Date: 2019-12-25 21:13:41 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 21512 rows and 52 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] 21512 52
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:pam | 3 | 1.000 | 0.961 | 0.984 | ** | 2 |
| SD:NMF | 3 | 1.000 | 0.963 | 0.984 | ** | |
| CV:pam | 3 | 1.000 | 0.969 | 0.990 | ** | 2 |
| CV:NMF | 3 | 1.000 | 0.986 | 0.994 | ** | |
| ATC:kmeans | 3 | 1.000 | 0.968 | 0.988 | ** | 2 |
| ATC:pam | 2 | 1.000 | 0.997 | 0.999 | ** | |
| MAD:pam | 3 | 0.999 | 0.956 | 0.981 | ** | 2 |
| CV:skmeans | 4 | 0.964 | 0.936 | 0.973 | ** | 2,3 |
| MAD:skmeans | 4 | 0.961 | 0.942 | 0.975 | ** | 2 |
| SD:skmeans | 4 | 0.942 | 0.892 | 0.958 | * | 2,3 |
| ATC:skmeans | 4 | 0.923 | 0.890 | 0.954 | * | 2,3 |
| MAD:NMF | 2 | 0.920 | 0.945 | 0.974 | * | |
| MAD:mclust | 5 | 0.786 | 0.774 | 0.893 | ||
| MAD:kmeans | 3 | 0.742 | 0.902 | 0.932 | ||
| MAD:hclust | 2 | 0.701 | 0.854 | 0.935 | ||
| SD:kmeans | 3 | 0.693 | 0.883 | 0.928 | ||
| CV:mclust | 3 | 0.679 | 0.834 | 0.910 | ||
| CV:hclust | 2 | 0.675 | 0.893 | 0.944 | ||
| ATC:NMF | 4 | 0.645 | 0.785 | 0.904 | ||
| ATC:hclust | 5 | 0.634 | 0.695 | 0.858 | ||
| CV:kmeans | 3 | 0.631 | 0.867 | 0.901 | ||
| SD:hclust | 2 | 0.618 | 0.892 | 0.938 | ||
| SD:mclust | 3 | 0.543 | 0.665 | 0.855 | ||
| ATC:mclust | 5 | 0.538 | 0.780 | 0.854 |
**: 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 0.707 0.8808 0.947 0.483 0.509 0.509
#> CV:NMF 2 0.778 0.8855 0.952 0.474 0.527 0.527
#> MAD:NMF 2 0.920 0.9447 0.974 0.484 0.509 0.509
#> ATC:NMF 2 0.662 0.9312 0.947 0.239 0.735 0.735
#> SD:skmeans 2 1.000 0.9698 0.987 0.501 0.497 0.497
#> CV:skmeans 2 0.959 0.9492 0.979 0.493 0.509 0.509
#> MAD:skmeans 2 1.000 0.9802 0.991 0.502 0.497 0.497
#> ATC:skmeans 2 0.959 0.9639 0.983 0.496 0.509 0.509
#> SD:mclust 2 0.487 0.6468 0.793 0.389 0.660 0.660
#> CV:mclust 2 0.442 0.7007 0.750 0.405 0.566 0.566
#> MAD:mclust 2 0.453 0.8646 0.894 0.412 0.599 0.599
#> ATC:mclust 2 0.674 0.9132 0.949 0.289 0.683 0.683
#> SD:kmeans 2 0.413 0.8512 0.855 0.415 0.566 0.566
#> CV:kmeans 2 0.470 0.9023 0.901 0.418 0.566 0.566
#> MAD:kmeans 2 0.471 0.8892 0.897 0.435 0.566 0.566
#> ATC:kmeans 2 1.000 0.9500 0.981 0.366 0.638 0.638
#> SD:pam 2 0.959 0.9471 0.978 0.371 0.638 0.638
#> CV:pam 2 0.960 0.9297 0.942 0.385 0.599 0.599
#> MAD:pam 2 0.999 0.9603 0.983 0.390 0.618 0.618
#> ATC:pam 2 1.000 0.9975 0.999 0.339 0.660 0.660
#> SD:hclust 2 0.618 0.8925 0.938 0.413 0.581 0.581
#> CV:hclust 2 0.675 0.8934 0.944 0.394 0.581 0.581
#> MAD:hclust 2 0.701 0.8535 0.935 0.433 0.581 0.581
#> ATC:hclust 2 0.481 0.0879 0.599 0.413 0.683 0.683
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 1.000 0.963 0.984 0.300 0.689 0.481
#> CV:NMF 3 1.000 0.986 0.994 0.312 0.729 0.538
#> MAD:NMF 3 0.770 0.796 0.922 0.335 0.798 0.620
#> ATC:NMF 3 0.895 0.931 0.972 0.651 0.871 0.825
#> SD:skmeans 3 0.978 0.914 0.966 0.305 0.697 0.474
#> CV:skmeans 3 0.969 0.903 0.962 0.324 0.733 0.527
#> MAD:skmeans 3 0.825 0.874 0.944 0.314 0.697 0.474
#> ATC:skmeans 3 0.953 0.928 0.956 0.275 0.821 0.656
#> SD:mclust 3 0.543 0.665 0.855 0.518 0.672 0.512
#> CV:mclust 3 0.679 0.834 0.910 0.445 0.491 0.329
#> MAD:mclust 3 0.588 0.803 0.892 0.563 0.602 0.399
#> ATC:mclust 3 0.455 0.657 0.837 0.608 0.855 0.799
#> SD:kmeans 3 0.693 0.883 0.928 0.470 0.799 0.648
#> CV:kmeans 3 0.631 0.867 0.901 0.432 0.785 0.633
#> MAD:kmeans 3 0.742 0.902 0.932 0.406 0.817 0.676
#> ATC:kmeans 3 1.000 0.968 0.988 0.747 0.684 0.518
#> SD:pam 3 1.000 0.961 0.984 0.635 0.701 0.551
#> CV:pam 3 1.000 0.969 0.990 0.549 0.664 0.496
#> MAD:pam 3 0.999 0.956 0.981 0.594 0.689 0.527
#> ATC:pam 3 0.629 0.705 0.882 0.781 0.618 0.463
#> SD:hclust 3 0.580 0.846 0.925 0.206 0.947 0.909
#> CV:hclust 3 0.623 0.806 0.902 0.269 0.947 0.909
#> MAD:hclust 3 0.745 0.855 0.937 0.129 0.947 0.909
#> ATC:hclust 3 0.466 0.590 0.808 0.267 0.607 0.509
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.662 0.598 0.831 0.1454 0.855 0.637
#> CV:NMF 4 0.713 0.676 0.835 0.1624 0.839 0.591
#> MAD:NMF 4 0.771 0.771 0.883 0.1092 0.837 0.596
#> ATC:NMF 4 0.645 0.785 0.904 0.7185 0.701 0.512
#> SD:skmeans 4 0.942 0.892 0.958 0.1456 0.885 0.680
#> CV:skmeans 4 0.964 0.936 0.973 0.1529 0.885 0.680
#> MAD:skmeans 4 0.961 0.942 0.975 0.1334 0.879 0.668
#> ATC:skmeans 4 0.923 0.890 0.954 0.1167 0.927 0.798
#> SD:mclust 4 0.770 0.856 0.918 0.0197 0.775 0.556
#> CV:mclust 4 0.638 0.341 0.709 0.0826 0.774 0.515
#> MAD:mclust 4 0.870 0.920 0.955 -0.0335 0.761 0.501
#> ATC:mclust 4 0.361 0.408 0.727 0.1490 0.864 0.799
#> SD:kmeans 4 0.705 0.680 0.849 0.1464 0.861 0.655
#> CV:kmeans 4 0.676 0.683 0.841 0.1660 0.826 0.588
#> MAD:kmeans 4 0.747 0.732 0.870 0.1285 0.937 0.837
#> ATC:kmeans 4 0.586 0.599 0.721 0.1180 0.790 0.488
#> SD:pam 4 0.766 0.810 0.916 0.2357 0.784 0.497
#> CV:pam 4 0.732 0.773 0.895 0.2390 0.802 0.530
#> MAD:pam 4 0.787 0.752 0.884 0.2137 0.855 0.631
#> ATC:pam 4 0.572 0.708 0.830 0.1585 0.844 0.617
#> SD:hclust 4 0.602 0.843 0.881 0.2201 0.837 0.692
#> CV:hclust 4 0.640 0.865 0.894 0.1957 0.837 0.692
#> MAD:hclust 4 0.571 0.782 0.861 0.3372 0.837 0.692
#> ATC:hclust 4 0.484 0.701 0.731 0.1734 0.756 0.534
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.670 0.667 0.787 0.0929 0.828 0.482
#> CV:NMF 5 0.681 0.665 0.784 0.0893 0.865 0.548
#> MAD:NMF 5 0.690 0.641 0.745 0.0906 0.851 0.540
#> ATC:NMF 5 0.568 0.597 0.802 0.0765 0.898 0.695
#> SD:skmeans 5 0.810 0.751 0.876 0.0588 0.931 0.744
#> CV:skmeans 5 0.804 0.736 0.878 0.0548 0.941 0.775
#> MAD:skmeans 5 0.799 0.778 0.882 0.0612 0.961 0.846
#> ATC:skmeans 5 0.775 0.778 0.875 0.0930 0.897 0.663
#> SD:mclust 5 0.639 0.636 0.823 0.2003 0.798 0.556
#> CV:mclust 5 0.762 0.742 0.857 0.1606 0.779 0.409
#> MAD:mclust 5 0.786 0.774 0.893 0.1355 0.925 0.807
#> ATC:mclust 5 0.538 0.780 0.854 0.2513 0.652 0.465
#> SD:kmeans 5 0.661 0.702 0.835 0.0854 0.890 0.653
#> CV:kmeans 5 0.684 0.717 0.838 0.0933 0.900 0.678
#> MAD:kmeans 5 0.691 0.635 0.807 0.1013 0.880 0.647
#> ATC:kmeans 5 0.588 0.614 0.755 0.0765 0.922 0.718
#> SD:pam 5 0.734 0.535 0.776 0.0504 0.873 0.578
#> CV:pam 5 0.710 0.582 0.777 0.0520 0.875 0.586
#> MAD:pam 5 0.766 0.671 0.825 0.0514 0.928 0.723
#> ATC:pam 5 0.746 0.793 0.876 0.1046 0.888 0.627
#> SD:hclust 5 0.720 0.740 0.859 0.1515 0.959 0.889
#> CV:hclust 5 0.701 0.820 0.890 0.1477 0.932 0.817
#> MAD:hclust 5 0.651 0.652 0.806 0.1062 0.863 0.642
#> ATC:hclust 5 0.634 0.695 0.858 0.1523 0.956 0.848
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.721 0.730 0.804 0.0516 0.939 0.734
#> CV:NMF 6 0.786 0.751 0.855 0.0470 0.902 0.605
#> MAD:NMF 6 0.738 0.675 0.826 0.0554 0.924 0.666
#> ATC:NMF 6 0.526 0.484 0.746 0.0445 0.900 0.656
#> SD:skmeans 6 0.774 0.683 0.814 0.0376 0.954 0.797
#> CV:skmeans 6 0.768 0.615 0.808 0.0389 0.965 0.838
#> MAD:skmeans 6 0.772 0.638 0.819 0.0397 0.959 0.814
#> ATC:skmeans 6 0.813 0.747 0.857 0.0329 0.987 0.940
#> SD:mclust 6 0.873 0.834 0.929 0.0417 0.909 0.700
#> CV:mclust 6 0.852 0.836 0.922 0.0429 0.885 0.614
#> MAD:mclust 6 0.749 0.701 0.807 0.0733 0.855 0.571
#> ATC:mclust 6 0.649 0.627 0.801 0.1183 0.843 0.578
#> SD:kmeans 6 0.711 0.744 0.813 0.0651 0.953 0.808
#> CV:kmeans 6 0.727 0.754 0.833 0.0554 0.919 0.687
#> MAD:kmeans 6 0.688 0.592 0.757 0.0655 0.941 0.758
#> ATC:kmeans 6 0.619 0.588 0.713 0.0405 0.961 0.835
#> SD:pam 6 0.855 0.774 0.912 0.0477 0.891 0.573
#> CV:pam 6 0.781 0.685 0.860 0.0455 0.904 0.623
#> MAD:pam 6 0.854 0.801 0.911 0.0381 0.959 0.799
#> ATC:pam 6 0.814 0.825 0.902 0.0425 0.971 0.865
#> SD:hclust 6 0.734 0.674 0.827 0.0740 0.911 0.734
#> CV:hclust 6 0.727 0.851 0.884 0.0464 0.991 0.971
#> MAD:hclust 6 0.676 0.556 0.727 0.0539 0.884 0.636
#> ATC:hclust 6 0.639 0.665 0.800 0.0725 0.989 0.957
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 disease.state(p) k
#> SD:NMF 50 2.37e-01 2
#> CV:NMF 50 2.99e-01 2
#> MAD:NMF 51 2.06e-01 2
#> ATC:NMF 51 9.92e-01 2
#> SD:skmeans 52 3.51e-01 2
#> CV:skmeans 51 4.76e-01 2
#> MAD:skmeans 52 3.51e-01 2
#> ATC:skmeans 52 5.14e-01 2
#> SD:mclust 50 4.65e-10 2
#> CV:mclust 51 3.04e-02 2
#> MAD:mclust 49 4.52e-02 2
#> ATC:mclust 52 2.33e-01 2
#> SD:kmeans 52 5.15e-01 2
#> CV:kmeans 52 5.15e-01 2
#> MAD:kmeans 52 5.15e-01 2
#> ATC:kmeans 51 1.00e+00 2
#> SD:pam 51 3.64e-09 2
#> CV:pam 52 5.58e-07 2
#> MAD:pam 52 1.20e-07 2
#> ATC:pam 52 1.00e+00 2
#> SD:hclust 52 2.10e-01 2
#> CV:hclust 52 2.10e-01 2
#> MAD:hclust 48 2.95e-01 2
#> ATC:hclust 10 NA 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) k
#> SD:NMF 52 8.38e-11 3
#> CV:NMF 52 8.38e-11 3
#> MAD:NMF 46 3.44e-08 3
#> ATC:NMF 52 8.85e-01 3
#> SD:skmeans 49 6.32e-08 3
#> CV:skmeans 48 9.12e-08 3
#> MAD:skmeans 50 2.80e-07 3
#> ATC:skmeans 50 8.74e-02 3
#> SD:mclust 40 2.38e-08 3
#> CV:mclust 50 3.28e-09 3
#> MAD:mclust 50 3.37e-05 3
#> ATC:mclust 40 1.00e+00 3
#> SD:kmeans 50 2.53e-10 3
#> CV:kmeans 51 1.60e-10 3
#> MAD:kmeans 51 2.17e-09 3
#> ATC:kmeans 51 6.43e-01 3
#> SD:pam 52 1.15e-08 3
#> CV:pam 51 1.82e-09 3
#> MAD:pam 51 1.89e-09 3
#> ATC:pam 41 5.58e-01 3
#> SD:hclust 51 7.39e-03 3
#> CV:hclust 52 9.08e-03 3
#> MAD:hclust 49 8.29e-03 3
#> ATC:hclust 47 6.23e-01 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) k
#> SD:NMF 37 8.86e-07 4
#> CV:NMF 41 9.19e-08 4
#> MAD:NMF 45 1.14e-05 4
#> ATC:NMF 47 1.14e-01 4
#> SD:skmeans 48 7.35e-08 4
#> CV:skmeans 51 8.58e-07 4
#> MAD:skmeans 52 7.19e-06 4
#> ATC:skmeans 51 1.20e-01 4
#> SD:mclust 51 1.12e-08 4
#> CV:mclust 17 1.55e-03 4
#> MAD:mclust 52 7.78e-09 4
#> ATC:mclust 26 1.19e-02 4
#> SD:kmeans 38 6.55e-08 4
#> CV:kmeans 41 8.21e-08 4
#> MAD:kmeans 46 1.34e-08 4
#> ATC:kmeans 36 2.18e-01 4
#> SD:pam 49 2.10e-08 4
#> CV:pam 44 1.53e-08 4
#> MAD:pam 43 2.59e-07 4
#> ATC:pam 45 6.19e-01 4
#> SD:hclust 51 8.90e-10 4
#> CV:hclust 52 4.65e-10 4
#> MAD:hclust 46 8.29e-09 4
#> ATC:hclust 47 1.21e-01 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) k
#> SD:NMF 41 4.46e-07 5
#> CV:NMF 43 5.48e-06 5
#> MAD:NMF 43 7.53e-06 5
#> ATC:NMF 35 3.79e-02 5
#> SD:skmeans 45 8.83e-07 5
#> CV:skmeans 45 5.17e-08 5
#> MAD:skmeans 46 3.89e-06 5
#> ATC:skmeans 47 4.89e-02 5
#> SD:mclust 38 3.48e-07 5
#> CV:mclust 44 7.17e-08 5
#> MAD:mclust 47 2.16e-08 5
#> ATC:mclust 49 1.16e-02 5
#> SD:kmeans 39 5.59e-07 5
#> CV:kmeans 45 3.96e-08 5
#> MAD:kmeans 37 5.89e-07 5
#> ATC:kmeans 45 3.40e-02 5
#> SD:pam 29 2.37e-04 5
#> CV:pam 36 2.09e-06 5
#> MAD:pam 45 4.32e-07 5
#> ATC:pam 49 7.73e-01 5
#> SD:hclust 49 6.19e-09 5
#> CV:hclust 51 2.54e-09 5
#> MAD:hclust 40 1.07e-07 5
#> ATC:hclust 45 1.63e-01 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) k
#> SD:NMF 48 5.00e-07 6
#> CV:NMF 47 7.36e-07 6
#> MAD:NMF 43 3.44e-06 6
#> ATC:NMF 30 2.41e-02 6
#> SD:skmeans 43 4.14e-07 6
#> CV:skmeans 38 1.15e-06 6
#> MAD:skmeans 42 5.99e-06 6
#> ATC:skmeans 43 1.54e-01 6
#> SD:mclust 48 4.05e-08 6
#> CV:mclust 49 2.64e-08 6
#> MAD:mclust 43 2.07e-07 6
#> ATC:mclust 38 4.70e-02 6
#> SD:kmeans 51 1.02e-08 6
#> CV:kmeans 49 2.23e-08 6
#> MAD:kmeans 37 1.52e-06 6
#> ATC:kmeans 40 7.61e-02 6
#> SD:pam 43 3.33e-07 6
#> CV:pam 40 1.17e-06 6
#> MAD:pam 45 1.30e-06 6
#> ATC:pam 50 8.05e-01 6
#> SD:hclust 44 1.95e-07 6
#> CV:hclust 51 6.96e-09 6
#> MAD:hclust 34 1.58e-06 6
#> ATC:hclust 47 2.72e-01 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 21512 rows and 52 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 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 0.618 0.892 0.938 0.413 0.581 0.581
#> 3 3 0.580 0.846 0.925 0.206 0.947 0.909
#> 4 4 0.602 0.843 0.881 0.220 0.837 0.692
#> 5 5 0.720 0.740 0.859 0.152 0.959 0.889
#> 6 6 0.734 0.674 0.827 0.074 0.911 0.734
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
#> GSM559433 1 0.0000 0.946 1.000 0.000
#> GSM559434 2 0.6247 0.873 0.156 0.844
#> GSM559436 1 0.0000 0.946 1.000 0.000
#> GSM559437 1 0.0000 0.946 1.000 0.000
#> GSM559438 2 0.7883 0.794 0.236 0.764
#> GSM559440 2 0.7883 0.794 0.236 0.764
#> GSM559441 1 0.1414 0.936 0.980 0.020
#> GSM559442 1 0.6048 0.821 0.852 0.148
#> GSM559444 2 0.5946 0.881 0.144 0.856
#> GSM559445 1 0.0000 0.946 1.000 0.000
#> GSM559446 1 0.0000 0.946 1.000 0.000
#> GSM559448 1 0.0000 0.946 1.000 0.000
#> GSM559450 2 0.5946 0.881 0.144 0.856
#> GSM559451 1 0.0000 0.946 1.000 0.000
#> GSM559452 2 0.8207 0.757 0.256 0.744
#> GSM559454 1 0.0000 0.946 1.000 0.000
#> GSM559455 1 0.1414 0.936 0.980 0.020
#> GSM559456 1 0.0000 0.946 1.000 0.000
#> GSM559457 1 0.0000 0.946 1.000 0.000
#> GSM559458 1 0.1414 0.936 0.980 0.020
#> GSM559459 1 0.0000 0.946 1.000 0.000
#> GSM559460 1 0.0000 0.946 1.000 0.000
#> GSM559461 1 0.0000 0.946 1.000 0.000
#> GSM559462 1 0.0000 0.946 1.000 0.000
#> GSM559463 1 0.0000 0.946 1.000 0.000
#> GSM559464 1 0.0000 0.946 1.000 0.000
#> GSM559465 1 0.0000 0.946 1.000 0.000
#> GSM559467 1 0.8267 0.632 0.740 0.260
#> GSM559468 1 0.5629 0.838 0.868 0.132
#> GSM559469 1 0.5946 0.826 0.856 0.144
#> GSM559470 1 0.8608 0.585 0.716 0.284
#> GSM559471 1 0.0672 0.943 0.992 0.008
#> GSM559472 1 0.0000 0.946 1.000 0.000
#> GSM559473 2 0.4161 0.904 0.084 0.916
#> GSM559475 2 0.4161 0.904 0.084 0.916
#> GSM559477 2 0.1414 0.906 0.020 0.980
#> GSM559478 2 0.1414 0.906 0.020 0.980
#> GSM559479 2 0.1414 0.906 0.020 0.980
#> GSM559480 2 0.1414 0.906 0.020 0.980
#> GSM559481 2 0.1414 0.906 0.020 0.980
#> GSM559482 2 0.1414 0.906 0.020 0.980
#> GSM559435 1 0.1414 0.938 0.980 0.020
#> GSM559439 1 0.1414 0.938 0.980 0.020
#> GSM559443 1 0.1414 0.938 0.980 0.020
#> GSM559447 1 0.1414 0.938 0.980 0.020
#> GSM559449 1 0.1414 0.938 0.980 0.020
#> GSM559453 1 0.1414 0.938 0.980 0.020
#> GSM559466 1 0.1414 0.938 0.980 0.020
#> GSM559474 1 0.8608 0.646 0.716 0.284
#> GSM559476 1 0.1414 0.938 0.980 0.020
#> GSM559483 2 0.1414 0.906 0.020 0.980
#> GSM559484 1 0.8608 0.646 0.716 0.284
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0000 0.914 1.000 0.000 0.000
#> GSM559434 2 0.4731 0.824 0.128 0.840 0.032
#> GSM559436 1 0.0000 0.914 1.000 0.000 0.000
#> GSM559437 1 0.0237 0.913 0.996 0.000 0.004
#> GSM559438 2 0.5803 0.734 0.212 0.760 0.028
#> GSM559440 2 0.5803 0.734 0.212 0.760 0.028
#> GSM559441 1 0.1315 0.902 0.972 0.008 0.020
#> GSM559442 1 0.4677 0.791 0.840 0.132 0.028
#> GSM559444 2 0.4397 0.835 0.116 0.856 0.028
#> GSM559445 1 0.0237 0.913 0.996 0.000 0.004
#> GSM559446 1 0.0237 0.913 0.996 0.000 0.004
#> GSM559448 1 0.0000 0.914 1.000 0.000 0.000
#> GSM559450 2 0.4397 0.835 0.116 0.856 0.028
#> GSM559451 1 0.0000 0.914 1.000 0.000 0.000
#> GSM559452 2 0.6402 0.684 0.236 0.724 0.040
#> GSM559454 1 0.0000 0.914 1.000 0.000 0.000
#> GSM559455 1 0.1315 0.902 0.972 0.008 0.020
#> GSM559456 1 0.0000 0.914 1.000 0.000 0.000
#> GSM559457 1 0.0000 0.914 1.000 0.000 0.000
#> GSM559458 1 0.1453 0.900 0.968 0.008 0.024
#> GSM559459 1 0.0000 0.914 1.000 0.000 0.000
#> GSM559460 1 0.0000 0.914 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.914 1.000 0.000 0.000
#> GSM559462 1 0.0000 0.914 1.000 0.000 0.000
#> GSM559463 1 0.0000 0.914 1.000 0.000 0.000
#> GSM559464 1 0.0000 0.914 1.000 0.000 0.000
#> GSM559465 1 0.0000 0.914 1.000 0.000 0.000
#> GSM559467 1 0.5737 0.607 0.732 0.256 0.012
#> GSM559468 1 0.4397 0.807 0.856 0.116 0.028
#> GSM559469 1 0.4609 0.794 0.844 0.128 0.028
#> GSM559470 1 0.5986 0.553 0.704 0.284 0.012
#> GSM559471 1 0.0829 0.909 0.984 0.004 0.012
#> GSM559472 1 0.0237 0.913 0.996 0.000 0.004
#> GSM559473 2 0.2743 0.860 0.052 0.928 0.020
#> GSM559475 2 0.2743 0.860 0.052 0.928 0.020
#> GSM559477 2 0.0000 0.857 0.000 1.000 0.000
#> GSM559478 2 0.0000 0.857 0.000 1.000 0.000
#> GSM559479 2 0.0000 0.857 0.000 1.000 0.000
#> GSM559480 2 0.0000 0.857 0.000 1.000 0.000
#> GSM559481 2 0.0000 0.857 0.000 1.000 0.000
#> GSM559482 2 0.0000 0.857 0.000 1.000 0.000
#> GSM559435 1 0.3551 0.833 0.868 0.000 0.132
#> GSM559439 1 0.3551 0.833 0.868 0.000 0.132
#> GSM559443 1 0.3551 0.833 0.868 0.000 0.132
#> GSM559447 1 0.3551 0.833 0.868 0.000 0.132
#> GSM559449 1 0.3941 0.814 0.844 0.000 0.156
#> GSM559453 1 0.6291 0.221 0.532 0.000 0.468
#> GSM559466 1 0.3551 0.833 0.868 0.000 0.132
#> GSM559474 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559476 1 0.3551 0.833 0.868 0.000 0.132
#> GSM559483 2 0.0000 0.857 0.000 1.000 0.000
#> GSM559484 3 0.0000 1.000 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM559434 2 0.3681 0.748 0.124 0.848 0.024 0.004
#> GSM559436 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM559437 1 0.0188 0.935 0.996 0.004 0.000 0.000
#> GSM559438 2 0.4464 0.672 0.208 0.768 0.024 0.000
#> GSM559440 2 0.4464 0.672 0.208 0.768 0.024 0.000
#> GSM559441 1 0.1297 0.917 0.964 0.016 0.020 0.000
#> GSM559442 1 0.4206 0.775 0.816 0.136 0.048 0.000
#> GSM559444 2 0.3278 0.756 0.116 0.864 0.020 0.000
#> GSM559445 1 0.0188 0.935 0.996 0.004 0.000 0.000
#> GSM559446 1 0.0188 0.935 0.996 0.004 0.000 0.000
#> GSM559448 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM559450 2 0.3278 0.756 0.116 0.864 0.020 0.000
#> GSM559451 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM559452 2 0.5349 0.639 0.212 0.732 0.048 0.008
#> GSM559454 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM559455 1 0.1297 0.917 0.964 0.016 0.020 0.000
#> GSM559456 1 0.0707 0.919 0.980 0.000 0.020 0.000
#> GSM559457 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM559458 1 0.1520 0.911 0.956 0.020 0.024 0.000
#> GSM559459 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM559460 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM559461 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM559462 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM559463 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM559464 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM559465 1 0.0000 0.936 1.000 0.000 0.000 0.000
#> GSM559467 1 0.4576 0.626 0.728 0.260 0.012 0.000
#> GSM559468 1 0.3991 0.793 0.832 0.120 0.048 0.000
#> GSM559469 1 0.4153 0.779 0.820 0.132 0.048 0.000
#> GSM559470 1 0.4770 0.580 0.700 0.288 0.012 0.000
#> GSM559471 1 0.0804 0.928 0.980 0.012 0.008 0.000
#> GSM559472 1 0.0188 0.935 0.996 0.004 0.000 0.000
#> GSM559473 2 0.1474 0.773 0.052 0.948 0.000 0.000
#> GSM559475 2 0.1474 0.773 0.052 0.948 0.000 0.000
#> GSM559477 2 0.3024 0.757 0.000 0.852 0.148 0.000
#> GSM559478 2 0.4008 0.711 0.000 0.756 0.244 0.000
#> GSM559479 2 0.3024 0.757 0.000 0.852 0.148 0.000
#> GSM559480 2 0.4008 0.711 0.000 0.756 0.244 0.000
#> GSM559481 2 0.4008 0.711 0.000 0.756 0.244 0.000
#> GSM559482 2 0.3024 0.757 0.000 0.852 0.148 0.000
#> GSM559435 3 0.4164 0.932 0.264 0.000 0.736 0.000
#> GSM559439 3 0.4164 0.932 0.264 0.000 0.736 0.000
#> GSM559443 3 0.4164 0.932 0.264 0.000 0.736 0.000
#> GSM559447 3 0.4164 0.932 0.264 0.000 0.736 0.000
#> GSM559449 3 0.4776 0.907 0.244 0.000 0.732 0.024
#> GSM559453 3 0.6367 0.348 0.080 0.000 0.584 0.336
#> GSM559466 3 0.4164 0.932 0.264 0.000 0.736 0.000
#> GSM559474 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM559476 3 0.4193 0.927 0.268 0.000 0.732 0.000
#> GSM559483 2 0.3024 0.757 0.000 0.852 0.148 0.000
#> GSM559484 4 0.0000 1.000 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
#> GSM559433 1 0.0510 0.878 0.984 0.000 0.000 0.016 0.000
#> GSM559434 4 0.4805 0.848 0.008 0.432 0.004 0.552 0.004
#> GSM559436 1 0.0000 0.875 1.000 0.000 0.000 0.000 0.000
#> GSM559437 1 0.3224 0.835 0.824 0.000 0.016 0.160 0.000
#> GSM559438 4 0.5566 0.831 0.068 0.364 0.004 0.564 0.000
#> GSM559440 4 0.5566 0.831 0.068 0.364 0.004 0.564 0.000
#> GSM559441 1 0.2890 0.839 0.836 0.000 0.004 0.160 0.000
#> GSM559442 1 0.4310 0.610 0.604 0.000 0.004 0.392 0.000
#> GSM559444 4 0.4273 0.837 0.000 0.448 0.000 0.552 0.000
#> GSM559445 1 0.3224 0.835 0.824 0.000 0.016 0.160 0.000
#> GSM559446 1 0.3224 0.835 0.824 0.000 0.016 0.160 0.000
#> GSM559448 1 0.0000 0.875 1.000 0.000 0.000 0.000 0.000
#> GSM559450 4 0.4273 0.837 0.000 0.448 0.000 0.552 0.000
#> GSM559451 1 0.0404 0.877 0.988 0.000 0.000 0.012 0.000
#> GSM559452 4 0.4299 0.784 0.000 0.316 0.004 0.672 0.008
#> GSM559454 1 0.0000 0.875 1.000 0.000 0.000 0.000 0.000
#> GSM559455 1 0.2890 0.839 0.836 0.000 0.004 0.160 0.000
#> GSM559456 1 0.3970 0.810 0.800 0.000 0.096 0.104 0.000
#> GSM559457 1 0.1197 0.873 0.952 0.000 0.000 0.048 0.000
#> GSM559458 1 0.3123 0.827 0.812 0.000 0.004 0.184 0.000
#> GSM559459 1 0.0000 0.875 1.000 0.000 0.000 0.000 0.000
#> GSM559460 1 0.0162 0.876 0.996 0.000 0.000 0.004 0.000
#> GSM559461 1 0.0162 0.876 0.996 0.000 0.000 0.004 0.000
#> GSM559462 1 0.0404 0.877 0.988 0.000 0.000 0.012 0.000
#> GSM559463 1 0.0000 0.875 1.000 0.000 0.000 0.000 0.000
#> GSM559464 1 0.0162 0.875 0.996 0.000 0.000 0.004 0.000
#> GSM559465 1 0.0162 0.875 0.996 0.000 0.000 0.004 0.000
#> GSM559467 1 0.4299 0.517 0.608 0.000 0.004 0.388 0.000
#> GSM559468 1 0.4251 0.638 0.624 0.000 0.004 0.372 0.000
#> GSM559469 1 0.4288 0.619 0.612 0.000 0.004 0.384 0.000
#> GSM559470 1 0.5002 0.420 0.548 0.024 0.004 0.424 0.000
#> GSM559471 1 0.0955 0.876 0.968 0.000 0.004 0.028 0.000
#> GSM559472 1 0.0404 0.877 0.988 0.000 0.000 0.012 0.000
#> GSM559473 2 0.4273 -0.652 0.000 0.552 0.000 0.448 0.000
#> GSM559475 2 0.4273 -0.652 0.000 0.552 0.000 0.448 0.000
#> GSM559477 2 0.0000 0.599 0.000 1.000 0.000 0.000 0.000
#> GSM559478 2 0.3895 0.526 0.000 0.680 0.000 0.320 0.000
#> GSM559479 2 0.0000 0.599 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.3895 0.526 0.000 0.680 0.000 0.320 0.000
#> GSM559481 2 0.3895 0.526 0.000 0.680 0.000 0.320 0.000
#> GSM559482 2 0.0000 0.599 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.0510 0.945 0.016 0.000 0.984 0.000 0.000
#> GSM559439 3 0.0510 0.945 0.016 0.000 0.984 0.000 0.000
#> GSM559443 3 0.0510 0.945 0.016 0.000 0.984 0.000 0.000
#> GSM559447 3 0.0510 0.945 0.016 0.000 0.984 0.000 0.000
#> GSM559449 3 0.1106 0.929 0.012 0.000 0.964 0.000 0.024
#> GSM559453 3 0.3966 0.502 0.000 0.000 0.664 0.000 0.336
#> GSM559466 3 0.0510 0.945 0.016 0.000 0.984 0.000 0.000
#> GSM559474 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM559476 3 0.0609 0.940 0.020 0.000 0.980 0.000 0.000
#> GSM559483 2 0.0000 0.599 0.000 1.000 0.000 0.000 0.000
#> GSM559484 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.1196 0.672 0.952 0.000 0.000 0.040 0.000 0.008
#> GSM559434 6 0.2445 0.881 0.008 0.120 0.000 0.004 0.000 0.868
#> GSM559436 1 0.0000 0.692 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559437 4 0.4682 0.916 0.396 0.000 0.000 0.556 0.000 0.048
#> GSM559438 6 0.3178 0.839 0.012 0.052 0.000 0.092 0.000 0.844
#> GSM559440 6 0.3178 0.839 0.012 0.052 0.000 0.092 0.000 0.844
#> GSM559441 1 0.4422 0.161 0.680 0.000 0.000 0.252 0.000 0.068
#> GSM559442 1 0.4619 0.227 0.600 0.000 0.000 0.052 0.000 0.348
#> GSM559444 6 0.2234 0.882 0.000 0.124 0.000 0.004 0.000 0.872
#> GSM559445 4 0.4682 0.916 0.396 0.000 0.000 0.556 0.000 0.048
#> GSM559446 4 0.4682 0.916 0.396 0.000 0.000 0.556 0.000 0.048
#> GSM559448 1 0.0000 0.692 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559450 6 0.2234 0.882 0.000 0.124 0.000 0.004 0.000 0.872
#> GSM559451 1 0.2416 0.528 0.844 0.000 0.000 0.156 0.000 0.000
#> GSM559452 6 0.1141 0.761 0.000 0.000 0.000 0.052 0.000 0.948
#> GSM559454 1 0.0000 0.692 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559455 1 0.4422 0.161 0.680 0.000 0.000 0.252 0.000 0.068
#> GSM559456 4 0.5034 0.749 0.404 0.000 0.076 0.520 0.000 0.000
#> GSM559457 1 0.2230 0.618 0.892 0.000 0.000 0.084 0.000 0.024
#> GSM559458 1 0.4663 0.151 0.660 0.000 0.000 0.252 0.000 0.088
#> GSM559459 1 0.0000 0.692 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559460 1 0.0146 0.692 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM559461 1 0.0146 0.692 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM559462 1 0.2378 0.533 0.848 0.000 0.000 0.152 0.000 0.000
#> GSM559463 1 0.0000 0.692 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559464 1 0.0146 0.692 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM559465 1 0.0146 0.692 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM559467 1 0.5855 -0.267 0.448 0.000 0.000 0.200 0.000 0.352
#> GSM559468 1 0.4607 0.251 0.616 0.000 0.000 0.056 0.000 0.328
#> GSM559469 1 0.4687 0.233 0.604 0.000 0.000 0.060 0.000 0.336
#> GSM559470 1 0.6425 -0.307 0.388 0.024 0.000 0.208 0.000 0.380
#> GSM559471 1 0.1168 0.680 0.956 0.000 0.000 0.028 0.000 0.016
#> GSM559472 1 0.0713 0.682 0.972 0.000 0.000 0.028 0.000 0.000
#> GSM559473 6 0.3136 0.804 0.000 0.228 0.000 0.004 0.000 0.768
#> GSM559475 6 0.3136 0.804 0.000 0.228 0.000 0.004 0.000 0.768
#> GSM559477 2 0.4899 0.784 0.000 0.560 0.016 0.388 0.000 0.036
#> GSM559478 2 0.0000 0.695 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559479 2 0.4899 0.784 0.000 0.560 0.016 0.388 0.000 0.036
#> GSM559480 2 0.0000 0.695 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559481 2 0.0000 0.695 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559482 2 0.4899 0.784 0.000 0.560 0.016 0.388 0.000 0.036
#> GSM559435 3 0.0458 0.945 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM559439 3 0.0458 0.945 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM559443 3 0.0458 0.945 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM559447 3 0.0458 0.945 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM559449 3 0.0993 0.929 0.012 0.000 0.964 0.000 0.024 0.000
#> GSM559453 3 0.3563 0.502 0.000 0.000 0.664 0.000 0.336 0.000
#> GSM559466 3 0.0458 0.945 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM559474 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM559476 3 0.0547 0.941 0.020 0.000 0.980 0.000 0.000 0.000
#> GSM559483 2 0.4899 0.784 0.000 0.560 0.016 0.388 0.000 0.036
#> GSM559484 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 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 disease.state(p) k
#> SD:hclust 52 2.10e-01 2
#> SD:hclust 51 7.39e-03 3
#> SD:hclust 51 8.90e-10 4
#> SD:hclust 49 6.19e-09 5
#> SD:hclust 44 1.95e-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", "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 21512 rows and 52 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 0.413 0.851 0.855 0.4153 0.566 0.566
#> 3 3 0.693 0.883 0.928 0.4700 0.799 0.648
#> 4 4 0.705 0.680 0.849 0.1464 0.861 0.655
#> 5 5 0.661 0.702 0.835 0.0854 0.890 0.653
#> 6 6 0.711 0.744 0.813 0.0651 0.953 0.808
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
#> GSM559433 1 0.844 0.872 0.728 0.272
#> GSM559434 2 0.118 0.957 0.016 0.984
#> GSM559436 1 0.844 0.872 0.728 0.272
#> GSM559437 1 0.850 0.869 0.724 0.276
#> GSM559438 2 0.118 0.957 0.016 0.984
#> GSM559440 2 0.118 0.957 0.016 0.984
#> GSM559441 1 0.973 0.709 0.596 0.404
#> GSM559442 1 0.844 0.872 0.728 0.272
#> GSM559444 2 0.000 0.969 0.000 1.000
#> GSM559445 1 0.975 0.702 0.592 0.408
#> GSM559446 1 0.850 0.869 0.724 0.276
#> GSM559448 1 0.839 0.871 0.732 0.268
#> GSM559450 2 0.000 0.969 0.000 1.000
#> GSM559451 1 0.844 0.872 0.728 0.272
#> GSM559452 2 0.118 0.957 0.016 0.984
#> GSM559454 1 0.844 0.872 0.728 0.272
#> GSM559455 1 0.844 0.872 0.728 0.272
#> GSM559456 1 0.605 0.812 0.852 0.148
#> GSM559457 1 0.844 0.872 0.728 0.272
#> GSM559458 1 0.605 0.812 0.852 0.148
#> GSM559459 1 0.844 0.872 0.728 0.272
#> GSM559460 1 0.844 0.872 0.728 0.272
#> GSM559461 1 0.844 0.872 0.728 0.272
#> GSM559462 1 0.844 0.872 0.728 0.272
#> GSM559463 1 0.844 0.872 0.728 0.272
#> GSM559464 1 0.844 0.872 0.728 0.272
#> GSM559465 1 0.827 0.868 0.740 0.260
#> GSM559467 1 0.850 0.869 0.724 0.276
#> GSM559468 1 0.844 0.872 0.728 0.272
#> GSM559469 1 0.844 0.872 0.728 0.272
#> GSM559470 1 0.999 0.556 0.520 0.480
#> GSM559471 1 0.844 0.872 0.728 0.272
#> GSM559472 1 0.844 0.872 0.728 0.272
#> GSM559473 2 0.000 0.969 0.000 1.000
#> GSM559475 2 0.000 0.969 0.000 1.000
#> GSM559477 2 0.000 0.969 0.000 1.000
#> GSM559478 2 0.000 0.969 0.000 1.000
#> GSM559479 2 0.000 0.969 0.000 1.000
#> GSM559480 2 0.000 0.969 0.000 1.000
#> GSM559481 2 0.000 0.969 0.000 1.000
#> GSM559482 2 0.000 0.969 0.000 1.000
#> GSM559435 1 0.000 0.722 1.000 0.000
#> GSM559439 1 0.000 0.722 1.000 0.000
#> GSM559443 1 0.000 0.722 1.000 0.000
#> GSM559447 1 0.000 0.722 1.000 0.000
#> GSM559449 1 0.000 0.722 1.000 0.000
#> GSM559453 1 0.000 0.722 1.000 0.000
#> GSM559466 1 0.000 0.722 1.000 0.000
#> GSM559474 1 0.574 0.603 0.864 0.136
#> GSM559476 1 0.000 0.722 1.000 0.000
#> GSM559483 2 0.000 0.969 0.000 1.000
#> GSM559484 2 0.844 0.635 0.272 0.728
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0237 0.961 0.996 0.000 0.004
#> GSM559434 2 0.5961 0.785 0.096 0.792 0.112
#> GSM559436 1 0.0237 0.961 0.996 0.000 0.004
#> GSM559437 1 0.3267 0.883 0.884 0.000 0.116
#> GSM559438 2 0.8783 0.174 0.420 0.468 0.112
#> GSM559440 2 0.5961 0.785 0.096 0.792 0.112
#> GSM559441 1 0.3267 0.883 0.884 0.000 0.116
#> GSM559442 1 0.0237 0.959 0.996 0.004 0.000
#> GSM559444 2 0.3573 0.855 0.004 0.876 0.120
#> GSM559445 1 0.3845 0.874 0.872 0.012 0.116
#> GSM559446 1 0.3267 0.883 0.884 0.000 0.116
#> GSM559448 1 0.0424 0.958 0.992 0.000 0.008
#> GSM559450 2 0.3573 0.855 0.004 0.876 0.120
#> GSM559451 1 0.0000 0.960 1.000 0.000 0.000
#> GSM559452 2 0.4196 0.847 0.024 0.864 0.112
#> GSM559454 1 0.0237 0.961 0.996 0.000 0.004
#> GSM559455 1 0.1529 0.939 0.960 0.000 0.040
#> GSM559456 1 0.0424 0.960 0.992 0.000 0.008
#> GSM559457 1 0.0237 0.961 0.996 0.000 0.004
#> GSM559458 1 0.0237 0.961 0.996 0.000 0.004
#> GSM559459 1 0.0237 0.961 0.996 0.000 0.004
#> GSM559460 1 0.0237 0.961 0.996 0.000 0.004
#> GSM559461 1 0.0237 0.961 0.996 0.000 0.004
#> GSM559462 1 0.0000 0.960 1.000 0.000 0.000
#> GSM559463 1 0.0424 0.958 0.992 0.000 0.008
#> GSM559464 1 0.0237 0.961 0.996 0.000 0.004
#> GSM559465 1 0.0424 0.958 0.992 0.000 0.008
#> GSM559467 1 0.3349 0.888 0.888 0.004 0.108
#> GSM559468 1 0.0000 0.960 1.000 0.000 0.000
#> GSM559469 1 0.1267 0.947 0.972 0.004 0.024
#> GSM559470 1 0.4136 0.867 0.864 0.020 0.116
#> GSM559471 1 0.0237 0.959 0.996 0.004 0.000
#> GSM559472 1 0.0237 0.961 0.996 0.000 0.004
#> GSM559473 2 0.0661 0.892 0.004 0.988 0.008
#> GSM559475 2 0.0661 0.892 0.004 0.988 0.008
#> GSM559477 2 0.0661 0.891 0.004 0.988 0.008
#> GSM559478 2 0.0237 0.892 0.004 0.996 0.000
#> GSM559479 2 0.0661 0.891 0.004 0.988 0.008
#> GSM559480 2 0.0237 0.892 0.004 0.996 0.000
#> GSM559481 2 0.0237 0.892 0.004 0.996 0.000
#> GSM559482 2 0.0661 0.891 0.004 0.988 0.008
#> GSM559435 3 0.3412 0.917 0.124 0.000 0.876
#> GSM559439 3 0.3412 0.917 0.124 0.000 0.876
#> GSM559443 3 0.3412 0.917 0.124 0.000 0.876
#> GSM559447 3 0.3412 0.917 0.124 0.000 0.876
#> GSM559449 3 0.3412 0.917 0.124 0.000 0.876
#> GSM559453 3 0.3412 0.917 0.124 0.000 0.876
#> GSM559466 3 0.3412 0.917 0.124 0.000 0.876
#> GSM559474 3 0.0829 0.787 0.012 0.004 0.984
#> GSM559476 3 0.4346 0.858 0.184 0.000 0.816
#> GSM559483 2 0.0661 0.891 0.004 0.988 0.008
#> GSM559484 3 0.6095 0.124 0.000 0.392 0.608
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.2011 0.8487 0.920 0.000 0.000 0.080
#> GSM559434 4 0.5636 0.0288 0.024 0.424 0.000 0.552
#> GSM559436 1 0.1302 0.8580 0.956 0.000 0.000 0.044
#> GSM559437 4 0.4830 0.1317 0.392 0.000 0.000 0.608
#> GSM559438 4 0.7779 0.3194 0.356 0.244 0.000 0.400
#> GSM559440 4 0.5769 0.1736 0.036 0.376 0.000 0.588
#> GSM559441 4 0.4967 -0.0500 0.452 0.000 0.000 0.548
#> GSM559442 1 0.1474 0.8537 0.948 0.000 0.000 0.052
#> GSM559444 2 0.4804 0.3856 0.000 0.616 0.000 0.384
#> GSM559445 4 0.3791 0.4873 0.200 0.004 0.000 0.796
#> GSM559446 4 0.3975 0.4467 0.240 0.000 0.000 0.760
#> GSM559448 1 0.0707 0.8528 0.980 0.000 0.000 0.020
#> GSM559450 2 0.4776 0.4031 0.000 0.624 0.000 0.376
#> GSM559451 1 0.1792 0.8545 0.932 0.000 0.000 0.068
#> GSM559452 4 0.6089 0.2168 0.064 0.328 0.000 0.608
#> GSM559454 1 0.0817 0.8645 0.976 0.000 0.000 0.024
#> GSM559455 1 0.4843 0.4351 0.604 0.000 0.000 0.396
#> GSM559456 1 0.4406 0.6184 0.700 0.000 0.000 0.300
#> GSM559457 1 0.2973 0.8025 0.856 0.000 0.000 0.144
#> GSM559458 1 0.4277 0.6123 0.720 0.000 0.000 0.280
#> GSM559459 1 0.0817 0.8645 0.976 0.000 0.000 0.024
#> GSM559460 1 0.0000 0.8624 1.000 0.000 0.000 0.000
#> GSM559461 1 0.0000 0.8624 1.000 0.000 0.000 0.000
#> GSM559462 1 0.1792 0.8545 0.932 0.000 0.000 0.068
#> GSM559463 1 0.0707 0.8528 0.980 0.000 0.000 0.020
#> GSM559464 1 0.0000 0.8624 1.000 0.000 0.000 0.000
#> GSM559465 1 0.0336 0.8596 0.992 0.000 0.000 0.008
#> GSM559467 1 0.4661 0.5293 0.652 0.000 0.000 0.348
#> GSM559468 1 0.0921 0.8628 0.972 0.000 0.000 0.028
#> GSM559469 1 0.1716 0.8466 0.936 0.000 0.000 0.064
#> GSM559470 1 0.5296 0.0651 0.496 0.008 0.000 0.496
#> GSM559471 1 0.0921 0.8628 0.972 0.000 0.000 0.028
#> GSM559472 1 0.0817 0.8645 0.976 0.000 0.000 0.024
#> GSM559473 2 0.0779 0.8882 0.000 0.980 0.004 0.016
#> GSM559475 2 0.0779 0.8882 0.000 0.980 0.004 0.016
#> GSM559477 2 0.0592 0.8871 0.000 0.984 0.000 0.016
#> GSM559478 2 0.0927 0.8885 0.000 0.976 0.016 0.008
#> GSM559479 2 0.0592 0.8871 0.000 0.984 0.000 0.016
#> GSM559480 2 0.0927 0.8885 0.000 0.976 0.016 0.008
#> GSM559481 2 0.0927 0.8885 0.000 0.976 0.016 0.008
#> GSM559482 2 0.0592 0.8871 0.000 0.984 0.000 0.016
#> GSM559435 3 0.0592 0.9660 0.016 0.000 0.984 0.000
#> GSM559439 3 0.0592 0.9660 0.016 0.000 0.984 0.000
#> GSM559443 3 0.1297 0.9528 0.016 0.000 0.964 0.020
#> GSM559447 3 0.0592 0.9660 0.016 0.000 0.984 0.000
#> GSM559449 3 0.0592 0.9660 0.016 0.000 0.984 0.000
#> GSM559453 3 0.0592 0.9660 0.016 0.000 0.984 0.000
#> GSM559466 3 0.0592 0.9660 0.016 0.000 0.984 0.000
#> GSM559474 4 0.4916 -0.1917 0.000 0.000 0.424 0.576
#> GSM559476 3 0.3806 0.7601 0.156 0.000 0.824 0.020
#> GSM559483 2 0.0592 0.8871 0.000 0.984 0.000 0.016
#> GSM559484 4 0.7349 -0.1491 0.000 0.160 0.384 0.456
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 1 0.2249 0.835 0.896 0.000 0.000 0.096 0.008
#> GSM559434 4 0.6163 0.222 0.016 0.196 0.000 0.612 0.176
#> GSM559436 1 0.1444 0.879 0.948 0.000 0.000 0.012 0.040
#> GSM559437 4 0.4541 0.489 0.112 0.000 0.000 0.752 0.136
#> GSM559438 4 0.6212 0.405 0.120 0.108 0.000 0.668 0.104
#> GSM559440 4 0.5481 0.327 0.016 0.136 0.000 0.692 0.156
#> GSM559441 4 0.2648 0.569 0.152 0.000 0.000 0.848 0.000
#> GSM559442 1 0.4216 0.749 0.780 0.000 0.000 0.100 0.120
#> GSM559444 2 0.6477 0.284 0.000 0.464 0.000 0.340 0.196
#> GSM559445 4 0.2966 0.410 0.016 0.000 0.000 0.848 0.136
#> GSM559446 4 0.4010 0.459 0.072 0.000 0.000 0.792 0.136
#> GSM559448 1 0.1205 0.880 0.956 0.000 0.000 0.004 0.040
#> GSM559450 2 0.6439 0.302 0.000 0.476 0.000 0.332 0.192
#> GSM559451 1 0.2439 0.840 0.876 0.000 0.000 0.120 0.004
#> GSM559452 4 0.6530 0.109 0.032 0.104 0.000 0.524 0.340
#> GSM559454 1 0.0912 0.886 0.972 0.000 0.000 0.012 0.016
#> GSM559455 4 0.4118 0.482 0.336 0.000 0.000 0.660 0.004
#> GSM559456 4 0.4655 0.164 0.476 0.000 0.000 0.512 0.012
#> GSM559457 1 0.3715 0.564 0.736 0.000 0.000 0.260 0.004
#> GSM559458 4 0.5854 0.196 0.436 0.000 0.000 0.468 0.096
#> GSM559459 1 0.0807 0.887 0.976 0.000 0.000 0.012 0.012
#> GSM559460 1 0.0955 0.885 0.968 0.000 0.000 0.004 0.028
#> GSM559461 1 0.0609 0.887 0.980 0.000 0.000 0.000 0.020
#> GSM559462 1 0.1671 0.858 0.924 0.000 0.000 0.076 0.000
#> GSM559463 1 0.1121 0.880 0.956 0.000 0.000 0.000 0.044
#> GSM559464 1 0.1124 0.886 0.960 0.000 0.000 0.004 0.036
#> GSM559465 1 0.0963 0.886 0.964 0.000 0.000 0.000 0.036
#> GSM559467 4 0.4525 0.425 0.360 0.000 0.000 0.624 0.016
#> GSM559468 1 0.3849 0.782 0.808 0.000 0.000 0.080 0.112
#> GSM559469 1 0.4164 0.754 0.784 0.000 0.000 0.096 0.120
#> GSM559470 4 0.3586 0.572 0.188 0.000 0.000 0.792 0.020
#> GSM559471 1 0.3090 0.825 0.860 0.000 0.000 0.088 0.052
#> GSM559472 1 0.0807 0.887 0.976 0.000 0.000 0.012 0.012
#> GSM559473 2 0.3281 0.764 0.000 0.848 0.000 0.092 0.060
#> GSM559475 2 0.2914 0.778 0.000 0.872 0.000 0.076 0.052
#> GSM559477 2 0.0510 0.809 0.000 0.984 0.000 0.000 0.016
#> GSM559478 2 0.2700 0.793 0.000 0.884 0.004 0.024 0.088
#> GSM559479 2 0.0510 0.809 0.000 0.984 0.000 0.000 0.016
#> GSM559480 2 0.2700 0.793 0.000 0.884 0.004 0.024 0.088
#> GSM559481 2 0.2700 0.793 0.000 0.884 0.004 0.024 0.088
#> GSM559482 2 0.0510 0.809 0.000 0.984 0.000 0.000 0.016
#> GSM559435 3 0.0162 0.945 0.004 0.000 0.996 0.000 0.000
#> GSM559439 3 0.0162 0.945 0.004 0.000 0.996 0.000 0.000
#> GSM559443 3 0.0771 0.926 0.004 0.000 0.976 0.000 0.020
#> GSM559447 3 0.0162 0.945 0.004 0.000 0.996 0.000 0.000
#> GSM559449 3 0.0162 0.945 0.004 0.000 0.996 0.000 0.000
#> GSM559453 3 0.0162 0.945 0.004 0.000 0.996 0.000 0.000
#> GSM559466 3 0.0162 0.945 0.004 0.000 0.996 0.000 0.000
#> GSM559474 5 0.5354 0.837 0.000 0.000 0.208 0.128 0.664
#> GSM559476 3 0.3655 0.614 0.160 0.000 0.804 0.000 0.036
#> GSM559483 2 0.0510 0.809 0.000 0.984 0.000 0.000 0.016
#> GSM559484 5 0.5157 0.838 0.000 0.052 0.204 0.032 0.712
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.2212 0.747 0.880 0.000 0.000 0.112 0.008 0.000
#> GSM559434 6 0.4439 0.738 0.004 0.088 0.000 0.152 0.012 0.744
#> GSM559436 1 0.2058 0.766 0.916 0.000 0.000 0.024 0.048 0.012
#> GSM559437 4 0.2380 0.753 0.036 0.000 0.000 0.900 0.048 0.016
#> GSM559438 6 0.4917 0.695 0.036 0.052 0.000 0.200 0.008 0.704
#> GSM559440 6 0.4170 0.723 0.008 0.060 0.000 0.192 0.000 0.740
#> GSM559441 4 0.2679 0.758 0.040 0.000 0.000 0.864 0.000 0.096
#> GSM559442 1 0.6239 0.547 0.496 0.000 0.000 0.052 0.116 0.336
#> GSM559444 6 0.5840 0.592 0.000 0.324 0.000 0.068 0.060 0.548
#> GSM559445 4 0.2519 0.724 0.008 0.000 0.000 0.888 0.048 0.056
#> GSM559446 4 0.2450 0.740 0.016 0.000 0.000 0.896 0.048 0.040
#> GSM559448 1 0.2390 0.764 0.900 0.000 0.004 0.024 0.060 0.012
#> GSM559450 6 0.5687 0.564 0.000 0.340 0.000 0.052 0.060 0.548
#> GSM559451 1 0.3332 0.745 0.832 0.000 0.000 0.108 0.016 0.044
#> GSM559452 6 0.4033 0.613 0.004 0.036 0.000 0.068 0.092 0.800
#> GSM559454 1 0.0622 0.783 0.980 0.000 0.000 0.008 0.012 0.000
#> GSM559455 4 0.3124 0.759 0.140 0.000 0.000 0.828 0.008 0.024
#> GSM559456 4 0.3706 0.691 0.184 0.000 0.000 0.776 0.016 0.024
#> GSM559457 1 0.4086 -0.135 0.528 0.000 0.000 0.464 0.008 0.000
#> GSM559458 4 0.6153 0.535 0.124 0.000 0.000 0.592 0.088 0.196
#> GSM559459 1 0.0603 0.786 0.980 0.000 0.000 0.004 0.016 0.000
#> GSM559460 1 0.3677 0.772 0.816 0.000 0.000 0.024 0.088 0.072
#> GSM559461 1 0.3246 0.782 0.848 0.000 0.000 0.028 0.076 0.048
#> GSM559462 1 0.2786 0.759 0.864 0.000 0.000 0.100 0.024 0.012
#> GSM559463 1 0.2340 0.769 0.900 0.000 0.000 0.016 0.060 0.024
#> GSM559464 1 0.3314 0.773 0.828 0.000 0.000 0.004 0.092 0.076
#> GSM559465 1 0.3249 0.776 0.840 0.000 0.000 0.012 0.088 0.060
#> GSM559467 4 0.4670 0.695 0.152 0.000 0.000 0.708 0.008 0.132
#> GSM559468 1 0.6159 0.571 0.520 0.000 0.000 0.048 0.120 0.312
#> GSM559469 1 0.6230 0.550 0.500 0.000 0.000 0.052 0.116 0.332
#> GSM559470 4 0.4437 0.679 0.088 0.000 0.000 0.724 0.008 0.180
#> GSM559471 1 0.5242 0.670 0.668 0.000 0.000 0.052 0.072 0.208
#> GSM559472 1 0.1088 0.784 0.960 0.000 0.000 0.024 0.016 0.000
#> GSM559473 2 0.4330 0.607 0.000 0.680 0.000 0.008 0.036 0.276
#> GSM559475 2 0.3860 0.731 0.000 0.756 0.000 0.008 0.036 0.200
#> GSM559477 2 0.0000 0.847 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559478 2 0.3862 0.825 0.000 0.796 0.000 0.016 0.088 0.100
#> GSM559479 2 0.0000 0.847 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559480 2 0.3862 0.825 0.000 0.796 0.000 0.016 0.088 0.100
#> GSM559481 2 0.3862 0.825 0.000 0.796 0.000 0.016 0.088 0.100
#> GSM559482 2 0.0000 0.847 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559439 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559443 3 0.0363 0.940 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM559447 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559449 3 0.0508 0.942 0.000 0.000 0.984 0.004 0.000 0.012
#> GSM559453 3 0.0508 0.942 0.000 0.000 0.984 0.004 0.000 0.012
#> GSM559466 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559474 5 0.4917 0.896 0.000 0.000 0.128 0.116 0.716 0.040
#> GSM559476 3 0.4679 0.641 0.092 0.000 0.772 0.036 0.048 0.052
#> GSM559483 2 0.0000 0.847 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559484 5 0.5151 0.891 0.000 0.024 0.120 0.048 0.728 0.080
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 disease.state(p) k
#> SD:kmeans 52 5.15e-01 2
#> SD:kmeans 50 2.53e-10 3
#> SD:kmeans 38 6.55e-08 4
#> SD:kmeans 39 5.59e-07 5
#> SD:kmeans 51 1.02e-08 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 21512 rows and 52 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 1.000 0.970 0.987 0.5014 0.497 0.497
#> 3 3 0.978 0.914 0.966 0.3055 0.697 0.474
#> 4 4 0.942 0.892 0.958 0.1456 0.885 0.680
#> 5 5 0.810 0.751 0.876 0.0588 0.931 0.744
#> 6 6 0.774 0.683 0.814 0.0376 0.954 0.797
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM559433 1 0.000 0.994 1.000 0.000
#> GSM559434 2 0.000 0.975 0.000 1.000
#> GSM559436 1 0.000 0.994 1.000 0.000
#> GSM559437 1 0.634 0.802 0.840 0.160
#> GSM559438 2 0.000 0.975 0.000 1.000
#> GSM559440 2 0.000 0.975 0.000 1.000
#> GSM559441 2 0.605 0.824 0.148 0.852
#> GSM559442 1 0.000 0.994 1.000 0.000
#> GSM559444 2 0.000 0.975 0.000 1.000
#> GSM559445 2 0.000 0.975 0.000 1.000
#> GSM559446 2 0.891 0.557 0.308 0.692
#> GSM559448 1 0.000 0.994 1.000 0.000
#> GSM559450 2 0.000 0.975 0.000 1.000
#> GSM559451 1 0.000 0.994 1.000 0.000
#> GSM559452 2 0.000 0.975 0.000 1.000
#> GSM559454 1 0.000 0.994 1.000 0.000
#> GSM559455 1 0.000 0.994 1.000 0.000
#> GSM559456 1 0.000 0.994 1.000 0.000
#> GSM559457 1 0.000 0.994 1.000 0.000
#> GSM559458 1 0.000 0.994 1.000 0.000
#> GSM559459 1 0.000 0.994 1.000 0.000
#> GSM559460 1 0.000 0.994 1.000 0.000
#> GSM559461 1 0.000 0.994 1.000 0.000
#> GSM559462 1 0.000 0.994 1.000 0.000
#> GSM559463 1 0.000 0.994 1.000 0.000
#> GSM559464 1 0.000 0.994 1.000 0.000
#> GSM559465 1 0.000 0.994 1.000 0.000
#> GSM559467 2 0.000 0.975 0.000 1.000
#> GSM559468 1 0.000 0.994 1.000 0.000
#> GSM559469 2 0.388 0.908 0.076 0.924
#> GSM559470 2 0.000 0.975 0.000 1.000
#> GSM559471 1 0.000 0.994 1.000 0.000
#> GSM559472 1 0.000 0.994 1.000 0.000
#> GSM559473 2 0.000 0.975 0.000 1.000
#> GSM559475 2 0.000 0.975 0.000 1.000
#> GSM559477 2 0.000 0.975 0.000 1.000
#> GSM559478 2 0.000 0.975 0.000 1.000
#> GSM559479 2 0.000 0.975 0.000 1.000
#> GSM559480 2 0.000 0.975 0.000 1.000
#> GSM559481 2 0.000 0.975 0.000 1.000
#> GSM559482 2 0.000 0.975 0.000 1.000
#> GSM559435 1 0.000 0.994 1.000 0.000
#> GSM559439 1 0.000 0.994 1.000 0.000
#> GSM559443 1 0.000 0.994 1.000 0.000
#> GSM559447 1 0.000 0.994 1.000 0.000
#> GSM559449 1 0.000 0.994 1.000 0.000
#> GSM559453 1 0.000 0.994 1.000 0.000
#> GSM559466 1 0.000 0.994 1.000 0.000
#> GSM559474 2 0.000 0.975 0.000 1.000
#> GSM559476 1 0.000 0.994 1.000 0.000
#> GSM559483 2 0.000 0.975 0.000 1.000
#> GSM559484 2 0.000 0.975 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559434 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559436 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559437 1 0.1643 0.922 0.956 0.000 0.044
#> GSM559438 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559440 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559441 1 0.6373 0.338 0.588 0.408 0.004
#> GSM559442 1 0.0592 0.944 0.988 0.012 0.000
#> GSM559444 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559445 2 0.3148 0.883 0.048 0.916 0.036
#> GSM559446 1 0.1643 0.922 0.956 0.000 0.044
#> GSM559448 3 0.2711 0.899 0.088 0.000 0.912
#> GSM559450 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559451 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559452 2 0.3879 0.803 0.000 0.848 0.152
#> GSM559454 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559455 1 0.0237 0.950 0.996 0.000 0.004
#> GSM559456 1 0.1643 0.922 0.956 0.000 0.044
#> GSM559457 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559458 3 0.0000 0.990 0.000 0.000 1.000
#> GSM559459 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559460 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559462 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559463 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559464 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559465 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559467 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559468 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559469 1 0.1031 0.936 0.976 0.024 0.000
#> GSM559470 1 0.6225 0.277 0.568 0.432 0.000
#> GSM559471 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559472 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559473 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559475 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559477 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559478 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559479 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559480 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559481 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559482 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559435 3 0.0000 0.990 0.000 0.000 1.000
#> GSM559439 3 0.0000 0.990 0.000 0.000 1.000
#> GSM559443 3 0.0000 0.990 0.000 0.000 1.000
#> GSM559447 3 0.0000 0.990 0.000 0.000 1.000
#> GSM559449 3 0.0000 0.990 0.000 0.000 1.000
#> GSM559453 3 0.0000 0.990 0.000 0.000 1.000
#> GSM559466 3 0.0000 0.990 0.000 0.000 1.000
#> GSM559474 3 0.0000 0.990 0.000 0.000 1.000
#> GSM559476 3 0.0000 0.990 0.000 0.000 1.000
#> GSM559483 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559484 2 0.6235 0.232 0.000 0.564 0.436
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.3123 0.822 0.844 0.000 0.000 0.156
#> GSM559434 2 0.0188 0.961 0.000 0.996 0.000 0.004
#> GSM559436 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM559437 4 0.0188 0.931 0.004 0.000 0.000 0.996
