Date: 2019-12-26 00:26:17 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 17713 rows and 54 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] 17713 54
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 | ||
|---|---|---|---|---|---|---|
| CV:hclust | 3 | 1.000 | 0.972 | 0.988 | ** | 2 |
| CV:NMF | 3 | 1.000 | 0.957 | 0.981 | ** | |
| MAD:pam | 3 | 1.000 | 0.974 | 0.980 | ** | 2 |
| ATC:skmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:mclust | 3 | 0.969 | 0.942 | 0.973 | ** | |
| SD:hclust | 4 | 0.964 | 0.970 | 0.977 | ** | 2,3 |
| SD:skmeans | 3 | 0.958 | 0.917 | 0.963 | ** | |
| MAD:skmeans | 3 | 0.952 | 0.958 | 0.980 | ** | 2 |
| MAD:hclust | 6 | 0.946 | 0.940 | 0.967 | * | 4 |
| ATC:pam | 3 | 0.944 | 0.940 | 0.973 | * | |
| CV:skmeans | 2 | 0.925 | 0.947 | 0.978 | * | |
| ATC:kmeans | 2 | 0.925 | 0.925 | 0.973 | * | |
| SD:NMF | 6 | 0.916 | 0.848 | 0.902 | * | 2,3,5 |
| SD:pam | 4 | 0.826 | 0.876 | 0.914 | ||
| MAD:mclust | 3 | 0.759 | 0.901 | 0.890 | ||
| MAD:NMF | 2 | 0.753 | 0.914 | 0.955 | ||
| CV:mclust | 2 | 0.632 | 0.909 | 0.941 | ||
| ATC:hclust | 2 | 0.602 | 0.703 | 0.891 | ||
| ATC:NMF | 3 | 0.592 | 0.781 | 0.884 | ||
| CV:pam | 4 | 0.481 | 0.752 | 0.855 | ||
| SD:kmeans | 3 | 0.382 | 0.817 | 0.814 | ||
| ATC:mclust | 2 | 0.377 | 0.685 | 0.872 | ||
| MAD:kmeans | 3 | 0.255 | 0.726 | 0.764 | ||
| CV:kmeans | 3 | 0.229 | 0.669 | 0.759 |
**: 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 0.974 0.989 0.4691 0.525 0.525
#> CV:NMF 2 0.852 0.931 0.971 0.4357 0.547 0.547
#> MAD:NMF 2 0.753 0.914 0.955 0.4989 0.497 0.497
#> ATC:NMF 2 0.813 0.914 0.962 0.4481 0.547 0.547
#> SD:skmeans 2 0.683 0.948 0.968 0.4942 0.508 0.508
#> CV:skmeans 2 0.925 0.947 0.978 0.4934 0.508 0.508
#> MAD:skmeans 2 1.000 0.992 0.996 0.5025 0.497 0.497
#> ATC:skmeans 2 1.000 1.000 1.000 0.5036 0.497 0.497
#> SD:mclust 2 0.625 0.888 0.943 0.4726 0.525 0.525
#> CV:mclust 2 0.632 0.909 0.941 0.4795 0.508 0.508
#> MAD:mclust 2 0.755 0.917 0.939 0.4337 0.525 0.525
#> ATC:mclust 2 0.377 0.685 0.872 0.4834 0.508 0.508
#> SD:kmeans 2 0.249 0.703 0.814 0.4376 0.525 0.525
#> CV:kmeans 2 0.620 0.849 0.912 0.2706 0.743 0.743
#> MAD:kmeans 2 0.201 0.630 0.761 0.4427 0.508 0.508
#> ATC:kmeans 2 0.925 0.925 0.973 0.4930 0.508 0.508
#> SD:pam 2 0.478 0.895 0.897 0.4250 0.575 0.575
#> CV:pam 2 0.665 0.904 0.947 0.2366 0.743 0.743
#> MAD:pam 2 0.922 0.922 0.968 0.4748 0.525 0.525
#> ATC:pam 2 0.673 0.879 0.944 0.4820 0.497 0.497
#> SD:hclust 2 1.000 0.972 0.980 0.4005 0.609 0.609
#> CV:hclust 2 1.000 1.000 1.000 0.0736 0.927 0.927
#> MAD:hclust 2 0.852 0.947 0.961 0.4819 0.497 0.497
#> ATC:hclust 2 0.602 0.703 0.891 0.4446 0.525 0.525
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.973 0.965 0.983 0.397 0.793 0.616
#> CV:NMF 3 1.000 0.957 0.981 0.507 0.726 0.528
#> MAD:NMF 3 0.807 0.878 0.949 0.314 0.709 0.487
#> ATC:NMF 3 0.592 0.781 0.884 0.469 0.732 0.529
#> SD:skmeans 3 0.958 0.917 0.963 0.349 0.768 0.567
#> CV:skmeans 3 0.771 0.890 0.932 0.344 0.765 0.566
#> MAD:skmeans 3 0.952 0.958 0.980 0.327 0.723 0.499
#> ATC:skmeans 3 0.759 0.870 0.934 0.322 0.760 0.547
#> SD:mclust 3 0.969 0.942 0.973 0.369 0.832 0.680
#> CV:mclust 3 0.514 0.747 0.829 0.284 0.832 0.670
#> MAD:mclust 3 0.759 0.901 0.890 0.478 0.832 0.680
#> ATC:mclust 3 0.659 0.800 0.868 0.327 0.712 0.489
#> SD:kmeans 3 0.382 0.817 0.814 0.382 0.760 0.565
#> CV:kmeans 3 0.229 0.669 0.759 0.711 0.860 0.817
#> MAD:kmeans 3 0.255 0.726 0.764 0.380 0.804 0.625
#> ATC:kmeans 3 0.477 0.700 0.796 0.301 0.804 0.625
#> SD:pam 3 0.719 0.831 0.885 0.441 0.782 0.621
#> CV:pam 3 0.746 0.866 0.948 0.334 0.992 0.989
#> MAD:pam 3 1.000 0.974 0.980 0.365 0.793 0.616
#> ATC:pam 3 0.944 0.940 0.973 0.296 0.709 0.507
#> SD:hclust 3 0.913 0.949 0.965 0.340 0.857 0.766
#> CV:hclust 3 1.000 0.972 0.988 2.076 0.866 0.855
#> MAD:hclust 3 0.882 0.932 0.970 0.162 0.925 0.848
#> ATC:hclust 3 0.517 0.487 0.712 0.342 0.883 0.776
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.853 0.824 0.812 0.1117 0.866 0.627
#> CV:NMF 4 0.799 0.744 0.823 0.0899 0.962 0.887
#> MAD:NMF 4 0.777 0.819 0.874 0.1051 0.944 0.840
#> ATC:NMF 4 0.573 0.636 0.797 0.1105 0.896 0.695
#> SD:skmeans 4 0.855 0.930 0.942 0.1337 0.877 0.647
#> CV:skmeans 4 0.698 0.820 0.838 0.1323 0.902 0.713
#> MAD:skmeans 4 0.801 0.812 0.881 0.1280 0.880 0.653
#> ATC:skmeans 4 0.753 0.677 0.791 0.0944 0.927 0.781
#> SD:mclust 4 0.827 0.796 0.894 0.1249 0.871 0.653
#> CV:mclust 4 0.671 0.821 0.893 0.1060 0.894 0.720
#> MAD:mclust 4 0.716 0.820 0.900 0.1241 0.925 0.789
#> ATC:mclust 4 0.449 0.449 0.647 0.1088 0.939 0.826
#> SD:kmeans 4 0.502 0.723 0.789 0.1504 0.983 0.951
#> CV:kmeans 4 0.275 0.470 0.653 0.3073 0.681 0.507
#> MAD:kmeans 4 0.496 0.727 0.770 0.1546 1.000 1.000
#> ATC:kmeans 4 0.496 0.602 0.699 0.1027 0.855 0.643
#> SD:pam 4 0.826 0.876 0.914 0.1369 0.966 0.906
#> CV:pam 4 0.481 0.752 0.855 0.4810 0.871 0.826
#> MAD:pam 4 0.824 0.739 0.888 0.1034 0.978 0.935
#> ATC:pam 4 0.890 0.896 0.948 0.0673 0.961 0.900
#> SD:hclust 4 0.964 0.970 0.977 0.3184 0.816 0.604
#> CV:hclust 4 0.665 0.661 0.886 0.7175 0.877 0.845
#> MAD:hclust 4 0.913 0.934 0.970 0.2629 0.860 0.668
#> ATC:hclust 4 0.638 0.650 0.857 0.1230 0.888 0.731
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.946 0.958 0.954 0.0833 0.964 0.850
#> CV:NMF 5 0.749 0.792 0.786 0.0919 0.867 0.575
#> MAD:NMF 5 0.895 0.881 0.919 0.0830 0.916 0.716
#> ATC:NMF 5 0.545 0.560 0.748 0.0591 0.808 0.439
#> SD:skmeans 5 0.879 0.903 0.929 0.0639 0.939 0.755
#> CV:skmeans 5 0.834 0.739 0.867 0.0755 0.927 0.717
#> MAD:skmeans 5 0.816 0.792 0.870 0.0708 0.941 0.763
#> ATC:skmeans 5 0.677 0.638 0.761 0.0596 0.925 0.740
#> SD:mclust 5 0.864 0.815 0.859 0.0450 0.941 0.794
#> CV:mclust 5 0.695 0.847 0.871 0.0647 0.925 0.763
#> MAD:mclust 5 0.641 0.617 0.749 0.0855 0.897 0.650
#> ATC:mclust 5 0.560 0.505 0.642 0.0936 0.883 0.661
#> SD:kmeans 5 0.647 0.490 0.722 0.0849 0.913 0.739
#> CV:kmeans 5 0.318 0.372 0.630 0.1283 0.762 0.427
#> MAD:kmeans 5 0.590 0.310 0.664 0.0766 0.927 0.786
#> ATC:kmeans 5 0.496 0.411 0.625 0.0723 0.983 0.949
#> SD:pam 5 0.798 0.832 0.880 0.0870 0.916 0.741
#> CV:pam 5 0.652 0.681 0.811 0.3212 0.776 0.638
#> MAD:pam 5 0.885 0.773 0.905 0.0883 0.925 0.767
#> ATC:pam 5 0.662 0.794 0.840 0.0723 0.972 0.920
#> SD:hclust 5 0.852 0.927 0.902 0.0583 0.966 0.881
#> CV:hclust 5 0.716 0.872 0.928 0.2971 0.776 0.672
#> MAD:hclust 5 0.882 0.861 0.900 0.0473 0.994 0.980
#> ATC:hclust 5 0.614 0.762 0.784 0.1119 0.857 0.588
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.916 0.848 0.902 0.0468 0.944 0.743
#> CV:NMF 6 0.893 0.750 0.854 0.0575 0.952 0.766
#> MAD:NMF 6 0.851 0.791 0.854 0.0494 0.950 0.780
#> ATC:NMF 6 0.656 0.576 0.750 0.0521 0.881 0.556
#> SD:skmeans 6 0.867 0.840 0.868 0.0352 1.000 1.000
#> CV:skmeans 6 0.795 0.671 0.804 0.0361 0.947 0.752
#> MAD:skmeans 6 0.819 0.733 0.817 0.0376 0.952 0.766
#> ATC:skmeans 6 0.719 0.643 0.744 0.0390 0.939 0.758
#> SD:mclust 6 0.807 0.735 0.809 0.0513 0.966 0.871
#> CV:mclust 6 0.695 0.804 0.805 0.0668 0.978 0.910
#> MAD:mclust 6 0.743 0.688 0.799 0.0526 0.922 0.657
#> ATC:mclust 6 0.704 0.640 0.753 0.0394 0.939 0.768
#> SD:kmeans 6 0.665 0.692 0.734 0.0550 0.894 0.627
#> CV:kmeans 6 0.385 0.580 0.662 0.0869 0.916 0.702
#> MAD:kmeans 6 0.635 0.563 0.673 0.0513 0.869 0.556
#> ATC:kmeans 6 0.514 0.317 0.576 0.0453 0.936 0.794
#> SD:pam 6 0.861 0.845 0.919 0.0457 0.958 0.827
#> CV:pam 6 0.600 0.513 0.729 0.0744 0.734 0.434
#> MAD:pam 6 0.879 0.878 0.908 0.0207 0.947 0.791
#> ATC:pam 6 0.733 0.667 0.851 0.0997 0.888 0.654
#> SD:hclust 6 0.832 0.908 0.888 0.0192 0.994 0.977
#> CV:hclust 6 0.925 0.865 0.927 0.0683 0.997 0.994
#> MAD:hclust 6 0.946 0.940 0.967 0.0460 0.944 0.797
#> ATC:hclust 6 0.673 0.648 0.784 0.0791 0.950 0.788
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 = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 1.000 0.972 0.980 0.4005 0.609 0.609
#> 3 3 0.913 0.949 0.965 0.3402 0.857 0.766
#> 4 4 0.964 0.970 0.977 0.3184 0.816 0.604
#> 5 5 0.852 0.927 0.902 0.0583 0.966 0.881
#> 6 6 0.832 0.908 0.888 0.0192 0.994 0.977
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 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
#> SRR1617430 2 0.0938 0.991 0.012 0.988
#> SRR1617431 2 0.0938 0.991 0.012 0.988
#> SRR1617410 1 0.0938 0.979 0.988 0.012
#> SRR1617411 1 0.0938 0.979 0.988 0.012
#> SRR1617412 1 0.0938 0.974 0.988 0.012
#> SRR1617413 1 0.0938 0.974 0.988 0.012
#> SRR1617414 1 0.0938 0.979 0.988 0.012
#> SRR1617415 1 0.0938 0.979 0.988 0.012
#> SRR1617416 1 0.0938 0.974 0.988 0.012
#> SRR1617417 1 0.0938 0.974 0.988 0.012
#> SRR1617418 1 0.0938 0.974 0.988 0.012
#> SRR1617419 1 0.0938 0.974 0.988 0.012
#> SRR1617420 1 0.0938 0.979 0.988 0.012
#> SRR1617421 1 0.0938 0.979 0.988 0.012
#> SRR1617422 1 0.0938 0.979 0.988 0.012
#> SRR1617423 1 0.0938 0.979 0.988 0.012
#> SRR1617424 1 0.0938 0.979 0.988 0.012
#> SRR1617425 1 0.0938 0.979 0.988 0.012
#> SRR1617427 1 0.0938 0.979 0.988 0.012
#> SRR1617426 1 0.0938 0.979 0.988 0.012
#> SRR1617428 1 0.0376 0.975 0.996 0.004
#> SRR1617429 1 0.0376 0.975 0.996 0.004
#> SRR1617432 1 0.0938 0.979 0.988 0.012
#> SRR1617433 1 0.0938 0.979 0.988 0.012
#> SRR1617434 1 0.0938 0.979 0.988 0.012
#> SRR1617436 1 0.0938 0.974 0.988 0.012
#> SRR1617435 1 0.0938 0.979 0.988 0.012
#> SRR1617437 1 0.0938 0.974 0.988 0.012
#> SRR1617438 1 0.0938 0.974 0.988 0.012
#> SRR1617439 1 0.0938 0.974 0.988 0.012
#> SRR1617440 1 0.3274 0.940 0.940 0.060
#> SRR1617441 1 0.3274 0.940 0.940 0.060
#> SRR1617443 1 0.0938 0.974 0.988 0.012
#> SRR1617442 1 0.0938 0.974 0.988 0.012
#> SRR1617444 1 0.1184 0.977 0.984 0.016
#> SRR1617445 1 0.1184 0.977 0.984 0.016
#> SRR1617446 1 0.0938 0.979 0.988 0.012
#> SRR1617447 1 0.0938 0.979 0.988 0.012
#> SRR1617448 1 0.0938 0.979 0.988 0.012
#> SRR1617449 1 0.0938 0.979 0.988 0.012
#> SRR1617451 2 0.0938 0.991 0.012 0.988
#> SRR1617450 2 0.0938 0.991 0.012 0.988
#> SRR1617452 1 0.7139 0.773 0.804 0.196
#> SRR1617454 2 0.0938 0.991 0.012 0.988
#> SRR1617453 1 0.7139 0.773 0.804 0.196
#> SRR1617456 2 0.0376 0.991 0.004 0.996
#> SRR1617457 2 0.0376 0.991 0.004 0.996
#> SRR1617455 2 0.0938 0.991 0.012 0.988
#> SRR1617458 2 0.0376 0.991 0.004 0.996
#> SRR1617459 2 0.0376 0.991 0.004 0.996
#> SRR1617460 2 0.1184 0.990 0.016 0.984
#> SRR1617461 2 0.1184 0.990 0.016 0.984
#> SRR1617463 2 0.1184 0.990 0.016 0.984
#> SRR1617462 2 0.1184 0.990 0.016 0.984
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.1031 0.980 0.024 0.976 0.000
#> SRR1617431 2 0.1031 0.980 0.024 0.976 0.000
#> SRR1617410 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617411 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617412 1 0.2448 0.942 0.924 0.000 0.076
#> SRR1617413 1 0.2448 0.942 0.924 0.000 0.076
#> SRR1617414 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617415 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617416 3 0.3619 0.836 0.136 0.000 0.864
#> SRR1617417 3 0.3619 0.836 0.136 0.000 0.864
#> SRR1617418 1 0.2448 0.942 0.924 0.000 0.076
#> SRR1617419 1 0.2448 0.942 0.924 0.000 0.076
#> SRR1617420 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617421 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617422 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617423 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617424 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617425 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617427 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617426 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617428 3 0.0829 0.860 0.012 0.004 0.984
#> SRR1617429 3 0.0829 0.860 0.012 0.004 0.984
#> SRR1617432 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617433 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617434 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617436 1 0.2448 0.942 0.924 0.000 0.076
#> SRR1617435 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617437 1 0.2448 0.942 0.924 0.000 0.076
#> SRR1617438 1 0.2448 0.942 0.924 0.000 0.076
#> SRR1617439 1 0.2448 0.942 0.924 0.000 0.076
#> SRR1617440 1 0.4165 0.903 0.876 0.048 0.076
#> SRR1617441 1 0.4165 0.903 0.876 0.048 0.076
#> SRR1617443 1 0.2448 0.942 0.924 0.000 0.076
#> SRR1617442 1 0.2448 0.942 0.924 0.000 0.076
#> SRR1617444 1 0.0237 0.967 0.996 0.004 0.000
#> SRR1617445 1 0.0237 0.967 0.996 0.004 0.000
#> SRR1617446 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617447 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617448 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617449 1 0.0000 0.969 1.000 0.000 0.000
#> SRR1617451 2 0.1031 0.980 0.024 0.976 0.000
#> SRR1617450 2 0.1031 0.980 0.024 0.976 0.000
#> SRR1617452 3 0.4346 0.793 0.000 0.184 0.816
#> SRR1617454 2 0.1031 0.980 0.024 0.976 0.000
#> SRR1617453 3 0.4346 0.793 0.000 0.184 0.816
#> SRR1617456 2 0.0237 0.979 0.004 0.996 0.000
#> SRR1617457 2 0.0237 0.979 0.004 0.996 0.000
#> SRR1617455 2 0.1031 0.980 0.024 0.976 0.000
#> SRR1617458 2 0.0237 0.979 0.004 0.996 0.000
#> SRR1617459 2 0.0237 0.979 0.004 0.996 0.000
#> SRR1617460 2 0.0747 0.981 0.016 0.984 0.000
#> SRR1617461 2 0.0747 0.981 0.016 0.984 0.000
#> SRR1617463 2 0.0747 0.981 0.016 0.984 0.000
#> SRR1617462 2 0.0747 0.981 0.016 0.984 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.1406 0.973 0.024 0.960 0.016 0.000
#> SRR1617431 2 0.1406 0.973 0.024 0.960 0.016 0.000
#> SRR1617410 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617411 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617412 3 0.0592 0.989 0.016 0.000 0.984 0.000
#> SRR1617413 3 0.0592 0.989 0.016 0.000 0.984 0.000
#> SRR1617414 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617415 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617416 4 0.2868 0.836 0.136 0.000 0.000 0.864
#> SRR1617417 4 0.2868 0.836 0.136 0.000 0.000 0.864
#> SRR1617418 3 0.0592 0.989 0.016 0.000 0.984 0.000
#> SRR1617419 3 0.0592 0.989 0.016 0.000 0.984 0.000
#> SRR1617420 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617421 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617422 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617423 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617424 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617425 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617427 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617426 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617428 4 0.0657 0.858 0.012 0.000 0.004 0.984
#> SRR1617429 4 0.0657 0.858 0.012 0.000 0.004 0.984
#> SRR1617432 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617433 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617434 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617436 3 0.0592 0.989 0.016 0.000 0.984 0.000
#> SRR1617435 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617437 3 0.0592 0.989 0.016 0.000 0.984 0.000
#> SRR1617438 3 0.0592 0.989 0.016 0.000 0.984 0.000
#> SRR1617439 3 0.0592 0.989 0.016 0.000 0.984 0.000
#> SRR1617440 3 0.1975 0.944 0.016 0.048 0.936 0.000
#> SRR1617441 3 0.1975 0.944 0.016 0.048 0.936 0.000
#> SRR1617443 3 0.0592 0.989 0.016 0.000 0.984 0.000
#> SRR1617442 3 0.0592 0.989 0.016 0.000 0.984 0.000
#> SRR1617444 1 0.0376 0.991 0.992 0.004 0.004 0.000
#> SRR1617445 1 0.0376 0.991 0.992 0.004 0.004 0.000
#> SRR1617446 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617447 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617448 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617449 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> SRR1617451 2 0.1406 0.973 0.024 0.960 0.016 0.000
#> SRR1617450 2 0.1406 0.973 0.024 0.960 0.016 0.000
#> SRR1617452 4 0.3444 0.799 0.000 0.184 0.000 0.816
#> SRR1617454 2 0.1406 0.973 0.024 0.960 0.016 0.000
#> SRR1617453 4 0.3444 0.799 0.000 0.184 0.000 0.816
#> SRR1617456 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR1617457 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR1617455 2 0.1406 0.973 0.024 0.960 0.016 0.000
#> SRR1617458 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR1617459 2 0.0000 0.974 0.000 1.000 0.000 0.000
#> SRR1617460 2 0.0469 0.976 0.012 0.988 0.000 0.000
#> SRR1617461 2 0.0469 0.976 0.012 0.988 0.000 0.000
#> SRR1617463 2 0.0469 0.976 0.012 0.988 0.000 0.000
#> SRR1617462 2 0.0469 0.976 0.012 0.988 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 5 0.3983 1.000 0.000 0.340 0.000 0.000 0.660
#> SRR1617431 5 0.3983 1.000 0.000 0.340 0.000 0.000 0.660
#> SRR1617410 1 0.2471 0.919 0.864 0.000 0.000 0.000 0.136
#> SRR1617411 1 0.2471 0.919 0.864 0.000 0.000 0.000 0.136
#> SRR1617412 3 0.0963 0.974 0.000 0.000 0.964 0.000 0.036
#> SRR1617413 3 0.0963 0.974 0.000 0.000 0.964 0.000 0.036
#> SRR1617414 1 0.2471 0.919 0.864 0.000 0.000 0.000 0.136
#> SRR1617415 1 0.2471 0.919 0.864 0.000 0.000 0.000 0.136
#> SRR1617416 4 0.2753 0.794 0.136 0.000 0.000 0.856 0.008
#> SRR1617417 4 0.2753 0.794 0.136 0.000 0.000 0.856 0.008
#> SRR1617418 3 0.0290 0.982 0.000 0.000 0.992 0.000 0.008
#> SRR1617419 3 0.0290 0.982 0.000 0.000 0.992 0.000 0.008
#> SRR1617420 1 0.2471 0.919 0.864 0.000 0.000 0.000 0.136
#> SRR1617421 1 0.2471 0.919 0.864 0.000 0.000 0.000 0.136
#> SRR1617422 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000
#> SRR1617423 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000
#> SRR1617424 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000
#> SRR1617425 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000
#> SRR1617427 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000
#> SRR1617426 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000
#> SRR1617428 4 0.2891 0.786 0.000 0.000 0.000 0.824 0.176
#> SRR1617429 4 0.2891 0.786 0.000 0.000 0.000 0.824 0.176
#> SRR1617432 1 0.2471 0.919 0.864 0.000 0.000 0.000 0.136
#> SRR1617433 1 0.2471 0.919 0.864 0.000 0.000 0.000 0.136
#> SRR1617434 1 0.2471 0.919 0.864 0.000 0.000 0.000 0.136
#> SRR1617436 3 0.0609 0.980 0.000 0.000 0.980 0.000 0.020
#> SRR1617435 1 0.2471 0.919 0.864 0.000 0.000 0.000 0.136
#> SRR1617437 3 0.0609 0.980 0.000 0.000 0.980 0.000 0.020
#> SRR1617438 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
#> SRR1617439 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
#> SRR1617440 3 0.1331 0.955 0.000 0.040 0.952 0.000 0.008
#> SRR1617441 3 0.1331 0.955 0.000 0.040 0.952 0.000 0.008
#> SRR1617443 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
#> SRR1617442 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
#> SRR1617444 1 0.0324 0.927 0.992 0.000 0.004 0.000 0.004
#> SRR1617445 1 0.0324 0.927 0.992 0.000 0.004 0.000 0.004
#> SRR1617446 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000
#> SRR1617447 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000
#> SRR1617448 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000
#> SRR1617449 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000
#> SRR1617451 5 0.3983 1.000 0.000 0.340 0.000 0.000 0.660
#> SRR1617450 5 0.3983 1.000 0.000 0.340 0.000 0.000 0.660
#> SRR1617452 4 0.2966 0.745 0.000 0.184 0.000 0.816 0.000
#> SRR1617454 5 0.3983 1.000 0.000 0.340 0.000 0.000 0.660
#> SRR1617453 4 0.2966 0.745 0.000 0.184 0.000 0.816 0.000
#> SRR1617456 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> SRR1617457 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> SRR1617455 5 0.3983 1.000 0.000 0.340 0.000 0.000 0.660
#> SRR1617458 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> SRR1617459 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> SRR1617460 2 0.2069 0.915 0.012 0.912 0.000 0.000 0.076
#> SRR1617461 2 0.2069 0.915 0.012 0.912 0.000 0.000 0.076
#> SRR1617463 2 0.2069 0.915 0.012 0.912 0.000 0.000 0.076
#> SRR1617462 2 0.2069 0.915 0.012 0.912 0.000 0.000 0.076
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.1814 1.000 0.000 0.900 0.000 0.000 0.000 0.100
#> SRR1617431 2 0.1814 1.000 0.000 0.900 0.000 0.000 0.000 0.100
#> SRR1617410 1 0.2536 0.917 0.864 0.020 0.000 0.000 0.116 0.000
#> SRR1617411 1 0.2536 0.917 0.864 0.020 0.000 0.000 0.116 0.000
#> SRR1617412 3 0.2474 0.919 0.000 0.080 0.884 0.032 0.004 0.000
#> SRR1617413 3 0.2474 0.919 0.000 0.080 0.884 0.032 0.004 0.000
#> SRR1617414 1 0.2536 0.917 0.864 0.020 0.000 0.000 0.116 0.000
#> SRR1617415 1 0.2536 0.917 0.864 0.020 0.000 0.000 0.116 0.000
#> SRR1617416 5 0.2473 0.795 0.136 0.000 0.000 0.008 0.856 0.000
#> SRR1617417 5 0.2473 0.795 0.136 0.000 0.000 0.008 0.856 0.000
#> SRR1617418 3 0.0260 0.958 0.000 0.008 0.992 0.000 0.000 0.000
#> SRR1617419 3 0.0260 0.958 0.000 0.008 0.992 0.000 0.000 0.000
#> SRR1617420 1 0.2536 0.917 0.864 0.020 0.000 0.000 0.116 0.000
#> SRR1617421 1 0.2536 0.917 0.864 0.020 0.000 0.000 0.116 0.000
#> SRR1617422 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617423 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617424 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617425 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617427 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617426 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617428 4 0.0790 1.000 0.000 0.000 0.000 0.968 0.032 0.000
#> SRR1617429 4 0.0790 1.000 0.000 0.000 0.000 0.968 0.032 0.000
#> SRR1617432 1 0.2536 0.917 0.864 0.020 0.000 0.000 0.116 0.000
#> SRR1617433 1 0.2536 0.917 0.864 0.020 0.000 0.000 0.116 0.000
#> SRR1617434 1 0.2536 0.917 0.864 0.020 0.000 0.000 0.116 0.000
#> SRR1617436 3 0.1826 0.940 0.000 0.052 0.924 0.020 0.004 0.000
#> SRR1617435 1 0.2536 0.917 0.864 0.020 0.000 0.000 0.116 0.000
#> SRR1617437 3 0.1826 0.940 0.000 0.052 0.924 0.020 0.004 0.000
#> SRR1617438 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617439 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617440 3 0.1196 0.934 0.000 0.008 0.952 0.000 0.000 0.040
#> SRR1617441 3 0.1196 0.934 0.000 0.008 0.952 0.000 0.000 0.040
#> SRR1617443 3 0.0260 0.959 0.000 0.008 0.992 0.000 0.000 0.000
#> SRR1617442 3 0.0260 0.959 0.000 0.008 0.992 0.000 0.000 0.000
#> SRR1617444 1 0.0291 0.925 0.992 0.004 0.004 0.000 0.000 0.000
#> SRR1617445 1 0.0291 0.925 0.992 0.004 0.004 0.000 0.000 0.000
#> SRR1617446 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617447 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617448 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617449 1 0.0000 0.929 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617451 2 0.1814 1.000 0.000 0.900 0.000 0.000 0.000 0.100
#> SRR1617450 2 0.1814 1.000 0.000 0.900 0.000 0.000 0.000 0.100
#> SRR1617452 5 0.3364 0.792 0.000 0.036 0.000 0.012 0.820 0.132
#> SRR1617454 2 0.1814 1.000 0.000 0.900 0.000 0.000 0.000 0.100
#> SRR1617453 5 0.3364 0.792 0.000 0.036 0.000 0.012 0.820 0.132
#> SRR1617456 6 0.0000 0.798 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617457 6 0.0000 0.798 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617455 2 0.1814 1.000 0.000 0.900 0.000 0.000 0.000 0.100
#> SRR1617458 6 0.0000 0.798 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617459 6 0.0000 0.798 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617460 6 0.3541 0.757 0.012 0.260 0.000 0.000 0.000 0.728
#> SRR1617461 6 0.3541 0.757 0.012 0.260 0.000 0.000 0.000 0.728
#> SRR1617463 6 0.3541 0.757 0.012 0.260 0.000 0.000 0.000 0.728
#> SRR1617462 6 0.3541 0.757 0.012 0.260 0.000 0.000 0.000 0.728
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", "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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 0.249 0.703 0.814 0.4376 0.525 0.525
#> 3 3 0.382 0.817 0.814 0.3824 0.760 0.565
#> 4 4 0.502 0.723 0.789 0.1504 0.983 0.951
#> 5 5 0.647 0.490 0.722 0.0849 0.913 0.739
#> 6 6 0.665 0.692 0.734 0.0550 0.894 0.627
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
#> SRR1617430 2 0.7950 0.821 0.240 0.760
#> SRR1617431 2 0.7950 0.821 0.240 0.760
#> SRR1617410 1 0.0000 0.806 1.000 0.000
#> SRR1617411 1 0.0000 0.806 1.000 0.000
#> SRR1617412 1 0.9608 0.545 0.616 0.384
#> SRR1617413 1 0.9608 0.545 0.616 0.384
#> SRR1617414 1 0.1184 0.797 0.984 0.016
#> SRR1617415 1 0.1184 0.797 0.984 0.016
#> SRR1617416 1 0.4022 0.762 0.920 0.080
#> SRR1617417 1 0.4022 0.762 0.920 0.080
#> SRR1617418 1 0.9775 0.510 0.588 0.412
#> SRR1617419 1 0.9775 0.510 0.588 0.412
#> SRR1617420 1 0.1184 0.804 0.984 0.016
#> SRR1617421 1 0.1184 0.804 0.984 0.016
#> SRR1617422 1 0.1184 0.797 0.984 0.016
#> SRR1617423 1 0.1184 0.797 0.984 0.016
#> SRR1617424 1 0.0376 0.806 0.996 0.004
#> SRR1617425 1 0.0376 0.806 0.996 0.004
#> SRR1617427 1 0.0672 0.806 0.992 0.008
#> SRR1617426 1 0.0672 0.806 0.992 0.008
#> SRR1617428 2 0.9977 0.144 0.472 0.528
#> SRR1617429 2 0.9977 0.144 0.472 0.528
#> SRR1617432 1 0.0000 0.806 1.000 0.000
#> SRR1617433 1 0.0000 0.806 1.000 0.000
#> SRR1617434 1 0.0938 0.804 0.988 0.012
#> SRR1617436 1 0.9775 0.510 0.588 0.412
#> SRR1617435 1 0.0938 0.804 0.988 0.012
#> SRR1617437 1 0.9775 0.510 0.588 0.412
#> SRR1617438 1 0.9775 0.510 0.588 0.412
#> SRR1617439 1 0.9775 0.510 0.588 0.412
#> SRR1617440 2 0.8386 0.470 0.268 0.732
#> SRR1617441 2 0.8386 0.470 0.268 0.732
#> SRR1617443 1 0.9608 0.545 0.616 0.384
#> SRR1617442 1 0.9608 0.545 0.616 0.384
#> SRR1617444 1 0.5629 0.690 0.868 0.132
#> SRR1617445 1 0.5629 0.690 0.868 0.132
#> SRR1617446 1 0.0376 0.806 0.996 0.004
#> SRR1617447 1 0.0376 0.806 0.996 0.004
#> SRR1617448 1 0.0376 0.806 0.996 0.004
#> SRR1617449 1 0.0376 0.806 0.996 0.004
#> SRR1617451 2 0.7950 0.821 0.240 0.760
#> SRR1617450 2 0.7950 0.821 0.240 0.760
#> SRR1617452 2 0.8144 0.712 0.252 0.748
#> SRR1617454 2 0.7950 0.821 0.240 0.760
#> SRR1617453 2 0.8144 0.712 0.252 0.748
#> SRR1617456 2 0.7674 0.818 0.224 0.776
#> SRR1617457 2 0.7674 0.818 0.224 0.776
#> SRR1617455 2 0.7950 0.821 0.240 0.760
#> SRR1617458 2 0.7674 0.818 0.224 0.776
#> SRR1617459 2 0.7674 0.818 0.224 0.776
#> SRR1617460 2 0.9427 0.724 0.360 0.640
#> SRR1617461 2 0.9427 0.724 0.360 0.640
#> SRR1617463 2 0.9460 0.720 0.364 0.636
#> SRR1617462 2 0.9460 0.720 0.364 0.636
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.441 0.888 0.104 0.860 0.036
#> SRR1617431 2 0.441 0.888 0.104 0.860 0.036
#> SRR1617410 1 0.164 0.885 0.956 0.000 0.044
#> SRR1617411 1 0.164 0.885 0.956 0.000 0.044
#> SRR1617412 3 0.753 0.827 0.252 0.084 0.664
#> SRR1617413 3 0.753 0.827 0.252 0.084 0.664
#> SRR1617414 1 0.165 0.887 0.960 0.004 0.036
#> SRR1617415 1 0.165 0.887 0.960 0.004 0.036
#> SRR1617416 1 0.666 0.650 0.704 0.044 0.252
#> SRR1617417 1 0.666 0.650 0.704 0.044 0.252
#> SRR1617418 3 0.753 0.840 0.228 0.096 0.676
#> SRR1617419 3 0.753 0.840 0.228 0.096 0.676
#> SRR1617420 1 0.186 0.886 0.948 0.000 0.052
#> SRR1617421 1 0.186 0.886 0.948 0.000 0.052
#> SRR1617422 1 0.331 0.887 0.908 0.028 0.064
#> SRR1617423 1 0.331 0.887 0.908 0.028 0.064
#> SRR1617424 1 0.270 0.890 0.928 0.016 0.056
#> SRR1617425 1 0.270 0.890 0.928 0.016 0.056
#> SRR1617427 1 0.265 0.890 0.928 0.012 0.060
#> SRR1617426 1 0.265 0.890 0.928 0.012 0.060
#> SRR1617428 3 0.944 0.249 0.240 0.256 0.504
#> SRR1617429 3 0.944 0.249 0.240 0.256 0.504
#> SRR1617432 1 0.164 0.886 0.956 0.000 0.044
#> SRR1617433 1 0.164 0.886 0.956 0.000 0.044
#> SRR1617434 1 0.199 0.884 0.948 0.004 0.048
#> SRR1617436 3 0.718 0.838 0.240 0.072 0.688
#> SRR1617435 1 0.199 0.884 0.948 0.004 0.048
#> SRR1617437 3 0.718 0.838 0.240 0.072 0.688
#> SRR1617438 3 0.711 0.840 0.224 0.076 0.700
#> SRR1617439 3 0.711 0.840 0.224 0.076 0.700
#> SRR1617440 3 0.741 0.679 0.092 0.224 0.684
#> SRR1617441 3 0.741 0.679 0.092 0.224 0.684
#> SRR1617443 3 0.704 0.832 0.252 0.060 0.688
#> SRR1617442 3 0.704 0.832 0.252 0.060 0.688
#> SRR1617444 1 0.602 0.761 0.784 0.076 0.140
#> SRR1617445 1 0.602 0.761 0.784 0.076 0.140
#> SRR1617446 1 0.318 0.887 0.908 0.016 0.076
#> SRR1617447 1 0.318 0.887 0.908 0.016 0.076
#> SRR1617448 1 0.309 0.888 0.912 0.016 0.072
#> SRR1617449 1 0.309 0.888 0.912 0.016 0.072
#> SRR1617451 2 0.354 0.893 0.100 0.888 0.012
#> SRR1617450 2 0.354 0.893 0.100 0.888 0.012
#> SRR1617452 2 0.816 0.501 0.084 0.568 0.348
#> SRR1617454 2 0.338 0.894 0.100 0.892 0.008
#> SRR1617453 2 0.816 0.501 0.084 0.568 0.348
#> SRR1617456 2 0.473 0.884 0.088 0.852 0.060
#> SRR1617457 2 0.473 0.884 0.088 0.852 0.060
#> SRR1617455 2 0.338 0.894 0.100 0.892 0.008
#> SRR1617458 2 0.482 0.883 0.088 0.848 0.064
#> SRR1617459 2 0.482 0.883 0.088 0.848 0.064
#> SRR1617460 2 0.641 0.841 0.144 0.764 0.092
#> SRR1617461 2 0.641 0.841 0.144 0.764 0.092
#> SRR1617463 2 0.489 0.878 0.124 0.836 0.040
#> SRR1617462 2 0.489 0.878 0.124 0.836 0.040
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.463 0.7662 0.040 0.828 0.056 0.076
#> SRR1617431 2 0.463 0.7662 0.040 0.828 0.056 0.076
#> SRR1617410 1 0.507 0.7081 0.740 0.000 0.052 0.208
#> SRR1617411 1 0.507 0.7081 0.740 0.000 0.052 0.208
#> SRR1617412 3 0.483 0.8480 0.100 0.020 0.808 0.072
#> SRR1617413 3 0.483 0.8480 0.100 0.020 0.808 0.072
#> SRR1617414 1 0.545 0.6879 0.700 0.000 0.056 0.244
#> SRR1617415 1 0.545 0.6879 0.700 0.000 0.056 0.244
#> SRR1617416 1 0.702 0.1940 0.556 0.016 0.088 0.340
#> SRR1617417 1 0.702 0.1940 0.556 0.016 0.088 0.340
#> SRR1617418 3 0.355 0.8879 0.096 0.016 0.868 0.020
#> SRR1617419 3 0.355 0.8879 0.096 0.016 0.868 0.020
#> SRR1617420 1 0.522 0.7063 0.728 0.000 0.056 0.216
#> SRR1617421 1 0.522 0.7063 0.728 0.000 0.056 0.216
#> SRR1617422 1 0.244 0.7319 0.916 0.012 0.068 0.004
#> SRR1617423 1 0.244 0.7319 0.916 0.012 0.068 0.004
#> SRR1617424 1 0.182 0.7358 0.936 0.004 0.060 0.000
#> SRR1617425 1 0.182 0.7358 0.936 0.004 0.060 0.000
#> SRR1617427 1 0.247 0.7363 0.916 0.000 0.056 0.028
#> SRR1617426 1 0.247 0.7363 0.916 0.000 0.056 0.028
#> SRR1617428 4 0.910 1.0000 0.168 0.116 0.268 0.448
#> SRR1617429 4 0.910 1.0000 0.168 0.116 0.268 0.448
#> SRR1617432 1 0.526 0.6901 0.700 0.000 0.040 0.260
#> SRR1617433 1 0.526 0.6901 0.700 0.000 0.040 0.260
#> SRR1617434 1 0.529 0.7006 0.720 0.000 0.056 0.224
#> SRR1617436 3 0.297 0.8927 0.096 0.000 0.884 0.020
#> SRR1617435 1 0.529 0.7006 0.720 0.000 0.056 0.224
#> SRR1617437 3 0.297 0.8927 0.096 0.000 0.884 0.020
#> SRR1617438 3 0.297 0.8925 0.096 0.000 0.884 0.020
#> SRR1617439 3 0.297 0.8925 0.096 0.000 0.884 0.020
#> SRR1617440 3 0.582 0.6661 0.056 0.108 0.760 0.076
#> SRR1617441 3 0.582 0.6661 0.056 0.108 0.760 0.076
#> SRR1617443 3 0.298 0.8922 0.092 0.004 0.888 0.016
#> SRR1617442 3 0.298 0.8922 0.092 0.004 0.888 0.016
#> SRR1617444 1 0.508 0.6230 0.804 0.048 0.088 0.060
#> SRR1617445 1 0.508 0.6230 0.804 0.048 0.088 0.060
#> SRR1617446 1 0.280 0.7250 0.900 0.008 0.080 0.012
#> SRR1617447 1 0.280 0.7250 0.900 0.008 0.080 0.012
#> SRR1617448 1 0.280 0.7250 0.900 0.008 0.080 0.012
#> SRR1617449 1 0.280 0.7250 0.900 0.008 0.080 0.012
#> SRR1617451 2 0.376 0.7813 0.032 0.872 0.048 0.048
#> SRR1617450 2 0.376 0.7813 0.032 0.872 0.048 0.048
#> SRR1617452 2 0.776 0.0868 0.032 0.432 0.108 0.428
#> SRR1617454 2 0.231 0.7939 0.032 0.932 0.016 0.020
#> SRR1617453 2 0.776 0.0868 0.032 0.432 0.108 0.428
#> SRR1617456 2 0.505 0.7735 0.028 0.788 0.044 0.140
#> SRR1617457 2 0.505 0.7735 0.028 0.788 0.044 0.140
#> SRR1617455 2 0.231 0.7939 0.032 0.932 0.016 0.020
#> SRR1617458 2 0.521 0.7712 0.028 0.772 0.040 0.160
#> SRR1617459 2 0.521 0.7712 0.028 0.772 0.040 0.160
#> SRR1617460 2 0.533 0.7439 0.076 0.756 0.008 0.160
#> SRR1617461 2 0.533 0.7439 0.076 0.756 0.008 0.160
#> SRR1617463 2 0.347 0.7727 0.072 0.868 0.000 0.060
#> SRR1617462 2 0.347 0.7727 0.072 0.868 0.000 0.060
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 2 0.4148 0.731 0.008 0.816 0.016 0.056 0.104
#> SRR1617431 2 0.4148 0.731 0.008 0.816 0.016 0.056 0.104
#> SRR1617410 1 0.1721 0.489 0.944 0.000 0.020 0.020 0.016
#> SRR1617411 1 0.1721 0.489 0.944 0.000 0.020 0.020 0.016
#> SRR1617412 3 0.4368 0.836 0.032 0.000 0.796 0.056 0.116
#> SRR1617413 3 0.4368 0.836 0.032 0.000 0.796 0.056 0.116
#> SRR1617414 1 0.2647 0.463 0.892 0.000 0.008 0.024 0.076
#> SRR1617415 1 0.2647 0.463 0.892 0.000 0.008 0.024 0.076
#> SRR1617416 4 0.7749 0.148 0.308 0.004 0.056 0.408 0.224
#> SRR1617417 4 0.7749 0.148 0.308 0.004 0.056 0.408 0.224
#> SRR1617418 3 0.3161 0.874 0.016 0.008 0.880 0.048 0.048
#> SRR1617419 3 0.3161 0.874 0.016 0.008 0.880 0.048 0.048
#> SRR1617420 1 0.1597 0.490 0.948 0.000 0.024 0.008 0.020
#> SRR1617421 1 0.1597 0.490 0.948 0.000 0.024 0.008 0.020
#> SRR1617422 1 0.5869 -0.309 0.512 0.008 0.048 0.012 0.420
#> SRR1617423 1 0.5869 -0.309 0.512 0.008 0.048 0.012 0.420
#> SRR1617424 1 0.5590 -0.199 0.540 0.000 0.056 0.008 0.396
#> SRR1617425 1 0.5590 -0.199 0.540 0.000 0.056 0.008 0.396
#> SRR1617427 1 0.5612 -0.209 0.520 0.000 0.048 0.012 0.420
#> SRR1617426 1 0.5612 -0.209 0.520 0.000 0.048 0.012 0.420
#> SRR1617428 4 0.8659 0.543 0.104 0.060 0.140 0.432 0.264
#> SRR1617429 4 0.8659 0.543 0.104 0.060 0.140 0.432 0.264
#> SRR1617432 1 0.2036 0.474 0.928 0.000 0.008 0.028 0.036
#> SRR1617433 1 0.2036 0.474 0.928 0.000 0.008 0.028 0.036
#> SRR1617434 1 0.0898 0.492 0.972 0.000 0.020 0.008 0.000
#> SRR1617436 3 0.3104 0.859 0.016 0.004 0.880 0.044 0.056
#> SRR1617435 1 0.0898 0.492 0.972 0.000 0.020 0.008 0.000
#> SRR1617437 3 0.3104 0.859 0.016 0.004 0.880 0.044 0.056
#> SRR1617438 3 0.1419 0.883 0.016 0.000 0.956 0.012 0.016
#> SRR1617439 3 0.1419 0.883 0.016 0.000 0.956 0.012 0.016
#> SRR1617440 3 0.4795 0.780 0.008 0.056 0.788 0.084 0.064
#> SRR1617441 3 0.4795 0.780 0.008 0.056 0.788 0.084 0.064
#> SRR1617443 3 0.2002 0.883 0.028 0.000 0.932 0.020 0.020
#> SRR1617442 3 0.2002 0.883 0.028 0.000 0.932 0.020 0.020
#> SRR1617444 5 0.7419 1.000 0.360 0.020 0.100 0.056 0.464
#> SRR1617445 5 0.7419 1.000 0.360 0.020 0.100 0.056 0.464
#> SRR1617446 1 0.6062 -0.312 0.508 0.000 0.064 0.024 0.404
#> SRR1617447 1 0.6062 -0.312 0.508 0.000 0.064 0.024 0.404
#> SRR1617448 1 0.6091 -0.423 0.480 0.000 0.064 0.024 0.432
#> SRR1617449 1 0.6091 -0.423 0.480 0.000 0.064 0.024 0.432
#> SRR1617451 2 0.2788 0.776 0.004 0.892 0.008 0.032 0.064
#> SRR1617450 2 0.2788 0.776 0.004 0.892 0.008 0.032 0.064
#> SRR1617452 4 0.6995 0.327 0.028 0.252 0.096 0.580 0.044
#> SRR1617454 2 0.1130 0.789 0.004 0.968 0.004 0.012 0.012
#> SRR1617453 4 0.6995 0.327 0.028 0.252 0.096 0.580 0.044
#> SRR1617456 2 0.5128 0.723 0.004 0.716 0.016 0.200 0.064
#> SRR1617457 2 0.5128 0.723 0.004 0.716 0.016 0.200 0.064
#> SRR1617455 2 0.1130 0.789 0.004 0.968 0.004 0.012 0.012
#> SRR1617458 2 0.5189 0.721 0.004 0.704 0.016 0.216 0.060
#> SRR1617459 2 0.5189 0.721 0.004 0.704 0.016 0.216 0.060
#> SRR1617460 2 0.5833 0.640 0.036 0.668 0.000 0.196 0.100
#> SRR1617461 2 0.5833 0.640 0.036 0.668 0.000 0.196 0.100
#> SRR1617463 2 0.3574 0.751 0.004 0.836 0.000 0.088 0.072
#> SRR1617462 2 0.3574 0.751 0.004 0.836 0.000 0.088 0.072
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.410 0.609 0.024 0.812 0.012 0.096 0.020 0.036
#> SRR1617431 2 0.410 0.609 0.024 0.812 0.012 0.096 0.020 0.036
#> SRR1617410 5 0.534 0.816 0.312 0.000 0.012 0.024 0.604 0.048
#> SRR1617411 5 0.534 0.816 0.312 0.000 0.012 0.024 0.604 0.048
#> SRR1617412 3 0.476 0.753 0.020 0.000 0.732 0.020 0.060 0.168
#> SRR1617413 3 0.476 0.753 0.020 0.000 0.732 0.020 0.060 0.168
#> SRR1617414 5 0.554 0.777 0.244 0.000 0.004 0.036 0.628 0.088
#> SRR1617415 5 0.554 0.777 0.244 0.000 0.004 0.036 0.628 0.088
#> SRR1617416 1 0.749 0.214 0.444 0.000 0.036 0.244 0.200 0.076
#> SRR1617417 1 0.749 0.214 0.444 0.000 0.036 0.244 0.200 0.076
#> SRR1617418 3 0.320 0.826 0.036 0.000 0.860 0.008 0.032 0.064
#> SRR1617419 3 0.320 0.826 0.036 0.000 0.860 0.008 0.032 0.064
#> SRR1617420 5 0.536 0.818 0.304 0.000 0.020 0.036 0.612 0.028
#> SRR1617421 5 0.536 0.818 0.304 0.000 0.020 0.036 0.612 0.028
#> SRR1617422 1 0.282 0.748 0.872 0.008 0.000 0.040 0.076 0.004
#> SRR1617423 1 0.282 0.748 0.872 0.008 0.000 0.040 0.076 0.004
#> SRR1617424 1 0.259 0.746 0.892 0.004 0.012 0.016 0.068 0.008
#> SRR1617425 1 0.259 0.746 0.892 0.004 0.012 0.016 0.068 0.008
#> SRR1617427 1 0.422 0.695 0.792 0.000 0.020 0.024 0.104 0.060
#> SRR1617426 1 0.422 0.695 0.792 0.000 0.020 0.024 0.104 0.060
#> SRR1617428 4 0.570 0.645 0.092 0.076 0.092 0.704 0.028 0.008
#> SRR1617429 4 0.559 0.645 0.092 0.076 0.092 0.708 0.028 0.004
#> SRR1617432 5 0.534 0.797 0.228 0.000 0.004 0.032 0.652 0.084
#> SRR1617433 5 0.534 0.797 0.228 0.000 0.004 0.032 0.652 0.084
#> SRR1617434 5 0.450 0.831 0.284 0.000 0.012 0.024 0.672 0.008
#> SRR1617436 3 0.466 0.781 0.044 0.000 0.772 0.084 0.028 0.072
#> SRR1617435 5 0.450 0.831 0.284 0.000 0.012 0.024 0.672 0.008
#> SRR1617437 3 0.466 0.781 0.044 0.000 0.772 0.084 0.028 0.072
#> SRR1617438 3 0.204 0.830 0.048 0.000 0.920 0.016 0.008 0.008
#> SRR1617439 3 0.204 0.830 0.048 0.000 0.920 0.016 0.008 0.008
#> SRR1617440 3 0.588 0.667 0.044 0.096 0.688 0.048 0.008 0.116
#> SRR1617441 3 0.588 0.667 0.044 0.096 0.688 0.048 0.008 0.116
#> SRR1617443 3 0.248 0.826 0.028 0.000 0.904 0.012 0.024 0.032
#> SRR1617442 3 0.248 0.826 0.028 0.000 0.904 0.012 0.024 0.032
#> SRR1617444 1 0.438 0.680 0.800 0.016 0.028 0.092 0.028 0.036
#> SRR1617445 1 0.438 0.680 0.800 0.016 0.028 0.092 0.028 0.036
#> SRR1617446 1 0.214 0.762 0.924 0.004 0.016 0.020 0.016 0.020
#> SRR1617447 1 0.214 0.762 0.924 0.004 0.016 0.020 0.016 0.020
#> SRR1617448 1 0.160 0.763 0.944 0.004 0.012 0.020 0.000 0.020
#> SRR1617449 1 0.160 0.763 0.944 0.004 0.012 0.020 0.000 0.020
#> SRR1617451 2 0.228 0.666 0.012 0.912 0.000 0.024 0.012 0.040
#> SRR1617450 2 0.228 0.666 0.012 0.912 0.000 0.024 0.012 0.040
#> SRR1617452 4 0.840 0.564 0.016 0.176 0.100 0.416 0.088 0.204
#> SRR1617454 2 0.081 0.678 0.008 0.976 0.004 0.008 0.000 0.004
#> SRR1617453 4 0.840 0.564 0.016 0.176 0.100 0.416 0.088 0.204
#> SRR1617456 2 0.439 0.566 0.000 0.604 0.008 0.012 0.004 0.372
#> SRR1617457 2 0.439 0.566 0.000 0.604 0.008 0.012 0.004 0.372
#> SRR1617455 2 0.081 0.678 0.008 0.976 0.004 0.008 0.000 0.004
#> SRR1617458 2 0.433 0.558 0.000 0.576 0.008 0.012 0.000 0.404
#> SRR1617459 2 0.433 0.558 0.000 0.576 0.008 0.012 0.000 0.404
#> SRR1617460 2 0.697 0.469 0.076 0.556 0.000 0.156 0.044 0.168
#> SRR1617461 2 0.697 0.469 0.076 0.556 0.000 0.156 0.044 0.168
#> SRR1617463 2 0.541 0.589 0.032 0.708 0.004 0.132 0.028 0.096
#> SRR1617462 2 0.541 0.589 0.032 0.708 0.004 0.132 0.028 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)
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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 0.683 0.948 0.968 0.4942 0.508 0.508
#> 3 3 0.958 0.917 0.963 0.3488 0.768 0.567
#> 4 4 0.855 0.930 0.942 0.1337 0.877 0.647
#> 5 5 0.879 0.903 0.929 0.0639 0.939 0.755
#> 6 6 0.867 0.840 0.868 0.0352 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
#> SRR1617430 2 0.0000 0.984 0.000 1.000
#> SRR1617431 2 0.0000 0.984 0.000 1.000
#> SRR1617410 1 0.0000 0.952 1.000 0.000
#> SRR1617411 1 0.0000 0.952 1.000 0.000
#> SRR1617412 1 0.5519 0.894 0.872 0.128
#> SRR1617413 1 0.5519 0.894 0.872 0.128
#> SRR1617414 1 0.0000 0.952 1.000 0.000
#> SRR1617415 1 0.0000 0.952 1.000 0.000
#> SRR1617416 1 0.0000 0.952 1.000 0.000
#> SRR1617417 1 0.0000 0.952 1.000 0.000
#> SRR1617418 1 0.5737 0.888 0.864 0.136
#> SRR1617419 1 0.5737 0.888 0.864 0.136
#> SRR1617420 1 0.0000 0.952 1.000 0.000
#> SRR1617421 1 0.0000 0.952 1.000 0.000
#> SRR1617422 1 0.2236 0.932 0.964 0.036
#> SRR1617423 1 0.2236 0.932 0.964 0.036
#> SRR1617424 1 0.0000 0.952 1.000 0.000
#> SRR1617425 1 0.0000 0.952 1.000 0.000
#> SRR1617427 1 0.0000 0.952 1.000 0.000
#> SRR1617426 1 0.0000 0.952 1.000 0.000
#> SRR1617428 2 0.0000 0.984 0.000 1.000
#> SRR1617429 2 0.0000 0.984 0.000 1.000
#> SRR1617432 1 0.0000 0.952 1.000 0.000
#> SRR1617433 1 0.0000 0.952 1.000 0.000
#> SRR1617434 1 0.0000 0.952 1.000 0.000
#> SRR1617436 1 0.5629 0.891 0.868 0.132
#> SRR1617435 1 0.0000 0.952 1.000 0.000
#> SRR1617437 1 0.5629 0.891 0.868 0.132
#> SRR1617438 1 0.5737 0.888 0.864 0.136
#> SRR1617439 1 0.5737 0.888 0.864 0.136
#> SRR1617440 2 0.0000 0.984 0.000 1.000
#> SRR1617441 2 0.0000 0.984 0.000 1.000
#> SRR1617443 1 0.5519 0.894 0.872 0.128
#> SRR1617442 1 0.5519 0.894 0.872 0.128
#> SRR1617444 2 0.6048 0.837 0.148 0.852
#> SRR1617445 2 0.6048 0.837 0.148 0.852
#> SRR1617446 1 0.0000 0.952 1.000 0.000
#> SRR1617447 1 0.0000 0.952 1.000 0.000
#> SRR1617448 1 0.0000 0.952 1.000 0.000
#> SRR1617449 1 0.0000 0.952 1.000 0.000
#> SRR1617451 2 0.0000 0.984 0.000 1.000
#> SRR1617450 2 0.0000 0.984 0.000 1.000
#> SRR1617452 2 0.0000 0.984 0.000 1.000
#> SRR1617454 2 0.0000 0.984 0.000 1.000
#> SRR1617453 2 0.0000 0.984 0.000 1.000
#> SRR1617456 2 0.0000 0.984 0.000 1.000
#> SRR1617457 2 0.0000 0.984 0.000 1.000
#> SRR1617455 2 0.0000 0.984 0.000 1.000
#> SRR1617458 2 0.0000 0.984 0.000 1.000
#> SRR1617459 2 0.0000 0.984 0.000 1.000
#> SRR1617460 2 0.0376 0.982 0.004 0.996
#> SRR1617461 2 0.0376 0.982 0.004 0.996
#> SRR1617463 2 0.0376 0.982 0.004 0.996
#> SRR1617462 2 0.0376 0.982 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.0000 0.925 0.000 1.000 0.000
#> SRR1617431 2 0.0000 0.925 0.000 1.000 0.000
#> SRR1617410 1 0.0424 0.991 0.992 0.000 0.008
#> SRR1617411 1 0.0424 0.991 0.992 0.000 0.008
#> SRR1617412 3 0.0000 0.955 0.000 0.000 1.000
#> SRR1617413 3 0.0000 0.955 0.000 0.000 1.000
#> SRR1617414 1 0.0237 0.992 0.996 0.000 0.004
#> SRR1617415 1 0.0237 0.992 0.996 0.000 0.004
#> SRR1617416 1 0.1860 0.950 0.948 0.000 0.052
#> SRR1617417 1 0.1860 0.950 0.948 0.000 0.052
#> SRR1617418 3 0.0000 0.955 0.000 0.000 1.000
#> SRR1617419 3 0.0000 0.955 0.000 0.000 1.000
#> SRR1617420 1 0.0424 0.991 0.992 0.000 0.008
#> SRR1617421 1 0.0424 0.991 0.992 0.000 0.008
#> SRR1617422 1 0.0000 0.992 1.000 0.000 0.000
#> SRR1617423 1 0.0000 0.992 1.000 0.000 0.000
#> SRR1617424 1 0.0000 0.992 1.000 0.000 0.000
#> SRR1617425 1 0.0000 0.992 1.000 0.000 0.000
#> SRR1617427 1 0.0000 0.992 1.000 0.000 0.000
