Date: 2019-12-25 22:24:31 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 10269 rows and 62 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] 10269 62
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:kmeans | 2 | 1.000 | 0.981 | 0.992 | ** | |
| SD:skmeans | 2 | 1.000 | 0.960 | 0.984 | ** | |
| CV:hclust | 2 | 1.000 | 0.969 | 0.982 | ** | |
| CV:skmeans | 2 | 1.000 | 0.970 | 0.987 | ** | |
| MAD:kmeans | 2 | 1.000 | 0.984 | 0.993 | ** | |
| MAD:skmeans | 2 | 1.000 | 0.974 | 0.988 | ** | |
| ATC:skmeans | 2 | 1.000 | 0.981 | 0.991 | ** | |
| CV:kmeans | 2 | 0.965 | 0.912 | 0.967 | ** | |
| SD:pam | 3 | 0.942 | 0.919 | 0.968 | * | 2 |
| ATC:kmeans | 3 | 0.935 | 0.953 | 0.971 | * | 2 |
| MAD:pam | 3 | 0.930 | 0.936 | 0.972 | * | 2 |
| ATC:pam | 3 | 0.907 | 0.907 | 0.942 | * | |
| SD:NMF | 2 | 0.900 | 0.926 | 0.967 | ||
| MAD:NMF | 2 | 0.871 | 0.914 | 0.953 | ||
| CV:pam | 2 | 0.862 | 0.921 | 0.963 | ||
| ATC:NMF | 2 | 0.775 | 0.896 | 0.954 | ||
| SD:hclust | 3 | 0.750 | 0.835 | 0.933 | ||
| MAD:hclust | 5 | 0.738 | 0.810 | 0.925 | ||
| MAD:mclust | 5 | 0.673 | 0.791 | 0.884 | ||
| CV:NMF | 2 | 0.662 | 0.863 | 0.931 | ||
| ATC:hclust | 2 | 0.610 | 0.934 | 0.904 | ||
| CV:mclust | 6 | 0.547 | 0.653 | 0.807 | ||
| ATC:mclust | 2 | 0.528 | 0.887 | 0.923 | ||
| SD:mclust | 3 | 0.283 | 0.669 | 0.775 |
**: 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 0.900 0.926 0.967 0.4898 0.505 0.505
#> CV:NMF 2 0.662 0.863 0.931 0.4772 0.511 0.511
#> MAD:NMF 2 0.871 0.914 0.953 0.4977 0.497 0.497
#> ATC:NMF 2 0.775 0.896 0.954 0.4874 0.511 0.511
#> SD:skmeans 2 1.000 0.960 0.984 0.5010 0.497 0.497
#> CV:skmeans 2 1.000 0.970 0.987 0.5034 0.497 0.497
#> MAD:skmeans 2 1.000 0.974 0.988 0.5022 0.497 0.497
#> ATC:skmeans 2 1.000 0.981 0.991 0.5048 0.494 0.494
#> SD:mclust 2 0.492 0.737 0.866 0.3414 0.748 0.748
#> CV:mclust 2 0.903 0.944 0.980 0.0701 0.968 0.968
#> MAD:mclust 2 0.445 0.735 0.870 0.3247 0.748 0.748
#> ATC:mclust 2 0.528 0.887 0.923 0.4617 0.497 0.497
#> SD:kmeans 2 1.000 0.981 0.992 0.4846 0.518 0.518
#> CV:kmeans 2 0.965 0.912 0.967 0.4509 0.556 0.556
#> MAD:kmeans 2 1.000 0.984 0.993 0.4855 0.518 0.518
#> ATC:kmeans 2 1.000 0.978 0.989 0.4394 0.568 0.568
#> SD:pam 2 0.966 0.960 0.980 0.5011 0.500 0.500
#> CV:pam 2 0.862 0.921 0.963 0.4365 0.556 0.556
#> MAD:pam 2 0.932 0.933 0.971 0.5021 0.497 0.497
#> ATC:pam 2 0.784 0.908 0.946 0.4864 0.492 0.492
#> SD:hclust 2 0.594 0.872 0.879 0.2921 0.581 0.581
#> CV:hclust 2 1.000 0.969 0.982 0.0914 0.906 0.906
#> MAD:hclust 2 0.560 0.857 0.895 0.3502 0.568 0.568
#> ATC:hclust 2 0.610 0.934 0.904 0.3234 0.568 0.568
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.5463 0.649 0.847 0.298 0.791 0.615
#> CV:NMF 3 0.5287 0.727 0.868 0.155 0.867 0.763
#> MAD:NMF 3 0.5348 0.679 0.844 0.261 0.856 0.718
#> ATC:NMF 3 0.5324 0.772 0.859 0.359 0.796 0.609
#> SD:skmeans 3 0.8028 0.841 0.909 0.220 0.871 0.745
#> CV:skmeans 3 0.7344 0.799 0.902 0.241 0.847 0.701
#> MAD:skmeans 3 0.7864 0.812 0.893 0.222 0.871 0.745
#> ATC:skmeans 3 0.8542 0.855 0.927 0.181 0.911 0.820
#> SD:mclust 3 0.2825 0.669 0.775 0.581 0.675 0.575
#> CV:mclust 3 0.0926 0.477 0.728 5.448 0.604 0.591
#> MAD:mclust 3 0.3122 0.616 0.778 0.594 0.689 0.592
#> ATC:mclust 3 0.6122 0.761 0.853 0.238 0.840 0.709
#> SD:kmeans 3 0.8149 0.814 0.900 0.217 0.808 0.649
#> CV:kmeans 3 0.7592 0.811 0.888 0.266 0.778 0.621
#> MAD:kmeans 3 0.7477 0.779 0.894 0.245 0.788 0.616
#> ATC:kmeans 3 0.9350 0.953 0.971 0.368 0.714 0.539
#> SD:pam 3 0.9419 0.919 0.968 0.175 0.914 0.829
#> CV:pam 3 0.7139 0.810 0.930 0.104 0.990 0.982
#> MAD:pam 3 0.9298 0.936 0.972 0.181 0.882 0.771
#> ATC:pam 3 0.9071 0.907 0.942 0.218 0.889 0.776
#> SD:hclust 3 0.7502 0.835 0.933 0.652 0.887 0.814
#> CV:hclust 3 1.0000 0.961 0.987 0.270 0.999 0.999
#> MAD:hclust 3 0.6669 0.781 0.920 0.401 0.870 0.785
#> ATC:hclust 3 0.7528 0.946 0.971 0.460 0.975 0.955
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.520 0.569 0.749 0.1270 0.753 0.466
#> CV:NMF 4 0.465 0.651 0.821 0.2158 0.723 0.481
#> MAD:NMF 4 0.500 0.666 0.794 0.1305 0.750 0.474
#> ATC:NMF 4 0.537 0.593 0.771 0.1167 0.824 0.528
#> SD:skmeans 4 0.613 0.667 0.820 0.1323 0.922 0.803
#> CV:skmeans 4 0.520 0.625 0.774 0.1382 0.943 0.849
#> MAD:skmeans 4 0.549 0.631 0.793 0.1381 0.921 0.799
#> ATC:skmeans 4 0.776 0.723 0.853 0.0739 0.976 0.940
#> SD:mclust 4 0.615 0.758 0.868 0.1162 0.883 0.769
#> CV:mclust 4 0.234 0.531 0.771 0.2223 0.677 0.543
#> MAD:mclust 4 0.579 0.771 0.869 0.1427 0.896 0.795
#> ATC:mclust 4 0.618 0.739 0.779 0.1171 0.918 0.836
#> SD:kmeans 4 0.658 0.714 0.820 0.1253 0.968 0.919
#> CV:kmeans 4 0.843 0.857 0.924 0.0712 0.959 0.897
#> MAD:kmeans 4 0.679 0.652 0.817 0.1194 0.919 0.795
#> ATC:kmeans 4 0.739 0.777 0.881 0.1106 0.906 0.773
#> SD:pam 4 0.802 0.857 0.925 0.0506 0.996 0.990
#> CV:pam 4 0.698 0.795 0.911 0.0931 0.897 0.813
#> MAD:pam 4 0.770 0.878 0.852 0.0481 0.996 0.990
#> ATC:pam 4 1.000 0.940 0.980 0.0591 0.987 0.967
#> SD:hclust 4 0.738 0.852 0.948 0.0176 0.999 0.998
#> CV:hclust 4 0.662 0.845 0.932 2.1815 0.762 0.737
#> MAD:hclust 4 0.695 0.818 0.931 0.0257 0.979 0.959
#> ATC:hclust 4 0.754 0.793 0.903 0.0691 0.971 0.946
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.626 0.668 0.797 0.0807 0.885 0.643
#> CV:NMF 5 0.547 0.457 0.761 0.0943 0.948 0.843
#> MAD:NMF 5 0.563 0.638 0.759 0.0810 0.883 0.646
#> ATC:NMF 5 0.564 0.561 0.750 0.0472 0.946 0.791
#> SD:skmeans 5 0.564 0.576 0.749 0.0775 0.969 0.909
#> CV:skmeans 5 0.522 0.388 0.687 0.0716 0.929 0.795
#> MAD:skmeans 5 0.552 0.512 0.741 0.0668 0.964 0.890
#> ATC:skmeans 5 0.699 0.628 0.801 0.0599 0.999 0.997
#> SD:mclust 5 0.696 0.798 0.876 0.1471 0.878 0.726
#> CV:mclust 5 0.283 0.572 0.746 0.2190 0.785 0.596
#> MAD:mclust 5 0.673 0.791 0.884 0.1677 0.854 0.680
#> ATC:mclust 5 0.457 0.420 0.702 0.0858 0.834 0.653
#> SD:kmeans 5 0.723 0.636 0.828 0.1032 0.815 0.541
#> CV:kmeans 5 0.846 0.848 0.924 0.0385 0.999 0.997
#> MAD:kmeans 5 0.721 0.735 0.833 0.0912 0.802 0.486
#> ATC:kmeans 5 0.738 0.606 0.752 0.1003 0.867 0.649
#> SD:pam 5 0.786 0.873 0.928 0.0202 0.983 0.959
#> CV:pam 5 0.646 0.795 0.916 0.0678 0.997 0.994
#> MAD:pam 5 0.740 0.837 0.925 0.0242 0.991 0.978
#> ATC:pam 5 0.754 0.773 0.845 0.1019 0.973 0.929
#> SD:hclust 5 0.759 0.824 0.938 0.0979 0.958 0.918
#> CV:hclust 5 0.638 0.768 0.902 0.2649 0.860 0.791
#> MAD:hclust 5 0.738 0.810 0.925 0.1022 0.949 0.897
#> ATC:hclust 5 0.757 0.831 0.876 0.0563 0.979 0.959
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.607 0.480 0.716 0.0424 0.936 0.740
#> CV:NMF 6 0.566 0.478 0.697 0.0497 0.867 0.595
#> MAD:NMF 6 0.583 0.503 0.718 0.0449 0.970 0.870
#> ATC:NMF 6 0.615 0.547 0.720 0.0318 0.968 0.859
#> SD:skmeans 6 0.580 0.486 0.717 0.0461 0.966 0.889
#> CV:skmeans 6 0.540 0.328 0.629 0.0483 0.940 0.809
#> MAD:skmeans 6 0.565 0.488 0.710 0.0484 0.997 0.989
#> ATC:skmeans 6 0.655 0.601 0.776 0.0396 0.973 0.930
#> SD:mclust 6 0.679 0.688 0.831 0.0794 0.984 0.952
#> CV:mclust 6 0.547 0.653 0.807 0.0895 0.918 0.763
#> MAD:mclust 6 0.634 0.610 0.803 0.0772 0.969 0.907
#> ATC:mclust 6 0.555 0.330 0.652 0.0526 0.888 0.685
#> SD:kmeans 6 0.679 0.698 0.813 0.0598 0.919 0.715
#> CV:kmeans 6 0.835 0.770 0.896 0.0422 0.973 0.928
#> MAD:kmeans 6 0.693 0.737 0.823 0.0573 0.948 0.800
#> ATC:kmeans 6 0.786 0.847 0.845 0.0571 0.832 0.474
#> SD:pam 6 0.710 0.822 0.907 0.0280 0.987 0.968
#> CV:pam 6 0.619 0.756 0.893 0.0417 0.992 0.981
#> MAD:pam 6 0.728 0.837 0.892 0.0956 0.854 0.641
#> ATC:pam 6 0.714 0.731 0.833 0.0683 0.840 0.586
#> SD:hclust 6 0.777 0.751 0.904 0.0463 0.992 0.982
#> CV:hclust 6 0.610 0.787 0.899 0.0740 0.948 0.902
#> MAD:hclust 6 0.738 0.765 0.898 0.0310 0.937 0.870
#> ATC:hclust 6 0.754 0.781 0.864 0.0486 1.000 1.000
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 10269 rows and 62 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 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 0.594 0.872 0.879 0.2921 0.581 0.581
#> 3 3 0.750 0.835 0.933 0.6525 0.887 0.814
#> 4 4 0.738 0.852 0.948 0.0176 0.999 0.998
#> 5 5 0.759 0.824 0.938 0.0979 0.958 0.918
#> 6 6 0.777 0.751 0.904 0.0463 0.992 0.982
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
#> ERR184078 1 0.9775 0.833 0.588 0.412
#> ERR184093 2 0.0000 0.961 0.000 1.000
#> ERR184051 1 0.9881 0.844 0.564 0.436
#> ERR184076 1 0.9775 0.833 0.588 0.412
#> ERR184043 1 0.9881 0.844 0.564 0.436
#> ERR184037 2 0.7745 0.461 0.228 0.772
#> ERR184059 1 0.9881 0.844 0.564 0.436
#> ERR184055 2 0.6623 0.637 0.172 0.828
#> ERR184065 2 0.0000 0.961 0.000 1.000
#> ERR184069 2 0.0000 0.961 0.000 1.000
#> ERR184040 1 0.9754 0.830 0.592 0.408
#> ERR184057 2 0.0000 0.961 0.000 1.000
#> ERR184082 2 0.0000 0.961 0.000 1.000
#> ERR184083 2 0.0000 0.961 0.000 1.000
#> ERR184039 2 0.0000 0.961 0.000 1.000
#> ERR184064 1 0.9881 0.844 0.564 0.436
#> ERR184081 2 0.0000 0.961 0.000 1.000
#> ERR184095 2 0.0000 0.961 0.000 1.000
#> ERR184079 2 0.0000 0.961 0.000 1.000
#> ERR184084 1 0.9881 0.844 0.564 0.436
#> ERR184068 2 0.0000 0.961 0.000 1.000
#> ERR184067 2 0.0000 0.961 0.000 1.000
#> ERR184071 2 0.0000 0.961 0.000 1.000
#> ERR184042 1 0.0000 0.542 1.000 0.000
#> ERR184063 1 0.9881 0.844 0.564 0.436
#> ERR184091 2 0.0000 0.961 0.000 1.000
#> ERR184061 2 0.0000 0.961 0.000 1.000
#> ERR184077 2 0.0000 0.961 0.000 1.000
#> ERR184062 2 0.0376 0.956 0.004 0.996
#> ERR184053 2 0.0000 0.961 0.000 1.000
#> ERR184088 2 0.0000 0.961 0.000 1.000
#> ERR184075 2 0.0000 0.961 0.000 1.000
#> ERR184041 1 0.9881 0.844 0.564 0.436
#> ERR184060 2 0.0000 0.961 0.000 1.000
#> ERR184035 2 0.0000 0.961 0.000 1.000
#> ERR184086 2 0.0000 0.961 0.000 1.000
#> ERR184080 2 0.4562 0.818 0.096 0.904
#> ERR184050 2 0.0000 0.961 0.000 1.000
#> ERR184047 1 0.0000 0.542 1.000 0.000
#> ERR184092 2 0.0000 0.961 0.000 1.000
#> ERR184072 1 0.9896 0.837 0.560 0.440
#> ERR184073 1 0.9850 0.841 0.572 0.428
#> ERR184066 2 0.3879 0.851 0.076 0.924
#> ERR184098 2 0.0000 0.961 0.000 1.000
#> ERR184044 2 0.0672 0.951 0.008 0.992
#> ERR184054 2 0.9635 -0.336 0.388 0.612
#> ERR184085 2 0.0000 0.961 0.000 1.000
#> ERR184056 2 0.0000 0.961 0.000 1.000
#> ERR184052 2 0.0000 0.961 0.000 1.000
#> ERR184070 2 0.0000 0.961 0.000 1.000
#> ERR184096 1 0.0000 0.542 1.000 0.000
#> ERR184089 2 0.0000 0.961 0.000 1.000
#> ERR184049 2 0.0000 0.961 0.000 1.000
#> ERR184038 2 0.3431 0.870 0.064 0.936
#> ERR184087 1 0.9881 0.844 0.564 0.436
#> ERR184097 2 0.0000 0.961 0.000 1.000
#> ERR184094 1 0.9881 0.844 0.564 0.436
#> ERR184058 2 0.0000 0.961 0.000 1.000
#> ERR184036 2 0.0000 0.961 0.000 1.000
#> ERR184046 2 0.0000 0.961 0.000 1.000
#> ERR184074 1 0.9881 0.844 0.564 0.436
#> ERR184048 2 0.0000 0.961 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.1031 0.818 0.976 0.000 0.024
#> ERR184093 2 0.0747 0.936 0.016 0.984 0.000
#> ERR184051 1 0.0000 0.844 1.000 0.000 0.000
#> ERR184076 1 0.1031 0.818 0.976 0.000 0.024
#> ERR184043 1 0.0000 0.844 1.000 0.000 0.000
#> ERR184037 1 0.5988 0.281 0.632 0.368 0.000
#> ERR184059 1 0.0000 0.844 1.000 0.000 0.000
#> ERR184055 1 0.6235 0.155 0.564 0.436 0.000
#> ERR184065 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184069 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184040 1 0.1411 0.804 0.964 0.000 0.036
#> ERR184057 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184082 2 0.3038 0.875 0.104 0.896 0.000
#> ERR184083 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184039 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184064 1 0.0000 0.844 1.000 0.000 0.000
#> ERR184081 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184095 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184079 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184084 1 0.0000 0.844 1.000 0.000 0.000
#> ERR184068 2 0.2537 0.895 0.080 0.920 0.000
#> ERR184067 2 0.0237 0.940 0.004 0.996 0.000
#> ERR184071 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184042 3 0.0000 0.528 0.000 0.000 1.000
#> ERR184063 1 0.0000 0.844 1.000 0.000 0.000
#> ERR184091 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184061 2 0.3192 0.866 0.112 0.888 0.000
#> ERR184077 2 0.0592 0.937 0.012 0.988 0.000
#> ERR184062 2 0.5216 0.683 0.260 0.740 0.000
#> ERR184053 2 0.1860 0.913 0.052 0.948 0.000
#> ERR184088 2 0.0424 0.939 0.008 0.992 0.000
#> ERR184075 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184041 1 0.0000 0.844 1.000 0.000 0.000
#> ERR184060 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184035 2 0.3038 0.875 0.104 0.896 0.000
#> ERR184086 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184080 2 0.6104 0.505 0.348 0.648 0.004
#> ERR184050 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184047 3 0.6274 0.625 0.456 0.000 0.544
#> ERR184092 2 0.0747 0.936 0.016 0.984 0.000
#> ERR184072 1 0.0237 0.839 0.996 0.004 0.000
#> ERR184073 1 0.0592 0.833 0.988 0.000 0.012
#> ERR184066 2 0.6008 0.460 0.372 0.628 0.000
#> ERR184098 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184044 2 0.4062 0.816 0.164 0.836 0.000
#> ERR184054 1 0.4452 0.516 0.808 0.192 0.000
#> ERR184085 2 0.3192 0.868 0.112 0.888 0.000
#> ERR184056 2 0.0424 0.938 0.008 0.992 0.000
#> ERR184052 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184070 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184096 3 0.6274 0.625 0.456 0.000 0.544
#> ERR184089 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184049 2 0.0747 0.936 0.016 0.984 0.000
#> ERR184038 2 0.5733 0.565 0.324 0.676 0.000
#> ERR184087 1 0.0000 0.844 1.000 0.000 0.000
#> ERR184097 2 0.0592 0.938 0.012 0.988 0.000
#> ERR184094 1 0.0000 0.844 1.000 0.000 0.000
#> ERR184058 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184036 2 0.0747 0.936 0.016 0.984 0.000
#> ERR184046 2 0.0000 0.941 0.000 1.000 0.000
#> ERR184074 1 0.0000 0.844 1.000 0.000 0.000
#> ERR184048 2 0.0237 0.940 0.004 0.996 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.0817 0.870 0.976 0.000 0.024 0
#> ERR184093 2 0.0592 0.933 0.016 0.984 0.000 0
#> ERR184051 1 0.0000 0.887 1.000 0.000 0.000 0
#> ERR184076 1 0.0817 0.870 0.976 0.000 0.024 0
#> ERR184043 1 0.0000 0.887 1.000 0.000 0.000 0
#> ERR184037 1 0.4920 0.372 0.628 0.368 0.004 0
#> ERR184059 1 0.0000 0.887 1.000 0.000 0.000 0
#> ERR184055 1 0.4941 0.165 0.564 0.436 0.000 0
#> ERR184065 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184069 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184040 1 0.1118 0.862 0.964 0.000 0.036 0
#> ERR184057 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184082 2 0.2408 0.872 0.104 0.896 0.000 0
#> ERR184083 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184039 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184064 1 0.0000 0.887 1.000 0.000 0.000 0
#> ERR184081 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184095 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184079 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184084 1 0.0000 0.887 1.000 0.000 0.000 0
#> ERR184068 2 0.2011 0.892 0.080 0.920 0.000 0
#> ERR184067 2 0.0188 0.938 0.004 0.996 0.000 0
#> ERR184071 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184042 4 0.0000 0.000 0.000 0.000 0.000 1
#> ERR184063 1 0.0000 0.887 1.000 0.000 0.000 0
#> ERR184091 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184061 2 0.2530 0.862 0.112 0.888 0.000 0
#> ERR184077 2 0.0469 0.935 0.012 0.988 0.000 0
#> ERR184062 2 0.4134 0.681 0.260 0.740 0.000 0
#> ERR184053 2 0.1474 0.910 0.052 0.948 0.000 0
#> ERR184088 2 0.0336 0.937 0.008 0.992 0.000 0
#> ERR184075 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184041 1 0.0000 0.887 1.000 0.000 0.000 0
#> ERR184060 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184035 2 0.2408 0.872 0.104 0.896 0.000 0
#> ERR184086 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184080 2 0.4837 0.502 0.348 0.648 0.004 0
#> ERR184050 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184047 3 0.0000 1.000 0.000 0.000 1.000 0
#> ERR184092 2 0.0592 0.933 0.016 0.984 0.000 0
#> ERR184072 1 0.0188 0.884 0.996 0.004 0.000 0
#> ERR184073 1 0.0469 0.880 0.988 0.000 0.012 0
#> ERR184066 2 0.4761 0.456 0.372 0.628 0.000 0
#> ERR184098 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184044 2 0.3219 0.813 0.164 0.836 0.000 0
#> ERR184054 1 0.3528 0.625 0.808 0.192 0.000 0
#> ERR184085 2 0.2530 0.865 0.112 0.888 0.000 0
#> ERR184056 2 0.0336 0.936 0.008 0.992 0.000 0
#> ERR184052 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184070 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184096 3 0.0000 1.000 0.000 0.000 1.000 0
#> ERR184089 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184049 2 0.0592 0.934 0.016 0.984 0.000 0
#> ERR184038 2 0.4543 0.562 0.324 0.676 0.000 0
#> ERR184087 1 0.0000 0.887 1.000 0.000 0.000 0
#> ERR184097 2 0.0469 0.935 0.012 0.988 0.000 0
#> ERR184094 1 0.0000 0.887 1.000 0.000 0.000 0
#> ERR184058 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184036 2 0.0592 0.934 0.016 0.984 0.000 0
#> ERR184046 2 0.0000 0.938 0.000 1.000 0.000 0
#> ERR184074 1 0.0000 0.887 1.000 0.000 0.000 0
#> ERR184048 2 0.0188 0.938 0.004 0.996 0.000 0
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.0992 0.642 0.968 0.000 0.008 0 0.024
#> ERR184093 2 0.0510 0.933 0.016 0.984 0.000 0 0.000
#> ERR184051 3 0.0000 1.000 0.000 0.000 1.000 0 0.000
#> ERR184076 1 0.0865 0.641 0.972 0.000 0.004 0 0.024
#> ERR184043 3 0.0000 1.000 0.000 0.000 1.000 0 0.000
#> ERR184037 1 0.4225 0.372 0.632 0.364 0.000 0 0.004
#> ERR184059 3 0.0000 1.000 0.000 0.000 1.000 0 0.000
#> ERR184055 1 0.4249 0.196 0.568 0.432 0.000 0 0.000
#> ERR184065 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184069 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184040 1 0.1661 0.631 0.940 0.000 0.024 0 0.036
#> ERR184057 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184082 2 0.2074 0.869 0.104 0.896 0.000 0 0.000
#> ERR184083 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184039 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184064 3 0.0000 1.000 0.000 0.000 1.000 0 0.000
#> ERR184081 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184095 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184079 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184084 3 0.0000 1.000 0.000 0.000 1.000 0 0.000
#> ERR184068 2 0.1732 0.891 0.080 0.920 0.000 0 0.000
#> ERR184067 2 0.0162 0.938 0.004 0.996 0.000 0 0.000
#> ERR184071 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184042 4 0.0000 0.000 0.000 0.000 0.000 1 0.000
#> ERR184063 3 0.0000 1.000 0.000 0.000 1.000 0 0.000
#> ERR184091 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184061 2 0.2230 0.855 0.116 0.884 0.000 0 0.000
#> ERR184077 2 0.0404 0.935 0.012 0.988 0.000 0 0.000
#> ERR184062 2 0.3561 0.666 0.260 0.740 0.000 0 0.000
#> ERR184053 2 0.1270 0.910 0.052 0.948 0.000 0 0.000
#> ERR184088 2 0.0290 0.937 0.008 0.992 0.000 0 0.000
#> ERR184075 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184041 3 0.0000 1.000 0.000 0.000 1.000 0 0.000
#> ERR184060 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184035 2 0.2074 0.869 0.104 0.896 0.000 0 0.000
#> ERR184086 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184080 2 0.4182 0.466 0.352 0.644 0.000 0 0.004
#> ERR184050 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184047 5 0.0000 1.000 0.000 0.000 0.000 0 1.000
#> ERR184092 2 0.0510 0.933 0.016 0.984 0.000 0 0.000
#> ERR184072 1 0.0000 0.645 1.000 0.000 0.000 0 0.000
#> ERR184073 1 0.1106 0.642 0.964 0.000 0.024 0 0.012
#> ERR184066 2 0.4114 0.418 0.376 0.624 0.000 0 0.000
#> ERR184098 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184044 2 0.2813 0.801 0.168 0.832 0.000 0 0.000
#> ERR184054 1 0.3282 0.516 0.804 0.188 0.008 0 0.000
#> ERR184085 2 0.2179 0.862 0.112 0.888 0.000 0 0.000
#> ERR184056 2 0.0290 0.937 0.008 0.992 0.000 0 0.000
#> ERR184052 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184070 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184096 5 0.0000 1.000 0.000 0.000 0.000 0 1.000
#> ERR184089 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184049 2 0.0510 0.935 0.016 0.984 0.000 0 0.000
#> ERR184038 2 0.3932 0.532 0.328 0.672 0.000 0 0.000
#> ERR184087 3 0.0000 1.000 0.000 0.000 1.000 0 0.000
#> ERR184097 2 0.0404 0.936 0.012 0.988 0.000 0 0.000
#> ERR184094 1 0.4305 -0.136 0.512 0.000 0.488 0 0.000
#> ERR184058 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184036 2 0.0609 0.932 0.020 0.980 0.000 0 0.000
#> ERR184046 2 0.0000 0.939 0.000 1.000 0.000 0 0.000
#> ERR184074 1 0.0404 0.647 0.988 0.000 0.012 0 0.000
#> ERR184048 2 0.0162 0.938 0.004 0.996 0.000 0 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.3954 0.40342 0.620 0.000 0.004 0 0.004 0.372
#> ERR184093 2 0.0603 0.88864 0.004 0.980 0.000 0 0.000 0.016
#> ERR184051 3 0.0000 1.00000 0.000 0.000 1.000 0 0.000 0.000
#> ERR184076 1 0.3862 0.38874 0.608 0.000 0.000 0 0.004 0.388
#> ERR184043 3 0.0000 1.00000 0.000 0.000 1.000 0 0.000 0.000
#> ERR184037 6 0.5190 0.82150 0.128 0.280 0.000 0 0.000 0.592
#> ERR184059 3 0.0000 1.00000 0.000 0.000 1.000 0 0.000 0.000
#> ERR184055 6 0.5310 0.84091 0.116 0.348 0.000 0 0.000 0.536
#> ERR184065 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184069 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184040 1 0.1949 0.57374 0.924 0.000 0.020 0 0.020 0.036
#> ERR184057 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184082 2 0.2651 0.74700 0.028 0.860 0.000 0 0.000 0.112
#> ERR184083 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184039 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184064 3 0.0000 1.00000 0.000 0.000 1.000 0 0.000 0.000
#> ERR184081 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184095 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184079 2 0.0146 0.89806 0.000 0.996 0.000 0 0.000 0.004
#> ERR184084 3 0.0000 1.00000 0.000 0.000 1.000 0 0.000 0.000
#> ERR184068 2 0.1779 0.82803 0.016 0.920 0.000 0 0.000 0.064
#> ERR184067 2 0.0146 0.89793 0.000 0.996 0.000 0 0.000 0.004
#> ERR184071 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184042 4 0.0000 0.00000 0.000 0.000 0.000 1 0.000 0.000
#> ERR184063 3 0.0000 1.00000 0.000 0.000 1.000 0 0.000 0.000
#> ERR184091 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184061 2 0.3134 0.64728 0.024 0.808 0.000 0 0.000 0.168
#> ERR184077 2 0.0405 0.89344 0.004 0.988 0.000 0 0.000 0.008
#> ERR184062 2 0.4565 0.31259 0.096 0.684 0.000 0 0.000 0.220
#> ERR184053 2 0.1219 0.85611 0.004 0.948 0.000 0 0.000 0.048
#> ERR184088 2 0.0260 0.89603 0.000 0.992 0.000 0 0.000 0.008
#> ERR184075 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184041 3 0.0000 1.00000 0.000 0.000 1.000 0 0.000 0.000
#> ERR184060 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184035 2 0.2651 0.74700 0.028 0.860 0.000 0 0.000 0.112
#> ERR184086 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184080 2 0.5437 -0.18474 0.196 0.576 0.000 0 0.000 0.228
#> ERR184050 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184047 5 0.0000 1.00000 0.000 0.000 0.000 0 1.000 0.000
#> ERR184092 2 0.0603 0.88864 0.004 0.980 0.000 0 0.000 0.016
#> ERR184072 1 0.2491 0.55458 0.836 0.000 0.000 0 0.000 0.164
#> ERR184073 1 0.1364 0.57996 0.952 0.000 0.020 0 0.012 0.016
#> ERR184066 2 0.5506 -0.26545 0.180 0.556 0.000 0 0.000 0.264
#> ERR184098 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184044 2 0.3454 0.56857 0.024 0.768 0.000 0 0.000 0.208
#> ERR184054 1 0.4342 0.25621 0.740 0.152 0.008 0 0.000 0.100
#> ERR184085 2 0.2826 0.72143 0.028 0.844 0.000 0 0.000 0.128
#> ERR184056 2 0.0260 0.89479 0.008 0.992 0.000 0 0.000 0.000
#> ERR184052 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184070 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184096 5 0.0000 1.00000 0.000 0.000 0.000 0 1.000 0.000
#> ERR184089 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184049 2 0.0603 0.88957 0.004 0.980 0.000 0 0.000 0.016
#> ERR184038 2 0.5183 -0.04971 0.140 0.604 0.000 0 0.000 0.256
#> ERR184087 3 0.0000 1.00000 0.000 0.000 1.000 0 0.000 0.000
#> ERR184097 2 0.0405 0.89419 0.004 0.988 0.000 0 0.000 0.008
#> ERR184094 1 0.3866 0.00265 0.516 0.000 0.484 0 0.000 0.000
#> ERR184058 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184036 2 0.0777 0.88247 0.004 0.972 0.000 0 0.000 0.024
#> ERR184046 2 0.0000 0.89910 0.000 1.000 0.000 0 0.000 0.000
#> ERR184074 1 0.4089 0.30819 0.524 0.000 0.008 0 0.000 0.468
#> ERR184048 2 0.0146 0.89781 0.000 0.996 0.000 0 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
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 10269 rows and 62 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.981 0.992 0.4846 0.518 0.518
#> 3 3 0.815 0.814 0.900 0.2165 0.808 0.649
#> 4 4 0.658 0.714 0.820 0.1253 0.968 0.919
#> 5 5 0.723 0.636 0.828 0.1032 0.815 0.541
#> 6 6 0.679 0.698 0.813 0.0598 0.919 0.715
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
#> ERR184078 1 0.0000 0.995 1.000 0.000
#> ERR184093 2 0.0000 0.989 0.000 1.000
#> ERR184051 1 0.0000 0.995 1.000 0.000
#> ERR184076 1 0.0000 0.995 1.000 0.000
#> ERR184043 1 0.0000 0.995 1.000 0.000
#> ERR184037 1 0.0938 0.988 0.988 0.012
#> ERR184059 1 0.0000 0.995 1.000 0.000
#> ERR184055 1 0.2236 0.966 0.964 0.036
#> ERR184065 2 0.0000 0.989 0.000 1.000
#> ERR184069 2 0.0000 0.989 0.000 1.000
#> ERR184040 1 0.0000 0.995 1.000 0.000
#> ERR184057 2 0.0000 0.989 0.000 1.000
#> ERR184082 2 0.0000 0.989 0.000 1.000
#> ERR184083 2 0.0000 0.989 0.000 1.000
#> ERR184039 2 0.0000 0.989 0.000 1.000
#> ERR184064 1 0.0000 0.995 1.000 0.000
#> ERR184081 2 0.0000 0.989 0.000 1.000
#> ERR184095 2 0.0000 0.989 0.000 1.000
#> ERR184079 2 0.0000 0.989 0.000 1.000
#> ERR184084 1 0.0000 0.995 1.000 0.000
#> ERR184068 2 0.0000 0.989 0.000 1.000
#> ERR184067 2 0.0000 0.989 0.000 1.000
#> ERR184071 2 0.0000 0.989 0.000 1.000
#> ERR184042 1 0.0000 0.995 1.000 0.000
#> ERR184063 1 0.0000 0.995 1.000 0.000
#> ERR184091 2 0.0000 0.989 0.000 1.000
#> ERR184061 2 0.0000 0.989 0.000 1.000
#> ERR184077 2 0.0000 0.989 0.000 1.000
#> ERR184062 2 0.0000 0.989 0.000 1.000
#> ERR184053 2 0.0000 0.989 0.000 1.000
#> ERR184088 2 0.0000 0.989 0.000 1.000
#> ERR184075 2 0.0000 0.989 0.000 1.000
#> ERR184041 1 0.0000 0.995 1.000 0.000
#> ERR184060 2 0.0000 0.989 0.000 1.000
#> ERR184035 2 0.2778 0.944 0.048 0.952
#> ERR184086 2 0.0000 0.989 0.000 1.000
#> ERR184080 1 0.0938 0.988 0.988 0.012
#> ERR184050 2 0.0000 0.989 0.000 1.000
#> ERR184047 1 0.0000 0.995 1.000 0.000
#> ERR184092 2 0.0000 0.989 0.000 1.000
#> ERR184072 1 0.0000 0.995 1.000 0.000
#> ERR184073 1 0.0000 0.995 1.000 0.000
#> ERR184066 1 0.2236 0.966 0.964 0.036
#> ERR184098 2 0.0000 0.989 0.000 1.000
#> ERR184044 2 0.9000 0.536 0.316 0.684
#> ERR184054 1 0.0000 0.995 1.000 0.000
#> ERR184085 2 0.2948 0.940 0.052 0.948
#> ERR184056 2 0.0000 0.989 0.000 1.000
#> ERR184052 2 0.0000 0.989 0.000 1.000
#> ERR184070 2 0.0000 0.989 0.000 1.000
#> ERR184096 1 0.0000 0.995 1.000 0.000
#> ERR184089 2 0.0000 0.989 0.000 1.000
#> ERR184049 2 0.0000 0.989 0.000 1.000
#> ERR184038 1 0.0938 0.988 0.988 0.012
#> ERR184087 1 0.0000 0.995 1.000 0.000
#> ERR184097 2 0.0000 0.989 0.000 1.000
#> ERR184094 1 0.0000 0.995 1.000 0.000
#> ERR184058 2 0.0000 0.989 0.000 1.000
#> ERR184036 2 0.0000 0.989 0.000 1.000
#> ERR184046 2 0.0000 0.989 0.000 1.000
#> ERR184074 1 0.0000 0.995 1.000 0.000
#> ERR184048 2 0.0000 0.989 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.1964 0.6876 0.944 0.000 0.056
#> ERR184093 2 0.0592 0.9737 0.012 0.988 0.000
#> ERR184051 3 0.5138 0.7836 0.252 0.000 0.748
#> ERR184076 1 0.1643 0.7001 0.956 0.000 0.044
#> ERR184043 3 0.4702 0.8040 0.212 0.000 0.788
#> ERR184037 1 0.0237 0.7300 0.996 0.000 0.004
#> ERR184059 3 0.4555 0.8027 0.200 0.000 0.800
#> ERR184055 1 0.0592 0.7306 0.988 0.000 0.012
#> ERR184065 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184069 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184040 1 0.3879 0.5229 0.848 0.000 0.152
#> ERR184057 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184082 1 0.6244 0.2807 0.560 0.440 0.000
#> ERR184083 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184039 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184064 3 0.4702 0.8040 0.212 0.000 0.788
#> ERR184081 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184095 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184079 2 0.1289 0.9610 0.032 0.968 0.000
#> ERR184084 3 0.4654 0.8031 0.208 0.000 0.792
#> ERR184068 2 0.2165 0.9336 0.064 0.936 0.000
#> ERR184067 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184071 2 0.0592 0.9737 0.012 0.988 0.000
#> ERR184042 3 0.0424 0.6703 0.008 0.000 0.992
#> ERR184063 3 0.6079 0.6191 0.388 0.000 0.612
#> ERR184091 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184061 1 0.6309 0.0677 0.500 0.500 0.000
#> ERR184077 2 0.1643 0.9519 0.044 0.956 0.000
#> ERR184062 2 0.3482 0.8564 0.128 0.872 0.000
#> ERR184053 2 0.1643 0.9519 0.044 0.956 0.000
#> ERR184088 2 0.0592 0.9737 0.012 0.988 0.000
#> ERR184075 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184041 3 0.5785 0.7058 0.332 0.000 0.668
#> ERR184060 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184035 1 0.5397 0.5039 0.720 0.280 0.000
#> ERR184086 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184080 1 0.0237 0.7300 0.996 0.000 0.004
#> ERR184050 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184047 3 0.4974 0.6130 0.236 0.000 0.764
#> ERR184092 2 0.0592 0.9737 0.012 0.988 0.000
#> ERR184072 1 0.0592 0.7306 0.988 0.000 0.012
#> ERR184073 3 0.6305 0.5547 0.484 0.000 0.516
#> ERR184066 1 0.0592 0.7306 0.988 0.000 0.012
#> ERR184098 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184044 1 0.2866 0.6796 0.916 0.076 0.008
#> ERR184054 1 0.0747 0.7287 0.984 0.000 0.016
#> ERR184085 1 0.5465 0.4937 0.712 0.288 0.000
#> ERR184056 2 0.0592 0.9737 0.012 0.988 0.000
#> ERR184052 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184070 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184096 3 0.5216 0.5923 0.260 0.000 0.740
#> ERR184089 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184049 2 0.5216 0.6270 0.260 0.740 0.000
#> ERR184038 1 0.2796 0.6643 0.908 0.000 0.092
#> ERR184087 3 0.4702 0.8040 0.212 0.000 0.788
#> ERR184097 2 0.0592 0.9737 0.012 0.988 0.000
#> ERR184094 3 0.6244 0.6291 0.440 0.000 0.560
#> ERR184058 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184036 2 0.0592 0.9737 0.012 0.988 0.000
#> ERR184046 2 0.0000 0.9768 0.000 1.000 0.000
#> ERR184074 1 0.1289 0.7101 0.968 0.000 0.032
#> ERR184048 2 0.1643 0.9519 0.044 0.956 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.4671 0.539 0.752 0.000 0.028 0.220
#> ERR184093 2 0.4153 0.818 0.048 0.820 0.000 0.132
#> ERR184051 3 0.1284 0.852 0.024 0.000 0.964 0.012
#> ERR184076 1 0.4194 0.596 0.800 0.000 0.028 0.172
#> ERR184043 3 0.0592 0.857 0.016 0.000 0.984 0.000
#> ERR184037 1 0.0927 0.703 0.976 0.000 0.008 0.016
#> ERR184059 3 0.4356 0.465 0.000 0.000 0.708 0.292
#> ERR184055 1 0.0804 0.703 0.980 0.000 0.008 0.012
#> ERR184065 2 0.0188 0.867 0.000 0.996 0.000 0.004
#> ERR184069 2 0.0000 0.867 0.000 1.000 0.000 0.000
#> ERR184040 1 0.5527 0.284 0.616 0.000 0.028 0.356
#> ERR184057 2 0.0000 0.867 0.000 1.000 0.000 0.000
#> ERR184082 1 0.6714 0.438 0.616 0.208 0.000 0.176
#> ERR184083 2 0.0000 0.867 0.000 1.000 0.000 0.000
#> ERR184039 2 0.0188 0.867 0.000 0.996 0.000 0.004
#> ERR184064 3 0.0592 0.857 0.016 0.000 0.984 0.000
#> ERR184081 2 0.0000 0.867 0.000 1.000 0.000 0.000
#> ERR184095 2 0.0000 0.867 0.000 1.000 0.000 0.000
#> ERR184079 2 0.6323 0.695 0.176 0.660 0.000 0.164
#> ERR184084 3 0.4621 0.480 0.008 0.000 0.708 0.284
#> ERR184068 2 0.6695 0.635 0.220 0.616 0.000 0.164
#> ERR184067 2 0.0000 0.867 0.000 1.000 0.000 0.000
#> ERR184071 2 0.4898 0.791 0.072 0.772 0.000 0.156
#> ERR184042 4 0.4605 0.355 0.000 0.000 0.336 0.664
#> ERR184063 3 0.1936 0.828 0.028 0.000 0.940 0.032
#> ERR184091 2 0.0188 0.867 0.000 0.996 0.000 0.004
#> ERR184061 1 0.6071 0.526 0.684 0.144 0.000 0.172
#> ERR184077 2 0.6279 0.696 0.180 0.664 0.000 0.156
#> ERR184062 2 0.7079 0.534 0.276 0.556 0.000 0.168
#> ERR184053 2 0.6279 0.696 0.180 0.664 0.000 0.156
#> ERR184088 2 0.5174 0.777 0.092 0.756 0.000 0.152
#> ERR184075 2 0.0188 0.867 0.000 0.996 0.000 0.004
#> ERR184041 3 0.1510 0.847 0.028 0.000 0.956 0.016
#> ERR184060 2 0.0000 0.867 0.000 1.000 0.000 0.000
#> ERR184035 1 0.4544 0.622 0.788 0.048 0.000 0.164
#> ERR184086 2 0.0188 0.867 0.000 0.996 0.000 0.004
#> ERR184080 1 0.1042 0.701 0.972 0.000 0.008 0.020
#> ERR184050 2 0.0188 0.867 0.000 0.996 0.000 0.004
#> ERR184047 4 0.4318 0.698 0.116 0.000 0.068 0.816
#> ERR184092 2 0.3793 0.828 0.044 0.844 0.000 0.112
#> ERR184072 1 0.2949 0.667 0.888 0.000 0.024 0.088
#> ERR184073 1 0.6589 0.140 0.556 0.000 0.092 0.352
#> ERR184066 1 0.0804 0.703 0.980 0.000 0.008 0.012
#> ERR184098 2 0.0188 0.867 0.000 0.996 0.000 0.004
#> ERR184044 1 0.3311 0.647 0.828 0.000 0.000 0.172
#> ERR184054 1 0.3143 0.660 0.876 0.000 0.024 0.100
#> ERR184085 1 0.5376 0.584 0.736 0.088 0.000 0.176
#> ERR184056 2 0.3674 0.829 0.036 0.848 0.000 0.116
#> ERR184052 2 0.0469 0.866 0.000 0.988 0.000 0.012
#> ERR184070 2 0.0000 0.867 0.000 1.000 0.000 0.000
#> ERR184096 4 0.4282 0.695 0.124 0.000 0.060 0.816
#> ERR184089 2 0.0188 0.867 0.000 0.996 0.000 0.004
#> ERR184049 2 0.7426 0.278 0.376 0.452 0.000 0.172
#> ERR184038 1 0.3958 0.658 0.816 0.000 0.024 0.160
#> ERR184087 3 0.0592 0.857 0.016 0.000 0.984 0.000
#> ERR184097 2 0.3850 0.825 0.044 0.840 0.000 0.116
#> ERR184094 4 0.7474 0.312 0.176 0.000 0.400 0.424
#> ERR184058 2 0.0000 0.867 0.000 1.000 0.000 0.000
#> ERR184036 2 0.4740 0.801 0.080 0.788 0.000 0.132
#> ERR184046 2 0.0000 0.867 0.000 1.000 0.000 0.000
#> ERR184074 1 0.4238 0.593 0.796 0.000 0.028 0.176
#> ERR184048 2 0.6310 0.691 0.188 0.660 0.000 0.152
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.1750 0.5344 0.936 0.000 0.000 0.036 0.028
#> ERR184093 2 0.4948 -0.0561 0.000 0.536 0.000 0.436 0.028
#> ERR184051 3 0.0290 0.8413 0.000 0.000 0.992 0.008 0.000
#> ERR184076 1 0.3574 0.6528 0.804 0.000 0.000 0.168 0.028
#> ERR184043 3 0.0000 0.8422 0.000 0.000 1.000 0.000 0.000
#> ERR184037 1 0.4650 0.6139 0.520 0.000 0.000 0.468 0.012
#> ERR184059 3 0.6098 0.2832 0.196 0.000 0.568 0.000 0.236
#> ERR184055 1 0.4653 0.6114 0.516 0.000 0.000 0.472 0.012
#> ERR184065 2 0.1197 0.8616 0.000 0.952 0.000 0.000 0.048
#> ERR184069 2 0.0000 0.8670 0.000 1.000 0.000 0.000 0.000
#> ERR184040 1 0.1195 0.4997 0.960 0.000 0.000 0.012 0.028
#> ERR184057 2 0.0290 0.8656 0.000 0.992 0.000 0.000 0.008
#> ERR184082 4 0.0290 0.6179 0.000 0.000 0.000 0.992 0.008
#> ERR184083 2 0.0000 0.8670 0.000 1.000 0.000 0.000 0.000
#> ERR184039 2 0.1197 0.8616 0.000 0.952 0.000 0.000 0.048
#> ERR184064 3 0.0000 0.8422 0.000 0.000 1.000 0.000 0.000
#> ERR184081 2 0.0000 0.8670 0.000 1.000 0.000 0.000 0.000
#> ERR184095 2 0.0162 0.8665 0.000 0.996 0.000 0.000 0.004
#> ERR184079 4 0.4024 0.6589 0.000 0.220 0.000 0.752 0.028
#> ERR184084 3 0.6346 0.2553 0.212 0.000 0.548 0.004 0.236
#> ERR184068 4 0.3355 0.6805 0.000 0.184 0.000 0.804 0.012
#> ERR184067 2 0.0290 0.8656 0.000 0.992 0.000 0.000 0.008
#> ERR184071 4 0.5106 0.2421 0.000 0.456 0.000 0.508 0.036
#> ERR184042 5 0.2574 0.5966 0.012 0.000 0.112 0.000 0.876
#> ERR184063 3 0.0290 0.8413 0.000 0.000 0.992 0.008 0.000
#> ERR184091 2 0.1043 0.8622 0.000 0.960 0.000 0.000 0.040
#> ERR184061 4 0.1525 0.6200 0.012 0.004 0.000 0.948 0.036
#> ERR184077 4 0.4446 0.4346 0.000 0.400 0.000 0.592 0.008
#> ERR184062 4 0.3012 0.6741 0.000 0.124 0.000 0.852 0.024
#> ERR184053 4 0.4527 0.4489 0.000 0.392 0.000 0.596 0.012
#> ERR184088 4 0.4902 0.2431 0.000 0.468 0.000 0.508 0.024
#> ERR184075 2 0.1197 0.8616 0.000 0.952 0.000 0.000 0.048
#> ERR184041 3 0.0290 0.8413 0.000 0.000 0.992 0.008 0.000
#> ERR184060 2 0.0000 0.8670 0.000 1.000 0.000 0.000 0.000
#> ERR184035 4 0.0566 0.6168 0.004 0.000 0.000 0.984 0.012
#> ERR184086 2 0.1197 0.8616 0.000 0.952 0.000 0.000 0.048
#> ERR184080 1 0.4375 0.6397 0.576 0.000 0.000 0.420 0.004
#> ERR184050 2 0.1197 0.8616 0.000 0.952 0.000 0.000 0.048
#> ERR184047 5 0.4165 0.8201 0.320 0.000 0.008 0.000 0.672
#> ERR184092 2 0.4546 0.4014 0.000 0.668 0.000 0.304 0.028
#> ERR184072 1 0.3635 0.6815 0.748 0.000 0.000 0.248 0.004
#> ERR184073 1 0.0579 0.5159 0.984 0.000 0.008 0.008 0.000
#> ERR184066 1 0.4443 0.6158 0.524 0.000 0.000 0.472 0.004
#> ERR184098 2 0.1478 0.8578 0.000 0.936 0.000 0.000 0.064
#> ERR184044 4 0.1549 0.5709 0.040 0.000 0.000 0.944 0.016
#> ERR184054 1 0.3579 0.6824 0.756 0.000 0.000 0.240 0.004
#> ERR184085 4 0.0404 0.6162 0.000 0.000 0.000 0.988 0.012
#> ERR184056 2 0.4219 0.5009 0.000 0.716 0.000 0.260 0.024
#> ERR184052 2 0.1522 0.8363 0.000 0.944 0.000 0.044 0.012
#> ERR184070 2 0.0162 0.8665 0.000 0.996 0.000 0.000 0.004
#> ERR184096 5 0.4201 0.8164 0.328 0.000 0.008 0.000 0.664
#> ERR184089 2 0.1197 0.8616 0.000 0.952 0.000 0.000 0.048
#> ERR184049 4 0.1195 0.6386 0.000 0.028 0.000 0.960 0.012
#> ERR184038 4 0.2689 0.4763 0.084 0.000 0.016 0.888 0.012
#> ERR184087 3 0.0000 0.8422 0.000 0.000 1.000 0.000 0.000
#> ERR184097 2 0.4624 0.2974 0.000 0.636 0.000 0.340 0.024
#> ERR184094 1 0.6529 -0.4196 0.476 0.000 0.296 0.000 0.228
#> ERR184058 2 0.0404 0.8660 0.000 0.988 0.000 0.000 0.012
#> ERR184036 2 0.5296 -0.2292 0.000 0.480 0.000 0.472 0.048
#> ERR184046 2 0.0000 0.8670 0.000 1.000 0.000 0.000 0.000
#> ERR184074 1 0.2852 0.6647 0.828 0.000 0.000 0.172 0.000
#> ERR184048 4 0.4415 0.4582 0.000 0.388 0.000 0.604 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.2088 0.7182 0.904 0.000 0.000 NA 0.068 0.000
#> ERR184093 6 0.4592 0.6328 0.000 0.268 0.000 NA 0.004 0.664
#> ERR184051 3 0.0000 0.8350 0.000 0.000 1.000 NA 0.000 0.000
#> ERR184076 1 0.2251 0.7270 0.904 0.000 0.000 NA 0.052 0.008
#> ERR184043 3 0.0000 0.8350 0.000 0.000 1.000 NA 0.000 0.000
#> ERR184037 1 0.5522 0.5829 0.544 0.000 0.000 NA 0.000 0.168
#> ERR184059 3 0.4435 0.2442 0.004 0.000 0.576 NA 0.400 0.004
#> ERR184055 1 0.5523 0.6005 0.552 0.000 0.000 NA 0.000 0.180
#> ERR184065 2 0.2191 0.8854 0.000 0.876 0.000 NA 0.004 0.000
#> ERR184069 2 0.0000 0.9001 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184040 1 0.2667 0.6880 0.852 0.000 0.000 NA 0.128 0.000
#> ERR184057 2 0.0260 0.8978 0.000 0.992 0.000 NA 0.000 0.008
#> ERR184082 6 0.3673 0.5845 0.016 0.004 0.000 NA 0.000 0.736
#> ERR184083 2 0.0260 0.9006 0.000 0.992 0.000 NA 0.000 0.000
#> ERR184039 2 0.2191 0.8854 0.000 0.876 0.000 NA 0.004 0.000
#> ERR184064 3 0.0000 0.8350 0.000 0.000 1.000 NA 0.000 0.000
#> ERR184081 2 0.0146 0.8991 0.000 0.996 0.000 NA 0.000 0.004
#> ERR184095 2 0.0260 0.8978 0.000 0.992 0.000 NA 0.000 0.008
#> ERR184079 6 0.2711 0.7054 0.000 0.068 0.000 NA 0.004 0.872
#> ERR184084 3 0.6073 0.0191 0.016 0.000 0.460 NA 0.400 0.012
#> ERR184068 6 0.2138 0.6960 0.004 0.052 0.000 NA 0.000 0.908
#> ERR184067 2 0.0622 0.8942 0.000 0.980 0.000 NA 0.000 0.012
#> ERR184071 6 0.4294 0.6896 0.000 0.188 0.000 NA 0.004 0.728
#> ERR184042 5 0.4319 0.5709 0.000 0.000 0.032 NA 0.620 0.000
#> ERR184063 3 0.0000 0.8350 0.000 0.000 1.000 NA 0.000 0.000
#> ERR184091 2 0.2053 0.8881 0.000 0.888 0.000 NA 0.004 0.000
#> ERR184061 6 0.4111 0.6135 0.028 0.012 0.000 NA 0.000 0.716
#> ERR184077 6 0.3141 0.7068 0.000 0.200 0.000 NA 0.000 0.788
#> ERR184062 6 0.2822 0.6976 0.012 0.048 0.000 NA 0.004 0.876
#> ERR184053 6 0.3488 0.7072 0.000 0.184 0.000 NA 0.000 0.780
#> ERR184088 6 0.4145 0.6883 0.000 0.220 0.000 NA 0.004 0.724
#> ERR184075 2 0.2191 0.8854 0.000 0.876 0.000 NA 0.004 0.000
#> ERR184041 3 0.0000 0.8350 0.000 0.000 1.000 NA 0.000 0.000
#> ERR184060 2 0.0000 0.9001 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184035 6 0.3697 0.5826 0.016 0.004 0.000 NA 0.000 0.732
#> ERR184086 2 0.2234 0.8843 0.000 0.872 0.000 NA 0.004 0.000
#> ERR184080 1 0.4465 0.7020 0.712 0.000 0.000 NA 0.000 0.144
#> ERR184050 2 0.3314 0.8595 0.000 0.820 0.000 NA 0.004 0.048
#> ERR184047 5 0.0363 0.7016 0.012 0.000 0.000 NA 0.988 0.000
#> ERR184092 6 0.4968 0.3190 0.000 0.432 0.000 NA 0.004 0.508
#> ERR184072 1 0.1572 0.7585 0.936 0.000 0.000 NA 0.000 0.028
#> ERR184073 1 0.1913 0.7205 0.908 0.000 0.000 NA 0.080 0.000
#> ERR184066 1 0.4843 0.6721 0.664 0.000 0.000 NA 0.000 0.192
#> ERR184098 2 0.3494 0.8365 0.000 0.792 0.000 NA 0.004 0.036
#> ERR184044 6 0.3830 0.5713 0.044 0.000 0.000 NA 0.000 0.744
#> ERR184054 1 0.1151 0.7591 0.956 0.000 0.000 NA 0.000 0.032
#> ERR184085 6 0.3767 0.5704 0.016 0.004 0.000 NA 0.000 0.720
#> ERR184056 2 0.4835 -0.0795 0.000 0.540 0.000 NA 0.004 0.408
#> ERR184052 2 0.3066 0.8041 0.000 0.832 0.000 NA 0.000 0.124
#> ERR184070 2 0.0000 0.9001 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184096 5 0.0547 0.7017 0.020 0.000 0.000 NA 0.980 0.000
#> ERR184089 2 0.3314 0.8595 0.000 0.820 0.000 NA 0.004 0.048
#> ERR184049 6 0.3163 0.6301 0.008 0.012 0.000 NA 0.000 0.808
#> ERR184038 6 0.4969 0.4573 0.100 0.000 0.008 NA 0.000 0.652
#> ERR184087 3 0.0000 0.8350 0.000 0.000 1.000 NA 0.000 0.000
#> ERR184097 6 0.4829 0.4011 0.000 0.404 0.000 NA 0.004 0.544
#> ERR184094 5 0.6437 0.0730 0.220 0.000 0.344 NA 0.416 0.004
#> ERR184058 2 0.0790 0.8995 0.000 0.968 0.000 NA 0.000 0.000
#> ERR184036 6 0.5068 0.6392 0.000 0.240 0.000 NA 0.000 0.624
#> ERR184046 2 0.0260 0.9006 0.000 0.992 0.000 NA 0.000 0.000
#> ERR184074 1 0.3224 0.7430 0.824 0.000 0.000 NA 0.004 0.040
#> ERR184048 6 0.2730 0.7091 0.000 0.192 0.000 NA 0.000 0.808
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 10269 rows and 62 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.960 0.984 0.5010 0.497 0.497
#> 3 3 0.803 0.841 0.909 0.2197 0.871 0.745
#> 4 4 0.613 0.667 0.820 0.1323 0.922 0.803
#> 5 5 0.564 0.576 0.749 0.0775 0.969 0.909
#> 6 6 0.580 0.486 0.717 0.0461 0.966 0.889
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
#> ERR184078 1 0.000 0.969 1.000 0.000
#> ERR184093 2 0.000 0.993 0.000 1.000
#> ERR184051 1 0.000 0.969 1.000 0.000
#> ERR184076 1 0.000 0.969 1.000 0.000
#> ERR184043 1 0.000 0.969 1.000 0.000
#> ERR184037 1 0.000 0.969 1.000 0.000
#> ERR184059 1 0.000 0.969 1.000 0.000
#> ERR184055 1 0.000 0.969 1.000 0.000
#> ERR184065 2 0.000 0.993 0.000 1.000
#> ERR184069 2 0.000 0.993 0.000 1.000
#> ERR184040 1 0.000 0.969 1.000 0.000
#> ERR184057 2 0.000 0.993 0.000 1.000
#> ERR184082 1 0.988 0.251 0.564 0.436
#> ERR184083 2 0.000 0.993 0.000 1.000
#> ERR184039 2 0.000 0.993 0.000 1.000
#> ERR184064 1 0.000 0.969 1.000 0.000
#> ERR184081 2 0.000 0.993 0.000 1.000
#> ERR184095 2 0.000 0.993 0.000 1.000
#> ERR184079 2 0.000 0.993 0.000 1.000
#> ERR184084 1 0.000 0.969 1.000 0.000
#> ERR184068 2 0.000 0.993 0.000 1.000
#> ERR184067 2 0.000 0.993 0.000 1.000
#> ERR184071 2 0.000 0.993 0.000 1.000
#> ERR184042 1 0.000 0.969 1.000 0.000
#> ERR184063 1 0.000 0.969 1.000 0.000
#> ERR184091 2 0.000 0.993 0.000 1.000
#> ERR184061 2 0.697 0.756 0.188 0.812
#> ERR184077 2 0.000 0.993 0.000 1.000
#> ERR184062 2 0.118 0.978 0.016 0.984
#> ERR184053 2 0.000 0.993 0.000 1.000
#> ERR184088 2 0.000 0.993 0.000 1.000
#> ERR184075 2 0.000 0.993 0.000 1.000
#> ERR184041 1 0.000 0.969 1.000 0.000
#> ERR184060 2 0.000 0.993 0.000 1.000
#> ERR184035 1 0.833 0.648 0.736 0.264
#> ERR184086 2 0.000 0.993 0.000 1.000
#> ERR184080 1 0.000 0.969 1.000 0.000
#> ERR184050 2 0.000 0.993 0.000 1.000
#> ERR184047 1 0.000 0.969 1.000 0.000
#> ERR184092 2 0.000 0.993 0.000 1.000
#> ERR184072 1 0.000 0.969 1.000 0.000
#> ERR184073 1 0.000 0.969 1.000 0.000
#> ERR184066 1 0.000 0.969 1.000 0.000
#> ERR184098 2 0.000 0.993 0.000 1.000
#> ERR184044 1 0.000 0.969 1.000 0.000
#> ERR184054 1 0.000 0.969 1.000 0.000
#> ERR184085 1 0.518 0.856 0.884 0.116
#> ERR184056 2 0.000 0.993 0.000 1.000
#> ERR184052 2 0.000 0.993 0.000 1.000
#> ERR184070 2 0.000 0.993 0.000 1.000
#> ERR184096 1 0.000 0.969 1.000 0.000
#> ERR184089 2 0.000 0.993 0.000 1.000
#> ERR184049 2 0.000 0.993 0.000 1.000
#> ERR184038 1 0.000 0.969 1.000 0.000
#> ERR184087 1 0.000 0.969 1.000 0.000
#> ERR184097 2 0.000 0.993 0.000 1.000
#> ERR184094 1 0.000 0.969 1.000 0.000
#> ERR184058 2 0.000 0.993 0.000 1.000
#> ERR184036 2 0.000 0.993 0.000 1.000
#> ERR184046 2 0.000 0.993 0.000 1.000
#> ERR184074 1 0.000 0.969 1.000 0.000
#> ERR184048 2 0.000 0.993 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.4654 0.808 0.792 0.000 0.208
#> ERR184093 2 0.0892 0.969 0.020 0.980 0.000
#> ERR184051 3 0.0000 0.831 0.000 0.000 1.000
#> ERR184076 1 0.4887 0.798 0.772 0.000 0.228
#> ERR184043 3 0.0000 0.831 0.000 0.000 1.000
#> ERR184037 1 0.1964 0.772 0.944 0.000 0.056
#> ERR184059 3 0.3816 0.767 0.148 0.000 0.852
#> ERR184055 1 0.2796 0.788 0.908 0.000 0.092
#> ERR184065 2 0.0000 0.973 0.000 1.000 0.000
#> ERR184069 2 0.0000 0.973 0.000 1.000 0.000
#> ERR184040 1 0.4887 0.797 0.772 0.000 0.228
#> ERR184057 2 0.0000 0.973 0.000 1.000 0.000
#> ERR184082 3 0.8230 0.498 0.224 0.144 0.632
#> ERR184083 2 0.0000 0.973 0.000 1.000 0.000
#> ERR184039 2 0.0237 0.973 0.004 0.996 0.000
#> ERR184064 3 0.0000 0.831 0.000 0.000 1.000
#> ERR184081 2 0.0000 0.973 0.000 1.000 0.000
#> ERR184095 2 0.0000 0.973 0.000 1.000 0.000
#> ERR184079 2 0.2066 0.947 0.060 0.940 0.000
#> ERR184084 3 0.3816 0.768 0.148 0.000 0.852
#> ERR184068 2 0.3551 0.888 0.132 0.868 0.000
#> ERR184067 2 0.0000 0.973 0.000 1.000 0.000
#> ERR184071 2 0.0237 0.973 0.004 0.996 0.000
#> ERR184042 3 0.3816 0.768 0.148 0.000 0.852
#> ERR184063 3 0.0000 0.831 0.000 0.000 1.000
#> ERR184091 2 0.0000 0.973 0.000 1.000 0.000
#> ERR184061 1 0.6724 0.109 0.568 0.420 0.012
#> ERR184077 2 0.1289 0.964 0.032 0.968 0.000
#> ERR184062 2 0.4465 0.796 0.176 0.820 0.004
#> ERR184053 2 0.1163 0.965 0.028 0.972 0.000
#> ERR184088 2 0.1753 0.955 0.048 0.952 0.000
#> ERR184075 2 0.0000 0.973 0.000 1.000 0.000
#> ERR184041 3 0.0000 0.831 0.000 0.000 1.000
#> ERR184060 2 0.0000 0.973 0.000 1.000 0.000
#> ERR184035 1 0.1482 0.704 0.968 0.020 0.012
#> ERR184086 2 0.0000 0.973 0.000 1.000 0.000
#> ERR184080 1 0.2356 0.784 0.928 0.000 0.072
#> ERR184050 2 0.0237 0.973 0.004 0.996 0.000
#> ERR184047 1 0.5431 0.740 0.716 0.000 0.284
#> ERR184092 2 0.0592 0.970 0.012 0.988 0.000
#> ERR184072 1 0.3752 0.815 0.856 0.000 0.144
#> ERR184073 1 0.5327 0.757 0.728 0.000 0.272
#> ERR184066 1 0.4062 0.818 0.836 0.000 0.164
#> ERR184098 2 0.0000 0.973 0.000 1.000 0.000
#> ERR184044 1 0.6045 0.415 0.620 0.000 0.380
#> ERR184054 1 0.4121 0.818 0.832 0.000 0.168
#> ERR184085 3 0.5580 0.699 0.256 0.008 0.736
#> ERR184056 2 0.0747 0.969 0.016 0.984 0.000
#> ERR184052 2 0.0424 0.972 0.008 0.992 0.000
#> ERR184070 2 0.0000 0.973 0.000 1.000 0.000
#> ERR184096 1 0.5098 0.781 0.752 0.000 0.248
#> ERR184089 2 0.2301 0.931 0.004 0.936 0.060
#> ERR184049 2 0.5109 0.781 0.212 0.780 0.008
#> ERR184038 3 0.3340 0.790 0.120 0.000 0.880
#> ERR184087 3 0.0000 0.831 0.000 0.000 1.000
#> ERR184097 2 0.0592 0.970 0.012 0.988 0.000
#> ERR184094 3 0.6299 -0.163 0.476 0.000 0.524
#> ERR184058 2 0.0000 0.973 0.000 1.000 0.000
#> ERR184036 2 0.1964 0.945 0.056 0.944 0.000
#> ERR184046 2 0.0000 0.973 0.000 1.000 0.000
#> ERR184074 1 0.4062 0.818 0.836 0.000 0.164
#> ERR184048 2 0.1964 0.951 0.056 0.944 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.2334 0.8356 0.908 0.000 0.088 0.004
#> ERR184093 2 0.3668 0.7365 0.000 0.808 0.004 0.188
#> ERR184051 3 0.0469 0.8304 0.012 0.000 0.988 0.000
#> ERR184076 1 0.2593 0.8354 0.904 0.000 0.080 0.016
#> ERR184043 3 0.0469 0.8304 0.012 0.000 0.988 0.000
#> ERR184037 1 0.3311 0.7034 0.828 0.000 0.000 0.172
#> ERR184059 3 0.4277 0.6557 0.280 0.000 0.720 0.000
#> ERR184055 1 0.4289 0.7098 0.796 0.000 0.032 0.172
#> ERR184065 2 0.2081 0.8154 0.000 0.916 0.000 0.084
#> ERR184069 2 0.0188 0.8268 0.000 0.996 0.000 0.004
#> ERR184040 1 0.2654 0.8314 0.888 0.000 0.108 0.004
#> ERR184057 2 0.0469 0.8262 0.000 0.988 0.000 0.012
#> ERR184082 4 0.7609 0.3058 0.116 0.056 0.228 0.600
#> ERR184083 2 0.1211 0.8296 0.000 0.960 0.000 0.040
#> ERR184039 2 0.2281 0.8125 0.000 0.904 0.000 0.096
#> ERR184064 3 0.0469 0.8304 0.012 0.000 0.988 0.000
#> ERR184081 2 0.0336 0.8266 0.000 0.992 0.000 0.008
#> ERR184095 2 0.0817 0.8268 0.000 0.976 0.000 0.024
#> ERR184079 2 0.5653 0.1626 0.016 0.532 0.004 0.448
#> ERR184084 3 0.4836 0.5773 0.320 0.000 0.672 0.008
#> ERR184068 4 0.5937 0.1217 0.032 0.404 0.004 0.560
#> ERR184067 2 0.1022 0.8280 0.000 0.968 0.000 0.032
#> ERR184071 2 0.2999 0.8006 0.000 0.864 0.004 0.132
#> ERR184042 3 0.4331 0.6463 0.288 0.000 0.712 0.000
#> ERR184063 3 0.0336 0.8276 0.008 0.000 0.992 0.000
#> ERR184091 2 0.1867 0.8194 0.000 0.928 0.000 0.072
#> ERR184061 4 0.8010 0.3692 0.208 0.352 0.012 0.428
#> ERR184077 2 0.4655 0.5518 0.000 0.684 0.004 0.312
#> ERR184062 2 0.7660 -0.0485 0.116 0.468 0.024 0.392
#> ERR184053 2 0.4800 0.4771 0.000 0.656 0.004 0.340
#> ERR184088 2 0.3751 0.7085 0.004 0.800 0.000 0.196
#> ERR184075 2 0.2081 0.8159 0.000 0.916 0.000 0.084
#> ERR184041 3 0.0336 0.8276 0.008 0.000 0.992 0.000
#> ERR184060 2 0.0000 0.8272 0.000 1.000 0.000 0.000
#> ERR184035 4 0.5427 -0.0354 0.444 0.004 0.008 0.544
#> ERR184086 2 0.2081 0.8159 0.000 0.916 0.000 0.084
#> ERR184080 1 0.1824 0.7802 0.936 0.000 0.004 0.060
#> ERR184050 2 0.2530 0.8094 0.000 0.888 0.000 0.112
#> ERR184047 1 0.3311 0.7915 0.828 0.000 0.172 0.000
#> ERR184092 2 0.2773 0.7854 0.000 0.880 0.004 0.116
#> ERR184072 1 0.3081 0.8254 0.888 0.000 0.064 0.048
#> ERR184073 1 0.3311 0.7933 0.828 0.000 0.172 0.000
#> ERR184066 1 0.3547 0.7972 0.864 0.000 0.064 0.072
#> ERR184098 2 0.2216 0.8179 0.000 0.908 0.000 0.092
#> ERR184044 1 0.7782 0.1345 0.424 0.000 0.312 0.264
#> ERR184054 1 0.2179 0.8331 0.924 0.000 0.064 0.012
#> ERR184085 4 0.7756 -0.1677 0.236 0.000 0.364 0.400
#> ERR184056 2 0.3024 0.7677 0.000 0.852 0.000 0.148
#> ERR184052 2 0.1474 0.8271 0.000 0.948 0.000 0.052
#> ERR184070 2 0.0188 0.8275 0.000 0.996 0.000 0.004
#> ERR184096 1 0.2760 0.8229 0.872 0.000 0.128 0.000
#> ERR184089 2 0.5051 0.6825 0.000 0.768 0.100 0.132
#> ERR184049 4 0.6237 0.1527 0.044 0.448 0.004 0.504
#> ERR184038 3 0.5170 0.6968 0.228 0.000 0.724 0.048
#> ERR184087 3 0.0469 0.8304 0.012 0.000 0.988 0.000
#> ERR184097 2 0.3257 0.7568 0.000 0.844 0.004 0.152
#> ERR184094 1 0.4888 0.2942 0.588 0.000 0.412 0.000
#> ERR184058 2 0.1302 0.8283 0.000 0.956 0.000 0.044
#> ERR184036 2 0.4533 0.6412 0.012 0.764 0.008 0.216
#> ERR184046 2 0.0921 0.8292 0.000 0.972 0.000 0.028
#> ERR184074 1 0.2443 0.8296 0.916 0.000 0.060 0.024
#> ERR184048 2 0.4776 0.4021 0.000 0.624 0.000 0.376
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.1808 0.8228 0.936 0.000 0.044 0.012 0.008
#> ERR184093 2 0.5666 0.5779 0.000 0.640 0.008 0.112 0.240
#> ERR184051 3 0.0865 0.7483 0.024 0.000 0.972 0.004 0.000
#> ERR184076 1 0.2362 0.8180 0.916 0.000 0.032 0.024 0.028
#> ERR184043 3 0.0865 0.7478 0.024 0.000 0.972 0.004 0.000
#> ERR184037 1 0.5026 0.3295 0.588 0.000 0.000 0.372 0.040
#> ERR184059 3 0.4457 0.5051 0.368 0.000 0.620 0.012 0.000
#> ERR184055 1 0.5348 0.5111 0.656 0.000 0.028 0.276 0.040
#> ERR184065 2 0.3779 0.7158 0.000 0.812 0.004 0.136 0.048
#> ERR184069 2 0.1216 0.7533 0.000 0.960 0.000 0.020 0.020
#> ERR184040 1 0.1357 0.8210 0.948 0.000 0.048 0.000 0.004
#> ERR184057 2 0.1399 0.7494 0.000 0.952 0.000 0.020 0.028
#> ERR184082 5 0.8092 0.1333 0.068 0.076 0.112 0.228 0.516
#> ERR184083 2 0.1597 0.7551 0.000 0.940 0.000 0.048 0.012
#> ERR184039 2 0.3916 0.7185 0.000 0.804 0.004 0.136 0.056
#> ERR184064 3 0.0703 0.7485 0.024 0.000 0.976 0.000 0.000
#> ERR184081 2 0.1195 0.7524 0.000 0.960 0.000 0.012 0.028
#> ERR184095 2 0.2172 0.7421 0.000 0.908 0.000 0.016 0.076
#> ERR184079 2 0.7099 0.0263 0.008 0.416 0.008 0.220 0.348
#> ERR184084 3 0.5450 0.3819 0.412 0.000 0.540 0.024 0.024
#> ERR184068 5 0.5561 0.1552 0.016 0.236 0.000 0.088 0.660
#> ERR184067 2 0.2291 0.7480 0.000 0.908 0.000 0.056 0.036
#> ERR184071 2 0.5091 0.6138 0.000 0.676 0.000 0.088 0.236
#> ERR184042 3 0.4676 0.4622 0.392 0.000 0.592 0.012 0.004
#> ERR184063 3 0.1074 0.7378 0.016 0.000 0.968 0.012 0.004
#> ERR184091 2 0.3037 0.7375 0.000 0.860 0.000 0.100 0.040
#> ERR184061 4 0.6625 0.2574 0.100 0.144 0.020 0.656 0.080
#> ERR184077 2 0.5274 0.3924 0.000 0.572 0.000 0.056 0.372
#> ERR184062 5 0.7519 0.0539 0.048 0.264 0.008 0.200 0.480
#> ERR184053 2 0.5869 0.1910 0.000 0.484 0.004 0.084 0.428
#> ERR184088 2 0.5496 0.5833 0.004 0.668 0.000 0.164 0.164
