Date: 2019-12-25 22:00:25 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 29485 rows and 57 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] 29485 57
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 | ||
|---|---|---|---|---|---|---|
| ATC:kmeans | 3 | 0.980 | 0.935 | 0.972 | ** | |
| MAD:mclust | 2 | 0.980 | 0.957 | 0.975 | ** | |
| ATC:pam | 5 | 0.960 | 0.943 | 0.977 | ** | 2,3,4 |
| ATC:NMF | 3 | 0.952 | 0.928 | 0.971 | ** | 2 |
| MAD:skmeans | 3 | 0.943 | 0.927 | 0.969 | * | |
| ATC:mclust | 6 | 0.923 | 0.898 | 0.950 | * | 2,4,5 |
| CV:NMF | 3 | 0.918 | 0.903 | 0.960 | * | |
| ATC:skmeans | 4 | 0.901 | 0.861 | 0.943 | * | 3 |
| SD:NMF | 3 | 0.874 | 0.911 | 0.961 | ||
| MAD:NMF | 3 | 0.862 | 0.911 | 0.961 | ||
| SD:skmeans | 4 | 0.857 | 0.897 | 0.938 | ||
| CV:skmeans | 4 | 0.853 | 0.905 | 0.942 | ||
| CV:kmeans | 3 | 0.840 | 0.876 | 0.943 | ||
| SD:kmeans | 3 | 0.820 | 0.873 | 0.942 | ||
| CV:mclust | 2 | 0.804 | 0.936 | 0.940 | ||
| MAD:kmeans | 3 | 0.790 | 0.876 | 0.940 | ||
| ATC:hclust | 3 | 0.693 | 0.877 | 0.936 | ||
| SD:mclust | 2 | 0.669 | 0.915 | 0.921 | ||
| SD:pam | 4 | 0.661 | 0.817 | 0.857 | ||
| CV:hclust | 3 | 0.654 | 0.711 | 0.881 | ||
| MAD:pam | 4 | 0.652 | 0.817 | 0.869 | ||
| CV:pam | 4 | 0.635 | 0.815 | 0.872 | ||
| MAD:hclust | 3 | 0.584 | 0.722 | 0.871 | ||
| SD:hclust | 3 | 0.549 | 0.733 | 0.883 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 0.516 0.757 0.874 0.468 0.491 0.491
#> CV:NMF 2 0.514 0.771 0.885 0.472 0.491 0.491
#> MAD:NMF 2 0.419 0.793 0.877 0.488 0.499 0.499
#> ATC:NMF 2 0.999 0.961 0.983 0.476 0.526 0.526
#> SD:skmeans 2 0.556 0.842 0.907 0.506 0.492 0.492
#> CV:skmeans 2 0.535 0.829 0.905 0.507 0.491 0.491
#> MAD:skmeans 2 0.407 0.816 0.857 0.508 0.492 0.492
#> ATC:skmeans 2 0.707 0.840 0.926 0.504 0.495 0.495
#> SD:mclust 2 0.669 0.915 0.921 0.417 0.560 0.560
#> CV:mclust 2 0.804 0.936 0.940 0.423 0.560 0.560
#> MAD:mclust 2 0.980 0.957 0.975 0.263 0.754 0.754
#> ATC:mclust 2 1.000 0.982 0.992 0.386 0.623 0.623
#> SD:kmeans 2 0.217 0.635 0.823 0.439 0.589 0.589
#> CV:kmeans 2 0.210 0.637 0.787 0.448 0.589 0.589
#> MAD:kmeans 2 0.151 0.341 0.580 0.474 0.526 0.526
#> ATC:kmeans 2 0.294 0.722 0.842 0.426 0.574 0.574
#> SD:pam 2 0.363 0.726 0.821 0.433 0.560 0.560
#> CV:pam 2 0.364 0.692 0.799 0.422 0.560 0.560
#> MAD:pam 2 0.379 0.740 0.826 0.429 0.560 0.560
#> ATC:pam 2 1.000 0.981 0.985 0.345 0.662 0.662
#> SD:hclust 2 0.420 0.780 0.865 0.364 0.729 0.729
#> CV:hclust 2 0.425 0.669 0.853 0.378 0.683 0.683
#> MAD:hclust 2 0.323 0.640 0.833 0.399 0.623 0.623
#> ATC:hclust 2 0.846 0.960 0.979 0.343 0.662 0.662
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.874 0.911 0.961 0.421 0.682 0.443
#> CV:NMF 3 0.918 0.903 0.960 0.410 0.677 0.437
#> MAD:NMF 3 0.862 0.911 0.961 0.369 0.705 0.476
#> ATC:NMF 3 0.952 0.928 0.971 0.387 0.790 0.611
#> SD:skmeans 3 0.856 0.870 0.948 0.336 0.695 0.456
#> CV:skmeans 3 0.846 0.872 0.948 0.335 0.706 0.468
#> MAD:skmeans 3 0.943 0.927 0.969 0.331 0.706 0.469
#> ATC:skmeans 3 1.000 0.981 0.993 0.324 0.791 0.597
#> SD:mclust 3 0.656 0.863 0.928 0.344 0.612 0.441
#> CV:mclust 3 0.802 0.890 0.929 0.336 0.612 0.441
#> MAD:mclust 3 0.566 0.825 0.898 1.243 0.648 0.545
#> ATC:mclust 3 0.626 0.811 0.889 0.403 0.600 0.473
#> SD:kmeans 3 0.820 0.873 0.942 0.487 0.673 0.483
#> CV:kmeans 3 0.840 0.876 0.943 0.464 0.694 0.505
#> MAD:kmeans 3 0.790 0.876 0.940 0.402 0.737 0.534
#> ATC:kmeans 3 0.980 0.935 0.972 0.537 0.753 0.576
#> SD:pam 3 0.456 0.734 0.836 0.437 0.752 0.576
#> CV:pam 3 0.442 0.719 0.821 0.457 0.752 0.576
#> MAD:pam 3 0.590 0.776 0.854 0.453 0.752 0.576
#> ATC:pam 3 0.999 0.957 0.982 0.839 0.709 0.561
#> SD:hclust 3 0.549 0.733 0.883 0.566 0.715 0.609
#> CV:hclust 3 0.654 0.711 0.881 0.506 0.704 0.576
#> MAD:hclust 3 0.584 0.722 0.871 0.451 0.751 0.625
#> ATC:hclust 3 0.693 0.877 0.936 0.658 0.739 0.606
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.658 0.640 0.795 0.114 0.905 0.728
#> CV:NMF 4 0.680 0.663 0.807 0.115 0.888 0.679
#> MAD:NMF 4 0.678 0.737 0.848 0.110 0.897 0.705
#> ATC:NMF 4 0.693 0.716 0.843 0.118 0.857 0.616
#> SD:skmeans 4 0.857 0.897 0.938 0.125 0.840 0.556
#> CV:skmeans 4 0.853 0.905 0.942 0.124 0.836 0.547
#> MAD:skmeans 4 0.798 0.805 0.890 0.122 0.826 0.526
#> ATC:skmeans 4 0.901 0.861 0.943 0.124 0.893 0.688
#> SD:mclust 4 0.727 0.776 0.899 0.290 0.761 0.496
#> CV:mclust 4 0.727 0.809 0.912 0.293 0.761 0.496
#> MAD:mclust 4 0.750 0.814 0.870 0.252 0.698 0.391
#> ATC:mclust 4 0.927 0.912 0.967 0.306 0.713 0.460
#> SD:kmeans 4 0.624 0.627 0.816 0.134 0.841 0.587
#> CV:kmeans 4 0.633 0.423 0.673 0.132 0.887 0.683
#> MAD:kmeans 4 0.630 0.425 0.661 0.121 0.900 0.715
#> ATC:kmeans 4 0.796 0.882 0.934 0.123 0.771 0.451
#> SD:pam 4 0.661 0.817 0.857 0.161 0.894 0.710
#> CV:pam 4 0.635 0.815 0.872 0.176 0.904 0.737
#> MAD:pam 4 0.652 0.817 0.869 0.163 0.904 0.737
#> ATC:pam 4 0.957 0.947 0.977 0.174 0.872 0.661
#> SD:hclust 4 0.477 0.620 0.770 0.135 0.966 0.923
#> CV:hclust 4 0.477 0.496 0.741 0.174 0.852 0.672
#> MAD:hclust 4 0.480 0.575 0.734 0.145 0.977 0.951
#> ATC:hclust 4 0.690 0.834 0.884 0.287 0.840 0.602
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.699 0.702 0.818 0.0715 0.898 0.651
#> CV:NMF 5 0.635 0.630 0.769 0.0697 0.873 0.574
#> MAD:NMF 5 0.658 0.653 0.776 0.0704 0.911 0.684
#> ATC:NMF 5 0.645 0.570 0.754 0.0706 0.937 0.769
#> SD:skmeans 5 0.781 0.600 0.800 0.0513 0.867 0.543
#> CV:skmeans 5 0.780 0.630 0.816 0.0535 0.873 0.553
#> MAD:skmeans 5 0.771 0.698 0.850 0.0531 0.872 0.546
#> ATC:skmeans 5 0.832 0.748 0.886 0.0447 0.937 0.763
#> SD:mclust 5 0.744 0.760 0.843 0.0809 0.934 0.765
#> CV:mclust 5 0.820 0.799 0.892 0.0712 0.921 0.720
#> MAD:mclust 5 0.775 0.568 0.752 0.0678 0.887 0.600
#> ATC:mclust 5 0.948 0.915 0.952 0.0528 0.902 0.687
#> SD:kmeans 5 0.690 0.639 0.771 0.0679 0.845 0.499
#> CV:kmeans 5 0.690 0.655 0.782 0.0691 0.870 0.559
#> MAD:kmeans 5 0.683 0.589 0.737 0.0674 0.826 0.448
#> ATC:kmeans 5 0.754 0.771 0.870 0.0847 0.890 0.614
#> SD:pam 5 0.717 0.804 0.864 0.0600 0.883 0.623
#> CV:pam 5 0.708 0.799 0.869 0.0611 0.875 0.606
#> MAD:pam 5 0.726 0.775 0.841 0.0561 0.861 0.566
#> ATC:pam 5 0.960 0.943 0.977 0.0392 0.972 0.892
#> SD:hclust 5 0.611 0.709 0.821 0.1503 0.805 0.541
#> CV:hclust 5 0.642 0.669 0.808 0.1254 0.763 0.414
#> MAD:hclust 5 0.656 0.699 0.842 0.1413 0.774 0.514
#> ATC:hclust 5 0.736 0.832 0.899 0.0564 0.977 0.906
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.652 0.591 0.732 0.0439 0.888 0.550
#> CV:NMF 6 0.639 0.590 0.718 0.0447 0.886 0.537
#> MAD:NMF 6 0.647 0.559 0.704 0.0435 0.931 0.700
#> ATC:NMF 6 0.769 0.630 0.822 0.0486 0.883 0.543
#> SD:skmeans 6 0.792 0.662 0.820 0.0402 0.917 0.641
#> CV:skmeans 6 0.785 0.656 0.823 0.0393 0.911 0.612
#> MAD:skmeans 6 0.790 0.727 0.846 0.0400 0.937 0.712
#> ATC:skmeans 6 0.818 0.775 0.863 0.0354 0.951 0.790
#> SD:mclust 6 0.832 0.796 0.887 0.0536 0.900 0.591
#> CV:mclust 6 0.829 0.821 0.895 0.0625 0.904 0.598
#> MAD:mclust 6 0.759 0.467 0.663 0.0487 0.838 0.398
#> ATC:mclust 6 0.923 0.898 0.950 0.0489 0.975 0.900
#> SD:kmeans 6 0.711 0.638 0.776 0.0454 0.889 0.537
#> CV:kmeans 6 0.700 0.537 0.725 0.0416 0.916 0.635
#> MAD:kmeans 6 0.703 0.616 0.753 0.0427 0.905 0.584
#> ATC:kmeans 6 0.801 0.676 0.838 0.0435 0.944 0.729
#> SD:pam 6 0.738 0.707 0.829 0.0714 0.931 0.719
#> CV:pam 6 0.744 0.622 0.785 0.0675 0.952 0.805
#> MAD:pam 6 0.705 0.594 0.787 0.0698 0.927 0.695
#> ATC:pam 6 0.836 0.468 0.815 0.0506 0.932 0.730
#> SD:hclust 6 0.672 0.585 0.726 0.0725 0.978 0.912
#> CV:hclust 6 0.656 0.640 0.781 0.0568 0.929 0.711
#> MAD:hclust 6 0.733 0.612 0.779 0.0708 0.894 0.614
#> ATC:hclust 6 0.748 0.827 0.880 0.0233 0.987 0.943
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 time(p) individual(p) k
#> SD:NMF 53 0.677 0.006636 2
#> CV:NMF 52 0.588 0.007252 2
#> MAD:NMF 54 0.648 0.013584 2
#> ATC:NMF 56 0.857 0.032726 2
#> SD:skmeans 56 0.796 0.003293 2
#> CV:skmeans 54 0.678 0.004877 2
#> MAD:skmeans 56 0.796 0.003293 2
#> ATC:skmeans 52 0.389 0.012691 2
#> SD:mclust 57 0.377 0.234717 2
#> CV:mclust 57 0.377 0.234717 2
#> MAD:mclust 56 0.329 0.011870 2
#> ATC:mclust 57 0.292 0.173506 2
#> SD:kmeans 50 0.742 0.114040 2
#> CV:kmeans 42 0.870 0.042355 2
#> MAD:kmeans 15 NA NA 2
#> ATC:kmeans 53 0.558 0.001038 2
#> SD:pam 56 0.620 0.034995 2
#> CV:pam 54 0.526 0.034927 2
#> MAD:pam 56 0.620 0.034995 2
#> ATC:pam 57 0.387 0.000693 2
#> SD:hclust 54 0.989 0.038378 2
#> CV:hclust 50 0.913 0.062364 2
#> MAD:hclust 43 0.959 0.123137 2
#> ATC:hclust 57 0.387 0.000693 2
test_to_known_factors(res_list, k = 3)
#> n time(p) individual(p) k
#> SD:NMF 54 0.341 3.30e-02 3
#> CV:NMF 54 0.341 3.30e-02 3
#> MAD:NMF 56 0.344 2.92e-02 3
#> ATC:NMF 56 0.388 1.50e-02 3
#> SD:skmeans 52 0.759 7.69e-03 3
#> CV:skmeans 53 0.822 6.25e-03 3
#> MAD:skmeans 55 0.879 1.26e-03 3
#> ATC:skmeans 56 0.724 1.67e-02 3
#> SD:mclust 55 0.612 5.01e-04 3
#> CV:mclust 56 0.570 7.23e-04 3
#> MAD:mclust 55 0.787 4.21e-04 3
#> ATC:mclust 57 0.456 1.97e-04 3
#> SD:kmeans 55 0.497 6.96e-03 3
#> CV:kmeans 55 0.460 1.16e-02 3
#> MAD:kmeans 55 0.507 1.11e-02 3
#> ATC:kmeans 55 0.456 7.79e-04 3
#> SD:pam 53 0.762 7.10e-05 3
#> CV:pam 52 0.790 8.83e-05 3
#> MAD:pam 54 0.706 8.47e-05 3
#> ATC:pam 56 0.512 1.82e-03 3
#> SD:hclust 49 0.953 1.90e-04 3
#> CV:hclust 46 0.866 1.79e-03 3
#> MAD:hclust 48 0.929 3.04e-04 3
#> ATC:hclust 54 0.818 4.03e-04 3
test_to_known_factors(res_list, k = 4)
#> n time(p) individual(p) k
#> SD:NMF 46 0.598 2.06e-03 4
#> CV:NMF 49 0.547 4.18e-03 4
#> MAD:NMF 51 0.167 8.84e-03 4
#> ATC:NMF 49 0.367 1.89e-03 4
#> SD:skmeans 57 0.238 6.40e-03 4
#> CV:skmeans 57 0.238 6.40e-03 4
#> MAD:skmeans 55 0.334 3.37e-03 4
#> ATC:skmeans 54 0.634 2.57e-03 4
#> SD:mclust 50 0.251 4.11e-04 4
#> CV:mclust 53 0.395 1.70e-04 4
#> MAD:mclust 53 0.443 1.57e-03 4
#> ATC:mclust 55 0.748 2.99e-04 4
#> SD:kmeans 40 0.360 2.37e-04 4
#> CV:kmeans 22 0.518 4.61e-02 4
#> MAD:kmeans 23 0.779 1.17e-01 4
#> ATC:kmeans 57 0.831 1.19e-04 4
#> SD:pam 54 0.898 3.89e-05 4
#> CV:pam 55 0.890 2.59e-05 4
#> MAD:pam 55 0.935 1.13e-05 4
#> ATC:pam 56 0.862 5.32e-04 4
#> SD:hclust 45 0.724 4.50e-03 4
#> CV:hclust 38 0.909 6.47e-04 4
#> MAD:hclust 39 0.833 5.95e-04 4
#> ATC:hclust 54 0.764 5.15e-04 4
test_to_known_factors(res_list, k = 5)
#> n time(p) individual(p) k
#> SD:NMF 51 0.290 3.27e-04 5
#> CV:NMF 47 0.637 3.51e-04 5
#> MAD:NMF 46 0.788 1.65e-04 5
#> ATC:NMF 39 0.317 2.34e-04 5
#> SD:skmeans 45 0.550 1.20e-04 5
#> CV:skmeans 43 0.448 1.75e-04 5
#> MAD:skmeans 53 0.712 3.50e-06 5
#> ATC:skmeans 48 0.938 1.39e-03 5
#> SD:mclust 49 0.262 5.32e-03 5
#> CV:mclust 53 0.301 1.18e-03 5
#> MAD:mclust 37 0.269 3.67e-02 5
#> ATC:mclust 55 0.623 1.43e-04 5
#> SD:kmeans 42 0.107 5.09e-04 5
#> CV:kmeans 44 0.272 8.90e-05 5
#> MAD:kmeans 38 0.730 2.09e-04 5
#> ATC:kmeans 53 0.307 1.49e-05 5
#> SD:pam 55 0.563 4.64e-07 5
#> CV:pam 54 0.681 1.23e-06 5
#> MAD:pam 55 0.674 4.46e-07 5
#> ATC:pam 56 0.861 4.20e-03 5
#> SD:hclust 48 0.698 1.24e-04 5
#> CV:hclust 44 0.845 1.23e-04 5
#> MAD:hclust 48 0.698 1.24e-04 5
#> ATC:hclust 57 0.645 1.12e-02 5
test_to_known_factors(res_list, k = 6)
#> n time(p) individual(p) k
#> SD:NMF 42 0.183 4.56e-07 6
#> CV:NMF 42 0.335 7.74e-06 6
#> MAD:NMF 42 0.558 6.54e-05 6
#> ATC:NMF 42 0.585 1.60e-04 6
#> SD:skmeans 45 0.851 1.87e-06 6
#> CV:skmeans 47 0.896 1.53e-06 6
#> MAD:skmeans 51 0.905 5.65e-07 6
#> ATC:skmeans 52 0.880 3.17e-07 6
#> SD:mclust 52 0.198 2.50e-03 6
#> CV:mclust 53 0.237 3.68e-03 6
#> MAD:mclust 37 0.607 1.69e-02 6
#> ATC:mclust 55 0.565 5.85e-03 6
#> SD:kmeans 47 0.405 1.97e-06 6
#> CV:kmeans 33 0.641 1.12e-03 6
#> MAD:kmeans 38 0.626 2.18e-05 6
#> ATC:kmeans 41 0.497 3.02e-04 6
#> SD:pam 51 0.792 2.37e-07 6
#> CV:pam 47 0.647 8.00e-07 6
#> MAD:pam 43 0.956 7.05e-06 6
#> ATC:pam 38 0.632 1.62e-02 6
#> SD:hclust 32 0.672 3.13e-03 6
#> CV:hclust 44 0.569 2.46e-04 6
#> MAD:hclust 41 0.728 1.10e-04 6
#> ATC:hclust 57 0.465 9.01e-03 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 29485 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.420 0.780 0.865 0.3639 0.729 0.729
#> 3 3 0.549 0.733 0.883 0.5658 0.715 0.609
#> 4 4 0.477 0.620 0.770 0.1348 0.966 0.923
#> 5 5 0.611 0.709 0.821 0.1503 0.805 0.541
#> 6 6 0.672 0.585 0.726 0.0725 0.978 0.912
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
#> GSM872244 1 0.8955 0.726 0.688 0.312
#> GSM872245 1 0.0376 0.832 0.996 0.004
#> GSM872246 1 0.7528 0.788 0.784 0.216
#> GSM872247 1 0.8955 0.726 0.688 0.312
#> GSM872248 2 0.0000 0.923 0.000 1.000
#> GSM872249 1 0.8955 0.726 0.688 0.312
#> GSM872250 1 0.0000 0.832 1.000 0.000
#> GSM872251 1 0.8813 0.736 0.700 0.300
#> GSM872252 1 0.0000 0.832 1.000 0.000
#> GSM872253 1 0.3274 0.826 0.940 0.060
#> GSM872254 2 0.8327 0.686 0.264 0.736
#> GSM872255 1 0.0000 0.832 1.000 0.000
#> GSM872256 1 0.0672 0.832 0.992 0.008
#> GSM872257 2 0.0000 0.923 0.000 1.000
#> GSM872258 1 0.6887 0.801 0.816 0.184
#> GSM872259 1 0.0000 0.832 1.000 0.000
#> GSM872260 1 0.0000 0.832 1.000 0.000
#> GSM872261 1 0.9170 0.597 0.668 0.332
#> GSM872262 1 0.0000 0.832 1.000 0.000
#> GSM872263 1 0.8955 0.726 0.688 0.312
#> GSM872264 1 0.8443 0.753 0.728 0.272
#> GSM872265 1 0.8443 0.753 0.728 0.272
#> GSM872266 1 0.9522 0.568 0.628 0.372
#> GSM872267 2 0.0000 0.923 0.000 1.000
#> GSM872268 1 0.8955 0.726 0.688 0.312
#> GSM872269 2 0.8386 0.682 0.268 0.732
#> GSM872270 1 0.8955 0.726 0.688 0.312
#> GSM872271 1 0.9970 0.453 0.532 0.468
#> GSM872272 1 0.9970 0.453 0.532 0.468
#> GSM872273 1 0.0000 0.832 1.000 0.000
#> GSM872274 2 0.0000 0.923 0.000 1.000
#> GSM872275 1 0.4939 0.823 0.892 0.108
#> GSM872276 1 0.0000 0.832 1.000 0.000
#> GSM872277 1 0.0000 0.832 1.000 0.000
#> GSM872278 1 0.4431 0.826 0.908 0.092
#> GSM872279 1 0.0000 0.832 1.000 0.000
#> GSM872280 1 0.0000 0.832 1.000 0.000
#> GSM872281 1 0.4298 0.826 0.912 0.088
#> GSM872282 1 0.8955 0.726 0.688 0.312
#> GSM872283 1 0.8443 0.753 0.728 0.272
#> GSM872284 1 0.7674 0.783 0.776 0.224
#> GSM872285 1 0.6973 0.800 0.812 0.188
#> GSM872286 1 0.0000 0.832 1.000 0.000
#> GSM872287 1 0.8955 0.726 0.688 0.312
#> GSM872288 1 0.0000 0.832 1.000 0.000
#> GSM872289 1 0.7056 0.798 0.808 0.192
#> GSM872290 1 0.0000 0.832 1.000 0.000
#> GSM872291 1 0.0000 0.832 1.000 0.000
#> GSM872292 2 0.0000 0.923 0.000 1.000
#> GSM872293 1 0.0000 0.832 1.000 0.000
#> GSM872294 1 0.9909 0.204 0.556 0.444
#> GSM872295 2 0.0000 0.923 0.000 1.000
#> GSM872296 2 0.0000 0.923 0.000 1.000
#> GSM872297 1 0.0000 0.832 1.000 0.000
#> GSM872298 1 0.4431 0.826 0.908 0.092
#> GSM872299 1 0.0000 0.832 1.000 0.000
#> GSM872300 1 0.0000 0.832 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.8094 0.000 0.000 1.000
#> GSM872245 1 0.0237 0.8483 0.996 0.004 0.000
#> GSM872246 3 0.5926 0.4671 0.356 0.000 0.644
#> GSM872247 3 0.0000 0.8094 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.9127 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.8094 0.000 0.000 1.000
#> GSM872250 1 0.0000 0.8491 1.000 0.000 0.000
#> GSM872251 3 0.0592 0.8024 0.012 0.000 0.988
#> GSM872252 1 0.0000 0.8491 1.000 0.000 0.000
#> GSM872253 1 0.3502 0.8089 0.896 0.020 0.084
#> GSM872254 2 0.5254 0.6679 0.264 0.736 0.000
#> GSM872255 1 0.0000 0.8491 1.000 0.000 0.000
#> GSM872256 1 0.0424 0.8482 0.992 0.000 0.008
#> GSM872257 2 0.0000 0.9127 0.000 1.000 0.000
#> GSM872258 3 0.6095 0.3992 0.392 0.000 0.608
#> GSM872259 1 0.0000 0.8491 1.000 0.000 0.000
#> GSM872260 1 0.0000 0.8491 1.000 0.000 0.000
#> GSM872261 1 0.8566 0.5089 0.608 0.204 0.188
#> GSM872262 1 0.1163 0.8440 0.972 0.000 0.028
#> GSM872263 3 0.0000 0.8094 0.000 0.000 1.000
#> GSM872264 1 0.5905 0.5028 0.648 0.000 0.352
#> GSM872265 1 0.5905 0.5028 0.648 0.000 0.352
#> GSM872266 1 0.8950 0.4457 0.568 0.212 0.220
#> GSM872267 2 0.0000 0.9127 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.8094 0.000 0.000 1.000
#> GSM872269 2 0.5291 0.6637 0.268 0.732 0.000
#> GSM872270 3 0.0000 0.8094 0.000 0.000 1.000
#> GSM872271 1 0.9531 0.2196 0.456 0.200 0.344
#> GSM872272 1 0.9531 0.2196 0.456 0.200 0.344
#> GSM872273 1 0.0000 0.8491 1.000 0.000 0.000
#> GSM872274 2 0.0000 0.9127 0.000 1.000 0.000
#> GSM872275 1 0.4551 0.7698 0.840 0.020 0.140
#> GSM872276 1 0.1163 0.8440 0.972 0.000 0.028
#> GSM872277 1 0.0000 0.8491 1.000 0.000 0.000
#> GSM872278 1 0.3851 0.7786 0.860 0.004 0.136
#> GSM872279 1 0.0000 0.8491 1.000 0.000 0.000
#> GSM872280 1 0.1163 0.8440 0.972 0.000 0.028
#> GSM872281 1 0.3267 0.7962 0.884 0.000 0.116
#> GSM872282 3 0.0000 0.8094 0.000 0.000 1.000
#> GSM872283 1 0.5905 0.5028 0.648 0.000 0.352
#> GSM872284 1 0.5560 0.5868 0.700 0.000 0.300
#> GSM872285 3 0.6299 0.0564 0.476 0.000 0.524
#> GSM872286 1 0.0000 0.8491 1.000 0.000 0.000
#> GSM872287 3 0.0000 0.8094 0.000 0.000 1.000
#> GSM872288 1 0.0000 0.8491 1.000 0.000 0.000
#> GSM872289 3 0.5988 0.4532 0.368 0.000 0.632
#> GSM872290 1 0.0000 0.8491 1.000 0.000 0.000
#> GSM872291 1 0.1031 0.8450 0.976 0.000 0.024
#> GSM872292 2 0.0000 0.9127 0.000 1.000 0.000
#> GSM872293 1 0.0000 0.8491 1.000 0.000 0.000
#> GSM872294 1 0.6897 0.1761 0.548 0.436 0.016
#> GSM872295 2 0.0000 0.9127 0.000 1.000 0.000
#> GSM872296 2 0.0000 0.9127 0.000 1.000 0.000
#> GSM872297 1 0.0000 0.8491 1.000 0.000 0.000
#> GSM872298 1 0.3851 0.7786 0.860 0.004 0.136
#> GSM872299 1 0.0000 0.8491 1.000 0.000 0.000
#> GSM872300 1 0.1163 0.8440 0.972 0.000 0.028
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0000 0.799 0.000 0.000 1.000 0.000
#> GSM872245 1 0.5119 0.589 0.556 0.004 0.000 0.440
#> GSM872246 3 0.4776 0.434 0.376 0.000 0.624 0.000
#> GSM872247 3 0.0000 0.799 0.000 0.000 1.000 0.000
#> GSM872248 2 0.0000 0.767 0.000 1.000 0.000 0.000
#> GSM872249 3 0.0000 0.799 0.000 0.000 1.000 0.000
#> GSM872250 1 0.4948 0.591 0.560 0.000 0.000 0.440
#> GSM872251 3 0.0469 0.791 0.012 0.000 0.988 0.000
#> GSM872252 1 0.4356 0.684 0.708 0.000 0.000 0.292
#> GSM872253 1 0.2877 0.713 0.904 0.008 0.060 0.028
#> GSM872254 2 0.4431 0.588 0.000 0.696 0.000 0.304
#> GSM872255 1 0.0921 0.733 0.972 0.000 0.000 0.028
#> GSM872256 1 0.3545 0.720 0.828 0.000 0.008 0.164
#> GSM872257 2 0.0000 0.767 0.000 1.000 0.000 0.000
#> GSM872258 3 0.4888 0.372 0.412 0.000 0.588 0.000
#> GSM872259 1 0.3528 0.711 0.808 0.000 0.000 0.192
#> GSM872260 1 0.0921 0.733 0.972 0.000 0.000 0.028
#> GSM872261 1 0.7824 0.308 0.480 0.016 0.168 0.336
#> GSM872262 1 0.0336 0.731 0.992 0.000 0.008 0.000
#> GSM872263 3 0.0000 0.799 0.000 0.000 1.000 0.000
#> GSM872264 1 0.4978 0.471 0.664 0.000 0.324 0.012
#> GSM872265 1 0.4978 0.471 0.664 0.000 0.324 0.012
#> GSM872266 1 0.8231 0.244 0.432 0.024 0.200 0.344
#> GSM872267 2 0.0000 0.767 0.000 1.000 0.000 0.000
#> GSM872268 3 0.0000 0.799 0.000 0.000 1.000 0.000
#> GSM872269 2 0.4608 0.584 0.004 0.692 0.000 0.304
#> GSM872270 3 0.0000 0.799 0.000 0.000 1.000 0.000
#> GSM872271 1 0.7887 0.214 0.472 0.012 0.316 0.200
#> GSM872272 1 0.7887 0.214 0.472 0.012 0.316 0.200
#> GSM872273 1 0.3528 0.711 0.808 0.000 0.000 0.192
#> GSM872274 4 0.4981 0.528 0.000 0.464 0.000 0.536
#> GSM872275 1 0.3653 0.683 0.856 0.008 0.112 0.024
#> GSM872276 1 0.0336 0.731 0.992 0.000 0.008 0.000
#> GSM872277 1 0.3528 0.711 0.808 0.000 0.000 0.192
#> GSM872278 1 0.3048 0.688 0.876 0.000 0.108 0.016
#> GSM872279 1 0.4356 0.684 0.708 0.000 0.000 0.292
#> GSM872280 1 0.0336 0.731 0.992 0.000 0.008 0.000
#> GSM872281 1 0.2281 0.707 0.904 0.000 0.096 0.000
#> GSM872282 3 0.0000 0.799 0.000 0.000 1.000 0.000
#> GSM872283 1 0.4978 0.471 0.664 0.000 0.324 0.012
#> GSM872284 1 0.4663 0.532 0.716 0.000 0.272 0.012
#> GSM872285 3 0.5000 0.103 0.496 0.000 0.504 0.000
#> GSM872286 1 0.4948 0.591 0.560 0.000 0.000 0.440
#> GSM872287 3 0.0000 0.799 0.000 0.000 1.000 0.000
#> GSM872288 1 0.4948 0.591 0.560 0.000 0.000 0.440
#> GSM872289 3 0.4776 0.440 0.376 0.000 0.624 0.000
#> GSM872290 1 0.4356 0.684 0.708 0.000 0.000 0.292
#> GSM872291 1 0.0524 0.732 0.988 0.000 0.008 0.004
#> GSM872292 4 0.4981 0.528 0.000 0.464 0.000 0.536
#> GSM872293 1 0.3528 0.711 0.808 0.000 0.000 0.192
#> GSM872294 4 0.7141 0.111 0.328 0.120 0.008 0.544
#> GSM872295 2 0.1211 0.744 0.000 0.960 0.000 0.040
#> GSM872296 4 0.4981 0.528 0.000 0.464 0.000 0.536
#> GSM872297 1 0.3528 0.711 0.808 0.000 0.000 0.192
#> GSM872298 1 0.3048 0.688 0.876 0.000 0.108 0.016
#> GSM872299 1 0.4356 0.684 0.708 0.000 0.000 0.292
#> GSM872300 1 0.0336 0.731 0.992 0.000 0.008 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.0000 0.8552 0.000 0.000 1.000 0.000 0.000
#> GSM872245 1 0.1399 0.7863 0.952 0.000 0.000 0.020 0.028
#> GSM872246 3 0.4138 0.3928 0.000 0.000 0.616 0.384 0.000
#> GSM872247 3 0.0000 0.8552 0.000 0.000 1.000 0.000 0.000
#> GSM872248 5 0.4026 0.8304 0.020 0.244 0.000 0.000 0.736
#> GSM872249 3 0.0000 0.8552 0.000 0.000 1.000 0.000 0.000
#> GSM872250 1 0.1310 0.7905 0.956 0.000 0.000 0.020 0.024
#> GSM872251 3 0.0404 0.8455 0.000 0.000 0.988 0.012 0.000
#> GSM872252 1 0.2605 0.8780 0.852 0.000 0.000 0.148 0.000
#> GSM872253 4 0.2672 0.7376 0.064 0.000 0.024 0.896 0.016
#> GSM872254 5 0.3855 0.6384 0.240 0.008 0.000 0.004 0.748
#> GSM872255 4 0.2886 0.6817 0.148 0.000 0.000 0.844 0.008
#> GSM872256 1 0.4067 0.7977 0.692 0.000 0.000 0.300 0.008
#> GSM872257 5 0.4026 0.8304 0.020 0.244 0.000 0.000 0.736
#> GSM872258 3 0.4227 0.3296 0.000 0.000 0.580 0.420 0.000
#> GSM872259 1 0.3942 0.8653 0.748 0.000 0.000 0.232 0.020
#> GSM872260 4 0.2886 0.6817 0.148 0.000 0.000 0.844 0.008
#> GSM872261 4 0.7767 0.3883 0.136 0.156 0.088 0.568 0.052
#> GSM872262 4 0.2020 0.7279 0.100 0.000 0.000 0.900 0.000
#> GSM872263 3 0.0000 0.8552 0.000 0.000 1.000 0.000 0.000
#> GSM872264 4 0.3424 0.6370 0.000 0.000 0.240 0.760 0.000
#> GSM872265 4 0.3424 0.6370 0.000 0.000 0.240 0.760 0.000
#> GSM872266 4 0.8278 0.3454 0.136 0.160 0.124 0.520 0.060
#> GSM872267 5 0.4026 0.8304 0.020 0.244 0.000 0.000 0.736
#> GSM872268 3 0.0000 0.8552 0.000 0.000 1.000 0.000 0.000
#> GSM872269 5 0.1914 0.6727 0.056 0.008 0.000 0.008 0.928
#> GSM872270 3 0.0000 0.8552 0.000 0.000 1.000 0.000 0.000
#> GSM872271 4 0.6840 0.4485 0.004 0.156 0.232 0.568 0.040
#> GSM872272 4 0.6840 0.4485 0.004 0.156 0.232 0.568 0.040
#> GSM872273 1 0.3942 0.8653 0.748 0.000 0.000 0.232 0.020
#> GSM872274 2 0.0000 0.7019 0.000 1.000 0.000 0.000 0.000
#> GSM872275 4 0.3003 0.7411 0.040 0.000 0.064 0.880 0.016
#> GSM872276 4 0.2020 0.7279 0.100 0.000 0.000 0.900 0.000
#> GSM872277 1 0.3942 0.8653 0.748 0.000 0.000 0.232 0.020
#> GSM872278 4 0.2359 0.7431 0.036 0.000 0.060 0.904 0.000
#> GSM872279 1 0.2605 0.8780 0.852 0.000 0.000 0.148 0.000
#> GSM872280 4 0.2020 0.7279 0.100 0.000 0.000 0.900 0.000
#> GSM872281 4 0.3535 0.7410 0.088 0.000 0.080 0.832 0.000
#> GSM872282 3 0.0000 0.8552 0.000 0.000 1.000 0.000 0.000
#> GSM872283 4 0.3424 0.6370 0.000 0.000 0.240 0.760 0.000
#> GSM872284 4 0.3003 0.6773 0.000 0.000 0.188 0.812 0.000
#> GSM872285 4 0.4307 -0.0274 0.000 0.000 0.496 0.504 0.000
#> GSM872286 1 0.1310 0.7905 0.956 0.000 0.000 0.020 0.024
#> GSM872287 3 0.0000 0.8552 0.000 0.000 1.000 0.000 0.000
#> GSM872288 1 0.1310 0.7905 0.956 0.000 0.000 0.020 0.024
#> GSM872289 3 0.4114 0.4282 0.000 0.000 0.624 0.376 0.000
#> GSM872290 1 0.2605 0.8780 0.852 0.000 0.000 0.148 0.000
#> GSM872291 4 0.2179 0.7218 0.112 0.000 0.000 0.888 0.000
#> GSM872292 2 0.0000 0.7019 0.000 1.000 0.000 0.000 0.000
#> GSM872293 1 0.3942 0.8653 0.748 0.000 0.000 0.232 0.020
#> GSM872294 2 0.7116 0.1392 0.016 0.388 0.000 0.352 0.244
#> GSM872295 5 0.3550 0.8154 0.000 0.236 0.000 0.004 0.760
#> GSM872296 2 0.0000 0.7019 0.000 1.000 0.000 0.000 0.000
#> GSM872297 1 0.3942 0.8653 0.748 0.000 0.000 0.232 0.020
#> GSM872298 4 0.2359 0.7431 0.036 0.000 0.060 0.904 0.000
#> GSM872299 1 0.2605 0.8780 0.852 0.000 0.000 0.148 0.000
#> GSM872300 4 0.2020 0.7279 0.100 0.000 0.000 0.900 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.0146 0.8115 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM872245 1 0.2852 0.7610 0.856 0.000 0.000 0.000 0.064 0.080
#> GSM872246 3 0.4683 0.4546 0.000 0.000 0.616 0.320 0.000 0.064
#> GSM872247 3 0.0000 0.8126 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872248 5 0.2454 0.7556 0.000 0.160 0.000 0.000 0.840 0.000
#> GSM872249 3 0.0000 0.8126 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872250 1 0.2794 0.7651 0.860 0.000 0.000 0.000 0.060 0.080
#> GSM872251 3 0.0363 0.8064 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM872252 1 0.0547 0.8358 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM872253 4 0.5044 0.3978 0.068 0.000 0.024 0.648 0.000 0.260
#> GSM872254 5 0.5219 0.5362 0.124 0.000 0.000 0.000 0.580 0.296
#> GSM872255 4 0.5761 0.3806 0.172 0.000 0.000 0.432 0.000 0.396
#> GSM872256 1 0.4745 0.6775 0.672 0.000 0.000 0.124 0.000 0.204
#> GSM872257 5 0.2454 0.7556 0.000 0.160 0.000 0.000 0.840 0.000
#> GSM872258 3 0.5090 0.4006 0.012 0.000 0.580 0.344 0.000 0.064
#> GSM872259 1 0.3493 0.8099 0.800 0.000 0.000 0.064 0.000 0.136
#> GSM872260 4 0.5761 0.3806 0.172 0.000 0.000 0.432 0.000 0.396
#> GSM872261 4 0.7683 -0.1921 0.068 0.148 0.060 0.464 0.008 0.252
#> GSM872262 4 0.4738 0.4793 0.064 0.000 0.000 0.600 0.000 0.336
#> GSM872263 3 0.0146 0.8115 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM872264 4 0.2597 0.3702 0.000 0.000 0.176 0.824 0.000 0.000
#> GSM872265 4 0.2597 0.3702 0.000 0.000 0.176 0.824 0.000 0.000
#> GSM872266 4 0.8073 -0.1985 0.064 0.152 0.084 0.432 0.016 0.252
#> GSM872267 5 0.2454 0.7556 0.000 0.160 0.000 0.000 0.840 0.000
#> GSM872268 3 0.0000 0.8126 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872269 5 0.4446 0.5421 0.040 0.000 0.000 0.000 0.612 0.348
#> GSM872270 3 0.0000 0.8126 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872271 4 0.7138 -0.0539 0.004 0.148 0.172 0.500 0.004 0.172
#> GSM872272 4 0.7138 -0.0539 0.004 0.148 0.172 0.500 0.004 0.172
#> GSM872273 1 0.3786 0.7911 0.768 0.000 0.000 0.064 0.000 0.168
#> GSM872274 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872275 4 0.4125 0.3904 0.016 0.000 0.028 0.724 0.000 0.232
#> GSM872276 4 0.4738 0.4793 0.064 0.000 0.000 0.600 0.000 0.336
#> GSM872277 1 0.3493 0.8099 0.800 0.000 0.000 0.064 0.000 0.136
#> GSM872278 4 0.4364 0.4827 0.012 0.000 0.024 0.656 0.000 0.308
#> GSM872279 1 0.0547 0.8358 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM872280 4 0.4855 0.4694 0.064 0.000 0.000 0.556 0.000 0.380
#> GSM872281 4 0.4887 0.4769 0.020 0.000 0.040 0.608 0.000 0.332
#> GSM872282 3 0.0146 0.8115 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM872283 4 0.2597 0.3702 0.000 0.000 0.176 0.824 0.000 0.000
#> GSM872284 4 0.2092 0.3931 0.000 0.000 0.124 0.876 0.000 0.000
#> GSM872285 3 0.5870 0.1858 0.008 0.000 0.496 0.328 0.000 0.168
#> GSM872286 1 0.2794 0.7651 0.860 0.000 0.000 0.000 0.060 0.080
#> GSM872287 3 0.0000 0.8126 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872288 1 0.2794 0.7651 0.860 0.000 0.000 0.000 0.060 0.080
#> GSM872289 3 0.4647 0.4755 0.012 0.000 0.624 0.328 0.000 0.036
#> GSM872290 1 0.0547 0.8358 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM872291 4 0.4926 0.4729 0.080 0.000 0.000 0.584 0.000 0.336
#> GSM872292 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872293 1 0.3786 0.7911 0.768 0.000 0.000 0.064 0.000 0.168
#> GSM872294 6 0.6076 0.0000 0.000 0.380 0.000 0.044 0.100 0.476
#> GSM872295 5 0.5078 0.7193 0.000 0.160 0.000 0.000 0.632 0.208
#> GSM872296 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872297 1 0.3493 0.8099 0.800 0.000 0.000 0.064 0.000 0.136
#> GSM872298 4 0.4364 0.4827 0.012 0.000 0.024 0.656 0.000 0.308
#> GSM872299 1 0.0547 0.8358 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM872300 4 0.4738 0.4793 0.064 0.000 0.000 0.600 0.000 0.336
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 time(p) individual(p) k
#> SD:hclust 54 0.989 0.038378 2
#> SD:hclust 49 0.953 0.000190 3
#> SD:hclust 45 0.724 0.004503 4
#> SD:hclust 48 0.698 0.000124 5
#> SD:hclust 32 0.672 0.003131 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 29485 rows and 57 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 0.217 0.635 0.823 0.4388 0.589 0.589
#> 3 3 0.820 0.873 0.942 0.4868 0.673 0.483
#> 4 4 0.624 0.627 0.816 0.1340 0.841 0.587
#> 5 5 0.690 0.639 0.771 0.0679 0.845 0.499
#> 6 6 0.711 0.638 0.776 0.0454 0.889 0.537
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
#> GSM872244 1 0.9795 0.1734 0.584 0.416
#> GSM872245 2 0.9988 -0.1034 0.480 0.520
#> GSM872246 1 0.4562 0.7179 0.904 0.096
#> GSM872247 1 0.4562 0.7179 0.904 0.096
#> GSM872248 2 0.0000 0.8254 0.000 1.000
#> GSM872249 1 0.4690 0.7152 0.900 0.100
#> GSM872250 2 0.9635 0.0798 0.388 0.612
#> GSM872251 1 0.4562 0.7179 0.904 0.096
#> GSM872252 1 0.9358 0.5261 0.648 0.352
#> GSM872253 1 0.6048 0.7244 0.852 0.148
#> GSM872254 2 0.0000 0.8254 0.000 1.000
#> GSM872255 1 0.5629 0.7348 0.868 0.132
#> GSM872256 1 0.9358 0.5261 0.648 0.352
#> GSM872257 2 0.1184 0.8283 0.016 0.984
#> GSM872258 1 0.4562 0.7179 0.904 0.096
#> GSM872259 1 0.9358 0.5261 0.648 0.352
#> GSM872260 1 0.5629 0.7348 0.868 0.132
#> GSM872261 2 0.9635 0.0798 0.388 0.612
#> GSM872262 1 0.5519 0.7359 0.872 0.128
#> GSM872263 1 0.4562 0.7179 0.904 0.096
#> GSM872264 1 0.7950 0.6120 0.760 0.240
#> GSM872265 1 0.9129 0.5991 0.672 0.328
#> GSM872266 2 0.0376 0.8268 0.004 0.996
#> GSM872267 2 0.0000 0.8254 0.000 1.000
#> GSM872268 1 0.4562 0.7179 0.904 0.096
#> GSM872269 2 0.7139 0.5939 0.196 0.804
#> GSM872270 1 0.7528 0.5894 0.784 0.216
#> GSM872271 2 0.4562 0.7859 0.096 0.904
#> GSM872272 2 0.4562 0.7859 0.096 0.904
#> GSM872273 1 0.7139 0.7004 0.804 0.196
#> GSM872274 2 0.2043 0.8242 0.032 0.968
#> GSM872275 1 0.5519 0.7226 0.872 0.128
#> GSM872276 1 0.5519 0.7359 0.872 0.128
#> GSM872277 1 0.7139 0.7004 0.804 0.196
#> GSM872278 1 0.5408 0.7241 0.876 0.124
#> GSM872279 1 0.9358 0.5261 0.648 0.352
#> GSM872280 1 0.0000 0.7223 1.000 0.000
#> GSM872281 1 0.2043 0.7326 0.968 0.032
#> GSM872282 1 0.9795 0.1734 0.584 0.416
#> GSM872283 1 0.7139 0.7034 0.804 0.196
#> GSM872284 1 0.5178 0.7373 0.884 0.116
#> GSM872285 1 0.2948 0.7251 0.948 0.052
#> GSM872286 1 0.9881 0.3200 0.564 0.436
#> GSM872287 1 0.4562 0.7179 0.904 0.096
#> GSM872288 1 0.9393 0.5243 0.644 0.356
#> GSM872289 1 0.4562 0.7179 0.904 0.096
#> GSM872290 1 0.9358 0.5261 0.648 0.352
#> GSM872291 1 0.5629 0.7348 0.868 0.132
#> GSM872292 2 0.2043 0.8242 0.032 0.968
#> GSM872293 1 0.9358 0.5261 0.648 0.352
#> GSM872294 2 0.1414 0.8282 0.020 0.980
#> GSM872295 2 0.1843 0.8254 0.028 0.972
#> GSM872296 2 0.2043 0.8242 0.032 0.968
#> GSM872297 1 0.9358 0.5261 0.648 0.352
#> GSM872298 1 0.5519 0.7359 0.872 0.128
#> GSM872299 1 0.9954 0.2429 0.540 0.460
#> GSM872300 1 0.5519 0.7359 0.872 0.128
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.938 0.000 0.000 1.000
#> GSM872245 1 0.0747 0.910 0.984 0.016 0.000
#> GSM872246 3 0.0237 0.940 0.004 0.000 0.996
#> GSM872247 3 0.0237 0.940 0.004 0.000 0.996
#> GSM872248 2 0.0592 0.960 0.012 0.988 0.000
#> GSM872249 3 0.0000 0.938 0.000 0.000 1.000
#> GSM872250 1 0.4452 0.723 0.808 0.192 0.000
#> GSM872251 3 0.0237 0.940 0.004 0.000 0.996
#> GSM872252 1 0.0237 0.915 0.996 0.004 0.000
#> GSM872253 3 0.3482 0.836 0.128 0.000 0.872
#> GSM872254 2 0.1753 0.937 0.048 0.952 0.000
#> GSM872255 1 0.0592 0.912 0.988 0.000 0.012
#> GSM872256 1 0.0000 0.915 1.000 0.000 0.000
#> GSM872257 2 0.0000 0.960 0.000 1.000 0.000
#> GSM872258 3 0.0237 0.940 0.004 0.000 0.996
#> GSM872259 1 0.0237 0.915 0.996 0.004 0.000
#> GSM872260 1 0.0000 0.915 1.000 0.000 0.000
#> GSM872261 1 0.6111 0.313 0.604 0.396 0.000
#> GSM872262 1 0.1753 0.893 0.952 0.000 0.048
#> GSM872263 3 0.0237 0.940 0.004 0.000 0.996
#> GSM872264 3 0.6079 0.300 0.388 0.000 0.612
#> GSM872265 1 0.5678 0.573 0.684 0.000 0.316
#> GSM872266 2 0.0592 0.960 0.012 0.988 0.000
#> GSM872267 2 0.0592 0.960 0.012 0.988 0.000
#> GSM872268 3 0.0237 0.940 0.004 0.000 0.996
#> GSM872269 2 0.4555 0.762 0.200 0.800 0.000
#> GSM872270 3 0.0000 0.938 0.000 0.000 1.000
#> GSM872271 2 0.2749 0.919 0.012 0.924 0.064
#> GSM872272 2 0.2749 0.919 0.012 0.924 0.064
#> GSM872273 1 0.0000 0.915 1.000 0.000 0.000
#> GSM872274 2 0.0475 0.961 0.004 0.992 0.004
#> GSM872275 3 0.1163 0.928 0.028 0.000 0.972
#> GSM872276 1 0.1753 0.893 0.952 0.000 0.048
#> GSM872277 1 0.0000 0.915 1.000 0.000 0.000
#> GSM872278 3 0.1163 0.928 0.028 0.000 0.972
#> GSM872279 1 0.0237 0.915 0.996 0.004 0.000
#> GSM872280 3 0.5058 0.680 0.244 0.000 0.756
#> GSM872281 1 0.5859 0.509 0.656 0.000 0.344
#> GSM872282 3 0.0892 0.924 0.000 0.020 0.980
#> GSM872283 1 0.3686 0.811 0.860 0.000 0.140
#> GSM872284 1 0.5650 0.574 0.688 0.000 0.312
#> GSM872285 3 0.0237 0.940 0.004 0.000 0.996
#> GSM872286 1 0.0424 0.914 0.992 0.008 0.000
#> GSM872287 3 0.0237 0.940 0.004 0.000 0.996
#> GSM872288 1 0.0424 0.914 0.992 0.008 0.000
#> GSM872289 3 0.0892 0.932 0.020 0.000 0.980
#> GSM872290 1 0.0237 0.915 0.996 0.004 0.000
#> GSM872291 1 0.0000 0.915 1.000 0.000 0.000
#> GSM872292 2 0.0475 0.961 0.004 0.992 0.004
#> GSM872293 1 0.0237 0.915 0.996 0.004 0.000
#> GSM872294 2 0.0475 0.961 0.004 0.992 0.004
#> GSM872295 2 0.0000 0.960 0.000 1.000 0.000
#> GSM872296 2 0.0475 0.961 0.004 0.992 0.004
#> GSM872297 1 0.0237 0.915 0.996 0.004 0.000
#> GSM872298 1 0.1753 0.893 0.952 0.000 0.048
#> GSM872299 1 0.0424 0.914 0.992 0.008 0.000
#> GSM872300 1 0.0892 0.909 0.980 0.000 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0657 0.895 0.012 0.000 0.984 0.004
#> GSM872245 1 0.0817 0.709 0.976 0.000 0.000 0.024
#> GSM872246 3 0.0000 0.898 0.000 0.000 1.000 0.000
#> GSM872247 3 0.0336 0.899 0.008 0.000 0.992 0.000
#> GSM872248 2 0.4804 0.331 0.384 0.616 0.000 0.000
#> GSM872249 3 0.0469 0.898 0.012 0.000 0.988 0.000
#> GSM872250 1 0.0779 0.708 0.980 0.004 0.000 0.016
#> GSM872251 3 0.0336 0.899 0.008 0.000 0.992 0.000
#> GSM872252 1 0.4679 0.211 0.648 0.000 0.000 0.352
#> GSM872253 3 0.5997 0.648 0.084 0.004 0.680 0.232
#> GSM872254 1 0.4697 0.333 0.644 0.356 0.000 0.000
#> GSM872255 4 0.2345 0.696 0.100 0.000 0.000 0.900
#> GSM872256 4 0.4877 0.496 0.408 0.000 0.000 0.592
#> GSM872257 2 0.1211 0.726 0.040 0.960 0.000 0.000
#> GSM872258 3 0.0000 0.898 0.000 0.000 1.000 0.000
#> GSM872259 4 0.4981 0.424 0.464 0.000 0.000 0.536
#> GSM872260 4 0.3024 0.682 0.148 0.000 0.000 0.852
#> GSM872261 1 0.5293 0.532 0.748 0.100 0.000 0.152
#> GSM872262 4 0.0921 0.703 0.028 0.000 0.000 0.972
#> GSM872263 3 0.0469 0.896 0.012 0.000 0.988 0.000
#> GSM872264 4 0.6544 0.358 0.044 0.040 0.276 0.640
#> GSM872265 4 0.5691 0.551 0.044 0.040 0.172 0.744
#> GSM872266 1 0.5290 -0.135 0.516 0.476 0.000 0.008
#> GSM872267 2 0.4746 0.365 0.368 0.632 0.000 0.000
#> GSM872268 3 0.0336 0.899 0.008 0.000 0.992 0.000
#> GSM872269 1 0.4679 0.342 0.648 0.352 0.000 0.000
#> GSM872270 3 0.0524 0.898 0.008 0.000 0.988 0.004
#> GSM872271 2 0.8857 0.280 0.208 0.452 0.072 0.268
#> GSM872272 2 0.8857 0.280 0.208 0.452 0.072 0.268
#> GSM872273 4 0.3907 0.641 0.232 0.000 0.000 0.768
#> GSM872274 2 0.0000 0.740 0.000 1.000 0.000 0.000
#> GSM872275 3 0.5051 0.682 0.028 0.004 0.724 0.244
#> GSM872276 4 0.0921 0.703 0.028 0.000 0.000 0.972
#> GSM872277 4 0.3907 0.641 0.232 0.000 0.000 0.768
#> GSM872278 3 0.5746 0.481 0.028 0.004 0.600 0.368
#> GSM872279 4 0.4996 0.380 0.484 0.000 0.000 0.516
#> GSM872280 4 0.4391 0.475 0.008 0.000 0.252 0.740
#> GSM872281 4 0.2928 0.647 0.012 0.000 0.108 0.880
#> GSM872282 3 0.0844 0.894 0.012 0.004 0.980 0.004
#> GSM872283 4 0.4876 0.602 0.068 0.032 0.088 0.812
#> GSM872284 4 0.3464 0.638 0.032 0.000 0.108 0.860
#> GSM872285 3 0.3942 0.713 0.000 0.000 0.764 0.236
#> GSM872286 1 0.1022 0.706 0.968 0.000 0.000 0.032
#> GSM872287 3 0.0336 0.899 0.008 0.000 0.992 0.000
#> GSM872288 1 0.0707 0.709 0.980 0.000 0.000 0.020
#> GSM872289 3 0.1302 0.868 0.044 0.000 0.956 0.000
#> GSM872290 4 0.4972 0.435 0.456 0.000 0.000 0.544
#> GSM872291 4 0.1022 0.703 0.032 0.000 0.000 0.968
#> GSM872292 2 0.0000 0.740 0.000 1.000 0.000 0.000
#> GSM872293 4 0.4977 0.433 0.460 0.000 0.000 0.540
#> GSM872294 2 0.0000 0.740 0.000 1.000 0.000 0.000
#> GSM872295 2 0.1118 0.728 0.036 0.964 0.000 0.000
#> GSM872296 2 0.0000 0.740 0.000 1.000 0.000 0.000
#> GSM872297 4 0.4961 0.447 0.448 0.000 0.000 0.552
#> GSM872298 4 0.1489 0.699 0.044 0.000 0.004 0.952
#> GSM872299 1 0.2281 0.659 0.904 0.000 0.000 0.096
#> GSM872300 4 0.0921 0.703 0.028 0.000 0.000 0.972
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.1911 0.89911 0.004 0.000 0.932 0.036 0.028
#> GSM872245 5 0.4152 0.59201 0.296 0.000 0.000 0.012 0.692
#> GSM872246 3 0.1484 0.91208 0.000 0.000 0.944 0.048 0.008
#> GSM872247 3 0.0703 0.91390 0.000 0.000 0.976 0.024 0.000
#> GSM872248 5 0.4687 0.38829 0.000 0.336 0.000 0.028 0.636
#> GSM872249 3 0.0162 0.91113 0.000 0.000 0.996 0.004 0.000
#> GSM872250 5 0.2389 0.71340 0.116 0.000 0.000 0.004 0.880
#> GSM872251 3 0.1267 0.91152 0.004 0.000 0.960 0.024 0.012
#> GSM872252 1 0.6439 0.26740 0.448 0.000 0.000 0.180 0.372
#> GSM872253 4 0.6927 0.48762 0.036 0.000 0.240 0.532 0.192
#> GSM872254 5 0.3012 0.66757 0.000 0.124 0.000 0.024 0.852
#> GSM872255 1 0.4661 0.46598 0.656 0.000 0.000 0.312 0.032
#> GSM872256 1 0.1830 0.64985 0.924 0.000 0.000 0.008 0.068
#> GSM872257 2 0.2248 0.90542 0.000 0.900 0.000 0.012 0.088
#> GSM872258 3 0.2529 0.88407 0.004 0.000 0.900 0.056 0.040
#> GSM872259 1 0.2583 0.61216 0.864 0.000 0.000 0.004 0.132
#> GSM872260 1 0.4603 0.47970 0.668 0.000 0.000 0.300 0.032
#> GSM872261 5 0.5289 0.26395 0.064 0.000 0.000 0.340 0.596
#> GSM872262 1 0.4893 0.29234 0.568 0.000 0.000 0.404 0.028
#> GSM872263 3 0.1911 0.89911 0.004 0.000 0.932 0.036 0.028
#> GSM872264 4 0.4165 0.67483 0.072 0.032 0.056 0.828 0.012
#> GSM872265 4 0.4083 0.67263 0.084 0.032 0.036 0.832 0.016
#> GSM872266 5 0.4094 0.61100 0.000 0.128 0.000 0.084 0.788
#> GSM872267 5 0.4733 0.36330 0.000 0.348 0.000 0.028 0.624
#> GSM872268 3 0.0703 0.91390 0.000 0.000 0.976 0.024 0.000
#> GSM872269 5 0.3573 0.67118 0.012 0.124 0.000 0.032 0.832
#> GSM872270 3 0.0727 0.91383 0.004 0.000 0.980 0.012 0.004
#> GSM872271 4 0.5522 0.57650 0.012 0.148 0.020 0.716 0.104
#> GSM872272 4 0.5522 0.57650 0.012 0.148 0.020 0.716 0.104
#> GSM872273 1 0.1671 0.63197 0.924 0.000 0.000 0.076 0.000
#> GSM872274 2 0.0162 0.94698 0.000 0.996 0.000 0.000 0.004
#> GSM872275 4 0.5888 0.54169 0.028 0.000 0.276 0.620 0.076
#> GSM872276 1 0.4885 0.30205 0.572 0.000 0.000 0.400 0.028
#> GSM872277 1 0.2069 0.63252 0.912 0.000 0.000 0.076 0.012
#> GSM872278 4 0.4880 0.63095 0.028 0.000 0.196 0.732 0.044
#> GSM872279 1 0.3016 0.59107 0.848 0.000 0.000 0.020 0.132
#> GSM872280 4 0.6784 0.15933 0.356 0.000 0.120 0.488 0.036
#> GSM872281 4 0.3596 0.59490 0.212 0.000 0.012 0.776 0.000
#> GSM872282 3 0.1990 0.89722 0.004 0.000 0.928 0.040 0.028
#> GSM872283 4 0.3804 0.65813 0.104 0.032 0.008 0.836 0.020
#> GSM872284 4 0.3544 0.60334 0.200 0.000 0.008 0.788 0.004
#> GSM872285 3 0.6078 -0.00929 0.052 0.000 0.528 0.384 0.036
#> GSM872286 5 0.2813 0.70240 0.168 0.000 0.000 0.000 0.832
#> GSM872287 3 0.0703 0.91390 0.000 0.000 0.976 0.024 0.000
#> GSM872288 5 0.2674 0.71120 0.140 0.000 0.000 0.004 0.856
#> GSM872289 3 0.2928 0.85489 0.004 0.000 0.872 0.032 0.092
#> GSM872290 1 0.2462 0.62456 0.880 0.000 0.000 0.008 0.112
#> GSM872291 1 0.4836 0.39521 0.612 0.000 0.000 0.356 0.032
#> GSM872292 2 0.0162 0.94698 0.000 0.996 0.000 0.000 0.004
#> GSM872293 1 0.2179 0.62579 0.888 0.000 0.000 0.000 0.112
#> GSM872294 2 0.1251 0.91906 0.000 0.956 0.000 0.036 0.008
#> GSM872295 2 0.2351 0.90568 0.000 0.896 0.000 0.016 0.088
#> GSM872296 2 0.0000 0.94525 0.000 1.000 0.000 0.000 0.000
#> GSM872297 1 0.2513 0.62515 0.876 0.000 0.000 0.008 0.116
#> GSM872298 4 0.4808 0.29996 0.348 0.000 0.000 0.620 0.032
#> GSM872299 5 0.4872 0.36826 0.436 0.000 0.000 0.024 0.540
#> GSM872300 1 0.4893 0.29234 0.568 0.000 0.000 0.404 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.3127 0.8521 0.000 0.000 0.852 0.084 0.020 0.044
#> GSM872245 5 0.4846 0.1956 0.436 0.000 0.000 0.016 0.520 0.028
#> GSM872246 3 0.1036 0.8943 0.000 0.000 0.964 0.024 0.004 0.008
#> GSM872247 3 0.0260 0.8964 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM872248 5 0.5036 0.5403 0.000 0.188 0.000 0.076 0.692 0.044
#> GSM872249 3 0.0260 0.8948 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM872250 5 0.2112 0.7442 0.088 0.000 0.000 0.016 0.896 0.000
#> GSM872251 3 0.2024 0.8725 0.000 0.000 0.920 0.036 0.016 0.028
#> GSM872252 6 0.7234 0.1659 0.272 0.000 0.000 0.120 0.200 0.408
#> GSM872253 6 0.6501 0.1912 0.000 0.000 0.088 0.308 0.108 0.496
#> GSM872254 5 0.3215 0.7296 0.036 0.016 0.000 0.052 0.864 0.032
#> GSM872255 6 0.3489 0.5437 0.288 0.000 0.000 0.004 0.000 0.708
#> GSM872256 1 0.1949 0.8385 0.904 0.000 0.000 0.004 0.004 0.088
#> GSM872257 2 0.3579 0.8456 0.000 0.828 0.000 0.072 0.064 0.036
#> GSM872258 3 0.4668 0.5393 0.000 0.000 0.660 0.052 0.012 0.276
#> GSM872259 1 0.0622 0.8570 0.980 0.000 0.000 0.008 0.012 0.000
#> GSM872260 6 0.4303 0.5118 0.292 0.000 0.000 0.020 0.016 0.672
#> GSM872261 5 0.6586 0.0464 0.036 0.000 0.000 0.208 0.404 0.352
#> GSM872262 6 0.4093 0.5270 0.204 0.000 0.000 0.056 0.004 0.736
#> GSM872263 3 0.3059 0.8542 0.000 0.000 0.856 0.084 0.020 0.040
#> GSM872264 4 0.4634 0.7371 0.032 0.004 0.024 0.684 0.000 0.256
#> GSM872265 4 0.4680 0.7398 0.036 0.004 0.016 0.684 0.004 0.256
#> GSM872266 5 0.3208 0.6914 0.000 0.044 0.000 0.084 0.848 0.024
#> GSM872267 5 0.5093 0.5281 0.000 0.196 0.000 0.076 0.684 0.044
#> GSM872268 3 0.0405 0.8958 0.000 0.000 0.988 0.008 0.000 0.004
#> GSM872269 5 0.3655 0.7245 0.044 0.012 0.000 0.048 0.836 0.060
#> GSM872270 3 0.0870 0.8962 0.000 0.000 0.972 0.012 0.004 0.012
#> GSM872271 4 0.4833 0.6226 0.004 0.080 0.016 0.756 0.040 0.104
#> GSM872272 4 0.4833 0.6226 0.004 0.080 0.016 0.756 0.040 0.104
#> GSM872273 1 0.2680 0.7608 0.856 0.000 0.000 0.016 0.004 0.124
#> GSM872274 2 0.0146 0.9284 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM872275 6 0.5877 0.0111 0.000 0.000 0.116 0.420 0.020 0.444
#> GSM872276 6 0.4121 0.5277 0.208 0.000 0.000 0.056 0.004 0.732
#> GSM872277 1 0.2915 0.7653 0.848 0.000 0.000 0.024 0.008 0.120
#> GSM872278 6 0.5332 -0.0204 0.000 0.000 0.072 0.424 0.012 0.492
#> GSM872279 1 0.2393 0.8274 0.892 0.000 0.000 0.004 0.040 0.064
#> GSM872280 6 0.3297 0.5361 0.100 0.000 0.060 0.008 0.000 0.832
#> GSM872281 6 0.4978 -0.4646 0.032 0.000 0.012 0.468 0.004 0.484
#> GSM872282 3 0.3228 0.8469 0.000 0.000 0.844 0.092 0.020 0.044
#> GSM872283 4 0.4478 0.7369 0.036 0.000 0.012 0.688 0.004 0.260
#> GSM872284 4 0.4961 0.3919 0.040 0.000 0.012 0.492 0.000 0.456
#> GSM872285 6 0.4507 0.2704 0.000 0.000 0.372 0.020 0.012 0.596
#> GSM872286 5 0.2377 0.7298 0.124 0.000 0.000 0.004 0.868 0.004
#> GSM872287 3 0.0260 0.8964 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM872288 5 0.2358 0.7360 0.108 0.000 0.000 0.016 0.876 0.000
#> GSM872289 3 0.4714 0.6987 0.000 0.000 0.728 0.044 0.068 0.160
#> GSM872290 1 0.1781 0.8437 0.924 0.000 0.000 0.008 0.008 0.060
#> GSM872291 6 0.3445 0.5526 0.260 0.000 0.000 0.008 0.000 0.732
#> GSM872292 2 0.0146 0.9284 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM872293 1 0.0260 0.8589 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM872294 2 0.2220 0.8922 0.000 0.908 0.000 0.052 0.020 0.020
#> GSM872295 2 0.3298 0.8771 0.000 0.844 0.000 0.060 0.072 0.024
#> GSM872296 2 0.0146 0.9284 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM872297 1 0.0622 0.8575 0.980 0.000 0.000 0.012 0.008 0.000
#> GSM872298 6 0.3301 0.5029 0.084 0.000 0.004 0.072 0.004 0.836
#> GSM872299 1 0.4985 0.4084 0.636 0.000 0.000 0.008 0.268 0.088
#> GSM872300 6 0.4093 0.5270 0.204 0.000 0.000 0.056 0.004 0.736
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 time(p) individual(p) k
#> SD:kmeans 50 0.742 1.14e-01 2
#> SD:kmeans 55 0.497 6.96e-03 3
#> SD:kmeans 40 0.360 2.37e-04 4
#> SD:kmeans 42 0.107 5.09e-04 5
#> SD:kmeans 47 0.405 1.97e-06 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 29485 rows and 57 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.556 0.842 0.907 0.5058 0.492 0.492
#> 3 3 0.856 0.870 0.948 0.3359 0.695 0.456
#> 4 4 0.857 0.897 0.938 0.1249 0.840 0.556
#> 5 5 0.781 0.600 0.800 0.0513 0.867 0.543
#> 6 6 0.792 0.662 0.820 0.0402 0.917 0.641
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM872244 1 0.7883 0.757 0.764 0.236
#> GSM872245 2 0.1633 0.857 0.024 0.976
#> GSM872246 1 0.1414 0.922 0.980 0.020
#> GSM872247 1 0.2423 0.917 0.960 0.040
#> GSM872248 2 0.0000 0.861 0.000 1.000
#> GSM872249 1 0.7883 0.757 0.764 0.236
#> GSM872250 2 0.0938 0.861 0.012 0.988
#> GSM872251 1 0.2043 0.920 0.968 0.032
#> GSM872252 2 0.7883 0.796 0.236 0.764
#> GSM872253 1 0.1843 0.921 0.972 0.028
#> GSM872254 2 0.0000 0.861 0.000 1.000
#> GSM872255 1 0.0000 0.920 1.000 0.000
#> GSM872256 2 0.7883 0.796 0.236 0.764
#> GSM872257 2 0.0000 0.861 0.000 1.000
#> GSM872258 1 0.1414 0.922 0.980 0.020
#> GSM872259 2 0.7883 0.796 0.236 0.764
#> GSM872260 1 0.0000 0.920 1.000 0.000
#> GSM872261 2 0.0376 0.861 0.004 0.996
#> GSM872262 1 0.0000 0.920 1.000 0.000
#> GSM872263 1 0.2423 0.917 0.960 0.040
#> GSM872264 1 0.7745 0.760 0.772 0.228
#> GSM872265 2 0.8955 0.498 0.312 0.688
#> GSM872266 2 0.0000 0.861 0.000 1.000
#> GSM872267 2 0.0000 0.861 0.000 1.000
#> GSM872268 1 0.1633 0.922 0.976 0.024
#> GSM872269 2 0.0938 0.861 0.012 0.988
#> GSM872270 1 0.7883 0.757 0.764 0.236
#> GSM872271 2 0.0000 0.861 0.000 1.000
#> GSM872272 2 0.0000 0.861 0.000 1.000
#> GSM872273 2 0.9795 0.547 0.416 0.584
#> GSM872274 2 0.0000 0.861 0.000 1.000
#> GSM872275 1 0.7883 0.757 0.764 0.236
#> GSM872276 1 0.0000 0.920 1.000 0.000
#> GSM872277 2 0.9795 0.547 0.416 0.584
#> GSM872278 1 0.3274 0.905 0.940 0.060
#> GSM872279 2 0.7883 0.796 0.236 0.764
#> GSM872280 1 0.0000 0.920 1.000 0.000
#> GSM872281 1 0.0000 0.920 1.000 0.000
#> GSM872282 1 0.7883 0.757 0.764 0.236
#> GSM872283 2 0.4815 0.821 0.104 0.896
#> GSM872284 1 0.0000 0.920 1.000 0.000
#> GSM872285 1 0.0000 0.920 1.000 0.000
#> GSM872286 2 0.7883 0.796 0.236 0.764
#> GSM872287 1 0.2043 0.920 0.968 0.032
#> GSM872288 2 0.7883 0.796 0.236 0.764
#> GSM872289 1 0.1414 0.922 0.980 0.020
#> GSM872290 2 0.7883 0.796 0.236 0.764
#> GSM872291 1 0.0000 0.920 1.000 0.000
#> GSM872292 2 0.0000 0.861 0.000 1.000
#> GSM872293 2 0.7883 0.796 0.236 0.764
#> GSM872294 2 0.0000 0.861 0.000 1.000
#> GSM872295 2 0.0000 0.861 0.000 1.000
#> GSM872296 2 0.0000 0.861 0.000 1.000
#> GSM872297 2 0.7883 0.796 0.236 0.764
#> GSM872298 1 0.0000 0.920 1.000 0.000
#> GSM872299 2 0.7883 0.796 0.236 0.764
#> GSM872300 1 0.0000 0.920 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0237 0.952 0.000 0.004 0.996
#> GSM872245 2 0.0000 0.942 0.000 1.000 0.000
#> GSM872246 3 0.0000 0.954 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.954 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.942 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.954 0.000 0.000 1.000
#> GSM872250 2 0.0237 0.940 0.004 0.996 0.000
#> GSM872251 3 0.0000 0.954 0.000 0.000 1.000
#> GSM872252 1 0.0424 0.923 0.992 0.008 0.000
#> GSM872253 3 0.2261 0.894 0.068 0.000 0.932
#> GSM872254 2 0.0000 0.942 0.000 1.000 0.000
#> GSM872255 1 0.0000 0.928 1.000 0.000 0.000
#> GSM872256 1 0.0000 0.928 1.000 0.000 0.000
#> GSM872257 2 0.0000 0.942 0.000 1.000 0.000
#> GSM872258 3 0.0000 0.954 0.000 0.000 1.000
#> GSM872259 1 0.0000 0.928 1.000 0.000 0.000
#> GSM872260 1 0.0000 0.928 1.000 0.000 0.000
#> GSM872261 2 0.0237 0.940 0.004 0.996 0.000
#> GSM872262 1 0.0000 0.928 1.000 0.000 0.000
#> GSM872263 3 0.0000 0.954 0.000 0.000 1.000
#> GSM872264 3 0.5785 0.543 0.300 0.004 0.696
#> GSM872265 1 0.7424 0.322 0.572 0.388 0.040
#> GSM872266 2 0.0000 0.942 0.000 1.000 0.000
#> GSM872267 2 0.0000 0.942 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.954 0.000 0.000 1.000
#> GSM872269 2 0.0237 0.940 0.004 0.996 0.000
#> GSM872270 3 0.0000 0.954 0.000 0.000 1.000
#> GSM872271 2 0.0000 0.942 0.000 1.000 0.000
#> GSM872272 2 0.0000 0.942 0.000 1.000 0.000
#> GSM872273 1 0.0000 0.928 1.000 0.000 0.000
#> GSM872274 2 0.0000 0.942 0.000 1.000 0.000
#> GSM872275 3 0.0000 0.954 0.000 0.000 1.000
#> GSM872276 1 0.0000 0.928 1.000 0.000 0.000
#> GSM872277 1 0.0000 0.928 1.000 0.000 0.000
#> GSM872278 3 0.0000 0.954 0.000 0.000 1.000
#> GSM872279 1 0.0000 0.928 1.000 0.000 0.000
#> GSM872280 3 0.5882 0.472 0.348 0.000 0.652
#> GSM872281 1 0.4452 0.742 0.808 0.000 0.192
#> GSM872282 3 0.0237 0.952 0.000 0.004 0.996
#> GSM872283 1 0.4575 0.773 0.828 0.160 0.012
#> GSM872284 1 0.4178 0.768 0.828 0.000 0.172
#> GSM872285 3 0.0000 0.954 0.000 0.000 1.000
#> GSM872286 2 0.6215 0.260 0.428 0.572 0.000
#> GSM872287 3 0.0000 0.954 0.000 0.000 1.000
#> GSM872288 1 0.5905 0.407 0.648 0.352 0.000
#> GSM872289 3 0.0000 0.954 0.000 0.000 1.000
#> GSM872290 1 0.0000 0.928 1.000 0.000 0.000
#> GSM872291 1 0.0000 0.928 1.000 0.000 0.000
#> GSM872292 2 0.0000 0.942 0.000 1.000 0.000
#> GSM872293 1 0.0000 0.928 1.000 0.000 0.000
#> GSM872294 2 0.0000 0.942 0.000 1.000 0.000
#> GSM872295 2 0.0000 0.942 0.000 1.000 0.000
#> GSM872296 2 0.0000 0.942 0.000 1.000 0.000
#> GSM872297 1 0.0000 0.928 1.000 0.000 0.000
#> GSM872298 1 0.0237 0.926 0.996 0.000 0.004
#> GSM872299 2 0.6280 0.166 0.460 0.540 0.000
#> GSM872300 1 0.0000 0.928 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM872245 1 0.0336 0.888 0.992 0.008 0.000 0.000
