Date: 2019-12-25 20:44:12 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 51941 54
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| ATC:skmeans | 3 | 1.000 | 0.953 | 0.979 | ** | |
| ATC:mclust | 2 | 1.000 | 0.971 | 0.986 | ** | |
| ATC:NMF | 3 | 0.965 | 0.948 | 0.981 | ** | 2 |
| SD:NMF | 2 | 0.961 | 0.929 | 0.974 | ** | |
| CV:kmeans | 3 | 0.923 | 0.891 | 0.944 | * | |
| CV:NMF | 2 | 0.922 | 0.944 | 0.977 | * | |
| MAD:NMF | 2 | 0.922 | 0.943 | 0.977 | * | |
| ATC:kmeans | 2 | 0.891 | 0.981 | 0.989 | ||
| ATC:pam | 4 | 0.880 | 0.937 | 0.970 | ||
| SD:skmeans | 2 | 0.811 | 0.904 | 0.959 | ||
| ATC:hclust | 3 | 0.795 | 0.826 | 0.932 | ||
| SD:hclust | 2 | 0.769 | 0.887 | 0.930 | ||
| SD:kmeans | 3 | 0.769 | 0.873 | 0.919 | ||
| MAD:kmeans | 3 | 0.700 | 0.835 | 0.903 | ||
| CV:hclust | 3 | 0.656 | 0.858 | 0.931 | ||
| CV:skmeans | 2 | 0.652 | 0.791 | 0.913 | ||
| SD:mclust | 2 | 0.620 | 0.882 | 0.941 | ||
| MAD:mclust | 2 | 0.599 | 0.807 | 0.905 | ||
| CV:pam | 2 | 0.571 | 0.826 | 0.919 | ||
| CV:mclust | 2 | 0.507 | 0.795 | 0.903 | ||
| SD:pam | 3 | 0.504 | 0.693 | 0.856 | ||
| MAD:skmeans | 2 | 0.483 | 0.808 | 0.905 | ||
| MAD:hclust | 2 | 0.358 | 0.797 | 0.870 | ||
| MAD:pam | 3 | 0.260 | 0.631 | 0.777 |
**: 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 0.961 0.929 0.974 0.449 0.547 0.547
#> CV:NMF 2 0.922 0.944 0.977 0.443 0.560 0.560
#> MAD:NMF 2 0.922 0.943 0.977 0.463 0.535 0.535
#> ATC:NMF 2 0.922 0.899 0.964 0.274 0.743 0.743
#> SD:skmeans 2 0.811 0.904 0.959 0.481 0.525 0.525
#> CV:skmeans 2 0.652 0.791 0.913 0.491 0.516 0.516
#> MAD:skmeans 2 0.483 0.808 0.905 0.497 0.525 0.525
#> ATC:skmeans 2 0.717 0.837 0.927 0.499 0.525 0.525
#> SD:mclust 2 0.620 0.882 0.941 0.477 0.516 0.516
#> CV:mclust 2 0.507 0.795 0.903 0.455 0.560 0.560
#> MAD:mclust 2 0.599 0.807 0.905 0.451 0.525 0.525
#> ATC:mclust 2 1.000 0.971 0.986 0.502 0.497 0.497
#> SD:kmeans 2 0.534 0.954 0.943 0.400 0.560 0.560
#> CV:kmeans 2 0.484 0.896 0.883 0.369 0.575 0.575
#> MAD:kmeans 2 0.500 0.924 0.913 0.413 0.560 0.560
#> ATC:kmeans 2 0.891 0.981 0.989 0.445 0.547 0.547
#> SD:pam 2 0.883 0.918 0.964 0.418 0.575 0.575
#> CV:pam 2 0.571 0.826 0.919 0.458 0.560 0.560
#> MAD:pam 2 0.315 0.733 0.850 0.414 0.575 0.575
#> ATC:pam 2 0.418 0.694 0.809 0.434 0.609 0.609
#> SD:hclust 2 0.769 0.887 0.930 0.394 0.609 0.609
#> CV:hclust 2 0.496 0.609 0.815 0.290 0.860 0.860
#> MAD:hclust 2 0.358 0.797 0.870 0.406 0.591 0.591
#> ATC:hclust 2 0.693 0.897 0.938 0.308 0.648 0.648
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.590 0.710 0.869 0.466 0.704 0.496
#> CV:NMF 3 0.551 0.736 0.870 0.487 0.743 0.553
#> MAD:NMF 3 0.504 0.710 0.829 0.404 0.697 0.481
#> ATC:NMF 3 0.965 0.948 0.981 0.988 0.662 0.562
#> SD:skmeans 3 0.559 0.718 0.856 0.398 0.727 0.514
#> CV:skmeans 3 0.417 0.627 0.807 0.371 0.718 0.498
#> MAD:skmeans 3 0.329 0.565 0.764 0.354 0.725 0.511
#> ATC:skmeans 3 1.000 0.953 0.979 0.310 0.793 0.616
#> SD:mclust 3 0.424 0.579 0.740 0.161 0.799 0.667
#> CV:mclust 3 0.697 0.883 0.922 0.158 0.874 0.783
#> MAD:mclust 3 0.383 0.478 0.724 0.192 0.617 0.424
#> ATC:mclust 3 0.557 0.733 0.848 0.189 0.887 0.774
#> SD:kmeans 3 0.769 0.873 0.919 0.406 0.908 0.835
#> CV:kmeans 3 0.923 0.891 0.944 0.471 0.885 0.800
#> MAD:kmeans 3 0.700 0.835 0.903 0.465 0.824 0.686
#> ATC:kmeans 3 0.447 0.646 0.816 0.343 0.704 0.525
#> SD:pam 3 0.504 0.693 0.856 0.522 0.763 0.594
#> CV:pam 3 0.460 0.694 0.825 0.402 0.743 0.550
#> MAD:pam 3 0.260 0.631 0.777 0.497 0.774 0.613
#> ATC:pam 3 0.413 0.641 0.790 0.399 0.704 0.546
#> SD:hclust 3 0.725 0.843 0.924 0.326 0.899 0.835
#> CV:hclust 3 0.656 0.858 0.931 0.781 0.633 0.574
#> MAD:hclust 3 0.399 0.750 0.857 0.305 0.902 0.835
#> ATC:hclust 3 0.795 0.826 0.932 0.354 0.913 0.868
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.576 0.626 0.808 0.1189 0.902 0.722
#> CV:NMF 4 0.502 0.580 0.774 0.1258 0.817 0.527
#> MAD:NMF 4 0.510 0.499 0.703 0.1535 0.820 0.528
#> ATC:NMF 4 0.751 0.837 0.915 0.1304 0.940 0.870
#> SD:skmeans 4 0.511 0.531 0.713 0.1170 0.894 0.690
#> CV:skmeans 4 0.408 0.427 0.678 0.1181 0.928 0.784
#> MAD:skmeans 4 0.340 0.380 0.627 0.1182 0.933 0.796
#> ATC:skmeans 4 0.896 0.905 0.959 0.1348 0.881 0.671
#> SD:mclust 4 0.496 0.614 0.768 0.2385 0.690 0.425
#> CV:mclust 4 0.442 0.434 0.725 0.3161 0.744 0.481
#> MAD:mclust 4 0.421 0.574 0.746 0.2786 0.611 0.285
#> ATC:mclust 4 0.853 0.847 0.918 0.1973 0.837 0.602
#> SD:kmeans 4 0.584 0.560 0.744 0.2072 0.989 0.976
#> CV:kmeans 4 0.556 0.577 0.795 0.2384 0.881 0.746
#> MAD:kmeans 4 0.600 0.606 0.756 0.1553 0.810 0.554
#> ATC:kmeans 4 0.736 0.784 0.881 0.2037 0.764 0.477
#> SD:pam 4 0.466 0.656 0.808 0.0355 1.000 1.000
#> CV:pam 4 0.431 0.624 0.805 0.0574 0.964 0.892
#> MAD:pam 4 0.379 0.572 0.756 0.1067 0.891 0.720
#> ATC:pam 4 0.880 0.937 0.970 0.2260 0.806 0.538
#> SD:hclust 4 0.653 0.784 0.892 0.0497 0.998 0.996
#> CV:hclust 4 0.655 0.801 0.915 0.0662 0.973 0.946
#> MAD:hclust 4 0.464 0.712 0.866 0.0819 0.973 0.946
#> ATC:hclust 4 0.588 0.685 0.842 0.2690 0.948 0.911
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.573 0.536 0.756 0.0731 0.864 0.565
#> CV:NMF 5 0.524 0.466 0.699 0.0698 0.888 0.620
#> MAD:NMF 5 0.582 0.528 0.727 0.0685 0.853 0.509
#> ATC:NMF 5 0.647 0.717 0.849 0.1645 0.829 0.602
#> SD:skmeans 5 0.514 0.426 0.633 0.0618 0.934 0.758
#> CV:skmeans 5 0.466 0.360 0.603 0.0601 0.943 0.801
#> MAD:skmeans 5 0.420 0.362 0.585 0.0616 0.902 0.665
#> ATC:skmeans 5 0.813 0.732 0.851 0.0595 0.915 0.690
#> SD:mclust 5 0.539 0.513 0.714 0.0316 0.747 0.355
#> CV:mclust 5 0.534 0.475 0.692 0.0548 0.841 0.505
#> MAD:mclust 5 0.549 0.680 0.790 0.0721 0.864 0.596
#> ATC:mclust 5 0.896 0.843 0.935 0.0672 0.867 0.583
#> SD:kmeans 5 0.553 0.613 0.764 0.0958 0.771 0.509
#> CV:kmeans 5 0.576 0.558 0.751 0.1036 0.836 0.578
#> MAD:kmeans 5 0.577 0.568 0.735 0.0901 0.876 0.609
#> ATC:kmeans 5 0.736 0.777 0.866 0.0786 0.909 0.688
#> SD:pam 5 0.414 0.566 0.797 0.0181 0.984 0.955
#> CV:pam 5 0.429 0.605 0.789 0.0228 0.979 0.933
#> MAD:pam 5 0.384 0.532 0.760 0.0235 0.944 0.835
#> ATC:pam 5 0.769 0.831 0.911 0.0432 0.975 0.900
#> SD:hclust 5 0.573 0.649 0.834 0.0445 0.983 0.967
#> CV:hclust 5 0.544 0.746 0.857 0.0692 0.974 0.945
#> MAD:hclust 5 0.413 0.627 0.786 0.1177 1.000 1.000
#> ATC:hclust 5 0.535 0.609 0.741 0.0965 0.857 0.742
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.614 0.436 0.663 0.04400 0.937 0.721
#> CV:NMF 6 0.560 0.397 0.630 0.04285 0.920 0.666
#> MAD:NMF 6 0.620 0.430 0.668 0.04456 0.914 0.633
#> ATC:NMF 6 0.593 0.611 0.788 0.04809 0.944 0.820
#> SD:skmeans 6 0.550 0.362 0.577 0.03721 0.894 0.593
#> CV:skmeans 6 0.503 0.290 0.556 0.04076 0.948 0.794
#> MAD:skmeans 6 0.481 0.297 0.532 0.04162 0.925 0.687
#> ATC:skmeans 6 0.778 0.641 0.811 0.03558 0.965 0.838
#> SD:mclust 6 0.592 0.571 0.726 0.09767 0.867 0.549
#> CV:mclust 6 0.580 0.494 0.716 0.04415 0.820 0.438
#> MAD:mclust 6 0.625 0.532 0.773 0.06357 0.936 0.772
#> ATC:mclust 6 0.800 0.705 0.843 0.05302 0.931 0.729
#> SD:kmeans 6 0.593 0.569 0.717 0.06219 0.955 0.820
#> CV:kmeans 6 0.609 0.550 0.755 0.05768 0.955 0.829
#> MAD:kmeans 6 0.605 0.484 0.715 0.05490 0.949 0.792
#> ATC:kmeans 6 0.769 0.618 0.792 0.04478 0.928 0.699
#> SD:pam 6 0.464 0.538 0.777 0.01027 0.976 0.932
#> CV:pam 6 0.489 0.583 0.790 0.02448 0.990 0.966
#> MAD:pam 6 0.373 0.470 0.723 0.03698 0.989 0.965
#> ATC:pam 6 0.922 0.845 0.942 0.00142 0.997 0.988
#> SD:hclust 6 0.544 0.679 0.804 0.04526 0.990 0.979
#> CV:hclust 6 0.509 0.570 0.813 0.06682 0.982 0.959
#> MAD:hclust 6 0.476 0.226 0.683 0.07426 0.930 0.851
#> ATC:hclust 6 0.520 0.588 0.706 0.12389 0.723 0.438
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 development.stage(p) disease.state(p) k
#> SD:NMF 51 0.534 1.000 2
#> CV:NMF 52 0.473 1.000 2
#> MAD:NMF 53 0.565 0.977 2
#> ATC:NMF 50 1.000 0.481 2
#> SD:skmeans 52 0.876 0.739 2
#> CV:skmeans 47 0.923 0.891 2
#> MAD:skmeans 49 0.986 0.752 2
#> ATC:skmeans 46 0.249 0.776 2
#> SD:mclust 54 1.000 0.676 2
#> CV:mclust 49 0.773 0.704 2
#> MAD:mclust 50 1.000 1.000 2
#> ATC:mclust 54 1.000 0.729 2
#> SD:kmeans 54 0.688 0.902 2
#> CV:kmeans 53 0.601 1.000 2
#> MAD:kmeans 54 0.688 0.902 2
#> ATC:kmeans 54 0.290 0.921 2
#> SD:pam 51 0.820 0.854 2
#> CV:pam 51 0.534 0.736 2
#> MAD:pam 50 0.474 0.640 2
#> ATC:pam 49 0.440 1.000 2
#> SD:hclust 51 0.820 1.000 2
#> CV:hclust 37 0.637 1.000 2
#> MAD:hclust 49 0.821 1.000 2
#> ATC:hclust 52 1.000 1.000 2
test_to_known_factors(res_list, k = 3)
#> n development.stage(p) disease.state(p) k
#> SD:NMF 47 0.0596 0.827 3
#> CV:NMF 47 0.0336 0.989 3
#> MAD:NMF 47 0.1867 0.930 3
#> ATC:NMF 53 0.6664 0.402 3
#> SD:skmeans 48 0.2849 0.817 3
#> CV:skmeans 39 0.3557 0.978 3
#> MAD:skmeans 33 0.5176 0.883 3
#> ATC:skmeans 53 0.2285 0.530 3
#> SD:mclust 42 1.0000 1.000 3
#> CV:mclust 53 0.4535 0.821 3
#> MAD:mclust 27 1.0000 1.000 3
#> ATC:mclust 46 0.6028 0.853 3
#> SD:kmeans 51 0.3941 0.852 3
#> CV:kmeans 51 0.4536 0.828 3
#> MAD:kmeans 53 0.4278 0.921 3
#> ATC:kmeans 40 0.5136 0.202 3
#> SD:pam 43 0.8305 0.462 3
#> CV:pam 47 0.6489 0.923 3
#> MAD:pam 41 0.7405 0.715 3
#> ATC:pam 51 0.7564 0.780 3
#> SD:hclust 51 0.4999 0.859 3
#> CV:hclust 52 0.4594 0.817 3
#> MAD:hclust 48 0.5122 0.697 3
#> ATC:hclust 49 0.7690 0.256 3
test_to_known_factors(res_list, k = 4)
#> n development.stage(p) disease.state(p) k
#> SD:NMF 41 0.365 0.0222 4
#> CV:NMF 35 0.753 0.6316 4
#> MAD:NMF 32 0.727 0.4362 4
#> ATC:NMF 51 0.464 0.2757 4
#> SD:skmeans 29 0.762 0.4046 4
#> CV:skmeans 19 0.495 0.9755 4
#> MAD:skmeans 16 NA NA 4
#> ATC:skmeans 52 0.380 0.4589 4
#> SD:mclust 40 0.537 0.7060 4
#> CV:mclust 36 0.378 0.8991 4
#> MAD:mclust 41 0.574 0.5850 4
#> ATC:mclust 50 0.734 0.6920 4
#> SD:kmeans 35 0.382 0.6150 4
#> CV:kmeans 37 0.397 0.8046 4
#> MAD:kmeans 42 0.311 0.9401 4
#> ATC:kmeans 48 0.989 0.3512 4
#> SD:pam 42 0.928 0.6238 4
#> CV:pam 44 0.740 0.7924 4
#> MAD:pam 37 0.846 0.8144 4
#> ATC:pam 54 0.971 0.7561 4
#> SD:hclust 49 0.183 0.9949 4
#> CV:hclust 51 0.164 0.9126 4
#> MAD:hclust 46 0.201 0.9924 4
#> ATC:hclust 39 0.297 0.3803 4
test_to_known_factors(res_list, k = 5)
#> n development.stage(p) disease.state(p) k
#> SD:NMF 33 0.707 0.081 5
#> CV:NMF 27 0.773 0.457 5
#> MAD:NMF 34 0.568 0.783 5
#> ATC:NMF 45 0.730 0.606 5
#> SD:skmeans 17 1.000 1.000 5
#> CV:skmeans 15 NA NA 5
#> MAD:skmeans 13 NA NA 5
#> ATC:skmeans 46 0.228 0.206 5
#> SD:mclust 39 0.492 0.705 5
#> CV:mclust 32 0.501 0.911 5
#> MAD:mclust 49 0.220 0.244 5
#> ATC:mclust 50 0.867 0.593 5
#> SD:kmeans 45 0.627 0.931 5
#> CV:kmeans 38 0.183 0.843 5
#> MAD:kmeans 38 0.135 0.964 5
#> ATC:kmeans 51 0.965 0.474 5
#> SD:pam 37 0.427 0.765 5
#> CV:pam 45 0.461 0.922 5
#> MAD:pam 33 0.327 0.938 5
#> ATC:pam 51 0.966 0.575 5
#> SD:hclust 45 0.108 0.308 5
#> CV:hclust 50 0.308 0.847 5
#> MAD:hclust 42 0.224 0.952 5
#> ATC:hclust 47 0.764 0.525 5
test_to_known_factors(res_list, k = 6)
#> n development.stage(p) disease.state(p) k
#> SD:NMF 23 0.492 0.120 6
#> CV:NMF 16 0.460 0.227 6
#> MAD:NMF 20 0.927 0.454 6
#> ATC:NMF 40 0.727 0.444 6
#> SD:skmeans 17 1.000 1.000 6
#> CV:skmeans 14 NA NA 6
#> MAD:skmeans 11 NA NA 6
#> ATC:skmeans 42 0.516 0.406 6
#> SD:mclust 42 0.330 0.753 6
#> CV:mclust 33 0.417 0.360 6
#> MAD:mclust 40 0.440 0.794 6
#> ATC:mclust 38 0.376 0.299 6
#> SD:kmeans 42 0.632 0.753 6
#> CV:kmeans 39 0.422 0.967 6
#> MAD:kmeans 31 0.185 0.895 6
#> ATC:kmeans 40 0.620 0.328 6
#> SD:pam 38 0.721 0.548 6
#> CV:pam 42 0.485 0.952 6
#> MAD:pam 29 0.821 0.348 6
#> ATC:pam 48 0.924 0.665 6
#> SD:hclust 45 0.401 0.940 6
#> CV:hclust 37 0.375 0.814 6
#> MAD:hclust 16 0.120 0.949 6
#> ATC:hclust 41 0.912 0.866 6
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.769 0.887 0.930 0.3939 0.609 0.609
#> 3 3 0.725 0.843 0.924 0.3262 0.899 0.835
#> 4 4 0.653 0.784 0.892 0.0497 0.998 0.996
#> 5 5 0.573 0.649 0.834 0.0445 0.983 0.967
#> 6 6 0.544 0.679 0.804 0.0453 0.990 0.979
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
#> GSM213078 1 0.0376 0.9363 0.996 0.004
#> GSM213082 2 0.4022 0.9606 0.080 0.920
#> GSM213085 1 0.0938 0.9353 0.988 0.012
#> GSM213088 1 0.0000 0.9363 1.000 0.000
#> GSM213091 1 0.3274 0.9030 0.940 0.060
#> GSM213092 1 0.0938 0.9353 0.988 0.012
#> GSM213096 1 0.0672 0.9361 0.992 0.008
#> GSM213100 1 0.0672 0.9361 0.992 0.008
#> GSM213111 2 0.4690 0.9498 0.100 0.900
#> GSM213117 1 0.0938 0.9341 0.988 0.012
#> GSM213118 1 0.2778 0.9126 0.952 0.048
#> GSM213120 1 0.9954 0.0238 0.540 0.460
#> GSM213122 2 0.4022 0.9606 0.080 0.920
#> GSM213074 1 0.2423 0.9166 0.960 0.040
#> GSM213077 1 0.0376 0.9363 0.996 0.004
#> GSM213083 1 0.0376 0.9363 0.996 0.004
#> GSM213094 1 0.4022 0.8872 0.920 0.080
#> GSM213095 2 0.4431 0.9549 0.092 0.908
#> GSM213102 1 0.0000 0.9363 1.000 0.000
#> GSM213103 1 0.9129 0.4546 0.672 0.328
#> GSM213104 1 0.4161 0.8815 0.916 0.084
#> GSM213107 2 0.4022 0.9606 0.080 0.920
#> GSM213108 2 0.4022 0.9606 0.080 0.920
#> GSM213112 1 0.0938 0.9353 0.988 0.012
#> GSM213114 1 0.4022 0.8854 0.920 0.080
#> GSM213115 2 0.7528 0.8373 0.216 0.784
#> GSM213116 1 0.1184 0.9353 0.984 0.016
#> GSM213119 2 0.4022 0.9606 0.080 0.920
#> GSM213072 1 0.2603 0.9187 0.956 0.044
#> GSM213075 1 0.0938 0.9356 0.988 0.012
#> GSM213076 2 0.7376 0.8424 0.208 0.792
#> GSM213079 1 0.4022 0.8872 0.920 0.080
#> GSM213080 1 0.4161 0.8815 0.916 0.084
#> GSM213081 1 0.1414 0.9315 0.980 0.020
#> GSM213084 1 0.0376 0.9363 0.996 0.004
#> GSM213087 2 0.4022 0.9606 0.080 0.920
#> GSM213089 1 0.0938 0.9324 0.988 0.012
#> GSM213090 1 0.4022 0.8872 0.920 0.080
#> GSM213093 1 0.0000 0.9363 1.000 0.000
#> GSM213097 1 0.0000 0.9363 1.000 0.000
#> GSM213099 1 0.3274 0.9030 0.940 0.060
#> GSM213101 1 0.0376 0.9363 0.996 0.004
#> GSM213105 2 0.4022 0.9606 0.080 0.920
#> GSM213109 1 0.0000 0.9363 1.000 0.000
#> GSM213110 2 0.7528 0.8373 0.216 0.784
#> GSM213113 1 0.1633 0.9293 0.976 0.024
#> GSM213121 2 0.4022 0.9606 0.080 0.920
#> GSM213123 1 0.0938 0.9352 0.988 0.012
#> GSM213125 2 0.4022 0.9606 0.080 0.920
#> GSM213073 1 0.4022 0.8872 0.920 0.080
#> GSM213086 1 0.0938 0.9353 0.988 0.012
#> GSM213098 1 0.1843 0.9270 0.972 0.028
#> GSM213106 1 0.0000 0.9363 1.000 0.000
#> GSM213124 1 0.9686 0.2513 0.604 0.396
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.0000 0.9034 1.000 0.000 0.000
#> GSM213082 2 0.0424 0.9291 0.008 0.992 0.000
#> GSM213085 1 0.0592 0.9034 0.988 0.000 0.012
#> GSM213088 1 0.1289 0.8999 0.968 0.000 0.032
#> GSM213091 1 0.5325 0.6569 0.748 0.004 0.248
#> GSM213092 1 0.0592 0.9034 0.988 0.000 0.012
#> GSM213096 1 0.0237 0.9032 0.996 0.000 0.004
#> GSM213100 1 0.0237 0.9032 0.996 0.000 0.004
#> GSM213111 2 0.1289 0.9109 0.032 0.968 0.000
#> GSM213117 1 0.1878 0.8929 0.952 0.004 0.044
#> GSM213118 1 0.2116 0.8863 0.948 0.040 0.012
#> GSM213120 1 0.6822 0.0633 0.508 0.480 0.012
#> GSM213122 2 0.0424 0.9291 0.008 0.992 0.000
#> GSM213074 1 0.2860 0.8630 0.912 0.004 0.084
#> GSM213077 1 0.0000 0.9034 1.000 0.000 0.000
#> GSM213083 1 0.0000 0.9034 1.000 0.000 0.000
#> GSM213094 3 0.4110 0.8655 0.152 0.004 0.844
#> GSM213095 2 0.0829 0.9225 0.012 0.984 0.004
#> GSM213102 1 0.1163 0.8986 0.972 0.000 0.028
#> GSM213103 1 0.6880 0.5142 0.660 0.304 0.036
#> GSM213104 1 0.4075 0.8364 0.880 0.072 0.048
#> GSM213107 2 0.0237 0.9261 0.004 0.996 0.000
#> GSM213108 2 0.0424 0.9291 0.008 0.992 0.000
#> GSM213112 1 0.0592 0.9034 0.988 0.000 0.012
#> GSM213114 1 0.3983 0.8401 0.884 0.068 0.048
#> GSM213115 2 0.5435 0.7032 0.192 0.784 0.024
#> GSM213116 1 0.1878 0.8933 0.952 0.004 0.044
#> GSM213119 2 0.0424 0.9291 0.008 0.992 0.000
#> GSM213072 1 0.2400 0.8778 0.932 0.004 0.064
#> GSM213075 1 0.1525 0.9018 0.964 0.004 0.032
#> GSM213076 2 0.4047 0.7684 0.148 0.848 0.004
#> GSM213079 3 0.2261 0.9466 0.068 0.000 0.932
#> GSM213080 1 0.4075 0.8364 0.880 0.072 0.048
#> GSM213081 1 0.1411 0.8917 0.964 0.000 0.036
#> GSM213084 1 0.0000 0.9034 1.000 0.000 0.000
#> GSM213087 2 0.0237 0.9261 0.004 0.996 0.000
#> GSM213089 1 0.2625 0.8676 0.916 0.000 0.084
#> GSM213090 3 0.1643 0.9243 0.044 0.000 0.956
#> GSM213093 1 0.1411 0.8965 0.964 0.000 0.036
#> GSM213097 1 0.1163 0.8986 0.972 0.000 0.028
#> GSM213099 1 0.6386 0.2709 0.584 0.004 0.412
#> GSM213101 1 0.0000 0.9034 1.000 0.000 0.000
#> GSM213105 2 0.0424 0.9291 0.008 0.992 0.000
#> GSM213109 1 0.0237 0.9035 0.996 0.000 0.004
#> GSM213110 2 0.5435 0.7032 0.192 0.784 0.024
#> GSM213113 1 0.1765 0.8889 0.956 0.004 0.040
#> GSM213121 2 0.0237 0.9261 0.004 0.996 0.000
#> GSM213123 1 0.1289 0.9028 0.968 0.000 0.032
#> GSM213125 2 0.0424 0.9291 0.008 0.992 0.000
#> GSM213073 3 0.2261 0.9466 0.068 0.000 0.932
#> GSM213086 1 0.0592 0.9034 0.988 0.000 0.012
#> GSM213098 1 0.1950 0.8866 0.952 0.008 0.040
#> GSM213106 1 0.1289 0.8975 0.968 0.000 0.032
#> GSM213124 1 0.6935 0.3711 0.604 0.372 0.024
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.0469 0.8786 0.988 0.000 0.000 0.012
#> GSM213082 2 0.1004 0.8748 0.004 0.972 0.000 0.024
#> GSM213085 1 0.0469 0.8786 0.988 0.000 0.000 0.012
#> GSM213088 1 0.1356 0.8748 0.960 0.000 0.008 0.032
#> GSM213091 1 0.5421 0.6061 0.724 0.000 0.076 0.200
#> GSM213092 1 0.0469 0.8786 0.988 0.000 0.000 0.012
#> GSM213096 1 0.0469 0.8793 0.988 0.000 0.000 0.012
#> GSM213100 1 0.0469 0.8793 0.988 0.000 0.000 0.012
#> GSM213111 2 0.1510 0.8698 0.028 0.956 0.000 0.016
#> GSM213117 1 0.2125 0.8632 0.932 0.004 0.012 0.052
#> GSM213118 1 0.1913 0.8625 0.940 0.040 0.000 0.020
#> GSM213120 1 0.6551 0.0994 0.492 0.440 0.004 0.064
#> GSM213122 2 0.0779 0.8800 0.004 0.980 0.000 0.016
#> GSM213074 1 0.2741 0.8332 0.892 0.000 0.012 0.096
#> GSM213077 1 0.0336 0.8789 0.992 0.000 0.000 0.008
#> GSM213083 1 0.0336 0.8789 0.992 0.000 0.000 0.008
#> GSM213094 4 0.6630 0.0000 0.136 0.000 0.252 0.612
#> GSM213095 2 0.3166 0.8424 0.000 0.868 0.016 0.116
#> GSM213102 1 0.1545 0.8696 0.952 0.000 0.008 0.040
#> GSM213103 1 0.5990 0.4788 0.644 0.284 0.000 0.072
#> GSM213104 1 0.4215 0.7768 0.824 0.072 0.000 0.104
#> GSM213107 2 0.3351 0.8276 0.000 0.844 0.008 0.148
#> GSM213108 2 0.1004 0.8748 0.004 0.972 0.000 0.024
#> GSM213112 1 0.0469 0.8786 0.988 0.000 0.000 0.012
#> GSM213114 1 0.4155 0.7806 0.828 0.072 0.000 0.100
#> GSM213115 2 0.4761 0.6426 0.184 0.768 0.000 0.048
#> GSM213116 1 0.1953 0.8677 0.940 0.004 0.012 0.044
#> GSM213119 2 0.1305 0.8783 0.004 0.960 0.000 0.036
#> GSM213072 1 0.2197 0.8512 0.916 0.000 0.004 0.080
#> GSM213075 1 0.1762 0.8763 0.944 0.004 0.004 0.048