#> ERR184075 2 0.4014 0.7149 0.000 0.804 0.008 0.128 0.060
#> ERR184041 3 0.0833 0.7408 0.016 0.000 0.976 0.004 0.004
#> ERR184060 2 0.0771 0.7524 0.000 0.976 0.000 0.004 0.020
#> ERR184035 5 0.7574 -0.0126 0.296 0.024 0.012 0.260 0.408
#> ERR184086 2 0.3090 0.7402 0.000 0.860 0.004 0.104 0.032
#> ERR184080 1 0.2518 0.7807 0.896 0.000 0.008 0.080 0.016
#> ERR184050 2 0.4352 0.7004 0.000 0.772 0.008 0.160 0.060
#> ERR184047 1 0.2753 0.7779 0.856 0.000 0.136 0.008 0.000
#> ERR184092 2 0.5092 0.6346 0.000 0.708 0.008 0.092 0.192
#> ERR184072 1 0.3284 0.7908 0.864 0.000 0.028 0.080 0.028
#> ERR184073 1 0.2864 0.7808 0.852 0.000 0.136 0.012 0.000
#> ERR184066 1 0.4499 0.7149 0.788 0.000 0.028 0.076 0.108
#> ERR184098 2 0.4382 0.7116 0.000 0.772 0.004 0.140 0.084
#> ERR184044 4 0.8218 0.0267 0.340 0.004 0.208 0.340 0.108
#> ERR184054 1 0.2140 0.8151 0.924 0.000 0.024 0.040 0.012
#> ERR184085 5 0.8789 -0.0355 0.172 0.012 0.248 0.260 0.308
#> ERR184056 2 0.4799 0.6269 0.000 0.716 0.008 0.056 0.220
#> ERR184052 2 0.3176 0.7426 0.000 0.856 0.000 0.080 0.064
#> ERR184070 2 0.1626 0.7485 0.000 0.940 0.000 0.016 0.044
#> ERR184096 1 0.1892 0.8128 0.916 0.000 0.080 0.004 0.000
#> ERR184089 2 0.7057 0.4600 0.000 0.576 0.144 0.180 0.100
#> ERR184049 4 0.5887 0.1702 0.012 0.220 0.000 0.632 0.136
#> ERR184038 3 0.6401 0.4889 0.328 0.000 0.552 0.052 0.068
#> ERR184087 3 0.0865 0.7484 0.024 0.000 0.972 0.004 0.000
#> ERR184097 2 0.5001 0.5993 0.000 0.680 0.008 0.052 0.260
#> ERR184094 1 0.4184 0.5218 0.700 0.000 0.284 0.016 0.000
#> ERR184058 2 0.2388 0.7486 0.000 0.900 0.000 0.072 0.028
#> ERR184036 2 0.5938 0.2518 0.000 0.512 0.000 0.376 0.112
#> ERR184046 2 0.1211 0.7549 0.000 0.960 0.000 0.024 0.016
#> ERR184074 1 0.2438 0.8185 0.900 0.000 0.040 0.060 0.000
#> ERR184048 2 0.5942 0.2943 0.000 0.524 0.000 0.116 0.360
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.2051 0.7810 0.924 0.000 0.032 0.012 0.020 0.012
#> ERR184093 2 0.5525 0.1470 0.000 0.520 0.000 0.388 0.052 0.040
#> ERR184051 3 0.0260 0.7578 0.008 0.000 0.992 0.000 0.000 0.000
#> ERR184076 1 0.3391 0.7724 0.856 0.000 0.032 0.024 0.044 0.044
#> ERR184043 3 0.0508 0.7584 0.012 0.000 0.984 0.000 0.000 0.004
#> ERR184037 1 0.5115 0.4481 0.560 0.000 0.000 0.004 0.080 0.356
#> ERR184059 3 0.4514 0.5307 0.328 0.000 0.632 0.000 0.028 0.012
#> ERR184055 1 0.6000 0.5033 0.572 0.000 0.024 0.020 0.100 0.284
#> ERR184065 2 0.4225 0.6164 0.000 0.764 0.000 0.144 0.024 0.068
#> ERR184069 2 0.1151 0.6659 0.000 0.956 0.000 0.032 0.000 0.012
#> ERR184040 1 0.1555 0.7790 0.932 0.000 0.060 0.000 0.004 0.004
#> ERR184057 2 0.2136 0.6513 0.000 0.908 0.000 0.064 0.016 0.012
#> ERR184082 5 0.6204 0.2792 0.036 0.072 0.072 0.052 0.688 0.080
#> ERR184083 2 0.1952 0.6749 0.000 0.920 0.000 0.052 0.016 0.012
#> ERR184039 2 0.4708 0.6014 0.000 0.728 0.000 0.148 0.032 0.092
#> ERR184064 3 0.0363 0.7593 0.012 0.000 0.988 0.000 0.000 0.000
#> ERR184081 2 0.1692 0.6606 0.000 0.932 0.000 0.048 0.008 0.012
#> ERR184095 2 0.2742 0.6279 0.000 0.852 0.000 0.128 0.012 0.008
#> ERR184079 4 0.7215 0.3540 0.004 0.236 0.000 0.456 0.140 0.164
#> ERR184084 3 0.5507 0.3804 0.372 0.000 0.524 0.004 0.092 0.008
#> ERR184068 5 0.7679 -0.3144 0.004 0.192 0.004 0.300 0.348 0.152
#> ERR184067 2 0.3566 0.6297 0.000 0.812 0.000 0.104 0.008 0.076
#> ERR184071 2 0.5472 0.5383 0.000 0.676 0.000 0.136 0.096 0.092
#> ERR184042 3 0.4595 0.5441 0.320 0.000 0.636 0.004 0.032 0.008
#> ERR184063 3 0.0665 0.7445 0.004 0.000 0.980 0.000 0.008 0.008
#> ERR184091 2 0.3517 0.6470 0.000 0.824 0.000 0.104 0.024 0.048
#> ERR184061 6 0.6407 0.0763 0.088 0.096 0.004 0.116 0.052 0.644
#> ERR184077 2 0.6612 -0.1172 0.000 0.460 0.000 0.324 0.152 0.064
#> ERR184062 4 0.6749 0.3401 0.032 0.140 0.004 0.596 0.100 0.128
#> ERR184053 2 0.7066 -0.2482 0.004 0.400 0.004 0.324 0.212 0.056
#> ERR184088 2 0.6346 0.2376 0.000 0.576 0.000 0.152 0.172 0.100
#> ERR184075 2 0.4683 0.6065 0.000 0.728 0.000 0.156 0.032 0.084
#> ERR184041 3 0.0717 0.7556 0.016 0.000 0.976 0.000 0.008 0.000
#> ERR184060 2 0.1411 0.6667 0.000 0.936 0.000 0.060 0.004 0.000
#> ERR184035 5 0.6586 0.2228 0.208 0.012 0.000 0.064 0.552 0.164
#> ERR184086 2 0.3864 0.6429 0.000 0.796 0.000 0.128 0.032 0.044
#> ERR184080 1 0.4084 0.7315 0.796 0.000 0.008 0.024 0.084 0.088
#> ERR184050 2 0.5542 0.5204 0.000 0.636 0.000 0.208 0.040 0.116
#> ERR184047 1 0.3002 0.7370 0.836 0.000 0.136 0.000 0.020 0.008
#> ERR184092 2 0.4379 0.3953 0.000 0.632 0.000 0.336 0.008 0.024
#> ERR184072 1 0.4528 0.7204 0.772 0.000 0.020 0.032 0.068 0.108
#> ERR184073 1 0.3277 0.7510 0.832 0.000 0.128 0.008 0.016 0.016
#> ERR184066 1 0.5983 0.5875 0.656 0.000 0.020 0.096 0.096 0.132
#> ERR184098 2 0.4930 0.5884 0.000 0.696 0.000 0.184 0.028 0.092
#> ERR184044 6 0.8760 -0.1922 0.252 0.004 0.220 0.104 0.140 0.280
#> ERR184054 1 0.3412 0.7527 0.848 0.000 0.008 0.032 0.056 0.056
#> ERR184085 5 0.8103 0.2057 0.176 0.012 0.128 0.068 0.460 0.156
#> ERR184056 2 0.4777 0.3680 0.000 0.628 0.000 0.316 0.024 0.032
#> ERR184052 2 0.3844 0.6442 0.000 0.812 0.000 0.072 0.060 0.056
#> ERR184070 2 0.2001 0.6502 0.000 0.900 0.000 0.092 0.004 0.004
#> ERR184096 1 0.1843 0.7737 0.912 0.000 0.080 0.000 0.004 0.004
#> ERR184089 2 0.7042 0.3511 0.000 0.528 0.048 0.240 0.076 0.108
#> ERR184049 6 0.7030 0.0788 0.020 0.208 0.000 0.096 0.156 0.520
#> ERR184038 3 0.6874 0.4260 0.260 0.000 0.512 0.048 0.148 0.032
#> ERR184087 3 0.0363 0.7593 0.012 0.000 0.988 0.000 0.000 0.000
#> ERR184097 2 0.4817 0.2458 0.000 0.564 0.000 0.388 0.036 0.012
#> ERR184094 1 0.4504 0.4184 0.648 0.000 0.308 0.000 0.032 0.012
#> ERR184058 2 0.2136 0.6690 0.000 0.908 0.000 0.064 0.012 0.016
#> ERR184036 6 0.6599 -0.1089 0.008 0.396 0.000 0.124 0.052 0.420
#> ERR184046 2 0.1750 0.6720 0.000 0.932 0.000 0.040 0.012 0.016
#> ERR184074 1 0.3722 0.7726 0.820 0.000 0.048 0.008 0.024 0.100
#> ERR184048 2 0.7047 -0.0968 0.000 0.468 0.004 0.196 0.236 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", "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 10269 rows and 62 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 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 0.966 0.960 0.980 0.5011 0.500 0.500
#> 3 3 0.942 0.919 0.968 0.1751 0.914 0.829
#> 4 4 0.802 0.857 0.925 0.0506 0.996 0.990
#> 5 5 0.786 0.873 0.928 0.0202 0.983 0.959
#> 6 6 0.710 0.822 0.907 0.0280 0.987 0.968
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
#> ERR184078 1 0.0000 0.988 1.000 0.000
#> ERR184093 2 0.0000 0.972 0.000 1.000
#> ERR184051 1 0.0000 0.988 1.000 0.000
#> ERR184076 1 0.0000 0.988 1.000 0.000
#> ERR184043 1 0.0000 0.988 1.000 0.000
#> ERR184037 1 0.0000 0.988 1.000 0.000
#> ERR184059 1 0.0000 0.988 1.000 0.000
#> ERR184055 1 0.0000 0.988 1.000 0.000
#> ERR184065 2 0.0000 0.972 0.000 1.000
#> ERR184069 2 0.0000 0.972 0.000 1.000
#> ERR184040 1 0.0000 0.988 1.000 0.000
#> ERR184057 2 0.0000 0.972 0.000 1.000
#> ERR184082 2 0.1414 0.961 0.020 0.980
#> ERR184083 2 0.0000 0.972 0.000 1.000
#> ERR184039 2 0.0000 0.972 0.000 1.000
#> ERR184064 1 0.0000 0.988 1.000 0.000
#> ERR184081 2 0.0000 0.972 0.000 1.000
#> ERR184095 2 0.0000 0.972 0.000 1.000
#> ERR184079 2 0.0000 0.972 0.000 1.000
#> ERR184084 1 0.0000 0.988 1.000 0.000
#> ERR184068 2 0.7056 0.787 0.192 0.808
#> ERR184067 2 0.0000 0.972 0.000 1.000
#> ERR184071 2 0.2948 0.938 0.052 0.948
#> ERR184042 1 0.0000 0.988 1.000 0.000
#> ERR184063 1 0.1414 0.972 0.980 0.020
#> ERR184091 2 0.0000 0.972 0.000 1.000
#> ERR184061 1 0.7453 0.724 0.788 0.212
#> ERR184077 2 0.0376 0.970 0.004 0.996
#> ERR184062 2 0.8555 0.650 0.280 0.720
#> ERR184053 2 0.3879 0.919 0.076 0.924
#> ERR184088 2 0.1184 0.963 0.016 0.984
#> ERR184075 2 0.0000 0.972 0.000 1.000
#> ERR184041 1 0.0672 0.982 0.992 0.008
#> ERR184060 2 0.0000 0.972 0.000 1.000
#> ERR184035 1 0.2603 0.947 0.956 0.044
#> ERR184086 2 0.0000 0.972 0.000 1.000
#> ERR184080 1 0.0000 0.988 1.000 0.000
#> ERR184050 2 0.0000 0.972 0.000 1.000
#> ERR184047 1 0.0000 0.988 1.000 0.000
#> ERR184092 2 0.0000 0.972 0.000 1.000
#> ERR184072 1 0.0000 0.988 1.000 0.000
#> ERR184073 1 0.0000 0.988 1.000 0.000
#> ERR184066 1 0.0000 0.988 1.000 0.000
#> ERR184098 2 0.0000 0.972 0.000 1.000
#> ERR184044 1 0.0376 0.986 0.996 0.004
#> ERR184054 1 0.0000 0.988 1.000 0.000
#> ERR184085 2 0.4815 0.893 0.104 0.896
#> ERR184056 2 0.0376 0.970 0.004 0.996
#> ERR184052 2 0.0000 0.972 0.000 1.000
#> ERR184070 2 0.0000 0.972 0.000 1.000
#> ERR184096 1 0.0000 0.988 1.000 0.000
#> ERR184089 2 0.0000 0.972 0.000 1.000
#> ERR184049 2 0.5946 0.849 0.144 0.856
#> ERR184038 1 0.0000 0.988 1.000 0.000
#> ERR184087 1 0.0000 0.988 1.000 0.000
#> ERR184097 2 0.0000 0.972 0.000 1.000
#> ERR184094 1 0.0000 0.988 1.000 0.000
#> ERR184058 2 0.0000 0.972 0.000 1.000
#> ERR184036 2 0.0000 0.972 0.000 1.000
#> ERR184046 2 0.0000 0.972 0.000 1.000
#> ERR184074 1 0.0000 0.988 1.000 0.000
#> ERR184048 2 0.3879 0.918 0.076 0.924
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.0000 0.9577 1.000 0.000 0.000
#> ERR184093 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184051 3 0.0000 0.9346 0.000 0.000 1.000
#> ERR184076 1 0.0000 0.9577 1.000 0.000 0.000
#> ERR184043 3 0.0000 0.9346 0.000 0.000 1.000
#> ERR184037 1 0.0000 0.9577 1.000 0.000 0.000
#> ERR184059 3 0.0000 0.9346 0.000 0.000 1.000
#> ERR184055 1 0.0000 0.9577 1.000 0.000 0.000
#> ERR184065 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184069 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184040 1 0.0000 0.9577 1.000 0.000 0.000
#> ERR184057 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184082 2 0.0747 0.9631 0.016 0.984 0.000
#> ERR184083 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184039 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184064 3 0.0000 0.9346 0.000 0.000 1.000
#> ERR184081 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184095 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184079 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184084 3 0.6309 -0.0367 0.500 0.000 0.500
#> ERR184068 2 0.4452 0.7854 0.192 0.808 0.000
#> ERR184067 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184071 2 0.1860 0.9363 0.052 0.948 0.000
#> ERR184042 3 0.0000 0.9346 0.000 0.000 1.000
#> ERR184063 3 0.0000 0.9346 0.000 0.000 1.000
#> ERR184091 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184061 1 0.4346 0.6894 0.816 0.184 0.000
#> ERR184077 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184062 2 0.5016 0.7124 0.240 0.760 0.000
#> ERR184053 2 0.2448 0.9152 0.076 0.924 0.000
#> ERR184088 2 0.0592 0.9656 0.012 0.988 0.000
#> ERR184075 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184041 3 0.0000 0.9346 0.000 0.000 1.000
#> ERR184060 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184035 1 0.0000 0.9577 1.000 0.000 0.000
#> ERR184086 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184080 1 0.0000 0.9577 1.000 0.000 0.000
#> ERR184050 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184047 1 0.6140 0.2824 0.596 0.000 0.404
#> ERR184092 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184072 1 0.0000 0.9577 1.000 0.000 0.000
#> ERR184073 1 0.0000 0.9577 1.000 0.000 0.000
#> ERR184066 1 0.0000 0.9577 1.000 0.000 0.000
#> ERR184098 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184044 1 0.0237 0.9531 0.996 0.004 0.000
#> ERR184054 1 0.0000 0.9577 1.000 0.000 0.000
#> ERR184085 2 0.1964 0.9338 0.056 0.944 0.000
#> ERR184056 2 0.0237 0.9703 0.004 0.996 0.000
#> ERR184052 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184070 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184096 1 0.0000 0.9577 1.000 0.000 0.000
#> ERR184089 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184049 2 0.3686 0.8483 0.140 0.860 0.000
#> ERR184038 1 0.0000 0.9577 1.000 0.000 0.000
#> ERR184087 3 0.0000 0.9346 0.000 0.000 1.000
#> ERR184097 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184094 1 0.0000 0.9577 1.000 0.000 0.000
#> ERR184058 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184036 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184046 2 0.0000 0.9725 0.000 1.000 0.000
#> ERR184074 1 0.0000 0.9577 1.000 0.000 0.000
#> ERR184048 2 0.2448 0.9150 0.076 0.924 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.0000 0.9370 1.000 0.000 0.000 0.000
#> ERR184093 2 0.1637 0.9103 0.000 0.940 0.000 0.060
#> ERR184051 3 0.0000 0.8496 0.000 0.000 1.000 0.000
#> ERR184076 1 0.0000 0.9370 1.000 0.000 0.000 0.000
#> ERR184043 3 0.0000 0.8496 0.000 0.000 1.000 0.000
#> ERR184037 1 0.0000 0.9370 1.000 0.000 0.000 0.000
#> ERR184059 3 0.0000 0.8496 0.000 0.000 1.000 0.000
#> ERR184055 1 0.0000 0.9370 1.000 0.000 0.000 0.000
#> ERR184065 2 0.0000 0.9161 0.000 1.000 0.000 0.000
#> ERR184069 2 0.0000 0.9161 0.000 1.000 0.000 0.000
#> ERR184040 1 0.0000 0.9370 1.000 0.000 0.000 0.000
#> ERR184057 2 0.2589 0.9085 0.000 0.884 0.000 0.116
#> ERR184082 2 0.2053 0.9125 0.004 0.924 0.000 0.072
#> ERR184083 2 0.0000 0.9161 0.000 1.000 0.000 0.000
#> ERR184039 2 0.0000 0.9161 0.000 1.000 0.000 0.000
#> ERR184064 3 0.0000 0.8496 0.000 0.000 1.000 0.000
#> ERR184081 2 0.2589 0.9085 0.000 0.884 0.000 0.116
#> ERR184095 2 0.0817 0.9193 0.000 0.976 0.000 0.024
#> ERR184079 2 0.2281 0.9060 0.000 0.904 0.000 0.096
#> ERR184084 3 0.5000 -0.0381 0.500 0.000 0.500 0.000
#> ERR184068 2 0.4549 0.8536 0.096 0.804 0.000 0.100
#> ERR184067 2 0.2589 0.9085 0.000 0.884 0.000 0.116
#> ERR184071 2 0.3610 0.8849 0.000 0.800 0.000 0.200
#> ERR184042 4 0.3610 0.0000 0.000 0.000 0.200 0.800
#> ERR184063 3 0.0000 0.8496 0.000 0.000 1.000 0.000
#> ERR184091 2 0.0000 0.9161 0.000 1.000 0.000 0.000
#> ERR184061 1 0.6149 0.4407 0.676 0.180 0.000 0.144
#> ERR184077 2 0.3610 0.8849 0.000 0.800 0.000 0.200
#> ERR184062 2 0.5033 0.8432 0.072 0.760 0.000 0.168
#> ERR184053 2 0.3610 0.8849 0.000 0.800 0.000 0.200
#> ERR184088 2 0.3494 0.8964 0.004 0.824 0.000 0.172
#> ERR184075 2 0.0000 0.9161 0.000 1.000 0.000 0.000
#> ERR184041 3 0.0000 0.8496 0.000 0.000 1.000 0.000
#> ERR184060 2 0.0000 0.9161 0.000 1.000 0.000 0.000
#> ERR184035 1 0.0000 0.9370 1.000 0.000 0.000 0.000
#> ERR184086 2 0.0000 0.9161 0.000 1.000 0.000 0.000
#> ERR184080 1 0.0000 0.9370 1.000 0.000 0.000 0.000
#> ERR184050 2 0.0000 0.9161 0.000 1.000 0.000 0.000
#> ERR184047 1 0.4866 0.2633 0.596 0.000 0.404 0.000
#> ERR184092 2 0.3356 0.8956 0.000 0.824 0.000 0.176
#> ERR184072 1 0.0188 0.9340 0.996 0.000 0.000 0.004
#> ERR184073 1 0.0000 0.9370 1.000 0.000 0.000 0.000
#> ERR184066 1 0.0000 0.9370 1.000 0.000 0.000 0.000
#> ERR184098 2 0.0817 0.9189 0.000 0.976 0.000 0.024
#> ERR184044 1 0.2197 0.8536 0.916 0.004 0.000 0.080
#> ERR184054 1 0.0000 0.9370 1.000 0.000 0.000 0.000
#> ERR184085 2 0.3913 0.8923 0.028 0.824 0.000 0.148
#> ERR184056 2 0.3610 0.8849 0.000 0.800 0.000 0.200
#> ERR184052 2 0.2469 0.9106 0.000 0.892 0.000 0.108
#> ERR184070 2 0.0000 0.9161 0.000 1.000 0.000 0.000
#> ERR184096 1 0.0000 0.9370 1.000 0.000 0.000 0.000
#> ERR184089 2 0.0000 0.9161 0.000 1.000 0.000 0.000
#> ERR184049 2 0.4139 0.8870 0.040 0.816 0.000 0.144
#> ERR184038 1 0.0817 0.9162 0.976 0.000 0.000 0.024
#> ERR184087 3 0.0000 0.8496 0.000 0.000 1.000 0.000
#> ERR184097 2 0.3610 0.8849 0.000 0.800 0.000 0.200
#> ERR184094 1 0.0000 0.9370 1.000 0.000 0.000 0.000
#> ERR184058 2 0.0000 0.9161 0.000 1.000 0.000 0.000
#> ERR184036 2 0.1474 0.9186 0.000 0.948 0.000 0.052
#> ERR184046 2 0.0000 0.9161 0.000 1.000 0.000 0.000
#> ERR184074 1 0.0000 0.9370 1.000 0.000 0.000 0.000
#> ERR184048 2 0.3610 0.8849 0.000 0.800 0.000 0.200
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.0000 0.9498 1.000 0.000 0.0 0 0.000
#> ERR184093 2 0.1410 0.9099 0.000 0.940 0.0 0 0.060
#> ERR184051 3 0.0000 0.8800 0.000 0.000 1.0 0 0.000
#> ERR184076 1 0.0000 0.9498 1.000 0.000 0.0 0 0.000
#> ERR184043 3 0.0000 0.8800 0.000 0.000 1.0 0 0.000
#> ERR184037 1 0.0000 0.9498 1.000 0.000 0.0 0 0.000
#> ERR184059 3 0.0000 0.8800 0.000 0.000 1.0 0 0.000
#> ERR184055 1 0.0000 0.9498 1.000 0.000 0.0 0 0.000
#> ERR184065 2 0.0000 0.9158 0.000 1.000 0.0 0 0.000
#> ERR184069 2 0.0000 0.9158 0.000 1.000 0.0 0 0.000
#> ERR184040 1 0.0000 0.9498 1.000 0.000 0.0 0 0.000
#> ERR184057 2 0.2230 0.9081 0.000 0.884 0.0 0 0.116
#> ERR184082 2 0.1768 0.9121 0.004 0.924 0.0 0 0.072
#> ERR184083 2 0.0000 0.9158 0.000 1.000 0.0 0 0.000
#> ERR184039 2 0.0000 0.9158 0.000 1.000 0.0 0 0.000
#> ERR184064 3 0.0000 0.8800 0.000 0.000 1.0 0 0.000
#> ERR184081 2 0.2230 0.9081 0.000 0.884 0.0 0 0.116
#> ERR184095 2 0.0703 0.9189 0.000 0.976 0.0 0 0.024
#> ERR184079 2 0.1965 0.9055 0.000 0.904 0.0 0 0.096
#> ERR184084 3 0.4307 -0.0283 0.500 0.000 0.5 0 0.000
#> ERR184068 2 0.3918 0.8527 0.096 0.804 0.0 0 0.100
#> ERR184067 2 0.2230 0.9081 0.000 0.884 0.0 0 0.116
#> ERR184071 2 0.3109 0.8844 0.000 0.800 0.0 0 0.200
#> ERR184042 4 0.0000 0.0000 0.000 0.000 0.0 1 0.000
#> ERR184063 3 0.0000 0.8800 0.000 0.000 1.0 0 0.000
#> ERR184091 2 0.0000 0.9158 0.000 1.000 0.0 0 0.000
#> ERR184061 1 0.5296 0.3366 0.676 0.180 0.0 0 0.144
#> ERR184077 2 0.3109 0.8844 0.000 0.800 0.0 0 0.200
#> ERR184062 2 0.4335 0.8434 0.072 0.760 0.0 0 0.168
#> ERR184053 2 0.3109 0.8844 0.000 0.800 0.0 0 0.200
#> ERR184088 2 0.3010 0.8960 0.004 0.824 0.0 0 0.172
#> ERR184075 2 0.0000 0.9158 0.000 1.000 0.0 0 0.000
#> ERR184041 3 0.0000 0.8800 0.000 0.000 1.0 0 0.000
#> ERR184060 2 0.0000 0.9158 0.000 1.000 0.0 0 0.000
#> ERR184035 1 0.0000 0.9498 1.000 0.000 0.0 0 0.000
#> ERR184086 2 0.0000 0.9158 0.000 1.000 0.0 0 0.000
#> ERR184080 1 0.0000 0.9498 1.000 0.000 0.0 0 0.000
#> ERR184050 2 0.0000 0.9158 0.000 1.000 0.0 0 0.000
#> ERR184047 5 0.3109 0.9910 0.200 0.000 0.0 0 0.800
#> ERR184092 2 0.2891 0.8951 0.000 0.824 0.0 0 0.176
#> ERR184072 1 0.0162 0.9459 0.996 0.000 0.0 0 0.004
#> ERR184073 1 0.0000 0.9498 1.000 0.000 0.0 0 0.000
#> ERR184066 1 0.0000 0.9498 1.000 0.000 0.0 0 0.000
#> ERR184098 2 0.0703 0.9186 0.000 0.976 0.0 0 0.024
#> ERR184044 1 0.1892 0.8399 0.916 0.004 0.0 0 0.080
#> ERR184054 1 0.0000 0.9498 1.000 0.000 0.0 0 0.000
#> ERR184085 2 0.3370 0.8918 0.028 0.824 0.0 0 0.148
#> ERR184056 2 0.3109 0.8844 0.000 0.800 0.0 0 0.200
#> ERR184052 2 0.2127 0.9102 0.000 0.892 0.0 0 0.108
#> ERR184070 2 0.0000 0.9158 0.000 1.000 0.0 0 0.000
#> ERR184096 5 0.3143 0.9911 0.204 0.000 0.0 0 0.796
#> ERR184089 2 0.0000 0.9158 0.000 1.000 0.0 0 0.000
#> ERR184049 2 0.3565 0.8864 0.040 0.816 0.0 0 0.144
#> ERR184038 1 0.0703 0.9225 0.976 0.000 0.0 0 0.024
#> ERR184087 3 0.0000 0.8800 0.000 0.000 1.0 0 0.000
#> ERR184097 2 0.3109 0.8844 0.000 0.800 0.0 0 0.200
#> ERR184094 1 0.0000 0.9498 1.000 0.000 0.0 0 0.000
#> ERR184058 2 0.0000 0.9158 0.000 1.000 0.0 0 0.000
#> ERR184036 2 0.1270 0.9182 0.000 0.948 0.0 0 0.052
#> ERR184046 2 0.0000 0.9158 0.000 1.000 0.0 0 0.000
#> ERR184074 1 0.0000 0.9498 1.000 0.000 0.0 0 0.000
#> ERR184048 2 0.3109 0.8844 0.000 0.800 0.0 0 0.200
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.0000 0.9145 1.000 0.000 0.0 0 0.000 0.000
#> ERR184093 2 0.2300 0.8501 0.000 0.856 0.0 0 0.144 0.000
#> ERR184051 3 0.0000 1.0000 0.000 0.000 1.0 0 0.000 0.000
#> ERR184076 1 0.0000 0.9145 1.000 0.000 0.0 0 0.000 0.000
#> ERR184043 3 0.0000 1.0000 0.000 0.000 1.0 0 0.000 0.000
#> ERR184037 1 0.0000 0.9145 1.000 0.000 0.0 0 0.000 0.000
#> ERR184059 3 0.0000 1.0000 0.000 0.000 1.0 0 0.000 0.000
#> ERR184055 1 0.0000 0.9145 1.000 0.000 0.0 0 0.000 0.000
#> ERR184065 2 0.0000 0.8851 0.000 1.000 0.0 0 0.000 0.000
#> ERR184069 2 0.0000 0.8851 0.000 1.000 0.0 0 0.000 0.000
#> ERR184040 1 0.0000 0.9145 1.000 0.000 0.0 0 0.000 0.000
#> ERR184057 2 0.2003 0.8760 0.000 0.884 0.0 0 0.116 0.000
#> ERR184082 2 0.1757 0.8810 0.008 0.916 0.0 0 0.076 0.000
#> ERR184083 2 0.0000 0.8851 0.000 1.000 0.0 0 0.000 0.000
#> ERR184039 2 0.0000 0.8851 0.000 1.000 0.0 0 0.000 0.000
#> ERR184064 3 0.0000 1.0000 0.000 0.000 1.0 0 0.000 0.000
#> ERR184081 2 0.2003 0.8760 0.000 0.884 0.0 0 0.116 0.000
#> ERR184095 2 0.0632 0.8876 0.000 0.976 0.0 0 0.024 0.000
#> ERR184079 2 0.2762 0.8316 0.000 0.804 0.0 0 0.196 0.000
#> ERR184084 1 0.3869 0.0157 0.500 0.000 0.5 0 0.000 0.000
#> ERR184068 2 0.4459 0.7678 0.096 0.700 0.0 0 0.204 0.000
#> ERR184067 2 0.2003 0.8760 0.000 0.884 0.0 0 0.116 0.000
#> ERR184071 2 0.3409 0.8050 0.000 0.700 0.0 0 0.300 0.000
#> ERR184042 4 0.0000 0.0000 0.000 0.000 0.0 1 0.000 0.000
#> ERR184063 3 0.0000 1.0000 0.000 0.000 1.0 0 0.000 0.000
#> ERR184091 2 0.0000 0.8851 0.000 1.000 0.0 0 0.000 0.000
#> ERR184061 1 0.4728 0.4188 0.680 0.176 0.0 0 0.144 0.000
#> ERR184077 2 0.3428 0.8022 0.000 0.696 0.0 0 0.304 0.000
#> ERR184062 2 0.4193 0.7843 0.044 0.684 0.0 0 0.272 0.000
#> ERR184053 2 0.3428 0.8022 0.000 0.696 0.0 0 0.304 0.000
#> ERR184088 2 0.3136 0.8453 0.004 0.768 0.0 0 0.228 0.000
#> ERR184075 2 0.0000 0.8851 0.000 1.000 0.0 0 0.000 0.000
#> ERR184041 3 0.0000 1.0000 0.000 0.000 1.0 0 0.000 0.000
#> ERR184060 2 0.0000 0.8851 0.000 1.000 0.0 0 0.000 0.000
#> ERR184035 1 0.0000 0.9145 1.000 0.000 0.0 0 0.000 0.000
#> ERR184086 2 0.0000 0.8851 0.000 1.000 0.0 0 0.000 0.000
#> ERR184080 1 0.0000 0.9145 1.000 0.000 0.0 0 0.000 0.000
#> ERR184050 2 0.0000 0.8851 0.000 1.000 0.0 0 0.000 0.000
#> ERR184047 5 0.3428 0.0000 0.000 0.000 0.0 0 0.696 0.304
#> ERR184092 2 0.3309 0.8162 0.000 0.720 0.0 0 0.280 0.000
#> ERR184072 1 0.0146 0.9115 0.996 0.000 0.0 0 0.004 0.000
#> ERR184073 1 0.0000 0.9145 1.000 0.000 0.0 0 0.000 0.000
#> ERR184066 1 0.0000 0.9145 1.000 0.000 0.0 0 0.000 0.000
#> ERR184098 2 0.0632 0.8872 0.000 0.976 0.0 0 0.024 0.000
#> ERR184044 1 0.2805 0.6986 0.812 0.004 0.0 0 0.184 0.000
#> ERR184054 1 0.0000 0.9145 1.000 0.000 0.0 0 0.000 0.000
#> ERR184085 2 0.3101 0.8604 0.032 0.820 0.0 0 0.148 0.000
#> ERR184056 2 0.3428 0.8022 0.000 0.696 0.0 0 0.304 0.000
#> ERR184052 2 0.1910 0.8780 0.000 0.892 0.0 0 0.108 0.000
#> ERR184070 2 0.0000 0.8851 0.000 1.000 0.0 0 0.000 0.000
#> ERR184096 6 0.0713 0.0000 0.028 0.000 0.0 0 0.000 0.972
#> ERR184089 2 0.0000 0.8851 0.000 1.000 0.0 0 0.000 0.000
#> ERR184049 2 0.3240 0.8573 0.040 0.812 0.0 0 0.148 0.000
#> ERR184038 1 0.0632 0.8931 0.976 0.000 0.0 0 0.024 0.000
#> ERR184087 3 0.0000 1.0000 0.000 0.000 1.0 0 0.000 0.000
#> ERR184097 2 0.3428 0.8022 0.000 0.696 0.0 0 0.304 0.000
#> ERR184094 1 0.0000 0.9145 1.000 0.000 0.0 0 0.000 0.000
#> ERR184058 2 0.0000 0.8851 0.000 1.000 0.0 0 0.000 0.000
#> ERR184036 2 0.1141 0.8862 0.000 0.948 0.0 0 0.052 0.000
#> ERR184046 2 0.0000 0.8851 0.000 1.000 0.0 0 0.000 0.000
#> ERR184074 1 0.0000 0.9145 1.000 0.000 0.0 0 0.000 0.000
#> ERR184048 2 0.2823 0.8561 0.000 0.796 0.0 0 0.204 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 10269 rows and 62 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 0.492 0.737 0.866 0.3414 0.748 0.748
#> 3 3 0.283 0.669 0.775 0.5806 0.675 0.575
#> 4 4 0.615 0.758 0.868 0.1162 0.883 0.769
#> 5 5 0.696 0.798 0.876 0.1471 0.878 0.726
#> 6 6 0.679 0.688 0.831 0.0794 0.984 0.952
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
#> ERR184078 2 0.9795 0.476 0.416 0.584
#> ERR184093 2 0.0000 0.822 0.000 1.000
#> ERR184051 1 0.3114 0.904 0.944 0.056
#> ERR184076 2 0.9795 0.476 0.416 0.584
#> ERR184043 1 0.0000 0.903 1.000 0.000
#> ERR184037 2 0.9522 0.544 0.372 0.628
#> ERR184059 1 0.7056 0.736 0.808 0.192
#> ERR184055 2 0.9522 0.544 0.372 0.628
#> ERR184065 2 0.0672 0.821 0.008 0.992
#> ERR184069 2 0.0000 0.822 0.000 1.000
#> ERR184040 2 0.9795 0.476 0.416 0.584
#> ERR184057 2 0.0000 0.822 0.000 1.000
#> ERR184082 2 0.2948 0.808 0.052 0.948
#> ERR184083 2 0.0672 0.821 0.008 0.992
#> ERR184039 2 0.0672 0.821 0.008 0.992
#> ERR184064 1 0.0000 0.903 1.000 0.000
#> ERR184081 2 0.0000 0.822 0.000 1.000
#> ERR184095 2 0.0000 0.822 0.000 1.000
#> ERR184079 2 0.0000 0.822 0.000 1.000
#> ERR184084 1 0.7453 0.683 0.788 0.212
#> ERR184068 2 0.0938 0.820 0.012 0.988
#> ERR184067 2 0.0000 0.822 0.000 1.000
#> ERR184071 2 0.0672 0.821 0.008 0.992
#> ERR184042 1 0.0000 0.903 1.000 0.000
#> ERR184063 1 0.3114 0.904 0.944 0.056
#> ERR184091 2 0.0672 0.821 0.008 0.992
#> ERR184061 2 0.3431 0.801 0.064 0.936
#> ERR184077 2 0.0000 0.822 0.000 1.000
#> ERR184062 2 0.9209 0.576 0.336 0.664
#> ERR184053 2 0.2236 0.815 0.036 0.964
#> ERR184088 2 0.0000 0.822 0.000 1.000
#> ERR184075 2 0.0672 0.821 0.008 0.992
#> ERR184041 1 0.3114 0.904 0.944 0.056
#> ERR184060 2 0.0000 0.822 0.000 1.000
#> ERR184035 2 0.7299 0.711 0.204 0.796
#> ERR184086 2 0.0672 0.821 0.008 0.992
#> ERR184080 2 0.9522 0.544 0.372 0.628
#> ERR184050 2 0.0672 0.821 0.008 0.992
#> ERR184047 2 0.9795 0.476 0.416 0.584
#> ERR184092 2 0.0000 0.822 0.000 1.000
#> ERR184072 2 0.9795 0.476 0.416 0.584
#> ERR184073 2 0.9795 0.476 0.416 0.584
#> ERR184066 2 0.9795 0.476 0.416 0.584
#> ERR184098 2 0.0672 0.821 0.008 0.992
#> ERR184044 2 0.8713 0.631 0.292 0.708
#> ERR184054 2 0.9795 0.476 0.416 0.584
#> ERR184085 2 0.7674 0.700 0.224 0.776
#> ERR184056 2 0.0000 0.822 0.000 1.000
#> ERR184052 2 0.0672 0.821 0.008 0.992
#> ERR184070 2 0.0672 0.821 0.008 0.992
#> ERR184096 2 0.9795 0.476 0.416 0.584
#> ERR184089 2 0.4690 0.785 0.100 0.900
#> ERR184049 2 0.2236 0.813 0.036 0.964
#> ERR184038 2 0.9608 0.536 0.384 0.616
#> ERR184087 1 0.0000 0.903 1.000 0.000
#> ERR184097 2 0.0000 0.822 0.000 1.000
#> ERR184094 2 0.9833 0.470 0.424 0.576
#> ERR184058 2 0.0672 0.821 0.008 0.992
#> ERR184036 2 0.1414 0.818 0.020 0.980
#> ERR184046 2 0.0672 0.821 0.008 0.992
#> ERR184074 2 0.9522 0.544 0.372 0.628
#> ERR184048 2 0.0000 0.822 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.4865 0.7585 0.832 0.136 0.032
#> ERR184093 2 0.5360 0.7250 0.220 0.768 0.012
#> ERR184051 3 0.2063 0.9519 0.044 0.008 0.948
#> ERR184076 1 0.4931 0.7577 0.828 0.140 0.032
#> ERR184043 3 0.0892 0.9561 0.020 0.000 0.980
#> ERR184037 1 0.7797 0.5178 0.608 0.320 0.072
#> ERR184059 1 0.6950 0.1412 0.508 0.016 0.476
#> ERR184055 1 0.7095 0.5728 0.660 0.292 0.048
#> ERR184065 2 0.4475 0.7171 0.072 0.864 0.064
#> ERR184069 2 0.0237 0.7432 0.004 0.996 0.000
#> ERR184040 1 0.4848 0.7594 0.836 0.128 0.036
#> ERR184057 2 0.0424 0.7444 0.008 0.992 0.000
#> ERR184082 2 0.6570 0.6062 0.308 0.668 0.024
#> ERR184083 2 0.3573 0.7420 0.120 0.876 0.004
#> ERR184039 2 0.3764 0.7308 0.068 0.892 0.040
#> ERR184064 3 0.1163 0.9600 0.028 0.000 0.972
#> ERR184081 2 0.0237 0.7432 0.004 0.996 0.000
#> ERR184095 2 0.0424 0.7417 0.008 0.992 0.000
#> ERR184079 2 0.5698 0.6722 0.252 0.736 0.012
#> ERR184084 1 0.8834 0.1089 0.464 0.116 0.420
#> ERR184068 2 0.5775 0.6718 0.260 0.728 0.012
#> ERR184067 2 0.3412 0.7439 0.124 0.876 0.000
#> ERR184071 2 0.5919 0.6866 0.276 0.712 0.012
#> ERR184042 3 0.4750 0.7962 0.216 0.000 0.784
#> ERR184063 3 0.1711 0.9590 0.032 0.008 0.960
#> ERR184091 2 0.4288 0.7207 0.068 0.872 0.060
#> ERR184061 2 0.6587 0.4817 0.424 0.568 0.008
#> ERR184077 2 0.5843 0.6754 0.252 0.732 0.016
#> ERR184062 1 0.7072 -0.2032 0.504 0.476 0.020
#> ERR184053 2 0.6262 0.6401 0.284 0.696 0.020
#> ERR184088 2 0.6102 0.6541 0.320 0.672 0.008
#> ERR184075 2 0.4660 0.7113 0.072 0.856 0.072
#> ERR184041 3 0.1525 0.9607 0.032 0.004 0.964
#> ERR184060 2 0.5812 0.6944 0.264 0.724 0.012
#> ERR184035 2 0.7366 0.3329 0.400 0.564 0.036
#> ERR184086 2 0.3875 0.7292 0.068 0.888 0.044
#> ERR184080 1 0.6506 0.6754 0.720 0.236 0.044
#> ERR184050 2 0.4658 0.7137 0.076 0.856 0.068
#> ERR184047 1 0.5955 0.6390 0.772 0.048 0.180
#> ERR184092 2 0.3715 0.7451 0.128 0.868 0.004
#> ERR184072 1 0.4848 0.7590 0.836 0.128 0.036
#> ERR184073 1 0.7317 0.6790 0.696 0.096 0.208
#> ERR184066 1 0.5295 0.7517 0.808 0.156 0.036
#> ERR184098 2 0.4087 0.7253 0.068 0.880 0.052
#> ERR184044 2 0.6696 0.5688 0.348 0.632 0.020
#> ERR184054 1 0.4995 0.7560 0.824 0.144 0.032
#> ERR184085 2 0.6541 0.5925 0.304 0.672 0.024
#> ERR184056 2 0.3459 0.7539 0.096 0.892 0.012
#> ERR184052 2 0.2680 0.7426 0.068 0.924 0.008
#> ERR184070 2 0.5465 0.6705 0.288 0.712 0.000
#> ERR184096 1 0.6490 0.6817 0.752 0.076 0.172
#> ERR184089 2 0.6271 0.6276 0.088 0.772 0.140
#> ERR184049 2 0.5956 0.6504 0.324 0.672 0.004
#> ERR184038 2 0.8665 0.0417 0.384 0.508 0.108
#> ERR184087 3 0.1289 0.9605 0.032 0.000 0.968
#> ERR184097 2 0.4390 0.7422 0.148 0.840 0.012
#> ERR184094 1 0.7056 0.5246 0.656 0.044 0.300
#> ERR184058 2 0.0000 0.7423 0.000 1.000 0.000
#> ERR184036 2 0.5244 0.7181 0.240 0.756 0.004
#> ERR184046 2 0.1031 0.7503 0.024 0.976 0.000
#> ERR184074 1 0.6337 0.6943 0.736 0.220 0.044
#> ERR184048 2 0.5659 0.6759 0.248 0.740 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.1388 0.7853 0.960 0.012 0.000 0.028
#> ERR184093 2 0.1820 0.8779 0.020 0.944 0.000 0.036
#> ERR184051 3 0.0188 0.7336 0.000 0.000 0.996 0.004
#> ERR184076 1 0.1510 0.7858 0.956 0.016 0.000 0.028
#> ERR184043 3 0.0336 0.7237 0.000 0.000 0.992 0.008
#> ERR184037 1 0.6003 0.6911 0.736 0.068 0.044 0.152
#> ERR184059 3 0.4673 0.3163 0.132 0.000 0.792 0.076
#> ERR184055 1 0.5075 0.6927 0.776 0.120 0.004 0.100
#> ERR184065 2 0.4776 0.7683 0.000 0.712 0.016 0.272
#> ERR184069 2 0.2281 0.8850 0.000 0.904 0.000 0.096
#> ERR184040 1 0.0469 0.7904 0.988 0.012 0.000 0.000
#> ERR184057 2 0.2281 0.8850 0.000 0.904 0.000 0.096
#> ERR184082 2 0.0524 0.8896 0.008 0.988 0.000 0.004
#> ERR184083 2 0.2011 0.8861 0.000 0.920 0.000 0.080
#> ERR184039 2 0.4012 0.8330 0.000 0.800 0.016 0.184
#> ERR184064 3 0.0000 0.7316 0.000 0.000 1.000 0.000
#> ERR184081 2 0.2345 0.8844 0.000 0.900 0.000 0.100
#> ERR184095 2 0.2081 0.8858 0.000 0.916 0.000 0.084
#> ERR184079 2 0.1406 0.8828 0.016 0.960 0.000 0.024
#> ERR184084 2 0.8839 0.0179 0.148 0.460 0.296 0.096
#> ERR184068 2 0.1820 0.8784 0.020 0.944 0.000 0.036
#> ERR184067 2 0.2081 0.8875 0.000 0.916 0.000 0.084
#> ERR184071 2 0.0524 0.8895 0.000 0.988 0.004 0.008
#> ERR184042 4 0.6673 0.0000 0.140 0.000 0.252 0.608
#> ERR184063 3 0.0188 0.7336 0.000 0.000 0.996 0.004
#> ERR184091 2 0.4690 0.7714 0.000 0.724 0.016 0.260
#> ERR184061 1 0.6865 0.2732 0.548 0.368 0.020 0.064
#> ERR184077 2 0.0469 0.8866 0.000 0.988 0.000 0.012
#> ERR184062 2 0.3813 0.8022 0.148 0.828 0.000 0.024
#> ERR184053 2 0.0188 0.8883 0.000 0.996 0.000 0.004
#> ERR184088 2 0.1724 0.8792 0.020 0.948 0.000 0.032
#> ERR184075 2 0.4868 0.7643 0.000 0.720 0.024 0.256
#> ERR184041 3 0.0188 0.7336 0.000 0.000 0.996 0.004
#> ERR184060 2 0.2876 0.8880 0.008 0.892 0.008 0.092
#> ERR184035 2 0.4473 0.7788 0.152 0.804 0.008 0.036
#> ERR184086 2 0.4630 0.7732 0.000 0.732 0.016 0.252
#> ERR184080 1 0.3229 0.7786 0.880 0.048 0.000 0.072
#> ERR184050 2 0.4661 0.7717 0.000 0.728 0.016 0.256
#> ERR184047 1 0.4791 0.6825 0.784 0.000 0.080 0.136
#> ERR184092 2 0.1510 0.8818 0.016 0.956 0.000 0.028
#> ERR184072 1 0.1584 0.7844 0.952 0.012 0.000 0.036
#> ERR184073 1 0.3030 0.7562 0.892 0.004 0.076 0.028
#> ERR184066 1 0.3647 0.6921 0.852 0.108 0.000 0.040
#> ERR184098 2 0.4364 0.8016 0.000 0.764 0.016 0.220
#> ERR184044 2 0.2002 0.8727 0.044 0.936 0.000 0.020
#> ERR184054 1 0.1284 0.7864 0.964 0.012 0.000 0.024
#> ERR184085 2 0.0672 0.8899 0.008 0.984 0.000 0.008
#> ERR184056 2 0.1706 0.8819 0.016 0.948 0.000 0.036
#> ERR184052 2 0.2727 0.8829 0.004 0.900 0.012 0.084
#> ERR184070 2 0.2926 0.8880 0.012 0.888 0.004 0.096
#> ERR184096 1 0.4222 0.7237 0.832 0.004 0.080 0.084
#> ERR184089 3 0.7771 0.0249 0.000 0.320 0.424 0.256
#> ERR184049 2 0.1398 0.8856 0.004 0.956 0.000 0.040
#> ERR184038 2 0.5805 0.7066 0.140 0.752 0.052 0.056
#> ERR184087 3 0.1936 0.6630 0.028 0.000 0.940 0.032
#> ERR184097 2 0.1820 0.8789 0.020 0.944 0.000 0.036
#> ERR184094 1 0.5680 0.6759 0.752 0.020 0.108 0.120
#> ERR184058 2 0.2281 0.8831 0.000 0.904 0.000 0.096
#> ERR184036 2 0.1767 0.8850 0.012 0.944 0.000 0.044
#> ERR184046 2 0.2384 0.8862 0.004 0.916 0.008 0.072
#> ERR184074 1 0.3796 0.7711 0.852 0.044 0.004 0.100
#> ERR184048 2 0.1151 0.8846 0.008 0.968 0.000 0.024
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.0451 0.813 0.988 0.004 0.000 0.008 0.000
#> ERR184093 2 0.1471 0.877 0.004 0.952 0.000 0.024 0.020
#> ERR184051 3 0.0000 0.903 0.000 0.000 1.000 0.000 0.000
#> ERR184076 1 0.0451 0.813 0.988 0.004 0.000 0.008 0.000
#> ERR184043 3 0.0000 0.903 0.000 0.000 1.000 0.000 0.000
#> ERR184037 1 0.5528 0.620 0.644 0.036 0.008 0.288 0.024
#> ERR184059 3 0.4471 0.422 0.020 0.004 0.684 0.292 0.000
#> ERR184055 1 0.4034 0.765 0.812 0.080 0.000 0.096 0.012
#> ERR184065 5 0.1478 0.893 0.000 0.064 0.000 0.000 0.936
#> ERR184069 2 0.3574 0.823 0.000 0.804 0.000 0.028 0.168
#> ERR184040 1 0.0671 0.817 0.980 0.004 0.000 0.016 0.000
#> ERR184057 2 0.3535 0.827 0.000 0.808 0.000 0.028 0.164
#> ERR184082 2 0.0963 0.878 0.000 0.964 0.000 0.000 0.036
#> ERR184083 2 0.3409 0.823 0.000 0.816 0.000 0.024 0.160
#> ERR184039 5 0.3969 0.581 0.000 0.304 0.000 0.004 0.692
#> ERR184064 3 0.0000 0.903 0.000 0.000 1.000 0.000 0.000
#> ERR184081 2 0.3574 0.823 0.000 0.804 0.000 0.028 0.168
#> ERR184095 2 0.3368 0.826 0.000 0.820 0.000 0.024 0.156
#> ERR184079 2 0.0510 0.879 0.000 0.984 0.000 0.016 0.000
#> ERR184084 2 0.6476 0.432 0.028 0.584 0.072 0.296 0.020
#> ERR184068 2 0.0898 0.876 0.000 0.972 0.000 0.020 0.008
#> ERR184067 2 0.2674 0.856 0.000 0.868 0.000 0.012 0.120
#> ERR184071 2 0.0865 0.880 0.000 0.972 0.000 0.004 0.024
#> ERR184042 4 0.2208 0.000 0.020 0.000 0.072 0.908 0.000
#> ERR184063 3 0.0000 0.903 0.000 0.000 1.000 0.000 0.000
#> ERR184091 5 0.1478 0.893 0.000 0.064 0.000 0.000 0.936
#> ERR184061 1 0.5623 0.387 0.604 0.324 0.000 0.024 0.048
#> ERR184077 2 0.0324 0.880 0.000 0.992 0.000 0.004 0.004
#> ERR184062 2 0.2723 0.814 0.124 0.864 0.000 0.000 0.012
#> ERR184053 2 0.0880 0.878 0.000 0.968 0.000 0.000 0.032
#> ERR184088 2 0.1372 0.875 0.004 0.956 0.000 0.024 0.016
#> ERR184075 5 0.1478 0.893 0.000 0.064 0.000 0.000 0.936
#> ERR184041 3 0.0000 0.903 0.000 0.000 1.000 0.000 0.000
#> ERR184060 2 0.3566 0.827 0.004 0.812 0.000 0.024 0.160
#> ERR184035 2 0.2581 0.850 0.048 0.904 0.000 0.020 0.028
#> ERR184086 5 0.1792 0.882 0.000 0.084 0.000 0.000 0.916
#> ERR184080 1 0.2585 0.812 0.896 0.024 0.000 0.072 0.008
#> ERR184050 5 0.1478 0.893 0.000 0.064 0.000 0.000 0.936
#> ERR184047 1 0.4213 0.648 0.680 0.000 0.012 0.308 0.000
#> ERR184092 2 0.1471 0.879 0.004 0.952 0.000 0.024 0.020
#> ERR184072 1 0.0324 0.813 0.992 0.004 0.000 0.004 0.000
#> ERR184073 1 0.1651 0.817 0.944 0.008 0.012 0.036 0.000
#> ERR184066 1 0.2077 0.749 0.908 0.084 0.000 0.000 0.008
#> ERR184098 5 0.3074 0.767 0.000 0.196 0.000 0.000 0.804
#> ERR184044 2 0.1904 0.875 0.020 0.936 0.000 0.028 0.016
#> ERR184054 1 0.0162 0.814 0.996 0.004 0.000 0.000 0.000
#> ERR184085 2 0.2124 0.874 0.020 0.924 0.000 0.012 0.044
#> ERR184056 2 0.1278 0.878 0.004 0.960 0.000 0.020 0.016
#> ERR184052 2 0.2970 0.829 0.000 0.828 0.000 0.004 0.168
#> ERR184070 2 0.3691 0.826 0.004 0.804 0.000 0.028 0.164
#> ERR184096 1 0.3563 0.738 0.780 0.000 0.012 0.208 0.000
#> ERR184089 5 0.1740 0.876 0.000 0.056 0.012 0.000 0.932
#> ERR184049 2 0.1788 0.870 0.004 0.932 0.000 0.008 0.056
#> ERR184038 2 0.4918 0.776 0.088 0.780 0.012 0.080 0.040
#> ERR184087 3 0.2074 0.804 0.000 0.000 0.896 0.104 0.000
#> ERR184097 2 0.1377 0.878 0.004 0.956 0.000 0.020 0.020
#> ERR184094 1 0.5337 0.640 0.660 0.028 0.024 0.280 0.008
#> ERR184058 2 0.3602 0.807 0.000 0.796 0.000 0.024 0.180
#> ERR184036 2 0.2158 0.870 0.008 0.920 0.000 0.020 0.052
#> ERR184046 2 0.3461 0.825 0.004 0.812 0.000 0.016 0.168
#> ERR184074 1 0.2731 0.804 0.876 0.016 0.000 0.104 0.004
#> ERR184048 2 0.0566 0.880 0.000 0.984 0.000 0.012 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.0622 0.81398 0.980 0.000 0.000 0.012 0.008 0.000
#> ERR184093 2 0.0865 0.76579 0.000 0.964 0.000 0.000 0.036 0.000
#> ERR184051 3 0.0000 0.91454 0.000 0.000 1.000 0.000 0.000 0.000
#> ERR184076 1 0.0622 0.81398 0.980 0.000 0.000 0.012 0.008 0.000
#> ERR184043 3 0.0000 0.91454 0.000 0.000 1.000 0.000 0.000 0.000
#> ERR184037 1 0.5549 0.56388 0.600 0.008 0.004 0.152 0.236 0.000
#> ERR184059 3 0.4316 0.37226 0.000 0.000 0.648 0.312 0.040 0.000
#> ERR184055 1 0.3656 0.73259 0.808 0.124 0.000 0.020 0.048 0.000
#> ERR184065 6 0.0146 0.90111 0.000 0.004 0.000 0.000 0.000 0.996
#> ERR184069 2 0.4650 0.69125 0.000 0.688 0.000 0.004 0.212 0.096
#> ERR184040 1 0.0363 0.81476 0.988 0.000 0.000 0.012 0.000 0.000
#> ERR184057 2 0.4512 0.70750 0.000 0.708 0.000 0.004 0.192 0.096
#> ERR184082 2 0.4736 0.22647 0.012 0.576 0.000 0.000 0.380 0.032
#> ERR184083 2 0.4689 0.69406 0.000 0.696 0.000 0.004 0.172 0.128
#> ERR184039 6 0.3431 0.55370 0.000 0.228 0.000 0.000 0.016 0.756
#> ERR184064 3 0.0000 0.91454 0.000 0.000 1.000 0.000 0.000 0.000
#> ERR184081 2 0.4650 0.69125 0.000 0.688 0.000 0.004 0.212 0.096
#> ERR184095 2 0.4358 0.70457 0.000 0.728 0.000 0.004 0.172 0.096
#> ERR184079 2 0.0632 0.76801 0.000 0.976 0.000 0.000 0.024 0.000
#> ERR184084 5 0.6208 0.00000 0.020 0.088 0.032 0.348 0.512 0.000
#> ERR184068 2 0.1151 0.76757 0.012 0.956 0.000 0.000 0.032 0.000
#> ERR184067 2 0.3253 0.75473 0.000 0.832 0.000 0.004 0.068 0.096
#> ERR184071 2 0.1082 0.77030 0.000 0.956 0.000 0.000 0.004 0.040
#> ERR184042 4 0.1141 0.00000 0.000 0.000 0.052 0.948 0.000 0.000
#> ERR184063 3 0.0146 0.91176 0.000 0.000 0.996 0.000 0.004 0.000
#> ERR184091 6 0.0000 0.90254 0.000 0.000 0.000 0.000 0.000 1.000
#> ERR184061 1 0.4732 0.35897 0.612 0.320 0.000 0.000 0.068 0.000
#> ERR184077 2 0.0363 0.76874 0.000 0.988 0.000 0.000 0.012 0.000
#> ERR184062 2 0.2573 0.71776 0.112 0.864 0.000 0.000 0.024 0.000
#> ERR184053 2 0.4206 0.30350 0.000 0.620 0.000 0.000 0.356 0.024
#> ERR184088 2 0.0777 0.76718 0.004 0.972 0.000 0.000 0.024 0.000
#> ERR184075 6 0.0000 0.90254 0.000 0.000 0.000 0.000 0.000 1.000
#> ERR184041 3 0.0000 0.91454 0.000 0.000 1.000 0.000 0.000 0.000
#> ERR184060 2 0.4422 0.70055 0.000 0.720 0.000 0.004 0.180 0.096
#> ERR184035 2 0.5035 0.09799 0.068 0.548 0.000 0.004 0.380 0.000
#> ERR184086 6 0.0146 0.90124 0.000 0.000 0.000 0.000 0.004 0.996
#> ERR184080 1 0.2151 0.80501 0.912 0.048 0.000 0.016 0.024 0.000
#> ERR184050 6 0.0000 0.90254 0.000 0.000 0.000 0.000 0.000 1.000
#> ERR184047 1 0.5200 0.52485 0.588 0.000 0.004 0.304 0.104 0.000
#> ERR184092 2 0.1088 0.77160 0.000 0.960 0.000 0.000 0.024 0.016
#> ERR184072 1 0.0000 0.81486 1.000 0.000 0.000 0.000 0.000 0.000
#> ERR184073 1 0.1401 0.80962 0.948 0.000 0.004 0.028 0.020 0.000
#> ERR184066 1 0.1643 0.77702 0.924 0.068 0.000 0.000 0.008 0.000
#> ERR184098 6 0.2234 0.75873 0.000 0.124 0.000 0.000 0.004 0.872
#> ERR184044 2 0.2461 0.75866 0.048 0.900 0.000 0.004 0.020 0.028
#> ERR184054 1 0.0146 0.81454 0.996 0.000 0.000 0.000 0.004 0.000
#> ERR184085 2 0.4900 0.41526 0.036 0.636 0.000 0.000 0.296 0.032
#> ERR184056 2 0.0993 0.77183 0.000 0.964 0.000 0.000 0.024 0.012
#> ERR184052 2 0.2821 0.74722 0.000 0.832 0.000 0.000 0.016 0.152
#> ERR184070 2 0.4512 0.69780 0.000 0.708 0.000 0.004 0.192 0.096
#> ERR184096 1 0.4275 0.66599 0.728 0.000 0.004 0.192 0.076 0.000
#> ERR184089 6 0.0146 0.89936 0.000 0.000 0.000 0.004 0.000 0.996
#> ERR184049 2 0.1895 0.76203 0.016 0.912 0.000 0.000 0.072 0.000
#> ERR184038 2 0.6635 -0.00264 0.132 0.464 0.000 0.036 0.348 0.020
#> ERR184087 3 0.1141 0.87081 0.000 0.000 0.948 0.052 0.000 0.000
#> ERR184097 2 0.1049 0.76674 0.008 0.960 0.000 0.000 0.032 0.000
#> ERR184094 1 0.5121 0.58391 0.632 0.004 0.008 0.268 0.088 0.000
#> ERR184058 2 0.5173 0.64100 0.000 0.636 0.000 0.004 0.172 0.188
#> ERR184036 2 0.1802 0.76378 0.012 0.916 0.000 0.000 0.072 0.000
#> ERR184046 2 0.4768 0.68375 0.000 0.688 0.000 0.004 0.168 0.140
#> ERR184074 1 0.2477 0.80089 0.896 0.048 0.000 0.024 0.032 0.000
#> ERR184048 2 0.0363 0.76871 0.000 0.988 0.000 0.000 0.012 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 10269 rows and 62 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 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 0.900 0.926 0.967 0.4898 0.505 0.505
#> 3 3 0.546 0.649 0.847 0.2985 0.791 0.615
#> 4 4 0.520 0.569 0.749 0.1270 0.753 0.466
#> 5 5 0.626 0.668 0.797 0.0807 0.885 0.643
#> 6 6 0.607 0.480 0.716 0.0424 0.936 0.740
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
#> ERR184078 2 0.0000 0.978 0.000 1.000
#> ERR184093 2 0.0000 0.978 0.000 1.000
#> ERR184051 1 0.0000 0.945 1.000 0.000
#> ERR184076 2 0.0000 0.978 0.000 1.000
#> ERR184043 1 0.0000 0.945 1.000 0.000
#> ERR184037 2 0.0000 0.978 0.000 1.000
#> ERR184059 1 0.0000 0.945 1.000 0.000
#> ERR184055 2 0.0000 0.978 0.000 1.000
#> ERR184065 1 0.0000 0.945 1.000 0.000
#> ERR184069 2 0.8713 0.562 0.292 0.708
#> ERR184040 2 0.0000 0.978 0.000 1.000
#> ERR184057 2 0.0000 0.978 0.000 1.000
#> ERR184082 1 0.4690 0.873 0.900 0.100
#> ERR184083 1 0.0672 0.942 0.992 0.008
#> ERR184039 1 0.0000 0.945 1.000 0.000
#> ERR184064 1 0.0000 0.945 1.000 0.000
#> ERR184081 1 0.7815 0.722 0.768 0.232
#> ERR184095 2 0.0000 0.978 0.000 1.000
#> ERR184079 2 0.0000 0.978 0.000 1.000
#> ERR184084 1 0.1414 0.935 0.980 0.020
#> ERR184068 2 0.0000 0.978 0.000 1.000
#> ERR184067 2 0.3584 0.912 0.068 0.932
#> ERR184071 1 0.8016 0.703 0.756 0.244
#> ERR184042 1 0.0376 0.943 0.996 0.004
#> ERR184063 1 0.0000 0.945 1.000 0.000
#> ERR184091 1 0.0000 0.945 1.000 0.000
#> ERR184061 2 0.0000 0.978 0.000 1.000
#> ERR184077 2 0.0000 0.978 0.000 1.000
#> ERR184062 2 0.0000 0.978 0.000 1.000
#> ERR184053 2 0.0938 0.969 0.012 0.988
#> ERR184088 2 0.0000 0.978 0.000 1.000
#> ERR184075 1 0.0000 0.945 1.000 0.000
#> ERR184041 1 0.0000 0.945 1.000 0.000
#> ERR184060 2 0.0000 0.978 0.000 1.000
#> ERR184035 2 0.0000 0.978 0.000 1.000
#> ERR184086 1 0.0000 0.945 1.000 0.000
#> ERR184080 2 0.0000 0.978 0.000 1.000
#> ERR184050 1 0.0000 0.945 1.000 0.000
#> ERR184047 2 0.0000 0.978 0.000 1.000
#> ERR184092 2 0.0000 0.978 0.000 1.000
#> ERR184072 2 0.0000 0.978 0.000 1.000
#> ERR184073 2 0.0672 0.972 0.008 0.992
#> ERR184066 2 0.0000 0.978 0.000 1.000
#> ERR184098 1 0.0000 0.945 1.000 0.000
#> ERR184044 2 0.0672 0.972 0.008 0.992
#> ERR184054 2 0.0000 0.978 0.000 1.000
#> ERR184085 1 0.9491 0.462 0.632 0.368
#> ERR184056 2 0.0000 0.978 0.000 1.000
#> ERR184052 1 0.2603 0.919 0.956 0.044
#> ERR184070 2 0.0000 0.978 0.000 1.000
#> ERR184096 2 0.0000 0.978 0.000 1.000
#> ERR184089 1 0.0000 0.945 1.000 0.000
#> ERR184049 2 0.0938 0.968 0.012 0.988
#> ERR184038 1 0.8861 0.599 0.696 0.304
#> ERR184087 1 0.0000 0.945 1.000 0.000
#> ERR184097 2 0.0000 0.978 0.000 1.000
#> ERR184094 2 0.8955 0.519 0.312 0.688
#> ERR184058 1 0.0938 0.940 0.988 0.012
#> ERR184036 2 0.0000 0.978 0.000 1.000
#> ERR184046 1 0.0000 0.945 1.000 0.000
#> ERR184074 2 0.0000 0.978 0.000 1.000
#> ERR184048 2 0.0000 0.978 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.1031 0.8466 0.976 0.000 0.024
#> ERR184093 1 0.0237 0.8520 0.996 0.004 0.000
#> ERR184051 3 0.2261 0.7431 0.000 0.068 0.932
#> ERR184076 1 0.1529 0.8404 0.960 0.000 0.040
#> ERR184043 3 0.2261 0.7433 0.000 0.068 0.932
#> ERR184037 1 0.1411 0.8497 0.964 0.036 0.000
#> ERR184059 3 0.0475 0.7216 0.004 0.004 0.992
#> ERR184055 1 0.0424 0.8523 0.992 0.008 0.000
#> ERR184065 2 0.3038 0.6896 0.000 0.896 0.104
#> ERR184069 2 0.0592 0.7501 0.012 0.988 0.000
#> ERR184040 1 0.0237 0.8509 0.996 0.000 0.004
#> ERR184057 1 0.6309 0.2299 0.504 0.496 0.000
#> ERR184082 2 0.1643 0.7421 0.000 0.956 0.044
#> ERR184083 2 0.0424 0.7556 0.000 0.992 0.008
#> ERR184039 2 0.1964 0.7333 0.000 0.944 0.056
#> ERR184064 3 0.4452 0.7159 0.000 0.192 0.808
#> ERR184081 2 0.0000 0.7546 0.000 1.000 0.000
#> ERR184095 2 0.5988 0.1860 0.368 0.632 0.000
#> ERR184079 1 0.2066 0.8437 0.940 0.060 0.000
#> ERR184084 3 0.6516 0.1970 0.004 0.480 0.516
#> ERR184068 1 0.3412 0.8147 0.876 0.124 0.000
#> ERR184067 2 0.3482 0.6409 0.128 0.872 0.000
#> ERR184071 2 0.0829 0.7537 0.012 0.984 0.004
#> ERR184042 3 0.1529 0.7060 0.040 0.000 0.960
#> ERR184063 3 0.3941 0.7318 0.000 0.156 0.844
#> ERR184091 2 0.2448 0.7170 0.000 0.924 0.076
#> ERR184061 1 0.0592 0.8532 0.988 0.012 0.000
#> ERR184077 1 0.4121 0.7831 0.832 0.168 0.000
#> ERR184062 1 0.4178 0.7459 0.828 0.000 0.172
#> ERR184053 1 0.6309 0.2218 0.500 0.500 0.000
#> ERR184088 1 0.3619 0.8067 0.864 0.136 0.000
#> ERR184075 2 0.5948 0.2336 0.000 0.640 0.360
#> ERR184041 3 0.5327 0.6390 0.000 0.272 0.728
#> ERR184060 1 0.5497 0.6450 0.708 0.292 0.000
#> ERR184035 1 0.4178 0.7780 0.828 0.172 0.000
#> ERR184086 2 0.6267 -0.0728 0.000 0.548 0.452
#> ERR184080 1 0.0424 0.8523 0.992 0.008 0.000
#> ERR184050 2 0.6111 0.1237 0.000 0.604 0.396
#> ERR184047 1 0.5363 0.6072 0.724 0.000 0.276
#> ERR184092 1 0.1753 0.8473 0.952 0.048 0.000
#> ERR184072 1 0.1163 0.8451 0.972 0.000 0.028
#> ERR184073 1 0.4931 0.6715 0.768 0.000 0.232
#> ERR184066 1 0.2261 0.8270 0.932 0.000 0.068
#> ERR184098 2 0.6308 -0.2115 0.000 0.508 0.492
#> ERR184044 1 0.4605 0.7101 0.796 0.000 0.204
#> ERR184054 1 0.1289 0.8444 0.968 0.000 0.032
#> ERR184085 2 0.0983 0.7493 0.016 0.980 0.004
#> ERR184056 1 0.0424 0.8523 0.992 0.008 0.000
#> ERR184052 2 0.0237 0.7556 0.000 0.996 0.004
#> ERR184070 1 0.2537 0.8367 0.920 0.080 0.000
#> ERR184096 1 0.2165 0.8293 0.936 0.000 0.064
#> ERR184089 3 0.6235 0.3270 0.000 0.436 0.564
#> ERR184049 2 0.6095 0.1107 0.392 0.608 0.000
#> ERR184038 3 0.3267 0.6576 0.116 0.000 0.884
#> ERR184087 3 0.4654 0.7050 0.000 0.208 0.792
#> ERR184097 1 0.0237 0.8516 0.996 0.000 0.004
#> ERR184094 3 0.6111 0.2161 0.396 0.000 0.604
#> ERR184058 2 0.0424 0.7556 0.000 0.992 0.008
#> ERR184036 1 0.6215 0.4026 0.572 0.428 0.000
#> ERR184046 2 0.0424 0.7556 0.000 0.992 0.008
#> ERR184074 1 0.0000 0.8513 1.000 0.000 0.000
#> ERR184048 1 0.5905 0.5496 0.648 0.352 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.0927 0.726 0.976 0.008 0.000 0.016
#> ERR184093 1 0.1837 0.730 0.944 0.028 0.000 0.028
#> ERR184051 3 0.2466 0.609 0.004 0.000 0.900 0.096
#> ERR184076 1 0.0992 0.726 0.976 0.008 0.004 0.012
#> ERR184043 3 0.0817 0.685 0.000 0.000 0.976 0.024
#> ERR184037 1 0.7485 0.347 0.472 0.192 0.000 0.336
#> ERR184059 3 0.4098 0.426 0.012 0.000 0.784 0.204
#> ERR184055 1 0.5272 0.604 0.680 0.032 0.000 0.288
#> ERR184065 3 0.6350 0.546 0.000 0.364 0.564 0.072
#> ERR184069 2 0.4465 0.650 0.004 0.776 0.020 0.200
#> ERR184040 1 0.1042 0.730 0.972 0.008 0.000 0.020
#> ERR184057 2 0.4692 0.630 0.032 0.756 0.000 0.212
#> ERR184082 2 0.3752 0.692 0.056 0.872 0.036 0.036
#> ERR184083 2 0.1888 0.686 0.000 0.940 0.044 0.016
#> ERR184039 3 0.6751 0.447 0.000 0.396 0.508 0.096
#> ERR184064 3 0.1042 0.708 0.000 0.020 0.972 0.008
#> ERR184081 2 0.3398 0.686 0.000 0.872 0.060 0.068
#> ERR184095 2 0.3801 0.688 0.064 0.856 0.004 0.076
#> ERR184079 1 0.6586 0.176 0.544 0.368 0.000 0.088
#> ERR184084 2 0.7381 0.479 0.064 0.620 0.228 0.088
#> ERR184068 2 0.6011 0.197 0.480 0.480 0.000 0.040
#> ERR184067 2 0.5304 0.560 0.012 0.672 0.012 0.304
#> ERR184071 2 0.2853 0.673 0.008 0.900 0.076 0.016
#> ERR184042 4 0.5643 0.092 0.024 0.000 0.428 0.548
#> ERR184063 3 0.1576 0.672 0.000 0.004 0.948 0.048
#> ERR184091 3 0.6285 0.473 0.000 0.412 0.528 0.060
#> ERR184061 1 0.6041 0.546 0.608 0.060 0.000 0.332
#> ERR184077 2 0.5953 0.542 0.268 0.656 0.000 0.076
#> ERR184062 1 0.1929 0.703 0.940 0.000 0.036 0.024
#> ERR184053 2 0.4972 0.657 0.136 0.780 0.004 0.080
#> ERR184088 1 0.7518 0.348 0.496 0.260 0.000 0.244
#> ERR184075 3 0.5257 0.697 0.000 0.212 0.728 0.060
#> ERR184041 3 0.1211 0.719 0.000 0.040 0.960 0.000
#> ERR184060 1 0.7386 0.390 0.552 0.264 0.008 0.176
#> ERR184035 2 0.5839 0.452 0.352 0.604 0.000 0.044
#> ERR184086 3 0.4701 0.723 0.000 0.164 0.780 0.056
#> ERR184080 1 0.2593 0.726 0.904 0.016 0.000 0.080
#> ERR184050 3 0.5091 0.713 0.000 0.180 0.752 0.068
#> ERR184047 1 0.5559 0.618 0.740 0.004 0.136 0.120
#> ERR184092 1 0.4352 0.693 0.816 0.080 0.000 0.104
#> ERR184072 1 0.1443 0.729 0.960 0.008 0.004 0.028
#> ERR184073 1 0.4837 0.639 0.792 0.008 0.136 0.064
#> ERR184066 1 0.0927 0.725 0.976 0.000 0.016 0.008
#> ERR184098 3 0.4022 0.734 0.000 0.096 0.836 0.068
#> ERR184044 1 0.7196 0.442 0.568 0.020 0.104 0.308
#> ERR184054 1 0.0469 0.730 0.988 0.000 0.000 0.012
#> ERR184085 2 0.2644 0.695 0.000 0.908 0.032 0.060
#> ERR184056 1 0.1406 0.728 0.960 0.024 0.000 0.016
#> ERR184052 2 0.5522 0.480 0.000 0.716 0.204 0.080
#> ERR184070 1 0.7007 0.474 0.548 0.144 0.000 0.308
#> ERR184096 1 0.2214 0.725 0.928 0.000 0.028 0.044
#> ERR184089 3 0.3858 0.735 0.000 0.100 0.844 0.056
#> ERR184049 2 0.6860 0.404 0.084 0.564 0.012 0.340
#> ERR184038 4 0.8203 0.266 0.180 0.032 0.316 0.472
#> ERR184087 3 0.1042 0.696 0.000 0.008 0.972 0.020
#> ERR184097 1 0.1297 0.720 0.964 0.020 0.000 0.016
#> ERR184094 1 0.7783 0.131 0.468 0.008 0.328 0.196
#> ERR184058 2 0.4542 0.621 0.000 0.804 0.108 0.088
#> ERR184036 4 0.8074 -0.311 0.316 0.328 0.004 0.352
#> ERR184046 2 0.4920 0.515 0.000 0.756 0.192 0.052
#> ERR184074 1 0.4936 0.622 0.700 0.020 0.000 0.280
#> ERR184048 2 0.4713 0.641 0.172 0.776 0.000 0.052
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.1186 0.841 0.964 0.020 0.000 0.008 0.008
#> ERR184093 1 0.3287 0.815 0.848 0.008 0.008 0.012 0.124
#> ERR184051 3 0.3969 0.631 0.004 0.000 0.692 0.304 0.000
#> ERR184076 1 0.1488 0.843 0.956 0.008 0.008 0.012 0.016
#> ERR184043 3 0.3010 0.754 0.004 0.000 0.824 0.172 0.000
#> ERR184037 5 0.2511 0.715 0.088 0.016 0.000 0.004 0.892
#> ERR184059 3 0.4590 0.407 0.012 0.000 0.568 0.420 0.000
#> ERR184055 5 0.3289 0.709 0.172 0.004 0.000 0.008 0.816
#> ERR184065 3 0.2727 0.733 0.000 0.116 0.868 0.000 0.016
#> ERR184069 2 0.4622 0.318 0.000 0.548 0.012 0.000 0.440
#> ERR184040 1 0.1408 0.852 0.948 0.008 0.000 0.000 0.044
#> ERR184057 2 0.4209 0.654 0.016 0.732 0.000 0.008 0.244
#> ERR184082 2 0.2438 0.737 0.032 0.916 0.032 0.012 0.008
#> ERR184083 2 0.1492 0.736 0.000 0.948 0.040 0.004 0.008
#> ERR184039 3 0.3823 0.670 0.000 0.140 0.808 0.004 0.048
#> ERR184064 3 0.2648 0.768 0.000 0.000 0.848 0.152 0.000
#> ERR184081 2 0.4451 0.658 0.000 0.712 0.040 0.000 0.248
#> ERR184095 2 0.2804 0.724 0.020 0.892 0.004 0.016 0.068
#> ERR184079 5 0.7414 0.275 0.328 0.244 0.008 0.020 0.400
#> ERR184084 2 0.3484 0.704 0.032 0.868 0.028 0.056 0.016
#> ERR184068 2 0.5534 0.308 0.360 0.580 0.000 0.020 0.040
#> ERR184067 5 0.3826 0.493 0.008 0.236 0.004 0.000 0.752
#> ERR184071 2 0.3430 0.719 0.016 0.844 0.120 0.004 0.016
#> ERR184042 4 0.1569 0.612 0.008 0.000 0.032 0.948 0.012
#> ERR184063 3 0.3534 0.693 0.000 0.000 0.744 0.256 0.000
#> ERR184091 3 0.3039 0.703 0.000 0.152 0.836 0.000 0.012
#> ERR184061 5 0.2733 0.712 0.112 0.004 0.000 0.012 0.872
#> ERR184077 2 0.3514 0.698 0.056 0.852 0.000 0.020 0.072
#> ERR184062 1 0.1913 0.827 0.936 0.000 0.020 0.024 0.020
#> ERR184053 2 0.3519 0.701 0.040 0.848 0.000 0.020 0.092
#> ERR184088 5 0.5169 0.633 0.248 0.068 0.000 0.008 0.676
#> ERR184075 3 0.1492 0.797 0.000 0.040 0.948 0.008 0.004
#> ERR184041 3 0.1965 0.788 0.000 0.000 0.904 0.096 0.000
#> ERR184060 5 0.7565 0.243 0.368 0.136 0.064 0.008 0.424
#> ERR184035 2 0.4773 0.604 0.216 0.716 0.000 0.004 0.064
#> ERR184086 3 0.0992 0.795 0.000 0.024 0.968 0.000 0.008
#> ERR184080 1 0.4083 0.625 0.728 0.008 0.000 0.008 0.256
#> ERR184050 3 0.1828 0.785 0.000 0.032 0.936 0.004 0.028
#> ERR184047 1 0.5937 0.562 0.660 0.004 0.020 0.140 0.176
#> ERR184092 1 0.5291 0.436 0.632 0.044 0.004 0.008 0.312
#> ERR184072 1 0.2812 0.828 0.876 0.004 0.000 0.024 0.096
#> ERR184073 1 0.4773 0.728 0.744 0.004 0.024 0.036 0.192
#> ERR184066 1 0.0955 0.850 0.968 0.004 0.000 0.000 0.028
#> ERR184098 3 0.1173 0.799 0.000 0.004 0.964 0.020 0.012
#> ERR184044 5 0.7237 0.250 0.344 0.000 0.044 0.168 0.444
#> ERR184054 1 0.1522 0.852 0.944 0.000 0.000 0.012 0.044
#> ERR184085 2 0.3613 0.727 0.000 0.840 0.032 0.024 0.104
#> ERR184056 1 0.1653 0.845 0.944 0.028 0.000 0.004 0.024
#> ERR184052 2 0.6124 0.260 0.000 0.460 0.412 0.000 0.128
#> ERR184070 5 0.3376 0.723 0.108 0.032 0.000 0.012 0.848
#> ERR184096 1 0.2518 0.842 0.896 0.000 0.008 0.016 0.080
#> ERR184089 3 0.0693 0.800 0.000 0.008 0.980 0.012 0.000
#> ERR184049 5 0.2452 0.667 0.016 0.084 0.004 0.000 0.896
#> ERR184038 4 0.7139 0.587 0.260 0.124 0.048 0.552 0.016
#> ERR184087 3 0.3336 0.720 0.000 0.000 0.772 0.228 0.000
#> ERR184097 1 0.1492 0.831 0.948 0.040 0.000 0.004 0.008
#> ERR184094 5 0.6437 0.505 0.108 0.000 0.080 0.176 0.636
#> ERR184058 2 0.4847 0.628 0.000 0.692 0.240 0.000 0.068
#> ERR184036 5 0.2806 0.689 0.028 0.056 0.012 0.008 0.896
#> ERR184046 2 0.4313 0.608 0.008 0.704 0.276 0.000 0.012
#> ERR184074 5 0.3596 0.683 0.200 0.000 0.000 0.016 0.784
#> ERR184048 2 0.1597 0.733 0.048 0.940 0.000 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.1554 0.64534 0.940 0.008 0.000 0.004 0.044 0.004
