Date: 2019-12-25 23:46:44 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 9427 77
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:mclust | 2 | 1.000 | 0.963 | 0.984 | ** | |
| CV:kmeans | 2 | 1.000 | 0.996 | 0.998 | ** | |
| MAD:mclust | 2 | 1.000 | 0.981 | 0.991 | ** | |
| ATC:pam | 2 | 1.000 | 0.985 | 0.993 | ** | |
| SD:skmeans | 3 | 0.985 | 0.951 | 0.977 | ** | 2 |
| MAD:skmeans | 3 | 0.984 | 0.946 | 0.976 | ** | 2 |
| CV:NMF | 3 | 0.950 | 0.898 | 0.963 | ** | 2 |
| CV:pam | 2 | 0.946 | 0.954 | 0.980 | * | |
| CV:skmeans | 3 | 0.943 | 0.934 | 0.969 | * | 2 |
| SD:NMF | 3 | 0.924 | 0.910 | 0.963 | * | 2 |
| MAD:NMF | 3 | 0.904 | 0.907 | 0.959 | * | 2 |
| ATC:skmeans | 3 | 0.903 | 0.876 | 0.949 | * | 2 |
| ATC:kmeans | 4 | 0.902 | 0.915 | 0.951 | * | |
| MAD:kmeans | 4 | 0.901 | 0.932 | 0.943 | * | |
| ATC:NMF | 2 | 0.890 | 0.928 | 0.969 | ||
| SD:kmeans | 2 | 0.808 | 0.964 | 0.981 | ||
| MAD:pam | 2 | 0.793 | 0.882 | 0.951 | ||
| SD:pam | 2 | 0.791 | 0.899 | 0.956 | ||
| CV:mclust | 2 | 0.785 | 0.930 | 0.959 | ||
| ATC:mclust | 2 | 0.653 | 0.933 | 0.952 | ||
| ATC:hclust | 4 | 0.592 | 0.733 | 0.810 | ||
| CV:hclust | 3 | 0.568 | 0.742 | 0.795 | ||
| MAD:hclust | 2 | 0.430 | 0.838 | 0.903 | ||
| SD:hclust | 2 | 0.430 | 0.837 | 0.907 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 1.000 0.976 0.989 0.503 0.496 0.496
#> CV:NMF 2 1.000 0.981 0.991 0.505 0.496 0.496
#> MAD:NMF 2 1.000 0.978 0.991 0.503 0.496 0.496
#> ATC:NMF 2 0.890 0.928 0.969 0.485 0.518 0.518
#> SD:skmeans 2 1.000 0.994 0.997 0.507 0.494 0.494
#> CV:skmeans 2 0.920 0.937 0.974 0.501 0.500 0.500
#> MAD:skmeans 2 1.000 0.972 0.989 0.506 0.494 0.494
#> ATC:skmeans 2 1.000 0.969 0.986 0.507 0.494 0.494
#> SD:mclust 2 1.000 0.963 0.984 0.478 0.518 0.518
#> CV:mclust 2 0.785 0.930 0.959 0.467 0.518 0.518
#> MAD:mclust 2 1.000 0.981 0.991 0.479 0.518 0.518
#> ATC:mclust 2 0.653 0.933 0.952 0.466 0.504 0.504
#> SD:kmeans 2 0.808 0.964 0.981 0.504 0.494 0.494
#> CV:kmeans 2 1.000 0.996 0.998 0.476 0.524 0.524
#> MAD:kmeans 2 0.802 0.934 0.970 0.502 0.494 0.494
#> ATC:kmeans 2 0.781 0.905 0.953 0.476 0.539 0.539
#> SD:pam 2 0.791 0.899 0.956 0.503 0.494 0.494
#> CV:pam 2 0.946 0.954 0.980 0.374 0.623 0.623
#> MAD:pam 2 0.793 0.882 0.951 0.502 0.494 0.494
#> ATC:pam 2 1.000 0.985 0.993 0.506 0.494 0.494
#> SD:hclust 2 0.430 0.837 0.907 0.449 0.531 0.531
#> CV:hclust 2 0.566 0.795 0.908 0.283 0.771 0.771
#> MAD:hclust 2 0.430 0.838 0.903 0.445 0.531 0.531
#> ATC:hclust 2 0.701 0.804 0.917 0.394 0.576 0.576
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.924 0.910 0.963 0.3127 0.806 0.624
#> CV:NMF 3 0.950 0.898 0.963 0.3149 0.767 0.563
#> MAD:NMF 3 0.904 0.907 0.959 0.3140 0.794 0.603
#> ATC:NMF 3 0.715 0.816 0.912 0.3263 0.778 0.596
#> SD:skmeans 3 0.985 0.951 0.977 0.2889 0.807 0.625
#> CV:skmeans 3 0.943 0.934 0.969 0.3078 0.791 0.602
#> MAD:skmeans 3 0.984 0.946 0.976 0.2890 0.786 0.594
#> ATC:skmeans 3 0.903 0.876 0.949 0.2064 0.889 0.777
#> SD:mclust 3 0.528 0.573 0.773 0.2324 0.981 0.963
#> CV:mclust 3 0.607 0.848 0.863 0.1624 0.843 0.730
#> MAD:mclust 3 0.564 0.580 0.773 0.2212 0.972 0.947
#> ATC:mclust 3 0.752 0.853 0.931 0.2010 0.907 0.815
#> SD:kmeans 3 0.744 0.773 0.888 0.2774 0.800 0.620
#> CV:kmeans 3 0.639 0.798 0.883 0.1969 0.935 0.876
#> MAD:kmeans 3 0.750 0.742 0.897 0.2927 0.756 0.549
#> ATC:kmeans 3 0.793 0.625 0.866 0.3814 0.687 0.487
#> SD:pam 3 0.630 0.810 0.904 0.1883 0.900 0.801
#> CV:pam 3 0.944 0.934 0.976 0.0728 0.976 0.962
#> MAD:pam 3 0.612 0.713 0.851 0.2041 0.885 0.771
#> ATC:pam 3 0.675 0.672 0.869 0.2374 0.882 0.766
#> SD:hclust 3 0.588 0.726 0.873 0.2462 0.896 0.810
#> CV:hclust 3 0.568 0.742 0.795 0.3762 0.606 0.533
#> MAD:hclust 3 0.629 0.750 0.867 0.2875 0.933 0.875
#> ATC:hclust 3 0.522 0.506 0.800 0.4522 0.756 0.603
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.814 0.775 0.896 0.0975 0.880 0.670
#> CV:NMF 4 0.827 0.750 0.879 0.0674 0.960 0.884
#> MAD:NMF 4 0.837 0.791 0.896 0.1017 0.914 0.752
#> ATC:NMF 4 0.599 0.619 0.799 0.1266 0.897 0.730
#> SD:skmeans 4 0.839 0.862 0.924 0.1023 0.916 0.763
#> CV:skmeans 4 0.699 0.674 0.829 0.1063 0.913 0.751
#> MAD:skmeans 4 0.790 0.833 0.903 0.1007 0.923 0.781
#> ATC:skmeans 4 0.853 0.842 0.926 0.0736 0.955 0.887
#> SD:mclust 4 0.645 0.798 0.861 0.1847 0.773 0.564
#> CV:mclust 4 0.503 0.758 0.803 0.2935 0.767 0.532
#> MAD:mclust 4 0.728 0.769 0.878 0.2037 0.766 0.539
#> ATC:mclust 4 0.639 0.603 0.754 0.2342 0.798 0.546
#> SD:kmeans 4 0.887 0.900 0.934 0.1247 0.838 0.594
#> CV:kmeans 4 0.669 0.720 0.826 0.1845 0.792 0.567
#> MAD:kmeans 4 0.901 0.932 0.943 0.1169 0.855 0.621
#> ATC:kmeans 4 0.902 0.915 0.951 0.1125 0.791 0.506
#> SD:pam 4 0.811 0.799 0.914 0.1472 0.874 0.704
#> CV:pam 4 0.860 0.900 0.958 0.0501 0.999 0.998
#> MAD:pam 4 0.770 0.783 0.909 0.1368 0.876 0.702
#> ATC:pam 4 0.799 0.775 0.910 0.1254 0.824 0.591
#> SD:hclust 4 0.597 0.707 0.827 0.0985 0.961 0.916
#> CV:hclust 4 0.883 0.916 0.943 0.3425 0.911 0.835
#> MAD:hclust 4 0.586 0.604 0.770 0.1197 0.942 0.878
#> ATC:hclust 4 0.592 0.733 0.810 0.1904 0.758 0.474
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.744 0.656 0.793 0.0531 0.936 0.775
#> CV:NMF 5 0.777 0.713 0.840 0.0428 0.949 0.844
#> MAD:NMF 5 0.761 0.664 0.811 0.0465 0.952 0.834
#> ATC:NMF 5 0.584 0.543 0.757 0.0530 0.896 0.677
#> SD:skmeans 5 0.722 0.682 0.838 0.0670 0.911 0.700
#> CV:skmeans 5 0.649 0.606 0.796 0.0649 0.916 0.712
#> MAD:skmeans 5 0.702 0.634 0.828 0.0625 0.955 0.841
#> ATC:skmeans 5 0.797 0.740 0.889 0.0479 0.990 0.974
#> SD:mclust 5 0.713 0.715 0.827 0.1001 0.857 0.572
#> CV:mclust 5 0.812 0.870 0.906 0.1252 0.838 0.486
#> MAD:mclust 5 0.721 0.776 0.853 0.0928 0.895 0.655
#> ATC:mclust 5 0.702 0.646 0.826 0.1256 0.827 0.480
#> SD:kmeans 5 0.820 0.777 0.872 0.0675 0.899 0.661
#> CV:kmeans 5 0.669 0.717 0.828 0.0955 0.912 0.715
#> MAD:kmeans 5 0.836 0.795 0.870 0.0677 0.934 0.764
#> ATC:kmeans 5 0.812 0.677 0.792 0.0513 0.943 0.790
#> SD:pam 5 0.705 0.660 0.809 0.0521 0.940 0.816
#> CV:pam 5 0.827 0.870 0.949 0.0230 0.999 0.998
#> MAD:pam 5 0.737 0.653 0.830 0.0517 0.947 0.837
#> ATC:pam 5 0.747 0.721 0.876 0.0208 0.932 0.787
#> SD:hclust 5 0.652 0.610 0.789 0.0691 0.981 0.955
#> CV:hclust 5 0.906 0.910 0.941 0.0457 0.998 0.996
#> MAD:hclust 5 0.648 0.732 0.818 0.0765 0.808 0.563
#> ATC:hclust 5 0.758 0.766 0.866 0.0777 0.967 0.881
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.716 0.606 0.769 0.0357 0.961 0.842
#> CV:NMF 6 0.761 0.651 0.793 0.0309 0.976 0.916
#> MAD:NMF 6 0.711 0.613 0.756 0.0340 0.962 0.858
#> ATC:NMF 6 0.595 0.468 0.688 0.0364 0.947 0.796
#> SD:skmeans 6 0.693 0.587 0.782 0.0335 0.984 0.931
#> CV:skmeans 6 0.653 0.549 0.748 0.0334 0.944 0.780
#> MAD:skmeans 6 0.697 0.636 0.780 0.0373 0.933 0.746
#> ATC:skmeans 6 0.796 0.679 0.850 0.0335 0.976 0.933
#> SD:mclust 6 0.814 0.845 0.893 0.0466 0.993 0.966
#> CV:mclust 6 0.853 0.849 0.863 0.0217 0.928 0.689
#> MAD:mclust 6 0.813 0.841 0.902 0.0464 0.981 0.911
#> ATC:mclust 6 0.736 0.712 0.830 0.0465 0.873 0.518
#> SD:kmeans 6 0.806 0.750 0.855 0.0423 0.965 0.845
#> CV:kmeans 6 0.679 0.682 0.812 0.0405 0.957 0.826
#> MAD:kmeans 6 0.791 0.716 0.818 0.0391 0.964 0.844
#> ATC:kmeans 6 0.813 0.670 0.796 0.0373 0.949 0.780
#> SD:pam 6 0.718 0.745 0.842 0.0346 0.957 0.854
#> CV:pam 6 0.820 0.804 0.929 0.0667 0.957 0.927
#> MAD:pam 6 0.753 0.687 0.818 0.0370 0.964 0.881
#> ATC:pam 6 0.760 0.701 0.867 0.0204 0.974 0.909
#> SD:hclust 6 0.654 0.632 0.793 0.0892 0.824 0.590
#> CV:hclust 6 0.929 0.872 0.921 0.0376 1.000 1.000
#> MAD:hclust 6 0.649 0.723 0.820 0.0489 0.963 0.866
#> ATC:hclust 6 0.743 0.723 0.860 0.0282 0.993 0.973
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 943, method = "euler")
top_rows_overlap(res_list, top_n = 1886, method = "euler")
top_rows_overlap(res_list, top_n = 2828, method = "euler")
top_rows_overlap(res_list, top_n = 3771, method = "euler")
top_rows_overlap(res_list, top_n = 4714, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 943, method = "correspondance")
top_rows_overlap(res_list, top_n = 1886, method = "correspondance")
top_rows_overlap(res_list, top_n = 2828, method = "correspondance")
top_rows_overlap(res_list, top_n = 3771, method = "correspondance")
top_rows_overlap(res_list, top_n = 4714, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 943)
top_rows_heatmap(res_list, top_n = 1886)
top_rows_heatmap(res_list, top_n = 2828)
top_rows_heatmap(res_list, top_n = 3771)
top_rows_heatmap(res_list, top_n = 4714)
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.430 0.837 0.907 0.4488 0.531 0.531
#> 3 3 0.588 0.726 0.873 0.2462 0.896 0.810
#> 4 4 0.597 0.707 0.827 0.0985 0.961 0.916
#> 5 5 0.652 0.610 0.789 0.0691 0.981 0.955
#> 6 6 0.654 0.632 0.793 0.0892 0.824 0.590
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.7528 0.7679 0.216 0.784
#> SRR944012 1 0.7883 0.7976 0.764 0.236
#> SRR944014 2 0.0000 0.8950 0.000 1.000
#> SRR944013 2 0.1633 0.8900 0.024 0.976
#> SRR944015 1 0.0000 0.8777 1.000 0.000
#> SRR944016 1 0.6887 0.8566 0.816 0.184
#> SRR944017 2 0.1633 0.8900 0.024 0.976
#> SRR944018 1 0.4022 0.8846 0.920 0.080
#> SRR944019 1 0.6887 0.8564 0.816 0.184
#> SRR944020 1 0.0000 0.8777 1.000 0.000
#> SRR944021 2 0.0000 0.8950 0.000 1.000
#> SRR944022 1 0.0000 0.8777 1.000 0.000
#> SRR944023 2 1.0000 0.0384 0.500 0.500
#> SRR944024 1 0.7883 0.8011 0.764 0.236
#> SRR944026 2 0.0000 0.8950 0.000 1.000
#> SRR944025 2 0.0000 0.8950 0.000 1.000
#> SRR944028 2 0.0000 0.8950 0.000 1.000
#> SRR944029 2 0.6247 0.8204 0.156 0.844
#> SRR944030 2 0.0000 0.8950 0.000 1.000
#> SRR944031 2 0.9944 0.2003 0.456 0.544
#> SRR944032 2 0.0672 0.8939 0.008 0.992
#> SRR944033 2 0.0000 0.8950 0.000 1.000
#> SRR944034 2 0.0000 0.8950 0.000 1.000
#> SRR944036 2 0.6623 0.8080 0.172 0.828
#> SRR944035 2 0.0000 0.8950 0.000 1.000
#> SRR944038 1 0.0000 0.8777 1.000 0.000
#> SRR944037 1 0.2236 0.8877 0.964 0.036
#> SRR944039 1 0.6887 0.8564 0.816 0.184
#> SRR944040 2 0.2778 0.8803 0.048 0.952
#> SRR944041 1 0.6438 0.8656 0.836 0.164
#> SRR944042 2 0.7528 0.7679 0.216 0.784
#> SRR944043 1 0.1414 0.8843 0.980 0.020
#> SRR944044 2 0.0000 0.8950 0.000 1.000
#> SRR944046 2 0.7815 0.7498 0.232 0.768
#> SRR944045 2 0.0000 0.8950 0.000 1.000
#> SRR944047 2 0.0000 0.8950 0.000 1.000
#> SRR944048 1 0.7950 0.7972 0.760 0.240
#> SRR944049 2 0.0000 0.8950 0.000 1.000
#> SRR944050 1 0.6887 0.8566 0.816 0.184
#> SRR944051 2 0.0672 0.8939 0.008 0.992
#> SRR944052 2 0.0000 0.8950 0.000 1.000
#> SRR944053 1 0.0000 0.8777 1.000 0.000
#> SRR944054 2 0.0938 0.8930 0.012 0.988
#> SRR944055 2 0.4815 0.8557 0.104 0.896
#> SRR944056 2 0.0000 0.8950 0.000 1.000
#> SRR944057 1 0.6801 0.8599 0.820 0.180
#> SRR944058 1 0.6801 0.8599 0.820 0.180
#> SRR944059 2 0.7299 0.7813 0.204 0.796
#> SRR944060 1 0.0000 0.8777 1.000 0.000
#> SRR944061 2 0.0000 0.8950 0.000 1.000
#> SRR944062 1 0.3114 0.8874 0.944 0.056
#> SRR944063 1 0.0672 0.8808 0.992 0.008
#> SRR944064 2 0.0000 0.8950 0.000 1.000
#> SRR944065 1 0.2043 0.8872 0.968 0.032
#> SRR944066 1 0.6801 0.8599 0.820 0.180
#> SRR944067 2 0.0000 0.8950 0.000 1.000
#> SRR944068 1 0.0000 0.8777 1.000 0.000
#> SRR944069 2 0.0000 0.8950 0.000 1.000
#> SRR944070 1 0.0000 0.8777 1.000 0.000
#> SRR944071 2 0.7299 0.7810 0.204 0.796
#> SRR944072 1 0.6801 0.8599 0.820 0.180
#> SRR944073 2 0.0000 0.8950 0.000 1.000
#> SRR944075 2 0.4939 0.8535 0.108 0.892
#> SRR944074 2 0.0000 0.8950 0.000 1.000
#> SRR944076 2 0.8016 0.7332 0.244 0.756
#> SRR944077 2 0.0000 0.8950 0.000 1.000
#> SRR944078 2 0.4939 0.8535 0.108 0.892
#> SRR944079 2 0.0000 0.8950 0.000 1.000
#> SRR944080 2 0.0000 0.8950 0.000 1.000
#> SRR944081 2 0.9170 0.5278 0.332 0.668
#> SRR944082 1 0.2236 0.8876 0.964 0.036
#> SRR944083 1 0.6801 0.8599 0.820 0.180
#> SRR944084 2 0.7453 0.7750 0.212 0.788
#> SRR944085 2 0.8207 0.7147 0.256 0.744
#> SRR944086 2 0.6623 0.8087 0.172 0.828
#> SRR944088 2 0.6247 0.8204 0.156 0.844
#> SRR944087 2 0.7376 0.7771 0.208 0.792
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 2 0.6075 0.6665 0.316 0.676 0.008
#> SRR944012 1 0.3572 0.7291 0.900 0.060 0.040
#> SRR944014 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944013 2 0.2066 0.8629 0.060 0.940 0.000
#> SRR944015 3 0.0000 0.8134 0.000 0.000 1.000
#> SRR944016 1 0.0237 0.7669 0.996 0.004 0.000
#> SRR944017 2 0.2066 0.8629 0.060 0.940 0.000
#> SRR944018 1 0.5158 0.5617 0.764 0.004 0.232
#> SRR944019 1 0.1170 0.7658 0.976 0.008 0.016
#> SRR944020 3 0.0237 0.8130 0.004 0.000 0.996
#> SRR944021 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944022 3 0.0000 0.8134 0.000 0.000 1.000
#> SRR944023 1 0.7591 0.0872 0.544 0.412 0.044
#> SRR944024 1 0.1964 0.7365 0.944 0.056 0.000
#> SRR944026 2 0.0747 0.8723 0.016 0.984 0.000
#> SRR944025 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944028 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944029 2 0.5178 0.7372 0.256 0.744 0.000
#> SRR944030 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944031 1 0.6912 -0.0452 0.540 0.444 0.016
#> SRR944032 2 0.1860 0.8655 0.052 0.948 0.000
#> SRR944033 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944034 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944036 2 0.5397 0.7150 0.280 0.720 0.000
#> SRR944035 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944038 3 0.5905 0.4834 0.352 0.000 0.648
#> SRR944037 1 0.6204 0.1704 0.576 0.000 0.424
#> SRR944039 1 0.1170 0.7658 0.976 0.008 0.016
#> SRR944040 2 0.2261 0.8572 0.068 0.932 0.000
#> SRR944041 1 0.2096 0.7516 0.944 0.004 0.052
#> SRR944042 2 0.6075 0.6665 0.316 0.676 0.008
#> SRR944043 1 0.6299 -0.0344 0.524 0.000 0.476
#> SRR944044 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944046 2 0.6282 0.6479 0.324 0.664 0.012
#> SRR944045 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944047 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944048 1 0.2066 0.7341 0.940 0.060 0.000
#> SRR944049 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944050 1 0.0237 0.7669 0.996 0.004 0.000
#> SRR944051 2 0.1163 0.8706 0.028 0.972 0.000
#> SRR944052 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944053 3 0.0000 0.8134 0.000 0.000 1.000
#> SRR944054 2 0.1529 0.8684 0.040 0.960 0.000
#> SRR944055 2 0.3879 0.8159 0.152 0.848 0.000
#> SRR944056 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944057 1 0.0000 0.7660 1.000 0.000 0.000
#> SRR944058 1 0.0424 0.7666 0.992 0.000 0.008
#> SRR944059 2 0.5815 0.6861 0.304 0.692 0.004
#> SRR944060 3 0.5882 0.4929 0.348 0.000 0.652
#> SRR944061 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944062 1 0.4504 0.6157 0.804 0.000 0.196
#> SRR944063 3 0.2878 0.7694 0.096 0.000 0.904
#> SRR944064 2 0.1411 0.8687 0.036 0.964 0.000
#> SRR944065 1 0.6215 0.1561 0.572 0.000 0.428
#> SRR944066 1 0.0000 0.7660 1.000 0.000 0.000
#> SRR944067 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944068 3 0.0000 0.8134 0.000 0.000 1.000
#> SRR944069 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944070 3 0.5905 0.4834 0.352 0.000 0.648
#> SRR944071 2 0.5845 0.6809 0.308 0.688 0.004
#> SRR944072 1 0.0424 0.7666 0.992 0.000 0.008
#> SRR944073 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944075 2 0.3941 0.8133 0.156 0.844 0.000
#> SRR944074 2 0.0747 0.8723 0.016 0.984 0.000
#> SRR944076 2 0.6229 0.6260 0.340 0.652 0.008
#> SRR944077 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944078 2 0.3941 0.8133 0.156 0.844 0.000
#> SRR944079 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944080 2 0.0000 0.8732 0.000 1.000 0.000
#> SRR944081 2 0.6483 0.3094 0.452 0.544 0.004
#> SRR944082 1 0.5291 0.5190 0.732 0.000 0.268
#> SRR944083 1 0.0000 0.7660 1.000 0.000 0.000
#> SRR944084 2 0.5873 0.6801 0.312 0.684 0.004
#> SRR944085 2 0.6297 0.6035 0.352 0.640 0.008
#> SRR944086 2 0.5397 0.7158 0.280 0.720 0.000
#> SRR944088 2 0.5178 0.7372 0.256 0.744 0.000
#> SRR944087 2 0.6018 0.6777 0.308 0.684 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 2 0.6703 0.6383 0.156 0.612 0.232 0.000
#> SRR944012 1 0.5198 0.6438 0.708 0.000 0.252 0.040
#> SRR944014 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944013 2 0.3128 0.8272 0.040 0.884 0.076 0.000
#> SRR944015 4 0.2647 0.8897 0.000 0.000 0.120 0.880
#> SRR944016 1 0.0188 0.8129 0.996 0.004 0.000 0.000
#> SRR944017 2 0.3128 0.8272 0.040 0.884 0.076 0.000
#> SRR944018 1 0.7043 0.1431 0.500 0.004 0.388 0.108
#> SRR944019 1 0.3519 0.7672 0.852 0.004 0.128 0.016
#> SRR944020 4 0.0188 0.9267 0.000 0.000 0.004 0.996
#> SRR944021 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944022 4 0.0000 0.9274 0.000 0.000 0.000 1.000
#> SRR944023 3 0.8009 0.0129 0.184 0.388 0.412 0.016
#> SRR944024 1 0.2489 0.7697 0.912 0.020 0.068 0.000
#> SRR944026 2 0.1792 0.8374 0.000 0.932 0.068 0.000
#> SRR944025 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944028 2 0.0336 0.8426 0.000 0.992 0.008 0.000
#> SRR944029 2 0.6147 0.6985 0.128 0.672 0.200 0.000
#> SRR944030 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944031 3 0.7335 -0.1161 0.156 0.400 0.444 0.000
#> SRR944032 2 0.2861 0.8292 0.016 0.888 0.096 0.000
#> SRR944033 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944036 2 0.6473 0.6766 0.168 0.644 0.188 0.000
#> SRR944035 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944038 3 0.5716 0.3467 0.068 0.000 0.680 0.252
#> SRR944037 3 0.7039 0.2831 0.316 0.000 0.540 0.144
#> SRR944039 1 0.3519 0.7672 0.852 0.004 0.128 0.016
#> SRR944040 2 0.2578 0.8330 0.036 0.912 0.052 0.000
#> SRR944041 1 0.4638 0.7259 0.776 0.000 0.180 0.044
#> SRR944042 2 0.6703 0.6383 0.156 0.612 0.232 0.000
#> SRR944043 3 0.6514 0.4468 0.212 0.000 0.636 0.152
#> SRR944044 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944046 2 0.6758 0.6243 0.156 0.604 0.240 0.000
#> SRR944045 2 0.0188 0.8427 0.000 0.996 0.004 0.000
#> SRR944047 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944048 1 0.2596 0.7682 0.908 0.024 0.068 0.000
#> SRR944049 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944050 1 0.0188 0.8129 0.996 0.004 0.000 0.000
#> SRR944051 2 0.2222 0.8368 0.016 0.924 0.060 0.000
#> SRR944052 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944053 4 0.0000 0.9274 0.000 0.000 0.000 1.000
#> SRR944054 2 0.2662 0.8319 0.016 0.900 0.084 0.000
#> SRR944055 2 0.4458 0.7902 0.076 0.808 0.116 0.000
#> SRR944056 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944057 1 0.0000 0.8131 1.000 0.000 0.000 0.000
#> SRR944058 1 0.0524 0.8126 0.988 0.000 0.004 0.008
#> SRR944059 2 0.6531 0.6629 0.160 0.636 0.204 0.000
#> SRR944060 3 0.5662 0.3520 0.072 0.000 0.692 0.236
#> SRR944061 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944062 1 0.5161 0.2751 0.592 0.000 0.400 0.008
#> SRR944063 4 0.2739 0.8426 0.060 0.000 0.036 0.904
#> SRR944064 2 0.1902 0.8376 0.004 0.932 0.064 0.000
#> SRR944065 3 0.6750 0.3475 0.288 0.000 0.584 0.128
#> SRR944066 1 0.0000 0.8131 1.000 0.000 0.000 0.000
#> SRR944067 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944068 4 0.2647 0.8897 0.000 0.000 0.120 0.880
#> SRR944069 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944070 3 0.5716 0.3467 0.068 0.000 0.680 0.252
#> SRR944071 2 0.6626 0.6518 0.160 0.624 0.216 0.000
#> SRR944072 1 0.0524 0.8126 0.988 0.000 0.004 0.008
#> SRR944073 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944075 2 0.4513 0.7880 0.076 0.804 0.120 0.000
#> SRR944074 2 0.1792 0.8374 0.000 0.932 0.068 0.000
#> SRR944076 2 0.6823 0.6094 0.160 0.596 0.244 0.000
#> SRR944077 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944078 2 0.4513 0.7880 0.076 0.804 0.120 0.000
#> SRR944079 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944080 2 0.0000 0.8428 0.000 1.000 0.000 0.000
#> SRR944081 2 0.7472 0.3126 0.344 0.488 0.164 0.004
#> SRR944082 1 0.6197 0.0853 0.508 0.000 0.440 0.052
#> SRR944083 1 0.0000 0.8131 1.000 0.000 0.000 0.000
#> SRR944084 2 0.6594 0.6542 0.140 0.620 0.240 0.000
#> SRR944085 2 0.6885 0.5936 0.164 0.588 0.248 0.000
#> SRR944086 2 0.6473 0.6772 0.168 0.644 0.188 0.000
#> SRR944088 2 0.6147 0.6985 0.128 0.672 0.200 0.000
#> SRR944087 2 0.6656 0.6481 0.160 0.620 0.220 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 2 0.6581 0.5132 0.060 0.500 0.064 0.000 0.376
#> SRR944012 5 0.4937 0.0000 0.292 0.000 0.012 0.032 0.664
#> SRR944014 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944013 2 0.2969 0.7741 0.020 0.852 0.000 0.000 0.128
#> SRR944015 4 0.4298 0.8080 0.000 0.000 0.184 0.756 0.060
#> SRR944016 1 0.0162 0.7185 0.996 0.004 0.000 0.000 0.000
#> SRR944017 2 0.2969 0.7741 0.020 0.852 0.000 0.000 0.128
#> SRR944018 3 0.6691 0.0492 0.352 0.000 0.476 0.016 0.156
#> SRR944019 1 0.4539 0.2567 0.660 0.000 0.008 0.012 0.320
#> SRR944020 4 0.0290 0.8813 0.000 0.000 0.000 0.992 0.008
#> SRR944021 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944022 4 0.0162 0.8819 0.000 0.000 0.000 0.996 0.004
#> SRR944023 3 0.7753 0.0117 0.080 0.344 0.392 0.000 0.184
#> SRR944024 1 0.2237 0.6187 0.904 0.008 0.004 0.000 0.084
#> SRR944026 2 0.1851 0.7909 0.000 0.912 0.000 0.000 0.088
#> SRR944025 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944028 2 0.0290 0.7999 0.000 0.992 0.000 0.000 0.008
#> SRR944029 2 0.4866 0.5880 0.028 0.580 0.000 0.000 0.392
#> SRR944030 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944031 3 0.7786 -0.0904 0.064 0.348 0.348 0.000 0.240
#> SRR944032 2 0.2424 0.7815 0.000 0.868 0.000 0.000 0.132
#> SRR944033 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944036 2 0.5751 0.5376 0.076 0.516 0.004 0.000 0.404
#> SRR944035 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944038 3 0.1907 0.4523 0.000 0.000 0.928 0.028 0.044
#> SRR944037 3 0.6271 0.3375 0.144 0.000 0.632 0.040 0.184
#> SRR944039 1 0.4539 0.2567 0.660 0.000 0.008 0.012 0.320
#> SRR944040 2 0.2891 0.7560 0.000 0.824 0.000 0.000 0.176
#> SRR944041 1 0.6170 -0.3650 0.460 0.000 0.064 0.028 0.448
#> SRR944042 2 0.6581 0.5132 0.060 0.500 0.064 0.000 0.376
#> SRR944043 3 0.4248 0.4475 0.092 0.000 0.800 0.016 0.092
#> SRR944044 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944046 2 0.6743 0.5078 0.060 0.500 0.080 0.000 0.360
#> SRR944045 2 0.0404 0.7996 0.000 0.988 0.000 0.000 0.012
#> SRR944047 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944048 1 0.2349 0.6147 0.900 0.012 0.004 0.000 0.084
#> SRR944049 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944050 1 0.0162 0.7185 0.996 0.004 0.000 0.000 0.000
#> SRR944051 2 0.1965 0.7897 0.000 0.904 0.000 0.000 0.096
#> SRR944052 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944053 4 0.0000 0.8821 0.000 0.000 0.000 1.000 0.000
#> SRR944054 2 0.2329 0.7824 0.000 0.876 0.000 0.000 0.124
#> SRR944055 2 0.4229 0.6954 0.000 0.704 0.020 0.000 0.276
#> SRR944056 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944057 1 0.0000 0.7186 1.000 0.000 0.000 0.000 0.000
#> SRR944058 1 0.2068 0.6770 0.904 0.000 0.004 0.000 0.092
#> SRR944059 2 0.6403 0.5380 0.060 0.520 0.052 0.000 0.368
#> SRR944060 3 0.1285 0.4558 0.004 0.000 0.956 0.036 0.004
#> SRR944061 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944062 1 0.5939 0.1189 0.536 0.000 0.344 0.000 0.120
#> SRR944063 4 0.2888 0.8186 0.020 0.000 0.036 0.888 0.056
#> SRR944064 2 0.1732 0.7919 0.000 0.920 0.000 0.000 0.080
#> SRR944065 3 0.5489 0.3889 0.156 0.000 0.696 0.020 0.128
#> SRR944066 1 0.0162 0.7184 0.996 0.000 0.004 0.000 0.000
#> SRR944067 2 0.0162 0.7994 0.000 0.996 0.000 0.000 0.004
#> SRR944068 4 0.4298 0.8080 0.000 0.000 0.184 0.756 0.060
#> SRR944069 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944070 3 0.1907 0.4523 0.000 0.000 0.928 0.028 0.044
#> SRR944071 2 0.6383 0.5206 0.060 0.504 0.048 0.000 0.388
#> SRR944072 1 0.2124 0.6748 0.900 0.000 0.004 0.000 0.096
#> SRR944073 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944075 2 0.4252 0.6928 0.000 0.700 0.020 0.000 0.280
#> SRR944074 2 0.1851 0.7909 0.000 0.912 0.000 0.000 0.088
#> SRR944076 2 0.6857 0.4992 0.060 0.496 0.092 0.000 0.352
#> SRR944077 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944078 2 0.4252 0.6928 0.000 0.700 0.020 0.000 0.280
#> SRR944079 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.8001 0.000 1.000 0.000 0.000 0.000
#> SRR944081 2 0.6911 0.1000 0.252 0.444 0.004 0.004 0.296
#> SRR944082 3 0.6315 0.0418 0.420 0.000 0.452 0.008 0.120
#> SRR944083 1 0.0162 0.7184 0.996 0.000 0.004 0.000 0.000
#> SRR944084 2 0.5895 0.5128 0.032 0.500 0.040 0.000 0.428
#> SRR944085 2 0.6951 0.4936 0.060 0.496 0.104 0.000 0.340
#> SRR944086 2 0.5478 0.5343 0.064 0.516 0.000 0.000 0.420
#> SRR944088 2 0.4866 0.5880 0.028 0.580 0.000 0.000 0.392
#> SRR944087 2 0.6440 0.5158 0.060 0.500 0.052 0.000 0.388
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.4378 0.8658 0.016 0.240 0.704 0.000 0.000 0.040
#> SRR944012 5 0.5438 0.5625 0.120 0.000 0.200 0.016 0.652 0.012
#> SRR944014 2 0.0000 0.8363 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944013 2 0.3543 0.6201 0.000 0.768 0.200 0.000 0.032 0.000
#> SRR944015 4 0.5163 0.7169 0.000 0.000 0.136 0.652 0.012 0.200
#> SRR944016 1 0.0862 0.6681 0.972 0.004 0.016 0.000 0.008 0.000
#> SRR944017 2 0.3543 0.6201 0.000 0.768 0.200 0.000 0.032 0.000
#> SRR944018 6 0.6709 0.2442 0.264 0.000 0.048 0.000 0.244 0.444
#> SRR944019 1 0.4640 -0.1196 0.528 0.000 0.032 0.004 0.436 0.000
#> SRR944020 4 0.0603 0.8324 0.000 0.000 0.016 0.980 0.004 0.000
#> SRR944021 2 0.0146 0.8352 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944022 4 0.0458 0.8330 0.000 0.000 0.016 0.984 0.000 0.000
#> SRR944023 3 0.6881 0.4284 0.028 0.196 0.388 0.000 0.020 0.368
#> SRR944024 1 0.2373 0.6099 0.888 0.000 0.084 0.000 0.024 0.004
#> SRR944026 2 0.2723 0.7321 0.000 0.852 0.128 0.000 0.016 0.004
#> SRR944025 2 0.0000 0.8363 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944028 2 0.0291 0.8333 0.000 0.992 0.004 0.000 0.004 0.000
#> SRR944029 3 0.5148 0.6503 0.000 0.352 0.560 0.000 0.084 0.004
#> SRR944030 2 0.0000 0.8363 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944031 3 0.6251 0.5569 0.020 0.196 0.460 0.000 0.000 0.324
#> SRR944032 2 0.3245 0.6756 0.000 0.800 0.172 0.000 0.028 0.000
#> SRR944033 2 0.0000 0.8363 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.8363 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944036 3 0.4589 0.8410 0.024 0.248 0.692 0.000 0.032 0.004
#> SRR944035 2 0.0000 0.8363 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944038 6 0.1327 0.6970 0.000 0.000 0.064 0.000 0.000 0.936
#> SRR944037 6 0.4869 0.5646 0.016 0.000 0.008 0.024 0.360 0.592
#> SRR944039 1 0.4640 -0.1196 0.528 0.000 0.032 0.004 0.436 0.000
#> SRR944040 2 0.3634 0.1565 0.000 0.644 0.356 0.000 0.000 0.000
#> SRR944041 5 0.5559 0.4597 0.284 0.000 0.068 0.012 0.608 0.028
#> SRR944042 3 0.4378 0.8658 0.016 0.240 0.704 0.000 0.000 0.040
#> SRR944043 6 0.3802 0.6896 0.036 0.000 0.012 0.000 0.180 0.772
#> SRR944044 2 0.0000 0.8363 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944046 3 0.4618 0.8620 0.016 0.240 0.688 0.000 0.000 0.056
#> SRR944045 2 0.0632 0.8240 0.000 0.976 0.024 0.000 0.000 0.000
#> SRR944047 2 0.0000 0.8363 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944048 1 0.2516 0.6069 0.884 0.004 0.084 0.000 0.024 0.004
#> SRR944049 2 0.0000 0.8363 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944050 1 0.1534 0.6652 0.944 0.004 0.016 0.000 0.032 0.004
#> SRR944051 2 0.2790 0.7199 0.000 0.840 0.140 0.000 0.020 0.000
#> SRR944052 2 0.0146 0.8352 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944053 4 0.0000 0.8337 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR944054 2 0.3309 0.6712 0.000 0.800 0.172 0.000 0.024 0.004
#> SRR944055 2 0.4097 -0.3641 0.000 0.500 0.492 0.000 0.000 0.008
#> SRR944056 2 0.0000 0.8363 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944057 1 0.1390 0.6649 0.948 0.000 0.016 0.000 0.032 0.004
#> SRR944058 1 0.2833 0.5845 0.836 0.000 0.012 0.000 0.148 0.004
#> SRR944059 3 0.4268 0.8598 0.016 0.256 0.700 0.000 0.000 0.028
#> SRR944060 6 0.1053 0.7006 0.000 0.000 0.020 0.012 0.004 0.964
#> SRR944061 2 0.0000 0.8363 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944062 1 0.6729 0.0519 0.468 0.000 0.060 0.000 0.232 0.240
#> SRR944063 4 0.2311 0.7707 0.000 0.000 0.000 0.880 0.104 0.016
#> SRR944064 2 0.2009 0.7812 0.000 0.908 0.068 0.000 0.024 0.000
#> SRR944065 6 0.4834 0.6358 0.044 0.000 0.020 0.004 0.272 0.660
#> SRR944066 1 0.0748 0.6660 0.976 0.000 0.016 0.000 0.004 0.004
#> SRR944067 2 0.0146 0.8345 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944068 4 0.5163 0.7169 0.000 0.000 0.136 0.652 0.012 0.200
#> SRR944069 2 0.0146 0.8352 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944070 6 0.1327 0.6970 0.000 0.000 0.064 0.000 0.000 0.936
#> SRR944071 3 0.4100 0.8644 0.016 0.240 0.720 0.000 0.000 0.024
#> SRR944072 1 0.2848 0.5786 0.828 0.000 0.008 0.000 0.160 0.004
#> SRR944073 2 0.0000 0.8363 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944075 2 0.4098 -0.3765 0.000 0.496 0.496 0.000 0.000 0.008
#> SRR944074 2 0.2723 0.7321 0.000 0.852 0.128 0.000 0.016 0.004
#> SRR944076 3 0.4863 0.8591 0.016 0.240 0.676 0.000 0.004 0.064
#> SRR944077 2 0.0000 0.8363 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944078 2 0.4098 -0.3765 0.000 0.496 0.496 0.000 0.000 0.008
#> SRR944079 2 0.0000 0.8363 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.8363 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944081 2 0.7601 -0.3543 0.200 0.336 0.264 0.000 0.200 0.000
#> SRR944082 1 0.6963 -0.2725 0.352 0.000 0.060 0.000 0.244 0.344
#> SRR944083 1 0.0748 0.6660 0.976 0.000 0.016 0.000 0.004 0.004
#> SRR944084 3 0.4825 0.8356 0.004 0.248 0.676 0.000 0.052 0.020
#> SRR944085 3 0.5015 0.8528 0.016 0.240 0.664 0.000 0.004 0.076
#> SRR944086 3 0.5165 0.8183 0.036 0.248 0.656 0.000 0.056 0.004
#> SRR944088 3 0.5148 0.6503 0.000 0.352 0.560 0.000 0.084 0.004
#> SRR944087 3 0.4175 0.8650 0.016 0.240 0.716 0.000 0.000 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "kmeans"]
# you can also extract it by
# res = res_list["SD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.808 0.964 0.981 0.5039 0.494 0.494
#> 3 3 0.744 0.773 0.888 0.2774 0.800 0.620
#> 4 4 0.887 0.900 0.934 0.1247 0.838 0.594
#> 5 5 0.820 0.777 0.872 0.0675 0.899 0.661
#> 6 6 0.806 0.750 0.855 0.0423 0.965 0.845
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.469 0.886 0.100 0.900
#> SRR944012 1 0.000 0.970 1.000 0.000
#> SRR944014 2 0.000 0.990 0.000 1.000
#> SRR944013 2 0.000 0.990 0.000 1.000
#> SRR944015 1 0.000 0.970 1.000 0.000
#> SRR944016 1 0.295 0.940 0.948 0.052
#> SRR944017 2 0.000 0.990 0.000 1.000
#> SRR944018 1 0.000 0.970 1.000 0.000
#> SRR944019 1 0.000 0.970 1.000 0.000
#> SRR944020 1 0.000 0.970 1.000 0.000
#> SRR944021 2 0.000 0.990 0.000 1.000
#> SRR944022 1 0.000 0.970 1.000 0.000
#> SRR944023 1 0.000 0.970 1.000 0.000
#> SRR944024 1 0.000 0.970 1.000 0.000
#> SRR944026 2 0.000 0.990 0.000 1.000
#> SRR944025 2 0.000 0.990 0.000 1.000
#> SRR944028 2 0.000 0.990 0.000 1.000
#> SRR944029 1 0.541 0.884 0.876 0.124
#> SRR944030 2 0.000 0.990 0.000 1.000
#> SRR944031 1 0.204 0.953 0.968 0.032
#> SRR944032 2 0.000 0.990 0.000 1.000
#> SRR944033 2 0.000 0.990 0.000 1.000
#> SRR944034 2 0.000 0.990 0.000 1.000
#> SRR944036 1 0.552 0.880 0.872 0.128
#> SRR944035 2 0.000 0.990 0.000 1.000
#> SRR944038 1 0.000 0.970 1.000 0.000
#> SRR944037 1 0.000 0.970 1.000 0.000
#> SRR944039 1 0.000 0.970 1.000 0.000
#> SRR944040 2 0.000 0.990 0.000 1.000
#> SRR944041 1 0.000 0.970 1.000 0.000
#> SRR944042 1 0.000 0.970 1.000 0.000
#> SRR944043 1 0.000 0.970 1.000 0.000
#> SRR944044 2 0.000 0.990 0.000 1.000
#> SRR944046 1 0.000 0.970 1.000 0.000
#> SRR944045 2 0.000 0.990 0.000 1.000
#> SRR944047 2 0.000 0.990 0.000 1.000
#> SRR944048 2 0.541 0.854 0.124 0.876
#> SRR944049 2 0.000 0.990 0.000 1.000
#> SRR944050 1 0.671 0.822 0.824 0.176
#> SRR944051 2 0.000 0.990 0.000 1.000
#> SRR944052 2 0.000 0.990 0.000 1.000
#> SRR944053 1 0.000 0.970 1.000 0.000
#> SRR944054 2 0.000 0.990 0.000 1.000
#> SRR944055 2 0.000 0.990 0.000 1.000
#> SRR944056 2 0.000 0.990 0.000 1.000
#> SRR944057 1 0.000 0.970 1.000 0.000
#> SRR944058 1 0.000 0.970 1.000 0.000
#> SRR944059 2 0.000 0.990 0.000 1.000
#> SRR944060 1 0.000 0.970 1.000 0.000
#> SRR944061 2 0.000 0.990 0.000 1.000
#> SRR944062 1 0.000 0.970 1.000 0.000
#> SRR944063 1 0.000 0.970 1.000 0.000
#> SRR944064 2 0.000 0.990 0.000 1.000
#> SRR944065 1 0.000 0.970 1.000 0.000
#> SRR944066 1 0.000 0.970 1.000 0.000
#> SRR944067 2 0.000 0.990 0.000 1.000
#> SRR944068 1 0.000 0.970 1.000 0.000
#> SRR944069 2 0.000 0.990 0.000 1.000
#> SRR944070 1 0.000 0.970 1.000 0.000
#> SRR944071 1 0.552 0.880 0.872 0.128
#> SRR944072 1 0.000 0.970 1.000 0.000
#> SRR944073 2 0.000 0.990 0.000 1.000
#> SRR944075 2 0.000 0.990 0.000 1.000
#> SRR944074 2 0.000 0.990 0.000 1.000
#> SRR944076 1 0.552 0.880 0.872 0.128
#> SRR944077 2 0.000 0.990 0.000 1.000
#> SRR944078 2 0.000 0.990 0.000 1.000
#> SRR944079 2 0.000 0.990 0.000 1.000
#> SRR944080 2 0.000 0.990 0.000 1.000
#> SRR944081 1 0.482 0.902 0.896 0.104
#> SRR944082 1 0.000 0.970 1.000 0.000
#> SRR944083 1 0.000 0.970 1.000 0.000
#> SRR944084 1 0.518 0.892 0.884 0.116
#> SRR944085 2 0.584 0.834 0.140 0.860
#> SRR944086 1 0.494 0.899 0.892 0.108
#> SRR944088 2 0.000 0.990 0.000 1.000
#> SRR944087 1 0.141 0.960 0.980 0.020
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 1 0.1636 0.817 0.964 0.020 0.016
#> SRR944012 1 0.6140 0.382 0.596 0.000 0.404
#> SRR944014 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944013 2 0.4733 0.761 0.196 0.800 0.004
#> SRR944015 3 0.0237 0.877 0.004 0.000 0.996
#> SRR944016 1 0.2537 0.806 0.920 0.000 0.080
#> SRR944017 2 0.0983 0.921 0.016 0.980 0.004
#> SRR944018 1 0.6079 0.444 0.612 0.000 0.388
#> SRR944019 1 0.4452 0.721 0.808 0.000 0.192
#> SRR944020 3 0.0237 0.877 0.004 0.000 0.996
#> SRR944021 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944022 3 0.0237 0.877 0.004 0.000 0.996
#> SRR944023 1 0.1289 0.820 0.968 0.000 0.032
#> SRR944024 1 0.1289 0.820 0.968 0.000 0.032
#> SRR944026 2 0.0983 0.921 0.016 0.980 0.004
#> SRR944025 2 0.0983 0.921 0.016 0.980 0.004
#> SRR944028 2 0.0983 0.921 0.016 0.980 0.004
#> SRR944029 1 0.0424 0.819 0.992 0.000 0.008
#> SRR944030 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944031 1 0.1453 0.821 0.968 0.008 0.024
#> SRR944032 1 0.6386 0.121 0.584 0.412 0.004
#> SRR944033 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944034 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944036 1 0.1015 0.820 0.980 0.012 0.008
#> SRR944035 2 0.0475 0.923 0.004 0.992 0.004
#> SRR944038 3 0.3267 0.809 0.116 0.000 0.884
#> SRR944037 3 0.0237 0.877 0.004 0.000 0.996
#> SRR944039 1 0.4887 0.682 0.772 0.000 0.228
#> SRR944040 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944041 1 0.6168 0.368 0.588 0.000 0.412
#> SRR944042 1 0.1482 0.821 0.968 0.012 0.020
#> SRR944043 3 0.1163 0.869 0.028 0.000 0.972
#> SRR944044 2 0.0983 0.921 0.016 0.980 0.004
#> SRR944046 1 0.1482 0.821 0.968 0.012 0.020
#> SRR944045 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944047 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944048 1 0.2590 0.776 0.924 0.072 0.004
#> SRR944049 2 0.0475 0.923 0.004 0.992 0.004
#> SRR944050 1 0.2590 0.806 0.924 0.004 0.072
#> SRR944051 2 0.0983 0.921 0.016 0.980 0.004
#> SRR944052 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944053 3 0.0237 0.877 0.004 0.000 0.996
#> SRR944054 2 0.2400 0.891 0.064 0.932 0.004
#> SRR944055 2 0.6095 0.468 0.392 0.608 0.000
#> SRR944056 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944057 1 0.2537 0.806 0.920 0.000 0.080
#> SRR944058 1 0.6140 0.375 0.596 0.000 0.404
#> SRR944059 2 0.6307 0.217 0.488 0.512 0.000
#> SRR944060 3 0.1163 0.869 0.028 0.000 0.972
#> SRR944061 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944062 3 0.6235 0.118 0.436 0.000 0.564
#> SRR944063 3 0.0237 0.877 0.004 0.000 0.996
#> SRR944064 2 0.0983 0.921 0.016 0.980 0.004
#> SRR944065 3 0.3941 0.735 0.156 0.000 0.844
#> SRR944066 1 0.6140 0.384 0.596 0.000 0.404
#> SRR944067 2 0.0983 0.921 0.016 0.980 0.004
#> SRR944068 3 0.0237 0.877 0.004 0.000 0.996
#> SRR944069 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944070 3 0.3267 0.809 0.116 0.000 0.884
#> SRR944071 1 0.1482 0.821 0.968 0.012 0.020
#> SRR944072 1 0.6154 0.374 0.592 0.000 0.408
#> SRR944073 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944075 2 0.6154 0.433 0.408 0.592 0.000
#> SRR944074 2 0.0983 0.921 0.016 0.980 0.004
#> SRR944076 1 0.1482 0.821 0.968 0.012 0.020
#> SRR944077 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944078 2 0.6079 0.476 0.388 0.612 0.000
#> SRR944079 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944080 2 0.0000 0.925 0.000 1.000 0.000
#> SRR944081 1 0.2625 0.805 0.916 0.000 0.084
#> SRR944082 3 0.6225 0.125 0.432 0.000 0.568
#> SRR944083 1 0.2625 0.805 0.916 0.000 0.084
#> SRR944084 1 0.1453 0.821 0.968 0.008 0.024
#> SRR944085 1 0.1491 0.819 0.968 0.016 0.016
#> SRR944086 1 0.0237 0.818 0.996 0.000 0.004
#> SRR944088 2 0.4931 0.750 0.212 0.784 0.004
#> SRR944087 1 0.1482 0.821 0.968 0.012 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.1151 0.948 0.024 0.008 0.968 0.000
#> SRR944012 1 0.0804 0.926 0.980 0.000 0.012 0.008
#> SRR944014 2 0.0592 0.959 0.000 0.984 0.016 0.000
#> SRR944013 2 0.4472 0.738 0.220 0.760 0.020 0.000
#> SRR944015 4 0.0336 0.871 0.000 0.000 0.008 0.992
#> SRR944016 1 0.2081 0.939 0.916 0.000 0.084 0.000
#> SRR944017 2 0.0804 0.951 0.008 0.980 0.012 0.000
#> SRR944018 1 0.3858 0.884 0.844 0.000 0.056 0.100
#> SRR944019 1 0.0469 0.927 0.988 0.000 0.012 0.000
#> SRR944020 4 0.0336 0.873 0.008 0.000 0.000 0.992
#> SRR944021 2 0.0592 0.959 0.000 0.984 0.016 0.000
#> SRR944022 4 0.0336 0.873 0.008 0.000 0.000 0.992
#> SRR944023 3 0.1305 0.947 0.036 0.000 0.960 0.004
#> SRR944024 1 0.1940 0.942 0.924 0.000 0.076 0.000
#> SRR944026 2 0.0927 0.949 0.008 0.976 0.016 0.000
#> SRR944025 2 0.0336 0.955 0.000 0.992 0.008 0.000
#> SRR944028 2 0.0336 0.955 0.000 0.992 0.008 0.000
#> SRR944029 3 0.2412 0.900 0.084 0.008 0.908 0.000
#> SRR944030 2 0.0592 0.959 0.000 0.984 0.016 0.000
#> SRR944031 3 0.1388 0.948 0.028 0.000 0.960 0.012
#> SRR944032 2 0.5477 0.710 0.180 0.728 0.092 0.000
#> SRR944033 2 0.0592 0.959 0.000 0.984 0.016 0.000
#> SRR944034 2 0.0592 0.959 0.000 0.984 0.016 0.000
#> SRR944036 3 0.1211 0.945 0.040 0.000 0.960 0.000
#> SRR944035 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> SRR944038 4 0.5769 0.434 0.036 0.000 0.376 0.588
#> SRR944037 4 0.0592 0.872 0.016 0.000 0.000 0.984
#> SRR944039 1 0.1489 0.942 0.952 0.000 0.044 0.004
#> SRR944040 2 0.1211 0.946 0.000 0.960 0.040 0.000
#> SRR944041 1 0.0804 0.926 0.980 0.000 0.012 0.008
#> SRR944042 3 0.1388 0.948 0.028 0.000 0.960 0.012
#> SRR944043 4 0.2401 0.826 0.092 0.000 0.004 0.904
#> SRR944044 2 0.0927 0.949 0.008 0.976 0.016 0.000
#> SRR944046 3 0.1388 0.948 0.028 0.000 0.960 0.012
#> SRR944045 2 0.1211 0.946 0.000 0.960 0.040 0.000
#> SRR944047 2 0.0592 0.959 0.000 0.984 0.016 0.000
#> SRR944048 1 0.2281 0.932 0.904 0.000 0.096 0.000
#> SRR944049 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> SRR944050 1 0.2281 0.932 0.904 0.000 0.096 0.000
#> SRR944051 2 0.2142 0.915 0.056 0.928 0.016 0.000
#> SRR944052 2 0.0592 0.959 0.000 0.984 0.016 0.000
#> SRR944053 4 0.0336 0.873 0.008 0.000 0.000 0.992
#> SRR944054 2 0.3168 0.883 0.060 0.884 0.056 0.000
#> SRR944055 3 0.1940 0.895 0.000 0.076 0.924 0.000
#> SRR944056 2 0.0592 0.959 0.000 0.984 0.016 0.000
#> SRR944057 1 0.1940 0.942 0.924 0.000 0.076 0.000
#> SRR944058 1 0.2089 0.940 0.932 0.000 0.048 0.020
#> SRR944059 3 0.1978 0.906 0.004 0.068 0.928 0.000
#> SRR944060 4 0.2408 0.849 0.036 0.000 0.044 0.920
#> SRR944061 2 0.0592 0.959 0.000 0.984 0.016 0.000
#> SRR944062 1 0.3266 0.898 0.876 0.000 0.040 0.084
#> SRR944063 4 0.0336 0.873 0.008 0.000 0.000 0.992
#> SRR944064 2 0.0188 0.956 0.000 0.996 0.004 0.000
#> SRR944065 4 0.5112 0.363 0.384 0.000 0.008 0.608
#> SRR944066 1 0.2111 0.937 0.932 0.000 0.044 0.024
#> SRR944067 2 0.0188 0.956 0.000 0.996 0.004 0.000
#> SRR944068 4 0.0336 0.871 0.000 0.000 0.008 0.992
#> SRR944069 2 0.0592 0.959 0.000 0.984 0.016 0.000
#> SRR944070 4 0.5769 0.434 0.036 0.000 0.376 0.588
#> SRR944071 3 0.1209 0.949 0.032 0.000 0.964 0.004
#> SRR944072 1 0.2089 0.940 0.932 0.000 0.048 0.020
#> SRR944073 2 0.0592 0.959 0.000 0.984 0.016 0.000
#> SRR944075 3 0.1940 0.895 0.000 0.076 0.924 0.000
#> SRR944074 2 0.0927 0.949 0.008 0.976 0.016 0.000
#> SRR944076 3 0.1296 0.950 0.028 0.004 0.964 0.004
#> SRR944077 2 0.0592 0.959 0.000 0.984 0.016 0.000
#> SRR944078 3 0.1940 0.895 0.000 0.076 0.924 0.000
#> SRR944079 2 0.0592 0.959 0.000 0.984 0.016 0.000
#> SRR944080 2 0.0592 0.959 0.000 0.984 0.016 0.000
#> SRR944081 1 0.2737 0.869 0.888 0.008 0.104 0.000
#> SRR944082 1 0.3266 0.898 0.876 0.000 0.040 0.084
#> SRR944083 1 0.1940 0.942 0.924 0.000 0.076 0.000
#> SRR944084 3 0.2342 0.915 0.080 0.000 0.912 0.008
#> SRR944085 3 0.1209 0.949 0.032 0.004 0.964 0.000
#> SRR944086 1 0.2216 0.884 0.908 0.000 0.092 0.000
#> SRR944088 2 0.4990 0.741 0.060 0.756 0.184 0.000
#> SRR944087 3 0.1256 0.950 0.028 0.000 0.964 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.0162 0.9021 0.004 0.000 0.996 0.000 0.000
#> SRR944012 5 0.5245 0.3266 0.328 0.000 0.000 0.064 0.608
#> SRR944014 2 0.0162 0.9504 0.000 0.996 0.000 0.000 0.004
#> SRR944013 5 0.5371 0.4900 0.020 0.352 0.032 0.000 0.596
#> SRR944015 4 0.2068 0.8283 0.000 0.000 0.004 0.904 0.092
#> SRR944016 1 0.1942 0.8480 0.920 0.000 0.012 0.000 0.068
#> SRR944017 2 0.2971 0.8089 0.000 0.836 0.008 0.000 0.156
#> SRR944018 1 0.5847 0.5432 0.592 0.000 0.000 0.144 0.264
#> SRR944019 5 0.4824 -0.0291 0.468 0.000 0.000 0.020 0.512
#> SRR944020 4 0.0404 0.8520 0.012 0.000 0.000 0.988 0.000
#> SRR944021 2 0.0324 0.9487 0.000 0.992 0.004 0.000 0.004
#> SRR944022 4 0.0404 0.8520 0.012 0.000 0.000 0.988 0.000
#> SRR944023 3 0.2426 0.8520 0.036 0.000 0.900 0.000 0.064
#> SRR944024 1 0.0693 0.8739 0.980 0.000 0.008 0.000 0.012
#> SRR944026 2 0.3109 0.7475 0.000 0.800 0.000 0.000 0.200
#> SRR944025 2 0.0880 0.9366 0.000 0.968 0.000 0.000 0.032
#> SRR944028 2 0.0963 0.9341 0.000 0.964 0.000 0.000 0.036
#> SRR944029 5 0.3983 0.3678 0.000 0.000 0.340 0.000 0.660
#> SRR944030 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> SRR944031 3 0.1124 0.8949 0.004 0.000 0.960 0.000 0.036
#> SRR944032 5 0.6645 0.5653 0.076 0.292 0.072 0.000 0.560
#> SRR944033 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> SRR944036 3 0.0324 0.9016 0.004 0.000 0.992 0.000 0.004
#> SRR944035 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> SRR944038 3 0.7383 -0.0458 0.032 0.000 0.408 0.292 0.268
#> SRR944037 4 0.3081 0.8141 0.012 0.000 0.000 0.832 0.156
#> SRR944039 1 0.3690 0.7231 0.780 0.000 0.000 0.020 0.200
#> SRR944040 2 0.1357 0.9085 0.000 0.948 0.048 0.000 0.004
#> SRR944041 5 0.5364 0.2540 0.364 0.000 0.000 0.064 0.572
#> SRR944042 3 0.1041 0.8963 0.004 0.000 0.964 0.000 0.032
#> SRR944043 4 0.5625 0.6721 0.160 0.000 0.000 0.636 0.204
#> SRR944044 2 0.2929 0.7775 0.000 0.820 0.000 0.000 0.180
#> SRR944046 3 0.1041 0.8963 0.004 0.000 0.964 0.000 0.032
#> SRR944045 2 0.1357 0.9085 0.000 0.948 0.048 0.000 0.004
#> SRR944047 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> SRR944048 1 0.1942 0.8480 0.920 0.000 0.012 0.000 0.068
#> SRR944049 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> SRR944050 1 0.1942 0.8480 0.920 0.000 0.012 0.000 0.068
#> SRR944051 5 0.4948 0.3151 0.000 0.436 0.028 0.000 0.536
#> SRR944052 2 0.0162 0.9504 0.000 0.996 0.000 0.000 0.004
#> SRR944053 4 0.0404 0.8520 0.012 0.000 0.000 0.988 0.000
#> SRR944054 5 0.5360 0.4285 0.000 0.384 0.060 0.000 0.556
#> SRR944055 3 0.0324 0.9008 0.000 0.004 0.992 0.000 0.004
#> SRR944056 2 0.0162 0.9504 0.000 0.996 0.000 0.000 0.004
#> SRR944057 1 0.0898 0.8718 0.972 0.000 0.008 0.000 0.020
#> SRR944058 1 0.0162 0.8743 0.996 0.000 0.000 0.000 0.004
#> SRR944059 3 0.0324 0.9008 0.000 0.004 0.992 0.000 0.004
#> SRR944060 4 0.5610 0.7331 0.036 0.000 0.048 0.644 0.272
#> SRR944061 2 0.0162 0.9504 0.000 0.996 0.000 0.000 0.004
#> SRR944062 1 0.3209 0.7651 0.812 0.000 0.000 0.008 0.180
#> SRR944063 4 0.0404 0.8520 0.012 0.000 0.000 0.988 0.000
#> SRR944064 2 0.0880 0.9366 0.000 0.968 0.000 0.000 0.032
#> SRR944065 4 0.6237 0.5380 0.196 0.000 0.000 0.540 0.264
#> SRR944066 1 0.0290 0.8731 0.992 0.000 0.000 0.000 0.008
#> SRR944067 2 0.0963 0.9341 0.000 0.964 0.000 0.000 0.036
#> SRR944068 4 0.2068 0.8283 0.000 0.000 0.004 0.904 0.092
#> SRR944069 2 0.0324 0.9487 0.000 0.992 0.004 0.000 0.004
#> SRR944070 3 0.7383 -0.0458 0.032 0.000 0.408 0.292 0.268
#> SRR944071 3 0.0162 0.9021 0.004 0.000 0.996 0.000 0.000
#> SRR944072 1 0.1043 0.8651 0.960 0.000 0.000 0.000 0.040
#> SRR944073 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> SRR944075 3 0.0324 0.9008 0.000 0.004 0.992 0.000 0.004
#> SRR944074 2 0.3109 0.7475 0.000 0.800 0.000 0.000 0.200
#> SRR944076 3 0.0324 0.9016 0.004 0.000 0.992 0.000 0.004
#> SRR944077 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> SRR944078 3 0.0324 0.9008 0.000 0.004 0.992 0.000 0.004
#> SRR944079 2 0.0162 0.9504 0.000 0.996 0.000 0.000 0.004
#> SRR944080 2 0.0000 0.9508 0.000 1.000 0.000 0.000 0.000
#> SRR944081 5 0.5250 0.4995 0.188 0.000 0.084 0.020 0.708
#> SRR944082 1 0.3724 0.7476 0.776 0.000 0.000 0.020 0.204
#> SRR944083 1 0.0579 0.8743 0.984 0.000 0.008 0.000 0.008
#> SRR944084 3 0.1410 0.8569 0.000 0.000 0.940 0.000 0.060
#> SRR944085 3 0.0162 0.9021 0.004 0.000 0.996 0.000 0.000
#> SRR944086 5 0.5289 0.4567 0.252 0.000 0.096 0.000 0.652
#> SRR944088 5 0.5434 0.5914 0.000 0.208 0.136 0.000 0.656
#> SRR944087 3 0.1041 0.8963 0.004 0.000 0.964 0.000 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.0632 0.9567 0.000 0.000 0.976 0.000 0.024 0.000
#> SRR944012 5 0.5776 0.5353 0.100 0.000 0.000 0.056 0.608 0.236
#> SRR944014 2 0.0146 0.8985 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR944013 5 0.3925 0.6823 0.012 0.116 0.012 0.000 0.800 0.060
#> SRR944015 4 0.3046 0.7101 0.000 0.000 0.000 0.800 0.012 0.188
#> SRR944016 1 0.0935 0.8954 0.964 0.000 0.000 0.000 0.032 0.004
#> SRR944017 2 0.4314 0.7002 0.004 0.716 0.000 0.000 0.212 0.068
#> SRR944018 6 0.5870 0.4202 0.244 0.000 0.000 0.100 0.060 0.596
#> SRR944019 5 0.6189 0.3995 0.228 0.000 0.000 0.028 0.524 0.220
#> SRR944020 4 0.0291 0.8151 0.000 0.000 0.000 0.992 0.004 0.004
#> SRR944021 2 0.0363 0.8970 0.000 0.988 0.000 0.000 0.000 0.012
#> SRR944022 4 0.0000 0.8164 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR944023 3 0.2494 0.8231 0.016 0.000 0.864 0.000 0.000 0.120
#> SRR944024 1 0.1010 0.8930 0.960 0.000 0.000 0.000 0.004 0.036
#> SRR944026 2 0.4885 0.4267 0.000 0.560 0.000 0.000 0.372 0.068
#> SRR944025 2 0.2962 0.8318 0.000 0.848 0.000 0.000 0.084 0.068
#> SRR944028 2 0.3013 0.8289 0.000 0.844 0.000 0.000 0.088 0.068
#> SRR944029 5 0.3227 0.6562 0.000 0.000 0.116 0.000 0.824 0.060
#> SRR944030 2 0.0000 0.8990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944031 3 0.0632 0.9370 0.000 0.000 0.976 0.000 0.000 0.024
#> SRR944032 5 0.4587 0.6720 0.048 0.084 0.016 0.000 0.772 0.080
#> SRR944033 2 0.0000 0.8990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.8990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944036 3 0.1155 0.9543 0.004 0.000 0.956 0.000 0.036 0.004
#> SRR944035 2 0.1908 0.8699 0.000 0.916 0.000 0.000 0.028 0.056
#> SRR944038 6 0.5616 0.3143 0.000 0.000 0.284 0.128 0.016 0.572
#> SRR944037 4 0.4178 0.0981 0.000 0.000 0.000 0.608 0.020 0.372
#> SRR944039 1 0.5531 0.4651 0.616 0.000 0.000 0.028 0.116 0.240
#> SRR944040 2 0.1461 0.8675 0.000 0.940 0.044 0.000 0.000 0.016
#> SRR944041 5 0.6148 0.4817 0.108 0.000 0.000 0.072 0.564 0.256
#> SRR944042 3 0.0632 0.9370 0.000 0.000 0.976 0.000 0.000 0.024
#> SRR944043 6 0.5464 0.3456 0.072 0.000 0.000 0.336 0.028 0.564
#> SRR944044 2 0.4655 0.5705 0.000 0.632 0.000 0.000 0.300 0.068
#> SRR944046 3 0.0458 0.9406 0.000 0.000 0.984 0.000 0.000 0.016
#> SRR944045 2 0.1297 0.8724 0.000 0.948 0.040 0.000 0.000 0.012
#> SRR944047 2 0.0000 0.8990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944048 1 0.1151 0.8934 0.956 0.000 0.000 0.000 0.032 0.012
#> SRR944049 2 0.1176 0.8867 0.000 0.956 0.000 0.000 0.020 0.024
#> SRR944050 1 0.0935 0.8954 0.964 0.000 0.000 0.000 0.032 0.004
#> SRR944051 5 0.4166 0.6364 0.000 0.148 0.012 0.000 0.760 0.080
#> SRR944052 2 0.0363 0.8970 0.000 0.988 0.000 0.000 0.000 0.012
#> SRR944053 4 0.0000 0.8164 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR944054 5 0.3809 0.6697 0.000 0.116 0.020 0.000 0.800 0.064
#> SRR944055 3 0.1320 0.9535 0.000 0.000 0.948 0.000 0.036 0.016
#> SRR944056 2 0.0146 0.8985 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR944057 1 0.0632 0.8987 0.976 0.000 0.000 0.000 0.024 0.000
#> SRR944058 1 0.1049 0.8948 0.960 0.000 0.000 0.000 0.008 0.032
#> SRR944059 3 0.1124 0.9556 0.000 0.000 0.956 0.000 0.036 0.008
#> SRR944060 6 0.4985 0.1944 0.004 0.000 0.064 0.280 0.012 0.640
#> SRR944061 2 0.0146 0.8985 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR944062 6 0.4393 0.0848 0.480 0.000 0.000 0.004 0.016 0.500
#> SRR944063 4 0.0291 0.8151 0.000 0.000 0.000 0.992 0.004 0.004
#> SRR944064 2 0.2910 0.8350 0.000 0.852 0.000 0.000 0.080 0.068
#> SRR944065 6 0.5456 0.2724 0.056 0.000 0.000 0.388 0.032 0.524
#> SRR944066 1 0.0713 0.8925 0.972 0.000 0.000 0.000 0.000 0.028
#> SRR944067 2 0.2965 0.8324 0.000 0.848 0.000 0.000 0.080 0.072
#> SRR944068 4 0.3046 0.7101 0.000 0.000 0.000 0.800 0.012 0.188
#> SRR944069 2 0.0363 0.8970 0.000 0.988 0.000 0.000 0.000 0.012
#> SRR944070 6 0.5632 0.3113 0.000 0.000 0.288 0.128 0.016 0.568
#> SRR944071 3 0.0865 0.9565 0.000 0.000 0.964 0.000 0.036 0.000
#> SRR944072 1 0.2748 0.7840 0.848 0.000 0.000 0.000 0.024 0.128
#> SRR944073 2 0.0000 0.8990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944075 3 0.1320 0.9535 0.000 0.000 0.948 0.000 0.036 0.016
#> SRR944074 2 0.4923 0.4294 0.000 0.560 0.000 0.000 0.368 0.072
#> SRR944076 3 0.0632 0.9567 0.000 0.000 0.976 0.000 0.024 0.000
#> SRR944077 2 0.0000 0.8990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944078 3 0.1320 0.9535 0.000 0.000 0.948 0.000 0.036 0.016
#> SRR944079 2 0.0363 0.8970 0.000 0.988 0.000 0.000 0.000 0.012
#> SRR944080 2 0.0000 0.8990 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944081 5 0.3755 0.6651 0.048 0.000 0.008 0.008 0.800 0.136
#> SRR944082 6 0.4817 0.2535 0.408 0.000 0.000 0.020 0.024 0.548
#> SRR944083 1 0.0632 0.8962 0.976 0.000 0.000 0.000 0.000 0.024
#> SRR944084 3 0.2020 0.9015 0.000 0.000 0.896 0.000 0.096 0.008
#> SRR944085 3 0.0865 0.9565 0.000 0.000 0.964 0.000 0.036 0.000
#> SRR944086 5 0.4192 0.6665 0.088 0.000 0.028 0.000 0.776 0.108
#> SRR944088 5 0.2685 0.6999 0.000 0.052 0.040 0.000 0.884 0.024
#> SRR944087 3 0.0363 0.9426 0.000 0.000 0.988 0.000 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.994 0.997 0.5068 0.494 0.494
#> 3 3 0.985 0.951 0.977 0.2889 0.807 0.625
#> 4 4 0.839 0.862 0.924 0.1023 0.916 0.763
#> 5 5 0.722 0.682 0.838 0.0670 0.911 0.700
#> 6 6 0.693 0.587 0.782 0.0335 0.984 0.931
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.0376 0.991 0.004 0.996
#> SRR944012 1 0.0000 1.000 1.000 0.000
#> SRR944014 2 0.0000 0.994 0.000 1.000
#> SRR944013 2 0.0000 0.994 0.000 1.000
#> SRR944015 1 0.0000 1.000 1.000 0.000
#> SRR944016 1 0.0000 1.000 1.000 0.000
#> SRR944017 2 0.0000 0.994 0.000 1.000
#> SRR944018 1 0.0000 1.000 1.000 0.000
#> SRR944019 1 0.0000 1.000 1.000 0.000
#> SRR944020 1 0.0000 1.000 1.000 0.000
#> SRR944021 2 0.0000 0.994 0.000 1.000
#> SRR944022 1 0.0000 1.000 1.000 0.000
#> SRR944023 1 0.0000 1.000 1.000 0.000
#> SRR944024 1 0.0000 1.000 1.000 0.000
#> SRR944026 2 0.0000 0.994 0.000 1.000
#> SRR944025 2 0.0000 0.994 0.000 1.000
#> SRR944028 2 0.0000 0.994 0.000 1.000
#> SRR944029 1 0.0000 1.000 1.000 0.000
#> SRR944030 2 0.0000 0.994 0.000 1.000
#> SRR944031 1 0.0000 1.000 1.000 0.000
#> SRR944032 2 0.0000 0.994 0.000 1.000
#> SRR944033 2 0.0000 0.994 0.000 1.000
#> SRR944034 2 0.0000 0.994 0.000 1.000
#> SRR944036 1 0.0000 1.000 1.000 0.000
#> SRR944035 2 0.0000 0.994 0.000 1.000
#> SRR944038 1 0.0000 1.000 1.000 0.000
#> SRR944037 1 0.0000 1.000 1.000 0.000
#> SRR944039 1 0.0000 1.000 1.000 0.000
#> SRR944040 2 0.0000 0.994 0.000 1.000
#> SRR944041 1 0.0000 1.000 1.000 0.000
#> SRR944042 1 0.0000 1.000 1.000 0.000
#> SRR944043 1 0.0000 1.000 1.000 0.000
#> SRR944044 2 0.0000 0.994 0.000 1.000
#> SRR944046 1 0.0000 1.000 1.000 0.000
#> SRR944045 2 0.0000 0.994 0.000 1.000
#> SRR944047 2 0.0000 0.994 0.000 1.000
#> SRR944048 2 0.6623 0.793 0.172 0.828
#> SRR944049 2 0.0000 0.994 0.000 1.000
#> SRR944050 1 0.0672 0.992 0.992 0.008
#> SRR944051 2 0.0000 0.994 0.000 1.000
#> SRR944052 2 0.0000 0.994 0.000 1.000
#> SRR944053 1 0.0000 1.000 1.000 0.000
#> SRR944054 2 0.0000 0.994 0.000 1.000
#> SRR944055 2 0.0000 0.994 0.000 1.000
#> SRR944056 2 0.0000 0.994 0.000 1.000
#> SRR944057 1 0.0000 1.000 1.000 0.000
#> SRR944058 1 0.0000 1.000 1.000 0.000
#> SRR944059 2 0.0000 0.994 0.000 1.000
#> SRR944060 1 0.0000 1.000 1.000 0.000
#> SRR944061 2 0.0000 0.994 0.000 1.000
#> SRR944062 1 0.0000 1.000 1.000 0.000
#> SRR944063 1 0.0000 1.000 1.000 0.000
#> SRR944064 2 0.0000 0.994 0.000 1.000
#> SRR944065 1 0.0000 1.000 1.000 0.000
#> SRR944066 1 0.0000 1.000 1.000 0.000
#> SRR944067 2 0.0000 0.994 0.000 1.000
#> SRR944068 1 0.0000 1.000 1.000 0.000
#> SRR944069 2 0.0000 0.994 0.000 1.000
#> SRR944070 1 0.0000 1.000 1.000 0.000
#> SRR944071 1 0.0000 1.000 1.000 0.000
#> SRR944072 1 0.0000 1.000 1.000 0.000
#> SRR944073 2 0.0000 0.994 0.000 1.000
#> SRR944075 2 0.0000 0.994 0.000 1.000
#> SRR944074 2 0.0000 0.994 0.000 1.000
#> SRR944076 1 0.0000 1.000 1.000 0.000
#> SRR944077 2 0.0000 0.994 0.000 1.000
#> SRR944078 2 0.0000 0.994 0.000 1.000
#> SRR944079 2 0.0000 0.994 0.000 1.000
#> SRR944080 2 0.0000 0.994 0.000 1.000
#> SRR944081 1 0.0000 1.000 1.000 0.000
#> SRR944082 1 0.0000 1.000 1.000 0.000
#> SRR944083 1 0.0000 1.000 1.000 0.000
#> SRR944084 1 0.0000 1.000 1.000 0.000
#> SRR944085 2 0.2423 0.956 0.040 0.960
#> SRR944086 1 0.0000 1.000 1.000 0.000
#> SRR944088 2 0.0000 0.994 0.000 1.000
#> SRR944087 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 3 0.0424 0.951 0.000 0.008 0.992
#> SRR944012 1 0.0592 0.981 0.988 0.000 0.012
#> SRR944014 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944013 2 0.0592 0.970 0.012 0.988 0.000
#> SRR944015 1 0.0892 0.980 0.980 0.000 0.020
#> SRR944016 1 0.0237 0.979 0.996 0.000 0.004
#> SRR944017 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944018 1 0.0892 0.980 0.980 0.000 0.020
#> SRR944019 1 0.0000 0.980 1.000 0.000 0.000
#> SRR944020 1 0.0892 0.980 0.980 0.000 0.020
#> SRR944021 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944022 1 0.0892 0.980 0.980 0.000 0.020
#> SRR944023 3 0.3116 0.858 0.108 0.000 0.892
#> SRR944024 1 0.0237 0.979 0.996 0.000 0.004
#> SRR944026 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944025 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944028 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944029 1 0.2448 0.931 0.924 0.000 0.076
#> SRR944030 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944031 3 0.0000 0.952 0.000 0.000 1.000
#> SRR944032 2 0.0475 0.974 0.004 0.992 0.004
#> SRR944033 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944034 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944036 3 0.0424 0.950 0.008 0.000 0.992
#> SRR944035 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944038 3 0.1289 0.936 0.032 0.000 0.968
#> SRR944037 1 0.0892 0.980 0.980 0.000 0.020
#> SRR944039 1 0.0000 0.980 1.000 0.000 0.000
#> SRR944040 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944041 1 0.0592 0.981 0.988 0.000 0.012
#> SRR944042 3 0.0237 0.952 0.004 0.000 0.996
#> SRR944043 1 0.0892 0.980 0.980 0.000 0.020
#> SRR944044 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944046 3 0.0237 0.952 0.004 0.000 0.996
#> SRR944045 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944047 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944048 2 0.6509 0.103 0.472 0.524 0.004
#> SRR944049 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944050 1 0.0237 0.979 0.996 0.000 0.004
#> SRR944051 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944052 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944053 1 0.0892 0.980 0.980 0.000 0.020
#> SRR944054 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944055 3 0.1163 0.941 0.000 0.028 0.972
#> SRR944056 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944057 1 0.0237 0.979 0.996 0.000 0.004
#> SRR944058 1 0.0000 0.980 1.000 0.000 0.000
#> SRR944059 3 0.4654 0.757 0.000 0.208 0.792
#> SRR944060 1 0.4750 0.745 0.784 0.000 0.216
#> SRR944061 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944062 1 0.0424 0.981 0.992 0.000 0.008
#> SRR944063 1 0.0892 0.980 0.980 0.000 0.020
#> SRR944064 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944065 1 0.0892 0.980 0.980 0.000 0.020
#> SRR944066 1 0.0237 0.979 0.996 0.000 0.004
#> SRR944067 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944068 1 0.0892 0.980 0.980 0.000 0.020
#> SRR944069 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944070 3 0.0892 0.945 0.020 0.000 0.980
#> SRR944071 3 0.0000 0.952 0.000 0.000 1.000
#> SRR944072 1 0.0000 0.980 1.000 0.000 0.000
#> SRR944073 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944075 3 0.1163 0.941 0.000 0.028 0.972
#> SRR944074 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944076 3 0.0000 0.952 0.000 0.000 1.000
#> SRR944077 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944078 3 0.5178 0.684 0.000 0.256 0.744
#> SRR944079 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944080 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944081 1 0.0237 0.981 0.996 0.000 0.004
#> SRR944082 1 0.0592 0.981 0.988 0.000 0.012
#> SRR944083 1 0.0237 0.979 0.996 0.000 0.004
#> SRR944084 3 0.0592 0.949 0.012 0.000 0.988
#> SRR944085 3 0.0592 0.949 0.000 0.012 0.988
#> SRR944086 1 0.0424 0.980 0.992 0.000 0.008
#> SRR944088 2 0.0000 0.982 0.000 1.000 0.000
#> SRR944087 3 0.0237 0.952 0.004 0.000 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.0000 0.8861 0.000 0.000 1.000 0.000
#> SRR944012 4 0.0469 0.9022 0.012 0.000 0.000 0.988
#> SRR944014 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944013 2 0.2859 0.9075 0.112 0.880 0.000 0.008
#> SRR944015 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> SRR944016 1 0.2408 0.8835 0.896 0.000 0.000 0.104
#> SRR944017 2 0.1118 0.9574 0.036 0.964 0.000 0.000
#> SRR944018 4 0.0188 0.9053 0.004 0.000 0.000 0.996
#> SRR944019 4 0.3356 0.7517 0.176 0.000 0.000 0.824
#> SRR944020 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> SRR944021 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944022 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> SRR944023 3 0.5585 0.6564 0.084 0.000 0.712 0.204
#> SRR944024 1 0.2868 0.8877 0.864 0.000 0.000 0.136
#> SRR944026 2 0.1867 0.9418 0.072 0.928 0.000 0.000
#> SRR944025 2 0.1022 0.9583 0.032 0.968 0.000 0.000
#> SRR944028 2 0.1022 0.9583 0.032 0.968 0.000 0.000
#> SRR944029 4 0.2593 0.8428 0.080 0.000 0.016 0.904
#> SRR944030 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944031 3 0.0188 0.8860 0.000 0.000 0.996 0.004
#> SRR944032 2 0.4941 0.3446 0.436 0.564 0.000 0.000
#> SRR944033 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944036 3 0.2999 0.8020 0.132 0.000 0.864 0.004
#> SRR944035 2 0.0817 0.9604 0.024 0.976 0.000 0.000
#> SRR944038 3 0.4164 0.6617 0.000 0.000 0.736 0.264
#> SRR944037 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> SRR944039 4 0.3123 0.7617 0.156 0.000 0.000 0.844
#> SRR944040 2 0.0188 0.9623 0.004 0.996 0.000 0.000
#> SRR944041 4 0.0469 0.9025 0.012 0.000 0.000 0.988
#> SRR944042 3 0.0188 0.8860 0.000 0.000 0.996 0.004
#> SRR944043 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> SRR944044 2 0.1716 0.9460 0.064 0.936 0.000 0.000
#> SRR944046 3 0.0188 0.8860 0.000 0.000 0.996 0.004
#> SRR944045 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944047 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944048 1 0.2089 0.8387 0.932 0.020 0.000 0.048
#> SRR944049 2 0.0592 0.9620 0.016 0.984 0.000 0.000
#> SRR944050 1 0.2081 0.8712 0.916 0.000 0.000 0.084
#> SRR944051 2 0.2011 0.9378 0.080 0.920 0.000 0.000
#> SRR944052 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944053 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> SRR944054 2 0.2216 0.9304 0.092 0.908 0.000 0.000
#> SRR944055 3 0.2125 0.8413 0.004 0.076 0.920 0.000
#> SRR944056 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944057 1 0.2647 0.8888 0.880 0.000 0.000 0.120
#> SRR944058 1 0.3528 0.8534 0.808 0.000 0.000 0.192
#> SRR944059 3 0.3751 0.7219 0.004 0.196 0.800 0.000
#> SRR944060 4 0.2589 0.8062 0.000 0.000 0.116 0.884
#> SRR944061 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944062 4 0.4907 -0.0151 0.420 0.000 0.000 0.580
#> SRR944063 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> SRR944064 2 0.0921 0.9593 0.028 0.972 0.000 0.000
#> SRR944065 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> SRR944066 1 0.3074 0.8820 0.848 0.000 0.000 0.152
#> SRR944067 2 0.1022 0.9583 0.032 0.968 0.000 0.000
#> SRR944068 4 0.0000 0.9073 0.000 0.000 0.000 1.000
#> SRR944069 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944070 3 0.3726 0.7281 0.000 0.000 0.788 0.212
#> SRR944071 3 0.0000 0.8861 0.000 0.000 1.000 0.000
#> SRR944072 1 0.4994 0.2914 0.520 0.000 0.000 0.480
#> SRR944073 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944075 3 0.0524 0.8829 0.004 0.008 0.988 0.000
#> SRR944074 2 0.1867 0.9418 0.072 0.928 0.000 0.000
#> SRR944076 3 0.0000 0.8861 0.000 0.000 1.000 0.000
#> SRR944077 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944078 3 0.4155 0.6632 0.004 0.240 0.756 0.000
#> SRR944079 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944080 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944081 4 0.2149 0.8642 0.088 0.000 0.000 0.912
#> SRR944082 4 0.1940 0.8477 0.076 0.000 0.000 0.924
#> SRR944083 1 0.2704 0.8891 0.876 0.000 0.000 0.124
#> SRR944084 4 0.4833 0.6432 0.032 0.000 0.228 0.740
#> SRR944085 3 0.0188 0.8854 0.004 0.000 0.996 0.000
#> SRR944086 1 0.4535 0.6884 0.704 0.000 0.004 0.292
#> SRR944088 2 0.2345 0.9250 0.100 0.900 0.000 0.000
#> SRR944087 3 0.0000 0.8861 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.2179 0.8026 0.004 0.000 0.896 0.000 0.100
#> SRR944012 4 0.2017 0.8183 0.008 0.000 0.000 0.912 0.080
#> SRR944014 2 0.0000 0.8258 0.000 1.000 0.000 0.000 0.000
#> SRR944013 5 0.4567 0.5642 0.004 0.448 0.000 0.004 0.544
#> SRR944015 4 0.0671 0.8415 0.000 0.000 0.016 0.980 0.004
#> SRR944016 1 0.0451 0.8854 0.988 0.000 0.000 0.008 0.004
#> SRR944017 2 0.3274 0.5711 0.000 0.780 0.000 0.000 0.220
#> SRR944018 4 0.0854 0.8419 0.012 0.000 0.004 0.976 0.008
#> SRR944019 4 0.4364 0.7166 0.112 0.000 0.000 0.768 0.120
#> SRR944020 4 0.0000 0.8452 0.000 0.000 0.000 1.000 0.000
#> SRR944021 2 0.0000 0.8258 0.000 1.000 0.000 0.000 0.000
#> SRR944022 4 0.0000 0.8452 0.000 0.000 0.000 1.000 0.000
#> SRR944023 3 0.5948 0.5767 0.112 0.000 0.664 0.184 0.040
#> SRR944024 1 0.2270 0.8682 0.904 0.000 0.000 0.076 0.020
#> SRR944026 5 0.4304 0.5132 0.000 0.484 0.000 0.000 0.516
#> SRR944025 2 0.3143 0.5937 0.000 0.796 0.000 0.000 0.204
#> SRR944028 2 0.3274 0.5566 0.000 0.780 0.000 0.000 0.220
#> SRR944029 5 0.4655 -0.3892 0.000 0.000 0.012 0.476 0.512
#> SRR944030 2 0.0290 0.8244 0.000 0.992 0.000 0.000 0.008
#> SRR944031 3 0.0955 0.8127 0.000 0.000 0.968 0.004 0.028
#> SRR944032 5 0.6767 0.4410 0.272 0.348 0.000 0.000 0.380
#> SRR944033 2 0.0000 0.8258 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0290 0.8244 0.000 0.992 0.000 0.000 0.008
#> SRR944036 3 0.4837 0.6726 0.188 0.000 0.732 0.012 0.068
#> SRR944035 2 0.2471 0.7015 0.000 0.864 0.000 0.000 0.136
#> SRR944038 3 0.3779 0.6334 0.000 0.000 0.752 0.236 0.012
#> SRR944037 4 0.0000 0.8452 0.000 0.000 0.000 1.000 0.000
#> SRR944039 4 0.3400 0.7580 0.136 0.000 0.000 0.828 0.036
#> SRR944040 2 0.1792 0.7147 0.000 0.916 0.000 0.000 0.084
#> SRR944041 4 0.1430 0.8296 0.004 0.000 0.000 0.944 0.052
#> SRR944042 3 0.0162 0.8103 0.000 0.000 0.996 0.000 0.004
#> SRR944043 4 0.0613 0.8434 0.004 0.000 0.008 0.984 0.004
#> SRR944044 2 0.4262 -0.3435 0.000 0.560 0.000 0.000 0.440
#> SRR944046 3 0.0000 0.8110 0.000 0.000 1.000 0.000 0.000
#> SRR944045 2 0.0290 0.8184 0.000 0.992 0.000 0.000 0.008
#> SRR944047 2 0.0162 0.8257 0.000 0.996 0.000 0.000 0.004
#> SRR944048 1 0.0451 0.8858 0.988 0.000 0.000 0.008 0.004
#> SRR944049 2 0.2074 0.7409 0.000 0.896 0.000 0.000 0.104
#> SRR944050 1 0.0290 0.8862 0.992 0.000 0.000 0.008 0.000
