Date: 2019-12-25 21:49:25 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 51941 rows and 51 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, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 51941 51
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, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), 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:pam | 3 | 1.000 | 1.000 | 1.000 | ** | 2 |
| SD:NMF | 3 | 1.000 | 1.000 | 1.000 | ** | 2 |
| CV:hclust | 3 | 1.000 | 1.000 | 1.000 | ** | 2 |
| CV:kmeans | 3 | 1.000 | 0.991 | 0.964 | ** | |
| CV:NMF | 3 | 1.000 | 1.000 | 1.000 | ** | 2 |
| MAD:hclust | 3 | 1.000 | 0.968 | 0.987 | ** | 2 |
| MAD:kmeans | 3 | 1.000 | 0.977 | 0.943 | ** | |
| MAD:mclust | 3 | 1.000 | 0.998 | 0.999 | ** | |
| MAD:NMF | 3 | 1.000 | 1.000 | 1.000 | ** | 2 |
| ATC:hclust | 3 | 1.000 | 1.000 | 1.000 | ** | 2 |
| ATC:pam | 3 | 1.000 | 1.000 | 1.000 | ** | 2 |
| ATC:mclust | 3 | 1.000 | 0.999 | 1.000 | ** | 2 |
| ATC:NMF | 3 | 1.000 | 0.998 | 0.999 | ** | 2 |
| MAD:skmeans | 5 | 0.969 | 0.939 | 0.968 | ** | 2,3 |
| CV:skmeans | 5 | 0.947 | 0.922 | 0.956 | * | 3 |
| CV:mclust | 4 | 0.936 | 0.905 | 0.932 | * | 2,3 |
| ATC:skmeans | 4 | 0.936 | 0.966 | 0.978 | * | 2,3 |
| SD:hclust | 4 | 0.934 | 0.992 | 0.983 | * | 2,3 |
| MAD:pam | 5 | 0.924 | 0.921 | 0.962 | * | 2,3,4 |
| SD:skmeans | 5 | 0.909 | 0.819 | 0.929 | * | 3 |
| SD:mclust | 5 | 0.909 | 0.882 | 0.944 | * | 3,4 |
| CV:pam | 6 | 0.902 | 0.890 | 0.950 | * | 2,3 |
| SD:kmeans | 3 | 0.681 | 0.990 | 0.947 | ||
| ATC:kmeans | 3 | 0.681 | 0.996 | 0.973 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 1.000 1.000 1.000 0.297 0.704 0.704
#> CV:NMF 2 1.000 1.000 1.000 0.297 0.704 0.704
#> MAD:NMF 2 1.000 0.999 1.000 0.298 0.704 0.704
#> ATC:NMF 2 1.000 1.000 1.000 0.297 0.704 0.704
#> SD:skmeans 2 0.633 0.897 0.915 0.424 0.506 0.506
#> CV:skmeans 2 0.633 0.897 0.915 0.424 0.506 0.506
#> MAD:skmeans 2 1.000 1.000 1.000 0.495 0.506 0.506
#> ATC:skmeans 2 1.000 1.000 1.000 0.297 0.704 0.704
#> SD:mclust 2 0.639 0.932 0.945 0.464 0.506 0.506
#> CV:mclust 2 1.000 0.984 0.986 0.485 0.506 0.506
#> MAD:mclust 2 0.633 0.903 0.919 0.427 0.506 0.506
#> ATC:mclust 2 1.000 0.964 0.977 0.316 0.704 0.704
#> SD:kmeans 2 0.506 0.758 0.824 0.327 0.704 0.704
#> CV:kmeans 2 0.506 0.815 0.854 0.323 0.704 0.704
#> MAD:kmeans 2 0.421 0.676 0.802 0.386 0.633 0.633
#> ATC:kmeans 2 0.500 0.819 0.850 0.329 0.704 0.704
#> SD:pam 2 1.000 1.000 1.000 0.297 0.704 0.704
#> CV:pam 2 1.000 1.000 1.000 0.297 0.704 0.704
#> MAD:pam 2 1.000 1.000 1.000 0.297 0.704 0.704
#> ATC:pam 2 1.000 1.000 1.000 0.297 0.704 0.704
#> SD:hclust 2 1.000 1.000 1.000 0.297 0.704 0.704
#> CV:hclust 2 1.000 1.000 1.000 0.297 0.704 0.704
#> MAD:hclust 2 1.000 1.000 1.000 0.297 0.704 0.704
#> ATC:hclust 2 1.000 1.000 1.000 0.297 0.704 0.704
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 1.000 1.000 1.000 0.949 0.718 0.599
#> CV:NMF 3 1.000 1.000 1.000 0.949 0.718 0.599
#> MAD:NMF 3 1.000 1.000 1.000 0.946 0.718 0.599
#> ATC:NMF 3 1.000 0.998 0.999 0.952 0.718 0.599
#> SD:skmeans 3 1.000 1.000 1.000 0.367 0.915 0.833
#> CV:skmeans 3 1.000 1.000 1.000 0.367 0.915 0.833
#> MAD:skmeans 3 1.000 0.999 0.999 0.171 0.915 0.833
#> ATC:skmeans 3 1.000 0.959 0.985 1.004 0.693 0.563
#> SD:mclust 3 0.969 0.941 0.973 0.286 0.915 0.833
#> CV:mclust 3 0.977 0.967 0.984 0.215 0.915 0.833
#> MAD:mclust 3 1.000 0.998 0.999 0.356 0.915 0.833
#> ATC:mclust 3 1.000 0.999 1.000 0.834 0.718 0.599
#> SD:kmeans 3 0.681 0.990 0.947 0.630 0.718 0.599
#> CV:kmeans 3 1.000 0.991 0.964 0.705 0.718 0.599
#> MAD:kmeans 3 1.000 0.977 0.943 0.465 0.788 0.665
#> ATC:kmeans 3 0.681 0.996 0.973 0.677 0.718 0.599
#> SD:pam 3 1.000 1.000 1.000 0.949 0.718 0.599
#> CV:pam 3 1.000 1.000 1.000 0.949 0.718 0.599
#> MAD:pam 3 1.000 1.000 1.000 0.949 0.718 0.599
#> ATC:pam 3 1.000 1.000 1.000 0.949 0.718 0.599
#> SD:hclust 3 1.000 1.000 1.000 0.949 0.718 0.599
#> CV:hclust 3 1.000 1.000 1.000 0.949 0.718 0.599
#> MAD:hclust 3 1.000 0.968 0.987 0.977 0.718 0.599
#> ATC:hclust 3 1.000 1.000 1.000 0.949 0.718 0.599
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.895 0.924 0.946 0.1444 0.902 0.767
#> CV:NMF 4 0.824 0.838 0.921 0.1346 0.918 0.806
#> MAD:NMF 4 0.730 0.639 0.859 0.1833 0.956 0.896
#> ATC:NMF 4 0.778 0.887 0.904 0.1348 1.000 1.000
#> SD:skmeans 4 0.844 0.774 0.890 0.2200 0.902 0.767
#> CV:skmeans 4 0.731 0.435 0.766 0.2443 0.977 0.946
#> MAD:skmeans 4 0.860 0.905 0.933 0.2909 0.824 0.583
#> ATC:skmeans 4 0.936 0.966 0.978 0.2613 0.817 0.558
#> SD:mclust 4 1.000 0.966 0.989 0.0961 0.918 0.806
#> CV:mclust 4 0.936 0.905 0.932 0.1039 0.918 0.806
#> MAD:mclust 4 0.701 0.698 0.838 0.1957 0.956 0.896
#> ATC:mclust 4 0.833 0.883 0.925 0.1723 0.936 0.849
#> SD:kmeans 4 0.770 0.863 0.892 0.2027 0.936 0.849
#> CV:kmeans 4 0.727 0.868 0.874 0.1875 1.000 1.000
#> MAD:kmeans 4 0.708 0.356 0.785 0.2186 0.977 0.946
#> ATC:kmeans 4 0.731 0.669 0.729 0.2216 0.836 0.611
#> SD:pam 4 0.820 0.847 0.885 0.2357 0.824 0.583
#> CV:pam 4 0.860 0.900 0.943 0.1691 0.936 0.849
#> MAD:pam 4 0.956 0.939 0.975 0.2997 0.824 0.583
#> ATC:pam 4 0.824 0.880 0.915 0.2560 0.852 0.648
#> SD:hclust 4 0.934 0.992 0.983 0.0893 0.936 0.849
#> CV:hclust 4 0.845 0.874 0.932 0.1416 0.936 0.849
#> MAD:hclust 4 0.759 0.850 0.921 0.1370 0.956 0.896
#> ATC:hclust 4 0.785 0.914 0.949 0.0796 0.991 0.980
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.822 0.876 0.929 0.0596 0.977 0.930
#> CV:NMF 5 0.859 0.868 0.928 0.0808 0.977 0.934
#> MAD:NMF 5 0.736 0.765 0.858 0.1179 0.825 0.547
#> ATC:NMF 5 0.689 0.701 0.848 0.0747 0.902 0.767
#> SD:skmeans 5 0.909 0.819 0.929 0.1236 0.887 0.650
#> CV:skmeans 5 0.947 0.922 0.956 0.1099 0.780 0.457
#> MAD:skmeans 5 0.969 0.939 0.968 0.0766 0.938 0.752
#> ATC:skmeans 5 0.827 0.804 0.884 0.0752 0.928 0.716
#> SD:mclust 5 0.909 0.882 0.944 0.0903 0.941 0.828
#> CV:mclust 5 0.685 0.590 0.738 0.1488 0.941 0.828
#> MAD:mclust 5 0.652 0.532 0.743 0.0859 0.802 0.509
#> ATC:mclust 5 0.796 0.781 0.877 0.0820 0.920 0.779
#> SD:kmeans 5 0.684 0.774 0.824 0.1183 1.000 1.000
#> CV:kmeans 5 0.695 0.561 0.697 0.1158 0.817 0.566
#> MAD:kmeans 5 0.681 0.760 0.768 0.0887 0.776 0.450
#> ATC:kmeans 5 0.680 0.746 0.828 0.1072 0.836 0.535
#> SD:pam 5 0.822 0.794 0.883 0.0873 0.949 0.801
#> CV:pam 5 0.781 0.623 0.783 0.1004 0.865 0.641
#> MAD:pam 5 0.924 0.921 0.962 0.0371 0.973 0.888
#> ATC:pam 5 0.803 0.865 0.919 0.0456 0.973 0.899
#> SD:hclust 5 1.000 0.980 1.000 0.0324 0.991 0.976
#> CV:hclust 5 0.812 0.839 0.924 0.0623 0.961 0.890
#> MAD:hclust 5 0.773 0.779 0.886 0.1181 0.905 0.749
#> ATC:hclust 5 0.834 0.848 0.920 0.1092 0.918 0.802
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.757 0.799 0.873 0.0577 0.977 0.927
#> CV:NMF 6 0.786 0.814 0.881 0.0500 0.956 0.867
#> MAD:NMF 6 0.782 0.713 0.831 0.0352 1.000 1.000
#> ATC:NMF 6 0.682 0.673 0.813 0.0459 0.956 0.867
#> SD:skmeans 6 0.865 0.762 0.835 0.0392 0.964 0.830
#> CV:skmeans 6 0.871 0.876 0.910 0.0317 0.969 0.846
#> MAD:skmeans 6 0.869 0.772 0.839 0.0298 0.967 0.829
#> ATC:skmeans 6 0.846 0.752 0.861 0.0306 0.947 0.734
#> SD:mclust 6 0.780 0.811 0.904 0.0641 0.971 0.899
#> CV:mclust 6 0.695 0.561 0.740 0.0503 0.797 0.413
#> MAD:mclust 6 0.776 0.662 0.865 0.0650 0.823 0.418
#> ATC:mclust 6 0.774 0.829 0.886 0.0786 0.892 0.637
#> SD:kmeans 6 0.689 0.724 0.776 0.0840 0.881 0.667
#> CV:kmeans 6 0.713 0.781 0.801 0.0781 0.869 0.536
#> MAD:kmeans 6 0.689 0.811 0.801 0.0623 0.961 0.817
#> ATC:kmeans 6 0.697 0.774 0.807 0.0495 0.925 0.734
#> SD:pam 6 0.879 0.852 0.933 0.0315 0.973 0.873
#> CV:pam 6 0.902 0.890 0.950 0.0756 0.907 0.664
#> MAD:pam 6 0.877 0.771 0.927 0.0244 0.990 0.953
#> ATC:pam 6 0.819 0.849 0.930 0.0080 0.997 0.987
#> SD:hclust 6 0.802 0.834 0.881 0.1456 0.873 0.636
#> CV:hclust 6 0.811 0.844 0.919 0.0375 0.991 0.973
#> MAD:hclust 6 0.782 0.774 0.903 0.0133 0.991 0.970
#> ATC:hclust 6 0.790 0.782 0.905 0.1160 0.871 0.619
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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n agent(p) k
#> SD:NMF 51 0.648 2
#> CV:NMF 51 0.648 2
#> MAD:NMF 51 0.648 2
#> ATC:NMF 51 0.648 2
#> SD:skmeans 51 0.493 2
#> CV:skmeans 51 0.493 2
#> MAD:skmeans 51 0.493 2
#> ATC:skmeans 51 0.648 2
#> SD:mclust 51 0.493 2
#> CV:mclust 51 0.493 2
#> MAD:mclust 51 0.493 2
#> ATC:mclust 51 0.648 2
#> SD:kmeans 51 0.648 2
#> CV:kmeans 51 0.648 2
#> MAD:kmeans 42 0.557 2
#> ATC:kmeans 51 0.648 2
#> SD:pam 51 0.648 2
#> CV:pam 51 0.648 2
#> MAD:pam 51 0.648 2
#> ATC:pam 51 0.648 2
#> SD:hclust 51 0.648 2
#> CV:hclust 51 0.648 2
#> MAD:hclust 51 0.648 2
#> ATC:hclust 51 0.648 2
test_to_known_factors(res_list, k = 3)
#> n agent(p) k
#> SD:NMF 51 0.642 3
#> CV:NMF 51 0.642 3
#> MAD:NMF 51 0.642 3
#> ATC:NMF 51 0.642 3
#> SD:skmeans 51 0.642 3
#> CV:skmeans 51 0.642 3
#> MAD:skmeans 51 0.642 3
#> ATC:skmeans 50 0.627 3
#> SD:mclust 48 0.627 3
#> CV:mclust 51 0.642 3
#> MAD:mclust 51 0.642 3
#> ATC:mclust 51 0.642 3
#> SD:kmeans 51 0.642 3
#> CV:kmeans 51 0.642 3
#> MAD:kmeans 51 0.642 3
#> ATC:kmeans 51 0.642 3
#> SD:pam 51 0.642 3
#> CV:pam 51 0.642 3
#> MAD:pam 51 0.642 3
#> ATC:pam 51 0.642 3
#> SD:hclust 51 0.642 3
#> CV:hclust 51 0.642 3
#> MAD:hclust 51 0.642 3
#> ATC:hclust 51 0.642 3
test_to_known_factors(res_list, k = 4)
#> n agent(p) k
#> SD:NMF 50 0.502 4
#> CV:NMF 49 0.494 4
#> MAD:NMF 33 0.406 4
#> ATC:NMF 51 0.642 4
#> SD:skmeans 45 0.474 4
#> CV:skmeans 21 0.529 4
#> MAD:skmeans 51 0.544 4
#> ATC:skmeans 51 0.567 4
#> SD:mclust 50 0.497 4
#> CV:mclust 49 0.495 4
#> MAD:mclust 40 0.754 4
#> ATC:mclust 51 0.502 4
#> SD:kmeans 50 0.497 4
#> CV:kmeans 51 0.642 4
#> MAD:kmeans 21 0.529 4
#> ATC:kmeans 41 0.528 4
#> SD:pam 47 0.515 4
#> CV:pam 51 0.502 4
#> MAD:pam 49 0.551 4
#> ATC:pam 51 0.623 4
#> SD:hclust 51 0.502 4
#> CV:hclust 49 0.494 4
#> MAD:hclust 50 0.833 4
#> ATC:hclust 50 0.583 4
test_to_known_factors(res_list, k = 5)
#> n agent(p) k
#> SD:NMF 49 0.497 5
#> CV:NMF 49 0.497 5
#> MAD:NMF 44 0.403 5
#> ATC:NMF 44 0.474 5
#> SD:skmeans 46 0.476 5
#> CV:skmeans 51 0.502 5
#> MAD:skmeans 50 0.538 5
#> ATC:skmeans 47 0.440 5
#> SD:mclust 49 0.396 5
#> CV:mclust 34 0.352 5
#> MAD:mclust 25 0.428 5
#> ATC:mclust 45 0.395 5
#> SD:kmeans 50 0.497 5
#> CV:kmeans 39 0.425 5
#> MAD:kmeans 48 0.520 5
#> ATC:kmeans 46 0.600 5
#> SD:pam 47 0.452 5
#> CV:pam 37 0.491 5
#> MAD:pam 49 0.520 5
#> ATC:pam 51 0.626 5
#> SD:hclust 50 0.476 5
#> CV:hclust 50 0.711 5
#> MAD:hclust 49 0.632 5
#> ATC:hclust 48 0.747 5
test_to_known_factors(res_list, k = 6)
#> n agent(p) k
#> SD:NMF 47 0.487 6
#> CV:NMF 45 0.478 6
#> MAD:NMF 44 0.403 6
#> ATC:NMF 42 0.479 6
#> SD:skmeans 45 0.394 6
#> CV:skmeans 48 0.422 6
#> MAD:skmeans 46 0.403 6
#> ATC:skmeans 43 0.400 6
#> SD:mclust 46 0.394 6
#> CV:mclust 32 0.497 6
#> MAD:mclust 40 0.576 6
#> ATC:mclust 48 0.384 6
#> SD:kmeans 43 0.446 6
#> CV:kmeans 49 0.394 6
#> MAD:kmeans 50 0.494 6
#> ATC:kmeans 48 0.495 6
#> SD:pam 46 0.424 6
#> CV:pam 48 0.445 6
#> MAD:pam 46 0.523 6
#> ATC:pam 50 0.522 6
#> SD:hclust 48 0.472 6
#> CV:hclust 49 0.631 6
#> MAD:hclust 49 0.632 6
#> ATC:hclust 44 0.601 6
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 51941 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.2972 0.704 0.704
#> 3 3 1.000 1.000 1.000 0.9492 0.718 0.599
#> 4 4 0.934 0.992 0.983 0.0893 0.936 0.849
#> 5 5 1.000 0.980 1.000 0.0324 0.991 0.976
#> 6 6 0.802 0.834 0.881 0.1456 0.873 0.636
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM782696 1 0 1 1 0
#> GSM782697 1 0 1 1 0
#> GSM782698 1 0 1 1 0
#> GSM782699 1 0 1 1 0
#> GSM782700 2 0 1 0 1
#> GSM782701 1 0 1 1 0
#> GSM782702 1 0 1 1 0
#> GSM782703 1 0 1 1 0
#> GSM782704 1 0 1 1 0
#> GSM782705 1 0 1 1 0
#> GSM782706 1 0 1 1 0
#> GSM782707 1 0 1 1 0
#> GSM782708 1 0 1 1 0
#> GSM782709 1 0 1 1 0
#> GSM782710 1 0 1 1 0
#> GSM782711 1 0 1 1 0
#> GSM782712 1 0 1 1 0
#> GSM782713 1 0 1 1 0
#> GSM782714 2 0 1 0 1
#> GSM782715 1 0 1 1 0
#> GSM782716 1 0 1 1 0
#> GSM782717 1 0 1 1 0
#> GSM782718 1 0 1 1 0
#> GSM782719 1 0 1 1 0
#> GSM782720 1 0 1 1 0
#> GSM782721 1 0 1 1 0
#> GSM782722 1 0 1 1 0
#> GSM782723 2 0 1 0 1
#> GSM782724 2 0 1 0 1
#> GSM782725 1 0 1 1 0
#> GSM782726 1 0 1 1 0
#> GSM782727 1 0 1 1 0
#> GSM782728 2 0 1 0 1
#> GSM782729 1 0 1 1 0
#> GSM782730 1 0 1 1 0
#> GSM782731 1 0 1 1 0
#> GSM782732 1 0 1 1 0
#> GSM782733 1 0 1 1 0
#> GSM782734 1 0 1 1 0
#> GSM782735 2 0 1 0 1
#> GSM782736 1 0 1 1 0
#> GSM782737 2 0 1 0 1
#> GSM782738 1 0 1 1 0
#> GSM782739 1 0 1 1 0
#> GSM782740 2 0 1 0 1
#> GSM782741 1 0 1 1 0
#> GSM782742 1 0 1 1 0
#> GSM782743 1 0 1 1 0
#> GSM782744 1 0 1 1 0
#> GSM782745 1 0 1 1 0
#> GSM782746 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0 1 1 0 0
#> GSM782697 1 0 1 1 0 0
#> GSM782698 1 0 1 1 0 0
#> GSM782699 1 0 1 1 0 0
#> GSM782700 2 0 1 0 1 0
#> GSM782701 1 0 1 1 0 0
#> GSM782702 1 0 1 1 0 0
#> GSM782703 3 0 1 0 0 1
#> GSM782704 3 0 1 0 0 1
#> GSM782705 1 0 1 1 0 0
#> GSM782706 1 0 1 1 0 0
#> GSM782707 1 0 1 1 0 0
#> GSM782708 3 0 1 0 0 1
#> GSM782709 1 0 1 1 0 0
#> GSM782710 1 0 1 1 0 0
#> GSM782711 1 0 1 1 0 0
#> GSM782712 1 0 1 1 0 0
#> GSM782713 3 0 1 0 0 1
#> GSM782714 2 0 1 0 1 0
#> GSM782715 1 0 1 1 0 0
#> GSM782716 3 0 1 0 0 1
#> GSM782717 1 0 1 1 0 0
#> GSM782718 1 0 1 1 0 0
#> GSM782719 1 0 1 1 0 0
#> GSM782720 3 0 1 0 0 1
#> GSM782721 1 0 1 1 0 0
#> GSM782722 1 0 1 1 0 0
#> GSM782723 2 0 1 0 1 0
#> GSM782724 2 0 1 0 1 0
#> GSM782725 1 0 1 1 0 0
#> GSM782726 1 0 1 1 0 0
#> GSM782727 3 0 1 0 0 1
#> GSM782728 2 0 1 0 1 0
#> GSM782729 1 0 1 1 0 0
#> GSM782730 3 0 1 0 0 1
#> GSM782731 1 0 1 1 0 0
#> GSM782732 1 0 1 1 0 0
#> GSM782733 3 0 1 0 0 1
#> GSM782734 1 0 1 1 0 0
#> GSM782735 2 0 1 0 1 0
#> GSM782736 1 0 1 1 0 0
#> GSM782737 2 0 1 0 1 0
#> GSM782738 1 0 1 1 0 0
#> GSM782739 1 0 1 1 0 0
#> GSM782740 2 0 1 0 1 0
#> GSM782741 1 0 1 1 0 0
#> GSM782742 3 0 1 0 0 1
#> GSM782743 3 0 1 0 0 1
#> GSM782744 3 0 1 0 0 1
#> GSM782745 1 0 1 1 0 0
#> GSM782746 2 0 1 0 1 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782697 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782698 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782699 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782701 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782702 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782703 3 0.0000 0.983 0.000 0 1.000 0.000
#> GSM782704 3 0.0000 0.983 0.000 0 1.000 0.000
#> GSM782705 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782706 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782707 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782708 3 0.0000 0.983 0.000 0 1.000 0.000
#> GSM782709 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782710 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782711 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782712 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782713 3 0.0000 0.983 0.000 0 1.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782715 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782716 3 0.0000 0.983 0.000 0 1.000 0.000
#> GSM782717 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782718 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782719 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782720 3 0.0000 0.983 0.000 0 1.000 0.000
#> GSM782721 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782722 4 0.3764 1.000 0.216 0 0.000 0.784
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782725 4 0.3764 1.000 0.216 0 0.000 0.784
#> GSM782726 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782727 3 0.0000 0.983 0.000 0 1.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782729 4 0.3764 1.000 0.216 0 0.000 0.784
#> GSM782730 3 0.0000 0.983 0.000 0 1.000 0.000
#> GSM782731 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782732 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782733 3 0.0000 0.983 0.000 0 1.000 0.000
#> GSM782734 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782736 1 0.0188 0.995 0.996 0 0.000 0.004
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782738 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782739 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782741 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782742 3 0.0000 0.983 0.000 0 1.000 0.000
#> GSM782743 3 0.0000 0.983 0.000 0 1.000 0.000
#> GSM782744 3 0.3764 0.784 0.000 0 0.784 0.216
#> GSM782745 1 0.0000 1.000 1.000 0 0.000 0.000
#> GSM782746 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782697 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782698 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782699 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782700 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782701 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782702 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782703 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782704 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782705 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782706 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782707 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782708 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782709 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782710 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782711 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782712 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782713 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782714 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782715 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782716 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782717 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782718 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782719 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782720 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782721 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782722 4 0.0000 1.000 0.000 0 0 1.000 0
#> GSM782723 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782724 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782725 4 0.0000 1.000 0.000 0 0 1.000 0
#> GSM782726 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782727 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782728 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782729 4 0.0000 1.000 0.000 0 0 1.000 0
#> GSM782730 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782731 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782732 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782733 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782734 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782735 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782736 1 0.0162 0.996 0.996 0 0 0.004 0
#> GSM782737 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782738 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782739 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782740 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782741 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782742 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782743 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782744 5 0.0000 0.000 0.000 0 0 0.000 1
#> GSM782745 1 0.0000 1.000 1.000 0 0 0.000 0
#> GSM782746 2 0.0000 1.000 0.000 1 0 0.000 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM782696 1 0.0000 0.804 1.000 0 0 0.000 0.000 0.000
#> GSM782697 1 0.0146 0.803 0.996 0 0 0.000 0.000 0.004
#> GSM782698 1 0.0146 0.803 0.996 0 0 0.000 0.000 0.004
#> GSM782699 1 0.0146 0.803 0.996 0 0 0.000 0.000 0.004
#> GSM782700 2 0.0000 1.000 0.000 1 0 0.000 0.000 0.000
#> GSM782701 1 0.0000 0.804 1.000 0 0 0.000 0.000 0.000
#> GSM782702 1 0.0000 0.804 1.000 0 0 0.000 0.000 0.000
#> GSM782703 3 0.0000 1.000 0.000 0 1 0.000 0.000 0.000
#> GSM782704 3 0.0000 1.000 0.000 0 1 0.000 0.000 0.000
#> GSM782705 1 0.0260 0.801 0.992 0 0 0.000 0.008 0.000
#> GSM782706 1 0.2527 0.512 0.832 0 0 0.000 0.000 0.168
#> GSM782707 1 0.0000 0.804 1.000 0 0 0.000 0.000 0.000
#> GSM782708 3 0.0000 1.000 0.000 0 1 0.000 0.000 0.000
#> GSM782709 1 0.3797 -0.570 0.580 0 0 0.000 0.000 0.420
#> GSM782710 6 0.3843 0.829 0.452 0 0 0.000 0.000 0.548
#> GSM782711 1 0.0000 0.804 1.000 0 0 0.000 0.000 0.000
#> GSM782712 1 0.0000 0.804 1.000 0 0 0.000 0.000 0.000
#> GSM782713 3 0.0000 1.000 0.000 0 1 0.000 0.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0 0.000 0.000 0.000
#> GSM782715 1 0.4793 0.436 0.628 0 0 0.000 0.288 0.084
#> GSM782716 3 0.0000 1.000 0.000 0 1 0.000 0.000 0.000
#> GSM782717 6 0.3867 0.917 0.488 0 0 0.000 0.000 0.512
#> GSM782718 1 0.2491 0.666 0.836 0 0 0.000 0.164 0.000
#> GSM782719 1 0.0000 0.804 1.000 0 0 0.000 0.000 0.000
#> GSM782720 3 0.0000 1.000 0.000 0 1 0.000 0.000 0.000
#> GSM782721 1 0.2527 0.512 0.832 0 0 0.000 0.000 0.168
#> GSM782722 4 0.0000 1.000 0.000 0 0 1.000 0.000 0.000
#> GSM782723 2 0.0000 1.000 0.000 1 0 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0 0.000 0.000 0.000
#> GSM782725 4 0.0000 1.000 0.000 0 0 1.000 0.000 0.000
#> GSM782726 6 0.3695 0.829 0.376 0 0 0.000 0.000 0.624
#> GSM782727 3 0.0000 1.000 0.000 0 1 0.000 0.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0 0.000 0.000 0.000
#> GSM782729 4 0.0000 1.000 0.000 0 0 1.000 0.000 0.000
#> GSM782730 3 0.0000 1.000 0.000 0 1 0.000 0.000 0.000
#> GSM782731 6 0.3868 0.913 0.492 0 0 0.000 0.000 0.508
#> GSM782732 6 0.3868 0.913 0.492 0 0 0.000 0.000 0.508
#> GSM782733 3 0.0000 1.000 0.000 0 1 0.000 0.000 0.000
#> GSM782734 6 0.3866 0.916 0.484 0 0 0.000 0.000 0.516
#> GSM782735 2 0.0000 1.000 0.000 1 0 0.000 0.000 0.000
#> GSM782736 1 0.3733 0.520 0.700 0 0 0.004 0.288 0.008
#> GSM782737 2 0.0000 1.000 0.000 1 0 0.000 0.000 0.000
#> GSM782738 1 0.2491 0.666 0.836 0 0 0.000 0.164 0.000
#> GSM782739 6 0.3867 0.917 0.488 0 0 0.000 0.000 0.512
#> GSM782740 2 0.0000 1.000 0.000 1 0 0.000 0.000 0.000
#> GSM782741 6 0.3867 0.917 0.488 0 0 0.000 0.000 0.512
#> GSM782742 3 0.0000 1.000 0.000 0 1 0.000 0.000 0.000
#> GSM782743 3 0.0000 1.000 0.000 0 1 0.000 0.000 0.000
#> GSM782744 5 0.3351 0.000 0.000 0 0 0.000 0.712 0.288
#> GSM782745 6 0.3695 0.829 0.376 0 0 0.000 0.000 0.624
#> GSM782746 2 0.0000 1.000 0.000 1 0 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> SD:hclust 51 0.648 2
#> SD:hclust 51 0.642 3
#> SD:hclust 51 0.502 4
#> SD:hclust 50 0.476 5
#> SD:hclust 48 0.472 6
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 51941 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.506 0.758 0.824 0.327 0.704 0.704
#> 3 3 0.681 0.990 0.947 0.630 0.718 0.599
#> 4 4 0.770 0.863 0.892 0.203 0.936 0.849
#> 5 5 0.684 0.774 0.824 0.118 1.000 1.000
#> 6 6 0.689 0.724 0.776 0.084 0.881 0.667
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
#> GSM782696 1 0.985 0.781 0.572 0.428
#> GSM782697 1 0.985 0.781 0.572 0.428
#> GSM782698 1 0.985 0.781 0.572 0.428
#> GSM782699 1 0.985 0.781 0.572 0.428
#> GSM782700 2 0.000 1.000 0.000 1.000
#> GSM782701 1 0.985 0.781 0.572 0.428
#> GSM782702 1 0.985 0.781 0.572 0.428
#> GSM782703 1 0.000 0.519 1.000 0.000
#> GSM782704 1 0.000 0.519 1.000 0.000
#> GSM782705 1 0.985 0.781 0.572 0.428
#> GSM782706 1 0.985 0.781 0.572 0.428
#> GSM782707 1 0.985 0.781 0.572 0.428
#> GSM782708 1 0.000 0.519 1.000 0.000
#> GSM782709 1 0.985 0.781 0.572 0.428
#> GSM782710 1 0.985 0.781 0.572 0.428
#> GSM782711 1 0.985 0.781 0.572 0.428
#> GSM782712 1 0.985 0.781 0.572 0.428
#> GSM782713 1 0.000 0.519 1.000 0.000
#> GSM782714 2 0.000 1.000 0.000 1.000
#> GSM782715 1 0.985 0.781 0.572 0.428
#> GSM782716 1 0.000 0.519 1.000 0.000
#> GSM782717 1 0.985 0.781 0.572 0.428
#> GSM782718 1 0.985 0.781 0.572 0.428
#> GSM782719 1 0.985 0.781 0.572 0.428
#> GSM782720 1 0.000 0.519 1.000 0.000
#> GSM782721 1 0.985 0.781 0.572 0.428
#> GSM782722 1 0.985 0.781 0.572 0.428
#> GSM782723 2 0.000 1.000 0.000 1.000
#> GSM782724 2 0.000 1.000 0.000 1.000
#> GSM782725 1 0.985 0.781 0.572 0.428
#> GSM782726 1 0.985 0.781 0.572 0.428
#> GSM782727 1 0.000 0.519 1.000 0.000
#> GSM782728 2 0.000 1.000 0.000 1.000
#> GSM782729 1 0.985 0.781 0.572 0.428
#> GSM782730 1 0.000 0.519 1.000 0.000
#> GSM782731 1 0.985 0.781 0.572 0.428
#> GSM782732 1 0.985 0.781 0.572 0.428
#> GSM782733 1 0.000 0.519 1.000 0.000
#> GSM782734 1 0.985 0.781 0.572 0.428
#> GSM782735 2 0.000 1.000 0.000 1.000
#> GSM782736 1 0.985 0.781 0.572 0.428
#> GSM782737 2 0.000 1.000 0.000 1.000
#> GSM782738 1 0.985 0.781 0.572 0.428
#> GSM782739 1 0.985 0.781 0.572 0.428
#> GSM782740 2 0.000 1.000 0.000 1.000
#> GSM782741 1 0.985 0.781 0.572 0.428
#> GSM782742 1 0.000 0.519 1.000 0.000
#> GSM782743 1 0.000 0.519 1.000 0.000
#> GSM782744 1 0.000 0.519 1.000 0.000
#> GSM782745 1 0.985 0.781 0.572 0.428
#> GSM782746 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
#> GSM782696 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782697 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782698 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782699 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782700 2 0.2400 0.980 0.064 0.932 0.004
#> GSM782701 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782702 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782703 3 0.4609 0.981 0.128 0.028 0.844
#> GSM782704 3 0.5174 0.981 0.128 0.048 0.824
#> GSM782705 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782706 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782707 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782708 3 0.5174 0.981 0.128 0.048 0.824
#> GSM782709 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782710 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782711 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782712 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782713 3 0.3482 0.981 0.128 0.000 0.872
#> GSM782714 2 0.3310 0.979 0.064 0.908 0.028
#> GSM782715 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782716 3 0.5174 0.981 0.128 0.048 0.824
#> GSM782717 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782718 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782719 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782720 3 0.3482 0.981 0.128 0.000 0.872
#> GSM782721 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782722 1 0.0424 0.992 0.992 0.000 0.008
#> GSM782723 2 0.3310 0.979 0.064 0.908 0.028
#> GSM782724 2 0.4565 0.960 0.064 0.860 0.076
#> GSM782725 1 0.0424 0.992 0.992 0.000 0.008
#> GSM782726 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782727 3 0.3482 0.981 0.128 0.000 0.872
#> GSM782728 2 0.2165 0.980 0.064 0.936 0.000
#> GSM782729 1 0.0424 0.992 0.992 0.000 0.008
#> GSM782730 3 0.3482 0.981 0.128 0.000 0.872
#> GSM782731 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782732 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782733 3 0.5174 0.981 0.128 0.048 0.824
#> GSM782734 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782735 2 0.3780 0.968 0.064 0.892 0.044
#> GSM782736 1 0.0424 0.992 0.992 0.000 0.008
#> GSM782737 2 0.3310 0.979 0.064 0.908 0.028
#> GSM782738 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782739 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782740 2 0.2165 0.980 0.064 0.936 0.000
#> GSM782741 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782742 3 0.3482 0.981 0.128 0.000 0.872
#> GSM782743 3 0.5174 0.981 0.128 0.048 0.824
#> GSM782744 3 0.4848 0.976 0.128 0.036 0.836
#> GSM782745 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782746 2 0.3780 0.968 0.064 0.892 0.044
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.1557 0.826 0.944 0.000 0.000 0.056
#> GSM782697 1 0.0000 0.834 1.000 0.000 0.000 0.000
#> GSM782698 1 0.2704 0.780 0.876 0.000 0.000 0.124
#> GSM782699 1 0.0000 0.834 1.000 0.000 0.000 0.000
#> GSM782700 2 0.0895 0.972 0.020 0.976 0.004 0.000
#> GSM782701 1 0.2530 0.787 0.888 0.000 0.000 0.112
#> GSM782702 1 0.0000 0.834 1.000 0.000 0.000 0.000
#> GSM782703 3 0.2466 0.935 0.028 0.000 0.916 0.056
#> GSM782704 3 0.0921 0.933 0.028 0.000 0.972 0.000
#> GSM782705 1 0.1716 0.839 0.936 0.000 0.000 0.064
#> GSM782706 1 0.2921 0.787 0.860 0.000 0.000 0.140
#> GSM782707 1 0.2530 0.787 0.888 0.000 0.000 0.112
#> GSM782708 3 0.0921 0.933 0.028 0.000 0.972 0.000
#> GSM782709 1 0.0000 0.834 1.000 0.000 0.000 0.000
#> GSM782710 1 0.0000 0.834 1.000 0.000 0.000 0.000
#> GSM782711 1 0.0469 0.835 0.988 0.000 0.000 0.012
#> GSM782712 1 0.0469 0.835 0.988 0.000 0.000 0.012
#> GSM782713 3 0.3962 0.933 0.028 0.000 0.820 0.152
#> GSM782714 2 0.1520 0.971 0.020 0.956 0.000 0.024
#> GSM782715 1 0.4277 0.580 0.720 0.000 0.000 0.280
#> GSM782716 3 0.0921 0.933 0.028 0.000 0.972 0.000
#> GSM782717 1 0.1867 0.836 0.928 0.000 0.000 0.072
#> GSM782718 1 0.4164 0.623 0.736 0.000 0.000 0.264
#> GSM782719 1 0.2530 0.787 0.888 0.000 0.000 0.112
#> GSM782720 3 0.3962 0.933 0.028 0.000 0.820 0.152
#> GSM782721 1 0.2921 0.787 0.860 0.000 0.000 0.140
#> GSM782722 4 0.4697 0.991 0.356 0.000 0.000 0.644
#> GSM782723 2 0.1520 0.971 0.020 0.956 0.000 0.024
#> GSM782724 2 0.2973 0.942 0.020 0.884 0.000 0.096
#> GSM782725 4 0.4713 0.996 0.360 0.000 0.000 0.640
#> GSM782726 1 0.1867 0.836 0.928 0.000 0.000 0.072
#> GSM782727 3 0.3962 0.933 0.028 0.000 0.820 0.152
#> GSM782728 2 0.0707 0.972 0.020 0.980 0.000 0.000
#> GSM782729 4 0.4713 0.996 0.360 0.000 0.000 0.640
#> GSM782730 3 0.3962 0.933 0.028 0.000 0.820 0.152
#> GSM782731 1 0.2081 0.829 0.916 0.000 0.000 0.084
#> GSM782732 1 0.2081 0.829 0.916 0.000 0.000 0.084
#> GSM782733 3 0.0921 0.933 0.028 0.000 0.972 0.000
#> GSM782734 1 0.1867 0.836 0.928 0.000 0.000 0.072
#> GSM782735 2 0.2977 0.947 0.020 0.904 0.024 0.052
#> GSM782736 1 0.4454 0.478 0.692 0.000 0.000 0.308
#> GSM782737 2 0.1520 0.971 0.020 0.956 0.000 0.024
#> GSM782738 1 0.4164 0.623 0.736 0.000 0.000 0.264
#> GSM782739 1 0.1867 0.836 0.928 0.000 0.000 0.072
#> GSM782740 2 0.0707 0.972 0.020 0.980 0.000 0.000
#> GSM782741 1 0.1867 0.836 0.928 0.000 0.000 0.072
#> GSM782742 3 0.3962 0.933 0.028 0.000 0.820 0.152
#> GSM782743 3 0.0921 0.933 0.028 0.000 0.972 0.000
#> GSM782744 3 0.4640 0.906 0.028 0.020 0.800 0.152
#> GSM782745 1 0.1867 0.836 0.928 0.000 0.000 0.072
#> GSM782746 2 0.2977 0.947 0.020 0.904 0.024 0.052
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.4210 0.707 0.588 0.000 0.000 0.000 NA
#> GSM782697 1 0.4084 0.718 0.668 0.000 0.000 0.004 NA
#> GSM782698 1 0.4557 0.673 0.516 0.000 0.000 0.008 NA
#> GSM782699 1 0.4196 0.718 0.640 0.000 0.000 0.004 NA
#> GSM782700 2 0.0162 0.937 0.000 0.996 0.000 0.004 NA
#> GSM782701 1 0.4637 0.678 0.536 0.000 0.000 0.012 NA
#> GSM782702 1 0.3932 0.720 0.672 0.000 0.000 0.000 NA
#> GSM782703 3 0.0510 0.879 0.000 0.000 0.984 0.016 NA
#> GSM782704 3 0.2520 0.874 0.000 0.000 0.896 0.048 NA
#> GSM782705 1 0.4029 0.725 0.680 0.000 0.000 0.004 NA
#> GSM782706 1 0.4576 0.666 0.608 0.000 0.000 0.016 NA
#> GSM782707 1 0.4637 0.678 0.536 0.000 0.000 0.012 NA
#> GSM782708 3 0.2520 0.874 0.000 0.000 0.896 0.048 NA
#> GSM782709 1 0.2813 0.704 0.832 0.000 0.000 0.000 NA
#> GSM782710 1 0.2966 0.697 0.816 0.000 0.000 0.000 NA
#> GSM782711 1 0.4114 0.716 0.624 0.000 0.000 0.000 NA
#> GSM782712 1 0.4470 0.714 0.616 0.000 0.000 0.012 NA
#> GSM782713 3 0.3201 0.876 0.000 0.000 0.852 0.096 NA
#> GSM782714 2 0.1701 0.933 0.000 0.936 0.000 0.016 NA
#> GSM782715 1 0.5772 0.503 0.584 0.000 0.000 0.120 NA
#> GSM782716 3 0.2520 0.874 0.000 0.000 0.896 0.048 NA
#> GSM782717 1 0.0162 0.666 0.996 0.000 0.000 0.000 NA
#> GSM782718 1 0.5525 0.558 0.612 0.000 0.000 0.100 NA
#> GSM782719 1 0.4637 0.678 0.536 0.000 0.000 0.012 NA
#> GSM782720 3 0.3201 0.876 0.000 0.000 0.852 0.096 NA
#> GSM782721 1 0.4576 0.666 0.608 0.000 0.000 0.016 NA
#> GSM782722 4 0.4832 1.000 0.200 0.000 0.000 0.712 NA
#> GSM782723 2 0.1701 0.933 0.000 0.936 0.000 0.016 NA
#> GSM782724 2 0.3648 0.876 0.000 0.824 0.000 0.084 NA
#> GSM782725 4 0.4832 1.000 0.200 0.000 0.000 0.712 NA
#> GSM782726 1 0.0290 0.660 0.992 0.000 0.000 0.000 NA
#> GSM782727 3 0.3201 0.876 0.000 0.000 0.852 0.096 NA
#> GSM782728 2 0.0162 0.937 0.000 0.996 0.000 0.000 NA
#> GSM782729 4 0.4832 1.000 0.200 0.000 0.000 0.712 NA
#> GSM782730 3 0.3201 0.876 0.000 0.000 0.852 0.096 NA
#> GSM782731 1 0.0671 0.655 0.980 0.000 0.000 0.004 NA
#> GSM782732 1 0.0671 0.655 0.980 0.000 0.000 0.004 NA
#> GSM782733 3 0.2520 0.874 0.000 0.000 0.896 0.048 NA
#> GSM782734 1 0.0290 0.660 0.992 0.000 0.000 0.000 NA
#> GSM782735 2 0.2824 0.887 0.000 0.872 0.000 0.032 NA
#> GSM782736 1 0.5964 0.398 0.588 0.000 0.000 0.180 NA
#> GSM782737 2 0.1701 0.933 0.000 0.936 0.000 0.016 NA
#> GSM782738 1 0.5487 0.556 0.620 0.000 0.000 0.100 NA
#> GSM782739 1 0.0000 0.664 1.000 0.000 0.000 0.000 NA
#> GSM782740 2 0.0162 0.937 0.000 0.996 0.000 0.000 NA
#> GSM782741 1 0.0000 0.664 1.000 0.000 0.000 0.000 NA
#> GSM782742 3 0.3201 0.876 0.000 0.000 0.852 0.096 NA
#> GSM782743 3 0.2520 0.874 0.000 0.000 0.896 0.048 NA
#> GSM782744 3 0.5004 0.807 0.000 0.000 0.672 0.072 NA
#> GSM782745 1 0.0290 0.660 0.992 0.000 0.000 0.000 NA
#> GSM782746 2 0.2824 0.887 0.000 0.872 0.000 0.032 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM782696 1 0.0603 0.658 0.980 0.000 0.000 0.000 NA 0.016
#> GSM782697 1 0.2350 0.616 0.880 0.000 0.000 0.000 NA 0.100
#> GSM782698 1 0.1552 0.653 0.940 0.000 0.000 0.004 NA 0.020
#> GSM782699 1 0.2250 0.622 0.888 0.000 0.000 0.000 NA 0.092
#> GSM782700 2 0.0291 0.911 0.000 0.992 0.000 0.004 NA 0.000
#> GSM782701 1 0.2100 0.653 0.884 0.000 0.000 0.000 NA 0.004
#> GSM782702 1 0.2454 0.584 0.840 0.000 0.000 0.000 NA 0.160
#> GSM782703 3 0.2572 0.840 0.000 0.000 0.852 0.000 NA 0.012
#> GSM782704 3 0.3499 0.832 0.000 0.000 0.680 0.000 NA 0.000
#> GSM782705 1 0.3752 0.561 0.776 0.000 0.000 0.004 NA 0.168
#> GSM782706 1 0.5299 0.489 0.612 0.000 0.000 0.004 NA 0.156
#> GSM782707 1 0.1957 0.654 0.888 0.000 0.000 0.000 NA 0.000
#> GSM782708 3 0.3499 0.832 0.000 0.000 0.680 0.000 NA 0.000
#> GSM782709 1 0.4226 -0.287 0.504 0.000 0.000 0.004 NA 0.484
#> GSM782710 1 0.3999 -0.293 0.500 0.000 0.000 0.000 NA 0.496
#> GSM782711 1 0.1391 0.649 0.944 0.000 0.000 0.000 NA 0.040
#> GSM782712 1 0.2867 0.650 0.848 0.000 0.000 0.000 NA 0.040
#> GSM782713 3 0.0260 0.835 0.000 0.000 0.992 0.000 NA 0.008
#> GSM782714 2 0.1921 0.905 0.000 0.920 0.000 0.012 NA 0.012
#> GSM782715 1 0.6941 0.310 0.464 0.000 0.000 0.092 NA 0.212
#> GSM782716 3 0.3619 0.832 0.000 0.000 0.680 0.000 NA 0.004
#> GSM782717 6 0.2996 0.964 0.228 0.000 0.000 0.000 NA 0.772
#> GSM782718 1 0.6486 0.384 0.540 0.000 0.000 0.076 NA 0.188
#> GSM782719 1 0.1910 0.654 0.892 0.000 0.000 0.000 NA 0.000
#> GSM782720 3 0.0000 0.835 0.000 0.000 1.000 0.000 NA 0.000
#> GSM782721 1 0.5299 0.489 0.612 0.000 0.000 0.004 NA 0.156
#> GSM782722 4 0.2934 0.993 0.112 0.000 0.000 0.844 NA 0.044
#> GSM782723 2 0.2015 0.905 0.000 0.916 0.000 0.012 NA 0.016
#> GSM782724 2 0.4178 0.812 0.000 0.748 0.000 0.016 NA 0.052
#> GSM782725 4 0.2954 0.996 0.108 0.000 0.000 0.844 NA 0.048
#> GSM782726 6 0.2969 0.963 0.224 0.000 0.000 0.000 NA 0.776
#> GSM782727 3 0.0146 0.835 0.000 0.000 0.996 0.000 NA 0.004
#> GSM782728 2 0.0260 0.910 0.000 0.992 0.000 0.000 NA 0.000
#> GSM782729 4 0.2954 0.996 0.108 0.000 0.000 0.844 NA 0.048
#> GSM782730 3 0.0146 0.835 0.000 0.000 0.996 0.000 NA 0.004
#> GSM782731 6 0.4064 0.897 0.236 0.000 0.000 0.004 NA 0.720
#> GSM782732 6 0.4064 0.897 0.236 0.000 0.000 0.004 NA 0.720
#> GSM782733 3 0.3619 0.832 0.000 0.000 0.680 0.000 NA 0.004
#> GSM782734 6 0.2969 0.963 0.224 0.000 0.000 0.000 NA 0.776
#> GSM782735 2 0.3659 0.840 0.000 0.824 0.000 0.064 NA 0.044
#> GSM782736 1 0.7430 0.132 0.380 0.000 0.000 0.164 NA 0.268
#> GSM782737 2 0.1921 0.905 0.000 0.920 0.000 0.012 NA 0.012
#> GSM782738 1 0.6770 0.308 0.488 0.000 0.000 0.080 NA 0.232
#> GSM782739 6 0.2996 0.964 0.228 0.000 0.000 0.000 NA 0.772
#> GSM782740 2 0.0260 0.910 0.000 0.992 0.000 0.000 NA 0.000
#> GSM782741 6 0.2996 0.964 0.228 0.000 0.000 0.000 NA 0.772
#> GSM782742 3 0.0000 0.835 0.000 0.000 1.000 0.000 NA 0.000
#> GSM782743 3 0.3619 0.832 0.000 0.000 0.680 0.000 NA 0.004
#> GSM782744 3 0.4958 0.762 0.000 0.000 0.708 0.068 NA 0.056
#> GSM782745 6 0.2969 0.963 0.224 0.000 0.000 0.000 NA 0.776
#> GSM782746 2 0.3659 0.840 0.000 0.824 0.000 0.064 NA 0.044
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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> SD:kmeans 51 0.648 2
#> SD:kmeans 51 0.642 3
#> SD:kmeans 50 0.497 4
#> SD:kmeans 50 0.497 5
#> SD:kmeans 43 0.446 6
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 51941 rows and 51 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 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 0.633 0.897 0.915 0.4236 0.506 0.506
#> 3 3 1.000 1.000 1.000 0.3674 0.915 0.833
#> 4 4 0.844 0.774 0.890 0.2200 0.902 0.767
#> 5 5 0.909 0.819 0.929 0.1236 0.887 0.650
#> 6 6 0.865 0.762 0.835 0.0392 0.964 0.830
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 3
There is also optional best \(k\) = 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM782696 1 0.000 1.000 1.00 0.00
#> GSM782697 1 0.000 1.000 1.00 0.00
#> GSM782698 1 0.000 1.000 1.00 0.00
#> GSM782699 1 0.000 1.000 1.00 0.00
#> GSM782700 2 0.000 0.756 0.00 1.00
#> GSM782701 1 0.000 1.000 1.00 0.00
#> GSM782702 1 0.000 1.000 1.00 0.00
#> GSM782703 2 0.943 0.747 0.36 0.64
#> GSM782704 2 0.943 0.747 0.36 0.64
#> GSM782705 1 0.000 1.000 1.00 0.00
#> GSM782706 1 0.000 1.000 1.00 0.00
#> GSM782707 1 0.000 1.000 1.00 0.00
#> GSM782708 2 0.943 0.747 0.36 0.64
#> GSM782709 1 0.000 1.000 1.00 0.00
#> GSM782710 1 0.000 1.000 1.00 0.00
#> GSM782711 1 0.000 1.000 1.00 0.00
#> GSM782712 1 0.000 1.000 1.00 0.00
#> GSM782713 2 0.943 0.747 0.36 0.64
#> GSM782714 2 0.000 0.756 0.00 1.00
#> GSM782715 1 0.000 1.000 1.00 0.00
#> GSM782716 2 0.943 0.747 0.36 0.64
#> GSM782717 1 0.000 1.000 1.00 0.00
#> GSM782718 1 0.000 1.000 1.00 0.00
#> GSM782719 1 0.000 1.000 1.00 0.00
#> GSM782720 2 0.943 0.747 0.36 0.64
#> GSM782721 1 0.000 1.000 1.00 0.00
#> GSM782722 1 0.000 1.000 1.00 0.00
#> GSM782723 2 0.000 0.756 0.00 1.00
#> GSM782724 2 0.000 0.756 0.00 1.00
#> GSM782725 1 0.000 1.000 1.00 0.00
#> GSM782726 1 0.000 1.000 1.00 0.00
#> GSM782727 2 0.943 0.747 0.36 0.64
#> GSM782728 2 0.000 0.756 0.00 1.00