#> GSM213076 2 0.4565 0.7098 0.140 0.796 0.000 0.064
#> GSM213079 3 0.1635 0.8523 0.044 0.000 0.948 0.008
#> GSM213080 1 0.4215 0.7768 0.824 0.072 0.000 0.104
#> GSM213081 1 0.2081 0.8476 0.916 0.000 0.000 0.084
#> GSM213084 1 0.0188 0.8785 0.996 0.000 0.000 0.004
#> GSM213087 2 0.1902 0.8693 0.000 0.932 0.004 0.064
#> GSM213089 1 0.2908 0.8376 0.896 0.000 0.040 0.064
#> GSM213090 3 0.2799 0.7828 0.008 0.000 0.884 0.108
#> GSM213093 1 0.1807 0.8682 0.940 0.000 0.008 0.052
#> GSM213097 1 0.1452 0.8711 0.956 0.000 0.008 0.036
#> GSM213099 1 0.6649 0.1554 0.560 0.000 0.100 0.340
#> GSM213101 1 0.0469 0.8786 0.988 0.000 0.000 0.012
#> GSM213105 2 0.1305 0.8783 0.004 0.960 0.000 0.036
#> GSM213109 1 0.0707 0.8786 0.980 0.000 0.000 0.020
#> GSM213110 2 0.4761 0.6426 0.184 0.768 0.000 0.048
#> GSM213113 1 0.2401 0.8406 0.904 0.004 0.000 0.092
#> GSM213121 2 0.3157 0.8324 0.000 0.852 0.004 0.144
#> GSM213123 1 0.1635 0.8755 0.948 0.000 0.008 0.044
#> GSM213125 2 0.0657 0.8797 0.004 0.984 0.000 0.012
#> GSM213073 3 0.2919 0.8411 0.044 0.000 0.896 0.060
#> GSM213086 1 0.0469 0.8786 0.988 0.000 0.000 0.012
#> GSM213098 1 0.2546 0.8379 0.900 0.008 0.000 0.092
#> GSM213106 1 0.1545 0.8701 0.952 0.000 0.008 0.040
#> GSM213124 1 0.5929 0.3735 0.596 0.356 0.000 0.048
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.0510 0.870 0.984 0.000 0.000 0.016 0.000
#> GSM213082 2 0.2389 0.505 0.004 0.880 0.000 0.000 0.116
#> GSM213085 1 0.0451 0.870 0.988 0.000 0.000 0.008 0.004
#> GSM213088 1 0.1282 0.865 0.952 0.000 0.004 0.044 0.000
#> GSM213091 1 0.4067 0.580 0.692 0.000 0.008 0.300 0.000
#> GSM213092 1 0.0451 0.870 0.988 0.000 0.000 0.008 0.004
#> GSM213096 1 0.0771 0.871 0.976 0.000 0.000 0.020 0.004
#> GSM213100 1 0.0771 0.871 0.976 0.000 0.000 0.020 0.004
#> GSM213111 2 0.2450 0.525 0.028 0.896 0.000 0.000 0.076
#> GSM213117 1 0.1928 0.853 0.920 0.004 0.004 0.072 0.000
#> GSM213118 1 0.1756 0.858 0.940 0.036 0.000 0.016 0.008
#> GSM213120 1 0.6677 0.149 0.488 0.356 0.000 0.024 0.132
#> GSM213122 2 0.1041 0.544 0.004 0.964 0.000 0.000 0.032
#> GSM213074 1 0.2707 0.812 0.860 0.000 0.008 0.132 0.000
#> GSM213077 1 0.0404 0.871 0.988 0.000 0.000 0.012 0.000
#> GSM213083 1 0.0404 0.871 0.988 0.000 0.000 0.012 0.000
#> GSM213094 4 0.3493 0.000 0.108 0.000 0.060 0.832 0.000
#> GSM213095 5 0.4560 0.508 0.000 0.484 0.008 0.000 0.508
#> GSM213102 1 0.1430 0.860 0.944 0.000 0.004 0.052 0.000
#> GSM213103 1 0.5927 0.516 0.640 0.248 0.000 0.052 0.060
#> GSM213104 1 0.4405 0.752 0.788 0.052 0.000 0.132 0.028
#> GSM213107 5 0.4294 0.548 0.000 0.468 0.000 0.000 0.532
#> GSM213108 2 0.2389 0.505 0.004 0.880 0.000 0.000 0.116
#> GSM213112 1 0.0451 0.870 0.988 0.000 0.000 0.008 0.004
#> GSM213114 1 0.4320 0.755 0.792 0.052 0.000 0.132 0.024
#> GSM213115 2 0.4979 0.353 0.184 0.732 0.000 0.028 0.056
#> GSM213116 1 0.1798 0.858 0.928 0.004 0.004 0.064 0.000
#> GSM213119 2 0.2011 0.502 0.004 0.908 0.000 0.000 0.088
#> GSM213072 1 0.2074 0.838 0.896 0.000 0.000 0.104 0.000
#> GSM213075 1 0.1892 0.864 0.916 0.000 0.000 0.080 0.004
#> GSM213076 2 0.4950 0.252 0.140 0.732 0.000 0.008 0.120
#> GSM213079 3 0.2813 0.695 0.040 0.000 0.876 0.084 0.000
#> GSM213080 1 0.4405 0.752 0.788 0.052 0.000 0.132 0.028
#> GSM213081 1 0.2280 0.822 0.880 0.000 0.000 0.120 0.000
#> GSM213084 1 0.0290 0.870 0.992 0.000 0.000 0.008 0.000
#> GSM213087 2 0.3177 0.233 0.000 0.792 0.000 0.000 0.208
#> GSM213089 1 0.2286 0.832 0.888 0.000 0.004 0.108 0.000
#> GSM213090 3 0.4421 0.547 0.000 0.000 0.748 0.068 0.184
#> GSM213093 1 0.1831 0.856 0.920 0.000 0.004 0.076 0.000
#> GSM213097 1 0.1357 0.862 0.948 0.000 0.004 0.048 0.000
#> GSM213099 1 0.4437 0.122 0.532 0.000 0.004 0.464 0.000
#> GSM213101 1 0.0510 0.870 0.984 0.000 0.000 0.016 0.000
#> GSM213105 2 0.2011 0.502 0.004 0.908 0.000 0.000 0.088
#> GSM213109 1 0.0880 0.871 0.968 0.000 0.000 0.032 0.000
#> GSM213110 2 0.4979 0.353 0.184 0.732 0.000 0.028 0.056
#> GSM213113 1 0.2536 0.814 0.868 0.004 0.000 0.128 0.000
#> GSM213121 2 0.4306 -0.727 0.000 0.508 0.000 0.000 0.492
#> GSM213123 1 0.1571 0.867 0.936 0.000 0.004 0.060 0.000
#> GSM213125 2 0.1041 0.545 0.004 0.964 0.000 0.000 0.032
#> GSM213073 3 0.5453 0.648 0.040 0.000 0.712 0.088 0.160
#> GSM213086 1 0.0451 0.870 0.988 0.000 0.000 0.008 0.004
#> GSM213098 1 0.2694 0.811 0.864 0.004 0.000 0.128 0.004
#> GSM213106 1 0.1502 0.862 0.940 0.000 0.004 0.056 0.000
#> GSM213124 1 0.5923 0.417 0.592 0.316 0.000 0.032 0.060
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.0458 0.8546 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM213082 2 0.3394 0.6120 0.000 0.752 0.000 0.000 0.236 0.012
#> GSM213085 1 0.0405 0.8554 0.988 0.000 0.004 0.008 0.000 0.000
#> GSM213088 1 0.1075 0.8507 0.952 0.000 0.000 0.048 0.000 0.000
#> GSM213091 1 0.4216 0.5594 0.676 0.000 0.032 0.288 0.000 0.004
#> GSM213092 1 0.0405 0.8554 0.988 0.000 0.004 0.008 0.000 0.000
#> GSM213096 1 0.0692 0.8563 0.976 0.000 0.004 0.020 0.000 0.000
#> GSM213100 1 0.0692 0.8563 0.976 0.000 0.004 0.020 0.000 0.000
#> GSM213111 2 0.3799 0.6272 0.024 0.764 0.000 0.000 0.196 0.016
#> GSM213117 1 0.1843 0.8410 0.912 0.004 0.004 0.080 0.000 0.000
#> GSM213118 1 0.2001 0.8402 0.924 0.028 0.004 0.032 0.012 0.000
#> GSM213120 1 0.7079 0.1481 0.464 0.304 0.008 0.040 0.160 0.024
#> GSM213122 2 0.0458 0.6750 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM213074 1 0.2699 0.8003 0.856 0.000 0.008 0.124 0.000 0.012
#> GSM213077 1 0.0363 0.8554 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM213083 1 0.0363 0.8554 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM213094 4 0.4369 0.0000 0.092 0.000 0.056 0.772 0.000 0.080
#> GSM213095 5 0.2510 0.4416 0.000 0.100 0.000 0.000 0.872 0.028
#> GSM213102 1 0.1204 0.8458 0.944 0.000 0.000 0.056 0.000 0.000
#> GSM213103 1 0.6876 0.4785 0.592 0.184 0.012 0.072 0.052 0.088
#> GSM213104 1 0.4811 0.6888 0.724 0.040 0.004 0.188 0.032 0.012
#> GSM213107 5 0.3163 0.6813 0.000 0.232 0.000 0.004 0.764 0.000
#> GSM213108 2 0.3483 0.6105 0.000 0.748 0.000 0.000 0.236 0.016
#> GSM213112 1 0.0405 0.8554 0.988 0.000 0.004 0.008 0.000 0.000
#> GSM213114 1 0.4716 0.6926 0.728 0.040 0.004 0.188 0.032 0.008
#> GSM213115 2 0.5907 0.5012 0.156 0.672 0.012 0.028 0.040 0.092
#> GSM213116 1 0.1988 0.8426 0.912 0.004 0.008 0.072 0.000 0.004
#> GSM213119 2 0.1700 0.6459 0.000 0.916 0.000 0.000 0.080 0.004
#> GSM213072 1 0.2053 0.8242 0.888 0.000 0.000 0.108 0.000 0.004
#> GSM213075 1 0.2373 0.8403 0.888 0.000 0.000 0.084 0.004 0.024
#> GSM213076 2 0.5458 0.4164 0.136 0.624 0.000 0.008 0.224 0.008
#> GSM213079 3 0.4002 0.6336 0.012 0.000 0.740 0.032 0.000 0.216
#> GSM213080 1 0.4811 0.6888 0.724 0.040 0.004 0.188 0.032 0.012
#> GSM213081 1 0.2848 0.7676 0.816 0.000 0.000 0.176 0.000 0.008
#> GSM213084 1 0.0260 0.8547 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM213087 2 0.3023 0.4627 0.000 0.768 0.000 0.000 0.232 0.000
#> GSM213089 1 0.1957 0.8214 0.888 0.000 0.000 0.112 0.000 0.000
#> GSM213090 6 0.2092 0.0000 0.000 0.000 0.124 0.000 0.000 0.876
#> GSM213093 1 0.1610 0.8425 0.916 0.000 0.000 0.084 0.000 0.000
#> GSM213097 1 0.1141 0.8473 0.948 0.000 0.000 0.052 0.000 0.000
#> GSM213099 1 0.4523 0.0911 0.516 0.000 0.032 0.452 0.000 0.000
#> GSM213101 1 0.0458 0.8546 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM213105 2 0.1700 0.6459 0.000 0.916 0.000 0.000 0.080 0.004
#> GSM213109 1 0.0790 0.8560 0.968 0.000 0.000 0.032 0.000 0.000
#> GSM213110 2 0.5907 0.5012 0.156 0.672 0.012 0.028 0.040 0.092
#> GSM213113 1 0.3056 0.7586 0.804 0.000 0.000 0.184 0.004 0.008
#> GSM213121 5 0.3619 0.6715 0.000 0.316 0.000 0.004 0.680 0.000
#> GSM213123 1 0.1556 0.8464 0.920 0.000 0.000 0.080 0.000 0.000
#> GSM213125 2 0.0632 0.6761 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM213073 3 0.0363 0.6842 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM213086 1 0.0405 0.8554 0.988 0.000 0.004 0.008 0.000 0.000
#> GSM213098 1 0.3166 0.7554 0.800 0.000 0.000 0.184 0.008 0.008
#> GSM213106 1 0.1327 0.8481 0.936 0.000 0.000 0.064 0.000 0.000
#> GSM213124 1 0.6789 0.3958 0.560 0.248 0.012 0.036 0.052 0.092
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 development.stage(p) disease.state(p) k
#> SD:hclust 51 0.820 1.000 2
#> SD:hclust 51 0.500 0.859 3
#> SD:hclust 49 0.183 0.995 4
#> SD:hclust 45 0.108 0.308 5
#> SD:hclust 45 0.401 0.940 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "kmeans"]
# you can also extract it by
# res = res_list["SD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.534 0.954 0.943 0.4004 0.560 0.560
#> 3 3 0.769 0.873 0.919 0.4061 0.908 0.835
#> 4 4 0.584 0.560 0.744 0.2072 0.989 0.976
#> 5 5 0.553 0.613 0.764 0.0958 0.771 0.509
#> 6 6 0.593 0.569 0.717 0.0622 0.955 0.820
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
#> GSM213078 1 0.0000 0.981 1.000 0.000
#> GSM213082 2 0.5629 0.964 0.132 0.868
#> GSM213085 1 0.0000 0.981 1.000 0.000
#> GSM213088 1 0.0000 0.981 1.000 0.000
#> GSM213091 1 0.1843 0.958 0.972 0.028
#> GSM213092 1 0.0000 0.981 1.000 0.000
#> GSM213096 1 0.0000 0.981 1.000 0.000
#> GSM213100 1 0.0000 0.981 1.000 0.000
#> GSM213111 2 0.5629 0.964 0.132 0.868
#> GSM213117 1 0.0000 0.981 1.000 0.000
#> GSM213118 1 0.0000 0.981 1.000 0.000
#> GSM213120 2 0.5629 0.964 0.132 0.868
#> GSM213122 2 0.5629 0.964 0.132 0.868
#> GSM213074 1 0.0000 0.981 1.000 0.000
#> GSM213077 1 0.0000 0.981 1.000 0.000
#> GSM213083 1 0.0000 0.981 1.000 0.000
#> GSM213094 1 0.5629 0.856 0.868 0.132
#> GSM213095 2 0.1414 0.855 0.020 0.980
#> GSM213102 1 0.0000 0.981 1.000 0.000
#> GSM213103 2 0.8081 0.836 0.248 0.752
#> GSM213104 1 0.0000 0.981 1.000 0.000
#> GSM213107 2 0.5629 0.964 0.132 0.868
#> GSM213108 2 0.5629 0.964 0.132 0.868
#> GSM213112 1 0.0000 0.981 1.000 0.000
#> GSM213114 1 0.0000 0.981 1.000 0.000
#> GSM213115 2 0.5629 0.964 0.132 0.868
#> GSM213116 1 0.0000 0.981 1.000 0.000
#> GSM213119 2 0.5629 0.964 0.132 0.868
#> GSM213072 1 0.0672 0.974 0.992 0.008
#> GSM213075 1 0.0000 0.981 1.000 0.000
#> GSM213076 2 0.5629 0.964 0.132 0.868
#> GSM213079 1 0.5629 0.856 0.868 0.132
#> GSM213080 1 0.0000 0.981 1.000 0.000
#> GSM213081 1 0.0000 0.981 1.000 0.000
#> GSM213084 1 0.0000 0.981 1.000 0.000
#> GSM213087 2 0.5629 0.964 0.132 0.868
#> GSM213089 1 0.0000 0.981 1.000 0.000
#> GSM213090 1 0.5629 0.856 0.868 0.132
#> GSM213093 1 0.0000 0.981 1.000 0.000
#> GSM213097 1 0.0000 0.981 1.000 0.000
#> GSM213099 1 0.1843 0.958 0.972 0.028
#> GSM213101 1 0.0000 0.981 1.000 0.000
#> GSM213105 2 0.5629 0.964 0.132 0.868
#> GSM213109 1 0.0000 0.981 1.000 0.000
#> GSM213110 2 0.5629 0.964 0.132 0.868
#> GSM213113 1 0.0000 0.981 1.000 0.000
#> GSM213121 2 0.5629 0.964 0.132 0.868
#> GSM213123 1 0.0000 0.981 1.000 0.000
#> GSM213125 2 0.5629 0.964 0.132 0.868
#> GSM213073 1 0.5629 0.856 0.868 0.132
#> GSM213086 1 0.0000 0.981 1.000 0.000
#> GSM213098 1 0.0000 0.981 1.000 0.000
#> GSM213106 1 0.0000 0.981 1.000 0.000
#> GSM213124 2 0.9686 0.572 0.396 0.604
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.0747 0.904 0.984 0.000 0.016
#> GSM213082 2 0.0237 0.934 0.000 0.996 0.004
#> GSM213085 1 0.1163 0.901 0.972 0.000 0.028
#> GSM213088 1 0.0747 0.904 0.984 0.000 0.016
#> GSM213091 1 0.6026 0.490 0.624 0.000 0.376
#> GSM213092 1 0.1163 0.901 0.972 0.000 0.028
#> GSM213096 1 0.1643 0.892 0.956 0.000 0.044
#> GSM213100 1 0.0424 0.904 0.992 0.000 0.008
#> GSM213111 2 0.0424 0.934 0.000 0.992 0.008
#> GSM213117 1 0.3340 0.868 0.880 0.000 0.120
#> GSM213118 1 0.1411 0.896 0.964 0.000 0.036
#> GSM213120 2 0.1643 0.925 0.000 0.956 0.044
#> GSM213122 2 0.0237 0.934 0.000 0.996 0.004
#> GSM213074 1 0.4702 0.784 0.788 0.000 0.212
#> GSM213077 1 0.0892 0.904 0.980 0.000 0.020
#> GSM213083 1 0.0747 0.904 0.984 0.000 0.016
#> GSM213094 3 0.2711 0.967 0.088 0.000 0.912
#> GSM213095 2 0.1643 0.925 0.000 0.956 0.044
#> GSM213102 1 0.3340 0.868 0.880 0.000 0.120
#> GSM213103 2 0.6858 0.636 0.188 0.728 0.084
#> GSM213104 1 0.2537 0.868 0.920 0.000 0.080
#> GSM213107 2 0.1411 0.926 0.000 0.964 0.036
#> GSM213108 2 0.0592 0.933 0.000 0.988 0.012
#> GSM213112 1 0.1163 0.901 0.972 0.000 0.028
#> GSM213114 1 0.2066 0.883 0.940 0.000 0.060
#> GSM213115 2 0.0000 0.935 0.000 1.000 0.000
#> GSM213116 1 0.3267 0.870 0.884 0.000 0.116
#> GSM213119 2 0.0237 0.934 0.000 0.996 0.004
#> GSM213072 1 0.4346 0.820 0.816 0.000 0.184
#> GSM213075 1 0.4291 0.819 0.820 0.000 0.180
#> GSM213076 2 0.1529 0.926 0.000 0.960 0.040
#> GSM213079 3 0.2356 0.978 0.072 0.000 0.928
#> GSM213080 1 0.2537 0.868 0.920 0.000 0.080
#> GSM213081 1 0.1163 0.900 0.972 0.000 0.028
#> GSM213084 1 0.0592 0.904 0.988 0.000 0.012
#> GSM213087 2 0.0000 0.935 0.000 1.000 0.000
#> GSM213089 1 0.3686 0.855 0.860 0.000 0.140
#> GSM213090 3 0.2066 0.977 0.060 0.000 0.940
#> GSM213093 1 0.3482 0.863 0.872 0.000 0.128
#> GSM213097 1 0.3340 0.868 0.880 0.000 0.120
#> GSM213099 1 0.6026 0.490 0.624 0.000 0.376
#> GSM213101 1 0.0424 0.903 0.992 0.000 0.008
#> GSM213105 2 0.0237 0.934 0.000 0.996 0.004
#> GSM213109 1 0.1411 0.901 0.964 0.000 0.036
#> GSM213110 2 0.0592 0.933 0.000 0.988 0.012
#> GSM213113 1 0.1964 0.896 0.944 0.000 0.056
#> GSM213121 2 0.1411 0.926 0.000 0.964 0.036
#> GSM213123 1 0.1031 0.904 0.976 0.000 0.024
#> GSM213125 2 0.0237 0.934 0.000 0.996 0.004
#> GSM213073 3 0.1964 0.967 0.056 0.000 0.944
#> GSM213086 1 0.1163 0.901 0.972 0.000 0.028
#> GSM213098 1 0.2537 0.878 0.920 0.000 0.080
#> GSM213106 1 0.3340 0.868 0.880 0.000 0.120
#> GSM213124 2 0.7442 0.370 0.316 0.628 0.056
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.0921 0.594 0.972 0.000 0.000 0.028
#> GSM213082 2 0.4605 0.758 0.000 0.664 0.000 0.336
#> GSM213085 1 0.3969 0.539 0.804 0.000 0.016 0.180
#> GSM213088 1 0.4382 0.526 0.704 0.000 0.000 0.296
#> GSM213091 1 0.7788 0.166 0.380 0.000 0.244 0.376
#> GSM213092 1 0.3647 0.547 0.832 0.000 0.016 0.152
#> GSM213096 1 0.4019 0.515 0.792 0.000 0.012 0.196
#> GSM213100 1 0.2124 0.582 0.924 0.000 0.008 0.068
#> GSM213111 2 0.4624 0.754 0.000 0.660 0.000 0.340
#> GSM213117 1 0.6123 0.459 0.572 0.000 0.056 0.372
#> GSM213118 1 0.4963 0.527 0.696 0.000 0.020 0.284
#> GSM213120 2 0.2345 0.643 0.000 0.900 0.000 0.100
#> GSM213122 2 0.4222 0.771 0.000 0.728 0.000 0.272
#> GSM213074 1 0.6889 0.374 0.496 0.000 0.108 0.396
#> GSM213077 1 0.0524 0.594 0.988 0.000 0.008 0.004
#> GSM213083 1 0.0592 0.595 0.984 0.000 0.000 0.016
#> GSM213094 3 0.1929 0.945 0.024 0.000 0.940 0.036
#> GSM213095 2 0.2345 0.646 0.000 0.900 0.000 0.100
#> GSM213102 1 0.5986 0.485 0.620 0.000 0.060 0.320
#> GSM213103 2 0.5749 0.125 0.040 0.680 0.012 0.268
#> GSM213104 1 0.7606 0.154 0.564 0.212 0.020 0.204
#> GSM213107 2 0.0469 0.670 0.000 0.988 0.000 0.012
#> GSM213108 2 0.4872 0.749 0.000 0.640 0.004 0.356
#> GSM213112 1 0.3925 0.540 0.808 0.000 0.016 0.176
#> GSM213114 1 0.4163 0.494 0.792 0.000 0.020 0.188
#> GSM213115 2 0.4454 0.765 0.000 0.692 0.000 0.308
#> GSM213116 1 0.6135 0.455 0.568 0.000 0.056 0.376
#> GSM213119 2 0.4222 0.771 0.000 0.728 0.000 0.272
#> GSM213072 1 0.6884 0.375 0.464 0.000 0.104 0.432
#> GSM213075 1 0.6758 0.370 0.504 0.000 0.096 0.400
#> GSM213076 2 0.1940 0.656 0.000 0.924 0.000 0.076
#> GSM213079 3 0.0779 0.967 0.016 0.000 0.980 0.004
#> GSM213080 1 0.6942 0.282 0.640 0.144 0.020 0.196
#> GSM213081 1 0.2928 0.568 0.880 0.000 0.012 0.108
#> GSM213084 1 0.0336 0.595 0.992 0.000 0.000 0.008
#> GSM213087 2 0.4277 0.771 0.000 0.720 0.000 0.280
#> GSM213089 1 0.6264 0.435 0.560 0.000 0.064 0.376
#> GSM213090 3 0.0804 0.965 0.008 0.000 0.980 0.012
#> GSM213093 1 0.5926 0.492 0.632 0.000 0.060 0.308
#> GSM213097 1 0.5883 0.494 0.640 0.000 0.060 0.300
#> GSM213099 1 0.7746 0.185 0.392 0.000 0.232 0.376
#> GSM213101 1 0.1389 0.596 0.952 0.000 0.000 0.048
#> GSM213105 2 0.4222 0.771 0.000 0.728 0.000 0.272
#> GSM213109 1 0.2542 0.592 0.904 0.000 0.012 0.084
#> GSM213110 2 0.4720 0.761 0.000 0.672 0.004 0.324
#> GSM213113 1 0.5991 0.478 0.620 0.020 0.024 0.336
#> GSM213121 2 0.0469 0.670 0.000 0.988 0.000 0.012
#> GSM213123 1 0.4560 0.533 0.700 0.000 0.004 0.296
#> GSM213125 2 0.4164 0.773 0.000 0.736 0.000 0.264
#> GSM213073 3 0.0469 0.955 0.000 0.000 0.988 0.012
#> GSM213086 1 0.3881 0.541 0.812 0.000 0.016 0.172
#> GSM213098 1 0.8042 0.194 0.456 0.168 0.024 0.352
#> GSM213106 1 0.6041 0.472 0.608 0.000 0.060 0.332
#> GSM213124 4 0.6106 0.000 0.112 0.160 0.016 0.712
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.4817 0.643 0.656 0.000 0.000 0.300 0.044
#> GSM213082 2 0.3003 0.573 0.000 0.812 0.000 0.000 0.188
#> GSM213085 1 0.4180 0.708 0.768 0.000 0.012 0.192 0.028
#> GSM213088 4 0.4254 0.650 0.220 0.000 0.000 0.740 0.040
#> GSM213091 4 0.3806 0.634 0.000 0.000 0.104 0.812 0.084
#> GSM213092 1 0.4140 0.712 0.764 0.000 0.008 0.200 0.028
#> GSM213096 1 0.2846 0.714 0.864 0.000 0.008 0.120 0.008
#> GSM213100 1 0.4548 0.686 0.708 0.000 0.008 0.256 0.028
#> GSM213111 2 0.4385 0.359 0.004 0.672 0.012 0.000 0.312
#> GSM213117 4 0.2020 0.777 0.100 0.000 0.000 0.900 0.000
#> GSM213118 1 0.5314 0.587 0.652 0.000 0.016 0.280 0.052
#> GSM213120 5 0.5071 0.604 0.040 0.340 0.000 0.004 0.616
#> GSM213122 2 0.0000 0.694 0.000 1.000 0.000 0.000 0.000
#> GSM213074 4 0.3207 0.756 0.056 0.000 0.024 0.872 0.048
#> GSM213077 1 0.4900 0.652 0.656 0.000 0.004 0.300 0.040
#> GSM213083 1 0.5107 0.633 0.632 0.000 0.004 0.316 0.048
#> GSM213094 3 0.4127 0.872 0.004 0.000 0.796 0.100 0.100
#> GSM213095 5 0.4772 0.594 0.012 0.352 0.012 0.000 0.624
#> GSM213102 4 0.3238 0.748 0.136 0.000 0.000 0.836 0.028
#> GSM213103 5 0.7859 0.350 0.264 0.228 0.020 0.044 0.444
#> GSM213104 1 0.3840 0.477 0.772 0.000 0.012 0.008 0.208
#> GSM213107 2 0.5453 -0.362 0.044 0.528 0.008 0.000 0.420
#> GSM213108 2 0.4090 0.472 0.000 0.716 0.016 0.000 0.268
#> GSM213112 1 0.4180 0.708 0.768 0.000 0.012 0.192 0.028
#> GSM213114 1 0.2756 0.664 0.892 0.000 0.012 0.036 0.060
#> GSM213115 2 0.2455 0.667 0.004 0.896 0.008 0.004 0.088
#> GSM213116 4 0.2124 0.778 0.096 0.000 0.000 0.900 0.004
#> GSM213119 2 0.0510 0.690 0.000 0.984 0.000 0.000 0.016
#> GSM213072 4 0.4128 0.714 0.092 0.000 0.032 0.816 0.060
#> GSM213075 4 0.2790 0.768 0.060 0.000 0.020 0.892 0.028
#> GSM213076 5 0.4674 0.555 0.016 0.416 0.000 0.000 0.568
#> GSM213079 3 0.1282 0.937 0.004 0.000 0.952 0.044 0.000
#> GSM213080 1 0.2701 0.635 0.884 0.000 0.012 0.012 0.092
#> GSM213081 1 0.5182 0.652 0.708 0.000 0.012 0.184 0.096
#> GSM213084 1 0.4728 0.652 0.664 0.000 0.000 0.296 0.040
#> GSM213087 2 0.1282 0.678 0.000 0.952 0.004 0.000 0.044