#> GSM559438 2 0.0188 0.961 0.000 0.996 0.000 0.004
#> GSM559440 2 0.0188 0.961 0.000 0.996 0.000 0.004
#> GSM559441 4 0.0188 0.931 0.004 0.000 0.000 0.996
#> GSM559442 1 0.0188 0.970 0.996 0.000 0.000 0.004
#> GSM559444 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM559445 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM559446 4 0.0188 0.931 0.004 0.000 0.000 0.996
#> GSM559448 3 0.4877 0.298 0.408 0.000 0.592 0.000
#> GSM559450 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM559451 1 0.2469 0.882 0.892 0.000 0.000 0.108
#> GSM559452 2 0.2053 0.896 0.000 0.924 0.072 0.004
#> GSM559454 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM559455 4 0.0188 0.931 0.004 0.000 0.000 0.996
#> GSM559456 4 0.0188 0.931 0.004 0.000 0.000 0.996
#> GSM559457 4 0.4898 0.237 0.416 0.000 0.000 0.584
#> GSM559458 3 0.1118 0.885 0.000 0.000 0.964 0.036
#> GSM559459 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM559460 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM559461 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM559462 1 0.2281 0.893 0.904 0.000 0.000 0.096
#> GSM559463 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM559464 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM559465 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM559467 4 0.0336 0.928 0.008 0.000 0.000 0.992
#> GSM559468 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM559469 1 0.0188 0.970 0.996 0.000 0.000 0.004
#> GSM559470 4 0.1004 0.910 0.004 0.024 0.000 0.972
#> GSM559471 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM559472 1 0.0000 0.973 1.000 0.000 0.000 0.000
#> GSM559473 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM559475 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM559477 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM559478 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM559479 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM559480 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM559481 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM559482 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM559435 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM559439 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM559443 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM559447 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM559449 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM559453 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM559466 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM559474 3 0.4713 0.431 0.000 0.000 0.640 0.360
#> GSM559476 3 0.0000 0.909 0.000 0.000 1.000 0.000
#> GSM559483 2 0.0000 0.963 0.000 1.000 0.000 0.000
#> GSM559484 2 0.4955 0.216 0.000 0.556 0.444 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 1 0.2136 0.6670 0.904 0.000 0.000 0.088 0.008
#> GSM559434 2 0.1908 0.8663 0.000 0.908 0.000 0.000 0.092
#> GSM559436 1 0.0000 0.7174 1.000 0.000 0.000 0.000 0.000
#> GSM559437 4 0.0000 0.9061 0.000 0.000 0.000 1.000 0.000
#> GSM559438 2 0.3366 0.7277 0.000 0.768 0.000 0.000 0.232
#> GSM559440 2 0.2280 0.8449 0.000 0.880 0.000 0.000 0.120
#> GSM559441 4 0.0290 0.9056 0.000 0.000 0.000 0.992 0.008
#> GSM559442 5 0.2929 0.8131 0.180 0.000 0.000 0.000 0.820
#> GSM559444 2 0.0963 0.8924 0.000 0.964 0.000 0.000 0.036
#> GSM559445 4 0.0162 0.9059 0.000 0.000 0.000 0.996 0.004
#> GSM559446 4 0.0290 0.9048 0.000 0.000 0.000 0.992 0.008
#> GSM559448 1 0.4425 0.1092 0.544 0.000 0.452 0.000 0.004
#> GSM559450 2 0.0880 0.8937 0.000 0.968 0.000 0.000 0.032
#> GSM559451 1 0.3888 0.6265 0.804 0.000 0.000 0.076 0.120
#> GSM559452 2 0.4872 0.4244 0.000 0.540 0.024 0.000 0.436
#> GSM559454 1 0.0290 0.7188 0.992 0.000 0.000 0.000 0.008
#> GSM559455 4 0.1168 0.8956 0.032 0.000 0.000 0.960 0.008
#> GSM559456 4 0.2362 0.8555 0.084 0.000 0.008 0.900 0.008
#> GSM559457 1 0.4065 0.4530 0.720 0.000 0.000 0.264 0.016
#> GSM559458 3 0.5921 0.5509 0.000 0.000 0.596 0.184 0.220
#> GSM559459 1 0.1270 0.7178 0.948 0.000 0.000 0.000 0.052
#> GSM559460 1 0.3774 0.4695 0.704 0.000 0.000 0.000 0.296
#> GSM559461 1 0.3109 0.6186 0.800 0.000 0.000 0.000 0.200
#> GSM559462 1 0.4179 0.6398 0.776 0.000 0.000 0.072 0.152
#> GSM559463 1 0.1608 0.7088 0.928 0.000 0.000 0.000 0.072
#> GSM559464 1 0.3752 0.4780 0.708 0.000 0.000 0.000 0.292
#> GSM559465 1 0.3210 0.5988 0.788 0.000 0.000 0.000 0.212
#> GSM559467 4 0.4150 0.7238 0.036 0.000 0.000 0.748 0.216
#> GSM559468 5 0.3612 0.7982 0.268 0.000 0.000 0.000 0.732
#> GSM559469 5 0.2891 0.8200 0.176 0.000 0.000 0.000 0.824
#> GSM559470 4 0.4410 0.7410 0.008 0.044 0.000 0.752 0.196
#> GSM559471 5 0.4150 0.5840 0.388 0.000 0.000 0.000 0.612
#> GSM559472 1 0.0290 0.7170 0.992 0.000 0.000 0.000 0.008
#> GSM559473 2 0.0000 0.9029 0.000 1.000 0.000 0.000 0.000
#> GSM559475 2 0.0000 0.9029 0.000 1.000 0.000 0.000 0.000
#> GSM559477 2 0.0000 0.9029 0.000 1.000 0.000 0.000 0.000
#> GSM559478 2 0.0000 0.9029 0.000 1.000 0.000 0.000 0.000
#> GSM559479 2 0.0000 0.9029 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.0000 0.9029 0.000 1.000 0.000 0.000 0.000
#> GSM559481 2 0.0000 0.9029 0.000 1.000 0.000 0.000 0.000
#> GSM559482 2 0.0000 0.9029 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.9097 0.000 0.000 1.000 0.000 0.000
#> GSM559439 3 0.0000 0.9097 0.000 0.000 1.000 0.000 0.000
#> GSM559443 3 0.0000 0.9097 0.000 0.000 1.000 0.000 0.000
#> GSM559447 3 0.0000 0.9097 0.000 0.000 1.000 0.000 0.000
#> GSM559449 3 0.0000 0.9097 0.000 0.000 1.000 0.000 0.000
#> GSM559453 3 0.0000 0.9097 0.000 0.000 1.000 0.000 0.000
#> GSM559466 3 0.0000 0.9097 0.000 0.000 1.000 0.000 0.000
#> GSM559474 3 0.5989 0.3698 0.000 0.000 0.536 0.336 0.128
#> GSM559476 3 0.0000 0.9097 0.000 0.000 1.000 0.000 0.000
#> GSM559483 2 0.0000 0.9029 0.000 1.000 0.000 0.000 0.000
#> GSM559484 2 0.6161 -0.0241 0.000 0.444 0.424 0.000 0.132
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.4053 0.6080 0.788 0.000 0.000 0.100 0.084 0.028
#> GSM559434 2 0.3756 0.6957 0.000 0.712 0.000 0.000 0.268 0.020
#> GSM559436 1 0.0937 0.6859 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM559437 4 0.0458 0.7984 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM559438 2 0.5030 0.5607 0.000 0.632 0.000 0.004 0.256 0.108
#> GSM559440 2 0.4347 0.6318 0.000 0.668 0.000 0.004 0.288 0.040
#> GSM559441 4 0.1049 0.7972 0.000 0.000 0.000 0.960 0.032 0.008
#> GSM559442 6 0.3492 0.7439 0.076 0.000 0.000 0.000 0.120 0.804
#> GSM559444 2 0.2902 0.7662 0.000 0.800 0.000 0.000 0.196 0.004
#> GSM559445 4 0.1584 0.7853 0.000 0.000 0.000 0.928 0.064 0.008
#> GSM559446 4 0.1524 0.7873 0.000 0.000 0.000 0.932 0.060 0.008
#> GSM559448 3 0.4969 0.1510 0.436 0.000 0.508 0.000 0.048 0.008
#> GSM559450 2 0.2933 0.7626 0.000 0.796 0.000 0.000 0.200 0.004
#> GSM559451 1 0.5761 0.4828 0.628 0.000 0.000 0.052 0.156 0.164
#> GSM559452 5 0.5537 0.3873 0.000 0.236 0.004 0.000 0.576 0.184
#> GSM559454 1 0.0603 0.6912 0.980 0.000 0.000 0.000 0.016 0.004
#> GSM559455 4 0.2515 0.7752 0.052 0.000 0.000 0.892 0.040 0.016
#> GSM559456 4 0.4181 0.7040 0.104 0.000 0.028 0.796 0.052 0.020
#> GSM559457 1 0.5241 0.4846 0.652 0.000 0.000 0.224 0.096 0.028
#> GSM559458 3 0.7068 0.0298 0.004 0.000 0.492 0.140 0.184 0.180
#> GSM559459 1 0.1471 0.6932 0.932 0.000 0.000 0.000 0.004 0.064
#> GSM559460 1 0.4362 0.3662 0.584 0.000 0.000 0.000 0.028 0.388
#> GSM559461 1 0.3950 0.5447 0.696 0.000 0.000 0.000 0.028 0.276
#> GSM559462 1 0.5693 0.5188 0.628 0.000 0.000 0.044 0.144 0.184
#> GSM559463 1 0.2560 0.6714 0.872 0.000 0.000 0.000 0.036 0.092
#> GSM559464 1 0.3979 0.4365 0.628 0.000 0.000 0.000 0.012 0.360
#> GSM559465 1 0.4435 0.4967 0.648 0.000 0.004 0.000 0.040 0.308
#> GSM559467 4 0.6123 0.5648 0.048 0.004 0.000 0.584 0.152 0.212
#> GSM559468 6 0.2454 0.7751 0.160 0.000 0.000 0.000 0.000 0.840
#> GSM559469 6 0.2006 0.7925 0.080 0.000 0.000 0.000 0.016 0.904
#> GSM559470 4 0.6262 0.5467 0.008 0.048 0.000 0.576 0.160 0.208
#> GSM559471 6 0.4783 0.5566 0.276 0.000 0.000 0.000 0.088 0.636
#> GSM559472 1 0.1528 0.6882 0.936 0.000 0.000 0.000 0.048 0.016
#> GSM559473 2 0.0260 0.8703 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM559475 2 0.0260 0.8693 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM559477 2 0.0000 0.8712 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559478 2 0.0777 0.8634 0.000 0.972 0.000 0.000 0.024 0.004
#> GSM559479 2 0.0000 0.8712 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559480 2 0.0891 0.8620 0.000 0.968 0.000 0.000 0.024 0.008
#> GSM559481 2 0.0891 0.8620 0.000 0.968 0.000 0.000 0.024 0.008
#> GSM559482 2 0.0000 0.8712 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.8525 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559439 3 0.0000 0.8525 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559443 3 0.0000 0.8525 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559447 3 0.0000 0.8525 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559449 3 0.0000 0.8525 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559453 3 0.0363 0.8426 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM559466 3 0.0000 0.8525 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559474 5 0.6208 0.3394 0.000 0.000 0.296 0.236 0.456 0.012
#> GSM559476 3 0.0000 0.8525 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559483 2 0.0000 0.8712 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559484 5 0.6266 0.5499 0.000 0.276 0.232 0.004 0.476 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 disease.state(p) k
#> SD:skmeans 52 3.51e-01 2
#> SD:skmeans 49 6.32e-08 3
#> SD:skmeans 48 7.35e-08 4
#> SD:skmeans 45 8.83e-07 5
#> SD:skmeans 43 4.14e-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", "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 21512 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.959 0.947 0.978 0.3709 0.638 0.638
#> 3 3 1.000 0.961 0.984 0.6353 0.701 0.551
#> 4 4 0.766 0.810 0.916 0.2357 0.784 0.497
#> 5 5 0.734 0.535 0.776 0.0504 0.873 0.578
#> 6 6 0.855 0.774 0.912 0.0477 0.891 0.573
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
#> GSM559433 2 0.0000 0.979 0.000 1.000
#> GSM559434 2 0.0000 0.979 0.000 1.000
#> GSM559436 2 0.0000 0.979 0.000 1.000
#> GSM559437 2 0.0000 0.979 0.000 1.000
#> GSM559438 2 0.0000 0.979 0.000 1.000
#> GSM559440 2 0.0000 0.979 0.000 1.000
#> GSM559441 2 0.0000 0.979 0.000 1.000
#> GSM559442 2 0.0000 0.979 0.000 1.000
#> GSM559444 2 0.0000 0.979 0.000 1.000
#> GSM559445 2 0.0000 0.979 0.000 1.000
#> GSM559446 2 0.0000 0.979 0.000 1.000
#> GSM559448 1 0.0376 0.963 0.996 0.004
#> GSM559450 2 0.0000 0.979 0.000 1.000
#> GSM559451 2 0.0000 0.979 0.000 1.000
#> GSM559452 2 0.0376 0.975 0.004 0.996
#> GSM559454 2 0.0000 0.979 0.000 1.000
#> GSM559455 2 0.0000 0.979 0.000 1.000
#> GSM559456 2 0.7950 0.670 0.240 0.760
#> GSM559457 2 0.0000 0.979 0.000 1.000
#> GSM559458 1 0.9358 0.445 0.648 0.352
#> GSM559459 2 0.0000 0.979 0.000 1.000
#> GSM559460 2 0.0000 0.979 0.000 1.000
#> GSM559461 2 0.0000 0.979 0.000 1.000
#> GSM559462 2 0.0000 0.979 0.000 1.000
#> GSM559463 2 0.8267 0.647 0.260 0.740
#> GSM559464 2 0.0000 0.979 0.000 1.000
#> GSM559465 2 0.8386 0.632 0.268 0.732
#> GSM559467 2 0.0000 0.979 0.000 1.000
#> GSM559468 2 0.0000 0.979 0.000 1.000
#> GSM559469 2 0.0000 0.979 0.000 1.000
#> GSM559470 2 0.0000 0.979 0.000 1.000
#> GSM559471 2 0.0000 0.979 0.000 1.000
#> GSM559472 2 0.0000 0.979 0.000 1.000
#> GSM559473 2 0.0000 0.979 0.000 1.000
#> GSM559475 2 0.0000 0.979 0.000 1.000
#> GSM559477 2 0.0000 0.979 0.000 1.000
#> GSM559478 2 0.0000 0.979 0.000 1.000
#> GSM559479 2 0.0000 0.979 0.000 1.000
#> GSM559480 2 0.0000 0.979 0.000 1.000
#> GSM559481 2 0.0000 0.979 0.000 1.000
#> GSM559482 2 0.0000 0.979 0.000 1.000
#> GSM559435 1 0.0000 0.967 1.000 0.000
#> GSM559439 1 0.0000 0.967 1.000 0.000
#> GSM559443 1 0.0000 0.967 1.000 0.000
#> GSM559447 1 0.0000 0.967 1.000 0.000
#> GSM559449 1 0.0000 0.967 1.000 0.000
#> GSM559453 1 0.0000 0.967 1.000 0.000
#> GSM559466 1 0.0000 0.967 1.000 0.000
#> GSM559474 1 0.0000 0.967 1.000 0.000
#> GSM559476 1 0.0000 0.967 1.000 0.000
#> GSM559483 2 0.0000 0.979 0.000 1.000
#> GSM559484 1 0.0000 0.967 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559434 1 0.5098 0.678 0.752 0.248 0.000
#> GSM559436 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559437 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559438 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559440 1 0.5291 0.645 0.732 0.268 0.000
#> GSM559441 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559442 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559444 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559445 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559446 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559448 1 0.0424 0.973 0.992 0.000 0.008
#> GSM559450 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559451 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559452 3 0.3129 0.878 0.008 0.088 0.904
#> GSM559454 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559455 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559456 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559457 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559458 3 0.4887 0.681 0.228 0.000 0.772
#> GSM559459 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559460 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559462 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559463 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559464 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559465 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559467 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559468 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559469 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559470 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559471 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559472 1 0.0000 0.981 1.000 0.000 0.000
#> GSM559473 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559475 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559477 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559478 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559479 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559480 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559481 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559482 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559435 3 0.0000 0.964 0.000 0.000 1.000
#> GSM559439 3 0.0000 0.964 0.000 0.000 1.000
#> GSM559443 3 0.0000 0.964 0.000 0.000 1.000
#> GSM559447 3 0.0000 0.964 0.000 0.000 1.000
#> GSM559449 3 0.0000 0.964 0.000 0.000 1.000
#> GSM559453 3 0.0000 0.964 0.000 0.000 1.000
#> GSM559466 3 0.0000 0.964 0.000 0.000 1.000
#> GSM559474 3 0.0000 0.964 0.000 0.000 1.000
#> GSM559476 3 0.0000 0.964 0.000 0.000 1.000
#> GSM559483 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559484 3 0.0000 0.964 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 4 0.0000 0.852 0.000 0.000 0.000 1.000
#> GSM559434 4 0.3074 0.752 0.000 0.152 0.000 0.848
#> GSM559436 1 0.4585 0.565 0.668 0.000 0.000 0.332
#> GSM559437 4 0.0000 0.852 0.000 0.000 0.000 1.000
#> GSM559438 4 0.1118 0.840 0.036 0.000 0.000 0.964
#> GSM559440 4 0.1940 0.814 0.000 0.076 0.000 0.924
#> GSM559441 4 0.0000 0.852 0.000 0.000 0.000 1.000
#> GSM559442 1 0.1118 0.836 0.964 0.000 0.000 0.036
#> GSM559444 4 0.3528 0.703 0.000 0.192 0.000 0.808
#> GSM559445 4 0.0000 0.852 0.000 0.000 0.000 1.000
#> GSM559446 4 0.0000 0.852 0.000 0.000 0.000 1.000
#> GSM559448 3 0.7512 -0.035 0.348 0.000 0.460 0.192
#> GSM559450 2 0.1302 0.948 0.000 0.956 0.000 0.044
#> GSM559451 4 0.3726 0.676 0.212 0.000 0.000 0.788
#> GSM559452 4 0.4522 0.537 0.320 0.000 0.000 0.680
#> GSM559454 4 0.4500 0.487 0.316 0.000 0.000 0.684
#> GSM559455 4 0.0000 0.852 0.000 0.000 0.000 1.000
#> GSM559456 4 0.2011 0.811 0.080 0.000 0.000 0.920
#> GSM559457 4 0.4072 0.614 0.252 0.000 0.000 0.748
#> GSM559458 3 0.6469 0.573 0.192 0.000 0.644 0.164
#> GSM559459 1 0.3528 0.766 0.808 0.000 0.000 0.192
#> GSM559460 1 0.0000 0.855 1.000 0.000 0.000 0.000
#> GSM559461 1 0.3219 0.785 0.836 0.000 0.000 0.164
#> GSM559462 1 0.3528 0.766 0.808 0.000 0.000 0.192
#> GSM559463 1 0.0592 0.854 0.984 0.000 0.000 0.016
#> GSM559464 1 0.0000 0.855 1.000 0.000 0.000 0.000
#> GSM559465 1 0.0000 0.855 1.000 0.000 0.000 0.000
#> GSM559467 4 0.4134 0.626 0.260 0.000 0.000 0.740
#> GSM559468 1 0.0000 0.855 1.000 0.000 0.000 0.000
#> GSM559469 1 0.0000 0.855 1.000 0.000 0.000 0.000
#> GSM559470 4 0.0000 0.852 0.000 0.000 0.000 1.000
#> GSM559471 1 0.1792 0.823 0.932 0.000 0.000 0.068
#> GSM559472 1 0.4972 0.202 0.544 0.000 0.000 0.456
#> GSM559473 2 0.2345 0.887 0.000 0.900 0.000 0.100
#> GSM559475 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559477 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559478 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559479 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559480 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559481 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559482 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559435 3 0.0000 0.918 0.000 0.000 1.000 0.000
#> GSM559439 3 0.0000 0.918 0.000 0.000 1.000 0.000
#> GSM559443 3 0.0000 0.918 0.000 0.000 1.000 0.000
#> GSM559447 3 0.0000 0.918 0.000 0.000 1.000 0.000
#> GSM559449 3 0.0000 0.918 0.000 0.000 1.000 0.000
#> GSM559453 3 0.0000 0.918 0.000 0.000 1.000 0.000
#> GSM559466 3 0.0000 0.918 0.000 0.000 1.000 0.000
#> GSM559474 3 0.0000 0.918 0.000 0.000 1.000 0.000
#> GSM559476 3 0.0000 0.918 0.000 0.000 1.000 0.000
#> GSM559483 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559484 3 0.0000 0.918 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 4 0.223 0.55336 0.000 0.000 0.116 0.884 0.000
#> GSM559434 3 0.541 -0.57831 0.000 0.056 0.472 0.472 0.000
#> GSM559436 4 0.403 -0.08415 0.352 0.000 0.000 0.648 0.000
#> GSM559437 4 0.430 0.56970 0.000 0.000 0.472 0.528 0.000
#> GSM559438 4 0.455 0.56535 0.008 0.000 0.472 0.520 0.000
#> GSM559440 4 0.505 0.53752 0.000 0.032 0.472 0.496 0.000
#> GSM559441 4 0.430 0.56970 0.000 0.000 0.472 0.528 0.000
#> GSM559442 1 0.088 0.74392 0.968 0.000 0.000 0.032 0.000
#> GSM559444 3 0.551 -0.57144 0.000 0.064 0.472 0.464 0.000
#> GSM559445 4 0.430 0.56970 0.000 0.000 0.472 0.528 0.000
#> GSM559446 4 0.373 0.58851 0.000 0.000 0.288 0.712 0.000
#> GSM559448 4 0.635 -0.03700 0.176 0.000 0.288 0.532 0.004
#> GSM559450 2 0.252 0.82613 0.000 0.860 0.140 0.000 0.000
#> GSM559451 4 0.247 0.41232 0.136 0.000 0.000 0.864 0.000
#> GSM559452 1 0.595 -0.00795 0.520 0.000 0.116 0.364 0.000
#> GSM559454 4 0.285 0.36360 0.172 0.000 0.000 0.828 0.000
#> GSM559455 4 0.430 0.56970 0.000 0.000 0.472 0.528 0.000
#> GSM559456 4 0.152 0.49697 0.044 0.000 0.012 0.944 0.000
#> GSM559457 4 0.256 0.40276 0.144 0.000 0.000 0.856 0.000
#> GSM559458 3 0.724 -0.09714 0.300 0.000 0.472 0.044 0.184
#> GSM559459 1 0.424 0.40335 0.572 0.000 0.000 0.428 0.000
#> GSM559460 1 0.000 0.76505 1.000 0.000 0.000 0.000 0.000
#> GSM559461 1 0.402 0.49908 0.652 0.000 0.000 0.348 0.000
#> GSM559462 1 0.423 0.41078 0.580 0.000 0.000 0.420 0.000
#> GSM559463 1 0.285 0.70284 0.828 0.000 0.000 0.172 0.000
#> GSM559464 1 0.000 0.76505 1.000 0.000 0.000 0.000 0.000
#> GSM559465 1 0.000 0.76505 1.000 0.000 0.000 0.000 0.000
#> GSM559467 4 0.531 0.37216 0.220 0.000 0.116 0.664 0.000
#> GSM559468 1 0.000 0.76505 1.000 0.000 0.000 0.000 0.000
#> GSM559469 1 0.000 0.76505 1.000 0.000 0.000 0.000 0.000
#> GSM559470 4 0.430 0.56970 0.000 0.000 0.472 0.528 0.000
#> GSM559471 1 0.277 0.68977 0.836 0.000 0.000 0.164 0.000
#> GSM559472 4 0.382 0.07835 0.304 0.000 0.000 0.696 0.000
#> GSM559473 2 0.212 0.86155 0.000 0.900 0.004 0.096 0.000
#> GSM559475 2 0.000 0.96667 0.000 1.000 0.000 0.000 0.000
#> GSM559477 2 0.000 0.96667 0.000 1.000 0.000 0.000 0.000
#> GSM559478 2 0.000 0.96667 0.000 1.000 0.000 0.000 0.000
#> GSM559479 2 0.000 0.96667 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.000 0.96667 0.000 1.000 0.000 0.000 0.000
#> GSM559481 2 0.000 0.96667 0.000 1.000 0.000 0.000 0.000
#> GSM559482 2 0.000 0.96667 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.430 0.41260 0.000 0.000 0.528 0.000 0.472
#> GSM559439 3 0.430 0.41260 0.000 0.000 0.528 0.000 0.472
#> GSM559443 3 0.430 0.41260 0.000 0.000 0.528 0.000 0.472
#> GSM559447 3 0.430 0.41260 0.000 0.000 0.528 0.000 0.472
#> GSM559449 3 0.430 0.41260 0.000 0.000 0.528 0.000 0.472
#> GSM559453 3 0.430 0.41260 0.000 0.000 0.528 0.000 0.472
#> GSM559466 3 0.430 0.41260 0.000 0.000 0.528 0.000 0.472
#> GSM559474 5 0.000 1.00000 0.000 0.000 0.000 0.000 1.000
#> GSM559476 3 0.430 0.41260 0.000 0.000 0.528 0.000 0.472
#> GSM559483 2 0.000 0.96667 0.000 1.000 0.000 0.000 0.000
#> GSM559484 5 0.000 1.00000 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.3804 0.2952 0.576 0.000 0.000 0.424 0 0.000
#> GSM559434 4 0.0000 0.9524 0.000 0.000 0.000 1.000 0 0.000
#> GSM559436 1 0.0000 0.7639 1.000 0.000 0.000 0.000 0 0.000
#> GSM559437 4 0.0363 0.9549 0.012 0.000 0.000 0.988 0 0.000
#> GSM559438 4 0.0000 0.9524 0.000 0.000 0.000 1.000 0 0.000
#> GSM559440 4 0.0000 0.9524 0.000 0.000 0.000 1.000 0 0.000
#> GSM559441 4 0.0363 0.9549 0.012 0.000 0.000 0.988 0 0.000
#> GSM559442 6 0.0000 0.7333 0.000 0.000 0.000 0.000 0 1.000
#> GSM559444 4 0.0000 0.9524 0.000 0.000 0.000 1.000 0 0.000
#> GSM559445 4 0.0363 0.9549 0.012 0.000 0.000 0.988 0 0.000
#> GSM559446 4 0.3198 0.5674 0.260 0.000 0.000 0.740 0 0.000
#> GSM559448 1 0.0260 0.7599 0.992 0.000 0.008 0.000 0 0.000
#> GSM559450 2 0.2664 0.7452 0.000 0.816 0.000 0.184 0 0.000
#> GSM559451 1 0.0000 0.7639 1.000 0.000 0.000 0.000 0 0.000
#> GSM559452 6 0.3823 0.1440 0.000 0.000 0.000 0.436 0 0.564
#> GSM559454 1 0.0000 0.7639 1.000 0.000 0.000 0.000 0 0.000
#> GSM559455 4 0.0458 0.9519 0.016 0.000 0.000 0.984 0 0.000
#> GSM559456 1 0.2762 0.6556 0.804 0.000 0.000 0.196 0 0.000
#> GSM559457 1 0.0000 0.7639 1.000 0.000 0.000 0.000 0 0.000
#> GSM559458 3 0.4798 0.4272 0.000 0.000 0.612 0.076 0 0.312
#> GSM559459 1 0.3499 0.4764 0.680 0.000 0.000 0.000 0 0.320
#> GSM559460 6 0.0000 0.7333 0.000 0.000 0.000 0.000 0 1.000
#> GSM559461 6 0.3747 0.0513 0.396 0.000 0.000 0.000 0 0.604
#> GSM559462 1 0.3810 0.2974 0.572 0.000 0.000 0.000 0 0.428
#> GSM559463 6 0.3867 0.2341 0.488 0.000 0.000 0.000 0 0.512
#> GSM559464 6 0.0000 0.7333 0.000 0.000 0.000 0.000 0 1.000
#> GSM559465 6 0.0000 0.7333 0.000 0.000 0.000 0.000 0 1.000
#> GSM559467 1 0.5451 0.3955 0.532 0.000 0.000 0.328 0 0.140
#> GSM559468 6 0.0000 0.7333 0.000 0.000 0.000 0.000 0 1.000
#> GSM559469 6 0.0000 0.7333 0.000 0.000 0.000 0.000 0 1.000
#> GSM559470 4 0.0363 0.9549 0.012 0.000 0.000 0.988 0 0.000
#> GSM559471 6 0.3804 0.3541 0.424 0.000 0.000 0.000 0 0.576
#> GSM559472 1 0.0146 0.7621 0.996 0.000 0.000 0.000 0 0.004
#> GSM559473 2 0.1910 0.8401 0.000 0.892 0.000 0.108 0 0.000
#> GSM559475 2 0.0000 0.9574 0.000 1.000 0.000 0.000 0 0.000
#> GSM559477 2 0.0000 0.9574 0.000 1.000 0.000 0.000 0 0.000
#> GSM559478 2 0.0000 0.9574 0.000 1.000 0.000 0.000 0 0.000
#> GSM559479 2 0.0000 0.9574 0.000 1.000 0.000 0.000 0 0.000
#> GSM559480 2 0.0000 0.9574 0.000 1.000 0.000 0.000 0 0.000
#> GSM559481 2 0.0000 0.9574 0.000 1.000 0.000 0.000 0 0.000
#> GSM559482 2 0.0000 0.9574 0.000 1.000 0.000 0.000 0 0.000
#> GSM559435 3 0.0000 0.9416 0.000 0.000 1.000 0.000 0 0.000
#> GSM559439 3 0.0000 0.9416 0.000 0.000 1.000 0.000 0 0.000
#> GSM559443 3 0.0000 0.9416 0.000 0.000 1.000 0.000 0 0.000
#> GSM559447 3 0.0000 0.9416 0.000 0.000 1.000 0.000 0 0.000
#> GSM559449 3 0.0000 0.9416 0.000 0.000 1.000 0.000 0 0.000
#> GSM559453 3 0.0000 0.9416 0.000 0.000 1.000 0.000 0 0.000
#> GSM559466 3 0.0000 0.9416 0.000 0.000 1.000 0.000 0 0.000
#> GSM559474 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1 0.000
#> GSM559476 3 0.0000 0.9416 0.000 0.000 1.000 0.000 0 0.000
#> GSM559483 2 0.0000 0.9574 0.000 1.000 0.000 0.000 0 0.000
#> GSM559484 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1 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 disease.state(p) k
#> SD:pam 51 3.64e-09 2
#> SD:pam 52 1.15e-08 3
#> SD:pam 49 2.10e-08 4
#> SD:pam 29 2.37e-04 5
#> SD:pam 43 3.33e-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 21512 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.487 0.647 0.793 0.3893 0.660 0.660
#> 3 3 0.543 0.665 0.855 0.5185 0.672 0.512
#> 4 4 0.770 0.856 0.918 0.0197 0.775 0.556
#> 5 5 0.639 0.636 0.823 0.2003 0.798 0.556
#> 6 6 0.873 0.834 0.929 0.0417 0.909 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
#> GSM559433 2 0.000 0.651 0.000 1.000
#> GSM559434 2 0.995 0.572 0.460 0.540
#> GSM559436 2 0.000 0.651 0.000 1.000
#> GSM559437 2 0.995 0.572 0.460 0.540
#> GSM559438 2 0.402 0.651 0.080 0.920
#> GSM559440 2 0.995 0.572 0.460 0.540
#> GSM559441 2 0.995 0.572 0.460 0.540
#> GSM559442 2 0.184 0.654 0.028 0.972
#> GSM559444 2 0.995 0.572 0.460 0.540
#> GSM559445 2 0.995 0.572 0.460 0.540
#> GSM559446 2 0.995 0.572 0.460 0.540
#> GSM559448 2 1.000 0.496 0.496 0.504
#> GSM559450 2 0.995 0.572 0.460 0.540
#> GSM559451 2 0.000 0.651 0.000 1.000
#> GSM559452 1 1.000 -0.515 0.512 0.488
#> GSM559454 2 0.000 0.651 0.000 1.000
#> GSM559455 2 0.891 0.604 0.308 0.692
#> GSM559456 2 0.995 0.572 0.460 0.540
#> GSM559457 2 0.000 0.651 0.000 1.000
#> GSM559458 2 0.995 0.572 0.460 0.540
#> GSM559459 2 0.000 0.651 0.000 1.000
#> GSM559460 2 0.000 0.651 0.000 1.000
#> GSM559461 2 0.000 0.651 0.000 1.000
#> GSM559462 2 0.000 0.651 0.000 1.000
#> GSM559463 2 0.430 0.650 0.088 0.912
#> GSM559464 2 0.000 0.651 0.000 1.000
#> GSM559465 2 0.000 0.651 0.000 1.000
#> GSM559467 2 0.204 0.654 0.032 0.968
#> GSM559468 2 0.000 0.651 0.000 1.000
#> GSM559469 2 0.278 0.654 0.048 0.952
#> GSM559470 2 0.991 0.576 0.444 0.556
#> GSM559471 2 0.000 0.651 0.000 1.000
#> GSM559472 2 0.000 0.651 0.000 1.000
#> GSM559473 2 0.995 0.572 0.460 0.540
#> GSM559475 2 0.995 0.572 0.460 0.540
#> GSM559477 2 0.995 0.572 0.460 0.540
#> GSM559478 2 0.995 0.572 0.460 0.540
#> GSM559479 2 0.995 0.572 0.460 0.540
#> GSM559480 2 0.995 0.572 0.460 0.540
#> GSM559481 2 0.995 0.572 0.460 0.540
#> GSM559482 2 0.995 0.572 0.460 0.540
#> GSM559435 1 0.000 0.922 1.000 0.000
#> GSM559439 1 0.000 0.922 1.000 0.000
#> GSM559443 1 0.000 0.922 1.000 0.000
#> GSM559447 1 0.000 0.922 1.000 0.000
#> GSM559449 1 0.000 0.922 1.000 0.000
#> GSM559453 1 0.000 0.922 1.000 0.000
#> GSM559466 1 0.000 0.922 1.000 0.000
#> GSM559474 1 0.000 0.922 1.000 0.000
#> GSM559476 1 0.000 0.922 1.000 0.000
#> GSM559483 2 0.995 0.572 0.460 0.540
#> GSM559484 1 0.000 0.922 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0237 0.8560 0.996 0.000 0.004
#> GSM559434 2 0.6627 0.5358 0.336 0.644 0.020
#> GSM559436 1 0.0592 0.8526 0.988 0.000 0.012
#> GSM559437 2 0.6937 0.4315 0.404 0.576 0.020
#> GSM559438 1 0.6798 0.1697 0.584 0.400 0.016
#> GSM559440 2 0.6661 0.4443 0.400 0.588 0.012
#> GSM559441 2 0.6713 0.4092 0.416 0.572 0.012
#> GSM559442 1 0.0424 0.8550 0.992 0.008 0.000
#> GSM559444 2 0.2959 0.7063 0.100 0.900 0.000
#> GSM559445 2 0.6937 0.4315 0.404 0.576 0.020
#> GSM559446 2 0.6937 0.4315 0.404 0.576 0.020
#> GSM559448 1 0.6828 0.4209 0.656 0.312 0.032
#> GSM559450 2 0.2796 0.7081 0.092 0.908 0.000
#> GSM559451 1 0.0000 0.8567 1.000 0.000 0.000
#> GSM559452 2 0.7004 0.2226 0.428 0.552 0.020
#> GSM559454 1 0.0000 0.8567 1.000 0.000 0.000
#> GSM559455 1 0.3941 0.7227 0.844 0.156 0.000
#> GSM559456 1 0.6627 0.3685 0.644 0.336 0.020
#> GSM559457 1 0.0592 0.8531 0.988 0.012 0.000
#> GSM559458 1 0.7001 0.3624 0.628 0.340 0.032
#> GSM559459 1 0.0592 0.8526 0.988 0.000 0.012
#> GSM559460 1 0.0000 0.8567 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.8567 1.000 0.000 0.000
#> GSM559462 1 0.0592 0.8526 0.988 0.000 0.012
#> GSM559463 1 0.0592 0.8526 0.988 0.000 0.012
#> GSM559464 1 0.0237 0.8560 0.996 0.000 0.004
#> GSM559465 1 0.0424 0.8550 0.992 0.008 0.000
#> GSM559467 1 0.3686 0.7451 0.860 0.140 0.000
#> GSM559468 1 0.0000 0.8567 1.000 0.000 0.000
#> GSM559469 1 0.3412 0.7637 0.876 0.124 0.000
#> GSM559470 1 0.6600 0.2359 0.604 0.384 0.012
#> GSM559471 1 0.0237 0.8561 0.996 0.004 0.000
#> GSM559472 1 0.0592 0.8526 0.988 0.000 0.012
#> GSM559473 2 0.0592 0.7157 0.012 0.988 0.000
#> GSM559475 2 0.0592 0.7157 0.012 0.988 0.000
#> GSM559477 2 0.0592 0.7157 0.012 0.988 0.000
#> GSM559478 2 0.0592 0.7157 0.012 0.988 0.000
#> GSM559479 2 0.0592 0.7157 0.012 0.988 0.000
#> GSM559480 2 0.0000 0.7038 0.000 1.000 0.000
#> GSM559481 2 0.0000 0.7038 0.000 1.000 0.000
#> GSM559482 2 0.0592 0.7157 0.012 0.988 0.000
#> GSM559435 3 0.0000 0.7683 0.000 0.000 1.000
#> GSM559439 3 0.0000 0.7683 0.000 0.000 1.000
#> GSM559443 3 0.4750 0.7074 0.000 0.216 0.784
#> GSM559447 3 0.0000 0.7683 0.000 0.000 1.000
#> GSM559449 3 0.1411 0.7680 0.000 0.036 0.964
#> GSM559453 3 0.4750 0.7074 0.000 0.216 0.784
#> GSM559466 3 0.0000 0.7683 0.000 0.000 1.000
#> GSM559474 3 0.5760 0.5825 0.000 0.328 0.672
#> GSM559476 3 0.9991 -0.0274 0.344 0.312 0.344
#> GSM559483 2 0.0592 0.7157 0.012 0.988 0.000
#> GSM559484 3 0.5785 0.5779 0.000 0.332 0.668
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM559434 1 0.4574 0.670 0.756 0.220 0.000 0.024
#> GSM559436 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM559437 1 0.4543 0.657 0.676 0.000 0.000 0.324
#> GSM559438 1 0.1520 0.894 0.956 0.020 0.000 0.024
#> GSM559440 1 0.3143 0.832 0.876 0.100 0.000 0.024
#> GSM559441 1 0.1474 0.892 0.948 0.000 0.000 0.052
#> GSM559442 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM559444 2 0.4963 0.571 0.284 0.696 0.000 0.020
#> GSM559445 1 0.4543 0.657 0.676 0.000 0.000 0.324
#> GSM559446 1 0.4543 0.657 0.676 0.000 0.000 0.324
#> GSM559448 1 0.0469 0.906 0.988 0.000 0.000 0.012
#> GSM559450 2 0.4963 0.571 0.284 0.696 0.000 0.020
#> GSM559451 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM559452 1 0.5673 0.303 0.596 0.372 0.000 0.032
#> GSM559454 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM559455 1 0.1557 0.891 0.944 0.000 0.000 0.056
#> GSM559456 1 0.4543 0.657 0.676 0.000 0.000 0.324
#> GSM559457 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM559458 1 0.4585 0.649 0.668 0.000 0.000 0.332
#> GSM559459 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM559460 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM559461 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM559462 1 0.0000 0.907 1.000 0.000 0.000 0.000
#> GSM559463 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM559464 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM559465 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM559467 1 0.0817 0.903 0.976 0.000 0.000 0.024
#> GSM559468 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM559469 1 0.0469 0.905 0.988 0.000 0.000 0.012
#> GSM559470 1 0.1389 0.893 0.952 0.000 0.000 0.048
#> GSM559471 1 0.0000 0.907 1.000 0.000 0.000 0.000
#> GSM559472 1 0.0188 0.907 0.996 0.000 0.000 0.004
#> GSM559473 2 0.1302 0.843 0.044 0.956 0.000 0.000
#> GSM559475 2 0.2921 0.756 0.140 0.860 0.000 0.000
#> GSM559477 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM559478 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM559479 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM559480 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM559481 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM559482 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM559435 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM559439 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM559443 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM559447 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM559449 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM559453 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM559466 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM559474 4 0.4500 1.000 0.000 0.000 0.316 0.684
#> GSM559476 1 0.3581 0.819 0.852 0.000 0.116 0.032
#> GSM559483 2 0.0000 0.869 0.000 1.000 0.000 0.000
#> GSM559484 4 0.4500 1.000 0.000 0.000 0.316 0.684
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 1 0.0000 0.84372 1.000 0.000 0.000 0.000 0.000
#> GSM559434 4 0.2351 0.54674 0.016 0.088 0.000 0.896 0.000
#> GSM559436 1 0.0000 0.84372 1.000 0.000 0.000 0.000 0.000
#> GSM559437 5 0.6693 0.17486 0.240 0.000 0.000 0.364 0.396
#> GSM559438 4 0.5096 -0.07681 0.444 0.036 0.000 0.520 0.000
#> GSM559440 4 0.4010 0.44915 0.160 0.056 0.000 0.784 0.000
#> GSM559441 1 0.4074 0.44631 0.636 0.000 0.000 0.364 0.000
#> GSM559442 1 0.2561 0.76045 0.856 0.000 0.000 0.144 0.000
#> GSM559444 4 0.3849 0.56839 0.016 0.232 0.000 0.752 0.000
#> GSM559445 4 0.4949 -0.03274 0.032 0.000 0.000 0.572 0.396
#> GSM559446 5 0.6671 0.16925 0.232 0.000 0.000 0.372 0.396
#> GSM559448 1 0.5153 0.57871 0.684 0.000 0.112 0.204 0.000
#> GSM559450 4 0.4227 0.52014 0.016 0.292 0.000 0.692 0.000
#> GSM559451 1 0.0000 0.84372 1.000 0.000 0.000 0.000 0.000
#> GSM559452 4 0.4971 0.34891 0.004 0.080 0.212 0.704 0.000
#> GSM559454 1 0.0000 0.84372 1.000 0.000 0.000 0.000 0.000
#> GSM559455 1 0.2848 0.74170 0.840 0.000 0.000 0.156 0.004
#> GSM559456 1 0.6233 -0.00581 0.460 0.000 0.000 0.144 0.396
#> GSM559457 1 0.0000 0.84372 1.000 0.000 0.000 0.000 0.000
#> GSM559458 1 0.7428 -0.02561 0.456 0.000 0.324 0.148 0.072
#> GSM559459 1 0.0000 0.84372 1.000 0.000 0.000 0.000 0.000
#> GSM559460 1 0.0000 0.84372 1.000 0.000 0.000 0.000 0.000
#> GSM559461 1 0.0000 0.84372 1.000 0.000 0.000 0.000 0.000
#> GSM559462 1 0.0000 0.84372 1.000 0.000 0.000 0.000 0.000
#> GSM559463 1 0.2020 0.79222 0.900 0.000 0.000 0.100 0.000
#> GSM559464 1 0.0000 0.84372 1.000 0.000 0.000 0.000 0.000
#> GSM559465 1 0.0404 0.83779 0.988 0.000 0.000 0.012 0.000
#> GSM559467 1 0.3003 0.70154 0.812 0.000 0.000 0.188 0.000
#> GSM559468 1 0.0162 0.84254 0.996 0.000 0.000 0.004 0.000
#> GSM559469 1 0.3039 0.73181 0.808 0.000 0.000 0.192 0.000
#> GSM559470 1 0.3932 0.50596 0.672 0.000 0.000 0.328 0.000
#> GSM559471 1 0.2230 0.78105 0.884 0.000 0.000 0.116 0.000
#> GSM559472 1 0.0000 0.84372 1.000 0.000 0.000 0.000 0.000
#> GSM559473 4 0.4192 0.35230 0.000 0.404 0.000 0.596 0.000
#> GSM559475 4 0.4114 0.40084 0.000 0.376 0.000 0.624 0.000
#> GSM559477 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM559478 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM559479 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM559481 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM559482 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.85260 0.000 0.000 1.000 0.000 0.000
#> GSM559439 3 0.0000 0.85260 0.000 0.000 1.000 0.000 0.000
#> GSM559443 3 0.1197 0.80129 0.000 0.000 0.952 0.048 0.000
#> GSM559447 3 0.0000 0.85260 0.000 0.000 1.000 0.000 0.000
#> GSM559449 3 0.0000 0.85260 0.000 0.000 1.000 0.000 0.000
#> GSM559453 3 0.1341 0.81496 0.000 0.000 0.944 0.000 0.056
#> GSM559466 3 0.0000 0.85260 0.000 0.000 1.000 0.000 0.000
#> GSM559474 5 0.4171 -0.07705 0.000 0.000 0.396 0.000 0.604
#> GSM559476 3 0.5938 -0.03108 0.376 0.000 0.512 0.112 0.000
#> GSM559483 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM559484 5 0.4171 -0.07705 0.000 0.000 0.396 0.000 0.604
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559434 6 0.0692 0.8213 0.004 0.020 0.000 0.000 0.000 0.976
#> GSM559436 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559437 4 0.2263 0.6376 0.016 0.000 0.000 0.884 0.000 0.100
#> GSM559438 6 0.2624 0.6839 0.148 0.004 0.000 0.004 0.000 0.844
#> GSM559440 6 0.0881 0.8171 0.008 0.012 0.000 0.008 0.000 0.972
#> GSM559441 4 0.5220 0.4469 0.372 0.000 0.000 0.528 0.000 0.100
#> GSM559442 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559444 6 0.1082 0.8229 0.004 0.040 0.000 0.000 0.000 0.956
#> GSM559445 4 0.2100 0.6188 0.004 0.000 0.000 0.884 0.000 0.112
#> GSM559446 4 0.2263 0.6376 0.016 0.000 0.000 0.884 0.000 0.100
#> GSM559448 1 0.2121 0.8318 0.892 0.000 0.000 0.096 0.000 0.012
#> GSM559450 6 0.1471 0.8153 0.004 0.064 0.000 0.000 0.000 0.932
#> GSM559451 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559452 6 0.0547 0.8203 0.000 0.020 0.000 0.000 0.000 0.980
#> GSM559454 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559455 1 0.3418 0.6479 0.784 0.000 0.000 0.184 0.000 0.032
#> GSM559456 4 0.4118 0.5008 0.352 0.000 0.000 0.628 0.000 0.020
#> GSM559457 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559458 1 0.4326 0.0392 0.572 0.000 0.000 0.404 0.000 0.024
#> GSM559459 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559460 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559461 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559462 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559463 1 0.0405 0.9172 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM559464 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559465 1 0.0260 0.9195 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM559467 1 0.1204 0.8742 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM559468 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559469 1 0.0458 0.9106 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM559470 6 0.4326 0.1213 0.404 0.000 0.000 0.024 0.000 0.572
#> GSM559471 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559472 1 0.0000 0.9241 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559473 6 0.2378 0.7570 0.000 0.152 0.000 0.000 0.000 0.848
#> GSM559475 6 0.2260 0.7673 0.000 0.140 0.000 0.000 0.000 0.860
#> GSM559477 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559478 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559479 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559480 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559481 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559482 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.9864 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559439 3 0.0000 0.9864 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559443 3 0.1461 0.9439 0.000 0.000 0.940 0.044 0.000 0.016
#> GSM559447 3 0.0000 0.9864 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559449 3 0.0146 0.9851 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM559453 3 0.0632 0.9738 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM559466 3 0.0000 0.9864 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559474 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM559476 1 0.5829 0.1964 0.524 0.000 0.336 0.116 0.000 0.024
#> GSM559483 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559484 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000 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 disease.state(p) k
#> SD:mclust 50 4.65e-10 2
#> SD:mclust 40 2.38e-08 3
#> SD:mclust 51 1.12e-08 4
#> SD:mclust 38 3.48e-07 5
#> SD:mclust 48 4.05e-08 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 21512 rows and 52 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 0.707 0.881 0.947 0.4827 0.509 0.509
#> 3 3 1.000 0.963 0.984 0.2996 0.689 0.481
#> 4 4 0.662 0.598 0.831 0.1454 0.855 0.637
#> 5 5 0.670 0.667 0.787 0.0929 0.828 0.482
#> 6 6 0.721 0.730 0.804 0.0516 0.939 0.734
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM559433 1 0.4562 0.884 0.904 0.096
#> GSM559434 2 0.0000 0.919 0.000 1.000
#> GSM559436 1 0.0000 0.952 1.000 0.000
#> GSM559437 1 0.5946 0.836 0.856 0.144
#> GSM559438 2 0.0000 0.919 0.000 1.000
#> GSM559440 2 0.0000 0.919 0.000 1.000
#> GSM559441 2 0.9732 0.328 0.404 0.596
#> GSM559442 1 0.2948 0.919 0.948 0.052
#> GSM559444 2 0.0000 0.919 0.000 1.000
#> GSM559445 2 0.7056 0.741 0.192 0.808
#> GSM559446 1 0.7528 0.744 0.784 0.216
#> GSM559448 1 0.0000 0.952 1.000 0.000
#> GSM559450 2 0.0000 0.919 0.000 1.000
#> GSM559451 1 0.5294 0.863 0.880 0.120
#> GSM559452 2 0.0672 0.914 0.008 0.992
#> GSM559454 1 0.0000 0.952 1.000 0.000
#> GSM559455 1 0.5408 0.859 0.876 0.124
#> GSM559456 1 0.0000 0.952 1.000 0.000
#> GSM559457 1 0.0938 0.945 0.988 0.012
#> GSM559458 1 0.0000 0.952 1.000 0.000
#> GSM559459 1 0.0000 0.952 1.000 0.000
#> GSM559460 1 0.0000 0.952 1.000 0.000
#> GSM559461 1 0.0000 0.952 1.000 0.000
#> GSM559462 1 0.8016 0.700 0.756 0.244
#> GSM559463 1 0.0000 0.952 1.000 0.000
#> GSM559464 1 0.0000 0.952 1.000 0.000
#> GSM559465 1 0.0000 0.952 1.000 0.000
#> GSM559467 2 0.8267 0.643 0.260 0.740
#> GSM559468 1 0.0000 0.952 1.000 0.000
#> GSM559469 2 0.9754 0.317 0.408 0.592
#> GSM559470 2 0.0376 0.917 0.004 0.996
#> GSM559471 1 0.8608 0.626 0.716 0.284
#> GSM559472 1 0.0000 0.952 1.000 0.000
#> GSM559473 2 0.0000 0.919 0.000 1.000
#> GSM559475 2 0.0000 0.919 0.000 1.000
#> GSM559477 2 0.0000 0.919 0.000 1.000
#> GSM559478 2 0.0000 0.919 0.000 1.000
#> GSM559479 2 0.0000 0.919 0.000 1.000
#> GSM559480 2 0.0000 0.919 0.000 1.000
#> GSM559481 2 0.0000 0.919 0.000 1.000
#> GSM559482 2 0.0000 0.919 0.000 1.000
#> GSM559435 1 0.0000 0.952 1.000 0.000
#> GSM559439 1 0.0000 0.952 1.000 0.000
#> GSM559443 1 0.0000 0.952 1.000 0.000
#> GSM559447 1 0.0000 0.952 1.000 0.000
#> GSM559449 1 0.0000 0.952 1.000 0.000
#> GSM559453 1 0.0000 0.952 1.000 0.000
#> GSM559466 1 0.0000 0.952 1.000 0.000
#> GSM559474 1 0.0000 0.952 1.000 0.000
#> GSM559476 1 0.0000 0.952 1.000 0.000
#> GSM559483 2 0.0000 0.919 0.000 1.000
#> GSM559484 2 0.6973 0.745 0.188 0.812
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559434 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559436 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559437 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559438 2 0.2165 0.912 0.064 0.936 0.000
#> GSM559440 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559441 1 0.1163 0.953 0.972 0.028 0.000
#> GSM559442 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559444 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559445 1 0.5706 0.545 0.680 0.320 0.000
#> GSM559446 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559448 1 0.1031 0.955 0.976 0.000 0.024
#> GSM559450 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559451 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559452 2 0.3267 0.868 0.000 0.884 0.116
#> GSM559454 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559455 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559456 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559457 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559458 1 0.1031 0.956 0.976 0.000 0.024
#> GSM559459 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559460 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559462 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559463 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559464 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559465 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559467 1 0.0892 0.960 0.980 0.020 0.000
#> GSM559468 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559469 1 0.0424 0.968 0.992 0.008 0.000
#> GSM559470 1 0.4931 0.709 0.768 0.232 0.000
#> GSM559471 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559472 1 0.0000 0.973 1.000 0.000 0.000
#> GSM559473 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559475 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559477 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559478 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559479 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559480 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559481 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559482 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559435 3 0.0000 0.998 0.000 0.000 1.000
#> GSM559439 3 0.0000 0.998 0.000 0.000 1.000
#> GSM559443 3 0.0237 0.995 0.004 0.000 0.996
#> GSM559447 3 0.0000 0.998 0.000 0.000 1.000
#> GSM559449 3 0.0000 0.998 0.000 0.000 1.000
#> GSM559453 3 0.0000 0.998 0.000 0.000 1.000
#> GSM559466 3 0.0000 0.998 0.000 0.000 1.000
#> GSM559474 3 0.0000 0.998 0.000 0.000 1.000
#> GSM559476 3 0.0592 0.986 0.012 0.000 0.988
#> GSM559483 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559484 3 0.0000 0.998 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.1302 0.7582 0.956 0.000 0.000 0.044
#> GSM559434 2 0.0376 0.9486 0.000 0.992 0.004 0.004
#> GSM559436 4 0.4331 0.4158 0.288 0.000 0.000 0.712
#> GSM559437 1 0.1209 0.7479 0.964 0.000 0.032 0.004
#> GSM559438 2 0.4008 0.6358 0.244 0.756 0.000 0.000
#> GSM559440 2 0.2773 0.8522 0.116 0.880 0.000 0.004
#> GSM559441 1 0.0712 0.7600 0.984 0.004 0.004 0.008
#> GSM559442 4 0.4372 0.4155 0.268 0.000 0.004 0.728
#> GSM559444 2 0.2131 0.9167 0.040 0.936 0.016 0.008
#> GSM559445 1 0.4134 0.5852 0.796 0.008 0.188 0.008
#> GSM559446 1 0.2944 0.6628 0.868 0.000 0.128 0.004
#> GSM559448 4 0.0707 0.4386 0.020 0.000 0.000 0.980
#> GSM559450 2 0.1114 0.9405 0.004 0.972 0.016 0.008
#> GSM559451 1 0.1118 0.7613 0.964 0.000 0.000 0.036
#> GSM559452 2 0.2924 0.8676 0.000 0.884 0.100 0.016
#> GSM559454 1 0.4761 0.3956 0.628 0.000 0.000 0.372
#> GSM559455 1 0.0000 0.7640 1.000 0.000 0.000 0.000
#> GSM559456 1 0.0469 0.7654 0.988 0.000 0.000 0.012
#> GSM559457 1 0.0592 0.7652 0.984 0.000 0.000 0.016
#> GSM559458 1 0.2500 0.7430 0.916 0.000 0.044 0.040
#> GSM559459 1 0.4193 0.5702 0.732 0.000 0.000 0.268
#> GSM559460 1 0.3975 0.6068 0.760 0.000 0.000 0.240
#> GSM559461 1 0.4643 0.4319 0.656 0.000 0.000 0.344
#> GSM559462 1 0.0188 0.7650 0.996 0.000 0.000 0.004
#> GSM559463 4 0.2469 0.5135 0.108 0.000 0.000 0.892
#> GSM559464 4 0.4994 -0.0930 0.480 0.000 0.000 0.520
#> GSM559465 4 0.4994 -0.0868 0.480 0.000 0.000 0.520
#> GSM559467 1 0.0188 0.7639 0.996 0.004 0.000 0.000