#> GSM782729 1 0.000 1.000 1.00 0.00
#> GSM782730 2 0.943 0.747 0.36 0.64
#> GSM782731 1 0.000 1.000 1.00 0.00
#> GSM782732 1 0.000 1.000 1.00 0.00
#> GSM782733 2 0.943 0.747 0.36 0.64
#> GSM782734 1 0.000 1.000 1.00 0.00
#> GSM782735 2 0.000 0.756 0.00 1.00
#> GSM782736 1 0.000 1.000 1.00 0.00
#> GSM782737 2 0.000 0.756 0.00 1.00
#> GSM782738 1 0.000 1.000 1.00 0.00
#> GSM782739 1 0.000 1.000 1.00 0.00
#> GSM782740 2 0.000 0.756 0.00 1.00
#> GSM782741 1 0.000 1.000 1.00 0.00
#> GSM782742 2 0.943 0.747 0.36 0.64
#> GSM782743 2 0.943 0.747 0.36 0.64
#> GSM782744 2 0.943 0.747 0.36 0.64
#> GSM782745 1 0.000 1.000 1.00 0.00
#> GSM782746 2 0.000 0.756 0.00 1.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0 1 1 0 0
#> GSM782697 1 0 1 1 0 0
#> GSM782698 1 0 1 1 0 0
#> GSM782699 1 0 1 1 0 0
#> GSM782700 2 0 1 0 1 0
#> GSM782701 1 0 1 1 0 0
#> GSM782702 1 0 1 1 0 0
#> GSM782703 3 0 1 0 0 1
#> GSM782704 3 0 1 0 0 1
#> GSM782705 1 0 1 1 0 0
#> GSM782706 1 0 1 1 0 0
#> GSM782707 1 0 1 1 0 0
#> GSM782708 3 0 1 0 0 1
#> GSM782709 1 0 1 1 0 0
#> GSM782710 1 0 1 1 0 0
#> GSM782711 1 0 1 1 0 0
#> GSM782712 1 0 1 1 0 0
#> GSM782713 3 0 1 0 0 1
#> GSM782714 2 0 1 0 1 0
#> GSM782715 1 0 1 1 0 0
#> GSM782716 3 0 1 0 0 1
#> GSM782717 1 0 1 1 0 0
#> GSM782718 1 0 1 1 0 0
#> GSM782719 1 0 1 1 0 0
#> GSM782720 3 0 1 0 0 1
#> GSM782721 1 0 1 1 0 0
#> GSM782722 1 0 1 1 0 0
#> GSM782723 2 0 1 0 1 0
#> GSM782724 2 0 1 0 1 0
#> GSM782725 1 0 1 1 0 0
#> GSM782726 1 0 1 1 0 0
#> GSM782727 3 0 1 0 0 1
#> GSM782728 2 0 1 0 1 0
#> GSM782729 1 0 1 1 0 0
#> GSM782730 3 0 1 0 0 1
#> GSM782731 1 0 1 1 0 0
#> GSM782732 1 0 1 1 0 0
#> GSM782733 3 0 1 0 0 1
#> GSM782734 1 0 1 1 0 0
#> GSM782735 2 0 1 0 1 0
#> GSM782736 1 0 1 1 0 0
#> GSM782737 2 0 1 0 1 0
#> GSM782738 1 0 1 1 0 0
#> GSM782739 1 0 1 1 0 0
#> GSM782740 2 0 1 0 1 0
#> GSM782741 1 0 1 1 0 0
#> GSM782742 3 0 1 0 0 1
#> GSM782743 3 0 1 0 0 1
#> GSM782744 3 0 1 0 0 1
#> GSM782745 1 0 1 1 0 0
#> GSM782746 2 0 1 0 1 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.0336 0.726 0.992 0 0 0.008
#> GSM782697 1 0.1302 0.720 0.956 0 0 0.044
#> GSM782698 1 0.2216 0.666 0.908 0 0 0.092
#> GSM782699 1 0.0000 0.727 1.000 0 0 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782701 1 0.0336 0.726 0.992 0 0 0.008
#> GSM782702 1 0.1389 0.718 0.952 0 0 0.048
#> GSM782703 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782704 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782705 1 0.4877 0.401 0.592 0 0 0.408
#> GSM782706 1 0.0469 0.726 0.988 0 0 0.012
#> GSM782707 1 0.0336 0.726 0.992 0 0 0.008
#> GSM782708 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782709 1 0.2011 0.708 0.920 0 0 0.080
#> GSM782710 1 0.2011 0.708 0.920 0 0 0.080
#> GSM782711 1 0.0000 0.727 1.000 0 0 0.000
#> GSM782712 1 0.0188 0.726 0.996 0 0 0.004
#> GSM782713 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782715 4 0.5000 -0.289 0.496 0 0 0.504
#> GSM782716 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782717 1 0.4817 0.564 0.612 0 0 0.388
#> GSM782718 1 0.4925 0.361 0.572 0 0 0.428
#> GSM782719 1 0.0336 0.726 0.992 0 0 0.008
#> GSM782720 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782721 1 0.0469 0.726 0.988 0 0 0.012
#> GSM782722 4 0.1940 0.836 0.076 0 0 0.924
#> GSM782723 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782725 4 0.1940 0.836 0.076 0 0 0.924
#> GSM782726 1 0.4817 0.564 0.612 0 0 0.388
#> GSM782727 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782729 4 0.1940 0.836 0.076 0 0 0.924
#> GSM782730 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782731 1 0.4994 0.419 0.520 0 0 0.480
#> GSM782732 1 0.4994 0.419 0.520 0 0 0.480
#> GSM782733 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782734 1 0.4817 0.564 0.612 0 0 0.388
#> GSM782735 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782736 4 0.1940 0.836 0.076 0 0 0.924
#> GSM782737 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782738 1 0.4925 0.361 0.572 0 0 0.428
#> GSM782739 1 0.4830 0.559 0.608 0 0 0.392
#> GSM782740 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782741 1 0.4817 0.564 0.612 0 0 0.388
#> GSM782742 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782743 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782744 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782745 1 0.4817 0.564 0.612 0 0 0.388
#> GSM782746 2 0.0000 1.000 0.000 1 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.0162 0.8067 0.996 0 0 0.000 0.004
#> GSM782697 1 0.0000 0.8058 1.000 0 0 0.000 0.000
#> GSM782698 1 0.0000 0.8058 1.000 0 0 0.000 0.000
#> GSM782699 1 0.0000 0.8058 1.000 0 0 0.000 0.000
#> GSM782700 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782701 1 0.0290 0.8061 0.992 0 0 0.000 0.008
#> GSM782702 1 0.0794 0.7975 0.972 0 0 0.000 0.028
#> GSM782703 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782704 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782705 1 0.4496 0.5312 0.728 0 0 0.216 0.056
#> GSM782706 1 0.3838 0.5910 0.716 0 0 0.004 0.280
#> GSM782707 1 0.0162 0.8067 0.996 0 0 0.000 0.004
#> GSM782708 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782709 1 0.4307 0.0758 0.500 0 0 0.000 0.500
#> GSM782710 5 0.4219 0.2169 0.416 0 0 0.000 0.584
#> GSM782711 1 0.0000 0.8058 1.000 0 0 0.000 0.000
#> GSM782712 1 0.0290 0.8060 0.992 0 0 0.000 0.008
#> GSM782713 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782714 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782715 4 0.6563 0.0326 0.356 0 0 0.436 0.208
#> GSM782716 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782717 5 0.0451 0.9044 0.004 0 0 0.008 0.988
#> GSM782718 1 0.6145 0.2220 0.532 0 0 0.312 0.156
#> GSM782719 1 0.0162 0.8067 0.996 0 0 0.000 0.004
#> GSM782720 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782721 1 0.3906 0.5765 0.704 0 0 0.004 0.292
#> GSM782722 4 0.0000 0.8342 0.000 0 0 1.000 0.000
#> GSM782723 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782724 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782725 4 0.0000 0.8342 0.000 0 0 1.000 0.000
#> GSM782726 5 0.0000 0.9073 0.000 0 0 0.000 1.000
#> GSM782727 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782728 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782729 4 0.0000 0.8342 0.000 0 0 1.000 0.000
#> GSM782730 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782731 5 0.1478 0.8670 0.000 0 0 0.064 0.936
#> GSM782732 5 0.1704 0.8616 0.004 0 0 0.068 0.928
#> GSM782733 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782734 5 0.0000 0.9073 0.000 0 0 0.000 1.000
#> GSM782735 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782736 4 0.1408 0.8083 0.008 0 0 0.948 0.044
#> GSM782737 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782738 1 0.6652 -0.0239 0.420 0 0 0.348 0.232
#> GSM782739 5 0.0000 0.9073 0.000 0 0 0.000 1.000
#> GSM782740 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782741 5 0.0162 0.9063 0.004 0 0 0.000 0.996
#> GSM782742 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782743 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782744 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782745 5 0.0000 0.9073 0.000 0 0 0.000 1.000
#> GSM782746 2 0.0000 1.0000 0.000 1 0 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM782696 1 0.1444 0.679052 0.928 0 0.000 0.000 0.072 0.000
#> GSM782697 1 0.3838 0.536810 0.552 0 0.000 0.000 0.448 0.000
#> GSM782698 1 0.3833 0.536679 0.556 0 0.000 0.000 0.444 0.000
#> GSM782699 1 0.3838 0.536810 0.552 0 0.000 0.000 0.448 0.000
#> GSM782700 2 0.0000 1.000000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782701 1 0.0713 0.671091 0.972 0 0.000 0.000 0.028 0.000
#> GSM782702 1 0.2190 0.670095 0.900 0 0.000 0.000 0.060 0.040
#> GSM782703 3 0.0146 0.998077 0.000 0 0.996 0.000 0.004 0.000
#> GSM782704 3 0.0146 0.998077 0.000 0 0.996 0.000 0.004 0.000
#> GSM782705 5 0.6218 0.511471 0.332 0 0.000 0.076 0.508 0.084
#> GSM782706 1 0.4328 0.436348 0.716 0 0.000 0.000 0.192 0.092
#> GSM782707 1 0.0260 0.678474 0.992 0 0.000 0.000 0.008 0.000
#> GSM782708 3 0.0146 0.998077 0.000 0 0.996 0.000 0.004 0.000
#> GSM782709 1 0.5932 0.164048 0.396 0 0.000 0.000 0.212 0.392
#> GSM782710 6 0.5157 0.055179 0.404 0 0.000 0.000 0.088 0.508
#> GSM782711 1 0.3198 0.623507 0.740 0 0.000 0.000 0.260 0.000
#> GSM782712 1 0.0508 0.677154 0.984 0 0.000 0.000 0.012 0.004
#> GSM782713 3 0.0000 0.998077 0.000 0 1.000 0.000 0.000 0.000
#> GSM782714 2 0.0000 1.000000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782715 5 0.6841 0.748444 0.240 0 0.000 0.200 0.476 0.084
#> GSM782716 3 0.0146 0.998077 0.000 0 0.996 0.000 0.004 0.000
#> GSM782717 6 0.3253 0.693623 0.020 0 0.000 0.000 0.192 0.788
#> GSM782718 5 0.6573 0.771722 0.240 0 0.000 0.148 0.524 0.088
#> GSM782719 1 0.0790 0.683032 0.968 0 0.000 0.000 0.032 0.000
#> GSM782720 3 0.0000 0.998077 0.000 0 1.000 0.000 0.000 0.000
#> GSM782721 1 0.4418 0.429022 0.708 0 0.000 0.000 0.192 0.100
#> GSM782722 4 0.0146 0.804795 0.000 0 0.000 0.996 0.004 0.000
#> GSM782723 2 0.0000 1.000000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.000000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782725 4 0.0000 0.805807 0.000 0 0.000 1.000 0.000 0.000
#> GSM782726 6 0.0458 0.710849 0.000 0 0.000 0.000 0.016 0.984
#> GSM782727 3 0.0000 0.998077 0.000 0 1.000 0.000 0.000 0.000
#> GSM782728 2 0.0000 1.000000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782729 4 0.0000 0.805807 0.000 0 0.000 1.000 0.000 0.000
#> GSM782730 3 0.0000 0.998077 0.000 0 1.000 0.000 0.000 0.000
#> GSM782731 6 0.4722 0.516941 0.008 0 0.000 0.056 0.296 0.640
#> GSM782732 6 0.4901 0.492449 0.012 0 0.000 0.060 0.304 0.624
#> GSM782733 3 0.0146 0.998077 0.000 0 0.996 0.000 0.004 0.000
#> GSM782734 6 0.0146 0.715128 0.000 0 0.000 0.000 0.004 0.996
#> GSM782735 2 0.0000 1.000000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782736 4 0.4791 -0.000624 0.004 0 0.000 0.564 0.384 0.048
#> GSM782737 2 0.0000 1.000000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782738 5 0.6855 0.770632 0.264 0 0.000 0.172 0.472 0.092
#> GSM782739 6 0.2669 0.716749 0.008 0 0.000 0.000 0.156 0.836
#> GSM782740 2 0.0000 1.000000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782741 6 0.3190 0.708183 0.044 0 0.000 0.000 0.136 0.820
#> GSM782742 3 0.0000 0.998077 0.000 0 1.000 0.000 0.000 0.000
#> GSM782743 3 0.0146 0.998077 0.000 0 0.996 0.000 0.004 0.000
#> GSM782744 3 0.0000 0.998077 0.000 0 1.000 0.000 0.000 0.000
#> GSM782745 6 0.0458 0.710849 0.000 0 0.000 0.000 0.016 0.984
#> GSM782746 2 0.0000 1.000000 0.000 1 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> SD:skmeans 51 0.493 2
#> SD:skmeans 51 0.642 3
#> SD:skmeans 45 0.474 4
#> SD:skmeans 46 0.476 5
#> SD:skmeans 45 0.394 6
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 51941 rows and 51 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 1.000 1.000 1.000 0.2972 0.704 0.704
#> 3 3 1.000 1.000 1.000 0.9492 0.718 0.599
#> 4 4 0.820 0.847 0.885 0.2357 0.824 0.583
#> 5 5 0.822 0.794 0.883 0.0873 0.949 0.801
#> 6 6 0.879 0.852 0.933 0.0315 0.973 0.873
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
#> GSM782696 1 0 1 1 0
#> GSM782697 1 0 1 1 0
#> GSM782698 1 0 1 1 0
#> GSM782699 1 0 1 1 0
#> GSM782700 2 0 1 0 1
#> GSM782701 1 0 1 1 0
#> GSM782702 1 0 1 1 0
#> GSM782703 1 0 1 1 0
#> GSM782704 1 0 1 1 0
#> GSM782705 1 0 1 1 0
#> GSM782706 1 0 1 1 0
#> GSM782707 1 0 1 1 0
#> GSM782708 1 0 1 1 0
#> GSM782709 1 0 1 1 0
#> GSM782710 1 0 1 1 0
#> GSM782711 1 0 1 1 0
#> GSM782712 1 0 1 1 0
#> GSM782713 1 0 1 1 0
#> GSM782714 2 0 1 0 1
#> GSM782715 1 0 1 1 0
#> GSM782716 1 0 1 1 0
#> GSM782717 1 0 1 1 0
#> GSM782718 1 0 1 1 0
#> GSM782719 1 0 1 1 0
#> GSM782720 1 0 1 1 0
#> GSM782721 1 0 1 1 0
#> GSM782722 1 0 1 1 0
#> GSM782723 2 0 1 0 1
#> GSM782724 2 0 1 0 1
#> GSM782725 1 0 1 1 0
#> GSM782726 1 0 1 1 0
#> GSM782727 1 0 1 1 0
#> GSM782728 2 0 1 0 1
#> GSM782729 1 0 1 1 0
#> GSM782730 1 0 1 1 0
#> GSM782731 1 0 1 1 0
#> GSM782732 1 0 1 1 0
#> GSM782733 1 0 1 1 0
#> GSM782734 1 0 1 1 0
#> GSM782735 2 0 1 0 1
#> GSM782736 1 0 1 1 0
#> GSM782737 2 0 1 0 1
#> GSM782738 1 0 1 1 0
#> GSM782739 1 0 1 1 0
#> GSM782740 2 0 1 0 1
#> GSM782741 1 0 1 1 0
#> GSM782742 1 0 1 1 0
#> GSM782743 1 0 1 1 0
#> GSM782744 1 0 1 1 0
#> GSM782745 1 0 1 1 0
#> GSM782746 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0 1 1 0 0
#> GSM782697 1 0 1 1 0 0
#> GSM782698 1 0 1 1 0 0
#> GSM782699 1 0 1 1 0 0
#> GSM782700 2 0 1 0 1 0
#> GSM782701 1 0 1 1 0 0
#> GSM782702 1 0 1 1 0 0
#> GSM782703 3 0 1 0 0 1
#> GSM782704 3 0 1 0 0 1
#> GSM782705 1 0 1 1 0 0
#> GSM782706 1 0 1 1 0 0
#> GSM782707 1 0 1 1 0 0
#> GSM782708 3 0 1 0 0 1
#> GSM782709 1 0 1 1 0 0
#> GSM782710 1 0 1 1 0 0
#> GSM782711 1 0 1 1 0 0
#> GSM782712 1 0 1 1 0 0
#> GSM782713 3 0 1 0 0 1
#> GSM782714 2 0 1 0 1 0
#> GSM782715 1 0 1 1 0 0
#> GSM782716 3 0 1 0 0 1
#> GSM782717 1 0 1 1 0 0
#> GSM782718 1 0 1 1 0 0
#> GSM782719 1 0 1 1 0 0
#> GSM782720 3 0 1 0 0 1
#> GSM782721 1 0 1 1 0 0
#> GSM782722 1 0 1 1 0 0
#> GSM782723 2 0 1 0 1 0
#> GSM782724 2 0 1 0 1 0
#> GSM782725 1 0 1 1 0 0
#> GSM782726 1 0 1 1 0 0
#> GSM782727 3 0 1 0 0 1
#> GSM782728 2 0 1 0 1 0
#> GSM782729 1 0 1 1 0 0
#> GSM782730 3 0 1 0 0 1
#> GSM782731 1 0 1 1 0 0
#> GSM782732 1 0 1 1 0 0
#> GSM782733 3 0 1 0 0 1
#> GSM782734 1 0 1 1 0 0
#> GSM782735 2 0 1 0 1 0
#> GSM782736 1 0 1 1 0 0
#> GSM782737 2 0 1 0 1 0
#> GSM782738 1 0 1 1 0 0
#> GSM782739 1 0 1 1 0 0
#> GSM782740 2 0 1 0 1 0
#> GSM782741 1 0 1 1 0 0
#> GSM782742 3 0 1 0 0 1
#> GSM782743 3 0 1 0 0 1
#> GSM782744 3 0 1 0 0 1
#> GSM782745 1 0 1 1 0 0
#> GSM782746 2 0 1 0 1 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.4585 0.980 0.668 0 0 0.332
#> GSM782697 1 0.4585 0.980 0.668 0 0 0.332
#> GSM782698 1 0.4585 0.980 0.668 0 0 0.332
#> GSM782699 1 0.4585 0.980 0.668 0 0 0.332
#> GSM782700 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782701 1 0.4585 0.980 0.668 0 0 0.332
#> GSM782702 1 0.4585 0.980 0.668 0 0 0.332
#> GSM782703 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782704 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782705 4 0.2216 0.651 0.092 0 0 0.908
#> GSM782706 1 0.4585 0.980 0.668 0 0 0.332
#> GSM782707 1 0.4585 0.980 0.668 0 0 0.332
#> GSM782708 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782709 1 0.4697 0.944 0.644 0 0 0.356
#> GSM782710 1 0.4585 0.980 0.668 0 0 0.332
#> GSM782711 1 0.4585 0.980 0.668 0 0 0.332
#> GSM782712 1 0.4585 0.980 0.668 0 0 0.332
#> GSM782713 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782715 4 0.4250 0.287 0.276 0 0 0.724
#> GSM782716 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782717 4 0.0000 0.737 0.000 0 0 1.000
#> GSM782718 4 0.0000 0.737 0.000 0 0 1.000
#> GSM782719 1 0.4585 0.980 0.668 0 0 0.332
#> GSM782720 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782721 1 0.4972 0.738 0.544 0 0 0.456
#> GSM782722 4 0.4585 0.538 0.332 0 0 0.668
#> GSM782723 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782725 4 0.4585 0.538 0.332 0 0 0.668
#> GSM782726 4 0.4008 0.387 0.244 0 0 0.756
#> GSM782727 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782729 4 0.4585 0.538 0.332 0 0 0.668
#> GSM782730 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782731 4 0.0000 0.737 0.000 0 0 1.000
#> GSM782732 4 0.0000 0.737 0.000 0 0 1.000
#> GSM782733 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782734 4 0.3610 0.498 0.200 0 0 0.800
#> GSM782735 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782736 4 0.0469 0.732 0.012 0 0 0.988
#> GSM782737 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782738 4 0.0000 0.737 0.000 0 0 1.000
#> GSM782739 4 0.0000 0.737 0.000 0 0 1.000
#> GSM782740 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782741 4 0.4866 -0.356 0.404 0 0 0.596
#> GSM782742 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782743 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782744 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782745 4 0.3444 0.528 0.184 0 0 0.816
#> GSM782746 2 0.0000 1.000 0.000 1 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.0000 0.892 1.000 0 0.000 0.000 0.000
#> GSM782697 1 0.0000 0.892 1.000 0 0.000 0.000 0.000
#> GSM782698 1 0.0000 0.892 1.000 0 0.000 0.000 0.000
#> GSM782699 1 0.0000 0.892 1.000 0 0.000 0.000 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782701 1 0.0000 0.892 1.000 0 0.000 0.000 0.000
#> GSM782702 1 0.0000 0.892 1.000 0 0.000 0.000 0.000
#> GSM782703 3 0.4101 0.838 0.000 0 0.628 0.372 0.000
#> GSM782704 3 0.4101 0.838 0.000 0 0.628 0.372 0.000
#> GSM782705 5 0.3895 0.363 0.320 0 0.000 0.000 0.680
#> GSM782706 1 0.3210 0.675 0.788 0 0.000 0.000 0.212
#> GSM782707 1 0.0000 0.892 1.000 0 0.000 0.000 0.000
#> GSM782708 3 0.4101 0.838 0.000 0 0.628 0.372 0.000
#> GSM782709 1 0.3395 0.643 0.764 0 0.000 0.000 0.236
#> GSM782710 1 0.0000 0.892 1.000 0 0.000 0.000 0.000
#> GSM782711 1 0.0290 0.887 0.992 0 0.000 0.000 0.008
#> GSM782712 1 0.0000 0.892 1.000 0 0.000 0.000 0.000
#> GSM782713 3 0.0000 0.762 0.000 0 1.000 0.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782715 1 0.4126 0.170 0.620 0 0.000 0.000 0.380
#> GSM782716 3 0.4101 0.838 0.000 0 0.628 0.372 0.000
#> GSM782717 5 0.0609 0.691 0.020 0 0.000 0.000 0.980
#> GSM782718 5 0.2280 0.612 0.120 0 0.000 0.000 0.880
#> GSM782719 1 0.0000 0.892 1.000 0 0.000 0.000 0.000
#> GSM782720 3 0.0000 0.762 0.000 0 1.000 0.000 0.000
#> GSM782721 1 0.3966 0.449 0.664 0 0.000 0.000 0.336
#> GSM782722 4 0.4101 1.000 0.000 0 0.000 0.628 0.372
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782725 4 0.4101 1.000 0.000 0 0.000 0.628 0.372
#> GSM782726 5 0.3876 0.550 0.316 0 0.000 0.000 0.684
#> GSM782727 3 0.0000 0.762 0.000 0 1.000 0.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782729 4 0.4101 1.000 0.000 0 0.000 0.628 0.372
#> GSM782730 3 0.0000 0.762 0.000 0 1.000 0.000 0.000
#> GSM782731 5 0.0609 0.691 0.020 0 0.000 0.000 0.980
#> GSM782732 5 0.0609 0.691 0.020 0 0.000 0.000 0.980
#> GSM782733 3 0.4101 0.838 0.000 0 0.628 0.372 0.000
#> GSM782734 5 0.3586 0.597 0.264 0 0.000 0.000 0.736
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782736 5 0.0609 0.691 0.020 0 0.000 0.000 0.980
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782738 5 0.1197 0.680 0.048 0 0.000 0.000 0.952
#> GSM782739 5 0.0609 0.691 0.020 0 0.000 0.000 0.980
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782741 5 0.4278 0.192 0.452 0 0.000 0.000 0.548
#> GSM782742 3 0.0000 0.762 0.000 0 1.000 0.000 0.000
#> GSM782743 3 0.4101 0.838 0.000 0 0.628 0.372 0.000
#> GSM782744 3 0.4101 0.838 0.000 0 0.628 0.372 0.000
#> GSM782745 5 0.3452 0.612 0.244 0 0.000 0.000 0.756
#> GSM782746 2 0.0000 1.000 0.000 1 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
#> GSM782696 1 0.0000 0.907 1.000 0 0.000 0 0.000 0.000
#> GSM782697 1 0.0000 0.907 1.000 0 0.000 0 0.000 0.000
#> GSM782698 1 0.0000 0.907 1.000 0 0.000 0 0.000 0.000
#> GSM782699 1 0.0000 0.907 1.000 0 0.000 0 0.000 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782701 1 0.0000 0.907 1.000 0 0.000 0 0.000 0.000
#> GSM782702 1 0.0000 0.907 1.000 0 0.000 0 0.000 0.000
#> GSM782703 3 0.1327 0.986 0.000 0 0.936 0 0.064 0.000
#> GSM782704 3 0.1327 0.986 0.000 0 0.936 0 0.064 0.000
#> GSM782705 6 0.3309 0.539 0.280 0 0.000 0 0.000 0.720
#> GSM782706 1 0.2883 0.681 0.788 0 0.000 0 0.000 0.212
#> GSM782707 1 0.0000 0.907 1.000 0 0.000 0 0.000 0.000
#> GSM782708 3 0.1327 0.986 0.000 0 0.936 0 0.064 0.000
#> GSM782709 1 0.3050 0.648 0.764 0 0.000 0 0.000 0.236
#> GSM782710 1 0.0000 0.907 1.000 0 0.000 0 0.000 0.000
#> GSM782711 1 0.0260 0.902 0.992 0 0.000 0 0.000 0.008
#> GSM782712 1 0.0000 0.907 1.000 0 0.000 0 0.000 0.000
#> GSM782713 5 0.0000 1.000 0.000 0 0.000 0 1.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782715 1 0.2854 0.659 0.792 0 0.000 0 0.000 0.208
#> GSM782716 3 0.1387 0.983 0.000 0 0.932 0 0.068 0.000
#> GSM782717 6 0.0000 0.740 0.000 0 0.000 0 0.000 1.000
#> GSM782718 6 0.1814 0.692 0.100 0 0.000 0 0.000 0.900
#> GSM782719 1 0.0000 0.907 1.000 0 0.000 0 0.000 0.000
#> GSM782720 5 0.0000 1.000 0.000 0 0.000 0 1.000 0.000
#> GSM782721 1 0.3531 0.460 0.672 0 0.000 0 0.000 0.328
#> GSM782722 4 0.0000 1.000 0.000 0 0.000 1 0.000 0.000
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782725 4 0.0000 1.000 0.000 0 0.000 1 0.000 0.000
#> GSM782726 6 0.3810 0.304 0.428 0 0.000 0 0.000 0.572
#> GSM782727 5 0.0000 1.000 0.000 0 0.000 0 1.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782729 4 0.0000 1.000 0.000 0 0.000 1 0.000 0.000
#> GSM782730 5 0.0000 1.000 0.000 0 0.000 0 1.000 0.000
#> GSM782731 6 0.0000 0.740 0.000 0 0.000 0 0.000 1.000
#> GSM782732 6 0.0000 0.740 0.000 0 0.000 0 0.000 1.000
#> GSM782733 3 0.1327 0.986 0.000 0 0.936 0 0.064 0.000
#> GSM782734 6 0.3765 0.370 0.404 0 0.000 0 0.000 0.596
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782736 6 0.0000 0.740 0.000 0 0.000 0 0.000 1.000
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782738 6 0.0713 0.733 0.028 0 0.000 0 0.000 0.972
#> GSM782739 6 0.0000 0.740 0.000 0 0.000 0 0.000 1.000
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782741 6 0.3737 0.413 0.392 0 0.000 0 0.000 0.608
#> GSM782742 5 0.0000 1.000 0.000 0 0.000 0 1.000 0.000
#> GSM782743 3 0.1327 0.986 0.000 0 0.936 0 0.064 0.000
#> GSM782744 3 0.0713 0.914 0.000 0 0.972 0 0.028 0.000
#> GSM782745 6 0.3672 0.449 0.368 0 0.000 0 0.000 0.632
#> GSM782746 2 0.0000 1.000 0.000 1 0.000 0 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> SD:pam 51 0.648 2
#> SD:pam 51 0.642 3
#> SD:pam 47 0.515 4
#> SD:pam 47 0.452 5
#> SD:pam 46 0.424 6
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 51941 rows and 51 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 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 0.639 0.932 0.945 0.4637 0.506 0.506
#> 3 3 0.969 0.941 0.973 0.2855 0.915 0.833
#> 4 4 1.000 0.966 0.989 0.0961 0.918 0.806
#> 5 5 0.909 0.882 0.944 0.0903 0.941 0.828
#> 6 6 0.780 0.811 0.904 0.0641 0.971 0.899
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 3 4
There is also optional best \(k\) = 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM782696 1 0.000 0.985 1.000 0.000
#> GSM782697 1 0.000 0.985 1.000 0.000
#> GSM782698 1 0.000 0.985 1.000 0.000
#> GSM782699 1 0.000 0.985 1.000 0.000
#> GSM782700 2 0.000 0.870 0.000 1.000
#> GSM782701 1 0.000 0.985 1.000 0.000
#> GSM782702 1 0.000 0.985 1.000 0.000
#> GSM782703 2 0.714 0.887 0.196 0.804
#> GSM782704 2 0.714 0.887 0.196 0.804
#> GSM782705 1 0.000 0.985 1.000 0.000
#> GSM782706 1 0.000 0.985 1.000 0.000
#> GSM782707 1 0.000 0.985 1.000 0.000
#> GSM782708 2 0.714 0.887 0.196 0.804
#> GSM782709 1 0.000 0.985 1.000 0.000
#> GSM782710 1 0.000 0.985 1.000 0.000
#> GSM782711 1 0.000 0.985 1.000 0.000
#> GSM782712 1 0.000 0.985 1.000 0.000
#> GSM782713 2 0.714 0.887 0.196 0.804
#> GSM782714 2 0.000 0.870 0.000 1.000
#> GSM782715 1 0.000 0.985 1.000 0.000
#> GSM782716 2 0.714 0.887 0.196 0.804
#> GSM782717 1 0.000 0.985 1.000 0.000
#> GSM782718 1 0.000 0.985 1.000 0.000
#> GSM782719 1 0.000 0.985 1.000 0.000
#> GSM782720 2 0.714 0.887 0.196 0.804
#> GSM782721 1 0.000 0.985 1.000 0.000
#> GSM782722 1 0.584 0.838 0.860 0.140
#> GSM782723 2 0.000 0.870 0.000 1.000
#> GSM782724 2 0.000 0.870 0.000 1.000
#> GSM782725 1 0.584 0.838 0.860 0.140
#> GSM782726 1 0.000 0.985 1.000 0.000
#> GSM782727 2 0.714 0.887 0.196 0.804
#> GSM782728 2 0.000 0.870 0.000 1.000
#> GSM782729 1 0.443 0.889 0.908 0.092
#> GSM782730 2 0.714 0.887 0.196 0.804
#> GSM782731 1 0.000 0.985 1.000 0.000
#> GSM782732 1 0.000 0.985 1.000 0.000
#> GSM782733 2 0.714 0.887 0.196 0.804
#> GSM782734 1 0.000 0.985 1.000 0.000
#> GSM782735 2 0.000 0.870 0.000 1.000
#> GSM782736 1 0.000 0.985 1.000 0.000
#> GSM782737 2 0.000 0.870 0.000 1.000
#> GSM782738 1 0.000 0.985 1.000 0.000
#> GSM782739 1 0.000 0.985 1.000 0.000
#> GSM782740 2 0.000 0.870 0.000 1.000
#> GSM782741 1 0.000 0.985 1.000 0.000
#> GSM782742 2 0.714 0.887 0.196 0.804
#> GSM782743 2 0.738 0.875 0.208 0.792
#> GSM782744 2 0.844 0.794 0.272 0.728
#> GSM782745 1 0.000 0.985 1.000 0.000
#> GSM782746 2 0.000 0.870 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0.000 0.953 1.000 0.000 0.000
#> GSM782697 1 0.000 0.953 1.000 0.000 0.000
#> GSM782698 1 0.000 0.953 1.000 0.000 0.000
#> GSM782699 1 0.000 0.953 1.000 0.000 0.000
#> GSM782700 2 0.000 1.000 0.000 1.000 0.000
#> GSM782701 1 0.000 0.953 1.000 0.000 0.000
#> GSM782702 1 0.000 0.953 1.000 0.000 0.000
#> GSM782703 3 0.000 1.000 0.000 0.000 1.000
#> GSM782704 3 0.000 1.000 0.000 0.000 1.000
#> GSM782705 1 0.000 0.953 1.000 0.000 0.000
#> GSM782706 1 0.000 0.953 1.000 0.000 0.000
#> GSM782707 1 0.000 0.953 1.000 0.000 0.000
#> GSM782708 3 0.000 1.000 0.000 0.000 1.000
#> GSM782709 1 0.000 0.953 1.000 0.000 0.000
#> GSM782710 1 0.000 0.953 1.000 0.000 0.000
#> GSM782711 1 0.000 0.953 1.000 0.000 0.000
#> GSM782712 1 0.000 0.953 1.000 0.000 0.000
#> GSM782713 3 0.000 1.000 0.000 0.000 1.000
#> GSM782714 2 0.000 1.000 0.000 1.000 0.000
#> GSM782715 1 0.000 0.953 1.000 0.000 0.000
#> GSM782716 3 0.000 1.000 0.000 0.000 1.000
#> GSM782717 1 0.000 0.953 1.000 0.000 0.000
#> GSM782718 1 0.000 0.953 1.000 0.000 0.000
#> GSM782719 1 0.000 0.953 1.000 0.000 0.000
#> GSM782720 3 0.000 1.000 0.000 0.000 1.000
#> GSM782721 1 0.000 0.953 1.000 0.000 0.000
#> GSM782722 1 0.832 0.478 0.600 0.116 0.284
#> GSM782723 2 0.000 1.000 0.000 1.000 0.000
#> GSM782724 2 0.000 1.000 0.000 1.000 0.000
#> GSM782725 1 0.832 0.478 0.600 0.116 0.284
#> GSM782726 1 0.000 0.953 1.000 0.000 0.000
#> GSM782727 3 0.000 1.000 0.000 0.000 1.000
#> GSM782728 2 0.000 1.000 0.000 1.000 0.000
#> GSM782729 1 0.832 0.478 0.600 0.116 0.284
#> GSM782730 3 0.000 1.000 0.000 0.000 1.000
#> GSM782731 1 0.000 0.953 1.000 0.000 0.000
#> GSM782732 1 0.000 0.953 1.000 0.000 0.000
#> GSM782733 3 0.000 1.000 0.000 0.000 1.000
#> GSM782734 1 0.000 0.953 1.000 0.000 0.000
#> GSM782735 2 0.000 1.000 0.000 1.000 0.000
#> GSM782736 1 0.545 0.782 0.816 0.116 0.068
#> GSM782737 2 0.000 1.000 0.000 1.000 0.000
#> GSM782738 1 0.000 0.953 1.000 0.000 0.000
#> GSM782739 1 0.000 0.953 1.000 0.000 0.000
#> GSM782740 2 0.000 1.000 0.000 1.000 0.000
#> GSM782741 1 0.000 0.953 1.000 0.000 0.000
#> GSM782742 3 0.000 1.000 0.000 0.000 1.000
#> GSM782743 3 0.000 1.000 0.000 0.000 1.000
#> GSM782744 3 0.000 1.000 0.000 0.000 1.000
#> GSM782745 1 0.000 0.953 1.000 0.000 0.000
#> GSM782746 2 0.000 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
#> GSM782696 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782697 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782698 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782699 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782701 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782702 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782703 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782704 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782705 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782706 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782707 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782708 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782709 1 0.0336 0.989 0.992 0 0 0.008
#> GSM782710 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782711 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782712 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782713 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782715 1 0.1557 0.932 0.944 0 0 0.056
#> GSM782716 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782717 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782718 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782719 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782720 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782721 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782722 4 0.0188 0.760 0.004 0 0 0.996
#> GSM782723 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782725 4 0.0188 0.760 0.004 0 0 0.996
#> GSM782726 1 0.0188 0.993 0.996 0 0 0.004
#> GSM782727 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782729 4 0.0188 0.760 0.004 0 0 0.996
#> GSM782730 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782731 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782732 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782733 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782734 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782735 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782736 4 0.4981 0.131 0.464 0 0 0.536
#> GSM782737 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782738 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782739 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782740 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782741 1 0.0000 0.997 1.000 0 0 0.000
#> GSM782742 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782743 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782744 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782745 1 0.0188 0.993 0.996 0 0 0.004
#> GSM782746 2 0.0000 1.000 0.000 1 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.0290 0.9174 0.992 0 0.000 0.008 0.000
#> GSM782697 1 0.0000 0.9169 1.000 0 0.000 0.000 0.000
#> GSM782698 1 0.1732 0.8709 0.920 0 0.000 0.080 0.000
#> GSM782699 1 0.0000 0.9169 1.000 0 0.000 0.000 0.000
#> GSM782700 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782701 1 0.1043 0.9131 0.960 0 0.000 0.040 0.000
#> GSM782702 1 0.0000 0.9169 1.000 0 0.000 0.000 0.000
#> GSM782703 3 0.0000 0.9961 0.000 0 1.000 0.000 0.000
#> GSM782704 3 0.0000 0.9961 0.000 0 1.000 0.000 0.000
#> GSM782705 1 0.0963 0.9064 0.964 0 0.000 0.036 0.000
#> GSM782706 1 0.2516 0.8275 0.860 0 0.000 0.140 0.000
#> GSM782707 1 0.0794 0.9123 0.972 0 0.000 0.028 0.000
#> GSM782708 3 0.0290 0.9934 0.000 0 0.992 0.000 0.008
#> GSM782709 1 0.0880 0.9125 0.968 0 0.000 0.032 0.000
#> GSM782710 1 0.0000 0.9169 1.000 0 0.000 0.000 0.000
#> GSM782711 1 0.0000 0.9169 1.000 0 0.000 0.000 0.000
#> GSM782712 1 0.0000 0.9169 1.000 0 0.000 0.000 0.000
#> GSM782713 3 0.0000 0.9961 0.000 0 1.000 0.000 0.000
#> GSM782714 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782715 4 0.3689 0.6450 0.256 0 0.000 0.740 0.004
#> GSM782716 3 0.0162 0.9949 0.000 0 0.996 0.000 0.004
#> GSM782717 1 0.0794 0.9141 0.972 0 0.000 0.028 0.000
#> GSM782718 4 0.4273 0.5081 0.448 0 0.000 0.552 0.000
#> GSM782719 1 0.0963 0.9132 0.964 0 0.000 0.036 0.000
#> GSM782720 3 0.0000 0.9961 0.000 0 1.000 0.000 0.000
#> GSM782721 1 0.2179 0.8600 0.888 0 0.000 0.112 0.000
#> GSM782722 5 0.0671 0.9706 0.004 0 0.000 0.016 0.980
#> GSM782723 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782725 5 0.0798 0.9724 0.008 0 0.000 0.016 0.976
#> GSM782726 1 0.1952 0.8724 0.912 0 0.000 0.084 0.004
#> GSM782727 3 0.0000 0.9961 0.000 0 1.000 0.000 0.000
#> GSM782728 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782729 5 0.1942 0.9493 0.012 0 0.000 0.068 0.920
#> GSM782730 3 0.0000 0.9961 0.000 0 1.000 0.000 0.000
#> GSM782731 1 0.4304 -0.3853 0.516 0 0.000 0.484 0.000
#> GSM782732 1 0.2929 0.7535 0.820 0 0.000 0.180 0.000
#> GSM782733 3 0.0162 0.9949 0.000 0 0.996 0.000 0.004
#> GSM782734 1 0.1197 0.9042 0.952 0 0.000 0.048 0.000
#> GSM782735 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782736 4 0.2624 0.0356 0.012 0 0.000 0.872 0.116
#> GSM782737 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782738 4 0.4060 0.6506 0.360 0 0.000 0.640 0.000
#> GSM782739 1 0.0162 0.9175 0.996 0 0.000 0.004 0.000
#> GSM782740 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782741 1 0.0162 0.9176 0.996 0 0.000 0.004 0.000
#> GSM782742 3 0.0000 0.9961 0.000 0 1.000 0.000 0.000
#> GSM782743 3 0.0609 0.9859 0.000 0 0.980 0.000 0.020
#> GSM782744 3 0.0510 0.9873 0.000 0 0.984 0.000 0.016
#> GSM782745 1 0.1952 0.8724 0.912 0 0.000 0.084 0.004
#> GSM782746 2 0.0000 1.0000 0.000 1 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
#> GSM782696 1 0.1387 0.858 0.932 0 0.000 0.000 0.000 0.068
#> GSM782697 1 0.0000 0.865 1.000 0 0.000 0.000 0.000 0.000
#> GSM782698 1 0.2793 0.784 0.800 0 0.000 0.000 0.000 0.200
#> GSM782699 1 0.0146 0.864 0.996 0 0.000 0.000 0.000 0.004
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782701 1 0.2784 0.847 0.848 0 0.000 0.000 0.028 0.124
#> GSM782702 1 0.0000 0.865 1.000 0 0.000 0.000 0.000 0.000
#> GSM782703 3 0.0000 0.904 0.000 0 1.000 0.000 0.000 0.000
#> GSM782704 3 0.1327 0.851 0.000 0 0.936 0.000 0.064 0.000
#> GSM782705 1 0.2378 0.814 0.848 0 0.000 0.000 0.000 0.152
#> GSM782706 1 0.4355 0.452 0.556 0 0.000 0.000 0.024 0.420
#> GSM782707 1 0.1957 0.846 0.888 0 0.000 0.000 0.000 0.112
#> GSM782708 3 0.1387 0.846 0.000 0 0.932 0.000 0.068 0.000
#> GSM782709 1 0.2328 0.852 0.892 0 0.000 0.000 0.052 0.056
#> GSM782710 1 0.0260 0.866 0.992 0 0.000 0.000 0.008 0.000
#> GSM782711 1 0.0146 0.866 0.996 0 0.000 0.000 0.000 0.004
#> GSM782712 1 0.0000 0.865 1.000 0 0.000 0.000 0.000 0.000
#> GSM782713 3 0.0000 0.904 0.000 0 1.000 0.000 0.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782715 6 0.3033 0.782 0.076 0 0.000 0.012 0.056 0.856
#> GSM782716 3 0.0363 0.900 0.000 0 0.988 0.000 0.012 0.000
#> GSM782717 1 0.1765 0.860 0.924 0 0.000 0.000 0.024 0.052
#> GSM782718 6 0.1610 0.807 0.084 0 0.000 0.000 0.000 0.916
#> GSM782719 1 0.1910 0.852 0.892 0 0.000 0.000 0.000 0.108
#> GSM782720 3 0.0000 0.904 0.000 0 1.000 0.000 0.000 0.000
#> GSM782721 1 0.3993 0.677 0.676 0 0.000 0.000 0.024 0.300
#> GSM782722 4 0.0508 0.947 0.000 0 0.000 0.984 0.004 0.012
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782725 4 0.0405 0.949 0.004 0 0.000 0.988 0.000 0.008
#> GSM782726 1 0.3518 0.818 0.816 0 0.000 0.012 0.116 0.056
#> GSM782727 3 0.0000 0.904 0.000 0 1.000 0.000 0.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782729 4 0.2437 0.905 0.004 0 0.000 0.888 0.072 0.036
#> GSM782730 3 0.0000 0.904 0.000 0 1.000 0.000 0.000 0.000
#> GSM782731 6 0.2854 0.683 0.208 0 0.000 0.000 0.000 0.792
#> GSM782732 1 0.4246 0.491 0.580 0 0.000 0.000 0.020 0.400
#> GSM782733 3 0.0363 0.900 0.000 0 0.988 0.000 0.012 0.000
#> GSM782734 1 0.2660 0.842 0.868 0 0.000 0.000 0.048 0.084
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782736 6 0.4669 0.383 0.004 0 0.000 0.108 0.196 0.692
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782738 6 0.1610 0.807 0.084 0 0.000 0.000 0.000 0.916
#> GSM782739 1 0.1152 0.868 0.952 0 0.000 0.000 0.004 0.044
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782741 1 0.0937 0.867 0.960 0 0.000 0.000 0.000 0.040
#> GSM782742 3 0.0000 0.904 0.000 0 1.000 0.000 0.000 0.000
#> GSM782743 3 0.3866 -0.556 0.000 0 0.516 0.000 0.484 0.000
#> GSM782744 5 0.3499 0.000 0.000 0 0.320 0.000 0.680 0.000
#> GSM782745 1 0.3849 0.801 0.792 0 0.000 0.012 0.116 0.080
#> GSM782746 2 0.0000 1.000 0.000 1 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> SD:mclust 51 0.493 2
#> SD:mclust 48 0.627 3
#> SD:mclust 50 0.497 4
#> SD:mclust 49 0.396 5
#> SD:mclust 46 0.394 6
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 51941 rows and 51 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 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.2972 0.704 0.704
#> 3 3 1.000 1.000 1.000 0.9492 0.718 0.599
#> 4 4 0.895 0.924 0.946 0.1444 0.902 0.767
#> 5 5 0.822 0.876 0.929 0.0596 0.977 0.930
#> 6 6 0.757 0.799 0.873 0.0577 0.977 0.927
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
#> GSM782696 1 0 1 1 0
#> GSM782697 1 0 1 1 0
#> GSM782698 1 0 1 1 0
#> GSM782699 1 0 1 1 0
#> GSM782700 2 0 1 0 1
#> GSM782701 1 0 1 1 0
#> GSM782702 1 0 1 1 0
#> GSM782703 1 0 1 1 0
#> GSM782704 1 0 1 1 0
#> GSM782705 1 0 1 1 0
#> GSM782706 1 0 1 1 0
#> GSM782707 1 0 1 1 0
#> GSM782708 1 0 1 1 0
#> GSM782709 1 0 1 1 0
#> GSM782710 1 0 1 1 0
#> GSM782711 1 0 1 1 0
#> GSM782712 1 0 1 1 0
#> GSM782713 1 0 1 1 0
#> GSM782714 2 0 1 0 1
#> GSM782715 1 0 1 1 0
#> GSM782716 1 0 1 1 0
#> GSM782717 1 0 1 1 0
#> GSM782718 1 0 1 1 0
#> GSM782719 1 0 1 1 0
#> GSM782720 1 0 1 1 0
#> GSM782721 1 0 1 1 0
#> GSM782722 1 0 1 1 0
#> GSM782723 2 0 1 0 1
#> GSM782724 2 0 1 0 1
#> GSM782725 1 0 1 1 0
#> GSM782726 1 0 1 1 0
#> GSM782727 1 0 1 1 0
#> GSM782728 2 0 1 0 1
#> GSM782729 1 0 1 1 0
#> GSM782730 1 0 1 1 0
#> GSM782731 1 0 1 1 0
#> GSM782732 1 0 1 1 0
#> GSM782733 1 0 1 1 0
#> GSM782734 1 0 1 1 0
#> GSM782735 2 0 1 0 1
#> GSM782736 1 0 1 1 0
#> GSM782737 2 0 1 0 1
#> GSM782738 1 0 1 1 0
#> GSM782739 1 0 1 1 0
#> GSM782740 2 0 1 0 1
#> GSM782741 1 0 1 1 0
#> GSM782742 1 0 1 1 0
#> GSM782743 1 0 1 1 0
#> GSM782744 1 0 1 1 0
#> GSM782745 1 0 1 1 0
#> GSM782746 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0 1 1 0 0
#> GSM782697 1 0 1 1 0 0
#> GSM782698 1 0 1 1 0 0
#> GSM782699 1 0 1 1 0 0
#> GSM782700 2 0 1 0 1 0
#> GSM782701 1 0 1 1 0 0
#> GSM782702 1 0 1 1 0 0
#> GSM782703 3 0 1 0 0 1
#> GSM782704 3 0 1 0 0 1
#> GSM782705 1 0 1 1 0 0
#> GSM782706 1 0 1 1 0 0
#> GSM782707 1 0 1 1 0 0
#> GSM782708 3 0 1 0 0 1
#> GSM782709 1 0 1 1 0 0
#> GSM782710 1 0 1 1 0 0
#> GSM782711 1 0 1 1 0 0
#> GSM782712 1 0 1 1 0 0
#> GSM782713 3 0 1 0 0 1
#> GSM782714 2 0 1 0 1 0
#> GSM782715 1 0 1 1 0 0
#> GSM782716 3 0 1 0 0 1
#> GSM782717 1 0 1 1 0 0
#> GSM782718 1 0 1 1 0 0
#> GSM782719 1 0 1 1 0 0
#> GSM782720 3 0 1 0 0 1
#> GSM782721 1 0 1 1 0 0
#> GSM782722 1 0 1 1 0 0
#> GSM782723 2 0 1 0 1 0
#> GSM782724 2 0 1 0 1 0
#> GSM782725 1 0 1 1 0 0
#> GSM782726 1 0 1 1 0 0
#> GSM782727 3 0 1 0 0 1
#> GSM782728 2 0 1 0 1 0
#> GSM782729 1 0 1 1 0 0
#> GSM782730 3 0 1 0 0 1
#> GSM782731 1 0 1 1 0 0
#> GSM782732 1 0 1 1 0 0
#> GSM782733 3 0 1 0 0 1
#> GSM782734 1 0 1 1 0 0
#> GSM782735 2 0 1 0 1 0
#> GSM782736 1 0 1 1 0 0
#> GSM782737 2 0 1 0 1 0
#> GSM782738 1 0 1 1 0 0
#> GSM782739 1 0 1 1 0 0
#> GSM782740 2 0 1 0 1 0
#> GSM782741 1 0 1 1 0 0
#> GSM782742 3 0 1 0 0 1
#> GSM782743 3 0 1 0 0 1
#> GSM782744 3 0 1 0 0 1
#> GSM782745 1 0 1 1 0 0
#> GSM782746 2 0 1 0 1 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.1211 0.920 0.960 0 0.000 0.040
#> GSM782697 1 0.1302 0.911 0.956 0 0.000 0.044
#> GSM782698 1 0.0921 0.930 0.972 0 0.000 0.028
#> GSM782699 1 0.1211 0.914 0.960 0 0.000 0.040
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782701 1 0.0188 0.931 0.996 0 0.000 0.004
#> GSM782702 1 0.0707 0.928 0.980 0 0.000 0.020