#> SRR944051 5 0.4201 0.6189 0.000 0.408 0.000 0.000 0.592
#> SRR944052 2 0.0000 0.8258 0.000 1.000 0.000 0.000 0.000
#> SRR944053 4 0.0000 0.8452 0.000 0.000 0.000 1.000 0.000
#> SRR944054 5 0.4088 0.6312 0.000 0.368 0.000 0.000 0.632
#> SRR944055 3 0.6333 0.5485 0.008 0.252 0.560 0.000 0.180
#> SRR944056 2 0.0000 0.8258 0.000 1.000 0.000 0.000 0.000
#> SRR944057 1 0.0404 0.8875 0.988 0.000 0.000 0.012 0.000
#> SRR944058 1 0.3421 0.7406 0.788 0.000 0.000 0.204 0.008
#> SRR944059 3 0.6673 0.4022 0.008 0.324 0.476 0.000 0.192
#> SRR944060 4 0.3890 0.6169 0.000 0.000 0.252 0.736 0.012
#> SRR944061 2 0.0000 0.8258 0.000 1.000 0.000 0.000 0.000
#> SRR944062 4 0.5014 0.1996 0.412 0.000 0.008 0.560 0.020
#> SRR944063 4 0.0000 0.8452 0.000 0.000 0.000 1.000 0.000
#> SRR944064 2 0.2929 0.6364 0.000 0.820 0.000 0.000 0.180
#> SRR944065 4 0.0162 0.8448 0.000 0.000 0.004 0.996 0.000
#> SRR944066 1 0.2179 0.8573 0.896 0.000 0.000 0.100 0.004
#> SRR944067 2 0.3074 0.6083 0.000 0.804 0.000 0.000 0.196
#> SRR944068 4 0.0566 0.8430 0.000 0.000 0.012 0.984 0.004
#> SRR944069 2 0.0162 0.8256 0.000 0.996 0.000 0.000 0.004
#> SRR944070 3 0.3462 0.6851 0.000 0.000 0.792 0.196 0.012
#> SRR944071 3 0.2011 0.8075 0.004 0.000 0.908 0.000 0.088
#> SRR944072 4 0.4655 0.0272 0.476 0.000 0.000 0.512 0.012
#> SRR944073 2 0.0162 0.8257 0.000 0.996 0.000 0.000 0.004
#> SRR944075 3 0.4869 0.7254 0.008 0.088 0.732 0.000 0.172
#> SRR944074 5 0.4300 0.5314 0.000 0.476 0.000 0.000 0.524
#> SRR944076 3 0.0794 0.8130 0.000 0.000 0.972 0.000 0.028
#> SRR944077 2 0.0000 0.8258 0.000 1.000 0.000 0.000 0.000
#> SRR944078 2 0.6703 -0.2980 0.008 0.420 0.392 0.000 0.180
#> SRR944079 2 0.0000 0.8258 0.000 1.000 0.000 0.000 0.000
#> SRR944080 2 0.0510 0.8196 0.000 0.984 0.000 0.000 0.016
#> SRR944081 4 0.4679 0.5966 0.032 0.000 0.000 0.652 0.316
#> SRR944082 4 0.3446 0.7360 0.144 0.000 0.016 0.828 0.012
#> SRR944083 1 0.0794 0.8877 0.972 0.000 0.000 0.028 0.000
#> SRR944084 4 0.5797 0.4465 0.000 0.000 0.276 0.592 0.132
#> SRR944085 3 0.3394 0.7873 0.004 0.020 0.824 0.000 0.152
#> SRR944086 1 0.6804 0.3911 0.488 0.000 0.012 0.268 0.232
#> SRR944088 5 0.3741 0.5959 0.000 0.264 0.000 0.004 0.732
#> SRR944087 3 0.0703 0.8131 0.000 0.000 0.976 0.000 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.3259 0.4970 0.000 0.000 0.772 0.000 0.012 0.216
#> SRR944012 4 0.4099 0.7045 0.012 0.000 0.000 0.764 0.072 0.152
#> SRR944014 2 0.0146 0.8220 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR944013 5 0.5036 0.6320 0.008 0.312 0.000 0.000 0.604 0.076
#> SRR944015 4 0.0951 0.8004 0.000 0.000 0.020 0.968 0.004 0.008
#> SRR944016 1 0.1176 0.8237 0.956 0.000 0.000 0.000 0.024 0.020
#> SRR944017 2 0.3907 0.4658 0.000 0.704 0.000 0.000 0.268 0.028
#> SRR944018 4 0.1957 0.7950 0.024 0.000 0.012 0.928 0.008 0.028
#> SRR944019 4 0.5888 0.5814 0.112 0.000 0.000 0.636 0.124 0.128
#> SRR944020 4 0.0146 0.8020 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR944021 2 0.0260 0.8206 0.000 0.992 0.000 0.000 0.000 0.008
#> SRR944022 4 0.0146 0.8020 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR944023 3 0.6447 0.3877 0.064 0.000 0.576 0.180 0.012 0.168
#> SRR944024 1 0.3189 0.8104 0.844 0.000 0.004 0.084 0.004 0.064
#> SRR944026 5 0.4461 0.5533 0.000 0.404 0.000 0.000 0.564 0.032
#> SRR944025 2 0.3512 0.4864 0.000 0.720 0.000 0.000 0.272 0.008
#> SRR944028 2 0.3833 0.2766 0.000 0.648 0.000 0.000 0.344 0.008
#> SRR944029 5 0.6095 -0.0134 0.000 0.000 0.012 0.268 0.492 0.228
#> SRR944030 2 0.0547 0.8157 0.000 0.980 0.000 0.000 0.020 0.000
#> SRR944031 3 0.1524 0.6106 0.000 0.000 0.932 0.008 0.000 0.060
#> SRR944032 5 0.6677 0.5093 0.172 0.284 0.000 0.000 0.476 0.068
#> SRR944033 2 0.0000 0.8224 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944034 2 0.0458 0.8177 0.000 0.984 0.000 0.000 0.016 0.000
#> SRR944036 3 0.5790 0.4016 0.140 0.000 0.612 0.000 0.044 0.204
#> SRR944035 2 0.2948 0.6364 0.000 0.804 0.000 0.000 0.188 0.008
#> SRR944038 3 0.3543 0.4802 0.000 0.000 0.756 0.224 0.004 0.016
#> SRR944037 4 0.0291 0.8028 0.000 0.000 0.004 0.992 0.004 0.000
#> SRR944039 4 0.4740 0.6484 0.160 0.000 0.000 0.720 0.028 0.092
#> SRR944040 2 0.2431 0.6627 0.000 0.860 0.008 0.000 0.000 0.132
#> SRR944041 4 0.2764 0.7645 0.008 0.000 0.000 0.864 0.028 0.100
#> SRR944042 3 0.0858 0.6116 0.000 0.000 0.968 0.000 0.004 0.028
#> SRR944043 4 0.1293 0.7993 0.004 0.000 0.016 0.956 0.004 0.020
#> SRR944044 5 0.4473 0.3465 0.000 0.484 0.000 0.000 0.488 0.028
#> SRR944046 3 0.0260 0.6117 0.000 0.000 0.992 0.000 0.000 0.008
#> SRR944045 2 0.0458 0.8169 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944047 2 0.0000 0.8224 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944048 1 0.1480 0.8193 0.940 0.000 0.000 0.000 0.020 0.040
#> SRR944049 2 0.2178 0.7146 0.000 0.868 0.000 0.000 0.132 0.000
#> SRR944050 1 0.1421 0.8198 0.944 0.000 0.000 0.000 0.028 0.028
#> SRR944051 5 0.4370 0.6532 0.004 0.280 0.000 0.000 0.672 0.044
#> SRR944052 2 0.0458 0.8167 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944053 4 0.0000 0.8025 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR944054 5 0.4093 0.6172 0.004 0.204 0.000 0.000 0.736 0.056
#> SRR944055 3 0.6283 -0.7393 0.000 0.264 0.372 0.000 0.008 0.356
#> SRR944056 2 0.0146 0.8220 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR944057 1 0.1364 0.8314 0.952 0.000 0.000 0.012 0.016 0.020
#> SRR944058 1 0.3745 0.6491 0.732 0.000 0.000 0.240 0.000 0.028
#> SRR944059 6 0.6281 0.0000 0.000 0.276 0.320 0.000 0.008 0.396
#> SRR944060 4 0.4264 0.5128 0.000 0.000 0.284 0.676 0.004 0.036
#> SRR944061 2 0.0146 0.8220 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR944062 4 0.5123 0.2399 0.388 0.000 0.012 0.548 0.004 0.048
#> SRR944063 4 0.0000 0.8025 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR944064 2 0.3373 0.5378 0.000 0.744 0.000 0.000 0.248 0.008
#> SRR944065 4 0.0798 0.8019 0.004 0.000 0.012 0.976 0.004 0.004
#> SRR944066 1 0.2653 0.7797 0.844 0.000 0.000 0.144 0.000 0.012
#> SRR944067 2 0.3575 0.4596 0.000 0.708 0.000 0.000 0.284 0.008
#> SRR944068 4 0.0862 0.8009 0.000 0.000 0.016 0.972 0.004 0.008
#> SRR944069 2 0.0508 0.8201 0.000 0.984 0.000 0.000 0.004 0.012
#> SRR944070 3 0.3245 0.5164 0.000 0.000 0.796 0.184 0.004 0.016
#> SRR944071 3 0.3679 0.4794 0.004 0.000 0.724 0.000 0.012 0.260
#> SRR944072 4 0.5036 0.1580 0.416 0.000 0.000 0.524 0.012 0.048
#> SRR944073 2 0.0000 0.8224 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944075 3 0.5137 -0.0810 0.000 0.084 0.564 0.000 0.004 0.348
#> SRR944074 5 0.4273 0.5857 0.000 0.380 0.000 0.000 0.596 0.024
#> SRR944076 3 0.2489 0.5966 0.000 0.000 0.860 0.000 0.012 0.128
#> SRR944077 2 0.0000 0.8224 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944078 2 0.6199 -0.7660 0.000 0.392 0.228 0.000 0.008 0.372
#> SRR944079 2 0.0458 0.8170 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944080 2 0.0547 0.8152 0.000 0.980 0.000 0.000 0.020 0.000
#> SRR944081 4 0.6254 0.4656 0.036 0.000 0.000 0.528 0.228 0.208
#> SRR944082 4 0.3493 0.7311 0.112 0.000 0.016 0.828 0.008 0.036
#> SRR944083 1 0.1562 0.8300 0.940 0.000 0.000 0.032 0.004 0.024
#> SRR944084 4 0.7000 0.2676 0.000 0.000 0.192 0.464 0.108 0.236
#> SRR944085 3 0.4170 0.4071 0.004 0.004 0.644 0.000 0.012 0.336
#> SRR944086 1 0.7705 0.2859 0.348 0.000 0.004 0.216 0.196 0.236
#> SRR944088 5 0.4613 0.4433 0.000 0.116 0.000 0.000 0.688 0.196
#> SRR944087 3 0.2121 0.5988 0.000 0.000 0.892 0.000 0.012 0.096
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "pam"]
# you can also extract it by
# res = res_list["SD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.791 0.899 0.956 0.5028 0.494 0.494
#> 3 3 0.630 0.810 0.904 0.1883 0.900 0.801
#> 4 4 0.811 0.799 0.914 0.1472 0.874 0.704
#> 5 5 0.705 0.660 0.809 0.0521 0.940 0.816
#> 6 6 0.718 0.745 0.842 0.0346 0.957 0.854
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 1 0.6048 0.826 0.852 0.148
#> SRR944012 1 0.0000 0.942 1.000 0.000
#> SRR944014 2 0.0000 0.962 0.000 1.000
#> SRR944013 2 0.0672 0.956 0.008 0.992
#> SRR944015 1 0.0000 0.942 1.000 0.000
#> SRR944016 1 0.9580 0.406 0.620 0.380
#> SRR944017 2 0.0000 0.962 0.000 1.000
#> SRR944018 1 0.0000 0.942 1.000 0.000
#> SRR944019 1 0.9209 0.524 0.664 0.336
#> SRR944020 1 0.0000 0.942 1.000 0.000
#> SRR944021 2 0.0000 0.962 0.000 1.000
#> SRR944022 1 0.0000 0.942 1.000 0.000
#> SRR944023 1 0.0000 0.942 1.000 0.000
#> SRR944024 1 0.0000 0.942 1.000 0.000
#> SRR944026 2 0.0000 0.962 0.000 1.000
#> SRR944025 2 0.0000 0.962 0.000 1.000
#> SRR944028 2 0.0000 0.962 0.000 1.000
#> SRR944029 1 0.7056 0.778 0.808 0.192
#> SRR944030 2 0.0000 0.962 0.000 1.000
#> SRR944031 1 0.0000 0.942 1.000 0.000
#> SRR944032 2 0.0000 0.962 0.000 1.000
#> SRR944033 2 0.0000 0.962 0.000 1.000
#> SRR944034 2 0.0000 0.962 0.000 1.000
#> SRR944036 1 0.6148 0.817 0.848 0.152
#> SRR944035 2 0.0000 0.962 0.000 1.000
#> SRR944038 1 0.0000 0.942 1.000 0.000
#> SRR944037 1 0.0000 0.942 1.000 0.000
#> SRR944039 1 0.0000 0.942 1.000 0.000
#> SRR944040 2 0.0000 0.962 0.000 1.000
#> SRR944041 1 0.0000 0.942 1.000 0.000
#> SRR944042 1 0.0000 0.942 1.000 0.000
#> SRR944043 1 0.0000 0.942 1.000 0.000
#> SRR944044 2 0.0000 0.962 0.000 1.000
#> SRR944046 1 0.0000 0.942 1.000 0.000
#> SRR944045 2 0.0000 0.962 0.000 1.000
#> SRR944047 2 0.0000 0.962 0.000 1.000
#> SRR944048 2 0.3584 0.900 0.068 0.932
#> SRR944049 2 0.0000 0.962 0.000 1.000
#> SRR944050 2 0.7376 0.722 0.208 0.792
#> SRR944051 2 0.0000 0.962 0.000 1.000
#> SRR944052 2 0.0000 0.962 0.000 1.000
#> SRR944053 1 0.0000 0.942 1.000 0.000
#> SRR944054 2 0.0376 0.959 0.004 0.996
#> SRR944055 2 0.1414 0.947 0.020 0.980
#> SRR944056 2 0.0000 0.962 0.000 1.000
#> SRR944057 1 0.1633 0.927 0.976 0.024
#> SRR944058 1 0.0000 0.942 1.000 0.000
#> SRR944059 2 0.8555 0.602 0.280 0.720
#> SRR944060 1 0.0000 0.942 1.000 0.000
#> SRR944061 2 0.0000 0.962 0.000 1.000
#> SRR944062 1 0.0000 0.942 1.000 0.000
#> SRR944063 1 0.0000 0.942 1.000 0.000
#> SRR944064 2 0.0000 0.962 0.000 1.000
#> SRR944065 1 0.0000 0.942 1.000 0.000
#> SRR944066 1 0.0000 0.942 1.000 0.000
#> SRR944067 2 0.0000 0.962 0.000 1.000
#> SRR944068 1 0.0000 0.942 1.000 0.000
#> SRR944069 2 0.0000 0.962 0.000 1.000
#> SRR944070 1 0.0000 0.942 1.000 0.000
#> SRR944071 1 0.4431 0.875 0.908 0.092
#> SRR944072 1 0.0000 0.942 1.000 0.000
#> SRR944073 2 0.0000 0.962 0.000 1.000
#> SRR944075 2 0.8499 0.601 0.276 0.724
#> SRR944074 2 0.0000 0.962 0.000 1.000
#> SRR944076 1 0.0000 0.942 1.000 0.000
#> SRR944077 2 0.0000 0.962 0.000 1.000
#> SRR944078 2 0.0938 0.953 0.012 0.988
#> SRR944079 2 0.0000 0.962 0.000 1.000
#> SRR944080 2 0.0000 0.962 0.000 1.000
#> SRR944081 2 0.9815 0.232 0.420 0.580
#> SRR944082 1 0.0000 0.942 1.000 0.000
#> SRR944083 1 0.0672 0.938 0.992 0.008
#> SRR944084 1 0.7056 0.778 0.808 0.192
#> SRR944085 1 0.9522 0.441 0.628 0.372
#> SRR944086 1 0.6623 0.801 0.828 0.172
#> SRR944088 2 0.0000 0.962 0.000 1.000
#> SRR944087 1 0.0000 0.942 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 1 0.6827 0.685 0.728 0.192 0.080
#> SRR944012 1 0.3686 0.736 0.860 0.000 0.140
#> SRR944014 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944013 2 0.3412 0.835 0.124 0.876 0.000
#> SRR944015 3 0.0747 0.950 0.016 0.000 0.984
#> SRR944016 1 0.3769 0.749 0.880 0.104 0.016
#> SRR944017 2 0.0424 0.936 0.008 0.992 0.000
#> SRR944018 1 0.0000 0.803 1.000 0.000 0.000
#> SRR944019 1 0.8122 0.421 0.608 0.100 0.292
#> SRR944020 3 0.0892 0.950 0.020 0.000 0.980
#> SRR944021 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944022 3 0.1031 0.938 0.024 0.000 0.976
#> SRR944023 1 0.2537 0.801 0.920 0.000 0.080
#> SRR944024 1 0.0747 0.800 0.984 0.000 0.016
#> SRR944026 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944025 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944028 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944029 1 0.6758 0.679 0.728 0.200 0.072
#> SRR944030 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944031 1 0.2537 0.801 0.920 0.000 0.080
#> SRR944032 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944033 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944034 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944036 1 0.4423 0.784 0.864 0.088 0.048
#> SRR944035 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944038 1 0.5706 0.595 0.680 0.000 0.320
#> SRR944037 3 0.4178 0.765 0.172 0.000 0.828
#> SRR944039 1 0.4178 0.696 0.828 0.000 0.172
#> SRR944040 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944041 1 0.5905 0.448 0.648 0.000 0.352
#> SRR944042 1 0.2537 0.801 0.920 0.000 0.080
#> SRR944043 1 0.3038 0.777 0.896 0.000 0.104
#> SRR944044 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944046 1 0.2537 0.801 0.920 0.000 0.080
#> SRR944045 2 0.0592 0.933 0.012 0.988 0.000
#> SRR944047 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944048 2 0.5992 0.637 0.268 0.716 0.016
#> SRR944049 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944050 2 0.6879 0.174 0.428 0.556 0.016
#> SRR944051 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944052 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944053 3 0.0592 0.950 0.012 0.000 0.988
#> SRR944054 2 0.1031 0.925 0.024 0.976 0.000
#> SRR944055 2 0.2959 0.859 0.100 0.900 0.000
#> SRR944056 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944057 1 0.0747 0.800 0.984 0.000 0.016
#> SRR944058 1 0.5706 0.449 0.680 0.000 0.320
#> SRR944059 2 0.6140 0.295 0.404 0.596 0.000
#> SRR944060 1 0.3340 0.785 0.880 0.000 0.120
#> SRR944061 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944062 1 0.0237 0.803 0.996 0.000 0.004
#> SRR944063 3 0.2066 0.927 0.060 0.000 0.940
#> SRR944064 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944065 1 0.2448 0.794 0.924 0.000 0.076
#> SRR944066 1 0.1031 0.800 0.976 0.000 0.024
#> SRR944067 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944068 3 0.0747 0.950 0.016 0.000 0.984
#> SRR944069 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944070 1 0.5138 0.677 0.748 0.000 0.252
#> SRR944071 1 0.6728 0.691 0.736 0.184 0.080
#> SRR944072 1 0.3619 0.733 0.864 0.000 0.136
#> SRR944073 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944075 2 0.5291 0.600 0.268 0.732 0.000
#> SRR944074 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944076 1 0.2537 0.801 0.920 0.000 0.080
#> SRR944077 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944078 2 0.3551 0.826 0.132 0.868 0.000
#> SRR944079 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944080 2 0.0000 0.940 0.000 1.000 0.000
#> SRR944081 1 0.6758 0.472 0.620 0.360 0.020
#> SRR944082 1 0.0424 0.802 0.992 0.000 0.008
#> SRR944083 1 0.0747 0.800 0.984 0.000 0.016
#> SRR944084 1 0.6854 0.664 0.716 0.216 0.068
#> SRR944085 1 0.6451 0.583 0.684 0.292 0.024
#> SRR944086 1 0.6208 0.688 0.752 0.200 0.048
#> SRR944088 2 0.0892 0.928 0.020 0.980 0.000
#> SRR944087 1 0.2537 0.801 0.920 0.000 0.080
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.0188 0.8504 0.000 0.004 0.996 0.000
#> SRR944012 1 0.5184 0.5838 0.672 0.000 0.304 0.024
#> SRR944014 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944013 2 0.1474 0.9195 0.000 0.948 0.052 0.000
#> SRR944015 4 0.0000 0.9421 0.000 0.000 0.000 1.000
#> SRR944016 1 0.1118 0.7001 0.964 0.000 0.036 0.000
#> SRR944017 2 0.0188 0.9591 0.000 0.996 0.004 0.000
#> SRR944018 3 0.4103 0.5116 0.256 0.000 0.744 0.000
#> SRR944019 1 0.5038 0.4786 0.652 0.000 0.336 0.012
#> SRR944020 4 0.0000 0.9421 0.000 0.000 0.000 1.000
#> SRR944021 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944022 4 0.0000 0.9421 0.000 0.000 0.000 1.000
#> SRR944023 3 0.0000 0.8506 0.000 0.000 1.000 0.000
#> SRR944024 1 0.3172 0.6992 0.840 0.000 0.160 0.000
#> SRR944026 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944025 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944028 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944029 3 0.1302 0.8358 0.000 0.044 0.956 0.000
#> SRR944030 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944031 3 0.0000 0.8506 0.000 0.000 1.000 0.000
#> SRR944032 2 0.0188 0.9592 0.004 0.996 0.000 0.000
#> SRR944033 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944036 3 0.1211 0.8378 0.000 0.040 0.960 0.000
#> SRR944035 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944038 3 0.4454 0.5168 0.000 0.000 0.692 0.308
#> SRR944037 4 0.4222 0.5923 0.000 0.000 0.272 0.728
#> SRR944039 1 0.4817 0.3912 0.612 0.000 0.388 0.000
#> SRR944040 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944041 1 0.6011 0.2293 0.480 0.000 0.480 0.040
#> SRR944042 3 0.0000 0.8506 0.000 0.000 1.000 0.000
#> SRR944043 3 0.6219 0.1588 0.344 0.000 0.588 0.068
#> SRR944044 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944046 3 0.0000 0.8506 0.000 0.000 1.000 0.000
#> SRR944045 2 0.0336 0.9564 0.000 0.992 0.008 0.000
#> SRR944047 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944048 1 0.1489 0.7002 0.952 0.004 0.044 0.000
#> SRR944049 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944050 2 0.7030 0.0689 0.408 0.472 0.120 0.000
#> SRR944051 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944052 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944053 4 0.0000 0.9421 0.000 0.000 0.000 1.000
#> SRR944054 2 0.0336 0.9564 0.000 0.992 0.008 0.000
#> SRR944055 2 0.2760 0.8404 0.000 0.872 0.128 0.000
#> SRR944056 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944057 1 0.4830 0.3792 0.608 0.000 0.392 0.000
#> SRR944058 1 0.0000 0.6964 1.000 0.000 0.000 0.000
#> SRR944059 2 0.4522 0.5274 0.000 0.680 0.320 0.000
#> SRR944060 3 0.1637 0.8170 0.000 0.000 0.940 0.060
#> SRR944061 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944062 1 0.4222 0.6222 0.728 0.000 0.272 0.000
#> SRR944063 4 0.0000 0.9421 0.000 0.000 0.000 1.000
#> SRR944064 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944065 1 0.5143 0.3181 0.540 0.000 0.456 0.004
#> SRR944066 1 0.0000 0.6964 1.000 0.000 0.000 0.000
#> SRR944067 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944068 4 0.0000 0.9421 0.000 0.000 0.000 1.000
#> SRR944069 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944070 3 0.1940 0.8068 0.000 0.000 0.924 0.076
#> SRR944071 3 0.0000 0.8506 0.000 0.000 1.000 0.000
#> SRR944072 1 0.0000 0.6964 1.000 0.000 0.000 0.000
#> SRR944073 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944075 3 0.4697 0.3817 0.000 0.356 0.644 0.000
#> SRR944074 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944076 3 0.0000 0.8506 0.000 0.000 1.000 0.000
#> SRR944077 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944078 2 0.2589 0.8553 0.000 0.884 0.116 0.000
#> SRR944079 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944080 2 0.0000 0.9616 0.000 1.000 0.000 0.000
#> SRR944081 3 0.5332 0.5595 0.184 0.080 0.736 0.000
#> SRR944082 1 0.4040 0.6462 0.752 0.000 0.248 0.000
#> SRR944083 1 0.0000 0.6964 1.000 0.000 0.000 0.000
#> SRR944084 3 0.1302 0.8361 0.000 0.044 0.956 0.000
#> SRR944085 3 0.1637 0.8189 0.000 0.060 0.940 0.000
#> SRR944086 3 0.1356 0.8413 0.008 0.032 0.960 0.000
#> SRR944088 2 0.1557 0.9154 0.000 0.944 0.056 0.000
#> SRR944087 3 0.0000 0.8506 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.1018 0.6259 0.000 0.016 0.968 0.000 0.016
#> SRR944012 5 0.6166 0.1363 0.256 0.000 0.124 0.020 0.600
#> SRR944014 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> SRR944013 2 0.3445 0.8675 0.000 0.824 0.036 0.000 0.140
#> SRR944015 4 0.0703 0.9355 0.000 0.000 0.000 0.976 0.024
#> SRR944016 1 0.1270 0.5657 0.948 0.000 0.052 0.000 0.000
#> SRR944017 2 0.0324 0.9387 0.000 0.992 0.004 0.000 0.004
#> SRR944018 5 0.5111 0.1903 0.036 0.000 0.464 0.000 0.500
#> SRR944019 1 0.5203 0.4235 0.708 0.000 0.140 0.008 0.144
#> SRR944020 4 0.2732 0.8690 0.000 0.000 0.000 0.840 0.160
#> SRR944021 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> SRR944022 4 0.1121 0.9369 0.000 0.000 0.000 0.956 0.044
#> SRR944023 3 0.2648 0.5691 0.000 0.000 0.848 0.000 0.152
#> SRR944024 1 0.5352 0.1296 0.480 0.000 0.052 0.000 0.468
#> SRR944026 2 0.2561 0.8911 0.000 0.856 0.000 0.000 0.144
#> SRR944025 2 0.2020 0.9098 0.000 0.900 0.000 0.000 0.100
#> SRR944028 2 0.2605 0.8880 0.000 0.852 0.000 0.000 0.148
#> SRR944029 3 0.4873 0.4374 0.000 0.068 0.688 0.000 0.244
#> SRR944030 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> SRR944031 3 0.0000 0.6223 0.000 0.000 1.000 0.000 0.000
#> SRR944032 2 0.2488 0.8999 0.004 0.872 0.000 0.000 0.124
#> SRR944033 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> SRR944036 3 0.4404 0.5160 0.000 0.088 0.760 0.000 0.152
#> SRR944035 2 0.2020 0.9098 0.000 0.900 0.000 0.000 0.100
#> SRR944038 3 0.4577 0.3514 0.000 0.000 0.740 0.176 0.084
#> SRR944037 3 0.6766 -0.1894 0.000 0.000 0.396 0.320 0.284
#> SRR944039 1 0.5301 0.3827 0.676 0.000 0.176 0.000 0.148
#> SRR944040 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> SRR944041 5 0.5698 0.3021 0.036 0.000 0.440 0.024 0.500
#> SRR944042 3 0.1197 0.6149 0.000 0.000 0.952 0.000 0.048
#> SRR944043 5 0.6204 0.2307 0.028 0.000 0.420 0.068 0.484
#> SRR944044 2 0.1792 0.9199 0.000 0.916 0.000 0.000 0.084
#> SRR944046 3 0.1270 0.6134 0.000 0.000 0.948 0.000 0.052
#> SRR944045 2 0.0290 0.9381 0.000 0.992 0.008 0.000 0.000
#> SRR944047 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> SRR944048 1 0.4982 0.3998 0.556 0.000 0.032 0.000 0.412
#> SRR944049 2 0.0162 0.9403 0.000 0.996 0.000 0.000 0.004
#> SRR944050 1 0.4773 0.3308 0.716 0.216 0.064 0.000 0.004
#> SRR944051 2 0.2648 0.8854 0.000 0.848 0.000 0.000 0.152
#> SRR944052 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> SRR944053 4 0.0000 0.9384 0.000 0.000 0.000 1.000 0.000
#> SRR944054 2 0.1557 0.9232 0.000 0.940 0.008 0.000 0.052
#> SRR944055 2 0.1965 0.8814 0.000 0.904 0.096 0.000 0.000
#> SRR944056 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> SRR944057 1 0.2561 0.4967 0.856 0.000 0.144 0.000 0.000
#> SRR944058 1 0.3857 0.5004 0.688 0.000 0.000 0.000 0.312
#> SRR944059 2 0.5635 0.4242 0.000 0.620 0.252 0.000 0.128
#> SRR944060 3 0.2248 0.5807 0.000 0.000 0.900 0.012 0.088
#> SRR944061 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> SRR944062 1 0.6760 -0.0309 0.400 0.000 0.284 0.000 0.316
#> SRR944063 4 0.1671 0.9255 0.000 0.000 0.000 0.924 0.076
#> SRR944064 2 0.2020 0.9098 0.000 0.900 0.000 0.000 0.100
#> SRR944065 5 0.5911 0.3546 0.104 0.000 0.408 0.000 0.488
#> SRR944066 1 0.2929 0.5566 0.820 0.000 0.000 0.000 0.180
#> SRR944067 2 0.2020 0.9098 0.000 0.900 0.000 0.000 0.100
#> SRR944068 4 0.1043 0.9286 0.000 0.000 0.000 0.960 0.040
#> SRR944069 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> SRR944070 3 0.2189 0.5838 0.000 0.000 0.904 0.012 0.084
#> SRR944071 3 0.1908 0.6058 0.000 0.000 0.908 0.000 0.092
#> SRR944072 1 0.0880 0.5701 0.968 0.000 0.000 0.000 0.032
#> SRR944073 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> SRR944075 3 0.4833 0.1045 0.000 0.412 0.564 0.000 0.024
#> SRR944074 2 0.1908 0.9174 0.000 0.908 0.000 0.000 0.092
#> SRR944076 3 0.2648 0.5691 0.000 0.000 0.848 0.000 0.152
#> SRR944077 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> SRR944078 2 0.1851 0.8899 0.000 0.912 0.088 0.000 0.000
#> SRR944079 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.9409 0.000 1.000 0.000 0.000 0.000
#> SRR944081 5 0.6844 -0.0417 0.036 0.120 0.404 0.000 0.440
#> SRR944082 5 0.5895 -0.1868 0.440 0.000 0.100 0.000 0.460
#> SRR944083 1 0.3837 0.5030 0.692 0.000 0.000 0.000 0.308
#> SRR944084 3 0.4119 0.5410 0.000 0.068 0.780 0.000 0.152
#> SRR944085 3 0.4884 0.4534 0.000 0.128 0.720 0.000 0.152
#> SRR944086 3 0.5751 0.3630 0.036 0.068 0.652 0.000 0.244
#> SRR944088 2 0.2233 0.9080 0.000 0.904 0.016 0.000 0.080
#> SRR944087 3 0.1121 0.6157 0.000 0.000 0.956 0.000 0.044
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.2679 0.7199 0.000 0.000 0.864 0.000 0.040 0.096
#> SRR944012 1 0.6321 0.4872 0.564 0.000 0.180 0.000 0.184 0.072
#> SRR944014 2 0.0000 0.9270 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944013 2 0.3590 0.8610 0.000 0.808 0.044 0.000 0.016 0.132
#> SRR944015 4 0.0000 0.8108 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR944016 6 0.3922 0.8719 0.320 0.000 0.016 0.000 0.000 0.664
#> SRR944017 2 0.0520 0.9237 0.000 0.984 0.008 0.000 0.008 0.000
#> SRR944018 3 0.5350 0.3184 0.216 0.000 0.632 0.000 0.136 0.016
#> SRR944019 6 0.5628 0.7948 0.268 0.000 0.020 0.000 0.128 0.584
#> SRR944020 5 0.3578 0.1137 0.000 0.000 0.000 0.340 0.660 0.000
#> SRR944021 2 0.0000 0.9270 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944022 4 0.2883 0.7237 0.000 0.000 0.000 0.788 0.212 0.000
#> SRR944023 3 0.0000 0.7138 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR944024 1 0.2100 0.7069 0.884 0.000 0.112 0.000 0.000 0.004
#> SRR944026 2 0.3172 0.8678 0.000 0.816 0.000 0.000 0.036 0.148
#> SRR944025 2 0.2260 0.8840 0.000 0.860 0.000 0.000 0.000 0.140
#> SRR944028 2 0.2871 0.8596 0.000 0.804 0.000 0.000 0.004 0.192
#> SRR944029 3 0.3693 0.6253 0.000 0.036 0.816 0.000 0.100 0.048
#> SRR944030 2 0.0000 0.9270 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944031 3 0.3393 0.7117 0.000 0.000 0.820 0.004 0.068 0.108
#> SRR944032 2 0.2668 0.8727 0.004 0.828 0.000 0.000 0.000 0.168
#> SRR944033 2 0.0000 0.9270 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.9270 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944036 3 0.0937 0.7071 0.000 0.040 0.960 0.000 0.000 0.000
#> SRR944035 2 0.2260 0.8840 0.000 0.860 0.000 0.000 0.000 0.140
#> SRR944038 3 0.6972 0.2988 0.000 0.000 0.460 0.272 0.144 0.124
#> SRR944037 5 0.3328 0.5186 0.000 0.000 0.064 0.120 0.816 0.000
#> SRR944039 6 0.6812 0.6742 0.276 0.000 0.116 0.000 0.128 0.480
#> SRR944040 2 0.0000 0.9270 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944041 5 0.4262 0.5849 0.024 0.000 0.100 0.004 0.776 0.096
#> SRR944042 3 0.4100 0.6893 0.000 0.000 0.760 0.004 0.112 0.124
#> SRR944043 5 0.5014 0.5570 0.024 0.000 0.372 0.036 0.568 0.000
#> SRR944044 2 0.2457 0.8966 0.000 0.880 0.000 0.000 0.036 0.084
#> SRR944046 3 0.4100 0.6903 0.000 0.000 0.760 0.004 0.112 0.124
#> SRR944045 2 0.0458 0.9229 0.000 0.984 0.016 0.000 0.000 0.000
#> SRR944047 2 0.0000 0.9270 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944048 1 0.3054 0.6404 0.828 0.000 0.036 0.000 0.000 0.136
#> SRR944049 2 0.0260 0.9260 0.000 0.992 0.000 0.000 0.000 0.008
#> SRR944050 6 0.4339 0.8603 0.300 0.016 0.020 0.000 0.000 0.664
#> SRR944051 2 0.2871 0.8596 0.000 0.804 0.000 0.000 0.004 0.192
#> SRR944052 2 0.0000 0.9270 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944053 4 0.0713 0.8117 0.000 0.000 0.000 0.972 0.028 0.000
#> SRR944054 2 0.2066 0.9010 0.000 0.908 0.000 0.000 0.040 0.052
#> SRR944055 2 0.2212 0.8640 0.000 0.880 0.112 0.000 0.008 0.000
#> SRR944056 2 0.0000 0.9270 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944057 6 0.3684 0.8675 0.332 0.000 0.004 0.000 0.000 0.664
#> SRR944058 1 0.0146 0.6637 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR944059 2 0.3672 0.5147 0.000 0.632 0.368 0.000 0.000 0.000
#> SRR944060 3 0.5521 0.6096 0.000 0.000 0.652 0.048 0.176 0.124
#> SRR944061 2 0.0000 0.9270 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944062 1 0.3717 0.6386 0.812 0.000 0.056 0.000 0.028 0.104
#> SRR944063 4 0.3706 0.4440 0.000 0.000 0.000 0.620 0.380 0.000
#> SRR944064 2 0.2260 0.8840 0.000 0.860 0.000 0.000 0.000 0.140
#> SRR944065 5 0.5436 0.5980 0.088 0.000 0.264 0.000 0.616 0.032
#> SRR944066 1 0.3390 0.0224 0.704 0.000 0.000 0.000 0.000 0.296
#> SRR944067 2 0.2260 0.8840 0.000 0.860 0.000 0.000 0.000 0.140
#> SRR944068 4 0.0865 0.7893 0.000 0.000 0.000 0.964 0.036 0.000
#> SRR944069 2 0.0000 0.9270 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944070 3 0.5143 0.6473 0.000 0.000 0.692 0.040 0.144 0.124
#> SRR944071 3 0.1794 0.7260 0.000 0.000 0.924 0.000 0.036 0.040
#> SRR944072 6 0.3547 0.8661 0.332 0.000 0.000 0.000 0.000 0.668
#> SRR944073 2 0.0000 0.9270 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944075 3 0.5678 0.3054 0.000 0.352 0.536 0.000 0.036 0.076
#> SRR944074 2 0.2560 0.8941 0.000 0.872 0.000 0.000 0.036 0.092
#> SRR944076 3 0.0000 0.7138 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR944077 2 0.0000 0.9270 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944078 2 0.1908 0.8835 0.000 0.900 0.096 0.000 0.004 0.000
#> SRR944079 2 0.0000 0.9270 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.9270 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944081 3 0.5644 0.4236 0.000 0.040 0.632 0.000 0.172 0.156
#> SRR944082 1 0.2668 0.6883 0.828 0.000 0.168 0.000 0.004 0.000
#> SRR944083 1 0.0632 0.6491 0.976 0.000 0.000 0.000 0.000 0.024
#> SRR944084 3 0.1649 0.7020 0.000 0.036 0.932 0.000 0.032 0.000
#> SRR944085 3 0.1141 0.7012 0.000 0.052 0.948 0.000 0.000 0.000
#> SRR944086 3 0.3370 0.6553 0.056 0.028 0.856 0.000 0.024 0.036
#> SRR944088 2 0.3284 0.8545 0.000 0.832 0.008 0.000 0.104 0.056
#> SRR944087 3 0.3918 0.6922 0.000 0.000 0.768 0.000 0.108 0.124
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.963 0.984 0.4784 0.518 0.518
#> 3 3 0.528 0.573 0.773 0.2324 0.981 0.963
#> 4 4 0.645 0.798 0.861 0.1847 0.773 0.564
#> 5 5 0.713 0.715 0.827 0.1001 0.857 0.572
#> 6 6 0.814 0.845 0.893 0.0466 0.993 0.966
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.0000 0.97311 0.000 1.000
#> SRR944012 1 0.0376 0.99162 0.996 0.004
#> SRR944014 2 0.0000 0.97311 0.000 1.000
#> SRR944013 1 0.0376 0.99162 0.996 0.004
#> SRR944015 1 0.0376 0.99162 0.996 0.004
#> SRR944016 1 0.0000 0.98955 1.000 0.000
#> SRR944017 1 0.0376 0.99162 0.996 0.004
#> SRR944018 1 0.0376 0.99162 0.996 0.004
#> SRR944019 1 0.0376 0.99162 0.996 0.004
#> SRR944020 1 0.0376 0.99162 0.996 0.004
#> SRR944021 2 0.0000 0.97311 0.000 1.000
#> SRR944022 1 0.0376 0.99162 0.996 0.004
#> SRR944023 1 0.0376 0.99162 0.996 0.004
#> SRR944024 1 0.0000 0.98955 1.000 0.000
#> SRR944026 1 0.0376 0.99162 0.996 0.004
#> SRR944025 1 0.0376 0.99162 0.996 0.004
#> SRR944028 1 0.0376 0.99162 0.996 0.004
#> SRR944029 1 0.0376 0.99162 0.996 0.004
#> SRR944030 2 0.6712 0.77929 0.176 0.824
#> SRR944031 2 0.0672 0.96991 0.008 0.992
#> SRR944032 1 0.0376 0.99162 0.996 0.004
#> SRR944033 2 0.0000 0.97311 0.000 1.000
#> SRR944034 2 0.0000 0.97311 0.000 1.000
#> SRR944036 1 0.0672 0.98836 0.992 0.008
#> SRR944035 1 0.3274 0.93395 0.940 0.060
#> SRR944038 2 0.0376 0.97168 0.004 0.996
#> SRR944037 1 0.0376 0.99162 0.996 0.004
#> SRR944039 1 0.0376 0.99162 0.996 0.004
#> SRR944040 2 0.0000 0.97311 0.000 1.000
#> SRR944041 1 0.0376 0.99162 0.996 0.004
#> SRR944042 2 0.0000 0.97311 0.000 1.000
#> SRR944043 1 0.0376 0.99162 0.996 0.004
#> SRR944044 1 0.0376 0.99162 0.996 0.004
#> SRR944046 2 0.0000 0.97311 0.000 1.000
#> SRR944045 2 0.0000 0.97311 0.000 1.000
#> SRR944047 2 0.0000 0.97311 0.000 1.000
#> SRR944048 1 0.0000 0.98955 1.000 0.000
#> SRR944049 1 0.0376 0.99162 0.996 0.004
#> SRR944050 1 0.0000 0.98955 1.000 0.000
#> SRR944051 1 0.0376 0.99162 0.996 0.004
#> SRR944052 2 0.1414 0.95979 0.020 0.980
#> SRR944053 1 0.0376 0.99162 0.996 0.004
#> SRR944054 1 0.0376 0.99162 0.996 0.004
#> SRR944055 2 0.0000 0.97311 0.000 1.000
#> SRR944056 2 0.0000 0.97311 0.000 1.000
#> SRR944057 1 0.0000 0.98955 1.000 0.000
#> SRR944058 1 0.0000 0.98955 1.000 0.000
#> SRR944059 2 0.0672 0.96991 0.008 0.992
#> SRR944060 1 0.8386 0.62464 0.732 0.268
#> SRR944061 2 0.0000 0.97311 0.000 1.000
#> SRR944062 1 0.0000 0.98955 1.000 0.000
#> SRR944063 1 0.0376 0.99162 0.996 0.004
#> SRR944064 1 0.0376 0.99162 0.996 0.004
#> SRR944065 1 0.0376 0.99162 0.996 0.004
#> SRR944066 1 0.0000 0.98955 1.000 0.000
#> SRR944067 1 0.0376 0.99162 0.996 0.004
#> SRR944068 1 0.0376 0.99162 0.996 0.004
#> SRR944069 2 0.1414 0.95987 0.020 0.980
#> SRR944070 2 0.0000 0.97311 0.000 1.000
#> SRR944071 2 1.0000 0.00964 0.496 0.504
#> SRR944072 1 0.0000 0.98955 1.000 0.000
#> SRR944073 2 0.0000 0.97311 0.000 1.000
#> SRR944075 2 0.0672 0.96991 0.008 0.992
#> SRR944074 1 0.0376 0.99162 0.996 0.004
#> SRR944076 2 0.0672 0.96991 0.008 0.992
#> SRR944077 2 0.0000 0.97311 0.000 1.000
#> SRR944078 2 0.0000 0.97311 0.000 1.000
#> SRR944079 2 0.0000 0.97311 0.000 1.000
#> SRR944080 2 0.0672 0.96949 0.008 0.992
#> SRR944081 1 0.0376 0.99162 0.996 0.004
#> SRR944082 1 0.0000 0.98955 1.000 0.000
#> SRR944083 1 0.0000 0.98955 1.000 0.000
#> SRR944084 1 0.0376 0.99162 0.996 0.004
#> SRR944085 2 0.0672 0.96988 0.008 0.992
#> SRR944086 1 0.0376 0.99162 0.996 0.004
#> SRR944088 1 0.0376 0.99162 0.996 0.004
#> SRR944087 2 0.0000 0.97311 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 2 0.0000 0.5315 0.000 1.000 0.000
#> SRR944012 1 0.1964 0.8152 0.944 0.000 0.056
#> SRR944014 2 0.5882 -0.1260 0.000 0.652 0.348
#> SRR944013 1 0.4291 0.8470 0.820 0.000 0.180
#> SRR944015 1 0.6794 0.8027 0.648 0.028 0.324
#> SRR944016 1 0.5835 0.8395 0.660 0.000 0.340
#> SRR944017 1 0.4346 0.8466 0.816 0.000 0.184
#> SRR944018 1 0.5138 0.8431 0.748 0.000 0.252
#> SRR944019 1 0.1964 0.8152 0.944 0.000 0.056
#> SRR944020 1 0.1964 0.8152 0.944 0.000 0.056
#> SRR944021 2 0.6062 -0.2621 0.000 0.616 0.384
#> SRR944022 1 0.1964 0.8152 0.944 0.000 0.056
#> SRR944023 1 0.9303 0.6789 0.500 0.184 0.316
#> SRR944024 1 0.5835 0.8395 0.660 0.000 0.340
#> SRR944026 1 0.0000 0.8125 1.000 0.000 0.000
#> SRR944025 1 0.7364 0.7741 0.640 0.056 0.304
#> SRR944028 1 0.5327 0.8228 0.728 0.000 0.272
#> SRR944029 1 0.0000 0.8125 1.000 0.000 0.000
#> SRR944030 2 0.7801 -0.5316 0.052 0.520 0.428
#> SRR944031 2 0.0000 0.5315 0.000 1.000 0.000
#> SRR944032 1 0.5122 0.8485 0.788 0.012 0.200
#> SRR944033 2 0.6079 -0.2103 0.000 0.612 0.388
#> SRR944034 2 0.7104 -0.2713 0.032 0.608 0.360
#> SRR944036 1 0.9472 0.6513 0.480 0.204 0.316
#> SRR944035 1 0.8346 0.6536 0.548 0.092 0.360
#> SRR944038 2 0.0000 0.5315 0.000 1.000 0.000
#> SRR944037 1 0.1964 0.8152 0.944 0.000 0.056
#> SRR944039 1 0.5178 0.8490 0.744 0.000 0.256
#> SRR944040 2 0.5529 0.1040 0.000 0.704 0.296
#> SRR944041 1 0.1964 0.8152 0.944 0.000 0.056
#> SRR944042 2 0.0237 0.5303 0.000 0.996 0.004
#> SRR944043 1 0.5138 0.8431 0.748 0.000 0.252
#> SRR944044 1 0.0000 0.8125 1.000 0.000 0.000
#> SRR944046 2 0.0000 0.5315 0.000 1.000 0.000
#> SRR944045 2 0.5650 0.0396 0.000 0.688 0.312
#> SRR944047 2 0.6204 -0.3538 0.000 0.576 0.424
#> SRR944048 1 0.5835 0.8395 0.660 0.000 0.340
#> SRR944049 1 0.7620 0.7360 0.596 0.056 0.348
#> SRR944050 1 0.5835 0.8395 0.660 0.000 0.340
#> SRR944051 1 0.0000 0.8125 1.000 0.000 0.000
#> SRR944052 2 0.4047 0.4024 0.004 0.848 0.148
#> SRR944053 1 0.1964 0.8152 0.944 0.000 0.056
#> SRR944054 1 0.0000 0.8125 1.000 0.000 0.000
#> SRR944055 2 0.2711 0.4846 0.000 0.912 0.088
#> SRR944056 2 0.6111 -0.3321 0.000 0.604 0.396
#> SRR944057 1 0.5835 0.8395 0.660 0.000 0.340
#> SRR944058 1 0.5835 0.8395 0.660 0.000 0.340
#> SRR944059 2 0.0000 0.5315 0.000 1.000 0.000
#> SRR944060 1 0.9617 0.5006 0.472 0.280 0.248
#> SRR944061 2 0.4654 0.2892 0.000 0.792 0.208
#> SRR944062 1 0.5835 0.8395 0.660 0.000 0.340
#> SRR944063 1 0.1964 0.8152 0.944 0.000 0.056
#> SRR944064 1 0.6203 0.8366 0.760 0.056 0.184
#> SRR944065 1 0.5138 0.8431 0.748 0.000 0.252
#> SRR944066 1 0.5835 0.8395 0.660 0.000 0.340
#> SRR944067 1 0.7726 0.7074 0.572 0.056 0.372
#> SRR944068 1 0.6794 0.8027 0.648 0.028 0.324
#> SRR944069 3 0.6608 0.8970 0.008 0.432 0.560
#> SRR944070 2 0.0000 0.5315 0.000 1.000 0.000
#> SRR944071 2 0.8968 -0.1428 0.408 0.464 0.128
#> SRR944072 1 0.5835 0.8395 0.660 0.000 0.340
#> SRR944073 2 0.6079 -0.2197 0.000 0.612 0.388
#> SRR944075 2 0.0237 0.5303 0.000 0.996 0.004
#> SRR944074 1 0.0000 0.8125 1.000 0.000 0.000
#> SRR944076 2 0.0237 0.5285 0.004 0.996 0.000
#> SRR944077 2 0.6180 -0.3325 0.000 0.584 0.416
#> SRR944078 2 0.2448 0.4943 0.000 0.924 0.076
#> SRR944079 2 0.6008 -0.1762 0.000 0.628 0.372
#> SRR944080 3 0.6664 0.8922 0.008 0.464 0.528
#> SRR944081 1 0.0000 0.8125 1.000 0.000 0.000
#> SRR944082 1 0.5678 0.8430 0.684 0.000 0.316
#> SRR944083 1 0.5835 0.8395 0.660 0.000 0.340
#> SRR944084 1 0.6407 0.8293 0.700 0.028 0.272
#> SRR944085 2 0.3995 0.3265 0.116 0.868 0.016
#> SRR944086 1 0.4575 0.8468 0.812 0.004 0.184
#> SRR944088 1 0.0000 0.8125 1.000 0.000 0.000
#> SRR944087 2 0.0000 0.5315 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.0000 0.897 0.000 0.000 1.000 0.000
#> SRR944012 4 0.0336 0.790 0.008 0.000 0.000 0.992
#> SRR944014 2 0.3074 0.960 0.000 0.848 0.152 0.000
#> SRR944013 4 0.3322 0.774 0.076 0.024 0.016 0.884
#> SRR944015 4 0.4122 0.741 0.056 0.096 0.008 0.840
#> SRR944016 1 0.0000 0.940 1.000 0.000 0.000 0.000
#> SRR944017 4 0.5636 0.667 0.288 0.024 0.016 0.672
#> SRR944018 4 0.5852 0.639 0.328 0.024 0.016 0.632
#> SRR944019 4 0.0707 0.791 0.020 0.000 0.000 0.980
#> SRR944020 4 0.0376 0.790 0.004 0.004 0.000 0.992
#> SRR944021 2 0.2868 0.966 0.000 0.864 0.136 0.000
#> SRR944022 4 0.0376 0.790 0.004 0.004 0.000 0.992
#> SRR944023 4 0.7547 0.497 0.340 0.024 0.116 0.520
#> SRR944024 1 0.0000 0.940 1.000 0.000 0.000 0.000
#> SRR944026 4 0.0376 0.790 0.004 0.004 0.000 0.992
#> SRR944025 4 0.5951 0.653 0.296 0.036 0.016 0.652
#> SRR944028 4 0.5684 0.660 0.296 0.024 0.016 0.664
#> SRR944029 4 0.0188 0.791 0.004 0.000 0.000 0.996
#> SRR944030 2 0.3335 0.956 0.000 0.856 0.128 0.016
#> SRR944031 3 0.0000 0.897 0.000 0.000 1.000 0.000
#> SRR944032 4 0.5833 0.636 0.324 0.024 0.016 0.636
#> SRR944033 2 0.2814 0.967 0.000 0.868 0.132 0.000
#> SRR944034 4 0.9625 0.152 0.216 0.280 0.144 0.360
#> SRR944036 4 0.7711 0.471 0.340 0.024 0.132 0.504
#> SRR944035 4 0.6091 0.655 0.288 0.020 0.040 0.652
#> SRR944038 3 0.5263 0.551 0.032 0.004 0.704 0.260
#> SRR944037 4 0.0376 0.790 0.004 0.004 0.000 0.992
#> SRR944039 4 0.5856 0.672 0.280 0.036 0.016 0.668
#> SRR944040 3 0.2868 0.767 0.000 0.136 0.864 0.000
#> SRR944041 4 0.0336 0.790 0.008 0.000 0.000 0.992
#> SRR944042 3 0.0000 0.897 0.000 0.000 1.000 0.000
#> SRR944043 4 0.6134 0.602 0.352 0.032 0.016 0.600
#> SRR944044 4 0.0376 0.790 0.004 0.004 0.000 0.992
#> SRR944046 3 0.0000 0.897 0.000 0.000 1.000 0.000
#> SRR944045 2 0.3975 0.862 0.000 0.760 0.240 0.000
#> SRR944047 2 0.2760 0.966 0.000 0.872 0.128 0.000
#> SRR944048 1 0.0000 0.940 1.000 0.000 0.000 0.000
#> SRR944049 4 0.6216 0.662 0.276 0.032 0.036 0.656
#> SRR944050 1 0.1174 0.929 0.968 0.020 0.000 0.012
#> SRR944051 4 0.0992 0.791 0.012 0.008 0.004 0.976
#> SRR944052 2 0.4088 0.887 0.000 0.764 0.232 0.004
#> SRR944053 4 0.0376 0.790 0.004 0.004 0.000 0.992
#> SRR944054 4 0.0376 0.790 0.004 0.004 0.000 0.992
#> SRR944055 3 0.0817 0.886 0.000 0.024 0.976 0.000
#> SRR944056 2 0.2973 0.964 0.000 0.856 0.144 0.000
#> SRR944057 1 0.0000 0.940 1.000 0.000 0.000 0.000
#> SRR944058 1 0.3706 0.833 0.848 0.040 0.000 0.112
#> SRR944059 3 0.0188 0.896 0.000 0.004 0.996 0.000
#> SRR944060 4 0.7655 0.416 0.076 0.056 0.340 0.528
#> SRR944061 2 0.3528 0.931 0.000 0.808 0.192 0.000
#> SRR944062 1 0.0000 0.940 1.000 0.000 0.000 0.000
#> SRR944063 4 0.0376 0.790 0.004 0.004 0.000 0.992
#> SRR944064 4 0.5775 0.597 0.356 0.016 0.016 0.612
#> SRR944065 4 0.3781 0.765 0.104 0.024 0.016 0.856
#> SRR944066 1 0.0000 0.940 1.000 0.000 0.000 0.000
#> SRR944067 4 0.5951 0.653 0.296 0.036 0.016 0.652
#> SRR944068 4 0.4122 0.741 0.056 0.096 0.008 0.840
#> SRR944069 2 0.2647 0.962 0.000 0.880 0.120 0.000
#> SRR944070 3 0.5523 0.545 0.032 0.012 0.696 0.260
#> SRR944071 3 0.2973 0.808 0.000 0.020 0.884 0.096
#> SRR944072 1 0.4553 0.714 0.780 0.040 0.000 0.180
#> SRR944073 2 0.2814 0.967 0.000 0.868 0.132 0.000
#> SRR944075 3 0.1256 0.880 0.000 0.028 0.964 0.008
#> SRR944074 4 0.0376 0.790 0.004 0.004 0.000 0.992
#> SRR944076 3 0.0188 0.896 0.000 0.000 0.996 0.004
#> SRR944077 2 0.2760 0.966 0.000 0.872 0.128 0.000
#> SRR944078 3 0.0707 0.889 0.000 0.020 0.980 0.000
#> SRR944079 2 0.2868 0.966 0.000 0.864 0.136 0.000
#> SRR944080 2 0.2958 0.956 0.004 0.876 0.116 0.004
#> SRR944081 4 0.0469 0.791 0.012 0.000 0.000 0.988
#> SRR944082 1 0.2737 0.846 0.888 0.008 0.000 0.104
#> SRR944083 1 0.0000 0.940 1.000 0.000 0.000 0.000
#> SRR944084 4 0.1854 0.781 0.012 0.048 0.000 0.940
#> SRR944085 3 0.1489 0.870 0.000 0.004 0.952 0.044
#> SRR944086 4 0.5537 0.673 0.288 0.020 0.016 0.676
#> SRR944088 4 0.0188 0.791 0.004 0.000 0.000 0.996
#> SRR944087 3 0.0000 0.897 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.0162 0.9832 0.000 0.004 0.996 0.000 0.000
#> SRR944012 4 0.1059 0.7786 0.008 0.004 0.000 0.968 0.020
#> SRR944014 2 0.1043 0.9633 0.000 0.960 0.040 0.000 0.000
#> SRR944013 4 0.3612 0.6261 0.028 0.000 0.000 0.800 0.172
#> SRR944015 4 0.4337 0.5336 0.004 0.016 0.000 0.696 0.284
#> SRR944016 1 0.0000 0.7863 1.000 0.000 0.000 0.000 0.000
#> SRR944017 5 0.6413 0.4417 0.172 0.000 0.000 0.396 0.432
#> SRR944018 4 0.6159 0.2844 0.208 0.000 0.004 0.580 0.208
#> SRR944019 4 0.1310 0.7783 0.024 0.000 0.000 0.956 0.020
#> SRR944020 4 0.2756 0.7567 0.004 0.024 0.000 0.880 0.092
#> SRR944021 2 0.0794 0.9617 0.000 0.972 0.028 0.000 0.000
#> SRR944022 4 0.2597 0.7560 0.000 0.024 0.000 0.884 0.092
#> SRR944023 1 0.7369 0.3897 0.544 0.004 0.112 0.120 0.220
#> SRR944024 1 0.0000 0.7863 1.000 0.000 0.000 0.000 0.000
#> SRR944026 4 0.1892 0.7517 0.004 0.000 0.000 0.916 0.080
#> SRR944025 5 0.6512 0.5673 0.176 0.004 0.004 0.292 0.524
#> SRR944028 5 0.6433 0.5652 0.176 0.004 0.000 0.312 0.508
#> SRR944029 4 0.0404 0.7780 0.000 0.000 0.000 0.988 0.012
#> SRR944030 2 0.2333 0.9065 0.000 0.916 0.016 0.028 0.040
#> SRR944031 3 0.0162 0.9838 0.000 0.004 0.996 0.000 0.000
#> SRR944032 1 0.6785 -0.2661 0.388 0.000 0.000 0.308 0.304
#> SRR944033 2 0.0963 0.9640 0.000 0.964 0.036 0.000 0.000
#> SRR944034 5 0.9001 0.4063 0.164 0.224 0.028 0.268 0.316
#> SRR944036 1 0.7525 0.3712 0.524 0.004 0.164 0.096 0.212
#> SRR944035 5 0.6623 0.5666 0.176 0.004 0.008 0.292 0.520
#> SRR944038 5 0.6409 -0.0975 0.004 0.000 0.404 0.148 0.444
#> SRR944037 4 0.2482 0.7585 0.000 0.024 0.000 0.892 0.084
#> SRR944039 4 0.5906 0.3166 0.204 0.000 0.004 0.616 0.176
#> SRR944040 3 0.1410 0.9262 0.000 0.060 0.940 0.000 0.000
#> SRR944041 4 0.0833 0.7780 0.004 0.004 0.000 0.976 0.016
#> SRR944042 3 0.0290 0.9801 0.000 0.000 0.992 0.000 0.008
#> SRR944043 4 0.6246 0.2336 0.236 0.000 0.004 0.564 0.196
#> SRR944044 4 0.2011 0.7479 0.004 0.000 0.000 0.908 0.088
#> SRR944046 3 0.0000 0.9827 0.000 0.000 1.000 0.000 0.000
#> SRR944045 2 0.3480 0.7265 0.000 0.752 0.248 0.000 0.000
#> SRR944047 2 0.0963 0.9640 0.000 0.964 0.036 0.000 0.000
#> SRR944048 1 0.0000 0.7863 1.000 0.000 0.000 0.000 0.000
#> SRR944049 5 0.6407 0.5669 0.176 0.004 0.000 0.304 0.516
#> SRR944050 1 0.1282 0.7753 0.952 0.000 0.000 0.004 0.044
#> SRR944051 4 0.2583 0.7166 0.004 0.000 0.000 0.864 0.132
#> SRR944052 2 0.1851 0.9277 0.000 0.912 0.088 0.000 0.000
#> SRR944053 4 0.2597 0.7560 0.000 0.024 0.000 0.884 0.092
#> SRR944054 4 0.1671 0.7550 0.000 0.000 0.000 0.924 0.076
#> SRR944055 3 0.0162 0.9832 0.000 0.004 0.996 0.000 0.000
#> SRR944056 2 0.1043 0.9635 0.000 0.960 0.040 0.000 0.000
#> SRR944057 1 0.0000 0.7863 1.000 0.000 0.000 0.000 0.000
#> SRR944058 1 0.3574 0.7230 0.836 0.004 0.000 0.072 0.088
#> SRR944059 3 0.0162 0.9838 0.000 0.004 0.996 0.000 0.000
#> SRR944060 5 0.8203 0.2121 0.092 0.008 0.292 0.224 0.384
#> SRR944061 2 0.1197 0.9599 0.000 0.952 0.048 0.000 0.000
#> SRR944062 1 0.0000 0.7863 1.000 0.000 0.000 0.000 0.000
#> SRR944063 4 0.2540 0.7571 0.000 0.024 0.000 0.888 0.088
#> SRR944064 1 0.5864 0.3309 0.560 0.000 0.000 0.120 0.320
#> SRR944065 4 0.4114 0.6867 0.040 0.000 0.004 0.772 0.184
#> SRR944066 1 0.0000 0.7863 1.000 0.000 0.000 0.000 0.000
#> SRR944067 5 0.6512 0.5673 0.176 0.004 0.004 0.292 0.524
#> SRR944068 4 0.4337 0.5336 0.004 0.016 0.000 0.696 0.284
#> SRR944069 2 0.0794 0.9617 0.000 0.972 0.028 0.000 0.000
#> SRR944070 5 0.6409 -0.0975 0.004 0.000 0.404 0.148 0.444
#> SRR944071 3 0.1202 0.9431 0.000 0.004 0.960 0.032 0.004
#> SRR944072 1 0.4127 0.6862 0.796 0.004 0.000 0.100 0.100
#> SRR944073 2 0.1568 0.9566 0.000 0.944 0.036 0.000 0.020
#> SRR944075 3 0.0290 0.9811 0.000 0.008 0.992 0.000 0.000
#> SRR944074 4 0.1952 0.7500 0.004 0.000 0.000 0.912 0.084
#> SRR944076 3 0.0162 0.9838 0.000 0.004 0.996 0.000 0.000
#> SRR944077 2 0.0963 0.9640 0.000 0.964 0.036 0.000 0.000
#> SRR944078 3 0.0404 0.9782 0.000 0.012 0.988 0.000 0.000
#> SRR944079 2 0.1341 0.9557 0.000 0.944 0.056 0.000 0.000
#> SRR944080 2 0.0794 0.9617 0.000 0.972 0.028 0.000 0.000
#> SRR944081 4 0.1082 0.7735 0.008 0.000 0.000 0.964 0.028
#> SRR944082 1 0.2974 0.7413 0.868 0.000 0.000 0.052 0.080
#> SRR944083 1 0.0000 0.7863 1.000 0.000 0.000 0.000 0.000
#> SRR944084 4 0.1608 0.7690 0.000 0.000 0.000 0.928 0.072
#> SRR944085 3 0.0451 0.9775 0.000 0.004 0.988 0.008 0.000
#> SRR944086 4 0.6025 0.1454 0.204 0.000 0.004 0.600 0.192
#> SRR944088 4 0.0880 0.7728 0.000 0.000 0.000 0.968 0.032
#> SRR944087 3 0.0162 0.9838 0.000 0.004 0.996 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.0937 0.944 0.000 0.040 0.960 0.000 0.000 0.000
#> SRR944012 4 0.0665 0.838 0.004 0.000 0.000 0.980 0.008 0.008
#> SRR944014 2 0.0146 0.977 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944013 4 0.3915 0.788 0.004 0.000 0.000 0.776 0.128 0.092
#> SRR944015 4 0.2902 0.742 0.000 0.000 0.000 0.800 0.004 0.196
#> SRR944016 1 0.0000 0.850 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR944017 5 0.3774 0.810 0.004 0.004 0.004 0.112 0.804 0.072
#> SRR944018 4 0.3547 0.752 0.096 0.000 0.004 0.824 0.012 0.064
#> SRR944019 4 0.0862 0.837 0.008 0.000 0.000 0.972 0.016 0.004
#> SRR944020 4 0.1921 0.820 0.000 0.004 0.004 0.924 0.044 0.024
#> SRR944021 2 0.0146 0.977 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944022 4 0.1921 0.820 0.000 0.004 0.004 0.924 0.044 0.024
#> SRR944023 1 0.6419 0.547 0.616 0.004 0.148 0.104 0.016 0.112
#> SRR944024 1 0.0146 0.850 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR944026 4 0.4338 0.741 0.000 0.000 0.004 0.716 0.072 0.208
#> SRR944025 5 0.1226 0.898 0.004 0.004 0.000 0.040 0.952 0.000
#> SRR944028 5 0.2154 0.893 0.004 0.004 0.000 0.064 0.908 0.020
#> SRR944029 4 0.2547 0.821 0.000 0.000 0.004 0.868 0.016 0.112
#> SRR944030 2 0.0725 0.956 0.000 0.976 0.000 0.012 0.012 0.000
#> SRR944031 3 0.0260 0.956 0.000 0.008 0.992 0.000 0.000 0.000
#> SRR944032 1 0.5471 0.610 0.632 0.000 0.000 0.080 0.240 0.048
#> SRR944033 2 0.0146 0.977 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944034 5 0.4360 0.713 0.004 0.188 0.004 0.056 0.740 0.008
#> SRR944036 1 0.6500 0.475 0.584 0.004 0.216 0.076 0.016 0.104
#> SRR944035 5 0.1442 0.897 0.004 0.012 0.000 0.040 0.944 0.000
#> SRR944038 6 0.4201 0.899 0.000 0.004 0.196 0.068 0.000 0.732
#> SRR944037 4 0.2000 0.819 0.000 0.004 0.004 0.920 0.044 0.028
#> SRR944039 4 0.3555 0.767 0.084 0.000 0.004 0.832 0.028 0.052
#> SRR944040 3 0.2454 0.773 0.000 0.160 0.840 0.000 0.000 0.000
#> SRR944041 4 0.0767 0.838 0.004 0.000 0.000 0.976 0.012 0.008
#> SRR944042 3 0.0405 0.954 0.000 0.008 0.988 0.000 0.000 0.004
#> SRR944043 4 0.5103 0.413 0.284 0.000 0.004 0.628 0.012 0.072
#> SRR944044 4 0.4389 0.739 0.000 0.000 0.004 0.712 0.076 0.208
#> SRR944046 3 0.0405 0.954 0.000 0.008 0.988 0.000 0.000 0.004
#> SRR944045 2 0.2697 0.732 0.000 0.812 0.188 0.000 0.000 0.000
#> SRR944047 2 0.0146 0.977 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944048 1 0.0146 0.850 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR944049 5 0.2761 0.892 0.004 0.036 0.004 0.060 0.884 0.012
#> SRR944050 1 0.1010 0.843 0.960 0.000 0.000 0.000 0.004 0.036
#> SRR944051 4 0.4033 0.773 0.000 0.004 0.000 0.760 0.156 0.080
#> SRR944052 2 0.0363 0.970 0.000 0.988 0.012 0.000 0.000 0.000
#> SRR944053 4 0.1921 0.820 0.000 0.004 0.004 0.924 0.044 0.024
#> SRR944054 4 0.3946 0.775 0.000 0.000 0.004 0.764 0.068 0.164
#> SRR944055 3 0.1141 0.937 0.000 0.052 0.948 0.000 0.000 0.000
#> SRR944056 2 0.0146 0.977 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944057 1 0.0146 0.850 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR944058 1 0.2908 0.799 0.864 0.000 0.000 0.076 0.012 0.048
#> SRR944059 3 0.0260 0.956 0.000 0.008 0.992 0.000 0.000 0.000
#> SRR944060 6 0.4516 0.802 0.012 0.004 0.080 0.144 0.008 0.752
#> SRR944061 2 0.0146 0.977 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944062 1 0.0146 0.850 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR944063 4 0.2000 0.819 0.000 0.004 0.004 0.920 0.044 0.028
#> SRR944064 1 0.5100 0.645 0.656 0.000 0.000 0.048 0.248 0.048
#> SRR944065 4 0.2145 0.824 0.016 0.000 0.004 0.916 0.020 0.044
#> SRR944066 1 0.0146 0.850 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR944067 5 0.1226 0.898 0.004 0.004 0.000 0.040 0.952 0.000
#> SRR944068 4 0.2902 0.742 0.000 0.000 0.000 0.800 0.004 0.196
#> SRR944069 2 0.0260 0.974 0.000 0.992 0.008 0.000 0.000 0.000
#> SRR944070 6 0.4150 0.894 0.000 0.004 0.204 0.060 0.000 0.732
#> SRR944071 3 0.0717 0.949 0.000 0.016 0.976 0.008 0.000 0.000
#> SRR944072 1 0.3522 0.753 0.812 0.000 0.000 0.128 0.012 0.048
#> SRR944073 2 0.0508 0.969 0.000 0.984 0.004 0.000 0.012 0.000
#> SRR944075 3 0.1141 0.937 0.000 0.052 0.948 0.000 0.000 0.000
#> SRR944074 4 0.4389 0.739 0.000 0.000 0.004 0.712 0.076 0.208
#> SRR944076 3 0.0260 0.956 0.000 0.008 0.992 0.000 0.000 0.000
#> SRR944077 2 0.0146 0.977 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944078 3 0.1141 0.937 0.000 0.052 0.948 0.000 0.000 0.000
#> SRR944079 2 0.0146 0.977 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944080 2 0.0405 0.972 0.000 0.988 0.004 0.000 0.008 0.000
#> SRR944081 4 0.1313 0.838 0.004 0.000 0.000 0.952 0.016 0.028
#> SRR944082 1 0.1738 0.834 0.928 0.000 0.000 0.016 0.004 0.052
#> SRR944083 1 0.0146 0.850 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR944084 4 0.2006 0.838 0.004 0.000 0.004 0.916 0.016 0.060
#> SRR944085 3 0.0260 0.956 0.000 0.008 0.992 0.000 0.000 0.000
#> SRR944086 4 0.3958 0.782 0.020 0.004 0.004 0.800 0.120 0.052
#> SRR944088 4 0.3048 0.802 0.000 0.000 0.004 0.824 0.020 0.152
#> SRR944087 3 0.0260 0.956 0.000 0.008 0.992 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.976 0.989 0.5032 0.496 0.496
#> 3 3 0.924 0.910 0.963 0.3127 0.806 0.624
#> 4 4 0.814 0.775 0.896 0.0975 0.880 0.670
#> 5 5 0.744 0.656 0.793 0.0531 0.936 0.775
#> 6 6 0.716 0.606 0.769 0.0357 0.961 0.842
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.0000 0.977 0.000 1.000
#> SRR944012 1 0.0000 0.999 1.000 0.000
#> SRR944014 2 0.0000 0.977 0.000 1.000
#> SRR944013 1 0.0000 0.999 1.000 0.000
#> SRR944015 1 0.1184 0.984 0.984 0.016
#> SRR944016 1 0.0000 0.999 1.000 0.000
#> SRR944017 1 0.0000 0.999 1.000 0.000
#> SRR944018 1 0.0000 0.999 1.000 0.000
#> SRR944019 1 0.0000 0.999 1.000 0.000
#> SRR944020 1 0.0000 0.999 1.000 0.000
#> SRR944021 2 0.0000 0.977 0.000 1.000
#> SRR944022 1 0.0000 0.999 1.000 0.000
#> SRR944023 2 0.0000 0.977 0.000 1.000
#> SRR944024 1 0.0000 0.999 1.000 0.000
#> SRR944026 1 0.0000 0.999 1.000 0.000
#> SRR944025 1 0.0000 0.999 1.000 0.000
#> SRR944028 1 0.0000 0.999 1.000 0.000
#> SRR944029 1 0.0000 0.999 1.000 0.000
#> SRR944030 2 0.0000 0.977 0.000 1.000
#> SRR944031 2 0.0000 0.977 0.000 1.000
#> SRR944032 1 0.0000 0.999 1.000 0.000
#> SRR944033 2 0.0000 0.977 0.000 1.000
#> SRR944034 2 0.0000 0.977 0.000 1.000
#> SRR944036 2 0.0000 0.977 0.000 1.000
#> SRR944035 2 0.7528 0.734 0.216 0.784
#> SRR944038 2 0.0000 0.977 0.000 1.000
#> SRR944037 1 0.0000 0.999 1.000 0.000
#> SRR944039 1 0.0000 0.999 1.000 0.000
#> SRR944040 2 0.0000 0.977 0.000 1.000
#> SRR944041 1 0.0000 0.999 1.000 0.000
#> SRR944042 2 0.0000 0.977 0.000 1.000
#> SRR944043 1 0.0000 0.999 1.000 0.000
#> SRR944044 1 0.0000 0.999 1.000 0.000
#> SRR944046 2 0.0000 0.977 0.000 1.000
#> SRR944045 2 0.0000 0.977 0.000 1.000
#> SRR944047 2 0.0000 0.977 0.000 1.000
#> SRR944048 1 0.0000 0.999 1.000 0.000
#> SRR944049 2 0.8267 0.663 0.260 0.740
#> SRR944050 1 0.0000 0.999 1.000 0.000
#> SRR944051 1 0.0000 0.999 1.000 0.000
#> SRR944052 2 0.0000 0.977 0.000 1.000
#> SRR944053 1 0.0000 0.999 1.000 0.000
#> SRR944054 1 0.0000 0.999 1.000 0.000
#> SRR944055 2 0.0000 0.977 0.000 1.000
#> SRR944056 2 0.0000 0.977 0.000 1.000
#> SRR944057 1 0.0000 0.999 1.000 0.000
#> SRR944058 1 0.0000 0.999 1.000 0.000
#> SRR944059 2 0.0000 0.977 0.000 1.000
#> SRR944060 2 0.0000 0.977 0.000 1.000
#> SRR944061 2 0.0000 0.977 0.000 1.000
#> SRR944062 1 0.0000 0.999 1.000 0.000
#> SRR944063 1 0.0000 0.999 1.000 0.000
#> SRR944064 1 0.0672 0.992 0.992 0.008
#> SRR944065 1 0.0000 0.999 1.000 0.000
#> SRR944066 1 0.0000 0.999 1.000 0.000
#> SRR944067 1 0.0000 0.999 1.000 0.000
#> SRR944068 1 0.0938 0.988 0.988 0.012
#> SRR944069 2 0.0000 0.977 0.000 1.000
#> SRR944070 2 0.0000 0.977 0.000 1.000
#> SRR944071 2 0.0000 0.977 0.000 1.000
#> SRR944072 1 0.0000 0.999 1.000 0.000
#> SRR944073 2 0.0000 0.977 0.000 1.000
#> SRR944075 2 0.0000 0.977 0.000 1.000
#> SRR944074 1 0.0000 0.999 1.000 0.000
#> SRR944076 2 0.0000 0.977 0.000 1.000
#> SRR944077 2 0.0000 0.977 0.000 1.000
#> SRR944078 2 0.0000 0.977 0.000 1.000
#> SRR944079 2 0.0000 0.977 0.000 1.000
#> SRR944080 2 0.0000 0.977 0.000 1.000
#> SRR944081 1 0.0000 0.999 1.000 0.000
#> SRR944082 1 0.0000 0.999 1.000 0.000
#> SRR944083 1 0.0000 0.999 1.000 0.000
#> SRR944084 2 0.8909 0.572 0.308 0.692
#> SRR944085 2 0.0000 0.977 0.000 1.000
#> SRR944086 1 0.0000 0.999 1.000 0.000
#> SRR944088 1 0.0000 0.999 1.000 0.000
#> SRR944087 2 0.0000 0.977 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944012 2 0.0237 0.928 0.004 0.996 0.000
#> SRR944014 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944013 2 0.0747 0.923 0.016 0.984 0.000
#> SRR944015 2 0.0000 0.930 0.000 1.000 0.000
#> SRR944016 1 0.0000 0.955 1.000 0.000 0.000
#> SRR944017 2 0.3340 0.841 0.120 0.880 0.000
#> SRR944018 2 0.6062 0.423 0.384 0.616 0.000
#> SRR944019 2 0.0747 0.923 0.016 0.984 0.000
#> SRR944020 2 0.0000 0.930 0.000 1.000 0.000
#> SRR944021 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944022 2 0.0000 0.930 0.000 1.000 0.000
#> SRR944023 1 0.5591 0.544 0.696 0.000 0.304
#> SRR944024 1 0.0000 0.955 1.000 0.000 0.000
#> SRR944026 2 0.0000 0.930 0.000 1.000 0.000
#> SRR944025 1 0.0000 0.955 1.000 0.000 0.000
#> SRR944028 1 0.0237 0.952 0.996 0.004 0.000
#> SRR944029 2 0.0000 0.930 0.000 1.000 0.000
#> SRR944030 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944031 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944032 1 0.0000 0.955 1.000 0.000 0.000
#> SRR944033 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944034 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944036 3 0.6215 0.225 0.428 0.000 0.572
#> SRR944035 1 0.0000 0.955 1.000 0.000 0.000
#> SRR944038 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944037 2 0.0000 0.930 0.000 1.000 0.000
#> SRR944039 2 0.5621 0.591 0.308 0.692 0.000
#> SRR944040 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944041 2 0.0237 0.928 0.004 0.996 0.000
#> SRR944042 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944043 2 0.6008 0.453 0.372 0.628 0.000
#> SRR944044 2 0.0000 0.930 0.000 1.000 0.000
#> SRR944046 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944045 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944047 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944048 1 0.0000 0.955 1.000 0.000 0.000
#> SRR944049 3 0.2434 0.929 0.036 0.024 0.940
#> SRR944050 1 0.0000 0.955 1.000 0.000 0.000
#> SRR944051 2 0.4399 0.765 0.188 0.812 0.000
#> SRR944052 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944053 2 0.0000 0.930 0.000 1.000 0.000
#> SRR944054 2 0.0000 0.930 0.000 1.000 0.000
#> SRR944055 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944056 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944057 1 0.0000 0.955 1.000 0.000 0.000
#> SRR944058 1 0.0000 0.955 1.000 0.000 0.000
#> SRR944059 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944060 3 0.2448 0.904 0.000 0.076 0.924
#> SRR944061 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944062 1 0.0000 0.955 1.000 0.000 0.000
#> SRR944063 2 0.0000 0.930 0.000 1.000 0.000
#> SRR944064 1 0.0000 0.955 1.000 0.000 0.000
#> SRR944065 2 0.4291 0.778 0.180 0.820 0.000
#> SRR944066 1 0.0000 0.955 1.000 0.000 0.000
#> SRR944067 1 0.0000 0.955 1.000 0.000 0.000
#> SRR944068 2 0.0000 0.930 0.000 1.000 0.000
#> SRR944069 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944070 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944071 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944072 1 0.0237 0.952 0.996 0.004 0.000
#> SRR944073 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944075 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944074 2 0.0237 0.928 0.004 0.996 0.000
#> SRR944076 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944077 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944078 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944079 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944080 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944081 2 0.0000 0.930 0.000 1.000 0.000
#> SRR944082 1 0.0000 0.955 1.000 0.000 0.000
#> SRR944083 1 0.0000 0.955 1.000 0.000 0.000
#> SRR944084 2 0.0237 0.927 0.000 0.996 0.004
#> SRR944085 3 0.0000 0.982 0.000 0.000 1.000
#> SRR944086 1 0.6026 0.299 0.624 0.376 0.000
#> SRR944088 2 0.0000 0.930 0.000 1.000 0.000
#> SRR944087 3 0.0000 0.982 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944012 4 0.0524 0.7491 0.008 0.000 0.004 0.988
#> SRR944014 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944013 4 0.3224 0.6966 0.016 0.000 0.120 0.864
#> SRR944015 3 0.3355 0.6439 0.000 0.004 0.836 0.160
#> SRR944016 1 0.2921 0.8505 0.860 0.000 0.140 0.000
#> SRR944017 3 0.1284 0.6864 0.024 0.000 0.964 0.012
#> SRR944018 3 0.2131 0.6904 0.032 0.000 0.932 0.036
#> SRR944019 3 0.5167 0.0665 0.004 0.000 0.508 0.488
#> SRR944020 4 0.4713 0.2847 0.000 0.000 0.360 0.640
#> SRR944021 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944022 4 0.4948 0.0224 0.000 0.000 0.440 0.560
#> SRR944023 1 0.6149 0.6137 0.676 0.180 0.144 0.000
#> SRR944024 1 0.0336 0.8797 0.992 0.000 0.008 0.000
#> SRR944026 4 0.0707 0.7561 0.000 0.000 0.020 0.980
#> SRR944025 1 0.1545 0.8802 0.952 0.000 0.040 0.008
#> SRR944028 1 0.1767 0.8791 0.944 0.000 0.044 0.012
#> SRR944029 4 0.0469 0.7557 0.000 0.000 0.012 0.988
#> SRR944030 3 0.4500 0.4358 0.000 0.316 0.684 0.000
#> SRR944031 2 0.1022 0.9627 0.000 0.968 0.032 0.000
#> SRR944032 1 0.0779 0.8767 0.980 0.000 0.016 0.004
#> SRR944033 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0188 0.9889 0.000 0.996 0.004 0.000
#> SRR944036 1 0.5842 0.2020 0.520 0.448 0.032 0.000
#> SRR944035 1 0.1305 0.8769 0.960 0.000 0.036 0.004
#> SRR944038 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944037 3 0.4992 0.1674 0.000 0.000 0.524 0.476
#> SRR944039 3 0.2775 0.6623 0.084 0.000 0.896 0.020
#> SRR944040 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944041 4 0.0817 0.7553 0.000 0.000 0.024 0.976
#> SRR944042 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944043 3 0.2021 0.6876 0.040 0.000 0.936 0.024
#> SRR944044 4 0.0336 0.7555 0.000 0.000 0.008 0.992
#> SRR944046 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944045 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944047 2 0.0188 0.9889 0.000 0.996 0.004 0.000
#> SRR944048 1 0.0707 0.8826 0.980 0.000 0.020 0.000
#> SRR944049 4 0.7515 0.1491 0.124 0.368 0.016 0.492
#> SRR944050 1 0.3219 0.8363 0.836 0.000 0.164 0.000
#> SRR944051 4 0.2706 0.6874 0.080 0.000 0.020 0.900
#> SRR944052 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944053 4 0.3649 0.5983 0.000 0.000 0.204 0.796
#> SRR944054 4 0.0336 0.7560 0.000 0.000 0.008 0.992
#> SRR944055 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944056 2 0.0992 0.9706 0.004 0.976 0.008 0.012
#> SRR944057 1 0.3074 0.8441 0.848 0.000 0.152 0.000
#> SRR944058 1 0.1174 0.8772 0.968 0.000 0.020 0.012
#> SRR944059 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944060 3 0.1978 0.6629 0.000 0.068 0.928 0.004
#> SRR944061 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944062 1 0.1389 0.8790 0.952 0.000 0.048 0.000
#> SRR944063 4 0.1211 0.7501 0.000 0.000 0.040 0.960
#> SRR944064 1 0.0592 0.8814 0.984 0.000 0.016 0.000
#> SRR944065 4 0.5228 0.4865 0.268 0.000 0.036 0.696
#> SRR944066 1 0.3942 0.7787 0.764 0.000 0.236 0.000
#> SRR944067 1 0.1004 0.8740 0.972 0.000 0.024 0.004
#> SRR944068 4 0.4477 0.4093 0.000 0.000 0.312 0.688
#> SRR944069 2 0.0188 0.9889 0.000 0.996 0.004 0.000
#> SRR944070 2 0.0188 0.9882 0.000 0.996 0.004 0.000
#> SRR944071 2 0.3266 0.7936 0.000 0.832 0.168 0.000
#> SRR944072 1 0.3942 0.7776 0.764 0.000 0.236 0.000
#> SRR944073 2 0.0188 0.9889 0.000 0.996 0.004 0.000
#> SRR944075 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944074 4 0.0000 0.7535 0.000 0.000 0.000 1.000
#> SRR944076 2 0.0188 0.9882 0.000 0.996 0.004 0.000
#> SRR944077 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944078 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944079 2 0.0188 0.9889 0.000 0.996 0.004 0.000
#> SRR944080 2 0.0188 0.9889 0.000 0.996 0.004 0.000
#> SRR944081 3 0.4925 0.3082 0.000 0.000 0.572 0.428
#> SRR944082 1 0.2281 0.8653 0.904 0.000 0.096 0.000
#> SRR944083 1 0.0592 0.8825 0.984 0.000 0.016 0.000
#> SRR944084 3 0.4855 0.4496 0.000 0.004 0.644 0.352
#> SRR944085 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> SRR944086 4 0.5906 0.2137 0.436 0.000 0.036 0.528
#> SRR944088 4 0.1022 0.7533 0.000 0.000 0.032 0.968
#> SRR944087 2 0.0000 0.9905 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 2 0.1568 0.9326 0.020 0.944 0.000 0.036 0.000
#> SRR944012 5 0.1484 0.7694 0.048 0.000 0.000 0.008 0.944
#> SRR944014 2 0.0162 0.9495 0.000 0.996 0.000 0.004 0.000
#> SRR944013 5 0.6032 0.4481 0.220 0.000 0.020 0.132 0.628
#> SRR944015 4 0.2251 0.6239 0.024 0.008 0.000 0.916 0.052
#> SRR944016 1 0.4978 0.5306 0.496 0.000 0.476 0.028 0.000
#> SRR944017 4 0.4350 0.1733 0.408 0.000 0.004 0.588 0.000
#> SRR944018 4 0.3068 0.5991 0.072 0.000 0.032 0.876 0.020
#> SRR944019 1 0.6739 -0.2370 0.400 0.000 0.000 0.336 0.264
#> SRR944020 5 0.4540 0.2766 0.020 0.000 0.000 0.340 0.640
#> SRR944021 2 0.0290 0.9502 0.008 0.992 0.000 0.000 0.000
#> SRR944022 4 0.5049 0.0826 0.032 0.000 0.000 0.484 0.484
#> SRR944023 3 0.5823 0.4947 0.096 0.084 0.700 0.120 0.000
#> SRR944024 3 0.0693 0.6540 0.012 0.000 0.980 0.008 0.000
#> SRR944026 5 0.0451 0.7781 0.008 0.000 0.000 0.004 0.988
#> SRR944025 1 0.4670 0.4724 0.548 0.000 0.440 0.008 0.004
#> SRR944028 3 0.4595 -0.1261 0.488 0.000 0.504 0.004 0.004
#> SRR944029 5 0.0510 0.7774 0.016 0.000 0.000 0.000 0.984
#> SRR944030 4 0.5981 0.1828 0.112 0.404 0.000 0.484 0.000
#> SRR944031 2 0.1270 0.9274 0.000 0.948 0.000 0.052 0.000
#> SRR944032 3 0.3551 0.6020 0.220 0.000 0.772 0.008 0.000
#> SRR944033 2 0.0000 0.9494 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0566 0.9490 0.012 0.984 0.000 0.004 0.000
#> SRR944036 3 0.6302 0.4212 0.132 0.156 0.648 0.064 0.000
#> SRR944035 3 0.4419 0.5133 0.344 0.008 0.644 0.004 0.000
#> SRR944038 2 0.3056 0.8840 0.056 0.876 0.012 0.056 0.000
#> SRR944037 4 0.5188 0.4155 0.056 0.000 0.000 0.600 0.344
#> SRR944039 1 0.5652 -0.0383 0.468 0.000 0.064 0.464 0.004
#> SRR944040 2 0.0000 0.9494 0.000 1.000 0.000 0.000 0.000
#> SRR944041 5 0.1399 0.7760 0.028 0.000 0.000 0.020 0.952
#> SRR944042 2 0.1300 0.9376 0.028 0.956 0.000 0.016 0.000
#> SRR944043 4 0.3256 0.5853 0.084 0.000 0.028 0.864 0.024
#> SRR944044 5 0.1082 0.7770 0.028 0.000 0.000 0.008 0.964
#> SRR944046 2 0.0798 0.9465 0.016 0.976 0.000 0.008 0.000
#> SRR944045 2 0.0162 0.9496 0.000 0.996 0.000 0.004 0.000
#> SRR944047 2 0.0162 0.9495 0.000 0.996 0.000 0.004 0.000
#> SRR944048 3 0.1851 0.5987 0.088 0.000 0.912 0.000 0.000
#> SRR944049 5 0.7319 0.2309 0.120 0.292 0.048 0.020 0.520
#> SRR944050 1 0.4855 0.5703 0.552 0.000 0.424 0.024 0.000
#> SRR944051 5 0.4291 0.6729 0.160 0.000 0.044 0.016 0.780
#> SRR944052 2 0.1012 0.9430 0.020 0.968 0.000 0.012 0.000
#> SRR944053 5 0.4192 0.5267 0.032 0.000 0.000 0.232 0.736
#> SRR944054 5 0.1943 0.7617 0.056 0.000 0.000 0.020 0.924
#> SRR944055 2 0.0324 0.9499 0.004 0.992 0.000 0.004 0.000
#> SRR944056 2 0.1932 0.9245 0.032 0.936 0.008 0.020 0.004
#> SRR944057 1 0.4965 0.5510 0.520 0.000 0.452 0.028 0.000
#> SRR944058 3 0.3861 0.3402 0.284 0.000 0.712 0.000 0.004
#> SRR944059 2 0.0162 0.9500 0.004 0.996 0.000 0.000 0.000
#> SRR944060 4 0.3649 0.5229 0.152 0.040 0.000 0.808 0.000
#> SRR944061 2 0.0451 0.9488 0.008 0.988 0.000 0.004 0.000
#> SRR944062 3 0.1877 0.6458 0.064 0.000 0.924 0.012 0.000
#> SRR944063 5 0.1725 0.7565 0.020 0.000 0.000 0.044 0.936
#> SRR944064 3 0.0566 0.6489 0.012 0.000 0.984 0.004 0.000
#> SRR944065 5 0.6735 0.2952 0.168 0.000 0.304 0.020 0.508
#> SRR944066 1 0.5693 0.5414 0.468 0.000 0.452 0.080 0.000
#> SRR944067 3 0.2806 0.6334 0.152 0.000 0.844 0.004 0.000
#> SRR944068 4 0.5573 0.4416 0.076 0.008 0.000 0.612 0.304
#> SRR944069 2 0.0798 0.9476 0.016 0.976 0.000 0.008 0.000