#> GSM559468 1 0.4981 0.1558 0.536 0.000 0.000 0.464
#> GSM559469 1 0.7210 0.0304 0.448 0.120 0.004 0.428
#> GSM559470 1 0.1256 0.7524 0.964 0.028 0.000 0.008
#> GSM559471 1 0.4998 0.0783 0.512 0.000 0.000 0.488
#> GSM559472 4 0.4994 -0.0623 0.480 0.000 0.000 0.520
#> GSM559473 2 0.0469 0.9468 0.000 0.988 0.000 0.012
#> GSM559475 2 0.0000 0.9495 0.000 1.000 0.000 0.000
#> GSM559477 2 0.0000 0.9495 0.000 1.000 0.000 0.000
#> GSM559478 2 0.0188 0.9492 0.000 0.996 0.000 0.004
#> GSM559479 2 0.0188 0.9489 0.000 0.996 0.000 0.004
#> GSM559480 2 0.0336 0.9485 0.000 0.992 0.000 0.008
#> GSM559481 2 0.0336 0.9485 0.000 0.992 0.000 0.008
#> GSM559482 2 0.0000 0.9495 0.000 1.000 0.000 0.000
#> GSM559435 4 0.4967 -0.5400 0.000 0.000 0.452 0.548
#> GSM559439 4 0.4961 -0.5318 0.000 0.000 0.448 0.552
#> GSM559443 4 0.2408 0.3166 0.000 0.000 0.104 0.896
#> GSM559447 3 0.4925 0.6503 0.000 0.000 0.572 0.428
#> GSM559449 3 0.4008 0.7710 0.000 0.000 0.756 0.244
#> GSM559453 3 0.2589 0.7846 0.000 0.000 0.884 0.116
#> GSM559466 3 0.4855 0.6810 0.000 0.000 0.600 0.400
#> GSM559474 3 0.0000 0.7518 0.000 0.000 1.000 0.000
#> GSM559476 4 0.1940 0.3600 0.000 0.000 0.076 0.924
#> GSM559483 2 0.0000 0.9495 0.000 1.000 0.000 0.000
#> GSM559484 3 0.0376 0.7520 0.000 0.004 0.992 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 4 0.1300 0.9169 0.028 0.000 0.000 0.956 0.016
#> GSM559434 2 0.5533 0.7612 0.192 0.680 0.000 0.016 0.112
#> GSM559436 5 0.8583 -0.2962 0.224 0.000 0.232 0.256 0.288
#> GSM559437 4 0.1012 0.9137 0.012 0.000 0.000 0.968 0.020
#> GSM559438 2 0.6500 0.6772 0.236 0.600 0.000 0.052 0.112
#> GSM559440 2 0.7530 0.6126 0.212 0.516 0.000 0.148 0.124
#> GSM559441 4 0.1059 0.9018 0.020 0.008 0.000 0.968 0.004
#> GSM559442 1 0.2529 0.6299 0.900 0.004 0.056 0.000 0.040
#> GSM559444 2 0.6440 0.7347 0.144 0.644 0.000 0.092 0.120
#> GSM559445 4 0.2577 0.8158 0.016 0.008 0.000 0.892 0.084
#> GSM559446 4 0.1357 0.8789 0.004 0.000 0.000 0.948 0.048
#> GSM559448 3 0.6244 0.4350 0.120 0.008 0.556 0.004 0.312
#> GSM559450 2 0.5370 0.7746 0.148 0.708 0.000 0.020 0.124
#> GSM559451 4 0.3067 0.7996 0.140 0.000 0.004 0.844 0.012
#> GSM559452 1 0.5685 0.0671 0.556 0.048 0.004 0.012 0.380
#> GSM559454 1 0.6060 0.6531 0.576 0.000 0.000 0.216 0.208
#> GSM559455 4 0.0609 0.9194 0.020 0.000 0.000 0.980 0.000
#> GSM559456 4 0.1043 0.9173 0.040 0.000 0.000 0.960 0.000
#> GSM559457 4 0.0794 0.9197 0.028 0.000 0.000 0.972 0.000
#> GSM559458 1 0.4642 0.7130 0.772 0.000 0.028 0.136 0.064
#> GSM559459 1 0.5638 0.6965 0.632 0.000 0.000 0.216 0.152
#> GSM559460 1 0.2648 0.7626 0.848 0.000 0.000 0.152 0.000
#> GSM559461 1 0.5159 0.7299 0.688 0.000 0.000 0.188 0.124
#> GSM559462 4 0.3010 0.7659 0.172 0.000 0.000 0.824 0.004
#> GSM559463 1 0.6743 0.3376 0.516 0.000 0.212 0.016 0.256
#> GSM559464 1 0.3247 0.7659 0.840 0.000 0.008 0.136 0.016
#> GSM559465 1 0.4409 0.7550 0.752 0.000 0.000 0.176 0.072
#> GSM559467 4 0.1956 0.8886 0.076 0.000 0.000 0.916 0.008
#> GSM559468 1 0.3155 0.7607 0.848 0.000 0.016 0.128 0.008
#> GSM559469 1 0.3460 0.7416 0.828 0.000 0.000 0.128 0.044
#> GSM559470 4 0.1173 0.9184 0.020 0.012 0.000 0.964 0.004
#> GSM559471 1 0.3151 0.7664 0.836 0.000 0.000 0.144 0.020
#> GSM559472 1 0.7335 0.4994 0.444 0.000 0.036 0.256 0.264
#> GSM559473 2 0.1251 0.8467 0.008 0.956 0.000 0.000 0.036
#> GSM559475 2 0.0703 0.8403 0.000 0.976 0.000 0.000 0.024
#> GSM559477 2 0.0798 0.8476 0.008 0.976 0.000 0.000 0.016
#> GSM559478 2 0.0794 0.8393 0.000 0.972 0.000 0.000 0.028
#> GSM559479 2 0.3967 0.8095 0.108 0.800 0.000 0.000 0.092
#> GSM559480 2 0.0955 0.8381 0.004 0.968 0.000 0.000 0.028
#> GSM559481 2 0.0955 0.8381 0.004 0.968 0.000 0.000 0.028
#> GSM559482 2 0.0162 0.8445 0.000 0.996 0.000 0.000 0.004
#> GSM559435 3 0.2873 0.5964 0.016 0.000 0.856 0.000 0.128
#> GSM559439 3 0.2573 0.5967 0.016 0.000 0.880 0.000 0.104
#> GSM559443 3 0.5641 0.4887 0.120 0.000 0.612 0.000 0.268
#> GSM559447 3 0.0162 0.5572 0.004 0.000 0.996 0.000 0.000
#> GSM559449 3 0.2516 0.3898 0.000 0.000 0.860 0.000 0.140
#> GSM559453 3 0.4114 -0.1702 0.000 0.000 0.624 0.000 0.376
#> GSM559466 3 0.0794 0.5334 0.000 0.000 0.972 0.000 0.028
#> GSM559474 5 0.4410 0.2496 0.000 0.000 0.440 0.004 0.556
#> GSM559476 3 0.5641 0.4870 0.120 0.000 0.612 0.000 0.268
#> GSM559483 2 0.0703 0.8475 0.000 0.976 0.000 0.000 0.024
#> GSM559484 5 0.4410 0.2496 0.000 0.000 0.440 0.004 0.556
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 4 0.3146 0.782 0.000 0.000 0.012 0.848 0.060 0.080
#> GSM559434 6 0.3771 0.748 0.044 0.172 0.000 0.008 0.000 0.776
#> GSM559436 4 0.8660 0.136 0.196 0.012 0.252 0.336 0.108 0.096
#> GSM559437 4 0.0632 0.802 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM559438 6 0.4516 0.732 0.084 0.184 0.000 0.012 0.000 0.720
#> GSM559440 6 0.3196 0.743 0.016 0.108 0.000 0.036 0.000 0.840
#> GSM559441 4 0.1814 0.782 0.000 0.000 0.000 0.900 0.000 0.100
#> GSM559442 1 0.2527 0.707 0.832 0.000 0.000 0.000 0.000 0.168
#> GSM559444 6 0.3807 0.717 0.000 0.192 0.000 0.052 0.000 0.756
#> GSM559445 4 0.2278 0.773 0.000 0.000 0.000 0.868 0.004 0.128
#> GSM559446 4 0.2274 0.802 0.008 0.000 0.000 0.892 0.012 0.088
#> GSM559448 3 0.3441 0.729 0.004 0.036 0.836 0.000 0.096 0.028
#> GSM559450 6 0.3163 0.718 0.000 0.232 0.000 0.004 0.000 0.764
#> GSM559451 4 0.5106 0.674 0.160 0.000 0.012 0.708 0.032 0.088
#> GSM559452 6 0.4607 0.354 0.328 0.000 0.000 0.000 0.056 0.616
#> GSM559454 1 0.6287 0.670 0.664 0.028 0.024 0.100 0.072 0.112
#> GSM559455 4 0.0547 0.802 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM559456 4 0.0717 0.803 0.016 0.000 0.000 0.976 0.000 0.008
#> GSM559457 4 0.0777 0.805 0.004 0.000 0.000 0.972 0.000 0.024
#> GSM559458 1 0.5180 0.560 0.680 0.000 0.004 0.020 0.148 0.148
#> GSM559459 1 0.5717 0.683 0.684 0.004 0.012 0.100 0.088 0.112
#> GSM559460 1 0.1714 0.759 0.908 0.000 0.000 0.000 0.000 0.092
#> GSM559461 1 0.4994 0.737 0.752 0.000 0.040 0.076 0.080 0.052
#> GSM559462 4 0.4881 0.508 0.276 0.000 0.000 0.644 0.012 0.068
#> GSM559463 1 0.6125 0.605 0.632 0.008 0.180 0.008 0.092 0.080
#> GSM559464 1 0.0363 0.774 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM559465 1 0.3116 0.763 0.868 0.004 0.004 0.044 0.028 0.052
#> GSM559467 4 0.5011 0.642 0.104 0.160 0.000 0.704 0.004 0.028
#> GSM559468 1 0.1957 0.750 0.888 0.000 0.000 0.000 0.000 0.112
#> GSM559469 1 0.1700 0.762 0.916 0.000 0.000 0.000 0.004 0.080
#> GSM559470 4 0.3812 0.747 0.056 0.028 0.000 0.812 0.004 0.100
#> GSM559471 1 0.1577 0.774 0.940 0.000 0.000 0.008 0.016 0.036
#> GSM559472 1 0.6693 0.523 0.580 0.020 0.012 0.212 0.068 0.108
#> GSM559473 2 0.2331 0.869 0.032 0.888 0.000 0.000 0.000 0.080
#> GSM559475 2 0.0692 0.907 0.004 0.976 0.000 0.000 0.000 0.020
#> GSM559477 2 0.2340 0.840 0.000 0.852 0.000 0.000 0.000 0.148
#> GSM559478 2 0.0260 0.908 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM559479 6 0.3828 0.381 0.000 0.440 0.000 0.000 0.000 0.560
#> GSM559480 2 0.0146 0.905 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM559481 2 0.0000 0.907 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559482 2 0.1910 0.879 0.000 0.892 0.000 0.000 0.000 0.108
#> GSM559435 3 0.0000 0.810 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559439 3 0.0937 0.811 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM559443 3 0.2191 0.759 0.004 0.000 0.876 0.000 0.120 0.000
#> GSM559447 3 0.1501 0.799 0.000 0.000 0.924 0.000 0.076 0.000
#> GSM559449 3 0.2631 0.713 0.000 0.000 0.820 0.000 0.180 0.000
#> GSM559453 3 0.3789 0.210 0.000 0.000 0.584 0.000 0.416 0.000
#> GSM559466 3 0.1957 0.779 0.000 0.000 0.888 0.000 0.112 0.000
#> GSM559474 5 0.2278 1.000 0.000 0.000 0.128 0.000 0.868 0.004
#> GSM559476 3 0.1806 0.782 0.004 0.000 0.908 0.000 0.088 0.000
#> GSM559483 2 0.2178 0.858 0.000 0.868 0.000 0.000 0.000 0.132
#> GSM559484 5 0.2278 1.000 0.000 0.000 0.128 0.000 0.868 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:NMF 50 2.37e-01 2
#> SD:NMF 52 8.38e-11 3
#> SD:NMF 37 8.86e-07 4
#> SD:NMF 41 4.46e-07 5
#> SD:NMF 48 5.00e-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", "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 21512 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.675 0.893 0.944 0.3941 0.581 0.581
#> 3 3 0.623 0.806 0.902 0.2687 0.947 0.909
#> 4 4 0.640 0.865 0.894 0.1957 0.837 0.692
#> 5 5 0.701 0.820 0.890 0.1477 0.932 0.817
#> 6 6 0.727 0.851 0.884 0.0464 0.991 0.971
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
#> GSM559433 1 0.0376 0.963 0.996 0.004
#> GSM559434 2 0.8713 0.711 0.292 0.708
#> GSM559436 1 0.0000 0.966 1.000 0.000
#> GSM559437 1 0.0000 0.966 1.000 0.000
#> GSM559438 2 0.9358 0.615 0.352 0.648
#> GSM559440 2 0.9358 0.615 0.352 0.648
#> GSM559441 1 0.0938 0.959 0.988 0.012
#> GSM559442 1 0.8144 0.615 0.748 0.252
#> GSM559444 2 0.6247 0.838 0.156 0.844
#> GSM559445 1 0.0000 0.966 1.000 0.000
#> GSM559446 1 0.0000 0.966 1.000 0.000
#> GSM559448 1 0.0000 0.966 1.000 0.000
#> GSM559450 2 0.6247 0.838 0.156 0.844
#> GSM559451 1 0.0000 0.966 1.000 0.000
#> GSM559452 2 0.8608 0.721 0.284 0.716
#> GSM559454 1 0.0000 0.966 1.000 0.000
#> GSM559455 1 0.0938 0.959 0.988 0.012
#> GSM559456 1 0.0000 0.966 1.000 0.000
#> GSM559457 1 0.0000 0.966 1.000 0.000
#> GSM559458 1 0.0938 0.959 0.988 0.012
#> GSM559459 1 0.0000 0.966 1.000 0.000
#> GSM559460 1 0.0000 0.966 1.000 0.000
#> GSM559461 1 0.0000 0.966 1.000 0.000
#> GSM559462 1 0.0000 0.966 1.000 0.000
#> GSM559463 1 0.0000 0.966 1.000 0.000
#> GSM559464 1 0.0000 0.966 1.000 0.000
#> GSM559465 1 0.0000 0.966 1.000 0.000
#> GSM559467 1 0.3431 0.907 0.936 0.064
#> GSM559468 1 0.2236 0.940 0.964 0.036
#> GSM559469 1 0.2236 0.940 0.964 0.036
#> GSM559470 1 0.3733 0.898 0.928 0.072
#> GSM559471 1 0.2236 0.941 0.964 0.036
#> GSM559472 1 0.0000 0.966 1.000 0.000
#> GSM559473 2 0.6048 0.842 0.148 0.852
#> GSM559475 2 0.6048 0.842 0.148 0.852
#> GSM559477 2 0.0000 0.854 0.000 1.000
#> GSM559478 2 0.0000 0.854 0.000 1.000
#> GSM559479 2 0.0000 0.854 0.000 1.000
#> GSM559480 2 0.0000 0.854 0.000 1.000
#> GSM559481 2 0.0000 0.854 0.000 1.000
#> GSM559482 2 0.0000 0.854 0.000 1.000
#> GSM559435 1 0.0000 0.966 1.000 0.000
#> GSM559439 1 0.0000 0.966 1.000 0.000
#> GSM559443 1 0.0000 0.966 1.000 0.000
#> GSM559447 1 0.0000 0.966 1.000 0.000
#> GSM559449 1 0.0000 0.966 1.000 0.000
#> GSM559453 1 0.0000 0.966 1.000 0.000
#> GSM559466 1 0.0000 0.966 1.000 0.000
#> GSM559474 1 0.8207 0.615 0.744 0.256
#> GSM559476 1 0.0000 0.966 1.000 0.000
#> GSM559483 2 0.0000 0.854 0.000 1.000
#> GSM559484 1 0.8207 0.615 0.744 0.256
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0237 0.897 0.996 0.000 0.004
#> GSM559434 2 0.6771 0.655 0.276 0.684 0.040
#> GSM559436 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559437 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559438 2 0.7186 0.588 0.336 0.624 0.040
#> GSM559440 2 0.7186 0.588 0.336 0.624 0.040
#> GSM559441 1 0.1031 0.888 0.976 0.000 0.024
#> GSM559442 1 0.6715 0.550 0.716 0.228 0.056
#> GSM559444 2 0.5159 0.778 0.140 0.820 0.040
#> GSM559445 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559446 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559448 1 0.0592 0.894 0.988 0.000 0.012
#> GSM559450 2 0.5159 0.778 0.140 0.820 0.040
#> GSM559451 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559452 2 0.6950 0.679 0.252 0.692 0.056
#> GSM559454 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559455 1 0.1031 0.888 0.976 0.000 0.024
#> GSM559456 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559457 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559458 1 0.1031 0.888 0.976 0.000 0.024
#> GSM559459 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559460 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559462 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559463 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559464 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559465 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559467 1 0.2165 0.855 0.936 0.064 0.000
#> GSM559468 1 0.2339 0.868 0.940 0.012 0.048
#> GSM559469 1 0.2339 0.868 0.940 0.012 0.048
#> GSM559470 1 0.2356 0.849 0.928 0.072 0.000
#> GSM559471 1 0.2031 0.879 0.952 0.016 0.032
#> GSM559472 1 0.0000 0.898 1.000 0.000 0.000
#> GSM559473 2 0.5028 0.781 0.132 0.828 0.040
#> GSM559475 2 0.5028 0.781 0.132 0.828 0.040
#> GSM559477 2 0.0000 0.771 0.000 1.000 0.000
#> GSM559478 2 0.0000 0.771 0.000 1.000 0.000
#> GSM559479 2 0.0000 0.771 0.000 1.000 0.000
#> GSM559480 2 0.0000 0.771 0.000 1.000 0.000
#> GSM559481 2 0.0000 0.771 0.000 1.000 0.000
#> GSM559482 2 0.0000 0.771 0.000 1.000 0.000
#> GSM559435 1 0.5591 0.641 0.696 0.000 0.304
#> GSM559439 1 0.5397 0.668 0.720 0.000 0.280
#> GSM559443 1 0.5397 0.668 0.720 0.000 0.280
#> GSM559447 1 0.5591 0.641 0.696 0.000 0.304
#> GSM559449 1 0.5591 0.641 0.696 0.000 0.304
#> GSM559453 1 0.5678 0.625 0.684 0.000 0.316
#> GSM559466 1 0.5591 0.641 0.696 0.000 0.304
#> GSM559474 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559476 1 0.5216 0.690 0.740 0.000 0.260
#> GSM559483 2 0.0000 0.771 0.000 1.000 0.000
#> GSM559484 3 0.0000 1.000 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.0188 0.962 0.996 0.004 0.000 0.000
#> GSM559434 2 0.4539 0.625 0.272 0.720 0.008 0.000
#> GSM559436 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM559437 1 0.0592 0.956 0.984 0.000 0.016 0.000
#> GSM559438 2 0.4781 0.559 0.336 0.660 0.004 0.000
#> GSM559440 2 0.4781 0.559 0.336 0.660 0.004 0.000
#> GSM559441 1 0.1004 0.951 0.972 0.024 0.004 0.000
#> GSM559442 1 0.4927 0.569 0.712 0.264 0.024 0.000
#> GSM559444 2 0.2921 0.725 0.140 0.860 0.000 0.000
#> GSM559445 1 0.0592 0.956 0.984 0.000 0.016 0.000
#> GSM559446 1 0.0592 0.956 0.984 0.000 0.016 0.000
#> GSM559448 1 0.0469 0.957 0.988 0.000 0.012 0.000
#> GSM559450 2 0.2921 0.725 0.140 0.860 0.000 0.000
#> GSM559451 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM559452 2 0.4807 0.639 0.248 0.728 0.024 0.000
#> GSM559454 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM559455 1 0.1004 0.951 0.972 0.024 0.004 0.000
#> GSM559456 1 0.1022 0.943 0.968 0.000 0.032 0.000
#> GSM559457 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM559458 1 0.1004 0.951 0.972 0.024 0.004 0.000
#> GSM559459 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM559460 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM559461 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM559462 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM559463 1 0.0188 0.961 0.996 0.000 0.004 0.000
#> GSM559464 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM559465 1 0.0188 0.961 0.996 0.000 0.004 0.000
#> GSM559467 1 0.1824 0.911 0.936 0.060 0.004 0.000
#> GSM559468 1 0.1854 0.926 0.940 0.048 0.012 0.000
#> GSM559469 1 0.1854 0.926 0.940 0.048 0.012 0.000
#> GSM559470 1 0.1978 0.904 0.928 0.068 0.004 0.000
#> GSM559471 1 0.1584 0.939 0.952 0.036 0.012 0.000
#> GSM559472 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM559473 2 0.2814 0.726 0.132 0.868 0.000 0.000
#> GSM559475 2 0.2814 0.726 0.132 0.868 0.000 0.000
#> GSM559477 2 0.3852 0.673 0.000 0.808 0.180 0.012
#> GSM559478 2 0.2888 0.698 0.000 0.872 0.124 0.004
#> GSM559479 2 0.3852 0.673 0.000 0.808 0.180 0.012
#> GSM559480 2 0.2888 0.698 0.000 0.872 0.124 0.004
#> GSM559481 2 0.2888 0.698 0.000 0.872 0.124 0.004
#> GSM559482 2 0.3852 0.673 0.000 0.808 0.180 0.012
#> GSM559435 3 0.3444 0.963 0.184 0.000 0.816 0.000
#> GSM559439 3 0.3837 0.944 0.224 0.000 0.776 0.000
#> GSM559443 3 0.3837 0.944 0.224 0.000 0.776 0.000
#> GSM559447 3 0.3444 0.963 0.184 0.000 0.816 0.000
#> GSM559449 3 0.3444 0.963 0.184 0.000 0.816 0.000
#> GSM559453 3 0.3764 0.946 0.172 0.000 0.816 0.012
#> GSM559466 3 0.3444 0.963 0.184 0.000 0.816 0.000
#> GSM559474 4 0.0469 1.000 0.000 0.000 0.012 0.988
#> GSM559476 3 0.4008 0.916 0.244 0.000 0.756 0.000
#> GSM559483 2 0.3852 0.673 0.000 0.808 0.180 0.012
#> GSM559484 4 0.0469 1.000 0.000 0.000 0.012 0.988
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 1 0.1908 0.909 0.908 0.000 0.000 0.092 0.000
#> GSM559434 4 0.5538 0.670 0.088 0.324 0.000 0.588 0.000
#> GSM559436 1 0.0162 0.912 0.996 0.000 0.000 0.004 0.000
#> GSM559437 1 0.2616 0.902 0.880 0.000 0.020 0.100 0.000
#> GSM559438 4 0.5797 0.642 0.132 0.276 0.000 0.592 0.000
#> GSM559440 4 0.5797 0.642 0.132 0.276 0.000 0.592 0.000
#> GSM559441 1 0.2891 0.868 0.824 0.000 0.000 0.176 0.000
#> GSM559442 4 0.4297 -0.198 0.472 0.000 0.000 0.528 0.000
#> GSM559444 4 0.4273 0.636 0.000 0.448 0.000 0.552 0.000
#> GSM559445 1 0.2616 0.902 0.880 0.000 0.020 0.100 0.000
#> GSM559446 1 0.2616 0.902 0.880 0.000 0.020 0.100 0.000
#> GSM559448 1 0.0693 0.908 0.980 0.000 0.012 0.008 0.000
#> GSM559450 4 0.4273 0.636 0.000 0.448 0.000 0.552 0.000
#> GSM559451 1 0.0794 0.916 0.972 0.000 0.000 0.028 0.000
#> GSM559452 4 0.4009 0.653 0.004 0.312 0.000 0.684 0.000
#> GSM559454 1 0.0162 0.912 0.996 0.000 0.000 0.004 0.000
#> GSM559455 1 0.2891 0.868 0.824 0.000 0.000 0.176 0.000
#> GSM559456 1 0.2959 0.896 0.864 0.000 0.036 0.100 0.000
#> GSM559457 1 0.0794 0.916 0.972 0.000 0.000 0.028 0.000
#> GSM559458 1 0.2891 0.868 0.824 0.000 0.000 0.176 0.000
#> GSM559459 1 0.0162 0.912 0.996 0.000 0.000 0.004 0.000
#> GSM559460 1 0.0162 0.912 0.996 0.000 0.000 0.004 0.000
#> GSM559461 1 0.0162 0.912 0.996 0.000 0.000 0.004 0.000
#> GSM559462 1 0.1043 0.915 0.960 0.000 0.000 0.040 0.000
#> GSM559463 1 0.0451 0.911 0.988 0.000 0.004 0.008 0.000
#> GSM559464 1 0.0290 0.911 0.992 0.000 0.000 0.008 0.000
#> GSM559465 1 0.0451 0.911 0.988 0.000 0.004 0.008 0.000
#> GSM559467 1 0.2891 0.863 0.824 0.000 0.000 0.176 0.000
#> GSM559468 1 0.3395 0.792 0.764 0.000 0.000 0.236 0.000
#> GSM559469 1 0.3395 0.792 0.764 0.000 0.000 0.236 0.000
#> GSM559470 1 0.3143 0.840 0.796 0.000 0.000 0.204 0.000
#> GSM559471 1 0.2690 0.872 0.844 0.000 0.000 0.156 0.000
#> GSM559472 1 0.0510 0.915 0.984 0.000 0.000 0.016 0.000
#> GSM559473 4 0.4287 0.623 0.000 0.460 0.000 0.540 0.000
#> GSM559475 4 0.4287 0.623 0.000 0.460 0.000 0.540 0.000
#> GSM559477 2 0.0000 0.741 0.000 1.000 0.000 0.000 0.000
#> GSM559478 2 0.4547 0.680 0.000 0.588 0.012 0.400 0.000
#> GSM559479 2 0.0000 0.741 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.4547 0.680 0.000 0.588 0.012 0.400 0.000
#> GSM559481 2 0.4547 0.680 0.000 0.588 0.012 0.400 0.000
#> GSM559482 2 0.0000 0.741 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.0404 0.960 0.012 0.000 0.988 0.000 0.000
#> GSM559439 3 0.1341 0.937 0.056 0.000 0.944 0.000 0.000
#> GSM559443 3 0.1341 0.937 0.056 0.000 0.944 0.000 0.000
#> GSM559447 3 0.0404 0.960 0.012 0.000 0.988 0.000 0.000
#> GSM559449 3 0.0404 0.960 0.012 0.000 0.988 0.000 0.000
#> GSM559453 3 0.0404 0.943 0.000 0.000 0.988 0.000 0.012
#> GSM559466 3 0.0404 0.960 0.012 0.000 0.988 0.000 0.000
#> GSM559474 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM559476 3 0.2046 0.911 0.068 0.000 0.916 0.016 0.000
#> GSM559483 2 0.0000 0.741 0.000 1.000 0.000 0.000 0.000
#> GSM559484 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.1700 0.877 0.928 0.000 0.000 0.024 0.000 0.048
#> GSM559434 6 0.3146 0.730 0.080 0.060 0.000 0.012 0.000 0.848
#> GSM559436 1 0.2003 0.864 0.884 0.000 0.000 0.116 0.000 0.000
#> GSM559437 1 0.2602 0.859 0.888 0.000 0.020 0.052 0.000 0.040
#> GSM559438 6 0.3313 0.679 0.160 0.024 0.000 0.008 0.000 0.808
#> GSM559440 6 0.3313 0.679 0.160 0.024 0.000 0.008 0.000 0.808
#> GSM559441 1 0.3457 0.825 0.820 0.000 0.012 0.052 0.000 0.116
#> GSM559442 6 0.4907 -0.140 0.464 0.000 0.012 0.036 0.000 0.488
#> GSM559444 6 0.2257 0.733 0.000 0.116 0.000 0.008 0.000 0.876
#> GSM559445 1 0.2602 0.859 0.888 0.000 0.020 0.052 0.000 0.040
#> GSM559446 1 0.2602 0.859 0.888 0.000 0.020 0.052 0.000 0.040
#> GSM559448 1 0.2357 0.865 0.872 0.000 0.012 0.116 0.000 0.000
#> GSM559450 6 0.2257 0.733 0.000 0.116 0.000 0.008 0.000 0.876
#> GSM559451 1 0.1296 0.879 0.948 0.000 0.004 0.044 0.000 0.004
#> GSM559452 6 0.0935 0.708 0.004 0.000 0.000 0.032 0.000 0.964
#> GSM559454 1 0.1814 0.870 0.900 0.000 0.000 0.100 0.000 0.000
#> GSM559455 1 0.3457 0.825 0.820 0.000 0.012 0.052 0.000 0.116
#> GSM559456 1 0.2911 0.854 0.872 0.000 0.036 0.052 0.000 0.040
#> GSM559457 1 0.0937 0.879 0.960 0.000 0.000 0.040 0.000 0.000
#> GSM559458 1 0.3457 0.825 0.820 0.000 0.012 0.052 0.000 0.116
#> GSM559459 1 0.2003 0.864 0.884 0.000 0.000 0.116 0.000 0.000
#> GSM559460 1 0.2006 0.869 0.892 0.000 0.004 0.104 0.000 0.000
#> GSM559461 1 0.2006 0.869 0.892 0.000 0.004 0.104 0.000 0.000
#> GSM559462 1 0.1528 0.876 0.936 0.000 0.000 0.048 0.000 0.016
#> GSM559463 1 0.2048 0.865 0.880 0.000 0.000 0.120 0.000 0.000
#> GSM559464 1 0.2048 0.863 0.880 0.000 0.000 0.120 0.000 0.000
#> GSM559465 1 0.2003 0.867 0.884 0.000 0.000 0.116 0.000 0.000
#> GSM559467 1 0.2972 0.829 0.836 0.000 0.000 0.036 0.000 0.128
#> GSM559468 1 0.3986 0.754 0.748 0.000 0.012 0.036 0.000 0.204
#> GSM559469 1 0.3957 0.756 0.752 0.000 0.012 0.036 0.000 0.200
#> GSM559470 1 0.3247 0.810 0.808 0.000 0.000 0.036 0.000 0.156
#> GSM559471 1 0.3358 0.841 0.824 0.000 0.008 0.052 0.000 0.116
#> GSM559472 1 0.1267 0.876 0.940 0.000 0.000 0.060 0.000 0.000
#> GSM559473 6 0.2389 0.728 0.000 0.128 0.000 0.008 0.000 0.864
#> GSM559475 6 0.2389 0.728 0.000 0.128 0.000 0.008 0.000 0.864
#> GSM559477 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559478 4 0.2980 1.000 0.000 0.192 0.000 0.800 0.000 0.008
#> GSM559479 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559480 4 0.2980 1.000 0.000 0.192 0.000 0.800 0.000 0.008
#> GSM559481 4 0.2980 1.000 0.000 0.192 0.000 0.800 0.000 0.008
#> GSM559482 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559439 3 0.1007 0.938 0.044 0.000 0.956 0.000 0.000 0.000
#> GSM559443 3 0.1007 0.938 0.044 0.000 0.956 0.000 0.000 0.000
#> GSM559447 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559449 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559453 3 0.0363 0.951 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM559466 3 0.0000 0.961 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559474 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM559476 3 0.1820 0.912 0.056 0.000 0.924 0.008 0.000 0.012
#> GSM559483 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559484 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 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 disease.state(p) k
#> CV:hclust 52 2.10e-01 2
#> CV:hclust 52 9.08e-03 3
#> CV:hclust 52 4.65e-10 4
#> CV:hclust 51 2.54e-09 5
#> CV:hclust 51 6.96e-09 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 21512 rows and 52 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 0.470 0.902 0.901 0.4179 0.566 0.566
#> 3 3 0.631 0.867 0.901 0.4323 0.785 0.633
#> 4 4 0.676 0.683 0.841 0.1660 0.826 0.588
#> 5 5 0.684 0.717 0.838 0.0933 0.900 0.678
#> 6 6 0.727 0.754 0.833 0.0554 0.919 0.687
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
#> GSM559433 1 0.000 0.923 1.000 0.000
#> GSM559434 2 0.802 0.919 0.244 0.756
#> GSM559436 1 0.000 0.923 1.000 0.000
#> GSM559437 1 0.000 0.923 1.000 0.000
#> GSM559438 2 0.802 0.919 0.244 0.756
#> GSM559440 2 0.802 0.919 0.244 0.756
#> GSM559441 1 0.327 0.869 0.940 0.060
#> GSM559442 1 0.000 0.923 1.000 0.000
#> GSM559444 2 0.689 0.962 0.184 0.816
#> GSM559445 1 0.327 0.869 0.940 0.060
#> GSM559446 1 0.000 0.923 1.000 0.000
#> GSM559448 1 0.184 0.914 0.972 0.028
#> GSM559450 2 0.689 0.962 0.184 0.816
#> GSM559451 1 0.000 0.923 1.000 0.000
#> GSM559452 2 0.861 0.867 0.284 0.716
#> GSM559454 1 0.000 0.923 1.000 0.000
#> GSM559455 1 0.000 0.923 1.000 0.000
#> GSM559456 1 0.402 0.891 0.920 0.080
#> GSM559457 1 0.000 0.923 1.000 0.000
#> GSM559458 1 0.402 0.891 0.920 0.080
#> GSM559459 1 0.000 0.923 1.000 0.000
#> GSM559460 1 0.000 0.923 1.000 0.000
#> GSM559461 1 0.000 0.923 1.000 0.000
#> GSM559462 1 0.000 0.923 1.000 0.000
#> GSM559463 1 0.000 0.923 1.000 0.000
#> GSM559464 1 0.000 0.923 1.000 0.000
#> GSM559465 1 0.260 0.908 0.956 0.044
#> GSM559467 1 0.000 0.923 1.000 0.000
#> GSM559468 1 0.000 0.923 1.000 0.000
#> GSM559469 1 0.000 0.923 1.000 0.000
#> GSM559470 1 0.518 0.798 0.884 0.116
#> GSM559471 1 0.000 0.923 1.000 0.000
#> GSM559472 1 0.000 0.923 1.000 0.000
#> GSM559473 2 0.689 0.962 0.184 0.816
#> GSM559475 2 0.689 0.962 0.184 0.816
#> GSM559477 2 0.689 0.962 0.184 0.816
#> GSM559478 2 0.689 0.962 0.184 0.816
#> GSM559479 2 0.689 0.962 0.184 0.816
#> GSM559480 2 0.689 0.962 0.184 0.816
#> GSM559481 2 0.689 0.962 0.184 0.816
#> GSM559482 2 0.689 0.962 0.184 0.816
#> GSM559435 1 0.689 0.828 0.816 0.184
#> GSM559439 1 0.689 0.828 0.816 0.184
#> GSM559443 1 0.689 0.828 0.816 0.184
#> GSM559447 1 0.689 0.828 0.816 0.184
#> GSM559449 1 0.689 0.828 0.816 0.184
#> GSM559453 1 0.689 0.828 0.816 0.184
#> GSM559466 1 0.689 0.828 0.816 0.184
#> GSM559474 1 0.891 0.726 0.692 0.308
#> GSM559476 1 0.689 0.828 0.816 0.184
#> GSM559483 2 0.689 0.962 0.184 0.816
#> GSM559484 2 0.000 0.770 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0237 0.932 0.996 0.000 0.004
#> GSM559434 2 0.8303 0.636 0.196 0.632 0.172
#> GSM559436 1 0.0000 0.933 1.000 0.000 0.000
#> GSM559437 1 0.4062 0.832 0.836 0.000 0.164
#> GSM559438 1 0.7165 0.691 0.716 0.112 0.172
#> GSM559440 2 0.8303 0.636 0.196 0.632 0.172
#> GSM559441 1 0.4178 0.826 0.828 0.000 0.172
#> GSM559442 1 0.0000 0.933 1.000 0.000 0.000
#> GSM559444 2 0.4062 0.807 0.000 0.836 0.164
#> GSM559445 1 0.4346 0.813 0.816 0.000 0.184
#> GSM559446 1 0.4235 0.822 0.824 0.000 0.176
#> GSM559448 1 0.0000 0.933 1.000 0.000 0.000
#> GSM559450 2 0.4002 0.808 0.000 0.840 0.160
#> GSM559451 1 0.0000 0.933 1.000 0.000 0.000
#> GSM559452 2 0.8683 0.577 0.236 0.592 0.172
#> GSM559454 1 0.0000 0.933 1.000 0.000 0.000
#> GSM559455 1 0.2796 0.884 0.908 0.000 0.092
#> GSM559456 1 0.0592 0.929 0.988 0.000 0.012
#> GSM559457 1 0.0424 0.931 0.992 0.000 0.008
#> GSM559458 1 0.0424 0.931 0.992 0.000 0.008
#> GSM559459 1 0.0000 0.933 1.000 0.000 0.000
#> GSM559460 1 0.0000 0.933 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.933 1.000 0.000 0.000
#> GSM559462 1 0.0237 0.932 0.996 0.000 0.004
#> GSM559463 1 0.0000 0.933 1.000 0.000 0.000
#> GSM559464 1 0.0000 0.933 1.000 0.000 0.000
#> GSM559465 1 0.0000 0.933 1.000 0.000 0.000
#> GSM559467 1 0.3816 0.845 0.852 0.000 0.148
#> GSM559468 1 0.0000 0.933 1.000 0.000 0.000
#> GSM559469 1 0.1163 0.921 0.972 0.000 0.028
#> GSM559470 1 0.4178 0.826 0.828 0.000 0.172
#> GSM559471 1 0.0000 0.933 1.000 0.000 0.000
#> GSM559472 1 0.0000 0.933 1.000 0.000 0.000
#> GSM559473 2 0.1860 0.848 0.000 0.948 0.052
#> GSM559475 2 0.1860 0.848 0.000 0.948 0.052
#> GSM559477 2 0.0237 0.852 0.000 0.996 0.004
#> GSM559478 2 0.0000 0.853 0.000 1.000 0.000
#> GSM559479 2 0.0237 0.852 0.000 0.996 0.004
#> GSM559480 2 0.0000 0.853 0.000 1.000 0.000
#> GSM559481 2 0.0000 0.853 0.000 1.000 0.000
#> GSM559482 2 0.0237 0.852 0.000 0.996 0.004
#> GSM559435 3 0.4654 0.960 0.208 0.000 0.792
#> GSM559439 3 0.4654 0.960 0.208 0.000 0.792
#> GSM559443 3 0.4654 0.960 0.208 0.000 0.792
#> GSM559447 3 0.4654 0.960 0.208 0.000 0.792
#> GSM559449 3 0.4654 0.960 0.208 0.000 0.792
#> GSM559453 3 0.4399 0.941 0.188 0.000 0.812
#> GSM559466 3 0.4654 0.960 0.208 0.000 0.792
#> GSM559474 3 0.0237 0.679 0.000 0.004 0.996
#> GSM559476 3 0.4702 0.956 0.212 0.000 0.788
#> GSM559483 2 0.0237 0.852 0.000 0.996 0.004
#> GSM559484 2 0.6291 0.458 0.000 0.532 0.468
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.2345 0.80506 0.900 0.000 0.000 0.100
#> GSM559434 4 0.4724 0.50650 0.076 0.136 0.000 0.788
#> GSM559436 1 0.0188 0.86666 0.996 0.000 0.000 0.004
#> GSM559437 4 0.4933 0.24978 0.432 0.000 0.000 0.568
#> GSM559438 4 0.5113 0.54895 0.252 0.036 0.000 0.712
#> GSM559440 4 0.4724 0.50650 0.076 0.136 0.000 0.788
#> GSM559441 4 0.4877 0.31952 0.408 0.000 0.000 0.592
#> GSM559442 1 0.2921 0.75473 0.860 0.000 0.000 0.140
#> GSM559444 4 0.4967 -0.25643 0.000 0.452 0.000 0.548
#> GSM559445 4 0.3801 0.55882 0.220 0.000 0.000 0.780
#> GSM559446 4 0.4855 0.32776 0.400 0.000 0.000 0.600
#> GSM559448 1 0.0000 0.86660 1.000 0.000 0.000 0.000
#> GSM559450 2 0.4981 0.34842 0.000 0.536 0.000 0.464
#> GSM559451 1 0.1389 0.84657 0.952 0.000 0.000 0.048
#> GSM559452 4 0.4784 0.54697 0.112 0.100 0.000 0.788
#> GSM559454 1 0.0188 0.86666 0.996 0.000 0.000 0.004
#> GSM559455 1 0.4989 0.00461 0.528 0.000 0.000 0.472
#> GSM559456 1 0.3975 0.62267 0.760 0.000 0.000 0.240
#> GSM559457 1 0.2281 0.80864 0.904 0.000 0.000 0.096
#> GSM559458 1 0.4866 0.24447 0.596 0.000 0.000 0.404
#> GSM559459 1 0.0188 0.86666 0.996 0.000 0.000 0.004
#> GSM559460 1 0.0000 0.86660 1.000 0.000 0.000 0.000
#> GSM559461 1 0.0000 0.86660 1.000 0.000 0.000 0.000
#> GSM559462 1 0.0336 0.86590 0.992 0.000 0.000 0.008
#> GSM559463 1 0.0000 0.86660 1.000 0.000 0.000 0.000
#> GSM559464 1 0.0000 0.86660 1.000 0.000 0.000 0.000
#> GSM559465 1 0.0000 0.86660 1.000 0.000 0.000 0.000
#> GSM559467 1 0.4866 0.25613 0.596 0.000 0.000 0.404
#> GSM559468 1 0.0188 0.86598 0.996 0.000 0.000 0.004
#> GSM559469 1 0.2973 0.74892 0.856 0.000 0.000 0.144
#> GSM559470 4 0.4941 0.25125 0.436 0.000 0.000 0.564
#> GSM559471 1 0.0188 0.86598 0.996 0.000 0.000 0.004
#> GSM559472 1 0.0188 0.86666 0.996 0.000 0.000 0.004
#> GSM559473 2 0.3486 0.80593 0.000 0.812 0.000 0.188
#> GSM559475 2 0.3486 0.80593 0.000 0.812 0.000 0.188
#> GSM559477 2 0.0188 0.88230 0.000 0.996 0.004 0.000
#> GSM559478 2 0.2142 0.88335 0.000 0.928 0.016 0.056
#> GSM559479 2 0.0188 0.88230 0.000 0.996 0.004 0.000
#> GSM559480 2 0.2142 0.88335 0.000 0.928 0.016 0.056
#> GSM559481 2 0.2142 0.88335 0.000 0.928 0.016 0.056
#> GSM559482 2 0.0188 0.88230 0.000 0.996 0.004 0.000
#> GSM559435 3 0.1004 0.99687 0.024 0.000 0.972 0.004
#> GSM559439 3 0.1004 0.99687 0.024 0.000 0.972 0.004
#> GSM559443 3 0.0921 0.99292 0.028 0.000 0.972 0.000
#> GSM559447 3 0.1004 0.99687 0.024 0.000 0.972 0.004
#> GSM559449 3 0.1004 0.99687 0.024 0.000 0.972 0.004
#> GSM559453 3 0.0707 0.98992 0.020 0.000 0.980 0.000
#> GSM559466 3 0.1004 0.99687 0.024 0.000 0.972 0.004
#> GSM559474 4 0.4989 -0.31382 0.000 0.000 0.472 0.528
#> GSM559476 3 0.1109 0.99265 0.028 0.000 0.968 0.004
#> GSM559483 2 0.0188 0.88230 0.000 0.996 0.004 0.000
#> GSM559484 4 0.7698 -0.16217 0.000 0.236 0.324 0.440
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 1 0.3551 0.6654 0.772 0.000 0.000 0.220 0.008
#> GSM559434 4 0.4347 0.4726 0.012 0.012 0.000 0.712 0.264
#> GSM559436 1 0.1356 0.8814 0.956 0.000 0.004 0.012 0.028
#> GSM559437 4 0.3163 0.6280 0.164 0.000 0.000 0.824 0.012
#> GSM559438 4 0.4757 0.4928 0.036 0.012 0.000 0.704 0.248
#> GSM559440 4 0.4296 0.4785 0.012 0.012 0.000 0.720 0.256
#> GSM559441 4 0.2462 0.6355 0.112 0.000 0.000 0.880 0.008
#> GSM559442 1 0.4879 0.6742 0.720 0.000 0.000 0.124 0.156
#> GSM559444 4 0.6823 -0.2483 0.000 0.336 0.000 0.344 0.320
#> GSM559445 4 0.1661 0.5807 0.036 0.000 0.000 0.940 0.024
#> GSM559446 4 0.3123 0.6288 0.160 0.000 0.000 0.828 0.012
#> GSM559448 1 0.1356 0.8814 0.956 0.000 0.004 0.012 0.028
#> GSM559450 2 0.6788 0.0925 0.000 0.384 0.000 0.296 0.320
#> GSM559451 1 0.2470 0.8341 0.884 0.000 0.000 0.104 0.012
#> GSM559452 4 0.5028 0.2935 0.012 0.016 0.000 0.560 0.412
#> GSM559454 1 0.0162 0.8899 0.996 0.000 0.000 0.004 0.000
#> GSM559455 4 0.3461 0.6147 0.224 0.000 0.000 0.772 0.004
#> GSM559456 4 0.4648 0.1588 0.464 0.000 0.000 0.524 0.012
#> GSM559457 1 0.3885 0.5780 0.724 0.000 0.000 0.268 0.008
#> GSM559458 4 0.5224 0.5206 0.276 0.000 0.000 0.644 0.080
#> GSM559459 1 0.0000 0.8904 1.000 0.000 0.000 0.000 0.000
#> GSM559460 1 0.0703 0.8896 0.976 0.000 0.000 0.000 0.024
#> GSM559461 1 0.0566 0.8907 0.984 0.000 0.000 0.004 0.012
#> GSM559462 1 0.0566 0.8898 0.984 0.000 0.000 0.004 0.012
#> GSM559463 1 0.1285 0.8833 0.956 0.000 0.004 0.004 0.036
#> GSM559464 1 0.0609 0.8901 0.980 0.000 0.000 0.000 0.020
#> GSM559465 1 0.0771 0.8904 0.976 0.000 0.000 0.004 0.020
#> GSM559467 4 0.4594 0.5684 0.284 0.000 0.000 0.680 0.036
#> GSM559468 1 0.3229 0.8177 0.840 0.000 0.000 0.032 0.128
#> GSM559469 1 0.4723 0.6880 0.736 0.000 0.000 0.136 0.128
#> GSM559470 4 0.3386 0.6381 0.128 0.000 0.000 0.832 0.040
#> GSM559471 1 0.2676 0.8465 0.884 0.000 0.000 0.036 0.080
#> GSM559472 1 0.0807 0.8880 0.976 0.000 0.000 0.012 0.012
#> GSM559473 2 0.5253 0.6356 0.000 0.676 0.000 0.124 0.200
#> GSM559475 2 0.5227 0.6401 0.000 0.676 0.000 0.116 0.208
#> GSM559477 2 0.0000 0.7747 0.000 1.000 0.000 0.000 0.000
#> GSM559478 2 0.3488 0.7614 0.000 0.808 0.000 0.024 0.168
#> GSM559479 2 0.0000 0.7747 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.3488 0.7614 0.000 0.808 0.000 0.024 0.168
#> GSM559481 2 0.3488 0.7614 0.000 0.808 0.000 0.024 0.168
#> GSM559482 2 0.0000 0.7747 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.0404 0.9824 0.012 0.000 0.988 0.000 0.000
#> GSM559439 3 0.0404 0.9824 0.012 0.000 0.988 0.000 0.000
#> GSM559443 3 0.0807 0.9731 0.012 0.000 0.976 0.000 0.012
#> GSM559447 3 0.0566 0.9825 0.012 0.000 0.984 0.000 0.004
#> GSM559449 3 0.0566 0.9825 0.012 0.000 0.984 0.000 0.004
#> GSM559453 3 0.0162 0.9643 0.000 0.000 0.996 0.000 0.004
#> GSM559466 3 0.0566 0.9825 0.012 0.000 0.984 0.000 0.004
#> GSM559474 5 0.6279 0.6878 0.000 0.000 0.280 0.192 0.528
#> GSM559476 3 0.1493 0.9377 0.028 0.000 0.948 0.000 0.024
#> GSM559483 2 0.0000 0.7747 0.000 1.000 0.000 0.000 0.000
#> GSM559484 5 0.6048 0.7094 0.000 0.092 0.220 0.044 0.644
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.4105 0.594 0.720 0.000 0.000 0.236 0.036 0.008
#> GSM559434 6 0.3337 0.641 0.000 0.000 0.000 0.260 0.004 0.736
#> GSM559436 1 0.2220 0.819 0.908 0.000 0.000 0.020 0.052 0.020
#> GSM559437 4 0.1873 0.773 0.048 0.000 0.000 0.924 0.020 0.008
#> GSM559438 6 0.4094 0.613 0.004 0.000 0.000 0.264 0.032 0.700
#> GSM559440 6 0.3383 0.636 0.004 0.000 0.000 0.268 0.000 0.728
#> GSM559441 4 0.1930 0.774 0.048 0.000 0.000 0.916 0.000 0.036
#> GSM559442 1 0.5955 0.576 0.576 0.000 0.000 0.052 0.112 0.260
#> GSM559444 6 0.5656 0.624 0.000 0.172 0.000 0.136 0.052 0.640
#> GSM559445 4 0.1594 0.710 0.000 0.000 0.000 0.932 0.016 0.052
#> GSM559446 4 0.1718 0.771 0.044 0.000 0.000 0.932 0.016 0.008
#> GSM559448 1 0.2279 0.820 0.904 0.000 0.000 0.024 0.056 0.016
#> GSM559450 6 0.5642 0.612 0.000 0.196 0.000 0.116 0.052 0.636
#> GSM559451 1 0.3815 0.745 0.792 0.000 0.000 0.136 0.056 0.016
#> GSM559452 6 0.3963 0.596 0.000 0.000 0.000 0.164 0.080 0.756
#> GSM559454 1 0.1194 0.833 0.956 0.000 0.000 0.008 0.032 0.004
#> GSM559455 4 0.2170 0.783 0.100 0.000 0.000 0.888 0.000 0.012
#> GSM559456 4 0.3516 0.689 0.220 0.000 0.000 0.760 0.016 0.004
#> GSM559457 4 0.4596 0.214 0.460 0.000 0.000 0.508 0.028 0.004
#> GSM559458 4 0.4691 0.707 0.112 0.000 0.000 0.744 0.056 0.088
#> GSM559459 1 0.0291 0.840 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM559460 1 0.1765 0.837 0.924 0.000 0.000 0.000 0.052 0.024
#> GSM559461 1 0.1464 0.842 0.944 0.000 0.000 0.004 0.036 0.016
#> GSM559462 1 0.1408 0.842 0.944 0.000 0.000 0.000 0.036 0.020
#> GSM559463 1 0.1914 0.828 0.920 0.000 0.000 0.008 0.056 0.016
#> GSM559464 1 0.1765 0.837 0.924 0.000 0.000 0.000 0.052 0.024
#> GSM559465 1 0.1461 0.840 0.940 0.000 0.000 0.000 0.044 0.016
#> GSM559467 4 0.4996 0.712 0.128 0.000 0.000 0.708 0.040 0.124
#> GSM559468 1 0.5332 0.668 0.652 0.000 0.000 0.028 0.120 0.200
#> GSM559469 1 0.5730 0.633 0.624 0.000 0.000 0.052 0.120 0.204
#> GSM559470 4 0.4198 0.698 0.056 0.000 0.000 0.772 0.036 0.136
#> GSM559471 1 0.4597 0.728 0.732 0.000 0.000 0.028 0.080 0.160
#> GSM559472 1 0.1794 0.829 0.924 0.000 0.000 0.040 0.036 0.000
#> GSM559473 6 0.4528 0.190 0.000 0.404 0.000 0.004 0.028 0.564
#> GSM559475 6 0.4549 0.155 0.000 0.416 0.000 0.004 0.028 0.552
#> GSM559477 2 0.0146 0.843 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM559478 2 0.4985 0.776 0.000 0.696 0.000 0.032 0.096 0.176
#> GSM559479 2 0.0146 0.843 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM559480 2 0.4985 0.776 0.000 0.696 0.000 0.032 0.096 0.176
#> GSM559481 2 0.4985 0.776 0.000 0.696 0.000 0.032 0.096 0.176
#> GSM559482 2 0.0146 0.843 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM559435 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559439 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559443 3 0.0146 0.984 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM559447 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559449 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559453 3 0.0458 0.977 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM559466 3 0.0000 0.987 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559474 5 0.4923 0.850 0.000 0.000 0.116 0.116 0.720 0.048
#> GSM559476 3 0.1498 0.931 0.012 0.000 0.948 0.004 0.012 0.024
#> GSM559483 2 0.0000 0.843 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559484 5 0.4947 0.841 0.000 0.016 0.112 0.024 0.728 0.120
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 disease.state(p) k
#> CV:kmeans 52 5.15e-01 2
#> CV:kmeans 51 1.60e-10 3
#> CV:kmeans 41 8.21e-08 4
#> CV:kmeans 45 3.96e-08 5
#> CV:kmeans 49 2.23e-08 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 21512 rows and 52 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 0.959 0.949 0.979 0.4926 0.509 0.509
#> 3 3 0.969 0.903 0.962 0.3243 0.733 0.527
#> 4 4 0.964 0.936 0.973 0.1529 0.885 0.680
#> 5 5 0.804 0.736 0.878 0.0548 0.941 0.775
#> 6 6 0.768 0.615 0.808 0.0389 0.965 0.838
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM559433 1 0.000 0.977 1.000 0.000
#> GSM559434 2 0.000 0.979 0.000 1.000
#> GSM559436 1 0.000 0.977 1.000 0.000
#> GSM559437 1 0.295 0.927 0.948 0.052
#> GSM559438 2 0.000 0.979 0.000 1.000
#> GSM559440 2 0.000 0.979 0.000 1.000
#> GSM559441 2 0.844 0.624 0.272 0.728
#> GSM559442 1 0.000 0.977 1.000 0.000
#> GSM559444 2 0.000 0.979 0.000 1.000
#> GSM559445 2 0.000 0.979 0.000 1.000
#> GSM559446 1 0.738 0.728 0.792 0.208
#> GSM559448 1 0.000 0.977 1.000 0.000
#> GSM559450 2 0.000 0.979 0.000 1.000
#> GSM559451 1 0.000 0.977 1.000 0.000
#> GSM559452 2 0.000 0.979 0.000 1.000
#> GSM559454 1 0.000 0.977 1.000 0.000
#> GSM559455 1 0.000 0.977 1.000 0.000
#> GSM559456 1 0.000 0.977 1.000 0.000
#> GSM559457 1 0.000 0.977 1.000 0.000
#> GSM559458 1 0.000 0.977 1.000 0.000
#> GSM559459 1 0.000 0.977 1.000 0.000
#> GSM559460 1 0.000 0.977 1.000 0.000
#> GSM559461 1 0.000 0.977 1.000 0.000
#> GSM559462 1 0.000 0.977 1.000 0.000
#> GSM559463 1 0.000 0.977 1.000 0.000
#> GSM559464 1 0.000 0.977 1.000 0.000
#> GSM559465 1 0.000 0.977 1.000 0.000
#> GSM559467 2 0.574 0.836 0.136 0.864
#> GSM559468 1 0.000 0.977 1.000 0.000
#> GSM559469 1 0.975 0.292 0.592 0.408
#> GSM559470 2 0.000 0.979 0.000 1.000
#> GSM559471 1 0.000 0.977 1.000 0.000
#> GSM559472 1 0.000 0.977 1.000 0.000
#> GSM559473 2 0.000 0.979 0.000 1.000
#> GSM559475 2 0.000 0.979 0.000 1.000
#> GSM559477 2 0.000 0.979 0.000 1.000
#> GSM559478 2 0.000 0.979 0.000 1.000
#> GSM559479 2 0.000 0.979 0.000 1.000
#> GSM559480 2 0.000 0.979 0.000 1.000
#> GSM559481 2 0.000 0.979 0.000 1.000
#> GSM559482 2 0.000 0.979 0.000 1.000
#> GSM559435 1 0.000 0.977 1.000 0.000
#> GSM559439 1 0.000 0.977 1.000 0.000
#> GSM559443 1 0.000 0.977 1.000 0.000
#> GSM559447 1 0.000 0.977 1.000 0.000
#> GSM559449 1 0.000 0.977 1.000 0.000
#> GSM559453 1 0.000 0.977 1.000 0.000
#> GSM559466 1 0.000 0.977 1.000 0.000
#> GSM559474 2 0.000 0.979 0.000 1.000
#> GSM559476 1 0.000 0.977 1.000 0.000
#> GSM559483 2 0.000 0.979 0.000 1.000
#> GSM559484 2 0.000 0.979 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559434 2 0.0000 0.940 0.000 1.000 0.000
#> GSM559436 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559437 1 0.2165 0.907 0.936 0.000 0.064
#> GSM559438 2 0.0000 0.940 0.000 1.000 0.000
#> GSM559440 2 0.0000 0.940 0.000 1.000 0.000
#> GSM559441 1 0.6667 0.400 0.616 0.368 0.016
#> GSM559442 1 0.0892 0.937 0.980 0.020 0.000
#> GSM559444 2 0.0000 0.940 0.000 1.000 0.000
#> GSM559445 2 0.8010 0.205 0.384 0.548 0.068
#> GSM559446 1 0.2066 0.910 0.940 0.000 0.060
#> GSM559448 3 0.2261 0.923 0.068 0.000 0.932
#> GSM559450 2 0.0000 0.940 0.000 1.000 0.000
#> GSM559451 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559452 2 0.1860 0.894 0.000 0.948 0.052
#> GSM559454 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559455 1 0.0892 0.940 0.980 0.000 0.020
#> GSM559456 1 0.2165 0.907 0.936 0.000 0.064
#> GSM559457 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559458 3 0.0000 0.992 0.000 0.000 1.000
#> GSM559459 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559460 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559462 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559463 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559464 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559465 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559467 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559468 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559469 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559470 1 0.6204 0.271 0.576 0.424 0.000
#> GSM559471 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559472 1 0.0000 0.952 1.000 0.000 0.000
#> GSM559473 2 0.0000 0.940 0.000 1.000 0.000
#> GSM559475 2 0.0000 0.940 0.000 1.000 0.000
#> GSM559477 2 0.0000 0.940 0.000 1.000 0.000
#> GSM559478 2 0.0000 0.940 0.000 1.000 0.000
#> GSM559479 2 0.0000 0.940 0.000 1.000 0.000
#> GSM559480 2 0.0000 0.940 0.000 1.000 0.000
#> GSM559481 2 0.0000 0.940 0.000 1.000 0.000
#> GSM559482 2 0.0000 0.940 0.000 1.000 0.000
#> GSM559435 3 0.0000 0.992 0.000 0.000 1.000
#> GSM559439 3 0.0000 0.992 0.000 0.000 1.000
#> GSM559443 3 0.0000 0.992 0.000 0.000 1.000
#> GSM559447 3 0.0000 0.992 0.000 0.000 1.000
#> GSM559449 3 0.0000 0.992 0.000 0.000 1.000
#> GSM559453 3 0.0000 0.992 0.000 0.000 1.000
#> GSM559466 3 0.0000 0.992 0.000 0.000 1.000
#> GSM559474 3 0.0000 0.992 0.000 0.000 1.000
#> GSM559476 3 0.0000 0.992 0.000 0.000 1.000
#> GSM559483 2 0.0000 0.940 0.000 1.000 0.000
#> GSM559484 2 0.5968 0.395 0.000 0.636 0.364
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.4933 0.224 0.568 0.000 0.000 0.432
#> GSM559434 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559436 1 0.0336 0.959 0.992 0.000 0.000 0.008
#> GSM559437 4 0.0000 0.967 0.000 0.000 0.000 1.000
#> GSM559438 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559440 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559441 4 0.0000 0.967 0.000 0.000 0.000 1.000
#> GSM559442 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM559444 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559445 4 0.0000 0.967 0.000 0.000 0.000 1.000
#> GSM559446 4 0.0000 0.967 0.000 0.000 0.000 1.000
#> GSM559448 3 0.2647 0.850 0.120 0.000 0.880 0.000
#> GSM559450 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559451 1 0.2216 0.879 0.908 0.000 0.000 0.092
#> GSM559452 2 0.1151 0.957 0.008 0.968 0.024 0.000
#> GSM559454 1 0.0336 0.959 0.992 0.000 0.000 0.008
#> GSM559455 4 0.0000 0.967 0.000 0.000 0.000 1.000
#> GSM559456 4 0.0000 0.967 0.000 0.000 0.000 1.000
#> GSM559457 4 0.3649 0.723 0.204 0.000 0.000 0.796
#> GSM559458 3 0.2342 0.899 0.008 0.000 0.912 0.080
#> GSM559459 1 0.0336 0.959 0.992 0.000 0.000 0.008
#> GSM559460 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM559461 1 0.0188 0.960 0.996 0.000 0.000 0.004
#> GSM559462 1 0.0336 0.959 0.992 0.000 0.000 0.008
#> GSM559463 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM559464 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM559465 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM559467 4 0.0592 0.955 0.016 0.000 0.000 0.984
#> GSM559468 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM559469 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM559470 4 0.0188 0.963 0.000 0.004 0.000 0.996
#> GSM559471 1 0.0188 0.960 0.996 0.000 0.000 0.004
#> GSM559472 1 0.0336 0.959 0.992 0.000 0.000 0.008
#> GSM559473 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559475 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559477 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559478 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559479 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559480 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559481 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559482 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559435 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM559439 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM559443 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM559447 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM559449 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM559453 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM559466 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM559474 3 0.2868 0.847 0.000 0.000 0.864 0.136
#> GSM559476 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM559483 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559484 2 0.3907 0.703 0.000 0.768 0.232 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 1 0.3954 0.597 0.772 0.000 0.000 0.192 0.036
#> GSM559434 2 0.3196 0.782 0.000 0.804 0.000 0.004 0.192
#> GSM559436 1 0.0510 0.790 0.984 0.000 0.000 0.000 0.016
#> GSM559437 4 0.0162 0.923 0.004 0.000 0.000 0.996 0.000
#> GSM559438 2 0.3715 0.687 0.000 0.736 0.000 0.004 0.260
#> GSM559440 2 0.3266 0.770 0.000 0.796 0.000 0.004 0.200
#> GSM559441 4 0.0162 0.922 0.000 0.000 0.000 0.996 0.004
#> GSM559442 5 0.2891 0.547 0.176 0.000 0.000 0.000 0.824
#> GSM559444 2 0.1638 0.874 0.000 0.932 0.000 0.004 0.064