#> GSM782703 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782704 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782705 1 0.0592 0.927 0.984 0 0.000 0.016
#> GSM782706 1 0.0592 0.927 0.984 0 0.000 0.016
#> GSM782707 1 0.0336 0.932 0.992 0 0.000 0.008
#> GSM782708 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782709 1 0.1022 0.922 0.968 0 0.000 0.032
#> GSM782710 1 0.0592 0.931 0.984 0 0.000 0.016
#> GSM782711 1 0.0707 0.931 0.980 0 0.000 0.020
#> GSM782712 1 0.0592 0.930 0.984 0 0.000 0.016
#> GSM782713 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782715 4 0.4907 0.755 0.420 0 0.000 0.580
#> GSM782716 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782717 1 0.0188 0.931 0.996 0 0.000 0.004
#> GSM782718 1 0.3942 0.525 0.764 0 0.000 0.236
#> GSM782719 1 0.1302 0.918 0.956 0 0.000 0.044
#> GSM782720 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782721 1 0.0469 0.931 0.988 0 0.000 0.012
#> GSM782722 4 0.4040 0.873 0.248 0 0.000 0.752
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782725 4 0.4250 0.899 0.276 0 0.000 0.724
#> GSM782726 1 0.0336 0.932 0.992 0 0.000 0.008
#> GSM782727 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782729 4 0.4356 0.902 0.292 0 0.000 0.708
#> GSM782730 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782731 1 0.3123 0.720 0.844 0 0.000 0.156
#> GSM782732 1 0.1792 0.870 0.932 0 0.000 0.068
#> GSM782733 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782734 1 0.0336 0.931 0.992 0 0.000 0.008
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782736 4 0.4679 0.867 0.352 0 0.000 0.648
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782738 1 0.4431 0.280 0.696 0 0.000 0.304
#> GSM782739 1 0.0000 0.932 1.000 0 0.000 0.000
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782741 1 0.0000 0.932 1.000 0 0.000 0.000
#> GSM782742 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782743 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782744 3 0.0817 0.977 0.000 0 0.976 0.024
#> GSM782745 1 0.0707 0.926 0.980 0 0.000 0.020
#> GSM782746 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.1544 0.895 0.932 0 0.00 0.000 0.068
#> GSM782697 1 0.2179 0.864 0.888 0 0.00 0.000 0.112
#> GSM782698 1 0.2674 0.847 0.856 0 0.00 0.004 0.140
#> GSM782699 1 0.1732 0.880 0.920 0 0.00 0.000 0.080
#> GSM782700 2 0.0000 1.000 0.000 1 0.00 0.000 0.000
#> GSM782701 1 0.0880 0.903 0.968 0 0.00 0.000 0.032
#> GSM782702 1 0.0798 0.903 0.976 0 0.00 0.008 0.016
#> GSM782703 3 0.0000 0.989 0.000 0 1.00 0.000 0.000
#> GSM782704 3 0.0000 0.989 0.000 0 1.00 0.000 0.000
#> GSM782705 1 0.1914 0.891 0.924 0 0.00 0.016 0.060
#> GSM782706 1 0.2669 0.859 0.876 0 0.00 0.020 0.104
#> GSM782707 1 0.1205 0.902 0.956 0 0.00 0.004 0.040
#> GSM782708 3 0.0000 0.989 0.000 0 1.00 0.000 0.000
#> GSM782709 1 0.1082 0.904 0.964 0 0.00 0.008 0.028
#> GSM782710 1 0.1195 0.903 0.960 0 0.00 0.012 0.028
#> GSM782711 1 0.0880 0.902 0.968 0 0.00 0.000 0.032
#> GSM782712 1 0.0963 0.902 0.964 0 0.00 0.000 0.036
#> GSM782713 3 0.0000 0.989 0.000 0 1.00 0.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.00 0.000 0.000
#> GSM782715 4 0.4927 0.663 0.296 0 0.00 0.652 0.052
#> GSM782716 3 0.0000 0.989 0.000 0 1.00 0.000 0.000
#> GSM782717 1 0.0693 0.902 0.980 0 0.00 0.008 0.012
#> GSM782718 1 0.5042 -0.276 0.508 0 0.00 0.460 0.032
#> GSM782719 1 0.1965 0.880 0.904 0 0.00 0.000 0.096
#> GSM782720 3 0.0000 0.989 0.000 0 1.00 0.000 0.000
#> GSM782721 1 0.2915 0.846 0.860 0 0.00 0.024 0.116
#> GSM782722 4 0.1484 0.744 0.048 0 0.00 0.944 0.008
#> GSM782723 2 0.0000 1.000 0.000 1 0.00 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.00 0.000 0.000
#> GSM782725 4 0.2110 0.772 0.072 0 0.00 0.912 0.016
#> GSM782726 1 0.1741 0.891 0.936 0 0.00 0.024 0.040
#> GSM782727 3 0.0000 0.989 0.000 0 1.00 0.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.00 0.000 0.000
#> GSM782729 4 0.2361 0.784 0.096 0 0.00 0.892 0.012
#> GSM782730 3 0.0000 0.989 0.000 0 1.00 0.000 0.000
#> GSM782731 1 0.3779 0.745 0.804 0 0.00 0.144 0.052
#> GSM782732 1 0.2409 0.862 0.900 0 0.00 0.068 0.032
#> GSM782733 3 0.0000 0.989 0.000 0 1.00 0.000 0.000
#> GSM782734 1 0.1310 0.896 0.956 0 0.00 0.020 0.024
#> GSM782735 2 0.0000 1.000 0.000 1 0.00 0.000 0.000
#> GSM782736 4 0.3639 0.780 0.184 0 0.00 0.792 0.024
#> GSM782737 2 0.0000 1.000 0.000 1 0.00 0.000 0.000
#> GSM782738 4 0.5049 0.207 0.484 0 0.00 0.484 0.032
#> GSM782739 1 0.0807 0.900 0.976 0 0.00 0.012 0.012
#> GSM782740 2 0.0000 1.000 0.000 1 0.00 0.000 0.000
#> GSM782741 1 0.0693 0.902 0.980 0 0.00 0.008 0.012
#> GSM782742 3 0.0000 0.989 0.000 0 1.00 0.000 0.000
#> GSM782743 3 0.0000 0.989 0.000 0 1.00 0.000 0.000
#> GSM782744 3 0.3037 0.869 0.000 0 0.86 0.040 0.100
#> GSM782745 1 0.2769 0.851 0.876 0 0.00 0.032 0.092
#> GSM782746 2 0.0000 1.000 0.000 1 0.00 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM782696 1 0.2554 0.797 0.876 0.000 0.000 0.000 NA 0.076
#> GSM782697 1 0.2738 0.751 0.820 0.000 0.000 0.000 NA 0.004
#> GSM782698 1 0.4719 0.613 0.680 0.000 0.000 0.044 NA 0.028
#> GSM782699 1 0.2513 0.774 0.852 0.000 0.000 0.000 NA 0.008
#> GSM782700 2 0.0000 0.999 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782701 1 0.2883 0.771 0.844 0.000 0.000 0.012 NA 0.132
#> GSM782702 1 0.0717 0.810 0.976 0.000 0.000 0.000 NA 0.016
#> GSM782703 3 0.0291 0.972 0.000 0.000 0.992 0.000 NA 0.004
#> GSM782704 3 0.0000 0.973 0.000 0.000 1.000 0.000 NA 0.000
#> GSM782705 1 0.4053 0.695 0.744 0.000 0.000 0.048 NA 0.008
#> GSM782706 1 0.5218 0.319 0.528 0.000 0.000 0.084 NA 0.384
#> GSM782707 1 0.2983 0.784 0.856 0.000 0.000 0.012 NA 0.092
#> GSM782708 3 0.0000 0.973 0.000 0.000 1.000 0.000 NA 0.000
#> GSM782709 1 0.2009 0.806 0.908 0.000 0.000 0.000 NA 0.068
#> GSM782710 1 0.1866 0.803 0.908 0.000 0.000 0.000 NA 0.008
#> GSM782711 1 0.1168 0.809 0.956 0.000 0.000 0.000 NA 0.016
#> GSM782712 1 0.2537 0.790 0.880 0.000 0.000 0.008 NA 0.088
#> GSM782713 3 0.0291 0.972 0.000 0.000 0.992 0.000 NA 0.004
#> GSM782714 2 0.0000 0.999 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782715 4 0.5960 0.527 0.284 0.000 0.000 0.544 NA 0.144
#> GSM782716 3 0.0000 0.973 0.000 0.000 1.000 0.000 NA 0.000
#> GSM782717 1 0.1410 0.806 0.944 0.000 0.000 0.004 NA 0.008
#> GSM782718 4 0.6043 0.216 0.428 0.000 0.000 0.440 NA 0.072
#> GSM782719 1 0.4531 0.669 0.716 0.000 0.000 0.004 NA 0.140
#> GSM782720 3 0.0291 0.972 0.000 0.000 0.992 0.000 NA 0.004
#> GSM782721 1 0.4952 0.329 0.524 0.000 0.000 0.068 NA 0.408
#> GSM782722 4 0.1462 0.669 0.008 0.000 0.000 0.936 NA 0.056
#> GSM782723 2 0.0000 0.999 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782724 2 0.0000 0.999 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782725 4 0.0976 0.668 0.008 0.000 0.000 0.968 NA 0.008
#> GSM782726 1 0.2916 0.790 0.860 0.000 0.000 0.024 NA 0.096
#> GSM782727 3 0.0508 0.970 0.000 0.000 0.984 0.000 NA 0.012
#> GSM782728 2 0.0000 0.999 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782729 4 0.2360 0.677 0.044 0.000 0.000 0.900 NA 0.012
#> GSM782730 3 0.0146 0.973 0.000 0.000 0.996 0.000 NA 0.004
#> GSM782731 1 0.4870 0.646 0.720 0.000 0.000 0.144 NA 0.092
#> GSM782732 1 0.4290 0.725 0.776 0.000 0.000 0.100 NA 0.048
#> GSM782733 3 0.0000 0.973 0.000 0.000 1.000 0.000 NA 0.000
#> GSM782734 1 0.2784 0.788 0.848 0.000 0.000 0.028 NA 0.124
#> GSM782735 2 0.0146 0.997 0.000 0.996 0.000 0.000 NA 0.004
#> GSM782736 4 0.4019 0.688 0.112 0.000 0.000 0.792 NA 0.056
#> GSM782737 2 0.0000 0.999 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782738 4 0.5924 0.247 0.412 0.000 0.000 0.420 NA 0.160
#> GSM782739 1 0.2039 0.804 0.916 0.000 0.000 0.012 NA 0.020
#> GSM782740 2 0.0000 0.999 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782741 1 0.1477 0.807 0.940 0.000 0.000 0.008 NA 0.048
#> GSM782742 3 0.0603 0.968 0.000 0.000 0.980 0.000 NA 0.016
#> GSM782743 3 0.0000 0.973 0.000 0.000 1.000 0.000 NA 0.000
#> GSM782744 3 0.4641 0.704 0.000 0.000 0.712 0.048 NA 0.204
#> GSM782745 1 0.3194 0.771 0.828 0.000 0.000 0.032 NA 0.132
#> GSM782746 2 0.0146 0.997 0.000 0.996 0.000 0.000 NA 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> SD:NMF 51 0.648 2
#> SD:NMF 51 0.642 3
#> SD:NMF 50 0.502 4
#> SD:NMF 49 0.497 5
#> SD:NMF 47 0.487 6
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 51941 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.2972 0.704 0.704
#> 3 3 1.000 1.000 1.000 0.9492 0.718 0.599
#> 4 4 0.845 0.874 0.932 0.1416 0.936 0.849
#> 5 5 0.812 0.839 0.924 0.0623 0.961 0.890
#> 6 6 0.811 0.844 0.919 0.0375 0.991 0.973
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
#> GSM782696 1 0 1 1 0
#> GSM782697 1 0 1 1 0
#> GSM782698 1 0 1 1 0
#> GSM782699 1 0 1 1 0
#> GSM782700 2 0 1 0 1
#> GSM782701 1 0 1 1 0
#> GSM782702 1 0 1 1 0
#> GSM782703 1 0 1 1 0
#> GSM782704 1 0 1 1 0
#> GSM782705 1 0 1 1 0
#> GSM782706 1 0 1 1 0
#> GSM782707 1 0 1 1 0
#> GSM782708 1 0 1 1 0
#> GSM782709 1 0 1 1 0
#> GSM782710 1 0 1 1 0
#> GSM782711 1 0 1 1 0
#> GSM782712 1 0 1 1 0
#> GSM782713 1 0 1 1 0
#> GSM782714 2 0 1 0 1
#> GSM782715 1 0 1 1 0
#> GSM782716 1 0 1 1 0
#> GSM782717 1 0 1 1 0
#> GSM782718 1 0 1 1 0
#> GSM782719 1 0 1 1 0
#> GSM782720 1 0 1 1 0
#> GSM782721 1 0 1 1 0
#> GSM782722 1 0 1 1 0
#> GSM782723 2 0 1 0 1
#> GSM782724 2 0 1 0 1
#> GSM782725 1 0 1 1 0
#> GSM782726 1 0 1 1 0
#> GSM782727 1 0 1 1 0
#> GSM782728 2 0 1 0 1
#> GSM782729 1 0 1 1 0
#> GSM782730 1 0 1 1 0
#> GSM782731 1 0 1 1 0
#> GSM782732 1 0 1 1 0
#> GSM782733 1 0 1 1 0
#> GSM782734 1 0 1 1 0
#> GSM782735 2 0 1 0 1
#> GSM782736 1 0 1 1 0
#> GSM782737 2 0 1 0 1
#> GSM782738 1 0 1 1 0
#> GSM782739 1 0 1 1 0
#> GSM782740 2 0 1 0 1
#> GSM782741 1 0 1 1 0
#> GSM782742 1 0 1 1 0
#> GSM782743 1 0 1 1 0
#> GSM782744 1 0 1 1 0
#> GSM782745 1 0 1 1 0
#> GSM782746 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0 1 1 0 0
#> GSM782697 1 0 1 1 0 0
#> GSM782698 1 0 1 1 0 0
#> GSM782699 1 0 1 1 0 0
#> GSM782700 2 0 1 0 1 0
#> GSM782701 1 0 1 1 0 0
#> GSM782702 1 0 1 1 0 0
#> GSM782703 3 0 1 0 0 1
#> GSM782704 3 0 1 0 0 1
#> GSM782705 1 0 1 1 0 0
#> GSM782706 1 0 1 1 0 0
#> GSM782707 1 0 1 1 0 0
#> GSM782708 3 0 1 0 0 1
#> GSM782709 1 0 1 1 0 0
#> GSM782710 1 0 1 1 0 0
#> GSM782711 1 0 1 1 0 0
#> GSM782712 1 0 1 1 0 0
#> GSM782713 3 0 1 0 0 1
#> GSM782714 2 0 1 0 1 0
#> GSM782715 1 0 1 1 0 0
#> GSM782716 3 0 1 0 0 1
#> GSM782717 1 0 1 1 0 0
#> GSM782718 1 0 1 1 0 0
#> GSM782719 1 0 1 1 0 0
#> GSM782720 3 0 1 0 0 1
#> GSM782721 1 0 1 1 0 0
#> GSM782722 1 0 1 1 0 0
#> GSM782723 2 0 1 0 1 0
#> GSM782724 2 0 1 0 1 0
#> GSM782725 1 0 1 1 0 0
#> GSM782726 1 0 1 1 0 0
#> GSM782727 3 0 1 0 0 1
#> GSM782728 2 0 1 0 1 0
#> GSM782729 1 0 1 1 0 0
#> GSM782730 3 0 1 0 0 1
#> GSM782731 1 0 1 1 0 0
#> GSM782732 1 0 1 1 0 0
#> GSM782733 3 0 1 0 0 1
#> GSM782734 1 0 1 1 0 0
#> GSM782735 2 0 1 0 1 0
#> GSM782736 1 0 1 1 0 0
#> GSM782737 2 0 1 0 1 0
#> GSM782738 1 0 1 1 0 0
#> GSM782739 1 0 1 1 0 0
#> GSM782740 2 0 1 0 1 0
#> GSM782741 1 0 1 1 0 0
#> GSM782742 3 0 1 0 0 1
#> GSM782743 3 0 1 0 0 1
#> GSM782744 3 0 1 0 0 1
#> GSM782745 1 0 1 1 0 0
#> GSM782746 2 0 1 0 1 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.0000 0.852 1.000 0 0 0.000
#> GSM782697 1 0.0000 0.852 1.000 0 0 0.000
#> GSM782698 1 0.3649 0.580 0.796 0 0 0.204
#> GSM782699 1 0.0000 0.852 1.000 0 0 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782701 1 0.0000 0.852 1.000 0 0 0.000
#> GSM782702 1 0.0000 0.852 1.000 0 0 0.000
#> GSM782703 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782704 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782705 1 0.0707 0.838 0.980 0 0 0.020
#> GSM782706 1 0.0000 0.852 1.000 0 0 0.000
#> GSM782707 1 0.0000 0.852 1.000 0 0 0.000
#> GSM782708 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782709 1 0.0000 0.852 1.000 0 0 0.000
#> GSM782710 1 0.2281 0.813 0.904 0 0 0.096
#> GSM782711 1 0.0000 0.852 1.000 0 0 0.000
#> GSM782712 1 0.0000 0.852 1.000 0 0 0.000
#> GSM782713 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782715 1 0.3649 0.580 0.796 0 0 0.204
#> GSM782716 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782717 1 0.2281 0.813 0.904 0 0 0.096
#> GSM782718 1 0.3649 0.580 0.796 0 0 0.204
#> GSM782719 1 0.0000 0.852 1.000 0 0 0.000
#> GSM782720 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782721 1 0.0000 0.852 1.000 0 0 0.000
#> GSM782722 4 0.4643 1.000 0.344 0 0 0.656
#> GSM782723 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782725 4 0.4643 1.000 0.344 0 0 0.656
#> GSM782726 1 0.4643 0.450 0.656 0 0 0.344
#> GSM782727 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782729 4 0.4643 1.000 0.344 0 0 0.656
#> GSM782730 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782731 1 0.2281 0.813 0.904 0 0 0.096
#> GSM782732 1 0.2281 0.813 0.904 0 0 0.096
#> GSM782733 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782734 1 0.2281 0.813 0.904 0 0 0.096
#> GSM782735 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782736 1 0.3649 0.580 0.796 0 0 0.204
#> GSM782737 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782738 1 0.3649 0.580 0.796 0 0 0.204
#> GSM782739 1 0.2281 0.813 0.904 0 0 0.096
#> GSM782740 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782741 1 0.2281 0.813 0.904 0 0 0.096
#> GSM782742 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782743 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782744 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782745 1 0.4643 0.450 0.656 0 0 0.344
#> GSM782746 2 0.0000 1.000 0.000 1 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.0000 0.815 1.000 0 0.000 0.000 0.000
#> GSM782697 1 0.0000 0.815 1.000 0 0.000 0.000 0.000
#> GSM782698 1 0.3266 0.617 0.796 0 0.000 0.200 0.004
#> GSM782699 1 0.0000 0.815 1.000 0 0.000 0.000 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782701 1 0.0000 0.815 1.000 0 0.000 0.000 0.000
#> GSM782702 1 0.0000 0.815 1.000 0 0.000 0.000 0.000
#> GSM782703 3 0.0000 0.966 0.000 0 1.000 0.000 0.000
#> GSM782704 3 0.0000 0.966 0.000 0 1.000 0.000 0.000
#> GSM782705 1 0.0609 0.803 0.980 0 0.000 0.020 0.000
#> GSM782706 1 0.0703 0.806 0.976 0 0.000 0.000 0.024
#> GSM782707 1 0.0000 0.815 1.000 0 0.000 0.000 0.000
#> GSM782708 3 0.0000 0.966 0.000 0 1.000 0.000 0.000
#> GSM782709 1 0.0510 0.809 0.984 0 0.000 0.000 0.016
#> GSM782710 1 0.3932 0.138 0.672 0 0.000 0.000 0.328
#> GSM782711 1 0.0000 0.815 1.000 0 0.000 0.000 0.000
#> GSM782712 1 0.0000 0.815 1.000 0 0.000 0.000 0.000
#> GSM782713 3 0.0000 0.966 0.000 0 1.000 0.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782715 1 0.3521 0.572 0.764 0 0.000 0.232 0.004
#> GSM782716 3 0.0000 0.966 0.000 0 1.000 0.000 0.000
#> GSM782717 1 0.2813 0.661 0.832 0 0.000 0.000 0.168
#> GSM782718 1 0.3333 0.608 0.788 0 0.000 0.208 0.004
#> GSM782719 1 0.0000 0.815 1.000 0 0.000 0.000 0.000
#> GSM782720 3 0.0000 0.966 0.000 0 1.000 0.000 0.000
#> GSM782721 1 0.0703 0.806 0.976 0 0.000 0.000 0.024
#> GSM782722 4 0.1197 1.000 0.048 0 0.000 0.952 0.000
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782725 4 0.1197 1.000 0.048 0 0.000 0.952 0.000
#> GSM782726 5 0.4088 1.000 0.368 0 0.000 0.000 0.632
#> GSM782727 3 0.0000 0.966 0.000 0 1.000 0.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782729 4 0.1197 1.000 0.048 0 0.000 0.952 0.000
#> GSM782730 3 0.0000 0.966 0.000 0 1.000 0.000 0.000
#> GSM782731 1 0.2813 0.661 0.832 0 0.000 0.000 0.168
#> GSM782732 1 0.2813 0.661 0.832 0 0.000 0.000 0.168
#> GSM782733 3 0.0000 0.966 0.000 0 1.000 0.000 0.000
#> GSM782734 1 0.2813 0.661 0.832 0 0.000 0.000 0.168
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782736 1 0.3333 0.608 0.788 0 0.000 0.208 0.004
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782738 1 0.3333 0.608 0.788 0 0.000 0.208 0.004
#> GSM782739 1 0.2813 0.661 0.832 0 0.000 0.000 0.168
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782741 1 0.2813 0.661 0.832 0 0.000 0.000 0.168
#> GSM782742 3 0.0000 0.966 0.000 0 1.000 0.000 0.000
#> GSM782743 3 0.0000 0.966 0.000 0 1.000 0.000 0.000
#> GSM782744 3 0.5131 0.501 0.000 0 0.588 0.048 0.364
#> GSM782745 5 0.4088 1.000 0.368 0 0.000 0.000 0.632
#> GSM782746 2 0.0000 1.000 0.000 1 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
#> GSM782696 1 0.0000 0.8217 1.000 0 0 0.000 0 0.000
#> GSM782697 1 0.0000 0.8217 1.000 0 0 0.000 0 0.000
#> GSM782698 1 0.3422 0.6811 0.792 0 0 0.040 0 0.168
#> GSM782699 1 0.0000 0.8217 1.000 0 0 0.000 0 0.000
#> GSM782700 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782701 1 0.0000 0.8217 1.000 0 0 0.000 0 0.000
#> GSM782702 1 0.0000 0.8217 1.000 0 0 0.000 0 0.000
#> GSM782703 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782704 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782705 1 0.0547 0.8140 0.980 0 0 0.000 0 0.020
#> GSM782706 1 0.1863 0.7844 0.896 0 0 0.000 0 0.104
#> GSM782707 1 0.0000 0.8217 1.000 0 0 0.000 0 0.000
#> GSM782708 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782709 1 0.1714 0.7922 0.908 0 0 0.000 0 0.092
#> GSM782710 1 0.3847 0.0436 0.544 0 0 0.000 0 0.456
#> GSM782711 1 0.0000 0.8217 1.000 0 0 0.000 0 0.000
#> GSM782712 1 0.0000 0.8217 1.000 0 0 0.000 0 0.000
#> GSM782713 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782714 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782715 1 0.4046 0.6332 0.748 0 0 0.084 0 0.168
#> GSM782716 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782717 1 0.2969 0.6834 0.776 0 0 0.000 0 0.224
#> GSM782718 1 0.3612 0.6745 0.780 0 0 0.052 0 0.168
#> GSM782719 1 0.0000 0.8217 1.000 0 0 0.000 0 0.000
#> GSM782720 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782721 1 0.1863 0.7844 0.896 0 0 0.000 0 0.104
#> GSM782722 4 0.0000 1.0000 0.000 0 0 1.000 0 0.000
#> GSM782723 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782724 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782725 4 0.0000 1.0000 0.000 0 0 1.000 0 0.000
#> GSM782726 6 0.2527 1.0000 0.168 0 0 0.000 0 0.832
#> GSM782727 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782728 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782729 4 0.0000 1.0000 0.000 0 0 1.000 0 0.000
#> GSM782730 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782731 1 0.2969 0.6834 0.776 0 0 0.000 0 0.224
#> GSM782732 1 0.2969 0.6834 0.776 0 0 0.000 0 0.224
#> GSM782733 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782734 1 0.2969 0.6834 0.776 0 0 0.000 0 0.224
#> GSM782735 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782736 1 0.3612 0.6694 0.780 0 0 0.052 0 0.168
#> GSM782737 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782738 1 0.3612 0.6745 0.780 0 0 0.052 0 0.168
#> GSM782739 1 0.2969 0.6834 0.776 0 0 0.000 0 0.224
#> GSM782740 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782741 1 0.2969 0.6834 0.776 0 0 0.000 0 0.224
#> GSM782742 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782743 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782744 5 0.0000 0.0000 0.000 0 0 0.000 1 0.000
#> GSM782745 6 0.2527 1.0000 0.168 0 0 0.000 0 0.832
#> GSM782746 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> CV:hclust 51 0.648 2
#> CV:hclust 51 0.642 3
#> CV:hclust 49 0.494 4
#> CV:hclust 50 0.711 5
#> CV:hclust 49 0.631 6
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 51941 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.506 0.815 0.854 0.3229 0.704 0.704
#> 3 3 1.000 0.991 0.964 0.7049 0.718 0.599
#> 4 4 0.727 0.868 0.874 0.1875 1.000 1.000
#> 5 5 0.695 0.561 0.697 0.1158 0.817 0.566
#> 6 6 0.713 0.781 0.801 0.0781 0.869 0.536
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
#> GSM782696 1 0.000 0.839 1.000 0.000
#> GSM782697 1 0.000 0.839 1.000 0.000
#> GSM782698 1 0.000 0.839 1.000 0.000
#> GSM782699 1 0.000 0.839 1.000 0.000
#> GSM782700 2 0.936 1.000 0.352 0.648
#> GSM782701 1 0.000 0.839 1.000 0.000
#> GSM782702 1 0.000 0.839 1.000 0.000
#> GSM782703 1 0.939 0.617 0.644 0.356
#> GSM782704 1 0.939 0.617 0.644 0.356
#> GSM782705 1 0.000 0.839 1.000 0.000
#> GSM782706 1 0.000 0.839 1.000 0.000
#> GSM782707 1 0.000 0.839 1.000 0.000
#> GSM782708 1 0.939 0.617 0.644 0.356
#> GSM782709 1 0.000 0.839 1.000 0.000
#> GSM782710 1 0.000 0.839 1.000 0.000
#> GSM782711 1 0.000 0.839 1.000 0.000
#> GSM782712 1 0.000 0.839 1.000 0.000
#> GSM782713 1 0.939 0.617 0.644 0.356
#> GSM782714 2 0.936 1.000 0.352 0.648
#> GSM782715 1 0.000 0.839 1.000 0.000
#> GSM782716 1 0.939 0.617 0.644 0.356
#> GSM782717 1 0.000 0.839 1.000 0.000
#> GSM782718 1 0.000 0.839 1.000 0.000
#> GSM782719 1 0.000 0.839 1.000 0.000
#> GSM782720 1 0.939 0.617 0.644 0.356
#> GSM782721 1 0.000 0.839 1.000 0.000
#> GSM782722 1 0.000 0.839 1.000 0.000
#> GSM782723 2 0.936 1.000 0.352 0.648
#> GSM782724 2 0.936 1.000 0.352 0.648
#> GSM782725 1 0.000 0.839 1.000 0.000
#> GSM782726 1 0.000 0.839 1.000 0.000
#> GSM782727 1 0.939 0.617 0.644 0.356
#> GSM782728 2 0.936 1.000 0.352 0.648
#> GSM782729 1 0.000 0.839 1.000 0.000
#> GSM782730 1 0.939 0.617 0.644 0.356
#> GSM782731 1 0.000 0.839 1.000 0.000
#> GSM782732 1 0.000 0.839 1.000 0.000
#> GSM782733 1 0.939 0.617 0.644 0.356
#> GSM782734 1 0.000 0.839 1.000 0.000
#> GSM782735 2 0.936 1.000 0.352 0.648
#> GSM782736 1 0.000 0.839 1.000 0.000
#> GSM782737 2 0.936 1.000 0.352 0.648
#> GSM782738 1 0.000 0.839 1.000 0.000
#> GSM782739 1 0.000 0.839 1.000 0.000
#> GSM782740 2 0.936 1.000 0.352 0.648
#> GSM782741 1 0.000 0.839 1.000 0.000
#> GSM782742 1 0.939 0.617 0.644 0.356
#> GSM782743 1 0.939 0.617 0.644 0.356
#> GSM782744 1 0.939 0.617 0.644 0.356
#> GSM782745 1 0.000 0.839 1.000 0.000
#> GSM782746 2 0.936 1.000 0.352 0.648
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0.000 1.000 1.000 0.000 0.000
#> GSM782697 1 0.000 1.000 1.000 0.000 0.000
#> GSM782698 1 0.000 1.000 1.000 0.000 0.000
#> GSM782699 1 0.000 1.000 1.000 0.000 0.000
#> GSM782700 2 0.216 0.991 0.064 0.936 0.000
#> GSM782701 1 0.000 1.000 1.000 0.000 0.000
#> GSM782702 1 0.000 1.000 1.000 0.000 0.000
#> GSM782703 3 0.378 0.974 0.064 0.044 0.892
#> GSM782704 3 0.429 0.972 0.064 0.064 0.872
#> GSM782705 1 0.000 1.000 1.000 0.000 0.000
#> GSM782706 1 0.000 1.000 1.000 0.000 0.000
#> GSM782707 1 0.000 1.000 1.000 0.000 0.000
#> GSM782708 3 0.429 0.972 0.064 0.064 0.872
#> GSM782709 1 0.000 1.000 1.000 0.000 0.000
#> GSM782710 1 0.000 1.000 1.000 0.000 0.000
#> GSM782711 1 0.000 1.000 1.000 0.000 0.000
#> GSM782712 1 0.000 1.000 1.000 0.000 0.000
#> GSM782713 3 0.216 0.975 0.064 0.000 0.936
#> GSM782714 2 0.216 0.991 0.064 0.936 0.000
#> GSM782715 1 0.000 1.000 1.000 0.000 0.000
#> GSM782716 3 0.429 0.972 0.064 0.064 0.872
#> GSM782717 1 0.000 1.000 1.000 0.000 0.000
#> GSM782718 1 0.000 1.000 1.000 0.000 0.000
#> GSM782719 1 0.000 1.000 1.000 0.000 0.000
#> GSM782720 3 0.216 0.975 0.064 0.000 0.936
#> GSM782721 1 0.000 1.000 1.000 0.000 0.000
#> GSM782722 1 0.000 1.000 1.000 0.000 0.000
#> GSM782723 2 0.216 0.991 0.064 0.936 0.000
#> GSM782724 2 0.305 0.983 0.064 0.916 0.020
#> GSM782725 1 0.000 1.000 1.000 0.000 0.000
#> GSM782726 1 0.000 1.000 1.000 0.000 0.000
#> GSM782727 3 0.216 0.975 0.064 0.000 0.936
#> GSM782728 2 0.216 0.991 0.064 0.936 0.000
#> GSM782729 1 0.000 1.000 1.000 0.000 0.000
#> GSM782730 3 0.216 0.975 0.064 0.000 0.936
#> GSM782731 1 0.000 1.000 1.000 0.000 0.000
#> GSM782732 1 0.000 1.000 1.000 0.000 0.000
#> GSM782733 3 0.429 0.972 0.064 0.064 0.872
#> GSM782734 1 0.000 1.000 1.000 0.000 0.000
#> GSM782735 2 0.378 0.974 0.064 0.892 0.044
#> GSM782736 1 0.000 1.000 1.000 0.000 0.000
#> GSM782737 2 0.216 0.991 0.064 0.936 0.000
#> GSM782738 1 0.000 1.000 1.000 0.000 0.000
#> GSM782739 1 0.000 1.000 1.000 0.000 0.000
#> GSM782740 2 0.216 0.991 0.064 0.936 0.000
#> GSM782741 1 0.000 1.000 1.000 0.000 0.000
#> GSM782742 3 0.216 0.975 0.064 0.000 0.936
#> GSM782743 3 0.429 0.972 0.064 0.064 0.872
#> GSM782744 3 0.216 0.975 0.064 0.000 0.936
#> GSM782745 1 0.000 1.000 1.000 0.000 0.000
#> GSM782746 2 0.378 0.974 0.064 0.892 0.044
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.3311 0.861 0.828 0.000 0.000 NA
#> GSM782697 1 0.1716 0.864 0.936 0.000 0.000 NA
#> GSM782698 1 0.3907 0.842 0.768 0.000 0.000 NA
#> GSM782699 1 0.2011 0.866 0.920 0.000 0.000 NA
#> GSM782700 2 0.0188 0.969 0.000 0.996 0.000 NA
#> GSM782701 1 0.3123 0.863 0.844 0.000 0.000 NA
#> GSM782702 1 0.1716 0.864 0.936 0.000 0.000 NA
#> GSM782703 3 0.3695 0.912 0.016 0.000 0.828 NA
#> GSM782704 3 0.4214 0.908 0.016 0.000 0.780 NA
#> GSM782705 1 0.2589 0.863 0.884 0.000 0.000 NA
#> GSM782706 1 0.3311 0.861 0.828 0.000 0.000 NA
#> GSM782707 1 0.3311 0.861 0.828 0.000 0.000 NA
#> GSM782708 3 0.4214 0.908 0.016 0.000 0.780 NA
#> GSM782709 1 0.1867 0.864 0.928 0.000 0.000 NA
#> GSM782710 1 0.1474 0.860 0.948 0.000 0.000 NA
#> GSM782711 1 0.1792 0.864 0.932 0.000 0.000 NA
#> GSM782712 1 0.1792 0.864 0.932 0.000 0.000 NA
#> GSM782713 3 0.0592 0.913 0.016 0.000 0.984 NA
#> GSM782714 2 0.0336 0.969 0.000 0.992 0.000 NA
#> GSM782715 1 0.3688 0.826 0.792 0.000 0.000 NA
#> GSM782716 3 0.4214 0.908 0.016 0.000 0.780 NA
#> GSM782717 1 0.1557 0.860 0.944 0.000 0.000 NA
#> GSM782718 1 0.3649 0.828 0.796 0.000 0.000 NA
#> GSM782719 1 0.3311 0.861 0.828 0.000 0.000 NA
#> GSM782720 3 0.0592 0.913 0.016 0.000 0.984 NA
#> GSM782721 1 0.3311 0.861 0.828 0.000 0.000 NA
#> GSM782722 1 0.4992 0.588 0.524 0.000 0.000 NA
#> GSM782723 2 0.0336 0.969 0.000 0.992 0.000 NA
#> GSM782724 2 0.2060 0.947 0.000 0.932 0.016 NA
#> GSM782725 1 0.4999 0.583 0.508 0.000 0.000 NA
#> GSM782726 1 0.1557 0.860 0.944 0.000 0.000 NA
#> GSM782727 3 0.0592 0.913 0.016 0.000 0.984 NA
#> GSM782728 2 0.0000 0.969 0.000 1.000 0.000 NA
#> GSM782729 1 0.4999 0.583 0.508 0.000 0.000 NA
#> GSM782730 3 0.0592 0.913 0.016 0.000 0.984 NA
#> GSM782731 1 0.1716 0.859 0.936 0.000 0.000 NA
#> GSM782732 1 0.1716 0.859 0.936 0.000 0.000 NA
#> GSM782733 3 0.4214 0.908 0.016 0.000 0.780 NA
#> GSM782734 1 0.1557 0.860 0.944 0.000 0.000 NA
#> GSM782735 2 0.2814 0.917 0.000 0.868 0.000 NA
#> GSM782736 1 0.4643 0.728 0.656 0.000 0.000 NA
#> GSM782737 2 0.0336 0.969 0.000 0.992 0.000 NA
#> GSM782738 1 0.3688 0.827 0.792 0.000 0.000 NA
#> GSM782739 1 0.1557 0.860 0.944 0.000 0.000 NA
#> GSM782740 2 0.0000 0.969 0.000 1.000 0.000 NA
#> GSM782741 1 0.1557 0.860 0.944 0.000 0.000 NA
#> GSM782742 3 0.0592 0.913 0.016 0.000 0.984 NA
#> GSM782743 3 0.4214 0.908 0.016 0.000 0.780 NA
#> GSM782744 3 0.1510 0.903 0.016 0.000 0.956 NA
#> GSM782745 1 0.1557 0.860 0.944 0.000 0.000 NA
#> GSM782746 2 0.2814 0.917 0.000 0.868 0.000 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 5 0.4227 0.8950 0.420 0.000 0.000 0.000 0.580
#> GSM782697 1 0.4552 -0.6551 0.524 0.000 0.000 0.008 0.468
#> GSM782698 5 0.4862 0.7959 0.364 0.000 0.000 0.032 0.604
#> GSM782699 5 0.4562 0.7035 0.492 0.000 0.000 0.008 0.500
#> GSM782700 2 0.0451 0.9540 0.000 0.988 0.004 0.000 0.008
#> GSM782701 5 0.4604 0.8933 0.428 0.000 0.000 0.012 0.560
#> GSM782702 1 0.4443 -0.6571 0.524 0.000 0.000 0.004 0.472
#> GSM782703 3 0.2349 0.8677 0.004 0.000 0.900 0.012 0.084
#> GSM782704 3 0.0162 0.8601 0.004 0.000 0.996 0.000 0.000
#> GSM782705 1 0.4882 -0.4789 0.532 0.000 0.000 0.024 0.444
#> GSM782706 5 0.4713 0.8584 0.440 0.000 0.000 0.016 0.544
#> GSM782707 5 0.4367 0.8961 0.416 0.000 0.000 0.004 0.580
#> GSM782708 3 0.0162 0.8601 0.004 0.000 0.996 0.000 0.000
#> GSM782709 1 0.4590 -0.5662 0.568 0.000 0.000 0.012 0.420
#> GSM782710 1 0.1410 0.4616 0.940 0.000 0.000 0.000 0.060
#> GSM782711 1 0.4560 -0.7011 0.508 0.000 0.000 0.008 0.484
#> GSM782712 1 0.4560 -0.7057 0.508 0.000 0.000 0.008 0.484
#> GSM782713 3 0.4910 0.8649 0.004 0.000 0.712 0.080 0.204
#> GSM782714 2 0.0000 0.9571 0.000 1.000 0.000 0.000 0.000
#> GSM782715 1 0.6426 -0.0447 0.468 0.000 0.000 0.184 0.348
#> GSM782716 3 0.0162 0.8601 0.004 0.000 0.996 0.000 0.000
#> GSM782717 1 0.0000 0.5076 1.000 0.000 0.000 0.000 0.000
#> GSM782718 1 0.6402 -0.0638 0.472 0.000 0.000 0.180 0.348
#> GSM782719 5 0.4590 0.8976 0.420 0.000 0.000 0.012 0.568
#> GSM782720 3 0.4910 0.8649 0.004 0.000 0.712 0.080 0.204
#> GSM782721 5 0.4713 0.8584 0.440 0.000 0.000 0.016 0.544
#> GSM782722 4 0.5400 0.9770 0.272 0.000 0.000 0.632 0.096
#> GSM782723 2 0.0000 0.9571 0.000 1.000 0.000 0.000 0.000
#> GSM782724 2 0.2597 0.9029 0.000 0.884 0.000 0.092 0.024
#> GSM782725 4 0.5296 0.9885 0.280 0.000 0.000 0.636 0.084
#> GSM782726 1 0.0000 0.5076 1.000 0.000 0.000 0.000 0.000
#> GSM782727 3 0.4910 0.8649 0.004 0.000 0.712 0.080 0.204
#> GSM782728 2 0.0000 0.9571 0.000 1.000 0.000 0.000 0.000
#> GSM782729 4 0.5296 0.9885 0.280 0.000 0.000 0.636 0.084
#> GSM782730 3 0.4910 0.8649 0.004 0.000 0.712 0.080 0.204
#> GSM782731 1 0.0992 0.4996 0.968 0.000 0.000 0.024 0.008
#> GSM782732 1 0.0865 0.5010 0.972 0.000 0.000 0.024 0.004
#> GSM782733 3 0.0162 0.8601 0.004 0.000 0.996 0.000 0.000
#> GSM782734 1 0.0000 0.5076 1.000 0.000 0.000 0.000 0.000
#> GSM782735 2 0.3390 0.8870 0.000 0.840 0.000 0.060 0.100
#> GSM782736 1 0.6630 -0.4690 0.404 0.000 0.000 0.376 0.220
#> GSM782737 2 0.0000 0.9571 0.000 1.000 0.000 0.000 0.000
#> GSM782738 1 0.6386 -0.0412 0.480 0.000 0.000 0.180 0.340
#> GSM782739 1 0.0162 0.5065 0.996 0.000 0.000 0.004 0.000
#> GSM782740 2 0.0000 0.9571 0.000 1.000 0.000 0.000 0.000
#> GSM782741 1 0.0000 0.5076 1.000 0.000 0.000 0.000 0.000
#> GSM782742 3 0.4910 0.8649 0.004 0.000 0.712 0.080 0.204
#> GSM782743 3 0.0162 0.8601 0.004 0.000 0.996 0.000 0.000
#> GSM782744 3 0.5689 0.8080 0.004 0.000 0.644 0.192 0.160
#> GSM782745 1 0.0000 0.5076 1.000 0.000 0.000 0.000 0.000
#> GSM782746 2 0.3390 0.8870 0.000 0.840 0.000 0.060 0.100
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM782696 1 0.0291 0.754 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM782697 1 0.2647 0.741 0.876 0.000 0.000 0.016 0.020 0.088
#> GSM782698 1 0.1657 0.703 0.928 0.000 0.000 0.016 0.056 0.000
#> GSM782699 1 0.2196 0.760 0.908 0.000 0.000 0.016 0.020 0.056
#> GSM782700 2 0.0653 0.925 0.000 0.980 0.000 0.004 0.004 0.012
#> GSM782701 1 0.1528 0.756 0.944 0.000 0.000 0.028 0.016 0.012
#> GSM782702 1 0.2006 0.744 0.892 0.000 0.000 0.000 0.004 0.104
#> GSM782703 3 0.3270 0.803 0.000 0.000 0.844 0.088 0.040 0.028
#> GSM782704 3 0.0547 0.787 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM782705 1 0.4259 0.325 0.752 0.000 0.000 0.016 0.160 0.072
#> GSM782706 1 0.3880 0.626 0.804 0.000 0.000 0.032 0.088 0.076
#> GSM782707 1 0.0777 0.754 0.972 0.000 0.000 0.024 0.004 0.000
#> GSM782708 3 0.0000 0.788 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM782709 1 0.3168 0.669 0.804 0.000 0.000 0.000 0.024 0.172
#> GSM782710 6 0.3309 0.832 0.280 0.000 0.000 0.000 0.000 0.720
#> GSM782711 1 0.2182 0.758 0.904 0.000 0.000 0.008 0.020 0.068
#> GSM782712 1 0.2422 0.762 0.892 0.000 0.000 0.024 0.012 0.072
#> GSM782713 3 0.5635 0.801 0.000 0.000 0.612 0.192 0.172 0.024
#> GSM782714 2 0.0146 0.930 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM782715 5 0.5681 0.827 0.432 0.000 0.000 0.016 0.452 0.100
#> GSM782716 3 0.0146 0.788 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM782717 6 0.3136 0.945 0.188 0.000 0.000 0.000 0.016 0.796
#> GSM782718 1 0.5075 -0.843 0.464 0.000 0.000 0.000 0.460 0.076
#> GSM782719 1 0.1168 0.753 0.956 0.000 0.000 0.028 0.016 0.000
#> GSM782720 3 0.5473 0.802 0.000 0.000 0.612 0.204 0.172 0.012
#> GSM782721 1 0.3880 0.626 0.804 0.000 0.000 0.032 0.088 0.076
#> GSM782722 4 0.5683 0.988 0.116 0.000 0.000 0.604 0.244 0.036
#> GSM782723 2 0.0260 0.929 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM782724 2 0.3895 0.816 0.000 0.800 0.000 0.032 0.108 0.060
#> GSM782725 4 0.5708 0.994 0.112 0.000 0.000 0.604 0.244 0.040
#> GSM782726 6 0.2838 0.941 0.188 0.000 0.000 0.000 0.004 0.808
#> GSM782727 3 0.5473 0.802 0.000 0.000 0.612 0.204 0.172 0.012
#> GSM782728 2 0.0000 0.930 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM782729 4 0.5708 0.994 0.112 0.000 0.000 0.604 0.244 0.040
#> GSM782730 3 0.5473 0.802 0.000 0.000 0.612 0.204 0.172 0.012
#> GSM782731 6 0.4314 0.881 0.184 0.000 0.000 0.000 0.096 0.720
#> GSM782732 6 0.4314 0.881 0.184 0.000 0.000 0.000 0.096 0.720
#> GSM782733 3 0.0000 0.788 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM782734 6 0.2697 0.942 0.188 0.000 0.000 0.000 0.000 0.812
#> GSM782735 2 0.4093 0.824 0.000 0.784 0.000 0.080 0.108 0.028
#> GSM782736 5 0.6812 0.550 0.300 0.000 0.000 0.160 0.456 0.084
#> GSM782737 2 0.0260 0.929 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM782738 5 0.5423 0.816 0.440 0.000 0.000 0.004 0.456 0.100
#> GSM782739 6 0.3136 0.945 0.188 0.000 0.000 0.000 0.016 0.796
#> GSM782740 2 0.0000 0.930 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM782741 6 0.3136 0.945 0.188 0.000 0.000 0.000 0.016 0.796
#> GSM782742 3 0.5473 0.802 0.000 0.000 0.612 0.204 0.172 0.012
#> GSM782743 3 0.0146 0.788 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM782744 3 0.6338 0.731 0.000 0.000 0.540 0.156 0.244 0.060
#> GSM782745 6 0.2838 0.941 0.188 0.000 0.000 0.000 0.004 0.808
#> GSM782746 2 0.4093 0.824 0.000 0.784 0.000 0.080 0.108 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> CV:kmeans 51 0.648 2
#> CV:kmeans 51 0.642 3
#> CV:kmeans 51 0.642 4
#> CV:kmeans 39 0.425 5
#> CV:kmeans 49 0.394 6
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 51941 rows and 51 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 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 0.633 0.897 0.915 0.4236 0.506 0.506
#> 3 3 1.000 1.000 1.000 0.3674 0.915 0.833
#> 4 4 0.731 0.435 0.766 0.2443 0.977 0.946
#> 5 5 0.947 0.922 0.956 0.1099 0.780 0.457
#> 6 6 0.871 0.876 0.910 0.0317 0.969 0.846
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 3
There is also optional best \(k\) = 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM782696 1 0.000 1.000 1.00 0.00
#> GSM782697 1 0.000 1.000 1.00 0.00
#> GSM782698 1 0.000 1.000 1.00 0.00
#> GSM782699 1 0.000 1.000 1.00 0.00
#> GSM782700 2 0.000 0.756 0.00 1.00
#> GSM782701 1 0.000 1.000 1.00 0.00
#> GSM782702 1 0.000 1.000 1.00 0.00
#> GSM782703 2 0.943 0.747 0.36 0.64
#> GSM782704 2 0.943 0.747 0.36 0.64
#> GSM782705 1 0.000 1.000 1.00 0.00
#> GSM782706 1 0.000 1.000 1.00 0.00
#> GSM782707 1 0.000 1.000 1.00 0.00
#> GSM782708 2 0.943 0.747 0.36 0.64
#> GSM782709 1 0.000 1.000 1.00 0.00
#> GSM782710 1 0.000 1.000 1.00 0.00
#> GSM782711 1 0.000 1.000 1.00 0.00
#> GSM782712 1 0.000 1.000 1.00 0.00
#> GSM782713 2 0.943 0.747 0.36 0.64
#> GSM782714 2 0.000 0.756 0.00 1.00
#> GSM782715 1 0.000 1.000 1.00 0.00
#> GSM782716 2 0.943 0.747 0.36 0.64
#> GSM782717 1 0.000 1.000 1.00 0.00
#> GSM782718 1 0.000 1.000 1.00 0.00
#> GSM782719 1 0.000 1.000 1.00 0.00
#> GSM782720 2 0.943 0.747 0.36 0.64
#> GSM782721 1 0.000 1.000 1.00 0.00
#> GSM782722 1 0.000 1.000 1.00 0.00
#> GSM782723 2 0.000 0.756 0.00 1.00
#> GSM782724 2 0.000 0.756 0.00 1.00
#> GSM782725 1 0.000 1.000 1.00 0.00
#> GSM782726 1 0.000 1.000 1.00 0.00
#> GSM782727 2 0.943 0.747 0.36 0.64
#> GSM782728 2 0.000 0.756 0.00 1.00
#> GSM782729 1 0.000 1.000 1.00 0.00
#> GSM782730 2 0.943 0.747 0.36 0.64
#> GSM782731 1 0.000 1.000 1.00 0.00
#> GSM782732 1 0.000 1.000 1.00 0.00
#> GSM782733 2 0.943 0.747 0.36 0.64
#> GSM782734 1 0.000 1.000 1.00 0.00
#> GSM782735 2 0.000 0.756 0.00 1.00
#> GSM782736 1 0.000 1.000 1.00 0.00
#> GSM782737 2 0.000 0.756 0.00 1.00
#> GSM782738 1 0.000 1.000 1.00 0.00
#> GSM782739 1 0.000 1.000 1.00 0.00
#> GSM782740 2 0.000 0.756 0.00 1.00
#> GSM782741 1 0.000 1.000 1.00 0.00
#> GSM782742 2 0.943 0.747 0.36 0.64
#> GSM782743 2 0.943 0.747 0.36 0.64
#> GSM782744 2 0.943 0.747 0.36 0.64
#> GSM782745 1 0.000 1.000 1.00 0.00
#> GSM782746 2 0.000 0.756 0.00 1.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0 1 1 0 0
#> GSM782697 1 0 1 1 0 0
#> GSM782698 1 0 1 1 0 0
#> GSM782699 1 0 1 1 0 0
#> GSM782700 2 0 1 0 1 0
#> GSM782701 1 0 1 1 0 0
#> GSM782702 1 0 1 1 0 0
#> GSM782703 3 0 1 0 0 1
#> GSM782704 3 0 1 0 0 1
#> GSM782705 1 0 1 1 0 0
#> GSM782706 1 0 1 1 0 0
#> GSM782707 1 0 1 1 0 0
#> GSM782708 3 0 1 0 0 1
#> GSM782709 1 0 1 1 0 0
#> GSM782710 1 0 1 1 0 0
#> GSM782711 1 0 1 1 0 0
#> GSM782712 1 0 1 1 0 0
#> GSM782713 3 0 1 0 0 1
#> GSM782714 2 0 1 0 1 0
#> GSM782715 1 0 1 1 0 0
#> GSM782716 3 0 1 0 0 1
#> GSM782717 1 0 1 1 0 0
#> GSM782718 1 0 1 1 0 0
#> GSM782719 1 0 1 1 0 0
#> GSM782720 3 0 1 0 0 1
#> GSM782721 1 0 1 1 0 0
#> GSM782722 1 0 1 1 0 0
#> GSM782723 2 0 1 0 1 0
#> GSM782724 2 0 1 0 1 0
#> GSM782725 1 0 1 1 0 0
#> GSM782726 1 0 1 1 0 0
#> GSM782727 3 0 1 0 0 1
#> GSM782728 2 0 1 0 1 0
#> GSM782729 1 0 1 1 0 0
#> GSM782730 3 0 1 0 0 1
#> GSM782731 1 0 1 1 0 0
#> GSM782732 1 0 1 1 0 0
#> GSM782733 3 0 1 0 0 1
#> GSM782734 1 0 1 1 0 0
#> GSM782735 2 0 1 0 1 0
#> GSM782736 1 0 1 1 0 0
#> GSM782737 2 0 1 0 1 0
#> GSM782738 1 0 1 1 0 0
#> GSM782739 1 0 1 1 0 0
#> GSM782740 2 0 1 0 1 0
#> GSM782741 1 0 1 1 0 0
#> GSM782742 3 0 1 0 0 1
#> GSM782743 3 0 1 0 0 1
#> GSM782744 3 0 1 0 0 1
#> GSM782745 1 0 1 1 0 0
#> GSM782746 2 0 1 0 1 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.445 0.395 0.692 0 0 0.308
#> GSM782697 1 0.496 0.250 0.552 0 0 0.448
#> GSM782698 1 0.422 0.389 0.728 0 0 0.272
#> GSM782699 1 0.456 0.393 0.672 0 0 0.328
#> GSM782700 2 0.000 1.000 0.000 1 0 0.000
#> GSM782701 1 0.460 0.388 0.664 0 0 0.336
#> GSM782702 1 0.496 0.250 0.552 0 0 0.448
#> GSM782703 3 0.000 1.000 0.000 0 1 0.000
#> GSM782704 3 0.000 1.000 0.000 0 1 0.000
#> GSM782705 1 0.000 0.253 1.000 0 0 0.000
#> GSM782706 1 0.456 0.393 0.672 0 0 0.328
#> GSM782707 1 0.454 0.394 0.676 0 0 0.324
#> GSM782708 3 0.000 1.000 0.000 0 1 0.000
#> GSM782709 1 0.499 0.207 0.532 0 0 0.468
#> GSM782710 4 0.489 0.000 0.412 0 0 0.588
#> GSM782711 1 0.476 0.357 0.628 0 0 0.372
#> GSM782712 1 0.483 0.335 0.608 0 0 0.392
#> GSM782713 3 0.000 1.000 0.000 0 1 0.000
#> GSM782714 2 0.000 1.000 0.000 1 0 0.000
#> GSM782715 1 0.000 0.253 1.000 0 0 0.000
#> GSM782716 3 0.000 1.000 0.000 0 1 0.000
#> GSM782717 1 0.499 -0.675 0.532 0 0 0.468
#> GSM782718 1 0.000 0.253 1.000 0 0 0.000
#> GSM782719 1 0.454 0.394 0.676 0 0 0.324
#> GSM782720 3 0.000 1.000 0.000 0 1 0.000
#> GSM782721 1 0.456 0.393 0.672 0 0 0.328
#> GSM782722 1 0.416 0.215 0.736 0 0 0.264
#> GSM782723 2 0.000 1.000 0.000 1 0 0.000
#> GSM782724 2 0.000 1.000 0.000 1 0 0.000
#> GSM782725 1 0.422 0.208 0.728 0 0 0.272
#> GSM782726 1 0.499 -0.675 0.532 0 0 0.468
#> GSM782727 3 0.000 1.000 0.000 0 1 0.000
#> GSM782728 2 0.000 1.000 0.000 1 0 0.000
#> GSM782729 1 0.422 0.208 0.728 0 0 0.272