#> SRR1617426 1 0.0000 0.992 1.000 0.000 0.000
#> SRR1617428 3 0.5138 0.670 0.000 0.252 0.748
#> SRR1617429 3 0.5138 0.670 0.000 0.252 0.748
#> SRR1617432 1 0.0424 0.991 0.992 0.000 0.008
#> SRR1617433 1 0.0424 0.991 0.992 0.000 0.008
#> SRR1617434 1 0.0424 0.991 0.992 0.000 0.008
#> SRR1617436 3 0.0000 0.955 0.000 0.000 1.000
#> SRR1617435 1 0.0424 0.991 0.992 0.000 0.008
#> SRR1617437 3 0.0000 0.955 0.000 0.000 1.000
#> SRR1617438 3 0.0000 0.955 0.000 0.000 1.000
#> SRR1617439 3 0.0000 0.955 0.000 0.000 1.000
#> SRR1617440 3 0.0592 0.948 0.000 0.012 0.988
#> SRR1617441 3 0.0592 0.948 0.000 0.012 0.988
#> SRR1617443 3 0.0000 0.955 0.000 0.000 1.000
#> SRR1617442 3 0.0000 0.955 0.000 0.000 1.000
#> SRR1617444 2 0.9907 0.132 0.288 0.400 0.312
#> SRR1617445 2 0.9907 0.132 0.288 0.400 0.312
#> SRR1617446 1 0.0000 0.992 1.000 0.000 0.000
#> SRR1617447 1 0.0000 0.992 1.000 0.000 0.000
#> SRR1617448 1 0.0000 0.992 1.000 0.000 0.000
#> SRR1617449 1 0.0000 0.992 1.000 0.000 0.000
#> SRR1617451 2 0.0000 0.925 0.000 1.000 0.000
#> SRR1617450 2 0.0000 0.925 0.000 1.000 0.000
#> SRR1617452 2 0.1411 0.895 0.000 0.964 0.036
#> SRR1617454 2 0.0000 0.925 0.000 1.000 0.000
#> SRR1617453 2 0.1411 0.895 0.000 0.964 0.036
#> SRR1617456 2 0.0000 0.925 0.000 1.000 0.000
#> SRR1617457 2 0.0000 0.925 0.000 1.000 0.000
#> SRR1617455 2 0.0000 0.925 0.000 1.000 0.000
#> SRR1617458 2 0.0000 0.925 0.000 1.000 0.000
#> SRR1617459 2 0.0000 0.925 0.000 1.000 0.000
#> SRR1617460 2 0.0000 0.925 0.000 1.000 0.000
#> SRR1617461 2 0.0000 0.925 0.000 1.000 0.000
#> SRR1617463 2 0.0000 0.925 0.000 1.000 0.000
#> SRR1617462 2 0.0000 0.925 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.0188 0.967 0.004 0.996 0.000 0.000
#> SRR1617431 2 0.0188 0.967 0.004 0.996 0.000 0.000
#> SRR1617410 4 0.0336 0.995 0.008 0.000 0.000 0.992
#> SRR1617411 4 0.0336 0.995 0.008 0.000 0.000 0.992
#> SRR1617412 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> SRR1617413 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> SRR1617414 4 0.0707 0.986 0.020 0.000 0.000 0.980
#> SRR1617415 4 0.0707 0.986 0.020 0.000 0.000 0.980
#> SRR1617416 1 0.5090 0.679 0.728 0.000 0.044 0.228
#> SRR1617417 1 0.5090 0.679 0.728 0.000 0.044 0.228
#> SRR1617418 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> SRR1617419 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> SRR1617420 4 0.0336 0.995 0.008 0.000 0.000 0.992
#> SRR1617421 4 0.0336 0.995 0.008 0.000 0.000 0.992
#> SRR1617422 1 0.2704 0.914 0.876 0.000 0.000 0.124
#> SRR1617423 1 0.2704 0.914 0.876 0.000 0.000 0.124
#> SRR1617424 1 0.2647 0.915 0.880 0.000 0.000 0.120
#> SRR1617425 1 0.2647 0.915 0.880 0.000 0.000 0.120
#> SRR1617427 1 0.2973 0.904 0.856 0.000 0.000 0.144
#> SRR1617426 1 0.2973 0.904 0.856 0.000 0.000 0.144
#> SRR1617428 3 0.6696 0.705 0.088 0.140 0.700 0.072
#> SRR1617429 3 0.6696 0.705 0.088 0.140 0.700 0.072
#> SRR1617432 4 0.0336 0.995 0.008 0.000 0.000 0.992
#> SRR1617433 4 0.0336 0.995 0.008 0.000 0.000 0.992
#> SRR1617434 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1617436 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> SRR1617435 4 0.0000 0.989 0.000 0.000 0.000 1.000
#> SRR1617437 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> SRR1617438 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> SRR1617439 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> SRR1617440 3 0.0804 0.944 0.012 0.008 0.980 0.000
#> SRR1617441 3 0.0804 0.944 0.012 0.008 0.980 0.000
#> SRR1617443 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> SRR1617442 3 0.0000 0.955 0.000 0.000 1.000 0.000
#> SRR1617444 1 0.0564 0.862 0.988 0.004 0.004 0.004
#> SRR1617445 1 0.0564 0.862 0.988 0.004 0.004 0.004
#> SRR1617446 1 0.2216 0.917 0.908 0.000 0.000 0.092
#> SRR1617447 1 0.2216 0.917 0.908 0.000 0.000 0.092
#> SRR1617448 1 0.2216 0.917 0.908 0.000 0.000 0.092
#> SRR1617449 1 0.2216 0.917 0.908 0.000 0.000 0.092
#> SRR1617451 2 0.0188 0.967 0.004 0.996 0.000 0.000
#> SRR1617450 2 0.0188 0.967 0.004 0.996 0.000 0.000
#> SRR1617452 2 0.4551 0.868 0.116 0.820 0.040 0.024
#> SRR1617454 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> SRR1617453 2 0.4551 0.868 0.116 0.820 0.040 0.024
#> SRR1617456 2 0.1022 0.963 0.032 0.968 0.000 0.000
#> SRR1617457 2 0.1022 0.963 0.032 0.968 0.000 0.000
#> SRR1617455 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> SRR1617458 2 0.1022 0.963 0.032 0.968 0.000 0.000
#> SRR1617459 2 0.1022 0.963 0.032 0.968 0.000 0.000
#> SRR1617460 2 0.1637 0.951 0.060 0.940 0.000 0.000
#> SRR1617461 2 0.1637 0.951 0.060 0.940 0.000 0.000
#> SRR1617463 2 0.0000 0.967 0.000 1.000 0.000 0.000
#> SRR1617462 2 0.0000 0.967 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
#> SRR1617430 2 0.0963 0.853 0.000 0.964 0.000 0.036 0.000
#> SRR1617431 2 0.0963 0.853 0.000 0.964 0.000 0.036 0.000
#> SRR1617410 5 0.0771 0.978 0.004 0.000 0.000 0.020 0.976
#> SRR1617411 5 0.0771 0.978 0.004 0.000 0.000 0.020 0.976
#> SRR1617412 3 0.0000 0.978 0.000 0.000 1.000 0.000 0.000
#> SRR1617413 3 0.0000 0.978 0.000 0.000 1.000 0.000 0.000
#> SRR1617414 5 0.0510 0.979 0.000 0.000 0.000 0.016 0.984
#> SRR1617415 5 0.0510 0.979 0.000 0.000 0.000 0.016 0.984
#> SRR1617416 4 0.4589 0.739 0.172 0.000 0.008 0.752 0.068
#> SRR1617417 4 0.4589 0.739 0.172 0.000 0.008 0.752 0.068
#> SRR1617418 3 0.0000 0.978 0.000 0.000 1.000 0.000 0.000
#> SRR1617419 3 0.0000 0.978 0.000 0.000 1.000 0.000 0.000
#> SRR1617420 5 0.0290 0.982 0.000 0.000 0.000 0.008 0.992
#> SRR1617421 5 0.0290 0.982 0.000 0.000 0.000 0.008 0.992
#> SRR1617422 1 0.1195 0.959 0.960 0.000 0.000 0.012 0.028
#> SRR1617423 1 0.1195 0.959 0.960 0.000 0.000 0.012 0.028
#> SRR1617424 1 0.0898 0.961 0.972 0.000 0.000 0.008 0.020
#> SRR1617425 1 0.0898 0.961 0.972 0.000 0.000 0.008 0.020
#> SRR1617427 1 0.1877 0.935 0.924 0.000 0.000 0.012 0.064
#> SRR1617426 1 0.1877 0.935 0.924 0.000 0.000 0.012 0.064
#> SRR1617428 4 0.4277 0.774 0.000 0.100 0.112 0.784 0.004
#> SRR1617429 4 0.4277 0.774 0.000 0.100 0.112 0.784 0.004
#> SRR1617432 5 0.0510 0.979 0.000 0.000 0.000 0.016 0.984
#> SRR1617433 5 0.0510 0.979 0.000 0.000 0.000 0.016 0.984
#> SRR1617434 5 0.0794 0.975 0.000 0.000 0.000 0.028 0.972
#> SRR1617436 3 0.0510 0.969 0.000 0.000 0.984 0.016 0.000
#> SRR1617435 5 0.0794 0.975 0.000 0.000 0.000 0.028 0.972
#> SRR1617437 3 0.0510 0.969 0.000 0.000 0.984 0.016 0.000
#> SRR1617438 3 0.0000 0.978 0.000 0.000 1.000 0.000 0.000
#> SRR1617439 3 0.0000 0.978 0.000 0.000 1.000 0.000 0.000
#> SRR1617440 3 0.2450 0.898 0.000 0.048 0.900 0.052 0.000
#> SRR1617441 3 0.2450 0.898 0.000 0.048 0.900 0.052 0.000
#> SRR1617443 3 0.0000 0.978 0.000 0.000 1.000 0.000 0.000
#> SRR1617442 3 0.0000 0.978 0.000 0.000 1.000 0.000 0.000
#> SRR1617444 1 0.1341 0.933 0.944 0.000 0.000 0.056 0.000
#> SRR1617445 1 0.1341 0.933 0.944 0.000 0.000 0.056 0.000
#> SRR1617446 1 0.1300 0.959 0.956 0.000 0.000 0.028 0.016
#> SRR1617447 1 0.1300 0.959 0.956 0.000 0.000 0.028 0.016
#> SRR1617448 1 0.1195 0.959 0.960 0.000 0.000 0.028 0.012
#> SRR1617449 1 0.1195 0.959 0.960 0.000 0.000 0.028 0.012
#> SRR1617451 2 0.0510 0.861 0.000 0.984 0.000 0.016 0.000
#> SRR1617450 2 0.0510 0.861 0.000 0.984 0.000 0.016 0.000
#> SRR1617452 4 0.2411 0.726 0.000 0.108 0.000 0.884 0.008
#> SRR1617454 2 0.0290 0.864 0.000 0.992 0.000 0.008 0.000
#> SRR1617453 4 0.2411 0.726 0.000 0.108 0.000 0.884 0.008
#> SRR1617456 2 0.3039 0.839 0.012 0.836 0.000 0.152 0.000
#> SRR1617457 2 0.3039 0.839 0.012 0.836 0.000 0.152 0.000
#> SRR1617455 2 0.0290 0.864 0.000 0.992 0.000 0.008 0.000
#> SRR1617458 2 0.3081 0.838 0.012 0.832 0.000 0.156 0.000
#> SRR1617459 2 0.3081 0.838 0.012 0.832 0.000 0.156 0.000
#> SRR1617460 2 0.4384 0.677 0.016 0.660 0.000 0.324 0.000
#> SRR1617461 2 0.4384 0.677 0.016 0.660 0.000 0.324 0.000
#> SRR1617463 2 0.2629 0.824 0.004 0.860 0.000 0.136 0.000
#> SRR1617462 2 0.2629 0.824 0.004 0.860 0.000 0.136 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.4010 0.727 0.000 0.584 0.000 0.008 0.000 0.408
#> SRR1617431 2 0.4010 0.727 0.000 0.584 0.000 0.008 0.000 0.408
#> SRR1617410 5 0.0363 0.937 0.000 0.000 0.000 0.012 0.988 0.000
#> SRR1617411 5 0.0363 0.937 0.000 0.000 0.000 0.012 0.988 0.000
#> SRR1617412 3 0.0820 0.921 0.000 0.000 0.972 0.012 0.000 0.016
#> SRR1617413 3 0.0820 0.921 0.000 0.000 0.972 0.012 0.000 0.016
#> SRR1617414 5 0.2871 0.909 0.008 0.000 0.000 0.024 0.852 0.116
#> SRR1617415 5 0.2871 0.909 0.008 0.000 0.000 0.024 0.852 0.116
#> SRR1617416 4 0.2017 0.893 0.020 0.000 0.004 0.920 0.048 0.008
#> SRR1617417 4 0.2017 0.893 0.020 0.000 0.004 0.920 0.048 0.008
#> SRR1617418 3 0.0520 0.923 0.000 0.000 0.984 0.008 0.000 0.008
#> SRR1617419 3 0.0520 0.923 0.000 0.000 0.984 0.008 0.000 0.008
#> SRR1617420 5 0.0000 0.938 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617421 5 0.0000 0.938 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617422 1 0.1429 0.887 0.940 0.000 0.000 0.004 0.004 0.052
#> SRR1617423 1 0.1429 0.887 0.940 0.000 0.000 0.004 0.004 0.052
#> SRR1617424 1 0.0146 0.894 0.996 0.000 0.000 0.004 0.000 0.000
#> SRR1617425 1 0.0146 0.894 0.996 0.000 0.000 0.004 0.000 0.000
#> SRR1617427 1 0.1624 0.875 0.936 0.000 0.000 0.004 0.040 0.020
#> SRR1617426 1 0.1624 0.875 0.936 0.000 0.000 0.004 0.040 0.020
#> SRR1617428 4 0.2214 0.884 0.000 0.004 0.012 0.892 0.000 0.092
#> SRR1617429 4 0.2214 0.884 0.000 0.004 0.012 0.892 0.000 0.092
#> SRR1617432 5 0.2760 0.911 0.004 0.000 0.000 0.024 0.856 0.116
#> SRR1617433 5 0.2760 0.911 0.004 0.000 0.000 0.024 0.856 0.116
#> SRR1617434 5 0.0363 0.937 0.000 0.000 0.000 0.012 0.988 0.000
#> SRR1617436 3 0.1563 0.900 0.000 0.000 0.932 0.012 0.000 0.056
#> SRR1617435 5 0.0363 0.937 0.000 0.000 0.000 0.012 0.988 0.000
#> SRR1617437 3 0.1563 0.900 0.000 0.000 0.932 0.012 0.000 0.056
#> SRR1617438 3 0.1007 0.922 0.000 0.000 0.956 0.000 0.000 0.044
#> SRR1617439 3 0.1007 0.922 0.000 0.000 0.956 0.000 0.000 0.044
#> SRR1617440 3 0.4459 0.739 0.000 0.204 0.708 0.004 0.000 0.084
#> SRR1617441 3 0.4459 0.739 0.000 0.204 0.708 0.004 0.000 0.084
#> SRR1617443 3 0.0937 0.923 0.000 0.000 0.960 0.000 0.000 0.040
#> SRR1617442 3 0.0937 0.923 0.000 0.000 0.960 0.000 0.000 0.040
#> SRR1617444 1 0.4173 0.840 0.732 0.012 0.000 0.044 0.000 0.212
#> SRR1617445 1 0.4173 0.840 0.732 0.012 0.000 0.044 0.000 0.212
#> SRR1617446 1 0.2831 0.891 0.840 0.000 0.000 0.024 0.000 0.136
#> SRR1617447 1 0.2831 0.891 0.840 0.000 0.000 0.024 0.000 0.136
#> SRR1617448 1 0.2831 0.891 0.840 0.000 0.000 0.024 0.000 0.136
#> SRR1617449 1 0.2831 0.891 0.840 0.000 0.000 0.024 0.000 0.136
#> SRR1617451 2 0.3847 0.745 0.000 0.644 0.000 0.008 0.000 0.348
#> SRR1617450 2 0.3847 0.745 0.000 0.644 0.000 0.008 0.000 0.348
#> SRR1617452 4 0.2408 0.875 0.000 0.108 0.004 0.876 0.000 0.012
#> SRR1617454 2 0.3684 0.750 0.000 0.628 0.000 0.000 0.000 0.372
#> SRR1617453 4 0.2408 0.875 0.000 0.108 0.004 0.876 0.000 0.012
#> SRR1617456 2 0.0000 0.703 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617457 2 0.0000 0.703 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617455 2 0.3684 0.750 0.000 0.628 0.000 0.000 0.000 0.372
#> SRR1617458 2 0.0000 0.703 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617459 2 0.0000 0.703 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617460 2 0.5660 0.518 0.000 0.516 0.000 0.184 0.000 0.300
#> SRR1617461 2 0.5660 0.518 0.000 0.516 0.000 0.184 0.000 0.300
#> SRR1617463 2 0.5181 0.637 0.000 0.484 0.000 0.088 0.000 0.428
#> SRR1617462 2 0.5181 0.637 0.000 0.484 0.000 0.088 0.000 0.428
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", "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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 0.478 0.895 0.897 0.4250 0.575 0.575
#> 3 3 0.719 0.831 0.885 0.4410 0.782 0.621
#> 4 4 0.826 0.876 0.914 0.1369 0.966 0.906
#> 5 5 0.798 0.832 0.880 0.0870 0.916 0.741
#> 6 6 0.861 0.845 0.919 0.0457 0.958 0.827
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
#> SRR1617430 2 0.000 1.000 0.000 1.000
#> SRR1617431 2 0.000 1.000 0.000 1.000
#> SRR1617410 1 0.000 0.833 1.000 0.000
#> SRR1617411 1 0.000 0.833 1.000 0.000
#> SRR1617412 1 0.714 0.891 0.804 0.196
#> SRR1617413 1 0.714 0.891 0.804 0.196
#> SRR1617414 1 0.000 0.833 1.000 0.000
#> SRR1617415 1 0.000 0.833 1.000 0.000
#> SRR1617416 1 0.000 0.833 1.000 0.000
#> SRR1617417 1 0.000 0.833 1.000 0.000
#> SRR1617418 1 0.722 0.890 0.800 0.200
#> SRR1617419 1 0.722 0.890 0.800 0.200
#> SRR1617420 1 0.000 0.833 1.000 0.000
#> SRR1617421 1 0.000 0.833 1.000 0.000
#> SRR1617422 1 0.697 0.894 0.812 0.188
#> SRR1617423 1 0.697 0.894 0.812 0.188
#> SRR1617424 1 0.697 0.894 0.812 0.188
#> SRR1617425 1 0.697 0.894 0.812 0.188
#> SRR1617427 1 0.689 0.894 0.816 0.184
#> SRR1617426 1 0.689 0.894 0.816 0.184
#> SRR1617428 1 0.850 0.759 0.724 0.276
#> SRR1617429 1 0.900 0.698 0.684 0.316
#> SRR1617432 1 0.000 0.833 1.000 0.000
#> SRR1617433 1 0.000 0.833 1.000 0.000
#> SRR1617434 1 0.000 0.833 1.000 0.000
#> SRR1617436 1 0.722 0.890 0.800 0.200
#> SRR1617435 1 0.000 0.833 1.000 0.000
#> SRR1617437 1 0.722 0.890 0.800 0.200
#> SRR1617438 1 0.722 0.890 0.800 0.200
#> SRR1617439 1 0.722 0.890 0.800 0.200
#> SRR1617440 1 0.971 0.629 0.600 0.400
#> SRR1617441 1 0.971 0.629 0.600 0.400
#> SRR1617443 1 0.680 0.891 0.820 0.180
#> SRR1617442 1 0.671 0.891 0.824 0.176
#> SRR1617444 1 0.697 0.894 0.812 0.188
#> SRR1617445 1 0.697 0.894 0.812 0.188
#> SRR1617446 1 0.697 0.894 0.812 0.188
#> SRR1617447 1 0.697 0.894 0.812 0.188
#> SRR1617448 1 0.697 0.894 0.812 0.188
#> SRR1617449 1 0.697 0.894 0.812 0.188
#> SRR1617451 2 0.000 1.000 0.000 1.000
#> SRR1617450 2 0.000 1.000 0.000 1.000
#> SRR1617452 2 0.000 1.000 0.000 1.000
#> SRR1617454 2 0.000 1.000 0.000 1.000
#> SRR1617453 2 0.000 1.000 0.000 1.000
#> SRR1617456 2 0.000 1.000 0.000 1.000
#> SRR1617457 2 0.000 1.000 0.000 1.000
#> SRR1617455 2 0.000 1.000 0.000 1.000
#> SRR1617458 2 0.000 1.000 0.000 1.000
#> SRR1617459 2 0.000 1.000 0.000 1.000
#> SRR1617460 2 0.000 1.000 0.000 1.000
#> SRR1617461 2 0.000 1.000 0.000 1.000
#> SRR1617463 2 0.000 1.000 0.000 1.000
#> SRR1617462 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.000 0.886 0.000 1.000 0.000
#> SRR1617431 2 0.000 0.886 0.000 1.000 0.000
#> SRR1617410 1 0.000 0.905 1.000 0.000 0.000
#> SRR1617411 1 0.000 0.905 1.000 0.000 0.000
#> SRR1617412 3 0.514 0.926 0.252 0.000 0.748
#> SRR1617413 3 0.514 0.926 0.252 0.000 0.748
#> SRR1617414 1 0.000 0.905 1.000 0.000 0.000
#> SRR1617415 1 0.000 0.905 1.000 0.000 0.000
#> SRR1617416 1 0.000 0.905 1.000 0.000 0.000
#> SRR1617417 1 0.000 0.905 1.000 0.000 0.000
#> SRR1617418 3 0.514 0.926 0.252 0.000 0.748
#> SRR1617419 3 0.514 0.926 0.252 0.000 0.748
#> SRR1617420 1 0.000 0.905 1.000 0.000 0.000
#> SRR1617421 1 0.000 0.905 1.000 0.000 0.000
#> SRR1617422 1 0.293 0.905 0.924 0.036 0.040
#> SRR1617423 1 0.293 0.905 0.924 0.036 0.040
#> SRR1617424 1 0.293 0.905 0.924 0.036 0.040
#> SRR1617425 1 0.293 0.905 0.924 0.036 0.040
#> SRR1617427 1 0.293 0.905 0.924 0.036 0.040
#> SRR1617426 1 0.293 0.905 0.924 0.036 0.040
#> SRR1617428 1 0.725 -0.198 0.536 0.028 0.436
#> SRR1617429 1 0.714 -0.197 0.540 0.024 0.436
#> SRR1617432 1 0.000 0.905 1.000 0.000 0.000
#> SRR1617433 1 0.000 0.905 1.000 0.000 0.000
#> SRR1617434 1 0.000 0.905 1.000 0.000 0.000
#> SRR1617436 3 0.518 0.921 0.256 0.000 0.744
#> SRR1617435 1 0.000 0.905 1.000 0.000 0.000
#> SRR1617437 3 0.518 0.921 0.256 0.000 0.744
#> SRR1617438 3 0.514 0.926 0.252 0.000 0.748
#> SRR1617439 3 0.514 0.926 0.252 0.000 0.748
#> SRR1617440 3 0.000 0.627 0.000 0.000 1.000
#> SRR1617441 3 0.000 0.627 0.000 0.000 1.000
#> SRR1617443 3 0.514 0.926 0.252 0.000 0.748
#> SRR1617442 3 0.514 0.926 0.252 0.000 0.748
#> SRR1617444 1 0.293 0.905 0.924 0.036 0.040
#> SRR1617445 1 0.293 0.905 0.924 0.036 0.040
#> SRR1617446 1 0.293 0.905 0.924 0.036 0.040
#> SRR1617447 1 0.293 0.905 0.924 0.036 0.040
#> SRR1617448 1 0.293 0.905 0.924 0.036 0.040
#> SRR1617449 1 0.293 0.905 0.924 0.036 0.040
#> SRR1617451 2 0.000 0.886 0.000 1.000 0.000
#> SRR1617450 2 0.000 0.886 0.000 1.000 0.000
#> SRR1617452 2 0.595 0.522 0.000 0.640 0.360
#> SRR1617454 2 0.000 0.886 0.000 1.000 0.000
#> SRR1617453 2 0.595 0.527 0.000 0.640 0.360
#> SRR1617456 2 0.514 0.798 0.000 0.748 0.252
#> SRR1617457 2 0.514 0.798 0.000 0.748 0.252
#> SRR1617455 2 0.000 0.886 0.000 1.000 0.000
#> SRR1617458 2 0.514 0.798 0.000 0.748 0.252
#> SRR1617459 2 0.514 0.798 0.000 0.748 0.252
#> SRR1617460 2 0.255 0.853 0.040 0.936 0.024
#> SRR1617461 2 0.255 0.853 0.040 0.936 0.024
#> SRR1617463 2 0.000 0.886 0.000 1.000 0.000
#> SRR1617462 2 0.000 0.886 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.0707 0.870 0.000 0.980 0.020 0.000
#> SRR1617431 2 0.0592 0.872 0.000 0.984 0.016 0.000
#> SRR1617410 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> SRR1617411 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> SRR1617412 3 0.0469 0.985 0.012 0.000 0.988 0.000
#> SRR1617413 3 0.0469 0.985 0.012 0.000 0.988 0.000
#> SRR1617414 1 0.0336 0.866 0.992 0.000 0.000 0.008
#> SRR1617415 1 0.0336 0.866 0.992 0.000 0.000 0.008
#> SRR1617416 1 0.3172 0.890 0.840 0.000 0.000 0.160
#> SRR1617417 1 0.2704 0.887 0.876 0.000 0.000 0.124
#> SRR1617418 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> SRR1617419 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> SRR1617420 1 0.0188 0.867 0.996 0.000 0.000 0.004
#> SRR1617421 1 0.0188 0.867 0.996 0.000 0.000 0.004
#> SRR1617422 1 0.3356 0.891 0.824 0.000 0.000 0.176
#> SRR1617423 1 0.3356 0.891 0.824 0.000 0.000 0.176
#> SRR1617424 1 0.3356 0.891 0.824 0.000 0.000 0.176
#> SRR1617425 1 0.3356 0.891 0.824 0.000 0.000 0.176
#> SRR1617427 1 0.3356 0.891 0.824 0.000 0.000 0.176
#> SRR1617426 1 0.3356 0.891 0.824 0.000 0.000 0.176
#> SRR1617428 1 0.5070 0.338 0.580 0.004 0.416 0.000
#> SRR1617429 1 0.5070 0.338 0.580 0.004 0.416 0.000
#> SRR1617432 1 0.0336 0.866 0.992 0.000 0.000 0.008
#> SRR1617433 1 0.0336 0.866 0.992 0.000 0.000 0.008
#> SRR1617434 1 0.0336 0.866 0.992 0.000 0.000 0.008
#> SRR1617436 3 0.0469 0.985 0.012 0.000 0.988 0.000
#> SRR1617435 1 0.0336 0.866 0.992 0.000 0.000 0.008
#> SRR1617437 3 0.0469 0.985 0.012 0.000 0.988 0.000
#> SRR1617438 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> SRR1617439 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> SRR1617440 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> SRR1617441 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> SRR1617443 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> SRR1617442 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> SRR1617444 1 0.3356 0.891 0.824 0.000 0.000 0.176
#> SRR1617445 1 0.3356 0.891 0.824 0.000 0.000 0.176
#> SRR1617446 1 0.3356 0.891 0.824 0.000 0.000 0.176
#> SRR1617447 1 0.3356 0.891 0.824 0.000 0.000 0.176
#> SRR1617448 1 0.3356 0.891 0.824 0.000 0.000 0.176
#> SRR1617449 1 0.3356 0.891 0.824 0.000 0.000 0.176
#> SRR1617451 2 0.3356 0.724 0.000 0.824 0.000 0.176
#> SRR1617450 2 0.3400 0.719 0.000 0.820 0.000 0.180
#> SRR1617452 2 0.5466 0.577 0.000 0.712 0.220 0.068
#> SRR1617454 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> SRR1617453 2 0.5533 0.572 0.000 0.708 0.220 0.072
#> SRR1617456 4 0.3444 1.000 0.000 0.184 0.000 0.816
#> SRR1617457 4 0.3444 1.000 0.000 0.184 0.000 0.816
#> SRR1617455 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> SRR1617458 4 0.3444 1.000 0.000 0.184 0.000 0.816
#> SRR1617459 4 0.3444 1.000 0.000 0.184 0.000 0.816
#> SRR1617460 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> SRR1617461 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> SRR1617463 2 0.0000 0.879 0.000 1.000 0.000 0.000
#> SRR1617462 2 0.0000 0.879 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
#> SRR1617430 2 0.5862 0.652 0.000 0.604 0.176 0.000 0.220
#> SRR1617431 2 0.5831 0.654 0.000 0.608 0.172 0.000 0.220
#> SRR1617410 1 0.3039 0.699 0.808 0.000 0.000 0.000 0.192
#> SRR1617411 1 0.2966 0.709 0.816 0.000 0.000 0.000 0.184
#> SRR1617412 3 0.0404 0.986 0.012 0.000 0.988 0.000 0.000
#> SRR1617413 3 0.0404 0.986 0.012 0.000 0.988 0.000 0.000
#> SRR1617414 5 0.3274 1.000 0.220 0.000 0.000 0.000 0.780
#> SRR1617415 5 0.3274 1.000 0.220 0.000 0.000 0.000 0.780
#> SRR1617416 1 0.0510 0.863 0.984 0.000 0.000 0.000 0.016
#> SRR1617417 1 0.1341 0.835 0.944 0.000 0.000 0.000 0.056
#> SRR1617418 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000
#> SRR1617419 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000
#> SRR1617420 1 0.3109 0.687 0.800 0.000 0.000 0.000 0.200
#> SRR1617421 1 0.3143 0.681 0.796 0.000 0.000 0.000 0.204
#> SRR1617422 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> SRR1617423 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> SRR1617424 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> SRR1617425 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> SRR1617427 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> SRR1617426 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> SRR1617428 1 0.5338 0.270 0.544 0.000 0.400 0.000 0.056
#> SRR1617429 1 0.5338 0.270 0.544 0.000 0.400 0.000 0.056
#> SRR1617432 5 0.3274 1.000 0.220 0.000 0.000 0.000 0.780
#> SRR1617433 5 0.3274 1.000 0.220 0.000 0.000 0.000 0.780
#> SRR1617434 5 0.3274 1.000 0.220 0.000 0.000 0.000 0.780
#> SRR1617436 3 0.0404 0.986 0.012 0.000 0.988 0.000 0.000
#> SRR1617435 5 0.3274 1.000 0.220 0.000 0.000 0.000 0.780
#> SRR1617437 3 0.0404 0.986 0.012 0.000 0.988 0.000 0.000
#> SRR1617438 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000
#> SRR1617439 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000
#> SRR1617440 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000
#> SRR1617441 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000
#> SRR1617443 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000
#> SRR1617442 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000
#> SRR1617444 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> SRR1617445 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> SRR1617446 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> SRR1617447 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> SRR1617448 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> SRR1617449 1 0.0000 0.872 1.000 0.000 0.000 0.000 0.000
#> SRR1617451 2 0.6423 0.550 0.000 0.504 0.000 0.276 0.220
#> SRR1617450 2 0.6438 0.545 0.000 0.500 0.000 0.280 0.220
#> SRR1617452 2 0.6031 0.418 0.000 0.576 0.180 0.244 0.000
#> SRR1617454 2 0.3274 0.711 0.000 0.780 0.000 0.000 0.220
#> SRR1617453 2 0.6080 0.406 0.000 0.568 0.184 0.248 0.000
#> SRR1617456 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617457 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617455 2 0.3274 0.711 0.000 0.780 0.000 0.000 0.220
#> SRR1617458 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617459 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617460 2 0.0000 0.725 0.000 1.000 0.000 0.000 0.000
#> SRR1617461 2 0.0000 0.725 0.000 1.000 0.000 0.000 0.000
#> SRR1617463 2 0.0000 0.725 0.000 1.000 0.000 0.000 0.000
#> SRR1617462 2 0.0000 0.725 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
#> SRR1617430 2 0.2805 0.625 0.000 0.812 0.184 0.004 0.000 0.000
#> SRR1617431 2 0.2772 0.629 0.000 0.816 0.180 0.004 0.000 0.000
#> SRR1617410 1 0.2730 0.766 0.808 0.000 0.000 0.000 0.192 0.000
#> SRR1617411 1 0.2664 0.775 0.816 0.000 0.000 0.000 0.184 0.000
#> SRR1617412 3 0.0363 0.985 0.012 0.000 0.988 0.000 0.000 0.000
#> SRR1617413 3 0.0363 0.985 0.012 0.000 0.988 0.000 0.000 0.000
#> SRR1617414 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617415 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617416 1 0.0363 0.927 0.988 0.000 0.000 0.000 0.012 0.000
#> SRR1617417 1 0.1007 0.905 0.956 0.000 0.000 0.000 0.044 0.000
#> SRR1617418 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617419 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617420 1 0.2793 0.756 0.800 0.000 0.000 0.000 0.200 0.000
#> SRR1617421 1 0.2823 0.751 0.796 0.000 0.000 0.000 0.204 0.000
#> SRR1617422 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617423 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617424 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617425 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617427 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617426 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617428 4 0.4727 0.360 0.368 0.000 0.056 0.576 0.000 0.000
#> SRR1617429 4 0.4727 0.360 0.368 0.000 0.056 0.576 0.000 0.000
#> SRR1617432 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617433 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617434 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617436 3 0.0363 0.985 0.012 0.000 0.988 0.000 0.000 0.000
#> SRR1617435 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617437 3 0.0363 0.985 0.012 0.000 0.988 0.000 0.000 0.000
#> SRR1617438 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617439 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617440 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617441 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617443 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617442 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617444 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617445 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617446 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617447 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617448 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617449 1 0.0000 0.934 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617451 2 0.3337 0.576 0.000 0.736 0.000 0.004 0.000 0.260
#> SRR1617450 2 0.3360 0.572 0.000 0.732 0.000 0.004 0.000 0.264
#> SRR1617452 4 0.5748 0.138 0.000 0.176 0.032 0.608 0.000 0.184
#> SRR1617454 2 0.0000 0.726 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617453 4 0.5785 0.144 0.000 0.172 0.036 0.608 0.000 0.184
#> SRR1617456 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617457 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617455 2 0.0000 0.726 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617458 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617459 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617460 2 0.3023 0.705 0.000 0.768 0.000 0.232 0.000 0.000
#> SRR1617461 2 0.3023 0.705 0.000 0.768 0.000 0.232 0.000 0.000
#> SRR1617463 2 0.3023 0.705 0.000 0.768 0.000 0.232 0.000 0.000
#> SRR1617462 2 0.3023 0.705 0.000 0.768 0.000 0.232 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", "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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 0.625 0.888 0.943 0.4726 0.525 0.525
#> 3 3 0.969 0.942 0.973 0.3686 0.832 0.680
#> 4 4 0.827 0.796 0.894 0.1249 0.871 0.653
#> 5 5 0.864 0.815 0.859 0.0450 0.941 0.794
#> 6 6 0.807 0.735 0.809 0.0513 0.966 0.871
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
#> SRR1617430 2 0.0672 0.926 0.008 0.992
#> SRR1617431 2 0.0672 0.926 0.008 0.992
#> SRR1617410 1 0.0000 0.951 1.000 0.000
#> SRR1617411 1 0.0000 0.951 1.000 0.000
#> SRR1617412 2 0.0000 0.923 0.000 1.000
#> SRR1617413 2 0.0000 0.923 0.000 1.000
#> SRR1617414 1 0.7139 0.767 0.804 0.196
#> SRR1617415 1 0.7139 0.767 0.804 0.196
#> SRR1617416 2 0.8327 0.702 0.264 0.736
#> SRR1617417 2 0.8327 0.702 0.264 0.736
#> SRR1617418 2 0.0000 0.923 0.000 1.000
#> SRR1617419 2 0.0000 0.923 0.000 1.000
#> SRR1617420 1 0.0000 0.951 1.000 0.000
#> SRR1617421 1 0.0000 0.951 1.000 0.000
#> SRR1617422 1 0.6801 0.789 0.820 0.180
#> SRR1617423 1 0.6887 0.784 0.816 0.184
#> SRR1617424 1 0.0000 0.951 1.000 0.000
#> SRR1617425 1 0.0000 0.951 1.000 0.000
#> SRR1617427 1 0.1414 0.941 0.980 0.020
#> SRR1617426 1 0.1414 0.941 0.980 0.020
#> SRR1617428 2 0.8327 0.702 0.264 0.736
#> SRR1617429 2 0.8327 0.702 0.264 0.736
#> SRR1617432 1 0.0000 0.951 1.000 0.000
#> SRR1617433 1 0.0000 0.951 1.000 0.000
#> SRR1617434 1 0.0000 0.951 1.000 0.000
#> SRR1617436 2 0.0000 0.923 0.000 1.000
#> SRR1617435 1 0.0672 0.948 0.992 0.008
#> SRR1617437 2 0.0000 0.923 0.000 1.000
#> SRR1617438 2 0.0000 0.923 0.000 1.000
#> SRR1617439 2 0.0000 0.923 0.000 1.000
#> SRR1617440 2 0.0672 0.926 0.008 0.992
#> SRR1617441 2 0.0672 0.926 0.008 0.992
#> SRR1617443 2 0.0000 0.923 0.000 1.000
#> SRR1617442 2 0.0000 0.923 0.000 1.000
#> SRR1617444 2 0.8327 0.702 0.264 0.736
#> SRR1617445 2 0.8327 0.702 0.264 0.736
#> SRR1617446 1 0.0000 0.951 1.000 0.000
#> SRR1617447 1 0.0000 0.951 1.000 0.000
#> SRR1617448 1 0.0000 0.951 1.000 0.000
#> SRR1617449 1 0.0000 0.951 1.000 0.000
#> SRR1617451 2 0.0672 0.926 0.008 0.992
#> SRR1617450 2 0.0672 0.926 0.008 0.992
#> SRR1617452 2 0.8327 0.702 0.264 0.736
#> SRR1617454 2 0.0672 0.926 0.008 0.992
#> SRR1617453 2 0.8327 0.702 0.264 0.736
#> SRR1617456 2 0.0672 0.926 0.008 0.992
#> SRR1617457 2 0.0672 0.926 0.008 0.992
#> SRR1617455 2 0.0672 0.926 0.008 0.992
#> SRR1617458 2 0.0672 0.926 0.008 0.992
#> SRR1617459 2 0.0672 0.926 0.008 0.992
#> SRR1617460 2 0.0938 0.924 0.012 0.988
#> SRR1617461 2 0.0938 0.924 0.012 0.988
#> SRR1617463 2 0.0938 0.924 0.012 0.988
#> SRR1617462 2 0.0938 0.924 0.012 0.988
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.0892 0.953 0.000 0.980 0.020
#> SRR1617431 2 0.0892 0.953 0.000 0.980 0.020
#> SRR1617410 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617411 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617412 3 0.0000 0.990 0.000 0.000 1.000
#> SRR1617413 3 0.0000 0.990 0.000 0.000 1.000
#> SRR1617414 1 0.4121 0.788 0.832 0.168 0.000
#> SRR1617415 1 0.4178 0.783 0.828 0.172 0.000
#> SRR1617416 2 0.1315 0.949 0.020 0.972 0.008
#> SRR1617417 2 0.1315 0.949 0.020 0.972 0.008
#> SRR1617418 3 0.0000 0.990 0.000 0.000 1.000
#> SRR1617419 3 0.0000 0.990 0.000 0.000 1.000
#> SRR1617420 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617421 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617422 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617423 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617424 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617425 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617427 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617426 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617428 2 0.0848 0.956 0.008 0.984 0.008
#> SRR1617429 2 0.0848 0.956 0.008 0.984 0.008
#> SRR1617432 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617433 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617434 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617436 3 0.1529 0.960 0.000 0.040 0.960
#> SRR1617435 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617437 3 0.1529 0.960 0.000 0.040 0.960
#> SRR1617438 3 0.0000 0.990 0.000 0.000 1.000
#> SRR1617439 3 0.0000 0.990 0.000 0.000 1.000
#> SRR1617440 2 0.6045 0.424 0.000 0.620 0.380
#> SRR1617441 2 0.6045 0.424 0.000 0.620 0.380
#> SRR1617443 3 0.0000 0.990 0.000 0.000 1.000
#> SRR1617442 3 0.0000 0.990 0.000 0.000 1.000
#> SRR1617444 2 0.1585 0.943 0.028 0.964 0.008
#> SRR1617445 2 0.1585 0.943 0.028 0.964 0.008
#> SRR1617446 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617447 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617448 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617449 1 0.0000 0.978 1.000 0.000 0.000
#> SRR1617451 2 0.0000 0.955 0.000 1.000 0.000
#> SRR1617450 2 0.0000 0.955 0.000 1.000 0.000
#> SRR1617452 2 0.0848 0.956 0.008 0.984 0.008
#> SRR1617454 2 0.0000 0.955 0.000 1.000 0.000
#> SRR1617453 2 0.0848 0.956 0.008 0.984 0.008
#> SRR1617456 2 0.0237 0.955 0.000 0.996 0.004
#> SRR1617457 2 0.0237 0.955 0.000 0.996 0.004
#> SRR1617455 2 0.0000 0.955 0.000 1.000 0.000
#> SRR1617458 2 0.0000 0.955 0.000 1.000 0.000
#> SRR1617459 2 0.0000 0.955 0.000 1.000 0.000
#> SRR1617460 2 0.0424 0.956 0.000 0.992 0.008
#> SRR1617461 2 0.0424 0.956 0.000 0.992 0.008
#> SRR1617463 2 0.0424 0.956 0.000 0.992 0.008
#> SRR1617462 2 0.0424 0.956 0.000 0.992 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.3448 0.643 0.000 0.828 0.004 0.168
#> SRR1617431 2 0.3448 0.643 0.000 0.828 0.004 0.168
#> SRR1617410 1 0.0188 0.988 0.996 0.000 0.004 0.000
#> SRR1617411 1 0.0188 0.988 0.996 0.000 0.004 0.000
#> SRR1617412 3 0.0000 0.905 0.000 0.000 1.000 0.000
#> SRR1617413 3 0.0000 0.905 0.000 0.000 1.000 0.000
#> SRR1617414 1 0.1798 0.933 0.944 0.016 0.000 0.040
#> SRR1617415 1 0.1798 0.933 0.944 0.016 0.000 0.040
#> SRR1617416 4 0.4817 0.621 0.088 0.128 0.000 0.784
#> SRR1617417 4 0.4817 0.621 0.088 0.128 0.000 0.784
#> SRR1617418 3 0.0000 0.905 0.000 0.000 1.000 0.000
#> SRR1617419 3 0.0000 0.905 0.000 0.000 1.000 0.000
#> SRR1617420 1 0.0188 0.988 0.996 0.000 0.004 0.000
#> SRR1617421 1 0.0188 0.988 0.996 0.000 0.004 0.000
#> SRR1617422 1 0.0564 0.986 0.988 0.004 0.004 0.004
#> SRR1617423 1 0.0524 0.983 0.988 0.004 0.000 0.008
#> SRR1617424 1 0.0376 0.987 0.992 0.004 0.004 0.000
#> SRR1617425 1 0.0376 0.987 0.992 0.004 0.004 0.000
#> SRR1617427 1 0.0188 0.987 0.996 0.004 0.000 0.000
#> SRR1617426 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> SRR1617428 4 0.4879 0.620 0.092 0.128 0.000 0.780
#> SRR1617429 4 0.4879 0.620 0.092 0.128 0.000 0.780
#> SRR1617432 1 0.0524 0.985 0.988 0.000 0.004 0.008
#> SRR1617433 1 0.0524 0.985 0.988 0.000 0.004 0.008
#> SRR1617434 1 0.0336 0.984 0.992 0.000 0.000 0.008
#> SRR1617436 3 0.0000 0.905 0.000 0.000 1.000 0.000
#> SRR1617435 1 0.0336 0.984 0.992 0.000 0.000 0.008
#> SRR1617437 3 0.0000 0.905 0.000 0.000 1.000 0.000
#> SRR1617438 3 0.0000 0.905 0.000 0.000 1.000 0.000
#> SRR1617439 3 0.0000 0.905 0.000 0.000 1.000 0.000
#> SRR1617440 3 0.7138 0.253 0.000 0.296 0.540 0.164
#> SRR1617441 3 0.7138 0.253 0.000 0.296 0.540 0.164
#> SRR1617443 3 0.0000 0.905 0.000 0.000 1.000 0.000
#> SRR1617442 3 0.0000 0.905 0.000 0.000 1.000 0.000
#> SRR1617444 4 0.8012 0.373 0.268 0.360 0.004 0.368
#> SRR1617445 4 0.8012 0.373 0.268 0.360 0.004 0.368
#> SRR1617446 1 0.0188 0.987 0.996 0.004 0.000 0.000
#> SRR1617447 1 0.0188 0.987 0.996 0.004 0.000 0.000
#> SRR1617448 1 0.0376 0.987 0.992 0.004 0.004 0.000
#> SRR1617449 1 0.0376 0.987 0.992 0.004 0.004 0.000
#> SRR1617451 2 0.0592 0.829 0.000 0.984 0.000 0.016
#> SRR1617450 2 0.0592 0.829 0.000 0.984 0.000 0.016
#> SRR1617452 4 0.1022 0.588 0.000 0.032 0.000 0.968
#> SRR1617454 2 0.0336 0.833 0.000 0.992 0.000 0.008
#> SRR1617453 4 0.1022 0.588 0.000 0.032 0.000 0.968
#> SRR1617456 2 0.2921 0.815 0.000 0.860 0.000 0.140
#> SRR1617457 2 0.2921 0.815 0.000 0.860 0.000 0.140
#> SRR1617455 2 0.0336 0.833 0.000 0.992 0.000 0.008
#> SRR1617458 2 0.2921 0.815 0.000 0.860 0.000 0.140
#> SRR1617459 2 0.2921 0.815 0.000 0.860 0.000 0.140
#> SRR1617460 4 0.4643 0.385 0.000 0.344 0.000 0.656
#> SRR1617461 4 0.4643 0.385 0.000 0.344 0.000 0.656
#> SRR1617463 4 0.4679 0.372 0.000 0.352 0.000 0.648
#> SRR1617462 4 0.4679 0.372 0.000 0.352 0.000 0.648
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 2 0.0510 0.8469 0.000 0.984 0.000 0.000 0.016
#> SRR1617431 2 0.0510 0.8469 0.000 0.984 0.000 0.000 0.016
#> SRR1617410 1 0.1012 0.8985 0.968 0.000 0.000 0.012 0.020
#> SRR1617411 1 0.1012 0.8985 0.968 0.000 0.000 0.012 0.020
#> SRR1617412 3 0.0000 0.8881 0.000 0.000 1.000 0.000 0.000
#> SRR1617413 3 0.0000 0.8881 0.000 0.000 1.000 0.000 0.000
#> SRR1617414 1 0.3898 0.8112 0.832 0.084 0.000 0.044 0.040
#> SRR1617415 1 0.3898 0.8112 0.832 0.084 0.000 0.044 0.040
#> SRR1617416 4 0.1872 0.8893 0.020 0.000 0.000 0.928 0.052
#> SRR1617417 4 0.1872 0.8893 0.020 0.000 0.000 0.928 0.052
#> SRR1617418 3 0.0000 0.8881 0.000 0.000 1.000 0.000 0.000
#> SRR1617419 3 0.0000 0.8881 0.000 0.000 1.000 0.000 0.000
#> SRR1617420 1 0.1399 0.8933 0.952 0.000 0.000 0.020 0.028
#> SRR1617421 1 0.1399 0.8933 0.952 0.000 0.000 0.020 0.028
#> SRR1617422 1 0.0898 0.8984 0.972 0.000 0.000 0.008 0.020
#> SRR1617423 1 0.0898 0.8984 0.972 0.000 0.000 0.008 0.020
#> SRR1617424 1 0.0000 0.9007 1.000 0.000 0.000 0.000 0.000
#> SRR1617425 1 0.0000 0.9007 1.000 0.000 0.000 0.000 0.000
#> SRR1617427 1 0.2221 0.8774 0.912 0.000 0.000 0.036 0.052
#> SRR1617426 1 0.2221 0.8774 0.912 0.000 0.000 0.036 0.052
#> SRR1617428 4 0.1743 0.8847 0.028 0.004 0.000 0.940 0.028
#> SRR1617429 4 0.1743 0.8847 0.028 0.004 0.000 0.940 0.028
#> SRR1617432 1 0.1549 0.8922 0.944 0.000 0.000 0.016 0.040
#> SRR1617433 1 0.1549 0.8922 0.944 0.000 0.000 0.016 0.040
#> SRR1617434 1 0.1444 0.8925 0.948 0.000 0.000 0.012 0.040
#> SRR1617436 3 0.0404 0.8822 0.000 0.000 0.988 0.000 0.012
#> SRR1617435 1 0.1444 0.8925 0.948 0.000 0.000 0.012 0.040
#> SRR1617437 3 0.0404 0.8822 0.000 0.000 0.988 0.000 0.012
#> SRR1617438 3 0.0000 0.8881 0.000 0.000 1.000 0.000 0.000
#> SRR1617439 3 0.0000 0.8881 0.000 0.000 1.000 0.000 0.000
#> SRR1617440 3 0.5114 -0.0202 0.000 0.476 0.488 0.000 0.036
#> SRR1617441 3 0.5114 -0.0202 0.000 0.476 0.488 0.000 0.036
#> SRR1617443 3 0.0000 0.8881 0.000 0.000 1.000 0.000 0.000
#> SRR1617442 3 0.0000 0.8881 0.000 0.000 1.000 0.000 0.000
#> SRR1617444 1 0.7478 -0.0473 0.400 0.220 0.000 0.336 0.044
#> SRR1617445 1 0.7478 -0.0473 0.400 0.220 0.000 0.336 0.044
#> SRR1617446 1 0.0451 0.9007 0.988 0.000 0.000 0.004 0.008
#> SRR1617447 1 0.0451 0.9007 0.988 0.000 0.000 0.004 0.008
#> SRR1617448 1 0.0794 0.8986 0.972 0.000 0.000 0.028 0.000
#> SRR1617449 1 0.0794 0.8986 0.972 0.000 0.000 0.028 0.000
#> SRR1617451 2 0.0162 0.8529 0.000 0.996 0.000 0.004 0.000
#> SRR1617450 2 0.0162 0.8529 0.000 0.996 0.000 0.004 0.000
#> SRR1617452 4 0.1485 0.8799 0.000 0.032 0.000 0.948 0.020
#> SRR1617454 2 0.0162 0.8523 0.000 0.996 0.000 0.004 0.000
#> SRR1617453 4 0.1485 0.8799 0.000 0.032 0.000 0.948 0.020
#> SRR1617456 2 0.3932 0.7851 0.000 0.672 0.000 0.000 0.328
#> SRR1617457 2 0.3932 0.7851 0.000 0.672 0.000 0.000 0.328
#> SRR1617455 2 0.0162 0.8523 0.000 0.996 0.000 0.004 0.000
#> SRR1617458 2 0.3932 0.7851 0.000 0.672 0.000 0.000 0.328
#> SRR1617459 2 0.3932 0.7851 0.000 0.672 0.000 0.000 0.328
#> SRR1617460 5 0.5731 0.9948 0.000 0.104 0.000 0.328 0.568
#> SRR1617461 5 0.5731 0.9948 0.000 0.104 0.000 0.328 0.568
#> SRR1617463 5 0.5717 0.9949 0.000 0.104 0.000 0.324 0.572
#> SRR1617462 5 0.5717 0.9949 0.000 0.104 0.000 0.324 0.572
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.3652 0.499 0.000 0.672 0.000 0.000 NA 0.004
#> SRR1617431 2 0.3652 0.499 0.000 0.672 0.000 0.000 NA 0.004
#> SRR1617410 1 0.1138 0.828 0.960 0.000 0.000 0.004 NA 0.012
#> SRR1617411 1 0.1138 0.828 0.960 0.000 0.000 0.004 NA 0.012
#> SRR1617412 3 0.0000 0.905 0.000 0.000 1.000 0.000 NA 0.000
#> SRR1617413 3 0.0000 0.905 0.000 0.000 1.000 0.000 NA 0.000
#> SRR1617414 1 0.5655 0.589 0.548 0.000 0.000 0.180 NA 0.004
#> SRR1617415 1 0.5655 0.589 0.548 0.000 0.000 0.180 NA 0.004
#> SRR1617416 4 0.2979 0.861 0.004 0.000 0.000 0.804 NA 0.188
#> SRR1617417 4 0.2979 0.861 0.004 0.000 0.000 0.804 NA 0.188
#> SRR1617418 3 0.0000 0.905 0.000 0.000 1.000 0.000 NA 0.000
#> SRR1617419 3 0.0000 0.905 0.000 0.000 1.000 0.000 NA 0.000
#> SRR1617420 1 0.2554 0.828 0.876 0.000 0.000 0.028 NA 0.004
#> SRR1617421 1 0.2554 0.828 0.876 0.000 0.000 0.028 NA 0.004
#> SRR1617422 1 0.4535 0.748 0.704 0.000 0.000 0.148 NA 0.000
#> SRR1617423 1 0.4535 0.748 0.704 0.000 0.000 0.148 NA 0.000
#> SRR1617424 1 0.0146 0.836 0.996 0.000 0.000 0.000 NA 0.000
#> SRR1617425 1 0.0405 0.837 0.988 0.000 0.000 0.004 NA 0.000
#> SRR1617427 1 0.4377 0.756 0.720 0.000 0.000 0.160 NA 0.000
#> SRR1617426 1 0.4377 0.756 0.720 0.000 0.000 0.160 NA 0.000
#> SRR1617428 4 0.3934 0.712 0.008 0.000 0.000 0.616 NA 0.376
#> SRR1617429 4 0.3934 0.712 0.008 0.000 0.000 0.616 NA 0.376
#> SRR1617432 1 0.2030 0.803 0.908 0.000 0.000 0.000 NA 0.028
#> SRR1617433 1 0.2030 0.803 0.908 0.000 0.000 0.000 NA 0.028
#> SRR1617434 1 0.2030 0.803 0.908 0.000 0.000 0.000 NA 0.028
#> SRR1617436 3 0.0458 0.897 0.000 0.000 0.984 0.000 NA 0.000
#> SRR1617435 1 0.2173 0.803 0.904 0.000 0.000 0.004 NA 0.028
#> SRR1617437 3 0.0458 0.897 0.000 0.000 0.984 0.000 NA 0.000
#> SRR1617438 3 0.0000 0.905 0.000 0.000 1.000 0.000 NA 0.000
#> SRR1617439 3 0.0000 0.905 0.000 0.000 1.000 0.000 NA 0.000
#> SRR1617440 3 0.5571 0.317 0.000 0.144 0.484 0.000 NA 0.000
#> SRR1617441 3 0.5571 0.317 0.000 0.144 0.484 0.000 NA 0.000
#> SRR1617443 3 0.0000 0.905 0.000 0.000 1.000 0.000 NA 0.000
#> SRR1617442 3 0.0000 0.905 0.000 0.000 1.000 0.000 NA 0.000
#> SRR1617444 6 0.6604 0.297 0.296 0.008 0.000 0.012 NA 0.372
#> SRR1617445 6 0.6604 0.297 0.296 0.008 0.000 0.012 NA 0.372
#> SRR1617446 1 0.0000 0.836 1.000 0.000 0.000 0.000 NA 0.000
#> SRR1617447 1 0.0000 0.836 1.000 0.000 0.000 0.000 NA 0.000
#> SRR1617448 1 0.3550 0.802 0.816 0.000 0.000 0.044 NA 0.020
#> SRR1617449 1 0.3550 0.802 0.816 0.000 0.000 0.044 NA 0.020
#> SRR1617451 2 0.0146 0.717 0.000 0.996 0.000 0.000 NA 0.004
#> SRR1617450 2 0.0146 0.717 0.000 0.996 0.000 0.000 NA 0.004
#> SRR1617452 4 0.3345 0.859 0.000 0.028 0.000 0.788 NA 0.184
#> SRR1617454 2 0.0146 0.717 0.000 0.996 0.000 0.004 NA 0.000
#> SRR1617453 4 0.3345 0.859 0.000 0.028 0.000 0.788 NA 0.184
#> SRR1617456 2 0.3847 0.655 0.000 0.544 0.000 0.000 NA 0.000
#> SRR1617457 2 0.3847 0.655 0.000 0.544 0.000 0.000 NA 0.000
#> SRR1617455 2 0.0146 0.717 0.000 0.996 0.000 0.004 NA 0.000
#> SRR1617458 2 0.3847 0.655 0.000 0.544 0.000 0.000 NA 0.000
#> SRR1617459 2 0.3847 0.655 0.000 0.544 0.000 0.000 NA 0.000
#> SRR1617460 6 0.0713 0.603 0.000 0.028 0.000 0.000 NA 0.972
#> SRR1617461 6 0.0713 0.603 0.000 0.028 0.000 0.000 NA 0.972
#> SRR1617463 6 0.0713 0.603 0.000 0.028 0.000 0.000 NA 0.972
#> SRR1617462 6 0.0713 0.603 0.000 0.028 0.000 0.000 NA 0.972
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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 6.