#> GSM213089 4 0.1818 0.777 0.044 0.000 0.000 0.932 0.024
#> GSM213090 3 0.2209 0.924 0.000 0.000 0.912 0.032 0.056
#> GSM213093 4 0.3445 0.746 0.140 0.000 0.000 0.824 0.036
#> GSM213097 4 0.3691 0.725 0.156 0.000 0.000 0.804 0.040
#> GSM213099 4 0.3639 0.662 0.000 0.000 0.076 0.824 0.100
#> GSM213101 1 0.4687 0.657 0.672 0.000 0.000 0.288 0.040
#> GSM213105 2 0.0510 0.690 0.000 0.984 0.000 0.000 0.016
#> GSM213109 1 0.5242 0.518 0.556 0.000 0.004 0.400 0.040
#> GSM213110 2 0.2880 0.647 0.004 0.864 0.008 0.004 0.120
#> GSM213113 1 0.6120 0.451 0.596 0.000 0.008 0.224 0.172
#> GSM213121 2 0.5396 -0.364 0.040 0.528 0.008 0.000 0.424
#> GSM213123 4 0.4337 0.637 0.204 0.000 0.000 0.744 0.052
#> GSM213125 2 0.0609 0.694 0.000 0.980 0.000 0.000 0.020
#> GSM213073 3 0.1728 0.933 0.004 0.000 0.940 0.036 0.020
#> GSM213086 1 0.4145 0.709 0.772 0.000 0.012 0.188 0.028
#> GSM213098 1 0.6415 0.286 0.540 0.000 0.012 0.152 0.296
#> GSM213106 4 0.3085 0.762 0.116 0.000 0.000 0.852 0.032
#> GSM213124 4 0.8341 0.041 0.108 0.252 0.016 0.420 0.204
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.2520 0.6129 0.872 0.000 0.000 0.108 0.008 0.012
#> GSM213082 2 0.3445 0.5720 0.000 0.732 0.000 0.000 0.260 0.008
#> GSM213085 1 0.4814 0.5208 0.668 0.000 0.000 0.076 0.012 0.244
#> GSM213088 4 0.4473 0.5463 0.396 0.000 0.000 0.576 0.008 0.020
#> GSM213091 4 0.3611 0.5640 0.004 0.000 0.072 0.832 0.052 0.040
#> GSM213092 1 0.4448 0.5585 0.708 0.000 0.000 0.068 0.008 0.216
#> GSM213096 1 0.4002 0.5633 0.736 0.000 0.000 0.036 0.008 0.220
#> GSM213100 1 0.2942 0.6338 0.860 0.000 0.000 0.068 0.008 0.064
#> GSM213111 2 0.4694 0.3223 0.000 0.572 0.000 0.000 0.376 0.052
#> GSM213117 4 0.3852 0.6763 0.180 0.000 0.000 0.764 0.004 0.052
#> GSM213118 1 0.6128 0.0748 0.444 0.000 0.000 0.192 0.012 0.352
#> GSM213120 5 0.5721 0.5979 0.000 0.188 0.000 0.008 0.556 0.248
#> GSM213122 2 0.0363 0.7663 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM213074 4 0.3439 0.6008 0.080 0.000 0.000 0.832 0.020 0.068
#> GSM213077 1 0.1757 0.6415 0.916 0.000 0.000 0.076 0.000 0.008
#> GSM213083 1 0.1958 0.6321 0.896 0.000 0.000 0.100 0.000 0.004
#> GSM213094 3 0.5803 0.6956 0.000 0.000 0.644 0.124 0.100 0.132
#> GSM213095 5 0.3543 0.6367 0.000 0.224 0.000 0.004 0.756 0.016
#> GSM213102 4 0.3547 0.6644 0.300 0.000 0.000 0.696 0.000 0.004
#> GSM213103 6 0.7213 0.0727 0.040 0.120 0.004 0.084 0.232 0.520
#> GSM213104 1 0.5300 0.0263 0.496 0.000 0.000 0.000 0.104 0.400
#> GSM213107 5 0.5673 0.6313 0.000 0.396 0.000 0.004 0.464 0.136
#> GSM213108 2 0.4952 0.4021 0.000 0.584 0.004 0.004 0.352 0.056
#> GSM213112 1 0.4814 0.5208 0.668 0.000 0.000 0.076 0.012 0.244
#> GSM213114 1 0.3969 0.4273 0.668 0.000 0.000 0.000 0.020 0.312
#> GSM213115 2 0.2512 0.7332 0.000 0.880 0.000 0.000 0.060 0.060
#> GSM213116 4 0.3819 0.6764 0.176 0.000 0.000 0.768 0.004 0.052
#> GSM213119 2 0.0405 0.7610 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM213072 4 0.4820 0.4959 0.112 0.000 0.000 0.716 0.028 0.144
#> GSM213075 4 0.3753 0.6297 0.072 0.000 0.000 0.812 0.028 0.088
#> GSM213076 5 0.4388 0.6599 0.000 0.276 0.000 0.000 0.668 0.056
#> GSM213079 3 0.0146 0.8804 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM213080 1 0.4144 0.3480 0.620 0.000 0.000 0.000 0.020 0.360
#> GSM213081 1 0.4913 0.4367 0.684 0.000 0.000 0.072 0.028 0.216
#> GSM213084 1 0.1866 0.6318 0.908 0.000 0.000 0.084 0.000 0.008
#> GSM213087 2 0.1296 0.7402 0.000 0.952 0.000 0.004 0.032 0.012
#> GSM213089 4 0.2323 0.6711 0.084 0.000 0.000 0.892 0.012 0.012
#> GSM213090 3 0.2001 0.8629 0.000 0.000 0.912 0.008 0.068 0.012
#> GSM213093 4 0.4199 0.6553 0.292 0.000 0.000 0.676 0.008 0.024
#> GSM213097 4 0.4365 0.6208 0.332 0.000 0.000 0.636 0.008 0.024
#> GSM213099 4 0.3965 0.5672 0.016 0.000 0.040 0.816 0.052 0.076
#> GSM213101 1 0.2547 0.6158 0.868 0.000 0.000 0.112 0.004 0.016
#> GSM213105 2 0.0405 0.7610 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM213109 1 0.3802 0.5429 0.748 0.000 0.000 0.208 0.000 0.044
#> GSM213110 2 0.3107 0.7119 0.000 0.844 0.004 0.000 0.080 0.072
#> GSM213113 6 0.6558 0.3815 0.252 0.000 0.000 0.124 0.100 0.524
#> GSM213121 5 0.5600 0.6251 0.000 0.412 0.000 0.004 0.460 0.124
#> GSM213123 4 0.5944 0.4844 0.344 0.000 0.000 0.504 0.024 0.128
#> GSM213125 2 0.1007 0.7635 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM213073 3 0.0508 0.8782 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM213086 1 0.4626 0.5403 0.688 0.000 0.000 0.076 0.008 0.228
#> GSM213098 6 0.5882 0.5358 0.172 0.000 0.000 0.088 0.112 0.628
#> GSM213106 4 0.3586 0.6770 0.268 0.000 0.000 0.720 0.000 0.012
#> GSM213124 4 0.8179 -0.1121 0.060 0.180 0.004 0.376 0.112 0.268
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 development.stage(p) disease.state(p) k
#> SD:kmeans 54 0.688 0.902 2
#> SD:kmeans 51 0.394 0.852 3
#> SD:kmeans 35 0.382 0.615 4
#> SD:kmeans 45 0.627 0.931 5
#> SD:kmeans 42 0.632 0.753 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.811 0.904 0.959 0.4814 0.525 0.525
#> 3 3 0.559 0.718 0.856 0.3976 0.727 0.514
#> 4 4 0.511 0.531 0.713 0.1170 0.894 0.690
#> 5 5 0.514 0.426 0.633 0.0618 0.934 0.758
#> 6 6 0.550 0.362 0.577 0.0372 0.894 0.593
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
#> GSM213078 1 0.0000 0.952 1.000 0.000
#> GSM213082 2 0.0000 0.960 0.000 1.000
#> GSM213085 1 0.0672 0.948 0.992 0.008
#> GSM213088 1 0.6148 0.804 0.848 0.152
#> GSM213091 1 0.0000 0.952 1.000 0.000
#> GSM213092 1 0.0000 0.952 1.000 0.000
#> GSM213096 1 0.0000 0.952 1.000 0.000
#> GSM213100 1 0.0000 0.952 1.000 0.000
#> GSM213111 2 0.0000 0.960 0.000 1.000
#> GSM213117 1 0.0000 0.952 1.000 0.000
#> GSM213118 1 0.1843 0.936 0.972 0.028
#> GSM213120 2 0.0000 0.960 0.000 1.000
#> GSM213122 2 0.0000 0.960 0.000 1.000
#> GSM213074 1 0.0000 0.952 1.000 0.000
#> GSM213077 1 0.0000 0.952 1.000 0.000
#> GSM213083 1 0.0000 0.952 1.000 0.000
#> GSM213094 1 0.4815 0.872 0.896 0.104
#> GSM213095 2 0.0000 0.960 0.000 1.000
#> GSM213102 1 0.0000 0.952 1.000 0.000
#> GSM213103 2 0.0000 0.960 0.000 1.000
#> GSM213104 2 0.1414 0.945 0.020 0.980
#> GSM213107 2 0.0000 0.960 0.000 1.000
#> GSM213108 2 0.0000 0.960 0.000 1.000
#> GSM213112 1 0.0376 0.950 0.996 0.004
#> GSM213114 1 0.0938 0.946 0.988 0.012
#> GSM213115 2 0.0000 0.960 0.000 1.000
#> GSM213116 1 0.0000 0.952 1.000 0.000
#> GSM213119 2 0.0000 0.960 0.000 1.000
#> GSM213072 1 0.0376 0.950 0.996 0.004
#> GSM213075 1 0.4161 0.891 0.916 0.084
#> GSM213076 2 0.0000 0.960 0.000 1.000
#> GSM213079 1 0.5737 0.839 0.864 0.136
#> GSM213080 2 0.8608 0.595 0.284 0.716
#> GSM213081 1 0.0000 0.952 1.000 0.000
#> GSM213084 1 0.0000 0.952 1.000 0.000
#> GSM213087 2 0.0000 0.960 0.000 1.000
#> GSM213089 1 0.0000 0.952 1.000 0.000
#> GSM213090 2 0.9608 0.327 0.384 0.616
#> GSM213093 1 0.0000 0.952 1.000 0.000
#> GSM213097 1 0.0000 0.952 1.000 0.000
#> GSM213099 1 0.0376 0.950 0.996 0.004
#> GSM213101 1 0.0000 0.952 1.000 0.000
#> GSM213105 2 0.0000 0.960 0.000 1.000
#> GSM213109 1 0.0000 0.952 1.000 0.000
#> GSM213110 2 0.0000 0.960 0.000 1.000
#> GSM213113 1 0.9170 0.529 0.668 0.332
#> GSM213121 2 0.0000 0.960 0.000 1.000
#> GSM213123 1 0.0000 0.952 1.000 0.000
#> GSM213125 2 0.0000 0.960 0.000 1.000
#> GSM213073 1 0.9732 0.358 0.596 0.404
#> GSM213086 1 0.0000 0.952 1.000 0.000
#> GSM213098 1 0.8016 0.694 0.756 0.244
#> GSM213106 1 0.0000 0.952 1.000 0.000
#> GSM213124 2 0.1633 0.941 0.024 0.976
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.1529 0.7562 0.960 0.000 0.040
#> GSM213082 2 0.0000 0.9728 0.000 1.000 0.000
#> GSM213085 1 0.4912 0.6897 0.796 0.008 0.196
#> GSM213088 1 0.7804 0.5026 0.664 0.120 0.216
#> GSM213091 3 0.1031 0.7535 0.024 0.000 0.976
#> GSM213092 1 0.3686 0.7367 0.860 0.000 0.140
#> GSM213096 1 0.1163 0.7582 0.972 0.000 0.028
#> GSM213100 1 0.2165 0.7641 0.936 0.000 0.064
#> GSM213111 2 0.0424 0.9707 0.000 0.992 0.008
#> GSM213117 3 0.6835 0.6182 0.284 0.040 0.676
#> GSM213118 1 0.6904 0.5759 0.684 0.048 0.268
#> GSM213120 2 0.1643 0.9508 0.000 0.956 0.044
#> GSM213122 2 0.0000 0.9728 0.000 1.000 0.000
#> GSM213074 3 0.3619 0.7483 0.136 0.000 0.864
#> GSM213077 1 0.3482 0.7438 0.872 0.000 0.128
#> GSM213083 1 0.2796 0.7517 0.908 0.000 0.092
#> GSM213094 3 0.0424 0.7486 0.008 0.000 0.992
#> GSM213095 2 0.1289 0.9602 0.000 0.968 0.032
#> GSM213102 3 0.6286 0.2444 0.464 0.000 0.536
#> GSM213103 2 0.3356 0.9102 0.056 0.908 0.036
#> GSM213104 1 0.7186 0.5402 0.696 0.224 0.080
#> GSM213107 2 0.0000 0.9728 0.000 1.000 0.000
#> GSM213108 2 0.1860 0.9458 0.000 0.948 0.052
#> GSM213112 1 0.5178 0.6397 0.744 0.000 0.256
#> GSM213114 1 0.0237 0.7522 0.996 0.000 0.004
#> GSM213115 2 0.0000 0.9728 0.000 1.000 0.000
#> GSM213116 3 0.5591 0.6052 0.304 0.000 0.696
#> GSM213119 2 0.0000 0.9728 0.000 1.000 0.000
#> GSM213072 3 0.3116 0.7382 0.108 0.000 0.892
#> GSM213075 3 0.6495 0.6850 0.200 0.060 0.740
#> GSM213076 2 0.1163 0.9623 0.000 0.972 0.028
#> GSM213079 3 0.0892 0.7475 0.020 0.000 0.980
#> GSM213080 1 0.3207 0.7238 0.904 0.084 0.012
#> GSM213081 1 0.3941 0.7203 0.844 0.000 0.156
#> GSM213084 1 0.2537 0.7611 0.920 0.000 0.080
#> GSM213087 2 0.0000 0.9728 0.000 1.000 0.000
#> GSM213089 3 0.3482 0.7484 0.128 0.000 0.872
#> GSM213090 3 0.3276 0.7186 0.024 0.068 0.908
#> GSM213093 3 0.5785 0.5617 0.332 0.000 0.668
#> GSM213097 1 0.6309 -0.1700 0.500 0.000 0.500
#> GSM213099 3 0.1163 0.7552 0.028 0.000 0.972
#> GSM213101 1 0.1529 0.7576 0.960 0.000 0.040
#> GSM213105 2 0.0000 0.9728 0.000 1.000 0.000
#> GSM213109 1 0.5465 0.5569 0.712 0.000 0.288
#> GSM213110 2 0.0592 0.9674 0.012 0.988 0.000
#> GSM213113 3 0.8775 0.1201 0.384 0.116 0.500
#> GSM213121 2 0.0000 0.9728 0.000 1.000 0.000
#> GSM213123 1 0.6280 0.0844 0.540 0.000 0.460
#> GSM213125 2 0.0000 0.9728 0.000 1.000 0.000
#> GSM213073 3 0.3276 0.7348 0.068 0.024 0.908
#> GSM213086 1 0.2165 0.7617 0.936 0.000 0.064
#> GSM213098 1 0.8652 0.1910 0.492 0.104 0.404
#> GSM213106 3 0.6675 0.4219 0.404 0.012 0.584
#> GSM213124 2 0.4999 0.8039 0.028 0.820 0.152
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.4994 0.3311 0.520 0.000 0.480 0.000
#> GSM213082 2 0.0712 0.9152 0.004 0.984 0.004 0.008
#> GSM213085 1 0.6539 0.4376 0.652 0.004 0.172 0.172
#> GSM213088 3 0.6964 0.2875 0.240 0.056 0.640 0.064
#> GSM213091 4 0.4453 0.5188 0.012 0.000 0.244 0.744
#> GSM213092 1 0.6102 0.4748 0.672 0.000 0.212 0.116
#> GSM213096 1 0.4321 0.5420 0.796 0.004 0.176 0.024
#> GSM213100 1 0.6055 0.4286 0.576 0.000 0.372 0.052
#> GSM213111 2 0.2360 0.9034 0.004 0.924 0.020 0.052
#> GSM213117 3 0.7080 0.2596 0.128 0.004 0.544 0.324
#> GSM213118 1 0.7799 0.2745 0.536 0.024 0.264 0.176
#> GSM213120 2 0.4372 0.8612 0.040 0.840 0.040 0.080
#> GSM213122 2 0.0188 0.9154 0.004 0.996 0.000 0.000
#> GSM213074 4 0.6465 0.1694 0.072 0.000 0.412 0.516
#> GSM213077 1 0.5773 0.4686 0.620 0.000 0.336 0.044
#> GSM213083 1 0.6334 0.2919 0.484 0.000 0.456 0.060
#> GSM213094 4 0.1637 0.5984 0.000 0.000 0.060 0.940
#> GSM213095 2 0.4288 0.8383 0.020 0.820 0.020 0.140
#> GSM213102 3 0.6110 0.5233 0.144 0.000 0.680 0.176
#> GSM213103 2 0.6510 0.6842 0.180 0.696 0.076 0.048
#> GSM213104 1 0.6967 0.3894 0.684 0.124 0.112 0.080
#> GSM213107 2 0.2170 0.9094 0.016 0.936 0.012 0.036
#> GSM213108 2 0.4129 0.8319 0.008 0.828 0.032 0.132
#> GSM213112 1 0.6742 0.3812 0.608 0.000 0.160 0.232
#> GSM213114 1 0.3538 0.5383 0.832 0.004 0.160 0.004
#> GSM213115 2 0.0000 0.9149 0.000 1.000 0.000 0.000
#> GSM213116 3 0.6928 0.2924 0.136 0.000 0.556 0.308
#> GSM213119 2 0.0188 0.9154 0.004 0.996 0.000 0.000
#> GSM213072 4 0.6585 0.3982 0.104 0.000 0.312 0.584
#> GSM213075 3 0.7946 0.0724 0.072 0.072 0.468 0.388
#> GSM213076 2 0.3159 0.8920 0.012 0.892 0.028 0.068
#> GSM213079 4 0.2124 0.5959 0.028 0.000 0.040 0.932
#> GSM213080 1 0.4747 0.5150 0.780 0.024 0.180 0.016
#> GSM213081 1 0.6702 0.2711 0.512 0.000 0.396 0.092
#> GSM213084 1 0.6090 0.4340 0.564 0.000 0.384 0.052
#> GSM213087 2 0.0188 0.9155 0.004 0.996 0.000 0.000
#> GSM213089 4 0.6631 0.1656 0.048 0.016 0.428 0.508
#> GSM213090 4 0.3991 0.5624 0.064 0.032 0.044 0.860
#> GSM213093 3 0.7184 0.3502 0.144 0.000 0.492 0.364
#> GSM213097 3 0.6545 0.4437 0.216 0.000 0.632 0.152
#> GSM213099 4 0.4855 0.5108 0.020 0.000 0.268 0.712
#> GSM213101 1 0.5161 0.3610 0.520 0.000 0.476 0.004
#> GSM213105 2 0.0000 0.9149 0.000 1.000 0.000 0.000
#> GSM213109 3 0.6995 -0.0438 0.384 0.000 0.496 0.120
#> GSM213110 2 0.1985 0.9021 0.040 0.940 0.004 0.016
#> GSM213113 4 0.8953 0.1062 0.296 0.068 0.220 0.416
#> GSM213121 2 0.1509 0.9123 0.008 0.960 0.012 0.020
#> GSM213123 3 0.7431 0.3304 0.244 0.008 0.552 0.196
#> GSM213125 2 0.0376 0.9150 0.000 0.992 0.004 0.004
#> GSM213073 4 0.4834 0.5279 0.096 0.028 0.064 0.812
#> GSM213086 1 0.5142 0.5224 0.744 0.000 0.192 0.064
#> GSM213098 1 0.8031 0.0375 0.452 0.028 0.152 0.368
#> GSM213106 3 0.6418 0.5201 0.112 0.012 0.672 0.204
#> GSM213124 2 0.7119 0.6183 0.068 0.668 0.132 0.132
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.5988 0.35302 0.508 0.000 0.004 0.388 0.100
#> GSM213082 2 0.2027 0.82412 0.000 0.928 0.024 0.008 0.040
#> GSM213085 1 0.5976 0.23171 0.644 0.000 0.060 0.060 0.236
#> GSM213088 4 0.6765 0.22716 0.200 0.056 0.036 0.632 0.076
#> GSM213091 3 0.5580 0.35117 0.020 0.000 0.620 0.304 0.056
#> GSM213092 1 0.6650 0.26302 0.608 0.000 0.084 0.104 0.204
#> GSM213096 1 0.5074 0.37322 0.724 0.000 0.020 0.076 0.180
#> GSM213100 1 0.5570 0.44249 0.712 0.000 0.048 0.120 0.120
#> GSM213111 2 0.3340 0.81591 0.004 0.860 0.028 0.016 0.092
#> GSM213117 4 0.8787 0.23209 0.164 0.032 0.244 0.396 0.164
#> GSM213118 5 0.7869 -0.00623 0.368 0.012 0.096 0.120 0.404
#> GSM213120 2 0.4782 0.74718 0.000 0.728 0.048 0.016 0.208
#> GSM213122 2 0.0404 0.82726 0.000 0.988 0.000 0.000 0.012
#> GSM213074 3 0.7884 0.03719 0.144 0.000 0.408 0.324 0.124
#> GSM213077 1 0.5216 0.48389 0.720 0.000 0.048 0.184 0.048
#> GSM213083 1 0.5337 0.43359 0.616 0.000 0.016 0.328 0.040
#> GSM213094 3 0.3257 0.52980 0.004 0.000 0.844 0.124 0.028
#> GSM213095 2 0.5809 0.63548 0.000 0.640 0.188 0.008 0.164
#> GSM213102 4 0.6402 0.40259 0.220 0.000 0.096 0.620 0.064
#> GSM213103 2 0.7705 0.09940 0.104 0.412 0.068 0.024 0.392
#> GSM213104 5 0.7351 0.04950 0.380 0.064 0.044 0.048 0.464
#> GSM213107 2 0.3840 0.77375 0.004 0.784 0.016 0.004 0.192
#> GSM213108 2 0.4108 0.76907 0.000 0.804 0.116 0.012 0.068
#> GSM213112 1 0.7079 0.15861 0.548 0.000 0.136 0.076 0.240
#> GSM213114 1 0.5625 0.35798 0.652 0.004 0.004 0.112 0.228
#> GSM213115 2 0.1197 0.82693 0.000 0.952 0.000 0.000 0.048
#> GSM213116 4 0.7894 0.14359 0.136 0.000 0.328 0.404 0.132
#> GSM213119 2 0.0404 0.82691 0.000 0.988 0.000 0.000 0.012
#> GSM213072 3 0.7969 0.22220 0.192 0.000 0.460 0.176 0.172
#> GSM213075 4 0.8118 0.03058 0.084 0.036 0.360 0.408 0.112
#> GSM213076 2 0.5259 0.74112 0.004 0.712 0.080 0.016 0.188
#> GSM213079 3 0.2710 0.53790 0.008 0.000 0.892 0.036 0.064
#> GSM213080 1 0.6870 0.06050 0.464 0.032 0.000 0.136 0.368
#> GSM213081 1 0.7795 0.18648 0.364 0.000 0.068 0.340 0.228
#> GSM213084 1 0.5404 0.49301 0.664 0.000 0.032 0.260 0.044
#> GSM213087 2 0.1571 0.82564 0.000 0.936 0.000 0.004 0.060
#> GSM213089 4 0.7132 -0.05421 0.060 0.008 0.396 0.448 0.088
#> GSM213090 3 0.4697 0.46968 0.040 0.020 0.768 0.012 0.160
#> GSM213093 4 0.6670 0.39002 0.148 0.000 0.208 0.592 0.052
#> GSM213097 4 0.5741 0.42487 0.140 0.000 0.100 0.700 0.060
#> GSM213099 3 0.6118 0.27289 0.052 0.000 0.572 0.328 0.048
#> GSM213101 1 0.5992 0.40627 0.560 0.000 0.008 0.328 0.104
#> GSM213105 2 0.0510 0.82542 0.000 0.984 0.000 0.000 0.016
#> GSM213109 1 0.6878 0.26670 0.496 0.000 0.076 0.352 0.076
#> GSM213110 2 0.3144 0.79967 0.020 0.872 0.004 0.020 0.084
#> GSM213113 5 0.8249 0.14902 0.092 0.036 0.352 0.120 0.400
#> GSM213121 2 0.3087 0.79824 0.000 0.836 0.008 0.004 0.152
#> GSM213123 4 0.7058 0.30560 0.208 0.000 0.096 0.568 0.128
#> GSM213125 2 0.0727 0.82909 0.000 0.980 0.004 0.004 0.012
#> GSM213073 3 0.5233 0.37811 0.052 0.008 0.728 0.032 0.180
#> GSM213086 1 0.6310 0.30451 0.632 0.000 0.052 0.116 0.200
#> GSM213098 5 0.7948 0.36137 0.112 0.040 0.252 0.088 0.508
#> GSM213106 4 0.5670 0.46178 0.096 0.000 0.144 0.704 0.056
#> GSM213124 2 0.8298 0.30130 0.080 0.500 0.092 0.100 0.228
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 5 0.6034 0.0385 0.120 0.000 0.000 0.412 0.440 0.028
#> GSM213082 2 0.2200 0.7781 0.004 0.900 0.012 0.000 0.004 0.080
#> GSM213085 1 0.6077 0.3673 0.620 0.000 0.048 0.040 0.224 0.068
#> GSM213088 4 0.6688 0.2555 0.068 0.028 0.020 0.596 0.208 0.080
#> GSM213091 3 0.5810 0.4449 0.032 0.000 0.616 0.232 0.012 0.108
#> GSM213092 1 0.6220 0.3491 0.612 0.000 0.044 0.084 0.216 0.044
#> GSM213096 1 0.6567 0.2549 0.448 0.004 0.000 0.080 0.372 0.096
#> GSM213100 1 0.6690 0.3590 0.508 0.000 0.012 0.216 0.220 0.044
#> GSM213111 2 0.3492 0.7585 0.004 0.816 0.028 0.000 0.016 0.136
#> GSM213117 4 0.8331 0.0927 0.124 0.004 0.184 0.340 0.064 0.284
#> GSM213118 1 0.8259 0.1135 0.328 0.012 0.060 0.072 0.272 0.256
#> GSM213120 2 0.5453 0.6052 0.012 0.660 0.032 0.012 0.048 0.236
#> GSM213122 2 0.1010 0.7877 0.000 0.960 0.000 0.000 0.004 0.036
#> GSM213074 3 0.7922 0.2157 0.220 0.000 0.384 0.212 0.028 0.156
#> GSM213077 1 0.6974 0.2974 0.412 0.000 0.028 0.288 0.252 0.020
#> GSM213083 1 0.7070 0.2055 0.368 0.000 0.036 0.328 0.252 0.016
#> GSM213094 3 0.3240 0.5188 0.032 0.000 0.856 0.052 0.004 0.056
#> GSM213095 2 0.6057 0.5748 0.032 0.644 0.128 0.000 0.048 0.148
#> GSM213102 4 0.6544 0.3589 0.156 0.000 0.076 0.616 0.060 0.092
#> GSM213103 6 0.7575 -0.0804 0.096 0.340 0.016 0.012 0.144 0.392
#> GSM213104 5 0.5718 0.2798 0.092 0.076 0.024 0.012 0.704 0.092
#> GSM213107 2 0.4105 0.7299 0.004 0.780 0.008 0.004 0.076 0.128
#> GSM213108 2 0.5111 0.6413 0.012 0.716 0.080 0.024 0.008 0.160
#> GSM213112 1 0.7028 0.3443 0.584 0.004 0.092 0.096 0.148 0.076
#> GSM213114 5 0.4677 0.2474 0.144 0.000 0.004 0.116 0.724 0.012
#> GSM213115 2 0.2006 0.7700 0.000 0.904 0.000 0.000 0.016 0.080
#> GSM213116 4 0.8397 0.0200 0.172 0.000 0.216 0.304 0.056 0.252
#> GSM213119 2 0.0632 0.7867 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM213072 3 0.7988 0.2382 0.216 0.000 0.400 0.088 0.068 0.228
#> GSM213075 6 0.8609 -0.3043 0.044 0.044 0.272 0.260 0.080 0.300
#> GSM213076 2 0.5368 0.6563 0.008 0.704 0.064 0.016 0.044 0.164
#> GSM213079 3 0.2783 0.5138 0.044 0.000 0.888 0.028 0.016 0.024
#> GSM213080 5 0.4838 0.3494 0.052 0.048 0.004 0.088 0.768 0.040