#> GSM782730 3 0.000 1.000 0.000 0 1 0.000
#> GSM782731 1 0.488 -0.587 0.592 0 0 0.408
#> GSM782732 1 0.488 -0.587 0.592 0 0 0.408
#> GSM782733 3 0.000 1.000 0.000 0 1 0.000
#> GSM782734 1 0.499 -0.675 0.532 0 0 0.468
#> GSM782735 2 0.000 1.000 0.000 1 0 0.000
#> GSM782736 1 0.416 0.215 0.736 0 0 0.264
#> GSM782737 2 0.000 1.000 0.000 1 0 0.000
#> GSM782738 1 0.000 0.253 1.000 0 0 0.000
#> GSM782739 1 0.499 -0.675 0.532 0 0 0.468
#> GSM782740 2 0.000 1.000 0.000 1 0 0.000
#> GSM782741 1 0.499 -0.675 0.532 0 0 0.468
#> GSM782742 3 0.000 1.000 0.000 0 1 0.000
#> GSM782743 3 0.000 1.000 0.000 0 1 0.000
#> GSM782744 3 0.000 1.000 0.000 0 1 0.000
#> GSM782745 1 0.499 -0.675 0.532 0 0 0.468
#> GSM782746 2 0.000 1.000 0.000 1 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.0000 0.968 1.000 0 0 0.000 0.000
#> GSM782697 1 0.0000 0.968 1.000 0 0 0.000 0.000
#> GSM782698 1 0.0000 0.968 1.000 0 0 0.000 0.000
#> GSM782699 1 0.0000 0.968 1.000 0 0 0.000 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782701 1 0.0671 0.962 0.980 0 0 0.004 0.016
#> GSM782702 1 0.0771 0.960 0.976 0 0 0.004 0.020
#> GSM782703 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782704 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782705 4 0.4547 0.572 0.400 0 0 0.588 0.012
#> GSM782706 1 0.1638 0.926 0.932 0 0 0.004 0.064
#> GSM782707 1 0.0162 0.967 0.996 0 0 0.004 0.000
#> GSM782708 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782709 1 0.2329 0.854 0.876 0 0 0.000 0.124
#> GSM782710 5 0.1768 0.865 0.072 0 0 0.004 0.924
#> GSM782711 1 0.0000 0.968 1.000 0 0 0.000 0.000
#> GSM782712 1 0.0324 0.967 0.992 0 0 0.004 0.004
#> GSM782713 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782715 4 0.4777 0.728 0.268 0 0 0.680 0.052
#> GSM782716 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782717 5 0.0000 0.925 0.000 0 0 0.000 1.000
#> GSM782718 4 0.4546 0.712 0.304 0 0 0.668 0.028
#> GSM782719 1 0.0000 0.968 1.000 0 0 0.000 0.000
#> GSM782720 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782721 1 0.1638 0.926 0.932 0 0 0.004 0.064
#> GSM782722 4 0.0162 0.762 0.000 0 0 0.996 0.004
#> GSM782723 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782725 4 0.0162 0.762 0.000 0 0 0.996 0.004
#> GSM782726 5 0.0000 0.925 0.000 0 0 0.000 1.000
#> GSM782727 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782729 4 0.0162 0.762 0.000 0 0 0.996 0.004
#> GSM782730 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782731 5 0.3210 0.742 0.000 0 0 0.212 0.788
#> GSM782732 5 0.3274 0.731 0.000 0 0 0.220 0.780
#> GSM782733 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782734 5 0.0000 0.925 0.000 0 0 0.000 1.000
#> GSM782735 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782736 4 0.0162 0.762 0.000 0 0 0.996 0.004
#> GSM782737 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782738 4 0.4914 0.730 0.260 0 0 0.676 0.064
#> GSM782739 5 0.0290 0.923 0.000 0 0 0.008 0.992
#> GSM782740 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782741 5 0.0162 0.924 0.004 0 0 0.000 0.996
#> GSM782742 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782743 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782744 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782745 5 0.0000 0.925 0.000 0 0 0.000 1.000
#> GSM782746 2 0.0000 1.000 0.000 1 0 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM782696 1 0.1471 0.880 0.932 0 0.000 0.004 0.064 0.000
#> GSM782697 1 0.3078 0.845 0.836 0 0.000 0.056 0.108 0.000
#> GSM782698 1 0.3316 0.837 0.812 0 0.000 0.052 0.136 0.000
#> GSM782699 1 0.3377 0.834 0.808 0 0.000 0.056 0.136 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782701 1 0.1700 0.880 0.936 0 0.000 0.024 0.028 0.012
#> GSM782702 1 0.1767 0.882 0.932 0 0.000 0.012 0.020 0.036
#> GSM782703 3 0.0000 0.995 0.000 0 1.000 0.000 0.000 0.000
#> GSM782704 3 0.0405 0.993 0.000 0 0.988 0.008 0.004 0.000
#> GSM782705 5 0.3323 0.605 0.204 0 0.000 0.008 0.780 0.008
#> GSM782706 1 0.3776 0.795 0.792 0 0.000 0.036 0.148 0.024
#> GSM782707 1 0.0891 0.884 0.968 0 0.000 0.008 0.024 0.000
#> GSM782708 3 0.0405 0.993 0.000 0 0.988 0.008 0.004 0.000
#> GSM782709 1 0.4225 0.808 0.780 0 0.000 0.056 0.056 0.108
#> GSM782710 6 0.2933 0.779 0.092 0 0.000 0.032 0.016 0.860
#> GSM782711 1 0.2420 0.868 0.884 0 0.000 0.040 0.076 0.000
#> GSM782712 1 0.1906 0.881 0.924 0 0.000 0.036 0.032 0.008
#> GSM782713 3 0.0000 0.995 0.000 0 1.000 0.000 0.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782715 5 0.3107 0.676 0.080 0 0.000 0.072 0.844 0.004
#> GSM782716 3 0.0405 0.993 0.000 0 0.988 0.008 0.004 0.000
#> GSM782717 6 0.2420 0.838 0.004 0 0.000 0.004 0.128 0.864
#> GSM782718 5 0.2964 0.688 0.108 0 0.000 0.040 0.848 0.004
#> GSM782719 1 0.0622 0.885 0.980 0 0.000 0.008 0.012 0.000
#> GSM782720 3 0.0000 0.995 0.000 0 1.000 0.000 0.000 0.000
#> GSM782721 1 0.3776 0.795 0.792 0 0.000 0.036 0.148 0.024
#> GSM782722 4 0.2378 0.984 0.000 0 0.000 0.848 0.152 0.000
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782725 4 0.2260 0.992 0.000 0 0.000 0.860 0.140 0.000
#> GSM782726 6 0.0790 0.866 0.000 0 0.000 0.032 0.000 0.968
#> GSM782727 3 0.0000 0.995 0.000 0 1.000 0.000 0.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782729 4 0.2260 0.992 0.000 0 0.000 0.860 0.140 0.000
#> GSM782730 3 0.0000 0.995 0.000 0 1.000 0.000 0.000 0.000
#> GSM782731 5 0.3717 0.381 0.000 0 0.000 0.000 0.616 0.384
#> GSM782732 5 0.3695 0.399 0.000 0 0.000 0.000 0.624 0.376
#> GSM782733 3 0.0405 0.993 0.000 0 0.988 0.008 0.004 0.000
#> GSM782734 6 0.0777 0.873 0.004 0 0.000 0.000 0.024 0.972
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782736 5 0.3508 0.423 0.004 0 0.000 0.292 0.704 0.000
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782738 5 0.3065 0.690 0.088 0 0.000 0.048 0.852 0.012
#> GSM782739 6 0.3104 0.743 0.004 0 0.000 0.004 0.204 0.788
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782741 6 0.2325 0.855 0.008 0 0.000 0.008 0.100 0.884
#> GSM782742 3 0.0000 0.995 0.000 0 1.000 0.000 0.000 0.000
#> GSM782743 3 0.0405 0.993 0.000 0 0.988 0.008 0.004 0.000
#> GSM782744 3 0.0000 0.995 0.000 0 1.000 0.000 0.000 0.000
#> GSM782745 6 0.0790 0.866 0.000 0 0.000 0.032 0.000 0.968
#> GSM782746 2 0.0000 1.000 0.000 1 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> CV:skmeans 51 0.493 2
#> CV:skmeans 51 0.642 3
#> CV:skmeans 21 0.529 4
#> CV:skmeans 51 0.502 5
#> CV:skmeans 48 0.422 6
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 51941 rows and 51 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.2972 0.704 0.704
#> 3 3 1.000 1.000 1.000 0.9492 0.718 0.599
#> 4 4 0.860 0.900 0.943 0.1691 0.936 0.849
#> 5 5 0.781 0.623 0.783 0.1004 0.865 0.641
#> 6 6 0.902 0.890 0.950 0.0756 0.907 0.664
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM782696 1 0 1 1 0
#> GSM782697 1 0 1 1 0
#> GSM782698 1 0 1 1 0
#> GSM782699 1 0 1 1 0
#> GSM782700 2 0 1 0 1
#> GSM782701 1 0 1 1 0
#> GSM782702 1 0 1 1 0
#> GSM782703 1 0 1 1 0
#> GSM782704 1 0 1 1 0
#> GSM782705 1 0 1 1 0
#> GSM782706 1 0 1 1 0
#> GSM782707 1 0 1 1 0
#> GSM782708 1 0 1 1 0
#> GSM782709 1 0 1 1 0
#> GSM782710 1 0 1 1 0
#> GSM782711 1 0 1 1 0
#> GSM782712 1 0 1 1 0
#> GSM782713 1 0 1 1 0
#> GSM782714 2 0 1 0 1
#> GSM782715 1 0 1 1 0
#> GSM782716 1 0 1 1 0
#> GSM782717 1 0 1 1 0
#> GSM782718 1 0 1 1 0
#> GSM782719 1 0 1 1 0
#> GSM782720 1 0 1 1 0
#> GSM782721 1 0 1 1 0
#> GSM782722 1 0 1 1 0
#> GSM782723 2 0 1 0 1
#> GSM782724 2 0 1 0 1
#> GSM782725 1 0 1 1 0
#> GSM782726 1 0 1 1 0
#> GSM782727 1 0 1 1 0
#> GSM782728 2 0 1 0 1
#> GSM782729 1 0 1 1 0
#> GSM782730 1 0 1 1 0
#> GSM782731 1 0 1 1 0
#> GSM782732 1 0 1 1 0
#> GSM782733 1 0 1 1 0
#> GSM782734 1 0 1 1 0
#> GSM782735 2 0 1 0 1
#> GSM782736 1 0 1 1 0
#> GSM782737 2 0 1 0 1
#> GSM782738 1 0 1 1 0
#> GSM782739 1 0 1 1 0
#> GSM782740 2 0 1 0 1
#> GSM782741 1 0 1 1 0
#> GSM782742 1 0 1 1 0
#> GSM782743 1 0 1 1 0
#> GSM782744 1 0 1 1 0
#> GSM782745 1 0 1 1 0
#> GSM782746 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0 1 1 0 0
#> GSM782697 1 0 1 1 0 0
#> GSM782698 1 0 1 1 0 0
#> GSM782699 1 0 1 1 0 0
#> GSM782700 2 0 1 0 1 0
#> GSM782701 1 0 1 1 0 0
#> GSM782702 1 0 1 1 0 0
#> GSM782703 3 0 1 0 0 1
#> GSM782704 3 0 1 0 0 1
#> GSM782705 1 0 1 1 0 0
#> GSM782706 1 0 1 1 0 0
#> GSM782707 1 0 1 1 0 0
#> GSM782708 3 0 1 0 0 1
#> GSM782709 1 0 1 1 0 0
#> GSM782710 1 0 1 1 0 0
#> GSM782711 1 0 1 1 0 0
#> GSM782712 1 0 1 1 0 0
#> GSM782713 3 0 1 0 0 1
#> GSM782714 2 0 1 0 1 0
#> GSM782715 1 0 1 1 0 0
#> GSM782716 3 0 1 0 0 1
#> GSM782717 1 0 1 1 0 0
#> GSM782718 1 0 1 1 0 0
#> GSM782719 1 0 1 1 0 0
#> GSM782720 3 0 1 0 0 1
#> GSM782721 1 0 1 1 0 0
#> GSM782722 1 0 1 1 0 0
#> GSM782723 2 0 1 0 1 0
#> GSM782724 2 0 1 0 1 0
#> GSM782725 1 0 1 1 0 0
#> GSM782726 1 0 1 1 0 0
#> GSM782727 3 0 1 0 0 1
#> GSM782728 2 0 1 0 1 0
#> GSM782729 1 0 1 1 0 0
#> GSM782730 3 0 1 0 0 1
#> GSM782731 1 0 1 1 0 0
#> GSM782732 1 0 1 1 0 0
#> GSM782733 3 0 1 0 0 1
#> GSM782734 1 0 1 1 0 0
#> GSM782735 2 0 1 0 1 0
#> GSM782736 1 0 1 1 0 0
#> GSM782737 2 0 1 0 1 0
#> GSM782738 1 0 1 1 0 0
#> GSM782739 1 0 1 1 0 0
#> GSM782740 2 0 1 0 1 0
#> GSM782741 1 0 1 1 0 0
#> GSM782742 3 0 1 0 0 1
#> GSM782743 3 0 1 0 0 1
#> GSM782744 3 0 1 0 0 1
#> GSM782745 1 0 1 1 0 0
#> GSM782746 2 0 1 0 1 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.000 0.876 1.000 0 0 0.000
#> GSM782697 1 0.000 0.876 1.000 0 0 0.000
#> GSM782698 1 0.000 0.876 1.000 0 0 0.000
#> GSM782699 1 0.000 0.876 1.000 0 0 0.000
#> GSM782700 2 0.000 1.000 0.000 1 0 0.000
#> GSM782701 1 0.000 0.876 1.000 0 0 0.000
#> GSM782702 1 0.000 0.876 1.000 0 0 0.000
#> GSM782703 3 0.000 1.000 0.000 0 1 0.000
#> GSM782704 3 0.000 1.000 0.000 0 1 0.000
#> GSM782705 1 0.448 0.691 0.688 0 0 0.312
#> GSM782706 1 0.000 0.876 1.000 0 0 0.000
#> GSM782707 1 0.000 0.876 1.000 0 0 0.000
#> GSM782708 3 0.000 1.000 0.000 0 1 0.000
#> GSM782709 1 0.000 0.876 1.000 0 0 0.000
#> GSM782710 1 0.000 0.876 1.000 0 0 0.000
#> GSM782711 1 0.000 0.876 1.000 0 0 0.000
#> GSM782712 1 0.000 0.876 1.000 0 0 0.000
#> GSM782713 3 0.000 1.000 0.000 0 1 0.000
#> GSM782714 2 0.000 1.000 0.000 1 0 0.000
#> GSM782715 1 0.000 0.876 1.000 0 0 0.000
#> GSM782716 3 0.000 1.000 0.000 0 1 0.000
#> GSM782717 1 0.448 0.691 0.688 0 0 0.312
#> GSM782718 1 0.448 0.691 0.688 0 0 0.312
#> GSM782719 1 0.000 0.876 1.000 0 0 0.000
#> GSM782720 3 0.000 1.000 0.000 0 1 0.000
#> GSM782721 1 0.000 0.876 1.000 0 0 0.000
#> GSM782722 4 0.000 1.000 0.000 0 0 1.000
#> GSM782723 2 0.000 1.000 0.000 1 0 0.000
#> GSM782724 2 0.000 1.000 0.000 1 0 0.000
#> GSM782725 4 0.000 1.000 0.000 0 0 1.000
#> GSM782726 1 0.164 0.860 0.940 0 0 0.060
#> GSM782727 3 0.000 1.000 0.000 0 1 0.000
#> GSM782728 2 0.000 1.000 0.000 1 0 0.000
#> GSM782729 4 0.000 1.000 0.000 0 0 1.000
#> GSM782730 3 0.000 1.000 0.000 0 1 0.000
#> GSM782731 1 0.448 0.691 0.688 0 0 0.312
#> GSM782732 1 0.448 0.691 0.688 0 0 0.312
#> GSM782733 3 0.000 1.000 0.000 0 1 0.000
#> GSM782734 1 0.139 0.864 0.952 0 0 0.048
#> GSM782735 2 0.000 1.000 0.000 1 0 0.000
#> GSM782736 1 0.492 0.501 0.576 0 0 0.424
#> GSM782737 2 0.000 1.000 0.000 1 0 0.000
#> GSM782738 1 0.448 0.691 0.688 0 0 0.312
#> GSM782739 1 0.448 0.691 0.688 0 0 0.312
#> GSM782740 2 0.000 1.000 0.000 1 0 0.000
#> GSM782741 1 0.194 0.853 0.924 0 0 0.076
#> GSM782742 3 0.000 1.000 0.000 0 1 0.000
#> GSM782743 3 0.000 1.000 0.000 0 1 0.000
#> GSM782744 3 0.000 1.000 0.000 0 1 0.000
#> GSM782745 1 0.276 0.826 0.872 0 0 0.128
#> GSM782746 2 0.000 1.000 0.000 1 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.0000 0.79905 1.000 0 0.0 0.000 0.000
#> GSM782697 1 0.0000 0.79905 1.000 0 0.0 0.000 0.000
#> GSM782698 1 0.0000 0.79905 1.000 0 0.0 0.000 0.000
#> GSM782699 1 0.0000 0.79905 1.000 0 0.0 0.000 0.000
#> GSM782700 2 0.0000 1.00000 0.000 1 0.0 0.000 0.000
#> GSM782701 1 0.0000 0.79905 1.000 0 0.0 0.000 0.000
#> GSM782702 1 0.0000 0.79905 1.000 0 0.0 0.000 0.000
#> GSM782703 3 0.0000 1.00000 0.000 0 1.0 0.000 0.000
#> GSM782704 3 0.0000 1.00000 0.000 0 1.0 0.000 0.000
#> GSM782705 1 0.6445 0.15834 0.496 0 0.0 0.288 0.216
#> GSM782706 1 0.2561 0.72642 0.856 0 0.0 0.000 0.144
#> GSM782707 1 0.0000 0.79905 1.000 0 0.0 0.000 0.000
#> GSM782708 3 0.0000 1.00000 0.000 0 1.0 0.000 0.000
#> GSM782709 1 0.0794 0.78977 0.972 0 0.0 0.000 0.028
#> GSM782710 1 0.0000 0.79905 1.000 0 0.0 0.000 0.000
#> GSM782711 1 0.0000 0.79905 1.000 0 0.0 0.000 0.000
#> GSM782712 1 0.0000 0.79905 1.000 0 0.0 0.000 0.000
#> GSM782713 5 0.4182 0.00701 0.000 0 0.4 0.000 0.600
#> GSM782714 2 0.0000 1.00000 0.000 1 0.0 0.000 0.000
#> GSM782715 1 0.1197 0.78089 0.952 0 0.0 0.000 0.048
#> GSM782716 3 0.0000 1.00000 0.000 0 1.0 0.000 0.000
#> GSM782717 5 0.6769 -0.12414 0.316 0 0.0 0.288 0.396
#> GSM782718 1 0.6605 0.10290 0.460 0 0.0 0.288 0.252
#> GSM782719 1 0.0000 0.79905 1.000 0 0.0 0.000 0.000
#> GSM782720 5 0.4182 0.00701 0.000 0 0.4 0.000 0.600
#> GSM782721 1 0.2852 0.71459 0.828 0 0.0 0.000 0.172
#> GSM782722 4 0.0000 0.71674 0.000 0 0.0 1.000 0.000
#> GSM782723 2 0.0000 1.00000 0.000 1 0.0 0.000 0.000
#> GSM782724 2 0.0000 1.00000 0.000 1 0.0 0.000 0.000
#> GSM782725 4 0.0000 0.71674 0.000 0 0.0 1.000 0.000
#> GSM782726 1 0.4987 0.54827 0.616 0 0.0 0.044 0.340
#> GSM782727 5 0.4182 0.00701 0.000 0 0.4 0.000 0.600
#> GSM782728 2 0.0000 1.00000 0.000 1 0.0 0.000 0.000
#> GSM782729 4 0.0000 0.71674 0.000 0 0.0 1.000 0.000
#> GSM782730 5 0.4182 0.00701 0.000 0 0.4 0.000 0.600
#> GSM782731 5 0.6763 -0.12431 0.312 0 0.0 0.288 0.400
#> GSM782732 5 0.6763 -0.12431 0.312 0 0.0 0.288 0.400
#> GSM782733 3 0.0000 1.00000 0.000 0 1.0 0.000 0.000
#> GSM782734 1 0.4731 0.57528 0.640 0 0.0 0.032 0.328
#> GSM782735 2 0.0000 1.00000 0.000 1 0.0 0.000 0.000
#> GSM782736 4 0.6819 -0.07978 0.320 0 0.0 0.356 0.324
#> GSM782737 2 0.0000 1.00000 0.000 1 0.0 0.000 0.000
#> GSM782738 1 0.6647 0.08671 0.448 0 0.0 0.288 0.264
#> GSM782739 5 0.6779 -0.12708 0.324 0 0.0 0.288 0.388
#> GSM782740 2 0.0000 1.00000 0.000 1 0.0 0.000 0.000
#> GSM782741 1 0.5036 0.55243 0.628 0 0.0 0.052 0.320
#> GSM782742 5 0.4182 0.00701 0.000 0 0.4 0.000 0.600
#> GSM782743 3 0.0000 1.00000 0.000 0 1.0 0.000 0.000
#> GSM782744 3 0.0000 1.00000 0.000 0 1.0 0.000 0.000
#> GSM782745 1 0.5901 0.36751 0.496 0 0.0 0.104 0.400
#> GSM782746 2 0.0000 1.00000 0.000 1 0.0 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM782696 1 0.0000 0.890 1.000 0.000 0 0.000 0 0.000
#> GSM782697 1 0.0000 0.890 1.000 0.000 0 0.000 0 0.000
#> GSM782698 1 0.0000 0.890 1.000 0.000 0 0.000 0 0.000
#> GSM782699 1 0.0000 0.890 1.000 0.000 0 0.000 0 0.000
#> GSM782700 2 0.0000 0.997 0.000 1.000 0 0.000 0 0.000
#> GSM782701 1 0.0000 0.890 1.000 0.000 0 0.000 0 0.000
#> GSM782702 1 0.0000 0.890 1.000 0.000 0 0.000 0 0.000
#> GSM782703 3 0.0000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM782704 3 0.0000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM782705 6 0.2697 0.786 0.188 0.000 0 0.000 0 0.812
#> GSM782706 1 0.2340 0.788 0.852 0.000 0 0.000 0 0.148
#> GSM782707 1 0.0000 0.890 1.000 0.000 0 0.000 0 0.000
#> GSM782708 3 0.0000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM782709 1 0.0713 0.877 0.972 0.000 0 0.000 0 0.028
#> GSM782710 1 0.0000 0.890 1.000 0.000 0 0.000 0 0.000
#> GSM782711 1 0.0000 0.890 1.000 0.000 0 0.000 0 0.000
#> GSM782712 1 0.0000 0.890 1.000 0.000 0 0.000 0 0.000
#> GSM782713 5 0.0000 1.000 0.000 0.000 0 0.000 1 0.000
#> GSM782714 2 0.0000 0.997 0.000 1.000 0 0.000 0 0.000
#> GSM782715 1 0.1075 0.861 0.952 0.000 0 0.000 0 0.048
#> GSM782716 3 0.0000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM782717 6 0.0146 0.854 0.004 0.000 0 0.000 0 0.996
#> GSM782718 6 0.2378 0.816 0.152 0.000 0 0.000 0 0.848
#> GSM782719 1 0.0000 0.890 1.000 0.000 0 0.000 0 0.000
#> GSM782720 5 0.0000 1.000 0.000 0.000 0 0.000 1 0.000
#> GSM782721 1 0.2597 0.768 0.824 0.000 0 0.000 0 0.176
#> GSM782722 4 0.0363 1.000 0.000 0.000 0 0.988 0 0.012
#> GSM782723 2 0.0000 0.997 0.000 1.000 0 0.000 0 0.000
#> GSM782724 2 0.0000 0.997 0.000 1.000 0 0.000 0 0.000
#> GSM782725 4 0.0363 1.000 0.000 0.000 0 0.988 0 0.012
#> GSM782726 1 0.3857 0.269 0.532 0.000 0 0.000 0 0.468
#> GSM782727 5 0.0000 1.000 0.000 0.000 0 0.000 1 0.000
#> GSM782728 2 0.0000 0.997 0.000 1.000 0 0.000 0 0.000
#> GSM782729 4 0.0363 1.000 0.000 0.000 0 0.988 0 0.012
#> GSM782730 5 0.0000 1.000 0.000 0.000 0 0.000 1 0.000
#> GSM782731 6 0.0000 0.853 0.000 0.000 0 0.000 0 1.000
#> GSM782732 6 0.0000 0.853 0.000 0.000 0 0.000 0 1.000
#> GSM782733 3 0.0000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM782734 1 0.3765 0.440 0.596 0.000 0 0.000 0 0.404
#> GSM782735 2 0.0363 0.991 0.000 0.988 0 0.012 0 0.000
#> GSM782736 6 0.1644 0.853 0.076 0.000 0 0.004 0 0.920
#> GSM782737 2 0.0000 0.997 0.000 1.000 0 0.000 0 0.000
#> GSM782738 6 0.2260 0.826 0.140 0.000 0 0.000 0 0.860
#> GSM782739 6 0.0363 0.855 0.012 0.000 0 0.000 0 0.988
#> GSM782740 2 0.0000 0.997 0.000 1.000 0 0.000 0 0.000
#> GSM782741 1 0.3847 0.277 0.544 0.000 0 0.000 0 0.456
#> GSM782742 5 0.0000 1.000 0.000 0.000 0 0.000 1 0.000
#> GSM782743 3 0.0000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM782744 3 0.0000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM782745 6 0.2854 0.659 0.208 0.000 0 0.000 0 0.792
#> GSM782746 2 0.0363 0.991 0.000 0.988 0 0.012 0 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> CV:pam 51 0.648 2
#> CV:pam 51 0.642 3
#> CV:pam 51 0.502 4
#> CV:pam 37 0.491 5
#> CV:pam 48 0.445 6
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 51941 rows and 51 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.984 0.986 0.4847 0.506 0.506
#> 3 3 0.977 0.967 0.984 0.2154 0.915 0.833
#> 4 4 0.936 0.905 0.932 0.1039 0.918 0.806
#> 5 5 0.685 0.590 0.738 0.1488 0.941 0.828
#> 6 6 0.695 0.561 0.740 0.0503 0.797 0.413
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM782696 1 0.0000 0.997 1.000 0.000
#> GSM782697 1 0.0000 0.997 1.000 0.000
#> GSM782698 1 0.0000 0.997 1.000 0.000
#> GSM782699 1 0.0000 0.997 1.000 0.000
#> GSM782700 2 0.0000 0.967 0.000 1.000
#> GSM782701 1 0.0000 0.997 1.000 0.000
#> GSM782702 1 0.0000 0.997 1.000 0.000
#> GSM782703 2 0.2948 0.974 0.052 0.948
#> GSM782704 2 0.2948 0.974 0.052 0.948
#> GSM782705 1 0.0000 0.997 1.000 0.000
#> GSM782706 1 0.0000 0.997 1.000 0.000
#> GSM782707 1 0.0000 0.997 1.000 0.000
#> GSM782708 2 0.2948 0.974 0.052 0.948
#> GSM782709 1 0.0000 0.997 1.000 0.000
#> GSM782710 1 0.0000 0.997 1.000 0.000
#> GSM782711 1 0.0000 0.997 1.000 0.000
#> GSM782712 1 0.0000 0.997 1.000 0.000
#> GSM782713 2 0.2948 0.974 0.052 0.948
#> GSM782714 2 0.0000 0.967 0.000 1.000
#> GSM782715 1 0.0000 0.997 1.000 0.000
#> GSM782716 2 0.2948 0.974 0.052 0.948
#> GSM782717 1 0.0000 0.997 1.000 0.000
#> GSM782718 1 0.0000 0.997 1.000 0.000
#> GSM782719 1 0.0000 0.997 1.000 0.000
#> GSM782720 2 0.2948 0.974 0.052 0.948
#> GSM782721 1 0.0000 0.997 1.000 0.000
#> GSM782722 1 0.1843 0.972 0.972 0.028
#> GSM782723 2 0.0000 0.967 0.000 1.000
#> GSM782724 2 0.0000 0.967 0.000 1.000
#> GSM782725 1 0.1843 0.972 0.972 0.028
#> GSM782726 1 0.0000 0.997 1.000 0.000
#> GSM782727 2 0.2948 0.974 0.052 0.948
#> GSM782728 2 0.0000 0.967 0.000 1.000
#> GSM782729 1 0.1633 0.976 0.976 0.024
#> GSM782730 2 0.2948 0.974 0.052 0.948
#> GSM782731 1 0.0000 0.997 1.000 0.000
#> GSM782732 1 0.0000 0.997 1.000 0.000
#> GSM782733 2 0.2948 0.974 0.052 0.948
#> GSM782734 1 0.0000 0.997 1.000 0.000
#> GSM782735 2 0.0000 0.967 0.000 1.000
#> GSM782736 1 0.0672 0.990 0.992 0.008
#> GSM782737 2 0.0000 0.967 0.000 1.000
#> GSM782738 1 0.0000 0.997 1.000 0.000
#> GSM782739 1 0.0000 0.997 1.000 0.000
#> GSM782740 2 0.0000 0.967 0.000 1.000
#> GSM782741 1 0.0000 0.997 1.000 0.000
#> GSM782742 2 0.2948 0.974 0.052 0.948
#> GSM782743 2 0.3114 0.971 0.056 0.944
#> GSM782744 2 0.3733 0.956 0.072 0.928
#> GSM782745 1 0.0000 0.997 1.000 0.000
#> GSM782746 2 0.0000 0.967 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0.000 0.971 1.000 0.000 0.000
#> GSM782697 1 0.000 0.971 1.000 0.000 0.000
#> GSM782698 1 0.000 0.971 1.000 0.000 0.000
#> GSM782699 1 0.000 0.971 1.000 0.000 0.000
#> GSM782700 2 0.000 1.000 0.000 1.000 0.000
#> GSM782701 1 0.000 0.971 1.000 0.000 0.000
#> GSM782702 1 0.000 0.971 1.000 0.000 0.000
#> GSM782703 3 0.000 1.000 0.000 0.000 1.000
#> GSM782704 3 0.000 1.000 0.000 0.000 1.000
#> GSM782705 1 0.000 0.971 1.000 0.000 0.000
#> GSM782706 1 0.000 0.971 1.000 0.000 0.000
#> GSM782707 1 0.000 0.971 1.000 0.000 0.000
#> GSM782708 3 0.000 1.000 0.000 0.000 1.000
#> GSM782709 1 0.000 0.971 1.000 0.000 0.000
#> GSM782710 1 0.000 0.971 1.000 0.000 0.000
#> GSM782711 1 0.000 0.971 1.000 0.000 0.000
#> GSM782712 1 0.000 0.971 1.000 0.000 0.000
#> GSM782713 3 0.000 1.000 0.000 0.000 1.000
#> GSM782714 2 0.000 1.000 0.000 1.000 0.000
#> GSM782715 1 0.000 0.971 1.000 0.000 0.000
#> GSM782716 3 0.000 1.000 0.000 0.000 1.000
#> GSM782717 1 0.000 0.971 1.000 0.000 0.000
#> GSM782718 1 0.000 0.971 1.000 0.000 0.000
#> GSM782719 1 0.000 0.971 1.000 0.000 0.000
#> GSM782720 3 0.000 1.000 0.000 0.000 1.000
#> GSM782721 1 0.000 0.971 1.000 0.000 0.000
#> GSM782722 1 0.606 0.733 0.760 0.044 0.196
#> GSM782723 2 0.000 1.000 0.000 1.000 0.000
#> GSM782724 2 0.000 1.000 0.000 1.000 0.000
#> GSM782725 1 0.606 0.733 0.760 0.044 0.196
#> GSM782726 1 0.000 0.971 1.000 0.000 0.000
#> GSM782727 3 0.000 1.000 0.000 0.000 1.000
#> GSM782728 2 0.000 1.000 0.000 1.000 0.000
#> GSM782729 1 0.606 0.733 0.760 0.044 0.196
#> GSM782730 3 0.000 1.000 0.000 0.000 1.000
#> GSM782731 1 0.000 0.971 1.000 0.000 0.000
#> GSM782732 1 0.000 0.971 1.000 0.000 0.000
#> GSM782733 3 0.000 1.000 0.000 0.000 1.000
#> GSM782734 1 0.000 0.971 1.000 0.000 0.000
#> GSM782735 2 0.000 1.000 0.000 1.000 0.000
#> GSM782736 1 0.377 0.877 0.888 0.028 0.084
#> GSM782737 2 0.000 1.000 0.000 1.000 0.000
#> GSM782738 1 0.000 0.971 1.000 0.000 0.000
#> GSM782739 1 0.000 0.971 1.000 0.000 0.000
#> GSM782740 2 0.000 1.000 0.000 1.000 0.000
#> GSM782741 1 0.000 0.971 1.000 0.000 0.000
#> GSM782742 3 0.000 1.000 0.000 0.000 1.000
#> GSM782743 3 0.000 1.000 0.000 0.000 1.000
#> GSM782744 3 0.000 1.000 0.000 0.000 1.000
#> GSM782745 1 0.000 0.971 1.000 0.000 0.000
#> GSM782746 2 0.000 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
#> GSM782696 1 0.0921 0.887 0.972 0 0.000 0.028
#> GSM782697 1 0.0592 0.892 0.984 0 0.000 0.016
#> GSM782698 1 0.1302 0.886 0.956 0 0.000 0.044
#> GSM782699 1 0.0921 0.887 0.972 0 0.000 0.028
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782701 1 0.1118 0.884 0.964 0 0.000 0.036
#> GSM782702 1 0.1118 0.888 0.964 0 0.000 0.036
#> GSM782703 3 0.0188 0.996 0.000 0 0.996 0.004
#> GSM782704 3 0.0469 0.995 0.000 0 0.988 0.012
#> GSM782705 1 0.0921 0.887 0.972 0 0.000 0.028
#> GSM782706 1 0.0921 0.889 0.972 0 0.000 0.028
#> GSM782707 1 0.1118 0.890 0.964 0 0.000 0.036
#> GSM782708 3 0.0469 0.995 0.000 0 0.988 0.012
#> GSM782709 1 0.0592 0.896 0.984 0 0.000 0.016
#> GSM782710 1 0.0707 0.891 0.980 0 0.000 0.020
#> GSM782711 1 0.1022 0.887 0.968 0 0.000 0.032
#> GSM782712 1 0.1211 0.888 0.960 0 0.000 0.040
#> GSM782713 3 0.0000 0.996 0.000 0 1.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782715 1 0.0921 0.889 0.972 0 0.000 0.028
#> GSM782716 3 0.0469 0.995 0.000 0 0.988 0.012
#> GSM782717 1 0.0817 0.889 0.976 0 0.000 0.024
#> GSM782718 1 0.1302 0.886 0.956 0 0.000 0.044
#> GSM782719 1 0.1302 0.886 0.956 0 0.000 0.044
#> GSM782720 3 0.0000 0.996 0.000 0 1.000 0.000
#> GSM782721 1 0.0921 0.889 0.972 0 0.000 0.028
#> GSM782722 4 0.4948 0.925 0.440 0 0.000 0.560
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782725 4 0.4972 0.938 0.456 0 0.000 0.544
#> GSM782726 1 0.4877 0.107 0.592 0 0.000 0.408
#> GSM782727 3 0.0000 0.996 0.000 0 1.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782729 4 0.4972 0.938 0.456 0 0.000 0.544
#> GSM782730 3 0.0000 0.996 0.000 0 1.000 0.000
#> GSM782731 1 0.0592 0.895 0.984 0 0.000 0.016
#> GSM782732 1 0.0469 0.897 0.988 0 0.000 0.012
#> GSM782733 3 0.0469 0.995 0.000 0 0.988 0.012
#> GSM782734 1 0.0592 0.892 0.984 0 0.000 0.016
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782736 4 0.5000 0.874 0.500 0 0.000 0.500
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782738 1 0.1211 0.888 0.960 0 0.000 0.040
#> GSM782739 1 0.0817 0.890 0.976 0 0.000 0.024
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782741 1 0.0707 0.891 0.980 0 0.000 0.020
#> GSM782742 3 0.0000 0.996 0.000 0 1.000 0.000
#> GSM782743 3 0.0469 0.995 0.000 0 0.988 0.012
#> GSM782744 3 0.0000 0.996 0.000 0 1.000 0.000
#> GSM782745 1 0.4877 0.107 0.592 0 0.000 0.408
#> GSM782746 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.5232 0.4358 0.668 0 0.000 0.228 0.104
#> GSM782697 1 0.2230 0.5246 0.884 0 0.000 0.116 0.000
#> GSM782698 1 0.6081 0.1342 0.476 0 0.000 0.400 0.124
#> GSM782699 1 0.4693 0.4745 0.700 0 0.000 0.244 0.056
#> GSM782700 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782701 1 0.5488 0.1433 0.608 0 0.000 0.300 0.092
#> GSM782702 1 0.0510 0.5619 0.984 0 0.000 0.016 0.000
#> GSM782703 3 0.2127 0.9013 0.000 0 0.892 0.000 0.108
#> GSM782704 3 0.3074 0.8888 0.000 0 0.804 0.000 0.196
#> GSM782705 1 0.5541 0.4151 0.636 0 0.000 0.236 0.128
#> GSM782706 1 0.6039 0.0647 0.552 0 0.000 0.300 0.148
#> GSM782707 1 0.5889 0.2307 0.544 0 0.000 0.340 0.116
#> GSM782708 3 0.3366 0.8801 0.000 0 0.768 0.000 0.232
#> GSM782709 1 0.4941 0.2355 0.628 0 0.000 0.328 0.044
#> GSM782710 1 0.1282 0.5669 0.952 0 0.000 0.044 0.004
#> GSM782711 1 0.3460 0.5465 0.828 0 0.000 0.128 0.044
#> GSM782712 1 0.1251 0.5639 0.956 0 0.000 0.036 0.008
#> GSM782713 3 0.0000 0.9051 0.000 0 1.000 0.000 0.000
#> GSM782714 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782715 5 0.6801 0.9002 0.308 0 0.000 0.316 0.376
#> GSM782716 3 0.3366 0.8801 0.000 0 0.768 0.000 0.232
#> GSM782717 1 0.1117 0.5445 0.964 0 0.000 0.020 0.016
#> GSM782718 4 0.6688 -0.7086 0.240 0 0.000 0.404 0.356
#> GSM782719 1 0.5946 0.1324 0.508 0 0.000 0.380 0.112
#> GSM782720 3 0.0000 0.9051 0.000 0 1.000 0.000 0.000
#> GSM782721 1 0.5765 0.0802 0.580 0 0.000 0.304 0.116
#> GSM782722 4 0.1732 0.5014 0.080 0 0.000 0.920 0.000
#> GSM782723 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782725 4 0.3480 0.5506 0.248 0 0.000 0.752 0.000
#> GSM782726 1 0.4642 0.3635 0.660 0 0.000 0.032 0.308
#> GSM782727 3 0.0000 0.9051 0.000 0 1.000 0.000 0.000
#> GSM782728 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782729 4 0.3395 0.5518 0.236 0 0.000 0.764 0.000
#> GSM782730 3 0.0000 0.9051 0.000 0 1.000 0.000 0.000
#> GSM782731 1 0.6420 -0.6063 0.484 0 0.000 0.192 0.324
#> GSM782732 1 0.4797 0.0245 0.660 0 0.000 0.044 0.296
#> GSM782733 3 0.3366 0.8801 0.000 0 0.768 0.000 0.232
#> GSM782734 1 0.3183 0.4979 0.828 0 0.000 0.156 0.016
#> GSM782735 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782736 4 0.5697 0.2441 0.116 0 0.000 0.596 0.288
#> GSM782737 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782738 5 0.6808 0.8987 0.324 0 0.000 0.308 0.368
#> GSM782739 1 0.1549 0.5549 0.944 0 0.000 0.040 0.016
#> GSM782740 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM782741 1 0.0912 0.5589 0.972 0 0.000 0.016 0.012
#> GSM782742 3 0.0000 0.9051 0.000 0 1.000 0.000 0.000
#> GSM782743 3 0.3366 0.8801 0.000 0 0.768 0.000 0.232
#> GSM782744 3 0.0404 0.8999 0.000 0 0.988 0.000 0.012
#> GSM782745 1 0.4786 0.3679 0.652 0 0.000 0.040 0.308
#> GSM782746 2 0.0000 1.0000 0.000 1 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
#> GSM782696 1 0.371 -0.1952 0.620 0 0.000 0.000 0.000 0.380
#> GSM782697 6 0.398 0.5408 0.392 0 0.000 0.008 0.000 0.600
#> GSM782698 1 0.356 0.5000 0.800 0 0.000 0.056 0.004 0.140
#> GSM782699 6 0.385 0.4693 0.456 0 0.000 0.000 0.000 0.544
#> GSM782700 2 0.000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782701 1 0.135 0.4586 0.940 0 0.000 0.004 0.000 0.056
#> GSM782702 6 0.390 0.5447 0.404 0 0.000 0.004 0.000 0.592
#> GSM782703 3 0.150 0.7183 0.000 0 0.924 0.000 0.076 0.000
#> GSM782704 3 0.350 0.0584 0.000 0 0.680 0.000 0.320 0.000
#> GSM782705 6 0.561 0.2449 0.380 0 0.000 0.148 0.000 0.472
#> GSM782706 1 0.382 0.5149 0.768 0 0.000 0.176 0.004 0.052
#> GSM782707 1 0.310 0.2351 0.756 0 0.000 0.000 0.000 0.244
#> GSM782708 5 0.382 0.8903 0.000 0 0.432 0.000 0.568 0.000
#> GSM782709 1 0.374 -0.1280 0.672 0 0.000 0.008 0.000 0.320
#> GSM782710 6 0.581 0.2175 0.360 0 0.000 0.188 0.000 0.452
#> GSM782711 6 0.394 0.5183 0.428 0 0.000 0.004 0.000 0.568
#> GSM782712 6 0.372 0.5438 0.384 0 0.000 0.000 0.000 0.616
#> GSM782713 3 0.000 0.7878 0.000 0 1.000 0.000 0.000 0.000
#> GSM782714 2 0.000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782715 1 0.468 0.4885 0.628 0 0.000 0.312 0.004 0.056
#> GSM782716 5 0.387 0.8767 0.000 0 0.488 0.000 0.512 0.000
#> GSM782717 6 0.427 0.5357 0.412 0 0.000 0.020 0.000 0.568
#> GSM782718 1 0.456 0.4924 0.628 0 0.000 0.316 0.000 0.056
#> GSM782719 1 0.159 0.5056 0.924 0 0.000 0.004 0.000 0.072
#> GSM782720 3 0.000 0.7878 0.000 0 1.000 0.000 0.000 0.000
#> GSM782721 1 0.115 0.5047 0.960 0 0.000 0.020 0.004 0.016
#> GSM782722 6 0.666 -0.2828 0.388 0 0.000 0.064 0.148 0.400
#> GSM782723 2 0.000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782724 2 0.000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782725 6 0.544 0.0797 0.092 0 0.000 0.084 0.148 0.676
#> GSM782726 4 0.514 0.9788 0.316 0 0.000 0.596 0.012 0.076
#> GSM782727 3 0.000 0.7878 0.000 0 1.000 0.000 0.000 0.000
#> GSM782728 2 0.000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782729 6 0.545 0.0955 0.088 0 0.000 0.068 0.180 0.664
#> GSM782730 3 0.000 0.7878 0.000 0 1.000 0.000 0.000 0.000
#> GSM782731 6 0.607 0.0432 0.292 0 0.000 0.304 0.000 0.404
#> GSM782732 6 0.598 0.1234 0.272 0 0.000 0.284 0.000 0.444
#> GSM782733 5 0.386 0.8895 0.000 0 0.480 0.000 0.520 0.000
#> GSM782734 6 0.478 0.4530 0.476 0 0.000 0.040 0.004 0.480
#> GSM782735 2 0.000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782736 1 0.674 0.2195 0.472 0 0.000 0.160 0.288 0.080
#> GSM782737 2 0.000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782738 1 0.555 0.3969 0.528 0 0.000 0.312 0.000 0.160
#> GSM782739 6 0.433 0.5363 0.408 0 0.000 0.024 0.000 0.568
#> GSM782740 2 0.000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782741 6 0.435 0.5385 0.384 0 0.000 0.028 0.000 0.588
#> GSM782742 3 0.200 0.6897 0.000 0 0.884 0.000 0.116 0.000
#> GSM782743 5 0.376 0.8518 0.000 0 0.400 0.000 0.600 0.000
#> GSM782744 3 0.343 0.3275 0.000 0 0.696 0.000 0.304 0.000
#> GSM782745 4 0.514 0.9788 0.304 0 0.000 0.604 0.012 0.080
#> GSM782746 2 0.000 1.0000 0.000 1 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> CV:mclust 51 0.493 2
#> CV:mclust 51 0.642 3
#> CV:mclust 49 0.495 4
#> CV:mclust 34 0.352 5
#> CV:mclust 32 0.497 6
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 51941 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.2972 0.704 0.704
#> 3 3 1.000 1.000 1.000 0.9492 0.718 0.599
#> 4 4 0.824 0.838 0.921 0.1346 0.918 0.806
#> 5 5 0.859 0.868 0.928 0.0808 0.977 0.934
#> 6 6 0.786 0.814 0.881 0.0500 0.956 0.867
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
#> GSM782696 1 0 1 1 0
#> GSM782697 1 0 1 1 0
#> GSM782698 1 0 1 1 0
#> GSM782699 1 0 1 1 0
#> GSM782700 2 0 1 0 1
#> GSM782701 1 0 1 1 0
#> GSM782702 1 0 1 1 0
#> GSM782703 1 0 1 1 0
#> GSM782704 1 0 1 1 0
#> GSM782705 1 0 1 1 0
#> GSM782706 1 0 1 1 0
#> GSM782707 1 0 1 1 0
#> GSM782708 1 0 1 1 0
#> GSM782709 1 0 1 1 0
#> GSM782710 1 0 1 1 0
#> GSM782711 1 0 1 1 0
#> GSM782712 1 0 1 1 0
#> GSM782713 1 0 1 1 0
#> GSM782714 2 0 1 0 1
#> GSM782715 1 0 1 1 0
#> GSM782716 1 0 1 1 0
#> GSM782717 1 0 1 1 0
#> GSM782718 1 0 1 1 0
#> GSM782719 1 0 1 1 0
#> GSM782720 1 0 1 1 0
#> GSM782721 1 0 1 1 0
#> GSM782722 1 0 1 1 0
#> GSM782723 2 0 1 0 1
#> GSM782724 2 0 1 0 1
#> GSM782725 1 0 1 1 0
#> GSM782726 1 0 1 1 0
#> GSM782727 1 0 1 1 0
#> GSM782728 2 0 1 0 1
#> GSM782729 1 0 1 1 0
#> GSM782730 1 0 1 1 0
#> GSM782731 1 0 1 1 0
#> GSM782732 1 0 1 1 0
#> GSM782733 1 0 1 1 0
#> GSM782734 1 0 1 1 0
#> GSM782735 2 0 1 0 1
#> GSM782736 1 0 1 1 0
#> GSM782737 2 0 1 0 1
#> GSM782738 1 0 1 1 0
#> GSM782739 1 0 1 1 0
#> GSM782740 2 0 1 0 1
#> GSM782741 1 0 1 1 0
#> GSM782742 1 0 1 1 0
#> GSM782743 1 0 1 1 0
#> GSM782744 1 0 1 1 0
#> GSM782745 1 0 1 1 0
#> GSM782746 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0 1 1 0 0
#> GSM782697 1 0 1 1 0 0
#> GSM782698 1 0 1 1 0 0
#> GSM782699 1 0 1 1 0 0
#> GSM782700 2 0 1 0 1 0
#> GSM782701 1 0 1 1 0 0
#> GSM782702 1 0 1 1 0 0
#> GSM782703 3 0 1 0 0 1
#> GSM782704 3 0 1 0 0 1
#> GSM782705 1 0 1 1 0 0
#> GSM782706 1 0 1 1 0 0
#> GSM782707 1 0 1 1 0 0
#> GSM782708 3 0 1 0 0 1
#> GSM782709 1 0 1 1 0 0
#> GSM782710 1 0 1 1 0 0
#> GSM782711 1 0 1 1 0 0
#> GSM782712 1 0 1 1 0 0
#> GSM782713 3 0 1 0 0 1
#> GSM782714 2 0 1 0 1 0
#> GSM782715 1 0 1 1 0 0
#> GSM782716 3 0 1 0 0 1
#> GSM782717 1 0 1 1 0 0
#> GSM782718 1 0 1 1 0 0
#> GSM782719 1 0 1 1 0 0
#> GSM782720 3 0 1 0 0 1
#> GSM782721 1 0 1 1 0 0
#> GSM782722 1 0 1 1 0 0
#> GSM782723 2 0 1 0 1 0
#> GSM782724 2 0 1 0 1 0
#> GSM782725 1 0 1 1 0 0
#> GSM782726 1 0 1 1 0 0
#> GSM782727 3 0 1 0 0 1
#> GSM782728 2 0 1 0 1 0
#> GSM782729 1 0 1 1 0 0
#> GSM782730 3 0 1 0 0 1
#> GSM782731 1 0 1 1 0 0
#> GSM782732 1 0 1 1 0 0
#> GSM782733 3 0 1 0 0 1
#> GSM782734 1 0 1 1 0 0
#> GSM782735 2 0 1 0 1 0
#> GSM782736 1 0 1 1 0 0
#> GSM782737 2 0 1 0 1 0
#> GSM782738 1 0 1 1 0 0
#> GSM782739 1 0 1 1 0 0
#> GSM782740 2 0 1 0 1 0
#> GSM782741 1 0 1 1 0 0
#> GSM782742 3 0 1 0 0 1
#> GSM782743 3 0 1 0 0 1
#> GSM782744 3 0 1 0 0 1
#> GSM782745 1 0 1 1 0 0
#> GSM782746 2 0 1 0 1 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.1302 0.829 0.956 0 0.000 0.044
#> GSM782697 1 0.2973 0.705 0.856 0 0.000 0.144
#> GSM782698 1 0.3266 0.675 0.832 0 0.000 0.168
#> GSM782699 1 0.2081 0.788 0.916 0 0.000 0.084
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782701 1 0.0592 0.846 0.984 0 0.000 0.016
#> GSM782702 1 0.0336 0.847 0.992 0 0.000 0.008
#> GSM782703 3 0.0000 0.997 0.000 0 1.000 0.000
#> GSM782704 3 0.0000 0.997 0.000 0 1.000 0.000
#> GSM782705 1 0.0921 0.836 0.972 0 0.000 0.028
#> GSM782706 1 0.0188 0.847 0.996 0 0.000 0.004
#> GSM782707 1 0.0817 0.843 0.976 0 0.000 0.024
#> GSM782708 3 0.0000 0.997 0.000 0 1.000 0.000
#> GSM782709 1 0.0817 0.842 0.976 0 0.000 0.024
#> GSM782710 1 0.0469 0.848 0.988 0 0.000 0.012
#> GSM782711 1 0.0817 0.843 0.976 0 0.000 0.024
#> GSM782712 1 0.0707 0.843 0.980 0 0.000 0.020
#> GSM782713 3 0.0000 0.997 0.000 0 1.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782715 1 0.4985 -0.791 0.532 0 0.000 0.468
#> GSM782716 3 0.0000 0.997 0.000 0 1.000 0.000
#> GSM782717 1 0.0336 0.845 0.992 0 0.000 0.008
#> GSM782718 1 0.3486 0.546 0.812 0 0.000 0.188
#> GSM782719 1 0.3172 0.675 0.840 0 0.000 0.160
#> GSM782720 3 0.0000 0.997 0.000 0 1.000 0.000
#> GSM782721 1 0.0000 0.847 1.000 0 0.000 0.000
#> GSM782722 4 0.4746 0.797 0.368 0 0.000 0.632
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782725 4 0.4981 0.905 0.464 0 0.000 0.536
#> GSM782726 1 0.1022 0.834 0.968 0 0.000 0.032
#> GSM782727 3 0.0000 0.997 0.000 0 1.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782729 4 0.4985 0.905 0.468 0 0.000 0.532
#> GSM782730 3 0.0000 0.997 0.000 0 1.000 0.000
#> GSM782731 1 0.3400 0.554 0.820 0 0.000 0.180
#> GSM782732 1 0.2589 0.714 0.884 0 0.000 0.116
#> GSM782733 3 0.0000 0.997 0.000 0 1.000 0.000
#> GSM782734 1 0.0592 0.842 0.984 0 0.000 0.016
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782736 4 0.4996 0.878 0.484 0 0.000 0.516
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782738 1 0.4193 0.197 0.732 0 0.000 0.268
#> GSM782739 1 0.0469 0.843 0.988 0 0.000 0.012
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782741 1 0.0336 0.845 0.992 0 0.000 0.008
#> GSM782742 3 0.0188 0.995 0.000 0 0.996 0.004
#> GSM782743 3 0.0000 0.997 0.000 0 1.000 0.000
#> GSM782744 3 0.1022 0.974 0.000 0 0.968 0.032
#> GSM782745 1 0.2149 0.765 0.912 0 0.000 0.088
#> GSM782746 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.1792 0.8556 0.916 0.000 0.000 0.000 0.084
#> GSM782697 1 0.2852 0.7954 0.828 0.000 0.000 0.000 0.172
#> GSM782698 1 0.4425 0.5228 0.600 0.000 0.000 0.008 0.392
#> GSM782699 1 0.2230 0.8391 0.884 0.000 0.000 0.000 0.116
#> GSM782700 2 0.0000 0.9988 0.000 1.000 0.000 0.000 0.000
#> GSM782701 1 0.0566 0.8751 0.984 0.000 0.000 0.004 0.012
#> GSM782702 1 0.0609 0.8738 0.980 0.000 0.000 0.000 0.020
#> GSM782703 3 0.0162 0.9935 0.000 0.000 0.996 0.004 0.000
#> GSM782704 3 0.0000 0.9938 0.000 0.000 1.000 0.000 0.000
#> GSM782705 1 0.1485 0.8739 0.948 0.000 0.000 0.032 0.020
#> GSM782706 1 0.1282 0.8721 0.952 0.000 0.000 0.004 0.044
#> GSM782707 1 0.1764 0.8649 0.928 0.000 0.000 0.008 0.064
#> GSM782708 3 0.0000 0.9938 0.000 0.000 1.000 0.000 0.000
#> GSM782709 1 0.0898 0.8730 0.972 0.000 0.000 0.008 0.020
#> GSM782710 1 0.0671 0.8747 0.980 0.000 0.000 0.004 0.016
#> GSM782711 1 0.0794 0.8722 0.972 0.000 0.000 0.000 0.028
#> GSM782712 1 0.0609 0.8731 0.980 0.000 0.000 0.000 0.020
#> GSM782713 3 0.0324 0.9928 0.000 0.000 0.992 0.004 0.004
#> GSM782714 2 0.0000 0.9988 0.000 1.000 0.000 0.000 0.000
#> GSM782715 4 0.4575 0.6934 0.236 0.000 0.000 0.712 0.052
#> GSM782716 3 0.0000 0.9938 0.000 0.000 1.000 0.000 0.000
#> GSM782717 1 0.0807 0.8750 0.976 0.000 0.000 0.012 0.012
#> GSM782718 1 0.5024 0.0865 0.528 0.000 0.000 0.440 0.032
#> GSM782719 1 0.3305 0.7509 0.776 0.000 0.000 0.000 0.224
#> GSM782720 3 0.0324 0.9928 0.000 0.000 0.992 0.004 0.004
#> GSM782721 1 0.1205 0.8687 0.956 0.000 0.000 0.004 0.040
#> GSM782722 4 0.0794 0.8745 0.028 0.000 0.000 0.972 0.000
#> GSM782723 2 0.0000 0.9988 0.000 1.000 0.000 0.000 0.000
#> GSM782724 2 0.0162 0.9976 0.000 0.996 0.000 0.000 0.004
#> GSM782725 4 0.1251 0.8820 0.036 0.000 0.000 0.956 0.008
#> GSM782726 1 0.2144 0.8529 0.912 0.000 0.000 0.020 0.068
#> GSM782727 3 0.0324 0.9928 0.000 0.000 0.992 0.004 0.004
#> GSM782728 2 0.0000 0.9988 0.000 1.000 0.000 0.000 0.000
#> GSM782729 4 0.1502 0.8875 0.056 0.000 0.000 0.940 0.004
#> GSM782730 3 0.0000 0.9938 0.000 0.000 1.000 0.000 0.000
#> GSM782731 1 0.4226 0.7034 0.764 0.000 0.000 0.176 0.060
#> GSM782732 1 0.2754 0.8276 0.880 0.000 0.000 0.080 0.040
#> GSM782733 3 0.0000 0.9938 0.000 0.000 1.000 0.000 0.000
#> GSM782734 1 0.1670 0.8610 0.936 0.000 0.000 0.012 0.052