#> GSM559445 4 0.0162 0.922 0.000 0.000 0.000 0.996 0.004
#> GSM559446 4 0.0451 0.922 0.004 0.000 0.000 0.988 0.008
#> GSM559448 3 0.4627 0.185 0.444 0.000 0.544 0.000 0.012
#> GSM559450 2 0.1430 0.880 0.000 0.944 0.000 0.004 0.052
#> GSM559451 1 0.2514 0.758 0.896 0.000 0.000 0.044 0.060
#> GSM559452 5 0.4410 -0.252 0.000 0.440 0.000 0.004 0.556
#> GSM559454 1 0.0404 0.794 0.988 0.000 0.000 0.000 0.012
#> GSM559455 4 0.0807 0.919 0.012 0.000 0.000 0.976 0.012
#> GSM559456 4 0.2228 0.881 0.056 0.000 0.008 0.916 0.020
#> GSM559457 1 0.4798 0.253 0.580 0.000 0.000 0.396 0.024
#> GSM559458 3 0.6131 0.391 0.000 0.000 0.536 0.156 0.308
#> GSM559459 1 0.1270 0.799 0.948 0.000 0.000 0.000 0.052
#> GSM559460 1 0.2813 0.749 0.832 0.000 0.000 0.000 0.168
#> GSM559461 1 0.2280 0.778 0.880 0.000 0.000 0.000 0.120
#> GSM559462 1 0.2305 0.786 0.896 0.000 0.000 0.012 0.092
#> GSM559463 1 0.1121 0.798 0.956 0.000 0.000 0.000 0.044
#> GSM559464 1 0.2773 0.751 0.836 0.000 0.000 0.000 0.164
#> GSM559465 1 0.2848 0.756 0.840 0.000 0.004 0.000 0.156
#> GSM559467 4 0.4593 0.732 0.080 0.000 0.000 0.736 0.184
#> GSM559468 5 0.4088 0.316 0.368 0.000 0.000 0.000 0.632
#> GSM559469 5 0.3635 0.519 0.248 0.004 0.000 0.000 0.748
#> GSM559470 4 0.3694 0.822 0.024 0.020 0.000 0.824 0.132
#> GSM559471 1 0.4262 0.146 0.560 0.000 0.000 0.000 0.440
#> GSM559472 1 0.0609 0.791 0.980 0.000 0.000 0.000 0.020
#> GSM559473 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM559475 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM559477 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM559478 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM559479 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM559481 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM559482 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.869 0.000 0.000 1.000 0.000 0.000
#> GSM559439 3 0.0000 0.869 0.000 0.000 1.000 0.000 0.000
#> GSM559443 3 0.0000 0.869 0.000 0.000 1.000 0.000 0.000
#> GSM559447 3 0.0000 0.869 0.000 0.000 1.000 0.000 0.000
#> GSM559449 3 0.0000 0.869 0.000 0.000 1.000 0.000 0.000
#> GSM559453 3 0.0000 0.869 0.000 0.000 1.000 0.000 0.000
#> GSM559466 3 0.0000 0.869 0.000 0.000 1.000 0.000 0.000
#> GSM559474 3 0.5264 0.600 0.000 0.000 0.676 0.196 0.128
#> GSM559476 3 0.0000 0.869 0.000 0.000 1.000 0.000 0.000
#> GSM559483 2 0.0000 0.903 0.000 1.000 0.000 0.000 0.000
#> GSM559484 2 0.5977 0.279 0.000 0.540 0.332 0.000 0.128
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.5821 0.474 0.632 0.000 0.000 0.176 0.080 0.112
#> GSM559434 2 0.4639 -0.430 0.000 0.512 0.000 0.000 0.040 0.448
#> GSM559436 1 0.1723 0.725 0.928 0.000 0.000 0.000 0.036 0.036
#> GSM559437 4 0.0458 0.797 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM559438 6 0.5421 0.480 0.000 0.432 0.000 0.004 0.100 0.464
#> GSM559440 6 0.5108 0.469 0.000 0.432 0.000 0.004 0.068 0.496
#> GSM559441 4 0.1572 0.792 0.000 0.000 0.000 0.936 0.028 0.036
#> GSM559442 5 0.4494 0.518 0.092 0.000 0.000 0.000 0.692 0.216
#> GSM559444 2 0.3266 0.365 0.000 0.728 0.000 0.000 0.000 0.272
#> GSM559445 4 0.1391 0.791 0.000 0.000 0.000 0.944 0.016 0.040
#> GSM559446 4 0.1528 0.791 0.000 0.000 0.000 0.936 0.016 0.048
#> GSM559448 3 0.4802 0.340 0.368 0.000 0.584 0.000 0.028 0.020
#> GSM559450 2 0.3221 0.386 0.000 0.736 0.000 0.000 0.000 0.264
#> GSM559451 1 0.4666 0.603 0.736 0.000 0.000 0.036 0.092 0.136
#> GSM559452 6 0.5365 0.273 0.000 0.164 0.000 0.000 0.256 0.580
#> GSM559454 1 0.0909 0.744 0.968 0.000 0.000 0.000 0.020 0.012
#> GSM559455 4 0.2745 0.771 0.012 0.000 0.000 0.876 0.056 0.056
#> GSM559456 4 0.4611 0.682 0.100 0.000 0.008 0.764 0.060 0.068
#> GSM559457 1 0.6253 0.278 0.512 0.000 0.000 0.320 0.068 0.100
#> GSM559458 3 0.7131 0.208 0.004 0.000 0.448 0.256 0.192 0.100
#> GSM559459 1 0.1563 0.742 0.932 0.000 0.000 0.000 0.056 0.012
#> GSM559460 1 0.3403 0.624 0.768 0.000 0.000 0.000 0.212 0.020
#> GSM559461 1 0.2491 0.720 0.868 0.000 0.000 0.000 0.112 0.020
#> GSM559462 1 0.4210 0.630 0.756 0.000 0.000 0.008 0.120 0.116
#> GSM559463 1 0.1049 0.744 0.960 0.000 0.000 0.000 0.032 0.008
#> GSM559464 1 0.3136 0.657 0.796 0.000 0.000 0.000 0.188 0.016
#> GSM559465 1 0.2872 0.693 0.832 0.000 0.000 0.004 0.152 0.012
#> GSM559467 4 0.6712 0.302 0.084 0.000 0.000 0.456 0.324 0.136
#> GSM559468 5 0.3126 0.690 0.248 0.000 0.000 0.000 0.752 0.000
#> GSM559469 5 0.2744 0.717 0.144 0.000 0.000 0.000 0.840 0.016
#> GSM559470 4 0.5992 0.530 0.020 0.008 0.000 0.572 0.236 0.164
#> GSM559471 5 0.5001 0.384 0.384 0.000 0.000 0.000 0.540 0.076
#> GSM559472 1 0.2265 0.717 0.896 0.000 0.000 0.000 0.052 0.052
#> GSM559473 2 0.0458 0.766 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM559475 2 0.0520 0.772 0.000 0.984 0.000 0.000 0.008 0.008
#> GSM559477 2 0.0000 0.776 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559478 2 0.0291 0.775 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM559479 2 0.0000 0.776 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559480 2 0.0291 0.775 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM559481 2 0.0291 0.775 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM559482 2 0.0000 0.776 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559435 3 0.0146 0.842 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM559439 3 0.0000 0.842 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559443 3 0.0146 0.842 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM559447 3 0.0000 0.842 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559449 3 0.0000 0.842 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559453 3 0.0260 0.839 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM559466 3 0.0000 0.842 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559474 3 0.6589 0.214 0.000 0.000 0.420 0.216 0.036 0.328
#> GSM559476 3 0.0146 0.842 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM559483 2 0.0146 0.776 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM559484 2 0.6559 -0.164 0.000 0.428 0.208 0.000 0.036 0.328
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 disease.state(p) k
#> CV:skmeans 51 4.76e-01 2
#> CV:skmeans 48 9.12e-08 3
#> CV:skmeans 51 8.58e-07 4
#> CV:skmeans 45 5.17e-08 5
#> CV:skmeans 38 1.15e-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 21512 rows and 52 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 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 0.960 0.930 0.942 0.3852 0.599 0.599
#> 3 3 1.000 0.969 0.990 0.5489 0.664 0.496
#> 4 4 0.732 0.773 0.895 0.2390 0.802 0.530
#> 5 5 0.710 0.582 0.777 0.0520 0.875 0.586
#> 6 6 0.781 0.685 0.860 0.0455 0.904 0.623
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
#> GSM559433 2 0.000 0.965 0.000 1.000
#> GSM559434 2 0.000 0.965 0.000 1.000
#> GSM559436 2 0.000 0.965 0.000 1.000
#> GSM559437 2 0.000 0.965 0.000 1.000
#> GSM559438 2 0.000 0.965 0.000 1.000
#> GSM559440 2 0.000 0.965 0.000 1.000
#> GSM559441 2 0.000 0.965 0.000 1.000
#> GSM559442 2 0.000 0.965 0.000 1.000
#> GSM559444 2 0.456 0.916 0.096 0.904
#> GSM559445 2 0.000 0.965 0.000 1.000
#> GSM559446 2 0.000 0.965 0.000 1.000
#> GSM559448 1 0.529 0.919 0.880 0.120
#> GSM559450 2 0.456 0.916 0.096 0.904
#> GSM559451 2 0.000 0.965 0.000 1.000
#> GSM559452 2 0.163 0.945 0.024 0.976
#> GSM559454 2 0.000 0.965 0.000 1.000
#> GSM559455 2 0.000 0.965 0.000 1.000
#> GSM559456 2 0.000 0.965 0.000 1.000
#> GSM559457 2 0.000 0.965 0.000 1.000
#> GSM559458 1 0.925 0.662 0.660 0.340
#> GSM559459 2 0.000 0.965 0.000 1.000
#> GSM559460 2 0.000 0.965 0.000 1.000
#> GSM559461 2 0.000 0.965 0.000 1.000
#> GSM559462 2 0.000 0.965 0.000 1.000
#> GSM559463 1 0.795 0.813 0.760 0.240
#> GSM559464 2 0.000 0.965 0.000 1.000
#> GSM559465 1 0.955 0.591 0.624 0.376
#> GSM559467 2 0.000 0.965 0.000 1.000
#> GSM559468 2 0.000 0.965 0.000 1.000
#> GSM559469 2 0.000 0.965 0.000 1.000
#> GSM559470 2 0.000 0.965 0.000 1.000
#> GSM559471 2 0.000 0.965 0.000 1.000
#> GSM559472 2 0.000 0.965 0.000 1.000
#> GSM559473 2 0.456 0.916 0.096 0.904
#> GSM559475 2 0.456 0.916 0.096 0.904
#> GSM559477 2 0.456 0.916 0.096 0.904
#> GSM559478 2 0.456 0.916 0.096 0.904
#> GSM559479 2 0.456 0.916 0.096 0.904
#> GSM559480 2 0.456 0.916 0.096 0.904
#> GSM559481 2 0.456 0.916 0.096 0.904
#> GSM559482 2 0.456 0.916 0.096 0.904
#> GSM559435 1 0.456 0.932 0.904 0.096
#> GSM559439 1 0.456 0.932 0.904 0.096
#> GSM559443 1 0.456 0.932 0.904 0.096
#> GSM559447 1 0.456 0.932 0.904 0.096
#> GSM559449 1 0.456 0.932 0.904 0.096
#> GSM559453 1 0.456 0.932 0.904 0.096
#> GSM559466 1 0.456 0.932 0.904 0.096
#> GSM559474 1 0.456 0.932 0.904 0.096
#> GSM559476 1 0.456 0.932 0.904 0.096
#> GSM559483 2 0.456 0.916 0.096 0.904
#> GSM559484 1 0.000 0.852 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0237 0.9977 0.996 0.004 0.000
#> GSM559434 1 0.0237 0.9977 0.996 0.004 0.000
#> GSM559436 1 0.0000 0.9979 1.000 0.000 0.000
#> GSM559437 1 0.0237 0.9977 0.996 0.004 0.000
#> GSM559438 1 0.0237 0.9977 0.996 0.004 0.000
#> GSM559440 1 0.0237 0.9977 0.996 0.004 0.000
#> GSM559441 1 0.0237 0.9977 0.996 0.004 0.000
#> GSM559442 1 0.0000 0.9979 1.000 0.000 0.000
#> GSM559444 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM559445 1 0.0237 0.9977 0.996 0.004 0.000
#> GSM559446 1 0.0237 0.9977 0.996 0.004 0.000
#> GSM559448 1 0.0000 0.9979 1.000 0.000 0.000
#> GSM559450 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM559451 1 0.0237 0.9977 0.996 0.004 0.000
#> GSM559452 3 0.0475 0.9331 0.004 0.004 0.992
#> GSM559454 1 0.0000 0.9979 1.000 0.000 0.000
#> GSM559455 1 0.0237 0.9977 0.996 0.004 0.000
#> GSM559456 1 0.0237 0.9977 0.996 0.004 0.000
#> GSM559457 1 0.0000 0.9979 1.000 0.000 0.000
#> GSM559458 3 0.6509 0.0965 0.472 0.004 0.524
#> GSM559459 1 0.0000 0.9979 1.000 0.000 0.000
#> GSM559460 1 0.0000 0.9979 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.9979 1.000 0.000 0.000
#> GSM559462 1 0.0000 0.9979 1.000 0.000 0.000
#> GSM559463 1 0.0000 0.9979 1.000 0.000 0.000
#> GSM559464 1 0.0000 0.9979 1.000 0.000 0.000
#> GSM559465 1 0.0000 0.9979 1.000 0.000 0.000
#> GSM559467 1 0.0237 0.9977 0.996 0.004 0.000
#> GSM559468 1 0.0000 0.9979 1.000 0.000 0.000
#> GSM559469 1 0.0000 0.9979 1.000 0.000 0.000
#> GSM559470 1 0.0237 0.9977 0.996 0.004 0.000
#> GSM559471 1 0.0000 0.9979 1.000 0.000 0.000
#> GSM559472 1 0.0237 0.9977 0.996 0.004 0.000
#> GSM559473 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM559475 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM559477 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM559478 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM559479 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM559480 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM559481 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM559482 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM559435 3 0.0000 0.9406 0.000 0.000 1.000
#> GSM559439 3 0.0000 0.9406 0.000 0.000 1.000
#> GSM559443 3 0.0000 0.9406 0.000 0.000 1.000
#> GSM559447 3 0.0000 0.9406 0.000 0.000 1.000
#> GSM559449 3 0.0000 0.9406 0.000 0.000 1.000
#> GSM559453 3 0.0000 0.9406 0.000 0.000 1.000
#> GSM559466 3 0.0000 0.9406 0.000 0.000 1.000
#> GSM559474 3 0.0000 0.9406 0.000 0.000 1.000
#> GSM559476 3 0.0000 0.9406 0.000 0.000 1.000
#> GSM559483 2 0.0000 1.0000 0.000 1.000 0.000
#> GSM559484 3 0.0000 0.9406 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 4 0.0592 0.843 0.016 0.000 0.000 0.984
#> GSM559434 4 0.0817 0.829 0.024 0.000 0.000 0.976
#> GSM559436 1 0.4222 0.715 0.728 0.000 0.000 0.272
#> GSM559437 4 0.0469 0.844 0.012 0.000 0.000 0.988
#> GSM559438 4 0.1211 0.821 0.040 0.000 0.000 0.960
#> GSM559440 4 0.0817 0.829 0.024 0.000 0.000 0.976
#> GSM559441 4 0.0469 0.844 0.012 0.000 0.000 0.988
#> GSM559442 1 0.3400 0.595 0.820 0.000 0.000 0.180
#> GSM559444 4 0.4222 0.475 0.000 0.272 0.000 0.728
#> GSM559445 4 0.0469 0.844 0.012 0.000 0.000 0.988
#> GSM559446 4 0.0469 0.844 0.012 0.000 0.000 0.988
#> GSM559448 1 0.7799 0.384 0.420 0.000 0.308 0.272
#> GSM559450 2 0.2469 0.843 0.000 0.892 0.000 0.108
#> GSM559451 4 0.4331 0.489 0.288 0.000 0.000 0.712
#> GSM559452 4 0.4222 0.553 0.272 0.000 0.000 0.728
#> GSM559454 1 0.4972 0.337 0.544 0.000 0.000 0.456
#> GSM559455 4 0.0469 0.844 0.012 0.000 0.000 0.988
#> GSM559456 4 0.1716 0.813 0.064 0.000 0.000 0.936
#> GSM559457 4 0.4431 0.452 0.304 0.000 0.000 0.696
#> GSM559458 3 0.5110 0.462 0.016 0.000 0.656 0.328
#> GSM559459 1 0.4222 0.715 0.728 0.000 0.000 0.272
#> GSM559460 1 0.1118 0.769 0.964 0.000 0.000 0.036
#> GSM559461 1 0.4222 0.715 0.728 0.000 0.000 0.272
#> GSM559462 1 0.4222 0.715 0.728 0.000 0.000 0.272
#> GSM559463 1 0.3801 0.740 0.780 0.000 0.000 0.220
#> GSM559464 1 0.0817 0.765 0.976 0.000 0.000 0.024
#> GSM559465 1 0.1867 0.771 0.928 0.000 0.000 0.072
#> GSM559467 4 0.2868 0.754 0.136 0.000 0.000 0.864
#> GSM559468 1 0.0000 0.755 1.000 0.000 0.000 0.000
#> GSM559469 1 0.0188 0.754 0.996 0.000 0.000 0.004
#> GSM559470 4 0.0469 0.844 0.012 0.000 0.000 0.988
#> GSM559471 1 0.1022 0.763 0.968 0.000 0.000 0.032
#> GSM559472 4 0.4817 0.193 0.388 0.000 0.000 0.612
#> GSM559473 2 0.4941 0.235 0.000 0.564 0.000 0.436
#> GSM559475 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM559477 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM559478 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM559479 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM559480 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM559481 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM559482 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM559435 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM559439 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM559443 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM559447 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM559449 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM559453 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM559466 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM559474 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM559476 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM559483 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM559484 3 0.0000 0.960 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 4 0.4201 0.4418 0.408 0.000 0.000 0.592 0.000
#> GSM559434 4 0.0000 0.7288 0.000 0.000 0.000 1.000 0.000
#> GSM559436 1 0.1608 0.5498 0.928 0.000 0.000 0.072 0.000
#> GSM559437 4 0.2329 0.7502 0.124 0.000 0.000 0.876 0.000
#> GSM559438 4 0.0000 0.7288 0.000 0.000 0.000 1.000 0.000
#> GSM559440 4 0.0000 0.7288 0.000 0.000 0.000 1.000 0.000
#> GSM559441 4 0.2329 0.7502 0.124 0.000 0.000 0.876 0.000
#> GSM559442 3 0.6451 -0.4734 0.364 0.000 0.452 0.184 0.000
#> GSM559444 4 0.1908 0.6683 0.000 0.092 0.000 0.908 0.000
#> GSM559445 4 0.2329 0.7502 0.124 0.000 0.000 0.876 0.000
#> GSM559446 4 0.3966 0.5489 0.336 0.000 0.000 0.664 0.000
#> GSM559448 1 0.4736 0.4020 0.712 0.000 0.216 0.072 0.000
#> GSM559450 2 0.3395 0.6906 0.000 0.764 0.000 0.236 0.000
#> GSM559451 1 0.4030 0.1378 0.648 0.000 0.000 0.352 0.000
#> GSM559452 4 0.5322 0.3661 0.072 0.000 0.320 0.608 0.000
#> GSM559454 1 0.3452 0.3612 0.756 0.000 0.000 0.244 0.000
#> GSM559455 4 0.2516 0.7420 0.140 0.000 0.000 0.860 0.000
#> GSM559456 4 0.4305 0.2803 0.488 0.000 0.000 0.512 0.000
#> GSM559457 1 0.4015 0.1493 0.652 0.000 0.000 0.348 0.000
#> GSM559458 3 0.7515 0.0615 0.252 0.000 0.500 0.140 0.108
#> GSM559459 1 0.3471 0.5813 0.836 0.000 0.092 0.072 0.000
#> GSM559460 1 0.4242 0.5069 0.572 0.000 0.428 0.000 0.000
#> GSM559461 1 0.3966 0.5888 0.796 0.000 0.132 0.072 0.000
#> GSM559462 1 0.3966 0.5888 0.796 0.000 0.132 0.072 0.000
#> GSM559463 1 0.3764 0.5942 0.800 0.000 0.156 0.044 0.000
#> GSM559464 1 0.4278 0.4914 0.548 0.000 0.452 0.000 0.000
#> GSM559465 1 0.4717 0.5326 0.584 0.000 0.396 0.020 0.000
#> GSM559467 1 0.4897 -0.2211 0.516 0.000 0.024 0.460 0.000
#> GSM559468 1 0.4811 0.4742 0.528 0.000 0.452 0.020 0.000
#> GSM559469 1 0.4890 0.4718 0.524 0.000 0.452 0.024 0.000
#> GSM559470 4 0.2329 0.7502 0.124 0.000 0.000 0.876 0.000
#> GSM559471 1 0.4768 0.4986 0.592 0.000 0.384 0.024 0.000
#> GSM559472 1 0.3837 0.2442 0.692 0.000 0.000 0.308 0.000
#> GSM559473 4 0.4306 -0.0383 0.000 0.492 0.000 0.508 0.000
#> GSM559475 2 0.1043 0.9364 0.000 0.960 0.000 0.040 0.000
#> GSM559477 2 0.0000 0.9532 0.000 1.000 0.000 0.000 0.000
#> GSM559478 2 0.0404 0.9499 0.000 0.988 0.000 0.012 0.000
#> GSM559479 2 0.0000 0.9532 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.1043 0.9364 0.000 0.960 0.000 0.040 0.000
#> GSM559481 2 0.0000 0.9532 0.000 1.000 0.000 0.000 0.000
#> GSM559482 2 0.0000 0.9532 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.4278 0.6545 0.000 0.000 0.548 0.000 0.452
#> GSM559439 3 0.4278 0.6545 0.000 0.000 0.548 0.000 0.452
#> GSM559443 3 0.4278 0.6545 0.000 0.000 0.548 0.000 0.452
#> GSM559447 3 0.4278 0.6545 0.000 0.000 0.548 0.000 0.452
#> GSM559449 3 0.4278 0.6545 0.000 0.000 0.548 0.000 0.452
#> GSM559453 3 0.4278 0.6545 0.000 0.000 0.548 0.000 0.452
#> GSM559466 3 0.4278 0.6545 0.000 0.000 0.548 0.000 0.452
#> GSM559474 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM559476 3 0.4278 0.6545 0.000 0.000 0.548 0.000 0.452
#> GSM559483 2 0.0000 0.9532 0.000 1.000 0.000 0.000 0.000
#> GSM559484 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.3804 0.0243 0.576 0.000 0.000 0.424 0 0.000
#> GSM559434 4 0.0146 0.6877 0.004 0.000 0.000 0.996 0 0.000
#> GSM559436 1 0.0000 0.7121 1.000 0.000 0.000 0.000 0 0.000
#> GSM559437 4 0.2996 0.6924 0.228 0.000 0.000 0.772 0 0.000
#> GSM559438 4 0.0000 0.6857 0.000 0.000 0.000 1.000 0 0.000
#> GSM559440 4 0.0000 0.6857 0.000 0.000 0.000 1.000 0 0.000
#> GSM559441 4 0.2996 0.6924 0.228 0.000 0.000 0.772 0 0.000
#> GSM559442 6 0.0865 0.8302 0.000 0.000 0.000 0.036 0 0.964
#> GSM559444 4 0.0000 0.6857 0.000 0.000 0.000 1.000 0 0.000
#> GSM559445 4 0.2996 0.6924 0.228 0.000 0.000 0.772 0 0.000
#> GSM559446 4 0.3851 0.2344 0.460 0.000 0.000 0.540 0 0.000
#> GSM559448 1 0.0000 0.7121 1.000 0.000 0.000 0.000 0 0.000
#> GSM559450 2 0.3151 0.6333 0.000 0.748 0.000 0.252 0 0.000
#> GSM559451 1 0.0000 0.7121 1.000 0.000 0.000 0.000 0 0.000
#> GSM559452 4 0.3862 0.1650 0.000 0.000 0.000 0.524 0 0.476
#> GSM559454 1 0.0000 0.7121 1.000 0.000 0.000 0.000 0 0.000
#> GSM559455 4 0.3221 0.6525 0.264 0.000 0.000 0.736 0 0.000
#> GSM559456 1 0.3330 0.3935 0.716 0.000 0.000 0.284 0 0.000
#> GSM559457 1 0.0000 0.7121 1.000 0.000 0.000 0.000 0 0.000
#> GSM559458 3 0.5360 0.2808 0.344 0.000 0.556 0.088 0 0.012
#> GSM559459 1 0.3817 0.3153 0.568 0.000 0.000 0.000 0 0.432
#> GSM559460 6 0.1267 0.8585 0.060 0.000 0.000 0.000 0 0.940
#> GSM559461 1 0.3867 0.2031 0.512 0.000 0.000 0.000 0 0.488
#> GSM559462 1 0.3867 0.2031 0.512 0.000 0.000 0.000 0 0.488
#> GSM559463 1 0.3351 0.3456 0.712 0.000 0.000 0.000 0 0.288
#> GSM559464 6 0.0865 0.8652 0.036 0.000 0.000 0.000 0 0.964
#> GSM559465 6 0.2300 0.7599 0.144 0.000 0.000 0.000 0 0.856
#> GSM559467 1 0.4587 0.3678 0.640 0.000 0.000 0.296 0 0.064
#> GSM559468 6 0.1007 0.8649 0.044 0.000 0.000 0.000 0 0.956
#> GSM559469 6 0.0865 0.8652 0.036 0.000 0.000 0.000 0 0.964
#> GSM559470 4 0.2996 0.6924 0.228 0.000 0.000 0.772 0 0.000
#> GSM559471 6 0.3804 0.3361 0.424 0.000 0.000 0.000 0 0.576
#> GSM559472 1 0.0000 0.7121 1.000 0.000 0.000 0.000 0 0.000
#> GSM559473 4 0.4537 -0.0304 0.000 0.412 0.000 0.552 0 0.036
#> GSM559475 2 0.1714 0.8790 0.000 0.908 0.000 0.092 0 0.000
#> GSM559477 2 0.0000 0.9205 0.000 1.000 0.000 0.000 0 0.000
#> GSM559478 2 0.1320 0.9109 0.000 0.948 0.000 0.016 0 0.036
#> GSM559479 2 0.0000 0.9205 0.000 1.000 0.000 0.000 0 0.000
#> GSM559480 2 0.2560 0.8664 0.000 0.872 0.000 0.092 0 0.036
#> GSM559481 2 0.0865 0.9132 0.000 0.964 0.000 0.000 0 0.036
#> GSM559482 2 0.0000 0.9205 0.000 1.000 0.000 0.000 0 0.000
#> GSM559435 3 0.0000 0.9293 0.000 0.000 1.000 0.000 0 0.000
#> GSM559439 3 0.0000 0.9293 0.000 0.000 1.000 0.000 0 0.000
#> GSM559443 3 0.0000 0.9293 0.000 0.000 1.000 0.000 0 0.000
#> GSM559447 3 0.0000 0.9293 0.000 0.000 1.000 0.000 0 0.000
#> GSM559449 3 0.0000 0.9293 0.000 0.000 1.000 0.000 0 0.000
#> GSM559453 3 0.0000 0.9293 0.000 0.000 1.000 0.000 0 0.000
#> GSM559466 3 0.0000 0.9293 0.000 0.000 1.000 0.000 0 0.000
#> GSM559474 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1 0.000
#> GSM559476 3 0.0000 0.9293 0.000 0.000 1.000 0.000 0 0.000
#> GSM559483 2 0.0000 0.9205 0.000 1.000 0.000 0.000 0 0.000
#> GSM559484 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1 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 disease.state(p) k
#> CV:pam 52 5.58e-07 2
#> CV:pam 51 1.82e-09 3
#> CV:pam 44 1.53e-08 4
#> CV:pam 36 2.09e-06 5
#> CV:pam 40 1.17e-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", "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 21512 rows and 52 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 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 0.442 0.701 0.750 0.4046 0.566 0.566
#> 3 3 0.679 0.834 0.910 0.4448 0.491 0.329
#> 4 4 0.638 0.341 0.709 0.0826 0.774 0.515
#> 5 5 0.762 0.742 0.857 0.1606 0.779 0.409
#> 6 6 0.852 0.836 0.922 0.0429 0.885 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
#> GSM559433 1 0.9970 0.913 0.532 0.468
#> GSM559434 2 0.0000 0.711 0.000 1.000
#> GSM559436 1 0.9661 0.941 0.608 0.392
#> GSM559437 2 0.0376 0.708 0.004 0.996
#> GSM559438 2 0.4562 0.536 0.096 0.904
#> GSM559440 2 0.0000 0.711 0.000 1.000
#> GSM559441 2 0.0376 0.708 0.004 0.996
#> GSM559442 1 0.9977 0.915 0.528 0.472
#> GSM559444 2 0.0000 0.711 0.000 1.000
#> GSM559445 2 0.0376 0.708 0.004 0.996
#> GSM559446 2 0.0376 0.708 0.004 0.996
#> GSM559448 2 0.4690 0.639 0.100 0.900
#> GSM559450 2 0.0000 0.711 0.000 1.000
#> GSM559451 1 0.9944 0.924 0.544 0.456
#> GSM559452 2 0.4022 0.665 0.080 0.920
#> GSM559454 1 0.9661 0.941 0.608 0.392
#> GSM559455 2 0.3879 0.586 0.076 0.924
#> GSM559456 2 0.0376 0.708 0.004 0.996
#> GSM559457 2 0.9983 -0.840 0.476 0.524
#> GSM559458 2 0.3733 0.668 0.072 0.928
#> GSM559459 1 0.9661 0.941 0.608 0.392
#> GSM559460 1 0.9661 0.941 0.608 0.392
#> GSM559461 1 0.9710 0.942 0.600 0.400
#> GSM559462 1 0.9661 0.941 0.608 0.392
#> GSM559463 2 0.5842 0.577 0.140 0.860
#> GSM559464 1 0.9661 0.941 0.608 0.392
#> GSM559465 1 0.9661 0.941 0.608 0.392
#> GSM559467 1 0.9983 0.908 0.524 0.476
#> GSM559468 1 0.9850 0.938 0.572 0.428
#> GSM559469 1 0.9977 0.912 0.528 0.472
#> GSM559470 2 0.0376 0.708 0.004 0.996
#> GSM559471 1 0.9963 0.918 0.536 0.464
#> GSM559472 1 0.9795 0.941 0.584 0.416
#> GSM559473 2 0.0376 0.713 0.004 0.996
#> GSM559475 2 0.0376 0.713 0.004 0.996
#> GSM559477 2 0.0376 0.713 0.004 0.996
#> GSM559478 2 0.0376 0.713 0.004 0.996
#> GSM559479 2 0.0376 0.713 0.004 0.996
#> GSM559480 2 0.0376 0.713 0.004 0.996
#> GSM559481 2 0.0376 0.713 0.004 0.996
#> GSM559482 2 0.0376 0.713 0.004 0.996
#> GSM559435 2 0.9970 0.520 0.468 0.532
#> GSM559439 2 0.9970 0.520 0.468 0.532
#> GSM559443 2 0.9970 0.520 0.468 0.532
#> GSM559447 2 0.9970 0.520 0.468 0.532
#> GSM559449 2 0.9970 0.520 0.468 0.532
#> GSM559453 2 0.9970 0.520 0.468 0.532
#> GSM559466 2 0.9970 0.520 0.468 0.532
#> GSM559474 2 0.9970 0.520 0.468 0.532
#> GSM559476 2 0.9970 0.520 0.468 0.532
#> GSM559483 2 0.0376 0.713 0.004 0.996
#> GSM559484 2 0.9970 0.520 0.468 0.532
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0000 0.869 1.000 0.000 0.000
#> GSM559434 1 0.6274 0.391 0.544 0.456 0.000
#> GSM559436 1 0.0000 0.869 1.000 0.000 0.000
#> GSM559437 1 0.6079 0.541 0.612 0.388 0.000
#> GSM559438 1 0.5650 0.626 0.688 0.312 0.000
#> GSM559440 1 0.6215 0.412 0.572 0.428 0.000
#> GSM559441 1 0.5216 0.719 0.740 0.260 0.000
#> GSM559442 1 0.1031 0.870 0.976 0.024 0.000
#> GSM559444 2 0.4062 0.758 0.164 0.836 0.000
#> GSM559445 1 0.6126 0.518 0.600 0.400 0.000
#> GSM559446 1 0.6045 0.555 0.620 0.380 0.000
#> GSM559448 1 0.1643 0.864 0.956 0.044 0.000
#> GSM559450 2 0.2711 0.865 0.088 0.912 0.000
#> GSM559451 1 0.0892 0.870 0.980 0.020 0.000
#> GSM559452 1 0.5643 0.726 0.760 0.220 0.020
#> GSM559454 1 0.0000 0.869 1.000 0.000 0.000
#> GSM559455 1 0.3038 0.845 0.896 0.104 0.000
#> GSM559456 1 0.3038 0.845 0.896 0.104 0.000
#> GSM559457 1 0.2625 0.855 0.916 0.084 0.000
#> GSM559458 1 0.2625 0.849 0.916 0.084 0.000
#> GSM559459 1 0.0000 0.869 1.000 0.000 0.000
#> GSM559460 1 0.0000 0.869 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.869 1.000 0.000 0.000
#> GSM559462 1 0.0000 0.869 1.000 0.000 0.000
#> GSM559463 1 0.0237 0.869 0.996 0.004 0.000
#> GSM559464 1 0.0000 0.869 1.000 0.000 0.000
#> GSM559465 1 0.2066 0.863 0.940 0.060 0.000
#> GSM559467 1 0.1031 0.870 0.976 0.024 0.000
#> GSM559468 1 0.0892 0.870 0.980 0.020 0.000
#> GSM559469 1 0.1031 0.870 0.976 0.024 0.000
#> GSM559470 1 0.4702 0.749 0.788 0.212 0.000
#> GSM559471 1 0.1031 0.870 0.976 0.024 0.000
#> GSM559472 1 0.0000 0.869 1.000 0.000 0.000
#> GSM559473 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559475 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559477 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559478 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559479 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559480 2 0.0892 0.940 0.000 0.980 0.020
#> GSM559481 2 0.0892 0.940 0.000 0.980 0.020
#> GSM559482 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559435 3 0.0892 0.943 0.020 0.000 0.980
#> GSM559439 3 0.0892 0.943 0.020 0.000 0.980
#> GSM559443 3 0.1129 0.942 0.020 0.004 0.976
#> GSM559447 3 0.0892 0.943 0.020 0.000 0.980
#> GSM559449 3 0.0892 0.943 0.020 0.000 0.980
#> GSM559453 3 0.1129 0.942 0.020 0.004 0.976
#> GSM559466 3 0.0892 0.943 0.020 0.000 0.980
#> GSM559474 3 0.4291 0.769 0.000 0.180 0.820
#> GSM559476 1 0.5069 0.766 0.828 0.044 0.128
#> GSM559483 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559484 3 0.4399 0.760 0.000 0.188 0.812
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.4999 -2.84e-01 0.508 0.000 0.000 0.492
#> GSM559434 4 0.5147 9.81e-02 0.460 0.004 0.000 0.536
#> GSM559436 4 0.5000 2.40e-01 0.496 0.000 0.000 0.504
#> GSM559437 1 0.0000 3.18e-01 1.000 0.000 0.000 0.000
#> GSM559438 1 0.4907 -5.64e-03 0.580 0.000 0.000 0.420
#> GSM559440 1 0.4977 -6.59e-02 0.540 0.000 0.000 0.460
#> GSM559441 1 0.3024 2.99e-01 0.852 0.000 0.000 0.148
#> GSM559442 1 0.4998 -1.16e-01 0.512 0.000 0.000 0.488
#> GSM559444 4 0.6648 7.70e-02 0.092 0.372 0.000 0.536
#> GSM559445 1 0.0000 3.18e-01 1.000 0.000 0.000 0.000
#> GSM559446 1 0.0000 3.18e-01 1.000 0.000 0.000 0.000
#> GSM559448 4 0.5143 7.76e-02 0.456 0.000 0.004 0.540
#> GSM559450 4 0.5894 -9.88e-02 0.036 0.428 0.000 0.536
#> GSM559451 4 0.5000 2.40e-01 0.496 0.000 0.000 0.504
#> GSM559452 4 0.6009 1.15e-01 0.380 0.048 0.000 0.572
#> GSM559454 4 0.5000 2.40e-01 0.496 0.000 0.000 0.504
#> GSM559455 1 0.3649 2.72e-01 0.796 0.000 0.000 0.204
#> GSM559456 1 0.0188 3.16e-01 0.996 0.000 0.004 0.000
#> GSM559457 1 0.4624 1.38e-01 0.660 0.000 0.000 0.340
#> GSM559458 1 0.1305 2.89e-01 0.960 0.000 0.004 0.036
#> GSM559459 4 0.5000 2.21e-01 0.500 0.000 0.000 0.500
#> GSM559460 4 0.5000 2.40e-01 0.496 0.000 0.000 0.504
#> GSM559461 4 0.5000 2.40e-01 0.496 0.000 0.000 0.504
#> GSM559462 1 0.4992 -2.03e-01 0.524 0.000 0.000 0.476
#> GSM559463 1 0.4992 -2.03e-01 0.524 0.000 0.000 0.476
#> GSM559464 4 0.5000 2.40e-01 0.496 0.000 0.000 0.504
#> GSM559465 1 0.4972 -1.58e-01 0.544 0.000 0.000 0.456
#> GSM559467 1 0.4888 -6.82e-05 0.588 0.000 0.000 0.412
#> GSM559468 1 0.5000 -2.96e-01 0.504 0.000 0.000 0.496
#> GSM559469 1 0.4948 -3.31e-02 0.560 0.000 0.000 0.440
#> GSM559470 1 0.4888 -6.82e-05 0.588 0.000 0.000 0.412
#> GSM559471 1 0.4994 -2.04e-01 0.520 0.000 0.000 0.480
#> GSM559472 4 0.5000 2.40e-01 0.496 0.000 0.000 0.504
#> GSM559473 2 0.4562 7.16e-01 0.028 0.764 0.000 0.208
#> GSM559475 2 0.5768 2.39e-01 0.028 0.516 0.000 0.456
#> GSM559477 2 0.0000 8.93e-01 0.000 1.000 0.000 0.000
#> GSM559478 2 0.0000 8.93e-01 0.000 1.000 0.000 0.000
#> GSM559479 2 0.0000 8.93e-01 0.000 1.000 0.000 0.000
#> GSM559480 2 0.0000 8.93e-01 0.000 1.000 0.000 0.000
#> GSM559481 2 0.0000 8.93e-01 0.000 1.000 0.000 0.000
#> GSM559482 2 0.0000 8.93e-01 0.000 1.000 0.000 0.000
#> GSM559435 3 0.0000 8.74e-01 0.000 0.000 1.000 0.000
#> GSM559439 3 0.0000 8.74e-01 0.000 0.000 1.000 0.000
#> GSM559443 3 0.0000 8.74e-01 0.000 0.000 1.000 0.000
#> GSM559447 3 0.0000 8.74e-01 0.000 0.000 1.000 0.000
#> GSM559449 3 0.0000 8.74e-01 0.000 0.000 1.000 0.000
#> GSM559453 3 0.0000 8.74e-01 0.000 0.000 1.000 0.000
#> GSM559466 3 0.0000 8.74e-01 0.000 0.000 1.000 0.000
#> GSM559474 3 0.4605 7.14e-01 0.000 0.000 0.664 0.336
#> GSM559476 3 0.6648 1.37e-01 0.372 0.000 0.536 0.092
#> GSM559483 2 0.0000 8.93e-01 0.000 1.000 0.000 0.000
#> GSM559484 3 0.4605 7.14e-01 0.000 0.000 0.664 0.336
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 1 0.0000 0.8956 1.000 0.000 0.000 0.000 0.000
#> GSM559434 4 0.0162 0.6171 0.004 0.000 0.000 0.996 0.000
#> GSM559436 1 0.0000 0.8956 1.000 0.000 0.000 0.000 0.000
#> GSM559437 4 0.6038 0.6366 0.184 0.000 0.000 0.576 0.240
#> GSM559438 4 0.3336 0.6164 0.228 0.000 0.000 0.772 0.000
#> GSM559440 4 0.0963 0.6254 0.036 0.000 0.000 0.964 0.000
#> GSM559441 4 0.6044 0.6362 0.188 0.000 0.000 0.576 0.236
#> GSM559442 1 0.0510 0.8886 0.984 0.000 0.000 0.016 0.000
#> GSM559444 4 0.2763 0.4671 0.004 0.148 0.000 0.848 0.000
#> GSM559445 4 0.5309 0.6438 0.104 0.000 0.000 0.656 0.240
#> GSM559446 4 0.6038 0.6366 0.184 0.000 0.000 0.576 0.240
#> GSM559448 1 0.1638 0.8528 0.932 0.000 0.004 0.064 0.000
#> GSM559450 2 0.4425 0.4987 0.000 0.544 0.000 0.452 0.004
#> GSM559451 1 0.0000 0.8956 1.000 0.000 0.000 0.000 0.000
#> GSM559452 4 0.0613 0.6182 0.008 0.004 0.004 0.984 0.000
#> GSM559454 1 0.0000 0.8956 1.000 0.000 0.000 0.000 0.000
#> GSM559455 1 0.5779 0.4143 0.616 0.000 0.000 0.212 0.172
#> GSM559456 1 0.5565 0.4746 0.632 0.000 0.000 0.128 0.240
#> GSM559457 1 0.2536 0.7900 0.868 0.000 0.000 0.004 0.128
#> GSM559458 1 0.6076 0.3814 0.588 0.000 0.004 0.172 0.236
#> GSM559459 1 0.0000 0.8956 1.000 0.000 0.000 0.000 0.000
#> GSM559460 1 0.0000 0.8956 1.000 0.000 0.000 0.000 0.000
#> GSM559461 1 0.0000 0.8956 1.000 0.000 0.000 0.000 0.000
#> GSM559462 1 0.0000 0.8956 1.000 0.000 0.000 0.000 0.000
#> GSM559463 1 0.0290 0.8920 0.992 0.000 0.000 0.008 0.000
#> GSM559464 1 0.0000 0.8956 1.000 0.000 0.000 0.000 0.000
#> GSM559465 1 0.0000 0.8956 1.000 0.000 0.000 0.000 0.000
#> GSM559467 1 0.4171 0.1382 0.604 0.000 0.000 0.396 0.000
#> GSM559468 1 0.0000 0.8956 1.000 0.000 0.000 0.000 0.000
#> GSM559469 1 0.1478 0.8550 0.936 0.000 0.000 0.064 0.000
#> GSM559470 4 0.4182 0.4480 0.400 0.000 0.000 0.600 0.000
#> GSM559471 1 0.0290 0.8920 0.992 0.000 0.000 0.008 0.000
#> GSM559472 1 0.0000 0.8956 1.000 0.000 0.000 0.000 0.000
#> GSM559473 2 0.3861 0.6750 0.000 0.712 0.000 0.284 0.004
#> GSM559475 2 0.4375 0.5517 0.000 0.576 0.000 0.420 0.004
#> GSM559477 2 0.0000 0.8530 0.000 1.000 0.000 0.000 0.000
#> GSM559478 2 0.0162 0.8515 0.000 0.996 0.000 0.000 0.004
#> GSM559479 2 0.0000 0.8530 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.0000 0.8530 0.000 1.000 0.000 0.000 0.000
#> GSM559481 2 0.0000 0.8530 0.000 1.000 0.000 0.000 0.000
#> GSM559482 2 0.0000 0.8530 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.8157 0.000 0.000 1.000 0.000 0.000
#> GSM559439 3 0.0000 0.8157 0.000 0.000 1.000 0.000 0.000
#> GSM559443 3 0.1341 0.7512 0.000 0.000 0.944 0.056 0.000
#> GSM559447 3 0.0000 0.8157 0.000 0.000 1.000 0.000 0.000
#> GSM559449 3 0.0000 0.8157 0.000 0.000 1.000 0.000 0.000
#> GSM559453 3 0.1608 0.7491 0.000 0.000 0.928 0.000 0.072
#> GSM559466 3 0.0000 0.8157 0.000 0.000 1.000 0.000 0.000
#> GSM559474 5 0.3452 1.0000 0.000 0.000 0.244 0.000 0.756
#> GSM559476 3 0.5697 0.0508 0.404 0.000 0.512 0.084 0.000
#> GSM559483 2 0.0000 0.8530 0.000 1.000 0.000 0.000 0.000
#> GSM559484 5 0.3452 1.0000 0.000 0.000 0.244 0.000 0.756
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.0146 0.944 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM559434 6 0.2288 0.870 0.000 0.004 0.000 0.116 0.004 0.876
#> GSM559436 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559437 4 0.1168 0.631 0.016 0.000 0.000 0.956 0.000 0.028
#> GSM559438 6 0.2553 0.742 0.144 0.000 0.000 0.008 0.000 0.848
#> GSM559440 6 0.2361 0.874 0.012 0.004 0.000 0.104 0.000 0.880
#> GSM559441 4 0.2868 0.673 0.132 0.000 0.000 0.840 0.000 0.028
#> GSM559442 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559444 6 0.2554 0.884 0.000 0.028 0.000 0.092 0.004 0.876
#> GSM559445 4 0.1151 0.625 0.012 0.000 0.000 0.956 0.000 0.032
#> GSM559446 4 0.1168 0.631 0.016 0.000 0.000 0.956 0.000 0.028
#> GSM559448 1 0.2800 0.792 0.860 0.000 0.000 0.036 0.004 0.100
#> GSM559450 6 0.2358 0.865 0.000 0.108 0.000 0.016 0.000 0.876
#> GSM559451 1 0.0146 0.944 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM559452 6 0.2637 0.883 0.000 0.024 0.000 0.096 0.008 0.872
#> GSM559454 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559455 4 0.4338 0.307 0.484 0.000 0.000 0.496 0.000 0.020
#> GSM559456 4 0.3734 0.651 0.264 0.000 0.000 0.716 0.000 0.020
#> GSM559457 1 0.0508 0.935 0.984 0.000 0.000 0.012 0.000 0.004
#> GSM559458 4 0.4131 0.592 0.356 0.000 0.000 0.624 0.000 0.020
#> GSM559459 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559460 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559461 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559462 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559463 1 0.0363 0.936 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM559464 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559465 1 0.0146 0.945 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM559467 1 0.0547 0.931 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM559468 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559469 1 0.0363 0.937 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM559470 1 0.6227 -0.410 0.376 0.000 0.000 0.320 0.004 0.300
#> GSM559471 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559472 1 0.0000 0.946 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559473 6 0.2730 0.793 0.000 0.192 0.000 0.000 0.000 0.808
#> GSM559475 6 0.2278 0.853 0.000 0.128 0.000 0.004 0.000 0.868
#> GSM559477 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559478 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559479 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559480 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559481 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559482 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.875 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559439 3 0.0000 0.875 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559443 3 0.2740 0.769 0.000 0.000 0.852 0.028 0.000 0.120
#> GSM559447 3 0.0000 0.875 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559449 3 0.0000 0.875 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559453 3 0.0458 0.866 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM559466 3 0.0000 0.875 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559474 5 0.0260 0.995 0.000 0.000 0.008 0.000 0.992 0.000
#> GSM559476 3 0.6292 0.220 0.340 0.000 0.496 0.036 0.008 0.120
#> GSM559483 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559484 5 0.0146 0.995 0.000 0.000 0.004 0.000 0.996 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 disease.state(p) k
#> CV:mclust 51 3.04e-02 2
#> CV:mclust 50 3.28e-09 3
#> CV:mclust 17 1.55e-03 4
#> CV:mclust 44 7.17e-08 5
#> CV:mclust 49 2.64e-08 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 21512 rows and 52 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 0.778 0.885 0.952 0.4737 0.527 0.527
#> 3 3 1.000 0.986 0.994 0.3120 0.729 0.538
#> 4 4 0.713 0.676 0.835 0.1624 0.839 0.591
#> 5 5 0.681 0.665 0.784 0.0893 0.865 0.548
#> 6 6 0.786 0.751 0.855 0.0470 0.902 0.605
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
#> GSM559433 1 0.2603 0.9260 0.956 0.044
#> GSM559434 2 0.0000 0.9423 0.000 1.000
#> GSM559436 1 0.0000 0.9488 1.000 0.000
#> GSM559437 1 0.3733 0.9066 0.928 0.072
#> GSM559438 2 0.0000 0.9423 0.000 1.000
#> GSM559440 2 0.0000 0.9423 0.000 1.000
#> GSM559441 1 0.9998 0.0482 0.508 0.492
#> GSM559442 1 0.1184 0.9414 0.984 0.016
#> GSM559444 2 0.0000 0.9423 0.000 1.000
#> GSM559445 2 0.8443 0.5935 0.272 0.728
#> GSM559446 1 0.5519 0.8590 0.872 0.128
#> GSM559448 1 0.0000 0.9488 1.000 0.000
#> GSM559450 2 0.0000 0.9423 0.000 1.000
#> GSM559451 1 0.2778 0.9234 0.952 0.048
#> GSM559452 2 0.0376 0.9396 0.004 0.996
#> GSM559454 1 0.0000 0.9488 1.000 0.000
#> GSM559455 1 0.4562 0.8880 0.904 0.096
#> GSM559456 1 0.0000 0.9488 1.000 0.000
#> GSM559457 1 0.0000 0.9488 1.000 0.000
#> GSM559458 1 0.0000 0.9488 1.000 0.000
#> GSM559459 1 0.0000 0.9488 1.000 0.000
#> GSM559460 1 0.0000 0.9488 1.000 0.000
#> GSM559461 1 0.0000 0.9488 1.000 0.000
#> GSM559462 1 0.5629 0.8540 0.868 0.132
#> GSM559463 1 0.0000 0.9488 1.000 0.000
#> GSM559464 1 0.0000 0.9488 1.000 0.000
#> GSM559465 1 0.0000 0.9488 1.000 0.000
#> GSM559467 2 0.9977 0.0225 0.472 0.528
#> GSM559468 1 0.0000 0.9488 1.000 0.000
#> GSM559469 1 0.8081 0.6924 0.752 0.248
#> GSM559470 2 0.2043 0.9173 0.032 0.968
#> GSM559471 1 0.5294 0.8669 0.880 0.120
#> GSM559472 1 0.0000 0.9488 1.000 0.000
#> GSM559473 2 0.0000 0.9423 0.000 1.000
#> GSM559475 2 0.0000 0.9423 0.000 1.000
#> GSM559477 2 0.0000 0.9423 0.000 1.000
#> GSM559478 2 0.0000 0.9423 0.000 1.000
#> GSM559479 2 0.0000 0.9423 0.000 1.000
#> GSM559480 2 0.0000 0.9423 0.000 1.000
#> GSM559481 2 0.0000 0.9423 0.000 1.000
#> GSM559482 2 0.0000 0.9423 0.000 1.000
#> GSM559435 1 0.0000 0.9488 1.000 0.000
#> GSM559439 1 0.0000 0.9488 1.000 0.000
#> GSM559443 1 0.0000 0.9488 1.000 0.000
#> GSM559447 1 0.0000 0.9488 1.000 0.000
#> GSM559449 1 0.0000 0.9488 1.000 0.000
#> GSM559453 1 0.0000 0.9488 1.000 0.000
#> GSM559466 1 0.0000 0.9488 1.000 0.000
#> GSM559474 1 0.5946 0.8194 0.856 0.144
#> GSM559476 1 0.0000 0.9488 1.000 0.000
#> GSM559483 2 0.0000 0.9423 0.000 1.000
#> GSM559484 2 0.6531 0.7795 0.168 0.832
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559434 2 0.0000 0.982 0.000 1.000 0.000
#> GSM559436 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559437 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559438 2 0.4291 0.747 0.180 0.820 0.000
#> GSM559440 2 0.0000 0.982 0.000 1.000 0.000
#> GSM559441 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559442 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559444 2 0.0000 0.982 0.000 1.000 0.000
#> GSM559445 1 0.1031 0.975 0.976 0.024 0.000
#> GSM559446 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559448 1 0.0424 0.990 0.992 0.000 0.008
#> GSM559450 2 0.0000 0.982 0.000 1.000 0.000
#> GSM559451 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559452 2 0.0892 0.965 0.000 0.980 0.020
#> GSM559454 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559455 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559456 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559457 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559458 1 0.1031 0.976 0.976 0.000 0.024
#> GSM559459 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559460 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559462 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559463 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559464 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559465 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559467 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559468 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559469 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559470 1 0.1031 0.975 0.976 0.024 0.000
#> GSM559471 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559472 1 0.0000 0.997 1.000 0.000 0.000
#> GSM559473 2 0.0000 0.982 0.000 1.000 0.000
#> GSM559475 2 0.0000 0.982 0.000 1.000 0.000
#> GSM559477 2 0.0000 0.982 0.000 1.000 0.000
#> GSM559478 2 0.0000 0.982 0.000 1.000 0.000
#> GSM559479 2 0.0000 0.982 0.000 1.000 0.000
#> GSM559480 2 0.0000 0.982 0.000 1.000 0.000
#> GSM559481 2 0.0000 0.982 0.000 1.000 0.000
#> GSM559482 2 0.0000 0.982 0.000 1.000 0.000
#> GSM559435 3 0.0000 0.997 0.000 0.000 1.000
#> GSM559439 3 0.0000 0.997 0.000 0.000 1.000
#> GSM559443 3 0.0000 0.997 0.000 0.000 1.000
#> GSM559447 3 0.0000 0.997 0.000 0.000 1.000
#> GSM559449 3 0.0000 0.997 0.000 0.000 1.000
#> GSM559453 3 0.0000 0.997 0.000 0.000 1.000
#> GSM559466 3 0.0000 0.997 0.000 0.000 1.000
#> GSM559474 3 0.0000 0.997 0.000 0.000 1.000
#> GSM559476 3 0.0424 0.989 0.008 0.000 0.992
#> GSM559483 2 0.0000 0.982 0.000 1.000 0.000
#> GSM559484 3 0.0747 0.984 0.000 0.016 0.984
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.0921 0.82599 0.972 0.000 0.000 0.028
#> GSM559434 2 0.0188 0.92638 0.000 0.996 0.000 0.004
#> GSM559436 4 0.4040 0.61257 0.248 0.000 0.000 0.752
#> GSM559437 1 0.0657 0.82546 0.984 0.000 0.012 0.004
#> GSM559438 2 0.5244 0.31115 0.388 0.600 0.000 0.012
#> GSM559440 2 0.4819 0.52238 0.344 0.652 0.000 0.004
#> GSM559441 1 0.0336 0.82961 0.992 0.000 0.000 0.008
#> GSM559442 4 0.3801 0.61714 0.220 0.000 0.000 0.780
#> GSM559444 2 0.1398 0.89766 0.040 0.956 0.000 0.004
#> GSM559445 1 0.2799 0.72477 0.884 0.000 0.108 0.008
#> GSM559446 1 0.2124 0.77146 0.924 0.000 0.068 0.008
#> GSM559448 4 0.0921 0.41478 0.028 0.000 0.000 0.972
#> GSM559450 2 0.0188 0.92638 0.000 0.996 0.000 0.004
#> GSM559451 1 0.1118 0.82006 0.964 0.000 0.000 0.036
#> GSM559452 2 0.1629 0.89801 0.000 0.952 0.024 0.024
#> GSM559454 1 0.4933 -0.19512 0.568 0.000 0.000 0.432
#> GSM559455 1 0.0000 0.83230 1.000 0.000 0.000 0.000
#> GSM559456 1 0.0469 0.83290 0.988 0.000 0.000 0.012
#> GSM559457 1 0.0336 0.83329 0.992 0.000 0.000 0.008
#> GSM559458 1 0.3793 0.72332 0.844 0.000 0.044 0.112
#> GSM559459 1 0.4585 0.22819 0.668 0.000 0.000 0.332
#> GSM559460 1 0.4843 -0.00856 0.604 0.000 0.000 0.396
#> GSM559461 4 0.4989 0.45322 0.472 0.000 0.000 0.528
#> GSM559462 1 0.0707 0.83049 0.980 0.000 0.000 0.020
#> GSM559463 4 0.1557 0.48859 0.056 0.000 0.000 0.944
#> GSM559464 4 0.4898 0.54352 0.416 0.000 0.000 0.584
#> GSM559465 4 0.4761 0.58118 0.372 0.000 0.000 0.628
#> GSM559467 1 0.0188 0.83302 0.996 0.000 0.000 0.004
#> GSM559468 4 0.4961 0.48680 0.448 0.000 0.000 0.552
#> GSM559469 4 0.5070 0.53943 0.416 0.004 0.000 0.580
#> GSM559470 1 0.0895 0.82024 0.976 0.020 0.000 0.004
#> GSM559471 4 0.4961 0.49138 0.448 0.000 0.000 0.552
#> GSM559472 4 0.4898 0.54960 0.416 0.000 0.000 0.584
#> GSM559473 2 0.0000 0.92793 0.000 1.000 0.000 0.000
#> GSM559475 2 0.0000 0.92793 0.000 1.000 0.000 0.000
#> GSM559477 2 0.0000 0.92793 0.000 1.000 0.000 0.000
#> GSM559478 2 0.0000 0.92793 0.000 1.000 0.000 0.000
#> GSM559479 2 0.0000 0.92793 0.000 1.000 0.000 0.000
#> GSM559480 2 0.0000 0.92793 0.000 1.000 0.000 0.000
#> GSM559481 2 0.0000 0.92793 0.000 1.000 0.000 0.000
#> GSM559482 2 0.0000 0.92793 0.000 1.000 0.000 0.000
#> GSM559435 3 0.4972 0.74125 0.000 0.000 0.544 0.456
#> GSM559439 3 0.4967 0.74448 0.000 0.000 0.548 0.452
#> GSM559443 4 0.4072 -0.20395 0.000 0.000 0.252 0.748
#> GSM559447 3 0.4661 0.81064 0.000 0.000 0.652 0.348
#> GSM559449 3 0.3610 0.81758 0.000 0.000 0.800 0.200
#> GSM559453 3 0.2011 0.79593 0.000 0.000 0.920 0.080
#> GSM559466 3 0.4624 0.81302 0.000 0.000 0.660 0.340
#> GSM559474 3 0.0188 0.76328 0.000 0.000 0.996 0.004
#> GSM559476 4 0.3569 -0.03512 0.000 0.000 0.196 0.804
#> GSM559483 2 0.0000 0.92793 0.000 1.000 0.000 0.000
#> GSM559484 3 0.0336 0.76154 0.000 0.008 0.992 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 4 0.0451 0.94150 0.008 0.000 0.004 0.988 0.000
#> GSM559434 2 0.5684 0.70802 0.248 0.644 0.096 0.008 0.004
#> GSM559436 3 0.6146 -0.10914 0.240 0.000 0.560 0.200 0.000
#> GSM559437 4 0.0162 0.94149 0.000 0.000 0.000 0.996 0.004
#> GSM559438 2 0.6291 0.57063 0.368 0.516 0.096 0.020 0.000
#> GSM559440 2 0.8130 0.31371 0.200 0.360 0.100 0.336 0.004
#> GSM559441 4 0.0290 0.93895 0.008 0.000 0.000 0.992 0.000
#> GSM559442 1 0.1502 0.66674 0.940 0.000 0.056 0.004 0.000
#> GSM559444 2 0.6163 0.73306 0.144 0.676 0.100 0.076 0.004
#> GSM559445 4 0.1704 0.88010 0.004 0.000 0.000 0.928 0.068
#> GSM559446 4 0.1285 0.92032 0.004 0.000 0.004 0.956 0.036
#> GSM559448 3 0.2230 0.50892 0.116 0.000 0.884 0.000 0.000
#> GSM559450 2 0.4909 0.76750 0.144 0.744 0.100 0.008 0.004
#> GSM559451 4 0.2017 0.87451 0.080 0.000 0.008 0.912 0.000
#> GSM559452 1 0.6646 -0.00366 0.520 0.032 0.100 0.004 0.344
#> GSM559454 1 0.5784 0.71678 0.616 0.000 0.208 0.176 0.000
#> GSM559455 4 0.0162 0.94255 0.000 0.000 0.004 0.996 0.000
#> GSM559456 4 0.0451 0.94192 0.008 0.000 0.004 0.988 0.000
#> GSM559457 4 0.0324 0.94215 0.004 0.000 0.004 0.992 0.000
#> GSM559458 1 0.4871 0.70558 0.760 0.000 0.032 0.128 0.080
#> GSM559459 1 0.5761 0.72038 0.620 0.000 0.184 0.196 0.000
#> GSM559460 1 0.3039 0.77418 0.836 0.000 0.012 0.152 0.000
#> GSM559461 1 0.5680 0.70404 0.620 0.000 0.240 0.140 0.000
#> GSM559462 4 0.3366 0.66628 0.212 0.000 0.004 0.784 0.000
#> GSM559463 1 0.4735 0.39984 0.524 0.000 0.460 0.016 0.000
#> GSM559464 1 0.3339 0.77693 0.836 0.000 0.040 0.124 0.000
#> GSM559465 1 0.4717 0.76418 0.736 0.000 0.120 0.144 0.000
#> GSM559467 4 0.1357 0.91473 0.048 0.000 0.004 0.948 0.000
#> GSM559468 1 0.2921 0.77313 0.856 0.000 0.020 0.124 0.000
#> GSM559469 1 0.2951 0.76899 0.860 0.000 0.028 0.112 0.000
#> GSM559470 4 0.0162 0.94209 0.000 0.000 0.004 0.996 0.000
#> GSM559471 1 0.3194 0.77635 0.832 0.000 0.020 0.148 0.000
#> GSM559472 1 0.6482 0.56122 0.468 0.000 0.332 0.200 0.000
#> GSM559473 2 0.2291 0.81597 0.036 0.908 0.056 0.000 0.000