#> SRR944070 2 0.2260 0.9100 0.028 0.908 0.000 0.064 0.000
#> SRR944071 2 0.3534 0.6755 0.000 0.744 0.000 0.256 0.000
#> SRR944072 1 0.5775 0.5382 0.496 0.000 0.424 0.076 0.004
#> SRR944073 2 0.0451 0.9488 0.008 0.988 0.000 0.004 0.000
#> SRR944075 2 0.0671 0.9467 0.016 0.980 0.000 0.004 0.000
#> SRR944074 5 0.1041 0.7749 0.032 0.000 0.000 0.004 0.964
#> SRR944076 2 0.5543 0.7030 0.088 0.724 0.096 0.092 0.000
#> SRR944077 2 0.0451 0.9488 0.008 0.988 0.000 0.004 0.000
#> SRR944078 2 0.0404 0.9483 0.012 0.988 0.000 0.000 0.000
#> SRR944079 2 0.0162 0.9495 0.000 0.996 0.000 0.004 0.000
#> SRR944080 2 0.1569 0.9339 0.032 0.948 0.008 0.012 0.000
#> SRR944081 4 0.5547 0.3809 0.080 0.000 0.000 0.564 0.356
#> SRR944082 3 0.2735 0.6301 0.084 0.000 0.880 0.036 0.000
#> SRR944083 3 0.3160 0.4648 0.188 0.000 0.808 0.004 0.000
#> SRR944084 4 0.4384 0.5956 0.032 0.020 0.000 0.764 0.184
#> SRR944085 2 0.3279 0.8790 0.048 0.864 0.016 0.072 0.000
#> SRR944086 3 0.6708 0.3753 0.288 0.000 0.520 0.020 0.172
#> SRR944088 5 0.1018 0.7754 0.016 0.000 0.000 0.016 0.968
#> SRR944087 2 0.3142 0.8780 0.056 0.868 0.008 0.068 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 2 0.0551 0.9209 0.000 0.984 0.004 0.004 0.000 0.008
#> SRR944012 5 0.2757 0.6810 0.004 0.000 0.008 0.004 0.848 0.136
#> SRR944014 2 0.0146 0.9215 0.000 0.996 0.000 0.004 0.000 0.000
#> SRR944013 5 0.7735 0.2134 0.156 0.000 0.028 0.184 0.432 0.200
#> SRR944015 4 0.3227 0.5693 0.000 0.008 0.036 0.860 0.040 0.056
#> SRR944016 1 0.2058 0.7215 0.908 0.000 0.072 0.012 0.000 0.008
#> SRR944017 4 0.5476 0.3329 0.380 0.000 0.036 0.536 0.004 0.044
#> SRR944018 4 0.3538 0.5562 0.028 0.000 0.084 0.836 0.008 0.044
#> SRR944019 4 0.7893 0.2812 0.284 0.000 0.020 0.344 0.180 0.172
#> SRR944020 5 0.4945 -0.0054 0.000 0.000 0.000 0.452 0.484 0.064
#> SRR944021 2 0.0767 0.9214 0.004 0.976 0.008 0.000 0.000 0.012
#> SRR944022 4 0.5768 0.2414 0.004 0.000 0.012 0.536 0.324 0.124
#> SRR944023 3 0.6453 0.2429 0.064 0.040 0.620 0.172 0.004 0.100
#> SRR944024 3 0.3731 0.5937 0.240 0.000 0.736 0.004 0.000 0.020
#> SRR944026 5 0.0622 0.7205 0.000 0.000 0.000 0.008 0.980 0.012
#> SRR944025 1 0.3400 0.6707 0.832 0.000 0.064 0.008 0.004 0.092
#> SRR944028 1 0.6366 -0.1035 0.436 0.000 0.144 0.016 0.016 0.388
#> SRR944029 5 0.0665 0.7184 0.000 0.000 0.004 0.008 0.980 0.008
#> SRR944030 4 0.6564 0.2288 0.096 0.364 0.040 0.472 0.000 0.028
#> SRR944031 2 0.2130 0.8910 0.008 0.916 0.020 0.048 0.000 0.008
#> SRR944032 6 0.6050 0.1981 0.276 0.000 0.312 0.000 0.000 0.412
#> SRR944033 2 0.0291 0.9218 0.000 0.992 0.000 0.004 0.000 0.004
#> SRR944034 2 0.1375 0.9162 0.008 0.952 0.008 0.004 0.000 0.028
#> SRR944036 3 0.5879 0.2258 0.032 0.112 0.660 0.044 0.000 0.152
#> SRR944035 6 0.5879 0.3923 0.228 0.000 0.260 0.004 0.000 0.508
#> SRR944038 2 0.3525 0.8005 0.000 0.800 0.156 0.012 0.000 0.032
#> SRR944037 4 0.5225 0.3808 0.004 0.000 0.008 0.620 0.272 0.096
#> SRR944039 4 0.6558 0.2850 0.356 0.000 0.052 0.468 0.012 0.112
#> SRR944040 2 0.0260 0.9218 0.000 0.992 0.000 0.000 0.000 0.008
#> SRR944041 5 0.1882 0.7125 0.000 0.000 0.008 0.012 0.920 0.060
#> SRR944042 2 0.1257 0.9124 0.000 0.952 0.028 0.000 0.000 0.020
#> SRR944043 4 0.4493 0.5041 0.056 0.000 0.120 0.764 0.004 0.056
#> SRR944044 5 0.1668 0.7140 0.000 0.000 0.004 0.008 0.928 0.060
#> SRR944046 2 0.0291 0.9215 0.000 0.992 0.000 0.004 0.000 0.004
#> SRR944045 2 0.0551 0.9219 0.000 0.984 0.004 0.004 0.000 0.008
#> SRR944047 2 0.0653 0.9215 0.004 0.980 0.000 0.004 0.000 0.012
#> SRR944048 3 0.4362 0.4580 0.392 0.000 0.584 0.004 0.000 0.020
#> SRR944049 5 0.7454 0.2937 0.056 0.168 0.060 0.020 0.536 0.160
#> SRR944050 1 0.0964 0.7334 0.968 0.000 0.012 0.016 0.000 0.004
#> SRR944051 5 0.5011 0.1058 0.004 0.000 0.048 0.004 0.492 0.452
#> SRR944052 2 0.1931 0.8958 0.004 0.916 0.008 0.004 0.000 0.068
#> SRR944053 5 0.5887 0.3284 0.012 0.000 0.008 0.260 0.564 0.156
#> SRR944054 5 0.3037 0.6916 0.008 0.000 0.012 0.008 0.840 0.132
#> SRR944055 2 0.0508 0.9222 0.000 0.984 0.000 0.004 0.000 0.012
#> SRR944056 2 0.2572 0.8768 0.004 0.884 0.008 0.008 0.008 0.088
#> SRR944057 1 0.1148 0.7370 0.960 0.000 0.020 0.016 0.000 0.004
#> SRR944058 1 0.5969 0.2164 0.560 0.000 0.260 0.016 0.008 0.156
#> SRR944059 2 0.0777 0.9200 0.000 0.972 0.004 0.000 0.000 0.024
#> SRR944060 4 0.4586 0.5253 0.156 0.036 0.036 0.752 0.000 0.020
#> SRR944061 2 0.0582 0.9216 0.004 0.984 0.004 0.004 0.000 0.004
#> SRR944062 3 0.3012 0.5929 0.196 0.000 0.796 0.000 0.000 0.008
#> SRR944063 5 0.4077 0.6387 0.000 0.000 0.008 0.100 0.768 0.124
#> SRR944064 3 0.3756 0.5854 0.268 0.000 0.712 0.000 0.000 0.020
#> SRR944065 6 0.6562 0.4454 0.032 0.000 0.240 0.016 0.192 0.520
#> SRR944066 1 0.2789 0.7149 0.864 0.000 0.088 0.044 0.000 0.004
#> SRR944067 3 0.5631 -0.1902 0.156 0.000 0.484 0.000 0.000 0.360
#> SRR944068 4 0.6631 0.2153 0.000 0.008 0.048 0.476 0.316 0.152
#> SRR944069 2 0.1760 0.9088 0.004 0.936 0.020 0.012 0.000 0.028
#> SRR944070 2 0.2274 0.8915 0.000 0.908 0.028 0.028 0.000 0.036
#> SRR944071 2 0.4991 0.3454 0.012 0.576 0.024 0.372 0.000 0.016
#> SRR944072 1 0.3728 0.6821 0.816 0.000 0.052 0.040 0.000 0.092
#> SRR944073 2 0.0146 0.9215 0.000 0.996 0.000 0.004 0.000 0.000
#> SRR944075 2 0.0717 0.9199 0.000 0.976 0.008 0.000 0.000 0.016
#> SRR944074 5 0.1714 0.7082 0.000 0.000 0.000 0.000 0.908 0.092
#> SRR944076 2 0.5246 0.6126 0.000 0.652 0.228 0.032 0.000 0.088
#> SRR944077 2 0.0291 0.9213 0.000 0.992 0.000 0.004 0.000 0.004
#> SRR944078 2 0.0603 0.9215 0.000 0.980 0.004 0.000 0.000 0.016
#> SRR944079 2 0.0146 0.9215 0.000 0.996 0.000 0.004 0.000 0.000
#> SRR944080 2 0.3896 0.8064 0.008 0.796 0.048 0.008 0.004 0.136
#> SRR944081 4 0.5786 0.3875 0.020 0.000 0.016 0.604 0.252 0.108
#> SRR944082 3 0.3492 0.5688 0.168 0.000 0.796 0.020 0.000 0.016
#> SRR944083 3 0.4315 0.2460 0.492 0.000 0.492 0.004 0.000 0.012
#> SRR944084 4 0.4388 0.5420 0.000 0.012 0.028 0.776 0.108 0.076
#> SRR944085 2 0.5208 0.6879 0.000 0.684 0.180 0.060 0.000 0.076
#> SRR944086 6 0.5924 0.5048 0.060 0.000 0.164 0.028 0.092 0.656
#> SRR944088 5 0.1536 0.7135 0.000 0.000 0.004 0.016 0.940 0.040
#> SRR944087 2 0.3077 0.8591 0.000 0.860 0.068 0.032 0.000 0.040
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.566 0.795 0.908 0.2828 0.771 0.771
#> 3 3 0.568 0.742 0.795 0.3762 0.606 0.533
#> 4 4 0.883 0.916 0.943 0.3425 0.911 0.835
#> 5 5 0.906 0.910 0.941 0.0457 0.998 0.996
#> 6 6 0.929 0.872 0.921 0.0376 1.000 1.000
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.0376 0.886 0.004 0.996
#> SRR944012 1 0.9866 0.209 0.568 0.432
#> SRR944014 2 0.0000 0.889 0.000 1.000
#> SRR944013 2 0.0000 0.889 0.000 1.000
#> SRR944015 1 0.0672 0.828 0.992 0.008
#> SRR944016 2 0.8499 0.640 0.276 0.724
#> SRR944017 2 0.0000 0.889 0.000 1.000
#> SRR944018 2 0.8909 0.594 0.308 0.692
#> SRR944019 2 0.8608 0.630 0.284 0.716
#> SRR944020 1 0.0000 0.828 1.000 0.000
#> SRR944021 2 0.0000 0.889 0.000 1.000
#> SRR944022 1 0.0000 0.828 1.000 0.000
#> SRR944023 2 0.6712 0.740 0.176 0.824
#> SRR944024 2 0.8713 0.618 0.292 0.708
#> SRR944026 2 0.0000 0.889 0.000 1.000
#> SRR944025 2 0.0000 0.889 0.000 1.000
#> SRR944028 2 0.0000 0.889 0.000 1.000
#> SRR944029 2 0.0000 0.889 0.000 1.000
#> SRR944030 2 0.0000 0.889 0.000 1.000
#> SRR944031 2 0.6801 0.735 0.180 0.820
#> SRR944032 2 0.0000 0.889 0.000 1.000
#> SRR944033 2 0.0000 0.889 0.000 1.000
#> SRR944034 2 0.0000 0.889 0.000 1.000
#> SRR944036 2 0.0000 0.889 0.000 1.000
#> SRR944035 2 0.0000 0.889 0.000 1.000
#> SRR944038 1 0.8327 0.658 0.736 0.264
#> SRR944037 2 0.9044 0.571 0.320 0.680
#> SRR944039 2 0.8763 0.613 0.296 0.704
#> SRR944040 2 0.0000 0.889 0.000 1.000
#> SRR944041 2 0.8955 0.584 0.312 0.688
#> SRR944042 2 0.0672 0.883 0.008 0.992
#> SRR944043 2 0.8608 0.629 0.284 0.716
#> SRR944044 2 0.0000 0.889 0.000 1.000
#> SRR944046 2 0.0672 0.883 0.008 0.992
#> SRR944045 2 0.0000 0.889 0.000 1.000
#> SRR944047 2 0.0000 0.889 0.000 1.000
#> SRR944048 2 0.8713 0.618 0.292 0.708
#> SRR944049 2 0.0000 0.889 0.000 1.000
#> SRR944050 2 0.8499 0.640 0.276 0.724
#> SRR944051 2 0.0000 0.889 0.000 1.000
#> SRR944052 2 0.0000 0.889 0.000 1.000
#> SRR944053 1 0.0000 0.828 1.000 0.000
#> SRR944054 2 0.0000 0.889 0.000 1.000
#> SRR944055 2 0.0000 0.889 0.000 1.000
#> SRR944056 2 0.0000 0.889 0.000 1.000
#> SRR944057 2 0.8661 0.624 0.288 0.712
#> SRR944058 2 0.8955 0.586 0.312 0.688
#> SRR944059 2 0.0376 0.886 0.004 0.996
#> SRR944060 1 0.8763 0.610 0.704 0.296
#> SRR944061 2 0.0000 0.889 0.000 1.000
#> SRR944062 2 0.8813 0.606 0.300 0.700
#> SRR944063 1 0.0000 0.828 1.000 0.000
#> SRR944064 2 0.0000 0.889 0.000 1.000
#> SRR944065 2 0.9427 0.482 0.360 0.640
#> SRR944066 2 0.8661 0.624 0.288 0.712
#> SRR944067 2 0.0000 0.889 0.000 1.000
#> SRR944068 1 0.0672 0.828 0.992 0.008
#> SRR944069 2 0.0000 0.889 0.000 1.000
#> SRR944070 1 0.8327 0.658 0.736 0.264
#> SRR944071 2 0.0000 0.889 0.000 1.000
#> SRR944072 2 0.8909 0.593 0.308 0.692
#> SRR944073 2 0.0000 0.889 0.000 1.000
#> SRR944075 2 0.0000 0.889 0.000 1.000
#> SRR944074 2 0.0000 0.889 0.000 1.000
#> SRR944076 2 0.0938 0.880 0.012 0.988
#> SRR944077 2 0.0000 0.889 0.000 1.000
#> SRR944078 2 0.0000 0.889 0.000 1.000
#> SRR944079 2 0.0000 0.889 0.000 1.000
#> SRR944080 2 0.0000 0.889 0.000 1.000
#> SRR944081 2 0.0000 0.889 0.000 1.000
#> SRR944082 2 0.8763 0.613 0.296 0.704
#> SRR944083 2 0.8661 0.624 0.288 0.712
#> SRR944084 2 0.0000 0.889 0.000 1.000
#> SRR944085 2 0.0672 0.883 0.008 0.992
#> SRR944086 2 0.0000 0.889 0.000 1.000
#> SRR944088 2 0.0000 0.889 0.000 1.000
#> SRR944087 2 0.0000 0.889 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 2 0.6495 0.822 0.460 0.536 0.004
#> SRR944012 1 0.6853 0.389 0.712 0.224 0.064
#> SRR944014 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944013 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944015 3 0.0424 0.812 0.000 0.008 0.992
#> SRR944016 1 0.1289 0.883 0.968 0.032 0.000
#> SRR944017 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944018 1 0.1491 0.896 0.968 0.016 0.016
#> SRR944019 1 0.1964 0.879 0.944 0.056 0.000
#> SRR944020 2 0.9823 -0.644 0.260 0.420 0.320
#> SRR944021 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944022 2 0.9823 -0.644 0.260 0.420 0.320
#> SRR944023 1 0.9191 -0.300 0.428 0.424 0.148
#> SRR944024 1 0.0592 0.902 0.988 0.012 0.000
#> SRR944026 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944025 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944028 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944029 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944030 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944031 2 0.9224 0.221 0.408 0.440 0.152
#> SRR944032 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944033 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944034 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944036 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944035 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944038 3 0.6811 0.843 0.220 0.064 0.716
#> SRR944037 1 0.2187 0.881 0.948 0.024 0.028
#> SRR944039 1 0.1643 0.890 0.956 0.044 0.000
#> SRR944040 2 0.6286 0.835 0.464 0.536 0.000
#> SRR944041 1 0.2261 0.875 0.932 0.068 0.000
#> SRR944042 2 0.6633 0.789 0.444 0.548 0.008
#> SRR944043 1 0.1267 0.895 0.972 0.024 0.004
#> SRR944044 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944046 2 0.6641 0.806 0.448 0.544 0.008
#> SRR944045 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944047 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944048 1 0.0592 0.902 0.988 0.012 0.000
#> SRR944049 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944050 1 0.1289 0.883 0.968 0.032 0.000
#> SRR944051 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944052 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944053 2 0.9823 -0.644 0.260 0.420 0.320
#> SRR944054 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944055 2 0.6280 0.831 0.460 0.540 0.000
#> SRR944056 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944057 1 0.0747 0.901 0.984 0.016 0.000
#> SRR944058 1 0.0592 0.895 0.988 0.012 0.000
#> SRR944059 2 0.6495 0.813 0.460 0.536 0.004
#> SRR944060 3 0.7758 0.776 0.280 0.084 0.636
#> SRR944061 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944062 1 0.0424 0.901 0.992 0.008 0.000
#> SRR944063 2 0.9823 -0.644 0.260 0.420 0.320
#> SRR944064 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944065 1 0.3528 0.827 0.892 0.016 0.092
#> SRR944066 1 0.0747 0.901 0.984 0.016 0.000
#> SRR944067 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944068 3 0.0424 0.812 0.000 0.008 0.992
#> SRR944069 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944070 3 0.6811 0.843 0.220 0.064 0.716
#> SRR944071 2 0.6286 0.835 0.464 0.536 0.000
#> SRR944072 1 0.0424 0.897 0.992 0.008 0.000
#> SRR944073 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944075 2 0.6280 0.831 0.460 0.540 0.000
#> SRR944074 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944076 2 0.6786 0.795 0.448 0.540 0.012
#> SRR944077 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944078 2 0.6280 0.831 0.460 0.540 0.000
#> SRR944079 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944080 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944081 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944082 1 0.0983 0.902 0.980 0.016 0.004
#> SRR944083 1 0.0747 0.901 0.984 0.016 0.000
#> SRR944084 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944085 2 0.6641 0.795 0.448 0.544 0.008
#> SRR944086 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944088 2 0.6295 0.842 0.472 0.528 0.000
#> SRR944087 2 0.6286 0.827 0.464 0.536 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 2 0.0937 0.967 0.012 0.976 0.012 0.000
#> SRR944012 1 0.7153 0.239 0.444 0.132 0.000 0.424
#> SRR944014 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944013 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944015 3 0.1637 0.656 0.000 0.000 0.940 0.060
#> SRR944016 1 0.2011 0.889 0.920 0.080 0.000 0.000
#> SRR944017 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944018 1 0.3593 0.877 0.868 0.092 0.016 0.024
#> SRR944019 1 0.4322 0.808 0.804 0.152 0.000 0.044
#> SRR944020 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> SRR944021 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944022 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> SRR944023 2 0.5800 0.607 0.128 0.708 0.164 0.000
#> SRR944024 1 0.1557 0.888 0.944 0.056 0.000 0.000
#> SRR944026 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944025 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944028 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944029 2 0.0188 0.979 0.004 0.996 0.000 0.000
#> SRR944030 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944031 2 0.5863 0.602 0.120 0.700 0.180 0.000
#> SRR944032 2 0.0188 0.979 0.004 0.996 0.000 0.000
#> SRR944033 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944036 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944035 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944038 3 0.4387 0.780 0.236 0.012 0.752 0.000
#> SRR944037 1 0.4792 0.838 0.808 0.120 0.028 0.044
#> SRR944039 1 0.4123 0.829 0.820 0.136 0.000 0.044
#> SRR944040 2 0.0376 0.977 0.004 0.992 0.004 0.000
#> SRR944041 1 0.4804 0.779 0.776 0.160 0.000 0.064
#> SRR944042 2 0.1624 0.948 0.020 0.952 0.028 0.000
#> SRR944043 1 0.2256 0.877 0.924 0.056 0.020 0.000
#> SRR944044 2 0.0188 0.979 0.004 0.996 0.000 0.000
#> SRR944046 2 0.1297 0.957 0.020 0.964 0.016 0.000
#> SRR944045 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944047 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944048 1 0.1557 0.888 0.944 0.056 0.000 0.000
#> SRR944049 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944050 1 0.2081 0.888 0.916 0.084 0.000 0.000
#> SRR944051 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944052 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944053 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> SRR944054 2 0.0188 0.979 0.004 0.996 0.000 0.000
#> SRR944055 2 0.0524 0.974 0.004 0.988 0.008 0.000
#> SRR944056 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944057 1 0.1792 0.893 0.932 0.068 0.000 0.000
#> SRR944058 1 0.2214 0.873 0.928 0.044 0.000 0.028
#> SRR944059 2 0.1182 0.962 0.016 0.968 0.016 0.000
#> SRR944060 3 0.5206 0.711 0.308 0.024 0.668 0.000
#> SRR944061 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944062 1 0.1675 0.874 0.948 0.044 0.004 0.004
#> SRR944063 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> SRR944064 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944065 1 0.5145 0.817 0.792 0.092 0.092 0.024
#> SRR944066 1 0.1792 0.893 0.932 0.068 0.000 0.000
#> SRR944067 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944068 3 0.1637 0.656 0.000 0.000 0.940 0.060
#> SRR944069 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944070 3 0.4387 0.780 0.236 0.012 0.752 0.000
#> SRR944071 2 0.0376 0.977 0.004 0.992 0.004 0.000
#> SRR944072 1 0.2197 0.878 0.928 0.048 0.000 0.024
#> SRR944073 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944075 2 0.0524 0.974 0.004 0.988 0.008 0.000
#> SRR944074 2 0.0188 0.979 0.004 0.996 0.000 0.000
#> SRR944076 2 0.1520 0.952 0.020 0.956 0.024 0.000
#> SRR944077 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944078 2 0.0524 0.974 0.004 0.988 0.008 0.000
#> SRR944079 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944080 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944081 2 0.0188 0.979 0.004 0.996 0.000 0.000
#> SRR944082 1 0.2311 0.894 0.916 0.076 0.004 0.004
#> SRR944083 1 0.1792 0.893 0.932 0.068 0.000 0.000
#> SRR944084 2 0.0188 0.979 0.004 0.996 0.000 0.000
#> SRR944085 2 0.1520 0.952 0.020 0.956 0.024 0.000
#> SRR944086 2 0.0000 0.981 0.000 1.000 0.000 0.000
#> SRR944088 2 0.0188 0.979 0.004 0.996 0.000 0.000
#> SRR944087 2 0.0672 0.972 0.008 0.984 0.008 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 2 0.0955 0.962 0.004 0.968 0.028 0.000 0.000
#> SRR944012 1 0.7356 0.113 0.420 0.116 0.080 0.384 0.000
#> SRR944014 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944013 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944015 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR944016 1 0.2074 0.850 0.920 0.036 0.044 0.000 0.000
#> SRR944017 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944018 1 0.2989 0.824 0.868 0.060 0.072 0.000 0.000
#> SRR944019 1 0.4107 0.752 0.804 0.132 0.040 0.024 0.000
#> SRR944020 4 0.0000 0.965 0.000 0.000 0.000 1.000 0.000
#> SRR944021 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944022 4 0.2230 0.890 0.000 0.000 0.116 0.884 0.000
#> SRR944023 2 0.4633 0.594 0.036 0.696 0.264 0.000 0.004
#> SRR944024 1 0.1444 0.847 0.948 0.012 0.040 0.000 0.000
#> SRR944026 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944025 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944028 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944029 2 0.0162 0.977 0.000 0.996 0.004 0.000 0.000
#> SRR944030 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944031 2 0.4359 0.593 0.016 0.692 0.288 0.000 0.004
#> SRR944032 2 0.0162 0.977 0.004 0.996 0.000 0.000 0.000
#> SRR944033 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944036 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944035 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944038 3 0.4016 0.919 0.012 0.000 0.716 0.000 0.272
#> SRR944037 1 0.4537 0.770 0.784 0.096 0.096 0.024 0.000
#> SRR944039 1 0.3920 0.770 0.820 0.116 0.040 0.024 0.000
#> SRR944040 2 0.0510 0.971 0.000 0.984 0.016 0.000 0.000
#> SRR944041 1 0.4692 0.716 0.768 0.144 0.052 0.036 0.000
#> SRR944042 2 0.1430 0.943 0.004 0.944 0.052 0.000 0.000
#> SRR944043 1 0.3661 0.641 0.724 0.000 0.276 0.000 0.000
#> SRR944044 2 0.0162 0.977 0.000 0.996 0.004 0.000 0.000
#> SRR944046 2 0.1205 0.953 0.004 0.956 0.040 0.000 0.000
#> SRR944045 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944047 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944048 1 0.1444 0.847 0.948 0.012 0.040 0.000 0.000
#> SRR944049 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944050 1 0.2153 0.848 0.916 0.040 0.044 0.000 0.000
#> SRR944051 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944052 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944053 4 0.0000 0.965 0.000 0.000 0.000 1.000 0.000
#> SRR944054 2 0.0162 0.977 0.000 0.996 0.004 0.000 0.000
#> SRR944055 2 0.0609 0.969 0.000 0.980 0.020 0.000 0.000
#> SRR944056 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944057 1 0.1965 0.852 0.924 0.024 0.052 0.000 0.000
#> SRR944058 1 0.0963 0.832 0.964 0.000 0.036 0.000 0.000
#> SRR944059 2 0.1124 0.956 0.004 0.960 0.036 0.000 0.000
#> SRR944060 3 0.3919 0.845 0.036 0.000 0.776 0.000 0.188
#> SRR944061 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944062 1 0.1671 0.820 0.924 0.000 0.076 0.000 0.000
#> SRR944063 4 0.0000 0.965 0.000 0.000 0.000 1.000 0.000
#> SRR944064 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944065 1 0.4656 0.752 0.768 0.052 0.148 0.000 0.032
#> SRR944066 1 0.1965 0.852 0.924 0.024 0.052 0.000 0.000
#> SRR944067 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944068 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR944069 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944070 3 0.4016 0.919 0.012 0.000 0.716 0.000 0.272
#> SRR944071 2 0.0510 0.971 0.000 0.984 0.016 0.000 0.000
#> SRR944072 1 0.1041 0.836 0.964 0.004 0.032 0.000 0.000
#> SRR944073 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944075 2 0.0609 0.969 0.000 0.980 0.020 0.000 0.000
#> SRR944074 2 0.0162 0.977 0.000 0.996 0.004 0.000 0.000
#> SRR944076 2 0.1357 0.947 0.004 0.948 0.048 0.000 0.000
#> SRR944077 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944078 2 0.0609 0.969 0.000 0.980 0.020 0.000 0.000
#> SRR944079 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> SRR944081 2 0.0162 0.977 0.000 0.996 0.004 0.000 0.000
#> SRR944082 1 0.1818 0.851 0.932 0.024 0.044 0.000 0.000
#> SRR944083 1 0.1725 0.850 0.936 0.020 0.044 0.000 0.000
#> SRR944084 2 0.0162 0.977 0.000 0.996 0.004 0.000 0.000
#> SRR944085 2 0.1357 0.946 0.004 0.948 0.048 0.000 0.000
#> SRR944086 2 0.0162 0.977 0.004 0.996 0.000 0.000 0.000
#> SRR944088 2 0.0162 0.977 0.000 0.996 0.004 0.000 0.000
#> SRR944087 2 0.0771 0.967 0.004 0.976 0.020 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 2 0.0790 0.960 0.000 0.968 NA 0.000 0.000 0.032
#> SRR944012 1 0.6484 -0.314 0.464 0.024 NA 0.336 0.000 0.012
#> SRR944014 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944013 2 0.0405 0.971 0.008 0.988 NA 0.000 0.000 0.000
#> SRR944015 5 0.0146 1.000 0.000 0.000 NA 0.000 0.996 0.004
#> SRR944016 1 0.4266 0.781 0.620 0.020 NA 0.000 0.000 0.004
#> SRR944017 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944018 1 0.4734 0.756 0.692 0.024 NA 0.000 0.000 0.060
#> SRR944019 1 0.2345 0.553 0.904 0.052 NA 0.012 0.000 0.004
#> SRR944020 4 0.0000 0.891 0.000 0.000 NA 1.000 0.000 0.000
#> SRR944021 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944022 4 0.3940 0.627 0.000 0.000 NA 0.652 0.004 0.008
#> SRR944023 2 0.4406 0.592 0.016 0.692 NA 0.000 0.000 0.256
#> SRR944024 1 0.3747 0.781 0.604 0.000 NA 0.000 0.000 0.000
#> SRR944026 2 0.0508 0.969 0.012 0.984 NA 0.000 0.000 0.000
#> SRR944025 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944028 2 0.0508 0.969 0.012 0.984 NA 0.000 0.000 0.000
#> SRR944029 2 0.0717 0.966 0.016 0.976 NA 0.000 0.000 0.000
#> SRR944030 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944031 2 0.4063 0.597 0.008 0.692 NA 0.000 0.000 0.280
#> SRR944032 2 0.0146 0.973 0.000 0.996 NA 0.000 0.000 0.000
#> SRR944033 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944036 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944035 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944038 6 0.1556 0.930 0.000 0.000 NA 0.000 0.080 0.920
#> SRR944037 1 0.2433 0.556 0.900 0.016 NA 0.012 0.000 0.060
#> SRR944039 1 0.1729 0.581 0.936 0.036 NA 0.012 0.000 0.004
#> SRR944040 2 0.0458 0.969 0.000 0.984 NA 0.000 0.000 0.016
#> SRR944041 1 0.3318 0.499 0.848 0.052 NA 0.024 0.000 0.004
#> SRR944042 2 0.1204 0.943 0.000 0.944 NA 0.000 0.000 0.056
#> SRR944043 1 0.5836 0.580 0.420 0.000 NA 0.000 0.000 0.188
#> SRR944044 2 0.0717 0.966 0.016 0.976 NA 0.000 0.000 0.000
#> SRR944046 2 0.1007 0.953 0.000 0.956 NA 0.000 0.000 0.044
#> SRR944045 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944047 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944048 1 0.3747 0.781 0.604 0.000 NA 0.000 0.000 0.000
#> SRR944049 2 0.0603 0.968 0.016 0.980 NA 0.000 0.000 0.000
#> SRR944050 1 0.4254 0.781 0.624 0.020 NA 0.000 0.000 0.004
#> SRR944051 2 0.0146 0.973 0.004 0.996 NA 0.000 0.000 0.000
#> SRR944052 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944053 4 0.0000 0.891 0.000 0.000 NA 1.000 0.000 0.000
#> SRR944054 2 0.0717 0.966 0.016 0.976 NA 0.000 0.000 0.000
#> SRR944055 2 0.0547 0.967 0.000 0.980 NA 0.000 0.000 0.020
#> SRR944056 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944057 1 0.4034 0.784 0.624 0.004 NA 0.000 0.000 0.008
#> SRR944058 1 0.3833 0.775 0.648 0.000 NA 0.000 0.000 0.008
#> SRR944059 2 0.0937 0.956 0.000 0.960 NA 0.000 0.000 0.040
#> SRR944060 6 0.1657 0.865 0.016 0.000 NA 0.000 0.000 0.928
#> SRR944061 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944062 1 0.4685 0.730 0.520 0.000 NA 0.000 0.000 0.044
#> SRR944063 4 0.0000 0.891 0.000 0.000 NA 1.000 0.000 0.000
#> SRR944064 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944065 1 0.5577 0.690 0.604 0.016 NA 0.000 0.000 0.168
#> SRR944066 1 0.4034 0.784 0.624 0.004 NA 0.000 0.000 0.008
#> SRR944067 2 0.0291 0.972 0.004 0.992 NA 0.000 0.000 0.000
#> SRR944068 5 0.0146 1.000 0.000 0.000 NA 0.000 0.996 0.004
#> SRR944069 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944070 6 0.1556 0.930 0.000 0.000 NA 0.000 0.080 0.920
#> SRR944071 2 0.0458 0.969 0.000 0.984 NA 0.000 0.000 0.016
#> SRR944072 1 0.3774 0.777 0.664 0.000 NA 0.000 0.000 0.008
#> SRR944073 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944075 2 0.0547 0.967 0.000 0.980 NA 0.000 0.000 0.020
#> SRR944074 2 0.0717 0.966 0.016 0.976 NA 0.000 0.000 0.000
#> SRR944076 2 0.1141 0.947 0.000 0.948 NA 0.000 0.000 0.052
#> SRR944077 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944078 2 0.0547 0.967 0.000 0.980 NA 0.000 0.000 0.020
#> SRR944079 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.974 0.000 1.000 NA 0.000 0.000 0.000
#> SRR944081 2 0.0717 0.966 0.016 0.976 NA 0.000 0.000 0.000
#> SRR944082 1 0.4397 0.784 0.632 0.012 NA 0.000 0.000 0.020
#> SRR944083 1 0.3830 0.783 0.620 0.004 NA 0.000 0.000 0.000
#> SRR944084 2 0.0603 0.968 0.016 0.980 NA 0.000 0.000 0.000
#> SRR944085 2 0.1141 0.946 0.000 0.948 NA 0.000 0.000 0.052
#> SRR944086 2 0.0713 0.961 0.028 0.972 NA 0.000 0.000 0.000
#> SRR944088 2 0.0717 0.966 0.016 0.976 NA 0.000 0.000 0.000
#> SRR944087 2 0.0632 0.965 0.000 0.976 NA 0.000 0.000 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "kmeans"]
# you can also extract it by
# res = res_list["CV:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.996 0.998 0.4762 0.524 0.524
#> 3 3 0.639 0.798 0.883 0.1969 0.935 0.876
#> 4 4 0.669 0.720 0.826 0.1845 0.792 0.567
#> 5 5 0.669 0.717 0.828 0.0955 0.912 0.715
#> 6 6 0.679 0.682 0.812 0.0405 0.957 0.826
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.0000 0.998 0.000 1.000
#> SRR944012 1 0.0000 0.997 1.000 0.000
#> SRR944014 2 0.0000 0.998 0.000 1.000
#> SRR944013 2 0.0000 0.998 0.000 1.000
#> SRR944015 1 0.0000 0.997 1.000 0.000
#> SRR944016 1 0.0672 0.991 0.992 0.008
#> SRR944017 2 0.0000 0.998 0.000 1.000
#> SRR944018 1 0.0000 0.997 1.000 0.000
#> SRR944019 1 0.0000 0.997 1.000 0.000
#> SRR944020 1 0.0000 0.997 1.000 0.000
#> SRR944021 2 0.0000 0.998 0.000 1.000
#> SRR944022 1 0.0000 0.997 1.000 0.000
#> SRR944023 1 0.0000 0.997 1.000 0.000
#> SRR944024 1 0.0000 0.997 1.000 0.000
#> SRR944026 2 0.0000 0.998 0.000 1.000
#> SRR944025 2 0.0000 0.998 0.000 1.000
#> SRR944028 2 0.0000 0.998 0.000 1.000
#> SRR944029 2 0.0938 0.988 0.012 0.988
#> SRR944030 2 0.0000 0.998 0.000 1.000
#> SRR944031 2 0.0000 0.998 0.000 1.000
#> SRR944032 2 0.0938 0.988 0.012 0.988
#> SRR944033 2 0.0000 0.998 0.000 1.000
#> SRR944034 2 0.0000 0.998 0.000 1.000
#> SRR944036 2 0.0000 0.998 0.000 1.000
#> SRR944035 2 0.0000 0.998 0.000 1.000
#> SRR944038 1 0.0000 0.997 1.000 0.000
#> SRR944037 1 0.0000 0.997 1.000 0.000
#> SRR944039 1 0.0000 0.997 1.000 0.000
#> SRR944040 2 0.0000 0.998 0.000 1.000
#> SRR944041 1 0.0000 0.997 1.000 0.000
#> SRR944042 2 0.0000 0.998 0.000 1.000
#> SRR944043 1 0.0000 0.997 1.000 0.000
#> SRR944044 2 0.0000 0.998 0.000 1.000
#> SRR944046 2 0.0000 0.998 0.000 1.000
#> SRR944045 2 0.0000 0.998 0.000 1.000
#> SRR944047 2 0.0000 0.998 0.000 1.000
#> SRR944048 1 0.0938 0.988 0.988 0.012
#> SRR944049 2 0.0000 0.998 0.000 1.000
#> SRR944050 1 0.2603 0.955 0.956 0.044
#> SRR944051 2 0.0000 0.998 0.000 1.000
#> SRR944052 2 0.0000 0.998 0.000 1.000
#> SRR944053 1 0.0000 0.997 1.000 0.000
#> SRR944054 2 0.0000 0.998 0.000 1.000
#> SRR944055 2 0.0000 0.998 0.000 1.000
#> SRR944056 2 0.0000 0.998 0.000 1.000
#> SRR944057 1 0.0000 0.997 1.000 0.000
#> SRR944058 1 0.0000 0.997 1.000 0.000
#> SRR944059 2 0.0000 0.998 0.000 1.000
#> SRR944060 1 0.0000 0.997 1.000 0.000
#> SRR944061 2 0.0000 0.998 0.000 1.000
#> SRR944062 1 0.0000 0.997 1.000 0.000
#> SRR944063 1 0.0000 0.997 1.000 0.000
#> SRR944064 2 0.0000 0.998 0.000 1.000
#> SRR944065 1 0.0000 0.997 1.000 0.000
#> SRR944066 1 0.0000 0.997 1.000 0.000
#> SRR944067 2 0.0000 0.998 0.000 1.000
#> SRR944068 1 0.0000 0.997 1.000 0.000
#> SRR944069 2 0.0000 0.998 0.000 1.000
#> SRR944070 1 0.0938 0.988 0.988 0.012
#> SRR944071 2 0.0000 0.998 0.000 1.000
#> SRR944072 1 0.0000 0.997 1.000 0.000
#> SRR944073 2 0.0000 0.998 0.000 1.000
#> SRR944075 2 0.0000 0.998 0.000 1.000
#> SRR944074 2 0.0000 0.998 0.000 1.000
#> SRR944076 2 0.0000 0.998 0.000 1.000
#> SRR944077 2 0.0000 0.998 0.000 1.000
#> SRR944078 2 0.0000 0.998 0.000 1.000
#> SRR944079 2 0.0000 0.998 0.000 1.000
#> SRR944080 2 0.0000 0.998 0.000 1.000
#> SRR944081 2 0.1414 0.980 0.020 0.980
#> SRR944082 1 0.0000 0.997 1.000 0.000
#> SRR944083 1 0.0000 0.997 1.000 0.000
#> SRR944084 2 0.0000 0.998 0.000 1.000
#> SRR944085 2 0.0000 0.998 0.000 1.000
#> SRR944086 2 0.2236 0.964 0.036 0.964
#> SRR944088 2 0.0000 0.998 0.000 1.000
#> SRR944087 2 0.0000 0.998 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 2 0.6266 0.79635 0.156 0.768 0.076
#> SRR944012 3 0.5650 0.62741 0.312 0.000 0.688
#> SRR944014 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944013 2 0.1585 0.89519 0.008 0.964 0.028
#> SRR944015 3 0.3267 0.74895 0.116 0.000 0.884
#> SRR944016 1 0.0592 0.83687 0.988 0.000 0.012
#> SRR944017 2 0.1031 0.89961 0.000 0.976 0.024
#> SRR944018 1 0.2448 0.83395 0.924 0.000 0.076
#> SRR944019 1 0.1964 0.83237 0.944 0.000 0.056
#> SRR944020 3 0.4062 0.77252 0.164 0.000 0.836
#> SRR944021 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944022 3 0.4062 0.77252 0.164 0.000 0.836
#> SRR944023 1 0.3340 0.69433 0.880 0.000 0.120
#> SRR944024 1 0.2448 0.83122 0.924 0.000 0.076
#> SRR944026 2 0.1163 0.89847 0.000 0.972 0.028
#> SRR944025 2 0.1031 0.89961 0.000 0.976 0.024
#> SRR944028 2 0.1031 0.89961 0.000 0.976 0.024
#> SRR944029 2 0.6542 0.77807 0.204 0.736 0.060
#> SRR944030 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944031 2 0.7588 0.72267 0.196 0.684 0.120
#> SRR944032 2 0.6601 0.68466 0.296 0.676 0.028
#> SRR944033 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944034 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944036 2 0.6304 0.78048 0.192 0.752 0.056
#> SRR944035 2 0.0237 0.90325 0.000 0.996 0.004
#> SRR944038 3 0.6140 0.30635 0.404 0.000 0.596
#> SRR944037 3 0.6295 0.29205 0.472 0.000 0.528
#> SRR944039 1 0.1529 0.84061 0.960 0.000 0.040
#> SRR944040 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944041 1 0.4121 0.78637 0.832 0.000 0.168
#> SRR944042 2 0.7524 0.72694 0.196 0.688 0.116
#> SRR944043 1 0.3192 0.80503 0.888 0.000 0.112
#> SRR944044 2 0.1163 0.89847 0.000 0.972 0.028
#> SRR944046 2 0.6827 0.76423 0.192 0.728 0.080
#> SRR944045 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944047 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944048 1 0.0000 0.83481 1.000 0.000 0.000
#> SRR944049 2 0.0892 0.90051 0.000 0.980 0.020
#> SRR944050 1 0.0747 0.83557 0.984 0.000 0.016
#> SRR944051 2 0.1163 0.89847 0.000 0.972 0.028
#> SRR944052 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944053 3 0.4062 0.77252 0.164 0.000 0.836
#> SRR944054 2 0.1163 0.89847 0.000 0.972 0.028
#> SRR944055 2 0.2448 0.87624 0.000 0.924 0.076
#> SRR944056 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944057 1 0.0747 0.83557 0.984 0.000 0.016
#> SRR944058 1 0.4654 0.65664 0.792 0.000 0.208
#> SRR944059 2 0.4749 0.84617 0.072 0.852 0.076
#> SRR944060 1 0.4121 0.64860 0.832 0.000 0.168
#> SRR944061 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944062 1 0.3192 0.80503 0.888 0.000 0.112
#> SRR944063 3 0.4062 0.77252 0.164 0.000 0.836
#> SRR944064 2 0.0237 0.90325 0.000 0.996 0.004
#> SRR944065 1 0.6192 -0.00734 0.580 0.000 0.420
#> SRR944066 1 0.0892 0.84250 0.980 0.000 0.020
#> SRR944067 2 0.0747 0.90130 0.000 0.984 0.016
#> SRR944068 3 0.3267 0.74895 0.116 0.000 0.884
#> SRR944069 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944070 3 0.7895 0.17434 0.436 0.056 0.508
#> SRR944071 2 0.6490 0.78446 0.172 0.752 0.076
#> SRR944072 1 0.3816 0.77412 0.852 0.000 0.148
#> SRR944073 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944075 2 0.2682 0.87499 0.004 0.920 0.076
#> SRR944074 2 0.1163 0.89847 0.000 0.972 0.028
#> SRR944076 2 0.6984 0.75775 0.192 0.720 0.088
#> SRR944077 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944078 2 0.2165 0.88164 0.000 0.936 0.064
#> SRR944079 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944080 2 0.0000 0.90368 0.000 1.000 0.000
#> SRR944081 2 0.5921 0.78440 0.212 0.756 0.032
#> SRR944082 1 0.3192 0.80503 0.888 0.000 0.112
#> SRR944083 1 0.0237 0.83766 0.996 0.000 0.004
#> SRR944084 2 0.6906 0.77438 0.192 0.724 0.084
#> SRR944085 2 0.6906 0.76107 0.192 0.724 0.084
#> SRR944086 2 0.6744 0.67705 0.300 0.668 0.032
#> SRR944088 2 0.1163 0.89847 0.000 0.972 0.028
#> SRR944087 2 0.6746 0.76723 0.192 0.732 0.076
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.5028 0.7353 0.004 0.400 0.596 0.000
#> SRR944012 4 0.7314 0.3016 0.336 0.000 0.168 0.496
#> SRR944014 2 0.0000 0.8618 0.000 1.000 0.000 0.000
#> SRR944013 2 0.4715 0.7138 0.024 0.776 0.188 0.012
#> SRR944015 4 0.3946 0.7494 0.020 0.000 0.168 0.812
#> SRR944016 1 0.1557 0.8826 0.944 0.000 0.056 0.000
#> SRR944017 2 0.1716 0.8468 0.000 0.936 0.064 0.000
#> SRR944018 1 0.1042 0.8929 0.972 0.000 0.020 0.008
#> SRR944019 1 0.4716 0.6714 0.764 0.000 0.196 0.040
#> SRR944020 4 0.1557 0.8159 0.056 0.000 0.000 0.944
#> SRR944021 2 0.0000 0.8618 0.000 1.000 0.000 0.000
#> SRR944022 4 0.1557 0.8159 0.056 0.000 0.000 0.944
#> SRR944023 3 0.5004 0.2020 0.392 0.000 0.604 0.004
#> SRR944024 1 0.1209 0.8921 0.964 0.000 0.032 0.004
#> SRR944026 2 0.3300 0.7849 0.000 0.848 0.144 0.008
#> SRR944025 2 0.1716 0.8468 0.000 0.936 0.064 0.000
#> SRR944028 2 0.2216 0.8299 0.000 0.908 0.092 0.000
#> SRR944029 3 0.5651 0.5096 0.028 0.260 0.692 0.020
#> SRR944030 2 0.0000 0.8618 0.000 1.000 0.000 0.000
#> SRR944031 3 0.4991 0.7378 0.004 0.388 0.608 0.000
#> SRR944032 2 0.8091 0.1210 0.264 0.444 0.280 0.012
#> SRR944033 2 0.0000 0.8618 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0188 0.8617 0.000 0.996 0.004 0.000
#> SRR944036 3 0.5105 0.6946 0.004 0.432 0.564 0.000
#> SRR944035 2 0.0817 0.8590 0.000 0.976 0.024 0.000
#> SRR944038 3 0.6097 0.2423 0.120 0.012 0.708 0.160
#> SRR944037 4 0.6302 0.3534 0.368 0.000 0.068 0.564
#> SRR944039 1 0.2730 0.8309 0.896 0.000 0.088 0.016
#> SRR944040 2 0.0188 0.8583 0.000 0.996 0.004 0.000
#> SRR944041 1 0.6646 0.4549 0.624 0.000 0.204 0.172
#> SRR944042 3 0.5085 0.7353 0.008 0.376 0.616 0.000
#> SRR944043 1 0.0927 0.8915 0.976 0.000 0.016 0.008
#> SRR944044 2 0.3088 0.7986 0.000 0.864 0.128 0.008
#> SRR944046 3 0.5016 0.7379 0.004 0.396 0.600 0.000
#> SRR944045 2 0.0000 0.8618 0.000 1.000 0.000 0.000
#> SRR944047 2 0.0000 0.8618 0.000 1.000 0.000 0.000
#> SRR944048 1 0.1637 0.8835 0.940 0.000 0.060 0.000
#> SRR944049 2 0.1637 0.8485 0.000 0.940 0.060 0.000
#> SRR944050 1 0.1637 0.8810 0.940 0.000 0.060 0.000
#> SRR944051 2 0.4503 0.7233 0.016 0.784 0.188 0.012
#> SRR944052 2 0.0000 0.8618 0.000 1.000 0.000 0.000
#> SRR944053 4 0.1743 0.8162 0.056 0.000 0.004 0.940
#> SRR944054 2 0.3672 0.7637 0.000 0.824 0.164 0.012
#> SRR944055 3 0.4961 0.6747 0.000 0.448 0.552 0.000
#> SRR944056 2 0.0000 0.8618 0.000 1.000 0.000 0.000
#> SRR944057 1 0.1389 0.8858 0.952 0.000 0.048 0.000
#> SRR944058 1 0.1576 0.8732 0.948 0.000 0.004 0.048
#> SRR944059 3 0.4898 0.7183 0.000 0.416 0.584 0.000
#> SRR944060 3 0.5025 0.3098 0.252 0.000 0.716 0.032
#> SRR944061 2 0.0000 0.8618 0.000 1.000 0.000 0.000
#> SRR944062 1 0.1151 0.8921 0.968 0.000 0.024 0.008
#> SRR944063 4 0.1743 0.8162 0.056 0.000 0.004 0.940
#> SRR944064 2 0.0921 0.8582 0.000 0.972 0.028 0.000
#> SRR944065 1 0.4770 0.5037 0.700 0.000 0.012 0.288
#> SRR944066 1 0.1305 0.8926 0.960 0.000 0.036 0.004
#> SRR944067 2 0.1557 0.8501 0.000 0.944 0.056 0.000
#> SRR944068 4 0.3946 0.7494 0.020 0.000 0.168 0.812
#> SRR944069 2 0.0000 0.8618 0.000 1.000 0.000 0.000
#> SRR944070 3 0.6117 0.3266 0.092 0.040 0.732 0.136
#> SRR944071 3 0.5028 0.7353 0.004 0.400 0.596 0.000
#> SRR944072 1 0.1004 0.8861 0.972 0.000 0.004 0.024
#> SRR944073 2 0.0000 0.8618 0.000 1.000 0.000 0.000
#> SRR944075 3 0.4972 0.6639 0.000 0.456 0.544 0.000
#> SRR944074 2 0.3300 0.7849 0.000 0.848 0.144 0.008
#> SRR944076 3 0.5016 0.7379 0.004 0.396 0.600 0.000
#> SRR944077 2 0.0000 0.8618 0.000 1.000 0.000 0.000
#> SRR944078 2 0.4605 -0.0320 0.000 0.664 0.336 0.000
#> SRR944079 2 0.0000 0.8618 0.000 1.000 0.000 0.000
#> SRR944080 2 0.0000 0.8618 0.000 1.000 0.000 0.000
#> SRR944081 2 0.8217 0.0302 0.192 0.416 0.368 0.024
#> SRR944082 1 0.1151 0.8921 0.968 0.000 0.024 0.008
#> SRR944083 1 0.1022 0.8933 0.968 0.000 0.032 0.000
#> SRR944084 3 0.4798 0.5801 0.012 0.232 0.744 0.012
#> SRR944085 3 0.5016 0.7379 0.004 0.396 0.600 0.000
#> SRR944086 3 0.8254 0.0379 0.340 0.280 0.368 0.012
#> SRR944088 2 0.4301 0.7298 0.008 0.788 0.192 0.012
#> SRR944087 3 0.5016 0.7379 0.004 0.396 0.600 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.3242 0.8259 0.000 0.216 0.784 0.000 0.000
#> SRR944012 5 0.3832 0.2765 0.060 0.000 0.012 0.104 0.824
#> SRR944014 2 0.0609 0.8924 0.000 0.980 0.020 0.000 0.000
#> SRR944013 5 0.4779 0.2987 0.004 0.448 0.012 0.000 0.536
#> SRR944015 4 0.3048 0.7014 0.000 0.000 0.176 0.820 0.004
#> SRR944016 1 0.1124 0.9001 0.960 0.000 0.004 0.000 0.036
#> SRR944017 2 0.1965 0.8267 0.000 0.904 0.000 0.000 0.096
#> SRR944018 1 0.2295 0.8603 0.900 0.000 0.008 0.004 0.088
#> SRR944019 5 0.4591 0.2350 0.332 0.000 0.012 0.008 0.648
#> SRR944020 4 0.3642 0.8357 0.008 0.000 0.000 0.760 0.232
#> SRR944021 2 0.0609 0.8924 0.000 0.980 0.020 0.000 0.000
#> SRR944022 4 0.3671 0.8338 0.008 0.000 0.000 0.756 0.236
#> SRR944023 3 0.4192 0.5544 0.232 0.000 0.736 0.000 0.032
#> SRR944024 1 0.0671 0.9009 0.980 0.000 0.016 0.000 0.004
#> SRR944026 2 0.3039 0.7052 0.000 0.808 0.000 0.000 0.192
#> SRR944025 2 0.1965 0.8267 0.000 0.904 0.000 0.000 0.096
#> SRR944028 2 0.2179 0.8084 0.000 0.888 0.000 0.000 0.112
#> SRR944029 5 0.5051 0.5089 0.004 0.068 0.248 0.000 0.680
#> SRR944030 2 0.0609 0.8924 0.000 0.980 0.020 0.000 0.000
#> SRR944031 3 0.3421 0.8238 0.000 0.204 0.788 0.000 0.008
#> SRR944032 5 0.6881 0.5742 0.064 0.232 0.136 0.000 0.568
#> SRR944033 2 0.0609 0.8924 0.000 0.980 0.020 0.000 0.000
#> SRR944034 2 0.0290 0.8899 0.000 0.992 0.008 0.000 0.000
#> SRR944036 3 0.3884 0.7645 0.000 0.288 0.708 0.000 0.004
#> SRR944035 2 0.0703 0.8769 0.000 0.976 0.000 0.000 0.024
#> SRR944038 3 0.4618 0.4043 0.024 0.000 0.748 0.192 0.036
#> SRR944037 5 0.6011 -0.2440 0.092 0.000 0.016 0.316 0.576
#> SRR944039 1 0.4730 0.3542 0.568 0.000 0.012 0.004 0.416
#> SRR944040 2 0.1197 0.8651 0.000 0.952 0.048 0.000 0.000
#> SRR944041 5 0.3241 0.3915 0.104 0.000 0.012 0.028 0.856
#> SRR944042 3 0.3333 0.8265 0.000 0.208 0.788 0.000 0.004
#> SRR944043 1 0.1444 0.8837 0.948 0.000 0.012 0.000 0.040
#> SRR944044 2 0.2852 0.7374 0.000 0.828 0.000 0.000 0.172
#> SRR944046 3 0.3177 0.8270 0.000 0.208 0.792 0.000 0.000
#> SRR944045 2 0.0609 0.8924 0.000 0.980 0.020 0.000 0.000
#> SRR944047 2 0.0609 0.8924 0.000 0.980 0.020 0.000 0.000
#> SRR944048 1 0.1018 0.9012 0.968 0.000 0.016 0.000 0.016
#> SRR944049 2 0.1671 0.8442 0.000 0.924 0.000 0.000 0.076
#> SRR944050 1 0.1124 0.9001 0.960 0.000 0.004 0.000 0.036
#> SRR944051 5 0.4641 0.2757 0.000 0.456 0.012 0.000 0.532
#> SRR944052 2 0.0609 0.8924 0.000 0.980 0.020 0.000 0.000
#> SRR944053 4 0.3421 0.8411 0.008 0.000 0.000 0.788 0.204
#> SRR944054 2 0.4276 0.2369 0.000 0.616 0.004 0.000 0.380
#> SRR944055 3 0.3612 0.7887 0.000 0.268 0.732 0.000 0.000
#> SRR944056 2 0.0609 0.8924 0.000 0.980 0.020 0.000 0.000
#> SRR944057 1 0.0955 0.9016 0.968 0.000 0.004 0.000 0.028
#> SRR944058 1 0.1921 0.8749 0.932 0.000 0.012 0.012 0.044
#> SRR944059 3 0.3242 0.8259 0.000 0.216 0.784 0.000 0.000
#> SRR944060 3 0.5390 0.4824 0.128 0.000 0.728 0.092 0.052
#> SRR944061 2 0.0609 0.8924 0.000 0.980 0.020 0.000 0.000
#> SRR944062 1 0.0671 0.9009 0.980 0.000 0.016 0.000 0.004
#> SRR944063 4 0.3455 0.8413 0.008 0.000 0.000 0.784 0.208
#> SRR944064 2 0.0794 0.8748 0.000 0.972 0.000 0.000 0.028
#> SRR944065 1 0.6465 0.2800 0.480 0.000 0.016 0.120 0.384
#> SRR944066 1 0.0703 0.9025 0.976 0.000 0.000 0.000 0.024
#> SRR944067 2 0.1544 0.8505 0.000 0.932 0.000 0.000 0.068
#> SRR944068 4 0.3048 0.7014 0.000 0.000 0.176 0.820 0.004
#> SRR944069 2 0.0609 0.8924 0.000 0.980 0.020 0.000 0.000
#> SRR944070 3 0.4206 0.4544 0.008 0.004 0.780 0.172 0.036
#> SRR944071 3 0.3395 0.8134 0.000 0.236 0.764 0.000 0.000
#> SRR944072 1 0.0898 0.8997 0.972 0.000 0.008 0.000 0.020
#> SRR944073 2 0.0609 0.8924 0.000 0.980 0.020 0.000 0.000
#> SRR944075 3 0.3752 0.7628 0.000 0.292 0.708 0.000 0.000
#> SRR944074 2 0.3109 0.6927 0.000 0.800 0.000 0.000 0.200
#> SRR944076 3 0.3177 0.8270 0.000 0.208 0.792 0.000 0.000
#> SRR944077 2 0.0609 0.8924 0.000 0.980 0.020 0.000 0.000
#> SRR944078 2 0.4242 -0.0804 0.000 0.572 0.428 0.000 0.000
#> SRR944079 2 0.0609 0.8924 0.000 0.980 0.020 0.000 0.000
#> SRR944080 2 0.0290 0.8899 0.000 0.992 0.008 0.000 0.000
#> SRR944081 5 0.5444 0.5829 0.032 0.112 0.144 0.000 0.712
#> SRR944082 1 0.0671 0.9009 0.980 0.000 0.016 0.000 0.004
#> SRR944083 1 0.1018 0.9012 0.968 0.000 0.016 0.000 0.016
#> SRR944084 3 0.5080 0.2653 0.000 0.044 0.588 0.000 0.368
#> SRR944085 3 0.3177 0.8270 0.000 0.208 0.792 0.000 0.000
#> SRR944086 5 0.5867 0.5664 0.068 0.080 0.168 0.000 0.684
#> SRR944088 5 0.5703 0.3603 0.000 0.408 0.084 0.000 0.508
#> SRR944087 3 0.3210 0.8268 0.000 0.212 0.788 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.2048 0.8019 0.000 0.120 0.880 0.000 0.000 0.000
#> SRR944012 5 0.4132 0.1792 0.008 0.000 0.004 0.352 0.632 0.004
#> SRR944014 2 0.0790 0.9284 0.000 0.968 0.032 0.000 0.000 0.000
#> SRR944013 5 0.4015 0.5627 0.000 0.328 0.008 0.008 0.656 0.000
#> SRR944015 6 0.0260 0.6061 0.000 0.000 0.008 0.000 0.000 0.992
#> SRR944016 1 0.2278 0.8494 0.900 0.000 0.004 0.044 0.052 0.000
#> SRR944017 2 0.1556 0.8696 0.000 0.920 0.000 0.000 0.080 0.000
#> SRR944018 1 0.3907 0.7665 0.792 0.000 0.016 0.104 0.088 0.000
#> SRR944019 5 0.4314 0.3629 0.156 0.000 0.004 0.104 0.736 0.000
#> SRR944020 4 0.4275 0.3513 0.004 0.000 0.000 0.592 0.016 0.388
#> SRR944021 2 0.0790 0.9284 0.000 0.968 0.032 0.000 0.000 0.000
#> SRR944022 4 0.4657 0.3503 0.004 0.000 0.016 0.588 0.016 0.376
#> SRR944023 3 0.3982 0.6241 0.116 0.000 0.792 0.060 0.032 0.000
#> SRR944024 1 0.2020 0.8579 0.920 0.000 0.020 0.040 0.020 0.000
#> SRR944026 2 0.2762 0.7199 0.000 0.804 0.000 0.000 0.196 0.000
#> SRR944025 2 0.1556 0.8696 0.000 0.920 0.000 0.000 0.080 0.000
#> SRR944028 2 0.1863 0.8422 0.000 0.896 0.000 0.000 0.104 0.000
#> SRR944029 5 0.3973 0.5147 0.000 0.048 0.148 0.024 0.780 0.000
#> SRR944030 2 0.0713 0.9282 0.000 0.972 0.028 0.000 0.000 0.000
#> SRR944031 3 0.2756 0.7876 0.000 0.084 0.872 0.028 0.016 0.000
#> SRR944032 5 0.5027 0.5813 0.024 0.196 0.064 0.016 0.700 0.000
#> SRR944033 2 0.0790 0.9284 0.000 0.968 0.032 0.000 0.000 0.000
#> SRR944034 2 0.0713 0.9282 0.000 0.972 0.028 0.000 0.000 0.000
#> SRR944036 3 0.2955 0.7670 0.000 0.172 0.816 0.008 0.004 0.000
#> SRR944035 2 0.0260 0.9127 0.000 0.992 0.000 0.000 0.008 0.000
#> SRR944038 3 0.6180 0.1911 0.004 0.000 0.476 0.104 0.040 0.376
#> SRR944037 4 0.6058 0.1051 0.068 0.000 0.008 0.484 0.392 0.048
#> SRR944039 5 0.5578 -0.0611 0.388 0.000 0.004 0.124 0.484 0.000
#> SRR944040 2 0.1204 0.9041 0.000 0.944 0.056 0.000 0.000 0.000
#> SRR944041 5 0.3619 0.3450 0.024 0.000 0.000 0.232 0.744 0.000
#> SRR944042 3 0.1866 0.7981 0.000 0.084 0.908 0.000 0.008 0.000
#> SRR944043 1 0.4189 0.7846 0.772 0.000 0.028 0.148 0.048 0.004
#> SRR944044 2 0.2762 0.7199 0.000 0.804 0.000 0.000 0.196 0.000
#> SRR944046 3 0.1663 0.8017 0.000 0.088 0.912 0.000 0.000 0.000
#> SRR944045 2 0.0790 0.9284 0.000 0.968 0.032 0.000 0.000 0.000
#> SRR944047 2 0.0790 0.9284 0.000 0.968 0.032 0.000 0.000 0.000
#> SRR944048 1 0.2594 0.8549 0.884 0.000 0.016 0.072 0.028 0.000
#> SRR944049 2 0.1556 0.8696 0.000 0.920 0.000 0.000 0.080 0.000
#> SRR944050 1 0.2340 0.8473 0.896 0.000 0.004 0.044 0.056 0.000
#> SRR944051 5 0.4015 0.5622 0.000 0.328 0.008 0.008 0.656 0.000
#> SRR944052 2 0.0790 0.9284 0.000 0.968 0.032 0.000 0.000 0.000
#> SRR944053 6 0.4310 -0.4614 0.004 0.000 0.000 0.472 0.012 0.512
#> SRR944054 5 0.3998 0.1686 0.000 0.492 0.004 0.000 0.504 0.000
#> SRR944055 3 0.2664 0.7684 0.000 0.184 0.816 0.000 0.000 0.000
#> SRR944056 2 0.0790 0.9284 0.000 0.968 0.032 0.000 0.000 0.000
#> SRR944057 1 0.1933 0.8568 0.920 0.000 0.004 0.044 0.032 0.000
#> SRR944058 1 0.2744 0.8355 0.876 0.000 0.012 0.060 0.052 0.000
#> SRR944059 3 0.1910 0.8036 0.000 0.108 0.892 0.000 0.000 0.000
#> SRR944060 3 0.6298 0.4922 0.072 0.000 0.644 0.124 0.056 0.104
#> SRR944061 2 0.0790 0.9284 0.000 0.968 0.032 0.000 0.000 0.000
#> SRR944062 1 0.2172 0.8563 0.912 0.000 0.020 0.044 0.024 0.000
#> SRR944063 4 0.4390 0.1540 0.004 0.000 0.000 0.508 0.016 0.472
#> SRR944064 2 0.0547 0.9066 0.000 0.980 0.000 0.000 0.020 0.000
#> SRR944065 1 0.6509 0.0438 0.392 0.000 0.020 0.368 0.216 0.004
#> SRR944066 1 0.1552 0.8624 0.940 0.000 0.004 0.036 0.020 0.000
#> SRR944067 2 0.1501 0.8725 0.000 0.924 0.000 0.000 0.076 0.000
#> SRR944068 6 0.0260 0.6061 0.000 0.000 0.008 0.000 0.000 0.992
#> SRR944069 2 0.0790 0.9284 0.000 0.968 0.032 0.000 0.000 0.000
#> SRR944070 3 0.6004 0.3295 0.004 0.000 0.544 0.100 0.040 0.312
#> SRR944071 3 0.2260 0.7944 0.000 0.140 0.860 0.000 0.000 0.000
#> SRR944072 1 0.1716 0.8560 0.932 0.000 0.004 0.028 0.036 0.000
#> SRR944073 2 0.0713 0.9282 0.000 0.972 0.028 0.000 0.000 0.000
#> SRR944075 3 0.3050 0.7200 0.000 0.236 0.764 0.000 0.000 0.000
#> SRR944074 2 0.2762 0.7199 0.000 0.804 0.000 0.000 0.196 0.000
#> SRR944076 3 0.1663 0.8017 0.000 0.088 0.912 0.000 0.000 0.000
#> SRR944077 2 0.0790 0.9284 0.000 0.968 0.032 0.000 0.000 0.000
#> SRR944078 3 0.3797 0.4162 0.000 0.420 0.580 0.000 0.000 0.000
#> SRR944079 2 0.0790 0.9284 0.000 0.968 0.032 0.000 0.000 0.000
#> SRR944080 2 0.0713 0.9282 0.000 0.972 0.028 0.000 0.000 0.000
#> SRR944081 5 0.3569 0.5549 0.016 0.064 0.056 0.024 0.840 0.000
#> SRR944082 1 0.2366 0.8538 0.900 0.000 0.020 0.056 0.024 0.000
#> SRR944083 1 0.2288 0.8589 0.900 0.000 0.016 0.068 0.016 0.000
#> SRR944084 3 0.4738 0.3111 0.000 0.036 0.596 0.012 0.356 0.000
#> SRR944085 3 0.1714 0.8025 0.000 0.092 0.908 0.000 0.000 0.000
#> SRR944086 5 0.4284 0.5380 0.028 0.052 0.072 0.048 0.800 0.000
#> SRR944088 5 0.4355 0.5629 0.000 0.320 0.032 0.004 0.644 0.000
#> SRR944087 3 0.2003 0.8028 0.000 0.116 0.884 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "skmeans"]
# you can also extract it by
# res = res_list["CV:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.920 0.937 0.974 0.5007 0.500 0.500
#> 3 3 0.943 0.934 0.969 0.3078 0.791 0.602
#> 4 4 0.699 0.674 0.829 0.1063 0.913 0.751
#> 5 5 0.649 0.606 0.796 0.0649 0.916 0.712
#> 6 6 0.653 0.549 0.748 0.0334 0.944 0.780
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.0000 0.970 0.000 1.000
#> SRR944012 1 0.0000 0.975 1.000 0.000
#> SRR944014 2 0.0000 0.970 0.000 1.000
#> SRR944013 2 0.6801 0.773 0.180 0.820
#> SRR944015 1 0.0000 0.975 1.000 0.000
#> SRR944016 1 0.0000 0.975 1.000 0.000
#> SRR944017 2 0.0000 0.970 0.000 1.000
#> SRR944018 1 0.0000 0.975 1.000 0.000
#> SRR944019 1 0.0000 0.975 1.000 0.000
#> SRR944020 1 0.0000 0.975 1.000 0.000
#> SRR944021 2 0.0000 0.970 0.000 1.000
#> SRR944022 1 0.0000 0.975 1.000 0.000
#> SRR944023 1 0.0000 0.975 1.000 0.000
#> SRR944024 1 0.0000 0.975 1.000 0.000
#> SRR944026 2 0.0000 0.970 0.000 1.000
#> SRR944025 2 0.0000 0.970 0.000 1.000
#> SRR944028 2 0.0000 0.970 0.000 1.000
#> SRR944029 1 0.0000 0.975 1.000 0.000
#> SRR944030 2 0.0000 0.970 0.000 1.000
#> SRR944031 2 0.9661 0.353 0.392 0.608
#> SRR944032 2 0.9000 0.537 0.316 0.684
#> SRR944033 2 0.0000 0.970 0.000 1.000
#> SRR944034 2 0.0000 0.970 0.000 1.000
#> SRR944036 2 0.0376 0.967 0.004 0.996
#> SRR944035 2 0.0000 0.970 0.000 1.000
#> SRR944038 1 0.0000 0.975 1.000 0.000
#> SRR944037 1 0.0000 0.975 1.000 0.000
#> SRR944039 1 0.0000 0.975 1.000 0.000
#> SRR944040 2 0.0000 0.970 0.000 1.000
#> SRR944041 1 0.0000 0.975 1.000 0.000
#> SRR944042 1 0.9635 0.355 0.612 0.388
#> SRR944043 1 0.0000 0.975 1.000 0.000
#> SRR944044 2 0.0000 0.970 0.000 1.000
#> SRR944046 2 0.4690 0.879 0.100 0.900
#> SRR944045 2 0.0000 0.970 0.000 1.000
#> SRR944047 2 0.0000 0.970 0.000 1.000
#> SRR944048 1 0.0000 0.975 1.000 0.000
#> SRR944049 2 0.0000 0.970 0.000 1.000
#> SRR944050 1 0.0000 0.975 1.000 0.000
#> SRR944051 2 0.0000 0.970 0.000 1.000
#> SRR944052 2 0.0000 0.970 0.000 1.000
#> SRR944053 1 0.0000 0.975 1.000 0.000
#> SRR944054 2 0.0000 0.970 0.000 1.000
#> SRR944055 2 0.0000 0.970 0.000 1.000
#> SRR944056 2 0.0000 0.970 0.000 1.000
#> SRR944057 1 0.0000 0.975 1.000 0.000
#> SRR944058 1 0.0000 0.975 1.000 0.000
#> SRR944059 2 0.0000 0.970 0.000 1.000
#> SRR944060 1 0.0000 0.975 1.000 0.000
#> SRR944061 2 0.0000 0.970 0.000 1.000
#> SRR944062 1 0.0000 0.975 1.000 0.000
#> SRR944063 1 0.0000 0.975 1.000 0.000
#> SRR944064 2 0.0000 0.970 0.000 1.000
#> SRR944065 1 0.0000 0.975 1.000 0.000
#> SRR944066 1 0.0000 0.975 1.000 0.000
#> SRR944067 2 0.0000 0.970 0.000 1.000
#> SRR944068 1 0.0000 0.975 1.000 0.000
#> SRR944069 2 0.0000 0.970 0.000 1.000
#> SRR944070 1 0.0000 0.975 1.000 0.000
#> SRR944071 2 0.0000 0.970 0.000 1.000
#> SRR944072 1 0.0000 0.975 1.000 0.000
#> SRR944073 2 0.0000 0.970 0.000 1.000
#> SRR944075 2 0.0000 0.970 0.000 1.000
#> SRR944074 2 0.0000 0.970 0.000 1.000
#> SRR944076 2 0.4690 0.879 0.100 0.900
#> SRR944077 2 0.0000 0.970 0.000 1.000
#> SRR944078 2 0.0000 0.970 0.000 1.000
#> SRR944079 2 0.0000 0.970 0.000 1.000
#> SRR944080 2 0.0000 0.970 0.000 1.000
#> SRR944081 1 0.0000 0.975 1.000 0.000
#> SRR944082 1 0.0000 0.975 1.000 0.000
#> SRR944083 1 0.0000 0.975 1.000 0.000
#> SRR944084 1 0.9358 0.448 0.648 0.352
#> SRR944085 2 0.0376 0.967 0.004 0.996
#> SRR944086 1 0.3114 0.920 0.944 0.056
#> SRR944088 2 0.0000 0.970 0.000 1.000
#> SRR944087 2 0.4298 0.892 0.088 0.912
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 3 0.0424 0.918 0.000 0.008 0.992
#> SRR944012 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944014 2 0.0424 0.982 0.000 0.992 0.008
#> SRR944013 2 0.2496 0.907 0.068 0.928 0.004
#> SRR944015 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944016 1 0.0424 0.976 0.992 0.000 0.008
#> SRR944017 2 0.0000 0.981 0.000 1.000 0.000
#> SRR944018 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944019 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944020 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944021 2 0.0424 0.982 0.000 0.992 0.008
#> SRR944022 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944023 3 0.3686 0.811 0.140 0.000 0.860
#> SRR944024 1 0.0237 0.978 0.996 0.000 0.004
#> SRR944026 2 0.0237 0.980 0.000 0.996 0.004
#> SRR944025 2 0.0000 0.981 0.000 1.000 0.000
#> SRR944028 2 0.0237 0.980 0.000 0.996 0.004
#> SRR944029 1 0.6255 0.685 0.748 0.048 0.204
#> SRR944030 2 0.0424 0.982 0.000 0.992 0.008
#> SRR944031 3 0.0237 0.918 0.000 0.004 0.996
#> SRR944032 2 0.5285 0.665 0.244 0.752 0.004
#> SRR944033 2 0.0424 0.982 0.000 0.992 0.008
#> SRR944034 2 0.0424 0.982 0.000 0.992 0.008
#> SRR944036 3 0.2772 0.880 0.004 0.080 0.916
#> SRR944035 2 0.0237 0.982 0.000 0.996 0.004
#> SRR944038 3 0.1860 0.893 0.052 0.000 0.948
#> SRR944037 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944039 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944040 2 0.1031 0.969 0.000 0.976 0.024
#> SRR944041 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944042 3 0.0237 0.917 0.004 0.000 0.996
#> SRR944043 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944044 2 0.0237 0.980 0.000 0.996 0.004
#> SRR944046 3 0.0237 0.918 0.000 0.004 0.996
#> SRR944045 2 0.0424 0.982 0.000 0.992 0.008
#> SRR944047 2 0.0424 0.982 0.000 0.992 0.008
#> SRR944048 1 0.0424 0.976 0.992 0.000 0.008
#> SRR944049 2 0.0000 0.981 0.000 1.000 0.000
#> SRR944050 1 0.0424 0.976 0.992 0.000 0.008
#> SRR944051 2 0.0237 0.980 0.000 0.996 0.004
#> SRR944052 2 0.0424 0.982 0.000 0.992 0.008
#> SRR944053 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944054 2 0.0237 0.980 0.000 0.996 0.004
#> SRR944055 3 0.2959 0.866 0.000 0.100 0.900
#> SRR944056 2 0.0424 0.982 0.000 0.992 0.008
#> SRR944057 1 0.0424 0.976 0.992 0.000 0.008
#> SRR944058 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944059 3 0.1411 0.909 0.000 0.036 0.964
#> SRR944060 3 0.5926 0.457 0.356 0.000 0.644
#> SRR944061 2 0.0424 0.982 0.000 0.992 0.008
#> SRR944062 1 0.0237 0.978 0.996 0.000 0.004
#> SRR944063 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944064 2 0.0237 0.982 0.000 0.996 0.004
#> SRR944065 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944066 1 0.0424 0.976 0.992 0.000 0.008
#> SRR944067 2 0.0000 0.981 0.000 1.000 0.000
#> SRR944068 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944069 2 0.0424 0.982 0.000 0.992 0.008
#> SRR944070 3 0.0747 0.913 0.016 0.000 0.984
#> SRR944071 3 0.0237 0.918 0.000 0.004 0.996
#> SRR944072 1 0.0000 0.979 1.000 0.000 0.000
#> SRR944073 2 0.0424 0.982 0.000 0.992 0.008
#> SRR944075 3 0.2878 0.870 0.000 0.096 0.904
#> SRR944074 2 0.0237 0.980 0.000 0.996 0.004
#> SRR944076 3 0.0237 0.918 0.000 0.004 0.996
#> SRR944077 2 0.0424 0.982 0.000 0.992 0.008
#> SRR944078 3 0.6244 0.230 0.000 0.440 0.560
#> SRR944079 2 0.0424 0.982 0.000 0.992 0.008
#> SRR944080 2 0.0424 0.982 0.000 0.992 0.008
#> SRR944081 1 0.1878 0.934 0.952 0.044 0.004
#> SRR944082 1 0.0237 0.978 0.996 0.000 0.004
#> SRR944083 1 0.0424 0.976 0.992 0.000 0.008
#> SRR944084 3 0.1170 0.913 0.016 0.008 0.976
#> SRR944085 3 0.0237 0.918 0.000 0.004 0.996
#> SRR944086 1 0.4692 0.768 0.820 0.168 0.012
#> SRR944088 2 0.0237 0.980 0.000 0.996 0.004
#> SRR944087 3 0.0237 0.918 0.000 0.004 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.1059 0.807 0.012 0.016 0.972 0.000
#> SRR944012 4 0.1792 0.645 0.068 0.000 0.000 0.932
#> SRR944014 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> SRR944013 2 0.6835 0.602 0.264 0.600 0.004 0.132
#> SRR944015 4 0.0804 0.665 0.012 0.000 0.008 0.980
#> SRR944016 1 0.4543 0.768 0.676 0.000 0.000 0.324
#> SRR944017 2 0.1389 0.917 0.048 0.952 0.000 0.000
#> SRR944018 4 0.4193 0.219 0.268 0.000 0.000 0.732
#> SRR944019 4 0.3688 0.540 0.208 0.000 0.000 0.792
#> SRR944020 4 0.0592 0.666 0.016 0.000 0.000 0.984
#> SRR944021 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> SRR944022 4 0.0188 0.664 0.004 0.000 0.000 0.996
#> SRR944023 3 0.6919 0.206 0.352 0.000 0.528 0.120
#> SRR944024 1 0.4817 0.733 0.612 0.000 0.000 0.388
#> SRR944026 2 0.3626 0.833 0.184 0.812 0.004 0.000
#> SRR944025 2 0.1792 0.907 0.068 0.932 0.000 0.000
#> SRR944028 2 0.2011 0.902 0.080 0.920 0.000 0.000
#> SRR944029 4 0.5277 0.443 0.304 0.000 0.028 0.668
#> SRR944030 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> SRR944031 3 0.0779 0.805 0.016 0.000 0.980 0.004
#> SRR944032 1 0.5921 0.268 0.672 0.256 0.004 0.068
#> SRR944033 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> SRR944036 3 0.6163 0.648 0.164 0.160 0.676 0.000
#> SRR944035 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> SRR944038 3 0.3280 0.732 0.016 0.000 0.860 0.124
#> SRR944037 4 0.0188 0.667 0.004 0.000 0.000 0.996
#> SRR944039 4 0.3942 0.370 0.236 0.000 0.000 0.764
#> SRR944040 2 0.1545 0.895 0.008 0.952 0.040 0.000
#> SRR944041 4 0.2469 0.626 0.108 0.000 0.000 0.892
#> SRR944042 3 0.0376 0.806 0.004 0.000 0.992 0.004
#> SRR944043 4 0.4961 -0.436 0.448 0.000 0.000 0.552
#> SRR944044 2 0.3074 0.858 0.152 0.848 0.000 0.000
#> SRR944046 3 0.0376 0.806 0.004 0.000 0.992 0.004
#> SRR944045 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> SRR944047 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> SRR944048 1 0.4564 0.770 0.672 0.000 0.000 0.328
#> SRR944049 2 0.1302 0.918 0.044 0.956 0.000 0.000
#> SRR944050 1 0.4500 0.762 0.684 0.000 0.000 0.316
#> SRR944051 2 0.4690 0.755 0.268 0.720 0.004 0.008
#> SRR944052 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> SRR944053 4 0.0000 0.666 0.000 0.000 0.000 1.000
#> SRR944054 2 0.4198 0.799 0.224 0.768 0.004 0.004
#> SRR944055 3 0.4690 0.669 0.016 0.260 0.724 0.000
#> SRR944056 2 0.0188 0.928 0.004 0.996 0.000 0.000
#> SRR944057 1 0.4624 0.768 0.660 0.000 0.000 0.340
#> SRR944058 4 0.5000 -0.562 0.500 0.000 0.000 0.500
#> SRR944059 3 0.3392 0.767 0.020 0.124 0.856 0.000
#> SRR944060 3 0.7495 0.112 0.192 0.000 0.468 0.340
#> SRR944061 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> SRR944062 1 0.4843 0.722 0.604 0.000 0.000 0.396
#> SRR944063 4 0.0000 0.666 0.000 0.000 0.000 1.000
#> SRR944064 2 0.0336 0.929 0.008 0.992 0.000 0.000
#> SRR944065 4 0.2647 0.545 0.120 0.000 0.000 0.880
#> SRR944066 1 0.4730 0.755 0.636 0.000 0.000 0.364
#> SRR944067 2 0.0817 0.925 0.024 0.976 0.000 0.000
#> SRR944068 4 0.0657 0.666 0.012 0.000 0.004 0.984
#> SRR944069 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> SRR944070 3 0.2060 0.783 0.016 0.000 0.932 0.052
#> SRR944071 3 0.2521 0.795 0.024 0.064 0.912 0.000
#> SRR944072 4 0.4999 -0.545 0.492 0.000 0.000 0.508
#> SRR944073 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> SRR944075 3 0.4857 0.635 0.016 0.284 0.700 0.000
#> SRR944074 2 0.3610 0.824 0.200 0.800 0.000 0.000
#> SRR944076 3 0.0657 0.806 0.012 0.000 0.984 0.004
#> SRR944077 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> SRR944078 3 0.5606 0.184 0.020 0.480 0.500 0.000
#> SRR944079 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> SRR944080 2 0.0000 0.930 0.000 1.000 0.000 0.000
#> SRR944081 4 0.5012 0.445 0.320 0.008 0.004 0.668
#> SRR944082 1 0.4994 0.563 0.520 0.000 0.000 0.480
#> SRR944083 1 0.4585 0.770 0.668 0.000 0.000 0.332
#> SRR944084 4 0.7358 0.168 0.140 0.008 0.332 0.520
#> SRR944085 3 0.0779 0.807 0.016 0.004 0.980 0.000
#> SRR944086 1 0.6141 0.112 0.620 0.060 0.004 0.316
#> SRR944088 2 0.6027 0.682 0.272 0.656 0.004 0.068
#> SRR944087 3 0.0844 0.807 0.004 0.012 0.980 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.2282 0.7234 0.004 0.032 0.920 0.008 0.036
#> SRR944012 4 0.2645 0.7527 0.068 0.000 0.000 0.888 0.044
#> SRR944014 2 0.0000 0.8139 0.000 1.000 0.000 0.000 0.000
#> SRR944013 5 0.5157 0.5811 0.016 0.288 0.000 0.040 0.656
#> SRR944015 4 0.2291 0.7520 0.072 0.000 0.008 0.908 0.012
#> SRR944016 1 0.0912 0.8017 0.972 0.000 0.000 0.012 0.016
#> SRR944017 2 0.3143 0.6556 0.000 0.796 0.000 0.000 0.204
#> SRR944018 4 0.4798 0.2077 0.396 0.000 0.000 0.580 0.024
#> SRR944019 4 0.6024 0.4670 0.288 0.000 0.000 0.560 0.152
#> SRR944020 4 0.2189 0.7587 0.084 0.000 0.000 0.904 0.012
#> SRR944021 2 0.0000 0.8139 0.000 1.000 0.000 0.000 0.000
#> SRR944022 4 0.2179 0.7564 0.100 0.000 0.000 0.896 0.004
#> SRR944023 3 0.6794 0.1455 0.388 0.000 0.468 0.096 0.048
#> SRR944024 1 0.2462 0.8084 0.880 0.000 0.000 0.112 0.008
#> SRR944026 2 0.4735 -0.0945 0.000 0.524 0.000 0.016 0.460
#> SRR944025 2 0.4047 0.4593 0.000 0.676 0.000 0.004 0.320
#> SRR944028 2 0.3990 0.4754 0.000 0.688 0.000 0.004 0.308
#> SRR944029 4 0.4705 0.4034 0.000 0.004 0.012 0.580 0.404
#> SRR944030 2 0.0000 0.8139 0.000 1.000 0.000 0.000 0.000
#> SRR944031 3 0.1774 0.7276 0.000 0.000 0.932 0.016 0.052
#> SRR944032 5 0.6057 0.2414 0.392 0.060 0.004 0.020 0.524
#> SRR944033 2 0.0000 0.8139 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.8139 0.000 1.000 0.000 0.000 0.000
#> SRR944036 3 0.8629 0.2650 0.216 0.260 0.392 0.032 0.100
#> SRR944035 2 0.2230 0.7477 0.000 0.884 0.000 0.000 0.116
#> SRR944038 3 0.4422 0.5771 0.020 0.000 0.732 0.232 0.016
#> SRR944037 4 0.2249 0.7582 0.096 0.000 0.000 0.896 0.008
#> SRR944039 4 0.5314 0.2226 0.420 0.000 0.000 0.528 0.052
#> SRR944040 2 0.1960 0.7484 0.000 0.928 0.048 0.004 0.020
#> SRR944041 4 0.4069 0.7068 0.096 0.000 0.000 0.792 0.112
#> SRR944042 3 0.1082 0.7297 0.000 0.000 0.964 0.008 0.028
#> SRR944043 1 0.4597 0.3274 0.564 0.000 0.000 0.424 0.012
#> SRR944044 2 0.4473 0.1285 0.000 0.580 0.000 0.008 0.412
#> SRR944046 3 0.1153 0.7295 0.004 0.000 0.964 0.008 0.024
#> SRR944045 2 0.0162 0.8116 0.000 0.996 0.000 0.004 0.000
#> SRR944047 2 0.0000 0.8139 0.000 1.000 0.000 0.000 0.000
#> SRR944048 1 0.1211 0.8025 0.960 0.000 0.000 0.016 0.024
#> SRR944049 2 0.3550 0.6009 0.000 0.760 0.000 0.004 0.236
#> SRR944050 1 0.1043 0.7844 0.960 0.000 0.000 0.000 0.040
#> SRR944051 5 0.4217 0.6101 0.012 0.244 0.000 0.012 0.732
#> SRR944052 2 0.0000 0.8139 0.000 1.000 0.000 0.000 0.000
#> SRR944053 4 0.1965 0.7576 0.096 0.000 0.000 0.904 0.000
#> SRR944054 5 0.4752 0.3336 0.000 0.412 0.000 0.020 0.568
#> SRR944055 3 0.5654 0.3842 0.004 0.384 0.552 0.008 0.052
#> SRR944056 2 0.0000 0.8139 0.000 1.000 0.000 0.000 0.000
#> SRR944057 1 0.1106 0.8095 0.964 0.000 0.000 0.024 0.012
#> SRR944058 1 0.3857 0.6164 0.688 0.000 0.000 0.312 0.000
#> SRR944059 3 0.4684 0.6312 0.000 0.176 0.744 0.008 0.072
#> SRR944060 3 0.7647 0.1630 0.244 0.000 0.408 0.292 0.056
#> SRR944061 2 0.0000 0.8139 0.000 1.000 0.000 0.000 0.000
#> SRR944062 1 0.2997 0.7916 0.840 0.000 0.000 0.148 0.012
#> SRR944063 4 0.2020 0.7562 0.100 0.000 0.000 0.900 0.000
#> SRR944064 2 0.2886 0.7143 0.008 0.844 0.000 0.000 0.148
#> SRR944065 4 0.3550 0.6725 0.184 0.000 0.000 0.796 0.020
#> SRR944066 1 0.2011 0.8145 0.908 0.000 0.000 0.088 0.004
#> SRR944067 2 0.3242 0.6453 0.000 0.784 0.000 0.000 0.216
#> SRR944068 4 0.2077 0.7540 0.084 0.000 0.000 0.908 0.008
#> SRR944069 2 0.0162 0.8116 0.000 0.996 0.000 0.004 0.000
#> SRR944070 3 0.3218 0.6889 0.004 0.000 0.844 0.128 0.024
#> SRR944071 3 0.5736 0.6180 0.016 0.176 0.692 0.016 0.100
#> SRR944072 1 0.4118 0.5614 0.660 0.000 0.000 0.336 0.004
#> SRR944073 2 0.0000 0.8139 0.000 1.000 0.000 0.000 0.000
#> SRR944075 3 0.5786 0.3439 0.004 0.400 0.532 0.012 0.052
#> SRR944074 2 0.4747 -0.1857 0.000 0.500 0.000 0.016 0.484
#> SRR944076 3 0.1195 0.7303 0.000 0.000 0.960 0.012 0.028
#> SRR944077 2 0.0000 0.8139 0.000 1.000 0.000 0.000 0.000
#> SRR944078 2 0.5322 0.1514 0.000 0.580 0.372 0.012 0.036
#> SRR944079 2 0.0000 0.8139 0.000 1.000 0.000 0.000 0.000
#> SRR944080 2 0.0794 0.8015 0.000 0.972 0.000 0.000 0.028
#> SRR944081 4 0.4907 0.2407 0.024 0.000 0.000 0.488 0.488
#> SRR944082 1 0.3988 0.7017 0.732 0.000 0.000 0.252 0.016
#> SRR944083 1 0.1124 0.8128 0.960 0.000 0.000 0.036 0.004
#> SRR944084 4 0.6274 0.4413 0.012 0.008 0.172 0.616 0.192
#> SRR944085 3 0.2102 0.7286 0.004 0.000 0.916 0.012 0.068
#> SRR944086 5 0.7111 0.1291 0.272 0.024 0.008 0.192 0.504
#> SRR944088 5 0.4938 0.5498 0.000 0.312 0.000 0.048 0.640
#> SRR944087 3 0.1731 0.7287 0.000 0.008 0.940 0.012 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.4160 0.6761 0.004 0.068 0.760 0.000 0.008 NA
#> SRR944012 4 0.3189 0.7188 0.016 0.000 0.000 0.848 0.064 NA
#> SRR944014 2 0.0146 0.7676 0.000 0.996 0.000 0.000 0.000 NA
#> SRR944013 5 0.5867 0.5658 0.020 0.200 0.000 0.024 0.624 NA
#> SRR944015 4 0.2145 0.7296 0.012 0.000 0.028 0.916 0.004 NA
#> SRR944016 1 0.2825 0.7613 0.876 0.000 0.000 0.040 0.028 NA
#> SRR944017 2 0.4354 0.4495 0.008 0.684 0.000 0.000 0.268 NA
#> SRR944018 4 0.5317 0.2606 0.288 0.000 0.000 0.608 0.024 NA
#> SRR944019 4 0.6553 0.4824 0.132 0.000 0.000 0.552 0.132 NA