#> GSM213081 5 0.7161 0.1406 0.108 0.000 0.044 0.348 0.436 0.064
#> GSM213084 4 0.7117 -0.2535 0.324 0.000 0.020 0.352 0.272 0.032
#> GSM213087 2 0.1779 0.7814 0.000 0.920 0.000 0.000 0.016 0.064
#> GSM213089 3 0.7549 0.1580 0.096 0.000 0.380 0.344 0.032 0.148
#> GSM213090 3 0.4739 0.4576 0.120 0.000 0.744 0.020 0.016 0.100
#> GSM213093 4 0.7268 0.3327 0.116 0.000 0.168 0.544 0.080 0.092
#> GSM213097 4 0.5165 0.3819 0.076 0.000 0.064 0.740 0.080 0.040
#> GSM213099 3 0.6108 0.4650 0.044 0.000 0.608 0.216 0.020 0.112
#> GSM213101 4 0.7043 -0.0781 0.256 0.000 0.004 0.416 0.260 0.064
#> GSM213105 2 0.0790 0.7844 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM213109 1 0.6981 0.2281 0.460 0.000 0.048 0.340 0.104 0.048
#> GSM213110 2 0.4227 0.6882 0.020 0.784 0.004 0.016 0.040 0.136
#> GSM213113 3 0.9175 0.0168 0.200 0.032 0.304 0.100 0.192 0.172
#> GSM213121 2 0.3065 0.7644 0.000 0.844 0.004 0.000 0.052 0.100
#> GSM213123 4 0.7879 0.2218 0.176 0.000 0.084 0.468 0.132 0.140
#> GSM213125 2 0.0632 0.7879 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM213073 3 0.4933 0.4534 0.088 0.004 0.756 0.020 0.072 0.060
#> GSM213086 1 0.6381 0.3033 0.540 0.000 0.016 0.064 0.296 0.084
#> GSM213098 5 0.7973 0.1724 0.120 0.004 0.172 0.056 0.440 0.208
#> GSM213106 4 0.6451 0.3910 0.092 0.000 0.104 0.628 0.048 0.128
#> GSM213124 2 0.7815 -0.2044 0.112 0.396 0.044 0.048 0.044 0.356
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 development.stage(p) disease.state(p) k
#> SD:skmeans 52 0.876 0.739 2
#> SD:skmeans 48 0.285 0.817 3
#> SD:skmeans 29 0.762 0.405 4
#> SD:skmeans 17 1.000 1.000 5
#> SD:skmeans 17 1.000 1.000 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "pam"]
# you can also extract it by
# res = res_list["SD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.883 0.918 0.964 0.4180 0.575 0.575
#> 3 3 0.504 0.693 0.856 0.5224 0.763 0.594
#> 4 4 0.466 0.656 0.808 0.0355 1.000 1.000
#> 5 5 0.414 0.566 0.797 0.0181 0.984 0.955
#> 6 6 0.464 0.538 0.777 0.0103 0.976 0.932
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
#> GSM213078 1 0.0000 0.976 1.000 0.000
#> GSM213082 2 0.0000 0.921 0.000 1.000
#> GSM213085 1 0.0000 0.976 1.000 0.000
#> GSM213088 1 0.1414 0.963 0.980 0.020
#> GSM213091 1 0.0000 0.976 1.000 0.000
#> GSM213092 1 0.0000 0.976 1.000 0.000
#> GSM213096 1 0.0000 0.976 1.000 0.000
#> GSM213100 1 0.0000 0.976 1.000 0.000
#> GSM213111 2 0.0000 0.921 0.000 1.000
#> GSM213117 1 0.0000 0.976 1.000 0.000
#> GSM213118 1 0.0000 0.976 1.000 0.000
#> GSM213120 2 0.9522 0.462 0.372 0.628
#> GSM213122 2 0.0000 0.921 0.000 1.000
#> GSM213074 1 0.0000 0.976 1.000 0.000
#> GSM213077 1 0.0000 0.976 1.000 0.000
#> GSM213083 1 0.0000 0.976 1.000 0.000
#> GSM213094 1 0.2948 0.933 0.948 0.052
#> GSM213095 2 0.1414 0.910 0.020 0.980
#> GSM213102 1 0.0672 0.971 0.992 0.008
#> GSM213103 2 0.9815 0.334 0.420 0.580
#> GSM213104 1 0.2603 0.942 0.956 0.044
#> GSM213107 2 0.0000 0.921 0.000 1.000
#> GSM213108 2 0.0000 0.921 0.000 1.000
#> GSM213112 1 0.0672 0.972 0.992 0.008
#> GSM213114 1 0.0000 0.976 1.000 0.000
#> GSM213115 2 0.0000 0.921 0.000 1.000
#> GSM213116 1 0.0000 0.976 1.000 0.000
#> GSM213119 2 0.0000 0.921 0.000 1.000
#> GSM213072 1 0.1633 0.959 0.976 0.024
#> GSM213075 1 0.4298 0.894 0.912 0.088
#> GSM213076 1 0.9286 0.475 0.656 0.344
#> GSM213079 1 0.0000 0.976 1.000 0.000
#> GSM213080 1 0.1414 0.963 0.980 0.020
#> GSM213081 1 0.0000 0.976 1.000 0.000
#> GSM213084 1 0.0000 0.976 1.000 0.000
#> GSM213087 2 0.0000 0.921 0.000 1.000
#> GSM213089 1 0.0000 0.976 1.000 0.000
#> GSM213090 1 0.7376 0.734 0.792 0.208
#> GSM213093 1 0.0000 0.976 1.000 0.000
#> GSM213097 1 0.0000 0.976 1.000 0.000
#> GSM213099 1 0.0000 0.976 1.000 0.000
#> GSM213101 1 0.0000 0.976 1.000 0.000
#> GSM213105 2 0.0000 0.921 0.000 1.000
#> GSM213109 1 0.0000 0.976 1.000 0.000
#> GSM213110 2 0.6343 0.801 0.160 0.840
#> GSM213113 1 0.0000 0.976 1.000 0.000
#> GSM213121 2 0.0000 0.921 0.000 1.000
#> GSM213123 1 0.0000 0.976 1.000 0.000
#> GSM213125 2 0.0000 0.921 0.000 1.000
#> GSM213073 1 0.0376 0.974 0.996 0.004
#> GSM213086 1 0.0000 0.976 1.000 0.000
#> GSM213098 1 0.0000 0.976 1.000 0.000
#> GSM213106 1 0.0000 0.976 1.000 0.000
#> GSM213124 2 0.6343 0.801 0.160 0.840
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.000 0.798 1.000 0.000 0.000
#> GSM213082 2 0.000 0.901 0.000 1.000 0.000
#> GSM213085 3 0.418 0.781 0.172 0.000 0.828
#> GSM213088 1 0.000 0.798 1.000 0.000 0.000
#> GSM213091 1 0.621 0.365 0.572 0.000 0.428
#> GSM213092 3 0.429 0.779 0.180 0.000 0.820
#> GSM213096 1 0.129 0.798 0.968 0.000 0.032
#> GSM213100 1 0.116 0.799 0.972 0.000 0.028
#> GSM213111 2 0.000 0.901 0.000 1.000 0.000
#> GSM213117 1 0.236 0.774 0.928 0.000 0.072
#> GSM213118 3 0.484 0.752 0.224 0.000 0.776
#> GSM213120 2 0.610 0.471 0.348 0.648 0.004
#> GSM213122 2 0.000 0.901 0.000 1.000 0.000
#> GSM213074 1 0.565 0.452 0.688 0.000 0.312
#> GSM213077 1 0.424 0.706 0.824 0.000 0.176
#> GSM213083 1 0.116 0.800 0.972 0.000 0.028
#> GSM213094 3 0.103 0.751 0.024 0.000 0.976
#> GSM213095 3 0.562 0.504 0.000 0.308 0.692
#> GSM213102 1 0.116 0.796 0.972 0.000 0.028
#> GSM213103 2 0.647 0.239 0.444 0.552 0.004
#> GSM213104 3 0.631 0.620 0.328 0.012 0.660
#> GSM213107 2 0.000 0.901 0.000 1.000 0.000
#> GSM213108 2 0.000 0.901 0.000 1.000 0.000
#> GSM213112 3 0.435 0.779 0.184 0.000 0.816
#> GSM213114 1 0.000 0.798 1.000 0.000 0.000
#> GSM213115 2 0.000 0.901 0.000 1.000 0.000
#> GSM213116 1 0.362 0.734 0.864 0.000 0.136
#> GSM213119 2 0.000 0.901 0.000 1.000 0.000
#> GSM213072 1 0.576 0.462 0.672 0.000 0.328
#> GSM213075 1 0.186 0.781 0.948 0.052 0.000
#> GSM213076 1 0.719 0.407 0.608 0.356 0.036
#> GSM213079 3 0.000 0.741 0.000 0.000 1.000
#> GSM213080 1 0.000 0.798 1.000 0.000 0.000
#> GSM213081 1 0.153 0.797 0.960 0.000 0.040
#> GSM213084 1 0.288 0.767 0.904 0.000 0.096
#> GSM213087 2 0.000 0.901 0.000 1.000 0.000
#> GSM213089 1 0.630 0.166 0.520 0.000 0.480
#> GSM213090 3 0.000 0.741 0.000 0.000 1.000
#> GSM213093 1 0.556 0.521 0.700 0.000 0.300
#> GSM213097 1 0.288 0.779 0.904 0.000 0.096
#> GSM213099 1 0.631 0.087 0.512 0.000 0.488
#> GSM213101 1 0.000 0.798 1.000 0.000 0.000
#> GSM213105 2 0.000 0.901 0.000 1.000 0.000
#> GSM213109 1 0.196 0.796 0.944 0.000 0.056
#> GSM213110 2 0.400 0.762 0.160 0.840 0.000
#> GSM213113 3 0.629 0.235 0.468 0.000 0.532
#> GSM213121 2 0.000 0.901 0.000 1.000 0.000
#> GSM213123 1 0.627 0.132 0.548 0.000 0.452
#> GSM213125 2 0.000 0.901 0.000 1.000 0.000
#> GSM213073 3 0.129 0.757 0.032 0.000 0.968
#> GSM213086 3 0.440 0.778 0.188 0.000 0.812
#> GSM213098 3 0.621 0.359 0.428 0.000 0.572
#> GSM213106 1 0.288 0.769 0.904 0.000 0.096
#> GSM213124 2 0.439 0.767 0.148 0.840 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.0188 0.78331 0.996 0.000 0.000 0.004
#> GSM213082 2 0.3444 0.83104 0.000 0.816 0.000 0.184
#> GSM213085 3 0.3172 0.73465 0.160 0.000 0.840 0.000
#> GSM213088 1 0.0000 0.78340 1.000 0.000 0.000 0.000
#> GSM213091 1 0.6554 0.33732 0.540 0.000 0.376 0.084
#> GSM213092 3 0.3266 0.73339 0.168 0.000 0.832 0.000
#> GSM213096 1 0.1305 0.78265 0.960 0.000 0.036 0.004
#> GSM213100 1 0.1209 0.78354 0.964 0.000 0.032 0.004
#> GSM213111 2 0.0188 0.84269 0.000 0.996 0.000 0.004
#> GSM213117 1 0.3216 0.74507 0.880 0.000 0.044 0.076
#> GSM213118 3 0.3831 0.71599 0.204 0.000 0.792 0.004
#> GSM213120 2 0.4855 0.45634 0.352 0.644 0.004 0.000
#> GSM213122 2 0.2647 0.83956 0.000 0.880 0.000 0.120
#> GSM213074 1 0.4857 0.41393 0.668 0.000 0.324 0.008
#> GSM213077 1 0.3583 0.69481 0.816 0.000 0.180 0.004
#> GSM213083 1 0.1109 0.78567 0.968 0.000 0.028 0.004
#> GSM213094 3 0.5378 0.51980 0.012 0.000 0.540 0.448
#> GSM213095 3 0.4837 0.46127 0.000 0.348 0.648 0.004
#> GSM213102 1 0.1936 0.77660 0.940 0.000 0.032 0.028
#> GSM213103 2 0.5408 0.25471 0.432 0.556 0.008 0.004
#> GSM213104 3 0.5266 0.58207 0.324 0.016 0.656 0.004
#> GSM213107 2 0.0469 0.84207 0.000 0.988 0.000 0.012
#> GSM213108 2 0.0000 0.84322 0.000 1.000 0.000 0.000
#> GSM213112 3 0.3266 0.73373 0.168 0.000 0.832 0.000
#> GSM213114 1 0.0188 0.78331 0.996 0.000 0.000 0.004
#> GSM213115 2 0.1302 0.84778 0.000 0.956 0.000 0.044
#> GSM213116 1 0.3052 0.72020 0.860 0.000 0.136 0.004
#> GSM213119 2 0.3444 0.83104 0.000 0.816 0.000 0.184
#> GSM213072 1 0.4761 0.44656 0.664 0.000 0.332 0.004
#> GSM213075 1 0.1792 0.76337 0.932 0.068 0.000 0.000
#> GSM213076 1 0.6009 0.34983 0.560 0.400 0.036 0.004
#> GSM213079 3 0.2973 0.66380 0.000 0.000 0.856 0.144
#> GSM213080 1 0.0188 0.78331 0.996 0.000 0.000 0.004
#> GSM213081 1 0.1398 0.78315 0.956 0.000 0.040 0.004
#> GSM213084 1 0.2466 0.75481 0.900 0.000 0.096 0.004
#> GSM213087 2 0.3444 0.83104 0.000 0.816 0.000 0.184
#> GSM213089 1 0.6491 0.16247 0.496 0.000 0.432 0.072
#> GSM213090 3 0.0921 0.69216 0.000 0.000 0.972 0.028
#> GSM213093 1 0.4608 0.51199 0.692 0.000 0.304 0.004
#> GSM213097 1 0.3156 0.76009 0.884 0.000 0.068 0.048
#> GSM213099 1 0.6661 -0.00213 0.460 0.000 0.456 0.084
#> GSM213101 1 0.0000 0.78340 1.000 0.000 0.000 0.000
#> GSM213105 2 0.3444 0.83104 0.000 0.816 0.000 0.184
#> GSM213109 1 0.1743 0.78364 0.940 0.000 0.056 0.004
#> GSM213110 2 0.3266 0.73867 0.168 0.832 0.000 0.000
#> GSM213113 3 0.4977 0.23116 0.460 0.000 0.540 0.000
#> GSM213121 2 0.1389 0.84622 0.000 0.952 0.000 0.048
#> GSM213123 1 0.5543 0.18899 0.556 0.000 0.424 0.020
#> GSM213125 2 0.0817 0.84732 0.000 0.976 0.000 0.024
#> GSM213073 3 0.5367 0.60327 0.032 0.000 0.664 0.304
#> GSM213086 3 0.3356 0.73243 0.176 0.000 0.824 0.000
#> GSM213098 3 0.4877 0.36825 0.408 0.000 0.592 0.000
#> GSM213106 1 0.3320 0.74172 0.876 0.000 0.056 0.068
#> GSM213124 2 0.4075 0.75433 0.128 0.832 0.032 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.0000 0.7725 1.000 0.000 0.000 0.000 0.000
#> GSM213082 2 0.3636 0.7461 0.000 0.728 0.000 0.000 0.272
#> GSM213085 4 0.2773 0.6399 0.164 0.000 0.000 0.836 0.000
#> GSM213088 1 0.0162 0.7729 0.996 0.000 0.000 0.004 0.000
#> GSM213091 1 0.6133 0.3257 0.540 0.000 0.160 0.300 0.000
#> GSM213092 4 0.2929 0.6437 0.180 0.000 0.000 0.820 0.000
#> GSM213096 1 0.1357 0.7698 0.948 0.000 0.000 0.048 0.004
#> GSM213100 1 0.1282 0.7710 0.952 0.000 0.000 0.044 0.004
#> GSM213111 2 0.0162 0.7778 0.000 0.996 0.000 0.000 0.004
#> GSM213117 1 0.2886 0.7332 0.864 0.000 0.116 0.016 0.004
#> GSM213118 4 0.3300 0.6410 0.204 0.000 0.000 0.792 0.004
#> GSM213120 2 0.4298 0.4277 0.352 0.640 0.008 0.000 0.000
#> GSM213122 2 0.2773 0.7704 0.000 0.836 0.000 0.000 0.164
#> GSM213074 1 0.4147 0.4345 0.676 0.000 0.008 0.316 0.000
#> GSM213077 1 0.3039 0.6756 0.808 0.000 0.000 0.192 0.000
#> GSM213083 1 0.0880 0.7753 0.968 0.000 0.000 0.032 0.000
#> GSM213094 3 0.2719 0.0000 0.004 0.000 0.852 0.144 0.000
#> GSM213095 4 0.4227 0.0117 0.000 0.420 0.000 0.580 0.000
#> GSM213102 1 0.2067 0.7639 0.920 0.000 0.048 0.032 0.000
#> GSM213103 2 0.4764 0.2461 0.436 0.548 0.000 0.012 0.004
#> GSM213104 4 0.4859 0.5325 0.364 0.024 0.000 0.608 0.004
#> GSM213107 2 0.0912 0.7769 0.000 0.972 0.016 0.000 0.012
#> GSM213108 2 0.0000 0.7787 0.000 1.000 0.000 0.000 0.000
#> GSM213112 4 0.2929 0.6474 0.180 0.000 0.000 0.820 0.000
#> GSM213114 1 0.0000 0.7725 1.000 0.000 0.000 0.000 0.000
#> GSM213115 2 0.1608 0.7873 0.000 0.928 0.000 0.000 0.072
#> GSM213116 1 0.2798 0.7076 0.852 0.000 0.008 0.140 0.000
#> GSM213119 2 0.3636 0.7461 0.000 0.728 0.000 0.000 0.272
#> GSM213072 1 0.4302 0.4091 0.648 0.000 0.004 0.344 0.004
#> GSM213075 1 0.1704 0.7534 0.928 0.068 0.000 0.004 0.000
#> GSM213076 1 0.5272 0.3015 0.540 0.416 0.000 0.040 0.004
#> GSM213079 4 0.6033 -0.3586 0.000 0.000 0.200 0.580 0.220
#> GSM213080 1 0.0162 0.7736 0.996 0.000 0.000 0.004 0.000
#> GSM213081 1 0.1043 0.7726 0.960 0.000 0.000 0.040 0.000
#> GSM213084 1 0.1965 0.7432 0.904 0.000 0.000 0.096 0.000
#> GSM213087 2 0.3636 0.7461 0.000 0.728 0.000 0.000 0.272
#> GSM213089 1 0.6077 0.1008 0.480 0.000 0.124 0.396 0.000
#> GSM213090 4 0.2889 0.1441 0.000 0.000 0.084 0.872 0.044
#> GSM213093 1 0.4088 0.4796 0.688 0.000 0.008 0.304 0.000
#> GSM213097 1 0.2616 0.7522 0.888 0.000 0.076 0.036 0.000
#> GSM213099 1 0.6321 0.0216 0.464 0.000 0.160 0.376 0.000
#> GSM213101 1 0.0162 0.7729 0.996 0.000 0.000 0.004 0.000
#> GSM213105 2 0.3636 0.7461 0.000 0.728 0.000 0.000 0.272
#> GSM213109 1 0.1341 0.7742 0.944 0.000 0.000 0.056 0.000
#> GSM213110 2 0.2891 0.6911 0.176 0.824 0.000 0.000 0.000
#> GSM213113 4 0.4291 0.2574 0.464 0.000 0.000 0.536 0.000
#> GSM213121 2 0.1626 0.7805 0.000 0.940 0.016 0.000 0.044
#> GSM213123 1 0.4885 0.1614 0.572 0.000 0.028 0.400 0.000
#> GSM213125 2 0.0880 0.7850 0.000 0.968 0.000 0.000 0.032
#> GSM213073 5 0.5772 0.0000 0.004 0.000 0.104 0.300 0.592
#> GSM213086 4 0.3074 0.6458 0.196 0.000 0.000 0.804 0.000
#> GSM213098 4 0.4182 0.4248 0.400 0.000 0.000 0.600 0.000
#> GSM213106 1 0.3051 0.7228 0.852 0.000 0.120 0.028 0.000
#> GSM213124 2 0.3817 0.7186 0.108 0.824 0.012 0.056 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 4 0.0260 0.73234 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM213082 2 0.3464 0.68763 0.000 0.688 0.000 0.000 0.312 0.000
#> GSM213085 1 0.2912 0.74195 0.784 0.000 0.000 0.216 0.000 0.000
#> GSM213088 4 0.0260 0.73284 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM213091 4 0.5752 0.19484 0.288 0.000 0.184 0.524 0.000 0.004
#> GSM213092 1 0.3244 0.72671 0.732 0.000 0.000 0.268 0.000 0.000
#> GSM213096 4 0.1753 0.70802 0.084 0.000 0.000 0.912 0.004 0.000
#> GSM213100 4 0.1753 0.70861 0.084 0.000 0.000 0.912 0.004 0.000
#> GSM213111 2 0.0146 0.73189 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM213117 4 0.3548 0.65412 0.048 0.000 0.152 0.796 0.004 0.000
#> GSM213118 1 0.3360 0.73458 0.732 0.000 0.000 0.264 0.004 0.000
#> GSM213120 2 0.4622 0.42300 0.008 0.628 0.020 0.332 0.000 0.012
#> GSM213122 2 0.2697 0.71870 0.000 0.812 0.000 0.000 0.188 0.000
#> GSM213074 4 0.3586 0.46714 0.268 0.000 0.012 0.720 0.000 0.000
#> GSM213077 4 0.2697 0.62925 0.188 0.000 0.000 0.812 0.000 0.000
#> GSM213083 4 0.0937 0.73378 0.040 0.000 0.000 0.960 0.000 0.000
#> GSM213094 3 0.1829 0.00000 0.056 0.000 0.920 0.000 0.000 0.024
#> GSM213095 2 0.3860 -0.01609 0.472 0.528 0.000 0.000 0.000 0.000
#> GSM213102 4 0.2134 0.71953 0.044 0.000 0.052 0.904 0.000 0.000
#> GSM213103 2 0.5271 0.18876 0.052 0.508 0.004 0.424 0.004 0.008
#> GSM213104 1 0.4484 0.56145 0.560 0.012 0.000 0.416 0.004 0.008
#> GSM213107 2 0.1768 0.72903 0.004 0.932 0.020 0.000 0.004 0.040
#> GSM213108 2 0.0000 0.73161 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM213112 1 0.2996 0.74402 0.772 0.000 0.000 0.228 0.000 0.000
#> GSM213114 4 0.0260 0.73234 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM213115 2 0.1988 0.73908 0.004 0.912 0.004 0.000 0.072 0.008
#> GSM213116 4 0.2593 0.65690 0.148 0.000 0.008 0.844 0.000 0.000
#> GSM213119 2 0.3464 0.68763 0.000 0.688 0.000 0.000 0.312 0.000
#> GSM213072 4 0.3878 0.28336 0.348 0.000 0.004 0.644 0.004 0.000
#> GSM213075 4 0.1644 0.70950 0.004 0.076 0.000 0.920 0.000 0.000
#> GSM213076 4 0.5037 0.22505 0.064 0.408 0.000 0.524 0.004 0.000
#> GSM213079 5 0.5949 0.00000 0.120 0.000 0.024 0.000 0.472 0.384
#> GSM213080 4 0.0458 0.73429 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM213081 4 0.1007 0.73110 0.044 0.000 0.000 0.956 0.000 0.000
#> GSM213084 4 0.1910 0.69374 0.108 0.000 0.000 0.892 0.000 0.000
#> GSM213087 2 0.3464 0.68763 0.000 0.688 0.000 0.000 0.312 0.000
#> GSM213089 4 0.5626 0.07986 0.344 0.000 0.160 0.496 0.000 0.000
#> GSM213090 1 0.4984 -0.26152 0.676 0.000 0.052 0.000 0.228 0.044
#> GSM213093 4 0.3748 0.38301 0.300 0.000 0.012 0.688 0.000 0.000
#> GSM213097 4 0.2747 0.69988 0.044 0.000 0.096 0.860 0.000 0.000
#> GSM213099 4 0.5831 -0.07806 0.348 0.000 0.196 0.456 0.000 0.000
#> GSM213101 4 0.0260 0.73284 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM213105 2 0.3464 0.68763 0.000 0.688 0.000 0.000 0.312 0.000
#> GSM213109 4 0.1327 0.73316 0.064 0.000 0.000 0.936 0.000 0.000
#> GSM213110 2 0.3025 0.66421 0.004 0.820 0.004 0.164 0.000 0.008
#> GSM213113 1 0.3857 0.44637 0.532 0.000 0.000 0.468 0.000 0.000
#> GSM213121 2 0.2032 0.72890 0.000 0.920 0.020 0.000 0.024 0.036
#> GSM213123 4 0.4482 0.00869 0.384 0.000 0.036 0.580 0.000 0.000
#> GSM213125 2 0.0777 0.73665 0.000 0.972 0.004 0.000 0.024 0.000
#> GSM213073 6 0.2624 0.00000 0.148 0.000 0.004 0.004 0.000 0.844
#> GSM213086 1 0.3330 0.72839 0.716 0.000 0.000 0.284 0.000 0.000
#> GSM213098 1 0.3797 0.55178 0.580 0.000 0.000 0.420 0.000 0.000
#> GSM213106 4 0.2945 0.65712 0.020 0.000 0.156 0.824 0.000 0.000
#> GSM213124 2 0.3671 0.69112 0.072 0.820 0.012 0.088 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n development.stage(p) disease.state(p) k
#> SD:pam 51 0.820 0.854 2
#> SD:pam 43 0.831 0.462 3
#> SD:pam 42 0.928 0.624 4
#> SD:pam 37 0.427 0.765 5
#> SD:pam 38 0.721 0.548 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "mclust"]
# you can also extract it by
# res = res_list["SD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.620 0.882 0.941 0.4766 0.516 0.516
#> 3 3 0.424 0.579 0.740 0.1607 0.799 0.667
#> 4 4 0.496 0.614 0.768 0.2385 0.690 0.425
#> 5 5 0.539 0.513 0.714 0.0316 0.747 0.355
#> 6 6 0.592 0.571 0.726 0.0977 0.867 0.549
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
#> GSM213078 1 0.0000 0.942 1.000 0.000
#> GSM213082 2 0.0000 0.917 0.000 1.000
#> GSM213085 1 0.0000 0.942 1.000 0.000
#> GSM213088 1 0.7528 0.743 0.784 0.216
#> GSM213091 1 0.3274 0.904 0.940 0.060
#> GSM213092 1 0.0000 0.942 1.000 0.000
#> GSM213096 1 0.0000 0.942 1.000 0.000
#> GSM213100 1 0.0000 0.942 1.000 0.000
#> GSM213111 2 0.0000 0.917 0.000 1.000
#> GSM213117 1 0.0000 0.942 1.000 0.000
#> GSM213118 1 0.0938 0.936 0.988 0.012
#> GSM213120 2 0.4815 0.861 0.104 0.896
#> GSM213122 2 0.0000 0.917 0.000 1.000
#> GSM213074 1 0.1633 0.929 0.976 0.024
#> GSM213077 1 0.0000 0.942 1.000 0.000
#> GSM213083 1 0.0000 0.942 1.000 0.000
#> GSM213094 2 0.8499 0.666 0.276 0.724
#> GSM213095 2 0.0000 0.917 0.000 1.000
#> GSM213102 1 0.0000 0.942 1.000 0.000
#> GSM213103 2 0.5519 0.846 0.128 0.872
#> GSM213104 1 0.8713 0.623 0.708 0.292
#> GSM213107 2 0.0000 0.917 0.000 1.000
#> GSM213108 2 0.0000 0.917 0.000 1.000
#> GSM213112 1 0.0000 0.942 1.000 0.000
#> GSM213114 1 0.7602 0.732 0.780 0.220
#> GSM213115 2 0.0000 0.917 0.000 1.000
#> GSM213116 1 0.0000 0.942 1.000 0.000
#> GSM213119 2 0.0000 0.917 0.000 1.000
#> GSM213072 1 0.0000 0.942 1.000 0.000
#> GSM213075 1 0.3114 0.906 0.944 0.056