#>
#> 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 0.974 0.989 0.4691 0.525 0.525
#> 3 3 0.973 0.965 0.983 0.3972 0.793 0.616
#> 4 4 0.853 0.824 0.812 0.1117 0.866 0.627
#> 5 5 0.946 0.958 0.954 0.0833 0.964 0.850
#> 6 6 0.916 0.848 0.902 0.0468 0.944 0.743
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 5
There is also optional best \(k\) = 2 3 5 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
#> SRR1617430 2 0.000 0.968 0.000 1.000
#> SRR1617431 2 0.000 0.968 0.000 1.000
#> SRR1617410 1 0.000 1.000 1.000 0.000
#> SRR1617411 1 0.000 1.000 1.000 0.000
#> SRR1617412 1 0.000 1.000 1.000 0.000
#> SRR1617413 1 0.000 1.000 1.000 0.000
#> SRR1617414 1 0.000 1.000 1.000 0.000
#> SRR1617415 1 0.000 1.000 1.000 0.000
#> SRR1617416 1 0.000 1.000 1.000 0.000
#> SRR1617417 1 0.000 1.000 1.000 0.000
#> SRR1617418 1 0.000 1.000 1.000 0.000
#> SRR1617419 1 0.000 1.000 1.000 0.000
#> SRR1617420 1 0.000 1.000 1.000 0.000
#> SRR1617421 1 0.000 1.000 1.000 0.000
#> SRR1617422 1 0.000 1.000 1.000 0.000
#> SRR1617423 1 0.000 1.000 1.000 0.000
#> SRR1617424 1 0.000 1.000 1.000 0.000
#> SRR1617425 1 0.000 1.000 1.000 0.000
#> SRR1617427 1 0.000 1.000 1.000 0.000
#> SRR1617426 1 0.000 1.000 1.000 0.000
#> SRR1617428 2 0.904 0.553 0.320 0.680
#> SRR1617429 2 0.850 0.635 0.276 0.724
#> SRR1617432 1 0.000 1.000 1.000 0.000
#> SRR1617433 1 0.000 1.000 1.000 0.000
#> SRR1617434 1 0.000 1.000 1.000 0.000
#> SRR1617436 1 0.000 1.000 1.000 0.000
#> SRR1617435 1 0.000 1.000 1.000 0.000
#> SRR1617437 1 0.000 1.000 1.000 0.000
#> SRR1617438 1 0.000 1.000 1.000 0.000
#> SRR1617439 1 0.000 1.000 1.000 0.000
#> SRR1617440 2 0.000 0.968 0.000 1.000
#> SRR1617441 2 0.000 0.968 0.000 1.000
#> SRR1617443 1 0.000 1.000 1.000 0.000
#> SRR1617442 1 0.000 1.000 1.000 0.000
#> SRR1617444 1 0.000 1.000 1.000 0.000
#> SRR1617445 1 0.000 1.000 1.000 0.000
#> SRR1617446 1 0.000 1.000 1.000 0.000
#> SRR1617447 1 0.000 1.000 1.000 0.000
#> SRR1617448 1 0.000 1.000 1.000 0.000
#> SRR1617449 1 0.000 1.000 1.000 0.000
#> SRR1617451 2 0.000 0.968 0.000 1.000
#> SRR1617450 2 0.000 0.968 0.000 1.000
#> SRR1617452 2 0.000 0.968 0.000 1.000
#> SRR1617454 2 0.000 0.968 0.000 1.000
#> SRR1617453 2 0.000 0.968 0.000 1.000
#> SRR1617456 2 0.000 0.968 0.000 1.000
#> SRR1617457 2 0.000 0.968 0.000 1.000
#> SRR1617455 2 0.000 0.968 0.000 1.000
#> SRR1617458 2 0.000 0.968 0.000 1.000
#> SRR1617459 2 0.000 0.968 0.000 1.000
#> SRR1617460 2 0.000 0.968 0.000 1.000
#> SRR1617461 2 0.000 0.968 0.000 1.000
#> SRR1617463 2 0.000 0.968 0.000 1.000
#> SRR1617462 2 0.000 0.968 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.000 0.966 0.000 1.000 0.000
#> SRR1617431 2 0.000 0.966 0.000 1.000 0.000
#> SRR1617410 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617411 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617412 3 0.000 1.000 0.000 0.000 1.000
#> SRR1617413 3 0.000 1.000 0.000 0.000 1.000
#> SRR1617414 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617415 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617416 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617417 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617418 3 0.000 1.000 0.000 0.000 1.000
#> SRR1617419 3 0.000 1.000 0.000 0.000 1.000
#> SRR1617420 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617421 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617422 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617423 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617424 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617425 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617427 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617426 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617428 2 0.745 0.655 0.184 0.696 0.120
#> SRR1617429 2 0.714 0.686 0.160 0.720 0.120
#> SRR1617432 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617433 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617434 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617436 3 0.000 1.000 0.000 0.000 1.000
#> SRR1617435 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617437 3 0.000 1.000 0.000 0.000 1.000
#> SRR1617438 3 0.000 1.000 0.000 0.000 1.000
#> SRR1617439 3 0.000 1.000 0.000 0.000 1.000
#> SRR1617440 3 0.000 1.000 0.000 0.000 1.000
#> SRR1617441 3 0.000 1.000 0.000 0.000 1.000
#> SRR1617443 3 0.000 1.000 0.000 0.000 1.000
#> SRR1617442 3 0.000 1.000 0.000 0.000 1.000
#> SRR1617444 1 0.532 0.817 0.824 0.072 0.104
#> SRR1617445 1 0.542 0.813 0.820 0.080 0.100
#> SRR1617446 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617447 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617448 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617449 1 0.000 0.985 1.000 0.000 0.000
#> SRR1617451 2 0.000 0.966 0.000 1.000 0.000
#> SRR1617450 2 0.000 0.966 0.000 1.000 0.000
#> SRR1617452 2 0.000 0.966 0.000 1.000 0.000
#> SRR1617454 2 0.000 0.966 0.000 1.000 0.000
#> SRR1617453 2 0.000 0.966 0.000 1.000 0.000
#> SRR1617456 2 0.000 0.966 0.000 1.000 0.000
#> SRR1617457 2 0.000 0.966 0.000 1.000 0.000
#> SRR1617455 2 0.000 0.966 0.000 1.000 0.000
#> SRR1617458 2 0.000 0.966 0.000 1.000 0.000
#> SRR1617459 2 0.000 0.966 0.000 1.000 0.000
#> SRR1617460 2 0.000 0.966 0.000 1.000 0.000
#> SRR1617461 2 0.000 0.966 0.000 1.000 0.000
#> SRR1617463 2 0.000 0.966 0.000 1.000 0.000
#> SRR1617462 2 0.000 0.966 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.4977 0.564 0.000 0.540 0.000 0.460
#> SRR1617431 2 0.4977 0.564 0.000 0.540 0.000 0.460
#> SRR1617410 4 0.4999 0.709 0.492 0.000 0.000 0.508
#> SRR1617411 4 0.4999 0.709 0.492 0.000 0.000 0.508
#> SRR1617412 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR1617413 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR1617414 4 0.4998 0.706 0.488 0.000 0.000 0.512
#> SRR1617415 4 0.4998 0.706 0.488 0.000 0.000 0.512
#> SRR1617416 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR1617417 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR1617418 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR1617419 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR1617420 4 0.4999 0.709 0.492 0.000 0.000 0.508
#> SRR1617421 4 0.4999 0.709 0.492 0.000 0.000 0.508
#> SRR1617422 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR1617423 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR1617424 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR1617425 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR1617427 1 0.0592 0.894 0.984 0.000 0.000 0.016
#> SRR1617426 1 0.0592 0.894 0.984 0.000 0.000 0.016
#> SRR1617428 4 0.7774 -0.339 0.060 0.324 0.084 0.532
#> SRR1617429 4 0.7774 -0.339 0.060 0.324 0.084 0.532
#> SRR1617432 4 0.4999 0.709 0.492 0.000 0.000 0.508
#> SRR1617433 4 0.4999 0.709 0.492 0.000 0.000 0.508
#> SRR1617434 4 0.4999 0.709 0.492 0.000 0.000 0.508
#> SRR1617436 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR1617435 4 0.4999 0.709 0.492 0.000 0.000 0.508
#> SRR1617437 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR1617438 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR1617439 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR1617440 3 0.0336 0.994 0.000 0.000 0.992 0.008
#> SRR1617441 3 0.0336 0.994 0.000 0.000 0.992 0.008
#> SRR1617443 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR1617442 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> SRR1617444 1 0.4604 0.548 0.756 0.224 0.008 0.012
#> SRR1617445 1 0.4533 0.540 0.752 0.232 0.004 0.012
#> SRR1617446 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR1617447 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR1617448 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR1617449 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> SRR1617451 2 0.2149 0.892 0.000 0.912 0.000 0.088
#> SRR1617450 2 0.2216 0.890 0.000 0.908 0.000 0.092
#> SRR1617452 2 0.0188 0.931 0.000 0.996 0.000 0.004
#> SRR1617454 2 0.0817 0.925 0.000 0.976 0.000 0.024
#> SRR1617453 2 0.0188 0.931 0.000 0.996 0.000 0.004
#> SRR1617456 2 0.0336 0.931 0.000 0.992 0.000 0.008
#> SRR1617457 2 0.0336 0.931 0.000 0.992 0.000 0.008
#> SRR1617455 2 0.0817 0.925 0.000 0.976 0.000 0.024
#> SRR1617458 2 0.0336 0.931 0.000 0.992 0.000 0.008
#> SRR1617459 2 0.0336 0.931 0.000 0.992 0.000 0.008
#> SRR1617460 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> SRR1617461 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> SRR1617463 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> SRR1617462 2 0.0000 0.932 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
#> SRR1617430 4 0.0794 0.975 0.000 0.028 0.000 0.972 0.000
#> SRR1617431 4 0.0794 0.975 0.000 0.028 0.000 0.972 0.000
#> SRR1617410 5 0.1732 0.998 0.080 0.000 0.000 0.000 0.920
#> SRR1617411 5 0.1732 0.998 0.080 0.000 0.000 0.000 0.920
#> SRR1617412 3 0.0912 0.970 0.000 0.000 0.972 0.016 0.012
#> SRR1617413 3 0.0912 0.970 0.000 0.000 0.972 0.016 0.012
#> SRR1617414 5 0.1732 0.998 0.080 0.000 0.000 0.000 0.920
#> SRR1617415 5 0.1732 0.998 0.080 0.000 0.000 0.000 0.920
#> SRR1617416 1 0.0609 0.973 0.980 0.000 0.000 0.000 0.020
#> SRR1617417 1 0.0609 0.973 0.980 0.000 0.000 0.000 0.020
#> SRR1617418 3 0.0798 0.972 0.000 0.000 0.976 0.016 0.008
#> SRR1617419 3 0.0798 0.972 0.000 0.000 0.976 0.016 0.008
#> SRR1617420 5 0.1732 0.998 0.080 0.000 0.000 0.000 0.920
#> SRR1617421 5 0.1732 0.998 0.080 0.000 0.000 0.000 0.920
#> SRR1617422 1 0.0290 0.976 0.992 0.000 0.000 0.000 0.008
#> SRR1617423 1 0.0290 0.976 0.992 0.000 0.000 0.000 0.008
#> SRR1617424 1 0.0404 0.976 0.988 0.000 0.000 0.000 0.012
#> SRR1617425 1 0.0404 0.976 0.988 0.000 0.000 0.000 0.012
#> SRR1617427 1 0.0865 0.968 0.972 0.000 0.000 0.004 0.024
#> SRR1617426 1 0.0865 0.968 0.972 0.000 0.000 0.004 0.024
#> SRR1617428 4 0.0960 0.975 0.004 0.000 0.008 0.972 0.016
#> SRR1617429 4 0.0960 0.975 0.004 0.000 0.008 0.972 0.016
#> SRR1617432 5 0.1892 0.997 0.080 0.000 0.000 0.004 0.916
#> SRR1617433 5 0.1892 0.997 0.080 0.000 0.000 0.004 0.916
#> SRR1617434 5 0.1892 0.997 0.080 0.000 0.000 0.004 0.916
#> SRR1617436 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> SRR1617435 5 0.1892 0.997 0.080 0.000 0.000 0.004 0.916
#> SRR1617437 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> SRR1617438 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> SRR1617439 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> SRR1617440 3 0.2130 0.921 0.000 0.016 0.924 0.016 0.044
#> SRR1617441 3 0.2130 0.921 0.000 0.016 0.924 0.016 0.044
#> SRR1617443 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> SRR1617442 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> SRR1617444 1 0.2288 0.906 0.924 0.020 0.020 0.008 0.028
#> SRR1617445 1 0.2288 0.906 0.924 0.020 0.020 0.008 0.028
#> SRR1617446 1 0.0290 0.977 0.992 0.000 0.000 0.000 0.008
#> SRR1617447 1 0.0290 0.977 0.992 0.000 0.000 0.000 0.008
#> SRR1617448 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> SRR1617449 1 0.0000 0.974 1.000 0.000 0.000 0.000 0.000
#> SRR1617451 2 0.3438 0.824 0.000 0.808 0.000 0.172 0.020
#> SRR1617450 2 0.3438 0.824 0.000 0.808 0.000 0.172 0.020
#> SRR1617452 2 0.0968 0.932 0.004 0.972 0.000 0.012 0.012
#> SRR1617454 2 0.1942 0.911 0.000 0.920 0.000 0.068 0.012
#> SRR1617453 2 0.0968 0.932 0.004 0.972 0.000 0.012 0.012
#> SRR1617456 2 0.1626 0.928 0.000 0.940 0.000 0.016 0.044
#> SRR1617457 2 0.1626 0.928 0.000 0.940 0.000 0.016 0.044
#> SRR1617455 2 0.1877 0.913 0.000 0.924 0.000 0.064 0.012
#> SRR1617458 2 0.1626 0.928 0.000 0.940 0.000 0.016 0.044
#> SRR1617459 2 0.1626 0.928 0.000 0.940 0.000 0.016 0.044
#> SRR1617460 2 0.1211 0.925 0.024 0.960 0.000 0.000 0.016
#> SRR1617461 2 0.1211 0.925 0.024 0.960 0.000 0.000 0.016
#> SRR1617463 2 0.1117 0.927 0.020 0.964 0.000 0.000 0.016
#> SRR1617462 2 0.1117 0.927 0.020 0.964 0.000 0.000 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 4 0.0363 0.9913 0.000 0.012 0.000 0.988 0.000 0.000
#> SRR1617431 4 0.0363 0.9913 0.000 0.012 0.000 0.988 0.000 0.000
#> SRR1617410 5 0.0000 0.9985 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617411 5 0.0000 0.9985 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617412 3 0.0790 0.8613 0.000 0.000 0.968 0.000 0.000 0.032
#> SRR1617413 3 0.0790 0.8613 0.000 0.000 0.968 0.000 0.000 0.032
#> SRR1617414 5 0.0146 0.9978 0.000 0.000 0.000 0.000 0.996 0.004
#> SRR1617415 5 0.0146 0.9978 0.000 0.000 0.000 0.000 0.996 0.004
#> SRR1617416 1 0.1074 0.9611 0.960 0.012 0.000 0.000 0.000 0.028
#> SRR1617417 1 0.1074 0.9611 0.960 0.012 0.000 0.000 0.000 0.028
#> SRR1617418 3 0.0000 0.8778 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617419 3 0.0000 0.8778 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617420 5 0.0000 0.9985 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617421 5 0.0000 0.9985 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617422 1 0.0508 0.9757 0.984 0.004 0.000 0.000 0.000 0.012
#> SRR1617423 1 0.0508 0.9757 0.984 0.004 0.000 0.000 0.000 0.012
#> SRR1617424 1 0.0000 0.9805 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617425 1 0.0000 0.9805 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617427 1 0.0146 0.9794 0.996 0.000 0.004 0.000 0.000 0.000
#> SRR1617426 1 0.0146 0.9794 0.996 0.000 0.004 0.000 0.000 0.000
#> SRR1617428 4 0.0000 0.9913 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1617429 4 0.0000 0.9913 0.000 0.000 0.000 1.000 0.000 0.000
#> SRR1617432 5 0.0146 0.9978 0.000 0.000 0.000 0.000 0.996 0.004
#> SRR1617433 5 0.0146 0.9978 0.000 0.000 0.000 0.000 0.996 0.004
#> SRR1617434 5 0.0000 0.9985 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617436 3 0.2778 0.9120 0.000 0.000 0.824 0.008 0.000 0.168
#> SRR1617435 5 0.0000 0.9985 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617437 3 0.2778 0.9120 0.000 0.000 0.824 0.008 0.000 0.168
#> SRR1617438 3 0.2793 0.8995 0.000 0.000 0.800 0.000 0.000 0.200
#> SRR1617439 3 0.2793 0.8995 0.000 0.000 0.800 0.000 0.000 0.200
#> SRR1617440 6 0.2378 0.4912 0.000 0.000 0.152 0.000 0.000 0.848
#> SRR1617441 6 0.2378 0.4912 0.000 0.000 0.152 0.000 0.000 0.848
#> SRR1617443 3 0.2527 0.9126 0.000 0.000 0.832 0.000 0.000 0.168
#> SRR1617442 3 0.2527 0.9126 0.000 0.000 0.832 0.000 0.000 0.168
#> SRR1617444 1 0.1686 0.9345 0.924 0.012 0.000 0.000 0.000 0.064
#> SRR1617445 1 0.1686 0.9345 0.924 0.012 0.000 0.000 0.000 0.064
#> SRR1617446 1 0.0000 0.9805 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617447 1 0.0000 0.9805 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617448 1 0.0000 0.9805 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617449 1 0.0000 0.9805 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617451 6 0.5969 0.4451 0.000 0.244 0.000 0.316 0.000 0.440
#> SRR1617450 6 0.5969 0.4451 0.000 0.244 0.000 0.316 0.000 0.440
#> SRR1617452 2 0.3804 0.0699 0.000 0.576 0.000 0.000 0.000 0.424
#> SRR1617454 2 0.1124 0.7900 0.000 0.956 0.000 0.036 0.000 0.008
#> SRR1617453 2 0.3804 0.0699 0.000 0.576 0.000 0.000 0.000 0.424
#> SRR1617456 6 0.3309 0.6366 0.000 0.280 0.000 0.000 0.000 0.720
#> SRR1617457 6 0.3309 0.6366 0.000 0.280 0.000 0.000 0.000 0.720
#> SRR1617455 2 0.1124 0.7900 0.000 0.956 0.000 0.036 0.000 0.008
#> SRR1617458 6 0.3309 0.6366 0.000 0.280 0.000 0.000 0.000 0.720
#> SRR1617459 6 0.3309 0.6366 0.000 0.280 0.000 0.000 0.000 0.720
#> SRR1617460 2 0.0508 0.8022 0.004 0.984 0.000 0.000 0.000 0.012
#> SRR1617461 2 0.0508 0.8022 0.004 0.984 0.000 0.000 0.000 0.012
#> SRR1617463 2 0.0146 0.8027 0.004 0.996 0.000 0.000 0.000 0.000
#> SRR1617462 2 0.0000 0.8038 0.000 1.000 0.000 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["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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 1.000 1.000 1.000 0.0736 0.927 0.927
#> 3 3 1.000 0.972 0.988 2.0760 0.866 0.855
#> 4 4 0.665 0.661 0.886 0.7175 0.877 0.845
#> 5 5 0.716 0.872 0.928 0.2971 0.776 0.672
#> 6 6 0.925 0.865 0.927 0.0683 0.997 0.994
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
#> SRR1617430 2 0 1 0 1
#> SRR1617431 2 0 1 0 1
#> SRR1617410 1 0 1 1 0
#> SRR1617411 1 0 1 1 0
#> SRR1617412 1 0 1 1 0
#> SRR1617413 1 0 1 1 0
#> SRR1617414 1 0 1 1 0
#> SRR1617415 1 0 1 1 0
#> SRR1617416 1 0 1 1 0
#> SRR1617417 1 0 1 1 0
#> SRR1617418 1 0 1 1 0
#> SRR1617419 1 0 1 1 0
#> SRR1617420 1 0 1 1 0
#> SRR1617421 1 0 1 1 0
#> SRR1617422 1 0 1 1 0
#> SRR1617423 1 0 1 1 0
#> SRR1617424 1 0 1 1 0
#> SRR1617425 1 0 1 1 0
#> SRR1617427 1 0 1 1 0
#> SRR1617426 1 0 1 1 0
#> SRR1617428 1 0 1 1 0
#> SRR1617429 1 0 1 1 0
#> SRR1617432 1 0 1 1 0
#> SRR1617433 1 0 1 1 0
#> SRR1617434 1 0 1 1 0
#> SRR1617436 1 0 1 1 0
#> SRR1617435 1 0 1 1 0
#> SRR1617437 1 0 1 1 0
#> SRR1617438 1 0 1 1 0
#> SRR1617439 1 0 1 1 0
#> SRR1617440 1 0 1 1 0
#> SRR1617441 1 0 1 1 0
#> SRR1617443 1 0 1 1 0
#> SRR1617442 1 0 1 1 0
#> SRR1617444 1 0 1 1 0
#> SRR1617445 1 0 1 1 0
#> SRR1617446 1 0 1 1 0
#> SRR1617447 1 0 1 1 0
#> SRR1617448 1 0 1 1 0
#> SRR1617449 1 0 1 1 0
#> SRR1617451 1 0 1 1 0
#> SRR1617450 1 0 1 1 0
#> SRR1617452 1 0 1 1 0
#> SRR1617454 1 0 1 1 0
#> SRR1617453 1 0 1 1 0
#> SRR1617456 1 0 1 1 0
#> SRR1617457 1 0 1 1 0
#> SRR1617455 1 0 1 1 0
#> SRR1617458 1 0 1 1 0
#> SRR1617459 1 0 1 1 0
#> SRR1617460 1 0 1 1 0
#> SRR1617461 1 0 1 1 0
#> SRR1617463 1 0 1 1 0
#> SRR1617462 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 3 0.0000 1.000 0.000 0.000 1
#> SRR1617431 3 0.0000 1.000 0.000 0.000 1
#> SRR1617410 1 0.0000 0.986 1.000 0.000 0
#> SRR1617411 1 0.0000 0.986 1.000 0.000 0
#> SRR1617412 1 0.0000 0.986 1.000 0.000 0
#> SRR1617413 1 0.0000 0.986 1.000 0.000 0
#> SRR1617414 1 0.0000 0.986 1.000 0.000 0
#> SRR1617415 1 0.0000 0.986 1.000 0.000 0
#> SRR1617416 1 0.0000 0.986 1.000 0.000 0
#> SRR1617417 1 0.0000 0.986 1.000 0.000 0
#> SRR1617418 1 0.0000 0.986 1.000 0.000 0
#> SRR1617419 1 0.0000 0.986 1.000 0.000 0
#> SRR1617420 1 0.0000 0.986 1.000 0.000 0
#> SRR1617421 1 0.0000 0.986 1.000 0.000 0
#> SRR1617422 1 0.0000 0.986 1.000 0.000 0
#> SRR1617423 1 0.0000 0.986 1.000 0.000 0
#> SRR1617424 1 0.0000 0.986 1.000 0.000 0
#> SRR1617425 1 0.0000 0.986 1.000 0.000 0
#> SRR1617427 1 0.0000 0.986 1.000 0.000 0
#> SRR1617426 1 0.0000 0.986 1.000 0.000 0
#> SRR1617428 1 0.0000 0.986 1.000 0.000 0
#> SRR1617429 1 0.0000 0.986 1.000 0.000 0
#> SRR1617432 1 0.0000 0.986 1.000 0.000 0
#> SRR1617433 1 0.0000 0.986 1.000 0.000 0
#> SRR1617434 1 0.0000 0.986 1.000 0.000 0
#> SRR1617436 1 0.0000 0.986 1.000 0.000 0
#> SRR1617435 1 0.0000 0.986 1.000 0.000 0
#> SRR1617437 1 0.0000 0.986 1.000 0.000 0
#> SRR1617438 1 0.0000 0.986 1.000 0.000 0
#> SRR1617439 1 0.0000 0.986 1.000 0.000 0
#> SRR1617440 1 0.0000 0.986 1.000 0.000 0
#> SRR1617441 1 0.0000 0.986 1.000 0.000 0
#> SRR1617443 1 0.0000 0.986 1.000 0.000 0
#> SRR1617442 1 0.0000 0.986 1.000 0.000 0
#> SRR1617444 1 0.0000 0.986 1.000 0.000 0
#> SRR1617445 1 0.0000 0.986 1.000 0.000 0
#> SRR1617446 1 0.0000 0.986 1.000 0.000 0
#> SRR1617447 1 0.0000 0.986 1.000 0.000 0
#> SRR1617448 1 0.0000 0.986 1.000 0.000 0
#> SRR1617449 1 0.0000 0.986 1.000 0.000 0
#> SRR1617451 2 0.0000 1.000 0.000 1.000 0
#> SRR1617450 2 0.0000 1.000 0.000 1.000 0
#> SRR1617452 1 0.0000 0.986 1.000 0.000 0
#> SRR1617454 2 0.0000 1.000 0.000 1.000 0
#> SRR1617453 1 0.0000 0.986 1.000 0.000 0
#> SRR1617456 1 0.0424 0.980 0.992 0.008 0
#> SRR1617457 1 0.0424 0.980 0.992 0.008 0
#> SRR1617455 2 0.0000 1.000 0.000 1.000 0
#> SRR1617458 1 0.0424 0.980 0.992 0.008 0
#> SRR1617459 1 0.0424 0.980 0.992 0.008 0
#> SRR1617460 1 0.0592 0.977 0.988 0.012 0
#> SRR1617461 1 0.0592 0.977 0.988 0.012 0
#> SRR1617463 1 0.5560 0.585 0.700 0.300 0
#> SRR1617462 1 0.5560 0.585 0.700 0.300 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 3 0.4989 1.0000 0.000 0.000 0.528 0.472
#> SRR1617431 3 0.4989 1.0000 0.000 0.000 0.528 0.472
#> SRR1617410 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617411 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617412 1 0.0188 0.8008 0.996 0.000 0.004 0.000
#> SRR1617413 1 0.0188 0.8008 0.996 0.000 0.004 0.000
#> SRR1617414 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617415 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617416 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617417 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617418 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617419 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617420 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617421 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617422 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617423 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617424 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617425 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617427 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617426 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617428 1 0.4989 0.0616 0.528 0.000 0.472 0.000
#> SRR1617429 1 0.4989 0.0616 0.528 0.000 0.472 0.000
#> SRR1617432 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617433 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617434 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617436 1 0.4989 0.0616 0.528 0.000 0.472 0.000
#> SRR1617435 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617437 1 0.4989 0.0616 0.528 0.000 0.472 0.000
#> SRR1617438 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617439 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617440 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617441 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617443 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617442 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617444 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617445 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617446 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617447 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617448 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617449 1 0.0000 0.8059 1.000 0.000 0.000 0.000
#> SRR1617451 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> SRR1617450 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> SRR1617452 1 0.3873 0.1501 0.772 0.000 0.000 0.228
#> SRR1617454 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> SRR1617453 1 0.3873 0.1501 0.772 0.000 0.000 0.228
#> SRR1617456 4 0.4992 1.0000 0.476 0.000 0.000 0.524
#> SRR1617457 4 0.4992 1.0000 0.476 0.000 0.000 0.524
#> SRR1617455 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> SRR1617458 4 0.4992 1.0000 0.476 0.000 0.000 0.524
#> SRR1617459 4 0.4992 1.0000 0.476 0.000 0.000 0.524
#> SRR1617460 1 0.4605 -0.4183 0.664 0.000 0.000 0.336
#> SRR1617461 1 0.4605 -0.4183 0.664 0.000 0.000 0.336
#> SRR1617463 1 0.7883 -0.6966 0.376 0.288 0.000 0.336
#> SRR1617462 1 0.7883 -0.6966 0.376 0.288 0.000 0.336
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> SRR1617431 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> SRR1617410 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617411 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617412 1 0.0162 0.959 0.996 0.000 0.004 0 0.000
#> SRR1617413 1 0.0162 0.959 0.996 0.000 0.004 0 0.000
#> SRR1617414 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617415 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617416 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617417 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617418 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617419 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617420 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617421 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617422 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617423 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617424 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617425 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617427 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617426 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617428 3 0.3366 0.998 0.212 0.004 0.784 0 0.000
#> SRR1617429 3 0.3366 0.998 0.212 0.004 0.784 0 0.000
#> SRR1617432 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617433 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617434 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617436 3 0.3210 0.998 0.212 0.000 0.788 0 0.000
#> SRR1617435 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617437 3 0.3210 0.998 0.212 0.000 0.788 0 0.000
#> SRR1617438 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617439 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617440 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617441 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617443 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617442 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617444 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617445 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617446 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617447 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617448 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617449 1 0.0000 0.964 1.000 0.000 0.000 0 0.000
#> SRR1617451 5 0.0000 0.782 0.000 0.000 0.000 0 1.000
#> SRR1617450 5 0.0000 0.782 0.000 0.000 0.000 0 1.000
#> SRR1617452 1 0.4283 -0.087 0.544 0.456 0.000 0 0.000
#> SRR1617454 5 0.4974 0.786 0.000 0.092 0.212 0 0.696
#> SRR1617453 1 0.4283 -0.087 0.544 0.456 0.000 0 0.000
#> SRR1617456 2 0.2074 0.782 0.104 0.896 0.000 0 0.000
#> SRR1617457 2 0.2074 0.782 0.104 0.896 0.000 0 0.000
#> SRR1617455 5 0.4974 0.786 0.000 0.092 0.212 0 0.696
#> SRR1617458 2 0.2074 0.782 0.104 0.896 0.000 0 0.000
#> SRR1617459 2 0.2074 0.782 0.104 0.896 0.000 0 0.000
#> SRR1617460 2 0.3752 0.552 0.292 0.708 0.000 0 0.000
#> SRR1617461 2 0.3752 0.552 0.292 0.708 0.000 0 0.000
#> SRR1617463 2 0.3352 0.572 0.004 0.800 0.192 0 0.004
#> SRR1617462 2 0.3352 0.572 0.004 0.800 0.192 0 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> SRR1617431 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> SRR1617410 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617411 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617412 1 0.0363 0.957 0.988 0.000 0.000 0.012 0 0.000
#> SRR1617413 1 0.0363 0.957 0.988 0.000 0.000 0.012 0 0.000
#> SRR1617414 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617415 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617416 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617417 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617418 1 0.0260 0.960 0.992 0.000 0.000 0.008 0 0.000
#> SRR1617419 1 0.0260 0.960 0.992 0.000 0.000 0.008 0 0.000
#> SRR1617420 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617421 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617422 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617423 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617424 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617425 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617427 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617426 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617428 4 0.0865 1.000 0.036 0.000 0.000 0.964 0 0.000
#> SRR1617429 4 0.0865 1.000 0.036 0.000 0.000 0.964 0 0.000
#> SRR1617432 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617433 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617434 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617436 3 0.4453 1.000 0.036 0.000 0.592 0.372 0 0.000
#> SRR1617435 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617437 3 0.4453 1.000 0.036 0.000 0.592 0.372 0 0.000
#> SRR1617438 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617439 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617440 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617441 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617443 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617442 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617444 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617445 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617446 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617447 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617448 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617449 1 0.0000 0.967 1.000 0.000 0.000 0.000 0 0.000
#> SRR1617451 2 0.0000 0.722 0.000 1.000 0.000 0.000 0 0.000
#> SRR1617450 2 0.0000 0.722 0.000 1.000 0.000 0.000 0 0.000
#> SRR1617452 1 0.4591 -0.128 0.500 0.000 0.000 0.036 0 0.464
#> SRR1617454 2 0.5190 0.727 0.000 0.596 0.132 0.000 0 0.272
#> SRR1617453 1 0.4591 -0.128 0.500 0.000 0.000 0.036 0 0.464
#> SRR1617456 6 0.3534 0.744 0.008 0.000 0.276 0.000 0 0.716
#> SRR1617457 6 0.3534 0.744 0.008 0.000 0.276 0.000 0 0.716
#> SRR1617455 2 0.5190 0.727 0.000 0.596 0.132 0.000 0 0.272
#> SRR1617458 6 0.3534 0.744 0.008 0.000 0.276 0.000 0 0.716
#> SRR1617459 6 0.3534 0.744 0.008 0.000 0.276 0.000 0 0.716
#> SRR1617460 6 0.3309 0.517 0.280 0.000 0.000 0.000 0 0.720
#> SRR1617461 6 0.3309 0.517 0.280 0.000 0.000 0.000 0 0.720
#> SRR1617463 6 0.0458 0.619 0.000 0.000 0.016 0.000 0 0.984
#> SRR1617462 6 0.0458 0.619 0.000 0.000 0.016 0.000 0 0.984
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", "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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 0.620 0.849 0.912 0.2706 0.743 0.743
#> 3 3 0.229 0.669 0.759 0.7107 0.860 0.817
#> 4 4 0.275 0.470 0.653 0.3073 0.681 0.507
#> 5 5 0.318 0.372 0.630 0.1283 0.762 0.427
#> 6 6 0.385 0.580 0.662 0.0869 0.916 0.702
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
#> SRR1617430 2 0.3733 0.783 0.072 0.928
#> SRR1617431 2 0.3733 0.783 0.072 0.928
#> SRR1617410 1 0.2236 0.914 0.964 0.036
#> SRR1617411 1 0.2236 0.914 0.964 0.036
#> SRR1617412 1 0.3114 0.906 0.944 0.056
#> SRR1617413 1 0.3114 0.906 0.944 0.056
#> SRR1617414 1 0.2423 0.913 0.960 0.040
#> SRR1617415 1 0.2423 0.913 0.960 0.040
#> SRR1617416 1 0.1414 0.919 0.980 0.020
#> SRR1617417 1 0.1414 0.919 0.980 0.020
#> SRR1617418 1 0.3274 0.906 0.940 0.060
#> SRR1617419 1 0.3274 0.906 0.940 0.060
#> SRR1617420 1 0.2423 0.913 0.960 0.040
#> SRR1617421 1 0.2423 0.913 0.960 0.040
#> SRR1617422 1 0.0938 0.919 0.988 0.012
#> SRR1617423 1 0.0938 0.919 0.988 0.012
#> SRR1617424 1 0.1184 0.919 0.984 0.016
#> SRR1617425 1 0.1184 0.919 0.984 0.016
#> SRR1617427 1 0.1633 0.918 0.976 0.024
#> SRR1617426 1 0.1633 0.918 0.976 0.024
#> SRR1617428 1 0.4815 0.837 0.896 0.104
#> SRR1617429 1 0.4815 0.837 0.896 0.104
#> SRR1617432 1 0.2423 0.913 0.960 0.040
#> SRR1617433 1 0.2423 0.913 0.960 0.040
#> SRR1617434 1 0.2236 0.914 0.964 0.036
#> SRR1617436 1 0.2043 0.918 0.968 0.032
#> SRR1617435 1 0.2236 0.914 0.964 0.036
#> SRR1617437 1 0.2043 0.918 0.968 0.032
#> SRR1617438 1 0.3114 0.904 0.944 0.056
#> SRR1617439 1 0.3114 0.904 0.944 0.056
#> SRR1617440 1 0.3114 0.904 0.944 0.056
#> SRR1617441 1 0.3114 0.904 0.944 0.056
#> SRR1617443 1 0.3114 0.904 0.944 0.056
#> SRR1617442 1 0.3114 0.904 0.944 0.056
#> SRR1617444 1 0.1414 0.918 0.980 0.020
#> SRR1617445 1 0.1414 0.918 0.980 0.020
#> SRR1617446 1 0.1184 0.919 0.984 0.016
#> SRR1617447 1 0.1184 0.919 0.984 0.016
#> SRR1617448 1 0.0938 0.919 0.988 0.012
#> SRR1617449 1 0.0938 0.919 0.988 0.012
#> SRR1617451 2 0.7815 0.873 0.232 0.768
#> SRR1617450 2 0.7815 0.873 0.232 0.768
#> SRR1617452 1 0.1843 0.916 0.972 0.028
#> SRR1617454 2 0.8016 0.871 0.244 0.756
#> SRR1617453 1 0.1843 0.916 0.972 0.028
#> SRR1617456 1 0.9358 0.275 0.648 0.352
#> SRR1617457 1 0.9358 0.275 0.648 0.352
#> SRR1617455 2 0.8016 0.871 0.244 0.756
#> SRR1617458 1 0.9358 0.275 0.648 0.352
#> SRR1617459 1 0.9358 0.275 0.648 0.352
#> SRR1617460 1 0.0938 0.919 0.988 0.012
#> SRR1617461 1 0.0938 0.919 0.988 0.012
#> SRR1617463 2 0.9460 0.730 0.364 0.636
#> SRR1617462 2 0.9460 0.730 0.364 0.636
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.6229 0.572 0.008 0.652 0.340
#> SRR1617431 2 0.6252 0.572 0.008 0.648 0.344
#> SRR1617410 1 0.5171 0.689 0.784 0.012 0.204
#> SRR1617411 1 0.5171 0.689 0.784 0.012 0.204
#> SRR1617412 1 0.6016 0.700 0.724 0.020 0.256
#> SRR1617413 1 0.6016 0.700 0.724 0.020 0.256
#> SRR1617414 1 0.5360 0.679 0.768 0.012 0.220
#> SRR1617415 1 0.5360 0.679 0.768 0.012 0.220
#> SRR1617416 1 0.2590 0.766 0.924 0.004 0.072
#> SRR1617417 1 0.2590 0.766 0.924 0.004 0.072
#> SRR1617418 1 0.6597 0.675 0.696 0.036 0.268
#> SRR1617419 1 0.6597 0.675 0.696 0.036 0.268
#> SRR1617420 1 0.5360 0.687 0.768 0.012 0.220
#> SRR1617421 1 0.5360 0.687 0.768 0.012 0.220
#> SRR1617422 1 0.1337 0.765 0.972 0.012 0.016
#> SRR1617423 1 0.1337 0.765 0.972 0.012 0.016
#> SRR1617424 1 0.1015 0.765 0.980 0.012 0.008
#> SRR1617425 1 0.1015 0.765 0.980 0.012 0.008
#> SRR1617427 1 0.2804 0.756 0.924 0.016 0.060
#> SRR1617426 1 0.2804 0.756 0.924 0.016 0.060
#> SRR1617428 1 0.7205 0.611 0.708 0.100 0.192
#> SRR1617429 1 0.7205 0.611 0.708 0.100 0.192
#> SRR1617432 1 0.5360 0.679 0.768 0.012 0.220
#> SRR1617433 1 0.5360 0.679 0.768 0.012 0.220
#> SRR1617434 1 0.5171 0.690 0.784 0.012 0.204
#> SRR1617436 1 0.6742 0.629 0.656 0.028 0.316
#> SRR1617435 1 0.5171 0.690 0.784 0.012 0.204
#> SRR1617437 1 0.6742 0.629 0.656 0.028 0.316
#> SRR1617438 1 0.5817 0.701 0.744 0.020 0.236
#> SRR1617439 1 0.5817 0.701 0.744 0.020 0.236
#> SRR1617440 1 0.6646 0.673 0.712 0.048 0.240
#> SRR1617441 1 0.6646 0.673 0.712 0.048 0.240
#> SRR1617443 1 0.5858 0.705 0.740 0.020 0.240
#> SRR1617442 1 0.5858 0.705 0.740 0.020 0.240
#> SRR1617444 1 0.2550 0.758 0.932 0.012 0.056
#> SRR1617445 1 0.2550 0.758 0.932 0.012 0.056
#> SRR1617446 1 0.1015 0.765 0.980 0.012 0.008
#> SRR1617447 1 0.1015 0.765 0.980 0.012 0.008
#> SRR1617448 1 0.0661 0.766 0.988 0.004 0.008
#> SRR1617449 1 0.0661 0.766 0.988 0.004 0.008
#> SRR1617451 2 0.5094 0.713 0.112 0.832 0.056
#> SRR1617450 2 0.5094 0.713 0.112 0.832 0.056
#> SRR1617452 1 0.7807 0.567 0.656 0.108 0.236
#> SRR1617454 2 0.3500 0.715 0.116 0.880 0.004
#> SRR1617453 1 0.7807 0.567 0.656 0.108 0.236
#> SRR1617456 2 0.9649 0.416 0.388 0.404 0.208
#> SRR1617457 2 0.9649 0.416 0.388 0.404 0.208
#> SRR1617455 2 0.3500 0.715 0.116 0.880 0.004
#> SRR1617458 2 0.9649 0.416 0.388 0.404 0.208
#> SRR1617459 2 0.9649 0.416 0.388 0.404 0.208
#> SRR1617460 1 0.7451 0.523 0.700 0.156 0.144
#> SRR1617461 1 0.7451 0.523 0.700 0.156 0.144
#> SRR1617463 2 0.6586 0.682 0.216 0.728 0.056
#> SRR1617462 2 0.6586 0.682 0.216 0.728 0.056
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 4 0.517 0.99526 0.004 0.484 0.000 0.512
#> SRR1617431 4 0.530 0.99526 0.008 0.488 0.000 0.504
#> SRR1617410 1 0.381 0.64028 0.812 0.000 0.176 0.012
#> SRR1617411 1 0.381 0.64028 0.812 0.000 0.176 0.012
#> SRR1617412 3 0.344 0.57646 0.084 0.000 0.868 0.048
#> SRR1617413 3 0.344 0.57646 0.084 0.000 0.868 0.048
#> SRR1617414 1 0.371 0.62660 0.836 0.000 0.140 0.024
#> SRR1617415 1 0.371 0.62660 0.836 0.000 0.140 0.024
#> SRR1617416 3 0.752 -0.06201 0.380 0.036 0.500 0.084
#> SRR1617417 3 0.752 -0.06201 0.380 0.036 0.500 0.084
#> SRR1617418 3 0.260 0.58658 0.040 0.004 0.916 0.040
#> SRR1617419 3 0.260 0.58658 0.040 0.004 0.916 0.040
#> SRR1617420 1 0.428 0.62836 0.780 0.000 0.200 0.020
#> SRR1617421 1 0.428 0.62836 0.780 0.000 0.200 0.020
#> SRR1617422 1 0.712 0.44434 0.500 0.040 0.412 0.048
#> SRR1617423 1 0.712 0.44434 0.500 0.040 0.412 0.048
#> SRR1617424 1 0.719 0.44690 0.496 0.044 0.412 0.048
#> SRR1617425 1 0.719 0.44690 0.496 0.044 0.412 0.048
#> SRR1617427 1 0.707 0.49403 0.544 0.036 0.364 0.056
#> SRR1617426 1 0.707 0.49403 0.544 0.036 0.364 0.056
#> SRR1617428 3 0.842 0.25494 0.256 0.084 0.524 0.136
#> SRR1617429 3 0.842 0.25494 0.256 0.084 0.524 0.136
#> SRR1617432 1 0.366 0.62502 0.840 0.000 0.136 0.024
#> SRR1617433 1 0.366 0.62502 0.840 0.000 0.136 0.024
#> SRR1617434 1 0.374 0.63923 0.824 0.000 0.160 0.016
#> SRR1617436 3 0.550 0.50676 0.112 0.004 0.744 0.140
#> SRR1617435 1 0.374 0.63923 0.824 0.000 0.160 0.016
#> SRR1617437 3 0.550 0.50676 0.112 0.004 0.744 0.140
#> SRR1617438 3 0.252 0.59656 0.076 0.000 0.908 0.016
#> SRR1617439 3 0.252 0.59656 0.076 0.000 0.908 0.016
#> SRR1617440 3 0.310 0.59274 0.080 0.004 0.888 0.028
#> SRR1617441 3 0.310 0.59274 0.080 0.004 0.888 0.028
#> SRR1617443 3 0.317 0.58634 0.116 0.000 0.868 0.016
#> SRR1617442 3 0.317 0.58634 0.116 0.000 0.868 0.016
#> SRR1617444 3 0.724 0.00535 0.348 0.048 0.548 0.056
#> SRR1617445 3 0.724 0.00535 0.348 0.048 0.548 0.056
#> SRR1617446 1 0.734 0.39505 0.468 0.048 0.432 0.052
#> SRR1617447 1 0.734 0.39505 0.468 0.048 0.432 0.052
#> SRR1617448 1 0.728 0.34695 0.452 0.048 0.452 0.048
#> SRR1617449 3 0.728 -0.40822 0.452 0.048 0.452 0.048
#> SRR1617451 2 0.490 0.32785 0.060 0.816 0.060 0.064
#> SRR1617450 2 0.490 0.32785 0.060 0.816 0.060 0.064
#> SRR1617452 3 0.816 0.44861 0.216 0.080 0.564 0.140
#> SRR1617454 2 0.267 0.43281 0.044 0.908 0.048 0.000
#> SRR1617453 3 0.816 0.44861 0.216 0.080 0.564 0.140
#> SRR1617456 2 0.939 0.61849 0.148 0.412 0.272 0.168
#> SRR1617457 2 0.939 0.61849 0.148 0.412 0.272 0.168
#> SRR1617455 2 0.267 0.43281 0.044 0.908 0.048 0.000
#> SRR1617458 2 0.941 0.60845 0.144 0.404 0.280 0.172
#> SRR1617459 2 0.941 0.60845 0.144 0.404 0.280 0.172
#> SRR1617460 3 0.966 0.10144 0.260 0.232 0.360 0.148
#> SRR1617461 3 0.966 0.10144 0.260 0.232 0.360 0.148
#> SRR1617463 2 0.673 0.59660 0.096 0.704 0.096 0.104
#> SRR1617462 2 0.673 0.59660 0.096 0.704 0.096 0.104
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 4 0.0932 0.5778 0.004 0.020 0.004 0.972 0.000
#> SRR1617431 4 0.1093 0.5778 0.004 0.020 0.004 0.968 0.004
#> SRR1617410 1 0.5582 -0.5663 0.568 0.024 0.036 0.000 0.372
#> SRR1617411 1 0.5582 -0.5663 0.568 0.024 0.036 0.000 0.372
#> SRR1617412 3 0.6143 0.7214 0.292 0.032 0.604 0.008 0.064
#> SRR1617413 3 0.6143 0.7214 0.292 0.032 0.604 0.008 0.064
#> SRR1617414 5 0.5573 0.9972 0.460 0.024 0.028 0.000 0.488
#> SRR1617415 5 0.5573 0.9972 0.460 0.024 0.028 0.000 0.488
#> SRR1617416 1 0.4299 0.4807 0.784 0.016 0.160 0.004 0.036
#> SRR1617417 1 0.4299 0.4807 0.784 0.016 0.160 0.004 0.036
#> SRR1617418 3 0.5314 0.7212 0.280 0.016 0.652 0.000 0.052
#> SRR1617419 3 0.5314 0.7212 0.280 0.016 0.652 0.000 0.052
#> SRR1617420 1 0.5282 -0.7291 0.524 0.008 0.024 0.004 0.440
#> SRR1617421 1 0.5282 -0.7291 0.524 0.008 0.024 0.004 0.440
#> SRR1617422 1 0.0510 0.5631 0.984 0.000 0.000 0.000 0.016
#> SRR1617423 1 0.0510 0.5631 0.984 0.000 0.000 0.000 0.016
#> SRR1617424 1 0.0290 0.5666 0.992 0.000 0.000 0.000 0.008
#> SRR1617425 1 0.0290 0.5666 0.992 0.000 0.000 0.000 0.008
#> SRR1617427 1 0.2305 0.4855 0.896 0.000 0.012 0.000 0.092
#> SRR1617426 1 0.2305 0.4855 0.896 0.000 0.012 0.000 0.092
#> SRR1617428 1 0.7912 -0.0739 0.476 0.052 0.288 0.040 0.144
#> SRR1617429 1 0.7912 -0.0739 0.476 0.052 0.288 0.040 0.144
#> SRR1617432 5 0.5573 0.9972 0.460 0.028 0.024 0.000 0.488
#> SRR1617433 5 0.5573 0.9972 0.460 0.028 0.024 0.000 0.488
#> SRR1617434 1 0.5320 -0.7413 0.524 0.016 0.024 0.000 0.436
#> SRR1617436 3 0.7131 0.5535 0.304 0.020 0.512 0.024 0.140
#> SRR1617435 1 0.5320 -0.7413 0.524 0.016 0.024 0.000 0.436
#> SRR1617437 3 0.7131 0.5535 0.304 0.020 0.512 0.024 0.140
#> SRR1617438 3 0.5088 0.7360 0.340 0.024 0.620 0.000 0.016
#> SRR1617439 3 0.5088 0.7360 0.340 0.024 0.620 0.000 0.016
#> SRR1617440 3 0.5338 0.7210 0.328 0.060 0.608 0.000 0.004
#> SRR1617441 3 0.5338 0.7210 0.328 0.060 0.608 0.000 0.004
#> SRR1617443 3 0.5307 0.7334 0.332 0.024 0.616 0.000 0.028
#> SRR1617442 3 0.5307 0.7334 0.332 0.024 0.616 0.000 0.028
#> SRR1617444 1 0.3416 0.5025 0.840 0.020 0.124 0.000 0.016
#> SRR1617445 1 0.3416 0.5025 0.840 0.020 0.124 0.000 0.016
#> SRR1617446 1 0.0898 0.5738 0.972 0.000 0.020 0.000 0.008
#> SRR1617447 1 0.0898 0.5738 0.972 0.000 0.020 0.000 0.008
#> SRR1617448 1 0.1251 0.5739 0.956 0.000 0.036 0.000 0.008
#> SRR1617449 1 0.1251 0.5739 0.956 0.000 0.036 0.000 0.008
#> SRR1617451 4 0.7258 0.3757 0.020 0.420 0.052 0.424 0.084
#> SRR1617450 4 0.7258 0.3757 0.020 0.420 0.052 0.424 0.084
#> SRR1617452 3 0.8363 0.1880 0.300 0.196 0.372 0.008 0.124
#> SRR1617454 2 0.7254 -0.3566 0.020 0.456 0.028 0.368 0.128
#> SRR1617453 3 0.8363 0.1880 0.300 0.196 0.372 0.008 0.124
#> SRR1617456 2 0.4795 0.5143 0.120 0.752 0.116 0.000 0.012
#> SRR1617457 2 0.4795 0.5143 0.120 0.752 0.116 0.000 0.012
#> SRR1617455 2 0.7254 -0.3566 0.020 0.456 0.028 0.368 0.128
#> SRR1617458 2 0.4894 0.5148 0.120 0.748 0.116 0.000 0.016
#> SRR1617459 2 0.4894 0.5148 0.120 0.748 0.116 0.000 0.016
#> SRR1617460 2 0.7585 0.2320 0.380 0.388 0.156 0.000 0.076
#> SRR1617461 2 0.7585 0.2320 0.380 0.388 0.156 0.000 0.076
#> SRR1617463 2 0.7400 0.1866 0.068 0.592 0.040 0.152 0.148
#> SRR1617462 2 0.7400 0.1866 0.068 0.592 0.040 0.152 0.148
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.279 0.563 0.000 0.864 0.004 NA 0.020 0.008
#> SRR1617431 2 0.275 0.563 0.000 0.868 0.004 NA 0.020 0.008
#> SRR1617410 5 0.509 0.787 0.364 0.004 0.012 NA 0.580 0.012
#> SRR1617411 5 0.509 0.787 0.364 0.004 0.012 NA 0.580 0.012
#> SRR1617412 3 0.600 0.658 0.180 0.000 0.604 NA 0.036 0.008
#> SRR1617413 3 0.600 0.658 0.180 0.000 0.604 NA 0.036 0.008
#> SRR1617414 5 0.492 0.839 0.276 0.000 0.000 NA 0.632 0.004
#> SRR1617415 5 0.492 0.839 0.276 0.000 0.000 NA 0.632 0.004
#> SRR1617416 1 0.456 0.660 0.768 0.004 0.120 NA 0.044 0.008
#> SRR1617417 1 0.456 0.660 0.768 0.004 0.120 NA 0.044 0.008
#> SRR1617418 3 0.510 0.686 0.200 0.000 0.664 NA 0.004 0.008
#> SRR1617419 3 0.510 0.686 0.200 0.000 0.664 NA 0.004 0.008
#> SRR1617420 5 0.547 0.818 0.332 0.004 0.032 NA 0.584 0.008
#> SRR1617421 5 0.547 0.818 0.332 0.004 0.032 NA 0.584 0.008
#> SRR1617422 1 0.144 0.764 0.944 0.000 0.000 NA 0.040 0.004
#> SRR1617423 1 0.144 0.764 0.944 0.000 0.000 NA 0.040 0.004
#> SRR1617424 1 0.151 0.763 0.944 0.000 0.004 NA 0.036 0.004
#> SRR1617425 1 0.151 0.763 0.944 0.000 0.004 NA 0.036 0.004
#> SRR1617427 1 0.329 0.689 0.840 0.000 0.016 NA 0.104 0.004
#> SRR1617426 1 0.329 0.689 0.840 0.000 0.016 NA 0.104 0.004
#> SRR1617428 1 0.742 0.152 0.440 0.028 0.104 NA 0.040 0.044
#> SRR1617429 1 0.742 0.152 0.440 0.028 0.104 NA 0.040 0.044
#> SRR1617432 5 0.490 0.840 0.272 0.000 0.000 NA 0.636 0.004
#> SRR1617433 5 0.490 0.840 0.272 0.000 0.000 NA 0.636 0.004
#> SRR1617434 5 0.432 0.850 0.324 0.000 0.016 NA 0.648 0.004
#> SRR1617436 3 0.712 0.493 0.244 0.008 0.460 NA 0.056 0.008
#> SRR1617435 5 0.432 0.850 0.324 0.000 0.016 NA 0.648 0.004
#> SRR1617437 3 0.712 0.493 0.244 0.008 0.460 NA 0.056 0.008
#> SRR1617438 3 0.449 0.700 0.236 0.000 0.708 NA 0.016 0.028
#> SRR1617439 3 0.449 0.700 0.236 0.000 0.708 NA 0.016 0.028
#> SRR1617440 3 0.517 0.679 0.240 0.000 0.656 NA 0.016 0.080
#> SRR1617441 3 0.517 0.679 0.240 0.000 0.656 NA 0.016 0.080
#> SRR1617443 3 0.459 0.696 0.228 0.000 0.708 NA 0.032 0.020
#> SRR1617442 3 0.459 0.696 0.228 0.000 0.708 NA 0.032 0.020
#> SRR1617444 1 0.291 0.723 0.864 0.000 0.096 NA 0.008 0.020
#> SRR1617445 1 0.291 0.723 0.864 0.000 0.096 NA 0.008 0.020
#> SRR1617446 1 0.213 0.775 0.920 0.000 0.028 NA 0.016 0.008
#> SRR1617447 1 0.213 0.775 0.920 0.000 0.028 NA 0.016 0.008
#> SRR1617448 1 0.201 0.776 0.924 0.000 0.032 NA 0.008 0.008
#> SRR1617449 1 0.201 0.776 0.924 0.000 0.032 NA 0.008 0.008
#> SRR1617451 2 0.599 0.351 0.020 0.524 0.032 NA 0.024 0.376
#> SRR1617450 2 0.599 0.351 0.020 0.524 0.032 NA 0.024 0.376
#> SRR1617452 3 0.863 0.114 0.276 0.004 0.284 NA 0.108 0.224
#> SRR1617454 6 0.644 -0.226 0.016 0.400 0.024 NA 0.028 0.468
#> SRR1617453 3 0.863 0.114 0.276 0.004 0.284 NA 0.108 0.224
#> SRR1617456 6 0.370 0.503 0.096 0.000 0.116 NA 0.000 0.788
#> SRR1617457 6 0.370 0.503 0.096 0.000 0.116 NA 0.000 0.788
#> SRR1617455 6 0.644 -0.226 0.016 0.400 0.024 NA 0.028 0.468
#> SRR1617458 6 0.397 0.504 0.100 0.000 0.124 NA 0.000 0.772
#> SRR1617459 6 0.397 0.504 0.100 0.000 0.124 NA 0.000 0.772
#> SRR1617460 6 0.716 0.262 0.388 0.004 0.112 NA 0.052 0.404
#> SRR1617461 6 0.716 0.262 0.388 0.004 0.112 NA 0.052 0.404
#> SRR1617463 6 0.723 0.247 0.088 0.184 0.036 NA 0.032 0.568
#> SRR1617462 6 0.723 0.247 0.088 0.184 0.036 NA 0.032 0.568
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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 0.925 0.947 0.978 0.4934 0.508 0.508
#> 3 3 0.771 0.890 0.932 0.3440 0.765 0.566
#> 4 4 0.698 0.820 0.838 0.1323 0.902 0.713
#> 5 5 0.834 0.739 0.867 0.0755 0.927 0.717
#> 6 6 0.795 0.671 0.804 0.0361 0.947 0.752
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
#> SRR1617430 2 0.0000 0.974 0.000 1.000
#> SRR1617431 2 0.0000 0.974 0.000 1.000
#> SRR1617410 1 0.0000 0.977 1.000 0.000
#> SRR1617411 1 0.0000 0.977 1.000 0.000
#> SRR1617412 1 0.0000 0.977 1.000 0.000
#> SRR1617413 1 0.0000 0.977 1.000 0.000
#> SRR1617414 1 0.0000 0.977 1.000 0.000
#> SRR1617415 1 0.0000 0.977 1.000 0.000
#> SRR1617416 1 0.0000 0.977 1.000 0.000
#> SRR1617417 1 0.0000 0.977 1.000 0.000
#> SRR1617418 2 0.0672 0.970 0.008 0.992
#> SRR1617419 2 0.0672 0.970 0.008 0.992
#> SRR1617420 1 0.0000 0.977 1.000 0.000
#> SRR1617421 1 0.0000 0.977 1.000 0.000
#> SRR1617422 1 0.0000 0.977 1.000 0.000
#> SRR1617423 1 0.0000 0.977 1.000 0.000
#> SRR1617424 1 0.0000 0.977 1.000 0.000
#> SRR1617425 1 0.0000 0.977 1.000 0.000
#> SRR1617427 1 0.0000 0.977 1.000 0.000
#> SRR1617426 1 0.0000 0.977 1.000 0.000
#> SRR1617428 2 0.0000 0.974 0.000 1.000
#> SRR1617429 2 0.0000 0.974 0.000 1.000
#> SRR1617432 1 0.0000 0.977 1.000 0.000
#> SRR1617433 1 0.0000 0.977 1.000 0.000
#> SRR1617434 1 0.0000 0.977 1.000 0.000
#> SRR1617436 2 0.7815 0.705 0.232 0.768
#> SRR1617435 1 0.0000 0.977 1.000 0.000
#> SRR1617437 2 0.7815 0.705 0.232 0.768
#> SRR1617438 1 0.0000 0.977 1.000 0.000
#> SRR1617439 1 0.0000 0.977 1.000 0.000
#> SRR1617440 1 0.9286 0.486 0.656 0.344
#> SRR1617441 1 0.9286 0.486 0.656 0.344
#> SRR1617443 1 0.0000 0.977 1.000 0.000
#> SRR1617442 1 0.0000 0.977 1.000 0.000
#> SRR1617444 1 0.0000 0.977 1.000 0.000
#> SRR1617445 1 0.0000 0.977 1.000 0.000
#> SRR1617446 1 0.0000 0.977 1.000 0.000
#> SRR1617447 1 0.0000 0.977 1.000 0.000
#> SRR1617448 1 0.0000 0.977 1.000 0.000
#> SRR1617449 1 0.0000 0.977 1.000 0.000
#> SRR1617451 2 0.0000 0.974 0.000 1.000
#> SRR1617450 2 0.0000 0.974 0.000 1.000
#> SRR1617452 2 0.1184 0.963 0.016 0.984
#> SRR1617454 2 0.0000 0.974 0.000 1.000
#> SRR1617453 2 0.1184 0.963 0.016 0.984
#> SRR1617456 2 0.0000 0.974 0.000 1.000
#> SRR1617457 2 0.0000 0.974 0.000 1.000
#> SRR1617455 2 0.0000 0.974 0.000 1.000
#> SRR1617458 2 0.0000 0.974 0.000 1.000
#> SRR1617459 2 0.0000 0.974 0.000 1.000
#> SRR1617460 2 0.0000 0.974 0.000 1.000
#> SRR1617461 2 0.0000 0.974 0.000 1.000
#> SRR1617463 2 0.0000 0.974 0.000 1.000
#> SRR1617462 2 0.0000 0.974 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.1031 0.900 0.000 0.976 0.024
#> SRR1617431 2 0.1031 0.900 0.000 0.976 0.024
#> SRR1617410 1 0.0892 0.930 0.980 0.000 0.020
#> SRR1617411 1 0.0892 0.930 0.980 0.000 0.020
#> SRR1617412 3 0.0424 0.928 0.008 0.000 0.992
#> SRR1617413 3 0.0424 0.928 0.008 0.000 0.992
#> SRR1617414 1 0.2165 0.921 0.936 0.000 0.064
#> SRR1617415 1 0.2165 0.921 0.936 0.000 0.064
#> SRR1617416 1 0.3879 0.831 0.848 0.000 0.152
#> SRR1617417 1 0.3879 0.831 0.848 0.000 0.152
#> SRR1617418 3 0.3816 0.855 0.000 0.148 0.852
#> SRR1617419 3 0.3816 0.855 0.000 0.148 0.852
#> SRR1617420 1 0.2165 0.921 0.936 0.000 0.064
#> SRR1617421 1 0.2165 0.921 0.936 0.000 0.064
#> SRR1617422 1 0.0592 0.932 0.988 0.000 0.012
#> SRR1617423 1 0.0592 0.932 0.988 0.000 0.012
#> SRR1617424 1 0.0592 0.932 0.988 0.000 0.012
#> SRR1617425 1 0.0592 0.932 0.988 0.000 0.012
#> SRR1617427 1 0.0592 0.932 0.988 0.000 0.012
#> SRR1617426 1 0.0592 0.932 0.988 0.000 0.012
#> SRR1617428 2 0.4834 0.726 0.004 0.792 0.204
#> SRR1617429 2 0.4834 0.726 0.004 0.792 0.204
#> SRR1617432 1 0.2165 0.921 0.936 0.000 0.064
#> SRR1617433 1 0.2165 0.921 0.936 0.000 0.064
#> SRR1617434 1 0.1860 0.925 0.948 0.000 0.052
#> SRR1617436 3 0.4033 0.860 0.008 0.136 0.856
#> SRR1617435 1 0.1860 0.925 0.948 0.000 0.052
#> SRR1617437 3 0.4033 0.860 0.008 0.136 0.856
#> SRR1617438 3 0.0892 0.930 0.020 0.000 0.980
#> SRR1617439 3 0.0892 0.930 0.020 0.000 0.980
#> SRR1617440 3 0.1399 0.928 0.028 0.004 0.968
#> SRR1617441 3 0.1399 0.928 0.028 0.004 0.968
#> SRR1617443 3 0.1289 0.925 0.032 0.000 0.968
#> SRR1617442 3 0.1289 0.925 0.032 0.000 0.968
#> SRR1617444 1 0.5591 0.615 0.696 0.000 0.304
#> SRR1617445 1 0.5591 0.615 0.696 0.000 0.304
#> SRR1617446 1 0.0592 0.932 0.988 0.000 0.012
#> SRR1617447 1 0.0592 0.932 0.988 0.000 0.012
#> SRR1617448 1 0.0892 0.930 0.980 0.000 0.020
#> SRR1617449 1 0.0892 0.930 0.980 0.000 0.020
#> SRR1617451 2 0.0000 0.908 0.000 1.000 0.000
#> SRR1617450 2 0.0000 0.908 0.000 1.000 0.000
#> SRR1617452 3 0.1950 0.908 0.008 0.040 0.952
#> SRR1617454 2 0.0000 0.908 0.000 1.000 0.000
#> SRR1617453 3 0.1950 0.908 0.008 0.040 0.952
#> SRR1617456 2 0.3412 0.882 0.000 0.876 0.124
#> SRR1617457 2 0.3412 0.882 0.000 0.876 0.124
#> SRR1617455 2 0.0000 0.908 0.000 1.000 0.000
#> SRR1617458 2 0.3412 0.882 0.000 0.876 0.124
#> SRR1617459 2 0.3412 0.882 0.000 0.876 0.124
#> SRR1617460 2 0.3896 0.875 0.008 0.864 0.128
#> SRR1617461 2 0.3896 0.875 0.008 0.864 0.128
#> SRR1617463 2 0.0000 0.908 0.000 1.000 0.000
#> SRR1617462 2 0.0000 0.908 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.5982 0.673 0.112 0.684 0.204 0.000
#> SRR1617431 2 0.5982 0.673 0.112 0.684 0.204 0.000
#> SRR1617410 1 0.3610 0.989 0.800 0.000 0.000 0.200
#> SRR1617411 1 0.3610 0.989 0.800 0.000 0.000 0.200
#> SRR1617412 3 0.3439 0.824 0.048 0.000 0.868 0.084
#> SRR1617413 3 0.3439 0.824 0.048 0.000 0.868 0.084
#> SRR1617414 1 0.3569 0.992 0.804 0.000 0.000 0.196
#> SRR1617415 1 0.3569 0.992 0.804 0.000 0.000 0.196
#> SRR1617416 4 0.2376 0.833 0.016 0.000 0.068 0.916
#> SRR1617417 4 0.2376 0.833 0.016 0.000 0.068 0.916
#> SRR1617418 3 0.3236 0.730 0.088 0.028 0.880 0.004
#> SRR1617419 3 0.3236 0.730 0.088 0.028 0.880 0.004
#> SRR1617420 1 0.3969 0.974 0.804 0.000 0.016 0.180
#> SRR1617421 1 0.3969 0.974 0.804 0.000 0.016 0.180
#> SRR1617422 4 0.2408 0.862 0.104 0.000 0.000 0.896
#> SRR1617423 4 0.2408 0.862 0.104 0.000 0.000 0.896
#> SRR1617424 4 0.2345 0.865 0.100 0.000 0.000 0.900
#> SRR1617425 4 0.2345 0.865 0.100 0.000 0.000 0.900
#> SRR1617427 4 0.2973 0.823 0.144 0.000 0.000 0.856
#> SRR1617426 4 0.2973 0.823 0.144 0.000 0.000 0.856
#> SRR1617428 2 0.7152 0.423 0.124 0.512 0.360 0.004
#> SRR1617429 2 0.7152 0.423 0.124 0.512 0.360 0.004
#> SRR1617432 1 0.3569 0.992 0.804 0.000 0.000 0.196
#> SRR1617433 1 0.3569 0.992 0.804 0.000 0.000 0.196
#> SRR1617434 1 0.3569 0.992 0.804 0.000 0.000 0.196
#> SRR1617436 3 0.3934 0.695 0.116 0.048 0.836 0.000
#> SRR1617435 1 0.3569 0.992 0.804 0.000 0.000 0.196
#> SRR1617437 3 0.3934 0.695 0.116 0.048 0.836 0.000
#> SRR1617438 3 0.4706 0.823 0.072 0.000 0.788 0.140
#> SRR1617439 3 0.4706 0.823 0.072 0.000 0.788 0.140
#> SRR1617440 3 0.5157 0.821 0.068 0.020 0.784 0.128
#> SRR1617441 3 0.5157 0.821 0.068 0.020 0.784 0.128
#> SRR1617443 3 0.4841 0.821 0.080 0.000 0.780 0.140
#> SRR1617442 3 0.4841 0.821 0.080 0.000 0.780 0.140
#> SRR1617444 4 0.3146 0.805 0.036 0.008 0.064 0.892
#> SRR1617445 4 0.3146 0.805 0.036 0.008 0.064 0.892
#> SRR1617446 4 0.1118 0.883 0.036 0.000 0.000 0.964
#> SRR1617447 4 0.1118 0.883 0.036 0.000 0.000 0.964
#> SRR1617448 4 0.0188 0.878 0.004 0.000 0.000 0.996
#> SRR1617449 4 0.0188 0.878 0.004 0.000 0.000 0.996
#> SRR1617451 2 0.3521 0.787 0.052 0.864 0.084 0.000
#> SRR1617450 2 0.3521 0.787 0.052 0.864 0.084 0.000
#> SRR1617452 3 0.7275 0.628 0.176 0.136 0.640 0.048
#> SRR1617454 2 0.1174 0.818 0.012 0.968 0.020 0.000
#> SRR1617453 3 0.7275 0.628 0.176 0.136 0.640 0.048
#> SRR1617456 2 0.3370 0.799 0.080 0.872 0.048 0.000
#> SRR1617457 2 0.3370 0.799 0.080 0.872 0.048 0.000
#> SRR1617455 2 0.1174 0.818 0.012 0.968 0.020 0.000
#> SRR1617458 2 0.3370 0.799 0.080 0.872 0.048 0.000
#> SRR1617459 2 0.3370 0.799 0.080 0.872 0.048 0.000
#> SRR1617460 2 0.3902 0.793 0.080 0.860 0.036 0.024
#> SRR1617461 2 0.3902 0.793 0.080 0.860 0.036 0.024
#> SRR1617463 2 0.0469 0.820 0.000 0.988 0.012 0.000
#> SRR1617462 2 0.0469 0.820 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