#> SRR944020 4 0.0984 0.7469 0.012 0.000 0.000 0.968 0.008 NA
#> SRR944021 2 0.0692 0.7643 0.000 0.976 0.000 0.000 0.004 NA
#> SRR944022 4 0.0777 0.7428 0.024 0.000 0.000 0.972 0.000 NA
#> SRR944023 3 0.6876 0.2837 0.316 0.000 0.444 0.048 0.012 NA
#> SRR944024 1 0.3663 0.7583 0.796 0.000 0.000 0.128 0.004 NA
#> SRR944026 5 0.4172 0.1751 0.000 0.460 0.000 0.000 0.528 NA
#> SRR944025 2 0.4794 0.2523 0.004 0.596 0.000 0.000 0.344 NA
#> SRR944028 2 0.4763 0.1751 0.004 0.576 0.000 0.000 0.372 NA
#> SRR944029 4 0.6403 0.2917 0.004 0.000 0.032 0.468 0.336 NA
#> SRR944030 2 0.0146 0.7669 0.000 0.996 0.000 0.000 0.004 NA
#> SRR944031 3 0.2698 0.7096 0.008 0.000 0.860 0.004 0.008 NA
#> SRR944032 5 0.7141 0.1269 0.296 0.052 0.004 0.008 0.408 NA
#> SRR944033 2 0.0000 0.7675 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944034 2 0.0260 0.7657 0.000 0.992 0.000 0.000 0.008 NA
#> SRR944036 3 0.8838 0.2187 0.144 0.216 0.304 0.012 0.092 NA
#> SRR944035 2 0.3567 0.6280 0.008 0.804 0.000 0.000 0.136 NA
#> SRR944038 3 0.4500 0.6207 0.016 0.000 0.740 0.160 0.004 NA
#> SRR944037 4 0.1938 0.7412 0.020 0.000 0.000 0.920 0.008 NA
#> SRR944039 4 0.6485 0.1277 0.336 0.000 0.000 0.468 0.060 NA
#> SRR944040 2 0.2290 0.6990 0.000 0.892 0.020 0.000 0.004 NA
#> SRR944041 4 0.4470 0.6757 0.044 0.000 0.000 0.760 0.092 NA
#> SRR944042 3 0.1082 0.7186 0.004 0.000 0.956 0.000 0.000 NA
#> SRR944043 1 0.5647 0.2285 0.464 0.000 0.008 0.440 0.016 NA
#> SRR944044 2 0.4172 -0.0797 0.000 0.528 0.000 0.000 0.460 NA
#> SRR944046 3 0.2545 0.7151 0.004 0.008 0.884 0.000 0.020 NA
#> SRR944045 2 0.0632 0.7631 0.000 0.976 0.000 0.000 0.000 NA
#> SRR944047 2 0.0000 0.7675 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944048 1 0.2390 0.7712 0.896 0.000 0.000 0.044 0.008 NA
#> SRR944049 2 0.3719 0.5297 0.000 0.728 0.000 0.000 0.248 NA
#> SRR944050 1 0.3113 0.7371 0.856 0.000 0.000 0.028 0.040 NA
#> SRR944051 5 0.5463 0.5588 0.024 0.200 0.000 0.008 0.652 NA
#> SRR944052 2 0.0547 0.7643 0.000 0.980 0.000 0.000 0.000 NA
#> SRR944053 4 0.0717 0.7453 0.016 0.000 0.000 0.976 0.000 NA
#> SRR944054 5 0.4616 0.4781 0.000 0.316 0.000 0.000 0.624 NA
#> SRR944055 2 0.5980 -0.2080 0.000 0.408 0.396 0.000 0.004 NA
#> SRR944056 2 0.0935 0.7582 0.000 0.964 0.000 0.000 0.004 NA
#> SRR944057 1 0.2577 0.7637 0.888 0.000 0.000 0.040 0.016 NA
#> SRR944058 1 0.4770 0.5116 0.584 0.000 0.000 0.368 0.012 NA
#> SRR944059 3 0.5761 0.4805 0.000 0.236 0.536 0.000 0.004 NA
#> SRR944060 3 0.7531 0.2184 0.164 0.000 0.396 0.272 0.008 NA
#> SRR944061 2 0.0363 0.7669 0.000 0.988 0.000 0.000 0.000 NA
#> SRR944062 1 0.3980 0.7392 0.760 0.000 0.000 0.168 0.004 NA
#> SRR944063 4 0.0717 0.7453 0.016 0.000 0.000 0.976 0.000 NA
#> SRR944064 2 0.3527 0.6332 0.008 0.808 0.000 0.000 0.132 NA
#> SRR944065 4 0.4166 0.5929 0.156 0.000 0.000 0.764 0.024 NA
#> SRR944066 1 0.2679 0.7756 0.868 0.000 0.000 0.096 0.004 NA
#> SRR944067 2 0.4515 0.4616 0.008 0.688 0.000 0.000 0.244 NA
#> SRR944068 4 0.1578 0.7385 0.012 0.000 0.012 0.944 0.004 NA
#> SRR944069 2 0.0508 0.7665 0.000 0.984 0.000 0.000 0.004 NA
#> SRR944070 3 0.3427 0.6838 0.008 0.000 0.824 0.088 0.000 NA
#> SRR944071 3 0.6357 0.4937 0.008 0.212 0.488 0.000 0.016 NA
#> SRR944072 1 0.5536 0.4610 0.540 0.000 0.000 0.356 0.024 NA
#> SRR944073 2 0.0000 0.7675 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944075 2 0.6182 -0.1678 0.000 0.416 0.372 0.000 0.012 NA
#> SRR944074 5 0.4123 0.2814 0.000 0.420 0.000 0.000 0.568 NA
#> SRR944076 3 0.2890 0.7192 0.012 0.000 0.848 0.000 0.016 NA
#> SRR944077 2 0.0000 0.7675 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944078 2 0.5663 0.2940 0.000 0.576 0.244 0.000 0.012 NA
#> SRR944079 2 0.0146 0.7676 0.000 0.996 0.000 0.000 0.000 NA
#> SRR944080 2 0.1225 0.7463 0.000 0.952 0.000 0.000 0.036 NA
#> SRR944081 5 0.6629 -0.2214 0.028 0.000 0.004 0.356 0.396 NA
#> SRR944082 1 0.4552 0.6163 0.640 0.000 0.000 0.300 0.000 NA
#> SRR944083 1 0.2201 0.7755 0.904 0.000 0.000 0.056 0.004 NA
#> SRR944084 4 0.7228 0.2923 0.000 0.004 0.176 0.460 0.144 NA
#> SRR944085 3 0.3514 0.7115 0.008 0.004 0.804 0.004 0.020 NA
#> SRR944086 5 0.7912 0.1269 0.160 0.012 0.016 0.144 0.380 NA
#> SRR944088 5 0.5364 0.5488 0.000 0.228 0.004 0.012 0.632 NA
#> SRR944087 3 0.3773 0.6966 0.004 0.028 0.796 0.000 0.024 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.946 0.954 0.980 0.3740 0.623 0.623
#> 3 3 0.944 0.934 0.976 0.0728 0.976 0.962
#> 4 4 0.860 0.900 0.958 0.0501 0.999 0.998
#> 5 5 0.827 0.870 0.949 0.0230 0.999 0.998
#> 6 6 0.820 0.804 0.929 0.0667 0.957 0.927
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.0000 0.987 0.000 1.000
#> SRR944012 2 0.8813 0.548 0.300 0.700
#> SRR944014 2 0.0000 0.987 0.000 1.000
#> SRR944013 2 0.0000 0.987 0.000 1.000
#> SRR944015 1 0.0000 0.951 1.000 0.000
#> SRR944016 2 0.6712 0.776 0.176 0.824
#> SRR944017 2 0.0000 0.987 0.000 1.000
#> SRR944018 1 0.0000 0.951 1.000 0.000
#> SRR944019 2 0.0000 0.987 0.000 1.000
#> SRR944020 1 0.8386 0.660 0.732 0.268
#> SRR944021 2 0.0000 0.987 0.000 1.000
#> SRR944022 1 0.0000 0.951 1.000 0.000
#> SRR944023 2 0.0000 0.987 0.000 1.000
#> SRR944024 1 0.0000 0.951 1.000 0.000
#> SRR944026 2 0.0000 0.987 0.000 1.000
#> SRR944025 2 0.0000 0.987 0.000 1.000
#> SRR944028 2 0.0000 0.987 0.000 1.000
#> SRR944029 2 0.0000 0.987 0.000 1.000
#> SRR944030 2 0.0000 0.987 0.000 1.000
#> SRR944031 2 0.0000 0.987 0.000 1.000
#> SRR944032 2 0.0000 0.987 0.000 1.000
#> SRR944033 2 0.0000 0.987 0.000 1.000
#> SRR944034 2 0.0000 0.987 0.000 1.000
#> SRR944036 2 0.0000 0.987 0.000 1.000
#> SRR944035 2 0.0000 0.987 0.000 1.000
#> SRR944038 1 0.7376 0.753 0.792 0.208
#> SRR944037 1 0.9129 0.551 0.672 0.328
#> SRR944039 2 0.0000 0.987 0.000 1.000
#> SRR944040 2 0.0000 0.987 0.000 1.000
#> SRR944041 2 0.0000 0.987 0.000 1.000
#> SRR944042 2 0.0000 0.987 0.000 1.000
#> SRR944043 1 0.0000 0.951 1.000 0.000
#> SRR944044 2 0.0000 0.987 0.000 1.000
#> SRR944046 2 0.0000 0.987 0.000 1.000
#> SRR944045 2 0.0000 0.987 0.000 1.000
#> SRR944047 2 0.0000 0.987 0.000 1.000
#> SRR944048 1 0.0000 0.951 1.000 0.000
#> SRR944049 2 0.0000 0.987 0.000 1.000
#> SRR944050 2 0.0000 0.987 0.000 1.000
#> SRR944051 2 0.0000 0.987 0.000 1.000
#> SRR944052 2 0.0000 0.987 0.000 1.000
#> SRR944053 1 0.0000 0.951 1.000 0.000
#> SRR944054 2 0.0000 0.987 0.000 1.000
#> SRR944055 2 0.0000 0.987 0.000 1.000
#> SRR944056 2 0.0000 0.987 0.000 1.000
#> SRR944057 2 0.0000 0.987 0.000 1.000
#> SRR944058 1 0.0000 0.951 1.000 0.000
#> SRR944059 2 0.0000 0.987 0.000 1.000
#> SRR944060 2 0.0000 0.987 0.000 1.000
#> SRR944061 2 0.0000 0.987 0.000 1.000
#> SRR944062 1 0.0000 0.951 1.000 0.000
#> SRR944063 1 0.0000 0.951 1.000 0.000
#> SRR944064 2 0.0000 0.987 0.000 1.000
#> SRR944065 1 0.3431 0.905 0.936 0.064
#> SRR944066 1 0.0000 0.951 1.000 0.000
#> SRR944067 2 0.0000 0.987 0.000 1.000
#> SRR944068 1 0.0000 0.951 1.000 0.000
#> SRR944069 2 0.0000 0.987 0.000 1.000
#> SRR944070 2 0.7219 0.734 0.200 0.800
#> SRR944071 2 0.0000 0.987 0.000 1.000
#> SRR944072 1 0.0376 0.948 0.996 0.004
#> SRR944073 2 0.0000 0.987 0.000 1.000
#> SRR944075 2 0.0000 0.987 0.000 1.000
#> SRR944074 2 0.0000 0.987 0.000 1.000
#> SRR944076 2 0.0000 0.987 0.000 1.000
#> SRR944077 2 0.0000 0.987 0.000 1.000
#> SRR944078 2 0.0000 0.987 0.000 1.000
#> SRR944079 2 0.0000 0.987 0.000 1.000
#> SRR944080 2 0.0000 0.987 0.000 1.000
#> SRR944081 2 0.0000 0.987 0.000 1.000
#> SRR944082 1 0.0000 0.951 1.000 0.000
#> SRR944083 1 0.0000 0.951 1.000 0.000
#> SRR944084 2 0.0000 0.987 0.000 1.000
#> SRR944085 2 0.0000 0.987 0.000 1.000
#> SRR944086 2 0.0000 0.987 0.000 1.000
#> SRR944088 2 0.0000 0.987 0.000 1.000
#> SRR944087 2 0.0000 0.987 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944012 2 0.5560 0.550 0.300 0.700 0.000
#> SRR944014 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944013 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944015 3 0.0000 0.903 0.000 0.000 1.000
#> SRR944016 2 0.4291 0.774 0.180 0.820 0.000
#> SRR944017 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944018 1 0.0892 0.870 0.980 0.020 0.000
#> SRR944019 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944020 3 0.1525 0.898 0.032 0.004 0.964
#> SRR944021 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944022 3 0.5497 0.588 0.292 0.000 0.708
#> SRR944023 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944024 1 0.0000 0.887 1.000 0.000 0.000
#> SRR944026 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944025 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944028 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944029 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944030 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944031 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944032 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944033 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944034 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944036 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944035 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944038 1 0.4834 0.577 0.792 0.204 0.004
#> SRR944037 1 0.5706 0.382 0.680 0.320 0.000
#> SRR944039 2 0.0747 0.972 0.016 0.984 0.000
#> SRR944040 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944041 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944042 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944043 1 0.0000 0.887 1.000 0.000 0.000
#> SRR944044 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944046 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944045 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944047 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944048 1 0.0000 0.887 1.000 0.000 0.000
#> SRR944049 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944050 2 0.0747 0.972 0.016 0.984 0.000
#> SRR944051 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944052 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944053 3 0.0000 0.903 0.000 0.000 1.000
#> SRR944054 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944055 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944056 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944057 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944058 1 0.0000 0.887 1.000 0.000 0.000
#> SRR944059 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944060 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944061 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944062 1 0.0000 0.887 1.000 0.000 0.000
#> SRR944063 1 0.3412 0.779 0.876 0.000 0.124
#> SRR944064 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944065 1 0.2165 0.813 0.936 0.064 0.000
#> SRR944066 1 0.0000 0.887 1.000 0.000 0.000
#> SRR944067 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944068 3 0.1529 0.895 0.040 0.000 0.960
#> SRR944069 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944070 2 0.4555 0.735 0.200 0.800 0.000
#> SRR944071 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944072 1 0.0237 0.885 0.996 0.004 0.000
#> SRR944073 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944075 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944074 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944076 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944077 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944078 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944079 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944080 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944081 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944082 1 0.0000 0.887 1.000 0.000 0.000
#> SRR944083 1 0.0000 0.887 1.000 0.000 0.000
#> SRR944084 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944085 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944086 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944088 2 0.0000 0.987 0.000 1.000 0.000
#> SRR944087 2 0.0000 0.987 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944012 2 0.4406 0.564 0.300 0.700 0.000 0.000
#> SRR944014 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944013 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944015 4 0.0000 0.876 0.000 0.000 0.000 1.000
#> SRR944016 2 0.4121 0.765 0.020 0.796 0.184 0.000
#> SRR944017 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944018 1 0.0524 0.863 0.988 0.004 0.008 0.000
#> SRR944019 2 0.3400 0.795 0.000 0.820 0.180 0.000
#> SRR944020 4 0.4044 0.754 0.024 0.004 0.152 0.820
#> SRR944021 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944022 3 0.4267 0.000 0.024 0.000 0.788 0.188
#> SRR944023 2 0.0657 0.961 0.004 0.984 0.012 0.000
#> SRR944024 1 0.0188 0.863 0.996 0.000 0.004 0.000
#> SRR944026 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944025 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944028 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944029 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944030 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944031 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944032 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944033 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944036 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944035 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944038 1 0.4012 0.556 0.788 0.204 0.004 0.004
#> SRR944037 1 0.6805 0.440 0.592 0.148 0.260 0.000
#> SRR944039 2 0.2530 0.881 0.004 0.896 0.100 0.000
#> SRR944040 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944041 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944042 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944043 1 0.0469 0.862 0.988 0.000 0.012 0.000
#> SRR944044 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944046 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944045 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944047 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944048 1 0.0188 0.863 0.996 0.000 0.004 0.000
#> SRR944049 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944050 2 0.3444 0.790 0.000 0.816 0.184 0.000
#> SRR944051 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944052 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944053 4 0.1211 0.871 0.000 0.000 0.040 0.960
#> SRR944054 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944055 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944056 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944057 2 0.3444 0.790 0.000 0.816 0.184 0.000
#> SRR944058 1 0.1302 0.853 0.956 0.000 0.044 0.000
#> SRR944059 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944060 2 0.1109 0.950 0.004 0.968 0.028 0.000
#> SRR944061 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944062 1 0.0188 0.863 0.996 0.000 0.004 0.000
#> SRR944063 1 0.3647 0.771 0.852 0.000 0.040 0.108
#> SRR944064 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944065 1 0.1824 0.808 0.936 0.060 0.004 0.000
#> SRR944066 1 0.3486 0.761 0.812 0.000 0.188 0.000
#> SRR944067 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944068 4 0.1211 0.848 0.040 0.000 0.000 0.960
#> SRR944069 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944070 2 0.3937 0.741 0.188 0.800 0.012 0.000
#> SRR944071 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944072 1 0.3528 0.760 0.808 0.000 0.192 0.000
#> SRR944073 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944075 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944074 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944076 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944077 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944078 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944079 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944080 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944081 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944082 1 0.0469 0.862 0.988 0.000 0.012 0.000
#> SRR944083 1 0.0188 0.863 0.996 0.000 0.004 0.000
#> SRR944084 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944085 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944086 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944088 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR944087 2 0.0000 0.974 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944012 2 0.3796 0.566 0.300 0.700 0.000 0.000 0.000
#> SRR944014 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944013 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944015 4 0.4129 0.811 0.000 0.000 0.040 0.756 0.204
#> SRR944016 2 0.3883 0.691 0.004 0.744 0.008 0.244 0.000
#> SRR944017 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944018 1 0.0671 0.843 0.980 0.004 0.016 0.000 0.000
#> SRR944019 2 0.3074 0.771 0.000 0.804 0.000 0.196 0.000
#> SRR944020 3 0.0162 0.000 0.004 0.000 0.996 0.000 0.000
#> SRR944021 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944022 5 0.3366 0.000 0.000 0.000 0.232 0.000 0.768
#> SRR944023 2 0.0771 0.948 0.004 0.976 0.020 0.000 0.000
#> SRR944024 1 0.0162 0.844 0.996 0.000 0.004 0.000 0.000
#> SRR944026 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944025 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944028 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944029 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944030 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944031 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944032 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944033 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944036 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944035 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944038 1 0.4408 0.518 0.752 0.204 0.008 0.004 0.032
#> SRR944037 1 0.6238 0.551 0.620 0.080 0.056 0.244 0.000
#> SRR944039 2 0.3044 0.817 0.004 0.840 0.008 0.148 0.000
#> SRR944040 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944041 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944042 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944043 1 0.0609 0.842 0.980 0.000 0.020 0.000 0.000
#> SRR944044 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944046 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944045 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944047 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944048 1 0.0162 0.844 0.996 0.000 0.004 0.000 0.000
#> SRR944049 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944050 2 0.3728 0.697 0.000 0.748 0.008 0.244 0.000
#> SRR944051 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944052 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944053 4 0.3913 0.513 0.000 0.000 0.324 0.676 0.000
#> SRR944054 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944055 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944056 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944057 2 0.3728 0.697 0.000 0.748 0.008 0.244 0.000
#> SRR944058 1 0.1205 0.836 0.956 0.000 0.004 0.040 0.000
#> SRR944059 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944060 2 0.2666 0.889 0.004 0.904 0.020 0.044 0.028
#> SRR944061 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944062 1 0.0162 0.844 0.996 0.000 0.004 0.000 0.000
#> SRR944063 1 0.3790 0.622 0.724 0.000 0.272 0.004 0.000
#> SRR944064 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944065 1 0.1809 0.790 0.928 0.060 0.012 0.000 0.000
#> SRR944066 1 0.3934 0.697 0.740 0.000 0.016 0.244 0.000
#> SRR944067 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944068 4 0.4129 0.811 0.000 0.000 0.040 0.756 0.204
#> SRR944069 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944070 2 0.4153 0.741 0.152 0.796 0.020 0.004 0.028
#> SRR944071 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944072 1 0.3934 0.697 0.740 0.000 0.016 0.244 0.000
#> SRR944073 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944075 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944074 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944076 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944077 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944078 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944079 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944081 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944082 1 0.0609 0.842 0.980 0.000 0.020 0.000 0.000
#> SRR944083 1 0.0162 0.844 0.996 0.000 0.004 0.000 0.000
#> SRR944084 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944085 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944086 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944088 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> SRR944087 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944012 2 0.3729 0.149 0.296 0.692 0.000 0.000 0 0.012
#> SRR944014 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944013 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944015 4 0.3672 0.772 0.000 0.000 0.000 0.632 0 0.368
#> SRR944016 2 0.3672 0.156 0.000 0.632 0.000 0.368 0 0.000
#> SRR944017 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944018 1 0.0603 0.832 0.980 0.004 0.000 0.000 0 0.016
#> SRR944019 2 0.2793 0.596 0.000 0.800 0.000 0.200 0 0.000
#> SRR944020 3 0.0000 0.000 0.000 0.000 1.000 0.000 0 0.000
#> SRR944021 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944022 5 0.0000 0.000 0.000 0.000 0.000 0.000 1 0.000
#> SRR944023 2 0.0790 0.898 0.000 0.968 0.000 0.000 0 0.032
#> SRR944024 1 0.0000 0.833 1.000 0.000 0.000 0.000 0 0.000
#> SRR944026 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944025 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944028 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944029 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944030 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944031 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944032 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944033 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944034 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944036 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944035 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944038 6 0.5691 0.186 0.276 0.204 0.000 0.000 0 0.520
#> SRR944037 1 0.5133 0.535 0.572 0.028 0.004 0.364 0 0.032
#> SRR944039 2 0.3240 0.482 0.004 0.752 0.000 0.244 0 0.000
#> SRR944040 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944041 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944042 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944043 1 0.0865 0.828 0.964 0.000 0.000 0.000 0 0.036
#> SRR944044 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944046 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944045 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944047 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944048 1 0.0000 0.833 1.000 0.000 0.000 0.000 0 0.000
#> SRR944049 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944050 2 0.3672 0.156 0.000 0.632 0.000 0.368 0 0.000
#> SRR944051 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944052 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944053 4 0.5408 0.383 0.000 0.000 0.304 0.552 0 0.144
#> SRR944054 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944055 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944056 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944057 2 0.3672 0.156 0.000 0.632 0.000 0.368 0 0.000
#> SRR944058 1 0.0937 0.824 0.960 0.000 0.000 0.040 0 0.000
#> SRR944059 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944060 6 0.4615 0.697 0.000 0.424 0.000 0.040 0 0.536
#> SRR944061 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944062 1 0.0000 0.833 1.000 0.000 0.000 0.000 0 0.000
#> SRR944063 1 0.4653 0.487 0.644 0.000 0.292 0.004 0 0.060
#> SRR944064 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944065 1 0.1970 0.758 0.912 0.060 0.000 0.000 0 0.028
#> SRR944066 1 0.4167 0.578 0.612 0.000 0.000 0.368 0 0.020
#> SRR944067 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944068 4 0.3672 0.772 0.000 0.000 0.000 0.632 0 0.368
#> SRR944069 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944070 6 0.3854 0.685 0.000 0.464 0.000 0.000 0 0.536
#> SRR944071 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944072 1 0.4167 0.578 0.612 0.000 0.000 0.368 0 0.020
#> SRR944073 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944075 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944074 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944076 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944077 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944078 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944079 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944080 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944081 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944082 1 0.0790 0.829 0.968 0.000 0.000 0.000 0 0.032
#> SRR944083 1 0.0000 0.833 1.000 0.000 0.000 0.000 0 0.000
#> SRR944084 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944085 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944086 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944088 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
#> SRR944087 2 0.0000 0.944 0.000 1.000 0.000 0.000 0 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.785 0.930 0.959 0.4670 0.518 0.518
#> 3 3 0.607 0.848 0.863 0.1624 0.843 0.730
#> 4 4 0.503 0.758 0.803 0.2935 0.767 0.532
#> 5 5 0.812 0.870 0.906 0.1252 0.838 0.486
#> 6 6 0.853 0.849 0.863 0.0217 0.928 0.689
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.5294 0.9240 0.120 0.880
#> SRR944012 1 0.0000 0.9756 1.000 0.000
#> SRR944014 2 0.0000 0.9259 0.000 1.000
#> SRR944013 1 0.0000 0.9756 1.000 0.000
#> SRR944015 1 0.0000 0.9756 1.000 0.000
#> SRR944016 1 0.0000 0.9756 1.000 0.000
#> SRR944017 1 0.2778 0.9338 0.952 0.048
#> SRR944018 1 0.0000 0.9756 1.000 0.000
#> SRR944019 1 0.0000 0.9756 1.000 0.000
#> SRR944020 1 0.0000 0.9756 1.000 0.000
#> SRR944021 2 0.0000 0.9259 0.000 1.000
#> SRR944022 1 0.0000 0.9756 1.000 0.000
#> SRR944023 1 0.0000 0.9756 1.000 0.000
#> SRR944024 1 0.0000 0.9756 1.000 0.000
#> SRR944026 1 0.0000 0.9756 1.000 0.000
#> SRR944025 1 0.0376 0.9721 0.996 0.004
#> SRR944028 1 0.2423 0.9403 0.960 0.040
#> SRR944029 1 0.0000 0.9756 1.000 0.000
#> SRR944030 2 0.0376 0.9269 0.004 0.996
#> SRR944031 2 0.5408 0.9215 0.124 0.876
#> SRR944032 1 0.0000 0.9756 1.000 0.000
#> SRR944033 2 0.0000 0.9259 0.000 1.000
#> SRR944034 2 0.3733 0.9317 0.072 0.928
#> SRR944036 1 0.0000 0.9756 1.000 0.000
#> SRR944035 1 0.9996 -0.0478 0.512 0.488
#> SRR944038 2 0.5629 0.9154 0.132 0.868
#> SRR944037 1 0.0000 0.9756 1.000 0.000
#> SRR944039 1 0.0000 0.9756 1.000 0.000
#> SRR944040 2 0.4161 0.9307 0.084 0.916
#> SRR944041 1 0.0000 0.9756 1.000 0.000
#> SRR944042 2 0.5294 0.9240 0.120 0.880
#> SRR944043 1 0.0000 0.9756 1.000 0.000
#> SRR944044 1 0.0000 0.9756 1.000 0.000
#> SRR944046 2 0.5408 0.9214 0.124 0.876
#> SRR944045 2 0.0000 0.9259 0.000 1.000
#> SRR944047 2 0.0000 0.9259 0.000 1.000
#> SRR944048 1 0.0000 0.9756 1.000 0.000
#> SRR944049 1 0.2778 0.9338 0.952 0.048
#> SRR944050 1 0.0000 0.9756 1.000 0.000
#> SRR944051 1 0.0000 0.9756 1.000 0.000
#> SRR944052 2 0.0672 0.9258 0.008 0.992
#> SRR944053 1 0.0000 0.9756 1.000 0.000
#> SRR944054 1 0.0000 0.9756 1.000 0.000
#> SRR944055 2 0.4562 0.9298 0.096 0.904
#> SRR944056 2 0.0000 0.9259 0.000 1.000
#> SRR944057 1 0.0000 0.9756 1.000 0.000
#> SRR944058 1 0.0000 0.9756 1.000 0.000
#> SRR944059 2 0.5294 0.9240 0.120 0.880
#> SRR944060 1 0.9393 0.3679 0.644 0.356
#> SRR944061 2 0.0000 0.9259 0.000 1.000
#> SRR944062 1 0.0000 0.9756 1.000 0.000
#> SRR944063 1 0.0000 0.9756 1.000 0.000
#> SRR944064 1 0.0000 0.9756 1.000 0.000
#> SRR944065 1 0.0000 0.9756 1.000 0.000
#> SRR944066 1 0.0000 0.9756 1.000 0.000
#> SRR944067 1 0.2948 0.9307 0.948 0.052
#> SRR944068 1 0.0000 0.9756 1.000 0.000
#> SRR944069 2 0.0000 0.9259 0.000 1.000
#> SRR944070 2 0.5629 0.9154 0.132 0.868
#> SRR944071 2 0.6887 0.8577 0.184 0.816
#> SRR944072 1 0.0000 0.9756 1.000 0.000
#> SRR944073 2 0.3584 0.9318 0.068 0.932
#> SRR944075 2 0.8267 0.7484 0.260 0.740
#> SRR944074 1 0.0000 0.9756 1.000 0.000
#> SRR944076 2 0.5294 0.9240 0.120 0.880
#> SRR944077 2 0.0000 0.9259 0.000 1.000
#> SRR944078 2 0.4562 0.9298 0.096 0.904
#> SRR944079 2 0.0000 0.9259 0.000 1.000
#> SRR944080 2 0.0938 0.9282 0.012 0.988
#> SRR944081 1 0.0000 0.9756 1.000 0.000
#> SRR944082 1 0.0000 0.9756 1.000 0.000
#> SRR944083 1 0.0000 0.9756 1.000 0.000
#> SRR944084 1 0.0000 0.9756 1.000 0.000
#> SRR944085 2 0.5294 0.9240 0.120 0.880
#> SRR944086 1 0.0000 0.9756 1.000 0.000
#> SRR944088 1 0.0000 0.9756 1.000 0.000
#> SRR944087 2 0.5294 0.9240 0.120 0.880
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 3 0.6452 0.913 0.036 0.252 0.712
#> SRR944012 1 0.1643 0.884 0.956 0.000 0.044
#> SRR944014 2 0.0237 0.925 0.000 0.996 0.004
#> SRR944013 1 0.2066 0.881 0.940 0.000 0.060
#> SRR944015 1 0.3482 0.872 0.872 0.000 0.128
#> SRR944016 1 0.4178 0.846 0.828 0.000 0.172
#> SRR944017 1 0.3456 0.866 0.904 0.036 0.060
#> SRR944018 1 0.2878 0.875 0.904 0.000 0.096
#> SRR944019 1 0.0747 0.888 0.984 0.000 0.016
#> SRR944020 1 0.2066 0.880 0.940 0.000 0.060
#> SRR944021 2 0.0424 0.924 0.000 0.992 0.008
#> SRR944022 1 0.2066 0.880 0.940 0.000 0.060
#> SRR944023 1 0.3752 0.868 0.856 0.000 0.144
#> SRR944024 1 0.4178 0.846 0.828 0.000 0.172
#> SRR944026 1 0.2066 0.881 0.940 0.000 0.060
#> SRR944025 1 0.2651 0.878 0.928 0.012 0.060
#> SRR944028 1 0.3213 0.870 0.912 0.028 0.060
#> SRR944029 1 0.0892 0.888 0.980 0.000 0.020
#> SRR944030 2 0.1015 0.912 0.012 0.980 0.008
#> SRR944031 3 0.6559 0.912 0.040 0.252 0.708
#> SRR944032 1 0.1860 0.882 0.948 0.000 0.052
#> SRR944033 2 0.0237 0.925 0.000 0.996 0.004
#> SRR944034 1 0.6566 0.503 0.636 0.348 0.016
#> SRR944036 1 0.3359 0.880 0.900 0.016 0.084
#> SRR944035 1 0.5884 0.774 0.788 0.148 0.064
#> SRR944038 1 0.7113 0.731 0.720 0.168 0.112
#> SRR944037 1 0.1964 0.881 0.944 0.000 0.056
#> SRR944039 1 0.0237 0.887 0.996 0.000 0.004
#> SRR944040 1 0.9147 0.128 0.496 0.348 0.156
#> SRR944041 1 0.0592 0.887 0.988 0.000 0.012
#> SRR944042 3 0.9857 0.322 0.368 0.252 0.380
#> SRR944043 1 0.4062 0.850 0.836 0.000 0.164
#> SRR944044 1 0.2066 0.881 0.940 0.000 0.060
#> SRR944046 3 0.6452 0.913 0.036 0.252 0.712
#> SRR944045 2 0.0592 0.922 0.000 0.988 0.012
#> SRR944047 2 0.0237 0.925 0.000 0.996 0.004
#> SRR944048 1 0.4178 0.846 0.828 0.000 0.172
#> SRR944049 1 0.3572 0.864 0.900 0.040 0.060
#> SRR944050 1 0.4002 0.852 0.840 0.000 0.160
#> SRR944051 1 0.2066 0.881 0.940 0.000 0.060
#> SRR944052 2 0.0829 0.922 0.004 0.984 0.012
#> SRR944053 1 0.2066 0.880 0.940 0.000 0.060
#> SRR944054 1 0.2066 0.881 0.940 0.000 0.060
#> SRR944055 3 0.6597 0.901 0.036 0.268 0.696
#> SRR944056 2 0.0237 0.925 0.000 0.996 0.004
#> SRR944057 1 0.4178 0.846 0.828 0.000 0.172
#> SRR944058 1 0.4062 0.850 0.836 0.000 0.164
#> SRR944059 3 0.6452 0.913 0.036 0.252 0.712
#> SRR944060 1 0.4514 0.857 0.832 0.012 0.156
#> SRR944061 2 0.0424 0.924 0.000 0.992 0.008
#> SRR944062 1 0.4178 0.846 0.828 0.000 0.172
#> SRR944063 1 0.2066 0.880 0.940 0.000 0.060
#> SRR944064 1 0.2066 0.881 0.940 0.000 0.060
#> SRR944065 1 0.2796 0.881 0.908 0.000 0.092
#> SRR944066 1 0.4178 0.846 0.828 0.000 0.172
#> SRR944067 1 0.3791 0.860 0.892 0.048 0.060
#> SRR944068 1 0.3482 0.872 0.872 0.000 0.128
#> SRR944069 2 0.0237 0.925 0.000 0.996 0.004
#> SRR944070 1 0.7126 0.734 0.720 0.164 0.116
#> SRR944071 3 0.7065 0.878 0.072 0.228 0.700
#> SRR944072 1 0.3941 0.854 0.844 0.000 0.156
#> SRR944073 2 0.6566 0.163 0.376 0.612 0.012
#> SRR944075 3 0.7145 0.877 0.072 0.236 0.692
#> SRR944074 1 0.2066 0.881 0.940 0.000 0.060
#> SRR944076 3 0.6452 0.913 0.036 0.252 0.712
#> SRR944077 2 0.0237 0.925 0.000 0.996 0.004
#> SRR944078 3 0.6597 0.901 0.036 0.268 0.696
#> SRR944079 2 0.0000 0.923 0.000 1.000 0.000
#> SRR944080 2 0.1267 0.888 0.024 0.972 0.004
#> SRR944081 1 0.1860 0.882 0.948 0.000 0.052
#> SRR944082 1 0.4178 0.846 0.828 0.000 0.172
#> SRR944083 1 0.4178 0.846 0.828 0.000 0.172
#> SRR944084 1 0.1753 0.884 0.952 0.000 0.048
#> SRR944085 3 0.6646 0.905 0.048 0.240 0.712
#> SRR944086 1 0.1860 0.882 0.948 0.000 0.052
#> SRR944088 1 0.2066 0.881 0.940 0.000 0.060
#> SRR944087 3 0.6452 0.913 0.036 0.252 0.712
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.3725 0.966 0.000 0.180 0.812 0.008
#> SRR944012 4 0.5653 0.710 0.192 0.000 0.096 0.712
#> SRR944014 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> SRR944013 4 0.0707 0.775 0.000 0.000 0.020 0.980
#> SRR944015 1 0.6330 0.557 0.656 0.000 0.144 0.200
#> SRR944016 1 0.4977 0.121 0.540 0.000 0.000 0.460
#> SRR944017 4 0.0895 0.776 0.000 0.004 0.020 0.976
#> SRR944018 4 0.5108 0.561 0.308 0.000 0.020 0.672
#> SRR944019 4 0.4378 0.728 0.164 0.000 0.040 0.796
#> SRR944020 4 0.5799 0.675 0.264 0.000 0.068 0.668
#> SRR944021 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> SRR944022 4 0.6027 0.675 0.244 0.000 0.092 0.664
#> SRR944023 1 0.6858 0.616 0.672 0.108 0.044 0.176
#> SRR944024 1 0.2760 0.733 0.872 0.000 0.000 0.128
#> SRR944026 4 0.2053 0.768 0.004 0.000 0.072 0.924
#> SRR944025 4 0.0707 0.775 0.000 0.000 0.020 0.980
#> SRR944028 4 0.0895 0.776 0.004 0.000 0.020 0.976
#> SRR944029 4 0.6122 0.707 0.160 0.000 0.160 0.680
#> SRR944030 2 0.1022 0.912 0.000 0.968 0.000 0.032
#> SRR944031 3 0.3725 0.966 0.000 0.180 0.812 0.008
#> SRR944032 4 0.1624 0.779 0.028 0.000 0.020 0.952
#> SRR944033 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> SRR944034 2 0.5435 0.257 0.000 0.564 0.016 0.420
#> SRR944036 1 0.8039 0.551 0.544 0.112 0.068 0.276
#> SRR944035 4 0.4175 0.593 0.000 0.200 0.016 0.784
#> SRR944038 1 0.6928 0.587 0.652 0.132 0.028 0.188
#> SRR944037 4 0.5648 0.690 0.252 0.000 0.064 0.684
#> SRR944039 4 0.3708 0.728 0.148 0.000 0.020 0.832
#> SRR944040 3 0.6522 0.714 0.000 0.280 0.608 0.112
#> SRR944041 4 0.5066 0.738 0.148 0.000 0.088 0.764
#> SRR944042 3 0.5650 0.868 0.068 0.180 0.736 0.016
#> SRR944043 1 0.3444 0.728 0.816 0.000 0.000 0.184
#> SRR944044 4 0.1940 0.770 0.000 0.000 0.076 0.924
#> SRR944046 3 0.3725 0.966 0.000 0.180 0.812 0.008
#> SRR944045 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> SRR944047 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> SRR944048 1 0.3219 0.725 0.836 0.000 0.000 0.164
#> SRR944049 4 0.1610 0.762 0.000 0.032 0.016 0.952
#> SRR944050 4 0.4916 0.234 0.424 0.000 0.000 0.576
#> SRR944051 4 0.0895 0.776 0.004 0.000 0.020 0.976
#> SRR944052 2 0.0336 0.928 0.000 0.992 0.008 0.000
#> SRR944053 4 0.5970 0.677 0.244 0.000 0.088 0.668
#> SRR944054 4 0.2760 0.762 0.000 0.000 0.128 0.872
#> SRR944055 3 0.3725 0.966 0.000 0.180 0.812 0.008
#> SRR944056 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> SRR944057 1 0.3444 0.718 0.816 0.000 0.000 0.184
#> SRR944058 1 0.4372 0.693 0.728 0.000 0.004 0.268
#> SRR944059 3 0.3725 0.966 0.000 0.180 0.812 0.008
#> SRR944060 1 0.7148 0.592 0.648 0.116 0.048 0.188
#> SRR944061 2 0.0188 0.931 0.000 0.996 0.004 0.000
#> SRR944062 1 0.2760 0.733 0.872 0.000 0.000 0.128
#> SRR944063 4 0.5968 0.674 0.252 0.000 0.084 0.664
#> SRR944064 4 0.2099 0.760 0.004 0.040 0.020 0.936
#> SRR944065 4 0.5453 0.448 0.388 0.000 0.020 0.592
#> SRR944066 1 0.2760 0.733 0.872 0.000 0.000 0.128
#> SRR944067 4 0.0895 0.774 0.000 0.004 0.020 0.976
#> SRR944068 1 0.6330 0.557 0.656 0.000 0.144 0.200
#> SRR944069 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> SRR944070 1 0.6928 0.587 0.652 0.132 0.028 0.188
#> SRR944071 3 0.3681 0.962 0.000 0.176 0.816 0.008
#> SRR944072 1 0.4955 0.595 0.648 0.000 0.008 0.344
#> SRR944073 2 0.3142 0.786 0.000 0.860 0.008 0.132
#> SRR944075 3 0.4095 0.944 0.000 0.172 0.804 0.024
#> SRR944074 4 0.2266 0.768 0.004 0.000 0.084 0.912
#> SRR944076 3 0.3725 0.966 0.000 0.180 0.812 0.008
#> SRR944077 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> SRR944078 3 0.3768 0.962 0.000 0.184 0.808 0.008
#> SRR944079 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> SRR944080 2 0.1256 0.911 0.000 0.964 0.008 0.028
#> SRR944081 4 0.4542 0.763 0.108 0.000 0.088 0.804
#> SRR944082 1 0.2921 0.735 0.860 0.000 0.000 0.140
#> SRR944083 1 0.2973 0.731 0.856 0.000 0.000 0.144
#> SRR944084 4 0.6754 0.647 0.204 0.000 0.184 0.612
#> SRR944085 3 0.3725 0.966 0.000 0.180 0.812 0.008
#> SRR944086 4 0.2563 0.772 0.072 0.000 0.020 0.908
#> SRR944088 4 0.3306 0.751 0.004 0.000 0.156 0.840
#> SRR944087 3 0.3725 0.966 0.000 0.180 0.812 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.1197 0.967 0.000 0.000 0.952 0.000 0.048
#> SRR944012 4 0.2389 0.891 0.004 0.116 0.000 0.880 0.000
#> SRR944014 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> SRR944013 2 0.0404 0.936 0.012 0.988 0.000 0.000 0.000
#> SRR944015 4 0.1836 0.833 0.036 0.000 0.032 0.932 0.000
#> SRR944016 1 0.1341 0.858 0.944 0.056 0.000 0.000 0.000
#> SRR944017 2 0.0290 0.936 0.008 0.992 0.000 0.000 0.000
#> SRR944018 1 0.5373 0.578 0.652 0.112 0.000 0.236 0.000
#> SRR944019 4 0.4101 0.648 0.004 0.332 0.000 0.664 0.000
#> SRR944020 4 0.3090 0.892 0.032 0.104 0.004 0.860 0.000
#> SRR944021 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> SRR944022 4 0.1965 0.894 0.000 0.096 0.000 0.904 0.000
#> SRR944023 1 0.6079 0.262 0.524 0.020 0.016 0.400 0.040
#> SRR944024 1 0.0880 0.860 0.968 0.032 0.000 0.000 0.000
#> SRR944026 2 0.1280 0.929 0.008 0.960 0.008 0.024 0.000
#> SRR944025 2 0.0290 0.936 0.008 0.992 0.000 0.000 0.000
#> SRR944028 2 0.0510 0.935 0.016 0.984 0.000 0.000 0.000
#> SRR944029 4 0.3001 0.872 0.004 0.144 0.008 0.844 0.000
#> SRR944030 5 0.2605 0.822 0.000 0.148 0.000 0.000 0.852
#> SRR944031 3 0.1484 0.962 0.000 0.000 0.944 0.008 0.048
#> SRR944032 2 0.0510 0.935 0.016 0.984 0.000 0.000 0.000
#> SRR944033 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> SRR944034 2 0.2230 0.850 0.000 0.884 0.000 0.000 0.116
#> SRR944036 1 0.7949 0.445 0.484 0.212 0.044 0.220 0.040
#> SRR944035 2 0.1124 0.921 0.004 0.960 0.000 0.000 0.036
#> SRR944038 4 0.2494 0.832 0.044 0.000 0.016 0.908 0.032
#> SRR944037 4 0.2927 0.890 0.040 0.092 0.000 0.868 0.000
#> SRR944039 4 0.5253 0.738 0.108 0.188 0.008 0.696 0.000
#> SRR944040 3 0.5405 0.634 0.000 0.204 0.660 0.000 0.136
#> SRR944041 4 0.2488 0.889 0.004 0.124 0.000 0.872 0.000
#> SRR944042 3 0.2903 0.903 0.000 0.000 0.872 0.080 0.048
#> SRR944043 1 0.1364 0.858 0.952 0.036 0.000 0.012 0.000
#> SRR944044 2 0.1455 0.926 0.008 0.952 0.008 0.032 0.000
#> SRR944046 3 0.1197 0.967 0.000 0.000 0.952 0.000 0.048
#> SRR944045 5 0.0290 0.958 0.000 0.008 0.000 0.000 0.992
#> SRR944047 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> SRR944048 1 0.1197 0.861 0.952 0.048 0.000 0.000 0.000
#> SRR944049 2 0.0451 0.936 0.008 0.988 0.000 0.000 0.004
#> SRR944050 1 0.1965 0.842 0.904 0.096 0.000 0.000 0.000
#> SRR944051 2 0.0566 0.936 0.012 0.984 0.000 0.004 0.000
#> SRR944052 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> SRR944053 4 0.2068 0.895 0.004 0.092 0.000 0.904 0.000
#> SRR944054 2 0.1569 0.921 0.008 0.944 0.004 0.044 0.000
#> SRR944055 3 0.1197 0.967 0.000 0.000 0.952 0.000 0.048
#> SRR944056 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> SRR944057 1 0.1197 0.861 0.952 0.048 0.000 0.000 0.000
#> SRR944058 1 0.5717 0.614 0.640 0.124 0.008 0.228 0.000
#> SRR944059 3 0.1197 0.967 0.000 0.000 0.952 0.000 0.048
#> SRR944060 4 0.2474 0.827 0.040 0.000 0.012 0.908 0.040
#> SRR944061 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> SRR944062 1 0.0963 0.861 0.964 0.036 0.000 0.000 0.000
#> SRR944063 4 0.2068 0.895 0.004 0.092 0.000 0.904 0.000
#> SRR944064 2 0.1195 0.922 0.028 0.960 0.000 0.000 0.012
#> SRR944065 4 0.4046 0.859 0.068 0.120 0.008 0.804 0.000
#> SRR944066 1 0.0963 0.861 0.964 0.036 0.000 0.000 0.000
#> SRR944067 2 0.0290 0.936 0.008 0.992 0.000 0.000 0.000
#> SRR944068 4 0.1836 0.833 0.036 0.000 0.032 0.932 0.000
#> SRR944069 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> SRR944070 4 0.2494 0.832 0.044 0.000 0.016 0.908 0.032
#> SRR944071 3 0.1197 0.967 0.000 0.000 0.952 0.000 0.048
#> SRR944072 1 0.4539 0.766 0.768 0.124 0.008 0.100 0.000
#> SRR944073 2 0.3837 0.554 0.000 0.692 0.000 0.000 0.308
#> SRR944075 3 0.1197 0.967 0.000 0.000 0.952 0.000 0.048
#> SRR944074 2 0.1393 0.930 0.012 0.956 0.008 0.024 0.000
#> SRR944076 3 0.1197 0.967 0.000 0.000 0.952 0.000 0.048
#> SRR944077 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> SRR944078 3 0.1197 0.967 0.000 0.000 0.952 0.000 0.048
#> SRR944079 5 0.0000 0.966 0.000 0.000 0.000 0.000 1.000
#> SRR944080 5 0.3003 0.767 0.000 0.188 0.000 0.000 0.812
#> SRR944081 2 0.3461 0.691 0.000 0.772 0.004 0.224 0.000
#> SRR944082 1 0.1364 0.858 0.952 0.036 0.000 0.012 0.000
#> SRR944083 1 0.1043 0.861 0.960 0.040 0.000 0.000 0.000
#> SRR944084 4 0.2775 0.893 0.004 0.100 0.020 0.876 0.000
#> SRR944085 3 0.1197 0.967 0.000 0.000 0.952 0.000 0.048
#> SRR944086 2 0.0404 0.936 0.012 0.988 0.000 0.000 0.000
#> SRR944088 2 0.2588 0.874 0.008 0.884 0.008 0.100 0.000
#> SRR944087 3 0.1197 0.967 0.000 0.000 0.952 0.000 0.048
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.0713 0.944 0.000 0.028 0.972 0.000 0.000 0.000
#> SRR944012 4 0.2654 0.817 0.004 0.000 0.008 0.864 0.116 0.008
#> SRR944014 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944013 5 0.1584 0.853 0.000 0.000 0.000 0.064 0.928 0.008
#> SRR944015 6 0.0547 0.969 0.000 0.000 0.000 0.020 0.000 0.980
#> SRR944016 1 0.1082 0.894 0.956 0.000 0.000 0.000 0.040 0.004
#> SRR944017 5 0.1231 0.840 0.000 0.004 0.012 0.012 0.960 0.012
#> SRR944018 1 0.2195 0.858 0.908 0.000 0.004 0.028 0.056 0.004
#> SRR944019 5 0.3093 0.812 0.012 0.000 0.000 0.164 0.816 0.008
#> SRR944020 4 0.1860 0.901 0.028 0.000 0.004 0.928 0.004 0.036
#> SRR944021 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944022 4 0.0972 0.910 0.000 0.000 0.008 0.964 0.000 0.028
#> SRR944023 1 0.4566 0.617 0.704 0.020 0.024 0.008 0.004 0.240
#> SRR944024 1 0.0291 0.892 0.992 0.000 0.004 0.004 0.000 0.000
#> SRR944026 5 0.2400 0.846 0.000 0.000 0.008 0.116 0.872 0.004
#> SRR944025 5 0.0870 0.840 0.000 0.000 0.004 0.012 0.972 0.012
#> SRR944028 5 0.1590 0.846 0.000 0.012 0.008 0.028 0.944 0.008
#> SRR944029 5 0.3320 0.788 0.000 0.000 0.016 0.212 0.772 0.000
#> SRR944030 2 0.3231 0.749 0.000 0.800 0.000 0.012 0.180 0.008
#> SRR944031 3 0.1908 0.902 0.000 0.028 0.916 0.000 0.000 0.056
#> SRR944032 5 0.1410 0.837 0.044 0.000 0.000 0.008 0.944 0.004
#> SRR944033 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944034 5 0.1757 0.823 0.000 0.052 0.000 0.012 0.928 0.008
#> SRR944036 1 0.5287 0.629 0.692 0.024 0.028 0.016 0.208 0.032
#> SRR944035 5 0.1223 0.839 0.000 0.016 0.004 0.012 0.960 0.008
#> SRR944038 6 0.0870 0.974 0.000 0.004 0.012 0.012 0.000 0.972
#> SRR944037 4 0.2924 0.860 0.028 0.000 0.000 0.864 0.084 0.024
#> SRR944039 5 0.5414 0.517 0.248 0.000 0.000 0.144 0.600 0.008
#> SRR944040 3 0.2905 0.828 0.000 0.084 0.852 0.000 0.064 0.000
#> SRR944041 5 0.4034 0.584 0.004 0.000 0.008 0.364 0.624 0.000
#> SRR944042 3 0.4410 0.288 0.000 0.028 0.560 0.000 0.000 0.412
#> SRR944043 1 0.0405 0.891 0.988 0.000 0.004 0.008 0.000 0.000
#> SRR944044 5 0.2445 0.846 0.000 0.000 0.008 0.120 0.868 0.004
#> SRR944046 3 0.0713 0.944 0.000 0.028 0.972 0.000 0.000 0.000
#> SRR944045 2 0.0508 0.944 0.000 0.984 0.012 0.000 0.004 0.000
#> SRR944047 2 0.0146 0.952 0.000 0.996 0.000 0.000 0.004 0.000
#> SRR944048 1 0.0865 0.897 0.964 0.000 0.000 0.000 0.036 0.000
#> SRR944049 5 0.1344 0.839 0.000 0.012 0.012 0.012 0.956 0.008
#> SRR944050 1 0.1285 0.892 0.944 0.000 0.000 0.000 0.052 0.004
#> SRR944051 5 0.1753 0.852 0.000 0.000 0.000 0.084 0.912 0.004
#> SRR944052 2 0.0146 0.951 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944053 4 0.1155 0.912 0.004 0.000 0.004 0.956 0.000 0.036
#> SRR944054 5 0.2655 0.839 0.000 0.000 0.008 0.140 0.848 0.004
#> SRR944055 3 0.0790 0.942 0.000 0.032 0.968 0.000 0.000 0.000
#> SRR944056 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944057 1 0.0865 0.897 0.964 0.000 0.000 0.000 0.036 0.000
#> SRR944058 1 0.1672 0.890 0.932 0.000 0.000 0.016 0.048 0.004
#> SRR944059 3 0.0713 0.944 0.000 0.028 0.972 0.000 0.000 0.000
#> SRR944060 6 0.1592 0.948 0.004 0.024 0.016 0.012 0.000 0.944
#> SRR944061 2 0.0146 0.951 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944062 1 0.0436 0.892 0.988 0.000 0.004 0.004 0.004 0.000
#> SRR944063 4 0.1116 0.914 0.008 0.000 0.004 0.960 0.000 0.028
#> SRR944064 5 0.2343 0.817 0.080 0.004 0.004 0.004 0.896 0.012
#> SRR944065 1 0.5929 0.325 0.568 0.000 0.004 0.164 0.244 0.020
#> SRR944066 1 0.0405 0.894 0.988 0.000 0.004 0.000 0.008 0.000
#> SRR944067 5 0.0984 0.840 0.000 0.000 0.008 0.012 0.968 0.012
#> SRR944068 6 0.0547 0.969 0.000 0.000 0.000 0.020 0.000 0.980
#> SRR944069 2 0.0146 0.951 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944070 6 0.0984 0.973 0.000 0.008 0.012 0.012 0.000 0.968
#> SRR944071 3 0.1010 0.937 0.000 0.036 0.960 0.000 0.004 0.000
#> SRR944072 1 0.1801 0.888 0.924 0.000 0.000 0.016 0.056 0.004
#> SRR944073 5 0.4312 0.297 0.000 0.396 0.000 0.012 0.584 0.008
#> SRR944075 3 0.0632 0.941 0.000 0.024 0.976 0.000 0.000 0.000
#> SRR944074 5 0.2400 0.846 0.000 0.000 0.008 0.116 0.872 0.004
#> SRR944076 3 0.0713 0.944 0.000 0.028 0.972 0.000 0.000 0.000
#> SRR944077 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944078 3 0.0790 0.942 0.000 0.032 0.968 0.000 0.000 0.000
#> SRR944079 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944080 2 0.3560 0.717 0.000 0.772 0.004 0.012 0.204 0.008
#> SRR944081 5 0.3023 0.816 0.000 0.000 0.008 0.180 0.808 0.004
#> SRR944082 1 0.0405 0.891 0.988 0.000 0.004 0.008 0.000 0.000
#> SRR944083 1 0.0713 0.897 0.972 0.000 0.000 0.000 0.028 0.000
#> SRR944084 5 0.5711 0.568 0.000 0.000 0.016 0.212 0.584 0.188
#> SRR944085 3 0.0713 0.944 0.000 0.028 0.972 0.000 0.000 0.000
#> SRR944086 5 0.1471 0.854 0.000 0.000 0.000 0.064 0.932 0.004
#> SRR944088 5 0.2848 0.829 0.000 0.000 0.008 0.160 0.828 0.004
#> SRR944087 3 0.0713 0.944 0.000 0.028 0.972 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "NMF"]
# you can also extract it by
# res = res_list["CV:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.981 0.991 0.5045 0.496 0.496
#> 3 3 0.950 0.898 0.963 0.3149 0.767 0.563
#> 4 4 0.827 0.750 0.879 0.0674 0.960 0.884
#> 5 5 0.777 0.713 0.840 0.0428 0.949 0.844
#> 6 6 0.761 0.651 0.793 0.0309 0.976 0.916
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.0000 0.989 0.000 1.000
#> SRR944012 1 0.0000 0.992 1.000 0.000
#> SRR944014 2 0.0000 0.989 0.000 1.000
#> SRR944013 1 0.0000 0.992 1.000 0.000
#> SRR944015 2 0.7745 0.708 0.228 0.772
#> SRR944016 1 0.0000 0.992 1.000 0.000
#> SRR944017 1 0.0000 0.992 1.000 0.000
#> SRR944018 1 0.0000 0.992 1.000 0.000
#> SRR944019 1 0.0000 0.992 1.000 0.000
#> SRR944020 1 0.0000 0.992 1.000 0.000
#> SRR944021 2 0.0000 0.989 0.000 1.000
#> SRR944022 1 0.0000 0.992 1.000 0.000
#> SRR944023 2 0.0000 0.989 0.000 1.000
#> SRR944024 1 0.0000 0.992 1.000 0.000
#> SRR944026 1 0.0000 0.992 1.000 0.000
#> SRR944025 1 0.0000 0.992 1.000 0.000
#> SRR944028 1 0.0000 0.992 1.000 0.000
#> SRR944029 1 0.0000 0.992 1.000 0.000
#> SRR944030 2 0.0000 0.989 0.000 1.000
#> SRR944031 2 0.0000 0.989 0.000 1.000
#> SRR944032 1 0.0000 0.992 1.000 0.000
#> SRR944033 2 0.0000 0.989 0.000 1.000
#> SRR944034 2 0.0000 0.989 0.000 1.000
#> SRR944036 2 0.0000 0.989 0.000 1.000
#> SRR944035 2 0.2423 0.953 0.040 0.960
#> SRR944038 2 0.0000 0.989 0.000 1.000
#> SRR944037 1 0.0000 0.992 1.000 0.000
#> SRR944039 1 0.0000 0.992 1.000 0.000
#> SRR944040 2 0.0000 0.989 0.000 1.000
#> SRR944041 1 0.0000 0.992 1.000 0.000
#> SRR944042 2 0.0000 0.989 0.000 1.000
#> SRR944043 1 0.0000 0.992 1.000 0.000
#> SRR944044 1 0.0000 0.992 1.000 0.000
#> SRR944046 2 0.0000 0.989 0.000 1.000
#> SRR944045 2 0.0000 0.989 0.000 1.000
#> SRR944047 2 0.0000 0.989 0.000 1.000
#> SRR944048 1 0.0000 0.992 1.000 0.000
#> SRR944049 1 0.7056 0.761 0.808 0.192
#> SRR944050 1 0.0000 0.992 1.000 0.000
#> SRR944051 1 0.0000 0.992 1.000 0.000
#> SRR944052 2 0.0000 0.989 0.000 1.000
#> SRR944053 1 0.0000 0.992 1.000 0.000
#> SRR944054 1 0.0000 0.992 1.000 0.000
#> SRR944055 2 0.0000 0.989 0.000 1.000
#> SRR944056 2 0.0000 0.989 0.000 1.000
#> SRR944057 1 0.0000 0.992 1.000 0.000
#> SRR944058 1 0.0000 0.992 1.000 0.000
#> SRR944059 2 0.0000 0.989 0.000 1.000
#> SRR944060 2 0.0000 0.989 0.000 1.000
#> SRR944061 2 0.0000 0.989 0.000 1.000
#> SRR944062 1 0.0000 0.992 1.000 0.000
#> SRR944063 1 0.0000 0.992 1.000 0.000
#> SRR944064 1 0.0376 0.988 0.996 0.004
#> SRR944065 1 0.0000 0.992 1.000 0.000
#> SRR944066 1 0.0000 0.992 1.000 0.000
#> SRR944067 1 0.0000 0.992 1.000 0.000
#> SRR944068 1 0.5178 0.868 0.884 0.116
#> SRR944069 2 0.0000 0.989 0.000 1.000
#> SRR944070 2 0.0000 0.989 0.000 1.000
#> SRR944071 2 0.0000 0.989 0.000 1.000
#> SRR944072 1 0.0000 0.992 1.000 0.000
#> SRR944073 2 0.0000 0.989 0.000 1.000
#> SRR944075 2 0.0000 0.989 0.000 1.000
#> SRR944074 1 0.0000 0.992 1.000 0.000
#> SRR944076 2 0.0000 0.989 0.000 1.000
#> SRR944077 2 0.0000 0.989 0.000 1.000
#> SRR944078 2 0.0000 0.989 0.000 1.000
#> SRR944079 2 0.0000 0.989 0.000 1.000
#> SRR944080 2 0.0000 0.989 0.000 1.000
#> SRR944081 1 0.0000 0.992 1.000 0.000
#> SRR944082 1 0.0000 0.992 1.000 0.000
#> SRR944083 1 0.0000 0.992 1.000 0.000
#> SRR944084 2 0.4815 0.883 0.104 0.896
#> SRR944085 2 0.0000 0.989 0.000 1.000
#> SRR944086 1 0.0000 0.992 1.000 0.000
#> SRR944088 1 0.0000 0.992 1.000 0.000
#> SRR944087 2 0.0000 0.989 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944012 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944014 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944013 3 0.0424 0.9394 0.008 0.000 0.992
#> SRR944015 3 0.0424 0.9383 0.000 0.008 0.992
#> SRR944016 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944017 1 0.6305 -0.0277 0.516 0.000 0.484
#> SRR944018 1 0.0237 0.9527 0.996 0.000 0.004
#> SRR944019 3 0.1031 0.9268 0.024 0.000 0.976
#> SRR944020 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944021 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944022 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944023 2 0.6274 0.1436 0.456 0.544 0.000
#> SRR944024 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944026 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944025 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944028 1 0.0592 0.9458 0.988 0.000 0.012
#> SRR944029 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944030 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944031 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944032 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944033 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944034 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944036 1 0.5327 0.6044 0.728 0.272 0.000
#> SRR944035 1 0.0747 0.9408 0.984 0.016 0.000
#> SRR944038 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944037 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944039 3 0.6260 0.1973 0.448 0.000 0.552
#> SRR944040 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944041 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944042 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944043 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944044 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944046 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944045 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944047 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944048 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944049 2 0.7337 0.1836 0.032 0.540 0.428
#> SRR944050 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944051 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944052 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944053 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944054 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944055 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944056 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944057 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944058 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944059 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944060 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944061 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944062 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944063 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944064 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944065 3 0.5058 0.6721 0.244 0.000 0.756
#> SRR944066 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944067 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944068 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944069 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944070 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944071 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944072 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944073 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944075 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944074 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944076 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944077 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944078 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944079 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944080 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944081 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944082 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944083 1 0.0000 0.9558 1.000 0.000 0.000
#> SRR944084 3 0.0424 0.9382 0.000 0.008 0.992
#> SRR944085 2 0.0000 0.9707 0.000 1.000 0.000
#> SRR944086 3 0.6215 0.2696 0.428 0.000 0.572
#> SRR944088 3 0.0000 0.9445 0.000 0.000 1.000
#> SRR944087 2 0.0000 0.9707 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944012 4 0.1211 0.9111 0.000 0.000 0.040 0.960
#> SRR944014 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944013 4 0.1398 0.9171 0.004 0.000 0.040 0.956
#> SRR944015 4 0.4203 0.8016 0.000 0.068 0.108 0.824
#> SRR944016 1 0.3610 0.7068 0.800 0.000 0.200 0.000
#> SRR944017 3 0.6677 -0.2226 0.348 0.000 0.552 0.100
#> SRR944018 1 0.3801 0.7036 0.780 0.000 0.220 0.000
#> SRR944019 4 0.3695 0.8183 0.016 0.000 0.156 0.828
#> SRR944020 4 0.1022 0.9176 0.000 0.000 0.032 0.968
#> SRR944021 2 0.0921 0.9147 0.000 0.972 0.028 0.000
#> SRR944022 4 0.2011 0.9051 0.000 0.000 0.080 0.920
#> SRR944023 2 0.7553 -0.1856 0.308 0.476 0.216 0.000
#> SRR944024 1 0.1637 0.7150 0.940 0.000 0.060 0.000
#> SRR944026 4 0.0188 0.9176 0.000 0.000 0.004 0.996
#> SRR944025 1 0.4624 0.5640 0.660 0.000 0.340 0.000
#> SRR944028 1 0.3401 0.6869 0.840 0.000 0.152 0.008
#> SRR944029 4 0.0469 0.9181 0.000 0.000 0.012 0.988
#> SRR944030 2 0.3710 0.7202 0.004 0.804 0.192 0.000
#> SRR944031 2 0.1389 0.8979 0.000 0.952 0.048 0.000
#> SRR944032 1 0.3945 0.6756 0.780 0.000 0.216 0.004
#> SRR944033 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944036 1 0.6617 0.2355 0.628 0.196 0.176 0.000
#> SRR944035 1 0.5396 0.2568 0.524 0.012 0.464 0.000
#> SRR944038 2 0.0188 0.9306 0.000 0.996 0.004 0.000
#> SRR944037 4 0.3074 0.8522 0.000 0.000 0.152 0.848
#> SRR944039 1 0.7580 0.1358 0.476 0.000 0.296 0.228
#> SRR944040 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944041 4 0.0707 0.9183 0.000 0.000 0.020 0.980
#> SRR944042 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944043 1 0.3975 0.6835 0.760 0.000 0.240 0.000
#> SRR944044 4 0.0817 0.9175 0.000 0.000 0.024 0.976
#> SRR944046 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944045 2 0.0188 0.9309 0.000 0.996 0.004 0.000
#> SRR944047 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944048 1 0.0592 0.7290 0.984 0.000 0.016 0.000
#> SRR944049 2 0.9015 -0.3411 0.232 0.360 0.064 0.344
#> SRR944050 1 0.4134 0.6752 0.740 0.000 0.260 0.000
#> SRR944051 4 0.3539 0.7927 0.004 0.000 0.176 0.820
#> SRR944052 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944053 4 0.1022 0.9179 0.000 0.000 0.032 0.968
#> SRR944054 4 0.1557 0.9131 0.000 0.000 0.056 0.944
#> SRR944055 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944056 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944057 1 0.3907 0.6890 0.768 0.000 0.232 0.000
#> SRR944058 1 0.1792 0.7215 0.932 0.000 0.068 0.000
#> SRR944059 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944060 3 0.6211 -0.0967 0.052 0.460 0.488 0.000
#> SRR944061 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944062 1 0.0592 0.7290 0.984 0.000 0.016 0.000
#> SRR944063 4 0.0336 0.9180 0.000 0.000 0.008 0.992
#> SRR944064 1 0.1022 0.7251 0.968 0.000 0.032 0.000
#> SRR944065 4 0.6468 0.3636 0.084 0.000 0.348 0.568
#> SRR944066 1 0.4382 0.6456 0.704 0.000 0.296 0.000
#> SRR944067 1 0.4277 0.5051 0.720 0.000 0.280 0.000
#> SRR944068 4 0.1211 0.9162 0.000 0.000 0.040 0.960
#> SRR944069 2 0.1867 0.8759 0.000 0.928 0.072 0.000
#> SRR944070 2 0.0188 0.9306 0.000 0.996 0.004 0.000
#> SRR944071 2 0.1557 0.8931 0.000 0.944 0.056 0.000
#> SRR944072 1 0.3942 0.6973 0.764 0.000 0.236 0.000
#> SRR944073 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944075 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944074 4 0.0336 0.9182 0.000 0.000 0.008 0.992
#> SRR944076 2 0.0188 0.9309 0.000 0.996 0.004 0.000
#> SRR944077 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944078 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944079 2 0.0000 0.9328 0.000 1.000 0.000 0.000
#> SRR944080 2 0.2921 0.7967 0.000 0.860 0.140 0.000
#> SRR944081 4 0.2081 0.8985 0.000 0.000 0.084 0.916
#> SRR944082 1 0.1211 0.7362 0.960 0.000 0.040 0.000
#> SRR944083 1 0.1474 0.7359 0.948 0.000 0.052 0.000
#> SRR944084 4 0.2623 0.8857 0.000 0.028 0.064 0.908
#> SRR944085 2 0.0188 0.9309 0.000 0.996 0.004 0.000
#> SRR944086 3 0.7627 -0.0434 0.272 0.000 0.472 0.256
#> SRR944088 4 0.0336 0.9182 0.000 0.000 0.008 0.992
#> SRR944087 2 0.0336 0.9282 0.000 0.992 0.008 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000
#> SRR944012 4 0.2370 0.795 0.000 0.000 0.056 0.904 0.040
#> SRR944014 2 0.0162 0.958 0.000 0.996 0.000 0.000 0.004
#> SRR944013 4 0.4554 0.763 0.028 0.000 0.128 0.780 0.064
#> SRR944015 4 0.5558 0.644 0.000 0.052 0.240 0.668 0.040
#> SRR944016 1 0.3010 0.691 0.824 0.000 0.172 0.000 0.004
#> SRR944017 3 0.4237 0.206 0.152 0.000 0.772 0.076 0.000
#> SRR944018 1 0.5023 0.602 0.708 0.000 0.192 0.004 0.096
#> SRR944019 4 0.6187 0.629 0.104 0.000 0.152 0.664 0.080
#> SRR944020 4 0.3291 0.800 0.000 0.000 0.120 0.840 0.040
#> SRR944021 2 0.1197 0.926 0.000 0.952 0.048 0.000 0.000
#> SRR944022 4 0.4457 0.763 0.000 0.000 0.152 0.756 0.092
#> SRR944023 3 0.7328 0.265 0.272 0.292 0.408 0.000 0.028
#> SRR944024 1 0.2067 0.657 0.920 0.000 0.032 0.000 0.048
#> SRR944026 4 0.0912 0.813 0.000 0.000 0.016 0.972 0.012
#> SRR944025 1 0.4359 0.477 0.584 0.000 0.412 0.000 0.004
#> SRR944028 1 0.4429 0.547 0.764 0.000 0.060 0.008 0.168
#> SRR944029 4 0.1493 0.805 0.000 0.000 0.028 0.948 0.024
#> SRR944030 2 0.4375 0.370 0.004 0.628 0.364 0.000 0.004
#> SRR944031 2 0.1638 0.908 0.000 0.932 0.064 0.000 0.004
#> SRR944032 1 0.5509 0.226 0.564 0.000 0.076 0.000 0.360
#> SRR944033 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0162 0.958 0.000 0.996 0.004 0.000 0.000
#> SRR944036 1 0.7684 -0.349 0.388 0.136 0.100 0.000 0.376
#> SRR944035 5 0.4818 0.533 0.180 0.000 0.100 0.000 0.720
#> SRR944038 2 0.0324 0.957 0.000 0.992 0.004 0.000 0.004
#> SRR944037 4 0.4087 0.759 0.000 0.000 0.208 0.756 0.036
#> SRR944039 1 0.6651 0.449 0.584 0.000 0.252 0.092 0.072
#> SRR944040 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000
#> SRR944041 4 0.1648 0.811 0.000 0.000 0.040 0.940 0.020
#> SRR944042 2 0.0162 0.958 0.000 0.996 0.000 0.000 0.004
#> SRR944043 1 0.4620 0.574 0.652 0.000 0.320 0.000 0.028
#> SRR944044 4 0.2104 0.806 0.000 0.000 0.024 0.916 0.060
#> SRR944046 2 0.0162 0.958 0.000 0.996 0.004 0.000 0.000
#> SRR944045 2 0.0162 0.958 0.000 0.996 0.004 0.000 0.000
#> SRR944047 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000
#> SRR944048 1 0.1493 0.673 0.948 0.000 0.024 0.000 0.028
#> SRR944049 4 0.8917 -0.207 0.276 0.248 0.088 0.336 0.052
#> SRR944050 1 0.3916 0.655 0.732 0.000 0.256 0.000 0.012
#> SRR944051 4 0.5733 0.481 0.004 0.000 0.092 0.580 0.324
#> SRR944052 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000
#> SRR944053 4 0.3237 0.802 0.000 0.000 0.104 0.848 0.048
#> SRR944054 4 0.2519 0.810 0.000 0.000 0.100 0.884 0.016
#> SRR944055 2 0.0324 0.957 0.000 0.992 0.004 0.000 0.004
#> SRR944056 2 0.0162 0.958 0.000 0.996 0.000 0.000 0.004
#> SRR944057 1 0.3487 0.677 0.780 0.000 0.212 0.000 0.008
#> SRR944058 1 0.2713 0.652 0.888 0.000 0.036 0.004 0.072
#> SRR944059 2 0.0162 0.958 0.000 0.996 0.004 0.000 0.000
#> SRR944060 3 0.5325 0.363 0.060 0.260 0.664 0.000 0.016
#> SRR944061 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000
#> SRR944062 1 0.1582 0.672 0.944 0.000 0.028 0.000 0.028
#> SRR944063 4 0.2149 0.816 0.000 0.000 0.048 0.916 0.036
#> SRR944064 1 0.2012 0.665 0.920 0.000 0.020 0.000 0.060
#> SRR944065 3 0.7783 -0.149 0.056 0.000 0.320 0.320 0.304
#> SRR944066 1 0.4009 0.618 0.684 0.000 0.312 0.000 0.004
#> SRR944067 5 0.4549 0.200 0.464 0.000 0.008 0.000 0.528
#> SRR944068 4 0.3112 0.794 0.000 0.000 0.100 0.856 0.044
#> SRR944069 2 0.1410 0.915 0.000 0.940 0.060 0.000 0.000
#> SRR944070 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000
#> SRR944071 2 0.2771 0.829 0.000 0.860 0.128 0.000 0.012
#> SRR944072 1 0.3612 0.690 0.800 0.000 0.172 0.000 0.028
#> SRR944073 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000
#> SRR944075 2 0.0451 0.954 0.000 0.988 0.004 0.000 0.008
#> SRR944074 4 0.1386 0.811 0.000 0.000 0.032 0.952 0.016
#> SRR944076 2 0.0000 0.959 0.000 1.000 0.000 0.000 0.000
#> SRR944077 2 0.0162 0.958 0.000 0.996 0.000 0.000 0.004
#> SRR944078 2 0.0162 0.958 0.000 0.996 0.000 0.000 0.004
#> SRR944079 2 0.0162 0.958 0.000 0.996 0.004 0.000 0.000
#> SRR944080 2 0.4121 0.587 0.004 0.720 0.264 0.000 0.012
#> SRR944081 4 0.3565 0.791 0.000 0.000 0.144 0.816 0.040
#> SRR944082 1 0.1493 0.693 0.948 0.000 0.028 0.000 0.024
#> SRR944083 1 0.0865 0.696 0.972 0.000 0.024 0.000 0.004
#> SRR944084 4 0.4933 0.710 0.000 0.048 0.176 0.740 0.036
#> SRR944085 2 0.0451 0.954 0.000 0.988 0.008 0.000 0.004
#> SRR944086 5 0.5039 0.421 0.052 0.000 0.076 0.116 0.756
#> SRR944088 4 0.1310 0.807 0.000 0.000 0.020 0.956 0.024
#> SRR944087 2 0.0566 0.951 0.000 0.984 0.004 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 2 0.0000 0.94161 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944012 4 0.3637 0.63314 0.000 0.000 0.052 0.820 0.096 0.032
#> SRR944014 2 0.0260 0.94098 0.000 0.992 0.008 0.000 0.000 0.000
#> SRR944013 4 0.6811 0.50711 0.064 0.000 0.092 0.596 0.136 0.112
#> SRR944015 4 0.7197 0.42734 0.000 0.068 0.112 0.452 0.044 0.324
#> SRR944016 1 0.3122 0.66898 0.816 0.000 0.020 0.000 0.004 0.160
#> SRR944017 6 0.3345 0.24280 0.144 0.000 0.004 0.032 0.004 0.816
#> SRR944018 1 0.6221 0.49141 0.600 0.000 0.072 0.016 0.092 0.220
#> SRR944019 4 0.7536 0.41111 0.112 0.000 0.088 0.508 0.100 0.192
#> SRR944020 4 0.3778 0.69879 0.000 0.000 0.020 0.796 0.048 0.136
#> SRR944021 2 0.1528 0.90405 0.000 0.936 0.016 0.000 0.000 0.048
#> SRR944022 4 0.6202 0.56300 0.000 0.000 0.076 0.580 0.140 0.204
#> SRR944023 6 0.7783 0.38460 0.276 0.216 0.100 0.000 0.032 0.376
#> SRR944024 1 0.3154 0.62636 0.836 0.000 0.124 0.000 0.020 0.020
#> SRR944026 4 0.1409 0.70210 0.000 0.000 0.008 0.948 0.032 0.012
#> SRR944025 1 0.4800 0.37330 0.580 0.000 0.032 0.000 0.016 0.372
#> SRR944028 1 0.6260 0.37454 0.616 0.000 0.092 0.020 0.184 0.088
#> SRR944029 4 0.2316 0.67965 0.000 0.000 0.040 0.904 0.040 0.016
#> SRR944030 2 0.5349 0.06461 0.012 0.540 0.068 0.000 0.004 0.376
#> SRR944031 2 0.2255 0.86280 0.000 0.892 0.028 0.000 0.000 0.080
#> SRR944032 5 0.4763 0.13915 0.392 0.000 0.012 0.000 0.564 0.032
#> SRR944033 2 0.0000 0.94161 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944034 2 0.0363 0.93866 0.000 0.988 0.000 0.000 0.000 0.012
#> SRR944036 3 0.6058 0.42861 0.268 0.080 0.588 0.000 0.040 0.024
#> SRR944035 3 0.5269 0.32425 0.084 0.000 0.548 0.000 0.360 0.008
#> SRR944038 2 0.0458 0.93828 0.000 0.984 0.016 0.000 0.000 0.000
#> SRR944037 4 0.5293 0.63022 0.000 0.000 0.056 0.624 0.044 0.276
#> SRR944039 1 0.7676 0.26466 0.468 0.000 0.084 0.128 0.084 0.236
#> SRR944040 2 0.0146 0.94154 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944041 4 0.2424 0.70332 0.000 0.000 0.036 0.900 0.036 0.028
#> SRR944042 2 0.0000 0.94161 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944043 1 0.4910 0.47936 0.644 0.000 0.040 0.000 0.032 0.284
#> SRR944044 4 0.3135 0.67809 0.000 0.000 0.048 0.856 0.068 0.028