#> GSM213076 2 0.0000 0.917 0.000 1.000
#> GSM213079 2 0.8144 0.701 0.252 0.748
#> GSM213080 1 0.8144 0.689 0.748 0.252
#> GSM213081 1 0.0000 0.942 1.000 0.000
#> GSM213084 1 0.0000 0.942 1.000 0.000
#> GSM213087 2 0.0000 0.917 0.000 1.000
#> GSM213089 1 0.0000 0.942 1.000 0.000
#> GSM213090 2 0.8016 0.711 0.244 0.756
#> GSM213093 1 0.0000 0.942 1.000 0.000
#> GSM213097 1 0.0000 0.942 1.000 0.000
#> GSM213099 1 0.3879 0.891 0.924 0.076
#> GSM213101 1 0.0000 0.942 1.000 0.000
#> GSM213105 2 0.0000 0.917 0.000 1.000
#> GSM213109 1 0.0000 0.942 1.000 0.000
#> GSM213110 2 0.4815 0.861 0.104 0.896
#> GSM213113 1 0.7815 0.717 0.768 0.232
#> GSM213121 2 0.0000 0.917 0.000 1.000
#> GSM213123 1 0.0376 0.940 0.996 0.004
#> GSM213125 2 0.0000 0.917 0.000 1.000
#> GSM213073 2 0.8016 0.711 0.244 0.756
#> GSM213086 1 0.0000 0.942 1.000 0.000
#> GSM213098 1 0.7815 0.716 0.768 0.232
#> GSM213106 1 0.0000 0.942 1.000 0.000
#> GSM213124 2 0.5629 0.843 0.132 0.868
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.7091 0.22324 0.560 0.416 NA
#> GSM213082 2 0.3619 0.70640 0.000 0.864 NA
#> GSM213085 1 0.4452 0.58688 0.808 0.192 NA
#> GSM213088 1 0.7748 0.09806 0.500 0.452 NA
#> GSM213091 2 0.7987 -0.00617 0.448 0.492 NA
#> GSM213092 1 0.0592 0.68014 0.988 0.012 NA
#> GSM213096 1 0.2165 0.64635 0.936 0.064 NA
#> GSM213100 1 0.0000 0.68052 1.000 0.000 NA
#> GSM213111 2 0.0000 0.73218 0.000 1.000 NA
#> GSM213117 1 0.6252 0.70734 0.556 0.000 NA
#> GSM213118 1 0.1411 0.67369 0.964 0.036 NA
#> GSM213120 2 0.0000 0.73218 0.000 1.000 NA
#> GSM213122 2 0.3879 0.70032 0.000 0.848 NA
#> GSM213074 1 0.8009 0.68315 0.524 0.064 NA
#> GSM213077 1 0.0000 0.68052 1.000 0.000 NA
#> GSM213083 1 0.2492 0.69064 0.936 0.016 NA
#> GSM213094 2 0.6811 0.56431 0.016 0.580 NA
#> GSM213095 2 0.0000 0.73218 0.000 1.000 NA
#> GSM213102 1 0.6260 0.70677 0.552 0.000 NA
#> GSM213103 2 0.4654 0.58262 0.208 0.792 NA
#> GSM213104 2 0.6140 0.26175 0.404 0.596 NA
#> GSM213107 2 0.0424 0.73211 0.000 0.992 NA
#> GSM213108 2 0.0000 0.73218 0.000 1.000 NA
#> GSM213112 1 0.4399 0.59069 0.812 0.188 NA
#> GSM213114 2 0.6168 0.24761 0.412 0.588 NA
#> GSM213115 2 0.3879 0.70032 0.000 0.848 NA
#> GSM213116 1 0.6252 0.70734 0.556 0.000 NA
#> GSM213119 2 0.3879 0.70032 0.000 0.848 NA
#> GSM213072 1 0.8749 0.45328 0.560 0.300 NA
#> GSM213075 1 0.6280 0.70223 0.540 0.000 NA
#> GSM213076 2 0.0000 0.73218 0.000 1.000 NA
#> GSM213079 2 0.6513 0.57204 0.008 0.592 NA
#> GSM213080 2 0.6140 0.26175 0.404 0.596 NA
#> GSM213081 1 0.0000 0.68052 1.000 0.000 NA
#> GSM213084 1 0.0000 0.68052 1.000 0.000 NA
#> GSM213087 2 0.3619 0.70486 0.000 0.864 NA
#> GSM213089 1 0.6260 0.70659 0.552 0.000 NA
#> GSM213090 2 0.6513 0.57204 0.008 0.592 NA
#> GSM213093 1 0.6260 0.70659 0.552 0.000 NA
#> GSM213097 1 0.6267 0.70562 0.548 0.000 NA
#> GSM213099 1 0.7838 0.07102 0.488 0.460 NA
#> GSM213101 1 0.7192 0.23273 0.560 0.412 NA
#> GSM213105 2 0.3879 0.70032 0.000 0.848 NA
#> GSM213109 1 0.6267 0.70562 0.548 0.000 NA
#> GSM213110 2 0.1170 0.73006 0.008 0.976 NA
#> GSM213113 2 0.6168 0.24761 0.412 0.588 NA
#> GSM213121 2 0.0424 0.73211 0.000 0.992 NA
#> GSM213123 1 0.6737 0.70872 0.600 0.016 NA
#> GSM213125 2 0.3686 0.70349 0.000 0.860 NA
#> GSM213073 2 0.6513 0.57204 0.008 0.592 NA
#> GSM213086 1 0.0000 0.68052 1.000 0.000 NA
#> GSM213098 2 0.6180 0.23862 0.416 0.584 NA
#> GSM213106 1 0.6260 0.70659 0.552 0.000 NA
#> GSM213124 2 0.6783 0.26567 0.396 0.588 NA
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 3 0.7756 0.0101 0.320 0.000 0.428 0.252
#> GSM213082 2 0.5016 0.1782 0.000 0.600 0.396 0.004
#> GSM213085 1 0.3831 0.6716 0.792 0.000 0.204 0.004
#> GSM213088 3 0.7569 0.0935 0.188 0.004 0.492 0.316
#> GSM213091 4 0.7425 0.1509 0.168 0.000 0.412 0.420
#> GSM213092 1 0.1489 0.8529 0.952 0.000 0.044 0.004
#> GSM213096 1 0.2197 0.8218 0.916 0.000 0.080 0.004
#> GSM213100 1 0.0707 0.8574 0.980 0.000 0.000 0.020
#> GSM213111 3 0.4855 0.3144 0.000 0.400 0.600 0.000
#> GSM213117 4 0.3528 0.7989 0.192 0.000 0.000 0.808
#> GSM213118 1 0.1637 0.8464 0.940 0.000 0.060 0.000
#> GSM213120 3 0.3400 0.6317 0.000 0.180 0.820 0.000
#> GSM213122 2 0.1722 0.8218 0.000 0.944 0.048 0.008
#> GSM213074 4 0.4589 0.7743 0.168 0.000 0.048 0.784
#> GSM213077 1 0.0469 0.8610 0.988 0.000 0.000 0.012
#> GSM213083 1 0.4690 0.4309 0.724 0.000 0.016 0.260
#> GSM213094 3 0.4256 0.6329 0.008 0.040 0.824 0.128
#> GSM213095 3 0.3402 0.6433 0.000 0.164 0.832 0.004
#> GSM213102 4 0.3356 0.8034 0.176 0.000 0.000 0.824
#> GSM213103 3 0.2908 0.6737 0.040 0.064 0.896 0.000
#> GSM213104 3 0.3295 0.6759 0.072 0.008 0.884 0.036
#> GSM213107 3 0.3539 0.6409 0.000 0.176 0.820 0.004
#> GSM213108 3 0.5060 0.2891 0.000 0.412 0.584 0.004
#> GSM213112 1 0.4049 0.6579 0.780 0.000 0.212 0.008
#> GSM213114 3 0.3616 0.6700 0.112 0.000 0.852 0.036
#> GSM213115 2 0.1722 0.8218 0.000 0.944 0.048 0.008
#> GSM213116 4 0.3569 0.7906 0.196 0.000 0.000 0.804
#> GSM213119 2 0.1389 0.8226 0.000 0.952 0.048 0.000
#> GSM213072 4 0.7220 0.4602 0.176 0.000 0.292 0.532
#> GSM213075 4 0.3539 0.7990 0.176 0.004 0.000 0.820
#> GSM213076 3 0.3801 0.5977 0.000 0.220 0.780 0.000
#> GSM213079 3 0.4316 0.6277 0.008 0.048 0.824 0.120
#> GSM213080 3 0.3436 0.6753 0.080 0.008 0.876 0.036
#> GSM213081 1 0.0336 0.8602 0.992 0.000 0.000 0.008
#> GSM213084 1 0.0469 0.8610 0.988 0.000 0.000 0.012
#> GSM213087 2 0.4804 0.2851 0.000 0.616 0.384 0.000
#> GSM213089 4 0.3400 0.8026 0.180 0.000 0.000 0.820
#> GSM213090 3 0.4316 0.6277 0.008 0.048 0.824 0.120
#> GSM213093 4 0.3266 0.8026 0.168 0.000 0.000 0.832
#> GSM213097 4 0.3266 0.8026 0.168 0.000 0.000 0.832
#> GSM213099 4 0.7421 0.1878 0.168 0.000 0.400 0.432
#> GSM213101 3 0.7884 -0.1399 0.308 0.000 0.384 0.308
#> GSM213105 2 0.1389 0.8226 0.000 0.952 0.048 0.000
#> GSM213109 4 0.3266 0.8026 0.168 0.000 0.000 0.832
#> GSM213110 3 0.5183 0.2950 0.000 0.408 0.584 0.008
#> GSM213113 3 0.3401 0.6631 0.152 0.008 0.840 0.000
#> GSM213121 3 0.3539 0.6409 0.000 0.176 0.820 0.004
#> GSM213123 4 0.5512 0.2222 0.488 0.000 0.016 0.496
#> GSM213125 2 0.1557 0.8202 0.000 0.944 0.056 0.000
#> GSM213073 3 0.4443 0.6271 0.012 0.048 0.820 0.120
#> GSM213086 1 0.0469 0.8610 0.988 0.000 0.000 0.012
#> GSM213098 3 0.3024 0.6633 0.148 0.000 0.852 0.000
#> GSM213106 4 0.3356 0.8001 0.176 0.000 0.000 0.824
#> GSM213124 3 0.7472 0.4438 0.120 0.244 0.596 0.040
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 4 0.7072 -0.2502 0.288 0.156 0.000 0.508 0.048
#> GSM213082 2 0.3242 0.5510 0.000 0.784 0.000 0.000 0.216
#> GSM213085 1 0.5742 0.5257 0.508 0.088 0.000 0.404 0.000
#> GSM213088 4 0.3509 0.5830 0.008 0.196 0.000 0.792 0.004
#> GSM213091 4 0.2911 0.6574 0.008 0.136 0.004 0.852 0.000
#> GSM213092 1 0.4557 0.5698 0.584 0.012 0.000 0.404 0.000
#> GSM213096 1 0.4416 0.5706 0.668 0.008 0.008 0.316 0.000
#> GSM213100 1 0.5405 0.4831 0.484 0.000 0.000 0.460 0.056
#> GSM213111 2 0.0162 0.4048 0.004 0.996 0.000 0.000 0.000
#> GSM213117 4 0.0000 0.7474 0.000 0.000 0.000 1.000 0.000
#> GSM213118 1 0.4630 0.5729 0.588 0.016 0.000 0.396 0.000
#> GSM213120 2 0.4300 0.0456 0.108 0.792 0.012 0.000 0.088
#> GSM213122 2 0.4101 0.5664 0.000 0.628 0.000 0.000 0.372
#> GSM213074 4 0.0162 0.7481 0.000 0.004 0.000 0.996 0.000
#> GSM213077 1 0.5396 0.5203 0.500 0.000 0.000 0.444 0.056
#> GSM213083 4 0.5322 -0.3104 0.408 0.004 0.000 0.544 0.044
#> GSM213094 3 0.1341 0.8967 0.000 0.056 0.944 0.000 0.000
#> GSM213095 5 0.4958 0.9130 0.012 0.424 0.012 0.000 0.552
#> GSM213102 4 0.0162 0.7466 0.004 0.000 0.000 0.996 0.000
#> GSM213103 2 0.6474 -0.2662 0.356 0.532 0.012 0.076 0.024
#> GSM213104 1 0.4401 0.1577 0.776 0.172 0.012 0.016 0.024
#> GSM213107 5 0.4801 0.9365 0.008 0.396 0.012 0.000 0.584
#> GSM213108 2 0.2230 0.5122 0.000 0.884 0.000 0.000 0.116
#> GSM213112 1 0.5680 0.5023 0.492 0.080 0.000 0.428 0.000
#> GSM213114 1 0.5507 0.3183 0.716 0.164 0.012 0.084 0.024
#> GSM213115 2 0.4225 0.5677 0.004 0.632 0.000 0.000 0.364
#> GSM213116 4 0.0693 0.7433 0.012 0.000 0.000 0.980 0.008
#> GSM213119 2 0.4088 0.5667 0.000 0.632 0.000 0.000 0.368
#> GSM213072 4 0.1965 0.6995 0.000 0.096 0.000 0.904 0.000
#> GSM213075 4 0.0324 0.7444 0.004 0.000 0.000 0.992 0.004
#> GSM213076 2 0.3206 0.1623 0.024 0.856 0.012 0.000 0.108
#> GSM213079 3 0.0000 0.9539 0.000 0.000 1.000 0.000 0.000
#> GSM213080 1 0.5007 0.2268 0.744 0.176 0.012 0.044 0.024
#> GSM213081 1 0.5211 0.5391 0.524 0.000 0.000 0.432 0.044
#> GSM213084 1 0.5450 0.5160 0.496 0.000 0.000 0.444 0.060
#> GSM213087 2 0.3508 0.5559 0.000 0.748 0.000 0.000 0.252
#> GSM213089 4 0.0000 0.7474 0.000 0.000 0.000 1.000 0.000
#> GSM213090 3 0.0000 0.9539 0.000 0.000 1.000 0.000 0.000
#> GSM213093 4 0.0000 0.7474 0.000 0.000 0.000 1.000 0.000
#> GSM213097 4 0.1608 0.7015 0.072 0.000 0.000 0.928 0.000
#> GSM213099 4 0.2909 0.6532 0.012 0.140 0.000 0.848 0.000
#> GSM213101 4 0.6789 -0.0544 0.244 0.152 0.000 0.560 0.044
#> GSM213105 2 0.4088 0.5667 0.000 0.632 0.000 0.000 0.368
#> GSM213109 4 0.1478 0.7102 0.064 0.000 0.000 0.936 0.000
#> GSM213110 2 0.1764 0.3428 0.064 0.928 0.000 0.000 0.008
#> GSM213113 4 0.7071 -0.1454 0.364 0.172 0.012 0.440 0.012
#> GSM213121 5 0.4696 0.9061 0.004 0.400 0.012 0.000 0.584
#> GSM213123 4 0.2329 0.6547 0.124 0.000 0.000 0.876 0.000
#> GSM213125 2 0.4088 0.5667 0.000 0.632 0.000 0.000 0.368
#> GSM213073 3 0.0981 0.9463 0.008 0.008 0.972 0.000 0.012
#> GSM213086 1 0.5389 0.5319 0.508 0.000 0.000 0.436 0.056
#> GSM213098 1 0.6053 0.3732 0.664 0.168 0.012 0.136 0.020
#> GSM213106 4 0.0324 0.7444 0.004 0.000 0.000 0.992 0.004
#> GSM213124 2 0.5757 -0.2377 0.064 0.480 0.000 0.448 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.5307 0.62955 0.664 0.000 0.000 0.176 0.032 0.128
#> GSM213082 2 0.1663 0.74154 0.000 0.912 0.000 0.000 0.000 0.088
#> GSM213085 1 0.5993 0.61772 0.612 0.000 0.000 0.188 0.088 0.112
#> GSM213088 4 0.6743 0.21571 0.284 0.024 0.000 0.464 0.020 0.208
#> GSM213091 4 0.3541 0.60344 0.000 0.000 0.000 0.748 0.232 0.020
#> GSM213092 1 0.3803 0.74196 0.808 0.000 0.000 0.092 0.072 0.028
#> GSM213096 1 0.3413 0.72766 0.836 0.000 0.000 0.068 0.072 0.024
#> GSM213100 1 0.2020 0.76896 0.896 0.000 0.000 0.096 0.008 0.000
#> GSM213111 2 0.4698 0.54670 0.064 0.660 0.000 0.000 0.008 0.268
#> GSM213117 4 0.2191 0.70976 0.120 0.000 0.000 0.876 0.004 0.000
#> GSM213118 1 0.4971 0.64795 0.688 0.000 0.000 0.204 0.072 0.036
#> GSM213120 6 0.6844 -0.00845 0.068 0.360 0.000 0.000 0.180 0.392
#> GSM213122 2 0.0000 0.75708 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM213074 4 0.2593 0.67191 0.008 0.000 0.000 0.844 0.148 0.000
#> GSM213077 1 0.1858 0.77056 0.904 0.000 0.000 0.092 0.004 0.000
#> GSM213083 1 0.3406 0.70793 0.792 0.000 0.000 0.180 0.020 0.008
#> GSM213094 3 0.1226 0.93940 0.000 0.000 0.952 0.004 0.040 0.004
#> GSM213095 6 0.0790 0.34196 0.000 0.032 0.000 0.000 0.000 0.968
#> GSM213102 4 0.2632 0.69997 0.164 0.000 0.000 0.832 0.004 0.000
#> GSM213103 6 0.7458 -0.05533 0.176 0.168 0.000 0.000 0.316 0.340
#> GSM213104 5 0.5378 0.66216 0.088 0.000 0.000 0.020 0.592 0.300
#> GSM213107 6 0.1075 0.34328 0.000 0.048 0.000 0.000 0.000 0.952
#> GSM213108 2 0.4545 0.57008 0.064 0.688 0.000 0.000 0.008 0.240
#> GSM213112 1 0.6120 0.59188 0.588 0.000 0.000 0.216 0.084 0.112
#> GSM213114 5 0.5842 0.80637 0.228 0.000 0.000 0.000 0.484 0.288
#> GSM213115 2 0.0146 0.75823 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM213116 4 0.2969 0.65252 0.224 0.000 0.000 0.776 0.000 0.000
#> GSM213119 2 0.0000 0.75708 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM213072 4 0.3331 0.68875 0.044 0.000 0.000 0.816 0.136 0.004
#> GSM213075 4 0.1615 0.72248 0.064 0.004 0.000 0.928 0.004 0.000
#> GSM213076 2 0.5471 0.14471 0.064 0.480 0.000 0.000 0.024 0.432
#> GSM213079 3 0.0000 0.95309 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM213080 5 0.5735 0.82314 0.200 0.000 0.000 0.000 0.504 0.296
#> GSM213081 1 0.1753 0.77008 0.912 0.000 0.000 0.084 0.004 0.000
#> GSM213084 1 0.1970 0.76953 0.900 0.000 0.000 0.092 0.008 0.000
#> GSM213087 2 0.1765 0.73620 0.000 0.904 0.000 0.000 0.000 0.096
#> GSM213089 4 0.1719 0.72268 0.060 0.000 0.000 0.924 0.016 0.000
#> GSM213090 3 0.0000 0.95309 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM213093 4 0.2234 0.72173 0.124 0.000 0.000 0.872 0.004 0.000
#> GSM213097 4 0.3126 0.62988 0.248 0.000 0.000 0.752 0.000 0.000
#> GSM213099 4 0.3720 0.59326 0.000 0.000 0.000 0.736 0.236 0.028
#> GSM213101 1 0.5393 0.61775 0.652 0.000 0.000 0.188 0.032 0.128
#> GSM213105 2 0.0000 0.75708 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM213109 4 0.3126 0.62967 0.248 0.000 0.000 0.752 0.000 0.000
#> GSM213110 2 0.6508 0.23283 0.064 0.508 0.000 0.000 0.160 0.268
#> GSM213113 6 0.7739 -0.32417 0.296 0.008 0.000 0.144 0.252 0.300
#> GSM213121 6 0.2300 0.34985 0.000 0.144 0.000 0.000 0.000 0.856
#> GSM213123 4 0.4984 0.12638 0.392 0.000 0.000 0.552 0.036 0.020
#> GSM213125 2 0.0146 0.75799 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM213073 3 0.1501 0.88731 0.000 0.000 0.924 0.000 0.000 0.076
#> GSM213086 1 0.2001 0.77103 0.900 0.000 0.000 0.092 0.004 0.004
#> GSM213098 1 0.7369 -0.44760 0.312 0.004 0.000 0.088 0.312 0.284
#> GSM213106 4 0.2146 0.72219 0.116 0.000 0.000 0.880 0.004 0.000
#> GSM213124 4 0.8626 -0.37037 0.096 0.192 0.000 0.276 0.160 0.276
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 development.stage(p) disease.state(p) k
#> SD:mclust 54 1.000 0.676 2
#> SD:mclust 42 1.000 1.000 3
#> SD:mclust 40 0.537 0.706 4
#> SD:mclust 39 0.492 0.705 5
#> SD:mclust 42 0.330 0.753 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "NMF"]
# you can also extract it by
# res = res_list["SD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.961 0.929 0.974 0.4489 0.547 0.547
#> 3 3 0.590 0.710 0.869 0.4662 0.704 0.496
#> 4 4 0.576 0.626 0.808 0.1189 0.902 0.722
#> 5 5 0.573 0.536 0.756 0.0731 0.864 0.565
#> 6 6 0.614 0.436 0.663 0.0440 0.937 0.721
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
#> GSM213078 1 0.000 0.9829 1.000 0.000
#> GSM213082 2 0.000 0.9500 0.000 1.000
#> GSM213085 1 0.000 0.9829 1.000 0.000
#> GSM213088 1 0.494 0.8638 0.892 0.108
#> GSM213091 1 0.000 0.9829 1.000 0.000
#> GSM213092 1 0.000 0.9829 1.000 0.000
#> GSM213096 1 0.000 0.9829 1.000 0.000
#> GSM213100 1 0.000 0.9829 1.000 0.000
#> GSM213111 2 0.000 0.9500 0.000 1.000
#> GSM213117 1 0.000 0.9829 1.000 0.000
#> GSM213118 1 0.000 0.9829 1.000 0.000
#> GSM213120 2 0.000 0.9500 0.000 1.000
#> GSM213122 2 0.000 0.9500 0.000 1.000
#> GSM213074 1 0.000 0.9829 1.000 0.000
#> GSM213077 1 0.000 0.9829 1.000 0.000
#> GSM213083 1 0.000 0.9829 1.000 0.000
#> GSM213094 1 0.000 0.9829 1.000 0.000
#> GSM213095 2 0.000 0.9500 0.000 1.000
#> GSM213102 1 0.000 0.9829 1.000 0.000
#> GSM213103 2 0.118 0.9371 0.016 0.984
#> GSM213104 2 0.921 0.4979 0.336 0.664
#> GSM213107 2 0.000 0.9500 0.000 1.000
#> GSM213108 2 0.000 0.9500 0.000 1.000
#> GSM213112 1 0.000 0.9829 1.000 0.000
#> GSM213114 1 0.000 0.9829 1.000 0.000
#> GSM213115 2 0.000 0.9500 0.000 1.000
#> GSM213116 1 0.000 0.9829 1.000 0.000
#> GSM213119 2 0.000 0.9500 0.000 1.000
#> GSM213072 1 0.000 0.9829 1.000 0.000
#> GSM213075 1 0.000 0.9829 1.000 0.000
#> GSM213076 2 0.000 0.9500 0.000 1.000
#> GSM213079 1 0.000 0.9829 1.000 0.000
#> GSM213080 2 0.998 0.1256 0.472 0.528
#> GSM213081 1 0.000 0.9829 1.000 0.000
#> GSM213084 1 0.000 0.9829 1.000 0.000
#> GSM213087 2 0.000 0.9500 0.000 1.000
#> GSM213089 1 0.000 0.9829 1.000 0.000
#> GSM213090 1 0.000 0.9829 1.000 0.000
#> GSM213093 1 0.000 0.9829 1.000 0.000
#> GSM213097 1 0.000 0.9829 1.000 0.000
#> GSM213099 1 0.000 0.9829 1.000 0.000
#> GSM213101 1 0.000 0.9829 1.000 0.000
#> GSM213105 2 0.000 0.9500 0.000 1.000
#> GSM213109 1 0.000 0.9829 1.000 0.000
#> GSM213110 2 0.000 0.9500 0.000 1.000
#> GSM213113 1 0.000 0.9829 1.000 0.000
#> GSM213121 2 0.000 0.9500 0.000 1.000
#> GSM213123 1 0.000 0.9829 1.000 0.000
#> GSM213125 2 0.000 0.9500 0.000 1.000
#> GSM213073 1 0.000 0.9829 1.000 0.000
#> GSM213086 1 0.000 0.9829 1.000 0.000
#> GSM213098 1 0.000 0.9829 1.000 0.000
#> GSM213106 1 0.000 0.9829 1.000 0.000
#> GSM213124 1 0.994 0.0855 0.544 0.456
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.0237 0.7904 0.996 0.000 0.004
#> GSM213082 2 0.0000 0.9230 0.000 1.000 0.000
#> GSM213085 1 0.4002 0.7326 0.840 0.000 0.160
#> GSM213088 1 0.2743 0.7741 0.928 0.052 0.020
#> GSM213091 3 0.0892 0.7933 0.020 0.000 0.980
#> GSM213092 1 0.4555 0.6937 0.800 0.000 0.200
#> GSM213096 1 0.0000 0.7886 1.000 0.000 0.000
#> GSM213100 1 0.0592 0.7927 0.988 0.000 0.012
#> GSM213111 2 0.0424 0.9207 0.000 0.992 0.008
#> GSM213117 1 0.5835 0.5301 0.660 0.000 0.340
#> GSM213118 1 0.2165 0.7879 0.936 0.000 0.064
#> GSM213120 2 0.0237 0.9221 0.000 0.996 0.004
#> GSM213122 2 0.0000 0.9230 0.000 1.000 0.000
#> GSM213074 3 0.3116 0.7650 0.108 0.000 0.892
#> GSM213077 1 0.3412 0.7618 0.876 0.000 0.124
#> GSM213083 1 0.2711 0.7811 0.912 0.000 0.088
#> GSM213094 3 0.0424 0.7916 0.008 0.000 0.992
#> GSM213095 2 0.3267 0.8481 0.000 0.884 0.116
#> GSM213102 1 0.5968 0.4832 0.636 0.000 0.364
#> GSM213103 2 0.5058 0.6890 0.244 0.756 0.000
#> GSM213104 1 0.6404 0.3236 0.644 0.344 0.012
#> GSM213107 2 0.0424 0.9210 0.000 0.992 0.008
#> GSM213108 2 0.5859 0.5513 0.000 0.656 0.344
#> GSM213112 1 0.6305 0.0292 0.516 0.000 0.484
#> GSM213114 1 0.0237 0.7863 0.996 0.000 0.004
#> GSM213115 2 0.0000 0.9230 0.000 1.000 0.000
#> GSM213116 3 0.6267 0.1051 0.452 0.000 0.548
#> GSM213119 2 0.0000 0.9230 0.000 1.000 0.000
#> GSM213072 3 0.3551 0.7654 0.132 0.000 0.868
#> GSM213075 3 0.5706 0.5241 0.320 0.000 0.680
#> GSM213076 2 0.0747 0.9177 0.000 0.984 0.016
#> GSM213079 3 0.0424 0.7910 0.008 0.000 0.992
#> GSM213080 1 0.0661 0.7821 0.988 0.004 0.008
#> GSM213081 1 0.0592 0.7926 0.988 0.000 0.012
#> GSM213084 1 0.0892 0.7935 0.980 0.000 0.020
#> GSM213087 2 0.0000 0.9230 0.000 1.000 0.000
#> GSM213089 3 0.2261 0.7851 0.068 0.000 0.932
#> GSM213090 3 0.0237 0.7901 0.004 0.000 0.996
#> GSM213093 3 0.5254 0.5845 0.264 0.000 0.736
#> GSM213097 1 0.6295 0.1853 0.528 0.000 0.472
#> GSM213099 3 0.0592 0.7927 0.012 0.000 0.988
#> GSM213101 1 0.0237 0.7904 0.996 0.000 0.004
#> GSM213105 2 0.0000 0.9230 0.000 1.000 0.000
#> GSM213109 1 0.5465 0.6137 0.712 0.000 0.288
#> GSM213110 2 0.1643 0.8968 0.044 0.956 0.000
#> GSM213113 3 0.4842 0.6590 0.224 0.000 0.776
#> GSM213121 2 0.0000 0.9230 0.000 1.000 0.000
#> GSM213123 3 0.6291 0.1153 0.468 0.000 0.532