#> GSM559475 2 0.0671 0.82199 0.004 0.980 0.016 0.000 0.000
#> GSM559477 2 0.0162 0.82591 0.000 0.996 0.004 0.000 0.000
#> GSM559478 2 0.0671 0.82199 0.004 0.980 0.016 0.000 0.000
#> GSM559479 2 0.4225 0.78493 0.112 0.788 0.096 0.000 0.004
#> GSM559480 2 0.0671 0.82199 0.004 0.980 0.016 0.000 0.000
#> GSM559481 2 0.0671 0.82199 0.004 0.980 0.016 0.000 0.000
#> GSM559482 2 0.0162 0.82598 0.000 0.996 0.004 0.000 0.000
#> GSM559435 3 0.4193 0.39865 0.012 0.000 0.684 0.000 0.304
#> GSM559439 3 0.4290 0.39955 0.016 0.000 0.680 0.000 0.304
#> GSM559443 3 0.3346 0.54173 0.092 0.000 0.844 0.000 0.064
#> GSM559447 3 0.4287 0.02077 0.000 0.000 0.540 0.000 0.460
#> GSM559449 5 0.4283 -0.03062 0.000 0.000 0.456 0.000 0.544
#> GSM559453 5 0.3274 0.56251 0.000 0.000 0.220 0.000 0.780
#> GSM559466 3 0.4291 0.00578 0.000 0.000 0.536 0.000 0.464
#> GSM559474 5 0.0162 0.66632 0.000 0.000 0.004 0.000 0.996
#> GSM559476 3 0.3812 0.54257 0.096 0.000 0.812 0.000 0.092
#> GSM559483 2 0.0404 0.82510 0.000 0.988 0.012 0.000 0.000
#> GSM559484 5 0.0162 0.66632 0.000 0.000 0.004 0.000 0.996
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 4 0.0551 0.9238 0.004 0.000 0.000 0.984 0.004 0.008
#> GSM559434 6 0.2939 0.7088 0.024 0.052 0.000 0.040 0.008 0.876
#> GSM559436 1 0.7094 0.0925 0.388 0.004 0.196 0.336 0.076 0.000
#> GSM559437 4 0.0000 0.9235 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM559438 6 0.2907 0.7260 0.028 0.096 0.000 0.016 0.000 0.860
#> GSM559440 6 0.2664 0.6729 0.000 0.016 0.000 0.136 0.000 0.848
#> GSM559441 4 0.1007 0.9129 0.000 0.000 0.000 0.956 0.000 0.044
#> GSM559442 1 0.3844 0.6120 0.676 0.000 0.004 0.000 0.008 0.312
#> GSM559444 6 0.4278 0.6593 0.000 0.212 0.000 0.076 0.000 0.712
#> GSM559445 4 0.0865 0.9151 0.000 0.000 0.000 0.964 0.000 0.036
#> GSM559446 4 0.0806 0.9222 0.008 0.000 0.000 0.972 0.000 0.020
#> GSM559448 3 0.2398 0.8102 0.028 0.004 0.888 0.000 0.080 0.000
#> GSM559450 6 0.3756 0.6139 0.000 0.268 0.000 0.020 0.000 0.712
#> GSM559451 4 0.3304 0.7624 0.172 0.000 0.004 0.804 0.008 0.012
#> GSM559452 6 0.2949 0.5256 0.140 0.000 0.000 0.000 0.028 0.832
#> GSM559454 1 0.2389 0.7262 0.888 0.000 0.000 0.052 0.060 0.000
#> GSM559455 4 0.0000 0.9235 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM559456 4 0.0937 0.9107 0.040 0.000 0.000 0.960 0.000 0.000
#> GSM559457 4 0.0790 0.9152 0.032 0.000 0.000 0.968 0.000 0.000
#> GSM559458 1 0.6120 0.3967 0.500 0.000 0.008 0.008 0.184 0.300
#> GSM559459 1 0.2328 0.7255 0.892 0.000 0.000 0.052 0.056 0.000
#> GSM559460 1 0.2389 0.7249 0.864 0.000 0.000 0.000 0.008 0.128
#> GSM559461 1 0.2992 0.7230 0.864 0.000 0.024 0.044 0.068 0.000
#> GSM559462 1 0.4440 0.1993 0.556 0.000 0.000 0.420 0.008 0.016
#> GSM559463 1 0.2884 0.7085 0.864 0.000 0.064 0.008 0.064 0.000
#> GSM559464 1 0.1524 0.7402 0.932 0.000 0.000 0.000 0.008 0.060
#> GSM559465 1 0.1080 0.7427 0.960 0.000 0.000 0.004 0.004 0.032
#> GSM559467 4 0.3883 0.7489 0.144 0.088 0.000 0.768 0.000 0.000
#> GSM559468 1 0.3490 0.6521 0.724 0.000 0.000 0.000 0.008 0.268
#> GSM559469 1 0.3271 0.6698 0.760 0.000 0.000 0.000 0.008 0.232
#> GSM559470 4 0.2106 0.8861 0.032 0.000 0.000 0.904 0.000 0.064
#> GSM559471 1 0.1411 0.7418 0.936 0.000 0.000 0.000 0.004 0.060
#> GSM559472 1 0.3896 0.6695 0.792 0.008 0.008 0.132 0.060 0.000
#> GSM559473 2 0.3301 0.7318 0.008 0.772 0.000 0.000 0.004 0.216
#> GSM559475 2 0.0405 0.8792 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM559477 2 0.2762 0.7873 0.000 0.804 0.000 0.000 0.000 0.196
#> GSM559478 2 0.0146 0.8788 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM559479 6 0.3756 0.3653 0.000 0.400 0.000 0.000 0.000 0.600
#> GSM559480 2 0.0146 0.8788 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM559481 2 0.0260 0.8774 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM559482 2 0.2300 0.8411 0.000 0.856 0.000 0.000 0.000 0.144
#> GSM559435 3 0.0000 0.8821 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559439 3 0.0458 0.8830 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM559443 3 0.1643 0.8418 0.008 0.000 0.924 0.000 0.068 0.000
#> GSM559447 3 0.0937 0.8789 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM559449 3 0.1610 0.8485 0.000 0.000 0.916 0.000 0.084 0.000
#> GSM559453 3 0.3756 0.2721 0.000 0.000 0.600 0.000 0.400 0.000
#> GSM559466 3 0.0937 0.8787 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM559474 5 0.1714 1.0000 0.000 0.000 0.092 0.000 0.908 0.000
#> GSM559476 3 0.0725 0.8754 0.012 0.000 0.976 0.000 0.012 0.000
#> GSM559483 2 0.1863 0.8620 0.000 0.896 0.000 0.000 0.000 0.104
#> GSM559484 5 0.1714 1.0000 0.000 0.000 0.092 0.000 0.908 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 disease.state(p) k
#> CV:NMF 50 2.99e-01 2
#> CV:NMF 52 8.38e-11 3
#> CV:NMF 41 9.19e-08 4
#> CV:NMF 43 5.48e-06 5
#> CV:NMF 47 7.36e-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", "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 21512 rows and 52 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 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 0.701 0.854 0.935 0.4330 0.581 0.581
#> 3 3 0.745 0.855 0.937 0.1293 0.947 0.909
#> 4 4 0.571 0.782 0.861 0.3372 0.837 0.692
#> 5 5 0.651 0.652 0.806 0.1062 0.863 0.642
#> 6 6 0.676 0.556 0.727 0.0539 0.884 0.636
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
#> GSM559433 1 0.0000 0.927 1.000 0.000
#> GSM559434 2 0.5178 0.864 0.116 0.884
#> GSM559436 1 0.0000 0.927 1.000 0.000
#> GSM559437 1 0.0672 0.924 0.992 0.008
#> GSM559438 2 0.7528 0.758 0.216 0.784
#> GSM559440 2 0.7453 0.764 0.212 0.788
#> GSM559441 1 0.1414 0.917 0.980 0.020
#> GSM559442 1 0.9358 0.465 0.648 0.352
#> GSM559444 2 0.0376 0.924 0.004 0.996
#> GSM559445 1 0.0672 0.924 0.992 0.008
#> GSM559446 1 0.0672 0.924 0.992 0.008
#> GSM559448 1 0.0000 0.927 1.000 0.000
#> GSM559450 2 0.0376 0.924 0.004 0.996
#> GSM559451 1 0.0000 0.927 1.000 0.000
#> GSM559452 2 0.8267 0.677 0.260 0.740
#> GSM559454 1 0.0000 0.927 1.000 0.000
#> GSM559455 1 0.1414 0.917 0.980 0.020
#> GSM559456 1 0.0000 0.927 1.000 0.000
#> GSM559457 1 0.0000 0.927 1.000 0.000
#> GSM559458 1 0.3431 0.883 0.936 0.064
#> GSM559459 1 0.0000 0.927 1.000 0.000
#> GSM559460 1 0.0000 0.927 1.000 0.000
#> GSM559461 1 0.0000 0.927 1.000 0.000
#> GSM559462 1 0.0000 0.927 1.000 0.000
#> GSM559463 1 0.0000 0.927 1.000 0.000
#> GSM559464 1 0.0000 0.927 1.000 0.000
#> GSM559465 1 0.0000 0.927 1.000 0.000
#> GSM559467 1 0.8861 0.566 0.696 0.304
#> GSM559468 1 0.5059 0.835 0.888 0.112
#> GSM559469 1 0.9248 0.493 0.660 0.340
#> GSM559470 1 0.8909 0.559 0.692 0.308
#> GSM559471 1 0.1184 0.919 0.984 0.016
#> GSM559472 1 0.0672 0.923 0.992 0.008
#> GSM559473 2 0.3584 0.900 0.068 0.932
#> GSM559475 2 0.3584 0.900 0.068 0.932
#> GSM559477 2 0.0000 0.924 0.000 1.000
#> GSM559478 2 0.0000 0.924 0.000 1.000
#> GSM559479 2 0.0000 0.924 0.000 1.000
#> GSM559480 2 0.0000 0.924 0.000 1.000
#> GSM559481 2 0.0000 0.924 0.000 1.000
#> GSM559482 2 0.0000 0.924 0.000 1.000
#> GSM559435 1 0.0000 0.927 1.000 0.000
#> GSM559439 1 0.0000 0.927 1.000 0.000
#> GSM559443 1 0.0000 0.927 1.000 0.000
#> GSM559447 1 0.0000 0.927 1.000 0.000
#> GSM559449 1 0.0000 0.927 1.000 0.000
#> GSM559453 1 0.0000 0.927 1.000 0.000
#> GSM559466 1 0.0000 0.927 1.000 0.000
#> GSM559474 1 0.9833 0.286 0.576 0.424
#> GSM559476 1 0.0000 0.927 1.000 0.000
#> GSM559483 2 0.0000 0.924 0.000 1.000
#> GSM559484 1 0.9833 0.286 0.576 0.424
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0000 0.931 1.000 0.000 0.000
#> GSM559434 2 0.4196 0.800 0.112 0.864 0.024
#> GSM559436 1 0.0000 0.931 1.000 0.000 0.000
#> GSM559437 1 0.0592 0.928 0.988 0.000 0.012
#> GSM559438 2 0.5921 0.677 0.212 0.756 0.032
#> GSM559440 2 0.5874 0.682 0.208 0.760 0.032
#> GSM559441 1 0.1031 0.921 0.976 0.000 0.024
#> GSM559442 1 0.6906 0.463 0.644 0.324 0.032
#> GSM559444 2 0.0829 0.871 0.004 0.984 0.012
#> GSM559445 1 0.0592 0.928 0.988 0.000 0.012
#> GSM559446 1 0.0592 0.928 0.988 0.000 0.012
#> GSM559448 1 0.0000 0.931 1.000 0.000 0.000
#> GSM559450 2 0.0829 0.871 0.004 0.984 0.012
#> GSM559451 1 0.0000 0.931 1.000 0.000 0.000
#> GSM559452 2 0.7331 0.558 0.256 0.672 0.072
#> GSM559454 1 0.0000 0.931 1.000 0.000 0.000
#> GSM559455 1 0.1031 0.921 0.976 0.000 0.024
#> GSM559456 1 0.0000 0.931 1.000 0.000 0.000
#> GSM559457 1 0.0000 0.931 1.000 0.000 0.000
#> GSM559458 1 0.2261 0.892 0.932 0.000 0.068
#> GSM559459 1 0.0000 0.931 1.000 0.000 0.000
#> GSM559460 1 0.0000 0.931 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.931 1.000 0.000 0.000
#> GSM559462 1 0.0000 0.931 1.000 0.000 0.000
#> GSM559463 1 0.0000 0.931 1.000 0.000 0.000
#> GSM559464 1 0.0000 0.931 1.000 0.000 0.000
#> GSM559465 1 0.0000 0.931 1.000 0.000 0.000
#> GSM559467 1 0.6475 0.566 0.692 0.280 0.028
#> GSM559468 1 0.3722 0.843 0.888 0.088 0.024
#> GSM559469 1 0.6828 0.491 0.656 0.312 0.032
#> GSM559470 1 0.6507 0.558 0.688 0.284 0.028
#> GSM559471 1 0.0848 0.926 0.984 0.008 0.008
#> GSM559472 1 0.0424 0.929 0.992 0.000 0.008
#> GSM559473 2 0.3045 0.843 0.064 0.916 0.020
#> GSM559475 2 0.3045 0.843 0.064 0.916 0.020
#> GSM559477 2 0.0000 0.873 0.000 1.000 0.000
#> GSM559478 2 0.0000 0.873 0.000 1.000 0.000
#> GSM559479 2 0.0000 0.873 0.000 1.000 0.000
#> GSM559480 2 0.0000 0.873 0.000 1.000 0.000
#> GSM559481 2 0.0000 0.873 0.000 1.000 0.000
#> GSM559482 2 0.0000 0.873 0.000 1.000 0.000
#> GSM559435 1 0.0237 0.930 0.996 0.000 0.004
#> GSM559439 1 0.0237 0.930 0.996 0.000 0.004
#> GSM559443 1 0.0237 0.930 0.996 0.000 0.004
#> GSM559447 1 0.0747 0.925 0.984 0.000 0.016
#> GSM559449 1 0.2878 0.859 0.904 0.000 0.096
#> GSM559453 1 0.5948 0.455 0.640 0.000 0.360
#> GSM559466 1 0.0747 0.925 0.984 0.000 0.016
#> GSM559474 3 0.0237 1.000 0.000 0.004 0.996
#> GSM559476 1 0.0237 0.930 0.996 0.000 0.004
#> GSM559483 2 0.0000 0.873 0.000 1.000 0.000
#> GSM559484 3 0.0237 1.000 0.000 0.004 0.996
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.0592 0.821 0.984 0.000 0.016 0.000
#> GSM559434 2 0.3899 0.832 0.052 0.840 0.108 0.000
#> GSM559436 1 0.1389 0.816 0.952 0.000 0.048 0.000
#> GSM559437 1 0.2345 0.795 0.900 0.000 0.100 0.000
#> GSM559438 2 0.5630 0.723 0.136 0.724 0.140 0.000
#> GSM559440 2 0.5581 0.728 0.132 0.728 0.140 0.000
#> GSM559441 1 0.2868 0.780 0.864 0.000 0.136 0.000
#> GSM559442 1 0.7664 0.211 0.460 0.292 0.248 0.000
#> GSM559444 2 0.1356 0.889 0.008 0.960 0.032 0.000
#> GSM559445 1 0.2345 0.795 0.900 0.000 0.100 0.000
#> GSM559446 1 0.2345 0.795 0.900 0.000 0.100 0.000
#> GSM559448 1 0.1389 0.816 0.952 0.000 0.048 0.000
#> GSM559450 2 0.1356 0.889 0.008 0.960 0.032 0.000
#> GSM559451 1 0.0817 0.821 0.976 0.000 0.024 0.000
#> GSM559452 2 0.6917 0.639 0.080 0.640 0.240 0.040
#> GSM559454 1 0.1389 0.816 0.952 0.000 0.048 0.000
#> GSM559455 1 0.2868 0.780 0.864 0.000 0.136 0.000
#> GSM559456 1 0.4855 0.209 0.600 0.000 0.400 0.000
#> GSM559457 1 0.0707 0.822 0.980 0.000 0.020 0.000
#> GSM559458 1 0.4888 0.688 0.740 0.000 0.224 0.036
#> GSM559459 1 0.1389 0.816 0.952 0.000 0.048 0.000
#> GSM559460 1 0.1557 0.814 0.944 0.000 0.056 0.000
#> GSM559461 1 0.1557 0.814 0.944 0.000 0.056 0.000
#> GSM559462 1 0.0817 0.821 0.976 0.000 0.024 0.000
#> GSM559463 1 0.1389 0.816 0.952 0.000 0.048 0.000
#> GSM559464 1 0.1557 0.814 0.944 0.000 0.056 0.000
#> GSM559465 1 0.1867 0.806 0.928 0.000 0.072 0.000
#> GSM559467 1 0.6690 0.475 0.608 0.248 0.144 0.000
#> GSM559468 1 0.4364 0.721 0.808 0.056 0.136 0.000
#> GSM559469 1 0.7622 0.248 0.472 0.280 0.248 0.000
#> GSM559470 1 0.6715 0.466 0.604 0.252 0.144 0.000
#> GSM559471 1 0.1356 0.819 0.960 0.008 0.032 0.000
#> GSM559472 1 0.1118 0.822 0.964 0.000 0.036 0.000
#> GSM559473 2 0.2796 0.862 0.016 0.892 0.092 0.000
#> GSM559475 2 0.2796 0.862 0.016 0.892 0.092 0.000
#> GSM559477 2 0.0336 0.888 0.000 0.992 0.008 0.000
#> GSM559478 2 0.0000 0.890 0.000 1.000 0.000 0.000
#> GSM559479 2 0.0336 0.888 0.000 0.992 0.008 0.000
#> GSM559480 2 0.0000 0.890 0.000 1.000 0.000 0.000
#> GSM559481 2 0.0000 0.890 0.000 1.000 0.000 0.000
#> GSM559482 2 0.0336 0.888 0.000 0.992 0.008 0.000
#> GSM559435 3 0.3610 0.919 0.200 0.000 0.800 0.000
#> GSM559439 3 0.3649 0.918 0.204 0.000 0.796 0.000
#> GSM559443 3 0.3649 0.918 0.204 0.000 0.796 0.000
#> GSM559447 3 0.3852 0.916 0.192 0.000 0.800 0.008
#> GSM559449 3 0.4920 0.839 0.136 0.000 0.776 0.088
#> GSM559453 3 0.6785 0.470 0.108 0.000 0.540 0.352
#> GSM559466 3 0.3852 0.916 0.192 0.000 0.800 0.008
#> GSM559474 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM559476 3 0.3649 0.918 0.204 0.000 0.796 0.000
#> GSM559483 2 0.0336 0.888 0.000 0.992 0.008 0.000
#> GSM559484 4 0.0000 1.000 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
#> GSM559433 1 0.161 0.846 0.928 0.000 0.000 0.072 0.000
#> GSM559434 4 0.475 -0.201 0.016 0.484 0.000 0.500 0.000
#> GSM559436 1 0.029 0.847 0.992 0.000 0.008 0.000 0.000
#> GSM559437 1 0.489 0.676 0.680 0.000 0.064 0.256 0.000
#> GSM559438 4 0.499 0.235 0.044 0.340 0.000 0.616 0.000
#> GSM559440 4 0.494 0.226 0.040 0.344 0.000 0.616 0.000
#> GSM559441 1 0.450 0.695 0.712 0.000 0.044 0.244 0.000
#> GSM559442 4 0.557 0.363 0.364 0.000 0.080 0.556 0.000
#> GSM559444 2 0.269 0.691 0.000 0.844 0.000 0.156 0.000
#> GSM559445 1 0.489 0.676 0.680 0.000 0.064 0.256 0.000
#> GSM559446 1 0.489 0.676 0.680 0.000 0.064 0.256 0.000
#> GSM559448 1 0.029 0.847 0.992 0.000 0.008 0.000 0.000
#> GSM559450 2 0.269 0.691 0.000 0.844 0.000 0.156 0.000
#> GSM559451 1 0.228 0.829 0.880 0.000 0.000 0.120 0.000
#> GSM559452 4 0.607 0.240 0.000 0.260 0.080 0.620 0.040
#> GSM559454 1 0.029 0.847 0.992 0.000 0.008 0.000 0.000
#> GSM559455 1 0.450 0.695 0.712 0.000 0.044 0.244 0.000
#> GSM559456 3 0.642 -0.174 0.412 0.000 0.416 0.172 0.000
#> GSM559457 1 0.213 0.843 0.908 0.000 0.012 0.080 0.000
#> GSM559458 1 0.594 0.591 0.660 0.000 0.112 0.192 0.036
#> GSM559459 1 0.029 0.847 0.992 0.000 0.008 0.000 0.000
#> GSM559460 1 0.051 0.845 0.984 0.000 0.016 0.000 0.000
#> GSM559461 1 0.051 0.845 0.984 0.000 0.016 0.000 0.000
#> GSM559462 1 0.218 0.832 0.888 0.000 0.000 0.112 0.000
#> GSM559463 1 0.029 0.847 0.992 0.000 0.008 0.000 0.000
#> GSM559464 1 0.051 0.845 0.984 0.000 0.016 0.000 0.000
#> GSM559465 1 0.088 0.838 0.968 0.000 0.032 0.000 0.000
#> GSM559467 4 0.432 0.187 0.396 0.004 0.000 0.600 0.000
#> GSM559468 1 0.423 0.659 0.748 0.000 0.044 0.208 0.000
#> GSM559469 4 0.560 0.338 0.376 0.000 0.080 0.544 0.000
#> GSM559470 4 0.430 0.210 0.388 0.004 0.000 0.608 0.000
#> GSM559471 1 0.262 0.827 0.872 0.000 0.012 0.116 0.000
#> GSM559472 1 0.252 0.835 0.884 0.000 0.016 0.100 0.000
#> GSM559473 2 0.420 0.348 0.000 0.592 0.000 0.408 0.000
#> GSM559475 2 0.420 0.348 0.000 0.592 0.000 0.408 0.000
#> GSM559477 2 0.000 0.766 0.000 1.000 0.000 0.000 0.000
#> GSM559478 2 0.399 0.678 0.000 0.720 0.012 0.268 0.000
#> GSM559479 2 0.000 0.766 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.399 0.678 0.000 0.720 0.012 0.268 0.000
#> GSM559481 2 0.399 0.678 0.000 0.720 0.012 0.268 0.000
#> GSM559482 2 0.000 0.766 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.179 0.817 0.084 0.000 0.916 0.000 0.000
#> GSM559439 3 0.185 0.817 0.088 0.000 0.912 0.000 0.000
#> GSM559443 3 0.185 0.817 0.088 0.000 0.912 0.000 0.000
#> GSM559447 3 0.196 0.814 0.076 0.000 0.916 0.000 0.008
#> GSM559449 3 0.235 0.733 0.016 0.000 0.896 0.000 0.088
#> GSM559453 3 0.403 0.362 0.000 0.000 0.648 0.000 0.352
#> GSM559466 3 0.196 0.814 0.076 0.000 0.916 0.000 0.008
#> GSM559474 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM559476 3 0.185 0.817 0.088 0.000 0.912 0.000 0.000
#> GSM559483 2 0.000 0.766 0.000 1.000 0.000 0.000 0.000
#> GSM559484 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.1753 0.72676 0.912 0.000 0.000 0.084 0.000 NA
#> GSM559434 2 0.5671 0.32562 0.016 0.472 0.000 0.412 0.000 NA
#> GSM559436 1 0.0547 0.73867 0.980 0.000 0.000 0.000 0.000 NA
#> GSM559437 4 0.6367 0.18410 0.332 0.000 0.012 0.384 0.000 NA
#> GSM559438 4 0.5486 -0.15228 0.020 0.332 0.000 0.560 0.000 NA
#> GSM559440 4 0.5420 -0.16221 0.016 0.336 0.000 0.560 0.000 NA
#> GSM559441 1 0.5579 0.33768 0.532 0.000 0.008 0.336 0.000 NA
#> GSM559442 1 0.6232 -0.13094 0.356 0.000 0.004 0.348 0.000 NA
#> GSM559444 2 0.2821 0.68641 0.000 0.832 0.000 0.152 0.000 NA
#> GSM559445 4 0.6367 0.18410 0.332 0.000 0.012 0.384 0.000 NA
#> GSM559446 4 0.6367 0.18410 0.332 0.000 0.012 0.384 0.000 NA
#> GSM559448 1 0.0547 0.73867 0.980 0.000 0.000 0.000 0.000 NA
#> GSM559450 2 0.2821 0.68641 0.000 0.832 0.000 0.152 0.000 NA
#> GSM559451 1 0.3163 0.63510 0.764 0.000 0.000 0.232 0.000 NA
#> GSM559452 4 0.6761 -0.11207 0.000 0.248 0.004 0.420 0.036 NA
#> GSM559454 1 0.0146 0.74165 0.996 0.000 0.000 0.004 0.000 NA
#> GSM559455 1 0.5579 0.33768 0.532 0.000 0.008 0.336 0.000 NA
#> GSM559456 4 0.7143 -0.00682 0.124 0.000 0.156 0.400 0.000 NA
#> GSM559457 1 0.2445 0.71628 0.872 0.000 0.000 0.108 0.000 NA
#> GSM559458 1 0.6773 0.27877 0.500 0.000 0.024 0.208 0.032 NA
#> GSM559459 1 0.0000 0.74088 1.000 0.000 0.000 0.000 0.000 NA
#> GSM559460 1 0.0363 0.74001 0.988 0.000 0.000 0.000 0.000 NA
#> GSM559461 1 0.0363 0.74001 0.988 0.000 0.000 0.000 0.000 NA
#> GSM559462 1 0.3109 0.64181 0.772 0.000 0.000 0.224 0.000 NA
#> GSM559463 1 0.0547 0.73867 0.980 0.000 0.000 0.000 0.000 NA
#> GSM559464 1 0.0363 0.74001 0.988 0.000 0.000 0.000 0.000 NA
#> GSM559465 1 0.0862 0.73590 0.972 0.000 0.004 0.008 0.000 NA
#> GSM559467 4 0.3337 0.31954 0.260 0.000 0.000 0.736 0.000 NA
#> GSM559468 1 0.4382 0.58000 0.720 0.000 0.000 0.156 0.000 NA
#> GSM559469 1 0.6224 -0.10704 0.368 0.000 0.004 0.340 0.000 NA
#> GSM559470 4 0.3290 0.32931 0.252 0.000 0.000 0.744 0.000 NA
#> GSM559471 1 0.3699 0.64653 0.752 0.000 0.000 0.212 0.000 NA
#> GSM559472 1 0.3572 0.65206 0.764 0.000 0.000 0.204 0.000 NA
#> GSM559473 2 0.4228 0.49661 0.000 0.588 0.000 0.392 0.000 NA
#> GSM559475 2 0.4228 0.49661 0.000 0.588 0.000 0.392 0.000 NA
#> GSM559477 2 0.0000 0.73107 0.000 1.000 0.000 0.000 0.000 NA
#> GSM559478 2 0.4525 0.59109 0.000 0.664 0.004 0.056 0.000 NA
#> GSM559479 2 0.0000 0.73107 0.000 1.000 0.000 0.000 0.000 NA
#> GSM559480 2 0.4525 0.59109 0.000 0.664 0.004 0.056 0.000 NA
#> GSM559481 2 0.4525 0.59109 0.000 0.664 0.004 0.056 0.000 NA
#> GSM559482 2 0.0000 0.73107 0.000 1.000 0.000 0.000 0.000 NA
#> GSM559435 3 0.1866 0.91726 0.084 0.000 0.908 0.000 0.000 NA
#> GSM559439 3 0.1918 0.91654 0.088 0.000 0.904 0.000 0.000 NA
#> GSM559443 3 0.1918 0.91654 0.088 0.000 0.904 0.000 0.000 NA
#> GSM559447 3 0.1501 0.91467 0.076 0.000 0.924 0.000 0.000 NA
#> GSM559449 3 0.2006 0.83641 0.016 0.000 0.904 0.000 0.080 NA
#> GSM559453 3 0.3592 0.47605 0.000 0.000 0.656 0.000 0.344 NA
#> GSM559466 3 0.1501 0.91467 0.076 0.000 0.924 0.000 0.000 NA
#> GSM559474 5 0.0000 1.00000 0.000 0.000 0.000 0.000 1.000 NA
#> GSM559476 3 0.1918 0.91654 0.088 0.000 0.904 0.000 0.000 NA
#> GSM559483 2 0.0000 0.73107 0.000 1.000 0.000 0.000 0.000 NA
#> GSM559484 5 0.0000 1.00000 0.000 0.000 0.000 0.000 1.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:hclust 48 2.95e-01 2
#> MAD:hclust 49 8.29e-03 3
#> MAD:hclust 46 8.29e-09 4
#> MAD:hclust 40 1.07e-07 5
#> MAD:hclust 34 1.58e-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", "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 21512 rows and 52 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 0.471 0.889 0.897 0.4345 0.566 0.566
#> 3 3 0.742 0.902 0.932 0.4063 0.817 0.676
#> 4 4 0.747 0.732 0.870 0.1285 0.937 0.837
#> 5 5 0.691 0.635 0.807 0.1013 0.880 0.647
#> 6 6 0.688 0.592 0.757 0.0655 0.941 0.758
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
#> GSM559433 1 0.000 0.901 1.000 0.000
#> GSM559434 2 0.680 0.985 0.180 0.820
#> GSM559436 1 0.000 0.901 1.000 0.000
#> GSM559437 1 0.295 0.888 0.948 0.052
#> GSM559438 2 0.680 0.985 0.180 0.820
#> GSM559440 2 0.680 0.985 0.180 0.820
#> GSM559441 1 0.662 0.704 0.828 0.172
#> GSM559442 1 0.000 0.901 1.000 0.000
#> GSM559444 2 0.680 0.985 0.180 0.820
#> GSM559445 1 0.760 0.620 0.780 0.220
#> GSM559446 1 0.000 0.901 1.000 0.000
#> GSM559448 1 0.118 0.898 0.984 0.016
#> GSM559450 2 0.680 0.985 0.180 0.820
#> GSM559451 1 0.000 0.901 1.000 0.000
#> GSM559452 2 0.680 0.985 0.180 0.820
#> GSM559454 1 0.000 0.901 1.000 0.000
#> GSM559455 1 0.000 0.901 1.000 0.000
#> GSM559456 1 0.634 0.843 0.840 0.160
#> GSM559457 1 0.000 0.901 1.000 0.000
#> GSM559458 1 0.662 0.838 0.828 0.172
#> GSM559459 1 0.000 0.901 1.000 0.000
#> GSM559460 1 0.000 0.901 1.000 0.000
#> GSM559461 1 0.000 0.901 1.000 0.000
#> GSM559462 1 0.000 0.901 1.000 0.000
#> GSM559463 1 0.118 0.898 0.984 0.016
#> GSM559464 1 0.000 0.901 1.000 0.000
#> GSM559465 1 0.373 0.881 0.928 0.072
#> GSM559467 1 0.000 0.901 1.000 0.000
#> GSM559468 1 0.000 0.901 1.000 0.000
#> GSM559469 1 0.000 0.901 1.000 0.000
#> GSM559470 1 0.767 0.612 0.776 0.224
#> GSM559471 1 0.000 0.901 1.000 0.000
#> GSM559472 1 0.000 0.901 1.000 0.000
#> GSM559473 2 0.680 0.985 0.180 0.820
#> GSM559475 2 0.680 0.985 0.180 0.820
#> GSM559477 2 0.680 0.985 0.180 0.820
#> GSM559478 2 0.680 0.985 0.180 0.820
#> GSM559479 2 0.680 0.985 0.180 0.820
#> GSM559480 2 0.680 0.985 0.180 0.820
#> GSM559481 2 0.680 0.985 0.180 0.820
#> GSM559482 2 0.680 0.985 0.180 0.820
#> GSM559435 1 0.680 0.833 0.820 0.180
#> GSM559439 1 0.680 0.833 0.820 0.180
#> GSM559443 1 0.680 0.833 0.820 0.180
#> GSM559447 1 0.680 0.833 0.820 0.180
#> GSM559449 1 0.680 0.833 0.820 0.180
#> GSM559453 1 0.680 0.833 0.820 0.180
#> GSM559466 1 0.680 0.833 0.820 0.180
#> GSM559474 1 0.971 0.613 0.600 0.400
#> GSM559476 1 0.680 0.833 0.820 0.180
#> GSM559483 2 0.680 0.985 0.180 0.820
#> GSM559484 2 0.000 0.777 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0237 0.953 0.996 0.000 0.004
#> GSM559434 2 0.3030 0.910 0.004 0.904 0.092
#> GSM559436 1 0.0000 0.953 1.000 0.000 0.000
#> GSM559437 1 0.3851 0.865 0.860 0.004 0.136
#> GSM559438 2 0.7372 0.614 0.220 0.688 0.092
#> GSM559440 2 0.3030 0.910 0.004 0.904 0.092
#> GSM559441 1 0.3771 0.875 0.876 0.012 0.112
#> GSM559442 1 0.0237 0.952 0.996 0.000 0.004
#> GSM559444 2 0.2400 0.923 0.004 0.932 0.064
#> GSM559445 1 0.6486 0.750 0.760 0.096 0.144
#> GSM559446 1 0.3918 0.861 0.856 0.004 0.140
#> GSM559448 1 0.0000 0.953 1.000 0.000 0.000
#> GSM559450 2 0.2200 0.926 0.004 0.940 0.056
#> GSM559451 1 0.0237 0.953 0.996 0.000 0.004
#> GSM559452 2 0.3272 0.904 0.004 0.892 0.104
#> GSM559454 1 0.0000 0.953 1.000 0.000 0.000
#> GSM559455 1 0.1647 0.937 0.960 0.004 0.036
#> GSM559456 1 0.1267 0.943 0.972 0.004 0.024
#> GSM559457 1 0.0424 0.952 0.992 0.000 0.008
#> GSM559458 1 0.0829 0.945 0.984 0.004 0.012
#> GSM559459 1 0.0000 0.953 1.000 0.000 0.000
#> GSM559460 1 0.0000 0.953 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.953 1.000 0.000 0.000
#> GSM559462 1 0.0424 0.952 0.992 0.000 0.008
#> GSM559463 1 0.0000 0.953 1.000 0.000 0.000
#> GSM559464 1 0.0000 0.953 1.000 0.000 0.000
#> GSM559465 1 0.0000 0.953 1.000 0.000 0.000
#> GSM559467 1 0.3112 0.893 0.900 0.004 0.096
#> GSM559468 1 0.0000 0.953 1.000 0.000 0.000
#> GSM559469 1 0.1989 0.927 0.948 0.004 0.048
#> GSM559470 1 0.4892 0.839 0.840 0.048 0.112
#> GSM559471 1 0.0475 0.951 0.992 0.004 0.004
#> GSM559472 1 0.0000 0.953 1.000 0.000 0.000
#> GSM559473 2 0.0661 0.936 0.004 0.988 0.008
#> GSM559475 2 0.0475 0.936 0.004 0.992 0.004
#> GSM559477 2 0.0475 0.935 0.004 0.992 0.004
#> GSM559478 2 0.0475 0.936 0.004 0.992 0.004
#> GSM559479 2 0.0475 0.935 0.004 0.992 0.004
#> GSM559480 2 0.0475 0.936 0.004 0.992 0.004
#> GSM559481 2 0.0475 0.936 0.004 0.992 0.004
#> GSM559482 2 0.0475 0.935 0.004 0.992 0.004
#> GSM559435 3 0.3619 0.917 0.136 0.000 0.864
#> GSM559439 3 0.3619 0.917 0.136 0.000 0.864
#> GSM559443 3 0.3619 0.917 0.136 0.000 0.864
#> GSM559447 3 0.3619 0.917 0.136 0.000 0.864
#> GSM559449 3 0.3340 0.909 0.120 0.000 0.880
#> GSM559453 3 0.3340 0.909 0.120 0.000 0.880
#> GSM559466 3 0.3619 0.917 0.136 0.000 0.864
#> GSM559474 3 0.1860 0.737 0.000 0.052 0.948
#> GSM559476 3 0.6280 0.371 0.460 0.000 0.540
#> GSM559483 2 0.0475 0.935 0.004 0.992 0.004
#> GSM559484 2 0.5098 0.762 0.000 0.752 0.248
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.0188 0.8850 0.996 0.000 0.004 0.000
#> GSM559434 2 0.1902 0.6498 0.004 0.932 0.000 0.064
#> GSM559436 1 0.0524 0.8811 0.988 0.000 0.004 0.008
#> GSM559437 4 0.7519 0.5040 0.364 0.136 0.012 0.488
#> GSM559438 2 0.5861 0.2827 0.296 0.644 0.000 0.060
#> GSM559440 2 0.1824 0.6525 0.004 0.936 0.000 0.060
#> GSM559441 1 0.7054 -0.0399 0.536 0.144 0.000 0.320
#> GSM559442 1 0.0376 0.8820 0.992 0.004 0.000 0.004
#> GSM559444 2 0.0469 0.6666 0.000 0.988 0.000 0.012
#> GSM559445 4 0.7810 0.7648 0.192 0.308 0.012 0.488
#> GSM559446 4 0.7875 0.7693 0.216 0.284 0.012 0.488
#> GSM559448 1 0.0524 0.8811 0.988 0.000 0.004 0.008
#> GSM559450 2 0.0336 0.6694 0.000 0.992 0.000 0.008
#> GSM559451 1 0.0469 0.8815 0.988 0.000 0.000 0.012
#> GSM559452 2 0.2466 0.5791 0.004 0.900 0.000 0.096
#> GSM559454 1 0.0188 0.8850 0.996 0.000 0.004 0.000
#> GSM559455 1 0.4356 0.5490 0.708 0.000 0.000 0.292
#> GSM559456 1 0.4584 0.5319 0.696 0.000 0.004 0.300
#> GSM559457 1 0.1661 0.8532 0.944 0.000 0.004 0.052
#> GSM559458 1 0.4868 0.5101 0.684 0.000 0.012 0.304
#> GSM559459 1 0.0188 0.8850 0.996 0.000 0.004 0.000
#> GSM559460 1 0.0188 0.8850 0.996 0.000 0.004 0.000
#> GSM559461 1 0.0188 0.8850 0.996 0.000 0.004 0.000
#> GSM559462 1 0.0188 0.8839 0.996 0.000 0.000 0.004
#> GSM559463 1 0.0524 0.8811 0.988 0.000 0.004 0.008
#> GSM559464 1 0.0188 0.8850 0.996 0.000 0.004 0.000
#> GSM559465 1 0.0188 0.8850 0.996 0.000 0.004 0.000
#> GSM559467 1 0.3870 0.6813 0.788 0.004 0.000 0.208
#> GSM559468 1 0.0188 0.8835 0.996 0.000 0.000 0.004
#> GSM559469 1 0.0657 0.8762 0.984 0.004 0.000 0.012
#> GSM559470 1 0.5998 0.4802 0.680 0.108 0.000 0.212
#> GSM559471 1 0.0376 0.8820 0.992 0.004 0.000 0.004
#> GSM559472 1 0.0188 0.8850 0.996 0.000 0.004 0.000
#> GSM559473 2 0.4605 0.7877 0.000 0.664 0.000 0.336
#> GSM559475 2 0.4605 0.7877 0.000 0.664 0.000 0.336
#> GSM559477 2 0.4454 0.7872 0.000 0.692 0.000 0.308
#> GSM559478 2 0.4955 0.7856 0.000 0.648 0.008 0.344
#> GSM559479 2 0.4454 0.7872 0.000 0.692 0.000 0.308
#> GSM559480 2 0.4955 0.7856 0.000 0.648 0.008 0.344
#> GSM559481 2 0.4955 0.7856 0.000 0.648 0.008 0.344
#> GSM559482 2 0.4454 0.7872 0.000 0.692 0.000 0.308
#> GSM559435 3 0.0707 0.8984 0.020 0.000 0.980 0.000
#> GSM559439 3 0.0707 0.8984 0.020 0.000 0.980 0.000
#> GSM559443 3 0.1042 0.8944 0.020 0.000 0.972 0.008
#> GSM559447 3 0.0707 0.8984 0.020 0.000 0.980 0.000
#> GSM559449 3 0.0336 0.8887 0.008 0.000 0.992 0.000
#> GSM559453 3 0.0336 0.8887 0.008 0.000 0.992 0.000
#> GSM559466 3 0.0707 0.8984 0.020 0.000 0.980 0.000
#> GSM559474 4 0.6987 0.4768 0.004 0.276 0.140 0.580
#> GSM559476 3 0.5244 0.1382 0.436 0.000 0.556 0.008
#> GSM559483 2 0.4454 0.7872 0.000 0.692 0.000 0.308
#> GSM559484 2 0.6446 -0.0202 0.000 0.584 0.088 0.328
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 1 0.1764 0.84577 0.928 0.000 0.000 0.064 0.008
#> GSM559434 2 0.6620 0.01156 0.000 0.436 0.000 0.228 0.336
#> GSM559436 1 0.1918 0.85407 0.928 0.000 0.000 0.036 0.036
#> GSM559437 4 0.1774 0.43414 0.052 0.000 0.000 0.932 0.016
#> GSM559438 2 0.8011 -0.04282 0.092 0.376 0.000 0.292 0.240
#> GSM559440 2 0.6890 -0.01232 0.004 0.404 0.000 0.300 0.292
#> GSM559441 4 0.4502 0.57339 0.180 0.000 0.000 0.744 0.076
#> GSM559442 1 0.3462 0.77028 0.792 0.000 0.000 0.012 0.196
#> GSM559444 2 0.5894 0.30227 0.000 0.532 0.000 0.112 0.356
#> GSM559445 4 0.1661 0.36826 0.024 0.000 0.000 0.940 0.036
#> GSM559446 4 0.1668 0.38486 0.028 0.000 0.000 0.940 0.032
#> GSM559448 1 0.1579 0.85801 0.944 0.000 0.000 0.024 0.032
#> GSM559450 2 0.5894 0.30227 0.000 0.532 0.000 0.112 0.356
#> GSM559451 1 0.1943 0.85706 0.924 0.000 0.000 0.056 0.020
#> GSM559452 5 0.5982 0.00162 0.000 0.312 0.000 0.136 0.552
#> GSM559454 1 0.0798 0.87325 0.976 0.000 0.000 0.016 0.008
#> GSM559455 4 0.4446 0.55462 0.400 0.000 0.000 0.592 0.008
#> GSM559456 4 0.4884 0.52617 0.392 0.000 0.008 0.584 0.016
#> GSM559457 1 0.3635 0.48117 0.748 0.000 0.000 0.248 0.004
#> GSM559458 4 0.5750 0.40774 0.436 0.000 0.008 0.492 0.064
#> GSM559459 1 0.1018 0.87465 0.968 0.000 0.000 0.016 0.016
#> GSM559460 1 0.1608 0.87075 0.928 0.000 0.000 0.000 0.072
#> GSM559461 1 0.1544 0.87137 0.932 0.000 0.000 0.000 0.068
#> GSM559462 1 0.1579 0.87111 0.944 0.000 0.000 0.032 0.024
#> GSM559463 1 0.1281 0.86608 0.956 0.000 0.000 0.012 0.032
#> GSM559464 1 0.1671 0.87152 0.924 0.000 0.000 0.000 0.076
#> GSM559465 1 0.1704 0.87317 0.928 0.000 0.000 0.004 0.068
#> GSM559467 4 0.5872 0.44928 0.408 0.000 0.000 0.492 0.100
#> GSM559468 1 0.3039 0.81647 0.836 0.000 0.000 0.012 0.152
#> GSM559469 1 0.3745 0.75705 0.780 0.000 0.000 0.024 0.196
#> GSM559470 4 0.5781 0.56913 0.308 0.000 0.000 0.576 0.116
#> GSM559471 1 0.3319 0.79797 0.820 0.000 0.000 0.020 0.160
#> GSM559472 1 0.0671 0.87357 0.980 0.000 0.000 0.016 0.004
#> GSM559473 2 0.1430 0.67509 0.000 0.944 0.000 0.004 0.052
#> GSM559475 2 0.1571 0.67607 0.000 0.936 0.000 0.004 0.060
#> GSM559477 2 0.1608 0.68020 0.000 0.928 0.000 0.000 0.072
#> GSM559478 2 0.0955 0.67769 0.000 0.968 0.000 0.004 0.028
#> GSM559479 2 0.1608 0.68020 0.000 0.928 0.000 0.000 0.072
#> GSM559480 2 0.0955 0.67769 0.000 0.968 0.000 0.004 0.028
#> GSM559481 2 0.0955 0.67769 0.000 0.968 0.000 0.004 0.028
#> GSM559482 2 0.1608 0.68020 0.000 0.928 0.000 0.000 0.072
#> GSM559435 3 0.0000 0.89896 0.000 0.000 1.000 0.000 0.000
#> GSM559439 3 0.0000 0.89896 0.000 0.000 1.000 0.000 0.000
#> GSM559443 3 0.0162 0.89602 0.000 0.000 0.996 0.000 0.004
#> GSM559447 3 0.0000 0.89896 0.000 0.000 1.000 0.000 0.000
#> GSM559449 3 0.0000 0.89896 0.000 0.000 1.000 0.000 0.000
#> GSM559453 3 0.0000 0.89896 0.000 0.000 1.000 0.000 0.000
#> GSM559466 3 0.0000 0.89896 0.000 0.000 1.000 0.000 0.000
#> GSM559474 5 0.5181 0.30447 0.000 0.004 0.032 0.452 0.512
#> GSM559476 3 0.5149 0.11718 0.424 0.000 0.540 0.004 0.032
#> GSM559483 2 0.1671 0.67991 0.000 0.924 0.000 0.000 0.076
#> GSM559484 5 0.5944 0.49670 0.000 0.136 0.028 0.180 0.656
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.1588 0.7630 0.924 0.000 0.000 0.072 0.000 0.004
#> GSM559434 6 0.6416 0.2914 0.000 0.208 0.000 0.088 0.148 0.556
#> GSM559436 1 0.2403 0.7470 0.900 0.000 0.000 0.040 0.040 0.020
#> GSM559437 4 0.2615 0.5336 0.004 0.000 0.000 0.852 0.136 0.008
#> GSM559438 6 0.5666 0.3435 0.016 0.180 0.000 0.152 0.016 0.636
#> GSM559440 6 0.5973 0.3448 0.000 0.196 0.000 0.124 0.072 0.608
#> GSM559441 4 0.3501 0.6267 0.080 0.000 0.000 0.804 0.000 0.116
#> GSM559442 6 0.5381 -0.3071 0.424 0.000 0.000 0.096 0.004 0.476
#> GSM559444 2 0.6109 0.0722 0.000 0.424 0.000 0.008 0.204 0.364
#> GSM559445 4 0.3027 0.5011 0.000 0.000 0.000 0.824 0.148 0.028
#> GSM559446 4 0.2613 0.5241 0.000 0.000 0.000 0.848 0.140 0.012
#> GSM559448 1 0.2259 0.7491 0.908 0.000 0.000 0.032 0.040 0.020
#> GSM559450 2 0.6109 0.0722 0.000 0.424 0.000 0.008 0.204 0.364
#> GSM559451 1 0.3535 0.7135 0.800 0.000 0.000 0.144 0.004 0.052
#> GSM559452 6 0.5906 0.1425 0.000 0.108 0.000 0.044 0.284 0.564
#> GSM559454 1 0.0692 0.7697 0.976 0.000 0.000 0.020 0.000 0.004
#> GSM559455 4 0.2994 0.6215 0.208 0.000 0.000 0.788 0.000 0.004
#> GSM559456 4 0.3705 0.5884 0.180 0.000 0.000 0.776 0.008 0.036
#> GSM559457 1 0.3684 0.3596 0.664 0.000 0.000 0.332 0.000 0.004
#> GSM559458 4 0.5481 0.4570 0.188 0.000 0.000 0.612 0.012 0.188
#> GSM559459 1 0.1148 0.7705 0.960 0.000 0.000 0.020 0.004 0.016
#> GSM559460 1 0.3943 0.6963 0.756 0.000 0.000 0.056 0.004 0.184
#> GSM559461 1 0.3943 0.6963 0.756 0.000 0.000 0.056 0.004 0.184
#> GSM559462 1 0.3229 0.7336 0.828 0.000 0.000 0.120 0.004 0.048
#> GSM559463 1 0.1536 0.7565 0.940 0.000 0.000 0.004 0.040 0.016
#> GSM559464 1 0.3884 0.6969 0.760 0.000 0.000 0.052 0.004 0.184
#> GSM559465 1 0.3695 0.7025 0.776 0.000 0.000 0.044 0.004 0.176
#> GSM559467 4 0.5504 0.4819 0.164 0.008 0.000 0.592 0.000 0.236
#> GSM559468 1 0.5452 0.3736 0.520 0.000 0.000 0.100 0.008 0.372
#> GSM559469 6 0.5424 -0.3469 0.444 0.000 0.000 0.100 0.004 0.452
#> GSM559470 4 0.5553 0.4685 0.148 0.008 0.000 0.572 0.000 0.272
#> GSM559471 1 0.5093 0.3222 0.528 0.000 0.000 0.084 0.000 0.388
#> GSM559472 1 0.1644 0.7669 0.932 0.000 0.000 0.052 0.004 0.012
#> GSM559473 2 0.2540 0.7560 0.000 0.872 0.000 0.004 0.020 0.104
#> GSM559475 2 0.2492 0.7571 0.000 0.876 0.000 0.004 0.020 0.100
#> GSM559477 2 0.0935 0.7726 0.000 0.964 0.000 0.000 0.032 0.004
#> GSM559478 2 0.3341 0.7350 0.000 0.816 0.000 0.000 0.068 0.116
#> GSM559479 2 0.1010 0.7717 0.000 0.960 0.000 0.000 0.036 0.004
#> GSM559480 2 0.3341 0.7350 0.000 0.816 0.000 0.000 0.068 0.116
#> GSM559481 2 0.3341 0.7350 0.000 0.816 0.000 0.000 0.068 0.116
#> GSM559482 2 0.0935 0.7726 0.000 0.964 0.000 0.000 0.032 0.004
#> GSM559435 3 0.0260 0.8962 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM559439 3 0.0260 0.8962 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM559443 3 0.0405 0.8943 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM559447 3 0.0000 0.8970 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559449 3 0.0146 0.8960 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM559453 3 0.0146 0.8960 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM559466 3 0.0000 0.8970 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559474 5 0.3052 0.7649 0.000 0.000 0.004 0.216 0.780 0.000
#> GSM559476 3 0.6709 0.1096 0.312 0.000 0.480 0.044 0.016 0.148
#> GSM559483 2 0.1010 0.7725 0.000 0.960 0.000 0.000 0.036 0.004
#> GSM559484 5 0.3134 0.7816 0.000 0.044 0.004 0.068 0.860 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:kmeans 52 5.15e-01 2
#> MAD:kmeans 51 2.17e-09 3
#> MAD:kmeans 46 1.34e-08 4
#> MAD:kmeans 37 5.89e-07 5
#> MAD:kmeans 37 1.52e-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", "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 21512 rows and 52 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.980 0.991 0.5023 0.497 0.497
#> 3 3 0.825 0.874 0.944 0.3135 0.697 0.474
#> 4 4 0.961 0.942 0.975 0.1334 0.879 0.668
#> 5 5 0.799 0.778 0.882 0.0612 0.961 0.846
#> 6 6 0.772 0.638 0.819 0.0397 0.959 0.814
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2
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
#> GSM559433 1 0.0000 0.995 1.000 0.000
#> GSM559434 2 0.0000 0.984 0.000 1.000
#> GSM559436 1 0.0000 0.995 1.000 0.000
#> GSM559437 1 0.5408 0.856 0.876 0.124
#> GSM559438 2 0.0000 0.984 0.000 1.000
#> GSM559440 2 0.0000 0.984 0.000 1.000
#> GSM559441 2 0.0672 0.978 0.008 0.992
#> GSM559442 1 0.0000 0.995 1.000 0.000
#> GSM559444 2 0.0000 0.984 0.000 1.000
#> GSM559445 2 0.0000 0.984 0.000 1.000
#> GSM559446 2 0.7950 0.684 0.240 0.760
#> GSM559448 1 0.0000 0.995 1.000 0.000
#> GSM559450 2 0.0000 0.984 0.000 1.000
#> GSM559451 1 0.0000 0.995 1.000 0.000
#> GSM559452 2 0.0000 0.984 0.000 1.000
#> GSM559454 1 0.0000 0.995 1.000 0.000
#> GSM559455 1 0.0000 0.995 1.000 0.000
#> GSM559456 1 0.0000 0.995 1.000 0.000
#> GSM559457 1 0.0000 0.995 1.000 0.000
#> GSM559458 1 0.0000 0.995 1.000 0.000
#> GSM559459 1 0.0000 0.995 1.000 0.000
#> GSM559460 1 0.0000 0.995 1.000 0.000
#> GSM559461 1 0.0000 0.995 1.000 0.000
#> GSM559462 1 0.0000 0.995 1.000 0.000
#> GSM559463 1 0.0000 0.995 1.000 0.000
#> GSM559464 1 0.0000 0.995 1.000 0.000
#> GSM559465 1 0.0000 0.995 1.000 0.000
#> GSM559467 2 0.0000 0.984 0.000 1.000
#> GSM559468 1 0.0000 0.995 1.000 0.000
#> GSM559469 2 0.4431 0.894 0.092 0.908
#> GSM559470 2 0.0000 0.984 0.000 1.000
#> GSM559471 1 0.0000 0.995 1.000 0.000
#> GSM559472 1 0.0000 0.995 1.000 0.000
#> GSM559473 2 0.0000 0.984 0.000 1.000
#> GSM559475 2 0.0000 0.984 0.000 1.000
#> GSM559477 2 0.0000 0.984 0.000 1.000
#> GSM559478 2 0.0000 0.984 0.000 1.000
#> GSM559479 2 0.0000 0.984 0.000 1.000
#> GSM559480 2 0.0000 0.984 0.000 1.000
#> GSM559481 2 0.0000 0.984 0.000 1.000
#> GSM559482 2 0.0000 0.984 0.000 1.000
#> GSM559435 1 0.0000 0.995 1.000 0.000
#> GSM559439 1 0.0000 0.995 1.000 0.000
#> GSM559443 1 0.0000 0.995 1.000 0.000
#> GSM559447 1 0.0000 0.995 1.000 0.000
#> GSM559449 1 0.0000 0.995 1.000 0.000
#> GSM559453 1 0.0000 0.995 1.000 0.000
#> GSM559466 1 0.0000 0.995 1.000 0.000
#> GSM559474 2 0.0000 0.984 0.000 1.000
#> GSM559476 1 0.0000 0.995 1.000 0.000
#> GSM559483 2 0.0000 0.984 0.000 1.000
#> GSM559484 2 0.0000 0.984 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0000 0.896 1.000 0.000 0.000
#> GSM559434 2 0.0000 0.970 0.000 1.000 0.000
#> GSM559436 1 0.0000 0.896 1.000 0.000 0.000
#> GSM559437 1 0.5465 0.623 0.712 0.000 0.288
#> GSM559438 2 0.0000 0.970 0.000 1.000 0.000
#> GSM559440 2 0.0000 0.970 0.000 1.000 0.000
#> GSM559441 1 0.8869 0.270 0.496 0.380 0.124
#> GSM559442 1 0.1753 0.864 0.952 0.048 0.000
#> GSM559444 2 0.0000 0.970 0.000 1.000 0.000
#> GSM559445 2 0.4521 0.763 0.004 0.816 0.180
#> GSM559446 1 0.5431 0.629 0.716 0.000 0.284
#> GSM559448 3 0.5138 0.644 0.252 0.000 0.748
#> GSM559450 2 0.0000 0.970 0.000 1.000 0.000
#> GSM559451 1 0.0000 0.896 1.000 0.000 0.000
#> GSM559452 2 0.0000 0.970 0.000 1.000 0.000
#> GSM559454 1 0.0000 0.896 1.000 0.000 0.000
#> GSM559455 1 0.3879 0.781 0.848 0.000 0.152
#> GSM559456 1 0.5560 0.604 0.700 0.000 0.300
#> GSM559457 1 0.0000 0.896 1.000 0.000 0.000
#> GSM559458 3 0.0000 0.972 0.000 0.000 1.000
#> GSM559459 1 0.0000 0.896 1.000 0.000 0.000
#> GSM559460 1 0.0000 0.896 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.896 1.000 0.000 0.000
#> GSM559462 1 0.0000 0.896 1.000 0.000 0.000
#> GSM559463 1 0.0000 0.896 1.000 0.000 0.000
#> GSM559464 1 0.0000 0.896 1.000 0.000 0.000
#> GSM559465 1 0.0000 0.896 1.000 0.000 0.000
#> GSM559467 1 0.0237 0.894 0.996 0.004 0.000
#> GSM559468 1 0.0000 0.896 1.000 0.000 0.000
#> GSM559469 1 0.4399 0.736 0.812 0.188 0.000
#> GSM559470 1 0.6192 0.305 0.580 0.420 0.000
#> GSM559471 1 0.0000 0.896 1.000 0.000 0.000
#> GSM559472 1 0.0000 0.896 1.000 0.000 0.000
#> GSM559473 2 0.0000 0.970 0.000 1.000 0.000
#> GSM559475 2 0.0000 0.970 0.000 1.000 0.000
#> GSM559477 2 0.0000 0.970 0.000 1.000 0.000
#> GSM559478 2 0.0000 0.970 0.000 1.000 0.000
#> GSM559479 2 0.0000 0.970 0.000 1.000 0.000
#> GSM559480 2 0.0000 0.970 0.000 1.000 0.000
#> GSM559481 2 0.0000 0.970 0.000 1.000 0.000
#> GSM559482 2 0.0000 0.970 0.000 1.000 0.000
#> GSM559435 3 0.0000 0.972 0.000 0.000 1.000
#> GSM559439 3 0.0000 0.972 0.000 0.000 1.000
#> GSM559443 3 0.0000 0.972 0.000 0.000 1.000
#> GSM559447 3 0.0000 0.972 0.000 0.000 1.000
#> GSM559449 3 0.0000 0.972 0.000 0.000 1.000
#> GSM559453 3 0.0000 0.972 0.000 0.000 1.000
#> GSM559466 3 0.0000 0.972 0.000 0.000 1.000
#> GSM559474 3 0.0000 0.972 0.000 0.000 1.000
#> GSM559476 3 0.0000 0.972 0.000 0.000 1.000
#> GSM559483 2 0.0000 0.970 0.000 1.000 0.000
#> GSM559484 2 0.5254 0.632 0.000 0.736 0.264
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.0921 0.950 0.972 0.000 0.000 0.028
#> GSM559434 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM559436 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM559437 4 0.0000 0.949 0.000 0.000 0.000 1.000
#> GSM559438 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM559440 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM559441 4 0.0000 0.949 0.000 0.000 0.000 1.000
#> GSM559442 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM559444 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM559445 4 0.0000 0.949 0.000 0.000 0.000 1.000
#> GSM559446 4 0.0000 0.949 0.000 0.000 0.000 1.000
#> GSM559448 3 0.3486 0.745 0.188 0.000 0.812 0.000
#> GSM559450 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM559451 1 0.2345 0.887 0.900 0.000 0.000 0.100
#> GSM559452 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM559454 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM559455 4 0.0188 0.948 0.004 0.000 0.000 0.996
#> GSM559456 4 0.1004 0.935 0.004 0.000 0.024 0.972
#> GSM559457 1 0.4500 0.571 0.684 0.000 0.000 0.316
#> GSM559458 3 0.0707 0.955 0.000 0.000 0.980 0.020
#> GSM559459 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM559460 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM559461 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM559462 1 0.1716 0.921 0.936 0.000 0.000 0.064
#> GSM559463 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM559464 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM559465 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM559467 4 0.0469 0.944 0.012 0.000 0.000 0.988
#> GSM559468 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM559469 1 0.0817 0.947 0.976 0.024 0.000 0.000
#> GSM559470 4 0.0707 0.938 0.020 0.000 0.000 0.980
#> GSM559471 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM559472 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM559473 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM559475 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM559477 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM559478 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM559479 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM559480 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM559481 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM559482 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM559435 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM559439 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM559443 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM559447 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM559449 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM559453 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM559466 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM559474 4 0.4543 0.512 0.000 0.000 0.324 0.676
#> GSM559476 3 0.0000 0.971 0.000 0.000 1.000 0.000
#> GSM559483 2 0.0000 0.987 0.000 1.000 0.000 0.000
#> GSM559484 2 0.3583 0.775 0.000 0.816 0.180 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 1 0.1310 0.720 0.956 0.000 0.000 0.024 0.020
#> GSM559434 2 0.1478 0.919 0.000 0.936 0.000 0.000 0.064
#> GSM559436 1 0.0000 0.740 1.000 0.000 0.000 0.000 0.000
#> GSM559437 4 0.0162 0.831 0.000 0.000 0.000 0.996 0.004
#> GSM559438 2 0.3109 0.777 0.000 0.800 0.000 0.000 0.200
#> GSM559440 2 0.2020 0.898 0.000 0.900 0.000 0.000 0.100
#> GSM559441 4 0.0451 0.830 0.004 0.000 0.000 0.988 0.008
#> GSM559442 5 0.3074 0.875 0.196 0.000 0.000 0.000 0.804
#> GSM559444 2 0.1043 0.926 0.000 0.960 0.000 0.000 0.040
#> GSM559445 4 0.0703 0.829 0.000 0.000 0.000 0.976 0.024
#> GSM559446 4 0.0609 0.829 0.000 0.000 0.000 0.980 0.020
#> GSM559448 3 0.4219 0.325 0.416 0.000 0.584 0.000 0.000
#> GSM559450 2 0.0963 0.927 0.000 0.964 0.000 0.000 0.036
#> GSM559451 1 0.2879 0.703 0.868 0.000 0.000 0.032 0.100
#> GSM559452 2 0.3534 0.762 0.000 0.744 0.000 0.000 0.256
#> GSM559454 1 0.0703 0.745 0.976 0.000 0.000 0.000 0.024
#> GSM559455 4 0.2130 0.808 0.080 0.000 0.000 0.908 0.012
#> GSM559456 4 0.4361 0.728 0.144 0.000 0.052 0.784 0.020
#> GSM559457 1 0.2920 0.612 0.852 0.000 0.000 0.132 0.016
#> GSM559458 3 0.4307 0.704 0.000 0.000 0.772 0.128 0.100
#> GSM559459 1 0.1341 0.743 0.944 0.000 0.000 0.000 0.056
#> GSM559460 1 0.4242 0.205 0.572 0.000 0.000 0.000 0.428
#> GSM559461 1 0.4074 0.399 0.636 0.000 0.000 0.000 0.364
#> GSM559462 1 0.3409 0.684 0.816 0.000 0.000 0.024 0.160
#> GSM559463 1 0.2011 0.728 0.908 0.000 0.004 0.000 0.088
#> GSM559464 1 0.4161 0.326 0.608 0.000 0.000 0.000 0.392
#> GSM559465 1 0.3966 0.444 0.664 0.000 0.000 0.000 0.336
#> GSM559467 4 0.4649 0.680 0.068 0.000 0.000 0.720 0.212
#> GSM559468 5 0.3561 0.851 0.260 0.000 0.000 0.000 0.740
#> GSM559469 5 0.2753 0.829 0.136 0.008 0.000 0.000 0.856
#> GSM559470 4 0.5204 0.638 0.076 0.008 0.000 0.680 0.236
#> GSM559471 5 0.3534 0.856 0.256 0.000 0.000 0.000 0.744
#> GSM559472 1 0.0451 0.739 0.988 0.000 0.000 0.004 0.008
#> GSM559473 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000
#> GSM559475 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000
#> GSM559477 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000
#> GSM559478 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000
#> GSM559479 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000
#> GSM559481 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000
#> GSM559482 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM559439 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM559443 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM559447 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM559449 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM559453 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM559466 3 0.0000 0.921 0.000 0.000 1.000 0.000 0.000
#> GSM559474 4 0.5847 0.446 0.000 0.000 0.264 0.592 0.144
#> GSM559476 3 0.0162 0.918 0.000 0.000 0.996 0.000 0.004
#> GSM559483 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000
#> GSM559484 2 0.5808 0.608 0.000 0.648 0.188 0.012 0.152
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.3699 0.6153 0.812 0.000 0.000 0.104 0.060 0.024
#> GSM559434 2 0.3468 0.6628 0.000 0.728 0.000 0.000 0.264 0.008
#> GSM559436 1 0.0862 0.6752 0.972 0.000 0.000 0.004 0.016 0.008
#> GSM559437 4 0.0935 0.6924 0.004 0.000 0.000 0.964 0.032 0.000
#> GSM559438 2 0.4672 0.5625 0.000 0.684 0.000 0.000 0.188 0.128
#> GSM559440 2 0.3834 0.6738 0.000 0.732 0.000 0.000 0.232 0.036
#> GSM559441 4 0.1297 0.6938 0.012 0.000 0.000 0.948 0.040 0.000
#> GSM559442 6 0.2857 0.7087 0.072 0.000 0.000 0.000 0.072 0.856
#> GSM559444 2 0.3265 0.6611 0.000 0.748 0.000 0.000 0.248 0.004
#> GSM559445 4 0.2278 0.6524 0.000 0.000 0.000 0.868 0.128 0.004
#> GSM559446 4 0.2278 0.6549 0.000 0.000 0.000 0.868 0.128 0.004