#> ERR184093 5 0.6280 0.04849 0.384 0.060 0.004 0.008 0.480 0.064
#> ERR184051 3 0.3894 0.62305 0.008 0.000 0.732 0.240 0.016 0.004
#> ERR184076 1 0.1296 0.63748 0.948 0.004 0.000 0.004 0.044 0.000
#> ERR184043 3 0.2908 0.71139 0.008 0.000 0.840 0.140 0.004 0.008
#> ERR184037 6 0.2157 0.62376 0.076 0.008 0.000 0.004 0.008 0.904
#> ERR184059 3 0.4461 0.43544 0.016 0.000 0.604 0.368 0.008 0.004
#> ERR184055 6 0.3827 0.55741 0.256 0.000 0.000 0.004 0.020 0.720
#> ERR184065 3 0.3578 0.65535 0.000 0.152 0.800 0.000 0.016 0.032
#> ERR184069 6 0.4954 -0.14809 0.000 0.444 0.012 0.000 0.040 0.504
#> ERR184040 1 0.1857 0.63666 0.924 0.004 0.000 0.000 0.028 0.044
#> ERR184057 2 0.6091 0.26325 0.020 0.452 0.000 0.000 0.152 0.376
#> ERR184082 2 0.3146 0.59771 0.028 0.868 0.008 0.016 0.068 0.012
#> ERR184083 2 0.2122 0.63458 0.000 0.916 0.024 0.000 0.032 0.028
#> ERR184039 3 0.6051 0.29950 0.000 0.320 0.540 0.008 0.040 0.092
#> ERR184064 3 0.2101 0.73407 0.004 0.000 0.892 0.100 0.000 0.004
#> ERR184081 2 0.6042 0.30593 0.000 0.476 0.024 0.004 0.116 0.380
#> ERR184095 2 0.5055 0.52608 0.012 0.624 0.000 0.004 0.296 0.064
#> ERR184079 5 0.7278 0.12878 0.076 0.344 0.000 0.008 0.348 0.224
#> ERR184084 2 0.4652 0.56899 0.024 0.776 0.020 0.088 0.080 0.012
#> ERR184068 2 0.5920 0.04937 0.188 0.536 0.000 0.004 0.264 0.008
#> ERR184067 6 0.3695 0.50558 0.000 0.176 0.000 0.004 0.044 0.776
#> ERR184071 2 0.5612 0.60701 0.024 0.692 0.116 0.000 0.104 0.064
#> ERR184042 4 0.0820 0.51682 0.000 0.000 0.012 0.972 0.016 0.000
#> ERR184063 3 0.3468 0.67395 0.008 0.000 0.784 0.192 0.012 0.004
#> ERR184091 3 0.3178 0.67896 0.000 0.128 0.832 0.000 0.012 0.028
#> ERR184061 6 0.3526 0.50868 0.028 0.004 0.000 0.004 0.172 0.792
#> ERR184077 2 0.5062 0.40044 0.024 0.532 0.000 0.008 0.416 0.020
#> ERR184062 1 0.3990 0.46989 0.728 0.000 0.016 0.004 0.240 0.012
#> ERR184053 2 0.5410 0.40720 0.020 0.516 0.000 0.004 0.404 0.056
#> ERR184088 6 0.6264 0.30877 0.332 0.124 0.000 0.004 0.040 0.500
#> ERR184075 3 0.1096 0.75029 0.000 0.020 0.964 0.004 0.008 0.004
#> ERR184041 3 0.1573 0.74763 0.004 0.004 0.936 0.052 0.000 0.004
#> ERR184060 1 0.7430 -0.16577 0.400 0.172 0.036 0.004 0.052 0.336
#> ERR184035 2 0.4942 0.46840 0.180 0.704 0.000 0.000 0.052 0.064
#> ERR184086 3 0.1621 0.74786 0.000 0.016 0.944 0.008 0.020 0.012
#> ERR184080 1 0.3304 0.56158 0.816 0.004 0.000 0.000 0.040 0.140
#> ERR184050 3 0.3832 0.69345 0.000 0.044 0.820 0.008 0.080 0.048
#> ERR184047 1 0.5774 0.39872 0.644 0.000 0.016 0.140 0.032 0.168
#> ERR184092 5 0.7151 0.32271 0.288 0.080 0.000 0.000 0.364 0.268
#> ERR184072 1 0.5246 -0.00801 0.496 0.008 0.000 0.004 0.432 0.060
#> ERR184073 1 0.5909 -0.05664 0.456 0.000 0.012 0.012 0.420 0.100
#> ERR184066 1 0.2537 0.63587 0.880 0.000 0.008 0.000 0.088 0.024
#> ERR184098 3 0.1490 0.75020 0.000 0.008 0.948 0.004 0.024 0.016
#> ERR184044 6 0.7175 0.16223 0.352 0.000 0.044 0.128 0.052 0.424
#> ERR184054 1 0.3593 0.58865 0.788 0.004 0.000 0.000 0.164 0.044
#> ERR184085 2 0.3897 0.57973 0.000 0.780 0.004 0.016 0.036 0.164
#> ERR184056 1 0.2002 0.63310 0.916 0.008 0.000 0.000 0.056 0.020
#> ERR184052 3 0.7186 -0.13157 0.016 0.320 0.404 0.000 0.060 0.200
#> ERR184070 6 0.3194 0.61008 0.168 0.020 0.000 0.000 0.004 0.808
#> ERR184096 1 0.4841 0.51473 0.696 0.004 0.008 0.004 0.204 0.084
#> ERR184089 3 0.0146 0.75168 0.000 0.004 0.996 0.000 0.000 0.000
#> ERR184049 6 0.2312 0.58236 0.000 0.080 0.004 0.008 0.012 0.896
#> ERR184038 4 0.7650 0.45256 0.232 0.092 0.044 0.464 0.164 0.004
#> ERR184087 3 0.2845 0.70035 0.004 0.000 0.820 0.172 0.000 0.004
#> ERR184097 1 0.1908 0.62777 0.900 0.000 0.000 0.000 0.096 0.004
#> ERR184094 6 0.6097 0.43738 0.068 0.000 0.084 0.176 0.032 0.640
#> ERR184058 2 0.5172 0.52339 0.000 0.676 0.184 0.000 0.032 0.108
#> ERR184036 6 0.2512 0.58608 0.004 0.028 0.004 0.008 0.060 0.896
#> ERR184046 2 0.4726 0.52401 0.000 0.708 0.196 0.000 0.068 0.028
#> ERR184074 6 0.4354 0.50995 0.240 0.000 0.000 0.000 0.068 0.692
#> ERR184048 2 0.2778 0.61893 0.032 0.872 0.000 0.000 0.080 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
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 10269 rows and 62 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.969 0.982 0.0914 0.906 0.906
#> 3 3 1.000 0.961 0.987 0.2705 0.999 0.999
#> 4 4 0.662 0.845 0.932 2.1815 0.762 0.737
#> 5 5 0.638 0.768 0.902 0.2649 0.860 0.791
#> 6 6 0.610 0.787 0.899 0.0740 0.948 0.902
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
#> ERR184078 2 0.0000 0.988 0.000 1.000
#> ERR184093 2 0.0000 0.988 0.000 1.000
#> ERR184051 2 0.3114 0.938 0.056 0.944
#> ERR184076 2 0.0000 0.988 0.000 1.000
#> ERR184043 2 0.3114 0.938 0.056 0.944
#> ERR184037 2 0.0000 0.988 0.000 1.000
#> ERR184059 2 0.3431 0.929 0.064 0.936
#> ERR184055 2 0.0000 0.988 0.000 1.000
#> ERR184065 2 0.0000 0.988 0.000 1.000
#> ERR184069 2 0.0000 0.988 0.000 1.000
#> ERR184040 2 0.2778 0.945 0.048 0.952
#> ERR184057 2 0.0000 0.988 0.000 1.000
#> ERR184082 2 0.0000 0.988 0.000 1.000
#> ERR184083 2 0.0000 0.988 0.000 1.000
#> ERR184039 2 0.0000 0.988 0.000 1.000
#> ERR184064 2 0.3114 0.938 0.056 0.944
#> ERR184081 2 0.0000 0.988 0.000 1.000
#> ERR184095 2 0.0000 0.988 0.000 1.000
#> ERR184079 2 0.0000 0.988 0.000 1.000
#> ERR184084 2 0.0000 0.988 0.000 1.000
#> ERR184068 2 0.0000 0.988 0.000 1.000
#> ERR184067 2 0.0000 0.988 0.000 1.000
#> ERR184071 2 0.0000 0.988 0.000 1.000
#> ERR184042 1 0.0000 0.709 1.000 0.000
#> ERR184063 2 0.3114 0.938 0.056 0.944
#> ERR184091 2 0.0000 0.988 0.000 1.000
#> ERR184061 2 0.0000 0.988 0.000 1.000
#> ERR184077 2 0.0000 0.988 0.000 1.000
#> ERR184062 2 0.0000 0.988 0.000 1.000
#> ERR184053 2 0.0000 0.988 0.000 1.000
#> ERR184088 2 0.0000 0.988 0.000 1.000
#> ERR184075 2 0.0000 0.988 0.000 1.000
#> ERR184041 2 0.3114 0.938 0.056 0.944
#> ERR184060 2 0.0000 0.988 0.000 1.000
#> ERR184035 2 0.0000 0.988 0.000 1.000
#> ERR184086 2 0.0000 0.988 0.000 1.000
#> ERR184080 2 0.0000 0.988 0.000 1.000
#> ERR184050 2 0.0000 0.988 0.000 1.000
#> ERR184047 1 0.8555 0.799 0.720 0.280
#> ERR184092 2 0.0000 0.988 0.000 1.000
#> ERR184072 2 0.0000 0.988 0.000 1.000
#> ERR184073 2 0.2778 0.946 0.048 0.952
#> ERR184066 2 0.0000 0.988 0.000 1.000
#> ERR184098 2 0.0000 0.988 0.000 1.000
#> ERR184044 2 0.0000 0.988 0.000 1.000
#> ERR184054 2 0.0938 0.978 0.012 0.988
#> ERR184085 2 0.0000 0.988 0.000 1.000
#> ERR184056 2 0.0000 0.988 0.000 1.000
#> ERR184052 2 0.0000 0.988 0.000 1.000
#> ERR184070 2 0.0000 0.988 0.000 1.000
#> ERR184096 1 0.8555 0.799 0.720 0.280
#> ERR184089 2 0.0000 0.988 0.000 1.000
#> ERR184049 2 0.0000 0.988 0.000 1.000
#> ERR184038 2 0.0000 0.988 0.000 1.000
#> ERR184087 2 0.3114 0.938 0.056 0.944
#> ERR184097 2 0.0000 0.988 0.000 1.000
#> ERR184094 2 0.2778 0.946 0.048 0.952
#> ERR184058 2 0.0000 0.988 0.000 1.000
#> ERR184036 2 0.0000 0.988 0.000 1.000
#> ERR184046 2 0.0000 0.988 0.000 1.000
#> ERR184074 2 0.1414 0.972 0.020 0.980
#> ERR184048 2 0.0000 0.988 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 2 0.0000 0.986 0.000 1.000 0
#> ERR184093 2 0.0000 0.986 0.000 1.000 0
#> ERR184051 2 0.2066 0.945 0.060 0.940 0
#> ERR184076 2 0.0000 0.986 0.000 1.000 0
#> ERR184043 2 0.2625 0.924 0.084 0.916 0
#> ERR184037 2 0.0000 0.986 0.000 1.000 0
#> ERR184059 2 0.2959 0.908 0.100 0.900 0
#> ERR184055 2 0.0000 0.986 0.000 1.000 0
#> ERR184065 2 0.0000 0.986 0.000 1.000 0
#> ERR184069 2 0.0000 0.986 0.000 1.000 0
#> ERR184040 2 0.2959 0.902 0.100 0.900 0
#> ERR184057 2 0.0000 0.986 0.000 1.000 0
#> ERR184082 2 0.0000 0.986 0.000 1.000 0
#> ERR184083 2 0.0000 0.986 0.000 1.000 0
#> ERR184039 2 0.0000 0.986 0.000 1.000 0
#> ERR184064 2 0.2625 0.924 0.084 0.916 0
#> ERR184081 2 0.0000 0.986 0.000 1.000 0
#> ERR184095 2 0.0000 0.986 0.000 1.000 0
#> ERR184079 2 0.0000 0.986 0.000 1.000 0
#> ERR184084 2 0.0237 0.984 0.004 0.996 0
#> ERR184068 2 0.0000 0.986 0.000 1.000 0
#> ERR184067 2 0.0000 0.986 0.000 1.000 0
#> ERR184071 2 0.0000 0.986 0.000 1.000 0
#> ERR184042 3 0.0000 0.000 0.000 0.000 1
#> ERR184063 2 0.2066 0.945 0.060 0.940 0
#> ERR184091 2 0.0000 0.986 0.000 1.000 0
#> ERR184061 2 0.0000 0.986 0.000 1.000 0
#> ERR184077 2 0.0000 0.986 0.000 1.000 0
#> ERR184062 2 0.0000 0.986 0.000 1.000 0
#> ERR184053 2 0.0000 0.986 0.000 1.000 0
#> ERR184088 2 0.0000 0.986 0.000 1.000 0
#> ERR184075 2 0.0000 0.986 0.000 1.000 0
#> ERR184041 2 0.2066 0.945 0.060 0.940 0
#> ERR184060 2 0.0000 0.986 0.000 1.000 0
#> ERR184035 2 0.0000 0.986 0.000 1.000 0
#> ERR184086 2 0.0000 0.986 0.000 1.000 0
#> ERR184080 2 0.0000 0.986 0.000 1.000 0
#> ERR184050 2 0.0000 0.986 0.000 1.000 0
#> ERR184047 1 0.0000 1.000 1.000 0.000 0
#> ERR184092 2 0.0000 0.986 0.000 1.000 0
#> ERR184072 2 0.0000 0.986 0.000 1.000 0
#> ERR184073 2 0.1860 0.951 0.052 0.948 0
#> ERR184066 2 0.0237 0.984 0.004 0.996 0
#> ERR184098 2 0.0000 0.986 0.000 1.000 0
#> ERR184044 2 0.0000 0.986 0.000 1.000 0
#> ERR184054 2 0.0747 0.976 0.016 0.984 0
#> ERR184085 2 0.0000 0.986 0.000 1.000 0
#> ERR184056 2 0.0000 0.986 0.000 1.000 0
#> ERR184052 2 0.0000 0.986 0.000 1.000 0
#> ERR184070 2 0.0000 0.986 0.000 1.000 0
#> ERR184096 1 0.0000 1.000 1.000 0.000 0
#> ERR184089 2 0.0000 0.986 0.000 1.000 0
#> ERR184049 2 0.0000 0.986 0.000 1.000 0
#> ERR184038 2 0.0000 0.986 0.000 1.000 0
#> ERR184087 2 0.2625 0.924 0.084 0.916 0
#> ERR184097 2 0.0000 0.986 0.000 1.000 0
#> ERR184094 2 0.2448 0.931 0.076 0.924 0
#> ERR184058 2 0.0000 0.986 0.000 1.000 0
#> ERR184036 2 0.0000 0.986 0.000 1.000 0
#> ERR184046 2 0.0000 0.986 0.000 1.000 0
#> ERR184074 2 0.1031 0.972 0.024 0.976 0
#> ERR184048 2 0.0000 0.986 0.000 1.000 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 2 0.3024 0.833 0.000 0.852 0.148 0
#> ERR184093 2 0.0188 0.930 0.000 0.996 0.004 0
#> ERR184051 3 0.3649 0.739 0.000 0.204 0.796 0
#> ERR184076 2 0.3172 0.816 0.000 0.840 0.160 0
#> ERR184043 3 0.1792 0.857 0.000 0.068 0.932 0
#> ERR184037 2 0.2281 0.876 0.000 0.904 0.096 0
#> ERR184059 3 0.1489 0.811 0.004 0.044 0.952 0
#> ERR184055 2 0.1940 0.894 0.000 0.924 0.076 0
#> ERR184065 2 0.0336 0.930 0.000 0.992 0.008 0
#> ERR184069 2 0.0000 0.930 0.000 1.000 0.000 0
#> ERR184040 2 0.6396 0.239 0.076 0.564 0.360 0
#> ERR184057 2 0.0000 0.930 0.000 1.000 0.000 0
#> ERR184082 2 0.4431 0.549 0.000 0.696 0.304 0
#> ERR184083 2 0.0000 0.930 0.000 1.000 0.000 0
#> ERR184039 2 0.0336 0.930 0.000 0.992 0.008 0
#> ERR184064 3 0.1792 0.857 0.000 0.068 0.932 0
#> ERR184081 2 0.0000 0.930 0.000 1.000 0.000 0
#> ERR184095 2 0.0000 0.930 0.000 1.000 0.000 0
#> ERR184079 2 0.0817 0.923 0.000 0.976 0.024 0
#> ERR184084 2 0.4855 0.315 0.000 0.600 0.400 0
#> ERR184068 2 0.1211 0.913 0.000 0.960 0.040 0
#> ERR184067 2 0.0000 0.930 0.000 1.000 0.000 0
#> ERR184071 2 0.0000 0.930 0.000 1.000 0.000 0
#> ERR184042 4 0.0000 0.000 0.000 0.000 0.000 1
#> ERR184063 3 0.2408 0.860 0.000 0.104 0.896 0
#> ERR184091 2 0.0188 0.930 0.000 0.996 0.004 0
#> ERR184061 2 0.1211 0.921 0.000 0.960 0.040 0
#> ERR184077 2 0.0000 0.930 0.000 1.000 0.000 0
#> ERR184062 2 0.0336 0.929 0.000 0.992 0.008 0
#> ERR184053 2 0.1211 0.913 0.000 0.960 0.040 0
#> ERR184088 2 0.0592 0.928 0.000 0.984 0.016 0
#> ERR184075 2 0.0336 0.930 0.000 0.992 0.008 0
#> ERR184041 3 0.2281 0.863 0.000 0.096 0.904 0
#> ERR184060 2 0.0000 0.930 0.000 1.000 0.000 0
#> ERR184035 2 0.3356 0.786 0.000 0.824 0.176 0
#> ERR184086 2 0.0188 0.930 0.000 0.996 0.004 0
#> ERR184080 2 0.0592 0.928 0.000 0.984 0.016 0
#> ERR184050 2 0.0336 0.930 0.000 0.992 0.008 0
#> ERR184047 1 0.0000 0.989 1.000 0.000 0.000 0
#> ERR184092 2 0.0188 0.930 0.000 0.996 0.004 0
#> ERR184072 2 0.1211 0.914 0.000 0.960 0.040 0
#> ERR184073 3 0.4304 0.597 0.000 0.284 0.716 0
#> ERR184066 2 0.2408 0.867 0.000 0.896 0.104 0
#> ERR184098 2 0.0336 0.930 0.000 0.992 0.008 0
#> ERR184044 2 0.1557 0.902 0.000 0.944 0.056 0
#> ERR184054 2 0.4624 0.483 0.000 0.660 0.340 0
#> ERR184085 2 0.3074 0.813 0.000 0.848 0.152 0
#> ERR184056 2 0.0336 0.929 0.000 0.992 0.008 0
#> ERR184052 2 0.0592 0.928 0.000 0.984 0.016 0
#> ERR184070 2 0.0000 0.930 0.000 1.000 0.000 0
#> ERR184096 1 0.0336 0.989 0.992 0.000 0.008 0
#> ERR184089 2 0.0336 0.930 0.000 0.992 0.008 0
#> ERR184049 2 0.0592 0.928 0.000 0.984 0.016 0
#> ERR184038 2 0.0336 0.929 0.000 0.992 0.008 0
#> ERR184087 3 0.1716 0.852 0.000 0.064 0.936 0
#> ERR184097 2 0.0000 0.930 0.000 1.000 0.000 0
#> ERR184094 3 0.2469 0.842 0.000 0.108 0.892 0
#> ERR184058 2 0.0000 0.930 0.000 1.000 0.000 0
#> ERR184036 2 0.0707 0.928 0.000 0.980 0.020 0
#> ERR184046 2 0.0000 0.930 0.000 1.000 0.000 0
#> ERR184074 2 0.4746 0.419 0.000 0.632 0.368 0
#> ERR184048 2 0.0336 0.929 0.000 0.992 0.008 0
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.2719 0.378 0.852 0.144 0.004 0 0.000
#> ERR184093 2 0.0162 0.921 0.004 0.996 0.000 0 0.000
#> ERR184051 3 0.3039 0.658 0.000 0.192 0.808 0 0.000
#> ERR184076 1 0.1877 0.138 0.924 0.064 0.012 0 0.000
#> ERR184043 3 0.1341 0.867 0.000 0.056 0.944 0 0.000
#> ERR184037 2 0.3916 0.686 0.092 0.804 0.104 0 0.000
#> ERR184059 3 0.1124 0.833 0.004 0.036 0.960 0 0.000
#> ERR184055 2 0.3169 0.777 0.060 0.856 0.084 0 0.000
#> ERR184065 2 0.0290 0.920 0.000 0.992 0.008 0 0.000
#> ERR184069 2 0.0000 0.922 0.000 1.000 0.000 0 0.000
#> ERR184040 1 0.7865 0.356 0.344 0.260 0.328 0 0.068
#> ERR184057 2 0.0000 0.922 0.000 1.000 0.000 0 0.000
#> ERR184082 1 0.6685 0.473 0.388 0.376 0.236 0 0.000
#> ERR184083 2 0.0000 0.922 0.000 1.000 0.000 0 0.000
#> ERR184039 2 0.0290 0.920 0.000 0.992 0.008 0 0.000
#> ERR184064 3 0.1341 0.867 0.000 0.056 0.944 0 0.000
#> ERR184081 2 0.0000 0.922 0.000 1.000 0.000 0 0.000
#> ERR184095 2 0.0000 0.922 0.000 1.000 0.000 0 0.000
#> ERR184079 2 0.0798 0.909 0.008 0.976 0.016 0 0.000
#> ERR184084 1 0.6629 0.428 0.436 0.232 0.332 0 0.000
#> ERR184068 2 0.2193 0.849 0.060 0.912 0.028 0 0.000
#> ERR184067 2 0.0000 0.922 0.000 1.000 0.000 0 0.000
#> ERR184071 2 0.0000 0.922 0.000 1.000 0.000 0 0.000
#> ERR184042 4 0.0000 0.000 0.000 0.000 0.000 1 0.000
#> ERR184063 3 0.1908 0.853 0.000 0.092 0.908 0 0.000
#> ERR184091 2 0.0162 0.921 0.000 0.996 0.004 0 0.000
#> ERR184061 2 0.1364 0.898 0.012 0.952 0.036 0 0.000
#> ERR184077 2 0.0000 0.922 0.000 1.000 0.000 0 0.000
#> ERR184062 2 0.0290 0.918 0.000 0.992 0.008 0 0.000
#> ERR184053 2 0.2260 0.845 0.064 0.908 0.028 0 0.000
#> ERR184088 2 0.0566 0.917 0.004 0.984 0.012 0 0.000
#> ERR184075 2 0.0290 0.920 0.000 0.992 0.008 0 0.000
#> ERR184041 3 0.1792 0.861 0.000 0.084 0.916 0 0.000
#> ERR184060 2 0.0000 0.922 0.000 1.000 0.000 0 0.000
#> ERR184035 1 0.5751 0.577 0.552 0.348 0.100 0 0.000
#> ERR184086 2 0.0162 0.921 0.000 0.996 0.004 0 0.000
#> ERR184080 2 0.0566 0.917 0.004 0.984 0.012 0 0.000
#> ERR184050 2 0.0290 0.920 0.000 0.992 0.008 0 0.000
#> ERR184047 5 0.0000 0.983 0.000 0.000 0.000 0 1.000
#> ERR184092 2 0.0162 0.921 0.004 0.996 0.000 0 0.000
#> ERR184072 2 0.2824 0.806 0.096 0.872 0.032 0 0.000
#> ERR184073 3 0.4496 0.478 0.056 0.216 0.728 0 0.000
#> ERR184066 2 0.3035 0.775 0.032 0.856 0.112 0 0.000
#> ERR184098 2 0.0290 0.920 0.000 0.992 0.008 0 0.000
#> ERR184044 2 0.1628 0.870 0.008 0.936 0.056 0 0.000
#> ERR184054 2 0.6790 -0.581 0.300 0.384 0.316 0 0.000
#> ERR184085 2 0.4808 0.498 0.136 0.728 0.136 0 0.000
#> ERR184056 2 0.0324 0.919 0.004 0.992 0.004 0 0.000
#> ERR184052 2 0.0566 0.917 0.004 0.984 0.012 0 0.000
#> ERR184070 2 0.0000 0.922 0.000 1.000 0.000 0 0.000
#> ERR184096 5 0.0510 0.983 0.016 0.000 0.000 0 0.984
#> ERR184089 2 0.0290 0.920 0.000 0.992 0.008 0 0.000
#> ERR184049 2 0.0566 0.917 0.004 0.984 0.012 0 0.000
#> ERR184038 2 0.0290 0.918 0.000 0.992 0.008 0 0.000
#> ERR184087 3 0.1270 0.863 0.000 0.052 0.948 0 0.000
#> ERR184097 2 0.0000 0.922 0.000 1.000 0.000 0 0.000
#> ERR184094 3 0.2344 0.842 0.032 0.064 0.904 0 0.000
#> ERR184058 2 0.0000 0.922 0.000 1.000 0.000 0 0.000
#> ERR184036 2 0.0671 0.917 0.004 0.980 0.016 0 0.000
#> ERR184046 2 0.0000 0.922 0.000 1.000 0.000 0 0.000
#> ERR184074 2 0.6799 -0.601 0.296 0.372 0.332 0 0.000
#> ERR184048 2 0.0324 0.919 0.004 0.992 0.004 0 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.4575 -0.297 0.600 0.048 0.000 0 0.000 0.352
#> ERR184093 2 0.0146 0.948 0.000 0.996 0.000 0 0.000 0.004
#> ERR184051 3 0.2912 0.640 0.012 0.172 0.816 0 0.000 0.000
#> ERR184076 6 0.2237 0.000 0.080 0.020 0.004 0 0.000 0.896
#> ERR184043 3 0.1007 0.841 0.000 0.044 0.956 0 0.000 0.000
#> ERR184037 2 0.4410 0.608 0.176 0.740 0.056 0 0.000 0.028
#> ERR184059 3 0.2775 0.732 0.052 0.016 0.876 0 0.000 0.056
#> ERR184055 2 0.3649 0.741 0.136 0.804 0.040 0 0.000 0.020
#> ERR184065 2 0.0363 0.945 0.000 0.988 0.012 0 0.000 0.000
#> ERR184069 2 0.0000 0.949 0.000 1.000 0.000 0 0.000 0.000
#> ERR184040 1 0.7039 0.362 0.484 0.132 0.292 0 0.048 0.044
#> ERR184057 2 0.0000 0.949 0.000 1.000 0.000 0 0.000 0.000
#> ERR184082 1 0.5980 0.451 0.496 0.288 0.208 0 0.000 0.008
#> ERR184083 2 0.0000 0.949 0.000 1.000 0.000 0 0.000 0.000
#> ERR184039 2 0.0363 0.945 0.000 0.988 0.012 0 0.000 0.000
#> ERR184064 3 0.1007 0.841 0.000 0.044 0.956 0 0.000 0.000
#> ERR184081 2 0.0000 0.949 0.000 1.000 0.000 0 0.000 0.000
#> ERR184095 2 0.0000 0.949 0.000 1.000 0.000 0 0.000 0.000
#> ERR184079 2 0.0951 0.932 0.020 0.968 0.008 0 0.000 0.004
#> ERR184084 1 0.5249 0.305 0.592 0.100 0.300 0 0.000 0.008
#> ERR184068 2 0.2473 0.839 0.104 0.876 0.008 0 0.000 0.012
#> ERR184067 2 0.0000 0.949 0.000 1.000 0.000 0 0.000 0.000
#> ERR184071 2 0.0000 0.949 0.000 1.000 0.000 0 0.000 0.000
#> ERR184042 4 0.0000 0.000 0.000 0.000 0.000 1 0.000 0.000
#> ERR184063 3 0.1610 0.828 0.000 0.084 0.916 0 0.000 0.000
#> ERR184091 2 0.0146 0.948 0.000 0.996 0.004 0 0.000 0.000
#> ERR184061 2 0.1642 0.914 0.032 0.936 0.028 0 0.000 0.004
#> ERR184077 2 0.0000 0.949 0.000 1.000 0.000 0 0.000 0.000
#> ERR184062 2 0.0405 0.944 0.004 0.988 0.008 0 0.000 0.000
#> ERR184053 2 0.2473 0.839 0.104 0.876 0.008 0 0.000 0.012
#> ERR184088 2 0.0665 0.943 0.008 0.980 0.008 0 0.000 0.004
#> ERR184075 2 0.0363 0.945 0.000 0.988 0.012 0 0.000 0.000
#> ERR184041 3 0.1501 0.835 0.000 0.076 0.924 0 0.000 0.000
#> ERR184060 2 0.0000 0.949 0.000 1.000 0.000 0 0.000 0.000
#> ERR184035 1 0.4331 0.413 0.728 0.208 0.040 0 0.000 0.024
#> ERR184086 2 0.0146 0.948 0.000 0.996 0.004 0 0.000 0.000
#> ERR184080 2 0.0665 0.943 0.008 0.980 0.008 0 0.000 0.004
#> ERR184050 2 0.0363 0.945 0.000 0.988 0.012 0 0.000 0.000
#> ERR184047 5 0.0000 0.939 0.000 0.000 0.000 0 1.000 0.000
#> ERR184092 2 0.0146 0.948 0.000 0.996 0.000 0 0.000 0.004
#> ERR184072 2 0.3515 0.702 0.192 0.780 0.012 0 0.000 0.016
#> ERR184073 3 0.4699 0.446 0.100 0.184 0.704 0 0.000 0.012
#> ERR184066 2 0.3321 0.778 0.072 0.832 0.088 0 0.000 0.008
#> ERR184098 2 0.0260 0.947 0.000 0.992 0.008 0 0.000 0.000
#> ERR184044 2 0.1657 0.893 0.016 0.928 0.056 0 0.000 0.000
#> ERR184054 1 0.6818 0.445 0.380 0.300 0.276 0 0.000 0.044
#> ERR184085 2 0.4742 0.465 0.184 0.688 0.124 0 0.000 0.004
#> ERR184056 2 0.0291 0.946 0.000 0.992 0.004 0 0.000 0.004
#> ERR184052 2 0.0551 0.945 0.004 0.984 0.008 0 0.000 0.004
#> ERR184070 2 0.0000 0.949 0.000 1.000 0.000 0 0.000 0.000
#> ERR184096 5 0.1708 0.939 0.040 0.000 0.004 0 0.932 0.024
#> ERR184089 2 0.0363 0.945 0.000 0.988 0.012 0 0.000 0.000
#> ERR184049 2 0.0665 0.943 0.008 0.980 0.008 0 0.000 0.004
#> ERR184038 2 0.0405 0.944 0.004 0.988 0.008 0 0.000 0.000
#> ERR184087 3 0.0937 0.837 0.000 0.040 0.960 0 0.000 0.000
#> ERR184097 2 0.0000 0.949 0.000 1.000 0.000 0 0.000 0.000
#> ERR184094 3 0.2556 0.799 0.052 0.048 0.888 0 0.000 0.012
#> ERR184058 2 0.0000 0.949 0.000 1.000 0.000 0 0.000 0.000
#> ERR184036 2 0.0767 0.943 0.008 0.976 0.012 0 0.000 0.004
#> ERR184046 2 0.0000 0.949 0.000 1.000 0.000 0 0.000 0.000
#> ERR184074 1 0.6617 0.460 0.432 0.248 0.284 0 0.000 0.036
#> ERR184048 2 0.0291 0.946 0.000 0.992 0.004 0 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5, scale_rows = FALSE)
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 10269 rows and 62 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 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 0.965 0.912 0.967 0.4509 0.556 0.556
#> 3 3 0.759 0.811 0.888 0.2657 0.778 0.621
#> 4 4 0.843 0.857 0.924 0.0712 0.959 0.897
#> 5 5 0.846 0.848 0.924 0.0385 0.999 0.997
#> 6 6 0.835 0.770 0.896 0.0422 0.973 0.928
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
#> ERR184078 1 0.0000 0.965 1.000 0.000
#> ERR184093 2 0.0000 0.963 0.000 1.000
#> ERR184051 1 0.0000 0.965 1.000 0.000
#> ERR184076 1 0.0000 0.965 1.000 0.000
#> ERR184043 1 0.0000 0.965 1.000 0.000
#> ERR184037 2 0.9970 0.121 0.468 0.532
#> ERR184059 1 0.0000 0.965 1.000 0.000
#> ERR184055 2 0.2948 0.921 0.052 0.948
#> ERR184065 2 0.0000 0.963 0.000 1.000
#> ERR184069 2 0.0000 0.963 0.000 1.000
#> ERR184040 1 0.0000 0.965 1.000 0.000
#> ERR184057 2 0.0000 0.963 0.000 1.000
#> ERR184082 2 0.9970 0.120 0.468 0.532
#> ERR184083 2 0.0000 0.963 0.000 1.000
#> ERR184039 2 0.0000 0.963 0.000 1.000
#> ERR184064 1 0.0000 0.965 1.000 0.000
#> ERR184081 2 0.0000 0.963 0.000 1.000
#> ERR184095 2 0.0000 0.963 0.000 1.000
#> ERR184079 2 0.0000 0.963 0.000 1.000
#> ERR184084 1 0.0000 0.965 1.000 0.000
#> ERR184068 2 0.0000 0.963 0.000 1.000
#> ERR184067 2 0.0000 0.963 0.000 1.000
#> ERR184071 2 0.0000 0.963 0.000 1.000
#> ERR184042 1 0.0000 0.965 1.000 0.000
#> ERR184063 1 0.0000 0.965 1.000 0.000
#> ERR184091 2 0.0000 0.963 0.000 1.000
#> ERR184061 2 0.0000 0.963 0.000 1.000
#> ERR184077 2 0.0000 0.963 0.000 1.000
#> ERR184062 2 0.0000 0.963 0.000 1.000
#> ERR184053 2 0.0000 0.963 0.000 1.000
#> ERR184088 2 0.0000 0.963 0.000 1.000
#> ERR184075 2 0.0000 0.963 0.000 1.000
#> ERR184041 1 0.0000 0.965 1.000 0.000
#> ERR184060 2 0.0000 0.963 0.000 1.000
#> ERR184035 1 0.7139 0.733 0.804 0.196
#> ERR184086 2 0.0000 0.963 0.000 1.000
#> ERR184080 2 0.8081 0.665 0.248 0.752
#> ERR184050 2 0.0000 0.963 0.000 1.000
#> ERR184047 1 0.0000 0.965 1.000 0.000
#> ERR184092 2 0.0000 0.963 0.000 1.000
#> ERR184072 2 0.3584 0.905 0.068 0.932
#> ERR184073 1 0.0000 0.965 1.000 0.000
#> ERR184066 2 0.2948 0.921 0.052 0.948
#> ERR184098 2 0.0000 0.963 0.000 1.000
#> ERR184044 2 0.0000 0.963 0.000 1.000
#> ERR184054 1 0.0000 0.965 1.000 0.000
#> ERR184085 1 0.9833 0.220 0.576 0.424
#> ERR184056 2 0.0000 0.963 0.000 1.000
#> ERR184052 2 0.0000 0.963 0.000 1.000
#> ERR184070 2 0.0000 0.963 0.000 1.000
#> ERR184096 1 0.0000 0.965 1.000 0.000
#> ERR184089 2 0.0000 0.963 0.000 1.000
#> ERR184049 2 0.0000 0.963 0.000 1.000
#> ERR184038 2 0.4022 0.893 0.080 0.920
#> ERR184087 1 0.0000 0.965 1.000 0.000
#> ERR184097 2 0.0000 0.963 0.000 1.000
#> ERR184094 1 0.0000 0.965 1.000 0.000
#> ERR184058 2 0.0000 0.963 0.000 1.000
#> ERR184036 2 0.0000 0.963 0.000 1.000
#> ERR184046 2 0.0000 0.963 0.000 1.000
#> ERR184074 1 0.0376 0.961 0.996 0.004
#> ERR184048 2 0.0000 0.963 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.0000 0.660 1.000 0.000 0.000
#> ERR184093 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184051 3 0.6095 0.754 0.392 0.000 0.608
#> ERR184076 1 0.0000 0.660 1.000 0.000 0.000
#> ERR184043 3 0.5706 0.804 0.320 0.000 0.680
#> ERR184037 1 0.2066 0.685 0.940 0.060 0.000
#> ERR184059 3 0.5431 0.801 0.284 0.000 0.716
#> ERR184055 1 0.4346 0.644 0.816 0.184 0.000
#> ERR184065 2 0.0237 0.975 0.000 0.996 0.004
#> ERR184069 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184040 1 0.0000 0.660 1.000 0.000 0.000
#> ERR184057 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184082 1 0.6977 0.483 0.712 0.076 0.212
#> ERR184083 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184039 2 0.0237 0.975 0.000 0.996 0.004
#> ERR184064 3 0.5706 0.804 0.320 0.000 0.680
#> ERR184081 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184095 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184079 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184084 3 0.5926 0.792 0.356 0.000 0.644
#> ERR184068 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184067 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184071 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184042 3 0.0424 0.600 0.008 0.000 0.992
#> ERR184063 3 0.6095 0.754 0.392 0.000 0.608
#> ERR184091 2 0.0237 0.975 0.000 0.996 0.004
#> ERR184061 1 0.6204 0.433 0.576 0.424 0.000
#> ERR184077 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184062 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184053 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184088 2 0.0592 0.965 0.012 0.988 0.000
#> ERR184075 2 0.0237 0.975 0.000 0.996 0.004
#> ERR184041 3 0.6095 0.754 0.392 0.000 0.608
#> ERR184060 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184035 1 0.0661 0.666 0.988 0.008 0.004
#> ERR184086 2 0.0237 0.975 0.000 0.996 0.004
#> ERR184080 1 0.2066 0.685 0.940 0.060 0.000
#> ERR184050 2 0.0237 0.975 0.000 0.996 0.004
#> ERR184047 3 0.5760 0.502 0.328 0.000 0.672
#> ERR184092 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184072 1 0.5835 0.544 0.660 0.340 0.000
#> ERR184073 3 0.6252 0.707 0.444 0.000 0.556
#> ERR184066 1 0.5678 0.564 0.684 0.316 0.000
#> ERR184098 2 0.0237 0.975 0.000 0.996 0.004
#> ERR184044 2 0.3412 0.818 0.124 0.876 0.000
#> ERR184054 1 0.0000 0.660 1.000 0.000 0.000
#> ERR184085 1 0.6541 0.456 0.732 0.056 0.212
#> ERR184056 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184052 2 0.0237 0.975 0.000 0.996 0.004
#> ERR184070 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184096 3 0.5926 0.477 0.356 0.000 0.644
#> ERR184089 2 0.0237 0.975 0.000 0.996 0.004
#> ERR184049 2 0.6286 -0.120 0.464 0.536 0.000
#> ERR184038 1 0.5956 0.553 0.672 0.324 0.004
#> ERR184087 3 0.5397 0.801 0.280 0.000 0.720
#> ERR184097 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184094 3 0.5431 0.801 0.284 0.000 0.716
#> ERR184058 2 0.0237 0.975 0.000 0.996 0.004
#> ERR184036 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184046 2 0.0000 0.977 0.000 1.000 0.000
#> ERR184074 1 0.0000 0.660 1.000 0.000 0.000
#> ERR184048 2 0.0000 0.977 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.1489 0.684 0.952 0.000 0.004 0.044
#> ERR184093 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184051 3 0.2197 0.902 0.048 0.000 0.928 0.024
#> ERR184076 1 0.1489 0.684 0.952 0.000 0.004 0.044
#> ERR184043 3 0.1118 0.911 0.036 0.000 0.964 0.000
#> ERR184037 1 0.0469 0.711 0.988 0.000 0.012 0.000
#> ERR184059 3 0.1022 0.908 0.032 0.000 0.968 0.000
#> ERR184055 1 0.3367 0.697 0.876 0.092 0.012 0.020
#> ERR184065 2 0.0336 0.987 0.000 0.992 0.000 0.008
#> ERR184069 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184040 1 0.1677 0.683 0.948 0.000 0.012 0.040
#> ERR184057 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184082 1 0.5876 0.490 0.660 0.012 0.288 0.040
#> ERR184083 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184039 2 0.0336 0.987 0.000 0.992 0.000 0.008
#> ERR184064 3 0.1118 0.911 0.036 0.000 0.964 0.000
#> ERR184081 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184095 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184079 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184084 3 0.2662 0.862 0.084 0.000 0.900 0.016
#> ERR184068 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184067 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184071 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184042 4 0.2704 0.641 0.000 0.000 0.124 0.876
#> ERR184063 3 0.2399 0.900 0.048 0.000 0.920 0.032
#> ERR184091 2 0.0336 0.987 0.000 0.992 0.000 0.008
#> ERR184061 1 0.5191 0.550 0.684 0.292 0.004 0.020
#> ERR184077 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184062 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184053 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184088 2 0.0921 0.966 0.028 0.972 0.000 0.000
#> ERR184075 2 0.0336 0.987 0.000 0.992 0.000 0.008
#> ERR184041 3 0.2399 0.900 0.048 0.000 0.920 0.032
#> ERR184060 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184035 1 0.1284 0.706 0.964 0.000 0.012 0.024
#> ERR184086 2 0.0336 0.987 0.000 0.992 0.000 0.008
#> ERR184080 1 0.0469 0.711 0.988 0.000 0.012 0.000
#> ERR184050 2 0.0336 0.987 0.000 0.992 0.000 0.008
#> ERR184047 4 0.6664 0.797 0.232 0.000 0.152 0.616
#> ERR184092 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184072 1 0.4092 0.651 0.800 0.184 0.008 0.008
#> ERR184073 3 0.5217 0.375 0.380 0.000 0.608 0.012
#> ERR184066 1 0.4773 0.625 0.756 0.216 0.012 0.016
#> ERR184098 2 0.0336 0.987 0.000 0.992 0.000 0.008
#> ERR184044 2 0.3266 0.831 0.108 0.868 0.000 0.024
#> ERR184054 1 0.0469 0.711 0.988 0.000 0.012 0.000
#> ERR184085 1 0.5876 0.496 0.660 0.012 0.288 0.040
#> ERR184056 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184052 2 0.0895 0.972 0.004 0.976 0.000 0.020
#> ERR184070 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184096 4 0.6547 0.792 0.260 0.000 0.124 0.616
#> ERR184089 2 0.0817 0.976 0.000 0.976 0.000 0.024
#> ERR184049 1 0.5657 0.358 0.540 0.436 0.000 0.024
#> ERR184038 1 0.5603 0.515 0.644 0.324 0.008 0.024
#> ERR184087 3 0.1118 0.911 0.036 0.000 0.964 0.000
#> ERR184097 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184094 3 0.1118 0.911 0.036 0.000 0.964 0.000
#> ERR184058 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184036 2 0.0188 0.988 0.004 0.996 0.000 0.000
#> ERR184046 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> ERR184074 1 0.0469 0.711 0.988 0.000 0.012 0.000
#> ERR184048 2 0.0000 0.991 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
#> ERR184078 1 0.2504 0.736 0.896 0.000 0.000 0.040 0.064
#> ERR184093 2 0.0579 0.976 0.000 0.984 0.000 0.008 0.008
#> ERR184051 3 0.1195 0.866 0.012 0.000 0.960 0.000 0.028
#> ERR184076 1 0.2438 0.739 0.900 0.000 0.000 0.040 0.060
#> ERR184043 3 0.0000 0.874 0.000 0.000 1.000 0.000 0.000
#> ERR184037 1 0.0162 0.771 0.996 0.000 0.000 0.004 0.000
#> ERR184059 3 0.1124 0.863 0.000 0.000 0.960 0.004 0.036
#> ERR184055 1 0.2180 0.768 0.924 0.024 0.000 0.020 0.032
#> ERR184065 2 0.1195 0.969 0.000 0.960 0.000 0.012 0.028
#> ERR184069 2 0.0162 0.977 0.000 0.996 0.000 0.004 0.000
#> ERR184040 1 0.2615 0.728 0.892 0.000 0.008 0.020 0.080
#> ERR184057 2 0.0162 0.977 0.000 0.996 0.000 0.004 0.000
#> ERR184082 1 0.6560 0.509 0.588 0.004 0.252 0.120 0.036
#> ERR184083 2 0.0566 0.975 0.000 0.984 0.000 0.004 0.012
#> ERR184039 2 0.1195 0.969 0.000 0.960 0.000 0.012 0.028
#> ERR184064 3 0.0000 0.874 0.000 0.000 1.000 0.000 0.000
#> ERR184081 2 0.0162 0.977 0.000 0.996 0.000 0.004 0.000
#> ERR184095 2 0.0162 0.977 0.000 0.996 0.000 0.004 0.000
#> ERR184079 2 0.0451 0.976 0.000 0.988 0.000 0.008 0.004
#> ERR184084 3 0.4163 0.750 0.056 0.000 0.816 0.088 0.040
#> ERR184068 2 0.1310 0.965 0.000 0.956 0.000 0.024 0.020
#> ERR184067 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> ERR184071 2 0.0566 0.976 0.000 0.984 0.000 0.012 0.004
#> ERR184042 4 0.3081 0.000 0.000 0.000 0.012 0.832 0.156
#> ERR184063 3 0.1195 0.866 0.012 0.000 0.960 0.000 0.028
#> ERR184091 2 0.1195 0.969 0.000 0.960 0.000 0.012 0.028
#> ERR184061 1 0.4787 0.650 0.744 0.184 0.000 0.032 0.040
#> ERR184077 2 0.0290 0.975 0.000 0.992 0.000 0.008 0.000
#> ERR184062 2 0.0451 0.976 0.000 0.988 0.000 0.008 0.004
#> ERR184053 2 0.0290 0.975 0.000 0.992 0.000 0.008 0.000
#> ERR184088 2 0.1018 0.963 0.016 0.968 0.000 0.016 0.000
#> ERR184075 2 0.1195 0.969 0.000 0.960 0.000 0.012 0.028
#> ERR184041 3 0.1281 0.865 0.012 0.000 0.956 0.000 0.032
#> ERR184060 2 0.0324 0.976 0.000 0.992 0.000 0.004 0.004
#> ERR184035 1 0.2813 0.737 0.868 0.000 0.000 0.108 0.024
#> ERR184086 2 0.0992 0.971 0.000 0.968 0.000 0.008 0.024
#> ERR184080 1 0.0162 0.771 0.996 0.000 0.000 0.000 0.004
#> ERR184050 2 0.1195 0.968 0.000 0.960 0.000 0.012 0.028
#> ERR184047 5 0.2230 0.987 0.044 0.000 0.044 0.000 0.912
#> ERR184092 2 0.0290 0.975 0.000 0.992 0.000 0.008 0.000
#> ERR184072 1 0.3584 0.717 0.828 0.132 0.000 0.028 0.012
#> ERR184073 3 0.5131 0.140 0.436 0.000 0.532 0.008 0.024
#> ERR184066 1 0.3204 0.742 0.860 0.100 0.000 0.016 0.024
#> ERR184098 2 0.1082 0.969 0.000 0.964 0.000 0.008 0.028
#> ERR184044 2 0.3850 0.798 0.116 0.824 0.000 0.028 0.032
#> ERR184054 1 0.0162 0.771 0.996 0.000 0.000 0.000 0.004
#> ERR184085 1 0.6330 0.563 0.632 0.004 0.212 0.108 0.044
#> ERR184056 2 0.0404 0.976 0.000 0.988 0.000 0.012 0.000
#> ERR184052 2 0.1934 0.937 0.008 0.932 0.000 0.020 0.040
#> ERR184070 2 0.0162 0.977 0.000 0.996 0.000 0.004 0.000
#> ERR184096 5 0.2228 0.987 0.048 0.000 0.040 0.000 0.912
#> ERR184089 2 0.1522 0.958 0.000 0.944 0.000 0.012 0.044
#> ERR184049 1 0.5808 0.365 0.552 0.376 0.000 0.032 0.040
#> ERR184038 1 0.5161 0.540 0.668 0.272 0.000 0.020 0.040
#> ERR184087 3 0.0000 0.874 0.000 0.000 1.000 0.000 0.000
#> ERR184097 2 0.0290 0.975 0.000 0.992 0.000 0.008 0.000
#> ERR184094 3 0.1285 0.861 0.004 0.000 0.956 0.004 0.036
#> ERR184058 2 0.1106 0.971 0.000 0.964 0.000 0.012 0.024
#> ERR184036 2 0.0693 0.974 0.000 0.980 0.000 0.012 0.008
#> ERR184046 2 0.0566 0.975 0.000 0.984 0.000 0.004 0.012
#> ERR184074 1 0.0000 0.771 1.000 0.000 0.000 0.000 0.000
#> ERR184048 2 0.0290 0.975 0.000 0.992 0.000 0.008 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 6 0.4474 0.9510 0.360 0.000 0.000 0.012 0.020 0.608
#> ERR184093 2 0.0000 0.9595 0.000 1.000 0.000 0.000 0.000 0.000
#> ERR184051 3 0.0000 0.9122 0.000 0.000 1.000 0.000 0.000 0.000
#> ERR184076 6 0.4418 0.9510 0.368 0.000 0.000 0.012 0.016 0.604
#> ERR184043 3 0.0146 0.9127 0.000 0.000 0.996 0.000 0.004 0.000
#> ERR184037 1 0.1753 0.5278 0.912 0.000 0.004 0.000 0.000 0.084
#> ERR184059 3 0.2474 0.8560 0.000 0.000 0.880 0.000 0.080 0.040
#> ERR184055 1 0.1226 0.5491 0.952 0.004 0.004 0.000 0.000 0.040
#> ERR184065 2 0.1340 0.9456 0.000 0.948 0.000 0.008 0.004 0.040
#> ERR184069 2 0.0000 0.9595 0.000 1.000 0.000 0.000 0.000 0.000
#> ERR184040 1 0.5145 -0.4054 0.572 0.000 0.004 0.000 0.088 0.336
#> ERR184057 2 0.0000 0.9595 0.000 1.000 0.000 0.000 0.000 0.000
#> ERR184082 1 0.5478 0.2889 0.512 0.000 0.136 0.000 0.000 0.352
#> ERR184083 2 0.0260 0.9581 0.000 0.992 0.000 0.000 0.000 0.008
#> ERR184039 2 0.1872 0.9352 0.004 0.920 0.000 0.008 0.004 0.064
#> ERR184064 3 0.0146 0.9127 0.000 0.000 0.996 0.000 0.004 0.000
#> ERR184081 2 0.0000 0.9595 0.000 1.000 0.000 0.000 0.000 0.000
#> ERR184095 2 0.0000 0.9595 0.000 1.000 0.000 0.000 0.000 0.000
#> ERR184079 2 0.0260 0.9583 0.008 0.992 0.000 0.000 0.000 0.000
#> ERR184084 3 0.5186 0.4692 0.012 0.000 0.572 0.000 0.072 0.344
#> ERR184068 2 0.1564 0.9354 0.040 0.936 0.000 0.000 0.000 0.024
#> ERR184067 2 0.0000 0.9595 0.000 1.000 0.000 0.000 0.000 0.000
#> ERR184071 2 0.0551 0.9584 0.004 0.984 0.000 0.008 0.000 0.004
#> ERR184042 4 0.0547 0.0000 0.000 0.000 0.000 0.980 0.020 0.000
#> ERR184063 3 0.0000 0.9122 0.000 0.000 1.000 0.000 0.000 0.000
#> ERR184091 2 0.1268 0.9467 0.000 0.952 0.000 0.008 0.004 0.036
#> ERR184061 1 0.2776 0.5332 0.860 0.088 0.000 0.000 0.000 0.052
#> ERR184077 2 0.0146 0.9590 0.004 0.996 0.000 0.000 0.000 0.000
#> ERR184062 2 0.0547 0.9535 0.020 0.980 0.000 0.000 0.000 0.000
#> ERR184053 2 0.0146 0.9590 0.004 0.996 0.000 0.000 0.000 0.000
#> ERR184088 2 0.1913 0.9040 0.080 0.908 0.000 0.000 0.000 0.012
#> ERR184075 2 0.1554 0.9434 0.004 0.940 0.000 0.008 0.004 0.044
#> ERR184041 3 0.0146 0.9104 0.000 0.000 0.996 0.000 0.000 0.004
#> ERR184060 2 0.0000 0.9595 0.000 1.000 0.000 0.000 0.000 0.000
#> ERR184035 1 0.4126 0.1770 0.512 0.000 0.004 0.000 0.004 0.480
#> ERR184086 2 0.1268 0.9467 0.000 0.952 0.000 0.008 0.004 0.036
#> ERR184080 1 0.1788 0.5096 0.916 0.000 0.004 0.000 0.004 0.076
#> ERR184050 2 0.1985 0.9335 0.008 0.916 0.000 0.008 0.004 0.064
#> ERR184047 5 0.0291 0.9967 0.004 0.000 0.000 0.000 0.992 0.004
#> ERR184092 2 0.0000 0.9595 0.000 1.000 0.000 0.000 0.000 0.000
#> ERR184072 1 0.1686 0.5521 0.924 0.064 0.000 0.000 0.000 0.012
#> ERR184073 1 0.5360 -0.0475 0.508 0.000 0.412 0.000 0.056 0.024
#> ERR184066 1 0.1578 0.5555 0.936 0.048 0.004 0.000 0.000 0.012
#> ERR184098 2 0.1925 0.9356 0.008 0.920 0.000 0.008 0.004 0.060
#> ERR184044 2 0.4486 0.4972 0.292 0.656 0.000 0.004 0.000 0.048
#> ERR184054 1 0.1555 0.5204 0.932 0.000 0.004 0.000 0.004 0.060
#> ERR184085 1 0.5160 0.3461 0.564 0.000 0.104 0.000 0.000 0.332
#> ERR184056 2 0.0146 0.9590 0.004 0.996 0.000 0.000 0.000 0.000
#> ERR184052 2 0.2579 0.8986 0.048 0.884 0.000 0.008 0.000 0.060
#> ERR184070 2 0.0000 0.9595 0.000 1.000 0.000 0.000 0.000 0.000
#> ERR184096 5 0.0146 0.9967 0.004 0.000 0.000 0.000 0.996 0.000
#> ERR184089 2 0.2128 0.9314 0.008 0.912 0.004 0.008 0.004 0.064
#> ERR184049 1 0.4469 0.3206 0.668 0.276 0.000 0.004 0.000 0.052
#> ERR184038 1 0.3779 0.3967 0.760 0.204 0.004 0.004 0.000 0.028
#> ERR184087 3 0.0146 0.9127 0.000 0.000 0.996 0.000 0.004 0.000
#> ERR184097 2 0.0146 0.9590 0.004 0.996 0.000 0.000 0.000 0.000
#> ERR184094 3 0.2474 0.8560 0.000 0.000 0.880 0.000 0.080 0.040
#> ERR184058 2 0.1686 0.9413 0.004 0.932 0.000 0.008 0.004 0.052
#> ERR184036 2 0.1832 0.9357 0.032 0.928 0.000 0.008 0.000 0.032
#> ERR184046 2 0.0260 0.9581 0.000 0.992 0.000 0.000 0.000 0.008
#> ERR184074 1 0.1588 0.5145 0.924 0.000 0.004 0.000 0.000 0.072
#> ERR184048 2 0.0146 0.9590 0.004 0.996 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", "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 10269 rows and 62 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 1.000 0.970 0.987 0.5034 0.497 0.497
#> 3 3 0.734 0.799 0.902 0.2412 0.847 0.701
#> 4 4 0.520 0.625 0.774 0.1382 0.943 0.849
#> 5 5 0.522 0.388 0.687 0.0716 0.929 0.795
#> 6 6 0.540 0.328 0.629 0.0483 0.940 0.809
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
#> ERR184078 1 0.000 0.983 1.000 0.000
#> ERR184093 2 0.000 0.989 0.000 1.000
#> ERR184051 1 0.000 0.983 1.000 0.000
#> ERR184076 1 0.000 0.983 1.000 0.000
#> ERR184043 1 0.000 0.983 1.000 0.000
#> ERR184037 1 0.000 0.983 1.000 0.000
#> ERR184059 1 0.000 0.983 1.000 0.000
#> ERR184055 1 0.000 0.983 1.000 0.000
#> ERR184065 2 0.000 0.989 0.000 1.000
#> ERR184069 2 0.000 0.989 0.000 1.000
#> ERR184040 1 0.000 0.983 1.000 0.000
#> ERR184057 2 0.000 0.989 0.000 1.000
#> ERR184082 1 0.000 0.983 1.000 0.000
#> ERR184083 2 0.000 0.989 0.000 1.000
#> ERR184039 2 0.000 0.989 0.000 1.000
#> ERR184064 1 0.000 0.983 1.000 0.000
#> ERR184081 2 0.000 0.989 0.000 1.000
#> ERR184095 2 0.000 0.989 0.000 1.000
#> ERR184079 2 0.000 0.989 0.000 1.000
#> ERR184084 1 0.000 0.983 1.000 0.000
#> ERR184068 2 0.000 0.989 0.000 1.000
#> ERR184067 2 0.000 0.989 0.000 1.000
#> ERR184071 2 0.000 0.989 0.000 1.000
#> ERR184042 1 0.000 0.983 1.000 0.000
#> ERR184063 1 0.000 0.983 1.000 0.000
#> ERR184091 2 0.000 0.989 0.000 1.000
#> ERR184061 1 0.808 0.683 0.752 0.248
#> ERR184077 2 0.000 0.989 0.000 1.000
#> ERR184062 2 0.000 0.989 0.000 1.000
#> ERR184053 2 0.000 0.989 0.000 1.000
#> ERR184088 2 0.000 0.989 0.000 1.000
#> ERR184075 2 0.000 0.989 0.000 1.000
#> ERR184041 1 0.000 0.983 1.000 0.000
#> ERR184060 2 0.000 0.989 0.000 1.000
#> ERR184035 1 0.000 0.983 1.000 0.000
#> ERR184086 2 0.000 0.989 0.000 1.000
#> ERR184080 1 0.000 0.983 1.000 0.000
#> ERR184050 2 0.000 0.989 0.000 1.000
#> ERR184047 1 0.000 0.983 1.000 0.000
#> ERR184092 2 0.000 0.989 0.000 1.000
#> ERR184072 1 0.644 0.809 0.836 0.164
#> ERR184073 1 0.000 0.983 1.000 0.000
#> ERR184066 1 0.000 0.983 1.000 0.000
#> ERR184098 2 0.000 0.989 0.000 1.000
#> ERR184044 2 0.358 0.921 0.068 0.932
#> ERR184054 1 0.000 0.983 1.000 0.000
#> ERR184085 1 0.000 0.983 1.000 0.000
#> ERR184056 2 0.000 0.989 0.000 1.000
#> ERR184052 2 0.000 0.989 0.000 1.000
#> ERR184070 2 0.000 0.989 0.000 1.000
#> ERR184096 1 0.000 0.983 1.000 0.000
#> ERR184089 2 0.000 0.989 0.000 1.000
#> ERR184049 2 0.871 0.590 0.292 0.708
#> ERR184038 1 0.260 0.944 0.956 0.044
#> ERR184087 1 0.000 0.983 1.000 0.000
#> ERR184097 2 0.000 0.989 0.000 1.000
#> ERR184094 1 0.000 0.983 1.000 0.000
#> ERR184058 2 0.000 0.989 0.000 1.000
#> ERR184036 2 0.000 0.989 0.000 1.000
#> ERR184046 2 0.000 0.989 0.000 1.000
#> ERR184074 1 0.000 0.983 1.000 0.000
#> ERR184048 2 0.000 0.989 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.3816 0.7927 0.852 0.000 0.148
#> ERR184093 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184051 3 0.0000 0.7987 0.000 0.000 1.000
#> ERR184076 1 0.4062 0.7864 0.836 0.000 0.164
#> ERR184043 3 0.0000 0.7987 0.000 0.000 1.000
#> ERR184037 1 0.0747 0.7842 0.984 0.000 0.016
#> ERR184059 3 0.2878 0.7804 0.096 0.000 0.904
#> ERR184055 1 0.0661 0.7779 0.988 0.008 0.004
#> ERR184065 2 0.0237 0.9562 0.000 0.996 0.004
#> ERR184069 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184040 1 0.5098 0.7099 0.752 0.000 0.248
#> ERR184057 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184082 3 0.3879 0.7528 0.152 0.000 0.848
#> ERR184083 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184039 2 0.0848 0.9522 0.008 0.984 0.008
#> ERR184064 3 0.0000 0.7987 0.000 0.000 1.000
#> ERR184081 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184095 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184079 2 0.1411 0.9386 0.036 0.964 0.000
#> ERR184084 3 0.4346 0.7149 0.184 0.000 0.816
#> ERR184068 2 0.1267 0.9452 0.024 0.972 0.004
#> ERR184067 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184071 2 0.0237 0.9564 0.004 0.996 0.000
#> ERR184042 3 0.3267 0.7720 0.116 0.000 0.884
#> ERR184063 3 0.0237 0.7963 0.004 0.000 0.996
#> ERR184091 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184061 1 0.6363 0.6221 0.768 0.136 0.096
#> ERR184077 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184062 2 0.2625 0.8945 0.084 0.916 0.000
#> ERR184053 2 0.0237 0.9564 0.004 0.996 0.000
#> ERR184088 2 0.5656 0.6127 0.284 0.712 0.004
#> ERR184075 2 0.1964 0.9217 0.000 0.944 0.056
#> ERR184041 3 0.0000 0.7987 0.000 0.000 1.000
#> ERR184060 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184035 1 0.4178 0.7699 0.828 0.000 0.172
#> ERR184086 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184080 1 0.1031 0.7874 0.976 0.000 0.024
#> ERR184050 2 0.1529 0.9356 0.000 0.960 0.040
#> ERR184047 1 0.6280 0.2594 0.540 0.000 0.460
#> ERR184092 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184072 1 0.3134 0.7835 0.916 0.032 0.052
#> ERR184073 3 0.6140 0.1878 0.404 0.000 0.596
#> ERR184066 1 0.3826 0.7859 0.868 0.008 0.124
#> ERR184098 2 0.0892 0.9485 0.000 0.980 0.020
#> ERR184044 2 0.9129 0.0837 0.372 0.480 0.148
#> ERR184054 1 0.3551 0.7984 0.868 0.000 0.132
#> ERR184085 3 0.4750 0.7069 0.216 0.000 0.784
#> ERR184056 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184052 2 0.5471 0.7918 0.128 0.812 0.060
#> ERR184070 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184096 1 0.5650 0.6164 0.688 0.000 0.312
#> ERR184089 3 0.6521 -0.0957 0.004 0.496 0.500
#> ERR184049 1 0.7979 0.4397 0.640 0.248 0.112
#> ERR184038 3 0.5708 0.6672 0.204 0.028 0.768
#> ERR184087 3 0.0000 0.7987 0.000 0.000 1.000
#> ERR184097 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184094 3 0.4504 0.6926 0.196 0.000 0.804
#> ERR184058 2 0.0237 0.9563 0.004 0.996 0.000
#> ERR184036 2 0.1643 0.9335 0.044 0.956 0.000
#> ERR184046 2 0.0000 0.9577 0.000 1.000 0.000
#> ERR184074 1 0.3752 0.7948 0.856 0.000 0.144
#> ERR184048 2 0.0000 0.9577 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.3015 0.7568 0.884 0.000 0.092 0.024
#> ERR184093 2 0.2480 0.7775 0.008 0.904 0.000 0.088
#> ERR184051 3 0.0188 0.7894 0.000 0.000 0.996 0.004
#> ERR184076 1 0.3224 0.7564 0.864 0.000 0.120 0.016
#> ERR184043 3 0.0469 0.7875 0.000 0.000 0.988 0.012
#> ERR184037 1 0.3577 0.6790 0.832 0.000 0.012 0.156
#> ERR184059 3 0.3529 0.7508 0.152 0.000 0.836 0.012
#> ERR184055 1 0.5684 0.4948 0.664 0.016 0.024 0.296
#> ERR184065 2 0.4164 0.6773 0.000 0.736 0.000 0.264
#> ERR184069 2 0.1716 0.7800 0.000 0.936 0.000 0.064
#> ERR184040 1 0.4121 0.7196 0.796 0.000 0.184 0.020
#> ERR184057 2 0.0817 0.7777 0.000 0.976 0.000 0.024
#> ERR184082 3 0.6357 0.6013 0.184 0.000 0.656 0.160
#> ERR184083 2 0.2216 0.7795 0.000 0.908 0.000 0.092
#> ERR184039 2 0.4406 0.6505 0.000 0.700 0.000 0.300
#> ERR184064 3 0.0188 0.7890 0.000 0.000 0.996 0.004
#> ERR184081 2 0.1637 0.7816 0.000 0.940 0.000 0.060
#> ERR184095 2 0.0921 0.7765 0.000 0.972 0.000 0.028
#> ERR184079 2 0.4501 0.6902 0.024 0.764 0.000 0.212
#> ERR184084 3 0.4399 0.7018 0.212 0.000 0.768 0.020
#> ERR184068 2 0.5449 0.5172 0.032 0.676 0.004 0.288
#> ERR184067 2 0.2408 0.7684 0.000 0.896 0.000 0.104
#> ERR184071 2 0.3490 0.7653 0.004 0.836 0.004 0.156
#> ERR184042 3 0.3271 0.7623 0.132 0.000 0.856 0.012
#> ERR184063 3 0.0921 0.7835 0.000 0.000 0.972 0.028
#> ERR184091 2 0.4103 0.6854 0.000 0.744 0.000 0.256
#> ERR184061 4 0.7556 -0.0898 0.420 0.072 0.044 0.464
#> ERR184077 2 0.2814 0.7621 0.000 0.868 0.000 0.132
#> ERR184062 2 0.6117 0.4486 0.072 0.648 0.004 0.276
#> ERR184053 2 0.3257 0.7169 0.004 0.844 0.000 0.152
#> ERR184088 2 0.7427 -0.1560 0.200 0.500 0.000 0.300
#> ERR184075 2 0.5557 0.5878 0.000 0.652 0.040 0.308
#> ERR184041 3 0.1305 0.7773 0.004 0.000 0.960 0.036
#> ERR184060 2 0.0817 0.7777 0.000 0.976 0.000 0.024
#> ERR184035 1 0.5352 0.6914 0.740 0.000 0.092 0.168
#> ERR184086 2 0.3726 0.7181 0.000 0.788 0.000 0.212
#> ERR184080 1 0.3335 0.7022 0.860 0.000 0.020 0.120
#> ERR184050 2 0.5786 0.4807 0.004 0.588 0.028 0.380
#> ERR184047 1 0.5310 0.2760 0.576 0.000 0.412 0.012
#> ERR184092 2 0.2011 0.7758 0.000 0.920 0.000 0.080
#> ERR184072 1 0.6963 0.4470 0.636 0.076 0.044 0.244
#> ERR184073 3 0.5602 0.2641 0.408 0.000 0.568 0.024
#> ERR184066 1 0.6097 0.6333 0.724 0.028 0.096 0.152
#> ERR184098 2 0.5498 0.4671 0.000 0.576 0.020 0.404
#> ERR184044 4 0.9449 0.4432 0.204 0.312 0.120 0.364
#> ERR184054 1 0.3821 0.7556 0.840 0.000 0.120 0.040
#> ERR184085 3 0.6875 0.5387 0.220 0.000 0.596 0.184
#> ERR184056 2 0.0817 0.7772 0.000 0.976 0.000 0.024
#> ERR184052 4 0.7176 0.1395 0.052 0.408 0.040 0.500
#> ERR184070 2 0.1022 0.7773 0.000 0.968 0.000 0.032
#> ERR184096 1 0.4372 0.6160 0.728 0.000 0.268 0.004
#> ERR184089 4 0.8310 0.3051 0.016 0.260 0.360 0.364
#> ERR184049 4 0.8592 0.3286 0.248 0.160 0.084 0.508
#> ERR184038 3 0.8302 0.3505 0.264 0.052 0.512 0.172
#> ERR184087 3 0.0524 0.7893 0.004 0.000 0.988 0.008
#> ERR184097 2 0.2480 0.7669 0.008 0.904 0.000 0.088
#> ERR184094 3 0.4019 0.7158 0.196 0.000 0.792 0.012
#> ERR184058 2 0.4356 0.6377 0.000 0.708 0.000 0.292
#> ERR184036 2 0.5430 0.4563 0.036 0.664 0.000 0.300
#> ERR184046 2 0.2081 0.7761 0.000 0.916 0.000 0.084
#> ERR184074 1 0.4638 0.7477 0.788 0.000 0.152 0.060
#> ERR184048 2 0.2345 0.7556 0.000 0.900 0.000 0.100
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.3323 0.5791 0.864 0.000 0.056 0.020 0.060
#> ERR184093 2 0.4149 0.5091 0.004 0.768 0.000 0.188 0.040
#> ERR184051 3 0.1405 0.7268 0.008 0.000 0.956 0.016 0.020
#> ERR184076 1 0.4500 0.5810 0.784 0.000 0.100 0.020 0.096
#> ERR184043 3 0.0693 0.7263 0.008 0.000 0.980 0.012 0.000
#> ERR184037 1 0.5031 0.1914 0.656 0.000 0.012 0.036 0.296
#> ERR184059 3 0.4065 0.6378 0.212 0.000 0.760 0.008 0.020
#> ERR184055 5 0.5850 0.3294 0.396 0.024 0.004 0.040 0.536
#> ERR184065 2 0.4482 0.0926 0.000 0.612 0.000 0.376 0.012
#> ERR184069 2 0.3184 0.5490 0.000 0.852 0.000 0.100 0.048
#> ERR184040 1 0.3387 0.6004 0.836 0.000 0.132 0.008 0.024
#> ERR184057 2 0.1484 0.5711 0.000 0.944 0.000 0.048 0.008
#> ERR184082 3 0.8038 0.3569 0.192 0.004 0.464 0.144 0.196
#> ERR184083 2 0.3304 0.5206 0.000 0.816 0.000 0.168 0.016
#> ERR184039 2 0.5223 -0.1659 0.000 0.512 0.000 0.444 0.044
#> ERR184064 3 0.0451 0.7268 0.008 0.000 0.988 0.004 0.000
#> ERR184081 2 0.2770 0.5659 0.000 0.880 0.000 0.076 0.044
#> ERR184095 2 0.1877 0.5711 0.000 0.924 0.000 0.064 0.012
#> ERR184079 2 0.5847 0.3309 0.000 0.608 0.000 0.204 0.188
#> ERR184084 3 0.6220 0.4604 0.296 0.000 0.588 0.048 0.068
#> ERR184068 2 0.6607 0.2196 0.012 0.536 0.004 0.284 0.164
#> ERR184067 2 0.4210 0.5366 0.000 0.780 0.000 0.124 0.096
#> ERR184071 2 0.5390 0.3031 0.004 0.620 0.008 0.320 0.048
#> ERR184042 3 0.4173 0.6413 0.212 0.000 0.756 0.012 0.020
#> ERR184063 3 0.1399 0.7183 0.000 0.000 0.952 0.028 0.020
#> ERR184091 2 0.4540 0.1752 0.000 0.640 0.000 0.340 0.020
#> ERR184061 5 0.7323 0.5453 0.216 0.080 0.032 0.092 0.580
#> ERR184077 2 0.4179 0.5315 0.000 0.776 0.000 0.152 0.072
#> ERR184062 2 0.7475 0.1193 0.040 0.492 0.016 0.280 0.172
#> ERR184053 2 0.4045 0.5196 0.004 0.792 0.000 0.148 0.056
#> ERR184088 2 0.7830 -0.0473 0.148 0.460 0.000 0.136 0.256
#> ERR184075 2 0.5084 -0.2264 0.000 0.488 0.020 0.484 0.008
#> ERR184041 3 0.1557 0.7111 0.000 0.000 0.940 0.052 0.008
#> ERR184060 2 0.0955 0.5656 0.000 0.968 0.000 0.028 0.004
#> ERR184035 1 0.6121 0.4396 0.656 0.000 0.076 0.076 0.192
#> ERR184086 2 0.3949 0.3059 0.000 0.696 0.000 0.300 0.004
#> ERR184080 1 0.3523 0.4427 0.824 0.004 0.000 0.032 0.140
#> ERR184050 4 0.6324 0.1774 0.000 0.444 0.024 0.448 0.084
#> ERR184047 1 0.4557 0.3998 0.656 0.000 0.324 0.012 0.008
#> ERR184092 2 0.3242 0.5597 0.000 0.844 0.000 0.116 0.040
#> ERR184072 1 0.7662 -0.1934 0.448 0.048 0.032 0.116 0.356
#> ERR184073 1 0.5605 -0.0489 0.472 0.000 0.468 0.008 0.052
#> ERR184066 1 0.7859 0.0234 0.512 0.048 0.072 0.104 0.264
#> ERR184098 4 0.5161 0.0730 0.000 0.480 0.008 0.488 0.024
#> ERR184044 2 0.9124 -0.1794 0.096 0.332 0.068 0.252 0.252
#> ERR184054 1 0.3709 0.5766 0.840 0.000 0.068 0.020 0.072
#> ERR184085 3 0.7852 0.2896 0.260 0.000 0.436 0.096 0.208
#> ERR184056 2 0.2959 0.5696 0.000 0.864 0.000 0.100 0.036
#> ERR184052 4 0.8128 0.2097 0.036 0.296 0.028 0.340 0.300
#> ERR184070 2 0.2209 0.5694 0.000 0.912 0.000 0.056 0.032
#> ERR184096 1 0.4230 0.5749 0.764 0.000 0.196 0.016 0.024
#> ERR184089 4 0.7239 0.2842 0.004 0.160 0.328 0.468 0.040
#> ERR184049 5 0.7549 0.5360 0.164 0.080 0.036 0.144 0.576
#> ERR184038 3 0.8418 0.1979 0.264 0.020 0.424 0.136 0.156
#> ERR184087 3 0.0833 0.7281 0.016 0.000 0.976 0.004 0.004
#> ERR184097 2 0.3595 0.5417 0.000 0.816 0.000 0.140 0.044
#> ERR184094 3 0.4747 0.5462 0.284 0.000 0.676 0.004 0.036
#> ERR184058 2 0.5554 0.1105 0.000 0.592 0.000 0.316 0.092
#> ERR184036 2 0.6910 -0.0226 0.016 0.480 0.000 0.236 0.268
#> ERR184046 2 0.2813 0.5394 0.000 0.868 0.000 0.108 0.024
#> ERR184074 1 0.4922 0.5235 0.744 0.000 0.072 0.024 0.160
#> ERR184048 2 0.4505 0.5083 0.004 0.760 0.000 0.152 0.084
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.452 0.5100 0.780 0.000 0.064 0.024 0.044 0.088
#> ERR184093 2 0.545 0.4491 0.000 0.636 0.000 0.144 0.196 0.024
#> ERR184051 3 0.249 0.6602 0.024 0.000 0.900 0.048 0.020 0.008
#> ERR184076 1 0.475 0.5200 0.748 0.000 0.100 0.008 0.040 0.104
#> ERR184043 3 0.155 0.6555 0.004 0.000 0.940 0.044 0.004 0.008
#> ERR184037 1 0.483 0.0672 0.520 0.000 0.012 0.004 0.024 0.440
#> ERR184059 3 0.394 0.5981 0.192 0.000 0.764 0.020 0.016 0.008
#> ERR184055 6 0.662 0.2391 0.328 0.016 0.028 0.032 0.080 0.516
#> ERR184065 2 0.492 -0.2412 0.000 0.508 0.000 0.436 0.052 0.004
#> ERR184069 2 0.326 0.5193 0.000 0.840 0.000 0.080 0.068 0.012
#> ERR184040 1 0.403 0.5367 0.784 0.000 0.144 0.004 0.036 0.032
#> ERR184057 2 0.271 0.5514 0.000 0.860 0.000 0.036 0.104 0.000
#> ERR184082 3 0.857 0.2187 0.172 0.016 0.408 0.148 0.096 0.160
#> ERR184083 2 0.337 0.5009 0.000 0.820 0.000 0.116 0.060 0.004
#> ERR184039 4 0.549 0.2894 0.000 0.440 0.004 0.480 0.044 0.032
#> ERR184064 3 0.137 0.6620 0.008 0.000 0.952 0.028 0.008 0.004
#> ERR184081 2 0.208 0.5365 0.000 0.916 0.000 0.036 0.036 0.012
#> ERR184095 2 0.296 0.5507 0.000 0.856 0.000 0.036 0.096 0.012
#> ERR184079 2 0.728 0.2574 0.032 0.524 0.004 0.124 0.196 0.120
#> ERR184084 3 0.650 0.3925 0.288 0.000 0.544 0.076 0.032 0.060
#> ERR184068 2 0.721 0.0106 0.036 0.444 0.004 0.088 0.344 0.084
#> ERR184067 2 0.525 0.4663 0.004 0.704 0.000 0.116 0.112 0.064
#> ERR184071 2 0.548 0.4015 0.004 0.648 0.000 0.156 0.168 0.024
#> ERR184042 3 0.439 0.5935 0.184 0.000 0.748 0.020 0.024 0.024
#> ERR184063 3 0.313 0.6321 0.008 0.000 0.860 0.080 0.024 0.028
#> ERR184091 2 0.462 -0.0954 0.000 0.572 0.000 0.388 0.036 0.004
#> ERR184061 6 0.839 0.3528 0.188 0.080 0.032 0.120 0.128 0.452
#> ERR184077 2 0.509 0.5054 0.004 0.696 0.000 0.072 0.184 0.044
#> ERR184062 2 0.756 -0.2047 0.020 0.364 0.000 0.152 0.344 0.120
#> ERR184053 2 0.596 0.3103 0.012 0.572 0.000 0.072 0.296 0.048
#> ERR184088 2 0.835 -0.3068 0.112 0.336 0.004 0.064 0.244 0.240
#> ERR184075 4 0.584 0.3672 0.000 0.408 0.028 0.492 0.052 0.020
#> ERR184041 3 0.291 0.6322 0.008 0.000 0.864 0.096 0.016 0.016
#> ERR184060 2 0.201 0.5349 0.000 0.916 0.000 0.036 0.044 0.004
#> ERR184035 1 0.669 0.2957 0.584 0.000 0.036 0.096 0.096 0.188