#> GSM872246 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM872247 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM872248 2 0.1940 0.901 0.076 0.924 0.000 0.000
#> GSM872249 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM872250 1 0.0336 0.888 0.992 0.008 0.000 0.000
#> GSM872251 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM872252 1 0.0921 0.897 0.972 0.000 0.000 0.028
#> GSM872253 3 0.0817 0.976 0.024 0.000 0.976 0.000
#> GSM872254 2 0.4382 0.706 0.296 0.704 0.000 0.000
#> GSM872255 4 0.1118 0.893 0.036 0.000 0.000 0.964
#> GSM872256 1 0.3764 0.805 0.784 0.000 0.000 0.216
#> GSM872257 2 0.1118 0.911 0.036 0.964 0.000 0.000
#> GSM872258 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM872259 1 0.2216 0.896 0.908 0.000 0.000 0.092
#> GSM872260 1 0.4522 0.653 0.680 0.000 0.000 0.320
#> GSM872261 2 0.4331 0.716 0.288 0.712 0.000 0.000
#> GSM872262 4 0.0336 0.906 0.008 0.000 0.000 0.992
#> GSM872263 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM872264 4 0.4040 0.720 0.000 0.248 0.000 0.752
#> GSM872265 4 0.4072 0.715 0.000 0.252 0.000 0.748
#> GSM872266 2 0.1940 0.901 0.076 0.924 0.000 0.000
#> GSM872267 2 0.1557 0.908 0.056 0.944 0.000 0.000
#> GSM872268 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM872269 2 0.4522 0.672 0.320 0.680 0.000 0.000
#> GSM872270 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM872271 2 0.0336 0.905 0.000 0.992 0.000 0.008
#> GSM872272 2 0.0336 0.905 0.000 0.992 0.000 0.008
#> GSM872273 4 0.1022 0.896 0.032 0.000 0.000 0.968
#> GSM872274 2 0.0000 0.909 0.000 1.000 0.000 0.000
#> GSM872275 3 0.0469 0.988 0.000 0.012 0.988 0.000
#> GSM872276 4 0.0336 0.906 0.008 0.000 0.000 0.992
#> GSM872277 4 0.0921 0.898 0.028 0.000 0.000 0.972
#> GSM872278 3 0.0336 0.991 0.000 0.000 0.992 0.008
#> GSM872279 1 0.2281 0.896 0.904 0.000 0.000 0.096
#> GSM872280 4 0.3356 0.746 0.000 0.000 0.176 0.824
#> GSM872281 4 0.0000 0.905 0.000 0.000 0.000 1.000
#> GSM872282 3 0.0707 0.979 0.000 0.020 0.980 0.000
#> GSM872283 4 0.4040 0.720 0.000 0.248 0.000 0.752
#> GSM872284 4 0.0000 0.905 0.000 0.000 0.000 1.000
#> GSM872285 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM872286 1 0.0336 0.888 0.992 0.008 0.000 0.000
#> GSM872287 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM872288 1 0.0188 0.889 0.996 0.004 0.000 0.000
#> GSM872289 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM872290 1 0.2469 0.892 0.892 0.000 0.000 0.108
#> GSM872291 4 0.0707 0.902 0.020 0.000 0.000 0.980
#> GSM872292 2 0.0000 0.909 0.000 1.000 0.000 0.000
#> GSM872293 1 0.2921 0.877 0.860 0.000 0.000 0.140
#> GSM872294 2 0.0000 0.909 0.000 1.000 0.000 0.000
#> GSM872295 2 0.1118 0.911 0.036 0.964 0.000 0.000
#> GSM872296 2 0.0000 0.909 0.000 1.000 0.000 0.000
#> GSM872297 1 0.3074 0.869 0.848 0.000 0.000 0.152
#> GSM872298 4 0.0188 0.906 0.004 0.000 0.000 0.996
#> GSM872299 1 0.0336 0.888 0.992 0.008 0.000 0.000
#> GSM872300 4 0.0336 0.906 0.008 0.000 0.000 0.992
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.0000 0.9564 0.000 0.000 1.000 0.000 0.000
#> GSM872245 5 0.1341 0.6352 0.056 0.000 0.000 0.000 0.944
#> GSM872246 3 0.0000 0.9564 0.000 0.000 1.000 0.000 0.000
#> GSM872247 3 0.0000 0.9564 0.000 0.000 1.000 0.000 0.000
#> GSM872248 5 0.4305 0.0805 0.000 0.488 0.000 0.000 0.512
#> GSM872249 3 0.0000 0.9564 0.000 0.000 1.000 0.000 0.000
#> GSM872250 5 0.0162 0.6693 0.000 0.004 0.000 0.000 0.996
#> GSM872251 3 0.0000 0.9564 0.000 0.000 1.000 0.000 0.000
#> GSM872252 1 0.4307 0.1857 0.500 0.000 0.000 0.000 0.500
#> GSM872253 3 0.3205 0.8642 0.052 0.020 0.876 0.004 0.048
#> GSM872254 5 0.3561 0.5078 0.000 0.260 0.000 0.000 0.740
#> GSM872255 1 0.1544 0.5520 0.932 0.000 0.000 0.068 0.000
#> GSM872256 1 0.3790 0.5870 0.724 0.000 0.000 0.004 0.272
#> GSM872257 2 0.1043 0.7724 0.000 0.960 0.000 0.000 0.040
#> GSM872258 3 0.0000 0.9564 0.000 0.000 1.000 0.000 0.000
#> GSM872259 1 0.3861 0.5774 0.712 0.000 0.000 0.004 0.284
#> GSM872260 1 0.1341 0.5582 0.944 0.000 0.000 0.056 0.000
#> GSM872261 2 0.4161 0.2047 0.000 0.608 0.000 0.000 0.392
#> GSM872262 1 0.4305 -0.2008 0.512 0.000 0.000 0.488 0.000
#> GSM872263 3 0.0000 0.9564 0.000 0.000 1.000 0.000 0.000
#> GSM872264 4 0.1892 0.7639 0.000 0.080 0.004 0.916 0.000
#> GSM872265 4 0.1792 0.7625 0.000 0.084 0.000 0.916 0.000
#> GSM872266 5 0.4306 0.0683 0.000 0.492 0.000 0.000 0.508
#> GSM872267 2 0.4440 -0.1295 0.000 0.528 0.000 0.004 0.468
#> GSM872268 3 0.0000 0.9564 0.000 0.000 1.000 0.000 0.000
#> GSM872269 5 0.3480 0.5208 0.000 0.248 0.000 0.000 0.752
#> GSM872270 3 0.0000 0.9564 0.000 0.000 1.000 0.000 0.000
#> GSM872271 2 0.3452 0.6333 0.000 0.756 0.000 0.244 0.000
#> GSM872272 2 0.3480 0.6281 0.000 0.752 0.000 0.248 0.000
#> GSM872273 1 0.2293 0.5619 0.900 0.000 0.000 0.084 0.016
#> GSM872274 2 0.0162 0.7933 0.000 0.996 0.000 0.004 0.000
#> GSM872275 3 0.3142 0.8366 0.004 0.108 0.856 0.032 0.000
#> GSM872276 1 0.4287 -0.1376 0.540 0.000 0.000 0.460 0.000
#> GSM872277 1 0.4630 0.5174 0.736 0.000 0.000 0.176 0.088
#> GSM872278 3 0.4956 0.4924 0.048 0.000 0.636 0.316 0.000
#> GSM872279 1 0.3730 0.5718 0.712 0.000 0.000 0.000 0.288
#> GSM872280 1 0.6695 -0.1466 0.428 0.000 0.308 0.264 0.000
#> GSM872281 4 0.3305 0.6403 0.224 0.000 0.000 0.776 0.000
#> GSM872282 3 0.0771 0.9409 0.000 0.020 0.976 0.004 0.000
#> GSM872283 4 0.1544 0.7680 0.000 0.068 0.000 0.932 0.000
#> GSM872284 4 0.1732 0.7403 0.080 0.000 0.000 0.920 0.000
#> GSM872285 3 0.0162 0.9544 0.000 0.000 0.996 0.004 0.000
#> GSM872286 5 0.0510 0.6695 0.016 0.000 0.000 0.000 0.984
#> GSM872287 3 0.0000 0.9564 0.000 0.000 1.000 0.000 0.000
#> GSM872288 5 0.0404 0.6699 0.012 0.000 0.000 0.000 0.988
#> GSM872289 3 0.0290 0.9520 0.000 0.000 0.992 0.000 0.008
#> GSM872290 1 0.3766 0.5861 0.728 0.000 0.000 0.004 0.268
#> GSM872291 1 0.1608 0.5478 0.928 0.000 0.000 0.072 0.000
#> GSM872292 2 0.0162 0.7933 0.000 0.996 0.000 0.004 0.000
#> GSM872293 1 0.3814 0.5842 0.720 0.000 0.000 0.004 0.276
#> GSM872294 2 0.0162 0.7933 0.000 0.996 0.000 0.004 0.000
#> GSM872295 2 0.0963 0.7745 0.000 0.964 0.000 0.000 0.036
#> GSM872296 2 0.0162 0.7933 0.000 0.996 0.000 0.004 0.000
#> GSM872297 1 0.3790 0.5870 0.724 0.000 0.000 0.004 0.272
#> GSM872298 4 0.4268 0.2808 0.444 0.000 0.000 0.556 0.000
#> GSM872299 5 0.4088 0.0485 0.368 0.000 0.000 0.000 0.632
#> GSM872300 1 0.4305 -0.2008 0.512 0.000 0.000 0.488 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.1036 0.91933 0.000 0.000 0.964 0.008 0.004 0.024
#> GSM872245 5 0.4537 0.12573 0.412 0.000 0.000 0.000 0.552 0.036
#> GSM872246 3 0.0603 0.92002 0.000 0.000 0.980 0.000 0.004 0.016
#> GSM872247 3 0.0146 0.92193 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM872248 5 0.3659 0.47994 0.000 0.364 0.000 0.000 0.636 0.000
#> GSM872249 3 0.0405 0.92094 0.000 0.000 0.988 0.004 0.000 0.008
#> GSM872250 5 0.1141 0.70995 0.052 0.000 0.000 0.000 0.948 0.000
#> GSM872251 3 0.0622 0.91964 0.000 0.000 0.980 0.000 0.008 0.012
#> GSM872252 1 0.6431 0.34815 0.452 0.012 0.000 0.008 0.244 0.284
#> GSM872253 6 0.6779 -0.17673 0.040 0.020 0.408 0.012 0.096 0.424
#> GSM872254 5 0.3974 0.63716 0.000 0.116 0.000 0.004 0.772 0.108
#> GSM872255 6 0.3672 0.61322 0.304 0.000 0.000 0.008 0.000 0.688
#> GSM872256 1 0.0508 0.79773 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM872257 2 0.0937 0.76641 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM872258 3 0.0935 0.91603 0.000 0.000 0.964 0.000 0.004 0.032
#> GSM872259 1 0.0260 0.79928 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM872260 6 0.3872 0.59832 0.264 0.000 0.000 0.004 0.020 0.712
#> GSM872261 2 0.6043 0.00333 0.016 0.484 0.000 0.008 0.368 0.124
#> GSM872262 6 0.5180 0.57851 0.164 0.000 0.000 0.220 0.000 0.616
#> GSM872263 3 0.0692 0.92070 0.000 0.000 0.976 0.000 0.004 0.020
#> GSM872264 4 0.0458 0.79170 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM872265 4 0.0632 0.79021 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM872266 5 0.3684 0.46890 0.000 0.372 0.000 0.000 0.628 0.000
#> GSM872267 5 0.3747 0.42699 0.000 0.396 0.000 0.000 0.604 0.000
#> GSM872268 3 0.0000 0.92182 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872269 5 0.3552 0.65854 0.008 0.068 0.000 0.004 0.820 0.100
#> GSM872270 3 0.0665 0.91970 0.000 0.000 0.980 0.008 0.004 0.008
#> GSM872271 2 0.4066 0.45865 0.000 0.596 0.000 0.392 0.000 0.012
#> GSM872272 2 0.4076 0.45191 0.000 0.592 0.000 0.396 0.000 0.012
#> GSM872273 1 0.2706 0.67878 0.852 0.000 0.000 0.024 0.000 0.124
#> GSM872274 2 0.0363 0.79231 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM872275 3 0.4987 0.68633 0.000 0.144 0.728 0.056 0.012 0.060
#> GSM872276 6 0.4982 0.60990 0.172 0.000 0.000 0.180 0.000 0.648
#> GSM872277 1 0.2954 0.68570 0.852 0.000 0.000 0.048 0.004 0.096
#> GSM872278 3 0.6501 0.00850 0.000 0.004 0.424 0.224 0.020 0.328
#> GSM872279 1 0.2258 0.77047 0.896 0.000 0.000 0.000 0.044 0.060
#> GSM872280 6 0.4602 0.55571 0.056 0.000 0.128 0.068 0.000 0.748
#> GSM872281 4 0.3890 0.27607 0.004 0.000 0.000 0.596 0.000 0.400
#> GSM872282 3 0.0891 0.91929 0.000 0.000 0.968 0.008 0.000 0.024
#> GSM872283 4 0.0881 0.79147 0.008 0.012 0.000 0.972 0.000 0.008
#> GSM872284 4 0.2933 0.66474 0.004 0.000 0.000 0.796 0.000 0.200
#> GSM872285 3 0.1588 0.87293 0.000 0.000 0.924 0.004 0.000 0.072
#> GSM872286 5 0.1444 0.70775 0.072 0.000 0.000 0.000 0.928 0.000
#> GSM872287 3 0.0146 0.92193 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM872288 5 0.1327 0.71001 0.064 0.000 0.000 0.000 0.936 0.000
#> GSM872289 3 0.1088 0.91267 0.000 0.000 0.960 0.000 0.024 0.016
#> GSM872290 1 0.2504 0.75986 0.880 0.000 0.000 0.004 0.028 0.088
#> GSM872291 6 0.4363 0.58406 0.272 0.000 0.000 0.024 0.020 0.684
#> GSM872292 2 0.0363 0.79231 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM872293 1 0.0146 0.79929 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM872294 2 0.0458 0.79254 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM872295 2 0.0603 0.77607 0.000 0.980 0.000 0.000 0.016 0.004
#> GSM872296 2 0.0458 0.79254 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM872297 1 0.0146 0.79929 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM872298 6 0.4467 0.51026 0.056 0.000 0.000 0.216 0.016 0.712
#> GSM872299 1 0.5860 0.34271 0.532 0.008 0.000 0.004 0.296 0.160
#> GSM872300 6 0.5162 0.58639 0.168 0.000 0.000 0.212 0.000 0.620
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 time(p) individual(p) k
#> SD:skmeans 56 0.796 3.29e-03 2
#> SD:skmeans 52 0.759 7.69e-03 3
#> SD:skmeans 57 0.238 6.40e-03 4
#> SD:skmeans 45 0.550 1.20e-04 5
#> SD:skmeans 45 0.851 1.87e-06 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 29485 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.363 0.726 0.821 0.4327 0.560 0.560
#> 3 3 0.456 0.734 0.836 0.4371 0.752 0.576
#> 4 4 0.661 0.817 0.857 0.1609 0.894 0.710
#> 5 5 0.717 0.804 0.864 0.0600 0.883 0.623
#> 6 6 0.738 0.707 0.829 0.0714 0.931 0.719
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM872244 2 0.966 0.7992 0.392 0.608
#> GSM872245 2 0.000 0.5777 0.000 1.000
#> GSM872246 1 0.000 0.8054 1.000 0.000
#> GSM872247 1 0.000 0.8054 1.000 0.000
#> GSM872248 2 0.966 0.7992 0.392 0.608
#> GSM872249 1 0.000 0.8054 1.000 0.000
#> GSM872250 2 0.625 0.6977 0.156 0.844
#> GSM872251 1 0.000 0.8054 1.000 0.000
#> GSM872252 1 0.855 0.6482 0.720 0.280
#> GSM872253 1 0.000 0.8054 1.000 0.000
#> GSM872254 2 0.552 0.6781 0.128 0.872
#> GSM872255 1 0.839 0.6556 0.732 0.268
#> GSM872256 1 0.861 0.6543 0.716 0.284
#> GSM872257 2 0.966 0.7992 0.392 0.608
#> GSM872258 1 0.000 0.8054 1.000 0.000
#> GSM872259 1 0.966 0.5866 0.608 0.392
#> GSM872260 1 0.506 0.7446 0.888 0.112
#> GSM872261 2 0.966 0.7992 0.392 0.608
#> GSM872262 1 0.000 0.8054 1.000 0.000
#> GSM872263 1 0.000 0.8054 1.000 0.000
#> GSM872264 1 0.000 0.8054 1.000 0.000
#> GSM872265 1 0.000 0.8054 1.000 0.000
#> GSM872266 2 0.966 0.7992 0.392 0.608
#> GSM872267 2 0.966 0.7992 0.392 0.608
#> GSM872268 1 0.000 0.8054 1.000 0.000
#> GSM872269 2 0.753 0.7283 0.216 0.784
#> GSM872270 1 0.000 0.8054 1.000 0.000
#> GSM872271 2 0.966 0.7992 0.392 0.608
#> GSM872272 2 0.966 0.7992 0.392 0.608
#> GSM872273 1 0.966 0.5866 0.608 0.392
#> GSM872274 2 0.966 0.7992 0.392 0.608
#> GSM872275 1 0.000 0.8054 1.000 0.000
#> GSM872276 1 0.966 0.5866 0.608 0.392
#> GSM872277 1 0.963 0.5898 0.612 0.388
#> GSM872278 1 0.000 0.8054 1.000 0.000
#> GSM872279 1 0.966 0.5866 0.608 0.392
#> GSM872280 1 0.000 0.8054 1.000 0.000
#> GSM872281 1 0.000 0.8054 1.000 0.000
#> GSM872282 1 0.163 0.7770 0.976 0.024
#> GSM872283 1 0.141 0.7964 0.980 0.020
#> GSM872284 1 0.000 0.8054 1.000 0.000
#> GSM872285 1 0.000 0.8054 1.000 0.000
#> GSM872286 2 0.000 0.5777 0.000 1.000
#> GSM872287 1 0.000 0.8054 1.000 0.000
#> GSM872288 2 0.689 0.6520 0.184 0.816
#> GSM872289 1 0.000 0.8054 1.000 0.000
#> GSM872290 1 0.966 0.5866 0.608 0.392
#> GSM872291 1 0.929 0.6156 0.656 0.344
#> GSM872292 2 0.966 0.7992 0.392 0.608
#> GSM872293 1 0.966 0.5866 0.608 0.392
#> GSM872294 1 0.000 0.8054 1.000 0.000
#> GSM872295 2 0.966 0.7992 0.392 0.608
#> GSM872296 1 0.327 0.7252 0.940 0.060
#> GSM872297 1 0.966 0.5866 0.608 0.392
#> GSM872298 1 0.000 0.8054 1.000 0.000
#> GSM872299 2 0.900 0.0401 0.316 0.684
#> GSM872300 1 0.955 0.5969 0.624 0.376
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.974 0.000 0.000 1.000
#> GSM872245 2 0.5706 0.691 0.320 0.680 0.000
#> GSM872246 3 0.0000 0.974 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.974 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.785 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.974 0.000 0.000 1.000
#> GSM872250 2 0.6348 0.764 0.188 0.752 0.060
#> GSM872251 3 0.0237 0.970 0.004 0.000 0.996
#> GSM872252 1 0.3267 0.731 0.884 0.000 0.116
#> GSM872253 1 0.6079 0.643 0.612 0.000 0.388
#> GSM872254 2 0.4002 0.774 0.160 0.840 0.000
#> GSM872255 1 0.3619 0.729 0.864 0.000 0.136
#> GSM872256 1 0.3116 0.724 0.892 0.000 0.108
#> GSM872257 2 0.0000 0.785 0.000 1.000 0.000
#> GSM872258 3 0.0000 0.974 0.000 0.000 1.000
#> GSM872259 1 0.0000 0.708 1.000 0.000 0.000
#> GSM872260 1 0.5397 0.695 0.720 0.000 0.280
#> GSM872261 2 0.6079 0.446 0.000 0.612 0.388
#> GSM872262 1 0.6079 0.643 0.612 0.000 0.388
#> GSM872263 3 0.0000 0.974 0.000 0.000 1.000
#> GSM872264 1 0.6079 0.643 0.612 0.000 0.388
#> GSM872265 1 0.6079 0.643 0.612 0.000 0.388
#> GSM872266 2 0.5098 0.656 0.000 0.752 0.248
#> GSM872267 2 0.0000 0.785 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.974 0.000 0.000 1.000
#> GSM872269 2 0.7113 0.750 0.168 0.720 0.112
#> GSM872270 3 0.0000 0.974 0.000 0.000 1.000
#> GSM872271 2 0.6079 0.446 0.000 0.612 0.388
#> GSM872272 2 0.6079 0.446 0.000 0.612 0.388
#> GSM872273 1 0.0000 0.708 1.000 0.000 0.000
#> GSM872274 2 0.0424 0.786 0.000 0.992 0.008
#> GSM872275 1 0.6079 0.643 0.612 0.000 0.388
#> GSM872276 1 0.0000 0.708 1.000 0.000 0.000
#> GSM872277 1 0.0237 0.710 0.996 0.000 0.004
#> GSM872278 1 0.6079 0.643 0.612 0.000 0.388
#> GSM872279 1 0.0000 0.708 1.000 0.000 0.000
#> GSM872280 1 0.6079 0.643 0.612 0.000 0.388
#> GSM872281 1 0.6079 0.643 0.612 0.000 0.388
#> GSM872282 3 0.0000 0.974 0.000 0.000 1.000
#> GSM872283 1 0.6008 0.650 0.628 0.000 0.372
#> GSM872284 1 0.6079 0.643 0.612 0.000 0.388
#> GSM872285 3 0.0592 0.962 0.012 0.000 0.988
#> GSM872286 2 0.5098 0.738 0.248 0.752 0.000
#> GSM872287 3 0.0000 0.974 0.000 0.000 1.000
#> GSM872288 2 0.7248 0.706 0.256 0.676 0.068
#> GSM872289 3 0.4555 0.617 0.200 0.000 0.800
#> GSM872290 1 0.0000 0.708 1.000 0.000 0.000
#> GSM872291 1 0.1753 0.724 0.952 0.000 0.048
#> GSM872292 2 0.0424 0.786 0.000 0.992 0.008
#> GSM872293 1 0.0000 0.708 1.000 0.000 0.000
#> GSM872294 1 0.8459 0.647 0.612 0.156 0.232
#> GSM872295 2 0.0424 0.786 0.000 0.992 0.008
#> GSM872296 1 0.9087 0.569 0.544 0.268 0.188
#> GSM872297 1 0.0000 0.708 1.000 0.000 0.000
#> GSM872298 1 0.6079 0.643 0.612 0.000 0.388
#> GSM872299 1 0.5591 0.154 0.696 0.304 0.000
#> GSM872300 1 0.0892 0.716 0.980 0.000 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.1389 0.9152 0.000 0.000 0.952 0.048
#> GSM872245 1 0.2530 0.7932 0.888 0.112 0.000 0.000
#> GSM872246 3 0.0000 0.9284 0.000 0.000 1.000 0.000
#> GSM872247 3 0.0000 0.9284 0.000 0.000 1.000 0.000
#> GSM872248 2 0.0188 0.8546 0.000 0.996 0.000 0.004
#> GSM872249 3 0.0000 0.9284 0.000 0.000 1.000 0.000
#> GSM872250 2 0.1824 0.8435 0.060 0.936 0.000 0.004
#> GSM872251 3 0.2281 0.8837 0.000 0.000 0.904 0.096
#> GSM872252 4 0.3649 0.7739 0.204 0.000 0.000 0.796
#> GSM872253 4 0.3123 0.8552 0.000 0.000 0.156 0.844
#> GSM872254 2 0.1474 0.8463 0.052 0.948 0.000 0.000
#> GSM872255 4 0.3486 0.7786 0.188 0.000 0.000 0.812
#> GSM872256 4 0.4499 0.8291 0.124 0.000 0.072 0.804
#> GSM872257 2 0.2921 0.8450 0.000 0.860 0.000 0.140
#> GSM872258 3 0.0336 0.9279 0.000 0.000 0.992 0.008
#> GSM872259 1 0.0000 0.8897 1.000 0.000 0.000 0.000
#> GSM872260 4 0.4236 0.8445 0.088 0.000 0.088 0.824
#> GSM872261 2 0.4609 0.7699 0.000 0.788 0.156 0.056
#> GSM872262 4 0.3052 0.8592 0.004 0.000 0.136 0.860
#> GSM872263 3 0.0000 0.9284 0.000 0.000 1.000 0.000
#> GSM872264 4 0.3123 0.8552 0.000 0.000 0.156 0.844
#> GSM872265 4 0.3123 0.8552 0.000 0.000 0.156 0.844
#> GSM872266 2 0.1975 0.8481 0.000 0.936 0.016 0.048
#> GSM872267 2 0.2921 0.8450 0.000 0.860 0.000 0.140
#> GSM872268 3 0.0000 0.9284 0.000 0.000 1.000 0.000
#> GSM872269 2 0.1938 0.8470 0.052 0.936 0.000 0.012
#> GSM872270 3 0.1557 0.9116 0.000 0.000 0.944 0.056
#> GSM872271 2 0.4609 0.7699 0.000 0.788 0.156 0.056
#> GSM872272 2 0.4609 0.7699 0.000 0.788 0.156 0.056
#> GSM872273 1 0.0592 0.8842 0.984 0.000 0.000 0.016
#> GSM872274 2 0.3024 0.8451 0.000 0.852 0.000 0.148
#> GSM872275 4 0.3123 0.8552 0.000 0.000 0.156 0.844
#> GSM872276 4 0.3569 0.7722 0.196 0.000 0.000 0.804
#> GSM872277 1 0.0592 0.8842 0.984 0.000 0.000 0.016
#> GSM872278 4 0.3123 0.8552 0.000 0.000 0.156 0.844
#> GSM872279 4 0.4564 0.6133 0.328 0.000 0.000 0.672
#> GSM872280 4 0.3626 0.8423 0.004 0.000 0.184 0.812
#> GSM872281 4 0.3157 0.8584 0.004 0.000 0.144 0.852
#> GSM872282 3 0.1474 0.9140 0.000 0.000 0.948 0.052
#> GSM872283 4 0.3306 0.8555 0.004 0.000 0.156 0.840
#> GSM872284 4 0.2921 0.8584 0.000 0.000 0.140 0.860
#> GSM872285 3 0.1557 0.8974 0.000 0.000 0.944 0.056
#> GSM872286 2 0.1940 0.8341 0.076 0.924 0.000 0.000
#> GSM872287 3 0.0000 0.9284 0.000 0.000 1.000 0.000
#> GSM872288 2 0.4037 0.7589 0.056 0.832 0.000 0.112
#> GSM872289 3 0.6574 0.2714 0.000 0.084 0.532 0.384
#> GSM872290 1 0.0000 0.8897 1.000 0.000 0.000 0.000
#> GSM872291 4 0.3649 0.7739 0.204 0.000 0.000 0.796
#> GSM872292 2 0.3024 0.8451 0.000 0.852 0.000 0.148
#> GSM872293 1 0.0000 0.8897 1.000 0.000 0.000 0.000
#> GSM872294 4 0.1722 0.7619 0.000 0.048 0.008 0.944
#> GSM872295 2 0.3024 0.8451 0.000 0.852 0.000 0.148
#> GSM872296 4 0.4406 0.3789 0.000 0.300 0.000 0.700
#> GSM872297 1 0.0000 0.8897 1.000 0.000 0.000 0.000
#> GSM872298 4 0.3123 0.8552 0.000 0.000 0.156 0.844
#> GSM872299 1 0.7893 0.0593 0.376 0.300 0.000 0.324
#> GSM872300 4 0.3528 0.7759 0.192 0.000 0.000 0.808
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.2732 0.813 0.000 0.000 0.840 0.160 0.000
#> GSM872245 1 0.2966 0.751 0.816 0.000 0.000 0.000 0.184
#> GSM872246 3 0.0000 0.859 0.000 0.000 1.000 0.000 0.000
#> GSM872247 3 0.0000 0.859 0.000 0.000 1.000 0.000 0.000
#> GSM872248 5 0.0290 0.823 0.000 0.008 0.000 0.000 0.992
#> GSM872249 3 0.0000 0.859 0.000 0.000 1.000 0.000 0.000
#> GSM872250 5 0.1124 0.839 0.004 0.000 0.000 0.036 0.960
#> GSM872251 3 0.3366 0.762 0.000 0.000 0.768 0.232 0.000
#> GSM872252 4 0.3160 0.787 0.188 0.000 0.000 0.808 0.004
#> GSM872253 4 0.1341 0.843 0.000 0.000 0.056 0.944 0.000
#> GSM872254 5 0.0000 0.826 0.000 0.000 0.000 0.000 1.000
#> GSM872255 4 0.4696 0.767 0.108 0.156 0.000 0.736 0.000
#> GSM872256 4 0.5112 0.799 0.152 0.080 0.024 0.740 0.004
#> GSM872257 2 0.2690 0.897 0.000 0.844 0.000 0.000 0.156
#> GSM872258 3 0.1341 0.851 0.000 0.000 0.944 0.056 0.000
#> GSM872259 1 0.0162 0.930 0.996 0.000 0.000 0.000 0.004
#> GSM872260 4 0.2130 0.835 0.080 0.000 0.012 0.908 0.000
#> GSM872261 4 0.1502 0.842 0.000 0.000 0.056 0.940 0.004
#> GSM872262 4 0.2971 0.815 0.008 0.156 0.000 0.836 0.000
#> GSM872263 3 0.0000 0.859 0.000 0.000 1.000 0.000 0.000
#> GSM872264 4 0.1608 0.832 0.000 0.000 0.072 0.928 0.000
#> GSM872265 4 0.1341 0.843 0.000 0.000 0.056 0.944 0.000
#> GSM872266 5 0.1121 0.835 0.000 0.000 0.000 0.044 0.956
#> GSM872267 5 0.3210 0.578 0.000 0.212 0.000 0.000 0.788
#> GSM872268 3 0.0000 0.859 0.000 0.000 1.000 0.000 0.000
#> GSM872269 5 0.1608 0.811 0.000 0.000 0.000 0.072 0.928
#> GSM872270 3 0.3586 0.728 0.000 0.000 0.736 0.264 0.000
#> GSM872271 4 0.1341 0.843 0.000 0.000 0.056 0.944 0.000
#> GSM872272 4 0.1341 0.843 0.000 0.000 0.056 0.944 0.000
#> GSM872273 1 0.2124 0.894 0.916 0.028 0.000 0.056 0.000
#> GSM872274 2 0.2690 0.897 0.000 0.844 0.000 0.000 0.156
#> GSM872275 4 0.1341 0.843 0.000 0.000 0.056 0.944 0.000
#> GSM872276 4 0.4696 0.767 0.108 0.156 0.000 0.736 0.000
#> GSM872277 1 0.2124 0.894 0.916 0.028 0.000 0.056 0.000
#> GSM872278 4 0.1341 0.843 0.000 0.000 0.056 0.944 0.000
#> GSM872279 4 0.4276 0.569 0.380 0.000 0.000 0.616 0.004
#> GSM872280 4 0.4873 0.762 0.008 0.156 0.100 0.736 0.000
#> GSM872281 4 0.2971 0.815 0.008 0.156 0.000 0.836 0.000
#> GSM872282 3 0.2690 0.815 0.000 0.000 0.844 0.156 0.000
#> GSM872283 4 0.1788 0.844 0.008 0.004 0.056 0.932 0.000
#> GSM872284 4 0.3087 0.820 0.004 0.152 0.008 0.836 0.000
#> GSM872285 3 0.2438 0.822 0.000 0.040 0.900 0.060 0.000
#> GSM872286 5 0.1043 0.823 0.040 0.000 0.000 0.000 0.960
#> GSM872287 3 0.0000 0.859 0.000 0.000 1.000 0.000 0.000
#> GSM872288 5 0.1364 0.838 0.012 0.000 0.000 0.036 0.952
#> GSM872289 3 0.5906 0.333 0.000 0.000 0.492 0.404 0.104
#> GSM872290 1 0.0162 0.930 0.996 0.000 0.000 0.000 0.004
#> GSM872291 4 0.5354 0.752 0.188 0.128 0.000 0.680 0.004
#> GSM872292 2 0.2690 0.897 0.000 0.844 0.000 0.000 0.156
#> GSM872293 1 0.0162 0.930 0.996 0.000 0.000 0.000 0.004
#> GSM872294 2 0.2773 0.798 0.000 0.836 0.000 0.164 0.000
#> GSM872295 2 0.2690 0.897 0.000 0.844 0.000 0.000 0.156
#> GSM872296 2 0.2690 0.806 0.000 0.844 0.000 0.156 0.000
#> GSM872297 1 0.0162 0.930 0.996 0.000 0.000 0.000 0.004
#> GSM872298 4 0.1341 0.843 0.000 0.000 0.056 0.944 0.000
#> GSM872299 5 0.6739 0.023 0.348 0.000 0.000 0.260 0.392
#> GSM872300 4 0.4696 0.767 0.108 0.156 0.000 0.736 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.2300 0.7198 0.000 0.000 0.856 0.000 0.000 0.144
#> GSM872245 1 0.3168 0.7055 0.792 0.000 0.000 0.000 0.192 0.016
#> GSM872246 3 0.3717 0.7967 0.000 0.000 0.616 0.000 0.000 0.384
#> GSM872247 3 0.3847 0.8025 0.000 0.000 0.544 0.000 0.000 0.456
#> GSM872248 5 0.0146 0.8675 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM872249 3 0.3847 0.8025 0.000 0.000 0.544 0.000 0.000 0.456
#> GSM872250 5 0.0000 0.8683 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872251 3 0.2100 0.6215 0.000 0.000 0.884 0.004 0.000 0.112
#> GSM872252 6 0.6775 0.6216 0.196 0.000 0.184 0.108 0.000 0.512
#> GSM872253 6 0.5205 0.4873 0.000 0.000 0.384 0.096 0.000 0.520
#> GSM872254 5 0.3868 -0.0405 0.000 0.000 0.000 0.000 0.508 0.492
#> GSM872255 4 0.0000 0.6952 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872256 4 0.4327 0.6513 0.140 0.000 0.092 0.752 0.016 0.000
#> GSM872257 2 0.0000 0.9344 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872258 3 0.3714 0.7996 0.000 0.000 0.656 0.004 0.000 0.340
#> GSM872259 1 0.0000 0.8224 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872260 4 0.4624 0.6894 0.080 0.000 0.220 0.692 0.000 0.008
#> GSM872261 4 0.4610 0.6979 0.000 0.000 0.384 0.580 0.024 0.012
#> GSM872262 4 0.0000 0.6952 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872263 3 0.3717 0.7967 0.000 0.000 0.616 0.000 0.000 0.384
#> GSM872264 4 0.4543 0.6985 0.000 0.000 0.384 0.576 0.000 0.040
#> GSM872265 4 0.4543 0.6985 0.000 0.000 0.384 0.576 0.000 0.040
#> GSM872266 5 0.0000 0.8683 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872267 5 0.3394 0.5944 0.000 0.236 0.000 0.000 0.752 0.012
#> GSM872268 3 0.3847 0.8025 0.000 0.000 0.544 0.000 0.000 0.456
#> GSM872269 5 0.0713 0.8536 0.000 0.000 0.000 0.000 0.972 0.028
#> GSM872270 3 0.1556 0.5646 0.000 0.000 0.920 0.000 0.000 0.080
#> GSM872271 6 0.5190 0.4927 0.000 0.000 0.384 0.072 0.008 0.536
#> GSM872272 4 0.5168 0.6773 0.000 0.000 0.384 0.548 0.028 0.040
#> GSM872273 1 0.2697 0.7775 0.812 0.000 0.000 0.188 0.000 0.000
#> GSM872274 2 0.0000 0.9344 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872275 4 0.3955 0.7112 0.000 0.000 0.384 0.608 0.000 0.008
#> GSM872276 4 0.0000 0.6952 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872277 1 0.2697 0.7775 0.812 0.000 0.000 0.188 0.000 0.000
#> GSM872278 4 0.3955 0.7112 0.000 0.000 0.384 0.608 0.000 0.008
#> GSM872279 6 0.5358 0.5005 0.392 0.000 0.000 0.112 0.000 0.496
#> GSM872280 4 0.0000 0.6952 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872281 4 0.0000 0.6952 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872282 3 0.2219 0.7146 0.000 0.000 0.864 0.000 0.000 0.136
#> GSM872283 4 0.4607 0.7120 0.012 0.000 0.356 0.604 0.000 0.028
#> GSM872284 4 0.0632 0.7002 0.000 0.000 0.024 0.976 0.000 0.000
#> GSM872285 3 0.5309 0.7345 0.000 0.000 0.560 0.128 0.000 0.312
#> GSM872286 5 0.0146 0.8677 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM872287 3 0.3847 0.8025 0.000 0.000 0.544 0.000 0.000 0.456
#> GSM872288 5 0.0260 0.8643 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM872289 3 0.5410 0.4988 0.000 0.000 0.680 0.128 0.120 0.072
#> GSM872290 6 0.3869 0.3037 0.500 0.000 0.000 0.000 0.000 0.500
#> GSM872291 6 0.5716 0.5346 0.188 0.000 0.000 0.312 0.000 0.500
#> GSM872292 2 0.0000 0.9344 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872293 1 0.0000 0.8224 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872294 2 0.0146 0.9309 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM872295 2 0.3907 0.5746 0.000 0.704 0.000 0.000 0.028 0.268
#> GSM872296 2 0.0000 0.9344 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872297 1 0.0000 0.8224 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872298 4 0.3955 0.7112 0.000 0.000 0.384 0.608 0.000 0.008
#> GSM872299 6 0.5735 0.3371 0.200 0.000 0.000 0.000 0.296 0.504
#> GSM872300 4 0.0000 0.6952 0.000 0.000 0.000 1.000 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 time(p) individual(p) k
#> SD:pam 56 0.620 3.50e-02 2
#> SD:pam 53 0.762 7.10e-05 3
#> SD:pam 54 0.898 3.89e-05 4
#> SD:pam 55 0.563 4.64e-07 5
#> SD:pam 51 0.792 2.37e-07 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 29485 rows and 57 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.669 0.915 0.921 0.4171 0.560 0.560
#> 3 3 0.656 0.863 0.928 0.3441 0.612 0.441
#> 4 4 0.727 0.776 0.899 0.2896 0.761 0.496
#> 5 5 0.744 0.760 0.843 0.0809 0.934 0.765
#> 6 6 0.832 0.796 0.887 0.0536 0.900 0.591
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM872244 1 0.4431 0.903 0.908 0.092
#> GSM872245 1 0.8144 0.588 0.748 0.252
#> GSM872246 1 0.4431 0.903 0.908 0.092
#> GSM872247 1 0.4431 0.903 0.908 0.092
#> GSM872248 2 0.4431 0.925 0.092 0.908
#> GSM872249 1 0.4431 0.903 0.908 0.092
#> GSM872250 1 0.0376 0.944 0.996 0.004
#> GSM872251 1 0.4298 0.906 0.912 0.088
#> GSM872252 1 0.0000 0.946 1.000 0.000
#> GSM872253 1 0.0000 0.946 1.000 0.000
#> GSM872254 2 0.7950 0.882 0.240 0.760
#> GSM872255 1 0.0000 0.946 1.000 0.000
#> GSM872256 1 0.1414 0.937 0.980 0.020
#> GSM872257 2 0.4431 0.925 0.092 0.908
#> GSM872258 1 0.4161 0.908 0.916 0.084
#> GSM872259 1 0.0000 0.946 1.000 0.000
#> GSM872260 1 0.0000 0.946 1.000 0.000
#> GSM872261 2 0.6712 0.937 0.176 0.824
#> GSM872262 1 0.1843 0.931 0.972 0.028
#> GSM872263 1 0.4431 0.903 0.908 0.092
#> GSM872264 2 0.6623 0.939 0.172 0.828
#> GSM872265 2 0.6623 0.939 0.172 0.828
#> GSM872266 2 0.6623 0.939 0.172 0.828
#> GSM872267 2 0.4431 0.925 0.092 0.908
#> GSM872268 1 0.4431 0.903 0.908 0.092
#> GSM872269 2 0.8386 0.848 0.268 0.732
#> GSM872270 1 0.4431 0.903 0.908 0.092
#> GSM872271 2 0.6623 0.939 0.172 0.828
#> GSM872272 2 0.6623 0.939 0.172 0.828
#> GSM872273 1 0.1414 0.937 0.980 0.020
#> GSM872274 2 0.4431 0.925 0.092 0.908
#> GSM872275 1 0.1184 0.939 0.984 0.016
#> GSM872276 1 0.1414 0.937 0.980 0.020
#> GSM872277 1 0.1414 0.937 0.980 0.020
#> GSM872278 1 0.0938 0.941 0.988 0.012
#> GSM872279 1 0.0000 0.946 1.000 0.000
#> GSM872280 1 0.0000 0.946 1.000 0.000
#> GSM872281 1 0.7674 0.649 0.776 0.224
#> GSM872282 1 0.6247 0.848 0.844 0.156
#> GSM872283 2 0.6712 0.937 0.176 0.824
#> GSM872284 2 0.8386 0.834 0.268 0.732
#> GSM872285 1 0.0000 0.946 1.000 0.000
#> GSM872286 1 0.0000 0.946 1.000 0.000
#> GSM872287 1 0.4431 0.903 0.908 0.092
#> GSM872288 1 0.0000 0.946 1.000 0.000
#> GSM872289 1 0.1414 0.939 0.980 0.020
#> GSM872290 1 0.0000 0.946 1.000 0.000
#> GSM872291 1 0.0000 0.946 1.000 0.000
#> GSM872292 2 0.4431 0.925 0.092 0.908
#> GSM872293 1 0.0000 0.946 1.000 0.000
#> GSM872294 2 0.6531 0.939 0.168 0.832
#> GSM872295 2 0.4431 0.925 0.092 0.908
#> GSM872296 2 0.4431 0.925 0.092 0.908
#> GSM872297 1 0.0000 0.946 1.000 0.000
#> GSM872298 1 0.0938 0.941 0.988 0.012
#> GSM872299 1 0.0000 0.946 1.000 0.000
#> GSM872300 1 0.1414 0.937 0.980 0.020
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.955 0.000 0.000 1.000
#> GSM872245 1 0.3752 0.887 0.856 0.144 0.000
#> GSM872246 3 0.0000 0.955 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.955 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.806 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.955 0.000 0.000 1.000
#> GSM872250 1 0.3752 0.887 0.856 0.144 0.000
#> GSM872251 3 0.0000 0.955 0.000 0.000 1.000
#> GSM872252 1 0.3752 0.887 0.856 0.144 0.000
#> GSM872253 1 0.4209 0.888 0.860 0.120 0.020
#> GSM872254 2 0.3482 0.753 0.128 0.872 0.000
#> GSM872255 1 0.1411 0.907 0.964 0.036 0.000
#> GSM872256 1 0.3116 0.897 0.892 0.108 0.000
#> GSM872257 2 0.0000 0.806 0.000 1.000 0.000
#> GSM872258 3 0.0000 0.955 0.000 0.000 1.000
#> GSM872259 1 0.3752 0.887 0.856 0.144 0.000
#> GSM872260 1 0.3482 0.893 0.872 0.128 0.000
#> GSM872261 1 0.3752 0.887 0.856 0.144 0.000
#> GSM872262 1 0.0000 0.907 1.000 0.000 0.000
#> GSM872263 3 0.0000 0.955 0.000 0.000 1.000
#> GSM872264 1 0.0424 0.903 0.992 0.008 0.000
#> GSM872265 1 0.0237 0.905 0.996 0.004 0.000
#> GSM872266 2 0.4842 0.673 0.224 0.776 0.000
#> GSM872267 2 0.0000 0.806 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.955 0.000 0.000 1.000
#> GSM872269 2 0.6168 0.206 0.412 0.588 0.000
#> GSM872270 3 0.0000 0.955 0.000 0.000 1.000
#> GSM872271 1 0.2625 0.840 0.916 0.084 0.000
#> GSM872272 1 0.2796 0.830 0.908 0.092 0.000
#> GSM872273 1 0.0000 0.907 1.000 0.000 0.000
#> GSM872274 2 0.3752 0.759 0.144 0.856 0.000
#> GSM872275 1 0.0000 0.907 1.000 0.000 0.000
#> GSM872276 1 0.0000 0.907 1.000 0.000 0.000
#> GSM872277 1 0.0000 0.907 1.000 0.000 0.000
#> GSM872278 1 0.0000 0.907 1.000 0.000 0.000
#> GSM872279 1 0.3752 0.887 0.856 0.144 0.000
#> GSM872280 1 0.0000 0.907 1.000 0.000 0.000
#> GSM872281 1 0.0000 0.907 1.000 0.000 0.000
#> GSM872282 3 0.0000 0.955 0.000 0.000 1.000
#> GSM872283 1 0.0237 0.905 0.996 0.004 0.000
#> GSM872284 1 0.0000 0.907 1.000 0.000 0.000
#> GSM872285 1 0.2711 0.871 0.912 0.000 0.088
#> GSM872286 1 0.3752 0.887 0.856 0.144 0.000
#> GSM872287 3 0.0000 0.955 0.000 0.000 1.000
#> GSM872288 1 0.3752 0.887 0.856 0.144 0.000
#> GSM872289 3 0.6047 0.422 0.312 0.008 0.680
#> GSM872290 1 0.3752 0.887 0.856 0.144 0.000
#> GSM872291 1 0.1031 0.908 0.976 0.024 0.000
#> GSM872292 2 0.3752 0.759 0.144 0.856 0.000
#> GSM872293 1 0.3752 0.887 0.856 0.144 0.000
#> GSM872294 1 0.3686 0.767 0.860 0.140 0.000
#> GSM872295 2 0.0000 0.806 0.000 1.000 0.000
#> GSM872296 2 0.3752 0.759 0.144 0.856 0.000
#> GSM872297 1 0.3752 0.887 0.856 0.144 0.000
#> GSM872298 1 0.0000 0.907 1.000 0.000 0.000
#> GSM872299 1 0.3752 0.887 0.856 0.144 0.000
#> GSM872300 1 0.0000 0.907 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM872245 1 0.0188 0.758 0.996 0.004 0.000 0.000
#> GSM872246 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM872247 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM872248 2 0.4948 0.402 0.440 0.560 0.000 0.000
#> GSM872249 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM872250 1 0.0188 0.758 0.996 0.004 0.000 0.000
#> GSM872251 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM872252 1 0.4122 0.761 0.760 0.004 0.000 0.236
#> GSM872253 3 0.5827 0.123 0.024 0.004 0.536 0.436
#> GSM872254 1 0.0188 0.758 0.996 0.004 0.000 0.000
#> GSM872255 4 0.0000 0.878 0.000 0.000 0.000 1.000
#> GSM872256 4 0.3539 0.672 0.176 0.004 0.000 0.820
#> GSM872257 2 0.1389 0.843 0.048 0.952 0.000 0.000
#> GSM872258 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM872259 1 0.4222 0.746 0.728 0.000 0.000 0.272
#> GSM872260 4 0.0817 0.863 0.024 0.000 0.000 0.976
#> GSM872261 1 0.3539 0.771 0.820 0.004 0.000 0.176
#> GSM872262 4 0.0469 0.878 0.000 0.012 0.000 0.988
#> GSM872263 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM872264 4 0.1510 0.871 0.000 0.028 0.016 0.956
#> GSM872265 4 0.1510 0.871 0.000 0.028 0.016 0.956
#> GSM872266 1 0.4661 0.134 0.652 0.348 0.000 0.000
#> GSM872267 2 0.1389 0.843 0.048 0.952 0.000 0.000
#> GSM872268 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM872269 1 0.0188 0.758 0.996 0.004 0.000 0.000
#> GSM872270 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM872271 4 0.4843 0.360 0.000 0.396 0.000 0.604
#> GSM872272 4 0.4746 0.427 0.000 0.368 0.000 0.632
#> GSM872273 4 0.0000 0.878 0.000 0.000 0.000 1.000
#> GSM872274 2 0.0000 0.846 0.000 1.000 0.000 0.000
#> GSM872275 4 0.4313 0.616 0.000 0.004 0.260 0.736
#> GSM872276 4 0.0817 0.876 0.000 0.024 0.000 0.976
#> GSM872277 4 0.0000 0.878 0.000 0.000 0.000 1.000
#> GSM872278 4 0.2125 0.836 0.000 0.004 0.076 0.920
#> GSM872279 1 0.4250 0.744 0.724 0.000 0.000 0.276
#> GSM872280 4 0.0000 0.878 0.000 0.000 0.000 1.000
#> GSM872281 4 0.0817 0.876 0.000 0.024 0.000 0.976
#> GSM872282 3 0.0188 0.947 0.000 0.004 0.996 0.000
#> GSM872283 4 0.0921 0.875 0.000 0.028 0.000 0.972
#> GSM872284 4 0.0817 0.876 0.000 0.024 0.000 0.976
#> GSM872285 4 0.4624 0.479 0.000 0.000 0.340 0.660
#> GSM872286 1 0.0188 0.758 0.996 0.004 0.000 0.000
#> GSM872287 3 0.0000 0.950 0.000 0.000 1.000 0.000
#> GSM872288 1 0.4018 0.764 0.772 0.004 0.000 0.224
#> GSM872289 3 0.0524 0.940 0.000 0.004 0.988 0.008
#> GSM872290 1 0.4564 0.673 0.672 0.000 0.000 0.328
#> GSM872291 4 0.0000 0.878 0.000 0.000 0.000 1.000
#> GSM872292 2 0.0000 0.846 0.000 1.000 0.000 0.000
#> GSM872293 1 0.4250 0.744 0.724 0.000 0.000 0.276
#> GSM872294 2 0.3801 0.626 0.000 0.780 0.000 0.220
#> GSM872295 2 0.3610 0.714 0.200 0.800 0.000 0.000
#> GSM872296 2 0.0000 0.846 0.000 1.000 0.000 0.000
#> GSM872297 4 0.4500 0.367 0.316 0.000 0.000 0.684
#> GSM872298 4 0.0000 0.878 0.000 0.000 0.000 1.000
#> GSM872299 1 0.0188 0.758 0.996 0.004 0.000 0.000
#> GSM872300 4 0.0000 0.878 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.0000 0.9821 0.000 0.000 1.000 0.000 0.000
#> GSM872245 5 0.3561 0.7385 0.260 0.000 0.000 0.000 0.740
#> GSM872246 3 0.0000 0.9821 0.000 0.000 1.000 0.000 0.000
#> GSM872247 3 0.0000 0.9821 0.000 0.000 1.000 0.000 0.000
#> GSM872248 5 0.3274 0.3862 0.000 0.220 0.000 0.000 0.780
#> GSM872249 3 0.0000 0.9821 0.000 0.000 1.000 0.000 0.000
#> GSM872250 5 0.2424 0.7651 0.132 0.000 0.000 0.000 0.868
#> GSM872251 3 0.0000 0.9821 0.000 0.000 1.000 0.000 0.000
#> GSM872252 5 0.4434 0.4536 0.460 0.000 0.000 0.004 0.536
#> GSM872253 3 0.3674 0.7915 0.020 0.000 0.832 0.116 0.032
#> GSM872254 5 0.0510 0.7053 0.016 0.000 0.000 0.000 0.984
#> GSM872255 4 0.3636 0.6906 0.272 0.000 0.000 0.728 0.000
#> GSM872256 1 0.1124 0.9374 0.960 0.000 0.004 0.036 0.000
#> GSM872257 2 0.4060 0.5743 0.000 0.640 0.000 0.000 0.360
#> GSM872258 3 0.0162 0.9787 0.000 0.000 0.996 0.004 0.000
#> GSM872259 1 0.0510 0.9742 0.984 0.000 0.000 0.000 0.016
#> GSM872260 4 0.4287 0.3297 0.460 0.000 0.000 0.540 0.000
#> GSM872261 5 0.4867 0.6971 0.180 0.000 0.000 0.104 0.716
#> GSM872262 4 0.2230 0.8124 0.116 0.000 0.000 0.884 0.000
#> GSM872263 3 0.0000 0.9821 0.000 0.000 1.000 0.000 0.000
#> GSM872264 4 0.1278 0.7849 0.004 0.000 0.020 0.960 0.016
#> GSM872265 4 0.1278 0.7849 0.004 0.000 0.020 0.960 0.016
#> GSM872266 5 0.2251 0.7210 0.052 0.024 0.008 0.000 0.916
#> GSM872267 2 0.3109 0.6940 0.000 0.800 0.000 0.000 0.200
#> GSM872268 3 0.0000 0.9821 0.000 0.000 1.000 0.000 0.000
#> GSM872269 5 0.0510 0.7053 0.016 0.000 0.000 0.000 0.984
#> GSM872270 3 0.0000 0.9821 0.000 0.000 1.000 0.000 0.000
#> GSM872271 4 0.4737 0.5049 0.004 0.256 0.020 0.704 0.016
#> GSM872272 4 0.4762 0.4983 0.004 0.260 0.020 0.700 0.016
#> GSM872273 4 0.4287 0.2912 0.460 0.000 0.000 0.540 0.000
#> GSM872274 2 0.0000 0.7364 0.000 1.000 0.000 0.000 0.000
#> GSM872275 4 0.2020 0.7516 0.000 0.000 0.100 0.900 0.000
#> GSM872276 4 0.2230 0.8124 0.116 0.000 0.000 0.884 0.000
#> GSM872277 4 0.2230 0.8124 0.116 0.000 0.000 0.884 0.000
#> GSM872278 4 0.0963 0.7885 0.000 0.000 0.036 0.964 0.000
#> GSM872279 1 0.0510 0.9742 0.984 0.000 0.000 0.000 0.016
#> GSM872280 4 0.2230 0.8124 0.116 0.000 0.000 0.884 0.000
#> GSM872281 4 0.2144 0.8101 0.068 0.000 0.020 0.912 0.000
#> GSM872282 3 0.0000 0.9821 0.000 0.000 1.000 0.000 0.000
#> GSM872283 4 0.1117 0.7866 0.000 0.000 0.020 0.964 0.016
#> GSM872284 4 0.2012 0.8087 0.060 0.000 0.020 0.920 0.000
#> GSM872285 4 0.4161 0.4250 0.000 0.000 0.392 0.608 0.000
#> GSM872286 5 0.3424 0.7490 0.240 0.000 0.000 0.000 0.760
#> GSM872287 3 0.0000 0.9821 0.000 0.000 1.000 0.000 0.000
#> GSM872288 5 0.3961 0.7406 0.248 0.000 0.000 0.016 0.736
#> GSM872289 3 0.0510 0.9673 0.000 0.000 0.984 0.016 0.000
#> GSM872290 1 0.0162 0.9730 0.996 0.000 0.000 0.004 0.000
#> GSM872291 4 0.3612 0.6933 0.268 0.000 0.000 0.732 0.000
#> GSM872292 2 0.0000 0.7364 0.000 1.000 0.000 0.000 0.000
#> GSM872293 1 0.0510 0.9742 0.984 0.000 0.000 0.000 0.016
#> GSM872294 2 0.4446 -0.0339 0.004 0.520 0.000 0.476 0.000
#> GSM872295 2 0.4171 0.5411 0.000 0.604 0.000 0.000 0.396
#> GSM872296 2 0.0000 0.7364 0.000 1.000 0.000 0.000 0.000
#> GSM872297 1 0.0162 0.9730 0.996 0.000 0.000 0.004 0.000
#> GSM872298 4 0.2230 0.8124 0.116 0.000 0.000 0.884 0.000
#> GSM872299 5 0.4283 0.4692 0.456 0.000 0.000 0.000 0.544
#> GSM872300 4 0.2230 0.8124 0.116 0.000 0.000 0.884 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.0000 0.928 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872245 5 0.2260 0.836 0.140 0.000 0.000 0.000 0.860 0.000
#> GSM872246 3 0.0000 0.928 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872247 3 0.0000 0.928 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872248 2 0.3747 0.533 0.000 0.604 0.000 0.000 0.396 0.000
#> GSM872249 3 0.0000 0.928 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872250 5 0.1588 0.858 0.072 0.000 0.000 0.004 0.924 0.000
#> GSM872251 3 0.0790 0.914 0.000 0.000 0.968 0.032 0.000 0.000
#> GSM872252 5 0.4466 0.539 0.336 0.000 0.000 0.044 0.620 0.000
#> GSM872253 3 0.4804 0.709 0.000 0.000 0.728 0.096 0.132 0.044
#> GSM872254 5 0.1141 0.800 0.000 0.052 0.000 0.000 0.948 0.000
#> GSM872255 6 0.0806 0.950 0.008 0.000 0.000 0.020 0.000 0.972
#> GSM872256 1 0.3464 0.469 0.688 0.000 0.000 0.000 0.000 0.312
#> GSM872257 2 0.2340 0.836 0.000 0.852 0.000 0.000 0.148 0.000
#> GSM872258 3 0.1610 0.884 0.000 0.000 0.916 0.084 0.000 0.000
#> GSM872259 1 0.0000 0.832 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872260 6 0.2999 0.789 0.112 0.000 0.000 0.048 0.000 0.840
#> GSM872261 5 0.2896 0.806 0.016 0.000 0.000 0.160 0.824 0.000
#> GSM872262 6 0.0000 0.966 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872263 3 0.0000 0.928 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872264 4 0.3563 0.638 0.000 0.000 0.000 0.664 0.000 0.336
#> GSM872265 4 0.3515 0.650 0.000 0.000 0.000 0.676 0.000 0.324
#> GSM872266 5 0.0291 0.840 0.004 0.004 0.000 0.000 0.992 0.000
#> GSM872267 2 0.2980 0.831 0.000 0.808 0.000 0.012 0.180 0.000
#> GSM872268 3 0.0000 0.928 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872269 5 0.0000 0.838 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872270 3 0.0000 0.928 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872271 4 0.2511 0.684 0.000 0.056 0.000 0.880 0.000 0.064
#> GSM872272 4 0.2511 0.684 0.000 0.056 0.000 0.880 0.000 0.064
#> GSM872273 6 0.1267 0.906 0.060 0.000 0.000 0.000 0.000 0.940
#> GSM872274 2 0.1387 0.815 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM872275 4 0.4408 0.403 0.000 0.000 0.320 0.636 0.000 0.044
#> GSM872276 6 0.0000 0.966 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872277 6 0.0000 0.966 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872278 4 0.4871 0.631 0.000 0.000 0.196 0.660 0.000 0.144
#> GSM872279 1 0.0000 0.832 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872280 6 0.0547 0.953 0.000 0.000 0.000 0.020 0.000 0.980
#> GSM872281 6 0.0000 0.966 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872282 3 0.0000 0.928 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872283 4 0.3857 0.405 0.000 0.000 0.000 0.532 0.000 0.468
#> GSM872284 6 0.0000 0.966 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872285 3 0.4902 0.450 0.000 0.000 0.608 0.088 0.000 0.304
#> GSM872286 5 0.2178 0.841 0.132 0.000 0.000 0.000 0.868 0.000
#> GSM872287 3 0.0000 0.928 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872288 5 0.3274 0.830 0.096 0.000 0.000 0.080 0.824 0.000
#> GSM872289 3 0.2214 0.866 0.000 0.000 0.888 0.096 0.016 0.000
#> GSM872290 1 0.0000 0.832 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872291 6 0.0363 0.960 0.012 0.000 0.000 0.000 0.000 0.988
#> GSM872292 2 0.1387 0.815 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM872293 1 0.0000 0.832 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872294 4 0.2474 0.661 0.000 0.080 0.000 0.880 0.000 0.040
#> GSM872295 2 0.2664 0.825 0.000 0.816 0.000 0.000 0.184 0.000
#> GSM872296 2 0.1387 0.815 0.000 0.932 0.000 0.068 0.000 0.000
#> GSM872297 1 0.0000 0.832 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872298 6 0.0000 0.966 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872299 1 0.3862 -0.192 0.524 0.000 0.000 0.000 0.476 0.000
#> GSM872300 6 0.0000 0.966 0.000 0.000 0.000 0.000 0.000 1.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 time(p) individual(p) k
#> SD:mclust 57 0.377 0.234717 2
#> SD:mclust 55 0.612 0.000501 3
#> SD:mclust 50 0.251 0.000411 4
#> SD:mclust 49 0.262 0.005321 5
#> SD:mclust 52 0.198 0.002496 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 29485 rows and 57 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 0.516 0.757 0.874 0.4676 0.491 0.491
#> 3 3 0.874 0.911 0.961 0.4214 0.682 0.443
#> 4 4 0.658 0.640 0.795 0.1137 0.905 0.728
#> 5 5 0.699 0.702 0.818 0.0715 0.898 0.651
#> 6 6 0.652 0.591 0.732 0.0439 0.888 0.550
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
#> GSM872244 1 0.3274 0.867 0.940 0.060
#> GSM872245 2 0.7883 0.742 0.236 0.764
#> GSM872246 1 0.0000 0.914 1.000 0.000
#> GSM872247 1 0.0000 0.914 1.000 0.000
#> GSM872248 2 0.0000 0.763 0.000 1.000
#> GSM872249 1 0.2778 0.880 0.952 0.048
#> GSM872250 2 0.7815 0.739 0.232 0.768
#> GSM872251 1 0.0000 0.914 1.000 0.000
#> GSM872252 2 0.9491 0.676 0.368 0.632
#> GSM872253 1 0.2236 0.895 0.964 0.036
#> GSM872254 2 0.0000 0.763 0.000 1.000
#> GSM872255 1 0.0000 0.914 1.000 0.000
#> GSM872256 2 0.9358 0.696 0.352 0.648
#> GSM872257 2 0.0000 0.763 0.000 1.000
#> GSM872258 1 0.0000 0.914 1.000 0.000
#> GSM872259 2 0.9358 0.696 0.352 0.648
#> GSM872260 1 0.9129 0.262 0.672 0.328
#> GSM872261 2 0.7376 0.745 0.208 0.792
#> GSM872262 1 0.0000 0.914 1.000 0.000
#> GSM872263 1 0.1184 0.905 0.984 0.016
#> GSM872264 1 0.0000 0.914 1.000 0.000
#> GSM872265 1 0.9988 -0.351 0.520 0.480
#> GSM872266 2 0.0000 0.763 0.000 1.000
#> GSM872267 2 0.0000 0.763 0.000 1.000
#> GSM872268 1 0.0000 0.914 1.000 0.000
#> GSM872269 2 0.1184 0.763 0.016 0.984
#> GSM872270 1 0.2603 0.883 0.956 0.044
#> GSM872271 2 0.0000 0.763 0.000 1.000
#> GSM872272 2 0.0000 0.763 0.000 1.000
#> GSM872273 2 0.9754 0.606 0.408 0.592
#> GSM872274 2 0.0000 0.763 0.000 1.000
#> GSM872275 1 0.2778 0.880 0.952 0.048
#> GSM872276 1 0.0000 0.914 1.000 0.000
#> GSM872277 2 0.9996 0.409 0.488 0.512
#> GSM872278 1 0.0000 0.914 1.000 0.000
#> GSM872279 2 0.9358 0.696 0.352 0.648
#> GSM872280 1 0.0000 0.914 1.000 0.000
#> GSM872281 1 0.0000 0.914 1.000 0.000
#> GSM872282 1 0.8144 0.598 0.748 0.252
#> GSM872283 2 0.9635 0.643 0.388 0.612
#> GSM872284 1 0.0000 0.914 1.000 0.000
#> GSM872285 1 0.0000 0.914 1.000 0.000
#> GSM872286 2 0.9248 0.703 0.340 0.660
#> GSM872287 1 0.0000 0.914 1.000 0.000
#> GSM872288 2 0.9460 0.681 0.364 0.636
#> GSM872289 1 0.0000 0.914 1.000 0.000
#> GSM872290 2 0.9393 0.691 0.356 0.644
#> GSM872291 1 0.9393 0.156 0.644 0.356
#> GSM872292 2 0.0000 0.763 0.000 1.000
#> GSM872293 2 0.9358 0.696 0.352 0.648
#> GSM872294 2 0.0000 0.763 0.000 1.000
#> GSM872295 2 0.0000 0.763 0.000 1.000
#> GSM872296 2 0.0000 0.763 0.000 1.000
#> GSM872297 2 0.9393 0.691 0.356 0.644
#> GSM872298 1 0.0000 0.914 1.000 0.000
#> GSM872299 2 0.9286 0.701 0.344 0.656
#> GSM872300 1 0.0672 0.909 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.978 0.000 0.000 1.000
#> GSM872245 1 0.1031 0.927 0.976 0.024 0.000
#> GSM872246 3 0.0000 0.978 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.978 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.940 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.978 0.000 0.000 1.000
#> GSM872250 2 0.5988 0.490 0.368 0.632 0.000
#> GSM872251 3 0.0000 0.978 0.000 0.000 1.000
#> GSM872252 1 0.0000 0.947 1.000 0.000 0.000
#> GSM872253 3 0.4002 0.802 0.160 0.000 0.840
#> GSM872254 2 0.1529 0.917 0.040 0.960 0.000
#> GSM872255 1 0.0000 0.947 1.000 0.000 0.000
#> GSM872256 1 0.0000 0.947 1.000 0.000 0.000
#> GSM872257 2 0.0000 0.940 0.000 1.000 0.000
#> GSM872258 3 0.0000 0.978 0.000 0.000 1.000
#> GSM872259 1 0.0000 0.947 1.000 0.000 0.000
#> GSM872260 1 0.0000 0.947 1.000 0.000 0.000
#> GSM872261 2 0.5363 0.661 0.276 0.724 0.000
#> GSM872262 1 0.2066 0.902 0.940 0.000 0.060
#> GSM872263 3 0.0000 0.978 0.000 0.000 1.000
#> GSM872264 3 0.0000 0.978 0.000 0.000 1.000
#> GSM872265 1 0.6735 0.283 0.564 0.012 0.424
#> GSM872266 2 0.0000 0.940 0.000 1.000 0.000
#> GSM872267 2 0.0000 0.940 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.978 0.000 0.000 1.000
#> GSM872269 2 0.3551 0.841 0.132 0.868 0.000
#> GSM872270 3 0.0000 0.978 0.000 0.000 1.000
#> GSM872271 2 0.0000 0.940 0.000 1.000 0.000
#> GSM872272 2 0.0000 0.940 0.000 1.000 0.000
#> GSM872273 1 0.0000 0.947 1.000 0.000 0.000
#> GSM872274 2 0.0000 0.940 0.000 1.000 0.000
#> GSM872275 3 0.0000 0.978 0.000 0.000 1.000
#> GSM872276 1 0.0747 0.937 0.984 0.000 0.016
#> GSM872277 1 0.0000 0.947 1.000 0.000 0.000
#> GSM872278 3 0.0000 0.978 0.000 0.000 1.000
#> GSM872279 1 0.0000 0.947 1.000 0.000 0.000
#> GSM872280 3 0.0424 0.972 0.008 0.000 0.992
#> GSM872281 3 0.3267 0.861 0.116 0.000 0.884
#> GSM872282 3 0.0000 0.978 0.000 0.000 1.000
#> GSM872283 1 0.1031 0.932 0.976 0.000 0.024
#> GSM872284 1 0.5948 0.468 0.640 0.000 0.360
#> GSM872285 3 0.0000 0.978 0.000 0.000 1.000
#> GSM872286 1 0.0000 0.947 1.000 0.000 0.000
#> GSM872287 3 0.0000 0.978 0.000 0.000 1.000
#> GSM872288 1 0.0000 0.947 1.000 0.000 0.000
#> GSM872289 3 0.1964 0.928 0.056 0.000 0.944
#> GSM872290 1 0.0000 0.947 1.000 0.000 0.000
#> GSM872291 1 0.0000 0.947 1.000 0.000 0.000
#> GSM872292 2 0.0000 0.940 0.000 1.000 0.000
#> GSM872293 1 0.0000 0.947 1.000 0.000 0.000
#> GSM872294 2 0.0000 0.940 0.000 1.000 0.000
#> GSM872295 2 0.0000 0.940 0.000 1.000 0.000
#> GSM872296 2 0.0000 0.940 0.000 1.000 0.000
#> GSM872297 1 0.0000 0.947 1.000 0.000 0.000
#> GSM872298 1 0.3340 0.845 0.880 0.000 0.120
#> GSM872299 1 0.0000 0.947 1.000 0.000 0.000
#> GSM872300 1 0.0000 0.947 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0469 0.8147 0.000 0.000 0.988 0.012
#> GSM872245 1 0.2385 0.5777 0.920 0.052 0.000 0.028
#> GSM872246 3 0.1389 0.8289 0.000 0.000 0.952 0.048
#> GSM872247 3 0.3123 0.8239 0.000 0.000 0.844 0.156
#> GSM872248 2 0.4561 0.7243 0.176 0.788 0.008 0.028
#> GSM872249 3 0.0000 0.8194 0.000 0.000 1.000 0.000
#> GSM872250 1 0.7900 -0.0172 0.480 0.140 0.352 0.028
#> GSM872251 3 0.0817 0.8252 0.000 0.000 0.976 0.024
#> GSM872252 1 0.0000 0.6285 1.000 0.000 0.000 0.000
#> GSM872253 3 0.2342 0.7651 0.080 0.000 0.912 0.008
#> GSM872254 2 0.7401 0.6028 0.244 0.592 0.136 0.028
#> GSM872255 1 0.3907 0.6997 0.768 0.000 0.000 0.232
#> GSM872256 1 0.3569 0.7154 0.804 0.000 0.000 0.196
#> GSM872257 2 0.0000 0.7789 0.000 1.000 0.000 0.000
#> GSM872258 3 0.1452 0.8269 0.008 0.000 0.956 0.036
#> GSM872259 1 0.3486 0.7152 0.812 0.000 0.000 0.188
#> GSM872260 1 0.3688 0.7115 0.792 0.000 0.000 0.208
#> GSM872261 2 0.5427 0.4981 0.416 0.568 0.000 0.016
#> GSM872262 4 0.5126 0.0281 0.444 0.000 0.004 0.552
#> GSM872263 3 0.0188 0.8208 0.000 0.000 0.996 0.004
#> GSM872264 4 0.3401 0.3704 0.000 0.008 0.152 0.840
#> GSM872265 4 0.3556 0.5736 0.036 0.096 0.004 0.864
#> GSM872266 2 0.4742 0.7095 0.208 0.760 0.004 0.028
#> GSM872267 2 0.1151 0.7778 0.024 0.968 0.000 0.008
#> GSM872268 3 0.3123 0.8239 0.000 0.000 0.844 0.156
#> GSM872269 2 0.6896 0.6177 0.272 0.616 0.088 0.024
#> GSM872270 3 0.4382 0.7664 0.000 0.000 0.704 0.296