#> GSM559448 3 0.4361 0.2285 0.436 0.000 0.544 0.000 0.016 0.004
#> GSM559450 2 0.3265 0.6610 0.000 0.748 0.000 0.000 0.248 0.004
#> GSM559451 1 0.5073 0.5302 0.680 0.000 0.000 0.020 0.160 0.140
#> GSM559452 5 0.5115 0.3442 0.000 0.356 0.004 0.000 0.560 0.080
#> GSM559454 1 0.0858 0.6786 0.968 0.000 0.000 0.000 0.004 0.028
#> GSM559455 4 0.3261 0.6591 0.104 0.000 0.000 0.824 0.072 0.000
#> GSM559456 4 0.5159 0.5585 0.172 0.000 0.044 0.700 0.076 0.008
#> GSM559457 1 0.4600 0.5552 0.728 0.000 0.000 0.156 0.096 0.020
#> GSM559458 3 0.5043 0.5622 0.000 0.000 0.692 0.124 0.156 0.028
#> GSM559459 1 0.2147 0.6689 0.896 0.000 0.000 0.000 0.020 0.084
#> GSM559460 6 0.3979 -0.0948 0.456 0.000 0.000 0.000 0.004 0.540
#> GSM559461 1 0.3989 0.0803 0.528 0.000 0.000 0.000 0.004 0.468
#> GSM559462 1 0.5436 0.4930 0.632 0.000 0.000 0.020 0.152 0.196
#> GSM559463 1 0.2673 0.6392 0.852 0.000 0.004 0.000 0.012 0.132
#> GSM559464 1 0.3993 0.0551 0.520 0.000 0.000 0.000 0.004 0.476
#> GSM559465 1 0.4127 0.2441 0.588 0.000 0.000 0.008 0.004 0.400
#> GSM559467 4 0.6883 0.4521 0.068 0.004 0.000 0.472 0.224 0.232
#> GSM559468 6 0.1765 0.7314 0.096 0.000 0.000 0.000 0.000 0.904
#> GSM559469 6 0.1644 0.7179 0.028 0.000 0.000 0.000 0.040 0.932
#> GSM559470 4 0.6795 0.4370 0.032 0.016 0.000 0.468 0.228 0.256
#> GSM559471 6 0.3806 0.6611 0.152 0.000 0.000 0.000 0.076 0.772
#> GSM559472 1 0.2152 0.6747 0.912 0.000 0.000 0.012 0.040 0.036
#> GSM559473 2 0.0146 0.8590 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM559475 2 0.0547 0.8563 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM559477 2 0.0146 0.8591 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM559478 2 0.0632 0.8534 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM559479 2 0.0363 0.8572 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM559480 2 0.0632 0.8534 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM559481 2 0.0632 0.8534 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM559482 2 0.0000 0.8595 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.9014 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559439 3 0.0000 0.9014 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559443 3 0.0000 0.9014 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559447 3 0.0000 0.9014 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559449 3 0.0000 0.9014 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559453 3 0.0000 0.9014 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559466 3 0.0000 0.9014 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559474 5 0.5498 -0.0342 0.000 0.000 0.116 0.376 0.504 0.004
#> GSM559476 3 0.0146 0.8984 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM559483 2 0.0000 0.8595 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559484 5 0.5526 0.5156 0.000 0.320 0.076 0.032 0.572 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 disease.state(p) k
#> MAD:skmeans 52 3.51e-01 2
#> MAD:skmeans 50 2.80e-07 3
#> MAD:skmeans 52 7.19e-06 4
#> MAD:skmeans 46 3.89e-06 5
#> MAD:skmeans 42 5.99e-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", "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 21512 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.999 0.960 0.983 0.3896 0.618 0.618
#> 3 3 0.999 0.956 0.981 0.5940 0.689 0.527
#> 4 4 0.787 0.752 0.884 0.2137 0.855 0.631
#> 5 5 0.766 0.671 0.825 0.0514 0.928 0.723
#> 6 6 0.854 0.801 0.911 0.0381 0.959 0.799
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
#> GSM559433 2 0.0000 0.983 0.000 1.000
#> GSM559434 2 0.0000 0.983 0.000 1.000
#> GSM559436 2 0.0000 0.983 0.000 1.000
#> GSM559437 2 0.0000 0.983 0.000 1.000
#> GSM559438 2 0.0000 0.983 0.000 1.000
#> GSM559440 2 0.0000 0.983 0.000 1.000
#> GSM559441 2 0.0000 0.983 0.000 1.000
#> GSM559442 2 0.0000 0.983 0.000 1.000
#> GSM559444 2 0.0000 0.983 0.000 1.000
#> GSM559445 2 0.0000 0.983 0.000 1.000
#> GSM559446 2 0.0000 0.983 0.000 1.000
#> GSM559448 1 0.0672 0.970 0.992 0.008
#> GSM559450 2 0.0000 0.983 0.000 1.000
#> GSM559451 2 0.0000 0.983 0.000 1.000
#> GSM559452 2 0.2043 0.954 0.032 0.968
#> GSM559454 2 0.0000 0.983 0.000 1.000
#> GSM559455 2 0.0000 0.983 0.000 1.000
#> GSM559456 1 0.8267 0.647 0.740 0.260
#> GSM559457 2 0.0000 0.983 0.000 1.000
#> GSM559458 1 0.0000 0.977 1.000 0.000
#> GSM559459 2 0.0000 0.983 0.000 1.000
#> GSM559460 2 0.0000 0.983 0.000 1.000
#> GSM559461 2 0.3584 0.917 0.068 0.932
#> GSM559462 2 0.0000 0.983 0.000 1.000
#> GSM559463 2 0.8327 0.650 0.264 0.736
#> GSM559464 2 0.0000 0.983 0.000 1.000
#> GSM559465 2 0.8327 0.650 0.264 0.736
#> GSM559467 2 0.0000 0.983 0.000 1.000
#> GSM559468 2 0.0000 0.983 0.000 1.000
#> GSM559469 2 0.0000 0.983 0.000 1.000
#> GSM559470 2 0.0000 0.983 0.000 1.000
#> GSM559471 2 0.0000 0.983 0.000 1.000
#> GSM559472 2 0.0000 0.983 0.000 1.000
#> GSM559473 2 0.0000 0.983 0.000 1.000
#> GSM559475 2 0.0000 0.983 0.000 1.000
#> GSM559477 2 0.0000 0.983 0.000 1.000
#> GSM559478 2 0.0000 0.983 0.000 1.000
#> GSM559479 2 0.0000 0.983 0.000 1.000
#> GSM559480 2 0.0000 0.983 0.000 1.000
#> GSM559481 2 0.0000 0.983 0.000 1.000
#> GSM559482 2 0.0000 0.983 0.000 1.000
#> GSM559435 1 0.0000 0.977 1.000 0.000
#> GSM559439 1 0.0000 0.977 1.000 0.000
#> GSM559443 1 0.0000 0.977 1.000 0.000
#> GSM559447 1 0.0000 0.977 1.000 0.000
#> GSM559449 1 0.0000 0.977 1.000 0.000
#> GSM559453 1 0.0000 0.977 1.000 0.000
#> GSM559466 1 0.0000 0.977 1.000 0.000
#> GSM559474 1 0.0000 0.977 1.000 0.000
#> GSM559476 1 0.0000 0.977 1.000 0.000
#> GSM559483 2 0.0000 0.983 0.000 1.000
#> GSM559484 1 0.0000 0.977 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559434 1 0.6192 0.266 0.580 0.420 0.000
#> GSM559436 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559437 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559438 1 0.1411 0.942 0.964 0.036 0.000
#> GSM559440 2 0.2878 0.874 0.096 0.904 0.000
#> GSM559441 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559442 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559444 2 0.0000 0.976 0.000 1.000 0.000
#> GSM559445 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559446 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559448 1 0.4452 0.760 0.808 0.000 0.192
#> GSM559450 2 0.0000 0.976 0.000 1.000 0.000
#> GSM559451 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559452 2 0.5000 0.825 0.044 0.832 0.124
#> GSM559454 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559455 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559456 1 0.1753 0.930 0.952 0.000 0.048
#> GSM559457 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559458 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559459 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559460 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559462 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559463 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559464 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559465 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559467 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559468 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559469 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559470 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559471 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559472 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559473 2 0.0592 0.966 0.012 0.988 0.000
#> GSM559475 2 0.0000 0.976 0.000 1.000 0.000
#> GSM559477 2 0.0000 0.976 0.000 1.000 0.000
#> GSM559478 2 0.0000 0.976 0.000 1.000 0.000
#> GSM559479 2 0.0000 0.976 0.000 1.000 0.000
#> GSM559480 2 0.0000 0.976 0.000 1.000 0.000
#> GSM559481 2 0.0000 0.976 0.000 1.000 0.000
#> GSM559482 2 0.0000 0.976 0.000 1.000 0.000
#> GSM559435 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559439 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559443 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559447 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559449 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559453 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559466 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559474 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559476 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559483 2 0.0000 0.976 0.000 1.000 0.000
#> GSM559484 3 0.0000 1.000 0.000 0.000 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.0000 0.7043 1.000 0.000 0.000 0.000
#> GSM559434 1 0.6837 -0.0143 0.504 0.392 0.000 0.104
#> GSM559436 1 0.4222 0.6065 0.728 0.000 0.000 0.272
#> GSM559437 1 0.0000 0.7043 1.000 0.000 0.000 0.000
#> GSM559438 1 0.5376 0.1599 0.588 0.016 0.000 0.396
#> GSM559440 2 0.6795 0.1373 0.432 0.472 0.000 0.096
#> GSM559441 1 0.0000 0.7043 1.000 0.000 0.000 0.000
#> GSM559442 4 0.2149 0.7781 0.088 0.000 0.000 0.912
#> GSM559444 2 0.1302 0.9105 0.044 0.956 0.000 0.000
#> GSM559445 1 0.0000 0.7043 1.000 0.000 0.000 0.000
#> GSM559446 1 0.0000 0.7043 1.000 0.000 0.000 0.000
#> GSM559448 1 0.7468 0.3315 0.464 0.000 0.352 0.184
#> GSM559450 2 0.0000 0.9457 0.000 1.000 0.000 0.000
#> GSM559451 1 0.4134 0.6497 0.740 0.000 0.000 0.260
#> GSM559452 4 0.4872 0.3738 0.356 0.004 0.000 0.640
#> GSM559454 1 0.3528 0.6693 0.808 0.000 0.000 0.192
#> GSM559455 1 0.0000 0.7043 1.000 0.000 0.000 0.000
#> GSM559456 1 0.4916 0.6531 0.760 0.000 0.056 0.184
#> GSM559457 1 0.3444 0.6723 0.816 0.000 0.000 0.184
#> GSM559458 3 0.1389 0.9496 0.000 0.000 0.952 0.048
#> GSM559459 1 0.4916 0.3844 0.576 0.000 0.000 0.424
#> GSM559460 4 0.2281 0.8268 0.096 0.000 0.000 0.904
#> GSM559461 4 0.3569 0.6291 0.196 0.000 0.000 0.804
#> GSM559462 1 0.4933 0.3767 0.568 0.000 0.000 0.432
#> GSM559463 4 0.1118 0.8436 0.036 0.000 0.000 0.964
#> GSM559464 4 0.2281 0.8268 0.096 0.000 0.000 0.904
#> GSM559465 4 0.2281 0.8268 0.096 0.000 0.000 0.904
#> GSM559467 1 0.4955 0.1945 0.556 0.000 0.000 0.444
#> GSM559468 4 0.0000 0.8441 0.000 0.000 0.000 1.000
#> GSM559469 4 0.0000 0.8441 0.000 0.000 0.000 1.000
#> GSM559470 1 0.1474 0.6790 0.948 0.000 0.000 0.052
#> GSM559471 4 0.0336 0.8437 0.008 0.000 0.000 0.992
#> GSM559472 1 0.4817 0.4963 0.612 0.000 0.000 0.388
#> GSM559473 2 0.0469 0.9369 0.000 0.988 0.000 0.012
#> GSM559475 2 0.0000 0.9457 0.000 1.000 0.000 0.000
#> GSM559477 2 0.0000 0.9457 0.000 1.000 0.000 0.000
#> GSM559478 2 0.0000 0.9457 0.000 1.000 0.000 0.000
#> GSM559479 2 0.0000 0.9457 0.000 1.000 0.000 0.000
#> GSM559480 2 0.0000 0.9457 0.000 1.000 0.000 0.000
#> GSM559481 2 0.0000 0.9457 0.000 1.000 0.000 0.000
#> GSM559482 2 0.0000 0.9457 0.000 1.000 0.000 0.000
#> GSM559435 3 0.0000 0.9952 0.000 0.000 1.000 0.000
#> GSM559439 3 0.0000 0.9952 0.000 0.000 1.000 0.000
#> GSM559443 3 0.0000 0.9952 0.000 0.000 1.000 0.000
#> GSM559447 3 0.0000 0.9952 0.000 0.000 1.000 0.000
#> GSM559449 3 0.0000 0.9952 0.000 0.000 1.000 0.000
#> GSM559453 3 0.0000 0.9952 0.000 0.000 1.000 0.000
#> GSM559466 3 0.0000 0.9952 0.000 0.000 1.000 0.000
#> GSM559474 3 0.0000 0.9952 0.000 0.000 1.000 0.000
#> GSM559476 3 0.0000 0.9952 0.000 0.000 1.000 0.000
#> GSM559483 2 0.0000 0.9457 0.000 1.000 0.000 0.000
#> GSM559484 3 0.0000 0.9952 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 1 0.3752 -0.00719 0.708 0.000 0.000 0.292 0.000
#> GSM559434 4 0.6697 0.52385 0.108 0.212 0.000 0.600 0.080
#> GSM559436 1 0.0162 0.60529 0.996 0.000 0.000 0.000 0.004
#> GSM559437 4 0.4304 0.57297 0.484 0.000 0.000 0.516 0.000
#> GSM559438 4 0.6118 0.57333 0.256 0.016 0.000 0.600 0.128
#> GSM559440 4 0.6697 0.52385 0.108 0.212 0.000 0.600 0.080
#> GSM559441 4 0.4304 0.57297 0.484 0.000 0.000 0.516 0.000
#> GSM559442 5 0.0000 0.80265 0.000 0.000 0.000 0.000 1.000
#> GSM559444 2 0.2890 0.81220 0.004 0.836 0.000 0.160 0.000
#> GSM559445 4 0.4304 0.57297 0.484 0.000 0.000 0.516 0.000
#> GSM559446 1 0.4307 -0.61612 0.504 0.000 0.000 0.496 0.000
#> GSM559448 1 0.3366 0.45892 0.768 0.000 0.232 0.000 0.000
#> GSM559450 2 0.0404 0.97409 0.000 0.988 0.000 0.012 0.000
#> GSM559451 1 0.1608 0.57789 0.928 0.000 0.000 0.000 0.072
#> GSM559452 5 0.5289 0.30728 0.064 0.000 0.000 0.340 0.596
#> GSM559454 1 0.0162 0.60529 0.996 0.000 0.000 0.000 0.004
#> GSM559455 1 0.4297 -0.56294 0.528 0.000 0.000 0.472 0.000
#> GSM559456 1 0.1168 0.60150 0.960 0.000 0.032 0.008 0.000
#> GSM559457 1 0.0000 0.60251 1.000 0.000 0.000 0.000 0.000
#> GSM559458 3 0.1197 0.89591 0.000 0.000 0.952 0.000 0.048
#> GSM559459 1 0.2377 0.58199 0.872 0.000 0.000 0.000 0.128
#> GSM559460 5 0.1732 0.79630 0.080 0.000 0.000 0.000 0.920
#> GSM559461 5 0.2891 0.65497 0.176 0.000 0.000 0.000 0.824
#> GSM559462 1 0.4201 0.30633 0.592 0.000 0.000 0.000 0.408
#> GSM559463 5 0.3837 0.58386 0.308 0.000 0.000 0.000 0.692
#> GSM559464 5 0.1732 0.79630 0.080 0.000 0.000 0.000 0.920
#> GSM559465 5 0.1732 0.79630 0.080 0.000 0.000 0.000 0.920
#> GSM559467 1 0.6645 0.06612 0.400 0.000 0.000 0.224 0.376
#> GSM559468 5 0.0000 0.80265 0.000 0.000 0.000 0.000 1.000
#> GSM559469 5 0.0000 0.80265 0.000 0.000 0.000 0.000 1.000
#> GSM559470 4 0.5381 0.57716 0.428 0.000 0.000 0.516 0.056
#> GSM559471 5 0.3752 0.59399 0.292 0.000 0.000 0.000 0.708
#> GSM559472 1 0.2732 0.56741 0.840 0.000 0.000 0.000 0.160
#> GSM559473 2 0.0404 0.97130 0.000 0.988 0.000 0.000 0.012
#> GSM559475 2 0.0000 0.98111 0.000 1.000 0.000 0.000 0.000
#> GSM559477 2 0.0000 0.98111 0.000 1.000 0.000 0.000 0.000
#> GSM559478 2 0.0000 0.98111 0.000 1.000 0.000 0.000 0.000
#> GSM559479 2 0.0000 0.98111 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.0000 0.98111 0.000 1.000 0.000 0.000 0.000
#> GSM559481 2 0.0000 0.98111 0.000 1.000 0.000 0.000 0.000
#> GSM559482 2 0.0000 0.98111 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.93052 0.000 0.000 1.000 0.000 0.000
#> GSM559439 3 0.0000 0.93052 0.000 0.000 1.000 0.000 0.000
#> GSM559443 3 0.0000 0.93052 0.000 0.000 1.000 0.000 0.000
#> GSM559447 3 0.0000 0.93052 0.000 0.000 1.000 0.000 0.000
#> GSM559449 3 0.0000 0.93052 0.000 0.000 1.000 0.000 0.000
#> GSM559453 3 0.0000 0.93052 0.000 0.000 1.000 0.000 0.000
#> GSM559466 3 0.0000 0.93052 0.000 0.000 1.000 0.000 0.000
#> GSM559474 3 0.4182 0.66460 0.000 0.000 0.600 0.400 0.000
#> GSM559476 3 0.0000 0.93052 0.000 0.000 1.000 0.000 0.000
#> GSM559483 2 0.0000 0.98111 0.000 1.000 0.000 0.000 0.000
#> GSM559484 3 0.4182 0.66460 0.000 0.000 0.600 0.400 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.3684 0.167 0.628 0.000 0.000 0.372 0 0.000
#> GSM559434 4 0.0363 0.803 0.000 0.000 0.000 0.988 0 0.012
#> GSM559436 1 0.0000 0.813 1.000 0.000 0.000 0.000 0 0.000
#> GSM559437 4 0.2454 0.871 0.160 0.000 0.000 0.840 0 0.000
#> GSM559438 4 0.0547 0.804 0.000 0.000 0.000 0.980 0 0.020
#> GSM559440 4 0.0000 0.799 0.000 0.000 0.000 1.000 0 0.000
#> GSM559441 4 0.2416 0.873 0.156 0.000 0.000 0.844 0 0.000
#> GSM559442 6 0.0000 0.786 0.000 0.000 0.000 0.000 0 1.000
#> GSM559444 2 0.3737 0.434 0.000 0.608 0.000 0.392 0 0.000
#> GSM559445 4 0.2416 0.873 0.156 0.000 0.000 0.844 0 0.000
#> GSM559446 4 0.3547 0.621 0.332 0.000 0.000 0.668 0 0.000
#> GSM559448 1 0.2416 0.678 0.844 0.000 0.156 0.000 0 0.000
#> GSM559450 2 0.1007 0.915 0.000 0.956 0.000 0.044 0 0.000
#> GSM559451 1 0.0692 0.806 0.976 0.000 0.000 0.004 0 0.020
#> GSM559452 6 0.3847 0.167 0.000 0.000 0.000 0.456 0 0.544
#> GSM559454 1 0.0000 0.813 1.000 0.000 0.000 0.000 0 0.000
#> GSM559455 4 0.2996 0.811 0.228 0.000 0.000 0.772 0 0.000
#> GSM559456 1 0.0692 0.807 0.976 0.000 0.004 0.020 0 0.000
#> GSM559457 1 0.0000 0.813 1.000 0.000 0.000 0.000 0 0.000
#> GSM559458 3 0.1075 0.936 0.000 0.000 0.952 0.000 0 0.048
#> GSM559459 1 0.0632 0.807 0.976 0.000 0.000 0.000 0 0.024
#> GSM559460 6 0.0547 0.787 0.020 0.000 0.000 0.000 0 0.980
#> GSM559461 6 0.2454 0.661 0.160 0.000 0.000 0.000 0 0.840
#> GSM559462 1 0.3672 0.390 0.632 0.000 0.000 0.000 0 0.368
#> GSM559463 6 0.3684 0.450 0.372 0.000 0.000 0.000 0 0.628
#> GSM559464 6 0.0547 0.787 0.020 0.000 0.000 0.000 0 0.980
#> GSM559465 6 0.0547 0.787 0.020 0.000 0.000 0.000 0 0.980
#> GSM559467 1 0.5925 0.174 0.456 0.000 0.000 0.236 0 0.308
#> GSM559468 6 0.0000 0.786 0.000 0.000 0.000 0.000 0 1.000
#> GSM559469 6 0.0000 0.786 0.000 0.000 0.000 0.000 0 1.000
#> GSM559470 4 0.2790 0.869 0.140 0.000 0.000 0.840 0 0.020
#> GSM559471 6 0.3672 0.456 0.368 0.000 0.000 0.000 0 0.632
#> GSM559472 1 0.0458 0.808 0.984 0.000 0.000 0.000 0 0.016
#> GSM559473 2 0.0000 0.951 0.000 1.000 0.000 0.000 0 0.000
#> GSM559475 2 0.0000 0.951 0.000 1.000 0.000 0.000 0 0.000
#> GSM559477 2 0.0000 0.951 0.000 1.000 0.000 0.000 0 0.000
#> GSM559478 2 0.0000 0.951 0.000 1.000 0.000 0.000 0 0.000
#> GSM559479 2 0.0000 0.951 0.000 1.000 0.000 0.000 0 0.000
#> GSM559480 2 0.0000 0.951 0.000 1.000 0.000 0.000 0 0.000
#> GSM559481 2 0.0000 0.951 0.000 1.000 0.000 0.000 0 0.000
#> GSM559482 2 0.0000 0.951 0.000 1.000 0.000 0.000 0 0.000
#> GSM559435 3 0.0000 0.992 0.000 0.000 1.000 0.000 0 0.000
#> GSM559439 3 0.0000 0.992 0.000 0.000 1.000 0.000 0 0.000
#> GSM559443 3 0.0000 0.992 0.000 0.000 1.000 0.000 0 0.000
#> GSM559447 3 0.0000 0.992 0.000 0.000 1.000 0.000 0 0.000
#> GSM559449 3 0.0000 0.992 0.000 0.000 1.000 0.000 0 0.000
#> GSM559453 3 0.0000 0.992 0.000 0.000 1.000 0.000 0 0.000
#> GSM559466 3 0.0000 0.992 0.000 0.000 1.000 0.000 0 0.000
#> GSM559474 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 0.000
#> GSM559476 3 0.0000 0.992 0.000 0.000 1.000 0.000 0 0.000
#> GSM559483 2 0.0000 0.951 0.000 1.000 0.000 0.000 0 0.000
#> GSM559484 5 0.0000 1.000 0.000 0.000 0.000 0.000 1 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 disease.state(p) k
#> MAD:pam 52 1.20e-07 2
#> MAD:pam 51 1.89e-09 3
#> MAD:pam 43 2.59e-07 4
#> MAD:pam 45 4.32e-07 5
#> MAD:pam 45 1.30e-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 21512 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.453 0.865 0.894 0.4122 0.599 0.599
#> 3 3 0.588 0.803 0.892 0.5632 0.602 0.399
#> 4 4 0.870 0.920 0.955 -0.0335 0.761 0.501
#> 5 5 0.786 0.774 0.893 0.1355 0.925 0.807
#> 6 6 0.749 0.701 0.807 0.0733 0.855 0.571
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM559433 1 0.6438 0.992 0.836 0.164
#> GSM559434 2 0.0000 0.893 0.000 1.000
#> GSM559436 1 0.6343 0.994 0.840 0.160
#> GSM559437 2 0.0000 0.893 0.000 1.000
#> GSM559438 2 0.8763 0.467 0.296 0.704
#> GSM559440 2 0.0000 0.893 0.000 1.000
#> GSM559441 2 0.0000 0.893 0.000 1.000
#> GSM559442 2 0.9608 0.202 0.384 0.616
#> GSM559444 2 0.0000 0.893 0.000 1.000
#> GSM559445 2 0.0000 0.893 0.000 1.000
#> GSM559446 2 0.0000 0.893 0.000 1.000
#> GSM559448 2 0.1184 0.889 0.016 0.984
#> GSM559450 2 0.0000 0.893 0.000 1.000
#> GSM559451 1 0.6438 0.992 0.836 0.164
#> GSM559452 2 0.4939 0.852 0.108 0.892
#> GSM559454 1 0.6343 0.994 0.840 0.160
#> GSM559455 2 0.1633 0.877 0.024 0.976
#> GSM559456 2 0.0000 0.893 0.000 1.000
#> GSM559457 1 0.6712 0.983 0.824 0.176
#> GSM559458 2 0.1184 0.889 0.016 0.984
#> GSM559459 1 0.6343 0.994 0.840 0.160
#> GSM559460 1 0.6343 0.994 0.840 0.160
#> GSM559461 1 0.6343 0.994 0.840 0.160
#> GSM559462 1 0.6973 0.966 0.812 0.188
#> GSM559463 2 0.7139 0.677 0.196 0.804
#> GSM559464 1 0.6343 0.994 0.840 0.160
#> GSM559465 1 0.6531 0.989 0.832 0.168
#> GSM559467 2 0.7299 0.658 0.204 0.796
#> GSM559468 1 0.6343 0.994 0.840 0.160
#> GSM559469 2 0.9209 0.360 0.336 0.664
#> GSM559470 2 0.0672 0.888 0.008 0.992
#> GSM559471 1 0.6531 0.990 0.832 0.168
#> GSM559472 1 0.6343 0.994 0.840 0.160
#> GSM559473 2 0.0000 0.893 0.000 1.000
#> GSM559475 2 0.0000 0.893 0.000 1.000
#> GSM559477 2 0.0000 0.893 0.000 1.000
#> GSM559478 2 0.0000 0.893 0.000 1.000
#> GSM559479 2 0.0000 0.893 0.000 1.000
#> GSM559480 2 0.0000 0.893 0.000 1.000
#> GSM559481 2 0.0000 0.893 0.000 1.000
#> GSM559482 2 0.0000 0.893 0.000 1.000
#> GSM559435 2 0.6438 0.826 0.164 0.836
#> GSM559439 2 0.6438 0.826 0.164 0.836
#> GSM559443 2 0.6438 0.826 0.164 0.836
#> GSM559447 2 0.6438 0.826 0.164 0.836
#> GSM559449 2 0.6438 0.826 0.164 0.836
#> GSM559453 2 0.6438 0.826 0.164 0.836
#> GSM559466 2 0.6438 0.826 0.164 0.836
#> GSM559474 2 0.6438 0.826 0.164 0.836
#> GSM559476 2 0.6438 0.826 0.164 0.836
#> GSM559483 2 0.0000 0.893 0.000 1.000
#> GSM559484 2 0.6438 0.826 0.164 0.836
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0000 0.9169 1.000 0.000 0.000
#> GSM559434 2 0.4968 0.6961 0.012 0.800 0.188
#> GSM559436 1 0.0592 0.9114 0.988 0.000 0.012
#> GSM559437 3 0.8392 0.6992 0.200 0.176 0.624
#> GSM559438 2 0.6596 0.5714 0.256 0.704 0.040
#> GSM559440 2 0.4178 0.7447 0.172 0.828 0.000
#> GSM559441 3 0.9319 0.4724 0.340 0.176 0.484
#> GSM559442 1 0.2550 0.8684 0.936 0.040 0.024
#> GSM559444 2 0.0592 0.9335 0.012 0.988 0.000
#> GSM559445 3 0.8392 0.6992 0.200 0.176 0.624
#> GSM559446 3 0.8392 0.6992 0.200 0.176 0.624
#> GSM559448 3 0.7564 0.6379 0.296 0.068 0.636
#> GSM559450 2 0.0592 0.9335 0.012 0.988 0.000
#> GSM559451 1 0.0000 0.9169 1.000 0.000 0.000
#> GSM559452 3 0.7613 0.6147 0.064 0.316 0.620
#> GSM559454 1 0.0000 0.9169 1.000 0.000 0.000
#> GSM559455 1 0.5253 0.7541 0.828 0.076 0.096
#> GSM559456 3 0.8009 0.6592 0.276 0.100 0.624
#> GSM559457 1 0.0000 0.9169 1.000 0.000 0.000
#> GSM559458 3 0.8013 0.6780 0.252 0.112 0.636
#> GSM559459 1 0.0592 0.9114 0.988 0.000 0.012
#> GSM559460 1 0.0000 0.9169 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.9169 1.000 0.000 0.000
#> GSM559462 1 0.0592 0.9114 0.988 0.000 0.012
#> GSM559463 1 0.0747 0.9106 0.984 0.000 0.016
#> GSM559464 1 0.0000 0.9169 1.000 0.000 0.000
#> GSM559465 1 0.0000 0.9169 1.000 0.000 0.000
#> GSM559467 1 0.6438 0.6613 0.764 0.100 0.136
#> GSM559468 1 0.0000 0.9169 1.000 0.000 0.000
#> GSM559469 1 0.7036 0.5801 0.720 0.096 0.184
#> GSM559470 1 0.8663 -0.0275 0.524 0.112 0.364
#> GSM559471 1 0.0000 0.9169 1.000 0.000 0.000
#> GSM559472 1 0.0592 0.9114 0.988 0.000 0.012
#> GSM559473 2 0.0592 0.9335 0.012 0.988 0.000
#> GSM559475 2 0.0592 0.9335 0.012 0.988 0.000
#> GSM559477 2 0.0592 0.9335 0.012 0.988 0.000
#> GSM559478 2 0.0592 0.9335 0.012 0.988 0.000
#> GSM559479 2 0.0592 0.9335 0.012 0.988 0.000
#> GSM559480 2 0.0000 0.9237 0.000 1.000 0.000
#> GSM559481 2 0.0000 0.9237 0.000 1.000 0.000
#> GSM559482 2 0.0592 0.9335 0.012 0.988 0.000
#> GSM559435 3 0.0000 0.7770 0.000 0.000 1.000
#> GSM559439 3 0.0000 0.7770 0.000 0.000 1.000
#> GSM559443 3 0.0424 0.7791 0.000 0.008 0.992
#> GSM559447 3 0.0000 0.7770 0.000 0.000 1.000
#> GSM559449 3 0.0237 0.7782 0.000 0.004 0.996
#> GSM559453 3 0.0424 0.7791 0.000 0.008 0.992
#> GSM559466 3 0.0000 0.7770 0.000 0.000 1.000
#> GSM559474 3 0.3412 0.7682 0.000 0.124 0.876
#> GSM559476 3 0.5060 0.7766 0.064 0.100 0.836
#> GSM559483 2 0.0592 0.9335 0.012 0.988 0.000
#> GSM559484 3 0.3412 0.7682 0.000 0.124 0.876
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.0336 0.947 0.992 0.000 0.000 0.008
#> GSM559434 2 0.5109 0.578 0.212 0.736 0.000 0.052
#> GSM559436 1 0.0336 0.947 0.992 0.000 0.000 0.008
#> GSM559437 1 0.2868 0.893 0.864 0.000 0.000 0.136
#> GSM559438 1 0.3858 0.847 0.844 0.100 0.000 0.056
#> GSM559440 2 0.4916 0.633 0.184 0.760 0.000 0.056
#> GSM559441 1 0.2345 0.915 0.900 0.000 0.000 0.100
#> GSM559442 1 0.0592 0.947 0.984 0.000 0.000 0.016
#> GSM559444 2 0.1406 0.903 0.016 0.960 0.000 0.024
#> GSM559445 1 0.2868 0.893 0.864 0.000 0.000 0.136
#> GSM559446 1 0.2868 0.893 0.864 0.000 0.000 0.136
#> GSM559448 1 0.1118 0.943 0.964 0.000 0.000 0.036
#> GSM559450 2 0.0779 0.916 0.016 0.980 0.000 0.004
#> GSM559451 1 0.0336 0.947 0.992 0.000 0.000 0.008
#> GSM559452 2 0.2853 0.853 0.016 0.900 0.008 0.076
#> GSM559454 1 0.0336 0.947 0.992 0.000 0.000 0.008
#> GSM559455 1 0.1637 0.932 0.940 0.000 0.000 0.060
#> GSM559456 1 0.2530 0.909 0.888 0.000 0.000 0.112
#> GSM559457 1 0.0188 0.948 0.996 0.000 0.000 0.004
#> GSM559458 1 0.3037 0.906 0.880 0.000 0.020 0.100
#> GSM559459 1 0.0336 0.947 0.992 0.000 0.000 0.008
#> GSM559460 1 0.0336 0.947 0.992 0.000 0.000 0.008
#> GSM559461 1 0.0336 0.947 0.992 0.000 0.000 0.008
#> GSM559462 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM559463 1 0.0336 0.947 0.992 0.000 0.000 0.008
#> GSM559464 1 0.0336 0.947 0.992 0.000 0.000 0.008
#> GSM559465 1 0.0336 0.947 0.992 0.000 0.000 0.008
#> GSM559467 1 0.1211 0.940 0.960 0.000 0.000 0.040
#> GSM559468 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM559469 1 0.1389 0.939 0.952 0.000 0.000 0.048
#> GSM559470 1 0.1867 0.927 0.928 0.000 0.000 0.072
#> GSM559471 1 0.0000 0.948 1.000 0.000 0.000 0.000
#> GSM559472 1 0.0188 0.948 0.996 0.000 0.000 0.004
#> GSM559473 2 0.0000 0.925 0.000 1.000 0.000 0.000
#> GSM559475 2 0.0336 0.922 0.008 0.992 0.000 0.000
#> GSM559477 2 0.0000 0.925 0.000 1.000 0.000 0.000
#> GSM559478 2 0.0000 0.925 0.000 1.000 0.000 0.000
#> GSM559479 2 0.0000 0.925 0.000 1.000 0.000 0.000
#> GSM559480 2 0.0000 0.925 0.000 1.000 0.000 0.000
#> GSM559481 2 0.0000 0.925 0.000 1.000 0.000 0.000
#> GSM559482 2 0.0000 0.925 0.000 1.000 0.000 0.000
#> GSM559435 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM559439 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM559443 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM559447 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM559449 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM559453 3 0.0707 0.971 0.000 0.000 0.980 0.020
#> GSM559466 3 0.0000 0.995 0.000 0.000 1.000 0.000
#> GSM559474 4 0.1474 0.962 0.000 0.000 0.052 0.948
#> GSM559476 1 0.5041 0.690 0.728 0.000 0.232 0.040
#> GSM559483 2 0.0000 0.925 0.000 1.000 0.000 0.000
#> GSM559484 4 0.2282 0.962 0.000 0.024 0.052 0.924
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 1 0.0000 0.8564 1.000 0.000 0.000 0.000 0.000
#> GSM559434 2 0.1960 0.8305 0.004 0.928 0.000 0.048 0.020
#> GSM559436 1 0.0000 0.8564 1.000 0.000 0.000 0.000 0.000
#> GSM559437 4 0.2179 0.7019 0.112 0.000 0.000 0.888 0.000
#> GSM559438 1 0.5907 0.0679 0.496 0.428 0.000 0.020 0.056
#> GSM559440 2 0.3347 0.7529 0.056 0.864 0.000 0.024 0.056
#> GSM559441 1 0.5338 0.0680 0.544 0.000 0.000 0.400 0.056
#> GSM559442 1 0.1168 0.8383 0.960 0.000 0.000 0.008 0.032
#> GSM559444 2 0.0451 0.8629 0.000 0.988 0.000 0.008 0.004
#> GSM559445 4 0.2127 0.6940 0.108 0.000 0.000 0.892 0.000
#> GSM559446 4 0.2179 0.7019 0.112 0.000 0.000 0.888 0.000
#> GSM559448 1 0.4347 0.6487 0.780 0.000 0.076 0.136 0.008
#> GSM559450 2 0.0324 0.8644 0.000 0.992 0.000 0.004 0.004
#> GSM559451 1 0.0000 0.8564 1.000 0.000 0.000 0.000 0.000
#> GSM559452 2 0.2286 0.7917 0.000 0.888 0.004 0.108 0.000
#> GSM559454 1 0.0000 0.8564 1.000 0.000 0.000 0.000 0.000
#> GSM559455 1 0.3055 0.7242 0.840 0.000 0.000 0.144 0.016
#> GSM559456 4 0.4304 0.1398 0.484 0.000 0.000 0.516 0.000
#> GSM559457 1 0.0000 0.8564 1.000 0.000 0.000 0.000 0.000
#> GSM559458 1 0.3741 0.5868 0.732 0.000 0.004 0.264 0.000
#> GSM559459 1 0.0000 0.8564 1.000 0.000 0.000 0.000 0.000
#> GSM559460 1 0.0000 0.8564 1.000 0.000 0.000 0.000 0.000
#> GSM559461 1 0.0000 0.8564 1.000 0.000 0.000 0.000 0.000
#> GSM559462 1 0.0000 0.8564 1.000 0.000 0.000 0.000 0.000
#> GSM559463 1 0.0290 0.8516 0.992 0.000 0.000 0.008 0.000
#> GSM559464 1 0.0000 0.8564 1.000 0.000 0.000 0.000 0.000
#> GSM559465 1 0.0000 0.8564 1.000 0.000 0.000 0.000 0.000
#> GSM559467 1 0.1845 0.8188 0.928 0.000 0.000 0.016 0.056
#> GSM559468 1 0.0000 0.8564 1.000 0.000 0.000 0.000 0.000
#> GSM559469 1 0.1845 0.8188 0.928 0.000 0.000 0.016 0.056
#> GSM559470 1 0.5274 0.1679 0.572 0.000 0.000 0.372 0.056
#> GSM559471 1 0.0703 0.8463 0.976 0.000 0.000 0.000 0.024
#> GSM559472 1 0.0000 0.8564 1.000 0.000 0.000 0.000 0.000
#> GSM559473 2 0.0162 0.8653 0.000 0.996 0.000 0.004 0.000
#> GSM559475 2 0.0324 0.8644 0.000 0.992 0.000 0.004 0.004
#> GSM559477 2 0.3123 0.8794 0.000 0.828 0.000 0.012 0.160
#> GSM559478 2 0.3236 0.8804 0.000 0.828 0.000 0.020 0.152
#> GSM559479 2 0.3123 0.8794 0.000 0.828 0.000 0.012 0.160
#> GSM559480 2 0.3236 0.8804 0.000 0.828 0.000 0.020 0.152
#> GSM559481 2 0.3236 0.8804 0.000 0.828 0.000 0.020 0.152
#> GSM559482 2 0.3123 0.8794 0.000 0.828 0.000 0.012 0.160
#> GSM559435 3 0.0162 0.9727 0.000 0.000 0.996 0.000 0.004
#> GSM559439 3 0.0162 0.9727 0.000 0.000 0.996 0.000 0.004
#> GSM559443 3 0.1942 0.9260 0.000 0.000 0.920 0.068 0.012
#> GSM559447 3 0.0000 0.9732 0.000 0.000 1.000 0.000 0.000
#> GSM559449 3 0.0000 0.9732 0.000 0.000 1.000 0.000 0.000
#> GSM559453 3 0.1341 0.9258 0.000 0.000 0.944 0.056 0.000
#> GSM559466 3 0.0000 0.9732 0.000 0.000 1.000 0.000 0.000
#> GSM559474 5 0.3491 0.7626 0.000 0.000 0.004 0.228 0.768
#> GSM559476 1 0.6281 0.1817 0.532 0.000 0.324 0.136 0.008
#> GSM559483 2 0.3123 0.8794 0.000 0.828 0.000 0.012 0.160
#> GSM559484 5 0.4409 0.7828 0.000 0.148 0.004 0.080 0.768
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.0146 0.91529 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM559434 6 0.3898 0.80398 0.000 0.336 0.000 0.012 0.000 0.652
#> GSM559436 1 0.1387 0.86637 0.932 0.000 0.000 0.000 0.068 0.000
#> GSM559437 4 0.0547 0.68149 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM559438 6 0.5630 0.05616 0.416 0.104 0.000 0.012 0.000 0.468
#> GSM559440 6 0.3898 0.80398 0.000 0.336 0.000 0.012 0.000 0.652
#> GSM559441 4 0.4504 0.30719 0.432 0.000 0.000 0.536 0.000 0.032
#> GSM559442 1 0.2420 0.83636 0.888 0.000 0.000 0.004 0.076 0.032
#> GSM559444 6 0.3847 0.80450 0.000 0.348 0.000 0.008 0.000 0.644
#> GSM559445 4 0.0622 0.66857 0.008 0.000 0.000 0.980 0.000 0.012
#> GSM559446 4 0.0547 0.68149 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM559448 5 0.4594 0.00530 0.480 0.000 0.000 0.000 0.484 0.036
#> GSM559450 6 0.3756 0.80239 0.000 0.352 0.000 0.004 0.000 0.644
#> GSM559451 1 0.0146 0.91529 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM559452 6 0.3912 0.80478 0.000 0.340 0.000 0.012 0.000 0.648
#> GSM559454 1 0.0000 0.91546 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559455 1 0.2597 0.70826 0.824 0.000 0.000 0.176 0.000 0.000
#> GSM559456 4 0.2491 0.63431 0.164 0.000 0.000 0.836 0.000 0.000
#> GSM559457 1 0.0146 0.91529 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM559458 4 0.5310 0.31359 0.392 0.000 0.000 0.512 0.092 0.004
#> GSM559459 1 0.0000 0.91546 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559460 1 0.0000 0.91546 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559461 1 0.0000 0.91546 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559462 1 0.0146 0.91529 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM559463 1 0.2915 0.72349 0.808 0.000 0.000 0.000 0.184 0.008
#> GSM559464 1 0.0146 0.91462 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM559465 1 0.1471 0.86757 0.932 0.000 0.000 0.000 0.064 0.004
#> GSM559467 1 0.0622 0.90798 0.980 0.000 0.000 0.012 0.000 0.008
#> GSM559468 1 0.0146 0.91506 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM559469 1 0.2649 0.83335 0.880 0.000 0.000 0.012 0.072 0.036
#> GSM559470 1 0.4490 0.48040 0.700 0.000 0.000 0.104 0.000 0.196
#> GSM559471 1 0.2039 0.85309 0.908 0.000 0.000 0.004 0.072 0.016
#> GSM559472 1 0.0000 0.91546 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559473 6 0.3991 0.63812 0.000 0.472 0.000 0.004 0.000 0.524
#> GSM559475 6 0.3944 0.71874 0.000 0.428 0.000 0.004 0.000 0.568
#> GSM559477 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559478 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559479 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559480 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559481 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559482 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559435 3 0.3866 0.64743 0.000 0.000 0.516 0.000 0.484 0.000
#> GSM559439 3 0.3868 0.64443 0.000 0.000 0.508 0.000 0.492 0.000
#> GSM559443 5 0.3023 -0.53042 0.000 0.000 0.232 0.000 0.768 0.000
#> GSM559447 3 0.3867 0.64606 0.000 0.000 0.512 0.000 0.488 0.000
#> GSM559449 3 0.4096 0.64622 0.000 0.000 0.508 0.000 0.484 0.008
#> GSM559453 3 0.4184 0.64449 0.000 0.000 0.504 0.000 0.484 0.012
#> GSM559466 3 0.3866 0.64743 0.000 0.000 0.516 0.000 0.484 0.000
#> GSM559474 3 0.5798 -0.09075 0.000 0.000 0.484 0.204 0.000 0.312
#> GSM559476 5 0.3409 0.34432 0.300 0.000 0.000 0.000 0.700 0.000
#> GSM559483 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559484 3 0.4407 0.00871 0.000 0.000 0.492 0.024 0.000 0.484
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 disease.state(p) k
#> MAD:mclust 49 4.52e-02 2
#> MAD:mclust 50 3.37e-05 3
#> MAD:mclust 52 7.78e-09 4
#> MAD:mclust 47 2.16e-08 5
#> MAD:mclust 43 2.07e-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", "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 21512 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.920 0.945 0.974 0.4839 0.509 0.509
#> 3 3 0.770 0.796 0.922 0.3351 0.798 0.620
#> 4 4 0.771 0.771 0.883 0.1092 0.837 0.596
#> 5 5 0.690 0.641 0.745 0.0906 0.851 0.540
#> 6 6 0.738 0.675 0.826 0.0554 0.924 0.666
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
#> GSM559433 1 0.0000 0.987 1.000 0.000
#> GSM559434 2 0.0000 0.950 0.000 1.000
#> GSM559436 1 0.0000 0.987 1.000 0.000
#> GSM559437 1 0.0938 0.979 0.988 0.012
#> GSM559438 2 0.0000 0.950 0.000 1.000
#> GSM559440 2 0.0000 0.950 0.000 1.000
#> GSM559441 2 0.9491 0.459 0.368 0.632
#> GSM559442 1 0.3733 0.923 0.928 0.072
#> GSM559444 2 0.0000 0.950 0.000 1.000
#> GSM559445 2 0.6148 0.821 0.152 0.848
#> GSM559446 1 0.3879 0.921 0.924 0.076
#> GSM559448 1 0.0000 0.987 1.000 0.000
#> GSM559450 2 0.0000 0.950 0.000 1.000
#> GSM559451 1 0.0376 0.984 0.996 0.004
#> GSM559452 2 0.0000 0.950 0.000 1.000
#> GSM559454 1 0.0000 0.987 1.000 0.000
#> GSM559455 1 0.0672 0.982 0.992 0.008
#> GSM559456 1 0.0000 0.987 1.000 0.000
#> GSM559457 1 0.0000 0.987 1.000 0.000
#> GSM559458 1 0.0000 0.987 1.000 0.000
#> GSM559459 1 0.0000 0.987 1.000 0.000
#> GSM559460 1 0.0000 0.987 1.000 0.000
#> GSM559461 1 0.0000 0.987 1.000 0.000
#> GSM559462 1 0.2423 0.956 0.960 0.040
#> GSM559463 1 0.0000 0.987 1.000 0.000
#> GSM559464 1 0.0000 0.987 1.000 0.000
#> GSM559465 1 0.0000 0.987 1.000 0.000
#> GSM559467 2 0.7219 0.765 0.200 0.800
#> GSM559468 1 0.0000 0.987 1.000 0.000
#> GSM559469 2 0.8081 0.697 0.248 0.752
#> GSM559470 2 0.0672 0.945 0.008 0.992
#> GSM559471 1 0.5737 0.845 0.864 0.136
#> GSM559472 1 0.0000 0.987 1.000 0.000
#> GSM559473 2 0.0000 0.950 0.000 1.000
#> GSM559475 2 0.0000 0.950 0.000 1.000
#> GSM559477 2 0.0000 0.950 0.000 1.000
#> GSM559478 2 0.0000 0.950 0.000 1.000
#> GSM559479 2 0.0000 0.950 0.000 1.000
#> GSM559480 2 0.0000 0.950 0.000 1.000
#> GSM559481 2 0.0000 0.950 0.000 1.000
#> GSM559482 2 0.0000 0.950 0.000 1.000
#> GSM559435 1 0.0000 0.987 1.000 0.000
#> GSM559439 1 0.0000 0.987 1.000 0.000
#> GSM559443 1 0.0000 0.987 1.000 0.000
#> GSM559447 1 0.0000 0.987 1.000 0.000
#> GSM559449 1 0.0000 0.987 1.000 0.000
#> GSM559453 1 0.0000 0.987 1.000 0.000
#> GSM559466 1 0.0000 0.987 1.000 0.000
#> GSM559474 1 0.2236 0.960 0.964 0.036
#> GSM559476 1 0.0000 0.987 1.000 0.000
#> GSM559483 2 0.0000 0.950 0.000 1.000
#> GSM559484 2 0.0000 0.950 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559434 2 0.0000 0.8949 0.000 1.000 0.000
#> GSM559436 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559437 1 0.1529 0.8834 0.960 0.000 0.040
#> GSM559438 2 0.0747 0.8845 0.016 0.984 0.000
#> GSM559440 2 0.0000 0.8949 0.000 1.000 0.000
#> GSM559441 1 0.6307 -0.0927 0.512 0.488 0.000
#> GSM559442 1 0.1163 0.8933 0.972 0.028 0.000
#> GSM559444 2 0.0000 0.8949 0.000 1.000 0.000
#> GSM559445 2 0.7592 0.6068 0.112 0.680 0.208
#> GSM559446 1 0.8332 0.3160 0.580 0.104 0.316
#> GSM559448 1 0.3116 0.8034 0.892 0.000 0.108
#> GSM559450 2 0.0000 0.8949 0.000 1.000 0.000
#> GSM559451 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559452 2 0.4842 0.6634 0.000 0.776 0.224
#> GSM559454 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559455 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559456 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559457 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559458 3 0.5733 0.5233 0.324 0.000 0.676
#> GSM559459 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559460 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559462 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559463 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559464 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559465 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559467 2 0.6274 0.2095 0.456 0.544 0.000
#> GSM559468 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559469 2 0.5988 0.4514 0.368 0.632 0.000
#> GSM559470 2 0.5098 0.6654 0.248 0.752 0.000
#> GSM559471 1 0.1289 0.8897 0.968 0.032 0.000
#> GSM559472 1 0.0000 0.9147 1.000 0.000 0.000
#> GSM559473 2 0.0000 0.8949 0.000 1.000 0.000
#> GSM559475 2 0.0000 0.8949 0.000 1.000 0.000
#> GSM559477 2 0.0000 0.8949 0.000 1.000 0.000
#> GSM559478 2 0.0000 0.8949 0.000 1.000 0.000
#> GSM559479 2 0.0000 0.8949 0.000 1.000 0.000
#> GSM559480 2 0.0000 0.8949 0.000 1.000 0.000
#> GSM559481 2 0.0000 0.8949 0.000 1.000 0.000
#> GSM559482 2 0.0000 0.8949 0.000 1.000 0.000
#> GSM559435 3 0.1031 0.8903 0.024 0.000 0.976
#> GSM559439 3 0.0237 0.8997 0.004 0.000 0.996
#> GSM559443 1 0.6309 -0.1170 0.504 0.000 0.496
#> GSM559447 3 0.0000 0.9006 0.000 0.000 1.000
#> GSM559449 3 0.0000 0.9006 0.000 0.000 1.000
#> GSM559453 3 0.0000 0.9006 0.000 0.000 1.000
#> GSM559466 3 0.0000 0.9006 0.000 0.000 1.000
#> GSM559474 3 0.0000 0.9006 0.000 0.000 1.000
#> GSM559476 3 0.6045 0.3865 0.380 0.000 0.620
#> GSM559483 2 0.0000 0.8949 0.000 1.000 0.000
#> GSM559484 3 0.1964 0.8567 0.000 0.056 0.944
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.1118 0.851 0.964 0.000 0.036 0.000
#> GSM559434 2 0.0817 0.945 0.000 0.976 0.000 0.024
#> GSM559436 1 0.4955 0.390 0.556 0.000 0.444 0.000
#> GSM559437 1 0.1792 0.799 0.932 0.000 0.000 0.068
#> GSM559438 2 0.2275 0.899 0.048 0.928 0.004 0.020
#> GSM559440 2 0.0895 0.946 0.004 0.976 0.000 0.020
#> GSM559441 1 0.1174 0.832 0.968 0.012 0.000 0.020
#> GSM559442 3 0.7560 0.331 0.172 0.216 0.584 0.028
#> GSM559444 2 0.0921 0.944 0.000 0.972 0.000 0.028
#> GSM559445 4 0.5663 0.292 0.440 0.024 0.000 0.536
#> GSM559446 1 0.4961 -0.151 0.552 0.000 0.000 0.448
#> GSM559448 3 0.1369 0.781 0.016 0.004 0.964 0.016
#> GSM559450 2 0.1022 0.942 0.000 0.968 0.000 0.032
#> GSM559451 1 0.0921 0.851 0.972 0.000 0.028 0.000
#> GSM559452 2 0.2546 0.899 0.000 0.912 0.028 0.060
#> GSM559454 1 0.2814 0.836 0.868 0.000 0.132 0.000
#> GSM559455 1 0.0336 0.841 0.992 0.000 0.000 0.008
#> GSM559456 1 0.0524 0.846 0.988 0.000 0.008 0.004
#> GSM559457 1 0.0188 0.843 0.996 0.000 0.000 0.004
#> GSM559458 4 0.6141 0.553 0.300 0.000 0.076 0.624
#> GSM559459 1 0.2281 0.846 0.904 0.000 0.096 0.000
#> GSM559460 1 0.2149 0.848 0.912 0.000 0.088 0.000
#> GSM559461 1 0.2973 0.831 0.856 0.000 0.144 0.000
#> GSM559462 1 0.0188 0.843 0.996 0.000 0.000 0.004
#> GSM559463 3 0.1863 0.762 0.040 0.004 0.944 0.012
#> GSM559464 1 0.3486 0.807 0.812 0.000 0.188 0.000
#> GSM559465 1 0.3688 0.790 0.792 0.000 0.208 0.000
#> GSM559467 1 0.0524 0.841 0.988 0.004 0.000 0.008
#> GSM559468 1 0.3591 0.817 0.824 0.000 0.168 0.008
#> GSM559469 2 0.6460 0.468 0.268 0.648 0.056 0.028
#> GSM559470 1 0.1182 0.832 0.968 0.016 0.000 0.016
#> GSM559471 1 0.5322 0.758 0.752 0.036 0.188 0.024
#> GSM559472 1 0.3356 0.813 0.824 0.000 0.176 0.000
#> GSM559473 2 0.0524 0.945 0.000 0.988 0.004 0.008
#> GSM559475 2 0.0469 0.948 0.000 0.988 0.000 0.012
#> GSM559477 2 0.0336 0.948 0.000 0.992 0.000 0.008
#> GSM559478 2 0.0524 0.945 0.000 0.988 0.004 0.008
#> GSM559479 2 0.0592 0.947 0.000 0.984 0.000 0.016
#> GSM559480 2 0.1151 0.936 0.000 0.968 0.008 0.024
#> GSM559481 2 0.1004 0.939 0.000 0.972 0.004 0.024
#> GSM559482 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM559435 3 0.2081 0.790 0.000 0.000 0.916 0.084
#> GSM559439 3 0.1792 0.795 0.000 0.000 0.932 0.068
#> GSM559443 3 0.0672 0.797 0.008 0.000 0.984 0.008
#> GSM559447 3 0.3311 0.730 0.000 0.000 0.828 0.172
#> GSM559449 3 0.4761 0.453 0.000 0.000 0.628 0.372
#> GSM559453 4 0.3688 0.485 0.000 0.000 0.208 0.792
#> GSM559466 3 0.3569 0.711 0.000 0.000 0.804 0.196
#> GSM559474 4 0.1488 0.649 0.000 0.012 0.032 0.956
#> GSM559476 3 0.0524 0.797 0.004 0.000 0.988 0.008
#> GSM559483 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM559484 4 0.1624 0.648 0.000 0.020 0.028 0.952
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 4 0.4074 0.6859 0.364 0.000 0.000 0.636 0.000
#> GSM559434 2 0.4538 0.7601 0.004 0.724 0.000 0.044 0.228
#> GSM559436 4 0.6908 0.2493 0.276 0.000 0.340 0.380 0.004
#> GSM559437 4 0.3343 0.6885 0.172 0.000 0.000 0.812 0.016
#> GSM559438 2 0.5944 0.6821 0.108 0.636 0.000 0.024 0.232
#> GSM559440 2 0.5484 0.7269 0.016 0.664 0.000 0.080 0.240
#> GSM559441 4 0.4095 0.7131 0.220 0.004 0.000 0.752 0.024
#> GSM559442 1 0.5306 0.5004 0.748 0.064 0.096 0.004 0.088
#> GSM559444 2 0.5389 0.7223 0.004 0.660 0.000 0.100 0.236
#> GSM559445 4 0.2692 0.4512 0.016 0.008 0.000 0.884 0.092
#> GSM559446 4 0.2438 0.5508 0.040 0.000 0.000 0.900 0.060
#> GSM559448 3 0.1748 0.8815 0.028 0.016 0.944 0.008 0.004
#> GSM559450 2 0.5013 0.7376 0.000 0.680 0.000 0.080 0.240
#> GSM559451 4 0.4586 0.6967 0.336 0.000 0.016 0.644 0.004
#> GSM559452 5 0.6576 0.2237 0.192 0.172 0.004 0.032 0.600
#> GSM559454 1 0.5490 0.0320 0.592 0.000 0.084 0.324 0.000
#> GSM559455 4 0.3752 0.7305 0.292 0.000 0.000 0.708 0.000
#> GSM559456 4 0.3999 0.7115 0.344 0.000 0.000 0.656 0.000
#> GSM559457 4 0.3932 0.7253 0.328 0.000 0.000 0.672 0.000
#> GSM559458 1 0.7603 -0.3120 0.380 0.000 0.052 0.224 0.344
#> GSM559459 1 0.4644 0.2524 0.680 0.000 0.040 0.280 0.000
#> GSM559460 1 0.1502 0.6631 0.940 0.000 0.004 0.056 0.000
#> GSM559461 1 0.2300 0.6556 0.904 0.000 0.024 0.072 0.000
#> GSM559462 4 0.4273 0.5698 0.448 0.000 0.000 0.552 0.000
#> GSM559463 3 0.3177 0.6812 0.208 0.000 0.792 0.000 0.000
#> GSM559464 1 0.1549 0.6695 0.944 0.000 0.016 0.040 0.000
#> GSM559465 1 0.2362 0.6532 0.900 0.000 0.024 0.076 0.000
#> GSM559467 4 0.5924 0.4977 0.376 0.096 0.000 0.524 0.004
#> GSM559468 1 0.0693 0.6663 0.980 0.000 0.008 0.000 0.012
#> GSM559469 1 0.3885 0.5241 0.784 0.176 0.000 0.000 0.040
#> GSM559470 4 0.4252 0.7171 0.340 0.008 0.000 0.652 0.000
#> GSM559471 1 0.1243 0.6613 0.960 0.028 0.008 0.004 0.000
#> GSM559472 1 0.5373 0.0934 0.620 0.000 0.084 0.296 0.000
#> GSM559473 2 0.0671 0.8311 0.016 0.980 0.000 0.000 0.004
#> GSM559475 2 0.1673 0.8177 0.032 0.944 0.000 0.008 0.016
#> GSM559477 2 0.0566 0.8325 0.000 0.984 0.000 0.004 0.012
#> GSM559478 2 0.1787 0.8167 0.032 0.940 0.000 0.012 0.016
#> GSM559479 2 0.3628 0.7792 0.000 0.772 0.000 0.012 0.216
#> GSM559480 2 0.1756 0.8165 0.036 0.940 0.000 0.008 0.016
#> GSM559481 2 0.1588 0.8195 0.028 0.948 0.000 0.008 0.016
#> GSM559482 2 0.0000 0.8322 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.0693 0.8904 0.012 0.000 0.980 0.000 0.008
#> GSM559439 3 0.0671 0.8913 0.016 0.000 0.980 0.000 0.004
#> GSM559443 3 0.1121 0.8839 0.044 0.000 0.956 0.000 0.000
#> GSM559447 3 0.1282 0.8722 0.004 0.000 0.952 0.000 0.044
#> GSM559449 3 0.3141 0.7381 0.000 0.000 0.832 0.016 0.152
#> GSM559453 5 0.6350 0.1631 0.000 0.000 0.420 0.160 0.420
#> GSM559466 3 0.1638 0.8522 0.000 0.000 0.932 0.004 0.064
#> GSM559474 5 0.4302 0.6581 0.000 0.000 0.048 0.208 0.744
#> GSM559476 3 0.1768 0.8721 0.072 0.000 0.924 0.000 0.004
#> GSM559483 2 0.0324 0.8323 0.004 0.992 0.000 0.000 0.004
#> GSM559484 5 0.4302 0.6581 0.000 0.000 0.048 0.208 0.744
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 4 0.4239 0.72331 0.092 0.000 0.024 0.796 0.028 0.060
#> GSM559434 6 0.3014 0.77748 0.000 0.184 0.000 0.012 0.000 0.804
#> GSM559436 4 0.7360 0.40477 0.184 0.024 0.236 0.488 0.024 0.044
#> GSM559437 4 0.1492 0.75037 0.000 0.000 0.000 0.940 0.024 0.036
#> GSM559438 6 0.4418 0.76759 0.072 0.144 0.000 0.024 0.004 0.756
#> GSM559440 6 0.2320 0.80153 0.000 0.080 0.000 0.024 0.004 0.892
#> GSM559441 4 0.2462 0.72305 0.000 0.004 0.000 0.860 0.004 0.132
#> GSM559442 1 0.2462 0.70283 0.860 0.000 0.004 0.000 0.004 0.132
#> GSM559444 6 0.2625 0.77539 0.000 0.072 0.000 0.056 0.000 0.872
#> GSM559445 4 0.4290 0.64947 0.000 0.008 0.000 0.736 0.076 0.180
#> GSM559446 4 0.4222 0.69512 0.004 0.000 0.000 0.748 0.116 0.132
#> GSM559448 3 0.2169 0.79016 0.012 0.060 0.912 0.004 0.004 0.008
#> GSM559450 6 0.2302 0.80201 0.000 0.120 0.000 0.008 0.000 0.872
#> GSM559451 4 0.5227 0.57951 0.216 0.000 0.024 0.672 0.012 0.076
#> GSM559452 6 0.5547 0.35604 0.200 0.004 0.004 0.000 0.196 0.596
#> GSM559454 1 0.5814 0.32607 0.552 0.000 0.044 0.344 0.024 0.036
#> GSM559455 4 0.0748 0.75649 0.004 0.004 0.000 0.976 0.000 0.016
#> GSM559456 4 0.3219 0.71167 0.112 0.000 0.000 0.836 0.012 0.040
#> GSM559457 4 0.1036 0.76174 0.024 0.000 0.000 0.964 0.004 0.008
#> GSM559458 5 0.5709 0.49406 0.292 0.000 0.024 0.024 0.596 0.064
#> GSM559459 1 0.5026 0.54462 0.664 0.000 0.028 0.260 0.020 0.028
#> GSM559460 1 0.1405 0.80010 0.948 0.000 0.000 0.024 0.004 0.024
#> GSM559461 1 0.2367 0.79590 0.900 0.000 0.012 0.064 0.004 0.020
#> GSM559462 4 0.4569 0.21743 0.396 0.000 0.000 0.564 0.000 0.040
#> GSM559463 3 0.5088 -0.00132 0.452 0.000 0.496 0.008 0.028 0.016
#> GSM559464 1 0.1321 0.80008 0.952 0.000 0.000 0.024 0.004 0.020
#> GSM559465 1 0.1745 0.79303 0.920 0.000 0.000 0.068 0.000 0.012
#> GSM559467 2 0.6323 0.04642 0.140 0.492 0.000 0.332 0.012 0.024
#> GSM559468 1 0.1410 0.77643 0.944 0.000 0.000 0.004 0.008 0.044
#> GSM559469 1 0.0717 0.78569 0.976 0.000 0.000 0.000 0.008 0.016
#> GSM559470 4 0.3494 0.75103 0.076 0.024 0.000 0.836 0.004 0.060
#> GSM559471 1 0.1282 0.79981 0.956 0.004 0.000 0.024 0.012 0.004
#> GSM559472 1 0.4860 0.35346 0.584 0.008 0.004 0.372 0.008 0.024
#> GSM559473 2 0.2378 0.75041 0.000 0.848 0.000 0.000 0.000 0.152