#> ERR184086 2 0.460 0.1190 0.000 0.628 0.000 0.320 0.048 0.004
#> ERR184080 1 0.464 0.3761 0.716 0.000 0.000 0.020 0.080 0.184
#> ERR184050 4 0.625 0.4659 0.004 0.312 0.024 0.548 0.076 0.036
#> ERR184047 1 0.463 0.1319 0.572 0.000 0.396 0.008 0.008 0.016
#> ERR184092 2 0.451 0.5160 0.000 0.740 0.000 0.068 0.160 0.032
#> ERR184072 1 0.779 -0.1760 0.404 0.040 0.032 0.028 0.240 0.256
#> ERR184073 3 0.569 0.1012 0.424 0.000 0.476 0.012 0.012 0.076
#> ERR184066 1 0.834 -0.0317 0.372 0.024 0.080 0.056 0.196 0.272
#> ERR184098 4 0.580 0.4121 0.000 0.340 0.000 0.520 0.120 0.020
#> ERR184044 5 0.922 0.0000 0.052 0.228 0.072 0.152 0.288 0.208
#> ERR184054 1 0.528 0.5037 0.712 0.000 0.100 0.012 0.064 0.112
#> ERR184085 3 0.880 0.0999 0.196 0.004 0.312 0.128 0.140 0.220
#> ERR184056 2 0.397 0.5252 0.000 0.744 0.000 0.048 0.204 0.004
#> ERR184052 4 0.889 -0.1971 0.052 0.260 0.036 0.304 0.156 0.192
#> ERR184070 2 0.248 0.5501 0.000 0.888 0.000 0.032 0.072 0.008
#> ERR184096 1 0.448 0.4753 0.720 0.000 0.220 0.016 0.024 0.020
#> ERR184089 4 0.612 0.1489 0.004 0.108 0.212 0.616 0.040 0.020
#> ERR184049 6 0.771 0.2814 0.092 0.064 0.040 0.152 0.108 0.544
#> ERR184038 3 0.892 0.1078 0.228 0.032 0.348 0.084 0.160 0.148
#> ERR184087 3 0.133 0.6627 0.020 0.000 0.948 0.032 0.000 0.000
#> ERR184097 2 0.462 0.4918 0.004 0.696 0.000 0.056 0.232 0.012
#> ERR184094 3 0.460 0.5545 0.228 0.000 0.708 0.016 0.016 0.032
#> ERR184058 2 0.567 -0.0411 0.004 0.552 0.000 0.344 0.056 0.044
#> ERR184036 2 0.748 -0.0906 0.008 0.428 0.000 0.192 0.156 0.216
#> ERR184046 2 0.282 0.5009 0.000 0.852 0.000 0.108 0.040 0.000
#> ERR184074 1 0.596 0.4488 0.616 0.000 0.128 0.012 0.040 0.204
#> ERR184048 2 0.564 0.4236 0.016 0.604 0.000 0.056 0.288 0.036
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 10269 rows and 62 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 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 0.862 0.921 0.963 0.4365 0.556 0.556
#> 3 3 0.714 0.810 0.930 0.1043 0.990 0.982
#> 4 4 0.698 0.795 0.911 0.0931 0.897 0.813
#> 5 5 0.646 0.795 0.916 0.0678 0.997 0.994
#> 6 6 0.619 0.756 0.893 0.0417 0.992 0.981
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
#> ERR184078 1 0.0376 0.926 0.996 0.004
#> ERR184093 2 0.0000 0.976 0.000 1.000
#> ERR184051 2 0.2043 0.951 0.032 0.968
#> ERR184076 1 0.0376 0.926 0.996 0.004
#> ERR184043 2 0.2043 0.951 0.032 0.968
#> ERR184037 1 0.0376 0.926 0.996 0.004
#> ERR184059 1 0.1184 0.921 0.984 0.016
#> ERR184055 1 0.1184 0.921 0.984 0.016
#> ERR184065 2 0.0000 0.976 0.000 1.000
#> ERR184069 2 0.0000 0.976 0.000 1.000
#> ERR184040 1 0.0376 0.926 0.996 0.004
#> ERR184057 2 0.0000 0.976 0.000 1.000
#> ERR184082 1 0.8763 0.630 0.704 0.296
#> ERR184083 2 0.0000 0.976 0.000 1.000
#> ERR184039 2 0.0000 0.976 0.000 1.000
#> ERR184064 2 0.2423 0.944 0.040 0.960
#> ERR184081 2 0.0000 0.976 0.000 1.000
#> ERR184095 2 0.0000 0.976 0.000 1.000
#> ERR184079 2 0.0000 0.976 0.000 1.000
#> ERR184084 1 0.1414 0.919 0.980 0.020
#> ERR184068 2 0.0000 0.976 0.000 1.000
#> ERR184067 2 0.0000 0.976 0.000 1.000
#> ERR184071 2 0.0000 0.976 0.000 1.000
#> ERR184042 1 0.4939 0.856 0.892 0.108
#> ERR184063 2 0.0376 0.973 0.004 0.996
#> ERR184091 2 0.0000 0.976 0.000 1.000
#> ERR184061 1 0.9732 0.395 0.596 0.404
#> ERR184077 2 0.0000 0.976 0.000 1.000
#> ERR184062 2 0.0000 0.976 0.000 1.000
#> ERR184053 2 0.0000 0.976 0.000 1.000
#> ERR184088 2 0.4431 0.883 0.092 0.908
#> ERR184075 2 0.0000 0.976 0.000 1.000
#> ERR184041 2 0.0376 0.973 0.004 0.996
#> ERR184060 2 0.0000 0.976 0.000 1.000
#> ERR184035 1 0.0376 0.926 0.996 0.004
#> ERR184086 2 0.0000 0.976 0.000 1.000
#> ERR184080 1 0.0376 0.926 0.996 0.004
#> ERR184050 2 0.0000 0.976 0.000 1.000
#> ERR184047 1 0.0000 0.925 1.000 0.000
#> ERR184092 2 0.0000 0.976 0.000 1.000
#> ERR184072 1 0.7950 0.713 0.760 0.240
#> ERR184073 1 0.0000 0.925 1.000 0.000
#> ERR184066 1 0.8144 0.696 0.748 0.252
#> ERR184098 2 0.0000 0.976 0.000 1.000
#> ERR184044 2 0.0000 0.976 0.000 1.000
#> ERR184054 1 0.0376 0.926 0.996 0.004
#> ERR184085 2 0.8327 0.625 0.264 0.736
#> ERR184056 2 0.0000 0.976 0.000 1.000
#> ERR184052 2 0.0000 0.976 0.000 1.000
#> ERR184070 2 0.0000 0.976 0.000 1.000
#> ERR184096 1 0.0000 0.925 1.000 0.000
#> ERR184089 2 0.0000 0.976 0.000 1.000
#> ERR184049 2 0.0376 0.973 0.004 0.996
#> ERR184038 2 0.8386 0.616 0.268 0.732
#> ERR184087 2 0.6531 0.791 0.168 0.832
#> ERR184097 2 0.0000 0.976 0.000 1.000
#> ERR184094 1 0.0000 0.925 1.000 0.000
#> ERR184058 2 0.0000 0.976 0.000 1.000
#> ERR184036 2 0.0000 0.976 0.000 1.000
#> ERR184046 2 0.0000 0.976 0.000 1.000
#> ERR184074 1 0.0376 0.926 0.996 0.004
#> ERR184048 2 0.0000 0.976 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.0000 0.825 1.000 0.000 0.000
#> ERR184093 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184051 2 0.5905 0.527 0.000 0.648 0.352
#> ERR184076 1 0.0000 0.825 1.000 0.000 0.000
#> ERR184043 2 0.5905 0.527 0.000 0.648 0.352
#> ERR184037 1 0.0000 0.825 1.000 0.000 0.000
#> ERR184059 1 0.6427 0.383 0.640 0.012 0.348
#> ERR184055 1 0.0000 0.825 1.000 0.000 0.000
#> ERR184065 2 0.0424 0.938 0.000 0.992 0.008
#> ERR184069 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184040 1 0.0000 0.825 1.000 0.000 0.000
#> ERR184057 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184082 1 0.5656 0.487 0.712 0.284 0.004
#> ERR184083 2 0.0237 0.939 0.000 0.996 0.004
#> ERR184039 2 0.0424 0.938 0.000 0.992 0.008
#> ERR184064 2 0.5905 0.527 0.000 0.648 0.352
#> ERR184081 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184095 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184079 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184084 1 0.2743 0.787 0.928 0.020 0.052
#> ERR184068 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184067 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184071 2 0.0424 0.938 0.000 0.992 0.008
#> ERR184042 3 0.0000 0.000 0.000 0.000 1.000
#> ERR184063 2 0.3941 0.808 0.000 0.844 0.156
#> ERR184091 2 0.0424 0.938 0.000 0.992 0.008
#> ERR184061 1 0.6379 0.335 0.624 0.368 0.008
#> ERR184077 2 0.0237 0.939 0.000 0.996 0.004
#> ERR184062 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184053 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184088 2 0.2711 0.853 0.088 0.912 0.000
#> ERR184075 2 0.0424 0.938 0.000 0.992 0.008
#> ERR184041 2 0.0747 0.934 0.000 0.984 0.016
#> ERR184060 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184035 1 0.0000 0.825 1.000 0.000 0.000
#> ERR184086 2 0.0424 0.938 0.000 0.992 0.008
#> ERR184080 1 0.0000 0.825 1.000 0.000 0.000
#> ERR184050 2 0.0424 0.938 0.000 0.992 0.008
#> ERR184047 1 0.5785 0.423 0.668 0.000 0.332
#> ERR184092 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184072 1 0.5335 0.549 0.760 0.232 0.008
#> ERR184073 1 0.0000 0.825 1.000 0.000 0.000
#> ERR184066 1 0.5216 0.528 0.740 0.260 0.000
#> ERR184098 2 0.0424 0.938 0.000 0.992 0.008
#> ERR184044 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184054 1 0.0000 0.825 1.000 0.000 0.000
#> ERR184085 2 0.5692 0.623 0.268 0.724 0.008
#> ERR184056 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184052 2 0.0424 0.938 0.000 0.992 0.008
#> ERR184070 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184096 1 0.0000 0.825 1.000 0.000 0.000
#> ERR184089 2 0.0424 0.938 0.000 0.992 0.008
#> ERR184049 2 0.0848 0.934 0.008 0.984 0.008
#> ERR184038 2 0.5692 0.624 0.268 0.724 0.008
#> ERR184087 2 0.5905 0.527 0.000 0.648 0.352
#> ERR184097 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184094 1 0.3116 0.746 0.892 0.000 0.108
#> ERR184058 2 0.0424 0.938 0.000 0.992 0.008
#> ERR184036 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184046 2 0.0000 0.939 0.000 1.000 0.000
#> ERR184074 1 0.0000 0.825 1.000 0.000 0.000
#> ERR184048 2 0.0000 0.939 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.0000 0.8395 1.000 0.000 0.000 0.000
#> ERR184093 2 0.0592 0.9411 0.000 0.984 0.016 0.000
#> ERR184051 3 0.5093 0.6169 0.012 0.348 0.640 0.000
#> ERR184076 1 0.0000 0.8395 1.000 0.000 0.000 0.000
#> ERR184043 3 0.4795 0.6771 0.012 0.292 0.696 0.000
#> ERR184037 1 0.0000 0.8395 1.000 0.000 0.000 0.000
#> ERR184059 3 0.5038 0.1493 0.336 0.012 0.652 0.000
#> ERR184055 1 0.0336 0.8348 0.992 0.008 0.000 0.000
#> ERR184065 2 0.1576 0.9328 0.000 0.948 0.048 0.004
#> ERR184069 2 0.0469 0.9413 0.000 0.988 0.012 0.000
#> ERR184040 1 0.0000 0.8395 1.000 0.000 0.000 0.000
#> ERR184057 2 0.0188 0.9392 0.000 0.996 0.004 0.000
#> ERR184082 1 0.4850 0.4299 0.696 0.292 0.008 0.004
#> ERR184083 2 0.1489 0.9347 0.000 0.952 0.044 0.004
#> ERR184039 2 0.1576 0.9328 0.000 0.948 0.048 0.004
#> ERR184064 3 0.4795 0.6771 0.012 0.292 0.696 0.000
#> ERR184081 2 0.0188 0.9392 0.000 0.996 0.004 0.000
#> ERR184095 2 0.0188 0.9392 0.000 0.996 0.004 0.000
#> ERR184079 2 0.0779 0.9408 0.000 0.980 0.016 0.004
#> ERR184084 1 0.3408 0.7452 0.860 0.016 0.120 0.004
#> ERR184068 2 0.0376 0.9394 0.000 0.992 0.004 0.004
#> ERR184067 2 0.0376 0.9394 0.000 0.992 0.004 0.004
#> ERR184071 2 0.1022 0.9386 0.000 0.968 0.032 0.000
#> ERR184042 4 0.0188 0.0000 0.000 0.000 0.004 0.996
#> ERR184063 2 0.3726 0.7052 0.000 0.788 0.212 0.000
#> ERR184091 2 0.1576 0.9328 0.000 0.948 0.048 0.004
#> ERR184061 1 0.5964 0.2391 0.612 0.340 0.044 0.004
#> ERR184077 2 0.0707 0.9409 0.000 0.980 0.020 0.000
#> ERR184062 2 0.0188 0.9392 0.000 0.996 0.004 0.000
#> ERR184053 2 0.0188 0.9392 0.000 0.996 0.004 0.000
#> ERR184088 2 0.2266 0.8381 0.084 0.912 0.004 0.000
#> ERR184075 2 0.1576 0.9328 0.000 0.948 0.048 0.004
#> ERR184041 2 0.1637 0.9269 0.000 0.940 0.060 0.000
#> ERR184060 2 0.0188 0.9392 0.000 0.996 0.004 0.000
#> ERR184035 1 0.0188 0.8376 0.996 0.000 0.000 0.004
#> ERR184086 2 0.1389 0.9334 0.000 0.952 0.048 0.000
#> ERR184080 1 0.0000 0.8395 1.000 0.000 0.000 0.000
#> ERR184050 2 0.1576 0.9328 0.000 0.948 0.048 0.004
#> ERR184047 3 0.3726 -0.0645 0.212 0.000 0.788 0.000
#> ERR184092 2 0.0188 0.9392 0.000 0.996 0.004 0.000
#> ERR184072 1 0.4707 0.5346 0.760 0.204 0.036 0.000
#> ERR184073 1 0.0000 0.8395 1.000 0.000 0.000 0.000
#> ERR184066 1 0.4428 0.4852 0.720 0.276 0.004 0.000
#> ERR184098 2 0.1576 0.9328 0.000 0.948 0.048 0.004
#> ERR184044 2 0.0336 0.9402 0.000 0.992 0.008 0.000
#> ERR184054 1 0.0000 0.8395 1.000 0.000 0.000 0.000
#> ERR184085 2 0.5648 0.4632 0.268 0.680 0.048 0.004
#> ERR184056 2 0.0188 0.9392 0.000 0.996 0.004 0.000
#> ERR184052 2 0.1302 0.9351 0.000 0.956 0.044 0.000
#> ERR184070 2 0.0188 0.9392 0.000 0.996 0.004 0.000
#> ERR184096 1 0.0000 0.8395 1.000 0.000 0.000 0.000
#> ERR184089 2 0.1576 0.9328 0.000 0.948 0.048 0.004
#> ERR184049 2 0.1822 0.9343 0.008 0.944 0.044 0.004
#> ERR184038 2 0.5471 0.4654 0.268 0.684 0.048 0.000
#> ERR184087 3 0.4795 0.6771 0.012 0.292 0.696 0.000
#> ERR184097 2 0.0188 0.9392 0.000 0.996 0.004 0.000
#> ERR184094 1 0.4222 0.5526 0.728 0.000 0.272 0.000
#> ERR184058 2 0.1576 0.9328 0.000 0.948 0.048 0.004
#> ERR184036 2 0.0188 0.9406 0.000 0.996 0.000 0.004
#> ERR184046 2 0.0592 0.9411 0.000 0.984 0.016 0.000
#> ERR184074 1 0.0000 0.8395 1.000 0.000 0.000 0.000
#> ERR184048 2 0.0336 0.9404 0.000 0.992 0.008 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.0000 0.832 1.000 0.000 0.000 0 0.000
#> ERR184093 2 0.1043 0.920 0.000 0.960 0.040 0 0.000
#> ERR184051 3 0.3607 0.446 0.004 0.244 0.752 0 0.000
#> ERR184076 1 0.0000 0.832 1.000 0.000 0.000 0 0.000
#> ERR184043 3 0.0865 0.781 0.004 0.024 0.972 0 0.000
#> ERR184037 1 0.0000 0.832 1.000 0.000 0.000 0 0.000
#> ERR184059 3 0.2020 0.559 0.100 0.000 0.900 0 0.000
#> ERR184055 1 0.0290 0.828 0.992 0.008 0.000 0 0.000
#> ERR184065 2 0.2470 0.906 0.000 0.884 0.104 0 0.012
#> ERR184069 2 0.0963 0.920 0.000 0.964 0.036 0 0.000
#> ERR184040 1 0.0000 0.832 1.000 0.000 0.000 0 0.000
#> ERR184057 2 0.0000 0.916 0.000 1.000 0.000 0 0.000
#> ERR184082 1 0.4604 0.482 0.680 0.292 0.016 0 0.012
#> ERR184083 2 0.2304 0.909 0.000 0.892 0.100 0 0.008
#> ERR184039 2 0.2470 0.906 0.000 0.884 0.104 0 0.012
#> ERR184064 3 0.0865 0.781 0.004 0.024 0.972 0 0.000
#> ERR184081 2 0.0000 0.916 0.000 1.000 0.000 0 0.000
#> ERR184095 2 0.0000 0.916 0.000 1.000 0.000 0 0.000
#> ERR184079 2 0.1205 0.920 0.000 0.956 0.040 0 0.004
#> ERR184084 1 0.3783 0.607 0.740 0.000 0.252 0 0.008
#> ERR184068 2 0.0162 0.916 0.000 0.996 0.000 0 0.004
#> ERR184067 2 0.0162 0.916 0.000 0.996 0.000 0 0.004
#> ERR184071 2 0.1894 0.915 0.000 0.920 0.072 0 0.008
#> ERR184042 4 0.0000 0.000 0.000 0.000 0.000 1 0.000
#> ERR184063 2 0.3980 0.694 0.000 0.708 0.284 0 0.008
#> ERR184091 2 0.2358 0.907 0.000 0.888 0.104 0 0.008
#> ERR184061 1 0.5815 0.377 0.616 0.272 0.100 0 0.012
#> ERR184077 2 0.1357 0.919 0.000 0.948 0.048 0 0.004
#> ERR184062 2 0.0000 0.916 0.000 1.000 0.000 0 0.000
#> ERR184053 2 0.0000 0.916 0.000 1.000 0.000 0 0.000
#> ERR184088 2 0.1732 0.846 0.080 0.920 0.000 0 0.000
#> ERR184075 2 0.2470 0.906 0.000 0.884 0.104 0 0.012
#> ERR184041 2 0.2439 0.901 0.000 0.876 0.120 0 0.004
#> ERR184060 2 0.0000 0.916 0.000 1.000 0.000 0 0.000
#> ERR184035 1 0.0162 0.830 0.996 0.000 0.000 0 0.004
#> ERR184086 2 0.2233 0.908 0.000 0.892 0.104 0 0.004
#> ERR184080 1 0.0000 0.832 1.000 0.000 0.000 0 0.000
#> ERR184050 2 0.2470 0.906 0.000 0.884 0.104 0 0.012
#> ERR184047 5 0.0404 0.000 0.012 0.000 0.000 0 0.988
#> ERR184092 2 0.0162 0.917 0.000 0.996 0.004 0 0.000
#> ERR184072 1 0.4489 0.608 0.760 0.156 0.080 0 0.004
#> ERR184073 1 0.0000 0.832 1.000 0.000 0.000 0 0.000
#> ERR184066 1 0.3796 0.508 0.700 0.300 0.000 0 0.000
#> ERR184098 2 0.2470 0.906 0.000 0.884 0.104 0 0.012
#> ERR184044 2 0.0162 0.917 0.000 0.996 0.004 0 0.000
#> ERR184054 1 0.0000 0.832 1.000 0.000 0.000 0 0.000
#> ERR184085 2 0.5795 0.526 0.268 0.620 0.100 0 0.012
#> ERR184056 2 0.0000 0.916 0.000 1.000 0.000 0 0.000
#> ERR184052 2 0.2304 0.908 0.000 0.892 0.100 0 0.008
#> ERR184070 2 0.0000 0.916 0.000 1.000 0.000 0 0.000
#> ERR184096 1 0.0162 0.830 0.996 0.000 0.004 0 0.000
#> ERR184089 2 0.2470 0.906 0.000 0.884 0.104 0 0.012
#> ERR184049 2 0.2414 0.911 0.008 0.900 0.080 0 0.012
#> ERR184038 2 0.5737 0.526 0.268 0.620 0.104 0 0.008
#> ERR184087 3 0.0865 0.781 0.004 0.024 0.972 0 0.000
#> ERR184097 2 0.0000 0.916 0.000 1.000 0.000 0 0.000
#> ERR184094 1 0.3684 0.552 0.720 0.000 0.280 0 0.000
#> ERR184058 2 0.2470 0.906 0.000 0.884 0.104 0 0.012
#> ERR184036 2 0.0451 0.918 0.000 0.988 0.004 0 0.008
#> ERR184046 2 0.1197 0.920 0.000 0.952 0.048 0 0.000
#> ERR184074 1 0.0000 0.832 1.000 0.000 0.000 0 0.000
#> ERR184048 2 0.0609 0.920 0.000 0.980 0.020 0 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.0000 0.776 1.000 0.000 0.000 0 0 0.000
#> ERR184093 2 0.1219 0.902 0.000 0.948 0.004 0 0 0.048
#> ERR184051 3 0.4091 0.391 0.000 0.224 0.720 0 0 0.056
#> ERR184076 1 0.0458 0.768 0.984 0.000 0.000 0 0 0.016
#> ERR184043 3 0.0458 0.814 0.000 0.016 0.984 0 0 0.000
#> ERR184037 1 0.0000 0.776 1.000 0.000 0.000 0 0 0.000
#> ERR184059 3 0.0632 0.749 0.000 0.000 0.976 0 0 0.024
#> ERR184055 1 0.0405 0.770 0.988 0.008 0.000 0 0 0.004
#> ERR184065 2 0.2750 0.887 0.000 0.844 0.020 0 0 0.136
#> ERR184069 2 0.1010 0.903 0.000 0.960 0.004 0 0 0.036
#> ERR184040 1 0.0000 0.776 1.000 0.000 0.000 0 0 0.000
#> ERR184057 2 0.0458 0.895 0.000 0.984 0.000 0 0 0.016
#> ERR184082 1 0.4630 0.391 0.660 0.280 0.012 0 0 0.048
#> ERR184083 2 0.2581 0.892 0.000 0.860 0.020 0 0 0.120
#> ERR184039 2 0.2750 0.887 0.000 0.844 0.020 0 0 0.136
#> ERR184064 3 0.0458 0.814 0.000 0.016 0.984 0 0 0.000
#> ERR184081 2 0.0458 0.895 0.000 0.984 0.000 0 0 0.016
#> ERR184095 2 0.0458 0.895 0.000 0.984 0.000 0 0 0.016
#> ERR184079 2 0.1584 0.903 0.000 0.928 0.008 0 0 0.064
#> ERR184084 1 0.3952 0.415 0.672 0.000 0.308 0 0 0.020
#> ERR184068 2 0.0547 0.899 0.000 0.980 0.000 0 0 0.020
#> ERR184067 2 0.0632 0.898 0.000 0.976 0.000 0 0 0.024
#> ERR184071 2 0.2350 0.898 0.000 0.880 0.020 0 0 0.100
#> ERR184042 4 0.0000 0.000 0.000 0.000 0.000 1 0 0.000
#> ERR184063 2 0.4594 0.683 0.000 0.676 0.232 0 0 0.092
#> ERR184091 2 0.2624 0.890 0.000 0.856 0.020 0 0 0.124
#> ERR184061 1 0.5473 0.349 0.616 0.236 0.020 0 0 0.128
#> ERR184077 2 0.1895 0.903 0.000 0.912 0.016 0 0 0.072
#> ERR184062 2 0.0458 0.895 0.000 0.984 0.000 0 0 0.016
#> ERR184053 2 0.0458 0.895 0.000 0.984 0.000 0 0 0.016
#> ERR184088 2 0.1951 0.834 0.076 0.908 0.000 0 0 0.016
#> ERR184075 2 0.2750 0.887 0.000 0.844 0.020 0 0 0.136
#> ERR184041 2 0.2912 0.886 0.000 0.844 0.040 0 0 0.116
#> ERR184060 2 0.0458 0.895 0.000 0.984 0.000 0 0 0.016
#> ERR184035 1 0.0146 0.775 0.996 0.000 0.000 0 0 0.004
#> ERR184086 2 0.2581 0.891 0.000 0.860 0.020 0 0 0.120
#> ERR184080 1 0.0000 0.776 1.000 0.000 0.000 0 0 0.000
#> ERR184050 2 0.2750 0.887 0.000 0.844 0.020 0 0 0.136
#> ERR184047 5 0.0000 0.000 0.000 0.000 0.000 0 1 0.000
#> ERR184092 2 0.0146 0.899 0.000 0.996 0.000 0 0 0.004
#> ERR184072 1 0.4250 0.557 0.760 0.132 0.016 0 0 0.092
#> ERR184073 1 0.0146 0.775 0.996 0.000 0.000 0 0 0.004
#> ERR184066 1 0.3990 0.407 0.676 0.304 0.004 0 0 0.016
#> ERR184098 2 0.2750 0.887 0.000 0.844 0.020 0 0 0.136
#> ERR184044 2 0.0972 0.901 0.000 0.964 0.008 0 0 0.028
#> ERR184054 1 0.0000 0.776 1.000 0.000 0.000 0 0 0.000
#> ERR184085 2 0.5644 0.531 0.264 0.584 0.020 0 0 0.132
#> ERR184056 2 0.0458 0.895 0.000 0.984 0.000 0 0 0.016
#> ERR184052 2 0.2581 0.892 0.000 0.860 0.020 0 0 0.120
#> ERR184070 2 0.0458 0.895 0.000 0.984 0.000 0 0 0.016
#> ERR184096 6 0.2762 0.000 0.196 0.000 0.000 0 0 0.804
#> ERR184089 2 0.2750 0.887 0.000 0.844 0.020 0 0 0.136
#> ERR184049 2 0.2501 0.896 0.004 0.872 0.016 0 0 0.108
#> ERR184038 2 0.5610 0.532 0.264 0.588 0.020 0 0 0.128
#> ERR184087 3 0.0458 0.814 0.000 0.016 0.984 0 0 0.000
#> ERR184097 2 0.0458 0.895 0.000 0.984 0.000 0 0 0.016
#> ERR184094 1 0.3371 0.407 0.708 0.000 0.292 0 0 0.000
#> ERR184058 2 0.2750 0.887 0.000 0.844 0.020 0 0 0.136
#> ERR184036 2 0.0935 0.901 0.000 0.964 0.004 0 0 0.032
#> ERR184046 2 0.1434 0.904 0.000 0.940 0.012 0 0 0.048
#> ERR184074 1 0.0000 0.776 1.000 0.000 0.000 0 0 0.000
#> ERR184048 2 0.1320 0.902 0.000 0.948 0.016 0 0 0.036
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 10269 rows and 62 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 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 0.9032 0.944 0.980 0.0701 0.968 0.968
#> 3 3 0.0926 0.477 0.728 5.4481 0.604 0.591
#> 4 4 0.2341 0.531 0.771 0.2223 0.677 0.543
#> 5 5 0.2831 0.572 0.746 0.2190 0.785 0.596
#> 6 6 0.5475 0.653 0.807 0.0895 0.918 0.763
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
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
#> ERR184078 2 0.1414 0.967 0.020 0.980
#> ERR184093 2 0.0000 0.979 0.000 1.000
#> ERR184051 2 0.0672 0.975 0.008 0.992
#> ERR184076 2 0.2423 0.951 0.040 0.960
#> ERR184043 2 0.5737 0.854 0.136 0.864
#> ERR184037 2 0.0376 0.977 0.004 0.996
#> ERR184059 2 0.1184 0.970 0.016 0.984
#> ERR184055 2 0.0000 0.979 0.000 1.000
#> ERR184065 2 0.0000 0.979 0.000 1.000
#> ERR184069 2 0.0000 0.979 0.000 1.000
#> ERR184040 2 0.1843 0.961 0.028 0.972
#> ERR184057 2 0.0000 0.979 0.000 1.000
#> ERR184082 2 0.0000 0.979 0.000 1.000
#> ERR184083 2 0.0000 0.979 0.000 1.000
#> ERR184039 2 0.0000 0.979 0.000 1.000
#> ERR184064 2 0.5737 0.854 0.136 0.864
#> ERR184081 2 0.0000 0.979 0.000 1.000
#> ERR184095 2 0.0000 0.979 0.000 1.000
#> ERR184079 2 0.0672 0.975 0.008 0.992
#> ERR184084 2 0.9170 0.517 0.332 0.668
#> ERR184068 2 0.0000 0.979 0.000 1.000
#> ERR184067 2 0.0000 0.979 0.000 1.000
#> ERR184071 2 0.0000 0.979 0.000 1.000
#> ERR184042 1 0.0000 0.000 1.000 0.000
#> ERR184063 2 0.2778 0.943 0.048 0.952
#> ERR184091 2 0.0000 0.979 0.000 1.000
#> ERR184061 2 0.0000 0.979 0.000 1.000
#> ERR184077 2 0.0000 0.979 0.000 1.000
#> ERR184062 2 0.0000 0.979 0.000 1.000
#> ERR184053 2 0.0938 0.972 0.012 0.988
#> ERR184088 2 0.0000 0.979 0.000 1.000
#> ERR184075 2 0.0000 0.979 0.000 1.000
#> ERR184041 2 0.2778 0.943 0.048 0.952
#> ERR184060 2 0.0000 0.979 0.000 1.000
#> ERR184035 2 0.1414 0.967 0.020 0.980
#> ERR184086 2 0.0000 0.979 0.000 1.000
#> ERR184080 2 0.0000 0.979 0.000 1.000
#> ERR184050 2 0.0000 0.979 0.000 1.000
#> ERR184047 2 0.5519 0.862 0.128 0.872
#> ERR184092 2 0.0000 0.979 0.000 1.000
#> ERR184072 2 0.0000 0.979 0.000 1.000
#> ERR184073 2 0.0000 0.979 0.000 1.000
#> ERR184066 2 0.0000 0.979 0.000 1.000
#> ERR184098 2 0.0000 0.979 0.000 1.000
#> ERR184044 2 0.0376 0.977 0.004 0.996
#> ERR184054 2 0.0376 0.977 0.004 0.996
#> ERR184085 2 0.0672 0.975 0.008 0.992
#> ERR184056 2 0.0000 0.979 0.000 1.000
#> ERR184052 2 0.0000 0.979 0.000 1.000
#> ERR184070 2 0.0000 0.979 0.000 1.000
#> ERR184096 2 0.4690 0.892 0.100 0.900
#> ERR184089 2 0.0000 0.979 0.000 1.000
#> ERR184049 2 0.0000 0.979 0.000 1.000
#> ERR184038 2 0.0000 0.979 0.000 1.000
#> ERR184087 2 0.5946 0.845 0.144 0.856
#> ERR184097 2 0.0000 0.979 0.000 1.000
#> ERR184094 2 0.0000 0.979 0.000 1.000
#> ERR184058 2 0.0000 0.979 0.000 1.000
#> ERR184036 2 0.0000 0.979 0.000 1.000
#> ERR184046 2 0.0000 0.979 0.000 1.000
#> ERR184074 2 0.0000 0.979 0.000 1.000
#> ERR184048 2 0.0000 0.979 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 2 0.6589 0.4978 0.032 0.688 0.280
#> ERR184093 2 0.1411 0.6257 0.000 0.964 0.036
#> ERR184051 3 0.4750 0.7028 0.000 0.216 0.784
#> ERR184076 2 0.7283 0.4782 0.068 0.672 0.260
#> ERR184043 3 0.6511 0.6849 0.072 0.180 0.748
#> ERR184037 2 0.5956 0.5208 0.016 0.720 0.264
#> ERR184059 3 0.6742 0.6730 0.052 0.240 0.708
#> ERR184055 2 0.5318 0.5576 0.016 0.780 0.204
#> ERR184065 2 0.5905 0.1790 0.000 0.648 0.352
#> ERR184069 2 0.4504 0.5044 0.000 0.804 0.196
#> ERR184040 2 0.6703 0.4963 0.040 0.692 0.268
#> ERR184057 2 0.3340 0.5916 0.000 0.880 0.120
#> ERR184082 3 0.6111 0.5789 0.000 0.396 0.604
#> ERR184083 2 0.4399 0.5302 0.000 0.812 0.188
#> ERR184039 2 0.5678 0.3081 0.000 0.684 0.316
#> ERR184064 3 0.5905 0.6959 0.044 0.184 0.772
#> ERR184081 2 0.3412 0.5928 0.000 0.876 0.124
#> ERR184095 2 0.4796 0.4505 0.000 0.780 0.220
#> ERR184079 2 0.6307 -0.2995 0.000 0.512 0.488
#> ERR184084 3 0.6319 0.5939 0.040 0.228 0.732
#> ERR184068 2 0.2448 0.6224 0.000 0.924 0.076
#> ERR184067 2 0.5016 0.4011 0.000 0.760 0.240
#> ERR184071 2 0.5968 0.0499 0.000 0.636 0.364
#> ERR184042 1 0.0592 0.0000 0.988 0.000 0.012
#> ERR184063 3 0.5850 0.6988 0.040 0.188 0.772
#> ERR184091 2 0.5621 0.3188 0.000 0.692 0.308
#> ERR184061 2 0.2261 0.6250 0.000 0.932 0.068
#> ERR184077 3 0.6309 0.4063 0.000 0.496 0.504
#> ERR184062 2 0.4702 0.5245 0.000 0.788 0.212
#> ERR184053 3 0.6244 0.4312 0.000 0.440 0.560
#> ERR184088 2 0.2400 0.6187 0.004 0.932 0.064
#> ERR184075 3 0.6299 0.4561 0.000 0.476 0.524
#> ERR184041 3 0.5728 0.7012 0.032 0.196 0.772
#> ERR184060 2 0.3879 0.5664 0.000 0.848 0.152
#> ERR184035 2 0.7156 0.3296 0.028 0.572 0.400
#> ERR184086 2 0.5465 0.3712 0.000 0.712 0.288
#> ERR184080 2 0.5817 0.5350 0.020 0.744 0.236
#> ERR184050 3 0.6280 0.4996 0.000 0.460 0.540
#> ERR184047 2 0.9299 0.2648 0.196 0.512 0.292
#> ERR184092 2 0.3116 0.5944 0.000 0.892 0.108
#> ERR184072 2 0.5578 0.5459 0.012 0.748 0.240
#> ERR184073 2 0.6647 0.2417 0.008 0.540 0.452
#> ERR184066 2 0.3644 0.6000 0.004 0.872 0.124
#> ERR184098 2 0.5650 0.3357 0.000 0.688 0.312
#> ERR184044 2 0.3425 0.6109 0.004 0.884 0.112
#> ERR184054 2 0.5623 0.5264 0.004 0.716 0.280
#> ERR184085 3 0.5497 0.5850 0.000 0.292 0.708
#> ERR184056 2 0.1031 0.6288 0.000 0.976 0.024
#> ERR184052 2 0.3412 0.5988 0.000 0.876 0.124
#> ERR184070 2 0.2537 0.6143 0.000 0.920 0.080
#> ERR184096 2 0.8734 0.3700 0.168 0.584 0.248
#> ERR184089 3 0.6045 0.6137 0.000 0.380 0.620
#> ERR184049 2 0.4504 0.5760 0.000 0.804 0.196
#> ERR184038 3 0.6225 0.4137 0.000 0.432 0.568
#> ERR184087 3 0.6059 0.6975 0.048 0.188 0.764
#> ERR184097 2 0.0892 0.6281 0.000 0.980 0.020
#> ERR184094 3 0.7295 0.1412 0.028 0.484 0.488
#> ERR184058 2 0.6267 -0.3678 0.000 0.548 0.452
#> ERR184036 2 0.3816 0.5793 0.000 0.852 0.148
#> ERR184046 2 0.4399 0.5312 0.000 0.812 0.188
#> ERR184074 2 0.5956 0.5180 0.016 0.720 0.264
#> ERR184048 2 0.1411 0.6284 0.000 0.964 0.036
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.4372 0.6409 0.728 0.268 0.004 0.000
#> ERR184093 2 0.1151 0.7006 0.024 0.968 0.008 0.000
#> ERR184051 3 0.1624 0.6941 0.020 0.028 0.952 0.000
#> ERR184076 1 0.4632 0.6576 0.688 0.308 0.004 0.000
#> ERR184043 3 0.1443 0.6948 0.008 0.004 0.960 0.028
#> ERR184037 1 0.5295 0.3554 0.504 0.488 0.008 0.000
#> ERR184059 3 0.7590 0.4413 0.140 0.124 0.636 0.100
#> ERR184055 2 0.5232 0.2307 0.340 0.644 0.012 0.004
#> ERR184065 2 0.6166 0.4320 0.024 0.572 0.384 0.020
#> ERR184069 2 0.2466 0.7088 0.028 0.916 0.056 0.000
#> ERR184040 1 0.3547 0.5039 0.840 0.144 0.016 0.000
#> ERR184057 2 0.0927 0.7043 0.016 0.976 0.008 0.000
#> ERR184082 2 0.6664 0.4151 0.112 0.580 0.308 0.000
#> ERR184083 2 0.2782 0.7151 0.024 0.904 0.068 0.004
#> ERR184039 2 0.6134 0.4843 0.032 0.620 0.328 0.020
#> ERR184064 3 0.1114 0.6984 0.008 0.004 0.972 0.016
#> ERR184081 2 0.0707 0.7099 0.000 0.980 0.020 0.000
#> ERR184095 2 0.2660 0.7122 0.036 0.908 0.056 0.000
#> ERR184079 2 0.6159 0.5846 0.172 0.676 0.152 0.000
#> ERR184084 3 0.8577 0.2631 0.184 0.316 0.448 0.052
#> ERR184068 2 0.2706 0.6950 0.080 0.900 0.020 0.000
#> ERR184067 2 0.2408 0.7108 0.036 0.920 0.044 0.000
#> ERR184071 2 0.4144 0.6929 0.068 0.828 0.104 0.000
#> ERR184042 4 0.0817 0.0000 0.000 0.000 0.024 0.976
#> ERR184063 3 0.1394 0.7000 0.012 0.008 0.964 0.016
#> ERR184091 2 0.6206 0.4481 0.028 0.584 0.368 0.020
#> ERR184061 2 0.3344 0.6760 0.108 0.868 0.020 0.004
#> ERR184077 2 0.5574 0.6219 0.124 0.728 0.148 0.000
#> ERR184062 2 0.3617 0.7067 0.064 0.860 0.076 0.000
#> ERR184053 2 0.6439 0.5611 0.180 0.648 0.172 0.000
#> ERR184088 2 0.3462 0.6661 0.116 0.860 0.020 0.004
#> ERR184075 2 0.6200 0.3399 0.020 0.508 0.452 0.020
#> ERR184041 3 0.1007 0.7016 0.008 0.008 0.976 0.008
#> ERR184060 2 0.1488 0.7145 0.012 0.956 0.032 0.000
#> ERR184035 1 0.6585 0.4032 0.520 0.412 0.060 0.008
#> ERR184086 2 0.6170 0.4895 0.032 0.612 0.336 0.020
#> ERR184080 2 0.5296 -0.4302 0.492 0.500 0.008 0.000
#> ERR184050 2 0.6205 0.2829 0.024 0.488 0.472 0.016
#> ERR184047 1 0.4652 0.2399 0.820 0.076 0.020 0.084
#> ERR184092 2 0.1510 0.7129 0.016 0.956 0.028 0.000
#> ERR184072 2 0.5070 0.1535 0.372 0.620 0.008 0.000
#> ERR184073 2 0.8066 0.0826 0.256 0.472 0.256 0.016
#> ERR184066 2 0.3647 0.6353 0.152 0.832 0.016 0.000
#> ERR184098 2 0.5788 0.5354 0.024 0.660 0.296 0.020
#> ERR184044 2 0.4093 0.6734 0.120 0.836 0.032 0.012
#> ERR184054 2 0.5558 0.0860 0.364 0.608 0.028 0.000
#> ERR184085 2 0.7045 0.3098 0.140 0.532 0.328 0.000
#> ERR184056 2 0.1635 0.6952 0.044 0.948 0.008 0.000
#> ERR184052 2 0.3785 0.6986 0.084 0.856 0.056 0.004
#> ERR184070 2 0.0707 0.7001 0.020 0.980 0.000 0.000
#> ERR184096 1 0.5387 0.4324 0.764 0.144 0.016 0.076
#> ERR184089 3 0.5248 0.4353 0.012 0.248 0.716 0.024
#> ERR184049 2 0.2830 0.7090 0.060 0.900 0.040 0.000
#> ERR184038 2 0.6167 0.5584 0.124 0.668 0.208 0.000
#> ERR184087 3 0.1543 0.6929 0.008 0.004 0.956 0.032
#> ERR184097 2 0.1722 0.6954 0.048 0.944 0.008 0.000
#> ERR184094 3 0.8477 0.3519 0.196 0.228 0.512 0.064
#> ERR184058 2 0.5023 0.6687 0.056 0.772 0.164 0.008
#> ERR184036 2 0.1936 0.7120 0.032 0.940 0.028 0.000
#> ERR184046 2 0.2715 0.7076 0.004 0.892 0.100 0.004
#> ERR184074 1 0.5388 0.4397 0.532 0.456 0.012 0.000
#> ERR184048 2 0.2198 0.6888 0.072 0.920 0.008 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.3688 0.6512 0.816 0.124 0.000 0.000 0.060
#> ERR184093 2 0.1399 0.7633 0.028 0.952 0.000 0.000 0.020
#> ERR184051 3 0.4270 0.6274 0.000 0.048 0.748 0.000 0.204
#> ERR184076 1 0.4350 0.6721 0.764 0.152 0.000 0.000 0.084
#> ERR184043 3 0.0000 0.7970 0.000 0.000 1.000 0.000 0.000
#> ERR184037 1 0.5199 0.6187 0.636 0.292 0.000 0.000 0.072
#> ERR184059 3 0.5751 0.5747 0.024 0.012 0.692 0.092 0.180
#> ERR184055 2 0.5849 0.0968 0.392 0.508 0.000 0.000 0.100
#> ERR184065 5 0.5348 0.6294 0.012 0.140 0.148 0.000 0.700
#> ERR184069 2 0.1644 0.7500 0.008 0.940 0.004 0.000 0.048
#> ERR184040 1 0.3231 0.5576 0.864 0.076 0.004 0.004 0.052
#> ERR184057 2 0.1106 0.7616 0.024 0.964 0.000 0.000 0.012
#> ERR184082 5 0.6591 0.3386 0.068 0.356 0.060 0.000 0.516
#> ERR184083 2 0.1892 0.7528 0.000 0.916 0.004 0.000 0.080
#> ERR184039 5 0.5604 0.6446 0.020 0.184 0.116 0.000 0.680
#> ERR184064 3 0.0162 0.7992 0.000 0.000 0.996 0.000 0.004
#> ERR184081 2 0.1124 0.7582 0.004 0.960 0.000 0.000 0.036
#> ERR184095 2 0.2032 0.7552 0.020 0.924 0.004 0.000 0.052
#> ERR184079 2 0.4592 0.6804 0.140 0.756 0.004 0.000 0.100
#> ERR184084 5 0.9121 0.2848 0.116 0.248 0.172 0.080 0.384
#> ERR184068 2 0.3346 0.7488 0.092 0.844 0.000 0.000 0.064
#> ERR184067 2 0.1731 0.7492 0.004 0.932 0.004 0.000 0.060
#> ERR184071 2 0.4007 0.6342 0.020 0.756 0.004 0.000 0.220
#> ERR184042 4 0.0000 0.0000 0.000 0.000 0.000 1.000 0.000
#> ERR184063 3 0.0794 0.7933 0.000 0.000 0.972 0.000 0.028
#> ERR184091 5 0.5481 0.6389 0.016 0.156 0.136 0.000 0.692
#> ERR184061 2 0.5399 0.6232 0.148 0.664 0.000 0.000 0.188
#> ERR184077 2 0.4612 0.6893 0.124 0.756 0.004 0.000 0.116
#> ERR184062 2 0.3741 0.7374 0.076 0.816 0.000 0.000 0.108
#> ERR184053 2 0.4829 0.6673 0.164 0.732 0.004 0.000 0.100
#> ERR184088 2 0.4835 0.6361 0.156 0.724 0.000 0.000 0.120
#> ERR184075 5 0.5698 0.5990 0.012 0.128 0.204 0.000 0.656
#> ERR184041 3 0.0609 0.7970 0.000 0.000 0.980 0.000 0.020
#> ERR184060 2 0.2047 0.7600 0.020 0.928 0.012 0.000 0.040
#> ERR184035 1 0.5940 0.5333 0.568 0.292 0.000 0.000 0.140
#> ERR184086 5 0.6061 0.6259 0.016 0.268 0.116 0.000 0.600
#> ERR184080 1 0.5409 0.5953 0.612 0.304 0.000 0.000 0.084
#> ERR184050 5 0.5978 0.6066 0.024 0.148 0.180 0.000 0.648
#> ERR184047 1 0.5980 0.0860 0.668 0.000 0.068 0.188 0.076
#> ERR184092 2 0.1399 0.7649 0.028 0.952 0.000 0.000 0.020
#> ERR184072 2 0.5650 -0.0916 0.456 0.468 0.000 0.000 0.076
#> ERR184073 5 0.9236 0.2849 0.188 0.264 0.160 0.056 0.332
#> ERR184066 2 0.5060 0.5914 0.224 0.684 0.000 0.000 0.092
#> ERR184098 5 0.5842 0.6393 0.024 0.204 0.116 0.000 0.656
#> ERR184044 2 0.5400 0.5666 0.096 0.632 0.000 0.000 0.272
#> ERR184054 2 0.5836 -0.1348 0.448 0.468 0.004 0.000 0.080
#> ERR184085 5 0.6782 0.3598 0.100 0.332 0.052 0.000 0.516
#> ERR184056 2 0.2153 0.7639 0.040 0.916 0.000 0.000 0.044
#> ERR184052 2 0.5988 0.3859 0.080 0.552 0.016 0.000 0.352
#> ERR184070 2 0.1310 0.7623 0.024 0.956 0.000 0.000 0.020
#> ERR184096 1 0.6056 0.3917 0.712 0.052 0.044 0.124 0.068
#> ERR184089 5 0.6011 0.4258 0.016 0.092 0.316 0.000 0.576
#> ERR184049 2 0.4735 0.6621 0.072 0.728 0.004 0.000 0.196
#> ERR184038 2 0.6109 0.1666 0.104 0.516 0.008 0.000 0.372
#> ERR184087 3 0.0162 0.7992 0.000 0.000 0.996 0.000 0.004
#> ERR184097 2 0.2438 0.7548 0.040 0.900 0.000 0.000 0.060
#> ERR184094 3 0.8255 0.1493 0.080 0.072 0.388 0.080 0.380
#> ERR184058 2 0.5361 0.2283 0.024 0.580 0.024 0.000 0.372
#> ERR184036 2 0.2209 0.7644 0.032 0.912 0.000 0.000 0.056
#> ERR184046 2 0.2102 0.7561 0.012 0.916 0.004 0.000 0.068
#> ERR184074 1 0.4960 0.6619 0.668 0.268 0.000 0.000 0.064
#> ERR184048 2 0.1942 0.7617 0.068 0.920 0.000 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.2086 0.7016 0.912 0.008 0.004 0.000 0.064 0.012
#> ERR184093 2 0.0363 0.8234 0.000 0.988 0.000 0.000 0.000 0.012
#> ERR184051 3 0.3827 0.7026 0.000 0.008 0.776 0.000 0.052 0.164
#> ERR184076 1 0.2094 0.7186 0.908 0.024 0.000 0.000 0.064 0.004
#> ERR184043 3 0.0790 0.8226 0.000 0.000 0.968 0.000 0.000 0.032
#> ERR184037 1 0.2002 0.7291 0.920 0.052 0.004 0.000 0.012 0.012
#> ERR184059 3 0.3652 0.7053 0.004 0.004 0.796 0.000 0.148 0.048
#> ERR184055 1 0.5087 0.2186 0.592 0.332 0.000 0.000 0.060 0.016
#> ERR184065 6 0.1732 0.8891 0.004 0.072 0.004 0.000 0.000 0.920
#> ERR184069 2 0.0508 0.8232 0.004 0.984 0.000 0.000 0.000 0.012
#> ERR184040 1 0.2431 0.6636 0.872 0.004 0.004 0.000 0.116 0.004
#> ERR184057 2 0.0146 0.8225 0.000 0.996 0.000 0.000 0.000 0.004
#> ERR184082 5 0.7588 0.4111 0.092 0.220 0.028 0.000 0.420 0.240
#> ERR184083 2 0.1644 0.8176 0.004 0.932 0.000 0.000 0.012 0.052
#> ERR184039 6 0.2162 0.8859 0.004 0.088 0.000 0.000 0.012 0.896
#> ERR184064 3 0.0713 0.8226 0.000 0.000 0.972 0.000 0.000 0.028
#> ERR184081 2 0.0508 0.8230 0.004 0.984 0.000 0.000 0.000 0.012
#> ERR184095 2 0.0862 0.8234 0.004 0.972 0.000 0.000 0.008 0.016
#> ERR184079 2 0.4703 0.6537 0.112 0.720 0.000 0.000 0.148 0.020
#> ERR184084 5 0.7296 0.3472 0.072 0.072 0.188 0.032 0.568 0.068
#> ERR184068 2 0.2736 0.8035 0.048 0.880 0.000 0.000 0.052 0.020
#> ERR184067 2 0.0984 0.8250 0.008 0.968 0.000 0.000 0.012 0.012
#> ERR184071 2 0.3621 0.7511 0.024 0.808 0.000 0.000 0.036 0.132
#> ERR184042 4 0.0000 0.0000 0.000 0.000 0.000 1.000 0.000 0.000
#> ERR184063 3 0.1531 0.8136 0.000 0.000 0.928 0.000 0.004 0.068
#> ERR184091 6 0.2144 0.8868 0.004 0.092 0.004 0.000 0.004 0.896
#> ERR184061 2 0.5897 0.5690 0.124 0.632 0.000 0.000 0.148 0.096
#> ERR184077 2 0.3717 0.7493 0.084 0.808 0.000 0.000 0.092 0.016
#> ERR184062 2 0.3361 0.7827 0.068 0.848 0.004 0.000 0.040 0.040
#> ERR184053 2 0.4813 0.6437 0.116 0.708 0.000 0.000 0.156 0.020
#> ERR184088 2 0.4041 0.7335 0.076 0.788 0.000 0.000 0.108 0.028
#> ERR184075 6 0.1867 0.8613 0.000 0.036 0.036 0.000 0.004 0.924
#> ERR184041 3 0.1615 0.8157 0.000 0.004 0.928 0.000 0.004 0.064
#> ERR184060 2 0.0547 0.8230 0.000 0.980 0.000 0.000 0.000 0.020
#> ERR184035 1 0.3737 0.6257 0.772 0.036 0.000 0.000 0.184 0.008
#> ERR184086 6 0.3499 0.7318 0.008 0.196 0.004 0.000 0.012 0.780
#> ERR184080 1 0.1644 0.7292 0.932 0.052 0.000 0.000 0.004 0.012
#> ERR184050 6 0.2195 0.8612 0.008 0.052 0.020 0.000 0.008 0.912
#> ERR184047 5 0.6675 -0.2164 0.372 0.000 0.032 0.132 0.440 0.024
#> ERR184092 2 0.0146 0.8225 0.000 0.996 0.000 0.000 0.000 0.004
#> ERR184072 1 0.4239 0.5430 0.732 0.204 0.000 0.000 0.052 0.012
#> ERR184073 5 0.7999 0.4233 0.132 0.148 0.156 0.024 0.488 0.052
#> ERR184066 2 0.5623 0.3408 0.340 0.536 0.000 0.000 0.108 0.016
#> ERR184098 6 0.2425 0.8729 0.012 0.100 0.000 0.000 0.008 0.880
#> ERR184044 2 0.6059 0.4896 0.048 0.580 0.000 0.000 0.168 0.204
#> ERR184054 1 0.3725 0.6308 0.788 0.156 0.004 0.000 0.048 0.004
#> ERR184085 5 0.7459 0.4486 0.128 0.168 0.024 0.000 0.468 0.212
#> ERR184056 2 0.0551 0.8243 0.008 0.984 0.000 0.000 0.004 0.004
#> ERR184052 2 0.6182 0.2866 0.040 0.492 0.000 0.000 0.128 0.340
#> ERR184070 2 0.0547 0.8230 0.000 0.980 0.000 0.000 0.000 0.020
#> ERR184096 1 0.6655 0.1136 0.460 0.012 0.024 0.104 0.376 0.024
#> ERR184089 6 0.2868 0.7713 0.000 0.028 0.132 0.000 0.000 0.840
#> ERR184049 2 0.5028 0.6467 0.048 0.708 0.000 0.000 0.140 0.104
#> ERR184038 2 0.7236 -0.1521 0.124 0.408 0.004 0.000 0.312 0.152
#> ERR184087 3 0.0713 0.8226 0.000 0.000 0.972 0.000 0.000 0.028
#> ERR184097 2 0.1059 0.8228 0.004 0.964 0.000 0.000 0.016 0.016
#> ERR184094 3 0.6573 0.0622 0.004 0.032 0.436 0.012 0.388 0.128
#> ERR184058 2 0.3852 0.7023 0.020 0.764 0.000 0.000 0.024 0.192
#> ERR184036 2 0.0665 0.8245 0.008 0.980 0.000 0.000 0.008 0.004
#> ERR184046 2 0.1588 0.8072 0.000 0.924 0.000 0.000 0.004 0.072
#> ERR184074 1 0.1657 0.7297 0.936 0.040 0.000 0.000 0.012 0.012
#> ERR184048 2 0.1599 0.8174 0.028 0.940 0.000 0.000 0.024 0.008
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 10269 rows and 62 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 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 0.662 0.863 0.931 0.4772 0.511 0.511
#> 3 3 0.529 0.727 0.868 0.1550 0.867 0.763
#> 4 4 0.465 0.651 0.821 0.2158 0.723 0.481
#> 5 5 0.547 0.457 0.761 0.0943 0.948 0.843
#> 6 6 0.566 0.478 0.697 0.0497 0.867 0.595
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
#> ERR184078 2 0.0376 0.935 0.004 0.996
#> ERR184093 2 0.2236 0.932 0.036 0.964
#> ERR184051 1 0.0376 0.905 0.996 0.004
#> ERR184076 2 0.0376 0.935 0.004 0.996
#> ERR184043 1 0.0376 0.905 0.996 0.004
#> ERR184037 2 0.0000 0.937 0.000 1.000
#> ERR184059 1 0.0938 0.906 0.988 0.012
#> ERR184055 2 0.0000 0.937 0.000 1.000
#> ERR184065 1 0.0672 0.906 0.992 0.008
#> ERR184069 2 0.4161 0.900 0.084 0.916
#> ERR184040 2 0.0376 0.938 0.004 0.996
#> ERR184057 2 0.1633 0.937 0.024 0.976
#> ERR184082 1 0.7602 0.753 0.780 0.220
#> ERR184083 2 0.9552 0.384 0.376 0.624
#> ERR184039 1 0.1414 0.904 0.980 0.020
#> ERR184064 1 0.0376 0.905 0.996 0.004
#> ERR184081 2 0.4815 0.884 0.104 0.896
#> ERR184095 2 0.1633 0.937 0.024 0.976
#> ERR184079 2 0.0000 0.937 0.000 1.000
#> ERR184084 1 0.7745 0.744 0.772 0.228
#> ERR184068 2 0.1414 0.938 0.020 0.980
#> ERR184067 2 0.5059 0.876 0.112 0.888
#> ERR184071 1 0.6623 0.810 0.828 0.172
#> ERR184042 1 0.4562 0.852 0.904 0.096
#> ERR184063 1 0.0376 0.905 0.996 0.004
#> ERR184091 1 0.0938 0.906 0.988 0.012
#> ERR184061 2 0.3274 0.920 0.060 0.940
#> ERR184077 2 0.0938 0.939 0.012 0.988
#> ERR184062 2 0.4939 0.857 0.108 0.892
#> ERR184053 2 0.0376 0.938 0.004 0.996
#> ERR184088 2 0.1414 0.938 0.020 0.980
#> ERR184075 1 0.0376 0.905 0.996 0.004
#> ERR184041 1 0.0376 0.905 0.996 0.004
#> ERR184060 2 0.2778 0.926 0.048 0.952
#> ERR184035 2 0.0938 0.939 0.012 0.988
#> ERR184086 1 0.0672 0.906 0.992 0.008
#> ERR184080 2 0.0000 0.937 0.000 1.000
#> ERR184050 1 0.0672 0.906 0.992 0.008
#> ERR184047 2 0.3733 0.899 0.072 0.928
#> ERR184092 2 0.2423 0.930 0.040 0.960
#> ERR184072 2 0.0376 0.935 0.004 0.996
#> ERR184073 2 0.9850 0.196 0.428 0.572
#> ERR184066 2 0.0000 0.937 0.000 1.000
#> ERR184098 1 0.1184 0.905 0.984 0.016
#> ERR184044 2 0.8386 0.647 0.268 0.732
#> ERR184054 2 0.0376 0.935 0.004 0.996
#> ERR184085 1 0.9323 0.523 0.652 0.348
#> ERR184056 2 0.0376 0.938 0.004 0.996
#> ERR184052 1 0.8144 0.700 0.748 0.252
#> ERR184070 2 0.0938 0.939 0.012 0.988
#> ERR184096 2 0.0376 0.935 0.004 0.996
#> ERR184089 1 0.0376 0.905 0.996 0.004
#> ERR184049 2 0.5059 0.875 0.112 0.888
#> ERR184038 1 0.9881 0.286 0.564 0.436
#> ERR184087 1 0.0376 0.905 0.996 0.004
#> ERR184097 2 0.1184 0.939 0.016 0.984
#> ERR184094 1 0.1843 0.901 0.972 0.028
#> ERR184058 1 0.5408 0.847 0.876 0.124
#> ERR184036 2 0.2603 0.930 0.044 0.956
#> ERR184046 1 0.6623 0.808 0.828 0.172
#> ERR184074 2 0.0376 0.935 0.004 0.996
#> ERR184048 2 0.0938 0.939 0.012 0.988
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.0892 0.8640 0.980 0.000 0.020
#> ERR184093 1 0.1170 0.8681 0.976 0.008 0.016
#> ERR184051 2 0.1964 0.7646 0.000 0.944 0.056
#> ERR184076 1 0.1399 0.8574 0.968 0.004 0.028
#> ERR184043 2 0.2537 0.7420 0.000 0.920 0.080
#> ERR184037 1 0.1289 0.8664 0.968 0.000 0.032
#> ERR184059 2 0.1411 0.7789 0.000 0.964 0.036
#> ERR184055 1 0.1529 0.8664 0.960 0.000 0.040
#> ERR184065 2 0.1289 0.7864 0.000 0.968 0.032
#> ERR184069 2 0.9142 0.3141 0.324 0.512 0.164
#> ERR184040 1 0.0424 0.8629 0.992 0.000 0.008
#> ERR184057 1 0.3780 0.8521 0.892 0.044 0.064
#> ERR184082 2 0.3846 0.7567 0.016 0.876 0.108
#> ERR184083 2 0.5637 0.6985 0.040 0.788 0.172
#> ERR184039 2 0.0424 0.7880 0.000 0.992 0.008
#> ERR184064 2 0.1860 0.7677 0.000 0.948 0.052
#> ERR184081 2 0.9070 0.3460 0.308 0.528 0.164
#> ERR184095 1 0.6324 0.7746 0.764 0.076 0.160
#> ERR184079 1 0.4139 0.8402 0.860 0.016 0.124
#> ERR184084 2 0.5060 0.7317 0.064 0.836 0.100
#> ERR184068 1 0.7739 0.6916 0.676 0.136 0.188
#> ERR184067 2 0.9317 0.0833 0.388 0.448 0.164
#> ERR184071 2 0.5473 0.7132 0.052 0.808 0.140
#> ERR184042 3 0.4504 0.0000 0.000 0.196 0.804
#> ERR184063 2 0.1860 0.7677 0.000 0.948 0.052
#> ERR184091 2 0.0892 0.7868 0.000 0.980 0.020
#> ERR184061 1 0.3112 0.8570 0.916 0.056 0.028
#> ERR184077 1 0.5159 0.8147 0.820 0.040 0.140
#> ERR184062 1 0.2947 0.8431 0.920 0.020 0.060
#> ERR184053 1 0.5850 0.7862 0.772 0.040 0.188
#> ERR184088 1 0.1832 0.8661 0.956 0.008 0.036
#> ERR184075 2 0.0237 0.7878 0.000 0.996 0.004
#> ERR184041 2 0.1643 0.7736 0.000 0.956 0.044
#> ERR184060 1 0.7797 0.4473 0.608 0.320 0.072
#> ERR184035 1 0.3722 0.8495 0.888 0.024 0.088
#> ERR184086 2 0.0892 0.7839 0.000 0.980 0.020
#> ERR184080 1 0.0237 0.8642 0.996 0.000 0.004
#> ERR184050 2 0.0592 0.7862 0.000 0.988 0.012
#> ERR184047 1 0.1950 0.8536 0.952 0.008 0.040
#> ERR184092 1 0.6363 0.7798 0.768 0.096 0.136
#> ERR184072 1 0.1753 0.8533 0.952 0.000 0.048
#> ERR184073 1 0.6126 0.6417 0.712 0.268 0.020
#> ERR184066 1 0.1529 0.8541 0.960 0.000 0.040
#> ERR184098 2 0.0237 0.7871 0.000 0.996 0.004
#> ERR184044 1 0.5378 0.6602 0.756 0.236 0.008
#> ERR184054 1 0.1163 0.8579 0.972 0.000 0.028
#> ERR184085 2 0.5020 0.7358 0.056 0.836 0.108
#> ERR184056 1 0.0747 0.8668 0.984 0.000 0.016
#> ERR184052 2 0.5815 0.6979 0.096 0.800 0.104
#> ERR184070 1 0.3009 0.8624 0.920 0.028 0.052
#> ERR184096 1 0.1289 0.8566 0.968 0.000 0.032
#> ERR184089 2 0.1411 0.7789 0.000 0.964 0.036
#> ERR184049 1 0.9226 0.0329 0.436 0.412 0.152
#> ERR184038 2 0.7549 0.0383 0.436 0.524 0.040
#> ERR184087 2 0.1753 0.7709 0.000 0.952 0.048
#> ERR184097 1 0.0237 0.8640 0.996 0.000 0.004
#> ERR184094 2 0.1031 0.7836 0.000 0.976 0.024
#> ERR184058 2 0.4514 0.7317 0.012 0.832 0.156
#> ERR184036 1 0.7447 0.7089 0.700 0.160 0.140
#> ERR184046 2 0.4326 0.7402 0.012 0.844 0.144
#> ERR184074 1 0.0592 0.8618 0.988 0.000 0.012
#> ERR184048 1 0.2796 0.8564 0.908 0.000 0.092
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.2530 0.8361 0.896 0.100 0.000 0.004
#> ERR184093 1 0.2665 0.8382 0.900 0.088 0.008 0.004
#> ERR184051 3 0.0817 0.8643 0.000 0.000 0.976 0.024
#> ERR184076 1 0.2342 0.8446 0.912 0.080 0.000 0.008
#> ERR184043 3 0.0921 0.8621 0.000 0.000 0.972 0.028
#> ERR184037 1 0.4228 0.7192 0.760 0.232 0.000 0.008
#> ERR184059 3 0.0592 0.8688 0.000 0.000 0.984 0.016
#> ERR184055 1 0.4295 0.6988 0.752 0.240 0.000 0.008
#> ERR184065 3 0.1211 0.8500 0.000 0.040 0.960 0.000
#> ERR184069 2 0.4001 0.6652 0.048 0.840 0.108 0.004
#> ERR184040 1 0.1022 0.8508 0.968 0.032 0.000 0.000
#> ERR184057 2 0.5369 0.5370 0.296 0.676 0.016 0.012
#> ERR184082 2 0.5406 0.1842 0.000 0.508 0.480 0.012
#> ERR184083 2 0.4214 0.6095 0.000 0.780 0.204 0.016
#> ERR184039 3 0.0779 0.8647 0.000 0.016 0.980 0.004
#> ERR184064 3 0.0707 0.8665 0.000 0.000 0.980 0.020
#> ERR184081 2 0.5566 0.6700 0.080 0.744 0.164 0.012
#> ERR184095 2 0.1486 0.6264 0.024 0.960 0.008 0.008
#> ERR184079 2 0.4533 0.5815 0.232 0.752 0.004 0.012
#> ERR184084 2 0.5466 0.3012 0.000 0.548 0.436 0.016
#> ERR184068 2 0.4883 0.5855 0.128 0.800 0.048 0.024
#> ERR184067 2 0.4805 0.6712 0.068 0.796 0.128 0.008
#> ERR184071 3 0.5345 0.0495 0.000 0.428 0.560 0.012
#> ERR184042 4 0.1305 0.0000 0.004 0.000 0.036 0.960
#> ERR184063 3 0.0592 0.8688 0.000 0.000 0.984 0.016
#> ERR184091 3 0.1022 0.8563 0.000 0.032 0.968 0.000
#> ERR184061 1 0.4590 0.7759 0.804 0.144 0.040 0.012
#> ERR184077 2 0.2040 0.6259 0.048 0.936 0.004 0.012
#> ERR184062 1 0.1509 0.8408 0.960 0.008 0.020 0.012
#> ERR184053 2 0.3981 0.5999 0.100 0.848 0.012 0.040
#> ERR184088 1 0.5099 0.2531 0.612 0.380 0.000 0.008
#> ERR184075 3 0.0524 0.8678 0.000 0.008 0.988 0.004
#> ERR184041 3 0.0336 0.8702 0.000 0.000 0.992 0.008
#> ERR184060 2 0.7350 0.5000 0.336 0.508 0.152 0.004
#> ERR184035 2 0.4834 0.5886 0.252 0.728 0.012 0.008
#> ERR184086 3 0.0000 0.8700 0.000 0.000 1.000 0.000
#> ERR184080 1 0.2281 0.8404 0.904 0.096 0.000 0.000
#> ERR184050 3 0.0188 0.8704 0.000 0.000 0.996 0.004
#> ERR184047 1 0.1022 0.8514 0.968 0.032 0.000 0.000
#> ERR184092 2 0.5853 0.4821 0.332 0.628 0.028 0.012
#> ERR184072 1 0.3392 0.7922 0.856 0.124 0.000 0.020
#> ERR184073 1 0.6300 0.4417 0.636 0.072 0.284 0.008
#> ERR184066 1 0.1042 0.8514 0.972 0.020 0.000 0.008
#> ERR184098 3 0.0336 0.8686 0.000 0.008 0.992 0.000
#> ERR184044 1 0.4800 0.6752 0.760 0.044 0.196 0.000
#> ERR184054 1 0.0817 0.8510 0.976 0.024 0.000 0.000
#> ERR184085 2 0.5330 0.2207 0.004 0.516 0.476 0.004
#> ERR184056 1 0.3908 0.7408 0.784 0.212 0.000 0.004
#> ERR184052 3 0.5474 0.4263 0.024 0.280 0.684 0.012
#> ERR184070 2 0.5408 0.0621 0.488 0.500 0.000 0.012
#> ERR184096 1 0.0779 0.8501 0.980 0.016 0.000 0.004
#> ERR184089 3 0.0336 0.8702 0.000 0.000 0.992 0.008
#> ERR184049 2 0.5813 0.6598 0.088 0.716 0.188 0.008
#> ERR184038 3 0.6829 0.2801 0.332 0.084 0.572 0.012
#> ERR184087 3 0.0592 0.8688 0.000 0.000 0.984 0.016
#> ERR184097 1 0.2197 0.8484 0.916 0.080 0.000 0.004
#> ERR184094 3 0.1339 0.8519 0.024 0.004 0.964 0.008
#> ERR184058 2 0.5257 0.3099 0.000 0.548 0.444 0.008
#> ERR184036 2 0.7491 0.3728 0.352 0.500 0.136 0.012
#> ERR184046 3 0.5444 0.0423 0.000 0.424 0.560 0.016
#> ERR184074 1 0.1545 0.8472 0.952 0.040 0.000 0.008
#> ERR184048 2 0.4212 0.6145 0.216 0.772 0.000 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.4328 0.6480 0.756 0.032 0.000 0.012 0.200
#> ERR184093 1 0.5177 0.6317 0.672 0.052 0.008 0.004 0.264
#> ERR184051 3 0.0290 0.8878 0.000 0.000 0.992 0.008 0.000
#> ERR184076 1 0.3048 0.6779 0.820 0.000 0.000 0.004 0.176
#> ERR184043 3 0.0290 0.8878 0.000 0.000 0.992 0.008 0.000
#> ERR184037 1 0.5998 0.1852 0.464 0.424 0.000 0.000 0.112
#> ERR184059 3 0.0290 0.8879 0.000 0.000 0.992 0.008 0.000
#> ERR184055 1 0.6409 0.2504 0.444 0.404 0.000 0.004 0.148
#> ERR184065 3 0.1205 0.8626 0.000 0.040 0.956 0.000 0.004
#> ERR184069 2 0.1461 0.3378 0.004 0.952 0.016 0.000 0.028
#> ERR184040 1 0.1981 0.7152 0.920 0.016 0.000 0.000 0.064
#> ERR184057 2 0.5546 0.2352 0.208 0.656 0.004 0.000 0.132
#> ERR184082 2 0.6615 -0.1338 0.008 0.508 0.276 0.000 0.208
#> ERR184083 2 0.5258 -0.1734 0.004 0.636 0.064 0.000 0.296
#> ERR184039 3 0.0671 0.8827 0.000 0.016 0.980 0.000 0.004
#> ERR184064 3 0.0162 0.8888 0.000 0.000 0.996 0.004 0.000
#> ERR184081 2 0.2795 0.3706 0.024 0.892 0.060 0.000 0.024
#> ERR184095 2 0.3093 0.1795 0.008 0.824 0.000 0.000 0.168
#> ERR184079 2 0.5210 0.2571 0.132 0.684 0.000 0.000 0.184
#> ERR184084 2 0.6731 -0.1777 0.008 0.488 0.248 0.000 0.256
#> ERR184068 5 0.5903 0.0000 0.040 0.408 0.020 0.008 0.524
#> ERR184067 2 0.3138 0.3583 0.032 0.876 0.032 0.000 0.060
#> ERR184071 3 0.6271 -0.1267 0.004 0.384 0.480 0.000 0.132
#> ERR184042 4 0.0579 0.0000 0.008 0.000 0.008 0.984 0.000
#> ERR184063 3 0.0290 0.8878 0.000 0.000 0.992 0.008 0.000
#> ERR184091 3 0.0671 0.8828 0.000 0.016 0.980 0.000 0.004
#> ERR184061 1 0.6788 0.4798 0.544 0.292 0.028 0.008 0.128
#> ERR184077 2 0.4678 -0.0628 0.028 0.668 0.000 0.004 0.300
#> ERR184062 1 0.5244 0.6639 0.728 0.048 0.024 0.016 0.184
#> ERR184053 2 0.5193 -0.2563 0.032 0.484 0.000 0.004 0.480
#> ERR184088 2 0.5719 0.1668 0.416 0.508 0.000 0.004 0.072
#> ERR184075 3 0.0162 0.8889 0.000 0.000 0.996 0.000 0.004
#> ERR184041 3 0.0162 0.8888 0.000 0.000 0.996 0.004 0.000
#> ERR184060 2 0.5409 0.3094 0.260 0.664 0.040 0.000 0.036
#> ERR184035 2 0.5388 0.1267 0.152 0.680 0.004 0.000 0.164
#> ERR184086 3 0.0162 0.8889 0.000 0.000 0.996 0.000 0.004
#> ERR184080 1 0.4141 0.6951 0.800 0.104 0.000 0.008 0.088
#> ERR184050 3 0.0566 0.8853 0.000 0.012 0.984 0.000 0.004
#> ERR184047 1 0.1117 0.7196 0.964 0.016 0.000 0.000 0.020
#> ERR184092 2 0.5627 0.2378 0.184 0.652 0.000 0.004 0.160
#> ERR184072 1 0.5542 0.5006 0.560 0.032 0.000 0.024 0.384
#> ERR184073 1 0.7881 0.3638 0.472 0.156 0.260 0.008 0.104
#> ERR184066 1 0.2789 0.7178 0.880 0.020 0.000 0.008 0.092
#> ERR184098 3 0.0000 0.8893 0.000 0.000 1.000 0.000 0.000
#> ERR184044 1 0.6089 0.5505 0.652 0.084 0.204 0.000 0.060
#> ERR184054 1 0.2103 0.7182 0.920 0.020 0.000 0.004 0.056
#> ERR184085 2 0.4982 0.1559 0.000 0.692 0.220 0.000 0.088
#> ERR184056 1 0.6105 0.5307 0.568 0.148 0.000 0.004 0.280
#> ERR184052 3 0.5325 -0.0170 0.020 0.436 0.524 0.000 0.020
#> ERR184070 2 0.5878 0.2343 0.324 0.556 0.000 0.000 0.120
#> ERR184096 1 0.1364 0.7181 0.952 0.012 0.000 0.000 0.036
#> ERR184089 3 0.0000 0.8893 0.000 0.000 1.000 0.000 0.000
#> ERR184049 2 0.4345 0.3692 0.056 0.808 0.068 0.000 0.068
#> ERR184038 3 0.6502 0.2827 0.240 0.004 0.556 0.008 0.192
#> ERR184087 3 0.0324 0.8886 0.000 0.004 0.992 0.004 0.000
#> ERR184097 1 0.3292 0.6991 0.836 0.016 0.000 0.008 0.140
#> ERR184094 3 0.1569 0.8514 0.032 0.012 0.948 0.008 0.000
#> ERR184058 2 0.4547 0.1991 0.000 0.736 0.192 0.000 0.072
#> ERR184036 2 0.6307 0.2637 0.188 0.636 0.036 0.004 0.136
#> ERR184046 2 0.6728 -0.2157 0.000 0.416 0.308 0.000 0.276
#> ERR184074 1 0.4280 0.6872 0.788 0.120 0.000 0.008 0.084
#> ERR184048 2 0.5045 0.1128 0.108 0.696 0.000 0.000 0.196
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.5294 0.45375 0.688 0.048 0.000 0.004 0.160 0.100
#> ERR184093 1 0.6274 0.09274 0.456 0.028 0.004 0.004 0.388 0.120
#> ERR184051 3 0.0692 0.89584 0.004 0.000 0.976 0.000 0.020 0.000
#> ERR184076 1 0.3954 0.52450 0.764 0.008 0.000 0.000 0.172 0.056
#> ERR184043 3 0.0508 0.89765 0.004 0.000 0.984 0.000 0.012 0.000
#> ERR184037 6 0.5380 0.33283 0.304 0.080 0.000 0.000 0.024 0.592
#> ERR184059 3 0.0837 0.89582 0.004 0.004 0.972 0.000 0.020 0.000
#> ERR184055 6 0.4595 0.39808 0.264 0.040 0.000 0.000 0.020 0.676
#> ERR184065 3 0.2644 0.83306 0.000 0.072 0.884 0.004 0.012 0.028
#> ERR184069 6 0.4486 0.07692 0.000 0.464 0.008 0.000 0.016 0.512
#> ERR184040 1 0.2364 0.63253 0.892 0.000 0.000 0.004 0.032 0.072
#> ERR184057 2 0.5719 0.38523 0.148 0.620 0.000 0.000 0.040 0.192
#> ERR184082 2 0.3614 0.53099 0.000 0.812 0.120 0.000 0.048 0.020
#> ERR184083 2 0.1616 0.55902 0.000 0.940 0.028 0.000 0.012 0.020
#> ERR184039 3 0.1692 0.87339 0.000 0.048 0.932 0.000 0.008 0.012
#> ERR184064 3 0.0260 0.89938 0.000 0.000 0.992 0.000 0.008 0.000
#> ERR184081 6 0.4317 0.25507 0.000 0.408 0.016 0.000 0.004 0.572
#> ERR184095 2 0.3983 0.45145 0.000 0.736 0.000 0.000 0.056 0.208
#> ERR184079 6 0.5996 0.37192 0.048 0.288 0.000 0.004 0.096 0.564
#> ERR184084 2 0.3999 0.51237 0.004 0.800 0.120 0.004 0.036 0.036
#> ERR184068 5 0.6391 -0.12337 0.016 0.420 0.012 0.012 0.428 0.112
#> ERR184067 6 0.4716 0.35470 0.008 0.344 0.008 0.000 0.028 0.612
#> ERR184071 2 0.4780 0.33975 0.000 0.592 0.360 0.000 0.028 0.020
#> ERR184042 4 0.0146 0.00000 0.004 0.000 0.000 0.996 0.000 0.000
#> ERR184063 3 0.0777 0.89947 0.000 0.000 0.972 0.000 0.024 0.004
#> ERR184091 3 0.1483 0.88312 0.000 0.036 0.944 0.000 0.008 0.012
#> ERR184061 6 0.5757 0.35114 0.232 0.028 0.040 0.000 0.064 0.636
#> ERR184077 2 0.5246 0.37280 0.004 0.620 0.000 0.000 0.152 0.224
#> ERR184062 1 0.6306 0.40447 0.568 0.000 0.048 0.008 0.216 0.160
#> ERR184053 2 0.7069 0.00937 0.032 0.388 0.000 0.020 0.256 0.304
#> ERR184088 2 0.6718 -0.22876 0.300 0.340 0.000 0.000 0.032 0.328
#> ERR184075 3 0.0622 0.89731 0.000 0.012 0.980 0.000 0.008 0.000
#> ERR184041 3 0.0291 0.90024 0.000 0.000 0.992 0.000 0.004 0.004
#> ERR184060 2 0.6386 -0.12398 0.176 0.416 0.012 0.000 0.012 0.384
#> ERR184035 2 0.4164 0.51920 0.068 0.780 0.000 0.000 0.036 0.116
#> ERR184086 3 0.0146 0.89993 0.000 0.000 0.996 0.000 0.004 0.000
#> ERR184080 1 0.4515 0.59474 0.716 0.024 0.000 0.000 0.052 0.208
#> ERR184050 3 0.1657 0.88053 0.000 0.012 0.936 0.000 0.012 0.040
#> ERR184047 1 0.3833 0.63199 0.800 0.000 0.028 0.000 0.052 0.120
#> ERR184092 6 0.6635 0.47574 0.128 0.216 0.000 0.000 0.124 0.532
#> ERR184072 5 0.5560 -0.26063 0.360 0.016 0.000 0.000 0.528 0.096
#> ERR184073 6 0.7687 -0.14095 0.244 0.004 0.288 0.000 0.156 0.308
#> ERR184066 1 0.4176 0.62490 0.752 0.000 0.008 0.000 0.080 0.160
#> ERR184098 3 0.0520 0.89883 0.000 0.000 0.984 0.000 0.008 0.008
#> ERR184044 1 0.6720 0.33307 0.492 0.004 0.252 0.000 0.060 0.192
#> ERR184054 1 0.3261 0.63809 0.824 0.000 0.000 0.000 0.072 0.104
#> ERR184085 2 0.5599 0.45773 0.000 0.632 0.116 0.004 0.032 0.216
#> ERR184056 1 0.7363 -0.05244 0.380 0.176 0.000 0.000 0.292 0.152
#> ERR184052 3 0.6368 -0.29694 0.016 0.404 0.428 0.000 0.020 0.132
#> ERR184070 6 0.5439 0.52302 0.140 0.200 0.000 0.000 0.024 0.636
#> ERR184096 1 0.3297 0.62952 0.820 0.000 0.000 0.000 0.068 0.112
#> ERR184089 3 0.0146 0.89998 0.000 0.000 0.996 0.000 0.000 0.004
#> ERR184049 6 0.4680 0.43033 0.016 0.300 0.016 0.000 0.016 0.652
#> ERR184038 3 0.6379 0.36177 0.208 0.064 0.580 0.000 0.136 0.012
#> ERR184087 3 0.0291 0.90024 0.000 0.000 0.992 0.000 0.004 0.004
#> ERR184097 1 0.3974 0.60656 0.808 0.028 0.004 0.004 0.064 0.092
#> ERR184094 3 0.2361 0.83536 0.032 0.000 0.896 0.000 0.008 0.064
#> ERR184058 2 0.4958 0.47923 0.000 0.680 0.132 0.000 0.012 0.176
#> ERR184036 6 0.5393 0.54396 0.080 0.184 0.012 0.000 0.044 0.680
#> ERR184046 2 0.4988 0.40858 0.000 0.672 0.224 0.000 0.080 0.024
#> ERR184074 1 0.5122 0.43853 0.564 0.004 0.004 0.000 0.068 0.360
#> ERR184048 2 0.2725 0.55268 0.040 0.880 0.000 0.000 0.020 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", "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 10269 rows and 62 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 5.