#> GSM782735 2 0.0162 0.9976 0.000 0.996 0.000 0.000 0.004
#> GSM782736 4 0.3192 0.8625 0.112 0.000 0.000 0.848 0.040
#> GSM782737 2 0.0000 0.9988 0.000 1.000 0.000 0.000 0.000
#> GSM782738 1 0.5176 -0.0616 0.492 0.000 0.000 0.468 0.040
#> GSM782739 1 0.1018 0.8734 0.968 0.000 0.000 0.016 0.016
#> GSM782740 2 0.0000 0.9988 0.000 1.000 0.000 0.000 0.000
#> GSM782741 1 0.0579 0.8737 0.984 0.000 0.000 0.008 0.008
#> GSM782742 3 0.0324 0.9928 0.000 0.000 0.992 0.004 0.004
#> GSM782743 3 0.0000 0.9938 0.000 0.000 1.000 0.000 0.000
#> GSM782744 3 0.1399 0.9609 0.000 0.000 0.952 0.028 0.020
#> GSM782745 1 0.2554 0.8408 0.892 0.000 0.000 0.036 0.072
#> GSM782746 2 0.0162 0.9976 0.000 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM782696 1 0.2234 0.803 0.872 0 0.000 0.000 0.124 NA
#> GSM782697 1 0.2070 0.811 0.892 0 0.000 0.000 0.100 NA
#> GSM782698 1 0.4732 0.374 0.484 0 0.000 0.016 0.480 NA
#> GSM782699 1 0.2001 0.813 0.900 0 0.000 0.004 0.092 NA
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 NA
#> GSM782701 1 0.3784 0.755 0.792 0 0.000 0.008 0.124 NA
#> GSM782702 1 0.1334 0.819 0.948 0 0.000 0.000 0.032 NA
#> GSM782703 3 0.0146 0.973 0.000 0 0.996 0.000 0.000 NA
#> GSM782704 3 0.0146 0.973 0.000 0 0.996 0.000 0.000 NA
#> GSM782705 1 0.2528 0.802 0.892 0 0.000 0.056 0.028 NA
#> GSM782706 1 0.6302 0.322 0.476 0 0.000 0.044 0.136 NA
#> GSM782707 1 0.4369 0.720 0.740 0 0.000 0.020 0.176 NA
#> GSM782708 3 0.0146 0.973 0.000 0 0.996 0.000 0.000 NA
#> GSM782709 1 0.1970 0.818 0.912 0 0.000 0.000 0.060 NA
#> GSM782710 1 0.1275 0.819 0.956 0 0.000 0.016 0.012 NA
#> GSM782711 1 0.1643 0.816 0.924 0 0.000 0.000 0.068 NA
#> GSM782712 1 0.2365 0.805 0.888 0 0.000 0.000 0.072 NA
#> GSM782713 3 0.0260 0.973 0.000 0 0.992 0.000 0.000 NA
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 NA
#> GSM782715 4 0.5615 0.676 0.140 0 0.000 0.596 0.020 NA
#> GSM782716 3 0.0000 0.973 0.000 0 1.000 0.000 0.000 NA
#> GSM782717 1 0.1391 0.811 0.944 0 0.000 0.040 0.000 NA
#> GSM782718 4 0.5704 0.351 0.380 0 0.000 0.496 0.016 NA
#> GSM782719 1 0.4636 0.429 0.516 0 0.000 0.000 0.444 NA
#> GSM782720 3 0.0363 0.970 0.000 0 0.988 0.000 0.000 NA
#> GSM782721 1 0.5952 0.406 0.520 0 0.000 0.036 0.108 NA
#> GSM782722 4 0.1897 0.736 0.004 0 0.000 0.908 0.004 NA
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 NA
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 NA
#> GSM782725 4 0.1010 0.735 0.004 0 0.000 0.960 0.000 NA
#> GSM782726 1 0.1794 0.807 0.924 0 0.000 0.040 0.000 NA
#> GSM782727 3 0.0547 0.967 0.000 0 0.980 0.000 0.000 NA
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 NA
#> GSM782729 4 0.1245 0.741 0.016 0 0.000 0.952 0.000 NA
#> GSM782730 3 0.0000 0.973 0.000 0 1.000 0.000 0.000 NA
#> GSM782731 1 0.3602 0.700 0.792 0 0.000 0.136 0.000 NA
#> GSM782732 1 0.2863 0.769 0.860 0 0.000 0.096 0.008 NA
#> GSM782733 3 0.0146 0.973 0.000 0 0.996 0.000 0.000 NA
#> GSM782734 1 0.1845 0.812 0.920 0 0.000 0.028 0.000 NA
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 NA
#> GSM782736 4 0.2213 0.758 0.048 0 0.000 0.904 0.004 NA
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 NA
#> GSM782738 4 0.5961 0.443 0.328 0 0.000 0.480 0.008 NA
#> GSM782739 1 0.1480 0.809 0.940 0 0.000 0.040 0.000 NA
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 NA
#> GSM782741 1 0.1341 0.817 0.948 0 0.000 0.024 0.000 NA
#> GSM782742 3 0.0713 0.963 0.000 0 0.972 0.000 0.000 NA
#> GSM782743 3 0.0146 0.973 0.000 0 0.996 0.000 0.000 NA
#> GSM782744 3 0.3645 0.734 0.000 0 0.740 0.024 0.000 NA
#> GSM782745 1 0.2308 0.794 0.892 0 0.000 0.040 0.000 NA
#> GSM782746 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> CV:NMF 51 0.648 2
#> CV:NMF 51 0.642 3
#> CV:NMF 49 0.494 4
#> CV:NMF 49 0.497 5
#> CV:NMF 45 0.478 6
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 51941 rows and 51 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 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.2972 0.704 0.704
#> 3 3 1.000 0.968 0.987 0.9772 0.718 0.599
#> 4 4 0.759 0.850 0.921 0.1370 0.956 0.896
#> 5 5 0.773 0.779 0.886 0.1181 0.905 0.749
#> 6 6 0.782 0.774 0.903 0.0133 0.991 0.970
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
#> GSM782696 1 0 1 1 0
#> GSM782697 1 0 1 1 0
#> GSM782698 1 0 1 1 0
#> GSM782699 1 0 1 1 0
#> GSM782700 2 0 1 0 1
#> GSM782701 1 0 1 1 0
#> GSM782702 1 0 1 1 0
#> GSM782703 1 0 1 1 0
#> GSM782704 1 0 1 1 0
#> GSM782705 1 0 1 1 0
#> GSM782706 1 0 1 1 0
#> GSM782707 1 0 1 1 0
#> GSM782708 1 0 1 1 0
#> GSM782709 1 0 1 1 0
#> GSM782710 1 0 1 1 0
#> GSM782711 1 0 1 1 0
#> GSM782712 1 0 1 1 0
#> GSM782713 1 0 1 1 0
#> GSM782714 2 0 1 0 1
#> GSM782715 1 0 1 1 0
#> GSM782716 1 0 1 1 0
#> GSM782717 1 0 1 1 0
#> GSM782718 1 0 1 1 0
#> GSM782719 1 0 1 1 0
#> GSM782720 1 0 1 1 0
#> GSM782721 1 0 1 1 0
#> GSM782722 1 0 1 1 0
#> GSM782723 2 0 1 0 1
#> GSM782724 2 0 1 0 1
#> GSM782725 1 0 1 1 0
#> GSM782726 1 0 1 1 0
#> GSM782727 1 0 1 1 0
#> GSM782728 2 0 1 0 1
#> GSM782729 1 0 1 1 0
#> GSM782730 1 0 1 1 0
#> GSM782731 1 0 1 1 0
#> GSM782732 1 0 1 1 0
#> GSM782733 1 0 1 1 0
#> GSM782734 1 0 1 1 0
#> GSM782735 2 0 1 0 1
#> GSM782736 1 0 1 1 0
#> GSM782737 2 0 1 0 1
#> GSM782738 1 0 1 1 0
#> GSM782739 1 0 1 1 0
#> GSM782740 2 0 1 0 1
#> GSM782741 1 0 1 1 0
#> GSM782742 1 0 1 1 0
#> GSM782743 1 0 1 1 0
#> GSM782744 1 0 1 1 0
#> GSM782745 1 0 1 1 0
#> GSM782746 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0.000 0.976 1.000 0 0.000
#> GSM782697 1 0.000 0.976 1.000 0 0.000
#> GSM782698 1 0.000 0.976 1.000 0 0.000
#> GSM782699 1 0.000 0.976 1.000 0 0.000
#> GSM782700 2 0.000 1.000 0.000 1 0.000
#> GSM782701 1 0.000 0.976 1.000 0 0.000
#> GSM782702 1 0.000 0.976 1.000 0 0.000
#> GSM782703 3 0.000 1.000 0.000 0 1.000
#> GSM782704 3 0.000 1.000 0.000 0 1.000
#> GSM782705 1 0.000 0.976 1.000 0 0.000
#> GSM782706 1 0.000 0.976 1.000 0 0.000
#> GSM782707 1 0.000 0.976 1.000 0 0.000
#> GSM782708 3 0.000 1.000 0.000 0 1.000
#> GSM782709 1 0.000 0.976 1.000 0 0.000
#> GSM782710 1 0.000 0.976 1.000 0 0.000
#> GSM782711 1 0.000 0.976 1.000 0 0.000
#> GSM782712 1 0.000 0.976 1.000 0 0.000
#> GSM782713 3 0.000 1.000 0.000 0 1.000
#> GSM782714 2 0.000 1.000 0.000 1 0.000
#> GSM782715 1 0.000 0.976 1.000 0 0.000
#> GSM782716 3 0.000 1.000 0.000 0 1.000
#> GSM782717 1 0.000 0.976 1.000 0 0.000
#> GSM782718 1 0.000 0.976 1.000 0 0.000
#> GSM782719 1 0.000 0.976 1.000 0 0.000
#> GSM782720 3 0.000 1.000 0.000 0 1.000
#> GSM782721 1 0.000 0.976 1.000 0 0.000
#> GSM782722 1 0.000 0.976 1.000 0 0.000
#> GSM782723 2 0.000 1.000 0.000 1 0.000
#> GSM782724 2 0.000 1.000 0.000 1 0.000
#> GSM782725 1 0.000 0.976 1.000 0 0.000
#> GSM782726 1 0.579 0.520 0.668 0 0.332
#> GSM782727 3 0.000 1.000 0.000 0 1.000
#> GSM782728 2 0.000 1.000 0.000 1 0.000
#> GSM782729 1 0.000 0.976 1.000 0 0.000
#> GSM782730 3 0.000 1.000 0.000 0 1.000
#> GSM782731 1 0.000 0.976 1.000 0 0.000
#> GSM782732 1 0.000 0.976 1.000 0 0.000
#> GSM782733 3 0.000 1.000 0.000 0 1.000
#> GSM782734 1 0.000 0.976 1.000 0 0.000
#> GSM782735 2 0.000 1.000 0.000 1 0.000
#> GSM782736 1 0.000 0.976 1.000 0 0.000
#> GSM782737 2 0.000 1.000 0.000 1 0.000
#> GSM782738 1 0.000 0.976 1.000 0 0.000
#> GSM782739 1 0.000 0.976 1.000 0 0.000
#> GSM782740 2 0.000 1.000 0.000 1 0.000
#> GSM782741 1 0.000 0.976 1.000 0 0.000
#> GSM782742 3 0.000 1.000 0.000 0 1.000
#> GSM782743 3 0.000 1.000 0.000 0 1.000
#> GSM782744 3 0.000 1.000 0.000 0 1.000
#> GSM782745 1 0.579 0.520 0.668 0 0.332
#> GSM782746 2 0.000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.0469 0.837 0.988 0 0.000 0.012
#> GSM782697 1 0.1637 0.819 0.940 0 0.000 0.060
#> GSM782698 1 0.1022 0.834 0.968 0 0.000 0.032
#> GSM782699 1 0.0707 0.835 0.980 0 0.000 0.020
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782701 1 0.0188 0.838 0.996 0 0.000 0.004
#> GSM782702 1 0.0188 0.838 0.996 0 0.000 0.004
#> GSM782703 3 0.0000 0.971 0.000 0 1.000 0.000
#> GSM782704 3 0.0000 0.971 0.000 0 1.000 0.000
#> GSM782705 1 0.2081 0.812 0.916 0 0.000 0.084
#> GSM782706 1 0.0817 0.836 0.976 0 0.000 0.024
#> GSM782707 1 0.0188 0.838 0.996 0 0.000 0.004
#> GSM782708 3 0.0000 0.971 0.000 0 1.000 0.000
#> GSM782709 1 0.2704 0.779 0.876 0 0.000 0.124
#> GSM782710 1 0.4907 0.149 0.580 0 0.000 0.420
#> GSM782711 1 0.1474 0.823 0.948 0 0.000 0.052
#> GSM782712 1 0.0188 0.838 0.996 0 0.000 0.004
#> GSM782713 3 0.0000 0.971 0.000 0 1.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782715 1 0.3569 0.725 0.804 0 0.000 0.196
#> GSM782716 3 0.0000 0.971 0.000 0 1.000 0.000
#> GSM782717 1 0.3837 0.676 0.776 0 0.000 0.224
#> GSM782718 1 0.2281 0.806 0.904 0 0.000 0.096
#> GSM782719 1 0.0188 0.838 0.996 0 0.000 0.004
#> GSM782720 3 0.0000 0.971 0.000 0 1.000 0.000
#> GSM782721 1 0.0817 0.836 0.976 0 0.000 0.024
#> GSM782722 1 0.3688 0.711 0.792 0 0.000 0.208
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782725 1 0.3688 0.711 0.792 0 0.000 0.208
#> GSM782726 4 0.3688 1.000 0.208 0 0.000 0.792
#> GSM782727 3 0.0000 0.971 0.000 0 1.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782729 1 0.3688 0.711 0.792 0 0.000 0.208
#> GSM782730 3 0.0000 0.971 0.000 0 1.000 0.000
#> GSM782731 1 0.3726 0.691 0.788 0 0.000 0.212
#> GSM782732 1 0.3726 0.691 0.788 0 0.000 0.212
#> GSM782733 3 0.0000 0.971 0.000 0 1.000 0.000
#> GSM782734 1 0.3837 0.676 0.776 0 0.000 0.224
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782736 1 0.2281 0.806 0.904 0 0.000 0.096
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782738 1 0.2281 0.806 0.904 0 0.000 0.096
#> GSM782739 1 0.3837 0.676 0.776 0 0.000 0.224
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782741 1 0.3837 0.676 0.776 0 0.000 0.224
#> GSM782742 3 0.0000 0.971 0.000 0 1.000 0.000
#> GSM782743 3 0.0000 0.971 0.000 0 1.000 0.000
#> GSM782744 3 0.4585 0.573 0.000 0 0.668 0.332
#> GSM782745 4 0.3688 1.000 0.208 0 0.000 0.792
#> GSM782746 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.0404 0.739 0.988 0 0.000 0.012 0.000
#> GSM782697 1 0.1197 0.719 0.952 0 0.000 0.000 0.048
#> GSM782698 1 0.1121 0.736 0.956 0 0.000 0.044 0.000
#> GSM782699 1 0.0290 0.735 0.992 0 0.000 0.000 0.008
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782701 1 0.3039 0.670 0.808 0 0.000 0.192 0.000
#> GSM782702 1 0.1043 0.742 0.960 0 0.000 0.040 0.000
#> GSM782703 3 0.0000 0.964 0.000 0 1.000 0.000 0.000
#> GSM782704 3 0.0000 0.964 0.000 0 1.000 0.000 0.000
#> GSM782705 1 0.2773 0.695 0.836 0 0.000 0.164 0.000
#> GSM782706 1 0.3336 0.649 0.772 0 0.000 0.228 0.000
#> GSM782707 1 0.1270 0.740 0.948 0 0.000 0.052 0.000
#> GSM782708 3 0.0000 0.964 0.000 0 1.000 0.000 0.000
#> GSM782709 1 0.2891 0.645 0.824 0 0.000 0.000 0.176
#> GSM782710 5 0.4273 0.029 0.448 0 0.000 0.000 0.552
#> GSM782711 1 0.1043 0.723 0.960 0 0.000 0.000 0.040
#> GSM782712 1 0.1043 0.742 0.960 0 0.000 0.040 0.000
#> GSM782713 3 0.0000 0.964 0.000 0 1.000 0.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782715 4 0.2674 0.862 0.140 0 0.000 0.856 0.004
#> GSM782716 3 0.0000 0.964 0.000 0 1.000 0.000 0.000
#> GSM782717 1 0.3990 0.516 0.688 0 0.000 0.004 0.308
#> GSM782718 1 0.3949 0.539 0.668 0 0.000 0.332 0.000
#> GSM782719 1 0.3039 0.670 0.808 0 0.000 0.192 0.000
#> GSM782720 3 0.0000 0.964 0.000 0 1.000 0.000 0.000
#> GSM782721 1 0.3336 0.649 0.772 0 0.000 0.228 0.000
#> GSM782722 4 0.1410 0.955 0.060 0 0.000 0.940 0.000
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782725 4 0.1410 0.955 0.060 0 0.000 0.940 0.000
#> GSM782726 5 0.1121 0.660 0.044 0 0.000 0.000 0.956
#> GSM782727 3 0.0000 0.964 0.000 0 1.000 0.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782729 4 0.1410 0.955 0.060 0 0.000 0.940 0.000
#> GSM782730 3 0.0000 0.964 0.000 0 1.000 0.000 0.000
#> GSM782731 1 0.4046 0.531 0.696 0 0.000 0.008 0.296
#> GSM782732 1 0.4046 0.531 0.696 0 0.000 0.008 0.296
#> GSM782733 3 0.0000 0.964 0.000 0 1.000 0.000 0.000
#> GSM782734 1 0.3990 0.516 0.688 0 0.000 0.004 0.308
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782736 1 0.3949 0.539 0.668 0 0.000 0.332 0.000
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782738 1 0.3949 0.539 0.668 0 0.000 0.332 0.000
#> GSM782739 1 0.3990 0.516 0.688 0 0.000 0.004 0.308
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782741 1 0.3990 0.516 0.688 0 0.000 0.004 0.308
#> GSM782742 3 0.0000 0.964 0.000 0 1.000 0.000 0.000
#> GSM782743 3 0.0000 0.964 0.000 0 1.000 0.000 0.000
#> GSM782744 3 0.5341 0.429 0.000 0 0.564 0.060 0.376
#> GSM782745 5 0.1121 0.660 0.044 0 0.000 0.000 0.956
#> GSM782746 2 0.0000 1.000 0.000 1 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
#> GSM782696 1 0.0508 0.7438 0.984 0 0 0.012 0 0.004
#> GSM782697 1 0.1141 0.7319 0.948 0 0 0.000 0 0.052
#> GSM782698 1 0.1196 0.7402 0.952 0 0 0.040 0 0.008
#> GSM782699 1 0.0363 0.7407 0.988 0 0 0.000 0 0.012
#> GSM782700 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782701 1 0.2697 0.6733 0.812 0 0 0.188 0 0.000
#> GSM782702 1 0.0865 0.7457 0.964 0 0 0.036 0 0.000
#> GSM782703 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782704 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782705 1 0.2706 0.6976 0.832 0 0 0.160 0 0.008
#> GSM782706 1 0.2969 0.6575 0.776 0 0 0.224 0 0.000
#> GSM782707 1 0.1075 0.7437 0.952 0 0 0.048 0 0.000
#> GSM782708 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782709 1 0.2631 0.6616 0.820 0 0 0.000 0 0.180
#> GSM782710 6 0.3828 -0.0246 0.440 0 0 0.000 0 0.560
#> GSM782711 1 0.1007 0.7344 0.956 0 0 0.000 0 0.044
#> GSM782712 1 0.0865 0.7457 0.964 0 0 0.036 0 0.000
#> GSM782713 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782714 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782715 4 0.2070 0.8077 0.092 0 0 0.896 0 0.012
#> GSM782716 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782717 1 0.3619 0.5340 0.680 0 0 0.004 0 0.316
#> GSM782718 1 0.3774 0.5740 0.664 0 0 0.328 0 0.008
#> GSM782719 1 0.2697 0.6733 0.812 0 0 0.188 0 0.000
#> GSM782720 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782721 1 0.2969 0.6575 0.776 0 0 0.224 0 0.000
#> GSM782722 4 0.0000 0.9349 0.000 0 0 1.000 0 0.000
#> GSM782723 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782724 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782725 4 0.0000 0.9349 0.000 0 0 1.000 0 0.000
#> GSM782726 6 0.0260 0.5029 0.008 0 0 0.000 0 0.992
#> GSM782727 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782728 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782729 4 0.0000 0.9349 0.000 0 0 1.000 0 0.000
#> GSM782730 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782731 1 0.3672 0.5482 0.688 0 0 0.008 0 0.304
#> GSM782732 1 0.3672 0.5482 0.688 0 0 0.008 0 0.304
#> GSM782733 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782734 1 0.3619 0.5340 0.680 0 0 0.004 0 0.316
#> GSM782735 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782736 1 0.3774 0.5740 0.664 0 0 0.328 0 0.008
#> GSM782737 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782738 1 0.3774 0.5740 0.664 0 0 0.328 0 0.008
#> GSM782739 1 0.3619 0.5340 0.680 0 0 0.004 0 0.316
#> GSM782740 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
#> GSM782741 1 0.3619 0.5340 0.680 0 0 0.004 0 0.316
#> GSM782742 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782743 3 0.0000 1.0000 0.000 0 1 0.000 0 0.000
#> GSM782744 5 0.0000 0.0000 0.000 0 0 0.000 1 0.000
#> GSM782745 6 0.0260 0.5029 0.008 0 0 0.000 0 0.992
#> GSM782746 2 0.0000 1.0000 0.000 1 0 0.000 0 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> MAD:hclust 51 0.648 2
#> MAD:hclust 51 0.642 3
#> MAD:hclust 50 0.833 4
#> MAD:hclust 49 0.632 5
#> MAD:hclust 49 0.632 6
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 51941 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.421 0.676 0.802 0.3855 0.633 0.633
#> 3 3 1.000 0.977 0.943 0.4650 0.788 0.665
#> 4 4 0.708 0.356 0.785 0.2186 0.977 0.946
#> 5 5 0.681 0.760 0.768 0.0887 0.776 0.450
#> 6 6 0.689 0.811 0.801 0.0623 0.961 0.817
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
#> GSM782696 1 0.925 0.7690 0.660 0.340
#> GSM782697 1 0.925 0.7690 0.660 0.340
#> GSM782698 1 0.925 0.7690 0.660 0.340
#> GSM782699 1 0.925 0.7690 0.660 0.340
#> GSM782700 1 0.913 -0.0649 0.672 0.328
#> GSM782701 1 0.925 0.7690 0.660 0.340
#> GSM782702 1 0.925 0.7690 0.660 0.340
#> GSM782703 2 0.000 1.0000 0.000 1.000
#> GSM782704 2 0.000 1.0000 0.000 1.000
#> GSM782705 1 0.925 0.7690 0.660 0.340
#> GSM782706 1 0.925 0.7690 0.660 0.340
#> GSM782707 1 0.925 0.7690 0.660 0.340
#> GSM782708 2 0.000 1.0000 0.000 1.000
#> GSM782709 1 0.925 0.7690 0.660 0.340
#> GSM782710 1 0.925 0.7690 0.660 0.340
#> GSM782711 1 0.925 0.7690 0.660 0.340
#> GSM782712 1 0.925 0.7690 0.660 0.340
#> GSM782713 2 0.000 1.0000 0.000 1.000
#> GSM782714 1 0.913 -0.0649 0.672 0.328
#> GSM782715 1 0.925 0.7690 0.660 0.340
#> GSM782716 2 0.000 1.0000 0.000 1.000
#> GSM782717 1 0.925 0.7690 0.660 0.340
#> GSM782718 1 0.925 0.7690 0.660 0.340
#> GSM782719 1 0.925 0.7690 0.660 0.340
#> GSM782720 2 0.000 1.0000 0.000 1.000
#> GSM782721 1 0.925 0.7690 0.660 0.340
#> GSM782722 1 0.925 0.7690 0.660 0.340
#> GSM782723 1 0.913 -0.0649 0.672 0.328
#> GSM782724 1 0.913 -0.0649 0.672 0.328
#> GSM782725 1 0.925 0.7690 0.660 0.340
#> GSM782726 1 0.925 0.7690 0.660 0.340
#> GSM782727 2 0.000 1.0000 0.000 1.000
#> GSM782728 1 0.913 -0.0649 0.672 0.328
#> GSM782729 1 0.925 0.7690 0.660 0.340
#> GSM782730 2 0.000 1.0000 0.000 1.000
#> GSM782731 1 0.925 0.7690 0.660 0.340
#> GSM782732 1 0.925 0.7690 0.660 0.340
#> GSM782733 2 0.000 1.0000 0.000 1.000
#> GSM782734 1 0.925 0.7690 0.660 0.340
#> GSM782735 1 0.913 -0.0649 0.672 0.328
#> GSM782736 1 0.925 0.7690 0.660 0.340
#> GSM782737 1 0.913 -0.0649 0.672 0.328
#> GSM782738 1 0.925 0.7690 0.660 0.340
#> GSM782739 1 0.925 0.7690 0.660 0.340
#> GSM782740 1 0.913 -0.0649 0.672 0.328
#> GSM782741 1 0.925 0.7690 0.660 0.340
#> GSM782742 2 0.000 1.0000 0.000 1.000
#> GSM782743 2 0.000 1.0000 0.000 1.000
#> GSM782744 2 0.000 1.0000 0.000 1.000
#> GSM782745 1 0.925 0.7690 0.660 0.340
#> GSM782746 1 0.913 -0.0649 0.672 0.328
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0.1289 0.975 0.968 0.032 0.000
#> GSM782697 1 0.0424 0.976 0.992 0.008 0.000
#> GSM782698 1 0.1753 0.972 0.952 0.048 0.000
#> GSM782699 1 0.0424 0.976 0.992 0.008 0.000
#> GSM782700 2 0.4007 0.990 0.036 0.880 0.084
#> GSM782701 1 0.1289 0.975 0.968 0.032 0.000
#> GSM782702 1 0.0424 0.976 0.992 0.008 0.000
#> GSM782703 3 0.1860 0.985 0.052 0.000 0.948
#> GSM782704 3 0.3253 0.982 0.052 0.036 0.912
#> GSM782705 1 0.0424 0.977 0.992 0.008 0.000
#> GSM782706 1 0.1529 0.973 0.960 0.040 0.000
#> GSM782707 1 0.1289 0.975 0.968 0.032 0.000
#> GSM782708 3 0.3253 0.982 0.052 0.036 0.912
#> GSM782709 1 0.0424 0.976 0.992 0.008 0.000
#> GSM782710 1 0.0237 0.976 0.996 0.004 0.000
#> GSM782711 1 0.0424 0.976 0.992 0.008 0.000
#> GSM782712 1 0.0592 0.976 0.988 0.012 0.000
#> GSM782713 3 0.1860 0.985 0.052 0.000 0.948
#> GSM782714 2 0.4174 0.989 0.036 0.872 0.092
#> GSM782715 1 0.2261 0.960 0.932 0.068 0.000
#> GSM782716 3 0.3253 0.982 0.052 0.036 0.912
#> GSM782717 1 0.0424 0.976 0.992 0.008 0.000
#> GSM782718 1 0.2261 0.960 0.932 0.068 0.000
#> GSM782719 1 0.1289 0.975 0.968 0.032 0.000
#> GSM782720 3 0.1860 0.985 0.052 0.000 0.948
#> GSM782721 1 0.1529 0.973 0.960 0.040 0.000
#> GSM782722 1 0.2356 0.959 0.928 0.072 0.000
#> GSM782723 2 0.4489 0.985 0.036 0.856 0.108
#> GSM782724 2 0.4489 0.985 0.036 0.856 0.108
#> GSM782725 1 0.2356 0.960 0.928 0.072 0.000
#> GSM782726 1 0.0424 0.976 0.992 0.008 0.000
#> GSM782727 3 0.1860 0.985 0.052 0.000 0.948
#> GSM782728 2 0.4007 0.990 0.036 0.880 0.084
#> GSM782729 1 0.2356 0.960 0.928 0.072 0.000
#> GSM782730 3 0.1860 0.985 0.052 0.000 0.948
#> GSM782731 1 0.0892 0.974 0.980 0.020 0.000
#> GSM782732 1 0.0892 0.974 0.980 0.020 0.000
#> GSM782733 3 0.3253 0.982 0.052 0.036 0.912
#> GSM782734 1 0.0424 0.976 0.992 0.008 0.000
#> GSM782735 2 0.4563 0.980 0.036 0.852 0.112
#> GSM782736 1 0.2356 0.959 0.928 0.072 0.000
#> GSM782737 2 0.4174 0.989 0.036 0.872 0.092
#> GSM782738 1 0.2261 0.960 0.932 0.068 0.000
#> GSM782739 1 0.0424 0.976 0.992 0.008 0.000
#> GSM782740 2 0.4007 0.990 0.036 0.880 0.084
#> GSM782741 1 0.0424 0.976 0.992 0.008 0.000
#> GSM782742 3 0.1860 0.985 0.052 0.000 0.948
#> GSM782743 3 0.3253 0.982 0.052 0.036 0.912
#> GSM782744 3 0.2599 0.981 0.052 0.016 0.932
#> GSM782745 1 0.0424 0.976 0.992 0.008 0.000
#> GSM782746 2 0.4563 0.980 0.036 0.852 0.112
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.4925 -0.6920 0.572 0.000 0.000 0.428
#> GSM782697 1 0.4134 -0.1144 0.740 0.000 0.000 0.260
#> GSM782698 4 0.5000 0.0000 0.496 0.000 0.000 0.504
#> GSM782699 1 0.4134 -0.1144 0.740 0.000 0.000 0.260
#> GSM782700 2 0.1109 0.9744 0.000 0.968 0.028 0.004
#> GSM782701 1 0.5088 -0.6940 0.572 0.004 0.000 0.424
#> GSM782702 1 0.4134 -0.1144 0.740 0.000 0.000 0.260
#> GSM782703 3 0.0469 0.9434 0.012 0.000 0.988 0.000
#> GSM782704 3 0.3324 0.9324 0.012 0.000 0.852 0.136
#> GSM782705 1 0.2647 0.2515 0.880 0.000 0.000 0.120
#> GSM782706 1 0.5257 -0.7666 0.548 0.008 0.000 0.444
#> GSM782707 1 0.4925 -0.6920 0.572 0.000 0.000 0.428
#> GSM782708 3 0.3324 0.9324 0.012 0.000 0.852 0.136
#> GSM782709 1 0.4134 -0.1144 0.740 0.000 0.000 0.260
#> GSM782710 1 0.2216 0.2264 0.908 0.000 0.000 0.092
#> GSM782711 1 0.4331 -0.2027 0.712 0.000 0.000 0.288
#> GSM782712 1 0.4500 -0.2981 0.684 0.000 0.000 0.316
#> GSM782713 3 0.0469 0.9434 0.012 0.000 0.988 0.000
#> GSM782714 2 0.1256 0.9742 0.000 0.964 0.028 0.008
#> GSM782715 1 0.5526 0.0573 0.564 0.020 0.000 0.416
#> GSM782716 3 0.3324 0.9324 0.012 0.000 0.852 0.136
#> GSM782717 1 0.0000 0.3265 1.000 0.000 0.000 0.000
#> GSM782718 1 0.5452 0.0276 0.556 0.016 0.000 0.428
#> GSM782719 1 0.5088 -0.6940 0.572 0.004 0.000 0.424
#> GSM782720 3 0.0469 0.9434 0.012 0.000 0.988 0.000
#> GSM782721 1 0.5257 -0.7666 0.548 0.008 0.000 0.444
#> GSM782722 1 0.5643 0.0557 0.548 0.024 0.000 0.428
#> GSM782723 2 0.2623 0.9568 0.000 0.908 0.028 0.064
#> GSM782724 2 0.2845 0.9536 0.000 0.896 0.028 0.076
#> GSM782725 1 0.5510 0.1105 0.600 0.024 0.000 0.376
#> GSM782726 1 0.0817 0.3242 0.976 0.000 0.000 0.024
#> GSM782727 3 0.0469 0.9434 0.012 0.000 0.988 0.000
#> GSM782728 2 0.0921 0.9743 0.000 0.972 0.028 0.000
#> GSM782729 1 0.5510 0.1105 0.600 0.024 0.000 0.376
#> GSM782730 3 0.0469 0.9434 0.012 0.000 0.988 0.000
#> GSM782731 1 0.1867 0.3052 0.928 0.000 0.000 0.072
#> GSM782732 1 0.1867 0.3052 0.928 0.000 0.000 0.072
#> GSM782733 3 0.3324 0.9324 0.012 0.000 0.852 0.136
#> GSM782734 1 0.0336 0.3272 0.992 0.000 0.000 0.008
#> GSM782735 2 0.2830 0.9510 0.000 0.900 0.040 0.060
#> GSM782736 1 0.5517 0.0626 0.568 0.020 0.000 0.412
#> GSM782737 2 0.1256 0.9742 0.000 0.964 0.028 0.008
#> GSM782738 1 0.5517 0.0562 0.568 0.020 0.000 0.412
#> GSM782739 1 0.0000 0.3265 1.000 0.000 0.000 0.000
#> GSM782740 2 0.0921 0.9743 0.000 0.972 0.028 0.000
#> GSM782741 1 0.0000 0.3265 1.000 0.000 0.000 0.000
#> GSM782742 3 0.0469 0.9434 0.012 0.000 0.988 0.000
#> GSM782743 3 0.3324 0.9324 0.012 0.000 0.852 0.136
#> GSM782744 3 0.3427 0.9106 0.028 0.000 0.860 0.112
#> GSM782745 1 0.0817 0.3242 0.976 0.000 0.000 0.024
#> GSM782746 2 0.2830 0.9510 0.000 0.900 0.040 0.060
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.3661 0.836 0.724 0.000 0.000 0.276 0.000
#> GSM782697 1 0.4251 0.771 0.756 0.004 0.000 0.200 0.040
#> GSM782698 1 0.4118 0.776 0.660 0.004 0.000 0.336 0.000
#> GSM782699 1 0.4251 0.771 0.756 0.004 0.000 0.200 0.040
#> GSM782700 2 0.0510 0.950 0.000 0.984 0.016 0.000 0.000
#> GSM782701 1 0.4656 0.834 0.692 0.004 0.000 0.268 0.036
#> GSM782702 1 0.4400 0.750 0.744 0.000 0.000 0.196 0.060
#> GSM782703 3 0.0162 0.898 0.000 0.000 0.996 0.004 0.000
#> GSM782704 3 0.3521 0.879 0.000 0.000 0.764 0.004 0.232
#> GSM782705 4 0.5635 -0.181 0.428 0.000 0.000 0.496 0.076
#> GSM782706 1 0.5256 0.738 0.592 0.004 0.000 0.356 0.048
#> GSM782707 1 0.4581 0.835 0.696 0.004 0.000 0.268 0.032
#> GSM782708 3 0.3521 0.879 0.000 0.000 0.764 0.004 0.232
#> GSM782709 1 0.4540 0.743 0.748 0.004 0.000 0.180 0.068
#> GSM782710 5 0.6739 0.783 0.336 0.000 0.000 0.264 0.400
#> GSM782711 1 0.3074 0.809 0.804 0.000 0.000 0.196 0.000
#> GSM782712 1 0.4335 0.829 0.740 0.004 0.000 0.220 0.036
#> GSM782713 3 0.0162 0.898 0.000 0.000 0.996 0.004 0.000
#> GSM782714 2 0.1179 0.949 0.004 0.964 0.016 0.000 0.016
#> GSM782715 4 0.2067 0.662 0.048 0.000 0.000 0.920 0.032
#> GSM782716 3 0.3521 0.879 0.000 0.000 0.764 0.004 0.232
#> GSM782717 5 0.6721 0.926 0.252 0.000 0.000 0.352 0.396
#> GSM782718 4 0.2020 0.635 0.100 0.000 0.000 0.900 0.000
#> GSM782719 1 0.4656 0.834 0.692 0.004 0.000 0.268 0.036
#> GSM782720 3 0.0162 0.898 0.000 0.000 0.996 0.004 0.000
#> GSM782721 1 0.5256 0.738 0.592 0.004 0.000 0.356 0.048
#> GSM782722 4 0.2011 0.637 0.020 0.008 0.000 0.928 0.044
#> GSM782723 2 0.2857 0.926 0.028 0.888 0.020 0.000 0.064
#> GSM782724 2 0.3423 0.917 0.068 0.856 0.016 0.000 0.060
#> GSM782725 4 0.2204 0.642 0.036 0.008 0.000 0.920 0.036
#> GSM782726 5 0.6597 0.890 0.224 0.000 0.000 0.332 0.444
#> GSM782727 3 0.0162 0.898 0.000 0.000 0.996 0.004 0.000
#> GSM782728 2 0.0510 0.950 0.000 0.984 0.016 0.000 0.000
#> GSM782729 4 0.2122 0.643 0.036 0.008 0.000 0.924 0.032
#> GSM782730 3 0.0162 0.898 0.000 0.000 0.996 0.004 0.000
#> GSM782731 4 0.6337 -0.541 0.192 0.000 0.000 0.512 0.296
#> GSM782732 4 0.6337 -0.541 0.192 0.000 0.000 0.512 0.296
#> GSM782733 3 0.3521 0.879 0.000 0.000 0.764 0.004 0.232
#> GSM782734 5 0.6718 0.925 0.252 0.000 0.000 0.348 0.400
#> GSM782735 2 0.3783 0.891 0.040 0.824 0.016 0.000 0.120
#> GSM782736 4 0.1386 0.666 0.032 0.000 0.000 0.952 0.016
#> GSM782737 2 0.1179 0.949 0.004 0.964 0.016 0.000 0.016
#> GSM782738 4 0.2046 0.655 0.068 0.000 0.000 0.916 0.016
#> GSM782739 5 0.6721 0.926 0.252 0.000 0.000 0.352 0.396
#> GSM782740 2 0.0510 0.950 0.000 0.984 0.016 0.000 0.000
#> GSM782741 5 0.6721 0.926 0.252 0.000 0.000 0.352 0.396
#> GSM782742 3 0.0162 0.898 0.000 0.000 0.996 0.004 0.000
#> GSM782743 3 0.3521 0.879 0.000 0.000 0.764 0.004 0.232
#> GSM782744 3 0.4621 0.818 0.076 0.000 0.744 0.004 0.176
#> GSM782745 5 0.6597 0.890 0.224 0.000 0.000 0.332 0.444
#> GSM782746 2 0.3783 0.891 0.040 0.824 0.016 0.000 0.120
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM782696 1 0.3837 0.785 0.752 0.000 0.000 0.052 NA 0.196
#> GSM782697 1 0.3933 0.741 0.676 0.000 0.000 0.008 NA 0.308
#> GSM782698 1 0.4371 0.721 0.740 0.000 0.000 0.132 NA 0.120
#> GSM782699 1 0.3933 0.741 0.676 0.000 0.000 0.008 NA 0.308
#> GSM782700 2 0.0458 0.923 0.016 0.984 0.000 0.000 NA 0.000
#> GSM782701 1 0.5866 0.774 0.612 0.000 0.000 0.056 NA 0.200
#> GSM782702 1 0.3728 0.732 0.652 0.000 0.000 0.004 NA 0.344
#> GSM782703 3 0.0692 0.821 0.020 0.000 0.976 0.000 NA 0.004
#> GSM782704 3 0.4265 0.787 0.016 0.000 0.596 0.000 NA 0.004
#> GSM782705 1 0.5820 0.201 0.416 0.000 0.000 0.184 NA 0.400
#> GSM782706 1 0.7155 0.658 0.456 0.000 0.000 0.160 NA 0.216
#> GSM782707 1 0.5806 0.777 0.620 0.000 0.000 0.056 NA 0.196
#> GSM782708 3 0.3890 0.786 0.000 0.000 0.596 0.000 NA 0.004
#> GSM782709 1 0.3925 0.731 0.656 0.000 0.000 0.004 NA 0.332
#> GSM782710 6 0.1716 0.863 0.036 0.000 0.000 0.004 NA 0.932
#> GSM782711 1 0.3380 0.776 0.748 0.000 0.000 0.004 NA 0.244
#> GSM782712 1 0.5495 0.769 0.600 0.000 0.000 0.016 NA 0.256
#> GSM782713 3 0.0508 0.821 0.012 0.000 0.984 0.000 NA 0.004
#> GSM782714 2 0.0603 0.924 0.004 0.980 0.000 0.000 NA 0.000
#> GSM782715 4 0.4025 0.897 0.052 0.000 0.000 0.760 NA 0.176
#> GSM782716 3 0.3890 0.786 0.000 0.000 0.596 0.000 NA 0.004
#> GSM782717 6 0.0508 0.902 0.004 0.000 0.000 0.012 NA 0.984
#> GSM782718 4 0.4054 0.874 0.072 0.000 0.000 0.740 NA 0.188
#> GSM782719 1 0.5787 0.776 0.620 0.000 0.000 0.052 NA 0.196
#> GSM782720 3 0.0146 0.822 0.000 0.000 0.996 0.000 NA 0.004
#> GSM782721 1 0.7155 0.658 0.456 0.000 0.000 0.160 NA 0.216
#> GSM782722 4 0.4052 0.876 0.036 0.000 0.000 0.788 NA 0.116
#> GSM782723 2 0.2841 0.892 0.028 0.872 0.000 0.028 NA 0.000
#> GSM782724 2 0.3775 0.872 0.048 0.816 0.000 0.060 NA 0.000
#> GSM782725 4 0.3971 0.876 0.012 0.000 0.000 0.772 NA 0.156
#> GSM782726 6 0.1075 0.888 0.000 0.000 0.000 0.000 NA 0.952
#> GSM782727 3 0.0291 0.821 0.004 0.000 0.992 0.000 NA 0.004
#> GSM782728 2 0.0000 0.924 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782729 4 0.4017 0.880 0.012 0.000 0.000 0.764 NA 0.168
#> GSM782730 3 0.0291 0.822 0.000 0.000 0.992 0.004 NA 0.004
#> GSM782731 6 0.2871 0.706 0.004 0.000 0.000 0.192 NA 0.804
#> GSM782732 6 0.2871 0.706 0.004 0.000 0.000 0.192 NA 0.804
#> GSM782733 3 0.3890 0.786 0.000 0.000 0.596 0.000 NA 0.004
#> GSM782734 6 0.0951 0.899 0.004 0.000 0.000 0.008 NA 0.968
#> GSM782735 2 0.3991 0.831 0.044 0.764 0.000 0.016 NA 0.000
#> GSM782736 4 0.3440 0.899 0.028 0.000 0.000 0.776 NA 0.196
#> GSM782737 2 0.0748 0.924 0.004 0.976 0.004 0.000 NA 0.000
#> GSM782738 4 0.3683 0.896 0.044 0.000 0.000 0.764 NA 0.192
#> GSM782739 6 0.0508 0.902 0.004 0.000 0.000 0.012 NA 0.984
#> GSM782740 2 0.0000 0.924 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782741 6 0.0508 0.902 0.004 0.000 0.000 0.012 NA 0.984
#> GSM782742 3 0.0146 0.822 0.000 0.000 0.996 0.000 NA 0.004
#> GSM782743 3 0.4015 0.786 0.000 0.000 0.596 0.004 NA 0.004
#> GSM782744 3 0.5606 0.746 0.076 0.000 0.664 0.052 NA 0.016
#> GSM782745 6 0.1075 0.888 0.000 0.000 0.000 0.000 NA 0.952
#> GSM782746 2 0.3991 0.831 0.044 0.764 0.000 0.016 NA 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> MAD:kmeans 42 0.557 2
#> MAD:kmeans 51 0.642 3
#> MAD:kmeans 21 0.529 4
#> MAD:kmeans 48 0.520 5
#> MAD:kmeans 50 0.494 6
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 51941 rows and 51 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 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 1.000 1.000 1.000 0.4946 0.506 0.506
#> 3 3 1.000 0.999 0.999 0.1715 0.915 0.833
#> 4 4 0.860 0.905 0.933 0.2909 0.824 0.583
#> 5 5 0.969 0.939 0.968 0.0766 0.938 0.752
#> 6 6 0.869 0.772 0.839 0.0298 0.967 0.829
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM782696 1 0 1 1 0
#> GSM782697 1 0 1 1 0
#> GSM782698 1 0 1 1 0
#> GSM782699 1 0 1 1 0
#> GSM782700 2 0 1 0 1
#> GSM782701 1 0 1 1 0
#> GSM782702 1 0 1 1 0
#> GSM782703 2 0 1 0 1
#> GSM782704 2 0 1 0 1
#> GSM782705 1 0 1 1 0
#> GSM782706 1 0 1 1 0
#> GSM782707 1 0 1 1 0
#> GSM782708 2 0 1 0 1
#> GSM782709 1 0 1 1 0
#> GSM782710 1 0 1 1 0
#> GSM782711 1 0 1 1 0
#> GSM782712 1 0 1 1 0
#> GSM782713 2 0 1 0 1
#> GSM782714 2 0 1 0 1
#> GSM782715 1 0 1 1 0
#> GSM782716 2 0 1 0 1
#> GSM782717 1 0 1 1 0
#> GSM782718 1 0 1 1 0
#> GSM782719 1 0 1 1 0
#> GSM782720 2 0 1 0 1
#> GSM782721 1 0 1 1 0
#> GSM782722 1 0 1 1 0
#> GSM782723 2 0 1 0 1
#> GSM782724 2 0 1 0 1
#> GSM782725 1 0 1 1 0
#> GSM782726 1 0 1 1 0
#> GSM782727 2 0 1 0 1
#> GSM782728 2 0 1 0 1
#> GSM782729 1 0 1 1 0
#> GSM782730 2 0 1 0 1
#> GSM782731 1 0 1 1 0
#> GSM782732 1 0 1 1 0
#> GSM782733 2 0 1 0 1
#> GSM782734 1 0 1 1 0
#> GSM782735 2 0 1 0 1
#> GSM782736 1 0 1 1 0
#> GSM782737 2 0 1 0 1
#> GSM782738 1 0 1 1 0
#> GSM782739 1 0 1 1 0
#> GSM782740 2 0 1 0 1
#> GSM782741 1 0 1 1 0
#> GSM782742 2 0 1 0 1
#> GSM782743 2 0 1 0 1
#> GSM782744 2 0 1 0 1
#> GSM782745 1 0 1 1 0
#> GSM782746 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782697 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782698 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782699 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782700 2 0.0237 1.000 0.000 0.996 0.004
#> GSM782701 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782702 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782703 3 0.0000 1.000 0.000 0.000 1.000
#> GSM782704 3 0.0000 1.000 0.000 0.000 1.000
#> GSM782705 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782706 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782707 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782708 3 0.0000 1.000 0.000 0.000 1.000
#> GSM782709 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782710 1 0.0237 0.997 0.996 0.004 0.000
#> GSM782711 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782712 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782713 3 0.0000 1.000 0.000 0.000 1.000
#> GSM782714 2 0.0237 1.000 0.000 0.996 0.004
#> GSM782715 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782716 3 0.0000 1.000 0.000 0.000 1.000
#> GSM782717 1 0.0237 0.997 0.996 0.004 0.000
#> GSM782718 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782719 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782720 3 0.0000 1.000 0.000 0.000 1.000
#> GSM782721 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782722 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782723 2 0.0237 1.000 0.000 0.996 0.004
#> GSM782724 2 0.0237 1.000 0.000 0.996 0.004
#> GSM782725 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782726 1 0.0237 0.997 0.996 0.004 0.000
#> GSM782727 3 0.0000 1.000 0.000 0.000 1.000
#> GSM782728 2 0.0237 1.000 0.000 0.996 0.004
#> GSM782729 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782730 3 0.0000 1.000 0.000 0.000 1.000
#> GSM782731 1 0.0237 0.997 0.996 0.004 0.000
#> GSM782732 1 0.0237 0.997 0.996 0.004 0.000
#> GSM782733 3 0.0000 1.000 0.000 0.000 1.000
#> GSM782734 1 0.0237 0.997 0.996 0.004 0.000
#> GSM782735 2 0.0237 1.000 0.000 0.996 0.004
#> GSM782736 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782737 2 0.0237 1.000 0.000 0.996 0.004
#> GSM782738 1 0.0000 0.999 1.000 0.000 0.000
#> GSM782739 1 0.0237 0.997 0.996 0.004 0.000
#> GSM782740 2 0.0237 1.000 0.000 0.996 0.004
#> GSM782741 1 0.0237 0.997 0.996 0.004 0.000
#> GSM782742 3 0.0000 1.000 0.000 0.000 1.000
#> GSM782743 3 0.0000 1.000 0.000 0.000 1.000
#> GSM782744 3 0.0000 1.000 0.000 0.000 1.000
#> GSM782745 1 0.0237 0.997 0.996 0.004 0.000
#> GSM782746 2 0.0237 1.000 0.000 0.996 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.0188 0.932 0.996 0 0.000 0.004
#> GSM782697 1 0.2081 0.891 0.916 0 0.000 0.084
#> GSM782698 1 0.1389 0.887 0.952 0 0.000 0.048
#> GSM782699 1 0.1211 0.923 0.960 0 0.000 0.040
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782701 1 0.0000 0.934 1.000 0 0.000 0.000
#> GSM782702 1 0.1940 0.897 0.924 0 0.000 0.076
#> GSM782703 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782704 3 0.0188 0.998 0.000 0 0.996 0.004
#> GSM782705 4 0.4543 0.742 0.324 0 0.000 0.676
#> GSM782706 1 0.0188 0.933 0.996 0 0.000 0.004
#> GSM782707 1 0.0188 0.932 0.996 0 0.000 0.004
#> GSM782708 3 0.0188 0.998 0.000 0 0.996 0.004
#> GSM782709 1 0.2814 0.843 0.868 0 0.000 0.132
#> GSM782710 1 0.4277 0.638 0.720 0 0.000 0.280
#> GSM782711 1 0.0469 0.932 0.988 0 0.000 0.012
#> GSM782712 1 0.0000 0.934 1.000 0 0.000 0.000
#> GSM782713 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782715 4 0.4382 0.776 0.296 0 0.000 0.704
#> GSM782716 3 0.0188 0.998 0.000 0 0.996 0.004
#> GSM782717 4 0.1557 0.803 0.056 0 0.000 0.944
#> GSM782718 4 0.4454 0.764 0.308 0 0.000 0.692
#> GSM782719 1 0.0000 0.934 1.000 0 0.000 0.000
#> GSM782720 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782721 1 0.0188 0.933 0.996 0 0.000 0.004
#> GSM782722 4 0.4304 0.785 0.284 0 0.000 0.716
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782725 4 0.4250 0.790 0.276 0 0.000 0.724
#> GSM782726 4 0.1474 0.799 0.052 0 0.000 0.948
#> GSM782727 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782729 4 0.4250 0.790 0.276 0 0.000 0.724
#> GSM782730 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782731 4 0.0817 0.804 0.024 0 0.000 0.976
#> GSM782732 4 0.1022 0.806 0.032 0 0.000 0.968
#> GSM782733 3 0.0188 0.998 0.000 0 0.996 0.004
#> GSM782734 4 0.1474 0.799 0.052 0 0.000 0.948
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782736 4 0.4277 0.788 0.280 0 0.000 0.720
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782738 4 0.4356 0.780 0.292 0 0.000 0.708
#> GSM782739 4 0.1389 0.802 0.048 0 0.000 0.952
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782741 4 0.1557 0.801 0.056 0 0.000 0.944
#> GSM782742 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782743 3 0.0188 0.998 0.000 0 0.996 0.004
#> GSM782744 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782745 4 0.1474 0.799 0.052 0 0.000 0.948
#> GSM782746 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.0290 0.986 0.992 0 0 0.008 0.000
#> GSM782697 1 0.0404 0.982 0.988 0 0 0.000 0.012
#> GSM782698 1 0.0566 0.980 0.984 0 0 0.012 0.004
#> GSM782699 1 0.0324 0.983 0.992 0 0 0.004 0.004
#> GSM782700 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782701 1 0.0566 0.987 0.984 0 0 0.012 0.004
#> GSM782702 1 0.0771 0.978 0.976 0 0 0.004 0.020
#> GSM782703 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782704 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782705 4 0.2597 0.824 0.092 0 0 0.884 0.024
#> GSM782706 1 0.0671 0.985 0.980 0 0 0.016 0.004
#> GSM782707 1 0.0566 0.987 0.984 0 0 0.012 0.004
#> GSM782708 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782709 1 0.0963 0.965 0.964 0 0 0.000 0.036
#> GSM782710 5 0.2377 0.811 0.128 0 0 0.000 0.872
#> GSM782711 1 0.0000 0.984 1.000 0 0 0.000 0.000
#> GSM782712 1 0.0566 0.987 0.984 0 0 0.012 0.004
#> GSM782713 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782715 4 0.0566 0.885 0.012 0 0 0.984 0.004
#> GSM782716 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782717 5 0.2377 0.854 0.000 0 0 0.128 0.872
#> GSM782718 4 0.1205 0.871 0.040 0 0 0.956 0.004
#> GSM782719 1 0.0566 0.987 0.984 0 0 0.012 0.004
#> GSM782720 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782721 1 0.0798 0.984 0.976 0 0 0.016 0.008
#> GSM782722 4 0.0000 0.885 0.000 0 0 1.000 0.000
#> GSM782723 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782725 4 0.0162 0.885 0.000 0 0 0.996 0.004
#> GSM782726 5 0.0290 0.919 0.000 0 0 0.008 0.992
#> GSM782727 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782729 4 0.0162 0.885 0.000 0 0 0.996 0.004
#> GSM782730 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782731 4 0.4161 0.392 0.000 0 0 0.608 0.392
#> GSM782732 4 0.3966 0.517 0.000 0 0 0.664 0.336
#> GSM782733 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782734 5 0.0404 0.919 0.000 0 0 0.012 0.988
#> GSM782735 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782736 4 0.0162 0.885 0.000 0 0 0.996 0.004
#> GSM782737 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782738 4 0.0798 0.884 0.016 0 0 0.976 0.008