#> GSM213125 2 0.0000 0.9230 0.000 1.000 0.000
#> GSM213073 3 0.0424 0.7910 0.008 0.000 0.992
#> GSM213086 1 0.2066 0.7908 0.940 0.000 0.060
#> GSM213098 3 0.5138 0.6044 0.252 0.000 0.748
#> GSM213106 1 0.5926 0.5039 0.644 0.000 0.356
#> GSM213124 2 0.9017 0.3216 0.212 0.560 0.228
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.0469 0.739 0.988 0.000 0.012 0.000
#> GSM213082 2 0.0469 0.865 0.000 0.988 0.000 0.012
#> GSM213085 1 0.5535 0.523 0.656 0.000 0.304 0.040
#> GSM213088 1 0.3781 0.696 0.844 0.028 0.004 0.124
#> GSM213091 4 0.0672 0.742 0.008 0.000 0.008 0.984
#> GSM213092 1 0.5787 0.578 0.680 0.000 0.244 0.076
#> GSM213096 1 0.2589 0.694 0.884 0.000 0.116 0.000
#> GSM213100 1 0.0804 0.742 0.980 0.000 0.012 0.008
#> GSM213111 2 0.0188 0.869 0.000 0.996 0.000 0.004
#> GSM213117 1 0.5016 0.409 0.600 0.000 0.004 0.396
#> GSM213118 1 0.3913 0.693 0.824 0.000 0.148 0.028
#> GSM213120 2 0.3725 0.701 0.000 0.812 0.180 0.008
#> GSM213122 2 0.0000 0.870 0.000 1.000 0.000 0.000
#> GSM213074 4 0.3205 0.726 0.104 0.000 0.024 0.872
#> GSM213077 1 0.2224 0.743 0.928 0.000 0.032 0.040
#> GSM213083 1 0.1211 0.745 0.960 0.000 0.000 0.040
#> GSM213094 4 0.1940 0.727 0.000 0.000 0.076 0.924
#> GSM213095 3 0.5227 0.567 0.000 0.256 0.704 0.040
#> GSM213102 1 0.4456 0.574 0.716 0.000 0.004 0.280
#> GSM213103 3 0.7218 0.447 0.120 0.352 0.520 0.008
#> GSM213104 3 0.2799 0.670 0.108 0.008 0.884 0.000
#> GSM213107 3 0.4406 0.566 0.000 0.300 0.700 0.000
#> GSM213108 2 0.4635 0.602 0.000 0.756 0.028 0.216
#> GSM213112 1 0.7669 0.267 0.444 0.000 0.328 0.228
#> GSM213114 1 0.4981 0.112 0.536 0.000 0.464 0.000
#> GSM213115 2 0.0000 0.870 0.000 1.000 0.000 0.000
#> GSM213116 1 0.5151 0.162 0.532 0.000 0.004 0.464
#> GSM213119 2 0.0000 0.870 0.000 1.000 0.000 0.000
#> GSM213072 4 0.4175 0.662 0.200 0.000 0.016 0.784
#> GSM213075 4 0.5093 0.425 0.336 0.008 0.004 0.652
#> GSM213076 2 0.2101 0.830 0.000 0.928 0.060 0.012
#> GSM213079 4 0.3610 0.663 0.000 0.000 0.200 0.800
#> GSM213080 3 0.4454 0.457 0.308 0.000 0.692 0.000
#> GSM213081 1 0.2760 0.691 0.872 0.000 0.128 0.000
#> GSM213084 1 0.1118 0.732 0.964 0.000 0.036 0.000
#> GSM213087 2 0.0469 0.866 0.000 0.988 0.012 0.000
#> GSM213089 4 0.1792 0.736 0.068 0.000 0.000 0.932
#> GSM213090 4 0.3649 0.660 0.000 0.000 0.204 0.796
#> GSM213093 4 0.4194 0.586 0.228 0.000 0.008 0.764
#> GSM213097 1 0.5155 0.243 0.528 0.000 0.004 0.468
#> GSM213099 4 0.0895 0.741 0.004 0.000 0.020 0.976
#> GSM213101 1 0.0657 0.742 0.984 0.000 0.004 0.012
#> GSM213105 2 0.0000 0.870 0.000 1.000 0.000 0.000
#> GSM213109 1 0.3196 0.701 0.856 0.000 0.008 0.136
#> GSM213110 2 0.0921 0.853 0.028 0.972 0.000 0.000
#> GSM213113 4 0.5724 0.326 0.028 0.000 0.424 0.548
#> GSM213121 2 0.3356 0.703 0.000 0.824 0.176 0.000
#> GSM213123 4 0.6374 0.308 0.324 0.000 0.084 0.592
#> GSM213125 2 0.0000 0.870 0.000 1.000 0.000 0.000
#> GSM213073 4 0.4730 0.485 0.000 0.000 0.364 0.636
#> GSM213086 1 0.1733 0.744 0.948 0.000 0.028 0.024
#> GSM213098 3 0.2589 0.636 0.044 0.000 0.912 0.044
#> GSM213106 1 0.5178 0.426 0.600 0.004 0.004 0.392
#> GSM213124 2 0.8348 0.104 0.232 0.468 0.032 0.268
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.1357 0.7383 0.948 0.000 0.000 0.048 0.004
#> GSM213082 2 0.0451 0.8140 0.000 0.988 0.008 0.000 0.004
#> GSM213085 3 0.6488 -0.1115 0.408 0.000 0.472 0.032 0.088
#> GSM213088 1 0.4201 0.3772 0.664 0.008 0.000 0.328 0.000
#> GSM213091 4 0.2516 0.5750 0.000 0.000 0.140 0.860 0.000
#> GSM213092 1 0.6698 0.1838 0.488 0.000 0.364 0.032 0.116
#> GSM213096 1 0.3996 0.7017 0.816 0.000 0.052 0.020 0.112
#> GSM213100 1 0.3746 0.7090 0.840 0.000 0.084 0.040 0.036
#> GSM213111 2 0.0566 0.8141 0.000 0.984 0.000 0.004 0.012
#> GSM213117 4 0.4425 0.6432 0.204 0.000 0.048 0.744 0.004
#> GSM213118 1 0.7418 0.3622 0.496 0.000 0.092 0.136 0.276
#> GSM213120 2 0.6471 0.1629 0.000 0.488 0.000 0.216 0.296
#> GSM213122 2 0.0000 0.8165 0.000 1.000 0.000 0.000 0.000
#> GSM213074 4 0.5968 0.3141 0.084 0.000 0.416 0.492 0.008
#> GSM213077 1 0.3092 0.7310 0.880 0.000 0.036 0.048 0.036
#> GSM213083 1 0.0451 0.7422 0.988 0.000 0.008 0.004 0.000
#> GSM213094 4 0.4009 0.3796 0.000 0.000 0.312 0.684 0.004
#> GSM213095 3 0.6514 0.1387 0.004 0.136 0.528 0.012 0.320
#> GSM213102 1 0.4416 0.3468 0.632 0.000 0.012 0.356 0.000
#> GSM213103 5 0.6635 0.4742 0.140 0.104 0.068 0.028 0.660
#> GSM213104 5 0.1493 0.5866 0.028 0.000 0.024 0.000 0.948
#> GSM213107 5 0.2930 0.5360 0.000 0.164 0.004 0.000 0.832
#> GSM213108 2 0.4506 0.6002 0.000 0.716 0.244 0.036 0.004
#> GSM213112 3 0.5462 0.3765 0.204 0.000 0.688 0.024 0.084
#> GSM213114 1 0.4470 0.3604 0.596 0.000 0.004 0.004 0.396
#> GSM213115 2 0.0324 0.8164 0.000 0.992 0.004 0.000 0.004
#> GSM213116 4 0.4832 0.6379 0.208 0.000 0.064 0.720 0.008
#> GSM213119 2 0.0000 0.8165 0.000 1.000 0.000 0.000 0.000
#> GSM213072 4 0.6526 0.3358 0.160 0.000 0.348 0.484 0.008
#> GSM213075 4 0.5616 0.6102 0.232 0.000 0.112 0.648 0.008
#> GSM213076 2 0.4675 0.6600 0.000 0.760 0.012 0.136 0.092
#> GSM213079 3 0.4584 0.3541 0.000 0.000 0.660 0.312 0.028
#> GSM213080 5 0.4313 0.4426 0.276 0.000 0.008 0.012 0.704
#> GSM213081 1 0.4244 0.6793 0.788 0.000 0.008 0.132 0.072
#> GSM213084 1 0.2095 0.7372 0.928 0.000 0.028 0.020 0.024
#> GSM213087 2 0.0609 0.8110 0.000 0.980 0.000 0.000 0.020
#> GSM213089 4 0.1996 0.6386 0.032 0.000 0.036 0.928 0.004
#> GSM213090 3 0.2270 0.4808 0.000 0.000 0.904 0.076 0.020
#> GSM213093 4 0.4615 0.6439 0.220 0.000 0.052 0.724 0.004
#> GSM213097 4 0.4350 0.3230 0.408 0.000 0.004 0.588 0.000
#> GSM213099 4 0.2536 0.5813 0.004 0.000 0.128 0.868 0.000
#> GSM213101 1 0.1518 0.7427 0.944 0.000 0.004 0.048 0.004
#> GSM213105 2 0.0162 0.8159 0.000 0.996 0.004 0.000 0.000
#> GSM213109 1 0.3191 0.7182 0.860 0.000 0.084 0.052 0.004
#> GSM213110 2 0.1704 0.7759 0.068 0.928 0.004 0.000 0.000
#> GSM213113 5 0.6360 0.0332 0.004 0.000 0.140 0.420 0.436
#> GSM213121 2 0.4101 0.3984 0.000 0.628 0.000 0.000 0.372
#> GSM213123 4 0.4055 0.6421 0.140 0.000 0.012 0.800 0.048
#> GSM213125 2 0.0000 0.8165 0.000 1.000 0.000 0.000 0.000
#> GSM213073 3 0.5974 0.3680 0.000 0.000 0.564 0.292 0.144
#> GSM213086 1 0.5407 0.6206 0.704 0.000 0.192 0.060 0.044
#> GSM213098 5 0.3141 0.5779 0.004 0.000 0.040 0.096 0.860
#> GSM213106 4 0.3967 0.6054 0.264 0.000 0.012 0.724 0.000
#> GSM213124 2 0.8507 -0.1060 0.116 0.336 0.308 0.228 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.1370 0.6355 0.948 0.000 0.004 0.036 0.000 0.012
#> GSM213082 2 0.0909 0.8132 0.000 0.968 0.020 0.012 0.000 0.000
#> GSM213085 6 0.6498 -0.0314 0.212 0.000 0.376 0.000 0.028 0.384
#> GSM213088 1 0.4355 0.3146 0.644 0.004 0.000 0.320 0.000 0.032
#> GSM213091 4 0.3261 0.5585 0.000 0.000 0.072 0.824 0.000 0.104
#> GSM213092 1 0.6825 -0.1465 0.360 0.000 0.312 0.004 0.032 0.292
#> GSM213096 1 0.5108 0.1854 0.552 0.000 0.000 0.000 0.092 0.356
#> GSM213100 1 0.4476 0.3903 0.672 0.000 0.028 0.008 0.008 0.284
#> GSM213111 2 0.1325 0.8108 0.000 0.956 0.004 0.016 0.012 0.012
#> GSM213117 4 0.4945 0.3724 0.068 0.000 0.000 0.584 0.004 0.344
#> GSM213118 6 0.6523 0.3128 0.152 0.000 0.004 0.048 0.312 0.484
#> GSM213120 2 0.6643 -0.0360 0.000 0.392 0.020 0.232 0.348 0.008
#> GSM213122 2 0.0291 0.8175 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM213074 6 0.4999 0.2875 0.036 0.000 0.068 0.216 0.000 0.680
#> GSM213077 1 0.3820 0.6077 0.820 0.000 0.056 0.080 0.008 0.036
#> GSM213083 1 0.0972 0.6355 0.964 0.000 0.008 0.000 0.000 0.028
#> GSM213094 4 0.5366 0.3242 0.000 0.000 0.224 0.604 0.004 0.168
#> GSM213095 3 0.5173 0.4443 0.004 0.096 0.704 0.000 0.144 0.052
#> GSM213102 1 0.5673 0.0255 0.484 0.000 0.004 0.372 0.000 0.140
#> GSM213103 6 0.6067 0.0940 0.096 0.028 0.000 0.008 0.412 0.456
#> GSM213104 5 0.2322 0.5797 0.048 0.000 0.024 0.000 0.904 0.024
#> GSM213107 5 0.2420 0.5322 0.000 0.128 0.004 0.004 0.864 0.000
#> GSM213108 2 0.5497 0.4759 0.004 0.640 0.176 0.020 0.000 0.160
#> GSM213112 3 0.5904 0.0812 0.148 0.000 0.528 0.004 0.012 0.308
#> GSM213114 1 0.4406 0.3628 0.648 0.000 0.004 0.004 0.316 0.028
#> GSM213115 2 0.0777 0.8148 0.000 0.972 0.000 0.000 0.004 0.024
#> GSM213116 4 0.4905 0.2949 0.052 0.000 0.000 0.524 0.004 0.420
#> GSM213119 2 0.0508 0.8168 0.000 0.984 0.000 0.004 0.000 0.012
#> GSM213072 6 0.4862 0.2859 0.068 0.000 0.028 0.216 0.000 0.688
#> GSM213075 4 0.6939 0.1932 0.168 0.000 0.084 0.376 0.000 0.372
#> GSM213076 2 0.6159 0.4860 0.000 0.608 0.056 0.216 0.100 0.020
#> GSM213079 3 0.4883 0.4834 0.000 0.000 0.684 0.212 0.020 0.084
#> GSM213080 5 0.5010 0.2262 0.368 0.000 0.000 0.032 0.572 0.028
#> GSM213081 1 0.5705 0.4858 0.684 0.000 0.040 0.136 0.044 0.096
#> GSM213084 1 0.1465 0.6343 0.948 0.000 0.020 0.004 0.004 0.024
#> GSM213087 2 0.0458 0.8158 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM213089 4 0.2956 0.5862 0.040 0.000 0.000 0.840 0.000 0.120
#> GSM213090 3 0.2890 0.5231 0.008 0.000 0.852 0.016 0.004 0.120
#> GSM213093 4 0.6370 0.4193 0.288 0.000 0.088 0.524 0.000 0.100
#> GSM213097 4 0.4751 0.2468 0.392 0.000 0.004 0.560 0.000 0.044
#> GSM213099 4 0.3047 0.5503 0.000 0.000 0.064 0.848 0.004 0.084
#> GSM213101 1 0.1642 0.6379 0.936 0.000 0.000 0.028 0.004 0.032
#> GSM213105 2 0.0291 0.8174 0.000 0.992 0.004 0.000 0.000 0.004
#> GSM213109 1 0.3893 0.4994 0.744 0.000 0.020 0.016 0.000 0.220
#> GSM213110 2 0.2579 0.7465 0.088 0.876 0.000 0.000 0.004 0.032
#> GSM213113 5 0.7507 0.1092 0.024 0.000 0.136 0.340 0.384 0.116
#> GSM213121 2 0.4124 0.1854 0.000 0.516 0.000 0.004 0.476 0.004
#> GSM213123 4 0.5597 0.5540 0.168 0.000 0.040 0.680 0.032 0.080
#> GSM213125 2 0.0146 0.8168 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM213073 3 0.6091 0.4133 0.000 0.000 0.576 0.248 0.088 0.088
#> GSM213086 6 0.6019 -0.0568 0.424 0.000 0.128 0.004 0.016 0.428
#> GSM213098 5 0.3124 0.5696 0.008 0.000 0.008 0.116 0.844 0.024
#> GSM213106 4 0.4411 0.5598 0.204 0.000 0.004 0.712 0.000 0.080
#> GSM213124 6 0.5716 0.4079 0.036 0.116 0.044 0.108 0.004 0.692
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n development.stage(p) disease.state(p) k
#> SD:NMF 51 0.5337 1.0000 2
#> SD:NMF 47 0.0596 0.8272 3
#> SD:NMF 41 0.3645 0.0222 4
#> SD:NMF 33 0.7067 0.0810 5
#> SD:NMF 23 0.4921 0.1196 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "hclust"]
# you can also extract it by
# res = res_list["CV:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.496 0.609 0.815 0.2897 0.860 0.860
#> 3 3 0.656 0.858 0.931 0.7814 0.633 0.574
#> 4 4 0.655 0.801 0.915 0.0662 0.973 0.946
#> 5 5 0.544 0.746 0.857 0.0692 0.974 0.945
#> 6 6 0.509 0.570 0.813 0.0668 0.982 0.959
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
#> GSM213078 1 0.0376 0.700 0.996 0.004
#> GSM213082 1 0.9988 0.443 0.520 0.480
#> GSM213085 1 0.0376 0.699 0.996 0.004
#> GSM213088 1 0.0376 0.700 0.996 0.004
#> GSM213091 1 0.8499 -0.255 0.724 0.276
#> GSM213092 1 0.0376 0.700 0.996 0.004
#> GSM213096 1 0.0000 0.698 1.000 0.000
#> GSM213100 1 0.0000 0.698 1.000 0.000
#> GSM213111 1 0.9983 0.446 0.524 0.476
#> GSM213117 1 0.0376 0.700 0.996 0.004
#> GSM213118 1 0.0376 0.699 0.996 0.004
#> GSM213120 1 0.9608 0.490 0.616 0.384
#> GSM213122 1 0.9988 0.443 0.520 0.480
#> GSM213074 1 0.1184 0.679 0.984 0.016
#> GSM213077 1 0.0376 0.695 0.996 0.004
#> GSM213083 1 0.0376 0.695 0.996 0.004
#> GSM213094 2 0.9988 0.997 0.480 0.520
#> GSM213095 1 0.9970 0.450 0.532 0.468
#> GSM213102 1 0.0376 0.695 0.996 0.004
#> GSM213103 1 0.2423 0.688 0.960 0.040
#> GSM213104 1 0.2948 0.684 0.948 0.052
#> GSM213107 1 0.9988 0.443 0.520 0.480
#> GSM213108 1 0.9944 0.457 0.544 0.456
#> GSM213112 1 0.0938 0.699 0.988 0.012
#> GSM213114 1 0.2236 0.691 0.964 0.036
#> GSM213115 1 0.9710 0.487 0.600 0.400
#> GSM213116 1 0.0000 0.698 1.000 0.000
#> GSM213119 1 0.9988 0.443 0.520 0.480
#> GSM213072 1 0.0938 0.685 0.988 0.012
#> GSM213075 1 0.0938 0.697 0.988 0.012
#> GSM213076 1 0.9686 0.488 0.604 0.396
#> GSM213079 2 0.9988 0.997 0.480 0.520
#> GSM213080 1 0.2236 0.691 0.964 0.036
#> GSM213081 1 0.0376 0.700 0.996 0.004
#> GSM213084 1 0.0000 0.698 1.000 0.000
#> GSM213087 1 0.9988 0.443 0.520 0.480
#> GSM213089 1 0.0672 0.698 0.992 0.008
#> GSM213090 2 0.9983 0.992 0.476 0.524
#> GSM213093 1 0.0000 0.698 1.000 0.000
#> GSM213097 1 0.0376 0.695 0.996 0.004
#> GSM213099 1 0.9393 -0.575 0.644 0.356
#> GSM213101 1 0.0376 0.700 0.996 0.004
#> GSM213105 1 0.9988 0.443 0.520 0.480
#> GSM213109 1 0.0376 0.695 0.996 0.004
#> GSM213110 1 0.9661 0.491 0.608 0.392
#> GSM213113 1 0.1843 0.692 0.972 0.028
#> GSM213121 1 0.9988 0.443 0.520 0.480
#> GSM213123 1 0.0376 0.700 0.996 0.004
#> GSM213125 1 0.9988 0.443 0.520 0.480
#> GSM213073 2 0.9988 0.997 0.480 0.520
#> GSM213086 1 0.0376 0.700 0.996 0.004
#> GSM213098 1 0.1414 0.698 0.980 0.020
#> GSM213106 1 0.0672 0.697 0.992 0.008
#> GSM213124 1 0.6438 0.603 0.836 0.164
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.0475 0.925 0.992 0.004 0.004
#> GSM213082 2 0.1411 0.902 0.036 0.964 0.000
#> GSM213085 1 0.0829 0.924 0.984 0.004 0.012
#> GSM213088 1 0.0475 0.925 0.992 0.004 0.004
#> GSM213091 1 0.6667 0.326 0.616 0.016 0.368
#> GSM213092 1 0.0829 0.925 0.984 0.004 0.012
#> GSM213096 1 0.0237 0.925 0.996 0.000 0.004
#> GSM213100 1 0.0237 0.925 0.996 0.000 0.004
#> GSM213111 2 0.1860 0.896 0.052 0.948 0.000
#> GSM213117 1 0.0237 0.925 0.996 0.000 0.004
#> GSM213118 1 0.1170 0.922 0.976 0.016 0.008
#> GSM213120 2 0.5202 0.699 0.220 0.772 0.008
#> GSM213122 2 0.0747 0.902 0.016 0.984 0.000
#> GSM213074 1 0.1989 0.904 0.948 0.004 0.048
#> GSM213077 1 0.0424 0.925 0.992 0.000 0.008
#> GSM213083 1 0.0592 0.925 0.988 0.000 0.012
#> GSM213094 3 0.4209 0.898 0.128 0.016 0.856
#> GSM213095 2 0.1832 0.901 0.036 0.956 0.008
#> GSM213102 1 0.0237 0.925 0.996 0.000 0.004
#> GSM213103 1 0.3295 0.858 0.896 0.096 0.008
#> GSM213104 1 0.5247 0.697 0.768 0.224 0.008
#> GSM213107 2 0.0747 0.902 0.016 0.984 0.000
#> GSM213108 2 0.2651 0.888 0.060 0.928 0.012
#> GSM213112 1 0.1585 0.916 0.964 0.028 0.008
#> GSM213114 1 0.4682 0.740 0.804 0.192 0.004
#> GSM213115 2 0.4700 0.764 0.180 0.812 0.008
#> GSM213116 1 0.0237 0.925 0.996 0.000 0.004
#> GSM213119 2 0.0747 0.902 0.016 0.984 0.000
#> GSM213072 1 0.0829 0.922 0.984 0.004 0.012
#> GSM213075 1 0.1015 0.923 0.980 0.012 0.008
#> GSM213076 2 0.4452 0.748 0.192 0.808 0.000
#> GSM213079 3 0.3116 0.930 0.108 0.000 0.892
#> GSM213080 1 0.4682 0.740 0.804 0.192 0.004
#> GSM213081 1 0.0237 0.925 0.996 0.000 0.004
#> GSM213084 1 0.0237 0.925 0.996 0.000 0.004
#> GSM213087 2 0.0747 0.902 0.016 0.984 0.000
#> GSM213089 1 0.0747 0.923 0.984 0.000 0.016
#> GSM213090 3 0.0237 0.841 0.004 0.000 0.996
#> GSM213093 1 0.0592 0.925 0.988 0.000 0.012
#> GSM213097 1 0.0237 0.925 0.996 0.000 0.004
#> GSM213099 1 0.6925 0.011 0.532 0.016 0.452
#> GSM213101 1 0.0475 0.925 0.992 0.004 0.004
#> GSM213105 2 0.0747 0.902 0.016 0.984 0.000
#> GSM213109 1 0.0592 0.925 0.988 0.000 0.012
#> GSM213110 2 0.4808 0.753 0.188 0.804 0.008
#> GSM213113 1 0.3148 0.881 0.916 0.036 0.048
#> GSM213121 2 0.1031 0.904 0.024 0.976 0.000
#> GSM213123 1 0.0661 0.925 0.988 0.008 0.004
#> GSM213125 2 0.0747 0.902 0.016 0.984 0.000
#> GSM213073 3 0.3116 0.930 0.108 0.000 0.892
#> GSM213086 1 0.0661 0.925 0.988 0.004 0.008
#> GSM213098 1 0.2584 0.886 0.928 0.064 0.008
#> GSM213106 1 0.0475 0.924 0.992 0.004 0.004
#> GSM213124 1 0.4915 0.729 0.804 0.184 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.0844 0.902 0.980 0.004 0.004 0.012
#> GSM213082 2 0.1059 0.899 0.016 0.972 0.000 0.012
#> GSM213085 1 0.0859 0.904 0.980 0.004 0.008 0.008
#> GSM213088 1 0.1109 0.903 0.968 0.004 0.000 0.028
#> GSM213091 1 0.5396 -0.277 0.524 0.000 0.012 0.464
#> GSM213092 1 0.0712 0.904 0.984 0.004 0.004 0.008
#> GSM213096 1 0.0376 0.902 0.992 0.000 0.004 0.004
#> GSM213100 1 0.0188 0.902 0.996 0.000 0.004 0.000
#> GSM213111 2 0.1724 0.892 0.032 0.948 0.000 0.020
#> GSM213117 1 0.1305 0.901 0.960 0.004 0.000 0.036
#> GSM213118 1 0.1707 0.899 0.952 0.020 0.004 0.024
#> GSM213120 2 0.4887 0.699 0.184 0.772 0.016 0.028
#> GSM213122 2 0.0000 0.899 0.000 1.000 0.000 0.000
#> GSM213074 1 0.2342 0.871 0.912 0.000 0.008 0.080
#> GSM213077 1 0.0524 0.903 0.988 0.000 0.004 0.008
#> GSM213083 1 0.0804 0.903 0.980 0.000 0.008 0.012
#> GSM213094 4 0.2670 -0.294 0.024 0.000 0.072 0.904
#> GSM213095 2 0.1749 0.894 0.012 0.952 0.012 0.024
#> GSM213102 1 0.0895 0.901 0.976 0.000 0.004 0.020
#> GSM213103 1 0.3264 0.822 0.876 0.096 0.004 0.024
#> GSM213104 1 0.5930 0.539 0.700 0.228 0.024 0.048
#> GSM213107 2 0.0592 0.898 0.000 0.984 0.000 0.016
#> GSM213108 2 0.2115 0.886 0.036 0.936 0.004 0.024
#> GSM213112 1 0.1443 0.897 0.960 0.028 0.004 0.008
#> GSM213114 1 0.4114 0.657 0.788 0.200 0.004 0.008
#> GSM213115 2 0.3695 0.756 0.156 0.828 0.000 0.016
#> GSM213116 1 0.1004 0.904 0.972 0.004 0.000 0.024
#> GSM213119 2 0.0000 0.899 0.000 1.000 0.000 0.000
#> GSM213072 1 0.1305 0.899 0.960 0.000 0.004 0.036
#> GSM213075 1 0.2039 0.894 0.940 0.008 0.016 0.036
#> GSM213076 2 0.3958 0.746 0.160 0.816 0.000 0.024
#> GSM213079 3 0.3215 0.871 0.032 0.000 0.876 0.092
#> GSM213080 1 0.4732 0.638 0.768 0.200 0.012 0.020
#> GSM213081 1 0.2002 0.879 0.936 0.000 0.020 0.044
#> GSM213084 1 0.0376 0.902 0.992 0.000 0.004 0.004
#> GSM213087 2 0.0336 0.898 0.000 0.992 0.000 0.008
#> GSM213089 1 0.1211 0.899 0.960 0.000 0.000 0.040
#> GSM213090 3 0.3528 0.753 0.000 0.000 0.808 0.192
#> GSM213093 1 0.1584 0.899 0.952 0.000 0.012 0.036
#> GSM213097 1 0.0895 0.901 0.976 0.000 0.004 0.020
#> GSM213099 4 0.5088 0.218 0.424 0.000 0.004 0.572
#> GSM213101 1 0.0844 0.902 0.980 0.004 0.004 0.012
#> GSM213105 2 0.0000 0.899 0.000 1.000 0.000 0.000
#> GSM213109 1 0.0804 0.903 0.980 0.000 0.008 0.012
#> GSM213110 2 0.3853 0.747 0.160 0.820 0.000 0.020
#> GSM213113 1 0.4520 0.782 0.832 0.032 0.080 0.056
#> GSM213121 2 0.0804 0.900 0.008 0.980 0.000 0.012
#> GSM213123 1 0.0992 0.904 0.976 0.008 0.004 0.012
#> GSM213125 2 0.0000 0.899 0.000 1.000 0.000 0.000
#> GSM213073 3 0.2943 0.869 0.032 0.000 0.892 0.076
#> GSM213086 1 0.0712 0.904 0.984 0.004 0.004 0.008
#> GSM213098 1 0.3777 0.819 0.868 0.060 0.020 0.052
#> GSM213106 1 0.1118 0.900 0.964 0.000 0.000 0.036
#> GSM213124 1 0.4448 0.672 0.784 0.188 0.004 0.024
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.1026 0.875 0.968 0.004 0.000 0.004 0.024
#> GSM213082 2 0.3551 0.773 0.008 0.772 0.000 0.000 0.220
#> GSM213085 1 0.0833 0.877 0.976 0.000 0.004 0.004 0.016
#> GSM213088 1 0.1278 0.876 0.960 0.004 0.000 0.020 0.016