#> SRR944046 2 0.0146 0.94166 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944045 2 0.0806 0.93096 0.000 0.972 0.008 0.000 0.000 0.020
#> SRR944047 2 0.0146 0.94166 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944048 1 0.2687 0.64830 0.872 0.000 0.092 0.000 0.012 0.024
#> SRR944049 4 0.8734 -0.13417 0.280 0.140 0.100 0.360 0.048 0.072
#> SRR944050 1 0.3972 0.61830 0.732 0.000 0.020 0.000 0.016 0.232
#> SRR944051 5 0.6332 -0.00165 0.012 0.000 0.068 0.388 0.468 0.064
#> SRR944052 2 0.0405 0.93952 0.000 0.988 0.004 0.000 0.000 0.008
#> SRR944053 4 0.4471 0.68615 0.000 0.000 0.040 0.752 0.068 0.140
#> SRR944054 4 0.2847 0.71207 0.000 0.000 0.012 0.852 0.016 0.120
#> SRR944055 2 0.0260 0.94061 0.000 0.992 0.008 0.000 0.000 0.000
#> SRR944056 2 0.0508 0.93805 0.000 0.984 0.012 0.000 0.004 0.000
#> SRR944057 1 0.3691 0.64117 0.764 0.000 0.020 0.000 0.012 0.204
#> SRR944058 1 0.4276 0.59430 0.784 0.000 0.080 0.004 0.088 0.044
#> SRR944059 2 0.0622 0.93775 0.000 0.980 0.008 0.000 0.000 0.012
#> SRR944060 6 0.5664 0.46709 0.088 0.224 0.052 0.000 0.004 0.632
#> SRR944061 2 0.0146 0.94155 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944062 1 0.2895 0.63746 0.852 0.000 0.116 0.000 0.016 0.016
#> SRR944063 4 0.4561 0.69008 0.000 0.000 0.072 0.756 0.064 0.108
#> SRR944064 1 0.2218 0.65024 0.884 0.000 0.104 0.000 0.012 0.000
#> SRR944065 5 0.7348 0.27682 0.112 0.000 0.048 0.132 0.516 0.192
#> SRR944066 1 0.4564 0.54291 0.664 0.000 0.032 0.000 0.020 0.284
#> SRR944067 5 0.5792 -0.04723 0.368 0.000 0.144 0.000 0.480 0.008
#> SRR944068 4 0.6297 0.57444 0.000 0.012 0.108 0.588 0.072 0.220
#> SRR944069 2 0.2006 0.87560 0.000 0.904 0.016 0.000 0.000 0.080
#> SRR944070 2 0.0405 0.94070 0.000 0.988 0.008 0.000 0.000 0.004
#> SRR944071 2 0.3370 0.76475 0.000 0.812 0.064 0.000 0.000 0.124
#> SRR944072 1 0.4785 0.65203 0.720 0.000 0.040 0.004 0.056 0.180
#> SRR944073 2 0.0000 0.94161 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944075 2 0.0260 0.94061 0.000 0.992 0.008 0.000 0.000 0.000
#> SRR944074 4 0.2038 0.69568 0.000 0.000 0.028 0.920 0.032 0.020
#> SRR944076 2 0.0520 0.93968 0.000 0.984 0.008 0.000 0.000 0.008
#> SRR944077 2 0.0363 0.93956 0.000 0.988 0.012 0.000 0.000 0.000
#> SRR944078 2 0.0291 0.94191 0.000 0.992 0.004 0.000 0.000 0.004
#> SRR944079 2 0.0000 0.94161 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944080 2 0.5103 0.44364 0.016 0.664 0.040 0.000 0.028 0.252
#> SRR944081 4 0.4673 0.66961 0.000 0.000 0.040 0.708 0.044 0.208
#> SRR944082 1 0.1555 0.68111 0.940 0.000 0.040 0.000 0.012 0.008
#> SRR944083 1 0.1257 0.69020 0.952 0.000 0.020 0.000 0.000 0.028
#> SRR944084 4 0.6636 0.51359 0.000 0.040 0.100 0.520 0.040 0.300
#> SRR944085 2 0.1341 0.91640 0.000 0.948 0.024 0.000 0.000 0.028
#> SRR944086 5 0.3277 0.09423 0.024 0.000 0.040 0.068 0.856 0.012
#> SRR944088 4 0.2401 0.68708 0.000 0.000 0.036 0.900 0.044 0.020
#> SRR944087 2 0.0922 0.92809 0.000 0.968 0.024 0.000 0.004 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "hclust"]
# you can also extract it by
# res = res_list["MAD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.430 0.838 0.903 0.4452 0.531 0.531
#> 3 3 0.629 0.750 0.867 0.2875 0.933 0.875
#> 4 4 0.586 0.604 0.770 0.1197 0.942 0.878
#> 5 5 0.648 0.732 0.818 0.0765 0.808 0.563
#> 6 6 0.649 0.723 0.820 0.0489 0.963 0.866
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.8144 0.735 0.252 0.748
#> SRR944012 1 0.7883 0.796 0.764 0.236
#> SRR944014 2 0.0000 0.889 0.000 1.000
#> SRR944013 2 0.2043 0.881 0.032 0.968
#> SRR944015 1 0.0000 0.869 1.000 0.000
#> SRR944016 1 0.7219 0.837 0.800 0.200
#> SRR944017 2 0.2043 0.881 0.032 0.968
#> SRR944018 1 0.2778 0.872 0.952 0.048
#> SRR944019 1 0.7299 0.834 0.796 0.204
#> SRR944020 1 0.0000 0.869 1.000 0.000
#> SRR944021 2 0.0000 0.889 0.000 1.000
#> SRR944022 1 0.0000 0.869 1.000 0.000
#> SRR944023 2 0.9087 0.621 0.324 0.676
#> SRR944024 1 0.7950 0.791 0.760 0.240
#> SRR944026 2 0.0000 0.889 0.000 1.000
#> SRR944025 2 0.0000 0.889 0.000 1.000
#> SRR944028 2 0.0000 0.889 0.000 1.000
#> SRR944029 2 0.6438 0.812 0.164 0.836
#> SRR944030 2 0.0000 0.889 0.000 1.000
#> SRR944031 2 0.8713 0.678 0.292 0.708
#> SRR944032 2 0.0376 0.888 0.004 0.996
#> SRR944033 2 0.0000 0.889 0.000 1.000
#> SRR944034 2 0.0000 0.889 0.000 1.000
#> SRR944036 2 0.7528 0.768 0.216 0.784
#> SRR944035 2 0.0000 0.889 0.000 1.000
#> SRR944038 1 0.0000 0.869 1.000 0.000
#> SRR944037 1 0.0376 0.870 0.996 0.004
#> SRR944039 1 0.7299 0.834 0.796 0.204
#> SRR944040 2 0.2236 0.879 0.036 0.964
#> SRR944041 1 0.7299 0.834 0.796 0.204
#> SRR944042 2 0.8386 0.715 0.268 0.732
#> SRR944043 1 0.0672 0.871 0.992 0.008
#> SRR944044 2 0.0000 0.889 0.000 1.000
#> SRR944046 2 0.8443 0.709 0.272 0.728
#> SRR944045 2 0.0376 0.888 0.004 0.996
#> SRR944047 2 0.0000 0.889 0.000 1.000
#> SRR944048 1 0.7950 0.791 0.760 0.240
#> SRR944049 2 0.0000 0.889 0.000 1.000
#> SRR944050 1 0.7219 0.837 0.800 0.200
#> SRR944051 2 0.0000 0.889 0.000 1.000
#> SRR944052 2 0.0000 0.889 0.000 1.000
#> SRR944053 1 0.0000 0.869 1.000 0.000
#> SRR944054 2 0.1184 0.885 0.016 0.984
#> SRR944055 2 0.5737 0.832 0.136 0.864
#> SRR944056 2 0.0000 0.889 0.000 1.000
#> SRR944057 1 0.7219 0.837 0.800 0.200
#> SRR944058 1 0.7219 0.837 0.800 0.200
#> SRR944059 2 0.7950 0.749 0.240 0.760
#> SRR944060 1 0.0000 0.869 1.000 0.000
#> SRR944061 2 0.0000 0.889 0.000 1.000
#> SRR944062 1 0.3431 0.871 0.936 0.064
#> SRR944063 1 0.0000 0.869 1.000 0.000
#> SRR944064 2 0.0000 0.889 0.000 1.000
#> SRR944065 1 0.0938 0.871 0.988 0.012
#> SRR944066 1 0.7139 0.839 0.804 0.196
#> SRR944067 2 0.0000 0.889 0.000 1.000
#> SRR944068 1 0.0000 0.869 1.000 0.000
#> SRR944069 2 0.0000 0.889 0.000 1.000
#> SRR944070 1 0.0000 0.869 1.000 0.000
#> SRR944071 2 0.8207 0.730 0.256 0.744
#> SRR944072 1 0.7219 0.837 0.800 0.200
#> SRR944073 2 0.0000 0.889 0.000 1.000
#> SRR944075 2 0.5519 0.837 0.128 0.872
#> SRR944074 2 0.0000 0.889 0.000 1.000
#> SRR944076 2 0.8608 0.692 0.284 0.716
#> SRR944077 2 0.0000 0.889 0.000 1.000
#> SRR944078 2 0.5408 0.839 0.124 0.876
#> SRR944079 2 0.0000 0.889 0.000 1.000
#> SRR944080 2 0.0000 0.889 0.000 1.000
#> SRR944081 2 0.8909 0.596 0.308 0.692
#> SRR944082 1 0.2948 0.872 0.948 0.052
#> SRR944083 1 0.7219 0.837 0.800 0.200
#> SRR944084 2 0.7602 0.766 0.220 0.780
#> SRR944085 2 0.8713 0.679 0.292 0.708
#> SRR944086 2 0.7745 0.757 0.228 0.772
#> SRR944088 2 0.5629 0.835 0.132 0.868
#> SRR944087 2 0.8267 0.725 0.260 0.740
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 2 0.6832 0.5962 0.376 0.604 0.020
#> SRR944012 1 0.1711 0.8779 0.960 0.032 0.008
#> SRR944014 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944013 2 0.2356 0.8226 0.072 0.928 0.000
#> SRR944015 3 0.0000 0.8383 0.000 0.000 1.000
#> SRR944016 1 0.0237 0.9072 0.996 0.000 0.004
#> SRR944017 2 0.2356 0.8226 0.072 0.928 0.000
#> SRR944018 1 0.6451 -0.0695 0.560 0.004 0.436
#> SRR944019 1 0.0661 0.9046 0.988 0.004 0.008
#> SRR944020 3 0.0000 0.8383 0.000 0.000 1.000
#> SRR944021 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944022 3 0.0000 0.8383 0.000 0.000 1.000
#> SRR944023 2 0.7690 0.4810 0.416 0.536 0.048
#> SRR944024 1 0.1411 0.8761 0.964 0.036 0.000
#> SRR944026 2 0.0892 0.8322 0.020 0.980 0.000
#> SRR944025 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944028 2 0.0237 0.8329 0.004 0.996 0.000
#> SRR944029 2 0.5497 0.6990 0.292 0.708 0.000
#> SRR944030 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944031 2 0.6973 0.5315 0.416 0.564 0.020
#> SRR944032 2 0.2356 0.8226 0.072 0.928 0.000
#> SRR944033 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944034 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944036 2 0.6008 0.6236 0.372 0.628 0.000
#> SRR944035 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944038 3 0.2448 0.8309 0.076 0.000 0.924
#> SRR944037 3 0.5621 0.6295 0.308 0.000 0.692
#> SRR944039 1 0.0661 0.9046 0.988 0.004 0.008
#> SRR944040 2 0.2878 0.8127 0.096 0.904 0.000
#> SRR944041 1 0.0829 0.9027 0.984 0.004 0.012
#> SRR944042 2 0.7001 0.5745 0.388 0.588 0.024
#> SRR944043 3 0.5810 0.5918 0.336 0.000 0.664
#> SRR944044 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944046 2 0.6910 0.5669 0.396 0.584 0.020
#> SRR944045 2 0.0747 0.8329 0.016 0.984 0.000
#> SRR944047 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944048 1 0.1411 0.8761 0.964 0.036 0.000
#> SRR944049 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944050 1 0.0237 0.9072 0.996 0.000 0.004
#> SRR944051 2 0.1163 0.8315 0.028 0.972 0.000
#> SRR944052 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944053 3 0.0000 0.8383 0.000 0.000 1.000
#> SRR944054 2 0.1964 0.8267 0.056 0.944 0.000
#> SRR944055 2 0.4974 0.7395 0.236 0.764 0.000
#> SRR944056 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944057 1 0.0237 0.9072 0.996 0.000 0.004
#> SRR944058 1 0.0237 0.9072 0.996 0.000 0.004
#> SRR944059 2 0.6566 0.6322 0.348 0.636 0.016
#> SRR944060 3 0.2066 0.8359 0.060 0.000 0.940
#> SRR944061 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944062 1 0.6126 0.1543 0.600 0.000 0.400
#> SRR944063 3 0.1163 0.8373 0.028 0.000 0.972
#> SRR944064 2 0.1753 0.8268 0.048 0.952 0.000
#> SRR944065 3 0.5926 0.5561 0.356 0.000 0.644
#> SRR944066 1 0.0424 0.9048 0.992 0.000 0.008
#> SRR944067 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944068 3 0.0000 0.8383 0.000 0.000 1.000
#> SRR944069 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944070 3 0.2448 0.8309 0.076 0.000 0.924
#> SRR944071 2 0.6849 0.5905 0.380 0.600 0.020
#> SRR944072 1 0.0237 0.9072 0.996 0.000 0.004
#> SRR944073 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944075 2 0.4842 0.7476 0.224 0.776 0.000
#> SRR944074 2 0.0892 0.8322 0.020 0.980 0.000
#> SRR944076 2 0.7056 0.5490 0.404 0.572 0.024
#> SRR944077 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944078 2 0.4654 0.7574 0.208 0.792 0.000
#> SRR944079 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944080 2 0.0000 0.8329 0.000 1.000 0.000
#> SRR944081 2 0.6509 0.3662 0.472 0.524 0.004
#> SRR944082 3 0.6309 0.1652 0.500 0.000 0.500
#> SRR944083 1 0.0237 0.9072 0.996 0.000 0.004
#> SRR944084 2 0.6339 0.6310 0.360 0.632 0.008
#> SRR944085 2 0.7181 0.5363 0.408 0.564 0.028
#> SRR944086 2 0.6045 0.6153 0.380 0.620 0.000
#> SRR944088 2 0.5138 0.7314 0.252 0.748 0.000
#> SRR944087 2 0.6865 0.5843 0.384 0.596 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 2 0.7502 0.4210 0.156 0.436 0.404 0.004
#> SRR944012 1 0.4452 0.6173 0.732 0.000 0.260 0.008
#> SRR944014 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944013 2 0.3870 0.7104 0.004 0.788 0.208 0.000
#> SRR944015 4 0.2011 0.9334 0.000 0.000 0.080 0.920
#> SRR944016 1 0.0336 0.8321 0.992 0.000 0.008 0.000
#> SRR944017 2 0.3870 0.7104 0.004 0.788 0.208 0.000
#> SRR944018 1 0.7442 0.1577 0.496 0.000 0.304 0.200
#> SRR944019 1 0.1970 0.8141 0.932 0.000 0.060 0.008
#> SRR944020 4 0.0000 0.9601 0.000 0.000 0.000 1.000
#> SRR944021 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944022 4 0.0000 0.9601 0.000 0.000 0.000 1.000
#> SRR944023 3 0.7965 -0.4137 0.176 0.400 0.408 0.016
#> SRR944024 1 0.2256 0.8022 0.924 0.020 0.056 0.000
#> SRR944026 2 0.1211 0.7549 0.000 0.960 0.040 0.000
#> SRR944025 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944028 2 0.0188 0.7578 0.000 0.996 0.004 0.000
#> SRR944029 2 0.6725 0.5510 0.104 0.548 0.348 0.000
#> SRR944030 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944031 3 0.7562 -0.4545 0.164 0.412 0.420 0.004
#> SRR944032 2 0.4079 0.7177 0.020 0.800 0.180 0.000
#> SRR944033 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944036 2 0.7349 0.4570 0.160 0.456 0.384 0.000
#> SRR944035 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944038 3 0.5643 -0.0644 0.024 0.000 0.548 0.428
#> SRR944037 3 0.7651 0.1875 0.248 0.000 0.464 0.288
#> SRR944039 1 0.1970 0.8141 0.932 0.000 0.060 0.008
#> SRR944040 2 0.4012 0.7140 0.016 0.800 0.184 0.000
#> SRR944041 1 0.2928 0.7781 0.880 0.000 0.108 0.012
#> SRR944042 2 0.7679 0.4043 0.164 0.432 0.396 0.008
#> SRR944043 3 0.7421 0.2421 0.268 0.000 0.512 0.220
#> SRR944044 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944046 2 0.7559 0.3988 0.164 0.428 0.404 0.004
#> SRR944045 2 0.0921 0.7568 0.000 0.972 0.028 0.000
#> SRR944047 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944048 1 0.2256 0.8022 0.924 0.020 0.056 0.000
#> SRR944049 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944050 1 0.0336 0.8321 0.992 0.000 0.008 0.000
#> SRR944051 2 0.2973 0.7324 0.000 0.856 0.144 0.000
#> SRR944052 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944053 4 0.0000 0.9601 0.000 0.000 0.000 1.000
#> SRR944054 2 0.3626 0.7195 0.004 0.812 0.184 0.000
#> SRR944055 2 0.6079 0.6133 0.072 0.628 0.300 0.000
#> SRR944056 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944057 1 0.0336 0.8321 0.992 0.000 0.008 0.000
#> SRR944058 1 0.0188 0.8308 0.996 0.000 0.004 0.000
#> SRR944059 2 0.7358 0.4614 0.140 0.468 0.388 0.004
#> SRR944060 3 0.5244 -0.1040 0.008 0.000 0.556 0.436
#> SRR944061 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944062 1 0.5526 0.2896 0.564 0.000 0.416 0.020
#> SRR944063 4 0.1004 0.9390 0.024 0.000 0.004 0.972
#> SRR944064 2 0.1975 0.7466 0.016 0.936 0.048 0.000
#> SRR944065 3 0.7407 0.2258 0.288 0.000 0.508 0.204
#> SRR944066 1 0.0469 0.8306 0.988 0.000 0.012 0.000
#> SRR944067 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944068 4 0.2011 0.9334 0.000 0.000 0.080 0.920
#> SRR944069 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944070 3 0.5643 -0.0644 0.024 0.000 0.548 0.428
#> SRR944071 2 0.7529 0.4190 0.160 0.436 0.400 0.004
#> SRR944072 1 0.0188 0.8308 0.996 0.000 0.004 0.000
#> SRR944073 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944075 2 0.5972 0.6225 0.068 0.640 0.292 0.000
#> SRR944074 2 0.1211 0.7549 0.000 0.960 0.040 0.000
#> SRR944076 2 0.7613 0.3823 0.172 0.420 0.404 0.004
#> SRR944077 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944078 2 0.5697 0.6341 0.052 0.656 0.292 0.000
#> SRR944079 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944080 2 0.0000 0.7581 0.000 1.000 0.000 0.000
#> SRR944081 2 0.8020 0.2404 0.340 0.380 0.276 0.004
#> SRR944082 1 0.7182 0.0161 0.452 0.000 0.412 0.136
#> SRR944083 1 0.0336 0.8321 0.992 0.000 0.008 0.000
#> SRR944084 2 0.7179 0.4583 0.136 0.456 0.408 0.000
#> SRR944085 2 0.7638 0.3717 0.176 0.416 0.404 0.004
#> SRR944086 2 0.7431 0.4478 0.172 0.448 0.380 0.000
#> SRR944088 2 0.6351 0.5874 0.080 0.588 0.332 0.000
#> SRR944087 2 0.7504 0.4116 0.156 0.432 0.408 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.5299 0.876 0.028 0.280 0.656 0.000 0.036
#> SRR944012 1 0.5565 0.414 0.552 0.000 0.384 0.008 0.056
#> SRR944014 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944013 2 0.3883 0.520 0.000 0.744 0.244 0.004 0.008
#> SRR944015 4 0.4852 0.764 0.000 0.000 0.100 0.716 0.184
#> SRR944016 1 0.0609 0.837 0.980 0.000 0.020 0.000 0.000
#> SRR944017 2 0.3883 0.520 0.000 0.744 0.244 0.004 0.008
#> SRR944018 5 0.5707 0.393 0.388 0.000 0.052 0.016 0.544
#> SRR944019 1 0.3187 0.790 0.860 0.000 0.096 0.008 0.036
#> SRR944020 4 0.0324 0.886 0.000 0.000 0.004 0.992 0.004
#> SRR944021 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944022 4 0.0162 0.887 0.000 0.000 0.000 0.996 0.004
#> SRR944023 3 0.6722 0.828 0.048 0.276 0.556 0.000 0.120
#> SRR944024 1 0.2304 0.800 0.892 0.000 0.100 0.000 0.008
#> SRR944026 2 0.1430 0.836 0.000 0.944 0.052 0.000 0.004
#> SRR944025 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944028 2 0.0162 0.870 0.000 0.996 0.004 0.000 0.000
#> SRR944029 3 0.5210 0.733 0.020 0.388 0.576 0.004 0.012
#> SRR944030 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944031 3 0.5963 0.866 0.032 0.276 0.616 0.000 0.076
#> SRR944032 2 0.3851 0.598 0.000 0.768 0.212 0.004 0.016
#> SRR944033 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944036 3 0.4832 0.858 0.032 0.292 0.668 0.000 0.008
#> SRR944035 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944038 5 0.3051 0.618 0.000 0.000 0.060 0.076 0.864
#> SRR944037 5 0.5840 0.657 0.136 0.000 0.044 0.136 0.684
#> SRR944039 1 0.3187 0.790 0.860 0.000 0.096 0.008 0.036
#> SRR944040 2 0.3932 0.211 0.000 0.672 0.328 0.000 0.000
#> SRR944041 1 0.4160 0.718 0.780 0.000 0.168 0.008 0.044
#> SRR944042 3 0.5622 0.875 0.032 0.276 0.640 0.000 0.052
#> SRR944043 5 0.4000 0.713 0.172 0.000 0.012 0.028 0.788
#> SRR944044 2 0.0324 0.869 0.000 0.992 0.004 0.000 0.004
#> SRR944046 3 0.5622 0.874 0.032 0.276 0.640 0.000 0.052
#> SRR944045 2 0.0880 0.852 0.000 0.968 0.032 0.000 0.000
#> SRR944047 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944048 1 0.2304 0.800 0.892 0.000 0.100 0.000 0.008
#> SRR944049 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944050 1 0.0609 0.837 0.980 0.000 0.020 0.000 0.000
#> SRR944051 2 0.3006 0.697 0.000 0.836 0.156 0.004 0.004
#> SRR944052 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944053 4 0.0162 0.887 0.000 0.000 0.000 0.996 0.004
#> SRR944054 2 0.3643 0.596 0.000 0.776 0.212 0.004 0.008
#> SRR944055 3 0.4561 0.525 0.008 0.488 0.504 0.000 0.000
#> SRR944056 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944057 1 0.0609 0.837 0.980 0.000 0.020 0.000 0.000
#> SRR944058 1 0.1753 0.828 0.936 0.000 0.032 0.000 0.032
#> SRR944059 3 0.5321 0.859 0.028 0.316 0.628 0.000 0.028
#> SRR944060 5 0.3425 0.595 0.004 0.000 0.044 0.112 0.840
#> SRR944061 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944062 1 0.6202 -0.164 0.496 0.000 0.148 0.000 0.356
#> SRR944063 4 0.1074 0.876 0.004 0.000 0.016 0.968 0.012
#> SRR944064 2 0.1894 0.812 0.000 0.920 0.072 0.000 0.008
#> SRR944065 5 0.4351 0.712 0.164 0.000 0.040 0.020 0.776
#> SRR944066 1 0.0510 0.834 0.984 0.000 0.016 0.000 0.000
#> SRR944067 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944068 4 0.4852 0.764 0.000 0.000 0.100 0.716 0.184
#> SRR944069 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944070 5 0.3051 0.618 0.000 0.000 0.060 0.076 0.864
#> SRR944071 3 0.5302 0.876 0.032 0.280 0.656 0.000 0.032
#> SRR944072 1 0.1668 0.828 0.940 0.000 0.028 0.000 0.032
#> SRR944073 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944075 2 0.4560 -0.504 0.008 0.508 0.484 0.000 0.000
#> SRR944074 2 0.1430 0.836 0.000 0.944 0.052 0.000 0.004
#> SRR944076 3 0.5873 0.871 0.036 0.276 0.624 0.000 0.064
#> SRR944077 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944078 2 0.4300 -0.448 0.000 0.524 0.476 0.000 0.000
#> SRR944079 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.872 0.000 1.000 0.000 0.000 0.000
#> SRR944081 3 0.7263 0.477 0.300 0.308 0.376 0.008 0.008
#> SRR944082 5 0.5812 0.434 0.372 0.000 0.100 0.000 0.528
#> SRR944083 1 0.0609 0.837 0.980 0.000 0.020 0.000 0.000
#> SRR944084 3 0.4715 0.861 0.020 0.296 0.672 0.000 0.012
#> SRR944085 3 0.5983 0.867 0.036 0.276 0.616 0.000 0.072
#> SRR944086 3 0.5587 0.836 0.056 0.292 0.632 0.004 0.016
#> SRR944088 3 0.5023 0.630 0.008 0.436 0.540 0.004 0.012
#> SRR944087 3 0.5425 0.876 0.032 0.276 0.652 0.000 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.3351 0.8379 0.004 0.168 0.800 0.000 0.000 0.028
#> SRR944012 1 0.7483 -0.1034 0.352 0.000 0.264 0.000 0.240 0.144
#> SRR944014 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944013 2 0.3900 0.5869 0.000 0.728 0.232 0.000 0.040 0.000
#> SRR944015 4 0.0146 0.6259 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR944016 1 0.0508 0.7715 0.984 0.000 0.012 0.000 0.004 0.000
#> SRR944017 2 0.3900 0.5869 0.000 0.728 0.232 0.000 0.040 0.000
#> SRR944018 6 0.4370 0.1856 0.268 0.000 0.048 0.000 0.004 0.680
#> SRR944019 1 0.3789 0.6711 0.808 0.000 0.040 0.000 0.044 0.108
#> SRR944020 4 0.4301 0.8211 0.000 0.000 0.004 0.580 0.400 0.016
#> SRR944021 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944022 4 0.4176 0.8216 0.000 0.000 0.000 0.580 0.404 0.016
#> SRR944023 3 0.4946 0.7923 0.016 0.168 0.688 0.000 0.000 0.128
#> SRR944024 1 0.2328 0.7185 0.892 0.000 0.052 0.000 0.056 0.000
#> SRR944026 2 0.1644 0.8772 0.000 0.932 0.040 0.000 0.028 0.000
#> SRR944025 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944028 2 0.0146 0.9164 0.000 0.996 0.000 0.000 0.004 0.000
#> SRR944029 3 0.4983 0.7522 0.004 0.268 0.644 0.000 0.076 0.008
#> SRR944030 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944031 3 0.4185 0.8275 0.012 0.168 0.752 0.000 0.000 0.068
#> SRR944032 2 0.3927 0.6654 0.000 0.756 0.172 0.000 0.072 0.000
#> SRR944033 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944036 3 0.4371 0.8173 0.016 0.180 0.736 0.000 0.068 0.000
#> SRR944035 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944038 6 0.3748 0.5994 0.000 0.000 0.012 0.300 0.000 0.688
#> SRR944037 6 0.4077 0.5057 0.040 0.000 0.012 0.092 0.052 0.804
#> SRR944039 1 0.3789 0.6711 0.808 0.000 0.040 0.000 0.044 0.108
#> SRR944040 2 0.3852 0.0674 0.000 0.612 0.384 0.000 0.004 0.000
#> SRR944041 1 0.5411 0.5072 0.684 0.000 0.108 0.000 0.092 0.116
#> SRR944042 3 0.3834 0.8365 0.012 0.168 0.776 0.000 0.000 0.044
#> SRR944043 6 0.2103 0.5703 0.056 0.000 0.020 0.012 0.000 0.912
#> SRR944044 2 0.0405 0.9131 0.000 0.988 0.004 0.000 0.008 0.000
#> SRR944046 3 0.3834 0.8351 0.012 0.168 0.776 0.000 0.000 0.044
#> SRR944045 2 0.0790 0.8992 0.000 0.968 0.032 0.000 0.000 0.000
#> SRR944047 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944048 1 0.2328 0.7185 0.892 0.000 0.052 0.000 0.056 0.000
#> SRR944049 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944050 1 0.0363 0.7724 0.988 0.000 0.012 0.000 0.000 0.000
#> SRR944051 2 0.3101 0.7431 0.000 0.820 0.148 0.000 0.032 0.000
#> SRR944052 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944053 4 0.4176 0.8216 0.000 0.000 0.000 0.580 0.404 0.016
#> SRR944054 2 0.3679 0.6534 0.000 0.760 0.200 0.000 0.040 0.000
#> SRR944055 3 0.3923 0.5796 0.000 0.416 0.580 0.000 0.004 0.000
#> SRR944056 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944057 1 0.0363 0.7724 0.988 0.000 0.012 0.000 0.000 0.000
#> SRR944058 1 0.3154 0.7030 0.848 0.000 0.012 0.000 0.068 0.072
#> SRR944059 3 0.3799 0.8366 0.012 0.208 0.756 0.000 0.000 0.024
#> SRR944060 6 0.3725 0.5844 0.000 0.000 0.008 0.316 0.000 0.676
#> SRR944061 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944062 5 0.7409 0.0000 0.308 0.000 0.116 0.000 0.312 0.264
#> SRR944063 4 0.4543 0.8098 0.000 0.000 0.000 0.576 0.384 0.040
#> SRR944064 2 0.1863 0.8632 0.000 0.920 0.036 0.000 0.044 0.000
#> SRR944065 6 0.1932 0.5677 0.040 0.000 0.020 0.000 0.016 0.924
#> SRR944066 1 0.0767 0.7685 0.976 0.000 0.012 0.000 0.008 0.004
#> SRR944067 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944068 4 0.0146 0.6259 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR944069 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944070 6 0.3748 0.5994 0.000 0.000 0.012 0.300 0.000 0.688
#> SRR944071 3 0.3516 0.8387 0.012 0.172 0.792 0.000 0.000 0.024
#> SRR944072 1 0.2883 0.7105 0.864 0.000 0.008 0.000 0.060 0.068
#> SRR944073 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944075 3 0.3961 0.5247 0.000 0.440 0.556 0.000 0.004 0.000
#> SRR944074 2 0.1644 0.8772 0.000 0.932 0.040 0.000 0.028 0.000
#> SRR944076 3 0.4131 0.8310 0.012 0.168 0.756 0.000 0.000 0.064
#> SRR944077 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944078 3 0.3982 0.4716 0.000 0.460 0.536 0.000 0.004 0.000
#> SRR944079 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.9185 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944081 3 0.7633 0.3570 0.280 0.248 0.364 0.000 0.084 0.024
#> SRR944082 6 0.6062 -0.1944 0.236 0.000 0.104 0.000 0.076 0.584
#> SRR944083 1 0.0622 0.7699 0.980 0.000 0.012 0.000 0.008 0.000
#> SRR944084 3 0.3121 0.8347 0.000 0.180 0.804 0.000 0.012 0.004
#> SRR944085 3 0.4238 0.8279 0.012 0.168 0.748 0.000 0.000 0.072
#> SRR944086 3 0.5143 0.7854 0.032 0.180 0.680 0.000 0.108 0.000
#> SRR944088 3 0.5185 0.6901 0.004 0.316 0.596 0.000 0.076 0.008
#> SRR944087 3 0.3631 0.8375 0.012 0.168 0.788 0.000 0.000 0.032
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.802 0.934 0.970 0.5022 0.494 0.494
#> 3 3 0.750 0.742 0.897 0.2927 0.756 0.549
#> 4 4 0.901 0.932 0.943 0.1169 0.855 0.621
#> 5 5 0.836 0.795 0.870 0.0677 0.934 0.764
#> 6 6 0.791 0.716 0.818 0.0391 0.964 0.844
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 1 0.900 0.591 0.684 0.316
#> SRR944012 1 0.000 0.958 1.000 0.000
#> SRR944014 2 0.000 0.977 0.000 1.000
#> SRR944013 2 0.000 0.977 0.000 1.000
#> SRR944015 1 0.000 0.958 1.000 0.000
#> SRR944016 1 0.482 0.891 0.896 0.104
#> SRR944017 2 0.000 0.977 0.000 1.000
#> SRR944018 1 0.000 0.958 1.000 0.000
#> SRR944019 1 0.000 0.958 1.000 0.000
#> SRR944020 1 0.000 0.958 1.000 0.000
#> SRR944021 2 0.000 0.977 0.000 1.000
#> SRR944022 1 0.000 0.958 1.000 0.000
#> SRR944023 1 0.000 0.958 1.000 0.000
#> SRR944024 1 0.000 0.958 1.000 0.000
#> SRR944026 2 0.000 0.977 0.000 1.000
#> SRR944025 2 0.000 0.977 0.000 1.000
#> SRR944028 2 0.000 0.977 0.000 1.000
#> SRR944029 1 0.584 0.863 0.860 0.140
#> SRR944030 2 0.000 0.977 0.000 1.000
#> SRR944031 1 0.000 0.958 1.000 0.000
#> SRR944032 2 0.000 0.977 0.000 1.000
#> SRR944033 2 0.000 0.977 0.000 1.000
#> SRR944034 2 0.000 0.977 0.000 1.000
#> SRR944036 1 0.584 0.863 0.860 0.140
#> SRR944035 2 0.000 0.977 0.000 1.000
#> SRR944038 1 0.000 0.958 1.000 0.000
#> SRR944037 1 0.000 0.958 1.000 0.000
#> SRR944039 1 0.000 0.958 1.000 0.000
#> SRR944040 2 0.000 0.977 0.000 1.000
#> SRR944041 1 0.000 0.958 1.000 0.000
#> SRR944042 1 0.000 0.958 1.000 0.000
#> SRR944043 1 0.000 0.958 1.000 0.000
#> SRR944044 2 0.000 0.977 0.000 1.000
#> SRR944046 1 0.000 0.958 1.000 0.000
#> SRR944045 2 0.000 0.977 0.000 1.000
#> SRR944047 2 0.000 0.977 0.000 1.000
#> SRR944048 2 0.969 0.290 0.396 0.604
#> SRR944049 2 0.000 0.977 0.000 1.000
#> SRR944050 1 0.625 0.845 0.844 0.156
#> SRR944051 2 0.000 0.977 0.000 1.000
#> SRR944052 2 0.000 0.977 0.000 1.000
#> SRR944053 1 0.000 0.958 1.000 0.000
#> SRR944054 2 0.000 0.977 0.000 1.000
#> SRR944055 2 0.000 0.977 0.000 1.000
#> SRR944056 2 0.000 0.977 0.000 1.000
#> SRR944057 1 0.000 0.958 1.000 0.000
#> SRR944058 1 0.000 0.958 1.000 0.000
#> SRR944059 2 0.000 0.977 0.000 1.000
#> SRR944060 1 0.000 0.958 1.000 0.000
#> SRR944061 2 0.000 0.977 0.000 1.000
#> SRR944062 1 0.000 0.958 1.000 0.000
#> SRR944063 1 0.000 0.958 1.000 0.000
#> SRR944064 2 0.000 0.977 0.000 1.000
#> SRR944065 1 0.000 0.958 1.000 0.000
#> SRR944066 1 0.000 0.958 1.000 0.000
#> SRR944067 2 0.000 0.977 0.000 1.000
#> SRR944068 1 0.000 0.958 1.000 0.000
#> SRR944069 2 0.000 0.977 0.000 1.000
#> SRR944070 1 0.000 0.958 1.000 0.000
#> SRR944071 1 0.584 0.863 0.860 0.140
#> SRR944072 1 0.000 0.958 1.000 0.000
#> SRR944073 2 0.000 0.977 0.000 1.000
#> SRR944075 2 0.000 0.977 0.000 1.000
#> SRR944074 2 0.000 0.977 0.000 1.000
#> SRR944076 1 0.584 0.863 0.860 0.140
#> SRR944077 2 0.000 0.977 0.000 1.000
#> SRR944078 2 0.000 0.977 0.000 1.000
#> SRR944079 2 0.000 0.977 0.000 1.000
#> SRR944080 2 0.000 0.977 0.000 1.000
#> SRR944081 1 0.563 0.870 0.868 0.132
#> SRR944082 1 0.000 0.958 1.000 0.000
#> SRR944083 1 0.000 0.958 1.000 0.000
#> SRR944084 1 0.584 0.863 0.860 0.140
#> SRR944085 2 0.958 0.334 0.380 0.620
#> SRR944086 1 0.584 0.863 0.860 0.140
#> SRR944088 2 0.000 0.977 0.000 1.000
#> SRR944087 1 0.000 0.958 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 1 0.1877 0.7798 0.956 0.012 0.032
#> SRR944012 1 0.6274 -0.0234 0.544 0.000 0.456
#> SRR944014 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944013 2 0.4504 0.7514 0.196 0.804 0.000
#> SRR944015 3 0.0237 0.8252 0.004 0.000 0.996
#> SRR944016 1 0.2796 0.7579 0.908 0.000 0.092
#> SRR944017 2 0.0747 0.9607 0.016 0.984 0.000
#> SRR944018 3 0.6291 0.1548 0.468 0.000 0.532
#> SRR944019 1 0.4235 0.6720 0.824 0.000 0.176
#> SRR944020 3 0.0000 0.8262 0.000 0.000 1.000
#> SRR944021 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944022 3 0.0000 0.8262 0.000 0.000 1.000
#> SRR944023 1 0.1643 0.7833 0.956 0.000 0.044
#> SRR944024 1 0.2537 0.7653 0.920 0.000 0.080
#> SRR944026 2 0.0747 0.9607 0.016 0.984 0.000
#> SRR944025 2 0.0747 0.9607 0.016 0.984 0.000
#> SRR944028 2 0.0747 0.9607 0.016 0.984 0.000
#> SRR944029 1 0.0424 0.7797 0.992 0.000 0.008
#> SRR944030 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944031 1 0.1643 0.7833 0.956 0.000 0.044
#> SRR944032 1 0.6295 0.0887 0.528 0.472 0.000
#> SRR944033 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944034 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944036 1 0.0747 0.7811 0.984 0.000 0.016
#> SRR944035 2 0.0424 0.9626 0.008 0.992 0.000
#> SRR944038 3 0.2537 0.7729 0.080 0.000 0.920
#> SRR944037 3 0.0000 0.8262 0.000 0.000 1.000
#> SRR944039 1 0.5465 0.4851 0.712 0.000 0.288
#> SRR944040 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944041 1 0.6286 -0.0538 0.536 0.000 0.464
#> SRR944042 1 0.1643 0.7833 0.956 0.000 0.044
#> SRR944043 3 0.0000 0.8262 0.000 0.000 1.000
#> SRR944044 2 0.0747 0.9607 0.016 0.984 0.000
#> SRR944046 1 0.1643 0.7833 0.956 0.000 0.044
#> SRR944045 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944047 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944048 1 0.2496 0.7483 0.928 0.068 0.004
#> SRR944049 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944050 1 0.2590 0.7616 0.924 0.004 0.072
#> SRR944051 2 0.0747 0.9607 0.016 0.984 0.000
#> SRR944052 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944053 3 0.0000 0.8262 0.000 0.000 1.000
#> SRR944054 2 0.1411 0.9463 0.036 0.964 0.000
#> SRR944055 1 0.6309 -0.0318 0.504 0.496 0.000
#> SRR944056 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944057 1 0.2796 0.7579 0.908 0.000 0.092
#> SRR944058 1 0.6305 -0.1311 0.516 0.000 0.484
#> SRR944059 1 0.5882 0.4177 0.652 0.348 0.000
#> SRR944060 3 0.0237 0.8252 0.004 0.000 0.996
#> SRR944061 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944062 3 0.5397 0.6008 0.280 0.000 0.720
#> SRR944063 3 0.0000 0.8262 0.000 0.000 1.000
#> SRR944064 2 0.0747 0.9607 0.016 0.984 0.000
#> SRR944065 3 0.2711 0.7783 0.088 0.000 0.912
#> SRR944066 3 0.6309 0.1090 0.500 0.000 0.500
#> SRR944067 2 0.0747 0.9607 0.016 0.984 0.000
#> SRR944068 3 0.0237 0.8252 0.004 0.000 0.996
#> SRR944069 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944070 3 0.2537 0.7729 0.080 0.000 0.920
#> SRR944071 1 0.1643 0.7833 0.956 0.000 0.044
#> SRR944072 3 0.6308 0.1354 0.492 0.000 0.508
#> SRR944073 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944075 1 0.6111 0.2972 0.604 0.396 0.000
#> SRR944074 2 0.0747 0.9607 0.016 0.984 0.000
#> SRR944076 1 0.1643 0.7833 0.956 0.000 0.044
#> SRR944077 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944078 2 0.6286 0.1176 0.464 0.536 0.000
#> SRR944079 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944080 2 0.0000 0.9643 0.000 1.000 0.000
#> SRR944081 1 0.2356 0.7628 0.928 0.000 0.072
#> SRR944082 3 0.5397 0.6008 0.280 0.000 0.720
#> SRR944083 1 0.2878 0.7554 0.904 0.000 0.096
#> SRR944084 1 0.1643 0.7833 0.956 0.000 0.044
#> SRR944085 1 0.1585 0.7740 0.964 0.028 0.008
#> SRR944086 1 0.0237 0.7787 0.996 0.000 0.004
#> SRR944088 2 0.4235 0.7813 0.176 0.824 0.000
#> SRR944087 1 0.1643 0.7833 0.956 0.000 0.044
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.1452 0.971 0.036 0.000 0.956 0.008
#> SRR944012 1 0.0937 0.924 0.976 0.000 0.012 0.012
#> SRR944014 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944013 2 0.3550 0.886 0.096 0.860 0.044 0.000
#> SRR944015 4 0.0000 0.926 0.000 0.000 0.000 1.000
#> SRR944016 1 0.2216 0.924 0.908 0.000 0.092 0.000
#> SRR944017 2 0.1510 0.954 0.016 0.956 0.028 0.000
#> SRR944018 1 0.3658 0.851 0.836 0.000 0.020 0.144
#> SRR944019 1 0.0927 0.929 0.976 0.000 0.016 0.008
#> SRR944020 4 0.0707 0.929 0.020 0.000 0.000 0.980
#> SRR944021 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944022 4 0.0707 0.929 0.020 0.000 0.000 0.980
#> SRR944023 3 0.1677 0.971 0.040 0.000 0.948 0.012
#> SRR944024 1 0.1867 0.931 0.928 0.000 0.072 0.000
#> SRR944026 2 0.1510 0.954 0.016 0.956 0.028 0.000
#> SRR944025 2 0.1059 0.959 0.012 0.972 0.016 0.000
#> SRR944028 2 0.1059 0.959 0.012 0.972 0.016 0.000
#> SRR944029 3 0.2125 0.935 0.076 0.004 0.920 0.000
#> SRR944030 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944031 3 0.1677 0.971 0.040 0.000 0.948 0.012
#> SRR944032 2 0.4155 0.854 0.072 0.828 0.100 0.000
#> SRR944033 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944034 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944036 3 0.1545 0.969 0.040 0.000 0.952 0.008
#> SRR944035 2 0.0779 0.961 0.004 0.980 0.016 0.000
#> SRR944038 4 0.4307 0.768 0.024 0.000 0.192 0.784
#> SRR944037 4 0.1004 0.929 0.024 0.000 0.004 0.972
#> SRR944039 1 0.1284 0.933 0.964 0.000 0.024 0.012
#> SRR944040 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944041 1 0.0804 0.925 0.980 0.000 0.008 0.012
#> SRR944042 3 0.1677 0.971 0.040 0.000 0.948 0.012
#> SRR944043 4 0.1489 0.917 0.044 0.000 0.004 0.952
#> SRR944044 2 0.1510 0.954 0.016 0.956 0.028 0.000
#> SRR944046 3 0.1677 0.971 0.040 0.000 0.948 0.012
#> SRR944045 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944047 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944048 1 0.2216 0.924 0.908 0.000 0.092 0.000
#> SRR944049 2 0.0188 0.964 0.004 0.996 0.000 0.000
#> SRR944050 1 0.2216 0.924 0.908 0.000 0.092 0.000
#> SRR944051 2 0.2385 0.932 0.052 0.920 0.028 0.000
#> SRR944052 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944053 4 0.0592 0.929 0.016 0.000 0.000 0.984
#> SRR944054 2 0.2670 0.925 0.052 0.908 0.040 0.000
#> SRR944055 3 0.1302 0.932 0.000 0.044 0.956 0.000
#> SRR944056 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944057 1 0.1940 0.930 0.924 0.000 0.076 0.000
#> SRR944058 1 0.1820 0.927 0.944 0.000 0.020 0.036
#> SRR944059 3 0.1610 0.951 0.016 0.032 0.952 0.000
#> SRR944060 4 0.1174 0.922 0.020 0.000 0.012 0.968
#> SRR944061 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944062 1 0.2867 0.882 0.884 0.000 0.012 0.104
#> SRR944063 4 0.0707 0.929 0.020 0.000 0.000 0.980
#> SRR944064 2 0.1059 0.959 0.012 0.972 0.016 0.000
#> SRR944065 4 0.4220 0.695 0.248 0.000 0.004 0.748
#> SRR944066 1 0.1929 0.928 0.940 0.000 0.024 0.036
#> SRR944067 2 0.1059 0.959 0.012 0.972 0.016 0.000
#> SRR944068 4 0.0000 0.926 0.000 0.000 0.000 1.000
#> SRR944069 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944070 4 0.4307 0.768 0.024 0.000 0.192 0.784
#> SRR944071 3 0.1584 0.971 0.036 0.000 0.952 0.012
#> SRR944072 1 0.1677 0.923 0.948 0.000 0.012 0.040
#> SRR944073 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944075 3 0.1305 0.940 0.004 0.036 0.960 0.000
#> SRR944074 2 0.1510 0.954 0.016 0.956 0.028 0.000
#> SRR944076 3 0.1584 0.971 0.036 0.000 0.952 0.012
#> SRR944077 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944078 3 0.1474 0.922 0.000 0.052 0.948 0.000
#> SRR944079 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944080 2 0.0592 0.966 0.000 0.984 0.016 0.000
#> SRR944081 1 0.3088 0.859 0.864 0.008 0.128 0.000
#> SRR944082 1 0.2988 0.875 0.876 0.000 0.012 0.112
#> SRR944083 1 0.1867 0.931 0.928 0.000 0.072 0.000
#> SRR944084 3 0.2329 0.950 0.072 0.000 0.916 0.012
#> SRR944085 3 0.1452 0.971 0.036 0.000 0.956 0.008
#> SRR944086 1 0.2814 0.865 0.868 0.000 0.132 0.000
#> SRR944088 2 0.4234 0.838 0.052 0.816 0.132 0.000
#> SRR944087 3 0.1677 0.971 0.040 0.000 0.948 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.0162 0.9758 0.004 0.000 0.996 0.000 0.000
#> SRR944012 1 0.5230 0.3310 0.504 0.000 0.000 0.044 0.452
#> SRR944014 2 0.0162 0.9276 0.000 0.996 0.000 0.000 0.004
#> SRR944013 5 0.5023 0.6190 0.012 0.348 0.024 0.000 0.616
#> SRR944015 4 0.3521 0.8089 0.004 0.000 0.000 0.764 0.232
#> SRR944016 1 0.1628 0.8192 0.936 0.000 0.008 0.000 0.056
#> SRR944017 2 0.3123 0.7459 0.000 0.812 0.004 0.000 0.184
#> SRR944018 1 0.5470 0.5459 0.628 0.000 0.000 0.268 0.104
#> SRR944019 1 0.4425 0.5049 0.600 0.000 0.000 0.008 0.392
#> SRR944020 4 0.3197 0.8221 0.024 0.000 0.000 0.836 0.140
#> SRR944021 2 0.0162 0.9276 0.000 0.996 0.000 0.000 0.004
#> SRR944022 4 0.3197 0.8221 0.024 0.000 0.000 0.836 0.140
#> SRR944023 3 0.1251 0.9592 0.008 0.000 0.956 0.000 0.036
#> SRR944024 1 0.0992 0.8268 0.968 0.000 0.008 0.000 0.024
#> SRR944026 2 0.3730 0.5521 0.000 0.712 0.000 0.000 0.288
#> SRR944025 2 0.1792 0.8740 0.000 0.916 0.000 0.000 0.084
#> SRR944028 2 0.1792 0.8740 0.000 0.916 0.000 0.000 0.084
#> SRR944029 5 0.4276 0.2184 0.004 0.000 0.380 0.000 0.616
#> SRR944030 2 0.0000 0.9279 0.000 1.000 0.000 0.000 0.000
#> SRR944031 3 0.1026 0.9659 0.004 0.000 0.968 0.004 0.024
#> SRR944032 5 0.5893 0.6359 0.052 0.320 0.036 0.000 0.592
#> SRR944033 2 0.0000 0.9279 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.9279 0.000 1.000 0.000 0.000 0.000
#> SRR944036 3 0.0566 0.9763 0.004 0.000 0.984 0.000 0.012
#> SRR944035 2 0.0290 0.9251 0.000 0.992 0.000 0.000 0.008
#> SRR944038 4 0.5898 0.5867 0.004 0.000 0.252 0.604 0.140
#> SRR944037 4 0.1278 0.8084 0.020 0.000 0.004 0.960 0.016
#> SRR944039 1 0.2624 0.8009 0.872 0.000 0.000 0.012 0.116
#> SRR944040 2 0.0324 0.9243 0.000 0.992 0.004 0.000 0.004
#> SRR944041 1 0.5281 0.4308 0.548 0.000 0.000 0.052 0.400
#> SRR944042 3 0.1026 0.9659 0.004 0.000 0.968 0.004 0.024
#> SRR944043 4 0.3120 0.7600 0.084 0.000 0.004 0.864 0.048
#> SRR944044 2 0.3366 0.6697 0.000 0.768 0.000 0.000 0.232
#> SRR944046 3 0.1026 0.9659 0.004 0.000 0.968 0.004 0.024
#> SRR944045 2 0.0162 0.9276 0.000 0.996 0.000 0.000 0.004
#> SRR944047 2 0.0000 0.9279 0.000 1.000 0.000 0.000 0.000
#> SRR944048 1 0.1628 0.8192 0.936 0.000 0.008 0.000 0.056
#> SRR944049 2 0.0162 0.9268 0.000 0.996 0.000 0.000 0.004
#> SRR944050 1 0.1628 0.8192 0.936 0.000 0.008 0.000 0.056
#> SRR944051 5 0.4875 0.5272 0.004 0.400 0.020 0.000 0.576
#> SRR944052 2 0.0162 0.9276 0.000 0.996 0.000 0.000 0.004
#> SRR944053 4 0.2920 0.8222 0.016 0.000 0.000 0.852 0.132
#> SRR944054 5 0.4883 0.5797 0.004 0.372 0.024 0.000 0.600
#> SRR944055 3 0.0771 0.9744 0.000 0.004 0.976 0.000 0.020
#> SRR944056 2 0.0162 0.9276 0.000 0.996 0.000 0.000 0.004
#> SRR944057 1 0.1168 0.8244 0.960 0.000 0.008 0.000 0.032
#> SRR944058 1 0.0510 0.8274 0.984 0.000 0.000 0.000 0.016
#> SRR944059 3 0.0771 0.9744 0.000 0.004 0.976 0.000 0.020
#> SRR944060 4 0.3441 0.7802 0.004 0.000 0.028 0.828 0.140
#> SRR944061 2 0.0162 0.9276 0.000 0.996 0.000 0.000 0.004
#> SRR944062 1 0.3978 0.7249 0.796 0.000 0.004 0.148 0.052
#> SRR944063 4 0.3197 0.8221 0.024 0.000 0.000 0.836 0.140
#> SRR944064 2 0.1792 0.8740 0.000 0.916 0.000 0.000 0.084
#> SRR944065 4 0.4510 0.6473 0.164 0.000 0.004 0.756 0.076
#> SRR944066 1 0.0451 0.8249 0.988 0.000 0.000 0.008 0.004
#> SRR944067 2 0.1792 0.8740 0.000 0.916 0.000 0.000 0.084
#> SRR944068 4 0.3521 0.8089 0.004 0.000 0.000 0.764 0.232
#> SRR944069 2 0.0162 0.9276 0.000 0.996 0.000 0.000 0.004
#> SRR944070 4 0.5898 0.5867 0.004 0.000 0.252 0.604 0.140
#> SRR944071 3 0.0566 0.9763 0.004 0.000 0.984 0.000 0.012
#> SRR944072 1 0.1041 0.8222 0.964 0.000 0.000 0.004 0.032
#> SRR944073 2 0.0000 0.9279 0.000 1.000 0.000 0.000 0.000
#> SRR944075 3 0.0771 0.9744 0.000 0.004 0.976 0.000 0.020
#> SRR944074 2 0.3730 0.5521 0.000 0.712 0.000 0.000 0.288
#> SRR944076 3 0.0324 0.9764 0.004 0.000 0.992 0.000 0.004
#> SRR944077 2 0.0000 0.9279 0.000 1.000 0.000 0.000 0.000
#> SRR944078 3 0.0771 0.9744 0.000 0.004 0.976 0.000 0.020
#> SRR944079 2 0.0162 0.9276 0.000 0.996 0.000 0.000 0.004
#> SRR944080 2 0.0000 0.9279 0.000 1.000 0.000 0.000 0.000
#> SRR944081 5 0.5070 0.2179 0.272 0.000 0.052 0.008 0.668
#> SRR944082 1 0.4332 0.7118 0.768 0.000 0.004 0.164 0.064
#> SRR944083 1 0.0798 0.8266 0.976 0.000 0.008 0.000 0.016
#> SRR944084 3 0.1282 0.9548 0.004 0.000 0.952 0.000 0.044
#> SRR944085 3 0.0671 0.9750 0.004 0.000 0.980 0.000 0.016
#> SRR944086 5 0.5449 -0.0542 0.376 0.000 0.068 0.000 0.556
#> SRR944088 5 0.5059 0.6495 0.004 0.292 0.052 0.000 0.652
#> SRR944087 3 0.1026 0.9659 0.004 0.000 0.968 0.004 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.0260 0.9696 0.000 0.000 0.992 0.000 0.008 0.000
#> SRR944012 5 0.4776 0.4912 0.136 0.000 0.000 0.032 0.724 0.108
#> SRR944014 2 0.0363 0.8938 0.000 0.988 0.000 0.000 0.000 0.012
#> SRR944013 5 0.5225 0.6531 0.004 0.140 0.012 0.000 0.660 0.184
#> SRR944015 4 0.2994 0.4815 0.000 0.000 0.000 0.788 0.004 0.208
#> SRR944016 1 0.1957 0.7788 0.888 0.000 0.000 0.000 0.112 0.000
#> SRR944017 2 0.4552 0.7003 0.000 0.700 0.004 0.000 0.092 0.204
#> SRR944018 6 0.7456 -0.1626 0.300 0.000 0.004 0.116 0.224 0.356
#> SRR944019 5 0.4447 0.4615 0.148 0.000 0.000 0.016 0.740 0.096
#> SRR944020 4 0.0260 0.6405 0.000 0.000 0.000 0.992 0.008 0.000
#> SRR944021 2 0.0458 0.8929 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944022 4 0.0000 0.6403 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR944023 3 0.1398 0.9297 0.000 0.000 0.940 0.000 0.008 0.052
#> SRR944024 1 0.1285 0.7909 0.944 0.000 0.000 0.000 0.004 0.052
#> SRR944026 2 0.5249 0.5338 0.000 0.600 0.000 0.000 0.156 0.244
#> SRR944025 2 0.2980 0.8031 0.000 0.808 0.000 0.000 0.012 0.180
#> SRR944028 2 0.3014 0.7999 0.000 0.804 0.000 0.000 0.012 0.184
#> SRR944029 5 0.3754 0.5768 0.000 0.000 0.152 0.000 0.776 0.072
#> SRR944030 2 0.0000 0.8951 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944031 3 0.0858 0.9538 0.000 0.000 0.968 0.000 0.004 0.028
#> SRR944032 5 0.5487 0.6361 0.012 0.116 0.012 0.000 0.632 0.228
#> SRR944033 2 0.0000 0.8951 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.8951 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944036 3 0.0603 0.9694 0.000 0.000 0.980 0.000 0.016 0.004
#> SRR944035 2 0.2135 0.8434 0.000 0.872 0.000 0.000 0.000 0.128
#> SRR944038 6 0.5799 0.4295 0.000 0.000 0.232 0.236 0.004 0.528
#> SRR944037 4 0.4139 0.3522 0.004 0.000 0.000 0.700 0.036 0.260
#> SRR944039 1 0.5728 0.5099 0.560 0.000 0.000 0.016 0.280 0.144
#> SRR944040 2 0.0603 0.8913 0.000 0.980 0.004 0.000 0.000 0.016
#> SRR944041 5 0.5429 0.4317 0.152 0.000 0.000 0.052 0.668 0.128
#> SRR944042 3 0.0713 0.9563 0.000 0.000 0.972 0.000 0.000 0.028
#> SRR944043 4 0.6278 0.0125 0.104 0.000 0.000 0.436 0.056 0.404
#> SRR944044 2 0.4809 0.6241 0.000 0.652 0.000 0.000 0.108 0.240
#> SRR944046 3 0.0713 0.9563 0.000 0.000 0.972 0.000 0.000 0.028
#> SRR944045 2 0.0603 0.8909 0.000 0.980 0.004 0.000 0.000 0.016
#> SRR944047 2 0.0000 0.8951 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944048 1 0.2121 0.7810 0.892 0.000 0.000 0.000 0.096 0.012
#> SRR944049 2 0.1204 0.8776 0.000 0.944 0.000 0.000 0.000 0.056
#> SRR944050 1 0.1957 0.7788 0.888 0.000 0.000 0.000 0.112 0.000
#> SRR944051 5 0.5678 0.5914 0.000 0.184 0.008 0.000 0.564 0.244
#> SRR944052 2 0.0363 0.8938 0.000 0.988 0.000 0.000 0.000 0.012
#> SRR944053 4 0.0146 0.6398 0.000 0.000 0.000 0.996 0.004 0.000
#> SRR944054 5 0.5567 0.6210 0.000 0.160 0.012 0.000 0.592 0.236
#> SRR944055 3 0.0964 0.9642 0.000 0.004 0.968 0.000 0.012 0.016
#> SRR944056 2 0.0146 0.8950 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR944057 1 0.1444 0.7913 0.928 0.000 0.000 0.000 0.072 0.000
#> SRR944058 1 0.1408 0.7949 0.944 0.000 0.000 0.000 0.020 0.036
#> SRR944059 3 0.0820 0.9670 0.000 0.000 0.972 0.000 0.016 0.012
#> SRR944060 6 0.4576 -0.0417 0.000 0.000 0.028 0.436 0.004 0.532
#> SRR944061 2 0.0260 0.8946 0.000 0.992 0.000 0.000 0.000 0.008
#> SRR944062 1 0.4791 0.3945 0.564 0.000 0.000 0.004 0.048 0.384
#> SRR944063 4 0.0260 0.6405 0.000 0.000 0.000 0.992 0.008 0.000
#> SRR944064 2 0.2805 0.8174 0.000 0.828 0.000 0.000 0.012 0.160
#> SRR944065 4 0.7010 -0.0558 0.108 0.000 0.004 0.396 0.124 0.368
#> SRR944066 1 0.0458 0.7956 0.984 0.000 0.000 0.000 0.000 0.016
#> SRR944067 2 0.2841 0.8147 0.000 0.824 0.000 0.000 0.012 0.164
#> SRR944068 4 0.2994 0.4815 0.000 0.000 0.000 0.788 0.004 0.208
#> SRR944069 2 0.0458 0.8929 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944070 6 0.5799 0.4295 0.000 0.000 0.232 0.236 0.004 0.528
#> SRR944071 3 0.0458 0.9693 0.000 0.000 0.984 0.000 0.016 0.000
#> SRR944072 1 0.3472 0.7286 0.808 0.000 0.000 0.000 0.092 0.100
#> SRR944073 2 0.0000 0.8951 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944075 3 0.0870 0.9662 0.000 0.004 0.972 0.000 0.012 0.012
#> SRR944074 2 0.5249 0.5338 0.000 0.600 0.000 0.000 0.156 0.244
#> SRR944076 3 0.0363 0.9696 0.000 0.000 0.988 0.000 0.012 0.000
#> SRR944077 2 0.0146 0.8950 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR944078 3 0.0964 0.9642 0.000 0.004 0.968 0.000 0.012 0.016
#> SRR944079 2 0.0458 0.8929 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944080 2 0.0000 0.8951 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944081 5 0.1528 0.6265 0.028 0.000 0.016 0.000 0.944 0.012
#> SRR944082 1 0.5562 0.3207 0.512 0.000 0.000 0.020 0.084 0.384
#> SRR944083 1 0.0777 0.7953 0.972 0.000 0.000 0.000 0.004 0.024
#> SRR944084 3 0.1501 0.9165 0.000 0.000 0.924 0.000 0.076 0.000
#> SRR944085 3 0.0458 0.9693 0.000 0.000 0.984 0.000 0.016 0.000
#> SRR944086 5 0.2255 0.6202 0.044 0.000 0.024 0.000 0.908 0.024
#> SRR944088 5 0.5131 0.6581 0.000 0.108 0.028 0.000 0.676 0.188
#> SRR944087 3 0.0363 0.9625 0.000 0.000 0.988 0.000 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "skmeans"]
# you can also extract it by
# res = res_list["MAD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.972 0.989 0.5064 0.494 0.494
#> 3 3 0.984 0.946 0.976 0.2890 0.786 0.594
#> 4 4 0.790 0.833 0.903 0.1007 0.923 0.781
#> 5 5 0.702 0.634 0.828 0.0625 0.955 0.841
#> 6 6 0.697 0.636 0.780 0.0373 0.933 0.746
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.988 0.241 0.436 0.564
#> SRR944012 1 0.000 0.999 1.000 0.000
#> SRR944014 2 0.000 0.977 0.000 1.000
#> SRR944013 2 0.000 0.977 0.000 1.000
#> SRR944015 1 0.000 0.999 1.000 0.000
#> SRR944016 1 0.000 0.999 1.000 0.000
#> SRR944017 2 0.000 0.977 0.000 1.000
#> SRR944018 1 0.000 0.999 1.000 0.000
#> SRR944019 1 0.000 0.999 1.000 0.000
#> SRR944020 1 0.000 0.999 1.000 0.000
#> SRR944021 2 0.000 0.977 0.000 1.000
#> SRR944022 1 0.000 0.999 1.000 0.000
#> SRR944023 1 0.000 0.999 1.000 0.000
#> SRR944024 1 0.000 0.999 1.000 0.000
#> SRR944026 2 0.000 0.977 0.000 1.000
#> SRR944025 2 0.000 0.977 0.000 1.000
#> SRR944028 2 0.000 0.977 0.000 1.000
#> SRR944029 1 0.000 0.999 1.000 0.000
#> SRR944030 2 0.000 0.977 0.000 1.000
#> SRR944031 1 0.000 0.999 1.000 0.000
#> SRR944032 2 0.000 0.977 0.000 1.000
#> SRR944033 2 0.000 0.977 0.000 1.000
#> SRR944034 2 0.000 0.977 0.000 1.000
#> SRR944036 1 0.000 0.999 1.000 0.000
#> SRR944035 2 0.000 0.977 0.000 1.000
#> SRR944038 1 0.000 0.999 1.000 0.000
#> SRR944037 1 0.000 0.999 1.000 0.000
#> SRR944039 1 0.000 0.999 1.000 0.000
#> SRR944040 2 0.000 0.977 0.000 1.000
#> SRR944041 1 0.000 0.999 1.000 0.000
#> SRR944042 1 0.000 0.999 1.000 0.000
#> SRR944043 1 0.000 0.999 1.000 0.000
#> SRR944044 2 0.000 0.977 0.000 1.000
#> SRR944046 1 0.000 0.999 1.000 0.000
#> SRR944045 2 0.000 0.977 0.000 1.000
#> SRR944047 2 0.000 0.977 0.000 1.000
#> SRR944048 2 0.891 0.558 0.308 0.692
#> SRR944049 2 0.000 0.977 0.000 1.000
#> SRR944050 1 0.242 0.957 0.960 0.040
#> SRR944051 2 0.000 0.977 0.000 1.000
#> SRR944052 2 0.000 0.977 0.000 1.000
#> SRR944053 1 0.000 0.999 1.000 0.000
#> SRR944054 2 0.000 0.977 0.000 1.000
#> SRR944055 2 0.000 0.977 0.000 1.000
#> SRR944056 2 0.000 0.977 0.000 1.000
#> SRR944057 1 0.000 0.999 1.000 0.000
#> SRR944058 1 0.000 0.999 1.000 0.000
#> SRR944059 2 0.000 0.977 0.000 1.000
#> SRR944060 1 0.000 0.999 1.000 0.000
#> SRR944061 2 0.000 0.977 0.000 1.000
#> SRR944062 1 0.000 0.999 1.000 0.000
#> SRR944063 1 0.000 0.999 1.000 0.000
#> SRR944064 2 0.000 0.977 0.000 1.000
#> SRR944065 1 0.000 0.999 1.000 0.000
#> SRR944066 1 0.000 0.999 1.000 0.000
#> SRR944067 2 0.000 0.977 0.000 1.000
#> SRR944068 1 0.000 0.999 1.000 0.000
#> SRR944069 2 0.000 0.977 0.000 1.000
#> SRR944070 1 0.000 0.999 1.000 0.000
#> SRR944071 1 0.000 0.999 1.000 0.000
#> SRR944072 1 0.000 0.999 1.000 0.000
#> SRR944073 2 0.000 0.977 0.000 1.000
#> SRR944075 2 0.000 0.977 0.000 1.000
#> SRR944074 2 0.000 0.977 0.000 1.000
#> SRR944076 1 0.000 0.999 1.000 0.000
#> SRR944077 2 0.000 0.977 0.000 1.000
#> SRR944078 2 0.000 0.977 0.000 1.000
#> SRR944079 2 0.000 0.977 0.000 1.000
#> SRR944080 2 0.000 0.977 0.000 1.000
#> SRR944081 1 0.000 0.999 1.000 0.000
#> SRR944082 1 0.000 0.999 1.000 0.000
#> SRR944083 1 0.000 0.999 1.000 0.000
#> SRR944084 1 0.000 0.999 1.000 0.000
#> SRR944085 2 0.416 0.895 0.084 0.916
#> SRR944086 1 0.000 0.999 1.000 0.000
#> SRR944088 2 0.000 0.977 0.000 1.000
#> SRR944087 1 0.000 0.999 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 3 0.0000 0.934 0.000 0.000 1.000
#> SRR944012 1 0.0424 0.967 0.992 0.000 0.008
#> SRR944014 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944013 2 0.0237 0.996 0.004 0.996 0.000
#> SRR944015 1 0.0892 0.966 0.980 0.000 0.020
#> SRR944016 1 0.0000 0.967 1.000 0.000 0.000
#> SRR944017 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944018 1 0.0892 0.966 0.980 0.000 0.020
#> SRR944019 1 0.0000 0.967 1.000 0.000 0.000
#> SRR944020 1 0.0892 0.966 0.980 0.000 0.020
#> SRR944021 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944022 1 0.0892 0.966 0.980 0.000 0.020
#> SRR944023 3 0.3267 0.830 0.116 0.000 0.884
#> SRR944024 1 0.0000 0.967 1.000 0.000 0.000
#> SRR944026 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944025 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944028 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944029 1 0.2165 0.930 0.936 0.000 0.064
#> SRR944030 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944031 3 0.0000 0.934 0.000 0.000 1.000
#> SRR944032 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944033 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944034 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944036 3 0.1031 0.925 0.024 0.000 0.976
#> SRR944035 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944038 3 0.1289 0.916 0.032 0.000 0.968
#> SRR944037 1 0.0892 0.966 0.980 0.000 0.020
#> SRR944039 1 0.0000 0.967 1.000 0.000 0.000
#> SRR944040 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944041 1 0.0237 0.968 0.996 0.000 0.004
#> SRR944042 3 0.0000 0.934 0.000 0.000 1.000
#> SRR944043 1 0.0892 0.966 0.980 0.000 0.020
#> SRR944044 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944046 3 0.0000 0.934 0.000 0.000 1.000
#> SRR944045 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944047 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944048 1 0.4750 0.700 0.784 0.216 0.000
#> SRR944049 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944050 1 0.0000 0.967 1.000 0.000 0.000
#> SRR944051 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944052 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944053 1 0.0892 0.966 0.980 0.000 0.020
#> SRR944054 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944055 3 0.1753 0.906 0.000 0.048 0.952
#> SRR944056 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944057 1 0.0000 0.967 1.000 0.000 0.000
#> SRR944058 1 0.0000 0.967 1.000 0.000 0.000
#> SRR944059 3 0.5138 0.670 0.000 0.252 0.748
#> SRR944060 1 0.6008 0.430 0.628 0.000 0.372
#> SRR944061 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944062 1 0.0237 0.968 0.996 0.000 0.004
#> SRR944063 1 0.0892 0.966 0.980 0.000 0.020
#> SRR944064 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944065 1 0.0892 0.966 0.980 0.000 0.020
#> SRR944066 1 0.0000 0.967 1.000 0.000 0.000
#> SRR944067 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944068 1 0.0892 0.966 0.980 0.000 0.020
#> SRR944069 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944070 3 0.0592 0.929 0.012 0.000 0.988
#> SRR944071 3 0.0000 0.934 0.000 0.000 1.000
#> SRR944072 1 0.0000 0.967 1.000 0.000 0.000
#> SRR944073 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944075 3 0.0892 0.924 0.000 0.020 0.980
#> SRR944074 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944076 3 0.0000 0.934 0.000 0.000 1.000
#> SRR944077 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944078 3 0.6291 0.168 0.000 0.468 0.532
#> SRR944079 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944080 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944081 1 0.0237 0.968 0.996 0.000 0.004
#> SRR944082 1 0.0747 0.966 0.984 0.000 0.016
#> SRR944083 1 0.0000 0.967 1.000 0.000 0.000
#> SRR944084 3 0.0747 0.927 0.016 0.000 0.984
#> SRR944085 3 0.0000 0.934 0.000 0.000 1.000
#> SRR944086 1 0.0000 0.967 1.000 0.000 0.000
#> SRR944088 2 0.0000 1.000 0.000 1.000 0.000
#> SRR944087 3 0.0000 0.934 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.0712 0.838 0.008 0.004 0.984 0.004
#> SRR944012 4 0.0921 0.863 0.028 0.000 0.000 0.972
#> SRR944014 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> SRR944013 2 0.3102 0.912 0.116 0.872 0.008 0.004
#> SRR944015 4 0.0469 0.871 0.000 0.000 0.012 0.988
#> SRR944016 1 0.3024 0.872 0.852 0.000 0.000 0.148
#> SRR944017 2 0.1151 0.959 0.024 0.968 0.008 0.000
#> SRR944018 4 0.0657 0.868 0.012 0.000 0.004 0.984
#> SRR944019 4 0.4072 0.602 0.252 0.000 0.000 0.748
#> SRR944020 4 0.0188 0.873 0.000 0.000 0.004 0.996
#> SRR944021 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> SRR944022 4 0.0188 0.873 0.000 0.000 0.004 0.996
#> SRR944023 3 0.6519 0.438 0.096 0.000 0.584 0.320
#> SRR944024 1 0.3444 0.872 0.816 0.000 0.000 0.184
#> SRR944026 2 0.2597 0.930 0.084 0.904 0.008 0.004
#> SRR944025 2 0.1256 0.958 0.028 0.964 0.008 0.000
#> SRR944028 2 0.1356 0.956 0.032 0.960 0.008 0.000
#> SRR944029 4 0.3335 0.768 0.128 0.000 0.016 0.856
#> SRR944030 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> SRR944031 3 0.0804 0.838 0.008 0.000 0.980 0.012
#> SRR944032 2 0.4374 0.778 0.228 0.760 0.008 0.004
#> SRR944033 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> SRR944036 3 0.5069 0.512 0.320 0.000 0.664 0.016
#> SRR944035 2 0.0779 0.962 0.016 0.980 0.004 0.000
#> SRR944038 3 0.4897 0.514 0.008 0.000 0.660 0.332
#> SRR944037 4 0.0336 0.872 0.000 0.000 0.008 0.992
#> SRR944039 4 0.3486 0.678 0.188 0.000 0.000 0.812
#> SRR944040 2 0.0336 0.961 0.000 0.992 0.008 0.000
#> SRR944041 4 0.0921 0.865 0.028 0.000 0.000 0.972
#> SRR944042 3 0.0672 0.839 0.008 0.000 0.984 0.008
#> SRR944043 4 0.0188 0.873 0.000 0.000 0.004 0.996
#> SRR944044 2 0.2384 0.936 0.072 0.916 0.008 0.004
#> SRR944046 3 0.0524 0.839 0.004 0.000 0.988 0.008
#> SRR944045 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> SRR944047 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> SRR944048 1 0.3308 0.824 0.872 0.036 0.000 0.092
#> SRR944049 2 0.0188 0.965 0.004 0.996 0.000 0.000
#> SRR944050 1 0.2760 0.862 0.872 0.000 0.000 0.128
#> SRR944051 2 0.3102 0.910 0.116 0.872 0.008 0.004
#> SRR944052 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> SRR944053 4 0.0188 0.873 0.000 0.000 0.004 0.996
#> SRR944054 2 0.2983 0.916 0.108 0.880 0.008 0.004
#> SRR944055 3 0.2610 0.792 0.012 0.088 0.900 0.000
#> SRR944056 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> SRR944057 1 0.3074 0.874 0.848 0.000 0.000 0.152
#> SRR944058 1 0.4193 0.812 0.732 0.000 0.000 0.268
#> SRR944059 3 0.4019 0.689 0.012 0.196 0.792 0.000
#> SRR944060 4 0.3157 0.747 0.004 0.000 0.144 0.852
#> SRR944061 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> SRR944062 4 0.4916 -0.109 0.424 0.000 0.000 0.576
#> SRR944063 4 0.0188 0.873 0.000 0.000 0.004 0.996
#> SRR944064 2 0.0895 0.961 0.020 0.976 0.004 0.000
#> SRR944065 4 0.0188 0.873 0.000 0.000 0.004 0.996
#> SRR944066 1 0.3837 0.851 0.776 0.000 0.000 0.224
#> SRR944067 2 0.1256 0.958 0.028 0.964 0.008 0.000
#> SRR944068 4 0.0469 0.871 0.000 0.000 0.012 0.988
#> SRR944069 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> SRR944070 3 0.4567 0.608 0.008 0.000 0.716 0.276
#> SRR944071 3 0.0804 0.838 0.012 0.000 0.980 0.008
#> SRR944072 1 0.4992 0.389 0.524 0.000 0.000 0.476
#> SRR944073 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> SRR944075 3 0.1388 0.828 0.012 0.028 0.960 0.000
#> SRR944074 2 0.2597 0.930 0.084 0.904 0.008 0.004
#> SRR944076 3 0.0524 0.839 0.004 0.000 0.988 0.008
#> SRR944077 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> SRR944078 3 0.4868 0.558 0.012 0.304 0.684 0.000
#> SRR944079 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> SRR944080 2 0.0000 0.965 0.000 1.000 0.000 0.000
#> SRR944081 4 0.3498 0.765 0.160 0.000 0.008 0.832
#> SRR944082 4 0.2530 0.778 0.112 0.000 0.000 0.888
#> SRR944083 1 0.3266 0.874 0.832 0.000 0.000 0.168
#> SRR944084 4 0.5417 0.525 0.040 0.000 0.284 0.676
#> SRR944085 3 0.1139 0.838 0.012 0.008 0.972 0.008
#> SRR944086 1 0.4690 0.657 0.712 0.000 0.012 0.276
#> SRR944088 2 0.3272 0.900 0.128 0.860 0.008 0.004
#> SRR944087 3 0.0672 0.839 0.008 0.000 0.984 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.2011 0.7467 0.004 0.000 0.908 0.000 0.088
#> SRR944012 4 0.3214 0.7731 0.036 0.000 0.000 0.844 0.120
#> SRR944014 2 0.0000 0.8264 0.000 1.000 0.000 0.000 0.000
#> SRR944013 5 0.4904 0.4160 0.024 0.472 0.000 0.000 0.504
#> SRR944015 4 0.0566 0.8394 0.000 0.000 0.004 0.984 0.012
#> SRR944016 1 0.0898 0.8077 0.972 0.000 0.000 0.020 0.008
#> SRR944017 2 0.3086 0.6560 0.004 0.816 0.000 0.000 0.180
#> SRR944018 4 0.0912 0.8373 0.012 0.000 0.000 0.972 0.016
#> SRR944019 4 0.4960 0.6247 0.180 0.000 0.000 0.708 0.112
#> SRR944020 4 0.0000 0.8411 0.000 0.000 0.000 1.000 0.000
#> SRR944021 2 0.0162 0.8243 0.000 0.996 0.000 0.000 0.004
#> SRR944022 4 0.0000 0.8411 0.000 0.000 0.000 1.000 0.000
#> SRR944023 3 0.7099 0.2178 0.132 0.000 0.472 0.344 0.052
#> SRR944024 1 0.2921 0.7985 0.856 0.000 0.000 0.124 0.020
#> SRR944026 2 0.4235 -0.2219 0.000 0.576 0.000 0.000 0.424
#> SRR944025 2 0.2648 0.6985 0.000 0.848 0.000 0.000 0.152
#> SRR944028 2 0.2891 0.6606 0.000 0.824 0.000 0.000 0.176
#> SRR944029 5 0.4985 -0.3814 0.008 0.000 0.016 0.452 0.524
#> SRR944030 2 0.0162 0.8258 0.000 0.996 0.000 0.000 0.004
#> SRR944031 3 0.1377 0.7492 0.004 0.000 0.956 0.020 0.020
#> SRR944032 2 0.6260 -0.3288 0.152 0.476 0.000 0.000 0.372
#> SRR944033 2 0.0000 0.8264 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0290 0.8246 0.000 0.992 0.000 0.000 0.008
#> SRR944036 3 0.6308 0.4142 0.284 0.000 0.588 0.044 0.084
#> SRR944035 2 0.1671 0.7806 0.000 0.924 0.000 0.000 0.076
#> SRR944038 3 0.4832 0.3923 0.004 0.000 0.616 0.356 0.024
#> SRR944037 4 0.0162 0.8407 0.000 0.000 0.000 0.996 0.004
#> SRR944039 4 0.4465 0.6414 0.204 0.000 0.000 0.736 0.060
#> SRR944040 2 0.2464 0.6839 0.004 0.892 0.012 0.000 0.092
#> SRR944041 4 0.2249 0.8038 0.008 0.000 0.000 0.896 0.096
#> SRR944042 3 0.1018 0.7523 0.000 0.000 0.968 0.016 0.016
#> SRR944043 4 0.0854 0.8383 0.008 0.000 0.004 0.976 0.012
#> SRR944044 2 0.4074 0.0595 0.000 0.636 0.000 0.000 0.364
#> SRR944046 3 0.0579 0.7531 0.000 0.000 0.984 0.008 0.008
#> SRR944045 2 0.0609 0.8075 0.000 0.980 0.000 0.000 0.020
#> SRR944047 2 0.0000 0.8264 0.000 1.000 0.000 0.000 0.000
#> SRR944048 1 0.0960 0.7986 0.972 0.004 0.000 0.008 0.016
#> SRR944049 2 0.1270 0.7999 0.000 0.948 0.000 0.000 0.052
#> SRR944050 1 0.0693 0.7998 0.980 0.000 0.000 0.008 0.012
#> SRR944051 5 0.4659 0.3864 0.012 0.488 0.000 0.000 0.500
#> SRR944052 2 0.0000 0.8264 0.000 1.000 0.000 0.000 0.000
#> SRR944053 4 0.0000 0.8411 0.000 0.000 0.000 1.000 0.000
#> SRR944054 5 0.4304 0.4088 0.000 0.484 0.000 0.000 0.516
#> SRR944055 3 0.5991 0.5847 0.008 0.204 0.616 0.000 0.172
#> SRR944056 2 0.0000 0.8264 0.000 1.000 0.000 0.000 0.000
#> SRR944057 1 0.1168 0.8127 0.960 0.000 0.000 0.032 0.008
#> SRR944058 1 0.3550 0.6984 0.760 0.000 0.000 0.236 0.004
#> SRR944059 3 0.6315 0.5418 0.008 0.228 0.568 0.000 0.196
#> SRR944060 4 0.3942 0.6176 0.000 0.000 0.232 0.748 0.020
#> SRR944061 2 0.0000 0.8264 0.000 1.000 0.000 0.000 0.000
#> SRR944062 4 0.4861 0.0244 0.428 0.000 0.000 0.548 0.024
#> SRR944063 4 0.0000 0.8411 0.000 0.000 0.000 1.000 0.000
#> SRR944064 2 0.2488 0.7306 0.004 0.872 0.000 0.000 0.124
#> SRR944065 4 0.0566 0.8400 0.004 0.000 0.000 0.984 0.012
#> SRR944066 1 0.3010 0.7718 0.824 0.000 0.000 0.172 0.004
#> SRR944067 2 0.2605 0.7045 0.000 0.852 0.000 0.000 0.148
#> SRR944068 4 0.0451 0.8399 0.000 0.000 0.004 0.988 0.008
#> SRR944069 2 0.0162 0.8243 0.000 0.996 0.000 0.000 0.004
#> SRR944070 3 0.4338 0.5282 0.000 0.000 0.696 0.280 0.024
#> SRR944071 3 0.2228 0.7505 0.004 0.000 0.900 0.004 0.092
#> SRR944072 1 0.4826 0.1444 0.508 0.000 0.000 0.472 0.020
#> SRR944073 2 0.0000 0.8264 0.000 1.000 0.000 0.000 0.000
#> SRR944075 3 0.4012 0.7106 0.008 0.036 0.788 0.000 0.168
#> SRR944074 2 0.4256 -0.2776 0.000 0.564 0.000 0.000 0.436
#> SRR944076 3 0.1043 0.7528 0.000 0.000 0.960 0.000 0.040
#> SRR944077 2 0.0000 0.8264 0.000 1.000 0.000 0.000 0.000
#> SRR944078 3 0.6646 0.2941 0.008 0.376 0.444 0.000 0.172
#> SRR944079 2 0.0000 0.8264 0.000 1.000 0.000 0.000 0.000
#> SRR944080 2 0.0404 0.8230 0.000 0.988 0.000 0.000 0.012
#> SRR944081 4 0.5144 0.5558 0.064 0.000 0.000 0.632 0.304
#> SRR944082 4 0.3169 0.7276 0.140 0.000 0.004 0.840 0.016
#> SRR944083 1 0.1830 0.8150 0.924 0.000 0.000 0.068 0.008
#> SRR944084 4 0.5908 0.4874 0.004 0.000 0.224 0.612 0.160
#> SRR944085 3 0.3516 0.7310 0.008 0.020 0.820 0.000 0.152
#> SRR944086 1 0.7055 0.3906 0.440 0.000 0.016 0.264 0.280
#> SRR944088 5 0.3895 0.4990 0.000 0.320 0.000 0.000 0.680
#> SRR944087 3 0.0992 0.7527 0.000 0.000 0.968 0.008 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.2778 0.7245 0.000 0.000 0.824 0.000 0.008 NA
#> SRR944012 4 0.3875 0.7352 0.028 0.000 0.000 0.796 0.052 NA
#> SRR944014 2 0.0000 0.8236 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944013 5 0.5170 0.5619 0.008 0.312 0.000 0.000 0.592 NA
#> SRR944015 4 0.0717 0.8027 0.000 0.000 0.016 0.976 0.000 NA
#> SRR944016 1 0.1844 0.8783 0.924 0.000 0.000 0.004 0.024 NA
#> SRR944017 2 0.4014 0.5209 0.000 0.716 0.000 0.000 0.240 NA
#> SRR944018 4 0.1901 0.7943 0.028 0.000 0.000 0.924 0.008 NA
#> SRR944019 4 0.6149 0.5617 0.124 0.000 0.000 0.604 0.112 NA
#> SRR944020 4 0.0146 0.8052 0.000 0.000 0.000 0.996 0.000 NA
#> SRR944021 2 0.0000 0.8236 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944022 4 0.0000 0.8052 0.000 0.000 0.000 1.000 0.000 NA
#> SRR944023 3 0.7124 0.4316 0.104 0.000 0.508 0.240 0.028 NA
#> SRR944024 1 0.2973 0.8550 0.860 0.000 0.000 0.084 0.016 NA
#> SRR944026 5 0.4039 0.4426 0.000 0.424 0.000 0.000 0.568 NA
#> SRR944025 2 0.3582 0.5352 0.000 0.732 0.000 0.000 0.252 NA
#> SRR944028 2 0.4101 0.3774 0.000 0.664 0.000 0.000 0.308 NA
#> SRR944029 5 0.6645 -0.0943 0.004 0.000 0.024 0.296 0.408 NA
#> SRR944030 2 0.0777 0.8152 0.000 0.972 0.000 0.000 0.024 NA
#> SRR944031 3 0.2182 0.7333 0.004 0.000 0.900 0.020 0.000 NA
#> SRR944032 5 0.6090 0.5290 0.076 0.268 0.000 0.000 0.564 NA
#> SRR944033 2 0.0000 0.8236 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944034 2 0.0777 0.8152 0.000 0.972 0.000 0.000 0.024 NA
#> SRR944036 3 0.6809 0.3726 0.256 0.000 0.496 0.024 0.036 NA
#> SRR944035 2 0.3245 0.6511 0.000 0.800 0.000 0.000 0.172 NA
#> SRR944038 3 0.3938 0.4680 0.000 0.000 0.672 0.312 0.004 NA
#> SRR944037 4 0.0405 0.8059 0.000 0.000 0.000 0.988 0.004 NA
#> SRR944039 4 0.4763 0.6777 0.132 0.000 0.000 0.728 0.036 NA
#> SRR944040 2 0.2513 0.6574 0.000 0.852 0.000 0.000 0.008 NA
#> SRR944041 4 0.3194 0.7605 0.012 0.000 0.000 0.840 0.044 NA
#> SRR944042 3 0.0717 0.7309 0.000 0.000 0.976 0.016 0.000 NA
#> SRR944043 4 0.0810 0.8043 0.004 0.000 0.008 0.976 0.004 NA
#> SRR944044 5 0.4262 0.3085 0.000 0.476 0.000 0.000 0.508 NA
#> SRR944046 3 0.0951 0.7345 0.000 0.000 0.968 0.008 0.004 NA
#> SRR944045 2 0.0713 0.8026 0.000 0.972 0.000 0.000 0.000 NA
#> SRR944047 2 0.0146 0.8232 0.000 0.996 0.000 0.000 0.004 NA
#> SRR944048 1 0.1232 0.8796 0.956 0.000 0.000 0.004 0.016 NA
#> SRR944049 2 0.2212 0.7450 0.000 0.880 0.000 0.000 0.112 NA
#> SRR944050 1 0.2594 0.8666 0.880 0.000 0.000 0.004 0.056 NA
#> SRR944051 5 0.4514 0.5909 0.008 0.288 0.000 0.000 0.660 NA
#> SRR944052 2 0.0260 0.8198 0.000 0.992 0.000 0.000 0.000 NA
#> SRR944053 4 0.0000 0.8052 0.000 0.000 0.000 1.000 0.000 NA
#> SRR944054 5 0.4233 0.6014 0.000 0.268 0.000 0.000 0.684 NA
#> SRR944055 3 0.6312 0.4253 0.000 0.252 0.412 0.000 0.012 NA
#> SRR944056 2 0.0000 0.8236 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944057 1 0.1663 0.8835 0.940 0.000 0.004 0.008 0.024 NA
#> SRR944058 1 0.4158 0.6396 0.716 0.000 0.000 0.240 0.012 NA
#> SRR944059 3 0.6403 0.3473 0.000 0.300 0.364 0.000 0.012 NA
#> SRR944060 4 0.4130 0.4836 0.004 0.000 0.300 0.672 0.000 NA
#> SRR944061 2 0.0000 0.8236 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944062 4 0.5118 0.2463 0.400 0.000 0.012 0.544 0.016 NA
#> SRR944063 4 0.0146 0.8053 0.000 0.000 0.000 0.996 0.004 NA
#> SRR944064 2 0.3834 0.5479 0.000 0.732 0.000 0.000 0.232 NA
#> SRR944065 4 0.0767 0.8036 0.012 0.000 0.000 0.976 0.008 NA
#> SRR944066 1 0.2992 0.8439 0.852 0.000 0.004 0.112 0.016 NA
#> SRR944067 2 0.3950 0.4603 0.000 0.696 0.000 0.000 0.276 NA
#> SRR944068 4 0.0520 0.8042 0.000 0.000 0.008 0.984 0.000 NA