#> GSM872271 2 0.4761 0.4707 0.000 0.628 0.000 0.372
#> GSM872272 2 0.4730 0.4824 0.000 0.636 0.000 0.364
#> GSM872273 1 0.4164 0.6737 0.736 0.000 0.000 0.264
#> GSM872274 2 0.1389 0.7713 0.000 0.952 0.000 0.048
#> GSM872275 3 0.4175 0.8066 0.000 0.012 0.776 0.212
#> GSM872276 1 0.5097 0.3141 0.568 0.000 0.004 0.428
#> GSM872277 1 0.4222 0.6718 0.728 0.000 0.000 0.272
#> GSM872278 3 0.4925 0.6318 0.000 0.000 0.572 0.428
#> GSM872279 1 0.2281 0.6842 0.904 0.000 0.000 0.096
#> GSM872280 3 0.7258 0.4077 0.164 0.000 0.508 0.328
#> GSM872281 4 0.2965 0.6213 0.072 0.000 0.036 0.892
#> GSM872282 3 0.4643 0.7198 0.000 0.000 0.656 0.344
#> GSM872283 4 0.5299 0.1978 0.388 0.008 0.004 0.600
#> GSM872284 4 0.4446 0.5709 0.196 0.000 0.028 0.776
#> GSM872285 3 0.5519 0.7451 0.052 0.000 0.684 0.264
#> GSM872286 1 0.3978 0.5150 0.860 0.048 0.064 0.028
#> GSM872287 3 0.4164 0.7857 0.000 0.000 0.736 0.264
#> GSM872288 1 0.4164 0.4949 0.844 0.036 0.096 0.024
#> GSM872289 3 0.1256 0.8030 0.028 0.000 0.964 0.008
#> GSM872290 1 0.3528 0.7159 0.808 0.000 0.000 0.192
#> GSM872291 1 0.4040 0.6878 0.752 0.000 0.000 0.248
#> GSM872292 2 0.1389 0.7713 0.000 0.952 0.000 0.048
#> GSM872293 1 0.3400 0.7153 0.820 0.000 0.000 0.180
#> GSM872294 2 0.2704 0.7368 0.000 0.876 0.000 0.124
#> GSM872295 2 0.0524 0.7793 0.004 0.988 0.000 0.008
#> GSM872296 2 0.2081 0.7593 0.000 0.916 0.000 0.084
#> GSM872297 1 0.3975 0.6984 0.760 0.000 0.000 0.240
#> GSM872298 1 0.5273 0.2084 0.536 0.000 0.008 0.456
#> GSM872299 1 0.1677 0.5911 0.948 0.040 0.000 0.012
#> GSM872300 1 0.4677 0.5940 0.680 0.000 0.004 0.316
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.3201 0.7819 0.000 0.000 0.852 0.096 0.052
#> GSM872245 5 0.2782 0.7837 0.048 0.000 0.000 0.072 0.880
#> GSM872246 3 0.0510 0.8314 0.000 0.000 0.984 0.016 0.000
#> GSM872247 3 0.2077 0.8286 0.000 0.000 0.908 0.084 0.008
#> GSM872248 5 0.3526 0.7891 0.000 0.096 0.000 0.072 0.832
#> GSM872249 3 0.2654 0.7970 0.000 0.000 0.884 0.084 0.032
#> GSM872250 5 0.5016 0.6081 0.016 0.000 0.160 0.092 0.732
#> GSM872251 3 0.1915 0.8159 0.000 0.000 0.928 0.032 0.040
#> GSM872252 1 0.2079 0.7981 0.916 0.000 0.000 0.020 0.064
#> GSM872253 3 0.6859 0.5432 0.212 0.004 0.596 0.092 0.096
#> GSM872254 2 0.7546 0.2443 0.008 0.468 0.092 0.104 0.328
#> GSM872255 1 0.0912 0.8213 0.972 0.000 0.016 0.012 0.000
#> GSM872256 1 0.2376 0.8145 0.904 0.000 0.000 0.044 0.052
#> GSM872257 2 0.0404 0.8495 0.000 0.988 0.000 0.000 0.012
#> GSM872258 3 0.1278 0.8297 0.020 0.000 0.960 0.016 0.004
#> GSM872259 1 0.2648 0.7588 0.848 0.000 0.000 0.000 0.152
#> GSM872260 1 0.0798 0.8243 0.976 0.000 0.008 0.016 0.000
#> GSM872261 2 0.5280 0.5873 0.240 0.676 0.000 0.012 0.072
#> GSM872262 4 0.5534 0.1196 0.424 0.000 0.068 0.508 0.000
#> GSM872263 3 0.2946 0.7910 0.000 0.000 0.868 0.088 0.044
#> GSM872264 4 0.4625 0.6279 0.000 0.008 0.036 0.712 0.244
#> GSM872265 4 0.4330 0.6527 0.016 0.008 0.024 0.776 0.176
#> GSM872266 5 0.2989 0.7931 0.000 0.060 0.000 0.072 0.868
#> GSM872267 5 0.3966 0.7696 0.000 0.132 0.000 0.072 0.796
#> GSM872268 3 0.2424 0.8179 0.000 0.000 0.868 0.132 0.000
#> GSM872269 2 0.4774 0.7349 0.064 0.780 0.008 0.032 0.116
#> GSM872270 3 0.2984 0.8266 0.000 0.000 0.860 0.108 0.032
#> GSM872271 4 0.5296 0.5225 0.000 0.280 0.000 0.636 0.084
#> GSM872272 4 0.5026 0.5844 0.000 0.064 0.000 0.656 0.280
#> GSM872273 1 0.4768 0.5072 0.656 0.000 0.000 0.304 0.040
#> GSM872274 2 0.0162 0.8513 0.000 0.996 0.000 0.000 0.004
#> GSM872275 3 0.3517 0.8240 0.016 0.004 0.844 0.112 0.024
#> GSM872276 1 0.4323 0.4791 0.656 0.000 0.012 0.332 0.000
#> GSM872277 4 0.6032 0.0551 0.424 0.000 0.000 0.460 0.116
#> GSM872278 3 0.4651 0.6845 0.016 0.008 0.680 0.292 0.004
#> GSM872279 1 0.1082 0.8252 0.964 0.000 0.000 0.008 0.028
#> GSM872280 3 0.5713 0.2318 0.416 0.000 0.500 0.084 0.000
#> GSM872281 4 0.3975 0.5771 0.064 0.000 0.144 0.792 0.000
#> GSM872282 3 0.3484 0.8228 0.000 0.004 0.824 0.144 0.028
#> GSM872283 4 0.4477 0.6094 0.016 0.008 0.000 0.688 0.288
#> GSM872284 4 0.5105 0.6404 0.040 0.000 0.104 0.748 0.108
#> GSM872285 3 0.3482 0.7964 0.012 0.000 0.812 0.168 0.008
#> GSM872286 5 0.2470 0.7581 0.104 0.000 0.000 0.012 0.884
#> GSM872287 3 0.2971 0.8064 0.000 0.000 0.836 0.156 0.008
#> GSM872288 5 0.2645 0.7655 0.096 0.000 0.012 0.008 0.884
#> GSM872289 3 0.4020 0.7433 0.000 0.000 0.796 0.108 0.096
#> GSM872290 1 0.0992 0.8291 0.968 0.000 0.000 0.008 0.024
#> GSM872291 1 0.1012 0.8290 0.968 0.000 0.000 0.020 0.012
#> GSM872292 2 0.0162 0.8509 0.000 0.996 0.000 0.004 0.000
#> GSM872293 1 0.0963 0.8269 0.964 0.000 0.000 0.000 0.036
#> GSM872294 2 0.0290 0.8500 0.000 0.992 0.000 0.008 0.000
#> GSM872295 2 0.0290 0.8505 0.000 0.992 0.000 0.000 0.008
#> GSM872296 2 0.1205 0.8299 0.000 0.956 0.000 0.040 0.004
#> GSM872297 1 0.3749 0.7558 0.816 0.000 0.000 0.080 0.104
#> GSM872298 1 0.5086 0.4390 0.636 0.000 0.060 0.304 0.000
#> GSM872299 1 0.2046 0.7956 0.916 0.000 0.000 0.016 0.068
#> GSM872300 1 0.4153 0.6399 0.740 0.000 0.016 0.236 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.4377 0.7540 0.000 0.000 0.716 0.016 0.048 0.220
#> GSM872245 5 0.6332 0.3846 0.300 0.000 0.000 0.092 0.520 0.088
#> GSM872246 3 0.1503 0.8504 0.008 0.000 0.944 0.000 0.016 0.032
#> GSM872247 3 0.0870 0.8447 0.012 0.000 0.972 0.004 0.000 0.012
#> GSM872248 5 0.3105 0.7320 0.000 0.080 0.000 0.064 0.848 0.008
#> GSM872249 3 0.2279 0.8443 0.000 0.000 0.900 0.004 0.048 0.048
#> GSM872250 5 0.4005 0.6739 0.016 0.000 0.052 0.008 0.788 0.136
#> GSM872251 3 0.3032 0.8356 0.008 0.000 0.864 0.016 0.080 0.032
#> GSM872252 6 0.4238 0.2758 0.340 0.000 0.000 0.008 0.016 0.636
#> GSM872253 6 0.4758 0.4691 0.040 0.012 0.108 0.056 0.016 0.768
#> GSM872254 6 0.6663 0.1770 0.004 0.260 0.024 0.008 0.232 0.472
#> GSM872255 1 0.2463 0.5559 0.888 0.000 0.024 0.004 0.004 0.080
#> GSM872256 1 0.3407 0.5447 0.820 0.000 0.004 0.008 0.132 0.036
#> GSM872257 2 0.1812 0.8860 0.000 0.912 0.000 0.008 0.080 0.000
#> GSM872258 3 0.4025 0.6188 0.016 0.000 0.668 0.000 0.004 0.312
#> GSM872259 1 0.4171 0.5320 0.776 0.000 0.000 0.048 0.132 0.044
#> GSM872260 1 0.3989 0.0134 0.528 0.000 0.000 0.004 0.000 0.468
#> GSM872261 6 0.7048 0.5119 0.128 0.212 0.000 0.032 0.096 0.532
#> GSM872262 1 0.6113 0.0835 0.504 0.000 0.088 0.348 0.000 0.060
#> GSM872263 3 0.3487 0.8027 0.000 0.000 0.788 0.000 0.044 0.168
#> GSM872264 4 0.3724 0.6806 0.000 0.004 0.032 0.816 0.108 0.040
#> GSM872265 4 0.4843 0.6856 0.072 0.016 0.028 0.776 0.056 0.052
#> GSM872266 5 0.1657 0.7516 0.000 0.016 0.000 0.056 0.928 0.000
#> GSM872267 5 0.4702 0.6744 0.000 0.164 0.000 0.080 0.724 0.032
#> GSM872268 3 0.1794 0.8353 0.024 0.000 0.932 0.016 0.000 0.028
#> GSM872269 6 0.6219 0.3432 0.028 0.340 0.000 0.004 0.140 0.488
#> GSM872270 3 0.2036 0.8364 0.000 0.000 0.916 0.048 0.008 0.028
#> GSM872271 4 0.3840 0.6514 0.000 0.136 0.000 0.788 0.064 0.012
#> GSM872272 4 0.3897 0.6271 0.000 0.048 0.000 0.772 0.168 0.012
#> GSM872273 1 0.3668 0.5647 0.824 0.000 0.020 0.108 0.024 0.024
#> GSM872274 2 0.0146 0.9504 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM872275 3 0.5973 0.6646 0.040 0.036 0.696 0.120 0.052 0.056
#> GSM872276 1 0.5453 0.2258 0.544 0.000 0.008 0.340 0.000 0.108
#> GSM872277 1 0.5877 0.4190 0.640 0.000 0.012 0.192 0.084 0.072
#> GSM872278 4 0.5511 0.5570 0.020 0.012 0.188 0.652 0.000 0.128
#> GSM872279 1 0.3023 0.4596 0.784 0.000 0.000 0.004 0.000 0.212
#> GSM872280 1 0.7217 0.0346 0.356 0.000 0.284 0.088 0.000 0.272
#> GSM872281 4 0.5426 0.6102 0.112 0.000 0.180 0.668 0.008 0.032
#> GSM872282 3 0.3622 0.8144 0.000 0.000 0.792 0.024 0.020 0.164
#> GSM872283 4 0.4629 0.6429 0.056 0.004 0.004 0.764 0.104 0.068
#> GSM872284 4 0.5564 0.6475 0.132 0.000 0.116 0.684 0.052 0.016
#> GSM872285 3 0.2886 0.8072 0.060 0.000 0.876 0.028 0.004 0.032
#> GSM872286 5 0.3278 0.6884 0.152 0.000 0.000 0.000 0.808 0.040
#> GSM872287 3 0.2339 0.8297 0.028 0.000 0.908 0.024 0.004 0.036
#> GSM872288 5 0.4734 0.7109 0.056 0.000 0.024 0.056 0.764 0.100
#> GSM872289 3 0.3823 0.7907 0.000 0.000 0.764 0.004 0.048 0.184
#> GSM872290 1 0.4356 0.0773 0.548 0.000 0.000 0.016 0.004 0.432
#> GSM872291 6 0.5576 0.0791 0.376 0.000 0.000 0.144 0.000 0.480
#> GSM872292 2 0.0405 0.9505 0.000 0.988 0.000 0.004 0.000 0.008
#> GSM872293 1 0.2081 0.5689 0.916 0.000 0.000 0.012 0.036 0.036
#> GSM872294 2 0.0858 0.9417 0.000 0.968 0.000 0.028 0.004 0.000
#> GSM872295 2 0.0622 0.9468 0.000 0.980 0.000 0.000 0.012 0.008
#> GSM872296 2 0.1524 0.9141 0.000 0.932 0.000 0.060 0.000 0.008
#> GSM872297 1 0.4167 0.5376 0.784 0.000 0.000 0.080 0.096 0.040
#> GSM872298 4 0.6786 0.2162 0.252 0.000 0.076 0.476 0.000 0.196
#> GSM872299 1 0.4072 0.0312 0.544 0.000 0.000 0.008 0.000 0.448
#> GSM872300 1 0.3524 0.5582 0.832 0.000 0.040 0.076 0.000 0.052
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 time(p) individual(p) k
#> SD:NMF 53 0.677 6.64e-03 2
#> SD:NMF 54 0.341 3.30e-02 3
#> SD:NMF 46 0.598 2.06e-03 4
#> SD:NMF 51 0.290 3.27e-04 5
#> SD:NMF 42 0.183 4.56e-07 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 29485 rows and 57 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 0.425 0.669 0.853 0.3783 0.683 0.683
#> 3 3 0.654 0.711 0.881 0.5057 0.704 0.576
#> 4 4 0.477 0.496 0.741 0.1738 0.852 0.672
#> 5 5 0.642 0.669 0.808 0.1254 0.763 0.414
#> 6 6 0.656 0.640 0.781 0.0568 0.929 0.711
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
#> GSM872244 1 0.9580 0.5342 0.620 0.380
#> GSM872245 1 0.0000 0.8045 1.000 0.000
#> GSM872246 1 0.9248 0.5837 0.660 0.340
#> GSM872247 1 0.9580 0.5342 0.620 0.380
#> GSM872248 2 0.0000 0.7952 0.000 1.000
#> GSM872249 1 0.9580 0.5342 0.620 0.380
#> GSM872250 1 0.0000 0.8045 1.000 0.000
#> GSM872251 1 0.9580 0.5342 0.620 0.380
#> GSM872252 1 0.0000 0.8045 1.000 0.000
#> GSM872253 1 0.1184 0.7989 0.984 0.016
#> GSM872254 2 0.9358 0.4735 0.352 0.648
#> GSM872255 1 0.0000 0.8045 1.000 0.000
#> GSM872256 1 0.0000 0.8045 1.000 0.000
#> GSM872257 2 0.0000 0.7952 0.000 1.000
#> GSM872258 1 0.7528 0.6964 0.784 0.216
#> GSM872259 1 0.0000 0.8045 1.000 0.000
#> GSM872260 1 0.0000 0.8045 1.000 0.000
#> GSM872261 1 0.9491 0.3790 0.632 0.368
#> GSM872262 1 0.0000 0.8045 1.000 0.000
#> GSM872263 1 0.9580 0.5342 0.620 0.380
#> GSM872264 1 0.8861 0.6132 0.696 0.304
#> GSM872265 1 0.8861 0.6132 0.696 0.304
#> GSM872266 1 0.9661 0.3414 0.608 0.392
#> GSM872267 2 0.0000 0.7952 0.000 1.000
#> GSM872268 1 0.9580 0.5342 0.620 0.380
#> GSM872269 2 0.9323 0.4799 0.348 0.652
#> GSM872270 1 0.9580 0.5342 0.620 0.380
#> GSM872271 2 0.9970 -0.0888 0.468 0.532
#> GSM872272 2 0.9970 -0.0888 0.468 0.532
#> GSM872273 1 0.0000 0.8045 1.000 0.000
#> GSM872274 2 0.0000 0.7952 0.000 1.000
#> GSM872275 1 0.3114 0.7670 0.944 0.056
#> GSM872276 1 0.0000 0.8045 1.000 0.000
#> GSM872277 1 0.0000 0.8045 1.000 0.000
#> GSM872278 1 0.0376 0.8035 0.996 0.004
#> GSM872279 1 0.0000 0.8045 1.000 0.000
#> GSM872280 1 0.0000 0.8045 1.000 0.000
#> GSM872281 1 0.0000 0.8045 1.000 0.000
#> GSM872282 1 0.9580 0.5342 0.620 0.380
#> GSM872283 1 0.8861 0.6132 0.696 0.304
#> GSM872284 1 0.7139 0.7091 0.804 0.196
#> GSM872285 1 0.7602 0.6949 0.780 0.220
#> GSM872286 1 0.0000 0.8045 1.000 0.000
#> GSM872287 1 0.9580 0.5342 0.620 0.380
#> GSM872288 1 0.0000 0.8045 1.000 0.000
#> GSM872289 1 0.7602 0.6933 0.780 0.220
#> GSM872290 1 0.0000 0.8045 1.000 0.000
#> GSM872291 1 0.0000 0.8045 1.000 0.000
#> GSM872292 2 0.0000 0.7952 0.000 1.000
#> GSM872293 1 0.0000 0.8045 1.000 0.000
#> GSM872294 1 0.9710 0.1616 0.600 0.400
#> GSM872295 2 0.0000 0.7952 0.000 1.000
#> GSM872296 2 0.0000 0.7952 0.000 1.000
#> GSM872297 1 0.0000 0.8045 1.000 0.000
#> GSM872298 1 0.0376 0.8035 0.996 0.004
#> GSM872299 1 0.0000 0.8045 1.000 0.000
#> GSM872300 1 0.0000 0.8045 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.732 0.000 0.000 1.000
#> GSM872245 1 0.0000 0.875 1.000 0.000 0.000
#> GSM872246 3 0.5678 0.527 0.316 0.000 0.684
#> GSM872247 3 0.0000 0.732 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.880 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.732 0.000 0.000 1.000
#> GSM872250 1 0.0000 0.875 1.000 0.000 0.000
#> GSM872251 3 0.0000 0.732 0.000 0.000 1.000
#> GSM872252 1 0.0000 0.875 1.000 0.000 0.000
#> GSM872253 1 0.2384 0.855 0.936 0.008 0.056
#> GSM872254 2 0.5905 0.523 0.352 0.648 0.000
#> GSM872255 1 0.0592 0.875 0.988 0.000 0.012
#> GSM872256 1 0.0592 0.875 0.988 0.000 0.012
#> GSM872257 2 0.0000 0.880 0.000 1.000 0.000
#> GSM872258 3 0.6244 0.303 0.440 0.000 0.560
#> GSM872259 1 0.0000 0.875 1.000 0.000 0.000
#> GSM872260 1 0.0592 0.875 0.988 0.000 0.012
#> GSM872261 1 0.8907 0.337 0.572 0.228 0.200
#> GSM872262 1 0.1529 0.868 0.960 0.000 0.040
#> GSM872263 3 0.0000 0.732 0.000 0.000 1.000
#> GSM872264 1 0.6079 0.314 0.612 0.000 0.388
#> GSM872265 1 0.6079 0.314 0.612 0.000 0.388
#> GSM872266 1 0.9119 0.279 0.548 0.228 0.224
#> GSM872267 2 0.0000 0.880 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.732 0.000 0.000 1.000
#> GSM872269 2 0.5882 0.531 0.348 0.652 0.000
#> GSM872270 3 0.0000 0.732 0.000 0.000 1.000
#> GSM872271 3 0.9757 0.107 0.384 0.228 0.388
#> GSM872272 3 0.9757 0.107 0.384 0.228 0.388
#> GSM872273 1 0.0000 0.875 1.000 0.000 0.000
#> GSM872274 2 0.0000 0.880 0.000 1.000 0.000
#> GSM872275 1 0.3692 0.829 0.896 0.048 0.056
#> GSM872276 1 0.1529 0.868 0.960 0.000 0.040
#> GSM872277 1 0.0000 0.875 1.000 0.000 0.000
#> GSM872278 1 0.1643 0.866 0.956 0.000 0.044
#> GSM872279 1 0.0000 0.875 1.000 0.000 0.000
#> GSM872280 1 0.1529 0.868 0.960 0.000 0.040
#> GSM872281 1 0.1529 0.868 0.960 0.000 0.040
#> GSM872282 3 0.0000 0.732 0.000 0.000 1.000
#> GSM872283 1 0.6079 0.314 0.612 0.000 0.388
#> GSM872284 1 0.5397 0.553 0.720 0.000 0.280
#> GSM872285 3 0.6079 0.414 0.388 0.000 0.612
#> GSM872286 1 0.0000 0.875 1.000 0.000 0.000
#> GSM872287 3 0.0000 0.732 0.000 0.000 1.000
#> GSM872288 1 0.0000 0.875 1.000 0.000 0.000
#> GSM872289 3 0.6225 0.324 0.432 0.000 0.568
#> GSM872290 1 0.0000 0.875 1.000 0.000 0.000
#> GSM872291 1 0.1529 0.868 0.960 0.000 0.040
#> GSM872292 2 0.0000 0.880 0.000 1.000 0.000
#> GSM872293 1 0.0000 0.875 1.000 0.000 0.000
#> GSM872294 1 0.6513 0.217 0.592 0.400 0.008
#> GSM872295 2 0.0000 0.880 0.000 1.000 0.000
#> GSM872296 2 0.0000 0.880 0.000 1.000 0.000
#> GSM872297 1 0.0000 0.875 1.000 0.000 0.000
#> GSM872298 1 0.1643 0.866 0.956 0.000 0.044
#> GSM872299 1 0.0000 0.875 1.000 0.000 0.000
#> GSM872300 1 0.1529 0.868 0.960 0.000 0.040
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.000 0.5840 0.000 0.000 1.000 0.000
#> GSM872245 1 0.441 0.4180 0.700 0.000 0.000 0.300
#> GSM872246 3 0.534 0.4246 0.300 0.000 0.668 0.032
#> GSM872247 3 0.000 0.5840 0.000 0.000 1.000 0.000
#> GSM872248 2 0.483 0.7498 0.000 0.608 0.000 0.392
#> GSM872249 3 0.000 0.5840 0.000 0.000 1.000 0.000
#> GSM872250 1 0.438 0.4236 0.704 0.000 0.000 0.296
#> GSM872251 3 0.000 0.5840 0.000 0.000 1.000 0.000
#> GSM872252 1 0.307 0.6004 0.848 0.000 0.000 0.152
#> GSM872253 1 0.526 0.6690 0.684 0.004 0.024 0.288
#> GSM872254 4 0.567 -0.2198 0.056 0.276 0.000 0.668
#> GSM872255 1 0.436 0.6905 0.744 0.000 0.008 0.248
#> GSM872256 1 0.292 0.6924 0.876 0.000 0.008 0.116
#> GSM872257 2 0.483 0.7498 0.000 0.608 0.000 0.392
#> GSM872258 3 0.610 0.2429 0.420 0.000 0.532 0.048
#> GSM872259 1 0.000 0.6742 1.000 0.000 0.000 0.000
#> GSM872260 1 0.436 0.6905 0.744 0.000 0.008 0.248
#> GSM872261 4 0.966 0.2526 0.200 0.224 0.188 0.388
#> GSM872262 1 0.459 0.6853 0.712 0.000 0.008 0.280
#> GSM872263 3 0.000 0.5840 0.000 0.000 1.000 0.000
#> GSM872264 3 0.784 -0.0122 0.364 0.000 0.372 0.264
#> GSM872265 3 0.784 -0.0122 0.364 0.000 0.372 0.264
#> GSM872266 4 0.964 0.2339 0.176 0.224 0.212 0.388
#> GSM872267 2 0.483 0.7498 0.000 0.608 0.000 0.392
#> GSM872268 3 0.000 0.5840 0.000 0.000 1.000 0.000
#> GSM872269 4 0.520 -0.2564 0.032 0.276 0.000 0.692
#> GSM872270 3 0.000 0.5840 0.000 0.000 1.000 0.000
#> GSM872271 3 0.957 -0.0770 0.136 0.224 0.372 0.268
#> GSM872272 3 0.957 -0.0770 0.136 0.224 0.372 0.268
#> GSM872273 1 0.000 0.6742 1.000 0.000 0.000 0.000
#> GSM872274 2 0.000 0.6628 0.000 1.000 0.000 0.000
#> GSM872275 1 0.624 0.6265 0.648 0.044 0.024 0.284
#> GSM872276 1 0.459 0.6853 0.712 0.000 0.008 0.280
#> GSM872277 1 0.000 0.6742 1.000 0.000 0.000 0.000
#> GSM872278 1 0.474 0.6840 0.704 0.000 0.012 0.284
#> GSM872279 1 0.307 0.6004 0.848 0.000 0.000 0.152
#> GSM872280 1 0.462 0.6855 0.708 0.000 0.008 0.284
#> GSM872281 1 0.459 0.6853 0.712 0.000 0.008 0.280
#> GSM872282 3 0.000 0.5840 0.000 0.000 1.000 0.000
#> GSM872283 3 0.784 -0.0122 0.364 0.000 0.372 0.264
#> GSM872284 1 0.764 0.2862 0.468 0.000 0.256 0.276
#> GSM872285 3 0.623 0.3660 0.348 0.000 0.584 0.068
#> GSM872286 1 0.438 0.4236 0.704 0.000 0.000 0.296
#> GSM872287 3 0.000 0.5840 0.000 0.000 1.000 0.000
#> GSM872288 1 0.438 0.4236 0.704 0.000 0.000 0.296
#> GSM872289 3 0.596 0.2538 0.420 0.000 0.540 0.040
#> GSM872290 1 0.307 0.6004 0.848 0.000 0.000 0.152
#> GSM872291 1 0.462 0.6855 0.708 0.000 0.008 0.284
#> GSM872292 2 0.000 0.6628 0.000 1.000 0.000 0.000
#> GSM872293 1 0.000 0.6742 1.000 0.000 0.000 0.000
#> GSM872294 4 0.674 0.3143 0.096 0.392 0.000 0.512
#> GSM872295 2 0.476 0.7418 0.000 0.628 0.000 0.372
#> GSM872296 2 0.000 0.6628 0.000 1.000 0.000 0.000
#> GSM872297 1 0.000 0.6742 1.000 0.000 0.000 0.000
#> GSM872298 1 0.474 0.6840 0.704 0.000 0.012 0.284
#> GSM872299 1 0.307 0.6004 0.848 0.000 0.000 0.152
#> GSM872300 1 0.459 0.6853 0.712 0.000 0.008 0.280
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.000 0.818 0.000 0.000 1.000 0.000 0.000
#> GSM872245 1 0.265 0.762 0.880 0.000 0.000 0.024 0.096
#> GSM872246 3 0.395 0.490 0.000 0.000 0.668 0.332 0.000
#> GSM872247 3 0.000 0.818 0.000 0.000 1.000 0.000 0.000
#> GSM872248 5 0.458 0.760 0.020 0.352 0.000 0.000 0.628
#> GSM872249 3 0.000 0.818 0.000 0.000 1.000 0.000 0.000
#> GSM872250 1 0.256 0.766 0.884 0.000 0.000 0.020 0.096
#> GSM872251 3 0.000 0.818 0.000 0.000 1.000 0.000 0.000
#> GSM872252 1 0.173 0.843 0.920 0.000 0.000 0.080 0.000
#> GSM872253 4 0.161 0.741 0.040 0.000 0.012 0.944 0.004
#> GSM872254 5 0.384 0.486 0.256 0.004 0.000 0.004 0.736
#> GSM872255 4 0.297 0.648 0.184 0.000 0.000 0.816 0.000
#> GSM872256 1 0.442 0.611 0.632 0.000 0.000 0.356 0.012
#> GSM872257 5 0.458 0.760 0.020 0.352 0.000 0.000 0.628
#> GSM872258 3 0.429 0.282 0.000 0.000 0.532 0.468 0.000
#> GSM872259 1 0.390 0.823 0.768 0.000 0.000 0.204 0.028
#> GSM872260 4 0.297 0.648 0.184 0.000 0.000 0.816 0.000
#> GSM872261 4 0.889 0.241 0.108 0.204 0.152 0.444 0.092
#> GSM872262 4 0.112 0.742 0.044 0.000 0.000 0.956 0.000
#> GSM872263 3 0.000 0.818 0.000 0.000 1.000 0.000 0.000
#> GSM872264 4 0.408 0.488 0.004 0.000 0.328 0.668 0.000
#> GSM872265 4 0.408 0.488 0.004 0.000 0.328 0.668 0.000
#> GSM872266 4 0.900 0.227 0.104 0.204 0.176 0.424 0.092
#> GSM872267 5 0.458 0.760 0.020 0.352 0.000 0.000 0.628
#> GSM872268 3 0.000 0.818 0.000 0.000 1.000 0.000 0.000
#> GSM872269 5 0.120 0.532 0.032 0.004 0.000 0.004 0.960
#> GSM872270 3 0.000 0.818 0.000 0.000 1.000 0.000 0.000
#> GSM872271 4 0.715 0.301 0.004 0.204 0.328 0.444 0.020
#> GSM872272 4 0.715 0.301 0.004 0.204 0.328 0.444 0.020
#> GSM872273 1 0.390 0.823 0.768 0.000 0.000 0.204 0.028
#> GSM872274 2 0.000 0.688 0.000 1.000 0.000 0.000 0.000
#> GSM872275 4 0.274 0.723 0.040 0.024 0.012 0.904 0.020
#> GSM872276 4 0.112 0.742 0.044 0.000 0.000 0.956 0.000
#> GSM872277 1 0.390 0.823 0.768 0.000 0.000 0.204 0.028
#> GSM872278 4 0.136 0.743 0.048 0.000 0.004 0.948 0.000
#> GSM872279 1 0.173 0.843 0.920 0.000 0.000 0.080 0.000
#> GSM872280 4 0.120 0.742 0.048 0.000 0.000 0.952 0.000
#> GSM872281 4 0.112 0.742 0.044 0.000 0.000 0.956 0.000
#> GSM872282 3 0.000 0.818 0.000 0.000 1.000 0.000 0.000
#> GSM872283 4 0.408 0.488 0.004 0.000 0.328 0.668 0.000
#> GSM872284 4 0.337 0.598 0.004 0.000 0.212 0.784 0.000
#> GSM872285 3 0.436 0.383 0.004 0.000 0.584 0.412 0.000
#> GSM872286 1 0.256 0.766 0.884 0.000 0.000 0.020 0.096
#> GSM872287 3 0.000 0.818 0.000 0.000 1.000 0.000 0.000
#> GSM872288 1 0.256 0.766 0.884 0.000 0.000 0.020 0.096
#> GSM872289 3 0.429 0.303 0.000 0.000 0.540 0.460 0.000
#> GSM872290 1 0.173 0.843 0.920 0.000 0.000 0.080 0.000
#> GSM872291 4 0.161 0.730 0.072 0.000 0.000 0.928 0.000
#> GSM872292 2 0.000 0.688 0.000 1.000 0.000 0.000 0.000
#> GSM872293 1 0.390 0.823 0.768 0.000 0.000 0.204 0.028
#> GSM872294 2 0.743 0.244 0.032 0.372 0.000 0.264 0.332
#> GSM872295 5 0.418 0.746 0.000 0.352 0.000 0.004 0.644
#> GSM872296 2 0.000 0.688 0.000 1.000 0.000 0.000 0.000
#> GSM872297 1 0.390 0.823 0.768 0.000 0.000 0.204 0.028
#> GSM872298 4 0.136 0.743 0.048 0.000 0.004 0.948 0.000
#> GSM872299 1 0.173 0.843 0.920 0.000 0.000 0.080 0.000
#> GSM872300 4 0.112 0.742 0.044 0.000 0.000 0.956 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.0000 0.784 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872245 1 0.2933 0.723 0.796 0.200 0.000 0.004 0.000 0.000
#> GSM872246 3 0.3547 0.429 0.000 0.000 0.668 0.000 0.000 0.332
#> GSM872247 3 0.0000 0.784 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872248 5 0.0000 0.739 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.784 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872250 1 0.2933 0.727 0.796 0.200 0.000 0.000 0.000 0.004
#> GSM872251 3 0.0000 0.784 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872252 1 0.0146 0.818 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM872253 6 0.3163 0.674 0.008 0.000 0.012 0.172 0.000 0.808
#> GSM872254 5 0.7526 0.373 0.156 0.200 0.000 0.252 0.388 0.004
#> GSM872255 6 0.2730 0.664 0.192 0.000 0.000 0.000 0.000 0.808
#> GSM872256 1 0.4015 0.558 0.656 0.008 0.000 0.008 0.000 0.328
#> GSM872257 5 0.0000 0.739 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872258 3 0.3857 0.298 0.000 0.000 0.532 0.000 0.000 0.468
#> GSM872259 1 0.3142 0.803 0.832 0.024 0.000 0.012 0.000 0.132
#> GSM872260 6 0.2730 0.664 0.192 0.000 0.000 0.000 0.000 0.808
#> GSM872261 4 0.7321 0.425 0.016 0.344 0.136 0.396 0.000 0.108
#> GSM872262 6 0.1010 0.819 0.004 0.000 0.000 0.036 0.000 0.960
#> GSM872263 3 0.0000 0.784 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872264 4 0.6116 0.404 0.000 0.000 0.312 0.368 0.000 0.320
#> GSM872265 4 0.6116 0.404 0.000 0.000 0.312 0.368 0.000 0.320
#> GSM872266 4 0.7294 0.438 0.016 0.340 0.160 0.396 0.000 0.088
#> GSM872267 5 0.0000 0.739 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.784 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872269 4 0.4531 -0.575 0.008 0.012 0.000 0.584 0.388 0.008
#> GSM872270 3 0.0000 0.784 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872271 4 0.7155 0.506 0.000 0.184 0.312 0.396 0.000 0.108
#> GSM872272 4 0.7155 0.506 0.000 0.184 0.312 0.396 0.000 0.108
#> GSM872273 1 0.3142 0.803 0.832 0.024 0.000 0.012 0.000 0.132
#> GSM872274 2 0.2996 1.000 0.000 0.772 0.000 0.000 0.228 0.000
#> GSM872275 6 0.3698 0.590 0.004 0.004 0.012 0.240 0.000 0.740
#> GSM872276 6 0.1010 0.819 0.004 0.000 0.000 0.036 0.000 0.960
#> GSM872277 1 0.3142 0.803 0.832 0.024 0.000 0.012 0.000 0.132
#> GSM872278 6 0.0922 0.815 0.004 0.000 0.004 0.024 0.000 0.968
#> GSM872279 1 0.0146 0.818 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM872280 6 0.0146 0.816 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM872281 6 0.1010 0.819 0.004 0.000 0.000 0.036 0.000 0.960
#> GSM872282 3 0.0000 0.784 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872283 4 0.6116 0.404 0.000 0.000 0.312 0.368 0.000 0.320
#> GSM872284 6 0.5852 -0.260 0.000 0.000 0.196 0.364 0.000 0.440
#> GSM872285 3 0.3789 0.373 0.000 0.000 0.584 0.000 0.000 0.416
#> GSM872286 1 0.2933 0.727 0.796 0.200 0.000 0.000 0.000 0.004
#> GSM872287 3 0.0000 0.784 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872288 1 0.2933 0.727 0.796 0.200 0.000 0.000 0.000 0.004
#> GSM872289 3 0.3851 0.316 0.000 0.000 0.540 0.000 0.000 0.460
#> GSM872290 1 0.0146 0.818 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM872291 6 0.0865 0.806 0.036 0.000 0.000 0.000 0.000 0.964
#> GSM872292 2 0.2996 1.000 0.000 0.772 0.000 0.000 0.228 0.000
#> GSM872293 1 0.3142 0.803 0.832 0.024 0.000 0.012 0.000 0.132
#> GSM872294 4 0.6121 -0.306 0.004 0.356 0.000 0.404 0.000 0.236
#> GSM872295 5 0.3429 0.621 0.004 0.000 0.000 0.252 0.740 0.004
#> GSM872296 2 0.2996 1.000 0.000 0.772 0.000 0.000 0.228 0.000
#> GSM872297 1 0.3142 0.803 0.832 0.024 0.000 0.012 0.000 0.132
#> GSM872298 6 0.0922 0.815 0.004 0.000 0.004 0.024 0.000 0.968
#> GSM872299 1 0.0146 0.818 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM872300 6 0.1010 0.819 0.004 0.000 0.000 0.036 0.000 0.960
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 time(p) individual(p) k
#> CV:hclust 50 0.913 0.062364 2
#> CV:hclust 46 0.866 0.001793 3
#> CV:hclust 38 0.909 0.000647 4
#> CV:hclust 44 0.845 0.000123 5
#> CV:hclust 44 0.569 0.000246 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 29485 rows and 57 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 0.210 0.637 0.787 0.4478 0.589 0.589
#> 3 3 0.840 0.876 0.943 0.4644 0.694 0.505
#> 4 4 0.633 0.423 0.673 0.1317 0.887 0.683
#> 5 5 0.690 0.655 0.782 0.0691 0.870 0.559
#> 6 6 0.700 0.537 0.725 0.0416 0.916 0.635
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
#> GSM872244 1 0.9580 0.326 0.620 0.380
#> GSM872245 2 0.9635 0.253 0.388 0.612
#> GSM872246 1 0.5629 0.691 0.868 0.132
#> GSM872247 1 0.5737 0.689 0.864 0.136
#> GSM872248 2 0.0000 0.870 0.000 1.000
#> GSM872249 1 0.5842 0.686 0.860 0.140
#> GSM872250 2 0.9087 0.278 0.324 0.676
#> GSM872251 1 0.5629 0.691 0.868 0.132
#> GSM872252 1 0.9710 0.407 0.600 0.400
#> GSM872253 1 0.7528 0.693 0.784 0.216
#> GSM872254 2 0.0672 0.870 0.008 0.992
#> GSM872255 1 0.5178 0.712 0.884 0.116
#> GSM872256 1 0.9710 0.407 0.600 0.400
#> GSM872257 2 0.0672 0.870 0.008 0.992
#> GSM872258 1 0.5629 0.691 0.868 0.132
#> GSM872259 1 0.9710 0.407 0.600 0.400
#> GSM872260 1 0.5178 0.712 0.884 0.116
#> GSM872261 2 0.8386 0.456 0.268 0.732
#> GSM872262 1 0.5178 0.712 0.884 0.116
#> GSM872263 1 0.5737 0.689 0.864 0.136
#> GSM872264 1 0.7883 0.655 0.764 0.236
#> GSM872265 1 0.9209 0.612 0.664 0.336
#> GSM872266 2 0.0000 0.870 0.000 1.000
#> GSM872267 2 0.0000 0.870 0.000 1.000
#> GSM872268 1 0.5629 0.691 0.868 0.132
#> GSM872269 2 0.3733 0.815 0.072 0.928
#> GSM872270 1 0.7376 0.622 0.792 0.208
#> GSM872271 2 0.4022 0.822 0.080 0.920
#> GSM872272 2 0.4022 0.822 0.080 0.920
#> GSM872273 1 0.7453 0.656 0.788 0.212
#> GSM872274 2 0.1414 0.866 0.020 0.980
#> GSM872275 1 0.6712 0.694 0.824 0.176
#> GSM872276 1 0.5178 0.712 0.884 0.116
#> GSM872277 1 0.7453 0.656 0.788 0.212
#> GSM872278 1 0.6623 0.696 0.828 0.172
#> GSM872279 1 0.9710 0.407 0.600 0.400
#> GSM872280 1 0.0000 0.696 1.000 0.000
#> GSM872281 1 0.2603 0.708 0.956 0.044
#> GSM872282 1 0.9580 0.326 0.620 0.380
#> GSM872283 1 0.7674 0.658 0.776 0.224
#> GSM872284 1 0.5059 0.713 0.888 0.112
#> GSM872285 1 0.4161 0.700 0.916 0.084
#> GSM872286 1 0.9963 0.228 0.536 0.464
#> GSM872287 1 0.5737 0.689 0.864 0.136
#> GSM872288 1 0.9775 0.398 0.588 0.412
#> GSM872289 1 0.5629 0.691 0.868 0.132
#> GSM872290 1 0.9710 0.407 0.600 0.400
#> GSM872291 1 0.5178 0.712 0.884 0.116
#> GSM872292 2 0.1414 0.866 0.020 0.980
#> GSM872293 1 0.9710 0.407 0.600 0.400
#> GSM872294 2 0.0000 0.870 0.000 1.000
#> GSM872295 2 0.1414 0.866 0.020 0.980
#> GSM872296 2 0.1414 0.866 0.020 0.980
#> GSM872297 1 0.9710 0.407 0.600 0.400
#> GSM872298 1 0.5059 0.713 0.888 0.112
#> GSM872299 1 1.0000 0.113 0.504 0.496
#> GSM872300 1 0.5178 0.712 0.884 0.116
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872245 1 0.1289 0.897 0.968 0.032 0.000
#> GSM872246 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872248 2 0.0829 0.939 0.012 0.984 0.004
#> GSM872249 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872250 1 0.5982 0.426 0.668 0.328 0.004
#> GSM872251 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872252 1 0.0000 0.918 1.000 0.000 0.000
#> GSM872253 3 0.2711 0.887 0.088 0.000 0.912
#> GSM872254 2 0.1765 0.927 0.040 0.956 0.004
#> GSM872255 1 0.0592 0.913 0.988 0.000 0.012
#> GSM872256 1 0.0000 0.918 1.000 0.000 0.000
#> GSM872257 2 0.0237 0.939 0.000 0.996 0.004
#> GSM872258 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872259 1 0.0000 0.918 1.000 0.000 0.000
#> GSM872260 1 0.0000 0.918 1.000 0.000 0.000
#> GSM872261 2 0.6209 0.465 0.368 0.628 0.004
#> GSM872262 1 0.1989 0.894 0.948 0.004 0.048
#> GSM872263 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872264 3 0.5158 0.677 0.232 0.004 0.764
#> GSM872265 1 0.5956 0.557 0.672 0.004 0.324
#> GSM872266 2 0.0829 0.939 0.012 0.984 0.004
#> GSM872267 2 0.0592 0.939 0.012 0.988 0.000
#> GSM872268 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872269 2 0.4172 0.824 0.156 0.840 0.004
#> GSM872270 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872271 2 0.2903 0.902 0.028 0.924 0.048
#> GSM872272 2 0.2903 0.902 0.028 0.924 0.048
#> GSM872273 1 0.0000 0.918 1.000 0.000 0.000
#> GSM872274 2 0.0237 0.939 0.000 0.996 0.004
#> GSM872275 3 0.1411 0.931 0.036 0.000 0.964
#> GSM872276 1 0.1989 0.894 0.948 0.004 0.048
#> GSM872277 1 0.0000 0.918 1.000 0.000 0.000
#> GSM872278 3 0.1647 0.929 0.036 0.004 0.960
#> GSM872279 1 0.0000 0.918 1.000 0.000 0.000
#> GSM872280 3 0.5553 0.627 0.272 0.004 0.724
#> GSM872281 1 0.6126 0.500 0.644 0.004 0.352
#> GSM872282 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872283 1 0.4629 0.758 0.808 0.004 0.188
#> GSM872284 1 0.5982 0.551 0.668 0.004 0.328
#> GSM872285 3 0.0237 0.952 0.004 0.000 0.996
#> GSM872286 1 0.0000 0.918 1.000 0.000 0.000
#> GSM872287 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872288 1 0.0000 0.918 1.000 0.000 0.000
#> GSM872289 3 0.0424 0.949 0.008 0.000 0.992
#> GSM872290 1 0.0000 0.918 1.000 0.000 0.000
#> GSM872291 1 0.0000 0.918 1.000 0.000 0.000
#> GSM872292 2 0.0237 0.939 0.000 0.996 0.004
#> GSM872293 1 0.0000 0.918 1.000 0.000 0.000
#> GSM872294 2 0.0000 0.939 0.000 1.000 0.000
#> GSM872295 2 0.0237 0.939 0.000 0.996 0.004
#> GSM872296 2 0.0000 0.939 0.000 1.000 0.000
#> GSM872297 1 0.0000 0.918 1.000 0.000 0.000
#> GSM872298 1 0.2096 0.891 0.944 0.004 0.052
#> GSM872299 1 0.0000 0.918 1.000 0.000 0.000
#> GSM872300 1 0.0829 0.913 0.984 0.004 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0592 0.86480 0.000 0.000 0.984 0.016
#> GSM872245 1 0.5685 0.14299 0.516 0.460 0.000 0.024
#> GSM872246 3 0.0188 0.86912 0.000 0.000 0.996 0.004
#> GSM872247 3 0.0469 0.86931 0.000 0.000 0.988 0.012
#> GSM872248 2 0.2799 0.64536 0.008 0.884 0.000 0.108
#> GSM872249 3 0.0592 0.86855 0.000 0.000 0.984 0.016
#> GSM872250 1 0.6147 0.11113 0.488 0.464 0.000 0.048
#> GSM872251 3 0.0336 0.86950 0.000 0.000 0.992 0.008
#> GSM872252 1 0.6316 0.32957 0.612 0.300 0.000 0.088
#> GSM872253 3 0.6773 0.37513 0.012 0.080 0.576 0.332
#> GSM872254 2 0.4175 0.41091 0.212 0.776 0.000 0.012
#> GSM872255 1 0.4888 -0.10421 0.588 0.000 0.000 0.412
#> GSM872256 1 0.2345 0.37403 0.900 0.000 0.000 0.100
#> GSM872257 2 0.4933 0.68919 0.000 0.568 0.000 0.432
#> GSM872258 3 0.0000 0.86876 0.000 0.000 1.000 0.000
#> GSM872259 1 0.0000 0.44183 1.000 0.000 0.000 0.000
#> GSM872260 1 0.4697 -0.00531 0.644 0.000 0.000 0.356
#> GSM872261 2 0.7216 0.03290 0.284 0.536 0.000 0.180
#> GSM872262 1 0.5277 -0.23560 0.532 0.000 0.008 0.460
#> GSM872263 3 0.0188 0.86873 0.000 0.000 0.996 0.004
#> GSM872264 4 0.7816 0.33542 0.176 0.012 0.352 0.460
#> GSM872265 4 0.7819 0.48076 0.340 0.012 0.180 0.468
#> GSM872266 2 0.2973 0.59121 0.020 0.884 0.000 0.096
#> GSM872267 2 0.3681 0.66089 0.008 0.816 0.000 0.176
#> GSM872268 3 0.0469 0.86931 0.000 0.000 0.988 0.012
#> GSM872269 2 0.4327 0.39988 0.216 0.768 0.000 0.016
#> GSM872270 3 0.0469 0.86895 0.000 0.000 0.988 0.012
#> GSM872271 4 0.7272 -0.27598 0.028 0.444 0.072 0.456
#> GSM872272 4 0.7272 -0.27598 0.028 0.444 0.072 0.456
#> GSM872273 1 0.4222 0.17965 0.728 0.000 0.000 0.272
#> GSM872274 2 0.4977 0.68508 0.000 0.540 0.000 0.460
#> GSM872275 3 0.4800 0.47721 0.004 0.000 0.656 0.340
#> GSM872276 1 0.5277 -0.23560 0.532 0.000 0.008 0.460
#> GSM872277 1 0.4222 0.17965 0.728 0.000 0.000 0.272
#> GSM872278 3 0.5097 0.26538 0.004 0.000 0.568 0.428
#> GSM872279 1 0.1004 0.43890 0.972 0.024 0.000 0.004
#> GSM872280 4 0.7384 0.37554 0.352 0.000 0.172 0.476
#> GSM872281 4 0.6882 0.44021 0.392 0.000 0.108 0.500
#> GSM872282 3 0.0707 0.86279 0.000 0.000 0.980 0.020
#> GSM872283 4 0.7412 0.46529 0.360 0.028 0.092 0.520
#> GSM872284 4 0.7252 0.45921 0.372 0.012 0.108 0.508
#> GSM872285 3 0.4382 0.54171 0.000 0.000 0.704 0.296
#> GSM872286 1 0.5497 0.15114 0.524 0.460 0.000 0.016
#> GSM872287 3 0.0469 0.86931 0.000 0.000 0.988 0.012
#> GSM872288 1 0.6145 0.12061 0.492 0.460 0.000 0.048
#> GSM872289 3 0.1118 0.84500 0.000 0.036 0.964 0.000
#> GSM872290 1 0.0000 0.44183 1.000 0.000 0.000 0.000
#> GSM872291 1 0.4972 -0.21160 0.544 0.000 0.000 0.456
#> GSM872292 2 0.4977 0.68508 0.000 0.540 0.000 0.460
#> GSM872293 1 0.0000 0.44183 1.000 0.000 0.000 0.000
#> GSM872294 2 0.4977 0.68508 0.000 0.540 0.000 0.460
#> GSM872295 2 0.4948 0.68909 0.000 0.560 0.000 0.440
#> GSM872296 2 0.4977 0.68508 0.000 0.540 0.000 0.460
#> GSM872297 1 0.0188 0.44030 0.996 0.000 0.000 0.004
#> GSM872298 4 0.5407 0.22101 0.484 0.000 0.012 0.504
#> GSM872299 1 0.5097 0.19246 0.568 0.428 0.000 0.004
#> GSM872300 1 0.5277 -0.23560 0.532 0.000 0.008 0.460
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.1525 0.911 0.004 0.000 0.948 0.036 0.012
#> GSM872245 5 0.3819 0.644 0.228 0.000 0.000 0.016 0.756
#> GSM872246 3 0.0671 0.925 0.000 0.000 0.980 0.016 0.004
#> GSM872247 3 0.0324 0.927 0.000 0.000 0.992 0.004 0.004
#> GSM872248 5 0.4957 0.431 0.000 0.332 0.000 0.044 0.624
#> GSM872249 3 0.0162 0.926 0.000 0.000 0.996 0.000 0.004
#> GSM872250 5 0.1894 0.744 0.072 0.000 0.000 0.008 0.920
#> GSM872251 3 0.0451 0.925 0.000 0.000 0.988 0.008 0.004
#> GSM872252 1 0.6643 0.175 0.404 0.000 0.000 0.224 0.372
#> GSM872253 4 0.5796 0.599 0.020 0.004 0.164 0.676 0.136
#> GSM872254 5 0.2828 0.716 0.004 0.104 0.000 0.020 0.872
#> GSM872255 1 0.4298 0.461 0.640 0.000 0.000 0.352 0.008
#> GSM872256 1 0.2172 0.646 0.908 0.000 0.000 0.016 0.076
#> GSM872257 2 0.1670 0.938 0.000 0.936 0.000 0.012 0.052
#> GSM872258 3 0.2052 0.875 0.004 0.000 0.912 0.080 0.004
#> GSM872259 1 0.2660 0.616 0.864 0.000 0.000 0.008 0.128
#> GSM872260 1 0.4183 0.484 0.668 0.000 0.000 0.324 0.008
#> GSM872261 5 0.5428 0.439 0.064 0.008 0.000 0.308 0.620
#> GSM872262 1 0.4440 0.177 0.528 0.000 0.004 0.468 0.000
#> GSM872263 3 0.1267 0.916 0.004 0.000 0.960 0.024 0.012
#> GSM872264 4 0.4949 0.702 0.096 0.020 0.072 0.780 0.032
#> GSM872265 4 0.4930 0.699 0.108 0.020 0.056 0.780 0.036
#> GSM872266 5 0.4269 0.652 0.000 0.116 0.000 0.108 0.776
#> GSM872267 5 0.5167 0.267 0.000 0.404 0.000 0.044 0.552
#> GSM872268 3 0.0324 0.927 0.000 0.000 0.992 0.004 0.004
#> GSM872269 5 0.2575 0.718 0.004 0.100 0.000 0.012 0.884
#> GSM872270 3 0.0162 0.927 0.000 0.000 0.996 0.004 0.000
#> GSM872271 4 0.5953 0.581 0.012 0.192 0.020 0.668 0.108
#> GSM872272 4 0.5953 0.581 0.012 0.192 0.020 0.668 0.108
#> GSM872273 1 0.2068 0.615 0.904 0.000 0.000 0.092 0.004
#> GSM872274 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM872275 4 0.4384 0.644 0.012 0.004 0.208 0.752 0.024
#> GSM872276 1 0.4437 0.188 0.532 0.000 0.004 0.464 0.000
#> GSM872277 1 0.2536 0.598 0.868 0.000 0.000 0.128 0.004
#> GSM872278 4 0.3730 0.677 0.016 0.004 0.156 0.812 0.012
#> GSM872279 1 0.3573 0.566 0.812 0.000 0.000 0.036 0.152
#> GSM872280 4 0.5394 0.222 0.328 0.000 0.056 0.608 0.008
#> GSM872281 4 0.4584 0.623 0.208 0.000 0.032 0.740 0.020
#> GSM872282 3 0.1605 0.908 0.004 0.000 0.944 0.040 0.012
#> GSM872283 4 0.4577 0.690 0.116 0.020 0.024 0.796 0.044
#> GSM872284 4 0.4723 0.630 0.204 0.000 0.032 0.736 0.028
#> GSM872285 3 0.4997 0.133 0.020 0.000 0.568 0.404 0.008
#> GSM872286 5 0.2286 0.733 0.108 0.000 0.000 0.004 0.888
#> GSM872287 3 0.0324 0.927 0.000 0.000 0.992 0.004 0.004
#> GSM872288 5 0.2077 0.743 0.084 0.000 0.000 0.008 0.908
#> GSM872289 3 0.2929 0.852 0.004 0.000 0.876 0.044 0.076
#> GSM872290 1 0.2825 0.612 0.860 0.000 0.000 0.016 0.124
#> GSM872291 1 0.4455 0.363 0.588 0.000 0.000 0.404 0.008
#> GSM872292 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM872293 1 0.2377 0.616 0.872 0.000 0.000 0.000 0.128
#> GSM872294 2 0.0579 0.959 0.000 0.984 0.000 0.008 0.008
#> GSM872295 2 0.1430 0.943 0.000 0.944 0.000 0.004 0.052
#> GSM872296 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM872297 1 0.2563 0.621 0.872 0.000 0.000 0.008 0.120
#> GSM872298 4 0.3883 0.501 0.244 0.000 0.004 0.744 0.008
#> GSM872299 5 0.4833 0.356 0.412 0.000 0.000 0.024 0.564
#> GSM872300 1 0.4440 0.177 0.528 0.000 0.004 0.468 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.3198 0.78979 0.012 0.000 0.816 0.004 0.008 0.160
#> GSM872245 5 0.4127 0.57156 0.284 0.000 0.000 0.000 0.680 0.036
#> GSM872246 3 0.0748 0.84861 0.000 0.000 0.976 0.016 0.004 0.004
#> GSM872247 3 0.0146 0.85143 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM872248 5 0.4877 0.49967 0.000 0.192 0.000 0.000 0.660 0.148
#> GSM872249 3 0.0405 0.85035 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM872250 5 0.1349 0.72201 0.056 0.000 0.000 0.000 0.940 0.004
#> GSM872251 3 0.1779 0.82843 0.000 0.000 0.920 0.016 0.000 0.064
#> GSM872252 6 0.6866 0.00109 0.248 0.000 0.000 0.052 0.312 0.388
#> GSM872253 6 0.6240 0.42554 0.000 0.000 0.100 0.208 0.112 0.580
#> GSM872254 5 0.2076 0.71500 0.012 0.016 0.000 0.000 0.912 0.060
#> GSM872255 4 0.6117 0.08770 0.372 0.000 0.000 0.392 0.004 0.232
#> GSM872256 1 0.2137 0.80192 0.912 0.000 0.000 0.048 0.012 0.028
#> GSM872257 2 0.3252 0.84758 0.000 0.824 0.000 0.000 0.068 0.108
#> GSM872258 3 0.3776 0.65508 0.000 0.000 0.760 0.052 0.000 0.188
#> GSM872259 1 0.0909 0.80759 0.968 0.000 0.000 0.000 0.020 0.012
#> GSM872260 1 0.6463 -0.16815 0.364 0.000 0.000 0.336 0.016 0.284
#> GSM872261 5 0.5334 0.13650 0.028 0.000 0.000 0.052 0.536 0.384
#> GSM872262 4 0.5374 0.34847 0.276 0.000 0.000 0.584 0.004 0.136
#> GSM872263 3 0.3020 0.79398 0.012 0.000 0.824 0.000 0.008 0.156
#> GSM872264 4 0.4924 0.10714 0.020 0.008 0.040 0.688 0.008 0.236
#> GSM872265 4 0.4936 0.11405 0.024 0.008 0.036 0.688 0.008 0.236
#> GSM872266 5 0.3084 0.66629 0.000 0.032 0.000 0.004 0.832 0.132
#> GSM872267 5 0.5167 0.41537 0.000 0.240 0.000 0.000 0.612 0.148
#> GSM872268 3 0.0146 0.85143 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM872269 5 0.2558 0.71305 0.012 0.016 0.000 0.004 0.884 0.084
#> GSM872270 3 0.0777 0.84934 0.000 0.000 0.972 0.004 0.000 0.024
#> GSM872271 4 0.6624 -0.14479 0.000 0.084 0.028 0.460 0.052 0.376
#> GSM872272 4 0.6624 -0.14479 0.000 0.084 0.028 0.460 0.052 0.376
#> GSM872273 1 0.2378 0.72524 0.848 0.000 0.000 0.152 0.000 0.000
#> GSM872274 2 0.0000 0.93712 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872275 6 0.5692 0.38059 0.000 0.000 0.112 0.412 0.012 0.464
#> GSM872276 4 0.5390 0.34705 0.280 0.000 0.000 0.580 0.004 0.136
#> GSM872277 1 0.2730 0.72138 0.836 0.000 0.000 0.152 0.000 0.012
#> GSM872278 6 0.5243 0.33048 0.000 0.000 0.080 0.452 0.004 0.464
#> GSM872279 1 0.3052 0.75965 0.848 0.000 0.000 0.004 0.068 0.080
#> GSM872280 4 0.6134 0.20250 0.124 0.000 0.056 0.580 0.004 0.236
#> GSM872281 4 0.1225 0.27532 0.036 0.000 0.012 0.952 0.000 0.000
#> GSM872282 3 0.3308 0.78700 0.012 0.000 0.812 0.008 0.008 0.160
#> GSM872283 4 0.4787 0.12520 0.028 0.004 0.024 0.696 0.012 0.236
#> GSM872284 4 0.2307 0.25205 0.032 0.000 0.016 0.904 0.000 0.048
#> GSM872285 3 0.5771 -0.11574 0.000 0.000 0.444 0.380 0.000 0.176
#> GSM872286 5 0.2312 0.71530 0.112 0.000 0.000 0.000 0.876 0.012
#> GSM872287 3 0.0146 0.85143 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM872288 5 0.1753 0.71798 0.084 0.000 0.000 0.000 0.912 0.004
#> GSM872289 3 0.4066 0.73618 0.000 0.000 0.788 0.036 0.064 0.112
#> GSM872290 1 0.2547 0.78357 0.880 0.000 0.000 0.004 0.036 0.080
#> GSM872291 4 0.6228 0.17996 0.332 0.000 0.000 0.412 0.008 0.248
#> GSM872292 2 0.0000 0.93712 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872293 1 0.0547 0.80949 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM872294 2 0.1364 0.91913 0.000 0.944 0.000 0.004 0.004 0.048
#> GSM872295 2 0.2705 0.89257 0.000 0.872 0.000 0.004 0.072 0.052
#> GSM872296 2 0.0260 0.93642 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM872297 1 0.1078 0.80809 0.964 0.000 0.000 0.008 0.016 0.012
#> GSM872298 4 0.4314 0.16332 0.044 0.000 0.004 0.704 0.004 0.244
#> GSM872299 5 0.5479 0.23805 0.416 0.000 0.000 0.004 0.472 0.108
#> GSM872300 4 0.5374 0.34847 0.276 0.000 0.000 0.584 0.004 0.136
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 time(p) individual(p) k
#> CV:kmeans 42 0.870 0.042355 2
#> CV:kmeans 55 0.460 0.011551 3
#> CV:kmeans 22 0.518 0.046063 4
#> CV:kmeans 44 0.272 0.000089 5
#> CV:kmeans 33 0.641 0.001118 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 29485 rows and 57 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.535 0.829 0.905 0.5065 0.491 0.491
#> 3 3 0.846 0.872 0.948 0.3349 0.706 0.468
#> 4 4 0.853 0.905 0.942 0.1240 0.836 0.547
#> 5 5 0.780 0.630 0.816 0.0535 0.873 0.553
#> 6 6 0.785 0.656 0.823 0.0393 0.911 0.612
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM872244 1 0.7528 0.773 0.784 0.216
#> GSM872245 2 0.0938 0.864 0.012 0.988
#> GSM872246 1 0.0938 0.909 0.988 0.012
#> GSM872247 1 0.0938 0.909 0.988 0.012
#> GSM872248 2 0.0000 0.866 0.000 1.000
#> GSM872249 1 0.7453 0.777 0.788 0.212
#> GSM872250 2 0.0376 0.866 0.004 0.996
#> GSM872251 1 0.0938 0.909 0.988 0.012
#> GSM872252 2 0.7528 0.805 0.216 0.784
#> GSM872253 1 0.0938 0.909 0.988 0.012
#> GSM872254 2 0.0376 0.866 0.004 0.996
#> GSM872255 1 0.0000 0.908 1.000 0.000
#> GSM872256 2 0.7528 0.805 0.216 0.784
#> GSM872257 2 0.0000 0.866 0.000 1.000
#> GSM872258 1 0.0672 0.909 0.992 0.008
#> GSM872259 2 0.7528 0.805 0.216 0.784
#> GSM872260 1 0.0000 0.908 1.000 0.000
#> GSM872261 2 0.0376 0.866 0.004 0.996
#> GSM872262 1 0.0000 0.908 1.000 0.000
#> GSM872263 1 0.1184 0.908 0.984 0.016
#> GSM872264 1 0.7453 0.775 0.788 0.212
#> GSM872265 1 0.9998 0.192 0.508 0.492
#> GSM872266 2 0.0000 0.866 0.000 1.000
#> GSM872267 2 0.0000 0.866 0.000 1.000
#> GSM872268 1 0.0938 0.909 0.988 0.012
#> GSM872269 2 0.0376 0.866 0.004 0.996
#> GSM872270 1 0.7528 0.773 0.784 0.216
#> GSM872271 2 0.0000 0.866 0.000 1.000
#> GSM872272 2 0.0000 0.866 0.000 1.000
#> GSM872273 2 0.9909 0.454 0.444 0.556
#> GSM872274 2 0.0000 0.866 0.000 1.000
#> GSM872275 1 0.7528 0.773 0.784 0.216
#> GSM872276 1 0.0000 0.908 1.000 0.000
#> GSM872277 2 0.9909 0.454 0.444 0.556
#> GSM872278 1 0.7376 0.780 0.792 0.208
#> GSM872279 2 0.7528 0.805 0.216 0.784
#> GSM872280 1 0.0000 0.908 1.000 0.000
#> GSM872281 1 0.0376 0.909 0.996 0.004
#> GSM872282 1 0.7528 0.773 0.784 0.216
#> GSM872283 2 0.7815 0.628 0.232 0.768
#> GSM872284 1 0.0376 0.909 0.996 0.004
#> GSM872285 1 0.0000 0.908 1.000 0.000
#> GSM872286 2 0.7528 0.805 0.216 0.784
#> GSM872287 1 0.0938 0.909 0.988 0.012
#> GSM872288 2 0.7453 0.806 0.212 0.788
#> GSM872289 1 0.0672 0.909 0.992 0.008
#> GSM872290 2 0.7528 0.805 0.216 0.784
#> GSM872291 1 0.0000 0.908 1.000 0.000
#> GSM872292 2 0.0000 0.866 0.000 1.000
#> GSM872293 2 0.7528 0.805 0.216 0.784
#> GSM872294 2 0.0000 0.866 0.000 1.000
#> GSM872295 2 0.0000 0.866 0.000 1.000
#> GSM872296 2 0.0000 0.866 0.000 1.000
#> GSM872297 2 0.7528 0.805 0.216 0.784
#> GSM872298 1 0.0000 0.908 1.000 0.000
#> GSM872299 2 0.7528 0.805 0.216 0.784
#> GSM872300 1 0.0000 0.908 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.000 0.9594 0.000 0.000 1.000
#> GSM872245 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872246 3 0.000 0.9594 0.000 0.000 1.000
#> GSM872247 3 0.000 0.9594 0.000 0.000 1.000
#> GSM872248 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872249 3 0.000 0.9594 0.000 0.000 1.000
#> GSM872250 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872251 3 0.000 0.9594 0.000 0.000 1.000
#> GSM872252 1 0.000 0.9441 1.000 0.000 0.000
#> GSM872253 3 0.164 0.9203 0.044 0.000 0.956
#> GSM872254 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872255 1 0.000 0.9441 1.000 0.000 0.000
#> GSM872256 1 0.000 0.9441 1.000 0.000 0.000
#> GSM872257 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872258 3 0.000 0.9594 0.000 0.000 1.000
#> GSM872259 1 0.000 0.9441 1.000 0.000 0.000
#> GSM872260 1 0.000 0.9441 1.000 0.000 0.000
#> GSM872261 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872262 1 0.000 0.9441 1.000 0.000 0.000
#> GSM872263 3 0.000 0.9594 0.000 0.000 1.000
#> GSM872264 3 0.400 0.7811 0.160 0.000 0.840
#> GSM872265 1 0.836 0.5287 0.620 0.232 0.148
#> GSM872266 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872267 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872268 3 0.000 0.9594 0.000 0.000 1.000
#> GSM872269 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872270 3 0.000 0.9594 0.000 0.000 1.000
#> GSM872271 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872272 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872273 1 0.000 0.9441 1.000 0.000 0.000
#> GSM872274 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872275 3 0.000 0.9594 0.000 0.000 1.000
#> GSM872276 1 0.000 0.9441 1.000 0.000 0.000
#> GSM872277 1 0.000 0.9441 1.000 0.000 0.000
#> GSM872278 3 0.000 0.9594 0.000 0.000 1.000
#> GSM872279 1 0.000 0.9441 1.000 0.000 0.000
#> GSM872280 3 0.625 0.2000 0.444 0.000 0.556
#> GSM872281 1 0.502 0.6883 0.760 0.000 0.240
#> GSM872282 3 0.000 0.9594 0.000 0.000 1.000
#> GSM872283 1 0.500 0.7767 0.820 0.152 0.028
#> GSM872284 1 0.465 0.7352 0.792 0.000 0.208
#> GSM872285 3 0.000 0.9594 0.000 0.000 1.000
#> GSM872286 2 0.604 0.4364 0.380 0.620 0.000
#> GSM872287 3 0.000 0.9594 0.000 0.000 1.000
#> GSM872288 2 0.631 0.0797 0.500 0.500 0.000
#> GSM872289 3 0.000 0.9594 0.000 0.000 1.000
#> GSM872290 1 0.000 0.9441 1.000 0.000 0.000
#> GSM872291 1 0.000 0.9441 1.000 0.000 0.000
#> GSM872292 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872293 1 0.000 0.9441 1.000 0.000 0.000
#> GSM872294 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872295 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872296 2 0.000 0.9234 0.000 1.000 0.000
#> GSM872297 1 0.000 0.9441 1.000 0.000 0.000
#> GSM872298 1 0.000 0.9441 1.000 0.000 0.000
#> GSM872299 2 0.625 0.2838 0.444 0.556 0.000
#> GSM872300 1 0.000 0.9441 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> GSM872245 1 0.0188 0.879 0.996 0.004 0.000 0.000
#> GSM872246 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> GSM872247 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> GSM872248 2 0.0921 0.933 0.028 0.972 0.000 0.000
#> GSM872249 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> GSM872250 1 0.0592 0.870 0.984 0.016 0.000 0.000
#> GSM872251 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> GSM872252 1 0.0188 0.882 0.996 0.000 0.000 0.004
#> GSM872253 3 0.1716 0.937 0.064 0.000 0.936 0.000
#> GSM872254 2 0.4072 0.758 0.252 0.748 0.000 0.000
#> GSM872255 4 0.2011 0.855 0.080 0.000 0.000 0.920
#> GSM872256 1 0.3649 0.845 0.796 0.000 0.000 0.204
#> GSM872257 2 0.0707 0.935 0.020 0.980 0.000 0.000
#> GSM872258 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> GSM872259 1 0.2921 0.881 0.860 0.000 0.000 0.140
#> GSM872260 1 0.4134 0.777 0.740 0.000 0.000 0.260
#> GSM872261 2 0.4008 0.765 0.244 0.756 0.000 0.000
#> GSM872262 4 0.0000 0.906 0.000 0.000 0.000 1.000
#> GSM872263 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> GSM872264 4 0.4426 0.754 0.000 0.204 0.024 0.772
#> GSM872265 4 0.3873 0.741 0.000 0.228 0.000 0.772
#> GSM872266 2 0.0817 0.934 0.024 0.976 0.000 0.000
#> GSM872267 2 0.0817 0.934 0.024 0.976 0.000 0.000
#> GSM872268 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> GSM872269 2 0.4164 0.743 0.264 0.736 0.000 0.000
#> GSM872270 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> GSM872271 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM872272 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM872273 4 0.1118 0.893 0.036 0.000 0.000 0.964
#> GSM872274 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM872275 3 0.0336 0.988 0.000 0.008 0.992 0.000
#> GSM872276 4 0.0000 0.906 0.000 0.000 0.000 1.000
#> GSM872277 4 0.0817 0.899 0.024 0.000 0.000 0.976
#> GSM872278 3 0.0817 0.974 0.000 0.000 0.976 0.024
#> GSM872279 1 0.2921 0.880 0.860 0.000 0.000 0.140
#> GSM872280 4 0.2814 0.798 0.000 0.000 0.132 0.868
#> GSM872281 4 0.0336 0.905 0.000 0.000 0.008 0.992
#> GSM872282 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> GSM872283 4 0.3726 0.759 0.000 0.212 0.000 0.788
#> GSM872284 4 0.0336 0.905 0.000 0.000 0.008 0.992
#> GSM872285 3 0.0188 0.990 0.000 0.000 0.996 0.004
#> GSM872286 1 0.0000 0.881 1.000 0.000 0.000 0.000
#> GSM872287 3 0.0000 0.993 0.000 0.000 1.000 0.000
#> GSM872288 1 0.0000 0.881 1.000 0.000 0.000 0.000
#> GSM872289 3 0.0469 0.985 0.012 0.000 0.988 0.000
#> GSM872290 1 0.2921 0.881 0.860 0.000 0.000 0.140
#> GSM872291 4 0.1557 0.878 0.056 0.000 0.000 0.944
#> GSM872292 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM872293 1 0.3528 0.854 0.808 0.000 0.000 0.192
#> GSM872294 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM872295 2 0.0707 0.935 0.020 0.980 0.000 0.000
#> GSM872296 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM872297 1 0.3610 0.849 0.800 0.000 0.000 0.200