#> GSM782739 5 0.2329 0.858 0.000 0 0 0.124 0.876
#> GSM782740 2 0.0000 1.000 0.000 1 0 0.000 0.000
#> GSM782741 5 0.1485 0.914 0.020 0 0 0.032 0.948
#> GSM782742 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782743 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782744 3 0.0000 1.000 0.000 0 1 0.000 0.000
#> GSM782745 5 0.0290 0.919 0.000 0 0 0.008 0.992
#> GSM782746 2 0.0000 1.000 0.000 1 0 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM782696 1 0.3810 -0.550 0.572 0 0.000 0.000 0.428 0.000
#> GSM782697 1 0.0551 0.635 0.984 0 0.000 0.004 0.008 0.004
#> GSM782698 1 0.0717 0.643 0.976 0 0.000 0.008 0.016 0.000
#> GSM782699 1 0.0146 0.642 0.996 0 0.000 0.004 0.000 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782701 5 0.3847 0.778 0.456 0 0.000 0.000 0.544 0.000
#> GSM782702 1 0.3827 0.139 0.680 0 0.000 0.004 0.308 0.008
#> GSM782703 3 0.0000 0.998 0.000 0 1.000 0.000 0.000 0.000
#> GSM782704 3 0.0146 0.998 0.000 0 0.996 0.000 0.004 0.000
#> GSM782705 4 0.4165 0.656 0.172 0 0.000 0.756 0.052 0.020
#> GSM782706 5 0.4316 0.709 0.312 0 0.000 0.040 0.648 0.000
#> GSM782707 5 0.3866 0.739 0.484 0 0.000 0.000 0.516 0.000
#> GSM782708 3 0.0146 0.998 0.000 0 0.996 0.000 0.004 0.000
#> GSM782709 1 0.2333 0.607 0.884 0 0.000 0.000 0.092 0.024
#> GSM782710 6 0.4451 0.616 0.148 0 0.000 0.004 0.124 0.724
#> GSM782711 1 0.3288 0.196 0.724 0 0.000 0.000 0.276 0.000
#> GSM782712 5 0.3797 0.785 0.420 0 0.000 0.000 0.580 0.000
#> GSM782713 3 0.0000 0.998 0.000 0 1.000 0.000 0.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782715 4 0.1556 0.770 0.000 0 0.000 0.920 0.080 0.000
#> GSM782716 3 0.0146 0.998 0.000 0 0.996 0.000 0.004 0.000
#> GSM782717 6 0.4412 0.650 0.008 0 0.000 0.236 0.056 0.700
#> GSM782718 4 0.1745 0.768 0.020 0 0.000 0.924 0.056 0.000
#> GSM782719 5 0.3866 0.735 0.484 0 0.000 0.000 0.516 0.000
#> GSM782720 3 0.0000 0.998 0.000 0 1.000 0.000 0.000 0.000
#> GSM782721 5 0.4316 0.709 0.312 0 0.000 0.040 0.648 0.000
#> GSM782722 4 0.2912 0.724 0.000 0 0.000 0.784 0.216 0.000
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782725 4 0.3076 0.712 0.000 0 0.000 0.760 0.240 0.000
#> GSM782726 6 0.1007 0.768 0.000 0 0.000 0.000 0.044 0.956
#> GSM782727 3 0.0000 0.998 0.000 0 1.000 0.000 0.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782729 4 0.3076 0.712 0.000 0 0.000 0.760 0.240 0.000
#> GSM782730 3 0.0000 0.998 0.000 0 1.000 0.000 0.000 0.000
#> GSM782731 4 0.4278 0.381 0.000 0 0.000 0.632 0.032 0.336
#> GSM782732 4 0.4152 0.448 0.000 0 0.000 0.664 0.032 0.304
#> GSM782733 3 0.0146 0.998 0.000 0 0.996 0.000 0.004 0.000
#> GSM782734 6 0.1572 0.774 0.000 0 0.000 0.036 0.028 0.936
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782736 4 0.0146 0.771 0.000 0 0.000 0.996 0.004 0.000
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782738 4 0.1411 0.771 0.004 0 0.000 0.936 0.060 0.000
#> GSM782739 6 0.4520 0.627 0.012 0 0.000 0.248 0.052 0.688
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782741 6 0.4871 0.685 0.008 0 0.000 0.112 0.204 0.676
#> GSM782742 3 0.0000 0.998 0.000 0 1.000 0.000 0.000 0.000
#> GSM782743 3 0.0146 0.998 0.000 0 0.996 0.000 0.004 0.000
#> GSM782744 3 0.0000 0.998 0.000 0 1.000 0.000 0.000 0.000
#> GSM782745 6 0.1007 0.768 0.000 0 0.000 0.000 0.044 0.956
#> GSM782746 2 0.0000 1.000 0.000 1 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> MAD:skmeans 51 0.493 2
#> MAD:skmeans 51 0.642 3
#> MAD:skmeans 51 0.544 4
#> MAD:skmeans 50 0.538 5
#> MAD:skmeans 46 0.403 6
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 51941 rows and 51 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 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 1.000 1.000 1.000 0.2972 0.704 0.704
#> 3 3 1.000 1.000 1.000 0.9492 0.718 0.599
#> 4 4 0.956 0.939 0.975 0.2997 0.824 0.583
#> 5 5 0.924 0.921 0.962 0.0371 0.973 0.888
#> 6 6 0.877 0.771 0.927 0.0244 0.990 0.953
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM782696 1 0 1 1 0
#> GSM782697 1 0 1 1 0
#> GSM782698 1 0 1 1 0
#> GSM782699 1 0 1 1 0
#> GSM782700 2 0 1 0 1
#> GSM782701 1 0 1 1 0
#> GSM782702 1 0 1 1 0
#> GSM782703 1 0 1 1 0
#> GSM782704 1 0 1 1 0
#> GSM782705 1 0 1 1 0
#> GSM782706 1 0 1 1 0
#> GSM782707 1 0 1 1 0
#> GSM782708 1 0 1 1 0
#> GSM782709 1 0 1 1 0
#> GSM782710 1 0 1 1 0
#> GSM782711 1 0 1 1 0
#> GSM782712 1 0 1 1 0
#> GSM782713 1 0 1 1 0
#> GSM782714 2 0 1 0 1
#> GSM782715 1 0 1 1 0
#> GSM782716 1 0 1 1 0
#> GSM782717 1 0 1 1 0
#> GSM782718 1 0 1 1 0
#> GSM782719 1 0 1 1 0
#> GSM782720 1 0 1 1 0
#> GSM782721 1 0 1 1 0
#> GSM782722 1 0 1 1 0
#> GSM782723 2 0 1 0 1
#> GSM782724 2 0 1 0 1
#> GSM782725 1 0 1 1 0
#> GSM782726 1 0 1 1 0
#> GSM782727 1 0 1 1 0
#> GSM782728 2 0 1 0 1
#> GSM782729 1 0 1 1 0
#> GSM782730 1 0 1 1 0
#> GSM782731 1 0 1 1 0
#> GSM782732 1 0 1 1 0
#> GSM782733 1 0 1 1 0
#> GSM782734 1 0 1 1 0
#> GSM782735 2 0 1 0 1
#> GSM782736 1 0 1 1 0
#> GSM782737 2 0 1 0 1
#> GSM782738 1 0 1 1 0
#> GSM782739 1 0 1 1 0
#> GSM782740 2 0 1 0 1
#> GSM782741 1 0 1 1 0
#> GSM782742 1 0 1 1 0
#> GSM782743 1 0 1 1 0
#> GSM782744 1 0 1 1 0
#> GSM782745 1 0 1 1 0
#> GSM782746 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0 1 1 0 0
#> GSM782697 1 0 1 1 0 0
#> GSM782698 1 0 1 1 0 0
#> GSM782699 1 0 1 1 0 0
#> GSM782700 2 0 1 0 1 0
#> GSM782701 1 0 1 1 0 0
#> GSM782702 1 0 1 1 0 0
#> GSM782703 3 0 1 0 0 1
#> GSM782704 3 0 1 0 0 1
#> GSM782705 1 0 1 1 0 0
#> GSM782706 1 0 1 1 0 0
#> GSM782707 1 0 1 1 0 0
#> GSM782708 3 0 1 0 0 1
#> GSM782709 1 0 1 1 0 0
#> GSM782710 1 0 1 1 0 0
#> GSM782711 1 0 1 1 0 0
#> GSM782712 1 0 1 1 0 0
#> GSM782713 3 0 1 0 0 1
#> GSM782714 2 0 1 0 1 0
#> GSM782715 1 0 1 1 0 0
#> GSM782716 3 0 1 0 0 1
#> GSM782717 1 0 1 1 0 0
#> GSM782718 1 0 1 1 0 0
#> GSM782719 1 0 1 1 0 0
#> GSM782720 3 0 1 0 0 1
#> GSM782721 1 0 1 1 0 0
#> GSM782722 1 0 1 1 0 0
#> GSM782723 2 0 1 0 1 0
#> GSM782724 2 0 1 0 1 0
#> GSM782725 1 0 1 1 0 0
#> GSM782726 1 0 1 1 0 0
#> GSM782727 3 0 1 0 0 1
#> GSM782728 2 0 1 0 1 0
#> GSM782729 1 0 1 1 0 0
#> GSM782730 3 0 1 0 0 1
#> GSM782731 1 0 1 1 0 0
#> GSM782732 1 0 1 1 0 0
#> GSM782733 3 0 1 0 0 1
#> GSM782734 1 0 1 1 0 0
#> GSM782735 2 0 1 0 1 0
#> GSM782736 1 0 1 1 0 0
#> GSM782737 2 0 1 0 1 0
#> GSM782738 1 0 1 1 0 0
#> GSM782739 1 0 1 1 0 0
#> GSM782740 2 0 1 0 1 0
#> GSM782741 1 0 1 1 0 0
#> GSM782742 3 0 1 0 0 1
#> GSM782743 3 0 1 0 0 1
#> GSM782744 3 0 1 0 0 1
#> GSM782745 1 0 1 1 0 0
#> GSM782746 2 0 1 0 1 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.0000 0.966 1.000 0 0 0.000
#> GSM782697 1 0.0000 0.966 1.000 0 0 0.000
#> GSM782698 1 0.0000 0.966 1.000 0 0 0.000
#> GSM782699 1 0.0000 0.966 1.000 0 0 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782701 1 0.0000 0.966 1.000 0 0 0.000
#> GSM782702 1 0.0000 0.966 1.000 0 0 0.000
#> GSM782703 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782704 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782705 4 0.2345 0.855 0.100 0 0 0.900
#> GSM782706 1 0.0000 0.966 1.000 0 0 0.000
#> GSM782707 1 0.0000 0.966 1.000 0 0 0.000
#> GSM782708 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782709 1 0.0000 0.966 1.000 0 0 0.000
#> GSM782710 1 0.0000 0.966 1.000 0 0 0.000
#> GSM782711 1 0.0000 0.966 1.000 0 0 0.000
#> GSM782712 1 0.0000 0.966 1.000 0 0 0.000
#> GSM782713 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782715 1 0.1118 0.936 0.964 0 0 0.036
#> GSM782716 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782717 4 0.0000 0.931 0.000 0 0 1.000
#> GSM782718 4 0.0000 0.931 0.000 0 0 1.000
#> GSM782719 1 0.0000 0.966 1.000 0 0 0.000
#> GSM782720 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782721 1 0.2216 0.878 0.908 0 0 0.092
#> GSM782722 4 0.0000 0.931 0.000 0 0 1.000
#> GSM782723 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782725 4 0.0188 0.929 0.004 0 0 0.996
#> GSM782726 4 0.4955 0.193 0.444 0 0 0.556
#> GSM782727 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782729 4 0.0000 0.931 0.000 0 0 1.000
#> GSM782730 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782731 4 0.0000 0.931 0.000 0 0 1.000
#> GSM782732 4 0.0000 0.931 0.000 0 0 1.000
#> GSM782733 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782734 4 0.2704 0.842 0.124 0 0 0.876
#> GSM782735 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782736 4 0.0000 0.931 0.000 0 0 1.000
#> GSM782737 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782738 4 0.0000 0.931 0.000 0 0 1.000
#> GSM782739 4 0.0000 0.931 0.000 0 0 1.000
#> GSM782740 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782741 1 0.4624 0.456 0.660 0 0 0.340
#> GSM782742 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782743 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782744 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782745 4 0.2530 0.854 0.112 0 0 0.888
#> GSM782746 2 0.0000 1.000 0.000 1 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.0000 0.962 1.000 0 0.000 0.000 0.000
#> GSM782697 1 0.0000 0.962 1.000 0 0.000 0.000 0.000
#> GSM782698 1 0.0000 0.962 1.000 0 0.000 0.000 0.000
#> GSM782699 1 0.0000 0.962 1.000 0 0.000 0.000 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782701 1 0.0000 0.962 1.000 0 0.000 0.000 0.000
#> GSM782702 1 0.0000 0.962 1.000 0 0.000 0.000 0.000
#> GSM782703 3 0.3424 0.676 0.000 0 0.760 0.000 0.240
#> GSM782704 3 0.0290 0.953 0.000 0 0.992 0.000 0.008
#> GSM782705 4 0.2074 0.842 0.104 0 0.000 0.896 0.000
#> GSM782706 1 0.0693 0.951 0.980 0 0.000 0.008 0.012
#> GSM782707 1 0.0000 0.962 1.000 0 0.000 0.000 0.000
#> GSM782708 3 0.0000 0.955 0.000 0 1.000 0.000 0.000
#> GSM782709 1 0.0290 0.957 0.992 0 0.000 0.008 0.000
#> GSM782710 1 0.0000 0.962 1.000 0 0.000 0.000 0.000
#> GSM782711 1 0.0000 0.962 1.000 0 0.000 0.000 0.000
#> GSM782712 1 0.0000 0.962 1.000 0 0.000 0.000 0.000
#> GSM782713 5 0.0880 1.000 0.000 0 0.032 0.000 0.968
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782715 1 0.1281 0.931 0.956 0 0.000 0.032 0.012
#> GSM782716 3 0.0000 0.955 0.000 0 1.000 0.000 0.000
#> GSM782717 4 0.0000 0.914 0.000 0 0.000 1.000 0.000
#> GSM782718 4 0.0404 0.914 0.000 0 0.000 0.988 0.012
#> GSM782719 1 0.0000 0.962 1.000 0 0.000 0.000 0.000
#> GSM782720 5 0.0880 1.000 0.000 0 0.032 0.000 0.968
#> GSM782721 1 0.2248 0.876 0.900 0 0.000 0.088 0.012
#> GSM782722 4 0.0880 0.910 0.000 0 0.000 0.968 0.032
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782725 4 0.1041 0.909 0.004 0 0.000 0.964 0.032
#> GSM782726 4 0.4268 0.181 0.444 0 0.000 0.556 0.000
#> GSM782727 5 0.0880 1.000 0.000 0 0.032 0.000 0.968
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782729 4 0.1012 0.910 0.012 0 0.000 0.968 0.020
#> GSM782730 5 0.0880 1.000 0.000 0 0.032 0.000 0.968
#> GSM782731 4 0.0000 0.914 0.000 0 0.000 1.000 0.000
#> GSM782732 4 0.0000 0.914 0.000 0 0.000 1.000 0.000
#> GSM782733 3 0.0000 0.955 0.000 0 1.000 0.000 0.000
#> GSM782734 4 0.2329 0.824 0.124 0 0.000 0.876 0.000
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782736 4 0.0510 0.914 0.000 0 0.000 0.984 0.016
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782738 4 0.0693 0.914 0.008 0 0.000 0.980 0.012
#> GSM782739 4 0.0000 0.914 0.000 0 0.000 1.000 0.000
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782741 1 0.3983 0.469 0.660 0 0.000 0.340 0.000
#> GSM782742 5 0.0880 1.000 0.000 0 0.032 0.000 0.968
#> GSM782743 3 0.0000 0.955 0.000 0 1.000 0.000 0.000
#> GSM782744 3 0.0290 0.953 0.000 0 0.992 0.000 0.008
#> GSM782745 4 0.2179 0.836 0.112 0 0.000 0.888 0.000
#> GSM782746 2 0.0000 1.000 0.000 1 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
#> GSM782696 1 0.0146 0.9431 0.996 0.00 0.000 0.004 0.000 0.000
#> GSM782697 1 0.0000 0.9433 1.000 0.00 0.000 0.000 0.000 0.000
#> GSM782698 1 0.0146 0.9431 0.996 0.00 0.000 0.004 0.000 0.000
#> GSM782699 1 0.0146 0.9431 0.996 0.00 0.000 0.004 0.000 0.000
#> GSM782700 2 0.0000 0.9916 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM782701 1 0.0000 0.9433 1.000 0.00 0.000 0.000 0.000 0.000
#> GSM782702 1 0.0000 0.9433 1.000 0.00 0.000 0.000 0.000 0.000
#> GSM782703 3 0.3266 0.6136 0.000 0.00 0.728 0.000 0.272 0.000
#> GSM782704 3 0.0260 0.8997 0.000 0.00 0.992 0.000 0.008 0.000
#> GSM782705 6 0.1204 0.6468 0.056 0.00 0.000 0.000 0.000 0.944
#> GSM782706 1 0.2841 0.8188 0.824 0.00 0.000 0.164 0.000 0.012
#> GSM782707 1 0.0000 0.9433 1.000 0.00 0.000 0.000 0.000 0.000
#> GSM782708 3 0.0000 0.9027 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM782709 1 0.0260 0.9401 0.992 0.00 0.000 0.000 0.000 0.008
#> GSM782710 1 0.0000 0.9433 1.000 0.00 0.000 0.000 0.000 0.000
#> GSM782711 1 0.0146 0.9431 0.996 0.00 0.000 0.004 0.000 0.000
#> GSM782712 1 0.0000 0.9433 1.000 0.00 0.000 0.000 0.000 0.000
#> GSM782713 5 0.0000 1.0000 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM782714 2 0.0000 0.9916 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM782715 1 0.1074 0.9193 0.960 0.00 0.000 0.012 0.000 0.028
#> GSM782716 3 0.0000 0.9027 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM782717 6 0.0000 0.6920 0.000 0.00 0.000 0.000 0.000 1.000
#> GSM782718 6 0.0458 0.6873 0.000 0.00 0.000 0.016 0.000 0.984
#> GSM782719 1 0.1007 0.9227 0.956 0.00 0.000 0.044 0.000 0.000
#> GSM782720 5 0.0000 1.0000 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM782721 1 0.3578 0.7815 0.784 0.00 0.000 0.164 0.000 0.052
#> GSM782722 4 0.3672 0.0000 0.000 0.00 0.000 0.632 0.000 0.368
#> GSM782723 2 0.0000 0.9916 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM782724 2 0.0000 0.9916 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM782725 6 0.3866 -0.6393 0.000 0.00 0.000 0.484 0.000 0.516
#> GSM782726 6 0.3860 0.0581 0.472 0.00 0.000 0.000 0.000 0.528
#> GSM782727 5 0.0000 1.0000 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM782728 2 0.0000 0.9916 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM782729 6 0.4179 -0.6362 0.012 0.00 0.000 0.472 0.000 0.516
#> GSM782730 5 0.0000 1.0000 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM782731 6 0.0000 0.6920 0.000 0.00 0.000 0.000 0.000 1.000
#> GSM782732 6 0.0000 0.6920 0.000 0.00 0.000 0.000 0.000 1.000
#> GSM782733 3 0.0000 0.9027 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM782734 6 0.2416 0.5280 0.156 0.00 0.000 0.000 0.000 0.844
#> GSM782735 2 0.0937 0.9701 0.000 0.96 0.000 0.040 0.000 0.000
#> GSM782736 6 0.0547 0.6836 0.000 0.00 0.000 0.020 0.000 0.980
#> GSM782737 2 0.0000 0.9916 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM782738 6 0.0725 0.6844 0.012 0.00 0.000 0.012 0.000 0.976
#> GSM782739 6 0.0000 0.6920 0.000 0.00 0.000 0.000 0.000 1.000
#> GSM782740 2 0.0000 0.9916 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM782741 1 0.3547 0.4873 0.668 0.00 0.000 0.000 0.000 0.332
#> GSM782742 5 0.0000 1.0000 0.000 0.00 0.000 0.000 1.000 0.000
#> GSM782743 3 0.0000 0.9027 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM782744 3 0.3758 0.6688 0.000 0.00 0.668 0.324 0.008 0.000
#> GSM782745 6 0.2260 0.5512 0.140 0.00 0.000 0.000 0.000 0.860
#> GSM782746 2 0.0937 0.9701 0.000 0.96 0.000 0.040 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> MAD:pam 51 0.648 2
#> MAD:pam 51 0.642 3
#> MAD:pam 49 0.551 4
#> MAD:pam 49 0.520 5
#> MAD:pam 46 0.523 6
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 51941 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.633 0.903 0.919 0.4268 0.506 0.506
#> 3 3 1.000 0.998 0.999 0.3560 0.915 0.833
#> 4 4 0.701 0.698 0.838 0.1957 0.956 0.896
#> 5 5 0.652 0.532 0.743 0.0859 0.802 0.509
#> 6 6 0.776 0.662 0.865 0.0650 0.823 0.418
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
#> GSM782696 1 0.000 1.000 1.000 0.000
#> GSM782697 1 0.000 1.000 1.000 0.000
#> GSM782698 1 0.000 1.000 1.000 0.000
#> GSM782699 1 0.000 1.000 1.000 0.000
#> GSM782700 2 0.000 0.767 0.000 1.000
#> GSM782701 1 0.000 1.000 1.000 0.000
#> GSM782702 1 0.000 1.000 1.000 0.000
#> GSM782703 2 0.929 0.764 0.344 0.656
#> GSM782704 2 0.929 0.764 0.344 0.656
#> GSM782705 1 0.000 1.000 1.000 0.000
#> GSM782706 1 0.000 1.000 1.000 0.000
#> GSM782707 1 0.000 1.000 1.000 0.000
#> GSM782708 2 0.929 0.764 0.344 0.656
#> GSM782709 1 0.000 1.000 1.000 0.000
#> GSM782710 1 0.000 1.000 1.000 0.000
#> GSM782711 1 0.000 1.000 1.000 0.000
#> GSM782712 1 0.000 1.000 1.000 0.000
#> GSM782713 2 0.929 0.764 0.344 0.656
#> GSM782714 2 0.000 0.767 0.000 1.000
#> GSM782715 1 0.000 1.000 1.000 0.000
#> GSM782716 2 0.929 0.764 0.344 0.656
#> GSM782717 1 0.000 1.000 1.000 0.000
#> GSM782718 1 0.000 1.000 1.000 0.000
#> GSM782719 1 0.000 1.000 1.000 0.000
#> GSM782720 2 0.929 0.764 0.344 0.656
#> GSM782721 1 0.000 1.000 1.000 0.000
#> GSM782722 1 0.000 1.000 1.000 0.000
#> GSM782723 2 0.000 0.767 0.000 1.000
#> GSM782724 2 0.000 0.767 0.000 1.000
#> GSM782725 1 0.000 1.000 1.000 0.000
#> GSM782726 1 0.000 1.000 1.000 0.000
#> GSM782727 2 0.929 0.764 0.344 0.656
#> GSM782728 2 0.000 0.767 0.000 1.000
#> GSM782729 1 0.000 1.000 1.000 0.000
#> GSM782730 2 0.929 0.764 0.344 0.656
#> GSM782731 1 0.000 1.000 1.000 0.000
#> GSM782732 1 0.000 1.000 1.000 0.000
#> GSM782733 2 0.929 0.764 0.344 0.656
#> GSM782734 1 0.000 1.000 1.000 0.000
#> GSM782735 2 0.000 0.767 0.000 1.000
#> GSM782736 1 0.000 1.000 1.000 0.000
#> GSM782737 2 0.000 0.767 0.000 1.000
#> GSM782738 1 0.000 1.000 1.000 0.000
#> GSM782739 1 0.000 1.000 1.000 0.000
#> GSM782740 2 0.000 0.767 0.000 1.000
#> GSM782741 1 0.000 1.000 1.000 0.000
#> GSM782742 2 0.929 0.764 0.344 0.656
#> GSM782743 2 0.929 0.764 0.344 0.656
#> GSM782744 2 0.929 0.764 0.344 0.656
#> GSM782745 1 0.000 1.000 1.000 0.000
#> GSM782746 2 0.000 0.767 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782697 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782698 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782699 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782700 2 0.0000 1.000 0.000 1.000 0.000
#> GSM782701 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782702 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782703 3 0.0237 0.993 0.000 0.004 0.996
#> GSM782704 3 0.0000 0.993 0.000 0.000 1.000
#> GSM782705 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782706 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782707 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782708 3 0.0000 0.993 0.000 0.000 1.000
#> GSM782709 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782710 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782711 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782712 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782713 3 0.0237 0.993 0.000 0.004 0.996
#> GSM782714 2 0.0000 1.000 0.000 1.000 0.000
#> GSM782715 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782716 3 0.0000 0.993 0.000 0.000 1.000
#> GSM782717 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782718 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782719 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782720 3 0.0237 0.993 0.000 0.004 0.996
#> GSM782721 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782722 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782723 2 0.0000 1.000 0.000 1.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1.000 0.000
#> GSM782725 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782726 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782727 3 0.0237 0.993 0.000 0.004 0.996
#> GSM782728 2 0.0000 1.000 0.000 1.000 0.000
#> GSM782729 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782730 3 0.0237 0.993 0.000 0.004 0.996
#> GSM782731 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782732 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782733 3 0.0000 0.993 0.000 0.000 1.000
#> GSM782734 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782735 2 0.0000 1.000 0.000 1.000 0.000
#> GSM782736 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782737 2 0.0000 1.000 0.000 1.000 0.000
#> GSM782738 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782739 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782740 2 0.0000 1.000 0.000 1.000 0.000
#> GSM782741 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782742 3 0.0237 0.993 0.000 0.004 0.996
#> GSM782743 3 0.0000 0.993 0.000 0.000 1.000
#> GSM782744 3 0.1411 0.948 0.036 0.000 0.964
#> GSM782745 1 0.0000 1.000 1.000 0.000 0.000
#> GSM782746 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
#> GSM782696 1 0.2973 0.518 0.856 0 0.000 0.144
#> GSM782697 1 0.1211 0.563 0.960 0 0.000 0.040
#> GSM782698 1 0.4477 0.502 0.688 0 0.000 0.312
#> GSM782699 1 0.2704 0.509 0.876 0 0.000 0.124
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782701 1 0.4804 0.474 0.616 0 0.000 0.384
#> GSM782702 1 0.0469 0.566 0.988 0 0.000 0.012
#> GSM782703 3 0.0000 0.980 0.000 0 1.000 0.000
#> GSM782704 3 0.0000 0.980 0.000 0 1.000 0.000
#> GSM782705 1 0.0921 0.569 0.972 0 0.000 0.028
#> GSM782706 1 0.4790 0.480 0.620 0 0.000 0.380
#> GSM782707 1 0.4222 0.534 0.728 0 0.000 0.272
#> GSM782708 3 0.0000 0.980 0.000 0 1.000 0.000
#> GSM782709 1 0.4277 0.500 0.720 0 0.000 0.280
#> GSM782710 1 0.3266 0.275 0.832 0 0.000 0.168
#> GSM782711 1 0.2704 0.509 0.876 0 0.000 0.124
#> GSM782712 1 0.2345 0.528 0.900 0 0.000 0.100
#> GSM782713 3 0.0000 0.980 0.000 0 1.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782715 1 0.4977 0.227 0.540 0 0.000 0.460
#> GSM782716 3 0.0188 0.978 0.000 0 0.996 0.004
#> GSM782717 1 0.3219 0.502 0.836 0 0.000 0.164
#> GSM782718 1 0.3610 0.592 0.800 0 0.000 0.200
#> GSM782719 1 0.4431 0.515 0.696 0 0.000 0.304
#> GSM782720 3 0.0000 0.980 0.000 0 1.000 0.000
#> GSM782721 1 0.4817 0.474 0.612 0 0.000 0.388
#> GSM782722 1 0.4277 0.555 0.720 0 0.000 0.280
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782725 1 0.4406 -0.150 0.700 0 0.000 0.300
#> GSM782726 4 0.4916 0.989 0.424 0 0.000 0.576
#> GSM782727 3 0.0000 0.980 0.000 0 1.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782729 1 0.1389 0.548 0.952 0 0.000 0.048
#> GSM782730 3 0.0000 0.980 0.000 0 1.000 0.000
#> GSM782731 1 0.4585 0.474 0.668 0 0.000 0.332
#> GSM782732 1 0.4222 0.505 0.728 0 0.000 0.272
#> GSM782733 3 0.0000 0.980 0.000 0 1.000 0.000
#> GSM782734 1 0.4643 0.353 0.656 0 0.000 0.344
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782736 1 0.4916 0.437 0.576 0 0.000 0.424
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782738 1 0.4661 0.514 0.652 0 0.000 0.348
#> GSM782739 1 0.1867 0.558 0.928 0 0.000 0.072
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782741 1 0.3569 0.473 0.804 0 0.000 0.196
#> GSM782742 3 0.0000 0.980 0.000 0 1.000 0.000
#> GSM782743 3 0.0000 0.980 0.000 0 1.000 0.000
#> GSM782744 3 0.4827 0.741 0.092 0 0.784 0.124
#> GSM782745 4 0.4925 0.989 0.428 0 0.000 0.572
#> GSM782746 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.4235 0.520 0.576 0 0.000 0.424 0.000
#> GSM782697 1 0.4437 0.483 0.532 0 0.000 0.464 0.004
#> GSM782698 1 0.4227 0.398 0.580 0 0.000 0.420 0.000
#> GSM782699 1 0.3913 0.578 0.676 0 0.000 0.324 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782701 4 0.4201 -0.351 0.408 0 0.000 0.592 0.000
#> GSM782702 1 0.4283 0.457 0.544 0 0.000 0.456 0.000
#> GSM782703 3 0.3774 0.850 0.000 0 0.704 0.000 0.296
#> GSM782704 3 0.4101 0.756 0.000 0 0.628 0.000 0.372
#> GSM782705 1 0.3983 0.576 0.660 0 0.000 0.340 0.000
#> GSM782706 4 0.4307 -0.441 0.500 0 0.000 0.500 0.000
#> GSM782707 1 0.4306 0.397 0.508 0 0.000 0.492 0.000
#> GSM782708 5 0.0794 0.964 0.000 0 0.028 0.000 0.972
#> GSM782709 4 0.4430 -0.463 0.456 0 0.000 0.540 0.004
#> GSM782710 4 0.4789 0.253 0.392 0 0.024 0.584 0.000
#> GSM782711 1 0.4030 0.576 0.648 0 0.000 0.352 0.000
#> GSM782712 1 0.4126 0.557 0.620 0 0.000 0.380 0.000
#> GSM782713 3 0.3480 0.883 0.000 0 0.752 0.000 0.248
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782715 4 0.2011 0.413 0.088 0 0.000 0.908 0.004
#> GSM782716 5 0.0162 0.972 0.000 0 0.004 0.000 0.996
#> GSM782717 4 0.3109 0.342 0.200 0 0.000 0.800 0.000
#> GSM782718 4 0.3837 0.184 0.308 0 0.000 0.692 0.000
#> GSM782719 1 0.4307 0.364 0.500 0 0.000 0.500 0.000
#> GSM782720 3 0.3336 0.880 0.000 0 0.772 0.000 0.228
#> GSM782721 4 0.4114 -0.290 0.376 0 0.000 0.624 0.000
#> GSM782722 4 0.3983 0.250 0.340 0 0.000 0.660 0.000
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782725 1 0.4440 -0.309 0.528 0 0.004 0.468 0.000
#> GSM782726 4 0.7479 0.224 0.320 0 0.164 0.448 0.068
#> GSM782727 3 0.3508 0.882 0.000 0 0.748 0.000 0.252
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782729 4 0.4074 0.274 0.364 0 0.000 0.636 0.000
#> GSM782730 3 0.3395 0.883 0.000 0 0.764 0.000 0.236
#> GSM782731 4 0.0162 0.419 0.004 0 0.000 0.996 0.000
#> GSM782732 4 0.2020 0.392 0.100 0 0.000 0.900 0.000
#> GSM782733 5 0.0162 0.972 0.000 0 0.004 0.000 0.996
#> GSM782734 4 0.0963 0.419 0.036 0 0.000 0.964 0.000
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782736 4 0.3480 0.308 0.248 0 0.000 0.752 0.000
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782738 4 0.2813 0.366 0.168 0 0.000 0.832 0.000
#> GSM782739 4 0.3003 0.343 0.188 0 0.000 0.812 0.000
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782741 4 0.3003 0.348 0.188 0 0.000 0.812 0.000
#> GSM782742 3 0.3461 0.876 0.004 0 0.772 0.000 0.224
#> GSM782743 5 0.0880 0.959 0.000 0 0.032 0.000 0.968
#> GSM782744 3 0.6490 0.443 0.028 0 0.584 0.160 0.228
#> GSM782745 4 0.7469 0.224 0.328 0 0.160 0.444 0.068
#> GSM782746 2 0.0000 1.000 0.000 1 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
#> GSM782696 1 0.2912 0.5856 0.784 0 0.000 0.000 0.000 0.216
#> GSM782697 1 0.3995 0.0995 0.516 0 0.000 0.000 0.004 0.480
#> GSM782698 1 0.0508 0.6440 0.984 0 0.000 0.000 0.004 0.012
#> GSM782699 1 0.3833 0.2193 0.556 0 0.000 0.000 0.000 0.444
#> GSM782700 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782701 1 0.1918 0.6749 0.904 0 0.000 0.000 0.008 0.088
#> GSM782702 6 0.2135 0.6196 0.128 0 0.000 0.000 0.000 0.872
#> GSM782703 3 0.0405 0.8629 0.000 0 0.988 0.008 0.004 0.000
#> GSM782704 3 0.3789 0.3270 0.000 0 0.584 0.416 0.000 0.000
#> GSM782705 6 0.3862 -0.1562 0.476 0 0.000 0.000 0.000 0.524
#> GSM782706 1 0.1524 0.6706 0.932 0 0.000 0.000 0.008 0.060
#> GSM782707 1 0.1765 0.6716 0.904 0 0.000 0.000 0.000 0.096
#> GSM782708 4 0.0000 1.0000 0.000 0 0.000 1.000 0.000 0.000
#> GSM782709 1 0.4093 0.1515 0.516 0 0.000 0.000 0.008 0.476
#> GSM782710 6 0.3290 0.5008 0.004 0 0.000 0.000 0.252 0.744
#> GSM782711 6 0.3869 -0.1876 0.500 0 0.000 0.000 0.000 0.500
#> GSM782712 6 0.3838 -0.0383 0.448 0 0.000 0.000 0.000 0.552
#> GSM782713 3 0.0260 0.8637 0.000 0 0.992 0.008 0.000 0.000
#> GSM782714 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782715 6 0.3110 0.5248 0.196 0 0.000 0.000 0.012 0.792
#> GSM782716 4 0.0000 1.0000 0.000 0 0.000 1.000 0.000 0.000
#> GSM782717 6 0.0520 0.7128 0.008 0 0.000 0.000 0.008 0.984
#> GSM782718 1 0.3309 0.5214 0.720 0 0.000 0.000 0.000 0.280
#> GSM782719 1 0.1075 0.6705 0.952 0 0.000 0.000 0.000 0.048
#> GSM782720 3 0.0000 0.8637 0.000 0 1.000 0.000 0.000 0.000
#> GSM782721 1 0.2513 0.6656 0.852 0 0.000 0.000 0.008 0.140
#> GSM782722 1 0.3795 0.2794 0.632 0 0.000 0.000 0.004 0.364
#> GSM782723 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782725 6 0.3394 0.5671 0.012 0 0.000 0.000 0.236 0.752
#> GSM782726 5 0.0291 0.9926 0.004 0 0.000 0.000 0.992 0.004
#> GSM782727 3 0.0260 0.8637 0.000 0 0.992 0.008 0.000 0.000
#> GSM782728 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782729 6 0.1168 0.7078 0.016 0 0.000 0.000 0.028 0.956
#> GSM782730 3 0.0000 0.8637 0.000 0 1.000 0.000 0.000 0.000
#> GSM782731 6 0.0806 0.7105 0.020 0 0.000 0.000 0.008 0.972
#> GSM782732 6 0.0000 0.7117 0.000 0 0.000 0.000 0.000 1.000
#> GSM782733 4 0.0000 1.0000 0.000 0 0.000 1.000 0.000 0.000
#> GSM782734 6 0.0858 0.7091 0.004 0 0.000 0.000 0.028 0.968
#> GSM782735 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782736 1 0.3930 0.1639 0.576 0 0.000 0.000 0.004 0.420
#> GSM782737 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782738 6 0.3841 0.1728 0.380 0 0.000 0.000 0.004 0.616
#> GSM782739 6 0.0622 0.7133 0.008 0 0.000 0.000 0.012 0.980
#> GSM782740 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782741 6 0.0146 0.7126 0.004 0 0.000 0.000 0.000 0.996
#> GSM782742 3 0.0000 0.8637 0.000 0 1.000 0.000 0.000 0.000
#> GSM782743 4 0.0000 1.0000 0.000 0 0.000 1.000 0.000 0.000
#> GSM782744 3 0.4212 0.2688 0.000 0 0.560 0.016 0.424 0.000
#> GSM782745 5 0.0260 0.9926 0.000 0 0.000 0.000 0.992 0.008
#> GSM782746 2 0.0000 1.0000 0.000 1 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> MAD:mclust 51 0.493 2
#> MAD:mclust 51 0.642 3
#> MAD:mclust 40 0.754 4
#> MAD:mclust 25 0.428 5
#> MAD:mclust 40 0.576 6
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 51941 rows and 51 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 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 0.999 1.000 0.2977 0.704 0.704
#> 3 3 1.000 1.000 1.000 0.9456 0.718 0.599
#> 4 4 0.730 0.639 0.859 0.1833 0.956 0.896
#> 5 5 0.736 0.765 0.858 0.1179 0.825 0.547
#> 6 6 0.782 0.713 0.831 0.0352 1.000 1.000
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> 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
#> GSM782696 1 0.0000 0.999 1.000 0.000
#> GSM782697 1 0.0000 0.999 1.000 0.000
#> GSM782698 1 0.0000 0.999 1.000 0.000
#> GSM782699 1 0.0000 0.999 1.000 0.000
#> GSM782700 2 0.0000 1.000 0.000 1.000
#> GSM782701 1 0.0000 0.999 1.000 0.000
#> GSM782702 1 0.0000 0.999 1.000 0.000
#> GSM782703 1 0.1414 0.980 0.980 0.020
#> GSM782704 1 0.0000 0.999 1.000 0.000
#> GSM782705 1 0.0000 0.999 1.000 0.000
#> GSM782706 1 0.0000 0.999 1.000 0.000
#> GSM782707 1 0.0000 0.999 1.000 0.000
#> GSM782708 1 0.0000 0.999 1.000 0.000
#> GSM782709 1 0.0000 0.999 1.000 0.000
#> GSM782710 1 0.0000 0.999 1.000 0.000
#> GSM782711 1 0.0000 0.999 1.000 0.000
#> GSM782712 1 0.0000 0.999 1.000 0.000
#> GSM782713 1 0.0376 0.996 0.996 0.004
#> GSM782714 2 0.0000 1.000 0.000 1.000
#> GSM782715 1 0.0000 0.999 1.000 0.000
#> GSM782716 1 0.0000 0.999 1.000 0.000
#> GSM782717 1 0.0000 0.999 1.000 0.000
#> GSM782718 1 0.0000 0.999 1.000 0.000
#> GSM782719 1 0.0000 0.999 1.000 0.000
#> GSM782720 1 0.0000 0.999 1.000 0.000
#> GSM782721 1 0.0000 0.999 1.000 0.000
#> GSM782722 1 0.0000 0.999 1.000 0.000
#> GSM782723 2 0.0000 1.000 0.000 1.000
#> GSM782724 2 0.0000 1.000 0.000 1.000
#> GSM782725 1 0.0000 0.999 1.000 0.000
#> GSM782726 1 0.0000 0.999 1.000 0.000
#> GSM782727 1 0.0000 0.999 1.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1.000
#> GSM782729 1 0.0000 0.999 1.000 0.000
#> GSM782730 1 0.0000 0.999 1.000 0.000
#> GSM782731 1 0.0000 0.999 1.000 0.000
#> GSM782732 1 0.0000 0.999 1.000 0.000
#> GSM782733 1 0.0000 0.999 1.000 0.000
#> GSM782734 1 0.0000 0.999 1.000 0.000
#> GSM782735 2 0.0000 1.000 0.000 1.000
#> GSM782736 1 0.0000 0.999 1.000 0.000
#> GSM782737 2 0.0000 1.000 0.000 1.000
#> GSM782738 1 0.0000 0.999 1.000 0.000
#> GSM782739 1 0.0000 0.999 1.000 0.000
#> GSM782740 2 0.0000 1.000 0.000 1.000
#> GSM782741 1 0.0000 0.999 1.000 0.000
#> GSM782742 1 0.0000 0.999 1.000 0.000
#> GSM782743 1 0.0000 0.999 1.000 0.000
#> GSM782744 1 0.0000 0.999 1.000 0.000
#> GSM782745 1 0.0000 0.999 1.000 0.000
#> GSM782746 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
#> GSM782696 1 0 1 1 0 0
#> GSM782697 1 0 1 1 0 0
#> GSM782698 1 0 1 1 0 0
#> GSM782699 1 0 1 1 0 0
#> GSM782700 2 0 1 0 1 0
#> GSM782701 1 0 1 1 0 0
#> GSM782702 1 0 1 1 0 0
#> GSM782703 3 0 1 0 0 1
#> GSM782704 3 0 1 0 0 1
#> GSM782705 1 0 1 1 0 0
#> GSM782706 1 0 1 1 0 0
#> GSM782707 1 0 1 1 0 0
#> GSM782708 3 0 1 0 0 1
#> GSM782709 1 0 1 1 0 0
#> GSM782710 1 0 1 1 0 0
#> GSM782711 1 0 1 1 0 0
#> GSM782712 1 0 1 1 0 0
#> GSM782713 3 0 1 0 0 1
#> GSM782714 2 0 1 0 1 0
#> GSM782715 1 0 1 1 0 0
#> GSM782716 3 0 1 0 0 1
#> GSM782717 1 0 1 1 0 0
#> GSM782718 1 0 1 1 0 0
#> GSM782719 1 0 1 1 0 0
#> GSM782720 3 0 1 0 0 1
#> GSM782721 1 0 1 1 0 0
#> GSM782722 1 0 1 1 0 0
#> GSM782723 2 0 1 0 1 0
#> GSM782724 2 0 1 0 1 0
#> GSM782725 1 0 1 1 0 0
#> GSM782726 1 0 1 1 0 0
#> GSM782727 3 0 1 0 0 1
#> GSM782728 2 0 1 0 1 0
#> GSM782729 1 0 1 1 0 0
#> GSM782730 3 0 1 0 0 1
#> GSM782731 1 0 1 1 0 0
#> GSM782732 1 0 1 1 0 0
#> GSM782733 3 0 1 0 0 1
#> GSM782734 1 0 1 1 0 0
#> GSM782735 2 0 1 0 1 0
#> GSM782736 1 0 1 1 0 0
#> GSM782737 2 0 1 0 1 0
#> GSM782738 1 0 1 1 0 0
#> GSM782739 1 0 1 1 0 0
#> GSM782740 2 0 1 0 1 0
#> GSM782741 1 0 1 1 0 0
#> GSM782742 3 0 1 0 0 1
#> GSM782743 3 0 1 0 0 1
#> GSM782744 3 0 1 0 0 1
#> GSM782745 1 0 1 1 0 0
#> GSM782746 2 0 1 0 1 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.3726 0.392 0.788 0 0.000 0.212
#> GSM782697 1 0.4843 -0.278 0.604 0 0.000 0.396
#> GSM782698 1 0.4008 0.352 0.756 0 0.000 0.244
#> GSM782699 1 0.3172 0.479 0.840 0 0.000 0.160
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782701 1 0.4817 -0.255 0.612 0 0.000 0.388
#> GSM782702 1 0.2647 0.524 0.880 0 0.000 0.120
#> GSM782703 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782704 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782705 1 0.1474 0.599 0.948 0 0.000 0.052
#> GSM782706 4 0.4992 0.291 0.476 0 0.000 0.524
#> GSM782707 1 0.4304 0.217 0.716 0 0.000 0.284
#> GSM782708 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782709 1 0.3444 0.430 0.816 0 0.000 0.184
#> GSM782710 1 0.1211 0.596 0.960 0 0.000 0.040
#> GSM782711 1 0.4040 0.292 0.752 0 0.000 0.248
#> GSM782712 1 0.4679 -0.108 0.648 0 0.000 0.352
#> GSM782713 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782715 1 0.4277 0.460 0.720 0 0.000 0.280
#> GSM782716 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782717 1 0.0188 0.601 0.996 0 0.000 0.004
#> GSM782718 1 0.3975 0.495 0.760 0 0.000 0.240
#> GSM782719 4 0.4790 0.502 0.380 0 0.000 0.620
#> GSM782720 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782721 1 0.4888 -0.252 0.588 0 0.000 0.412
#> GSM782722 1 0.4697 0.374 0.644 0 0.000 0.356
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782725 1 0.4356 0.446 0.708 0 0.000 0.292
#> GSM782726 1 0.1716 0.602 0.936 0 0.000 0.064
#> GSM782727 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782729 1 0.3975 0.489 0.760 0 0.000 0.240
#> GSM782730 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782731 1 0.2973 0.566 0.856 0 0.000 0.144
#> GSM782732 1 0.2469 0.585 0.892 0 0.000 0.108
#> GSM782733 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782734 1 0.1022 0.600 0.968 0 0.000 0.032
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782736 1 0.4382 0.446 0.704 0 0.000 0.296
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782738 1 0.4382 0.455 0.704 0 0.000 0.296
#> GSM782739 1 0.0817 0.606 0.976 0 0.000 0.024
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782741 1 0.2469 0.548 0.892 0 0.000 0.108
#> GSM782742 3 0.0000 0.998 0.000 0 1.000 0.000
#> GSM782743 3 0.0188 0.996 0.000 0 0.996 0.004
#> GSM782744 3 0.0707 0.982 0.000 0 0.980 0.020
#> GSM782745 1 0.2216 0.590 0.908 0 0.000 0.092
#> GSM782746 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.4425 -0.346 0.544 0 0.000 0.004 0.452
#> GSM782697 1 0.4272 0.508 0.752 0 0.000 0.052 0.196
#> GSM782698 1 0.5144 0.342 0.640 0 0.000 0.068 0.292
#> GSM782699 1 0.3389 0.625 0.836 0 0.000 0.048 0.116
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782701 5 0.5320 0.801 0.368 0 0.000 0.060 0.572
#> GSM782702 1 0.2795 0.649 0.872 0 0.000 0.028 0.100
#> GSM782703 3 0.0000 0.994 0.000 0 1.000 0.000 0.000
#> GSM782704 3 0.0000 0.994 0.000 0 1.000 0.000 0.000
#> GSM782705 1 0.2653 0.703 0.880 0 0.000 0.096 0.024
#> GSM782706 4 0.6117 0.287 0.136 0 0.000 0.504 0.360
#> GSM782707 5 0.5707 0.762 0.364 0 0.000 0.092 0.544
#> GSM782708 3 0.0000 0.994 0.000 0 1.000 0.000 0.000
#> GSM782709 1 0.3696 0.498 0.772 0 0.000 0.016 0.212
#> GSM782710 1 0.0451 0.714 0.988 0 0.000 0.004 0.008
#> GSM782711 1 0.3837 0.307 0.692 0 0.000 0.000 0.308
#> GSM782712 5 0.4958 0.793 0.372 0 0.000 0.036 0.592
#> GSM782713 3 0.0000 0.994 0.000 0 1.000 0.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782715 4 0.3366 0.776 0.212 0 0.000 0.784 0.004
#> GSM782716 3 0.0000 0.994 0.000 0 1.000 0.000 0.000
#> GSM782717 1 0.1608 0.728 0.928 0 0.000 0.072 0.000
#> GSM782718 4 0.3663 0.777 0.208 0 0.000 0.776 0.016
#> GSM782719 5 0.3419 0.649 0.180 0 0.000 0.016 0.804
#> GSM782720 3 0.0000 0.994 0.000 0 1.000 0.000 0.000
#> GSM782721 4 0.6447 0.198 0.192 0 0.000 0.472 0.336
#> GSM782722 4 0.2824 0.764 0.116 0 0.000 0.864 0.020
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782725 4 0.2719 0.782 0.144 0 0.000 0.852 0.004
#> GSM782726 1 0.1877 0.728 0.924 0 0.000 0.064 0.012
#> GSM782727 3 0.0000 0.994 0.000 0 1.000 0.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782729 4 0.4356 0.563 0.340 0 0.000 0.648 0.012
#> GSM782730 3 0.0000 0.994 0.000 0 1.000 0.000 0.000
#> GSM782731 1 0.4161 0.500 0.704 0 0.000 0.280 0.016
#> GSM782732 1 0.3565 0.659 0.800 0 0.000 0.176 0.024
#> GSM782733 3 0.0162 0.992 0.000 0 0.996 0.004 0.000
#> GSM782734 1 0.2411 0.716 0.884 0 0.000 0.108 0.008
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782736 4 0.3093 0.784 0.168 0 0.000 0.824 0.008
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782738 4 0.3438 0.787 0.172 0 0.000 0.808 0.020
#> GSM782739 1 0.1965 0.724 0.904 0 0.000 0.096 0.000
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782741 1 0.4155 0.642 0.780 0 0.000 0.144 0.076
#> GSM782742 3 0.0000 0.994 0.000 0 1.000 0.000 0.000
#> GSM782743 3 0.0162 0.992 0.000 0 0.996 0.004 0.000
#> GSM782744 3 0.1571 0.934 0.000 0 0.936 0.060 0.004
#> GSM782745 1 0.2361 0.718 0.892 0 0.000 0.096 0.012
#> GSM782746 2 0.0000 1.000 0.000 1 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
#> GSM782696 6 0.4561 -0.174 0.428 0.000 0.000 0.000 NA 0.536
#> GSM782697 6 0.4624 0.562 0.120 0.000 0.000 0.000 NA 0.688
#> GSM782698 6 0.6329 0.139 0.308 0.000 0.000 0.012 NA 0.412
#> GSM782699 6 0.3412 0.640 0.064 0.000 0.000 0.000 NA 0.808
#> GSM782700 2 0.0146 0.998 0.000 0.996 0.000 0.000 NA 0.000
#> GSM782701 1 0.4464 0.749 0.624 0.000 0.000 0.028 NA 0.340
#> GSM782702 6 0.3121 0.567 0.192 0.000 0.000 0.004 NA 0.796
#> GSM782703 3 0.0146 0.981 0.000 0.000 0.996 0.000 NA 0.000
#> GSM782704 3 0.0000 0.981 0.000 0.000 1.000 0.000 NA 0.000
#> GSM782705 6 0.3732 0.576 0.004 0.000 0.000 0.024 NA 0.744
#> GSM782706 4 0.6721 -0.197 0.352 0.000 0.000 0.404 NA 0.192
#> GSM782707 1 0.4552 0.778 0.684 0.000 0.000 0.040 NA 0.256