#> SRR944069 2 0.0000 0.8236 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944070 3 0.3543 0.5942 0.000 0.000 0.756 0.224 0.004 NA
#> SRR944071 3 0.3819 0.7185 0.012 0.000 0.768 0.004 0.024 NA
#> SRR944072 4 0.5319 0.1617 0.408 0.000 0.000 0.516 0.028 NA
#> SRR944073 2 0.0363 0.8212 0.000 0.988 0.000 0.000 0.012 NA
#> SRR944075 3 0.5315 0.6190 0.000 0.084 0.584 0.000 0.016 NA
#> SRR944074 5 0.4101 0.4734 0.000 0.408 0.000 0.000 0.580 NA
#> SRR944076 3 0.2723 0.7315 0.000 0.000 0.856 0.004 0.020 NA
#> SRR944077 2 0.0000 0.8236 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944078 2 0.6516 -0.3346 0.000 0.360 0.272 0.000 0.020 NA
#> SRR944079 2 0.0146 0.8216 0.000 0.996 0.000 0.000 0.000 NA
#> SRR944080 2 0.1219 0.8012 0.000 0.948 0.000 0.000 0.048 NA
#> SRR944081 4 0.6316 0.3836 0.016 0.000 0.000 0.448 0.272 NA
#> SRR944082 4 0.3635 0.7085 0.156 0.000 0.016 0.800 0.008 NA
#> SRR944083 1 0.1168 0.8862 0.956 0.000 0.000 0.028 0.000 NA
#> SRR944084 4 0.6828 0.3124 0.004 0.000 0.216 0.496 0.076 NA
#> SRR944085 3 0.4901 0.6880 0.004 0.028 0.660 0.000 0.040 NA
#> SRR944086 5 0.8030 -0.2812 0.272 0.000 0.020 0.168 0.280 NA
#> SRR944088 5 0.5022 0.5721 0.000 0.204 0.000 0.000 0.640 NA
#> SRR944087 3 0.1615 0.7358 0.000 0.000 0.928 0.004 0.004 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "pam"]
# you can also extract it by
# res = res_list["MAD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.793 0.882 0.951 0.5018 0.494 0.494
#> 3 3 0.612 0.713 0.851 0.2041 0.885 0.771
#> 4 4 0.770 0.783 0.909 0.1368 0.876 0.702
#> 5 5 0.737 0.653 0.830 0.0517 0.947 0.837
#> 6 6 0.753 0.687 0.818 0.0370 0.964 0.881
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 1 0.802 0.6880 0.756 0.244
#> SRR944012 1 0.000 0.9373 1.000 0.000
#> SRR944014 2 0.000 0.9518 0.000 1.000
#> SRR944013 2 0.163 0.9360 0.024 0.976
#> SRR944015 1 0.000 0.9373 1.000 0.000
#> SRR944016 1 0.917 0.5051 0.668 0.332
#> SRR944017 2 0.000 0.9518 0.000 1.000
#> SRR944018 1 0.000 0.9373 1.000 0.000
#> SRR944019 1 0.821 0.6634 0.744 0.256
#> SRR944020 1 0.000 0.9373 1.000 0.000
#> SRR944021 2 0.000 0.9518 0.000 1.000
#> SRR944022 1 0.000 0.9373 1.000 0.000
#> SRR944023 1 0.000 0.9373 1.000 0.000
#> SRR944024 1 0.000 0.9373 1.000 0.000
#> SRR944026 2 0.000 0.9518 0.000 1.000
#> SRR944025 2 0.000 0.9518 0.000 1.000
#> SRR944028 2 0.000 0.9518 0.000 1.000
#> SRR944029 1 0.821 0.6714 0.744 0.256
#> SRR944030 2 0.000 0.9518 0.000 1.000
#> SRR944031 1 0.000 0.9373 1.000 0.000
#> SRR944032 2 0.000 0.9518 0.000 1.000
#> SRR944033 2 0.000 0.9518 0.000 1.000
#> SRR944034 2 0.000 0.9518 0.000 1.000
#> SRR944036 1 0.184 0.9180 0.972 0.028
#> SRR944035 2 0.000 0.9518 0.000 1.000
#> SRR944038 1 0.000 0.9373 1.000 0.000
#> SRR944037 1 0.000 0.9373 1.000 0.000
#> SRR944039 1 0.000 0.9373 1.000 0.000
#> SRR944040 2 0.000 0.9518 0.000 1.000
#> SRR944041 1 0.000 0.9373 1.000 0.000
#> SRR944042 1 0.000 0.9373 1.000 0.000
#> SRR944043 1 0.000 0.9373 1.000 0.000
#> SRR944044 2 0.000 0.9518 0.000 1.000
#> SRR944046 1 0.000 0.9373 1.000 0.000
#> SRR944045 2 0.000 0.9518 0.000 1.000
#> SRR944047 2 0.000 0.9518 0.000 1.000
#> SRR944048 2 0.358 0.8965 0.068 0.932
#> SRR944049 2 0.000 0.9518 0.000 1.000
#> SRR944050 2 0.745 0.7109 0.212 0.788
#> SRR944051 2 0.000 0.9518 0.000 1.000
#> SRR944052 2 0.000 0.9518 0.000 1.000
#> SRR944053 1 0.000 0.9373 1.000 0.000
#> SRR944054 2 0.141 0.9392 0.020 0.980
#> SRR944055 2 0.295 0.9109 0.052 0.948
#> SRR944056 2 0.000 0.9518 0.000 1.000
#> SRR944057 1 0.000 0.9373 1.000 0.000
#> SRR944058 1 0.000 0.9373 1.000 0.000
#> SRR944059 2 0.861 0.5853 0.284 0.716
#> SRR944060 1 0.000 0.9373 1.000 0.000
#> SRR944061 2 0.000 0.9518 0.000 1.000
#> SRR944062 1 0.000 0.9373 1.000 0.000
#> SRR944063 1 0.000 0.9373 1.000 0.000
#> SRR944064 2 0.000 0.9518 0.000 1.000
#> SRR944065 1 0.000 0.9373 1.000 0.000
#> SRR944066 1 0.000 0.9373 1.000 0.000
#> SRR944067 2 0.000 0.9518 0.000 1.000
#> SRR944068 1 0.000 0.9373 1.000 0.000
#> SRR944069 2 0.000 0.9518 0.000 1.000
#> SRR944070 1 0.000 0.9373 1.000 0.000
#> SRR944071 1 0.745 0.7324 0.788 0.212
#> SRR944072 1 0.000 0.9373 1.000 0.000
#> SRR944073 2 0.000 0.9518 0.000 1.000
#> SRR944075 2 1.000 -0.0218 0.488 0.512
#> SRR944074 2 0.000 0.9518 0.000 1.000
#> SRR944076 1 0.000 0.9373 1.000 0.000
#> SRR944077 2 0.000 0.9518 0.000 1.000
#> SRR944078 2 0.118 0.9419 0.016 0.984
#> SRR944079 2 0.000 0.9518 0.000 1.000
#> SRR944080 2 0.000 0.9518 0.000 1.000
#> SRR944081 2 0.966 0.3322 0.392 0.608
#> SRR944082 1 0.000 0.9373 1.000 0.000
#> SRR944083 1 0.000 0.9373 1.000 0.000
#> SRR944084 1 0.866 0.6194 0.712 0.288
#> SRR944085 1 0.767 0.7187 0.776 0.224
#> SRR944086 1 0.929 0.5082 0.656 0.344
#> SRR944088 2 0.327 0.9046 0.060 0.940
#> SRR944087 1 0.000 0.9373 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 1 0.9718 0.3611 0.452 0.288 0.260
#> SRR944012 1 0.2625 0.6630 0.916 0.000 0.084
#> SRR944014 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944013 2 0.3412 0.8263 0.124 0.876 0.000
#> SRR944015 3 0.0000 0.8313 0.000 0.000 1.000
#> SRR944016 1 0.0892 0.6589 0.980 0.020 0.000
#> SRR944017 2 0.0237 0.9270 0.004 0.996 0.000
#> SRR944018 1 0.2356 0.6739 0.928 0.000 0.072
#> SRR944019 1 0.4446 0.5809 0.856 0.032 0.112
#> SRR944020 3 0.0592 0.8299 0.012 0.000 0.988
#> SRR944021 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944022 3 0.0592 0.8288 0.012 0.000 0.988
#> SRR944023 1 0.5216 0.6256 0.740 0.000 0.260
#> SRR944024 1 0.1289 0.6752 0.968 0.000 0.032
#> SRR944026 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944025 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944028 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944029 1 0.9676 0.3690 0.460 0.288 0.252
#> SRR944030 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944031 1 0.5216 0.6256 0.740 0.000 0.260
#> SRR944032 2 0.0237 0.9269 0.004 0.996 0.000
#> SRR944033 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944034 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944036 1 0.6224 0.6286 0.728 0.032 0.240
#> SRR944035 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944038 3 0.5835 0.3749 0.340 0.000 0.660
#> SRR944037 3 0.5178 0.5282 0.256 0.000 0.744
#> SRR944039 1 0.3038 0.5985 0.896 0.000 0.104
#> SRR944040 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944041 1 0.6154 0.4262 0.592 0.000 0.408
#> SRR944042 1 0.5216 0.6256 0.740 0.000 0.260
#> SRR944043 1 0.5529 0.5732 0.704 0.000 0.296
#> SRR944044 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944046 1 0.5216 0.6256 0.740 0.000 0.260
#> SRR944045 2 0.1289 0.9086 0.032 0.968 0.000
#> SRR944047 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944048 2 0.6244 0.3176 0.440 0.560 0.000
#> SRR944049 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944050 2 0.6095 0.3439 0.392 0.608 0.000
#> SRR944051 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944052 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944053 3 0.0237 0.8306 0.004 0.000 0.996
#> SRR944054 2 0.2878 0.8554 0.096 0.904 0.000
#> SRR944055 2 0.3349 0.8406 0.108 0.888 0.004
#> SRR944056 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944057 1 0.0000 0.6648 1.000 0.000 0.000
#> SRR944058 1 0.4062 0.5140 0.836 0.000 0.164
#> SRR944059 2 0.6314 0.2998 0.392 0.604 0.004
#> SRR944060 1 0.6267 0.3115 0.548 0.000 0.452
#> SRR944061 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944062 1 0.2066 0.6741 0.940 0.000 0.060
#> SRR944063 3 0.2959 0.7508 0.100 0.000 0.900
#> SRR944064 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944065 1 0.5098 0.6254 0.752 0.000 0.248
#> SRR944066 1 0.0747 0.6612 0.984 0.000 0.016
#> SRR944067 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944068 3 0.0000 0.8313 0.000 0.000 1.000
#> SRR944069 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944070 3 0.4974 0.5916 0.236 0.000 0.764
#> SRR944071 1 0.9536 0.4000 0.488 0.252 0.260
#> SRR944072 1 0.1753 0.6455 0.952 0.000 0.048
#> SRR944073 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944075 2 0.8402 0.0829 0.376 0.532 0.092
#> SRR944074 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944076 1 0.5216 0.6256 0.740 0.000 0.260
#> SRR944077 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944078 2 0.3192 0.8399 0.112 0.888 0.000
#> SRR944079 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944080 2 0.0000 0.9291 0.000 1.000 0.000
#> SRR944081 1 0.6495 0.1398 0.536 0.460 0.004
#> SRR944082 1 0.1753 0.6762 0.952 0.000 0.048
#> SRR944083 1 0.0000 0.6648 1.000 0.000 0.000
#> SRR944084 1 0.9633 0.3694 0.464 0.300 0.236
#> SRR944085 1 0.7878 0.5689 0.668 0.172 0.160
#> SRR944086 1 0.9442 0.3357 0.456 0.360 0.184
#> SRR944088 2 0.2066 0.8868 0.060 0.940 0.000
#> SRR944087 1 0.5216 0.6256 0.740 0.000 0.260
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.0336 0.8309 0.000 0.008 0.992 0.000
#> SRR944012 1 0.4123 0.6926 0.772 0.000 0.220 0.008
#> SRR944014 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944013 2 0.1211 0.9298 0.000 0.960 0.040 0.000
#> SRR944015 4 0.0000 0.8513 0.000 0.000 0.000 1.000
#> SRR944016 1 0.3123 0.7170 0.844 0.000 0.156 0.000
#> SRR944017 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944018 3 0.4482 0.5124 0.264 0.000 0.728 0.008
#> SRR944019 1 0.5204 0.4504 0.612 0.000 0.376 0.012
#> SRR944020 4 0.0000 0.8513 0.000 0.000 0.000 1.000
#> SRR944021 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944022 4 0.0000 0.8513 0.000 0.000 0.000 1.000
#> SRR944023 3 0.0000 0.8312 0.000 0.000 1.000 0.000
#> SRR944024 1 0.3356 0.7252 0.824 0.000 0.176 0.000
#> SRR944026 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944025 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944028 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944029 3 0.0336 0.8307 0.000 0.008 0.992 0.000
#> SRR944030 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944031 3 0.0000 0.8312 0.000 0.000 1.000 0.000
#> SRR944032 2 0.0188 0.9577 0.000 0.996 0.004 0.000
#> SRR944033 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944036 3 0.0469 0.8296 0.000 0.012 0.988 0.000
#> SRR944035 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944038 4 0.4994 0.1480 0.000 0.000 0.480 0.520
#> SRR944037 4 0.4730 0.4403 0.000 0.000 0.364 0.636
#> SRR944039 1 0.4936 0.4608 0.624 0.000 0.372 0.004
#> SRR944040 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944041 3 0.5982 -0.0699 0.436 0.000 0.524 0.040
#> SRR944042 3 0.0000 0.8312 0.000 0.000 1.000 0.000
#> SRR944043 3 0.6637 0.2458 0.324 0.000 0.572 0.104
#> SRR944044 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944046 3 0.0000 0.8312 0.000 0.000 1.000 0.000
#> SRR944045 2 0.0188 0.9577 0.000 0.996 0.004 0.000
#> SRR944047 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944048 1 0.0921 0.7451 0.972 0.000 0.028 0.000
#> SRR944049 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944050 2 0.6374 0.4007 0.324 0.592 0.084 0.000
#> SRR944051 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944052 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944053 4 0.0000 0.8513 0.000 0.000 0.000 1.000
#> SRR944054 2 0.0921 0.9394 0.000 0.972 0.028 0.000
#> SRR944055 2 0.3764 0.7188 0.000 0.784 0.216 0.000
#> SRR944056 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944057 1 0.4888 0.3514 0.588 0.000 0.412 0.000
#> SRR944058 1 0.0000 0.7410 1.000 0.000 0.000 0.000
#> SRR944059 2 0.4746 0.4109 0.000 0.632 0.368 0.000
#> SRR944060 3 0.2530 0.7543 0.000 0.000 0.888 0.112
#> SRR944061 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944062 1 0.3569 0.7038 0.804 0.000 0.196 0.000
#> SRR944063 4 0.0000 0.8513 0.000 0.000 0.000 1.000
#> SRR944064 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944065 1 0.5517 0.3126 0.568 0.000 0.412 0.020
#> SRR944066 1 0.0000 0.7410 1.000 0.000 0.000 0.000
#> SRR944067 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944068 4 0.0000 0.8513 0.000 0.000 0.000 1.000
#> SRR944069 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944070 3 0.3610 0.6432 0.000 0.000 0.800 0.200
#> SRR944071 3 0.0000 0.8312 0.000 0.000 1.000 0.000
#> SRR944072 1 0.0000 0.7410 1.000 0.000 0.000 0.000
#> SRR944073 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944075 3 0.4356 0.4865 0.000 0.292 0.708 0.000
#> SRR944074 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944076 3 0.0000 0.8312 0.000 0.000 1.000 0.000
#> SRR944077 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944078 2 0.2216 0.8806 0.000 0.908 0.092 0.000
#> SRR944079 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944080 2 0.0000 0.9604 0.000 1.000 0.000 0.000
#> SRR944081 3 0.5944 0.5019 0.140 0.164 0.696 0.000
#> SRR944082 1 0.3311 0.7264 0.828 0.000 0.172 0.000
#> SRR944083 1 0.0000 0.7410 1.000 0.000 0.000 0.000
#> SRR944084 3 0.0817 0.8229 0.000 0.024 0.976 0.000
#> SRR944085 3 0.2973 0.6998 0.000 0.144 0.856 0.000
#> SRR944086 3 0.1545 0.8092 0.008 0.040 0.952 0.000
#> SRR944088 2 0.2149 0.8838 0.000 0.912 0.088 0.000
#> SRR944087 3 0.0000 0.8312 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.2583 0.5941 0.000 0.004 0.864 0.000 0.132
#> SRR944012 1 0.5823 0.3259 0.628 0.000 0.184 0.004 0.184
#> SRR944014 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944013 2 0.3400 0.8560 0.000 0.828 0.036 0.000 0.136
#> SRR944015 4 0.0162 0.9408 0.000 0.000 0.000 0.996 0.004
#> SRR944016 1 0.6420 0.0154 0.496 0.000 0.204 0.000 0.300
#> SRR944017 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944018 3 0.5847 0.1417 0.204 0.000 0.608 0.000 0.188
#> SRR944019 5 0.6608 0.1616 0.300 0.000 0.244 0.000 0.456
#> SRR944020 4 0.2690 0.8616 0.000 0.000 0.000 0.844 0.156
#> SRR944021 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944022 4 0.1341 0.9364 0.000 0.000 0.000 0.944 0.056
#> SRR944023 3 0.0000 0.6015 0.000 0.000 1.000 0.000 0.000
#> SRR944024 1 0.3527 0.4940 0.804 0.000 0.172 0.000 0.024
#> SRR944026 2 0.1732 0.9238 0.000 0.920 0.000 0.000 0.080
#> SRR944025 2 0.0880 0.9424 0.000 0.968 0.000 0.000 0.032
#> SRR944028 2 0.1478 0.9318 0.000 0.936 0.000 0.000 0.064
#> SRR944029 3 0.2605 0.5019 0.000 0.000 0.852 0.000 0.148
#> SRR944030 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944031 3 0.2561 0.5848 0.000 0.000 0.856 0.000 0.144
#> SRR944032 2 0.1608 0.9281 0.000 0.928 0.000 0.000 0.072
#> SRR944033 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944036 3 0.0451 0.6030 0.000 0.008 0.988 0.000 0.004
#> SRR944035 2 0.0880 0.9424 0.000 0.968 0.000 0.000 0.032
#> SRR944038 3 0.6763 0.0400 0.000 0.000 0.392 0.332 0.276
#> SRR944037 5 0.6403 0.0128 0.000 0.000 0.256 0.232 0.512
#> SRR944039 5 0.6655 0.1829 0.296 0.000 0.260 0.000 0.444
#> SRR944040 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944041 5 0.6453 0.0964 0.184 0.000 0.272 0.008 0.536
#> SRR944042 3 0.3636 0.5365 0.000 0.000 0.728 0.000 0.272
#> SRR944043 3 0.6947 0.1090 0.172 0.000 0.584 0.084 0.160
#> SRR944044 2 0.1478 0.9299 0.000 0.936 0.000 0.000 0.064
#> SRR944046 3 0.3636 0.5365 0.000 0.000 0.728 0.000 0.272
#> SRR944045 2 0.0290 0.9465 0.000 0.992 0.008 0.000 0.000
#> SRR944047 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944048 1 0.1386 0.5750 0.952 0.000 0.032 0.000 0.016
#> SRR944049 2 0.0290 0.9478 0.000 0.992 0.000 0.000 0.008
#> SRR944050 1 0.7737 0.0168 0.324 0.324 0.052 0.000 0.300
#> SRR944051 2 0.1732 0.9238 0.000 0.920 0.000 0.000 0.080
#> SRR944052 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944053 4 0.0000 0.9414 0.000 0.000 0.000 1.000 0.000
#> SRR944054 2 0.3064 0.8706 0.000 0.856 0.036 0.000 0.108
#> SRR944055 2 0.3419 0.7637 0.000 0.804 0.180 0.000 0.016
#> SRR944056 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944057 1 0.6248 0.1076 0.524 0.000 0.176 0.000 0.300
#> SRR944058 1 0.0000 0.5794 1.000 0.000 0.000 0.000 0.000
#> SRR944059 2 0.4210 0.3423 0.000 0.588 0.412 0.000 0.000
#> SRR944060 3 0.4768 0.4753 0.000 0.000 0.656 0.040 0.304
#> SRR944061 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944062 1 0.4634 0.3754 0.744 0.000 0.120 0.000 0.136
#> SRR944063 4 0.1608 0.9298 0.000 0.000 0.000 0.928 0.072
#> SRR944064 2 0.0880 0.9424 0.000 0.968 0.000 0.000 0.032
#> SRR944065 3 0.6917 -0.0907 0.312 0.000 0.388 0.004 0.296
#> SRR944066 1 0.1792 0.5556 0.916 0.000 0.000 0.000 0.084
#> SRR944067 2 0.0880 0.9424 0.000 0.968 0.000 0.000 0.032
#> SRR944068 4 0.0162 0.9408 0.000 0.000 0.000 0.996 0.004
#> SRR944069 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944070 3 0.5275 0.4558 0.000 0.000 0.640 0.084 0.276
#> SRR944071 3 0.0609 0.6041 0.000 0.000 0.980 0.000 0.020
#> SRR944072 1 0.3966 0.3633 0.664 0.000 0.000 0.000 0.336
#> SRR944073 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944075 3 0.5490 0.1973 0.000 0.372 0.556 0.000 0.072
#> SRR944074 2 0.1671 0.9256 0.000 0.924 0.000 0.000 0.076
#> SRR944076 3 0.0000 0.6015 0.000 0.000 1.000 0.000 0.000
#> SRR944077 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944078 2 0.1544 0.9089 0.000 0.932 0.068 0.000 0.000
#> SRR944079 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.9492 0.000 1.000 0.000 0.000 0.000
#> SRR944081 3 0.5606 0.1619 0.000 0.104 0.600 0.000 0.296
#> SRR944082 1 0.3282 0.4875 0.804 0.000 0.188 0.000 0.008
#> SRR944083 1 0.0162 0.5795 0.996 0.000 0.000 0.000 0.004
#> SRR944084 3 0.1800 0.5785 0.000 0.020 0.932 0.000 0.048
#> SRR944085 3 0.2561 0.4860 0.000 0.144 0.856 0.000 0.000
#> SRR944086 3 0.2582 0.5531 0.004 0.024 0.892 0.000 0.080
#> SRR944088 2 0.3409 0.8385 0.000 0.824 0.032 0.000 0.144
#> SRR944087 3 0.3636 0.5365 0.000 0.000 0.728 0.000 0.272
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.3888 0.4181 0.028 0.008 0.740 0.000 0.000 0.224
#> SRR944012 1 0.4633 0.6739 0.744 0.000 0.124 0.000 0.044 0.088
#> SRR944014 2 0.0000 0.9312 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944013 2 0.3589 0.8507 0.148 0.800 0.040 0.000 0.000 0.012
#> SRR944015 4 0.0146 0.7946 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR944016 5 0.0972 0.8578 0.028 0.000 0.008 0.000 0.964 0.000
#> SRR944017 2 0.0260 0.9305 0.008 0.992 0.000 0.000 0.000 0.000
#> SRR944018 3 0.5294 0.3417 0.156 0.000 0.668 0.000 0.032 0.144
#> SRR944019 5 0.2264 0.8055 0.012 0.000 0.004 0.000 0.888 0.096
#> SRR944020 4 0.4242 0.5289 0.016 0.000 0.000 0.536 0.000 0.448
#> SRR944021 2 0.0000 0.9312 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944022 4 0.3104 0.7709 0.016 0.000 0.000 0.800 0.000 0.184
#> SRR944023 3 0.0146 0.5725 0.004 0.000 0.996 0.000 0.000 0.000
#> SRR944024 1 0.4042 0.7911 0.784 0.000 0.096 0.000 0.100 0.020
#> SRR944026 2 0.2558 0.8770 0.156 0.840 0.000 0.000 0.000 0.004
#> SRR944025 2 0.1267 0.9194 0.060 0.940 0.000 0.000 0.000 0.000
#> SRR944028 2 0.2100 0.9008 0.112 0.884 0.000 0.000 0.000 0.004
#> SRR944029 3 0.3253 0.5160 0.044 0.008 0.844 0.000 0.008 0.096
#> SRR944030 2 0.0000 0.9312 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944031 3 0.3755 0.4094 0.036 0.000 0.744 0.000 0.000 0.220
#> SRR944032 2 0.2260 0.8892 0.140 0.860 0.000 0.000 0.000 0.000
#> SRR944033 2 0.0000 0.9312 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.9312 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944036 3 0.0717 0.5740 0.000 0.008 0.976 0.000 0.000 0.016
#> SRR944035 2 0.1267 0.9194 0.060 0.940 0.000 0.000 0.000 0.000
#> SRR944038 6 0.6706 0.3629 0.036 0.000 0.220 0.312 0.004 0.428
#> SRR944037 6 0.3827 0.4939 0.028 0.000 0.096 0.036 0.020 0.820
#> SRR944039 5 0.4948 0.6015 0.024 0.000 0.168 0.000 0.696 0.112
#> SRR944040 2 0.0000 0.9312 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944041 6 0.3514 0.4279 0.040 0.000 0.096 0.000 0.036 0.828
#> SRR944042 3 0.4524 0.1147 0.036 0.000 0.560 0.000 0.000 0.404
#> SRR944043 3 0.5415 -0.2342 0.048 0.000 0.464 0.032 0.000 0.456
#> SRR944044 2 0.2278 0.8894 0.128 0.868 0.000 0.000 0.000 0.004
#> SRR944046 3 0.4524 0.1147 0.036 0.000 0.560 0.000 0.000 0.404
#> SRR944045 2 0.0363 0.9284 0.000 0.988 0.012 0.000 0.000 0.000
#> SRR944047 2 0.0000 0.9312 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944048 1 0.3319 0.7857 0.800 0.000 0.036 0.000 0.164 0.000
#> SRR944049 2 0.0260 0.9301 0.008 0.992 0.000 0.000 0.000 0.000
#> SRR944050 5 0.0865 0.8313 0.000 0.036 0.000 0.000 0.964 0.000
#> SRR944051 2 0.2558 0.8770 0.156 0.840 0.000 0.000 0.000 0.004
#> SRR944052 2 0.0000 0.9312 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944053 4 0.0260 0.7967 0.000 0.000 0.000 0.992 0.000 0.008
#> SRR944054 2 0.3233 0.8641 0.132 0.828 0.016 0.000 0.000 0.024
#> SRR944055 2 0.3522 0.7553 0.000 0.784 0.172 0.000 0.000 0.044
#> SRR944056 2 0.0000 0.9312 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944057 5 0.0972 0.8558 0.008 0.000 0.028 0.000 0.964 0.000
#> SRR944058 1 0.2996 0.7727 0.772 0.000 0.000 0.000 0.228 0.000
#> SRR944059 2 0.3868 0.1243 0.000 0.504 0.496 0.000 0.000 0.000
#> SRR944060 6 0.5430 0.0272 0.036 0.000 0.432 0.036 0.004 0.492
#> SRR944061 2 0.0000 0.9312 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944062 1 0.3803 0.6962 0.808 0.000 0.060 0.000 0.032 0.100
#> SRR944063 4 0.3717 0.7186 0.016 0.000 0.000 0.708 0.000 0.276
#> SRR944064 2 0.1267 0.9194 0.060 0.940 0.000 0.000 0.000 0.000
#> SRR944065 6 0.4756 0.5014 0.112 0.000 0.224 0.000 0.000 0.664
#> SRR944066 1 0.3828 0.4753 0.560 0.000 0.000 0.000 0.440 0.000
#> SRR944067 2 0.1267 0.9194 0.060 0.940 0.000 0.000 0.000 0.000
#> SRR944068 4 0.0146 0.7946 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR944069 2 0.0000 0.9312 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944070 3 0.5539 -0.0620 0.036 0.000 0.488 0.044 0.004 0.428
#> SRR944071 3 0.1327 0.5564 0.000 0.000 0.936 0.000 0.000 0.064
#> SRR944072 5 0.0865 0.8517 0.036 0.000 0.000 0.000 0.964 0.000
#> SRR944073 2 0.0000 0.9312 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944075 3 0.5632 0.1075 0.024 0.384 0.508 0.000 0.000 0.084
#> SRR944074 2 0.2482 0.8812 0.148 0.848 0.000 0.000 0.000 0.004
#> SRR944076 3 0.0000 0.5726 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR944077 2 0.0000 0.9312 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944078 2 0.1556 0.8974 0.000 0.920 0.080 0.000 0.000 0.000
#> SRR944079 2 0.0000 0.9312 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.9312 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944081 3 0.5513 0.3913 0.148 0.020 0.680 0.000 0.032 0.120
#> SRR944082 1 0.3976 0.7773 0.776 0.000 0.128 0.000 0.088 0.008
#> SRR944083 1 0.3126 0.7621 0.752 0.000 0.000 0.000 0.248 0.000
#> SRR944084 3 0.1552 0.5677 0.004 0.020 0.940 0.000 0.000 0.036
#> SRR944085 3 0.2278 0.4770 0.004 0.128 0.868 0.000 0.000 0.000
#> SRR944086 3 0.2372 0.5538 0.056 0.012 0.904 0.000 0.012 0.016
#> SRR944088 2 0.3875 0.8323 0.120 0.796 0.024 0.000 0.000 0.060
#> SRR944087 3 0.4524 0.1147 0.036 0.000 0.560 0.000 0.000 0.404
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "mclust"]
# you can also extract it by
# res = res_list["MAD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.981 0.991 0.4787 0.518 0.518
#> 3 3 0.564 0.580 0.773 0.2212 0.972 0.947
#> 4 4 0.728 0.769 0.878 0.2037 0.766 0.539
#> 5 5 0.721 0.776 0.853 0.0928 0.895 0.655
#> 6 6 0.813 0.841 0.902 0.0464 0.981 0.911
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.0000 0.979 0.000 1.000
#> SRR944012 1 0.0000 0.997 1.000 0.000
#> SRR944014 2 0.0000 0.979 0.000 1.000
#> SRR944013 1 0.0000 0.997 1.000 0.000
#> SRR944015 1 0.0000 0.997 1.000 0.000
#> SRR944016 1 0.0000 0.997 1.000 0.000
#> SRR944017 1 0.0000 0.997 1.000 0.000
#> SRR944018 1 0.0000 0.997 1.000 0.000
#> SRR944019 1 0.0000 0.997 1.000 0.000
#> SRR944020 1 0.0000 0.997 1.000 0.000
#> SRR944021 2 0.0000 0.979 0.000 1.000
#> SRR944022 1 0.0000 0.997 1.000 0.000
#> SRR944023 1 0.0000 0.997 1.000 0.000
#> SRR944024 1 0.0000 0.997 1.000 0.000
#> SRR944026 1 0.0000 0.997 1.000 0.000
#> SRR944025 1 0.0000 0.997 1.000 0.000
#> SRR944028 1 0.0000 0.997 1.000 0.000
#> SRR944029 1 0.0000 0.997 1.000 0.000
#> SRR944030 2 0.4690 0.887 0.100 0.900
#> SRR944031 2 0.1184 0.975 0.016 0.984
#> SRR944032 1 0.0000 0.997 1.000 0.000
#> SRR944033 2 0.0000 0.979 0.000 1.000
#> SRR944034 2 0.0000 0.979 0.000 1.000
#> SRR944036 1 0.0000 0.997 1.000 0.000
#> SRR944035 1 0.0672 0.990 0.992 0.008
#> SRR944038 2 0.1184 0.975 0.016 0.984
#> SRR944037 1 0.0000 0.997 1.000 0.000
#> SRR944039 1 0.0000 0.997 1.000 0.000
#> SRR944040 2 0.0000 0.979 0.000 1.000
#> SRR944041 1 0.0000 0.997 1.000 0.000
#> SRR944042 2 0.1184 0.975 0.016 0.984
#> SRR944043 1 0.0000 0.997 1.000 0.000
#> SRR944044 1 0.0000 0.997 1.000 0.000
#> SRR944046 2 0.0000 0.979 0.000 1.000
#> SRR944045 2 0.0000 0.979 0.000 1.000
#> SRR944047 2 0.0000 0.979 0.000 1.000
#> SRR944048 1 0.0000 0.997 1.000 0.000
#> SRR944049 1 0.0672 0.990 0.992 0.008
#> SRR944050 1 0.0000 0.997 1.000 0.000
#> SRR944051 1 0.0000 0.997 1.000 0.000
#> SRR944052 2 0.1414 0.972 0.020 0.980
#> SRR944053 1 0.0000 0.997 1.000 0.000
#> SRR944054 1 0.0000 0.997 1.000 0.000
#> SRR944055 2 0.0000 0.979 0.000 1.000
#> SRR944056 2 0.0000 0.979 0.000 1.000
#> SRR944057 1 0.0000 0.997 1.000 0.000
#> SRR944058 1 0.0000 0.997 1.000 0.000
#> SRR944059 2 0.1184 0.975 0.016 0.984
#> SRR944060 1 0.4815 0.881 0.896 0.104
#> SRR944061 2 0.1184 0.975 0.016 0.984
#> SRR944062 1 0.0000 0.997 1.000 0.000
#> SRR944063 1 0.0000 0.997 1.000 0.000
#> SRR944064 1 0.0000 0.997 1.000 0.000
#> SRR944065 1 0.0000 0.997 1.000 0.000
#> SRR944066 1 0.0000 0.997 1.000 0.000
#> SRR944067 1 0.0000 0.997 1.000 0.000
#> SRR944068 1 0.0000 0.997 1.000 0.000
#> SRR944069 2 0.0376 0.978 0.004 0.996
#> SRR944070 2 0.0376 0.978 0.004 0.996
#> SRR944071 2 0.9209 0.509 0.336 0.664
#> SRR944072 1 0.0000 0.997 1.000 0.000
#> SRR944073 2 0.0000 0.979 0.000 1.000
#> SRR944075 2 0.1184 0.975 0.016 0.984
#> SRR944074 1 0.0000 0.997 1.000 0.000
#> SRR944076 2 0.1184 0.975 0.016 0.984
#> SRR944077 2 0.0000 0.979 0.000 1.000
#> SRR944078 2 0.0000 0.979 0.000 1.000
#> SRR944079 2 0.0000 0.979 0.000 1.000
#> SRR944080 2 0.0000 0.979 0.000 1.000
#> SRR944081 1 0.0000 0.997 1.000 0.000
#> SRR944082 1 0.0000 0.997 1.000 0.000
#> SRR944083 1 0.0000 0.997 1.000 0.000
#> SRR944084 1 0.0000 0.997 1.000 0.000
#> SRR944085 2 0.1184 0.975 0.016 0.984
#> SRR944086 1 0.0000 0.997 1.000 0.000
#> SRR944088 1 0.0000 0.997 1.000 0.000
#> SRR944087 2 0.1184 0.975 0.016 0.984
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 2 0.6267 -0.2314 0.000 0.548 0.452
#> SRR944012 1 0.1163 0.8713 0.972 0.000 0.028
#> SRR944014 2 0.1031 0.5427 0.000 0.976 0.024
#> SRR944013 1 0.0237 0.8723 0.996 0.000 0.004
#> SRR944015 1 0.5621 0.7500 0.692 0.000 0.308
#> SRR944016 1 0.5058 0.8205 0.756 0.000 0.244
#> SRR944017 1 0.0424 0.8717 0.992 0.008 0.000
#> SRR944018 1 0.4062 0.8432 0.836 0.000 0.164
#> SRR944019 1 0.1163 0.8713 0.972 0.000 0.028
#> SRR944020 1 0.1643 0.8720 0.956 0.000 0.044
#> SRR944021 2 0.1753 0.5410 0.000 0.952 0.048
#> SRR944022 1 0.1529 0.8719 0.960 0.000 0.040
#> SRR944023 1 0.6217 0.7665 0.712 0.024 0.264
#> SRR944024 1 0.5058 0.8205 0.756 0.000 0.244
#> SRR944026 1 0.1031 0.8708 0.976 0.000 0.024
#> SRR944025 1 0.3966 0.8146 0.876 0.024 0.100
#> SRR944028 1 0.3528 0.8253 0.892 0.016 0.092
#> SRR944029 1 0.1031 0.8708 0.976 0.000 0.024
#> SRR944030 2 0.3120 0.5049 0.012 0.908 0.080
#> SRR944031 2 0.6286 -0.2620 0.000 0.536 0.464
#> SRR944032 1 0.0747 0.8698 0.984 0.016 0.000
#> SRR944033 2 0.0892 0.5424 0.000 0.980 0.020
#> SRR944034 2 0.4324 0.3739 0.112 0.860 0.028
#> SRR944036 1 0.6322 0.7525 0.700 0.024 0.276
#> SRR944035 1 0.4609 0.7889 0.844 0.028 0.128
#> SRR944038 2 0.6664 -0.3081 0.008 0.528 0.464
#> SRR944037 1 0.1753 0.8739 0.952 0.000 0.048
#> SRR944039 1 0.1163 0.8733 0.972 0.000 0.028
#> SRR944040 2 0.5363 0.2246 0.000 0.724 0.276
#> SRR944041 1 0.1163 0.8713 0.972 0.000 0.028
#> SRR944042 2 0.6280 -0.2514 0.000 0.540 0.460
#> SRR944043 1 0.4062 0.8432 0.836 0.000 0.164
#> SRR944044 1 0.1031 0.8708 0.976 0.000 0.024
#> SRR944046 2 0.6274 -0.2392 0.000 0.544 0.456
#> SRR944045 2 0.1411 0.5342 0.000 0.964 0.036
#> SRR944047 2 0.1289 0.5371 0.000 0.968 0.032
#> SRR944048 1 0.5058 0.8205 0.756 0.000 0.244
#> SRR944049 1 0.6250 0.7136 0.776 0.104 0.120
#> SRR944050 1 0.5058 0.8205 0.756 0.000 0.244
#> SRR944051 1 0.1031 0.8708 0.976 0.000 0.024
#> SRR944052 2 0.5450 0.4152 0.012 0.760 0.228
#> SRR944053 1 0.1529 0.8719 0.960 0.000 0.040
#> SRR944054 1 0.1031 0.8708 0.976 0.000 0.024
#> SRR944055 2 0.6126 -0.0994 0.000 0.600 0.400
#> SRR944056 2 0.2165 0.5355 0.000 0.936 0.064
#> SRR944057 1 0.5058 0.8205 0.756 0.000 0.244
#> SRR944058 1 0.5016 0.8220 0.760 0.000 0.240
#> SRR944059 2 0.6305 -0.3425 0.000 0.516 0.484
#> SRR944060 1 0.8065 0.3435 0.484 0.064 0.452
#> SRR944061 2 0.4555 0.4587 0.000 0.800 0.200
#> SRR944062 1 0.5058 0.8205 0.756 0.000 0.244
#> SRR944063 1 0.1529 0.8719 0.960 0.000 0.040
#> SRR944064 1 0.1015 0.8707 0.980 0.012 0.008
#> SRR944065 1 0.4531 0.8419 0.824 0.008 0.168
#> SRR944066 1 0.5058 0.8205 0.756 0.000 0.244
#> SRR944067 1 0.4349 0.7943 0.852 0.020 0.128
#> SRR944068 1 0.5621 0.7500 0.692 0.000 0.308
#> SRR944069 2 0.3551 0.4660 0.000 0.868 0.132
#> SRR944070 2 0.6664 -0.3024 0.008 0.528 0.464
#> SRR944071 3 0.9836 0.2221 0.268 0.312 0.420
#> SRR944072 1 0.5016 0.8220 0.760 0.000 0.240
#> SRR944073 2 0.0237 0.5438 0.000 0.996 0.004
#> SRR944075 2 0.6286 -0.2652 0.000 0.536 0.464
#> SRR944074 1 0.1031 0.8708 0.976 0.000 0.024
#> SRR944076 3 0.6302 0.1965 0.000 0.480 0.520
#> SRR944077 2 0.0424 0.5440 0.000 0.992 0.008
#> SRR944078 2 0.6111 -0.0887 0.000 0.604 0.396
#> SRR944079 2 0.0747 0.5440 0.000 0.984 0.016
#> SRR944080 2 0.3941 0.4475 0.000 0.844 0.156
#> SRR944081 1 0.1031 0.8708 0.976 0.000 0.024
#> SRR944082 1 0.4504 0.8375 0.804 0.000 0.196
#> SRR944083 1 0.5058 0.8205 0.756 0.000 0.244
#> SRR944084 1 0.4002 0.8454 0.840 0.000 0.160
#> SRR944085 3 0.7072 0.2531 0.020 0.476 0.504
#> SRR944086 1 0.0661 0.8717 0.988 0.008 0.004
#> SRR944088 1 0.1031 0.8708 0.976 0.000 0.024
#> SRR944087 2 0.6280 -0.2514 0.000 0.540 0.460
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.2011 0.9034 0.000 0.080 0.920 0.000
#> SRR944012 4 0.0336 0.8245 0.008 0.000 0.000 0.992
#> SRR944014 2 0.0469 0.9325 0.000 0.988 0.012 0.000
#> SRR944013 4 0.1706 0.8154 0.016 0.000 0.036 0.948
#> SRR944015 4 0.3168 0.7723 0.060 0.000 0.056 0.884
#> SRR944016 1 0.0000 0.8640 1.000 0.000 0.000 0.000
#> SRR944017 4 0.5705 0.6317 0.280 0.008 0.040 0.672
#> SRR944018 4 0.5300 0.6264 0.308 0.000 0.028 0.664
#> SRR944019 4 0.0469 0.8245 0.012 0.000 0.000 0.988
#> SRR944020 4 0.0524 0.8245 0.008 0.000 0.004 0.988
#> SRR944021 2 0.0469 0.9325 0.000 0.988 0.012 0.000
#> SRR944022 4 0.0336 0.8245 0.008 0.000 0.000 0.992
#> SRR944023 1 0.7389 -0.1750 0.448 0.024 0.088 0.440
#> SRR944024 1 0.0000 0.8640 1.000 0.000 0.000 0.000
#> SRR944026 4 0.0376 0.8215 0.000 0.004 0.004 0.992
#> SRR944025 4 0.5852 0.6216 0.284 0.012 0.040 0.664
#> SRR944028 4 0.5827 0.6270 0.280 0.012 0.040 0.668
#> SRR944029 4 0.0188 0.8237 0.004 0.000 0.000 0.996
#> SRR944030 2 0.0188 0.9274 0.000 0.996 0.000 0.004
#> SRR944031 3 0.2011 0.9034 0.000 0.080 0.920 0.000
#> SRR944032 4 0.5517 0.5927 0.316 0.000 0.036 0.648
#> SRR944033 2 0.0336 0.9320 0.000 0.992 0.008 0.000
#> SRR944034 2 0.8384 -0.2183 0.228 0.376 0.024 0.372
#> SRR944036 4 0.7435 0.0967 0.440 0.024 0.092 0.444
#> SRR944035 4 0.5960 0.6217 0.280 0.020 0.036 0.664
#> SRR944038 3 0.5287 0.7486 0.008 0.076 0.760 0.156
#> SRR944037 4 0.0336 0.8245 0.008 0.000 0.000 0.992
#> SRR944039 4 0.5022 0.6968 0.220 0.000 0.044 0.736
#> SRR944040 3 0.3942 0.7369 0.000 0.236 0.764 0.000
#> SRR944041 4 0.0188 0.8237 0.004 0.000 0.000 0.996
#> SRR944042 3 0.2011 0.9034 0.000 0.080 0.920 0.000
#> SRR944043 4 0.5535 0.6192 0.304 0.000 0.040 0.656
#> SRR944044 4 0.0376 0.8215 0.000 0.004 0.004 0.992
#> SRR944046 3 0.2011 0.9034 0.000 0.080 0.920 0.000
#> SRR944045 2 0.1635 0.9027 0.000 0.948 0.044 0.008
#> SRR944047 2 0.0469 0.9325 0.000 0.988 0.012 0.000
#> SRR944048 1 0.0000 0.8640 1.000 0.000 0.000 0.000
#> SRR944049 4 0.5887 0.6325 0.272 0.016 0.040 0.672
#> SRR944050 1 0.1938 0.8403 0.936 0.000 0.012 0.052
#> SRR944051 4 0.0844 0.8236 0.012 0.004 0.004 0.980
#> SRR944052 2 0.1706 0.8955 0.000 0.948 0.036 0.016
#> SRR944053 4 0.0336 0.8245 0.008 0.000 0.000 0.992
#> SRR944054 4 0.0188 0.8224 0.000 0.004 0.000 0.996
#> SRR944055 3 0.2011 0.9034 0.000 0.080 0.920 0.000
#> SRR944056 2 0.0188 0.9304 0.000 0.996 0.004 0.000
#> SRR944057 1 0.0000 0.8640 1.000 0.000 0.000 0.000
#> SRR944058 1 0.3862 0.7553 0.824 0.000 0.024 0.152
#> SRR944059 3 0.2011 0.9034 0.000 0.080 0.920 0.000
#> SRR944060 3 0.6591 0.0736 0.028 0.032 0.524 0.416
#> SRR944061 2 0.0336 0.9303 0.000 0.992 0.008 0.000
#> SRR944062 1 0.0000 0.8640 1.000 0.000 0.000 0.000
#> SRR944063 4 0.0336 0.8245 0.008 0.000 0.000 0.992
#> SRR944064 4 0.5882 0.3106 0.436 0.012 0.016 0.536
#> SRR944065 4 0.3013 0.7891 0.080 0.000 0.032 0.888
#> SRR944066 1 0.0000 0.8640 1.000 0.000 0.000 0.000
#> SRR944067 4 0.5852 0.6216 0.284 0.012 0.040 0.664
#> SRR944068 4 0.3168 0.7723 0.060 0.000 0.056 0.884
#> SRR944069 2 0.0336 0.9319 0.000 0.992 0.008 0.000
#> SRR944070 3 0.5219 0.7467 0.008 0.072 0.764 0.156
#> SRR944071 3 0.3611 0.8594 0.000 0.080 0.860 0.060
#> SRR944072 1 0.4898 0.5719 0.716 0.000 0.024 0.260
#> SRR944073 2 0.0657 0.9318 0.000 0.984 0.012 0.004
#> SRR944075 3 0.1978 0.8961 0.000 0.068 0.928 0.004
#> SRR944074 4 0.0376 0.8215 0.000 0.004 0.004 0.992
#> SRR944076 3 0.2011 0.9034 0.000 0.080 0.920 0.000
#> SRR944077 2 0.0469 0.9325 0.000 0.988 0.012 0.000
#> SRR944078 3 0.2081 0.9010 0.000 0.084 0.916 0.000
#> SRR944079 2 0.0469 0.9325 0.000 0.988 0.012 0.000
#> SRR944080 2 0.0188 0.9308 0.000 0.996 0.004 0.000
#> SRR944081 4 0.0188 0.8237 0.004 0.000 0.000 0.996
#> SRR944082 1 0.3577 0.7476 0.832 0.000 0.012 0.156
#> SRR944083 1 0.0000 0.8640 1.000 0.000 0.000 0.000
#> SRR944084 4 0.0657 0.8223 0.004 0.000 0.012 0.984
#> SRR944085 3 0.2197 0.9018 0.000 0.080 0.916 0.004
#> SRR944086 4 0.4379 0.7382 0.172 0.000 0.036 0.792
#> SRR944088 4 0.0188 0.8237 0.004 0.000 0.000 0.996
#> SRR944087 3 0.2011 0.9034 0.000 0.080 0.920 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.1732 0.882 0.000 0.080 0.920 0.000 0.000
#> SRR944012 4 0.1043 0.791 0.000 0.000 0.000 0.960 0.040
#> SRR944014 2 0.0510 0.978 0.000 0.984 0.016 0.000 0.000
#> SRR944013 4 0.3920 0.641 0.004 0.000 0.004 0.724 0.268
#> SRR944015 4 0.3740 0.543 0.012 0.000 0.008 0.784 0.196
#> SRR944016 1 0.0162 0.856 0.996 0.000 0.000 0.000 0.004
#> SRR944017 5 0.5470 0.663 0.080 0.000 0.000 0.332 0.588
#> SRR944018 4 0.3590 0.639 0.092 0.000 0.000 0.828 0.080
#> SRR944019 4 0.1197 0.791 0.000 0.000 0.000 0.952 0.048
#> SRR944020 4 0.0324 0.781 0.000 0.000 0.004 0.992 0.004
#> SRR944021 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> SRR944022 4 0.0324 0.781 0.000 0.000 0.004 0.992 0.004
#> SRR944023 1 0.7045 0.512 0.596 0.008 0.168 0.084 0.144
#> SRR944024 1 0.0000 0.856 1.000 0.000 0.000 0.000 0.000
#> SRR944026 4 0.3366 0.727 0.000 0.000 0.004 0.784 0.212
#> SRR944025 5 0.5232 0.744 0.084 0.000 0.000 0.268 0.648
#> SRR944028 5 0.5466 0.735 0.084 0.000 0.004 0.284 0.628
#> SRR944029 4 0.2890 0.762 0.000 0.000 0.004 0.836 0.160
#> SRR944030 2 0.0579 0.974 0.000 0.984 0.000 0.008 0.008
#> SRR944031 3 0.0609 0.894 0.000 0.020 0.980 0.000 0.000
#> SRR944032 5 0.6758 0.508 0.304 0.000 0.000 0.292 0.404
#> SRR944033 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> SRR944034 5 0.7849 0.516 0.080 0.244 0.000 0.264 0.412
#> SRR944036 1 0.6980 0.520 0.600 0.008 0.168 0.076 0.148
#> SRR944035 5 0.5232 0.744 0.084 0.000 0.000 0.268 0.648
#> SRR944038 3 0.6230 0.496 0.000 0.020 0.528 0.092 0.360
#> SRR944037 4 0.0324 0.781 0.000 0.000 0.004 0.992 0.004
#> SRR944039 4 0.3359 0.687 0.052 0.000 0.000 0.840 0.108
#> SRR944040 3 0.2690 0.824 0.000 0.156 0.844 0.000 0.000
#> SRR944041 4 0.0963 0.791 0.000 0.000 0.000 0.964 0.036
#> SRR944042 3 0.1399 0.885 0.000 0.020 0.952 0.000 0.028
#> SRR944043 4 0.3460 0.668 0.076 0.000 0.004 0.844 0.076
#> SRR944044 4 0.3366 0.727 0.000 0.000 0.004 0.784 0.212
#> SRR944046 3 0.0609 0.894 0.000 0.020 0.980 0.000 0.000
#> SRR944045 2 0.1608 0.925 0.000 0.928 0.072 0.000 0.000
#> SRR944047 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> SRR944048 1 0.0000 0.856 1.000 0.000 0.000 0.000 0.000
#> SRR944049 5 0.5542 0.737 0.084 0.008 0.000 0.276 0.632
#> SRR944050 1 0.0912 0.849 0.972 0.000 0.000 0.012 0.016
#> SRR944051 4 0.3333 0.726 0.000 0.000 0.004 0.788 0.208
#> SRR944052 2 0.1197 0.950 0.000 0.952 0.048 0.000 0.000
#> SRR944053 4 0.0324 0.781 0.000 0.000 0.004 0.992 0.004
#> SRR944054 4 0.3300 0.733 0.000 0.000 0.004 0.792 0.204
#> SRR944055 3 0.2020 0.873 0.000 0.100 0.900 0.000 0.000
#> SRR944056 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> SRR944057 1 0.0000 0.856 1.000 0.000 0.000 0.000 0.000
#> SRR944058 1 0.3141 0.771 0.852 0.000 0.000 0.108 0.040
#> SRR944059 3 0.0609 0.894 0.000 0.020 0.980 0.000 0.000
#> SRR944060 5 0.6951 -0.280 0.012 0.008 0.388 0.164 0.428
#> SRR944061 2 0.0162 0.983 0.000 0.996 0.004 0.000 0.000
#> SRR944062 1 0.0000 0.856 1.000 0.000 0.000 0.000 0.000
#> SRR944063 4 0.0324 0.781 0.000 0.000 0.004 0.992 0.004
#> SRR944064 1 0.5107 0.464 0.632 0.000 0.004 0.048 0.316
#> SRR944065 4 0.2490 0.774 0.020 0.000 0.004 0.896 0.080
#> SRR944066 1 0.0000 0.856 1.000 0.000 0.000 0.000 0.000
#> SRR944067 5 0.5232 0.744 0.084 0.000 0.000 0.268 0.648
#> SRR944068 4 0.3740 0.543 0.012 0.000 0.008 0.784 0.196
#> SRR944069 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> SRR944070 3 0.6230 0.496 0.000 0.020 0.528 0.092 0.360
#> SRR944071 3 0.3046 0.818 0.000 0.020 0.876 0.028 0.076
#> SRR944072 1 0.3983 0.700 0.784 0.000 0.000 0.164 0.052
#> SRR944073 2 0.0609 0.974 0.000 0.980 0.000 0.000 0.020
#> SRR944075 3 0.1965 0.875 0.000 0.096 0.904 0.000 0.000
#> SRR944074 4 0.3366 0.727 0.000 0.000 0.004 0.784 0.212
#> SRR944076 3 0.0609 0.894 0.000 0.020 0.980 0.000 0.000
#> SRR944077 2 0.0290 0.982 0.000 0.992 0.008 0.000 0.000
#> SRR944078 3 0.2074 0.871 0.000 0.104 0.896 0.000 0.000
#> SRR944079 2 0.0510 0.978 0.000 0.984 0.016 0.000 0.000
#> SRR944080 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> SRR944081 4 0.2020 0.786 0.000 0.000 0.000 0.900 0.100
#> SRR944082 1 0.2172 0.815 0.908 0.000 0.000 0.076 0.016
#> SRR944083 1 0.0000 0.856 1.000 0.000 0.000 0.000 0.000
#> SRR944084 4 0.2629 0.769 0.000 0.000 0.004 0.860 0.136
#> SRR944085 3 0.0609 0.894 0.000 0.020 0.980 0.000 0.000
#> SRR944086 4 0.4885 0.507 0.056 0.000 0.000 0.668 0.276
#> SRR944088 4 0.3196 0.743 0.000 0.000 0.004 0.804 0.192
#> SRR944087 3 0.0609 0.894 0.000 0.020 0.980 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.2219 0.811 0.000 0.136 0.864 0.000 0.000 0.000
#> SRR944012 4 0.0146 0.868 0.000 0.000 0.000 0.996 0.004 0.000
#> SRR944014 2 0.0146 0.988 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944013 4 0.4560 0.731 0.000 0.000 0.000 0.692 0.200 0.108
#> SRR944015 4 0.1863 0.815 0.000 0.000 0.000 0.896 0.000 0.104
#> SRR944016 1 0.0000 0.870 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR944017 5 0.3098 0.771 0.000 0.004 0.000 0.064 0.844 0.088
#> SRR944018 4 0.0976 0.865 0.008 0.000 0.000 0.968 0.016 0.008
#> SRR944019 4 0.0260 0.868 0.000 0.000 0.000 0.992 0.008 0.000
#> SRR944020 4 0.0520 0.867 0.000 0.000 0.000 0.984 0.008 0.008
#> SRR944021 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944022 4 0.0520 0.867 0.000 0.000 0.000 0.984 0.008 0.008
#> SRR944023 1 0.5535 0.621 0.692 0.000 0.160 0.060 0.044 0.044
#> SRR944024 1 0.0000 0.870 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR944026 4 0.4371 0.681 0.000 0.000 0.000 0.620 0.036 0.344
#> SRR944025 5 0.0000 0.880 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR944028 5 0.0858 0.872 0.000 0.000 0.000 0.004 0.968 0.028
#> SRR944029 4 0.2805 0.818 0.000 0.000 0.000 0.812 0.004 0.184
#> SRR944030 2 0.0146 0.987 0.000 0.996 0.000 0.000 0.004 0.000
#> SRR944031 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR944032 1 0.5083 0.320 0.520 0.000 0.000 0.068 0.408 0.004
#> SRR944033 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944034 5 0.3076 0.635 0.000 0.240 0.000 0.000 0.760 0.000
#> SRR944036 1 0.5504 0.618 0.692 0.000 0.164 0.060 0.044 0.040
#> SRR944035 5 0.0146 0.880 0.000 0.004 0.000 0.000 0.996 0.000
#> SRR944038 6 0.4682 0.866 0.000 0.000 0.284 0.076 0.000 0.640
#> SRR944037 4 0.0146 0.868 0.000 0.000 0.000 0.996 0.004 0.000
#> SRR944039 4 0.1434 0.859 0.024 0.000 0.000 0.948 0.020 0.008
#> SRR944040 3 0.3076 0.652 0.000 0.240 0.760 0.000 0.000 0.000
#> SRR944041 4 0.0146 0.868 0.000 0.000 0.000 0.996 0.004 0.000
#> SRR944042 3 0.0865 0.832 0.000 0.000 0.964 0.000 0.000 0.036
#> SRR944043 4 0.1180 0.861 0.012 0.000 0.000 0.960 0.012 0.016
#> SRR944044 4 0.4371 0.681 0.000 0.000 0.000 0.620 0.036 0.344
#> SRR944046 3 0.0146 0.859 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR944045 2 0.1267 0.927 0.000 0.940 0.060 0.000 0.000 0.000
#> SRR944047 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944048 1 0.0000 0.870 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR944049 5 0.1501 0.837 0.000 0.076 0.000 0.000 0.924 0.000
#> SRR944050 1 0.0291 0.868 0.992 0.000 0.000 0.000 0.004 0.004
#> SRR944051 4 0.4140 0.782 0.000 0.000 0.000 0.744 0.152 0.104
#> SRR944052 2 0.0858 0.964 0.000 0.968 0.028 0.000 0.004 0.000
#> SRR944053 4 0.0405 0.867 0.000 0.000 0.000 0.988 0.004 0.008
#> SRR944054 4 0.3841 0.769 0.000 0.000 0.000 0.724 0.032 0.244
#> SRR944055 3 0.2260 0.808 0.000 0.140 0.860 0.000 0.000 0.000
#> SRR944056 2 0.0146 0.988 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944057 1 0.0000 0.870 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR944058 1 0.2325 0.794 0.884 0.000 0.000 0.100 0.008 0.008
#> SRR944059 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR944060 6 0.5669 0.802 0.004 0.004 0.184 0.148 0.024 0.636
#> SRR944061 2 0.0260 0.985 0.000 0.992 0.008 0.000 0.000 0.000
#> SRR944062 1 0.0000 0.870 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR944063 4 0.0146 0.868 0.000 0.000 0.000 0.996 0.004 0.000
#> SRR944064 1 0.3536 0.696 0.736 0.000 0.000 0.008 0.252 0.004
#> SRR944065 4 0.0837 0.867 0.004 0.000 0.000 0.972 0.020 0.004
#> SRR944066 1 0.0000 0.870 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR944067 5 0.0000 0.880 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR944068 4 0.1863 0.815 0.000 0.000 0.000 0.896 0.000 0.104
#> SRR944069 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944070 6 0.4196 0.819 0.000 0.000 0.332 0.028 0.000 0.640
#> SRR944071 3 0.1837 0.805 0.000 0.004 0.928 0.044 0.020 0.004
#> SRR944072 1 0.2685 0.766 0.852 0.000 0.000 0.132 0.008 0.008
#> SRR944073 2 0.0146 0.987 0.000 0.996 0.000 0.000 0.004 0.000
#> SRR944075 3 0.2219 0.811 0.000 0.136 0.864 0.000 0.000 0.000
#> SRR944074 4 0.4371 0.681 0.000 0.000 0.000 0.620 0.036 0.344
#> SRR944076 3 0.0146 0.859 0.000 0.004 0.996 0.000 0.000 0.000
#> SRR944077 2 0.0146 0.988 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944078 3 0.2300 0.803 0.000 0.144 0.856 0.000 0.000 0.000
#> SRR944079 2 0.0146 0.988 0.000 0.996 0.004 0.000 0.000 0.000
#> SRR944080 2 0.0146 0.987 0.000 0.996 0.000 0.000 0.004 0.000
#> SRR944081 4 0.1398 0.864 0.000 0.000 0.000 0.940 0.008 0.052
#> SRR944082 1 0.0837 0.861 0.972 0.000 0.000 0.020 0.004 0.004
#> SRR944083 1 0.0000 0.870 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR944084 4 0.2416 0.831 0.000 0.000 0.000 0.844 0.000 0.156
#> SRR944085 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR944086 4 0.3409 0.775 0.024 0.000 0.000 0.788 0.184 0.004
#> SRR944088 4 0.3298 0.786 0.000 0.000 0.000 0.756 0.008 0.236
#> SRR944087 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.978 0.991 0.5033 0.496 0.496
#> 3 3 0.904 0.907 0.959 0.3140 0.794 0.603
#> 4 4 0.837 0.791 0.896 0.1017 0.914 0.752
#> 5 5 0.761 0.664 0.811 0.0465 0.952 0.834
#> 6 6 0.711 0.613 0.756 0.0340 0.962 0.858
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.0000 0.979 0.000 1.000
#> SRR944012 1 0.0000 1.000 1.000 0.000
#> SRR944014 2 0.0000 0.979 0.000 1.000
#> SRR944013 1 0.0000 1.000 1.000 0.000
#> SRR944015 1 0.0938 0.987 0.988 0.012
#> SRR944016 1 0.0000 1.000 1.000 0.000
#> SRR944017 1 0.0000 1.000 1.000 0.000
#> SRR944018 1 0.0000 1.000 1.000 0.000
#> SRR944019 1 0.0000 1.000 1.000 0.000
#> SRR944020 1 0.0000 1.000 1.000 0.000
#> SRR944021 2 0.0000 0.979 0.000 1.000
#> SRR944022 1 0.0000 1.000 1.000 0.000
#> SRR944023 2 0.1843 0.956 0.028 0.972
#> SRR944024 1 0.0000 1.000 1.000 0.000
#> SRR944026 1 0.0000 1.000 1.000 0.000
#> SRR944025 1 0.0000 1.000 1.000 0.000
#> SRR944028 1 0.0000 1.000 1.000 0.000
#> SRR944029 1 0.0000 1.000 1.000 0.000
#> SRR944030 2 0.0000 0.979 0.000 1.000
#> SRR944031 2 0.0000 0.979 0.000 1.000
#> SRR944032 1 0.0000 1.000 1.000 0.000
#> SRR944033 2 0.0000 0.979 0.000 1.000
#> SRR944034 2 0.0000 0.979 0.000 1.000
#> SRR944036 2 0.0000 0.979 0.000 1.000
#> SRR944035 2 0.9248 0.502 0.340 0.660
#> SRR944038 2 0.0000 0.979 0.000 1.000
#> SRR944037 1 0.0000 1.000 1.000 0.000
#> SRR944039 1 0.0000 1.000 1.000 0.000
#> SRR944040 2 0.0000 0.979 0.000 1.000
#> SRR944041 1 0.0000 1.000 1.000 0.000
#> SRR944042 2 0.0000 0.979 0.000 1.000
#> SRR944043 1 0.0000 1.000 1.000 0.000
#> SRR944044 1 0.0000 1.000 1.000 0.000
#> SRR944046 2 0.0000 0.979 0.000 1.000
#> SRR944045 2 0.0000 0.979 0.000 1.000
#> SRR944047 2 0.0000 0.979 0.000 1.000
#> SRR944048 1 0.0000 1.000 1.000 0.000
#> SRR944049 2 0.3431 0.922 0.064 0.936
#> SRR944050 1 0.0000 1.000 1.000 0.000
#> SRR944051 1 0.0000 1.000 1.000 0.000
#> SRR944052 2 0.0000 0.979 0.000 1.000
#> SRR944053 1 0.0000 1.000 1.000 0.000
#> SRR944054 1 0.0000 1.000 1.000 0.000
#> SRR944055 2 0.0000 0.979 0.000 1.000
#> SRR944056 2 0.0000 0.979 0.000 1.000
#> SRR944057 1 0.0000 1.000 1.000 0.000
#> SRR944058 1 0.0000 1.000 1.000 0.000
#> SRR944059 2 0.0000 0.979 0.000 1.000
#> SRR944060 2 0.0376 0.976 0.004 0.996
#> SRR944061 2 0.0000 0.979 0.000 1.000
#> SRR944062 1 0.0000 1.000 1.000 0.000
#> SRR944063 1 0.0000 1.000 1.000 0.000
#> SRR944064 1 0.0000 1.000 1.000 0.000
#> SRR944065 1 0.0000 1.000 1.000 0.000
#> SRR944066 1 0.0000 1.000 1.000 0.000
#> SRR944067 1 0.0000 1.000 1.000 0.000
#> SRR944068 1 0.0000 1.000 1.000 0.000
#> SRR944069 2 0.0000 0.979 0.000 1.000
#> SRR944070 2 0.0000 0.979 0.000 1.000
#> SRR944071 2 0.0000 0.979 0.000 1.000
#> SRR944072 1 0.0000 1.000 1.000 0.000
#> SRR944073 2 0.0000 0.979 0.000 1.000
#> SRR944075 2 0.0000 0.979 0.000 1.000
#> SRR944074 1 0.0000 1.000 1.000 0.000
#> SRR944076 2 0.0000 0.979 0.000 1.000
#> SRR944077 2 0.0000 0.979 0.000 1.000
#> SRR944078 2 0.0000 0.979 0.000 1.000
#> SRR944079 2 0.0000 0.979 0.000 1.000
#> SRR944080 2 0.0000 0.979 0.000 1.000
#> SRR944081 1 0.0000 1.000 1.000 0.000
#> SRR944082 1 0.0000 1.000 1.000 0.000
#> SRR944083 1 0.0000 1.000 1.000 0.000
#> SRR944084 2 0.8555 0.623 0.280 0.720
#> SRR944085 2 0.0000 0.979 0.000 1.000
#> SRR944086 1 0.0000 1.000 1.000 0.000
#> SRR944088 1 0.0000 1.000 1.000 0.000
#> SRR944087 2 0.0000 0.979 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944012 1 0.0237 0.910 0.996 0.004 0.000
#> SRR944014 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944013 1 0.3482 0.837 0.872 0.128 0.000
#> SRR944015 1 0.0000 0.911 1.000 0.000 0.000
#> SRR944016 2 0.0000 0.948 0.000 1.000 0.000
#> SRR944017 1 0.2537 0.870 0.920 0.080 0.000
#> SRR944018 1 0.6267 0.276 0.548 0.452 0.000
#> SRR944019 1 0.1289 0.897 0.968 0.032 0.000
#> SRR944020 1 0.0000 0.911 1.000 0.000 0.000
#> SRR944021 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944022 1 0.0000 0.911 1.000 0.000 0.000
#> SRR944023 2 0.5988 0.438 0.000 0.632 0.368
#> SRR944024 2 0.0000 0.948 0.000 1.000 0.000
#> SRR944026 1 0.0000 0.911 1.000 0.000 0.000
#> SRR944025 2 0.0000 0.948 0.000 1.000 0.000
#> SRR944028 2 0.0747 0.937 0.016 0.984 0.000
#> SRR944029 1 0.0000 0.911 1.000 0.000 0.000
#> SRR944030 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944031 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944032 2 0.0000 0.948 0.000 1.000 0.000
#> SRR944033 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944034 3 0.0237 0.988 0.000 0.004 0.996
#> SRR944036 2 0.5591 0.577 0.000 0.696 0.304
#> SRR944035 2 0.0000 0.948 0.000 1.000 0.000
#> SRR944038 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944037 1 0.0000 0.911 1.000 0.000 0.000
#> SRR944039 1 0.5988 0.504 0.632 0.368 0.000
#> SRR944040 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944041 1 0.0000 0.911 1.000 0.000 0.000
#> SRR944042 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944043 1 0.4121 0.795 0.832 0.168 0.000
#> SRR944044 1 0.0000 0.911 1.000 0.000 0.000
#> SRR944046 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944045 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944047 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944048 2 0.0000 0.948 0.000 1.000 0.000
#> SRR944049 3 0.2261 0.923 0.000 0.068 0.932
#> SRR944050 2 0.0000 0.948 0.000 1.000 0.000
#> SRR944051 1 0.4974 0.717 0.764 0.236 0.000
#> SRR944052 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944053 1 0.0237 0.910 0.996 0.004 0.000
#> SRR944054 1 0.0000 0.911 1.000 0.000 0.000
#> SRR944055 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944056 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944057 2 0.0000 0.948 0.000 1.000 0.000
#> SRR944058 2 0.0592 0.940 0.012 0.988 0.000
#> SRR944059 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944060 3 0.4235 0.782 0.176 0.000 0.824
#> SRR944061 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944062 2 0.0000 0.948 0.000 1.000 0.000
#> SRR944063 1 0.0000 0.911 1.000 0.000 0.000
#> SRR944064 2 0.0000 0.948 0.000 1.000 0.000
#> SRR944065 1 0.4750 0.743 0.784 0.216 0.000
#> SRR944066 2 0.0000 0.948 0.000 1.000 0.000
#> SRR944067 2 0.0000 0.948 0.000 1.000 0.000
#> SRR944068 1 0.0000 0.911 1.000 0.000 0.000
#> SRR944069 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944070 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944071 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944072 2 0.1289 0.922 0.032 0.968 0.000
#> SRR944073 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944075 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944074 1 0.0000 0.911 1.000 0.000 0.000
#> SRR944076 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944077 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944078 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944079 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944080 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944081 1 0.0000 0.911 1.000 0.000 0.000
#> SRR944082 2 0.0892 0.934 0.020 0.980 0.000
#> SRR944083 2 0.0000 0.948 0.000 1.000 0.000
#> SRR944084 1 0.0747 0.900 0.984 0.000 0.016
#> SRR944085 3 0.0000 0.991 0.000 0.000 1.000
#> SRR944086 1 0.6299 0.238 0.524 0.476 0.000
#> SRR944088 1 0.0000 0.911 1.000 0.000 0.000
#> SRR944087 3 0.0000 0.991 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 2 0.0188 0.9623 0.000 0.996 0.004 0.000
#> SRR944012 4 0.0804 0.8305 0.012 0.000 0.008 0.980
#> SRR944014 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944013 4 0.5280 0.6274 0.156 0.000 0.096 0.748
#> SRR944015 3 0.2081 0.6824 0.000 0.000 0.916 0.084
#> SRR944016 1 0.2704 0.8812 0.876 0.000 0.124 0.000
#> SRR944017 3 0.1042 0.6783 0.020 0.000 0.972 0.008
#> SRR944018 3 0.1109 0.6741 0.028 0.000 0.968 0.004
#> SRR944019 3 0.4936 0.4776 0.004 0.000 0.624 0.372
#> SRR944020 3 0.4898 0.4565 0.000 0.000 0.584 0.416
#> SRR944021 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944022 3 0.4730 0.5392 0.000 0.000 0.636 0.364
#> SRR944023 1 0.7179 0.3230 0.480 0.140 0.380 0.000
#> SRR944024 1 0.0817 0.9032 0.976 0.000 0.024 0.000
#> SRR944026 4 0.0336 0.8344 0.000 0.000 0.008 0.992
#> SRR944025 1 0.1059 0.9026 0.972 0.000 0.016 0.012
#> SRR944028 1 0.1174 0.9001 0.968 0.000 0.012 0.020
#> SRR944029 4 0.0469 0.8342 0.000 0.000 0.012 0.988
#> SRR944030 3 0.4985 0.0435 0.000 0.468 0.532 0.000
#> SRR944031 2 0.1867 0.8991 0.000 0.928 0.072 0.000
#> SRR944032 1 0.0524 0.9020 0.988 0.000 0.004 0.008
#> SRR944033 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0188 0.9623 0.004 0.996 0.000 0.000
#> SRR944036 1 0.4483 0.8056 0.808 0.088 0.104 0.000
#> SRR944035 1 0.0657 0.8997 0.984 0.000 0.012 0.004
#> SRR944038 2 0.0336 0.9605 0.000 0.992 0.008 0.000
#> SRR944037 3 0.4713 0.5470 0.000 0.000 0.640 0.360
#> SRR944039 3 0.2796 0.6407 0.092 0.000 0.892 0.016
#> SRR944040 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944041 4 0.0921 0.8306 0.000 0.000 0.028 0.972
#> SRR944042 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944043 3 0.0927 0.6793 0.016 0.000 0.976 0.008
#> SRR944044 4 0.0592 0.8342 0.000 0.000 0.016 0.984
#> SRR944046 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944045 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944047 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944048 1 0.0469 0.9042 0.988 0.000 0.012 0.000
#> SRR944049 2 0.7583 -0.0525 0.196 0.420 0.000 0.384
#> SRR944050 1 0.2814 0.8768 0.868 0.000 0.132 0.000
#> SRR944051 4 0.1743 0.7957 0.056 0.000 0.004 0.940
#> SRR944052 2 0.0469 0.9576 0.012 0.988 0.000 0.000
#> SRR944053 4 0.4981 -0.2218 0.000 0.000 0.464 0.536
#> SRR944054 4 0.0469 0.8340 0.000 0.000 0.012 0.988
#> SRR944055 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944056 2 0.0937 0.9497 0.012 0.976 0.000 0.012
#> SRR944057 1 0.2921 0.8744 0.860 0.000 0.140 0.000
#> SRR944058 1 0.0927 0.9010 0.976 0.000 0.008 0.016
#> SRR944059 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944060 3 0.1389 0.6652 0.000 0.048 0.952 0.000
#> SRR944061 2 0.0712 0.9563 0.008 0.984 0.004 0.004
#> SRR944062 1 0.1792 0.9004 0.932 0.000 0.068 0.000
#> SRR944063 4 0.1302 0.8189 0.000 0.000 0.044 0.956
#> SRR944064 1 0.0707 0.9034 0.980 0.000 0.020 0.000
#> SRR944065 4 0.4955 0.5664 0.268 0.000 0.024 0.708
#> SRR944066 1 0.3837 0.8180 0.776 0.000 0.224 0.000
#> SRR944067 1 0.0937 0.8974 0.976 0.000 0.012 0.012
#> SRR944068 3 0.4977 0.3598 0.000 0.000 0.540 0.460
#> SRR944069 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944070 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944071 2 0.4040 0.6530 0.000 0.752 0.248 0.000
#> SRR944072 1 0.3649 0.8335 0.796 0.000 0.204 0.000
#> SRR944073 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944075 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944074 4 0.0000 0.8323 0.000 0.000 0.000 1.000
#> SRR944076 2 0.0592 0.9555 0.000 0.984 0.016 0.000
#> SRR944077 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944078 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944079 2 0.0000 0.9641 0.000 1.000 0.000 0.000
#> SRR944080 2 0.0188 0.9623 0.000 0.996 0.000 0.004
#> SRR944081 3 0.4888 0.4585 0.000 0.000 0.588 0.412
#> SRR944082 1 0.3528 0.8431 0.808 0.000 0.192 0.000
#> SRR944083 1 0.1022 0.9044 0.968 0.000 0.032 0.000
#> SRR944084 3 0.4502 0.6351 0.000 0.016 0.748 0.236
#> SRR944085 2 0.0469 0.9586 0.000 0.988 0.012 0.000
#> SRR944086 4 0.5823 0.4446 0.348 0.000 0.044 0.608
#> SRR944088 4 0.0921 0.8300 0.000 0.000 0.028 0.972
#> SRR944087 2 0.0469 0.9580 0.000 0.988 0.012 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 2 0.0771 0.9312 0.000 0.976 0.020 0.004 0.000
#> SRR944012 5 0.2054 0.7885 0.004 0.000 0.072 0.008 0.916
#> SRR944014 2 0.0000 0.9331 0.000 1.000 0.000 0.000 0.000
#> SRR944013 5 0.7469 0.2419 0.160 0.000 0.132 0.176 0.532
#> SRR944015 4 0.2409 0.6501 0.000 0.000 0.068 0.900 0.032
#> SRR944016 1 0.4555 0.5440 0.720 0.000 0.224 0.056 0.000
#> SRR944017 4 0.4264 0.5206 0.044 0.000 0.212 0.744 0.000
#> SRR944018 4 0.2995 0.6235 0.032 0.000 0.088 0.872 0.008
#> SRR944019 4 0.7487 0.4757 0.088 0.000 0.180 0.504 0.228
#> SRR944020 4 0.4836 0.5841 0.000 0.000 0.036 0.628 0.336
#> SRR944021 2 0.0162 0.9333 0.000 0.996 0.004 0.000 0.000
#> SRR944022 4 0.4378 0.6643 0.000 0.000 0.036 0.716 0.248
#> SRR944023 3 0.8008 0.2978 0.348 0.132 0.368 0.152 0.000
#> SRR944024 1 0.3177 0.4675 0.792 0.000 0.208 0.000 0.000
#> SRR944026 5 0.0324 0.8020 0.000 0.000 0.004 0.004 0.992
#> SRR944025 1 0.4677 0.5221 0.688 0.008 0.280 0.020 0.004
#> SRR944028 1 0.3467 0.5711 0.832 0.000 0.128 0.004 0.036
#> SRR944029 5 0.0898 0.8018 0.000 0.000 0.020 0.008 0.972
#> SRR944030 2 0.5440 0.2756 0.000 0.540 0.064 0.396 0.000
#> SRR944031 2 0.1668 0.9154 0.000 0.940 0.028 0.032 0.000
#> SRR944032 1 0.2818 0.5403 0.856 0.000 0.132 0.000 0.012
#> SRR944033 2 0.0000 0.9331 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0510 0.9324 0.000 0.984 0.016 0.000 0.000
#> SRR944036 1 0.6469 -0.4072 0.448 0.068 0.440 0.044 0.000
#> SRR944035 1 0.4273 0.2107 0.552 0.000 0.448 0.000 0.000
#> SRR944038 2 0.2286 0.8745 0.000 0.888 0.108 0.004 0.000
#> SRR944037 4 0.4184 0.6476 0.000 0.000 0.016 0.700 0.284
#> SRR944039 4 0.5877 0.4100 0.184 0.000 0.176 0.632 0.008
#> SRR944040 2 0.0404 0.9334 0.000 0.988 0.012 0.000 0.000
#> SRR944041 5 0.0703 0.7968 0.000 0.000 0.000 0.024 0.976
#> SRR944042 2 0.1121 0.9226 0.000 0.956 0.044 0.000 0.000
#> SRR944043 4 0.3218 0.6236 0.020 0.000 0.108 0.856 0.016
#> SRR944044 5 0.1205 0.7998 0.000 0.000 0.040 0.004 0.956
#> SRR944046 2 0.0771 0.9310 0.000 0.976 0.020 0.004 0.000
#> SRR944045 2 0.0404 0.9329 0.000 0.988 0.012 0.000 0.000
#> SRR944047 2 0.0290 0.9331 0.000 0.992 0.008 0.000 0.000
#> SRR944048 1 0.2233 0.5566 0.892 0.000 0.104 0.004 0.000
#> SRR944049 5 0.7571 0.0133 0.120 0.340 0.104 0.000 0.436
#> SRR944050 1 0.5309 0.5038 0.644 0.000 0.264 0.092 0.000
#> SRR944051 5 0.2712 0.7647 0.032 0.000 0.088 0.000 0.880
#> SRR944052 2 0.0880 0.9243 0.000 0.968 0.032 0.000 0.000
#> SRR944053 4 0.5658 0.4198 0.000 0.000 0.080 0.512 0.408
#> SRR944054 5 0.1043 0.7930 0.000 0.000 0.040 0.000 0.960
#> SRR944055 2 0.0000 0.9331 0.000 1.000 0.000 0.000 0.000
#> SRR944056 2 0.1408 0.9128 0.000 0.948 0.044 0.000 0.008
#> SRR944057 1 0.5215 0.5145 0.656 0.000 0.256 0.088 0.000
#> SRR944058 1 0.2012 0.5832 0.920 0.000 0.060 0.000 0.020
#> SRR944059 2 0.0404 0.9343 0.000 0.988 0.012 0.000 0.000
#> SRR944060 4 0.2484 0.6146 0.004 0.028 0.068 0.900 0.000
#> SRR944061 2 0.0609 0.9295 0.000 0.980 0.020 0.000 0.000
#> SRR944062 1 0.3607 0.4075 0.752 0.000 0.244 0.004 0.000
#> SRR944063 5 0.1981 0.7633 0.000 0.000 0.016 0.064 0.920
#> SRR944064 1 0.3039 0.4818 0.808 0.000 0.192 0.000 0.000
#> SRR944065 5 0.7276 0.1871 0.224 0.000 0.172 0.076 0.528
#> SRR944066 1 0.5848 0.4607 0.604 0.000 0.228 0.168 0.000
#> SRR944067 1 0.3353 0.4871 0.796 0.000 0.196 0.000 0.008
#> SRR944068 4 0.6333 0.4936 0.000 0.000 0.196 0.516 0.288
#> SRR944069 2 0.0671 0.9313 0.000 0.980 0.016 0.004 0.000
#> SRR944070 2 0.1478 0.9131 0.000 0.936 0.064 0.000 0.000
#> SRR944071 2 0.4309 0.5439 0.000 0.676 0.016 0.308 0.000
#> SRR944072 1 0.5756 0.4589 0.620 0.000 0.204 0.176 0.000
#> SRR944073 2 0.0290 0.9337 0.000 0.992 0.008 0.000 0.000
#> SRR944075 2 0.0510 0.9322 0.000 0.984 0.016 0.000 0.000
#> SRR944074 5 0.0609 0.7996 0.000 0.000 0.020 0.000 0.980
#> SRR944076 2 0.4372 0.6354 0.004 0.712 0.260 0.024 0.000
#> SRR944077 2 0.0290 0.9330 0.000 0.992 0.008 0.000 0.000
#> SRR944078 2 0.0703 0.9311 0.000 0.976 0.024 0.000 0.000
#> SRR944079 2 0.0000 0.9331 0.000 1.000 0.000 0.000 0.000
#> SRR944080 2 0.1197 0.9186 0.000 0.952 0.048 0.000 0.000
#> SRR944081 4 0.4594 0.6412 0.000 0.000 0.036 0.680 0.284
#> SRR944082 1 0.5150 0.2316 0.652 0.000 0.272 0.076 0.000
#> SRR944083 1 0.0955 0.5888 0.968 0.000 0.028 0.004 0.000
#> SRR944084 4 0.4838 0.6423 0.000 0.012 0.112 0.748 0.128
#> SRR944085 2 0.2270 0.8926 0.000 0.904 0.076 0.020 0.000
#> SRR944086 3 0.6717 0.3608 0.252 0.000 0.540 0.024 0.184
#> SRR944088 5 0.1907 0.7861 0.000 0.000 0.044 0.028 0.928
#> SRR944087 2 0.2361 0.8814 0.000 0.892 0.096 0.012 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 2 0.0696 0.90561 0.004 0.980 0.004 0.008 0.000 0.004
#> SRR944012 5 0.4052 0.62685 0.020 0.000 0.008 0.020 0.756 0.196
#> SRR944014 2 0.0291 0.90650 0.004 0.992 0.000 0.000 0.000 0.004
#> SRR944013 5 0.8011 0.09925 0.208 0.000 0.072 0.232 0.400 0.088
#> SRR944015 4 0.1773 0.66262 0.016 0.000 0.000 0.932 0.016 0.036
#> SRR944016 1 0.3874 0.76887 0.636 0.000 0.356 0.008 0.000 0.000
#> SRR944017 4 0.4396 0.50849 0.352 0.000 0.000 0.612 0.000 0.036
#> SRR944018 4 0.3469 0.65071 0.060 0.000 0.020 0.840 0.008 0.072
#> SRR944019 4 0.7282 0.39029 0.280 0.000 0.020 0.448 0.164 0.088
#> SRR944020 4 0.4405 0.60999 0.024 0.000 0.000 0.696 0.252 0.028
#> SRR944021 2 0.1675 0.89762 0.024 0.936 0.000 0.008 0.000 0.032
#> SRR944022 4 0.4411 0.65218 0.016 0.000 0.000 0.740 0.160 0.084
#> SRR944023 3 0.7575 -0.00452 0.096 0.064 0.492 0.188 0.000 0.160
#> SRR944024 3 0.1594 0.48656 0.052 0.000 0.932 0.000 0.000 0.016
#> SRR944026 5 0.1777 0.71311 0.004 0.000 0.000 0.024 0.928 0.044
#> SRR944025 1 0.5079 0.58931 0.620 0.000 0.288 0.000 0.012 0.080
#> SRR944028 3 0.6809 -0.14987 0.324 0.000 0.388 0.004 0.036 0.248
#> SRR944029 5 0.1844 0.70980 0.012 0.004 0.000 0.024 0.932 0.028
#> SRR944030 2 0.6450 0.20424 0.140 0.476 0.000 0.328 0.000 0.056
#> SRR944031 2 0.2016 0.88969 0.024 0.920 0.000 0.040 0.000 0.016
#> SRR944032 3 0.5776 0.24942 0.188 0.000 0.520 0.000 0.004 0.288
#> SRR944033 2 0.0291 0.90650 0.004 0.992 0.000 0.000 0.000 0.004
#> SRR944034 2 0.1723 0.89409 0.036 0.928 0.000 0.000 0.000 0.036
#> SRR944036 3 0.6253 -0.03339 0.068 0.044 0.552 0.032 0.000 0.304
#> SRR944035 6 0.6067 0.09507 0.240 0.004 0.308 0.000 0.000 0.448
#> SRR944038 2 0.2962 0.85501 0.028 0.876 0.056 0.012 0.000 0.028
#> SRR944037 4 0.4282 0.64374 0.028 0.000 0.000 0.736 0.200 0.036
#> SRR944039 4 0.6130 0.30394 0.368 0.000 0.092 0.496 0.012 0.032
#> SRR944040 2 0.0291 0.90650 0.004 0.992 0.000 0.000 0.000 0.004
#> SRR944041 5 0.1951 0.70741 0.004 0.000 0.000 0.060 0.916 0.020
#> SRR944042 2 0.1317 0.89743 0.016 0.956 0.016 0.004 0.000 0.008
#> SRR944043 4 0.3369 0.62159 0.072 0.000 0.012 0.832 0.000 0.084
#> SRR944044 5 0.3608 0.67102 0.048 0.000 0.000 0.024 0.816 0.112
#> SRR944046 2 0.0665 0.90636 0.004 0.980 0.000 0.008 0.000 0.008
#> SRR944045 2 0.0748 0.90655 0.004 0.976 0.000 0.004 0.000 0.016
#> SRR944047 2 0.0508 0.90659 0.012 0.984 0.000 0.000 0.000 0.004
#> SRR944048 3 0.2933 0.33450 0.200 0.000 0.796 0.000 0.000 0.004
#> SRR944049 5 0.7659 0.10612 0.080 0.232 0.084 0.004 0.484 0.116
#> SRR944050 1 0.3840 0.81255 0.696 0.000 0.288 0.008 0.000 0.008
#> SRR944051 5 0.5636 0.25976 0.020 0.000 0.072 0.012 0.564 0.332
#> SRR944052 2 0.1930 0.89139 0.028 0.924 0.012 0.000 0.000 0.036
#> SRR944053 4 0.6041 0.51803 0.060 0.000 0.000 0.572 0.256 0.112
#> SRR944054 5 0.2664 0.68806 0.040 0.000 0.000 0.020 0.884 0.056
#> SRR944055 2 0.0291 0.90669 0.004 0.992 0.000 0.000 0.000 0.004
#> SRR944056 2 0.3018 0.85275 0.028 0.872 0.008 0.000 0.040 0.052
#> SRR944057 1 0.3767 0.80695 0.708 0.000 0.276 0.012 0.000 0.004
#> SRR944058 3 0.5825 -0.19117 0.368 0.000 0.496 0.000 0.020 0.116
#> SRR944059 2 0.2222 0.88820 0.032 0.912 0.012 0.004 0.000 0.040
#> SRR944060 4 0.4104 0.59745 0.160 0.036 0.000 0.768 0.000 0.036
#> SRR944061 2 0.0405 0.90639 0.004 0.988 0.000 0.000 0.000 0.008
#> SRR944062 3 0.2380 0.48189 0.036 0.000 0.892 0.004 0.000 0.068
#> SRR944063 5 0.4674 0.58805 0.016 0.000 0.004 0.148 0.728 0.104
#> SRR944064 3 0.2384 0.47290 0.084 0.000 0.884 0.000 0.000 0.032
#> SRR944065 6 0.7426 0.15954 0.020 0.000 0.152 0.108 0.300 0.420
#> SRR944066 1 0.4738 0.77291 0.640 0.000 0.288 0.068 0.000 0.004
#> SRR944067 3 0.4895 0.31018 0.104 0.000 0.632 0.000 0.000 0.264
#> SRR944068 4 0.6283 0.46689 0.024 0.004 0.024 0.592 0.172 0.184
#> SRR944069 2 0.2853 0.86577 0.068 0.868 0.000 0.004 0.004 0.056
#> SRR944070 2 0.1811 0.88963 0.020 0.936 0.012 0.012 0.000 0.020
#> SRR944071 2 0.5154 0.49296 0.040 0.608 0.000 0.312 0.000 0.040
#> SRR944072 1 0.5803 0.69689 0.576 0.000 0.296 0.044 0.004 0.080
#> SRR944073 2 0.0405 0.90639 0.004 0.988 0.000 0.000 0.000 0.008
#> SRR944075 2 0.0291 0.90645 0.004 0.992 0.000 0.000 0.000 0.004
#> SRR944074 5 0.1857 0.70274 0.012 0.000 0.000 0.028 0.928 0.032
#> SRR944076 2 0.6036 0.57319 0.056 0.640 0.112 0.024 0.000 0.168
#> SRR944077 2 0.0291 0.90669 0.004 0.992 0.000 0.000 0.000 0.004
#> SRR944078 2 0.0146 0.90637 0.004 0.996 0.000 0.000 0.000 0.000
#> SRR944079 2 0.0405 0.90639 0.004 0.988 0.000 0.000 0.000 0.008
#> SRR944080 2 0.4231 0.79871 0.072 0.796 0.024 0.000 0.024 0.084
#> SRR944081 4 0.5062 0.63170 0.060 0.000 0.000 0.688 0.196 0.056
#> SRR944082 3 0.3884 0.41471 0.048 0.000 0.808 0.064 0.000 0.080
#> SRR944083 3 0.3499 0.05442 0.320 0.000 0.680 0.000 0.000 0.000
#> SRR944084 4 0.3548 0.65011 0.016 0.008 0.000 0.832 0.080 0.064
#> SRR944085 2 0.5137 0.74263 0.048 0.740 0.100 0.048 0.000 0.064
#> SRR944086 6 0.5583 0.41461 0.040 0.000 0.196 0.020 0.080 0.664
#> SRR944088 5 0.3517 0.68483 0.024 0.000 0.000 0.048 0.824 0.104