#> GSM872298 4 0.0000 0.906 0.000 0.000 0.000 1.000
#> GSM872299 1 0.0000 0.881 1.000 0.000 0.000 0.000
#> GSM872300 4 0.0000 0.906 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM872245 5 0.1877 0.7052 0.064 0.000 0.000 0.012 0.924
#> GSM872246 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM872247 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM872248 2 0.4307 0.2551 0.000 0.504 0.000 0.000 0.496
#> GSM872249 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM872250 5 0.0000 0.7147 0.000 0.000 0.000 0.000 1.000
#> GSM872251 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM872252 5 0.4448 0.0204 0.480 0.000 0.000 0.004 0.516
#> GSM872253 3 0.3473 0.8313 0.052 0.008 0.852 0.004 0.084
#> GSM872254 5 0.3579 0.4018 0.000 0.240 0.000 0.004 0.756
#> GSM872255 1 0.1544 0.6250 0.932 0.000 0.000 0.068 0.000
#> GSM872256 1 0.3579 0.5799 0.756 0.000 0.000 0.004 0.240
#> GSM872257 2 0.1197 0.7504 0.000 0.952 0.000 0.000 0.048
#> GSM872258 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM872259 1 0.3906 0.5728 0.744 0.000 0.000 0.016 0.240
#> GSM872260 1 0.1571 0.6289 0.936 0.000 0.000 0.060 0.004
#> GSM872261 2 0.4403 0.2256 0.000 0.560 0.000 0.004 0.436
#> GSM872262 1 0.4307 -0.0109 0.504 0.000 0.000 0.496 0.000
#> GSM872263 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM872264 4 0.2349 0.7194 0.012 0.084 0.004 0.900 0.000
#> GSM872265 4 0.2248 0.7173 0.012 0.088 0.000 0.900 0.000
#> GSM872266 2 0.4304 0.2834 0.000 0.516 0.000 0.000 0.484
#> GSM872267 2 0.4171 0.4369 0.000 0.604 0.000 0.000 0.396
#> GSM872268 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM872269 5 0.3579 0.4018 0.000 0.240 0.000 0.004 0.756
#> GSM872270 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM872271 2 0.2852 0.6504 0.000 0.828 0.000 0.172 0.000
#> GSM872272 2 0.2891 0.6474 0.000 0.824 0.000 0.176 0.000
#> GSM872273 1 0.2464 0.6272 0.888 0.000 0.000 0.096 0.016
#> GSM872274 2 0.0000 0.7608 0.000 1.000 0.000 0.000 0.000
#> GSM872275 3 0.2719 0.8145 0.000 0.144 0.852 0.004 0.000
#> GSM872276 1 0.4287 0.0784 0.540 0.000 0.000 0.460 0.000
#> GSM872277 1 0.4010 0.6114 0.784 0.000 0.000 0.160 0.056
#> GSM872278 4 0.5574 0.1172 0.044 0.012 0.440 0.504 0.000
#> GSM872279 1 0.3741 0.5549 0.732 0.000 0.000 0.004 0.264
#> GSM872280 1 0.6543 -0.1024 0.456 0.000 0.212 0.332 0.000
#> GSM872281 4 0.2929 0.6140 0.180 0.000 0.000 0.820 0.000
#> GSM872282 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM872283 4 0.2130 0.7202 0.012 0.080 0.000 0.908 0.000
#> GSM872284 4 0.1544 0.6901 0.068 0.000 0.000 0.932 0.000
#> GSM872285 3 0.0404 0.9658 0.000 0.000 0.988 0.012 0.000
#> GSM872286 5 0.0609 0.7171 0.020 0.000 0.000 0.000 0.980
#> GSM872287 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM872288 5 0.0162 0.7163 0.004 0.000 0.000 0.000 0.996
#> GSM872289 3 0.0162 0.9726 0.000 0.000 0.996 0.000 0.004
#> GSM872290 1 0.3395 0.5771 0.764 0.000 0.000 0.000 0.236
#> GSM872291 1 0.1544 0.6239 0.932 0.000 0.000 0.068 0.000
#> GSM872292 2 0.0000 0.7608 0.000 1.000 0.000 0.000 0.000
#> GSM872293 1 0.3635 0.5727 0.748 0.000 0.000 0.004 0.248
#> GSM872294 2 0.0000 0.7608 0.000 1.000 0.000 0.000 0.000
#> GSM872295 2 0.1197 0.7504 0.000 0.952 0.000 0.000 0.048
#> GSM872296 2 0.0000 0.7608 0.000 1.000 0.000 0.000 0.000
#> GSM872297 1 0.3878 0.5766 0.748 0.000 0.000 0.016 0.236
#> GSM872298 4 0.4060 0.3623 0.360 0.000 0.000 0.640 0.000
#> GSM872299 5 0.4009 0.4079 0.312 0.000 0.000 0.004 0.684
#> GSM872300 1 0.4306 0.0020 0.508 0.000 0.000 0.492 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.0717 0.9163 0.000 0.000 0.976 0.000 0.016 0.008
#> GSM872245 5 0.4614 0.0963 0.416 0.000 0.000 0.004 0.548 0.032
#> GSM872246 3 0.0725 0.9165 0.000 0.000 0.976 0.000 0.012 0.012
#> GSM872247 3 0.0260 0.9171 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM872248 5 0.3881 0.4128 0.000 0.396 0.000 0.000 0.600 0.004
#> GSM872249 3 0.0146 0.9171 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM872250 5 0.1327 0.6955 0.064 0.000 0.000 0.000 0.936 0.000
#> GSM872251 3 0.0291 0.9172 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM872252 1 0.6151 0.3705 0.484 0.000 0.000 0.016 0.296 0.204
#> GSM872253 3 0.6916 0.1570 0.024 0.016 0.432 0.040 0.096 0.392
#> GSM872254 5 0.3444 0.6598 0.000 0.124 0.000 0.008 0.816 0.052
#> GSM872255 6 0.3719 0.7017 0.248 0.000 0.000 0.024 0.000 0.728
#> GSM872256 1 0.0748 0.7953 0.976 0.000 0.000 0.004 0.004 0.016
#> GSM872257 2 0.0777 0.7892 0.000 0.972 0.000 0.000 0.024 0.004
#> GSM872258 3 0.1088 0.9118 0.000 0.000 0.960 0.000 0.016 0.024
#> GSM872259 1 0.0405 0.7969 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM872260 6 0.3384 0.6675 0.228 0.000 0.000 0.004 0.008 0.760
#> GSM872261 2 0.5619 -0.0895 0.004 0.476 0.000 0.012 0.420 0.088
#> GSM872262 6 0.4590 0.6866 0.096 0.000 0.000 0.224 0.000 0.680
#> GSM872263 3 0.0717 0.9163 0.000 0.000 0.976 0.000 0.016 0.008
#> GSM872264 4 0.0692 0.6618 0.000 0.020 0.004 0.976 0.000 0.000
#> GSM872265 4 0.0692 0.6614 0.000 0.020 0.000 0.976 0.000 0.004
#> GSM872266 5 0.3915 0.3874 0.000 0.412 0.000 0.000 0.584 0.004
#> GSM872267 5 0.4114 0.2748 0.000 0.460 0.000 0.004 0.532 0.004
#> GSM872268 3 0.0260 0.9171 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM872269 5 0.3113 0.6723 0.000 0.100 0.000 0.008 0.844 0.048
#> GSM872270 3 0.0291 0.9165 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM872271 2 0.4058 0.5587 0.000 0.660 0.000 0.320 0.004 0.016
#> GSM872272 2 0.4195 0.5462 0.000 0.648 0.000 0.328 0.008 0.016
#> GSM872273 1 0.3417 0.6128 0.796 0.000 0.000 0.044 0.000 0.160
#> GSM872274 2 0.0000 0.8052 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872275 3 0.5740 0.5476 0.000 0.192 0.660 0.056 0.028 0.064
#> GSM872276 6 0.4545 0.7185 0.124 0.000 0.000 0.176 0.000 0.700
#> GSM872277 1 0.3017 0.6883 0.844 0.000 0.000 0.072 0.000 0.084
#> GSM872278 4 0.6665 0.1274 0.000 0.000 0.312 0.348 0.028 0.312
#> GSM872279 1 0.2321 0.7704 0.900 0.000 0.000 0.008 0.040 0.052
#> GSM872280 6 0.3714 0.6742 0.044 0.000 0.064 0.072 0.000 0.820
#> GSM872281 4 0.3999 -0.1850 0.000 0.000 0.004 0.500 0.000 0.496
#> GSM872282 3 0.0717 0.9163 0.000 0.000 0.976 0.000 0.016 0.008
#> GSM872283 4 0.1003 0.6563 0.016 0.020 0.000 0.964 0.000 0.000
#> GSM872284 4 0.2933 0.5186 0.000 0.000 0.004 0.796 0.000 0.200
#> GSM872285 3 0.1524 0.8718 0.000 0.000 0.932 0.008 0.000 0.060
#> GSM872286 5 0.1556 0.6887 0.080 0.000 0.000 0.000 0.920 0.000
#> GSM872287 3 0.0260 0.9171 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM872288 5 0.1444 0.6932 0.072 0.000 0.000 0.000 0.928 0.000
#> GSM872289 3 0.0909 0.9104 0.000 0.000 0.968 0.000 0.020 0.012
#> GSM872290 1 0.2741 0.7489 0.868 0.000 0.000 0.008 0.032 0.092
#> GSM872291 6 0.4341 0.5904 0.284 0.000 0.000 0.016 0.024 0.676
#> GSM872292 2 0.0000 0.8052 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872293 1 0.0436 0.7969 0.988 0.000 0.000 0.004 0.004 0.004
#> GSM872294 2 0.0000 0.8052 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872295 2 0.1053 0.7863 0.000 0.964 0.000 0.004 0.020 0.012
#> GSM872296 2 0.0146 0.8041 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM872297 1 0.0405 0.7969 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM872298 6 0.3837 0.5828 0.020 0.000 0.000 0.212 0.016 0.752
#> GSM872299 1 0.5449 0.2917 0.536 0.000 0.000 0.016 0.364 0.084
#> GSM872300 6 0.4582 0.6948 0.100 0.000 0.000 0.216 0.000 0.684
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 time(p) individual(p) k
#> CV:skmeans 54 0.678 4.88e-03 2
#> CV:skmeans 53 0.822 6.25e-03 3
#> CV:skmeans 57 0.238 6.40e-03 4
#> CV:skmeans 43 0.448 1.75e-04 5
#> CV:skmeans 47 0.896 1.53e-06 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 29485 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.364 0.692 0.799 0.4222 0.560 0.560
#> 3 3 0.442 0.719 0.821 0.4569 0.752 0.576
#> 4 4 0.635 0.815 0.872 0.1763 0.904 0.737
#> 5 5 0.708 0.799 0.869 0.0611 0.875 0.606
#> 6 6 0.744 0.622 0.785 0.0675 0.952 0.805
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM872244 2 0.983 0.799 0.424 0.576
#> GSM872245 2 0.000 0.489 0.000 1.000
#> GSM872246 1 0.000 0.780 1.000 0.000
#> GSM872247 1 0.000 0.780 1.000 0.000
#> GSM872248 2 0.983 0.799 0.424 0.576
#> GSM872249 1 0.000 0.780 1.000 0.000
#> GSM872250 2 0.861 0.727 0.284 0.716
#> GSM872251 1 0.000 0.780 1.000 0.000
#> GSM872252 1 0.850 0.627 0.724 0.276
#> GSM872253 1 0.000 0.780 1.000 0.000
#> GSM872254 2 0.775 0.680 0.228 0.772
#> GSM872255 1 0.844 0.629 0.728 0.272
#> GSM872256 1 0.969 0.552 0.604 0.396
#> GSM872257 2 0.983 0.799 0.424 0.576
#> GSM872258 1 0.000 0.780 1.000 0.000
#> GSM872259 1 0.985 0.530 0.572 0.428
#> GSM872260 1 0.260 0.758 0.956 0.044
#> GSM872261 2 0.983 0.799 0.424 0.576
#> GSM872262 1 0.184 0.769 0.972 0.028
#> GSM872263 1 0.000 0.780 1.000 0.000
#> GSM872264 1 0.000 0.780 1.000 0.000
#> GSM872265 1 0.000 0.780 1.000 0.000
#> GSM872266 2 0.983 0.799 0.424 0.576
#> GSM872267 2 0.983 0.799 0.424 0.576
#> GSM872268 1 0.000 0.780 1.000 0.000
#> GSM872269 2 0.886 0.740 0.304 0.696
#> GSM872270 1 0.000 0.780 1.000 0.000
#> GSM872271 2 0.983 0.799 0.424 0.576
#> GSM872272 2 0.983 0.799 0.424 0.576
#> GSM872273 1 0.983 0.534 0.576 0.424
#> GSM872274 2 0.983 0.799 0.424 0.576
#> GSM872275 1 0.000 0.780 1.000 0.000
#> GSM872276 1 0.983 0.534 0.576 0.424
#> GSM872277 1 0.983 0.534 0.576 0.424
#> GSM872278 1 0.000 0.780 1.000 0.000
#> GSM872279 1 0.983 0.534 0.576 0.424
#> GSM872280 1 0.000 0.780 1.000 0.000
#> GSM872281 1 0.000 0.780 1.000 0.000
#> GSM872282 1 0.163 0.748 0.976 0.024
#> GSM872283 1 0.295 0.752 0.948 0.052
#> GSM872284 1 0.000 0.780 1.000 0.000
#> GSM872285 1 0.000 0.780 1.000 0.000
#> GSM872286 2 0.000 0.489 0.000 1.000
#> GSM872287 1 0.000 0.780 1.000 0.000
#> GSM872288 2 0.952 0.536 0.372 0.628
#> GSM872289 1 0.000 0.780 1.000 0.000
#> GSM872290 1 0.983 0.534 0.576 0.424
#> GSM872291 1 0.881 0.614 0.700 0.300
#> GSM872292 2 0.983 0.799 0.424 0.576
#> GSM872293 1 0.983 0.534 0.576 0.424
#> GSM872294 1 0.000 0.780 1.000 0.000
#> GSM872295 2 0.983 0.799 0.424 0.576
#> GSM872296 1 0.416 0.646 0.916 0.084
#> GSM872297 1 0.983 0.534 0.576 0.424
#> GSM872298 1 0.000 0.780 1.000 0.000
#> GSM872299 2 0.987 -0.343 0.432 0.568
#> GSM872300 1 0.886 0.611 0.696 0.304
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.965 0.000 0.000 1.000
#> GSM872245 2 0.5988 0.625 0.368 0.632 0.000
#> GSM872246 3 0.0000 0.965 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.965 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.764 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.965 0.000 0.000 1.000
#> GSM872250 2 0.6594 0.750 0.116 0.756 0.128
#> GSM872251 3 0.0747 0.954 0.016 0.000 0.984
#> GSM872252 1 0.4062 0.716 0.836 0.000 0.164
#> GSM872253 1 0.6180 0.614 0.584 0.000 0.416
#> GSM872254 2 0.4742 0.770 0.104 0.848 0.048
#> GSM872255 1 0.4062 0.716 0.836 0.000 0.164
#> GSM872256 1 0.1399 0.695 0.968 0.004 0.028
#> GSM872257 2 0.0000 0.764 0.000 1.000 0.000
#> GSM872258 3 0.1163 0.942 0.028 0.000 0.972
#> GSM872259 1 0.0424 0.679 0.992 0.008 0.000
#> GSM872260 1 0.6008 0.646 0.628 0.000 0.372
#> GSM872261 2 0.6045 0.488 0.000 0.620 0.380
#> GSM872262 1 0.6062 0.639 0.616 0.000 0.384
#> GSM872263 3 0.0000 0.965 0.000 0.000 1.000
#> GSM872264 1 0.6180 0.614 0.584 0.000 0.416
#> GSM872265 1 0.6180 0.614 0.584 0.000 0.416
#> GSM872266 2 0.5058 0.672 0.000 0.756 0.244
#> GSM872267 2 0.0000 0.764 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.965 0.000 0.000 1.000
#> GSM872269 2 0.6254 0.759 0.108 0.776 0.116
#> GSM872270 3 0.0000 0.965 0.000 0.000 1.000
#> GSM872271 2 0.6180 0.411 0.000 0.584 0.416
#> GSM872272 2 0.6180 0.411 0.000 0.584 0.416
#> GSM872273 1 0.0000 0.685 1.000 0.000 0.000
#> GSM872274 2 0.1964 0.768 0.000 0.944 0.056
#> GSM872275 1 0.6180 0.614 0.584 0.000 0.416
#> GSM872276 1 0.0000 0.685 1.000 0.000 0.000
#> GSM872277 1 0.0000 0.685 1.000 0.000 0.000
#> GSM872278 1 0.6180 0.614 0.584 0.000 0.416
#> GSM872279 1 0.0000 0.685 1.000 0.000 0.000
#> GSM872280 1 0.6168 0.618 0.588 0.000 0.412
#> GSM872281 1 0.6168 0.618 0.588 0.000 0.412
#> GSM872282 3 0.0000 0.965 0.000 0.000 1.000
#> GSM872283 1 0.5968 0.637 0.636 0.000 0.364
#> GSM872284 1 0.6168 0.618 0.588 0.000 0.412
#> GSM872285 3 0.2356 0.891 0.072 0.000 0.928
#> GSM872286 2 0.5058 0.704 0.244 0.756 0.000
#> GSM872287 3 0.0000 0.965 0.000 0.000 1.000
#> GSM872288 2 0.8349 0.590 0.264 0.608 0.128
#> GSM872289 3 0.4121 0.702 0.168 0.000 0.832
#> GSM872290 1 0.0000 0.685 1.000 0.000 0.000
#> GSM872291 1 0.3482 0.717 0.872 0.000 0.128
#> GSM872292 2 0.1964 0.768 0.000 0.944 0.056
#> GSM872293 1 0.0000 0.685 1.000 0.000 0.000
#> GSM872294 1 0.8748 0.620 0.584 0.172 0.244
#> GSM872295 2 0.1964 0.768 0.000 0.944 0.056
#> GSM872296 1 0.9355 0.497 0.492 0.320 0.188
#> GSM872297 1 0.0000 0.685 1.000 0.000 0.000
#> GSM872298 1 0.6180 0.614 0.584 0.000 0.416
#> GSM872299 1 0.5327 0.394 0.728 0.272 0.000
#> GSM872300 1 0.3267 0.717 0.884 0.000 0.116
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.2647 0.870 0.000 0.000 0.880 0.120
#> GSM872245 1 0.1585 0.939 0.952 0.040 0.004 0.004
#> GSM872246 3 0.0188 0.888 0.000 0.000 0.996 0.004
#> GSM872247 3 0.0188 0.888 0.000 0.000 0.996 0.004
#> GSM872248 2 0.0376 0.818 0.000 0.992 0.004 0.004
#> GSM872249 3 0.0188 0.888 0.000 0.000 0.996 0.004
#> GSM872250 2 0.5082 0.793 0.108 0.776 0.004 0.112
#> GSM872251 3 0.3219 0.847 0.000 0.000 0.836 0.164
#> GSM872252 4 0.3585 0.809 0.164 0.004 0.004 0.828
#> GSM872253 4 0.1389 0.848 0.000 0.000 0.048 0.952
#> GSM872254 2 0.3765 0.800 0.116 0.848 0.004 0.032
#> GSM872255 4 0.2973 0.813 0.144 0.000 0.000 0.856
#> GSM872256 4 0.3810 0.798 0.188 0.000 0.008 0.804
#> GSM872257 2 0.0336 0.817 0.000 0.992 0.000 0.008
#> GSM872258 3 0.2216 0.873 0.000 0.000 0.908 0.092
#> GSM872259 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM872260 4 0.2214 0.854 0.044 0.000 0.028 0.928
#> GSM872261 2 0.5031 0.780 0.000 0.740 0.048 0.212
#> GSM872262 4 0.1388 0.853 0.028 0.000 0.012 0.960
#> GSM872263 3 0.0188 0.888 0.000 0.000 0.996 0.004
#> GSM872264 4 0.1557 0.845 0.000 0.000 0.056 0.944
#> GSM872265 4 0.1389 0.848 0.000 0.000 0.048 0.952
#> GSM872266 2 0.4285 0.807 0.000 0.804 0.040 0.156
#> GSM872267 2 0.0336 0.817 0.000 0.992 0.000 0.008
#> GSM872268 3 0.0188 0.888 0.000 0.000 0.996 0.004
#> GSM872269 2 0.4606 0.809 0.100 0.808 0.004 0.088
#> GSM872270 3 0.2868 0.859 0.000 0.000 0.864 0.136
#> GSM872271 2 0.5031 0.780 0.000 0.740 0.048 0.212
#> GSM872272 2 0.5031 0.780 0.000 0.740 0.048 0.212
#> GSM872273 1 0.1118 0.959 0.964 0.000 0.000 0.036
#> GSM872274 2 0.1118 0.822 0.000 0.964 0.000 0.036
#> GSM872275 4 0.1389 0.848 0.000 0.000 0.048 0.952
#> GSM872276 4 0.3311 0.793 0.172 0.000 0.000 0.828
#> GSM872277 1 0.1118 0.959 0.964 0.000 0.000 0.036
#> GSM872278 4 0.1389 0.848 0.000 0.000 0.048 0.952
#> GSM872279 4 0.4746 0.569 0.368 0.000 0.000 0.632
#> GSM872280 4 0.2345 0.828 0.000 0.000 0.100 0.900
#> GSM872281 4 0.1022 0.853 0.000 0.000 0.032 0.968
#> GSM872282 3 0.2469 0.873 0.000 0.000 0.892 0.108
#> GSM872283 4 0.1389 0.848 0.000 0.000 0.048 0.952
#> GSM872284 4 0.0469 0.853 0.000 0.000 0.012 0.988
#> GSM872285 3 0.3311 0.801 0.000 0.000 0.828 0.172
#> GSM872286 2 0.4198 0.710 0.224 0.768 0.004 0.004
#> GSM872287 3 0.0188 0.888 0.000 0.000 0.996 0.004
#> GSM872288 2 0.6758 0.548 0.104 0.580 0.004 0.312
#> GSM872289 3 0.4843 0.484 0.000 0.000 0.604 0.396
#> GSM872290 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM872291 4 0.3486 0.800 0.188 0.000 0.000 0.812
#> GSM872292 2 0.1118 0.822 0.000 0.964 0.000 0.036
#> GSM872293 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM872294 4 0.3583 0.767 0.000 0.180 0.004 0.816
#> GSM872295 2 0.1118 0.822 0.000 0.964 0.000 0.036
#> GSM872296 4 0.4730 0.523 0.000 0.364 0.000 0.636
#> GSM872297 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM872298 4 0.1389 0.848 0.000 0.000 0.048 0.952
#> GSM872299 4 0.7519 0.176 0.392 0.184 0.000 0.424
#> GSM872300 4 0.3074 0.809 0.152 0.000 0.000 0.848
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.2970 0.822 0.000 0.000 0.828 0.168 0.004
#> GSM872245 1 0.3143 0.818 0.796 0.000 0.000 0.000 0.204
#> GSM872246 3 0.0000 0.853 0.000 0.000 1.000 0.000 0.000
#> GSM872247 3 0.0000 0.853 0.000 0.000 1.000 0.000 0.000
#> GSM872248 5 0.2471 0.717 0.000 0.136 0.000 0.000 0.864
#> GSM872249 3 0.0000 0.853 0.000 0.000 1.000 0.000 0.000
#> GSM872250 5 0.1121 0.797 0.000 0.000 0.000 0.044 0.956
#> GSM872251 3 0.3336 0.784 0.000 0.000 0.772 0.228 0.000
#> GSM872252 4 0.3780 0.786 0.072 0.000 0.000 0.812 0.116
#> GSM872253 4 0.0000 0.845 0.000 0.000 0.000 1.000 0.000
#> GSM872254 5 0.1197 0.788 0.000 0.048 0.000 0.000 0.952
#> GSM872255 4 0.5625 0.788 0.160 0.096 0.000 0.700 0.044
#> GSM872256 4 0.5582 0.774 0.112 0.060 0.000 0.716 0.112
#> GSM872257 2 0.1965 0.923 0.000 0.904 0.000 0.000 0.096
#> GSM872258 3 0.2230 0.830 0.000 0.000 0.884 0.116 0.000
#> GSM872259 1 0.1908 0.921 0.908 0.000 0.000 0.000 0.092
#> GSM872260 4 0.1485 0.844 0.020 0.000 0.000 0.948 0.032
#> GSM872261 4 0.1270 0.828 0.000 0.000 0.000 0.948 0.052
#> GSM872262 4 0.5125 0.811 0.112 0.096 0.000 0.748 0.044
#> GSM872263 3 0.0000 0.853 0.000 0.000 1.000 0.000 0.000
#> GSM872264 4 0.0609 0.835 0.000 0.000 0.020 0.980 0.000
#> GSM872265 4 0.0000 0.845 0.000 0.000 0.000 1.000 0.000
#> GSM872266 5 0.2471 0.723 0.000 0.000 0.000 0.136 0.864
#> GSM872267 5 0.4074 0.352 0.000 0.364 0.000 0.000 0.636
#> GSM872268 3 0.0000 0.853 0.000 0.000 1.000 0.000 0.000
#> GSM872269 5 0.1579 0.796 0.000 0.032 0.000 0.024 0.944
#> GSM872270 3 0.3534 0.750 0.000 0.000 0.744 0.256 0.000
#> GSM872271 4 0.0000 0.845 0.000 0.000 0.000 1.000 0.000
#> GSM872272 4 0.0000 0.845 0.000 0.000 0.000 1.000 0.000
#> GSM872273 1 0.0794 0.855 0.972 0.028 0.000 0.000 0.000
#> GSM872274 2 0.1965 0.923 0.000 0.904 0.000 0.000 0.096
#> GSM872275 4 0.0000 0.845 0.000 0.000 0.000 1.000 0.000
#> GSM872276 4 0.5625 0.788 0.160 0.096 0.000 0.700 0.044
#> GSM872277 1 0.0794 0.855 0.972 0.028 0.000 0.000 0.000
#> GSM872278 4 0.0000 0.845 0.000 0.000 0.000 1.000 0.000
#> GSM872279 4 0.6152 0.459 0.332 0.020 0.000 0.556 0.092
#> GSM872280 4 0.6244 0.786 0.092 0.096 0.064 0.704 0.044
#> GSM872281 4 0.5031 0.815 0.092 0.096 0.004 0.764 0.044
#> GSM872282 3 0.2690 0.820 0.000 0.000 0.844 0.156 0.000
#> GSM872283 4 0.1121 0.847 0.000 0.044 0.000 0.956 0.000
#> GSM872284 4 0.4569 0.821 0.092 0.096 0.000 0.784 0.028
#> GSM872285 3 0.4052 0.757 0.000 0.024 0.784 0.176 0.016
#> GSM872286 5 0.1121 0.779 0.044 0.000 0.000 0.000 0.956
#> GSM872287 3 0.0000 0.853 0.000 0.000 1.000 0.000 0.000
#> GSM872288 5 0.1282 0.797 0.004 0.000 0.000 0.044 0.952
#> GSM872289 3 0.5470 0.527 0.000 0.000 0.564 0.364 0.072
#> GSM872290 1 0.1908 0.921 0.908 0.000 0.000 0.000 0.092
#> GSM872291 4 0.5771 0.764 0.096 0.068 0.000 0.700 0.136
#> GSM872292 2 0.1965 0.923 0.000 0.904 0.000 0.000 0.096
#> GSM872293 1 0.1908 0.921 0.908 0.000 0.000 0.000 0.092
#> GSM872294 2 0.2329 0.841 0.000 0.876 0.000 0.124 0.000
#> GSM872295 2 0.1965 0.923 0.000 0.904 0.000 0.000 0.096
#> GSM872296 2 0.2179 0.853 0.000 0.888 0.000 0.112 0.000
#> GSM872297 1 0.1908 0.921 0.908 0.000 0.000 0.000 0.092
#> GSM872298 4 0.0000 0.845 0.000 0.000 0.000 1.000 0.000
#> GSM872299 5 0.6682 0.133 0.192 0.008 0.000 0.328 0.472
#> GSM872300 4 0.5625 0.788 0.160 0.096 0.000 0.700 0.044
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.4898 0.737 0.000 0.000 0.656 0.200 0.000 0.144
#> GSM872245 1 0.3221 0.586 0.792 0.000 0.000 0.000 0.188 0.020
#> GSM872246 3 0.2300 0.783 0.000 0.000 0.856 0.000 0.000 0.144
#> GSM872247 3 0.0000 0.791 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872248 5 0.0000 0.859 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.791 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872250 5 0.0000 0.859 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872251 3 0.3101 0.702 0.000 0.000 0.756 0.244 0.000 0.000
#> GSM872252 6 0.6139 0.425 0.188 0.000 0.000 0.388 0.012 0.412
#> GSM872253 4 0.3765 -0.249 0.000 0.000 0.000 0.596 0.000 0.404
#> GSM872254 5 0.3672 0.219 0.000 0.000 0.000 0.000 0.632 0.368
#> GSM872255 4 0.3804 0.587 0.000 0.000 0.000 0.576 0.000 0.424
#> GSM872256 4 0.5384 0.489 0.184 0.000 0.000 0.604 0.004 0.208
#> GSM872257 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872258 3 0.4154 0.765 0.000 0.000 0.744 0.112 0.000 0.144
#> GSM872259 1 0.0000 0.699 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872260 4 0.2448 0.621 0.064 0.000 0.000 0.884 0.000 0.052
#> GSM872261 4 0.0000 0.647 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872262 4 0.3804 0.587 0.000 0.000 0.000 0.576 0.000 0.424
#> GSM872263 3 0.2300 0.783 0.000 0.000 0.856 0.000 0.000 0.144
#> GSM872264 4 0.0547 0.640 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM872265 4 0.0547 0.640 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM872266 5 0.0000 0.859 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872267 5 0.3756 0.271 0.000 0.400 0.000 0.000 0.600 0.000
#> GSM872268 3 0.0000 0.791 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872269 5 0.0000 0.859 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872270 3 0.3464 0.605 0.000 0.000 0.688 0.312 0.000 0.000
#> GSM872271 4 0.3810 -0.266 0.000 0.000 0.000 0.572 0.000 0.428
#> GSM872272 4 0.0547 0.640 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM872273 1 0.2597 0.646 0.824 0.000 0.000 0.000 0.000 0.176
#> GSM872274 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872275 4 0.0000 0.647 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872276 4 0.3804 0.587 0.000 0.000 0.000 0.576 0.000 0.424
#> GSM872277 1 0.2597 0.646 0.824 0.000 0.000 0.000 0.000 0.176
#> GSM872278 4 0.0000 0.647 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872279 1 0.5392 -0.315 0.448 0.000 0.000 0.112 0.000 0.440
#> GSM872280 4 0.3804 0.587 0.000 0.000 0.000 0.576 0.000 0.424
#> GSM872281 4 0.3804 0.587 0.000 0.000 0.000 0.576 0.000 0.424
#> GSM872282 3 0.4634 0.752 0.000 0.000 0.692 0.164 0.000 0.144
#> GSM872283 4 0.2006 0.643 0.004 0.000 0.000 0.892 0.000 0.104
#> GSM872284 4 0.3747 0.595 0.000 0.000 0.000 0.604 0.000 0.396
#> GSM872285 3 0.4793 0.534 0.000 0.000 0.628 0.288 0.000 0.084
#> GSM872286 5 0.0000 0.859 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872287 3 0.0000 0.791 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872288 5 0.0000 0.859 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872289 3 0.6847 0.596 0.000 0.000 0.504 0.216 0.136 0.144
#> GSM872290 1 0.3782 0.081 0.588 0.000 0.000 0.000 0.000 0.412
#> GSM872291 6 0.4892 0.418 0.176 0.000 0.000 0.164 0.000 0.660
#> GSM872292 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872293 1 0.0000 0.699 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872294 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872295 2 0.1501 0.909 0.000 0.924 0.000 0.000 0.000 0.076
#> GSM872296 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872297 1 0.0000 0.699 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872298 4 0.0000 0.647 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872299 6 0.6010 0.133 0.200 0.000 0.000 0.004 0.384 0.412
#> GSM872300 4 0.3804 0.587 0.000 0.000 0.000 0.576 0.000 0.424
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 time(p) individual(p) k
#> CV:pam 54 0.526 3.49e-02 2
#> CV:pam 52 0.790 8.83e-05 3
#> CV:pam 55 0.890 2.59e-05 4
#> CV:pam 54 0.681 1.23e-06 5
#> CV:pam 47 0.647 8.00e-07 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 29485 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.804 0.936 0.940 0.4229 0.560 0.560
#> 3 3 0.802 0.890 0.929 0.3359 0.612 0.441
#> 4 4 0.727 0.809 0.912 0.2930 0.761 0.496
#> 5 5 0.820 0.799 0.892 0.0712 0.921 0.720
#> 6 6 0.829 0.821 0.895 0.0625 0.904 0.598
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM872244 1 0.000 0.923 1.000 0.000
#> GSM872245 1 0.952 0.507 0.628 0.372
#> GSM872246 1 0.000 0.923 1.000 0.000
#> GSM872247 1 0.000 0.923 1.000 0.000
#> GSM872248 2 0.000 0.953 0.000 1.000
#> GSM872249 1 0.000 0.923 1.000 0.000
#> GSM872250 1 0.430 0.956 0.912 0.088
#> GSM872251 1 0.000 0.923 1.000 0.000
#> GSM872252 1 0.402 0.961 0.920 0.080
#> GSM872253 1 0.402 0.961 0.920 0.080
#> GSM872254 2 0.388 0.926 0.076 0.924
#> GSM872255 1 0.402 0.961 0.920 0.080
#> GSM872256 1 0.402 0.961 0.920 0.080
#> GSM872257 2 0.000 0.953 0.000 1.000
#> GSM872258 1 0.204 0.939 0.968 0.032
#> GSM872259 1 0.402 0.961 0.920 0.080
#> GSM872260 1 0.402 0.961 0.920 0.080
#> GSM872261 2 0.373 0.930 0.072 0.928
#> GSM872262 1 0.402 0.961 0.920 0.080
#> GSM872263 1 0.000 0.923 1.000 0.000
#> GSM872264 2 0.224 0.956 0.036 0.964
#> GSM872265 2 0.224 0.956 0.036 0.964
#> GSM872266 2 0.184 0.958 0.028 0.972
#> GSM872267 2 0.000 0.953 0.000 1.000
#> GSM872268 1 0.000 0.923 1.000 0.000
#> GSM872269 2 0.689 0.800 0.184 0.816
#> GSM872270 1 0.000 0.923 1.000 0.000
#> GSM872271 2 0.184 0.958 0.028 0.972
#> GSM872272 2 0.184 0.958 0.028 0.972
#> GSM872273 1 0.402 0.961 0.920 0.080
#> GSM872274 2 0.000 0.953 0.000 1.000
#> GSM872275 1 0.416 0.959 0.916 0.084
#> GSM872276 1 0.402 0.961 0.920 0.080
#> GSM872277 1 0.402 0.961 0.920 0.080
#> GSM872278 1 0.541 0.925 0.876 0.124
#> GSM872279 1 0.402 0.961 0.920 0.080
#> GSM872280 1 0.402 0.961 0.920 0.080
#> GSM872281 1 0.634 0.884 0.840 0.160
#> GSM872282 1 0.000 0.923 1.000 0.000
#> GSM872283 2 0.224 0.956 0.036 0.964
#> GSM872284 2 0.689 0.799 0.184 0.816
#> GSM872285 1 0.402 0.961 0.920 0.080
#> GSM872286 1 0.416 0.959 0.916 0.084
#> GSM872287 1 0.000 0.923 1.000 0.000
#> GSM872288 1 0.402 0.961 0.920 0.080
#> GSM872289 1 0.402 0.961 0.920 0.080
#> GSM872290 1 0.402 0.961 0.920 0.080
#> GSM872291 1 0.402 0.961 0.920 0.080
#> GSM872292 2 0.000 0.953 0.000 1.000
#> GSM872293 1 0.402 0.961 0.920 0.080
#> GSM872294 2 0.184 0.958 0.028 0.972
#> GSM872295 2 0.000 0.953 0.000 1.000
#> GSM872296 2 0.000 0.953 0.000 1.000
#> GSM872297 1 0.402 0.961 0.920 0.080
#> GSM872298 1 0.402 0.961 0.920 0.080
#> GSM872299 1 0.402 0.961 0.920 0.080
#> GSM872300 1 0.402 0.961 0.920 0.080
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.956 0.000 0.000 1.000
#> GSM872245 1 0.2625 0.922 0.916 0.084 0.000
#> GSM872246 3 0.0000 0.956 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.956 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.870 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.956 0.000 0.000 1.000
#> GSM872250 1 0.2625 0.922 0.916 0.084 0.000
#> GSM872251 3 0.0000 0.956 0.000 0.000 1.000
#> GSM872252 1 0.2625 0.922 0.916 0.084 0.000
#> GSM872253 1 0.2625 0.922 0.916 0.084 0.000
#> GSM872254 2 0.3752 0.792 0.144 0.856 0.000
#> GSM872255 1 0.0747 0.924 0.984 0.016 0.000
#> GSM872256 1 0.2448 0.924 0.924 0.076 0.000
#> GSM872257 2 0.0000 0.870 0.000 1.000 0.000
#> GSM872258 3 0.0000 0.956 0.000 0.000 1.000
#> GSM872259 1 0.2625 0.922 0.916 0.084 0.000
#> GSM872260 1 0.2261 0.925 0.932 0.068 0.000
#> GSM872261 1 0.2625 0.922 0.916 0.084 0.000
#> GSM872262 1 0.0000 0.922 1.000 0.000 0.000
#> GSM872263 3 0.0000 0.956 0.000 0.000 1.000
#> GSM872264 1 0.1964 0.899 0.944 0.000 0.056
#> GSM872265 1 0.1964 0.899 0.944 0.000 0.056
#> GSM872266 2 0.3340 0.813 0.120 0.880 0.000
#> GSM872267 2 0.0000 0.870 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.956 0.000 0.000 1.000
#> GSM872269 2 0.5650 0.553 0.312 0.688 0.000
#> GSM872270 3 0.0000 0.956 0.000 0.000 1.000
#> GSM872271 1 0.4519 0.814 0.852 0.116 0.032
#> GSM872272 1 0.4551 0.802 0.844 0.132 0.024
#> GSM872273 1 0.0000 0.922 1.000 0.000 0.000
#> GSM872274 2 0.2625 0.843 0.084 0.916 0.000
#> GSM872275 1 0.1964 0.899 0.944 0.000 0.056
#> GSM872276 1 0.0000 0.922 1.000 0.000 0.000
#> GSM872277 1 0.0000 0.922 1.000 0.000 0.000
#> GSM872278 1 0.1964 0.899 0.944 0.000 0.056
#> GSM872279 1 0.2625 0.922 0.916 0.084 0.000
#> GSM872280 1 0.0000 0.922 1.000 0.000 0.000
#> GSM872281 1 0.1964 0.899 0.944 0.000 0.056
#> GSM872282 3 0.0000 0.956 0.000 0.000 1.000
#> GSM872283 1 0.0237 0.921 0.996 0.000 0.004
#> GSM872284 1 0.1964 0.899 0.944 0.000 0.056
#> GSM872285 1 0.2959 0.881 0.900 0.000 0.100
#> GSM872286 1 0.2625 0.922 0.916 0.084 0.000
#> GSM872287 3 0.0000 0.956 0.000 0.000 1.000
#> GSM872288 1 0.2625 0.922 0.916 0.084 0.000
#> GSM872289 3 0.5785 0.451 0.332 0.000 0.668
#> GSM872290 1 0.2625 0.922 0.916 0.084 0.000
#> GSM872291 1 0.2165 0.925 0.936 0.064 0.000
#> GSM872292 2 0.2625 0.843 0.084 0.916 0.000
#> GSM872293 1 0.2625 0.922 0.916 0.084 0.000
#> GSM872294 1 0.5254 0.614 0.736 0.264 0.000
#> GSM872295 2 0.0000 0.870 0.000 1.000 0.000
#> GSM872296 2 0.2625 0.843 0.084 0.916 0.000
#> GSM872297 1 0.2625 0.922 0.916 0.084 0.000
#> GSM872298 1 0.0000 0.922 1.000 0.000 0.000
#> GSM872299 1 0.2625 0.922 0.916 0.084 0.000
#> GSM872300 1 0.0000 0.922 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM872245 1 0.0000 0.871 1.000 0.000 0.000 0.000
#> GSM872246 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM872247 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM872248 2 0.3873 0.713 0.228 0.772 0.000 0.000
#> GSM872249 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM872250 1 0.0000 0.871 1.000 0.000 0.000 0.000
#> GSM872251 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM872252 1 0.2011 0.860 0.920 0.000 0.000 0.080
#> GSM872253 3 0.7302 0.166 0.168 0.000 0.500 0.332
#> GSM872254 1 0.0000 0.871 1.000 0.000 0.000 0.000
#> GSM872255 4 0.0000 0.860 0.000 0.000 0.000 1.000
#> GSM872256 4 0.3975 0.611 0.240 0.000 0.000 0.760
#> GSM872257 2 0.0000 0.898 0.000 1.000 0.000 0.000
#> GSM872258 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM872259 1 0.3311 0.817 0.828 0.000 0.000 0.172
#> GSM872260 4 0.3172 0.727 0.160 0.000 0.000 0.840
#> GSM872261 1 0.0707 0.871 0.980 0.000 0.000 0.020
#> GSM872262 4 0.0000 0.860 0.000 0.000 0.000 1.000
#> GSM872263 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM872264 4 0.2469 0.835 0.000 0.000 0.108 0.892
#> GSM872265 4 0.2469 0.835 0.000 0.000 0.108 0.892
#> GSM872266 1 0.4888 0.171 0.588 0.412 0.000 0.000
#> GSM872267 2 0.0000 0.898 0.000 1.000 0.000 0.000
#> GSM872268 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM872269 1 0.0000 0.871 1.000 0.000 0.000 0.000
#> GSM872270 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM872271 4 0.5923 0.340 0.000 0.376 0.044 0.580
#> GSM872272 4 0.5699 0.342 0.000 0.380 0.032 0.588
#> GSM872273 4 0.0188 0.859 0.004 0.000 0.000 0.996
#> GSM872274 2 0.0000 0.898 0.000 1.000 0.000 0.000
#> GSM872275 4 0.2704 0.824 0.000 0.000 0.124 0.876
#> GSM872276 4 0.0000 0.860 0.000 0.000 0.000 1.000
#> GSM872277 4 0.0000 0.860 0.000 0.000 0.000 1.000
#> GSM872278 4 0.2589 0.830 0.000 0.000 0.116 0.884
#> GSM872279 1 0.3311 0.817 0.828 0.000 0.000 0.172
#> GSM872280 4 0.1022 0.854 0.000 0.000 0.032 0.968
#> GSM872281 4 0.2011 0.848 0.000 0.000 0.080 0.920
#> GSM872282 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM872283 4 0.1389 0.856 0.000 0.000 0.048 0.952
#> GSM872284 4 0.2149 0.845 0.000 0.000 0.088 0.912
#> GSM872285 4 0.4477 0.602 0.000 0.000 0.312 0.688
#> GSM872286 1 0.0000 0.871 1.000 0.000 0.000 0.000
#> GSM872287 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM872288 1 0.2011 0.853 0.920 0.000 0.000 0.080
#> GSM872289 3 0.0707 0.931 0.000 0.000 0.980 0.020
#> GSM872290 1 0.4222 0.695 0.728 0.000 0.000 0.272
#> GSM872291 4 0.0000 0.860 0.000 0.000 0.000 1.000
#> GSM872292 2 0.0000 0.898 0.000 1.000 0.000 0.000
#> GSM872293 1 0.3311 0.817 0.828 0.000 0.000 0.172
#> GSM872294 2 0.3610 0.693 0.000 0.800 0.000 0.200
#> GSM872295 2 0.3266 0.767 0.168 0.832 0.000 0.000
#> GSM872296 2 0.0000 0.898 0.000 1.000 0.000 0.000
#> GSM872297 4 0.4331 0.522 0.288 0.000 0.000 0.712
#> GSM872298 4 0.0000 0.860 0.000 0.000 0.000 1.000
#> GSM872299 1 0.0000 0.871 1.000 0.000 0.000 0.000
#> GSM872300 4 0.0000 0.860 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000
#> GSM872245 5 0.2690 0.825 0.156 0.000 0.000 0.000 0.844
#> GSM872246 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000
#> GSM872247 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000
#> GSM872248 5 0.3966 0.445 0.000 0.336 0.000 0.000 0.664
#> GSM872249 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000
#> GSM872250 5 0.2208 0.840 0.072 0.000 0.000 0.020 0.908
#> GSM872251 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000
#> GSM872252 5 0.4341 0.558 0.404 0.000 0.000 0.004 0.592
#> GSM872253 3 0.6388 0.241 0.000 0.000 0.496 0.312 0.192
#> GSM872254 5 0.1410 0.836 0.060 0.000 0.000 0.000 0.940
#> GSM872255 4 0.2813 0.714 0.168 0.000 0.000 0.832 0.000
#> GSM872256 1 0.1908 0.839 0.908 0.000 0.000 0.092 0.000
#> GSM872257 2 0.1608 0.839 0.000 0.928 0.000 0.000 0.072
#> GSM872258 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000
#> GSM872259 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM872260 4 0.4074 0.353 0.364 0.000 0.000 0.636 0.000
#> GSM872261 5 0.2505 0.839 0.092 0.000 0.000 0.020 0.888
#> GSM872262 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000
#> GSM872263 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000
#> GSM872264 4 0.3336 0.832 0.000 0.000 0.096 0.844 0.060
#> GSM872265 4 0.3401 0.830 0.000 0.000 0.096 0.840 0.064
#> GSM872266 5 0.2407 0.750 0.004 0.088 0.012 0.000 0.896
#> GSM872267 2 0.0703 0.861 0.000 0.976 0.000 0.000 0.024
#> GSM872268 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000
#> GSM872269 5 0.1410 0.836 0.060 0.000 0.000 0.000 0.940
#> GSM872270 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000
#> GSM872271 4 0.6589 0.535 0.000 0.252 0.096 0.588 0.064
#> GSM872272 4 0.6546 0.550 0.000 0.244 0.096 0.596 0.064
#> GSM872273 1 0.3966 0.538 0.664 0.000 0.000 0.336 0.000
#> GSM872274 2 0.0000 0.864 0.000 1.000 0.000 0.000 0.000
#> GSM872275 4 0.2074 0.845 0.000 0.000 0.104 0.896 0.000
#> GSM872276 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000
#> GSM872277 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000
#> GSM872278 4 0.1965 0.848 0.000 0.000 0.096 0.904 0.000
#> GSM872279 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM872280 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000
#> GSM872281 4 0.1965 0.848 0.000 0.000 0.096 0.904 0.000
#> GSM872282 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000
#> GSM872283 4 0.3401 0.830 0.000 0.000 0.096 0.840 0.064
#> GSM872284 4 0.1965 0.848 0.000 0.000 0.096 0.904 0.000
#> GSM872285 4 0.2605 0.820 0.000 0.000 0.148 0.852 0.000
#> GSM872286 5 0.2561 0.831 0.144 0.000 0.000 0.000 0.856
#> GSM872287 3 0.0000 0.949 0.000 0.000 1.000 0.000 0.000
#> GSM872288 5 0.3454 0.806 0.100 0.000 0.000 0.064 0.836
#> GSM872289 3 0.1478 0.884 0.000 0.000 0.936 0.064 0.000
#> GSM872290 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM872291 4 0.2690 0.726 0.156 0.000 0.000 0.844 0.000
#> GSM872292 2 0.0000 0.864 0.000 1.000 0.000 0.000 0.000
#> GSM872293 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM872294 2 0.4219 0.147 0.000 0.584 0.000 0.416 0.000
#> GSM872295 2 0.2605 0.782 0.000 0.852 0.000 0.000 0.148
#> GSM872296 2 0.0000 0.864 0.000 1.000 0.000 0.000 0.000
#> GSM872297 1 0.0000 0.905 1.000 0.000 0.000 0.000 0.000
#> GSM872298 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000
#> GSM872299 5 0.4060 0.642 0.360 0.000 0.000 0.000 0.640
#> GSM872300 4 0.0000 0.846 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.0000 0.9035 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872245 5 0.2260 0.8000 0.140 0.000 0.000 0.000 0.860 0.000
#> GSM872246 3 0.0000 0.9035 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872247 3 0.0000 0.9035 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872248 2 0.3868 0.0522 0.000 0.508 0.000 0.000 0.492 0.000
#> GSM872249 3 0.0000 0.9035 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872250 5 0.0520 0.8506 0.008 0.000 0.000 0.008 0.984 0.000
#> GSM872251 3 0.0713 0.8918 0.000 0.000 0.972 0.028 0.000 0.000
#> GSM872252 5 0.4193 0.6421 0.272 0.000 0.000 0.044 0.684 0.000
#> GSM872253 3 0.5703 0.4407 0.000 0.000 0.540 0.188 0.268 0.004
#> GSM872254 5 0.1141 0.8215 0.000 0.052 0.000 0.000 0.948 0.000
#> GSM872255 6 0.1957 0.8606 0.000 0.000 0.000 0.112 0.000 0.888
#> GSM872256 1 0.2178 0.8169 0.868 0.000 0.000 0.000 0.000 0.132
#> GSM872257 2 0.0458 0.8378 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM872258 3 0.2527 0.8116 0.000 0.000 0.832 0.168 0.000 0.000
#> GSM872259 1 0.0000 0.9641 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872260 6 0.3495 0.7849 0.060 0.000 0.000 0.128 0.004 0.808
#> GSM872261 5 0.1204 0.8412 0.000 0.000 0.000 0.056 0.944 0.000
#> GSM872262 6 0.0000 0.9410 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872263 3 0.0000 0.9035 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872264 4 0.3290 0.8258 0.000 0.000 0.004 0.744 0.000 0.252
#> GSM872265 4 0.3290 0.8258 0.000 0.000 0.004 0.744 0.000 0.252
#> GSM872266 5 0.0146 0.8470 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM872267 2 0.1333 0.8531 0.000 0.944 0.000 0.048 0.008 0.000
#> GSM872268 3 0.0000 0.9035 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872269 5 0.0000 0.8475 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872270 3 0.0000 0.9035 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872271 4 0.3240 0.8262 0.000 0.040 0.000 0.812 0.000 0.148
#> GSM872272 4 0.3240 0.8262 0.000 0.040 0.000 0.812 0.000 0.148
#> GSM872273 6 0.1204 0.8968 0.056 0.000 0.000 0.000 0.000 0.944
#> GSM872274 2 0.1204 0.8533 0.000 0.944 0.000 0.056 0.000 0.000
#> GSM872275 4 0.1765 0.6985 0.000 0.000 0.052 0.924 0.000 0.024
#> GSM872276 6 0.0000 0.9410 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872277 6 0.0000 0.9410 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872278 4 0.3046 0.8331 0.000 0.000 0.012 0.800 0.000 0.188
#> GSM872279 1 0.0000 0.9641 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872280 6 0.1957 0.8611 0.000 0.000 0.000 0.112 0.000 0.888
#> GSM872281 6 0.0146 0.9389 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM872282 3 0.0000 0.9035 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872283 4 0.3961 0.5391 0.000 0.000 0.004 0.556 0.000 0.440
#> GSM872284 6 0.0146 0.9389 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM872285 3 0.5539 0.4762 0.000 0.000 0.552 0.188 0.000 0.260
#> GSM872286 5 0.0790 0.8497 0.032 0.000 0.000 0.000 0.968 0.000
#> GSM872287 3 0.0000 0.9035 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872288 5 0.2980 0.7481 0.012 0.000 0.000 0.180 0.808 0.000
#> GSM872289 3 0.3221 0.7852 0.000 0.000 0.792 0.188 0.020 0.000
#> GSM872290 1 0.0000 0.9641 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872291 6 0.0146 0.9401 0.000 0.000 0.000 0.004 0.000 0.996
#> GSM872292 2 0.1204 0.8533 0.000 0.944 0.000 0.056 0.000 0.000
#> GSM872293 1 0.0000 0.9641 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872294 4 0.3247 0.7067 0.000 0.156 0.000 0.808 0.000 0.036
#> GSM872295 2 0.2491 0.7432 0.000 0.836 0.000 0.000 0.164 0.000
#> GSM872296 2 0.1204 0.8533 0.000 0.944 0.000 0.056 0.000 0.000
#> GSM872297 1 0.0000 0.9641 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872298 6 0.0000 0.9410 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872299 5 0.3843 0.2936 0.452 0.000 0.000 0.000 0.548 0.000
#> GSM872300 6 0.0000 0.9410 0.000 0.000 0.000 0.000 0.000 1.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 time(p) individual(p) k
#> CV:mclust 57 0.377 0.234717 2
#> CV:mclust 56 0.570 0.000723 3
#> CV:mclust 53 0.395 0.000170 4
#> CV:mclust 53 0.301 0.001181 5
#> CV:mclust 53 0.237 0.003681 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 29485 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.514 0.771 0.885 0.4721 0.491 0.491
#> 3 3 0.918 0.903 0.960 0.4103 0.677 0.437
#> 4 4 0.680 0.663 0.807 0.1151 0.888 0.679
#> 5 5 0.635 0.630 0.769 0.0697 0.873 0.574
#> 6 6 0.639 0.590 0.718 0.0447 0.886 0.537
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
#> GSM872244 1 0.3584 0.8565 0.932 0.068
#> GSM872245 2 0.7745 0.7703 0.228 0.772
#> GSM872246 1 0.0000 0.9055 1.000 0.000
#> GSM872247 1 0.0000 0.9055 1.000 0.000
#> GSM872248 2 0.0000 0.7990 0.000 1.000
#> GSM872249 1 0.2948 0.8714 0.948 0.052
#> GSM872250 2 0.7056 0.7759 0.192 0.808
#> GSM872251 1 0.0000 0.9055 1.000 0.000
#> GSM872252 2 0.9000 0.7304 0.316 0.684
#> GSM872253 1 0.2236 0.8886 0.964 0.036
#> GSM872254 2 0.0000 0.7990 0.000 1.000
#> GSM872255 1 0.0000 0.9055 1.000 0.000
#> GSM872256 2 0.9000 0.7304 0.316 0.684
#> GSM872257 2 0.0000 0.7990 0.000 1.000
#> GSM872258 1 0.0000 0.9055 1.000 0.000
#> GSM872259 2 0.9000 0.7304 0.316 0.684
#> GSM872260 1 0.9286 0.2800 0.656 0.344
#> GSM872261 2 0.6801 0.7787 0.180 0.820
#> GSM872262 1 0.0000 0.9055 1.000 0.000
#> GSM872263 1 0.1843 0.8893 0.972 0.028
#> GSM872264 1 0.0000 0.9055 1.000 0.000
#> GSM872265 1 0.9775 0.0133 0.588 0.412
#> GSM872266 2 0.0000 0.7990 0.000 1.000
#> GSM872267 2 0.0000 0.7990 0.000 1.000
#> GSM872268 1 0.0000 0.9055 1.000 0.000
#> GSM872269 2 0.0000 0.7990 0.000 1.000
#> GSM872270 1 0.2948 0.8714 0.948 0.052
#> GSM872271 2 0.0000 0.7990 0.000 1.000
#> GSM872272 2 0.0000 0.7990 0.000 1.000
#> GSM872273 2 0.9909 0.4692 0.444 0.556
#> GSM872274 2 0.0000 0.7990 0.000 1.000
#> GSM872275 1 0.3431 0.8605 0.936 0.064
#> GSM872276 1 0.0000 0.9055 1.000 0.000
#> GSM872277 1 0.9963 -0.2090 0.536 0.464
#> GSM872278 1 0.0000 0.9055 1.000 0.000
#> GSM872279 2 0.9000 0.7304 0.316 0.684
#> GSM872280 1 0.0000 0.9055 1.000 0.000
#> GSM872281 1 0.0000 0.9055 1.000 0.000
#> GSM872282 1 0.6531 0.7344 0.832 0.168
#> GSM872283 2 0.9427 0.6597 0.360 0.640
#> GSM872284 1 0.0000 0.9055 1.000 0.000
#> GSM872285 1 0.0000 0.9055 1.000 0.000
#> GSM872286 2 0.8813 0.7410 0.300 0.700
#> GSM872287 1 0.0000 0.9055 1.000 0.000
#> GSM872288 2 0.9044 0.7249 0.320 0.680
#> GSM872289 1 0.0000 0.9055 1.000 0.000
#> GSM872290 2 0.9000 0.7304 0.316 0.684
#> GSM872291 1 0.8813 0.4114 0.700 0.300
#> GSM872292 2 0.0000 0.7990 0.000 1.000
#> GSM872293 2 0.9000 0.7304 0.316 0.684
#> GSM872294 2 0.0000 0.7990 0.000 1.000
#> GSM872295 2 0.0000 0.7990 0.000 1.000
#> GSM872296 2 0.0000 0.7990 0.000 1.000
#> GSM872297 2 0.9000 0.7304 0.316 0.684
#> GSM872298 1 0.0000 0.9055 1.000 0.000
#> GSM872299 2 0.8813 0.7410 0.300 0.700
#> GSM872300 1 0.0376 0.9029 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872245 1 0.1289 0.907 0.968 0.032 0.000
#> GSM872246 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.945 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872250 2 0.6111 0.414 0.396 0.604 0.000
#> GSM872251 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872252 1 0.0000 0.933 1.000 0.000 0.000
#> GSM872253 3 0.3715 0.837 0.128 0.004 0.868
#> GSM872254 2 0.0892 0.933 0.020 0.980 0.000
#> GSM872255 1 0.0000 0.933 1.000 0.000 0.000
#> GSM872256 1 0.0000 0.933 1.000 0.000 0.000
#> GSM872257 2 0.0000 0.945 0.000 1.000 0.000
#> GSM872258 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872259 1 0.0000 0.933 1.000 0.000 0.000
#> GSM872260 1 0.0000 0.933 1.000 0.000 0.000
#> GSM872261 2 0.5291 0.664 0.268 0.732 0.000
#> GSM872262 1 0.2711 0.871 0.912 0.000 0.088
#> GSM872263 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872264 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872265 1 0.6950 0.130 0.508 0.016 0.476
#> GSM872266 2 0.0000 0.945 0.000 1.000 0.000
#> GSM872267 2 0.0000 0.945 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872269 2 0.2356 0.893 0.072 0.928 0.000
#> GSM872270 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872271 2 0.0000 0.945 0.000 1.000 0.000
#> GSM872272 2 0.0000 0.945 0.000 1.000 0.000
#> GSM872273 1 0.0000 0.933 1.000 0.000 0.000
#> GSM872274 2 0.0000 0.945 0.000 1.000 0.000
#> GSM872275 3 0.0237 0.984 0.000 0.004 0.996
#> GSM872276 1 0.2066 0.895 0.940 0.000 0.060
#> GSM872277 1 0.0000 0.933 1.000 0.000 0.000
#> GSM872278 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872279 1 0.0000 0.933 1.000 0.000 0.000
#> GSM872280 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872281 3 0.2066 0.928 0.060 0.000 0.940
#> GSM872282 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872283 1 0.1643 0.906 0.956 0.000 0.044
#> GSM872284 1 0.6286 0.199 0.536 0.000 0.464
#> GSM872285 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872286 1 0.0000 0.933 1.000 0.000 0.000
#> GSM872287 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872288 1 0.0000 0.933 1.000 0.000 0.000
#> GSM872289 3 0.0592 0.976 0.012 0.000 0.988
#> GSM872290 1 0.0000 0.933 1.000 0.000 0.000
#> GSM872291 1 0.0000 0.933 1.000 0.000 0.000
#> GSM872292 2 0.0000 0.945 0.000 1.000 0.000
#> GSM872293 1 0.0000 0.933 1.000 0.000 0.000
#> GSM872294 2 0.0000 0.945 0.000 1.000 0.000
#> GSM872295 2 0.0000 0.945 0.000 1.000 0.000
#> GSM872296 2 0.0000 0.945 0.000 1.000 0.000
#> GSM872297 1 0.0000 0.933 1.000 0.000 0.000
#> GSM872298 1 0.3482 0.832 0.872 0.000 0.128
#> GSM872299 1 0.0000 0.933 1.000 0.000 0.000
#> GSM872300 1 0.0237 0.931 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0707 0.849 0.000 0.000 0.980 0.020
#> GSM872245 1 0.0927 0.638 0.976 0.008 0.000 0.016
#> GSM872246 3 0.1211 0.867 0.000 0.000 0.960 0.040
#> GSM872247 3 0.2408 0.866 0.000 0.000 0.896 0.104
#> GSM872248 2 0.4426 0.729 0.204 0.772 0.000 0.024
#> GSM872249 3 0.0188 0.859 0.000 0.000 0.996 0.004
#> GSM872250 1 0.7186 0.175 0.600 0.116 0.260 0.024
#> GSM872251 3 0.0707 0.864 0.000 0.000 0.980 0.020
#> GSM872252 1 0.0000 0.653 1.000 0.000 0.000 0.000
#> GSM872253 3 0.2345 0.790 0.100 0.000 0.900 0.000
#> GSM872254 2 0.6814 0.634 0.300 0.604 0.072 0.024
#> GSM872255 1 0.4277 0.668 0.720 0.000 0.000 0.280
#> GSM872256 1 0.3942 0.704 0.764 0.000 0.000 0.236
#> GSM872257 2 0.0707 0.787 0.000 0.980 0.000 0.020
#> GSM872258 3 0.0921 0.865 0.000 0.000 0.972 0.028
#> GSM872259 1 0.3486 0.715 0.812 0.000 0.000 0.188
#> GSM872260 1 0.3975 0.702 0.760 0.000 0.000 0.240
#> GSM872261 2 0.5500 0.445 0.464 0.520 0.000 0.016
#> GSM872262 4 0.4585 0.427 0.332 0.000 0.000 0.668
#> GSM872263 3 0.0000 0.857 0.000 0.000 1.000 0.000
#> GSM872264 4 0.3052 0.460 0.000 0.004 0.136 0.860
#> GSM872265 4 0.2662 0.595 0.016 0.084 0.000 0.900
#> GSM872266 2 0.4678 0.716 0.232 0.744 0.000 0.024
#> GSM872267 2 0.0592 0.788 0.016 0.984 0.000 0.000
#> GSM872268 3 0.2530 0.865 0.000 0.000 0.888 0.112
#> GSM872269 2 0.6396 0.641 0.312 0.620 0.044 0.024
#> GSM872270 3 0.4040 0.817 0.000 0.000 0.752 0.248
#> GSM872271 2 0.4866 0.380 0.000 0.596 0.000 0.404
#> GSM872272 2 0.4877 0.373 0.000 0.592 0.000 0.408
#> GSM872273 1 0.4543 0.606 0.676 0.000 0.000 0.324
#> GSM872274 2 0.0336 0.786 0.000 0.992 0.000 0.008
#> GSM872275 3 0.3991 0.847 0.000 0.020 0.808 0.172
#> GSM872276 4 0.4999 -0.110 0.492 0.000 0.000 0.508
#> GSM872277 1 0.4585 0.592 0.668 0.000 0.000 0.332
#> GSM872278 3 0.4843 0.660 0.000 0.000 0.604 0.396
#> GSM872279 1 0.2149 0.691 0.912 0.000 0.000 0.088
#> GSM872280 3 0.6508 0.519 0.088 0.000 0.568 0.344
#> GSM872281 4 0.1356 0.622 0.008 0.000 0.032 0.960
#> GSM872282 3 0.4103 0.811 0.000 0.000 0.744 0.256
#> GSM872283 4 0.4663 0.502 0.272 0.012 0.000 0.716
#> GSM872284 4 0.2699 0.629 0.068 0.000 0.028 0.904
#> GSM872285 3 0.4248 0.827 0.012 0.000 0.768 0.220
#> GSM872286 1 0.1739 0.618 0.952 0.008 0.016 0.024
#> GSM872287 3 0.3688 0.839 0.000 0.000 0.792 0.208
#> GSM872288 1 0.2125 0.598 0.932 0.004 0.052 0.012
#> GSM872289 3 0.0817 0.848 0.024 0.000 0.976 0.000
#> GSM872290 1 0.3764 0.712 0.784 0.000 0.000 0.216
#> GSM872291 1 0.4382 0.649 0.704 0.000 0.000 0.296
#> GSM872292 2 0.0336 0.786 0.000 0.992 0.000 0.008
#> GSM872293 1 0.3528 0.715 0.808 0.000 0.000 0.192
#> GSM872294 2 0.1211 0.776 0.000 0.960 0.000 0.040
#> GSM872295 2 0.0188 0.787 0.000 0.996 0.000 0.004
#> GSM872296 2 0.1022 0.779 0.000 0.968 0.000 0.032
#> GSM872297 1 0.4277 0.669 0.720 0.000 0.000 0.280
#> GSM872298 4 0.4941 0.130 0.436 0.000 0.000 0.564
#> GSM872299 1 0.0188 0.651 0.996 0.004 0.000 0.000
#> GSM872300 1 0.4713 0.530 0.640 0.000 0.000 0.360
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.3821 0.7443 0.000 0.000 0.764 0.216 0.020
#> GSM872245 5 0.1430 0.7166 0.052 0.000 0.000 0.004 0.944
#> GSM872246 3 0.1591 0.8022 0.004 0.000 0.940 0.052 0.004
#> GSM872247 3 0.1043 0.7991 0.000 0.000 0.960 0.040 0.000
#> GSM872248 5 0.2719 0.7113 0.000 0.144 0.000 0.004 0.852
#> GSM872249 3 0.3003 0.7671 0.000 0.000 0.812 0.188 0.000
#> GSM872250 5 0.6107 0.5479 0.020 0.000 0.132 0.232 0.616
#> GSM872251 3 0.2488 0.7917 0.000 0.000 0.872 0.124 0.004
#> GSM872252 1 0.2535 0.6816 0.892 0.000 0.000 0.076 0.032
#> GSM872253 3 0.7967 0.3343 0.276 0.016 0.404 0.256 0.048
#> GSM872254 2 0.7994 0.1644 0.012 0.432 0.068 0.252 0.236
#> GSM872255 1 0.1617 0.7269 0.948 0.000 0.012 0.020 0.020
#> GSM872256 1 0.3970 0.6871 0.788 0.000 0.000 0.056 0.156
#> GSM872257 2 0.0963 0.8134 0.000 0.964 0.000 0.000 0.036
#> GSM872258 3 0.3658 0.7863 0.044 0.000 0.832 0.112 0.012
#> GSM872259 1 0.4248 0.6303 0.728 0.000 0.000 0.032 0.240
#> GSM872260 1 0.1082 0.7208 0.964 0.000 0.000 0.028 0.008
#> GSM872261 2 0.6395 0.5303 0.212 0.624 0.000 0.064 0.100
#> GSM872262 4 0.5684 -0.0315 0.432 0.000 0.080 0.488 0.000
#> GSM872263 3 0.3789 0.7472 0.000 0.000 0.768 0.212 0.020
#> GSM872264 4 0.6245 0.5893 0.008 0.008 0.120 0.580 0.284
#> GSM872265 4 0.6425 0.6274 0.060 0.012 0.056 0.612 0.260
#> GSM872266 5 0.2228 0.7289 0.000 0.092 0.004 0.004 0.900
#> GSM872267 5 0.3366 0.6443 0.000 0.232 0.000 0.000 0.768