#> SRR1617430 4 0.2124 0.7697 0.000 0.096 0.004 0.900 0.000
#> SRR1617431 4 0.2124 0.7697 0.000 0.096 0.004 0.900 0.000
#> SRR1617410 5 0.0703 0.9752 0.024 0.000 0.000 0.000 0.976
#> SRR1617411 5 0.0703 0.9752 0.024 0.000 0.000 0.000 0.976
#> SRR1617412 3 0.2017 0.7895 0.000 0.000 0.912 0.080 0.008
#> SRR1617413 3 0.2017 0.7895 0.000 0.000 0.912 0.080 0.008
#> SRR1617414 5 0.0162 0.9915 0.000 0.000 0.000 0.004 0.996
#> SRR1617415 5 0.0162 0.9915 0.000 0.000 0.000 0.004 0.996
#> SRR1617416 1 0.4797 0.7445 0.756 0.004 0.168 0.040 0.032
#> SRR1617417 1 0.4797 0.7445 0.756 0.004 0.168 0.040 0.032
#> SRR1617418 3 0.3966 0.6237 0.000 0.000 0.664 0.336 0.000
#> SRR1617419 3 0.3966 0.6237 0.000 0.000 0.664 0.336 0.000
#> SRR1617420 5 0.0162 0.9906 0.004 0.000 0.000 0.000 0.996
#> SRR1617421 5 0.0162 0.9906 0.004 0.000 0.000 0.000 0.996
#> SRR1617422 1 0.0955 0.9368 0.968 0.000 0.000 0.004 0.028
#> SRR1617423 1 0.0955 0.9368 0.968 0.000 0.000 0.004 0.028
#> SRR1617424 1 0.0771 0.9387 0.976 0.000 0.000 0.004 0.020
#> SRR1617425 1 0.0771 0.9387 0.976 0.000 0.000 0.004 0.020
#> SRR1617427 1 0.1768 0.9116 0.924 0.000 0.000 0.004 0.072
#> SRR1617426 1 0.1768 0.9116 0.924 0.000 0.000 0.004 0.072
#> SRR1617428 4 0.1652 0.7274 0.004 0.004 0.040 0.944 0.008
#> SRR1617429 4 0.1652 0.7274 0.004 0.004 0.040 0.944 0.008
#> SRR1617432 5 0.0162 0.9915 0.000 0.000 0.000 0.004 0.996
#> SRR1617433 5 0.0162 0.9915 0.000 0.000 0.000 0.004 0.996
#> SRR1617434 5 0.0000 0.9912 0.000 0.000 0.000 0.000 1.000
#> SRR1617436 3 0.4443 0.4347 0.000 0.000 0.524 0.472 0.004
#> SRR1617435 5 0.0000 0.9912 0.000 0.000 0.000 0.000 1.000
#> SRR1617437 3 0.4443 0.4347 0.000 0.000 0.524 0.472 0.004
#> SRR1617438 3 0.1117 0.8043 0.020 0.000 0.964 0.000 0.016
#> SRR1617439 3 0.1117 0.8043 0.020 0.000 0.964 0.000 0.016
#> SRR1617440 3 0.2217 0.7891 0.024 0.044 0.920 0.000 0.012
#> SRR1617441 3 0.2217 0.7891 0.024 0.044 0.920 0.000 0.012
#> SRR1617443 3 0.1564 0.8014 0.024 0.004 0.948 0.000 0.024
#> SRR1617442 3 0.1564 0.8014 0.024 0.004 0.948 0.000 0.024
#> SRR1617444 1 0.1106 0.9305 0.964 0.024 0.012 0.000 0.000
#> SRR1617445 1 0.1106 0.9305 0.964 0.024 0.012 0.000 0.000
#> SRR1617446 1 0.0579 0.9395 0.984 0.008 0.000 0.000 0.008
#> SRR1617447 1 0.0579 0.9395 0.984 0.008 0.000 0.000 0.008
#> SRR1617448 1 0.0451 0.9386 0.988 0.008 0.000 0.000 0.004
#> SRR1617449 1 0.0451 0.9386 0.988 0.008 0.000 0.000 0.004
#> SRR1617451 4 0.4066 0.5261 0.004 0.324 0.000 0.672 0.000
#> SRR1617450 4 0.4066 0.5261 0.004 0.324 0.000 0.672 0.000
#> SRR1617452 2 0.6294 0.3434 0.004 0.560 0.296 0.132 0.008
#> SRR1617454 2 0.4449 -0.0774 0.004 0.512 0.000 0.484 0.000
#> SRR1617453 2 0.6294 0.3434 0.004 0.560 0.296 0.132 0.008
#> SRR1617456 2 0.1012 0.6493 0.000 0.968 0.012 0.020 0.000
#> SRR1617457 2 0.1012 0.6493 0.000 0.968 0.012 0.020 0.000
#> SRR1617455 2 0.4449 -0.0774 0.004 0.512 0.000 0.484 0.000
#> SRR1617458 2 0.1018 0.6508 0.000 0.968 0.016 0.016 0.000
#> SRR1617459 2 0.1018 0.6508 0.000 0.968 0.016 0.016 0.000
#> SRR1617460 2 0.1557 0.6352 0.000 0.940 0.008 0.052 0.000
#> SRR1617461 2 0.1557 0.6352 0.000 0.940 0.008 0.052 0.000
#> SRR1617463 2 0.4470 0.2131 0.004 0.596 0.004 0.396 0.000
#> SRR1617462 2 0.4470 0.2131 0.004 0.596 0.004 0.396 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.2544 0.362 0.000 0.864 0.004 0.120 0.000 0.012
#> SRR1617431 2 0.2544 0.362 0.000 0.864 0.004 0.120 0.000 0.012
#> SRR1617410 5 0.1511 0.934 0.012 0.000 0.004 0.044 0.940 0.000
#> SRR1617411 5 0.1511 0.934 0.012 0.000 0.004 0.044 0.940 0.000
#> SRR1617412 3 0.3558 0.535 0.000 0.016 0.736 0.248 0.000 0.000
#> SRR1617413 3 0.3558 0.535 0.000 0.016 0.736 0.248 0.000 0.000
#> SRR1617414 5 0.1444 0.944 0.000 0.000 0.000 0.072 0.928 0.000
#> SRR1617415 5 0.1444 0.944 0.000 0.000 0.000 0.072 0.928 0.000
#> SRR1617416 1 0.6508 0.498 0.540 0.000 0.224 0.176 0.052 0.008
#> SRR1617417 1 0.6508 0.498 0.540 0.000 0.224 0.176 0.052 0.008
#> SRR1617418 3 0.5847 -0.363 0.000 0.196 0.444 0.360 0.000 0.000
#> SRR1617419 3 0.5847 -0.363 0.000 0.196 0.444 0.360 0.000 0.000
#> SRR1617420 5 0.0632 0.948 0.000 0.000 0.000 0.024 0.976 0.000
#> SRR1617421 5 0.0632 0.948 0.000 0.000 0.000 0.024 0.976 0.000
#> SRR1617422 1 0.2300 0.861 0.856 0.000 0.000 0.144 0.000 0.000
#> SRR1617423 1 0.2300 0.861 0.856 0.000 0.000 0.144 0.000 0.000
#> SRR1617424 1 0.2260 0.861 0.860 0.000 0.000 0.140 0.000 0.000
#> SRR1617425 1 0.2260 0.861 0.860 0.000 0.000 0.140 0.000 0.000
#> SRR1617427 1 0.3312 0.835 0.792 0.000 0.000 0.180 0.028 0.000
#> SRR1617426 1 0.3312 0.835 0.792 0.000 0.000 0.180 0.028 0.000
#> SRR1617428 2 0.4357 -0.246 0.000 0.608 0.004 0.368 0.004 0.016
#> SRR1617429 2 0.4357 -0.246 0.000 0.608 0.004 0.368 0.004 0.016
#> SRR1617432 5 0.1444 0.944 0.000 0.000 0.000 0.072 0.928 0.000
#> SRR1617433 5 0.1444 0.944 0.000 0.000 0.000 0.072 0.928 0.000
#> SRR1617434 5 0.0547 0.950 0.000 0.000 0.000 0.020 0.980 0.000
#> SRR1617436 4 0.5888 1.000 0.000 0.320 0.220 0.460 0.000 0.000
#> SRR1617435 5 0.0547 0.950 0.000 0.000 0.000 0.020 0.980 0.000
#> SRR1617437 4 0.5888 1.000 0.000 0.320 0.220 0.460 0.000 0.000
#> SRR1617438 3 0.0291 0.714 0.000 0.000 0.992 0.004 0.004 0.000
#> SRR1617439 3 0.0291 0.714 0.000 0.000 0.992 0.004 0.004 0.000
#> SRR1617440 3 0.2355 0.657 0.000 0.004 0.876 0.008 0.000 0.112
#> SRR1617441 3 0.2355 0.657 0.000 0.004 0.876 0.008 0.000 0.112
#> SRR1617443 3 0.0291 0.714 0.000 0.000 0.992 0.004 0.004 0.000
#> SRR1617442 3 0.0291 0.714 0.000 0.000 0.992 0.004 0.004 0.000
#> SRR1617444 1 0.1401 0.851 0.948 0.000 0.028 0.020 0.000 0.004
#> SRR1617445 1 0.1401 0.851 0.948 0.000 0.028 0.020 0.000 0.004
#> SRR1617446 1 0.0146 0.865 0.996 0.000 0.000 0.004 0.000 0.000
#> SRR1617447 1 0.0146 0.865 0.996 0.000 0.000 0.004 0.000 0.000
#> SRR1617448 1 0.0291 0.864 0.992 0.000 0.004 0.004 0.000 0.000
#> SRR1617449 1 0.0291 0.864 0.992 0.000 0.004 0.004 0.000 0.000
#> SRR1617451 2 0.2730 0.617 0.000 0.808 0.000 0.000 0.000 0.192
#> SRR1617450 2 0.2730 0.617 0.000 0.808 0.000 0.000 0.000 0.192
#> SRR1617452 6 0.6237 0.566 0.004 0.020 0.164 0.288 0.004 0.520
#> SRR1617454 2 0.4389 0.546 0.000 0.660 0.000 0.052 0.000 0.288
#> SRR1617453 6 0.6237 0.566 0.004 0.020 0.164 0.288 0.004 0.520
#> SRR1617456 6 0.0713 0.762 0.000 0.028 0.000 0.000 0.000 0.972
#> SRR1617457 6 0.0713 0.762 0.000 0.028 0.000 0.000 0.000 0.972
#> SRR1617455 2 0.4389 0.546 0.000 0.660 0.000 0.052 0.000 0.288
#> SRR1617458 6 0.0547 0.766 0.000 0.020 0.000 0.000 0.000 0.980
#> SRR1617459 6 0.0547 0.766 0.000 0.020 0.000 0.000 0.000 0.980
#> SRR1617460 6 0.3819 0.711 0.004 0.040 0.000 0.200 0.000 0.756
#> SRR1617461 6 0.3819 0.711 0.004 0.040 0.000 0.200 0.000 0.756
#> SRR1617463 2 0.5303 0.419 0.000 0.548 0.000 0.120 0.000 0.332
#> SRR1617462 2 0.5303 0.419 0.000 0.548 0.000 0.120 0.000 0.332
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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 0.665 0.904 0.947 0.2366 0.743 0.743
#> 3 3 0.746 0.866 0.948 0.3337 0.992 0.989
#> 4 4 0.481 0.752 0.855 0.4810 0.871 0.826
#> 5 5 0.652 0.681 0.811 0.3212 0.776 0.638
#> 6 6 0.600 0.513 0.729 0.0744 0.734 0.434
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
#> SRR1617430 2 0.000 0.745 0.000 1.000
#> SRR1617431 2 0.000 0.745 0.000 1.000
#> SRR1617410 1 0.000 0.963 1.000 0.000
#> SRR1617411 1 0.000 0.963 1.000 0.000
#> SRR1617412 1 0.000 0.963 1.000 0.000
#> SRR1617413 1 0.000 0.963 1.000 0.000
#> SRR1617414 1 0.000 0.963 1.000 0.000
#> SRR1617415 1 0.000 0.963 1.000 0.000
#> SRR1617416 1 0.000 0.963 1.000 0.000
#> SRR1617417 1 0.000 0.963 1.000 0.000
#> SRR1617418 1 0.000 0.963 1.000 0.000
#> SRR1617419 1 0.000 0.963 1.000 0.000
#> SRR1617420 1 0.000 0.963 1.000 0.000
#> SRR1617421 1 0.000 0.963 1.000 0.000
#> SRR1617422 1 0.000 0.963 1.000 0.000
#> SRR1617423 1 0.000 0.963 1.000 0.000
#> SRR1617424 1 0.000 0.963 1.000 0.000
#> SRR1617425 1 0.000 0.963 1.000 0.000
#> SRR1617427 1 0.000 0.963 1.000 0.000
#> SRR1617426 1 0.000 0.963 1.000 0.000
#> SRR1617428 1 0.000 0.963 1.000 0.000
#> SRR1617429 1 0.000 0.963 1.000 0.000
#> SRR1617432 1 0.000 0.963 1.000 0.000
#> SRR1617433 1 0.000 0.963 1.000 0.000
#> SRR1617434 1 0.000 0.963 1.000 0.000
#> SRR1617436 1 0.000 0.963 1.000 0.000
#> SRR1617435 1 0.000 0.963 1.000 0.000
#> SRR1617437 1 0.000 0.963 1.000 0.000
#> SRR1617438 1 0.000 0.963 1.000 0.000
#> SRR1617439 1 0.000 0.963 1.000 0.000
#> SRR1617440 1 0.000 0.963 1.000 0.000
#> SRR1617441 1 0.000 0.963 1.000 0.000
#> SRR1617443 1 0.000 0.963 1.000 0.000
#> SRR1617442 1 0.000 0.963 1.000 0.000
#> SRR1617444 1 0.000 0.963 1.000 0.000
#> SRR1617445 1 0.000 0.963 1.000 0.000
#> SRR1617446 1 0.000 0.963 1.000 0.000
#> SRR1617447 1 0.000 0.963 1.000 0.000
#> SRR1617448 1 0.000 0.963 1.000 0.000
#> SRR1617449 1 0.000 0.963 1.000 0.000
#> SRR1617451 2 0.958 0.651 0.380 0.620
#> SRR1617450 2 0.949 0.675 0.368 0.632
#> SRR1617452 1 0.000 0.963 1.000 0.000
#> SRR1617454 2 0.760 0.850 0.220 0.780
#> SRR1617453 1 0.000 0.963 1.000 0.000
#> SRR1617456 1 0.738 0.678 0.792 0.208
#> SRR1617457 1 0.738 0.678 0.792 0.208
#> SRR1617455 2 0.760 0.850 0.220 0.780
#> SRR1617458 1 0.738 0.678 0.792 0.208
#> SRR1617459 1 0.738 0.678 0.792 0.208
#> SRR1617460 1 0.738 0.678 0.792 0.208
#> SRR1617461 1 0.738 0.678 0.792 0.208
#> SRR1617463 2 0.760 0.850 0.220 0.780
#> SRR1617462 2 0.760 0.850 0.220 0.780
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617431 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617410 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617411 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617412 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617413 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617414 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617415 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617416 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617417 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617418 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617419 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617420 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617421 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617422 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617423 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617424 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617425 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617427 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617426 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617428 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617429 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617432 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617433 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617434 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617436 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617435 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617437 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617438 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617439 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617440 1 0.0237 0.938 0.996 0.004 0.000
#> SRR1617441 1 0.0237 0.938 0.996 0.004 0.000
#> SRR1617443 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617442 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617444 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617445 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617446 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617447 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617448 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617449 1 0.0000 0.941 1.000 0.000 0.000
#> SRR1617451 2 0.3551 0.734 0.132 0.868 0.000
#> SRR1617450 2 0.3267 0.761 0.116 0.884 0.000
#> SRR1617452 1 0.0424 0.935 0.992 0.008 0.000
#> SRR1617454 2 0.1289 0.849 0.000 0.968 0.032
#> SRR1617453 1 0.0424 0.935 0.992 0.008 0.000
#> SRR1617456 1 0.6154 0.343 0.592 0.408 0.000
#> SRR1617457 1 0.6154 0.343 0.592 0.408 0.000
#> SRR1617455 2 0.1289 0.849 0.000 0.968 0.032
#> SRR1617458 1 0.6154 0.343 0.592 0.408 0.000
#> SRR1617459 1 0.6154 0.343 0.592 0.408 0.000
#> SRR1617460 1 0.5988 0.427 0.632 0.368 0.000
#> SRR1617461 1 0.5988 0.427 0.632 0.368 0.000
#> SRR1617463 2 0.2031 0.858 0.016 0.952 0.032
#> SRR1617462 2 0.2031 0.858 0.016 0.952 0.032
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 3 0.0000 1.0000 0.000 0.000 1 0.000
#> SRR1617431 3 0.0000 1.0000 0.000 0.000 1 0.000
#> SRR1617410 1 0.3311 0.7495 0.828 0.172 0 0.000
#> SRR1617411 1 0.3311 0.7495 0.828 0.172 0 0.000
#> SRR1617412 1 0.1637 0.8349 0.940 0.060 0 0.000
#> SRR1617413 1 0.1716 0.8335 0.936 0.064 0 0.000
#> SRR1617414 1 0.3907 0.7031 0.768 0.232 0 0.000
#> SRR1617415 1 0.3907 0.7031 0.768 0.232 0 0.000
#> SRR1617416 1 0.0000 0.8458 1.000 0.000 0 0.000
#> SRR1617417 1 0.0000 0.8458 1.000 0.000 0 0.000
#> SRR1617418 1 0.2281 0.8168 0.904 0.096 0 0.000
#> SRR1617419 1 0.2345 0.8147 0.900 0.100 0 0.000
#> SRR1617420 1 0.3907 0.7031 0.768 0.232 0 0.000
#> SRR1617421 1 0.3907 0.7031 0.768 0.232 0 0.000
#> SRR1617422 1 0.0000 0.8458 1.000 0.000 0 0.000
#> SRR1617423 1 0.0000 0.8458 1.000 0.000 0 0.000
#> SRR1617424 1 0.0000 0.8458 1.000 0.000 0 0.000
#> SRR1617425 1 0.0000 0.8458 1.000 0.000 0 0.000
#> SRR1617427 1 0.0000 0.8458 1.000 0.000 0 0.000
#> SRR1617426 1 0.0000 0.8458 1.000 0.000 0 0.000
#> SRR1617428 1 0.0469 0.8448 0.988 0.012 0 0.000
#> SRR1617429 1 0.0707 0.8438 0.980 0.020 0 0.000
#> SRR1617432 1 0.3907 0.7031 0.768 0.232 0 0.000
#> SRR1617433 1 0.3907 0.7031 0.768 0.232 0 0.000
#> SRR1617434 1 0.3907 0.7031 0.768 0.232 0 0.000
#> SRR1617436 1 0.0000 0.8458 1.000 0.000 0 0.000
#> SRR1617435 1 0.3907 0.7031 0.768 0.232 0 0.000
#> SRR1617437 1 0.0000 0.8458 1.000 0.000 0 0.000
#> SRR1617438 1 0.2647 0.8028 0.880 0.120 0 0.000
#> SRR1617439 1 0.2647 0.8028 0.880 0.120 0 0.000
#> SRR1617440 1 0.3942 0.6791 0.764 0.236 0 0.000
#> SRR1617441 1 0.4250 0.6138 0.724 0.276 0 0.000
#> SRR1617443 1 0.2647 0.8028 0.880 0.120 0 0.000
#> SRR1617442 1 0.2647 0.8028 0.880 0.120 0 0.000
#> SRR1617444 1 0.1637 0.8349 0.940 0.060 0 0.000
#> SRR1617445 1 0.1637 0.8349 0.940 0.060 0 0.000
#> SRR1617446 1 0.0000 0.8458 1.000 0.000 0 0.000
#> SRR1617447 1 0.0000 0.8458 1.000 0.000 0 0.000
#> SRR1617448 1 0.1637 0.8349 0.940 0.060 0 0.000
#> SRR1617449 1 0.1637 0.8349 0.940 0.060 0 0.000
#> SRR1617451 2 0.5294 -0.0803 0.008 0.508 0 0.484
#> SRR1617450 2 0.5294 -0.0803 0.008 0.508 0 0.484
#> SRR1617452 1 0.3837 0.6959 0.776 0.224 0 0.000
#> SRR1617454 4 0.0000 1.0000 0.000 0.000 0 1.000
#> SRR1617453 1 0.3764 0.7064 0.784 0.216 0 0.000
#> SRR1617456 2 0.3907 0.7090 0.232 0.768 0 0.000
#> SRR1617457 2 0.3907 0.7090 0.232 0.768 0 0.000
#> SRR1617455 4 0.0000 1.0000 0.000 0.000 0 1.000
#> SRR1617458 2 0.3907 0.7090 0.232 0.768 0 0.000
#> SRR1617459 2 0.3907 0.7090 0.232 0.768 0 0.000
#> SRR1617460 1 0.6179 0.2008 0.552 0.056 0 0.392
#> SRR1617461 1 0.6179 0.2008 0.552 0.056 0 0.392
#> SRR1617463 4 0.0000 1.0000 0.000 0.000 0 1.000
#> SRR1617462 4 0.0000 1.0000 0.000 0.000 0 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> SRR1617431 4 0.0000 1.000 0.000 0.000 0.000 1 0.000
#> SRR1617410 1 0.3999 0.122 0.656 0.000 0.344 0 0.000
#> SRR1617411 1 0.4045 0.066 0.644 0.000 0.356 0 0.000
#> SRR1617412 3 0.0000 0.608 0.000 0.000 1.000 0 0.000
#> SRR1617413 3 0.0000 0.608 0.000 0.000 1.000 0 0.000
#> SRR1617414 1 0.0703 0.876 0.976 0.000 0.024 0 0.000
#> SRR1617415 1 0.0703 0.876 0.976 0.000 0.024 0 0.000
#> SRR1617416 3 0.4268 0.588 0.444 0.000 0.556 0 0.000
#> SRR1617417 3 0.4268 0.588 0.444 0.000 0.556 0 0.000
#> SRR1617418 3 0.2471 0.615 0.136 0.000 0.864 0 0.000
#> SRR1617419 3 0.1544 0.612 0.068 0.000 0.932 0 0.000
#> SRR1617420 1 0.0703 0.876 0.976 0.000 0.024 0 0.000
#> SRR1617421 1 0.0703 0.876 0.976 0.000 0.024 0 0.000
#> SRR1617422 3 0.4268 0.588 0.444 0.000 0.556 0 0.000
#> SRR1617423 3 0.4268 0.588 0.444 0.000 0.556 0 0.000
#> SRR1617424 3 0.4268 0.588 0.444 0.000 0.556 0 0.000
#> SRR1617425 3 0.4268 0.588 0.444 0.000 0.556 0 0.000
#> SRR1617427 3 0.4268 0.588 0.444 0.000 0.556 0 0.000
#> SRR1617426 3 0.4268 0.588 0.444 0.000 0.556 0 0.000
#> SRR1617428 3 0.4249 0.594 0.432 0.000 0.568 0 0.000
#> SRR1617429 3 0.4201 0.604 0.408 0.000 0.592 0 0.000
#> SRR1617432 1 0.0703 0.876 0.976 0.000 0.024 0 0.000
#> SRR1617433 1 0.0703 0.876 0.976 0.000 0.024 0 0.000
#> SRR1617434 1 0.0703 0.876 0.976 0.000 0.024 0 0.000
#> SRR1617436 3 0.4268 0.588 0.444 0.000 0.556 0 0.000
#> SRR1617435 1 0.0703 0.876 0.976 0.000 0.024 0 0.000
#> SRR1617437 3 0.4268 0.588 0.444 0.000 0.556 0 0.000
#> SRR1617438 3 0.0000 0.608 0.000 0.000 1.000 0 0.000
#> SRR1617439 3 0.0000 0.608 0.000 0.000 1.000 0 0.000
#> SRR1617440 3 0.0000 0.608 0.000 0.000 1.000 0 0.000
#> SRR1617441 3 0.0000 0.608 0.000 0.000 1.000 0 0.000
#> SRR1617443 3 0.0000 0.608 0.000 0.000 1.000 0 0.000
#> SRR1617442 3 0.0000 0.608 0.000 0.000 1.000 0 0.000
#> SRR1617444 3 0.4074 0.620 0.364 0.000 0.636 0 0.000
#> SRR1617445 3 0.4074 0.620 0.364 0.000 0.636 0 0.000
#> SRR1617446 3 0.4268 0.588 0.444 0.000 0.556 0 0.000
#> SRR1617447 3 0.4268 0.588 0.444 0.000 0.556 0 0.000
#> SRR1617448 3 0.4074 0.620 0.364 0.000 0.636 0 0.000
#> SRR1617449 3 0.4074 0.620 0.364 0.000 0.636 0 0.000
#> SRR1617451 2 0.4735 0.631 0.024 0.664 0.008 0 0.304
#> SRR1617450 2 0.4735 0.631 0.024 0.664 0.008 0 0.304
#> SRR1617452 3 0.0451 0.610 0.008 0.004 0.988 0 0.000
#> SRR1617454 5 0.0000 1.000 0.000 0.000 0.000 0 1.000
#> SRR1617453 3 0.0671 0.612 0.016 0.004 0.980 0 0.000
#> SRR1617456 2 0.0000 0.844 0.000 1.000 0.000 0 0.000
#> SRR1617457 2 0.0000 0.844 0.000 1.000 0.000 0 0.000
#> SRR1617455 5 0.0000 1.000 0.000 0.000 0.000 0 1.000
#> SRR1617458 2 0.0000 0.844 0.000 1.000 0.000 0 0.000
#> SRR1617459 2 0.0000 0.844 0.000 1.000 0.000 0 0.000
#> SRR1617460 3 0.4150 0.439 0.000 0.000 0.612 0 0.388
#> SRR1617461 3 0.4150 0.439 0.000 0.000 0.612 0 0.388
#> SRR1617463 5 0.0000 1.000 0.000 0.000 0.000 0 1.000
#> SRR1617462 5 0.0000 1.000 0.000 0.000 0.000 0 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 1 0.5114 -0.5140 0.468 0.000 0.000 0.452 0.080 0.000
#> SRR1617431 1 0.5114 -0.5140 0.468 0.000 0.000 0.452 0.080 0.000
#> SRR1617410 1 0.5431 0.4131 0.532 0.000 0.332 0.000 0.136 0.000
#> SRR1617411 1 0.5367 0.4164 0.532 0.000 0.344 0.000 0.124 0.000
#> SRR1617412 3 0.0000 0.6984 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617413 3 0.0000 0.6984 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617414 5 0.1556 1.0000 0.080 0.000 0.000 0.000 0.920 0.000
#> SRR1617415 5 0.1556 1.0000 0.080 0.000 0.000 0.000 0.920 0.000
#> SRR1617416 1 0.3857 0.4508 0.532 0.000 0.468 0.000 0.000 0.000
#> SRR1617417 1 0.3857 0.4508 0.532 0.000 0.468 0.000 0.000 0.000
#> SRR1617418 3 0.2219 0.5931 0.136 0.000 0.864 0.000 0.000 0.000
#> SRR1617419 3 0.1387 0.6584 0.068 0.000 0.932 0.000 0.000 0.000
#> SRR1617420 1 0.4083 -0.0534 0.532 0.000 0.008 0.000 0.460 0.000
#> SRR1617421 1 0.4083 -0.0534 0.532 0.000 0.008 0.000 0.460 0.000
#> SRR1617422 1 0.3857 0.4508 0.532 0.000 0.468 0.000 0.000 0.000
#> SRR1617423 1 0.3857 0.4508 0.532 0.000 0.468 0.000 0.000 0.000
#> SRR1617424 1 0.3857 0.4508 0.532 0.000 0.468 0.000 0.000 0.000
#> SRR1617425 1 0.3857 0.4508 0.532 0.000 0.468 0.000 0.000 0.000
#> SRR1617427 1 0.3857 0.4508 0.532 0.000 0.468 0.000 0.000 0.000
#> SRR1617426 1 0.3857 0.4508 0.532 0.000 0.468 0.000 0.000 0.000
#> SRR1617428 3 0.3868 -0.3959 0.496 0.000 0.504 0.000 0.000 0.000
#> SRR1617429 3 0.3843 -0.2454 0.452 0.000 0.548 0.000 0.000 0.000
#> SRR1617432 5 0.1556 1.0000 0.080 0.000 0.000 0.000 0.920 0.000
#> SRR1617433 5 0.1556 1.0000 0.080 0.000 0.000 0.000 0.920 0.000
#> SRR1617434 1 0.3989 -0.0757 0.528 0.000 0.004 0.000 0.468 0.000
#> SRR1617436 1 0.3857 0.4508 0.532 0.000 0.468 0.000 0.000 0.000
#> SRR1617435 1 0.3989 -0.0757 0.528 0.000 0.004 0.000 0.468 0.000
#> SRR1617437 1 0.3857 0.4508 0.532 0.000 0.468 0.000 0.000 0.000
#> SRR1617438 3 0.0000 0.6984 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617439 3 0.0000 0.6984 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617440 3 0.0000 0.6984 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617441 3 0.0000 0.6984 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617443 3 0.0000 0.6984 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617442 3 0.0000 0.6984 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617444 3 0.3672 0.1159 0.368 0.000 0.632 0.000 0.000 0.000
#> SRR1617445 3 0.3672 0.1159 0.368 0.000 0.632 0.000 0.000 0.000
#> SRR1617446 1 0.3857 0.4508 0.532 0.000 0.468 0.000 0.000 0.000
#> SRR1617447 1 0.3857 0.4508 0.532 0.000 0.468 0.000 0.000 0.000
#> SRR1617448 3 0.3672 0.1159 0.368 0.000 0.632 0.000 0.000 0.000
#> SRR1617449 3 0.3672 0.1159 0.368 0.000 0.632 0.000 0.000 0.000
#> SRR1617451 4 0.5468 1.0000 0.000 0.156 0.000 0.548 0.000 0.296
#> SRR1617450 4 0.5468 1.0000 0.000 0.156 0.000 0.548 0.000 0.296
#> SRR1617452 3 0.0508 0.6945 0.004 0.000 0.984 0.000 0.000 0.012
#> SRR1617454 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617453 3 0.0820 0.6909 0.016 0.000 0.972 0.000 0.000 0.012
#> SRR1617456 6 0.0000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617457 6 0.0000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617455 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617458 6 0.0000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617459 6 0.0000 1.0000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617460 3 0.3847 0.3386 0.000 0.456 0.544 0.000 0.000 0.000
#> SRR1617461 3 0.3847 0.3386 0.000 0.456 0.544 0.000 0.000 0.000
#> SRR1617463 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617462 2 0.0000 1.0000 0.000 1.000 0.000 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["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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 0.632 0.909 0.941 0.4795 0.508 0.508
#> 3 3 0.514 0.747 0.829 0.2845 0.832 0.670
#> 4 4 0.671 0.821 0.893 0.1060 0.894 0.720
#> 5 5 0.695 0.847 0.871 0.0647 0.925 0.763
#> 6 6 0.695 0.804 0.805 0.0668 0.978 0.910
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
#> SRR1617430 2 0.0000 0.919 0.000 1.000
#> SRR1617431 2 0.0000 0.919 0.000 1.000
#> SRR1617410 1 0.0000 0.956 1.000 0.000
#> SRR1617411 1 0.0000 0.956 1.000 0.000
#> SRR1617412 2 0.6148 0.880 0.152 0.848
#> SRR1617413 2 0.6148 0.880 0.152 0.848
#> SRR1617414 1 0.0938 0.952 0.988 0.012
#> SRR1617415 1 0.0938 0.952 0.988 0.012
#> SRR1617416 1 0.6887 0.770 0.816 0.184
#> SRR1617417 1 0.6887 0.770 0.816 0.184
#> SRR1617418 2 0.3733 0.922 0.072 0.928
#> SRR1617419 2 0.3733 0.922 0.072 0.928
#> SRR1617420 1 0.6438 0.808 0.836 0.164
#> SRR1617421 1 0.6438 0.808 0.836 0.164
#> SRR1617422 1 0.0000 0.956 1.000 0.000
#> SRR1617423 1 0.0000 0.956 1.000 0.000
#> SRR1617424 1 0.0000 0.956 1.000 0.000
#> SRR1617425 1 0.0000 0.956 1.000 0.000
#> SRR1617427 1 0.0000 0.956 1.000 0.000
#> SRR1617426 1 0.0000 0.956 1.000 0.000
#> SRR1617428 2 0.3733 0.922 0.072 0.928
#> SRR1617429 2 0.3733 0.922 0.072 0.928
#> SRR1617432 1 0.1184 0.951 0.984 0.016
#> SRR1617433 1 0.1184 0.951 0.984 0.016
#> SRR1617434 1 0.0000 0.956 1.000 0.000
#> SRR1617436 2 0.3733 0.922 0.072 0.928
#> SRR1617435 1 0.0000 0.956 1.000 0.000
#> SRR1617437 2 0.3733 0.922 0.072 0.928
#> SRR1617438 2 0.6887 0.855 0.184 0.816
#> SRR1617439 2 0.6887 0.855 0.184 0.816
#> SRR1617440 2 0.5629 0.894 0.132 0.868
#> SRR1617441 2 0.5629 0.894 0.132 0.868
#> SRR1617443 2 0.6887 0.855 0.184 0.816
#> SRR1617442 2 0.6887 0.855 0.184 0.816
#> SRR1617444 2 0.7950 0.786 0.240 0.760
#> SRR1617445 2 0.7950 0.786 0.240 0.760
#> SRR1617446 1 0.0000 0.956 1.000 0.000
#> SRR1617447 1 0.0000 0.956 1.000 0.000
#> SRR1617448 1 0.2043 0.942 0.968 0.032
#> SRR1617449 1 0.2043 0.942 0.968 0.032
#> SRR1617451 2 0.0000 0.919 0.000 1.000
#> SRR1617450 2 0.0000 0.919 0.000 1.000
#> SRR1617452 2 0.3879 0.921 0.076 0.924
#> SRR1617454 2 0.0000 0.919 0.000 1.000
#> SRR1617453 2 0.3879 0.921 0.076 0.924
#> SRR1617456 2 0.0000 0.919 0.000 1.000
#> SRR1617457 2 0.0000 0.919 0.000 1.000
#> SRR1617455 2 0.0000 0.919 0.000 1.000
#> SRR1617458 2 0.0000 0.919 0.000 1.000
#> SRR1617459 2 0.0000 0.919 0.000 1.000
#> SRR1617460 2 0.0000 0.919 0.000 1.000
#> SRR1617461 2 0.0000 0.919 0.000 1.000
#> SRR1617463 2 0.0000 0.919 0.000 1.000
#> SRR1617462 2 0.0000 0.919 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.375 0.775 0.000 0.856 0.144
#> SRR1617431 2 0.375 0.775 0.000 0.856 0.144
#> SRR1617410 1 0.000 0.887 1.000 0.000 0.000
#> SRR1617411 1 0.000 0.887 1.000 0.000 0.000
#> SRR1617412 3 0.271 0.819 0.088 0.000 0.912
#> SRR1617413 3 0.271 0.819 0.088 0.000 0.912
#> SRR1617414 1 0.319 0.807 0.888 0.000 0.112
#> SRR1617415 1 0.319 0.807 0.888 0.000 0.112
#> SRR1617416 1 0.729 -0.305 0.492 0.028 0.480
#> SRR1617417 1 0.729 -0.305 0.492 0.028 0.480
#> SRR1617418 3 0.236 0.812 0.072 0.000 0.928
#> SRR1617419 3 0.236 0.812 0.072 0.000 0.928
#> SRR1617420 1 0.369 0.784 0.860 0.000 0.140
#> SRR1617421 1 0.369 0.784 0.860 0.000 0.140
#> SRR1617422 1 0.000 0.887 1.000 0.000 0.000
#> SRR1617423 1 0.000 0.887 1.000 0.000 0.000
#> SRR1617424 1 0.000 0.887 1.000 0.000 0.000
#> SRR1617425 1 0.000 0.887 1.000 0.000 0.000
#> SRR1617427 1 0.000 0.887 1.000 0.000 0.000
#> SRR1617426 1 0.000 0.887 1.000 0.000 0.000
#> SRR1617428 3 0.377 0.799 0.084 0.028 0.888
#> SRR1617429 3 0.377 0.799 0.084 0.028 0.888
#> SRR1617432 1 0.000 0.887 1.000 0.000 0.000
#> SRR1617433 1 0.000 0.887 1.000 0.000 0.000
#> SRR1617434 1 0.000 0.887 1.000 0.000 0.000
#> SRR1617436 3 0.245 0.814 0.076 0.000 0.924
#> SRR1617435 1 0.000 0.887 1.000 0.000 0.000
#> SRR1617437 3 0.245 0.814 0.076 0.000 0.924
#> SRR1617438 3 0.288 0.821 0.096 0.000 0.904
#> SRR1617439 3 0.288 0.821 0.096 0.000 0.904
#> SRR1617440 3 0.625 0.707 0.268 0.024 0.708
#> SRR1617441 3 0.625 0.707 0.268 0.024 0.708
#> SRR1617443 3 0.288 0.821 0.096 0.000 0.904
#> SRR1617442 3 0.288 0.821 0.096 0.000 0.904
#> SRR1617444 3 0.722 0.439 0.424 0.028 0.548
#> SRR1617445 3 0.722 0.439 0.424 0.028 0.548
#> SRR1617446 1 0.000 0.887 1.000 0.000 0.000
#> SRR1617447 1 0.000 0.887 1.000 0.000 0.000
#> SRR1617448 1 0.375 0.756 0.856 0.000 0.144
#> SRR1617449 1 0.394 0.739 0.844 0.000 0.156
#> SRR1617451 2 0.465 0.886 0.000 0.792 0.208
#> SRR1617450 2 0.465 0.886 0.000 0.792 0.208
#> SRR1617452 3 0.630 0.713 0.260 0.028 0.712
#> SRR1617454 2 0.341 0.899 0.000 0.876 0.124
#> SRR1617453 3 0.630 0.713 0.260 0.028 0.712
#> SRR1617456 2 0.434 0.901 0.016 0.848 0.136
#> SRR1617457 2 0.434 0.901 0.016 0.848 0.136
#> SRR1617455 2 0.341 0.899 0.000 0.876 0.124
#> SRR1617458 2 0.434 0.901 0.016 0.848 0.136
#> SRR1617459 2 0.434 0.901 0.016 0.848 0.136
#> SRR1617460 3 0.661 0.015 0.016 0.356 0.628
#> SRR1617461 3 0.661 0.015 0.016 0.356 0.628
#> SRR1617463 2 0.529 0.794 0.000 0.732 0.268
#> SRR1617462 2 0.529 0.794 0.000 0.732 0.268
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 4 0.4643 1.000 0.000 0.344 0.000 0.656
#> SRR1617431 4 0.4643 1.000 0.000 0.344 0.000 0.656
#> SRR1617410 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> SRR1617411 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> SRR1617412 3 0.0188 0.877 0.004 0.000 0.996 0.000
#> SRR1617413 3 0.0188 0.877 0.004 0.000 0.996 0.000
#> SRR1617414 1 0.2831 0.822 0.876 0.000 0.120 0.004
#> SRR1617415 1 0.2831 0.822 0.876 0.000 0.120 0.004
#> SRR1617416 3 0.5701 0.683 0.276 0.048 0.672 0.004
#> SRR1617417 3 0.5701 0.683 0.276 0.048 0.672 0.004
#> SRR1617418 3 0.0000 0.875 0.000 0.000 1.000 0.000
#> SRR1617419 3 0.0000 0.875 0.000 0.000 1.000 0.000
#> SRR1617420 1 0.4088 0.709 0.764 0.000 0.232 0.004
#> SRR1617421 1 0.4088 0.709 0.764 0.000 0.232 0.004
#> SRR1617422 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> SRR1617423 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> SRR1617424 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> SRR1617425 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> SRR1617427 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> SRR1617426 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> SRR1617428 3 0.1576 0.870 0.000 0.048 0.948 0.004
#> SRR1617429 3 0.1576 0.870 0.000 0.048 0.948 0.004
#> SRR1617432 1 0.0188 0.917 0.996 0.000 0.004 0.000
#> SRR1617433 1 0.0188 0.917 0.996 0.000 0.004 0.000
#> SRR1617434 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> SRR1617436 3 0.0000 0.875 0.000 0.000 1.000 0.000
#> SRR1617435 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> SRR1617437 3 0.0000 0.875 0.000 0.000 1.000 0.000
#> SRR1617438 3 0.1940 0.868 0.076 0.000 0.924 0.000
#> SRR1617439 3 0.1940 0.868 0.076 0.000 0.924 0.000
#> SRR1617440 3 0.2759 0.875 0.044 0.052 0.904 0.000
#> SRR1617441 3 0.2759 0.875 0.044 0.052 0.904 0.000
#> SRR1617443 3 0.1940 0.868 0.076 0.000 0.924 0.000
#> SRR1617442 3 0.1940 0.868 0.076 0.000 0.924 0.000
#> SRR1617444 3 0.5669 0.701 0.260 0.052 0.684 0.004
#> SRR1617445 3 0.5669 0.701 0.260 0.052 0.684 0.004
#> SRR1617446 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> SRR1617447 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> SRR1617448 1 0.3982 0.685 0.776 0.000 0.220 0.004
#> SRR1617449 1 0.4018 0.678 0.772 0.000 0.224 0.004
#> SRR1617451 2 0.3024 0.719 0.000 0.852 0.148 0.000
#> SRR1617450 2 0.3024 0.719 0.000 0.852 0.148 0.000
#> SRR1617452 3 0.1474 0.869 0.000 0.052 0.948 0.000
#> SRR1617454 2 0.0000 0.705 0.000 1.000 0.000 0.000
#> SRR1617453 3 0.1474 0.869 0.000 0.052 0.948 0.000
#> SRR1617456 2 0.4936 0.675 0.000 0.652 0.008 0.340
#> SRR1617457 2 0.4936 0.675 0.000 0.652 0.008 0.340
#> SRR1617455 2 0.0000 0.705 0.000 1.000 0.000 0.000
#> SRR1617458 2 0.4936 0.675 0.000 0.652 0.008 0.340
#> SRR1617459 2 0.4936 0.675 0.000 0.652 0.008 0.340
#> SRR1617460 2 0.3569 0.672 0.000 0.804 0.196 0.000
#> SRR1617461 2 0.3486 0.683 0.000 0.812 0.188 0.000
#> SRR1617463 2 0.0000 0.705 0.000 1.000 0.000 0.000
#> SRR1617462 2 0.0000 0.705 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
#> SRR1617430 4 0.1121 1.000 0.000 0.044 0.000 0.956 0.000
#> SRR1617431 4 0.1121 1.000 0.000 0.044 0.000 0.956 0.000
#> SRR1617410 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> SRR1617411 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> SRR1617412 3 0.0000 0.933 0.000 0.000 1.000 0.000 0.000
#> SRR1617413 3 0.0000 0.933 0.000 0.000 1.000 0.000 0.000
#> SRR1617414 1 0.3209 0.757 0.848 0.000 0.120 0.028 0.004
#> SRR1617415 1 0.3209 0.757 0.848 0.000 0.120 0.028 0.004
#> SRR1617416 5 0.6120 0.904 0.256 0.000 0.184 0.000 0.560
#> SRR1617417 5 0.6120 0.904 0.256 0.000 0.184 0.000 0.560
#> SRR1617418 3 0.0771 0.933 0.000 0.000 0.976 0.004 0.020
#> SRR1617419 3 0.0771 0.933 0.000 0.000 0.976 0.004 0.020
#> SRR1617420 1 0.4121 0.557 0.720 0.000 0.264 0.012 0.004
#> SRR1617421 1 0.4121 0.557 0.720 0.000 0.264 0.012 0.004
#> SRR1617422 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> SRR1617423 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> SRR1617424 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> SRR1617425 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> SRR1617427 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> SRR1617426 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> SRR1617428 3 0.1026 0.932 0.004 0.000 0.968 0.004 0.024
#> SRR1617429 3 0.1026 0.932 0.004 0.000 0.968 0.004 0.024
#> SRR1617432 1 0.0162 0.917 0.996 0.000 0.004 0.000 0.000
#> SRR1617433 1 0.0162 0.917 0.996 0.000 0.004 0.000 0.000
#> SRR1617434 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> SRR1617436 3 0.0771 0.933 0.000 0.000 0.976 0.004 0.020
#> SRR1617435 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> SRR1617437 3 0.0771 0.933 0.000 0.000 0.976 0.004 0.020
#> SRR1617438 3 0.2325 0.873 0.068 0.000 0.904 0.028 0.000
#> SRR1617439 3 0.2325 0.873 0.068 0.000 0.904 0.028 0.000
#> SRR1617440 3 0.1412 0.924 0.008 0.004 0.952 0.036 0.000
#> SRR1617441 3 0.1412 0.924 0.008 0.004 0.952 0.036 0.000
#> SRR1617443 3 0.2491 0.870 0.068 0.000 0.896 0.036 0.000
#> SRR1617442 3 0.2491 0.870 0.068 0.000 0.896 0.036 0.000
#> SRR1617444 5 0.6272 0.867 0.200 0.000 0.236 0.004 0.560
#> SRR1617445 5 0.6272 0.867 0.200 0.000 0.236 0.004 0.560
#> SRR1617446 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> SRR1617447 1 0.0000 0.920 1.000 0.000 0.000 0.000 0.000
#> SRR1617448 5 0.6121 0.870 0.324 0.000 0.148 0.000 0.528
#> SRR1617449 5 0.6121 0.870 0.324 0.000 0.148 0.000 0.528
#> SRR1617451 2 0.2886 0.725 0.000 0.844 0.148 0.000 0.008
#> SRR1617450 2 0.2886 0.725 0.000 0.844 0.148 0.000 0.008
#> SRR1617452 3 0.1697 0.894 0.000 0.060 0.932 0.008 0.000
#> SRR1617454 2 0.0000 0.735 0.000 1.000 0.000 0.000 0.000
#> SRR1617453 3 0.1697 0.894 0.000 0.060 0.932 0.008 0.000
#> SRR1617456 2 0.4383 0.657 0.000 0.572 0.000 0.004 0.424
#> SRR1617457 2 0.4383 0.657 0.000 0.572 0.000 0.004 0.424
#> SRR1617455 2 0.0000 0.735 0.000 1.000 0.000 0.000 0.000
#> SRR1617458 2 0.4383 0.657 0.000 0.572 0.000 0.004 0.424
#> SRR1617459 2 0.4383 0.657 0.000 0.572 0.000 0.004 0.424
#> SRR1617460 2 0.4035 0.670 0.000 0.756 0.220 0.008 0.016
#> SRR1617461 2 0.4035 0.670 0.000 0.756 0.220 0.008 0.016
#> SRR1617463 2 0.0000 0.735 0.000 1.000 0.000 0.000 0.000
#> SRR1617462 2 0.0000 0.735 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
#> SRR1617430 4 0.5916 1.000 0.336 0.000 0.000 0.444 0.000 0.220
#> SRR1617431 4 0.5916 1.000 0.336 0.000 0.000 0.444 0.000 0.220
#> SRR1617410 5 0.0291 0.875 0.004 0.000 0.004 0.000 0.992 0.000
#> SRR1617411 5 0.0291 0.875 0.004 0.000 0.004 0.000 0.992 0.000
#> SRR1617412 3 0.2020 0.734 0.008 0.000 0.896 0.096 0.000 0.000
#> SRR1617413 3 0.2020 0.734 0.008 0.000 0.896 0.096 0.000 0.000
#> SRR1617414 5 0.3789 0.721 0.040 0.000 0.160 0.016 0.784 0.000
#> SRR1617415 5 0.3789 0.721 0.040 0.000 0.160 0.016 0.784 0.000
#> SRR1617416 1 0.4632 0.875 0.656 0.000 0.064 0.004 0.276 0.000
#> SRR1617417 1 0.4598 0.874 0.656 0.000 0.060 0.004 0.280 0.000
#> SRR1617418 3 0.4062 0.624 0.008 0.000 0.552 0.440 0.000 0.000
#> SRR1617419 3 0.4062 0.624 0.008 0.000 0.552 0.440 0.000 0.000
#> SRR1617420 5 0.4023 0.677 0.016 0.000 0.124 0.080 0.780 0.000
#> SRR1617421 5 0.4023 0.677 0.016 0.000 0.124 0.080 0.780 0.000
#> SRR1617422 5 0.0777 0.872 0.024 0.000 0.004 0.000 0.972 0.000
#> SRR1617423 5 0.0777 0.872 0.024 0.000 0.004 0.000 0.972 0.000
#> SRR1617424 5 0.1757 0.844 0.076 0.000 0.008 0.000 0.916 0.000
#> SRR1617425 5 0.1757 0.844 0.076 0.000 0.008 0.000 0.916 0.000
#> SRR1617427 5 0.1349 0.860 0.056 0.000 0.004 0.000 0.940 0.000
#> SRR1617426 5 0.1349 0.860 0.056 0.000 0.004 0.000 0.940 0.000
#> SRR1617428 3 0.5464 0.559 0.016 0.000 0.456 0.452 0.076 0.000
#> SRR1617429 3 0.5464 0.559 0.016 0.000 0.456 0.452 0.076 0.000
#> SRR1617432 5 0.1434 0.865 0.020 0.000 0.024 0.008 0.948 0.000
#> SRR1617433 5 0.1434 0.865 0.020 0.000 0.024 0.008 0.948 0.000
#> SRR1617434 5 0.0146 0.875 0.000 0.000 0.004 0.000 0.996 0.000
#> SRR1617436 3 0.4083 0.617 0.008 0.000 0.532 0.460 0.000 0.000
#> SRR1617435 5 0.0146 0.875 0.000 0.000 0.004 0.000 0.996 0.000
#> SRR1617437 3 0.4083 0.617 0.008 0.000 0.532 0.460 0.000 0.000
#> SRR1617438 3 0.1605 0.714 0.004 0.000 0.936 0.000 0.044 0.016
#> SRR1617439 3 0.1605 0.714 0.004 0.000 0.936 0.000 0.044 0.016
#> SRR1617440 3 0.2925 0.685 0.016 0.000 0.880 0.024 0.048 0.032
#> SRR1617441 3 0.2925 0.685 0.016 0.000 0.880 0.024 0.048 0.032
#> SRR1617443 3 0.2706 0.699 0.048 0.016 0.888 0.008 0.040 0.000
#> SRR1617442 3 0.2706 0.699 0.048 0.016 0.888 0.008 0.040 0.000
#> SRR1617444 1 0.5055 0.790 0.652 0.004 0.184 0.000 0.160 0.000
#> SRR1617445 1 0.5055 0.790 0.652 0.004 0.184 0.000 0.160 0.000
#> SRR1617446 5 0.1843 0.846 0.080 0.000 0.004 0.004 0.912 0.000
#> SRR1617447 5 0.1956 0.848 0.080 0.000 0.004 0.008 0.908 0.000
#> SRR1617448 1 0.4660 0.844 0.612 0.000 0.060 0.000 0.328 0.000
#> SRR1617449 1 0.4660 0.844 0.612 0.000 0.060 0.000 0.328 0.000
#> SRR1617451 2 0.3061 0.860 0.008 0.840 0.020 0.128 0.000 0.004
#> SRR1617450 2 0.3061 0.860 0.008 0.840 0.020 0.128 0.000 0.004
#> SRR1617452 3 0.2720 0.729 0.004 0.016 0.884 0.056 0.000 0.040
#> SRR1617454 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617453 3 0.2720 0.729 0.004 0.016 0.884 0.056 0.000 0.040
#> SRR1617456 6 0.3449 0.995 0.008 0.196 0.016 0.000 0.000 0.780
#> SRR1617457 6 0.3449 0.995 0.008 0.196 0.016 0.000 0.000 0.780
#> SRR1617455 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617458 6 0.3457 0.995 0.012 0.196 0.012 0.000 0.000 0.780
#> SRR1617459 6 0.3457 0.995 0.012 0.196 0.012 0.000 0.000 0.780
#> SRR1617460 2 0.4529 0.823 0.020 0.776 0.068 0.096 0.000 0.040
#> SRR1617461 2 0.4529 0.823 0.020 0.776 0.068 0.096 0.000 0.040
#> SRR1617463 2 0.0993 0.864 0.000 0.964 0.000 0.012 0.000 0.024
#> SRR1617462 2 0.0993 0.864 0.000 0.964 0.000 0.012 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)
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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 0.852 0.931 0.971 0.4357 0.547 0.547
#> 3 3 1.000 0.957 0.981 0.5071 0.726 0.528
#> 4 4 0.799 0.744 0.823 0.0899 0.962 0.887
#> 5 5 0.749 0.792 0.786 0.0919 0.867 0.575
#> 6 6 0.893 0.750 0.854 0.0575 0.952 0.766
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
#> SRR1617430 2 0.295 0.891 0.052 0.948
#> SRR1617431 2 0.204 0.903 0.032 0.968
#> SRR1617410 1 0.000 0.993 1.000 0.000
#> SRR1617411 1 0.000 0.993 1.000 0.000
#> SRR1617412 1 0.000 0.993 1.000 0.000
#> SRR1617413 1 0.000 0.993 1.000 0.000
#> SRR1617414 1 0.000 0.993 1.000 0.000
#> SRR1617415 1 0.000 0.993 1.000 0.000
#> SRR1617416 1 0.000 0.993 1.000 0.000
#> SRR1617417 1 0.000 0.993 1.000 0.000
#> SRR1617418 1 0.000 0.993 1.000 0.000
#> SRR1617419 1 0.000 0.993 1.000 0.000
#> SRR1617420 1 0.000 0.993 1.000 0.000
#> SRR1617421 1 0.000 0.993 1.000 0.000
#> SRR1617422 1 0.000 0.993 1.000 0.000
#> SRR1617423 1 0.000 0.993 1.000 0.000
#> SRR1617424 1 0.000 0.993 1.000 0.000
#> SRR1617425 1 0.000 0.993 1.000 0.000
#> SRR1617427 1 0.000 0.993 1.000 0.000
#> SRR1617426 1 0.000 0.993 1.000 0.000
#> SRR1617428 1 0.469 0.878 0.900 0.100
#> SRR1617429 1 0.563 0.833 0.868 0.132
#> SRR1617432 1 0.000 0.993 1.000 0.000
#> SRR1617433 1 0.000 0.993 1.000 0.000
#> SRR1617434 1 0.000 0.993 1.000 0.000
#> SRR1617436 1 0.000 0.993 1.000 0.000
#> SRR1617435 1 0.000 0.993 1.000 0.000
#> SRR1617437 1 0.000 0.993 1.000 0.000
#> SRR1617438 1 0.000 0.993 1.000 0.000
#> SRR1617439 1 0.000 0.993 1.000 0.000
#> SRR1617440 2 0.998 0.190 0.476 0.524
#> SRR1617441 2 0.994 0.252 0.456 0.544
#> SRR1617443 1 0.000 0.993 1.000 0.000
#> SRR1617442 1 0.000 0.993 1.000 0.000
#> SRR1617444 1 0.000 0.993 1.000 0.000
#> SRR1617445 1 0.000 0.993 1.000 0.000
#> SRR1617446 1 0.000 0.993 1.000 0.000
#> SRR1617447 1 0.000 0.993 1.000 0.000
#> SRR1617448 1 0.000 0.993 1.000 0.000
#> SRR1617449 1 0.000 0.993 1.000 0.000
#> SRR1617451 2 0.000 0.918 0.000 1.000
#> SRR1617450 2 0.000 0.918 0.000 1.000
#> SRR1617452 2 0.662 0.788 0.172 0.828
#> SRR1617454 2 0.000 0.918 0.000 1.000
#> SRR1617453 2 0.662 0.788 0.172 0.828
#> SRR1617456 2 0.000 0.918 0.000 1.000
#> SRR1617457 2 0.000 0.918 0.000 1.000
#> SRR1617455 2 0.000 0.918 0.000 1.000
#> SRR1617458 2 0.000 0.918 0.000 1.000
#> SRR1617459 2 0.000 0.918 0.000 1.000
#> SRR1617460 2 0.000 0.918 0.000 1.000
#> SRR1617461 2 0.000 0.918 0.000 1.000
#> SRR1617463 2 0.000 0.918 0.000 1.000
#> SRR1617462 2 0.000 0.918 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 3 0.0000 0.989 0.000 0.000 1.000
#> SRR1617431 3 0.0000 0.989 0.000 0.000 1.000
#> SRR1617410 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617411 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617412 3 0.0424 0.995 0.008 0.000 0.992
#> SRR1617413 3 0.0424 0.995 0.008 0.000 0.992
#> SRR1617414 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617415 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617416 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617417 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617418 3 0.0424 0.995 0.008 0.000 0.992
#> SRR1617419 3 0.0424 0.995 0.008 0.000 0.992
#> SRR1617420 1 0.0424 0.992 0.992 0.000 0.008
#> SRR1617421 1 0.0424 0.992 0.992 0.000 0.008
#> SRR1617422 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617423 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617424 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617425 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617427 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617426 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617428 3 0.0424 0.995 0.008 0.000 0.992
#> SRR1617429 3 0.0424 0.995 0.008 0.000 0.992
#> SRR1617432 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617433 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617434 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617436 3 0.0424 0.995 0.008 0.000 0.992
#> SRR1617435 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617437 3 0.0424 0.995 0.008 0.000 0.992
#> SRR1617438 3 0.0424 0.995 0.008 0.000 0.992
#> SRR1617439 3 0.0424 0.995 0.008 0.000 0.992
#> SRR1617440 3 0.0592 0.986 0.000 0.012 0.988
#> SRR1617441 3 0.1289 0.967 0.000 0.032 0.968
#> SRR1617443 3 0.0424 0.995 0.008 0.000 0.992
#> SRR1617442 3 0.0424 0.995 0.008 0.000 0.992
#> SRR1617444 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617445 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617446 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617447 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617448 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617449 1 0.0000 0.999 1.000 0.000 0.000
#> SRR1617451 2 0.0424 0.931 0.000 0.992 0.008
#> SRR1617450 2 0.0424 0.931 0.000 0.992 0.008
#> SRR1617452 2 0.6168 0.343 0.000 0.588 0.412
#> SRR1617454 2 0.0424 0.931 0.000 0.992 0.008
#> SRR1617453 2 0.6180 0.333 0.000 0.584 0.416
#> SRR1617456 2 0.0000 0.931 0.000 1.000 0.000
#> SRR1617457 2 0.0000 0.931 0.000 1.000 0.000
#> SRR1617455 2 0.0424 0.931 0.000 0.992 0.008
#> SRR1617458 2 0.0000 0.931 0.000 1.000 0.000
#> SRR1617459 2 0.0000 0.931 0.000 1.000 0.000
#> SRR1617460 2 0.0000 0.931 0.000 1.000 0.000
#> SRR1617461 2 0.0000 0.931 0.000 1.000 0.000
#> SRR1617463 2 0.0424 0.931 0.000 0.992 0.008
#> SRR1617462 2 0.0424 0.931 0.000 0.992 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 4 0.4624 0.8201 0.000 0.000 0.340 0.660
#> SRR1617431 4 0.4624 0.8201 0.000 0.000 0.340 0.660
#> SRR1617410 1 0.0000 0.8772 1.000 0.000 0.000 0.000
#> SRR1617411 1 0.0000 0.8772 1.000 0.000 0.000 0.000
#> SRR1617412 3 0.1302 0.7323 0.000 0.000 0.956 0.044
#> SRR1617413 3 0.1302 0.7323 0.000 0.000 0.956 0.044
#> SRR1617414 1 0.0000 0.8772 1.000 0.000 0.000 0.000
#> SRR1617415 1 0.0000 0.8772 1.000 0.000 0.000 0.000
#> SRR1617416 1 0.4426 0.9039 0.772 0.000 0.024 0.204
#> SRR1617417 1 0.4361 0.9041 0.772 0.000 0.020 0.208
#> SRR1617418 4 0.4999 0.6904 0.000 0.000 0.492 0.508
#> SRR1617419 3 0.4999 -0.7388 0.000 0.000 0.508 0.492
#> SRR1617420 1 0.0376 0.8722 0.992 0.000 0.004 0.004
#> SRR1617421 1 0.0376 0.8722 0.992 0.000 0.004 0.004
#> SRR1617422 1 0.3791 0.9088 0.796 0.000 0.004 0.200
#> SRR1617423 1 0.3933 0.9087 0.792 0.000 0.008 0.200
#> SRR1617424 1 0.4175 0.9078 0.784 0.000 0.016 0.200
#> SRR1617425 1 0.4175 0.9078 0.784 0.000 0.016 0.200
#> SRR1617427 1 0.3610 0.9086 0.800 0.000 0.000 0.200
#> SRR1617426 1 0.3610 0.9086 0.800 0.000 0.000 0.200
#> SRR1617428 4 0.4907 0.8484 0.000 0.000 0.420 0.580
#> SRR1617429 4 0.4907 0.8484 0.000 0.000 0.420 0.580
#> SRR1617432 1 0.0000 0.8772 1.000 0.000 0.000 0.000
#> SRR1617433 1 0.0000 0.8772 1.000 0.000 0.000 0.000
#> SRR1617434 1 0.0000 0.8772 1.000 0.000 0.000 0.000
#> SRR1617436 3 0.4277 0.1746 0.000 0.000 0.720 0.280
#> SRR1617435 1 0.0000 0.8772 1.000 0.000 0.000 0.000
#> SRR1617437 3 0.4431 0.0564 0.000 0.000 0.696 0.304
#> SRR1617438 3 0.0000 0.7556 0.000 0.000 1.000 0.000
#> SRR1617439 3 0.0000 0.7556 0.000 0.000 1.000 0.000
#> SRR1617440 3 0.2124 0.6886 0.000 0.068 0.924 0.008
#> SRR1617441 3 0.2048 0.6934 0.000 0.064 0.928 0.008
#> SRR1617443 3 0.0000 0.7556 0.000 0.000 1.000 0.000
#> SRR1617442 3 0.0000 0.7556 0.000 0.000 1.000 0.000
#> SRR1617444 1 0.4793 0.8947 0.756 0.000 0.040 0.204
#> SRR1617445 1 0.4793 0.8947 0.756 0.000 0.040 0.204
#> SRR1617446 1 0.4175 0.9078 0.784 0.000 0.016 0.200
#> SRR1617447 1 0.4175 0.9078 0.784 0.000 0.016 0.200
#> SRR1617448 1 0.4214 0.9068 0.780 0.000 0.016 0.204
#> SRR1617449 1 0.4214 0.9068 0.780 0.000 0.016 0.204
#> SRR1617451 2 0.4356 0.7671 0.000 0.708 0.000 0.292
#> SRR1617450 2 0.4382 0.7648 0.000 0.704 0.000 0.296
#> SRR1617452 2 0.7937 -0.0812 0.008 0.452 0.236 0.304
#> SRR1617454 2 0.4103 0.7837 0.000 0.744 0.000 0.256
#> SRR1617453 2 0.7937 -0.0812 0.008 0.452 0.236 0.304
#> SRR1617456 2 0.0524 0.8046 0.000 0.988 0.004 0.008
#> SRR1617457 2 0.0524 0.8046 0.000 0.988 0.004 0.008
#> SRR1617455 2 0.4103 0.7837 0.000 0.744 0.000 0.256
#> SRR1617458 2 0.0524 0.8046 0.000 0.988 0.004 0.008
#> SRR1617459 2 0.0524 0.8046 0.000 0.988 0.004 0.008
#> SRR1617460 2 0.0336 0.8055 0.000 0.992 0.000 0.008
#> SRR1617461 2 0.0336 0.8055 0.000 0.992 0.000 0.008
#> SRR1617463 2 0.3764 0.7953 0.000 0.784 0.000 0.216
#> SRR1617462 2 0.3764 0.7953 0.000 0.784 0.000 0.216
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 4 0.2605 0.699 0.000 0.000 0.148 0.852 0.000
#> SRR1617431 4 0.2605 0.699 0.000 0.000 0.148 0.852 0.000
#> SRR1617410 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617411 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617412 3 0.1478 0.808 0.000 0.000 0.936 0.064 0.000
#> SRR1617413 3 0.1478 0.808 0.000 0.000 0.936 0.064 0.000
#> SRR1617414 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617415 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617416 1 0.5379 0.852 0.676 0.000 0.016 0.076 0.232
#> SRR1617417 1 0.5379 0.852 0.676 0.000 0.016 0.076 0.232
#> SRR1617418 4 0.4126 0.494 0.000 0.000 0.380 0.620 0.000
#> SRR1617419 4 0.4227 0.415 0.000 0.000 0.420 0.580 0.000
#> SRR1617420 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617421 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617422 1 0.3966 0.961 0.664 0.000 0.000 0.000 0.336
#> SRR1617423 1 0.3966 0.961 0.664 0.000 0.000 0.000 0.336
#> SRR1617424 1 0.3949 0.963 0.668 0.000 0.000 0.000 0.332
#> SRR1617425 1 0.3949 0.963 0.668 0.000 0.000 0.000 0.332
#> SRR1617427 1 0.3966 0.961 0.664 0.000 0.000 0.000 0.336
#> SRR1617426 1 0.3966 0.961 0.664 0.000 0.000 0.000 0.336
#> SRR1617428 4 0.3003 0.700 0.000 0.000 0.188 0.812 0.000
#> SRR1617429 4 0.3003 0.700 0.000 0.000 0.188 0.812 0.000
#> SRR1617432 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617433 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617434 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617436 3 0.4166 0.325 0.004 0.000 0.648 0.348 0.000
#> SRR1617435 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617437 3 0.4182 0.313 0.004 0.000 0.644 0.352 0.000
#> SRR1617438 3 0.0290 0.836 0.008 0.000 0.992 0.000 0.000
#> SRR1617439 3 0.0290 0.836 0.008 0.000 0.992 0.000 0.000
#> SRR1617440 3 0.2387 0.776 0.040 0.048 0.908 0.004 0.000
#> SRR1617441 3 0.2609 0.765 0.052 0.048 0.896 0.004 0.000
#> SRR1617443 3 0.0290 0.836 0.008 0.000 0.992 0.000 0.000
#> SRR1617442 3 0.0290 0.836 0.008 0.000 0.992 0.000 0.000
#> SRR1617444 1 0.4492 0.933 0.680 0.020 0.004 0.000 0.296
#> SRR1617445 1 0.4492 0.933 0.680 0.020 0.004 0.000 0.296
#> SRR1617446 1 0.3949 0.963 0.668 0.000 0.000 0.000 0.332
#> SRR1617447 1 0.3949 0.963 0.668 0.000 0.000 0.000 0.332
#> SRR1617448 1 0.3949 0.963 0.668 0.000 0.000 0.000 0.332
#> SRR1617449 1 0.3949 0.963 0.668 0.000 0.000 0.000 0.332
#> SRR1617451 2 0.6517 0.573 0.192 0.416 0.000 0.392 0.000
#> SRR1617450 2 0.6519 0.562 0.192 0.408 0.000 0.400 0.000
#> SRR1617452 4 0.8123 0.323 0.128 0.332 0.124 0.404 0.012
#> SRR1617454 2 0.5618 0.683 0.136 0.628 0.000 0.236 0.000
#> SRR1617453 4 0.8112 0.341 0.128 0.324 0.124 0.412 0.012
#> SRR1617456 2 0.3289 0.682 0.172 0.816 0.008 0.004 0.000
#> SRR1617457 2 0.3289 0.682 0.172 0.816 0.008 0.004 0.000
#> SRR1617455 2 0.5618 0.683 0.136 0.628 0.000 0.236 0.000
#> SRR1617458 2 0.3289 0.682 0.172 0.816 0.008 0.004 0.000
#> SRR1617459 2 0.3289 0.682 0.172 0.816 0.008 0.004 0.000
#> SRR1617460 2 0.0404 0.707 0.012 0.988 0.000 0.000 0.000
#> SRR1617461 2 0.0404 0.707 0.012 0.988 0.000 0.000 0.000
#> SRR1617463 2 0.5264 0.702 0.128 0.676 0.000 0.196 0.000
#> SRR1617462 2 0.5264 0.702 0.128 0.676 0.000 0.196 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 4 0.1059 0.574 0.000 0.016 0.016 0.964 0.004 0.000
#> SRR1617431 4 0.1059 0.574 0.000 0.016 0.016 0.964 0.004 0.000
#> SRR1617410 5 0.1387 0.996 0.068 0.000 0.000 0.000 0.932 0.000
#> SRR1617411 5 0.1387 0.996 0.068 0.000 0.000 0.000 0.932 0.000
#> SRR1617412 3 0.3739 0.637 0.004 0.020 0.772 0.192 0.012 0.000
#> SRR1617413 3 0.3739 0.637 0.004 0.020 0.772 0.192 0.012 0.000
#> SRR1617414 5 0.1787 0.993 0.068 0.008 0.000 0.004 0.920 0.000
#> SRR1617415 5 0.1787 0.993 0.068 0.008 0.000 0.004 0.920 0.000
#> SRR1617416 1 0.1837 0.921 0.932 0.032 0.004 0.012 0.020 0.000
#> SRR1617417 1 0.1837 0.921 0.932 0.032 0.004 0.012 0.020 0.000
#> SRR1617418 4 0.4302 0.307 0.004 0.012 0.344 0.632 0.008 0.000
#> SRR1617419 4 0.4398 0.244 0.004 0.012 0.376 0.600 0.008 0.000
#> SRR1617420 5 0.1387 0.996 0.068 0.000 0.000 0.000 0.932 0.000
#> SRR1617421 5 0.1387 0.996 0.068 0.000 0.000 0.000 0.932 0.000
#> SRR1617422 1 0.0363 0.984 0.988 0.000 0.000 0.000 0.012 0.000
#> SRR1617423 1 0.0363 0.984 0.988 0.000 0.000 0.000 0.012 0.000
#> SRR1617424 1 0.0363 0.984 0.988 0.000 0.000 0.000 0.012 0.000
#> SRR1617425 1 0.0363 0.984 0.988 0.000 0.000 0.000 0.012 0.000
#> SRR1617427 1 0.0458 0.981 0.984 0.000 0.000 0.000 0.016 0.000
#> SRR1617426 1 0.0458 0.981 0.984 0.000 0.000 0.000 0.016 0.000
#> SRR1617428 4 0.2837 0.595 0.008 0.060 0.032 0.880 0.020 0.000
#> SRR1617429 4 0.2837 0.595 0.008 0.060 0.032 0.880 0.020 0.000
#> SRR1617432 5 0.1787 0.993 0.068 0.008 0.000 0.004 0.920 0.000
#> SRR1617433 5 0.1787 0.993 0.068 0.008 0.000 0.004 0.920 0.000
#> SRR1617434 5 0.1387 0.996 0.068 0.000 0.000 0.000 0.932 0.000
#> SRR1617436 4 0.6188 0.299 0.012 0.088 0.396 0.468 0.036 0.000
#> SRR1617435 5 0.1387 0.996 0.068 0.000 0.000 0.000 0.932 0.000
#> SRR1617437 4 0.6184 0.306 0.012 0.088 0.392 0.472 0.036 0.000
#> SRR1617438 3 0.0146 0.839 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1617439 3 0.0146 0.839 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1617440 3 0.2631 0.725 0.000 0.000 0.820 0.000 0.000 0.180
#> SRR1617441 3 0.2631 0.725 0.000 0.000 0.820 0.000 0.000 0.180
#> SRR1617443 3 0.0146 0.839 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1617442 3 0.0146 0.839 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1617444 1 0.0405 0.978 0.988 0.000 0.008 0.000 0.000 0.004
#> SRR1617445 1 0.0405 0.978 0.988 0.000 0.008 0.000 0.000 0.004
#> SRR1617446 1 0.0363 0.984 0.988 0.000 0.000 0.000 0.012 0.000
#> SRR1617447 1 0.0363 0.984 0.988 0.000 0.000 0.000 0.012 0.000
#> SRR1617448 1 0.0405 0.983 0.988 0.000 0.004 0.000 0.008 0.000
#> SRR1617449 1 0.0405 0.983 0.988 0.000 0.004 0.000 0.008 0.000
#> SRR1617451 2 0.5702 0.386 0.000 0.480 0.000 0.384 0.008 0.128
#> SRR1617450 2 0.5677 0.383 0.000 0.480 0.000 0.388 0.008 0.124
#> SRR1617452 4 0.7886 0.154 0.008 0.212 0.072 0.376 0.040 0.292
#> SRR1617454 2 0.2048 0.678 0.000 0.880 0.000 0.000 0.000 0.120
#> SRR1617453 4 0.7886 0.154 0.008 0.212 0.072 0.376 0.040 0.292
#> SRR1617456 6 0.0146 0.760 0.000 0.000 0.004 0.000 0.000 0.996
#> SRR1617457 6 0.0146 0.760 0.000 0.000 0.004 0.000 0.000 0.996
#> SRR1617455 2 0.2048 0.678 0.000 0.880 0.000 0.000 0.000 0.120
#> SRR1617458 6 0.0146 0.760 0.000 0.000 0.004 0.000 0.000 0.996
#> SRR1617459 6 0.0146 0.760 0.000 0.000 0.004 0.000 0.000 0.996
#> SRR1617460 6 0.4566 0.276 0.000 0.452 0.000 0.012 0.016 0.520
#> SRR1617461 6 0.4566 0.276 0.000 0.452 0.000 0.012 0.016 0.520
#> SRR1617463 2 0.2473 0.661 0.000 0.856 0.000 0.000 0.008 0.136
#> SRR1617462 2 0.2473 0.661 0.000 0.856 0.000 0.000 0.008 0.136
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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 6.