#> SRR944087 2 0.3554 0.83337 0.024 0.844 0.048 0.024 0.000 0.060
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.701 0.804 0.917 0.3937 0.576 0.576
#> 3 3 0.522 0.506 0.800 0.4522 0.756 0.603
#> 4 4 0.592 0.733 0.810 0.1904 0.758 0.474
#> 5 5 0.758 0.766 0.866 0.0777 0.967 0.881
#> 6 6 0.743 0.723 0.860 0.0282 0.993 0.973
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.0938 0.9356 0.012 0.988
#> SRR944012 1 0.9286 0.5776 0.656 0.344
#> SRR944014 2 0.0000 0.9376 0.000 1.000
#> SRR944013 2 0.0376 0.9373 0.004 0.996
#> SRR944015 1 0.0000 0.8032 1.000 0.000
#> SRR944016 2 0.9044 0.4165 0.320 0.680
#> SRR944017 2 0.0376 0.9373 0.004 0.996
#> SRR944018 1 0.9044 0.6078 0.680 0.320
#> SRR944019 2 0.9850 0.0389 0.428 0.572
#> SRR944020 1 0.0000 0.8032 1.000 0.000
#> SRR944021 2 0.0000 0.9376 0.000 1.000
#> SRR944022 1 0.0000 0.8032 1.000 0.000
#> SRR944023 2 0.4022 0.8768 0.080 0.920
#> SRR944024 1 0.9922 0.3871 0.552 0.448
#> SRR944026 2 0.0000 0.9376 0.000 1.000
#> SRR944025 2 0.0000 0.9376 0.000 1.000
#> SRR944028 2 0.0000 0.9376 0.000 1.000
#> SRR944029 2 0.1843 0.9271 0.028 0.972
#> SRR944030 2 0.0000 0.9376 0.000 1.000
#> SRR944031 2 0.3274 0.8987 0.060 0.940
#> SRR944032 2 0.0938 0.9356 0.012 0.988
#> SRR944033 2 0.0000 0.9376 0.000 1.000
#> SRR944034 2 0.0000 0.9376 0.000 1.000
#> SRR944036 2 0.1843 0.9271 0.028 0.972
#> SRR944035 2 0.0000 0.9376 0.000 1.000
#> SRR944038 1 0.0000 0.8032 1.000 0.000
#> SRR944037 1 0.0000 0.8032 1.000 0.000
#> SRR944039 2 0.9896 -0.0159 0.440 0.560
#> SRR944040 2 0.0000 0.9376 0.000 1.000
#> SRR944041 1 0.8661 0.6410 0.712 0.288
#> SRR944042 2 0.2043 0.9247 0.032 0.968
#> SRR944043 1 0.3114 0.7872 0.944 0.056
#> SRR944044 2 0.0000 0.9376 0.000 1.000
#> SRR944046 2 0.2043 0.9247 0.032 0.968
#> SRR944045 2 0.0000 0.9376 0.000 1.000
#> SRR944047 2 0.0000 0.9376 0.000 1.000
#> SRR944048 2 0.9754 0.1149 0.408 0.592
#> SRR944049 2 0.0000 0.9376 0.000 1.000
#> SRR944050 2 0.9044 0.4165 0.320 0.680
#> SRR944051 2 0.0938 0.9356 0.012 0.988
#> SRR944052 2 0.0000 0.9376 0.000 1.000
#> SRR944053 1 0.0000 0.8032 1.000 0.000
#> SRR944054 2 0.0672 0.9366 0.008 0.992
#> SRR944055 2 0.0938 0.9356 0.012 0.988
#> SRR944056 2 0.0000 0.9376 0.000 1.000
#> SRR944057 1 0.9998 0.2523 0.508 0.492
#> SRR944058 1 0.9795 0.4615 0.584 0.416
#> SRR944059 2 0.0938 0.9356 0.012 0.988
#> SRR944060 1 0.5629 0.7539 0.868 0.132
#> SRR944061 2 0.0000 0.9376 0.000 1.000
#> SRR944062 1 0.0000 0.8032 1.000 0.000
#> SRR944063 1 0.0000 0.8032 1.000 0.000
#> SRR944064 2 0.0000 0.9376 0.000 1.000
#> SRR944065 1 0.0000 0.8032 1.000 0.000
#> SRR944066 1 0.9815 0.4533 0.580 0.420
#> SRR944067 2 0.0000 0.9376 0.000 1.000
#> SRR944068 1 0.0000 0.8032 1.000 0.000
#> SRR944069 2 0.0000 0.9376 0.000 1.000
#> SRR944070 1 0.0000 0.8032 1.000 0.000
#> SRR944071 2 0.1843 0.9271 0.028 0.972
#> SRR944072 1 0.9815 0.4536 0.580 0.420
#> SRR944073 2 0.0000 0.9376 0.000 1.000
#> SRR944075 2 0.0672 0.9366 0.008 0.992
#> SRR944074 2 0.0000 0.9376 0.000 1.000
#> SRR944076 2 0.1843 0.9271 0.028 0.972
#> SRR944077 2 0.0000 0.9376 0.000 1.000
#> SRR944078 2 0.0672 0.9366 0.008 0.992
#> SRR944079 2 0.0000 0.9376 0.000 1.000
#> SRR944080 2 0.0000 0.9376 0.000 1.000
#> SRR944081 2 0.5842 0.7960 0.140 0.860
#> SRR944082 1 0.0000 0.8032 1.000 0.000
#> SRR944083 1 0.9922 0.3871 0.552 0.448
#> SRR944084 2 0.2043 0.9247 0.032 0.968
#> SRR944085 2 0.0938 0.9356 0.012 0.988
#> SRR944086 2 0.4022 0.8772 0.080 0.920
#> SRR944088 2 0.1633 0.9295 0.024 0.976
#> SRR944087 2 0.2043 0.9247 0.032 0.968
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 2 0.6295 0.2328 0.472 0.528 0.000
#> SRR944012 1 0.3412 0.4366 0.876 0.000 0.124
#> SRR944014 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944013 2 0.5178 0.5300 0.256 0.744 0.000
#> SRR944015 3 0.0000 0.8062 0.000 0.000 1.000
#> SRR944016 1 0.4702 0.5415 0.788 0.212 0.000
#> SRR944017 2 0.5178 0.5300 0.256 0.744 0.000
#> SRR944018 1 0.4645 0.3420 0.816 0.008 0.176
#> SRR944019 1 0.3038 0.6361 0.896 0.104 0.000
#> SRR944020 3 0.4654 0.8150 0.208 0.000 0.792
#> SRR944021 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944022 3 0.0000 0.8062 0.000 0.000 1.000
#> SRR944023 1 0.6267 -0.0486 0.548 0.452 0.000
#> SRR944024 1 0.0892 0.5770 0.980 0.000 0.020
#> SRR944026 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944025 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944028 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944029 2 0.6309 0.1667 0.496 0.504 0.000
#> SRR944030 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944031 1 0.6295 -0.1171 0.528 0.472 0.000
#> SRR944032 2 0.6280 0.2570 0.460 0.540 0.000
#> SRR944033 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944034 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944036 2 0.6309 0.1667 0.496 0.504 0.000
#> SRR944035 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944038 3 0.5926 0.7621 0.356 0.000 0.644
#> SRR944037 3 0.4121 0.8238 0.168 0.000 0.832
#> SRR944039 1 0.3846 0.6338 0.876 0.108 0.016
#> SRR944040 2 0.2711 0.6658 0.088 0.912 0.000
#> SRR944041 1 0.4399 0.2918 0.812 0.000 0.188
#> SRR944042 1 0.6309 -0.2129 0.500 0.500 0.000
#> SRR944043 3 0.6308 0.5786 0.492 0.000 0.508
#> SRR944044 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944046 1 0.6309 -0.2129 0.500 0.500 0.000
#> SRR944045 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944047 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944048 1 0.3412 0.6269 0.876 0.124 0.000
#> SRR944049 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944050 1 0.4702 0.5415 0.788 0.212 0.000
#> SRR944051 2 0.6280 0.2570 0.460 0.540 0.000
#> SRR944052 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944053 3 0.0000 0.8062 0.000 0.000 1.000
#> SRR944054 2 0.6274 0.2643 0.456 0.544 0.000
#> SRR944055 2 0.6295 0.2328 0.472 0.528 0.000
#> SRR944056 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944057 1 0.1031 0.6017 0.976 0.024 0.000
#> SRR944058 1 0.1860 0.5486 0.948 0.000 0.052
#> SRR944059 2 0.6295 0.2328 0.472 0.528 0.000
#> SRR944060 1 0.6180 -0.4167 0.584 0.000 0.416
#> SRR944061 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944062 3 0.5926 0.7621 0.356 0.000 0.644
#> SRR944063 3 0.0592 0.8061 0.012 0.000 0.988
#> SRR944064 2 0.0424 0.7118 0.008 0.992 0.000
#> SRR944065 3 0.4062 0.8241 0.164 0.000 0.836
#> SRR944066 1 0.1753 0.5528 0.952 0.000 0.048
#> SRR944067 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944068 3 0.0000 0.8062 0.000 0.000 1.000
#> SRR944069 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944070 3 0.5926 0.7621 0.356 0.000 0.644
#> SRR944071 2 0.6309 0.1667 0.496 0.504 0.000
#> SRR944072 1 0.1753 0.5530 0.952 0.000 0.048
#> SRR944073 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944075 2 0.6286 0.2496 0.464 0.536 0.000
#> SRR944074 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944076 2 0.6309 0.1667 0.496 0.504 0.000
#> SRR944077 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944078 2 0.6267 0.2695 0.452 0.548 0.000
#> SRR944079 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944080 2 0.0000 0.7156 0.000 1.000 0.000
#> SRR944081 1 0.6095 0.1397 0.608 0.392 0.000
#> SRR944082 3 0.5926 0.7621 0.356 0.000 0.644
#> SRR944083 1 0.0892 0.5770 0.980 0.000 0.020
#> SRR944084 2 0.6309 0.1538 0.500 0.500 0.000
#> SRR944085 2 0.6295 0.2328 0.472 0.528 0.000
#> SRR944086 1 0.6267 -0.0630 0.548 0.452 0.000
#> SRR944088 2 0.6308 0.1786 0.492 0.508 0.000
#> SRR944087 2 0.6309 0.1538 0.500 0.500 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.4193 0.8538 0.000 0.268 0.732 0.000
#> SRR944012 1 0.3047 0.6427 0.872 0.000 0.116 0.012
#> SRR944014 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944013 2 0.4961 -0.1891 0.000 0.552 0.448 0.000
#> SRR944015 4 0.0000 0.7420 0.000 0.000 0.000 1.000
#> SRR944016 3 0.4746 0.1517 0.304 0.008 0.688 0.000
#> SRR944017 2 0.4961 -0.1891 0.000 0.552 0.448 0.000
#> SRR944018 1 0.5062 0.6162 0.752 0.000 0.184 0.064
#> SRR944019 1 0.4907 0.5857 0.580 0.000 0.420 0.000
#> SRR944020 4 0.5690 0.6953 0.268 0.000 0.060 0.672
#> SRR944021 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944022 4 0.0469 0.7402 0.000 0.000 0.012 0.988
#> SRR944023 3 0.4552 0.8237 0.044 0.172 0.784 0.000
#> SRR944024 1 0.3975 0.7478 0.760 0.000 0.240 0.000
#> SRR944026 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944025 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944028 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944029 3 0.3726 0.8660 0.000 0.212 0.788 0.000
#> SRR944030 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944031 3 0.4365 0.8435 0.028 0.188 0.784 0.000
#> SRR944032 3 0.4304 0.8389 0.000 0.284 0.716 0.000
#> SRR944033 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944036 3 0.3726 0.8660 0.000 0.212 0.788 0.000
#> SRR944035 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944038 4 0.6465 0.5923 0.412 0.000 0.072 0.516
#> SRR944037 4 0.4826 0.7237 0.264 0.000 0.020 0.716
#> SRR944039 1 0.4817 0.6363 0.612 0.000 0.388 0.000
#> SRR944040 2 0.3942 0.5641 0.000 0.764 0.236 0.000
#> SRR944041 1 0.4285 0.5798 0.820 0.000 0.104 0.076
#> SRR944042 3 0.4049 0.8652 0.008 0.212 0.780 0.000
#> SRR944043 1 0.6215 -0.3207 0.600 0.000 0.072 0.328
#> SRR944044 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944046 3 0.4049 0.8652 0.008 0.212 0.780 0.000
#> SRR944045 2 0.0336 0.9315 0.000 0.992 0.008 0.000
#> SRR944047 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944048 3 0.4925 -0.2412 0.428 0.000 0.572 0.000
#> SRR944049 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944050 3 0.4746 0.1517 0.304 0.008 0.688 0.000
#> SRR944051 3 0.4304 0.8389 0.000 0.284 0.716 0.000
#> SRR944052 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944053 4 0.0000 0.7420 0.000 0.000 0.000 1.000
#> SRR944054 3 0.4331 0.8344 0.000 0.288 0.712 0.000
#> SRR944055 3 0.4193 0.8538 0.000 0.268 0.732 0.000
#> SRR944056 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944057 1 0.4522 0.7081 0.680 0.000 0.320 0.000
#> SRR944058 1 0.4327 0.7462 0.768 0.000 0.216 0.016
#> SRR944059 3 0.4193 0.8538 0.000 0.268 0.732 0.000
#> SRR944060 1 0.5845 -0.0594 0.672 0.000 0.076 0.252
#> SRR944061 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944062 4 0.6465 0.5923 0.412 0.000 0.072 0.516
#> SRR944063 4 0.1302 0.7348 0.044 0.000 0.000 0.956
#> SRR944064 2 0.1118 0.8997 0.000 0.964 0.036 0.000
#> SRR944065 4 0.4642 0.7325 0.240 0.000 0.020 0.740
#> SRR944066 1 0.3444 0.7364 0.816 0.000 0.184 0.000
#> SRR944067 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944068 4 0.0000 0.7420 0.000 0.000 0.000 1.000
#> SRR944069 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944070 4 0.6465 0.5923 0.412 0.000 0.072 0.516
#> SRR944071 3 0.3726 0.8660 0.000 0.212 0.788 0.000
#> SRR944072 1 0.3945 0.7464 0.780 0.000 0.216 0.004
#> SRR944073 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944075 3 0.4250 0.8473 0.000 0.276 0.724 0.000
#> SRR944074 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944076 3 0.3726 0.8660 0.000 0.212 0.788 0.000
#> SRR944077 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944078 3 0.4382 0.8240 0.000 0.296 0.704 0.000
#> SRR944079 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944080 2 0.0000 0.9395 0.000 1.000 0.000 0.000
#> SRR944081 3 0.7249 0.5463 0.260 0.200 0.540 0.000
#> SRR944082 4 0.6465 0.5923 0.412 0.000 0.072 0.516
#> SRR944083 1 0.3975 0.7478 0.760 0.000 0.240 0.000
#> SRR944084 3 0.4049 0.8652 0.008 0.212 0.780 0.000
#> SRR944085 3 0.4193 0.8538 0.000 0.268 0.732 0.000
#> SRR944086 3 0.5929 0.7803 0.108 0.204 0.688 0.000
#> SRR944088 3 0.3764 0.8662 0.000 0.216 0.784 0.000
#> SRR944087 3 0.4049 0.8652 0.008 0.212 0.780 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.2561 0.8538 0.000 0.144 0.856 0.000 0.000
#> SRR944012 1 0.4717 0.5785 0.704 0.000 0.048 0.004 0.244
#> SRR944014 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944013 2 0.4302 -0.0888 0.000 0.520 0.480 0.000 0.000
#> SRR944015 4 0.0703 0.8068 0.000 0.000 0.000 0.976 0.024
#> SRR944016 3 0.4291 -0.0345 0.464 0.000 0.536 0.000 0.000
#> SRR944017 2 0.4302 -0.0888 0.000 0.520 0.480 0.000 0.000
#> SRR944018 1 0.5483 0.1912 0.512 0.000 0.064 0.000 0.424
#> SRR944019 1 0.3582 0.6629 0.768 0.000 0.224 0.000 0.008
#> SRR944020 4 0.5575 0.5858 0.016 0.000 0.056 0.604 0.324
#> SRR944021 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944022 4 0.0324 0.8063 0.000 0.000 0.004 0.992 0.004
#> SRR944023 3 0.2747 0.8300 0.060 0.048 0.888 0.000 0.004
#> SRR944024 1 0.1211 0.7494 0.960 0.000 0.024 0.000 0.016
#> SRR944026 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944025 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944028 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944029 3 0.1638 0.8649 0.000 0.064 0.932 0.000 0.004
#> SRR944030 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944031 3 0.2597 0.8471 0.040 0.060 0.896 0.000 0.004
#> SRR944032 3 0.2891 0.8313 0.000 0.176 0.824 0.000 0.000
#> SRR944033 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944036 3 0.1478 0.8647 0.000 0.064 0.936 0.000 0.000
#> SRR944035 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944038 5 0.4563 0.8361 0.048 0.000 0.000 0.244 0.708
#> SRR944037 4 0.5072 0.6126 0.032 0.000 0.016 0.652 0.300
#> SRR944039 1 0.3690 0.6856 0.780 0.000 0.200 0.000 0.020
#> SRR944040 2 0.3707 0.5317 0.000 0.716 0.284 0.000 0.000
#> SRR944041 1 0.5124 0.5046 0.628 0.000 0.040 0.008 0.324
#> SRR944042 3 0.1924 0.8640 0.008 0.064 0.924 0.000 0.004
#> SRR944043 5 0.2464 0.7078 0.092 0.000 0.004 0.012 0.892
#> SRR944044 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944046 3 0.1924 0.8640 0.008 0.064 0.924 0.000 0.004
#> SRR944045 2 0.0290 0.9313 0.000 0.992 0.008 0.000 0.000
#> SRR944047 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944048 1 0.4288 0.3596 0.612 0.000 0.384 0.000 0.004
#> SRR944049 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944050 3 0.4291 -0.0345 0.464 0.000 0.536 0.000 0.000
#> SRR944051 3 0.2891 0.8313 0.000 0.176 0.824 0.000 0.000
#> SRR944052 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944053 4 0.0703 0.8068 0.000 0.000 0.000 0.976 0.024
#> SRR944054 3 0.2929 0.8271 0.000 0.180 0.820 0.000 0.000
#> SRR944055 3 0.2561 0.8538 0.000 0.144 0.856 0.000 0.000
#> SRR944056 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944057 1 0.2462 0.7344 0.880 0.000 0.112 0.000 0.008
#> SRR944058 1 0.1612 0.7495 0.948 0.000 0.016 0.012 0.024
#> SRR944059 3 0.2561 0.8538 0.000 0.144 0.856 0.000 0.000
#> SRR944060 5 0.3873 0.6449 0.212 0.000 0.012 0.008 0.768
#> SRR944061 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944062 5 0.4589 0.8346 0.048 0.000 0.000 0.248 0.704
#> SRR944063 4 0.1908 0.7917 0.000 0.000 0.000 0.908 0.092
#> SRR944064 2 0.0963 0.9034 0.000 0.964 0.036 0.000 0.000
#> SRR944065 4 0.4805 0.6383 0.032 0.000 0.016 0.700 0.252
#> SRR944066 1 0.2505 0.7191 0.888 0.000 0.020 0.000 0.092
#> SRR944067 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944068 4 0.0703 0.8068 0.000 0.000 0.000 0.976 0.024
#> SRR944069 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944070 5 0.4563 0.8361 0.048 0.000 0.000 0.244 0.708
#> SRR944071 3 0.1638 0.8649 0.000 0.064 0.932 0.000 0.004
#> SRR944072 1 0.1701 0.7488 0.936 0.000 0.016 0.000 0.048
#> SRR944073 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944075 3 0.2648 0.8492 0.000 0.152 0.848 0.000 0.000
#> SRR944074 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944076 3 0.1638 0.8649 0.000 0.064 0.932 0.000 0.004
#> SRR944077 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944078 3 0.2852 0.8346 0.000 0.172 0.828 0.000 0.000
#> SRR944079 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.9384 0.000 1.000 0.000 0.000 0.000
#> SRR944081 3 0.5347 0.4357 0.316 0.064 0.616 0.000 0.004
#> SRR944082 5 0.4589 0.8346 0.048 0.000 0.000 0.248 0.704
#> SRR944083 1 0.1211 0.7494 0.960 0.000 0.024 0.000 0.016
#> SRR944084 3 0.1924 0.8640 0.008 0.064 0.924 0.000 0.004
#> SRR944085 3 0.2561 0.8538 0.000 0.144 0.856 0.000 0.000
#> SRR944086 3 0.4028 0.7773 0.104 0.060 0.816 0.000 0.020
#> SRR944088 3 0.1544 0.8654 0.000 0.068 0.932 0.000 0.000
#> SRR944087 3 0.1924 0.8640 0.008 0.064 0.924 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.1863 0.8293 0.000 0.104 0.896 0.000 0.000 0.000
#> SRR944012 5 0.3717 0.7768 0.384 0.000 0.000 0.000 0.616 0.000
#> SRR944014 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944013 2 0.3866 -0.0145 0.000 0.516 0.484 0.000 0.000 0.000
#> SRR944015 4 0.0146 0.7653 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR944016 3 0.3995 -0.0706 0.480 0.000 0.516 0.000 0.004 0.000
#> SRR944017 2 0.3866 -0.0145 0.000 0.516 0.484 0.000 0.000 0.000
#> SRR944018 1 0.6193 -0.0511 0.472 0.000 0.044 0.000 0.116 0.368
#> SRR944019 1 0.4915 0.3951 0.704 0.000 0.176 0.000 0.084 0.036
#> SRR944020 4 0.5115 0.4882 0.000 0.000 0.000 0.460 0.460 0.080
#> SRR944021 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944022 4 0.1814 0.7610 0.000 0.000 0.000 0.900 0.100 0.000
#> SRR944023 3 0.1674 0.8109 0.068 0.000 0.924 0.000 0.004 0.004
#> SRR944024 1 0.0405 0.5156 0.988 0.000 0.004 0.000 0.000 0.008
#> SRR944026 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944025 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944028 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944029 3 0.0291 0.8434 0.004 0.004 0.992 0.000 0.000 0.000
#> SRR944030 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944031 3 0.1440 0.8272 0.044 0.004 0.944 0.000 0.004 0.004
#> SRR944032 3 0.2340 0.7965 0.000 0.148 0.852 0.000 0.000 0.000
#> SRR944033 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944036 3 0.0146 0.8432 0.000 0.004 0.996 0.000 0.000 0.000
#> SRR944035 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944038 6 0.2854 0.8080 0.000 0.000 0.000 0.208 0.000 0.792
#> SRR944037 4 0.5547 0.5983 0.000 0.000 0.000 0.528 0.312 0.160
#> SRR944039 1 0.4041 0.4414 0.764 0.000 0.172 0.000 0.044 0.020
#> SRR944040 2 0.3371 0.5427 0.000 0.708 0.292 0.000 0.000 0.000
#> SRR944041 5 0.5029 0.7673 0.444 0.000 0.000 0.000 0.484 0.072
#> SRR944042 3 0.0653 0.8423 0.012 0.004 0.980 0.000 0.000 0.004
#> SRR944043 6 0.3566 0.5996 0.024 0.000 0.000 0.000 0.224 0.752
#> SRR944044 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944046 3 0.0653 0.8423 0.012 0.004 0.980 0.000 0.000 0.004
#> SRR944045 2 0.0260 0.9281 0.000 0.992 0.008 0.000 0.000 0.000
#> SRR944047 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944048 1 0.3659 0.2283 0.636 0.000 0.364 0.000 0.000 0.000
#> SRR944049 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944050 3 0.3995 -0.0706 0.480 0.000 0.516 0.000 0.004 0.000
#> SRR944051 3 0.2340 0.7965 0.000 0.148 0.852 0.000 0.000 0.000
#> SRR944052 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944053 4 0.0146 0.7653 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR944054 3 0.2378 0.7921 0.000 0.152 0.848 0.000 0.000 0.000
#> SRR944055 3 0.1863 0.8293 0.000 0.104 0.896 0.000 0.000 0.000
#> SRR944056 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944057 1 0.1858 0.5091 0.904 0.000 0.092 0.000 0.004 0.000
#> SRR944058 1 0.2613 0.4061 0.848 0.000 0.000 0.000 0.140 0.012
#> SRR944059 3 0.1863 0.8293 0.000 0.104 0.896 0.000 0.000 0.000
#> SRR944060 6 0.5073 0.5159 0.152 0.000 0.004 0.000 0.196 0.648
#> SRR944061 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944062 6 0.2883 0.8068 0.000 0.000 0.000 0.212 0.000 0.788
#> SRR944063 4 0.1865 0.7587 0.000 0.000 0.000 0.920 0.040 0.040
#> SRR944064 2 0.0865 0.8988 0.000 0.964 0.036 0.000 0.000 0.000
#> SRR944065 4 0.5289 0.6200 0.000 0.000 0.000 0.576 0.288 0.136
#> SRR944066 1 0.1956 0.4462 0.908 0.000 0.004 0.000 0.008 0.080
#> SRR944067 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944068 4 0.0146 0.7653 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR944069 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944070 6 0.2854 0.8080 0.000 0.000 0.000 0.208 0.000 0.792
#> SRR944071 3 0.0436 0.8434 0.004 0.004 0.988 0.000 0.000 0.004
#> SRR944072 1 0.2631 0.3675 0.820 0.000 0.000 0.000 0.180 0.000
#> SRR944073 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944075 3 0.1957 0.8245 0.000 0.112 0.888 0.000 0.000 0.000
#> SRR944074 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944076 3 0.0436 0.8434 0.004 0.004 0.988 0.000 0.000 0.004
#> SRR944077 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944078 3 0.2300 0.8004 0.000 0.144 0.856 0.000 0.000 0.000
#> SRR944079 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.9356 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944081 3 0.4600 0.4103 0.284 0.004 0.664 0.000 0.036 0.012
#> SRR944082 6 0.2883 0.8068 0.000 0.000 0.000 0.212 0.000 0.788
#> SRR944083 1 0.0405 0.5156 0.988 0.000 0.004 0.000 0.000 0.008
#> SRR944084 3 0.0653 0.8423 0.012 0.004 0.980 0.000 0.000 0.004
#> SRR944085 3 0.1863 0.8293 0.000 0.104 0.896 0.000 0.000 0.000
#> SRR944086 3 0.3507 0.7053 0.016 0.000 0.816 0.000 0.124 0.044
#> SRR944088 3 0.0260 0.8440 0.000 0.008 0.992 0.000 0.000 0.000
#> SRR944087 3 0.0653 0.8423 0.012 0.004 0.980 0.000 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "kmeans"]
# you can also extract it by
# res = res_list["ATC:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.781 0.905 0.953 0.4765 0.539 0.539
#> 3 3 0.793 0.625 0.866 0.3814 0.687 0.487
#> 4 4 0.902 0.915 0.951 0.1125 0.791 0.506
#> 5 5 0.812 0.677 0.792 0.0513 0.943 0.790
#> 6 6 0.813 0.670 0.796 0.0373 0.949 0.780
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.000 0.925 0.000 1.000
#> SRR944012 1 0.000 0.998 1.000 0.000
#> SRR944014 2 0.000 0.925 0.000 1.000
#> SRR944013 2 0.000 0.925 0.000 1.000
#> SRR944015 1 0.000 0.998 1.000 0.000
#> SRR944016 2 0.722 0.781 0.200 0.800
#> SRR944017 2 0.000 0.925 0.000 1.000
#> SRR944018 1 0.000 0.998 1.000 0.000
#> SRR944019 1 0.000 0.998 1.000 0.000
#> SRR944020 1 0.000 0.998 1.000 0.000
#> SRR944021 2 0.000 0.925 0.000 1.000
#> SRR944022 1 0.000 0.998 1.000 0.000
#> SRR944023 1 0.000 0.998 1.000 0.000
#> SRR944024 1 0.000 0.998 1.000 0.000
#> SRR944026 2 0.000 0.925 0.000 1.000
#> SRR944025 2 0.000 0.925 0.000 1.000
#> SRR944028 2 0.000 0.925 0.000 1.000
#> SRR944029 2 0.722 0.781 0.200 0.800
#> SRR944030 2 0.000 0.925 0.000 1.000
#> SRR944031 2 0.753 0.763 0.216 0.784
#> SRR944032 2 0.000 0.925 0.000 1.000
#> SRR944033 2 0.000 0.925 0.000 1.000
#> SRR944034 2 0.000 0.925 0.000 1.000
#> SRR944036 2 0.730 0.776 0.204 0.796
#> SRR944035 2 0.000 0.925 0.000 1.000
#> SRR944038 1 0.000 0.998 1.000 0.000
#> SRR944037 1 0.000 0.998 1.000 0.000
#> SRR944039 1 0.000 0.998 1.000 0.000
#> SRR944040 2 0.000 0.925 0.000 1.000
#> SRR944041 1 0.000 0.998 1.000 0.000
#> SRR944042 1 0.000 0.998 1.000 0.000
#> SRR944043 1 0.000 0.998 1.000 0.000
#> SRR944044 2 0.000 0.925 0.000 1.000
#> SRR944046 2 0.963 0.486 0.388 0.612
#> SRR944045 2 0.000 0.925 0.000 1.000
#> SRR944047 2 0.000 0.925 0.000 1.000
#> SRR944048 2 0.680 0.799 0.180 0.820
#> SRR944049 2 0.000 0.925 0.000 1.000
#> SRR944050 2 0.689 0.795 0.184 0.816
#> SRR944051 2 0.000 0.925 0.000 1.000
#> SRR944052 2 0.000 0.925 0.000 1.000
#> SRR944053 1 0.000 0.998 1.000 0.000
#> SRR944054 2 0.000 0.925 0.000 1.000
#> SRR944055 2 0.000 0.925 0.000 1.000
#> SRR944056 2 0.000 0.925 0.000 1.000
#> SRR944057 1 0.311 0.932 0.944 0.056
#> SRR944058 1 0.000 0.998 1.000 0.000
#> SRR944059 2 0.000 0.925 0.000 1.000
#> SRR944060 1 0.000 0.998 1.000 0.000
#> SRR944061 2 0.000 0.925 0.000 1.000
#> SRR944062 1 0.000 0.998 1.000 0.000
#> SRR944063 1 0.000 0.998 1.000 0.000
#> SRR944064 2 0.000 0.925 0.000 1.000
#> SRR944065 1 0.000 0.998 1.000 0.000
#> SRR944066 1 0.000 0.998 1.000 0.000
#> SRR944067 2 0.000 0.925 0.000 1.000
#> SRR944068 1 0.000 0.998 1.000 0.000
#> SRR944069 2 0.000 0.925 0.000 1.000
#> SRR944070 1 0.000 0.998 1.000 0.000
#> SRR944071 2 0.722 0.781 0.200 0.800
#> SRR944072 1 0.000 0.998 1.000 0.000
#> SRR944073 2 0.000 0.925 0.000 1.000
#> SRR944075 2 0.000 0.925 0.000 1.000
#> SRR944074 2 0.000 0.925 0.000 1.000
#> SRR944076 2 0.722 0.781 0.200 0.800
#> SRR944077 2 0.000 0.925 0.000 1.000
#> SRR944078 2 0.000 0.925 0.000 1.000
#> SRR944079 2 0.000 0.925 0.000 1.000
#> SRR944080 2 0.000 0.925 0.000 1.000
#> SRR944081 2 0.983 0.404 0.424 0.576
#> SRR944082 1 0.000 0.998 1.000 0.000
#> SRR944083 1 0.000 0.998 1.000 0.000
#> SRR944084 2 0.983 0.404 0.424 0.576
#> SRR944085 2 0.000 0.925 0.000 1.000
#> SRR944086 2 0.990 0.363 0.440 0.560
#> SRR944088 2 0.000 0.925 0.000 1.000
#> SRR944087 2 0.844 0.690 0.272 0.728
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944012 1 0.5706 -0.65283 0.680 0.000 0.320
#> SRR944014 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944013 2 0.5968 0.77639 0.000 0.636 0.364
#> SRR944015 3 0.6267 1.00000 0.452 0.000 0.548
#> SRR944016 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944017 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944018 1 0.6225 0.78150 0.568 0.432 0.000
#> SRR944019 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944020 3 0.6267 1.00000 0.452 0.000 0.548
#> SRR944021 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944022 3 0.6267 1.00000 0.452 0.000 0.548
#> SRR944023 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944024 1 0.1643 -0.00831 0.956 0.000 0.044
#> SRR944026 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944025 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944028 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944029 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944030 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944031 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944032 1 0.6307 0.75186 0.512 0.488 0.000
#> SRR944033 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944034 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944036 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944035 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944038 3 0.6267 1.00000 0.452 0.000 0.548
#> SRR944037 3 0.6267 1.00000 0.452 0.000 0.548
#> SRR944039 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944040 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944041 1 0.5706 -0.65283 0.680 0.000 0.320
#> SRR944042 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944043 3 0.6267 1.00000 0.452 0.000 0.548
#> SRR944044 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944046 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944045 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944047 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944048 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944049 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944050 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944051 2 0.5327 -0.36848 0.272 0.728 0.000
#> SRR944052 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944053 3 0.6267 1.00000 0.452 0.000 0.548
#> SRR944054 2 0.0747 0.28011 0.016 0.984 0.000
#> SRR944055 2 0.0424 0.29647 0.008 0.992 0.000
#> SRR944056 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944057 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944058 1 0.6299 -0.90709 0.524 0.000 0.476
#> SRR944059 2 0.1289 0.24491 0.032 0.968 0.000
#> SRR944060 1 0.5363 -0.57398 0.724 0.000 0.276
#> SRR944061 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944062 3 0.6267 1.00000 0.452 0.000 0.548
#> SRR944063 3 0.6267 1.00000 0.452 0.000 0.548
#> SRR944064 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944065 3 0.6267 1.00000 0.452 0.000 0.548
#> SRR944066 1 0.5216 -0.54401 0.740 0.000 0.260
#> SRR944067 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944068 3 0.6267 1.00000 0.452 0.000 0.548
#> SRR944069 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944070 3 0.6267 1.00000 0.452 0.000 0.548
#> SRR944071 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944072 1 0.5706 -0.65283 0.680 0.000 0.320
#> SRR944073 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944075 2 0.5785 -0.48840 0.332 0.668 0.000
#> SRR944074 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944076 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944077 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944078 2 0.0661 0.31927 0.004 0.988 0.008
#> SRR944079 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944080 2 0.6267 0.83669 0.000 0.548 0.452
#> SRR944081 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944082 3 0.6267 1.00000 0.452 0.000 0.548
#> SRR944083 1 0.6252 0.78862 0.556 0.444 0.000
#> SRR944084 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944085 2 0.6280 -0.69873 0.460 0.540 0.000
#> SRR944086 1 0.6267 0.79280 0.548 0.452 0.000
#> SRR944088 2 0.5327 -0.36848 0.272 0.728 0.000
#> SRR944087 1 0.6267 0.79280 0.548 0.452 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.0188 0.923 0.004 0.000 0.996 0.000
#> SRR944012 1 0.2334 0.882 0.908 0.000 0.004 0.088
#> SRR944014 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944013 3 0.4655 0.532 0.004 0.312 0.684 0.000
#> SRR944015 4 0.0000 0.901 0.000 0.000 0.000 1.000
#> SRR944016 3 0.3528 0.840 0.192 0.000 0.808 0.000
#> SRR944017 2 0.2149 0.904 0.000 0.912 0.088 0.000
#> SRR944018 1 0.0188 0.918 0.996 0.000 0.004 0.000
#> SRR944019 1 0.1118 0.897 0.964 0.000 0.036 0.000
#> SRR944020 4 0.0000 0.901 0.000 0.000 0.000 1.000
#> SRR944021 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944022 4 0.0000 0.901 0.000 0.000 0.000 1.000
#> SRR944023 1 0.1118 0.899 0.964 0.000 0.036 0.000
#> SRR944024 1 0.0376 0.919 0.992 0.000 0.004 0.004
#> SRR944026 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944025 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944028 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944029 3 0.0336 0.921 0.008 0.000 0.992 0.000
#> SRR944030 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944031 3 0.2216 0.921 0.092 0.000 0.908 0.000
#> SRR944032 3 0.0188 0.922 0.004 0.000 0.996 0.000
#> SRR944033 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944036 3 0.2216 0.921 0.092 0.000 0.908 0.000
#> SRR944035 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944038 4 0.3074 0.807 0.152 0.000 0.000 0.848
#> SRR944037 4 0.0000 0.901 0.000 0.000 0.000 1.000
#> SRR944039 1 0.0336 0.917 0.992 0.000 0.008 0.000
#> SRR944040 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944041 1 0.2281 0.878 0.904 0.000 0.000 0.096
#> SRR944042 3 0.2216 0.921 0.092 0.000 0.908 0.000
#> SRR944043 1 0.2530 0.864 0.888 0.000 0.000 0.112
#> SRR944044 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944046 3 0.2216 0.921 0.092 0.000 0.908 0.000
#> SRR944045 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944047 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944048 3 0.3528 0.840 0.192 0.000 0.808 0.000
#> SRR944049 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944050 3 0.3528 0.840 0.192 0.000 0.808 0.000
#> SRR944051 3 0.0336 0.921 0.008 0.000 0.992 0.000
#> SRR944052 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944053 4 0.0000 0.901 0.000 0.000 0.000 1.000
#> SRR944054 3 0.0376 0.920 0.004 0.004 0.992 0.000
#> SRR944055 3 0.0336 0.921 0.000 0.008 0.992 0.000
#> SRR944056 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944057 1 0.3219 0.734 0.836 0.000 0.164 0.000
#> SRR944058 1 0.2345 0.876 0.900 0.000 0.000 0.100
#> SRR944059 3 0.0336 0.921 0.000 0.008 0.992 0.000
#> SRR944060 1 0.0592 0.917 0.984 0.000 0.000 0.016
#> SRR944061 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944062 4 0.2921 0.818 0.140 0.000 0.000 0.860
#> SRR944063 4 0.0000 0.901 0.000 0.000 0.000 1.000
#> SRR944064 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944065 4 0.0000 0.901 0.000 0.000 0.000 1.000
#> SRR944066 1 0.0376 0.919 0.992 0.000 0.004 0.004
#> SRR944067 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944068 4 0.0000 0.901 0.000 0.000 0.000 1.000
#> SRR944069 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944070 4 0.4624 0.538 0.340 0.000 0.000 0.660
#> SRR944071 3 0.1557 0.925 0.056 0.000 0.944 0.000
#> SRR944072 1 0.2345 0.876 0.900 0.000 0.000 0.100
#> SRR944073 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944075 3 0.0188 0.923 0.004 0.000 0.996 0.000
#> SRR944074 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944076 3 0.2216 0.921 0.092 0.000 0.908 0.000
#> SRR944077 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944078 3 0.0336 0.921 0.000 0.008 0.992 0.000
#> SRR944079 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944080 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> SRR944081 3 0.2281 0.921 0.096 0.000 0.904 0.000
#> SRR944082 4 0.4776 0.441 0.376 0.000 0.000 0.624
#> SRR944083 1 0.0336 0.917 0.992 0.000 0.008 0.000
#> SRR944084 3 0.2281 0.921 0.096 0.000 0.904 0.000
#> SRR944085 3 0.0188 0.923 0.004 0.000 0.996 0.000
#> SRR944086 3 0.2281 0.921 0.096 0.000 0.904 0.000
#> SRR944088 3 0.0336 0.921 0.008 0.000 0.992 0.000
#> SRR944087 3 0.2216 0.921 0.092 0.000 0.908 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 5 0.3586 0.3805 0.000 0.000 0.264 0.000 0.736
#> SRR944012 1 0.2646 0.7677 0.868 0.000 0.124 0.004 0.004
#> SRR944014 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944013 5 0.3521 0.2696 0.000 0.232 0.004 0.000 0.764
#> SRR944015 4 0.0000 0.7925 0.000 0.000 0.000 1.000 0.000
#> SRR944016 3 0.6338 0.4409 0.160 0.000 0.448 0.000 0.392
#> SRR944017 2 0.3480 0.6903 0.000 0.752 0.000 0.000 0.248
#> SRR944018 1 0.1544 0.8000 0.932 0.000 0.068 0.000 0.000
#> SRR944019 1 0.5102 0.6326 0.696 0.000 0.176 0.000 0.128
#> SRR944020 4 0.2536 0.7859 0.004 0.000 0.128 0.868 0.000
#> SRR944021 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944022 4 0.0162 0.7922 0.000 0.000 0.004 0.996 0.000
#> SRR944023 3 0.6202 0.1664 0.372 0.000 0.484 0.000 0.144
#> SRR944024 1 0.2280 0.7914 0.880 0.000 0.120 0.000 0.000
#> SRR944026 2 0.0451 0.9792 0.000 0.988 0.004 0.000 0.008
#> SRR944025 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944028 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944029 5 0.2605 0.4299 0.000 0.000 0.148 0.000 0.852
#> SRR944030 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944031 3 0.4306 0.5022 0.000 0.000 0.508 0.000 0.492
#> SRR944032 5 0.0510 0.5521 0.000 0.000 0.016 0.000 0.984
#> SRR944033 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944036 3 0.4302 0.5032 0.000 0.000 0.520 0.000 0.480
#> SRR944035 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944038 4 0.6130 0.6016 0.180 0.000 0.264 0.556 0.000
#> SRR944037 4 0.3048 0.7799 0.004 0.000 0.176 0.820 0.000
#> SRR944039 1 0.3326 0.7343 0.824 0.000 0.152 0.000 0.024
#> SRR944040 2 0.0510 0.9743 0.000 0.984 0.000 0.000 0.016
#> SRR944041 1 0.3128 0.7434 0.824 0.000 0.168 0.004 0.004
#> SRR944042 3 0.4305 0.5015 0.000 0.000 0.512 0.000 0.488
#> SRR944043 1 0.4866 0.5530 0.620 0.000 0.344 0.036 0.000
#> SRR944044 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944046 3 0.4306 0.5022 0.000 0.000 0.508 0.000 0.492
#> SRR944045 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944047 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944048 3 0.6330 0.4455 0.160 0.000 0.456 0.000 0.384
#> SRR944049 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944050 3 0.6338 0.4409 0.160 0.000 0.448 0.000 0.392
#> SRR944051 5 0.0703 0.5511 0.000 0.000 0.024 0.000 0.976
#> SRR944052 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944053 4 0.0000 0.7925 0.000 0.000 0.000 1.000 0.000
#> SRR944054 5 0.0510 0.5541 0.000 0.000 0.016 0.000 0.984
#> SRR944055 5 0.2852 0.5440 0.000 0.000 0.172 0.000 0.828
#> SRR944056 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944057 1 0.5369 0.3192 0.552 0.000 0.388 0.000 0.060
#> SRR944058 1 0.1571 0.7886 0.936 0.000 0.060 0.004 0.000
#> SRR944059 5 0.2852 0.5440 0.000 0.000 0.172 0.000 0.828
#> SRR944060 1 0.3969 0.6521 0.692 0.000 0.304 0.004 0.000
#> SRR944061 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944062 4 0.6111 0.6063 0.180 0.000 0.260 0.560 0.000
#> SRR944063 4 0.0510 0.7945 0.000 0.000 0.016 0.984 0.000
#> SRR944064 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944065 4 0.2930 0.7829 0.004 0.000 0.164 0.832 0.000
#> SRR944066 1 0.2127 0.7919 0.892 0.000 0.108 0.000 0.000
#> SRR944067 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944068 4 0.0000 0.7925 0.000 0.000 0.000 1.000 0.000
#> SRR944069 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944070 4 0.6734 0.3285 0.324 0.000 0.268 0.408 0.000
#> SRR944071 5 0.4304 -0.5064 0.000 0.000 0.484 0.000 0.516
#> SRR944072 1 0.0451 0.7989 0.988 0.000 0.008 0.004 0.000
#> SRR944073 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944075 5 0.2891 0.5400 0.000 0.000 0.176 0.000 0.824
#> SRR944074 2 0.0451 0.9792 0.000 0.988 0.004 0.000 0.008
#> SRR944076 3 0.4307 0.4903 0.000 0.000 0.504 0.000 0.496
#> SRR944077 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944078 5 0.2773 0.5455 0.000 0.000 0.164 0.000 0.836
#> SRR944079 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.9880 0.000 1.000 0.000 0.000 0.000
#> SRR944081 5 0.4608 -0.0776 0.024 0.000 0.336 0.000 0.640
#> SRR944082 4 0.6678 0.4464 0.264 0.000 0.300 0.436 0.000
#> SRR944083 1 0.2377 0.7904 0.872 0.000 0.128 0.000 0.000
#> SRR944084 5 0.4306 -0.4710 0.000 0.000 0.492 0.000 0.508
#> SRR944085 5 0.2852 0.5440 0.000 0.000 0.172 0.000 0.828
#> SRR944086 5 0.4886 -0.1739 0.032 0.000 0.372 0.000 0.596
#> SRR944088 5 0.0703 0.5511 0.000 0.000 0.024 0.000 0.976
#> SRR944087 3 0.4306 0.5022 0.000 0.000 0.508 0.000 0.492
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 5 0.3126 0.110 0.000 0.000 0.248 0.000 0.752 0.000
#> SRR944012 1 0.3920 0.578 0.736 0.000 0.048 0.000 0.000 0.216
#> SRR944014 2 0.0458 0.965 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944013 5 0.5680 0.454 0.000 0.088 0.264 0.000 0.600 0.048
#> SRR944015 4 0.0405 0.887 0.000 0.000 0.004 0.988 0.000 0.008
#> SRR944016 3 0.6607 0.443 0.200 0.000 0.508 0.000 0.224 0.068
#> SRR944017 2 0.4587 0.427 0.000 0.596 0.000 0.000 0.356 0.048
#> SRR944018 1 0.4232 0.647 0.732 0.000 0.100 0.000 0.000 0.168
#> SRR944019 1 0.3190 0.536 0.772 0.000 0.220 0.000 0.000 0.008
#> SRR944020 4 0.3253 0.831 0.032 0.000 0.032 0.844 0.000 0.092
#> SRR944021 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944022 4 0.0000 0.888 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR944023 3 0.5952 0.447 0.184 0.000 0.616 0.000 0.120 0.080
#> SRR944024 1 0.4692 0.490 0.512 0.000 0.044 0.000 0.000 0.444
#> SRR944026 2 0.2461 0.882 0.000 0.888 0.004 0.000 0.064 0.044
#> SRR944025 2 0.0260 0.963 0.000 0.992 0.000 0.000 0.000 0.008
#> SRR944028 2 0.0547 0.964 0.000 0.980 0.000 0.000 0.000 0.020
#> SRR944029 3 0.4527 -0.288 0.004 0.000 0.516 0.000 0.456 0.024
#> SRR944030 2 0.0458 0.965 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944031 3 0.3847 0.556 0.000 0.000 0.544 0.000 0.456 0.000
#> SRR944032 5 0.4476 0.539 0.008 0.000 0.268 0.000 0.676 0.048
#> SRR944033 2 0.0458 0.965 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944034 2 0.0458 0.965 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944036 3 0.4189 0.558 0.004 0.000 0.552 0.000 0.436 0.008
#> SRR944035 2 0.0458 0.965 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944038 6 0.3744 0.745 0.016 0.000 0.004 0.256 0.000 0.724
#> SRR944037 4 0.4100 0.754 0.032 0.000 0.032 0.760 0.000 0.176
#> SRR944039 1 0.2100 0.608 0.884 0.000 0.112 0.000 0.000 0.004
#> SRR944040 2 0.1563 0.921 0.000 0.932 0.000 0.000 0.056 0.012
#> SRR944041 1 0.4332 0.477 0.664 0.000 0.048 0.000 0.000 0.288
#> SRR944042 3 0.3838 0.562 0.000 0.000 0.552 0.000 0.448 0.000
#> SRR944043 6 0.3503 0.547 0.180 0.000 0.020 0.012 0.000 0.788
#> SRR944044 2 0.0260 0.963 0.000 0.992 0.000 0.000 0.000 0.008
#> SRR944046 3 0.3838 0.562 0.000 0.000 0.552 0.000 0.448 0.000
#> SRR944045 2 0.0146 0.964 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR944047 2 0.0458 0.965 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944048 3 0.6622 0.444 0.196 0.000 0.504 0.000 0.232 0.068
#> SRR944049 2 0.0260 0.963 0.000 0.992 0.000 0.000 0.000 0.008
#> SRR944050 3 0.6607 0.443 0.200 0.000 0.508 0.000 0.224 0.068
#> SRR944051 5 0.4518 0.542 0.004 0.000 0.264 0.000 0.672 0.060
#> SRR944052 2 0.0146 0.964 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR944053 4 0.0146 0.888 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR944054 5 0.4464 0.543 0.004 0.000 0.264 0.000 0.676 0.056
#> SRR944055 5 0.1327 0.534 0.000 0.000 0.064 0.000 0.936 0.000
#> SRR944056 2 0.0260 0.965 0.000 0.992 0.000 0.000 0.000 0.008
#> SRR944057 1 0.5477 0.213 0.456 0.000 0.420 0.000 0.000 0.124
#> SRR944058 1 0.3665 0.619 0.728 0.000 0.020 0.000 0.000 0.252
#> SRR944059 5 0.1327 0.534 0.000 0.000 0.064 0.000 0.936 0.000
#> SRR944060 6 0.3694 0.456 0.232 0.000 0.028 0.000 0.000 0.740
#> SRR944061 2 0.0458 0.965 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944062 6 0.3650 0.709 0.012 0.000 0.000 0.280 0.000 0.708
#> SRR944063 4 0.1003 0.886 0.004 0.000 0.004 0.964 0.000 0.028
#> SRR944064 2 0.0363 0.962 0.000 0.988 0.000 0.000 0.000 0.012
#> SRR944065 4 0.4060 0.749 0.032 0.000 0.028 0.760 0.000 0.180
#> SRR944066 1 0.4780 0.521 0.552 0.000 0.056 0.000 0.000 0.392
#> SRR944067 2 0.0260 0.963 0.000 0.992 0.000 0.000 0.000 0.008
#> SRR944068 4 0.0405 0.887 0.000 0.000 0.004 0.988 0.000 0.008
#> SRR944069 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944070 6 0.3974 0.760 0.056 0.000 0.004 0.188 0.000 0.752
#> SRR944071 5 0.3868 -0.563 0.000 0.000 0.496 0.000 0.504 0.000
#> SRR944072 1 0.3368 0.641 0.756 0.000 0.012 0.000 0.000 0.232
#> SRR944073 2 0.0458 0.965 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944075 5 0.1327 0.534 0.000 0.000 0.064 0.000 0.936 0.000
#> SRR944074 2 0.2461 0.882 0.000 0.888 0.004 0.000 0.064 0.044
#> SRR944076 3 0.3847 0.556 0.000 0.000 0.544 0.000 0.456 0.000
#> SRR944077 2 0.0458 0.965 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944078 5 0.0000 0.547 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR944079 2 0.0458 0.965 0.000 0.984 0.000 0.000 0.000 0.016
#> SRR944080 2 0.0146 0.964 0.000 0.996 0.000 0.000 0.000 0.004
#> SRR944081 3 0.5564 0.181 0.160 0.000 0.628 0.000 0.184 0.028
#> SRR944082 6 0.3688 0.739 0.020 0.000 0.000 0.256 0.000 0.724
#> SRR944083 1 0.4646 0.552 0.616 0.000 0.060 0.000 0.000 0.324
#> SRR944084 3 0.4051 0.551 0.000 0.000 0.560 0.000 0.432 0.008
#> SRR944085 5 0.1327 0.534 0.000 0.000 0.064 0.000 0.936 0.000
#> SRR944086 3 0.5259 0.215 0.148 0.000 0.668 0.000 0.156 0.028
#> SRR944088 5 0.4518 0.542 0.004 0.000 0.264 0.000 0.672 0.060
#> SRR944087 3 0.3838 0.562 0.000 0.000 0.552 0.000 0.448 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "skmeans"]
# you can also extract it by
# res = res_list["ATC:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.969 0.986 0.5065 0.494 0.494
#> 3 3 0.903 0.876 0.949 0.2064 0.889 0.777
#> 4 4 0.853 0.842 0.926 0.0736 0.955 0.887
#> 5 5 0.797 0.740 0.889 0.0479 0.990 0.974
#> 6 6 0.796 0.679 0.850 0.0335 0.976 0.933
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.0000 1.000 0.000 1.000
#> SRR944012 1 0.0000 0.973 1.000 0.000
#> SRR944014 2 0.0000 1.000 0.000 1.000
#> SRR944013 2 0.0000 1.000 0.000 1.000
#> SRR944015 1 0.0000 0.973 1.000 0.000
#> SRR944016 1 0.7453 0.742 0.788 0.212
#> SRR944017 2 0.0000 1.000 0.000 1.000
#> SRR944018 1 0.0000 0.973 1.000 0.000
#> SRR944019 1 0.0000 0.973 1.000 0.000
#> SRR944020 1 0.0000 0.973 1.000 0.000
#> SRR944021 2 0.0000 1.000 0.000 1.000
#> SRR944022 1 0.0000 0.973 1.000 0.000
#> SRR944023 1 0.0000 0.973 1.000 0.000
#> SRR944024 1 0.0000 0.973 1.000 0.000
#> SRR944026 2 0.0000 1.000 0.000 1.000
#> SRR944025 2 0.0000 1.000 0.000 1.000
#> SRR944028 2 0.0000 1.000 0.000 1.000
#> SRR944029 1 0.2236 0.943 0.964 0.036
#> SRR944030 2 0.0000 1.000 0.000 1.000
#> SRR944031 1 0.0000 0.973 1.000 0.000
#> SRR944032 2 0.0000 1.000 0.000 1.000
#> SRR944033 2 0.0000 1.000 0.000 1.000
#> SRR944034 2 0.0000 1.000 0.000 1.000
#> SRR944036 1 0.0000 0.973 1.000 0.000
#> SRR944035 2 0.0000 1.000 0.000 1.000
#> SRR944038 1 0.0000 0.973 1.000 0.000
#> SRR944037 1 0.0000 0.973 1.000 0.000
#> SRR944039 1 0.0000 0.973 1.000 0.000
#> SRR944040 2 0.0000 1.000 0.000 1.000
#> SRR944041 1 0.0000 0.973 1.000 0.000
#> SRR944042 1 0.0000 0.973 1.000 0.000
#> SRR944043 1 0.0000 0.973 1.000 0.000
#> SRR944044 2 0.0000 1.000 0.000 1.000
#> SRR944046 1 0.0000 0.973 1.000 0.000
#> SRR944045 2 0.0000 1.000 0.000 1.000
#> SRR944047 2 0.0000 1.000 0.000 1.000
#> SRR944048 1 0.8443 0.644 0.728 0.272
#> SRR944049 2 0.0000 1.000 0.000 1.000
#> SRR944050 1 0.9661 0.391 0.608 0.392
#> SRR944051 2 0.0000 1.000 0.000 1.000
#> SRR944052 2 0.0000 1.000 0.000 1.000
#> SRR944053 1 0.0000 0.973 1.000 0.000
#> SRR944054 2 0.0000 1.000 0.000 1.000
#> SRR944055 2 0.0000 1.000 0.000 1.000
#> SRR944056 2 0.0000 1.000 0.000 1.000
#> SRR944057 1 0.0000 0.973 1.000 0.000
#> SRR944058 1 0.0000 0.973 1.000 0.000
#> SRR944059 2 0.0000 1.000 0.000 1.000
#> SRR944060 1 0.0000 0.973 1.000 0.000
#> SRR944061 2 0.0000 1.000 0.000 1.000
#> SRR944062 1 0.0000 0.973 1.000 0.000
#> SRR944063 1 0.0000 0.973 1.000 0.000
#> SRR944064 2 0.0000 1.000 0.000 1.000
#> SRR944065 1 0.0000 0.973 1.000 0.000
#> SRR944066 1 0.0000 0.973 1.000 0.000
#> SRR944067 2 0.0000 1.000 0.000 1.000
#> SRR944068 1 0.0000 0.973 1.000 0.000
#> SRR944069 2 0.0000 1.000 0.000 1.000
#> SRR944070 1 0.0000 0.973 1.000 0.000
#> SRR944071 1 0.5519 0.851 0.872 0.128
#> SRR944072 1 0.0000 0.973 1.000 0.000
#> SRR944073 2 0.0000 1.000 0.000 1.000
#> SRR944075 2 0.0000 1.000 0.000 1.000
#> SRR944074 2 0.0000 1.000 0.000 1.000
#> SRR944076 1 0.0376 0.970 0.996 0.004
#> SRR944077 2 0.0000 1.000 0.000 1.000
#> SRR944078 2 0.0000 1.000 0.000 1.000
#> SRR944079 2 0.0000 1.000 0.000 1.000
#> SRR944080 2 0.0000 1.000 0.000 1.000
#> SRR944081 1 0.0000 0.973 1.000 0.000
#> SRR944082 1 0.0000 0.973 1.000 0.000
#> SRR944083 1 0.0000 0.973 1.000 0.000
#> SRR944084 1 0.0000 0.973 1.000 0.000
#> SRR944085 2 0.0000 1.000 0.000 1.000
#> SRR944086 1 0.0000 0.973 1.000 0.000
#> SRR944088 2 0.0000 1.000 0.000 1.000
#> SRR944087 1 0.0000 0.973 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 3 0.4654 0.6419 0.000 0.208 0.792
#> SRR944012 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944014 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944013 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944015 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944016 1 0.7710 0.2488 0.576 0.056 0.368
#> SRR944017 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944018 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944019 1 0.0592 0.9224 0.988 0.000 0.012
#> SRR944020 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944021 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944022 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944023 1 0.1163 0.9073 0.972 0.000 0.028
#> SRR944024 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944026 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944025 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944028 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944029 1 0.7114 0.0832 0.584 0.028 0.388
#> SRR944030 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944031 3 0.1860 0.7949 0.052 0.000 0.948
#> SRR944032 2 0.0424 0.9821 0.000 0.992 0.008
#> SRR944033 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944034 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944036 3 0.0000 0.7774 0.000 0.000 1.000
#> SRR944035 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944038 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944037 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944039 1 0.0592 0.9224 0.988 0.000 0.012
#> SRR944040 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944041 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944042 3 0.5706 0.5859 0.320 0.000 0.680
#> SRR944043 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944044 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944046 3 0.3619 0.7718 0.136 0.000 0.864
#> SRR944045 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944047 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944048 3 0.7382 0.0657 0.456 0.032 0.512
#> SRR944049 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944050 1 0.8304 0.0315 0.504 0.080 0.416
#> SRR944051 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944052 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944053 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944054 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944055 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944056 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944057 1 0.4887 0.6552 0.772 0.000 0.228
#> SRR944058 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944059 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944060 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944061 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944062 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944063 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944064 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944065 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944066 1 0.0237 0.9275 0.996 0.000 0.004
#> SRR944067 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944068 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944069 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944070 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944071 3 0.1832 0.7936 0.036 0.008 0.956
#> SRR944072 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944073 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944075 2 0.5650 0.5346 0.000 0.688 0.312
#> SRR944074 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944076 3 0.0892 0.7877 0.020 0.000 0.980
#> SRR944077 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944078 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944079 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944080 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944081 1 0.0424 0.9248 0.992 0.000 0.008
#> SRR944082 1 0.0000 0.9298 1.000 0.000 0.000
#> SRR944083 1 0.1163 0.9097 0.972 0.000 0.028
#> SRR944084 3 0.6260 0.3366 0.448 0.000 0.552
#> SRR944085 2 0.1411 0.9542 0.000 0.964 0.036
#> SRR944086 1 0.2878 0.8256 0.904 0.000 0.096
#> SRR944088 2 0.0000 0.9894 0.000 1.000 0.000
#> SRR944087 3 0.3038 0.7866 0.104 0.000 0.896
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.3301 0.7458 0.048 0.076 0.876 0.000
#> SRR944012 4 0.0000 0.8921 0.000 0.000 0.000 1.000
#> SRR944014 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944013 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944015 4 0.0000 0.8921 0.000 0.000 0.000 1.000
#> SRR944016 1 0.2859 0.8061 0.880 0.000 0.008 0.112
#> SRR944017 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944018 4 0.0592 0.8871 0.016 0.000 0.000 0.984
#> SRR944019 4 0.3625 0.7569 0.160 0.000 0.012 0.828
#> SRR944020 4 0.0000 0.8921 0.000 0.000 0.000 1.000
#> SRR944021 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944022 4 0.0000 0.8921 0.000 0.000 0.000 1.000
#> SRR944023 4 0.2483 0.8397 0.032 0.000 0.052 0.916
#> SRR944024 4 0.1474 0.8691 0.052 0.000 0.000 0.948
#> SRR944026 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944025 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944028 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944029 4 0.7919 -0.0973 0.156 0.020 0.392 0.432
#> SRR944030 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944031 3 0.3959 0.7950 0.092 0.000 0.840 0.068
#> SRR944032 2 0.4814 0.5677 0.316 0.676 0.008 0.000
#> SRR944033 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944036 3 0.4857 0.5660 0.324 0.000 0.668 0.008
#> SRR944035 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944038 4 0.0188 0.8912 0.004 0.000 0.000 0.996
#> SRR944037 4 0.0000 0.8921 0.000 0.000 0.000 1.000
#> SRR944039 4 0.2469 0.8262 0.108 0.000 0.000 0.892
#> SRR944040 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944041 4 0.0000 0.8921 0.000 0.000 0.000 1.000
#> SRR944042 3 0.4252 0.5418 0.004 0.000 0.744 0.252
#> SRR944043 4 0.0000 0.8921 0.000 0.000 0.000 1.000
#> SRR944044 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944046 3 0.2363 0.8231 0.024 0.000 0.920 0.056
#> SRR944045 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944047 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944048 1 0.3605 0.7910 0.864 0.004 0.044 0.088
#> SRR944049 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944050 1 0.2813 0.7873 0.896 0.000 0.024 0.080
#> SRR944051 2 0.2813 0.8871 0.080 0.896 0.024 0.000
#> SRR944052 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944053 4 0.0000 0.8921 0.000 0.000 0.000 1.000
#> SRR944054 2 0.1938 0.9207 0.052 0.936 0.012 0.000
#> SRR944055 2 0.1059 0.9477 0.012 0.972 0.016 0.000
#> SRR944056 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944057 1 0.5110 0.5474 0.636 0.000 0.012 0.352
#> SRR944058 4 0.0921 0.8815 0.028 0.000 0.000 0.972
#> SRR944059 2 0.1109 0.9445 0.004 0.968 0.028 0.000
#> SRR944060 4 0.0524 0.8891 0.008 0.000 0.004 0.988
#> SRR944061 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944062 4 0.0336 0.8905 0.008 0.000 0.000 0.992
#> SRR944063 4 0.0000 0.8921 0.000 0.000 0.000 1.000
#> SRR944064 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944065 4 0.0000 0.8921 0.000 0.000 0.000 1.000
#> SRR944066 4 0.2345 0.8290 0.100 0.000 0.000 0.900
#> SRR944067 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944068 4 0.0000 0.8921 0.000 0.000 0.000 1.000
#> SRR944069 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944070 4 0.0188 0.8912 0.004 0.000 0.000 0.996
#> SRR944071 3 0.2101 0.8147 0.060 0.000 0.928 0.012
#> SRR944072 4 0.1118 0.8777 0.036 0.000 0.000 0.964
#> SRR944073 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944075 2 0.5174 0.4164 0.012 0.620 0.368 0.000
#> SRR944074 2 0.0188 0.9621 0.004 0.996 0.000 0.000
#> SRR944076 3 0.1722 0.8158 0.048 0.000 0.944 0.008
#> SRR944077 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944078 2 0.0927 0.9504 0.016 0.976 0.008 0.000
#> SRR944079 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944080 2 0.0000 0.9643 0.000 1.000 0.000 0.000
#> SRR944081 4 0.4922 0.6269 0.228 0.000 0.036 0.736
#> SRR944082 4 0.0188 0.8912 0.004 0.000 0.000 0.996
#> SRR944083 4 0.4304 0.5433 0.284 0.000 0.000 0.716
#> SRR944084 4 0.6120 0.0833 0.048 0.000 0.432 0.520
#> SRR944085 2 0.4307 0.7823 0.048 0.808 0.144 0.000
#> SRR944086 4 0.6084 0.4744 0.244 0.000 0.096 0.660
#> SRR944088 2 0.3149 0.8729 0.088 0.880 0.032 0.000
#> SRR944087 3 0.2174 0.8249 0.020 0.000 0.928 0.052
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.5625 0.451 0.028 0.112 0.688 0.000 0.172
#> SRR944012 4 0.0404 0.882 0.000 0.000 0.000 0.988 0.012
#> SRR944014 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944013 2 0.1282 0.891 0.004 0.952 0.000 0.000 0.044
#> SRR944015 4 0.0000 0.883 0.000 0.000 0.000 1.000 0.000
#> SRR944016 1 0.1087 0.686 0.968 0.000 0.008 0.008 0.016
#> SRR944017 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944018 4 0.0833 0.880 0.004 0.000 0.004 0.976 0.016
#> SRR944019 4 0.4320 0.685 0.096 0.000 0.004 0.780 0.120
#> SRR944020 4 0.0000 0.883 0.000 0.000 0.000 1.000 0.000
#> SRR944021 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944022 4 0.0000 0.883 0.000 0.000 0.000 1.000 0.000
#> SRR944023 4 0.4065 0.751 0.056 0.000 0.076 0.824 0.044
#> SRR944024 4 0.2284 0.840 0.056 0.000 0.004 0.912 0.028
#> SRR944026 2 0.0794 0.902 0.000 0.972 0.000 0.000 0.028
#> SRR944025 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944028 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944029 5 0.6313 0.000 0.048 0.000 0.148 0.168 0.636
#> SRR944030 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944031 3 0.4918 0.609 0.084 0.000 0.764 0.044 0.108
#> SRR944032 2 0.6562 0.202 0.264 0.504 0.004 0.000 0.228
#> SRR944033 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944036 3 0.5887 0.446 0.252 0.000 0.592 0.000 0.156
#> SRR944035 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944038 4 0.0451 0.882 0.000 0.000 0.004 0.988 0.008
#> SRR944037 4 0.0000 0.883 0.000 0.000 0.000 1.000 0.000
#> SRR944039 4 0.2888 0.809 0.060 0.000 0.004 0.880 0.056
#> SRR944040 2 0.0162 0.915 0.000 0.996 0.000 0.000 0.004
#> SRR944041 4 0.0290 0.883 0.000 0.000 0.000 0.992 0.008
#> SRR944042 3 0.5162 0.241 0.004 0.000 0.672 0.248 0.076
#> SRR944043 4 0.0290 0.883 0.000 0.000 0.000 0.992 0.008
#> SRR944044 2 0.0162 0.915 0.000 0.996 0.000 0.000 0.004
#> SRR944046 3 0.2995 0.644 0.008 0.000 0.872 0.032 0.088
#> SRR944045 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944047 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944048 1 0.2492 0.663 0.900 0.000 0.020 0.008 0.072
#> SRR944049 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944050 1 0.0740 0.686 0.980 0.000 0.008 0.004 0.008
#> SRR944051 2 0.5059 0.314 0.036 0.548 0.000 0.000 0.416
#> SRR944052 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944053 4 0.0000 0.883 0.000 0.000 0.000 1.000 0.000
#> SRR944054 2 0.3961 0.666 0.016 0.736 0.000 0.000 0.248
#> SRR944055 2 0.3216 0.814 0.004 0.856 0.044 0.000 0.096
#> SRR944056 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944057 1 0.4837 0.152 0.628 0.000 0.012 0.344 0.016
#> SRR944058 4 0.0579 0.882 0.008 0.000 0.000 0.984 0.008
#> SRR944059 2 0.2813 0.835 0.004 0.880 0.032 0.000 0.084
#> SRR944060 4 0.0693 0.881 0.000 0.000 0.008 0.980 0.012
#> SRR944061 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944062 4 0.0671 0.880 0.000 0.000 0.004 0.980 0.016
#> SRR944063 4 0.0000 0.883 0.000 0.000 0.000 1.000 0.000
#> SRR944064 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944065 4 0.0000 0.883 0.000 0.000 0.000 1.000 0.000
#> SRR944066 4 0.2608 0.820 0.088 0.000 0.004 0.888 0.020
#> SRR944067 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944068 4 0.0000 0.883 0.000 0.000 0.000 1.000 0.000
#> SRR944069 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944070 4 0.0566 0.881 0.000 0.000 0.004 0.984 0.012
#> SRR944071 3 0.4323 0.590 0.044 0.004 0.752 0.000 0.200
#> SRR944072 4 0.1211 0.873 0.024 0.000 0.000 0.960 0.016
#> SRR944073 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944075 2 0.6207 0.362 0.004 0.568 0.244 0.000 0.184
#> SRR944074 2 0.0703 0.905 0.000 0.976 0.000 0.000 0.024
#> SRR944076 3 0.3273 0.646 0.036 0.000 0.848 0.004 0.112
#> SRR944077 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944078 2 0.2632 0.846 0.004 0.892 0.032 0.000 0.072
#> SRR944079 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.917 0.000 1.000 0.000 0.000 0.000
#> SRR944081 4 0.6462 0.118 0.124 0.000 0.024 0.548 0.304
#> SRR944082 4 0.0324 0.883 0.000 0.000 0.004 0.992 0.004
#> SRR944083 4 0.4541 0.534 0.288 0.000 0.000 0.680 0.032
#> SRR944084 4 0.6953 -0.267 0.016 0.000 0.292 0.464 0.228
#> SRR944085 2 0.5673 0.573 0.016 0.668 0.128 0.000 0.188
#> SRR944086 4 0.7420 -0.144 0.100 0.000 0.120 0.488 0.292
#> SRR944088 2 0.4871 0.317 0.008 0.548 0.012 0.000 0.432
#> SRR944087 3 0.3595 0.638 0.040 0.000 0.852 0.044 0.064
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.6297 0.4775 0.008 0.084 0.480 0.000 0.056 NA
#> SRR944012 4 0.0622 0.8527 0.000 0.000 0.000 0.980 0.008 NA
#> SRR944014 2 0.0146 0.8823 0.000 0.996 0.000 0.000 0.000 NA
#> SRR944013 2 0.2307 0.7935 0.004 0.896 0.000 0.000 0.068 NA
#> SRR944015 4 0.0000 0.8547 0.000 0.000 0.000 1.000 0.000 NA
#> SRR944016 1 0.1623 0.7329 0.940 0.000 0.004 0.004 0.020 NA
#> SRR944017 2 0.0622 0.8734 0.000 0.980 0.000 0.000 0.012 NA
#> SRR944018 4 0.1680 0.8443 0.024 0.000 0.004 0.940 0.020 NA
#> SRR944019 4 0.5843 0.5227 0.088 0.000 0.000 0.636 0.152 NA
#> SRR944020 4 0.0000 0.8547 0.000 0.000 0.000 1.000 0.000 NA
#> SRR944021 2 0.0000 0.8827 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944022 4 0.0000 0.8547 0.000 0.000 0.000 1.000 0.000 NA
#> SRR944023 4 0.5129 0.6493 0.080 0.000 0.128 0.724 0.016 NA
#> SRR944024 4 0.2971 0.7953 0.100 0.000 0.012 0.860 0.012 NA
#> SRR944026 2 0.1584 0.8251 0.000 0.928 0.000 0.000 0.064 NA
#> SRR944025 2 0.0508 0.8781 0.000 0.984 0.000 0.000 0.004 NA
#> SRR944028 2 0.0146 0.8819 0.000 0.996 0.000 0.000 0.000 NA
#> SRR944029 5 0.5688 -0.2718 0.036 0.000 0.088 0.088 0.696 NA
#> SRR944030 2 0.0000 0.8827 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944031 3 0.6886 0.5461 0.056 0.000 0.560 0.064 0.112 NA
#> SRR944032 2 0.7156 -0.4159 0.208 0.456 0.004 0.000 0.224 NA
#> SRR944033 2 0.0000 0.8827 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944034 2 0.0000 0.8827 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944036 3 0.6409 0.4535 0.192 0.000 0.556 0.004 0.060 NA
#> SRR944035 2 0.0146 0.8819 0.000 0.996 0.000 0.000 0.000 NA
#> SRR944038 4 0.0363 0.8539 0.000 0.000 0.012 0.988 0.000 NA
#> SRR944037 4 0.0000 0.8547 0.000 0.000 0.000 1.000 0.000 NA
#> SRR944039 4 0.4269 0.7200 0.092 0.000 0.000 0.780 0.068 NA
#> SRR944040 2 0.0260 0.8808 0.000 0.992 0.000 0.000 0.000 NA
#> SRR944041 4 0.0665 0.8540 0.008 0.000 0.000 0.980 0.008 NA
#> SRR944042 3 0.4854 0.4275 0.000 0.000 0.664 0.260 0.032 NA
#> SRR944043 4 0.0436 0.8550 0.004 0.000 0.004 0.988 0.000 NA
#> SRR944044 2 0.0547 0.8720 0.000 0.980 0.000 0.000 0.020 NA
#> SRR944046 3 0.3469 0.6583 0.012 0.000 0.848 0.044 0.044 NA
#> SRR944045 2 0.0000 0.8827 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944047 2 0.0000 0.8827 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944048 1 0.3198 0.7042 0.852 0.000 0.028 0.008 0.020 NA
#> SRR944049 2 0.0146 0.8823 0.000 0.996 0.000 0.000 0.000 NA
#> SRR944050 1 0.2270 0.7236 0.900 0.000 0.004 0.004 0.020 NA
#> SRR944051 5 0.5963 0.4235 0.036 0.416 0.000 0.000 0.452 NA
#> SRR944052 2 0.0146 0.8823 0.000 0.996 0.000 0.000 0.000 NA
#> SRR944053 4 0.0000 0.8547 0.000 0.000 0.000 1.000 0.000 NA
#> SRR944054 2 0.4782 0.0239 0.004 0.600 0.000 0.000 0.340 NA
#> SRR944055 2 0.3916 0.5789 0.000 0.760 0.032 0.000 0.016 NA
#> SRR944056 2 0.0146 0.8823 0.000 0.996 0.000 0.000 0.000 NA
#> SRR944057 1 0.5956 0.4301 0.608 0.000 0.012 0.236 0.048 NA
#> SRR944058 4 0.1307 0.8460 0.032 0.000 0.000 0.952 0.008 NA
#> SRR944059 2 0.3273 0.6899 0.000 0.824 0.016 0.000 0.024 NA
#> SRR944060 4 0.1526 0.8425 0.008 0.000 0.036 0.944 0.004 NA
#> SRR944061 2 0.0000 0.8827 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944062 4 0.0810 0.8537 0.008 0.000 0.004 0.976 0.004 NA
#> SRR944063 4 0.0146 0.8547 0.000 0.000 0.000 0.996 0.000 NA
#> SRR944064 2 0.0146 0.8819 0.000 0.996 0.000 0.000 0.000 NA
#> SRR944065 4 0.0000 0.8547 0.000 0.000 0.000 1.000 0.000 NA
#> SRR944066 4 0.3246 0.7730 0.120 0.000 0.008 0.836 0.008 NA
#> SRR944067 2 0.0146 0.8819 0.000 0.996 0.000 0.000 0.000 NA
#> SRR944068 4 0.0000 0.8547 0.000 0.000 0.000 1.000 0.000 NA
#> SRR944069 2 0.0146 0.8823 0.000 0.996 0.000 0.000 0.000 NA
#> SRR944070 4 0.0713 0.8502 0.000 0.000 0.028 0.972 0.000 NA
#> SRR944071 3 0.5214 0.5883 0.040 0.000 0.632 0.000 0.056 NA
#> SRR944072 4 0.1707 0.8357 0.056 0.000 0.000 0.928 0.004 NA
#> SRR944073 2 0.0000 0.8827 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944075 2 0.6698 -0.2857 0.004 0.432 0.220 0.000 0.036 NA
#> SRR944074 2 0.1838 0.8170 0.000 0.916 0.000 0.000 0.068 NA
#> SRR944076 3 0.4284 0.6350 0.020 0.000 0.760 0.004 0.060 NA
#> SRR944077 2 0.0146 0.8823 0.000 0.996 0.000 0.000 0.000 NA
#> SRR944078 2 0.3233 0.6969 0.000 0.828 0.016 0.000 0.024 NA
#> SRR944079 2 0.0146 0.8823 0.000 0.996 0.000 0.000 0.000 NA
#> SRR944080 2 0.0000 0.8827 0.000 1.000 0.000 0.000 0.000 NA
#> SRR944081 4 0.7122 0.0941 0.056 0.000 0.024 0.444 0.304 NA
#> SRR944082 4 0.0810 0.8538 0.004 0.000 0.004 0.976 0.008 NA
#> SRR944083 4 0.4864 0.2911 0.404 0.000 0.008 0.552 0.008 NA
#> SRR944084 4 0.7756 -0.3301 0.016 0.000 0.304 0.348 0.184 NA
#> SRR944085 2 0.5902 0.2311 0.020 0.624 0.080 0.000 0.048 NA
#> SRR944086 4 0.8183 -0.2089 0.084 0.000 0.080 0.340 0.272 NA
#> SRR944088 5 0.5103 0.4777 0.012 0.392 0.000 0.000 0.540 NA
#> SRR944087 3 0.3540 0.6511 0.012 0.000 0.832 0.036 0.020 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.985 0.993 0.5061 0.494 0.494
#> 3 3 0.675 0.672 0.869 0.2374 0.882 0.766
#> 4 4 0.799 0.775 0.910 0.1254 0.824 0.591
#> 5 5 0.747 0.721 0.876 0.0208 0.932 0.787
#> 6 6 0.760 0.701 0.867 0.0204 0.974 0.909
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.6148 0.821 0.152 0.848
#> SRR944012 1 0.0000 0.991 1.000 0.000
#> SRR944014 2 0.0000 0.994 0.000 1.000
#> SRR944013 2 0.0000 0.994 0.000 1.000
#> SRR944015 1 0.0000 0.991 1.000 0.000
#> SRR944016 1 0.1184 0.979 0.984 0.016
#> SRR944017 2 0.0000 0.994 0.000 1.000
#> SRR944018 1 0.0000 0.991 1.000 0.000
#> SRR944019 1 0.0000 0.991 1.000 0.000