#> GSM872268 3 0.2074 0.7813 0.000 0.000 0.896 0.104 0.000
#> GSM872269 2 0.5409 0.6811 0.100 0.740 0.004 0.092 0.064
#> GSM872270 3 0.2416 0.7824 0.000 0.000 0.888 0.100 0.012
#> GSM872271 4 0.5695 0.2258 0.000 0.444 0.004 0.484 0.068
#> GSM872272 4 0.6607 0.4479 0.000 0.212 0.004 0.484 0.300
#> GSM872273 1 0.5470 0.4882 0.612 0.000 0.000 0.296 0.092
#> GSM872274 2 0.0290 0.8244 0.000 0.992 0.000 0.000 0.008
#> GSM872275 3 0.2929 0.7844 0.012 0.004 0.856 0.128 0.000
#> GSM872276 1 0.4445 0.5021 0.676 0.000 0.024 0.300 0.000
#> GSM872277 1 0.7031 0.0924 0.424 0.000 0.020 0.356 0.200
#> GSM872278 3 0.5762 0.4984 0.068 0.012 0.624 0.288 0.008
#> GSM872279 1 0.1582 0.7264 0.944 0.000 0.000 0.028 0.028
#> GSM872280 1 0.5650 -0.0642 0.464 0.000 0.460 0.076 0.000
#> GSM872281 4 0.5289 0.5440 0.096 0.000 0.228 0.672 0.004
#> GSM872282 3 0.2873 0.7967 0.000 0.000 0.856 0.128 0.016
#> GSM872283 4 0.6315 0.5423 0.060 0.012 0.024 0.528 0.376
#> GSM872284 4 0.6873 0.6103 0.084 0.000 0.180 0.592 0.144
#> GSM872285 3 0.3001 0.7551 0.004 0.000 0.844 0.144 0.008
#> GSM872286 5 0.4170 0.7029 0.108 0.004 0.004 0.084 0.800
#> GSM872287 3 0.2660 0.7661 0.000 0.000 0.864 0.128 0.008
#> GSM872288 5 0.4636 0.6958 0.108 0.000 0.024 0.092 0.776
#> GSM872289 3 0.4315 0.6931 0.000 0.000 0.700 0.276 0.024
#> GSM872290 1 0.0703 0.7275 0.976 0.000 0.000 0.000 0.024
#> GSM872291 1 0.1195 0.7245 0.960 0.000 0.000 0.028 0.012
#> GSM872292 2 0.0000 0.8242 0.000 1.000 0.000 0.000 0.000
#> GSM872293 1 0.2249 0.7191 0.896 0.000 0.000 0.008 0.096
#> GSM872294 2 0.0703 0.8182 0.000 0.976 0.000 0.024 0.000
#> GSM872295 2 0.0290 0.8244 0.000 0.992 0.000 0.000 0.008
#> GSM872296 2 0.1124 0.8087 0.000 0.960 0.000 0.036 0.004
#> GSM872297 1 0.5059 0.6182 0.696 0.000 0.000 0.112 0.192
#> GSM872298 1 0.5301 0.4432 0.648 0.000 0.076 0.272 0.004
#> GSM872299 1 0.3110 0.6815 0.860 0.000 0.000 0.080 0.060
#> GSM872300 1 0.5149 0.5754 0.696 0.000 0.044 0.232 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.4720 0.7505 0.000 0.000 0.700 0.016 0.084 0.200
#> GSM872245 5 0.5780 0.2045 0.388 0.000 0.000 0.116 0.480 0.016
#> GSM872246 3 0.1873 0.8353 0.000 0.000 0.924 0.008 0.020 0.048
#> GSM872247 3 0.1323 0.8279 0.020 0.000 0.956 0.008 0.008 0.008
#> GSM872248 5 0.3570 0.7133 0.012 0.076 0.000 0.076 0.828 0.008
#> GSM872249 3 0.2884 0.8243 0.000 0.000 0.864 0.008 0.064 0.064
#> GSM872250 5 0.4078 0.6661 0.036 0.000 0.032 0.012 0.792 0.128
#> GSM872251 3 0.2789 0.8314 0.008 0.000 0.880 0.012 0.064 0.036
#> GSM872252 6 0.4072 0.5077 0.260 0.000 0.000 0.032 0.004 0.704
#> GSM872253 6 0.4722 0.4371 0.020 0.008 0.136 0.080 0.008 0.748
#> GSM872254 6 0.6466 -0.0222 0.008 0.236 0.008 0.004 0.292 0.452
#> GSM872255 1 0.3401 0.5087 0.820 0.000 0.028 0.004 0.012 0.136
#> GSM872256 1 0.4191 0.5450 0.752 0.000 0.004 0.004 0.164 0.076
#> GSM872257 2 0.1700 0.8919 0.000 0.916 0.000 0.004 0.080 0.000
#> GSM872258 3 0.4197 0.6466 0.016 0.000 0.676 0.008 0.004 0.296
#> GSM872259 1 0.4712 0.5592 0.732 0.000 0.000 0.084 0.144 0.040
#> GSM872260 6 0.4212 0.3989 0.392 0.000 0.000 0.008 0.008 0.592
#> GSM872261 6 0.7046 0.4566 0.092 0.240 0.000 0.060 0.076 0.532
#> GSM872262 1 0.6466 0.1417 0.500 0.000 0.116 0.316 0.004 0.064
#> GSM872263 3 0.3982 0.7892 0.000 0.000 0.764 0.004 0.076 0.156
#> GSM872264 4 0.2884 0.6522 0.036 0.004 0.016 0.872 0.072 0.000
#> GSM872265 4 0.3910 0.6525 0.088 0.028 0.020 0.824 0.032 0.008
#> GSM872266 5 0.2878 0.7220 0.020 0.028 0.000 0.076 0.872 0.004
#> GSM872267 5 0.4954 0.5794 0.004 0.232 0.000 0.100 0.660 0.004
#> GSM872268 3 0.2095 0.8113 0.052 0.000 0.916 0.016 0.004 0.012
#> GSM872269 6 0.5603 0.0832 0.008 0.416 0.004 0.000 0.096 0.476
#> GSM872270 3 0.2038 0.8265 0.000 0.000 0.920 0.032 0.020 0.028
#> GSM872271 4 0.4239 0.6118 0.000 0.148 0.004 0.764 0.068 0.016
#> GSM872272 4 0.4356 0.5603 0.000 0.084 0.000 0.740 0.164 0.012
#> GSM872273 1 0.3625 0.6184 0.820 0.000 0.016 0.120 0.028 0.016
#> GSM872274 2 0.0146 0.9587 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM872275 3 0.6139 0.5813 0.064 0.000 0.652 0.152 0.064 0.068
#> GSM872276 1 0.6228 0.1863 0.516 0.000 0.040 0.292 0.000 0.152
#> GSM872277 1 0.5042 0.5175 0.672 0.000 0.008 0.212 0.100 0.008
#> GSM872278 4 0.5760 0.5394 0.028 0.008 0.172 0.640 0.004 0.148
#> GSM872279 1 0.3784 0.2267 0.680 0.000 0.000 0.000 0.012 0.308
#> GSM872280 6 0.7517 0.0198 0.300 0.000 0.280 0.112 0.004 0.304
#> GSM872281 4 0.6645 0.4240 0.184 0.000 0.224 0.528 0.012 0.052
#> GSM872282 3 0.3739 0.7977 0.000 0.000 0.796 0.024 0.036 0.144
#> GSM872283 4 0.3652 0.6295 0.092 0.008 0.004 0.824 0.064 0.008
#> GSM872284 4 0.6099 0.5202 0.180 0.000 0.120 0.628 0.028 0.044
#> GSM872285 3 0.2931 0.7920 0.056 0.000 0.876 0.024 0.008 0.036
#> GSM872286 5 0.3587 0.6616 0.188 0.000 0.000 0.000 0.772 0.040
#> GSM872287 3 0.2189 0.8139 0.028 0.000 0.916 0.024 0.004 0.028
#> GSM872288 5 0.5553 0.6512 0.104 0.000 0.012 0.056 0.680 0.148
#> GSM872289 3 0.4293 0.7778 0.000 0.000 0.740 0.008 0.084 0.168
#> GSM872290 6 0.4520 0.3087 0.448 0.000 0.000 0.032 0.000 0.520
#> GSM872291 6 0.5138 0.4658 0.268 0.000 0.000 0.128 0.000 0.604
#> GSM872292 2 0.0146 0.9584 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM872293 1 0.2842 0.5564 0.852 0.000 0.000 0.000 0.044 0.104
#> GSM872294 2 0.0696 0.9565 0.004 0.980 0.000 0.004 0.004 0.008
#> GSM872295 2 0.0405 0.9578 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM872296 2 0.1471 0.9091 0.000 0.932 0.000 0.064 0.000 0.004
#> GSM872297 1 0.4013 0.5880 0.768 0.000 0.000 0.124 0.104 0.004
#> GSM872298 4 0.6751 0.2787 0.172 0.000 0.092 0.500 0.000 0.236
#> GSM872299 6 0.4045 0.3714 0.428 0.000 0.000 0.000 0.008 0.564
#> GSM872300 1 0.4616 0.5279 0.760 0.000 0.092 0.084 0.004 0.060
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 time(p) individual(p) k
#> CV:NMF 52 0.588 7.25e-03 2
#> CV:NMF 54 0.341 3.30e-02 3
#> CV:NMF 49 0.547 4.18e-03 4
#> CV:NMF 47 0.637 3.51e-04 5
#> CV:NMF 42 0.335 7.74e-06 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 29485 rows and 57 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 0.323 0.640 0.833 0.3993 0.623 0.623
#> 3 3 0.584 0.722 0.871 0.4510 0.751 0.625
#> 4 4 0.480 0.575 0.734 0.1451 0.977 0.951
#> 5 5 0.656 0.699 0.842 0.1413 0.774 0.514
#> 6 6 0.733 0.612 0.779 0.0708 0.894 0.614
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
#> GSM872244 1 0.9933 0.396 0.548 0.452
#> GSM872245 1 0.7139 0.667 0.804 0.196
#> GSM872246 1 0.8327 0.652 0.736 0.264
#> GSM872247 1 0.9933 0.396 0.548 0.452
#> GSM872248 2 0.0000 0.771 0.000 1.000
#> GSM872249 1 0.9933 0.396 0.548 0.452
#> GSM872250 1 0.0376 0.767 0.996 0.004
#> GSM872251 1 0.9933 0.396 0.548 0.452
#> GSM872252 1 0.0376 0.767 0.996 0.004
#> GSM872253 1 0.5294 0.735 0.880 0.120
#> GSM872254 2 0.1633 0.767 0.024 0.976
#> GSM872255 1 0.0000 0.769 1.000 0.000
#> GSM872256 1 0.0000 0.769 1.000 0.000
#> GSM872257 2 0.0000 0.771 0.000 1.000
#> GSM872258 1 0.8327 0.652 0.736 0.264
#> GSM872259 1 0.0000 0.769 1.000 0.000
#> GSM872260 1 0.0000 0.769 1.000 0.000
#> GSM872261 2 0.9866 0.231 0.432 0.568
#> GSM872262 1 0.0000 0.769 1.000 0.000
#> GSM872263 1 0.9933 0.396 0.548 0.452
#> GSM872264 1 0.8861 0.599 0.696 0.304
#> GSM872265 1 0.8861 0.599 0.696 0.304
#> GSM872266 2 0.9580 0.329 0.380 0.620
#> GSM872267 2 0.0000 0.771 0.000 1.000
#> GSM872268 1 0.9933 0.396 0.548 0.452
#> GSM872269 2 0.7602 0.579 0.220 0.780
#> GSM872270 1 0.9933 0.396 0.548 0.452
#> GSM872271 2 0.9866 0.229 0.432 0.568
#> GSM872272 2 0.9866 0.229 0.432 0.568
#> GSM872273 1 0.0000 0.769 1.000 0.000
#> GSM872274 2 0.0000 0.771 0.000 1.000
#> GSM872275 1 0.7815 0.659 0.768 0.232
#> GSM872276 1 0.0000 0.769 1.000 0.000
#> GSM872277 1 0.0000 0.769 1.000 0.000
#> GSM872278 1 0.6343 0.719 0.840 0.160
#> GSM872279 1 0.0376 0.767 0.996 0.004
#> GSM872280 1 0.0000 0.769 1.000 0.000
#> GSM872281 1 0.2603 0.761 0.956 0.044
#> GSM872282 1 0.9933 0.396 0.548 0.452
#> GSM872283 1 0.8861 0.599 0.696 0.304
#> GSM872284 1 0.8763 0.609 0.704 0.296
#> GSM872285 1 0.8081 0.668 0.752 0.248
#> GSM872286 1 0.0376 0.767 0.996 0.004
#> GSM872287 1 0.9933 0.396 0.548 0.452
#> GSM872288 1 0.0376 0.767 0.996 0.004
#> GSM872289 1 0.8386 0.648 0.732 0.268
#> GSM872290 1 0.0376 0.767 0.996 0.004
#> GSM872291 1 0.0000 0.769 1.000 0.000
#> GSM872292 2 0.0000 0.771 0.000 1.000
#> GSM872293 1 0.0000 0.769 1.000 0.000
#> GSM872294 2 0.8955 0.499 0.312 0.688
#> GSM872295 2 0.1633 0.767 0.024 0.976
#> GSM872296 2 0.0000 0.771 0.000 1.000
#> GSM872297 1 0.0000 0.769 1.000 0.000
#> GSM872298 1 0.6343 0.719 0.840 0.160
#> GSM872299 1 0.0376 0.767 0.996 0.004
#> GSM872300 1 0.0000 0.769 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 1.00000 0.000 0.000 1.000
#> GSM872245 1 0.4733 0.65446 0.800 0.196 0.004
#> GSM872246 1 0.6299 0.30257 0.524 0.000 0.476
#> GSM872247 3 0.0000 1.00000 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.78737 0.000 1.000 0.000
#> GSM872249 3 0.0000 1.00000 0.000 0.000 1.000
#> GSM872250 1 0.0475 0.81963 0.992 0.004 0.004
#> GSM872251 3 0.0000 1.00000 0.000 0.000 1.000
#> GSM872252 1 0.0475 0.81963 0.992 0.004 0.004
#> GSM872253 1 0.3619 0.76955 0.864 0.000 0.136
#> GSM872254 2 0.1129 0.78257 0.020 0.976 0.004
#> GSM872255 1 0.0237 0.82163 0.996 0.000 0.004
#> GSM872256 1 0.0000 0.82094 1.000 0.000 0.000
#> GSM872257 2 0.0000 0.78737 0.000 1.000 0.000
#> GSM872258 1 0.6299 0.30257 0.524 0.000 0.476
#> GSM872259 1 0.0000 0.82094 1.000 0.000 0.000
#> GSM872260 1 0.0237 0.82163 0.996 0.000 0.004
#> GSM872261 2 0.9024 0.05546 0.420 0.448 0.132
#> GSM872262 1 0.0892 0.82059 0.980 0.000 0.020
#> GSM872263 3 0.0000 1.00000 0.000 0.000 1.000
#> GSM872264 1 0.5810 0.61888 0.664 0.000 0.336
#> GSM872265 1 0.5810 0.61888 0.664 0.000 0.336
#> GSM872266 2 0.8936 0.21411 0.368 0.500 0.132
#> GSM872267 2 0.0000 0.78737 0.000 1.000 0.000
#> GSM872268 3 0.0000 1.00000 0.000 0.000 1.000
#> GSM872269 2 0.4978 0.62093 0.216 0.780 0.004
#> GSM872270 3 0.0000 1.00000 0.000 0.000 1.000
#> GSM872271 1 0.9778 -0.00557 0.408 0.356 0.236
#> GSM872272 1 0.9778 -0.00557 0.408 0.356 0.236
#> GSM872273 1 0.0000 0.82094 1.000 0.000 0.000
#> GSM872274 2 0.0000 0.78737 0.000 1.000 0.000
#> GSM872275 1 0.6662 0.69336 0.736 0.072 0.192
#> GSM872276 1 0.0892 0.82059 0.980 0.000 0.020
#> GSM872277 1 0.0000 0.82094 1.000 0.000 0.000
#> GSM872278 1 0.4399 0.74490 0.812 0.000 0.188
#> GSM872279 1 0.0475 0.81963 0.992 0.004 0.004
#> GSM872280 1 0.1031 0.82005 0.976 0.000 0.024
#> GSM872281 1 0.2165 0.80772 0.936 0.000 0.064
#> GSM872282 3 0.0000 1.00000 0.000 0.000 1.000
#> GSM872283 1 0.5810 0.61888 0.664 0.000 0.336
#> GSM872284 1 0.5760 0.62874 0.672 0.000 0.328
#> GSM872285 1 0.6244 0.41502 0.560 0.000 0.440
#> GSM872286 1 0.0475 0.81963 0.992 0.004 0.004
#> GSM872287 3 0.0000 1.00000 0.000 0.000 1.000
#> GSM872288 1 0.0475 0.81963 0.992 0.004 0.004
#> GSM872289 1 0.6302 0.29160 0.520 0.000 0.480
#> GSM872290 1 0.0475 0.81963 0.992 0.004 0.004
#> GSM872291 1 0.0237 0.82154 0.996 0.000 0.004
#> GSM872292 2 0.0000 0.78737 0.000 1.000 0.000
#> GSM872293 1 0.0000 0.82094 1.000 0.000 0.000
#> GSM872294 2 0.9072 0.35226 0.300 0.532 0.168
#> GSM872295 2 0.1129 0.78257 0.020 0.976 0.004
#> GSM872296 2 0.0000 0.78737 0.000 1.000 0.000
#> GSM872297 1 0.0000 0.82094 1.000 0.000 0.000
#> GSM872298 1 0.4399 0.74490 0.812 0.000 0.188
#> GSM872299 1 0.0475 0.81963 0.992 0.004 0.004
#> GSM872300 1 0.0892 0.82059 0.980 0.000 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872245 1 0.7283 0.465 0.524 0.292 0.000 0.184
#> GSM872246 1 0.4967 0.315 0.548 0.000 0.452 0.000
#> GSM872247 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872248 2 0.4999 0.885 0.000 0.508 0.000 0.492
#> GSM872249 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872250 1 0.4989 0.548 0.528 0.472 0.000 0.000
#> GSM872251 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872252 1 0.4989 0.548 0.528 0.472 0.000 0.000
#> GSM872253 1 0.4046 0.543 0.828 0.048 0.124 0.000
#> GSM872254 2 0.5000 0.871 0.000 0.504 0.000 0.496
#> GSM872255 1 0.0817 0.611 0.976 0.024 0.000 0.000
#> GSM872256 1 0.4331 0.602 0.712 0.288 0.000 0.000
#> GSM872257 2 0.4999 0.885 0.000 0.508 0.000 0.492
#> GSM872258 1 0.4967 0.315 0.548 0.000 0.452 0.000
#> GSM872259 1 0.4522 0.599 0.680 0.320 0.000 0.000
#> GSM872260 1 0.0707 0.610 0.980 0.020 0.000 0.000
#> GSM872261 4 0.8174 0.364 0.388 0.048 0.124 0.440
#> GSM872262 1 0.0469 0.609 0.988 0.012 0.000 0.000
#> GSM872263 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872264 1 0.5108 0.439 0.672 0.020 0.308 0.000
#> GSM872265 1 0.5108 0.439 0.672 0.020 0.308 0.000
#> GSM872266 4 0.7961 0.438 0.344 0.040 0.124 0.492
#> GSM872267 2 0.4999 0.885 0.000 0.508 0.000 0.492
#> GSM872268 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872269 2 0.4769 0.620 0.008 0.684 0.000 0.308
#> GSM872270 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872271 1 0.8406 -0.346 0.400 0.028 0.216 0.356
#> GSM872272 1 0.8406 -0.346 0.400 0.028 0.216 0.356
#> GSM872273 1 0.4522 0.599 0.680 0.320 0.000 0.000
#> GSM872274 4 0.0000 0.107 0.000 0.000 0.000 1.000
#> GSM872275 1 0.5855 0.431 0.736 0.028 0.164 0.072
#> GSM872276 1 0.0469 0.609 0.988 0.012 0.000 0.000
#> GSM872277 1 0.4522 0.599 0.680 0.320 0.000 0.000
#> GSM872278 1 0.3402 0.531 0.832 0.004 0.164 0.000
#> GSM872279 1 0.4989 0.548 0.528 0.472 0.000 0.000
#> GSM872280 1 0.0188 0.607 0.996 0.004 0.000 0.000
#> GSM872281 1 0.1767 0.606 0.944 0.012 0.044 0.000
#> GSM872282 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872283 1 0.5108 0.439 0.672 0.020 0.308 0.000
#> GSM872284 1 0.5062 0.444 0.680 0.020 0.300 0.000
#> GSM872285 1 0.4898 0.338 0.584 0.000 0.416 0.000
#> GSM872286 1 0.4989 0.548 0.528 0.472 0.000 0.000
#> GSM872287 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872288 1 0.4989 0.548 0.528 0.472 0.000 0.000
#> GSM872289 1 0.4972 0.309 0.544 0.000 0.456 0.000
#> GSM872290 1 0.4989 0.548 0.528 0.472 0.000 0.000
#> GSM872291 1 0.1022 0.611 0.968 0.032 0.000 0.000
#> GSM872292 4 0.0000 0.107 0.000 0.000 0.000 1.000
#> GSM872293 1 0.4522 0.599 0.680 0.320 0.000 0.000
#> GSM872294 4 0.7687 0.457 0.288 0.020 0.160 0.532
#> GSM872295 2 0.5000 0.871 0.000 0.504 0.000 0.496
#> GSM872296 4 0.0000 0.107 0.000 0.000 0.000 1.000
#> GSM872297 1 0.4522 0.599 0.680 0.320 0.000 0.000
#> GSM872298 1 0.3402 0.531 0.832 0.004 0.164 0.000
#> GSM872299 1 0.4989 0.548 0.528 0.472 0.000 0.000
#> GSM872300 1 0.0469 0.609 0.988 0.012 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM872245 1 0.3333 0.7570 0.788 0.004 0.000 0.000 0.208
#> GSM872246 4 0.4278 0.2589 0.000 0.000 0.452 0.548 0.000
#> GSM872247 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM872248 5 0.0510 0.9126 0.000 0.016 0.000 0.000 0.984
#> GSM872249 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM872250 1 0.0510 0.8847 0.984 0.000 0.000 0.000 0.016
#> GSM872251 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM872252 1 0.0290 0.8875 0.992 0.000 0.000 0.000 0.008
#> GSM872253 4 0.0794 0.6256 0.028 0.000 0.000 0.972 0.000
#> GSM872254 5 0.1281 0.9018 0.012 0.032 0.000 0.000 0.956
#> GSM872255 4 0.3455 0.6287 0.208 0.008 0.000 0.784 0.000
#> GSM872256 1 0.3691 0.8326 0.804 0.040 0.000 0.156 0.000
#> GSM872257 5 0.0510 0.9126 0.000 0.016 0.000 0.000 0.984
#> GSM872258 4 0.4278 0.2589 0.000 0.000 0.452 0.548 0.000
#> GSM872259 1 0.3620 0.8688 0.824 0.068 0.000 0.108 0.000
#> GSM872260 4 0.3421 0.6312 0.204 0.008 0.000 0.788 0.000
#> GSM872261 4 0.6583 -0.0381 0.012 0.256 0.000 0.532 0.200
#> GSM872262 4 0.3231 0.6350 0.196 0.004 0.000 0.800 0.000
#> GSM872263 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM872264 4 0.3086 0.5754 0.000 0.004 0.180 0.816 0.000
#> GSM872265 4 0.3086 0.5754 0.000 0.004 0.180 0.816 0.000
#> GSM872266 4 0.6730 -0.1259 0.008 0.260 0.000 0.488 0.244
#> GSM872267 5 0.0510 0.9126 0.000 0.016 0.000 0.000 0.984
#> GSM872268 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM872269 5 0.4010 0.6947 0.208 0.032 0.000 0.000 0.760
#> GSM872270 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM872271 4 0.6821 0.0688 0.008 0.308 0.092 0.544 0.048
#> GSM872272 4 0.6821 0.0688 0.008 0.308 0.092 0.544 0.048
#> GSM872273 1 0.3620 0.8688 0.824 0.068 0.000 0.108 0.000
#> GSM872274 2 0.1608 0.7701 0.000 0.928 0.000 0.000 0.072
#> GSM872275 4 0.2916 0.5903 0.008 0.072 0.040 0.880 0.000
#> GSM872276 4 0.3266 0.6332 0.200 0.004 0.000 0.796 0.000
#> GSM872277 1 0.3620 0.8688 0.824 0.068 0.000 0.108 0.000
#> GSM872278 4 0.2569 0.6457 0.068 0.000 0.040 0.892 0.000
#> GSM872279 1 0.0290 0.8875 0.992 0.000 0.000 0.000 0.008
#> GSM872280 4 0.3160 0.6377 0.188 0.004 0.000 0.808 0.000
#> GSM872281 4 0.4290 0.6427 0.196 0.004 0.044 0.756 0.000
#> GSM872282 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM872283 4 0.3086 0.5754 0.000 0.004 0.180 0.816 0.000
#> GSM872284 4 0.3010 0.5800 0.000 0.004 0.172 0.824 0.000
#> GSM872285 4 0.5420 0.3538 0.060 0.000 0.416 0.524 0.000
#> GSM872286 1 0.0510 0.8847 0.984 0.000 0.000 0.000 0.016
#> GSM872287 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM872288 1 0.0510 0.8847 0.984 0.000 0.000 0.000 0.016
#> GSM872289 4 0.4283 0.2495 0.000 0.000 0.456 0.544 0.000
#> GSM872290 1 0.0290 0.8875 0.992 0.000 0.000 0.000 0.008
#> GSM872291 4 0.3430 0.6236 0.220 0.004 0.000 0.776 0.000
#> GSM872292 2 0.1608 0.7701 0.000 0.928 0.000 0.000 0.072
#> GSM872293 1 0.3620 0.8688 0.824 0.068 0.000 0.108 0.000
#> GSM872294 2 0.7463 0.2012 0.084 0.480 0.036 0.348 0.052
#> GSM872295 5 0.1281 0.9018 0.012 0.032 0.000 0.000 0.956
#> GSM872296 2 0.1608 0.7701 0.000 0.928 0.000 0.000 0.072
#> GSM872297 1 0.3620 0.8688 0.824 0.068 0.000 0.108 0.000
#> GSM872298 4 0.2569 0.6457 0.068 0.000 0.040 0.892 0.000
#> GSM872299 1 0.0290 0.8875 0.992 0.000 0.000 0.000 0.008
#> GSM872300 4 0.3231 0.6350 0.196 0.004 0.000 0.800 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872245 1 0.2933 0.565 0.796 0.000 0.000 0.000 0.200 0.004
#> GSM872246 6 0.4165 0.341 0.000 0.000 0.452 0.012 0.000 0.536
#> GSM872247 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872248 5 0.0806 0.911 0.000 0.008 0.000 0.020 0.972 0.000
#> GSM872249 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872250 1 0.0260 0.716 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM872251 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872252 1 0.0000 0.719 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872253 6 0.3454 0.545 0.024 0.000 0.000 0.208 0.000 0.768
#> GSM872254 5 0.1787 0.900 0.020 0.016 0.000 0.032 0.932 0.000
#> GSM872255 6 0.0976 0.712 0.016 0.008 0.000 0.008 0.000 0.968
#> GSM872256 1 0.6108 0.119 0.376 0.304 0.000 0.000 0.000 0.320
#> GSM872257 5 0.0806 0.911 0.000 0.008 0.000 0.020 0.972 0.000
#> GSM872258 6 0.4165 0.341 0.000 0.000 0.452 0.012 0.000 0.536
#> GSM872259 1 0.5724 0.281 0.456 0.376 0.000 0.000 0.000 0.168
#> GSM872260 6 0.1078 0.713 0.016 0.008 0.000 0.012 0.000 0.964
#> GSM872261 4 0.4229 0.526 0.008 0.000 0.000 0.732 0.200 0.060
#> GSM872262 6 0.0000 0.717 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872263 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872264 4 0.5661 0.550 0.000 0.008 0.140 0.532 0.000 0.320
#> GSM872265 4 0.5661 0.550 0.000 0.008 0.140 0.532 0.000 0.320
#> GSM872266 4 0.3682 0.460 0.004 0.004 0.000 0.752 0.224 0.016
#> GSM872267 5 0.0806 0.911 0.000 0.008 0.000 0.020 0.972 0.000
#> GSM872268 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872269 5 0.4091 0.710 0.216 0.016 0.000 0.032 0.736 0.000
#> GSM872270 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872271 4 0.2938 0.575 0.004 0.004 0.056 0.868 0.004 0.064
#> GSM872272 4 0.2938 0.575 0.004 0.004 0.056 0.868 0.004 0.064
#> GSM872273 2 0.6025 -0.328 0.372 0.384 0.000 0.000 0.000 0.244
#> GSM872274 2 0.3774 0.366 0.000 0.592 0.000 0.408 0.000 0.000
#> GSM872275 6 0.3892 0.313 0.004 0.000 0.004 0.352 0.000 0.640
#> GSM872276 6 0.0146 0.716 0.000 0.004 0.000 0.000 0.000 0.996
#> GSM872277 1 0.5724 0.281 0.456 0.376 0.000 0.000 0.000 0.168
#> GSM872278 6 0.2913 0.594 0.004 0.000 0.004 0.180 0.000 0.812
#> GSM872279 1 0.0000 0.719 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872280 6 0.0260 0.717 0.000 0.000 0.000 0.008 0.000 0.992
#> GSM872281 6 0.1124 0.703 0.000 0.000 0.008 0.036 0.000 0.956
#> GSM872282 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872283 4 0.5661 0.550 0.000 0.008 0.140 0.532 0.000 0.320
#> GSM872284 4 0.5632 0.532 0.000 0.008 0.132 0.528 0.000 0.332
#> GSM872285 6 0.4116 0.391 0.000 0.000 0.416 0.012 0.000 0.572
#> GSM872286 1 0.0260 0.716 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM872287 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872288 1 0.0260 0.716 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM872289 6 0.4169 0.331 0.000 0.000 0.456 0.012 0.000 0.532
#> GSM872290 1 0.0000 0.719 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872291 6 0.0692 0.708 0.020 0.004 0.000 0.000 0.000 0.976
#> GSM872292 2 0.3774 0.366 0.000 0.592 0.000 0.408 0.000 0.000
#> GSM872293 2 0.6025 -0.328 0.372 0.384 0.000 0.000 0.000 0.244
#> GSM872294 4 0.5793 0.175 0.004 0.124 0.020 0.568 0.000 0.284
#> GSM872295 5 0.1787 0.900 0.020 0.016 0.000 0.032 0.932 0.000
#> GSM872296 2 0.3774 0.366 0.000 0.592 0.000 0.408 0.000 0.000
#> GSM872297 1 0.5724 0.281 0.456 0.376 0.000 0.000 0.000 0.168
#> GSM872298 6 0.2913 0.594 0.004 0.000 0.004 0.180 0.000 0.812
#> GSM872299 1 0.0000 0.719 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872300 6 0.0000 0.717 0.000 0.000 0.000 0.000 0.000 1.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 time(p) individual(p) k
#> MAD:hclust 43 0.959 0.123137 2
#> MAD:hclust 48 0.929 0.000304 3
#> MAD:hclust 39 0.833 0.000595 4
#> MAD:hclust 48 0.698 0.000124 5
#> MAD:hclust 41 0.728 0.000110 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 29485 rows and 57 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 0.151 0.341 0.580 0.4740 0.526 0.526
#> 3 3 0.790 0.876 0.940 0.4016 0.737 0.534
#> 4 4 0.630 0.425 0.661 0.1206 0.900 0.715
#> 5 5 0.683 0.589 0.737 0.0674 0.826 0.448
#> 6 6 0.703 0.616 0.753 0.0427 0.905 0.584
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
#> GSM872244 2 0.3584 0.4311 0.068 0.932
#> GSM872245 1 0.6712 0.3693 0.824 0.176
#> GSM872246 2 0.7528 0.6678 0.216 0.784
#> GSM872247 2 0.6973 0.6739 0.188 0.812
#> GSM872248 1 0.9909 0.2329 0.556 0.444
#> GSM872249 2 0.5842 0.6519 0.140 0.860
#> GSM872250 1 0.9248 0.2671 0.660 0.340
#> GSM872251 2 0.7453 0.6699 0.212 0.788
#> GSM872252 1 0.5842 0.4372 0.860 0.140
#> GSM872253 2 0.8207 0.6118 0.256 0.744
#> GSM872254 1 0.9881 0.2373 0.564 0.436
#> GSM872255 1 0.9732 0.1349 0.596 0.404
#> GSM872256 1 0.5842 0.4372 0.860 0.140
#> GSM872257 1 0.9933 0.2238 0.548 0.452
#> GSM872258 2 0.7674 0.6613 0.224 0.776
#> GSM872259 1 0.5842 0.4372 0.860 0.140
#> GSM872260 1 0.9686 0.1474 0.604 0.396
#> GSM872261 1 0.9491 0.2635 0.632 0.368
#> GSM872262 1 0.9775 0.1202 0.588 0.412
#> GSM872263 2 0.6887 0.6735 0.184 0.816
#> GSM872264 2 0.7745 0.5355 0.228 0.772
#> GSM872265 1 0.9983 0.0796 0.524 0.476
#> GSM872266 1 0.9909 0.2329 0.556 0.444
#> GSM872267 1 0.9909 0.2329 0.556 0.444
#> GSM872268 2 0.7528 0.6678 0.216 0.784
#> GSM872269 1 0.9087 0.2763 0.676 0.324
#> GSM872270 2 0.4431 0.6104 0.092 0.908
#> GSM872271 1 1.0000 0.1605 0.500 0.500
#> GSM872272 2 1.0000 -0.2227 0.500 0.500
#> GSM872273 1 0.8443 0.3228 0.728 0.272
#> GSM872274 1 1.0000 0.1660 0.504 0.496
#> GSM872275 2 0.7453 0.6491 0.212 0.788
#> GSM872276 1 0.9775 0.1202 0.588 0.412
#> GSM872277 1 0.8443 0.3228 0.728 0.272
#> GSM872278 2 0.7883 0.6468 0.236 0.764
#> GSM872279 1 0.5842 0.4372 0.860 0.140
#> GSM872280 2 0.9909 0.1903 0.444 0.556
#> GSM872281 1 0.9983 -0.0487 0.524 0.476
#> GSM872282 2 0.3431 0.4357 0.064 0.936
#> GSM872283 1 0.9087 0.2767 0.676 0.324
#> GSM872284 1 0.9881 0.0711 0.564 0.436
#> GSM872285 2 0.7815 0.6515 0.232 0.768
#> GSM872286 1 0.0672 0.4220 0.992 0.008
#> GSM872287 2 0.7299 0.6720 0.204 0.796
#> GSM872288 1 0.8555 0.3135 0.720 0.280
#> GSM872289 2 0.7745 0.6571 0.228 0.772
#> GSM872290 1 0.5842 0.4372 0.860 0.140
#> GSM872291 1 0.9580 0.1746 0.620 0.380
#> GSM872292 2 1.0000 -0.2171 0.496 0.504
#> GSM872293 1 0.5842 0.4372 0.860 0.140
#> GSM872294 1 0.9460 0.2876 0.636 0.364
#> GSM872295 1 0.9977 0.1973 0.528 0.472
#> GSM872296 2 1.0000 -0.2171 0.496 0.504
#> GSM872297 1 0.5842 0.4372 0.860 0.140
#> GSM872298 1 0.9833 0.0918 0.576 0.424
#> GSM872299 1 0.0672 0.4220 0.992 0.008
#> GSM872300 1 0.9732 0.1349 0.596 0.404
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.2796 0.884 0.000 0.092 0.908
#> GSM872245 1 0.5810 0.463 0.664 0.336 0.000
#> GSM872246 3 0.0000 0.964 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.964 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.953 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.964 0.000 0.000 1.000
#> GSM872250 2 0.4504 0.792 0.196 0.804 0.000
#> GSM872251 3 0.0000 0.964 0.000 0.000 1.000
#> GSM872252 1 0.0000 0.896 1.000 0.000 0.000
#> GSM872253 3 0.2261 0.904 0.068 0.000 0.932
#> GSM872254 2 0.0000 0.953 0.000 1.000 0.000
#> GSM872255 1 0.0237 0.896 0.996 0.000 0.004
#> GSM872256 1 0.0000 0.896 1.000 0.000 0.000
#> GSM872257 2 0.0000 0.953 0.000 1.000 0.000
#> GSM872258 3 0.0000 0.964 0.000 0.000 1.000
#> GSM872259 1 0.0000 0.896 1.000 0.000 0.000
#> GSM872260 1 0.0000 0.896 1.000 0.000 0.000
#> GSM872261 2 0.4399 0.803 0.188 0.812 0.000
#> GSM872262 1 0.2711 0.863 0.912 0.000 0.088
#> GSM872263 3 0.0000 0.964 0.000 0.000 1.000
#> GSM872264 1 0.6305 0.189 0.516 0.000 0.484
#> GSM872265 1 0.5058 0.717 0.756 0.000 0.244
#> GSM872266 2 0.0000 0.953 0.000 1.000 0.000
#> GSM872267 2 0.0000 0.953 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.964 0.000 0.000 1.000
#> GSM872269 2 0.4605 0.782 0.204 0.796 0.000
#> GSM872270 3 0.0000 0.964 0.000 0.000 1.000
#> GSM872271 2 0.0424 0.950 0.008 0.992 0.000
#> GSM872272 2 0.0424 0.950 0.008 0.992 0.000
#> GSM872273 1 0.0000 0.896 1.000 0.000 0.000
#> GSM872274 2 0.0000 0.953 0.000 1.000 0.000
#> GSM872275 3 0.0424 0.959 0.008 0.000 0.992
#> GSM872276 1 0.2711 0.863 0.912 0.000 0.088
#> GSM872277 1 0.0000 0.896 1.000 0.000 0.000
#> GSM872278 3 0.0424 0.959 0.008 0.000 0.992
#> GSM872279 1 0.0000 0.896 1.000 0.000 0.000
#> GSM872280 3 0.5058 0.656 0.244 0.000 0.756
#> GSM872281 1 0.5016 0.722 0.760 0.000 0.240
#> GSM872282 3 0.2796 0.884 0.000 0.092 0.908
#> GSM872283 1 0.3116 0.850 0.892 0.000 0.108
#> GSM872284 1 0.4974 0.726 0.764 0.000 0.236
#> GSM872285 3 0.0000 0.964 0.000 0.000 1.000
#> GSM872286 1 0.4178 0.743 0.828 0.172 0.000
#> GSM872287 3 0.0000 0.964 0.000 0.000 1.000
#> GSM872288 1 0.0424 0.892 0.992 0.008 0.000
#> GSM872289 3 0.0237 0.962 0.004 0.000 0.996
#> GSM872290 1 0.0000 0.896 1.000 0.000 0.000
#> GSM872291 1 0.0000 0.896 1.000 0.000 0.000
#> GSM872292 2 0.0000 0.953 0.000 1.000 0.000
#> GSM872293 1 0.0000 0.896 1.000 0.000 0.000
#> GSM872294 2 0.0424 0.950 0.008 0.992 0.000
#> GSM872295 2 0.0000 0.953 0.000 1.000 0.000
#> GSM872296 2 0.0000 0.953 0.000 1.000 0.000
#> GSM872297 1 0.0000 0.896 1.000 0.000 0.000
#> GSM872298 1 0.2796 0.861 0.908 0.000 0.092
#> GSM872299 1 0.4062 0.751 0.836 0.164 0.000
#> GSM872300 1 0.0747 0.893 0.984 0.000 0.016
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0592 0.9116 0.000 0.000 0.984 0.016
#> GSM872245 1 0.7030 -0.1218 0.472 0.408 0.000 0.120
#> GSM872246 3 0.0188 0.9147 0.000 0.000 0.996 0.004
#> GSM872247 3 0.0469 0.9150 0.000 0.000 0.988 0.012
#> GSM872248 2 0.0376 0.6238 0.004 0.992 0.000 0.004
#> GSM872249 3 0.0707 0.9131 0.000 0.000 0.980 0.020
#> GSM872250 2 0.7006 0.1225 0.428 0.456 0.000 0.116
#> GSM872251 3 0.0336 0.9152 0.000 0.000 0.992 0.008
#> GSM872252 1 0.6386 0.3232 0.648 0.140 0.000 0.212
#> GSM872253 3 0.4718 0.6814 0.004 0.008 0.716 0.272
#> GSM872254 2 0.5637 0.4836 0.168 0.720 0.000 0.112
#> GSM872255 1 0.4898 0.0683 0.584 0.000 0.000 0.416
#> GSM872256 1 0.2216 0.4147 0.908 0.000 0.000 0.092
#> GSM872257 2 0.4331 0.5829 0.000 0.712 0.000 0.288
#> GSM872258 3 0.0188 0.9138 0.000 0.000 0.996 0.004
#> GSM872259 1 0.0188 0.4533 0.996 0.000 0.000 0.004
#> GSM872260 1 0.4477 0.2313 0.688 0.000 0.000 0.312
#> GSM872261 2 0.7628 0.2581 0.260 0.472 0.000 0.268
#> GSM872262 1 0.5088 0.0410 0.572 0.000 0.004 0.424
#> GSM872263 3 0.0469 0.9125 0.000 0.000 0.988 0.012
#> GSM872264 4 0.7587 0.3452 0.292 0.000 0.232 0.476
#> GSM872265 4 0.6898 0.3454 0.360 0.000 0.116 0.524
#> GSM872266 2 0.0657 0.6226 0.004 0.984 0.000 0.012
#> GSM872267 2 0.0376 0.6238 0.004 0.992 0.000 0.004
#> GSM872268 3 0.0469 0.9150 0.000 0.000 0.988 0.012
#> GSM872269 2 0.6400 0.3910 0.252 0.632 0.000 0.116
#> GSM872270 3 0.0336 0.9152 0.000 0.000 0.992 0.008
#> GSM872271 4 0.5512 -0.4205 0.016 0.492 0.000 0.492
#> GSM872272 2 0.5512 0.2825 0.016 0.492 0.000 0.492
#> GSM872273 1 0.4331 0.2479 0.712 0.000 0.000 0.288
#> GSM872274 2 0.4697 0.5502 0.000 0.644 0.000 0.356
#> GSM872275 3 0.4049 0.7316 0.000 0.008 0.780 0.212
#> GSM872276 1 0.5088 0.0410 0.572 0.000 0.004 0.424
#> GSM872277 1 0.4331 0.2479 0.712 0.000 0.000 0.288
#> GSM872278 3 0.4406 0.6031 0.000 0.000 0.700 0.300
#> GSM872279 1 0.2385 0.4345 0.920 0.028 0.000 0.052
#> GSM872280 4 0.7702 0.2422 0.260 0.000 0.288 0.452
#> GSM872281 4 0.6599 0.2438 0.432 0.000 0.080 0.488
#> GSM872282 3 0.1389 0.8941 0.000 0.000 0.952 0.048
#> GSM872283 4 0.5535 0.2267 0.420 0.000 0.020 0.560
#> GSM872284 4 0.6599 0.2502 0.432 0.000 0.080 0.488
#> GSM872285 3 0.3266 0.7802 0.000 0.000 0.832 0.168
#> GSM872286 1 0.7030 -0.1218 0.472 0.408 0.000 0.120
#> GSM872287 3 0.0469 0.9150 0.000 0.000 0.988 0.012
#> GSM872288 1 0.6995 -0.0782 0.496 0.384 0.000 0.120
#> GSM872289 3 0.1211 0.8930 0.000 0.000 0.960 0.040
#> GSM872290 1 0.0336 0.4530 0.992 0.000 0.000 0.008
#> GSM872291 1 0.4916 0.0491 0.576 0.000 0.000 0.424
#> GSM872292 2 0.4697 0.5502 0.000 0.644 0.000 0.356
#> GSM872293 1 0.0188 0.4533 0.996 0.000 0.000 0.004
#> GSM872294 4 0.4948 -0.4229 0.000 0.440 0.000 0.560
#> GSM872295 2 0.4382 0.5807 0.000 0.704 0.000 0.296
#> GSM872296 2 0.4898 0.4962 0.000 0.584 0.000 0.416
#> GSM872297 1 0.0469 0.4521 0.988 0.000 0.000 0.012
#> GSM872298 1 0.5406 -0.1488 0.508 0.000 0.012 0.480
#> GSM872299 1 0.6839 0.0361 0.552 0.328 0.000 0.120
#> GSM872300 1 0.5088 0.0410 0.572 0.000 0.004 0.424
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.1990 0.834 0.000 0.004 0.928 0.028 0.040
#> GSM872245 5 0.4522 0.452 0.440 0.000 0.000 0.008 0.552
#> GSM872246 3 0.0290 0.862 0.000 0.000 0.992 0.008 0.000
#> GSM872247 3 0.0451 0.862 0.000 0.004 0.988 0.008 0.000
#> GSM872248 5 0.4777 0.459 0.008 0.356 0.000 0.016 0.620
#> GSM872249 3 0.0324 0.859 0.000 0.004 0.992 0.000 0.004
#> GSM872250 5 0.3521 0.692 0.232 0.000 0.000 0.004 0.764
#> GSM872251 3 0.0671 0.861 0.000 0.004 0.980 0.016 0.000
#> GSM872252 1 0.5973 0.321 0.580 0.000 0.000 0.164 0.256
#> GSM872253 3 0.7767 0.190 0.016 0.032 0.408 0.280 0.264
#> GSM872254 5 0.5052 0.675 0.100 0.144 0.000 0.020 0.736
#> GSM872255 4 0.5390 0.386 0.420 0.000 0.008 0.532 0.040
#> GSM872256 1 0.2068 0.687 0.904 0.000 0.000 0.092 0.004
#> GSM872257 2 0.2864 0.602 0.000 0.852 0.000 0.012 0.136
#> GSM872258 3 0.2293 0.819 0.000 0.000 0.900 0.084 0.016
#> GSM872259 1 0.1106 0.743 0.964 0.000 0.000 0.024 0.012
#> GSM872260 4 0.5505 0.265 0.452 0.000 0.000 0.484 0.064
#> GSM872261 5 0.6505 0.526 0.172 0.056 0.000 0.152 0.620
#> GSM872262 4 0.4183 0.551 0.324 0.000 0.008 0.668 0.000
#> GSM872263 3 0.1830 0.837 0.000 0.000 0.932 0.028 0.040
#> GSM872264 4 0.6560 0.444 0.064 0.096 0.032 0.668 0.140
#> GSM872265 4 0.6541 0.451 0.068 0.096 0.028 0.668 0.140
#> GSM872266 5 0.4653 0.486 0.008 0.324 0.000 0.016 0.652
#> GSM872267 5 0.4777 0.459 0.008 0.356 0.000 0.016 0.620
#> GSM872268 3 0.0451 0.862 0.000 0.004 0.988 0.008 0.000
#> GSM872269 5 0.4686 0.700 0.188 0.052 0.000 0.016 0.744
#> GSM872270 3 0.0324 0.861 0.000 0.004 0.992 0.004 0.000
#> GSM872271 2 0.6634 0.415 0.004 0.452 0.000 0.348 0.196
#> GSM872272 2 0.6634 0.415 0.004 0.452 0.000 0.348 0.196
#> GSM872273 1 0.3684 0.400 0.720 0.000 0.000 0.280 0.000
#> GSM872274 2 0.0771 0.706 0.000 0.976 0.000 0.004 0.020
#> GSM872275 3 0.7183 0.260 0.008 0.040 0.484 0.332 0.136
#> GSM872276 4 0.4201 0.547 0.328 0.000 0.008 0.664 0.000
#> GSM872277 1 0.3990 0.363 0.688 0.000 0.000 0.308 0.004
#> GSM872278 4 0.6444 0.165 0.008 0.020 0.328 0.548 0.096
#> GSM872279 1 0.1197 0.726 0.952 0.000 0.000 0.000 0.048
#> GSM872280 4 0.5662 0.553 0.132 0.000 0.144 0.692 0.032
#> GSM872281 4 0.2951 0.615 0.084 0.004 0.016 0.880 0.016
#> GSM872282 3 0.3005 0.802 0.000 0.048 0.884 0.028 0.040
#> GSM872283 4 0.6076 0.461 0.076 0.096 0.004 0.684 0.140
#> GSM872284 4 0.3529 0.603 0.076 0.016 0.016 0.860 0.032
#> GSM872285 3 0.4329 0.520 0.000 0.000 0.672 0.312 0.016
#> GSM872286 5 0.4047 0.629 0.320 0.000 0.000 0.004 0.676
#> GSM872287 3 0.0451 0.862 0.000 0.004 0.988 0.008 0.000
#> GSM872288 5 0.3809 0.676 0.256 0.000 0.000 0.008 0.736
#> GSM872289 3 0.1997 0.840 0.000 0.000 0.924 0.036 0.040
#> GSM872290 1 0.1211 0.742 0.960 0.000 0.000 0.016 0.024
#> GSM872291 4 0.5206 0.396 0.428 0.000 0.000 0.528 0.044
#> GSM872292 2 0.0771 0.706 0.000 0.976 0.000 0.004 0.020
#> GSM872293 1 0.0693 0.744 0.980 0.000 0.000 0.012 0.008
#> GSM872294 2 0.5076 0.628 0.004 0.712 0.000 0.128 0.156
#> GSM872295 2 0.2625 0.638 0.000 0.876 0.000 0.016 0.108
#> GSM872296 2 0.1484 0.706 0.000 0.944 0.000 0.008 0.048
#> GSM872297 1 0.1251 0.739 0.956 0.000 0.000 0.036 0.008
#> GSM872298 4 0.3928 0.611 0.176 0.000 0.008 0.788 0.028
#> GSM872299 1 0.4666 -0.189 0.572 0.000 0.000 0.016 0.412
#> GSM872300 4 0.4183 0.551 0.324 0.000 0.008 0.668 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.3695 0.8294 0.008 0.004 0.832 0.068 0.024 0.064
#> GSM872245 5 0.4899 0.3325 0.356 0.000 0.000 0.036 0.588 0.020
#> GSM872246 3 0.1610 0.8803 0.020 0.004 0.944 0.004 0.004 0.024
#> GSM872247 3 0.0291 0.8915 0.004 0.000 0.992 0.000 0.000 0.004
#> GSM872248 5 0.4968 0.5410 0.000 0.208 0.000 0.060 0.688 0.044
#> GSM872249 3 0.0291 0.8905 0.004 0.000 0.992 0.000 0.000 0.004
#> GSM872250 5 0.1327 0.7320 0.064 0.000 0.000 0.000 0.936 0.000
#> GSM872251 3 0.1592 0.8736 0.016 0.000 0.944 0.012 0.004 0.024
#> GSM872252 6 0.7315 0.0543 0.204 0.000 0.000 0.136 0.256 0.404
#> GSM872253 6 0.7399 0.2558 0.020 0.004 0.140 0.232 0.124 0.480
#> GSM872254 5 0.3565 0.6975 0.004 0.028 0.000 0.080 0.832 0.056
#> GSM872255 6 0.3528 0.5038 0.296 0.000 0.000 0.004 0.000 0.700
#> GSM872256 1 0.1444 0.7837 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM872257 2 0.3496 0.7863 0.000 0.836 0.000 0.056 0.056 0.052
#> GSM872258 3 0.4601 0.4963 0.016 0.004 0.664 0.016 0.008 0.292
#> GSM872259 1 0.1408 0.8159 0.944 0.000 0.000 0.020 0.036 0.000
#> GSM872260 6 0.4111 0.4805 0.296 0.000 0.000 0.024 0.004 0.676
#> GSM872261 5 0.6577 0.2810 0.044 0.000 0.000 0.204 0.460 0.292
#> GSM872262 6 0.4750 0.4522 0.244 0.000 0.000 0.100 0.000 0.656
#> GSM872263 3 0.3695 0.8294 0.008 0.004 0.832 0.068 0.024 0.064
#> GSM872264 4 0.4502 0.7318 0.040 0.016 0.004 0.720 0.004 0.216
#> GSM872265 4 0.4502 0.7318 0.040 0.016 0.004 0.720 0.004 0.216
#> GSM872266 5 0.4605 0.5885 0.000 0.160 0.000 0.060 0.736 0.044
#> GSM872267 5 0.4994 0.5358 0.000 0.212 0.000 0.060 0.684 0.044
#> GSM872268 3 0.0291 0.8915 0.004 0.000 0.992 0.000 0.000 0.004
#> GSM872269 5 0.4266 0.6926 0.040 0.012 0.000 0.076 0.792 0.080
#> GSM872270 3 0.0000 0.8914 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872271 4 0.4492 0.4906 0.000 0.216 0.000 0.712 0.020 0.052
#> GSM872272 4 0.4492 0.4906 0.000 0.216 0.000 0.712 0.020 0.052
#> GSM872273 1 0.2593 0.6972 0.844 0.000 0.000 0.008 0.000 0.148
#> GSM872274 2 0.0260 0.8638 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM872275 6 0.6858 0.1720 0.020 0.000 0.288 0.288 0.016 0.388
#> GSM872276 6 0.4729 0.4537 0.248 0.000 0.000 0.096 0.000 0.656
#> GSM872277 1 0.3275 0.7019 0.816 0.000 0.000 0.036 0.004 0.144
#> GSM872278 6 0.6264 0.1198 0.020 0.000 0.152 0.340 0.008 0.480
#> GSM872279 1 0.2713 0.7841 0.880 0.000 0.000 0.016 0.052 0.052
#> GSM872280 6 0.4079 0.4879 0.096 0.000 0.084 0.032 0.000 0.788
#> GSM872281 4 0.4876 0.4533 0.048 0.000 0.004 0.504 0.000 0.444
#> GSM872282 3 0.4449 0.8024 0.008 0.040 0.796 0.068 0.024 0.064
#> GSM872283 4 0.4390 0.7308 0.040 0.016 0.000 0.720 0.004 0.220
#> GSM872284 4 0.4830 0.5838 0.044 0.000 0.004 0.580 0.004 0.368
#> GSM872285 6 0.4959 -0.0118 0.016 0.000 0.472 0.020 0.008 0.484
#> GSM872286 5 0.1918 0.7242 0.088 0.000 0.000 0.008 0.904 0.000
#> GSM872287 3 0.0291 0.8915 0.004 0.000 0.992 0.000 0.000 0.004
#> GSM872288 5 0.1501 0.7311 0.076 0.000 0.000 0.000 0.924 0.000
#> GSM872289 3 0.3936 0.7784 0.016 0.004 0.808 0.016 0.040 0.116
#> GSM872290 1 0.2341 0.7988 0.900 0.000 0.000 0.012 0.032 0.056
#> GSM872291 6 0.3636 0.4874 0.320 0.000 0.000 0.004 0.000 0.676
#> GSM872292 2 0.0260 0.8638 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM872293 1 0.0790 0.8166 0.968 0.000 0.000 0.000 0.032 0.000
#> GSM872294 2 0.4909 0.5174 0.004 0.644 0.000 0.288 0.020 0.044
#> GSM872295 2 0.3426 0.8078 0.000 0.840 0.000 0.064 0.048 0.048
#> GSM872296 2 0.0632 0.8572 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM872297 1 0.1408 0.8159 0.944 0.000 0.000 0.020 0.036 0.000
#> GSM872298 6 0.3678 0.4041 0.084 0.000 0.000 0.128 0.000 0.788
#> GSM872299 1 0.6302 -0.1530 0.432 0.000 0.000 0.064 0.408 0.096
#> GSM872300 6 0.4750 0.4522 0.244 0.000 0.000 0.100 0.000 0.656
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 time(p) individual(p) k
#> MAD:kmeans 15 NA NA 2
#> MAD:kmeans 55 0.507 1.11e-02 3
#> MAD:kmeans 23 0.779 1.17e-01 4
#> MAD:kmeans 38 0.730 2.09e-04 5
#> MAD:kmeans 38 0.626 2.18e-05 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 29485 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.407 0.816 0.857 0.5083 0.492 0.492
#> 3 3 0.943 0.927 0.969 0.3308 0.706 0.469
#> 4 4 0.798 0.805 0.890 0.1215 0.826 0.526
#> 5 5 0.771 0.698 0.850 0.0531 0.872 0.546
#> 6 6 0.790 0.727 0.846 0.0400 0.937 0.712
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
#> GSM872244 1 0.855 0.831 0.720 0.280
#> GSM872245 2 0.706 0.834 0.192 0.808
#> GSM872246 1 0.706 0.855 0.808 0.192
#> GSM872247 1 0.833 0.841 0.736 0.264
#> GSM872248 2 0.000 0.812 0.000 1.000
#> GSM872249 1 0.855 0.831 0.720 0.280
#> GSM872250 2 0.506 0.837 0.112 0.888
#> GSM872251 1 0.827 0.843 0.740 0.260
#> GSM872252 2 0.855 0.822 0.280 0.720
#> GSM872253 1 0.494 0.848 0.892 0.108
#> GSM872254 2 0.343 0.827 0.064 0.936
#> GSM872255 1 0.000 0.816 1.000 0.000
#> GSM872256 2 0.855 0.822 0.280 0.720
#> GSM872257 2 0.000 0.812 0.000 1.000
#> GSM872258 1 0.625 0.856 0.844 0.156
#> GSM872259 2 0.855 0.822 0.280 0.720
#> GSM872260 1 0.000 0.816 1.000 0.000
#> GSM872261 2 0.506 0.837 0.112 0.888
#> GSM872262 1 0.000 0.816 1.000 0.000
#> GSM872263 1 0.833 0.841 0.736 0.264
#> GSM872264 1 0.814 0.838 0.748 0.252
#> GSM872265 2 0.963 0.248 0.388 0.612
#> GSM872266 2 0.000 0.812 0.000 1.000
#> GSM872267 2 0.000 0.812 0.000 1.000
#> GSM872268 1 0.706 0.855 0.808 0.192
#> GSM872269 2 0.689 0.831 0.184 0.816
#> GSM872270 1 0.855 0.831 0.720 0.280
#> GSM872271 2 0.000 0.812 0.000 1.000
#> GSM872272 2 0.000 0.812 0.000 1.000
#> GSM872273 2 0.891 0.804 0.308 0.692
#> GSM872274 2 0.000 0.812 0.000 1.000
#> GSM872275 1 0.855 0.831 0.720 0.280
#> GSM872276 1 0.000 0.816 1.000 0.000
#> GSM872277 2 0.891 0.804 0.308 0.692
#> GSM872278 1 0.839 0.839 0.732 0.268
#> GSM872279 2 0.855 0.822 0.280 0.720
#> GSM872280 1 0.000 0.816 1.000 0.000
#> GSM872281 1 0.343 0.839 0.936 0.064
#> GSM872282 1 0.855 0.831 0.720 0.280
#> GSM872283 2 0.595 0.829 0.144 0.856
#> GSM872284 1 0.343 0.839 0.936 0.064
#> GSM872285 1 0.343 0.842 0.936 0.064
#> GSM872286 2 0.850 0.823 0.276 0.724
#> GSM872287 1 0.833 0.841 0.736 0.264
#> GSM872288 2 0.833 0.826 0.264 0.736
#> GSM872289 1 0.494 0.848 0.892 0.108
#> GSM872290 2 0.855 0.822 0.280 0.720
#> GSM872291 1 0.000 0.816 1.000 0.000
#> GSM872292 2 0.000 0.812 0.000 1.000
#> GSM872293 2 0.855 0.822 0.280 0.720
#> GSM872294 2 0.327 0.824 0.060 0.940
#> GSM872295 2 0.000 0.812 0.000 1.000
#> GSM872296 2 0.000 0.812 0.000 1.000
#> GSM872297 2 0.855 0.822 0.280 0.720
#> GSM872298 1 0.000 0.816 1.000 0.000
#> GSM872299 2 0.855 0.822 0.280 0.720
#> GSM872300 1 0.000 0.816 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0424 0.941 0.000 0.008 0.992
#> GSM872245 2 0.0237 0.972 0.004 0.996 0.000
#> GSM872246 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.974 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872250 2 0.0424 0.970 0.008 0.992 0.000
#> GSM872251 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872252 1 0.2878 0.885 0.904 0.096 0.000
#> GSM872253 3 0.0424 0.941 0.008 0.000 0.992
#> GSM872254 2 0.0000 0.974 0.000 1.000 0.000
#> GSM872255 1 0.0000 0.977 1.000 0.000 0.000
#> GSM872256 1 0.0000 0.977 1.000 0.000 0.000
#> GSM872257 2 0.0000 0.974 0.000 1.000 0.000
#> GSM872258 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872259 1 0.0000 0.977 1.000 0.000 0.000
#> GSM872260 1 0.0000 0.977 1.000 0.000 0.000
#> GSM872261 2 0.0000 0.974 0.000 1.000 0.000
#> GSM872262 1 0.0237 0.976 0.996 0.000 0.004
#> GSM872263 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872264 3 0.7059 0.104 0.460 0.020 0.520
#> GSM872265 1 0.5883 0.783 0.796 0.112 0.092
#> GSM872266 2 0.0000 0.974 0.000 1.000 0.000
#> GSM872267 2 0.0000 0.974 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872269 2 0.0424 0.970 0.008 0.992 0.000
#> GSM872270 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872271 2 0.0000 0.974 0.000 1.000 0.000
#> GSM872272 2 0.0000 0.974 0.000 1.000 0.000
#> GSM872273 1 0.0000 0.977 1.000 0.000 0.000
#> GSM872274 2 0.0000 0.974 0.000 1.000 0.000
#> GSM872275 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872276 1 0.0237 0.976 0.996 0.000 0.004
#> GSM872277 1 0.0000 0.977 1.000 0.000 0.000
#> GSM872278 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872279 1 0.0000 0.977 1.000 0.000 0.000
#> GSM872280 3 0.6026 0.400 0.376 0.000 0.624
#> GSM872281 1 0.1529 0.949 0.960 0.000 0.040
#> GSM872282 3 0.0424 0.941 0.000 0.008 0.992
#> GSM872283 1 0.1031 0.962 0.976 0.024 0.000
#> GSM872284 1 0.1529 0.949 0.960 0.000 0.040
#> GSM872285 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872286 2 0.3482 0.855 0.128 0.872 0.000
#> GSM872287 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872288 2 0.1031 0.958 0.024 0.976 0.000
#> GSM872289 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872290 1 0.0000 0.977 1.000 0.000 0.000
#> GSM872291 1 0.0000 0.977 1.000 0.000 0.000
#> GSM872292 2 0.0000 0.974 0.000 1.000 0.000
#> GSM872293 1 0.0000 0.977 1.000 0.000 0.000
#> GSM872294 2 0.0000 0.974 0.000 1.000 0.000
#> GSM872295 2 0.0000 0.974 0.000 1.000 0.000
#> GSM872296 2 0.0000 0.974 0.000 1.000 0.000
#> GSM872297 1 0.0000 0.977 1.000 0.000 0.000
#> GSM872298 1 0.0424 0.973 0.992 0.000 0.008
#> GSM872299 2 0.5431 0.622 0.284 0.716 0.000
#> GSM872300 1 0.0000 0.977 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0000 0.9968 0.000 0.000 1.000 0.000
#> GSM872245 1 0.0188 0.7384 0.996 0.004 0.000 0.000
#> GSM872246 3 0.0000 0.9968 0.000 0.000 1.000 0.000
#> GSM872247 3 0.0000 0.9968 0.000 0.000 1.000 0.000
#> GSM872248 2 0.3801 0.8279 0.220 0.780 0.000 0.000
#> GSM872249 3 0.0000 0.9968 0.000 0.000 1.000 0.000
#> GSM872250 1 0.0336 0.7346 0.992 0.008 0.000 0.000
#> GSM872251 3 0.0000 0.9968 0.000 0.000 1.000 0.000
#> GSM872252 1 0.2469 0.7749 0.892 0.000 0.000 0.108
#> GSM872253 3 0.0921 0.9720 0.028 0.000 0.972 0.000
#> GSM872254 2 0.4877 0.6095 0.408 0.592 0.000 0.000
#> GSM872255 4 0.0592 0.8239 0.016 0.000 0.000 0.984
#> GSM872256 1 0.4866 0.5767 0.596 0.000 0.000 0.404
#> GSM872257 2 0.3649 0.8330 0.204 0.796 0.000 0.000
#> GSM872258 3 0.0000 0.9968 0.000 0.000 1.000 0.000
#> GSM872259 1 0.4103 0.7524 0.744 0.000 0.000 0.256
#> GSM872260 1 0.4877 0.5688 0.592 0.000 0.000 0.408
#> GSM872261 2 0.4866 0.6136 0.404 0.596 0.000 0.000
#> GSM872262 4 0.0000 0.8324 0.000 0.000 0.000 1.000
#> GSM872263 3 0.0000 0.9968 0.000 0.000 1.000 0.000
#> GSM872264 4 0.4817 0.5181 0.000 0.388 0.000 0.612
#> GSM872265 4 0.4817 0.5181 0.000 0.388 0.000 0.612
#> GSM872266 2 0.3801 0.8279 0.220 0.780 0.000 0.000
#> GSM872267 2 0.3764 0.8297 0.216 0.784 0.000 0.000
#> GSM872268 3 0.0000 0.9968 0.000 0.000 1.000 0.000
#> GSM872269 1 0.4543 0.0731 0.676 0.324 0.000 0.000
#> GSM872270 3 0.0000 0.9968 0.000 0.000 1.000 0.000
#> GSM872271 2 0.0000 0.8326 0.000 1.000 0.000 0.000
#> GSM872272 2 0.0000 0.8326 0.000 1.000 0.000 0.000
#> GSM872273 4 0.0336 0.8293 0.008 0.000 0.000 0.992
#> GSM872274 2 0.0188 0.8341 0.004 0.996 0.000 0.000
#> GSM872275 3 0.0336 0.9908 0.000 0.008 0.992 0.000
#> GSM872276 4 0.0000 0.8324 0.000 0.000 0.000 1.000
#> GSM872277 4 0.0336 0.8291 0.008 0.000 0.000 0.992
#> GSM872278 3 0.0000 0.9968 0.000 0.000 1.000 0.000
#> GSM872279 1 0.3975 0.7581 0.760 0.000 0.000 0.240
#> GSM872280 4 0.4830 0.3373 0.000 0.000 0.392 0.608
#> GSM872281 4 0.0469 0.8301 0.000 0.012 0.000 0.988
#> GSM872282 3 0.0469 0.9872 0.000 0.012 0.988 0.000
#> GSM872283 4 0.4790 0.5300 0.000 0.380 0.000 0.620
#> GSM872284 4 0.2011 0.7965 0.000 0.080 0.000 0.920
#> GSM872285 3 0.0000 0.9968 0.000 0.000 1.000 0.000
#> GSM872286 1 0.0000 0.7411 1.000 0.000 0.000 0.000
#> GSM872287 3 0.0000 0.9968 0.000 0.000 1.000 0.000
#> GSM872288 1 0.0000 0.7411 1.000 0.000 0.000 0.000
#> GSM872289 3 0.0000 0.9968 0.000 0.000 1.000 0.000
#> GSM872290 1 0.4103 0.7524 0.744 0.000 0.000 0.256
#> GSM872291 4 0.0592 0.8238 0.016 0.000 0.000 0.984
#> GSM872292 2 0.0188 0.8341 0.004 0.996 0.000 0.000
#> GSM872293 1 0.4250 0.7395 0.724 0.000 0.000 0.276
#> GSM872294 2 0.0000 0.8326 0.000 1.000 0.000 0.000
#> GSM872295 2 0.3649 0.8330 0.204 0.796 0.000 0.000
#> GSM872296 2 0.0000 0.8326 0.000 1.000 0.000 0.000
#> GSM872297 1 0.4250 0.7395 0.724 0.000 0.000 0.276
#> GSM872298 4 0.0000 0.8324 0.000 0.000 0.000 1.000
#> GSM872299 1 0.0000 0.7411 1.000 0.000 0.000 0.000
#> GSM872300 4 0.0000 0.8324 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.0290 0.9191 0.000 0.008 0.992 0.000 0.000
#> GSM872245 5 0.2179 0.6756 0.100 0.000 0.000 0.004 0.896
#> GSM872246 3 0.0000 0.9226 0.000 0.000 1.000 0.000 0.000
#> GSM872247 3 0.0000 0.9226 0.000 0.000 1.000 0.000 0.000
#> GSM872248 5 0.3913 0.5285 0.000 0.324 0.000 0.000 0.676
#> GSM872249 3 0.0000 0.9226 0.000 0.000 1.000 0.000 0.000
#> GSM872250 5 0.0510 0.7300 0.000 0.016 0.000 0.000 0.984
#> GSM872251 3 0.0000 0.9226 0.000 0.000 1.000 0.000 0.000
#> GSM872252 1 0.4029 0.6053 0.680 0.004 0.000 0.000 0.316
#> GSM872253 3 0.3731 0.8129 0.036 0.060 0.844 0.000 0.060
#> GSM872254 5 0.2813 0.6687 0.000 0.168 0.000 0.000 0.832
#> GSM872255 1 0.2605 0.6448 0.852 0.000 0.000 0.148 0.000
#> GSM872256 1 0.2674 0.8172 0.856 0.000 0.000 0.004 0.140
#> GSM872257 2 0.2891 0.6863 0.000 0.824 0.000 0.000 0.176
#> GSM872258 3 0.0000 0.9226 0.000 0.000 1.000 0.000 0.000
#> GSM872259 1 0.2806 0.8163 0.844 0.000 0.000 0.004 0.152
#> GSM872260 1 0.2719 0.6552 0.852 0.000 0.000 0.144 0.004
#> GSM872261 2 0.4307 -0.0531 0.000 0.500 0.000 0.000 0.500
#> GSM872262 4 0.4210 0.5081 0.412 0.000 0.000 0.588 0.000
#> GSM872263 3 0.0000 0.9226 0.000 0.000 1.000 0.000 0.000
#> GSM872264 4 0.2516 0.6055 0.000 0.140 0.000 0.860 0.000
#> GSM872265 4 0.2516 0.6055 0.000 0.140 0.000 0.860 0.000
#> GSM872266 5 0.3913 0.5285 0.000 0.324 0.000 0.000 0.676
#> GSM872267 5 0.3932 0.5216 0.000 0.328 0.000 0.000 0.672
#> GSM872268 3 0.0000 0.9226 0.000 0.000 1.000 0.000 0.000
#> GSM872269 5 0.2068 0.7140 0.004 0.092 0.000 0.000 0.904
#> GSM872270 3 0.0000 0.9226 0.000 0.000 1.000 0.000 0.000
#> GSM872271 2 0.2813 0.7459 0.000 0.832 0.000 0.168 0.000
#> GSM872272 2 0.2813 0.7459 0.000 0.832 0.000 0.168 0.000
#> GSM872273 1 0.2464 0.7168 0.888 0.000 0.000 0.096 0.016
#> GSM872274 2 0.0000 0.8244 0.000 1.000 0.000 0.000 0.000
#> GSM872275 3 0.3177 0.7160 0.000 0.208 0.792 0.000 0.000
#> GSM872276 4 0.4291 0.4082 0.464 0.000 0.000 0.536 0.000
#> GSM872277 1 0.4337 0.6141 0.748 0.000 0.000 0.196 0.056
#> GSM872278 3 0.2848 0.7886 0.004 0.000 0.840 0.156 0.000
#> GSM872279 1 0.2690 0.8169 0.844 0.000 0.000 0.000 0.156
#> GSM872280 3 0.6799 -0.2745 0.296 0.000 0.372 0.332 0.000
#> GSM872281 4 0.1908 0.6832 0.092 0.000 0.000 0.908 0.000
#> GSM872282 3 0.0963 0.9022 0.000 0.036 0.964 0.000 0.000
#> GSM872283 4 0.2753 0.6051 0.008 0.136 0.000 0.856 0.000
#> GSM872284 4 0.0794 0.6858 0.028 0.000 0.000 0.972 0.000
#> GSM872285 3 0.0290 0.9192 0.000 0.000 0.992 0.008 0.000
#> GSM872286 5 0.0703 0.7228 0.024 0.000 0.000 0.000 0.976
#> GSM872287 3 0.0000 0.9226 0.000 0.000 1.000 0.000 0.000
#> GSM872288 5 0.0290 0.7277 0.008 0.000 0.000 0.000 0.992
#> GSM872289 3 0.0162 0.9210 0.000 0.000 0.996 0.000 0.004
#> GSM872290 1 0.2516 0.8159 0.860 0.000 0.000 0.000 0.140
#> GSM872291 1 0.2561 0.6472 0.856 0.000 0.000 0.144 0.000
#> GSM872292 2 0.0000 0.8244 0.000 1.000 0.000 0.000 0.000
#> GSM872293 1 0.2648 0.8174 0.848 0.000 0.000 0.000 0.152
#> GSM872294 2 0.0451 0.8226 0.008 0.988 0.000 0.004 0.000
#> GSM872295 2 0.2377 0.7359 0.000 0.872 0.000 0.000 0.128
#> GSM872296 2 0.0290 0.8240 0.000 0.992 0.000 0.008 0.000
#> GSM872297 1 0.2763 0.8175 0.848 0.000 0.000 0.004 0.148
#> GSM872298 4 0.3966 0.5835 0.336 0.000 0.000 0.664 0.000
#> GSM872299 5 0.4434 -0.1598 0.460 0.004 0.000 0.000 0.536