#>
#> 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 0.852 0.947 0.961 0.4819 0.497 0.497
#> 3 3 0.882 0.932 0.970 0.1624 0.925 0.848
#> 4 4 0.913 0.934 0.970 0.2629 0.860 0.668
#> 5 5 0.882 0.861 0.900 0.0473 0.994 0.980
#> 6 6 0.946 0.940 0.967 0.0460 0.944 0.797
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 4
There is also optional best \(k\) = 4 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
#> SRR1617430 2 0.278 0.930 0.048 0.952
#> SRR1617431 2 0.278 0.930 0.048 0.952
#> SRR1617410 1 0.000 1.000 1.000 0.000
#> SRR1617411 1 0.000 1.000 1.000 0.000
#> SRR1617412 1 0.000 1.000 1.000 0.000
#> SRR1617413 1 0.000 1.000 1.000 0.000
#> SRR1617414 1 0.000 1.000 1.000 0.000
#> SRR1617415 1 0.000 1.000 1.000 0.000
#> SRR1617416 2 0.541 0.855 0.124 0.876
#> SRR1617417 2 0.541 0.855 0.124 0.876
#> SRR1617418 1 0.000 1.000 1.000 0.000
#> SRR1617419 1 0.000 1.000 1.000 0.000
#> SRR1617420 1 0.000 1.000 1.000 0.000
#> SRR1617421 1 0.000 1.000 1.000 0.000
#> SRR1617422 1 0.000 1.000 1.000 0.000
#> SRR1617423 1 0.000 1.000 1.000 0.000
#> SRR1617424 1 0.000 1.000 1.000 0.000
#> SRR1617425 1 0.000 1.000 1.000 0.000
#> SRR1617427 1 0.000 1.000 1.000 0.000
#> SRR1617426 1 0.000 1.000 1.000 0.000
#> SRR1617428 2 0.909 0.627 0.324 0.676
#> SRR1617429 2 0.909 0.627 0.324 0.676
#> SRR1617432 1 0.000 1.000 1.000 0.000
#> SRR1617433 1 0.000 1.000 1.000 0.000
#> SRR1617434 1 0.000 1.000 1.000 0.000
#> SRR1617436 1 0.000 1.000 1.000 0.000
#> SRR1617435 1 0.000 1.000 1.000 0.000
#> SRR1617437 1 0.000 1.000 1.000 0.000
#> SRR1617438 1 0.000 1.000 1.000 0.000
#> SRR1617439 1 0.000 1.000 1.000 0.000
#> SRR1617440 2 0.388 0.916 0.076 0.924
#> SRR1617441 2 0.388 0.916 0.076 0.924
#> SRR1617443 1 0.000 1.000 1.000 0.000
#> SRR1617442 1 0.000 1.000 1.000 0.000
#> SRR1617444 2 0.833 0.722 0.264 0.736
#> SRR1617445 2 0.833 0.722 0.264 0.736
#> SRR1617446 1 0.000 1.000 1.000 0.000
#> SRR1617447 1 0.000 1.000 1.000 0.000
#> SRR1617448 1 0.000 1.000 1.000 0.000
#> SRR1617449 1 0.000 1.000 1.000 0.000
#> SRR1617451 2 0.224 0.933 0.036 0.964
#> SRR1617450 2 0.224 0.933 0.036 0.964
#> SRR1617452 2 0.000 0.909 0.000 1.000
#> SRR1617454 2 0.224 0.933 0.036 0.964
#> SRR1617453 2 0.000 0.909 0.000 1.000
#> SRR1617456 2 0.224 0.933 0.036 0.964
#> SRR1617457 2 0.224 0.933 0.036 0.964
#> SRR1617455 2 0.224 0.933 0.036 0.964
#> SRR1617458 2 0.224 0.933 0.036 0.964
#> SRR1617459 2 0.224 0.933 0.036 0.964
#> SRR1617460 2 0.224 0.933 0.036 0.964
#> SRR1617461 2 0.224 0.933 0.036 0.964
#> SRR1617463 2 0.224 0.933 0.036 0.964
#> SRR1617462 2 0.224 0.933 0.036 0.964
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.0592 0.937 0.012 0.988 0.00
#> SRR1617431 2 0.0592 0.937 0.012 0.988 0.00
#> SRR1617410 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617411 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617412 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617413 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617414 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617415 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617416 3 0.0000 0.756 0.000 0.000 1.00
#> SRR1617417 3 0.0000 0.756 0.000 0.000 1.00
#> SRR1617418 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617419 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617420 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617421 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617422 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617423 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617424 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617425 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617427 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617426 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617428 3 0.4555 0.717 0.200 0.000 0.80
#> SRR1617429 3 0.4555 0.717 0.200 0.000 0.80
#> SRR1617432 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617433 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617434 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617436 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617435 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617437 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617438 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617439 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617440 2 0.1529 0.909 0.040 0.960 0.00
#> SRR1617441 2 0.1529 0.909 0.040 0.960 0.00
#> SRR1617443 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617442 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617444 2 0.4887 0.608 0.228 0.772 0.00
#> SRR1617445 2 0.4887 0.608 0.228 0.772 0.00
#> SRR1617446 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617447 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617448 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617449 1 0.0000 1.000 1.000 0.000 0.00
#> SRR1617451 2 0.0000 0.945 0.000 1.000 0.00
#> SRR1617450 2 0.0000 0.945 0.000 1.000 0.00
#> SRR1617452 3 0.5706 0.553 0.000 0.320 0.68
#> SRR1617454 2 0.0000 0.945 0.000 1.000 0.00
#> SRR1617453 3 0.5706 0.553 0.000 0.320 0.68
#> SRR1617456 2 0.0000 0.945 0.000 1.000 0.00
#> SRR1617457 2 0.0000 0.945 0.000 1.000 0.00
#> SRR1617455 2 0.0000 0.945 0.000 1.000 0.00
#> SRR1617458 2 0.0000 0.945 0.000 1.000 0.00
#> SRR1617459 2 0.0000 0.945 0.000 1.000 0.00
#> SRR1617460 2 0.0000 0.945 0.000 1.000 0.00
#> SRR1617461 2 0.0000 0.945 0.000 1.000 0.00
#> SRR1617463 2 0.0000 0.945 0.000 1.000 0.00
#> SRR1617462 2 0.0000 0.945 0.000 1.000 0.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.0469 0.946 0.000 0.988 0.012 0.00
#> SRR1617431 2 0.0469 0.946 0.000 0.988 0.012 0.00
#> SRR1617410 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617411 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617412 3 0.0000 1.000 0.000 0.000 1.000 0.00
#> SRR1617413 3 0.0000 1.000 0.000 0.000 1.000 0.00
#> SRR1617414 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617415 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617416 4 0.0000 0.730 0.000 0.000 0.000 1.00
#> SRR1617417 4 0.0000 0.730 0.000 0.000 0.000 1.00
#> SRR1617418 3 0.0000 1.000 0.000 0.000 1.000 0.00
#> SRR1617419 3 0.0000 1.000 0.000 0.000 1.000 0.00
#> SRR1617420 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617421 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617422 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617423 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617424 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617425 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617427 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617426 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617428 4 0.3610 0.693 0.200 0.000 0.000 0.80
#> SRR1617429 4 0.3610 0.693 0.200 0.000 0.000 0.80
#> SRR1617432 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617433 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617434 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617436 3 0.0000 1.000 0.000 0.000 1.000 0.00
#> SRR1617435 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617437 3 0.0000 1.000 0.000 0.000 1.000 0.00
#> SRR1617438 3 0.0000 1.000 0.000 0.000 1.000 0.00
#> SRR1617439 3 0.0000 1.000 0.000 0.000 1.000 0.00
#> SRR1617440 2 0.1211 0.923 0.000 0.960 0.040 0.00
#> SRR1617441 2 0.1211 0.923 0.000 0.960 0.040 0.00
#> SRR1617443 3 0.0000 1.000 0.000 0.000 1.000 0.00
#> SRR1617442 3 0.0000 1.000 0.000 0.000 1.000 0.00
#> SRR1617444 2 0.4212 0.648 0.216 0.772 0.012 0.00
#> SRR1617445 2 0.4212 0.648 0.216 0.772 0.012 0.00
#> SRR1617446 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617447 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617448 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617449 1 0.0000 1.000 1.000 0.000 0.000 0.00
#> SRR1617451 2 0.0000 0.954 0.000 1.000 0.000 0.00
#> SRR1617450 2 0.0000 0.954 0.000 1.000 0.000 0.00
#> SRR1617452 4 0.4522 0.564 0.000 0.320 0.000 0.68
#> SRR1617454 2 0.0000 0.954 0.000 1.000 0.000 0.00
#> SRR1617453 4 0.4522 0.564 0.000 0.320 0.000 0.68
#> SRR1617456 2 0.0000 0.954 0.000 1.000 0.000 0.00
#> SRR1617457 2 0.0000 0.954 0.000 1.000 0.000 0.00
#> SRR1617455 2 0.0000 0.954 0.000 1.000 0.000 0.00
#> SRR1617458 2 0.0000 0.954 0.000 1.000 0.000 0.00
#> SRR1617459 2 0.0000 0.954 0.000 1.000 0.000 0.00
#> SRR1617460 2 0.0000 0.954 0.000 1.000 0.000 0.00
#> SRR1617461 2 0.0000 0.954 0.000 1.000 0.000 0.00
#> SRR1617463 2 0.0000 0.954 0.000 1.000 0.000 0.00
#> SRR1617462 2 0.0000 0.954 0.000 1.000 0.000 0.00
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 2 0.088 0.729 0.000 0.968 0.000 0.032 0.000
#> SRR1617431 2 0.088 0.729 0.000 0.968 0.000 0.032 0.000
#> SRR1617410 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617411 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617412 3 0.411 0.995 0.000 0.000 0.624 0.376 0.000
#> SRR1617413 3 0.411 0.995 0.000 0.000 0.624 0.376 0.000
#> SRR1617414 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617415 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617416 4 0.423 0.443 0.000 0.000 0.000 0.580 0.420
#> SRR1617417 4 0.423 0.443 0.000 0.000 0.000 0.580 0.420
#> SRR1617418 3 0.415 0.992 0.000 0.000 0.612 0.388 0.000
#> SRR1617419 3 0.415 0.992 0.000 0.000 0.612 0.388 0.000
#> SRR1617420 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617421 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617422 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617423 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617424 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617425 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617427 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617426 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617428 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617429 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617432 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617433 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617434 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617436 3 0.411 0.995 0.000 0.000 0.624 0.376 0.000
#> SRR1617435 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617437 3 0.411 0.995 0.000 0.000 0.624 0.376 0.000
#> SRR1617438 3 0.415 0.992 0.000 0.000 0.612 0.388 0.000
#> SRR1617439 3 0.415 0.992 0.000 0.000 0.612 0.388 0.000
#> SRR1617440 2 0.163 0.714 0.000 0.940 0.016 0.044 0.000
#> SRR1617441 2 0.163 0.714 0.000 0.940 0.016 0.044 0.000
#> SRR1617443 3 0.411 0.995 0.000 0.000 0.624 0.376 0.000
#> SRR1617442 3 0.411 0.995 0.000 0.000 0.624 0.376 0.000
#> SRR1617444 2 0.407 0.536 0.216 0.752 0.000 0.032 0.000
#> SRR1617445 2 0.407 0.536 0.216 0.752 0.000 0.032 0.000
#> SRR1617446 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617447 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617448 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617449 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617451 2 0.000 0.739 0.000 1.000 0.000 0.000 0.000
#> SRR1617450 2 0.000 0.739 0.000 1.000 0.000 0.000 0.000
#> SRR1617452 4 0.663 0.612 0.000 0.052 0.268 0.572 0.108
#> SRR1617454 2 0.000 0.739 0.000 1.000 0.000 0.000 0.000
#> SRR1617453 4 0.663 0.612 0.000 0.052 0.268 0.572 0.108
#> SRR1617456 2 0.411 0.693 0.000 0.624 0.376 0.000 0.000
#> SRR1617457 2 0.411 0.693 0.000 0.624 0.376 0.000 0.000
#> SRR1617455 2 0.000 0.739 0.000 1.000 0.000 0.000 0.000
#> SRR1617458 2 0.411 0.693 0.000 0.624 0.376 0.000 0.000
#> SRR1617459 2 0.411 0.693 0.000 0.624 0.376 0.000 0.000
#> SRR1617460 2 0.411 0.693 0.000 0.624 0.376 0.000 0.000
#> SRR1617461 2 0.411 0.693 0.000 0.624 0.376 0.000 0.000
#> SRR1617463 2 0.411 0.693 0.000 0.624 0.376 0.000 0.000
#> SRR1617462 2 0.411 0.693 0.000 0.624 0.376 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.0632 0.896 0.000 0.976 0.000 0.000 0.000 0.024
#> SRR1617431 2 0.0632 0.896 0.000 0.976 0.000 0.000 0.000 0.024
#> SRR1617410 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617411 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617412 3 0.0146 0.988 0.000 0.004 0.996 0.000 0.000 0.000
#> SRR1617413 3 0.0146 0.988 0.000 0.004 0.996 0.000 0.000 0.000
#> SRR1617414 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617415 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617416 4 0.0632 0.653 0.000 0.000 0.000 0.976 0.024 0.000
#> SRR1617417 4 0.0632 0.653 0.000 0.000 0.000 0.976 0.024 0.000
#> SRR1617418 3 0.0547 0.987 0.000 0.020 0.980 0.000 0.000 0.000
#> SRR1617419 3 0.0547 0.987 0.000 0.020 0.980 0.000 0.000 0.000
#> SRR1617420 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617421 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617422 1 0.0632 0.987 0.976 0.000 0.000 0.024 0.000 0.000
#> SRR1617423 1 0.0632 0.987 0.976 0.000 0.000 0.024 0.000 0.000
#> SRR1617424 1 0.0632 0.987 0.976 0.000 0.000 0.024 0.000 0.000
#> SRR1617425 1 0.0632 0.987 0.976 0.000 0.000 0.024 0.000 0.000
#> SRR1617427 1 0.0632 0.987 0.976 0.000 0.000 0.024 0.000 0.000
#> SRR1617426 1 0.0632 0.987 0.976 0.000 0.000 0.024 0.000 0.000
#> SRR1617428 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617429 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617432 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617433 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617434 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617436 3 0.0146 0.990 0.000 0.004 0.996 0.000 0.000 0.000
#> SRR1617435 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617437 3 0.0146 0.990 0.000 0.004 0.996 0.000 0.000 0.000
#> SRR1617438 3 0.0547 0.987 0.000 0.020 0.980 0.000 0.000 0.000
#> SRR1617439 3 0.0547 0.987 0.000 0.020 0.980 0.000 0.000 0.000
#> SRR1617440 2 0.0260 0.884 0.000 0.992 0.008 0.000 0.000 0.000
#> SRR1617441 2 0.0260 0.884 0.000 0.992 0.008 0.000 0.000 0.000
#> SRR1617443 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617442 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617444 2 0.3473 0.671 0.192 0.780 0.000 0.024 0.000 0.004
#> SRR1617445 2 0.3473 0.671 0.192 0.780 0.000 0.024 0.000 0.004
#> SRR1617446 1 0.0632 0.987 0.976 0.000 0.000 0.024 0.000 0.000
#> SRR1617447 1 0.0632 0.987 0.976 0.000 0.000 0.024 0.000 0.000
#> SRR1617448 1 0.0632 0.987 0.976 0.000 0.000 0.024 0.000 0.000
#> SRR1617449 1 0.0632 0.987 0.976 0.000 0.000 0.024 0.000 0.000
#> SRR1617451 2 0.1204 0.896 0.000 0.944 0.000 0.000 0.000 0.056
#> SRR1617450 2 0.1204 0.896 0.000 0.944 0.000 0.000 0.000 0.056
#> SRR1617452 4 0.4211 0.680 0.000 0.008 0.000 0.660 0.020 0.312
#> SRR1617454 2 0.1204 0.896 0.000 0.944 0.000 0.000 0.000 0.056
#> SRR1617453 4 0.4211 0.680 0.000 0.008 0.000 0.660 0.020 0.312
#> SRR1617456 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617457 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617455 2 0.1204 0.896 0.000 0.944 0.000 0.000 0.000 0.056
#> SRR1617458 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617459 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617460 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617461 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617463 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617462 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
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", "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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 0.201 0.630 0.761 0.4427 0.508 0.508
#> 3 3 0.255 0.726 0.764 0.3798 0.804 0.625
#> 4 4 0.496 0.727 0.770 0.1546 1.000 1.000
#> 5 5 0.590 0.310 0.664 0.0766 0.927 0.786
#> 6 6 0.635 0.563 0.673 0.0513 0.869 0.556
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
#> SRR1617430 2 0.760 0.577 0.220 0.780
#> SRR1617431 2 0.760 0.577 0.220 0.780
#> SRR1617410 1 0.921 0.705 0.664 0.336
#> SRR1617411 1 0.921 0.705 0.664 0.336
#> SRR1617412 1 0.584 0.487 0.860 0.140
#> SRR1617413 1 0.584 0.487 0.860 0.140
#> SRR1617414 1 0.943 0.681 0.640 0.360
#> SRR1617415 1 0.943 0.681 0.640 0.360
#> SRR1617416 1 0.886 0.602 0.696 0.304
#> SRR1617417 1 0.886 0.602 0.696 0.304
#> SRR1617418 1 0.644 0.467 0.836 0.164
#> SRR1617419 1 0.644 0.467 0.836 0.164
#> SRR1617420 1 0.876 0.706 0.704 0.296
#> SRR1617421 1 0.876 0.706 0.704 0.296
#> SRR1617422 1 0.988 0.515 0.564 0.436
#> SRR1617423 1 0.988 0.515 0.564 0.436
#> SRR1617424 1 0.917 0.703 0.668 0.332
#> SRR1617425 1 0.917 0.703 0.668 0.332
#> SRR1617427 1 0.891 0.706 0.692 0.308
#> SRR1617426 1 0.891 0.706 0.692 0.308
#> SRR1617428 2 0.921 0.456 0.336 0.664
#> SRR1617429 2 0.921 0.456 0.336 0.664
#> SRR1617432 1 0.932 0.699 0.652 0.348
#> SRR1617433 1 0.932 0.699 0.652 0.348
#> SRR1617434 1 0.917 0.702 0.668 0.332
#> SRR1617436 1 0.662 0.489 0.828 0.172
#> SRR1617435 1 0.917 0.702 0.668 0.332
#> SRR1617437 1 0.662 0.489 0.828 0.172
#> SRR1617438 1 0.634 0.470 0.840 0.160
#> SRR1617439 1 0.634 0.470 0.840 0.160
#> SRR1617440 2 0.994 0.414 0.456 0.544
#> SRR1617441 2 0.994 0.414 0.456 0.544
#> SRR1617443 1 0.625 0.468 0.844 0.156
#> SRR1617442 1 0.625 0.468 0.844 0.156
#> SRR1617444 2 0.802 0.576 0.244 0.756
#> SRR1617445 2 0.802 0.576 0.244 0.756
#> SRR1617446 1 0.913 0.705 0.672 0.328
#> SRR1617447 1 0.913 0.705 0.672 0.328
#> SRR1617448 1 0.917 0.702 0.668 0.332
#> SRR1617449 1 0.917 0.702 0.668 0.332
#> SRR1617451 2 0.242 0.771 0.040 0.960
#> SRR1617450 2 0.242 0.771 0.040 0.960
#> SRR1617452 2 0.697 0.638 0.188 0.812
#> SRR1617454 2 0.242 0.771 0.040 0.960
#> SRR1617453 2 0.697 0.638 0.188 0.812
#> SRR1617456 2 0.343 0.767 0.064 0.936
#> SRR1617457 2 0.343 0.767 0.064 0.936
#> SRR1617455 2 0.242 0.771 0.040 0.960
#> SRR1617458 2 0.358 0.763 0.068 0.932
#> SRR1617459 2 0.358 0.763 0.068 0.932
#> SRR1617460 2 0.443 0.729 0.092 0.908
#> SRR1617461 2 0.443 0.729 0.092 0.908
#> SRR1617463 2 0.443 0.729 0.092 0.908
#> SRR1617462 2 0.443 0.729 0.092 0.908
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.848 0.581 0.332 0.560 0.108
#> SRR1617431 2 0.848 0.581 0.332 0.560 0.108
#> SRR1617410 1 0.243 0.835 0.940 0.024 0.036
#> SRR1617411 1 0.243 0.835 0.940 0.024 0.036
#> SRR1617412 3 0.672 0.830 0.248 0.048 0.704
#> SRR1617413 3 0.672 0.830 0.248 0.048 0.704
#> SRR1617414 1 0.380 0.820 0.888 0.080 0.032
#> SRR1617415 1 0.380 0.820 0.888 0.080 0.032
#> SRR1617416 1 0.863 0.456 0.580 0.140 0.280
#> SRR1617417 1 0.863 0.456 0.580 0.140 0.280
#> SRR1617418 3 0.638 0.843 0.224 0.044 0.732
#> SRR1617419 3 0.638 0.843 0.224 0.044 0.732
#> SRR1617420 1 0.255 0.832 0.932 0.012 0.056
#> SRR1617421 1 0.255 0.832 0.932 0.012 0.056
#> SRR1617422 1 0.621 0.679 0.756 0.192 0.052
#> SRR1617423 1 0.621 0.679 0.756 0.192 0.052
#> SRR1617424 1 0.392 0.831 0.884 0.036 0.080
#> SRR1617425 1 0.392 0.831 0.884 0.036 0.080
#> SRR1617427 1 0.417 0.833 0.872 0.036 0.092
#> SRR1617426 1 0.417 0.833 0.872 0.036 0.092
#> SRR1617428 2 0.963 0.362 0.220 0.452 0.328
#> SRR1617429 2 0.963 0.362 0.220 0.452 0.328
#> SRR1617432 1 0.266 0.834 0.932 0.024 0.044
#> SRR1617433 1 0.266 0.834 0.932 0.024 0.044
#> SRR1617434 1 0.326 0.819 0.912 0.040 0.048
#> SRR1617436 3 0.660 0.826 0.256 0.040 0.704
#> SRR1617435 1 0.326 0.819 0.912 0.040 0.048
#> SRR1617437 3 0.660 0.826 0.256 0.040 0.704
#> SRR1617438 3 0.623 0.845 0.220 0.040 0.740
#> SRR1617439 3 0.623 0.845 0.220 0.040 0.740
#> SRR1617440 3 0.809 0.104 0.068 0.416 0.516
#> SRR1617441 3 0.809 0.104 0.068 0.416 0.516
#> SRR1617443 3 0.638 0.840 0.244 0.036 0.720
#> SRR1617442 3 0.638 0.840 0.244 0.036 0.720
#> SRR1617444 2 0.874 0.569 0.340 0.536 0.124
#> SRR1617445 2 0.874 0.569 0.340 0.536 0.124
#> SRR1617446 1 0.409 0.831 0.876 0.036 0.088
#> SRR1617447 1 0.409 0.831 0.876 0.036 0.088
#> SRR1617448 1 0.453 0.827 0.860 0.052 0.088
#> SRR1617449 1 0.453 0.827 0.860 0.052 0.088
#> SRR1617451 2 0.520 0.780 0.136 0.820 0.044
#> SRR1617450 2 0.520 0.780 0.136 0.820 0.044
#> SRR1617452 2 0.666 0.590 0.052 0.716 0.232
#> SRR1617454 2 0.514 0.780 0.132 0.824 0.044
#> SRR1617453 2 0.666 0.590 0.052 0.716 0.232
#> SRR1617456 2 0.566 0.753 0.104 0.808 0.088
#> SRR1617457 2 0.566 0.753 0.104 0.808 0.088
#> SRR1617455 2 0.514 0.780 0.132 0.824 0.044
#> SRR1617458 2 0.574 0.751 0.100 0.804 0.096
#> SRR1617459 2 0.574 0.751 0.100 0.804 0.096
#> SRR1617460 2 0.535 0.776 0.152 0.808 0.040
#> SRR1617461 2 0.535 0.776 0.152 0.808 0.040
#> SRR1617463 2 0.524 0.776 0.168 0.804 0.028
#> SRR1617462 2 0.524 0.776 0.168 0.804 0.028
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.731 0.644 0.164 0.652 0.080 0.104
#> SRR1617431 2 0.731 0.644 0.164 0.652 0.080 0.104
#> SRR1617410 1 0.256 0.798 0.920 0.008 0.032 0.040
#> SRR1617411 1 0.256 0.798 0.920 0.008 0.032 0.040
#> SRR1617412 3 0.402 0.854 0.068 0.000 0.836 0.096
#> SRR1617413 3 0.402 0.854 0.068 0.000 0.836 0.096
#> SRR1617414 1 0.372 0.789 0.872 0.048 0.024 0.056
#> SRR1617415 1 0.372 0.789 0.872 0.048 0.024 0.056
#> SRR1617416 1 0.740 0.492 0.460 0.044 0.060 0.436
#> SRR1617417 1 0.740 0.492 0.460 0.044 0.060 0.436
#> SRR1617418 3 0.324 0.869 0.064 0.000 0.880 0.056
#> SRR1617419 3 0.324 0.869 0.064 0.000 0.880 0.056
#> SRR1617420 1 0.264 0.791 0.908 0.000 0.060 0.032
#> SRR1617421 1 0.264 0.791 0.908 0.000 0.060 0.032
#> SRR1617422 1 0.665 0.723 0.688 0.124 0.036 0.152
#> SRR1617423 1 0.665 0.723 0.688 0.124 0.036 0.152
#> SRR1617424 1 0.518 0.799 0.780 0.028 0.048 0.144
#> SRR1617425 1 0.518 0.799 0.780 0.028 0.048 0.144
#> SRR1617427 1 0.509 0.805 0.784 0.024 0.048 0.144
#> SRR1617426 1 0.509 0.805 0.784 0.024 0.048 0.144
#> SRR1617428 2 0.920 0.412 0.120 0.388 0.152 0.340
#> SRR1617429 2 0.920 0.412 0.120 0.388 0.152 0.340
#> SRR1617432 1 0.322 0.796 0.892 0.016 0.032 0.060
#> SRR1617433 1 0.322 0.796 0.892 0.016 0.032 0.060
#> SRR1617434 1 0.333 0.781 0.880 0.004 0.044 0.072
#> SRR1617436 3 0.320 0.859 0.072 0.008 0.888 0.032
#> SRR1617435 1 0.333 0.781 0.880 0.004 0.044 0.072
#> SRR1617437 3 0.320 0.859 0.072 0.008 0.888 0.032
#> SRR1617438 3 0.270 0.870 0.068 0.000 0.904 0.028
#> SRR1617439 3 0.270 0.870 0.068 0.000 0.904 0.028
#> SRR1617440 3 0.739 0.303 0.016 0.312 0.544 0.128
#> SRR1617441 3 0.739 0.303 0.016 0.312 0.544 0.128
#> SRR1617443 3 0.281 0.865 0.080 0.000 0.896 0.024
#> SRR1617442 3 0.281 0.865 0.080 0.000 0.896 0.024
#> SRR1617444 2 0.845 0.553 0.212 0.540 0.092 0.156
#> SRR1617445 2 0.845 0.553 0.212 0.540 0.092 0.156
#> SRR1617446 1 0.542 0.794 0.756 0.020 0.056 0.168
#> SRR1617447 1 0.542 0.794 0.756 0.020 0.056 0.168
#> SRR1617448 1 0.620 0.779 0.708 0.040 0.060 0.192
#> SRR1617449 1 0.620 0.779 0.708 0.040 0.060 0.192
#> SRR1617451 2 0.353 0.752 0.044 0.876 0.012 0.068
#> SRR1617450 2 0.353 0.752 0.044 0.876 0.012 0.068
#> SRR1617452 2 0.684 0.609 0.028 0.556 0.052 0.364
#> SRR1617454 2 0.259 0.757 0.036 0.920 0.012 0.032
#> SRR1617453 2 0.684 0.609 0.028 0.556 0.052 0.364
#> SRR1617456 2 0.460 0.716 0.012 0.796 0.032 0.160
#> SRR1617457 2 0.460 0.716 0.012 0.796 0.032 0.160
#> SRR1617455 2 0.259 0.757 0.036 0.920 0.012 0.032
#> SRR1617458 2 0.478 0.713 0.012 0.780 0.032 0.176
#> SRR1617459 2 0.478 0.713 0.012 0.780 0.032 0.176
#> SRR1617460 2 0.469 0.753 0.052 0.804 0.012 0.132
#> SRR1617461 2 0.469 0.753 0.052 0.804 0.012 0.132
#> SRR1617463 2 0.378 0.756 0.056 0.864 0.012 0.068
#> SRR1617462 2 0.378 0.756 0.056 0.864 0.012 0.068
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 2 0.6535 0.2467 0.060 0.668 0.044 0.068 0.160
#> SRR1617431 2 0.6535 0.2467 0.060 0.668 0.044 0.068 0.160
#> SRR1617410 1 0.1699 0.4189 0.944 0.008 0.036 0.004 0.008
#> SRR1617411 1 0.1699 0.4189 0.944 0.008 0.036 0.004 0.008
#> SRR1617412 3 0.4759 0.7457 0.016 0.004 0.760 0.068 0.152
#> SRR1617413 3 0.4759 0.7457 0.016 0.004 0.760 0.068 0.152
#> SRR1617414 1 0.5187 0.3338 0.752 0.048 0.008 0.060 0.132
#> SRR1617415 1 0.5187 0.3338 0.752 0.048 0.008 0.060 0.132
#> SRR1617416 1 0.7620 0.0523 0.388 0.004 0.040 0.328 0.240
#> SRR1617417 1 0.7620 0.0523 0.388 0.004 0.040 0.328 0.240
#> SRR1617418 3 0.3413 0.7951 0.008 0.008 0.852 0.028 0.104
#> SRR1617419 3 0.3413 0.7951 0.008 0.008 0.852 0.028 0.104
#> SRR1617420 1 0.3460 0.3978 0.860 0.004 0.076 0.024 0.036
#> SRR1617421 1 0.3460 0.3978 0.860 0.004 0.076 0.024 0.036
#> SRR1617422 1 0.6967 -0.5089 0.424 0.120 0.008 0.028 0.420
#> SRR1617423 1 0.6967 -0.5089 0.424 0.120 0.008 0.028 0.420
#> SRR1617424 1 0.5979 -0.6406 0.540 0.024 0.036 0.012 0.388
#> SRR1617425 1 0.5979 -0.6406 0.540 0.024 0.036 0.012 0.388
#> SRR1617427 1 0.6268 -0.3515 0.572 0.016 0.036 0.044 0.332
#> SRR1617426 1 0.6268 -0.3515 0.572 0.016 0.036 0.044 0.332
#> SRR1617428 4 0.8533 0.3780 0.064 0.348 0.084 0.384 0.120
#> SRR1617429 4 0.8533 0.3780 0.064 0.348 0.084 0.384 0.120
#> SRR1617432 1 0.3142 0.4100 0.876 0.004 0.012 0.048 0.060
#> SRR1617433 1 0.3142 0.4100 0.876 0.004 0.012 0.048 0.060
#> SRR1617434 1 0.2061 0.4211 0.928 0.004 0.040 0.024 0.004
#> SRR1617436 3 0.4184 0.7725 0.016 0.012 0.820 0.072 0.080
#> SRR1617435 1 0.2061 0.4211 0.928 0.004 0.040 0.024 0.004
#> SRR1617437 3 0.4184 0.7725 0.016 0.012 0.820 0.072 0.080
#> SRR1617438 3 0.2082 0.8018 0.012 0.004 0.928 0.012 0.044
#> SRR1617439 3 0.2082 0.8018 0.012 0.004 0.928 0.012 0.044
#> SRR1617440 3 0.7312 0.2871 0.000 0.264 0.516 0.096 0.124
#> SRR1617441 3 0.7312 0.2871 0.000 0.264 0.516 0.096 0.124
#> SRR1617443 3 0.1893 0.8013 0.024 0.000 0.936 0.012 0.028
#> SRR1617442 3 0.1893 0.8013 0.024 0.000 0.936 0.012 0.028
#> SRR1617444 2 0.8717 0.0120 0.108 0.372 0.084 0.092 0.344
#> SRR1617445 2 0.8717 0.0120 0.108 0.372 0.084 0.092 0.344
#> SRR1617446 1 0.6121 -0.8060 0.488 0.020 0.040 0.016 0.436
#> SRR1617447 1 0.6121 -0.8060 0.488 0.020 0.040 0.016 0.436
#> SRR1617448 5 0.6221 1.0000 0.436 0.036 0.040 0.008 0.480
#> SRR1617449 5 0.6221 1.0000 0.436 0.036 0.040 0.008 0.480
#> SRR1617451 2 0.2590 0.4756 0.012 0.908 0.008 0.028 0.044
#> SRR1617450 2 0.2590 0.4756 0.012 0.908 0.008 0.028 0.044
#> SRR1617452 4 0.6086 0.2407 0.032 0.404 0.032 0.520 0.012
#> SRR1617454 2 0.0981 0.4998 0.012 0.972 0.008 0.000 0.008
#> SRR1617453 4 0.6086 0.2407 0.032 0.404 0.032 0.520 0.012
#> SRR1617456 2 0.5114 0.3626 0.000 0.708 0.032 0.216 0.044
#> SRR1617457 2 0.5114 0.3626 0.000 0.708 0.032 0.216 0.044
#> SRR1617455 2 0.0981 0.4998 0.012 0.972 0.008 0.000 0.008
#> SRR1617458 2 0.5302 0.3507 0.000 0.688 0.036 0.232 0.044
#> SRR1617459 2 0.5302 0.3507 0.000 0.688 0.036 0.232 0.044
#> SRR1617460 2 0.5488 0.4077 0.028 0.696 0.000 0.184 0.092
#> SRR1617461 2 0.5488 0.4077 0.028 0.696 0.000 0.184 0.092
#> SRR1617463 2 0.4528 0.4545 0.024 0.784 0.000 0.108 0.084
#> SRR1617462 2 0.4528 0.4545 0.024 0.784 0.000 0.108 0.084
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.6683 0.0518 0.160 0.620 0.020 0.064 0.040 0.096
#> SRR1617431 2 0.6683 0.0518 0.160 0.620 0.020 0.064 0.040 0.096
#> SRR1617410 5 0.2398 0.8144 0.080 0.000 0.000 0.028 0.888 0.004
#> SRR1617411 5 0.2398 0.8144 0.080 0.000 0.000 0.028 0.888 0.004
#> SRR1617412 3 0.4225 0.7029 0.028 0.000 0.696 0.000 0.012 0.264
#> SRR1617413 3 0.4225 0.7029 0.028 0.000 0.696 0.000 0.012 0.264
#> SRR1617414 5 0.4662 0.7108 0.096 0.028 0.000 0.008 0.748 0.120
#> SRR1617415 5 0.4662 0.7108 0.096 0.028 0.000 0.008 0.748 0.120
#> SRR1617416 4 0.7564 0.2445 0.304 0.000 0.024 0.328 0.276 0.068
#> SRR1617417 4 0.7564 0.2445 0.304 0.000 0.024 0.328 0.276 0.068
#> SRR1617418 3 0.2573 0.7638 0.000 0.000 0.856 0.004 0.008 0.132
#> SRR1617419 3 0.2573 0.7638 0.000 0.000 0.856 0.004 0.008 0.132
#> SRR1617420 5 0.3342 0.7924 0.084 0.000 0.012 0.020 0.848 0.036
#> SRR1617421 5 0.3342 0.7924 0.084 0.000 0.012 0.020 0.848 0.036
#> SRR1617422 1 0.6034 0.6436 0.588 0.044 0.012 0.016 0.288 0.052
#> SRR1617423 1 0.6034 0.6436 0.588 0.044 0.012 0.016 0.288 0.052
#> SRR1617424 1 0.4977 0.6661 0.640 0.020 0.024 0.008 0.300 0.008
#> SRR1617425 1 0.4977 0.6661 0.640 0.020 0.024 0.008 0.300 0.008
#> SRR1617427 1 0.5738 0.5108 0.540 0.012 0.012 0.008 0.360 0.068
#> SRR1617426 1 0.5738 0.5108 0.540 0.012 0.012 0.008 0.360 0.068
#> SRR1617428 6 0.8943 1.0000 0.100 0.244 0.052 0.244 0.060 0.300
#> SRR1617429 6 0.8943 1.0000 0.100 0.244 0.052 0.244 0.060 0.300
#> SRR1617432 5 0.2864 0.7936 0.028 0.000 0.000 0.012 0.860 0.100
#> SRR1617433 5 0.2864 0.7936 0.028 0.000 0.000 0.012 0.860 0.100
#> SRR1617434 5 0.1657 0.8136 0.056 0.000 0.000 0.016 0.928 0.000
#> SRR1617436 3 0.3854 0.7218 0.036 0.000 0.804 0.016 0.016 0.128
#> SRR1617435 5 0.1657 0.8136 0.056 0.000 0.000 0.016 0.928 0.000
#> SRR1617437 3 0.3854 0.7218 0.036 0.000 0.804 0.016 0.016 0.128
#> SRR1617438 3 0.1337 0.7726 0.008 0.000 0.956 0.012 0.008 0.016
#> SRR1617439 3 0.1337 0.7726 0.008 0.000 0.956 0.012 0.008 0.016
#> SRR1617440 3 0.7510 0.2535 0.080 0.192 0.508 0.128 0.000 0.092
#> SRR1617441 3 0.7510 0.2535 0.080 0.192 0.508 0.128 0.000 0.092
#> SRR1617443 3 0.2600 0.7723 0.020 0.000 0.892 0.008 0.020 0.060
#> SRR1617442 3 0.2600 0.7723 0.020 0.000 0.892 0.008 0.020 0.060
#> SRR1617444 1 0.8677 -0.1653 0.364 0.296 0.072 0.120 0.088 0.060
#> SRR1617445 1 0.8677 -0.1653 0.364 0.296 0.072 0.120 0.088 0.060
#> SRR1617446 1 0.4806 0.6759 0.688 0.008 0.028 0.012 0.248 0.016
#> SRR1617447 1 0.4806 0.6759 0.688 0.008 0.028 0.012 0.248 0.016
#> SRR1617448 1 0.4817 0.6807 0.708 0.016 0.028 0.012 0.220 0.016
#> SRR1617449 1 0.4817 0.6807 0.708 0.016 0.028 0.012 0.220 0.016
#> SRR1617451 2 0.3474 0.4417 0.052 0.852 0.004 0.044 0.012 0.036
#> SRR1617450 2 0.3474 0.4417 0.052 0.852 0.004 0.044 0.012 0.036
#> SRR1617452 4 0.4967 0.1427 0.016 0.276 0.016 0.660 0.024 0.008
#> SRR1617454 2 0.0767 0.5301 0.012 0.976 0.000 0.000 0.008 0.004
#> SRR1617453 4 0.4967 0.1427 0.016 0.276 0.016 0.660 0.024 0.008
#> SRR1617456 2 0.5490 0.4571 0.012 0.596 0.008 0.288 0.000 0.096
#> SRR1617457 2 0.5490 0.4571 0.012 0.596 0.008 0.288 0.000 0.096
#> SRR1617455 2 0.0767 0.5301 0.012 0.976 0.000 0.000 0.008 0.004
#> SRR1617458 2 0.5524 0.4390 0.012 0.572 0.008 0.320 0.000 0.088
#> SRR1617459 2 0.5524 0.4390 0.012 0.572 0.008 0.320 0.000 0.088
#> SRR1617460 2 0.6163 0.4724 0.060 0.580 0.004 0.276 0.016 0.064
#> SRR1617461 2 0.6163 0.4724 0.060 0.580 0.004 0.276 0.016 0.064
#> SRR1617463 2 0.5351 0.5018 0.060 0.692 0.004 0.176 0.008 0.060
#> SRR1617462 2 0.5351 0.5018 0.060 0.692 0.004 0.176 0.008 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["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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 0.992 0.996 0.5025 0.497 0.497
#> 3 3 0.952 0.958 0.980 0.3274 0.723 0.499
#> 4 4 0.801 0.812 0.881 0.1280 0.880 0.653
#> 5 5 0.816 0.792 0.870 0.0708 0.941 0.763
#> 6 6 0.819 0.733 0.817 0.0376 0.952 0.766
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
#> SRR1617430 2 0.000 0.991 0.000 1.000
#> SRR1617431 2 0.000 0.991 0.000 1.000
#> SRR1617410 1 0.000 1.000 1.000 0.000
#> SRR1617411 1 0.000 1.000 1.000 0.000
#> SRR1617412 1 0.000 1.000 1.000 0.000
#> SRR1617413 1 0.000 1.000 1.000 0.000
#> SRR1617414 1 0.000 1.000 1.000 0.000
#> SRR1617415 1 0.000 1.000 1.000 0.000
#> SRR1617416 1 0.000 1.000 1.000 0.000
#> SRR1617417 1 0.000 1.000 1.000 0.000
#> SRR1617418 1 0.000 1.000 1.000 0.000
#> SRR1617419 1 0.000 1.000 1.000 0.000
#> SRR1617420 1 0.000 1.000 1.000 0.000
#> SRR1617421 1 0.000 1.000 1.000 0.000
#> SRR1617422 2 0.482 0.889 0.104 0.896
#> SRR1617423 2 0.482 0.889 0.104 0.896
#> SRR1617424 1 0.000 1.000 1.000 0.000
#> SRR1617425 1 0.000 1.000 1.000 0.000
#> SRR1617427 1 0.000 1.000 1.000 0.000
#> SRR1617426 1 0.000 1.000 1.000 0.000
#> SRR1617428 2 0.000 0.991 0.000 1.000
#> SRR1617429 2 0.000 0.991 0.000 1.000
#> SRR1617432 1 0.000 1.000 1.000 0.000
#> SRR1617433 1 0.000 1.000 1.000 0.000
#> SRR1617434 1 0.000 1.000 1.000 0.000
#> SRR1617436 1 0.000 1.000 1.000 0.000
#> SRR1617435 1 0.000 1.000 1.000 0.000
#> SRR1617437 1 0.000 1.000 1.000 0.000
#> SRR1617438 1 0.000 1.000 1.000 0.000
#> SRR1617439 1 0.000 1.000 1.000 0.000
#> SRR1617440 2 0.000 0.991 0.000 1.000
#> SRR1617441 2 0.000 0.991 0.000 1.000
#> SRR1617443 1 0.000 1.000 1.000 0.000
#> SRR1617442 1 0.000 1.000 1.000 0.000
#> SRR1617444 2 0.000 0.991 0.000 1.000
#> SRR1617445 2 0.000 0.991 0.000 1.000
#> SRR1617446 1 0.000 1.000 1.000 0.000
#> SRR1617447 1 0.000 1.000 1.000 0.000
#> SRR1617448 1 0.000 1.000 1.000 0.000
#> SRR1617449 1 0.000 1.000 1.000 0.000
#> SRR1617451 2 0.000 0.991 0.000 1.000
#> SRR1617450 2 0.000 0.991 0.000 1.000
#> SRR1617452 2 0.000 0.991 0.000 1.000
#> SRR1617454 2 0.000 0.991 0.000 1.000
#> SRR1617453 2 0.000 0.991 0.000 1.000
#> SRR1617456 2 0.000 0.991 0.000 1.000
#> SRR1617457 2 0.000 0.991 0.000 1.000
#> SRR1617455 2 0.000 0.991 0.000 1.000
#> SRR1617458 2 0.000 0.991 0.000 1.000
#> SRR1617459 2 0.000 0.991 0.000 1.000
#> SRR1617460 2 0.000 0.991 0.000 1.000
#> SRR1617461 2 0.000 0.991 0.000 1.000
#> SRR1617463 2 0.000 0.991 0.000 1.000
#> SRR1617462 2 0.000 0.991 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1617431 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1617410 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617411 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617412 3 0.0000 0.947 0.000 0.000 1.000
#> SRR1617413 3 0.0000 0.947 0.000 0.000 1.000
#> SRR1617414 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617415 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617416 1 0.3412 0.867 0.876 0.000 0.124
#> SRR1617417 1 0.3412 0.867 0.876 0.000 0.124
#> SRR1617418 3 0.0000 0.947 0.000 0.000 1.000
#> SRR1617419 3 0.0000 0.947 0.000 0.000 1.000
#> SRR1617420 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617421 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617422 1 0.0424 0.982 0.992 0.008 0.000
#> SRR1617423 1 0.0424 0.982 0.992 0.008 0.000
#> SRR1617424 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617425 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617427 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617426 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617428 3 0.5733 0.567 0.000 0.324 0.676
#> SRR1617429 3 0.5733 0.567 0.000 0.324 0.676
#> SRR1617432 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617433 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617434 1 0.0237 0.985 0.996 0.000 0.004
#> SRR1617436 3 0.0237 0.944 0.004 0.000 0.996
#> SRR1617435 1 0.0237 0.985 0.996 0.000 0.004
#> SRR1617437 3 0.0237 0.944 0.004 0.000 0.996
#> SRR1617438 3 0.0000 0.947 0.000 0.000 1.000
#> SRR1617439 3 0.0000 0.947 0.000 0.000 1.000
#> SRR1617440 3 0.0592 0.941 0.000 0.012 0.988
#> SRR1617441 3 0.0592 0.941 0.000 0.012 0.988
#> SRR1617443 3 0.0000 0.947 0.000 0.000 1.000
#> SRR1617442 3 0.0000 0.947 0.000 0.000 1.000
#> SRR1617444 2 0.1163 0.975 0.000 0.972 0.028
#> SRR1617445 2 0.1163 0.975 0.000 0.972 0.028
#> SRR1617446 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617447 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617448 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617449 1 0.0000 0.987 1.000 0.000 0.000
#> SRR1617451 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1617450 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1617452 2 0.0892 0.983 0.000 0.980 0.020
#> SRR1617454 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1617453 2 0.0892 0.983 0.000 0.980 0.020
#> SRR1617456 2 0.0237 0.992 0.000 0.996 0.004
#> SRR1617457 2 0.0237 0.992 0.000 0.996 0.004
#> SRR1617455 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1617458 2 0.0237 0.992 0.000 0.996 0.004
#> SRR1617459 2 0.0237 0.992 0.000 0.996 0.004
#> SRR1617460 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1617461 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1617463 2 0.0000 0.993 0.000 1.000 0.000
#> SRR1617462 2 0.0000 0.993 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.3160 0.890 0.060 0.892 0.008 0.040
#> SRR1617431 2 0.3160 0.890 0.060 0.892 0.008 0.040
#> SRR1617410 4 0.3726 0.871 0.212 0.000 0.000 0.788
#> SRR1617411 4 0.3726 0.871 0.212 0.000 0.000 0.788
#> SRR1617412 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> SRR1617413 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> SRR1617414 4 0.4008 0.829 0.244 0.000 0.000 0.756
#> SRR1617415 4 0.4008 0.829 0.244 0.000 0.000 0.756
#> SRR1617416 4 0.5581 0.370 0.340 0.008 0.020 0.632
#> SRR1617417 4 0.5581 0.370 0.340 0.008 0.020 0.632
#> SRR1617418 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> SRR1617419 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> SRR1617420 4 0.4053 0.864 0.228 0.000 0.004 0.768
#> SRR1617421 4 0.4053 0.864 0.228 0.000 0.004 0.768
#> SRR1617422 1 0.1635 0.804 0.948 0.008 0.000 0.044
#> SRR1617423 1 0.1635 0.804 0.948 0.008 0.000 0.044
#> SRR1617424 1 0.1022 0.818 0.968 0.000 0.000 0.032
#> SRR1617425 1 0.1022 0.818 0.968 0.000 0.000 0.032
#> SRR1617427 1 0.1716 0.790 0.936 0.000 0.000 0.064
#> SRR1617426 1 0.1716 0.790 0.936 0.000 0.000 0.064
#> SRR1617428 3 0.8397 0.314 0.028 0.244 0.440 0.288
#> SRR1617429 3 0.8397 0.314 0.028 0.244 0.440 0.288
#> SRR1617432 4 0.3610 0.871 0.200 0.000 0.000 0.800
#> SRR1617433 4 0.3610 0.871 0.200 0.000 0.000 0.800
#> SRR1617434 4 0.3311 0.854 0.172 0.000 0.000 0.828
#> SRR1617436 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> SRR1617435 4 0.3311 0.854 0.172 0.000 0.000 0.828
#> SRR1617437 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> SRR1617438 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> SRR1617439 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> SRR1617440 3 0.1004 0.899 0.000 0.024 0.972 0.004
#> SRR1617441 3 0.1004 0.899 0.000 0.024 0.972 0.004
#> SRR1617443 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> SRR1617442 3 0.0000 0.915 0.000 0.000 1.000 0.000
#> SRR1617444 1 0.6768 0.103 0.480 0.452 0.024 0.044
#> SRR1617445 1 0.6768 0.103 0.480 0.452 0.024 0.044
#> SRR1617446 1 0.0707 0.820 0.980 0.000 0.000 0.020
#> SRR1617447 1 0.0707 0.820 0.980 0.000 0.000 0.020
#> SRR1617448 1 0.0469 0.820 0.988 0.000 0.000 0.012
#> SRR1617449 1 0.0469 0.820 0.988 0.000 0.000 0.012
#> SRR1617451 2 0.1488 0.932 0.012 0.956 0.000 0.032
#> SRR1617450 2 0.1488 0.932 0.012 0.956 0.000 0.032
#> SRR1617452 2 0.4011 0.799 0.000 0.784 0.008 0.208
#> SRR1617454 2 0.0817 0.939 0.000 0.976 0.000 0.024
#> SRR1617453 2 0.4011 0.799 0.000 0.784 0.008 0.208
#> SRR1617456 2 0.0592 0.941 0.000 0.984 0.000 0.016
#> SRR1617457 2 0.0592 0.941 0.000 0.984 0.000 0.016
#> SRR1617455 2 0.0817 0.939 0.000 0.976 0.000 0.024
#> SRR1617458 2 0.0592 0.941 0.000 0.984 0.000 0.016
#> SRR1617459 2 0.0592 0.941 0.000 0.984 0.000 0.016
#> SRR1617460 2 0.1151 0.939 0.008 0.968 0.000 0.024
#> SRR1617461 2 0.1151 0.939 0.008 0.968 0.000 0.024
#> SRR1617463 2 0.0927 0.941 0.008 0.976 0.000 0.016
#> SRR1617462 2 0.0927 0.941 0.008 0.976 0.000 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 2 0.3835 0.602 0.020 0.800 0.004 0.168 0.008
#> SRR1617431 2 0.3835 0.602 0.020 0.800 0.004 0.168 0.008
#> SRR1617410 5 0.0579 0.965 0.008 0.000 0.000 0.008 0.984
#> SRR1617411 5 0.0579 0.965 0.008 0.000 0.000 0.008 0.984
#> SRR1617412 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> SRR1617413 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> SRR1617414 5 0.2170 0.930 0.020 0.020 0.000 0.036 0.924
#> SRR1617415 5 0.2170 0.930 0.020 0.020 0.000 0.036 0.924
#> SRR1617416 4 0.5934 0.626 0.156 0.000 0.020 0.648 0.176
#> SRR1617417 4 0.5934 0.626 0.156 0.000 0.020 0.648 0.176
#> SRR1617418 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> SRR1617419 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> SRR1617420 5 0.0771 0.964 0.020 0.000 0.004 0.000 0.976
#> SRR1617421 5 0.0771 0.964 0.020 0.000 0.004 0.000 0.976
#> SRR1617422 1 0.1967 0.846 0.932 0.012 0.000 0.020 0.036
#> SRR1617423 1 0.1967 0.846 0.932 0.012 0.000 0.020 0.036
#> SRR1617424 1 0.1205 0.852 0.956 0.000 0.000 0.004 0.040
#> SRR1617425 1 0.1205 0.852 0.956 0.000 0.000 0.004 0.040
#> SRR1617427 1 0.2513 0.806 0.876 0.000 0.000 0.008 0.116
#> SRR1617426 1 0.2513 0.806 0.876 0.000 0.000 0.008 0.116
#> SRR1617428 4 0.5468 0.581 0.008 0.236 0.068 0.676 0.012
#> SRR1617429 4 0.5468 0.581 0.008 0.236 0.068 0.676 0.012
#> SRR1617432 5 0.0693 0.966 0.008 0.000 0.000 0.012 0.980
#> SRR1617433 5 0.0693 0.966 0.008 0.000 0.000 0.012 0.980
#> SRR1617434 5 0.0794 0.956 0.000 0.000 0.000 0.028 0.972
#> SRR1617436 3 0.0162 0.961 0.000 0.000 0.996 0.004 0.000
#> SRR1617435 5 0.0794 0.956 0.000 0.000 0.000 0.028 0.972
#> SRR1617437 3 0.0162 0.961 0.000 0.000 0.996 0.004 0.000
#> SRR1617438 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> SRR1617439 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> SRR1617440 3 0.4057 0.798 0.008 0.068 0.812 0.108 0.004
#> SRR1617441 3 0.4057 0.798 0.008 0.068 0.812 0.108 0.004
#> SRR1617443 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> SRR1617442 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> SRR1617444 1 0.6192 0.262 0.496 0.124 0.000 0.376 0.004
#> SRR1617445 1 0.6192 0.262 0.496 0.124 0.000 0.376 0.004
#> SRR1617446 1 0.1117 0.851 0.964 0.000 0.000 0.016 0.020
#> SRR1617447 1 0.1117 0.851 0.964 0.000 0.000 0.016 0.020
#> SRR1617448 1 0.0992 0.847 0.968 0.000 0.000 0.024 0.008
#> SRR1617449 1 0.0992 0.847 0.968 0.000 0.000 0.024 0.008
#> SRR1617451 2 0.1952 0.699 0.004 0.912 0.000 0.084 0.000
#> SRR1617450 2 0.1952 0.699 0.004 0.912 0.000 0.084 0.000
#> SRR1617452 4 0.3210 0.480 0.000 0.212 0.000 0.788 0.000
#> SRR1617454 2 0.0000 0.738 0.000 1.000 0.000 0.000 0.000
#> SRR1617453 4 0.3210 0.480 0.000 0.212 0.000 0.788 0.000
#> SRR1617456 2 0.3844 0.710 0.004 0.736 0.000 0.256 0.004
#> SRR1617457 2 0.3844 0.710 0.004 0.736 0.000 0.256 0.004
#> SRR1617455 2 0.0000 0.738 0.000 1.000 0.000 0.000 0.000
#> SRR1617458 2 0.3895 0.706 0.004 0.728 0.000 0.264 0.004
#> SRR1617459 2 0.3895 0.706 0.004 0.728 0.000 0.264 0.004
#> SRR1617460 2 0.4213 0.664 0.012 0.680 0.000 0.308 0.000
#> SRR1617461 2 0.4213 0.664 0.012 0.680 0.000 0.308 0.000
#> SRR1617463 2 0.3039 0.725 0.012 0.836 0.000 0.152 0.000
#> SRR1617462 2 0.3039 0.725 0.012 0.836 0.000 0.152 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.2989 0.3906 0.008 0.812 0.000 0.004 0.000 0.176
#> SRR1617431 2 0.2989 0.3906 0.008 0.812 0.000 0.004 0.000 0.176
#> SRR1617410 5 0.0146 0.9399 0.000 0.000 0.000 0.004 0.996 0.000
#> SRR1617411 5 0.0146 0.9399 0.000 0.000 0.000 0.004 0.996 0.000
#> SRR1617412 3 0.0767 0.9121 0.000 0.012 0.976 0.008 0.004 0.000
#> SRR1617413 3 0.0767 0.9121 0.000 0.012 0.976 0.008 0.004 0.000
#> SRR1617414 5 0.3135 0.9041 0.028 0.068 0.000 0.048 0.856 0.000
#> SRR1617415 5 0.3135 0.9041 0.028 0.068 0.000 0.048 0.856 0.000
#> SRR1617416 4 0.3261 0.7554 0.028 0.004 0.012 0.852 0.092 0.012
#> SRR1617417 4 0.3261 0.7554 0.028 0.004 0.012 0.852 0.092 0.012
#> SRR1617418 3 0.0622 0.9136 0.000 0.012 0.980 0.008 0.000 0.000
#> SRR1617419 3 0.0622 0.9136 0.000 0.012 0.980 0.008 0.000 0.000
#> SRR1617420 5 0.0146 0.9409 0.004 0.000 0.000 0.000 0.996 0.000
#> SRR1617421 5 0.0146 0.9409 0.004 0.000 0.000 0.000 0.996 0.000
#> SRR1617422 1 0.3268 0.8104 0.852 0.072 0.000 0.028 0.004 0.044
#> SRR1617423 1 0.3268 0.8104 0.852 0.072 0.000 0.028 0.004 0.044
#> SRR1617424 1 0.0260 0.8667 0.992 0.000 0.000 0.000 0.008 0.000
#> SRR1617425 1 0.0260 0.8667 0.992 0.000 0.000 0.000 0.008 0.000
#> SRR1617427 1 0.2493 0.8196 0.884 0.036 0.000 0.004 0.076 0.000
#> SRR1617426 1 0.2493 0.8196 0.884 0.036 0.000 0.004 0.076 0.000
#> SRR1617428 4 0.3633 0.6955 0.004 0.252 0.012 0.732 0.000 0.000
#> SRR1617429 4 0.3633 0.6955 0.004 0.252 0.012 0.732 0.000 0.000
#> SRR1617432 5 0.2614 0.9187 0.012 0.060 0.000 0.044 0.884 0.000
#> SRR1617433 5 0.2614 0.9187 0.012 0.060 0.000 0.044 0.884 0.000
#> SRR1617434 5 0.0632 0.9311 0.000 0.000 0.000 0.024 0.976 0.000
#> SRR1617436 3 0.1349 0.8892 0.000 0.056 0.940 0.004 0.000 0.000
#> SRR1617435 5 0.0632 0.9311 0.000 0.000 0.000 0.024 0.976 0.000
#> SRR1617437 3 0.1349 0.8892 0.000 0.056 0.940 0.004 0.000 0.000
#> SRR1617438 3 0.0260 0.9134 0.000 0.008 0.992 0.000 0.000 0.000
#> SRR1617439 3 0.0260 0.9134 0.000 0.008 0.992 0.000 0.000 0.000
#> SRR1617440 3 0.5460 0.5533 0.000 0.240 0.620 0.024 0.000 0.116
#> SRR1617441 3 0.5460 0.5533 0.000 0.240 0.620 0.024 0.000 0.116
#> SRR1617443 3 0.0146 0.9142 0.000 0.000 0.996 0.004 0.000 0.000
#> SRR1617442 3 0.0146 0.9142 0.000 0.000 0.996 0.004 0.000 0.000
#> SRR1617444 2 0.7595 0.2422 0.192 0.368 0.008 0.144 0.000 0.288
#> SRR1617445 2 0.7595 0.2422 0.192 0.368 0.008 0.144 0.000 0.288
#> SRR1617446 1 0.3104 0.8554 0.844 0.068 0.000 0.084 0.004 0.000
#> SRR1617447 1 0.3104 0.8554 0.844 0.068 0.000 0.084 0.004 0.000
#> SRR1617448 1 0.3104 0.8554 0.844 0.068 0.000 0.084 0.004 0.000
#> SRR1617449 1 0.3104 0.8554 0.844 0.068 0.000 0.084 0.004 0.000
#> SRR1617451 2 0.3695 0.0676 0.000 0.624 0.000 0.000 0.000 0.376
#> SRR1617450 2 0.3695 0.0676 0.000 0.624 0.000 0.000 0.000 0.376
#> SRR1617452 4 0.3380 0.7089 0.000 0.004 0.000 0.748 0.004 0.244
#> SRR1617454 6 0.3838 0.3329 0.000 0.448 0.000 0.000 0.000 0.552
#> SRR1617453 4 0.3380 0.7089 0.000 0.004 0.000 0.748 0.004 0.244
#> SRR1617456 6 0.2263 0.6848 0.000 0.100 0.000 0.016 0.000 0.884
#> SRR1617457 6 0.2263 0.6848 0.000 0.100 0.000 0.016 0.000 0.884
#> SRR1617455 6 0.3838 0.3329 0.000 0.448 0.000 0.000 0.000 0.552
#> SRR1617458 6 0.2263 0.6848 0.000 0.100 0.000 0.016 0.000 0.884