#> SRR944020 1 0.0000 0.991 1.000 0.000
#> SRR944021 2 0.0000 0.994 0.000 1.000
#> SRR944022 1 0.0000 0.991 1.000 0.000
#> SRR944023 1 0.0000 0.991 1.000 0.000
#> SRR944024 1 0.0000 0.991 1.000 0.000
#> SRR944026 2 0.0000 0.994 0.000 1.000
#> SRR944025 2 0.0000 0.994 0.000 1.000
#> SRR944028 2 0.0000 0.994 0.000 1.000
#> SRR944029 1 0.6048 0.830 0.852 0.148
#> SRR944030 2 0.0000 0.994 0.000 1.000
#> SRR944031 1 0.0000 0.991 1.000 0.000
#> SRR944032 2 0.0000 0.994 0.000 1.000
#> SRR944033 2 0.0000 0.994 0.000 1.000
#> SRR944034 2 0.0000 0.994 0.000 1.000
#> SRR944036 1 0.0000 0.991 1.000 0.000
#> SRR944035 2 0.0000 0.994 0.000 1.000
#> SRR944038 1 0.0000 0.991 1.000 0.000
#> SRR944037 1 0.0000 0.991 1.000 0.000
#> SRR944039 1 0.0000 0.991 1.000 0.000
#> SRR944040 2 0.0000 0.994 0.000 1.000
#> SRR944041 1 0.0000 0.991 1.000 0.000
#> SRR944042 1 0.0000 0.991 1.000 0.000
#> SRR944043 1 0.0000 0.991 1.000 0.000
#> SRR944044 2 0.0000 0.994 0.000 1.000
#> SRR944046 1 0.0000 0.991 1.000 0.000
#> SRR944045 2 0.0000 0.994 0.000 1.000
#> SRR944047 2 0.0000 0.994 0.000 1.000
#> SRR944048 1 0.1184 0.979 0.984 0.016
#> SRR944049 2 0.0000 0.994 0.000 1.000
#> SRR944050 1 0.1414 0.975 0.980 0.020
#> SRR944051 2 0.0000 0.994 0.000 1.000
#> SRR944052 2 0.0000 0.994 0.000 1.000
#> SRR944053 1 0.0000 0.991 1.000 0.000
#> SRR944054 2 0.0000 0.994 0.000 1.000
#> SRR944055 2 0.0000 0.994 0.000 1.000
#> SRR944056 2 0.0000 0.994 0.000 1.000
#> SRR944057 1 0.0000 0.991 1.000 0.000
#> SRR944058 1 0.0000 0.991 1.000 0.000
#> SRR944059 2 0.0000 0.994 0.000 1.000
#> SRR944060 1 0.0000 0.991 1.000 0.000
#> SRR944061 2 0.0000 0.994 0.000 1.000
#> SRR944062 1 0.0000 0.991 1.000 0.000
#> SRR944063 1 0.0000 0.991 1.000 0.000
#> SRR944064 2 0.0000 0.994 0.000 1.000
#> SRR944065 1 0.0000 0.991 1.000 0.000
#> SRR944066 1 0.0000 0.991 1.000 0.000
#> SRR944067 2 0.0000 0.994 0.000 1.000
#> SRR944068 1 0.0000 0.991 1.000 0.000
#> SRR944069 2 0.0000 0.994 0.000 1.000
#> SRR944070 1 0.0000 0.991 1.000 0.000
#> SRR944071 1 0.5519 0.856 0.872 0.128
#> SRR944072 1 0.0000 0.991 1.000 0.000
#> SRR944073 2 0.0000 0.994 0.000 1.000
#> SRR944075 2 0.1184 0.980 0.016 0.984
#> SRR944074 2 0.0000 0.994 0.000 1.000
#> SRR944076 1 0.0000 0.991 1.000 0.000
#> SRR944077 2 0.0000 0.994 0.000 1.000
#> SRR944078 2 0.0000 0.994 0.000 1.000
#> SRR944079 2 0.0000 0.994 0.000 1.000
#> SRR944080 2 0.0000 0.994 0.000 1.000
#> SRR944081 1 0.0000 0.991 1.000 0.000
#> SRR944082 1 0.0000 0.991 1.000 0.000
#> SRR944083 1 0.0000 0.991 1.000 0.000
#> SRR944084 1 0.0000 0.991 1.000 0.000
#> SRR944085 2 0.2948 0.944 0.052 0.948
#> SRR944086 1 0.0376 0.988 0.996 0.004
#> SRR944088 2 0.0376 0.990 0.004 0.996
#> SRR944087 1 0.0000 0.991 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 1 0.6192 -0.0967 0.580 0.420 0.000
#> SRR944012 1 0.6235 0.2656 0.564 0.000 0.436
#> SRR944014 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944013 2 0.5291 0.6741 0.268 0.732 0.000
#> SRR944015 3 0.0000 0.8847 0.000 0.000 1.000
#> SRR944016 1 0.1163 0.7122 0.972 0.028 0.000
#> SRR944017 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944018 1 0.0000 0.7300 1.000 0.000 0.000
#> SRR944019 1 0.0000 0.7300 1.000 0.000 0.000
#> SRR944020 3 0.5465 0.4853 0.288 0.000 0.712
#> SRR944021 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944022 3 0.0000 0.8847 0.000 0.000 1.000
#> SRR944023 1 0.0000 0.7300 1.000 0.000 0.000
#> SRR944024 1 0.6252 0.2542 0.556 0.000 0.444
#> SRR944026 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944025 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944028 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944029 1 0.3686 0.5946 0.860 0.140 0.000
#> SRR944030 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944031 1 0.0000 0.7300 1.000 0.000 0.000
#> SRR944032 2 0.6308 0.3176 0.492 0.508 0.000
#> SRR944033 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944034 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944036 1 0.0000 0.7300 1.000 0.000 0.000
#> SRR944035 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944038 1 0.6309 0.1112 0.504 0.000 0.496
#> SRR944037 3 0.0237 0.8821 0.004 0.000 0.996
#> SRR944039 1 0.0000 0.7300 1.000 0.000 0.000
#> SRR944040 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944041 1 0.6286 0.2106 0.536 0.000 0.464
#> SRR944042 1 0.0000 0.7300 1.000 0.000 0.000
#> SRR944043 1 0.6291 0.2013 0.532 0.000 0.468
#> SRR944044 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944046 1 0.0000 0.7300 1.000 0.000 0.000
#> SRR944045 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944047 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944048 1 0.1031 0.7151 0.976 0.024 0.000
#> SRR944049 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944050 1 0.1643 0.6990 0.956 0.044 0.000
#> SRR944051 2 0.6095 0.5031 0.392 0.608 0.000
#> SRR944052 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944053 3 0.0000 0.8847 0.000 0.000 1.000
#> SRR944054 2 0.2448 0.8439 0.076 0.924 0.000
#> SRR944055 2 0.4605 0.7426 0.204 0.796 0.000
#> SRR944056 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944057 1 0.0000 0.7300 1.000 0.000 0.000
#> SRR944058 1 0.6291 0.2013 0.532 0.000 0.468
#> SRR944059 2 0.6168 0.4743 0.412 0.588 0.000
#> SRR944060 1 0.6252 0.2542 0.556 0.000 0.444
#> SRR944061 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944062 3 0.6079 0.2098 0.388 0.000 0.612
#> SRR944063 3 0.0000 0.8847 0.000 0.000 1.000
#> SRR944064 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944065 3 0.0000 0.8847 0.000 0.000 1.000
#> SRR944066 1 0.6260 0.2461 0.552 0.000 0.448
#> SRR944067 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944068 3 0.0000 0.8847 0.000 0.000 1.000
#> SRR944069 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944070 1 0.6291 0.2013 0.532 0.000 0.468
#> SRR944071 1 0.3340 0.6182 0.880 0.120 0.000
#> SRR944072 1 0.6286 0.2112 0.536 0.000 0.464
#> SRR944073 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944075 2 0.6309 0.3074 0.496 0.504 0.000
#> SRR944074 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944076 1 0.0000 0.7300 1.000 0.000 0.000
#> SRR944077 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944078 2 0.3619 0.8014 0.136 0.864 0.000
#> SRR944079 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944080 2 0.0000 0.8901 0.000 1.000 0.000
#> SRR944081 1 0.0000 0.7300 1.000 0.000 0.000
#> SRR944082 1 0.6309 0.1105 0.504 0.000 0.496
#> SRR944083 1 0.3551 0.6428 0.868 0.000 0.132
#> SRR944084 1 0.0000 0.7300 1.000 0.000 0.000
#> SRR944085 2 0.6308 0.3176 0.492 0.508 0.000
#> SRR944086 1 0.0237 0.7278 0.996 0.004 0.000
#> SRR944088 2 0.6286 0.3745 0.464 0.536 0.000
#> SRR944087 1 0.0000 0.7300 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.0000 0.8189 0.000 0.000 1.000 0.000
#> SRR944012 1 0.1389 0.7789 0.952 0.000 0.048 0.000
#> SRR944014 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944013 2 0.4564 0.4825 0.000 0.672 0.328 0.000
#> SRR944015 4 0.0000 0.9439 0.000 0.000 0.000 1.000
#> SRR944016 3 0.1389 0.7888 0.048 0.000 0.952 0.000
#> SRR944017 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944018 1 0.4972 0.4009 0.544 0.000 0.456 0.000
#> SRR944019 3 0.0707 0.8113 0.020 0.000 0.980 0.000
#> SRR944020 4 0.3105 0.8233 0.140 0.000 0.004 0.856
#> SRR944021 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944022 4 0.0000 0.9439 0.000 0.000 0.000 1.000
#> SRR944023 1 0.4977 0.3932 0.540 0.000 0.460 0.000
#> SRR944024 1 0.0707 0.7706 0.980 0.000 0.020 0.000
#> SRR944026 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944025 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944028 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944029 3 0.0000 0.8189 0.000 0.000 1.000 0.000
#> SRR944030 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944031 3 0.0188 0.8187 0.004 0.000 0.996 0.000
#> SRR944032 3 0.4843 0.3407 0.000 0.396 0.604 0.000
#> SRR944033 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944034 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944036 3 0.0000 0.8189 0.000 0.000 1.000 0.000
#> SRR944035 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944038 1 0.1489 0.7786 0.952 0.000 0.044 0.004
#> SRR944037 4 0.0707 0.9357 0.020 0.000 0.000 0.980
#> SRR944039 1 0.4977 0.3932 0.540 0.000 0.460 0.000
#> SRR944040 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944041 1 0.1302 0.7797 0.956 0.000 0.044 0.000
#> SRR944042 3 0.4661 0.1401 0.348 0.000 0.652 0.000
#> SRR944043 1 0.1302 0.7797 0.956 0.000 0.044 0.000
#> SRR944044 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944046 3 0.0817 0.8081 0.024 0.000 0.976 0.000
#> SRR944045 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944047 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944048 3 0.4406 0.4814 0.300 0.000 0.700 0.000
#> SRR944049 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944050 3 0.1256 0.8070 0.028 0.008 0.964 0.000
#> SRR944051 2 0.4972 0.0997 0.000 0.544 0.456 0.000
#> SRR944052 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944053 4 0.0000 0.9439 0.000 0.000 0.000 1.000
#> SRR944054 2 0.2281 0.8605 0.000 0.904 0.096 0.000
#> SRR944055 2 0.3975 0.6600 0.000 0.760 0.240 0.000
#> SRR944056 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944057 1 0.4989 0.3659 0.528 0.000 0.472 0.000
#> SRR944058 1 0.0000 0.7669 1.000 0.000 0.000 0.000
#> SRR944059 3 0.4994 0.0806 0.000 0.480 0.520 0.000
#> SRR944060 1 0.4761 0.5315 0.628 0.000 0.372 0.000
#> SRR944061 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944062 1 0.4697 0.1562 0.644 0.000 0.000 0.356
#> SRR944063 4 0.0000 0.9439 0.000 0.000 0.000 1.000
#> SRR944064 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944065 4 0.3688 0.7606 0.208 0.000 0.000 0.792
#> SRR944066 1 0.0000 0.7669 1.000 0.000 0.000 0.000
#> SRR944067 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944068 4 0.0000 0.9439 0.000 0.000 0.000 1.000
#> SRR944069 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944070 1 0.1302 0.7797 0.956 0.000 0.044 0.000
#> SRR944071 3 0.0000 0.8189 0.000 0.000 1.000 0.000
#> SRR944072 1 0.0000 0.7669 1.000 0.000 0.000 0.000
#> SRR944073 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944075 3 0.2814 0.7269 0.000 0.132 0.868 0.000
#> SRR944074 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944076 3 0.0000 0.8189 0.000 0.000 1.000 0.000
#> SRR944077 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944078 2 0.3219 0.7765 0.000 0.836 0.164 0.000
#> SRR944079 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944080 2 0.0000 0.9510 0.000 1.000 0.000 0.000
#> SRR944081 3 0.0336 0.8175 0.008 0.000 0.992 0.000
#> SRR944082 1 0.0188 0.7652 0.996 0.000 0.000 0.004
#> SRR944083 1 0.0469 0.7704 0.988 0.000 0.012 0.000
#> SRR944084 3 0.0707 0.8117 0.020 0.000 0.980 0.000
#> SRR944085 3 0.3219 0.6968 0.000 0.164 0.836 0.000
#> SRR944086 3 0.0188 0.8186 0.004 0.000 0.996 0.000
#> SRR944088 3 0.4961 0.1930 0.000 0.448 0.552 0.000
#> SRR944087 3 0.0469 0.8162 0.012 0.000 0.988 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.0794 0.7719 0.000 0.000 0.972 0.000 0.028
#> SRR944012 1 0.1725 0.7623 0.936 0.000 0.020 0.000 0.044
#> SRR944014 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944013 2 0.4584 0.4891 0.000 0.660 0.312 0.000 0.028
#> SRR944015 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> SRR944016 3 0.1830 0.7658 0.040 0.000 0.932 0.000 0.028
#> SRR944017 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944018 3 0.5080 0.3775 0.368 0.000 0.588 0.000 0.044
#> SRR944019 3 0.0703 0.7779 0.024 0.000 0.976 0.000 0.000
#> SRR944020 5 0.4225 0.0664 0.004 0.000 0.000 0.364 0.632
#> SRR944021 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944022 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> SRR944023 3 0.4768 0.4972 0.304 0.000 0.656 0.000 0.040
#> SRR944024 1 0.1106 0.8006 0.964 0.000 0.024 0.000 0.012
#> SRR944026 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944025 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944028 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944029 3 0.0000 0.7794 0.000 0.000 1.000 0.000 0.000
#> SRR944030 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944031 3 0.0162 0.7802 0.000 0.000 0.996 0.000 0.004
#> SRR944032 3 0.4835 0.3368 0.000 0.380 0.592 0.000 0.028
#> SRR944033 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944036 3 0.0290 0.7800 0.008 0.000 0.992 0.000 0.000
#> SRR944035 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944038 5 0.4630 0.0878 0.396 0.000 0.016 0.000 0.588
#> SRR944037 5 0.3452 0.2494 0.000 0.000 0.000 0.244 0.756
#> SRR944039 3 0.4193 0.5247 0.304 0.000 0.684 0.000 0.012
#> SRR944040 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944041 1 0.4418 0.3669 0.652 0.000 0.016 0.000 0.332
#> SRR944042 3 0.4028 0.6221 0.192 0.000 0.768 0.000 0.040
#> SRR944043 5 0.4659 -0.0262 0.492 0.000 0.012 0.000 0.496
#> SRR944044 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944046 3 0.1915 0.7604 0.032 0.000 0.928 0.000 0.040
#> SRR944045 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944047 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944048 3 0.4252 0.4997 0.280 0.000 0.700 0.000 0.020
#> SRR944049 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944050 3 0.0898 0.7770 0.008 0.000 0.972 0.000 0.020
#> SRR944051 2 0.4937 0.1643 0.000 0.544 0.428 0.000 0.028
#> SRR944052 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944053 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> SRR944054 2 0.2740 0.8345 0.000 0.876 0.096 0.000 0.028
#> SRR944055 2 0.4024 0.6677 0.000 0.752 0.220 0.000 0.028
#> SRR944056 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944057 3 0.4777 0.5105 0.292 0.000 0.664 0.000 0.044
#> SRR944058 1 0.0290 0.8123 0.992 0.000 0.000 0.000 0.008
#> SRR944059 3 0.4974 0.0813 0.000 0.464 0.508 0.000 0.028
#> SRR944060 5 0.6705 0.1174 0.292 0.000 0.280 0.000 0.428
#> SRR944061 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944062 1 0.3720 0.6278 0.760 0.000 0.000 0.012 0.228
#> SRR944063 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> SRR944064 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944065 5 0.4757 0.0314 0.024 0.000 0.000 0.380 0.596
#> SRR944066 1 0.1965 0.7963 0.904 0.000 0.000 0.000 0.096
#> SRR944067 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944068 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> SRR944069 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944070 5 0.4620 0.0915 0.392 0.000 0.016 0.000 0.592
#> SRR944071 3 0.0609 0.7751 0.000 0.000 0.980 0.000 0.020
#> SRR944072 1 0.1544 0.8061 0.932 0.000 0.000 0.000 0.068
#> SRR944073 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944075 3 0.3002 0.6914 0.000 0.116 0.856 0.000 0.028
#> SRR944074 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944076 3 0.0162 0.7798 0.004 0.000 0.996 0.000 0.000
#> SRR944077 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944078 2 0.3412 0.7702 0.000 0.820 0.152 0.000 0.028
#> SRR944079 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.9475 0.000 1.000 0.000 0.000 0.000
#> SRR944081 3 0.0290 0.7801 0.008 0.000 0.992 0.000 0.000
#> SRR944082 1 0.2891 0.7271 0.824 0.000 0.000 0.000 0.176
#> SRR944083 1 0.0404 0.8076 0.988 0.000 0.012 0.000 0.000
#> SRR944084 3 0.1579 0.7683 0.024 0.000 0.944 0.000 0.032
#> SRR944085 3 0.3238 0.6685 0.000 0.136 0.836 0.000 0.028
#> SRR944086 3 0.0693 0.7794 0.008 0.000 0.980 0.000 0.012
#> SRR944088 3 0.4948 0.1782 0.000 0.436 0.536 0.000 0.028
#> SRR944087 3 0.1549 0.7686 0.016 0.000 0.944 0.000 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.0865 0.71927 0.000 0.000 0.964 0.000 0.036 0.000
#> SRR944012 1 0.4407 0.55138 0.496 0.000 0.000 0.000 0.024 0.480
#> SRR944014 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944013 2 0.4186 0.47146 0.000 0.656 0.312 0.000 0.032 0.000
#> SRR944015 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR944016 3 0.1713 0.70839 0.000 0.000 0.928 0.000 0.028 0.044
#> SRR944017 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944018 6 0.4932 0.12849 0.052 0.000 0.452 0.000 0.004 0.492
#> SRR944019 3 0.0993 0.71814 0.000 0.000 0.964 0.000 0.012 0.024
#> SRR944020 5 0.1588 0.78696 0.000 0.000 0.000 0.072 0.924 0.004
#> SRR944021 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944022 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR944023 3 0.3847 -0.07935 0.000 0.000 0.544 0.000 0.000 0.456
#> SRR944024 1 0.3470 0.76194 0.740 0.000 0.012 0.000 0.000 0.248
#> SRR944026 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944025 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944028 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944029 3 0.0000 0.72672 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR944030 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944031 3 0.0260 0.72742 0.000 0.000 0.992 0.000 0.000 0.008
#> SRR944032 3 0.4453 0.36042 0.000 0.372 0.592 0.000 0.036 0.000
#> SRR944033 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944034 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944036 3 0.0260 0.72629 0.000 0.000 0.992 0.000 0.000 0.008
#> SRR944035 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944038 6 0.3975 0.18302 0.392 0.000 0.000 0.000 0.008 0.600
#> SRR944037 5 0.1686 0.79029 0.012 0.000 0.000 0.064 0.924 0.000
#> SRR944039 3 0.4076 0.06441 0.000 0.000 0.592 0.000 0.012 0.396
#> SRR944040 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944041 5 0.5861 0.11287 0.264 0.000 0.000 0.000 0.484 0.252
#> SRR944042 3 0.3634 0.23810 0.000 0.000 0.644 0.000 0.000 0.356
#> SRR944043 6 0.2887 0.17398 0.036 0.000 0.000 0.000 0.120 0.844
#> SRR944044 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944046 3 0.2562 0.61204 0.000 0.000 0.828 0.000 0.000 0.172
#> SRR944045 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944047 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944048 3 0.3986 0.39254 0.316 0.000 0.664 0.000 0.020 0.000
#> SRR944049 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944050 3 0.0806 0.72531 0.000 0.000 0.972 0.000 0.020 0.008
#> SRR944051 2 0.4550 0.15192 0.000 0.544 0.420 0.000 0.036 0.000
#> SRR944052 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944053 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR944054 2 0.2560 0.82933 0.000 0.872 0.092 0.000 0.036 0.000
#> SRR944055 2 0.3727 0.65652 0.000 0.748 0.216 0.000 0.036 0.000
#> SRR944056 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944057 6 0.3868 -0.00661 0.000 0.000 0.496 0.000 0.000 0.504
#> SRR944058 1 0.3454 0.76264 0.768 0.000 0.000 0.000 0.024 0.208
#> SRR944059 3 0.4581 0.14596 0.000 0.448 0.516 0.000 0.036 0.000
#> SRR944060 6 0.1794 0.30148 0.036 0.000 0.040 0.000 0.000 0.924
#> SRR944061 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944062 1 0.1265 0.57835 0.948 0.000 0.000 0.000 0.008 0.044
#> SRR944063 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR944064 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944065 5 0.1528 0.79043 0.000 0.000 0.000 0.048 0.936 0.016
#> SRR944066 1 0.3907 0.69961 0.588 0.000 0.000 0.000 0.004 0.408
#> SRR944067 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944068 4 0.0000 1.00000 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR944069 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944070 6 0.3534 0.27573 0.276 0.000 0.000 0.000 0.008 0.716
#> SRR944071 3 0.0547 0.72425 0.000 0.000 0.980 0.000 0.020 0.000
#> SRR944072 1 0.3936 0.75518 0.688 0.000 0.000 0.000 0.024 0.288
#> SRR944073 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944075 3 0.3014 0.62550 0.000 0.132 0.832 0.000 0.036 0.000
#> SRR944074 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944076 3 0.0146 0.72671 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR944077 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944078 2 0.3172 0.76212 0.000 0.816 0.148 0.000 0.036 0.000
#> SRR944079 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944080 2 0.0000 0.94653 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944081 3 0.0508 0.72447 0.000 0.000 0.984 0.000 0.012 0.004
#> SRR944082 1 0.3445 0.65549 0.732 0.000 0.000 0.000 0.008 0.260
#> SRR944083 1 0.3101 0.76586 0.756 0.000 0.000 0.000 0.000 0.244
#> SRR944084 3 0.1957 0.66619 0.000 0.000 0.888 0.000 0.000 0.112
#> SRR944085 3 0.2887 0.63266 0.000 0.120 0.844 0.000 0.036 0.000
#> SRR944086 3 0.1297 0.71441 0.000 0.000 0.948 0.000 0.012 0.040
#> SRR944088 3 0.4565 0.20075 0.000 0.432 0.532 0.000 0.036 0.000
#> SRR944087 3 0.2378 0.63467 0.000 0.000 0.848 0.000 0.000 0.152
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "mclust"]
# you can also extract it by
# res = res_list["ATC:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.653 0.933 0.952 0.4659 0.504 0.504
#> 3 3 0.752 0.853 0.931 0.2010 0.907 0.815
#> 4 4 0.639 0.603 0.754 0.2342 0.798 0.546
#> 5 5 0.702 0.646 0.826 0.1256 0.827 0.480
#> 6 6 0.736 0.712 0.830 0.0465 0.873 0.518
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.5737 0.9032 0.136 0.864
#> SRR944012 1 0.0000 0.9975 1.000 0.000
#> SRR944014 2 0.0000 0.8832 0.000 1.000
#> SRR944013 1 0.0000 0.9975 1.000 0.000
#> SRR944015 1 0.0000 0.9975 1.000 0.000
#> SRR944016 1 0.0000 0.9975 1.000 0.000
#> SRR944017 1 0.0000 0.9975 1.000 0.000
#> SRR944018 1 0.0000 0.9975 1.000 0.000
#> SRR944019 1 0.0000 0.9975 1.000 0.000
#> SRR944020 1 0.0000 0.9975 1.000 0.000
#> SRR944021 2 0.0000 0.8832 0.000 1.000
#> SRR944022 1 0.0000 0.9975 1.000 0.000
#> SRR944023 1 0.3274 0.9262 0.940 0.060
#> SRR944024 1 0.0000 0.9975 1.000 0.000
#> SRR944026 1 0.0000 0.9975 1.000 0.000
#> SRR944025 1 0.0000 0.9975 1.000 0.000
#> SRR944028 1 0.0000 0.9975 1.000 0.000
#> SRR944029 1 0.0000 0.9975 1.000 0.000
#> SRR944030 2 0.2043 0.8900 0.032 0.968
#> SRR944031 2 0.5737 0.9032 0.136 0.864
#> SRR944032 1 0.0000 0.9975 1.000 0.000
#> SRR944033 2 0.0000 0.8832 0.000 1.000
#> SRR944034 2 0.5737 0.9032 0.136 0.864
#> SRR944036 1 0.2043 0.9611 0.968 0.032
#> SRR944035 2 0.0672 0.8852 0.008 0.992
#> SRR944038 2 0.5737 0.9032 0.136 0.864
#> SRR944037 1 0.0000 0.9975 1.000 0.000
#> SRR944039 1 0.0000 0.9975 1.000 0.000
#> SRR944040 2 0.5737 0.9032 0.136 0.864
#> SRR944041 1 0.0000 0.9975 1.000 0.000
#> SRR944042 2 0.5737 0.9032 0.136 0.864
#> SRR944043 1 0.0000 0.9975 1.000 0.000
#> SRR944044 1 0.0000 0.9975 1.000 0.000
#> SRR944046 2 0.5737 0.9032 0.136 0.864
#> SRR944045 2 0.5408 0.9024 0.124 0.876
#> SRR944047 2 0.0000 0.8832 0.000 1.000
#> SRR944048 1 0.0000 0.9975 1.000 0.000
#> SRR944049 2 0.9998 0.0247 0.492 0.508
#> SRR944050 1 0.0000 0.9975 1.000 0.000
#> SRR944051 1 0.0000 0.9975 1.000 0.000
#> SRR944052 2 0.0376 0.8844 0.004 0.996
#> SRR944053 1 0.0000 0.9975 1.000 0.000
#> SRR944054 1 0.0000 0.9975 1.000 0.000
#> SRR944055 2 0.5737 0.9032 0.136 0.864
#> SRR944056 2 0.0000 0.8832 0.000 1.000
#> SRR944057 1 0.0000 0.9975 1.000 0.000
#> SRR944058 1 0.0000 0.9975 1.000 0.000
#> SRR944059 2 0.5737 0.9032 0.136 0.864
#> SRR944060 2 0.9087 0.6669 0.324 0.676
#> SRR944061 2 0.0000 0.8832 0.000 1.000
#> SRR944062 1 0.0000 0.9975 1.000 0.000
#> SRR944063 1 0.0000 0.9975 1.000 0.000
#> SRR944064 1 0.0000 0.9975 1.000 0.000
#> SRR944065 1 0.0000 0.9975 1.000 0.000
#> SRR944066 1 0.0000 0.9975 1.000 0.000
#> SRR944067 1 0.0000 0.9975 1.000 0.000
#> SRR944068 1 0.0000 0.9975 1.000 0.000
#> SRR944069 2 0.0000 0.8832 0.000 1.000
#> SRR944070 2 0.5737 0.9032 0.136 0.864
#> SRR944071 2 0.5737 0.9032 0.136 0.864
#> SRR944072 1 0.0000 0.9975 1.000 0.000
#> SRR944073 2 0.5737 0.9032 0.136 0.864
#> SRR944075 2 0.5946 0.8973 0.144 0.856
#> SRR944074 1 0.0000 0.9975 1.000 0.000
#> SRR944076 2 0.5737 0.9032 0.136 0.864
#> SRR944077 2 0.0000 0.8832 0.000 1.000
#> SRR944078 2 0.6623 0.8715 0.172 0.828
#> SRR944079 2 0.0000 0.8832 0.000 1.000
#> SRR944080 2 0.0000 0.8832 0.000 1.000
#> SRR944081 1 0.0000 0.9975 1.000 0.000
#> SRR944082 1 0.0000 0.9975 1.000 0.000
#> SRR944083 1 0.0000 0.9975 1.000 0.000
#> SRR944084 1 0.0000 0.9975 1.000 0.000
#> SRR944085 2 0.9552 0.5653 0.376 0.624
#> SRR944086 1 0.0000 0.9975 1.000 0.000
#> SRR944088 1 0.0000 0.9975 1.000 0.000
#> SRR944087 2 0.5737 0.9032 0.136 0.864
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 3 0.0000 0.771 0.000 0.000 1.000
#> SRR944012 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944014 2 0.1411 0.827 0.000 0.964 0.036
#> SRR944013 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944015 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944016 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944017 1 0.4172 0.806 0.840 0.156 0.004
#> SRR944018 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944019 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944020 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944021 2 0.3038 0.813 0.000 0.896 0.104
#> SRR944022 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944023 1 0.2959 0.873 0.900 0.000 0.100
#> SRR944024 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944026 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944025 1 0.2261 0.922 0.932 0.068 0.000
#> SRR944028 1 0.0892 0.968 0.980 0.020 0.000
#> SRR944029 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944030 2 0.4683 0.783 0.024 0.836 0.140
#> SRR944031 3 0.0000 0.771 0.000 0.000 1.000
#> SRR944032 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944033 2 0.1860 0.828 0.000 0.948 0.052
#> SRR944034 2 0.9203 0.291 0.340 0.496 0.164
#> SRR944036 1 0.3551 0.828 0.868 0.000 0.132
#> SRR944035 2 0.2774 0.799 0.008 0.920 0.072
#> SRR944038 3 0.6154 0.451 0.408 0.000 0.592
#> SRR944037 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944039 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944040 3 0.9615 0.239 0.324 0.220 0.456
#> SRR944041 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944042 3 0.1529 0.757 0.040 0.000 0.960
#> SRR944043 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944044 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944046 3 0.0000 0.771 0.000 0.000 1.000
#> SRR944045 2 0.8787 0.463 0.228 0.584 0.188
#> SRR944047 2 0.3686 0.790 0.000 0.860 0.140
#> SRR944048 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944049 2 0.5220 0.601 0.208 0.780 0.012
#> SRR944050 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944051 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944052 2 0.4733 0.747 0.004 0.800 0.196
#> SRR944053 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944054 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944055 3 0.0237 0.769 0.000 0.004 0.996
#> SRR944056 2 0.0237 0.814 0.000 0.996 0.004
#> SRR944057 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944058 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944059 3 0.1031 0.755 0.000 0.024 0.976
#> SRR944060 3 0.6225 0.402 0.432 0.000 0.568
#> SRR944061 2 0.2448 0.825 0.000 0.924 0.076
#> SRR944062 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944063 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944064 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944065 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944066 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944067 1 0.2774 0.910 0.920 0.072 0.008
#> SRR944068 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944069 2 0.0892 0.816 0.000 0.980 0.020
#> SRR944070 3 0.6154 0.451 0.408 0.000 0.592
#> SRR944071 3 0.0000 0.771 0.000 0.000 1.000
#> SRR944072 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944073 2 0.8505 0.478 0.256 0.600 0.144
#> SRR944075 3 0.0000 0.771 0.000 0.000 1.000
#> SRR944074 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944076 3 0.0000 0.771 0.000 0.000 1.000
#> SRR944077 2 0.1753 0.828 0.000 0.952 0.048
#> SRR944078 3 0.4353 0.681 0.156 0.008 0.836
#> SRR944079 2 0.1860 0.829 0.000 0.948 0.052
#> SRR944080 2 0.0592 0.817 0.000 0.988 0.012
#> SRR944081 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944082 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944083 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944084 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944085 3 0.4782 0.665 0.164 0.016 0.820
#> SRR944086 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944088 1 0.0000 0.985 1.000 0.000 0.000
#> SRR944087 3 0.0000 0.771 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 3 0.0000 0.9317 0.000 0.000 1.000 0.000
#> SRR944012 1 0.4999 0.5505 0.508 0.000 0.000 0.492
#> SRR944014 2 0.0469 0.9112 0.000 0.988 0.012 0.000
#> SRR944013 4 0.0000 0.6940 0.000 0.000 0.000 1.000
#> SRR944015 1 0.4999 0.5505 0.508 0.000 0.000 0.492
#> SRR944016 1 0.0000 0.4750 1.000 0.000 0.000 0.000
#> SRR944017 4 0.1118 0.6642 0.000 0.036 0.000 0.964
#> SRR944018 1 0.4998 0.5513 0.512 0.000 0.000 0.488
#> SRR944019 1 0.4998 0.5513 0.512 0.000 0.000 0.488
#> SRR944020 1 0.4999 0.5505 0.508 0.000 0.000 0.492
#> SRR944021 2 0.0336 0.9124 0.000 0.992 0.008 0.000
#> SRR944022 1 0.4999 0.5505 0.508 0.000 0.000 0.492
#> SRR944023 1 0.7170 0.4962 0.548 0.000 0.184 0.268
#> SRR944024 1 0.0000 0.4750 1.000 0.000 0.000 0.000
#> SRR944026 4 0.0000 0.6940 0.000 0.000 0.000 1.000
#> SRR944025 4 0.0376 0.6911 0.004 0.004 0.000 0.992
#> SRR944028 4 0.0188 0.6932 0.004 0.000 0.000 0.996
#> SRR944029 4 0.4994 -0.5348 0.480 0.000 0.000 0.520
#> SRR944030 2 0.2473 0.8737 0.000 0.908 0.012 0.080
#> SRR944031 3 0.0000 0.9317 0.000 0.000 1.000 0.000
#> SRR944032 4 0.4564 -0.0717 0.328 0.000 0.000 0.672
#> SRR944033 2 0.0188 0.9119 0.000 0.996 0.004 0.000
#> SRR944034 4 0.5396 -0.3767 0.000 0.464 0.012 0.524
#> SRR944036 1 0.7576 0.4084 0.484 0.000 0.260 0.256
#> SRR944035 2 0.2480 0.8654 0.000 0.904 0.008 0.088
#> SRR944038 1 0.7643 0.4443 0.468 0.000 0.276 0.256
#> SRR944037 1 0.4999 0.5505 0.508 0.000 0.000 0.492
#> SRR944039 1 0.4996 0.5528 0.516 0.000 0.000 0.484
#> SRR944040 3 0.9146 0.0569 0.280 0.300 0.352 0.068
#> SRR944041 1 0.4999 0.5505 0.508 0.000 0.000 0.492
#> SRR944042 3 0.2928 0.8011 0.108 0.000 0.880 0.012
#> SRR944043 1 0.4998 0.5513 0.512 0.000 0.000 0.488
#> SRR944044 4 0.0000 0.6940 0.000 0.000 0.000 1.000
#> SRR944046 3 0.0000 0.9317 0.000 0.000 1.000 0.000
#> SRR944045 2 0.5909 0.7168 0.088 0.756 0.096 0.060
#> SRR944047 2 0.1059 0.9083 0.000 0.972 0.012 0.016
#> SRR944048 1 0.0000 0.4750 1.000 0.000 0.000 0.000
#> SRR944049 2 0.4500 0.5729 0.000 0.684 0.000 0.316
#> SRR944050 1 0.0000 0.4750 1.000 0.000 0.000 0.000
#> SRR944051 4 0.1792 0.6289 0.068 0.000 0.000 0.932
#> SRR944052 2 0.1004 0.9066 0.000 0.972 0.024 0.004
#> SRR944053 1 0.4999 0.5505 0.508 0.000 0.000 0.492
#> SRR944054 4 0.0188 0.6921 0.004 0.000 0.000 0.996
#> SRR944055 3 0.0000 0.9317 0.000 0.000 1.000 0.000
#> SRR944056 2 0.0000 0.9112 0.000 1.000 0.000 0.000
#> SRR944057 1 0.0000 0.4750 1.000 0.000 0.000 0.000
#> SRR944058 1 0.4522 0.5662 0.680 0.000 0.000 0.320
#> SRR944059 3 0.0188 0.9287 0.000 0.004 0.996 0.000
#> SRR944060 1 0.7643 0.4443 0.468 0.000 0.276 0.256
#> SRR944061 2 0.0469 0.9119 0.000 0.988 0.012 0.000
#> SRR944062 1 0.1637 0.4950 0.940 0.000 0.000 0.060
#> SRR944063 1 0.4999 0.5505 0.508 0.000 0.000 0.492
#> SRR944064 1 0.4843 0.5409 0.604 0.000 0.000 0.396
#> SRR944065 1 0.4999 0.5505 0.508 0.000 0.000 0.492
#> SRR944066 1 0.0000 0.4750 1.000 0.000 0.000 0.000
#> SRR944067 4 0.0188 0.6932 0.004 0.000 0.000 0.996
#> SRR944068 1 0.4999 0.5505 0.508 0.000 0.000 0.492
#> SRR944069 2 0.0336 0.9123 0.000 0.992 0.008 0.000
#> SRR944070 1 0.7643 0.4443 0.468 0.000 0.276 0.256
#> SRR944071 3 0.0000 0.9317 0.000 0.000 1.000 0.000
#> SRR944072 1 0.4522 0.5662 0.680 0.000 0.000 0.320
#> SRR944073 2 0.5383 0.4545 0.000 0.536 0.012 0.452
#> SRR944075 3 0.0000 0.9317 0.000 0.000 1.000 0.000
#> SRR944074 4 0.0000 0.6940 0.000 0.000 0.000 1.000
#> SRR944076 3 0.0000 0.9317 0.000 0.000 1.000 0.000
#> SRR944077 2 0.0188 0.9125 0.000 0.996 0.004 0.000
#> SRR944078 3 0.0657 0.9199 0.012 0.000 0.984 0.004
#> SRR944079 2 0.0188 0.9119 0.000 0.996 0.004 0.000
#> SRR944080 2 0.0188 0.9125 0.000 0.996 0.004 0.000
#> SRR944081 4 0.4989 -0.5193 0.472 0.000 0.000 0.528
#> SRR944082 1 0.4331 0.5660 0.712 0.000 0.000 0.288
#> SRR944083 1 0.0000 0.4750 1.000 0.000 0.000 0.000
#> SRR944084 1 0.4999 0.5505 0.508 0.000 0.000 0.492
#> SRR944085 3 0.0000 0.9317 0.000 0.000 1.000 0.000
#> SRR944086 4 0.5000 -0.5683 0.496 0.000 0.000 0.504
#> SRR944088 4 0.2704 0.5403 0.124 0.000 0.000 0.876
#> SRR944087 3 0.0000 0.9317 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 3 0.0000 0.8391 0.000 0.000 1.000 0.000 0.000
#> SRR944012 4 0.0579 0.6539 0.008 0.000 0.000 0.984 0.008
#> SRR944014 2 0.0000 0.8884 0.000 1.000 0.000 0.000 0.000
#> SRR944013 5 0.3216 0.7125 0.044 0.000 0.000 0.108 0.848
#> SRR944015 4 0.1106 0.6517 0.012 0.000 0.000 0.964 0.024
#> SRR944016 1 0.0000 0.9422 1.000 0.000 0.000 0.000 0.000
#> SRR944017 5 0.2152 0.7104 0.044 0.004 0.000 0.032 0.920
#> SRR944018 4 0.6176 0.4382 0.172 0.000 0.000 0.540 0.288
#> SRR944019 4 0.5195 0.5721 0.168 0.000 0.000 0.688 0.144
#> SRR944020 4 0.0000 0.6509 0.000 0.000 0.000 1.000 0.000
#> SRR944021 2 0.0000 0.8884 0.000 1.000 0.000 0.000 0.000
#> SRR944022 4 0.0162 0.6518 0.000 0.000 0.000 0.996 0.004
#> SRR944023 4 0.8372 0.2211 0.288 0.000 0.212 0.340 0.160
#> SRR944024 1 0.0000 0.9422 1.000 0.000 0.000 0.000 0.000
#> SRR944026 5 0.3752 0.5858 0.000 0.000 0.000 0.292 0.708
#> SRR944025 5 0.2074 0.7127 0.044 0.000 0.000 0.036 0.920
#> SRR944028 5 0.2230 0.7143 0.044 0.000 0.000 0.044 0.912
#> SRR944029 4 0.4104 0.5618 0.032 0.000 0.000 0.748 0.220
#> SRR944030 2 0.1121 0.8697 0.000 0.956 0.000 0.000 0.044
#> SRR944031 3 0.0000 0.8391 0.000 0.000 1.000 0.000 0.000
#> SRR944032 5 0.4634 0.6094 0.120 0.000 0.000 0.136 0.744
#> SRR944033 2 0.0000 0.8884 0.000 1.000 0.000 0.000 0.000
#> SRR944034 2 0.3928 0.6241 0.000 0.700 0.000 0.004 0.296
#> SRR944036 4 0.8434 0.1740 0.284 0.000 0.252 0.308 0.156
#> SRR944035 2 0.1732 0.8509 0.000 0.920 0.000 0.000 0.080
#> SRR944038 3 0.7232 -0.1231 0.044 0.000 0.400 0.396 0.160
#> SRR944037 4 0.0000 0.6509 0.000 0.000 0.000 1.000 0.000
#> SRR944039 4 0.6243 0.4609 0.216 0.000 0.000 0.544 0.240
#> SRR944040 2 0.6511 0.2931 0.000 0.500 0.376 0.036 0.088
#> SRR944041 4 0.1082 0.6549 0.028 0.000 0.000 0.964 0.008
#> SRR944042 3 0.1043 0.8121 0.000 0.000 0.960 0.040 0.000
#> SRR944043 4 0.6121 0.4732 0.164 0.000 0.004 0.576 0.256
#> SRR944044 5 0.3496 0.6771 0.012 0.000 0.000 0.200 0.788
#> SRR944046 3 0.0000 0.8391 0.000 0.000 1.000 0.000 0.000
#> SRR944045 2 0.4580 0.7301 0.000 0.776 0.136 0.028 0.060
#> SRR944047 2 0.0162 0.8875 0.000 0.996 0.000 0.000 0.004
#> SRR944048 1 0.0000 0.9422 1.000 0.000 0.000 0.000 0.000
#> SRR944049 2 0.5227 0.2781 0.032 0.556 0.000 0.008 0.404
#> SRR944050 1 0.0000 0.9422 1.000 0.000 0.000 0.000 0.000
#> SRR944051 5 0.4979 0.1999 0.028 0.000 0.000 0.480 0.492
#> SRR944052 2 0.0290 0.8866 0.000 0.992 0.000 0.000 0.008
#> SRR944053 4 0.0290 0.6517 0.000 0.000 0.000 0.992 0.008
#> SRR944054 5 0.3983 0.5156 0.000 0.000 0.000 0.340 0.660
#> SRR944055 3 0.0000 0.8391 0.000 0.000 1.000 0.000 0.000
#> SRR944056 2 0.0000 0.8884 0.000 1.000 0.000 0.000 0.000
#> SRR944057 1 0.0000 0.9422 1.000 0.000 0.000 0.000 0.000
#> SRR944058 4 0.5854 0.3598 0.436 0.000 0.000 0.468 0.096
#> SRR944059 3 0.0510 0.8274 0.000 0.016 0.984 0.000 0.000
#> SRR944060 3 0.7232 -0.1231 0.044 0.000 0.400 0.396 0.160
#> SRR944061 2 0.0000 0.8884 0.000 1.000 0.000 0.000 0.000
#> SRR944062 1 0.4065 0.4426 0.720 0.000 0.000 0.264 0.016
#> SRR944063 4 0.0162 0.6518 0.000 0.000 0.000 0.996 0.004
#> SRR944064 5 0.6963 0.1314 0.328 0.000 0.008 0.260 0.404
#> SRR944065 4 0.0290 0.6517 0.000 0.000 0.000 0.992 0.008
#> SRR944066 1 0.0000 0.9422 1.000 0.000 0.000 0.000 0.000
#> SRR944067 5 0.2074 0.7127 0.044 0.000 0.000 0.036 0.920
#> SRR944068 4 0.0000 0.6509 0.000 0.000 0.000 1.000 0.000
#> SRR944069 2 0.0000 0.8884 0.000 1.000 0.000 0.000 0.000
#> SRR944070 3 0.7232 -0.1231 0.044 0.000 0.400 0.396 0.160
#> SRR944071 3 0.0000 0.8391 0.000 0.000 1.000 0.000 0.000
#> SRR944072 4 0.5854 0.3598 0.436 0.000 0.000 0.468 0.096
#> SRR944073 2 0.3612 0.6683 0.000 0.732 0.000 0.000 0.268
#> SRR944075 3 0.0000 0.8391 0.000 0.000 1.000 0.000 0.000
#> SRR944074 5 0.3636 0.6069 0.000 0.000 0.000 0.272 0.728
#> SRR944076 3 0.0000 0.8391 0.000 0.000 1.000 0.000 0.000
#> SRR944077 2 0.0000 0.8884 0.000 1.000 0.000 0.000 0.000
#> SRR944078 3 0.0162 0.8371 0.000 0.000 0.996 0.000 0.004
#> SRR944079 2 0.0290 0.8850 0.000 0.992 0.008 0.000 0.000
#> SRR944080 2 0.0000 0.8884 0.000 1.000 0.000 0.000 0.000
#> SRR944081 4 0.4615 0.5142 0.048 0.000 0.000 0.700 0.252
#> SRR944082 4 0.6428 0.3602 0.384 0.000 0.000 0.440 0.176
#> SRR944083 1 0.0000 0.9422 1.000 0.000 0.000 0.000 0.000
#> SRR944084 4 0.4681 0.5648 0.084 0.000 0.000 0.728 0.188
#> SRR944085 3 0.0798 0.8259 0.008 0.000 0.976 0.000 0.016
#> SRR944086 4 0.5968 0.4508 0.156 0.000 0.000 0.576 0.268
#> SRR944088 4 0.4268 0.0695 0.000 0.000 0.000 0.556 0.444
#> SRR944087 3 0.0000 0.8391 0.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 3 0.0146 0.970 0.000 0.004 0.996 0.000 0.000 0.000
#> SRR944012 4 0.1501 0.814 0.000 0.000 0.000 0.924 0.000 0.076
#> SRR944014 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944013 5 0.1251 0.696 0.012 0.000 0.000 0.024 0.956 0.008
#> SRR944015 4 0.3473 0.739 0.000 0.000 0.000 0.808 0.096 0.096
#> SRR944016 1 0.0000 0.685 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR944017 5 0.2126 0.622 0.020 0.004 0.000 0.000 0.904 0.072
#> SRR944018 5 0.5930 0.563 0.136 0.000 0.000 0.260 0.568 0.036
#> SRR944019 4 0.6674 -0.301 0.112 0.000 0.000 0.428 0.368 0.092
#> SRR944020 4 0.1714 0.835 0.000 0.000 0.000 0.908 0.000 0.092
#> SRR944021 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944022 4 0.0146 0.864 0.000 0.000 0.000 0.996 0.000 0.004
#> SRR944023 1 0.7340 -0.135 0.380 0.000 0.164 0.048 0.044 0.364
#> SRR944024 1 0.0000 0.685 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR944026 5 0.3748 0.716 0.000 0.000 0.004 0.148 0.784 0.064
#> SRR944025 5 0.2201 0.617 0.028 0.000 0.000 0.000 0.896 0.076
#> SRR944028 5 0.0993 0.672 0.024 0.000 0.000 0.000 0.964 0.012
#> SRR944029 5 0.5638 0.463 0.000 0.000 0.004 0.368 0.492 0.136
#> SRR944030 2 0.1007 0.876 0.000 0.956 0.000 0.000 0.044 0.000
#> SRR944031 3 0.0146 0.970 0.000 0.004 0.996 0.000 0.000 0.000
#> SRR944032 5 0.2459 0.700 0.052 0.000 0.000 0.032 0.896 0.020
#> SRR944033 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944034 2 0.3023 0.740 0.004 0.784 0.000 0.000 0.212 0.000
#> SRR944036 1 0.7120 -0.128 0.384 0.000 0.184 0.028 0.040 0.364
#> SRR944035 2 0.1753 0.852 0.000 0.912 0.004 0.000 0.084 0.000
#> SRR944038 6 0.4710 0.987 0.000 0.004 0.136 0.084 0.036 0.740
#> SRR944037 4 0.1714 0.835 0.000 0.000 0.000 0.908 0.000 0.092
#> SRR944039 5 0.6871 0.393 0.176 0.000 0.000 0.304 0.440 0.080
#> SRR944040 2 0.4747 0.385 0.000 0.568 0.376 0.000 0.056 0.000
#> SRR944041 4 0.0622 0.863 0.000 0.000 0.000 0.980 0.012 0.008
#> SRR944042 3 0.2308 0.851 0.000 0.004 0.880 0.008 0.000 0.108
#> SRR944043 5 0.6082 0.497 0.044 0.000 0.000 0.328 0.516 0.112
#> SRR944044 5 0.2250 0.721 0.000 0.000 0.000 0.092 0.888 0.020
#> SRR944046 3 0.1010 0.945 0.000 0.004 0.960 0.000 0.000 0.036
#> SRR944045 2 0.3737 0.700 0.000 0.780 0.168 0.008 0.044 0.000
#> SRR944047 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944048 1 0.0000 0.685 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR944049 2 0.4929 0.430 0.004 0.600 0.000 0.000 0.324 0.072
#> SRR944050 1 0.0000 0.685 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR944051 5 0.4219 0.639 0.000 0.000 0.000 0.304 0.660 0.036
#> SRR944052 2 0.0405 0.893 0.000 0.988 0.004 0.000 0.008 0.000
#> SRR944053 4 0.0865 0.847 0.000 0.000 0.000 0.964 0.000 0.036
#> SRR944054 5 0.3946 0.713 0.000 0.000 0.004 0.152 0.768 0.076
#> SRR944055 3 0.0146 0.970 0.000 0.004 0.996 0.000 0.000 0.000
#> SRR944056 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944057 1 0.0000 0.685 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR944058 1 0.7048 0.204 0.420 0.000 0.000 0.312 0.156 0.112
#> SRR944059 3 0.0405 0.967 0.000 0.008 0.988 0.000 0.000 0.004
#> SRR944060 6 0.4862 0.974 0.004 0.000 0.140 0.088 0.040 0.728
#> SRR944061 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944062 1 0.3424 0.587 0.812 0.000 0.000 0.092 0.000 0.096
#> SRR944063 4 0.0000 0.864 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR944064 1 0.6017 0.395 0.572 0.000 0.000 0.036 0.196 0.196
#> SRR944065 4 0.0146 0.865 0.000 0.000 0.000 0.996 0.004 0.000
#> SRR944066 1 0.0000 0.685 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR944067 5 0.2066 0.624 0.024 0.000 0.000 0.000 0.904 0.072
#> SRR944068 4 0.1327 0.849 0.000 0.000 0.000 0.936 0.000 0.064
#> SRR944069 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944070 6 0.4710 0.987 0.000 0.004 0.136 0.084 0.036 0.740
#> SRR944071 3 0.0291 0.969 0.000 0.004 0.992 0.000 0.000 0.004
#> SRR944072 1 0.7048 0.204 0.420 0.000 0.000 0.312 0.156 0.112
#> SRR944073 2 0.2562 0.783 0.000 0.828 0.000 0.000 0.172 0.000
#> SRR944075 3 0.0146 0.970 0.000 0.004 0.996 0.000 0.000 0.000
#> SRR944074 5 0.3710 0.717 0.000 0.000 0.004 0.144 0.788 0.064
#> SRR944076 3 0.0146 0.970 0.000 0.004 0.996 0.000 0.000 0.000
#> SRR944077 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944078 3 0.0405 0.964 0.000 0.004 0.988 0.000 0.008 0.000
#> SRR944079 2 0.0291 0.894 0.000 0.992 0.004 0.000 0.004 0.000
#> SRR944080 2 0.0000 0.896 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR944081 5 0.4408 0.626 0.000 0.000 0.000 0.320 0.636 0.044
#> SRR944082 1 0.6885 0.275 0.468 0.000 0.000 0.228 0.220 0.084
#> SRR944083 1 0.0146 0.684 0.996 0.000 0.000 0.000 0.000 0.004
#> SRR944084 5 0.5672 0.441 0.024 0.000 0.000 0.384 0.504 0.088
#> SRR944085 3 0.1909 0.884 0.000 0.004 0.920 0.000 0.024 0.052
#> SRR944086 5 0.5148 0.529 0.032 0.000 0.000 0.372 0.560 0.036
#> SRR944088 5 0.4861 0.651 0.000 0.000 0.004 0.264 0.644 0.088
#> SRR944087 3 0.0291 0.969 0.000 0.004 0.992 0.000 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 9427 rows and 77 columns.
#> Top rows (943, 1886, 2828, 3771, 4714) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.890 0.928 0.969 0.4851 0.518 0.518
#> 3 3 0.715 0.816 0.912 0.3263 0.778 0.596
#> 4 4 0.599 0.619 0.799 0.1266 0.897 0.730
#> 5 5 0.584 0.543 0.757 0.0530 0.896 0.677
#> 6 6 0.595 0.468 0.688 0.0364 0.947 0.796
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> SRR944011 2 0.0000 0.964 0.000 1.000
#> SRR944012 1 0.0000 0.970 1.000 0.000
#> SRR944014 2 0.0000 0.964 0.000 1.000
#> SRR944013 1 0.0000 0.970 1.000 0.000
#> SRR944015 2 0.8661 0.610 0.288 0.712
#> SRR944016 1 0.8955 0.539 0.688 0.312
#> SRR944017 1 0.9044 0.515 0.680 0.320
#> SRR944018 1 0.3274 0.919 0.940 0.060
#> SRR944019 1 0.0000 0.970 1.000 0.000
#> SRR944020 1 0.0000 0.970 1.000 0.000
#> SRR944021 2 0.0000 0.964 0.000 1.000
#> SRR944022 1 0.0000 0.970 1.000 0.000
#> SRR944023 2 0.0000 0.964 0.000 1.000
#> SRR944024 2 0.0000 0.964 0.000 1.000
#> SRR944026 1 0.0000 0.970 1.000 0.000
#> SRR944025 1 0.2423 0.938 0.960 0.040
#> SRR944028 1 0.0000 0.970 1.000 0.000
#> SRR944029 1 0.0000 0.970 1.000 0.000
#> SRR944030 2 0.0000 0.964 0.000 1.000
#> SRR944031 2 0.0000 0.964 0.000 1.000
#> SRR944032 1 0.0000 0.970 1.000 0.000
#> SRR944033 2 0.0000 0.964 0.000 1.000
#> SRR944034 2 0.2948 0.923 0.052 0.948
#> SRR944036 2 0.0000 0.964 0.000 1.000
#> SRR944035 2 0.0376 0.962 0.004 0.996
#> SRR944038 2 0.0000 0.964 0.000 1.000
#> SRR944037 1 0.0000 0.970 1.000 0.000
#> SRR944039 1 0.0000 0.970 1.000 0.000
#> SRR944040 2 0.0000 0.964 0.000 1.000
#> SRR944041 1 0.0000 0.970 1.000 0.000
#> SRR944042 2 0.0000 0.964 0.000 1.000
#> SRR944043 2 0.6623 0.796 0.172 0.828
#> SRR944044 1 0.0000 0.970 1.000 0.000
#> SRR944046 2 0.0000 0.964 0.000 1.000
#> SRR944045 2 0.0000 0.964 0.000 1.000
#> SRR944047 2 0.0000 0.964 0.000 1.000
#> SRR944048 2 0.0672 0.959 0.008 0.992
#> SRR944049 2 0.0376 0.962 0.004 0.996
#> SRR944050 2 0.9661 0.360 0.392 0.608
#> SRR944051 1 0.0000 0.970 1.000 0.000
#> SRR944052 2 0.0000 0.964 0.000 1.000
#> SRR944053 1 0.0000 0.970 1.000 0.000
#> SRR944054 1 0.0000 0.970 1.000 0.000
#> SRR944055 2 0.0000 0.964 0.000 1.000
#> SRR944056 2 0.0000 0.964 0.000 1.000
#> SRR944057 2 0.2948 0.924 0.052 0.948
#> SRR944058 1 0.0000 0.970 1.000 0.000
#> SRR944059 2 0.0000 0.964 0.000 1.000
#> SRR944060 2 0.0000 0.964 0.000 1.000
#> SRR944061 2 0.0000 0.964 0.000 1.000
#> SRR944062 2 0.0000 0.964 0.000 1.000
#> SRR944063 1 0.0000 0.970 1.000 0.000
#> SRR944064 2 0.0000 0.964 0.000 1.000
#> SRR944065 1 0.0000 0.970 1.000 0.000
#> SRR944066 2 0.0000 0.964 0.000 1.000
#> SRR944067 1 0.0000 0.970 1.000 0.000
#> SRR944068 1 0.4298 0.890 0.912 0.088
#> SRR944069 2 0.0000 0.964 0.000 1.000
#> SRR944070 2 0.0000 0.964 0.000 1.000
#> SRR944071 2 0.0000 0.964 0.000 1.000
#> SRR944072 1 0.0000 0.970 1.000 0.000
#> SRR944073 2 0.0000 0.964 0.000 1.000
#> SRR944075 2 0.0000 0.964 0.000 1.000
#> SRR944074 1 0.0000 0.970 1.000 0.000
#> SRR944076 2 0.0000 0.964 0.000 1.000
#> SRR944077 2 0.0000 0.964 0.000 1.000
#> SRR944078 2 0.0000 0.964 0.000 1.000
#> SRR944079 2 0.0000 0.964 0.000 1.000
#> SRR944080 2 0.0000 0.964 0.000 1.000
#> SRR944081 1 0.0000 0.970 1.000 0.000
#> SRR944082 2 0.6438 0.807 0.164 0.836
#> SRR944083 2 0.6148 0.817 0.152 0.848
#> SRR944084 2 0.8713 0.600 0.292 0.708
#> SRR944085 2 0.0000 0.964 0.000 1.000
#> SRR944086 1 0.0000 0.970 1.000 0.000
#> SRR944088 1 0.0000 0.970 1.000 0.000
#> SRR944087 2 0.0000 0.964 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR944011 3 0.0424 0.92996 0.008 0.000 0.992
#> SRR944012 2 0.1643 0.87453 0.044 0.956 0.000
#> SRR944014 3 0.0237 0.92985 0.004 0.000 0.996
#> SRR944013 2 0.4452 0.74176 0.192 0.808 0.000
#> SRR944015 3 0.5058 0.66804 0.000 0.244 0.756
#> SRR944016 1 0.0237 0.84997 0.996 0.004 0.000
#> SRR944017 2 0.9136 0.15099 0.144 0.456 0.400
#> SRR944018 1 0.5138 0.65489 0.748 0.252 0.000
#> SRR944019 2 0.6079 0.35333 0.388 0.612 0.000
#> SRR944020 2 0.1411 0.86263 0.000 0.964 0.036
#> SRR944021 3 0.0592 0.92993 0.012 0.000 0.988
#> SRR944022 2 0.1031 0.87972 0.024 0.976 0.000
#> SRR944023 3 0.5905 0.50987 0.352 0.000 0.648
#> SRR944024 1 0.1289 0.84477 0.968 0.000 0.032
#> SRR944026 2 0.0592 0.87985 0.012 0.988 0.000
#> SRR944025 1 0.1411 0.84401 0.964 0.036 0.000
#> SRR944028 1 0.6079 0.34521 0.612 0.388 0.000
#> SRR944029 2 0.3192 0.80096 0.000 0.888 0.112
#> SRR944030 3 0.0892 0.92077 0.000 0.020 0.980
#> SRR944031 3 0.0424 0.93013 0.008 0.000 0.992
#> SRR944032 1 0.3340 0.80968 0.880 0.120 0.000
#> SRR944033 3 0.2066 0.90885 0.060 0.000 0.940
#> SRR944034 1 0.6936 -0.00742 0.524 0.016 0.460
#> SRR944036 3 0.4931 0.72996 0.232 0.000 0.768
#> SRR944035 3 0.6260 0.24641 0.448 0.000 0.552
#> SRR944038 3 0.0424 0.92996 0.008 0.000 0.992
#> SRR944037 2 0.2878 0.81650 0.000 0.904 0.096
#> SRR944039 1 0.3879 0.78252 0.848 0.152 0.000
#> SRR944040 3 0.0592 0.93002 0.012 0.000 0.988
#> SRR944041 2 0.0592 0.87985 0.012 0.988 0.000
#> SRR944042 3 0.0237 0.92985 0.004 0.000 0.996
#> SRR944043 3 0.4270 0.83245 0.024 0.116 0.860
#> SRR944044 2 0.0000 0.87793 0.000 1.000 0.000
#> SRR944046 3 0.0000 0.92899 0.000 0.000 1.000
#> SRR944045 3 0.0237 0.92788 0.000 0.004 0.996
#> SRR944047 3 0.1753 0.91564 0.048 0.000 0.952
#> SRR944048 1 0.0592 0.85187 0.988 0.000 0.012
#> SRR944049 3 0.4861 0.77840 0.192 0.008 0.800
#> SRR944050 1 0.0424 0.85240 0.992 0.000 0.008
#> SRR944051 2 0.2165 0.86619 0.064 0.936 0.000
#> SRR944052 3 0.2959 0.88141 0.100 0.000 0.900
#> SRR944053 2 0.2625 0.85306 0.084 0.916 0.000
#> SRR944054 2 0.0424 0.87584 0.000 0.992 0.008
#> SRR944055 3 0.0424 0.92996 0.008 0.000 0.992
#> SRR944056 3 0.1163 0.92512 0.028 0.000 0.972
#> SRR944057 1 0.0424 0.85240 0.992 0.000 0.008
#> SRR944058 1 0.3752 0.78964 0.856 0.144 0.000
#> SRR944059 3 0.0592 0.92993 0.012 0.000 0.988
#> SRR944060 3 0.0747 0.92923 0.016 0.000 0.984
#> SRR944061 3 0.2261 0.90319 0.068 0.000 0.932
#> SRR944062 1 0.3941 0.74203 0.844 0.000 0.156
#> SRR944063 2 0.1525 0.87938 0.032 0.964 0.004
#> SRR944064 1 0.1753 0.83567 0.952 0.000 0.048
#> SRR944065 2 0.1031 0.87993 0.024 0.976 0.000
#> SRR944066 1 0.0892 0.84982 0.980 0.000 0.020
#> SRR944067 1 0.3412 0.80636 0.876 0.124 0.000
#> SRR944068 2 0.4702 0.67867 0.000 0.788 0.212
#> SRR944069 3 0.0592 0.92467 0.000 0.012 0.988
#> SRR944070 3 0.0000 0.92899 0.000 0.000 1.000
#> SRR944071 3 0.0237 0.92788 0.000 0.004 0.996
#> SRR944072 1 0.3038 0.81852 0.896 0.104 0.000
#> SRR944073 3 0.2796 0.88866 0.092 0.000 0.908
#> SRR944075 3 0.0237 0.92788 0.000 0.004 0.996
#> SRR944074 2 0.0424 0.87925 0.008 0.992 0.000
#> SRR944076 3 0.0592 0.92993 0.012 0.000 0.988
#> SRR944077 3 0.0892 0.92821 0.020 0.000 0.980
#> SRR944078 3 0.0747 0.92292 0.000 0.016 0.984
#> SRR944079 3 0.0592 0.93004 0.012 0.000 0.988
#> SRR944080 3 0.1163 0.92548 0.028 0.000 0.972
#> SRR944081 2 0.2261 0.86355 0.068 0.932 0.000
#> SRR944082 1 0.3116 0.79143 0.892 0.000 0.108
#> SRR944083 1 0.0424 0.85240 0.992 0.000 0.008
#> SRR944084 3 0.5058 0.66774 0.000 0.244 0.756
#> SRR944085 3 0.0747 0.92275 0.000 0.016 0.984
#> SRR944086 2 0.3752 0.79827 0.144 0.856 0.000
#> SRR944088 2 0.0237 0.87723 0.000 0.996 0.004
#> SRR944087 3 0.0237 0.92985 0.004 0.000 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR944011 2 0.2647 0.7229 0.000 0.880 0.120 0.000
#> SRR944012 4 0.1305 0.8542 0.004 0.000 0.036 0.960
#> SRR944014 2 0.0779 0.7615 0.004 0.980 0.016 0.000
#> SRR944013 3 0.7587 -0.2966 0.196 0.000 0.412 0.392
#> SRR944015 2 0.6395 -0.1437 0.000 0.472 0.464 0.064
#> SRR944016 1 0.2149 0.7573 0.912 0.000 0.088 0.000
#> SRR944017 3 0.4903 0.4842 0.068 0.036 0.812 0.084
#> SRR944018 3 0.5594 0.1447 0.284 0.004 0.672 0.040
#> SRR944019 4 0.7598 0.3255 0.284 0.000 0.240 0.476
#> SRR944020 4 0.4137 0.7708 0.000 0.012 0.208 0.780
#> SRR944021 2 0.3123 0.6990 0.000 0.844 0.156 0.000
#> SRR944022 4 0.4745 0.7640 0.036 0.000 0.208 0.756
#> SRR944023 1 0.7906 -0.2629 0.352 0.348 0.300 0.000
#> SRR944024 1 0.4756 0.6581 0.784 0.144 0.072 0.000
#> SRR944026 4 0.1356 0.8552 0.008 0.000 0.032 0.960
#> SRR944025 1 0.2983 0.7628 0.896 0.016 0.076 0.012
#> SRR944028 1 0.7059 0.3104 0.528 0.000 0.140 0.332
#> SRR944029 4 0.3198 0.8324 0.000 0.040 0.080 0.880
#> SRR944030 3 0.5033 0.4582 0.004 0.324 0.664 0.008
#> SRR944031 2 0.4991 0.3197 0.004 0.608 0.388 0.000
#> SRR944032 1 0.4072 0.7107 0.828 0.000 0.052 0.120
#> SRR944033 2 0.2413 0.7354 0.064 0.916 0.020 0.000
#> SRR944034 2 0.8212 -0.0203 0.380 0.416 0.176 0.028
#> SRR944036 2 0.6229 0.5294 0.132 0.664 0.204 0.000
#> SRR944035 2 0.8440 0.1776 0.300 0.472 0.180 0.048
#> SRR944038 2 0.1109 0.7575 0.004 0.968 0.028 0.000
#> SRR944037 4 0.3301 0.8314 0.000 0.048 0.076 0.876
#> SRR944039 1 0.6052 0.3964 0.556 0.000 0.396 0.048
#> SRR944040 2 0.1388 0.7572 0.012 0.960 0.028 0.000
#> SRR944041 4 0.1545 0.8521 0.000 0.008 0.040 0.952
#> SRR944042 2 0.0817 0.7599 0.000 0.976 0.024 0.000
#> SRR944043 3 0.5938 0.5471 0.020 0.232 0.696 0.052
#> SRR944044 4 0.3351 0.8186 0.008 0.000 0.148 0.844
#> SRR944046 2 0.3801 0.6359 0.000 0.780 0.220 0.000
#> SRR944045 2 0.5070 0.2563 0.000 0.580 0.416 0.004
#> SRR944047 2 0.1743 0.7568 0.004 0.940 0.056 0.000
#> SRR944048 1 0.2224 0.7545 0.928 0.032 0.040 0.000
#> SRR944049 2 0.6456 0.5016 0.204 0.688 0.064 0.044
#> SRR944050 1 0.2334 0.7580 0.908 0.004 0.088 0.000
#> SRR944051 4 0.2924 0.8343 0.016 0.000 0.100 0.884
#> SRR944052 2 0.4552 0.6569 0.128 0.812 0.048 0.012
#> SRR944053 4 0.4428 0.8024 0.068 0.000 0.124 0.808
#> SRR944054 4 0.1296 0.8539 0.004 0.004 0.028 0.964
#> SRR944055 2 0.1022 0.7609 0.000 0.968 0.032 0.000
#> SRR944056 2 0.4808 0.6661 0.092 0.816 0.056 0.036
#> SRR944057 1 0.2805 0.7559 0.888 0.012 0.100 0.000
#> SRR944058 1 0.4282 0.7036 0.816 0.000 0.060 0.124
#> SRR944059 2 0.2589 0.7261 0.000 0.884 0.116 0.000
#> SRR944060 3 0.5186 0.4346 0.016 0.344 0.640 0.000
#> SRR944061 2 0.2300 0.7441 0.048 0.924 0.028 0.000
#> SRR944062 1 0.5994 0.4528 0.636 0.296 0.068 0.000
#> SRR944063 4 0.2010 0.8527 0.004 0.004 0.060 0.932
#> SRR944064 1 0.2739 0.7460 0.904 0.060 0.036 0.000
#> SRR944065 4 0.2302 0.8486 0.008 0.008 0.060 0.924
#> SRR944066 1 0.3280 0.7470 0.860 0.016 0.124 0.000
#> SRR944067 1 0.5062 0.6890 0.752 0.000 0.184 0.064
#> SRR944068 4 0.3071 0.8168 0.000 0.068 0.044 0.888
#> SRR944069 3 0.5838 0.1444 0.024 0.444 0.528 0.004
#> SRR944070 2 0.0921 0.7592 0.000 0.972 0.028 0.000
#> SRR944071 2 0.4250 0.5574 0.000 0.724 0.276 0.000
#> SRR944072 1 0.3280 0.7394 0.860 0.000 0.124 0.016
#> SRR944073 2 0.4024 0.7132 0.076 0.856 0.040 0.028
#> SRR944075 2 0.1637 0.7544 0.000 0.940 0.060 0.000
#> SRR944074 4 0.1022 0.8557 0.000 0.000 0.032 0.968
#> SRR944076 2 0.3311 0.6996 0.000 0.828 0.172 0.000
#> SRR944077 2 0.1624 0.7546 0.020 0.952 0.028 0.000
#> SRR944078 2 0.1733 0.7540 0.000 0.948 0.028 0.024
#> SRR944079 2 0.1890 0.7590 0.008 0.936 0.056 0.000
#> SRR944080 2 0.2870 0.7405 0.044 0.908 0.036 0.012
#> SRR944081 4 0.5929 0.6384 0.064 0.000 0.296 0.640
#> SRR944082 1 0.3463 0.7273 0.864 0.096 0.040 0.000
#> SRR944083 1 0.1833 0.7551 0.944 0.032 0.024 0.000
#> SRR944084 2 0.6810 0.3239 0.000 0.596 0.248 0.156
#> SRR944085 2 0.4991 0.3238 0.000 0.608 0.388 0.004
#> SRR944086 4 0.5646 0.7008 0.088 0.000 0.204 0.708
#> SRR944088 4 0.1474 0.8519 0.000 0.000 0.052 0.948
#> SRR944087 2 0.1256 0.7619 0.008 0.964 0.028 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR944011 2 0.2280 0.7432 0.000 0.880 0.120 0.000 0.000
#> SRR944012 4 0.2102 0.7471 0.012 0.000 0.004 0.916 0.068
#> SRR944014 2 0.0510 0.7976 0.000 0.984 0.000 0.000 0.016
#> SRR944013 3 0.7775 -0.1632 0.124 0.000 0.468 0.252 0.156
#> SRR944015 3 0.5741 0.4661 0.000 0.320 0.592 0.076 0.012
#> SRR944016 1 0.1809 0.6716 0.928 0.000 0.060 0.000 0.012
#> SRR944017 3 0.3530 0.4089 0.040 0.024 0.868 0.024 0.044
#> SRR944018 3 0.4082 0.3004 0.140 0.000 0.796 0.008 0.056
#> SRR944019 4 0.8299 0.1169 0.180 0.000 0.216 0.392 0.212
#> SRR944020 4 0.3967 0.6548 0.000 0.000 0.264 0.724 0.012
#> SRR944021 2 0.3897 0.6301 0.000 0.768 0.204 0.000 0.028
#> SRR944022 4 0.5976 0.5464 0.016 0.000 0.296 0.592 0.096
#> SRR944023 3 0.7675 0.2375 0.316 0.240 0.388 0.000 0.056
#> SRR944024 1 0.5481 0.5255 0.676 0.132 0.008 0.000 0.184
#> SRR944026 4 0.1828 0.7547 0.004 0.000 0.028 0.936 0.032
#> SRR944025 1 0.4609 0.6030 0.804 0.012 0.056 0.064 0.064
#> SRR944028 5 0.7466 -0.0422 0.340 0.000 0.060 0.172 0.428
#> SRR944029 4 0.2701 0.7375 0.000 0.032 0.036 0.900 0.032
#> SRR944030 3 0.3732 0.5440 0.000 0.176 0.792 0.000 0.032
#> SRR944031 3 0.4747 0.1342 0.000 0.488 0.496 0.000 0.016
#> SRR944032 1 0.5301 0.4591 0.648 0.000 0.004 0.076 0.272
#> SRR944033 2 0.1814 0.7901 0.024 0.940 0.004 0.004 0.028
#> SRR944034 1 0.8424 -0.0514 0.356 0.332 0.156 0.012 0.144
#> SRR944036 2 0.7734 0.1754 0.112 0.480 0.188 0.000 0.220
#> SRR944035 5 0.6868 0.1950 0.080 0.296 0.040 0.024 0.560
#> SRR944038 2 0.0671 0.7983 0.000 0.980 0.004 0.000 0.016
#> SRR944037 4 0.3294 0.7481 0.000 0.008 0.104 0.852 0.036
#> SRR944039 3 0.6493 -0.1879 0.396 0.000 0.476 0.024 0.104
#> SRR944040 2 0.1256 0.7959 0.012 0.964 0.008 0.004 0.012
#> SRR944041 4 0.2275 0.7456 0.004 0.008 0.008 0.912 0.068
#> SRR944042 2 0.1012 0.7979 0.000 0.968 0.020 0.000 0.012
#> SRR944043 3 0.3874 0.4943 0.020 0.092 0.836 0.044 0.008
#> SRR944044 4 0.3888 0.7348 0.008 0.000 0.112 0.816 0.064
#> SRR944046 2 0.4000 0.5902 0.000 0.748 0.228 0.000 0.024
#> SRR944045 3 0.5289 0.1993 0.000 0.452 0.500 0.000 0.048
#> SRR944047 2 0.1502 0.7871 0.000 0.940 0.056 0.000 0.004
#> SRR944048 1 0.3757 0.6543 0.816 0.040 0.008 0.000 0.136
#> SRR944049 2 0.6368 0.4401 0.188 0.652 0.012 0.052 0.096
#> SRR944050 1 0.1443 0.6722 0.948 0.004 0.044 0.000 0.004
#> SRR944051 4 0.4986 0.4849 0.008 0.000 0.024 0.600 0.368
#> SRR944052 2 0.4582 0.6724 0.112 0.792 0.008 0.028 0.060
#> SRR944053 4 0.6006 0.6217 0.036 0.000 0.184 0.656 0.124
#> SRR944054 4 0.2608 0.7206 0.000 0.020 0.004 0.888 0.088
#> SRR944055 2 0.1116 0.7986 0.000 0.964 0.028 0.004 0.004
#> SRR944056 2 0.4727 0.6788 0.060 0.796 0.012 0.056 0.076
#> SRR944057 1 0.2208 0.6595 0.908 0.000 0.072 0.000 0.020
#> SRR944058 1 0.5161 0.5083 0.672 0.000 0.016 0.048 0.264
#> SRR944059 2 0.3731 0.6845 0.000 0.800 0.160 0.000 0.040
#> SRR944060 3 0.3289 0.5467 0.008 0.172 0.816 0.000 0.004
#> SRR944061 2 0.1990 0.7855 0.028 0.928 0.004 0.000 0.040
#> SRR944062 1 0.6652 0.2084 0.512 0.304 0.016 0.000 0.168
#> SRR944063 4 0.3236 0.7315 0.004 0.004 0.016 0.844 0.132
#> SRR944064 1 0.3570 0.6616 0.836 0.048 0.008 0.000 0.108
#> SRR944065 4 0.3398 0.6838 0.000 0.000 0.004 0.780 0.216
#> SRR944066 1 0.2629 0.6475 0.880 0.004 0.104 0.000 0.012
#> SRR944067 1 0.6406 0.1829 0.480 0.000 0.064 0.044 0.412
#> SRR944068 4 0.4726 0.6784 0.000 0.088 0.036 0.776 0.100
#> SRR944069 3 0.5869 0.4357 0.032 0.344 0.584 0.012 0.028
#> SRR944070 2 0.0992 0.7986 0.000 0.968 0.024 0.000 0.008
#> SRR944071 2 0.4508 0.3637 0.000 0.648 0.332 0.000 0.020
#> SRR944072 1 0.3423 0.6421 0.852 0.000 0.092 0.016 0.040
#> SRR944073 2 0.3561 0.7460 0.064 0.860 0.008 0.028 0.040
#> SRR944075 2 0.1809 0.7834 0.000 0.928 0.060 0.000 0.012
#> SRR944074 4 0.1885 0.7495 0.004 0.000 0.020 0.932 0.044
#> SRR944076 2 0.5526 0.4875 0.000 0.648 0.200 0.000 0.152
#> SRR944077 2 0.2550 0.7693 0.044 0.908 0.004 0.012 0.032
#> SRR944078 2 0.1686 0.7979 0.000 0.944 0.020 0.028 0.008
#> SRR944079 2 0.1492 0.7984 0.008 0.948 0.040 0.000 0.004
#> SRR944080 2 0.4447 0.7131 0.064 0.816 0.020 0.036 0.064
#> SRR944081 4 0.7100 0.3373 0.028 0.000 0.344 0.440 0.188
#> SRR944082 1 0.5145 0.6115 0.724 0.092 0.020 0.000 0.164
#> SRR944083 1 0.1996 0.6716 0.928 0.032 0.004 0.000 0.036
#> SRR944084 2 0.7267 0.0152 0.000 0.496 0.304 0.108 0.092
#> SRR944085 3 0.4907 0.1185 0.000 0.488 0.488 0.000 0.024
#> SRR944086 5 0.4505 0.2444 0.016 0.000 0.028 0.220 0.736
#> SRR944088 4 0.1377 0.7539 0.004 0.000 0.020 0.956 0.020
#> SRR944087 2 0.1300 0.7989 0.000 0.956 0.016 0.000 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR944011 2 0.3118 0.6831 0.000 0.820 0.012 0.000 0.012 0.156
#> SRR944012 4 0.3642 0.6981 0.016 0.000 0.060 0.824 0.092 0.008
#> SRR944014 2 0.1867 0.7449 0.004 0.924 0.036 0.000 0.000 0.036
#> SRR944013 6 0.8210 -0.1033 0.112 0.000 0.252 0.180 0.080 0.376
#> SRR944015 6 0.5578 0.4601 0.000 0.248 0.036 0.040 0.036 0.640
#> SRR944016 1 0.1565 0.6356 0.940 0.000 0.028 0.000 0.004 0.028
#> SRR944017 6 0.4219 0.4121 0.088 0.012 0.076 0.004 0.024 0.796
#> SRR944018 6 0.4890 0.3488 0.144 0.004 0.064 0.016 0.032 0.740
#> SRR944019 3 0.8539 -0.3690 0.116 0.000 0.304 0.288 0.128 0.164
#> SRR944020 4 0.4784 0.6368 0.000 0.000 0.064 0.680 0.020 0.236
#> SRR944021 2 0.4564 0.5405 0.000 0.684 0.036 0.000 0.024 0.256
#> SRR944022 4 0.7054 0.4923 0.008 0.000 0.116 0.488 0.148 0.240
#> SRR944023 6 0.7939 0.0397 0.280 0.196 0.144 0.000 0.028 0.352
#> SRR944024 1 0.6376 0.3252 0.472 0.132 0.344 0.000 0.052 0.000
#> SRR944026 4 0.1864 0.7219 0.000 0.000 0.032 0.924 0.040 0.004
#> SRR944025 1 0.3720 0.5538 0.828 0.008 0.100 0.032 0.012 0.020
#> SRR944028 5 0.7556 0.2396 0.296 0.000 0.220 0.068 0.384 0.032
#> SRR944029 4 0.2789 0.7068 0.000 0.036 0.064 0.880 0.008 0.012
#> SRR944030 6 0.3696 0.5157 0.004 0.128 0.036 0.004 0.016 0.812
#> SRR944031 2 0.4500 0.0110 0.000 0.488 0.012 0.000 0.012 0.488
#> SRR944032 1 0.6064 0.2561 0.564 0.000 0.108 0.048 0.276 0.004
#> SRR944033 2 0.1719 0.7272 0.008 0.928 0.056 0.000 0.000 0.008
#> SRR944034 2 0.8820 -0.2717 0.244 0.300 0.148 0.004 0.132 0.172
#> SRR944036 3 0.7835 -0.0600 0.040 0.328 0.360 0.000 0.124 0.148
#> SRR944035 5 0.6946 0.0880 0.048 0.104 0.352 0.008 0.460 0.028
#> SRR944038 2 0.0865 0.7374 0.000 0.964 0.036 0.000 0.000 0.000
#> SRR944037 4 0.3938 0.7119 0.000 0.012 0.092 0.812 0.032 0.052
#> SRR944039 6 0.7757 -0.1882 0.292 0.000 0.256 0.048 0.060 0.344
#> SRR944040 2 0.1578 0.7397 0.012 0.936 0.048 0.000 0.000 0.004
#> SRR944041 4 0.3791 0.7024 0.000 0.016 0.136 0.804 0.028 0.016
#> SRR944042 2 0.1180 0.7438 0.000 0.960 0.016 0.000 0.012 0.012
#> SRR944043 6 0.3221 0.5078 0.048 0.080 0.024 0.000 0.000 0.848
#> SRR944044 4 0.4859 0.6777 0.020 0.000 0.072 0.756 0.080 0.072
#> SRR944046 2 0.4185 0.5911 0.000 0.724 0.024 0.000 0.024 0.228
#> SRR944045 6 0.5496 0.0494 0.000 0.428 0.080 0.000 0.016 0.476
#> SRR944047 2 0.3150 0.7207 0.000 0.840 0.036 0.000 0.012 0.112
#> SRR944048 1 0.5518 0.4647 0.568 0.032 0.336 0.000 0.060 0.004
#> SRR944049 2 0.5407 0.2955 0.052 0.632 0.272 0.032 0.008 0.004
#> SRR944050 1 0.1495 0.6320 0.948 0.004 0.020 0.000 0.008 0.020
#> SRR944051 4 0.5440 0.4660 0.004 0.000 0.100 0.540 0.352 0.004
#> SRR944052 2 0.4239 0.6100 0.080 0.780 0.116 0.004 0.008 0.012
#> SRR944053 4 0.7503 0.4898 0.068 0.000 0.116 0.512 0.128 0.176
#> SRR944054 4 0.3976 0.6907 0.004 0.016 0.132 0.800 0.028 0.020
#> SRR944055 2 0.0725 0.7451 0.000 0.976 0.012 0.000 0.000 0.012
#> SRR944056 2 0.3872 0.6328 0.032 0.812 0.116 0.024 0.004 0.012
#> SRR944057 1 0.2257 0.6005 0.904 0.000 0.040 0.000 0.008 0.048
#> SRR944058 1 0.5813 0.3932 0.596 0.000 0.224 0.024 0.152 0.004
#> SRR944059 2 0.3629 0.6798 0.000 0.804 0.032 0.000 0.024 0.140
#> SRR944060 6 0.3337 0.5226 0.036 0.136 0.004 0.000 0.004 0.820
#> SRR944061 2 0.1818 0.7250 0.004 0.920 0.068 0.000 0.004 0.004
#> SRR944062 3 0.6889 -0.1389 0.280 0.320 0.352 0.000 0.048 0.000
#> SRR944063 4 0.4555 0.6910 0.000 0.008 0.124 0.748 0.104 0.016
#> SRR944064 1 0.5537 0.4671 0.568 0.048 0.340 0.000 0.036 0.008
#> SRR944065 4 0.4508 0.5878 0.000 0.004 0.036 0.648 0.308 0.004
#> SRR944066 1 0.2492 0.5993 0.888 0.000 0.036 0.000 0.008 0.068
#> SRR944067 5 0.6791 0.0397 0.340 0.000 0.272 0.008 0.356 0.024
#> SRR944068 4 0.5057 0.6488 0.000 0.080 0.048 0.740 0.104 0.028
#> SRR944069 6 0.6167 0.3987 0.044 0.280 0.080 0.000 0.024 0.572
#> SRR944070 2 0.1245 0.7468 0.000 0.952 0.016 0.000 0.000 0.032
#> SRR944071 2 0.4629 0.3016 0.000 0.576 0.020 0.000 0.016 0.388
#> SRR944072 1 0.2228 0.6210 0.912 0.000 0.016 0.004 0.024 0.044
#> SRR944073 2 0.3712 0.6784 0.068 0.832 0.064 0.020 0.004 0.012
#> SRR944075 2 0.1226 0.7453 0.000 0.952 0.004 0.000 0.004 0.040
#> SRR944074 4 0.3011 0.7117 0.000 0.000 0.100 0.852 0.036 0.012
#> SRR944076 2 0.6510 0.3330 0.000 0.540 0.144 0.000 0.092 0.224
#> SRR944077 2 0.2543 0.7256 0.024 0.892 0.064 0.000 0.004 0.016
#> SRR944078 2 0.1967 0.7444 0.000 0.928 0.028 0.016 0.008 0.020
#> SRR944079 2 0.3501 0.7252 0.012 0.828 0.036 0.000 0.012 0.112
#> SRR944080 2 0.5584 0.5279 0.136 0.684 0.124 0.004 0.020 0.032
#> SRR944081 4 0.8035 0.1466 0.032 0.000 0.248 0.300 0.128 0.292
#> SRR944082 1 0.6230 0.4014 0.516 0.076 0.344 0.000 0.048 0.016
#> SRR944083 1 0.2865 0.6206 0.852 0.020 0.120 0.000 0.004 0.004
#> SRR944084 2 0.7829 -0.1181 0.000 0.392 0.060 0.108 0.128 0.312
#> SRR944085 6 0.4896 0.1040 0.000 0.424 0.032 0.000 0.016 0.528
#> SRR944086 5 0.2780 0.3052 0.012 0.000 0.012 0.092 0.872 0.012
#> SRR944088 4 0.2664 0.7119 0.000 0.000 0.056 0.884 0.040 0.020
#> SRR944087 2 0.1950 0.7422 0.000 0.924 0.032 0.000 0.028 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
sessionInfo()
#> R version 3.6.0 (2019-04-26)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: CentOS Linux 7 (Core)
#>
#> Matrix products: default
#> BLAS: /usr/lib64/libblas.so.3.4.2
#> LAPACK: /usr/lib64/liblapack.so.3.4.2
#>
#> locale:
#> [1] LC_CTYPE=en_GB.UTF-8 LC_NUMERIC=C LC_TIME=en_GB.UTF-8
#> [4] LC_COLLATE=en_GB.UTF-8 LC_MONETARY=en_GB.UTF-8 LC_MESSAGES=en_GB.UTF-8
#> [7] LC_PAPER=en_GB.UTF-8 LC_NAME=C LC_ADDRESS=C
#> [10] LC_TELEPHONE=C LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C
#>
#> attached base packages:
#> [1] grid stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] genefilter_1.66.0 ComplexHeatmap_2.3.1 markdown_1.1 knitr_1.26
#> [5] GetoptLong_0.1.7 cola_1.3.2
#>
#> loaded via a namespace (and not attached):
#> [1] circlize_0.4.8 shape_1.4.4 xfun_0.11 slam_0.1-46
#> [5] lattice_0.20-38 splines_3.6.0 colorspace_1.4-1 vctrs_0.2.0
#> [9] stats4_3.6.0 blob_1.2.0 XML_3.98-1.20 survival_2.44-1.1
#> [13] rlang_0.4.2 pillar_1.4.2 DBI_1.0.0 BiocGenerics_0.30.0
#> [17] bit64_0.9-7 RColorBrewer_1.1-2 matrixStats_0.55.0 stringr_1.4.0
#> [21] GlobalOptions_0.1.1 evaluate_0.14 memoise_1.1.0 Biobase_2.44.0
#> [25] IRanges_2.18.3 parallel_3.6.0 AnnotationDbi_1.46.1 highr_0.8
#> [29] Rcpp_1.0.3 xtable_1.8-4 backports_1.1.5 S4Vectors_0.22.1
#> [33] annotate_1.62.0 skmeans_0.2-11 bit_1.1-14 microbenchmark_1.4-7
#> [37] brew_1.0-6 impute_1.58.0 rjson_0.2.20 png_0.1-7
#> [41] digest_0.6.23 stringi_1.4.3 polyclip_1.10-0 clue_0.3-57
#> [45] tools_3.6.0 bitops_1.0-6 magrittr_1.5 eulerr_6.0.0
#> [49] RCurl_1.95-4.12 RSQLite_2.1.4 tibble_2.1.3 cluster_2.1.0
#> [53] crayon_1.3.4 pkgconfig_2.0.3 zeallot_0.1.0 Matrix_1.2-17
#> [57] xml2_1.2.2 httr_1.4.1 R6_2.4.1 mclust_5.4.5
#> [61] compiler_3.6.0