#> GSM872300 4 0.4219 0.5021 0.416 0.000 0.000 0.584 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.1026 0.9000 0.000 0.008 0.968 0.008 0.004 0.012
#> GSM872245 5 0.4386 0.1888 0.412 0.008 0.000 0.004 0.568 0.008
#> GSM872246 3 0.0748 0.9026 0.000 0.000 0.976 0.004 0.004 0.016
#> GSM872247 3 0.0146 0.9038 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM872248 5 0.3398 0.6430 0.000 0.252 0.000 0.000 0.740 0.008
#> GSM872249 3 0.0146 0.9034 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM872250 5 0.1230 0.7595 0.028 0.008 0.000 0.000 0.956 0.008
#> GSM872251 3 0.0260 0.9039 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM872252 1 0.6555 0.4017 0.504 0.008 0.000 0.036 0.208 0.244
#> GSM872253 3 0.7438 0.2391 0.016 0.060 0.432 0.052 0.088 0.352
#> GSM872254 5 0.3767 0.6977 0.000 0.092 0.000 0.016 0.804 0.088
#> GSM872255 6 0.2793 0.8029 0.200 0.000 0.000 0.000 0.000 0.800
#> GSM872256 1 0.1080 0.8295 0.960 0.000 0.000 0.004 0.004 0.032
#> GSM872257 2 0.2070 0.7437 0.000 0.892 0.000 0.000 0.100 0.008
#> GSM872258 3 0.1194 0.8982 0.000 0.000 0.956 0.008 0.004 0.032
#> GSM872259 1 0.0291 0.8399 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM872260 6 0.2902 0.7886 0.196 0.000 0.000 0.000 0.004 0.800
#> GSM872261 2 0.5913 -0.0382 0.004 0.444 0.000 0.020 0.428 0.104
#> GSM872262 6 0.4620 0.7671 0.132 0.000 0.000 0.176 0.000 0.692
#> GSM872263 3 0.0881 0.9016 0.000 0.000 0.972 0.008 0.008 0.012
#> GSM872264 4 0.1296 0.8310 0.000 0.044 0.004 0.948 0.000 0.004
#> GSM872265 4 0.1152 0.8304 0.004 0.044 0.000 0.952 0.000 0.000
#> GSM872266 5 0.3398 0.6430 0.000 0.252 0.000 0.000 0.740 0.008
#> GSM872267 5 0.3583 0.6292 0.000 0.260 0.000 0.004 0.728 0.008
#> GSM872268 3 0.0146 0.9038 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM872269 5 0.3655 0.7061 0.012 0.040 0.000 0.020 0.824 0.104
#> GSM872270 3 0.0146 0.9034 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM872271 2 0.3690 0.5696 0.000 0.684 0.000 0.308 0.000 0.008
#> GSM872272 2 0.3690 0.5696 0.000 0.684 0.000 0.308 0.000 0.008
#> GSM872273 1 0.2706 0.7259 0.852 0.000 0.000 0.024 0.000 0.124
#> GSM872274 2 0.0405 0.8017 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM872275 3 0.4664 0.5438 0.000 0.284 0.664 0.012 0.012 0.028
#> GSM872276 6 0.4014 0.8081 0.148 0.000 0.000 0.096 0.000 0.756
#> GSM872277 1 0.2318 0.7813 0.892 0.000 0.000 0.044 0.000 0.064
#> GSM872278 3 0.5587 0.5064 0.000 0.008 0.620 0.152 0.012 0.208
#> GSM872279 1 0.1138 0.8313 0.960 0.000 0.000 0.004 0.012 0.024
#> GSM872280 6 0.3259 0.7209 0.048 0.000 0.104 0.012 0.000 0.836
#> GSM872281 4 0.3899 0.2268 0.004 0.000 0.000 0.592 0.000 0.404
#> GSM872282 3 0.1514 0.8870 0.000 0.036 0.944 0.004 0.004 0.012
#> GSM872283 4 0.1297 0.8295 0.012 0.040 0.000 0.948 0.000 0.000
#> GSM872284 4 0.2092 0.7642 0.000 0.000 0.000 0.876 0.000 0.124
#> GSM872285 3 0.0935 0.8961 0.000 0.000 0.964 0.000 0.004 0.032
#> GSM872286 5 0.1701 0.7554 0.072 0.000 0.000 0.000 0.920 0.008
#> GSM872287 3 0.0146 0.9038 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM872288 5 0.1462 0.7580 0.056 0.000 0.000 0.000 0.936 0.008
#> GSM872289 3 0.0976 0.9008 0.000 0.000 0.968 0.008 0.008 0.016
#> GSM872290 1 0.1592 0.8246 0.944 0.004 0.000 0.016 0.012 0.024
#> GSM872291 6 0.4233 0.6645 0.304 0.004 0.000 0.016 0.008 0.668
#> GSM872292 2 0.0405 0.8017 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM872293 1 0.0146 0.8396 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM872294 2 0.1148 0.7985 0.000 0.960 0.000 0.020 0.004 0.016
#> GSM872295 2 0.2136 0.7631 0.000 0.908 0.000 0.016 0.064 0.012
#> GSM872296 2 0.0858 0.8001 0.000 0.968 0.000 0.028 0.004 0.000
#> GSM872297 1 0.0291 0.8399 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM872298 6 0.4164 0.7225 0.064 0.000 0.000 0.184 0.008 0.744
#> GSM872299 1 0.5544 0.4306 0.612 0.004 0.000 0.020 0.252 0.112
#> GSM872300 6 0.4620 0.7671 0.132 0.000 0.000 0.176 0.000 0.692
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 time(p) individual(p) k
#> MAD:skmeans 56 0.796 3.29e-03 2
#> MAD:skmeans 55 0.879 1.26e-03 3
#> MAD:skmeans 55 0.334 3.37e-03 4
#> MAD:skmeans 53 0.712 3.50e-06 5
#> MAD:skmeans 51 0.905 5.65e-07 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 29485 rows and 57 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.379 0.740 0.826 0.4288 0.560 0.560
#> 3 3 0.590 0.776 0.854 0.4528 0.752 0.576
#> 4 4 0.652 0.817 0.869 0.1631 0.904 0.737
#> 5 5 0.726 0.775 0.841 0.0561 0.861 0.566
#> 6 6 0.705 0.594 0.787 0.0698 0.927 0.695
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM872244 2 0.9491 0.820 0.368 0.632
#> GSM872245 2 0.0000 0.583 0.000 1.000
#> GSM872246 1 0.0000 0.821 1.000 0.000
#> GSM872247 1 0.0000 0.821 1.000 0.000
#> GSM872248 2 0.9491 0.820 0.368 0.632
#> GSM872249 1 0.0000 0.821 1.000 0.000
#> GSM872250 2 0.6801 0.734 0.180 0.820
#> GSM872251 1 0.0000 0.821 1.000 0.000
#> GSM872252 1 0.7219 0.706 0.800 0.200
#> GSM872253 1 0.0000 0.821 1.000 0.000
#> GSM872254 2 0.7219 0.748 0.200 0.800
#> GSM872255 1 0.7056 0.711 0.808 0.192
#> GSM872256 1 0.9170 0.643 0.668 0.332
#> GSM872257 2 0.9491 0.820 0.368 0.632
#> GSM872258 1 0.0000 0.821 1.000 0.000
#> GSM872259 1 0.9491 0.619 0.632 0.368
#> GSM872260 1 0.0000 0.821 1.000 0.000
#> GSM872261 2 0.9491 0.820 0.368 0.632
#> GSM872262 1 0.0376 0.819 0.996 0.004
#> GSM872263 1 0.0000 0.821 1.000 0.000
#> GSM872264 1 0.0000 0.821 1.000 0.000
#> GSM872265 1 0.0000 0.821 1.000 0.000
#> GSM872266 2 0.9491 0.820 0.368 0.632
#> GSM872267 2 0.9491 0.820 0.368 0.632
#> GSM872268 1 0.0000 0.821 1.000 0.000
#> GSM872269 2 0.7219 0.748 0.200 0.800
#> GSM872270 1 0.0376 0.817 0.996 0.004
#> GSM872271 2 0.9491 0.820 0.368 0.632
#> GSM872272 2 0.9491 0.820 0.368 0.632
#> GSM872273 1 0.9491 0.619 0.632 0.368
#> GSM872274 2 0.9491 0.820 0.368 0.632
#> GSM872275 1 0.0000 0.821 1.000 0.000
#> GSM872276 1 0.9491 0.619 0.632 0.368
#> GSM872277 1 0.9491 0.619 0.632 0.368
#> GSM872278 1 0.0000 0.821 1.000 0.000
#> GSM872279 1 0.9491 0.619 0.632 0.368
#> GSM872280 1 0.0000 0.821 1.000 0.000
#> GSM872281 1 0.0000 0.821 1.000 0.000
#> GSM872282 1 0.3879 0.718 0.924 0.076
#> GSM872283 1 0.6531 0.725 0.832 0.168
#> GSM872284 1 0.0000 0.821 1.000 0.000
#> GSM872285 1 0.0000 0.821 1.000 0.000
#> GSM872286 2 0.0000 0.583 0.000 1.000
#> GSM872287 1 0.0000 0.821 1.000 0.000
#> GSM872288 2 0.7745 0.689 0.228 0.772
#> GSM872289 1 0.0000 0.821 1.000 0.000
#> GSM872290 1 0.9491 0.619 0.632 0.368
#> GSM872291 1 0.9393 0.627 0.644 0.356
#> GSM872292 2 0.9491 0.820 0.368 0.632
#> GSM872293 1 0.9491 0.619 0.632 0.368
#> GSM872294 1 0.0000 0.821 1.000 0.000
#> GSM872295 2 0.9491 0.820 0.368 0.632
#> GSM872296 1 0.1843 0.788 0.972 0.028
#> GSM872297 1 0.9491 0.619 0.632 0.368
#> GSM872298 1 0.0000 0.821 1.000 0.000
#> GSM872299 2 0.9944 -0.363 0.456 0.544
#> GSM872300 1 0.8608 0.667 0.716 0.284
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872245 2 0.5905 0.671 0.352 0.648 0.000
#> GSM872246 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.821 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872250 2 0.4953 0.791 0.176 0.808 0.016
#> GSM872251 3 0.0424 0.980 0.008 0.000 0.992
#> GSM872252 1 0.4002 0.740 0.840 0.000 0.160
#> GSM872253 1 0.5988 0.699 0.632 0.000 0.368
#> GSM872254 2 0.0000 0.821 0.000 1.000 0.000
#> GSM872255 1 0.4399 0.738 0.812 0.000 0.188
#> GSM872256 1 0.1031 0.736 0.976 0.000 0.024
#> GSM872257 2 0.0000 0.821 0.000 1.000 0.000
#> GSM872258 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872259 1 0.0000 0.727 1.000 0.000 0.000
#> GSM872260 1 0.5988 0.699 0.632 0.000 0.368
#> GSM872261 2 0.5497 0.601 0.000 0.708 0.292
#> GSM872262 1 0.5968 0.701 0.636 0.000 0.364
#> GSM872263 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872264 1 0.5988 0.699 0.632 0.000 0.368
#> GSM872265 1 0.5988 0.699 0.632 0.000 0.368
#> GSM872266 2 0.2066 0.819 0.000 0.940 0.060
#> GSM872267 2 0.0000 0.821 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872269 2 0.5667 0.796 0.140 0.800 0.060
#> GSM872270 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872271 2 0.5968 0.466 0.000 0.636 0.364
#> GSM872272 2 0.5988 0.457 0.000 0.632 0.368
#> GSM872273 1 0.0000 0.727 1.000 0.000 0.000
#> GSM872274 2 0.2165 0.818 0.000 0.936 0.064
#> GSM872275 1 0.5988 0.699 0.632 0.000 0.368
#> GSM872276 1 0.0000 0.727 1.000 0.000 0.000
#> GSM872277 1 0.0000 0.727 1.000 0.000 0.000
#> GSM872278 1 0.5988 0.699 0.632 0.000 0.368
#> GSM872279 1 0.0000 0.727 1.000 0.000 0.000
#> GSM872280 1 0.5988 0.699 0.632 0.000 0.368
#> GSM872281 1 0.5988 0.699 0.632 0.000 0.368
#> GSM872282 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872283 1 0.4555 0.723 0.800 0.000 0.200
#> GSM872284 1 0.5988 0.699 0.632 0.000 0.368
#> GSM872285 3 0.0424 0.980 0.008 0.000 0.992
#> GSM872286 2 0.4555 0.780 0.200 0.800 0.000
#> GSM872287 3 0.0000 0.987 0.000 0.000 1.000
#> GSM872288 2 0.5138 0.739 0.252 0.748 0.000
#> GSM872289 3 0.2878 0.847 0.096 0.000 0.904
#> GSM872290 1 0.0000 0.727 1.000 0.000 0.000
#> GSM872291 1 0.0592 0.732 0.988 0.000 0.012
#> GSM872292 2 0.2165 0.818 0.000 0.936 0.064
#> GSM872293 1 0.0000 0.727 1.000 0.000 0.000
#> GSM872294 1 0.5988 0.699 0.632 0.000 0.368
#> GSM872295 2 0.2165 0.818 0.000 0.936 0.064
#> GSM872296 1 0.7032 0.671 0.604 0.028 0.368
#> GSM872297 1 0.0000 0.727 1.000 0.000 0.000
#> GSM872298 1 0.5988 0.699 0.632 0.000 0.368
#> GSM872299 1 0.5216 0.412 0.740 0.260 0.000
#> GSM872300 1 0.2448 0.743 0.924 0.000 0.076
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.2197 0.9104 0.000 0.004 0.916 0.080
#> GSM872245 1 0.1118 0.8833 0.964 0.036 0.000 0.000
#> GSM872246 3 0.0000 0.9330 0.000 0.000 1.000 0.000
#> GSM872247 3 0.0000 0.9330 0.000 0.000 1.000 0.000
#> GSM872248 2 0.0000 0.8537 0.000 1.000 0.000 0.000
#> GSM872249 3 0.0000 0.9330 0.000 0.000 1.000 0.000
#> GSM872250 2 0.3547 0.8208 0.144 0.840 0.000 0.016
#> GSM872251 3 0.2281 0.9035 0.000 0.000 0.904 0.096
#> GSM872252 4 0.2831 0.7750 0.120 0.004 0.000 0.876
#> GSM872253 4 0.3266 0.8106 0.000 0.000 0.168 0.832
#> GSM872254 2 0.1888 0.8518 0.044 0.940 0.000 0.016
#> GSM872255 4 0.1545 0.7995 0.040 0.000 0.008 0.952
#> GSM872256 4 0.2530 0.7491 0.112 0.000 0.000 0.888
#> GSM872257 2 0.1004 0.8495 0.024 0.972 0.000 0.004
#> GSM872258 3 0.0817 0.9298 0.000 0.000 0.976 0.024
#> GSM872259 1 0.1792 0.9536 0.932 0.000 0.000 0.068
#> GSM872260 4 0.1792 0.8277 0.000 0.000 0.068 0.932
#> GSM872261 2 0.5265 0.7422 0.000 0.748 0.160 0.092
#> GSM872262 4 0.0707 0.8157 0.000 0.000 0.020 0.980
#> GSM872263 3 0.0000 0.9330 0.000 0.000 1.000 0.000
#> GSM872264 4 0.3266 0.8106 0.000 0.000 0.168 0.832
#> GSM872265 4 0.3266 0.8106 0.000 0.000 0.168 0.832
#> GSM872266 2 0.2807 0.8557 0.044 0.912 0.024 0.020
#> GSM872267 2 0.0000 0.8537 0.000 1.000 0.000 0.000
#> GSM872268 3 0.0000 0.9330 0.000 0.000 1.000 0.000
#> GSM872269 2 0.3708 0.8201 0.148 0.832 0.000 0.020
#> GSM872270 3 0.2216 0.9036 0.000 0.000 0.908 0.092
#> GSM872271 2 0.5309 0.7375 0.000 0.744 0.164 0.092
#> GSM872272 2 0.5352 0.7321 0.000 0.740 0.168 0.092
#> GSM872273 1 0.3024 0.9121 0.852 0.000 0.000 0.148
#> GSM872274 2 0.2596 0.8455 0.024 0.908 0.000 0.068
#> GSM872275 4 0.3266 0.8106 0.000 0.000 0.168 0.832
#> GSM872276 4 0.2530 0.7491 0.112 0.000 0.000 0.888
#> GSM872277 1 0.3024 0.9121 0.852 0.000 0.000 0.148
#> GSM872278 4 0.3266 0.8106 0.000 0.000 0.168 0.832
#> GSM872279 4 0.4992 0.1165 0.476 0.000 0.000 0.524
#> GSM872280 4 0.1389 0.8118 0.000 0.000 0.048 0.952
#> GSM872281 4 0.1302 0.8142 0.000 0.000 0.044 0.956
#> GSM872282 3 0.3080 0.8991 0.024 0.000 0.880 0.096
#> GSM872283 4 0.4893 0.8064 0.064 0.000 0.168 0.768
#> GSM872284 4 0.2081 0.8265 0.000 0.000 0.084 0.916
#> GSM872285 3 0.1867 0.8737 0.000 0.000 0.928 0.072
#> GSM872286 2 0.3695 0.8143 0.156 0.828 0.000 0.016
#> GSM872287 3 0.0000 0.9330 0.000 0.000 1.000 0.000
#> GSM872288 2 0.5140 0.7655 0.144 0.760 0.000 0.096
#> GSM872289 3 0.5115 0.7461 0.028 0.012 0.740 0.220
#> GSM872290 1 0.1792 0.9536 0.932 0.000 0.000 0.068
#> GSM872291 4 0.3444 0.7271 0.184 0.000 0.000 0.816
#> GSM872292 2 0.2596 0.8455 0.024 0.908 0.000 0.068
#> GSM872293 1 0.1792 0.9536 0.932 0.000 0.000 0.068
#> GSM872294 4 0.3266 0.8106 0.000 0.000 0.168 0.832
#> GSM872295 2 0.2596 0.8455 0.024 0.908 0.000 0.068
#> GSM872296 4 0.4955 0.7869 0.024 0.044 0.140 0.792
#> GSM872297 1 0.1792 0.9536 0.932 0.000 0.000 0.068
#> GSM872298 4 0.3266 0.8106 0.000 0.000 0.168 0.832
#> GSM872299 4 0.7863 0.0139 0.344 0.276 0.000 0.380
#> GSM872300 4 0.2345 0.7598 0.100 0.000 0.000 0.900
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.3608 0.8176 0.000 0.112 0.824 0.064 0.000
#> GSM872245 1 0.2424 0.7307 0.868 0.000 0.000 0.000 0.132
#> GSM872246 3 0.0000 0.8683 0.000 0.000 1.000 0.000 0.000
#> GSM872247 3 0.0000 0.8683 0.000 0.000 1.000 0.000 0.000
#> GSM872248 5 0.2179 0.7731 0.000 0.112 0.000 0.000 0.888
#> GSM872249 3 0.0000 0.8683 0.000 0.000 1.000 0.000 0.000
#> GSM872250 5 0.1043 0.8536 0.040 0.000 0.000 0.000 0.960
#> GSM872251 3 0.3780 0.8113 0.000 0.116 0.812 0.072 0.000
#> GSM872252 4 0.5116 0.7643 0.188 0.120 0.000 0.692 0.000
#> GSM872253 4 0.4393 0.8135 0.000 0.168 0.076 0.756 0.000
#> GSM872254 5 0.0000 0.8432 0.000 0.000 0.000 0.000 1.000
#> GSM872255 4 0.1410 0.7829 0.060 0.000 0.000 0.940 0.000
#> GSM872256 4 0.1965 0.7720 0.096 0.000 0.000 0.904 0.000
#> GSM872257 2 0.2852 0.7816 0.000 0.828 0.000 0.000 0.172
#> GSM872258 3 0.2520 0.8508 0.000 0.048 0.896 0.056 0.000
#> GSM872259 1 0.0000 0.8324 1.000 0.000 0.000 0.000 0.000
#> GSM872260 4 0.3351 0.8190 0.028 0.132 0.004 0.836 0.000
#> GSM872261 4 0.5274 0.7849 0.000 0.096 0.076 0.744 0.084
#> GSM872262 4 0.1197 0.7901 0.048 0.000 0.000 0.952 0.000
#> GSM872263 3 0.0000 0.8683 0.000 0.000 1.000 0.000 0.000
#> GSM872264 4 0.4466 0.8104 0.000 0.176 0.076 0.748 0.000
#> GSM872265 4 0.4466 0.8104 0.000 0.176 0.076 0.748 0.000
#> GSM872266 5 0.0404 0.8425 0.000 0.012 0.000 0.000 0.988
#> GSM872267 5 0.2280 0.7668 0.000 0.120 0.000 0.000 0.880
#> GSM872268 3 0.0000 0.8683 0.000 0.000 1.000 0.000 0.000
#> GSM872269 5 0.1197 0.8510 0.048 0.000 0.000 0.000 0.952
#> GSM872270 3 0.4088 0.7772 0.000 0.168 0.776 0.056 0.000
#> GSM872271 4 0.4585 0.8107 0.000 0.172 0.076 0.748 0.004
#> GSM872272 4 0.4466 0.8104 0.000 0.176 0.076 0.748 0.000
#> GSM872273 1 0.2329 0.7792 0.876 0.000 0.000 0.124 0.000
#> GSM872274 2 0.2648 0.8089 0.000 0.848 0.000 0.000 0.152
#> GSM872275 4 0.4393 0.8135 0.000 0.168 0.076 0.756 0.000
#> GSM872276 4 0.1478 0.7797 0.064 0.000 0.000 0.936 0.000
#> GSM872277 1 0.2329 0.7792 0.876 0.000 0.000 0.124 0.000
#> GSM872278 4 0.4393 0.8135 0.000 0.168 0.076 0.756 0.000
#> GSM872279 1 0.4273 -0.0942 0.552 0.000 0.000 0.448 0.000
#> GSM872280 4 0.1862 0.7840 0.048 0.004 0.016 0.932 0.000
#> GSM872281 4 0.1197 0.7901 0.048 0.000 0.000 0.952 0.000
#> GSM872282 3 0.4495 0.7342 0.000 0.244 0.712 0.044 0.000
#> GSM872283 4 0.4753 0.7999 0.088 0.056 0.076 0.780 0.000
#> GSM872284 4 0.0000 0.8039 0.000 0.000 0.000 1.000 0.000
#> GSM872285 3 0.1251 0.8529 0.008 0.000 0.956 0.036 0.000
#> GSM872286 5 0.1197 0.8510 0.048 0.000 0.000 0.000 0.952
#> GSM872287 3 0.0000 0.8683 0.000 0.000 1.000 0.000 0.000
#> GSM872288 5 0.1043 0.8536 0.040 0.000 0.000 0.000 0.960
#> GSM872289 3 0.6524 0.6249 0.000 0.140 0.628 0.160 0.072
#> GSM872290 1 0.0000 0.8324 1.000 0.000 0.000 0.000 0.000
#> GSM872291 4 0.3003 0.7376 0.188 0.000 0.000 0.812 0.000
#> GSM872292 2 0.2648 0.8089 0.000 0.848 0.000 0.000 0.152
#> GSM872293 1 0.0000 0.8324 1.000 0.000 0.000 0.000 0.000
#> GSM872294 2 0.3791 0.5911 0.000 0.812 0.076 0.112 0.000
#> GSM872295 2 0.2648 0.8089 0.000 0.848 0.000 0.000 0.152
#> GSM872296 2 0.2592 0.6712 0.000 0.892 0.056 0.052 0.000
#> GSM872297 1 0.0000 0.8324 1.000 0.000 0.000 0.000 0.000
#> GSM872298 4 0.4393 0.8135 0.000 0.168 0.076 0.756 0.000
#> GSM872299 5 0.6614 0.1547 0.236 0.000 0.000 0.316 0.448
#> GSM872300 4 0.1478 0.7797 0.064 0.000 0.000 0.936 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.3672 0.6820 0.000 0.000 0.632 0.000 0.000 0.368
#> GSM872245 1 0.2664 0.6199 0.816 0.000 0.000 0.000 0.184 0.000
#> GSM872246 3 0.1501 0.7724 0.000 0.000 0.924 0.000 0.000 0.076
#> GSM872247 3 0.0000 0.7778 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872248 5 0.2416 0.7212 0.000 0.156 0.000 0.000 0.844 0.000
#> GSM872249 3 0.0000 0.7778 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872250 5 0.0000 0.7975 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872251 3 0.3428 0.6776 0.000 0.000 0.696 0.000 0.000 0.304
#> GSM872252 6 0.4643 0.3620 0.184 0.000 0.000 0.128 0.000 0.688
#> GSM872253 6 0.1501 0.4835 0.000 0.000 0.000 0.076 0.000 0.924
#> GSM872254 5 0.3843 0.2987 0.000 0.000 0.000 0.000 0.548 0.452
#> GSM872255 4 0.0000 0.7343 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872256 4 0.0865 0.7189 0.036 0.000 0.000 0.964 0.000 0.000
#> GSM872257 2 0.0000 0.8329 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872258 3 0.3101 0.7525 0.000 0.000 0.756 0.000 0.000 0.244
#> GSM872259 1 0.0000 0.7277 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872260 4 0.2793 0.6598 0.000 0.000 0.000 0.800 0.000 0.200
#> GSM872261 6 0.5852 -0.0361 0.000 0.000 0.000 0.328 0.208 0.464
#> GSM872262 4 0.0000 0.7343 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872263 3 0.1501 0.7724 0.000 0.000 0.924 0.000 0.000 0.076
#> GSM872264 4 0.3860 0.3990 0.000 0.000 0.000 0.528 0.000 0.472
#> GSM872265 4 0.3860 0.3990 0.000 0.000 0.000 0.528 0.000 0.472
#> GSM872266 5 0.0000 0.7975 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872267 5 0.3247 0.6964 0.000 0.156 0.000 0.000 0.808 0.036
#> GSM872268 3 0.0000 0.7778 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872269 5 0.3563 0.4877 0.000 0.000 0.000 0.000 0.664 0.336
#> GSM872270 3 0.3659 0.6092 0.000 0.000 0.636 0.000 0.000 0.364
#> GSM872271 6 0.1501 0.4835 0.000 0.000 0.000 0.076 0.000 0.924
#> GSM872272 6 0.5836 -0.0208 0.000 0.000 0.000 0.320 0.208 0.472
#> GSM872273 1 0.2697 0.6585 0.812 0.000 0.000 0.188 0.000 0.000
#> GSM872274 2 0.0000 0.8329 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872275 4 0.3672 0.5488 0.000 0.000 0.000 0.632 0.000 0.368
#> GSM872276 4 0.0000 0.7343 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872277 1 0.2664 0.6609 0.816 0.000 0.000 0.184 0.000 0.000
#> GSM872278 4 0.3672 0.5488 0.000 0.000 0.000 0.632 0.000 0.368
#> GSM872279 1 0.5428 0.1269 0.484 0.000 0.000 0.120 0.000 0.396
#> GSM872280 4 0.0146 0.7346 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM872281 4 0.0000 0.7343 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872282 3 0.4671 0.5864 0.000 0.044 0.532 0.000 0.000 0.424
#> GSM872283 4 0.4718 0.5812 0.124 0.000 0.000 0.676 0.000 0.200
#> GSM872284 4 0.0632 0.7329 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM872285 3 0.1858 0.7498 0.000 0.000 0.904 0.092 0.000 0.004
#> GSM872286 5 0.0000 0.7975 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM872287 3 0.0000 0.7778 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872288 5 0.0146 0.7954 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM872289 3 0.5718 0.6265 0.000 0.000 0.556 0.036 0.088 0.320
#> GSM872290 1 0.3843 0.2419 0.548 0.000 0.000 0.000 0.000 0.452
#> GSM872291 6 0.5795 0.1792 0.184 0.000 0.000 0.364 0.000 0.452
#> GSM872292 2 0.0000 0.8329 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872293 1 0.0000 0.7277 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872294 2 0.3373 0.6430 0.000 0.744 0.000 0.008 0.000 0.248
#> GSM872295 6 0.5903 -0.0594 0.000 0.364 0.000 0.000 0.208 0.428
#> GSM872296 2 0.2996 0.7078 0.000 0.772 0.000 0.000 0.000 0.228
#> GSM872297 1 0.0000 0.7277 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872298 4 0.3672 0.5488 0.000 0.000 0.000 0.632 0.000 0.368
#> GSM872299 6 0.6015 -0.1282 0.216 0.000 0.000 0.004 0.328 0.452
#> GSM872300 4 0.0000 0.7343 0.000 0.000 0.000 1.000 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 time(p) individual(p) k
#> MAD:pam 56 0.620 3.50e-02 2
#> MAD:pam 54 0.706 8.47e-05 3
#> MAD:pam 55 0.935 1.13e-05 4
#> MAD:pam 55 0.674 4.46e-07 5
#> MAD:pam 43 0.956 7.05e-06 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 29485 rows and 57 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.980 0.957 0.975 0.2633 0.754 0.754
#> 3 3 0.566 0.825 0.898 1.2430 0.648 0.545
#> 4 4 0.750 0.814 0.870 0.2523 0.698 0.391
#> 5 5 0.775 0.568 0.752 0.0678 0.887 0.600
#> 6 6 0.759 0.467 0.663 0.0487 0.838 0.398
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM872244 1 0.946 0.460 0.636 0.364
#> GSM872245 1 0.163 0.974 0.976 0.024
#> GSM872246 2 0.000 0.977 0.000 1.000
#> GSM872247 2 0.000 0.977 0.000 1.000
#> GSM872248 1 0.000 0.973 1.000 0.000
#> GSM872249 2 0.000 0.977 0.000 1.000
#> GSM872250 1 0.000 0.973 1.000 0.000
#> GSM872251 2 0.469 0.891 0.100 0.900
#> GSM872252 1 0.163 0.974 0.976 0.024
#> GSM872253 1 0.163 0.974 0.976 0.024
#> GSM872254 1 0.000 0.973 1.000 0.000
#> GSM872255 1 0.163 0.974 0.976 0.024
#> GSM872256 1 0.163 0.974 0.976 0.024
#> GSM872257 1 0.000 0.973 1.000 0.000
#> GSM872258 1 0.469 0.904 0.900 0.100
#> GSM872259 1 0.163 0.974 0.976 0.024
#> GSM872260 1 0.163 0.974 0.976 0.024
#> GSM872261 1 0.000 0.973 1.000 0.000
#> GSM872262 1 0.000 0.973 1.000 0.000
#> GSM872263 2 0.000 0.977 0.000 1.000
#> GSM872264 1 0.000 0.973 1.000 0.000
#> GSM872265 1 0.000 0.973 1.000 0.000
#> GSM872266 1 0.000 0.973 1.000 0.000
#> GSM872267 1 0.000 0.973 1.000 0.000
#> GSM872268 2 0.000 0.977 0.000 1.000
#> GSM872269 1 0.000 0.973 1.000 0.000
#> GSM872270 2 0.295 0.942 0.052 0.948
#> GSM872271 1 0.000 0.973 1.000 0.000
#> GSM872272 1 0.000 0.973 1.000 0.000
#> GSM872273 1 0.163 0.974 0.976 0.024
#> GSM872274 1 0.000 0.973 1.000 0.000
#> GSM872275 1 0.163 0.974 0.976 0.024
#> GSM872276 1 0.000 0.973 1.000 0.000
#> GSM872277 1 0.163 0.974 0.976 0.024
#> GSM872278 1 0.163 0.974 0.976 0.024
#> GSM872279 1 0.163 0.974 0.976 0.024
#> GSM872280 1 0.163 0.974 0.976 0.024
#> GSM872281 1 0.000 0.973 1.000 0.000
#> GSM872282 1 0.795 0.708 0.760 0.240
#> GSM872283 1 0.000 0.973 1.000 0.000
#> GSM872284 1 0.000 0.973 1.000 0.000
#> GSM872285 1 0.163 0.974 0.976 0.024
#> GSM872286 1 0.141 0.974 0.980 0.020
#> GSM872287 2 0.000 0.977 0.000 1.000
#> GSM872288 1 0.163 0.974 0.976 0.024
#> GSM872289 1 0.184 0.972 0.972 0.028
#> GSM872290 1 0.163 0.974 0.976 0.024
#> GSM872291 1 0.163 0.974 0.976 0.024
#> GSM872292 1 0.000 0.973 1.000 0.000
#> GSM872293 1 0.163 0.974 0.976 0.024
#> GSM872294 1 0.000 0.973 1.000 0.000
#> GSM872295 1 0.000 0.973 1.000 0.000
#> GSM872296 1 0.000 0.973 1.000 0.000
#> GSM872297 1 0.163 0.974 0.976 0.024
#> GSM872298 1 0.163 0.974 0.976 0.024
#> GSM872299 1 0.163 0.974 0.976 0.024
#> GSM872300 1 0.141 0.974 0.980 0.020
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.975 0.000 0.000 1.000
#> GSM872245 1 0.3752 0.851 0.856 0.144 0.000
#> GSM872246 3 0.0000 0.975 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.975 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.878 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.975 0.000 0.000 1.000
#> GSM872250 1 0.3752 0.851 0.856 0.144 0.000
#> GSM872251 3 0.0000 0.975 0.000 0.000 1.000
#> GSM872252 1 0.3752 0.851 0.856 0.144 0.000
#> GSM872253 1 0.5098 0.708 0.752 0.000 0.248
#> GSM872254 2 0.0000 0.878 0.000 1.000 0.000
#> GSM872255 1 0.4288 0.848 0.872 0.068 0.060
#> GSM872256 1 0.3482 0.853 0.872 0.128 0.000
#> GSM872257 2 0.0000 0.878 0.000 1.000 0.000
#> GSM872258 3 0.0000 0.975 0.000 0.000 1.000
#> GSM872259 1 0.3752 0.851 0.856 0.144 0.000
#> GSM872260 1 0.3851 0.852 0.860 0.136 0.004
#> GSM872261 1 0.3752 0.851 0.856 0.144 0.000
#> GSM872262 1 0.0000 0.843 1.000 0.000 0.000
#> GSM872263 3 0.0000 0.975 0.000 0.000 1.000
#> GSM872264 1 0.4346 0.721 0.816 0.000 0.184
#> GSM872265 1 0.2959 0.794 0.900 0.000 0.100
#> GSM872266 2 0.0000 0.878 0.000 1.000 0.000
#> GSM872267 2 0.0237 0.878 0.004 0.996 0.000
#> GSM872268 3 0.0000 0.975 0.000 0.000 1.000
#> GSM872269 2 0.5968 0.267 0.364 0.636 0.000
#> GSM872270 3 0.0000 0.975 0.000 0.000 1.000
#> GSM872271 1 0.5397 0.515 0.720 0.280 0.000
#> GSM872272 1 0.6095 0.217 0.608 0.392 0.000
#> GSM872273 1 0.0000 0.843 1.000 0.000 0.000
#> GSM872274 2 0.3752 0.805 0.144 0.856 0.000
#> GSM872275 1 0.5058 0.697 0.756 0.000 0.244
#> GSM872276 1 0.0000 0.843 1.000 0.000 0.000
#> GSM872277 1 0.0000 0.843 1.000 0.000 0.000
#> GSM872278 1 0.5058 0.689 0.756 0.000 0.244
#> GSM872279 1 0.3752 0.851 0.856 0.144 0.000
#> GSM872280 1 0.3686 0.815 0.860 0.000 0.140
#> GSM872281 1 0.3752 0.759 0.856 0.000 0.144
#> GSM872282 3 0.0000 0.975 0.000 0.000 1.000
#> GSM872283 1 0.0000 0.843 1.000 0.000 0.000
#> GSM872284 1 0.1163 0.835 0.972 0.000 0.028
#> GSM872285 1 0.6095 0.506 0.608 0.000 0.392
#> GSM872286 1 0.3752 0.851 0.856 0.144 0.000
#> GSM872287 3 0.0000 0.975 0.000 0.000 1.000
#> GSM872288 1 0.3752 0.851 0.856 0.144 0.000
#> GSM872289 3 0.4452 0.698 0.192 0.000 0.808
#> GSM872290 1 0.3752 0.851 0.856 0.144 0.000
#> GSM872291 1 0.2711 0.854 0.912 0.088 0.000
#> GSM872292 2 0.3752 0.805 0.144 0.856 0.000
#> GSM872293 1 0.3752 0.851 0.856 0.144 0.000
#> GSM872294 1 0.0000 0.843 1.000 0.000 0.000
#> GSM872295 2 0.0000 0.878 0.000 1.000 0.000
#> GSM872296 2 0.3752 0.805 0.144 0.856 0.000
#> GSM872297 1 0.3752 0.851 0.856 0.144 0.000
#> GSM872298 1 0.0000 0.843 1.000 0.000 0.000
#> GSM872299 1 0.3752 0.851 0.856 0.144 0.000
#> GSM872300 1 0.0000 0.843 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM872245 1 0.1209 0.750 0.964 0.032 0.000 0.004
#> GSM872246 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM872247 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM872248 2 0.3801 0.813 0.220 0.780 0.000 0.000
#> GSM872249 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM872250 1 0.1022 0.750 0.968 0.032 0.000 0.000
#> GSM872251 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM872252 1 0.4199 0.730 0.804 0.032 0.000 0.164
#> GSM872253 3 0.3860 0.847 0.012 0.032 0.852 0.104
#> GSM872254 1 0.3311 0.569 0.828 0.172 0.000 0.000
#> GSM872255 4 0.0188 0.906 0.004 0.000 0.000 0.996
#> GSM872256 4 0.4277 0.537 0.280 0.000 0.000 0.720
#> GSM872257 2 0.1792 0.889 0.068 0.932 0.000 0.000
#> GSM872258 3 0.0336 0.940 0.000 0.000 0.992 0.008
#> GSM872259 1 0.4843 0.462 0.604 0.000 0.000 0.396
#> GSM872260 4 0.4250 0.544 0.276 0.000 0.000 0.724
#> GSM872261 1 0.1209 0.751 0.964 0.032 0.000 0.004
#> GSM872262 4 0.0000 0.907 0.000 0.000 0.000 1.000
#> GSM872263 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM872264 4 0.4782 0.714 0.000 0.068 0.152 0.780
#> GSM872265 4 0.1837 0.881 0.000 0.028 0.028 0.944
#> GSM872266 2 0.3907 0.802 0.232 0.768 0.000 0.000
#> GSM872267 2 0.1557 0.892 0.056 0.944 0.000 0.000
#> GSM872268 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM872269 1 0.1022 0.750 0.968 0.032 0.000 0.000
#> GSM872270 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM872271 2 0.1716 0.857 0.000 0.936 0.000 0.064
#> GSM872272 2 0.0817 0.886 0.000 0.976 0.000 0.024
#> GSM872273 4 0.0336 0.905 0.000 0.008 0.000 0.992
#> GSM872274 2 0.0000 0.896 0.000 1.000 0.000 0.000
#> GSM872275 3 0.2982 0.880 0.004 0.032 0.896 0.068
#> GSM872276 4 0.0000 0.907 0.000 0.000 0.000 1.000
#> GSM872277 4 0.0336 0.905 0.000 0.008 0.000 0.992
#> GSM872278 3 0.5346 0.639 0.004 0.032 0.692 0.272
#> GSM872279 1 0.4830 0.469 0.608 0.000 0.000 0.392
#> GSM872280 4 0.1004 0.893 0.004 0.000 0.024 0.972
#> GSM872281 4 0.0000 0.907 0.000 0.000 0.000 1.000
#> GSM872282 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM872283 4 0.0817 0.898 0.000 0.024 0.000 0.976
#> GSM872284 4 0.0000 0.907 0.000 0.000 0.000 1.000
#> GSM872285 3 0.4053 0.729 0.004 0.000 0.768 0.228
#> GSM872286 1 0.1022 0.750 0.968 0.032 0.000 0.000
#> GSM872287 3 0.0000 0.943 0.000 0.000 1.000 0.000
#> GSM872288 1 0.3749 0.741 0.840 0.032 0.000 0.128
#> GSM872289 3 0.0592 0.936 0.000 0.000 0.984 0.016
#> GSM872290 1 0.4843 0.462 0.604 0.000 0.000 0.396
#> GSM872291 4 0.0000 0.907 0.000 0.000 0.000 1.000
#> GSM872292 2 0.0000 0.896 0.000 1.000 0.000 0.000
#> GSM872293 1 0.4843 0.462 0.604 0.000 0.000 0.396
#> GSM872294 4 0.2868 0.803 0.000 0.136 0.000 0.864
#> GSM872295 2 0.3907 0.803 0.232 0.768 0.000 0.000
#> GSM872296 2 0.0000 0.896 0.000 1.000 0.000 0.000
#> GSM872297 4 0.4072 0.618 0.252 0.000 0.000 0.748
#> GSM872298 4 0.0188 0.906 0.004 0.000 0.000 0.996
#> GSM872299 1 0.1209 0.750 0.964 0.032 0.000 0.004
#> GSM872300 4 0.0000 0.907 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.0162 0.9452 0.000 0.000 0.996 0.000 0.004
#> GSM872245 2 0.6715 0.0987 0.288 0.424 0.000 0.000 0.288
#> GSM872246 3 0.0162 0.9460 0.000 0.004 0.996 0.000 0.000
#> GSM872247 3 0.0000 0.9460 0.000 0.000 1.000 0.000 0.000
#> GSM872248 5 0.0510 0.4151 0.000 0.016 0.000 0.000 0.984
#> GSM872249 3 0.0162 0.9460 0.000 0.004 0.996 0.000 0.000
#> GSM872250 5 0.6274 -0.0610 0.148 0.424 0.000 0.000 0.428
#> GSM872251 3 0.0898 0.9426 0.008 0.020 0.972 0.000 0.000
#> GSM872252 2 0.6707 0.1069 0.308 0.424 0.000 0.000 0.268
#> GSM872253 3 0.1492 0.9350 0.008 0.040 0.948 0.000 0.004
#> GSM872254 5 0.5071 0.0920 0.036 0.424 0.000 0.000 0.540
#> GSM872255 4 0.3999 0.7212 0.344 0.000 0.000 0.656 0.000
#> GSM872256 1 0.1082 0.9202 0.964 0.000 0.000 0.028 0.008
#> GSM872257 5 0.3932 0.1753 0.000 0.328 0.000 0.000 0.672
#> GSM872258 3 0.1331 0.9366 0.008 0.040 0.952 0.000 0.000
#> GSM872259 1 0.0290 0.9301 0.992 0.000 0.000 0.000 0.008
#> GSM872260 1 0.3455 0.6129 0.784 0.000 0.000 0.208 0.008
#> GSM872261 2 0.6575 -0.0119 0.208 0.424 0.000 0.000 0.368
#> GSM872262 4 0.3966 0.7268 0.336 0.000 0.000 0.664 0.000
#> GSM872263 3 0.0162 0.9460 0.000 0.004 0.996 0.000 0.000
#> GSM872264 4 0.2249 0.6286 0.000 0.096 0.000 0.896 0.008
#> GSM872265 4 0.0992 0.6771 0.000 0.024 0.000 0.968 0.008
#> GSM872266 5 0.0510 0.4194 0.000 0.016 0.000 0.000 0.984
#> GSM872267 5 0.4310 0.1141 0.004 0.392 0.000 0.000 0.604
#> GSM872268 3 0.0000 0.9460 0.000 0.000 1.000 0.000 0.000
#> GSM872269 5 0.6219 -0.0466 0.140 0.424 0.000 0.000 0.436
#> GSM872270 3 0.0000 0.9460 0.000 0.000 1.000 0.000 0.000
#> GSM872271 2 0.6068 0.0183 0.000 0.452 0.000 0.428 0.120
#> GSM872272 2 0.5988 0.0134 0.000 0.516 0.000 0.364 0.120
#> GSM872273 4 0.3983 0.7228 0.340 0.000 0.000 0.660 0.000
#> GSM872274 2 0.4449 -0.1635 0.000 0.512 0.000 0.004 0.484
#> GSM872275 3 0.1960 0.9287 0.008 0.032 0.936 0.016 0.008
#> GSM872276 4 0.3966 0.7268 0.336 0.000 0.000 0.664 0.000
#> GSM872277 4 0.3966 0.7268 0.336 0.000 0.000 0.664 0.000
#> GSM872278 3 0.5384 0.1417 0.008 0.024 0.528 0.432 0.008
#> GSM872279 1 0.0290 0.9301 0.992 0.000 0.000 0.000 0.008
#> GSM872280 4 0.5499 0.6593 0.232 0.004 0.112 0.652 0.000
#> GSM872281 4 0.0510 0.6971 0.016 0.000 0.000 0.984 0.000
#> GSM872282 3 0.0609 0.9371 0.000 0.000 0.980 0.000 0.020
#> GSM872283 4 0.0693 0.6827 0.000 0.012 0.000 0.980 0.008
#> GSM872284 4 0.0404 0.6958 0.012 0.000 0.000 0.988 0.000
#> GSM872285 3 0.2201 0.9126 0.008 0.032 0.920 0.040 0.000
#> GSM872286 2 0.6681 0.0628 0.248 0.424 0.000 0.000 0.328
#> GSM872287 3 0.0000 0.9460 0.000 0.000 1.000 0.000 0.000
#> GSM872288 2 0.6703 0.0822 0.264 0.424 0.000 0.000 0.312
#> GSM872289 3 0.1412 0.9361 0.008 0.036 0.952 0.000 0.004
#> GSM872290 1 0.0290 0.9301 0.992 0.000 0.000 0.000 0.008
#> GSM872291 4 0.3983 0.7232 0.340 0.000 0.000 0.660 0.000
#> GSM872292 2 0.4304 -0.1653 0.000 0.516 0.000 0.000 0.484
#> GSM872293 1 0.0290 0.9301 0.992 0.000 0.000 0.000 0.008
#> GSM872294 4 0.2304 0.6252 0.000 0.100 0.000 0.892 0.008
#> GSM872295 5 0.0162 0.4214 0.000 0.004 0.000 0.000 0.996
#> GSM872296 2 0.4440 -0.1544 0.000 0.528 0.000 0.004 0.468
#> GSM872297 1 0.1408 0.9039 0.948 0.000 0.000 0.044 0.008
#> GSM872298 4 0.3796 0.7319 0.300 0.000 0.000 0.700 0.000
#> GSM872299 2 0.6665 0.1067 0.336 0.424 0.000 0.000 0.240
#> GSM872300 4 0.3966 0.7268 0.336 0.000 0.000 0.664 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.3672 0.68071 0.000 0.000 0.688 0.000 0.008 0.304
#> GSM872245 5 0.5258 0.27344 0.384 0.004 0.000 0.000 0.524 0.088
#> GSM872246 3 0.3672 0.65845 0.000 0.000 0.632 0.000 0.000 0.368
#> GSM872247 3 0.3578 0.68487 0.000 0.000 0.660 0.000 0.000 0.340
#> GSM872248 6 0.4570 -0.53316 0.000 0.436 0.000 0.000 0.036 0.528
#> GSM872249 3 0.3446 0.68464 0.000 0.000 0.692 0.000 0.000 0.308
#> GSM872250 5 0.4926 0.69660 0.068 0.000 0.000 0.000 0.540 0.392
#> GSM872251 6 0.5575 0.42376 0.000 0.000 0.140 0.000 0.400 0.460
#> GSM872252 5 0.6034 0.51521 0.308 0.000 0.000 0.000 0.420 0.272
#> GSM872253 6 0.5360 0.44896 0.000 0.000 0.108 0.000 0.436 0.456
#> GSM872254 5 0.4335 0.62611 0.020 0.000 0.000 0.000 0.508 0.472
#> GSM872255 3 0.8154 -0.51640 0.156 0.000 0.304 0.288 0.216 0.036
#> GSM872256 1 0.3168 0.63092 0.804 0.000 0.172 0.024 0.000 0.000
#> GSM872257 2 0.3984 0.57751 0.000 0.596 0.000 0.000 0.008 0.396
#> GSM872258 6 0.5475 0.44689 0.000 0.000 0.124 0.000 0.416 0.460
#> GSM872259 1 0.0000 0.85752 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872260 3 0.8255 -0.47356 0.188 0.000 0.296 0.236 0.244 0.036
#> GSM872261 5 0.4917 0.70304 0.076 0.000 0.000 0.000 0.576 0.348
#> GSM872262 4 0.5859 0.61497 0.156 0.000 0.304 0.528 0.004 0.008
#> GSM872263 3 0.3578 0.68487 0.000 0.000 0.660 0.000 0.000 0.340
#> GSM872264 4 0.3122 0.35590 0.000 0.176 0.000 0.804 0.020 0.000
#> GSM872265 4 0.1003 0.50807 0.000 0.016 0.000 0.964 0.020 0.000
#> GSM872266 6 0.5799 -0.47446 0.016 0.380 0.000 0.004 0.104 0.496
#> GSM872267 2 0.3833 0.63220 0.000 0.648 0.000 0.000 0.008 0.344
#> GSM872268 3 0.3620 0.67581 0.000 0.000 0.648 0.000 0.000 0.352
#> GSM872269 5 0.4926 0.69660 0.068 0.000 0.000 0.000 0.540 0.392
#> GSM872270 3 0.3446 0.68349 0.000 0.000 0.692 0.000 0.000 0.308
#> GSM872271 4 0.4705 -0.13900 0.000 0.440 0.000 0.520 0.036 0.004
#> GSM872272 4 0.4719 -0.17699 0.000 0.460 0.000 0.500 0.036 0.004
#> GSM872273 4 0.6118 0.39544 0.336 0.000 0.304 0.360 0.000 0.000
#> GSM872274 2 0.0000 0.77943 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872275 6 0.5417 0.45077 0.000 0.000 0.116 0.000 0.420 0.464
#> GSM872276 4 0.5859 0.61497 0.156 0.000 0.304 0.528 0.004 0.008
#> GSM872277 4 0.5625 0.60381 0.176 0.000 0.304 0.520 0.000 0.000
#> GSM872278 6 0.5739 0.43597 0.000 0.000 0.084 0.028 0.424 0.464
#> GSM872279 1 0.0000 0.85752 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872280 5 0.7309 -0.26551 0.024 0.000 0.332 0.088 0.416 0.140
#> GSM872281 4 0.3946 0.64034 0.004 0.000 0.304 0.680 0.004 0.008
#> GSM872282 3 0.3565 0.68146 0.000 0.000 0.692 0.000 0.004 0.304
#> GSM872283 4 0.0000 0.52981 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872284 4 0.3946 0.64034 0.004 0.000 0.304 0.680 0.004 0.008
#> GSM872285 6 0.5414 0.45124 0.000 0.000 0.116 0.000 0.416 0.468
#> GSM872286 5 0.5390 0.69433 0.128 0.000 0.000 0.000 0.532 0.340
#> GSM872287 3 0.3578 0.68487 0.000 0.000 0.660 0.000 0.000 0.340
#> GSM872288 5 0.4913 0.64956 0.112 0.000 0.000 0.000 0.636 0.252
#> GSM872289 6 0.5475 0.44689 0.000 0.000 0.124 0.000 0.416 0.460
#> GSM872290 1 0.0000 0.85752 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872291 4 0.6520 0.59777 0.156 0.000 0.304 0.492 0.040 0.008
#> GSM872292 2 0.0146 0.77930 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM872293 1 0.0000 0.85752 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872294 4 0.2728 0.42689 0.000 0.100 0.000 0.864 0.032 0.004
#> GSM872295 6 0.5122 -0.51075 0.016 0.420 0.000 0.000 0.048 0.516
#> GSM872296 2 0.1075 0.75276 0.000 0.952 0.000 0.048 0.000 0.000
#> GSM872297 1 0.0146 0.85466 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM872298 4 0.5881 0.63014 0.076 0.000 0.304 0.572 0.016 0.032
#> GSM872299 1 0.4938 -0.00603 0.568 0.000 0.000 0.000 0.356 0.076
#> GSM872300 4 0.5859 0.61497 0.156 0.000 0.304 0.528 0.004 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 time(p) individual(p) k
#> MAD:mclust 56 0.329 0.011870 2
#> MAD:mclust 55 0.787 0.000421 3
#> MAD:mclust 53 0.443 0.001565 4
#> MAD:mclust 37 0.269 0.036734 5
#> MAD:mclust 37 0.607 0.016924 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 29485 rows and 57 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 0.419 0.793 0.877 0.4884 0.499 0.499
#> 3 3 0.862 0.911 0.961 0.3689 0.705 0.476
#> 4 4 0.678 0.737 0.848 0.1097 0.897 0.705
#> 5 5 0.658 0.653 0.776 0.0704 0.911 0.684
#> 6 6 0.647 0.559 0.704 0.0435 0.931 0.700
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
#> GSM872244 1 0.0000 0.787 1.000 0.000
#> GSM872245 2 0.0000 0.872 0.000 1.000
#> GSM872246 1 0.6247 0.844 0.844 0.156
#> GSM872247 1 0.4161 0.833 0.916 0.084
#> GSM872248 2 0.6531 0.841 0.168 0.832
#> GSM872249 1 0.0000 0.787 1.000 0.000
#> GSM872250 2 0.4431 0.865 0.092 0.908
#> GSM872251 1 0.6148 0.845 0.848 0.152
#> GSM872252 2 0.0000 0.872 0.000 1.000
#> GSM872253 1 0.6343 0.821 0.840 0.160
#> GSM872254 2 0.6531 0.841 0.168 0.832
#> GSM872255 1 0.9963 0.514 0.536 0.464
#> GSM872256 2 0.0000 0.872 0.000 1.000
#> GSM872257 2 0.6531 0.841 0.168 0.832
#> GSM872258 1 0.6531 0.840 0.832 0.168
#> GSM872259 2 0.0000 0.872 0.000 1.000
#> GSM872260 2 0.5842 0.707 0.140 0.860
#> GSM872261 2 0.4562 0.864 0.096 0.904
#> GSM872262 1 0.9922 0.547 0.552 0.448
#> GSM872263 1 0.3733 0.827 0.928 0.072
#> GSM872264 1 0.3584 0.823 0.932 0.068
#> GSM872265 2 0.8499 0.416 0.276 0.724
#> GSM872266 2 0.6531 0.841 0.168 0.832
#> GSM872267 2 0.6531 0.841 0.168 0.832
#> GSM872268 1 0.6247 0.844 0.844 0.156
#> GSM872269 2 0.4431 0.865 0.092 0.908
#> GSM872270 1 0.0000 0.787 1.000 0.000
#> GSM872271 2 0.6801 0.838 0.180 0.820
#> GSM872272 2 0.6801 0.838 0.180 0.820
#> GSM872273 2 0.0000 0.872 0.000 1.000
#> GSM872274 2 0.6531 0.841 0.168 0.832
#> GSM872275 1 0.0672 0.793 0.992 0.008
#> GSM872276 1 0.9850 0.584 0.572 0.428
#> GSM872277 2 0.2043 0.850 0.032 0.968
#> GSM872278 1 0.5294 0.841 0.880 0.120
#> GSM872279 2 0.0000 0.872 0.000 1.000
#> GSM872280 1 0.6531 0.840 0.832 0.168
#> GSM872281 1 0.6712 0.838 0.824 0.176
#> GSM872282 1 0.0000 0.787 1.000 0.000
#> GSM872283 2 0.0672 0.868 0.008 0.992
#> GSM872284 1 0.9833 0.590 0.576 0.424
#> GSM872285 1 0.6531 0.840 0.832 0.168
#> GSM872286 2 0.0000 0.872 0.000 1.000
#> GSM872287 1 0.6048 0.845 0.852 0.148
#> GSM872288 2 0.0000 0.872 0.000 1.000
#> GSM872289 1 0.6343 0.843 0.840 0.160
#> GSM872290 2 0.0000 0.872 0.000 1.000
#> GSM872291 2 0.1414 0.859 0.020 0.980
#> GSM872292 2 0.9896 0.450 0.440 0.560
#> GSM872293 2 0.0000 0.872 0.000 1.000
#> GSM872294 2 0.6343 0.845 0.160 0.840
#> GSM872295 2 0.8955 0.688 0.312 0.688
#> GSM872296 2 0.7674 0.815 0.224 0.776
#> GSM872297 2 0.0000 0.872 0.000 1.000
#> GSM872298 1 0.9881 0.570 0.564 0.436
#> GSM872299 2 0.0000 0.872 0.000 1.000
#> GSM872300 1 1.0000 0.434 0.504 0.496
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0237 0.965 0.000 0.004 0.996
#> GSM872245 1 0.6126 0.298 0.600 0.400 0.000
#> GSM872246 3 0.0000 0.967 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.967 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.970 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.967 0.000 0.000 1.000
#> GSM872250 2 0.3116 0.888 0.108 0.892 0.000
#> GSM872251 3 0.0000 0.967 0.000 0.000 1.000
#> GSM872252 1 0.0000 0.937 1.000 0.000 0.000
#> GSM872253 3 0.4575 0.794 0.160 0.012 0.828
#> GSM872254 2 0.0000 0.970 0.000 1.000 0.000
#> GSM872255 1 0.0237 0.935 0.996 0.000 0.004
#> GSM872256 1 0.0000 0.937 1.000 0.000 0.000
#> GSM872257 2 0.0000 0.970 0.000 1.000 0.000
#> GSM872258 3 0.0000 0.967 0.000 0.000 1.000
#> GSM872259 1 0.0000 0.937 1.000 0.000 0.000
#> GSM872260 1 0.0000 0.937 1.000 0.000 0.000
#> GSM872261 2 0.2959 0.896 0.100 0.900 0.000
#> GSM872262 1 0.0237 0.935 0.996 0.000 0.004
#> GSM872263 3 0.0000 0.967 0.000 0.000 1.000
#> GSM872264 3 0.0000 0.967 0.000 0.000 1.000
#> GSM872265 1 0.5733 0.530 0.676 0.000 0.324
#> GSM872266 2 0.0000 0.970 0.000 1.000 0.000
#> GSM872267 2 0.0237 0.968 0.004 0.996 0.000
#> GSM872268 3 0.0000 0.967 0.000 0.000 1.000
#> GSM872269 2 0.4121 0.815 0.168 0.832 0.000
#> GSM872270 3 0.0000 0.967 0.000 0.000 1.000
#> GSM872271 2 0.0000 0.970 0.000 1.000 0.000
#> GSM872272 2 0.0000 0.970 0.000 1.000 0.000
#> GSM872273 1 0.0000 0.937 1.000 0.000 0.000
#> GSM872274 2 0.0000 0.970 0.000 1.000 0.000
#> GSM872275 3 0.0424 0.963 0.000 0.008 0.992
#> GSM872276 1 0.0237 0.935 0.996 0.000 0.004
#> GSM872277 1 0.0000 0.937 1.000 0.000 0.000
#> GSM872278 3 0.0000 0.967 0.000 0.000 1.000
#> GSM872279 1 0.0000 0.937 1.000 0.000 0.000
#> GSM872280 3 0.0747 0.956 0.016 0.000 0.984
#> GSM872281 3 0.5254 0.621 0.264 0.000 0.736
#> GSM872282 3 0.0237 0.965 0.000 0.004 0.996
#> GSM872283 1 0.0237 0.935 0.996 0.000 0.004
#> GSM872284 1 0.5431 0.609 0.716 0.000 0.284
#> GSM872285 3 0.0000 0.967 0.000 0.000 1.000
#> GSM872286 1 0.3879 0.786 0.848 0.152 0.000
#> GSM872287 3 0.0000 0.967 0.000 0.000 1.000
#> GSM872288 1 0.0000 0.937 1.000 0.000 0.000
#> GSM872289 3 0.2165 0.913 0.064 0.000 0.936
#> GSM872290 1 0.0000 0.937 1.000 0.000 0.000
#> GSM872291 1 0.0000 0.937 1.000 0.000 0.000
#> GSM872292 2 0.0000 0.970 0.000 1.000 0.000
#> GSM872293 1 0.0000 0.937 1.000 0.000 0.000
#> GSM872294 2 0.1031 0.956 0.024 0.976 0.000
#> GSM872295 2 0.0000 0.970 0.000 1.000 0.000
#> GSM872296 2 0.0000 0.970 0.000 1.000 0.000
#> GSM872297 1 0.0000 0.937 1.000 0.000 0.000
#> GSM872298 1 0.2796 0.864 0.908 0.000 0.092
#> GSM872299 1 0.0592 0.929 0.988 0.012 0.000
#> GSM872300 1 0.0237 0.935 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.1398 0.831 0.000 0.040 0.956 0.004
#> GSM872245 1 0.4776 0.459 0.624 0.376 0.000 0.000
#> GSM872246 3 0.0188 0.846 0.000 0.000 0.996 0.004
#> GSM872247 3 0.3311 0.835 0.000 0.000 0.828 0.172
#> GSM872248 2 0.0188 0.795 0.000 0.996 0.000 0.004
#> GSM872249 3 0.0336 0.845 0.000 0.008 0.992 0.000
#> GSM872250 2 0.6736 0.484 0.092 0.588 0.312 0.008
#> GSM872251 3 0.0000 0.846 0.000 0.000 1.000 0.000
#> GSM872252 1 0.3102 0.799 0.872 0.116 0.004 0.008
#> GSM872253 3 0.3029 0.791 0.028 0.068 0.896 0.008
#> GSM872254 2 0.1489 0.777 0.004 0.952 0.044 0.000
#> GSM872255 1 0.0188 0.867 0.996 0.000 0.004 0.000
#> GSM872256 1 0.0592 0.870 0.984 0.000 0.000 0.016
#> GSM872257 2 0.2216 0.779 0.000 0.908 0.000 0.092
#> GSM872258 3 0.0804 0.840 0.012 0.000 0.980 0.008
#> GSM872259 1 0.0592 0.870 0.984 0.000 0.000 0.016
#> GSM872260 1 0.0336 0.865 0.992 0.000 0.000 0.008
#> GSM872261 2 0.2530 0.711 0.112 0.888 0.000 0.000
#> GSM872262 1 0.5344 0.467 0.668 0.000 0.032 0.300
#> GSM872263 3 0.0336 0.845 0.000 0.008 0.992 0.000
#> GSM872264 4 0.2161 0.625 0.048 0.004 0.016 0.932
#> GSM872265 4 0.2334 0.644 0.088 0.004 0.000 0.908
#> GSM872266 2 0.0592 0.795 0.000 0.984 0.000 0.016
#> GSM872267 2 0.2081 0.783 0.000 0.916 0.000 0.084
#> GSM872268 3 0.2281 0.847 0.000 0.000 0.904 0.096
#> GSM872269 2 0.6743 0.491 0.100 0.600 0.292 0.008
#> GSM872270 3 0.4250 0.791 0.000 0.000 0.724 0.276
#> GSM872271 4 0.4720 0.536 0.004 0.324 0.000 0.672
#> GSM872272 4 0.4720 0.536 0.004 0.324 0.000 0.672
#> GSM872273 1 0.1389 0.859 0.952 0.000 0.000 0.048
#> GSM872274 2 0.3266 0.716 0.000 0.832 0.000 0.168
#> GSM872275 3 0.5334 0.796 0.000 0.088 0.740 0.172
#> GSM872276 1 0.3245 0.797 0.872 0.000 0.028 0.100
#> GSM872277 1 0.1211 0.862 0.960 0.000 0.000 0.040
#> GSM872278 3 0.4522 0.756 0.000 0.000 0.680 0.320
#> GSM872279 1 0.1211 0.853 0.960 0.040 0.000 0.000
#> GSM872280 3 0.6316 0.671 0.184 0.000 0.660 0.156
#> GSM872281 4 0.4562 0.606 0.152 0.000 0.056 0.792
#> GSM872282 3 0.5173 0.758 0.000 0.020 0.660 0.320
#> GSM872283 4 0.5050 0.306 0.408 0.004 0.000 0.588
#> GSM872284 4 0.4868 0.561 0.256 0.000 0.024 0.720
#> GSM872285 3 0.4295 0.808 0.008 0.000 0.752 0.240
#> GSM872286 1 0.4642 0.749 0.808 0.116 0.068 0.008
#> GSM872287 3 0.4008 0.809 0.000 0.000 0.756 0.244
#> GSM872288 1 0.5646 0.674 0.740 0.116 0.136 0.008
#> GSM872289 3 0.1617 0.831 0.024 0.012 0.956 0.008
#> GSM872290 1 0.0592 0.870 0.984 0.000 0.000 0.016
#> GSM872291 1 0.0592 0.870 0.984 0.000 0.000 0.016
#> GSM872292 2 0.3074 0.733 0.000 0.848 0.000 0.152
#> GSM872293 1 0.0592 0.870 0.984 0.000 0.000 0.016
#> GSM872294 4 0.4917 0.520 0.008 0.336 0.000 0.656
#> GSM872295 2 0.1867 0.789 0.000 0.928 0.000 0.072
#> GSM872296 4 0.4817 0.414 0.000 0.388 0.000 0.612
#> GSM872297 1 0.0707 0.869 0.980 0.000 0.000 0.020
#> GSM872298 1 0.5328 0.547 0.704 0.000 0.048 0.248
#> GSM872299 1 0.2918 0.801 0.876 0.116 0.000 0.008
#> GSM872300 1 0.2174 0.846 0.928 0.000 0.020 0.052
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.4546 0.7225 0.000 0.008 0.688 0.284 0.020
#> GSM872245 5 0.1831 0.6329 0.076 0.004 0.000 0.000 0.920
#> GSM872246 3 0.2193 0.7891 0.000 0.000 0.900 0.092 0.008
#> GSM872247 3 0.0794 0.7893 0.000 0.000 0.972 0.028 0.000
#> GSM872248 5 0.3039 0.6643 0.000 0.152 0.000 0.012 0.836
#> GSM872249 3 0.3967 0.7378 0.000 0.000 0.724 0.264 0.012
#> GSM872250 5 0.6447 0.4549 0.016 0.012 0.100 0.312 0.560
#> GSM872251 3 0.3671 0.7503 0.000 0.000 0.756 0.236 0.008
#> GSM872252 1 0.2900 0.7768 0.876 0.012 0.000 0.092 0.020
#> GSM872253 4 0.8775 -0.2769 0.204 0.304 0.164 0.312 0.016
#> GSM872254 2 0.4865 0.6139 0.000 0.684 0.000 0.252 0.064
#> GSM872255 1 0.1617 0.8219 0.948 0.000 0.020 0.020 0.012
#> GSM872256 1 0.3085 0.8125 0.852 0.000 0.000 0.032 0.116
#> GSM872257 2 0.1965 0.7661 0.000 0.904 0.000 0.000 0.096
#> GSM872258 3 0.4571 0.7637 0.048 0.004 0.772 0.156 0.020
#> GSM872259 1 0.2516 0.8016 0.860 0.000 0.000 0.000 0.140
#> GSM872260 1 0.1825 0.8100 0.940 0.008 0.008 0.036 0.008
#> GSM872261 2 0.3778 0.7167 0.108 0.820 0.000 0.068 0.004
#> GSM872262 1 0.5723 0.3634 0.532 0.000 0.076 0.388 0.004
#> GSM872263 3 0.4358 0.7267 0.000 0.008 0.696 0.284 0.012
#> GSM872264 4 0.6285 0.4941 0.008 0.020 0.068 0.504 0.400
#> GSM872265 4 0.6251 0.5063 0.028 0.028 0.028 0.524 0.392
#> GSM872266 5 0.2329 0.6738 0.000 0.124 0.000 0.000 0.876
#> GSM872267 5 0.2536 0.6674 0.000 0.128 0.000 0.004 0.868
#> GSM872268 3 0.0880 0.7816 0.000 0.000 0.968 0.032 0.000
#> GSM872269 2 0.7273 0.4317 0.184 0.500 0.004 0.268 0.044
#> GSM872270 3 0.1522 0.7887 0.000 0.000 0.944 0.044 0.012
#> GSM872271 4 0.5237 0.0552 0.000 0.468 0.000 0.488 0.044
#> GSM872272 4 0.6077 0.4471 0.000 0.124 0.000 0.480 0.396
#> GSM872273 1 0.4482 0.7527 0.752 0.000 0.000 0.160 0.088
#> GSM872274 2 0.0566 0.7891 0.000 0.984 0.000 0.004 0.012
#> GSM872275 3 0.4307 0.7317 0.008 0.104 0.800 0.080 0.008
#> GSM872276 1 0.3441 0.7697 0.828 0.000 0.028 0.140 0.004
#> GSM872277 1 0.6271 0.5162 0.572 0.000 0.008 0.240 0.180
#> GSM872278 3 0.4994 0.6025 0.052 0.008 0.732 0.192 0.016
#> GSM872279 1 0.1836 0.8226 0.932 0.000 0.000 0.032 0.036
#> GSM872280 3 0.5271 0.2921 0.392 0.000 0.564 0.036 0.008
#> GSM872281 4 0.5203 0.3727 0.060 0.000 0.332 0.608 0.000
#> GSM872282 3 0.3126 0.7693 0.000 0.028 0.868 0.088 0.016
#> GSM872283 4 0.5925 0.4369 0.036 0.028 0.004 0.468 0.464
#> GSM872284 4 0.7077 0.4701 0.044 0.000 0.156 0.492 0.308
#> GSM872285 3 0.1991 0.7576 0.004 0.000 0.916 0.076 0.004
#> GSM872286 5 0.5211 0.6311 0.120 0.004 0.012 0.140 0.724
#> GSM872287 3 0.1341 0.7695 0.000 0.000 0.944 0.056 0.000
#> GSM872288 5 0.5149 0.6446 0.088 0.000 0.028 0.152 0.732
#> GSM872289 3 0.4567 0.6673 0.004 0.000 0.628 0.356 0.012
#> GSM872290 1 0.0771 0.8249 0.976 0.004 0.000 0.000 0.020
#> GSM872291 1 0.1490 0.8160 0.952 0.008 0.004 0.032 0.004
#> GSM872292 2 0.0404 0.7885 0.000 0.988 0.000 0.000 0.012
#> GSM872293 1 0.2017 0.8204 0.912 0.000 0.000 0.008 0.080
#> GSM872294 2 0.3566 0.6717 0.024 0.812 0.000 0.160 0.004
#> GSM872295 2 0.1018 0.7882 0.000 0.968 0.000 0.016 0.016
#> GSM872296 2 0.2843 0.6914 0.000 0.848 0.000 0.144 0.008
#> GSM872297 1 0.2997 0.7955 0.840 0.000 0.000 0.012 0.148
#> GSM872298 1 0.5225 0.5768 0.656 0.000 0.072 0.268 0.004
#> GSM872299 1 0.2845 0.7822 0.876 0.008 0.000 0.096 0.020
#> GSM872300 1 0.3878 0.7923 0.820 0.000 0.020 0.120 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.495 0.7217 0.000 0.020 0.684 0.000 0.100 0.196
#> GSM872245 5 0.714 0.2098 0.332 0.012 0.000 0.232 0.372 0.052
#> GSM872246 3 0.198 0.7834 0.000 0.000 0.912 0.004 0.016 0.068
#> GSM872247 3 0.151 0.7690 0.016 0.000 0.948 0.004 0.016 0.016
#> GSM872248 5 0.419 0.6985 0.000 0.068 0.000 0.140 0.768 0.024
#> GSM872249 3 0.347 0.7724 0.000 0.000 0.808 0.000 0.092 0.100
#> GSM872250 5 0.451 0.6105 0.008 0.024 0.044 0.008 0.756 0.160
#> GSM872251 3 0.361 0.7735 0.000 0.000 0.804 0.004 0.100 0.092
#> GSM872252 6 0.401 0.2946 0.344 0.000 0.000 0.016 0.000 0.640
#> GSM872253 6 0.549 0.5345 0.036 0.176 0.056 0.036 0.004 0.692
#> GSM872254 6 0.562 0.1272 0.000 0.388 0.000 0.000 0.148 0.464
#> GSM872255 1 0.251 0.6161 0.884 0.000 0.040 0.004 0.000 0.072
#> GSM872256 1 0.388 0.5039 0.728 0.000 0.000 0.004 0.240 0.028
#> GSM872257 2 0.310 0.6929 0.000 0.784 0.000 0.000 0.208 0.008
#> GSM872258 3 0.417 0.5887 0.016 0.000 0.628 0.000 0.004 0.352
#> GSM872259 1 0.453 0.5947 0.768 0.004 0.000 0.088 0.068 0.072
#> GSM872260 1 0.384 0.0403 0.552 0.000 0.000 0.000 0.000 0.448
#> GSM872261 6 0.597 0.4006 0.080 0.380 0.000 0.012 0.028 0.500
#> GSM872262 1 0.623 0.3200 0.584 0.000 0.096 0.224 0.004 0.092
#> GSM872263 3 0.432 0.7501 0.000 0.012 0.740 0.000 0.076 0.172
#> GSM872264 4 0.271 0.5871 0.004 0.008 0.012 0.872 0.100 0.004
#> GSM872265 4 0.210 0.6019 0.024 0.004 0.000 0.916 0.048 0.008
#> GSM872266 5 0.383 0.7011 0.000 0.048 0.004 0.156 0.784 0.008