#>
#> 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 0.560 0.857 0.895 0.3502 0.568 0.568
#> 3 3 0.667 0.781 0.920 0.4007 0.870 0.785
#> 4 4 0.695 0.818 0.931 0.0257 0.979 0.959
#> 5 5 0.738 0.810 0.925 0.1022 0.949 0.897
#> 6 6 0.738 0.765 0.898 0.0310 0.937 0.870
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
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
#> ERR184078 1 0.8955 0.8766 0.688 0.312
#> ERR184093 2 0.0000 0.9441 0.000 1.000
#> ERR184051 1 0.8713 0.8929 0.708 0.292
#> ERR184076 1 0.8955 0.8766 0.688 0.312
#> ERR184043 1 0.8713 0.8929 0.708 0.292
#> ERR184037 2 0.9866 -0.2368 0.432 0.568
#> ERR184059 1 0.8661 0.8922 0.712 0.288
#> ERR184055 2 0.9580 0.0135 0.380 0.620
#> ERR184065 2 0.0000 0.9441 0.000 1.000
#> ERR184069 2 0.0000 0.9441 0.000 1.000
#> ERR184040 1 0.8267 0.8763 0.740 0.260
#> ERR184057 2 0.0000 0.9441 0.000 1.000
#> ERR184082 2 0.1414 0.9284 0.020 0.980
#> ERR184083 2 0.0000 0.9441 0.000 1.000
#> ERR184039 2 0.0000 0.9441 0.000 1.000
#> ERR184064 1 0.8713 0.8929 0.708 0.292
#> ERR184081 2 0.0000 0.9441 0.000 1.000
#> ERR184095 2 0.0000 0.9441 0.000 1.000
#> ERR184079 2 0.0000 0.9441 0.000 1.000
#> ERR184084 1 0.8661 0.8922 0.712 0.288
#> ERR184068 2 0.0938 0.9354 0.012 0.988
#> ERR184067 2 0.0000 0.9441 0.000 1.000
#> ERR184071 2 0.0000 0.9441 0.000 1.000
#> ERR184042 1 0.0000 0.6791 1.000 0.000
#> ERR184063 1 0.8713 0.8929 0.708 0.292
#> ERR184091 2 0.0000 0.9441 0.000 1.000
#> ERR184061 2 0.1184 0.9317 0.016 0.984
#> ERR184077 2 0.0000 0.9441 0.000 1.000
#> ERR184062 2 0.2948 0.8934 0.052 0.948
#> ERR184053 2 0.0376 0.9412 0.004 0.996
#> ERR184088 2 0.0000 0.9441 0.000 1.000
#> ERR184075 2 0.0000 0.9441 0.000 1.000
#> ERR184041 1 0.8713 0.8929 0.708 0.292
#> ERR184060 2 0.0000 0.9441 0.000 1.000
#> ERR184035 2 0.1414 0.9284 0.020 0.980
#> ERR184086 2 0.0000 0.9441 0.000 1.000
#> ERR184080 2 0.8327 0.4789 0.264 0.736
#> ERR184050 2 0.0000 0.9441 0.000 1.000
#> ERR184047 1 0.0000 0.6791 1.000 0.000
#> ERR184092 2 0.0000 0.9441 0.000 1.000
#> ERR184072 1 0.9087 0.8632 0.676 0.324
#> ERR184073 1 0.8267 0.8763 0.740 0.260
#> ERR184066 2 0.8327 0.4761 0.264 0.736
#> ERR184098 2 0.0000 0.9441 0.000 1.000
#> ERR184044 2 0.2603 0.9024 0.044 0.956
#> ERR184054 1 0.9896 0.6294 0.560 0.440
#> ERR184085 2 0.1633 0.9244 0.024 0.976
#> ERR184056 2 0.0000 0.9441 0.000 1.000
#> ERR184052 2 0.0000 0.9441 0.000 1.000
#> ERR184070 2 0.0000 0.9441 0.000 1.000
#> ERR184096 1 0.0000 0.6791 1.000 0.000
#> ERR184089 2 0.0000 0.9441 0.000 1.000
#> ERR184049 2 0.0000 0.9441 0.000 1.000
#> ERR184038 2 0.5946 0.7505 0.144 0.856
#> ERR184087 1 0.8713 0.8929 0.708 0.292
#> ERR184097 2 0.0000 0.9441 0.000 1.000
#> ERR184094 1 0.8386 0.8809 0.732 0.268
#> ERR184058 2 0.0000 0.9441 0.000 1.000
#> ERR184036 2 0.0000 0.9441 0.000 1.000
#> ERR184046 2 0.0000 0.9441 0.000 1.000
#> ERR184074 1 0.9044 0.8685 0.680 0.320
#> ERR184048 2 0.0000 0.9441 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.0829 0.7857 0.984 0.012 0.004
#> ERR184093 2 0.1163 0.9334 0.028 0.972 0.000
#> ERR184051 1 0.0592 0.7874 0.988 0.000 0.012
#> ERR184076 1 0.0829 0.7857 0.984 0.012 0.004
#> ERR184043 1 0.0592 0.7874 0.988 0.000 0.012
#> ERR184037 1 0.5254 0.5240 0.736 0.264 0.000
#> ERR184059 1 0.0747 0.7853 0.984 0.000 0.016
#> ERR184055 1 0.5678 0.4624 0.684 0.316 0.000
#> ERR184065 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184069 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184040 1 0.1964 0.7624 0.944 0.000 0.056
#> ERR184057 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184082 2 0.4399 0.7926 0.188 0.812 0.000
#> ERR184083 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184039 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184064 1 0.0592 0.7874 0.988 0.000 0.012
#> ERR184081 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184095 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184079 2 0.1031 0.9353 0.024 0.976 0.000
#> ERR184084 1 0.0747 0.7853 0.984 0.000 0.016
#> ERR184068 2 0.2959 0.8824 0.100 0.900 0.000
#> ERR184067 2 0.0237 0.9399 0.004 0.996 0.000
#> ERR184071 2 0.0237 0.9399 0.004 0.996 0.000
#> ERR184042 3 0.0000 0.0000 0.000 0.000 1.000
#> ERR184063 1 0.0592 0.7874 0.988 0.000 0.012
#> ERR184091 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184061 2 0.4002 0.8137 0.160 0.840 0.000
#> ERR184077 2 0.0892 0.9368 0.020 0.980 0.000
#> ERR184062 2 0.5216 0.6823 0.260 0.740 0.000
#> ERR184053 2 0.2537 0.8970 0.080 0.920 0.000
#> ERR184088 2 0.0424 0.9399 0.008 0.992 0.000
#> ERR184075 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184041 1 0.0592 0.7874 0.988 0.000 0.012
#> ERR184060 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184035 2 0.4399 0.7926 0.188 0.812 0.000
#> ERR184086 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184080 1 0.6521 -0.0222 0.500 0.496 0.004
#> ERR184050 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184047 1 0.6280 0.0530 0.540 0.000 0.460
#> ERR184092 2 0.1163 0.9334 0.028 0.972 0.000
#> ERR184072 1 0.0892 0.7818 0.980 0.020 0.000
#> ERR184073 1 0.1964 0.7624 0.944 0.000 0.056
#> ERR184066 1 0.6305 0.0239 0.516 0.484 0.000
#> ERR184098 2 0.0592 0.9387 0.012 0.988 0.000
#> ERR184044 2 0.4702 0.7585 0.212 0.788 0.000
#> ERR184054 1 0.3983 0.6625 0.852 0.144 0.004
#> ERR184085 2 0.4504 0.7820 0.196 0.804 0.000
#> ERR184056 2 0.1529 0.9264 0.040 0.960 0.000
#> ERR184052 2 0.0237 0.9399 0.004 0.996 0.000
#> ERR184070 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184096 1 0.6280 0.0530 0.540 0.000 0.460
#> ERR184089 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184049 2 0.0424 0.9399 0.008 0.992 0.000
#> ERR184038 2 0.6026 0.4177 0.376 0.624 0.000
#> ERR184087 1 0.0592 0.7874 0.988 0.000 0.012
#> ERR184097 2 0.1163 0.9331 0.028 0.972 0.000
#> ERR184094 1 0.1643 0.7702 0.956 0.000 0.044
#> ERR184058 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184036 2 0.1643 0.9181 0.044 0.956 0.000
#> ERR184046 2 0.0000 0.9400 0.000 1.000 0.000
#> ERR184074 1 0.0747 0.7840 0.984 0.016 0.000
#> ERR184048 2 0.0424 0.9399 0.008 0.992 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.0657 0.80938 0.984 0.012 0.004 0.000
#> ERR184093 2 0.0921 0.93378 0.028 0.972 0.000 0.000
#> ERR184051 1 0.0937 0.81011 0.976 0.000 0.012 0.012
#> ERR184076 1 0.0657 0.80938 0.984 0.012 0.004 0.000
#> ERR184043 1 0.0937 0.81011 0.976 0.000 0.012 0.012
#> ERR184037 1 0.4164 0.55160 0.736 0.264 0.000 0.000
#> ERR184059 1 0.1174 0.80624 0.968 0.000 0.020 0.012
#> ERR184055 1 0.4500 0.49036 0.684 0.316 0.000 0.000
#> ERR184065 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184069 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184040 1 0.2216 0.76391 0.908 0.000 0.092 0.000
#> ERR184057 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184082 2 0.3486 0.79087 0.188 0.812 0.000 0.000
#> ERR184083 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184039 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184064 1 0.0937 0.81011 0.976 0.000 0.012 0.012
#> ERR184081 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184095 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184079 2 0.0817 0.93557 0.024 0.976 0.000 0.000
#> ERR184084 1 0.1174 0.80624 0.968 0.000 0.020 0.012
#> ERR184068 2 0.2345 0.88228 0.100 0.900 0.000 0.000
#> ERR184067 2 0.0188 0.94020 0.004 0.996 0.000 0.000
#> ERR184071 2 0.0188 0.94020 0.004 0.996 0.000 0.000
#> ERR184042 4 0.0469 0.00000 0.000 0.000 0.012 0.988
#> ERR184063 1 0.0937 0.81011 0.976 0.000 0.012 0.012
#> ERR184091 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184061 2 0.3172 0.81049 0.160 0.840 0.000 0.000
#> ERR184077 2 0.0707 0.93715 0.020 0.980 0.000 0.000
#> ERR184062 2 0.4134 0.67827 0.260 0.740 0.000 0.000
#> ERR184053 2 0.2011 0.89770 0.080 0.920 0.000 0.000
#> ERR184088 2 0.0336 0.94019 0.008 0.992 0.000 0.000
#> ERR184075 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184041 1 0.0937 0.81011 0.976 0.000 0.012 0.012
#> ERR184060 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184035 2 0.3486 0.79087 0.188 0.812 0.000 0.000
#> ERR184086 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184080 1 0.5168 0.00069 0.500 0.496 0.004 0.000
#> ERR184050 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184047 3 0.0000 1.00000 0.000 0.000 1.000 0.000
#> ERR184092 2 0.0921 0.93378 0.028 0.972 0.000 0.000
#> ERR184072 1 0.0707 0.80663 0.980 0.020 0.000 0.000
#> ERR184073 1 0.2081 0.77018 0.916 0.000 0.084 0.000
#> ERR184066 1 0.4996 0.05033 0.516 0.484 0.000 0.000
#> ERR184098 2 0.0469 0.93905 0.012 0.988 0.000 0.000
#> ERR184044 2 0.3726 0.75719 0.212 0.788 0.000 0.000
#> ERR184054 1 0.3157 0.69069 0.852 0.144 0.004 0.000
#> ERR184085 2 0.3569 0.78043 0.196 0.804 0.000 0.000
#> ERR184056 2 0.1211 0.92674 0.040 0.960 0.000 0.000
#> ERR184052 2 0.0188 0.94020 0.004 0.996 0.000 0.000
#> ERR184070 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184096 3 0.0000 1.00000 0.000 0.000 1.000 0.000
#> ERR184089 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184049 2 0.0336 0.94012 0.008 0.992 0.000 0.000
#> ERR184038 2 0.4776 0.40768 0.376 0.624 0.000 0.000
#> ERR184087 1 0.0937 0.81011 0.976 0.000 0.012 0.012
#> ERR184097 2 0.0921 0.93340 0.028 0.972 0.000 0.000
#> ERR184094 1 0.2011 0.77424 0.920 0.000 0.080 0.000
#> ERR184058 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184036 2 0.1302 0.91794 0.044 0.956 0.000 0.000
#> ERR184046 2 0.0000 0.94034 0.000 1.000 0.000 0.000
#> ERR184074 1 0.0592 0.80837 0.984 0.016 0.000 0.000
#> ERR184048 2 0.0336 0.94018 0.008 0.992 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.0324 0.600 0.992 0.000 0.004 0 0.004
#> ERR184093 2 0.1043 0.923 0.040 0.960 0.000 0 0.000
#> ERR184051 3 0.0000 0.998 0.000 0.000 1.000 0 0.000
#> ERR184076 1 0.0162 0.599 0.996 0.000 0.000 0 0.004
#> ERR184043 3 0.0000 0.998 0.000 0.000 1.000 0 0.000
#> ERR184037 1 0.3508 0.548 0.748 0.252 0.000 0 0.000
#> ERR184059 3 0.0290 0.993 0.000 0.000 0.992 0 0.008
#> ERR184055 1 0.3816 0.515 0.696 0.304 0.000 0 0.000
#> ERR184065 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184069 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184040 1 0.3532 0.551 0.832 0.000 0.076 0 0.092
#> ERR184057 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184082 2 0.3109 0.763 0.200 0.800 0.000 0 0.000
#> ERR184083 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184039 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184064 3 0.0000 0.998 0.000 0.000 1.000 0 0.000
#> ERR184081 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184095 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184079 2 0.0880 0.927 0.032 0.968 0.000 0 0.000
#> ERR184084 3 0.0290 0.993 0.000 0.000 0.992 0 0.008
#> ERR184068 2 0.2020 0.870 0.100 0.900 0.000 0 0.000
#> ERR184067 2 0.0404 0.932 0.012 0.988 0.000 0 0.000
#> ERR184071 2 0.0404 0.932 0.012 0.988 0.000 0 0.000
#> ERR184042 4 0.0000 0.000 0.000 0.000 0.000 1 0.000
#> ERR184063 3 0.0000 0.998 0.000 0.000 1.000 0 0.000
#> ERR184091 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184061 2 0.2852 0.788 0.172 0.828 0.000 0 0.000
#> ERR184077 2 0.0794 0.929 0.028 0.972 0.000 0 0.000
#> ERR184062 2 0.3636 0.637 0.272 0.728 0.000 0 0.000
#> ERR184053 2 0.1732 0.887 0.080 0.920 0.000 0 0.000
#> ERR184088 2 0.0510 0.932 0.016 0.984 0.000 0 0.000
#> ERR184075 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184041 3 0.0000 0.998 0.000 0.000 1.000 0 0.000
#> ERR184060 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184035 2 0.3109 0.763 0.200 0.800 0.000 0 0.000
#> ERR184086 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184080 1 0.4449 0.119 0.512 0.484 0.000 0 0.004
#> ERR184050 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184047 5 0.0000 1.000 0.000 0.000 0.000 0 1.000
#> ERR184092 2 0.1043 0.923 0.040 0.960 0.000 0 0.000
#> ERR184072 1 0.0290 0.604 0.992 0.008 0.000 0 0.000
#> ERR184073 1 0.3479 0.552 0.836 0.000 0.080 0 0.084
#> ERR184066 1 0.4297 0.159 0.528 0.472 0.000 0 0.000
#> ERR184098 2 0.0404 0.932 0.012 0.988 0.000 0 0.000
#> ERR184044 2 0.3305 0.725 0.224 0.776 0.000 0 0.000
#> ERR184054 1 0.3513 0.602 0.828 0.132 0.036 0 0.004
#> ERR184085 2 0.3177 0.751 0.208 0.792 0.000 0 0.000
#> ERR184056 2 0.1197 0.917 0.048 0.952 0.000 0 0.000
#> ERR184052 2 0.0404 0.932 0.012 0.988 0.000 0 0.000
#> ERR184070 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184096 5 0.0000 1.000 0.000 0.000 0.000 0 1.000
#> ERR184089 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184049 2 0.0609 0.931 0.020 0.980 0.000 0 0.000
#> ERR184038 2 0.4150 0.327 0.388 0.612 0.000 0 0.000
#> ERR184087 3 0.0000 0.998 0.000 0.000 1.000 0 0.000
#> ERR184097 2 0.0963 0.924 0.036 0.964 0.000 0 0.000
#> ERR184094 1 0.4818 0.396 0.708 0.000 0.212 0 0.080
#> ERR184058 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184036 2 0.1270 0.910 0.052 0.948 0.000 0 0.000
#> ERR184046 2 0.0000 0.933 0.000 1.000 0.000 0 0.000
#> ERR184074 1 0.1502 0.605 0.940 0.004 0.056 0 0.000
#> ERR184048 2 0.0510 0.932 0.016 0.984 0.000 0 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.0405 0.485 0.988 0.000 0.004 0 0.000 0.008
#> ERR184093 2 0.0865 0.891 0.000 0.964 0.000 0 0.000 0.036
#> ERR184051 3 0.0000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> ERR184076 1 0.0000 0.474 1.000 0.000 0.000 0 0.000 0.000
#> ERR184043 3 0.0000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> ERR184037 6 0.3494 0.604 0.012 0.252 0.000 0 0.000 0.736
#> ERR184059 3 0.0260 0.993 0.000 0.000 0.992 0 0.008 0.000
#> ERR184055 6 0.4083 0.577 0.028 0.304 0.000 0 0.000 0.668
#> ERR184065 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184069 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184040 1 0.6283 0.668 0.492 0.000 0.076 0 0.088 0.344
#> ERR184057 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184082 2 0.2793 0.727 0.000 0.800 0.000 0 0.000 0.200
#> ERR184083 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184039 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184064 3 0.0000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> ERR184081 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184095 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184079 2 0.0713 0.895 0.000 0.972 0.000 0 0.000 0.028
#> ERR184084 3 0.0260 0.993 0.000 0.000 0.992 0 0.008 0.000
#> ERR184068 2 0.2039 0.842 0.020 0.904 0.000 0 0.000 0.076
#> ERR184067 2 0.0260 0.899 0.000 0.992 0.000 0 0.000 0.008
#> ERR184071 2 0.0260 0.899 0.000 0.992 0.000 0 0.000 0.008
#> ERR184042 4 0.0000 0.000 0.000 0.000 0.000 1 0.000 0.000
#> ERR184063 3 0.0000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> ERR184091 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184061 2 0.2562 0.748 0.000 0.828 0.000 0 0.000 0.172
#> ERR184077 2 0.0632 0.896 0.000 0.976 0.000 0 0.000 0.024
#> ERR184062 2 0.3980 0.608 0.052 0.732 0.000 0 0.000 0.216
#> ERR184053 2 0.1501 0.856 0.000 0.924 0.000 0 0.000 0.076
#> ERR184088 2 0.0363 0.899 0.000 0.988 0.000 0 0.000 0.012
#> ERR184075 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184041 3 0.0000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> ERR184060 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184035 2 0.2793 0.727 0.000 0.800 0.000 0 0.000 0.200
#> ERR184086 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184080 2 0.5860 -0.243 0.248 0.484 0.000 0 0.000 0.268
#> ERR184050 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184047 5 0.0000 1.000 0.000 0.000 0.000 0 1.000 0.000
#> ERR184092 2 0.0865 0.891 0.000 0.964 0.000 0 0.000 0.036
#> ERR184072 1 0.3862 0.600 0.524 0.000 0.000 0 0.000 0.476
#> ERR184073 1 0.6209 0.672 0.512 0.000 0.080 0 0.080 0.328
#> ERR184066 2 0.5772 -0.299 0.184 0.468 0.000 0 0.000 0.348
#> ERR184098 2 0.0260 0.900 0.000 0.992 0.000 0 0.000 0.008
#> ERR184044 2 0.2969 0.691 0.000 0.776 0.000 0 0.000 0.224
#> ERR184054 1 0.6097 0.340 0.516 0.132 0.036 0 0.000 0.316
#> ERR184085 2 0.2854 0.715 0.000 0.792 0.000 0 0.000 0.208
#> ERR184056 2 0.1082 0.886 0.004 0.956 0.000 0 0.000 0.040
#> ERR184052 2 0.0260 0.899 0.000 0.992 0.000 0 0.000 0.008
#> ERR184070 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184096 5 0.0000 1.000 0.000 0.000 0.000 0 1.000 0.000
#> ERR184089 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184049 2 0.0458 0.898 0.000 0.984 0.000 0 0.000 0.016
#> ERR184038 2 0.4480 0.297 0.044 0.616 0.000 0 0.000 0.340
#> ERR184087 3 0.0000 0.998 0.000 0.000 1.000 0 0.000 0.000
#> ERR184097 2 0.0790 0.892 0.000 0.968 0.000 0 0.000 0.032
#> ERR184094 1 0.7007 0.570 0.396 0.000 0.212 0 0.076 0.316
#> ERR184058 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184036 2 0.1075 0.877 0.000 0.952 0.000 0 0.000 0.048
#> ERR184046 2 0.0146 0.900 0.000 0.996 0.000 0 0.000 0.004
#> ERR184074 6 0.2129 -0.127 0.040 0.000 0.056 0 0.000 0.904
#> ERR184048 2 0.0363 0.899 0.000 0.988 0.000 0 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
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 10269 rows and 62 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.984 0.993 0.4855 0.518 0.518
#> 3 3 0.748 0.779 0.894 0.2446 0.788 0.616
#> 4 4 0.679 0.652 0.817 0.1194 0.919 0.795
#> 5 5 0.721 0.735 0.833 0.0912 0.802 0.486
#> 6 6 0.693 0.737 0.823 0.0573 0.948 0.800
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
#> ERR184078 1 0.0000 0.999 1.000 0.000
#> ERR184093 2 0.0000 0.988 0.000 1.000
#> ERR184051 1 0.0000 0.999 1.000 0.000
#> ERR184076 1 0.0000 0.999 1.000 0.000
#> ERR184043 1 0.0000 0.999 1.000 0.000
#> ERR184037 1 0.0000 0.999 1.000 0.000
#> ERR184059 1 0.0000 0.999 1.000 0.000
#> ERR184055 1 0.0672 0.992 0.992 0.008
#> ERR184065 2 0.0000 0.988 0.000 1.000
#> ERR184069 2 0.0000 0.988 0.000 1.000
#> ERR184040 1 0.0000 0.999 1.000 0.000
#> ERR184057 2 0.0000 0.988 0.000 1.000
#> ERR184082 2 0.0000 0.988 0.000 1.000
#> ERR184083 2 0.0000 0.988 0.000 1.000
#> ERR184039 2 0.0000 0.988 0.000 1.000
#> ERR184064 1 0.0000 0.999 1.000 0.000
#> ERR184081 2 0.0000 0.988 0.000 1.000
#> ERR184095 2 0.0000 0.988 0.000 1.000
#> ERR184079 2 0.0000 0.988 0.000 1.000
#> ERR184084 1 0.0000 0.999 1.000 0.000
#> ERR184068 2 0.0000 0.988 0.000 1.000
#> ERR184067 2 0.0000 0.988 0.000 1.000
#> ERR184071 2 0.0000 0.988 0.000 1.000
#> ERR184042 1 0.0000 0.999 1.000 0.000
#> ERR184063 1 0.0000 0.999 1.000 0.000
#> ERR184091 2 0.0000 0.988 0.000 1.000
#> ERR184061 2 0.0000 0.988 0.000 1.000
#> ERR184077 2 0.0000 0.988 0.000 1.000
#> ERR184062 2 0.0000 0.988 0.000 1.000
#> ERR184053 2 0.0000 0.988 0.000 1.000
#> ERR184088 2 0.0000 0.988 0.000 1.000
#> ERR184075 2 0.0000 0.988 0.000 1.000
#> ERR184041 1 0.0000 0.999 1.000 0.000
#> ERR184060 2 0.0000 0.988 0.000 1.000
#> ERR184035 2 0.4022 0.911 0.080 0.920
#> ERR184086 2 0.0000 0.988 0.000 1.000
#> ERR184080 1 0.0000 0.999 1.000 0.000
#> ERR184050 2 0.0000 0.988 0.000 1.000
#> ERR184047 1 0.0000 0.999 1.000 0.000
#> ERR184092 2 0.0000 0.988 0.000 1.000
#> ERR184072 1 0.0000 0.999 1.000 0.000
#> ERR184073 1 0.0000 0.999 1.000 0.000
#> ERR184066 1 0.0672 0.992 0.992 0.008
#> ERR184098 2 0.0000 0.988 0.000 1.000
#> ERR184044 2 0.8016 0.681 0.244 0.756
#> ERR184054 1 0.0000 0.999 1.000 0.000
#> ERR184085 2 0.4815 0.885 0.104 0.896
#> ERR184056 2 0.0000 0.988 0.000 1.000
#> ERR184052 2 0.0000 0.988 0.000 1.000
#> ERR184070 2 0.0000 0.988 0.000 1.000
#> ERR184096 1 0.0000 0.999 1.000 0.000
#> ERR184089 2 0.0000 0.988 0.000 1.000
#> ERR184049 2 0.0000 0.988 0.000 1.000
#> ERR184038 1 0.0000 0.999 1.000 0.000
#> ERR184087 1 0.0000 0.999 1.000 0.000
#> ERR184097 2 0.0000 0.988 0.000 1.000
#> ERR184094 1 0.0000 0.999 1.000 0.000
#> ERR184058 2 0.0000 0.988 0.000 1.000
#> ERR184036 2 0.0000 0.988 0.000 1.000
#> ERR184046 2 0.0000 0.988 0.000 1.000
#> ERR184074 1 0.0000 0.999 1.000 0.000
#> ERR184048 2 0.0000 0.988 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.2878 0.6447 0.904 0.000 0.096
#> ERR184093 2 0.1031 0.9477 0.024 0.976 0.000
#> ERR184051 3 0.4605 0.8168 0.204 0.000 0.796
#> ERR184076 1 0.2878 0.6447 0.904 0.000 0.096
#> ERR184043 3 0.4346 0.8261 0.184 0.000 0.816
#> ERR184037 1 0.0237 0.7269 0.996 0.000 0.004
#> ERR184059 3 0.3619 0.8224 0.136 0.000 0.864
#> ERR184055 1 0.0000 0.7266 1.000 0.000 0.000
#> ERR184065 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184069 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184040 1 0.6111 -0.1902 0.604 0.000 0.396
#> ERR184057 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184082 1 0.5465 0.5443 0.712 0.288 0.000
#> ERR184083 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184039 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184064 3 0.4346 0.8261 0.184 0.000 0.816
#> ERR184081 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184095 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184079 2 0.2537 0.9081 0.080 0.920 0.000
#> ERR184084 3 0.3752 0.8246 0.144 0.000 0.856
#> ERR184068 2 0.4702 0.7379 0.212 0.788 0.000
#> ERR184067 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184071 2 0.1529 0.9396 0.040 0.960 0.000
#> ERR184042 3 0.0000 0.7378 0.000 0.000 1.000
#> ERR184063 3 0.6299 0.3758 0.476 0.000 0.524
#> ERR184091 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184061 1 0.6252 0.2480 0.556 0.444 0.000
#> ERR184077 2 0.2878 0.8942 0.096 0.904 0.000
#> ERR184062 2 0.6291 0.0407 0.468 0.532 0.000
#> ERR184053 2 0.2959 0.8899 0.100 0.900 0.000
#> ERR184088 2 0.1289 0.9441 0.032 0.968 0.000
#> ERR184075 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184041 3 0.6204 0.5080 0.424 0.000 0.576
#> ERR184060 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184035 1 0.4605 0.6189 0.796 0.204 0.000
#> ERR184086 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184080 1 0.0237 0.7269 0.996 0.000 0.004
#> ERR184050 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184047 3 0.4002 0.7352 0.160 0.000 0.840
#> ERR184092 2 0.1163 0.9460 0.028 0.972 0.000
#> ERR184072 1 0.0237 0.7269 0.996 0.000 0.004
#> ERR184073 3 0.5859 0.7315 0.344 0.000 0.656
#> ERR184066 1 0.0000 0.7266 1.000 0.000 0.000
#> ERR184098 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184044 1 0.2261 0.7026 0.932 0.068 0.000
#> ERR184054 1 0.0592 0.7226 0.988 0.000 0.012
#> ERR184085 1 0.4654 0.6121 0.792 0.208 0.000
#> ERR184056 2 0.1411 0.9421 0.036 0.964 0.000
#> ERR184052 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184070 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184096 3 0.4235 0.7266 0.176 0.000 0.824
#> ERR184089 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184049 1 0.6309 0.0525 0.504 0.496 0.000
#> ERR184038 1 0.2066 0.6911 0.940 0.000 0.060
#> ERR184087 3 0.4235 0.8268 0.176 0.000 0.824
#> ERR184097 2 0.1411 0.9421 0.036 0.964 0.000
#> ERR184094 3 0.5497 0.7612 0.292 0.000 0.708
#> ERR184058 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184036 2 0.0747 0.9507 0.016 0.984 0.000
#> ERR184046 2 0.0000 0.9558 0.000 1.000 0.000
#> ERR184074 1 0.1964 0.6843 0.944 0.000 0.056
#> ERR184048 2 0.2796 0.8975 0.092 0.908 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.5581 0.310 0.532 0.000 0.020 0.448
#> ERR184093 2 0.4220 0.760 0.248 0.748 0.000 0.004
#> ERR184051 3 0.1452 0.799 0.036 0.000 0.956 0.008
#> ERR184076 1 0.5414 0.458 0.604 0.000 0.020 0.376
#> ERR184043 3 0.0336 0.807 0.008 0.000 0.992 0.000
#> ERR184037 1 0.4535 0.568 0.704 0.000 0.004 0.292
#> ERR184059 3 0.4955 0.318 0.008 0.000 0.648 0.344
#> ERR184055 1 0.4535 0.570 0.704 0.000 0.004 0.292
#> ERR184065 2 0.0188 0.880 0.000 0.996 0.000 0.004
#> ERR184069 2 0.0000 0.881 0.000 1.000 0.000 0.000
#> ERR184040 4 0.5730 0.111 0.344 0.000 0.040 0.616
#> ERR184057 2 0.0000 0.881 0.000 1.000 0.000 0.000
#> ERR184082 1 0.2266 0.556 0.912 0.084 0.000 0.004
#> ERR184083 2 0.0000 0.881 0.000 1.000 0.000 0.000
#> ERR184039 2 0.0188 0.880 0.000 0.996 0.000 0.004
#> ERR184064 3 0.0336 0.807 0.008 0.000 0.992 0.000
#> ERR184081 2 0.0000 0.881 0.000 1.000 0.000 0.000
#> ERR184095 2 0.0000 0.881 0.000 1.000 0.000 0.000
#> ERR184079 2 0.4936 0.612 0.372 0.624 0.000 0.004
#> ERR184084 3 0.5075 0.306 0.012 0.000 0.644 0.344
#> ERR184068 1 0.5294 -0.354 0.508 0.484 0.000 0.008
#> ERR184067 2 0.0000 0.881 0.000 1.000 0.000 0.000
#> ERR184071 2 0.4483 0.726 0.284 0.712 0.000 0.004
#> ERR184042 4 0.4746 0.129 0.000 0.000 0.368 0.632
#> ERR184063 3 0.2450 0.762 0.072 0.000 0.912 0.016
#> ERR184091 2 0.0188 0.880 0.000 0.996 0.000 0.004
#> ERR184061 1 0.3172 0.510 0.840 0.160 0.000 0.000
#> ERR184077 2 0.4819 0.654 0.344 0.652 0.000 0.004
#> ERR184062 1 0.5093 0.112 0.640 0.348 0.000 0.012
#> ERR184053 2 0.4837 0.648 0.348 0.648 0.000 0.004
#> ERR184088 2 0.4313 0.749 0.260 0.736 0.000 0.004
#> ERR184075 2 0.0188 0.880 0.000 0.996 0.000 0.004
#> ERR184041 3 0.2222 0.777 0.060 0.000 0.924 0.016
#> ERR184060 2 0.0000 0.881 0.000 1.000 0.000 0.000
#> ERR184035 1 0.1936 0.586 0.940 0.028 0.000 0.032
#> ERR184086 2 0.0188 0.880 0.000 0.996 0.000 0.004
#> ERR184080 1 0.4584 0.566 0.696 0.000 0.004 0.300
#> ERR184050 2 0.0188 0.880 0.000 0.996 0.000 0.004
#> ERR184047 4 0.3494 0.564 0.004 0.000 0.172 0.824
#> ERR184092 2 0.3870 0.787 0.208 0.788 0.000 0.004
#> ERR184072 1 0.5026 0.546 0.672 0.000 0.016 0.312
#> ERR184073 4 0.7290 0.449 0.168 0.000 0.328 0.504
#> ERR184066 1 0.4567 0.573 0.716 0.000 0.008 0.276
#> ERR184098 2 0.0188 0.880 0.000 0.996 0.000 0.004
#> ERR184044 1 0.0712 0.582 0.984 0.004 0.004 0.008
#> ERR184054 1 0.5069 0.539 0.664 0.000 0.016 0.320
#> ERR184085 1 0.1489 0.574 0.952 0.044 0.000 0.004
#> ERR184056 2 0.3306 0.816 0.156 0.840 0.000 0.004
#> ERR184052 2 0.1211 0.868 0.040 0.960 0.000 0.000
#> ERR184070 2 0.0000 0.881 0.000 1.000 0.000 0.000
#> ERR184096 4 0.3306 0.571 0.004 0.000 0.156 0.840
#> ERR184089 2 0.1109 0.869 0.028 0.968 0.000 0.004
#> ERR184049 1 0.3400 0.488 0.820 0.180 0.000 0.000
#> ERR184038 1 0.3176 0.555 0.880 0.000 0.084 0.036
#> ERR184087 3 0.0336 0.807 0.008 0.000 0.992 0.000
#> ERR184097 2 0.3945 0.783 0.216 0.780 0.000 0.004
#> ERR184094 4 0.5628 0.336 0.024 0.000 0.420 0.556
#> ERR184058 2 0.0188 0.880 0.000 0.996 0.000 0.004
#> ERR184036 2 0.4088 0.773 0.232 0.764 0.000 0.004
#> ERR184046 2 0.0000 0.881 0.000 1.000 0.000 0.000
#> ERR184074 1 0.5253 0.494 0.624 0.000 0.016 0.360
#> ERR184048 2 0.4837 0.648 0.348 0.648 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.2189 0.771 0.904 0.000 0.000 0.084 0.012
#> ERR184093 4 0.4825 0.461 0.000 0.408 0.000 0.568 0.024
#> ERR184051 3 0.0162 0.990 0.000 0.000 0.996 0.004 0.000
#> ERR184076 1 0.2997 0.824 0.840 0.000 0.000 0.148 0.012
#> ERR184043 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> ERR184037 1 0.4213 0.821 0.680 0.000 0.000 0.308 0.012
#> ERR184059 5 0.6390 0.583 0.168 0.000 0.396 0.000 0.436
#> ERR184055 1 0.4213 0.821 0.680 0.000 0.000 0.308 0.012
#> ERR184065 2 0.0880 0.891 0.000 0.968 0.000 0.000 0.032
#> ERR184069 2 0.0290 0.896 0.000 0.992 0.000 0.008 0.000
#> ERR184040 1 0.1493 0.675 0.948 0.000 0.000 0.024 0.028
#> ERR184057 2 0.0290 0.896 0.000 0.992 0.000 0.008 0.000
#> ERR184082 4 0.1413 0.650 0.020 0.012 0.000 0.956 0.012
#> ERR184083 2 0.0579 0.896 0.000 0.984 0.000 0.008 0.008
#> ERR184039 2 0.0880 0.891 0.000 0.968 0.000 0.000 0.032
#> ERR184064 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> ERR184081 2 0.0290 0.896 0.000 0.992 0.000 0.008 0.000
#> ERR184095 2 0.0290 0.896 0.000 0.992 0.000 0.008 0.000
#> ERR184079 4 0.3877 0.709 0.000 0.212 0.000 0.764 0.024
#> ERR184084 5 0.6529 0.587 0.168 0.000 0.392 0.004 0.436
#> ERR184068 4 0.3340 0.729 0.004 0.156 0.000 0.824 0.016
#> ERR184067 2 0.0510 0.893 0.000 0.984 0.000 0.016 0.000
#> ERR184071 4 0.4575 0.606 0.000 0.328 0.000 0.648 0.024
#> ERR184042 5 0.2692 0.577 0.008 0.000 0.092 0.016 0.884
#> ERR184063 3 0.0451 0.985 0.000 0.000 0.988 0.008 0.004
#> ERR184091 2 0.0880 0.891 0.000 0.968 0.000 0.000 0.032
#> ERR184061 4 0.2617 0.653 0.032 0.028 0.000 0.904 0.036
#> ERR184077 4 0.4025 0.662 0.000 0.292 0.000 0.700 0.008
#> ERR184062 4 0.2995 0.709 0.008 0.088 0.000 0.872 0.032
#> ERR184053 4 0.4206 0.664 0.000 0.288 0.000 0.696 0.016
#> ERR184088 4 0.4722 0.549 0.000 0.368 0.000 0.608 0.024
#> ERR184075 2 0.0880 0.891 0.000 0.968 0.000 0.000 0.032
#> ERR184041 3 0.0451 0.985 0.000 0.000 0.988 0.008 0.004
#> ERR184060 2 0.0290 0.896 0.000 0.992 0.000 0.008 0.000
#> ERR184035 4 0.1857 0.608 0.060 0.004 0.000 0.928 0.008
#> ERR184086 2 0.0880 0.891 0.000 0.968 0.000 0.000 0.032
#> ERR184080 1 0.3684 0.840 0.720 0.000 0.000 0.280 0.000
#> ERR184050 2 0.1661 0.882 0.000 0.940 0.000 0.024 0.036
#> ERR184047 5 0.4904 0.714 0.316 0.000 0.036 0.004 0.644
#> ERR184092 2 0.4746 0.162 0.000 0.600 0.000 0.376 0.024
#> ERR184072 1 0.3671 0.846 0.756 0.000 0.000 0.236 0.008
#> ERR184073 1 0.1981 0.595 0.920 0.000 0.064 0.000 0.016
#> ERR184066 1 0.4009 0.822 0.684 0.000 0.000 0.312 0.004
#> ERR184098 2 0.1597 0.879 0.000 0.940 0.000 0.012 0.048
#> ERR184044 4 0.1800 0.618 0.048 0.000 0.000 0.932 0.020
#> ERR184054 1 0.3242 0.850 0.784 0.000 0.000 0.216 0.000
#> ERR184085 4 0.1588 0.640 0.028 0.008 0.000 0.948 0.016
#> ERR184056 2 0.4484 0.369 0.000 0.668 0.000 0.308 0.024
#> ERR184052 2 0.2648 0.726 0.000 0.848 0.000 0.152 0.000
#> ERR184070 2 0.0290 0.896 0.000 0.992 0.000 0.008 0.000
#> ERR184096 5 0.4848 0.713 0.320 0.000 0.032 0.004 0.644
#> ERR184089 2 0.1750 0.880 0.000 0.936 0.000 0.028 0.036
#> ERR184049 4 0.1721 0.658 0.016 0.020 0.000 0.944 0.020
#> ERR184038 4 0.5087 -0.143 0.320 0.000 0.028 0.636 0.016
#> ERR184087 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000
#> ERR184097 2 0.4882 -0.123 0.000 0.532 0.000 0.444 0.024
#> ERR184094 5 0.6678 0.666 0.312 0.000 0.256 0.000 0.432
#> ERR184058 2 0.0510 0.894 0.000 0.984 0.000 0.000 0.016
#> ERR184036 4 0.4982 0.467 0.000 0.412 0.000 0.556 0.032
#> ERR184046 2 0.0451 0.896 0.000 0.988 0.000 0.008 0.004
#> ERR184074 1 0.3086 0.842 0.816 0.000 0.000 0.180 0.004
#> ERR184048 4 0.3730 0.664 0.000 0.288 0.000 0.712 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.0914 0.728 0.968 0.000 0.000 NA 0.016 0.000
#> ERR184093 6 0.3616 0.686 0.000 0.232 0.000 NA 0.008 0.748
#> ERR184051 3 0.0291 0.993 0.000 0.000 0.992 NA 0.000 0.004
#> ERR184076 1 0.1225 0.731 0.952 0.000 0.000 NA 0.012 0.000
#> ERR184043 3 0.0146 0.993 0.000 0.000 0.996 NA 0.004 0.000
#> ERR184037 1 0.5165 0.659 0.612 0.000 0.000 NA 0.004 0.116
#> ERR184059 5 0.3878 0.599 0.004 0.000 0.348 NA 0.644 0.000
#> ERR184055 1 0.4994 0.684 0.648 0.000 0.000 NA 0.004 0.120
#> ERR184065 2 0.2355 0.871 0.000 0.876 0.000 NA 0.008 0.004
#> ERR184069 2 0.0260 0.886 0.000 0.992 0.000 NA 0.000 0.008
#> ERR184040 1 0.3078 0.588 0.796 0.000 0.000 NA 0.192 0.000
#> ERR184057 2 0.0547 0.882 0.000 0.980 0.000 NA 0.000 0.020
#> ERR184082 6 0.3988 0.567 0.012 0.000 0.000 NA 0.004 0.660
#> ERR184083 2 0.0520 0.886 0.000 0.984 0.000 NA 0.000 0.008
#> ERR184039 2 0.2400 0.869 0.000 0.872 0.000 NA 0.008 0.004
#> ERR184064 3 0.0146 0.993 0.000 0.000 0.996 NA 0.004 0.000
#> ERR184081 2 0.0260 0.886 0.000 0.992 0.000 NA 0.000 0.008
#> ERR184095 2 0.0260 0.886 0.000 0.992 0.000 NA 0.000 0.008
#> ERR184079 6 0.1524 0.746 0.000 0.060 0.000 NA 0.008 0.932
#> ERR184084 5 0.4979 0.627 0.004 0.000 0.300 NA 0.624 0.008
#> ERR184068 6 0.3442 0.719 0.008 0.028 0.004 NA 0.012 0.832
#> ERR184067 2 0.0632 0.880 0.000 0.976 0.000 NA 0.000 0.024
#> ERR184071 6 0.2841 0.738 0.000 0.164 0.000 NA 0.000 0.824
#> ERR184042 5 0.4491 0.535 0.000 0.000 0.036 NA 0.576 0.000
#> ERR184063 3 0.0291 0.993 0.000 0.000 0.992 NA 0.000 0.004
#> ERR184091 2 0.2308 0.871 0.000 0.880 0.000 NA 0.008 0.004
#> ERR184061 6 0.3859 0.649 0.048 0.012 0.000 NA 0.004 0.788
#> ERR184077 6 0.4247 0.748 0.004 0.164 0.000 NA 0.008 0.752
#> ERR184062 6 0.2469 0.726 0.036 0.028 0.000 NA 0.012 0.904
#> ERR184053 6 0.4539 0.747 0.004 0.148 0.004 NA 0.008 0.740
#> ERR184088 6 0.2994 0.722 0.000 0.208 0.000 NA 0.000 0.788
#> ERR184075 2 0.2355 0.871 0.000 0.876 0.000 NA 0.008 0.004
#> ERR184041 3 0.0291 0.993 0.000 0.000 0.992 NA 0.000 0.004
#> ERR184060 2 0.0260 0.886 0.000 0.992 0.000 NA 0.000 0.008
#> ERR184035 6 0.4579 0.532 0.052 0.000 0.000 NA 0.004 0.644
#> ERR184086 2 0.2355 0.871 0.000 0.876 0.000 NA 0.008 0.004
#> ERR184080 1 0.3693 0.733 0.788 0.000 0.000 NA 0.000 0.092
#> ERR184050 2 0.3894 0.818 0.000 0.784 0.000 NA 0.008 0.088
#> ERR184047 5 0.1296 0.720 0.044 0.000 0.004 NA 0.948 0.000
#> ERR184092 6 0.3899 0.482 0.000 0.364 0.000 NA 0.008 0.628
#> ERR184072 1 0.1922 0.751 0.924 0.000 0.000 NA 0.012 0.040
#> ERR184073 1 0.3470 0.559 0.772 0.000 0.028 NA 0.200 0.000
#> ERR184066 1 0.4387 0.708 0.720 0.000 0.000 NA 0.000 0.152
#> ERR184098 2 0.4039 0.809 0.000 0.772 0.000 NA 0.008 0.104
#> ERR184044 6 0.4448 0.595 0.052 0.000 0.000 NA 0.008 0.688
#> ERR184054 1 0.0937 0.752 0.960 0.000 0.000 NA 0.000 0.040
#> ERR184085 6 0.4317 0.544 0.028 0.000 0.000 NA 0.004 0.640
#> ERR184056 2 0.4217 -0.107 0.000 0.524 0.000 NA 0.008 0.464
#> ERR184052 2 0.3671 0.666 0.000 0.756 0.000 NA 0.000 0.208
#> ERR184070 2 0.0260 0.886 0.000 0.992 0.000 NA 0.000 0.008
#> ERR184096 5 0.1493 0.719 0.056 0.000 0.004 NA 0.936 0.000
#> ERR184089 2 0.3989 0.811 0.000 0.776 0.000 NA 0.008 0.096
#> ERR184049 6 0.3618 0.644 0.012 0.008 0.000 NA 0.004 0.764
#> ERR184038 1 0.6564 0.189 0.368 0.000 0.012 NA 0.008 0.356
#> ERR184087 3 0.0146 0.993 0.000 0.000 0.996 NA 0.004 0.000
#> ERR184097 6 0.3940 0.543 0.000 0.336 0.000 NA 0.008 0.652
#> ERR184094 5 0.4888 0.657 0.116 0.000 0.240 NA 0.644 0.000
#> ERR184058 2 0.1219 0.882 0.000 0.948 0.000 NA 0.000 0.004
#> ERR184036 6 0.4178 0.696 0.000 0.208 0.000 NA 0.004 0.728
#> ERR184046 2 0.0260 0.886 0.000 0.992 0.000 NA 0.000 0.008
#> ERR184074 1 0.2883 0.745 0.860 0.000 0.000 NA 0.008 0.040
#> ERR184048 6 0.3522 0.753 0.004 0.148 0.000 NA 0.004 0.804
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 10269 rows and 62 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.974 0.988 0.5022 0.497 0.497
#> 3 3 0.786 0.812 0.893 0.2220 0.871 0.745
#> 4 4 0.549 0.631 0.793 0.1381 0.921 0.799
#> 5 5 0.552 0.512 0.741 0.0668 0.964 0.890
#> 6 6 0.565 0.488 0.710 0.0484 0.997 0.989
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
#> ERR184078 1 0.0000 0.979 1.000 0.000
#> ERR184093 2 0.0000 0.995 0.000 1.000
#> ERR184051 1 0.0000 0.979 1.000 0.000
#> ERR184076 1 0.0000 0.979 1.000 0.000
#> ERR184043 1 0.0000 0.979 1.000 0.000
#> ERR184037 1 0.0000 0.979 1.000 0.000
#> ERR184059 1 0.0000 0.979 1.000 0.000
#> ERR184055 1 0.0000 0.979 1.000 0.000
#> ERR184065 2 0.0000 0.995 0.000 1.000
#> ERR184069 2 0.0000 0.995 0.000 1.000
#> ERR184040 1 0.0000 0.979 1.000 0.000
#> ERR184057 2 0.0000 0.995 0.000 1.000
#> ERR184082 1 0.8909 0.570 0.692 0.308
#> ERR184083 2 0.0000 0.995 0.000 1.000
#> ERR184039 2 0.0000 0.995 0.000 1.000
#> ERR184064 1 0.0000 0.979 1.000 0.000
#> ERR184081 2 0.0000 0.995 0.000 1.000
#> ERR184095 2 0.0000 0.995 0.000 1.000
#> ERR184079 2 0.0000 0.995 0.000 1.000
#> ERR184084 1 0.0000 0.979 1.000 0.000
#> ERR184068 2 0.0376 0.991 0.004 0.996
#> ERR184067 2 0.0000 0.995 0.000 1.000
#> ERR184071 2 0.0000 0.995 0.000 1.000
#> ERR184042 1 0.0000 0.979 1.000 0.000
#> ERR184063 1 0.0000 0.979 1.000 0.000
#> ERR184091 2 0.0000 0.995 0.000 1.000
#> ERR184061 2 0.4431 0.896 0.092 0.908
#> ERR184077 2 0.0000 0.995 0.000 1.000
#> ERR184062 2 0.3879 0.916 0.076 0.924
#> ERR184053 2 0.0000 0.995 0.000 1.000
#> ERR184088 2 0.0000 0.995 0.000 1.000
#> ERR184075 2 0.0000 0.995 0.000 1.000
#> ERR184041 1 0.0000 0.979 1.000 0.000
#> ERR184060 2 0.0000 0.995 0.000 1.000
#> ERR184035 1 0.7602 0.726 0.780 0.220
#> ERR184086 2 0.0000 0.995 0.000 1.000
#> ERR184080 1 0.0000 0.979 1.000 0.000
#> ERR184050 2 0.0000 0.995 0.000 1.000
#> ERR184047 1 0.0000 0.979 1.000 0.000
#> ERR184092 2 0.0000 0.995 0.000 1.000
#> ERR184072 1 0.0000 0.979 1.000 0.000
#> ERR184073 1 0.0000 0.979 1.000 0.000
#> ERR184066 1 0.0000 0.979 1.000 0.000
#> ERR184098 2 0.0000 0.995 0.000 1.000
#> ERR184044 1 0.0000 0.979 1.000 0.000
#> ERR184054 1 0.0000 0.979 1.000 0.000
#> ERR184085 1 0.1843 0.955 0.972 0.028
#> ERR184056 2 0.0000 0.995 0.000 1.000
#> ERR184052 2 0.0000 0.995 0.000 1.000
#> ERR184070 2 0.0000 0.995 0.000 1.000
#> ERR184096 1 0.0000 0.979 1.000 0.000
#> ERR184089 2 0.0000 0.995 0.000 1.000
#> ERR184049 2 0.0000 0.995 0.000 1.000
#> ERR184038 1 0.0000 0.979 1.000 0.000
#> ERR184087 1 0.0000 0.979 1.000 0.000
#> ERR184097 2 0.0000 0.995 0.000 1.000
#> ERR184094 1 0.0000 0.979 1.000 0.000
#> ERR184058 2 0.0000 0.995 0.000 1.000
#> ERR184036 2 0.0000 0.995 0.000 1.000
#> ERR184046 2 0.0000 0.995 0.000 1.000
#> ERR184074 1 0.0000 0.979 1.000 0.000
#> ERR184048 2 0.0000 0.995 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.5397 0.7431 0.720 0.000 0.280
#> ERR184093 2 0.0892 0.9570 0.020 0.980 0.000
#> ERR184051 3 0.0000 0.8376 0.000 0.000 1.000
#> ERR184076 1 0.5465 0.7399 0.712 0.000 0.288
#> ERR184043 3 0.0000 0.8376 0.000 0.000 1.000
#> ERR184037 1 0.1529 0.6926 0.960 0.000 0.040
#> ERR184059 3 0.2959 0.8007 0.100 0.000 0.900
#> ERR184055 1 0.2796 0.7262 0.908 0.000 0.092
#> ERR184065 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184069 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184040 1 0.5678 0.7181 0.684 0.000 0.316
#> ERR184057 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184082 3 0.8142 0.4888 0.268 0.112 0.620
#> ERR184083 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184039 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184064 3 0.0000 0.8376 0.000 0.000 1.000
#> ERR184081 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184095 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184079 2 0.2448 0.9239 0.076 0.924 0.000
#> ERR184084 3 0.3116 0.7944 0.108 0.000 0.892
#> ERR184068 2 0.4978 0.7586 0.216 0.780 0.004
#> ERR184067 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184071 2 0.0424 0.9614 0.008 0.992 0.000
#> ERR184042 3 0.3192 0.7896 0.112 0.000 0.888
#> ERR184063 3 0.0000 0.8376 0.000 0.000 1.000
#> ERR184091 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184061 1 0.6936 -0.0843 0.524 0.460 0.016
#> ERR184077 2 0.1163 0.9535 0.028 0.972 0.000
#> ERR184062 2 0.5431 0.6269 0.284 0.716 0.000
#> ERR184053 2 0.1289 0.9521 0.032 0.968 0.000
#> ERR184088 2 0.1529 0.9462 0.040 0.960 0.000
#> ERR184075 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184041 3 0.0000 0.8376 0.000 0.000 1.000
#> ERR184060 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184035 1 0.1337 0.6561 0.972 0.012 0.016
#> ERR184086 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184080 1 0.2066 0.7088 0.940 0.000 0.060
#> ERR184050 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184047 1 0.5859 0.6849 0.656 0.000 0.344
#> ERR184092 2 0.0237 0.9622 0.004 0.996 0.000
#> ERR184072 1 0.4291 0.7590 0.820 0.000 0.180
#> ERR184073 1 0.5810 0.6963 0.664 0.000 0.336
#> ERR184066 1 0.4504 0.7608 0.804 0.000 0.196
#> ERR184098 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184044 1 0.6529 0.4050 0.620 0.012 0.368
#> ERR184054 1 0.4842 0.7606 0.776 0.000 0.224
#> ERR184085 3 0.5760 0.5808 0.328 0.000 0.672
#> ERR184056 2 0.0747 0.9585 0.016 0.984 0.000
#> ERR184052 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184070 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184096 1 0.5706 0.7144 0.680 0.000 0.320
#> ERR184089 2 0.2448 0.9075 0.000 0.924 0.076
#> ERR184049 2 0.6473 0.5905 0.312 0.668 0.020
#> ERR184038 3 0.2796 0.8073 0.092 0.000 0.908
#> ERR184087 3 0.0000 0.8376 0.000 0.000 1.000
#> ERR184097 2 0.0747 0.9585 0.016 0.984 0.000
#> ERR184094 3 0.6204 -0.0808 0.424 0.000 0.576
#> ERR184058 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184036 2 0.1860 0.9326 0.052 0.948 0.000
#> ERR184046 2 0.0000 0.9633 0.000 1.000 0.000
#> ERR184074 1 0.5016 0.7578 0.760 0.000 0.240
#> ERR184048 2 0.1529 0.9484 0.040 0.960 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.2888 0.7870 0.872 0.000 0.124 0.004
#> ERR184093 2 0.4331 0.5416 0.000 0.712 0.000 0.288
#> ERR184051 3 0.0707 0.8034 0.020 0.000 0.980 0.000
#> ERR184076 1 0.2888 0.7885 0.872 0.000 0.124 0.004
#> ERR184043 3 0.0707 0.8034 0.020 0.000 0.980 0.000
#> ERR184037 1 0.2944 0.6987 0.868 0.000 0.004 0.128
#> ERR184059 3 0.4164 0.6379 0.264 0.000 0.736 0.000
#> ERR184055 1 0.3354 0.7416 0.872 0.000 0.044 0.084
#> ERR184065 2 0.2402 0.7600 0.000 0.912 0.012 0.076
#> ERR184069 2 0.0817 0.7764 0.000 0.976 0.000 0.024
#> ERR184040 1 0.3219 0.7732 0.836 0.000 0.164 0.000
#> ERR184057 2 0.1389 0.7712 0.000 0.952 0.000 0.048
#> ERR184082 4 0.8449 0.2034 0.140 0.092 0.236 0.532
#> ERR184083 2 0.0817 0.7796 0.000 0.976 0.000 0.024
#> ERR184039 2 0.2676 0.7563 0.000 0.896 0.012 0.092
#> ERR184064 3 0.0817 0.8033 0.024 0.000 0.976 0.000
#> ERR184081 2 0.1109 0.7761 0.000 0.968 0.004 0.028
#> ERR184095 2 0.1940 0.7617 0.000 0.924 0.000 0.076
#> ERR184079 2 0.5597 -0.0889 0.020 0.516 0.000 0.464
#> ERR184084 3 0.4584 0.5722 0.300 0.000 0.696 0.004
#> ERR184068 4 0.6279 0.4275 0.060 0.348 0.004 0.588
#> ERR184067 2 0.1302 0.7770 0.000 0.956 0.000 0.044
#> ERR184071 2 0.3626 0.7041 0.004 0.812 0.000 0.184
#> ERR184042 3 0.4356 0.5959 0.292 0.000 0.708 0.000
#> ERR184063 3 0.0592 0.8020 0.016 0.000 0.984 0.000
#> ERR184091 2 0.2255 0.7623 0.000 0.920 0.012 0.068
#> ERR184061 4 0.8317 0.4931 0.224 0.324 0.024 0.428
#> ERR184077 2 0.5016 0.2660 0.004 0.600 0.000 0.396
#> ERR184062 4 0.7885 0.3930 0.148 0.352 0.024 0.476
#> ERR184053 2 0.5229 0.1293 0.008 0.564 0.000 0.428
#> ERR184088 2 0.4502 0.5819 0.016 0.748 0.000 0.236
#> ERR184075 2 0.2473 0.7610 0.000 0.908 0.012 0.080
#> ERR184041 3 0.0592 0.8020 0.016 0.000 0.984 0.000
#> ERR184060 2 0.0657 0.7775 0.000 0.984 0.004 0.012
#> ERR184035 1 0.5760 0.1245 0.520 0.020 0.004 0.456
#> ERR184086 2 0.2610 0.7576 0.000 0.900 0.012 0.088
#> ERR184080 1 0.2021 0.7568 0.936 0.000 0.024 0.040
#> ERR184050 2 0.2987 0.7518 0.000 0.880 0.016 0.104
#> ERR184047 1 0.3975 0.7111 0.760 0.000 0.240 0.000
#> ERR184092 2 0.3528 0.6670 0.000 0.808 0.000 0.192
#> ERR184072 1 0.4010 0.7789 0.836 0.000 0.100 0.064
#> ERR184073 1 0.4164 0.6824 0.736 0.000 0.264 0.000
#> ERR184066 1 0.4591 0.7483 0.800 0.000 0.116 0.084
#> ERR184098 2 0.2924 0.7519 0.000 0.884 0.016 0.100
#> ERR184044 1 0.7733 0.2032 0.476 0.004 0.292 0.228
#> ERR184054 1 0.3048 0.7890 0.876 0.000 0.108 0.016
#> ERR184085 3 0.7586 0.2931 0.200 0.000 0.436 0.364
#> ERR184056 2 0.3801 0.6329 0.000 0.780 0.000 0.220
#> ERR184052 2 0.2611 0.7557 0.000 0.896 0.008 0.096
#> ERR184070 2 0.0921 0.7745 0.000 0.972 0.000 0.028
#> ERR184096 1 0.3486 0.7582 0.812 0.000 0.188 0.000
#> ERR184089 2 0.5484 0.5410 0.000 0.736 0.132 0.132
#> ERR184049 4 0.6989 0.3909 0.100 0.412 0.004 0.484
#> ERR184038 3 0.4903 0.6496 0.248 0.000 0.724 0.028
#> ERR184087 3 0.0817 0.8033 0.024 0.000 0.976 0.000
#> ERR184097 2 0.3942 0.6029 0.000 0.764 0.000 0.236
#> ERR184094 1 0.4941 0.2776 0.564 0.000 0.436 0.000
#> ERR184058 2 0.1854 0.7695 0.000 0.940 0.012 0.048
#> ERR184036 2 0.4979 0.5583 0.032 0.740 0.004 0.224
#> ERR184046 2 0.0895 0.7797 0.000 0.976 0.004 0.020
#> ERR184074 1 0.3105 0.7884 0.868 0.000 0.120 0.012
#> ERR184048 2 0.5143 0.2834 0.012 0.628 0.000 0.360
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.1831 0.7571 0.920 0.000 0.076 0.004 0.000
#> ERR184093 2 0.4971 0.2412 0.004 0.628 0.000 0.036 0.332
#> ERR184051 3 0.0703 0.7594 0.024 0.000 0.976 0.000 0.000
#> ERR184076 1 0.2069 0.7533 0.924 0.000 0.052 0.012 0.012
#> ERR184043 3 0.0609 0.7597 0.020 0.000 0.980 0.000 0.000
#> ERR184037 1 0.4623 0.4574 0.640 0.000 0.008 0.340 0.012
#> ERR184059 3 0.4375 0.4802 0.364 0.000 0.628 0.004 0.004
#> ERR184055 1 0.4699 0.5916 0.716 0.000 0.016 0.236 0.032
#> ERR184065 2 0.3810 0.6333 0.000 0.792 0.000 0.040 0.168
#> ERR184069 2 0.1168 0.6809 0.000 0.960 0.000 0.032 0.008
#> ERR184040 1 0.2249 0.7543 0.896 0.000 0.096 0.008 0.000
#> ERR184057 2 0.2221 0.6633 0.000 0.912 0.000 0.036 0.052
#> ERR184082 4 0.8928 0.2764 0.112 0.072 0.140 0.384 0.292
#> ERR184083 2 0.1478 0.6865 0.000 0.936 0.000 0.000 0.064
#> ERR184039 2 0.3920 0.6369 0.000 0.796 0.004 0.044 0.156
#> ERR184064 3 0.0609 0.7597 0.020 0.000 0.980 0.000 0.000
#> ERR184081 2 0.1117 0.6810 0.000 0.964 0.000 0.016 0.020
#> ERR184095 2 0.2236 0.6569 0.000 0.908 0.000 0.024 0.068
#> ERR184079 5 0.6726 0.4117 0.000 0.388 0.004 0.208 0.400
#> ERR184084 3 0.4882 0.2716 0.440 0.000 0.540 0.012 0.008
#> ERR184068 5 0.7226 0.4619 0.028 0.284 0.004 0.212 0.472
#> ERR184067 2 0.2592 0.6710 0.000 0.892 0.000 0.056 0.052
#> ERR184071 2 0.5107 0.4936 0.000 0.688 0.000 0.108 0.204
#> ERR184042 3 0.4478 0.4810 0.360 0.000 0.628 0.004 0.008
#> ERR184063 3 0.0960 0.7494 0.016 0.000 0.972 0.004 0.008
#> ERR184091 2 0.3061 0.6611 0.000 0.844 0.000 0.020 0.136
#> ERR184061 4 0.7384 0.1447 0.080 0.200 0.016 0.564 0.140
#> ERR184077 2 0.5901 -0.2959 0.000 0.492 0.004 0.088 0.416
#> ERR184062 5 0.7019 0.3810 0.096 0.248 0.004 0.088 0.564
#> ERR184053 2 0.6586 -0.1750 0.004 0.524 0.012 0.148 0.312
#> ERR184088 2 0.5973 0.2567 0.008 0.632 0.004 0.204 0.152
#> ERR184075 2 0.3574 0.6490 0.000 0.804 0.000 0.028 0.168
#> ERR184041 3 0.0932 0.7562 0.020 0.000 0.972 0.004 0.004
#> ERR184060 2 0.0451 0.6809 0.000 0.988 0.000 0.004 0.008
#> ERR184035 4 0.7111 0.2904 0.316 0.008 0.016 0.464 0.196
#> ERR184086 2 0.2929 0.6620 0.000 0.840 0.000 0.008 0.152
#> ERR184080 1 0.3197 0.6778 0.836 0.000 0.000 0.140 0.024
#> ERR184050 2 0.4465 0.5880 0.000 0.732 0.000 0.056 0.212
#> ERR184047 1 0.3387 0.6756 0.796 0.000 0.196 0.004 0.004
#> ERR184092 2 0.3724 0.5416 0.000 0.788 0.000 0.028 0.184
#> ERR184072 1 0.4905 0.6767 0.768 0.000 0.052 0.096 0.084
#> ERR184073 1 0.3585 0.6511 0.772 0.000 0.220 0.004 0.004
#> ERR184066 1 0.4660 0.6527 0.772 0.000 0.028 0.068 0.132
#> ERR184098 2 0.4269 0.6120 0.000 0.756 0.000 0.056 0.188
#> ERR184044 1 0.8484 -0.0976 0.348 0.016 0.184 0.332 0.120
#> ERR184054 1 0.2684 0.7443 0.900 0.000 0.032 0.044 0.024
#> ERR184085 4 0.8547 0.2809 0.160 0.008 0.264 0.364 0.204
#> ERR184056 2 0.4347 0.4624 0.000 0.732 0.004 0.032 0.232
#> ERR184052 2 0.4094 0.6214 0.000 0.788 0.000 0.084 0.128
#> ERR184070 2 0.1117 0.6770 0.000 0.964 0.000 0.020 0.016
#> ERR184096 1 0.2660 0.7366 0.864 0.000 0.128 0.000 0.008
#> ERR184089 2 0.6917 0.3263 0.004 0.580 0.108 0.076 0.232
#> ERR184049 4 0.5876 0.0445 0.020 0.240 0.004 0.644 0.092
#> ERR184038 3 0.5781 0.5281 0.292 0.000 0.620 0.040 0.048
#> ERR184087 3 0.0609 0.7597 0.020 0.000 0.980 0.000 0.000
#> ERR184097 2 0.4086 0.3873 0.000 0.704 0.000 0.012 0.284
#> ERR184094 1 0.4530 0.2967 0.612 0.000 0.376 0.004 0.008
#> ERR184058 2 0.2464 0.6781 0.000 0.888 0.000 0.016 0.096
#> ERR184036 2 0.5759 0.2174 0.012 0.604 0.000 0.300 0.084
#> ERR184046 2 0.1124 0.6841 0.000 0.960 0.000 0.004 0.036
#> ERR184074 1 0.2795 0.7531 0.880 0.000 0.056 0.064 0.000
#> ERR184048 2 0.6403 -0.2250 0.000 0.512 0.000 0.232 0.256
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.2830 0.704 0.880 0.000 0.060 0.012 0.036 0.012
#> ERR184093 2 0.6143 0.147 0.000 0.516 0.000 0.324 0.052 0.108
#> ERR184051 3 0.0837 0.777 0.020 0.000 0.972 0.004 0.004 0.000
#> ERR184076 1 0.3954 0.697 0.820 0.000 0.068 0.052 0.036 0.024
#> ERR184043 3 0.0291 0.776 0.004 0.000 0.992 0.000 0.004 0.000
#> ERR184037 1 0.5985 0.393 0.596 0.000 0.004 0.044 0.136 0.220
#> ERR184059 3 0.3681 0.631 0.272 0.000 0.716 0.004 0.004 0.004
#> ERR184055 1 0.5839 0.513 0.648 0.000 0.012 0.088 0.072 0.180
#> ERR184065 2 0.3853 0.593 0.000 0.708 0.000 0.012 0.008 0.272
#> ERR184069 2 0.1257 0.644 0.000 0.952 0.000 0.020 0.000 0.028
#> ERR184040 1 0.2094 0.704 0.900 0.000 0.080 0.000 0.020 0.000
#> ERR184057 2 0.2151 0.623 0.000 0.904 0.000 0.072 0.008 0.016
#> ERR184082 5 0.7268 0.273 0.048 0.052 0.092 0.096 0.596 0.116
#> ERR184083 2 0.2462 0.650 0.000 0.876 0.000 0.028 0.000 0.096
#> ERR184039 2 0.4071 0.575 0.000 0.672 0.000 0.020 0.004 0.304
#> ERR184064 3 0.0260 0.779 0.008 0.000 0.992 0.000 0.000 0.000
#> ERR184081 2 0.1977 0.644 0.000 0.920 0.000 0.032 0.008 0.040
#> ERR184095 2 0.2491 0.614 0.000 0.868 0.000 0.112 0.000 0.020
#> ERR184079 4 0.7330 0.230 0.004 0.324 0.000 0.380 0.168 0.124
#> ERR184084 3 0.4832 0.513 0.324 0.000 0.612 0.000 0.056 0.008
#> ERR184068 4 0.6778 0.193 0.008 0.128 0.000 0.460 0.332 0.072
#> ERR184067 2 0.3185 0.622 0.000 0.852 0.000 0.060 0.024 0.064
#> ERR184071 2 0.6351 0.408 0.000 0.592 0.004 0.140 0.108 0.156
#> ERR184042 3 0.4088 0.571 0.308 0.000 0.668 0.000 0.020 0.004
#> ERR184063 3 0.0696 0.767 0.004 0.000 0.980 0.004 0.008 0.004
#> ERR184091 2 0.3189 0.616 0.000 0.760 0.000 0.004 0.000 0.236
#> ERR184061 6 0.8072 0.489 0.096 0.184 0.004 0.120 0.140 0.456
#> ERR184077 2 0.5951 -0.173 0.000 0.444 0.000 0.428 0.088 0.040
#> ERR184062 4 0.5727 0.258 0.044 0.156 0.000 0.680 0.068 0.052
#> ERR184053 2 0.6975 -0.181 0.000 0.412 0.000 0.340 0.128 0.120
#> ERR184088 2 0.6431 0.261 0.000 0.572 0.000 0.132 0.152 0.144
#> ERR184075 2 0.3809 0.581 0.000 0.684 0.000 0.004 0.008 0.304
#> ERR184041 3 0.0405 0.778 0.008 0.000 0.988 0.000 0.004 0.000
#> ERR184060 2 0.0291 0.641 0.000 0.992 0.000 0.004 0.000 0.004
#> ERR184035 5 0.5701 0.285 0.200 0.012 0.004 0.080 0.656 0.048
#> ERR184086 2 0.3781 0.624 0.000 0.756 0.000 0.036 0.004 0.204
#> ERR184080 1 0.3571 0.628 0.816 0.000 0.000 0.012 0.096 0.076
#> ERR184050 2 0.4871 0.500 0.000 0.592 0.000 0.040 0.016 0.352
#> ERR184047 1 0.3421 0.646 0.780 0.000 0.200 0.004 0.012 0.004
#> ERR184092 2 0.4948 0.413 0.000 0.660 0.000 0.244 0.016 0.080
#> ERR184072 1 0.5640 0.534 0.672 0.000 0.012 0.116 0.144 0.056
#> ERR184073 1 0.3686 0.632 0.756 0.000 0.220 0.008 0.008 0.008
#> ERR184066 1 0.6160 0.519 0.648 0.000 0.044 0.148 0.092 0.068
#> ERR184098 2 0.4319 0.586 0.000 0.696 0.000 0.036 0.012 0.256
#> ERR184044 1 0.9070 -0.225 0.272 0.016 0.144 0.260 0.144 0.164
#> ERR184054 1 0.3969 0.684 0.820 0.000 0.048 0.028 0.068 0.036
#> ERR184085 5 0.8127 0.328 0.124 0.008 0.204 0.100 0.452 0.112
#> ERR184056 2 0.4303 0.404 0.000 0.676 0.000 0.284 0.008 0.032
#> ERR184052 2 0.4529 0.594 0.000 0.748 0.000 0.052 0.056 0.144
#> ERR184070 2 0.1082 0.635 0.000 0.956 0.000 0.040 0.000 0.004
#> ERR184096 1 0.2386 0.694 0.876 0.000 0.112 0.004 0.004 0.004
#> ERR184089 2 0.6506 0.300 0.000 0.460 0.064 0.048 0.036 0.392
#> ERR184049 6 0.7452 0.488 0.032 0.164 0.000 0.092 0.260 0.452
#> ERR184038 3 0.6643 0.442 0.256 0.000 0.552 0.048 0.100 0.044
#> ERR184087 3 0.0363 0.779 0.012 0.000 0.988 0.000 0.000 0.000
#> ERR184097 2 0.5136 0.284 0.000 0.612 0.000 0.308 0.044 0.036
#> ERR184094 1 0.4409 0.284 0.596 0.000 0.380 0.004 0.008 0.012
#> ERR184058 2 0.2402 0.642 0.000 0.856 0.000 0.004 0.000 0.140
#> ERR184036 2 0.6801 0.114 0.016 0.496 0.000 0.104 0.084 0.300
#> ERR184046 2 0.1802 0.650 0.000 0.916 0.000 0.012 0.000 0.072
#> ERR184074 1 0.3559 0.698 0.840 0.000 0.056 0.008 0.052 0.044
#> ERR184048 2 0.7097 -0.200 0.000 0.420 0.000 0.232 0.256 0.092
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 10269 rows and 62 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 0.932 0.933 0.971 0.5021 0.497 0.497
#> 3 3 0.930 0.936 0.972 0.1806 0.882 0.771
#> 4 4 0.770 0.878 0.852 0.0481 0.996 0.990