#> GSM782708 3 0.0000 0.981 0.000 0.000 1.000 0.000 NA 0.000
#> GSM782709 6 0.3507 0.478 0.232 0.000 0.000 0.004 NA 0.752
#> GSM782710 6 0.2095 0.660 0.076 0.000 0.000 0.004 NA 0.904
#> GSM782711 6 0.4153 0.241 0.340 0.000 0.000 0.000 NA 0.636
#> GSM782712 1 0.4015 0.764 0.656 0.000 0.000 0.008 NA 0.328
#> GSM782713 3 0.0146 0.981 0.000 0.000 0.996 0.000 NA 0.000
#> GSM782714 2 0.0000 0.999 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782715 4 0.2595 0.735 0.020 0.000 0.000 0.880 NA 0.084
#> GSM782716 3 0.0000 0.981 0.000 0.000 1.000 0.000 NA 0.000
#> GSM782717 6 0.1364 0.680 0.012 0.000 0.000 0.020 NA 0.952
#> GSM782718 4 0.3174 0.727 0.012 0.000 0.000 0.840 NA 0.108
#> GSM782719 1 0.3657 0.629 0.792 0.000 0.000 0.000 NA 0.100
#> GSM782720 3 0.0146 0.981 0.000 0.000 0.996 0.000 NA 0.000
#> GSM782721 4 0.6994 -0.290 0.324 0.000 0.000 0.368 NA 0.244
#> GSM782722 4 0.1321 0.719 0.024 0.000 0.000 0.952 NA 0.020
#> GSM782723 2 0.0000 0.999 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782724 2 0.0000 0.999 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782725 4 0.1398 0.736 0.000 0.000 0.000 0.940 NA 0.052
#> GSM782726 6 0.1426 0.671 0.028 0.000 0.000 0.008 NA 0.948
#> GSM782727 3 0.0260 0.980 0.000 0.000 0.992 0.000 NA 0.000
#> GSM782728 2 0.0146 0.998 0.000 0.996 0.000 0.000 NA 0.000
#> GSM782729 4 0.4812 0.532 0.000 0.000 0.000 0.640 NA 0.264
#> GSM782730 3 0.0000 0.981 0.000 0.000 1.000 0.000 NA 0.000
#> GSM782731 6 0.4587 0.381 0.000 0.000 0.000 0.296 NA 0.640
#> GSM782732 6 0.4636 0.513 0.000 0.000 0.000 0.160 NA 0.692
#> GSM782733 3 0.0363 0.975 0.000 0.000 0.988 0.000 NA 0.000
#> GSM782734 6 0.2365 0.648 0.068 0.000 0.000 0.012 NA 0.896
#> GSM782735 2 0.0000 0.999 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782736 4 0.3402 0.719 0.004 0.000 0.000 0.820 NA 0.104
#> GSM782737 2 0.0000 0.999 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782738 4 0.2076 0.734 0.016 0.000 0.000 0.912 NA 0.060
#> GSM782739 6 0.1297 0.676 0.000 0.000 0.000 0.012 NA 0.948
#> GSM782740 2 0.0146 0.998 0.000 0.996 0.000 0.000 NA 0.000
#> GSM782741 6 0.3999 0.541 0.156 0.000 0.000 0.036 NA 0.776
#> GSM782742 3 0.0260 0.980 0.000 0.000 0.992 0.000 NA 0.000
#> GSM782743 3 0.0000 0.981 0.000 0.000 1.000 0.000 NA 0.000
#> GSM782744 3 0.3729 0.797 0.008 0.000 0.808 0.116 NA 0.008
#> GSM782745 6 0.1555 0.674 0.008 0.000 0.000 0.040 NA 0.940
#> GSM782746 2 0.0000 0.999 0.000 1.000 0.000 0.000 NA 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> MAD:NMF 51 0.648 2
#> MAD:NMF 51 0.642 3
#> MAD:NMF 33 0.406 4
#> MAD:NMF 44 0.403 5
#> MAD:NMF 44 0.403 6
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 51941 rows and 51 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 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.2972 0.704 0.704
#> 3 3 1.000 1.000 1.000 0.9492 0.718 0.599
#> 4 4 0.785 0.914 0.949 0.0796 0.991 0.980
#> 5 5 0.834 0.848 0.920 0.1092 0.918 0.802
#> 6 6 0.790 0.782 0.905 0.1160 0.871 0.619
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
#> GSM782696 1 0 1 1 0
#> GSM782697 1 0 1 1 0
#> GSM782698 1 0 1 1 0
#> GSM782699 1 0 1 1 0
#> GSM782700 2 0 1 0 1
#> GSM782701 1 0 1 1 0
#> GSM782702 1 0 1 1 0
#> GSM782703 1 0 1 1 0
#> GSM782704 1 0 1 1 0
#> GSM782705 1 0 1 1 0
#> GSM782706 1 0 1 1 0
#> GSM782707 1 0 1 1 0
#> GSM782708 1 0 1 1 0
#> GSM782709 1 0 1 1 0
#> GSM782710 1 0 1 1 0
#> GSM782711 1 0 1 1 0
#> GSM782712 1 0 1 1 0
#> GSM782713 1 0 1 1 0
#> GSM782714 2 0 1 0 1
#> GSM782715 1 0 1 1 0
#> GSM782716 1 0 1 1 0
#> GSM782717 1 0 1 1 0
#> GSM782718 1 0 1 1 0
#> GSM782719 1 0 1 1 0
#> GSM782720 1 0 1 1 0
#> GSM782721 1 0 1 1 0
#> GSM782722 1 0 1 1 0
#> GSM782723 2 0 1 0 1
#> GSM782724 2 0 1 0 1
#> GSM782725 1 0 1 1 0
#> GSM782726 1 0 1 1 0
#> GSM782727 1 0 1 1 0
#> GSM782728 2 0 1 0 1
#> GSM782729 1 0 1 1 0
#> GSM782730 1 0 1 1 0
#> GSM782731 1 0 1 1 0
#> GSM782732 1 0 1 1 0
#> GSM782733 1 0 1 1 0
#> GSM782734 1 0 1 1 0
#> GSM782735 2 0 1 0 1
#> GSM782736 1 0 1 1 0
#> GSM782737 2 0 1 0 1
#> GSM782738 1 0 1 1 0
#> GSM782739 1 0 1 1 0
#> GSM782740 2 0 1 0 1
#> GSM782741 1 0 1 1 0
#> GSM782742 1 0 1 1 0
#> GSM782743 1 0 1 1 0
#> GSM782744 1 0 1 1 0
#> GSM782745 1 0 1 1 0
#> GSM782746 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0 1 1 0 0
#> GSM782697 1 0 1 1 0 0
#> GSM782698 1 0 1 1 0 0
#> GSM782699 1 0 1 1 0 0
#> GSM782700 2 0 1 0 1 0
#> GSM782701 1 0 1 1 0 0
#> GSM782702 1 0 1 1 0 0
#> GSM782703 3 0 1 0 0 1
#> GSM782704 3 0 1 0 0 1
#> GSM782705 1 0 1 1 0 0
#> GSM782706 1 0 1 1 0 0
#> GSM782707 1 0 1 1 0 0
#> GSM782708 3 0 1 0 0 1
#> GSM782709 1 0 1 1 0 0
#> GSM782710 1 0 1 1 0 0
#> GSM782711 1 0 1 1 0 0
#> GSM782712 1 0 1 1 0 0
#> GSM782713 3 0 1 0 0 1
#> GSM782714 2 0 1 0 1 0
#> GSM782715 1 0 1 1 0 0
#> GSM782716 3 0 1 0 0 1
#> GSM782717 1 0 1 1 0 0
#> GSM782718 1 0 1 1 0 0
#> GSM782719 1 0 1 1 0 0
#> GSM782720 3 0 1 0 0 1
#> GSM782721 1 0 1 1 0 0
#> GSM782722 1 0 1 1 0 0
#> GSM782723 2 0 1 0 1 0
#> GSM782724 2 0 1 0 1 0
#> GSM782725 1 0 1 1 0 0
#> GSM782726 1 0 1 1 0 0
#> GSM782727 3 0 1 0 0 1
#> GSM782728 2 0 1 0 1 0
#> GSM782729 1 0 1 1 0 0
#> GSM782730 3 0 1 0 0 1
#> GSM782731 1 0 1 1 0 0
#> GSM782732 1 0 1 1 0 0
#> GSM782733 3 0 1 0 0 1
#> GSM782734 1 0 1 1 0 0
#> GSM782735 2 0 1 0 1 0
#> GSM782736 1 0 1 1 0 0
#> GSM782737 2 0 1 0 1 0
#> GSM782738 1 0 1 1 0 0
#> GSM782739 1 0 1 1 0 0
#> GSM782740 2 0 1 0 1 0
#> GSM782741 1 0 1 1 0 0
#> GSM782742 3 0 1 0 0 1
#> GSM782743 3 0 1 0 0 1
#> GSM782744 3 0 1 0 0 1
#> GSM782745 1 0 1 1 0 0
#> GSM782746 2 0 1 0 1 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.0188 0.924 0.996 0 0.00 0.004
#> GSM782697 1 0.0188 0.924 0.996 0 0.00 0.004
#> GSM782698 1 0.0188 0.924 0.996 0 0.00 0.004
#> GSM782699 1 0.0188 0.924 0.996 0 0.00 0.004
#> GSM782700 2 0.0000 1.000 0.000 1 0.00 0.000
#> GSM782701 1 0.0188 0.923 0.996 0 0.00 0.004
#> GSM782702 1 0.0000 0.924 1.000 0 0.00 0.000
#> GSM782703 3 0.0000 1.000 0.000 0 1.00 0.000
#> GSM782704 3 0.0000 1.000 0.000 0 1.00 0.000
#> GSM782705 1 0.0336 0.924 0.992 0 0.00 0.008
#> GSM782706 1 0.2530 0.874 0.888 0 0.00 0.112
#> GSM782707 1 0.0188 0.923 0.996 0 0.00 0.004
#> GSM782708 3 0.0000 1.000 0.000 0 1.00 0.000
#> GSM782709 1 0.3528 0.808 0.808 0 0.00 0.192
#> GSM782710 1 0.0188 0.924 0.996 0 0.00 0.004
#> GSM782711 1 0.0188 0.924 0.996 0 0.00 0.004
#> GSM782712 1 0.0188 0.923 0.996 0 0.00 0.004
#> GSM782713 3 0.0000 1.000 0.000 0 1.00 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.00 0.000
#> GSM782715 1 0.3266 0.843 0.832 0 0.00 0.168
#> GSM782716 3 0.0000 1.000 0.000 0 1.00 0.000
#> GSM782717 1 0.0188 0.924 0.996 0 0.00 0.004
#> GSM782718 1 0.3219 0.846 0.836 0 0.00 0.164
#> GSM782719 1 0.0188 0.923 0.996 0 0.00 0.004
#> GSM782720 3 0.0000 1.000 0.000 0 1.00 0.000
#> GSM782721 1 0.2530 0.874 0.888 0 0.00 0.112
#> GSM782722 1 0.3266 0.843 0.832 0 0.00 0.168
#> GSM782723 2 0.0000 1.000 0.000 1 0.00 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.00 0.000
#> GSM782725 1 0.3266 0.843 0.832 0 0.00 0.168
#> GSM782726 1 0.3528 0.808 0.808 0 0.00 0.192
#> GSM782727 3 0.0000 1.000 0.000 0 1.00 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.00 0.000
#> GSM782729 1 0.3266 0.843 0.832 0 0.00 0.168
#> GSM782730 3 0.0000 1.000 0.000 0 1.00 0.000
#> GSM782731 1 0.0188 0.924 0.996 0 0.00 0.004
#> GSM782732 1 0.0188 0.924 0.996 0 0.00 0.004
#> GSM782733 3 0.0000 1.000 0.000 0 1.00 0.000
#> GSM782734 1 0.3528 0.808 0.808 0 0.00 0.192
#> GSM782735 2 0.0000 1.000 0.000 1 0.00 0.000
#> GSM782736 1 0.3219 0.846 0.836 0 0.00 0.164
#> GSM782737 2 0.0000 1.000 0.000 1 0.00 0.000
#> GSM782738 1 0.3219 0.846 0.836 0 0.00 0.164
#> GSM782739 1 0.0336 0.923 0.992 0 0.00 0.008
#> GSM782740 2 0.0000 1.000 0.000 1 0.00 0.000
#> GSM782741 1 0.0336 0.923 0.992 0 0.00 0.008
#> GSM782742 3 0.0000 1.000 0.000 0 1.00 0.000
#> GSM782743 3 0.0000 1.000 0.000 0 1.00 0.000
#> GSM782744 4 0.4713 0.000 0.000 0 0.36 0.640
#> GSM782745 1 0.3528 0.808 0.808 0 0.00 0.192
#> GSM782746 2 0.0000 1.000 0.000 1 0.00 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.0290 0.829 0.992 0 0 0.008 0
#> GSM782697 1 0.0290 0.829 0.992 0 0 0.008 0
#> GSM782698 1 0.0290 0.829 0.992 0 0 0.008 0
#> GSM782699 1 0.0290 0.829 0.992 0 0 0.008 0
#> GSM782700 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782701 1 0.0290 0.828 0.992 0 0 0.008 0
#> GSM782702 1 0.0609 0.817 0.980 0 0 0.020 0
#> GSM782703 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782704 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782705 1 0.0404 0.829 0.988 0 0 0.012 0
#> GSM782706 1 0.3684 0.344 0.720 0 0 0.280 0
#> GSM782707 1 0.0162 0.828 0.996 0 0 0.004 0
#> GSM782708 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782709 4 0.3816 1.000 0.304 0 0 0.696 0
#> GSM782710 1 0.0290 0.829 0.992 0 0 0.008 0
#> GSM782711 1 0.0290 0.829 0.992 0 0 0.008 0
#> GSM782712 1 0.0162 0.828 0.996 0 0 0.004 0
#> GSM782713 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782714 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782715 1 0.3816 0.646 0.696 0 0 0.304 0
#> GSM782716 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782717 1 0.0404 0.827 0.988 0 0 0.012 0
#> GSM782718 1 0.3796 0.650 0.700 0 0 0.300 0
#> GSM782719 1 0.0162 0.828 0.996 0 0 0.004 0
#> GSM782720 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782721 1 0.3684 0.344 0.720 0 0 0.280 0
#> GSM782722 1 0.3816 0.646 0.696 0 0 0.304 0
#> GSM782723 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782724 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782725 1 0.3816 0.646 0.696 0 0 0.304 0
#> GSM782726 4 0.3816 1.000 0.304 0 0 0.696 0
#> GSM782727 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782728 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782729 1 0.3816 0.646 0.696 0 0 0.304 0
#> GSM782730 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782731 1 0.0290 0.829 0.992 0 0 0.008 0
#> GSM782732 1 0.0290 0.829 0.992 0 0 0.008 0
#> GSM782733 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782734 4 0.3816 1.000 0.304 0 0 0.696 0
#> GSM782735 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782736 1 0.3796 0.650 0.700 0 0 0.300 0
#> GSM782737 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782738 1 0.3796 0.650 0.700 0 0 0.300 0
#> GSM782739 1 0.1197 0.791 0.952 0 0 0.048 0
#> GSM782740 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM782741 1 0.1197 0.791 0.952 0 0 0.048 0
#> GSM782742 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782743 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM782744 5 0.0000 0.000 0.000 0 0 0.000 1
#> GSM782745 4 0.3816 1.000 0.304 0 0 0.696 0
#> GSM782746 2 0.0000 1.000 0.000 1 0 0.000 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM782696 1 0.0865 0.825 0.964 0 0.000 0.036 0 0.000
#> GSM782697 1 0.0146 0.814 0.996 0 0.000 0.004 0 0.000
#> GSM782698 1 0.0146 0.814 0.996 0 0.000 0.004 0 0.000
#> GSM782699 1 0.0146 0.814 0.996 0 0.000 0.004 0 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM782701 1 0.2772 0.773 0.816 0 0.000 0.180 0 0.004
#> GSM782702 1 0.3408 0.762 0.800 0 0.000 0.152 0 0.048
#> GSM782703 3 0.0000 0.992 0.000 0 1.000 0.000 0 0.000
#> GSM782704 3 0.0000 0.992 0.000 0 1.000 0.000 0 0.000
#> GSM782705 1 0.0458 0.812 0.984 0 0.000 0.016 0 0.000
#> GSM782706 6 0.4806 0.435 0.060 0 0.000 0.380 0 0.560
#> GSM782707 1 0.2631 0.775 0.820 0 0.000 0.180 0 0.000
#> GSM782708 3 0.0000 0.992 0.000 0 1.000 0.000 0 0.000
#> GSM782709 6 0.0000 0.743 0.000 0 0.000 0.000 0 1.000
#> GSM782710 1 0.0146 0.814 0.996 0 0.000 0.004 0 0.000
#> GSM782711 1 0.0146 0.814 0.996 0 0.000 0.004 0 0.000
#> GSM782712 1 0.2527 0.783 0.832 0 0.000 0.168 0 0.000
#> GSM782713 3 0.0000 0.992 0.000 0 1.000 0.000 0 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM782715 4 0.3847 0.464 0.456 0 0.000 0.544 0 0.000
#> GSM782716 3 0.0000 0.992 0.000 0 1.000 0.000 0 0.000
#> GSM782717 1 0.1958 0.821 0.896 0 0.000 0.100 0 0.004
#> GSM782718 1 0.3864 -0.416 0.520 0 0.000 0.480 0 0.000
#> GSM782719 1 0.1765 0.814 0.904 0 0.000 0.096 0 0.000
#> GSM782720 3 0.0000 0.992 0.000 0 1.000 0.000 0 0.000
#> GSM782721 6 0.4806 0.435 0.060 0 0.000 0.380 0 0.560
#> GSM782722 4 0.1714 0.623 0.092 0 0.000 0.908 0 0.000
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM782725 4 0.1957 0.650 0.112 0 0.000 0.888 0 0.000
#> GSM782726 6 0.0000 0.743 0.000 0 0.000 0.000 0 1.000
#> GSM782727 3 0.0000 0.992 0.000 0 1.000 0.000 0 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM782729 4 0.2219 0.653 0.136 0 0.000 0.864 0 0.000
#> GSM782730 3 0.0000 0.992 0.000 0 1.000 0.000 0 0.000
#> GSM782731 1 0.1765 0.823 0.904 0 0.000 0.096 0 0.000
#> GSM782732 1 0.1765 0.823 0.904 0 0.000 0.096 0 0.000
#> GSM782733 3 0.0000 0.992 0.000 0 1.000 0.000 0 0.000
#> GSM782734 6 0.0000 0.743 0.000 0 0.000 0.000 0 1.000
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM782736 4 0.3823 0.414 0.436 0 0.000 0.564 0 0.000
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM782738 4 0.3823 0.414 0.436 0 0.000 0.564 0 0.000
#> GSM782739 1 0.4242 0.671 0.736 0 0.000 0.136 0 0.128
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
#> GSM782741 1 0.4242 0.671 0.736 0 0.000 0.136 0 0.128
#> GSM782742 3 0.0000 0.992 0.000 0 1.000 0.000 0 0.000
#> GSM782743 3 0.1663 0.909 0.000 0 0.912 0.088 0 0.000
#> GSM782744 5 0.0000 0.000 0.000 0 0.000 0.000 1 0.000
#> GSM782745 6 0.0000 0.743 0.000 0 0.000 0.000 0 1.000
#> GSM782746 2 0.0000 1.000 0.000 1 0.000 0.000 0 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> ATC:hclust 51 0.648 2
#> ATC:hclust 51 0.642 3
#> ATC:hclust 50 0.583 4
#> ATC:hclust 48 0.747 5
#> ATC:hclust 44 0.601 6
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 51941 rows and 51 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 0.500 0.819 0.850 0.3293 0.704 0.704
#> 3 3 0.681 0.996 0.973 0.6771 0.718 0.599
#> 4 4 0.731 0.669 0.729 0.2216 0.836 0.611
#> 5 5 0.680 0.746 0.828 0.1072 0.836 0.535
#> 6 6 0.697 0.774 0.807 0.0495 0.925 0.734
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
#> GSM782696 1 0.929 0.835 0.656 0.344
#> GSM782697 1 0.929 0.835 0.656 0.344
#> GSM782698 1 0.929 0.835 0.656 0.344
#> GSM782699 1 0.929 0.835 0.656 0.344
#> GSM782700 2 0.000 1.000 0.000 1.000
#> GSM782701 1 0.929 0.835 0.656 0.344
#> GSM782702 1 0.929 0.835 0.656 0.344
#> GSM782703 1 0.000 0.660 1.000 0.000
#> GSM782704 1 0.000 0.660 1.000 0.000
#> GSM782705 1 0.929 0.835 0.656 0.344
#> GSM782706 1 0.929 0.835 0.656 0.344
#> GSM782707 1 0.929 0.835 0.656 0.344
#> GSM782708 1 0.000 0.660 1.000 0.000
#> GSM782709 1 0.850 0.804 0.724 0.276
#> GSM782710 1 0.929 0.835 0.656 0.344
#> GSM782711 1 0.929 0.835 0.656 0.344
#> GSM782712 1 0.929 0.835 0.656 0.344
#> GSM782713 1 0.000 0.660 1.000 0.000
#> GSM782714 2 0.000 1.000 0.000 1.000
#> GSM782715 1 0.929 0.835 0.656 0.344
#> GSM782716 1 0.000 0.660 1.000 0.000
#> GSM782717 1 0.929 0.835 0.656 0.344
#> GSM782718 1 0.929 0.835 0.656 0.344
#> GSM782719 1 0.929 0.835 0.656 0.344
#> GSM782720 1 0.000 0.660 1.000 0.000
#> GSM782721 1 0.929 0.835 0.656 0.344
#> GSM782722 1 0.929 0.835 0.656 0.344
#> GSM782723 2 0.000 1.000 0.000 1.000
#> GSM782724 2 0.000 1.000 0.000 1.000
#> GSM782725 1 0.929 0.835 0.656 0.344
#> GSM782726 1 0.402 0.699 0.920 0.080
#> GSM782727 1 0.000 0.660 1.000 0.000
#> GSM782728 2 0.000 1.000 0.000 1.000
#> GSM782729 1 0.929 0.835 0.656 0.344
#> GSM782730 1 0.000 0.660 1.000 0.000
#> GSM782731 1 0.929 0.835 0.656 0.344
#> GSM782732 1 0.929 0.835 0.656 0.344
#> GSM782733 1 0.000 0.660 1.000 0.000
#> GSM782734 1 0.886 0.818 0.696 0.304
#> GSM782735 2 0.000 1.000 0.000 1.000
#> GSM782736 1 0.929 0.835 0.656 0.344
#> GSM782737 2 0.000 1.000 0.000 1.000
#> GSM782738 1 0.929 0.835 0.656 0.344
#> GSM782739 1 0.929 0.835 0.656 0.344
#> GSM782740 2 0.000 1.000 0.000 1.000
#> GSM782741 1 0.929 0.835 0.656 0.344
#> GSM782742 1 0.000 0.660 1.000 0.000
#> GSM782743 1 0.000 0.660 1.000 0.000
#> GSM782744 1 0.000 0.660 1.000 0.000
#> GSM782745 1 0.886 0.818 0.696 0.304
#> GSM782746 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
#> GSM782696 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782697 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782698 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782699 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782700 2 0.0237 0.984 0.0 0.996 0.004
#> GSM782701 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782702 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782703 3 0.2959 1.000 0.1 0.000 0.900
#> GSM782704 3 0.2959 1.000 0.1 0.000 0.900
#> GSM782705 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782706 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782707 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782708 3 0.2959 1.000 0.1 0.000 0.900
#> GSM782709 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782710 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782711 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782712 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782713 3 0.2959 1.000 0.1 0.000 0.900
#> GSM782714 2 0.0000 0.984 0.0 1.000 0.000
#> GSM782715 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782716 3 0.2959 1.000 0.1 0.000 0.900
#> GSM782717 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782718 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782719 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782720 3 0.2959 1.000 0.1 0.000 0.900
#> GSM782721 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782722 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782723 2 0.1529 0.976 0.0 0.960 0.040
#> GSM782724 2 0.2165 0.966 0.0 0.936 0.064
#> GSM782725 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782726 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782727 3 0.2959 1.000 0.1 0.000 0.900
#> GSM782728 2 0.0000 0.984 0.0 1.000 0.000
#> GSM782729 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782730 3 0.2959 1.000 0.1 0.000 0.900
#> GSM782731 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782732 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782733 3 0.2959 1.000 0.1 0.000 0.900
#> GSM782734 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782735 2 0.1411 0.975 0.0 0.964 0.036
#> GSM782736 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782737 2 0.0892 0.982 0.0 0.980 0.020
#> GSM782738 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782739 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782740 2 0.0000 0.984 0.0 1.000 0.000
#> GSM782741 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782742 3 0.2959 1.000 0.1 0.000 0.900
#> GSM782743 3 0.2959 1.000 0.1 0.000 0.900
#> GSM782744 3 0.2959 1.000 0.1 0.000 0.900
#> GSM782745 1 0.0000 1.000 1.0 0.000 0.000
#> GSM782746 2 0.1411 0.975 0.0 0.964 0.036
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.4961 -0.569 0.552 0.000 0.000 0.448
#> GSM782697 1 0.4941 -0.556 0.564 0.000 0.000 0.436
#> GSM782698 4 0.4955 0.977 0.444 0.000 0.000 0.556
#> GSM782699 1 0.4941 -0.556 0.564 0.000 0.000 0.436
#> GSM782700 2 0.0188 0.966 0.000 0.996 0.000 0.004
#> GSM782701 1 0.0817 0.601 0.976 0.000 0.000 0.024
#> GSM782702 1 0.1867 0.575 0.928 0.000 0.000 0.072
#> GSM782703 3 0.0895 0.960 0.004 0.000 0.976 0.020
#> GSM782704 3 0.2593 0.936 0.004 0.000 0.892 0.104
#> GSM782705 4 0.4972 0.967 0.456 0.000 0.000 0.544
#> GSM782706 1 0.0592 0.600 0.984 0.000 0.000 0.016
#> GSM782707 1 0.4967 -0.575 0.548 0.000 0.000 0.452
#> GSM782708 3 0.2593 0.936 0.004 0.000 0.892 0.104
#> GSM782709 1 0.0000 0.604 1.000 0.000 0.000 0.000
#> GSM782710 1 0.4356 0.128 0.708 0.000 0.000 0.292
#> GSM782711 1 0.4961 -0.569 0.552 0.000 0.000 0.448
#> GSM782712 1 0.3356 0.480 0.824 0.000 0.000 0.176
#> GSM782713 3 0.0188 0.961 0.004 0.000 0.996 0.000
#> GSM782714 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM782715 4 0.4948 0.980 0.440 0.000 0.000 0.560
#> GSM782716 3 0.0895 0.960 0.004 0.000 0.976 0.020
#> GSM782717 1 0.3569 0.431 0.804 0.000 0.000 0.196
#> GSM782718 4 0.4948 0.980 0.440 0.000 0.000 0.560
#> GSM782719 1 0.4967 -0.575 0.548 0.000 0.000 0.452
#> GSM782720 3 0.0188 0.961 0.004 0.000 0.996 0.000
#> GSM782721 1 0.0592 0.600 0.984 0.000 0.000 0.016
#> GSM782722 4 0.4948 0.980 0.440 0.000 0.000 0.560
#> GSM782723 2 0.2281 0.942 0.000 0.904 0.000 0.096
#> GSM782724 2 0.2868 0.925 0.000 0.864 0.000 0.136
#> GSM782725 4 0.4948 0.980 0.440 0.000 0.000 0.560
#> GSM782726 1 0.0000 0.604 1.000 0.000 0.000 0.000
#> GSM782727 3 0.0188 0.961 0.004 0.000 0.996 0.000
#> GSM782728 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM782729 4 0.4972 0.967 0.456 0.000 0.000 0.544
#> GSM782730 3 0.0188 0.961 0.004 0.000 0.996 0.000
#> GSM782731 4 0.4972 0.967 0.456 0.000 0.000 0.544
#> GSM782732 4 0.4972 0.967 0.456 0.000 0.000 0.544
#> GSM782733 3 0.0895 0.960 0.004 0.000 0.976 0.020
#> GSM782734 1 0.0000 0.604 1.000 0.000 0.000 0.000
#> GSM782735 2 0.1743 0.950 0.000 0.940 0.004 0.056
#> GSM782736 4 0.4948 0.980 0.440 0.000 0.000 0.560
#> GSM782737 2 0.1637 0.954 0.000 0.940 0.000 0.060
#> GSM782738 4 0.4948 0.980 0.440 0.000 0.000 0.560
#> GSM782739 1 0.3356 0.468 0.824 0.000 0.000 0.176
#> GSM782740 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM782741 1 0.0000 0.604 1.000 0.000 0.000 0.000
#> GSM782742 3 0.0188 0.961 0.004 0.000 0.996 0.000
#> GSM782743 3 0.2593 0.936 0.004 0.000 0.892 0.104
#> GSM782744 3 0.4053 0.837 0.004 0.000 0.768 0.228
#> GSM782745 1 0.0000 0.604 1.000 0.000 0.000 0.000
#> GSM782746 2 0.1743 0.950 0.000 0.940 0.004 0.056
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 4 0.2763 0.6506 0.148 0.000 0.000 0.848 0.004
#> GSM782697 4 0.2921 0.6497 0.124 0.000 0.000 0.856 0.020
#> GSM782698 4 0.0000 0.6838 0.000 0.000 0.000 1.000 0.000
#> GSM782699 4 0.2825 0.6518 0.124 0.000 0.000 0.860 0.016
#> GSM782700 2 0.0740 0.9540 0.008 0.980 0.004 0.000 0.008
#> GSM782701 1 0.3456 0.8421 0.800 0.000 0.000 0.184 0.016
#> GSM782702 4 0.4902 0.0956 0.408 0.000 0.000 0.564 0.028
#> GSM782703 3 0.0451 0.9312 0.008 0.000 0.988 0.004 0.000
#> GSM782704 3 0.3684 0.8801 0.056 0.000 0.824 0.004 0.116
#> GSM782705 4 0.0162 0.6833 0.004 0.000 0.000 0.996 0.000
#> GSM782706 1 0.3495 0.8512 0.812 0.000 0.000 0.160 0.028
#> GSM782707 4 0.3885 0.5660 0.268 0.000 0.000 0.724 0.008
#> GSM782708 3 0.3684 0.8801 0.056 0.000 0.824 0.004 0.116
#> GSM782709 1 0.5379 0.8719 0.668 0.000 0.000 0.168 0.164
#> GSM782710 4 0.4223 0.5051 0.248 0.000 0.000 0.724 0.028
#> GSM782711 4 0.2763 0.6506 0.148 0.000 0.000 0.848 0.004
#> GSM782712 4 0.4533 0.1391 0.448 0.000 0.000 0.544 0.008
#> GSM782713 3 0.0865 0.9328 0.000 0.000 0.972 0.004 0.024
#> GSM782714 2 0.0000 0.9552 0.000 1.000 0.000 0.000 0.000
#> GSM782715 4 0.4777 0.5374 0.044 0.000 0.000 0.664 0.292
#> GSM782716 3 0.0162 0.9317 0.000 0.000 0.996 0.004 0.000
#> GSM782717 4 0.4703 0.3340 0.340 0.000 0.000 0.632 0.028
#> GSM782718 4 0.3967 0.5775 0.012 0.000 0.000 0.724 0.264
#> GSM782719 4 0.4063 0.5503 0.280 0.000 0.000 0.708 0.012
#> GSM782720 3 0.0955 0.9325 0.000 0.000 0.968 0.004 0.028
#> GSM782721 1 0.3495 0.8512 0.812 0.000 0.000 0.160 0.028
#> GSM782722 4 0.5714 0.4608 0.108 0.000 0.000 0.580 0.312
#> GSM782723 2 0.2278 0.9356 0.032 0.908 0.000 0.000 0.060
#> GSM782724 2 0.3413 0.9024 0.044 0.832 0.000 0.000 0.124
#> GSM782725 4 0.4040 0.5743 0.012 0.000 0.000 0.712 0.276
#> GSM782726 1 0.5379 0.8719 0.668 0.000 0.000 0.168 0.164
#> GSM782727 3 0.0955 0.9325 0.000 0.000 0.968 0.004 0.028
#> GSM782728 2 0.0000 0.9552 0.000 1.000 0.000 0.000 0.000
#> GSM782729 4 0.1357 0.6809 0.004 0.000 0.000 0.948 0.048
#> GSM782730 3 0.1116 0.9321 0.004 0.000 0.964 0.004 0.028
#> GSM782731 4 0.1041 0.6821 0.004 0.000 0.000 0.964 0.032
#> GSM782732 4 0.1041 0.6821 0.004 0.000 0.000 0.964 0.032
#> GSM782733 3 0.0451 0.9312 0.008 0.000 0.988 0.004 0.000
#> GSM782734 1 0.5379 0.8719 0.668 0.000 0.000 0.168 0.164
#> GSM782735 2 0.2370 0.9286 0.040 0.904 0.000 0.000 0.056
#> GSM782736 4 0.3942 0.5783 0.012 0.000 0.000 0.728 0.260
#> GSM782737 2 0.1668 0.9454 0.032 0.940 0.000 0.000 0.028
#> GSM782738 4 0.4326 0.5698 0.028 0.000 0.000 0.708 0.264
#> GSM782739 4 0.4733 0.3121 0.348 0.000 0.000 0.624 0.028
#> GSM782740 2 0.0000 0.9552 0.000 1.000 0.000 0.000 0.000
#> GSM782741 1 0.2929 0.8523 0.820 0.000 0.000 0.180 0.000
#> GSM782742 3 0.0955 0.9325 0.000 0.000 0.968 0.004 0.028
#> GSM782743 3 0.3750 0.8788 0.060 0.000 0.820 0.004 0.116
#> GSM782744 3 0.4118 0.7805 0.000 0.000 0.660 0.004 0.336
#> GSM782745 1 0.5379 0.8719 0.668 0.000 0.000 0.168 0.164
#> GSM782746 2 0.2370 0.9286 0.040 0.904 0.000 0.000 0.056
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM782696 1 0.0820 0.721 0.972 0.000 0.000 0.012 NA 0.000
#> GSM782697 1 0.0820 0.724 0.972 0.000 0.000 0.000 NA 0.016
#> GSM782698 1 0.1913 0.669 0.908 0.000 0.000 0.080 NA 0.000
#> GSM782699 1 0.0820 0.724 0.972 0.000 0.000 0.000 NA 0.016
#> GSM782700 2 0.0914 0.936 0.000 0.968 0.000 0.016 NA 0.016
#> GSM782701 6 0.6458 0.700 0.212 0.000 0.000 0.028 NA 0.432
#> GSM782702 1 0.3492 0.625 0.788 0.000 0.000 0.004 NA 0.176
#> GSM782703 3 0.2252 0.892 0.000 0.000 0.908 0.028 NA 0.020
#> GSM782704 3 0.4427 0.825 0.000 0.000 0.716 0.136 NA 0.000
#> GSM782705 1 0.2019 0.662 0.900 0.000 0.000 0.088 NA 0.000
#> GSM782706 6 0.6356 0.738 0.164 0.000 0.000 0.036 NA 0.464
#> GSM782707 1 0.3936 0.454 0.688 0.000 0.000 0.024 NA 0.000
#> GSM782708 3 0.4427 0.825 0.000 0.000 0.716 0.136 NA 0.000
#> GSM782709 6 0.2416 0.763 0.156 0.000 0.000 0.000 NA 0.844
#> GSM782710 1 0.1951 0.713 0.908 0.000 0.000 0.000 NA 0.076
#> GSM782711 1 0.0820 0.721 0.972 0.000 0.000 0.012 NA 0.000
#> GSM782712 1 0.5679 0.222 0.552 0.000 0.000 0.024 NA 0.104
#> GSM782713 3 0.0000 0.896 0.000 0.000 1.000 0.000 NA 0.000
#> GSM782714 2 0.0146 0.938 0.000 0.996 0.000 0.000 NA 0.000
#> GSM782715 4 0.4504 0.839 0.296 0.000 0.000 0.652 NA 0.004
#> GSM782716 3 0.1710 0.895 0.000 0.000 0.936 0.016 NA 0.020
#> GSM782717 1 0.3310 0.672 0.816 0.000 0.000 0.020 NA 0.148
#> GSM782718 4 0.3852 0.894 0.384 0.000 0.000 0.612 NA 0.000
#> GSM782719 1 0.4062 0.417 0.660 0.000 0.000 0.024 NA 0.000
#> GSM782720 3 0.0000 0.896 0.000 0.000 1.000 0.000 NA 0.000
#> GSM782721 6 0.6333 0.740 0.160 0.000 0.000 0.036 NA 0.468
#> GSM782722 4 0.4659 0.799 0.252 0.000 0.000 0.668 NA 0.004
#> GSM782723 2 0.2458 0.917 0.000 0.892 0.000 0.016 NA 0.024
#> GSM782724 2 0.4176 0.875 0.000 0.788 0.000 0.076 NA 0.060
#> GSM782725 4 0.4322 0.881 0.372 0.000 0.000 0.600 NA 0.000
#> GSM782726 6 0.2416 0.763 0.156 0.000 0.000 0.000 NA 0.844
#> GSM782727 3 0.0806 0.895 0.000 0.000 0.972 0.008 NA 0.020
#> GSM782728 2 0.0000 0.938 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782729 1 0.3248 0.541 0.804 0.000 0.000 0.164 NA 0.000
#> GSM782730 3 0.0458 0.893 0.000 0.000 0.984 0.016 NA 0.000
#> GSM782731 1 0.2631 0.600 0.840 0.000 0.000 0.152 NA 0.000
#> GSM782732 1 0.2631 0.600 0.840 0.000 0.000 0.152 NA 0.000
#> GSM782733 3 0.2252 0.892 0.000 0.000 0.908 0.028 NA 0.020
#> GSM782734 6 0.2416 0.763 0.156 0.000 0.000 0.000 NA 0.844
#> GSM782735 2 0.2677 0.902 0.000 0.876 0.000 0.016 NA 0.024
#> GSM782736 4 0.3841 0.896 0.380 0.000 0.000 0.616 NA 0.000
#> GSM782737 2 0.2318 0.922 0.000 0.904 0.000 0.020 NA 0.028
#> GSM782738 4 0.3841 0.896 0.380 0.000 0.000 0.616 NA 0.000
#> GSM782739 1 0.2964 0.680 0.836 0.000 0.000 0.012 NA 0.140
#> GSM782740 2 0.0000 0.938 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782741 6 0.6141 0.734 0.192 0.000 0.000 0.016 NA 0.476
#> GSM782742 3 0.0000 0.896 0.000 0.000 1.000 0.000 NA 0.000
#> GSM782743 3 0.4745 0.818 0.000 0.000 0.700 0.144 NA 0.008
#> GSM782744 3 0.4810 0.675 0.000 0.000 0.588 0.040 NA 0.012
#> GSM782745 6 0.2416 0.763 0.156 0.000 0.000 0.000 NA 0.844
#> GSM782746 2 0.2677 0.902 0.000 0.876 0.000 0.016 NA 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> ATC:kmeans 51 0.648 2
#> ATC:kmeans 51 0.642 3
#> ATC:kmeans 41 0.528 4
#> ATC:kmeans 46 0.600 5
#> ATC:kmeans 48 0.495 6
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 51941 rows and 51 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.2972 0.704 0.704
#> 3 3 1.000 0.959 0.985 1.0036 0.693 0.563
#> 4 4 0.936 0.966 0.978 0.2613 0.817 0.558
#> 5 5 0.827 0.804 0.884 0.0752 0.928 0.716
#> 6 6 0.846 0.752 0.861 0.0306 0.947 0.734
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM782696 1 0 1 1 0
#> GSM782697 1 0 1 1 0
#> GSM782698 1 0 1 1 0
#> GSM782699 1 0 1 1 0
#> GSM782700 2 0 1 0 1
#> GSM782701 1 0 1 1 0
#> GSM782702 1 0 1 1 0
#> GSM782703 1 0 1 1 0
#> GSM782704 1 0 1 1 0
#> GSM782705 1 0 1 1 0
#> GSM782706 1 0 1 1 0
#> GSM782707 1 0 1 1 0
#> GSM782708 1 0 1 1 0
#> GSM782709 1 0 1 1 0
#> GSM782710 1 0 1 1 0
#> GSM782711 1 0 1 1 0
#> GSM782712 1 0 1 1 0
#> GSM782713 1 0 1 1 0
#> GSM782714 2 0 1 0 1
#> GSM782715 1 0 1 1 0
#> GSM782716 1 0 1 1 0
#> GSM782717 1 0 1 1 0
#> GSM782718 1 0 1 1 0
#> GSM782719 1 0 1 1 0
#> GSM782720 1 0 1 1 0
#> GSM782721 1 0 1 1 0
#> GSM782722 1 0 1 1 0
#> GSM782723 2 0 1 0 1
#> GSM782724 2 0 1 0 1
#> GSM782725 1 0 1 1 0
#> GSM782726 1 0 1 1 0
#> GSM782727 1 0 1 1 0
#> GSM782728 2 0 1 0 1
#> GSM782729 1 0 1 1 0
#> GSM782730 1 0 1 1 0
#> GSM782731 1 0 1 1 0
#> GSM782732 1 0 1 1 0
#> GSM782733 1 0 1 1 0
#> GSM782734 1 0 1 1 0
#> GSM782735 2 0 1 0 1
#> GSM782736 1 0 1 1 0
#> GSM782737 2 0 1 0 1
#> GSM782738 1 0 1 1 0
#> GSM782739 1 0 1 1 0
#> GSM782740 2 0 1 0 1
#> GSM782741 1 0 1 1 0
#> GSM782742 1 0 1 1 0
#> GSM782743 1 0 1 1 0
#> GSM782744 1 0 1 1 0
#> GSM782745 1 0 1 1 0
#> GSM782746 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0.000 0.999 1.000 0 0.000
#> GSM782697 1 0.000 0.999 1.000 0 0.000
#> GSM782698 1 0.000 0.999 1.000 0 0.000
#> GSM782699 1 0.000 0.999 1.000 0 0.000
#> GSM782700 2 0.000 1.000 0.000 1 0.000
#> GSM782701 1 0.000 0.999 1.000 0 0.000
#> GSM782702 1 0.000 0.999 1.000 0 0.000
#> GSM782703 3 0.000 0.922 0.000 0 1.000
#> GSM782704 3 0.000 0.922 0.000 0 1.000
#> GSM782705 1 0.000 0.999 1.000 0 0.000
#> GSM782706 1 0.000 0.999 1.000 0 0.000
#> GSM782707 1 0.000 0.999 1.000 0 0.000
#> GSM782708 3 0.000 0.922 0.000 0 1.000
#> GSM782709 3 0.619 0.321 0.420 0 0.580
#> GSM782710 1 0.000 0.999 1.000 0 0.000
#> GSM782711 1 0.000 0.999 1.000 0 0.000
#> GSM782712 1 0.000 0.999 1.000 0 0.000
#> GSM782713 3 0.000 0.922 0.000 0 1.000
#> GSM782714 2 0.000 1.000 0.000 1 0.000
#> GSM782715 1 0.000 0.999 1.000 0 0.000
#> GSM782716 3 0.000 0.922 0.000 0 1.000
#> GSM782717 1 0.000 0.999 1.000 0 0.000
#> GSM782718 1 0.000 0.999 1.000 0 0.000
#> GSM782719 1 0.000 0.999 1.000 0 0.000
#> GSM782720 3 0.000 0.922 0.000 0 1.000
#> GSM782721 1 0.000 0.999 1.000 0 0.000
#> GSM782722 1 0.000 0.999 1.000 0 0.000
#> GSM782723 2 0.000 1.000 0.000 1 0.000
#> GSM782724 2 0.000 1.000 0.000 1 0.000
#> GSM782725 1 0.000 0.999 1.000 0 0.000
#> GSM782726 3 0.568 0.557 0.316 0 0.684
#> GSM782727 3 0.000 0.922 0.000 0 1.000
#> GSM782728 2 0.000 1.000 0.000 1 0.000
#> GSM782729 1 0.000 0.999 1.000 0 0.000
#> GSM782730 3 0.000 0.922 0.000 0 1.000
#> GSM782731 1 0.000 0.999 1.000 0 0.000
#> GSM782732 1 0.000 0.999 1.000 0 0.000
#> GSM782733 3 0.000 0.922 0.000 0 1.000
#> GSM782734 1 0.000 0.999 1.000 0 0.000
#> GSM782735 2 0.000 1.000 0.000 1 0.000
#> GSM782736 1 0.000 0.999 1.000 0 0.000
#> GSM782737 2 0.000 1.000 0.000 1 0.000
#> GSM782738 1 0.000 0.999 1.000 0 0.000
#> GSM782739 1 0.000 0.999 1.000 0 0.000
#> GSM782740 2 0.000 1.000 0.000 1 0.000
#> GSM782741 1 0.000 0.999 1.000 0 0.000
#> GSM782742 3 0.000 0.922 0.000 0 1.000
#> GSM782743 3 0.000 0.922 0.000 0 1.000
#> GSM782744 3 0.000 0.922 0.000 0 1.000
#> GSM782745 1 0.103 0.973 0.976 0 0.024
#> GSM782746 2 0.000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.2868 0.883 0.864 0 0 0.136
#> GSM782697 1 0.3444 0.848 0.816 0 0 0.184
#> GSM782698 1 0.0336 0.934 0.992 0 0 0.008
#> GSM782699 1 0.3528 0.839 0.808 0 0 0.192
#> GSM782700 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782701 4 0.0707 0.981 0.020 0 0 0.980
#> GSM782702 4 0.0000 0.987 0.000 0 0 1.000
#> GSM782703 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782704 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782705 1 0.0592 0.934 0.984 0 0 0.016
#> GSM782706 4 0.0592 0.983 0.016 0 0 0.984
#> GSM782707 1 0.2921 0.880 0.860 0 0 0.140
#> GSM782708 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782709 4 0.0000 0.987 0.000 0 0 1.000
#> GSM782710 4 0.0469 0.984 0.012 0 0 0.988
#> GSM782711 1 0.2868 0.883 0.864 0 0 0.136
#> GSM782712 4 0.0921 0.976 0.028 0 0 0.972
#> GSM782713 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782715 1 0.0000 0.935 1.000 0 0 0.000
#> GSM782716 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782717 4 0.1211 0.957 0.040 0 0 0.960
#> GSM782718 1 0.0000 0.935 1.000 0 0 0.000
#> GSM782719 1 0.2973 0.878 0.856 0 0 0.144
#> GSM782720 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782721 4 0.0469 0.984 0.012 0 0 0.988
#> GSM782722 1 0.0000 0.935 1.000 0 0 0.000
#> GSM782723 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782725 1 0.0000 0.935 1.000 0 0 0.000
#> GSM782726 4 0.0000 0.987 0.000 0 0 1.000
#> GSM782727 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782729 1 0.0469 0.933 0.988 0 0 0.012
#> GSM782730 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782731 1 0.0707 0.933 0.980 0 0 0.020
#> GSM782732 1 0.0336 0.934 0.992 0 0 0.008
#> GSM782733 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782734 4 0.0000 0.987 0.000 0 0 1.000
#> GSM782735 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782736 1 0.0000 0.935 1.000 0 0 0.000
#> GSM782737 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782738 1 0.0000 0.935 1.000 0 0 0.000
#> GSM782739 4 0.0469 0.983 0.012 0 0 0.988
#> GSM782740 2 0.0000 1.000 0.000 1 0 0.000
#> GSM782741 4 0.0000 0.987 0.000 0 0 1.000
#> GSM782742 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782743 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782744 3 0.0000 1.000 0.000 0 1 0.000
#> GSM782745 4 0.0000 0.987 0.000 0 0 1.000
#> GSM782746 2 0.0000 1.000 0.000 1 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 5 0.2763 0.6265 0.004 0 0 0.148 0.848
#> GSM782697 5 0.4822 0.5850 0.220 0 0 0.076 0.704
#> GSM782698 5 0.4403 0.2840 0.008 0 0 0.384 0.608
#> GSM782699 5 0.4449 0.6148 0.168 0 0 0.080 0.752
#> GSM782700 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782701 1 0.4963 0.6240 0.608 0 0 0.040 0.352
#> GSM782702 1 0.2471 0.7430 0.864 0 0 0.000 0.136
#> GSM782703 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782704 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782705 5 0.4976 0.0128 0.028 0 0 0.468 0.504
#> GSM782706 1 0.4714 0.6521 0.644 0 0 0.032 0.324
#> GSM782707 5 0.4613 0.5340 0.072 0 0 0.200 0.728
#> GSM782708 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782709 1 0.0000 0.7566 1.000 0 0 0.000 0.000
#> GSM782710 5 0.4211 0.3920 0.360 0 0 0.004 0.636
#> GSM782711 5 0.3151 0.6340 0.020 0 0 0.144 0.836
#> GSM782712 1 0.5351 0.4312 0.484 0 0 0.052 0.464
#> GSM782713 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782714 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782715 4 0.0703 0.8967 0.000 0 0 0.976 0.024
#> GSM782716 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782717 1 0.4234 0.5571 0.760 0 0 0.056 0.184
#> GSM782718 4 0.1270 0.8958 0.000 0 0 0.948 0.052
#> GSM782719 5 0.4953 0.5037 0.088 0 0 0.216 0.696
#> GSM782720 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782721 1 0.4309 0.6711 0.676 0 0 0.016 0.308
#> GSM782722 4 0.0609 0.8767 0.000 0 0 0.980 0.020
#> GSM782723 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782724 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782725 4 0.0703 0.8880 0.000 0 0 0.976 0.024
#> GSM782726 1 0.0000 0.7566 1.000 0 0 0.000 0.000
#> GSM782727 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782728 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782729 4 0.3055 0.8097 0.016 0 0 0.840 0.144
#> GSM782730 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782731 4 0.3532 0.8087 0.048 0 0 0.824 0.128
#> GSM782732 4 0.3586 0.7516 0.020 0 0 0.792 0.188
#> GSM782733 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782734 1 0.0162 0.7574 0.996 0 0 0.000 0.004
#> GSM782735 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782736 4 0.0963 0.8999 0.000 0 0 0.964 0.036
#> GSM782737 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782738 4 0.1043 0.8975 0.000 0 0 0.960 0.040
#> GSM782739 1 0.2813 0.6805 0.868 0 0 0.024 0.108
#> GSM782740 2 0.0000 1.0000 0.000 1 0 0.000 0.000
#> GSM782741 1 0.3388 0.7304 0.792 0 0 0.008 0.200
#> GSM782742 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782743 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782744 3 0.0000 1.0000 0.000 0 1 0.000 0.000
#> GSM782745 1 0.0000 0.7566 1.000 0 0 0.000 0.000
#> GSM782746 2 0.0000 1.0000 0.000 1 0 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM782696 1 0.4981 0.3198 0.584 0 0 0.072 0.340 0.004
#> GSM782697 5 0.2407 0.7061 0.048 0 0 0.004 0.892 0.056
#> GSM782698 5 0.3344 0.6548 0.044 0 0 0.152 0.804 0.000
#> GSM782699 5 0.2617 0.6950 0.080 0 0 0.004 0.876 0.040
#> GSM782700 2 0.0000 1.0000 0.000 1 0 0.000 0.000 0.000
#> GSM782701 1 0.3861 0.5242 0.672 0 0 0.004 0.008 0.316
#> GSM782702 6 0.4349 0.5399 0.208 0 0 0.000 0.084 0.708
#> GSM782703 3 0.0000 1.0000 0.000 0 1 0.000 0.000 0.000
#> GSM782704 3 0.0000 1.0000 0.000 0 1 0.000 0.000 0.000
#> GSM782705 5 0.3993 0.3563 0.024 0 0 0.300 0.676 0.000
#> GSM782706 1 0.3940 0.4923 0.652 0 0 0.004 0.008 0.336
#> GSM782707 1 0.4682 0.6056 0.740 0 0 0.064 0.136 0.060
#> GSM782708 3 0.0000 1.0000 0.000 0 1 0.000 0.000 0.000
#> GSM782709 6 0.0000 0.7521 0.000 0 0 0.000 0.000 1.000
#> GSM782710 5 0.5373 0.3551 0.136 0 0 0.000 0.552 0.312
#> GSM782711 1 0.5071 -0.0600 0.488 0 0 0.064 0.444 0.004
#> GSM782712 1 0.3780 0.5923 0.744 0 0 0.004 0.028 0.224
#> GSM782713 3 0.0000 1.0000 0.000 0 1 0.000 0.000 0.000
#> GSM782714 2 0.0000 1.0000 0.000 1 0 0.000 0.000 0.000
#> GSM782715 4 0.2250 0.7964 0.064 0 0 0.896 0.040 0.000
#> GSM782716 3 0.0000 1.0000 0.000 0 1 0.000 0.000 0.000
#> GSM782717 6 0.6197 0.4232 0.124 0 0 0.072 0.236 0.568
#> GSM782718 4 0.2384 0.7950 0.064 0 0 0.888 0.048 0.000
#> GSM782719 1 0.4327 0.6021 0.772 0 0 0.072 0.108 0.048
#> GSM782720 3 0.0000 1.0000 0.000 0 1 0.000 0.000 0.000
#> GSM782721 1 0.3975 0.3849 0.600 0 0 0.000 0.008 0.392
#> GSM782722 4 0.1858 0.7805 0.076 0 0 0.912 0.012 0.000