#> GSM872267 5 0.411 0.6630 0.000 0.040 0.000 0.212 0.736 0.012
#> GSM872268 3 0.209 0.7553 0.036 0.000 0.920 0.008 0.008 0.028
#> GSM872269 6 0.580 0.5504 0.100 0.124 0.000 0.000 0.132 0.644
#> GSM872270 3 0.189 0.7771 0.000 0.004 0.928 0.008 0.024 0.036
#> GSM872271 4 0.369 0.5187 0.000 0.204 0.000 0.764 0.020 0.012
#> GSM872272 4 0.381 0.5588 0.000 0.088 0.000 0.800 0.096 0.016
#> GSM872273 1 0.295 0.6338 0.864 0.000 0.008 0.092 0.016 0.020
#> GSM872274 2 0.183 0.8525 0.000 0.928 0.000 0.036 0.028 0.008
#> GSM872275 3 0.710 0.5252 0.068 0.168 0.596 0.040 0.068 0.060
#> GSM872276 1 0.567 0.3656 0.608 0.000 0.028 0.260 0.008 0.096
#> GSM872277 1 0.506 0.4660 0.640 0.004 0.000 0.280 0.052 0.024
#> GSM872278 4 0.743 0.4417 0.036 0.052 0.268 0.484 0.020 0.140
#> GSM872279 1 0.267 0.5826 0.836 0.000 0.000 0.000 0.008 0.156
#> GSM872280 3 0.723 -0.0146 0.300 0.000 0.392 0.064 0.012 0.232
#> GSM872281 4 0.717 0.4867 0.124 0.000 0.260 0.496 0.036 0.084
#> GSM872282 3 0.473 0.7386 0.000 0.072 0.744 0.008 0.040 0.136
#> GSM872283 4 0.286 0.5646 0.028 0.000 0.000 0.860 0.100 0.012
#> GSM872284 4 0.602 0.5769 0.096 0.000 0.104 0.672 0.068 0.060
#> GSM872285 3 0.279 0.7293 0.056 0.000 0.884 0.012 0.016 0.032
#> GSM872286 5 0.424 0.6474 0.156 0.008 0.012 0.004 0.768 0.052
#> GSM872287 3 0.190 0.7545 0.032 0.000 0.928 0.008 0.004 0.028
#> GSM872288 5 0.582 0.6398 0.088 0.000 0.032 0.068 0.676 0.136
#> GSM872289 3 0.462 0.7292 0.000 0.008 0.696 0.000 0.084 0.212
#> GSM872290 1 0.412 0.3125 0.628 0.000 0.000 0.020 0.000 0.352
#> GSM872291 6 0.541 0.0216 0.408 0.000 0.000 0.116 0.000 0.476
#> GSM872292 2 0.122 0.8490 0.000 0.948 0.004 0.048 0.000 0.000
#> GSM872293 1 0.212 0.6269 0.904 0.000 0.000 0.000 0.036 0.060
#> GSM872294 2 0.386 0.7973 0.020 0.796 0.000 0.144 0.012 0.028
#> GSM872295 2 0.158 0.8200 0.000 0.936 0.000 0.004 0.048 0.012
#> GSM872296 2 0.270 0.8099 0.000 0.836 0.000 0.156 0.004 0.004
#> GSM872297 1 0.433 0.5977 0.772 0.004 0.000 0.128 0.052 0.044
#> GSM872298 4 0.734 0.0029 0.360 0.000 0.092 0.372 0.016 0.160
#> GSM872299 1 0.392 0.1539 0.580 0.000 0.000 0.000 0.004 0.416
#> GSM872300 1 0.305 0.6180 0.864 0.000 0.048 0.040 0.000 0.048
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 time(p) individual(p) k
#> MAD:NMF 54 0.648 1.36e-02 2
#> MAD:NMF 56 0.344 2.92e-02 3
#> MAD:NMF 51 0.167 8.84e-03 4
#> MAD:NMF 46 0.788 1.65e-04 5
#> MAD:NMF 42 0.558 6.54e-05 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 29485 rows and 57 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 0.846 0.960 0.979 0.3433 0.662 0.662
#> 3 3 0.693 0.877 0.936 0.6577 0.739 0.606
#> 4 4 0.690 0.834 0.884 0.2870 0.840 0.602
#> 5 5 0.736 0.832 0.899 0.0564 0.977 0.906
#> 6 6 0.748 0.827 0.880 0.0233 0.987 0.943
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
#> GSM872244 2 0.0000 0.963 0.000 1.000
#> GSM872245 1 0.0000 0.981 1.000 0.000
#> GSM872246 2 0.0000 0.963 0.000 1.000
#> GSM872247 2 0.0000 0.963 0.000 1.000
#> GSM872248 1 0.0000 0.981 1.000 0.000
#> GSM872249 2 0.0000 0.963 0.000 1.000
#> GSM872250 1 0.1633 0.969 0.976 0.024
#> GSM872251 2 0.5408 0.877 0.124 0.876
#> GSM872252 1 0.0376 0.979 0.996 0.004
#> GSM872253 1 0.4815 0.895 0.896 0.104
#> GSM872254 1 0.0000 0.981 1.000 0.000
#> GSM872255 1 0.0000 0.981 1.000 0.000
#> GSM872256 1 0.0000 0.981 1.000 0.000
#> GSM872257 1 0.0000 0.981 1.000 0.000
#> GSM872258 2 0.5629 0.869 0.132 0.868
#> GSM872259 1 0.0000 0.981 1.000 0.000
#> GSM872260 1 0.0000 0.981 1.000 0.000
#> GSM872261 1 0.0376 0.979 0.996 0.004
#> GSM872262 1 0.0000 0.981 1.000 0.000
#> GSM872263 2 0.0000 0.963 0.000 1.000
#> GSM872264 1 0.1633 0.969 0.976 0.024
#> GSM872265 1 0.0000 0.981 1.000 0.000
#> GSM872266 1 0.0376 0.979 0.996 0.004
#> GSM872267 1 0.0000 0.981 1.000 0.000
#> GSM872268 2 0.0000 0.963 0.000 1.000
#> GSM872269 1 0.0000 0.981 1.000 0.000
#> GSM872270 2 0.0000 0.963 0.000 1.000
#> GSM872271 1 0.0376 0.979 0.996 0.004
#> GSM872272 1 0.0376 0.979 0.996 0.004
#> GSM872273 1 0.0000 0.981 1.000 0.000
#> GSM872274 1 0.0000 0.981 1.000 0.000
#> GSM872275 1 0.4815 0.895 0.896 0.104
#> GSM872276 1 0.0000 0.981 1.000 0.000
#> GSM872277 1 0.0000 0.981 1.000 0.000
#> GSM872278 1 0.4815 0.895 0.896 0.104
#> GSM872279 1 0.0000 0.981 1.000 0.000
#> GSM872280 1 0.4815 0.895 0.896 0.104
#> GSM872281 1 0.1633 0.969 0.976 0.024
#> GSM872282 2 0.0000 0.963 0.000 1.000
#> GSM872283 1 0.0000 0.981 1.000 0.000
#> GSM872284 1 0.1633 0.969 0.976 0.024
#> GSM872285 1 0.7674 0.730 0.776 0.224
#> GSM872286 1 0.1633 0.969 0.976 0.024
#> GSM872287 2 0.0000 0.963 0.000 1.000
#> GSM872288 1 0.1633 0.969 0.976 0.024
#> GSM872289 2 0.5629 0.869 0.132 0.868
#> GSM872290 1 0.0000 0.981 1.000 0.000
#> GSM872291 1 0.0000 0.981 1.000 0.000
#> GSM872292 1 0.0000 0.981 1.000 0.000
#> GSM872293 1 0.0000 0.981 1.000 0.000
#> GSM872294 1 0.0000 0.981 1.000 0.000
#> GSM872295 1 0.0000 0.981 1.000 0.000
#> GSM872296 1 0.0000 0.981 1.000 0.000
#> GSM872297 1 0.0000 0.981 1.000 0.000
#> GSM872298 1 0.1633 0.969 0.976 0.024
#> GSM872299 1 0.0000 0.981 1.000 0.000
#> GSM872300 1 0.0000 0.981 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.000 0.947 0.000 0.000 1.000
#> GSM872245 1 0.000 0.959 1.000 0.000 0.000
#> GSM872246 3 0.000 0.947 0.000 0.000 1.000
#> GSM872247 3 0.000 0.947 0.000 0.000 1.000
#> GSM872248 2 0.440 0.780 0.188 0.812 0.000
#> GSM872249 3 0.000 0.947 0.000 0.000 1.000
#> GSM872250 1 0.318 0.911 0.912 0.064 0.024
#> GSM872251 3 0.341 0.833 0.124 0.000 0.876
#> GSM872252 1 0.165 0.937 0.960 0.036 0.004
#> GSM872253 1 0.304 0.890 0.896 0.000 0.104
#> GSM872254 2 0.196 0.781 0.056 0.944 0.000
#> GSM872255 1 0.000 0.959 1.000 0.000 0.000
#> GSM872256 1 0.000 0.959 1.000 0.000 0.000
#> GSM872257 2 0.000 0.751 0.000 1.000 0.000
#> GSM872258 3 0.355 0.824 0.132 0.000 0.868
#> GSM872259 1 0.000 0.959 1.000 0.000 0.000
#> GSM872260 1 0.000 0.959 1.000 0.000 0.000
#> GSM872261 1 0.250 0.909 0.928 0.068 0.004
#> GSM872262 1 0.000 0.959 1.000 0.000 0.000
#> GSM872263 3 0.000 0.947 0.000 0.000 1.000
#> GSM872264 1 0.103 0.949 0.976 0.000 0.024
#> GSM872265 1 0.000 0.959 1.000 0.000 0.000
#> GSM872266 2 0.647 0.444 0.444 0.552 0.004
#> GSM872267 2 0.440 0.780 0.188 0.812 0.000
#> GSM872268 3 0.000 0.947 0.000 0.000 1.000
#> GSM872269 2 0.406 0.788 0.164 0.836 0.000
#> GSM872270 3 0.000 0.947 0.000 0.000 1.000
#> GSM872271 2 0.647 0.444 0.444 0.552 0.004
#> GSM872272 2 0.647 0.444 0.444 0.552 0.004
#> GSM872273 1 0.000 0.959 1.000 0.000 0.000
#> GSM872274 2 0.000 0.751 0.000 1.000 0.000
#> GSM872275 1 0.304 0.890 0.896 0.000 0.104
#> GSM872276 1 0.000 0.959 1.000 0.000 0.000
#> GSM872277 1 0.000 0.959 1.000 0.000 0.000
#> GSM872278 1 0.304 0.890 0.896 0.000 0.104
#> GSM872279 1 0.000 0.959 1.000 0.000 0.000
#> GSM872280 1 0.304 0.890 0.896 0.000 0.104
#> GSM872281 1 0.103 0.949 0.976 0.000 0.024
#> GSM872282 3 0.000 0.947 0.000 0.000 1.000
#> GSM872283 1 0.000 0.959 1.000 0.000 0.000
#> GSM872284 1 0.103 0.949 0.976 0.000 0.024
#> GSM872285 1 0.484 0.729 0.776 0.000 0.224
#> GSM872286 1 0.318 0.911 0.912 0.064 0.024
#> GSM872287 3 0.000 0.947 0.000 0.000 1.000
#> GSM872288 1 0.318 0.911 0.912 0.064 0.024
#> GSM872289 3 0.355 0.824 0.132 0.000 0.868
#> GSM872290 1 0.000 0.959 1.000 0.000 0.000
#> GSM872291 1 0.000 0.959 1.000 0.000 0.000
#> GSM872292 2 0.000 0.751 0.000 1.000 0.000
#> GSM872293 1 0.000 0.959 1.000 0.000 0.000
#> GSM872294 2 0.394 0.789 0.156 0.844 0.000
#> GSM872295 2 0.196 0.781 0.056 0.944 0.000
#> GSM872296 2 0.000 0.751 0.000 1.000 0.000
#> GSM872297 1 0.000 0.959 1.000 0.000 0.000
#> GSM872298 1 0.103 0.949 0.976 0.000 0.024
#> GSM872299 1 0.000 0.959 1.000 0.000 0.000
#> GSM872300 1 0.000 0.959 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM872245 1 0.0188 0.856 0.996 0.000 0.000 0.004
#> GSM872246 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM872247 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM872248 2 0.5229 0.798 0.084 0.748 0.000 0.168
#> GSM872249 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM872250 4 0.0592 0.885 0.016 0.000 0.000 0.984
#> GSM872251 3 0.3024 0.842 0.000 0.000 0.852 0.148
#> GSM872252 1 0.3764 0.793 0.784 0.000 0.000 0.216
#> GSM872253 4 0.2915 0.890 0.028 0.000 0.080 0.892
#> GSM872254 2 0.2928 0.812 0.012 0.880 0.000 0.108
#> GSM872255 1 0.4277 0.748 0.720 0.000 0.000 0.280
#> GSM872256 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM872257 2 0.0336 0.782 0.000 0.992 0.000 0.008
#> GSM872258 3 0.3123 0.833 0.000 0.000 0.844 0.156
#> GSM872259 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM872260 1 0.4277 0.748 0.720 0.000 0.000 0.280
#> GSM872261 4 0.2197 0.829 0.080 0.004 0.000 0.916
#> GSM872262 1 0.4277 0.748 0.720 0.000 0.000 0.280
#> GSM872263 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM872264 4 0.1940 0.902 0.076 0.000 0.000 0.924
#> GSM872265 4 0.2345 0.888 0.100 0.000 0.000 0.900
#> GSM872266 2 0.6646 0.492 0.084 0.488 0.000 0.428
#> GSM872267 2 0.5229 0.798 0.084 0.748 0.000 0.168
#> GSM872268 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM872269 2 0.4938 0.807 0.080 0.772 0.000 0.148
#> GSM872270 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM872271 2 0.6646 0.492 0.084 0.488 0.000 0.428
#> GSM872272 2 0.6646 0.492 0.084 0.488 0.000 0.428
#> GSM872273 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM872274 2 0.0336 0.782 0.000 0.992 0.000 0.008
#> GSM872275 4 0.2915 0.890 0.028 0.000 0.080 0.892
#> GSM872276 1 0.4277 0.748 0.720 0.000 0.000 0.280
#> GSM872277 1 0.0921 0.863 0.972 0.000 0.000 0.028
#> GSM872278 4 0.2915 0.890 0.028 0.000 0.080 0.892
#> GSM872279 1 0.0188 0.856 0.996 0.000 0.000 0.004
#> GSM872280 4 0.2915 0.890 0.028 0.000 0.080 0.892
#> GSM872281 4 0.2081 0.898 0.084 0.000 0.000 0.916
#> GSM872282 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM872283 4 0.3486 0.811 0.188 0.000 0.000 0.812
#> GSM872284 4 0.1940 0.902 0.076 0.000 0.000 0.924
#> GSM872285 4 0.4485 0.765 0.028 0.000 0.200 0.772
#> GSM872286 4 0.0592 0.885 0.016 0.000 0.000 0.984
#> GSM872287 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM872288 4 0.0592 0.885 0.016 0.000 0.000 0.984
#> GSM872289 3 0.3123 0.833 0.000 0.000 0.844 0.156
#> GSM872290 1 0.1940 0.854 0.924 0.000 0.000 0.076
#> GSM872291 1 0.3837 0.792 0.776 0.000 0.000 0.224
#> GSM872292 2 0.0336 0.782 0.000 0.992 0.000 0.008
#> GSM872293 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM872294 2 0.4841 0.808 0.080 0.780 0.000 0.140
#> GSM872295 2 0.2928 0.812 0.012 0.880 0.000 0.108
#> GSM872296 2 0.0336 0.782 0.000 0.992 0.000 0.008
#> GSM872297 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM872298 4 0.2281 0.891 0.096 0.000 0.000 0.904
#> GSM872299 1 0.0188 0.856 0.996 0.000 0.000 0.004
#> GSM872300 1 0.4277 0.748 0.720 0.000 0.000 0.280
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM872245 1 0.0510 0.825 0.984 0.000 0.000 0.000 0.016
#> GSM872246 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM872247 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM872248 5 0.1282 0.783 0.000 0.044 0.000 0.004 0.952
#> GSM872249 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM872250 4 0.2516 0.831 0.000 0.000 0.000 0.860 0.140
#> GSM872251 3 0.2798 0.838 0.000 0.008 0.852 0.140 0.000
#> GSM872252 1 0.4901 0.709 0.716 0.000 0.000 0.116 0.168
#> GSM872253 4 0.2017 0.866 0.000 0.008 0.080 0.912 0.000
#> GSM872254 5 0.2377 0.716 0.000 0.128 0.000 0.000 0.872
#> GSM872255 1 0.3949 0.714 0.668 0.000 0.000 0.332 0.000
#> GSM872256 1 0.0000 0.830 1.000 0.000 0.000 0.000 0.000
#> GSM872257 2 0.0290 1.000 0.000 0.992 0.000 0.000 0.008
#> GSM872258 3 0.2886 0.830 0.000 0.008 0.844 0.148 0.000
#> GSM872259 1 0.0000 0.830 1.000 0.000 0.000 0.000 0.000
#> GSM872260 1 0.3949 0.714 0.668 0.000 0.000 0.332 0.000
#> GSM872261 4 0.3395 0.702 0.000 0.000 0.000 0.764 0.236
#> GSM872262 1 0.3949 0.714 0.668 0.000 0.000 0.332 0.000
#> GSM872263 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM872264 4 0.0794 0.874 0.000 0.000 0.000 0.972 0.028
#> GSM872265 4 0.1493 0.864 0.024 0.000 0.000 0.948 0.028
#> GSM872266 5 0.4622 0.653 0.000 0.044 0.000 0.264 0.692
#> GSM872267 5 0.1282 0.783 0.000 0.044 0.000 0.004 0.952
#> GSM872268 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM872269 5 0.1082 0.778 0.000 0.028 0.000 0.008 0.964
#> GSM872270 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM872271 5 0.4622 0.653 0.000 0.044 0.000 0.264 0.692
#> GSM872272 5 0.4622 0.653 0.000 0.044 0.000 0.264 0.692
#> GSM872273 1 0.0000 0.830 1.000 0.000 0.000 0.000 0.000
#> GSM872274 2 0.0290 1.000 0.000 0.992 0.000 0.000 0.008
#> GSM872275 4 0.2017 0.866 0.000 0.008 0.080 0.912 0.000
#> GSM872276 1 0.3949 0.714 0.668 0.000 0.000 0.332 0.000
#> GSM872277 1 0.0510 0.831 0.984 0.000 0.000 0.016 0.000
#> GSM872278 4 0.2017 0.866 0.000 0.008 0.080 0.912 0.000
#> GSM872279 1 0.0510 0.825 0.984 0.000 0.000 0.000 0.016
#> GSM872280 4 0.2017 0.866 0.000 0.008 0.080 0.912 0.000
#> GSM872281 4 0.0162 0.870 0.004 0.000 0.000 0.996 0.000
#> GSM872282 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM872283 4 0.2824 0.797 0.116 0.000 0.000 0.864 0.020
#> GSM872284 4 0.0794 0.874 0.000 0.000 0.000 0.972 0.028
#> GSM872285 4 0.3388 0.740 0.000 0.008 0.200 0.792 0.000
#> GSM872286 4 0.2516 0.831 0.000 0.000 0.000 0.860 0.140
#> GSM872287 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000
#> GSM872288 4 0.2516 0.831 0.000 0.000 0.000 0.860 0.140
#> GSM872289 3 0.2886 0.830 0.000 0.008 0.844 0.148 0.000
#> GSM872290 1 0.1544 0.823 0.932 0.000 0.000 0.068 0.000
#> GSM872291 1 0.3561 0.764 0.740 0.000 0.000 0.260 0.000
#> GSM872292 2 0.0290 1.000 0.000 0.992 0.000 0.000 0.008
#> GSM872293 1 0.0000 0.830 1.000 0.000 0.000 0.000 0.000
#> GSM872294 5 0.0880 0.775 0.000 0.032 0.000 0.000 0.968
#> GSM872295 5 0.2377 0.716 0.000 0.128 0.000 0.000 0.872
#> GSM872296 2 0.0290 1.000 0.000 0.992 0.000 0.000 0.008
#> GSM872297 1 0.0000 0.830 1.000 0.000 0.000 0.000 0.000
#> GSM872298 4 0.0798 0.866 0.016 0.008 0.000 0.976 0.000
#> GSM872299 1 0.0510 0.825 0.984 0.000 0.000 0.000 0.016
#> GSM872300 1 0.3949 0.714 0.668 0.000 0.000 0.332 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872245 1 0.0458 0.823 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM872246 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872247 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872248 5 0.0632 0.634 0.000 0.000 0.000 0.000 0.976 0.024
#> GSM872249 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872250 4 0.2593 0.792 0.000 0.000 0.000 0.844 0.148 0.008
#> GSM872251 3 0.3900 0.797 0.000 0.000 0.796 0.088 0.020 0.096
#> GSM872252 1 0.4895 0.698 0.712 0.000 0.000 0.116 0.140 0.032
#> GSM872253 4 0.3093 0.814 0.000 0.000 0.024 0.848 0.024 0.104
#> GSM872254 6 0.3045 0.902 0.000 0.100 0.000 0.000 0.060 0.840
#> GSM872255 1 0.4034 0.714 0.652 0.000 0.000 0.328 0.000 0.020
#> GSM872256 1 0.0000 0.829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872257 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872258 3 0.3996 0.790 0.000 0.000 0.788 0.096 0.020 0.096
#> GSM872259 1 0.0000 0.829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872260 1 0.4034 0.714 0.652 0.000 0.000 0.328 0.000 0.020
#> GSM872261 4 0.3630 0.685 0.000 0.000 0.000 0.756 0.212 0.032
#> GSM872262 1 0.4034 0.714 0.652 0.000 0.000 0.328 0.000 0.020
#> GSM872263 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872264 4 0.0935 0.828 0.000 0.000 0.000 0.964 0.032 0.004
#> GSM872265 4 0.1693 0.811 0.012 0.000 0.000 0.936 0.032 0.020
#> GSM872266 5 0.3175 0.788 0.000 0.000 0.000 0.256 0.744 0.000
#> GSM872267 5 0.0632 0.634 0.000 0.000 0.000 0.000 0.976 0.024
#> GSM872268 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872269 6 0.2442 0.881 0.000 0.000 0.000 0.004 0.144 0.852
#> GSM872270 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872271 5 0.3175 0.788 0.000 0.000 0.000 0.256 0.744 0.000
#> GSM872272 5 0.3175 0.788 0.000 0.000 0.000 0.256 0.744 0.000
#> GSM872273 1 0.0000 0.829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872274 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872275 4 0.3093 0.814 0.000 0.000 0.024 0.848 0.024 0.104
#> GSM872276 1 0.4034 0.714 0.652 0.000 0.000 0.328 0.000 0.020
#> GSM872277 1 0.0458 0.829 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM872278 4 0.3093 0.814 0.000 0.000 0.024 0.848 0.024 0.104
#> GSM872279 1 0.0458 0.823 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM872280 4 0.3093 0.814 0.000 0.000 0.024 0.848 0.024 0.104
#> GSM872281 4 0.0260 0.821 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM872282 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872283 4 0.2925 0.761 0.104 0.000 0.000 0.856 0.024 0.016
#> GSM872284 4 0.1049 0.826 0.000 0.000 0.000 0.960 0.032 0.008
#> GSM872285 4 0.4661 0.668 0.000 0.000 0.144 0.728 0.024 0.104
#> GSM872286 4 0.2593 0.792 0.000 0.000 0.000 0.844 0.148 0.008
#> GSM872287 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872288 4 0.2593 0.792 0.000 0.000 0.000 0.844 0.148 0.008
#> GSM872289 3 0.3996 0.790 0.000 0.000 0.788 0.096 0.020 0.096
#> GSM872290 1 0.1444 0.820 0.928 0.000 0.000 0.072 0.000 0.000
#> GSM872291 1 0.3688 0.755 0.724 0.000 0.000 0.256 0.000 0.020
#> GSM872292 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872293 1 0.0000 0.829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872294 6 0.2092 0.897 0.000 0.000 0.000 0.000 0.124 0.876
#> GSM872295 6 0.3045 0.902 0.000 0.100 0.000 0.000 0.060 0.840
#> GSM872296 2 0.0146 0.997 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM872297 1 0.0000 0.829 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872298 4 0.1353 0.827 0.012 0.000 0.000 0.952 0.012 0.024
#> GSM872299 1 0.0458 0.823 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM872300 1 0.4034 0.714 0.652 0.000 0.000 0.328 0.000 0.020
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 time(p) individual(p) k
#> ATC:hclust 57 0.387 0.000693 2
#> ATC:hclust 54 0.818 0.000403 3
#> ATC:hclust 54 0.764 0.000515 4
#> ATC:hclust 57 0.645 0.011167 5
#> ATC:hclust 57 0.465 0.009007 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 29485 rows and 57 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 0.294 0.722 0.842 0.4261 0.574 0.574
#> 3 3 0.980 0.935 0.972 0.5369 0.753 0.576
#> 4 4 0.796 0.882 0.934 0.1227 0.771 0.451
#> 5 5 0.754 0.771 0.870 0.0847 0.890 0.614
#> 6 6 0.801 0.676 0.838 0.0435 0.944 0.729
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
#> GSM872244 1 0.529 0.878 0.880 0.120
#> GSM872245 2 0.529 0.748 0.120 0.880
#> GSM872246 1 0.529 0.878 0.880 0.120
#> GSM872247 1 0.529 0.878 0.880 0.120
#> GSM872248 2 0.987 0.533 0.432 0.568
#> GSM872249 1 0.529 0.878 0.880 0.120
#> GSM872250 2 0.895 0.509 0.312 0.688
#> GSM872251 1 0.529 0.878 0.880 0.120
#> GSM872252 2 0.000 0.809 0.000 1.000
#> GSM872253 1 0.991 0.343 0.556 0.444
#> GSM872254 2 0.987 0.533 0.432 0.568
#> GSM872255 2 0.000 0.809 0.000 1.000
#> GSM872256 2 0.000 0.809 0.000 1.000
#> GSM872257 2 0.987 0.533 0.432 0.568
#> GSM872258 1 0.529 0.878 0.880 0.120
#> GSM872259 2 0.000 0.809 0.000 1.000
#> GSM872260 2 0.000 0.809 0.000 1.000
#> GSM872261 2 0.443 0.765 0.092 0.908
#> GSM872262 2 0.000 0.809 0.000 1.000
#> GSM872263 1 0.529 0.878 0.880 0.120
#> GSM872264 2 0.821 0.598 0.256 0.744
#> GSM872265 2 0.000 0.809 0.000 1.000
#> GSM872266 2 0.978 0.560 0.412 0.588
#> GSM872267 2 0.753 0.728 0.216 0.784
#> GSM872268 1 0.529 0.878 0.880 0.120
#> GSM872269 2 0.985 0.533 0.428 0.572
#> GSM872270 1 0.529 0.878 0.880 0.120
#> GSM872271 2 0.961 0.595 0.384 0.616
#> GSM872272 2 0.961 0.595 0.384 0.616
#> GSM872273 2 0.000 0.809 0.000 1.000
#> GSM872274 2 0.987 0.533 0.432 0.568
#> GSM872275 1 0.992 0.330 0.552 0.448
#> GSM872276 2 0.000 0.809 0.000 1.000
#> GSM872277 2 0.000 0.809 0.000 1.000
#> GSM872278 1 0.988 0.365 0.564 0.436
#> GSM872279 2 0.000 0.809 0.000 1.000
#> GSM872280 1 1.000 0.204 0.500 0.500
#> GSM872281 2 0.204 0.783 0.032 0.968
#> GSM872282 1 0.529 0.878 0.880 0.120
#> GSM872283 2 0.000 0.809 0.000 1.000
#> GSM872284 2 0.000 0.809 0.000 1.000
#> GSM872285 1 0.529 0.878 0.880 0.120
#> GSM872286 2 0.000 0.809 0.000 1.000
#> GSM872287 1 0.529 0.878 0.880 0.120
#> GSM872288 2 0.697 0.681 0.188 0.812
#> GSM872289 1 0.529 0.878 0.880 0.120
#> GSM872290 2 0.000 0.809 0.000 1.000
#> GSM872291 2 0.000 0.809 0.000 1.000
#> GSM872292 2 0.987 0.533 0.432 0.568
#> GSM872293 2 0.000 0.809 0.000 1.000
#> GSM872294 2 0.529 0.748 0.120 0.880
#> GSM872295 2 0.987 0.533 0.432 0.568
#> GSM872296 2 0.987 0.533 0.432 0.568
#> GSM872297 2 0.000 0.809 0.000 1.000
#> GSM872298 2 0.000 0.809 0.000 1.000
#> GSM872299 2 0.518 0.751 0.116 0.884
#> GSM872300 2 0.000 0.809 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872245 1 0.0424 0.979 0.992 0.008 0.000
#> GSM872246 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872248 2 0.0424 0.968 0.000 0.992 0.008
#> GSM872249 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872250 2 0.3481 0.895 0.044 0.904 0.052
#> GSM872251 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872252 1 0.0000 0.979 1.000 0.000 0.000
#> GSM872253 3 0.5058 0.643 0.000 0.244 0.756
#> GSM872254 2 0.0424 0.968 0.000 0.992 0.008
#> GSM872255 1 0.0000 0.979 1.000 0.000 0.000
#> GSM872256 1 0.0424 0.979 0.992 0.008 0.000
#> GSM872257 2 0.0424 0.968 0.000 0.992 0.008
#> GSM872258 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872259 1 0.0424 0.979 0.992 0.008 0.000
#> GSM872260 1 0.0000 0.979 1.000 0.000 0.000
#> GSM872261 1 0.5988 0.397 0.632 0.368 0.000
#> GSM872262 1 0.0000 0.979 1.000 0.000 0.000
#> GSM872263 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872264 1 0.1163 0.956 0.972 0.000 0.028
#> GSM872265 1 0.0000 0.979 1.000 0.000 0.000
#> GSM872266 2 0.0424 0.968 0.000 0.992 0.008
#> GSM872267 2 0.0000 0.963 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872269 2 0.0424 0.968 0.000 0.992 0.008
#> GSM872270 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872271 2 0.0475 0.966 0.004 0.992 0.004
#> GSM872272 2 0.0475 0.966 0.004 0.992 0.004
#> GSM872273 1 0.0424 0.979 0.992 0.008 0.000
#> GSM872274 2 0.0424 0.968 0.000 0.992 0.008
#> GSM872275 2 0.5733 0.520 0.000 0.676 0.324
#> GSM872276 1 0.0000 0.979 1.000 0.000 0.000
#> GSM872277 1 0.0424 0.979 0.992 0.008 0.000
#> GSM872278 3 0.0424 0.947 0.008 0.000 0.992
#> GSM872279 1 0.0424 0.979 0.992 0.008 0.000
#> GSM872280 3 0.5859 0.486 0.344 0.000 0.656
#> GSM872281 1 0.0000 0.979 1.000 0.000 0.000
#> GSM872282 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872283 1 0.0424 0.979 0.992 0.008 0.000
#> GSM872284 1 0.0000 0.979 1.000 0.000 0.000
#> GSM872285 3 0.0424 0.947 0.008 0.000 0.992
#> GSM872286 1 0.0237 0.979 0.996 0.004 0.000
#> GSM872287 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872288 1 0.0892 0.963 0.980 0.000 0.020
#> GSM872289 3 0.0000 0.953 0.000 0.000 1.000
#> GSM872290 1 0.0424 0.979 0.992 0.008 0.000
#> GSM872291 1 0.0000 0.979 1.000 0.000 0.000
#> GSM872292 2 0.0424 0.968 0.000 0.992 0.008
#> GSM872293 1 0.0424 0.979 0.992 0.008 0.000
#> GSM872294 2 0.0000 0.963 0.000 1.000 0.000
#> GSM872295 2 0.0424 0.968 0.000 0.992 0.008
#> GSM872296 2 0.0424 0.968 0.000 0.992 0.008
#> GSM872297 1 0.0424 0.979 0.992 0.008 0.000
#> GSM872298 1 0.0000 0.979 1.000 0.000 0.000
#> GSM872299 1 0.0424 0.979 0.992 0.008 0.000
#> GSM872300 1 0.0000 0.979 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0000 0.977 0.000 0.000 1.000 0.000
#> GSM872245 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM872246 3 0.0000 0.977 0.000 0.000 1.000 0.000
#> GSM872247 3 0.0000 0.977 0.000 0.000 1.000 0.000
#> GSM872248 2 0.3486 0.816 0.000 0.812 0.000 0.188
#> GSM872249 3 0.0000 0.977 0.000 0.000 1.000 0.000
#> GSM872250 4 0.0000 0.878 0.000 0.000 0.000 1.000
#> GSM872251 3 0.0469 0.969 0.000 0.000 0.988 0.012
#> GSM872252 4 0.2011 0.874 0.080 0.000 0.000 0.920
#> GSM872253 4 0.0000 0.878 0.000 0.000 0.000 1.000
#> GSM872254 2 0.0000 0.865 0.000 1.000 0.000 0.000
#> GSM872255 4 0.3688 0.788 0.208 0.000 0.000 0.792
#> GSM872256 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM872257 2 0.0000 0.865 0.000 1.000 0.000 0.000
#> GSM872258 3 0.2408 0.885 0.000 0.000 0.896 0.104
#> GSM872259 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM872260 4 0.4008 0.753 0.244 0.000 0.000 0.756
#> GSM872261 4 0.0000 0.878 0.000 0.000 0.000 1.000
#> GSM872262 4 0.4585 0.640 0.332 0.000 0.000 0.668
#> GSM872263 3 0.0000 0.977 0.000 0.000 1.000 0.000
#> GSM872264 4 0.0000 0.878 0.000 0.000 0.000 1.000
#> GSM872265 4 0.0592 0.882 0.016 0.000 0.000 0.984
#> GSM872266 2 0.3610 0.807 0.000 0.800 0.000 0.200
#> GSM872267 2 0.3486 0.816 0.000 0.812 0.000 0.188
#> GSM872268 3 0.0000 0.977 0.000 0.000 1.000 0.000
#> GSM872269 4 0.2589 0.768 0.000 0.116 0.000 0.884
#> GSM872270 3 0.0000 0.977 0.000 0.000 1.000 0.000
#> GSM872271 2 0.4855 0.538 0.000 0.600 0.000 0.400
#> GSM872272 2 0.4855 0.538 0.000 0.600 0.000 0.400
#> GSM872273 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM872274 2 0.0000 0.865 0.000 1.000 0.000 0.000
#> GSM872275 4 0.0000 0.878 0.000 0.000 0.000 1.000
#> GSM872276 4 0.4605 0.634 0.336 0.000 0.000 0.664
#> GSM872277 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM872278 4 0.0000 0.878 0.000 0.000 0.000 1.000
#> GSM872279 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM872280 4 0.1637 0.880 0.060 0.000 0.000 0.940
#> GSM872281 4 0.1637 0.880 0.060 0.000 0.000 0.940
#> GSM872282 3 0.0000 0.977 0.000 0.000 1.000 0.000
#> GSM872283 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM872284 4 0.1118 0.883 0.036 0.000 0.000 0.964
#> GSM872285 4 0.1637 0.859 0.000 0.000 0.060 0.940
#> GSM872286 4 0.0707 0.880 0.020 0.000 0.000 0.980
#> GSM872287 3 0.0000 0.977 0.000 0.000 1.000 0.000
#> GSM872288 4 0.0000 0.878 0.000 0.000 0.000 1.000
#> GSM872289 3 0.2408 0.885 0.000 0.000 0.896 0.104
#> GSM872290 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM872291 4 0.4605 0.634 0.336 0.000 0.000 0.664
#> GSM872292 2 0.0000 0.865 0.000 1.000 0.000 0.000
#> GSM872293 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM872294 2 0.0000 0.865 0.000 1.000 0.000 0.000
#> GSM872295 2 0.0000 0.865 0.000 1.000 0.000 0.000
#> GSM872296 2 0.0000 0.865 0.000 1.000 0.000 0.000
#> GSM872297 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM872298 4 0.1637 0.880 0.060 0.000 0.000 0.940
#> GSM872299 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM872300 4 0.3649 0.791 0.204 0.000 0.000 0.796
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.0703 0.898 0.000 0.000 0.976 0.000 0.024
#> GSM872245 1 0.0865 0.950 0.972 0.000 0.000 0.004 0.024
#> GSM872246 3 0.0880 0.897 0.000 0.000 0.968 0.000 0.032
#> GSM872247 3 0.0000 0.900 0.000 0.000 1.000 0.000 0.000
#> GSM872248 5 0.4269 0.494 0.000 0.300 0.000 0.016 0.684
#> GSM872249 3 0.0703 0.898 0.000 0.000 0.976 0.000 0.024
#> GSM872250 5 0.2605 0.681 0.000 0.000 0.000 0.148 0.852
#> GSM872251 3 0.3284 0.814 0.000 0.000 0.828 0.024 0.148
#> GSM872252 4 0.4326 0.554 0.028 0.000 0.000 0.708 0.264
#> GSM872253 5 0.3242 0.657 0.000 0.000 0.000 0.216 0.784
#> GSM872254 2 0.3783 0.661 0.000 0.740 0.000 0.008 0.252
#> GSM872255 4 0.1282 0.835 0.044 0.000 0.000 0.952 0.004
#> GSM872256 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000
#> GSM872257 2 0.0000 0.886 0.000 1.000 0.000 0.000 0.000
#> GSM872258 3 0.5617 0.587 0.000 0.000 0.620 0.124 0.256
#> GSM872259 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000
#> GSM872260 4 0.1800 0.831 0.048 0.000 0.000 0.932 0.020
#> GSM872261 5 0.3636 0.643 0.000 0.000 0.000 0.272 0.728
#> GSM872262 4 0.2648 0.785 0.152 0.000 0.000 0.848 0.000
#> GSM872263 3 0.0703 0.898 0.000 0.000 0.976 0.000 0.024
#> GSM872264 4 0.2377 0.785 0.000 0.000 0.000 0.872 0.128
#> GSM872265 4 0.2179 0.795 0.000 0.000 0.000 0.888 0.112
#> GSM872266 5 0.4318 0.507 0.000 0.292 0.000 0.020 0.688
#> GSM872267 5 0.4269 0.494 0.000 0.300 0.000 0.016 0.684
#> GSM872268 3 0.0880 0.897 0.000 0.000 0.968 0.000 0.032
#> GSM872269 5 0.3039 0.661 0.000 0.012 0.000 0.152 0.836
#> GSM872270 3 0.0000 0.900 0.000 0.000 1.000 0.000 0.000
#> GSM872271 5 0.4933 0.561 0.000 0.236 0.000 0.076 0.688
#> GSM872272 5 0.4933 0.561 0.000 0.236 0.000 0.076 0.688
#> GSM872273 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000
#> GSM872274 2 0.0000 0.886 0.000 1.000 0.000 0.000 0.000
#> GSM872275 5 0.3177 0.662 0.000 0.000 0.000 0.208 0.792
#> GSM872276 4 0.2648 0.785 0.152 0.000 0.000 0.848 0.000
#> GSM872277 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000
#> GSM872278 4 0.3534 0.626 0.000 0.000 0.000 0.744 0.256
#> GSM872279 1 0.0609 0.955 0.980 0.000 0.000 0.000 0.020
#> GSM872280 4 0.3318 0.699 0.008 0.000 0.000 0.800 0.192
#> GSM872281 4 0.0290 0.830 0.008 0.000 0.000 0.992 0.000
#> GSM872282 3 0.0703 0.898 0.000 0.000 0.976 0.000 0.024
#> GSM872283 1 0.3480 0.645 0.752 0.000 0.000 0.248 0.000
#> GSM872284 4 0.1792 0.809 0.000 0.000 0.000 0.916 0.084
#> GSM872285 4 0.3916 0.630 0.000 0.000 0.012 0.732 0.256
#> GSM872286 5 0.4138 0.448 0.000 0.000 0.000 0.384 0.616
#> GSM872287 3 0.0794 0.898 0.000 0.000 0.972 0.000 0.028
#> GSM872288 5 0.4302 0.136 0.000 0.000 0.000 0.480 0.520
#> GSM872289 3 0.5617 0.587 0.000 0.000 0.620 0.124 0.256
#> GSM872290 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000
#> GSM872291 4 0.2648 0.785 0.152 0.000 0.000 0.848 0.000
#> GSM872292 2 0.0000 0.886 0.000 1.000 0.000 0.000 0.000
#> GSM872293 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000
#> GSM872294 2 0.3957 0.631 0.000 0.712 0.000 0.008 0.280
#> GSM872295 2 0.0865 0.877 0.000 0.972 0.000 0.004 0.024
#> GSM872296 2 0.0000 0.886 0.000 1.000 0.000 0.000 0.000
#> GSM872297 1 0.0000 0.963 1.000 0.000 0.000 0.000 0.000
#> GSM872298 4 0.0290 0.830 0.008 0.000 0.000 0.992 0.000
#> GSM872299 1 0.0955 0.947 0.968 0.000 0.000 0.004 0.028
#> GSM872300 4 0.1121 0.835 0.044 0.000 0.000 0.956 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.1082 0.8932 0.000 0.000 0.956 0.000 0.040 0.004
#> GSM872245 1 0.0951 0.9114 0.968 0.000 0.000 0.020 0.008 0.004
#> GSM872246 3 0.1863 0.8636 0.000 0.000 0.896 0.104 0.000 0.000
#> GSM872247 3 0.0000 0.8939 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872248 5 0.1524 0.7265 0.000 0.060 0.000 0.008 0.932 0.000
#> GSM872249 3 0.1082 0.8932 0.000 0.000 0.956 0.000 0.040 0.004
#> GSM872250 5 0.3784 0.4678 0.000 0.000 0.000 0.308 0.680 0.012
#> GSM872251 3 0.3899 0.3531 0.000 0.000 0.592 0.404 0.000 0.004
#> GSM872252 6 0.4431 0.5332 0.000 0.000 0.000 0.228 0.080 0.692
#> GSM872253 4 0.3500 0.3161 0.000 0.000 0.000 0.768 0.204 0.028
#> GSM872254 2 0.5866 0.4896 0.000 0.512 0.000 0.232 0.252 0.004
#> GSM872255 6 0.0653 0.8442 0.004 0.000 0.000 0.012 0.004 0.980
#> GSM872256 1 0.0146 0.9226 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM872257 2 0.0146 0.8169 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM872258 4 0.4078 0.2846 0.000 0.000 0.340 0.640 0.000 0.020
#> GSM872259 1 0.0000 0.9231 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872260 6 0.1251 0.8400 0.008 0.000 0.000 0.024 0.012 0.956
#> GSM872261 5 0.4480 0.4518 0.000 0.000 0.000 0.340 0.616 0.044
#> GSM872262 6 0.0777 0.8439 0.024 0.000 0.000 0.004 0.000 0.972
#> GSM872263 3 0.1082 0.8932 0.000 0.000 0.956 0.000 0.040 0.004
#> GSM872264 6 0.4475 0.6467 0.000 0.000 0.000 0.100 0.200 0.700
#> GSM872265 6 0.3650 0.7549 0.000 0.000 0.000 0.092 0.116 0.792
#> GSM872266 5 0.1524 0.7265 0.000 0.060 0.000 0.008 0.932 0.000
#> GSM872267 5 0.1524 0.7217 0.000 0.060 0.000 0.008 0.932 0.000
#> GSM872268 3 0.1814 0.8661 0.000 0.000 0.900 0.100 0.000 0.000
#> GSM872269 4 0.4310 -0.3056 0.000 0.004 0.000 0.512 0.472 0.012
#> GSM872270 3 0.0000 0.8939 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872271 5 0.2137 0.7281 0.000 0.048 0.000 0.028 0.912 0.012
#> GSM872272 5 0.2137 0.7281 0.000 0.048 0.000 0.028 0.912 0.012
#> GSM872273 1 0.0146 0.9226 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM872274 2 0.0146 0.8169 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM872275 4 0.4131 0.1528 0.000 0.000 0.000 0.624 0.356 0.020
#> GSM872276 6 0.0858 0.8420 0.028 0.000 0.000 0.004 0.000 0.968
#> GSM872277 1 0.0146 0.9226 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM872278 4 0.4057 0.2121 0.000 0.000 0.000 0.600 0.012 0.388
#> GSM872279 1 0.1053 0.9121 0.964 0.000 0.000 0.012 0.004 0.020
#> GSM872280 6 0.3854 -0.0337 0.000 0.000 0.000 0.464 0.000 0.536
#> GSM872281 6 0.1411 0.8361 0.000 0.000 0.000 0.060 0.004 0.936
#> GSM872282 3 0.1082 0.8932 0.000 0.000 0.956 0.000 0.040 0.004
#> GSM872283 1 0.5080 0.2073 0.552 0.000 0.000 0.056 0.012 0.380
#> GSM872284 6 0.2176 0.8251 0.000 0.000 0.000 0.080 0.024 0.896
#> GSM872285 4 0.3409 0.3837 0.000 0.000 0.000 0.700 0.000 0.300
#> GSM872286 5 0.5409 0.4215 0.000 0.000 0.000 0.188 0.580 0.232
#> GSM872287 3 0.1814 0.8661 0.000 0.000 0.900 0.100 0.000 0.000
#> GSM872288 5 0.5844 0.2156 0.000 0.000 0.000 0.324 0.468 0.208
#> GSM872289 4 0.4078 0.2846 0.000 0.000 0.340 0.640 0.000 0.020
#> GSM872290 1 0.0909 0.9132 0.968 0.000 0.000 0.012 0.000 0.020
#> GSM872291 6 0.1218 0.8397 0.028 0.000 0.000 0.012 0.004 0.956
#> GSM872292 2 0.0146 0.8169 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM872293 1 0.0000 0.9231 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872294 2 0.6030 0.4475 0.000 0.468 0.000 0.256 0.272 0.004
#> GSM872295 2 0.2784 0.7709 0.000 0.848 0.000 0.124 0.028 0.000
#> GSM872296 2 0.0291 0.8161 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM872297 1 0.0000 0.9231 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872298 6 0.1398 0.8389 0.000 0.000 0.000 0.052 0.008 0.940
#> GSM872299 1 0.3062 0.8167 0.844 0.000 0.000 0.116 0.016 0.024
#> GSM872300 6 0.0405 0.8462 0.004 0.000 0.000 0.000 0.008 0.988
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 time(p) individual(p) k
#> ATC:kmeans 53 0.558 1.04e-03 2
#> ATC:kmeans 55 0.456 7.79e-04 3
#> ATC:kmeans 57 0.831 1.19e-04 4
#> ATC:kmeans 53 0.307 1.49e-05 5
#> ATC:kmeans 41 0.497 3.02e-04 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 29485 rows and 57 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 0.707 0.840 0.926 0.5044 0.495 0.495
#> 3 3 1.000 0.981 0.993 0.3236 0.791 0.597
#> 4 4 0.901 0.861 0.943 0.1236 0.893 0.688
#> 5 5 0.832 0.748 0.886 0.0447 0.937 0.763
#> 6 6 0.818 0.775 0.863 0.0354 0.951 0.790
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] 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
#> GSM872244 2 0.000 0.857 0.000 1.000
#> GSM872245 1 0.000 0.983 1.000 0.000
#> GSM872246 2 0.000 0.857 0.000 1.000
#> GSM872247 2 0.000 0.857 0.000 1.000
#> GSM872248 2 0.909 0.612 0.324 0.676
#> GSM872249 2 0.000 0.857 0.000 1.000
#> GSM872250 2 0.000 0.857 0.000 1.000
#> GSM872251 2 0.000 0.857 0.000 1.000
#> GSM872252 1 0.000 0.983 1.000 0.000
#> GSM872253 2 0.000 0.857 0.000 1.000
#> GSM872254 2 0.909 0.612 0.324 0.676
#> GSM872255 1 0.000 0.983 1.000 0.000
#> GSM872256 1 0.000 0.983 1.000 0.000
#> GSM872257 2 0.909 0.612 0.324 0.676
#> GSM872258 2 0.000 0.857 0.000 1.000
#> GSM872259 1 0.000 0.983 1.000 0.000
#> GSM872260 1 0.000 0.983 1.000 0.000
#> GSM872261 1 0.000 0.983 1.000 0.000
#> GSM872262 1 0.000 0.983 1.000 0.000
#> GSM872263 2 0.000 0.857 0.000 1.000
#> GSM872264 2 0.827 0.624 0.260 0.740
#> GSM872265 1 0.000 0.983 1.000 0.000
#> GSM872266 2 0.909 0.612 0.324 0.676
#> GSM872267 1 0.163 0.954 0.976 0.024
#> GSM872268 2 0.000 0.857 0.000 1.000
#> GSM872269 2 0.204 0.842 0.032 0.968
#> GSM872270 2 0.000 0.857 0.000 1.000
#> GSM872271 2 0.988 0.412 0.436 0.564
#> GSM872272 2 0.980 0.456 0.416 0.584
#> GSM872273 1 0.000 0.983 1.000 0.000
#> GSM872274 2 0.909 0.612 0.324 0.676
#> GSM872275 2 0.000 0.857 0.000 1.000
#> GSM872276 1 0.000 0.983 1.000 0.000
#> GSM872277 1 0.000 0.983 1.000 0.000
#> GSM872278 2 0.000 0.857 0.000 1.000
#> GSM872279 1 0.000 0.983 1.000 0.000
#> GSM872280 2 0.996 0.135 0.464 0.536
#> GSM872281 1 0.909 0.440 0.676 0.324
#> GSM872282 2 0.000 0.857 0.000 1.000
#> GSM872283 1 0.000 0.983 1.000 0.000
#> GSM872284 1 0.000 0.983 1.000 0.000
#> GSM872285 2 0.000 0.857 0.000 1.000
#> GSM872286 1 0.000 0.983 1.000 0.000
#> GSM872287 2 0.000 0.857 0.000 1.000
#> GSM872288 2 0.929 0.480 0.344 0.656
#> GSM872289 2 0.000 0.857 0.000 1.000
#> GSM872290 1 0.000 0.983 1.000 0.000
#> GSM872291 1 0.000 0.983 1.000 0.000
#> GSM872292 2 0.000 0.857 0.000 1.000
#> GSM872293 1 0.000 0.983 1.000 0.000
#> GSM872294 1 0.000 0.983 1.000 0.000
#> GSM872295 2 0.000 0.857 0.000 1.000
#> GSM872296 2 0.909 0.612 0.324 0.676
#> GSM872297 1 0.000 0.983 1.000 0.000
#> GSM872298 1 0.000 0.983 1.000 0.000
#> GSM872299 1 0.000 0.983 1.000 0.000
#> GSM872300 1 0.000 0.983 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872245 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872246 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.972 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872250 2 0.6079 0.364 0.000 0.612 0.388
#> GSM872251 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872252 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872253 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872254 2 0.0000 0.972 0.000 1.000 0.000
#> GSM872255 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872256 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872257 2 0.0000 0.972 0.000 1.000 0.000
#> GSM872258 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872259 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872260 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872261 2 0.0000 0.972 0.000 1.000 0.000
#> GSM872262 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872263 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872264 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872265 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872266 2 0.0000 0.972 0.000 1.000 0.000
#> GSM872267 2 0.0000 0.972 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872269 2 0.0000 0.972 0.000 1.000 0.000
#> GSM872270 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872271 2 0.0000 0.972 0.000 1.000 0.000
#> GSM872272 2 0.0000 0.972 0.000 1.000 0.000
#> GSM872273 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872274 2 0.0000 0.972 0.000 1.000 0.000
#> GSM872275 3 0.0592 0.987 0.000 0.012 0.988
#> GSM872276 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872277 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872278 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872279 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872280 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872281 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872282 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872283 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872284 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872285 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872286 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872287 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872288 3 0.0424 0.991 0.008 0.000 0.992
#> GSM872289 3 0.0000 0.999 0.000 0.000 1.000
#> GSM872290 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872291 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872292 2 0.0000 0.972 0.000 1.000 0.000
#> GSM872293 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872294 2 0.0000 0.972 0.000 1.000 0.000
#> GSM872295 2 0.0000 0.972 0.000 1.000 0.000
#> GSM872296 2 0.0000 0.972 0.000 1.000 0.000
#> GSM872297 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872298 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872299 1 0.0000 1.000 1.000 0.000 0.000
#> GSM872300 1 0.0000 1.000 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0000 0.9864 0.000 0.000 1.000 0.000
#> GSM872245 1 0.0000 0.9167 1.000 0.000 0.000 0.000
#> GSM872246 3 0.0000 0.9864 0.000 0.000 1.000 0.000
#> GSM872247 3 0.0000 0.9864 0.000 0.000 1.000 0.000
#> GSM872248 2 0.0188 0.9660 0.000 0.996 0.000 0.004
#> GSM872249 3 0.0000 0.9864 0.000 0.000 1.000 0.000
#> GSM872250 2 0.5040 0.4212 0.000 0.628 0.364 0.008
#> GSM872251 3 0.0000 0.9864 0.000 0.000 1.000 0.000
#> GSM872252 1 0.0000 0.9167 1.000 0.000 0.000 0.000
#> GSM872253 3 0.0000 0.9864 0.000 0.000 1.000 0.000
#> GSM872254 2 0.0000 0.9668 0.000 1.000 0.000 0.000
#> GSM872255 1 0.4941 0.0784 0.564 0.000 0.000 0.436
#> GSM872256 1 0.0000 0.9167 1.000 0.000 0.000 0.000
#> GSM872257 2 0.0000 0.9668 0.000 1.000 0.000 0.000
#> GSM872258 3 0.0000 0.9864 0.000 0.000 1.000 0.000
#> GSM872259 1 0.0000 0.9167 1.000 0.000 0.000 0.000
#> GSM872260 1 0.1867 0.8548 0.928 0.000 0.000 0.072
#> GSM872261 2 0.0000 0.9668 0.000 1.000 0.000 0.000
#> GSM872262 4 0.4477 0.5556 0.312 0.000 0.000 0.688
#> GSM872263 3 0.0000 0.9864 0.000 0.000 1.000 0.000
#> GSM872264 4 0.1022 0.7608 0.000 0.000 0.032 0.968
#> GSM872265 4 0.1389 0.7609 0.048 0.000 0.000 0.952
#> GSM872266 2 0.0188 0.9660 0.000 0.996 0.000 0.004
#> GSM872267 2 0.0188 0.9660 0.000 0.996 0.000 0.004
#> GSM872268 3 0.0000 0.9864 0.000 0.000 1.000 0.000
#> GSM872269 2 0.0188 0.9648 0.000 0.996 0.000 0.004
#> GSM872270 3 0.0000 0.9864 0.000 0.000 1.000 0.000
#> GSM872271 2 0.0188 0.9660 0.000 0.996 0.000 0.004
#> GSM872272 2 0.0188 0.9660 0.000 0.996 0.000 0.004
#> GSM872273 1 0.0188 0.9141 0.996 0.000 0.000 0.004
#> GSM872274 2 0.0000 0.9668 0.000 1.000 0.000 0.000
#> GSM872275 3 0.0336 0.9780 0.000 0.008 0.992 0.000
#> GSM872276 4 0.4500 0.5491 0.316 0.000 0.000 0.684
#> GSM872277 1 0.2704 0.7789 0.876 0.000 0.000 0.124
#> GSM872278 3 0.0000 0.9864 0.000 0.000 1.000 0.000
#> GSM872279 1 0.0000 0.9167 1.000 0.000 0.000 0.000
#> GSM872280 3 0.3486 0.7491 0.000 0.000 0.812 0.188
#> GSM872281 4 0.0336 0.7709 0.008 0.000 0.000 0.992
#> GSM872282 3 0.0000 0.9864 0.000 0.000 1.000 0.000
#> GSM872283 4 0.4972 0.1653 0.456 0.000 0.000 0.544
#> GSM872284 4 0.0336 0.7709 0.008 0.000 0.000 0.992
#> GSM872285 3 0.0000 0.9864 0.000 0.000 1.000 0.000
#> GSM872286 1 0.0188 0.9135 0.996 0.000 0.000 0.004
#> GSM872287 3 0.0000 0.9864 0.000 0.000 1.000 0.000
#> GSM872288 4 0.3942 0.5818 0.000 0.000 0.236 0.764
#> GSM872289 3 0.0000 0.9864 0.000 0.000 1.000 0.000
#> GSM872290 1 0.0000 0.9167 1.000 0.000 0.000 0.000
#> GSM872291 1 0.4164 0.5640 0.736 0.000 0.000 0.264
#> GSM872292 2 0.0000 0.9668 0.000 1.000 0.000 0.000
#> GSM872293 1 0.0000 0.9167 1.000 0.000 0.000 0.000
#> GSM872294 2 0.0000 0.9668 0.000 1.000 0.000 0.000
#> GSM872295 2 0.0000 0.9668 0.000 1.000 0.000 0.000
#> GSM872296 2 0.0000 0.9668 0.000 1.000 0.000 0.000
#> GSM872297 1 0.0000 0.9167 1.000 0.000 0.000 0.000
#> GSM872298 4 0.0336 0.7709 0.008 0.000 0.000 0.992
#> GSM872299 1 0.0000 0.9167 1.000 0.000 0.000 0.000
#> GSM872300 4 0.4477 0.5556 0.312 0.000 0.000 0.688
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.0000 0.9557 0.000 0.000 1.000 0.000 0.000
#> GSM872245 1 0.0162 0.8772 0.996 0.000 0.000 0.000 0.004
#> GSM872246 3 0.0000 0.9557 0.000 0.000 1.000 0.000 0.000
#> GSM872247 3 0.0000 0.9557 0.000 0.000 1.000 0.000 0.000
#> GSM872248 2 0.3508 0.7520 0.000 0.748 0.000 0.000 0.252
#> GSM872249 3 0.0000 0.9557 0.000 0.000 1.000 0.000 0.000
#> GSM872250 5 0.4335 0.4148 0.000 0.168 0.072 0.000 0.760
#> GSM872251 3 0.0000 0.9557 0.000 0.000 1.000 0.000 0.000
#> GSM872252 1 0.0912 0.8618 0.972 0.000 0.000 0.012 0.016
#> GSM872253 3 0.1331 0.9169 0.000 0.008 0.952 0.000 0.040
#> GSM872254 2 0.0609 0.8755 0.000 0.980 0.000 0.000 0.020
#> GSM872255 4 0.3857 0.5549 0.312 0.000 0.000 0.688 0.000
#> GSM872256 1 0.0000 0.8794 1.000 0.000 0.000 0.000 0.000
#> GSM872257 2 0.0000 0.8819 0.000 1.000 0.000 0.000 0.000
#> GSM872258 3 0.0000 0.9557 0.000 0.000 1.000 0.000 0.000
#> GSM872259 1 0.0000 0.8794 1.000 0.000 0.000 0.000 0.000
#> GSM872260 1 0.4262 -0.0411 0.560 0.000 0.000 0.440 0.000
#> GSM872261 2 0.1956 0.8517 0.008 0.916 0.000 0.000 0.076
#> GSM872262 4 0.3074 0.6663 0.196 0.000 0.000 0.804 0.000
#> GSM872263 3 0.0000 0.9557 0.000 0.000 1.000 0.000 0.000
#> GSM872264 4 0.5154 0.2840 0.000 0.000 0.048 0.580 0.372
#> GSM872265 4 0.5405 0.4082 0.104 0.000 0.000 0.640 0.256
#> GSM872266 2 0.3452 0.7601 0.000 0.756 0.000 0.000 0.244
#> GSM872267 2 0.3508 0.7520 0.000 0.748 0.000 0.000 0.252
#> GSM872268 3 0.0000 0.9557 0.000 0.000 1.000 0.000 0.000
#> GSM872269 2 0.3109 0.7062 0.000 0.800 0.000 0.000 0.200
#> GSM872270 3 0.0000 0.9557 0.000 0.000 1.000 0.000 0.000
#> GSM872271 2 0.2605 0.8317 0.000 0.852 0.000 0.000 0.148
#> GSM872272 2 0.2732 0.8252 0.000 0.840 0.000 0.000 0.160
#> GSM872273 1 0.0290 0.8746 0.992 0.000 0.000 0.008 0.000
#> GSM872274 2 0.0000 0.8819 0.000 1.000 0.000 0.000 0.000
#> GSM872275 3 0.2848 0.8171 0.000 0.104 0.868 0.000 0.028
#> GSM872276 4 0.3143 0.6650 0.204 0.000 0.000 0.796 0.000
#> GSM872277 1 0.1478 0.8157 0.936 0.000 0.000 0.064 0.000
#> GSM872278 3 0.0000 0.9557 0.000 0.000 1.000 0.000 0.000
#> GSM872279 1 0.0000 0.8794 1.000 0.000 0.000 0.000 0.000
#> GSM872280 3 0.4262 0.2346 0.000 0.000 0.560 0.440 0.000
#> GSM872281 4 0.1732 0.5984 0.000 0.000 0.000 0.920 0.080
#> GSM872282 3 0.0000 0.9557 0.000 0.000 1.000 0.000 0.000
#> GSM872283 1 0.6430 0.0459 0.480 0.000 0.000 0.328 0.192
#> GSM872284 4 0.3480 0.5004 0.000 0.000 0.000 0.752 0.248
#> GSM872285 3 0.0000 0.9557 0.000 0.000 1.000 0.000 0.000
#> GSM872286 5 0.4306 0.0168 0.492 0.000 0.000 0.000 0.508
#> GSM872287 3 0.0000 0.9557 0.000 0.000 1.000 0.000 0.000
#> GSM872288 5 0.1981 0.4346 0.000 0.000 0.028 0.048 0.924
#> GSM872289 3 0.0000 0.9557 0.000 0.000 1.000 0.000 0.000
#> GSM872290 1 0.0000 0.8794 1.000 0.000 0.000 0.000 0.000
#> GSM872291 4 0.4287 0.2419 0.460 0.000 0.000 0.540 0.000
#> GSM872292 2 0.0000 0.8819 0.000 1.000 0.000 0.000 0.000
#> GSM872293 1 0.0000 0.8794 1.000 0.000 0.000 0.000 0.000
#> GSM872294 2 0.0000 0.8819 0.000 1.000 0.000 0.000 0.000
#> GSM872295 2 0.0510 0.8771 0.000 0.984 0.000 0.000 0.016
#> GSM872296 2 0.0000 0.8819 0.000 1.000 0.000 0.000 0.000
#> GSM872297 1 0.0000 0.8794 1.000 0.000 0.000 0.000 0.000
#> GSM872298 4 0.0963 0.6352 0.036 0.000 0.000 0.964 0.000
#> GSM872299 1 0.0162 0.8772 0.996 0.000 0.000 0.000 0.004
#> GSM872300 4 0.3143 0.6650 0.204 0.000 0.000 0.796 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.0146 0.973 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM872245 1 0.0937 0.926 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM872246 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872247 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872248 2 0.6129 0.514 0.000 0.536 0.000 0.116 0.296 0.052
#> GSM872249 3 0.0146 0.973 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM872250 5 0.0858 0.636 0.000 0.028 0.000 0.004 0.968 0.000
#> GSM872251 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872252 1 0.3652 0.800 0.816 0.000 0.000 0.084 0.020 0.080
#> GSM872253 3 0.3766 0.809 0.000 0.008 0.820 0.084 0.064 0.024
#> GSM872254 2 0.1788 0.714 0.000 0.928 0.000 0.028 0.040 0.004
#> GSM872255 6 0.2300 0.793 0.144 0.000 0.000 0.000 0.000 0.856
#> GSM872256 1 0.0146 0.955 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM872257 2 0.0000 0.732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872258 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872259 1 0.0146 0.955 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM872260 6 0.3271 0.712 0.232 0.000 0.000 0.008 0.000 0.760
#> GSM872261 2 0.6451 0.534 0.032 0.604 0.000 0.188 0.096 0.080
#> GSM872262 6 0.2257 0.798 0.116 0.000 0.000 0.008 0.000 0.876
#> GSM872263 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872264 4 0.3996 0.650 0.000 0.000 0.036 0.780 0.036 0.148
#> GSM872265 4 0.4001 0.686 0.112 0.000 0.000 0.760 0.000 0.128
#> GSM872266 2 0.6116 0.518 0.000 0.540 0.000 0.116 0.292 0.052
#> GSM872267 2 0.6169 0.516 0.000 0.536 0.000 0.124 0.288 0.052
#> GSM872268 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872269 2 0.5840 0.428 0.000 0.616 0.000 0.148 0.184 0.052
#> GSM872270 3 0.0146 0.973 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM872271 2 0.6072 0.565 0.000 0.584 0.000 0.184 0.180 0.052
#> GSM872272 2 0.6098 0.561 0.000 0.580 0.000 0.188 0.180 0.052
#> GSM872273 1 0.0260 0.953 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM872274 2 0.0000 0.732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872275 3 0.3676 0.791 0.000 0.120 0.816 0.032 0.024 0.008
#> GSM872276 6 0.2346 0.800 0.124 0.000 0.000 0.008 0.000 0.868
#> GSM872277 1 0.0458 0.947 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM872278 3 0.0291 0.971 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM872279 1 0.0291 0.953 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM872280 6 0.3795 0.342 0.000 0.000 0.364 0.004 0.000 0.632
#> GSM872281 6 0.3563 0.304 0.000 0.000 0.000 0.336 0.000 0.664
#> GSM872282 3 0.0146 0.973 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM872283 4 0.4552 0.390 0.388 0.000 0.000 0.572 0.000 0.040
#> GSM872284 4 0.3309 0.618 0.000 0.000 0.000 0.720 0.000 0.280
#> GSM872285 3 0.0146 0.972 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM872286 5 0.3515 0.463 0.324 0.000 0.000 0.000 0.676 0.000
#> GSM872287 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872288 5 0.2730 0.607 0.000 0.000 0.012 0.152 0.836 0.000
#> GSM872289 3 0.0146 0.972 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM872290 1 0.0405 0.953 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM872291 6 0.2933 0.754 0.200 0.000 0.000 0.004 0.000 0.796