#> GSM559475 2 0.0363 0.78581 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM559477 2 0.2941 0.68582 0.000 0.780 0.000 0.000 0.000 0.220
#> GSM559478 2 0.0146 0.78393 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM559479 6 0.3428 0.62559 0.000 0.304 0.000 0.000 0.000 0.696
#> GSM559480 2 0.0436 0.78436 0.004 0.988 0.000 0.000 0.004 0.004
#> GSM559481 2 0.0436 0.78000 0.004 0.988 0.004 0.000 0.004 0.000
#> GSM559482 2 0.2597 0.73460 0.000 0.824 0.000 0.000 0.000 0.176
#> GSM559435 3 0.0146 0.82279 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM559439 3 0.0291 0.82256 0.004 0.000 0.992 0.000 0.000 0.004
#> GSM559443 3 0.1313 0.81019 0.016 0.000 0.952 0.000 0.028 0.004
#> GSM559447 3 0.0790 0.81850 0.000 0.000 0.968 0.000 0.032 0.000
#> GSM559449 3 0.2048 0.77177 0.000 0.000 0.880 0.000 0.120 0.000
#> GSM559453 3 0.3659 0.42951 0.000 0.000 0.636 0.000 0.364 0.000
#> GSM559466 3 0.1387 0.80577 0.000 0.000 0.932 0.000 0.068 0.000
#> GSM559474 5 0.1007 0.78302 0.000 0.000 0.044 0.000 0.956 0.000
#> GSM559476 3 0.2056 0.78915 0.080 0.004 0.904 0.000 0.012 0.000
#> GSM559483 2 0.2854 0.70195 0.000 0.792 0.000 0.000 0.000 0.208
#> GSM559484 5 0.1007 0.78302 0.000 0.000 0.044 0.000 0.956 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 disease.state(p) k
#> MAD:NMF 51 2.06e-01 2
#> MAD:NMF 46 3.44e-08 3
#> MAD:NMF 45 1.14e-05 4
#> MAD:NMF 43 7.53e-06 5
#> MAD:NMF 43 3.44e-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["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 21512 rows and 52 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.481 0.0879 0.599 0.4131 0.683 0.683
#> 3 3 0.466 0.5902 0.808 0.2665 0.607 0.509
#> 4 4 0.484 0.7007 0.731 0.1734 0.756 0.534
#> 5 5 0.634 0.6947 0.858 0.1523 0.956 0.848
#> 6 6 0.639 0.6645 0.800 0.0725 0.989 0.957
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM559433 1 0.998 -0.90186 0.524 0.476
#> GSM559434 2 1.000 1.00000 0.488 0.512
#> GSM559436 1 0.000 0.30476 1.000 0.000
#> GSM559437 1 0.000 0.30476 1.000 0.000
#> GSM559438 1 0.697 0.00519 0.812 0.188
#> GSM559440 1 0.697 0.00519 0.812 0.188
#> GSM559441 1 0.994 -0.86218 0.544 0.456
#> GSM559442 1 0.000 0.30476 1.000 0.000
#> GSM559444 1 0.141 0.28600 0.980 0.020
#> GSM559445 2 1.000 1.00000 0.488 0.512
#> GSM559446 1 0.697 0.00519 0.812 0.188
#> GSM559448 2 1.000 1.00000 0.488 0.512
#> GSM559450 1 0.141 0.28600 0.980 0.020
#> GSM559451 1 0.697 0.00519 0.812 0.188
#> GSM559452 1 0.697 0.00519 0.812 0.188
#> GSM559454 1 0.998 -0.90186 0.524 0.476
#> GSM559455 1 0.998 -0.90186 0.524 0.476
#> GSM559456 2 1.000 1.00000 0.488 0.512
#> GSM559457 2 1.000 1.00000 0.488 0.512
#> GSM559458 2 1.000 1.00000 0.488 0.512
#> GSM559459 1 0.996 0.37494 0.536 0.464
#> GSM559460 1 0.998 -0.90186 0.524 0.476
#> GSM559461 1 0.697 0.00519 0.812 0.188
#> GSM559462 1 1.000 0.37583 0.512 0.488
#> GSM559463 1 1.000 0.37583 0.512 0.488
#> GSM559464 1 0.000 0.30476 1.000 0.000
#> GSM559465 1 0.998 -0.90186 0.524 0.476
#> GSM559467 1 0.000 0.30476 1.000 0.000
#> GSM559468 1 0.644 0.05665 0.836 0.164
#> GSM559469 2 1.000 1.00000 0.488 0.512
#> GSM559470 1 0.998 -0.90186 0.524 0.476
#> GSM559471 1 0.000 0.30476 1.000 0.000
#> GSM559472 2 1.000 1.00000 0.488 0.512
#> GSM559473 1 0.697 0.00519 0.812 0.188
#> GSM559475 1 0.963 -0.67773 0.612 0.388
#> GSM559477 1 1.000 0.37583 0.512 0.488
#> GSM559478 1 0.999 0.37626 0.516 0.484
#> GSM559479 1 1.000 0.37583 0.512 0.488
#> GSM559480 1 1.000 0.37583 0.512 0.488
#> GSM559481 1 0.999 0.37626 0.516 0.484
#> GSM559482 1 1.000 0.37583 0.512 0.488
#> GSM559435 1 0.998 -0.90186 0.524 0.476
#> GSM559439 1 0.998 -0.90186 0.524 0.476
#> GSM559443 1 0.000 0.30476 1.000 0.000
#> GSM559447 1 0.998 -0.90186 0.524 0.476
#> GSM559449 2 1.000 1.00000 0.488 0.512
#> GSM559453 1 0.998 -0.90186 0.524 0.476
#> GSM559466 1 0.998 -0.90186 0.524 0.476
#> GSM559474 2 1.000 1.00000 0.488 0.512
#> GSM559476 1 0.998 -0.90186 0.524 0.476
#> GSM559483 1 1.000 0.37583 0.512 0.488
#> GSM559484 1 0.999 0.37626 0.516 0.484
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.5465 0.560 0.712 0.000 0.288
#> GSM559434 1 0.5948 0.429 0.640 0.000 0.360
#> GSM559436 1 0.4897 0.502 0.812 0.172 0.016
#> GSM559437 1 0.4897 0.502 0.812 0.172 0.016
#> GSM559438 1 0.0000 0.609 1.000 0.000 0.000
#> GSM559440 1 0.0000 0.609 1.000 0.000 0.000
#> GSM559441 1 0.5291 0.566 0.732 0.000 0.268
#> GSM559442 1 0.4897 0.502 0.812 0.172 0.016
#> GSM559444 1 0.4121 0.514 0.832 0.168 0.000
#> GSM559445 3 0.5835 0.578 0.340 0.000 0.660
#> GSM559446 1 0.0000 0.609 1.000 0.000 0.000
#> GSM559448 1 0.5948 0.429 0.640 0.000 0.360
#> GSM559450 1 0.4121 0.514 0.832 0.168 0.000
#> GSM559451 1 0.0000 0.609 1.000 0.000 0.000
#> GSM559452 1 0.0000 0.609 1.000 0.000 0.000
#> GSM559454 1 0.5465 0.560 0.712 0.000 0.288
#> GSM559455 1 0.5465 0.560 0.712 0.000 0.288
#> GSM559456 3 0.5835 0.578 0.340 0.000 0.660
#> GSM559457 1 0.6308 -0.104 0.508 0.000 0.492
#> GSM559458 3 0.5835 0.520 0.340 0.000 0.660
#> GSM559459 2 0.2804 0.832 0.060 0.924 0.016
#> GSM559460 1 0.5465 0.560 0.712 0.000 0.288
#> GSM559461 1 0.0000 0.609 1.000 0.000 0.000
#> GSM559462 2 0.0000 0.871 0.000 1.000 0.000
#> GSM559463 2 0.0000 0.871 0.000 1.000 0.000
#> GSM559464 1 0.4897 0.502 0.812 0.172 0.016
#> GSM559465 1 0.5465 0.560 0.712 0.000 0.288
#> GSM559467 1 0.4897 0.502 0.812 0.172 0.016
#> GSM559468 1 0.1170 0.597 0.976 0.008 0.016
#> GSM559469 1 0.5948 0.429 0.640 0.000 0.360
#> GSM559470 1 0.5497 0.555 0.708 0.000 0.292
#> GSM559471 1 0.4897 0.502 0.812 0.172 0.016
#> GSM559472 1 0.5948 0.429 0.640 0.000 0.360
#> GSM559473 1 0.0000 0.609 1.000 0.000 0.000
#> GSM559475 1 0.4555 0.580 0.800 0.000 0.200
#> GSM559477 2 0.0000 0.871 0.000 1.000 0.000
#> GSM559478 2 0.5760 0.664 0.328 0.672 0.000
#> GSM559479 2 0.0000 0.871 0.000 1.000 0.000
#> GSM559480 2 0.0000 0.871 0.000 1.000 0.000
#> GSM559481 2 0.5760 0.664 0.328 0.672 0.000
#> GSM559482 2 0.0000 0.871 0.000 1.000 0.000
#> GSM559435 1 0.5465 0.560 0.712 0.000 0.288
#> GSM559439 1 0.5465 0.560 0.712 0.000 0.288
#> GSM559443 1 0.4897 0.502 0.812 0.172 0.016
#> GSM559447 1 0.5465 0.560 0.712 0.000 0.288
#> GSM559449 3 0.0747 0.612 0.016 0.000 0.984
#> GSM559453 1 0.5465 0.560 0.712 0.000 0.288
#> GSM559466 1 0.5465 0.560 0.712 0.000 0.288
#> GSM559474 3 0.0747 0.612 0.016 0.000 0.984
#> GSM559476 1 0.5465 0.560 0.712 0.000 0.288
#> GSM559483 2 0.0000 0.871 0.000 1.000 0.000
#> GSM559484 2 0.5760 0.664 0.328 0.672 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.454 0.9144 0.676 0.000 0.000 0.324
#> GSM559434 1 0.649 0.8337 0.604 0.000 0.104 0.292
#> GSM559436 4 0.000 0.7641 0.000 0.000 0.000 1.000
#> GSM559437 4 0.000 0.7641 0.000 0.000 0.000 1.000
#> GSM559438 4 0.401 0.6780 0.244 0.000 0.000 0.756
#> GSM559440 4 0.401 0.6780 0.244 0.000 0.000 0.756
#> GSM559441 1 0.475 0.8332 0.632 0.000 0.000 0.368
#> GSM559442 4 0.000 0.7641 0.000 0.000 0.000 1.000
#> GSM559444 4 0.139 0.7629 0.048 0.000 0.000 0.952
#> GSM559445 3 0.687 0.6015 0.264 0.000 0.584 0.152
#> GSM559446 4 0.398 0.6829 0.240 0.000 0.000 0.760
#> GSM559448 1 0.649 0.8337 0.604 0.000 0.104 0.292
#> GSM559450 4 0.139 0.7629 0.048 0.000 0.000 0.952
#> GSM559451 4 0.398 0.6829 0.240 0.000 0.000 0.760
#> GSM559452 4 0.401 0.6780 0.244 0.000 0.000 0.756
#> GSM559454 1 0.454 0.9144 0.676 0.000 0.000 0.324
#> GSM559455 1 0.454 0.9144 0.676 0.000 0.000 0.324
#> GSM559456 3 0.687 0.6015 0.264 0.000 0.584 0.152
#> GSM559457 1 0.752 -0.0156 0.412 0.000 0.404 0.184
#> GSM559458 3 0.701 0.5232 0.240 0.000 0.576 0.184
#> GSM559459 2 0.736 0.5183 0.320 0.500 0.000 0.180
#> GSM559460 1 0.454 0.9144 0.676 0.000 0.000 0.324
#> GSM559461 4 0.398 0.6829 0.240 0.000 0.000 0.760
#> GSM559462 2 0.454 0.5771 0.324 0.676 0.000 0.000
#> GSM559463 2 0.454 0.5771 0.324 0.676 0.000 0.000
#> GSM559464 4 0.000 0.7641 0.000 0.000 0.000 1.000
#> GSM559465 1 0.454 0.9144 0.676 0.000 0.000 0.324
#> GSM559467 4 0.000 0.7641 0.000 0.000 0.000 1.000
#> GSM559468 4 0.349 0.7068 0.188 0.000 0.000 0.812
#> GSM559469 1 0.649 0.8337 0.604 0.000 0.104 0.292
#> GSM559470 1 0.470 0.9113 0.676 0.000 0.004 0.320
#> GSM559471 4 0.000 0.7641 0.000 0.000 0.000 1.000
#> GSM559472 1 0.649 0.8337 0.604 0.000 0.104 0.292
#> GSM559473 4 0.401 0.6780 0.244 0.000 0.000 0.756
#> GSM559475 4 0.497 -0.2120 0.452 0.000 0.000 0.548
#> GSM559477 2 0.000 0.7039 0.000 1.000 0.000 0.000
#> GSM559478 2 0.500 0.4208 0.000 0.504 0.000 0.496
#> GSM559479 2 0.000 0.7039 0.000 1.000 0.000 0.000
#> GSM559480 2 0.000 0.7039 0.000 1.000 0.000 0.000
#> GSM559481 2 0.500 0.4208 0.000 0.504 0.000 0.496
#> GSM559482 2 0.000 0.7039 0.000 1.000 0.000 0.000
#> GSM559435 1 0.454 0.9144 0.676 0.000 0.000 0.324
#> GSM559439 1 0.454 0.9144 0.676 0.000 0.000 0.324
#> GSM559443 4 0.000 0.7641 0.000 0.000 0.000 1.000
#> GSM559447 1 0.454 0.9144 0.676 0.000 0.000 0.324
#> GSM559449 3 0.000 0.5028 0.000 0.000 1.000 0.000
#> GSM559453 1 0.454 0.9144 0.676 0.000 0.000 0.324
#> GSM559466 1 0.454 0.9144 0.676 0.000 0.000 0.324
#> GSM559474 3 0.000 0.5028 0.000 0.000 1.000 0.000
#> GSM559476 1 0.454 0.9144 0.676 0.000 0.000 0.324
#> GSM559483 2 0.000 0.7039 0.000 1.000 0.000 0.000
#> GSM559484 2 0.500 0.4208 0.000 0.504 0.000 0.496
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 3 0.0000 0.8589 0.000 0.000 1.000 0.000 0.000
#> GSM559434 3 0.2074 0.7865 0.000 0.000 0.896 0.000 0.104
#> GSM559436 4 0.0000 0.7779 0.000 0.000 0.000 1.000 0.000
#> GSM559437 4 0.0000 0.7779 0.000 0.000 0.000 1.000 0.000
#> GSM559438 4 0.4163 0.7723 0.032 0.000 0.228 0.740 0.000
#> GSM559440 4 0.4163 0.7723 0.032 0.000 0.228 0.740 0.000
#> GSM559441 3 0.3577 0.6253 0.032 0.000 0.808 0.160 0.000
#> GSM559442 4 0.0000 0.7779 0.000 0.000 0.000 1.000 0.000
#> GSM559444 4 0.1478 0.7887 0.000 0.000 0.064 0.936 0.000
#> GSM559445 5 0.4219 0.5997 0.000 0.000 0.416 0.000 0.584
#> GSM559446 4 0.4541 0.7208 0.032 0.000 0.288 0.680 0.000
#> GSM559448 3 0.2074 0.7865 0.000 0.000 0.896 0.000 0.104
#> GSM559450 4 0.1478 0.7887 0.000 0.000 0.064 0.936 0.000
#> GSM559451 4 0.4541 0.7208 0.032 0.000 0.288 0.680 0.000
#> GSM559452 4 0.4163 0.7723 0.032 0.000 0.228 0.740 0.000
#> GSM559454 3 0.0000 0.8589 0.000 0.000 1.000 0.000 0.000
#> GSM559455 3 0.0000 0.8589 0.000 0.000 1.000 0.000 0.000
#> GSM559456 5 0.4219 0.5997 0.000 0.000 0.416 0.000 0.584
#> GSM559457 3 0.4192 -0.0682 0.000 0.000 0.596 0.000 0.404
#> GSM559458 5 0.4235 0.5243 0.000 0.000 0.424 0.000 0.576
#> GSM559459 1 0.3368 0.7269 0.820 0.024 0.000 0.156 0.000
#> GSM559460 3 0.0000 0.8589 0.000 0.000 1.000 0.000 0.000
#> GSM559461 4 0.4541 0.7208 0.032 0.000 0.288 0.680 0.000
#> GSM559462 1 0.3336 0.7542 0.772 0.228 0.000 0.000 0.000
#> GSM559463 1 0.1792 0.8136 0.916 0.084 0.000 0.000 0.000
#> GSM559464 4 0.0000 0.7779 0.000 0.000 0.000 1.000 0.000
#> GSM559465 3 0.0880 0.8491 0.032 0.000 0.968 0.000 0.000
#> GSM559467 4 0.0000 0.7779 0.000 0.000 0.000 1.000 0.000
#> GSM559468 4 0.3536 0.7799 0.032 0.000 0.156 0.812 0.000
#> GSM559469 3 0.2074 0.7865 0.000 0.000 0.896 0.000 0.104
#> GSM559470 3 0.0162 0.8578 0.000 0.000 0.996 0.000 0.004
#> GSM559471 4 0.0000 0.7779 0.000 0.000 0.000 1.000 0.000
#> GSM559472 3 0.2074 0.7865 0.000 0.000 0.896 0.000 0.104
#> GSM559473 4 0.4163 0.7723 0.032 0.000 0.228 0.740 0.000
#> GSM559475 3 0.5028 -0.1439 0.032 0.000 0.524 0.444 0.000
#> GSM559477 2 0.0000 0.6341 0.000 1.000 0.000 0.000 0.000
#> GSM559478 2 0.4904 0.4342 0.024 0.504 0.000 0.472 0.000
#> GSM559479 2 0.0000 0.6341 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.0000 0.6341 0.000 1.000 0.000 0.000 0.000
#> GSM559481 2 0.4904 0.4342 0.024 0.504 0.000 0.472 0.000
#> GSM559482 2 0.0000 0.6341 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.8589 0.000 0.000 1.000 0.000 0.000
#> GSM559439 3 0.0880 0.8491 0.032 0.000 0.968 0.000 0.000
#> GSM559443 4 0.0000 0.7779 0.000 0.000 0.000 1.000 0.000
#> GSM559447 3 0.0880 0.8491 0.032 0.000 0.968 0.000 0.000
#> GSM559449 5 0.0794 0.3684 0.028 0.000 0.000 0.000 0.972
#> GSM559453 3 0.0880 0.8491 0.032 0.000 0.968 0.000 0.000
#> GSM559466 3 0.0000 0.8589 0.000 0.000 1.000 0.000 0.000
#> GSM559474 5 0.0000 0.3902 0.000 0.000 0.000 0.000 1.000
#> GSM559476 3 0.0510 0.8554 0.016 0.000 0.984 0.000 0.000
#> GSM559483 2 0.0000 0.6341 0.000 1.000 0.000 0.000 0.000
#> GSM559484 2 0.4904 0.4342 0.024 0.504 0.000 0.472 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 3 0.0260 0.7767 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM559434 3 0.2118 0.7088 0.000 0.000 0.888 0.104 0.008 0.000
#> GSM559436 6 0.2416 0.6402 0.000 0.000 0.000 0.000 0.156 0.844
#> GSM559437 6 0.2416 0.6402 0.000 0.000 0.000 0.000 0.156 0.844
#> GSM559438 6 0.4873 0.5831 0.000 0.000 0.080 0.000 0.320 0.600
#> GSM559440 6 0.4873 0.5831 0.000 0.000 0.080 0.000 0.320 0.600
#> GSM559441 3 0.3482 0.5088 0.000 0.000 0.684 0.000 0.000 0.316
#> GSM559442 6 0.2416 0.6402 0.000 0.000 0.000 0.000 0.156 0.844
#> GSM559444 6 0.4651 0.5641 0.000 0.000 0.040 0.000 0.476 0.484
#> GSM559445 4 0.4010 0.5740 0.000 0.000 0.408 0.584 0.008 0.000
#> GSM559446 6 0.2859 0.6240 0.000 0.000 0.156 0.000 0.016 0.828
#> GSM559448 3 0.2118 0.7088 0.000 0.000 0.888 0.104 0.008 0.000
#> GSM559450 6 0.4651 0.5641 0.000 0.000 0.040 0.000 0.476 0.484
#> GSM559451 6 0.2859 0.6240 0.000 0.000 0.156 0.000 0.016 0.828
#> GSM559452 6 0.4873 0.5831 0.000 0.000 0.080 0.000 0.320 0.600
#> GSM559454 3 0.0000 0.7809 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559455 3 0.0000 0.7809 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559456 4 0.4010 0.5740 0.000 0.000 0.408 0.584 0.008 0.000
#> GSM559457 3 0.4002 -0.1910 0.000 0.000 0.588 0.404 0.008 0.000
#> GSM559458 4 0.3804 0.4686 0.000 0.000 0.424 0.576 0.000 0.000
#> GSM559459 1 0.3285 0.6942 0.820 0.000 0.000 0.000 0.116 0.064
#> GSM559460 3 0.0000 0.7809 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559461 6 0.2859 0.6240 0.000 0.000 0.156 0.000 0.016 0.828
#> GSM559462 1 0.2454 0.7397 0.840 0.160 0.000 0.000 0.000 0.000
#> GSM559463 1 0.0260 0.8010 0.992 0.008 0.000 0.000 0.000 0.000
#> GSM559464 6 0.2416 0.6402 0.000 0.000 0.000 0.000 0.156 0.844
#> GSM559465 3 0.2416 0.7114 0.000 0.000 0.844 0.000 0.000 0.156
#> GSM559467 6 0.2416 0.6402 0.000 0.000 0.000 0.000 0.156 0.844
#> GSM559468 6 0.0790 0.6477 0.000 0.000 0.032 0.000 0.000 0.968
#> GSM559469 3 0.2118 0.7088 0.000 0.000 0.888 0.104 0.008 0.000
#> GSM559470 3 0.0146 0.7801 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM559471 6 0.2416 0.6402 0.000 0.000 0.000 0.000 0.156 0.844
#> GSM559472 3 0.2118 0.7088 0.000 0.000 0.888 0.104 0.008 0.000
#> GSM559473 6 0.4873 0.5831 0.000 0.000 0.080 0.000 0.320 0.600
#> GSM559475 3 0.6108 -0.0826 0.000 0.000 0.376 0.000 0.320 0.304
#> GSM559477 2 0.0000 0.9320 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559478 5 0.5461 1.0000 0.004 0.308 0.000 0.000 0.556 0.132
#> GSM559479 2 0.0000 0.9320 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559480 2 0.2762 0.6617 0.000 0.804 0.000 0.000 0.196 0.000
#> GSM559481 5 0.5461 1.0000 0.004 0.308 0.000 0.000 0.556 0.132
#> GSM559482 2 0.0000 0.9320 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.7809 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559439 3 0.2416 0.7114 0.000 0.000 0.844 0.000 0.000 0.156
#> GSM559443 6 0.2416 0.6402 0.000 0.000 0.000 0.000 0.156 0.844
#> GSM559447 3 0.2416 0.7114 0.000 0.000 0.844 0.000 0.000 0.156
#> GSM559449 4 0.0858 0.3726 0.004 0.000 0.000 0.968 0.028 0.000
#> GSM559453 3 0.2416 0.7114 0.000 0.000 0.844 0.000 0.000 0.156
#> GSM559466 3 0.0000 0.7809 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559474 4 0.0000 0.3965 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM559476 3 0.3125 0.7059 0.000 0.000 0.836 0.000 0.084 0.080
#> GSM559483 2 0.0000 0.9320 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559484 5 0.5461 1.0000 0.004 0.308 0.000 0.000 0.556 0.132
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 disease.state(p) k
#> ATC:hclust 10 NA 2
#> ATC:hclust 47 0.623 3
#> ATC:hclust 47 0.121 4
#> ATC:hclust 45 0.163 5
#> ATC:hclust 47 0.272 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 21512 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.950 0.981 0.3657 0.638 0.638
#> 3 3 1.000 0.968 0.988 0.7471 0.684 0.518
#> 4 4 0.586 0.599 0.721 0.1180 0.790 0.488
#> 5 5 0.588 0.614 0.755 0.0765 0.922 0.718
#> 6 6 0.619 0.588 0.713 0.0405 0.961 0.835
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
#> GSM559433 1 0.000 0.984 1.000 0.000
#> GSM559434 1 0.000 0.984 1.000 0.000
#> GSM559436 1 0.000 0.984 1.000 0.000
#> GSM559437 1 0.000 0.984 1.000 0.000
#> GSM559438 1 0.000 0.984 1.000 0.000
#> GSM559440 1 0.000 0.984 1.000 0.000
#> GSM559441 1 0.000 0.984 1.000 0.000
#> GSM559442 2 0.969 0.315 0.396 0.604
#> GSM559444 1 0.000 0.984 1.000 0.000
#> GSM559445 1 0.000 0.984 1.000 0.000
#> GSM559446 1 0.000 0.984 1.000 0.000
#> GSM559448 1 0.000 0.984 1.000 0.000
#> GSM559450 1 0.000 0.984 1.000 0.000
#> GSM559451 1 0.000 0.984 1.000 0.000
#> GSM559452 1 0.000 0.984 1.000 0.000
#> GSM559454 1 0.000 0.984 1.000 0.000
#> GSM559455 1 0.000 0.984 1.000 0.000
#> GSM559456 1 0.000 0.984 1.000 0.000
#> GSM559457 1 0.000 0.984 1.000 0.000
#> GSM559458 1 0.000 0.984 1.000 0.000
#> GSM559459 2 0.000 0.963 0.000 1.000
#> GSM559460 1 0.000 0.984 1.000 0.000
#> GSM559461 1 0.000 0.984 1.000 0.000
#> GSM559462 2 0.000 0.963 0.000 1.000
#> GSM559463 2 0.000 0.963 0.000 1.000
#> GSM559464 1 0.881 0.558 0.700 0.300
#> GSM559465 1 0.000 0.984 1.000 0.000
#> GSM559467 1 0.000 0.984 1.000 0.000
#> GSM559468 1 0.000 0.984 1.000 0.000
#> GSM559469 1 0.000 0.984 1.000 0.000
#> GSM559470 1 0.000 0.984 1.000 0.000
#> GSM559471 1 0.881 0.558 0.700 0.300
#> GSM559472 1 0.000 0.984 1.000 0.000
#> GSM559473 1 0.000 0.984 1.000 0.000
#> GSM559475 1 0.000 0.984 1.000 0.000
#> GSM559477 2 0.000 0.963 0.000 1.000
#> GSM559478 2 0.000 0.963 0.000 1.000
#> GSM559479 2 0.000 0.963 0.000 1.000
#> GSM559480 2 0.000 0.963 0.000 1.000
#> GSM559481 2 0.000 0.963 0.000 1.000
#> GSM559482 2 0.000 0.963 0.000 1.000
#> GSM559435 1 0.000 0.984 1.000 0.000
#> GSM559439 1 0.000 0.984 1.000 0.000
#> GSM559443 1 0.000 0.984 1.000 0.000
#> GSM559447 1 0.000 0.984 1.000 0.000
#> GSM559449 1 0.000 0.984 1.000 0.000
#> GSM559453 1 0.000 0.984 1.000 0.000
#> GSM559466 1 0.000 0.984 1.000 0.000
#> GSM559474 1 0.000 0.984 1.000 0.000
#> GSM559476 1 0.000 0.984 1.000 0.000
#> GSM559483 2 0.000 0.963 0.000 1.000
#> GSM559484 2 0.000 0.963 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559434 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559436 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559437 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559438 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559440 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559441 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559442 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559444 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559445 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559446 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559448 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559450 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559451 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559452 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559454 3 0.0237 0.995 0.004 0.000 0.996
#> GSM559455 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559456 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559457 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559458 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559459 2 0.0000 0.953 0.000 1.000 0.000
#> GSM559460 1 0.0424 0.983 0.992 0.000 0.008
#> GSM559461 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559462 2 0.0000 0.953 0.000 1.000 0.000
#> GSM559463 2 0.0000 0.953 0.000 1.000 0.000
#> GSM559464 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559465 1 0.0424 0.983 0.992 0.000 0.008
#> GSM559467 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559468 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559469 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559470 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559471 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559472 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559473 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559475 1 0.0424 0.983 0.992 0.000 0.008
#> GSM559477 2 0.0000 0.953 0.000 1.000 0.000
#> GSM559478 2 0.0424 0.947 0.008 0.992 0.000
#> GSM559479 2 0.0000 0.953 0.000 1.000 0.000
#> GSM559480 2 0.0000 0.953 0.000 1.000 0.000
#> GSM559481 2 0.0000 0.953 0.000 1.000 0.000
#> GSM559482 2 0.0000 0.953 0.000 1.000 0.000
#> GSM559435 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559439 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559443 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559447 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559449 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559453 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559466 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559474 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559476 1 0.4555 0.744 0.800 0.000 0.200
#> GSM559483 2 0.0000 0.953 0.000 1.000 0.000
#> GSM559484 2 0.6126 0.339 0.400 0.600 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.3356 0.80647 0.824 0.000 0.176 0.000
#> GSM559434 1 0.1557 0.91893 0.944 0.000 0.056 0.000
#> GSM559436 4 0.3688 0.57521 0.000 0.000 0.208 0.792
#> GSM559437 4 0.3688 0.57521 0.000 0.000 0.208 0.792
#> GSM559438 4 0.4817 0.33531 0.000 0.000 0.388 0.612
#> GSM559440 4 0.4972 0.14546 0.000 0.000 0.456 0.544
#> GSM559441 3 0.4843 0.40784 0.000 0.000 0.604 0.396
#> GSM559442 4 0.0592 0.59802 0.000 0.000 0.016 0.984
#> GSM559444 4 0.2589 0.61303 0.000 0.000 0.116 0.884
#> GSM559445 1 0.0592 0.91879 0.984 0.000 0.016 0.000
#> GSM559446 4 0.4843 0.30342 0.000 0.000 0.396 0.604
#> GSM559448 1 0.1474 0.91964 0.948 0.000 0.052 0.000
#> GSM559450 4 0.2647 0.61136 0.000 0.000 0.120 0.880
#> GSM559451 4 0.4941 0.21844 0.000 0.000 0.436 0.564
#> GSM559452 3 0.5193 0.34086 0.008 0.000 0.580 0.412
#> GSM559454 3 0.4697 0.47169 0.356 0.000 0.644 0.000
#> GSM559455 3 0.4830 0.40916 0.392 0.000 0.608 0.000
#> GSM559456 1 0.0921 0.91708 0.972 0.000 0.028 0.000
#> GSM559457 1 0.0336 0.91805 0.992 0.000 0.008 0.000
#> GSM559458 1 0.2149 0.87496 0.912 0.000 0.088 0.000
#> GSM559459 2 0.7091 0.58680 0.000 0.508 0.136 0.356
#> GSM559460 3 0.6084 0.60959 0.120 0.000 0.676 0.204
#> GSM559461 4 0.4855 0.30453 0.000 0.000 0.400 0.600
#> GSM559462 2 0.2760 0.85019 0.000 0.872 0.128 0.000
#> GSM559463 2 0.4791 0.82685 0.000 0.784 0.136 0.080
#> GSM559464 4 0.1118 0.60332 0.000 0.000 0.036 0.964
#> GSM559465 3 0.6112 0.60275 0.096 0.000 0.656 0.248
#> GSM559467 4 0.2011 0.61894 0.000 0.000 0.080 0.920
#> GSM559468 4 0.4454 0.46111 0.000 0.000 0.308 0.692
#> GSM559469 1 0.1557 0.91893 0.944 0.000 0.056 0.000
#> GSM559470 1 0.3172 0.82481 0.840 0.000 0.160 0.000
#> GSM559471 4 0.0188 0.60101 0.000 0.000 0.004 0.996
#> GSM559472 1 0.1474 0.91964 0.948 0.000 0.052 0.000
#> GSM559473 4 0.4941 0.20222 0.000 0.000 0.436 0.564
#> GSM559475 3 0.5903 0.50491 0.052 0.000 0.616 0.332
#> GSM559477 2 0.0000 0.88342 0.000 1.000 0.000 0.000
#> GSM559478 4 0.5971 -0.32985 0.000 0.428 0.040 0.532
#> GSM559479 2 0.0000 0.88342 0.000 1.000 0.000 0.000
#> GSM559480 2 0.0000 0.88342 0.000 1.000 0.000 0.000
#> GSM559481 2 0.5599 0.65560 0.000 0.644 0.040 0.316
#> GSM559482 2 0.0000 0.88342 0.000 1.000 0.000 0.000
#> GSM559435 3 0.4972 0.21750 0.456 0.000 0.544 0.000
#> GSM559439 3 0.5298 0.47160 0.016 0.000 0.612 0.372
#> GSM559443 4 0.1792 0.60059 0.000 0.000 0.068 0.932
#> GSM559447 3 0.5746 0.51930 0.040 0.000 0.612 0.348
#> GSM559449 1 0.2216 0.87265 0.908 0.000 0.092 0.000
#> GSM559453 3 0.5615 0.50687 0.032 0.000 0.612 0.356
#> GSM559466 3 0.4746 0.45764 0.368 0.000 0.632 0.000
#> GSM559474 1 0.2216 0.87265 0.908 0.000 0.092 0.000
#> GSM559476 3 0.5144 0.58384 0.052 0.000 0.732 0.216
#> GSM559483 2 0.0000 0.88342 0.000 1.000 0.000 0.000
#> GSM559484 4 0.5614 -0.00659 0.000 0.304 0.044 0.652
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 1 0.3949 0.515 0.696 0.000 0.300 0.000 0.004
#> GSM559434 1 0.1484 0.835 0.944 0.000 0.048 0.000 0.008
#> GSM559436 4 0.4836 0.605 0.000 0.000 0.304 0.652 0.044
#> GSM559437 4 0.4836 0.605 0.000 0.000 0.304 0.652 0.044
#> GSM559438 4 0.2773 0.632 0.000 0.000 0.164 0.836 0.000
#> GSM559440 4 0.3522 0.587 0.004 0.000 0.212 0.780 0.004
#> GSM559441 3 0.2773 0.642 0.000 0.000 0.836 0.164 0.000
#> GSM559442 4 0.5611 -0.157 0.000 0.000 0.076 0.516 0.408
#> GSM559444 4 0.0912 0.566 0.000 0.000 0.012 0.972 0.016
#> GSM559445 1 0.2790 0.815 0.880 0.000 0.052 0.000 0.068
#> GSM559446 4 0.4511 0.589 0.000 0.000 0.356 0.628 0.016
#> GSM559448 1 0.1197 0.837 0.952 0.000 0.048 0.000 0.000
#> GSM559450 4 0.0912 0.571 0.000 0.000 0.016 0.972 0.012
#> GSM559451 4 0.3636 0.619 0.000 0.000 0.272 0.728 0.000
#> GSM559452 4 0.4936 0.141 0.012 0.000 0.412 0.564 0.012
#> GSM559454 3 0.5169 0.595 0.304 0.000 0.640 0.048 0.008
#> GSM559455 3 0.4440 0.564 0.324 0.000 0.660 0.012 0.004
#> GSM559456 1 0.4078 0.750 0.784 0.000 0.148 0.000 0.068
#> GSM559457 1 0.0912 0.836 0.972 0.000 0.012 0.000 0.016
#> GSM559458 1 0.4049 0.767 0.780 0.000 0.056 0.000 0.164
#> GSM559459 5 0.5864 0.589 0.000 0.220 0.016 0.124 0.640
#> GSM559460 3 0.4779 0.712 0.144 0.000 0.740 0.112 0.004
#> GSM559461 4 0.4482 0.593 0.000 0.000 0.348 0.636 0.016
#> GSM559462 2 0.4350 0.629 0.000 0.704 0.028 0.000 0.268
#> GSM559463 2 0.5083 0.323 0.000 0.540 0.028 0.004 0.428
#> GSM559464 4 0.6262 0.155 0.000 0.000 0.164 0.504 0.332
#> GSM559465 3 0.2914 0.719 0.052 0.000 0.872 0.076 0.000
#> GSM559467 4 0.2074 0.573 0.000 0.000 0.044 0.920 0.036
#> GSM559468 4 0.4400 0.623 0.000 0.000 0.308 0.672 0.020
#> GSM559469 1 0.1484 0.835 0.944 0.000 0.048 0.000 0.008
#> GSM559470 1 0.3093 0.721 0.824 0.000 0.168 0.000 0.008
#> GSM559471 4 0.4576 0.198 0.000 0.000 0.040 0.692 0.268
#> GSM559472 1 0.1197 0.837 0.952 0.000 0.048 0.000 0.000
#> GSM559473 4 0.3242 0.612 0.000 0.000 0.172 0.816 0.012
#> GSM559475 4 0.6178 -0.051 0.080 0.000 0.404 0.496 0.020
#> GSM559477 2 0.0000 0.855 0.000 1.000 0.000 0.000 0.000
#> GSM559478 5 0.6553 0.713 0.000 0.236 0.000 0.292 0.472
#> GSM559479 2 0.0000 0.855 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.0510 0.847 0.000 0.984 0.000 0.000 0.016
#> GSM559481 5 0.6281 0.560 0.000 0.388 0.000 0.152 0.460
#> GSM559482 2 0.0000 0.855 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.3932 0.541 0.328 0.000 0.672 0.000 0.000
#> GSM559439 3 0.2732 0.649 0.000 0.000 0.840 0.160 0.000
#> GSM559443 4 0.6066 0.444 0.000 0.000 0.240 0.572 0.188
#> GSM559447 3 0.2886 0.665 0.008 0.000 0.844 0.148 0.000
#> GSM559449 1 0.4333 0.749 0.752 0.000 0.060 0.000 0.188
#> GSM559453 3 0.2806 0.661 0.004 0.000 0.844 0.152 0.000
#> GSM559466 3 0.3266 0.707 0.200 0.000 0.796 0.004 0.000
#> GSM559474 1 0.4333 0.749 0.752 0.000 0.060 0.000 0.188
#> GSM559476 3 0.5232 0.666 0.060 0.000 0.744 0.084 0.112
#> GSM559483 2 0.0000 0.855 0.000 1.000 0.000 0.000 0.000
#> GSM559484 5 0.5956 0.573 0.000 0.108 0.000 0.416 0.476
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.3547 0.459 0.696 0.000 0.300 NA 0.000 0.000
#> GSM559434 1 0.0405 0.793 0.988 0.000 0.008 NA 0.000 0.000
#> GSM559436 6 0.6362 0.491 0.000 0.000 0.292 NA 0.128 0.516
#> GSM559437 6 0.6362 0.491 0.000 0.000 0.292 NA 0.128 0.516
#> GSM559438 6 0.2907 0.619 0.000 0.000 0.152 NA 0.000 0.828
#> GSM559440 6 0.3194 0.612 0.004 0.000 0.168 NA 0.000 0.808
#> GSM559441 3 0.2222 0.682 0.000 0.000 0.896 NA 0.012 0.084
#> GSM559442 5 0.5549 0.361 0.000 0.000 0.072 NA 0.584 0.304
#> GSM559444 6 0.2624 0.532 0.000 0.000 0.028 NA 0.068 0.884
#> GSM559445 1 0.4390 0.714 0.720 0.000 0.148 NA 0.000 0.000
#> GSM559446 6 0.5053 0.585 0.000 0.000 0.368 NA 0.056 0.564
#> GSM559448 1 0.0260 0.794 0.992 0.000 0.008 NA 0.000 0.000
#> GSM559450 6 0.2255 0.544 0.000 0.000 0.024 NA 0.044 0.908
#> GSM559451 6 0.3690 0.625 0.000 0.000 0.288 NA 0.012 0.700
#> GSM559452 6 0.4868 0.359 0.016 0.000 0.332 NA 0.000 0.608
#> GSM559454 3 0.4452 0.604 0.312 0.000 0.644 NA 0.000 0.040
#> GSM559455 3 0.3351 0.635 0.288 0.000 0.712 NA 0.000 0.000
#> GSM559456 1 0.4967 0.627 0.640 0.000 0.228 NA 0.000 0.000
#> GSM559457 1 0.0790 0.791 0.968 0.000 0.000 NA 0.000 0.000
#> GSM559458 1 0.3607 0.680 0.652 0.000 0.000 NA 0.000 0.000
#> GSM559459 5 0.3263 0.542 0.000 0.024 0.000 NA 0.836 0.028
#> GSM559460 3 0.3865 0.728 0.192 0.000 0.752 NA 0.000 0.056
#> GSM559461 6 0.4943 0.592 0.000 0.000 0.360 NA 0.056 0.576
#> GSM559462 2 0.6223 0.235 0.000 0.420 0.008 NA 0.252 0.000
#> GSM559463 5 0.6291 -0.188 0.000 0.284 0.008 NA 0.392 0.000
#> GSM559464 5 0.6367 0.103 0.000 0.000 0.172 NA 0.492 0.296
#> GSM559465 3 0.1261 0.748 0.024 0.000 0.952 NA 0.000 0.024
#> GSM559467 6 0.3820 0.495 0.000 0.000 0.064 NA 0.144 0.784
#> GSM559468 6 0.5398 0.576 0.000 0.000 0.324 NA 0.064 0.580
#> GSM559469 1 0.0405 0.793 0.988 0.000 0.008 NA 0.000 0.000
#> GSM559470 1 0.2513 0.693 0.852 0.000 0.140 NA 0.000 0.000
#> GSM559471 6 0.5503 -0.180 0.000 0.000 0.056 NA 0.428 0.484
#> GSM559472 1 0.0260 0.794 0.992 0.000 0.008 NA 0.000 0.000
#> GSM559473 6 0.3054 0.586 0.000 0.000 0.116 NA 0.004 0.840
#> GSM559475 6 0.6011 0.278 0.096 0.000 0.292 NA 0.004 0.560
#> GSM559477 2 0.0000 0.881 0.000 1.000 0.000 NA 0.000 0.000
#> GSM559478 5 0.4388 0.607 0.000 0.092 0.000 NA 0.732 0.168
#> GSM559479 2 0.0000 0.881 0.000 1.000 0.000 NA 0.000 0.000
#> GSM559480 2 0.0858 0.863 0.000 0.968 0.004 NA 0.028 0.000
#> GSM559481 5 0.4468 0.530 0.000 0.184 0.000 NA 0.720 0.088
#> GSM559482 2 0.0000 0.881 0.000 1.000 0.000 NA 0.000 0.000
#> GSM559435 3 0.3390 0.613 0.296 0.000 0.704 NA 0.000 0.000
#> GSM559439 3 0.2013 0.709 0.008 0.000 0.908 NA 0.000 0.076
#> GSM559443 6 0.6957 0.240 0.000 0.000 0.260 NA 0.272 0.404
#> GSM559447 3 0.1655 0.733 0.008 0.000 0.932 NA 0.000 0.052
#> GSM559449 1 0.4171 0.643 0.604 0.000 0.000 NA 0.012 0.004
#> GSM559453 3 0.1655 0.733 0.008 0.000 0.932 NA 0.000 0.052
#> GSM559466 3 0.2632 0.746 0.164 0.000 0.832 NA 0.000 0.000
#> GSM559474 1 0.3747 0.645 0.604 0.000 0.000 NA 0.000 0.000
#> GSM559476 3 0.5145 0.575 0.028 0.000 0.696 NA 0.032 0.044
#> GSM559483 2 0.0000 0.881 0.000 1.000 0.000 NA 0.000 0.000
#> GSM559484 5 0.3770 0.601 0.000 0.032 0.000 NA 0.752 0.212
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 disease.state(p) k
#> ATC:kmeans 51 1.0000 2
#> ATC:kmeans 51 0.6430 3
#> ATC:kmeans 36 0.2183 4
#> ATC:kmeans 45 0.0340 5
#> ATC:kmeans 40 0.0761 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 21512 rows and 52 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 0.959 0.964 0.983 0.4964 0.509 0.509
#> 3 3 0.953 0.928 0.956 0.2753 0.821 0.656
#> 4 4 0.923 0.890 0.954 0.1167 0.927 0.798
#> 5 5 0.775 0.778 0.875 0.0930 0.897 0.663
#> 6 6 0.813 0.747 0.857 0.0329 0.987 0.940
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM559433 1 0.000 0.971 1.000 0.000
#> GSM559434 1 0.000 0.971 1.000 0.000
#> GSM559436 2 0.000 1.000 0.000 1.000
#> GSM559437 2 0.000 1.000 0.000 1.000
#> GSM559438 1 0.921 0.531 0.664 0.336
#> GSM559440 1 0.000 0.971 1.000 0.000
#> GSM559441 1 0.000 0.971 1.000 0.000
#> GSM559442 2 0.000 1.000 0.000 1.000
#> GSM559444 2 0.000 1.000 0.000 1.000
#> GSM559445 1 0.000 0.971 1.000 0.000
#> GSM559446 1 0.529 0.859 0.880 0.120
#> GSM559448 1 0.000 0.971 1.000 0.000
#> GSM559450 2 0.000 1.000 0.000 1.000
#> GSM559451 1 0.000 0.971 1.000 0.000
#> GSM559452 1 0.000 0.971 1.000 0.000
#> GSM559454 1 0.000 0.971 1.000 0.000
#> GSM559455 1 0.000 0.971 1.000 0.000
#> GSM559456 1 0.000 0.971 1.000 0.000
#> GSM559457 1 0.000 0.971 1.000 0.000
#> GSM559458 1 0.000 0.971 1.000 0.000
#> GSM559459 2 0.000 1.000 0.000 1.000
#> GSM559460 1 0.000 0.971 1.000 0.000
#> GSM559461 1 0.767 0.727 0.776 0.224
#> GSM559462 2 0.000 1.000 0.000 1.000
#> GSM559463 2 0.000 1.000 0.000 1.000
#> GSM559464 2 0.000 1.000 0.000 1.000
#> GSM559465 1 0.000 0.971 1.000 0.000
#> GSM559467 2 0.000 1.000 0.000 1.000
#> GSM559468 2 0.000 1.000 0.000 1.000
#> GSM559469 1 0.000 0.971 1.000 0.000
#> GSM559470 1 0.000 0.971 1.000 0.000
#> GSM559471 2 0.000 1.000 0.000 1.000
#> GSM559472 1 0.000 0.971 1.000 0.000
#> GSM559473 1 0.680 0.785 0.820 0.180
#> GSM559475 1 0.000 0.971 1.000 0.000
#> GSM559477 2 0.000 1.000 0.000 1.000
#> GSM559478 2 0.000 1.000 0.000 1.000
#> GSM559479 2 0.000 1.000 0.000 1.000
#> GSM559480 2 0.000 1.000 0.000 1.000
#> GSM559481 2 0.000 1.000 0.000 1.000
#> GSM559482 2 0.000 1.000 0.000 1.000
#> GSM559435 1 0.000 0.971 1.000 0.000
#> GSM559439 1 0.000 0.971 1.000 0.000
#> GSM559443 2 0.000 1.000 0.000 1.000
#> GSM559447 1 0.000 0.971 1.000 0.000
#> GSM559449 1 0.000 0.971 1.000 0.000
#> GSM559453 1 0.000 0.971 1.000 0.000
#> GSM559466 1 0.000 0.971 1.000 0.000
#> GSM559474 1 0.000 0.971 1.000 0.000
#> GSM559476 1 0.000 0.971 1.000 0.000
#> GSM559483 2 0.000 1.000 0.000 1.000
#> GSM559484 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 3 0.0000 0.985 0.000 0.000 1.000
#> GSM559434 3 0.0000 0.985 0.000 0.000 1.000
#> GSM559436 1 0.1643 0.954 0.956 0.044 0.000
#> GSM559437 1 0.1529 0.956 0.960 0.040 0.000
#> GSM559438 2 0.1289 0.822 0.000 0.968 0.032
#> GSM559440 2 0.1964 0.827 0.000 0.944 0.056
#> GSM559441 3 0.1529 0.965 0.000 0.040 0.960
#> GSM559442 1 0.0000 0.984 1.000 0.000 0.000
#> GSM559444 2 0.1529 0.800 0.040 0.960 0.000
#> GSM559445 3 0.0000 0.985 0.000 0.000 1.000
#> GSM559446 2 0.6753 0.424 0.016 0.596 0.388
#> GSM559448 3 0.0000 0.985 0.000 0.000 1.000
#> GSM559450 2 0.1529 0.800 0.040 0.960 0.000
#> GSM559451 2 0.1860 0.827 0.000 0.948 0.052
#> GSM559452 2 0.5397 0.682 0.000 0.720 0.280
#> GSM559454 3 0.0000 0.985 0.000 0.000 1.000
#> GSM559455 3 0.0000 0.985 0.000 0.000 1.000
#> GSM559456 3 0.1163 0.973 0.000 0.028 0.972
#> GSM559457 3 0.0000 0.985 0.000 0.000 1.000
#> GSM559458 3 0.0000 0.985 0.000 0.000 1.000
#> GSM559459 1 0.0000 0.984 1.000 0.000 0.000
#> GSM559460 3 0.0000 0.985 0.000 0.000 1.000
#> GSM559461 2 0.6753 0.424 0.016 0.596 0.388
#> GSM559462 1 0.0000 0.984 1.000 0.000 0.000
#> GSM559463 1 0.0000 0.984 1.000 0.000 0.000
#> GSM559464 1 0.0000 0.984 1.000 0.000 0.000
#> GSM559465 3 0.1289 0.970 0.000 0.032 0.968
#> GSM559467 1 0.0747 0.986 0.984 0.016 0.000
#> GSM559468 1 0.0237 0.982 0.996 0.004 0.000
#> GSM559469 3 0.0000 0.985 0.000 0.000 1.000
#> GSM559470 3 0.0000 0.985 0.000 0.000 1.000
#> GSM559471 1 0.0747 0.986 0.984 0.016 0.000
#> GSM559472 3 0.0000 0.985 0.000 0.000 1.000
#> GSM559473 2 0.1529 0.824 0.000 0.960 0.040
#> GSM559475 2 0.5397 0.682 0.000 0.720 0.280
#> GSM559477 1 0.0747 0.986 0.984 0.016 0.000
#> GSM559478 1 0.0747 0.986 0.984 0.016 0.000
#> GSM559479 1 0.0747 0.986 0.984 0.016 0.000
#> GSM559480 1 0.0747 0.986 0.984 0.016 0.000
#> GSM559481 1 0.0747 0.986 0.984 0.016 0.000
#> GSM559482 1 0.0747 0.986 0.984 0.016 0.000
#> GSM559435 3 0.1163 0.973 0.000 0.028 0.972
#> GSM559439 3 0.1529 0.965 0.000 0.040 0.960
#> GSM559443 1 0.1529 0.956 0.960 0.040 0.000
#> GSM559447 3 0.1529 0.965 0.000 0.040 0.960
#> GSM559449 3 0.0000 0.985 0.000 0.000 1.000
#> GSM559453 3 0.1529 0.965 0.000 0.040 0.960
#> GSM559466 3 0.1163 0.973 0.000 0.028 0.972
#> GSM559474 3 0.0000 0.985 0.000 0.000 1.000
#> GSM559476 3 0.0000 0.985 0.000 0.000 1.000
#> GSM559483 1 0.0747 0.986 0.984 0.016 0.000
#> GSM559484 1 0.0747 0.986 0.984 0.016 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 3 0.0188 0.944 0.000 0.004 0.996 0.000
#> GSM559434 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM559436 4 0.0336 0.847 0.008 0.000 0.000 0.992
#> GSM559437 4 0.0336 0.847 0.008 0.000 0.000 0.992
#> GSM559438 2 0.0188 0.909 0.000 0.996 0.000 0.004
#> GSM559440 2 0.0188 0.910 0.000 0.996 0.004 0.000
#> GSM559441 4 0.4819 0.387 0.000 0.004 0.344 0.652
#> GSM559442 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM559444 2 0.2973 0.771 0.144 0.856 0.000 0.000
#> GSM559445 3 0.0376 0.942 0.000 0.004 0.992 0.004
#> GSM559446 4 0.0817 0.840 0.000 0.024 0.000 0.976
#> GSM559448 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM559450 2 0.0188 0.909 0.004 0.996 0.000 0.000
#> GSM559451 2 0.2647 0.812 0.000 0.880 0.000 0.120
#> GSM559452 2 0.2149 0.858 0.000 0.912 0.088 0.000
#> GSM559454 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM559455 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM559456 3 0.0524 0.940 0.000 0.004 0.988 0.008
#> GSM559457 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM559458 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM559459 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM559460 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM559461 4 0.3400 0.705 0.000 0.180 0.000 0.820
#> GSM559462 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM559463 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM559464 1 0.2281 0.892 0.904 0.000 0.000 0.096
#> GSM559465 3 0.0657 0.938 0.000 0.004 0.984 0.012
#> GSM559467 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM559468 1 0.3688 0.756 0.792 0.000 0.000 0.208
#> GSM559469 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM559470 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM559471 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM559472 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM559473 2 0.0188 0.910 0.000 0.996 0.004 0.000
#> GSM559475 2 0.2149 0.858 0.000 0.912 0.088 0.000
#> GSM559477 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM559478 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM559479 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM559480 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM559481 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM559482 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM559435 3 0.0524 0.940 0.000 0.004 0.988 0.008
#> GSM559439 3 0.4699 0.529 0.000 0.004 0.676 0.320
#> GSM559443 4 0.0592 0.843 0.016 0.000 0.000 0.984
#> GSM559447 3 0.4677 0.537 0.000 0.004 0.680 0.316
#> GSM559449 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM559453 3 0.4699 0.529 0.000 0.004 0.676 0.320
#> GSM559466 3 0.0524 0.940 0.000 0.004 0.988 0.008
#> GSM559474 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM559476 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM559483 1 0.0000 0.980 1.000 0.000 0.000 0.000
#> GSM559484 1 0.0000 0.980 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 1 0.1908 0.8480 0.908 0.000 0.092 0.000 0.000
#> GSM559434 1 0.0609 0.9275 0.980 0.000 0.020 0.000 0.000
#> GSM559436 5 0.1410 0.7005 0.000 0.000 0.060 0.000 0.940
#> GSM559437 5 0.1270 0.7010 0.000 0.000 0.052 0.000 0.948
#> GSM559438 4 0.0290 0.7472 0.000 0.000 0.008 0.992 0.000
#> GSM559440 4 0.0290 0.7472 0.000 0.000 0.008 0.992 0.000
#> GSM559441 3 0.3234 0.7662 0.084 0.000 0.852 0.000 0.064
#> GSM559442 2 0.3177 0.7871 0.000 0.792 0.000 0.000 0.208
#> GSM559444 4 0.0794 0.7372 0.000 0.028 0.000 0.972 0.000
#> GSM559445 1 0.3876 0.3215 0.684 0.000 0.316 0.000 0.000
#> GSM559446 5 0.5083 0.5591 0.000 0.000 0.280 0.068 0.652
#> GSM559448 1 0.0000 0.9419 1.000 0.000 0.000 0.000 0.000
#> GSM559450 4 0.1041 0.7468 0.000 0.004 0.032 0.964 0.000
#> GSM559451 4 0.4080 0.5757 0.012 0.000 0.136 0.800 0.052
#> GSM559452 4 0.5721 0.3236 0.424 0.000 0.084 0.492 0.000
#> GSM559454 1 0.0000 0.9419 1.000 0.000 0.000 0.000 0.000
#> GSM559455 1 0.0703 0.9297 0.976 0.000 0.024 0.000 0.000
#> GSM559456 3 0.3876 0.8017 0.316 0.000 0.684 0.000 0.000
#> GSM559457 1 0.0162 0.9428 0.996 0.000 0.004 0.000 0.000
#> GSM559458 1 0.0290 0.9419 0.992 0.000 0.008 0.000 0.000
#> GSM559459 2 0.3074 0.7979 0.000 0.804 0.000 0.000 0.196
#> GSM559460 1 0.0000 0.9419 1.000 0.000 0.000 0.000 0.000
#> GSM559461 5 0.6721 0.2725 0.000 0.000 0.256 0.340 0.404
#> GSM559462 2 0.3074 0.7979 0.000 0.804 0.000 0.000 0.196
#> GSM559463 2 0.3109 0.7945 0.000 0.800 0.000 0.000 0.200
#> GSM559464 2 0.4074 0.5383 0.000 0.636 0.000 0.000 0.364
#> GSM559465 3 0.3684 0.8348 0.280 0.000 0.720 0.000 0.000
#> GSM559467 2 0.0000 0.9062 0.000 1.000 0.000 0.000 0.000
#> GSM559468 5 0.4760 -0.0645 0.000 0.416 0.020 0.000 0.564
#> GSM559469 1 0.0609 0.9275 0.980 0.000 0.020 0.000 0.000
#> GSM559470 1 0.0162 0.9428 0.996 0.000 0.004 0.000 0.000
#> GSM559471 2 0.0000 0.9062 0.000 1.000 0.000 0.000 0.000
#> GSM559472 1 0.0162 0.9428 0.996 0.000 0.004 0.000 0.000
#> GSM559473 4 0.2248 0.7291 0.012 0.000 0.088 0.900 0.000
#> GSM559475 4 0.5682 0.4354 0.372 0.000 0.088 0.540 0.000
#> GSM559477 2 0.0000 0.9062 0.000 1.000 0.000 0.000 0.000
#> GSM559478 2 0.0000 0.9062 0.000 1.000 0.000 0.000 0.000
#> GSM559479 2 0.0000 0.9062 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.0000 0.9062 0.000 1.000 0.000 0.000 0.000
#> GSM559481 2 0.0000 0.9062 0.000 1.000 0.000 0.000 0.000
#> GSM559482 2 0.0000 0.9062 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.3730 0.8300 0.288 0.000 0.712 0.000 0.000
#> GSM559439 3 0.2921 0.8258 0.124 0.000 0.856 0.000 0.020
#> GSM559443 5 0.0609 0.6893 0.000 0.000 0.020 0.000 0.980
#> GSM559447 3 0.2921 0.8258 0.124 0.000 0.856 0.000 0.020
#> GSM559449 1 0.0290 0.9419 0.992 0.000 0.008 0.000 0.000
#> GSM559453 3 0.2921 0.8258 0.124 0.000 0.856 0.000 0.020
#> GSM559466 3 0.3895 0.7964 0.320 0.000 0.680 0.000 0.000
#> GSM559474 1 0.0290 0.9419 0.992 0.000 0.008 0.000 0.000
#> GSM559476 1 0.2669 0.8455 0.876 0.000 0.104 0.000 0.020
#> GSM559483 2 0.0000 0.9062 0.000 1.000 0.000 0.000 0.000
#> GSM559484 2 0.0000 0.9062 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.1082 0.925 0.956 0.000 0.040 0.000 0.004 0.000
#> GSM559434 1 0.0458 0.940 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM559436 4 0.2350 0.658 0.000 0.000 0.036 0.888 0.076 0.000
#> GSM559437 4 0.1863 0.694 0.000 0.000 0.036 0.920 0.044 0.000
#> GSM559438 6 0.3907 0.425 0.000 0.000 0.004 0.000 0.408 0.588
#> GSM559440 6 0.3907 0.425 0.000 0.000 0.004 0.000 0.408 0.588
#> GSM559441 3 0.1138 0.872 0.024 0.000 0.960 0.012 0.004 0.000
#> GSM559442 2 0.3835 0.609 0.000 0.668 0.000 0.320 0.012 0.000
#> GSM559444 6 0.4289 0.462 0.000 0.024 0.004 0.000 0.340 0.632
#> GSM559445 1 0.3337 0.597 0.736 0.000 0.260 0.000 0.004 0.000
#> GSM559446 5 0.5160 0.416 0.000 0.000 0.108 0.320 0.572 0.000
#> GSM559448 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559450 6 0.1863 0.550 0.000 0.000 0.000 0.000 0.104 0.896
#> GSM559451 5 0.4866 0.274 0.020 0.000 0.024 0.028 0.684 0.244
#> GSM559452 6 0.4031 0.343 0.332 0.000 0.008 0.000 0.008 0.652
#> GSM559454 1 0.0146 0.948 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM559455 1 0.0458 0.946 0.984 0.000 0.016 0.000 0.000 0.000
#> GSM559456 3 0.2668 0.865 0.168 0.000 0.828 0.000 0.004 0.000
#> GSM559457 1 0.0291 0.949 0.992 0.000 0.004 0.000 0.004 0.000
#> GSM559458 1 0.0405 0.948 0.988 0.000 0.008 0.000 0.004 0.000
#> GSM559459 2 0.3729 0.639 0.000 0.692 0.000 0.296 0.012 0.000
#> GSM559460 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559461 5 0.4684 0.618 0.000 0.000 0.076 0.152 0.732 0.040
#> GSM559462 2 0.3690 0.647 0.000 0.700 0.000 0.288 0.012 0.000
#> GSM559463 2 0.3819 0.615 0.000 0.672 0.000 0.316 0.012 0.000
#> GSM559464 2 0.4328 0.292 0.000 0.520 0.000 0.460 0.020 0.000
#> GSM559465 3 0.2234 0.891 0.124 0.000 0.872 0.000 0.004 0.000
#> GSM559467 2 0.0870 0.838 0.000 0.972 0.000 0.012 0.012 0.004
#> GSM559468 4 0.6048 0.354 0.000 0.256 0.020 0.528 0.196 0.000
#> GSM559469 1 0.0547 0.936 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM559470 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559471 2 0.0603 0.845 0.000 0.980 0.000 0.016 0.004 0.000
#> GSM559472 1 0.0000 0.949 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559473 6 0.0291 0.534 0.000 0.000 0.004 0.000 0.004 0.992
#> GSM559475 6 0.3104 0.450 0.204 0.000 0.004 0.000 0.004 0.788
#> GSM559477 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559478 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559479 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559480 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559481 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559482 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559435 3 0.2442 0.883 0.144 0.000 0.852 0.000 0.004 0.000
#> GSM559439 3 0.0865 0.889 0.036 0.000 0.964 0.000 0.000 0.000
#> GSM559443 4 0.0520 0.693 0.000 0.000 0.008 0.984 0.008 0.000
#> GSM559447 3 0.0865 0.889 0.036 0.000 0.964 0.000 0.000 0.000
#> GSM559449 1 0.0405 0.948 0.988 0.000 0.008 0.000 0.004 0.000
#> GSM559453 3 0.0865 0.889 0.036 0.000 0.964 0.000 0.000 0.000
#> GSM559466 3 0.2738 0.855 0.176 0.000 0.820 0.000 0.004 0.000
#> GSM559474 1 0.0508 0.947 0.984 0.000 0.012 0.000 0.004 0.000
#> GSM559476 1 0.4589 0.734 0.764 0.000 0.060 0.008 0.108 0.060
#> GSM559483 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559484 2 0.0000 0.851 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 disease.state(p) k
#> ATC:skmeans 52 0.5143 2
#> ATC:skmeans 50 0.0874 3
#> ATC:skmeans 51 0.1201 4
#> ATC:skmeans 47 0.0489 5
#> ATC:skmeans 43 0.1542 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 21512 rows and 52 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.997 0.999 0.3393 0.660 0.660
#> 3 3 0.629 0.705 0.882 0.7811 0.618 0.463
#> 4 4 0.572 0.708 0.830 0.1585 0.844 0.617
#> 5 5 0.746 0.793 0.876 0.1046 0.888 0.627
#> 6 6 0.814 0.825 0.902 0.0425 0.971 0.865
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
#> GSM559433 1 0.000 1.000 1.000 0.000