#> 5 5 0.740 0.837 0.925 0.0242 0.991 0.978
#> 6 6 0.728 0.837 0.892 0.0956 0.854 0.641
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
#> ERR184078 1 0.0000 0.96524 1.000 0.000
#> ERR184093 2 0.0000 0.97225 0.000 1.000
#> ERR184051 1 0.0000 0.96524 1.000 0.000
#> ERR184076 1 0.0000 0.96524 1.000 0.000
#> ERR184043 1 0.0000 0.96524 1.000 0.000
#> ERR184037 1 0.0000 0.96524 1.000 0.000
#> ERR184059 1 0.0000 0.96524 1.000 0.000
#> ERR184055 1 0.0000 0.96524 1.000 0.000
#> ERR184065 2 0.0000 0.97225 0.000 1.000
#> ERR184069 2 0.0000 0.97225 0.000 1.000
#> ERR184040 1 0.0000 0.96524 1.000 0.000
#> ERR184057 2 0.0000 0.97225 0.000 1.000
#> ERR184082 2 0.3584 0.92444 0.068 0.932
#> ERR184083 2 0.0000 0.97225 0.000 1.000
#> ERR184039 2 0.0000 0.97225 0.000 1.000
#> ERR184064 1 0.0000 0.96524 1.000 0.000
#> ERR184081 2 0.0000 0.97225 0.000 1.000
#> ERR184095 2 0.0000 0.97225 0.000 1.000
#> ERR184079 2 0.3274 0.93032 0.060 0.940
#> ERR184084 1 0.0000 0.96524 1.000 0.000
#> ERR184068 2 0.7602 0.73191 0.220 0.780
#> ERR184067 2 0.0000 0.97225 0.000 1.000
#> ERR184071 2 0.0672 0.96783 0.008 0.992
#> ERR184042 1 0.0000 0.96524 1.000 0.000
#> ERR184063 1 0.1843 0.94193 0.972 0.028
#> ERR184091 2 0.0000 0.97225 0.000 1.000
#> ERR184061 1 0.7950 0.67699 0.760 0.240
#> ERR184077 2 0.0000 0.97225 0.000 1.000
#> ERR184062 1 0.9993 0.00075 0.516 0.484
#> ERR184053 2 0.4815 0.88809 0.104 0.896
#> ERR184088 2 0.0672 0.96784 0.008 0.992
#> ERR184075 2 0.0000 0.97225 0.000 1.000
#> ERR184041 1 0.0376 0.96213 0.996 0.004
#> ERR184060 2 0.0000 0.97225 0.000 1.000
#> ERR184035 1 0.5629 0.82914 0.868 0.132
#> ERR184086 2 0.0000 0.97225 0.000 1.000
#> ERR184080 1 0.0000 0.96524 1.000 0.000
#> ERR184050 2 0.0000 0.97225 0.000 1.000
#> ERR184047 1 0.0000 0.96524 1.000 0.000
#> ERR184092 2 0.0000 0.97225 0.000 1.000
#> ERR184072 1 0.0000 0.96524 1.000 0.000
#> ERR184073 1 0.0000 0.96524 1.000 0.000
#> ERR184066 1 0.0000 0.96524 1.000 0.000
#> ERR184098 2 0.0000 0.97225 0.000 1.000
#> ERR184044 1 0.0000 0.96524 1.000 0.000
#> ERR184054 1 0.0000 0.96524 1.000 0.000
#> ERR184085 2 0.8144 0.67031 0.252 0.748
#> ERR184056 2 0.0000 0.97225 0.000 1.000
#> ERR184052 2 0.0000 0.97225 0.000 1.000
#> ERR184070 2 0.0000 0.97225 0.000 1.000
#> ERR184096 1 0.0000 0.96524 1.000 0.000
#> ERR184089 2 0.0000 0.97225 0.000 1.000
#> ERR184049 2 0.4161 0.90971 0.084 0.916
#> ERR184038 1 0.0000 0.96524 1.000 0.000
#> ERR184087 1 0.0000 0.96524 1.000 0.000
#> ERR184097 2 0.0376 0.97015 0.004 0.996
#> ERR184094 1 0.0000 0.96524 1.000 0.000
#> ERR184058 2 0.0000 0.97225 0.000 1.000
#> ERR184036 2 0.0000 0.97225 0.000 1.000
#> ERR184046 2 0.0000 0.97225 0.000 1.000
#> ERR184074 1 0.0000 0.96524 1.000 0.000
#> ERR184048 2 0.3879 0.91653 0.076 0.924
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.0000 0.967 1.000 0.000 0.000
#> ERR184093 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184051 3 0.0000 0.984 0.000 0.000 1.000
#> ERR184076 1 0.0000 0.967 1.000 0.000 0.000
#> ERR184043 3 0.0000 0.984 0.000 0.000 1.000
#> ERR184037 1 0.0000 0.967 1.000 0.000 0.000
#> ERR184059 3 0.0000 0.984 0.000 0.000 1.000
#> ERR184055 1 0.0000 0.967 1.000 0.000 0.000
#> ERR184065 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184069 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184040 1 0.0000 0.967 1.000 0.000 0.000
#> ERR184057 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184082 2 0.2261 0.918 0.068 0.932 0.000
#> ERR184083 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184039 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184064 3 0.0000 0.984 0.000 0.000 1.000
#> ERR184081 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184095 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184079 2 0.2066 0.924 0.060 0.940 0.000
#> ERR184084 3 0.3412 0.852 0.124 0.000 0.876
#> ERR184068 2 0.4796 0.741 0.220 0.780 0.000
#> ERR184067 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184071 2 0.0424 0.959 0.008 0.992 0.000
#> ERR184042 3 0.0000 0.984 0.000 0.000 1.000
#> ERR184063 3 0.0000 0.984 0.000 0.000 1.000
#> ERR184091 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184061 1 0.4002 0.750 0.840 0.160 0.000
#> ERR184077 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184062 2 0.6111 0.386 0.396 0.604 0.000
#> ERR184053 2 0.3038 0.885 0.104 0.896 0.000
#> ERR184088 2 0.0424 0.959 0.008 0.992 0.000
#> ERR184075 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184041 3 0.0000 0.984 0.000 0.000 1.000
#> ERR184060 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184035 1 0.0000 0.967 1.000 0.000 0.000
#> ERR184086 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184080 1 0.0000 0.967 1.000 0.000 0.000
#> ERR184050 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184047 1 0.5591 0.566 0.696 0.000 0.304
#> ERR184092 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184072 1 0.0000 0.967 1.000 0.000 0.000
#> ERR184073 1 0.0237 0.964 0.996 0.000 0.004
#> ERR184066 1 0.0000 0.967 1.000 0.000 0.000
#> ERR184098 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184044 1 0.0424 0.959 0.992 0.008 0.000
#> ERR184054 1 0.0000 0.967 1.000 0.000 0.000
#> ERR184085 2 0.3482 0.855 0.128 0.872 0.000
#> ERR184056 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184052 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184070 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184096 1 0.0000 0.967 1.000 0.000 0.000
#> ERR184089 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184049 2 0.2625 0.905 0.084 0.916 0.000
#> ERR184038 1 0.0000 0.967 1.000 0.000 0.000
#> ERR184087 3 0.0000 0.984 0.000 0.000 1.000
#> ERR184097 2 0.0237 0.961 0.004 0.996 0.000
#> ERR184094 1 0.0424 0.961 0.992 0.000 0.008
#> ERR184058 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184036 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184046 2 0.0000 0.963 0.000 1.000 0.000
#> ERR184074 1 0.0000 0.967 1.000 0.000 0.000
#> ERR184048 2 0.2448 0.911 0.076 0.924 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> ERR184093 2 0.2814 0.881 0.000 0.868 0.000 0.132
#> ERR184051 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> ERR184076 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> ERR184043 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> ERR184037 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> ERR184059 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> ERR184055 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> ERR184065 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> ERR184069 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> ERR184040 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> ERR184057 2 0.1022 0.914 0.000 0.968 0.000 0.032
#> ERR184082 2 0.3383 0.885 0.052 0.872 0.000 0.076
#> ERR184083 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> ERR184039 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> ERR184064 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> ERR184081 2 0.1022 0.914 0.000 0.968 0.000 0.032
#> ERR184095 2 0.0336 0.917 0.000 0.992 0.000 0.008
#> ERR184079 2 0.3790 0.861 0.016 0.820 0.000 0.164
#> ERR184084 3 0.2704 0.730 0.124 0.000 0.876 0.000
#> ERR184068 2 0.4820 0.824 0.060 0.772 0.000 0.168
#> ERR184067 2 0.1022 0.914 0.000 0.968 0.000 0.032
#> ERR184071 2 0.3610 0.857 0.000 0.800 0.000 0.200
#> ERR184042 4 0.3610 0.000 0.000 0.000 0.200 0.800
#> ERR184063 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> ERR184091 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> ERR184061 1 0.4244 0.659 0.804 0.160 0.000 0.036
#> ERR184077 2 0.3610 0.857 0.000 0.800 0.000 0.200
#> ERR184062 2 0.6790 0.567 0.228 0.604 0.000 0.168
#> ERR184053 2 0.3610 0.857 0.000 0.800 0.000 0.200
#> ERR184088 2 0.3024 0.883 0.000 0.852 0.000 0.148
#> ERR184075 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> ERR184041 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> ERR184060 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> ERR184035 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> ERR184086 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> ERR184080 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> ERR184050 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> ERR184047 1 0.4431 0.528 0.696 0.000 0.304 0.000
#> ERR184092 2 0.3172 0.876 0.000 0.840 0.000 0.160
#> ERR184072 1 0.1211 0.913 0.960 0.000 0.000 0.040
#> ERR184073 1 0.0188 0.940 0.996 0.000 0.004 0.000
#> ERR184066 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> ERR184098 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> ERR184044 1 0.3636 0.748 0.820 0.008 0.000 0.172
#> ERR184054 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> ERR184085 2 0.4374 0.806 0.120 0.812 0.000 0.068
#> ERR184056 2 0.3610 0.857 0.000 0.800 0.000 0.200
#> ERR184052 2 0.0469 0.917 0.000 0.988 0.000 0.012
#> ERR184070 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> ERR184096 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> ERR184089 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> ERR184049 2 0.3090 0.889 0.056 0.888 0.000 0.056
#> ERR184038 1 0.1118 0.916 0.964 0.000 0.000 0.036
#> ERR184087 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> ERR184097 2 0.3610 0.857 0.000 0.800 0.000 0.200
#> ERR184094 1 0.0336 0.937 0.992 0.000 0.008 0.000
#> ERR184058 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> ERR184036 2 0.0817 0.915 0.000 0.976 0.000 0.024
#> ERR184046 2 0.0000 0.918 0.000 1.000 0.000 0.000
#> ERR184074 1 0.0000 0.942 1.000 0.000 0.000 0.000
#> ERR184048 2 0.3577 0.877 0.012 0.832 0.000 0.156
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.0000 0.913 1.000 0.000 0.000 0 0.000
#> ERR184093 2 0.2929 0.844 0.000 0.820 0.000 0 0.180
#> ERR184051 3 0.0000 0.971 0.000 0.000 1.000 0 0.000
#> ERR184076 1 0.0000 0.913 1.000 0.000 0.000 0 0.000
#> ERR184043 3 0.0000 0.971 0.000 0.000 1.000 0 0.000
#> ERR184037 1 0.0000 0.913 1.000 0.000 0.000 0 0.000
#> ERR184059 3 0.0000 0.971 0.000 0.000 1.000 0 0.000
#> ERR184055 1 0.0000 0.913 1.000 0.000 0.000 0 0.000
#> ERR184065 2 0.0000 0.903 0.000 1.000 0.000 0 0.000
#> ERR184069 2 0.0000 0.903 0.000 1.000 0.000 0 0.000
#> ERR184040 1 0.0000 0.913 1.000 0.000 0.000 0 0.000
#> ERR184057 2 0.0880 0.899 0.000 0.968 0.000 0 0.032
#> ERR184082 2 0.2974 0.869 0.052 0.868 0.000 0 0.080
#> ERR184083 2 0.0000 0.903 0.000 1.000 0.000 0 0.000
#> ERR184039 2 0.0000 0.903 0.000 1.000 0.000 0 0.000
#> ERR184064 3 0.0000 0.971 0.000 0.000 1.000 0 0.000
#> ERR184081 2 0.0880 0.899 0.000 0.968 0.000 0 0.032
#> ERR184095 2 0.0290 0.903 0.000 0.992 0.000 0 0.008
#> ERR184079 2 0.3487 0.826 0.008 0.780 0.000 0 0.212
#> ERR184084 3 0.2329 0.779 0.124 0.000 0.876 0 0.000
#> ERR184068 2 0.4295 0.798 0.044 0.740 0.000 0 0.216
#> ERR184067 2 0.0880 0.899 0.000 0.968 0.000 0 0.032
#> ERR184071 2 0.3452 0.820 0.000 0.756 0.000 0 0.244
#> ERR184042 4 0.0000 0.000 0.000 0.000 0.000 1 0.000
#> ERR184063 3 0.0000 0.971 0.000 0.000 1.000 0 0.000
#> ERR184091 2 0.0000 0.903 0.000 1.000 0.000 0 0.000
#> ERR184061 1 0.3655 0.530 0.804 0.160 0.000 0 0.036
#> ERR184077 2 0.3480 0.817 0.000 0.752 0.000 0 0.248
#> ERR184062 2 0.6008 0.556 0.200 0.584 0.000 0 0.216
#> ERR184053 2 0.3480 0.817 0.000 0.752 0.000 0 0.248
#> ERR184088 2 0.2813 0.861 0.000 0.832 0.000 0 0.168
#> ERR184075 2 0.0000 0.903 0.000 1.000 0.000 0 0.000
#> ERR184041 3 0.0000 0.971 0.000 0.000 1.000 0 0.000
#> ERR184060 2 0.0000 0.903 0.000 1.000 0.000 0 0.000
#> ERR184035 1 0.0000 0.913 1.000 0.000 0.000 0 0.000
#> ERR184086 2 0.0000 0.903 0.000 1.000 0.000 0 0.000
#> ERR184080 1 0.0000 0.913 1.000 0.000 0.000 0 0.000
#> ERR184050 2 0.0000 0.903 0.000 1.000 0.000 0 0.000
#> ERR184047 5 0.3607 0.000 0.244 0.000 0.004 0 0.752
#> ERR184092 2 0.3177 0.838 0.000 0.792 0.000 0 0.208
#> ERR184072 1 0.1043 0.875 0.960 0.000 0.000 0 0.040
#> ERR184073 1 0.0162 0.911 0.996 0.000 0.004 0 0.000
#> ERR184066 1 0.0000 0.913 1.000 0.000 0.000 0 0.000
#> ERR184098 2 0.0000 0.903 0.000 1.000 0.000 0 0.000
#> ERR184044 1 0.3551 0.558 0.772 0.008 0.000 0 0.220
#> ERR184054 1 0.0000 0.913 1.000 0.000 0.000 0 0.000
#> ERR184085 2 0.3814 0.792 0.124 0.808 0.000 0 0.068
#> ERR184056 2 0.3480 0.817 0.000 0.752 0.000 0 0.248
#> ERR184052 2 0.0404 0.902 0.000 0.988 0.000 0 0.012
#> ERR184070 2 0.0000 0.903 0.000 1.000 0.000 0 0.000
#> ERR184096 1 0.3913 0.269 0.676 0.000 0.000 0 0.324
#> ERR184089 2 0.0000 0.903 0.000 1.000 0.000 0 0.000
#> ERR184049 2 0.2729 0.873 0.056 0.884 0.000 0 0.060
#> ERR184038 1 0.0963 0.880 0.964 0.000 0.000 0 0.036
#> ERR184087 3 0.0000 0.971 0.000 0.000 1.000 0 0.000
#> ERR184097 2 0.3480 0.817 0.000 0.752 0.000 0 0.248
#> ERR184094 1 0.0290 0.907 0.992 0.000 0.008 0 0.000
#> ERR184058 2 0.0000 0.903 0.000 1.000 0.000 0 0.000
#> ERR184036 2 0.0703 0.901 0.000 0.976 0.000 0 0.024
#> ERR184046 2 0.0000 0.903 0.000 1.000 0.000 0 0.000
#> ERR184074 1 0.0000 0.913 1.000 0.000 0.000 0 0.000
#> ERR184048 2 0.3123 0.862 0.012 0.828 0.000 0 0.160
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.0000 0.942 1.000 0.000 0.000 0 0.000 0.000
#> ERR184093 6 0.3747 0.836 0.000 0.396 0.000 0 0.000 0.604
#> ERR184051 3 0.0000 0.971 0.000 0.000 1.000 0 0.000 0.000
#> ERR184076 1 0.0000 0.942 1.000 0.000 0.000 0 0.000 0.000
#> ERR184043 3 0.0000 0.971 0.000 0.000 1.000 0 0.000 0.000
#> ERR184037 1 0.0000 0.942 1.000 0.000 0.000 0 0.000 0.000
#> ERR184059 3 0.0000 0.971 0.000 0.000 1.000 0 0.000 0.000
#> ERR184055 1 0.0000 0.942 1.000 0.000 0.000 0 0.000 0.000
#> ERR184065 2 0.0000 0.925 0.000 1.000 0.000 0 0.000 0.000
#> ERR184069 2 0.0000 0.925 0.000 1.000 0.000 0 0.000 0.000
#> ERR184040 1 0.0000 0.942 1.000 0.000 0.000 0 0.000 0.000
#> ERR184057 2 0.0790 0.906 0.000 0.968 0.000 0 0.000 0.032
#> ERR184082 2 0.3496 0.681 0.052 0.804 0.000 0 0.004 0.140
#> ERR184083 2 0.0000 0.925 0.000 1.000 0.000 0 0.000 0.000
#> ERR184039 2 0.0000 0.925 0.000 1.000 0.000 0 0.000 0.000
#> ERR184064 3 0.0000 0.971 0.000 0.000 1.000 0 0.000 0.000
#> ERR184081 2 0.0790 0.906 0.000 0.968 0.000 0 0.000 0.032
#> ERR184095 2 0.0260 0.922 0.000 0.992 0.000 0 0.000 0.008
#> ERR184079 6 0.3887 0.873 0.008 0.360 0.000 0 0.000 0.632
#> ERR184084 3 0.2092 0.784 0.124 0.000 0.876 0 0.000 0.000
#> ERR184068 6 0.4249 0.875 0.032 0.328 0.000 0 0.000 0.640
#> ERR184067 2 0.0935 0.904 0.000 0.964 0.000 0 0.004 0.032
#> ERR184071 6 0.3756 0.803 0.000 0.400 0.000 0 0.000 0.600
#> ERR184042 4 0.0000 0.000 0.000 0.000 0.000 1 0.000 0.000
#> ERR184063 3 0.0000 0.971 0.000 0.000 1.000 0 0.000 0.000
#> ERR184091 2 0.0000 0.925 0.000 1.000 0.000 0 0.000 0.000
#> ERR184061 1 0.3236 0.675 0.820 0.140 0.000 0 0.004 0.036
#> ERR184077 6 0.3531 0.885 0.000 0.328 0.000 0 0.000 0.672
#> ERR184062 6 0.4393 0.864 0.044 0.316 0.000 0 0.000 0.640
#> ERR184053 6 0.3531 0.885 0.000 0.328 0.000 0 0.000 0.672
#> ERR184088 2 0.3244 0.471 0.000 0.732 0.000 0 0.000 0.268
#> ERR184075 2 0.0000 0.925 0.000 1.000 0.000 0 0.000 0.000
#> ERR184041 3 0.0000 0.971 0.000 0.000 1.000 0 0.000 0.000
#> ERR184060 2 0.0000 0.925 0.000 1.000 0.000 0 0.000 0.000
#> ERR184035 1 0.0000 0.942 1.000 0.000 0.000 0 0.000 0.000
#> ERR184086 2 0.0000 0.925 0.000 1.000 0.000 0 0.000 0.000
#> ERR184080 1 0.0000 0.942 1.000 0.000 0.000 0 0.000 0.000
#> ERR184050 2 0.0000 0.925 0.000 1.000 0.000 0 0.000 0.000
#> ERR184047 5 0.0146 0.000 0.004 0.000 0.000 0 0.996 0.000
#> ERR184092 6 0.3672 0.858 0.000 0.368 0.000 0 0.000 0.632
#> ERR184072 1 0.0937 0.910 0.960 0.000 0.000 0 0.000 0.040
#> ERR184073 1 0.0146 0.940 0.996 0.000 0.004 0 0.000 0.000
#> ERR184066 1 0.0363 0.934 0.988 0.000 0.000 0 0.000 0.012
#> ERR184098 2 0.0000 0.925 0.000 1.000 0.000 0 0.000 0.000
#> ERR184044 6 0.3983 0.163 0.348 0.008 0.000 0 0.004 0.640
#> ERR184054 1 0.0000 0.942 1.000 0.000 0.000 0 0.000 0.000
#> ERR184085 2 0.4078 0.577 0.180 0.748 0.000 0 0.004 0.068
#> ERR184056 6 0.3531 0.885 0.000 0.328 0.000 0 0.000 0.672
#> ERR184052 2 0.0363 0.920 0.000 0.988 0.000 0 0.000 0.012
#> ERR184070 2 0.0000 0.925 0.000 1.000 0.000 0 0.000 0.000
#> ERR184096 1 0.5325 0.265 0.548 0.000 0.000 0 0.124 0.328
#> ERR184089 2 0.0000 0.925 0.000 1.000 0.000 0 0.000 0.000
#> ERR184049 2 0.3395 0.729 0.056 0.816 0.000 0 0.004 0.124
#> ERR184038 1 0.0865 0.914 0.964 0.000 0.000 0 0.000 0.036
#> ERR184087 3 0.0000 0.971 0.000 0.000 1.000 0 0.000 0.000
#> ERR184097 6 0.3531 0.885 0.000 0.328 0.000 0 0.000 0.672
#> ERR184094 1 0.0260 0.937 0.992 0.000 0.008 0 0.000 0.000
#> ERR184058 2 0.0000 0.925 0.000 1.000 0.000 0 0.000 0.000
#> ERR184036 2 0.0777 0.910 0.000 0.972 0.000 0 0.004 0.024
#> ERR184046 2 0.0000 0.925 0.000 1.000 0.000 0 0.000 0.000
#> ERR184074 1 0.0000 0.942 1.000 0.000 0.000 0 0.000 0.000
#> ERR184048 2 0.3454 0.591 0.012 0.760 0.000 0 0.004 0.224
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 10269 rows and 62 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 5.
#>
#> 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 0.445 0.735 0.870 0.3247 0.748 0.748
#> 3 3 0.312 0.616 0.778 0.5944 0.689 0.592
#> 4 4 0.579 0.771 0.869 0.1427 0.896 0.795
#> 5 5 0.673 0.791 0.884 0.1677 0.854 0.680
#> 6 6 0.634 0.610 0.803 0.0772 0.969 0.907
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
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
#> ERR184078 2 0.9635 0.483 0.388 0.612
#> ERR184093 2 0.0000 0.823 0.000 1.000
#> ERR184051 1 0.6531 0.854 0.832 0.168
#> ERR184076 2 0.9635 0.483 0.388 0.612
#> ERR184043 1 0.2236 0.875 0.964 0.036
#> ERR184037 2 0.9427 0.527 0.360 0.640
#> ERR184059 1 0.7602 0.772 0.780 0.220
#> ERR184055 2 0.9427 0.527 0.360 0.640
#> ERR184065 2 0.0672 0.823 0.008 0.992
#> ERR184069 2 0.0000 0.823 0.000 1.000
#> ERR184040 2 0.9635 0.483 0.388 0.612
#> ERR184057 2 0.0000 0.823 0.000 1.000
#> ERR184082 2 0.1843 0.817 0.028 0.972
#> ERR184083 2 0.0672 0.823 0.008 0.992
#> ERR184039 2 0.0672 0.823 0.008 0.992
#> ERR184064 1 0.2236 0.875 0.964 0.036
#> ERR184081 2 0.0672 0.823 0.008 0.992
#> ERR184095 2 0.0000 0.823 0.000 1.000
#> ERR184079 2 0.0000 0.823 0.000 1.000
#> ERR184084 1 0.5294 0.852 0.880 0.120
#> ERR184068 2 0.3114 0.797 0.056 0.944
#> ERR184067 2 0.0000 0.823 0.000 1.000
#> ERR184071 2 0.0672 0.823 0.008 0.992
#> ERR184042 1 0.0000 0.840 1.000 0.000
#> ERR184063 1 0.6623 0.851 0.828 0.172
#> ERR184091 2 0.0672 0.823 0.008 0.992
#> ERR184061 2 0.0376 0.823 0.004 0.996
#> ERR184077 2 0.0000 0.823 0.000 1.000
#> ERR184062 2 0.9552 0.500 0.376 0.624
#> ERR184053 2 0.0672 0.823 0.008 0.992
#> ERR184088 2 0.0000 0.823 0.000 1.000
#> ERR184075 2 0.0672 0.823 0.008 0.992
#> ERR184041 1 0.6623 0.851 0.828 0.172
#> ERR184060 2 0.0000 0.823 0.000 1.000
#> ERR184035 2 0.6801 0.712 0.180 0.820
#> ERR184086 2 0.0672 0.823 0.008 0.992
#> ERR184080 2 0.9427 0.527 0.360 0.640
#> ERR184050 2 0.0672 0.823 0.008 0.992
#> ERR184047 2 0.9635 0.483 0.388 0.612
#> ERR184092 2 0.0000 0.823 0.000 1.000
#> ERR184072 2 0.9635 0.483 0.388 0.612
#> ERR184073 2 0.9635 0.483 0.388 0.612
#> ERR184066 2 0.9635 0.483 0.388 0.612
#> ERR184098 2 0.0672 0.823 0.008 0.992
#> ERR184044 2 0.8144 0.652 0.252 0.748
#> ERR184054 2 0.9635 0.483 0.388 0.612
#> ERR184085 2 0.7883 0.669 0.236 0.764
#> ERR184056 2 0.0000 0.823 0.000 1.000
#> ERR184052 2 0.0672 0.823 0.008 0.992
#> ERR184070 2 0.0672 0.823 0.008 0.992
#> ERR184096 2 0.9635 0.483 0.388 0.612
#> ERR184089 2 0.3114 0.803 0.056 0.944
#> ERR184049 2 0.0000 0.823 0.000 1.000
#> ERR184038 2 0.9552 0.512 0.376 0.624
#> ERR184087 1 0.2236 0.875 0.964 0.036
#> ERR184097 2 0.0000 0.823 0.000 1.000
#> ERR184094 2 0.9686 0.477 0.396 0.604
#> ERR184058 2 0.0672 0.823 0.008 0.992
#> ERR184036 2 0.0000 0.823 0.000 1.000
#> ERR184046 2 0.0376 0.823 0.004 0.996
#> ERR184074 2 0.9427 0.527 0.360 0.640
#> ERR184048 2 0.0000 0.823 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.6008 0.5766 0.664 0.332 0.004
#> ERR184093 2 0.4768 0.7559 0.100 0.848 0.052
#> ERR184051 3 0.3921 0.9411 0.112 0.016 0.872
#> ERR184076 1 0.6057 0.5715 0.656 0.340 0.004
#> ERR184043 3 0.2625 0.9354 0.084 0.000 0.916
#> ERR184037 2 0.7584 -0.3567 0.472 0.488 0.040
#> ERR184059 1 0.6701 -0.2321 0.576 0.012 0.412
#> ERR184055 1 0.6809 0.3439 0.524 0.464 0.012
#> ERR184065 2 0.2959 0.6986 0.000 0.900 0.100
#> ERR184069 2 0.0592 0.7613 0.012 0.988 0.000
#> ERR184040 1 0.5919 0.6134 0.724 0.260 0.016
#> ERR184057 2 0.0747 0.7621 0.016 0.984 0.000
#> ERR184082 2 0.7267 0.5678 0.268 0.668 0.064
#> ERR184083 2 0.2590 0.7671 0.072 0.924 0.004
#> ERR184039 2 0.2625 0.7108 0.000 0.916 0.084
#> ERR184064 3 0.2878 0.9499 0.096 0.000 0.904
#> ERR184081 2 0.0424 0.7605 0.008 0.992 0.000
#> ERR184095 2 0.1411 0.7623 0.036 0.964 0.000
#> ERR184079 2 0.6107 0.7031 0.184 0.764 0.052
#> ERR184084 1 0.7676 -0.0928 0.584 0.056 0.360
#> ERR184068 2 0.6703 0.6548 0.236 0.712 0.052
#> ERR184067 2 0.1647 0.7684 0.036 0.960 0.004
#> ERR184071 2 0.5442 0.7337 0.132 0.812 0.056
#> ERR184042 3 0.5254 0.7982 0.264 0.000 0.736
#> ERR184063 3 0.3539 0.9484 0.100 0.012 0.888
#> ERR184091 2 0.2796 0.7052 0.000 0.908 0.092
#> ERR184061 2 0.6578 0.6624 0.224 0.724 0.052
#> ERR184077 2 0.6678 0.6799 0.216 0.724 0.060
#> ERR184062 2 0.7430 0.0343 0.424 0.540 0.036
#> ERR184053 2 0.7308 0.5343 0.284 0.656 0.060
#> ERR184088 2 0.5891 0.7103 0.168 0.780 0.052
#> ERR184075 2 0.3193 0.6948 0.004 0.896 0.100
#> ERR184041 3 0.3375 0.9501 0.100 0.008 0.892
#> ERR184060 2 0.4634 0.7390 0.164 0.824 0.012
#> ERR184035 2 0.7537 0.4508 0.332 0.612 0.056
#> ERR184086 2 0.2625 0.7108 0.000 0.916 0.084
#> ERR184080 1 0.6641 0.3924 0.544 0.448 0.008
#> ERR184050 2 0.2959 0.6986 0.000 0.900 0.100
#> ERR184047 1 0.5931 0.4262 0.792 0.084 0.124
#> ERR184092 2 0.3589 0.7636 0.048 0.900 0.052
#> ERR184072 1 0.6104 0.5658 0.648 0.348 0.004
#> ERR184073 1 0.6696 0.3381 0.736 0.076 0.188
#> ERR184066 1 0.6111 0.5088 0.604 0.396 0.000
#> ERR184098 2 0.2625 0.7105 0.000 0.916 0.084
#> ERR184044 2 0.5558 0.7225 0.152 0.800 0.048
#> ERR184054 1 0.6298 0.5238 0.608 0.388 0.004
#> ERR184085 2 0.6897 0.5343 0.292 0.668 0.040
#> ERR184056 2 0.3694 0.7637 0.052 0.896 0.052
#> ERR184052 2 0.1765 0.7440 0.004 0.956 0.040
#> ERR184070 2 0.4062 0.7334 0.164 0.836 0.000
#> ERR184096 1 0.5576 0.4936 0.812 0.104 0.084
#> ERR184089 2 0.5667 0.6059 0.060 0.800 0.140
#> ERR184049 2 0.5408 0.7306 0.136 0.812 0.052
#> ERR184038 1 0.9189 0.3027 0.436 0.416 0.148
#> ERR184087 3 0.3192 0.9469 0.112 0.000 0.888
#> ERR184097 2 0.4768 0.7544 0.100 0.848 0.052
#> ERR184094 1 0.6927 0.1794 0.700 0.060 0.240
#> ERR184058 2 0.0983 0.7547 0.004 0.980 0.016
#> ERR184036 2 0.4845 0.7542 0.104 0.844 0.052
#> ERR184046 2 0.1453 0.7621 0.024 0.968 0.008
#> ERR184074 1 0.6769 0.5116 0.592 0.392 0.016
#> ERR184048 2 0.5947 0.7118 0.172 0.776 0.052
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.2644 0.7465 0.908 0.032 0.000 0.060
#> ERR184093 2 0.1854 0.8844 0.012 0.940 0.000 0.048
#> ERR184051 3 0.0469 0.8093 0.012 0.000 0.988 0.000
#> ERR184076 1 0.2965 0.7458 0.892 0.036 0.000 0.072
#> ERR184043 3 0.0657 0.8066 0.012 0.000 0.984 0.004
#> ERR184037 1 0.5898 0.6263 0.736 0.164 0.036 0.064
#> ERR184059 3 0.4605 0.5576 0.132 0.000 0.796 0.072
#> ERR184055 1 0.5900 0.4866 0.664 0.260 0.000 0.076
#> ERR184065 2 0.4284 0.8263 0.000 0.780 0.020 0.200
#> ERR184069 2 0.2060 0.8982 0.000 0.932 0.016 0.052
#> ERR184040 1 0.1109 0.7495 0.968 0.028 0.000 0.004
#> ERR184057 2 0.1938 0.8985 0.000 0.936 0.012 0.052
#> ERR184082 2 0.1807 0.8947 0.008 0.940 0.000 0.052
#> ERR184083 2 0.2489 0.8942 0.000 0.912 0.020 0.068
#> ERR184039 2 0.3708 0.8600 0.000 0.832 0.020 0.148
#> ERR184064 3 0.0469 0.8093 0.012 0.000 0.988 0.000
#> ERR184081 2 0.2413 0.8953 0.000 0.916 0.020 0.064
#> ERR184095 2 0.1854 0.8992 0.000 0.940 0.012 0.048
#> ERR184079 2 0.2197 0.8836 0.024 0.928 0.000 0.048
#> ERR184084 3 0.8216 0.0369 0.152 0.224 0.552 0.072
#> ERR184068 2 0.3323 0.8590 0.060 0.876 0.000 0.064
#> ERR184067 2 0.1389 0.9000 0.000 0.952 0.000 0.048
#> ERR184071 2 0.0469 0.8978 0.000 0.988 0.000 0.012
#> ERR184042 4 0.6463 0.0000 0.160 0.000 0.196 0.644
#> ERR184063 3 0.0469 0.8093 0.012 0.000 0.988 0.000
#> ERR184091 2 0.4284 0.8263 0.000 0.780 0.020 0.200
#> ERR184061 1 0.5288 0.2807 0.520 0.472 0.000 0.008
#> ERR184077 2 0.1302 0.8902 0.000 0.956 0.000 0.044
#> ERR184062 2 0.5432 0.6549 0.216 0.716 0.000 0.068
#> ERR184053 2 0.0524 0.8976 0.004 0.988 0.000 0.008
#> ERR184088 2 0.1624 0.8902 0.020 0.952 0.000 0.028
#> ERR184075 2 0.4464 0.8232 0.000 0.768 0.024 0.208
#> ERR184041 3 0.0469 0.8093 0.012 0.000 0.988 0.000
#> ERR184060 2 0.2825 0.8985 0.012 0.908 0.024 0.056
#> ERR184035 2 0.3383 0.8552 0.076 0.872 0.000 0.052
#> ERR184086 2 0.4163 0.8408 0.000 0.792 0.020 0.188
#> ERR184080 1 0.3621 0.7255 0.860 0.072 0.000 0.068
#> ERR184050 2 0.4361 0.8263 0.000 0.772 0.020 0.208
#> ERR184047 1 0.3497 0.6516 0.860 0.000 0.036 0.104
#> ERR184092 2 0.1677 0.8877 0.012 0.948 0.000 0.040
#> ERR184072 1 0.2871 0.7442 0.896 0.032 0.000 0.072
#> ERR184073 1 0.2540 0.7383 0.924 0.024 0.024 0.028
#> ERR184066 1 0.5533 0.5308 0.708 0.220 0.000 0.072
#> ERR184098 2 0.3606 0.8688 0.000 0.840 0.020 0.140
#> ERR184044 2 0.2761 0.8658 0.048 0.904 0.000 0.048
#> ERR184054 1 0.2816 0.7467 0.900 0.036 0.000 0.064
#> ERR184085 2 0.1888 0.8945 0.016 0.940 0.000 0.044
#> ERR184056 2 0.1975 0.8831 0.016 0.936 0.000 0.048
#> ERR184052 2 0.2706 0.8888 0.000 0.900 0.020 0.080
#> ERR184070 2 0.2483 0.8989 0.012 0.920 0.012 0.056
#> ERR184096 1 0.2546 0.7063 0.920 0.008 0.028 0.044
#> ERR184089 2 0.7188 0.4929 0.000 0.552 0.244 0.204
#> ERR184049 2 0.0188 0.8968 0.000 0.996 0.000 0.004
#> ERR184038 2 0.6616 0.6849 0.172 0.692 0.048 0.088
#> ERR184087 3 0.2412 0.7323 0.084 0.000 0.908 0.008
#> ERR184097 2 0.2060 0.8817 0.016 0.932 0.000 0.052
#> ERR184094 1 0.4997 0.6200 0.792 0.012 0.104 0.092
#> ERR184058 2 0.2742 0.8917 0.000 0.900 0.024 0.076
#> ERR184036 2 0.0376 0.8971 0.004 0.992 0.000 0.004
#> ERR184046 2 0.2852 0.8953 0.008 0.904 0.024 0.064
#> ERR184074 1 0.3970 0.7204 0.840 0.076 0.000 0.084
#> ERR184048 2 0.0937 0.8977 0.012 0.976 0.000 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.0510 0.792 0.984 0.000 0.000 0.016 0.000
#> ERR184093 2 0.1179 0.884 0.004 0.964 0.000 0.016 0.016
#> ERR184051 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> ERR184076 1 0.0771 0.794 0.976 0.004 0.000 0.020 0.000
#> ERR184043 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> ERR184037 1 0.5255 0.616 0.672 0.076 0.000 0.244 0.008
#> ERR184059 3 0.4547 0.499 0.044 0.000 0.704 0.252 0.000
#> ERR184055 1 0.4907 0.584 0.720 0.204 0.000 0.064 0.012
#> ERR184065 5 0.0609 0.893 0.000 0.020 0.000 0.000 0.980
#> ERR184069 2 0.3616 0.825 0.000 0.804 0.000 0.032 0.164
#> ERR184040 1 0.0703 0.794 0.976 0.000 0.000 0.024 0.000
#> ERR184057 2 0.3535 0.827 0.000 0.808 0.000 0.028 0.164
#> ERR184082 2 0.1124 0.881 0.000 0.960 0.000 0.004 0.036
#> ERR184083 2 0.3594 0.822 0.000 0.804 0.004 0.020 0.172
#> ERR184039 5 0.3243 0.742 0.000 0.180 0.004 0.004 0.812
#> ERR184064 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> ERR184081 2 0.3773 0.823 0.000 0.800 0.004 0.032 0.164
#> ERR184095 2 0.3409 0.829 0.000 0.816 0.000 0.024 0.160
#> ERR184079 2 0.0510 0.883 0.000 0.984 0.000 0.016 0.000
#> ERR184084 2 0.6375 0.466 0.048 0.604 0.080 0.264 0.004
#> ERR184068 2 0.1569 0.873 0.032 0.948 0.000 0.012 0.008
#> ERR184067 2 0.2920 0.847 0.000 0.852 0.000 0.016 0.132
#> ERR184071 2 0.0898 0.884 0.000 0.972 0.000 0.008 0.020
#> ERR184042 4 0.2770 0.000 0.044 0.000 0.076 0.880 0.000
#> ERR184063 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> ERR184091 5 0.0510 0.892 0.000 0.016 0.000 0.000 0.984
#> ERR184061 1 0.4779 0.348 0.584 0.396 0.000 0.016 0.004
#> ERR184077 2 0.0671 0.882 0.000 0.980 0.000 0.016 0.004
#> ERR184062 2 0.3770 0.718 0.188 0.788 0.000 0.016 0.008
#> ERR184053 2 0.0798 0.883 0.000 0.976 0.000 0.008 0.016
#> ERR184088 2 0.0162 0.884 0.000 0.996 0.000 0.000 0.004
#> ERR184075 5 0.0510 0.892 0.000 0.016 0.000 0.000 0.984
#> ERR184041 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> ERR184060 2 0.3566 0.827 0.000 0.812 0.004 0.024 0.160
#> ERR184035 2 0.1507 0.876 0.024 0.952 0.000 0.012 0.012
#> ERR184086 5 0.2052 0.858 0.000 0.080 0.004 0.004 0.912
#> ERR184080 1 0.2251 0.787 0.916 0.024 0.000 0.052 0.008
#> ERR184050 5 0.0671 0.890 0.000 0.016 0.004 0.000 0.980
#> ERR184047 1 0.3774 0.608 0.704 0.000 0.000 0.296 0.000
#> ERR184092 2 0.0912 0.884 0.000 0.972 0.000 0.016 0.012
#> ERR184072 1 0.0771 0.794 0.976 0.004 0.000 0.020 0.000
#> ERR184073 1 0.0404 0.795 0.988 0.000 0.000 0.012 0.000
#> ERR184066 1 0.3575 0.597 0.800 0.180 0.000 0.016 0.004
#> ERR184098 5 0.3128 0.765 0.000 0.168 0.004 0.004 0.824
#> ERR184044 2 0.1095 0.881 0.008 0.968 0.000 0.012 0.012
#> ERR184054 1 0.0798 0.793 0.976 0.008 0.000 0.016 0.000
#> ERR184085 2 0.1168 0.882 0.008 0.960 0.000 0.000 0.032
#> ERR184056 2 0.0960 0.883 0.004 0.972 0.000 0.016 0.008
#> ERR184052 2 0.3282 0.821 0.000 0.804 0.000 0.008 0.188
#> ERR184070 2 0.3454 0.831 0.000 0.816 0.000 0.028 0.156
#> ERR184096 1 0.2536 0.751 0.868 0.004 0.000 0.128 0.000
#> ERR184089 5 0.0865 0.888 0.000 0.024 0.004 0.000 0.972
#> ERR184049 2 0.0912 0.882 0.000 0.972 0.000 0.016 0.012
#> ERR184038 2 0.4629 0.750 0.172 0.764 0.008 0.036 0.020
#> ERR184087 3 0.3115 0.752 0.036 0.000 0.852 0.112 0.000
#> ERR184097 2 0.1419 0.882 0.012 0.956 0.000 0.016 0.016
#> ERR184094 1 0.4748 0.645 0.708 0.016 0.012 0.252 0.012
#> ERR184058 2 0.3812 0.802 0.000 0.780 0.004 0.020 0.196
#> ERR184036 2 0.0671 0.882 0.000 0.980 0.000 0.016 0.004
#> ERR184046 2 0.3556 0.824 0.000 0.808 0.004 0.020 0.168
#> ERR184074 1 0.2674 0.780 0.888 0.020 0.000 0.084 0.008
#> ERR184048 2 0.0693 0.882 0.000 0.980 0.000 0.008 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.0551 0.6741 0.984 0.000 0.000 0.004 0.004 0.008
#> ERR184093 2 0.2100 0.6907 0.004 0.884 0.000 0.000 0.000 0.112
#> ERR184051 3 0.0146 0.9297 0.000 0.000 0.996 0.000 0.000 0.004
#> ERR184076 1 0.0767 0.6737 0.976 0.000 0.000 0.004 0.012 0.008
#> ERR184043 3 0.0000 0.9304 0.000 0.000 1.000 0.000 0.000 0.000
#> ERR184037 1 0.6091 0.1536 0.544 0.032 0.000 0.000 0.172 0.252
#> ERR184059 3 0.3626 0.6327 0.004 0.000 0.704 0.000 0.288 0.004
#> ERR184055 1 0.4430 0.5548 0.760 0.120 0.000 0.000 0.040 0.080
#> ERR184065 4 0.0260 0.9415 0.000 0.008 0.000 0.992 0.000 0.000
#> ERR184069 2 0.4267 0.6487 0.000 0.732 0.000 0.152 0.000 0.116
#> ERR184040 1 0.1908 0.6560 0.900 0.000 0.000 0.000 0.096 0.004
#> ERR184057 2 0.4095 0.6600 0.000 0.748 0.000 0.152 0.000 0.100
#> ERR184082 2 0.4243 0.3416 0.008 0.704 0.000 0.040 0.000 0.248
#> ERR184083 2 0.4282 0.6384 0.000 0.720 0.000 0.192 0.000 0.088
#> ERR184039 4 0.2538 0.7835 0.000 0.124 0.000 0.860 0.000 0.016
#> ERR184064 3 0.0000 0.9304 0.000 0.000 1.000 0.000 0.000 0.000
#> ERR184081 2 0.4267 0.6487 0.000 0.732 0.000 0.152 0.000 0.116
#> ERR184095 2 0.4140 0.6553 0.000 0.744 0.000 0.152 0.000 0.104
#> ERR184079 2 0.1610 0.7014 0.000 0.916 0.000 0.000 0.000 0.084
#> ERR184084 6 0.7518 0.0000 0.016 0.256 0.056 0.008 0.328 0.336
#> ERR184068 2 0.2831 0.6712 0.024 0.840 0.000 0.000 0.000 0.136
#> ERR184067 2 0.3190 0.6928 0.000 0.820 0.000 0.136 0.000 0.044
#> ERR184071 2 0.1643 0.7147 0.000 0.924 0.000 0.068 0.000 0.008
#> ERR184042 5 0.4617 -0.0970 0.004 0.000 0.060 0.000 0.652 0.284
#> ERR184063 3 0.0146 0.9297 0.000 0.000 0.996 0.000 0.000 0.004
#> ERR184091 4 0.0146 0.9421 0.000 0.004 0.000 0.996 0.000 0.000
#> ERR184061 1 0.5806 0.1239 0.484 0.404 0.000 0.000 0.056 0.056
#> ERR184077 2 0.1951 0.7102 0.000 0.908 0.000 0.016 0.000 0.076
#> ERR184062 2 0.3529 0.5361 0.208 0.764 0.000 0.000 0.000 0.028
#> ERR184053 2 0.3766 0.3549 0.000 0.720 0.000 0.024 0.000 0.256
#> ERR184088 2 0.1421 0.7014 0.028 0.944 0.000 0.000 0.000 0.028
#> ERR184075 4 0.0146 0.9421 0.000 0.004 0.000 0.996 0.000 0.000
#> ERR184041 3 0.0000 0.9304 0.000 0.000 1.000 0.000 0.000 0.000
#> ERR184060 2 0.4267 0.6547 0.000 0.732 0.000 0.152 0.000 0.116
#> ERR184035 2 0.6024 -0.3010 0.268 0.492 0.000 0.000 0.008 0.232
#> ERR184086 4 0.0806 0.9319 0.000 0.020 0.000 0.972 0.000 0.008
#> ERR184080 1 0.3273 0.6339 0.848 0.036 0.000 0.000 0.044 0.072
#> ERR184050 4 0.0146 0.9421 0.000 0.004 0.000 0.996 0.000 0.000
#> ERR184047 5 0.4101 0.2296 0.408 0.000 0.000 0.000 0.580 0.012
#> ERR184092 2 0.1814 0.6977 0.000 0.900 0.000 0.000 0.000 0.100
#> ERR184072 1 0.1075 0.6644 0.952 0.000 0.000 0.000 0.048 0.000
#> ERR184073 1 0.3360 0.3651 0.732 0.004 0.000 0.000 0.264 0.000
#> ERR184066 1 0.1267 0.6473 0.940 0.060 0.000 0.000 0.000 0.000
#> ERR184098 4 0.2070 0.8474 0.000 0.100 0.000 0.892 0.000 0.008
#> ERR184044 2 0.1767 0.7085 0.012 0.932 0.000 0.020 0.000 0.036
#> ERR184054 1 0.0405 0.6765 0.988 0.004 0.000 0.000 0.008 0.000
#> ERR184085 2 0.3917 0.4570 0.012 0.752 0.000 0.032 0.000 0.204
#> ERR184056 2 0.1910 0.6938 0.000 0.892 0.000 0.000 0.000 0.108
#> ERR184052 2 0.3376 0.6568 0.000 0.764 0.000 0.220 0.000 0.016
#> ERR184070 2 0.4154 0.6591 0.000 0.744 0.000 0.144 0.000 0.112
#> ERR184096 1 0.3899 -0.0625 0.592 0.000 0.000 0.000 0.404 0.004
#> ERR184089 4 0.0291 0.9388 0.000 0.004 0.004 0.992 0.000 0.000
#> ERR184049 2 0.1296 0.7075 0.004 0.948 0.000 0.000 0.004 0.044
#> ERR184038 2 0.6827 0.0160 0.136 0.556 0.000 0.044 0.056 0.208
#> ERR184087 3 0.1610 0.8715 0.000 0.000 0.916 0.000 0.084 0.000
#> ERR184097 2 0.2450 0.6843 0.016 0.868 0.000 0.000 0.000 0.116
#> ERR184094 5 0.4910 0.2132 0.420 0.012 0.000 0.008 0.536 0.024
#> ERR184058 2 0.4475 0.6103 0.000 0.692 0.000 0.220 0.000 0.088
#> ERR184036 2 0.1155 0.7090 0.004 0.956 0.000 0.004 0.000 0.036
#> ERR184046 2 0.4141 0.6520 0.000 0.740 0.000 0.168 0.000 0.092
#> ERR184074 1 0.4151 0.6100 0.780 0.036 0.000 0.000 0.120 0.064
#> ERR184048 2 0.0363 0.7099 0.000 0.988 0.000 0.000 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
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 10269 rows and 62 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 0.871 0.914 0.953 0.4977 0.497 0.497
#> 3 3 0.535 0.679 0.844 0.2615 0.856 0.718
#> 4 4 0.500 0.666 0.794 0.1305 0.750 0.474
#> 5 5 0.563 0.638 0.759 0.0810 0.883 0.646
#> 6 6 0.583 0.503 0.718 0.0449 0.970 0.870
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
#> ERR184078 1 0.0376 0.954 0.996 0.004
#> ERR184093 1 0.0672 0.957 0.992 0.008
#> ERR184051 2 0.1414 0.936 0.020 0.980
#> ERR184076 1 0.0672 0.952 0.992 0.008
#> ERR184043 2 0.1414 0.936 0.020 0.980
#> ERR184037 1 0.0938 0.957 0.988 0.012
#> ERR184059 2 0.2603 0.926 0.044 0.956
#> ERR184055 1 0.0672 0.957 0.992 0.008
#> ERR184065 2 0.0672 0.949 0.008 0.992
#> ERR184069 2 0.5842 0.832 0.140 0.860
#> ERR184040 1 0.0376 0.956 0.996 0.004
#> ERR184057 1 0.4022 0.923 0.920 0.080
#> ERR184082 2 0.1843 0.941 0.028 0.972
#> ERR184083 2 0.0938 0.949 0.012 0.988
#> ERR184039 2 0.0938 0.949 0.012 0.988
#> ERR184064 2 0.0000 0.946 0.000 1.000
#> ERR184081 2 0.1843 0.941 0.028 0.972
#> ERR184095 1 0.5629 0.874 0.868 0.132
#> ERR184079 1 0.0938 0.957 0.988 0.012
#> ERR184084 2 0.0938 0.949 0.012 0.988
#> ERR184068 1 0.2778 0.946 0.952 0.048
#> ERR184067 2 0.9775 0.280 0.412 0.588
#> ERR184071 2 0.1633 0.944 0.024 0.976
#> ERR184042 2 0.5946 0.835 0.144 0.856
#> ERR184063 2 0.0000 0.946 0.000 1.000
#> ERR184091 2 0.0672 0.949 0.008 0.992
#> ERR184061 1 0.0938 0.957 0.988 0.012
#> ERR184077 1 0.1633 0.955 0.976 0.024
#> ERR184062 1 0.0672 0.953 0.992 0.008
#> ERR184053 1 0.3733 0.932 0.928 0.072
#> ERR184088 1 0.2778 0.946 0.952 0.048
#> ERR184075 2 0.0672 0.949 0.008 0.992
#> ERR184041 2 0.0672 0.949 0.008 0.992
#> ERR184060 1 0.5946 0.860 0.856 0.144
#> ERR184035 1 0.2948 0.944 0.948 0.052
#> ERR184086 2 0.0672 0.949 0.008 0.992
#> ERR184080 1 0.0672 0.957 0.992 0.008
#> ERR184050 2 0.0672 0.949 0.008 0.992
#> ERR184047 1 0.0938 0.951 0.988 0.012
#> ERR184092 1 0.2236 0.951 0.964 0.036
#> ERR184072 1 0.0376 0.954 0.996 0.004
#> ERR184073 1 0.0672 0.957 0.992 0.008
#> ERR184066 1 0.0376 0.954 0.996 0.004
#> ERR184098 2 0.0672 0.949 0.008 0.992
#> ERR184044 1 0.0672 0.953 0.992 0.008
#> ERR184054 1 0.0376 0.954 0.996 0.004
#> ERR184085 2 0.4022 0.898 0.080 0.920
#> ERR184056 1 0.0938 0.957 0.988 0.012
#> ERR184052 2 0.0938 0.949 0.012 0.988
#> ERR184070 1 0.2778 0.946 0.952 0.048
#> ERR184096 1 0.0376 0.954 0.996 0.004
#> ERR184089 2 0.0672 0.949 0.008 0.992
#> ERR184049 1 0.8386 0.673 0.732 0.268
#> ERR184038 2 0.9635 0.431 0.388 0.612
#> ERR184087 2 0.0000 0.946 0.000 1.000
#> ERR184097 1 0.0938 0.957 0.988 0.012
#> ERR184094 1 0.7950 0.684 0.760 0.240
#> ERR184058 2 0.0938 0.949 0.012 0.988
#> ERR184036 1 0.3431 0.936 0.936 0.064
#> ERR184046 2 0.0938 0.949 0.012 0.988
#> ERR184074 1 0.0376 0.956 0.996 0.004
#> ERR184048 1 0.2778 0.946 0.952 0.048
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.1163 0.833 0.972 0.000 0.028
#> ERR184093 1 0.0000 0.838 1.000 0.000 0.000
#> ERR184051 3 0.3482 0.701 0.000 0.128 0.872
#> ERR184076 1 0.3267 0.790 0.884 0.000 0.116
#> ERR184043 3 0.3551 0.699 0.000 0.132 0.868
#> ERR184037 1 0.1289 0.838 0.968 0.032 0.000
#> ERR184059 3 0.1860 0.686 0.000 0.052 0.948
#> ERR184055 1 0.0000 0.838 1.000 0.000 0.000
#> ERR184065 2 0.2261 0.772 0.000 0.932 0.068
#> ERR184069 2 0.0747 0.788 0.016 0.984 0.000
#> ERR184040 1 0.0747 0.836 0.984 0.000 0.016
#> ERR184057 1 0.5621 0.649 0.692 0.308 0.000
#> ERR184082 2 0.2400 0.777 0.004 0.932 0.064
#> ERR184083 2 0.0000 0.797 0.000 1.000 0.000
#> ERR184039 2 0.1753 0.784 0.000 0.952 0.048
#> ERR184064 3 0.5650 0.598 0.000 0.312 0.688
#> ERR184081 2 0.0424 0.794 0.008 0.992 0.000
#> ERR184095 1 0.6252 0.413 0.556 0.444 0.000
#> ERR184079 1 0.1643 0.836 0.956 0.044 0.000
#> ERR184084 3 0.6683 0.199 0.008 0.492 0.500
#> ERR184068 1 0.2772 0.828 0.916 0.080 0.004
#> ERR184067 2 0.3941 0.613 0.156 0.844 0.000
#> ERR184071 2 0.0424 0.794 0.008 0.992 0.000
#> ERR184042 3 0.0892 0.657 0.020 0.000 0.980
#> ERR184063 3 0.4887 0.667 0.000 0.228 0.772
#> ERR184091 2 0.2165 0.775 0.000 0.936 0.064
#> ERR184061 1 0.1643 0.838 0.956 0.044 0.000
#> ERR184077 1 0.2066 0.833 0.940 0.060 0.000
#> ERR184062 1 0.5650 0.571 0.688 0.000 0.312
#> ERR184053 1 0.5810 0.619 0.664 0.336 0.000
#> ERR184088 1 0.4291 0.773 0.820 0.180 0.000
#> ERR184075 2 0.5058 0.564 0.000 0.756 0.244
#> ERR184041 3 0.6295 0.264 0.000 0.472 0.528
#> ERR184060 1 0.6291 0.318 0.532 0.468 0.000
#> ERR184035 1 0.4121 0.781 0.832 0.168 0.000
#> ERR184086 2 0.5497 0.472 0.000 0.708 0.292
#> ERR184080 1 0.0000 0.838 1.000 0.000 0.000
#> ERR184050 2 0.5138 0.549 0.000 0.748 0.252
#> ERR184047 1 0.5363 0.628 0.724 0.000 0.276
#> ERR184092 1 0.1031 0.839 0.976 0.024 0.000
#> ERR184072 1 0.1411 0.830 0.964 0.000 0.036
#> ERR184073 1 0.5733 0.553 0.676 0.000 0.324
#> ERR184066 1 0.3816 0.765 0.852 0.000 0.148
#> ERR184098 2 0.5621 0.436 0.000 0.692 0.308
#> ERR184044 1 0.5733 0.564 0.676 0.000 0.324
#> ERR184054 1 0.1753 0.827 0.952 0.000 0.048
#> ERR184085 2 0.1620 0.789 0.024 0.964 0.012
#> ERR184056 1 0.0000 0.838 1.000 0.000 0.000
#> ERR184052 2 0.0000 0.797 0.000 1.000 0.000
#> ERR184070 1 0.3116 0.814 0.892 0.108 0.000
#> ERR184096 1 0.3192 0.793 0.888 0.000 0.112
#> ERR184089 2 0.5905 0.317 0.000 0.648 0.352
#> ERR184049 2 0.6095 0.102 0.392 0.608 0.000
#> ERR184038 3 0.3619 0.609 0.136 0.000 0.864
#> ERR184087 3 0.5760 0.578 0.000 0.328 0.672
#> ERR184097 1 0.1031 0.834 0.976 0.000 0.024
#> ERR184094 3 0.7056 0.123 0.404 0.024 0.572
#> ERR184058 2 0.0000 0.797 0.000 1.000 0.000
#> ERR184036 1 0.5397 0.684 0.720 0.280 0.000
#> ERR184046 2 0.0000 0.797 0.000 1.000 0.000
#> ERR184074 1 0.0424 0.837 0.992 0.000 0.008
#> ERR184048 1 0.4796 0.742 0.780 0.220 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.2983 0.7678 0.892 0.040 0.000 0.068
#> ERR184093 1 0.1406 0.7850 0.960 0.016 0.000 0.024
#> ERR184051 3 0.3801 0.5713 0.000 0.000 0.780 0.220
#> ERR184076 1 0.3266 0.7597 0.880 0.032 0.004 0.084
#> ERR184043 3 0.2921 0.6637 0.000 0.000 0.860 0.140
#> ERR184037 1 0.6245 0.6729 0.668 0.168 0.000 0.164
#> ERR184059 3 0.5050 0.0834 0.004 0.000 0.588 0.408
#> ERR184055 1 0.4440 0.7526 0.804 0.060 0.000 0.136
#> ERR184065 3 0.3907 0.6558 0.000 0.232 0.768 0.000
#> ERR184069 2 0.4449 0.7273 0.012 0.824 0.104 0.060
#> ERR184040 1 0.1610 0.7862 0.952 0.016 0.000 0.032
#> ERR184057 2 0.3856 0.6823 0.032 0.832 0.000 0.136
#> ERR184082 2 0.2803 0.7370 0.012 0.900 0.080 0.008
#> ERR184083 2 0.2216 0.7339 0.000 0.908 0.092 0.000
#> ERR184039 3 0.4661 0.6225 0.000 0.256 0.728 0.016
#> ERR184064 3 0.2654 0.6989 0.000 0.004 0.888 0.108
#> ERR184081 2 0.3142 0.7300 0.000 0.860 0.132 0.008
#> ERR184095 2 0.2782 0.7249 0.068 0.904 0.004 0.024
#> ERR184079 1 0.5279 0.6482 0.716 0.232 0.000 0.052
#> ERR184084 2 0.7798 0.4400 0.060 0.592 0.140 0.208
#> ERR184068 2 0.5698 0.4391 0.356 0.608 0.000 0.036
#> ERR184067 2 0.5317 0.6910 0.028 0.776 0.060 0.136
#> ERR184071 2 0.3688 0.6828 0.000 0.792 0.208 0.000
#> ERR184042 4 0.4035 0.7549 0.020 0.000 0.176 0.804
#> ERR184063 3 0.3764 0.5823 0.000 0.000 0.784 0.216
#> ERR184091 3 0.4382 0.5720 0.000 0.296 0.704 0.000
#> ERR184061 1 0.5567 0.7172 0.740 0.088 0.008 0.164
#> ERR184077 2 0.5464 0.5931 0.228 0.708 0.000 0.064
#> ERR184062 1 0.3736 0.7335 0.860 0.012 0.032 0.096
#> ERR184053 2 0.4336 0.6881 0.132 0.816 0.004 0.048
#> ERR184088 1 0.6920 0.4727 0.552 0.316 0.000 0.132
#> ERR184075 3 0.3306 0.7199 0.000 0.156 0.840 0.004
#> ERR184041 3 0.1820 0.7420 0.000 0.020 0.944 0.036
#> ERR184060 1 0.7865 0.3893 0.544 0.300 0.080 0.076
#> ERR184035 2 0.4295 0.6476 0.240 0.752 0.000 0.008
#> ERR184086 3 0.2149 0.7449 0.000 0.088 0.912 0.000
#> ERR184080 1 0.2565 0.7859 0.912 0.032 0.000 0.056
#> ERR184050 3 0.3105 0.7307 0.000 0.120 0.868 0.012
#> ERR184047 1 0.4203 0.7351 0.824 0.000 0.068 0.108
#> ERR184092 1 0.3542 0.7771 0.864 0.076 0.000 0.060
#> ERR184072 1 0.1488 0.7787 0.956 0.012 0.000 0.032
#> ERR184073 1 0.4337 0.7088 0.824 0.004 0.072 0.100
#> ERR184066 1 0.2667 0.7733 0.912 0.008 0.020 0.060
#> ERR184098 3 0.1771 0.7504 0.004 0.036 0.948 0.012
#> ERR184044 1 0.6398 0.6286 0.660 0.032 0.052 0.256
#> ERR184054 1 0.0657 0.7869 0.984 0.004 0.000 0.012
#> ERR184085 2 0.4333 0.7298 0.008 0.812 0.148 0.032
#> ERR184056 1 0.2399 0.7857 0.920 0.048 0.000 0.032
#> ERR184052 2 0.5143 0.4415 0.000 0.628 0.360 0.012
#> ERR184070 1 0.5950 0.6964 0.696 0.156 0.000 0.148
#> ERR184096 1 0.2089 0.7809 0.932 0.000 0.020 0.048
#> ERR184089 3 0.1452 0.7515 0.000 0.036 0.956 0.008
#> ERR184049 2 0.7701 0.5466 0.156 0.616 0.072 0.156
#> ERR184038 4 0.6381 0.7718 0.148 0.020 0.136 0.696
#> ERR184087 3 0.2469 0.6944 0.000 0.000 0.892 0.108
#> ERR184097 1 0.2670 0.7709 0.908 0.052 0.000 0.040
#> ERR184094 1 0.7346 0.3346 0.552 0.004 0.220 0.224
#> ERR184058 2 0.4608 0.5639 0.000 0.692 0.304 0.004
#> ERR184036 1 0.7492 0.5249 0.556 0.268 0.016 0.160
#> ERR184046 2 0.4252 0.6233 0.000 0.744 0.252 0.004
#> ERR184074 1 0.4356 0.7463 0.812 0.044 0.004 0.140
#> ERR184048 2 0.3718 0.6811 0.168 0.820 0.000 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.2476 0.794 0.904 0.012 0.000 0.020 0.064
#> ERR184093 1 0.4326 0.755 0.780 0.008 0.008 0.040 0.164
#> ERR184051 3 0.3866 0.709 0.024 0.000 0.780 0.192 0.004
#> ERR184076 1 0.1748 0.782 0.944 0.008 0.004 0.016 0.028
#> ERR184043 3 0.3080 0.766 0.020 0.000 0.852 0.124 0.004
#> ERR184037 5 0.3276 0.668 0.132 0.032 0.000 0.000 0.836
#> ERR184059 3 0.4705 0.587 0.040 0.000 0.692 0.264 0.004
#> ERR184055 5 0.3814 0.551 0.276 0.004 0.000 0.000 0.720
#> ERR184065 3 0.3876 0.677 0.000 0.168 0.796 0.012 0.024
#> ERR184069 2 0.5191 0.437 0.000 0.552 0.036 0.004 0.408
#> ERR184040 1 0.3129 0.778 0.832 0.004 0.000 0.008 0.156
#> ERR184057 2 0.4264 0.499 0.000 0.620 0.000 0.004 0.376
#> ERR184082 2 0.2702 0.717 0.008 0.904 0.040 0.016 0.032
#> ERR184083 2 0.2067 0.721 0.000 0.924 0.044 0.004 0.028
#> ERR184039 3 0.5275 0.589 0.000 0.188 0.712 0.032 0.068
#> ERR184064 3 0.2464 0.783 0.016 0.000 0.888 0.096 0.000
#> ERR184081 2 0.4409 0.681 0.000 0.736 0.040 0.004 0.220
#> ERR184095 2 0.2463 0.697 0.008 0.888 0.000 0.004 0.100
#> ERR184079 5 0.7206 0.176 0.388 0.128 0.008 0.040 0.436
#> ERR184084 2 0.5445 0.592 0.024 0.748 0.056 0.120 0.052
#> ERR184068 2 0.5646 0.301 0.336 0.584 0.000 0.008 0.072
#> ERR184067 5 0.4675 0.134 0.000 0.336 0.020 0.004 0.640
#> ERR184071 2 0.4490 0.693 0.000 0.756 0.168 0.004 0.072
#> ERR184042 4 0.1282 0.652 0.004 0.000 0.044 0.952 0.000
#> ERR184063 3 0.3586 0.721 0.020 0.000 0.792 0.188 0.000
#> ERR184091 3 0.4268 0.589 0.000 0.244 0.728 0.004 0.024
#> ERR184061 5 0.3734 0.615 0.204 0.004 0.004 0.008 0.780
#> ERR184077 2 0.4653 0.555 0.132 0.752 0.000 0.004 0.112
#> ERR184062 1 0.1682 0.762 0.944 0.000 0.032 0.012 0.012
#> ERR184053 2 0.4072 0.637 0.048 0.792 0.000 0.008 0.152
#> ERR184088 5 0.5233 0.642 0.164 0.136 0.000 0.004 0.696
#> ERR184075 3 0.1809 0.785 0.000 0.060 0.928 0.000 0.012
#> ERR184041 3 0.2026 0.799 0.016 0.012 0.928 0.044 0.000
#> ERR184060 5 0.7301 0.531 0.184 0.188 0.068 0.008 0.552
#> ERR184035 2 0.4848 0.665 0.092 0.736 0.000 0.008 0.164
#> ERR184086 3 0.1442 0.795 0.000 0.012 0.952 0.032 0.004
#> ERR184080 1 0.4182 0.391 0.600 0.000 0.000 0.000 0.400
#> ERR184050 3 0.2450 0.781 0.000 0.028 0.912 0.028 0.032
#> ERR184047 1 0.5715 0.560 0.636 0.000 0.020 0.080 0.264
#> ERR184092 1 0.5856 0.384 0.596 0.036 0.008 0.032 0.328
#> ERR184072 1 0.2731 0.793 0.876 0.016 0.000 0.004 0.104
#> ERR184073 1 0.4933 0.730 0.756 0.000 0.056 0.048 0.140
#> ERR184066 1 0.1843 0.799 0.932 0.000 0.008 0.008 0.052
#> ERR184098 3 0.1940 0.797 0.004 0.008 0.936 0.024 0.028
#> ERR184044 5 0.7191 0.275 0.320 0.000 0.056 0.144 0.480
#> ERR184054 1 0.3437 0.771 0.808 0.000 0.004 0.012 0.176
#> ERR184085 2 0.5558 0.690 0.000 0.696 0.080 0.040 0.184
#> ERR184056 1 0.3142 0.768 0.856 0.032 0.000 0.004 0.108
#> ERR184052 2 0.6418 0.486 0.000 0.508 0.316 0.004 0.172
#> ERR184070 5 0.3821 0.668 0.148 0.052 0.000 0.000 0.800
#> ERR184096 1 0.3430 0.778 0.824 0.000 0.012 0.012 0.152
#> ERR184089 3 0.0968 0.803 0.004 0.012 0.972 0.012 0.000
#> ERR184049 5 0.3898 0.511 0.004 0.188 0.020 0.004 0.784
#> ERR184038 4 0.7318 0.614 0.260 0.064 0.072 0.560 0.044
#> ERR184087 3 0.2536 0.775 0.004 0.000 0.868 0.128 0.000
#> ERR184097 1 0.1728 0.771 0.940 0.020 0.000 0.004 0.036
#> ERR184094 5 0.7491 0.421 0.204 0.000 0.136 0.136 0.524
#> ERR184058 2 0.5738 0.641 0.000 0.644 0.228 0.012 0.116
#> ERR184036 5 0.3775 0.665 0.056 0.084 0.008 0.012 0.840
#> ERR184046 2 0.4582 0.676 0.004 0.764 0.172 0.020 0.040
#> ERR184074 5 0.4240 0.479 0.304 0.000 0.004 0.008 0.684
#> ERR184048 2 0.2538 0.691 0.048 0.900 0.000 0.004 0.048
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.2602 0.6514 0.896 0.016 0.004 0.004 0.040 0.040
#> ERR184093 1 0.6126 0.4795 0.492 0.056 0.000 0.000 0.360 0.092
#> ERR184051 3 0.3299 0.7076 0.028 0.000 0.820 0.140 0.012 0.000
#> ERR184076 1 0.2613 0.6039 0.888 0.008 0.012 0.004 0.076 0.012
#> ERR184043 3 0.1938 0.7798 0.020 0.000 0.920 0.052 0.008 0.000
#> ERR184037 6 0.1881 0.7270 0.052 0.016 0.000 0.004 0.004 0.924
#> ERR184059 3 0.4124 0.5932 0.036 0.000 0.728 0.224 0.012 0.000
#> ERR184055 6 0.2872 0.6666 0.140 0.000 0.000 0.000 0.024 0.836
#> ERR184065 3 0.4400 0.6471 0.000 0.184 0.740 0.004 0.052 0.020
#> ERR184069 2 0.5106 0.3102 0.000 0.568 0.016 0.004 0.044 0.368
#> ERR184040 1 0.3823 0.6513 0.764 0.004 0.000 0.000 0.048 0.184
#> ERR184057 2 0.5738 0.0362 0.000 0.432 0.000 0.004 0.144 0.420
#> ERR184082 2 0.1956 0.3392 0.016 0.928 0.016 0.008 0.032 0.000
#> ERR184083 2 0.2268 0.3449 0.000 0.912 0.028 0.004 0.028 0.028
#> ERR184039 3 0.6088 0.2184 0.000 0.360 0.496 0.000 0.088 0.056
#> ERR184064 3 0.1434 0.7900 0.020 0.000 0.948 0.024 0.008 0.000
#> ERR184081 2 0.5759 0.2009 0.000 0.564 0.020 0.000 0.140 0.276
#> ERR184095 2 0.4721 -0.6206 0.004 0.584 0.000 0.004 0.372 0.036
#> ERR184079 2 0.7817 -0.0576 0.208 0.276 0.000 0.004 0.240 0.272
#> ERR184084 2 0.5098 0.0746 0.040 0.740 0.040 0.084 0.096 0.000
#> ERR184068 2 0.6144 -0.1837 0.296 0.472 0.000 0.000 0.220 0.012
#> ERR184067 6 0.4424 0.4924 0.000 0.208 0.004 0.008 0.060 0.720
#> ERR184071 2 0.4785 0.3516 0.000 0.720 0.180 0.004 0.056 0.040
#> ERR184042 4 0.0363 0.4830 0.000 0.000 0.012 0.988 0.000 0.000
#> ERR184063 3 0.2556 0.7627 0.028 0.000 0.884 0.076 0.012 0.000
#> ERR184091 3 0.4499 0.5709 0.000 0.252 0.692 0.004 0.040 0.012
#> ERR184061 6 0.3265 0.6863 0.056 0.000 0.000 0.004 0.112 0.828
#> ERR184077 5 0.5400 0.8679 0.064 0.460 0.000 0.008 0.460 0.008
#> ERR184062 1 0.2573 0.6271 0.856 0.000 0.008 0.000 0.132 0.004
#> ERR184053 5 0.5318 0.8675 0.024 0.452 0.000 0.012 0.484 0.028
#> ERR184088 6 0.4924 0.6334 0.112 0.156 0.000 0.000 0.028 0.704
#> ERR184075 3 0.1826 0.7811 0.000 0.052 0.924 0.004 0.020 0.000
#> ERR184041 3 0.1223 0.7949 0.016 0.004 0.960 0.008 0.012 0.000
#> ERR184060 6 0.7213 0.3375 0.172 0.228 0.040 0.000 0.064 0.496
#> ERR184035 2 0.4637 0.3557 0.112 0.748 0.000 0.008 0.024 0.108
#> ERR184086 3 0.3017 0.7571 0.000 0.084 0.844 0.000 0.072 0.000
#> ERR184080 1 0.4653 0.1641 0.488 0.012 0.000 0.000 0.020 0.480
#> ERR184050 3 0.4063 0.7107 0.000 0.072 0.768 0.000 0.148 0.012
#> ERR184047 1 0.6861 0.3176 0.476 0.000 0.048 0.080 0.056 0.340
#> ERR184092 1 0.6472 0.2007 0.392 0.024 0.000 0.000 0.224 0.360
#> ERR184072 1 0.4929 0.5980 0.644 0.004 0.000 0.000 0.252 0.100
#> ERR184073 1 0.5970 0.5607 0.572 0.000 0.036 0.008 0.280 0.104
#> ERR184066 1 0.2781 0.6517 0.876 0.000 0.008 0.004 0.048 0.064
#> ERR184098 3 0.1453 0.7928 0.000 0.008 0.944 0.000 0.040 0.008
#> ERR184044 6 0.7070 0.2772 0.280 0.004 0.068 0.108 0.036 0.504
#> ERR184054 1 0.4886 0.6550 0.680 0.000 0.000 0.008 0.128 0.184
#> ERR184085 2 0.4761 0.4141 0.000 0.752 0.024 0.032 0.064 0.128
#> ERR184056 1 0.3720 0.6204 0.816 0.036 0.000 0.000 0.056 0.092
#> ERR184052 2 0.6759 0.2858 0.000 0.484 0.276 0.004 0.068 0.168
#> ERR184070 6 0.1832 0.7319 0.032 0.032 0.000 0.000 0.008 0.928
#> ERR184096 1 0.5231 0.6522 0.688 0.000 0.012 0.020 0.156 0.124
#> ERR184089 3 0.0291 0.7955 0.000 0.004 0.992 0.000 0.004 0.000
#> ERR184049 6 0.2776 0.6778 0.000 0.112 0.004 0.004 0.020 0.860
#> ERR184038 4 0.7624 0.4502 0.260 0.032 0.116 0.432 0.160 0.000
#> ERR184087 3 0.1841 0.7843 0.008 0.000 0.920 0.064 0.008 0.000
#> ERR184097 1 0.1888 0.6257 0.916 0.012 0.000 0.000 0.068 0.004
#> ERR184094 6 0.6235 0.5343 0.084 0.000 0.120 0.124 0.032 0.640
#> ERR184058 2 0.4752 0.4178 0.000 0.740 0.136 0.004 0.048 0.072
#> ERR184036 6 0.3315 0.7050 0.004 0.056 0.000 0.004 0.104 0.832
#> ERR184046 2 0.3767 0.3883 0.000 0.808 0.092 0.004 0.084 0.012
#> ERR184074 6 0.3444 0.6572 0.124 0.000 0.008 0.000 0.052 0.816
#> ERR184048 2 0.3121 0.1606 0.032 0.844 0.000 0.004 0.112 0.008
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 10269 rows and 62 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 0.610 0.934 0.904 0.3234 0.568 0.568
#> 3 3 0.753 0.946 0.971 0.4596 0.975 0.955
#> 4 4 0.754 0.793 0.903 0.0691 0.971 0.946
#> 5 5 0.757 0.831 0.876 0.0563 0.979 0.959
#> 6 6 0.754 0.781 0.864 0.0486 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] 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