#> GSM872292 2 0.0000 0.732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872293 1 0.0000 0.954 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872294 2 0.2677 0.686 0.000 0.884 0.000 0.056 0.024 0.036
#> GSM872295 2 0.1642 0.716 0.000 0.936 0.000 0.028 0.032 0.004
#> GSM872296 2 0.0000 0.732 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872297 1 0.0146 0.955 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM872298 6 0.2629 0.742 0.060 0.000 0.000 0.068 0.000 0.872
#> GSM872299 1 0.2760 0.854 0.872 0.000 0.000 0.068 0.008 0.052
#> GSM872300 6 0.2302 0.800 0.120 0.000 0.000 0.008 0.000 0.872
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 time(p) individual(p) k
#> ATC:skmeans 52 0.389 1.27e-02 2
#> ATC:skmeans 56 0.724 1.67e-02 3
#> ATC:skmeans 54 0.634 2.57e-03 4
#> ATC:skmeans 48 0.938 1.39e-03 5
#> ATC:skmeans 52 0.880 3.17e-07 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 29485 rows and 57 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 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 0.981 0.985 0.3448 0.662 0.662
#> 3 3 0.999 0.957 0.982 0.8394 0.709 0.561
#> 4 4 0.957 0.947 0.977 0.1743 0.872 0.661
#> 5 5 0.960 0.943 0.977 0.0392 0.972 0.892
#> 6 6 0.836 0.468 0.815 0.0506 0.932 0.730
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
#> GSM872244 2 0.0000 0.977 0.000 1.000
#> GSM872245 1 0.1633 0.982 0.976 0.024
#> GSM872246 2 0.1633 0.991 0.024 0.976
#> GSM872247 2 0.1633 0.991 0.024 0.976
#> GSM872248 1 0.1633 0.982 0.976 0.024
#> GSM872249 2 0.1633 0.991 0.024 0.976
#> GSM872250 1 0.1633 0.982 0.976 0.024
#> GSM872251 2 0.1633 0.991 0.024 0.976
#> GSM872252 1 0.0000 0.986 1.000 0.000
#> GSM872253 1 0.0000 0.986 1.000 0.000
#> GSM872254 1 0.1633 0.982 0.976 0.024
#> GSM872255 1 0.0000 0.986 1.000 0.000
#> GSM872256 1 0.0000 0.986 1.000 0.000
#> GSM872257 1 0.1633 0.982 0.976 0.024
#> GSM872258 2 0.2948 0.969 0.052 0.948
#> GSM872259 1 0.0000 0.986 1.000 0.000
#> GSM872260 1 0.0000 0.986 1.000 0.000
#> GSM872261 1 0.1633 0.982 0.976 0.024
#> GSM872262 1 0.0000 0.986 1.000 0.000
#> GSM872263 2 0.1633 0.991 0.024 0.976
#> GSM872264 1 0.0000 0.986 1.000 0.000
#> GSM872265 1 0.0000 0.986 1.000 0.000
#> GSM872266 1 0.1633 0.982 0.976 0.024
#> GSM872267 1 0.1633 0.982 0.976 0.024
#> GSM872268 2 0.1633 0.991 0.024 0.976
#> GSM872269 1 0.1633 0.982 0.976 0.024
#> GSM872270 2 0.0938 0.986 0.012 0.988
#> GSM872271 1 0.1633 0.982 0.976 0.024
#> GSM872272 1 0.1633 0.982 0.976 0.024
#> GSM872273 1 0.0000 0.986 1.000 0.000
#> GSM872274 1 0.1633 0.982 0.976 0.024
#> GSM872275 1 0.0672 0.985 0.992 0.008
#> GSM872276 1 0.0000 0.986 1.000 0.000
#> GSM872277 1 0.0000 0.986 1.000 0.000
#> GSM872278 1 0.0000 0.986 1.000 0.000
#> GSM872279 1 0.0000 0.986 1.000 0.000
#> GSM872280 1 0.0000 0.986 1.000 0.000
#> GSM872281 1 0.0000 0.986 1.000 0.000
#> GSM872282 2 0.0000 0.977 0.000 1.000
#> GSM872283 1 0.0000 0.986 1.000 0.000
#> GSM872284 1 0.0000 0.986 1.000 0.000
#> GSM872285 1 0.6712 0.778 0.824 0.176
#> GSM872286 1 0.1633 0.982 0.976 0.024
#> GSM872287 2 0.1633 0.991 0.024 0.976
#> GSM872288 1 0.0000 0.986 1.000 0.000
#> GSM872289 2 0.2043 0.986 0.032 0.968
#> GSM872290 1 0.0000 0.986 1.000 0.000
#> GSM872291 1 0.0000 0.986 1.000 0.000
#> GSM872292 1 0.1633 0.982 0.976 0.024
#> GSM872293 1 0.0000 0.986 1.000 0.000
#> GSM872294 1 0.1633 0.982 0.976 0.024
#> GSM872295 1 0.1633 0.982 0.976 0.024
#> GSM872296 1 0.1633 0.982 0.976 0.024
#> GSM872297 1 0.0000 0.986 1.000 0.000
#> GSM872298 1 0.0000 0.986 1.000 0.000
#> GSM872299 1 0.1414 0.982 0.980 0.020
#> GSM872300 1 0.0000 0.986 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.988 0.000 0.000 1.000
#> GSM872245 2 0.0000 0.997 0.000 1.000 0.000
#> GSM872246 3 0.0000 0.988 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.988 0.000 0.000 1.000
#> GSM872248 2 0.0000 0.997 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.988 0.000 0.000 1.000
#> GSM872250 2 0.0000 0.997 0.000 1.000 0.000
#> GSM872251 3 0.0000 0.988 0.000 0.000 1.000
#> GSM872252 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872253 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872254 2 0.0000 0.997 0.000 1.000 0.000
#> GSM872255 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872256 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872257 2 0.0000 0.997 0.000 1.000 0.000
#> GSM872258 3 0.2878 0.884 0.096 0.000 0.904
#> GSM872259 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872260 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872261 2 0.1529 0.948 0.040 0.960 0.000
#> GSM872262 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872263 3 0.0000 0.988 0.000 0.000 1.000
#> GSM872264 1 0.2625 0.892 0.916 0.084 0.000
#> GSM872265 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872266 2 0.0000 0.997 0.000 1.000 0.000
#> GSM872267 2 0.0000 0.997 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.988 0.000 0.000 1.000
#> GSM872269 2 0.0000 0.997 0.000 1.000 0.000
#> GSM872270 3 0.0000 0.988 0.000 0.000 1.000
#> GSM872271 2 0.0000 0.997 0.000 1.000 0.000
#> GSM872272 2 0.0000 0.997 0.000 1.000 0.000
#> GSM872273 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872274 2 0.0000 0.997 0.000 1.000 0.000
#> GSM872275 1 0.6062 0.399 0.616 0.384 0.000
#> GSM872276 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872277 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872278 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872279 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872280 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872281 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872282 3 0.0000 0.988 0.000 0.000 1.000
#> GSM872283 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872284 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872285 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872286 1 0.4235 0.792 0.824 0.176 0.000
#> GSM872287 3 0.0000 0.988 0.000 0.000 1.000
#> GSM872288 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872289 3 0.0747 0.974 0.016 0.000 0.984
#> GSM872290 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872291 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872292 2 0.0000 0.997 0.000 1.000 0.000
#> GSM872293 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872294 2 0.0000 0.997 0.000 1.000 0.000
#> GSM872295 2 0.0000 0.997 0.000 1.000 0.000
#> GSM872296 2 0.0000 0.997 0.000 1.000 0.000
#> GSM872297 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872298 1 0.0000 0.966 1.000 0.000 0.000
#> GSM872299 1 0.5098 0.682 0.752 0.248 0.000
#> GSM872300 1 0.0000 0.966 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.000 0.978 0.000 0.000 1.000 0.000
#> GSM872245 1 0.000 0.953 1.000 0.000 0.000 0.000
#> GSM872246 3 0.000 0.978 0.000 0.000 1.000 0.000
#> GSM872247 3 0.000 0.978 0.000 0.000 1.000 0.000
#> GSM872248 2 0.000 0.996 0.000 1.000 0.000 0.000
#> GSM872249 3 0.000 0.978 0.000 0.000 1.000 0.000
#> GSM872250 2 0.000 0.996 0.000 1.000 0.000 0.000
#> GSM872251 3 0.000 0.978 0.000 0.000 1.000 0.000
#> GSM872252 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872253 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872254 2 0.000 0.996 0.000 1.000 0.000 0.000
#> GSM872255 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872256 1 0.000 0.953 1.000 0.000 0.000 0.000
#> GSM872257 2 0.000 0.996 0.000 1.000 0.000 0.000
#> GSM872258 3 0.317 0.797 0.000 0.000 0.840 0.160
#> GSM872259 1 0.000 0.953 1.000 0.000 0.000 0.000
#> GSM872260 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872261 2 0.130 0.944 0.000 0.956 0.000 0.044
#> GSM872262 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872263 3 0.000 0.978 0.000 0.000 1.000 0.000
#> GSM872264 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872265 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872266 2 0.000 0.996 0.000 1.000 0.000 0.000
#> GSM872267 2 0.000 0.996 0.000 1.000 0.000 0.000
#> GSM872268 3 0.000 0.978 0.000 0.000 1.000 0.000
#> GSM872269 2 0.000 0.996 0.000 1.000 0.000 0.000
#> GSM872270 3 0.000 0.978 0.000 0.000 1.000 0.000
#> GSM872271 2 0.000 0.996 0.000 1.000 0.000 0.000
#> GSM872272 2 0.000 0.996 0.000 1.000 0.000 0.000
#> GSM872273 1 0.000 0.953 1.000 0.000 0.000 0.000
#> GSM872274 2 0.000 0.996 0.000 1.000 0.000 0.000
#> GSM872275 4 0.428 0.616 0.000 0.280 0.000 0.720
#> GSM872276 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872277 1 0.000 0.953 1.000 0.000 0.000 0.000
#> GSM872278 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872279 1 0.000 0.953 1.000 0.000 0.000 0.000
#> GSM872280 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872281 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872282 3 0.000 0.978 0.000 0.000 1.000 0.000
#> GSM872283 4 0.365 0.730 0.204 0.000 0.000 0.796
#> GSM872284 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872285 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872286 4 0.281 0.832 0.000 0.132 0.000 0.868
#> GSM872287 3 0.000 0.978 0.000 0.000 1.000 0.000
#> GSM872288 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872289 3 0.112 0.945 0.000 0.000 0.964 0.036
#> GSM872290 1 0.000 0.953 1.000 0.000 0.000 0.000
#> GSM872291 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872292 2 0.000 0.996 0.000 1.000 0.000 0.000
#> GSM872293 1 0.000 0.953 1.000 0.000 0.000 0.000
#> GSM872294 2 0.000 0.996 0.000 1.000 0.000 0.000
#> GSM872295 2 0.000 0.996 0.000 1.000 0.000 0.000
#> GSM872296 2 0.000 0.996 0.000 1.000 0.000 0.000
#> GSM872297 1 0.000 0.953 1.000 0.000 0.000 0.000
#> GSM872298 4 0.000 0.964 0.000 0.000 0.000 1.000
#> GSM872299 1 0.701 0.412 0.552 0.300 0.000 0.148
#> GSM872300 4 0.000 0.964 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.0000 0.975 0.000 0 1.000 0.000 0.000
#> GSM872245 1 0.0000 0.944 1.000 0 0.000 0.000 0.000
#> GSM872246 3 0.0000 0.975 0.000 0 1.000 0.000 0.000
#> GSM872247 3 0.0000 0.975 0.000 0 1.000 0.000 0.000
#> GSM872248 5 0.0000 0.994 0.000 0 0.000 0.000 1.000
#> GSM872249 3 0.0000 0.975 0.000 0 1.000 0.000 0.000
#> GSM872250 5 0.0000 0.994 0.000 0 0.000 0.000 1.000
#> GSM872251 3 0.0000 0.975 0.000 0 1.000 0.000 0.000
#> GSM872252 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872253 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872254 5 0.0000 0.994 0.000 0 0.000 0.000 1.000
#> GSM872255 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872256 1 0.0000 0.944 1.000 0 0.000 0.000 0.000
#> GSM872257 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM872258 3 0.2732 0.763 0.000 0 0.840 0.160 0.000
#> GSM872259 1 0.0000 0.944 1.000 0 0.000 0.000 0.000
#> GSM872260 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872261 5 0.1121 0.935 0.000 0 0.000 0.044 0.956
#> GSM872262 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872263 3 0.0000 0.975 0.000 0 1.000 0.000 0.000
#> GSM872264 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872265 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872266 5 0.0000 0.994 0.000 0 0.000 0.000 1.000
#> GSM872267 5 0.0000 0.994 0.000 0 0.000 0.000 1.000
#> GSM872268 3 0.0000 0.975 0.000 0 1.000 0.000 0.000
#> GSM872269 5 0.0000 0.994 0.000 0 0.000 0.000 1.000
#> GSM872270 3 0.0000 0.975 0.000 0 1.000 0.000 0.000
#> GSM872271 5 0.0000 0.994 0.000 0 0.000 0.000 1.000
#> GSM872272 5 0.0000 0.994 0.000 0 0.000 0.000 1.000
#> GSM872273 1 0.0000 0.944 1.000 0 0.000 0.000 0.000
#> GSM872274 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM872275 4 0.3684 0.615 0.000 0 0.000 0.720 0.280
#> GSM872276 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872277 1 0.0000 0.944 1.000 0 0.000 0.000 0.000
#> GSM872278 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872279 1 0.0000 0.944 1.000 0 0.000 0.000 0.000
#> GSM872280 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872281 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872282 3 0.0000 0.975 0.000 0 1.000 0.000 0.000
#> GSM872283 4 0.3143 0.729 0.204 0 0.000 0.796 0.000
#> GSM872284 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872285 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872286 4 0.2424 0.827 0.000 0 0.000 0.868 0.132
#> GSM872287 3 0.0000 0.975 0.000 0 1.000 0.000 0.000
#> GSM872288 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872289 3 0.0963 0.937 0.000 0 0.964 0.036 0.000
#> GSM872290 1 0.0000 0.944 1.000 0 0.000 0.000 0.000
#> GSM872291 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872292 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM872293 1 0.0000 0.944 1.000 0 0.000 0.000 0.000
#> GSM872294 5 0.0000 0.994 0.000 0 0.000 0.000 1.000
#> GSM872295 5 0.0000 0.994 0.000 0 0.000 0.000 1.000
#> GSM872296 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM872297 1 0.0000 0.944 1.000 0 0.000 0.000 0.000
#> GSM872298 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
#> GSM872299 1 0.6039 0.383 0.552 0 0.000 0.148 0.300
#> GSM872300 4 0.0000 0.963 0.000 0 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.000 0.805 0.000 0 1.000 0.000 0.000 0.000
#> GSM872245 4 0.386 0.000 0.480 0 0.000 0.520 0.000 0.000
#> GSM872246 3 0.300 0.838 0.000 0 0.772 0.228 0.000 0.000
#> GSM872247 3 0.300 0.838 0.000 0 0.772 0.228 0.000 0.000
#> GSM872248 5 0.000 0.887 0.000 0 0.000 0.000 1.000 0.000
#> GSM872249 3 0.000 0.805 0.000 0 1.000 0.000 0.000 0.000
#> GSM872250 5 0.000 0.887 0.000 0 0.000 0.000 1.000 0.000
#> GSM872251 3 0.386 0.712 0.000 0 0.524 0.476 0.000 0.000
#> GSM872252 6 0.000 0.433 0.000 0 0.000 0.000 0.000 1.000
#> GSM872253 6 0.315 0.156 0.000 0 0.000 0.252 0.000 0.748
#> GSM872254 5 0.000 0.887 0.000 0 0.000 0.000 1.000 0.000
#> GSM872255 6 0.382 0.794 0.432 0 0.000 0.000 0.000 0.568
#> GSM872256 1 0.382 -0.799 0.568 0 0.000 0.432 0.000 0.000
#> GSM872257 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM872258 3 0.386 0.709 0.000 0 0.520 0.480 0.000 0.000
#> GSM872259 1 0.382 -0.799 0.568 0 0.000 0.432 0.000 0.000
#> GSM872260 6 0.382 0.794 0.432 0 0.000 0.000 0.000 0.568
#> GSM872261 5 0.101 0.843 0.000 0 0.000 0.000 0.956 0.044
#> GSM872262 6 0.382 0.794 0.432 0 0.000 0.000 0.000 0.568
#> GSM872263 3 0.000 0.805 0.000 0 1.000 0.000 0.000 0.000
#> GSM872264 6 0.382 0.794 0.432 0 0.000 0.000 0.000 0.568
#> GSM872265 6 0.382 0.794 0.432 0 0.000 0.000 0.000 0.568
#> GSM872266 5 0.000 0.887 0.000 0 0.000 0.000 1.000 0.000
#> GSM872267 5 0.000 0.887 0.000 0 0.000 0.000 1.000 0.000
#> GSM872268 3 0.300 0.838 0.000 0 0.772 0.228 0.000 0.000
#> GSM872269 5 0.444 0.455 0.000 0 0.000 0.028 0.540 0.432
#> GSM872270 3 0.171 0.826 0.000 0 0.908 0.092 0.000 0.000
#> GSM872271 5 0.000 0.887 0.000 0 0.000 0.000 1.000 0.000
#> GSM872272 5 0.000 0.887 0.000 0 0.000 0.000 1.000 0.000
#> GSM872273 1 0.382 -0.799 0.568 0 0.000 0.432 0.000 0.000
#> GSM872274 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM872275 1 0.765 -0.304 0.308 0 0.000 0.232 0.272 0.188
#> GSM872276 6 0.382 0.794 0.432 0 0.000 0.000 0.000 0.568
#> GSM872277 1 0.382 -0.799 0.568 0 0.000 0.432 0.000 0.000
#> GSM872278 6 0.382 0.794 0.432 0 0.000 0.000 0.000 0.568
#> GSM872279 1 0.562 -0.307 0.480 0 0.000 0.152 0.000 0.368
#> GSM872280 6 0.414 0.784 0.432 0 0.000 0.012 0.000 0.556
#> GSM872281 6 0.382 0.794 0.432 0 0.000 0.000 0.000 0.568
#> GSM872282 3 0.000 0.805 0.000 0 1.000 0.000 0.000 0.000
#> GSM872283 1 0.366 -0.577 0.636 0 0.000 0.000 0.000 0.364
#> GSM872284 6 0.382 0.794 0.432 0 0.000 0.000 0.000 0.568
#> GSM872285 1 0.599 -0.582 0.432 0 0.000 0.248 0.000 0.320
#> GSM872286 6 0.000 0.433 0.000 0 0.000 0.000 0.000 1.000
#> GSM872287 3 0.300 0.838 0.000 0 0.772 0.228 0.000 0.000
#> GSM872288 6 0.382 0.794 0.432 0 0.000 0.000 0.000 0.568
#> GSM872289 3 0.386 0.709 0.000 0 0.520 0.480 0.000 0.000
#> GSM872290 1 0.526 -0.412 0.568 0 0.000 0.124 0.000 0.308
#> GSM872291 6 0.000 0.433 0.000 0 0.000 0.000 0.000 1.000
#> GSM872292 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM872293 1 0.382 -0.799 0.568 0 0.000 0.432 0.000 0.000
#> GSM872294 5 0.518 0.394 0.000 0 0.000 0.088 0.480 0.432
#> GSM872295 5 0.000 0.887 0.000 0 0.000 0.000 1.000 0.000
#> GSM872296 2 0.000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM872297 1 0.382 -0.799 0.568 0 0.000 0.432 0.000 0.000
#> GSM872298 6 0.382 0.794 0.432 0 0.000 0.000 0.000 0.568
#> GSM872299 6 0.689 -0.418 0.296 0 0.000 0.088 0.168 0.448
#> GSM872300 6 0.382 0.794 0.432 0 0.000 0.000 0.000 0.568
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 time(p) individual(p) k
#> ATC:pam 57 0.387 0.000693 2
#> ATC:pam 56 0.512 0.001825 3
#> ATC:pam 56 0.862 0.000532 4
#> ATC:pam 56 0.861 0.004198 5
#> ATC:pam 38 0.632 0.016196 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 29485 rows and 57 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.982 0.992 0.3856 0.623 0.623
#> 3 3 0.626 0.811 0.889 0.4033 0.600 0.473
#> 4 4 0.927 0.912 0.967 0.3062 0.713 0.460
#> 5 5 0.948 0.915 0.952 0.0528 0.902 0.687
#> 6 6 0.923 0.898 0.950 0.0489 0.975 0.900
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 4 5
There is also optional best \(k\) = 2 4 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM872244 1 0.000 0.989 1.000 0.000
#> GSM872245 1 0.000 0.989 1.000 0.000
#> GSM872246 1 0.000 0.989 1.000 0.000
#> GSM872247 1 0.000 0.989 1.000 0.000
#> GSM872248 2 0.000 1.000 0.000 1.000
#> GSM872249 1 0.000 0.989 1.000 0.000
#> GSM872250 1 0.000 0.989 1.000 0.000
#> GSM872251 1 0.000 0.989 1.000 0.000
#> GSM872252 1 0.000 0.989 1.000 0.000
#> GSM872253 1 0.000 0.989 1.000 0.000
#> GSM872254 2 0.000 1.000 0.000 1.000
#> GSM872255 1 0.000 0.989 1.000 0.000
#> GSM872256 1 0.000 0.989 1.000 0.000
#> GSM872257 2 0.000 1.000 0.000 1.000
#> GSM872258 1 0.000 0.989 1.000 0.000
#> GSM872259 1 0.000 0.989 1.000 0.000
#> GSM872260 1 0.000 0.989 1.000 0.000
#> GSM872261 1 0.900 0.539 0.684 0.316
#> GSM872262 1 0.000 0.989 1.000 0.000
#> GSM872263 1 0.000 0.989 1.000 0.000
#> GSM872264 2 0.000 1.000 0.000 1.000
#> GSM872265 1 0.506 0.871 0.888 0.112
#> GSM872266 2 0.000 1.000 0.000 1.000
#> GSM872267 2 0.000 1.000 0.000 1.000
#> GSM872268 1 0.000 0.989 1.000 0.000
#> GSM872269 2 0.000 1.000 0.000 1.000
#> GSM872270 1 0.000 0.989 1.000 0.000
#> GSM872271 2 0.000 1.000 0.000 1.000
#> GSM872272 2 0.000 1.000 0.000 1.000
#> GSM872273 1 0.000 0.989 1.000 0.000
#> GSM872274 2 0.000 1.000 0.000 1.000
#> GSM872275 1 0.000 0.989 1.000 0.000
#> GSM872276 1 0.000 0.989 1.000 0.000
#> GSM872277 1 0.000 0.989 1.000 0.000
#> GSM872278 1 0.000 0.989 1.000 0.000
#> GSM872279 1 0.000 0.989 1.000 0.000
#> GSM872280 1 0.000 0.989 1.000 0.000
#> GSM872281 1 0.000 0.989 1.000 0.000
#> GSM872282 1 0.000 0.989 1.000 0.000
#> GSM872283 1 0.000 0.989 1.000 0.000
#> GSM872284 1 0.141 0.971 0.980 0.020
#> GSM872285 1 0.000 0.989 1.000 0.000
#> GSM872286 1 0.000 0.989 1.000 0.000
#> GSM872287 1 0.000 0.989 1.000 0.000
#> GSM872288 1 0.000 0.989 1.000 0.000
#> GSM872289 1 0.000 0.989 1.000 0.000
#> GSM872290 1 0.000 0.989 1.000 0.000
#> GSM872291 1 0.000 0.989 1.000 0.000
#> GSM872292 2 0.000 1.000 0.000 1.000
#> GSM872293 1 0.000 0.989 1.000 0.000
#> GSM872294 2 0.000 1.000 0.000 1.000
#> GSM872295 2 0.000 1.000 0.000 1.000
#> GSM872296 2 0.000 1.000 0.000 1.000
#> GSM872297 1 0.000 0.989 1.000 0.000
#> GSM872298 1 0.000 0.989 1.000 0.000
#> GSM872299 1 0.000 0.989 1.000 0.000
#> GSM872300 1 0.000 0.989 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.838 0.000 0.000 1.000
#> GSM872245 1 0.5678 0.712 0.684 0.316 0.000
#> GSM872246 3 0.5706 0.678 0.320 0.000 0.680
#> GSM872247 3 0.0000 0.838 0.000 0.000 1.000
#> GSM872248 2 0.0592 0.983 0.012 0.988 0.000
#> GSM872249 3 0.0000 0.838 0.000 0.000 1.000
#> GSM872250 1 0.5929 0.706 0.676 0.320 0.004
#> GSM872251 3 0.5706 0.678 0.320 0.000 0.680
#> GSM872252 1 0.5678 0.712 0.684 0.316 0.000
#> GSM872253 1 0.5678 0.712 0.684 0.316 0.000
#> GSM872254 2 0.0237 0.994 0.004 0.996 0.000
#> GSM872255 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872256 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872257 2 0.0000 0.995 0.000 1.000 0.000
#> GSM872258 3 0.5810 0.662 0.336 0.000 0.664
#> GSM872259 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872260 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872261 1 0.5733 0.705 0.676 0.324 0.000
#> GSM872262 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872263 3 0.0000 0.838 0.000 0.000 1.000
#> GSM872264 1 0.5254 0.744 0.736 0.264 0.000
#> GSM872265 1 0.4750 0.769 0.784 0.216 0.000
#> GSM872266 1 0.5733 0.705 0.676 0.324 0.000
#> GSM872267 1 0.5785 0.695 0.668 0.332 0.000
#> GSM872268 3 0.0000 0.838 0.000 0.000 1.000
#> GSM872269 1 0.5733 0.705 0.676 0.324 0.000
#> GSM872270 3 0.0000 0.838 0.000 0.000 1.000
#> GSM872271 1 0.5733 0.705 0.676 0.324 0.000
#> GSM872272 1 0.5733 0.705 0.676 0.324 0.000
#> GSM872273 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872274 2 0.0000 0.995 0.000 1.000 0.000
#> GSM872275 1 0.5929 0.706 0.676 0.320 0.004
#> GSM872276 1 0.1964 0.827 0.944 0.056 0.000
#> GSM872277 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872278 1 0.0237 0.836 0.996 0.000 0.004
#> GSM872279 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872280 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872281 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872282 3 0.0000 0.838 0.000 0.000 1.000
#> GSM872283 1 0.2165 0.825 0.936 0.064 0.000
#> GSM872284 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872285 1 0.0237 0.836 0.996 0.000 0.004
#> GSM872286 1 0.4399 0.781 0.812 0.188 0.000
#> GSM872287 3 0.0000 0.838 0.000 0.000 1.000
#> GSM872288 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872289 3 0.5810 0.662 0.336 0.000 0.664
#> GSM872290 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872291 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872292 2 0.0000 0.995 0.000 1.000 0.000
#> GSM872293 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872294 1 0.5733 0.705 0.676 0.324 0.000
#> GSM872295 2 0.0237 0.994 0.004 0.996 0.000
#> GSM872296 2 0.0000 0.995 0.000 1.000 0.000
#> GSM872297 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872298 1 0.0000 0.838 1.000 0.000 0.000
#> GSM872299 1 0.5678 0.712 0.684 0.316 0.000
#> GSM872300 1 0.0000 0.838 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872245 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM872246 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872247 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872248 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM872249 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872250 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872251 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872252 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872253 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872254 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM872255 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872256 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM872257 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM872258 4 0.0336 0.978 0.000 0.000 0.008 0.992
#> GSM872259 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM872260 4 0.3837 0.670 0.224 0.000 0.000 0.776
#> GSM872261 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872262 1 0.4955 0.266 0.556 0.000 0.000 0.444
#> GSM872263 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872264 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872265 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872266 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872267 2 0.4431 0.593 0.000 0.696 0.000 0.304
#> GSM872268 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872269 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872270 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872271 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872272 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872273 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM872274 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM872275 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872276 1 0.3486 0.733 0.812 0.000 0.000 0.188
#> GSM872277 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM872278 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872279 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM872280 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872281 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872282 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872283 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM872284 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872285 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872286 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872287 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM872288 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872289 4 0.1118 0.947 0.000 0.000 0.036 0.964
#> GSM872290 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM872291 1 0.3975 0.673 0.760 0.000 0.000 0.240
#> GSM872292 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM872293 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM872294 2 0.5132 0.275 0.004 0.548 0.000 0.448
#> GSM872295 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM872296 2 0.0000 0.874 0.000 1.000 0.000 0.000
#> GSM872297 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM872298 4 0.0000 0.986 0.000 0.000 0.000 1.000
#> GSM872299 1 0.0000 0.910 1.000 0.000 0.000 0.000
#> GSM872300 4 0.0000 0.986 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.0000 0.9983 0.000 0.000 1.000 0.000 0.000
#> GSM872245 1 0.1608 0.9078 0.928 0.000 0.000 0.072 0.000
#> GSM872246 3 0.0000 0.9983 0.000 0.000 1.000 0.000 0.000
#> GSM872247 3 0.0000 0.9983 0.000 0.000 1.000 0.000 0.000
#> GSM872248 5 0.2922 0.9151 0.000 0.072 0.000 0.056 0.872
#> GSM872249 3 0.0000 0.9983 0.000 0.000 1.000 0.000 0.000
#> GSM872250 4 0.0290 0.9464 0.000 0.000 0.000 0.992 0.008
#> GSM872251 3 0.0510 0.9843 0.000 0.000 0.984 0.000 0.016
#> GSM872252 4 0.0000 0.9483 0.000 0.000 0.000 1.000 0.000
#> GSM872253 4 0.0404 0.9451 0.000 0.000 0.000 0.988 0.012
#> GSM872254 2 0.2179 0.9274 0.004 0.896 0.000 0.000 0.100
#> GSM872255 4 0.0000 0.9483 0.000 0.000 0.000 1.000 0.000
#> GSM872256 1 0.1608 0.9078 0.928 0.000 0.000 0.072 0.000
#> GSM872257 2 0.0000 0.9648 0.000 1.000 0.000 0.000 0.000
#> GSM872258 4 0.1571 0.9018 0.000 0.000 0.004 0.936 0.060
#> GSM872259 1 0.0162 0.8944 0.996 0.000 0.000 0.004 0.000
#> GSM872260 4 0.1121 0.9132 0.044 0.000 0.000 0.956 0.000
#> GSM872261 4 0.0000 0.9483 0.000 0.000 0.000 1.000 0.000
#> GSM872262 4 0.2516 0.8037 0.140 0.000 0.000 0.860 0.000
#> GSM872263 3 0.0000 0.9983 0.000 0.000 1.000 0.000 0.000
#> GSM872264 4 0.0000 0.9483 0.000 0.000 0.000 1.000 0.000
#> GSM872265 4 0.0000 0.9483 0.000 0.000 0.000 1.000 0.000
#> GSM872266 5 0.2563 0.9423 0.000 0.008 0.000 0.120 0.872
#> GSM872267 5 0.2927 0.9292 0.000 0.060 0.000 0.068 0.872
#> GSM872268 3 0.0000 0.9983 0.000 0.000 1.000 0.000 0.000
#> GSM872269 4 0.1908 0.8836 0.000 0.000 0.000 0.908 0.092
#> GSM872270 3 0.0000 0.9983 0.000 0.000 1.000 0.000 0.000
#> GSM872271 5 0.2377 0.9400 0.000 0.000 0.000 0.128 0.872
#> GSM872272 5 0.2377 0.9400 0.000 0.000 0.000 0.128 0.872
#> GSM872273 1 0.0162 0.8944 0.996 0.000 0.000 0.004 0.000
#> GSM872274 2 0.0000 0.9648 0.000 1.000 0.000 0.000 0.000
#> GSM872275 4 0.0290 0.9464 0.000 0.000 0.000 0.992 0.008
#> GSM872276 1 0.4114 0.4459 0.624 0.000 0.000 0.376 0.000
#> GSM872277 1 0.1671 0.9054 0.924 0.000 0.000 0.076 0.000
#> GSM872278 4 0.0510 0.9432 0.000 0.000 0.000 0.984 0.016
#> GSM872279 1 0.1608 0.9078 0.928 0.000 0.000 0.072 0.000
#> GSM872280 4 0.0510 0.9432 0.000 0.000 0.000 0.984 0.016
#> GSM872281 4 0.0000 0.9483 0.000 0.000 0.000 1.000 0.000
#> GSM872282 3 0.0000 0.9983 0.000 0.000 1.000 0.000 0.000
#> GSM872283 1 0.1732 0.9021 0.920 0.000 0.000 0.080 0.000
#> GSM872284 4 0.0000 0.9483 0.000 0.000 0.000 1.000 0.000
#> GSM872285 4 0.0609 0.9407 0.000 0.000 0.000 0.980 0.020
#> GSM872286 4 0.0000 0.9483 0.000 0.000 0.000 1.000 0.000
#> GSM872287 3 0.0000 0.9983 0.000 0.000 1.000 0.000 0.000
#> GSM872288 4 0.0000 0.9483 0.000 0.000 0.000 1.000 0.000
#> GSM872289 4 0.2193 0.8824 0.000 0.000 0.028 0.912 0.060
#> GSM872290 1 0.0162 0.8944 0.996 0.000 0.000 0.004 0.000
#> GSM872291 4 0.4287 0.0239 0.460 0.000 0.000 0.540 0.000
#> GSM872292 2 0.0000 0.9648 0.000 1.000 0.000 0.000 0.000
#> GSM872293 1 0.0162 0.8944 0.996 0.000 0.000 0.004 0.000
#> GSM872294 5 0.1894 0.9254 0.000 0.008 0.000 0.072 0.920
#> GSM872295 2 0.2179 0.9274 0.004 0.896 0.000 0.000 0.100
#> GSM872296 2 0.0000 0.9648 0.000 1.000 0.000 0.000 0.000
#> GSM872297 1 0.0162 0.8944 0.996 0.000 0.000 0.004 0.000
#> GSM872298 4 0.0000 0.9483 0.000 0.000 0.000 1.000 0.000
#> GSM872299 1 0.1608 0.9078 0.928 0.000 0.000 0.072 0.000
#> GSM872300 4 0.0000 0.9483 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872245 1 0.0146 0.893 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM872246 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872247 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872248 4 0.1327 0.915 0.000 0.064 0.000 0.936 0.000 0.000
#> GSM872249 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872250 6 0.0790 0.921 0.000 0.000 0.000 0.000 0.032 0.968
#> GSM872251 3 0.0632 0.972 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM872252 6 0.0000 0.922 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872253 6 0.0790 0.921 0.000 0.000 0.000 0.000 0.032 0.968
#> GSM872254 5 0.0993 0.976 0.000 0.012 0.000 0.024 0.964 0.000
#> GSM872255 6 0.0000 0.922 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872256 1 0.0146 0.893 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM872257 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872258 6 0.0790 0.921 0.000 0.000 0.000 0.000 0.032 0.968
#> GSM872259 1 0.0000 0.894 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872260 6 0.0458 0.917 0.016 0.000 0.000 0.000 0.000 0.984
#> GSM872261 6 0.0547 0.920 0.000 0.000 0.000 0.020 0.000 0.980
#> GSM872262 6 0.1663 0.863 0.088 0.000 0.000 0.000 0.000 0.912
#> GSM872263 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872264 6 0.2902 0.766 0.000 0.000 0.000 0.196 0.004 0.800
#> GSM872265 6 0.2902 0.766 0.000 0.000 0.000 0.196 0.004 0.800
#> GSM872266 4 0.0000 0.979 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872267 4 0.0000 0.979 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872268 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872269 5 0.0891 0.969 0.000 0.000 0.000 0.024 0.968 0.008
#> GSM872270 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872271 4 0.0000 0.979 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872272 4 0.0000 0.979 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM872273 1 0.0000 0.894 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872274 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872275 6 0.0790 0.921 0.000 0.000 0.000 0.000 0.032 0.968
#> GSM872276 1 0.3843 0.129 0.548 0.000 0.000 0.000 0.000 0.452
#> GSM872277 1 0.0713 0.877 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM872278 6 0.0790 0.921 0.000 0.000 0.000 0.000 0.032 0.968
#> GSM872279 1 0.0146 0.893 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM872280 6 0.0790 0.921 0.000 0.000 0.000 0.000 0.032 0.968
#> GSM872281 6 0.1958 0.861 0.000 0.000 0.000 0.100 0.004 0.896
#> GSM872282 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872283 1 0.3582 0.679 0.768 0.000 0.000 0.196 0.000 0.036
#> GSM872284 6 0.2902 0.766 0.000 0.000 0.000 0.196 0.004 0.800
#> GSM872285 6 0.0790 0.921 0.000 0.000 0.000 0.000 0.032 0.968
#> GSM872286 6 0.0000 0.922 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872287 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM872288 6 0.0000 0.922 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872289 6 0.1245 0.913 0.000 0.000 0.016 0.000 0.032 0.952
#> GSM872290 1 0.0000 0.894 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872291 6 0.3756 0.244 0.400 0.000 0.000 0.000 0.000 0.600
#> GSM872292 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872293 1 0.0000 0.894 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872294 5 0.1531 0.952 0.000 0.000 0.000 0.068 0.928 0.004
#> GSM872295 5 0.0993 0.976 0.000 0.012 0.000 0.024 0.964 0.000
#> GSM872296 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM872297 1 0.0000 0.894 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM872298 6 0.0000 0.922 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM872299 1 0.2902 0.713 0.800 0.000 0.000 0.000 0.196 0.004
#> GSM872300 6 0.0000 0.922 0.000 0.000 0.000 0.000 0.000 1.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 time(p) individual(p) k
#> ATC:mclust 57 0.292 0.173506 2
#> ATC:mclust 57 0.456 0.000197 3
#> ATC:mclust 55 0.748 0.000299 4
#> ATC:mclust 55 0.623 0.000143 5
#> ATC:mclust 55 0.565 0.005855 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 29485 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.999 0.961 0.983 0.4762 0.526 0.526
#> 3 3 0.952 0.928 0.971 0.3874 0.790 0.611
#> 4 4 0.693 0.716 0.843 0.1180 0.857 0.616
#> 5 5 0.645 0.570 0.754 0.0706 0.937 0.769
#> 6 6 0.769 0.630 0.822 0.0486 0.883 0.543
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
#> GSM872244 1 0.0000 0.984 1.000 0.000
#> GSM872245 2 0.0000 0.981 0.000 1.000
#> GSM872246 1 0.0000 0.984 1.000 0.000
#> GSM872247 1 0.0000 0.984 1.000 0.000
#> GSM872248 2 0.0938 0.972 0.012 0.988
#> GSM872249 1 0.0000 0.984 1.000 0.000
#> GSM872250 1 0.2423 0.951 0.960 0.040
#> GSM872251 1 0.0000 0.984 1.000 0.000
#> GSM872252 2 0.0000 0.981 0.000 1.000
#> GSM872253 1 0.0000 0.984 1.000 0.000
#> GSM872254 2 0.0376 0.978 0.004 0.996
#> GSM872255 2 0.0000 0.981 0.000 1.000
#> GSM872256 2 0.0000 0.981 0.000 1.000
#> GSM872257 2 0.0000 0.981 0.000 1.000
#> GSM872258 1 0.0000 0.984 1.000 0.000
#> GSM872259 2 0.0000 0.981 0.000 1.000
#> GSM872260 2 0.0000 0.981 0.000 1.000
#> GSM872261 2 0.0000 0.981 0.000 1.000
#> GSM872262 2 0.0000 0.981 0.000 1.000
#> GSM872263 1 0.0000 0.984 1.000 0.000
#> GSM872264 1 0.7528 0.722 0.784 0.216
#> GSM872265 2 0.0000 0.981 0.000 1.000
#> GSM872266 2 0.0000 0.981 0.000 1.000
#> GSM872267 2 0.0000 0.981 0.000 1.000
#> GSM872268 1 0.0000 0.984 1.000 0.000
#> GSM872269 2 0.3114 0.930 0.056 0.944
#> GSM872270 1 0.0000 0.984 1.000 0.000
#> GSM872271 2 0.0000 0.981 0.000 1.000
#> GSM872272 2 0.0672 0.975 0.008 0.992
#> GSM872273 2 0.0000 0.981 0.000 1.000
#> GSM872274 2 0.0000 0.981 0.000 1.000
#> GSM872275 1 0.0000 0.984 1.000 0.000
#> GSM872276 2 0.0000 0.981 0.000 1.000
#> GSM872277 2 0.0000 0.981 0.000 1.000
#> GSM872278 1 0.0000 0.984 1.000 0.000
#> GSM872279 2 0.0000 0.981 0.000 1.000
#> GSM872280 1 0.0000 0.984 1.000 0.000
#> GSM872281 2 0.6973 0.765 0.188 0.812
#> GSM872282 1 0.0000 0.984 1.000 0.000
#> GSM872283 2 0.0000 0.981 0.000 1.000
#> GSM872284 2 0.0000 0.981 0.000 1.000
#> GSM872285 1 0.0000 0.984 1.000 0.000
#> GSM872286 2 0.0000 0.981 0.000 1.000
#> GSM872287 1 0.0000 0.984 1.000 0.000
#> GSM872288 2 0.9522 0.408 0.372 0.628
#> GSM872289 1 0.0000 0.984 1.000 0.000
#> GSM872290 2 0.0000 0.981 0.000 1.000
#> GSM872291 2 0.0000 0.981 0.000 1.000
#> GSM872292 1 0.0000 0.984 1.000 0.000
#> GSM872293 2 0.0000 0.981 0.000 1.000
#> GSM872294 2 0.0000 0.981 0.000 1.000
#> GSM872295 1 0.2778 0.944 0.952 0.048
#> GSM872296 2 0.0000 0.981 0.000 1.000
#> GSM872297 2 0.0000 0.981 0.000 1.000
#> GSM872298 2 0.0000 0.981 0.000 1.000
#> GSM872299 2 0.0000 0.981 0.000 1.000
#> GSM872300 2 0.0000 0.981 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM872244 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872245 1 0.0592 0.957 0.988 0.012 0.000
#> GSM872246 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872247 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872248 2 0.0000 1.000 0.000 1.000 0.000
#> GSM872249 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872250 3 0.5733 0.542 0.000 0.324 0.676
#> GSM872251 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872252 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872253 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872254 2 0.0000 1.000 0.000 1.000 0.000
#> GSM872255 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872256 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872257 2 0.0000 1.000 0.000 1.000 0.000
#> GSM872258 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872259 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872260 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872261 1 0.6168 0.311 0.588 0.412 0.000
#> GSM872262 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872263 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872264 3 0.5016 0.663 0.240 0.000 0.760
#> GSM872265 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872266 2 0.0000 1.000 0.000 1.000 0.000
#> GSM872267 2 0.0000 1.000 0.000 1.000 0.000
#> GSM872268 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872269 2 0.0000 1.000 0.000 1.000 0.000
#> GSM872270 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872271 2 0.0000 1.000 0.000 1.000 0.000
#> GSM872272 2 0.0000 1.000 0.000 1.000 0.000
#> GSM872273 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872274 2 0.0000 1.000 0.000 1.000 0.000
#> GSM872275 3 0.5859 0.507 0.000 0.344 0.656
#> GSM872276 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872277 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872278 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872279 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872280 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872281 1 0.1031 0.946 0.976 0.000 0.024
#> GSM872282 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872283 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872284 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872285 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872286 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872287 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872288 1 0.5733 0.504 0.676 0.000 0.324
#> GSM872289 3 0.0000 0.947 0.000 0.000 1.000
#> GSM872290 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872291 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872292 2 0.0000 1.000 0.000 1.000 0.000
#> GSM872293 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872294 2 0.0000 1.000 0.000 1.000 0.000
#> GSM872295 2 0.0000 1.000 0.000 1.000 0.000
#> GSM872296 2 0.0000 1.000 0.000 1.000 0.000
#> GSM872297 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872298 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872299 1 0.0000 0.967 1.000 0.000 0.000
#> GSM872300 1 0.0000 0.967 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM872244 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM872245 1 0.3105 0.777 0.868 0.012 0.000 0.120
#> GSM872246 3 0.0469 0.883 0.000 0.000 0.988 0.012
#> GSM872247 3 0.1940 0.883 0.000 0.000 0.924 0.076
#> GSM872248 2 0.3764 0.604 0.000 0.784 0.000 0.216
#> GSM872249 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM872250 3 0.4911 0.530 0.008 0.280 0.704 0.008
#> GSM872251 3 0.1389 0.885 0.000 0.000 0.952 0.048
#> GSM872252 1 0.3801 0.708 0.780 0.000 0.000 0.220
#> GSM872253 3 0.5973 0.648 0.052 0.024 0.700 0.224
#> GSM872254 2 0.0188 0.798 0.000 0.996 0.000 0.004
#> GSM872255 1 0.3610 0.728 0.800 0.000 0.000 0.200
#> GSM872256 1 0.2081 0.819 0.916 0.000 0.000 0.084
#> GSM872257 2 0.0000 0.799 0.000 1.000 0.000 0.000
#> GSM872258 3 0.1302 0.867 0.000 0.000 0.956 0.044
#> GSM872259 1 0.1211 0.847 0.960 0.000 0.000 0.040
#> GSM872260 1 0.3764 0.712 0.784 0.000 0.000 0.216
#> GSM872261 2 0.5427 0.204 0.416 0.568 0.000 0.016
#> GSM872262 1 0.0592 0.856 0.984 0.000 0.000 0.016
#> GSM872263 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM872264 4 0.4948 0.639 0.124 0.000 0.100 0.776
#> GSM872265 4 0.4500 0.600 0.316 0.000 0.000 0.684
#> GSM872266 2 0.3726 0.611 0.000 0.788 0.000 0.212
#> GSM872267 4 0.4790 0.375 0.000 0.380 0.000 0.620
#> GSM872268 3 0.2011 0.882 0.000 0.000 0.920 0.080
#> GSM872269 2 0.6488 0.487 0.004 0.648 0.128 0.220
#> GSM872270 3 0.2647 0.868 0.000 0.000 0.880 0.120
#> GSM872271 4 0.4843 0.337 0.000 0.396 0.000 0.604
#> GSM872272 4 0.4889 0.404 0.004 0.360 0.000 0.636
#> GSM872273 1 0.4103 0.557 0.744 0.000 0.000 0.256
#> GSM872274 2 0.0000 0.799 0.000 1.000 0.000 0.000
#> GSM872275 2 0.4804 0.294 0.000 0.616 0.384 0.000
#> GSM872276 1 0.0469 0.856 0.988 0.000 0.000 0.012
#> GSM872277 1 0.4843 0.142 0.604 0.000 0.000 0.396
#> GSM872278 3 0.2760 0.864 0.000 0.000 0.872 0.128
#> GSM872279 1 0.0921 0.848 0.972 0.000 0.000 0.028
#> GSM872280 3 0.6931 0.502 0.184 0.000 0.588 0.228
#> GSM872281 4 0.6796 0.574 0.252 0.000 0.152 0.596
#> GSM872282 3 0.1867 0.883 0.000 0.000 0.928 0.072
#> GSM872283 4 0.4713 0.538 0.360 0.000 0.000 0.640
#> GSM872284 4 0.4560 0.619 0.296 0.000 0.004 0.700
#> GSM872285 3 0.2345 0.876 0.000 0.000 0.900 0.100
#> GSM872286 1 0.0469 0.856 0.988 0.000 0.000 0.012
#> GSM872287 3 0.2760 0.864 0.000 0.000 0.872 0.128
#> GSM872288 4 0.7760 0.487 0.276 0.000 0.288 0.436
#> GSM872289 3 0.1792 0.854 0.000 0.000 0.932 0.068
#> GSM872290 1 0.0000 0.855 1.000 0.000 0.000 0.000
#> GSM872291 1 0.1211 0.843 0.960 0.000 0.000 0.040
#> GSM872292 2 0.0000 0.799 0.000 1.000 0.000 0.000
#> GSM872293 1 0.1022 0.850 0.968 0.000 0.000 0.032
#> GSM872294 2 0.0188 0.798 0.000 0.996 0.000 0.004
#> GSM872295 2 0.0000 0.799 0.000 1.000 0.000 0.000
#> GSM872296 2 0.0469 0.794 0.000 0.988 0.000 0.012
#> GSM872297 1 0.2081 0.819 0.916 0.000 0.000 0.084
#> GSM872298 1 0.1305 0.849 0.960 0.000 0.004 0.036
#> GSM872299 1 0.4079 0.728 0.800 0.020 0.000 0.180
#> GSM872300 1 0.0336 0.856 0.992 0.000 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM872244 3 0.0566 0.7778 0.000 0.000 0.984 0.004 0.012
#> GSM872245 1 0.3687 0.5624 0.792 0.000 0.000 0.180 0.028
#> GSM872246 3 0.2628 0.7728 0.000 0.000 0.884 0.028 0.088
#> GSM872247 3 0.3106 0.7535 0.000 0.000 0.844 0.024 0.132
#> GSM872248 4 0.6126 0.4178 0.016 0.344 0.008 0.560 0.072
#> GSM872249 3 0.0290 0.7805 0.000 0.000 0.992 0.000 0.008
#> GSM872250 3 0.6723 0.2723 0.032 0.008 0.592 0.180 0.188
#> GSM872251 3 0.1117 0.7868 0.000 0.000 0.964 0.020 0.016
#> GSM872252 5 0.4307 -0.2959 0.496 0.000 0.000 0.000 0.504
#> GSM872253 5 0.5071 0.2190 0.028 0.004 0.420 0.000 0.548
#> GSM872254 2 0.2286 0.8096 0.000 0.888 0.000 0.004 0.108
#> GSM872255 1 0.4327 0.4039 0.632 0.000 0.000 0.008 0.360
#> GSM872256 1 0.0703 0.6999 0.976 0.000 0.000 0.024 0.000
#> GSM872257 2 0.0000 0.8832 0.000 1.000 0.000 0.000 0.000
#> GSM872258 3 0.1952 0.7526 0.000 0.000 0.912 0.004 0.084
#> GSM872259 1 0.0290 0.7009 0.992 0.000 0.000 0.008 0.000
#> GSM872260 1 0.4210 0.2966 0.588 0.000 0.000 0.000 0.412
#> GSM872261 2 0.5699 0.3411 0.264 0.608 0.000 0.000 0.128
#> GSM872262 1 0.6261 0.3759 0.524 0.000 0.000 0.180 0.296
#> GSM872263 3 0.0290 0.7805 0.000 0.000 0.992 0.000 0.008
#> GSM872264 4 0.1560 0.5760 0.020 0.000 0.028 0.948 0.004
#> GSM872265 4 0.4269 0.5454 0.188 0.000 0.000 0.756 0.056
#> GSM872266 4 0.5603 0.4125 0.008 0.356 0.000 0.572 0.064
#> GSM872267 4 0.5678 0.5338 0.040 0.260 0.000 0.648 0.052
#> GSM872268 3 0.4555 0.6893 0.000 0.000 0.732 0.068 0.200
#> GSM872269 5 0.7084 0.3043 0.076 0.272 0.120 0.000 0.532
#> GSM872270 3 0.1310 0.7869 0.000 0.000 0.956 0.024 0.020
#> GSM872271 4 0.4446 0.3538 0.000 0.400 0.000 0.592 0.008
#> GSM872272 4 0.4347 0.5754 0.004 0.212 0.000 0.744 0.040
#> GSM872273 1 0.2017 0.6862 0.912 0.000 0.000 0.080 0.008
#> GSM872274 2 0.0000 0.8832 0.000 1.000 0.000 0.000 0.000
#> GSM872275 2 0.2732 0.7058 0.000 0.840 0.160 0.000 0.000
#> GSM872276 1 0.5864 0.4505 0.572 0.000 0.000 0.128 0.300
#> GSM872277 1 0.2727 0.6563 0.868 0.000 0.000 0.116 0.016
#> GSM872278 3 0.6815 0.1400 0.000 0.000 0.360 0.312 0.328
#> GSM872279 1 0.1341 0.6928 0.944 0.000 0.000 0.000 0.056
#> GSM872280 5 0.5468 0.2338 0.072 0.000 0.272 0.012 0.644
#> GSM872281 4 0.7196 0.0466 0.176 0.000 0.036 0.416 0.372
#> GSM872282 3 0.0671 0.7811 0.000 0.000 0.980 0.004 0.016
#> GSM872283 4 0.3814 0.5206 0.276 0.000 0.000 0.720 0.004
#> GSM872284 4 0.4743 0.5198 0.156 0.000 0.000 0.732 0.112
#> GSM872285 3 0.5032 0.6525 0.000 0.000 0.688 0.092 0.220
#> GSM872286 1 0.6707 0.2797 0.596 0.000 0.060 0.148 0.196
#> GSM872287 3 0.4618 0.6843 0.000 0.000 0.724 0.068 0.208
#> GSM872288 4 0.6858 0.4028 0.328 0.000 0.068 0.516 0.088
#> GSM872289 3 0.2886 0.6414 0.000 0.000 0.844 0.008 0.148
#> GSM872290 1 0.1043 0.6966 0.960 0.000 0.000 0.000 0.040
#> GSM872291 1 0.3884 0.5247 0.708 0.000 0.000 0.004 0.288
#> GSM872292 2 0.0000 0.8832 0.000 1.000 0.000 0.000 0.000
#> GSM872293 1 0.0771 0.7003 0.976 0.000 0.000 0.004 0.020
#> GSM872294 2 0.0794 0.8661 0.000 0.972 0.000 0.000 0.028
#> GSM872295 2 0.0000 0.8832 0.000 1.000 0.000 0.000 0.000
#> GSM872296 2 0.0000 0.8832 0.000 1.000 0.000 0.000 0.000
#> GSM872297 1 0.0880 0.6988 0.968 0.000 0.000 0.032 0.000
#> GSM872298 1 0.6037 0.4606 0.612 0.000 0.012 0.232 0.144
#> GSM872299 1 0.3561 0.5086 0.740 0.000 0.000 0.000 0.260
#> GSM872300 1 0.4871 0.5630 0.704 0.000 0.000 0.084 0.212
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM872244 3 0.0520 0.8628 0.000 0.000 0.984 0.000 0.008 0.008
#> GSM872245 1 0.1053 0.7730 0.964 0.012 0.000 0.004 0.020 0.000
#> GSM872246 3 0.2416 0.8603 0.000 0.000 0.844 0.156 0.000 0.000
#> GSM872247 3 0.2234 0.8689 0.000 0.000 0.872 0.124 0.000 0.004
#> GSM872248 5 0.1584 0.7018 0.004 0.032 0.004 0.004 0.944 0.012
#> GSM872249 3 0.0291 0.8661 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM872250 5 0.3857 0.5899 0.004 0.000 0.072 0.000 0.776 0.148
#> GSM872251 3 0.4117 0.8008 0.000 0.000 0.708 0.256 0.020 0.016
#> GSM872252 6 0.1714 0.6665 0.092 0.000 0.000 0.000 0.000 0.908
#> GSM872253 6 0.1925 0.6456 0.000 0.008 0.060 0.008 0.004 0.920
#> GSM872254 2 0.3292 0.7971 0.000 0.824 0.000 0.004 0.052 0.120
#> GSM872255 6 0.5020 0.1898 0.372 0.000 0.000 0.080 0.000 0.548
#> GSM872256 1 0.0146 0.7864 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM872257 2 0.0405 0.9545 0.000 0.988 0.000 0.004 0.000 0.008
#> GSM872258 3 0.1563 0.8752 0.000 0.000 0.932 0.056 0.000 0.012
#> GSM872259 1 0.0291 0.7869 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM872260 6 0.2473 0.6449 0.136 0.000 0.000 0.008 0.000 0.856
#> GSM872261 6 0.4662 0.1253 0.012 0.420 0.000 0.004 0.016 0.548
#> GSM872262 4 0.5097 0.1389 0.420 0.000 0.000 0.508 0.004 0.068
#> GSM872263 3 0.0146 0.8653 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM872264 5 0.3852 0.3671 0.000 0.000 0.000 0.384 0.612 0.004
#> GSM872265 5 0.5260 0.0620 0.072 0.000 0.000 0.456 0.464 0.008
#> GSM872266 5 0.1699 0.7028 0.012 0.040 0.000 0.004 0.936 0.008
#> GSM872267 5 0.1959 0.7003 0.020 0.032 0.000 0.024 0.924 0.000
#> GSM872268 3 0.3508 0.7941 0.000 0.000 0.704 0.292 0.000 0.004
#> GSM872269 6 0.2452 0.6474 0.000 0.056 0.008 0.000 0.044 0.892
#> GSM872270 3 0.1480 0.8734 0.000 0.000 0.940 0.040 0.020 0.000
#> GSM872271 5 0.5510 0.4868 0.000 0.220 0.000 0.164 0.604 0.012
#> GSM872272 5 0.2580 0.6834 0.004 0.036 0.000 0.072 0.884 0.004
#> GSM872273 1 0.0653 0.7833 0.980 0.000 0.000 0.004 0.012 0.004
#> GSM872274 2 0.0146 0.9555 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM872275 2 0.1116 0.9358 0.000 0.960 0.028 0.004 0.000 0.008
#> GSM872276 1 0.5160 -0.1983 0.476 0.000 0.000 0.448 0.004 0.072
#> GSM872277 1 0.0653 0.7834 0.980 0.000 0.000 0.004 0.012 0.004
#> GSM872278 4 0.2206 0.4294 0.000 0.000 0.064 0.904 0.008 0.024
#> GSM872279 1 0.2053 0.7490 0.888 0.000 0.000 0.000 0.004 0.108
#> GSM872280 6 0.4787 0.2591 0.020 0.000 0.020 0.440 0.000 0.520
#> GSM872281 4 0.0653 0.4615 0.004 0.000 0.012 0.980 0.004 0.000
#> GSM872282 3 0.1148 0.8598 0.000 0.000 0.960 0.004 0.020 0.016
#> GSM872283 1 0.5844 0.0936 0.548 0.000 0.000 0.200 0.240 0.012
#> GSM872284 4 0.4362 -0.1207 0.020 0.000 0.000 0.584 0.392 0.004
#> GSM872285 3 0.3634 0.7367 0.000 0.000 0.644 0.356 0.000 0.000
#> GSM872286 5 0.5852 0.1526 0.364 0.000 0.000 0.000 0.440 0.196
#> GSM872287 3 0.3606 0.7988 0.000 0.000 0.708 0.284 0.004 0.004
#> GSM872288 5 0.2262 0.6869 0.036 0.000 0.020 0.000 0.908 0.036
#> GSM872289 3 0.1714 0.8383 0.000 0.000 0.908 0.000 0.000 0.092
#> GSM872290 1 0.1714 0.7576 0.908 0.000 0.000 0.000 0.000 0.092
#> GSM872291 1 0.4620 0.1819 0.532 0.000 0.000 0.040 0.000 0.428
#> GSM872292 2 0.0622 0.9520 0.000 0.980 0.000 0.000 0.008 0.012
#> GSM872293 1 0.0146 0.7865 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM872294 2 0.1155 0.9381 0.000 0.956 0.000 0.004 0.004 0.036
#> GSM872295 2 0.0291 0.9554 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM872296 2 0.0291 0.9554 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM872297 1 0.0260 0.7856 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM872298 4 0.4181 0.0461 0.476 0.000 0.000 0.512 0.000 0.012
#> GSM872299 1 0.3584 0.5126 0.688 0.000 0.000 0.000 0.004 0.308
#> GSM872300 1 0.3045 0.7054 0.840 0.000 0.000 0.100 0.000 0.060
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 time(p) individual(p) k
#> ATC:NMF 56 0.857 0.032726 2
#> ATC:NMF 56 0.388 0.015038 3
#> ATC:NMF 49 0.367 0.001891 4
#> ATC:NMF 39 0.317 0.000234 5
#> ATC:NMF 42 0.585 0.000160 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
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