#> GSM213091 4 0.4913 0.333 0.488 0.000 0.012 0.492 0.008
#> GSM213092 1 0.0833 0.878 0.976 0.004 0.004 0.000 0.016
#> GSM213096 1 0.0955 0.876 0.968 0.000 0.000 0.004 0.028
#> GSM213100 1 0.0865 0.876 0.972 0.000 0.000 0.004 0.024
#> GSM213111 2 0.3877 0.783 0.024 0.764 0.000 0.000 0.212
#> GSM213117 1 0.1914 0.868 0.932 0.004 0.000 0.032 0.032
#> GSM213118 1 0.2217 0.867 0.920 0.012 0.000 0.024 0.044
#> GSM213120 2 0.6362 0.623 0.136 0.584 0.016 0.004 0.260
#> GSM213122 2 0.0000 0.810 0.000 1.000 0.000 0.000 0.000
#> GSM213074 1 0.2824 0.829 0.880 0.000 0.008 0.088 0.024
#> GSM213077 1 0.0579 0.876 0.984 0.000 0.000 0.008 0.008
#> GSM213083 1 0.0693 0.875 0.980 0.000 0.000 0.012 0.008
#> GSM213094 4 0.2243 -0.409 0.012 0.000 0.056 0.916 0.016
#> GSM213095 2 0.4440 0.731 0.000 0.660 0.012 0.004 0.324
#> GSM213102 1 0.0865 0.874 0.972 0.000 0.000 0.024 0.004
#> GSM213103 1 0.3976 0.766 0.824 0.084 0.000 0.024 0.068
#> GSM213104 1 0.6730 0.335 0.596 0.168 0.016 0.024 0.196
#> GSM213107 2 0.2997 0.771 0.000 0.840 0.000 0.012 0.148
#> GSM213108 2 0.4308 0.761 0.020 0.732 0.004 0.004 0.240
#> GSM213112 1 0.1372 0.874 0.956 0.016 0.000 0.004 0.024
#> GSM213114 1 0.4404 0.594 0.760 0.152 0.000 0.000 0.088
#> GSM213115 2 0.4512 0.699 0.136 0.772 0.000 0.012 0.080
#> GSM213116 1 0.1560 0.873 0.948 0.004 0.000 0.020 0.028
#> GSM213119 2 0.0579 0.809 0.000 0.984 0.000 0.008 0.008
#> GSM213072 1 0.1907 0.863 0.928 0.000 0.000 0.044 0.028
#> GSM213075 1 0.2784 0.852 0.896 0.004 0.012 0.048 0.040
#> GSM213076 2 0.5503 0.680 0.128 0.672 0.000 0.008 0.192
#> GSM213079 3 0.2321 0.949 0.016 0.000 0.916 0.044 0.024
#> GSM213080 1 0.5109 0.564 0.732 0.152 0.008 0.008 0.100
#> GSM213081 1 0.3689 0.761 0.820 0.000 0.016 0.024 0.140
#> GSM213084 1 0.0609 0.877 0.980 0.000 0.000 0.000 0.020
#> GSM213087 2 0.1557 0.804 0.000 0.940 0.000 0.008 0.052
#> GSM213089 1 0.1364 0.873 0.952 0.000 0.000 0.036 0.012
#> GSM213090 5 0.6384 0.000 0.000 0.000 0.388 0.168 0.444
#> GSM213093 1 0.2140 0.869 0.924 0.000 0.012 0.024 0.040
#> GSM213097 1 0.0865 0.874 0.972 0.000 0.000 0.024 0.004
#> GSM213099 4 0.4686 0.504 0.396 0.000 0.012 0.588 0.004
#> GSM213101 1 0.0932 0.875 0.972 0.004 0.000 0.004 0.020
#> GSM213105 2 0.0579 0.809 0.000 0.984 0.000 0.008 0.008
#> GSM213109 1 0.0912 0.876 0.972 0.000 0.000 0.016 0.012
#> GSM213110 2 0.4611 0.690 0.140 0.764 0.000 0.012 0.084
#> GSM213113 1 0.5846 0.544 0.688 0.008 0.092 0.036 0.176
#> GSM213121 2 0.2286 0.794 0.004 0.888 0.000 0.000 0.108
#> GSM213123 1 0.1153 0.878 0.964 0.000 0.004 0.008 0.024
#> GSM213125 2 0.0162 0.811 0.000 0.996 0.000 0.000 0.004
#> GSM213073 3 0.1469 0.950 0.016 0.000 0.948 0.036 0.000
#> GSM213086 1 0.1093 0.877 0.968 0.004 0.004 0.004 0.020
#> GSM213098 1 0.5122 0.632 0.732 0.028 0.024 0.024 0.192
#> GSM213106 1 0.1661 0.868 0.940 0.000 0.000 0.036 0.024
#> GSM213124 1 0.5126 0.616 0.744 0.128 0.004 0.024 0.100
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.1476 0.843 0.948 0.004 0.000 0.028 0.008 0.012
#> GSM213082 2 0.4051 -0.118 0.008 0.560 0.000 0.000 0.000 0.432
#> GSM213085 1 0.1350 0.846 0.952 0.000 0.000 0.020 0.008 0.020
#> GSM213088 1 0.1678 0.845 0.940 0.004 0.004 0.032 0.004 0.016
#> GSM213091 4 0.4698 0.386 0.436 0.000 0.024 0.528 0.000 0.012
#> GSM213092 1 0.1546 0.846 0.944 0.000 0.000 0.020 0.016 0.020
#> GSM213096 1 0.1350 0.844 0.952 0.000 0.000 0.020 0.008 0.020
#> GSM213100 1 0.1262 0.845 0.956 0.000 0.000 0.016 0.008 0.020
#> GSM213111 2 0.4355 -0.200 0.024 0.556 0.000 0.000 0.000 0.420
#> GSM213117 1 0.2144 0.832 0.908 0.000 0.004 0.048 0.000 0.040
#> GSM213118 1 0.2356 0.833 0.900 0.004 0.004 0.048 0.000 0.044
#> GSM213120 6 0.6540 0.237 0.100 0.372 0.012 0.016 0.028 0.472
#> GSM213122 2 0.0458 0.523 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM213074 1 0.3211 0.789 0.848 0.000 0.004 0.096 0.020 0.032
#> GSM213077 1 0.1346 0.846 0.952 0.000 0.000 0.024 0.008 0.016
#> GSM213083 1 0.1296 0.846 0.952 0.000 0.000 0.032 0.004 0.012
#> GSM213094 4 0.3536 -0.347 0.004 0.000 0.048 0.820 0.116 0.012
#> GSM213095 6 0.3426 0.322 0.000 0.220 0.012 0.004 0.000 0.764
#> GSM213102 1 0.1010 0.843 0.960 0.000 0.000 0.036 0.000 0.004
#> GSM213103 1 0.4172 0.734 0.792 0.036 0.004 0.052 0.004 0.112
#> GSM213104 1 0.7497 0.189 0.500 0.096 0.004 0.092 0.072 0.236
#> GSM213107 2 0.4151 0.133 0.000 0.576 0.000 0.008 0.004 0.412
#> GSM213108 2 0.4699 -0.153 0.016 0.528 0.000 0.008 0.008 0.440
#> GSM213112 1 0.1810 0.844 0.932 0.008 0.000 0.020 0.004 0.036
#> GSM213114 1 0.5016 0.564 0.720 0.084 0.000 0.024 0.020 0.152
#> GSM213115 2 0.4802 0.292 0.132 0.724 0.000 0.016 0.008 0.120
#> GSM213116 1 0.2010 0.837 0.920 0.000 0.004 0.036 0.004 0.036
#> GSM213119 2 0.0858 0.523 0.000 0.968 0.000 0.004 0.000 0.028
#> GSM213072 1 0.2288 0.824 0.896 0.000 0.004 0.072 0.000 0.028
#> GSM213075 1 0.2786 0.816 0.876 0.000 0.008 0.076 0.008 0.032
#> GSM213076 2 0.6435 -0.357 0.100 0.468 0.000 0.024 0.032 0.376
#> GSM213079 3 0.1152 0.948 0.004 0.000 0.952 0.000 0.044 0.000
#> GSM213080 1 0.5580 0.516 0.680 0.084 0.000 0.036 0.032 0.168
#> GSM213081 1 0.4866 0.663 0.740 0.000 0.004 0.088 0.068 0.100
#> GSM213084 1 0.1262 0.846 0.956 0.000 0.000 0.020 0.008 0.016
#> GSM213087 2 0.2101 0.489 0.000 0.892 0.000 0.004 0.004 0.100
#> GSM213089 1 0.1578 0.841 0.936 0.000 0.004 0.048 0.000 0.012
#> GSM213090 5 0.2165 0.000 0.000 0.000 0.108 0.008 0.884 0.000
#> GSM213093 1 0.2489 0.830 0.900 0.000 0.016 0.052 0.012 0.020
#> GSM213097 1 0.1010 0.843 0.960 0.000 0.000 0.036 0.000 0.004
#> GSM213099 4 0.4241 0.502 0.348 0.000 0.020 0.628 0.000 0.004
#> GSM213101 1 0.1375 0.843 0.952 0.004 0.000 0.028 0.008 0.008
#> GSM213105 2 0.0692 0.524 0.000 0.976 0.000 0.004 0.000 0.020
#> GSM213109 1 0.0891 0.845 0.968 0.000 0.000 0.024 0.000 0.008
#> GSM213110 2 0.4922 0.284 0.136 0.716 0.000 0.020 0.008 0.120
#> GSM213113 1 0.7191 0.341 0.572 0.004 0.100 0.088 0.104 0.132
#> GSM213121 2 0.3606 0.299 0.004 0.708 0.000 0.004 0.000 0.284
#> GSM213123 1 0.1590 0.848 0.944 0.000 0.008 0.012 0.008 0.028
#> GSM213125 2 0.0713 0.521 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM213073 3 0.0146 0.949 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM213086 1 0.1630 0.845 0.940 0.000 0.000 0.024 0.016 0.020
#> GSM213098 1 0.6011 0.481 0.636 0.000 0.012 0.088 0.092 0.172
#> GSM213106 1 0.2000 0.832 0.916 0.000 0.004 0.048 0.000 0.032
#> GSM213124 1 0.4931 0.604 0.732 0.080 0.000 0.040 0.012 0.136
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n development.stage(p) disease.state(p) k
#> CV:hclust 37 0.637 1.000 2
#> CV:hclust 52 0.459 0.817 3
#> CV:hclust 51 0.164 0.913 4
#> CV:hclust 50 0.308 0.847 5
#> CV:hclust 37 0.375 0.814 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "kmeans"]
# you can also extract it by
# res = res_list["CV:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.484 0.896 0.883 0.3687 0.575 0.575
#> 3 3 0.923 0.891 0.944 0.4710 0.885 0.800
#> 4 4 0.556 0.577 0.795 0.2384 0.881 0.746
#> 5 5 0.576 0.558 0.751 0.1036 0.836 0.578
#> 6 6 0.609 0.550 0.755 0.0577 0.955 0.829
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
#> GSM213078 1 0.8081 0.933 0.752 0.248
#> GSM213082 2 0.0672 0.967 0.008 0.992
#> GSM213085 1 0.8081 0.933 0.752 0.248
#> GSM213088 1 0.8081 0.933 0.752 0.248
#> GSM213091 1 0.2603 0.743 0.956 0.044
#> GSM213092 1 0.8081 0.933 0.752 0.248
#> GSM213096 1 0.8081 0.933 0.752 0.248
#> GSM213100 1 0.8081 0.933 0.752 0.248
#> GSM213111 2 0.0672 0.967 0.008 0.992
#> GSM213117 1 0.8081 0.933 0.752 0.248
#> GSM213118 1 0.8081 0.933 0.752 0.248
#> GSM213120 2 0.0672 0.967 0.008 0.992
#> GSM213122 2 0.0672 0.967 0.008 0.992
#> GSM213074 1 0.7139 0.894 0.804 0.196
#> GSM213077 1 0.8081 0.933 0.752 0.248
#> GSM213083 1 0.8081 0.933 0.752 0.248
#> GSM213094 1 0.3431 0.640 0.936 0.064
#> GSM213095 2 0.0672 0.950 0.008 0.992
#> GSM213102 1 0.8081 0.933 0.752 0.248
#> GSM213103 2 0.9129 0.236 0.328 0.672
#> GSM213104 1 0.8081 0.933 0.752 0.248
#> GSM213107 2 0.0672 0.967 0.008 0.992
#> GSM213108 2 0.0938 0.963 0.012 0.988
#> GSM213112 1 0.8081 0.933 0.752 0.248
#> GSM213114 1 0.8081 0.933 0.752 0.248
#> GSM213115 2 0.0672 0.967 0.008 0.992
#> GSM213116 1 0.8081 0.933 0.752 0.248
#> GSM213119 2 0.0672 0.967 0.008 0.992
#> GSM213072 1 0.7056 0.890 0.808 0.192
#> GSM213075 1 0.7950 0.930 0.760 0.240
#> GSM213076 2 0.0672 0.967 0.008 0.992
#> GSM213079 1 0.3431 0.640 0.936 0.064
#> GSM213080 1 0.8081 0.933 0.752 0.248
#> GSM213081 1 0.8016 0.932 0.756 0.244
#> GSM213084 1 0.8081 0.933 0.752 0.248
#> GSM213087 2 0.0672 0.967 0.008 0.992
#> GSM213089 1 0.7950 0.930 0.760 0.240
#> GSM213090 1 0.3431 0.640 0.936 0.064
#> GSM213093 1 0.7950 0.930 0.760 0.240
#> GSM213097 1 0.8081 0.933 0.752 0.248
#> GSM213099 1 0.2778 0.747 0.952 0.048
#> GSM213101 1 0.8081 0.933 0.752 0.248
#> GSM213105 2 0.0672 0.967 0.008 0.992
#> GSM213109 1 0.8016 0.932 0.756 0.244
#> GSM213110 2 0.1633 0.949 0.024 0.976
#> GSM213113 1 0.7883 0.927 0.764 0.236
#> GSM213121 2 0.0672 0.967 0.008 0.992
#> GSM213123 1 0.8081 0.933 0.752 0.248
#> GSM213125 2 0.0672 0.967 0.008 0.992
#> GSM213073 1 0.3431 0.640 0.936 0.064
#> GSM213086 1 0.8081 0.933 0.752 0.248
#> GSM213098 1 0.8081 0.933 0.752 0.248
#> GSM213106 1 0.8081 0.933 0.752 0.248
#> GSM213124 1 0.9427 0.781 0.640 0.360
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.0892 0.9481 0.980 0.000 0.020
#> GSM213082 2 0.0747 0.9375 0.000 0.984 0.016
#> GSM213085 1 0.0592 0.9513 0.988 0.000 0.012
#> GSM213088 1 0.1031 0.9489 0.976 0.000 0.024
#> GSM213091 3 0.6286 0.1835 0.464 0.000 0.536
#> GSM213092 1 0.0000 0.9517 1.000 0.000 0.000
#> GSM213096 1 0.0892 0.9481 0.980 0.000 0.020
#> GSM213100 1 0.0237 0.9517 0.996 0.000 0.004
#> GSM213111 2 0.0424 0.9386 0.000 0.992 0.008
#> GSM213117 1 0.1964 0.9304 0.944 0.000 0.056
#> GSM213118 1 0.0424 0.9523 0.992 0.000 0.008
#> GSM213120 2 0.1753 0.9224 0.000 0.952 0.048
#> GSM213122 2 0.0747 0.9375 0.000 0.984 0.016
#> GSM213074 1 0.2537 0.9101 0.920 0.000 0.080
#> GSM213077 1 0.0592 0.9507 0.988 0.000 0.012
#> GSM213083 1 0.0237 0.9515 0.996 0.000 0.004
#> GSM213094 3 0.2448 0.8577 0.076 0.000 0.924
#> GSM213095 2 0.1031 0.9356 0.000 0.976 0.024
#> GSM213102 1 0.1031 0.9474 0.976 0.000 0.024
#> GSM213103 2 0.7979 0.0842 0.440 0.500 0.060
#> GSM213104 1 0.1647 0.9365 0.960 0.004 0.036
#> GSM213107 2 0.1411 0.9335 0.000 0.964 0.036
#> GSM213108 2 0.0892 0.9372 0.000 0.980 0.020
#> GSM213112 1 0.0424 0.9515 0.992 0.000 0.008
#> GSM213114 1 0.1163 0.9447 0.972 0.000 0.028
#> GSM213115 2 0.0592 0.9386 0.000 0.988 0.012
#> GSM213116 1 0.1163 0.9469 0.972 0.000 0.028
#> GSM213119 2 0.1031 0.9366 0.000 0.976 0.024
#> GSM213072 1 0.2066 0.9276 0.940 0.000 0.060
#> GSM213075 1 0.1964 0.9409 0.944 0.000 0.056
#> GSM213076 2 0.1163 0.9360 0.000 0.972 0.028
#> GSM213079 3 0.2448 0.8577 0.076 0.000 0.924
#> GSM213080 1 0.1525 0.9396 0.964 0.004 0.032
#> GSM213081 1 0.1163 0.9491 0.972 0.000 0.028
#> GSM213084 1 0.0892 0.9481 0.980 0.000 0.020
#> GSM213087 2 0.0892 0.9378 0.000 0.980 0.020
#> GSM213089 1 0.1964 0.9304 0.944 0.000 0.056
#> GSM213090 3 0.2356 0.8547 0.072 0.000 0.928
#> GSM213093 1 0.1289 0.9450 0.968 0.000 0.032
#> GSM213097 1 0.0892 0.9487 0.980 0.000 0.020
#> GSM213099 1 0.5678 0.4700 0.684 0.000 0.316
#> GSM213101 1 0.0892 0.9481 0.980 0.000 0.020
#> GSM213105 2 0.1031 0.9366 0.000 0.976 0.024
#> GSM213109 1 0.0237 0.9515 0.996 0.000 0.004
#> GSM213110 2 0.1031 0.9365 0.000 0.976 0.024
#> GSM213113 1 0.2711 0.9140 0.912 0.000 0.088
#> GSM213121 2 0.1289 0.9339 0.000 0.968 0.032
#> GSM213123 1 0.1163 0.9502 0.972 0.000 0.028
#> GSM213125 2 0.0592 0.9379 0.000 0.988 0.012
#> GSM213073 3 0.2261 0.8526 0.068 0.000 0.932
#> GSM213086 1 0.0000 0.9517 1.000 0.000 0.000
#> GSM213098 1 0.1529 0.9455 0.960 0.000 0.040
#> GSM213106 1 0.1529 0.9410 0.960 0.000 0.040
#> GSM213124 1 0.5852 0.6789 0.776 0.180 0.044
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.1940 0.6370 0.924 0.000 0.000 0.076
#> GSM213082 2 0.2654 0.8680 0.000 0.888 0.004 0.108
#> GSM213085 1 0.2053 0.6491 0.924 0.000 0.004 0.072
#> GSM213088 1 0.3172 0.6192 0.840 0.000 0.000 0.160
#> GSM213091 4 0.7130 0.2649 0.132 0.000 0.396 0.472
#> GSM213092 1 0.1211 0.6590 0.960 0.000 0.000 0.040
#> GSM213096 1 0.2469 0.6398 0.892 0.000 0.000 0.108
#> GSM213100 1 0.1302 0.6594 0.956 0.000 0.000 0.044
#> GSM213111 2 0.3726 0.8550 0.000 0.788 0.000 0.212
#> GSM213117 1 0.5281 -0.0666 0.528 0.000 0.008 0.464
#> GSM213118 1 0.4585 0.2998 0.668 0.000 0.000 0.332
#> GSM213120 2 0.4950 0.7467 0.000 0.620 0.004 0.376
#> GSM213122 2 0.0188 0.8803 0.000 0.996 0.000 0.004
#> GSM213074 1 0.5695 -0.1659 0.500 0.000 0.024 0.476
#> GSM213077 1 0.0779 0.6547 0.980 0.000 0.004 0.016
#> GSM213083 1 0.0188 0.6575 0.996 0.000 0.000 0.004
#> GSM213094 3 0.1722 0.9586 0.008 0.000 0.944 0.048
#> GSM213095 2 0.4584 0.8138 0.000 0.696 0.004 0.300
#> GSM213102 1 0.3768 0.5499 0.808 0.000 0.008 0.184
#> GSM213103 4 0.6449 0.4208 0.140 0.220 0.000 0.640
#> GSM213104 1 0.4406 0.3038 0.700 0.000 0.000 0.300
#> GSM213107 2 0.3870 0.8358 0.000 0.788 0.004 0.208
#> GSM213108 2 0.3157 0.8630 0.000 0.852 0.004 0.144
#> GSM213112 1 0.2401 0.6381 0.904 0.000 0.004 0.092
#> GSM213114 1 0.2281 0.6262 0.904 0.000 0.000 0.096
#> GSM213115 2 0.1389 0.8782 0.000 0.952 0.000 0.048
#> GSM213116 1 0.5132 -0.0261 0.548 0.000 0.004 0.448
#> GSM213119 2 0.0524 0.8791 0.000 0.988 0.004 0.008
#> GSM213072 1 0.5295 -0.1514 0.504 0.000 0.008 0.488
#> GSM213075 4 0.4967 0.0954 0.452 0.000 0.000 0.548
#> GSM213076 2 0.4331 0.8074 0.000 0.712 0.000 0.288
#> GSM213079 3 0.0376 0.9802 0.004 0.000 0.992 0.004
#> GSM213080 1 0.2530 0.6156 0.888 0.000 0.000 0.112
#> GSM213081 1 0.3444 0.5809 0.816 0.000 0.000 0.184
#> GSM213084 1 0.1792 0.6410 0.932 0.000 0.000 0.068
#> GSM213087 2 0.0779 0.8789 0.000 0.980 0.004 0.016
#> GSM213089 1 0.5277 -0.0767 0.532 0.000 0.008 0.460
#> GSM213090 3 0.0657 0.9763 0.004 0.000 0.984 0.012
#> GSM213093 1 0.4991 0.1185 0.608 0.000 0.004 0.388
#> GSM213097 1 0.3142 0.5957 0.860 0.000 0.008 0.132
#> GSM213099 4 0.7290 0.4229 0.328 0.000 0.168 0.504
#> GSM213101 1 0.1867 0.6396 0.928 0.000 0.000 0.072
#> GSM213105 2 0.0524 0.8791 0.000 0.988 0.004 0.008
#> GSM213109 1 0.1305 0.6579 0.960 0.000 0.004 0.036
#> GSM213110 2 0.1978 0.8742 0.004 0.928 0.000 0.068
#> GSM213113 4 0.5466 0.4615 0.292 0.000 0.040 0.668
#> GSM213121 2 0.3539 0.8497 0.000 0.820 0.004 0.176
#> GSM213123 1 0.4222 0.4868 0.728 0.000 0.000 0.272
#> GSM213125 2 0.0469 0.8809 0.000 0.988 0.000 0.012
#> GSM213073 3 0.0336 0.9781 0.000 0.000 0.992 0.008
#> GSM213086 1 0.1389 0.6571 0.952 0.000 0.000 0.048
#> GSM213098 4 0.4761 0.3196 0.372 0.000 0.000 0.628
#> GSM213106 1 0.5268 -0.0390 0.540 0.000 0.008 0.452
#> GSM213124 4 0.6712 0.4147 0.344 0.104 0.000 0.552
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.0798 0.7587 0.976 0.000 0.000 0.016 0.008
#> GSM213082 2 0.3618 0.5948 0.000 0.788 0.004 0.012 0.196
#> GSM213085 1 0.2795 0.7465 0.872 0.000 0.000 0.100 0.028
#> GSM213088 1 0.4193 0.5057 0.720 0.000 0.000 0.256 0.024
#> GSM213091 4 0.5663 0.4620 0.052 0.000 0.208 0.680 0.060
#> GSM213092 1 0.2423 0.7543 0.896 0.000 0.000 0.080 0.024
#> GSM213096 1 0.1668 0.7572 0.940 0.000 0.000 0.032 0.028
#> GSM213100 1 0.1774 0.7646 0.932 0.000 0.000 0.052 0.016
#> GSM213111 2 0.4723 0.0955 0.000 0.536 0.000 0.016 0.448
#> GSM213117 4 0.3706 0.6860 0.236 0.000 0.004 0.756 0.004
#> GSM213118 1 0.5547 0.0491 0.532 0.000 0.004 0.404 0.060
#> GSM213120 5 0.4848 0.2088 0.000 0.304 0.004 0.036 0.656
#> GSM213122 2 0.0510 0.7337 0.000 0.984 0.000 0.000 0.016
#> GSM213074 4 0.4532 0.7020 0.216 0.000 0.012 0.736 0.036
#> GSM213077 1 0.2339 0.7465 0.892 0.000 0.004 0.100 0.004
#> GSM213083 1 0.1697 0.7616 0.932 0.000 0.000 0.060 0.008
#> GSM213094 3 0.3532 0.8840 0.000 0.000 0.832 0.092 0.076
#> GSM213095 5 0.4696 0.0849 0.000 0.400 0.004 0.012 0.584
#> GSM213102 1 0.4908 0.2120 0.560 0.000 0.004 0.416 0.020
#> GSM213103 4 0.8260 -0.1321 0.120 0.196 0.004 0.348 0.332
#> GSM213104 1 0.4946 0.5064 0.700 0.004 0.004 0.056 0.236
#> GSM213107 2 0.4789 0.1683 0.000 0.584 0.000 0.024 0.392
#> GSM213108 2 0.4556 0.4735 0.000 0.680 0.004 0.024 0.292
#> GSM213112 1 0.3051 0.7305 0.852 0.000 0.000 0.120 0.028
#> GSM213114 1 0.1893 0.7383 0.928 0.000 0.000 0.024 0.048
#> GSM213115 2 0.2304 0.7138 0.000 0.908 0.004 0.020 0.068
#> GSM213116 4 0.3870 0.6793 0.260 0.000 0.004 0.732 0.004
#> GSM213119 2 0.0000 0.7331 0.000 1.000 0.000 0.000 0.000
#> GSM213072 4 0.4423 0.6939 0.232 0.000 0.004 0.728 0.036
#> GSM213075 4 0.5409 0.6494 0.252 0.000 0.008 0.656 0.084
#> GSM213076 5 0.4565 0.1090 0.000 0.408 0.000 0.012 0.580
#> GSM213079 3 0.0451 0.9498 0.000 0.000 0.988 0.008 0.004
#> GSM213080 1 0.2504 0.7245 0.900 0.004 0.000 0.032 0.064
#> GSM213081 1 0.6217 0.3772 0.584 0.000 0.008 0.216 0.192
#> GSM213084 1 0.0693 0.7597 0.980 0.000 0.000 0.012 0.008
#> GSM213087 2 0.1124 0.7264 0.000 0.960 0.000 0.004 0.036
#> GSM213089 4 0.4095 0.6984 0.220 0.000 0.004 0.752 0.024
#> GSM213090 3 0.1399 0.9458 0.000 0.000 0.952 0.020 0.028
#> GSM213093 4 0.5539 0.5786 0.324 0.000 0.004 0.596 0.076
#> GSM213097 1 0.4832 0.3594 0.616 0.000 0.004 0.356 0.024
#> GSM213099 4 0.4814 0.6707 0.128 0.000 0.032 0.764 0.076
#> GSM213101 1 0.0898 0.7594 0.972 0.000 0.000 0.020 0.008
#> GSM213105 2 0.0162 0.7333 0.000 0.996 0.000 0.000 0.004
#> GSM213109 1 0.2519 0.7503 0.884 0.000 0.000 0.100 0.016
#> GSM213110 2 0.3269 0.6826 0.024 0.868 0.004 0.024 0.080
#> GSM213113 4 0.6898 0.2323 0.156 0.000 0.024 0.420 0.400
#> GSM213121 2 0.4639 0.2461 0.000 0.612 0.000 0.020 0.368
#> GSM213123 1 0.6068 0.0704 0.516 0.000 0.004 0.368 0.112
#> GSM213125 2 0.1121 0.7291 0.000 0.956 0.000 0.000 0.044
#> GSM213073 3 0.0324 0.9484 0.000 0.000 0.992 0.004 0.004
#> GSM213086 1 0.2653 0.7491 0.880 0.000 0.000 0.096 0.024
#> GSM213098 5 0.6871 -0.3971 0.220 0.000 0.008 0.368 0.404
#> GSM213106 4 0.4142 0.6680 0.252 0.000 0.004 0.728 0.016
#> GSM213124 4 0.6704 0.6186 0.156 0.096 0.004 0.628 0.116
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.1718 0.7115 0.932 0.000 0.000 0.016 0.008 0.044
#> GSM213082 2 0.3622 0.5074 0.000 0.760 0.000 0.004 0.212 0.024
#> GSM213085 1 0.3119 0.7068 0.856 0.000 0.000 0.076 0.032 0.036
#> GSM213088 1 0.4858 0.4164 0.660 0.000 0.000 0.252 0.012 0.076
#> GSM213091 4 0.5554 0.4889 0.004 0.000 0.096 0.676 0.084 0.140