#> ERR184078 1 0.9286 0.896 0.656 0.344
#> ERR184093 2 0.0000 0.981 0.000 1.000
#> ERR184051 1 0.9323 0.892 0.652 0.348
#> ERR184076 1 0.9286 0.896 0.656 0.344
#> ERR184043 1 0.9248 0.896 0.660 0.340
#> ERR184037 2 0.2778 0.943 0.048 0.952
#> ERR184059 1 0.7815 0.811 0.768 0.232
#> ERR184055 2 0.2778 0.943 0.048 0.952
#> ERR184065 2 0.0000 0.981 0.000 1.000
#> ERR184069 2 0.0000 0.981 0.000 1.000
#> ERR184040 1 0.9286 0.896 0.656 0.344
#> ERR184057 2 0.0000 0.981 0.000 1.000
#> ERR184082 2 0.2778 0.943 0.048 0.952
#> ERR184083 2 0.0000 0.981 0.000 1.000
#> ERR184039 2 0.0000 0.981 0.000 1.000
#> ERR184064 1 0.9248 0.896 0.660 0.340
#> ERR184081 2 0.0000 0.981 0.000 1.000
#> ERR184095 2 0.0000 0.981 0.000 1.000
#> ERR184079 2 0.0000 0.981 0.000 1.000
#> ERR184084 1 0.9248 0.895 0.660 0.340
#> ERR184068 2 0.0000 0.981 0.000 1.000
#> ERR184067 2 0.0000 0.981 0.000 1.000
#> ERR184071 2 0.0000 0.981 0.000 1.000
#> ERR184042 1 0.0000 0.652 1.000 0.000
#> ERR184063 1 0.9323 0.892 0.652 0.348
#> ERR184091 2 0.0000 0.981 0.000 1.000
#> ERR184061 2 0.3114 0.933 0.056 0.944
#> ERR184077 2 0.0000 0.981 0.000 1.000
#> ERR184062 2 0.2778 0.943 0.048 0.952
#> ERR184053 2 0.0000 0.981 0.000 1.000
#> ERR184088 2 0.0000 0.981 0.000 1.000
#> ERR184075 2 0.0000 0.981 0.000 1.000
#> ERR184041 1 0.9427 0.874 0.640 0.360
#> ERR184060 2 0.0000 0.981 0.000 1.000
#> ERR184035 2 0.2778 0.943 0.048 0.952
#> ERR184086 2 0.0000 0.981 0.000 1.000
#> ERR184080 2 0.2778 0.943 0.048 0.952
#> ERR184050 2 0.0000 0.981 0.000 1.000
#> ERR184047 1 0.0000 0.652 1.000 0.000
#> ERR184092 2 0.0000 0.981 0.000 1.000
#> ERR184072 1 0.9323 0.892 0.652 0.348
#> ERR184073 1 0.9248 0.896 0.660 0.340
#> ERR184066 2 0.2778 0.943 0.048 0.952
#> ERR184098 2 0.0000 0.981 0.000 1.000
#> ERR184044 2 0.2778 0.943 0.048 0.952
#> ERR184054 1 0.9286 0.896 0.656 0.344
#> ERR184085 2 0.2778 0.943 0.048 0.952
#> ERR184056 2 0.0000 0.981 0.000 1.000
#> ERR184052 2 0.0000 0.981 0.000 1.000
#> ERR184070 2 0.0000 0.981 0.000 1.000
#> ERR184096 1 0.0000 0.652 1.000 0.000
#> ERR184089 2 0.0376 0.978 0.004 0.996
#> ERR184049 2 0.0000 0.981 0.000 1.000
#> ERR184038 2 0.2778 0.943 0.048 0.952
#> ERR184087 1 0.9248 0.896 0.660 0.340
#> ERR184097 2 0.0000 0.981 0.000 1.000
#> ERR184094 1 0.9248 0.896 0.660 0.340
#> ERR184058 2 0.0000 0.981 0.000 1.000
#> ERR184036 2 0.0000 0.981 0.000 1.000
#> ERR184046 2 0.0000 0.981 0.000 1.000
#> ERR184074 1 0.9286 0.896 0.656 0.344
#> ERR184048 2 0.0000 0.981 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.0000 0.978 1.000 0.000 0.000
#> ERR184093 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184051 1 0.0237 0.976 0.996 0.004 0.000
#> ERR184076 1 0.0000 0.978 1.000 0.000 0.000
#> ERR184043 1 0.0424 0.977 0.992 0.000 0.008
#> ERR184037 2 0.3619 0.872 0.136 0.864 0.000
#> ERR184059 1 0.4974 0.695 0.764 0.000 0.236
#> ERR184055 2 0.3551 0.876 0.132 0.868 0.000
#> ERR184065 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184069 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184040 1 0.0000 0.978 1.000 0.000 0.000
#> ERR184057 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184082 2 0.3551 0.876 0.132 0.868 0.000
#> ERR184083 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184039 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184064 1 0.0424 0.977 0.992 0.000 0.008
#> ERR184081 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184095 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184079 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184084 1 0.0237 0.977 0.996 0.000 0.004
#> ERR184068 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184067 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184071 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184042 3 0.0000 1.000 0.000 0.000 1.000
#> ERR184063 1 0.0237 0.976 0.996 0.004 0.000
#> ERR184091 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184061 2 0.3879 0.855 0.152 0.848 0.000
#> ERR184077 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184062 2 0.3551 0.876 0.132 0.868 0.000
#> ERR184053 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184088 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184075 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184041 1 0.0747 0.959 0.984 0.016 0.000
#> ERR184060 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184035 2 0.3551 0.876 0.132 0.868 0.000
#> ERR184086 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184080 2 0.3551 0.876 0.132 0.868 0.000
#> ERR184050 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184047 3 0.0000 1.000 0.000 0.000 1.000
#> ERR184092 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184072 1 0.0237 0.976 0.996 0.004 0.000
#> ERR184073 1 0.0237 0.978 0.996 0.000 0.004
#> ERR184066 2 0.3551 0.876 0.132 0.868 0.000
#> ERR184098 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184044 2 0.3551 0.876 0.132 0.868 0.000
#> ERR184054 1 0.0000 0.978 1.000 0.000 0.000
#> ERR184085 2 0.3551 0.876 0.132 0.868 0.000
#> ERR184056 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184052 2 0.0237 0.957 0.004 0.996 0.000
#> ERR184070 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184096 3 0.0000 1.000 0.000 0.000 1.000
#> ERR184089 2 0.0424 0.955 0.008 0.992 0.000
#> ERR184049 2 0.0237 0.957 0.004 0.996 0.000
#> ERR184038 2 0.3551 0.876 0.132 0.868 0.000
#> ERR184087 1 0.0424 0.977 0.992 0.000 0.008
#> ERR184097 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184094 1 0.0237 0.978 0.996 0.000 0.004
#> ERR184058 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184036 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184046 2 0.0000 0.959 0.000 1.000 0.000
#> ERR184074 1 0.0000 0.978 1.000 0.000 0.000
#> ERR184048 2 0.0000 0.959 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.4999 0.703 0.508 0.000 0.492 0.000
#> ERR184093 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184051 3 0.1389 0.646 0.048 0.000 0.952 0.000
#> ERR184076 1 0.4888 0.673 0.588 0.000 0.412 0.000
#> ERR184043 3 0.0000 0.650 0.000 0.000 1.000 0.000
#> ERR184037 2 0.3351 0.870 0.148 0.844 0.008 0.000
#> ERR184059 3 0.4158 0.408 0.008 0.000 0.768 0.224
#> ERR184055 2 0.3300 0.873 0.144 0.848 0.008 0.000
#> ERR184065 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184069 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184040 3 0.4999 -0.748 0.492 0.000 0.508 0.000
#> ERR184057 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184082 2 0.3300 0.873 0.144 0.848 0.008 0.000
#> ERR184083 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184039 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184064 3 0.0000 0.650 0.000 0.000 1.000 0.000
#> ERR184081 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184095 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184079 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184084 3 0.2011 0.618 0.080 0.000 0.920 0.000
#> ERR184068 2 0.0188 0.957 0.004 0.996 0.000 0.000
#> ERR184067 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184071 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184042 4 0.3907 0.873 0.232 0.000 0.000 0.768
#> ERR184063 3 0.1389 0.646 0.048 0.000 0.952 0.000
#> ERR184091 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184061 2 0.3545 0.855 0.164 0.828 0.008 0.000
#> ERR184077 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184062 2 0.3300 0.873 0.144 0.848 0.008 0.000
#> ERR184053 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184088 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184075 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184041 3 0.1716 0.638 0.064 0.000 0.936 0.000
#> ERR184060 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184035 2 0.3300 0.873 0.144 0.848 0.008 0.000
#> ERR184086 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184080 2 0.3300 0.873 0.144 0.848 0.008 0.000
#> ERR184050 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184047 4 0.0000 0.938 0.000 0.000 0.000 1.000
#> ERR184092 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184072 1 0.4164 0.564 0.736 0.000 0.264 0.000
#> ERR184073 3 0.4998 -0.746 0.488 0.000 0.512 0.000
#> ERR184066 2 0.3300 0.873 0.144 0.848 0.008 0.000
#> ERR184098 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184044 2 0.3300 0.873 0.144 0.848 0.008 0.000
#> ERR184054 1 0.4998 0.714 0.512 0.000 0.488 0.000
#> ERR184085 2 0.3300 0.873 0.144 0.848 0.008 0.000
#> ERR184056 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184052 2 0.0188 0.957 0.004 0.996 0.000 0.000
#> ERR184070 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184096 4 0.0000 0.938 0.000 0.000 0.000 1.000
#> ERR184089 2 0.0817 0.947 0.024 0.976 0.000 0.000
#> ERR184049 2 0.0188 0.957 0.004 0.996 0.000 0.000
#> ERR184038 2 0.3300 0.873 0.144 0.848 0.008 0.000
#> ERR184087 3 0.0000 0.650 0.000 0.000 1.000 0.000
#> ERR184097 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184094 3 0.4907 -0.592 0.420 0.000 0.580 0.000
#> ERR184058 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184036 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184046 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> ERR184074 1 0.4981 0.727 0.536 0.000 0.464 0.000
#> ERR184048 2 0.0000 0.958 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
#> ERR184078 1 0.1357 0.776 0.948 0.000 0.004 0.000 0.048
#> ERR184093 2 0.0404 0.925 0.000 0.988 0.000 0.000 0.012
#> ERR184051 3 0.4604 0.888 0.428 0.000 0.560 0.000 0.012
#> ERR184076 1 0.4807 -0.358 0.532 0.000 0.020 0.000 0.448
#> ERR184043 3 0.4150 0.893 0.388 0.000 0.612 0.000 0.000
#> ERR184037 2 0.3912 0.780 0.020 0.752 0.000 0.000 0.228
#> ERR184059 3 0.6736 0.594 0.324 0.000 0.488 0.172 0.016
#> ERR184055 2 0.3819 0.784 0.016 0.756 0.000 0.000 0.228
#> ERR184065 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184069 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184040 1 0.0404 0.805 0.988 0.000 0.012 0.000 0.000
#> ERR184057 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184082 2 0.3819 0.784 0.016 0.756 0.000 0.000 0.228
#> ERR184083 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184039 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184064 3 0.4150 0.893 0.388 0.000 0.612 0.000 0.000
#> ERR184081 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184095 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184079 2 0.0880 0.919 0.000 0.968 0.000 0.000 0.032
#> ERR184084 3 0.4297 0.829 0.472 0.000 0.528 0.000 0.000
#> ERR184068 2 0.0880 0.919 0.000 0.968 0.000 0.000 0.032
#> ERR184067 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184071 2 0.0290 0.926 0.000 0.992 0.000 0.000 0.008
#> ERR184042 4 0.1608 0.606 0.000 0.000 0.000 0.928 0.072
#> ERR184063 3 0.4604 0.888 0.428 0.000 0.560 0.000 0.012
#> ERR184091 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184061 2 0.4026 0.763 0.020 0.736 0.000 0.000 0.244
#> ERR184077 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184062 2 0.3819 0.784 0.016 0.756 0.000 0.000 0.228
#> ERR184053 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184088 2 0.0404 0.925 0.000 0.988 0.000 0.000 0.012
#> ERR184075 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184041 3 0.4937 0.877 0.428 0.000 0.544 0.000 0.028
#> ERR184060 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184035 2 0.3819 0.784 0.016 0.756 0.000 0.000 0.228
#> ERR184086 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184080 2 0.3819 0.784 0.016 0.756 0.000 0.000 0.228
#> ERR184050 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184047 4 0.4088 0.819 0.000 0.000 0.368 0.632 0.000
#> ERR184092 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184072 5 0.4084 0.000 0.328 0.000 0.004 0.000 0.668
#> ERR184073 1 0.0609 0.804 0.980 0.000 0.020 0.000 0.000
#> ERR184066 2 0.3819 0.784 0.016 0.756 0.000 0.000 0.228
#> ERR184098 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184044 2 0.3819 0.784 0.016 0.756 0.000 0.000 0.228
#> ERR184054 1 0.0703 0.806 0.976 0.000 0.000 0.000 0.024
#> ERR184085 2 0.3819 0.784 0.016 0.756 0.000 0.000 0.228
#> ERR184056 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184052 2 0.0880 0.919 0.000 0.968 0.000 0.000 0.032
#> ERR184070 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184096 4 0.4088 0.819 0.000 0.000 0.368 0.632 0.000
#> ERR184089 2 0.1478 0.903 0.000 0.936 0.000 0.000 0.064
#> ERR184049 2 0.0963 0.917 0.000 0.964 0.000 0.000 0.036
#> ERR184038 2 0.3819 0.784 0.016 0.756 0.000 0.000 0.228
#> ERR184087 3 0.4150 0.893 0.388 0.000 0.612 0.000 0.000
#> ERR184097 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184094 1 0.2408 0.690 0.892 0.000 0.092 0.000 0.016
#> ERR184058 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184036 2 0.0404 0.925 0.000 0.988 0.000 0.000 0.012
#> ERR184046 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000
#> ERR184074 1 0.1121 0.784 0.956 0.000 0.000 0.000 0.044
#> ERR184048 2 0.0000 0.928 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
#> ERR184078 1 0.3969 0.763 0.668 0.000 0.312 NA 0.000 0.020
#> ERR184093 2 0.0547 0.889 0.000 0.980 0.000 NA 0.000 0.020
#> ERR184051 3 0.1390 0.854 0.032 0.000 0.948 NA 0.000 0.004
#> ERR184076 1 0.3679 -0.144 0.772 0.000 0.000 NA 0.000 0.052
#> ERR184043 3 0.0000 0.861 0.000 0.000 1.000 NA 0.000 0.000
#> ERR184037 2 0.3769 0.652 0.000 0.640 0.000 NA 0.000 0.356
#> ERR184059 3 0.5250 0.427 0.000 0.000 0.608 NA 0.208 0.000
#> ERR184055 2 0.3634 0.657 0.000 0.644 0.000 NA 0.000 0.356
#> ERR184065 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184069 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184040 1 0.4022 0.776 0.628 0.000 0.360 NA 0.000 0.008
#> ERR184057 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184082 2 0.3756 0.657 0.000 0.644 0.000 NA 0.000 0.352
#> ERR184083 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184039 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184064 3 0.0000 0.861 0.000 0.000 1.000 NA 0.000 0.000
#> ERR184081 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184095 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184079 2 0.0937 0.883 0.000 0.960 0.000 NA 0.000 0.040
#> ERR184084 3 0.3796 0.691 0.084 0.000 0.776 NA 0.000 0.000
#> ERR184068 2 0.0935 0.885 0.000 0.964 0.000 NA 0.000 0.032
#> ERR184067 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184071 2 0.0260 0.892 0.000 0.992 0.000 NA 0.000 0.008
#> ERR184042 5 0.3851 0.529 0.000 0.000 0.000 NA 0.540 0.000
#> ERR184063 3 0.1390 0.854 0.032 0.000 0.948 NA 0.000 0.004
#> ERR184091 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184061 2 0.3819 0.631 0.000 0.624 0.000 NA 0.000 0.372
#> ERR184077 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184062 2 0.3634 0.657 0.000 0.644 0.000 NA 0.000 0.356
#> ERR184053 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184088 2 0.0547 0.889 0.000 0.980 0.000 NA 0.000 0.020
#> ERR184075 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184041 3 0.1787 0.844 0.032 0.000 0.932 NA 0.000 0.020
#> ERR184060 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184035 2 0.3756 0.657 0.000 0.644 0.000 NA 0.000 0.352
#> ERR184086 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184080 2 0.3634 0.657 0.000 0.644 0.000 NA 0.000 0.356
#> ERR184050 2 0.0146 0.893 0.000 0.996 0.000 NA 0.000 0.004
#> ERR184047 5 0.0000 0.790 0.000 0.000 0.000 NA 1.000 0.000
#> ERR184092 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184072 6 0.4828 0.000 0.156 0.000 0.000 NA 0.000 0.668
#> ERR184073 1 0.4326 0.776 0.608 0.000 0.368 NA 0.000 0.008
#> ERR184066 2 0.3634 0.657 0.000 0.644 0.000 NA 0.000 0.356
#> ERR184098 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184044 2 0.3756 0.657 0.000 0.644 0.000 NA 0.000 0.352
#> ERR184054 1 0.4306 0.775 0.624 0.000 0.344 NA 0.000 0.032
#> ERR184085 2 0.3634 0.657 0.000 0.644 0.000 NA 0.000 0.356
#> ERR184056 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184052 2 0.1007 0.881 0.000 0.956 0.000 NA 0.000 0.044
#> ERR184070 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184096 5 0.0000 0.790 0.000 0.000 0.000 NA 1.000 0.000
#> ERR184089 2 0.1501 0.864 0.000 0.924 0.000 NA 0.000 0.076
#> ERR184049 2 0.1075 0.879 0.000 0.952 0.000 NA 0.000 0.048
#> ERR184038 2 0.3634 0.657 0.000 0.644 0.000 NA 0.000 0.356
#> ERR184087 3 0.0000 0.861 0.000 0.000 1.000 NA 0.000 0.000
#> ERR184097 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184094 1 0.4903 0.692 0.524 0.000 0.424 NA 0.000 0.008
#> ERR184058 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184036 2 0.0547 0.889 0.000 0.980 0.000 NA 0.000 0.020
#> ERR184046 2 0.0000 0.894 0.000 1.000 0.000 NA 0.000 0.000
#> ERR184074 1 0.5668 0.739 0.540 0.000 0.348 NA 0.000 0.036
#> ERR184048 2 0.0000 0.894 0.000 1.000 0.000 NA 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["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 10269 rows and 62 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 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.978 0.989 0.4394 0.568 0.568
#> 3 3 0.935 0.953 0.971 0.3683 0.714 0.539
#> 4 4 0.739 0.777 0.881 0.1106 0.906 0.773
#> 5 5 0.738 0.606 0.752 0.1003 0.867 0.649
#> 6 6 0.786 0.847 0.845 0.0571 0.832 0.474
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
#> ERR184078 1 0.000 1.000 1.000 0.000
#> ERR184093 2 0.000 0.984 0.000 1.000
#> ERR184051 1 0.000 1.000 1.000 0.000
#> ERR184076 1 0.000 1.000 1.000 0.000
#> ERR184043 1 0.000 1.000 1.000 0.000
#> ERR184037 2 0.327 0.939 0.060 0.940
#> ERR184059 1 0.000 1.000 1.000 0.000
#> ERR184055 2 0.163 0.969 0.024 0.976
#> ERR184065 2 0.000 0.984 0.000 1.000
#> ERR184069 2 0.000 0.984 0.000 1.000
#> ERR184040 1 0.000 1.000 1.000 0.000
#> ERR184057 2 0.000 0.984 0.000 1.000
#> ERR184082 2 0.163 0.969 0.024 0.976
#> ERR184083 2 0.000 0.984 0.000 1.000
#> ERR184039 2 0.000 0.984 0.000 1.000
#> ERR184064 1 0.000 1.000 1.000 0.000
#> ERR184081 2 0.000 0.984 0.000 1.000
#> ERR184095 2 0.000 0.984 0.000 1.000
#> ERR184079 2 0.000 0.984 0.000 1.000
#> ERR184084 1 0.000 1.000 1.000 0.000
#> ERR184068 2 0.000 0.984 0.000 1.000
#> ERR184067 2 0.000 0.984 0.000 1.000
#> ERR184071 2 0.000 0.984 0.000 1.000
#> ERR184042 1 0.000 1.000 1.000 0.000
#> ERR184063 1 0.000 1.000 1.000 0.000
#> ERR184091 2 0.000 0.984 0.000 1.000
#> ERR184061 2 0.163 0.969 0.024 0.976
#> ERR184077 2 0.000 0.984 0.000 1.000
#> ERR184062 2 0.000 0.984 0.000 1.000
#> ERR184053 2 0.000 0.984 0.000 1.000
#> ERR184088 2 0.000 0.984 0.000 1.000
#> ERR184075 2 0.000 0.984 0.000 1.000
#> ERR184041 1 0.000 1.000 1.000 0.000
#> ERR184060 2 0.000 0.984 0.000 1.000
#> ERR184035 2 0.327 0.939 0.060 0.940
#> ERR184086 2 0.000 0.984 0.000 1.000
#> ERR184080 2 0.833 0.666 0.264 0.736
#> ERR184050 2 0.000 0.984 0.000 1.000
#> ERR184047 1 0.000 1.000 1.000 0.000
#> ERR184092 2 0.000 0.984 0.000 1.000
#> ERR184072 1 0.000 1.000 1.000 0.000
#> ERR184073 1 0.000 1.000 1.000 0.000
#> ERR184066 2 0.163 0.969 0.024 0.976
#> ERR184098 2 0.000 0.984 0.000 1.000
#> ERR184044 2 0.000 0.984 0.000 1.000
#> ERR184054 1 0.000 1.000 1.000 0.000
#> ERR184085 2 0.327 0.939 0.060 0.940
#> ERR184056 2 0.000 0.984 0.000 1.000
#> ERR184052 2 0.000 0.984 0.000 1.000
#> ERR184070 2 0.000 0.984 0.000 1.000
#> ERR184096 1 0.000 1.000 1.000 0.000
#> ERR184089 2 0.000 0.984 0.000 1.000
#> ERR184049 2 0.000 0.984 0.000 1.000
#> ERR184038 2 0.584 0.851 0.140 0.860
#> ERR184087 1 0.000 1.000 1.000 0.000
#> ERR184097 2 0.000 0.984 0.000 1.000
#> ERR184094 1 0.000 1.000 1.000 0.000
#> ERR184058 2 0.000 0.984 0.000 1.000
#> ERR184036 2 0.000 0.984 0.000 1.000
#> ERR184046 2 0.000 0.984 0.000 1.000
#> ERR184074 1 0.000 1.000 1.000 0.000
#> ERR184048 2 0.000 0.984 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.1163 0.941 0.972 0.000 0.028
#> ERR184093 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184051 1 0.0000 0.961 1.000 0.000 0.000
#> ERR184076 1 0.0237 0.961 0.996 0.000 0.004
#> ERR184043 3 0.4399 0.875 0.188 0.000 0.812
#> ERR184037 1 0.0237 0.963 0.996 0.004 0.000
#> ERR184059 3 0.0000 0.851 0.000 0.000 1.000
#> ERR184055 1 0.0237 0.963 0.996 0.004 0.000
#> ERR184065 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184069 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184040 1 0.1163 0.941 0.972 0.000 0.028
#> ERR184057 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184082 1 0.0892 0.946 0.980 0.020 0.000
#> ERR184083 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184039 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184064 3 0.4504 0.871 0.196 0.000 0.804
#> ERR184081 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184095 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184079 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184084 3 0.5810 0.677 0.336 0.000 0.664
#> ERR184068 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184067 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184071 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184042 3 0.0000 0.851 0.000 0.000 1.000
#> ERR184063 1 0.0000 0.961 1.000 0.000 0.000
#> ERR184091 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184061 1 0.0592 0.955 0.988 0.012 0.000
#> ERR184077 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184062 1 0.5835 0.421 0.660 0.340 0.000
#> ERR184053 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184088 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184075 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184041 1 0.0000 0.961 1.000 0.000 0.000
#> ERR184060 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184035 1 0.0747 0.951 0.984 0.016 0.000
#> ERR184086 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184080 1 0.0237 0.963 0.996 0.004 0.000
#> ERR184050 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184047 3 0.0000 0.851 0.000 0.000 1.000
#> ERR184092 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184072 1 0.0237 0.961 0.996 0.000 0.004
#> ERR184073 3 0.4452 0.872 0.192 0.000 0.808
#> ERR184066 1 0.0237 0.963 0.996 0.004 0.000
#> ERR184098 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184044 1 0.0237 0.963 0.996 0.004 0.000
#> ERR184054 1 0.0237 0.961 0.996 0.000 0.004
#> ERR184085 1 0.0237 0.963 0.996 0.004 0.000
#> ERR184056 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184052 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184070 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184096 3 0.0000 0.851 0.000 0.000 1.000
#> ERR184089 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184049 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184038 1 0.0237 0.963 0.996 0.004 0.000
#> ERR184087 3 0.4399 0.875 0.188 0.000 0.812
#> ERR184097 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184094 3 0.4452 0.872 0.192 0.000 0.808
#> ERR184058 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184036 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184046 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184074 1 0.0237 0.961 0.996 0.000 0.004
#> ERR184048 2 0.0000 1.000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 3 0.4304 0.5350 0.284 0.000 0.716 0.000
#> ERR184093 2 0.2530 0.9172 0.000 0.888 0.000 0.112
#> ERR184051 3 0.3942 0.7156 0.236 0.000 0.764 0.000
#> ERR184076 1 0.4998 0.0707 0.512 0.000 0.488 0.000
#> ERR184043 3 0.2589 0.7559 0.000 0.000 0.884 0.116
#> ERR184037 1 0.0188 0.7681 0.996 0.000 0.000 0.004
#> ERR184059 3 0.3172 0.7066 0.000 0.000 0.840 0.160
#> ERR184055 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> ERR184065 2 0.0188 0.9225 0.000 0.996 0.000 0.004
#> ERR184069 2 0.0188 0.9225 0.000 0.996 0.000 0.004
#> ERR184040 3 0.4304 0.5350 0.284 0.000 0.716 0.000
#> ERR184057 2 0.0188 0.9225 0.000 0.996 0.000 0.004
#> ERR184082 1 0.0469 0.7666 0.988 0.000 0.000 0.012
#> ERR184083 2 0.0188 0.9225 0.000 0.996 0.000 0.004
#> ERR184039 2 0.0000 0.9228 0.000 1.000 0.000 0.000
#> ERR184064 3 0.2589 0.7559 0.000 0.000 0.884 0.116
#> ERR184081 2 0.0188 0.9225 0.000 0.996 0.000 0.004
#> ERR184095 2 0.0188 0.9225 0.000 0.996 0.000 0.004
#> ERR184079 2 0.3219 0.9057 0.020 0.868 0.000 0.112
#> ERR184084 3 0.3166 0.7606 0.016 0.000 0.868 0.116
#> ERR184068 2 0.6607 0.5269 0.296 0.592 0.000 0.112
#> ERR184067 2 0.0188 0.9225 0.000 0.996 0.000 0.004
#> ERR184071 2 0.2530 0.9172 0.000 0.888 0.000 0.112
#> ERR184042 4 0.2647 1.0000 0.000 0.000 0.120 0.880
#> ERR184063 3 0.4193 0.6864 0.268 0.000 0.732 0.000
#> ERR184091 2 0.0188 0.9225 0.000 0.996 0.000 0.004
#> ERR184061 1 0.0921 0.7605 0.972 0.000 0.000 0.028
#> ERR184077 2 0.2469 0.9185 0.000 0.892 0.000 0.108
#> ERR184062 1 0.5119 0.5177 0.764 0.124 0.000 0.112
#> ERR184053 2 0.2469 0.9185 0.000 0.892 0.000 0.108
#> ERR184088 2 0.2530 0.9172 0.000 0.888 0.000 0.112
#> ERR184075 2 0.1211 0.9242 0.000 0.960 0.000 0.040
#> ERR184041 3 0.4304 0.6664 0.284 0.000 0.716 0.000
#> ERR184060 2 0.0188 0.9225 0.000 0.996 0.000 0.004
#> ERR184035 1 0.0336 0.7681 0.992 0.000 0.000 0.008
#> ERR184086 2 0.2011 0.9230 0.000 0.920 0.000 0.080
#> ERR184080 1 0.1389 0.7473 0.952 0.000 0.048 0.000
#> ERR184050 2 0.2530 0.9172 0.000 0.888 0.000 0.112
#> ERR184047 4 0.2647 1.0000 0.000 0.000 0.120 0.880
#> ERR184092 2 0.2345 0.9204 0.000 0.900 0.000 0.100
#> ERR184072 1 0.5016 0.3257 0.600 0.000 0.396 0.004
#> ERR184073 3 0.0000 0.7374 0.000 0.000 1.000 0.000
#> ERR184066 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> ERR184098 2 0.2011 0.9230 0.000 0.920 0.000 0.080
#> ERR184044 1 0.1118 0.7528 0.964 0.000 0.000 0.036
#> ERR184054 1 0.4855 0.3179 0.600 0.000 0.400 0.000
#> ERR184085 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> ERR184056 2 0.0188 0.9225 0.000 0.996 0.000 0.004
#> ERR184052 2 0.3108 0.9088 0.016 0.872 0.000 0.112
#> ERR184070 2 0.0188 0.9225 0.000 0.996 0.000 0.004
#> ERR184096 4 0.2647 1.0000 0.000 0.000 0.120 0.880
#> ERR184089 2 0.6476 0.5761 0.272 0.616 0.000 0.112
#> ERR184049 1 0.6885 0.0546 0.516 0.372 0.000 0.112
#> ERR184038 1 0.0000 0.7684 1.000 0.000 0.000 0.000
#> ERR184087 3 0.2589 0.7559 0.000 0.000 0.884 0.116
#> ERR184097 2 0.2345 0.9204 0.000 0.900 0.000 0.100
#> ERR184094 3 0.2589 0.7559 0.000 0.000 0.884 0.116
#> ERR184058 2 0.0188 0.9225 0.000 0.996 0.000 0.004
#> ERR184036 2 0.2530 0.9172 0.000 0.888 0.000 0.112
#> ERR184046 2 0.0188 0.9225 0.000 0.996 0.000 0.004
#> ERR184074 1 0.5163 0.1003 0.516 0.000 0.480 0.004
#> ERR184048 2 0.2408 0.9195 0.000 0.896 0.000 0.104
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.2763 0.655 0.848 0.000 0.148 0.004 0.000
#> ERR184093 2 0.4291 0.631 0.000 0.536 0.000 0.464 0.000
#> ERR184051 3 0.4597 0.891 0.424 0.000 0.564 0.012 0.000
#> ERR184076 1 0.4025 0.714 0.700 0.000 0.292 0.008 0.000
#> ERR184043 3 0.5668 0.924 0.416 0.000 0.504 0.000 0.080
#> ERR184037 4 0.4304 0.528 0.000 0.000 0.484 0.516 0.000
#> ERR184059 3 0.5989 0.889 0.412 0.000 0.476 0.000 0.112
#> ERR184055 4 0.4300 0.531 0.000 0.000 0.476 0.524 0.000
#> ERR184065 2 0.0000 0.748 0.000 1.000 0.000 0.000 0.000
#> ERR184069 2 0.0000 0.748 0.000 1.000 0.000 0.000 0.000
#> ERR184040 1 0.2605 0.652 0.852 0.000 0.148 0.000 0.000
#> ERR184057 2 0.0000 0.748 0.000 1.000 0.000 0.000 0.000
#> ERR184082 4 0.4283 0.535 0.000 0.000 0.456 0.544 0.000
#> ERR184083 2 0.0000 0.748 0.000 1.000 0.000 0.000 0.000
#> ERR184039 2 0.0404 0.747 0.000 0.988 0.000 0.012 0.000
#> ERR184064 3 0.5668 0.924 0.416 0.000 0.504 0.000 0.080
#> ERR184081 2 0.0000 0.748 0.000 1.000 0.000 0.000 0.000
#> ERR184095 2 0.0000 0.748 0.000 1.000 0.000 0.000 0.000
#> ERR184079 2 0.4305 0.599 0.000 0.512 0.000 0.488 0.000
#> ERR184084 3 0.5649 0.907 0.452 0.000 0.472 0.000 0.076
#> ERR184068 4 0.2773 0.146 0.000 0.164 0.000 0.836 0.000
#> ERR184067 2 0.0000 0.748 0.000 1.000 0.000 0.000 0.000
#> ERR184071 2 0.4287 0.636 0.000 0.540 0.000 0.460 0.000
#> ERR184042 5 0.0566 0.988 0.000 0.000 0.004 0.012 0.984
#> ERR184063 3 0.4597 0.891 0.424 0.000 0.564 0.012 0.000
#> ERR184091 2 0.0000 0.748 0.000 1.000 0.000 0.000 0.000
#> ERR184061 4 0.4297 0.532 0.000 0.000 0.472 0.528 0.000
#> ERR184077 2 0.4287 0.636 0.000 0.540 0.000 0.460 0.000
#> ERR184062 4 0.2777 0.404 0.000 0.016 0.120 0.864 0.000
#> ERR184053 2 0.4287 0.636 0.000 0.540 0.000 0.460 0.000
#> ERR184088 4 0.4305 -0.601 0.000 0.488 0.000 0.512 0.000
#> ERR184075 2 0.3534 0.704 0.000 0.744 0.000 0.256 0.000
#> ERR184041 3 0.4582 0.881 0.416 0.000 0.572 0.012 0.000
#> ERR184060 2 0.0000 0.748 0.000 1.000 0.000 0.000 0.000
#> ERR184035 4 0.4304 0.528 0.000 0.000 0.484 0.516 0.000
#> ERR184086 2 0.4030 0.680 0.000 0.648 0.000 0.352 0.000
#> ERR184080 4 0.4971 0.503 0.028 0.000 0.460 0.512 0.000
#> ERR184050 2 0.4287 0.636 0.000 0.540 0.000 0.460 0.000
#> ERR184047 5 0.0162 0.994 0.004 0.000 0.000 0.000 0.996
#> ERR184092 2 0.4256 0.648 0.000 0.564 0.000 0.436 0.000
#> ERR184072 1 0.4836 0.684 0.628 0.000 0.336 0.036 0.000
#> ERR184073 1 0.0404 0.367 0.988 0.000 0.000 0.000 0.012
#> ERR184066 4 0.4302 0.530 0.000 0.000 0.480 0.520 0.000
#> ERR184098 2 0.4045 0.679 0.000 0.644 0.000 0.356 0.000
#> ERR184044 4 0.4126 0.513 0.000 0.000 0.380 0.620 0.000
#> ERR184054 1 0.4763 0.685 0.632 0.000 0.336 0.032 0.000
#> ERR184085 4 0.4294 0.534 0.000 0.000 0.468 0.532 0.000
#> ERR184056 2 0.0000 0.748 0.000 1.000 0.000 0.000 0.000
#> ERR184052 4 0.4300 -0.583 0.000 0.476 0.000 0.524 0.000
#> ERR184070 2 0.0000 0.748 0.000 1.000 0.000 0.000 0.000
#> ERR184096 5 0.0162 0.994 0.004 0.000 0.000 0.000 0.996
#> ERR184089 4 0.4166 -0.346 0.000 0.348 0.004 0.648 0.000
#> ERR184049 4 0.0703 0.339 0.000 0.024 0.000 0.976 0.000
#> ERR184038 4 0.4302 0.530 0.000 0.000 0.480 0.520 0.000
#> ERR184087 3 0.5668 0.924 0.416 0.000 0.504 0.000 0.080
#> ERR184097 2 0.4278 0.640 0.000 0.548 0.000 0.452 0.000
#> ERR184094 1 0.5124 -0.617 0.644 0.000 0.288 0.000 0.068
#> ERR184058 2 0.0000 0.748 0.000 1.000 0.000 0.000 0.000
#> ERR184036 2 0.4287 0.636 0.000 0.540 0.000 0.460 0.000
#> ERR184046 2 0.0000 0.748 0.000 1.000 0.000 0.000 0.000
#> ERR184074 1 0.4165 0.710 0.672 0.000 0.320 0.008 0.000
#> ERR184048 2 0.4287 0.636 0.000 0.540 0.000 0.460 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.1657 0.925 0.936 0.000 0.040 0.012 0.000 0.012
#> ERR184093 2 0.0508 0.825 0.012 0.984 0.000 0.000 0.004 0.000
#> ERR184051 3 0.2477 0.871 0.024 0.000 0.896 0.048 0.000 0.032
#> ERR184076 1 0.2819 0.911 0.880 0.000 0.024 0.056 0.004 0.036
#> ERR184043 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000 0.000
#> ERR184037 6 0.1785 0.893 0.016 0.000 0.000 0.048 0.008 0.928
#> ERR184059 3 0.1321 0.875 0.024 0.000 0.952 0.020 0.004 0.000
#> ERR184055 6 0.0508 0.907 0.012 0.000 0.000 0.004 0.000 0.984
#> ERR184065 4 0.3607 0.990 0.000 0.348 0.000 0.652 0.000 0.000
#> ERR184069 4 0.3607 0.990 0.000 0.348 0.000 0.652 0.000 0.000
#> ERR184040 1 0.1555 0.925 0.940 0.000 0.040 0.008 0.000 0.012
#> ERR184057 4 0.3607 0.990 0.000 0.348 0.000 0.652 0.000 0.000
#> ERR184082 6 0.1588 0.890 0.000 0.004 0.000 0.072 0.000 0.924
#> ERR184083 4 0.3607 0.990 0.000 0.348 0.000 0.652 0.000 0.000
#> ERR184039 4 0.4249 0.857 0.012 0.416 0.000 0.568 0.004 0.000
#> ERR184064 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000 0.000
#> ERR184081 4 0.3607 0.990 0.000 0.348 0.000 0.652 0.000 0.000
#> ERR184095 4 0.3607 0.990 0.000 0.348 0.000 0.652 0.000 0.000
#> ERR184079 2 0.1490 0.814 0.008 0.948 0.000 0.024 0.004 0.016
#> ERR184084 3 0.1564 0.883 0.040 0.000 0.936 0.024 0.000 0.000
#> ERR184068 2 0.4467 0.547 0.016 0.708 0.000 0.040 0.004 0.232
#> ERR184067 4 0.3607 0.990 0.000 0.348 0.000 0.652 0.000 0.000
#> ERR184071 2 0.0291 0.823 0.004 0.992 0.000 0.004 0.000 0.000
#> ERR184042 5 0.1552 0.986 0.004 0.000 0.036 0.020 0.940 0.000
#> ERR184063 3 0.2620 0.868 0.024 0.000 0.888 0.048 0.000 0.040
#> ERR184091 4 0.3607 0.990 0.000 0.348 0.000 0.652 0.000 0.000
#> ERR184061 6 0.2290 0.888 0.024 0.004 0.000 0.060 0.008 0.904
#> ERR184077 2 0.0551 0.824 0.008 0.984 0.000 0.004 0.004 0.000
#> ERR184062 6 0.4226 0.488 0.004 0.328 0.000 0.016 0.004 0.648
#> ERR184053 2 0.0551 0.824 0.008 0.984 0.000 0.004 0.004 0.000
#> ERR184088 2 0.2495 0.781 0.016 0.892 0.000 0.032 0.000 0.060
#> ERR184075 2 0.3875 0.157 0.016 0.700 0.000 0.280 0.004 0.000
#> ERR184041 3 0.2818 0.860 0.024 0.000 0.876 0.048 0.000 0.052
#> ERR184060 4 0.3607 0.990 0.000 0.348 0.000 0.652 0.000 0.000
#> ERR184035 6 0.2157 0.892 0.008 0.004 0.000 0.076 0.008 0.904
#> ERR184086 2 0.2886 0.614 0.016 0.836 0.000 0.144 0.004 0.000
#> ERR184080 6 0.1806 0.894 0.044 0.000 0.000 0.020 0.008 0.928
#> ERR184050 2 0.0748 0.818 0.016 0.976 0.000 0.004 0.004 0.000
#> ERR184047 5 0.0865 0.993 0.000 0.000 0.036 0.000 0.964 0.000
#> ERR184092 2 0.0653 0.820 0.004 0.980 0.000 0.012 0.004 0.000
#> ERR184072 1 0.4279 0.843 0.784 0.000 0.020 0.120 0.024 0.052
#> ERR184073 1 0.1588 0.904 0.924 0.000 0.072 0.004 0.000 0.000
#> ERR184066 6 0.0909 0.906 0.020 0.000 0.000 0.012 0.000 0.968
#> ERR184098 2 0.2846 0.623 0.016 0.840 0.000 0.140 0.004 0.000
#> ERR184044 6 0.1575 0.894 0.000 0.032 0.000 0.032 0.000 0.936
#> ERR184054 1 0.2539 0.916 0.896 0.000 0.020 0.020 0.008 0.056
#> ERR184085 6 0.1152 0.901 0.000 0.004 0.000 0.044 0.000 0.952
#> ERR184056 4 0.3607 0.990 0.000 0.348 0.000 0.652 0.000 0.000
#> ERR184052 2 0.3003 0.775 0.028 0.868 0.000 0.032 0.004 0.068
#> ERR184070 4 0.3607 0.990 0.000 0.348 0.000 0.652 0.000 0.000
#> ERR184096 5 0.0865 0.993 0.000 0.000 0.036 0.000 0.964 0.000
#> ERR184089 2 0.3625 0.722 0.020 0.816 0.000 0.040 0.004 0.120
#> ERR184049 2 0.5109 0.190 0.020 0.552 0.000 0.036 0.004 0.388
#> ERR184038 6 0.0909 0.906 0.020 0.000 0.000 0.012 0.000 0.968
#> ERR184087 3 0.0000 0.890 0.000 0.000 1.000 0.000 0.000 0.000
#> ERR184097 2 0.0436 0.824 0.004 0.988 0.000 0.004 0.004 0.000
#> ERR184094 3 0.4155 0.360 0.364 0.000 0.616 0.020 0.000 0.000
#> ERR184058 4 0.3742 0.985 0.000 0.348 0.000 0.648 0.004 0.000
#> ERR184036 2 0.0922 0.821 0.024 0.968 0.000 0.000 0.004 0.004
#> ERR184046 4 0.3607 0.990 0.000 0.348 0.000 0.652 0.000 0.000
#> ERR184074 1 0.2476 0.918 0.900 0.000 0.020 0.020 0.008 0.052
#> ERR184048 2 0.0551 0.824 0.008 0.984 0.000 0.004 0.004 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", "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 10269 rows and 62 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 0.981 0.991 0.5048 0.494 0.494
#> 3 3 0.854 0.855 0.927 0.1810 0.911 0.820
#> 4 4 0.776 0.723 0.853 0.0739 0.976 0.940
#> 5 5 0.699 0.628 0.801 0.0599 0.999 0.997
#> 6 6 0.655 0.601 0.776 0.0396 0.973 0.930
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
#> ERR184078 1 0.000 0.980 1.000 0.000
#> ERR184093 2 0.000 1.000 0.000 1.000
#> ERR184051 1 0.000 0.980 1.000 0.000
#> ERR184076 1 0.000 0.980 1.000 0.000
#> ERR184043 1 0.000 0.980 1.000 0.000
#> ERR184037 1 0.000 0.980 1.000 0.000
#> ERR184059 1 0.000 0.980 1.000 0.000
#> ERR184055 1 0.000 0.980 1.000 0.000
#> ERR184065 2 0.000 1.000 0.000 1.000
#> ERR184069 2 0.000 1.000 0.000 1.000
#> ERR184040 1 0.000 0.980 1.000 0.000
#> ERR184057 2 0.000 1.000 0.000 1.000
#> ERR184082 1 0.788 0.708 0.764 0.236
#> ERR184083 2 0.000 1.000 0.000 1.000
#> ERR184039 2 0.000 1.000 0.000 1.000
#> ERR184064 1 0.000 0.980 1.000 0.000
#> ERR184081 2 0.000 1.000 0.000 1.000
#> ERR184095 2 0.000 1.000 0.000 1.000
#> ERR184079 2 0.000 1.000 0.000 1.000
#> ERR184084 1 0.000 0.980 1.000 0.000
#> ERR184068 2 0.000 1.000 0.000 1.000
#> ERR184067 2 0.000 1.000 0.000 1.000
#> ERR184071 2 0.000 1.000 0.000 1.000
#> ERR184042 1 0.000 0.980 1.000 0.000
#> ERR184063 1 0.000 0.980 1.000 0.000
#> ERR184091 2 0.000 1.000 0.000 1.000
#> ERR184061 1 0.295 0.937 0.948 0.052
#> ERR184077 2 0.000 1.000 0.000 1.000
#> ERR184062 2 0.000 1.000 0.000 1.000
#> ERR184053 2 0.000 1.000 0.000 1.000
#> ERR184088 2 0.000 1.000 0.000 1.000
#> ERR184075 2 0.000 1.000 0.000 1.000
#> ERR184041 1 0.000 0.980 1.000 0.000
#> ERR184060 2 0.000 1.000 0.000 1.000
#> ERR184035 1 0.653 0.808 0.832 0.168
#> ERR184086 2 0.000 1.000 0.000 1.000
#> ERR184080 1 0.000 0.980 1.000 0.000
#> ERR184050 2 0.000 1.000 0.000 1.000
#> ERR184047 1 0.000 0.980 1.000 0.000
#> ERR184092 2 0.000 1.000 0.000 1.000
#> ERR184072 1 0.000 0.980 1.000 0.000
#> ERR184073 1 0.000 0.980 1.000 0.000
#> ERR184066 1 0.000 0.980 1.000 0.000
#> ERR184098 2 0.000 1.000 0.000 1.000
#> ERR184044 1 0.494 0.879 0.892 0.108
#> ERR184054 1 0.000 0.980 1.000 0.000
#> ERR184085 1 0.000 0.980 1.000 0.000
#> ERR184056 2 0.000 1.000 0.000 1.000
#> ERR184052 2 0.000 1.000 0.000 1.000
#> ERR184070 2 0.000 1.000 0.000 1.000
#> ERR184096 1 0.000 0.980 1.000 0.000
#> ERR184089 2 0.000 1.000 0.000 1.000
#> ERR184049 2 0.000 1.000 0.000 1.000
#> ERR184038 1 0.000 0.980 1.000 0.000
#> ERR184087 1 0.000 0.980 1.000 0.000
#> ERR184097 2 0.000 1.000 0.000 1.000
#> ERR184094 1 0.000 0.980 1.000 0.000
#> ERR184058 2 0.000 1.000 0.000 1.000
#> ERR184036 2 0.000 1.000 0.000 1.000
#> ERR184046 2 0.000 1.000 0.000 1.000
#> ERR184074 1 0.000 0.980 1.000 0.000
#> ERR184048 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
#> ERR184078 3 0.3267 0.833 0.116 0.000 0.884
#> ERR184093 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184051 3 0.0592 0.864 0.012 0.000 0.988
#> ERR184076 3 0.3340 0.831 0.120 0.000 0.880
#> ERR184043 3 0.0592 0.864 0.012 0.000 0.988
#> ERR184037 1 0.1643 0.707 0.956 0.000 0.044
#> ERR184059 3 0.0237 0.869 0.004 0.000 0.996
#> ERR184055 1 0.5291 0.663 0.732 0.000 0.268
#> ERR184065 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184069 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184040 3 0.2448 0.859 0.076 0.000 0.924
#> ERR184057 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184082 1 0.7080 0.470 0.564 0.024 0.412
#> ERR184083 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184039 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184064 3 0.0592 0.864 0.012 0.000 0.988
#> ERR184081 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184095 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184079 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184084 3 0.0424 0.868 0.008 0.000 0.992
#> ERR184068 2 0.0592 0.977 0.012 0.988 0.000
#> ERR184067 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184071 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184042 3 0.1031 0.870 0.024 0.000 0.976
#> ERR184063 3 0.0592 0.864 0.012 0.000 0.988
#> ERR184091 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184061 1 0.2261 0.717 0.932 0.000 0.068
#> ERR184077 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184062 2 0.5327 0.643 0.272 0.728 0.000
#> ERR184053 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184088 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184075 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184041 3 0.0592 0.864 0.012 0.000 0.988
#> ERR184060 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184035 1 0.3619 0.724 0.864 0.000 0.136
#> ERR184086 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184080 1 0.5988 0.516 0.632 0.000 0.368
#> ERR184050 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184047 3 0.1860 0.867 0.052 0.000 0.948
#> ERR184092 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184072 3 0.5948 0.362 0.360 0.000 0.640
#> ERR184073 3 0.2356 0.861 0.072 0.000 0.928
#> ERR184066 1 0.6260 0.329 0.552 0.000 0.448
#> ERR184098 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184044 1 0.6066 0.675 0.728 0.024 0.248
#> ERR184054 3 0.5178 0.626 0.256 0.000 0.744
#> ERR184085 3 0.6295 -0.232 0.472 0.000 0.528
#> ERR184056 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184052 2 0.0424 0.980 0.008 0.992 0.000
#> ERR184070 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184096 3 0.2356 0.861 0.072 0.000 0.928
#> ERR184089 2 0.0424 0.980 0.008 0.992 0.000
#> ERR184049 2 0.3619 0.847 0.136 0.864 0.000
#> ERR184038 3 0.3038 0.821 0.104 0.000 0.896
#> ERR184087 3 0.0592 0.864 0.012 0.000 0.988
#> ERR184097 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184094 3 0.1753 0.868 0.048 0.000 0.952
#> ERR184058 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184036 2 0.0747 0.973 0.016 0.984 0.000
#> ERR184046 2 0.0000 0.986 0.000 1.000 0.000
#> ERR184074 3 0.3686 0.809 0.140 0.000 0.860
#> ERR184048 2 0.0000 0.986 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 3 0.3691 0.7308 0.076 0.000 0.856 0.068
#> ERR184093 2 0.1004 0.9450 0.004 0.972 0.000 0.024
#> ERR184051 3 0.3311 0.7542 0.000 0.000 0.828 0.172
#> ERR184076 3 0.4100 0.7274 0.076 0.000 0.832 0.092
#> ERR184043 3 0.3266 0.7560 0.000 0.000 0.832 0.168
#> ERR184037 1 0.2915 0.4682 0.892 0.000 0.080 0.028
#> ERR184059 3 0.1792 0.7874 0.000 0.000 0.932 0.068
#> ERR184055 1 0.7603 0.3235 0.476 0.000 0.244 0.280
#> ERR184065 2 0.0188 0.9570 0.000 0.996 0.000 0.004
#> ERR184069 2 0.0000 0.9576 0.000 1.000 0.000 0.000
#> ERR184040 3 0.2565 0.7660 0.056 0.000 0.912 0.032
#> ERR184057 2 0.0000 0.9576 0.000 1.000 0.000 0.000
#> ERR184082 4 0.7888 -0.3066 0.244 0.020 0.216 0.520
#> ERR184083 2 0.0188 0.9570 0.000 0.996 0.000 0.004
#> ERR184039 2 0.0336 0.9560 0.000 0.992 0.000 0.008
#> ERR184064 3 0.3266 0.7560 0.000 0.000 0.832 0.168
#> ERR184081 2 0.0188 0.9570 0.000 0.996 0.000 0.004
#> ERR184095 2 0.0000 0.9576 0.000 1.000 0.000 0.000
#> ERR184079 2 0.2111 0.9100 0.024 0.932 0.000 0.044
#> ERR184084 3 0.1867 0.7868 0.000 0.000 0.928 0.072
#> ERR184068 2 0.4920 0.6652 0.052 0.756 0.000 0.192
#> ERR184067 2 0.0000 0.9576 0.000 1.000 0.000 0.000
#> ERR184071 2 0.0188 0.9568 0.000 0.996 0.000 0.004
#> ERR184042 3 0.0469 0.7906 0.000 0.000 0.988 0.012
#> ERR184063 3 0.3486 0.7452 0.000 0.000 0.812 0.188
#> ERR184091 2 0.0000 0.9576 0.000 1.000 0.000 0.000
#> ERR184061 1 0.5151 0.4550 0.760 0.000 0.100 0.140
#> ERR184077 2 0.0707 0.9510 0.000 0.980 0.000 0.020
#> ERR184062 4 0.7695 0.0453 0.220 0.372 0.000 0.408
#> ERR184053 2 0.1042 0.9447 0.008 0.972 0.000 0.020
#> ERR184088 2 0.1151 0.9428 0.008 0.968 0.000 0.024
#> ERR184075 2 0.0188 0.9570 0.000 0.996 0.000 0.004
#> ERR184041 3 0.3444 0.7479 0.000 0.000 0.816 0.184
#> ERR184060 2 0.0000 0.9576 0.000 1.000 0.000 0.000
#> ERR184035 1 0.7293 0.3016 0.476 0.000 0.156 0.368
#> ERR184086 2 0.0000 0.9576 0.000 1.000 0.000 0.000
#> ERR184080 1 0.7558 0.2390 0.428 0.000 0.380 0.192
#> ERR184050 2 0.0592 0.9526 0.000 0.984 0.000 0.016
#> ERR184047 3 0.0804 0.7881 0.012 0.000 0.980 0.008
#> ERR184092 2 0.0000 0.9576 0.000 1.000 0.000 0.000
#> ERR184072 3 0.6566 0.2828 0.288 0.000 0.600 0.112
#> ERR184073 3 0.1936 0.7768 0.032 0.000 0.940 0.028
#> ERR184066 4 0.7816 -0.3809 0.340 0.000 0.260 0.400
#> ERR184098 2 0.0188 0.9570 0.000 0.996 0.000 0.004
#> ERR184044 1 0.6260 0.3185 0.636 0.008 0.068 0.288
#> ERR184054 3 0.5470 0.5775 0.168 0.000 0.732 0.100
#> ERR184085 3 0.7796 -0.3100 0.248 0.000 0.392 0.360
#> ERR184056 2 0.0000 0.9576 0.000 1.000 0.000 0.000
#> ERR184052 2 0.2845 0.8732 0.028 0.896 0.000 0.076
#> ERR184070 2 0.0000 0.9576 0.000 1.000 0.000 0.000
#> ERR184096 3 0.1488 0.7820 0.032 0.000 0.956 0.012
#> ERR184089 2 0.3219 0.8374 0.020 0.868 0.000 0.112
#> ERR184049 2 0.6964 0.2385 0.228 0.584 0.000 0.188
#> ERR184038 3 0.5217 0.6277 0.108 0.000 0.756 0.136
#> ERR184087 3 0.3266 0.7560 0.000 0.000 0.832 0.168
#> ERR184097 2 0.0188 0.9568 0.000 0.996 0.000 0.004
#> ERR184094 3 0.0592 0.7888 0.016 0.000 0.984 0.000
#> ERR184058 2 0.0188 0.9567 0.000 0.996 0.000 0.004
#> ERR184036 2 0.1854 0.9163 0.048 0.940 0.000 0.012
#> ERR184046 2 0.0000 0.9576 0.000 1.000 0.000 0.000
#> ERR184074 3 0.4312 0.6947 0.132 0.000 0.812 0.056
#> ERR184048 2 0.0188 0.9569 0.004 0.996 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 3 0.4032 0.6588 0.164 0.000 0.792 0.024 0.020
#> ERR184093 2 0.2972 0.8474 0.004 0.864 0.000 0.024 0.108
#> ERR184051 3 0.3300 0.6720 0.000 0.000 0.792 0.204 0.004
#> ERR184076 3 0.5544 0.5896 0.148 0.000 0.712 0.052 0.088
#> ERR184043 3 0.3039 0.6794 0.000 0.000 0.808 0.192 0.000
#> ERR184037 1 0.4219 0.2870 0.816 0.000 0.068 0.060 0.056
#> ERR184059 3 0.1043 0.7317 0.000 0.000 0.960 0.040 0.000
#> ERR184055 1 0.8039 0.1118 0.432 0.000 0.132 0.212 0.224
#> ERR184065 2 0.0290 0.9071 0.000 0.992 0.000 0.000 0.008
#> ERR184069 2 0.0000 0.9070 0.000 1.000 0.000 0.000 0.000
#> ERR184040 3 0.3357 0.6919 0.136 0.000 0.836 0.016 0.012
#> ERR184057 2 0.0162 0.9070 0.000 0.996 0.000 0.000 0.004
#> ERR184082 4 0.8124 0.0000 0.168 0.020 0.172 0.496 0.144
#> ERR184083 2 0.0000 0.9070 0.000 1.000 0.000 0.000 0.000
#> ERR184039 2 0.1281 0.9011 0.000 0.956 0.000 0.012 0.032
#> ERR184064 3 0.3039 0.6798 0.000 0.000 0.808 0.192 0.000
#> ERR184081 2 0.0000 0.9070 0.000 1.000 0.000 0.000 0.000
#> ERR184095 2 0.0162 0.9070 0.000 0.996 0.000 0.000 0.004
#> ERR184079 2 0.4791 0.7081 0.020 0.748 0.000 0.064 0.168
#> ERR184084 3 0.1484 0.7321 0.008 0.000 0.944 0.048 0.000
#> ERR184068 2 0.7151 0.1510 0.048 0.504 0.000 0.176 0.272
#> ERR184067 2 0.0290 0.9074 0.000 0.992 0.000 0.000 0.008
#> ERR184071 2 0.1862 0.8937 0.004 0.932 0.000 0.016 0.048
#> ERR184042 3 0.0693 0.7357 0.012 0.000 0.980 0.008 0.000
#> ERR184063 3 0.3961 0.6284 0.000 0.000 0.736 0.248 0.016
#> ERR184091 2 0.0162 0.9066 0.000 0.996 0.000 0.000 0.004
#> ERR184061 1 0.5520 0.2189 0.692 0.000 0.024 0.180 0.104
#> ERR184077 2 0.1331 0.8989 0.000 0.952 0.000 0.008 0.040
#> ERR184062 5 0.4426 0.0513 0.052 0.196 0.000 0.004 0.748
#> ERR184053 2 0.2260 0.8762 0.000 0.908 0.000 0.028 0.064
#> ERR184088 2 0.3725 0.7998 0.008 0.816 0.000 0.036 0.140
#> ERR184075 2 0.1106 0.9028 0.000 0.964 0.000 0.012 0.024
#> ERR184041 3 0.3696 0.6612 0.000 0.000 0.772 0.212 0.016
#> ERR184060 2 0.0000 0.9070 0.000 1.000 0.000 0.000 0.000
#> ERR184035 1 0.7640 -0.2142 0.428 0.000 0.120 0.340 0.112
#> ERR184086 2 0.0693 0.9072 0.000 0.980 0.000 0.012 0.008
#> ERR184080 1 0.6974 0.0979 0.496 0.000 0.340 0.096 0.068
#> ERR184050 2 0.1960 0.8891 0.004 0.928 0.000 0.020 0.048
#> ERR184047 3 0.0794 0.7346 0.028 0.000 0.972 0.000 0.000
#> ERR184092 2 0.0510 0.9067 0.000 0.984 0.000 0.000 0.016
#> ERR184072 3 0.6905 0.0310 0.380 0.000 0.468 0.092 0.060
#> ERR184073 3 0.2011 0.7214 0.088 0.000 0.908 0.000 0.004
#> ERR184066 5 0.8044 -0.2567 0.240 0.000 0.188 0.140 0.432
#> ERR184098 2 0.0807 0.9072 0.000 0.976 0.000 0.012 0.012
#> ERR184044 1 0.8197 0.0671 0.400 0.024 0.072 0.180 0.324
#> ERR184054 3 0.5952 0.4542 0.260 0.000 0.628 0.036 0.076
#> ERR184085 3 0.8367 -0.4480 0.184 0.000 0.344 0.292 0.180
#> ERR184056 2 0.0703 0.9056 0.000 0.976 0.000 0.000 0.024
#> ERR184052 2 0.4750 0.7294 0.016 0.760 0.000 0.104 0.120
#> ERR184070 2 0.0000 0.9070 0.000 1.000 0.000 0.000 0.000
#> ERR184096 3 0.1591 0.7291 0.052 0.000 0.940 0.004 0.004
#> ERR184089 2 0.5523 0.6007 0.016 0.688 0.000 0.152 0.144
#> ERR184049 2 0.7611 0.1036 0.108 0.496 0.000 0.228 0.168
#> ERR184038 3 0.6852 0.3715 0.084 0.000 0.596 0.156 0.164
#> ERR184087 3 0.2966 0.6823 0.000 0.000 0.816 0.184 0.000
#> ERR184097 2 0.0865 0.9057 0.000 0.972 0.000 0.004 0.024
#> ERR184094 3 0.0609 0.7357 0.020 0.000 0.980 0.000 0.000
#> ERR184058 2 0.0510 0.9071 0.000 0.984 0.000 0.000 0.016
#> ERR184036 2 0.3779 0.8153 0.040 0.836 0.000 0.032 0.092
#> ERR184046 2 0.0000 0.9070 0.000 1.000 0.000 0.000 0.000
#> ERR184074 3 0.3883 0.6399 0.216 0.000 0.764 0.016 0.004
#> ERR184048 2 0.1408 0.8967 0.000 0.948 0.000 0.008 0.044
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.2898 0.6656 0.880 0.000 NA 0.016 0.016 0.048
#> ERR184093 2 0.3849 0.7981 0.000 0.812 NA 0.024 0.112 0.016
#> ERR184051 1 0.3861 0.6016 0.672 0.000 NA 0.004 0.008 0.000
#> ERR184076 1 0.4833 0.5862 0.760 0.000 NA 0.032 0.044 0.076
#> ERR184043 1 0.3446 0.6102 0.692 0.000 NA 0.000 0.000 0.000
#> ERR184037 6 0.4208 0.3081 0.076 0.000 NA 0.064 0.044 0.800
#> ERR184059 1 0.1714 0.6969 0.908 0.000 NA 0.000 0.000 0.000
#> ERR184055 6 0.8778 0.0266 0.216 0.000 NA 0.160 0.136 0.296
#> ERR184065 2 0.0951 0.8730 0.000 0.968 NA 0.000 0.020 0.004
#> ERR184069 2 0.0260 0.8731 0.000 0.992 NA 0.000 0.008 0.000
#> ERR184040 1 0.2138 0.6745 0.908 0.000 NA 0.004 0.000 0.052
#> ERR184057 2 0.0603 0.8726 0.000 0.980 NA 0.004 0.016 0.000
#> ERR184082 4 0.6059 0.3194 0.108 0.000 NA 0.668 0.088 0.052
#> ERR184083 2 0.0653 0.8735 0.000 0.980 NA 0.000 0.012 0.004
#> ERR184039 2 0.1440 0.8720 0.000 0.948 NA 0.004 0.032 0.004
#> ERR184064 1 0.3409 0.6150 0.700 0.000 NA 0.000 0.000 0.000
#> ERR184081 2 0.0291 0.8728 0.000 0.992 NA 0.000 0.004 0.000
#> ERR184095 2 0.0363 0.8739 0.000 0.988 NA 0.000 0.012 0.000
#> ERR184079 2 0.6036 0.5848 0.000 0.652 NA 0.088 0.160 0.036
#> ERR184084 1 0.2311 0.6905 0.880 0.000 NA 0.016 0.000 0.000
#> ERR184068 2 0.7408 0.1514 0.000 0.480 NA 0.164 0.232 0.044
#> ERR184067 2 0.0520 0.8750 0.000 0.984 NA 0.000 0.008 0.000
#> ERR184071 2 0.2596 0.8477 0.000 0.872 NA 0.004 0.104 0.004
#> ERR184042 1 0.1141 0.7018 0.948 0.000 NA 0.000 0.000 0.000
#> ERR184063 1 0.4552 0.5202 0.580 0.000 NA 0.016 0.016 0.000
#> ERR184091 2 0.0653 0.8722 0.000 0.980 NA 0.000 0.012 0.004
#> ERR184061 6 0.6157 0.2624 0.044 0.004 NA 0.116 0.088 0.664
#> ERR184077 2 0.3035 0.8370 0.000 0.868 NA 0.020 0.072 0.012
#> ERR184062 5 0.4246 0.0952 0.000 0.156 NA 0.024 0.764 0.052
#> ERR184053 2 0.3423 0.8263 0.000 0.848 NA 0.044 0.068 0.012
#> ERR184088 2 0.4990 0.7216 0.000 0.748 NA 0.072 0.080 0.024
#> ERR184075 2 0.1821 0.8646 0.000 0.928 NA 0.000 0.040 0.008
#> ERR184041 1 0.4371 0.5164 0.576 0.000 NA 0.008 0.008 0.004
#> ERR184060 2 0.0260 0.8728 0.000 0.992 NA 0.000 0.008 0.000
#> ERR184035 4 0.6005 0.1963 0.076 0.000 NA 0.644 0.040 0.188
#> ERR184086 2 0.1180 0.8753 0.000 0.960 NA 0.004 0.024 0.004
#> ERR184080 1 0.8173 -0.3155 0.364 0.000 NA 0.148 0.088 0.292
#> ERR184050 2 0.2881 0.8380 0.000 0.872 NA 0.012 0.064 0.004
#> ERR184047 1 0.0692 0.7011 0.976 0.000 NA 0.000 0.000 0.004
#> ERR184092 2 0.1010 0.8733 0.000 0.960 NA 0.004 0.036 0.000
#> ERR184072 1 0.7129 0.1545 0.516 0.000 NA 0.088 0.044 0.244
#> ERR184073 1 0.1080 0.6906 0.960 0.000 NA 0.004 0.000 0.032
#> ERR184066 5 0.8103 -0.1395 0.180 0.000 NA 0.092 0.436 0.144
#> ERR184098 2 0.1722 0.8680 0.000 0.936 NA 0.008 0.036 0.004
#> ERR184044 6 0.7896 0.1894 0.044 0.008 NA 0.112 0.240 0.440
#> ERR184054 1 0.6462 0.3823 0.616 0.000 NA 0.052 0.060 0.164
#> ERR184085 4 0.8362 0.1856 0.236 0.000 NA 0.368 0.092 0.132
#> ERR184056 2 0.1268 0.8730 0.000 0.952 NA 0.004 0.036 0.000
#> ERR184052 2 0.5485 0.6735 0.000 0.704 NA 0.112 0.096 0.024
#> ERR184070 2 0.0146 0.8725 0.000 0.996 NA 0.000 0.004 0.000
#> ERR184096 1 0.0508 0.6968 0.984 0.000 NA 0.000 0.000 0.012
#> ERR184089 2 0.7014 0.3692 0.000 0.552 NA 0.100 0.168 0.036
#> ERR184049 2 0.8590 -0.3138 0.000 0.340 NA 0.208 0.128 0.196
#> ERR184038 1 0.7381 0.1972 0.496 0.000 NA 0.076 0.096 0.084
#> ERR184087 1 0.3390 0.6172 0.704 0.000 NA 0.000 0.000 0.000
#> ERR184097 2 0.1442 0.8704 0.000 0.944 NA 0.004 0.040 0.000
#> ERR184094 1 0.0508 0.7010 0.984 0.000 NA 0.000 0.000 0.004
#> ERR184058 2 0.0798 0.8741 0.000 0.976 NA 0.004 0.012 0.004
#> ERR184036 2 0.4263 0.7720 0.000 0.800 NA 0.044 0.048 0.080
#> ERR184046 2 0.0508 0.8737 0.000 0.984 NA 0.000 0.012 0.000
#> ERR184074 1 0.4247 0.5926 0.784 0.000 NA 0.020 0.016 0.116
#> ERR184048 2 0.2820 0.8452 0.000 0.872 NA 0.024 0.084 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 10269 rows and 62 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 0.784 0.908 0.946 0.4864 0.492 0.492