#> GSM782723 2 0.0000 1.0000 0.000 1 0 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.0000 0.000 1 0 0.000 0.000 0.000
#> GSM782725 4 0.3757 0.7094 0.136 0 0 0.780 0.084 0.000
#> GSM782726 6 0.0000 0.7521 0.000 0 0 0.000 0.000 1.000
#> GSM782727 3 0.0000 1.0000 0.000 0 1 0.000 0.000 0.000
#> GSM782728 2 0.0000 1.0000 0.000 1 0 0.000 0.000 0.000
#> GSM782729 4 0.5144 0.5821 0.120 0 0 0.620 0.256 0.004
#> GSM782730 3 0.0000 1.0000 0.000 0 1 0.000 0.000 0.000
#> GSM782731 4 0.4779 0.6305 0.028 0 0 0.676 0.248 0.048
#> GSM782732 4 0.4576 0.6205 0.044 0 0 0.676 0.264 0.016
#> GSM782733 3 0.0000 1.0000 0.000 0 1 0.000 0.000 0.000
#> GSM782734 6 0.0146 0.7513 0.004 0 0 0.000 0.000 0.996
#> GSM782735 2 0.0000 1.0000 0.000 1 0 0.000 0.000 0.000
#> GSM782736 4 0.1616 0.8034 0.020 0 0 0.932 0.048 0.000
#> GSM782737 2 0.0000 1.0000 0.000 1 0 0.000 0.000 0.000
#> GSM782738 4 0.1794 0.8022 0.036 0 0 0.924 0.040 0.000
#> GSM782739 6 0.4410 0.6123 0.056 0 0 0.020 0.196 0.728
#> GSM782740 2 0.0000 1.0000 0.000 1 0 0.000 0.000 0.000
#> GSM782741 6 0.4025 0.0234 0.416 0 0 0.000 0.008 0.576
#> GSM782742 3 0.0000 1.0000 0.000 0 1 0.000 0.000 0.000
#> GSM782743 3 0.0000 1.0000 0.000 0 1 0.000 0.000 0.000
#> GSM782744 3 0.0000 1.0000 0.000 0 1 0.000 0.000 0.000
#> GSM782745 6 0.0000 0.7521 0.000 0 0 0.000 0.000 1.000
#> GSM782746 2 0.0000 1.0000 0.000 1 0 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> ATC:skmeans 51 0.648 2
#> ATC:skmeans 50 0.627 3
#> ATC:skmeans 51 0.567 4
#> ATC:skmeans 47 0.440 5
#> ATC:skmeans 43 0.400 6
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 51941 rows and 51 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 1.000 1.000 1.000 0.2972 0.704 0.704
#> 3 3 1.000 1.000 1.000 0.9492 0.718 0.599
#> 4 4 0.824 0.880 0.915 0.2560 0.852 0.648
#> 5 5 0.803 0.865 0.919 0.0456 0.973 0.899
#> 6 6 0.819 0.849 0.930 0.0080 0.997 0.987
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
#> GSM782696 1 0 1 1 0
#> GSM782697 1 0 1 1 0
#> GSM782698 1 0 1 1 0
#> GSM782699 1 0 1 1 0
#> GSM782700 2 0 1 0 1
#> GSM782701 1 0 1 1 0
#> GSM782702 1 0 1 1 0
#> GSM782703 1 0 1 1 0
#> GSM782704 1 0 1 1 0
#> GSM782705 1 0 1 1 0
#> GSM782706 1 0 1 1 0
#> GSM782707 1 0 1 1 0
#> GSM782708 1 0 1 1 0
#> GSM782709 1 0 1 1 0
#> GSM782710 1 0 1 1 0
#> GSM782711 1 0 1 1 0
#> GSM782712 1 0 1 1 0
#> GSM782713 1 0 1 1 0
#> GSM782714 2 0 1 0 1
#> GSM782715 1 0 1 1 0
#> GSM782716 1 0 1 1 0
#> GSM782717 1 0 1 1 0
#> GSM782718 1 0 1 1 0
#> GSM782719 1 0 1 1 0
#> GSM782720 1 0 1 1 0
#> GSM782721 1 0 1 1 0
#> GSM782722 1 0 1 1 0
#> GSM782723 2 0 1 0 1
#> GSM782724 2 0 1 0 1
#> GSM782725 1 0 1 1 0
#> GSM782726 1 0 1 1 0
#> GSM782727 1 0 1 1 0
#> GSM782728 2 0 1 0 1
#> GSM782729 1 0 1 1 0
#> GSM782730 1 0 1 1 0
#> GSM782731 1 0 1 1 0
#> GSM782732 1 0 1 1 0
#> GSM782733 1 0 1 1 0
#> GSM782734 1 0 1 1 0
#> GSM782735 2 0 1 0 1
#> GSM782736 1 0 1 1 0
#> GSM782737 2 0 1 0 1
#> GSM782738 1 0 1 1 0
#> GSM782739 1 0 1 1 0
#> GSM782740 2 0 1 0 1
#> GSM782741 1 0 1 1 0
#> GSM782742 1 0 1 1 0
#> GSM782743 1 0 1 1 0
#> GSM782744 1 0 1 1 0
#> GSM782745 1 0 1 1 0
#> GSM782746 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0 1 1 0 0
#> GSM782697 1 0 1 1 0 0
#> GSM782698 1 0 1 1 0 0
#> GSM782699 1 0 1 1 0 0
#> GSM782700 2 0 1 0 1 0
#> GSM782701 1 0 1 1 0 0
#> GSM782702 1 0 1 1 0 0
#> GSM782703 3 0 1 0 0 1
#> GSM782704 3 0 1 0 0 1
#> GSM782705 1 0 1 1 0 0
#> GSM782706 1 0 1 1 0 0
#> GSM782707 1 0 1 1 0 0
#> GSM782708 3 0 1 0 0 1
#> GSM782709 1 0 1 1 0 0
#> GSM782710 1 0 1 1 0 0
#> GSM782711 1 0 1 1 0 0
#> GSM782712 1 0 1 1 0 0
#> GSM782713 3 0 1 0 0 1
#> GSM782714 2 0 1 0 1 0
#> GSM782715 1 0 1 1 0 0
#> GSM782716 3 0 1 0 0 1
#> GSM782717 1 0 1 1 0 0
#> GSM782718 1 0 1 1 0 0
#> GSM782719 1 0 1 1 0 0
#> GSM782720 3 0 1 0 0 1
#> GSM782721 1 0 1 1 0 0
#> GSM782722 1 0 1 1 0 0
#> GSM782723 2 0 1 0 1 0
#> GSM782724 2 0 1 0 1 0
#> GSM782725 1 0 1 1 0 0
#> GSM782726 1 0 1 1 0 0
#> GSM782727 3 0 1 0 0 1
#> GSM782728 2 0 1 0 1 0
#> GSM782729 1 0 1 1 0 0
#> GSM782730 3 0 1 0 0 1
#> GSM782731 1 0 1 1 0 0
#> GSM782732 1 0 1 1 0 0
#> GSM782733 3 0 1 0 0 1
#> GSM782734 1 0 1 1 0 0
#> GSM782735 2 0 1 0 1 0
#> GSM782736 1 0 1 1 0 0
#> GSM782737 2 0 1 0 1 0
#> GSM782738 1 0 1 1 0 0
#> GSM782739 1 0 1 1 0 0
#> GSM782740 2 0 1 0 1 0
#> GSM782741 1 0 1 1 0 0
#> GSM782742 3 0 1 0 0 1
#> GSM782743 3 0 1 0 0 1
#> GSM782744 3 0 1 0 0 1
#> GSM782745 1 0 1 1 0 0
#> GSM782746 2 0 1 0 1 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.4761 0.581 0.628 0 0.000 0.372
#> GSM782697 1 0.4477 0.650 0.688 0 0.000 0.312
#> GSM782698 1 0.3486 0.757 0.812 0 0.000 0.188
#> GSM782699 1 0.4761 0.581 0.628 0 0.000 0.372
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782701 4 0.3172 0.852 0.160 0 0.000 0.840
#> GSM782702 4 0.1940 0.970 0.076 0 0.000 0.924
#> GSM782703 3 0.1716 0.972 0.000 0 0.936 0.064
#> GSM782704 3 0.1716 0.972 0.000 0 0.936 0.064
#> GSM782705 1 0.0000 0.822 1.000 0 0.000 0.000
#> GSM782706 4 0.1716 0.977 0.064 0 0.000 0.936
#> GSM782707 1 0.4761 0.581 0.628 0 0.000 0.372
#> GSM782708 3 0.1716 0.972 0.000 0 0.936 0.064
#> GSM782709 4 0.1716 0.977 0.064 0 0.000 0.936
#> GSM782710 1 0.4761 0.581 0.628 0 0.000 0.372
#> GSM782711 1 0.3764 0.738 0.784 0 0.000 0.216
#> GSM782712 1 0.4830 0.541 0.608 0 0.000 0.392
#> GSM782713 3 0.0000 0.977 0.000 0 1.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782715 1 0.0000 0.822 1.000 0 0.000 0.000
#> GSM782716 3 0.0000 0.977 0.000 0 1.000 0.000
#> GSM782717 1 0.0000 0.822 1.000 0 0.000 0.000
#> GSM782718 1 0.0000 0.822 1.000 0 0.000 0.000
#> GSM782719 1 0.3311 0.766 0.828 0 0.000 0.172
#> GSM782720 3 0.0000 0.977 0.000 0 1.000 0.000
#> GSM782721 4 0.1716 0.977 0.064 0 0.000 0.936
#> GSM782722 1 0.0000 0.822 1.000 0 0.000 0.000
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782725 1 0.0000 0.822 1.000 0 0.000 0.000
#> GSM782726 4 0.1716 0.977 0.064 0 0.000 0.936
#> GSM782727 3 0.0188 0.977 0.000 0 0.996 0.004
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782729 1 0.0000 0.822 1.000 0 0.000 0.000
#> GSM782730 3 0.0000 0.977 0.000 0 1.000 0.000
#> GSM782731 1 0.0000 0.822 1.000 0 0.000 0.000
#> GSM782732 1 0.0000 0.822 1.000 0 0.000 0.000
#> GSM782733 3 0.0817 0.976 0.000 0 0.976 0.024
#> GSM782734 4 0.1792 0.974 0.068 0 0.000 0.932
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782736 1 0.0000 0.822 1.000 0 0.000 0.000
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782738 1 0.0000 0.822 1.000 0 0.000 0.000
#> GSM782739 1 0.3528 0.738 0.808 0 0.000 0.192
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782741 4 0.2081 0.962 0.084 0 0.000 0.916
#> GSM782742 3 0.0000 0.977 0.000 0 1.000 0.000
#> GSM782743 3 0.1716 0.972 0.000 0 0.936 0.064
#> GSM782744 3 0.1716 0.972 0.000 0 0.936 0.064
#> GSM782745 4 0.1716 0.977 0.064 0 0.000 0.936
#> GSM782746 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 4 0.4138 0.602 0.384 0 0.000 0.616 0.000
#> GSM782697 4 0.3895 0.669 0.320 0 0.000 0.680 0.000
#> GSM782698 4 0.3074 0.765 0.196 0 0.000 0.804 0.000
#> GSM782699 4 0.4138 0.602 0.384 0 0.000 0.616 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782701 1 0.1965 0.863 0.904 0 0.000 0.096 0.000
#> GSM782702 1 0.0404 0.970 0.988 0 0.000 0.012 0.000
#> GSM782703 5 0.2561 0.954 0.000 0 0.144 0.000 0.856
#> GSM782704 5 0.2561 0.954 0.000 0 0.144 0.000 0.856
#> GSM782705 4 0.0000 0.827 0.000 0 0.000 1.000 0.000
#> GSM782706 1 0.0000 0.977 1.000 0 0.000 0.000 0.000
#> GSM782707 4 0.4138 0.602 0.384 0 0.000 0.616 0.000
#> GSM782708 5 0.2561 0.954 0.000 0 0.144 0.000 0.856
#> GSM782709 1 0.0000 0.977 1.000 0 0.000 0.000 0.000
#> GSM782710 4 0.4138 0.602 0.384 0 0.000 0.616 0.000
#> GSM782711 4 0.3336 0.745 0.228 0 0.000 0.772 0.000
#> GSM782712 4 0.4249 0.511 0.432 0 0.000 0.568 0.000
#> GSM782713 3 0.0000 0.936 0.000 0 1.000 0.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782715 4 0.0000 0.827 0.000 0 0.000 1.000 0.000
#> GSM782716 3 0.0000 0.936 0.000 0 1.000 0.000 0.000
#> GSM782717 4 0.0000 0.827 0.000 0 0.000 1.000 0.000
#> GSM782718 4 0.0000 0.827 0.000 0 0.000 1.000 0.000
#> GSM782719 4 0.2966 0.772 0.184 0 0.000 0.816 0.000
#> GSM782720 3 0.0000 0.936 0.000 0 1.000 0.000 0.000
#> GSM782721 1 0.0000 0.977 1.000 0 0.000 0.000 0.000
#> GSM782722 4 0.0000 0.827 0.000 0 0.000 1.000 0.000
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782725 4 0.0000 0.827 0.000 0 0.000 1.000 0.000
#> GSM782726 1 0.0000 0.977 1.000 0 0.000 0.000 0.000
#> GSM782727 3 0.0963 0.910 0.000 0 0.964 0.000 0.036
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782729 4 0.0000 0.827 0.000 0 0.000 1.000 0.000
#> GSM782730 3 0.0000 0.936 0.000 0 1.000 0.000 0.000
#> GSM782731 4 0.0000 0.827 0.000 0 0.000 1.000 0.000
#> GSM782732 4 0.0000 0.827 0.000 0 0.000 1.000 0.000
#> GSM782733 3 0.3707 0.521 0.000 0 0.716 0.000 0.284
#> GSM782734 1 0.0162 0.974 0.996 0 0.000 0.004 0.000
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782736 4 0.0000 0.827 0.000 0 0.000 1.000 0.000
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782738 4 0.0000 0.827 0.000 0 0.000 1.000 0.000
#> GSM782739 4 0.3039 0.752 0.192 0 0.000 0.808 0.000
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM782741 1 0.0609 0.963 0.980 0 0.000 0.020 0.000
#> GSM782742 3 0.0000 0.936 0.000 0 1.000 0.000 0.000
#> GSM782743 5 0.2561 0.954 0.000 0 0.144 0.000 0.856
#> GSM782744 5 0.0000 0.827 0.000 0 0.000 0.000 1.000
#> GSM782745 1 0.0000 0.977 1.000 0 0.000 0.000 0.000
#> GSM782746 2 0.0000 1.000 0.000 1 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
#> GSM782696 1 0.3717 0.602 0.616 0 0.000 0 0.000 0.384
#> GSM782697 1 0.3499 0.669 0.680 0 0.000 0 0.000 0.320
#> GSM782698 1 0.2762 0.765 0.804 0 0.000 0 0.000 0.196
#> GSM782699 1 0.3717 0.602 0.616 0 0.000 0 0.000 0.384
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782701 6 0.1765 0.845 0.096 0 0.000 0 0.000 0.904
#> GSM782702 6 0.0363 0.965 0.012 0 0.000 0 0.000 0.988
#> GSM782703 5 0.0146 0.994 0.000 0 0.004 0 0.996 0.000
#> GSM782704 5 0.0000 0.998 0.000 0 0.000 0 1.000 0.000
#> GSM782705 1 0.0000 0.809 1.000 0 0.000 0 0.000 0.000
#> GSM782706 6 0.0000 0.973 0.000 0 0.000 0 0.000 1.000
#> GSM782707 1 0.3717 0.602 0.616 0 0.000 0 0.000 0.384
#> GSM782708 5 0.0000 0.998 0.000 0 0.000 0 1.000 0.000
#> GSM782709 6 0.0000 0.973 0.000 0 0.000 0 0.000 1.000
#> GSM782710 1 0.3717 0.602 0.616 0 0.000 0 0.000 0.384
#> GSM782711 1 0.2996 0.745 0.772 0 0.000 0 0.000 0.228
#> GSM782712 1 0.3817 0.511 0.568 0 0.000 0 0.000 0.432
#> GSM782713 3 0.0000 0.934 0.000 0 1.000 0 0.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782715 1 0.0000 0.809 1.000 0 0.000 0 0.000 0.000
#> GSM782716 3 0.0000 0.934 0.000 0 1.000 0 0.000 0.000
#> GSM782717 1 0.0000 0.809 1.000 0 0.000 0 0.000 0.000
#> GSM782718 1 0.0000 0.809 1.000 0 0.000 0 0.000 0.000
#> GSM782719 1 0.2664 0.772 0.816 0 0.000 0 0.000 0.184
#> GSM782720 3 0.0000 0.934 0.000 0 1.000 0 0.000 0.000
#> GSM782721 6 0.0000 0.973 0.000 0 0.000 0 0.000 1.000
#> GSM782722 1 0.0000 0.809 1.000 0 0.000 0 0.000 0.000
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782725 1 0.0000 0.809 1.000 0 0.000 0 0.000 0.000
#> GSM782726 6 0.0000 0.973 0.000 0 0.000 0 0.000 1.000
#> GSM782727 3 0.0865 0.909 0.000 0 0.964 0 0.036 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782729 1 0.0000 0.809 1.000 0 0.000 0 0.000 0.000
#> GSM782730 3 0.0000 0.934 0.000 0 1.000 0 0.000 0.000
#> GSM782731 1 0.0000 0.809 1.000 0 0.000 0 0.000 0.000
#> GSM782732 1 0.0000 0.809 1.000 0 0.000 0 0.000 0.000
#> GSM782733 3 0.3371 0.590 0.000 0 0.708 0 0.292 0.000
#> GSM782734 6 0.0146 0.970 0.004 0 0.000 0 0.000 0.996
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782736 1 0.0000 0.809 1.000 0 0.000 0 0.000 0.000
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782738 1 0.0000 0.809 1.000 0 0.000 0 0.000 0.000
#> GSM782739 1 0.2730 0.752 0.808 0 0.000 0 0.000 0.192
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0 0.000 0.000
#> GSM782741 6 0.0547 0.957 0.020 0 0.000 0 0.000 0.980
#> GSM782742 3 0.0000 0.934 0.000 0 1.000 0 0.000 0.000
#> GSM782743 5 0.0000 0.998 0.000 0 0.000 0 1.000 0.000
#> GSM782744 4 0.0000 0.000 0.000 0 0.000 1 0.000 0.000
#> GSM782745 6 0.0000 0.973 0.000 0 0.000 0 0.000 1.000
#> GSM782746 2 0.0000 1.000 0.000 1 0.000 0 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> ATC:pam 51 0.648 2
#> ATC:pam 51 0.642 3
#> ATC:pam 51 0.623 4
#> ATC:pam 51 0.626 5
#> ATC:pam 50 0.522 6
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 51941 rows and 51 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 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 0.964 0.977 0.3160 0.704 0.704
#> 3 3 1.000 0.999 1.000 0.8338 0.718 0.599
#> 4 4 0.833 0.883 0.925 0.1723 0.936 0.849
#> 5 5 0.796 0.781 0.877 0.0820 0.920 0.779
#> 6 6 0.774 0.829 0.886 0.0786 0.892 0.637
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
#> GSM782696 1 0.000 0.971 1.000 0.000
#> GSM782697 1 0.000 0.971 1.000 0.000
#> GSM782698 1 0.000 0.971 1.000 0.000
#> GSM782699 1 0.000 0.971 1.000 0.000
#> GSM782700 2 0.000 1.000 0.000 1.000
#> GSM782701 1 0.000 0.971 1.000 0.000
#> GSM782702 1 0.000 0.971 1.000 0.000
#> GSM782703 1 0.456 0.922 0.904 0.096
#> GSM782704 1 0.456 0.922 0.904 0.096
#> GSM782705 1 0.000 0.971 1.000 0.000
#> GSM782706 1 0.000 0.971 1.000 0.000
#> GSM782707 1 0.000 0.971 1.000 0.000
#> GSM782708 1 0.456 0.922 0.904 0.096
#> GSM782709 1 0.000 0.971 1.000 0.000
#> GSM782710 1 0.000 0.971 1.000 0.000
#> GSM782711 1 0.000 0.971 1.000 0.000
#> GSM782712 1 0.000 0.971 1.000 0.000
#> GSM782713 1 0.456 0.922 0.904 0.096
#> GSM782714 2 0.000 1.000 0.000 1.000
#> GSM782715 1 0.000 0.971 1.000 0.000
#> GSM782716 1 0.456 0.922 0.904 0.096
#> GSM782717 1 0.000 0.971 1.000 0.000
#> GSM782718 1 0.000 0.971 1.000 0.000
#> GSM782719 1 0.000 0.971 1.000 0.000
#> GSM782720 1 0.456 0.922 0.904 0.096
#> GSM782721 1 0.000 0.971 1.000 0.000
#> GSM782722 1 0.000 0.971 1.000 0.000
#> GSM782723 2 0.000 1.000 0.000 1.000
#> GSM782724 2 0.000 1.000 0.000 1.000
#> GSM782725 1 0.000 0.971 1.000 0.000
#> GSM782726 1 0.000 0.971 1.000 0.000
#> GSM782727 1 0.456 0.922 0.904 0.096
#> GSM782728 2 0.000 1.000 0.000 1.000
#> GSM782729 1 0.000 0.971 1.000 0.000
#> GSM782730 1 0.456 0.922 0.904 0.096
#> GSM782731 1 0.000 0.971 1.000 0.000
#> GSM782732 1 0.000 0.971 1.000 0.000
#> GSM782733 1 0.456 0.922 0.904 0.096
#> GSM782734 1 0.000 0.971 1.000 0.000
#> GSM782735 2 0.000 1.000 0.000 1.000
#> GSM782736 1 0.000 0.971 1.000 0.000
#> GSM782737 2 0.000 1.000 0.000 1.000
#> GSM782738 1 0.000 0.971 1.000 0.000
#> GSM782739 1 0.000 0.971 1.000 0.000
#> GSM782740 2 0.000 1.000 0.000 1.000
#> GSM782741 1 0.000 0.971 1.000 0.000
#> GSM782742 1 0.456 0.922 0.904 0.096
#> GSM782743 1 0.456 0.922 0.904 0.096
#> GSM782744 1 0.456 0.922 0.904 0.096
#> GSM782745 1 0.000 0.971 1.000 0.000
#> GSM782746 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
#> GSM782696 1 0.0000 0.999 1.000 0 0.000
#> GSM782697 1 0.0000 0.999 1.000 0 0.000
#> GSM782698 1 0.0000 0.999 1.000 0 0.000
#> GSM782699 1 0.0000 0.999 1.000 0 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0.000
#> GSM782701 1 0.0000 0.999 1.000 0 0.000
#> GSM782702 1 0.0000 0.999 1.000 0 0.000
#> GSM782703 3 0.0000 1.000 0.000 0 1.000
#> GSM782704 3 0.0000 1.000 0.000 0 1.000
#> GSM782705 1 0.0000 0.999 1.000 0 0.000
#> GSM782706 1 0.0000 0.999 1.000 0 0.000
#> GSM782707 1 0.0000 0.999 1.000 0 0.000
#> GSM782708 3 0.0000 1.000 0.000 0 1.000
#> GSM782709 1 0.0000 0.999 1.000 0 0.000
#> GSM782710 1 0.0000 0.999 1.000 0 0.000
#> GSM782711 1 0.0000 0.999 1.000 0 0.000
#> GSM782712 1 0.0000 0.999 1.000 0 0.000
#> GSM782713 3 0.0000 1.000 0.000 0 1.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000
#> GSM782715 1 0.0424 0.992 0.992 0 0.008
#> GSM782716 3 0.0000 1.000 0.000 0 1.000
#> GSM782717 1 0.0000 0.999 1.000 0 0.000
#> GSM782718 1 0.0000 0.999 1.000 0 0.000
#> GSM782719 1 0.0000 0.999 1.000 0 0.000
#> GSM782720 3 0.0000 1.000 0.000 0 1.000
#> GSM782721 1 0.0000 0.999 1.000 0 0.000
#> GSM782722 1 0.0424 0.992 0.992 0 0.008
#> GSM782723 2 0.0000 1.000 0.000 1 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000
#> GSM782725 1 0.0000 0.999 1.000 0 0.000
#> GSM782726 1 0.0000 0.999 1.000 0 0.000
#> GSM782727 3 0.0000 1.000 0.000 0 1.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000
#> GSM782729 1 0.0000 0.999 1.000 0 0.000
#> GSM782730 3 0.0000 1.000 0.000 0 1.000
#> GSM782731 1 0.0000 0.999 1.000 0 0.000
#> GSM782732 1 0.0000 0.999 1.000 0 0.000
#> GSM782733 3 0.0000 1.000 0.000 0 1.000
#> GSM782734 1 0.0000 0.999 1.000 0 0.000
#> GSM782735 2 0.0000 1.000 0.000 1 0.000
#> GSM782736 1 0.0000 0.999 1.000 0 0.000
#> GSM782737 2 0.0000 1.000 0.000 1 0.000
#> GSM782738 1 0.0000 0.999 1.000 0 0.000
#> GSM782739 1 0.0000 0.999 1.000 0 0.000
#> GSM782740 2 0.0000 1.000 0.000 1 0.000
#> GSM782741 1 0.0000 0.999 1.000 0 0.000
#> GSM782742 3 0.0000 1.000 0.000 0 1.000
#> GSM782743 3 0.0000 1.000 0.000 0 1.000
#> GSM782744 3 0.0000 1.000 0.000 0 1.000
#> GSM782745 1 0.0000 0.999 1.000 0 0.000
#> GSM782746 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.3649 0.792 0.796 0 0.000 0.204
#> GSM782697 1 0.1940 0.838 0.924 0 0.000 0.076
#> GSM782698 1 0.4776 0.613 0.624 0 0.000 0.376
#> GSM782699 1 0.3726 0.788 0.788 0 0.000 0.212
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782701 1 0.0592 0.839 0.984 0 0.000 0.016
#> GSM782702 1 0.0188 0.844 0.996 0 0.000 0.004
#> GSM782703 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782704 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782705 1 0.3942 0.774 0.764 0 0.000 0.236
#> GSM782706 1 0.0921 0.836 0.972 0 0.000 0.028
#> GSM782707 1 0.3172 0.811 0.840 0 0.000 0.160
#> GSM782708 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782709 1 0.0707 0.840 0.980 0 0.000 0.020
#> GSM782710 1 0.1302 0.843 0.956 0 0.000 0.044
#> GSM782711 1 0.3649 0.792 0.796 0 0.000 0.204
#> GSM782712 1 0.0188 0.844 0.996 0 0.000 0.004
#> GSM782713 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782715 4 0.0707 0.940 0.020 0 0.000 0.980
#> GSM782716 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782717 1 0.0707 0.845 0.980 0 0.000 0.020
#> GSM782718 1 0.4585 0.664 0.668 0 0.000 0.332
#> GSM782719 1 0.0000 0.843 1.000 0 0.000 0.000
#> GSM782720 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782721 1 0.0817 0.836 0.976 0 0.000 0.024
#> GSM782722 4 0.0707 0.940 0.020 0 0.000 0.980
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782725 1 0.4103 0.761 0.744 0 0.000 0.256
#> GSM782726 1 0.0707 0.840 0.980 0 0.000 0.020
#> GSM782727 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782729 1 0.4605 0.674 0.664 0 0.000 0.336
#> GSM782730 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782731 1 0.4605 0.674 0.664 0 0.000 0.336
#> GSM782732 1 0.4222 0.737 0.728 0 0.000 0.272
#> GSM782733 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782734 1 0.0592 0.839 0.984 0 0.000 0.016
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782736 4 0.2345 0.880 0.100 0 0.000 0.900
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782738 1 0.4790 0.606 0.620 0 0.000 0.380
#> GSM782739 1 0.0336 0.844 0.992 0 0.000 0.008
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM782741 1 0.0592 0.839 0.984 0 0.000 0.016
#> GSM782742 3 0.0000 0.999 0.000 0 1.000 0.000
#> GSM782743 3 0.0336 0.994 0.000 0 0.992 0.008
#> GSM782744 3 0.0336 0.994 0.000 0 0.992 0.008
#> GSM782745 1 0.0592 0.839 0.984 0 0.000 0.016
#> GSM782746 2 0.0000 1.000 0.000 1 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.1697 0.77211 0.932 0 0.000 0.060 0.008
#> GSM782697 1 0.1205 0.77501 0.956 0 0.000 0.040 0.004
#> GSM782698 1 0.6282 0.26106 0.536 0 0.000 0.248 0.216
#> GSM782699 1 0.1430 0.77252 0.944 0 0.000 0.052 0.004
#> GSM782700 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000
#> GSM782701 1 0.2561 0.71397 0.856 0 0.000 0.000 0.144
#> GSM782702 1 0.0162 0.76442 0.996 0 0.000 0.000 0.004
#> GSM782703 3 0.0162 0.98382 0.000 0 0.996 0.000 0.004
#> GSM782704 3 0.0162 0.98382 0.000 0 0.996 0.004 0.000
#> GSM782705 1 0.4164 0.69698 0.784 0 0.000 0.096 0.120
#> GSM782706 1 0.3141 0.71176 0.832 0 0.000 0.016 0.152
#> GSM782707 1 0.3734 0.72748 0.812 0 0.000 0.060 0.128
#> GSM782708 3 0.0162 0.98382 0.000 0 0.996 0.004 0.000
#> GSM782709 5 0.3913 1.00000 0.324 0 0.000 0.000 0.676
#> GSM782710 1 0.1282 0.77427 0.952 0 0.000 0.044 0.004
#> GSM782711 1 0.1697 0.77211 0.932 0 0.000 0.060 0.008
#> GSM782712 1 0.0162 0.76438 0.996 0 0.000 0.000 0.004
#> GSM782713 3 0.0162 0.98382 0.000 0 0.996 0.004 0.000
#> GSM782714 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000
#> GSM782715 4 0.0290 0.53855 0.008 0 0.000 0.992 0.000
#> GSM782716 3 0.0324 0.98378 0.000 0 0.992 0.004 0.004
#> GSM782717 1 0.1300 0.76949 0.956 0 0.000 0.016 0.028
#> GSM782718 4 0.6652 0.28900 0.348 0 0.000 0.420 0.232
#> GSM782719 1 0.1981 0.76772 0.920 0 0.000 0.016 0.064
#> GSM782720 3 0.0451 0.98368 0.000 0 0.988 0.004 0.008
#> GSM782721 1 0.3039 0.70679 0.836 0 0.000 0.012 0.152
#> GSM782722 4 0.0404 0.54224 0.012 0 0.000 0.988 0.000
#> GSM782723 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000
#> GSM782725 1 0.4985 0.58186 0.680 0 0.000 0.076 0.244
#> GSM782726 5 0.3913 1.00000 0.324 0 0.000 0.000 0.676
#> GSM782727 3 0.0162 0.98382 0.000 0 0.996 0.000 0.004
#> GSM782728 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000
#> GSM782729 1 0.5775 0.47060 0.608 0 0.000 0.148 0.244
#> GSM782730 3 0.0324 0.98378 0.000 0 0.992 0.004 0.004
#> GSM782731 1 0.5941 0.42827 0.588 0 0.000 0.168 0.244
#> GSM782732 1 0.5628 0.51886 0.632 0 0.000 0.148 0.220
#> GSM782733 3 0.0162 0.98382 0.000 0 0.996 0.000 0.004
#> GSM782734 1 0.2377 0.67211 0.872 0 0.000 0.000 0.128
#> GSM782735 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000
#> GSM782736 4 0.3035 0.56200 0.032 0 0.000 0.856 0.112
#> GSM782737 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000
#> GSM782738 4 0.6652 0.28995 0.348 0 0.000 0.420 0.232
#> GSM782739 1 0.0290 0.76299 0.992 0 0.000 0.000 0.008
#> GSM782740 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000
#> GSM782741 1 0.1410 0.73690 0.940 0 0.000 0.000 0.060
#> GSM782742 3 0.0451 0.98368 0.000 0 0.988 0.004 0.008
#> GSM782743 3 0.1914 0.94368 0.000 0 0.924 0.016 0.060
#> GSM782744 3 0.2046 0.93792 0.000 0 0.916 0.016 0.068
#> GSM782745 1 0.4015 -0.00892 0.652 0 0.000 0.000 0.348
#> GSM782746 2 0.0000 1.00000 0.000 1 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
#> GSM782696 1 0.2416 0.776 0.844 0 0.000 0.156 0.000 0.000
#> GSM782697 1 0.0790 0.859 0.968 0 0.000 0.032 0.000 0.000
#> GSM782698 4 0.2489 0.811 0.128 0 0.000 0.860 0.012 0.000
#> GSM782699 1 0.1204 0.853 0.944 0 0.000 0.056 0.000 0.000
#> GSM782700 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782701 1 0.2221 0.844 0.896 0 0.000 0.072 0.000 0.032
#> GSM782702 1 0.0260 0.857 0.992 0 0.000 0.008 0.000 0.000
#> GSM782703 3 0.0260 0.918 0.000 0 0.992 0.000 0.000 0.008
#> GSM782704 3 0.3268 0.845 0.000 0 0.808 0.020 0.164 0.008
#> GSM782705 4 0.3330 0.699 0.284 0 0.000 0.716 0.000 0.000
#> GSM782706 1 0.2361 0.841 0.884 0 0.000 0.088 0.000 0.028
#> GSM782707 1 0.3464 0.591 0.688 0 0.000 0.312 0.000 0.000
#> GSM782708 3 0.3268 0.845 0.000 0 0.808 0.020 0.164 0.008
#> GSM782709 6 0.0713 0.700 0.028 0 0.000 0.000 0.000 0.972
#> GSM782710 1 0.0458 0.859 0.984 0 0.000 0.016 0.000 0.000
#> GSM782711 1 0.2416 0.776 0.844 0 0.000 0.156 0.000 0.000
#> GSM782712 1 0.0547 0.862 0.980 0 0.000 0.020 0.000 0.000
#> GSM782713 3 0.0146 0.919 0.000 0 0.996 0.000 0.000 0.004
#> GSM782714 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782715 5 0.3126 0.868 0.000 0 0.000 0.248 0.752 0.000
#> GSM782716 3 0.0146 0.919 0.000 0 0.996 0.000 0.000 0.004
#> GSM782717 1 0.2020 0.844 0.896 0 0.000 0.096 0.000 0.008
#> GSM782718 4 0.3950 0.343 0.040 0 0.000 0.720 0.240 0.000
#> GSM782719 1 0.3215 0.725 0.756 0 0.000 0.240 0.000 0.004
#> GSM782720 3 0.0146 0.919 0.000 0 0.996 0.000 0.000 0.004
#> GSM782721 1 0.2733 0.826 0.864 0 0.000 0.080 0.000 0.056
#> GSM782722 5 0.3175 0.871 0.000 0 0.000 0.256 0.744 0.000
#> GSM782723 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782724 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782725 4 0.2673 0.798 0.132 0 0.000 0.852 0.004 0.012
#> GSM782726 6 0.0713 0.700 0.028 0 0.000 0.000 0.000 0.972
#> GSM782727 3 0.0146 0.919 0.000 0 0.996 0.000 0.000 0.004
#> GSM782728 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782729 4 0.2219 0.827 0.136 0 0.000 0.864 0.000 0.000
#> GSM782730 3 0.0291 0.918 0.000 0 0.992 0.000 0.004 0.004
#> GSM782731 4 0.2340 0.826 0.148 0 0.000 0.852 0.000 0.000
#> GSM782732 4 0.2527 0.814 0.168 0 0.000 0.832 0.000 0.000
#> GSM782733 3 0.0146 0.919 0.000 0 0.996 0.000 0.000 0.004
#> GSM782734 1 0.3288 0.498 0.724 0 0.000 0.000 0.000 0.276
#> GSM782735 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782736 5 0.4502 0.689 0.016 0 0.000 0.404 0.568 0.012
#> GSM782737 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782738 4 0.3253 0.680 0.068 0 0.000 0.832 0.096 0.004
#> GSM782739 1 0.0260 0.857 0.992 0 0.000 0.008 0.000 0.000
#> GSM782740 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM782741 1 0.0972 0.859 0.964 0 0.000 0.028 0.000 0.008
#> GSM782742 3 0.0000 0.919 0.000 0 1.000 0.000 0.000 0.000
#> GSM782743 3 0.4176 0.776 0.000 0 0.708 0.044 0.244 0.004
#> GSM782744 3 0.4176 0.772 0.000 0 0.708 0.044 0.244 0.004
#> GSM782745 6 0.3684 0.364 0.372 0 0.000 0.000 0.000 0.628
#> GSM782746 2 0.0000 1.000 0.000 1 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> ATC:mclust 51 0.648 2
#> ATC:mclust 51 0.642 3
#> ATC:mclust 51 0.502 4
#> ATC:mclust 45 0.395 5
#> ATC:mclust 48 0.384 6
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 51941 rows and 51 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.2972 0.704 0.704
#> 3 3 1.000 0.998 0.999 0.9516 0.718 0.599
#> 4 4 0.778 0.887 0.904 0.1348 1.000 1.000
#> 5 5 0.689 0.701 0.848 0.0747 0.902 0.767
#> 6 6 0.682 0.673 0.813 0.0459 0.956 0.867
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
#> GSM782696 1 0 1 1 0
#> GSM782697 1 0 1 1 0
#> GSM782698 1 0 1 1 0
#> GSM782699 1 0 1 1 0
#> GSM782700 2 0 1 0 1
#> GSM782701 1 0 1 1 0
#> GSM782702 1 0 1 1 0
#> GSM782703 1 0 1 1 0
#> GSM782704 1 0 1 1 0
#> GSM782705 1 0 1 1 0
#> GSM782706 1 0 1 1 0
#> GSM782707 1 0 1 1 0
#> GSM782708 1 0 1 1 0
#> GSM782709 1 0 1 1 0
#> GSM782710 1 0 1 1 0
#> GSM782711 1 0 1 1 0
#> GSM782712 1 0 1 1 0
#> GSM782713 1 0 1 1 0
#> GSM782714 2 0 1 0 1
#> GSM782715 1 0 1 1 0
#> GSM782716 1 0 1 1 0
#> GSM782717 1 0 1 1 0
#> GSM782718 1 0 1 1 0
#> GSM782719 1 0 1 1 0
#> GSM782720 1 0 1 1 0
#> GSM782721 1 0 1 1 0
#> GSM782722 1 0 1 1 0
#> GSM782723 2 0 1 0 1
#> GSM782724 2 0 1 0 1
#> GSM782725 1 0 1 1 0
#> GSM782726 1 0 1 1 0
#> GSM782727 1 0 1 1 0
#> GSM782728 2 0 1 0 1
#> GSM782729 1 0 1 1 0
#> GSM782730 1 0 1 1 0
#> GSM782731 1 0 1 1 0
#> GSM782732 1 0 1 1 0
#> GSM782733 1 0 1 1 0
#> GSM782734 1 0 1 1 0
#> GSM782735 2 0 1 0 1
#> GSM782736 1 0 1 1 0
#> GSM782737 2 0 1 0 1
#> GSM782738 1 0 1 1 0
#> GSM782739 1 0 1 1 0
#> GSM782740 2 0 1 0 1
#> GSM782741 1 0 1 1 0
#> GSM782742 1 0 1 1 0
#> GSM782743 1 0 1 1 0
#> GSM782744 1 0 1 1 0
#> GSM782745 1 0 1 1 0
#> GSM782746 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM782696 1 0.000 0.998 1.000 0 0.000
#> GSM782697 1 0.000 0.998 1.000 0 0.000
#> GSM782698 1 0.000 0.998 1.000 0 0.000
#> GSM782699 1 0.000 0.998 1.000 0 0.000
#> GSM782700 2 0.000 1.000 0.000 1 0.000
#> GSM782701 1 0.000 0.998 1.000 0 0.000
#> GSM782702 1 0.000 0.998 1.000 0 0.000
#> GSM782703 3 0.000 1.000 0.000 0 1.000
#> GSM782704 3 0.000 1.000 0.000 0 1.000
#> GSM782705 1 0.000 0.998 1.000 0 0.000
#> GSM782706 1 0.000 0.998 1.000 0 0.000
#> GSM782707 1 0.000 0.998 1.000 0 0.000
#> GSM782708 3 0.000 1.000 0.000 0 1.000
#> GSM782709 1 0.000 0.998 1.000 0 0.000
#> GSM782710 1 0.000 0.998 1.000 0 0.000
#> GSM782711 1 0.000 0.998 1.000 0 0.000
#> GSM782712 1 0.000 0.998 1.000 0 0.000
#> GSM782713 3 0.000 1.000 0.000 0 1.000
#> GSM782714 2 0.000 1.000 0.000 1 0.000
#> GSM782715 1 0.000 0.998 1.000 0 0.000
#> GSM782716 3 0.000 1.000 0.000 0 1.000
#> GSM782717 1 0.000 0.998 1.000 0 0.000
#> GSM782718 1 0.000 0.998 1.000 0 0.000
#> GSM782719 1 0.000 0.998 1.000 0 0.000
#> GSM782720 3 0.000 1.000 0.000 0 1.000
#> GSM782721 1 0.000 0.998 1.000 0 0.000
#> GSM782722 1 0.000 0.998 1.000 0 0.000
#> GSM782723 2 0.000 1.000 0.000 1 0.000
#> GSM782724 2 0.000 1.000 0.000 1 0.000
#> GSM782725 1 0.000 0.998 1.000 0 0.000
#> GSM782726 1 0.196 0.939 0.944 0 0.056
#> GSM782727 3 0.000 1.000 0.000 0 1.000
#> GSM782728 2 0.000 1.000 0.000 1 0.000
#> GSM782729 1 0.000 0.998 1.000 0 0.000
#> GSM782730 3 0.000 1.000 0.000 0 1.000
#> GSM782731 1 0.000 0.998 1.000 0 0.000
#> GSM782732 1 0.000 0.998 1.000 0 0.000
#> GSM782733 3 0.000 1.000 0.000 0 1.000
#> GSM782734 1 0.000 0.998 1.000 0 0.000
#> GSM782735 2 0.000 1.000 0.000 1 0.000
#> GSM782736 1 0.000 0.998 1.000 0 0.000
#> GSM782737 2 0.000 1.000 0.000 1 0.000
#> GSM782738 1 0.000 0.998 1.000 0 0.000
#> GSM782739 1 0.000 0.998 1.000 0 0.000
#> GSM782740 2 0.000 1.000 0.000 1 0.000
#> GSM782741 1 0.000 0.998 1.000 0 0.000
#> GSM782742 3 0.000 1.000 0.000 0 1.000
#> GSM782743 3 0.000 1.000 0.000 0 1.000
#> GSM782744 3 0.000 1.000 0.000 0 1.000
#> GSM782745 1 0.000 0.998 1.000 0 0.000
#> GSM782746 2 0.000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM782696 1 0.0707 0.863 0.980 0.000 0.000 NA
#> GSM782697 1 0.1118 0.864 0.964 0.000 0.000 NA
#> GSM782698 1 0.4697 0.738 0.644 0.000 0.000 NA
#> GSM782699 1 0.0592 0.863 0.984 0.000 0.000 NA
#> GSM782700 2 0.0000 0.999 0.000 1.000 0.000 NA
#> GSM782701 1 0.1792 0.852 0.932 0.000 0.000 NA
#> GSM782702 1 0.1474 0.852 0.948 0.000 0.000 NA
#> GSM782703 3 0.0336 0.992 0.000 0.000 0.992 NA
#> GSM782704 3 0.0336 0.992 0.000 0.000 0.992 NA
#> GSM782705 1 0.3569 0.832 0.804 0.000 0.000 NA
#> GSM782706 1 0.2345 0.844 0.900 0.000 0.000 NA
#> GSM782707 1 0.2408 0.856 0.896 0.000 0.000 NA
#> GSM782708 3 0.0336 0.992 0.000 0.000 0.992 NA
#> GSM782709 1 0.4155 0.735 0.756 0.000 0.004 NA
#> GSM782710 1 0.0592 0.862 0.984 0.000 0.000 NA
#> GSM782711 1 0.1022 0.864 0.968 0.000 0.000 NA
#> GSM782712 1 0.1302 0.855 0.956 0.000 0.000 NA
#> GSM782713 3 0.0000 0.994 0.000 0.000 1.000 NA
#> GSM782714 2 0.0188 0.998 0.000 0.996 0.000 NA
#> GSM782715 1 0.4999 0.615 0.508 0.000 0.000 NA
#> GSM782716 3 0.0000 0.994 0.000 0.000 1.000 NA
#> GSM782717 1 0.0469 0.863 0.988 0.000 0.000 NA
#> GSM782718 1 0.4643 0.752 0.656 0.000 0.000 NA
#> GSM782719 1 0.1940 0.861 0.924 0.000 0.000 NA
#> GSM782720 3 0.0000 0.994 0.000 0.000 1.000 NA
#> GSM782721 1 0.3266 0.808 0.832 0.000 0.000 NA
#> GSM782722 1 0.4925 0.683 0.572 0.000 0.000 NA
#> GSM782723 2 0.0188 0.998 0.000 0.996 0.000 NA
#> GSM782724 2 0.0188 0.998 0.000 0.996 0.000 NA
#> GSM782725 1 0.3569 0.833 0.804 0.000 0.000 NA
#> GSM782726 1 0.5464 0.695 0.716 0.000 0.072 NA
#> GSM782727 3 0.0000 0.994 0.000 0.000 1.000 NA
#> GSM782728 2 0.0000 0.999 0.000 1.000 0.000 NA
#> GSM782729 1 0.4072 0.807 0.748 0.000 0.000 NA
#> GSM782730 3 0.0469 0.990 0.000 0.000 0.988 NA
#> GSM782731 1 0.3486 0.836 0.812 0.000 0.000 NA
#> GSM782732 1 0.3528 0.833 0.808 0.000 0.000 NA
#> GSM782733 3 0.0000 0.994 0.000 0.000 1.000 NA
#> GSM782734 1 0.2408 0.835 0.896 0.000 0.000 NA
#> GSM782735 2 0.0000 0.999 0.000 1.000 0.000 NA
#> GSM782736 1 0.4776 0.728 0.624 0.000 0.000 NA
#> GSM782737 2 0.0188 0.998 0.000 0.996 0.000 NA
#> GSM782738 1 0.3975 0.814 0.760 0.000 0.000 NA
#> GSM782739 1 0.0469 0.860 0.988 0.000 0.000 NA
#> GSM782740 2 0.0000 0.999 0.000 1.000 0.000 NA
#> GSM782741 1 0.1792 0.847 0.932 0.000 0.000 NA
#> GSM782742 3 0.0188 0.993 0.000 0.000 0.996 NA
#> GSM782743 3 0.0707 0.985 0.000 0.000 0.980 NA
#> GSM782744 3 0.0921 0.982 0.000 0.000 0.972 NA
#> GSM782745 1 0.2760 0.824 0.872 0.000 0.000 NA
#> GSM782746 2 0.0000 0.999 0.000 1.000 0.000 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM782696 1 0.2962 0.6499 0.868 0.000 0.000 0.084 NA
#> GSM782697 1 0.3688 0.6071 0.816 0.000 0.000 0.124 NA
#> GSM782698 4 0.5068 0.7198 0.388 0.000 0.000 0.572 NA
#> GSM782699 1 0.2795 0.6490 0.880 0.000 0.000 0.064 NA
#> GSM782700 2 0.0000 0.9987 0.000 1.000 0.000 0.000 NA
#> GSM782701 1 0.3184 0.6353 0.852 0.000 0.000 0.048 NA
#> GSM782702 1 0.2408 0.6576 0.892 0.000 0.000 0.016 NA
#> GSM782703 3 0.0404 0.9765 0.000 0.000 0.988 0.000 NA
#> GSM782704 3 0.0451 0.9772 0.000 0.000 0.988 0.004 NA
#> GSM782705 1 0.4905 0.0572 0.624 0.000 0.000 0.336 NA
#> GSM782706 1 0.4918 0.5054 0.708 0.000 0.000 0.100 NA
#> GSM782707 1 0.3488 0.5404 0.808 0.000 0.000 0.168 NA
#> GSM782708 3 0.0566 0.9761 0.000 0.000 0.984 0.004 NA
#> GSM782709 1 0.4153 0.5334 0.740 0.000 0.008 0.016 NA
#> GSM782710 1 0.2685 0.6519 0.880 0.000 0.000 0.028 NA
#> GSM782711 1 0.1670 0.6591 0.936 0.000 0.000 0.052 NA
#> GSM782712 1 0.2067 0.6627 0.920 0.000 0.000 0.032 NA
#> GSM782713 3 0.0162 0.9774 0.000 0.000 0.996 0.004 NA
#> GSM782714 2 0.0000 0.9987 0.000 1.000 0.000 0.000 NA
#> GSM782715 4 0.4642 0.7740 0.308 0.000 0.000 0.660 NA
#> GSM782716 3 0.0162 0.9776 0.000 0.000 0.996 0.004 NA
#> GSM782717 1 0.2830 0.6465 0.876 0.000 0.000 0.080 NA
#> GSM782718 4 0.4597 0.7403 0.424 0.000 0.000 0.564 NA
#> GSM782719 1 0.3578 0.5710 0.820 0.000 0.000 0.132 NA
#> GSM782720 3 0.0290 0.9772 0.000 0.000 0.992 0.000 NA
#> GSM782721 1 0.4693 0.5008 0.700 0.000 0.000 0.056 NA
#> GSM782722 4 0.5533 0.7652 0.336 0.000 0.000 0.580 NA
#> GSM782723 2 0.0162 0.9975 0.000 0.996 0.000 0.004 NA
#> GSM782724 2 0.0162 0.9975 0.000 0.996 0.000 0.004 NA
#> GSM782725 1 0.5426 0.1362 0.640 0.000 0.000 0.252 NA
#> GSM782726 1 0.4946 0.4839 0.700 0.000 0.060 0.008 NA
#> GSM782727 3 0.0404 0.9776 0.000 0.000 0.988 0.000 NA
#> GSM782728 2 0.0000 0.9987 0.000 1.000 0.000 0.000 NA
#> GSM782729 1 0.4582 -0.2740 0.572 0.000 0.000 0.416 NA
#> GSM782730 3 0.0451 0.9765 0.000 0.000 0.988 0.004 NA
#> GSM782731 1 0.4250 0.3586 0.720 0.000 0.000 0.252 NA
#> GSM782732 1 0.4196 0.0496 0.640 0.000 0.000 0.356 NA
#> GSM782733 3 0.0324 0.9776 0.000 0.000 0.992 0.004 NA
#> GSM782734 1 0.2548 0.6373 0.876 0.000 0.004 0.004 NA
#> GSM782735 2 0.0000 0.9987 0.000 1.000 0.000 0.000 NA
#> GSM782736 4 0.4779 0.8040 0.388 0.000 0.000 0.588 NA
#> GSM782737 2 0.0324 0.9955 0.000 0.992 0.000 0.004 NA
#> GSM782738 1 0.4803 -0.4650 0.536 0.000 0.000 0.444 NA
#> GSM782739 1 0.1408 0.6700 0.948 0.000 0.000 0.008 NA
#> GSM782740 2 0.0000 0.9987 0.000 1.000 0.000 0.000 NA
#> GSM782741 1 0.2351 0.6634 0.896 0.000 0.000 0.016 NA
#> GSM782742 3 0.0451 0.9764 0.000 0.000 0.988 0.004 NA
#> GSM782743 3 0.0963 0.9599 0.000 0.000 0.964 0.036 NA
#> GSM782744 3 0.3891 0.8426 0.016 0.000 0.812 0.036 NA
#> GSM782745 1 0.3320 0.6202 0.844 0.000 0.016 0.016 NA
#> GSM782746 2 0.0000 0.9987 0.000 1.000 0.000 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM782696 1 0.3717 0.5978 0.812 0.000 0.000 0.104 NA 0.028
#> GSM782697 1 0.4800 0.4820 0.688 0.000 0.000 0.116 NA 0.008
#> GSM782698 4 0.5819 0.5082 0.340 0.000 0.000 0.536 NA 0.048
#> GSM782699 1 0.3159 0.5968 0.832 0.000 0.000 0.068 NA 0.000
#> GSM782700 2 0.0260 0.9941 0.000 0.992 0.000 0.000 NA 0.008
#> GSM782701 1 0.4162 0.5095 0.744 0.000 0.000 0.120 NA 0.000
#> GSM782702 1 0.2272 0.6335 0.900 0.000 0.000 0.004 NA 0.040
#> GSM782703 3 0.0993 0.9476 0.000 0.000 0.964 0.000 NA 0.012
#> GSM782704 3 0.0603 0.9507 0.000 0.000 0.980 0.000 NA 0.004
#> GSM782705 1 0.5724 0.1652 0.560 0.000 0.000 0.292 NA 0.020
#> GSM782706 1 0.5983 0.0949 0.520 0.000 0.000 0.220 NA 0.012
#> GSM782707 1 0.4678 0.2094 0.640 0.000 0.000 0.304 NA 0.012
#> GSM782708 3 0.0713 0.9490 0.000 0.000 0.972 0.000 NA 0.000
#> GSM782709 1 0.3875 0.5788 0.776 0.000 0.012 0.004 NA 0.036
#> GSM782710 1 0.4312 0.5436 0.744 0.000 0.004 0.060 NA 0.012
#> GSM782711 1 0.2036 0.6277 0.916 0.000 0.000 0.048 NA 0.008
#> GSM782712 1 0.3424 0.5857 0.824 0.000 0.000 0.076 NA 0.008
#> GSM782713 3 0.0653 0.9516 0.000 0.000 0.980 0.004 NA 0.004
#> GSM782714 2 0.0000 0.9952 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782715 4 0.4084 0.6884 0.196 0.000 0.000 0.744 NA 0.008
#> GSM782716 3 0.0363 0.9519 0.000 0.000 0.988 0.000 NA 0.000
#> GSM782717 1 0.2344 0.6150 0.892 0.000 0.000 0.076 NA 0.004
#> GSM782718 4 0.3950 0.7379 0.312 0.000 0.000 0.672 NA 0.008
#> GSM782719 1 0.4862 0.3325 0.664 0.000 0.000 0.244 NA 0.012
#> GSM782720 3 0.1010 0.9480 0.000 0.000 0.960 0.004 NA 0.000
#> GSM782721 1 0.5715 0.2232 0.540 0.000 0.000 0.160 NA 0.008
#> GSM782722 4 0.5465 0.6668 0.208 0.000 0.000 0.644 NA 0.040
#> GSM782723 2 0.0146 0.9946 0.000 0.996 0.000 0.004 NA 0.000
#> GSM782724 2 0.0146 0.9946 0.000 0.996 0.000 0.004 NA 0.000
#> GSM782725 4 0.5772 0.5367 0.404 0.000 0.000 0.472 NA 0.020
#> GSM782726 1 0.4182 0.5466 0.760 0.000 0.040 0.012 NA 0.012
#> GSM782727 3 0.0937 0.9495 0.000 0.000 0.960 0.000 NA 0.000
#> GSM782728 2 0.0000 0.9952 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782729 1 0.5009 -0.3114 0.500 0.000 0.000 0.444 NA 0.012
#> GSM782730 3 0.1606 0.9417 0.000 0.000 0.932 0.004 NA 0.008
#> GSM782731 1 0.4443 0.2342 0.656 0.000 0.000 0.300 NA 0.008
#> GSM782732 1 0.4456 0.0301 0.596 0.000 0.000 0.372 NA 0.004
#> GSM782733 3 0.0436 0.9517 0.000 0.000 0.988 0.004 NA 0.004
#> GSM782734 1 0.2356 0.6218 0.884 0.000 0.000 0.004 NA 0.016
#> GSM782735 2 0.0458 0.9904 0.000 0.984 0.000 0.000 NA 0.016
#> GSM782736 4 0.4071 0.7388 0.304 0.000 0.000 0.672 NA 0.004
#> GSM782737 2 0.0000 0.9952 0.000 1.000 0.000 0.000 NA 0.000
#> GSM782738 4 0.4799 0.6783 0.356 0.000 0.000 0.592 NA 0.012
#> GSM782739 1 0.1296 0.6319 0.952 0.000 0.000 0.012 NA 0.004
#> GSM782740 2 0.0260 0.9932 0.000 0.992 0.000 0.000 NA 0.008
#> GSM782741 1 0.3387 0.6011 0.836 0.000 0.000 0.052 NA 0.024
#> GSM782742 3 0.1327 0.9405 0.000 0.000 0.936 0.000 NA 0.000
#> GSM782743 3 0.1478 0.9434 0.000 0.000 0.944 0.020 NA 0.004
#> GSM782744 3 0.5673 0.6708 0.008 0.000 0.628 0.052 NA 0.072
#> GSM782745 1 0.3248 0.5961 0.828 0.000 0.004 0.016 NA 0.016
#> GSM782746 2 0.0458 0.9904 0.000 0.984 0.000 0.000 NA 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)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n agent(p) k
#> ATC:NMF 51 0.648 2
#> ATC:NMF 51 0.642 3
#> ATC:NMF 51 0.642 4
#> ATC:NMF 44 0.474 5
#> ATC:NMF 42 0.479 6
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