#> GSM559434 1 0.000 1.000 1.000 0.000
#> GSM559436 1 0.000 1.000 1.000 0.000
#> GSM559437 1 0.000 1.000 1.000 0.000
#> GSM559438 1 0.000 1.000 1.000 0.000
#> GSM559440 1 0.000 1.000 1.000 0.000
#> GSM559441 1 0.000 1.000 1.000 0.000
#> GSM559442 1 0.000 1.000 1.000 0.000
#> GSM559444 1 0.000 1.000 1.000 0.000
#> GSM559445 1 0.000 1.000 1.000 0.000
#> GSM559446 1 0.000 1.000 1.000 0.000
#> GSM559448 1 0.000 1.000 1.000 0.000
#> GSM559450 1 0.000 1.000 1.000 0.000
#> GSM559451 1 0.000 1.000 1.000 0.000
#> GSM559452 1 0.000 1.000 1.000 0.000
#> GSM559454 1 0.000 1.000 1.000 0.000
#> GSM559455 1 0.000 1.000 1.000 0.000
#> GSM559456 1 0.000 1.000 1.000 0.000
#> GSM559457 1 0.000 1.000 1.000 0.000
#> GSM559458 1 0.000 1.000 1.000 0.000
#> GSM559459 2 0.000 0.994 0.000 1.000
#> GSM559460 1 0.000 1.000 1.000 0.000
#> GSM559461 1 0.000 1.000 1.000 0.000
#> GSM559462 2 0.000 0.994 0.000 1.000
#> GSM559463 2 0.000 0.994 0.000 1.000
#> GSM559464 1 0.000 1.000 1.000 0.000
#> GSM559465 1 0.000 1.000 1.000 0.000
#> GSM559467 1 0.000 1.000 1.000 0.000
#> GSM559468 1 0.000 1.000 1.000 0.000
#> GSM559469 1 0.000 1.000 1.000 0.000
#> GSM559470 1 0.000 1.000 1.000 0.000
#> GSM559471 1 0.000 1.000 1.000 0.000
#> GSM559472 1 0.000 1.000 1.000 0.000
#> GSM559473 1 0.000 1.000 1.000 0.000
#> GSM559475 1 0.000 1.000 1.000 0.000
#> GSM559477 2 0.000 0.994 0.000 1.000
#> GSM559478 2 0.000 0.994 0.000 1.000
#> GSM559479 2 0.000 0.994 0.000 1.000
#> GSM559480 2 0.000 0.994 0.000 1.000
#> GSM559481 2 0.000 0.994 0.000 1.000
#> GSM559482 2 0.000 0.994 0.000 1.000
#> GSM559435 1 0.000 1.000 1.000 0.000
#> GSM559439 1 0.000 1.000 1.000 0.000
#> GSM559443 1 0.000 1.000 1.000 0.000
#> GSM559447 1 0.000 1.000 1.000 0.000
#> GSM559449 1 0.000 1.000 1.000 0.000
#> GSM559453 1 0.000 1.000 1.000 0.000
#> GSM559466 1 0.000 1.000 1.000 0.000
#> GSM559474 1 0.000 1.000 1.000 0.000
#> GSM559476 1 0.000 1.000 1.000 0.000
#> GSM559483 2 0.000 0.994 0.000 1.000
#> GSM559484 2 0.343 0.932 0.064 0.936
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 3 0.000 0.8879 0.000 0.000 1.000
#> GSM559434 3 0.000 0.8879 0.000 0.000 1.000
#> GSM559436 1 0.000 0.7865 1.000 0.000 0.000
#> GSM559437 1 0.000 0.7865 1.000 0.000 0.000
#> GSM559438 1 0.000 0.7865 1.000 0.000 0.000
#> GSM559440 1 0.614 0.3794 0.596 0.000 0.404
#> GSM559441 1 0.614 0.3794 0.596 0.000 0.404
#> GSM559442 1 0.000 0.7865 1.000 0.000 0.000
#> GSM559444 1 0.000 0.7865 1.000 0.000 0.000
#> GSM559445 3 0.000 0.8879 0.000 0.000 1.000
#> GSM559446 1 0.000 0.7865 1.000 0.000 0.000
#> GSM559448 3 0.000 0.8879 0.000 0.000 1.000
#> GSM559450 1 0.000 0.7865 1.000 0.000 0.000
#> GSM559451 1 0.236 0.7538 0.928 0.000 0.072
#> GSM559452 1 0.614 0.3794 0.596 0.000 0.404
#> GSM559454 3 0.465 0.7119 0.208 0.000 0.792
#> GSM559455 3 0.465 0.7119 0.208 0.000 0.792
#> GSM559456 3 0.000 0.8879 0.000 0.000 1.000
#> GSM559457 3 0.000 0.8879 0.000 0.000 1.000
#> GSM559458 3 0.000 0.8879 0.000 0.000 1.000
#> GSM559459 1 0.613 -0.0311 0.600 0.400 0.000
#> GSM559460 1 0.614 0.3794 0.596 0.000 0.404
#> GSM559461 1 0.000 0.7865 1.000 0.000 0.000
#> GSM559462 2 0.000 0.8791 0.000 1.000 0.000
#> GSM559463 2 0.614 0.5094 0.404 0.596 0.000
#> GSM559464 1 0.000 0.7865 1.000 0.000 0.000
#> GSM559465 3 0.613 0.2645 0.400 0.000 0.600
#> GSM559467 1 0.000 0.7865 1.000 0.000 0.000
#> GSM559468 1 0.000 0.7865 1.000 0.000 0.000
#> GSM559469 3 0.000 0.8879 0.000 0.000 1.000
#> GSM559470 3 0.000 0.8879 0.000 0.000 1.000
#> GSM559471 1 0.000 0.7865 1.000 0.000 0.000
#> GSM559472 3 0.000 0.8879 0.000 0.000 1.000
#> GSM559473 1 0.000 0.7865 1.000 0.000 0.000
#> GSM559475 1 0.630 0.1607 0.524 0.000 0.476
#> GSM559477 2 0.000 0.8791 0.000 1.000 0.000
#> GSM559478 1 0.164 0.7411 0.956 0.044 0.000
#> GSM559479 2 0.000 0.8791 0.000 1.000 0.000
#> GSM559480 2 0.000 0.8791 0.000 1.000 0.000
#> GSM559481 2 0.614 0.5094 0.404 0.596 0.000
#> GSM559482 2 0.000 0.8791 0.000 1.000 0.000
#> GSM559435 3 0.296 0.8218 0.100 0.000 0.900
#> GSM559439 1 0.614 0.3794 0.596 0.000 0.404
#> GSM559443 1 0.000 0.7865 1.000 0.000 0.000
#> GSM559447 1 0.614 0.3794 0.596 0.000 0.404
#> GSM559449 3 0.000 0.8879 0.000 0.000 1.000
#> GSM559453 1 0.614 0.3794 0.596 0.000 0.404
#> GSM559466 3 0.460 0.7171 0.204 0.000 0.796
#> GSM559474 3 0.000 0.8879 0.000 0.000 1.000
#> GSM559476 3 0.599 0.4152 0.368 0.000 0.632
#> GSM559483 2 0.000 0.8791 0.000 1.000 0.000
#> GSM559484 1 0.000 0.7865 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.3257 0.82396 0.844 0.152 0.004 0.000
#> GSM559434 1 0.1209 0.85208 0.964 0.032 0.004 0.000
#> GSM559436 2 0.3074 0.60421 0.000 0.848 0.152 0.000
#> GSM559437 2 0.3074 0.60421 0.000 0.848 0.152 0.000
#> GSM559438 2 0.0000 0.75139 0.000 1.000 0.000 0.000
#> GSM559440 2 0.1022 0.75543 0.032 0.968 0.000 0.000
#> GSM559441 2 0.1022 0.75543 0.032 0.968 0.000 0.000
#> GSM559442 3 0.4406 0.75329 0.000 0.300 0.700 0.000
#> GSM559444 2 0.3837 0.50085 0.000 0.776 0.224 0.000
#> GSM559445 1 0.0188 0.85269 0.996 0.000 0.004 0.000
#> GSM559446 2 0.0000 0.75139 0.000 1.000 0.000 0.000
#> GSM559448 1 0.0336 0.85266 0.992 0.000 0.008 0.000
#> GSM559450 2 0.3726 0.52347 0.000 0.788 0.212 0.000
#> GSM559451 2 0.0336 0.75345 0.008 0.992 0.000 0.000
#> GSM559452 2 0.1209 0.75449 0.032 0.964 0.004 0.000
#> GSM559454 1 0.4401 0.71072 0.724 0.272 0.004 0.000
#> GSM559455 1 0.4401 0.71072 0.724 0.272 0.004 0.000
#> GSM559456 1 0.0336 0.85266 0.992 0.000 0.008 0.000
#> GSM559457 1 0.0336 0.85266 0.992 0.000 0.008 0.000
#> GSM559458 1 0.0336 0.85266 0.992 0.000 0.008 0.000
#> GSM559459 3 0.1902 0.71343 0.000 0.064 0.932 0.004
#> GSM559460 2 0.5004 0.21158 0.392 0.604 0.004 0.000
#> GSM559461 2 0.0000 0.75139 0.000 1.000 0.000 0.000
#> GSM559462 4 0.2921 0.88390 0.000 0.000 0.140 0.860
#> GSM559463 3 0.4713 0.00817 0.000 0.000 0.640 0.360
#> GSM559464 3 0.4431 0.75160 0.000 0.304 0.696 0.000
#> GSM559465 1 0.4898 0.40412 0.584 0.416 0.000 0.000
#> GSM559467 3 0.4431 0.75160 0.000 0.304 0.696 0.000
#> GSM559468 2 0.4830 0.02879 0.000 0.608 0.392 0.000
#> GSM559469 1 0.3257 0.82396 0.844 0.152 0.004 0.000
#> GSM559470 1 0.3257 0.82396 0.844 0.152 0.004 0.000
#> GSM559471 3 0.4431 0.75160 0.000 0.304 0.696 0.000
#> GSM559472 1 0.0336 0.85266 0.992 0.000 0.008 0.000
#> GSM559473 2 0.1474 0.71901 0.000 0.948 0.052 0.000
#> GSM559475 2 0.2593 0.71265 0.104 0.892 0.004 0.000
#> GSM559477 4 0.0000 0.97766 0.000 0.000 0.000 1.000
#> GSM559478 3 0.3501 0.76681 0.000 0.132 0.848 0.020
#> GSM559479 4 0.0000 0.97766 0.000 0.000 0.000 1.000
#> GSM559480 4 0.0000 0.97766 0.000 0.000 0.000 1.000
#> GSM559481 3 0.3501 0.64803 0.000 0.020 0.848 0.132
#> GSM559482 4 0.0000 0.97766 0.000 0.000 0.000 1.000
#> GSM559435 1 0.3751 0.79360 0.800 0.196 0.004 0.000
#> GSM559439 2 0.1211 0.75355 0.040 0.960 0.000 0.000
#> GSM559443 3 0.4605 0.70866 0.000 0.336 0.664 0.000
#> GSM559447 2 0.4776 0.26633 0.376 0.624 0.000 0.000
#> GSM559449 1 0.0336 0.85266 0.992 0.000 0.008 0.000
#> GSM559453 2 0.4776 0.26633 0.376 0.624 0.000 0.000
#> GSM559466 1 0.4401 0.71072 0.724 0.272 0.004 0.000
#> GSM559474 1 0.0336 0.85266 0.992 0.000 0.008 0.000
#> GSM559476 2 0.4193 0.49571 0.268 0.732 0.000 0.000
#> GSM559483 4 0.0000 0.97766 0.000 0.000 0.000 1.000
#> GSM559484 3 0.3074 0.77001 0.000 0.152 0.848 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 3 0.1544 0.843 0.000 0.000 0.932 0.000 0.068
#> GSM559434 3 0.3366 0.636 0.000 0.000 0.768 0.000 0.232
#> GSM559436 4 0.0566 0.859 0.012 0.000 0.004 0.984 0.000
#> GSM559437 4 0.0566 0.859 0.012 0.000 0.004 0.984 0.000
#> GSM559438 4 0.0404 0.863 0.000 0.000 0.012 0.988 0.000
#> GSM559440 4 0.1608 0.844 0.000 0.000 0.072 0.928 0.000
#> GSM559441 4 0.1341 0.855 0.000 0.000 0.056 0.944 0.000
#> GSM559442 1 0.3424 0.782 0.760 0.000 0.000 0.240 0.000
#> GSM559444 4 0.1341 0.833 0.056 0.000 0.000 0.944 0.000
#> GSM559445 3 0.4262 -0.155 0.000 0.000 0.560 0.000 0.440
#> GSM559446 4 0.0510 0.864 0.000 0.000 0.016 0.984 0.000
#> GSM559448 5 0.3109 0.982 0.000 0.000 0.200 0.000 0.800
#> GSM559450 4 0.1043 0.846 0.040 0.000 0.000 0.960 0.000
#> GSM559451 4 0.0510 0.864 0.000 0.000 0.016 0.984 0.000
#> GSM559452 4 0.2929 0.779 0.000 0.000 0.180 0.820 0.000
#> GSM559454 3 0.0000 0.887 0.000 0.000 1.000 0.000 0.000
#> GSM559455 3 0.0000 0.887 0.000 0.000 1.000 0.000 0.000
#> GSM559456 5 0.3508 0.916 0.000 0.000 0.252 0.000 0.748
#> GSM559457 5 0.3074 0.986 0.000 0.000 0.196 0.000 0.804
#> GSM559458 5 0.3074 0.986 0.000 0.000 0.196 0.000 0.804
#> GSM559459 1 0.0880 0.762 0.968 0.000 0.000 0.032 0.000
#> GSM559460 3 0.1341 0.836 0.000 0.000 0.944 0.056 0.000
#> GSM559461 4 0.0510 0.864 0.000 0.000 0.016 0.984 0.000
#> GSM559462 2 0.4654 0.785 0.052 0.740 0.000 0.012 0.196
#> GSM559463 1 0.6824 -0.221 0.452 0.340 0.000 0.012 0.196
#> GSM559464 1 0.3480 0.779 0.752 0.000 0.000 0.248 0.000
#> GSM559465 3 0.0162 0.886 0.000 0.000 0.996 0.004 0.000
#> GSM559467 1 0.3480 0.779 0.752 0.000 0.000 0.248 0.000
#> GSM559468 4 0.4249 -0.118 0.432 0.000 0.000 0.568 0.000
#> GSM559469 3 0.2516 0.789 0.000 0.000 0.860 0.000 0.140
#> GSM559470 3 0.1410 0.857 0.000 0.000 0.940 0.000 0.060
#> GSM559471 1 0.3480 0.779 0.752 0.000 0.000 0.248 0.000
#> GSM559472 5 0.3074 0.986 0.000 0.000 0.196 0.000 0.804
#> GSM559473 4 0.0451 0.862 0.004 0.000 0.008 0.988 0.000
#> GSM559475 4 0.3707 0.661 0.000 0.000 0.284 0.716 0.000
#> GSM559477 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM559478 1 0.1444 0.767 0.948 0.012 0.000 0.040 0.000
#> GSM559479 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM559481 1 0.1270 0.727 0.948 0.052 0.000 0.000 0.000
#> GSM559482 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.887 0.000 0.000 1.000 0.000 0.000
#> GSM559439 4 0.3074 0.768 0.000 0.000 0.196 0.804 0.000
#> GSM559443 1 0.3715 0.762 0.736 0.000 0.004 0.260 0.000
#> GSM559447 3 0.0162 0.886 0.000 0.000 0.996 0.004 0.000
#> GSM559449 5 0.3074 0.986 0.000 0.000 0.196 0.000 0.804
#> GSM559453 3 0.0404 0.883 0.000 0.000 0.988 0.012 0.000
#> GSM559466 3 0.0000 0.887 0.000 0.000 1.000 0.000 0.000
#> GSM559474 5 0.3074 0.986 0.000 0.000 0.196 0.000 0.804
#> GSM559476 4 0.3966 0.598 0.000 0.000 0.336 0.664 0.000
#> GSM559483 2 0.0000 0.960 0.000 1.000 0.000 0.000 0.000
#> GSM559484 1 0.1270 0.773 0.948 0.000 0.000 0.052 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 3 0.2664 0.775 0.000 0.000 0.816 0.000 0.184 0.000
#> GSM559434 3 0.5149 0.603 0.000 0.000 0.624 0.192 0.184 0.000
#> GSM559436 6 0.0000 0.879 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559437 6 0.0000 0.879 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559438 6 0.0000 0.879 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559440 6 0.0632 0.874 0.000 0.000 0.024 0.000 0.000 0.976
#> GSM559441 6 0.2178 0.823 0.000 0.000 0.132 0.000 0.000 0.868
#> GSM559442 1 0.1444 0.879 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM559444 6 0.0937 0.864 0.040 0.000 0.000 0.000 0.000 0.960
#> GSM559445 3 0.4084 0.319 0.000 0.000 0.588 0.400 0.012 0.000
#> GSM559446 6 0.0000 0.879 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559448 4 0.4222 0.694 0.000 0.000 0.088 0.728 0.184 0.000
#> GSM559450 6 0.1556 0.836 0.080 0.000 0.000 0.000 0.000 0.920
#> GSM559451 6 0.0000 0.879 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559452 6 0.2996 0.756 0.000 0.000 0.228 0.000 0.000 0.772
#> GSM559454 3 0.2009 0.806 0.000 0.000 0.908 0.000 0.024 0.068
#> GSM559455 3 0.0363 0.841 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM559456 4 0.2092 0.765 0.000 0.000 0.124 0.876 0.000 0.000
#> GSM559457 4 0.0000 0.883 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM559458 4 0.0000 0.883 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM559459 1 0.0146 0.859 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM559460 3 0.2092 0.753 0.000 0.000 0.876 0.000 0.000 0.124
#> GSM559461 6 0.0000 0.879 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559462 5 0.2664 1.000 0.000 0.184 0.000 0.000 0.816 0.000
#> GSM559463 5 0.2664 1.000 0.000 0.184 0.000 0.000 0.816 0.000
#> GSM559464 1 0.1556 0.879 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM559465 3 0.0146 0.841 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM559467 1 0.1556 0.879 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM559468 1 0.3867 0.244 0.512 0.000 0.000 0.000 0.000 0.488
#> GSM559469 3 0.4643 0.692 0.000 0.000 0.688 0.128 0.184 0.000
#> GSM559470 3 0.3453 0.781 0.000 0.000 0.804 0.064 0.132 0.000
#> GSM559471 1 0.1556 0.879 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM559472 4 0.2664 0.775 0.000 0.000 0.000 0.816 0.184 0.000
#> GSM559473 6 0.0000 0.879 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559475 6 0.3390 0.682 0.000 0.000 0.296 0.000 0.000 0.704
#> GSM559477 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559478 1 0.0000 0.861 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559479 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559480 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559481 1 0.0000 0.861 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559482 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559435 3 0.0000 0.840 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559439 6 0.3607 0.629 0.000 0.000 0.348 0.000 0.000 0.652
#> GSM559443 1 0.2135 0.842 0.872 0.000 0.000 0.000 0.000 0.128
#> GSM559447 3 0.0146 0.841 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM559449 4 0.0000 0.883 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM559453 3 0.0260 0.839 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM559466 3 0.0363 0.841 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM559474 4 0.0000 0.883 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM559476 6 0.3936 0.676 0.000 0.000 0.288 0.000 0.024 0.688
#> GSM559483 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559484 1 0.0000 0.861 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 disease.state(p) k
#> ATC:pam 52 1.000 2
#> ATC:pam 41 0.558 3
#> ATC:pam 45 0.619 4
#> ATC:pam 49 0.773 5
#> ATC:pam 50 0.805 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 21512 rows and 52 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.674 0.913 0.949 0.289 0.683 0.683
#> 3 3 0.455 0.657 0.837 0.608 0.855 0.799
#> 4 4 0.361 0.408 0.727 0.149 0.864 0.799
#> 5 5 0.538 0.780 0.854 0.251 0.652 0.465
#> 6 6 0.649 0.627 0.801 0.118 0.843 0.578
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM559433 1 0.0000 0.971 1.000 0.000
#> GSM559434 1 0.0000 0.971 1.000 0.000
#> GSM559436 1 0.0000 0.971 1.000 0.000
#> GSM559437 1 0.0000 0.971 1.000 0.000
#> GSM559438 1 0.0000 0.971 1.000 0.000
#> GSM559440 1 0.3733 0.899 0.928 0.072
#> GSM559441 1 0.0000 0.971 1.000 0.000
#> GSM559442 1 0.0000 0.971 1.000 0.000
#> GSM559444 1 0.6623 0.747 0.828 0.172
#> GSM559445 1 0.0000 0.971 1.000 0.000
#> GSM559446 1 0.0000 0.971 1.000 0.000
#> GSM559448 1 0.0000 0.971 1.000 0.000
#> GSM559450 1 0.4815 0.859 0.896 0.104
#> GSM559451 1 0.0000 0.971 1.000 0.000
#> GSM559452 1 0.0000 0.971 1.000 0.000
#> GSM559454 1 0.0000 0.971 1.000 0.000
#> GSM559455 1 0.0000 0.971 1.000 0.000
#> GSM559456 1 0.0000 0.971 1.000 0.000
#> GSM559457 1 0.0376 0.968 0.996 0.004
#> GSM559458 1 0.0000 0.971 1.000 0.000
#> GSM559459 1 0.0000 0.971 1.000 0.000
#> GSM559460 1 0.0000 0.971 1.000 0.000
#> GSM559461 1 0.0000 0.971 1.000 0.000
#> GSM559462 1 0.4690 0.865 0.900 0.100
#> GSM559463 1 0.3431 0.909 0.936 0.064
#> GSM559464 1 0.0000 0.971 1.000 0.000
#> GSM559465 1 0.0000 0.971 1.000 0.000
#> GSM559467 1 0.1184 0.958 0.984 0.016
#> GSM559468 1 0.0000 0.971 1.000 0.000
#> GSM559469 1 0.0000 0.971 1.000 0.000
#> GSM559470 1 0.0000 0.971 1.000 0.000
#> GSM559471 1 0.0000 0.971 1.000 0.000
#> GSM559472 1 0.0000 0.971 1.000 0.000
#> GSM559473 1 0.4815 0.859 0.896 0.104
#> GSM559475 1 0.4815 0.859 0.896 0.104
#> GSM559477 2 0.0000 0.788 0.000 1.000
#> GSM559478 2 0.8955 0.752 0.312 0.688
#> GSM559479 2 0.0000 0.788 0.000 1.000
#> GSM559480 2 0.7745 0.800 0.228 0.772
#> GSM559481 2 0.8499 0.788 0.276 0.724
#> GSM559482 2 0.0000 0.788 0.000 1.000
#> GSM559435 1 0.0000 0.971 1.000 0.000
#> GSM559439 1 0.0000 0.971 1.000 0.000
#> GSM559443 1 0.0000 0.971 1.000 0.000
#> GSM559447 1 0.0000 0.971 1.000 0.000
#> GSM559449 1 0.6801 0.732 0.820 0.180
#> GSM559453 1 0.0000 0.971 1.000 0.000
#> GSM559466 1 0.0000 0.971 1.000 0.000
#> GSM559474 2 0.9323 0.693 0.348 0.652
#> GSM559476 2 0.8661 0.781 0.288 0.712
#> GSM559483 2 0.0000 0.788 0.000 1.000
#> GSM559484 2 0.8661 0.781 0.288 0.712
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559434 1 0.0237 0.8343 0.996 0.000 0.004
#> GSM559436 1 0.0237 0.8343 0.996 0.004 0.000
#> GSM559437 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559438 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559440 1 0.6274 0.4091 0.544 0.000 0.456
#> GSM559441 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559442 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559444 1 0.6280 0.4027 0.540 0.000 0.460
#> GSM559445 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559446 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559448 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559450 1 0.5882 0.5965 0.652 0.000 0.348
#> GSM559451 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559452 1 0.5760 0.6147 0.672 0.000 0.328
#> GSM559454 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559455 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559456 1 0.6189 0.1417 0.632 0.004 0.364
#> GSM559457 1 0.3267 0.7839 0.884 0.000 0.116
#> GSM559458 1 0.2878 0.7958 0.904 0.000 0.096
#> GSM559459 1 0.0475 0.8324 0.992 0.004 0.004
#> GSM559460 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559462 3 0.9090 0.4356 0.332 0.156 0.512
#> GSM559463 3 0.9090 0.4356 0.332 0.156 0.512
#> GSM559464 1 0.0237 0.8338 0.996 0.000 0.004
#> GSM559465 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559467 1 0.6579 0.4728 0.652 0.328 0.020
#> GSM559468 1 0.4862 0.7114 0.820 0.160 0.020
#> GSM559469 1 0.5706 0.6235 0.680 0.000 0.320
#> GSM559470 1 0.4702 0.7181 0.788 0.000 0.212
#> GSM559471 1 0.4575 0.7162 0.828 0.160 0.012
#> GSM559472 1 0.5706 0.6238 0.680 0.000 0.320
#> GSM559473 1 0.5905 0.5921 0.648 0.000 0.352
#> GSM559475 1 0.5968 0.5778 0.636 0.000 0.364
#> GSM559477 2 0.0000 0.7375 0.000 1.000 0.000
#> GSM559478 1 0.8239 0.1854 0.532 0.388 0.080
#> GSM559479 2 0.0000 0.7375 0.000 1.000 0.000
#> GSM559480 2 0.4558 0.5786 0.044 0.856 0.100
#> GSM559481 2 0.8402 -0.0435 0.376 0.532 0.092
#> GSM559482 2 0.0000 0.7375 0.000 1.000 0.000
#> GSM559435 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559439 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559443 1 0.3412 0.7244 0.876 0.000 0.124
#> GSM559447 1 0.0000 0.8354 1.000 0.000 0.000
#> GSM559449 3 0.6026 0.3981 0.244 0.024 0.732
#> GSM559453 1 0.0237 0.8343 0.996 0.004 0.000
#> GSM559466 1 0.4172 0.6785 0.840 0.004 0.156
#> GSM559474 3 0.7874 0.3035 0.064 0.368 0.568
#> GSM559476 3 0.6625 0.1754 0.008 0.440 0.552
#> GSM559483 2 0.0000 0.7375 0.000 1.000 0.000
#> GSM559484 3 0.7652 0.2121 0.044 0.444 0.512
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 1 0.4744 0.5090 0.704 0.000 0.012 0.284
#> GSM559434 1 0.0524 0.5784 0.988 0.000 0.008 0.004
#> GSM559436 1 0.5972 0.4709 0.632 0.000 0.064 0.304
#> GSM559437 1 0.6187 0.4353 0.656 0.000 0.108 0.236
#> GSM559438 1 0.0469 0.5782 0.988 0.000 0.000 0.012
#> GSM559440 1 0.2216 0.5419 0.908 0.000 0.000 0.092
#> GSM559441 1 0.4516 0.4919 0.736 0.000 0.012 0.252
#> GSM559442 1 0.3942 0.5146 0.764 0.000 0.000 0.236
#> GSM559444 1 0.2216 0.5419 0.908 0.000 0.000 0.092
#> GSM559445 1 0.4744 0.5090 0.704 0.000 0.012 0.284
#> GSM559446 1 0.3123 0.5516 0.844 0.000 0.000 0.156
#> GSM559448 1 0.0817 0.5795 0.976 0.000 0.000 0.024
#> GSM559450 1 0.4776 0.2352 0.624 0.000 0.000 0.376
#> GSM559451 1 0.0000 0.5801 1.000 0.000 0.000 0.000
#> GSM559452 1 0.3569 0.4881 0.804 0.000 0.000 0.196
#> GSM559454 1 0.0592 0.5776 0.984 0.000 0.000 0.016
#> GSM559455 1 0.1867 0.5808 0.928 0.000 0.000 0.072
#> GSM559456 1 0.6048 0.3004 0.680 0.028 0.252 0.040
#> GSM559457 1 0.4901 0.5143 0.780 0.000 0.108 0.112
#> GSM559458 1 0.4827 0.5112 0.784 0.000 0.124 0.092
#> GSM559459 1 0.4630 0.4874 0.732 0.000 0.016 0.252
#> GSM559460 1 0.0469 0.5802 0.988 0.000 0.000 0.012
#> GSM559461 1 0.1716 0.5747 0.936 0.000 0.000 0.064
#> GSM559462 3 0.5713 0.3886 0.036 0.000 0.604 0.360
#> GSM559463 4 0.7890 -0.2294 0.352 0.000 0.288 0.360
#> GSM559464 1 0.3942 0.5146 0.764 0.000 0.000 0.236
#> GSM559465 1 0.5178 0.4886 0.716 0.020 0.012 0.252
#> GSM559467 1 0.6844 0.0934 0.588 0.152 0.000 0.260
#> GSM559468 4 0.8778 -0.2534 0.380 0.128 0.092 0.400
#> GSM559469 1 0.4746 0.2458 0.632 0.000 0.000 0.368
#> GSM559470 1 0.3219 0.5375 0.836 0.000 0.000 0.164
#> GSM559471 1 0.6844 0.0934 0.588 0.152 0.000 0.260
#> GSM559472 1 0.4332 0.5101 0.792 0.000 0.032 0.176
#> GSM559473 1 0.4776 0.2352 0.624 0.000 0.000 0.376
#> GSM559475 1 0.4776 0.2352 0.624 0.000 0.000 0.376
#> GSM559477 2 0.0000 0.8112 0.000 1.000 0.000 0.000
#> GSM559478 1 0.6973 0.0554 0.584 0.220 0.000 0.196
#> GSM559479 2 0.0000 0.8112 0.000 1.000 0.000 0.000
#> GSM559480 2 0.1004 0.7848 0.024 0.972 0.000 0.004
#> GSM559481 1 0.5360 -0.0673 0.552 0.436 0.000 0.012
#> GSM559482 2 0.0000 0.8112 0.000 1.000 0.000 0.000
#> GSM559435 1 0.4936 0.4918 0.672 0.000 0.012 0.316
#> GSM559439 1 0.4477 0.5092 0.688 0.000 0.000 0.312
#> GSM559443 1 0.4988 0.4834 0.728 0.000 0.036 0.236
#> GSM559447 1 0.4857 0.4900 0.668 0.000 0.008 0.324
#> GSM559449 1 0.5731 -0.0950 0.544 0.000 0.428 0.028
#> GSM559453 1 0.5178 0.4886 0.716 0.020 0.012 0.252
#> GSM559466 3 0.8377 -0.4709 0.376 0.032 0.400 0.192
#> GSM559474 3 0.1543 0.5116 0.032 0.004 0.956 0.008
#> GSM559476 3 0.1489 0.4952 0.000 0.044 0.952 0.004
#> GSM559483 2 0.0000 0.8112 0.000 1.000 0.000 0.000
#> GSM559484 2 0.7973 -0.3013 0.356 0.432 0.200 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 1 0.4358 0.5334 0.696 0.000 0.008 0.284 0.012
#> GSM559434 4 0.1399 0.8291 0.028 0.000 0.020 0.952 0.000
#> GSM559436 1 0.3868 0.8733 0.800 0.000 0.060 0.140 0.000
#> GSM559437 1 0.3683 0.8789 0.832 0.004 0.032 0.120 0.012
#> GSM559438 4 0.1569 0.8279 0.032 0.012 0.000 0.948 0.008
#> GSM559440 4 0.1808 0.8276 0.044 0.012 0.000 0.936 0.008
#> GSM559441 1 0.2513 0.8793 0.876 0.000 0.008 0.116 0.000
#> GSM559442 1 0.3197 0.8716 0.836 0.000 0.024 0.140 0.000
#> GSM559444 4 0.1969 0.8270 0.032 0.012 0.012 0.936 0.008
#> GSM559445 1 0.2362 0.8447 0.900 0.000 0.008 0.084 0.008
#> GSM559446 1 0.4542 0.7648 0.720 0.004 0.024 0.244 0.008
#> GSM559448 4 0.2067 0.8226 0.048 0.000 0.032 0.920 0.000
#> GSM559450 4 0.0290 0.8237 0.000 0.000 0.000 0.992 0.008
#> GSM559451 4 0.2474 0.8059 0.084 0.012 0.000 0.896 0.008
#> GSM559452 4 0.0960 0.8282 0.016 0.000 0.004 0.972 0.008
#> GSM559454 4 0.1651 0.8281 0.036 0.000 0.012 0.944 0.008
#> GSM559455 4 0.4942 0.5866 0.256 0.016 0.024 0.696 0.008
#> GSM559456 1 0.2299 0.7893 0.916 0.012 0.004 0.012 0.056
#> GSM559457 4 0.5416 0.6066 0.164 0.000 0.012 0.692 0.132
#> GSM559458 4 0.5673 0.5795 0.188 0.000 0.016 0.668 0.128
#> GSM559459 1 0.3688 0.8730 0.816 0.000 0.060 0.124 0.000
#> GSM559460 4 0.2549 0.8189 0.060 0.004 0.024 0.904 0.008
#> GSM559461 1 0.4948 0.5689 0.612 0.000 0.024 0.356 0.008
#> GSM559462 3 0.1341 0.9601 0.000 0.000 0.944 0.000 0.056
#> GSM559463 3 0.1469 0.9605 0.016 0.000 0.948 0.000 0.036
#> GSM559464 1 0.3310 0.8733 0.836 0.004 0.024 0.136 0.000
#> GSM559465 1 0.1408 0.8492 0.948 0.000 0.008 0.044 0.000
#> GSM559467 4 0.2378 0.8054 0.064 0.016 0.012 0.908 0.000
#> GSM559468 1 0.3777 0.8443 0.844 0.024 0.024 0.092 0.016
#> GSM559469 4 0.0960 0.8231 0.016 0.000 0.004 0.972 0.008
#> GSM559470 4 0.1579 0.8226 0.032 0.000 0.024 0.944 0.000
#> GSM559471 4 0.4755 0.4419 0.292 0.028 0.000 0.672 0.008
#> GSM559472 4 0.4101 0.7362 0.124 0.000 0.028 0.808 0.040
#> GSM559473 4 0.0451 0.8236 0.000 0.004 0.000 0.988 0.008
#> GSM559475 4 0.0451 0.8235 0.000 0.000 0.004 0.988 0.008
#> GSM559477 2 0.0000 0.9419 0.000 1.000 0.000 0.000 0.000
#> GSM559478 4 0.3861 0.6129 0.000 0.264 0.000 0.728 0.008
#> GSM559479 2 0.0404 0.9320 0.000 0.988 0.000 0.000 0.012
#> GSM559480 2 0.2358 0.7796 0.000 0.888 0.000 0.104 0.008
#> GSM559481 4 0.4489 0.3132 0.000 0.420 0.000 0.572 0.008
#> GSM559482 2 0.0000 0.9419 0.000 1.000 0.000 0.000 0.000
#> GSM559435 1 0.2707 0.8800 0.860 0.000 0.008 0.132 0.000
#> GSM559439 1 0.3197 0.8774 0.836 0.000 0.024 0.140 0.000
#> GSM559443 1 0.2886 0.8609 0.884 0.000 0.036 0.068 0.012
#> GSM559447 1 0.2707 0.8812 0.860 0.000 0.008 0.132 0.000
#> GSM559449 4 0.5652 0.5251 0.140 0.000 0.004 0.644 0.212
#> GSM559453 1 0.1956 0.8699 0.916 0.000 0.008 0.076 0.000
#> GSM559466 1 0.2484 0.7889 0.912 0.012 0.008 0.020 0.048
#> GSM559474 5 0.1701 0.8916 0.048 0.000 0.000 0.016 0.936
#> GSM559476 5 0.0992 0.8888 0.000 0.000 0.024 0.008 0.968
#> GSM559483 2 0.0000 0.9419 0.000 1.000 0.000 0.000 0.000
#> GSM559484 4 0.6722 -0.0257 0.000 0.408 0.020 0.432 0.140
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 3 0.3809 0.5443 0.304 0.000 0.684 0.000 0.004 0.008
#> GSM559434 6 0.0653 0.6373 0.012 0.000 0.000 0.004 0.004 0.980
#> GSM559436 3 0.0820 0.8566 0.012 0.000 0.972 0.016 0.000 0.000
#> GSM559437 3 0.0748 0.8552 0.000 0.000 0.976 0.016 0.004 0.004
#> GSM559438 6 0.4377 0.2817 0.436 0.000 0.024 0.000 0.000 0.540
#> GSM559440 6 0.3098 0.6281 0.164 0.000 0.024 0.000 0.000 0.812
#> GSM559441 3 0.0146 0.8569 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM559442 3 0.0622 0.8578 0.012 0.000 0.980 0.008 0.000 0.000
#> GSM559444 6 0.3017 0.6301 0.164 0.000 0.020 0.000 0.000 0.816
#> GSM559445 3 0.3189 0.6347 0.236 0.000 0.760 0.000 0.004 0.000
#> GSM559446 3 0.3189 0.7185 0.184 0.000 0.796 0.000 0.000 0.020
#> GSM559448 6 0.4062 0.4350 0.344 0.000 0.012 0.004 0.000 0.640
#> GSM559450 6 0.0146 0.6407 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM559451 1 0.5480 -0.0964 0.444 0.000 0.124 0.000 0.000 0.432
#> GSM559452 6 0.3151 0.5667 0.252 0.000 0.000 0.000 0.000 0.748
#> GSM559454 6 0.4139 0.4571 0.336 0.000 0.024 0.000 0.000 0.640
#> GSM559455 1 0.6031 0.1277 0.420 0.000 0.268 0.000 0.000 0.312
#> GSM559456 3 0.2902 0.7445 0.196 0.000 0.800 0.000 0.000 0.004
#> GSM559457 1 0.5022 0.4453 0.680 0.000 0.016 0.004 0.096 0.204
#> GSM559458 1 0.5042 0.4428 0.676 0.000 0.024 0.000 0.096 0.204
#> GSM559459 3 0.0820 0.8570 0.016 0.000 0.972 0.012 0.000 0.000
#> GSM559460 1 0.5531 -0.0626 0.452 0.000 0.132 0.000 0.000 0.416
#> GSM559461 3 0.5275 0.3654 0.232 0.000 0.600 0.000 0.000 0.168
#> GSM559462 4 0.0363 0.9767 0.000 0.000 0.000 0.988 0.012 0.000
#> GSM559463 4 0.0405 0.9768 0.008 0.000 0.004 0.988 0.000 0.000
#> GSM559464 3 0.0692 0.8577 0.020 0.000 0.976 0.000 0.000 0.004
#> GSM559465 3 0.0405 0.8569 0.008 0.000 0.988 0.000 0.004 0.000
#> GSM559467 6 0.5434 0.1552 0.148 0.004 0.268 0.000 0.000 0.580
#> GSM559468 3 0.2815 0.7947 0.132 0.004 0.848 0.000 0.004 0.012
#> GSM559469 6 0.0508 0.6377 0.012 0.000 0.000 0.004 0.000 0.984
#> GSM559470 6 0.3975 0.3614 0.392 0.000 0.008 0.000 0.000 0.600
#> GSM559471 3 0.5571 0.0425 0.148 0.000 0.496 0.000 0.000 0.356
#> GSM559472 1 0.5122 0.3291 0.564 0.000 0.004 0.004 0.068 0.360
#> GSM559473 6 0.0000 0.6400 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559475 6 0.0146 0.6407 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM559477 2 0.0000 0.8225 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559478 2 0.5128 0.6560 0.156 0.652 0.000 0.008 0.000 0.184
#> GSM559479 2 0.0000 0.8225 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559480 2 0.2956 0.8041 0.088 0.848 0.000 0.000 0.000 0.064
#> GSM559481 2 0.4445 0.7427 0.100 0.728 0.000 0.008 0.000 0.164
#> GSM559482 2 0.0000 0.8225 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559435 3 0.0291 0.8574 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM559439 3 0.0508 0.8574 0.012 0.000 0.984 0.000 0.000 0.004
#> GSM559443 3 0.0891 0.8531 0.008 0.000 0.968 0.024 0.000 0.000
#> GSM559447 3 0.0508 0.8574 0.012 0.000 0.984 0.000 0.000 0.004
#> GSM559449 1 0.5092 0.3968 0.660 0.000 0.012 0.000 0.128 0.200
#> GSM559453 3 0.0405 0.8569 0.008 0.000 0.988 0.000 0.004 0.000
#> GSM559466 3 0.3261 0.7382 0.192 0.004 0.792 0.000 0.008 0.004
#> GSM559474 5 0.3629 0.6463 0.276 0.000 0.012 0.000 0.712 0.000
#> GSM559476 5 0.0146 0.6195 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM559483 2 0.0000 0.8225 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559484 2 0.4744 0.7211 0.008 0.716 0.000 0.008 0.108 0.160
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 disease.state(p) k
#> ATC:mclust 52 0.2329 2
#> ATC:mclust 40 1.0000 3
#> ATC:mclust 26 0.0119 4
#> ATC:mclust 49 0.0116 5
#> ATC:mclust 38 0.0470 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 21512 rows and 52 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 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 0.662 0.931 0.947 0.2389 0.735 0.735
#> 3 3 0.895 0.931 0.972 0.6512 0.871 0.825
#> 4 4 0.645 0.785 0.904 0.7185 0.701 0.512
#> 5 5 0.568 0.597 0.802 0.0765 0.898 0.695
#> 6 6 0.526 0.484 0.746 0.0445 0.900 0.656
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
#> GSM559433 1 0.0000 0.972 1.000 0.000
#> GSM559434 1 0.0000 0.972 1.000 0.000
#> GSM559436 1 0.3733 0.894 0.928 0.072
#> GSM559437 1 0.6247 0.787 0.844 0.156
#> GSM559438 1 0.0000 0.972 1.000 0.000
#> GSM559440 1 0.0000 0.972 1.000 0.000
#> GSM559441 1 0.0376 0.968 0.996 0.004
#> GSM559442 1 0.0000 0.972 1.000 0.000
#> GSM559444 1 0.0000 0.972 1.000 0.000
#> GSM559445 1 0.0000 0.972 1.000 0.000
#> GSM559446 1 0.0000 0.972 1.000 0.000
#> GSM559448 1 0.0000 0.972 1.000 0.000
#> GSM559450 1 0.0000 0.972 1.000 0.000
#> GSM559451 1 0.0000 0.972 1.000 0.000
#> GSM559452 1 0.0000 0.972 1.000 0.000
#> GSM559454 1 0.0000 0.972 1.000 0.000
#> GSM559455 1 0.0000 0.972 1.000 0.000
#> GSM559456 1 0.0000 0.972 1.000 0.000
#> GSM559457 1 0.0000 0.972 1.000 0.000
#> GSM559458 1 0.0000 0.972 1.000 0.000
#> GSM559459 1 0.7056 0.734 0.808 0.192
#> GSM559460 1 0.0000 0.972 1.000 0.000
#> GSM559461 1 0.0000 0.972 1.000 0.000
#> GSM559462 2 0.9815 0.308 0.420 0.580
#> GSM559463 1 0.7219 0.721 0.800 0.200
#> GSM559464 1 0.0000 0.972 1.000 0.000
#> GSM559465 1 0.0000 0.972 1.000 0.000
#> GSM559467 1 0.0000 0.972 1.000 0.000
#> GSM559468 1 0.0000 0.972 1.000 0.000
#> GSM559469 1 0.0000 0.972 1.000 0.000
#> GSM559470 1 0.0000 0.972 1.000 0.000
#> GSM559471 1 0.0000 0.972 1.000 0.000
#> GSM559472 1 0.0000 0.972 1.000 0.000
#> GSM559473 1 0.0000 0.972 1.000 0.000
#> GSM559475 1 0.0000 0.972 1.000 0.000
#> GSM559477 2 0.7219 0.930 0.200 0.800
#> GSM559478 2 0.7674 0.911 0.224 0.776
#> GSM559479 2 0.7219 0.930 0.200 0.800
#> GSM559480 2 0.7219 0.930 0.200 0.800
#> GSM559481 2 0.7299 0.928 0.204 0.796
#> GSM559482 2 0.7219 0.930 0.200 0.800
#> GSM559435 1 0.0000 0.972 1.000 0.000
#> GSM559439 1 0.0000 0.972 1.000 0.000
#> GSM559443 1 0.6438 0.775 0.836 0.164
#> GSM559447 1 0.0000 0.972 1.000 0.000
#> GSM559449 1 0.0000 0.972 1.000 0.000
#> GSM559453 1 0.0000 0.972 1.000 0.000
#> GSM559466 1 0.0000 0.972 1.000 0.000
#> GSM559474 1 0.0000 0.972 1.000 0.000
#> GSM559476 1 0.0000 0.972 1.000 0.000
#> GSM559483 2 0.7219 0.930 0.200 0.800
#> GSM559484 1 0.5629 0.787 0.868 0.132
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559433 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559434 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559436 1 0.4654 0.724 0.792 0.000 0.208
#> GSM559437 3 0.5178 0.616 0.256 0.000 0.744
#> GSM559438 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559440 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559441 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559442 1 0.5680 0.679 0.764 0.024 0.212
#> GSM559444 1 0.1411 0.943 0.964 0.036 0.000
#> GSM559445 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559446 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559448 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559450 1 0.0747 0.963 0.984 0.016 0.000
#> GSM559451 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559452 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559454 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559455 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559456 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559457 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559458 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559459 3 0.2796 0.704 0.000 0.092 0.908
#> GSM559460 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559461 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559462 3 0.0000 0.750 0.000 0.000 1.000
#> GSM559463 3 0.0000 0.750 0.000 0.000 1.000
#> GSM559464 1 0.3482 0.838 0.872 0.000 0.128
#> GSM559465 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559467 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559468 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559469 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559470 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559471 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559472 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559473 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559475 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559477 2 0.0237 0.985 0.004 0.996 0.000
#> GSM559478 2 0.1529 0.927 0.040 0.960 0.000
#> GSM559479 2 0.0237 0.985 0.004 0.996 0.000
#> GSM559480 2 0.0237 0.985 0.004 0.996 0.000
#> GSM559481 2 0.0592 0.976 0.012 0.988 0.000
#> GSM559482 2 0.0237 0.985 0.004 0.996 0.000
#> GSM559435 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559439 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559443 3 0.4504 0.687 0.196 0.000 0.804
#> GSM559447 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559449 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559453 1 0.0000 0.975 1.000 0.000 0.000
#> GSM559466 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559474 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559476 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559483 2 0.0237 0.985 0.004 0.996 0.000
#> GSM559484 1 0.4346 0.758 0.816 0.184 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559433 3 0.2345 0.843 0.100 0.000 0.900 0.000
#> GSM559434 1 0.2704 0.785 0.876 0.000 0.124 0.000
#> GSM559436 1 0.3569 0.680 0.804 0.000 0.000 0.196
#> GSM559437 4 0.2345 0.846 0.100 0.000 0.000 0.900
#> GSM559438 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> GSM559440 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> GSM559441 3 0.5558 0.389 0.364 0.000 0.608 0.028
#> GSM559442 1 0.0469 0.824 0.988 0.000 0.000 0.012
#> GSM559444 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> GSM559445 3 0.2149 0.852 0.088 0.000 0.912 0.000
#> GSM559446 1 0.1302 0.825 0.956 0.000 0.044 0.000
#> GSM559448 1 0.4985 0.121 0.532 0.000 0.468 0.000
#> GSM559450 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> GSM559451 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> GSM559452 1 0.1118 0.827 0.964 0.000 0.036 0.000
#> GSM559454 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> GSM559455 1 0.3024 0.772 0.852 0.000 0.148 0.000
#> GSM559456 3 0.0000 0.869 0.000 0.000 1.000 0.000
#> GSM559457 3 0.0592 0.875 0.016 0.000 0.984 0.000
#> GSM559458 3 0.0336 0.874 0.008 0.000 0.992 0.000
#> GSM559459 4 0.3837 0.721 0.224 0.000 0.000 0.776
#> GSM559460 1 0.0188 0.832 0.996 0.000 0.004 0.000
#> GSM559461 1 0.0000 0.832 1.000 0.000 0.000 0.000
#> GSM559462 4 0.0000 0.883 0.000 0.000 0.000 1.000
#> GSM559463 4 0.0000 0.883 0.000 0.000 0.000 1.000
#> GSM559464 1 0.4382 0.522 0.704 0.000 0.000 0.296
#> GSM559465 3 0.1118 0.872 0.036 0.000 0.964 0.000
#> GSM559467 1 0.4382 0.588 0.704 0.000 0.296 0.000
#> GSM559468 3 0.0336 0.874 0.008 0.000 0.992 0.000
#> GSM559469 3 0.3873 0.709 0.228 0.000 0.772 0.000
#> GSM559470 3 0.4103 0.667 0.256 0.000 0.744 0.000
#> GSM559471 1 0.0336 0.832 0.992 0.000 0.008 0.000
#> GSM559472 3 0.0707 0.875 0.020 0.000 0.980 0.000
#> GSM559473 1 0.3123 0.757 0.844 0.000 0.156 0.000
#> GSM559475 1 0.4843 0.338 0.604 0.000 0.396 0.000
#> GSM559477 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM559478 2 0.1867 0.885 0.072 0.928 0.000 0.000
#> GSM559479 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM559480 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM559481 2 0.0188 0.977 0.004 0.996 0.000 0.000
#> GSM559482 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM559435 3 0.4697 0.440 0.356 0.000 0.644 0.000
#> GSM559439 1 0.3837 0.689 0.776 0.000 0.224 0.000
#> GSM559443 4 0.0188 0.882 0.000 0.000 0.004 0.996
#> GSM559447 1 0.4730 0.430 0.636 0.000 0.364 0.000
#> GSM559449 3 0.0188 0.873 0.004 0.000 0.996 0.000
#> GSM559453 3 0.3266 0.778 0.168 0.000 0.832 0.000
#> GSM559466 3 0.0188 0.873 0.004 0.000 0.996 0.000
#> GSM559474 3 0.0188 0.873 0.004 0.000 0.996 0.000
#> GSM559476 3 0.0188 0.873 0.004 0.000 0.996 0.000
#> GSM559483 2 0.0000 0.980 0.000 1.000 0.000 0.000
#> GSM559484 3 0.2654 0.804 0.004 0.108 0.888 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559433 1 0.4087 0.696 0.756 0.000 0.208 0.036 0.000
#> GSM559434 4 0.2395 0.759 0.072 0.000 0.016 0.904 0.008
#> GSM559436 3 0.5045 0.163 0.004 0.000 0.508 0.464 0.024
#> GSM559437 3 0.1547 0.361 0.004 0.000 0.948 0.016 0.032
#> GSM559438 4 0.1041 0.777 0.000 0.000 0.032 0.964 0.004
#> GSM559440 4 0.0771 0.781 0.000 0.000 0.020 0.976 0.004
#> GSM559441 3 0.5394 0.432 0.208 0.000 0.660 0.132 0.000
#> GSM559442 4 0.4125 0.622 0.000 0.000 0.172 0.772 0.056
#> GSM559444 4 0.1197 0.770 0.000 0.000 0.048 0.952 0.000
#> GSM559445 1 0.5523 0.416 0.564 0.000 0.368 0.064 0.004
#> GSM559446 4 0.4819 0.232 0.024 0.000 0.352 0.620 0.004
#> GSM559448 4 0.4947 0.287 0.396 0.000 0.024 0.576 0.004
#> GSM559450 4 0.0960 0.781 0.004 0.000 0.008 0.972 0.016
#> GSM559451 4 0.0566 0.783 0.000 0.000 0.012 0.984 0.004
#> GSM559452 4 0.1686 0.782 0.020 0.000 0.028 0.944 0.008
#> GSM559454 4 0.0693 0.786 0.012 0.000 0.008 0.980 0.000
#> GSM559455 4 0.6033 0.141 0.132 0.000 0.296 0.568 0.004
#> GSM559456 1 0.3684 0.651 0.720 0.000 0.280 0.000 0.000
#> GSM559457 1 0.2006 0.730 0.916 0.000 0.072 0.012 0.000
#> GSM559458 1 0.3163 0.725 0.824 0.000 0.164 0.012 0.000
#> GSM559459 5 0.4576 0.491 0.000 0.000 0.040 0.268 0.692
#> GSM559460 4 0.1661 0.780 0.024 0.000 0.036 0.940 0.000
#> GSM559461 4 0.0932 0.785 0.004 0.000 0.020 0.972 0.004
#> GSM559462 5 0.2011 0.537 0.000 0.004 0.088 0.000 0.908
#> GSM559463 3 0.4262 -0.393 0.000 0.000 0.560 0.000 0.440
#> GSM559464 4 0.5523 0.279 0.000 0.000 0.088 0.592 0.320
#> GSM559465 1 0.4063 0.645 0.708 0.000 0.280 0.012 0.000
#> GSM559467 4 0.4217 0.618 0.232 0.000 0.008 0.740 0.020
#> GSM559468 1 0.1059 0.710 0.968 0.000 0.020 0.008 0.004
#> GSM559469 1 0.4697 0.325 0.620 0.000 0.008 0.360 0.012
#> GSM559470 1 0.5013 0.360 0.612 0.000 0.028 0.352 0.008
#> GSM559471 4 0.1948 0.771 0.024 0.000 0.008 0.932 0.036
#> GSM559472 1 0.1628 0.678 0.936 0.000 0.008 0.056 0.000
#> GSM559473 4 0.3320 0.719 0.124 0.000 0.016 0.844 0.016
#> GSM559475 4 0.4524 0.535 0.280 0.000 0.008 0.692 0.020
#> GSM559477 2 0.0162 0.976 0.000 0.996 0.000 0.000 0.004
#> GSM559478 2 0.1544 0.880 0.000 0.932 0.000 0.068 0.000
#> GSM559479 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM559480 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM559481 2 0.0290 0.971 0.000 0.992 0.000 0.008 0.000
#> GSM559482 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM559435 3 0.6439 0.212 0.332 0.000 0.476 0.192 0.000
#> GSM559439 3 0.5028 0.219 0.032 0.000 0.524 0.444 0.000
#> GSM559443 3 0.1996 0.356 0.036 0.000 0.928 0.004 0.032
#> GSM559447 3 0.5122 0.464 0.060 0.000 0.628 0.312 0.000
#> GSM559449 1 0.3421 0.712 0.788 0.000 0.204 0.008 0.000
#> GSM559453 3 0.5268 0.199 0.320 0.000 0.612 0.068 0.000
#> GSM559466 1 0.3305 0.700 0.776 0.000 0.224 0.000 0.000
#> GSM559474 1 0.1892 0.725 0.916 0.000 0.080 0.000 0.004
#> GSM559476 1 0.1012 0.693 0.968 0.000 0.012 0.000 0.020
#> GSM559483 2 0.0162 0.976 0.000 0.996 0.000 0.000 0.004
#> GSM559484 1 0.5202 0.533 0.696 0.240 0.016 0.032 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559433 1 0.547 0.1427 0.484 0.000 0.432 0.000 0.036 0.048
#> GSM559434 6 0.352 0.6973 0.104 0.000 0.048 0.000 0.024 0.824
#> GSM559436 3 0.490 0.3973 0.004 0.000 0.684 0.004 0.136 0.172
#> GSM559437 3 0.228 0.3809 0.000 0.000 0.868 0.000 0.128 0.004
#> GSM559438 6 0.169 0.6809 0.000 0.000 0.064 0.000 0.012 0.924
#> GSM559440 6 0.180 0.6784 0.000 0.000 0.072 0.000 0.012 0.916
#> GSM559441 3 0.382 0.5147 0.140 0.000 0.792 0.000 0.048 0.020
#> GSM559442 6 0.580 0.0964 0.000 0.000 0.312 0.004 0.180 0.504
#> GSM559444 6 0.325 0.5976 0.000 0.000 0.156 0.000 0.036 0.808
#> GSM559445 3 0.555 0.0677 0.380 0.000 0.524 0.000 0.036 0.060
#> GSM559446 3 0.565 0.2378 0.060 0.000 0.524 0.000 0.044 0.372
#> GSM559448 6 0.639 0.1720 0.352 0.000 0.156 0.000 0.040 0.452
#> GSM559450 6 0.108 0.6957 0.008 0.000 0.016 0.000 0.012 0.964
#> GSM559451 6 0.231 0.6945 0.012 0.000 0.064 0.000 0.024 0.900
#> GSM559452 6 0.189 0.7131 0.020 0.000 0.056 0.000 0.004 0.920
#> GSM559454 6 0.245 0.7127 0.048 0.000 0.040 0.000 0.016 0.896
#> GSM559455 6 0.608 -0.0502 0.148 0.000 0.400 0.000 0.020 0.432
#> GSM559456 1 0.463 0.2132 0.520 0.000 0.440 0.000 0.040 0.000
#> GSM559457 1 0.405 0.5864 0.768 0.000 0.164 0.000 0.024 0.044
#> GSM559458 1 0.402 0.5542 0.720 0.000 0.244 0.000 0.008 0.028
#> GSM559459 4 0.734 0.1553 0.000 0.000 0.212 0.408 0.144 0.236
#> GSM559460 6 0.442 0.6456 0.080 0.000 0.148 0.000 0.024 0.748
#> GSM559461 6 0.402 0.6501 0.032 0.000 0.144 0.000 0.044 0.780
#> GSM559462 4 0.000 -0.0153 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM559463 5 0.495 0.0000 0.000 0.000 0.244 0.120 0.636 0.000
#> GSM559464 3 0.763 -0.1338 0.020 0.000 0.360 0.136 0.148 0.336
#> GSM559465 3 0.487 -0.1657 0.468 0.000 0.488 0.000 0.028 0.016
#> GSM559467 6 0.431 0.6410 0.184 0.000 0.012 0.000 0.068 0.736
#> GSM559468 1 0.314 0.5968 0.856 0.000 0.060 0.000 0.056 0.028
#> GSM559469 6 0.499 0.2025 0.472 0.000 0.016 0.000 0.036 0.476
#> GSM559470 1 0.582 -0.0285 0.484 0.000 0.104 0.000 0.024 0.388
#> GSM559471 6 0.186 0.6799 0.016 0.000 0.004 0.000 0.060 0.920
#> GSM559472 1 0.344 0.5493 0.828 0.000 0.036 0.000 0.028 0.108
#> GSM559473 6 0.352 0.6763 0.136 0.000 0.024 0.000 0.028 0.812
#> GSM559475 6 0.449 0.6095 0.228 0.000 0.016 0.000 0.052 0.704
#> GSM559477 2 0.000 0.9745 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559478 2 0.161 0.8633 0.000 0.916 0.000 0.000 0.000 0.084
#> GSM559479 2 0.000 0.9745 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559480 2 0.052 0.9636 0.000 0.984 0.000 0.000 0.008 0.008
#> GSM559481 2 0.000 0.9745 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559482 2 0.000 0.9745 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559435 3 0.452 0.4833 0.196 0.000 0.720 0.000 0.020 0.064
#> GSM559439 3 0.397 0.5433 0.044 0.000 0.772 0.000 0.020 0.164
#> GSM559443 3 0.417 0.2537 0.056 0.000 0.736 0.008 0.200 0.000
#> GSM559447 3 0.293 0.5660 0.040 0.000 0.860 0.000 0.012 0.088
#> GSM559449 1 0.401 0.5383 0.704 0.000 0.268 0.000 0.016 0.012
#> GSM559453 3 0.446 0.4748 0.160 0.000 0.736 0.000 0.088 0.016
#> GSM559466 1 0.421 0.4444 0.636 0.000 0.336 0.000 0.028 0.000
#> GSM559474 1 0.366 0.5665 0.800 0.000 0.100 0.000 0.096 0.004
#> GSM559476 1 0.292 0.4922 0.828 0.000 0.008 0.000 0.156 0.008
#> GSM559483 2 0.000 0.9745 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559484 1 0.628 0.2827 0.548 0.276 0.004 0.000 0.104 0.068
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 disease.state(p) k
#> ATC:NMF 51 0.9923 2
#> ATC:NMF 52 0.8845 3
#> ATC:NMF 47 0.1138 4
#> ATC:NMF 35 0.0379 5
#> ATC:NMF 30 0.0241 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
sessionInfo()
#> R version 3.6.0 (2019-04-26)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: CentOS Linux 7 (Core)
#>
#> Matrix products: default
#> BLAS: /usr/lib64/libblas.so.3.4.2
#> LAPACK: /usr/lib64/liblapack.so.3.4.2
#>
#> locale:
#> [1] LC_CTYPE=en_GB.UTF-8 LC_NUMERIC=C LC_TIME=en_GB.UTF-8
#> [4] LC_COLLATE=en_GB.UTF-8 LC_MONETARY=en_GB.UTF-8 LC_MESSAGES=en_GB.UTF-8
#> [7] LC_PAPER=en_GB.UTF-8 LC_NAME=C LC_ADDRESS=C
#> [10] LC_TELEPHONE=C LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C
#>
#> attached base packages:
#> [1] grid stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] genefilter_1.66.0 ComplexHeatmap_2.3.1 markdown_1.1 knitr_1.26
#> [5] GetoptLong_0.1.7 cola_1.3.2
#>
#> loaded via a namespace (and not attached):
#> [1] circlize_0.4.8 shape_1.4.4 xfun_0.11 slam_0.1-46
#> [5] lattice_0.20-38 splines_3.6.0 colorspace_1.4-1 vctrs_0.2.0
#> [9] stats4_3.6.0 blob_1.2.0 XML_3.98-1.20 survival_2.44-1.1
#> [13] rlang_0.4.2 pillar_1.4.2 DBI_1.0.0 BiocGenerics_0.30.0
#> [17] bit64_0.9-7 RColorBrewer_1.1-2 matrixStats_0.55.0 stringr_1.4.0
#> [21] GlobalOptions_0.1.1 evaluate_0.14 memoise_1.1.0 Biobase_2.44.0
#> [25] IRanges_2.18.3 parallel_3.6.0 AnnotationDbi_1.46.1 highr_0.8
#> [29] Rcpp_1.0.3 xtable_1.8-4 backports_1.1.5 S4Vectors_0.22.1
#> [33] annotate_1.62.0 skmeans_0.2-11 bit_1.1-14 microbenchmark_1.4-7
#> [37] brew_1.0-6 impute_1.58.0 rjson_0.2.20 png_0.1-7
#> [41] digest_0.6.23 stringi_1.4.3 polyclip_1.10-0 clue_0.3-57
#> [45] tools_3.6.0 bitops_1.0-6 magrittr_1.5 eulerr_6.0.0
#> [49] RCurl_1.95-4.12 RSQLite_2.1.4 tibble_2.1.3 cluster_2.1.0
#> [53] crayon_1.3.4 pkgconfig_2.0.3 zeallot_0.1.0 Matrix_1.2-17
#> [57] xml2_1.2.2 httr_1.4.1 R6_2.4.1 mclust_5.4.5
#> [61] compiler_3.6.0