#> 3 3 0.907 0.907 0.942 0.2182 0.889 0.776
#> 4 4 1.000 0.940 0.980 0.0591 0.987 0.967
#> 5 5 0.754 0.773 0.845 0.1019 0.973 0.929
#> 6 6 0.714 0.731 0.833 0.0683 0.840 0.586
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
#> ERR184078 1 0.0000 0.879 1.000 0.000
#> ERR184093 2 0.0000 1.000 0.000 1.000
#> ERR184051 1 0.0000 0.879 1.000 0.000
#> ERR184076 1 0.0000 0.879 1.000 0.000
#> ERR184043 1 0.0000 0.879 1.000 0.000
#> ERR184037 1 0.8144 0.764 0.748 0.252
#> ERR184059 1 0.0000 0.879 1.000 0.000
#> ERR184055 1 0.8144 0.764 0.748 0.252
#> ERR184065 2 0.0000 1.000 0.000 1.000
#> ERR184069 2 0.0000 1.000 0.000 1.000
#> ERR184040 1 0.0000 0.879 1.000 0.000
#> ERR184057 2 0.0000 1.000 0.000 1.000
#> ERR184082 1 0.9970 0.355 0.532 0.468
#> ERR184083 2 0.0000 1.000 0.000 1.000
#> ERR184039 2 0.0000 1.000 0.000 1.000
#> ERR184064 1 0.0000 0.879 1.000 0.000
#> ERR184081 2 0.0000 1.000 0.000 1.000
#> ERR184095 2 0.0000 1.000 0.000 1.000
#> ERR184079 2 0.0000 1.000 0.000 1.000
#> ERR184084 1 0.0000 0.879 1.000 0.000
#> ERR184068 2 0.0000 1.000 0.000 1.000
#> ERR184067 2 0.0000 1.000 0.000 1.000
#> ERR184071 2 0.0000 1.000 0.000 1.000
#> ERR184042 1 0.0000 0.879 1.000 0.000
#> ERR184063 1 0.0376 0.878 0.996 0.004
#> ERR184091 2 0.0000 1.000 0.000 1.000
#> ERR184061 1 0.8608 0.726 0.716 0.284
#> ERR184077 2 0.0000 1.000 0.000 1.000
#> ERR184062 1 0.9909 0.420 0.556 0.444
#> ERR184053 2 0.0000 1.000 0.000 1.000
#> ERR184088 2 0.0000 1.000 0.000 1.000
#> ERR184075 2 0.0000 1.000 0.000 1.000
#> ERR184041 1 0.1184 0.876 0.984 0.016
#> ERR184060 2 0.0000 1.000 0.000 1.000
#> ERR184035 1 0.8267 0.756 0.740 0.260
#> ERR184086 2 0.0000 1.000 0.000 1.000
#> ERR184080 1 0.8144 0.764 0.748 0.252
#> ERR184050 2 0.0000 1.000 0.000 1.000
#> ERR184047 1 0.0000 0.879 1.000 0.000
#> ERR184092 2 0.0000 1.000 0.000 1.000
#> ERR184072 1 0.3274 0.863 0.940 0.060
#> ERR184073 1 0.0000 0.879 1.000 0.000
#> ERR184066 1 0.8144 0.764 0.748 0.252
#> ERR184098 2 0.0000 1.000 0.000 1.000
#> ERR184044 1 0.8144 0.764 0.748 0.252
#> ERR184054 1 0.3274 0.863 0.940 0.060
#> ERR184085 1 0.8207 0.760 0.744 0.256
#> ERR184056 2 0.0000 1.000 0.000 1.000
#> ERR184052 2 0.0000 1.000 0.000 1.000
#> ERR184070 2 0.0000 1.000 0.000 1.000
#> ERR184096 1 0.0000 0.879 1.000 0.000
#> ERR184089 2 0.0000 1.000 0.000 1.000
#> ERR184049 2 0.0000 1.000 0.000 1.000
#> ERR184038 1 0.8144 0.764 0.748 0.252
#> ERR184087 1 0.0000 0.879 1.000 0.000
#> ERR184097 2 0.0000 1.000 0.000 1.000
#> ERR184094 1 0.0000 0.879 1.000 0.000
#> ERR184058 2 0.0000 1.000 0.000 1.000
#> ERR184036 2 0.0000 1.000 0.000 1.000
#> ERR184046 2 0.0000 1.000 0.000 1.000
#> ERR184074 1 0.0000 0.879 1.000 0.000
#> ERR184048 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.0000 0.932 1.000 0.000 0.000
#> ERR184093 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184051 3 0.6095 0.731 0.392 0.000 0.608
#> ERR184076 1 0.0000 0.932 1.000 0.000 0.000
#> ERR184043 3 0.6095 0.731 0.392 0.000 0.608
#> ERR184037 1 0.0000 0.932 1.000 0.000 0.000
#> ERR184059 3 0.1411 0.669 0.036 0.000 0.964
#> ERR184055 1 0.0000 0.932 1.000 0.000 0.000
#> ERR184065 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184069 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184040 1 0.0000 0.932 1.000 0.000 0.000
#> ERR184057 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184082 1 0.4974 0.518 0.764 0.236 0.000
#> ERR184083 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184039 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184064 3 0.6095 0.731 0.392 0.000 0.608
#> ERR184081 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184095 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184079 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184084 3 0.6140 0.715 0.404 0.000 0.596
#> ERR184068 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184067 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184071 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184042 3 0.0000 0.654 0.000 0.000 1.000
#> ERR184063 3 0.6095 0.731 0.392 0.000 0.608
#> ERR184091 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184061 1 0.0747 0.911 0.984 0.016 0.000
#> ERR184077 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184062 1 0.5465 0.408 0.712 0.288 0.000
#> ERR184053 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184088 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184075 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184041 3 0.6154 0.708 0.408 0.000 0.592
#> ERR184060 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184035 1 0.0237 0.928 0.996 0.004 0.000
#> ERR184086 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184080 1 0.0000 0.932 1.000 0.000 0.000
#> ERR184050 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184047 3 0.0000 0.654 0.000 0.000 1.000
#> ERR184092 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184072 1 0.0000 0.932 1.000 0.000 0.000
#> ERR184073 1 0.0000 0.932 1.000 0.000 0.000
#> ERR184066 1 0.0000 0.932 1.000 0.000 0.000
#> ERR184098 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184044 1 0.0000 0.932 1.000 0.000 0.000
#> ERR184054 1 0.0000 0.932 1.000 0.000 0.000
#> ERR184085 1 0.0237 0.928 0.996 0.004 0.000
#> ERR184056 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184052 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184070 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184096 3 0.3941 0.596 0.156 0.000 0.844
#> ERR184089 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184049 2 0.0424 0.990 0.008 0.992 0.000
#> ERR184038 1 0.0000 0.932 1.000 0.000 0.000
#> ERR184087 3 0.5905 0.733 0.352 0.000 0.648
#> ERR184097 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184094 1 0.2959 0.790 0.900 0.000 0.100
#> ERR184058 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184036 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184046 2 0.0000 1.000 0.000 1.000 0.000
#> ERR184074 1 0.0000 0.932 1.000 0.000 0.000
#> ERR184048 2 0.0000 1.000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.0000 0.924 1.000 0.000 0.000 0
#> ERR184093 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184051 3 0.0000 0.946 0.000 0.000 1.000 0
#> ERR184076 1 0.0000 0.924 1.000 0.000 0.000 0
#> ERR184043 3 0.0000 0.946 0.000 0.000 1.000 0
#> ERR184037 1 0.0000 0.924 1.000 0.000 0.000 0
#> ERR184059 3 0.0000 0.946 0.000 0.000 1.000 0
#> ERR184055 1 0.0000 0.924 1.000 0.000 0.000 0
#> ERR184065 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184069 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184040 1 0.0000 0.924 1.000 0.000 0.000 0
#> ERR184057 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184082 1 0.4040 0.572 0.752 0.248 0.000 0
#> ERR184083 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184039 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184064 3 0.0000 0.946 0.000 0.000 1.000 0
#> ERR184081 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184095 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184079 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184084 3 0.0592 0.930 0.016 0.000 0.984 0
#> ERR184068 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184067 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184071 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184042 4 0.0000 1.000 0.000 0.000 0.000 1
#> ERR184063 3 0.0000 0.946 0.000 0.000 1.000 0
#> ERR184091 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184061 1 0.0188 0.921 0.996 0.004 0.000 0
#> ERR184077 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184062 1 0.4543 0.438 0.676 0.324 0.000 0
#> ERR184053 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184088 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184075 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184041 3 0.3873 0.617 0.228 0.000 0.772 0
#> ERR184060 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184035 1 0.0000 0.924 1.000 0.000 0.000 0
#> ERR184086 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184080 1 0.0000 0.924 1.000 0.000 0.000 0
#> ERR184050 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184047 4 0.0000 1.000 0.000 0.000 0.000 1
#> ERR184092 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184072 1 0.0000 0.924 1.000 0.000 0.000 0
#> ERR184073 1 0.0000 0.924 1.000 0.000 0.000 0
#> ERR184066 1 0.0000 0.924 1.000 0.000 0.000 0
#> ERR184098 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184044 1 0.0188 0.921 0.996 0.004 0.000 0
#> ERR184054 1 0.0000 0.924 1.000 0.000 0.000 0
#> ERR184085 1 0.0336 0.917 0.992 0.008 0.000 0
#> ERR184056 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184052 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184070 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184096 4 0.0000 1.000 0.000 0.000 0.000 1
#> ERR184089 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184049 2 0.0336 0.990 0.008 0.992 0.000 0
#> ERR184038 1 0.0000 0.924 1.000 0.000 0.000 0
#> ERR184087 3 0.0000 0.946 0.000 0.000 1.000 0
#> ERR184097 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184094 1 0.4866 0.286 0.596 0.000 0.404 0
#> ERR184058 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184036 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184046 2 0.0000 1.000 0.000 1.000 0.000 0
#> ERR184074 1 0.0000 0.924 1.000 0.000 0.000 0
#> ERR184048 2 0.0000 1.000 0.000 1.000 0.000 0
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> ERR184093 2 0.0000 0.720 0.000 1.000 0.000 0.000 0.000
#> ERR184051 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000
#> ERR184076 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> ERR184043 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000
#> ERR184037 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> ERR184059 3 0.0162 0.941 0.000 0.000 0.996 0.000 0.004
#> ERR184055 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> ERR184065 2 0.4278 0.738 0.000 0.548 0.000 0.000 0.452
#> ERR184069 2 0.4287 0.735 0.000 0.540 0.000 0.000 0.460
#> ERR184040 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> ERR184057 2 0.4287 0.735 0.000 0.540 0.000 0.000 0.460
#> ERR184082 1 0.4150 0.380 0.612 0.388 0.000 0.000 0.000
#> ERR184083 2 0.4287 0.735 0.000 0.540 0.000 0.000 0.460
#> ERR184039 2 0.4161 0.745 0.000 0.608 0.000 0.000 0.392
#> ERR184064 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000
#> ERR184081 2 0.4287 0.735 0.000 0.540 0.000 0.000 0.460
#> ERR184095 2 0.4287 0.735 0.000 0.540 0.000 0.000 0.460
#> ERR184079 2 0.0000 0.720 0.000 1.000 0.000 0.000 0.000
#> ERR184084 3 0.0510 0.928 0.016 0.000 0.984 0.000 0.000
#> ERR184068 2 0.0000 0.720 0.000 1.000 0.000 0.000 0.000
#> ERR184067 2 0.4278 0.738 0.000 0.548 0.000 0.000 0.452
#> ERR184071 2 0.0703 0.730 0.000 0.976 0.000 0.000 0.024
#> ERR184042 4 0.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> ERR184063 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000
#> ERR184091 2 0.4287 0.735 0.000 0.540 0.000 0.000 0.460
#> ERR184061 1 0.2605 0.764 0.852 0.148 0.000 0.000 0.000
#> ERR184077 2 0.0290 0.723 0.000 0.992 0.000 0.000 0.008
#> ERR184062 2 0.3586 0.313 0.264 0.736 0.000 0.000 0.000
#> ERR184053 2 0.0290 0.723 0.000 0.992 0.000 0.000 0.008
#> ERR184088 2 0.0000 0.720 0.000 1.000 0.000 0.000 0.000
#> ERR184075 2 0.4273 0.739 0.000 0.552 0.000 0.000 0.448
#> ERR184041 3 0.3336 0.597 0.228 0.000 0.772 0.000 0.000
#> ERR184060 2 0.4287 0.735 0.000 0.540 0.000 0.000 0.460
#> ERR184035 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> ERR184086 2 0.3684 0.747 0.000 0.720 0.000 0.000 0.280
#> ERR184080 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> ERR184050 2 0.3452 0.749 0.000 0.756 0.000 0.000 0.244
#> ERR184047 5 0.4297 1.000 0.000 0.000 0.000 0.472 0.528
#> ERR184092 2 0.0609 0.728 0.000 0.980 0.000 0.000 0.020
#> ERR184072 1 0.0290 0.909 0.992 0.000 0.000 0.000 0.008
#> ERR184073 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> ERR184066 1 0.0703 0.896 0.976 0.024 0.000 0.000 0.000
#> ERR184098 2 0.3661 0.748 0.000 0.724 0.000 0.000 0.276
#> ERR184044 1 0.3003 0.722 0.812 0.188 0.000 0.000 0.000
#> ERR184054 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> ERR184085 1 0.0162 0.910 0.996 0.004 0.000 0.000 0.000
#> ERR184056 2 0.3210 0.733 0.000 0.788 0.000 0.000 0.212
#> ERR184052 2 0.0609 0.729 0.000 0.980 0.000 0.000 0.020
#> ERR184070 2 0.4287 0.735 0.000 0.540 0.000 0.000 0.460
#> ERR184096 5 0.4297 1.000 0.000 0.000 0.000 0.472 0.528
#> ERR184089 2 0.0000 0.720 0.000 1.000 0.000 0.000 0.000
#> ERR184049 2 0.0000 0.720 0.000 1.000 0.000 0.000 0.000
#> ERR184038 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> ERR184087 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000
#> ERR184097 2 0.2516 0.730 0.000 0.860 0.000 0.000 0.140
#> ERR184094 1 0.4192 0.332 0.596 0.000 0.404 0.000 0.000
#> ERR184058 2 0.4278 0.738 0.000 0.548 0.000 0.000 0.452
#> ERR184036 2 0.1544 0.738 0.000 0.932 0.000 0.000 0.068
#> ERR184046 2 0.4287 0.735 0.000 0.540 0.000 0.000 0.460
#> ERR184074 1 0.0000 0.913 1.000 0.000 0.000 0.000 0.000
#> ERR184048 2 0.0880 0.732 0.000 0.968 0.000 0.000 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.0146 0.8749 0.996 0.000 0.000 0.000 0.00 0.004
#> ERR184093 2 0.0000 0.7474 0.000 1.000 0.000 0.000 0.00 0.000
#> ERR184051 3 0.0000 0.9190 0.000 0.000 1.000 0.000 0.00 0.000
#> ERR184076 1 0.0146 0.8750 0.996 0.000 0.000 0.000 0.00 0.004
#> ERR184043 3 0.0000 0.9190 0.000 0.000 1.000 0.000 0.00 0.000
#> ERR184037 1 0.0000 0.8760 1.000 0.000 0.000 0.000 0.00 0.000
#> ERR184059 3 0.3278 0.7736 0.000 0.000 0.808 0.152 0.00 0.040
#> ERR184055 1 0.0146 0.8747 0.996 0.004 0.000 0.000 0.00 0.000
#> ERR184065 6 0.3023 0.9679 0.000 0.232 0.000 0.000 0.00 0.768
#> ERR184069 6 0.2969 0.9723 0.000 0.224 0.000 0.000 0.00 0.776
#> ERR184040 1 0.0000 0.8760 1.000 0.000 0.000 0.000 0.00 0.000
#> ERR184057 6 0.2969 0.9723 0.000 0.224 0.000 0.000 0.00 0.776
#> ERR184082 2 0.3843 -0.0574 0.452 0.548 0.000 0.000 0.00 0.000
#> ERR184083 6 0.2969 0.9723 0.000 0.224 0.000 0.000 0.00 0.776
#> ERR184039 6 0.3547 0.8035 0.000 0.332 0.000 0.000 0.00 0.668
#> ERR184064 3 0.0000 0.9190 0.000 0.000 1.000 0.000 0.00 0.000
#> ERR184081 6 0.2969 0.9723 0.000 0.224 0.000 0.000 0.00 0.776
#> ERR184095 6 0.2969 0.9723 0.000 0.224 0.000 0.000 0.00 0.776
#> ERR184079 2 0.0000 0.7474 0.000 1.000 0.000 0.000 0.00 0.000
#> ERR184084 3 0.0458 0.9069 0.016 0.000 0.984 0.000 0.00 0.000
#> ERR184068 2 0.0000 0.7474 0.000 1.000 0.000 0.000 0.00 0.000
#> ERR184067 6 0.3076 0.9632 0.000 0.240 0.000 0.000 0.00 0.760
#> ERR184071 2 0.2260 0.6894 0.000 0.860 0.000 0.000 0.00 0.140
#> ERR184042 4 0.3756 0.0000 0.000 0.000 0.000 0.600 0.40 0.000
#> ERR184063 3 0.0000 0.9190 0.000 0.000 1.000 0.000 0.00 0.000
#> ERR184091 6 0.2969 0.9723 0.000 0.224 0.000 0.000 0.00 0.776
#> ERR184061 1 0.3620 0.4456 0.648 0.352 0.000 0.000 0.00 0.000
#> ERR184077 2 0.0865 0.7440 0.000 0.964 0.000 0.000 0.00 0.036
#> ERR184062 2 0.1007 0.7175 0.044 0.956 0.000 0.000 0.00 0.000
#> ERR184053 2 0.2793 0.5831 0.000 0.800 0.000 0.000 0.00 0.200
#> ERR184088 2 0.0363 0.7484 0.000 0.988 0.000 0.000 0.00 0.012
#> ERR184075 6 0.3050 0.9648 0.000 0.236 0.000 0.000 0.00 0.764
#> ERR184041 3 0.2996 0.6086 0.228 0.000 0.772 0.000 0.00 0.000
#> ERR184060 6 0.2969 0.9723 0.000 0.224 0.000 0.000 0.00 0.776
#> ERR184035 1 0.0000 0.8760 1.000 0.000 0.000 0.000 0.00 0.000
#> ERR184086 2 0.3672 0.1922 0.000 0.632 0.000 0.000 0.00 0.368
#> ERR184080 1 0.0000 0.8760 1.000 0.000 0.000 0.000 0.00 0.000
#> ERR184050 2 0.3547 0.3035 0.000 0.668 0.000 0.000 0.00 0.332
#> ERR184047 5 0.0000 0.7633 0.000 0.000 0.000 0.000 1.00 0.000
#> ERR184092 2 0.2762 0.6016 0.000 0.804 0.000 0.000 0.00 0.196
#> ERR184072 1 0.3558 0.6364 0.736 0.000 0.000 0.248 0.00 0.016
#> ERR184073 1 0.0632 0.8645 0.976 0.000 0.000 0.024 0.00 0.000
#> ERR184066 1 0.0937 0.8489 0.960 0.040 0.000 0.000 0.00 0.000
#> ERR184098 2 0.3765 0.0963 0.000 0.596 0.000 0.000 0.00 0.404
#> ERR184044 1 0.3868 0.1940 0.508 0.492 0.000 0.000 0.00 0.000
#> ERR184054 1 0.0000 0.8760 1.000 0.000 0.000 0.000 0.00 0.000
#> ERR184085 1 0.0865 0.8513 0.964 0.036 0.000 0.000 0.00 0.000
#> ERR184056 2 0.3823 -0.0604 0.000 0.564 0.000 0.000 0.00 0.436
#> ERR184052 2 0.0632 0.7481 0.000 0.976 0.000 0.000 0.00 0.024
#> ERR184070 6 0.3151 0.9451 0.000 0.252 0.000 0.000 0.00 0.748
#> ERR184096 5 0.2454 0.7633 0.000 0.000 0.000 0.000 0.84 0.160
#> ERR184089 2 0.1007 0.7428 0.000 0.956 0.000 0.000 0.00 0.044
#> ERR184049 2 0.0000 0.7474 0.000 1.000 0.000 0.000 0.00 0.000
#> ERR184038 1 0.0000 0.8760 1.000 0.000 0.000 0.000 0.00 0.000
#> ERR184087 3 0.0000 0.9190 0.000 0.000 1.000 0.000 0.00 0.000
#> ERR184097 2 0.3672 0.1956 0.000 0.632 0.000 0.000 0.00 0.368
#> ERR184094 1 0.4273 0.3368 0.596 0.000 0.380 0.024 0.00 0.000
#> ERR184058 6 0.3244 0.9271 0.000 0.268 0.000 0.000 0.00 0.732
#> ERR184036 2 0.2260 0.6715 0.000 0.860 0.000 0.000 0.00 0.140
#> ERR184046 6 0.2969 0.9723 0.000 0.224 0.000 0.000 0.00 0.776
#> ERR184074 1 0.0000 0.8760 1.000 0.000 0.000 0.000 0.00 0.000
#> ERR184048 2 0.1765 0.7173 0.000 0.904 0.000 0.000 0.00 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["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 10269 rows and 62 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 0.528 0.887 0.923 0.4617 0.497 0.497
#> 3 3 0.612 0.761 0.853 0.2382 0.840 0.709
#> 4 4 0.618 0.739 0.779 0.1171 0.918 0.836
#> 5 5 0.457 0.420 0.702 0.0858 0.834 0.653
#> 6 6 0.555 0.330 0.652 0.0526 0.888 0.685
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
#> ERR184078 1 0.6247 0.886 0.844 0.156
#> ERR184093 2 0.0000 0.973 0.000 1.000
#> ERR184051 1 0.0000 0.838 1.000 0.000
#> ERR184076 1 0.6247 0.886 0.844 0.156
#> ERR184043 1 0.0000 0.838 1.000 0.000
#> ERR184037 1 0.6247 0.886 0.844 0.156
#> ERR184059 1 0.0938 0.844 0.988 0.012
#> ERR184055 1 0.9323 0.665 0.652 0.348
#> ERR184065 2 0.0000 0.973 0.000 1.000
#> ERR184069 2 0.0000 0.973 0.000 1.000
#> ERR184040 1 0.6247 0.886 0.844 0.156
#> ERR184057 2 0.0000 0.973 0.000 1.000
#> ERR184082 2 0.5737 0.807 0.136 0.864
#> ERR184083 2 0.0000 0.973 0.000 1.000
#> ERR184039 2 0.0000 0.973 0.000 1.000
#> ERR184064 1 0.0000 0.838 1.000 0.000
#> ERR184081 2 0.0000 0.973 0.000 1.000
#> ERR184095 2 0.0000 0.973 0.000 1.000
#> ERR184079 2 0.0000 0.973 0.000 1.000
#> ERR184084 1 0.1414 0.846 0.980 0.020
#> ERR184068 2 0.0000 0.973 0.000 1.000
#> ERR184067 2 0.0000 0.973 0.000 1.000
#> ERR184071 2 0.0000 0.973 0.000 1.000
#> ERR184042 1 0.0000 0.838 1.000 0.000
#> ERR184063 1 0.0000 0.838 1.000 0.000
#> ERR184091 2 0.0000 0.973 0.000 1.000
#> ERR184061 1 0.6247 0.886 0.844 0.156
#> ERR184077 2 0.0000 0.973 0.000 1.000
#> ERR184062 2 0.7219 0.692 0.200 0.800
#> ERR184053 2 0.0376 0.969 0.004 0.996
#> ERR184088 2 0.0000 0.973 0.000 1.000
#> ERR184075 2 0.1843 0.946 0.028 0.972
#> ERR184041 1 0.0000 0.838 1.000 0.000
#> ERR184060 2 0.0000 0.973 0.000 1.000
#> ERR184035 1 0.8813 0.734 0.700 0.300
#> ERR184086 2 0.0000 0.973 0.000 1.000
#> ERR184080 1 0.6247 0.886 0.844 0.156
#> ERR184050 2 0.0000 0.973 0.000 1.000
#> ERR184047 1 0.6247 0.886 0.844 0.156
#> ERR184092 2 0.0000 0.973 0.000 1.000
#> ERR184072 1 0.6247 0.886 0.844 0.156
#> ERR184073 1 0.6247 0.886 0.844 0.156
#> ERR184066 1 0.8555 0.767 0.720 0.280
#> ERR184098 2 0.0000 0.973 0.000 1.000
#> ERR184044 2 0.2423 0.934 0.040 0.960
#> ERR184054 1 0.6247 0.886 0.844 0.156
#> ERR184085 2 0.9087 0.383 0.324 0.676
#> ERR184056 2 0.0000 0.973 0.000 1.000
#> ERR184052 2 0.0000 0.973 0.000 1.000
#> ERR184070 2 0.0000 0.973 0.000 1.000
#> ERR184096 1 0.6247 0.886 0.844 0.156
#> ERR184089 1 0.9988 0.323 0.520 0.480
#> ERR184049 2 0.0000 0.973 0.000 1.000
#> ERR184038 1 0.7376 0.845 0.792 0.208
#> ERR184087 1 0.0000 0.838 1.000 0.000
#> ERR184097 2 0.0000 0.973 0.000 1.000
#> ERR184094 1 0.6247 0.886 0.844 0.156
#> ERR184058 2 0.0000 0.973 0.000 1.000
#> ERR184036 1 0.9580 0.609 0.620 0.380
#> ERR184046 2 0.0000 0.973 0.000 1.000
#> ERR184074 1 0.6247 0.886 0.844 0.156
#> ERR184048 2 0.0000 0.973 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 1 0.6722 0.800 0.720 0.060 0.220
#> ERR184093 2 0.4110 0.844 0.152 0.844 0.004
#> ERR184051 3 0.0424 0.903 0.008 0.000 0.992
#> ERR184076 1 0.6853 0.798 0.712 0.064 0.224
#> ERR184043 3 0.0424 0.903 0.008 0.000 0.992
#> ERR184037 1 0.6486 0.725 0.760 0.096 0.144
#> ERR184059 3 0.6204 -0.136 0.424 0.000 0.576
#> ERR184055 2 0.6598 0.508 0.428 0.564 0.008
#> ERR184065 2 0.0237 0.882 0.000 0.996 0.004
#> ERR184069 2 0.0000 0.883 0.000 1.000 0.000
#> ERR184040 1 0.6722 0.800 0.720 0.060 0.220
#> ERR184057 2 0.0000 0.883 0.000 1.000 0.000
#> ERR184082 2 0.6984 0.518 0.420 0.560 0.020
#> ERR184083 2 0.0000 0.883 0.000 1.000 0.000
#> ERR184039 2 0.0237 0.882 0.000 0.996 0.004
#> ERR184064 3 0.0424 0.903 0.008 0.000 0.992
#> ERR184081 2 0.0000 0.883 0.000 1.000 0.000
#> ERR184095 2 0.0000 0.883 0.000 1.000 0.000
#> ERR184079 2 0.3983 0.845 0.144 0.852 0.004
#> ERR184084 1 0.5926 0.641 0.644 0.000 0.356
#> ERR184068 2 0.5109 0.802 0.212 0.780 0.008
#> ERR184067 2 0.0000 0.883 0.000 1.000 0.000
#> ERR184071 2 0.2400 0.873 0.064 0.932 0.004
#> ERR184042 1 0.5810 0.625 0.664 0.000 0.336
#> ERR184063 3 0.0424 0.903 0.008 0.000 0.992
#> ERR184091 2 0.0237 0.882 0.000 0.996 0.004
#> ERR184061 1 0.6927 0.795 0.700 0.060 0.240
#> ERR184077 2 0.3030 0.866 0.092 0.904 0.004
#> ERR184062 2 0.5541 0.771 0.252 0.740 0.008
#> ERR184053 2 0.5775 0.716 0.260 0.728 0.012
#> ERR184088 2 0.4465 0.831 0.176 0.820 0.004
#> ERR184075 2 0.2703 0.853 0.016 0.928 0.056
#> ERR184041 3 0.0424 0.903 0.008 0.000 0.992
#> ERR184060 2 0.0000 0.883 0.000 1.000 0.000
#> ERR184035 1 0.4099 0.536 0.852 0.140 0.008
#> ERR184086 2 0.0237 0.882 0.000 0.996 0.004
#> ERR184080 1 0.5506 0.691 0.816 0.092 0.092
#> ERR184050 2 0.0237 0.882 0.000 0.996 0.004
#> ERR184047 1 0.5588 0.731 0.720 0.004 0.276
#> ERR184092 2 0.1647 0.879 0.036 0.960 0.004
#> ERR184072 1 0.6335 0.784 0.724 0.036 0.240
#> ERR184073 1 0.6836 0.795 0.704 0.056 0.240
#> ERR184066 1 0.6937 0.428 0.680 0.272 0.048
#> ERR184098 2 0.0237 0.882 0.000 0.996 0.004
#> ERR184044 2 0.5247 0.793 0.224 0.768 0.008
#> ERR184054 1 0.6630 0.800 0.724 0.056 0.220
#> ERR184085 2 0.7223 0.470 0.424 0.548 0.028
#> ERR184056 2 0.1989 0.877 0.048 0.948 0.004
#> ERR184052 2 0.0237 0.883 0.004 0.996 0.000
#> ERR184070 2 0.0000 0.883 0.000 1.000 0.000
#> ERR184096 1 0.5803 0.756 0.736 0.016 0.248
#> ERR184089 2 0.7061 0.488 0.036 0.632 0.332
#> ERR184049 2 0.4409 0.830 0.172 0.824 0.004
#> ERR184038 1 0.7012 0.338 0.652 0.308 0.040
#> ERR184087 3 0.0424 0.903 0.008 0.000 0.992
#> ERR184097 2 0.3112 0.864 0.096 0.900 0.004
#> ERR184094 1 0.6562 0.777 0.700 0.036 0.264
#> ERR184058 2 0.0000 0.883 0.000 1.000 0.000
#> ERR184036 2 0.9400 -0.206 0.356 0.464 0.180
#> ERR184046 2 0.0000 0.883 0.000 1.000 0.000
#> ERR184074 1 0.6895 0.799 0.708 0.064 0.228
#> ERR184048 2 0.2772 0.870 0.080 0.916 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 1 0.1492 0.852 0.956 0.004 0.004 NA
#> ERR184093 2 0.1978 0.734 0.068 0.928 0.000 NA
#> ERR184051 3 0.1489 0.942 0.044 0.000 0.952 NA
#> ERR184076 1 0.1492 0.852 0.956 0.004 0.004 NA
#> ERR184043 3 0.1888 0.938 0.044 0.000 0.940 NA
#> ERR184037 1 0.3213 0.834 0.896 0.040 0.024 NA
#> ERR184059 3 0.5309 0.600 0.256 0.000 0.700 NA
#> ERR184055 2 0.4326 0.669 0.088 0.840 0.036 NA
#> ERR184065 2 0.5155 0.728 0.000 0.528 0.004 NA
#> ERR184069 2 0.4907 0.753 0.000 0.580 0.000 NA
#> ERR184040 1 0.1082 0.854 0.972 0.004 0.004 NA
#> ERR184057 2 0.4790 0.763 0.000 0.620 0.000 NA
#> ERR184082 2 0.3403 0.728 0.028 0.888 0.040 NA
#> ERR184083 2 0.4898 0.754 0.000 0.584 0.000 NA
#> ERR184039 2 0.4916 0.748 0.000 0.576 0.000 NA
#> ERR184064 3 0.1489 0.942 0.044 0.000 0.952 NA
#> ERR184081 2 0.4907 0.753 0.000 0.580 0.000 NA
#> ERR184095 2 0.4898 0.755 0.000 0.584 0.000 NA
#> ERR184079 2 0.0967 0.731 0.004 0.976 0.004 NA
#> ERR184084 1 0.8643 0.216 0.456 0.216 0.276 NA
#> ERR184068 2 0.0895 0.728 0.000 0.976 0.004 NA
#> ERR184067 2 0.4800 0.766 0.000 0.656 0.004 NA
#> ERR184071 2 0.2859 0.761 0.000 0.880 0.008 NA
#> ERR184042 1 0.6961 0.508 0.512 0.000 0.120 NA
#> ERR184063 3 0.1635 0.942 0.044 0.000 0.948 NA
#> ERR184091 2 0.5163 0.724 0.000 0.516 0.004 NA
#> ERR184061 1 0.1284 0.859 0.964 0.012 0.000 NA
#> ERR184077 2 0.1890 0.748 0.000 0.936 0.008 NA
#> ERR184062 2 0.3907 0.688 0.064 0.864 0.036 NA
#> ERR184053 2 0.2742 0.756 0.008 0.900 0.008 NA
#> ERR184088 2 0.1296 0.735 0.028 0.964 0.004 NA
#> ERR184075 2 0.7345 0.689 0.016 0.532 0.116 NA
#> ERR184041 3 0.2111 0.936 0.044 0.000 0.932 NA
#> ERR184060 2 0.5060 0.755 0.004 0.584 0.000 NA
#> ERR184035 2 0.6619 0.422 0.304 0.616 0.036 NA
#> ERR184086 2 0.4907 0.749 0.000 0.580 0.000 NA
#> ERR184080 1 0.2521 0.835 0.924 0.028 0.032 NA
#> ERR184050 2 0.4961 0.736 0.000 0.552 0.000 NA
#> ERR184047 1 0.4504 0.808 0.772 0.004 0.020 NA
#> ERR184092 2 0.2831 0.762 0.000 0.876 0.004 NA
#> ERR184072 1 0.2197 0.855 0.916 0.004 0.000 NA
#> ERR184073 1 0.3534 0.837 0.840 0.004 0.008 NA
#> ERR184066 2 0.6696 0.299 0.320 0.600 0.036 NA
#> ERR184098 2 0.4907 0.749 0.000 0.580 0.000 NA
#> ERR184044 2 0.2392 0.726 0.012 0.928 0.036 NA
#> ERR184054 1 0.0712 0.857 0.984 0.004 0.004 NA
#> ERR184085 2 0.4329 0.703 0.056 0.844 0.036 NA
#> ERR184056 2 0.3142 0.763 0.000 0.860 0.008 NA
#> ERR184052 2 0.4843 0.758 0.000 0.604 0.000 NA
#> ERR184070 2 0.4905 0.766 0.004 0.632 0.000 NA
#> ERR184096 1 0.3992 0.822 0.800 0.004 0.008 NA
#> ERR184089 2 0.9053 0.332 0.076 0.408 0.296 NA
#> ERR184049 2 0.0707 0.745 0.000 0.980 0.000 NA
#> ERR184038 2 0.4723 0.665 0.108 0.816 0.036 NA
#> ERR184087 3 0.1489 0.941 0.044 0.000 0.952 NA
#> ERR184097 2 0.2737 0.759 0.000 0.888 0.008 NA
#> ERR184094 1 0.4420 0.812 0.776 0.008 0.012 NA
#> ERR184058 2 0.5039 0.757 0.004 0.592 0.000 NA
#> ERR184036 2 0.6031 0.245 0.420 0.536 0.000 NA
#> ERR184046 2 0.4916 0.752 0.000 0.576 0.000 NA
#> ERR184074 1 0.1004 0.858 0.972 0.004 0.000 NA
#> ERR184048 2 0.1909 0.745 0.004 0.940 0.008 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.3437 0.5857 0.808 0.000 0.004 0.176 0.012
#> ERR184093 2 0.1911 0.4934 0.036 0.932 0.000 0.004 0.028
#> ERR184051 3 0.2605 0.8389 0.148 0.000 0.852 0.000 0.000
#> ERR184076 1 0.3696 0.5617 0.772 0.000 0.000 0.212 0.016
#> ERR184043 3 0.1341 0.8423 0.056 0.000 0.944 0.000 0.000
#> ERR184037 1 0.3694 0.5566 0.796 0.032 0.000 0.172 0.000
#> ERR184059 3 0.4378 0.5883 0.216 0.000 0.740 0.040 0.004
#> ERR184055 2 0.5564 0.3778 0.200 0.664 0.000 0.128 0.008
#> ERR184065 5 0.5964 0.5031 0.000 0.340 0.000 0.124 0.536
#> ERR184069 5 0.4192 0.8150 0.000 0.404 0.000 0.000 0.596
#> ERR184040 1 0.2439 0.6456 0.876 0.000 0.004 0.120 0.000
#> ERR184057 5 0.4302 0.7232 0.000 0.480 0.000 0.000 0.520
#> ERR184082 2 0.5385 0.4093 0.124 0.724 0.000 0.112 0.040
#> ERR184083 5 0.4350 0.8180 0.000 0.408 0.000 0.004 0.588
#> ERR184039 2 0.5630 -0.3643 0.000 0.560 0.000 0.088 0.352
#> ERR184064 3 0.1341 0.8423 0.056 0.000 0.944 0.000 0.000
#> ERR184081 5 0.4219 0.8152 0.000 0.416 0.000 0.000 0.584
#> ERR184095 5 0.4262 0.7974 0.000 0.440 0.000 0.000 0.560
#> ERR184079 2 0.0798 0.5035 0.000 0.976 0.000 0.016 0.008
#> ERR184084 1 0.8160 -0.1210 0.428 0.180 0.268 0.116 0.008
#> ERR184068 2 0.0912 0.5034 0.000 0.972 0.000 0.016 0.012
#> ERR184067 2 0.3969 -0.1599 0.000 0.692 0.000 0.004 0.304
#> ERR184071 2 0.2233 0.4465 0.000 0.904 0.000 0.016 0.080
#> ERR184042 4 0.8269 0.0000 0.320 0.000 0.136 0.332 0.212
#> ERR184063 3 0.2605 0.8389 0.148 0.000 0.852 0.000 0.000
#> ERR184091 5 0.5739 0.5539 0.000 0.280 0.000 0.124 0.596
#> ERR184061 1 0.3190 0.6344 0.840 0.008 0.000 0.140 0.012
#> ERR184077 2 0.1493 0.4961 0.000 0.948 0.000 0.024 0.028
#> ERR184062 2 0.5108 0.4113 0.156 0.716 0.000 0.120 0.008
#> ERR184053 2 0.1893 0.4953 0.000 0.928 0.000 0.024 0.048
#> ERR184088 2 0.1597 0.4997 0.024 0.948 0.000 0.008 0.020
#> ERR184075 2 0.7719 -0.2392 0.008 0.448 0.092 0.124 0.328
#> ERR184041 3 0.2806 0.8334 0.152 0.000 0.844 0.000 0.004
#> ERR184060 5 0.4262 0.8029 0.000 0.440 0.000 0.000 0.560
#> ERR184035 2 0.6643 -0.0239 0.372 0.404 0.000 0.224 0.000
#> ERR184086 2 0.5778 -0.3529 0.000 0.528 0.000 0.096 0.376
#> ERR184080 1 0.3151 0.6137 0.836 0.020 0.000 0.144 0.000
#> ERR184050 2 0.6001 -0.3572 0.000 0.456 0.000 0.112 0.432
#> ERR184047 1 0.5778 0.1709 0.680 0.000 0.040 0.180 0.100
#> ERR184092 2 0.2104 0.4714 0.000 0.916 0.000 0.024 0.060
#> ERR184072 1 0.2361 0.6597 0.892 0.000 0.000 0.096 0.012
#> ERR184073 1 0.2740 0.6475 0.876 0.000 0.000 0.096 0.028
#> ERR184066 2 0.6464 0.1549 0.360 0.484 0.000 0.148 0.008
#> ERR184098 2 0.5845 -0.3479 0.000 0.540 0.000 0.108 0.352
#> ERR184044 2 0.4605 0.4265 0.132 0.772 0.000 0.076 0.020
#> ERR184054 1 0.1478 0.6744 0.936 0.000 0.000 0.064 0.000
#> ERR184085 2 0.5231 0.4131 0.140 0.728 0.000 0.104 0.028
#> ERR184056 2 0.1701 0.4851 0.000 0.936 0.000 0.016 0.048
#> ERR184052 2 0.4956 -0.2349 0.000 0.636 0.000 0.048 0.316
#> ERR184070 2 0.4268 -0.5348 0.000 0.556 0.000 0.000 0.444
#> ERR184096 1 0.5777 0.2018 0.676 0.000 0.040 0.192 0.092
#> ERR184089 2 0.9117 -0.1783 0.076 0.360 0.152 0.124 0.288
#> ERR184049 2 0.1408 0.4880 0.000 0.948 0.000 0.008 0.044
#> ERR184038 2 0.5407 0.3887 0.196 0.680 0.000 0.116 0.008
#> ERR184087 3 0.1341 0.8423 0.056 0.000 0.944 0.000 0.000
#> ERR184097 2 0.1701 0.4890 0.000 0.936 0.000 0.016 0.048
#> ERR184094 1 0.3110 0.6365 0.876 0.020 0.000 0.060 0.044
#> ERR184058 5 0.4450 0.6808 0.000 0.488 0.000 0.004 0.508
#> ERR184036 2 0.5392 0.2990 0.256 0.664 0.000 0.060 0.020
#> ERR184046 5 0.4192 0.8167 0.000 0.404 0.000 0.000 0.596
#> ERR184074 1 0.1764 0.6726 0.928 0.000 0.000 0.064 0.008
#> ERR184048 2 0.1493 0.4955 0.000 0.948 0.000 0.024 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 6 0.3586 0.7662 0.280 0.004 0.004 0.000 0.000 0.712
#> ERR184093 2 0.2307 0.4990 0.064 0.900 0.000 0.024 0.012 0.000
#> ERR184051 3 0.1080 0.8787 0.004 0.000 0.960 0.004 0.000 0.032
#> ERR184076 6 0.4027 0.7466 0.236 0.004 0.012 0.008 0.008 0.732
#> ERR184043 3 0.0767 0.8746 0.000 0.000 0.976 0.012 0.008 0.004
#> ERR184037 1 0.5876 -0.1178 0.500 0.012 0.000 0.064 0.032 0.392
#> ERR184059 3 0.3114 0.8056 0.052 0.000 0.864 0.004 0.032 0.048
#> ERR184055 2 0.4184 0.2346 0.488 0.500 0.000 0.000 0.012 0.000
#> ERR184065 4 0.5624 0.2766 0.000 0.356 0.000 0.488 0.156 0.000
#> ERR184069 4 0.4076 0.7304 0.000 0.452 0.000 0.540 0.008 0.000
#> ERR184040 6 0.4584 0.5555 0.428 0.008 0.004 0.000 0.016 0.544
#> ERR184057 2 0.4181 -0.6920 0.012 0.512 0.000 0.476 0.000 0.000
#> ERR184082 2 0.5734 0.2482 0.372 0.524 0.000 0.056 0.004 0.044
#> ERR184083 4 0.4308 0.7393 0.012 0.468 0.000 0.516 0.004 0.000
#> ERR184039 2 0.4710 0.0312 0.004 0.668 0.000 0.244 0.084 0.000
#> ERR184064 3 0.0767 0.8769 0.000 0.000 0.976 0.008 0.012 0.004
#> ERR184081 4 0.3993 0.7359 0.004 0.476 0.000 0.520 0.000 0.000
#> ERR184095 4 0.3998 0.7069 0.004 0.492 0.000 0.504 0.000 0.000
#> ERR184079 2 0.1194 0.5090 0.032 0.956 0.000 0.004 0.008 0.000
#> ERR184084 3 0.7589 0.3054 0.088 0.144 0.476 0.020 0.024 0.248
#> ERR184068 2 0.2067 0.5016 0.064 0.912 0.000 0.016 0.004 0.004
#> ERR184067 2 0.2879 0.2751 0.004 0.816 0.000 0.176 0.004 0.000
#> ERR184071 2 0.0951 0.4937 0.008 0.968 0.000 0.020 0.004 0.000
#> ERR184042 5 0.4690 0.4162 0.056 0.004 0.080 0.000 0.752 0.108
#> ERR184063 3 0.1225 0.8785 0.004 0.000 0.956 0.004 0.004 0.032
#> ERR184091 4 0.5464 0.4299 0.004 0.268 0.000 0.576 0.152 0.000
#> ERR184061 1 0.7574 -0.0851 0.428 0.008 0.016 0.152 0.112 0.284
#> ERR184077 2 0.0748 0.4958 0.004 0.976 0.000 0.016 0.004 0.000
#> ERR184062 2 0.4292 0.2761 0.416 0.568 0.000 0.004 0.008 0.004
#> ERR184053 2 0.1553 0.5043 0.008 0.944 0.000 0.032 0.004 0.012
#> ERR184088 2 0.2326 0.5013 0.092 0.888 0.000 0.012 0.008 0.000
#> ERR184075 2 0.6709 -0.0901 0.000 0.432 0.040 0.360 0.156 0.012
#> ERR184041 3 0.1371 0.8745 0.004 0.000 0.948 0.004 0.004 0.040
#> ERR184060 4 0.3979 0.7434 0.000 0.456 0.000 0.540 0.004 0.000
#> ERR184035 1 0.6432 0.0746 0.520 0.228 0.000 0.016 0.020 0.216
#> ERR184086 2 0.4729 0.0231 0.000 0.656 0.000 0.248 0.096 0.000
#> ERR184080 1 0.4509 -0.2244 0.620 0.016 0.000 0.000 0.020 0.344
#> ERR184050 2 0.5723 -0.1272 0.000 0.460 0.004 0.392 0.144 0.000
#> ERR184047 5 0.5297 0.4867 0.384 0.004 0.000 0.000 0.520 0.092
#> ERR184092 2 0.0508 0.4962 0.004 0.984 0.000 0.012 0.000 0.000
#> ERR184072 1 0.7284 -0.0949 0.436 0.000 0.016 0.152 0.100 0.296
#> ERR184073 1 0.7282 -0.0719 0.476 0.000 0.024 0.116 0.128 0.256
#> ERR184066 1 0.4802 -0.0069 0.588 0.364 0.000 0.004 0.008 0.036
#> ERR184098 2 0.4733 0.0475 0.004 0.668 0.000 0.240 0.088 0.000
#> ERR184044 2 0.4420 0.2935 0.360 0.604 0.000 0.036 0.000 0.000
#> ERR184054 1 0.5650 -0.3119 0.572 0.008 0.020 0.024 0.036 0.340
#> ERR184085 2 0.5176 0.2629 0.388 0.544 0.000 0.052 0.004 0.012
#> ERR184056 2 0.1036 0.5047 0.004 0.964 0.000 0.024 0.008 0.000
#> ERR184052 2 0.3409 0.2578 0.000 0.780 0.000 0.192 0.028 0.000
#> ERR184070 2 0.3881 -0.4351 0.000 0.600 0.000 0.396 0.004 0.000
#> ERR184096 5 0.4925 0.4838 0.448 0.000 0.000 0.008 0.500 0.044
#> ERR184089 2 0.7219 -0.0944 0.000 0.408 0.072 0.340 0.160 0.020
#> ERR184049 2 0.2201 0.4946 0.056 0.904 0.000 0.036 0.004 0.000
#> ERR184038 2 0.4878 0.2431 0.464 0.496 0.000 0.020 0.012 0.008
#> ERR184087 3 0.0665 0.8749 0.000 0.000 0.980 0.008 0.008 0.004
#> ERR184097 2 0.0935 0.5023 0.000 0.964 0.000 0.032 0.004 0.000
#> ERR184094 1 0.7405 -0.1399 0.480 0.044 0.028 0.036 0.124 0.288
#> ERR184058 2 0.4032 -0.4595 0.000 0.572 0.000 0.420 0.008 0.000
#> ERR184036 2 0.4556 0.3976 0.100 0.768 0.000 0.060 0.064 0.008
#> ERR184046 4 0.3982 0.7455 0.004 0.460 0.000 0.536 0.000 0.000
#> ERR184074 1 0.6932 -0.1661 0.476 0.004 0.020 0.108 0.068 0.324
#> ERR184048 2 0.1007 0.5079 0.016 0.968 0.000 0.008 0.004 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 10269 rows and 62 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 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 0.775 0.896 0.954 0.4874 0.511 0.511
#> 3 3 0.532 0.772 0.859 0.3587 0.796 0.609
#> 4 4 0.537 0.593 0.771 0.1167 0.824 0.528
#> 5 5 0.564 0.561 0.750 0.0472 0.946 0.791
#> 6 6 0.615 0.547 0.720 0.0318 0.968 0.859
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
#> ERR184078 2 0.0000 0.9509 0.000 1.000
#> ERR184093 2 0.0000 0.9509 0.000 1.000
#> ERR184051 1 0.0000 0.9470 1.000 0.000
#> ERR184076 2 0.0000 0.9509 0.000 1.000
#> ERR184043 1 0.0000 0.9470 1.000 0.000
#> ERR184037 2 0.0000 0.9509 0.000 1.000
#> ERR184059 1 0.0000 0.9470 1.000 0.000
#> ERR184055 2 0.0938 0.9474 0.012 0.988
#> ERR184065 1 0.0000 0.9470 1.000 0.000
#> ERR184069 2 0.9977 0.0827 0.472 0.528
#> ERR184040 2 0.0000 0.9509 0.000 1.000
#> ERR184057 2 0.0376 0.9499 0.004 0.996
#> ERR184082 1 0.6148 0.8258 0.848 0.152
#> ERR184083 1 0.0000 0.9470 1.000 0.000
#> ERR184039 1 0.0000 0.9470 1.000 0.000
#> ERR184064 1 0.0000 0.9470 1.000 0.000
#> ERR184081 1 0.6048 0.8298 0.852 0.148
#> ERR184095 2 0.5408 0.8587 0.124 0.876
#> ERR184079 2 0.0000 0.9509 0.000 1.000
#> ERR184084 1 0.0000 0.9470 1.000 0.000
#> ERR184068 2 0.0938 0.9472 0.012 0.988
#> ERR184067 2 0.5059 0.8681 0.112 0.888
#> ERR184071 2 0.9608 0.3747 0.384 0.616
#> ERR184042 1 0.6623 0.8008 0.828 0.172
#> ERR184063 1 0.0000 0.9470 1.000 0.000
#> ERR184091 1 0.0000 0.9470 1.000 0.000
#> ERR184061 2 0.0000 0.9509 0.000 1.000
#> ERR184077 2 0.1184 0.9452 0.016 0.984
#> ERR184062 2 0.0938 0.9473 0.012 0.988
#> ERR184053 2 0.6343 0.8145 0.160 0.840
#> ERR184088 2 0.0000 0.9509 0.000 1.000
#> ERR184075 1 0.0000 0.9470 1.000 0.000
#> ERR184041 1 0.0000 0.9470 1.000 0.000
#> ERR184060 2 0.0672 0.9488 0.008 0.992
#> ERR184035 2 0.0000 0.9509 0.000 1.000
#> ERR184086 1 0.0000 0.9470 1.000 0.000
#> ERR184080 2 0.0000 0.9509 0.000 1.000
#> ERR184050 1 0.0000 0.9470 1.000 0.000
#> ERR184047 2 0.3584 0.9109 0.068 0.932
#> ERR184092 2 0.0000 0.9509 0.000 1.000
#> ERR184072 2 0.0000 0.9509 0.000 1.000
#> ERR184073 2 0.0000 0.9509 0.000 1.000
#> ERR184066 2 0.0000 0.9509 0.000 1.000
#> ERR184098 1 0.0000 0.9470 1.000 0.000
#> ERR184044 2 0.2603 0.9282 0.044 0.956
#> ERR184054 2 0.0000 0.9509 0.000 1.000
#> ERR184085 1 0.7745 0.7112 0.772 0.228
#> ERR184056 2 0.0672 0.9488 0.008 0.992
#> ERR184052 1 0.3431 0.9049 0.936 0.064
#> ERR184070 2 0.0000 0.9509 0.000 1.000
#> ERR184096 2 0.0000 0.9509 0.000 1.000
#> ERR184089 1 0.0000 0.9470 1.000 0.000
#> ERR184049 2 0.2603 0.9285 0.044 0.956
#> ERR184038 1 0.9661 0.3368 0.608 0.392
#> ERR184087 1 0.0000 0.9470 1.000 0.000
#> ERR184097 2 0.3114 0.9206 0.056 0.944
#> ERR184094 2 0.5842 0.8379 0.140 0.860
#> ERR184058 1 0.1843 0.9308 0.972 0.028
#> ERR184036 2 0.0000 0.9509 0.000 1.000
#> ERR184046 1 0.0000 0.9470 1.000 0.000
#> ERR184074 2 0.0000 0.9509 0.000 1.000
#> ERR184048 2 0.0000 0.9509 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> ERR184078 2 0.2878 0.849 0.096 0.904 0.000
#> ERR184093 1 0.5948 0.413 0.640 0.360 0.000
#> ERR184051 3 0.0747 0.893 0.000 0.016 0.984
#> ERR184076 2 0.1753 0.843 0.048 0.952 0.000
#> ERR184043 3 0.0237 0.894 0.000 0.004 0.996
#> ERR184037 1 0.4062 0.770 0.836 0.164 0.000
#> ERR184059 3 0.0747 0.894 0.000 0.016 0.984
#> ERR184055 2 0.5497 0.662 0.292 0.708 0.000
#> ERR184065 3 0.0424 0.894 0.000 0.008 0.992
#> ERR184069 1 0.5357 0.704 0.820 0.064 0.116
#> ERR184040 2 0.3816 0.835 0.148 0.852 0.000
#> ERR184057 2 0.4702 0.735 0.212 0.788 0.000
#> ERR184082 3 0.7279 0.613 0.056 0.292 0.652
#> ERR184083 3 0.5315 0.766 0.012 0.216 0.772
#> ERR184039 3 0.2599 0.875 0.052 0.016 0.932
#> ERR184064 3 0.0424 0.894 0.000 0.008 0.992
#> ERR184081 3 0.7248 0.656 0.068 0.256 0.676
#> ERR184095 2 0.2998 0.823 0.068 0.916 0.016
#> ERR184079 2 0.4842 0.753 0.224 0.776 0.000
#> ERR184084 3 0.3682 0.847 0.008 0.116 0.876
#> ERR184068 2 0.2711 0.846 0.088 0.912 0.000
#> ERR184067 1 0.8093 0.265 0.516 0.416 0.068
#> ERR184071 2 0.3623 0.793 0.032 0.896 0.072
#> ERR184042 3 0.4174 0.849 0.036 0.092 0.872
#> ERR184063 3 0.0424 0.894 0.000 0.008 0.992
#> ERR184091 3 0.0237 0.894 0.000 0.004 0.996
#> ERR184061 1 0.1129 0.791 0.976 0.020 0.004
#> ERR184077 2 0.2165 0.849 0.064 0.936 0.000
#> ERR184062 2 0.3686 0.824 0.140 0.860 0.000
#> ERR184053 2 0.0747 0.827 0.016 0.984 0.000
#> ERR184088 1 0.4842 0.714 0.776 0.224 0.000
#> ERR184075 3 0.0747 0.894 0.000 0.016 0.984
#> ERR184041 3 0.0892 0.893 0.000 0.020 0.980
#> ERR184060 1 0.4293 0.752 0.832 0.164 0.004
#> ERR184035 1 0.6057 0.583 0.656 0.340 0.004
#> ERR184086 3 0.0424 0.893 0.008 0.000 0.992
#> ERR184080 2 0.5678 0.657 0.316 0.684 0.000
#> ERR184050 3 0.2584 0.870 0.064 0.008 0.928
#> ERR184047 1 0.7334 0.547 0.624 0.328 0.048
#> ERR184092 2 0.4796 0.776 0.220 0.780 0.000
#> ERR184072 1 0.2878 0.789 0.904 0.096 0.000
#> ERR184073 1 0.1529 0.792 0.960 0.040 0.000
#> ERR184066 2 0.3340 0.829 0.120 0.880 0.000
#> ERR184098 3 0.0829 0.894 0.004 0.012 0.984
#> ERR184044 1 0.6113 0.583 0.688 0.300 0.012
#> ERR184054 2 0.5706 0.641 0.320 0.680 0.000
#> ERR184085 3 0.8068 0.455 0.316 0.088 0.596
#> ERR184056 2 0.2356 0.851 0.072 0.928 0.000
#> ERR184052 3 0.6105 0.685 0.252 0.024 0.724
#> ERR184070 1 0.0892 0.794 0.980 0.020 0.000
#> ERR184096 1 0.3116 0.796 0.892 0.108 0.000
#> ERR184089 3 0.0000 0.893 0.000 0.000 1.000
#> ERR184049 1 0.3802 0.776 0.888 0.080 0.032
#> ERR184038 2 0.3551 0.743 0.000 0.868 0.132
#> ERR184087 3 0.0000 0.893 0.000 0.000 1.000
#> ERR184097 2 0.1964 0.843 0.056 0.944 0.000
#> ERR184094 1 0.4179 0.774 0.876 0.052 0.072
#> ERR184058 3 0.7683 0.530 0.328 0.064 0.608
#> ERR184036 1 0.0983 0.793 0.980 0.016 0.004
#> ERR184046 3 0.2066 0.882 0.000 0.060 0.940
#> ERR184074 1 0.2796 0.801 0.908 0.092 0.000
#> ERR184048 2 0.3619 0.825 0.136 0.864 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> ERR184078 4 0.2271 0.7885 0.008 0.076 0.000 0.916
#> ERR184093 1 0.5489 0.4585 0.700 0.060 0.000 0.240
#> ERR184051 3 0.0657 0.9041 0.000 0.012 0.984 0.004
#> ERR184076 4 0.1305 0.7909 0.004 0.036 0.000 0.960
#> ERR184043 3 0.0779 0.9009 0.000 0.016 0.980 0.004
#> ERR184037 1 0.6139 0.3430 0.544 0.404 0.000 0.052
#> ERR184059 3 0.0657 0.9048 0.000 0.012 0.984 0.004
#> ERR184055 4 0.6121 0.6278 0.156 0.164 0.000 0.680
#> ERR184065 3 0.1576 0.8884 0.004 0.048 0.948 0.000
#> ERR184069 2 0.6020 0.1660 0.376 0.580 0.040 0.004
#> ERR184040 4 0.3547 0.7842 0.072 0.064 0.000 0.864
#> ERR184057 2 0.5790 0.4806 0.080 0.684 0.000 0.236
#> ERR184082 2 0.4256 0.5772 0.008 0.824 0.128 0.040
#> ERR184083 2 0.5530 0.3998 0.000 0.632 0.336 0.032
#> ERR184039 3 0.5508 0.5567 0.056 0.252 0.692 0.000
#> ERR184064 3 0.0188 0.9044 0.000 0.000 0.996 0.004
#> ERR184081 2 0.5606 0.5532 0.068 0.756 0.148 0.028
#> ERR184095 2 0.3823 0.5460 0.008 0.824 0.008 0.160
#> ERR184079 2 0.6295 0.3304 0.088 0.616 0.000 0.296
#> ERR184084 2 0.5732 0.2876 0.004 0.580 0.392 0.024
#> ERR184068 2 0.6149 -0.2062 0.048 0.480 0.000 0.472
#> ERR184067 2 0.5722 0.4530 0.192 0.724 0.012 0.072
#> ERR184071 2 0.6569 -0.0323 0.008 0.476 0.056 0.460
#> ERR184042 3 0.4587 0.7656 0.020 0.140 0.808 0.032
#> ERR184063 3 0.0376 0.9050 0.000 0.004 0.992 0.004
#> ERR184091 3 0.1557 0.8830 0.000 0.056 0.944 0.000
#> ERR184061 1 0.1902 0.6701 0.932 0.064 0.000 0.004
#> ERR184077 4 0.5343 0.5353 0.028 0.316 0.000 0.656
#> ERR184062 4 0.3204 0.7680 0.064 0.028 0.016 0.892
#> ERR184053 4 0.5270 0.5393 0.012 0.320 0.008 0.660
#> ERR184088 1 0.6337 0.1566 0.472 0.468 0.000 0.060
#> ERR184075 3 0.0592 0.9030 0.000 0.016 0.984 0.000
#> ERR184041 3 0.0524 0.9032 0.000 0.004 0.988 0.008
#> ERR184060 1 0.6170 0.6143 0.700 0.084 0.020 0.196
#> ERR184035 2 0.4379 0.4890 0.172 0.792 0.000 0.036
#> ERR184086 3 0.0657 0.9034 0.004 0.012 0.984 0.000
#> ERR184080 4 0.7241 0.3748 0.196 0.264 0.000 0.540
#> ERR184050 3 0.3027 0.8340 0.088 0.020 0.888 0.004
#> ERR184047 1 0.8713 0.3386 0.444 0.236 0.052 0.268
#> ERR184092 4 0.3806 0.7297 0.156 0.020 0.000 0.824
#> ERR184072 1 0.3372 0.6357 0.868 0.036 0.000 0.096
#> ERR184073 1 0.1635 0.6602 0.948 0.008 0.000 0.044
#> ERR184066 4 0.2207 0.7860 0.056 0.012 0.004 0.928
#> ERR184098 3 0.1114 0.8994 0.008 0.016 0.972 0.004
#> ERR184044 1 0.8069 0.2188 0.468 0.064 0.092 0.376
#> ERR184054 4 0.5432 0.5365 0.316 0.032 0.000 0.652
#> ERR184085 2 0.5993 0.5104 0.144 0.712 0.136 0.008
#> ERR184056 4 0.2480 0.7820 0.008 0.088 0.000 0.904
#> ERR184052 3 0.7453 0.0231 0.192 0.324 0.484 0.000
#> ERR184070 1 0.3751 0.6247 0.800 0.196 0.000 0.004
#> ERR184096 1 0.3463 0.6752 0.864 0.040 0.000 0.096
#> ERR184089 3 0.0188 0.9052 0.000 0.004 0.996 0.000
#> ERR184049 2 0.5795 -0.1184 0.460 0.516 0.008 0.016
#> ERR184038 4 0.3771 0.7306 0.004 0.052 0.088 0.856
#> ERR184087 3 0.0336 0.9047 0.000 0.008 0.992 0.000
#> ERR184097 4 0.1452 0.7900 0.008 0.036 0.000 0.956
#> ERR184094 1 0.6429 0.4283 0.600 0.336 0.040 0.024
#> ERR184058 2 0.6878 0.4350 0.136 0.596 0.264 0.004
#> ERR184036 1 0.3024 0.6484 0.852 0.148 0.000 0.000
#> ERR184046 3 0.3647 0.8324 0.004 0.096 0.860 0.040
#> ERR184074 1 0.4234 0.6727 0.816 0.132 0.000 0.052
#> ERR184048 2 0.4706 0.4836 0.028 0.748 0.000 0.224
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> ERR184078 1 0.3409 0.6886 0.824 0.032 0.000 0.144 0.000
#> ERR184093 5 0.6261 0.3804 0.160 0.008 0.000 0.268 0.564
#> ERR184051 3 0.0324 0.9049 0.004 0.004 0.992 0.000 0.000
#> ERR184076 1 0.1830 0.7458 0.932 0.028 0.000 0.040 0.000
#> ERR184043 3 0.0613 0.9019 0.008 0.000 0.984 0.004 0.004
#> ERR184037 5 0.7079 0.1896 0.124 0.340 0.000 0.056 0.480
#> ERR184059 3 0.1186 0.9028 0.008 0.008 0.964 0.020 0.000
#> ERR184055 1 0.6479 0.4950 0.648 0.100 0.004 0.092 0.156
#> ERR184065 3 0.2068 0.8698 0.000 0.092 0.904 0.004 0.000
#> ERR184069 2 0.4625 0.4034 0.000 0.652 0.004 0.020 0.324
#> ERR184040 1 0.3224 0.7407 0.868 0.028 0.000 0.076 0.028
#> ERR184057 2 0.7129 0.2729 0.236 0.548 0.000 0.088 0.128
#> ERR184082 2 0.3317 0.4748 0.004 0.852 0.056 0.088 0.000
#> ERR184083 2 0.5249 0.3648 0.016 0.712 0.164 0.108 0.000
#> ERR184039 3 0.4905 0.4659 0.000 0.344 0.624 0.008 0.024
#> ERR184064 3 0.0162 0.9051 0.000 0.004 0.996 0.000 0.000
#> ERR184081 2 0.4075 0.5511 0.016 0.836 0.044 0.036 0.068
#> ERR184095 2 0.3575 0.4308 0.056 0.824 0.000 0.120 0.000
#> ERR184079 2 0.7018 -0.1206 0.180 0.536 0.000 0.236 0.048
#> ERR184084 2 0.5240 0.3298 0.000 0.660 0.244 0.096 0.000
#> ERR184068 4 0.7082 0.5132 0.236 0.308 0.004 0.440 0.012
#> ERR184067 2 0.6209 0.4501 0.068 0.640 0.000 0.080 0.212
#> ERR184071 2 0.6953 -0.2600 0.392 0.464 0.044 0.092 0.008
#> ERR184042 3 0.4826 0.7537 0.024 0.160 0.764 0.032 0.020
#> ERR184063 3 0.0486 0.9045 0.004 0.004 0.988 0.004 0.000
#> ERR184091 3 0.2233 0.8590 0.000 0.104 0.892 0.004 0.000
#> ERR184061 5 0.2157 0.5981 0.004 0.036 0.000 0.040 0.920
#> ERR184077 4 0.6971 0.6280 0.296 0.252 0.000 0.440 0.012
#> ERR184062 1 0.2930 0.7232 0.880 0.000 0.032 0.076 0.012
#> ERR184053 4 0.6352 0.5517 0.308 0.188 0.000 0.504 0.000
#> ERR184088 2 0.7000 0.0559 0.132 0.472 0.000 0.044 0.352
#> ERR184075 3 0.0609 0.9043 0.000 0.020 0.980 0.000 0.000
#> ERR184041 3 0.0451 0.9037 0.004 0.000 0.988 0.008 0.000
#> ERR184060 5 0.6504 0.3425 0.336 0.028 0.028 0.052 0.556
#> ERR184035 2 0.2264 0.5359 0.004 0.912 0.000 0.024 0.060
#> ERR184086 3 0.1186 0.9035 0.000 0.020 0.964 0.008 0.008
#> ERR184080 1 0.6456 0.4321 0.628 0.172 0.000 0.060 0.140
#> ERR184050 3 0.3280 0.7788 0.000 0.004 0.824 0.012 0.160
#> ERR184047 5 0.8311 0.1993 0.368 0.152 0.076 0.036 0.368
#> ERR184092 1 0.4414 0.6434 0.764 0.000 0.004 0.072 0.160
#> ERR184072 5 0.4958 0.4776 0.084 0.000 0.000 0.224 0.692
#> ERR184073 5 0.4170 0.5201 0.048 0.000 0.000 0.192 0.760
#> ERR184066 1 0.1787 0.7410 0.940 0.000 0.016 0.032 0.012
#> ERR184098 3 0.1347 0.8951 0.020 0.004 0.960 0.008 0.008
#> ERR184044 5 0.8261 0.2401 0.340 0.044 0.100 0.100 0.416
#> ERR184054 1 0.5355 0.5725 0.704 0.008 0.004 0.148 0.136
#> ERR184085 2 0.3586 0.5426 0.000 0.848 0.080 0.024 0.048
#> ERR184056 1 0.3019 0.7229 0.864 0.048 0.000 0.088 0.000
#> ERR184052 2 0.6036 0.2998 0.000 0.548 0.356 0.020 0.076
#> ERR184070 5 0.3984 0.5573 0.032 0.152 0.000 0.016 0.800
#> ERR184096 5 0.4844 0.5854 0.152 0.024 0.000 0.072 0.752
#> ERR184089 3 0.0566 0.9053 0.000 0.012 0.984 0.000 0.004
#> ERR184049 2 0.6168 0.1467 0.048 0.512 0.000 0.044 0.396
#> ERR184038 1 0.3882 0.6476 0.824 0.016 0.100 0.060 0.000
#> ERR184087 3 0.0854 0.9062 0.000 0.012 0.976 0.008 0.004
#> ERR184097 1 0.2513 0.7232 0.900 0.012 0.008 0.076 0.004
#> ERR184094 5 0.7449 0.2508 0.080 0.300 0.064 0.036 0.520
#> ERR184058 2 0.4112 0.5269 0.000 0.804 0.124 0.016 0.056
#> ERR184036 5 0.2289 0.6012 0.004 0.080 0.000 0.012 0.904
#> ERR184046 3 0.5424 0.6241 0.052 0.220 0.688 0.040 0.000
#> ERR184074 5 0.4797 0.5951 0.116 0.104 0.000 0.020 0.760
#> ERR184048 2 0.4937 0.3595 0.128 0.744 0.000 0.112 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> ERR184078 1 0.3722 0.7387 0.820 0.044 0.000 0.036 0.004 0.096
#> ERR184093 6 0.5071 0.5543 0.064 0.012 0.000 0.004 0.300 0.620
#> ERR184051 3 0.0508 0.8839 0.004 0.000 0.984 0.012 0.000 0.000
#> ERR184076 1 0.2377 0.7532 0.908 0.008 0.008 0.040 0.004 0.032
#> ERR184043 3 0.0841 0.8832 0.004 0.004 0.976 0.008 0.004 0.004
#> ERR184037 5 0.5693 0.4627 0.088 0.168 0.000 0.036 0.672 0.036
#> ERR184059 3 0.2132 0.8771 0.008 0.020 0.920 0.032 0.000 0.020
#> ERR184055 1 0.7016 0.4492 0.560 0.096 0.004 0.064 0.208 0.068
#> ERR184065 3 0.2270 0.8506 0.000 0.072 0.900 0.020 0.004 0.004
#> ERR184069 2 0.5274 0.2416 0.004 0.516 0.008 0.024 0.424 0.024
#> ERR184040 1 0.3566 0.7524 0.844 0.020 0.004 0.024 0.032 0.076
#> ERR184057 2 0.7565 0.0809 0.240 0.348 0.000 0.056 0.320 0.036
#> ERR184082 2 0.2594 0.5298 0.004 0.900 0.036 0.024 0.008 0.028
#> ERR184083 2 0.3879 0.4635 0.004 0.792 0.144 0.036 0.000 0.024
#> ERR184039 3 0.5598 0.3476 0.000 0.320 0.572 0.020 0.080 0.008
#> ERR184064 3 0.0551 0.8846 0.004 0.004 0.984 0.000 0.000 0.008
#> ERR184081 2 0.5006 0.5699 0.024 0.704 0.020 0.012 0.212 0.028
#> ERR184095 2 0.4280 0.5306 0.020 0.796 0.004 0.092 0.064 0.024
#> ERR184079 2 0.7266 0.1671 0.080 0.536 0.000 0.164 0.068 0.152
#> ERR184084 2 0.4681 0.4029 0.008 0.708 0.208 0.064 0.000 0.012
#> ERR184068 6 0.7440 -0.4865 0.104 0.248 0.000 0.320 0.004 0.324
#> ERR184067 2 0.6500 0.1948 0.064 0.456 0.000 0.032 0.396 0.052
#> ERR184071 2 0.7437 -0.0163 0.380 0.416 0.060 0.068 0.040 0.036
#> ERR184042 3 0.5405 0.7259 0.020 0.116 0.732 0.044 0.040 0.048
#> ERR184063 3 0.1129 0.8844 0.004 0.008 0.964 0.012 0.000 0.012
#> ERR184091 3 0.1555 0.8689 0.000 0.060 0.932 0.004 0.000 0.004
#> ERR184061 5 0.2915 0.2828 0.000 0.000 0.000 0.008 0.808 0.184
#> ERR184077 4 0.7268 0.5785 0.160 0.224 0.000 0.464 0.008 0.144
#> ERR184062 1 0.2587 0.7459 0.892 0.000 0.016 0.036 0.004 0.052
#> ERR184053 4 0.4827 0.5987 0.160 0.116 0.008 0.708 0.000 0.008
#> ERR184088 2 0.6975 0.2677 0.128 0.452 0.000 0.008 0.316 0.096
#> ERR184075 3 0.0665 0.8844 0.000 0.008 0.980 0.004 0.000 0.008
#> ERR184041 3 0.1312 0.8812 0.008 0.004 0.956 0.012 0.000 0.020
#> ERR184060 5 0.7728 -0.0529 0.312 0.072 0.016 0.012 0.340 0.248
#> ERR184035 2 0.3459 0.5858 0.008 0.820 0.000 0.004 0.124 0.044
#> ERR184086 3 0.1761 0.8758 0.000 0.008 0.936 0.008 0.016 0.032
#> ERR184080 1 0.5542 0.6004 0.676 0.096 0.000 0.012 0.164 0.052
#> ERR184050 3 0.5034 0.6763 0.004 0.004 0.720 0.036 0.136 0.100
#> ERR184047 5 0.6255 0.2690 0.360 0.060 0.024 0.012 0.516 0.028
#> ERR184092 1 0.5180 0.6421 0.708 0.012 0.000 0.056 0.160 0.064
#> ERR184072 6 0.4694 0.5639 0.024 0.008 0.000 0.008 0.360 0.600
#> ERR184073 6 0.4427 0.5155 0.016 0.008 0.000 0.000 0.412 0.564
#> ERR184066 1 0.1579 0.7601 0.944 0.000 0.004 0.024 0.008 0.020
#> ERR184098 3 0.2296 0.8618 0.024 0.004 0.916 0.016 0.012 0.028
#> ERR184044 5 0.7713 0.2795 0.288 0.032 0.048 0.104 0.464 0.064
#> ERR184054 1 0.5188 0.5502 0.648 0.004 0.000 0.024 0.072 0.252
#> ERR184085 2 0.4709 0.5843 0.004 0.744 0.024 0.044 0.164 0.020
#> ERR184056 1 0.3718 0.7391 0.836 0.060 0.000 0.032 0.028 0.044
#> ERR184052 2 0.5780 0.3719 0.000 0.576 0.292 0.008 0.100 0.024
#> ERR184070 5 0.2593 0.5329 0.012 0.068 0.000 0.000 0.884 0.036
#> ERR184096 5 0.4794 0.1441 0.100 0.000 0.000 0.004 0.668 0.228
#> ERR184089 3 0.1109 0.8853 0.004 0.016 0.964 0.004 0.000 0.012
#> ERR184049 5 0.4402 0.1942 0.016 0.336 0.000 0.000 0.632 0.016
#> ERR184038 1 0.4030 0.6876 0.820 0.004 0.060 0.056 0.020 0.040
#> ERR184087 3 0.1325 0.8849 0.000 0.016 0.956 0.012 0.004 0.012
#> ERR184097 1 0.2102 0.7626 0.920 0.020 0.004 0.032 0.000 0.024
#> ERR184094 5 0.4551 0.4927 0.024 0.172 0.016 0.012 0.752 0.024
#> ERR184058 2 0.4105 0.5911 0.000 0.780 0.048 0.008 0.144 0.020
#> ERR184036 5 0.2563 0.4861 0.000 0.040 0.000 0.004 0.880 0.076
#> ERR184046 3 0.6124 0.5347 0.080 0.196 0.640 0.048 0.016 0.020
#> ERR184074 5 0.3075 0.5438 0.080 0.020 0.000 0.016 0.864 0.020
#> ERR184048 2 0.5403 0.5025 0.048 0.716 0.000 0.044 0.076 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.
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