#> SRR1617459 6 0.2263 0.6848 0.000 0.100 0.000 0.016 0.000 0.884
#> SRR1617460 6 0.3039 0.6589 0.004 0.088 0.000 0.060 0.000 0.848
#> SRR1617461 6 0.3039 0.6589 0.004 0.088 0.000 0.060 0.000 0.848
#> SRR1617463 6 0.3758 0.6307 0.004 0.176 0.000 0.048 0.000 0.772
#> SRR1617462 6 0.3758 0.6307 0.004 0.176 0.000 0.048 0.000 0.772
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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 0.922 0.922 0.968 0.4748 0.525 0.525
#> 3 3 1.000 0.974 0.980 0.3646 0.793 0.616
#> 4 4 0.824 0.739 0.888 0.1034 0.978 0.935
#> 5 5 0.885 0.773 0.905 0.0883 0.925 0.767
#> 6 6 0.879 0.878 0.908 0.0207 0.947 0.791
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
#> SRR1617430 2 0.0376 0.956 0.004 0.996
#> SRR1617431 2 0.0376 0.956 0.004 0.996
#> SRR1617410 1 0.0000 0.967 1.000 0.000
#> SRR1617411 1 0.0000 0.967 1.000 0.000
#> SRR1617412 1 0.0000 0.967 1.000 0.000
#> SRR1617413 1 0.0000 0.967 1.000 0.000
#> SRR1617414 1 0.0000 0.967 1.000 0.000
#> SRR1617415 1 0.0000 0.967 1.000 0.000
#> SRR1617416 1 0.0000 0.967 1.000 0.000
#> SRR1617417 1 0.0000 0.967 1.000 0.000
#> SRR1617418 1 0.2236 0.942 0.964 0.036
#> SRR1617419 1 0.2603 0.936 0.956 0.044
#> SRR1617420 1 0.0000 0.967 1.000 0.000
#> SRR1617421 1 0.0000 0.967 1.000 0.000
#> SRR1617422 1 0.0000 0.967 1.000 0.000
#> SRR1617423 1 0.0000 0.967 1.000 0.000
#> SRR1617424 1 0.0000 0.967 1.000 0.000
#> SRR1617425 1 0.0000 0.967 1.000 0.000
#> SRR1617427 1 0.0000 0.967 1.000 0.000
#> SRR1617426 1 0.0000 0.967 1.000 0.000
#> SRR1617428 2 0.0000 0.959 0.000 1.000
#> SRR1617429 2 0.0000 0.959 0.000 1.000
#> SRR1617432 1 0.0000 0.967 1.000 0.000
#> SRR1617433 1 0.0000 0.967 1.000 0.000
#> SRR1617434 1 0.0000 0.967 1.000 0.000
#> SRR1617436 1 0.0000 0.967 1.000 0.000
#> SRR1617435 1 0.0000 0.967 1.000 0.000
#> SRR1617437 1 0.0000 0.967 1.000 0.000
#> SRR1617438 1 0.9087 0.531 0.676 0.324
#> SRR1617439 1 0.9170 0.513 0.668 0.332
#> SRR1617440 2 0.9427 0.422 0.360 0.640
#> SRR1617441 2 0.9427 0.422 0.360 0.640
#> SRR1617443 1 0.5842 0.834 0.860 0.140
#> SRR1617442 1 0.4562 0.885 0.904 0.096
#> SRR1617444 1 0.1633 0.952 0.976 0.024
#> SRR1617445 1 0.1843 0.949 0.972 0.028
#> SRR1617446 1 0.0000 0.967 1.000 0.000
#> SRR1617447 1 0.0000 0.967 1.000 0.000
#> SRR1617448 1 0.0000 0.967 1.000 0.000
#> SRR1617449 1 0.0000 0.967 1.000 0.000
#> SRR1617451 2 0.0000 0.959 0.000 1.000
#> SRR1617450 2 0.0000 0.959 0.000 1.000
#> SRR1617452 2 0.0000 0.959 0.000 1.000
#> SRR1617454 2 0.0000 0.959 0.000 1.000
#> SRR1617453 2 0.0000 0.959 0.000 1.000
#> SRR1617456 2 0.0000 0.959 0.000 1.000
#> SRR1617457 2 0.0000 0.959 0.000 1.000
#> SRR1617455 2 0.0000 0.959 0.000 1.000
#> SRR1617458 2 0.0000 0.959 0.000 1.000
#> SRR1617459 2 0.0000 0.959 0.000 1.000
#> SRR1617460 2 0.0000 0.959 0.000 1.000
#> SRR1617461 2 0.0000 0.959 0.000 1.000
#> SRR1617463 2 0.0000 0.959 0.000 1.000
#> SRR1617462 2 0.0000 0.959 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.429 0.777 0.180 0.820 0.000
#> SRR1617431 2 0.400 0.802 0.160 0.840 0.000
#> SRR1617410 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617411 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617412 3 0.164 0.990 0.044 0.000 0.956
#> SRR1617413 3 0.164 0.990 0.044 0.000 0.956
#> SRR1617414 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617415 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617416 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617417 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617418 3 0.164 0.990 0.044 0.000 0.956
#> SRR1617419 3 0.164 0.990 0.044 0.000 0.956
#> SRR1617420 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617421 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617422 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617423 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617424 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617425 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617427 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617426 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617428 2 0.000 0.963 0.000 1.000 0.000
#> SRR1617429 2 0.000 0.963 0.000 1.000 0.000
#> SRR1617432 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617433 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617434 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617436 3 0.164 0.990 0.044 0.000 0.956
#> SRR1617435 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617437 3 0.164 0.990 0.044 0.000 0.956
#> SRR1617438 3 0.164 0.990 0.044 0.000 0.956
#> SRR1617439 3 0.164 0.990 0.044 0.000 0.956
#> SRR1617440 3 0.000 0.950 0.000 0.000 1.000
#> SRR1617441 3 0.000 0.950 0.000 0.000 1.000
#> SRR1617443 3 0.164 0.990 0.044 0.000 0.956
#> SRR1617442 3 0.164 0.990 0.044 0.000 0.956
#> SRR1617444 1 0.103 0.973 0.976 0.024 0.000
#> SRR1617445 1 0.129 0.965 0.968 0.032 0.000
#> SRR1617446 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617447 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617448 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617449 1 0.000 0.997 1.000 0.000 0.000
#> SRR1617451 2 0.000 0.963 0.000 1.000 0.000
#> SRR1617450 2 0.000 0.963 0.000 1.000 0.000
#> SRR1617452 2 0.164 0.954 0.000 0.956 0.044
#> SRR1617454 2 0.000 0.963 0.000 1.000 0.000
#> SRR1617453 2 0.164 0.954 0.000 0.956 0.044
#> SRR1617456 2 0.164 0.954 0.000 0.956 0.044
#> SRR1617457 2 0.164 0.954 0.000 0.956 0.044
#> SRR1617455 2 0.000 0.963 0.000 1.000 0.000
#> SRR1617458 2 0.164 0.954 0.000 0.956 0.044
#> SRR1617459 2 0.164 0.954 0.000 0.956 0.044
#> SRR1617460 2 0.000 0.963 0.000 1.000 0.000
#> SRR1617461 2 0.000 0.963 0.000 1.000 0.000
#> SRR1617463 2 0.000 0.963 0.000 1.000 0.000
#> SRR1617462 2 0.000 0.963 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.1022 0.618 0.032 0.968 0.000 0.000
#> SRR1617431 2 0.0921 0.623 0.028 0.972 0.000 0.000
#> SRR1617410 1 0.3528 0.842 0.808 0.000 0.000 0.192
#> SRR1617411 1 0.3528 0.842 0.808 0.000 0.000 0.192
#> SRR1617412 3 0.0469 0.985 0.012 0.000 0.988 0.000
#> SRR1617413 3 0.0469 0.985 0.012 0.000 0.988 0.000
#> SRR1617414 1 0.4543 0.772 0.676 0.000 0.000 0.324
#> SRR1617415 1 0.4543 0.772 0.676 0.000 0.000 0.324
#> SRR1617416 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> SRR1617417 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> SRR1617418 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> SRR1617419 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> SRR1617420 1 0.1474 0.892 0.948 0.000 0.000 0.052
#> SRR1617421 1 0.1716 0.889 0.936 0.000 0.000 0.064
#> SRR1617422 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> SRR1617423 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> SRR1617424 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> SRR1617425 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> SRR1617427 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> SRR1617426 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> SRR1617428 2 0.0469 0.638 0.000 0.988 0.012 0.000
#> SRR1617429 2 0.0592 0.635 0.000 0.984 0.016 0.000
#> SRR1617432 1 0.4543 0.772 0.676 0.000 0.000 0.324
#> SRR1617433 1 0.4543 0.772 0.676 0.000 0.000 0.324
#> SRR1617434 1 0.4543 0.772 0.676 0.000 0.000 0.324
#> SRR1617436 3 0.0188 0.994 0.004 0.000 0.996 0.000
#> SRR1617435 1 0.4543 0.772 0.676 0.000 0.000 0.324
#> SRR1617437 3 0.0188 0.994 0.004 0.000 0.996 0.000
#> SRR1617438 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> SRR1617439 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> SRR1617440 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> SRR1617441 3 0.0188 0.993 0.000 0.004 0.996 0.000
#> SRR1617443 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> SRR1617442 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> SRR1617444 1 0.0817 0.892 0.976 0.024 0.000 0.000
#> SRR1617445 1 0.1022 0.888 0.968 0.032 0.000 0.000
#> SRR1617446 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> SRR1617447 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> SRR1617448 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> SRR1617449 1 0.0000 0.902 1.000 0.000 0.000 0.000
#> SRR1617451 2 0.0000 0.642 0.000 1.000 0.000 0.000
#> SRR1617450 2 0.0000 0.642 0.000 1.000 0.000 0.000
#> SRR1617452 4 0.4543 1.000 0.000 0.324 0.000 0.676
#> SRR1617454 2 0.0000 0.642 0.000 1.000 0.000 0.000
#> SRR1617453 4 0.4543 1.000 0.000 0.324 0.000 0.676
#> SRR1617456 2 0.4972 -0.400 0.000 0.544 0.000 0.456
#> SRR1617457 2 0.4972 -0.400 0.000 0.544 0.000 0.456
#> SRR1617455 2 0.0000 0.642 0.000 1.000 0.000 0.000
#> SRR1617458 2 0.4972 -0.400 0.000 0.544 0.000 0.456
#> SRR1617459 2 0.4972 -0.400 0.000 0.544 0.000 0.456
#> SRR1617460 2 0.3801 0.454 0.000 0.780 0.000 0.220
#> SRR1617461 2 0.3801 0.454 0.000 0.780 0.000 0.220
#> SRR1617463 2 0.3801 0.454 0.000 0.780 0.000 0.220
#> SRR1617462 2 0.3801 0.454 0.000 0.780 0.000 0.220
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 2 0.1043 0.566 0.040 0.960 0.000 0.000 0.000
#> SRR1617431 2 0.0794 0.571 0.028 0.972 0.000 0.000 0.000
#> SRR1617410 1 0.3039 0.799 0.808 0.000 0.000 0.000 0.192
#> SRR1617411 1 0.3039 0.799 0.808 0.000 0.000 0.000 0.192
#> SRR1617412 3 0.0404 0.986 0.012 0.000 0.988 0.000 0.000
#> SRR1617413 3 0.0404 0.986 0.012 0.000 0.988 0.000 0.000
#> SRR1617414 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617415 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617416 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> SRR1617417 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> SRR1617418 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000
#> SRR1617419 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000
#> SRR1617420 1 0.1270 0.935 0.948 0.000 0.000 0.000 0.052
#> SRR1617421 1 0.1478 0.927 0.936 0.000 0.000 0.000 0.064
#> SRR1617422 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> SRR1617423 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> SRR1617424 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> SRR1617425 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> SRR1617427 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> SRR1617426 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> SRR1617428 2 0.4190 0.471 0.000 0.768 0.060 0.172 0.000
#> SRR1617429 2 0.4252 0.469 0.000 0.764 0.064 0.172 0.000
#> SRR1617432 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617433 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617434 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617436 3 0.0162 0.994 0.004 0.000 0.996 0.000 0.000
#> SRR1617435 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617437 3 0.0162 0.994 0.004 0.000 0.996 0.000 0.000
#> SRR1617438 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000
#> SRR1617439 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000
#> SRR1617440 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000
#> SRR1617441 3 0.0162 0.993 0.000 0.004 0.996 0.000 0.000
#> SRR1617443 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000
#> SRR1617442 3 0.0000 0.996 0.000 0.000 1.000 0.000 0.000
#> SRR1617444 1 0.1300 0.937 0.956 0.016 0.000 0.028 0.000
#> SRR1617445 1 0.1493 0.930 0.948 0.024 0.000 0.028 0.000
#> SRR1617446 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> SRR1617447 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> SRR1617448 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> SRR1617449 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> SRR1617451 2 0.1197 0.564 0.000 0.952 0.000 0.048 0.000
#> SRR1617450 2 0.1197 0.564 0.000 0.952 0.000 0.048 0.000
#> SRR1617452 4 0.2852 1.000 0.000 0.172 0.000 0.828 0.000
#> SRR1617454 2 0.0000 0.572 0.000 1.000 0.000 0.000 0.000
#> SRR1617453 4 0.2852 1.000 0.000 0.172 0.000 0.828 0.000
#> SRR1617456 2 0.4304 -0.123 0.000 0.516 0.000 0.484 0.000
#> SRR1617457 2 0.4304 -0.123 0.000 0.516 0.000 0.484 0.000
#> SRR1617455 2 0.0000 0.572 0.000 1.000 0.000 0.000 0.000
#> SRR1617458 2 0.4304 -0.123 0.000 0.516 0.000 0.484 0.000
#> SRR1617459 2 0.4304 -0.123 0.000 0.516 0.000 0.484 0.000
#> SRR1617460 2 0.3999 0.263 0.000 0.656 0.000 0.344 0.000
#> SRR1617461 2 0.3999 0.263 0.000 0.656 0.000 0.344 0.000
#> SRR1617463 2 0.3999 0.263 0.000 0.656 0.000 0.344 0.000
#> SRR1617462 2 0.3999 0.263 0.000 0.656 0.000 0.344 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.5520 0.465 0.240 0.560 0.000 0.000 0.000 0.200
#> SRR1617431 2 0.5083 0.571 0.164 0.632 0.000 0.000 0.000 0.204
#> SRR1617410 1 0.2730 0.798 0.808 0.000 0.000 0.000 0.192 0.000
#> SRR1617411 1 0.2730 0.798 0.808 0.000 0.000 0.000 0.192 0.000
#> SRR1617412 3 0.0363 0.985 0.012 0.000 0.988 0.000 0.000 0.000
#> SRR1617413 3 0.0363 0.985 0.012 0.000 0.988 0.000 0.000 0.000
#> SRR1617414 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617415 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617416 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617417 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617418 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617419 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617420 1 0.1075 0.928 0.952 0.000 0.000 0.000 0.048 0.000
#> SRR1617421 1 0.1327 0.917 0.936 0.000 0.000 0.000 0.064 0.000
#> SRR1617422 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617423 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617424 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617425 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617427 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617426 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617428 4 0.2762 1.000 0.000 0.196 0.000 0.804 0.000 0.000
#> SRR1617429 4 0.2762 1.000 0.000 0.196 0.000 0.804 0.000 0.000
#> SRR1617432 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617433 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617434 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617436 3 0.0146 0.993 0.004 0.000 0.996 0.000 0.000 0.000
#> SRR1617435 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617437 3 0.0146 0.993 0.004 0.000 0.996 0.000 0.000 0.000
#> SRR1617438 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617439 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617440 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617441 3 0.0146 0.993 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1617443 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617442 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617444 1 0.2092 0.859 0.876 0.000 0.000 0.000 0.000 0.124
#> SRR1617445 1 0.2092 0.859 0.876 0.000 0.000 0.000 0.000 0.124
#> SRR1617446 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617447 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617448 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617449 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> SRR1617451 2 0.3695 0.595 0.000 0.624 0.000 0.000 0.000 0.376
#> SRR1617450 2 0.3695 0.595 0.000 0.624 0.000 0.000 0.000 0.376
#> SRR1617452 6 0.5202 0.627 0.000 0.188 0.000 0.196 0.000 0.616
#> SRR1617454 2 0.2762 0.697 0.000 0.804 0.000 0.000 0.000 0.196
#> SRR1617453 6 0.5202 0.627 0.000 0.188 0.000 0.196 0.000 0.616
#> SRR1617456 6 0.0000 0.832 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617457 6 0.0000 0.832 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617455 2 0.2762 0.697 0.000 0.804 0.000 0.000 0.000 0.196
#> SRR1617458 6 0.0000 0.832 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617459 6 0.0000 0.832 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617460 2 0.0000 0.680 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617461 2 0.0000 0.680 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617463 2 0.0000 0.680 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617462 2 0.0000 0.680 0.000 1.000 0.000 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", "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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 0.755 0.917 0.939 0.4337 0.525 0.525
#> 3 3 0.759 0.901 0.890 0.4782 0.832 0.680
#> 4 4 0.716 0.820 0.900 0.1241 0.925 0.789
#> 5 5 0.641 0.617 0.749 0.0855 0.897 0.650
#> 6 6 0.743 0.688 0.799 0.0526 0.922 0.657
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
#> SRR1617430 2 0.2423 0.983 0.040 0.960
#> SRR1617431 2 0.2423 0.983 0.040 0.960
#> SRR1617410 1 0.0000 0.870 1.000 0.000
#> SRR1617411 1 0.0000 0.870 1.000 0.000
#> SRR1617412 2 0.0000 0.966 0.000 1.000
#> SRR1617413 2 0.0000 0.966 0.000 1.000
#> SRR1617414 1 0.6343 0.851 0.840 0.160
#> SRR1617415 1 0.6623 0.842 0.828 0.172
#> SRR1617416 2 0.2778 0.978 0.048 0.952
#> SRR1617417 2 0.2778 0.978 0.048 0.952
#> SRR1617418 2 0.0000 0.966 0.000 1.000
#> SRR1617419 2 0.0000 0.966 0.000 1.000
#> SRR1617420 1 0.2423 0.880 0.960 0.040
#> SRR1617421 1 0.2423 0.880 0.960 0.040
#> SRR1617422 1 0.8016 0.769 0.756 0.244
#> SRR1617423 1 0.8443 0.733 0.728 0.272
#> SRR1617424 1 0.1633 0.878 0.976 0.024
#> SRR1617425 1 0.1633 0.878 0.976 0.024
#> SRR1617427 1 0.5519 0.867 0.872 0.128
#> SRR1617426 1 0.5519 0.867 0.872 0.128
#> SRR1617428 2 0.2423 0.983 0.040 0.960
#> SRR1617429 2 0.2423 0.983 0.040 0.960
#> SRR1617432 1 0.0672 0.873 0.992 0.008
#> SRR1617433 1 0.0672 0.873 0.992 0.008
#> SRR1617434 1 0.9795 0.448 0.584 0.416
#> SRR1617436 2 0.0000 0.966 0.000 1.000
#> SRR1617435 1 0.9795 0.448 0.584 0.416
#> SRR1617437 2 0.0000 0.966 0.000 1.000
#> SRR1617438 2 0.0000 0.966 0.000 1.000
#> SRR1617439 2 0.0000 0.966 0.000 1.000
#> SRR1617440 2 0.1414 0.976 0.020 0.980
#> SRR1617441 2 0.1414 0.976 0.020 0.980
#> SRR1617443 2 0.0000 0.966 0.000 1.000
#> SRR1617442 2 0.0000 0.966 0.000 1.000
#> SRR1617444 2 0.2423 0.983 0.040 0.960
#> SRR1617445 2 0.2423 0.983 0.040 0.960
#> SRR1617446 1 0.0000 0.870 1.000 0.000
#> SRR1617447 1 0.0000 0.870 1.000 0.000
#> SRR1617448 1 0.5842 0.863 0.860 0.140
#> SRR1617449 1 0.5842 0.863 0.860 0.140
#> SRR1617451 2 0.2423 0.983 0.040 0.960
#> SRR1617450 2 0.2423 0.983 0.040 0.960
#> SRR1617452 2 0.2423 0.983 0.040 0.960
#> SRR1617454 2 0.2423 0.983 0.040 0.960
#> SRR1617453 2 0.2423 0.983 0.040 0.960
#> SRR1617456 2 0.2423 0.983 0.040 0.960
#> SRR1617457 2 0.2423 0.983 0.040 0.960
#> SRR1617455 2 0.2423 0.983 0.040 0.960
#> SRR1617458 2 0.2423 0.983 0.040 0.960
#> SRR1617459 2 0.2423 0.983 0.040 0.960
#> SRR1617460 2 0.2423 0.983 0.040 0.960
#> SRR1617461 2 0.2423 0.983 0.040 0.960
#> SRR1617463 2 0.2423 0.983 0.040 0.960
#> SRR1617462 2 0.2423 0.983 0.040 0.960
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.2796 0.861 0.092 0.908 0.000
#> SRR1617431 2 0.2796 0.861 0.092 0.908 0.000
#> SRR1617410 1 0.0000 0.983 1.000 0.000 0.000
#> SRR1617411 1 0.0000 0.983 1.000 0.000 0.000
#> SRR1617412 3 0.0000 0.976 0.000 0.000 1.000
#> SRR1617413 3 0.0000 0.976 0.000 0.000 1.000
#> SRR1617414 1 0.1163 0.979 0.972 0.028 0.000
#> SRR1617415 1 0.1163 0.979 0.972 0.028 0.000
#> SRR1617416 2 0.4178 0.828 0.172 0.828 0.000
#> SRR1617417 2 0.4178 0.828 0.172 0.828 0.000
#> SRR1617418 3 0.0000 0.976 0.000 0.000 1.000
#> SRR1617419 3 0.0000 0.976 0.000 0.000 1.000
#> SRR1617420 1 0.0000 0.983 1.000 0.000 0.000
#> SRR1617421 1 0.0000 0.983 1.000 0.000 0.000
#> SRR1617422 1 0.1529 0.971 0.960 0.040 0.000
#> SRR1617423 1 0.1529 0.971 0.960 0.040 0.000
#> SRR1617424 1 0.0747 0.982 0.984 0.016 0.000
#> SRR1617425 1 0.0747 0.982 0.984 0.016 0.000
#> SRR1617427 1 0.0592 0.984 0.988 0.012 0.000
#> SRR1617426 1 0.0592 0.984 0.988 0.012 0.000
#> SRR1617428 2 0.3267 0.850 0.116 0.884 0.000
#> SRR1617429 2 0.3267 0.850 0.116 0.884 0.000
#> SRR1617432 1 0.0000 0.983 1.000 0.000 0.000
#> SRR1617433 1 0.0000 0.983 1.000 0.000 0.000
#> SRR1617434 1 0.0592 0.984 0.988 0.012 0.000
#> SRR1617436 3 0.2796 0.896 0.000 0.092 0.908
#> SRR1617435 1 0.0747 0.983 0.984 0.016 0.000
#> SRR1617437 3 0.2796 0.896 0.000 0.092 0.908
#> SRR1617438 3 0.0000 0.976 0.000 0.000 1.000
#> SRR1617439 3 0.0000 0.976 0.000 0.000 1.000
#> SRR1617440 2 0.6062 0.454 0.000 0.616 0.384
#> SRR1617441 2 0.6062 0.454 0.000 0.616 0.384
#> SRR1617443 3 0.0000 0.976 0.000 0.000 1.000
#> SRR1617442 3 0.0000 0.976 0.000 0.000 1.000
#> SRR1617444 2 0.2356 0.867 0.072 0.928 0.000
#> SRR1617445 2 0.2356 0.867 0.072 0.928 0.000
#> SRR1617446 1 0.0000 0.983 1.000 0.000 0.000
#> SRR1617447 1 0.0000 0.983 1.000 0.000 0.000
#> SRR1617448 1 0.1411 0.974 0.964 0.036 0.000
#> SRR1617449 1 0.1411 0.974 0.964 0.036 0.000
#> SRR1617451 2 0.0000 0.874 0.000 1.000 0.000
#> SRR1617450 2 0.0000 0.874 0.000 1.000 0.000
#> SRR1617452 2 0.0000 0.874 0.000 1.000 0.000
#> SRR1617454 2 0.0000 0.874 0.000 1.000 0.000
#> SRR1617453 2 0.0000 0.874 0.000 1.000 0.000
#> SRR1617456 2 0.0000 0.874 0.000 1.000 0.000
#> SRR1617457 2 0.0000 0.874 0.000 1.000 0.000
#> SRR1617455 2 0.0000 0.874 0.000 1.000 0.000
#> SRR1617458 2 0.0000 0.874 0.000 1.000 0.000
#> SRR1617459 2 0.0000 0.874 0.000 1.000 0.000
#> SRR1617460 2 0.4887 0.748 0.228 0.772 0.000
#> SRR1617461 2 0.4887 0.748 0.228 0.772 0.000
#> SRR1617463 2 0.4887 0.748 0.228 0.772 0.000
#> SRR1617462 2 0.4887 0.748 0.228 0.772 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.3521 0.739 0.084 0.864 0.000 0.052
#> SRR1617431 2 0.3521 0.739 0.084 0.864 0.000 0.052
#> SRR1617410 1 0.1118 0.916 0.964 0.000 0.000 0.036
#> SRR1617411 1 0.1118 0.916 0.964 0.000 0.000 0.036
#> SRR1617412 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR1617413 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR1617414 1 0.2124 0.901 0.924 0.068 0.000 0.008
#> SRR1617415 1 0.2124 0.901 0.924 0.068 0.000 0.008
#> SRR1617416 4 0.1059 0.774 0.012 0.016 0.000 0.972
#> SRR1617417 4 0.1059 0.774 0.012 0.016 0.000 0.972
#> SRR1617418 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR1617419 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR1617420 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> SRR1617421 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> SRR1617422 1 0.3647 0.817 0.832 0.152 0.000 0.016
#> SRR1617423 1 0.3647 0.817 0.832 0.152 0.000 0.016
#> SRR1617424 1 0.1004 0.921 0.972 0.024 0.000 0.004
#> SRR1617425 1 0.1004 0.921 0.972 0.024 0.000 0.004
#> SRR1617427 1 0.1488 0.915 0.956 0.012 0.000 0.032
#> SRR1617426 1 0.1488 0.915 0.956 0.012 0.000 0.032
#> SRR1617428 4 0.6135 0.534 0.056 0.376 0.000 0.568
#> SRR1617429 4 0.6135 0.534 0.056 0.376 0.000 0.568
#> SRR1617432 1 0.1118 0.917 0.964 0.000 0.000 0.036
#> SRR1617433 1 0.1118 0.917 0.964 0.000 0.000 0.036
#> SRR1617434 1 0.3528 0.792 0.808 0.000 0.000 0.192
#> SRR1617436 3 0.2593 0.863 0.000 0.104 0.892 0.004
#> SRR1617435 1 0.4040 0.727 0.752 0.000 0.000 0.248
#> SRR1617437 3 0.2593 0.863 0.000 0.104 0.892 0.004
#> SRR1617438 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR1617439 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR1617440 2 0.5097 0.351 0.000 0.568 0.428 0.004
#> SRR1617441 2 0.5097 0.351 0.000 0.568 0.428 0.004
#> SRR1617443 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR1617442 3 0.0000 0.968 0.000 0.000 1.000 0.000
#> SRR1617444 2 0.2635 0.773 0.020 0.904 0.000 0.076
#> SRR1617445 2 0.2635 0.773 0.020 0.904 0.000 0.076
#> SRR1617446 1 0.0336 0.920 0.992 0.000 0.000 0.008
#> SRR1617447 1 0.0336 0.920 0.992 0.000 0.000 0.008
#> SRR1617448 1 0.2973 0.883 0.884 0.096 0.000 0.020
#> SRR1617449 1 0.2861 0.884 0.888 0.096 0.000 0.016
#> SRR1617451 2 0.0592 0.801 0.000 0.984 0.000 0.016
#> SRR1617450 2 0.0592 0.801 0.000 0.984 0.000 0.016
#> SRR1617452 4 0.2530 0.796 0.000 0.112 0.000 0.888
#> SRR1617454 2 0.0937 0.802 0.012 0.976 0.000 0.012
#> SRR1617453 4 0.2530 0.796 0.000 0.112 0.000 0.888
#> SRR1617456 2 0.1637 0.796 0.000 0.940 0.000 0.060
#> SRR1617457 2 0.1637 0.796 0.000 0.940 0.000 0.060
#> SRR1617455 2 0.0937 0.802 0.012 0.976 0.000 0.012
#> SRR1617458 2 0.1637 0.796 0.000 0.940 0.000 0.060
#> SRR1617459 2 0.1637 0.796 0.000 0.940 0.000 0.060
#> SRR1617460 2 0.3942 0.679 0.000 0.764 0.000 0.236
#> SRR1617461 2 0.3942 0.679 0.000 0.764 0.000 0.236
#> SRR1617463 2 0.3837 0.692 0.000 0.776 0.000 0.224
#> SRR1617462 2 0.3837 0.692 0.000 0.776 0.000 0.224
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 2 0.6027 0.597 0.052 0.644 0.000 0.076 0.228
#> SRR1617431 2 0.6027 0.597 0.052 0.644 0.000 0.076 0.228
#> SRR1617410 1 0.0609 0.606 0.980 0.000 0.000 0.020 0.000
#> SRR1617411 1 0.0609 0.606 0.980 0.000 0.000 0.020 0.000
#> SRR1617412 3 0.0000 0.874 0.000 0.000 1.000 0.000 0.000
#> SRR1617413 3 0.0000 0.874 0.000 0.000 1.000 0.000 0.000
#> SRR1617414 5 0.5646 0.662 0.356 0.004 0.000 0.076 0.564
#> SRR1617415 5 0.5646 0.662 0.356 0.004 0.000 0.076 0.564
#> SRR1617416 4 0.3608 0.782 0.064 0.000 0.000 0.824 0.112
#> SRR1617417 4 0.3608 0.782 0.064 0.000 0.000 0.824 0.112
#> SRR1617418 3 0.0000 0.874 0.000 0.000 1.000 0.000 0.000
#> SRR1617419 3 0.0000 0.874 0.000 0.000 1.000 0.000 0.000
#> SRR1617420 1 0.5045 0.322 0.696 0.000 0.000 0.108 0.196
#> SRR1617421 1 0.5045 0.322 0.696 0.000 0.000 0.108 0.196
#> SRR1617422 5 0.4908 0.668 0.356 0.036 0.000 0.000 0.608
#> SRR1617423 5 0.4908 0.668 0.356 0.036 0.000 0.000 0.608
#> SRR1617424 1 0.5364 -0.190 0.572 0.000 0.000 0.064 0.364
#> SRR1617425 1 0.5364 -0.190 0.572 0.000 0.000 0.064 0.364
#> SRR1617427 5 0.6175 0.476 0.424 0.004 0.000 0.116 0.456
#> SRR1617426 5 0.6142 0.470 0.428 0.004 0.000 0.112 0.456
#> SRR1617428 4 0.5961 0.673 0.076 0.160 0.000 0.680 0.084
#> SRR1617429 4 0.5961 0.673 0.076 0.160 0.000 0.680 0.084
#> SRR1617432 1 0.0162 0.604 0.996 0.000 0.000 0.000 0.004
#> SRR1617433 1 0.0162 0.604 0.996 0.000 0.000 0.000 0.004
#> SRR1617434 1 0.3662 0.439 0.744 0.000 0.000 0.252 0.004
#> SRR1617436 3 0.2304 0.815 0.000 0.008 0.892 0.000 0.100
#> SRR1617435 1 0.3766 0.424 0.728 0.000 0.000 0.268 0.004
#> SRR1617437 3 0.2304 0.815 0.000 0.008 0.892 0.000 0.100
#> SRR1617438 3 0.0000 0.874 0.000 0.000 1.000 0.000 0.000
#> SRR1617439 3 0.0000 0.874 0.000 0.000 1.000 0.000 0.000
#> SRR1617440 3 0.5843 0.220 0.000 0.388 0.512 0.000 0.100
#> SRR1617441 3 0.5843 0.220 0.000 0.388 0.512 0.000 0.100
#> SRR1617443 3 0.0000 0.874 0.000 0.000 1.000 0.000 0.000
#> SRR1617442 3 0.0000 0.874 0.000 0.000 1.000 0.000 0.000
#> SRR1617444 2 0.5721 0.619 0.052 0.696 0.000 0.096 0.156
#> SRR1617445 2 0.5721 0.619 0.052 0.696 0.000 0.096 0.156
#> SRR1617446 1 0.3488 0.492 0.808 0.000 0.000 0.024 0.168
#> SRR1617447 1 0.3656 0.493 0.800 0.000 0.000 0.032 0.168
#> SRR1617448 5 0.6495 0.600 0.388 0.056 0.000 0.060 0.496
#> SRR1617449 5 0.6398 0.593 0.396 0.056 0.000 0.052 0.496
#> SRR1617451 2 0.1608 0.746 0.000 0.928 0.000 0.000 0.072
#> SRR1617450 2 0.1608 0.746 0.000 0.928 0.000 0.000 0.072
#> SRR1617452 4 0.0000 0.808 0.000 0.000 0.000 1.000 0.000
#> SRR1617454 2 0.1908 0.745 0.000 0.908 0.000 0.000 0.092
#> SRR1617453 4 0.0000 0.808 0.000 0.000 0.000 1.000 0.000
#> SRR1617456 2 0.1764 0.737 0.000 0.928 0.000 0.008 0.064
#> SRR1617457 2 0.1764 0.737 0.000 0.928 0.000 0.008 0.064
#> SRR1617455 2 0.1908 0.745 0.000 0.908 0.000 0.000 0.092
#> SRR1617458 2 0.1764 0.737 0.000 0.928 0.000 0.008 0.064
#> SRR1617459 2 0.1764 0.737 0.000 0.928 0.000 0.008 0.064
#> SRR1617460 2 0.5396 0.507 0.000 0.560 0.000 0.064 0.376
#> SRR1617461 2 0.5396 0.507 0.000 0.560 0.000 0.064 0.376
#> SRR1617463 2 0.5103 0.505 0.000 0.556 0.000 0.040 0.404
#> SRR1617462 2 0.5103 0.505 0.000 0.556 0.000 0.040 0.404
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.3565 0.692 0.092 0.808 0.000 0.000 0.004 0.096
#> SRR1617431 2 0.3565 0.692 0.092 0.808 0.000 0.000 0.004 0.096
#> SRR1617410 5 0.2145 0.682 0.072 0.000 0.000 0.028 0.900 0.000
#> SRR1617411 5 0.2145 0.682 0.072 0.000 0.000 0.028 0.900 0.000
#> SRR1617412 3 0.0146 0.884 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1617413 3 0.0146 0.884 0.000 0.000 0.996 0.000 0.000 0.004
#> SRR1617414 1 0.1471 0.735 0.932 0.000 0.000 0.000 0.064 0.004
#> SRR1617415 1 0.1471 0.735 0.932 0.000 0.000 0.000 0.064 0.004
#> SRR1617416 4 0.0508 0.835 0.000 0.000 0.000 0.984 0.012 0.004
#> SRR1617417 4 0.0508 0.835 0.000 0.000 0.000 0.984 0.012 0.004
#> SRR1617418 3 0.0000 0.886 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617419 3 0.0000 0.886 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617420 1 0.3868 0.277 0.508 0.000 0.000 0.000 0.492 0.000
#> SRR1617421 1 0.3998 0.269 0.504 0.000 0.000 0.004 0.492 0.000
#> SRR1617422 1 0.1080 0.700 0.960 0.032 0.000 0.000 0.004 0.004
#> SRR1617423 1 0.1080 0.700 0.960 0.032 0.000 0.000 0.004 0.004
#> SRR1617424 1 0.3805 0.593 0.664 0.000 0.000 0.004 0.328 0.004
#> SRR1617425 1 0.3805 0.593 0.664 0.000 0.000 0.004 0.328 0.004
#> SRR1617427 1 0.1588 0.732 0.924 0.000 0.000 0.000 0.072 0.004
#> SRR1617426 1 0.1588 0.732 0.924 0.000 0.000 0.000 0.072 0.004
#> SRR1617428 4 0.5132 0.602 0.080 0.028 0.000 0.656 0.000 0.236
#> SRR1617429 4 0.5132 0.602 0.080 0.028 0.000 0.656 0.000 0.236
#> SRR1617432 5 0.1663 0.674 0.088 0.000 0.000 0.000 0.912 0.000
#> SRR1617433 5 0.1663 0.674 0.088 0.000 0.000 0.000 0.912 0.000
#> SRR1617434 5 0.3907 0.274 0.004 0.000 0.000 0.408 0.588 0.000
#> SRR1617436 3 0.2911 0.826 0.044 0.060 0.876 0.008 0.008 0.004
#> SRR1617435 5 0.3907 0.274 0.004 0.000 0.000 0.408 0.588 0.000
#> SRR1617437 3 0.2911 0.826 0.044 0.060 0.876 0.008 0.008 0.004
#> SRR1617438 3 0.0000 0.886 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617439 3 0.0000 0.886 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617440 3 0.5426 0.351 0.044 0.372 0.552 0.008 0.004 0.020
#> SRR1617441 3 0.5426 0.351 0.044 0.372 0.552 0.008 0.004 0.020
#> SRR1617443 3 0.0000 0.886 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617442 3 0.0000 0.886 0.000 0.000 1.000 0.000 0.000 0.000
#> SRR1617444 2 0.5482 0.613 0.084 0.600 0.000 0.032 0.000 0.284
#> SRR1617445 2 0.5482 0.613 0.084 0.600 0.000 0.032 0.000 0.284
#> SRR1617446 5 0.3756 0.215 0.352 0.000 0.000 0.004 0.644 0.000
#> SRR1617447 5 0.3756 0.215 0.352 0.000 0.000 0.004 0.644 0.000
#> SRR1617448 1 0.4196 0.664 0.752 0.052 0.000 0.012 0.180 0.004
#> SRR1617449 1 0.4100 0.667 0.756 0.052 0.000 0.008 0.180 0.004
#> SRR1617451 2 0.3046 0.732 0.012 0.800 0.000 0.000 0.000 0.188
#> SRR1617450 2 0.3046 0.732 0.012 0.800 0.000 0.000 0.000 0.188
#> SRR1617452 4 0.0291 0.838 0.004 0.004 0.000 0.992 0.000 0.000
#> SRR1617454 2 0.2768 0.737 0.012 0.832 0.000 0.000 0.000 0.156
#> SRR1617453 4 0.0291 0.838 0.004 0.004 0.000 0.992 0.000 0.000
#> SRR1617456 2 0.4550 0.648 0.000 0.676 0.000 0.000 0.084 0.240
#> SRR1617457 2 0.4550 0.648 0.000 0.676 0.000 0.000 0.084 0.240
#> SRR1617455 2 0.2768 0.737 0.012 0.832 0.000 0.000 0.000 0.156
#> SRR1617458 2 0.4550 0.648 0.000 0.676 0.000 0.000 0.084 0.240
#> SRR1617459 2 0.4550 0.648 0.000 0.676 0.000 0.000 0.084 0.240
#> SRR1617460 6 0.1405 0.988 0.024 0.004 0.000 0.024 0.000 0.948
#> SRR1617461 6 0.1405 0.988 0.024 0.004 0.000 0.024 0.000 0.948
#> SRR1617463 6 0.1320 0.988 0.036 0.000 0.000 0.016 0.000 0.948
#> SRR1617462 6 0.1320 0.988 0.036 0.000 0.000 0.016 0.000 0.948
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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 0.753 0.914 0.955 0.4989 0.497 0.497
#> 3 3 0.807 0.878 0.949 0.3142 0.709 0.487
#> 4 4 0.777 0.819 0.874 0.1051 0.944 0.840
#> 5 5 0.895 0.881 0.919 0.0830 0.916 0.716
#> 6 6 0.851 0.791 0.854 0.0494 0.950 0.780
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
#> SRR1617430 2 0.0000 0.939 0.000 1.000
#> SRR1617431 2 0.0000 0.939 0.000 1.000
#> SRR1617410 1 0.2603 0.942 0.956 0.044
#> SRR1617411 1 0.2236 0.947 0.964 0.036
#> SRR1617412 1 0.1414 0.959 0.980 0.020
#> SRR1617413 1 0.1414 0.959 0.980 0.020
#> SRR1617414 1 0.3274 0.931 0.940 0.060
#> SRR1617415 1 0.3274 0.931 0.940 0.060
#> SRR1617416 1 0.4690 0.893 0.900 0.100
#> SRR1617417 1 0.5059 0.881 0.888 0.112
#> SRR1617418 1 0.1414 0.959 0.980 0.020
#> SRR1617419 1 0.1414 0.959 0.980 0.020
#> SRR1617420 1 0.0000 0.960 1.000 0.000
#> SRR1617421 1 0.0000 0.960 1.000 0.000
#> SRR1617422 2 0.5629 0.850 0.132 0.868
#> SRR1617423 2 0.5408 0.858 0.124 0.876
#> SRR1617424 1 0.0376 0.960 0.996 0.004
#> SRR1617425 1 0.0376 0.960 0.996 0.004
#> SRR1617427 1 0.0000 0.960 1.000 0.000
#> SRR1617426 1 0.0000 0.960 1.000 0.000
#> SRR1617428 2 0.9000 0.549 0.316 0.684
#> SRR1617429 2 0.8955 0.560 0.312 0.688
#> SRR1617432 1 0.0672 0.959 0.992 0.008
#> SRR1617433 1 0.0672 0.959 0.992 0.008
#> SRR1617434 1 0.0000 0.960 1.000 0.000
#> SRR1617436 1 0.1414 0.959 0.980 0.020
#> SRR1617435 1 0.0000 0.960 1.000 0.000
#> SRR1617437 1 0.1414 0.959 0.980 0.020
#> SRR1617438 1 0.1414 0.959 0.980 0.020
#> SRR1617439 1 0.1414 0.959 0.980 0.020
#> SRR1617440 2 0.6801 0.790 0.180 0.820
#> SRR1617441 2 0.6343 0.813 0.160 0.840
#> SRR1617443 1 0.1414 0.959 0.980 0.020
#> SRR1617442 1 0.1414 0.959 0.980 0.020
#> SRR1617444 2 0.0672 0.938 0.008 0.992
#> SRR1617445 2 0.0672 0.938 0.008 0.992
#> SRR1617446 1 0.0000 0.960 1.000 0.000
#> SRR1617447 1 0.0376 0.960 0.996 0.004
#> SRR1617448 1 0.7674 0.733 0.776 0.224
#> SRR1617449 1 0.7745 0.727 0.772 0.228
#> SRR1617451 2 0.0000 0.939 0.000 1.000
#> SRR1617450 2 0.0000 0.939 0.000 1.000
#> SRR1617452 2 0.0000 0.939 0.000 1.000
#> SRR1617454 2 0.0000 0.939 0.000 1.000
#> SRR1617453 2 0.0000 0.939 0.000 1.000
#> SRR1617456 2 0.0000 0.939 0.000 1.000
#> SRR1617457 2 0.0000 0.939 0.000 1.000
#> SRR1617455 2 0.0000 0.939 0.000 1.000
#> SRR1617458 2 0.0000 0.939 0.000 1.000
#> SRR1617459 2 0.0000 0.939 0.000 1.000
#> SRR1617460 2 0.1414 0.933 0.020 0.980
#> SRR1617461 2 0.1414 0.933 0.020 0.980
#> SRR1617463 2 0.1414 0.933 0.020 0.980
#> SRR1617462 2 0.1414 0.933 0.020 0.980
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.0000 0.9781 0.000 1.000 0.000
#> SRR1617431 2 0.0000 0.9781 0.000 1.000 0.000
#> SRR1617410 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617411 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617412 3 0.0000 0.9108 0.000 0.000 1.000
#> SRR1617413 3 0.0000 0.9108 0.000 0.000 1.000
#> SRR1617414 1 0.0237 0.9285 0.996 0.000 0.004
#> SRR1617415 1 0.0237 0.9285 0.996 0.000 0.004
#> SRR1617416 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617417 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617418 3 0.0000 0.9108 0.000 0.000 1.000
#> SRR1617419 3 0.0000 0.9108 0.000 0.000 1.000
#> SRR1617420 1 0.4452 0.7706 0.808 0.000 0.192
#> SRR1617421 1 0.4346 0.7802 0.816 0.000 0.184
#> SRR1617422 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617423 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617424 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617425 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617427 1 0.3482 0.8373 0.872 0.000 0.128
#> SRR1617426 1 0.3482 0.8373 0.872 0.000 0.128
#> SRR1617428 1 0.7919 0.3386 0.556 0.380 0.064
#> SRR1617429 1 0.7919 0.3386 0.556 0.380 0.064
#> SRR1617432 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617433 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617434 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617436 3 0.0000 0.9108 0.000 0.000 1.000
#> SRR1617435 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617437 3 0.0000 0.9108 0.000 0.000 1.000
#> SRR1617438 3 0.0000 0.9108 0.000 0.000 1.000
#> SRR1617439 3 0.0000 0.9108 0.000 0.000 1.000
#> SRR1617440 3 0.6260 0.2507 0.000 0.448 0.552
#> SRR1617441 3 0.6309 0.0892 0.000 0.500 0.500
#> SRR1617443 3 0.0000 0.9108 0.000 0.000 1.000
#> SRR1617442 3 0.0000 0.9108 0.000 0.000 1.000
#> SRR1617444 2 0.0000 0.9781 0.000 1.000 0.000
#> SRR1617445 2 0.0000 0.9781 0.000 1.000 0.000
#> SRR1617446 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617447 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617448 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617449 1 0.0000 0.9305 1.000 0.000 0.000
#> SRR1617451 2 0.0000 0.9781 0.000 1.000 0.000
#> SRR1617450 2 0.0000 0.9781 0.000 1.000 0.000
#> SRR1617452 2 0.0000 0.9781 0.000 1.000 0.000
#> SRR1617454 2 0.0000 0.9781 0.000 1.000 0.000
#> SRR1617453 2 0.0000 0.9781 0.000 1.000 0.000
#> SRR1617456 2 0.0000 0.9781 0.000 1.000 0.000
#> SRR1617457 2 0.0000 0.9781 0.000 1.000 0.000
#> SRR1617455 2 0.0000 0.9781 0.000 1.000 0.000
#> SRR1617458 2 0.0000 0.9781 0.000 1.000 0.000
#> SRR1617459 2 0.0000 0.9781 0.000 1.000 0.000
#> SRR1617460 2 0.3038 0.8786 0.104 0.896 0.000
#> SRR1617461 2 0.3038 0.8786 0.104 0.896 0.000
#> SRR1617463 2 0.1643 0.9439 0.044 0.956 0.000
#> SRR1617462 2 0.1643 0.9439 0.044 0.956 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 4 0.4967 0.535 0.000 0.452 0.000 0.548
#> SRR1617431 4 0.4989 0.501 0.000 0.472 0.000 0.528
#> SRR1617410 1 0.0000 0.748 1.000 0.000 0.000 0.000
#> SRR1617411 1 0.0000 0.748 1.000 0.000 0.000 0.000
#> SRR1617412 3 0.0469 0.940 0.000 0.000 0.988 0.012
#> SRR1617413 3 0.0469 0.940 0.000 0.000 0.988 0.012
#> SRR1617414 1 0.1174 0.733 0.968 0.000 0.012 0.020
#> SRR1617415 1 0.1174 0.733 0.968 0.000 0.012 0.020
#> SRR1617416 1 0.4888 0.752 0.588 0.000 0.000 0.412
#> SRR1617417 1 0.4888 0.752 0.588 0.000 0.000 0.412
#> SRR1617418 3 0.0592 0.938 0.000 0.000 0.984 0.016
#> SRR1617419 3 0.0592 0.938 0.000 0.000 0.984 0.016
#> SRR1617420 1 0.2466 0.712 0.900 0.000 0.096 0.004
#> SRR1617421 1 0.2466 0.712 0.900 0.000 0.096 0.004
#> SRR1617422 1 0.4776 0.762 0.624 0.000 0.000 0.376
#> SRR1617423 1 0.4790 0.761 0.620 0.000 0.000 0.380
#> SRR1617424 1 0.4866 0.756 0.596 0.000 0.000 0.404
#> SRR1617425 1 0.4866 0.756 0.596 0.000 0.000 0.404
#> SRR1617427 1 0.4706 0.766 0.748 0.000 0.028 0.224
#> SRR1617426 1 0.4808 0.766 0.736 0.000 0.028 0.236
#> SRR1617428 4 0.5784 0.683 0.112 0.116 0.024 0.748
#> SRR1617429 4 0.5880 0.679 0.116 0.112 0.028 0.744
#> SRR1617432 1 0.0000 0.748 1.000 0.000 0.000 0.000
#> SRR1617433 1 0.0000 0.748 1.000 0.000 0.000 0.000
#> SRR1617434 1 0.0188 0.747 0.996 0.000 0.004 0.000
#> SRR1617436 3 0.0336 0.940 0.000 0.000 0.992 0.008
#> SRR1617435 1 0.0188 0.747 0.996 0.000 0.004 0.000
#> SRR1617437 3 0.0336 0.940 0.000 0.000 0.992 0.008
#> SRR1617438 3 0.0188 0.941 0.000 0.000 0.996 0.004
#> SRR1617439 3 0.0188 0.941 0.000 0.000 0.996 0.004
#> SRR1617440 3 0.4284 0.704 0.000 0.200 0.780 0.020
#> SRR1617441 3 0.4399 0.684 0.000 0.212 0.768 0.020
#> SRR1617443 3 0.0188 0.941 0.000 0.000 0.996 0.004
#> SRR1617442 3 0.0188 0.941 0.000 0.000 0.996 0.004
#> SRR1617444 2 0.2704 0.815 0.000 0.876 0.000 0.124
#> SRR1617445 2 0.2760 0.808 0.000 0.872 0.000 0.128
#> SRR1617446 1 0.5060 0.753 0.584 0.000 0.004 0.412
#> SRR1617447 1 0.5060 0.753 0.584 0.000 0.004 0.412
#> SRR1617448 1 0.5080 0.748 0.576 0.000 0.004 0.420
#> SRR1617449 1 0.5080 0.748 0.576 0.000 0.004 0.420
#> SRR1617451 2 0.0336 0.937 0.000 0.992 0.000 0.008
#> SRR1617450 2 0.0336 0.937 0.000 0.992 0.000 0.008
#> SRR1617452 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> SRR1617454 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> SRR1617453 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> SRR1617456 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> SRR1617457 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> SRR1617455 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> SRR1617458 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> SRR1617459 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> SRR1617460 2 0.2197 0.879 0.080 0.916 0.000 0.004
#> SRR1617461 2 0.2197 0.879 0.080 0.916 0.000 0.004
#> SRR1617463 2 0.1743 0.904 0.056 0.940 0.000 0.004
#> SRR1617462 2 0.1743 0.904 0.056 0.940 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 4 0.1768 0.950 0.004 0.072 0.000 0.924 0.000
#> SRR1617431 4 0.1952 0.942 0.004 0.084 0.000 0.912 0.000
#> SRR1617410 5 0.0865 0.969 0.024 0.000 0.000 0.004 0.972
#> SRR1617411 5 0.0865 0.969 0.024 0.000 0.000 0.004 0.972
#> SRR1617412 3 0.1686 0.922 0.028 0.000 0.944 0.020 0.008
#> SRR1617413 3 0.1686 0.922 0.028 0.000 0.944 0.020 0.008
#> SRR1617414 5 0.0912 0.965 0.012 0.000 0.016 0.000 0.972
#> SRR1617415 5 0.0912 0.965 0.012 0.000 0.016 0.000 0.972
#> SRR1617416 1 0.2179 0.891 0.888 0.000 0.000 0.000 0.112
#> SRR1617417 1 0.2179 0.891 0.888 0.000 0.000 0.000 0.112
#> SRR1617418 3 0.1469 0.922 0.036 0.000 0.948 0.016 0.000
#> SRR1617419 3 0.1469 0.922 0.036 0.000 0.948 0.016 0.000
#> SRR1617420 5 0.1410 0.930 0.000 0.000 0.060 0.000 0.940
#> SRR1617421 5 0.1410 0.930 0.000 0.000 0.060 0.000 0.940
#> SRR1617422 1 0.2629 0.880 0.860 0.000 0.000 0.004 0.136
#> SRR1617423 1 0.2753 0.879 0.856 0.000 0.000 0.008 0.136
#> SRR1617424 1 0.2127 0.892 0.892 0.000 0.000 0.000 0.108
#> SRR1617425 1 0.2127 0.892 0.892 0.000 0.000 0.000 0.108
#> SRR1617427 1 0.4560 0.296 0.508 0.000 0.000 0.008 0.484
#> SRR1617426 1 0.4557 0.320 0.516 0.000 0.000 0.008 0.476
#> SRR1617428 4 0.1012 0.951 0.000 0.012 0.000 0.968 0.020
#> SRR1617429 4 0.1012 0.951 0.000 0.012 0.000 0.968 0.020
#> SRR1617432 5 0.0609 0.972 0.020 0.000 0.000 0.000 0.980
#> SRR1617433 5 0.0609 0.972 0.020 0.000 0.000 0.000 0.980
#> SRR1617434 5 0.0609 0.972 0.020 0.000 0.000 0.000 0.980
#> SRR1617436 3 0.0865 0.924 0.000 0.000 0.972 0.024 0.004
#> SRR1617435 5 0.0609 0.972 0.020 0.000 0.000 0.000 0.980
#> SRR1617437 3 0.0955 0.922 0.000 0.000 0.968 0.028 0.004
#> SRR1617438 3 0.0162 0.929 0.000 0.000 0.996 0.004 0.000
#> SRR1617439 3 0.0162 0.929 0.000 0.000 0.996 0.004 0.000
#> SRR1617440 3 0.4681 0.745 0.076 0.148 0.760 0.016 0.000
#> SRR1617441 3 0.4761 0.734 0.076 0.156 0.752 0.016 0.000
#> SRR1617443 3 0.0290 0.928 0.000 0.000 0.992 0.000 0.008
#> SRR1617442 3 0.0290 0.928 0.000 0.000 0.992 0.000 0.008
#> SRR1617444 2 0.4540 0.623 0.300 0.676 0.016 0.008 0.000
#> SRR1617445 2 0.4560 0.617 0.304 0.672 0.016 0.008 0.000
#> SRR1617446 1 0.1892 0.883 0.916 0.000 0.004 0.000 0.080
#> SRR1617447 1 0.1892 0.883 0.916 0.000 0.004 0.000 0.080
#> SRR1617448 1 0.1894 0.875 0.920 0.000 0.008 0.000 0.072
#> SRR1617449 1 0.1768 0.878 0.924 0.000 0.004 0.000 0.072
#> SRR1617451 2 0.1544 0.884 0.000 0.932 0.000 0.068 0.000
#> SRR1617450 2 0.1544 0.884 0.000 0.932 0.000 0.068 0.000
#> SRR1617452 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> SRR1617454 2 0.0162 0.920 0.000 0.996 0.000 0.000 0.004
#> SRR1617453 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> SRR1617456 2 0.0566 0.917 0.004 0.984 0.000 0.012 0.000
#> SRR1617457 2 0.0566 0.917 0.004 0.984 0.000 0.012 0.000
#> SRR1617455 2 0.0162 0.920 0.000 0.996 0.000 0.000 0.004
#> SRR1617458 2 0.0324 0.919 0.004 0.992 0.000 0.004 0.000
#> SRR1617459 2 0.0324 0.919 0.004 0.992 0.000 0.004 0.000
#> SRR1617460 2 0.2173 0.893 0.016 0.920 0.000 0.012 0.052
#> SRR1617461 2 0.2173 0.893 0.016 0.920 0.000 0.012 0.052
#> SRR1617463 2 0.1764 0.904 0.012 0.940 0.000 0.012 0.036
#> SRR1617462 2 0.1764 0.904 0.012 0.940 0.000 0.012 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 4 0.1408 0.956 0.000 0.020 0.000 0.944 0.000 0.036
#> SRR1617431 4 0.1480 0.951 0.000 0.020 0.000 0.940 0.000 0.040
#> SRR1617410 5 0.0291 0.991 0.000 0.004 0.000 0.004 0.992 0.000
#> SRR1617411 5 0.0291 0.991 0.000 0.004 0.000 0.004 0.992 0.000
#> SRR1617412 3 0.2558 0.715 0.004 0.156 0.840 0.000 0.000 0.000
#> SRR1617413 3 0.2558 0.715 0.004 0.156 0.840 0.000 0.000 0.000
#> SRR1617414 5 0.0260 0.992 0.000 0.008 0.000 0.000 0.992 0.000
#> SRR1617415 5 0.0260 0.992 0.000 0.008 0.000 0.000 0.992 0.000
#> SRR1617416 1 0.2121 0.793 0.892 0.096 0.000 0.012 0.000 0.000
#> SRR1617417 1 0.2121 0.793 0.892 0.096 0.000 0.012 0.000 0.000
#> SRR1617418 3 0.2178 0.731 0.000 0.132 0.868 0.000 0.000 0.000
#> SRR1617419 3 0.2178 0.731 0.000 0.132 0.868 0.000 0.000 0.000
#> SRR1617420 5 0.0405 0.988 0.000 0.000 0.008 0.004 0.988 0.000
#> SRR1617421 5 0.0405 0.988 0.000 0.000 0.008 0.004 0.988 0.000
#> SRR1617422 1 0.1959 0.821 0.924 0.032 0.000 0.000 0.024 0.020
#> SRR1617423 1 0.2201 0.817 0.912 0.032 0.000 0.000 0.028 0.028
#> SRR1617424 1 0.0260 0.833 0.992 0.008 0.000 0.000 0.000 0.000
#> SRR1617425 1 0.0260 0.833 0.992 0.008 0.000 0.000 0.000 0.000
#> SRR1617427 1 0.5083 0.614 0.668 0.084 0.028 0.000 0.220 0.000
#> SRR1617426 1 0.5006 0.626 0.680 0.084 0.028 0.000 0.208 0.000
#> SRR1617428 4 0.0436 0.959 0.000 0.000 0.004 0.988 0.004 0.004
#> SRR1617429 4 0.0436 0.959 0.000 0.000 0.004 0.988 0.004 0.004
#> SRR1617432 5 0.0363 0.991 0.000 0.012 0.000 0.000 0.988 0.000
#> SRR1617433 5 0.0363 0.991 0.000 0.012 0.000 0.000 0.988 0.000
#> SRR1617434 5 0.0000 0.993 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617436 3 0.2790 0.782 0.000 0.132 0.844 0.024 0.000 0.000
#> SRR1617435 5 0.0000 0.993 0.000 0.000 0.000 0.000 1.000 0.000
#> SRR1617437 3 0.2790 0.782 0.000 0.132 0.844 0.024 0.000 0.000
#> SRR1617438 3 0.2664 0.749 0.000 0.184 0.816 0.000 0.000 0.000
#> SRR1617439 3 0.2664 0.749 0.000 0.184 0.816 0.000 0.000 0.000
#> SRR1617440 2 0.4301 0.972 0.000 0.696 0.240 0.000 0.000 0.064
#> SRR1617441 2 0.4455 0.972 0.000 0.684 0.240 0.000 0.000 0.076
#> SRR1617443 3 0.2431 0.785 0.000 0.132 0.860 0.000 0.008 0.000
#> SRR1617442 3 0.2431 0.785 0.000 0.132 0.860 0.000 0.008 0.000
#> SRR1617444 1 0.5944 0.213 0.476 0.380 0.024 0.000 0.000 0.120
#> SRR1617445 1 0.5964 0.224 0.480 0.372 0.024 0.000 0.000 0.124
#> SRR1617446 1 0.0146 0.834 0.996 0.004 0.000 0.000 0.000 0.000
#> SRR1617447 1 0.0146 0.834 0.996 0.004 0.000 0.000 0.000 0.000
#> SRR1617448 1 0.0713 0.833 0.972 0.028 0.000 0.000 0.000 0.000
#> SRR1617449 1 0.0713 0.833 0.972 0.028 0.000 0.000 0.000 0.000
#> SRR1617451 6 0.5563 0.507 0.000 0.260 0.000 0.192 0.000 0.548
#> SRR1617450 6 0.5488 0.523 0.000 0.272 0.000 0.172 0.000 0.556
#> SRR1617452 6 0.1556 0.759 0.000 0.080 0.000 0.000 0.000 0.920
#> SRR1617454 6 0.1327 0.758 0.000 0.064 0.000 0.000 0.000 0.936
#> SRR1617453 6 0.1556 0.759 0.000 0.080 0.000 0.000 0.000 0.920
#> SRR1617456 6 0.3531 0.659 0.000 0.328 0.000 0.000 0.000 0.672
#> SRR1617457 6 0.3531 0.659 0.000 0.328 0.000 0.000 0.000 0.672
#> SRR1617455 6 0.1141 0.758 0.000 0.052 0.000 0.000 0.000 0.948
#> SRR1617458 6 0.3428 0.675 0.000 0.304 0.000 0.000 0.000 0.696
#> SRR1617459 6 0.3390 0.680 0.000 0.296 0.000 0.000 0.000 0.704
#> SRR1617460 6 0.2618 0.710 0.036 0.060 0.000 0.004 0.012 0.888
#> SRR1617461 6 0.2618 0.710 0.036 0.060 0.000 0.004 0.012 0.888
#> SRR1617463 6 0.2063 0.726 0.020 0.060 0.000 0.000 0.008 0.912
#> SRR1617462 6 0.2063 0.726 0.020 0.060 0.000 0.000 0.008 0.912
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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 0.602 0.703 0.891 0.4446 0.525 0.525
#> 3 3 0.517 0.487 0.712 0.3416 0.883 0.776
#> 4 4 0.638 0.650 0.857 0.1230 0.888 0.731
#> 5 5 0.614 0.762 0.784 0.1119 0.857 0.588
#> 6 6 0.673 0.648 0.784 0.0791 0.950 0.788
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
#> SRR1617430 1 0.000 0.8931 1.000 0.000
#> SRR1617431 1 0.000 0.8931 1.000 0.000
#> SRR1617410 1 0.996 -0.0607 0.536 0.464
#> SRR1617411 1 0.996 -0.0607 0.536 0.464
#> SRR1617412 1 0.000 0.8931 1.000 0.000
#> SRR1617413 1 0.000 0.8931 1.000 0.000
#> SRR1617414 1 0.000 0.8931 1.000 0.000
#> SRR1617415 1 0.000 0.8931 1.000 0.000
#> SRR1617416 2 0.000 0.7953 0.000 1.000
#> SRR1617417 2 0.000 0.7953 0.000 1.000
#> SRR1617418 2 0.388 0.7732 0.076 0.924
#> SRR1617419 2 0.388 0.7732 0.076 0.924
#> SRR1617420 1 0.260 0.8581 0.956 0.044
#> SRR1617421 1 0.260 0.8581 0.956 0.044
#> SRR1617422 1 0.000 0.8931 1.000 0.000
#> SRR1617423 1 0.000 0.8931 1.000 0.000
#> SRR1617424 1 0.000 0.8931 1.000 0.000
#> SRR1617425 1 0.000 0.8931 1.000 0.000
#> SRR1617427 1 0.000 0.8931 1.000 0.000
#> SRR1617426 1 0.000 0.8931 1.000 0.000
#> SRR1617428 1 0.000 0.8931 1.000 0.000
#> SRR1617429 1 0.000 0.8931 1.000 0.000
#> SRR1617432 1 0.000 0.8931 1.000 0.000
#> SRR1617433 1 0.000 0.8931 1.000 0.000
#> SRR1617434 2 0.000 0.7953 0.000 1.000
#> SRR1617436 1 0.000 0.8931 1.000 0.000
#> SRR1617435 2 0.000 0.7953 0.000 1.000
#> SRR1617437 1 0.000 0.8931 1.000 0.000
#> SRR1617438 1 0.980 0.1589 0.584 0.416
#> SRR1617439 1 0.980 0.1589 0.584 0.416
#> SRR1617440 2 0.999 0.1794 0.484 0.516
#> SRR1617441 2 0.999 0.1794 0.484 0.516
#> SRR1617443 2 0.000 0.7953 0.000 1.000
#> SRR1617442 2 0.000 0.7953 0.000 1.000
#> SRR1617444 2 0.998 0.2017 0.476 0.524
#> SRR1617445 2 0.998 0.2017 0.476 0.524
#> SRR1617446 1 0.000 0.8931 1.000 0.000
#> SRR1617447 1 0.000 0.8931 1.000 0.000
#> SRR1617448 1 0.000 0.8931 1.000 0.000
#> SRR1617449 1 0.000 0.8931 1.000 0.000
#> SRR1617451 1 0.000 0.8931 1.000 0.000
#> SRR1617450 1 0.000 0.8931 1.000 0.000
#> SRR1617452 2 0.000 0.7953 0.000 1.000
#> SRR1617454 1 0.506 0.7900 0.888 0.112
#> SRR1617453 2 0.000 0.7953 0.000 1.000
#> SRR1617456 2 0.204 0.7953 0.032 0.968
#> SRR1617457 2 0.204 0.7953 0.032 0.968
#> SRR1617455 1 0.506 0.7900 0.888 0.112
#> SRR1617458 2 0.204 0.7953 0.032 0.968
#> SRR1617459 2 0.204 0.7953 0.032 0.968
#> SRR1617460 2 1.000 0.1531 0.492 0.508
#> SRR1617461 2 1.000 0.1531 0.492 0.508
#> SRR1617463 1 0.904 0.4329 0.680 0.320
#> SRR1617462 1 0.904 0.4329 0.680 0.320
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.630 1.000 0.480 0.520 0.000
#> SRR1617431 2 0.630 1.000 0.480 0.520 0.000
#> SRR1617410 1 0.630 0.224 0.528 0.000 0.472
#> SRR1617411 1 0.630 0.224 0.528 0.000 0.472
#> SRR1617412 1 0.000 0.680 1.000 0.000 0.000
#> SRR1617413 1 0.000 0.680 1.000 0.000 0.000
#> SRR1617414 1 0.000 0.680 1.000 0.000 0.000
#> SRR1617415 1 0.000 0.680 1.000 0.000 0.000
#> SRR1617416 3 0.630 0.601 0.000 0.480 0.520
#> SRR1617417 3 0.630 0.601 0.000 0.480 0.520
#> SRR1617418 3 0.226 0.459 0.068 0.000 0.932
#> SRR1617419 3 0.226 0.459 0.068 0.000 0.932
#> SRR1617420 1 0.164 0.665 0.956 0.000 0.044
#> SRR1617421 1 0.164 0.665 0.956 0.000 0.044
#> SRR1617422 1 0.000 0.680 1.000 0.000 0.000
#> SRR1617423 1 0.000 0.680 1.000 0.000 0.000
#> SRR1617424 1 0.000 0.680 1.000 0.000 0.000
#> SRR1617425 1 0.000 0.680 1.000 0.000 0.000
#> SRR1617427 1 0.622 -0.784 0.568 0.432 0.000
#> SRR1617426 1 0.622 -0.784 0.568 0.432 0.000
#> SRR1617428 2 0.630 1.000 0.480 0.520 0.000
#> SRR1617429 2 0.630 1.000 0.480 0.520 0.000
#> SRR1617432 1 0.000 0.680 1.000 0.000 0.000
#> SRR1617433 1 0.000 0.680 1.000 0.000 0.000
#> SRR1617434 3 0.618 0.611 0.000 0.416 0.584
#> SRR1617436 1 0.334 0.507 0.880 0.120 0.000
#> SRR1617435 3 0.618 0.611 0.000 0.416 0.584
#> SRR1617437 1 0.334 0.507 0.880 0.120 0.000
#> SRR1617438 1 0.620 0.342 0.576 0.000 0.424
#> SRR1617439 1 0.620 0.342 0.576 0.000 0.424
#> SRR1617440 3 0.630 -0.177 0.476 0.000 0.524
#> SRR1617441 3 0.630 -0.177 0.476 0.000 0.524
#> SRR1617443 3 0.618 0.611 0.000 0.416 0.584
#> SRR1617442 3 0.618 0.611 0.000 0.416 0.584
#> SRR1617444 3 0.629 -0.162 0.468 0.000 0.532
#> SRR1617445 3 0.629 -0.162 0.468 0.000 0.532
#> SRR1617446 1 0.288 0.560 0.904 0.096 0.000
#> SRR1617447 1 0.288 0.560 0.904 0.096 0.000
#> SRR1617448 1 0.288 0.560 0.904 0.096 0.000
#> SRR1617449 1 0.288 0.560 0.904 0.096 0.000
#> SRR1617451 2 0.630 1.000 0.480 0.520 0.000
#> SRR1617450 2 0.630 1.000 0.480 0.520 0.000
#> SRR1617452 3 0.630 0.601 0.000 0.480 0.520
#> SRR1617454 1 0.447 0.614 0.852 0.028 0.120
#> SRR1617453 3 0.630 0.601 0.000 0.480 0.520
#> SRR1617456 3 0.730 0.611 0.032 0.412 0.556
#> SRR1617457 3 0.730 0.611 0.032 0.412 0.556
#> SRR1617455 1 0.447 0.614 0.852 0.028 0.120
#> SRR1617458 3 0.730 0.611 0.032 0.412 0.556
#> SRR1617459 3 0.730 0.611 0.032 0.412 0.556
#> SRR1617460 3 0.630 -0.194 0.484 0.000 0.516
#> SRR1617461 3 0.630 -0.194 0.484 0.000 0.516
#> SRR1617463 1 0.576 0.491 0.672 0.000 0.328
#> SRR1617462 1 0.576 0.491 0.672 0.000 0.328
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.000 0.8984 0.000 1.000 0.000 0.000
#> SRR1617431 2 0.000 0.8984 0.000 1.000 0.000 0.000
#> SRR1617410 1 0.500 -0.5520 0.516 0.000 0.484 0.000
#> SRR1617411 1 0.500 -0.5520 0.516 0.000 0.484 0.000
#> SRR1617412 1 0.000 0.7563 1.000 0.000 0.000 0.000
#> SRR1617413 1 0.000 0.7563 1.000 0.000 0.000 0.000
#> SRR1617414 1 0.000 0.7563 1.000 0.000 0.000 0.000
#> SRR1617415 1 0.000 0.7563 1.000 0.000 0.000 0.000
#> SRR1617416 4 0.000 0.9200 0.000 0.000 0.000 1.000
#> SRR1617417 4 0.000 0.9200 0.000 0.000 0.000 1.000
#> SRR1617418 3 0.000 0.3895 0.000 0.000 1.000 0.000
#> SRR1617419 3 0.000 0.3895 0.000 0.000 1.000 0.000
#> SRR1617420 1 0.130 0.7267 0.956 0.000 0.044 0.000
#> SRR1617421 1 0.130 0.7267 0.956 0.000 0.044 0.000
#> SRR1617422 1 0.000 0.7563 1.000 0.000 0.000 0.000
#> SRR1617423 1 0.000 0.7563 1.000 0.000 0.000 0.000
#> SRR1617424 1 0.000 0.7563 1.000 0.000 0.000 0.000
#> SRR1617425 1 0.000 0.7563 1.000 0.000 0.000 0.000
#> SRR1617427 2 0.407 0.7137 0.252 0.748 0.000 0.000
#> SRR1617426 2 0.407 0.7137 0.252 0.748 0.000 0.000
#> SRR1617428 2 0.102 0.8966 0.032 0.968 0.000 0.000
#> SRR1617429 2 0.102 0.8966 0.032 0.968 0.000 0.000
#> SRR1617432 1 0.000 0.7563 1.000 0.000 0.000 0.000
#> SRR1617433 1 0.000 0.7563 1.000 0.000 0.000 0.000
#> SRR1617434 4 0.234 0.9046 0.000 0.000 0.100 0.900
#> SRR1617436 1 0.281 0.6731 0.868 0.132 0.000 0.000
#> SRR1617435 4 0.234 0.9046 0.000 0.000 0.100 0.900
#> SRR1617437 1 0.281 0.6731 0.868 0.132 0.000 0.000
#> SRR1617438 1 0.496 -0.3925 0.552 0.000 0.448 0.000
#> SRR1617439 1 0.496 -0.3925 0.552 0.000 0.448 0.000
#> SRR1617440 3 0.495 0.6909 0.440 0.000 0.560 0.000
#> SRR1617441 3 0.495 0.6909 0.440 0.000 0.560 0.000
#> SRR1617443 4 0.234 0.9046 0.000 0.000 0.100 0.900
#> SRR1617442 4 0.234 0.9046 0.000 0.000 0.100 0.900
#> SRR1617444 3 0.524 0.6937 0.432 0.000 0.560 0.008
#> SRR1617445 3 0.524 0.6937 0.432 0.000 0.560 0.008
#> SRR1617446 1 0.228 0.7063 0.904 0.096 0.000 0.000
#> SRR1617447 1 0.228 0.7063 0.904 0.096 0.000 0.000
#> SRR1617448 1 0.228 0.7063 0.904 0.096 0.000 0.000
#> SRR1617449 1 0.228 0.7063 0.904 0.096 0.000 0.000
#> SRR1617451 2 0.000 0.8984 0.000 1.000 0.000 0.000
#> SRR1617450 2 0.000 0.8984 0.000 1.000 0.000 0.000
#> SRR1617452 4 0.000 0.9200 0.000 0.000 0.000 1.000
#> SRR1617454 1 0.410 0.5807 0.808 0.028 0.164 0.000
#> SRR1617453 4 0.000 0.9200 0.000 0.000 0.000 1.000
#> SRR1617456 4 0.234 0.9056 0.000 0.000 0.100 0.900
#> SRR1617457 4 0.234 0.9056 0.000 0.000 0.100 0.900
#> SRR1617455 1 0.410 0.5807 0.808 0.028 0.164 0.000
#> SRR1617458 4 0.234 0.9056 0.000 0.000 0.100 0.900
#> SRR1617459 4 0.234 0.9056 0.000 0.000 0.100 0.900
#> SRR1617460 3 0.498 0.6593 0.460 0.000 0.540 0.000
#> SRR1617461 3 0.498 0.6593 0.460 0.000 0.540 0.000
#> SRR1617463 1 0.462 0.0301 0.660 0.000 0.340 0.000
#> SRR1617462 1 0.462 0.0301 0.660 0.000 0.340 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 4 0.0000 0.837 0.000 0.000 0.000 1.000 0.000
#> SRR1617431 4 0.0000 0.837 0.000 0.000 0.000 1.000 0.000
#> SRR1617410 2 0.2424 0.715 0.132 0.868 0.000 0.000 0.000
#> SRR1617411 2 0.2424 0.715 0.132 0.868 0.000 0.000 0.000
#> SRR1617412 1 0.3861 0.738 0.804 0.128 0.068 0.000 0.000
#> SRR1617413 1 0.3861 0.738 0.804 0.128 0.068 0.000 0.000
#> SRR1617414 1 0.5426 0.750 0.640 0.252 0.108 0.000 0.000
#> SRR1617415 1 0.5426 0.750 0.640 0.252 0.108 0.000 0.000
#> SRR1617416 5 0.0162 0.907 0.000 0.000 0.004 0.000 0.996
#> SRR1617417 5 0.0162 0.907 0.000 0.000 0.004 0.000 0.996
#> SRR1617418 3 0.3242 1.000 0.000 0.216 0.784 0.000 0.000
#> SRR1617419 3 0.3242 1.000 0.000 0.216 0.784 0.000 0.000
#> SRR1617420 1 0.4687 0.722 0.672 0.288 0.040 0.000 0.000
#> SRR1617421 1 0.4687 0.722 0.672 0.288 0.040 0.000 0.000
#> SRR1617422 1 0.4883 0.703 0.652 0.300 0.048 0.000 0.000
#> SRR1617423 1 0.4883 0.703 0.652 0.300 0.048 0.000 0.000
#> SRR1617424 1 0.4883 0.703 0.652 0.300 0.048 0.000 0.000
#> SRR1617425 1 0.4883 0.703 0.652 0.300 0.048 0.000 0.000
#> SRR1617427 4 0.4101 0.569 0.372 0.000 0.000 0.628 0.000
#> SRR1617426 4 0.4101 0.569 0.372 0.000 0.000 0.628 0.000
#> SRR1617428 4 0.1341 0.831 0.056 0.000 0.000 0.944 0.000
#> SRR1617429 4 0.1341 0.831 0.056 0.000 0.000 0.944 0.000
#> SRR1617432 1 0.5426 0.750 0.640 0.252 0.108 0.000 0.000
#> SRR1617433 1 0.5426 0.750 0.640 0.252 0.108 0.000 0.000
#> SRR1617434 5 0.2020 0.877 0.000 0.100 0.000 0.000 0.900
#> SRR1617436 1 0.1952 0.646 0.912 0.000 0.084 0.004 0.000
#> SRR1617435 5 0.2020 0.877 0.000 0.100 0.000 0.000 0.900
#> SRR1617437 1 0.1952 0.646 0.912 0.000 0.084 0.004 0.000
#> SRR1617438 2 0.2770 0.767 0.076 0.880 0.044 0.000 0.000
#> SRR1617439 2 0.2770 0.767 0.076 0.880 0.044 0.000 0.000
#> SRR1617440 2 0.0324 0.777 0.004 0.992 0.004 0.000 0.000
#> SRR1617441 2 0.0324 0.777 0.004 0.992 0.004 0.000 0.000
#> SRR1617443 5 0.2020 0.877 0.000 0.100 0.000 0.000 0.900
#> SRR1617442 5 0.2020 0.877 0.000 0.100 0.000 0.000 0.900
#> SRR1617444 2 0.0613 0.772 0.004 0.984 0.004 0.000 0.008
#> SRR1617445 2 0.0613 0.772 0.004 0.984 0.004 0.000 0.008
#> SRR1617446 1 0.3033 0.748 0.864 0.084 0.052 0.000 0.000
#> SRR1617447 1 0.3033 0.748 0.864 0.084 0.052 0.000 0.000
#> SRR1617448 1 0.3033 0.748 0.864 0.084 0.052 0.000 0.000
#> SRR1617449 1 0.3033 0.748 0.864 0.084 0.052 0.000 0.000
#> SRR1617451 4 0.0000 0.837 0.000 0.000 0.000 1.000 0.000
#> SRR1617450 4 0.0000 0.837 0.000 0.000 0.000 1.000 0.000
#> SRR1617452 5 0.0162 0.907 0.000 0.000 0.004 0.000 0.996
#> SRR1617454 2 0.6451 0.129 0.372 0.504 0.096 0.028 0.000
#> SRR1617453 5 0.0162 0.907 0.000 0.000 0.004 0.000 0.996
#> SRR1617456 5 0.2450 0.887 0.000 0.052 0.048 0.000 0.900
#> SRR1617457 5 0.2450 0.887 0.000 0.052 0.048 0.000 0.900
#> SRR1617455 2 0.6451 0.129 0.372 0.504 0.096 0.028 0.000
#> SRR1617458 5 0.2450 0.887 0.000 0.052 0.048 0.000 0.900
#> SRR1617459 5 0.2450 0.887 0.000 0.052 0.048 0.000 0.900
#> SRR1617460 2 0.0671 0.784 0.016 0.980 0.004 0.000 0.000
#> SRR1617461 2 0.0671 0.784 0.016 0.980 0.004 0.000 0.000
#> SRR1617463 2 0.4021 0.696 0.168 0.780 0.052 0.000 0.000
#> SRR1617462 2 0.4021 0.696 0.168 0.780 0.052 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.0000 0.854 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617431 2 0.0000 0.854 0.000 1.000 0.000 0.000 0.000 0.000
#> SRR1617410 3 0.3309 0.460 0.000 0.000 0.720 0.000 0.280 0.000
#> SRR1617411 3 0.3309 0.460 0.000 0.000 0.720 0.000 0.280 0.000
#> SRR1617412 1 0.3364 0.392 0.780 0.000 0.024 0.000 0.196 0.000
#> SRR1617413 1 0.3364 0.392 0.780 0.000 0.024 0.000 0.196 0.000
#> SRR1617414 5 0.1807 0.752 0.020 0.000 0.060 0.000 0.920 0.000
#> SRR1617415 5 0.1807 0.752 0.020 0.000 0.060 0.000 0.920 0.000
#> SRR1617416 6 0.2178 0.863 0.000 0.000 0.000 0.132 0.000 0.868
#> SRR1617417 6 0.2178 0.863 0.000 0.000 0.000 0.132 0.000 0.868
#> SRR1617418 4 0.2219 1.000 0.000 0.000 0.136 0.864 0.000 0.000
#> SRR1617419 4 0.2219 1.000 0.000 0.000 0.136 0.864 0.000 0.000
#> SRR1617420 5 0.5271 0.283 0.380 0.000 0.104 0.000 0.516 0.000
#> SRR1617421 5 0.5271 0.283 0.380 0.000 0.104 0.000 0.516 0.000
#> SRR1617422 1 0.6075 0.118 0.396 0.000 0.280 0.000 0.324 0.000
#> SRR1617423 1 0.6075 0.118 0.396 0.000 0.280 0.000 0.324 0.000
#> SRR1617424 1 0.6075 0.118 0.396 0.000 0.280 0.000 0.324 0.000
#> SRR1617425 1 0.6075 0.118 0.396 0.000 0.280 0.000 0.324 0.000
#> SRR1617427 2 0.3684 0.612 0.372 0.628 0.000 0.000 0.000 0.000
#> SRR1617426 2 0.3684 0.612 0.372 0.628 0.000 0.000 0.000 0.000
#> SRR1617428 2 0.1204 0.850 0.056 0.944 0.000 0.000 0.000 0.000
#> SRR1617429 2 0.1204 0.850 0.056 0.944 0.000 0.000 0.000 0.000
#> SRR1617432 5 0.1807 0.752 0.020 0.000 0.060 0.000 0.920 0.000
#> SRR1617433 5 0.1807 0.752 0.020 0.000 0.060 0.000 0.920 0.000
#> SRR1617434 6 0.1814 0.866 0.000 0.000 0.100 0.000 0.000 0.900
#> SRR1617436 1 0.0713 0.447 0.972 0.000 0.000 0.000 0.028 0.000
#> SRR1617435 6 0.1814 0.866 0.000 0.000 0.100 0.000 0.000 0.900
#> SRR1617437 1 0.0713 0.447 0.972 0.000 0.000 0.000 0.028 0.000
#> SRR1617438 3 0.2617 0.745 0.100 0.000 0.872 0.016 0.012 0.000
#> SRR1617439 3 0.2617 0.745 0.100 0.000 0.872 0.016 0.012 0.000
#> SRR1617440 3 0.0458 0.760 0.000 0.000 0.984 0.016 0.000 0.000
#> SRR1617441 3 0.0458 0.760 0.000 0.000 0.984 0.016 0.000 0.000
#> SRR1617443 6 0.1814 0.866 0.000 0.000 0.100 0.000 0.000 0.900
#> SRR1617442 6 0.1814 0.866 0.000 0.000 0.100 0.000 0.000 0.900
#> SRR1617444 3 0.0717 0.759 0.000 0.000 0.976 0.016 0.000 0.008
#> SRR1617445 3 0.0717 0.759 0.000 0.000 0.976 0.016 0.000 0.008
#> SRR1617446 1 0.3852 0.409 0.664 0.000 0.012 0.000 0.324 0.000
#> SRR1617447 1 0.3852 0.409 0.664 0.000 0.012 0.000 0.324 0.000
#> SRR1617448 1 0.3852 0.409 0.664 0.000 0.012 0.000 0.324 0.000
#> SRR1617449 1 0.3852 0.409 0.664 0.000 0.012 0.000 0.324 0.000
#> SRR1617451 2 0.0777 0.851 0.000 0.972 0.000 0.004 0.024 0.000
#> SRR1617450 2 0.0777 0.851 0.000 0.972 0.000 0.004 0.024 0.000
#> SRR1617452 6 0.2178 0.863 0.000 0.000 0.000 0.132 0.000 0.868
#> SRR1617454 3 0.5420 0.335 0.104 0.000 0.500 0.004 0.392 0.000
#> SRR1617453 6 0.2178 0.863 0.000 0.000 0.000 0.132 0.000 0.868
#> SRR1617456 6 0.2263 0.846 0.000 0.000 0.048 0.000 0.056 0.896
#> SRR1617457 6 0.2263 0.846 0.000 0.000 0.048 0.000 0.056 0.896
#> SRR1617455 3 0.5420 0.335 0.104 0.000 0.500 0.004 0.392 0.000
#> SRR1617458 6 0.2263 0.846 0.000 0.000 0.048 0.000 0.056 0.896
#> SRR1617459 6 0.2263 0.846 0.000 0.000 0.048 0.000 0.056 0.896
#> SRR1617460 3 0.0146 0.764 0.000 0.000 0.996 0.000 0.004 0.000
#> SRR1617461 3 0.0146 0.764 0.000 0.000 0.996 0.000 0.004 0.000
#> SRR1617463 3 0.3563 0.686 0.072 0.000 0.796 0.000 0.132 0.000
#> SRR1617462 3 0.3563 0.686 0.072 0.000 0.796 0.000 0.132 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["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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 0.925 0.925 0.973 0.4930 0.508 0.508
#> 3 3 0.477 0.700 0.796 0.3011 0.804 0.625
#> 4 4 0.496 0.602 0.699 0.1027 0.855 0.643
#> 5 5 0.496 0.411 0.625 0.0723 0.983 0.949
#> 6 6 0.514 0.317 0.576 0.0453 0.936 0.794
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
#> SRR1617430 1 0.000 0.969 1.000 0.000
#> SRR1617431 1 0.000 0.969 1.000 0.000
#> SRR1617410 2 0.850 0.615 0.276 0.724
#> SRR1617411 2 0.850 0.615 0.276 0.724
#> SRR1617412 1 0.000 0.969 1.000 0.000
#> SRR1617413 1 0.000 0.969 1.000 0.000
#> SRR1617414 1 0.000 0.969 1.000 0.000
#> SRR1617415 1 0.000 0.969 1.000 0.000
#> SRR1617416 2 0.000 0.972 0.000 1.000
#> SRR1617417 2 0.000 0.972 0.000 1.000
#> SRR1617418 2 0.000 0.972 0.000 1.000
#> SRR1617419 2 0.000 0.972 0.000 1.000
#> SRR1617420 1 0.000 0.969 1.000 0.000
#> SRR1617421 1 0.000 0.969 1.000 0.000
#> SRR1617422 1 0.000 0.969 1.000 0.000
#> SRR1617423 1 0.000 0.969 1.000 0.000
#> SRR1617424 1 0.000 0.969 1.000 0.000
#> SRR1617425 1 0.000 0.969 1.000 0.000
#> SRR1617427 1 0.000 0.969 1.000 0.000
#> SRR1617426 1 0.000 0.969 1.000 0.000
#> SRR1617428 1 0.000 0.969 1.000 0.000
#> SRR1617429 1 0.000 0.969 1.000 0.000
#> SRR1617432 1 0.000 0.969 1.000 0.000
#> SRR1617433 1 0.000 0.969 1.000 0.000
#> SRR1617434 2 0.000 0.972 0.000 1.000
#> SRR1617436 1 0.000 0.969 1.000 0.000
#> SRR1617435 2 0.000 0.972 0.000 1.000
#> SRR1617437 1 0.000 0.969 1.000 0.000
#> SRR1617438 1 0.995 0.120 0.540 0.460
#> SRR1617439 1 0.995 0.120 0.540 0.460
#> SRR1617440 2 0.000 0.972 0.000 1.000
#> SRR1617441 2 0.000 0.972 0.000 1.000
#> SRR1617443 2 0.000 0.972 0.000 1.000
#> SRR1617442 2 0.000 0.972 0.000 1.000
#> SRR1617444 2 0.000 0.972 0.000 1.000
#> SRR1617445 2 0.000 0.972 0.000 1.000
#> SRR1617446 1 0.000 0.969 1.000 0.000
#> SRR1617447 1 0.000 0.969 1.000 0.000
#> SRR1617448 1 0.000 0.969 1.000 0.000
#> SRR1617449 1 0.000 0.969 1.000 0.000
#> SRR1617451 1 0.000 0.969 1.000 0.000
#> SRR1617450 1 0.000 0.969 1.000 0.000
#> SRR1617452 2 0.000 0.972 0.000 1.000
#> SRR1617454 1 0.000 0.969 1.000 0.000
#> SRR1617453 2 0.000 0.972 0.000 1.000
#> SRR1617456 2 0.000 0.972 0.000 1.000
#> SRR1617457 2 0.000 0.972 0.000 1.000
#> SRR1617455 1 0.000 0.969 1.000 0.000
#> SRR1617458 2 0.000 0.972 0.000 1.000
#> SRR1617459 2 0.000 0.972 0.000 1.000
#> SRR1617460 2 0.000 0.972 0.000 1.000
#> SRR1617461 2 0.000 0.972 0.000 1.000
#> SRR1617463 1 0.000 0.969 1.000 0.000
#> SRR1617462 1 0.000 0.969 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.0000 0.679 0.000 1.000 0.000
#> SRR1617431 2 0.0000 0.679 0.000 1.000 0.000
#> SRR1617410 1 0.3669 0.765 0.896 0.040 0.064
#> SRR1617411 1 0.3669 0.765 0.896 0.040 0.064
#> SRR1617412 1 0.4842 0.815 0.776 0.224 0.000
#> SRR1617413 1 0.4842 0.815 0.776 0.224 0.000
#> SRR1617414 2 0.4555 0.688 0.200 0.800 0.000
#> SRR1617415 2 0.4555 0.688 0.200 0.800 0.000
#> SRR1617416 3 0.1860 0.851 0.052 0.000 0.948
#> SRR1617417 3 0.1860 0.851 0.052 0.000 0.948
#> SRR1617418 3 0.6244 0.576 0.440 0.000 0.560
#> SRR1617419 3 0.6244 0.576 0.440 0.000 0.560
#> SRR1617420 1 0.4504 0.848 0.804 0.196 0.000
#> SRR1617421 1 0.4504 0.848 0.804 0.196 0.000
#> SRR1617422 2 0.4346 0.686 0.184 0.816 0.000
#> SRR1617423 2 0.4346 0.686 0.184 0.816 0.000
#> SRR1617424 1 0.4605 0.844 0.796 0.204 0.000
#> SRR1617425 1 0.4605 0.844 0.796 0.204 0.000
#> SRR1617427 2 0.2711 0.696 0.088 0.912 0.000
#> SRR1617426 2 0.2711 0.696 0.088 0.912 0.000
#> SRR1617428 2 0.0237 0.677 0.004 0.996 0.000
#> SRR1617429 2 0.0237 0.677 0.004 0.996 0.000
#> SRR1617432 1 0.4504 0.833 0.804 0.196 0.000
#> SRR1617433 1 0.4504 0.833 0.804 0.196 0.000
#> SRR1617434 3 0.2878 0.875 0.096 0.000 0.904
#> SRR1617436 2 0.6252 0.321 0.444 0.556 0.000
#> SRR1617435 3 0.2878 0.875 0.096 0.000 0.904
#> SRR1617437 2 0.6252 0.321 0.444 0.556 0.000
#> SRR1617438 1 0.3481 0.768 0.904 0.044 0.052
#> SRR1617439 1 0.3481 0.768 0.904 0.044 0.052
#> SRR1617440 3 0.5785 0.775 0.332 0.000 0.668
#> SRR1617441 3 0.5785 0.775 0.332 0.000 0.668
#> SRR1617443 3 0.2448 0.873 0.076 0.000 0.924
#> SRR1617442 3 0.2448 0.873 0.076 0.000 0.924
#> SRR1617444 3 0.4796 0.852 0.220 0.000 0.780
#> SRR1617445 3 0.4796 0.852 0.220 0.000 0.780
#> SRR1617446 2 0.6308 0.182 0.492 0.508 0.000
#> SRR1617447 2 0.6308 0.182 0.492 0.508 0.000
#> SRR1617448 2 0.6308 0.182 0.492 0.508 0.000
#> SRR1617449 2 0.6308 0.182 0.492 0.508 0.000
#> SRR1617451 2 0.0000 0.679 0.000 1.000 0.000
#> SRR1617450 2 0.0000 0.679 0.000 1.000 0.000
#> SRR1617452 3 0.1411 0.851 0.036 0.000 0.964
#> SRR1617454 2 0.5988 0.556 0.304 0.688 0.008
#> SRR1617453 3 0.1411 0.851 0.036 0.000 0.964
#> SRR1617456 3 0.2878 0.870 0.096 0.000 0.904
#> SRR1617457 3 0.2878 0.870 0.096 0.000 0.904
#> SRR1617455 2 0.5988 0.556 0.304 0.688 0.008
#> SRR1617458 3 0.2878 0.870 0.096 0.000 0.904
#> SRR1617459 3 0.2878 0.870 0.096 0.000 0.904
#> SRR1617460 3 0.4931 0.844 0.232 0.000 0.768
#> SRR1617461 3 0.4931 0.844 0.232 0.000 0.768
#> SRR1617463 2 0.6483 0.458 0.392 0.600 0.008
#> SRR1617462 2 0.6483 0.458 0.392 0.600 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.260 0.7236 0.068 0.908 0.000 0.024
#> SRR1617431 2 0.260 0.7236 0.068 0.908 0.000 0.024
#> SRR1617410 1 0.536 0.5587 0.744 0.000 0.108 0.148
#> SRR1617411 1 0.536 0.5587 0.744 0.000 0.108 0.148
#> SRR1617412 1 0.328 0.6568 0.872 0.032 0.000 0.096
#> SRR1617413 1 0.328 0.6568 0.872 0.032 0.000 0.096
#> SRR1617414 2 0.684 0.5830 0.280 0.580 0.000 0.140
#> SRR1617415 2 0.684 0.5830 0.280 0.580 0.000 0.140
#> SRR1617416 3 0.438 0.7186 0.000 0.036 0.792 0.172
#> SRR1617417 3 0.438 0.7186 0.000 0.036 0.792 0.172
#> SRR1617418 3 0.814 0.4133 0.280 0.016 0.452 0.252
#> SRR1617419 3 0.814 0.4133 0.280 0.016 0.452 0.252
#> SRR1617420 1 0.152 0.6669 0.956 0.020 0.000 0.024
#> SRR1617421 1 0.152 0.6669 0.956 0.020 0.000 0.024
#> SRR1617422 2 0.643 0.5755 0.324 0.588 0.000 0.088
#> SRR1617423 2 0.643 0.5755 0.324 0.588 0.000 0.088
#> SRR1617424 1 0.115 0.6669 0.968 0.024 0.000 0.008
#> SRR1617425 1 0.115 0.6669 0.968 0.024 0.000 0.008
#> SRR1617427 2 0.541 0.6799 0.192 0.728 0.000 0.080
#> SRR1617426 2 0.541 0.6799 0.192 0.728 0.000 0.080
#> SRR1617428 2 0.205 0.7294 0.072 0.924 0.000 0.004
#> SRR1617429 2 0.205 0.7294 0.072 0.924 0.000 0.004
#> SRR1617432 1 0.461 0.6117 0.796 0.040 0.008 0.156
#> SRR1617433 1 0.461 0.6117 0.796 0.040 0.008 0.156
#> SRR1617434 3 0.191 0.7739 0.020 0.000 0.940 0.040
#> SRR1617436 1 0.703 0.2615 0.552 0.296 0.000 0.152
#> SRR1617435 3 0.191 0.7739 0.020 0.000 0.940 0.040
#> SRR1617437 1 0.703 0.2615 0.552 0.296 0.000 0.152
#> SRR1617438 1 0.566 0.5457 0.728 0.004 0.104 0.164
#> SRR1617439 1 0.566 0.5457 0.728 0.004 0.104 0.164
#> SRR1617440 3 0.680 0.6981 0.160 0.004 0.620 0.216
#> SRR1617441 3 0.680 0.6981 0.160 0.004 0.620 0.216
#> SRR1617443 3 0.187 0.7722 0.016 0.012 0.948 0.024
#> SRR1617442 3 0.187 0.7722 0.016 0.012 0.948 0.024
#> SRR1617444 3 0.500 0.7668 0.084 0.000 0.768 0.148
#> SRR1617445 3 0.500 0.7668 0.084 0.000 0.768 0.148
#> SRR1617446 1 0.591 0.4616 0.668 0.252 0.000 0.080
#> SRR1617447 1 0.591 0.4616 0.668 0.252 0.000 0.080
#> SRR1617448 1 0.591 0.4616 0.668 0.252 0.000 0.080
#> SRR1617449 1 0.591 0.4616 0.668 0.252 0.000 0.080
#> SRR1617451 2 0.262 0.7244 0.064 0.908 0.000 0.028
#> SRR1617450 2 0.262 0.7244 0.064 0.908 0.000 0.028
#> SRR1617452 3 0.467 0.7167 0.000 0.036 0.764 0.200
#> SRR1617454 2 0.728 0.2705 0.408 0.444 0.000 0.148
#> SRR1617453 3 0.467 0.7167 0.000 0.036 0.764 0.200
#> SRR1617456 3 0.498 0.7590 0.012 0.000 0.664 0.324
#> SRR1617457 3 0.498 0.7590 0.012 0.000 0.664 0.324
#> SRR1617455 2 0.728 0.2705 0.408 0.444 0.000 0.148
#> SRR1617458 3 0.498 0.7590 0.012 0.000 0.664 0.324
#> SRR1617459 3 0.498 0.7590 0.012 0.000 0.664 0.324
#> SRR1617460 3 0.634 0.7336 0.116 0.004 0.660 0.220
#> SRR1617461 3 0.634 0.7336 0.116 0.004 0.660 0.220
#> SRR1617463 1 0.721 -0.0362 0.516 0.324 0.000 0.160
#> SRR1617462 1 0.721 -0.0362 0.516 0.324 0.000 0.160
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 4 0.243 0.4296 0.020 NA 0.000 0.912 0.028
#> SRR1617431 4 0.243 0.4296 0.020 NA 0.000 0.912 0.028
#> SRR1617410 1 0.620 0.4702 0.664 NA 0.128 0.000 0.076
#> SRR1617411 1 0.620 0.4702 0.664 NA 0.128 0.000 0.076
#> SRR1617412 1 0.433 0.5473 0.792 NA 0.000 0.016 0.116
#> SRR1617413 1 0.433 0.5473 0.792 NA 0.000 0.016 0.116
#> SRR1617414 5 0.657 1.0000 0.204 NA 0.000 0.388 0.408
#> SRR1617415 5 0.657 1.0000 0.204 NA 0.000 0.388 0.408
#> SRR1617416 3 0.467 0.6066 0.000 NA 0.752 0.008 0.156
#> SRR1617417 3 0.467 0.6066 0.000 NA 0.752 0.008 0.156
#> SRR1617418 3 0.828 0.2253 0.264 NA 0.352 0.004 0.104
#> SRR1617419 3 0.828 0.2253 0.264 NA 0.352 0.004 0.104
#> SRR1617420 1 0.290 0.5683 0.884 NA 0.000 0.012 0.064
#> SRR1617421 1 0.290 0.5683 0.884 NA 0.000 0.012 0.064
#> SRR1617422 4 0.662 -0.5778 0.256 NA 0.000 0.492 0.248
#> SRR1617423 4 0.662 -0.5778 0.256 NA 0.000 0.492 0.248
#> SRR1617424 1 0.152 0.5677 0.952 NA 0.000 0.012 0.020
#> SRR1617425 1 0.152 0.5677 0.952 NA 0.000 0.012 0.020
#> SRR1617427 4 0.645 -0.1541 0.152 NA 0.000 0.596 0.220
#> SRR1617426 4 0.645 -0.1541 0.152 NA 0.000 0.596 0.220
#> SRR1617428 4 0.288 0.3950 0.024 NA 0.000 0.880 0.084
#> SRR1617429 4 0.288 0.3950 0.024 NA 0.000 0.880 0.084
#> SRR1617432 1 0.547 0.2967 0.596 NA 0.016 0.008 0.352
#> SRR1617433 1 0.547 0.2967 0.596 NA 0.016 0.008 0.352
#> SRR1617434 3 0.241 0.6839 0.012 NA 0.908 0.000 0.020
#> SRR1617436 1 0.763 0.0225 0.456 NA 0.000 0.200 0.268
#> SRR1617435 3 0.241 0.6839 0.012 NA 0.908 0.000 0.020
#> SRR1617437 1 0.763 0.0225 0.456 NA 0.000 0.200 0.268
#> SRR1617438 1 0.589 0.4937 0.684 NA 0.080 0.000 0.072
#> SRR1617439 1 0.589 0.4937 0.684 NA 0.080 0.000 0.072
#> SRR1617440 3 0.668 0.6108 0.112 NA 0.484 0.000 0.032
#> SRR1617441 3 0.668 0.6108 0.112 NA 0.484 0.000 0.032
#> SRR1617443 3 0.213 0.6782 0.016 NA 0.928 0.004 0.016
#> SRR1617442 3 0.213 0.6782 0.016 NA 0.928 0.004 0.016
#> SRR1617444 3 0.534 0.6777 0.060 NA 0.648 0.000 0.012
#> SRR1617445 3 0.534 0.6777 0.060 NA 0.648 0.000 0.012
#> SRR1617446 1 0.632 0.3665 0.628 NA 0.000 0.160 0.172
#> SRR1617447 1 0.632 0.3665 0.628 NA 0.000 0.160 0.172
#> SRR1617448 1 0.632 0.3665 0.628 NA 0.000 0.160 0.172
#> SRR1617449 1 0.632 0.3665 0.628 NA 0.000 0.160 0.172
#> SRR1617451 4 0.225 0.4365 0.016 NA 0.000 0.920 0.028
#> SRR1617450 4 0.225 0.4365 0.016 NA 0.000 0.920 0.028
#> SRR1617452 3 0.526 0.5989 0.000 NA 0.708 0.012 0.156
#> SRR1617454 4 0.834 -0.0588 0.296 NA 0.004 0.372 0.156
#> SRR1617453 3 0.526 0.5989 0.000 NA 0.708 0.012 0.156
#> SRR1617456 3 0.456 0.6675 0.000 NA 0.500 0.000 0.008
#> SRR1617457 3 0.456 0.6675 0.000 NA 0.500 0.000 0.008
#> SRR1617455 4 0.834 -0.0588 0.296 NA 0.004 0.372 0.156
#> SRR1617458 3 0.456 0.6675 0.000 NA 0.500 0.000 0.008
#> SRR1617459 3 0.456 0.6675 0.000 NA 0.500 0.000 0.008
#> SRR1617460 3 0.620 0.6325 0.092 NA 0.504 0.000 0.016
#> SRR1617461 3 0.620 0.6325 0.092 NA 0.504 0.000 0.016
#> SRR1617463 1 0.829 -0.1099 0.416 NA 0.004 0.232 0.176
#> SRR1617462 1 0.829 -0.1099 0.416 NA 0.004 0.232 0.176
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.243 0.4113 0.012 0.900 0.036 0.048 0.004 0.000
#> SRR1617431 2 0.243 0.4113 0.012 0.900 0.036 0.048 0.004 0.000
#> SRR1617410 1 0.644 -0.0200 0.556 0.000 0.160 0.012 0.048 0.224
#> SRR1617411 1 0.644 -0.0200 0.556 0.000 0.160 0.012 0.048 0.224
#> SRR1617412 1 0.513 0.4365 0.716 0.008 0.140 0.036 0.096 0.004
#> SRR1617413 1 0.513 0.4365 0.716 0.008 0.140 0.036 0.096 0.004
#> SRR1617414 5 0.585 1.0000 0.172 0.356 0.004 0.000 0.468 0.000
#> SRR1617415 5 0.585 1.0000 0.172 0.356 0.004 0.000 0.468 0.000
#> SRR1617416 4 0.417 0.8556 0.000 0.000 0.008 0.692 0.028 0.272
#> SRR1617417 4 0.417 0.8556 0.000 0.000 0.008 0.692 0.028 0.272
#> SRR1617418 3 0.667 1.0000 0.172 0.000 0.508 0.084 0.000 0.236
#> SRR1617419 3 0.667 1.0000 0.172 0.000 0.508 0.084 0.000 0.236
#> SRR1617420 1 0.288 0.4644 0.880 0.008 0.064 0.004 0.028 0.016
#> SRR1617421 1 0.288 0.4644 0.880 0.008 0.064 0.004 0.028 0.016
#> SRR1617422 2 0.642 -0.4695 0.232 0.476 0.016 0.008 0.268 0.000
#> SRR1617423 2 0.642 -0.4695 0.232 0.476 0.016 0.008 0.268 0.000
#> SRR1617424 1 0.258 0.4873 0.896 0.008 0.020 0.000 0.044 0.032
#> SRR1617425 1 0.258 0.4873 0.896 0.008 0.020 0.000 0.044 0.032
#> SRR1617427 2 0.611 0.0301 0.120 0.592 0.044 0.012 0.232 0.000
#> SRR1617426 2 0.611 0.0301 0.120 0.592 0.044 0.012 0.232 0.000
#> SRR1617428 2 0.281 0.3749 0.016 0.872 0.016 0.008 0.088 0.000
#> SRR1617429 2 0.281 0.3749 0.016 0.872 0.016 0.008 0.088 0.000
#> SRR1617432 1 0.550 0.1387 0.528 0.000 0.016 0.008 0.384 0.064
#> SRR1617433 1 0.550 0.1387 0.528 0.000 0.016 0.008 0.384 0.064
#> SRR1617434 6 0.561 0.0712 0.016 0.000 0.052 0.332 0.028 0.572
#> SRR1617436 1 0.791 0.0775 0.392 0.192 0.168 0.028 0.220 0.000
#> SRR1617435 6 0.561 0.0712 0.016 0.000 0.052 0.332 0.028 0.572
#> SRR1617437 1 0.791 0.0775 0.392 0.192 0.168 0.028 0.220 0.000
#> SRR1617438 1 0.643 0.0540 0.556 0.000 0.180 0.012 0.044 0.208
#> SRR1617439 1 0.643 0.0540 0.556 0.000 0.180 0.012 0.044 0.208
#> SRR1617440 6 0.409 0.2903 0.100 0.000 0.112 0.008 0.004 0.776
#> SRR1617441 6 0.409 0.2903 0.100 0.000 0.112 0.008 0.004 0.776
#> SRR1617443 6 0.591 -0.0976 0.016 0.000 0.080 0.376 0.020 0.508
#> SRR1617442 6 0.591 -0.0976 0.016 0.000 0.080 0.376 0.020 0.508
#> SRR1617444 6 0.332 0.4774 0.044 0.000 0.028 0.076 0.004 0.848
#> SRR1617445 6 0.332 0.4774 0.044 0.000 0.028 0.076 0.004 0.848
#> SRR1617446 1 0.679 0.3072 0.544 0.148 0.060 0.028 0.220 0.000
#> SRR1617447 1 0.679 0.3072 0.544 0.148 0.060 0.028 0.220 0.000
#> SRR1617448 1 0.679 0.3072 0.544 0.148 0.060 0.028 0.220 0.000
#> SRR1617449 1 0.679 0.3072 0.544 0.148 0.060 0.028 0.220 0.000
#> SRR1617451 2 0.258 0.4153 0.012 0.896 0.020 0.020 0.052 0.000
#> SRR1617450 2 0.258 0.4153 0.012 0.896 0.020 0.020 0.052 0.000
#> SRR1617452 4 0.340 0.8596 0.000 0.004 0.000 0.776 0.016 0.204
#> SRR1617454 2 0.882 -0.0451 0.264 0.308 0.048 0.044 0.220 0.116
#> SRR1617453 4 0.340 0.8596 0.000 0.004 0.000 0.776 0.016 0.204
#> SRR1617456 6 0.617 0.3744 0.004 0.004 0.096 0.192 0.092 0.612
#> SRR1617457 6 0.617 0.3744 0.004 0.004 0.096 0.192 0.092 0.612
#> SRR1617455 2 0.882 -0.0451 0.264 0.308 0.048 0.044 0.220 0.116
#> SRR1617458 6 0.626 0.3737 0.004 0.004 0.096 0.192 0.100 0.604
#> SRR1617459 6 0.626 0.3737 0.004 0.004 0.096 0.192 0.100 0.604
#> SRR1617460 6 0.313 0.4977 0.036 0.004 0.028 0.012 0.048 0.872
#> SRR1617461 6 0.313 0.4977 0.036 0.004 0.028 0.012 0.048 0.872
#> SRR1617463 1 0.875 -0.1167 0.352 0.200 0.060 0.036 0.236 0.116
#> SRR1617462 1 0.875 -0.1167 0.352 0.200 0.060 0.036 0.236 0.116
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", "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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 1.000 1.000 0.5036 0.497 0.497
#> 3 3 0.759 0.870 0.934 0.3223 0.760 0.547
#> 4 4 0.753 0.677 0.791 0.0944 0.927 0.781
#> 5 5 0.677 0.638 0.761 0.0596 0.925 0.740
#> 6 6 0.719 0.643 0.744 0.0390 0.939 0.758
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
#> SRR1617430 1 0 1 1 0
#> SRR1617431 1 0 1 1 0
#> SRR1617410 2 0 1 0 1
#> SRR1617411 2 0 1 0 1
#> SRR1617412 1 0 1 1 0
#> SRR1617413 1 0 1 1 0
#> SRR1617414 1 0 1 1 0
#> SRR1617415 1 0 1 1 0
#> SRR1617416 2 0 1 0 1
#> SRR1617417 2 0 1 0 1
#> SRR1617418 2 0 1 0 1
#> SRR1617419 2 0 1 0 1
#> SRR1617420 1 0 1 1 0
#> SRR1617421 1 0 1 1 0
#> SRR1617422 1 0 1 1 0
#> SRR1617423 1 0 1 1 0
#> SRR1617424 1 0 1 1 0
#> SRR1617425 1 0 1 1 0
#> SRR1617427 1 0 1 1 0
#> SRR1617426 1 0 1 1 0
#> SRR1617428 1 0 1 1 0
#> SRR1617429 1 0 1 1 0
#> SRR1617432 1 0 1 1 0
#> SRR1617433 1 0 1 1 0
#> SRR1617434 2 0 1 0 1
#> SRR1617436 1 0 1 1 0
#> SRR1617435 2 0 1 0 1
#> SRR1617437 1 0 1 1 0
#> SRR1617438 2 0 1 0 1
#> SRR1617439 2 0 1 0 1
#> SRR1617440 2 0 1 0 1
#> SRR1617441 2 0 1 0 1
#> SRR1617443 2 0 1 0 1
#> SRR1617442 2 0 1 0 1
#> SRR1617444 2 0 1 0 1
#> SRR1617445 2 0 1 0 1
#> SRR1617446 1 0 1 1 0
#> SRR1617447 1 0 1 1 0
#> SRR1617448 1 0 1 1 0
#> SRR1617449 1 0 1 1 0
#> SRR1617451 1 0 1 1 0
#> SRR1617450 1 0 1 1 0
#> SRR1617452 2 0 1 0 1
#> SRR1617454 1 0 1 1 0
#> SRR1617453 2 0 1 0 1
#> SRR1617456 2 0 1 0 1
#> SRR1617457 2 0 1 0 1
#> SRR1617455 1 0 1 1 0
#> SRR1617458 2 0 1 0 1
#> SRR1617459 2 0 1 0 1
#> SRR1617460 2 0 1 0 1
#> SRR1617461 2 0 1 0 1
#> SRR1617463 1 0 1 1 0
#> SRR1617462 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.0000 0.968 0.000 1.000 0.000
#> SRR1617431 2 0.0000 0.968 0.000 1.000 0.000
#> SRR1617410 1 0.6225 0.270 0.568 0.000 0.432
#> SRR1617411 1 0.6215 0.280 0.572 0.000 0.428
#> SRR1617412 1 0.0237 0.808 0.996 0.004 0.000
#> SRR1617413 1 0.0237 0.808 0.996 0.004 0.000
#> SRR1617414 2 0.0000 0.968 0.000 1.000 0.000
#> SRR1617415 2 0.0000 0.968 0.000 1.000 0.000
#> SRR1617416 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617417 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617418 3 0.4291 0.756 0.180 0.000 0.820
#> SRR1617419 3 0.4291 0.756 0.180 0.000 0.820
#> SRR1617420 1 0.0000 0.806 1.000 0.000 0.000
#> SRR1617421 1 0.0000 0.806 1.000 0.000 0.000
#> SRR1617422 2 0.0000 0.968 0.000 1.000 0.000
#> SRR1617423 2 0.0000 0.968 0.000 1.000 0.000
#> SRR1617424 1 0.0592 0.808 0.988 0.012 0.000
#> SRR1617425 1 0.0592 0.808 0.988 0.012 0.000
#> SRR1617427 2 0.0424 0.962 0.008 0.992 0.000
#> SRR1617426 2 0.0424 0.962 0.008 0.992 0.000
#> SRR1617428 2 0.0000 0.968 0.000 1.000 0.000
#> SRR1617429 2 0.0000 0.968 0.000 1.000 0.000
#> SRR1617432 2 0.5058 0.691 0.244 0.756 0.000
#> SRR1617433 2 0.5058 0.691 0.244 0.756 0.000
#> SRR1617434 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617436 1 0.5835 0.582 0.660 0.340 0.000
#> SRR1617435 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617437 1 0.5835 0.582 0.660 0.340 0.000
#> SRR1617438 1 0.4452 0.699 0.808 0.000 0.192
#> SRR1617439 1 0.4452 0.699 0.808 0.000 0.192
#> SRR1617440 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617441 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617443 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617442 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617444 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617445 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617446 1 0.4291 0.761 0.820 0.180 0.000
#> SRR1617447 1 0.4291 0.761 0.820 0.180 0.000
#> SRR1617448 1 0.4291 0.761 0.820 0.180 0.000
#> SRR1617449 1 0.4291 0.761 0.820 0.180 0.000
#> SRR1617451 2 0.0000 0.968 0.000 1.000 0.000
#> SRR1617450 2 0.0000 0.968 0.000 1.000 0.000
#> SRR1617452 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617454 2 0.0000 0.968 0.000 1.000 0.000
#> SRR1617453 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617456 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617457 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617455 2 0.0000 0.968 0.000 1.000 0.000
#> SRR1617458 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617459 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617460 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617461 3 0.0000 0.978 0.000 0.000 1.000
#> SRR1617463 2 0.0000 0.968 0.000 1.000 0.000
#> SRR1617462 2 0.0000 0.968 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.0469 0.9211 0.012 0.988 0.000 0.000
#> SRR1617431 2 0.0469 0.9211 0.012 0.988 0.000 0.000
#> SRR1617410 1 0.7090 0.0626 0.496 0.000 0.372 0.132
#> SRR1617411 1 0.7090 0.0626 0.496 0.000 0.372 0.132
#> SRR1617412 3 0.4485 0.4713 0.248 0.012 0.740 0.000
#> SRR1617413 3 0.4485 0.4713 0.248 0.012 0.740 0.000
#> SRR1617414 2 0.3528 0.7951 0.192 0.808 0.000 0.000
#> SRR1617415 2 0.3528 0.7951 0.192 0.808 0.000 0.000
#> SRR1617416 4 0.0779 0.9325 0.016 0.000 0.004 0.980
#> SRR1617417 4 0.0779 0.9325 0.016 0.000 0.004 0.980
#> SRR1617418 4 0.5744 0.3408 0.028 0.000 0.436 0.536
#> SRR1617419 4 0.5744 0.3408 0.028 0.000 0.436 0.536
#> SRR1617420 3 0.5000 0.3100 0.496 0.000 0.504 0.000
#> SRR1617421 3 0.5000 0.3100 0.496 0.000 0.504 0.000
#> SRR1617422 2 0.0592 0.9210 0.016 0.984 0.000 0.000
#> SRR1617423 2 0.0592 0.9210 0.016 0.984 0.000 0.000
#> SRR1617424 3 0.5700 0.2372 0.412 0.028 0.560 0.000
#> SRR1617425 3 0.5700 0.2372 0.412 0.028 0.560 0.000
#> SRR1617427 2 0.4798 0.7282 0.180 0.768 0.052 0.000
#> SRR1617426 2 0.4798 0.7282 0.180 0.768 0.052 0.000
#> SRR1617428 2 0.0592 0.9210 0.016 0.984 0.000 0.000
#> SRR1617429 2 0.0592 0.9210 0.016 0.984 0.000 0.000
#> SRR1617432 1 0.3711 0.3038 0.836 0.140 0.024 0.000
#> SRR1617433 1 0.3711 0.3038 0.836 0.140 0.024 0.000
#> SRR1617434 4 0.0895 0.9311 0.020 0.000 0.004 0.976
#> SRR1617436 3 0.7574 0.1667 0.248 0.268 0.484 0.000
#> SRR1617435 4 0.0895 0.9311 0.020 0.000 0.004 0.976
#> SRR1617437 3 0.7574 0.1667 0.248 0.268 0.484 0.000
#> SRR1617438 3 0.1452 0.4135 0.008 0.000 0.956 0.036
#> SRR1617439 3 0.1452 0.4135 0.008 0.000 0.956 0.036
#> SRR1617440 4 0.1174 0.9284 0.012 0.000 0.020 0.968
#> SRR1617441 4 0.1174 0.9284 0.012 0.000 0.020 0.968
#> SRR1617443 4 0.0779 0.9325 0.016 0.000 0.004 0.980
#> SRR1617442 4 0.0779 0.9325 0.016 0.000 0.004 0.980
#> SRR1617444 4 0.0000 0.9362 0.000 0.000 0.000 1.000
#> SRR1617445 4 0.0000 0.9362 0.000 0.000 0.000 1.000
#> SRR1617446 1 0.6444 0.2757 0.612 0.104 0.284 0.000
#> SRR1617447 1 0.6444 0.2757 0.612 0.104 0.284 0.000
#> SRR1617448 1 0.6444 0.2757 0.612 0.104 0.284 0.000
#> SRR1617449 1 0.6444 0.2757 0.612 0.104 0.284 0.000
#> SRR1617451 2 0.0000 0.9191 0.000 1.000 0.000 0.000
#> SRR1617450 2 0.0000 0.9191 0.000 1.000 0.000 0.000
#> SRR1617452 4 0.0000 0.9362 0.000 0.000 0.000 1.000
#> SRR1617454 2 0.1406 0.9036 0.024 0.960 0.016 0.000
#> SRR1617453 4 0.0000 0.9362 0.000 0.000 0.000 1.000
#> SRR1617456 4 0.0592 0.9343 0.016 0.000 0.000 0.984
#> SRR1617457 4 0.0592 0.9343 0.016 0.000 0.000 0.984
#> SRR1617455 2 0.1406 0.9036 0.024 0.960 0.016 0.000
#> SRR1617458 4 0.0592 0.9343 0.016 0.000 0.000 0.984
#> SRR1617459 4 0.0592 0.9343 0.016 0.000 0.000 0.984
#> SRR1617460 4 0.0592 0.9343 0.016 0.000 0.000 0.984
#> SRR1617461 4 0.0592 0.9343 0.016 0.000 0.000 0.984
#> SRR1617463 2 0.1406 0.9036 0.024 0.960 0.016 0.000
#> SRR1617462 2 0.1406 0.9036 0.024 0.960 0.016 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 4 0.0162 0.796 0.004 0.000 0.000 0.996 0.000
#> SRR1617431 4 0.0162 0.796 0.004 0.000 0.000 0.996 0.000
#> SRR1617410 5 0.8022 0.300 0.192 0.112 0.304 0.000 0.392
#> SRR1617411 5 0.8022 0.300 0.192 0.112 0.304 0.000 0.392
#> SRR1617412 1 0.4909 0.354 0.560 0.000 0.412 0.000 0.028
#> SRR1617413 1 0.4909 0.354 0.560 0.000 0.412 0.000 0.028
#> SRR1617414 4 0.5533 0.354 0.060 0.000 0.004 0.540 0.396
#> SRR1617415 4 0.5533 0.354 0.060 0.000 0.004 0.540 0.396
#> SRR1617416 2 0.1211 0.890 0.000 0.960 0.024 0.000 0.016
#> SRR1617417 2 0.1211 0.890 0.000 0.960 0.024 0.000 0.016
#> SRR1617418 3 0.6562 0.165 0.028 0.368 0.496 0.000 0.108
#> SRR1617419 3 0.6562 0.165 0.028 0.368 0.496 0.000 0.108
#> SRR1617420 3 0.6685 0.128 0.280 0.000 0.436 0.000 0.284
#> SRR1617421 3 0.6685 0.128 0.280 0.000 0.436 0.000 0.284
#> SRR1617422 4 0.2238 0.777 0.020 0.000 0.004 0.912 0.064
#> SRR1617423 4 0.2238 0.777 0.020 0.000 0.004 0.912 0.064
#> SRR1617424 1 0.4969 0.501 0.752 0.000 0.116 0.028 0.104
#> SRR1617425 1 0.4969 0.501 0.752 0.000 0.116 0.028 0.104
#> SRR1617427 4 0.5576 0.463 0.268 0.000 0.004 0.628 0.100
#> SRR1617426 4 0.5576 0.463 0.268 0.000 0.004 0.628 0.100
#> SRR1617428 4 0.1018 0.794 0.016 0.000 0.000 0.968 0.016
#> SRR1617429 4 0.1018 0.794 0.016 0.000 0.000 0.968 0.016
#> SRR1617432 5 0.5563 0.465 0.244 0.004 0.008 0.088 0.656
#> SRR1617433 5 0.5563 0.465 0.244 0.004 0.008 0.088 0.656
#> SRR1617434 2 0.1403 0.887 0.000 0.952 0.024 0.000 0.024
#> SRR1617436 1 0.7370 0.403 0.404 0.000 0.316 0.248 0.032
#> SRR1617435 2 0.1403 0.887 0.000 0.952 0.024 0.000 0.024
#> SRR1617437 1 0.7370 0.403 0.404 0.000 0.316 0.248 0.032
#> SRR1617438 3 0.2464 0.372 0.096 0.016 0.888 0.000 0.000
#> SRR1617439 3 0.2464 0.372 0.096 0.016 0.888 0.000 0.000
#> SRR1617440 2 0.3772 0.796 0.000 0.792 0.172 0.000 0.036
#> SRR1617441 2 0.3772 0.796 0.000 0.792 0.172 0.000 0.036
#> SRR1617443 2 0.1469 0.887 0.000 0.948 0.036 0.000 0.016
#> SRR1617442 2 0.1469 0.887 0.000 0.948 0.036 0.000 0.016
#> SRR1617444 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> SRR1617445 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> SRR1617446 1 0.2573 0.625 0.880 0.000 0.000 0.104 0.016
#> SRR1617447 1 0.2573 0.625 0.880 0.000 0.000 0.104 0.016
#> SRR1617448 1 0.2573 0.625 0.880 0.000 0.000 0.104 0.016
#> SRR1617449 1 0.2573 0.625 0.880 0.000 0.000 0.104 0.016
#> SRR1617451 4 0.0880 0.791 0.000 0.000 0.000 0.968 0.032
#> SRR1617450 4 0.0880 0.791 0.000 0.000 0.000 0.968 0.032
#> SRR1617452 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> SRR1617454 4 0.3942 0.718 0.016 0.000 0.032 0.804 0.148
#> SRR1617453 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> SRR1617456 2 0.3180 0.869 0.000 0.856 0.076 0.000 0.068
#> SRR1617457 2 0.3180 0.869 0.000 0.856 0.076 0.000 0.068
#> SRR1617455 4 0.3942 0.718 0.016 0.000 0.032 0.804 0.148
#> SRR1617458 2 0.3180 0.869 0.000 0.856 0.076 0.000 0.068
#> SRR1617459 2 0.3180 0.869 0.000 0.856 0.076 0.000 0.068
#> SRR1617460 2 0.3242 0.865 0.000 0.852 0.076 0.000 0.072
#> SRR1617461 2 0.3242 0.865 0.000 0.852 0.076 0.000 0.072
#> SRR1617463 4 0.4062 0.715 0.016 0.000 0.036 0.796 0.152
#> SRR1617462 4 0.4062 0.715 0.016 0.000 0.036 0.796 0.152
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.0547 0.737 0.020 0.980 0.000 0.000 0.000 0.000
#> SRR1617431 2 0.0547 0.737 0.020 0.980 0.000 0.000 0.000 0.000
#> SRR1617410 4 0.7903 0.649 0.084 0.000 0.112 0.456 0.200 0.148
#> SRR1617411 4 0.7903 0.649 0.084 0.000 0.112 0.456 0.200 0.148
#> SRR1617412 3 0.4697 0.433 0.396 0.004 0.568 0.020 0.012 0.000
#> SRR1617413 3 0.4697 0.433 0.396 0.004 0.568 0.020 0.012 0.000
#> SRR1617414 5 0.4076 0.573 0.012 0.396 0.000 0.000 0.592 0.000
#> SRR1617415 5 0.4076 0.573 0.012 0.396 0.000 0.000 0.592 0.000
#> SRR1617416 6 0.1141 0.788 0.000 0.000 0.000 0.052 0.000 0.948
#> SRR1617417 6 0.1141 0.788 0.000 0.000 0.000 0.052 0.000 0.948
#> SRR1617418 4 0.6399 0.663 0.012 0.000 0.272 0.436 0.004 0.276
#> SRR1617419 4 0.6399 0.663 0.012 0.000 0.272 0.436 0.004 0.276
#> SRR1617420 3 0.6066 0.509 0.196 0.000 0.580 0.048 0.176 0.000
#> SRR1617421 3 0.6066 0.509 0.196 0.000 0.580 0.048 0.176 0.000
#> SRR1617422 2 0.2208 0.703 0.032 0.908 0.004 0.004 0.052 0.000
#> SRR1617423 2 0.2208 0.703 0.032 0.908 0.004 0.004 0.052 0.000
#> SRR1617424 1 0.5760 0.513 0.632 0.012 0.108 0.212 0.036 0.000
#> SRR1617425 1 0.5760 0.513 0.632 0.012 0.108 0.212 0.036 0.000
#> SRR1617427 2 0.4995 0.363 0.252 0.652 0.008 0.004 0.084 0.000
#> SRR1617426 2 0.4995 0.363 0.252 0.652 0.008 0.004 0.084 0.000
#> SRR1617428 2 0.1049 0.733 0.032 0.960 0.000 0.000 0.008 0.000
#> SRR1617429 2 0.1049 0.733 0.032 0.960 0.000 0.000 0.008 0.000
#> SRR1617432 5 0.2933 0.605 0.096 0.040 0.008 0.000 0.856 0.000
#> SRR1617433 5 0.2933 0.605 0.096 0.040 0.008 0.000 0.856 0.000
#> SRR1617434 6 0.1349 0.783 0.000 0.000 0.000 0.056 0.004 0.940
#> SRR1617436 3 0.6062 0.310 0.320 0.232 0.444 0.000 0.004 0.000
#> SRR1617435 6 0.1349 0.783 0.000 0.000 0.000 0.056 0.004 0.940
#> SRR1617437 3 0.6062 0.310 0.320 0.232 0.444 0.000 0.004 0.000
#> SRR1617438 3 0.2723 0.362 0.008 0.000 0.872 0.096 0.008 0.016
#> SRR1617439 3 0.2723 0.362 0.008 0.000 0.872 0.096 0.008 0.016
#> SRR1617440 6 0.5061 0.606 0.000 0.000 0.132 0.204 0.008 0.656
#> SRR1617441 6 0.5061 0.606 0.000 0.000 0.132 0.204 0.008 0.656
#> SRR1617443 6 0.1049 0.796 0.000 0.000 0.008 0.032 0.000 0.960
#> SRR1617442 6 0.1049 0.796 0.000 0.000 0.008 0.032 0.000 0.960
#> SRR1617444 6 0.0000 0.808 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617445 6 0.0000 0.808 0.000 0.000 0.000 0.000 0.000 1.000
#> SRR1617446 1 0.2068 0.774 0.904 0.080 0.008 0.000 0.008 0.000
#> SRR1617447 1 0.2068 0.774 0.904 0.080 0.008 0.000 0.008 0.000
#> SRR1617448 1 0.2068 0.774 0.904 0.080 0.008 0.000 0.008 0.000
#> SRR1617449 1 0.2068 0.774 0.904 0.080 0.008 0.000 0.008 0.000
#> SRR1617451 2 0.1138 0.731 0.000 0.960 0.004 0.012 0.024 0.000
#> SRR1617450 2 0.1138 0.731 0.000 0.960 0.004 0.012 0.024 0.000
#> SRR1617452 6 0.0146 0.809 0.000 0.000 0.000 0.004 0.000 0.996
#> SRR1617454 2 0.5633 0.568 0.028 0.652 0.016 0.188 0.116 0.000
#> SRR1617453 6 0.0146 0.809 0.000 0.000 0.000 0.004 0.000 0.996
#> SRR1617456 6 0.3476 0.748 0.000 0.000 0.004 0.260 0.004 0.732
#> SRR1617457 6 0.3476 0.748 0.000 0.000 0.004 0.260 0.004 0.732
#> SRR1617455 2 0.5633 0.568 0.028 0.652 0.016 0.188 0.116 0.000
#> SRR1617458 6 0.3476 0.748 0.000 0.000 0.004 0.260 0.004 0.732
#> SRR1617459 6 0.3476 0.748 0.000 0.000 0.004 0.260 0.004 0.732
#> SRR1617460 6 0.3746 0.731 0.000 0.000 0.004 0.272 0.012 0.712
#> SRR1617461 6 0.3746 0.731 0.000 0.000 0.004 0.272 0.012 0.712
#> SRR1617463 2 0.5776 0.556 0.028 0.632 0.016 0.204 0.120 0.000
#> SRR1617462 2 0.5776 0.556 0.028 0.632 0.016 0.204 0.120 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["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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 0.673 0.879 0.944 0.4820 0.497 0.497
#> 3 3 0.944 0.940 0.973 0.2965 0.709 0.507
#> 4 4 0.890 0.896 0.948 0.0673 0.961 0.900
#> 5 5 0.662 0.794 0.840 0.0723 0.972 0.920
#> 6 6 0.733 0.667 0.851 0.0997 0.888 0.654
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
#> SRR1617430 1 0.000 0.990 1.000 0.000
#> SRR1617431 1 0.000 0.990 1.000 0.000
#> SRR1617410 2 0.978 0.443 0.412 0.588
#> SRR1617411 2 0.978 0.443 0.412 0.588
#> SRR1617412 1 0.000 0.990 1.000 0.000
#> SRR1617413 1 0.000 0.990 1.000 0.000
#> SRR1617414 1 0.000 0.990 1.000 0.000
#> SRR1617415 1 0.000 0.990 1.000 0.000
#> SRR1617416 2 0.000 0.869 0.000 1.000
#> SRR1617417 2 0.000 0.869 0.000 1.000
#> SRR1617418 2 0.978 0.443 0.412 0.588
#> SRR1617419 2 0.978 0.443 0.412 0.588
#> SRR1617420 1 0.000 0.990 1.000 0.000
#> SRR1617421 1 0.000 0.990 1.000 0.000
#> SRR1617422 1 0.000 0.990 1.000 0.000
#> SRR1617423 1 0.000 0.990 1.000 0.000
#> SRR1617424 1 0.000 0.990 1.000 0.000
#> SRR1617425 1 0.000 0.990 1.000 0.000
#> SRR1617427 1 0.000 0.990 1.000 0.000
#> SRR1617426 1 0.000 0.990 1.000 0.000
#> SRR1617428 1 0.000 0.990 1.000 0.000
#> SRR1617429 1 0.000 0.990 1.000 0.000
#> SRR1617432 1 0.574 0.813 0.864 0.136
#> SRR1617433 1 0.469 0.867 0.900 0.100
#> SRR1617434 2 0.000 0.869 0.000 1.000
#> SRR1617436 1 0.000 0.990 1.000 0.000
#> SRR1617435 2 0.000 0.869 0.000 1.000
#> SRR1617437 1 0.000 0.990 1.000 0.000
#> SRR1617438 2 0.978 0.443 0.412 0.588
#> SRR1617439 2 0.978 0.443 0.412 0.588
#> SRR1617440 2 0.000 0.869 0.000 1.000
#> SRR1617441 2 0.000 0.869 0.000 1.000
#> SRR1617443 2 0.000 0.869 0.000 1.000
#> SRR1617442 2 0.000 0.869 0.000 1.000
#> SRR1617444 2 0.000 0.869 0.000 1.000
#> SRR1617445 2 0.000 0.869 0.000 1.000
#> SRR1617446 1 0.000 0.990 1.000 0.000
#> SRR1617447 1 0.000 0.990 1.000 0.000
#> SRR1617448 1 0.000 0.990 1.000 0.000
#> SRR1617449 1 0.000 0.990 1.000 0.000
#> SRR1617451 1 0.000 0.990 1.000 0.000
#> SRR1617450 1 0.000 0.990 1.000 0.000
#> SRR1617452 2 0.000 0.869 0.000 1.000
#> SRR1617454 1 0.000 0.990 1.000 0.000
#> SRR1617453 2 0.000 0.869 0.000 1.000
#> SRR1617456 2 0.000 0.869 0.000 1.000
#> SRR1617457 2 0.000 0.869 0.000 1.000
#> SRR1617455 1 0.000 0.990 1.000 0.000
#> SRR1617458 2 0.000 0.869 0.000 1.000
#> SRR1617459 2 0.000 0.869 0.000 1.000
#> SRR1617460 2 0.605 0.762 0.148 0.852
#> SRR1617461 2 0.605 0.762 0.148 0.852
#> SRR1617463 1 0.000 0.990 1.000 0.000
#> SRR1617462 1 0.000 0.990 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1617431 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1617410 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617411 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617412 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617413 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617414 1 0.4796 0.735 0.780 0.220 0.000
#> SRR1617415 1 0.4974 0.713 0.764 0.236 0.000
#> SRR1617416 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617417 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617418 1 0.2261 0.888 0.932 0.000 0.068
#> SRR1617419 1 0.3482 0.827 0.872 0.000 0.128
#> SRR1617420 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617421 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617422 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617423 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617424 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617425 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617427 1 0.6126 0.416 0.600 0.400 0.000
#> SRR1617426 1 0.6126 0.416 0.600 0.400 0.000
#> SRR1617428 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1617429 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1617432 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617433 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617434 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617436 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617435 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617437 1 0.0237 0.942 0.996 0.004 0.000
#> SRR1617438 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617439 1 0.0237 0.941 0.996 0.000 0.004
#> SRR1617440 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617441 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617443 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617442 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617444 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617445 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617446 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617447 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617448 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617449 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617451 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1617450 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1617452 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617454 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1617453 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617456 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617457 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617455 2 0.0000 1.000 0.000 1.000 0.000
#> SRR1617458 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617459 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617460 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617461 3 0.0000 1.000 0.000 0.000 1.000
#> SRR1617463 1 0.0000 0.944 1.000 0.000 0.000
#> SRR1617462 1 0.0000 0.944 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> SRR1617431 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> SRR1617410 1 0.0336 0.936 0.992 0.000 0.008 0.000
#> SRR1617411 1 0.0336 0.936 0.992 0.000 0.008 0.000
#> SRR1617412 1 0.0336 0.938 0.992 0.000 0.000 0.008
#> SRR1617413 1 0.0336 0.938 0.992 0.000 0.000 0.008
#> SRR1617414 1 0.3764 0.739 0.784 0.216 0.000 0.000
#> SRR1617415 1 0.3907 0.718 0.768 0.232 0.000 0.000
#> SRR1617416 4 0.3649 0.833 0.000 0.000 0.204 0.796
#> SRR1617417 4 0.3649 0.833 0.000 0.000 0.204 0.796
#> SRR1617418 1 0.1940 0.881 0.924 0.000 0.076 0.000
#> SRR1617419 1 0.2868 0.818 0.864 0.000 0.136 0.000
#> SRR1617420 1 0.0000 0.938 1.000 0.000 0.000 0.000
#> SRR1617421 1 0.0000 0.938 1.000 0.000 0.000 0.000
#> SRR1617422 1 0.0000 0.938 1.000 0.000 0.000 0.000
#> SRR1617423 1 0.0000 0.938 1.000 0.000 0.000 0.000
#> SRR1617424 1 0.0000 0.938 1.000 0.000 0.000 0.000
#> SRR1617425 1 0.0000 0.938 1.000 0.000 0.000 0.000
#> SRR1617427 1 0.5016 0.426 0.600 0.396 0.000 0.004
#> SRR1617426 1 0.5016 0.426 0.600 0.396 0.000 0.004
#> SRR1617428 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> SRR1617429 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> SRR1617432 1 0.0000 0.938 1.000 0.000 0.000 0.000
#> SRR1617433 1 0.0000 0.938 1.000 0.000 0.000 0.000
#> SRR1617434 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> SRR1617436 1 0.0336 0.938 0.992 0.000 0.000 0.008
#> SRR1617435 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> SRR1617437 1 0.0524 0.937 0.988 0.004 0.000 0.008
#> SRR1617438 1 0.0336 0.936 0.992 0.000 0.008 0.000
#> SRR1617439 1 0.0469 0.934 0.988 0.000 0.012 0.000
#> SRR1617440 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> SRR1617441 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> SRR1617443 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> SRR1617442 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> SRR1617444 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> SRR1617445 3 0.0000 0.926 0.000 0.000 1.000 0.000
#> SRR1617446 1 0.0336 0.938 0.992 0.000 0.000 0.008
#> SRR1617447 1 0.0336 0.938 0.992 0.000 0.000 0.008
#> SRR1617448 1 0.0336 0.938 0.992 0.000 0.000 0.008
#> SRR1617449 1 0.0336 0.938 0.992 0.000 0.000 0.008
#> SRR1617451 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> SRR1617450 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> SRR1617452 4 0.0336 0.839 0.000 0.000 0.008 0.992
#> SRR1617454 2 0.0336 0.991 0.008 0.992 0.000 0.000
#> SRR1617453 4 0.0336 0.839 0.000 0.000 0.008 0.992
#> SRR1617456 3 0.3569 0.806 0.000 0.000 0.804 0.196
#> SRR1617457 3 0.3569 0.806 0.000 0.000 0.804 0.196
#> SRR1617455 2 0.0336 0.991 0.008 0.992 0.000 0.000
#> SRR1617458 3 0.3569 0.806 0.000 0.000 0.804 0.196
#> SRR1617459 3 0.3569 0.806 0.000 0.000 0.804 0.196
#> SRR1617460 3 0.0336 0.920 0.008 0.000 0.992 0.000
#> SRR1617461 3 0.0336 0.920 0.008 0.000 0.992 0.000
#> SRR1617463 1 0.0000 0.938 1.000 0.000 0.000 0.000
#> SRR1617462 1 0.0000 0.938 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 4 0.000 0.892 0.000 0.000 0.000 1.000 0
#> SRR1617431 4 0.000 0.892 0.000 0.000 0.000 1.000 0
#> SRR1617410 1 0.368 0.661 0.720 0.000 0.280 0.000 0
#> SRR1617411 1 0.368 0.661 0.720 0.000 0.280 0.000 0
#> SRR1617412 1 0.368 0.759 0.720 0.280 0.000 0.000 0
#> SRR1617413 1 0.368 0.759 0.720 0.280 0.000 0.000 0
#> SRR1617414 1 0.467 0.703 0.736 0.100 0.000 0.164 0
#> SRR1617415 1 0.473 0.696 0.728 0.096 0.000 0.176 0
#> SRR1617416 5 0.000 1.000 0.000 0.000 0.000 0.000 1
#> SRR1617417 5 0.000 1.000 0.000 0.000 0.000 0.000 1
#> SRR1617418 1 0.368 0.661 0.720 0.000 0.280 0.000 0
#> SRR1617419 1 0.371 0.658 0.716 0.000 0.284 0.000 0
#> SRR1617420 1 0.000 0.787 1.000 0.000 0.000 0.000 0
#> SRR1617421 1 0.029 0.788 0.992 0.008 0.000 0.000 0
#> SRR1617422 1 0.000 0.787 1.000 0.000 0.000 0.000 0
#> SRR1617423 1 0.000 0.787 1.000 0.000 0.000 0.000 0
#> SRR1617424 1 0.000 0.787 1.000 0.000 0.000 0.000 0
#> SRR1617425 1 0.000 0.787 1.000 0.000 0.000 0.000 0
#> SRR1617427 1 0.634 0.522 0.508 0.188 0.000 0.304 0
#> SRR1617426 1 0.634 0.522 0.508 0.188 0.000 0.304 0
#> SRR1617428 4 0.000 0.892 0.000 0.000 0.000 1.000 0
#> SRR1617429 4 0.000 0.892 0.000 0.000 0.000 1.000 0
#> SRR1617432 1 0.000 0.787 1.000 0.000 0.000 0.000 0
#> SRR1617433 1 0.000 0.787 1.000 0.000 0.000 0.000 0
#> SRR1617434 3 0.000 0.866 0.000 0.000 1.000 0.000 0
#> SRR1617436 1 0.375 0.755 0.708 0.292 0.000 0.000 0
#> SRR1617435 3 0.000 0.866 0.000 0.000 1.000 0.000 0
#> SRR1617437 1 0.375 0.755 0.708 0.292 0.000 0.000 0
#> SRR1617438 1 0.324 0.711 0.784 0.000 0.216 0.000 0
#> SRR1617439 1 0.307 0.723 0.804 0.000 0.196 0.000 0
#> SRR1617440 3 0.000 0.866 0.000 0.000 1.000 0.000 0
#> SRR1617441 3 0.000 0.866 0.000 0.000 1.000 0.000 0
#> SRR1617443 3 0.000 0.866 0.000 0.000 1.000 0.000 0
#> SRR1617442 3 0.000 0.866 0.000 0.000 1.000 0.000 0
#> SRR1617444 3 0.000 0.866 0.000 0.000 1.000 0.000 0
#> SRR1617445 3 0.000 0.866 0.000 0.000 1.000 0.000 0
#> SRR1617446 1 0.417 0.713 0.604 0.396 0.000 0.000 0
#> SRR1617447 1 0.417 0.713 0.604 0.396 0.000 0.000 0
#> SRR1617448 1 0.417 0.713 0.604 0.396 0.000 0.000 0
#> SRR1617449 1 0.417 0.713 0.604 0.396 0.000 0.000 0
#> SRR1617451 4 0.000 0.892 0.000 0.000 0.000 1.000 0
#> SRR1617450 4 0.000 0.892 0.000 0.000 0.000 1.000 0
#> SRR1617452 5 0.000 1.000 0.000 0.000 0.000 0.000 1
#> SRR1617454 4 0.368 0.658 0.280 0.000 0.000 0.720 0
#> SRR1617453 5 0.000 1.000 0.000 0.000 0.000 0.000 1
#> SRR1617456 2 0.417 1.000 0.000 0.604 0.396 0.000 0
#> SRR1617457 2 0.417 1.000 0.000 0.604 0.396 0.000 0
#> SRR1617455 4 0.368 0.658 0.280 0.000 0.000 0.720 0
#> SRR1617458 2 0.417 1.000 0.000 0.604 0.396 0.000 0
#> SRR1617459 2 0.417 1.000 0.000 0.604 0.396 0.000 0
#> SRR1617460 3 0.364 0.468 0.272 0.000 0.728 0.000 0
#> SRR1617461 3 0.327 0.545 0.220 0.000 0.780 0.000 0
#> SRR1617463 1 0.000 0.787 1.000 0.000 0.000 0.000 0
#> SRR1617462 1 0.000 0.787 1.000 0.000 0.000 0.000 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.0000 0.869 0.000 1.000 0.000 0 0.000 0
#> SRR1617431 2 0.0000 0.869 0.000 1.000 0.000 0 0.000 0
#> SRR1617410 3 0.3563 0.548 0.000 0.000 0.664 0 0.336 0
#> SRR1617411 3 0.3563 0.548 0.000 0.000 0.664 0 0.336 0
#> SRR1617412 3 0.3563 0.418 0.336 0.000 0.664 0 0.000 0
#> SRR1617413 3 0.3563 0.418 0.336 0.000 0.664 0 0.000 0
#> SRR1617414 1 0.5298 0.315 0.592 0.160 0.248 0 0.000 0
#> SRR1617415 1 0.5344 0.310 0.588 0.172 0.240 0 0.000 0
#> SRR1617416 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0
#> SRR1617417 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0
#> SRR1617418 3 0.3563 0.548 0.000 0.000 0.664 0 0.336 0
#> SRR1617419 3 0.3578 0.544 0.000 0.000 0.660 0 0.340 0
#> SRR1617420 3 0.0000 0.661 0.000 0.000 1.000 0 0.000 0
#> SRR1617421 3 0.0363 0.658 0.012 0.000 0.988 0 0.000 0
#> SRR1617422 3 0.0000 0.661 0.000 0.000 1.000 0 0.000 0
#> SRR1617423 3 0.0000 0.661 0.000 0.000 1.000 0 0.000 0
#> SRR1617424 3 0.0000 0.661 0.000 0.000 1.000 0 0.000 0
#> SRR1617425 3 0.0000 0.661 0.000 0.000 1.000 0 0.000 0
#> SRR1617427 1 0.3076 0.332 0.760 0.240 0.000 0 0.000 0
#> SRR1617426 1 0.3050 0.336 0.764 0.236 0.000 0 0.000 0
#> SRR1617428 2 0.0000 0.869 0.000 1.000 0.000 0 0.000 0
#> SRR1617429 2 0.0000 0.869 0.000 1.000 0.000 0 0.000 0
#> SRR1617432 3 0.3672 0.133 0.368 0.000 0.632 0 0.000 0
#> SRR1617433 3 0.3672 0.133 0.368 0.000 0.632 0 0.000 0
#> SRR1617434 5 0.0000 0.905 0.000 0.000 0.000 0 1.000 0
#> SRR1617436 3 0.3607 0.399 0.348 0.000 0.652 0 0.000 0
#> SRR1617435 5 0.0000 0.905 0.000 0.000 0.000 0 1.000 0
#> SRR1617437 3 0.3607 0.399 0.348 0.000 0.652 0 0.000 0
#> SRR1617438 3 0.3244 0.591 0.000 0.000 0.732 0 0.268 0
#> SRR1617439 3 0.3126 0.601 0.000 0.000 0.752 0 0.248 0
#> SRR1617440 5 0.0000 0.905 0.000 0.000 0.000 0 1.000 0
#> SRR1617441 5 0.0000 0.905 0.000 0.000 0.000 0 1.000 0
#> SRR1617443 5 0.0000 0.905 0.000 0.000 0.000 0 1.000 0
#> SRR1617442 5 0.0000 0.905 0.000 0.000 0.000 0 1.000 0
#> SRR1617444 5 0.0000 0.905 0.000 0.000 0.000 0 1.000 0
#> SRR1617445 5 0.0000 0.905 0.000 0.000 0.000 0 1.000 0
#> SRR1617446 1 0.3672 0.362 0.632 0.000 0.368 0 0.000 0
#> SRR1617447 1 0.3672 0.362 0.632 0.000 0.368 0 0.000 0
#> SRR1617448 1 0.3672 0.362 0.632 0.000 0.368 0 0.000 0
#> SRR1617449 1 0.3672 0.362 0.632 0.000 0.368 0 0.000 0
#> SRR1617451 2 0.0000 0.869 0.000 1.000 0.000 0 0.000 0
#> SRR1617450 2 0.0000 0.869 0.000 1.000 0.000 0 0.000 0
#> SRR1617452 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0
#> SRR1617454 2 0.3563 0.565 0.000 0.664 0.336 0 0.000 0
#> SRR1617453 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0
#> SRR1617456 6 0.0000 1.000 0.000 0.000 0.000 0 0.000 1
#> SRR1617457 6 0.0000 1.000 0.000 0.000 0.000 0 0.000 1
#> SRR1617455 2 0.3563 0.565 0.000 0.664 0.336 0 0.000 0
#> SRR1617458 6 0.0000 1.000 0.000 0.000 0.000 0 0.000 1
#> SRR1617459 6 0.0000 1.000 0.000 0.000 0.000 0 0.000 1
#> SRR1617460 5 0.3531 0.535 0.000 0.000 0.328 0 0.672 0
#> SRR1617461 5 0.3288 0.606 0.000 0.000 0.276 0 0.724 0
#> SRR1617463 3 0.0000 0.661 0.000 0.000 1.000 0 0.000 0
#> SRR1617462 3 0.0000 0.661 0.000 0.000 1.000 0 0.000 0
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", "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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 0.377 0.685 0.872 0.4834 0.508 0.508
#> 3 3 0.659 0.800 0.868 0.3270 0.712 0.489
#> 4 4 0.449 0.449 0.647 0.1088 0.939 0.826
#> 5 5 0.560 0.505 0.642 0.0936 0.883 0.661
#> 6 6 0.704 0.640 0.753 0.0394 0.939 0.768
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
#> SRR1617430 2 0.0672 0.82776 0.008 0.992
#> SRR1617431 2 0.0672 0.82776 0.008 0.992
#> SRR1617410 1 0.0000 0.82226 1.000 0.000
#> SRR1617411 1 0.0000 0.82226 1.000 0.000
#> SRR1617412 1 0.0000 0.82226 1.000 0.000
#> SRR1617413 1 0.0000 0.82226 1.000 0.000
#> SRR1617414 2 0.9896 -0.02673 0.440 0.560
#> SRR1617415 2 0.9896 -0.02673 0.440 0.560
#> SRR1617416 1 0.8555 0.52552 0.720 0.280
#> SRR1617417 1 0.9087 0.45438 0.676 0.324
#> SRR1617418 1 0.0000 0.82226 1.000 0.000
#> SRR1617419 1 0.0000 0.82226 1.000 0.000
#> SRR1617420 1 0.0000 0.82226 1.000 0.000
#> SRR1617421 1 0.0000 0.82226 1.000 0.000
#> SRR1617422 2 0.0938 0.83037 0.012 0.988
#> SRR1617423 2 0.0938 0.83037 0.012 0.988
#> SRR1617424 1 0.0000 0.82226 1.000 0.000
#> SRR1617425 1 0.0000 0.82226 1.000 0.000
#> SRR1617427 1 0.5946 0.70258 0.856 0.144
#> SRR1617426 1 0.5946 0.70258 0.856 0.144
#> SRR1617428 2 0.0000 0.82757 0.000 1.000
#> SRR1617429 2 0.0000 0.82757 0.000 1.000
#> SRR1617432 1 0.9686 0.27149 0.604 0.396
#> SRR1617433 1 0.9686 0.27149 0.604 0.396
#> SRR1617434 1 0.8955 0.46454 0.688 0.312
#> SRR1617436 1 0.0000 0.82226 1.000 0.000
#> SRR1617435 1 0.9686 0.27149 0.604 0.396
#> SRR1617437 1 0.0000 0.82226 1.000 0.000
#> SRR1617438 1 0.0000 0.82226 1.000 0.000
#> SRR1617439 1 0.0000 0.82226 1.000 0.000
#> SRR1617440 1 0.9970 0.01732 0.532 0.468
#> SRR1617441 1 0.9983 -0.00753 0.524 0.476
#> SRR1617443 1 0.0000 0.82226 1.000 0.000
#> SRR1617442 1 0.0000 0.82226 1.000 0.000
#> SRR1617444 1 0.9963 0.02889 0.536 0.464
#> SRR1617445 1 0.9963 0.02889 0.536 0.464
#> SRR1617446 1 0.0000 0.82226 1.000 0.000
#> SRR1617447 1 0.0000 0.82226 1.000 0.000
#> SRR1617448 1 0.0000 0.82226 1.000 0.000
#> SRR1617449 1 0.0000 0.82226 1.000 0.000
#> SRR1617451 2 0.0672 0.83234 0.008 0.992
#> SRR1617450 2 0.0672 0.83234 0.008 0.992
#> SRR1617452 2 0.6438 0.82976 0.164 0.836
#> SRR1617454 2 0.5737 0.85870 0.136 0.864
#> SRR1617453 2 0.6438 0.82976 0.164 0.836
#> SRR1617456 2 0.5737 0.85870 0.136 0.864
#> SRR1617457 2 0.5737 0.85870 0.136 0.864
#> SRR1617455 2 0.5737 0.85870 0.136 0.864
#> SRR1617458 2 0.5737 0.85870 0.136 0.864
#> SRR1617459 2 0.5737 0.85870 0.136 0.864
#> SRR1617460 2 0.5737 0.85870 0.136 0.864
#> SRR1617461 2 0.5737 0.85870 0.136 0.864
#> SRR1617463 2 0.5737 0.85870 0.136 0.864
#> SRR1617462 2 0.5737 0.85870 0.136 0.864
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.0475 0.809 0.004 0.992 0.004
#> SRR1617431 2 0.0475 0.809 0.004 0.992 0.004
#> SRR1617410 3 0.0424 0.974 0.008 0.000 0.992
#> SRR1617411 3 0.0424 0.974 0.008 0.000 0.992
#> SRR1617412 3 0.0475 0.976 0.004 0.004 0.992
#> SRR1617413 3 0.0475 0.976 0.004 0.004 0.992
#> SRR1617414 2 0.4121 0.864 0.168 0.832 0.000
#> SRR1617415 2 0.4121 0.864 0.168 0.832 0.000
#> SRR1617416 1 0.1905 0.636 0.956 0.028 0.016
#> SRR1617417 1 0.1905 0.636 0.956 0.028 0.016
#> SRR1617418 3 0.0475 0.975 0.004 0.004 0.992
#> SRR1617419 3 0.0475 0.975 0.004 0.004 0.992
#> SRR1617420 3 0.0000 0.976 0.000 0.000 1.000
#> SRR1617421 3 0.0000 0.976 0.000 0.000 1.000
#> SRR1617422 2 0.3377 0.831 0.092 0.896 0.012
#> SRR1617423 2 0.3213 0.834 0.092 0.900 0.008
#> SRR1617424 3 0.0475 0.975 0.004 0.004 0.992
#> SRR1617425 3 0.0475 0.975 0.004 0.004 0.992
#> SRR1617427 3 0.4807 0.810 0.060 0.092 0.848
#> SRR1617426 3 0.4709 0.816 0.056 0.092 0.852
#> SRR1617428 2 0.3272 0.848 0.104 0.892 0.004
#> SRR1617429 2 0.3272 0.848 0.104 0.892 0.004
#> SRR1617432 2 0.6597 0.823 0.268 0.696 0.036
#> SRR1617433 2 0.6252 0.833 0.268 0.708 0.024
#> SRR1617434 1 0.7292 0.165 0.500 0.028 0.472
#> SRR1617436 3 0.0475 0.975 0.004 0.004 0.992
#> SRR1617435 1 0.7292 0.165 0.500 0.028 0.472
#> SRR1617437 3 0.0475 0.975 0.004 0.004 0.992
#> SRR1617438 3 0.0475 0.975 0.004 0.004 0.992
#> SRR1617439 3 0.0475 0.975 0.004 0.004 0.992
#> SRR1617440 1 0.6483 0.470 0.600 0.008 0.392
#> SRR1617441 1 0.6483 0.470 0.600 0.008 0.392
#> SRR1617443 3 0.0661 0.973 0.004 0.008 0.988
#> SRR1617442 3 0.0661 0.973 0.004 0.008 0.988
#> SRR1617444 1 0.6584 0.483 0.608 0.012 0.380
#> SRR1617445 1 0.6566 0.488 0.612 0.012 0.376
#> SRR1617446 3 0.0237 0.975 0.000 0.004 0.996
#> SRR1617447 3 0.0237 0.975 0.000 0.004 0.996
#> SRR1617448 3 0.0237 0.975 0.000 0.004 0.996
#> SRR1617449 3 0.0424 0.975 0.000 0.008 0.992
#> SRR1617451 2 0.2945 0.845 0.088 0.908 0.004
#> SRR1617450 2 0.2945 0.845 0.088 0.908 0.004
#> SRR1617452 1 0.1877 0.632 0.956 0.032 0.012
#> SRR1617454 2 0.4682 0.814 0.192 0.804 0.004
#> SRR1617453 1 0.1877 0.632 0.956 0.032 0.012
#> SRR1617456 1 0.4834 0.557 0.792 0.204 0.004
#> SRR1617457 1 0.5070 0.533 0.772 0.224 0.004
#> SRR1617455 2 0.4682 0.814 0.192 0.804 0.004
#> SRR1617458 1 0.3573 0.610 0.876 0.120 0.004
#> SRR1617459 1 0.3573 0.610 0.876 0.120 0.004
#> SRR1617460 2 0.5928 0.818 0.296 0.696 0.008
#> SRR1617461 2 0.5928 0.818 0.296 0.696 0.008
#> SRR1617463 2 0.5327 0.835 0.272 0.728 0.000
#> SRR1617462 2 0.5327 0.835 0.272 0.728 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.4591 0.3633 0.084 0.800 0.116 0.000
#> SRR1617431 2 0.4591 0.3633 0.084 0.800 0.116 0.000
#> SRR1617410 1 0.6336 0.0932 0.480 0.000 0.060 0.460
#> SRR1617411 1 0.6276 0.0942 0.480 0.000 0.056 0.464
#> SRR1617412 1 0.3668 0.6667 0.808 0.000 0.188 0.004
#> SRR1617413 1 0.3668 0.6667 0.808 0.000 0.188 0.004
#> SRR1617414 2 0.7130 0.2271 0.020 0.536 0.360 0.084
#> SRR1617415 2 0.7130 0.2271 0.020 0.536 0.360 0.084
#> SRR1617416 4 0.4419 0.5742 0.072 0.012 0.088 0.828
#> SRR1617417 4 0.4419 0.5742 0.072 0.012 0.088 0.828
#> SRR1617418 1 0.8500 0.4196 0.472 0.044 0.236 0.248
#> SRR1617419 1 0.8500 0.4196 0.472 0.044 0.236 0.248
#> SRR1617420 1 0.1510 0.6812 0.956 0.000 0.016 0.028
#> SRR1617421 1 0.1510 0.6812 0.956 0.000 0.016 0.028
#> SRR1617422 2 0.7510 0.3199 0.044 0.556 0.312 0.088
#> SRR1617423 2 0.7357 0.3241 0.036 0.564 0.312 0.088
#> SRR1617424 1 0.2706 0.6713 0.900 0.000 0.020 0.080
#> SRR1617425 1 0.2775 0.6703 0.896 0.000 0.020 0.084
#> SRR1617427 1 0.6311 0.5075 0.708 0.180 0.048 0.064
#> SRR1617426 1 0.6311 0.5075 0.708 0.180 0.048 0.064
#> SRR1617428 2 0.6567 0.3395 0.004 0.592 0.316 0.088
#> SRR1617429 2 0.6567 0.3395 0.004 0.592 0.316 0.088
#> SRR1617432 3 0.7649 1.0000 0.004 0.204 0.484 0.308
#> SRR1617433 3 0.7649 1.0000 0.004 0.204 0.484 0.308
#> SRR1617434 4 0.5250 0.5537 0.072 0.040 0.096 0.792
#> SRR1617436 1 0.5203 0.6464 0.720 0.000 0.232 0.048
#> SRR1617435 4 0.5335 0.5497 0.072 0.044 0.096 0.788
#> SRR1617437 1 0.5203 0.6464 0.720 0.000 0.232 0.048
#> SRR1617438 1 0.7434 0.4716 0.512 0.000 0.232 0.256
#> SRR1617439 1 0.7434 0.4716 0.512 0.000 0.232 0.256
#> SRR1617440 4 0.6122 0.4043 0.276 0.008 0.064 0.652
#> SRR1617441 4 0.6355 0.4383 0.260 0.020 0.064 0.656
#> SRR1617443 1 0.6315 0.1601 0.508 0.000 0.060 0.432
#> SRR1617442 1 0.6319 0.1532 0.504 0.000 0.060 0.436
#> SRR1617444 4 0.4442 0.5725 0.236 0.004 0.008 0.752
#> SRR1617445 4 0.4464 0.5858 0.224 0.004 0.012 0.760
#> SRR1617446 1 0.1733 0.6837 0.948 0.000 0.028 0.024
#> SRR1617447 1 0.1733 0.6837 0.948 0.000 0.028 0.024
#> SRR1617448 1 0.0524 0.6834 0.988 0.000 0.008 0.004
#> SRR1617449 1 0.0524 0.6834 0.988 0.000 0.008 0.004
#> SRR1617451 2 0.2297 0.4229 0.032 0.932 0.012 0.024
#> SRR1617450 2 0.2297 0.4229 0.032 0.932 0.012 0.024
#> SRR1617452 4 0.3414 0.5837 0.004 0.072 0.048 0.876
#> SRR1617454 2 0.3637 0.4006 0.004 0.864 0.052 0.080
#> SRR1617453 4 0.3414 0.5837 0.004 0.072 0.048 0.876
#> SRR1617456 2 0.7822 -0.0811 0.000 0.380 0.256 0.364
#> SRR1617457 2 0.7822 -0.0811 0.000 0.380 0.256 0.364
#> SRR1617455 2 0.3292 0.3976 0.004 0.880 0.036 0.080
#> SRR1617458 4 0.7512 0.3187 0.004 0.336 0.172 0.488
#> SRR1617459 4 0.7512 0.3187 0.004 0.336 0.172 0.488
#> SRR1617460 2 0.8246 0.0512 0.024 0.400 0.196 0.380
#> SRR1617461 2 0.8162 0.0541 0.020 0.404 0.196 0.380
#> SRR1617463 2 0.6374 0.3614 0.000 0.644 0.228 0.128
#> SRR1617462 2 0.6403 0.3632 0.000 0.640 0.232 0.128
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 2 0.5715 0.5557 0.048 0.676 0.000 0.208 0.068
#> SRR1617431 2 0.5715 0.5557 0.048 0.676 0.000 0.208 0.068
#> SRR1617410 1 0.6536 0.3344 0.632 0.016 0.200 0.112 0.040
#> SRR1617411 1 0.6536 0.3344 0.632 0.016 0.200 0.112 0.040
#> SRR1617412 3 0.1087 0.4770 0.016 0.000 0.968 0.008 0.008
#> SRR1617413 3 0.1087 0.4770 0.016 0.000 0.968 0.008 0.008
#> SRR1617414 2 0.3343 0.3087 0.016 0.812 0.000 0.172 0.000
#> SRR1617415 2 0.3343 0.3087 0.016 0.812 0.000 0.172 0.000
#> SRR1617416 1 0.5061 0.4532 0.624 0.004 0.012 0.340 0.020
#> SRR1617417 1 0.4842 0.4482 0.632 0.004 0.004 0.340 0.020
#> SRR1617418 3 0.7327 0.0878 0.136 0.004 0.544 0.092 0.224
#> SRR1617419 3 0.7327 0.0878 0.136 0.004 0.544 0.092 0.224
#> SRR1617420 3 0.6395 0.5474 0.356 0.008 0.528 0.092 0.016
#> SRR1617421 3 0.6395 0.5474 0.356 0.008 0.528 0.092 0.016
#> SRR1617422 2 0.1894 0.5205 0.072 0.920 0.000 0.008 0.000
#> SRR1617423 2 0.1764 0.5278 0.064 0.928 0.000 0.008 0.000
#> SRR1617424 3 0.6289 0.5437 0.400 0.008 0.492 0.092 0.008
#> SRR1617425 3 0.6289 0.5437 0.400 0.008 0.492 0.092 0.008
#> SRR1617427 3 0.7022 0.4795 0.384 0.100 0.464 0.044 0.008
#> SRR1617426 3 0.7022 0.4795 0.384 0.100 0.464 0.044 0.008
#> SRR1617428 2 0.0671 0.5516 0.016 0.980 0.000 0.004 0.000
#> SRR1617429 2 0.0671 0.5516 0.016 0.980 0.000 0.004 0.000
#> SRR1617432 4 0.6076 1.0000 0.076 0.432 0.000 0.476 0.016
#> SRR1617433 4 0.6076 1.0000 0.076 0.432 0.000 0.476 0.016
#> SRR1617434 1 0.6127 0.4313 0.528 0.008 0.072 0.380 0.012
#> SRR1617436 3 0.1444 0.4637 0.012 0.000 0.948 0.040 0.000
#> SRR1617435 1 0.6127 0.4313 0.528 0.008 0.072 0.380 0.012
#> SRR1617437 3 0.1444 0.4637 0.012 0.000 0.948 0.040 0.000
#> SRR1617438 3 0.6129 0.2017 0.124 0.000 0.668 0.068 0.140
#> SRR1617439 3 0.6129 0.2017 0.124 0.000 0.668 0.068 0.140
#> SRR1617440 1 0.7719 0.2877 0.476 0.004 0.172 0.088 0.260
#> SRR1617441 1 0.7579 0.2984 0.492 0.004 0.164 0.080 0.260
#> SRR1617443 1 0.4737 0.4320 0.680 0.000 0.284 0.012 0.024
#> SRR1617442 1 0.4737 0.4320 0.680 0.000 0.284 0.012 0.024
#> SRR1617444 1 0.4026 0.5603 0.832 0.024 0.036 0.016 0.092
#> SRR1617445 1 0.4080 0.5594 0.828 0.024 0.036 0.016 0.096
#> SRR1617446 3 0.6229 0.5511 0.384 0.000 0.500 0.104 0.012
#> SRR1617447 3 0.6229 0.5511 0.384 0.000 0.500 0.104 0.012
#> SRR1617448 3 0.6159 0.5540 0.380 0.004 0.508 0.104 0.004
#> SRR1617449 3 0.6159 0.5540 0.380 0.004 0.508 0.104 0.004
#> SRR1617451 2 0.5584 0.5787 0.000 0.584 0.000 0.324 0.092
#> SRR1617450 2 0.5584 0.5787 0.000 0.584 0.000 0.324 0.092
#> SRR1617452 1 0.6702 0.4569 0.588 0.008 0.028 0.200 0.176
#> SRR1617454 2 0.6639 0.4878 0.004 0.476 0.000 0.304 0.216
#> SRR1617453 1 0.6702 0.4569 0.588 0.008 0.028 0.200 0.176
#> SRR1617456 5 0.3646 0.8718 0.052 0.100 0.000 0.012 0.836
#> SRR1617457 5 0.3646 0.8718 0.052 0.100 0.000 0.012 0.836
#> SRR1617455 2 0.6677 0.4751 0.004 0.468 0.000 0.304 0.224
#> SRR1617458 5 0.2124 0.8715 0.096 0.004 0.000 0.000 0.900
#> SRR1617459 5 0.2124 0.8715 0.096 0.004 0.000 0.000 0.900
#> SRR1617460 2 0.6881 0.4320 0.168 0.604 0.004 0.144 0.080
#> SRR1617461 2 0.6830 0.4366 0.168 0.608 0.004 0.144 0.076
#> SRR1617463 2 0.4255 0.5858 0.068 0.800 0.000 0.112 0.020
#> SRR1617462 2 0.4255 0.5858 0.068 0.800 0.000 0.112 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.3956 0.654 0.068 0.788 0.004 0.012 0.128 0.000
#> SRR1617431 2 0.3956 0.654 0.068 0.788 0.004 0.012 0.128 0.000
#> SRR1617410 4 0.7245 0.559 0.132 0.000 0.148 0.416 0.300 0.004
#> SRR1617411 4 0.7245 0.559 0.132 0.000 0.148 0.416 0.300 0.004
#> SRR1617412 1 0.4652 0.469 0.560 0.000 0.404 0.024 0.000 0.012
#> SRR1617413 1 0.4652 0.469 0.560 0.000 0.404 0.024 0.000 0.012
#> SRR1617414 2 0.4082 0.420 0.004 0.560 0.000 0.004 0.432 0.000
#> SRR1617415 2 0.4082 0.420 0.004 0.560 0.000 0.004 0.432 0.000
#> SRR1617416 4 0.5386 0.582 0.000 0.000 0.120 0.512 0.368 0.000
#> SRR1617417 4 0.5386 0.582 0.000 0.000 0.120 0.512 0.368 0.000
#> SRR1617418 3 0.1410 0.777 0.008 0.000 0.944 0.044 0.000 0.004
#> SRR1617419 3 0.1410 0.777 0.008 0.000 0.944 0.044 0.000 0.004
#> SRR1617420 1 0.1606 0.751 0.932 0.000 0.056 0.004 0.000 0.008
#> SRR1617421 1 0.1542 0.752 0.936 0.000 0.052 0.004 0.000 0.008
#> SRR1617422 2 0.4937 0.682 0.064 0.696 0.000 0.032 0.204 0.004
#> SRR1617423 2 0.4867 0.684 0.064 0.700 0.000 0.028 0.204 0.004
#> SRR1617424 1 0.1437 0.759 0.952 0.004 0.020 0.004 0.004 0.016
#> SRR1617425 1 0.1348 0.759 0.956 0.004 0.016 0.004 0.004 0.016
#> SRR1617427 1 0.5655 0.376 0.608 0.280 0.020 0.028 0.064 0.000
#> SRR1617426 1 0.5655 0.376 0.608 0.280 0.020 0.028 0.064 0.000
#> SRR1617428 2 0.3441 0.697 0.004 0.768 0.000 0.008 0.216 0.004
#> SRR1617429 2 0.3441 0.697 0.004 0.768 0.000 0.008 0.216 0.004
#> SRR1617432 5 0.2149 1.000 0.000 0.080 0.004 0.016 0.900 0.000
#> SRR1617433 5 0.2149 1.000 0.000 0.080 0.004 0.016 0.900 0.000
#> SRR1617434 4 0.6423 0.570 0.020 0.024 0.124 0.464 0.368 0.000
#> SRR1617436 1 0.4580 0.419 0.528 0.000 0.440 0.028 0.004 0.000
#> SRR1617435 4 0.6423 0.570 0.020 0.024 0.124 0.464 0.368 0.000
#> SRR1617437 1 0.4580 0.419 0.528 0.000 0.440 0.028 0.004 0.000
#> SRR1617438 3 0.1620 0.768 0.024 0.000 0.940 0.024 0.000 0.012
#> SRR1617439 3 0.1620 0.768 0.024 0.000 0.940 0.024 0.000 0.012
#> SRR1617440 3 0.5277 0.524 0.008 0.000 0.568 0.332 0.000 0.092
#> SRR1617441 3 0.5265 0.531 0.008 0.000 0.572 0.328 0.000 0.092
#> SRR1617443 4 0.4507 0.474 0.052 0.000 0.284 0.660 0.000 0.004
#> SRR1617442 4 0.4507 0.474 0.052 0.000 0.284 0.660 0.000 0.004
#> SRR1617444 4 0.4529 0.542 0.092 0.008 0.152 0.740 0.004 0.004
#> SRR1617445 4 0.4529 0.542 0.092 0.008 0.152 0.740 0.004 0.004
#> SRR1617446 1 0.0551 0.759 0.984 0.004 0.000 0.000 0.004 0.008
#> SRR1617447 1 0.0551 0.759 0.984 0.004 0.000 0.000 0.004 0.008
#> SRR1617448 1 0.0508 0.759 0.984 0.004 0.012 0.000 0.000 0.000
#> SRR1617449 1 0.0508 0.759 0.984 0.004 0.012 0.000 0.000 0.000
#> SRR1617451 2 0.1788 0.676 0.004 0.916 0.000 0.004 0.076 0.000
#> SRR1617450 2 0.1788 0.676 0.004 0.916 0.000 0.004 0.076 0.000
#> SRR1617452 4 0.3270 0.369 0.000 0.004 0.004 0.816 0.024 0.152
#> SRR1617454 2 0.0893 0.700 0.004 0.972 0.004 0.004 0.000 0.016
#> SRR1617453 4 0.3270 0.369 0.000 0.004 0.004 0.816 0.024 0.152
#> SRR1617456 6 0.0291 0.996 0.000 0.004 0.000 0.004 0.000 0.992
#> SRR1617457 6 0.0291 0.996 0.000 0.004 0.000 0.004 0.000 0.992
#> SRR1617455 2 0.0893 0.700 0.004 0.972 0.004 0.004 0.000 0.016
#> SRR1617458 6 0.0146 0.996 0.000 0.000 0.000 0.004 0.000 0.996
#> SRR1617459 6 0.0146 0.996 0.000 0.000 0.000 0.004 0.000 0.996
#> SRR1617460 2 0.6579 0.305 0.012 0.532 0.132 0.276 0.040 0.008
#> SRR1617461 2 0.6579 0.305 0.012 0.532 0.132 0.276 0.040 0.008
#> SRR1617463 2 0.3456 0.703 0.004 0.800 0.004 0.028 0.164 0.000
#> SRR1617462 2 0.3456 0.703 0.004 0.800 0.004 0.028 0.164 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["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 17713 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) 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 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 0.813 0.914 0.962 0.4481 0.547 0.547
#> 3 3 0.592 0.781 0.884 0.4691 0.732 0.529
#> 4 4 0.573 0.636 0.797 0.1105 0.896 0.695
#> 5 5 0.545 0.560 0.748 0.0591 0.808 0.439
#> 6 6 0.656 0.576 0.750 0.0521 0.881 0.556
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
#> SRR1617430 2 0.7602 0.738 0.220 0.780
#> SRR1617431 2 0.7674 0.733 0.224 0.776
#> SRR1617410 1 0.0000 0.971 1.000 0.000
#> SRR1617411 1 0.0000 0.971 1.000 0.000
#> SRR1617412 1 0.0000 0.971 1.000 0.000
#> SRR1617413 1 0.0000 0.971 1.000 0.000
#> SRR1617414 1 0.1184 0.959 0.984 0.016
#> SRR1617415 1 0.1184 0.959 0.984 0.016
#> SRR1617416 1 0.0000 0.971 1.000 0.000
#> SRR1617417 1 0.0000 0.971 1.000 0.000
#> SRR1617418 1 0.0000 0.971 1.000 0.000
#> SRR1617419 1 0.0000 0.971 1.000 0.000
#> SRR1617420 1 0.0000 0.971 1.000 0.000
#> SRR1617421 1 0.0000 0.971 1.000 0.000
#> SRR1617422 1 0.5408 0.844 0.876 0.124
#> SRR1617423 1 0.6531 0.788 0.832 0.168
#> SRR1617424 1 0.0000 0.971 1.000 0.000
#> SRR1617425 1 0.0000 0.971 1.000 0.000
#> SRR1617427 1 0.0000 0.971 1.000 0.000
#> SRR1617426 1 0.0000 0.971 1.000 0.000
#> SRR1617428 2 0.9323 0.524 0.348 0.652
#> SRR1617429 2 0.9087 0.573 0.324 0.676
#> SRR1617432 1 0.0000 0.971 1.000 0.000
#> SRR1617433 1 0.0000 0.971 1.000 0.000
#> SRR1617434 1 0.0000 0.971 1.000 0.000
#> SRR1617436 1 0.0000 0.971 1.000 0.000
#> SRR1617435 1 0.0000 0.971 1.000 0.000
#> SRR1617437 1 0.0000 0.971 1.000 0.000
#> SRR1617438 1 0.0000 0.971 1.000 0.000
#> SRR1617439 1 0.0000 0.971 1.000 0.000
#> SRR1617440 1 0.7139 0.754 0.804 0.196
#> SRR1617441 1 0.9775 0.294 0.588 0.412
#> SRR1617443 1 0.0000 0.971 1.000 0.000
#> SRR1617442 1 0.0000 0.971 1.000 0.000
#> SRR1617444 1 0.0376 0.969 0.996 0.004
#> SRR1617445 1 0.0376 0.969 0.996 0.004
#> SRR1617446 1 0.0000 0.971 1.000 0.000
#> SRR1617447 1 0.0000 0.971 1.000 0.000
#> SRR1617448 1 0.0000 0.971 1.000 0.000
#> SRR1617449 1 0.0000 0.971 1.000 0.000
#> SRR1617451 2 0.0000 0.931 0.000 1.000
#> SRR1617450 2 0.0000 0.931 0.000 1.000
#> SRR1617452 2 0.0000 0.931 0.000 1.000
#> SRR1617454 2 0.0000 0.931 0.000 1.000
#> SRR1617453 2 0.0000 0.931 0.000 1.000
#> SRR1617456 2 0.0000 0.931 0.000 1.000
#> SRR1617457 2 0.0000 0.931 0.000 1.000
#> SRR1617455 2 0.0000 0.931 0.000 1.000
#> SRR1617458 2 0.0000 0.931 0.000 1.000
#> SRR1617459 2 0.0000 0.931 0.000 1.000
#> SRR1617460 2 0.0000 0.931 0.000 1.000
#> SRR1617461 2 0.0000 0.931 0.000 1.000
#> SRR1617463 2 0.0000 0.931 0.000 1.000
#> SRR1617462 2 0.0000 0.931 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> SRR1617430 2 0.5835 0.535 0.340 0.660 0.000
#> SRR1617431 2 0.5882 0.526 0.348 0.652 0.000
#> SRR1617410 1 0.5254 0.648 0.736 0.000 0.264
#> SRR1617411 1 0.5431 0.614 0.716 0.000 0.284
#> SRR1617412 3 0.0000 0.864 0.000 0.000 1.000
#> SRR1617413 3 0.0237 0.865 0.004 0.000 0.996
#> SRR1617414 1 0.3832 0.830 0.888 0.076 0.036
#> SRR1617415 1 0.4092 0.824 0.876 0.088 0.036
#> SRR1617416 1 0.1411 0.821 0.964 0.000 0.036
#> SRR1617417 1 0.0237 0.832 0.996 0.000 0.004
#> SRR1617418 3 0.1411 0.850 0.036 0.000 0.964
#> SRR1617419 3 0.1411 0.850 0.036 0.000 0.964
#> SRR1617420 3 0.2878 0.838 0.096 0.000 0.904
#> SRR1617421 3 0.2959 0.836 0.100 0.000 0.900
#> SRR1617422 1 0.5812 0.641 0.724 0.264 0.012
#> SRR1617423 1 0.5986 0.608 0.704 0.284 0.012
#> SRR1617424 1 0.5859 0.482 0.656 0.000 0.344
#> SRR1617425 1 0.5291 0.639 0.732 0.000 0.268
#> SRR1617427 1 0.4744 0.807 0.836 0.028 0.136
#> SRR1617426 1 0.5223 0.776 0.800 0.024 0.176
#> SRR1617428 1 0.2261 0.823 0.932 0.068 0.000
#> SRR1617429 1 0.2356 0.821 0.928 0.072 0.000
#> SRR1617432 1 0.1411 0.841 0.964 0.000 0.036
#> SRR1617433 1 0.1411 0.841 0.964 0.000 0.036
#> SRR1617434 1 0.1411 0.841 0.964 0.000 0.036
#> SRR1617436 3 0.0892 0.867 0.020 0.000 0.980
#> SRR1617435 1 0.1411 0.841 0.964 0.000 0.036
#> SRR1617437 3 0.1163 0.866 0.028 0.000 0.972
#> SRR1617438 3 0.0000 0.864 0.000 0.000 1.000
#> SRR1617439 3 0.0000 0.864 0.000 0.000 1.000
#> SRR1617440 3 0.1411 0.854 0.000 0.036 0.964
#> SRR1617441 3 0.3686 0.785 0.000 0.140 0.860
#> SRR1617443 3 0.1031 0.867 0.024 0.000 0.976
#> SRR1617442 3 0.0424 0.866 0.008 0.000 0.992
#> SRR1617444 3 0.4887 0.718 0.228 0.000 0.772
#> SRR1617445 3 0.5541 0.679 0.252 0.008 0.740
#> SRR1617446 3 0.5178 0.689 0.256 0.000 0.744
#> SRR1617447 3 0.5785 0.554 0.332 0.000 0.668
#> SRR1617448 3 0.5560 0.619 0.300 0.000 0.700
#> SRR1617449 3 0.5706 0.581 0.320 0.000 0.680
#> SRR1617451 2 0.0000 0.893 0.000 1.000 0.000
#> SRR1617450 2 0.0000 0.893 0.000 1.000 0.000
#> SRR1617452 2 0.0000 0.893 0.000 1.000 0.000
#> SRR1617454 2 0.0000 0.893 0.000 1.000 0.000
#> SRR1617453 2 0.0000 0.893 0.000 1.000 0.000
#> SRR1617456 2 0.0000 0.893 0.000 1.000 0.000
#> SRR1617457 2 0.0000 0.893 0.000 1.000 0.000
#> SRR1617455 2 0.0000 0.893 0.000 1.000 0.000
#> SRR1617458 2 0.0000 0.893 0.000 1.000 0.000
#> SRR1617459 2 0.0000 0.893 0.000 1.000 0.000
#> SRR1617460 2 0.5497 0.562 0.292 0.708 0.000
#> SRR1617461 2 0.5397 0.584 0.280 0.720 0.000
#> SRR1617463 2 0.2448 0.852 0.076 0.924 0.000
#> SRR1617462 2 0.2356 0.853 0.072 0.928 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> SRR1617430 2 0.5297 0.640 0.292 0.676 0.000 0.032
#> SRR1617431 2 0.5207 0.644 0.292 0.680 0.000 0.028
#> SRR1617410 1 0.6352 0.644 0.656 0.000 0.188 0.156
#> SRR1617411 1 0.6193 0.621 0.672 0.000 0.148 0.180
#> SRR1617412 4 0.4989 0.211 0.000 0.000 0.472 0.528
#> SRR1617413 4 0.4998 0.160 0.000 0.000 0.488 0.512
#> SRR1617414 1 0.5478 0.521 0.540 0.016 0.444 0.000
#> SRR1617415 1 0.5508 0.461 0.508 0.016 0.476 0.000
#> SRR1617416 1 0.2704 0.574 0.876 0.000 0.000 0.124
#> SRR1617417 1 0.2281 0.595 0.904 0.000 0.000 0.096
#> SRR1617418 4 0.0707 0.690 0.000 0.000 0.020 0.980
#> SRR1617419 4 0.0707 0.690 0.000 0.000 0.020 0.980
#> SRR1617420 3 0.1302 0.724 0.000 0.000 0.956 0.044
#> SRR1617421 3 0.0921 0.725 0.000 0.000 0.972 0.028
#> SRR1617422 1 0.5067 0.680 0.736 0.048 0.216 0.000
#> SRR1617423 1 0.5188 0.676 0.716 0.044 0.240 0.000
#> SRR1617424 1 0.6903 0.348 0.508 0.000 0.112 0.380
#> SRR1617425 1 0.6686 0.521 0.596 0.000 0.128 0.276
#> SRR1617427 3 0.4695 0.386 0.252 0.012 0.732 0.004
#> SRR1617426 3 0.4355 0.463 0.212 0.012 0.772 0.004
#> SRR1617428 1 0.2342 0.620 0.912 0.080 0.000 0.008
#> SRR1617429 1 0.2266 0.620 0.912 0.084 0.000 0.004
#> SRR1617432 1 0.5244 0.589 0.600 0.012 0.388 0.000
#> SRR1617433 1 0.5466 0.531 0.548 0.016 0.436 0.000
#> SRR1617434 1 0.4632 0.649 0.688 0.004 0.308 0.000
#> SRR1617436 3 0.2868 0.674 0.000 0.000 0.864 0.136
#> SRR1617435 1 0.5212 0.558 0.572 0.008 0.420 0.000
#> SRR1617437 3 0.2408 0.702 0.000 0.000 0.896 0.104
#> SRR1617438 3 0.4994 -0.215 0.000 0.000 0.520 0.480
#> SRR1617439 3 0.4907 0.014 0.000 0.000 0.580 0.420
#> SRR1617440 4 0.6315 0.476 0.004 0.076 0.300 0.620
#> SRR1617441 3 0.7083 0.206 0.004 0.164 0.580 0.252
#> SRR1617443 3 0.2216 0.709 0.000 0.000 0.908 0.092
#> SRR1617442 3 0.2530 0.696 0.000 0.000 0.888 0.112
#> SRR1617444 3 0.0859 0.719 0.008 0.008 0.980 0.004
#> SRR1617445 3 0.0992 0.718 0.008 0.012 0.976 0.004
#> SRR1617446 4 0.1767 0.675 0.044 0.000 0.012 0.944
#> SRR1617447 4 0.3471 0.611 0.072 0.000 0.060 0.868
#> SRR1617448 3 0.5121 0.579 0.116 0.000 0.764 0.120
#> SRR1617449 3 0.3877 0.613 0.112 0.000 0.840 0.048
#> SRR1617451 2 0.1284 0.916 0.024 0.964 0.000 0.012
#> SRR1617450 2 0.1284 0.916 0.024 0.964 0.000 0.012
#> SRR1617452 2 0.1022 0.916 0.032 0.968 0.000 0.000
#> SRR1617454 2 0.0188 0.915 0.004 0.996 0.000 0.000
#> SRR1617453 2 0.0921 0.917 0.028 0.972 0.000 0.000
#> SRR1617456 2 0.1484 0.905 0.004 0.960 0.016 0.020
#> SRR1617457 2 0.1484 0.905 0.004 0.960 0.016 0.020
#> SRR1617455 2 0.0188 0.915 0.004 0.996 0.000 0.000
#> SRR1617458 2 0.1598 0.905 0.004 0.956 0.020 0.020
#> SRR1617459 2 0.1598 0.905 0.004 0.956 0.020 0.020
#> SRR1617460 2 0.4102 0.843 0.104 0.836 0.056 0.004
#> SRR1617461 2 0.4193 0.837 0.100 0.832 0.064 0.004
#> SRR1617463 2 0.1771 0.915 0.036 0.948 0.012 0.004
#> SRR1617462 2 0.1545 0.916 0.040 0.952 0.008 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> SRR1617430 4 0.3063 0.6434 0.004 0.036 0.000 0.864 0.096
#> SRR1617431 4 0.3063 0.6434 0.004 0.036 0.000 0.864 0.096
#> SRR1617410 1 0.0960 0.6764 0.972 0.000 0.008 0.016 0.004
#> SRR1617411 1 0.0833 0.6751 0.976 0.000 0.004 0.016 0.004
#> SRR1617412 3 0.4101 0.5358 0.004 0.000 0.664 0.000 0.332
#> SRR1617413 3 0.3969 0.5722 0.004 0.000 0.692 0.000 0.304
#> SRR1617414 1 0.4915 0.6623 0.728 0.000 0.144 0.124 0.004
#> SRR1617415 1 0.5347 0.6341 0.684 0.000 0.168 0.144 0.004
#> SRR1617416 1 0.5029 0.4837 0.648 0.000 0.000 0.292 0.060
#> SRR1617417 1 0.4777 0.4999 0.664 0.000 0.000 0.292 0.044
#> SRR1617418 5 0.0404 0.7133 0.000 0.000 0.012 0.000 0.988
#> SRR1617419 5 0.0404 0.7133 0.000 0.000 0.012 0.000 0.988
#> SRR1617420 3 0.3001 0.7129 0.144 0.000 0.844 0.004 0.008
#> SRR1617421 3 0.3129 0.7031 0.156 0.000 0.832 0.004 0.008
#> SRR1617422 1 0.6845 0.4102 0.524 0.052 0.072 0.340 0.012
#> SRR1617423 1 0.6891 0.3848 0.500 0.048 0.076 0.364 0.012
#> SRR1617424 1 0.4892 0.5913 0.764 0.028 0.012 0.048 0.148
#> SRR1617425 1 0.4612 0.6082 0.788 0.028 0.008 0.056 0.120
#> SRR1617427 1 0.6528 0.1541 0.432 0.004 0.416 0.144 0.004
#> SRR1617426 3 0.6525 -0.1878 0.408 0.004 0.440 0.144 0.004
#> SRR1617428 4 0.1043 0.6301 0.040 0.000 0.000 0.960 0.000
#> SRR1617429 4 0.1121 0.6283 0.044 0.000 0.000 0.956 0.000
#> SRR1617432 1 0.3994 0.6811 0.792 0.000 0.140 0.068 0.000
#> SRR1617433 1 0.4599 0.6685 0.752 0.000 0.156 0.088 0.004
#> SRR1617434 1 0.3622 0.6862 0.820 0.000 0.124 0.056 0.000
#> SRR1617436 3 0.0963 0.7525 0.000 0.000 0.964 0.000 0.036
#> SRR1617435 1 0.4289 0.6590 0.760 0.000 0.176 0.064 0.000
#> SRR1617437 3 0.0703 0.7552 0.000 0.000 0.976 0.000 0.024
#> SRR1617438 3 0.3724 0.6401 0.000 0.020 0.776 0.000 0.204
#> SRR1617439 3 0.3183 0.6870 0.000 0.016 0.828 0.000 0.156
#> SRR1617440 5 0.6373 0.1445 0.000 0.416 0.164 0.000 0.420
#> SRR1617441 2 0.5974 0.0802 0.000 0.568 0.284 0.000 0.148
#> SRR1617443 3 0.0613 0.7558 0.004 0.000 0.984 0.004 0.008
#> SRR1617442 3 0.0727 0.7561 0.004 0.000 0.980 0.004 0.012
#> SRR1617444 3 0.4062 0.6967 0.148 0.024 0.804 0.012 0.012
#> SRR1617445 3 0.4020 0.6988 0.144 0.024 0.808 0.012 0.012
#> SRR1617446 1 0.5274 0.2366 0.564 0.012 0.012 0.012 0.400
#> SRR1617447 1 0.5023 0.3423 0.620 0.012 0.008 0.012 0.348
#> SRR1617448 1 0.4980 0.6266 0.752 0.044 0.164 0.012 0.028
#> SRR1617449 1 0.4689 0.6217 0.756 0.048 0.176 0.012 0.008
#> SRR1617451 4 0.3639 0.6860 0.000 0.144 0.000 0.812 0.044
#> SRR1617450 4 0.3821 0.6845 0.000 0.148 0.000 0.800 0.052
#> SRR1617452 4 0.4088 0.6091 0.000 0.368 0.000 0.632 0.000
#> SRR1617454 4 0.4211 0.6157 0.000 0.360 0.000 0.636 0.004
#> SRR1617453 4 0.4088 0.6091 0.000 0.368 0.000 0.632 0.000
#> SRR1617456 2 0.0880 0.6747 0.000 0.968 0.000 0.032 0.000
#> SRR1617457 2 0.0880 0.6747 0.000 0.968 0.000 0.032 0.000
#> SRR1617455 4 0.4196 0.6186 0.000 0.356 0.000 0.640 0.004
#> SRR1617458 2 0.0609 0.6744 0.000 0.980 0.000 0.020 0.000
#> SRR1617459 2 0.0609 0.6744 0.000 0.980 0.000 0.020 0.000
#> SRR1617460 2 0.6637 0.3784 0.224 0.568 0.020 0.184 0.004
#> SRR1617461 2 0.6848 0.3341 0.244 0.532 0.020 0.200 0.004
#> SRR1617463 4 0.6575 0.2198 0.152 0.400 0.004 0.440 0.004
#> SRR1617462 4 0.6575 0.2221 0.152 0.400 0.004 0.440 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> SRR1617430 2 0.1700 0.7673 0.000 0.916 0.000 0.080 0.004 0.000
#> SRR1617431 2 0.1644 0.7703 0.000 0.920 0.000 0.076 0.004 0.000
#> SRR1617410 5 0.2418 0.8029 0.092 0.000 0.000 0.016 0.884 0.008
#> SRR1617411 5 0.2648 0.7972 0.092 0.000 0.004 0.020 0.876 0.008
#> SRR1617412 3 0.3384 0.6096 0.004 0.000 0.760 0.228 0.008 0.000
#> SRR1617413 3 0.3056 0.6447 0.004 0.000 0.804 0.184 0.008 0.000
#> SRR1617414 5 0.1555 0.8656 0.008 0.040 0.012 0.000 0.940 0.000
#> SRR1617415 5 0.1821 0.8635 0.008 0.040 0.024 0.000 0.928 0.000
#> SRR1617416 1 0.5653 0.2139 0.640 0.120 0.000 0.056 0.184 0.000
#> SRR1617417 1 0.5596 0.2167 0.640 0.120 0.000 0.048 0.192 0.000
#> SRR1617418 4 0.0603 1.0000 0.000 0.004 0.016 0.980 0.000 0.000
#> SRR1617419 4 0.0603 1.0000 0.000 0.004 0.016 0.980 0.000 0.000
#> SRR1617420 3 0.4033 0.2736 0.004 0.000 0.588 0.004 0.404 0.000
#> SRR1617421 3 0.3944 0.2092 0.004 0.000 0.568 0.000 0.428 0.000
#> SRR1617422 1 0.5928 0.3439 0.584 0.272 0.064 0.000 0.076 0.004
#> SRR1617423 1 0.6312 0.2987 0.540 0.300 0.064 0.000 0.084 0.012
#> SRR1617424 1 0.3212 0.3216 0.840 0.000 0.012 0.100 0.048 0.000
#> SRR1617425 1 0.2648 0.3485 0.884 0.004 0.008 0.064 0.040 0.000
#> SRR1617427 5 0.4679 0.6584 0.012 0.164 0.100 0.004 0.720 0.000
#> SRR1617426 5 0.4807 0.6466 0.012 0.164 0.112 0.004 0.708 0.000
#> SRR1617428 2 0.2520 0.7369 0.108 0.872 0.012 0.000 0.008 0.000
#> SRR1617429 2 0.2473 0.7399 0.104 0.876 0.012 0.000 0.008 0.000
#> SRR1617432 5 0.0508 0.8689 0.004 0.012 0.000 0.000 0.984 0.000
#> SRR1617433 5 0.0748 0.8696 0.004 0.016 0.004 0.000 0.976 0.000
#> SRR1617434 5 0.1237 0.8662 0.020 0.004 0.020 0.000 0.956 0.000
#> SRR1617436 3 0.1219 0.7223 0.048 0.000 0.948 0.004 0.000 0.000
#> SRR1617435 5 0.1116 0.8666 0.008 0.004 0.028 0.000 0.960 0.000
#> SRR1617437 3 0.1141 0.7224 0.052 0.000 0.948 0.000 0.000 0.000
#> SRR1617438 3 0.3253 0.7054 0.096 0.000 0.832 0.068 0.004 0.000
#> SRR1617439 3 0.2968 0.7084 0.092 0.000 0.852 0.052 0.004 0.000
#> SRR1617440 6 0.6747 0.2848 0.044 0.000 0.276 0.224 0.004 0.452
#> SRR1617441 6 0.5640 0.2440 0.044 0.004 0.400 0.036 0.004 0.512
#> SRR1617443 3 0.0937 0.7111 0.000 0.000 0.960 0.000 0.040 0.000
#> SRR1617442 3 0.1196 0.7103 0.000 0.000 0.952 0.008 0.040 0.000
#> SRR1617444 3 0.4689 0.4426 0.340 0.004 0.612 0.004 0.040 0.000
#> SRR1617445 3 0.4615 0.4436 0.340 0.004 0.612 0.000 0.044 0.000
#> SRR1617446 1 0.6523 0.0973 0.356 0.000 0.008 0.348 0.280 0.008
#> SRR1617447 1 0.6503 0.1934 0.380 0.000 0.008 0.272 0.332 0.008
#> SRR1617448 1 0.5512 0.1785 0.504 0.000 0.020 0.032 0.420 0.024
#> SRR1617449 1 0.5353 0.1766 0.512 0.000 0.016 0.016 0.420 0.036
#> SRR1617451 2 0.0713 0.8127 0.000 0.972 0.000 0.000 0.000 0.028
#> SRR1617450 2 0.0713 0.8127 0.000 0.972 0.000 0.000 0.000 0.028
#> SRR1617452 2 0.2613 0.8049 0.012 0.848 0.000 0.000 0.000 0.140
#> SRR1617454 2 0.2482 0.8019 0.004 0.848 0.000 0.000 0.000 0.148
#> SRR1617453 2 0.2613 0.8049 0.012 0.848 0.000 0.000 0.000 0.140
#> SRR1617456 6 0.0458 0.7340 0.000 0.016 0.000 0.000 0.000 0.984
#> SRR1617457 6 0.0458 0.7340 0.000 0.016 0.000 0.000 0.000 0.984
#> SRR1617455 2 0.2482 0.8019 0.004 0.848 0.000 0.000 0.000 0.148
#> SRR1617458 6 0.0405 0.7338 0.004 0.008 0.000 0.000 0.000 0.988
#> SRR1617459 6 0.0405 0.7338 0.004 0.008 0.000 0.000 0.000 0.988
#> SRR1617460 1 0.7564 0.2727 0.388 0.240 0.056 0.000 0.040 0.276
#> SRR1617461 1 0.7767 0.2728 0.376 0.240 0.068 0.000 0.048 0.268
#> SRR1617463 2 0.6138 -0.0842 0.424 0.436 0.028 0.000 0.008 0.104
#> SRR1617462 1 0.6004 -0.0640 0.444 0.432 0.028 0.000 0.008 0.088
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