#> GSM213092 1 0.2624 0.7217 0.884 0.000 0.000 0.068 0.020 0.028
#> GSM213096 1 0.2071 0.7157 0.916 0.000 0.000 0.028 0.012 0.044
#> GSM213100 1 0.2375 0.7309 0.896 0.000 0.000 0.068 0.016 0.020
#> GSM213111 5 0.4778 0.4091 0.000 0.464 0.000 0.004 0.492 0.040
#> GSM213117 4 0.2478 0.6484 0.076 0.000 0.000 0.888 0.012 0.024
#> GSM213118 1 0.6102 0.0240 0.464 0.000 0.000 0.384 0.036 0.116
#> GSM213120 5 0.5377 0.5942 0.000 0.216 0.000 0.004 0.604 0.176
#> GSM213122 2 0.0508 0.7238 0.000 0.984 0.000 0.000 0.012 0.004
#> GSM213074 4 0.4262 0.6378 0.072 0.000 0.008 0.792 0.056 0.072
#> GSM213077 1 0.2196 0.7084 0.884 0.000 0.000 0.108 0.004 0.004
#> GSM213083 1 0.1718 0.7289 0.932 0.000 0.000 0.044 0.016 0.008
#> GSM213094 3 0.5654 0.7200 0.000 0.000 0.628 0.040 0.140 0.192
#> GSM213095 5 0.3738 0.6843 0.000 0.280 0.000 0.000 0.704 0.016
#> GSM213102 1 0.4847 0.2495 0.528 0.000 0.000 0.424 0.008 0.040
#> GSM213103 4 0.7867 -0.0443 0.052 0.080 0.000 0.348 0.200 0.320
#> GSM213104 1 0.4328 0.4051 0.708 0.000 0.000 0.000 0.080 0.212
#> GSM213107 5 0.5063 0.4961 0.000 0.432 0.000 0.004 0.500 0.064
#> GSM213108 2 0.4868 0.0953 0.000 0.588 0.000 0.008 0.352 0.052
#> GSM213112 1 0.3714 0.6765 0.816 0.000 0.000 0.096 0.040 0.048
#> GSM213114 1 0.1967 0.6845 0.904 0.000 0.000 0.000 0.012 0.084
#> GSM213115 2 0.2719 0.6832 0.000 0.876 0.000 0.012 0.072 0.040
#> GSM213116 4 0.2933 0.6372 0.092 0.000 0.000 0.860 0.016 0.032
#> GSM213119 2 0.0291 0.7269 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM213072 4 0.4081 0.6300 0.088 0.000 0.000 0.788 0.032 0.092
#> GSM213075 4 0.5006 0.5244 0.100 0.000 0.000 0.668 0.016 0.216
#> GSM213076 5 0.4236 0.6895 0.000 0.308 0.000 0.000 0.656 0.036
#> GSM213079 3 0.0000 0.8826 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM213080 1 0.2214 0.6773 0.892 0.000 0.000 0.004 0.012 0.092
#> GSM213081 6 0.5862 0.2710 0.404 0.000 0.000 0.136 0.012 0.448
#> GSM213084 1 0.1320 0.7189 0.948 0.000 0.000 0.016 0.000 0.036
#> GSM213087 2 0.1592 0.7057 0.000 0.940 0.000 0.008 0.032 0.020
#> GSM213089 4 0.2444 0.6387 0.068 0.000 0.000 0.892 0.012 0.028
#> GSM213090 3 0.2445 0.8694 0.000 0.000 0.892 0.008 0.060 0.040
#> GSM213093 4 0.5708 0.3202 0.232 0.000 0.000 0.588 0.020 0.160
#> GSM213097 1 0.4824 0.3430 0.588 0.000 0.000 0.356 0.008 0.048
#> GSM213099 4 0.5053 0.5212 0.028 0.000 0.012 0.708 0.084 0.168
#> GSM213101 1 0.1409 0.7155 0.948 0.000 0.000 0.012 0.008 0.032
#> GSM213105 2 0.0291 0.7269 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM213109 1 0.2736 0.7214 0.876 0.000 0.000 0.076 0.020 0.028
#> GSM213110 2 0.3682 0.6413 0.016 0.824 0.000 0.012 0.092 0.056
#> GSM213113 6 0.6209 0.5157 0.088 0.000 0.012 0.224 0.080 0.596
#> GSM213121 2 0.5117 -0.5662 0.000 0.480 0.000 0.004 0.448 0.068
#> GSM213123 1 0.6338 -0.3592 0.344 0.000 0.000 0.336 0.008 0.312
#> GSM213125 2 0.1007 0.7220 0.000 0.956 0.000 0.000 0.044 0.000
#> GSM213073 3 0.0291 0.8810 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM213086 1 0.2684 0.7203 0.880 0.000 0.000 0.072 0.024 0.024
#> GSM213098 6 0.6064 0.5934 0.132 0.000 0.000 0.192 0.076 0.600
#> GSM213106 4 0.2964 0.6209 0.108 0.000 0.000 0.848 0.004 0.040
#> GSM213124 4 0.6651 0.4687 0.056 0.072 0.000 0.604 0.116 0.152
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 development.stage(p) disease.state(p) k
#> CV:kmeans 53 0.601 1.000 2
#> CV:kmeans 51 0.454 0.828 3
#> CV:kmeans 37 0.397 0.805 4
#> CV:kmeans 38 0.183 0.843 5
#> CV:kmeans 39 0.422 0.967 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "skmeans"]
# you can also extract it by
# res = res_list["CV:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.652 0.791 0.913 0.4907 0.516 0.516
#> 3 3 0.417 0.627 0.807 0.3705 0.718 0.498
#> 4 4 0.408 0.427 0.678 0.1181 0.928 0.784
#> 5 5 0.466 0.360 0.603 0.0601 0.943 0.801
#> 6 6 0.503 0.290 0.556 0.0408 0.948 0.794
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM213078 1 0.0000 0.8982 1.000 0.000
#> GSM213082 2 0.0000 0.8993 0.000 1.000
#> GSM213085 1 0.2236 0.8951 0.964 0.036
#> GSM213088 1 0.9323 0.4385 0.652 0.348
#> GSM213091 1 0.4161 0.8649 0.916 0.084
#> GSM213092 1 0.0000 0.8982 1.000 0.000
#> GSM213096 1 0.1184 0.8985 0.984 0.016
#> GSM213100 1 0.0000 0.8982 1.000 0.000
#> GSM213111 2 0.0000 0.8993 0.000 1.000
#> GSM213117 1 0.2948 0.8889 0.948 0.052
#> GSM213118 1 0.5059 0.8406 0.888 0.112
#> GSM213120 2 0.0000 0.8993 0.000 1.000
#> GSM213122 2 0.0000 0.8993 0.000 1.000
#> GSM213074 1 0.1633 0.8979 0.976 0.024
#> GSM213077 1 0.0000 0.8982 1.000 0.000
#> GSM213083 1 0.0000 0.8982 1.000 0.000
#> GSM213094 1 0.8608 0.6250 0.716 0.284
#> GSM213095 2 0.0000 0.8993 0.000 1.000
#> GSM213102 1 0.0000 0.8982 1.000 0.000
#> GSM213103 2 0.2043 0.8805 0.032 0.968
#> GSM213104 2 0.7815 0.6664 0.232 0.768
#> GSM213107 2 0.0000 0.8993 0.000 1.000
#> GSM213108 2 0.0000 0.8993 0.000 1.000
#> GSM213112 1 0.3733 0.8764 0.928 0.072
#> GSM213114 1 0.2603 0.8887 0.956 0.044
#> GSM213115 2 0.0000 0.8993 0.000 1.000
#> GSM213116 1 0.0376 0.8987 0.996 0.004
#> GSM213119 2 0.0000 0.8993 0.000 1.000
#> GSM213072 1 0.2778 0.8894 0.952 0.048
#> GSM213075 1 0.9427 0.4526 0.640 0.360
#> GSM213076 2 0.0000 0.8993 0.000 1.000
#> GSM213079 1 0.9491 0.4502 0.632 0.368
#> GSM213080 2 0.9996 0.0357 0.488 0.512
#> GSM213081 1 0.2603 0.8916 0.956 0.044
#> GSM213084 1 0.0000 0.8982 1.000 0.000
#> GSM213087 2 0.0000 0.8993 0.000 1.000
#> GSM213089 1 0.0938 0.8993 0.988 0.012
#> GSM213090 2 0.9732 0.2543 0.404 0.596
#> GSM213093 1 0.1184 0.8992 0.984 0.016
#> GSM213097 1 0.0000 0.8982 1.000 0.000
#> GSM213099 1 0.4431 0.8608 0.908 0.092
#> GSM213101 1 0.0376 0.8989 0.996 0.004
#> GSM213105 2 0.0000 0.8993 0.000 1.000
#> GSM213109 1 0.0000 0.8982 1.000 0.000
#> GSM213110 2 0.2236 0.8774 0.036 0.964
#> GSM213113 1 0.9996 0.0708 0.512 0.488
#> GSM213121 2 0.0000 0.8993 0.000 1.000
#> GSM213123 1 0.3584 0.8783 0.932 0.068
#> GSM213125 2 0.0000 0.8993 0.000 1.000
#> GSM213073 2 0.9993 -0.0347 0.484 0.516
#> GSM213086 1 0.0000 0.8982 1.000 0.000
#> GSM213098 1 0.9170 0.5336 0.668 0.332
#> GSM213106 1 0.1184 0.8994 0.984 0.016
#> GSM213124 2 0.5059 0.8127 0.112 0.888
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.1289 0.6828 0.968 0.000 0.032
#> GSM213082 2 0.0237 0.9265 0.000 0.996 0.004
#> GSM213085 1 0.7279 0.3162 0.588 0.036 0.376
#> GSM213088 1 0.8689 0.3628 0.588 0.248 0.164
#> GSM213091 3 0.2496 0.6699 0.068 0.004 0.928
#> GSM213092 1 0.4002 0.6735 0.840 0.000 0.160
#> GSM213096 1 0.2066 0.6913 0.940 0.000 0.060
#> GSM213100 1 0.4121 0.6616 0.832 0.000 0.168
#> GSM213111 2 0.1031 0.9207 0.000 0.976 0.024
#> GSM213117 3 0.7442 0.4149 0.348 0.048 0.604
#> GSM213118 1 0.8425 0.2480 0.552 0.100 0.348
#> GSM213120 2 0.3445 0.8723 0.016 0.896 0.088
#> GSM213122 2 0.0000 0.9275 0.000 1.000 0.000
#> GSM213074 3 0.5109 0.6195 0.212 0.008 0.780
#> GSM213077 1 0.3340 0.6924 0.880 0.000 0.120
#> GSM213083 1 0.3116 0.6917 0.892 0.000 0.108
#> GSM213094 3 0.1015 0.6619 0.012 0.008 0.980
#> GSM213095 2 0.2796 0.8851 0.000 0.908 0.092
#> GSM213102 1 0.6019 0.5348 0.700 0.012 0.288
#> GSM213103 2 0.6663 0.6956 0.096 0.748 0.156
#> GSM213104 1 0.8900 0.2099 0.512 0.356 0.132
#> GSM213107 2 0.0000 0.9275 0.000 1.000 0.000
#> GSM213108 2 0.3425 0.8616 0.004 0.884 0.112
#> GSM213112 1 0.7339 0.2731 0.572 0.036 0.392
#> GSM213114 1 0.1620 0.6823 0.964 0.012 0.024
#> GSM213115 2 0.0000 0.9275 0.000 1.000 0.000
#> GSM213116 3 0.6701 0.3100 0.412 0.012 0.576
#> GSM213119 2 0.0000 0.9275 0.000 1.000 0.000
#> GSM213072 3 0.4521 0.6450 0.180 0.004 0.816
#> GSM213075 3 0.9040 0.3628 0.320 0.156 0.524
#> GSM213076 2 0.2384 0.9030 0.008 0.936 0.056
#> GSM213079 3 0.1620 0.6627 0.024 0.012 0.964
#> GSM213080 1 0.5455 0.5448 0.776 0.204 0.020
#> GSM213081 1 0.7490 0.2693 0.576 0.044 0.380
#> GSM213084 1 0.3116 0.6927 0.892 0.000 0.108
#> GSM213087 2 0.0000 0.9275 0.000 1.000 0.000
#> GSM213089 3 0.5737 0.5647 0.256 0.012 0.732
#> GSM213090 3 0.3434 0.6560 0.032 0.064 0.904
#> GSM213093 3 0.6675 0.2771 0.404 0.012 0.584
#> GSM213097 1 0.5058 0.5986 0.756 0.000 0.244
#> GSM213099 3 0.4413 0.6673 0.124 0.024 0.852
#> GSM213101 1 0.1643 0.6882 0.956 0.000 0.044
#> GSM213105 2 0.0000 0.9275 0.000 1.000 0.000
#> GSM213109 1 0.5016 0.6116 0.760 0.000 0.240
#> GSM213110 2 0.2165 0.8902 0.064 0.936 0.000
#> GSM213113 3 0.8835 0.4288 0.244 0.180 0.576
#> GSM213121 2 0.0000 0.9275 0.000 1.000 0.000
#> GSM213123 1 0.7245 0.3421 0.596 0.036 0.368
#> GSM213125 2 0.0000 0.9275 0.000 1.000 0.000
#> GSM213073 3 0.3550 0.6512 0.024 0.080 0.896
#> GSM213086 1 0.3412 0.6901 0.876 0.000 0.124
#> GSM213098 3 0.9457 0.2368 0.352 0.188 0.460
#> GSM213106 3 0.7188 0.0871 0.484 0.024 0.492
#> GSM213124 2 0.8375 0.4209 0.132 0.608 0.260
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.3047 0.47387 0.872 0.000 0.012 0.116
#> GSM213082 2 0.1510 0.86157 0.000 0.956 0.028 0.016
#> GSM213085 1 0.8208 -0.00693 0.392 0.012 0.264 0.332
#> GSM213088 1 0.8885 0.01814 0.404 0.156 0.084 0.356
#> GSM213091 3 0.4655 0.45660 0.032 0.000 0.760 0.208
#> GSM213092 1 0.6587 0.32198 0.596 0.000 0.112 0.292
#> GSM213096 1 0.4900 0.44291 0.732 0.000 0.032 0.236
#> GSM213100 1 0.5722 0.42293 0.660 0.004 0.044 0.292
#> GSM213111 2 0.2772 0.85050 0.004 0.908 0.048 0.040
#> GSM213117 4 0.8133 0.31896 0.172 0.032 0.312 0.484
#> GSM213118 4 0.7978 -0.07956 0.404 0.040 0.116 0.440
#> GSM213120 2 0.5659 0.74996 0.028 0.760 0.108 0.104
#> GSM213122 2 0.0895 0.86502 0.000 0.976 0.004 0.020
#> GSM213074 3 0.7065 0.11039 0.128 0.004 0.548 0.320
#> GSM213077 1 0.5448 0.42195 0.724 0.000 0.080 0.196
#> GSM213083 1 0.5662 0.42403 0.692 0.000 0.072 0.236
#> GSM213094 3 0.2737 0.52266 0.008 0.000 0.888 0.104
#> GSM213095 2 0.4713 0.76862 0.004 0.788 0.156 0.052
#> GSM213102 4 0.7629 0.08877 0.416 0.008 0.156 0.420
#> GSM213103 2 0.8356 0.37873 0.132 0.532 0.084 0.252
#> GSM213104 1 0.8712 0.21837 0.528 0.148 0.144 0.180
#> GSM213107 2 0.1492 0.86157 0.004 0.956 0.004 0.036
#> GSM213108 2 0.4401 0.78809 0.000 0.812 0.112 0.076
#> GSM213112 1 0.8210 0.05404 0.420 0.016 0.240 0.324
#> GSM213114 1 0.2676 0.47795 0.896 0.000 0.012 0.092
#> GSM213115 2 0.0592 0.86411 0.000 0.984 0.000 0.016
#> GSM213116 4 0.8007 0.34922 0.216 0.016 0.292 0.476
#> GSM213119 2 0.0376 0.86431 0.000 0.992 0.004 0.004
#> GSM213072 3 0.6988 0.12268 0.120 0.000 0.500 0.380
#> GSM213075 3 0.8897 0.02511 0.192 0.076 0.440 0.292
#> GSM213076 2 0.4713 0.78865 0.012 0.808 0.112 0.068
#> GSM213079 3 0.1771 0.53342 0.012 0.004 0.948 0.036
#> GSM213080 1 0.6275 0.37533 0.700 0.136 0.016 0.148
#> GSM213081 1 0.8121 0.16610 0.520 0.036 0.200 0.244
#> GSM213084 1 0.5172 0.46025 0.744 0.000 0.068 0.188
#> GSM213087 2 0.0336 0.86368 0.000 0.992 0.000 0.008
#> GSM213089 4 0.7830 0.17640 0.156 0.016 0.396 0.432
#> GSM213090 3 0.3538 0.52090 0.004 0.044 0.868 0.084
#> GSM213093 4 0.8458 0.23245 0.252 0.024 0.360 0.364
#> GSM213097 1 0.6817 -0.03723 0.492 0.000 0.100 0.408
#> GSM213099 3 0.5883 0.36017 0.064 0.000 0.648 0.288
#> GSM213101 1 0.3790 0.47089 0.820 0.000 0.016 0.164
#> GSM213105 2 0.0188 0.86392 0.000 0.996 0.000 0.004
#> GSM213109 1 0.6839 0.22771 0.552 0.000 0.120 0.328
#> GSM213110 2 0.4524 0.77719 0.104 0.820 0.012 0.064
#> GSM213113 3 0.8142 0.26369 0.120 0.076 0.548 0.256
#> GSM213121 2 0.1004 0.86433 0.000 0.972 0.004 0.024
#> GSM213123 1 0.8400 -0.04351 0.428 0.036 0.188 0.348
#> GSM213125 2 0.0469 0.86367 0.000 0.988 0.000 0.012
#> GSM213073 3 0.3363 0.52727 0.040 0.020 0.888 0.052
#> GSM213086 1 0.5907 0.37330 0.668 0.000 0.080 0.252
#> GSM213098 3 0.9505 -0.02325 0.240 0.116 0.360 0.284
#> GSM213106 4 0.8035 0.39474 0.244 0.012 0.288 0.456
#> GSM213124 2 0.9086 0.02111 0.092 0.424 0.192 0.292
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.3427 0.4069 0.844 0.000 0.012 0.112 0.032
#> GSM213082 2 0.2522 0.8012 0.000 0.904 0.012 0.028 0.056
#> GSM213085 1 0.7952 -0.1212 0.368 0.000 0.156 0.120 0.356
#> GSM213088 1 0.7648 0.0817 0.412 0.128 0.016 0.384 0.060
#> GSM213091 3 0.5274 0.3903 0.008 0.000 0.664 0.256 0.072
#> GSM213092 1 0.6803 0.1649 0.512 0.000 0.048 0.108 0.332
#> GSM213096 1 0.6001 0.2472 0.616 0.000 0.020 0.108 0.256
#> GSM213100 1 0.7042 0.2201 0.544 0.000 0.080 0.116 0.260
#> GSM213111 2 0.4278 0.7712 0.004 0.816 0.064 0.040 0.076
#> GSM213117 4 0.7523 0.3250 0.084 0.008 0.192 0.532 0.184
#> GSM213118 5 0.7760 0.1152 0.280 0.020 0.060 0.160 0.480
#> GSM213120 2 0.6261 0.6623 0.016 0.672 0.048 0.104 0.160
#> GSM213122 2 0.0693 0.8069 0.000 0.980 0.000 0.008 0.012
#> GSM213074 3 0.7551 0.1770 0.052 0.008 0.484 0.204 0.252
#> GSM213077 1 0.5829 0.3607 0.692 0.000 0.056 0.124 0.128
#> GSM213083 1 0.6229 0.3481 0.656 0.000 0.064 0.148 0.132
#> GSM213094 3 0.3715 0.4893 0.000 0.004 0.824 0.108 0.064
#> GSM213095 2 0.5625 0.6485 0.000 0.676 0.208 0.028 0.088
#> GSM213102 1 0.7745 -0.0271 0.384 0.004 0.076 0.376 0.160
#> GSM213103 2 0.8720 -0.0305 0.096 0.372 0.084 0.104 0.344
#> GSM213104 1 0.9081 -0.1282 0.396 0.124 0.108 0.112 0.260
#> GSM213107 2 0.3380 0.7964 0.012 0.864 0.020 0.020 0.084
#> GSM213108 2 0.5472 0.7195 0.012 0.744 0.096 0.060 0.088
#> GSM213112 5 0.8555 0.0465 0.312 0.012 0.208 0.132 0.336
#> GSM213114 1 0.4270 0.3840 0.788 0.000 0.008 0.124 0.080
#> GSM213115 2 0.1757 0.8049 0.004 0.936 0.000 0.012 0.048
#> GSM213116 4 0.8406 0.2294 0.164 0.004 0.252 0.384 0.196
#> GSM213119 2 0.1041 0.8084 0.000 0.964 0.000 0.004 0.032
#> GSM213072 3 0.7872 0.1085 0.100 0.000 0.412 0.180 0.308
#> GSM213075 3 0.9317 -0.0368 0.128 0.072 0.328 0.228 0.244
#> GSM213076 2 0.5518 0.7199 0.020 0.744 0.088 0.048 0.100
#> GSM213079 3 0.3086 0.4959 0.016 0.000 0.876 0.048 0.060
#> GSM213080 1 0.7248 0.2219 0.592 0.096 0.016 0.140 0.156
#> GSM213081 1 0.8098 0.0690 0.392 0.004 0.168 0.320 0.116
#> GSM213084 1 0.4943 0.3731 0.752 0.000 0.028 0.132 0.088
#> GSM213087 2 0.1365 0.8071 0.004 0.952 0.000 0.004 0.040
#> GSM213089 4 0.7784 0.2200 0.104 0.004 0.300 0.452 0.140
#> GSM213090 3 0.4430 0.4900 0.020 0.016 0.796 0.036 0.132
#> GSM213093 4 0.8423 0.2067 0.212 0.008 0.232 0.400 0.148
#> GSM213097 1 0.6975 0.0710 0.460 0.000 0.076 0.384 0.080
#> GSM213099 3 0.6115 0.2987 0.040 0.000 0.612 0.268 0.080
#> GSM213101 1 0.4895 0.4000 0.756 0.004 0.016 0.128 0.096
#> GSM213105 2 0.0865 0.8064 0.004 0.972 0.000 0.000 0.024
#> GSM213109 1 0.7312 0.2268 0.532 0.000 0.084 0.204 0.180
#> GSM213110 2 0.5743 0.6722 0.096 0.724 0.020 0.044 0.116
#> GSM213113 3 0.8749 0.1121 0.088 0.076 0.428 0.152 0.256
#> GSM213121 2 0.1970 0.8054 0.000 0.924 0.004 0.012 0.060
#> GSM213123 4 0.8738 0.0530 0.308 0.028 0.132 0.352 0.180
#> GSM213125 2 0.0854 0.8082 0.000 0.976 0.012 0.008 0.004
#> GSM213073 3 0.4091 0.4732 0.012 0.000 0.808 0.084 0.096
#> GSM213086 1 0.6776 0.2071 0.536 0.000 0.036 0.144 0.284
#> GSM213098 5 0.9565 0.0570 0.216 0.068 0.240 0.232 0.244
#> GSM213106 4 0.7049 0.2948 0.216 0.008 0.156 0.568 0.052
#> GSM213124 2 0.8617 -0.0064 0.056 0.372 0.084 0.148 0.340
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.3706 0.30681 0.824 0.004 0.000 0.072 0.032 0.068
#> GSM213082 2 0.3759 0.73901 0.004 0.824 0.020 0.020 0.104 0.028
#> GSM213085 6 0.7750 0.27663 0.256 0.008 0.192 0.064 0.048 0.432
#> GSM213088 1 0.7983 0.03169 0.416 0.088 0.032 0.320 0.084 0.060
#> GSM213091 3 0.6219 0.36022 0.012 0.000 0.596 0.220 0.072 0.100
#> GSM213092 6 0.6520 0.11258 0.396 0.000 0.060 0.040 0.048 0.456
#> GSM213096 1 0.6899 0.05352 0.540 0.004 0.024 0.104 0.088 0.240
#> GSM213100 1 0.7341 -0.00759 0.460 0.000 0.048 0.116 0.080 0.296
#> GSM213111 2 0.4513 0.72770 0.008 0.788 0.044 0.028 0.096 0.036
#> GSM213117 4 0.6702 0.25808 0.076 0.012 0.092 0.632 0.080 0.108
#> GSM213118 6 0.8619 0.02774 0.204 0.012 0.052 0.228 0.184 0.320
#> GSM213120 2 0.6121 0.57946 0.008 0.616 0.060 0.040 0.240 0.036
#> GSM213122 2 0.1870 0.75810 0.004 0.928 0.000 0.012 0.044 0.012
#> GSM213074 3 0.7982 0.06103 0.076 0.000 0.340 0.212 0.064 0.308
#> GSM213077 1 0.6409 0.16671 0.588 0.000 0.040 0.124 0.036 0.212
#> GSM213083 1 0.6128 0.17503 0.584 0.000 0.024 0.104 0.032 0.256
#> GSM213094 3 0.4590 0.41660 0.004 0.004 0.752 0.148 0.036 0.056
#> GSM213095 2 0.6591 0.48438 0.000 0.548 0.208 0.012 0.172 0.060
#> GSM213102 4 0.7983 0.01841 0.312 0.004 0.072 0.348 0.056 0.208
#> GSM213103 2 0.9010 -0.11305 0.056 0.304 0.068 0.124 0.292 0.156
#> GSM213104 1 0.9018 -0.04382 0.304 0.100 0.088 0.052 0.292 0.164
#> GSM213107 2 0.3540 0.73543 0.008 0.816 0.016 0.004 0.140 0.016
#> GSM213108 2 0.6591 0.59833 0.008 0.624 0.116 0.044 0.136 0.072
#> GSM213112 6 0.7958 0.27537 0.292 0.020 0.168 0.056 0.056 0.408
#> GSM213114 1 0.4064 0.26681 0.800 0.004 0.004 0.024 0.080 0.088
#> GSM213115 2 0.2658 0.75495 0.004 0.884 0.000 0.016 0.072 0.024
#> GSM213116 4 0.7697 0.21251 0.096 0.004 0.164 0.500 0.076 0.160
#> GSM213119 2 0.0603 0.75662 0.000 0.980 0.000 0.000 0.016 0.004
#> GSM213072 3 0.8341 0.01609 0.076 0.000 0.308 0.292 0.116 0.208
#> GSM213075 3 0.9288 -0.04294 0.108 0.040 0.300 0.188 0.192 0.172
#> GSM213076 2 0.5883 0.62332 0.012 0.632 0.060 0.024 0.240 0.032
#> GSM213079 3 0.3548 0.38146 0.004 0.000 0.836 0.048 0.072 0.040
#> GSM213080 1 0.7338 0.22632 0.556 0.080 0.008 0.084 0.156 0.116
#> GSM213081 1 0.8199 0.03436 0.380 0.008 0.068 0.140 0.292 0.112
#> GSM213084 1 0.6711 0.11915 0.536 0.000 0.032 0.084 0.076 0.272
#> GSM213087 2 0.1728 0.75696 0.000 0.924 0.000 0.004 0.064 0.008
#> GSM213089 4 0.7502 0.13114 0.048 0.000 0.236 0.456 0.068 0.192
#> GSM213090 3 0.3923 0.37591 0.012 0.008 0.824 0.032 0.048 0.076
#> GSM213093 4 0.8727 0.07187 0.172 0.000 0.208 0.264 0.104 0.252
#> GSM213097 1 0.8122 0.03537 0.380 0.012 0.044 0.276 0.096 0.192
#> GSM213099 3 0.7459 0.21508 0.032 0.000 0.460 0.252 0.104 0.152
#> GSM213101 1 0.4857 0.28164 0.748 0.004 0.004 0.084 0.064 0.096
#> GSM213105 2 0.1297 0.75771 0.000 0.948 0.000 0.000 0.040 0.012
#> GSM213109 1 0.6767 -0.07217 0.424 0.000 0.068 0.112 0.012 0.384
#> GSM213110 2 0.6228 0.61404 0.060 0.668 0.016 0.044 0.120 0.092
#> GSM213113 5 0.8057 0.06586 0.056 0.016 0.356 0.108 0.356 0.108
#> GSM213121 2 0.2609 0.75147 0.000 0.868 0.004 0.008 0.112 0.008
#> GSM213123 5 0.8948 -0.05265 0.208 0.012 0.112 0.260 0.268 0.140
#> GSM213125 2 0.1484 0.75906 0.000 0.944 0.004 0.008 0.040 0.004
#> GSM213073 3 0.4451 0.30834 0.008 0.004 0.764 0.040 0.148 0.036
#> GSM213086 1 0.6659 -0.12257 0.456 0.000 0.032 0.076 0.056 0.380
#> GSM213098 5 0.8152 0.23956 0.140 0.036 0.192 0.064 0.476 0.092
#> GSM213106 4 0.6969 0.28301 0.112 0.012 0.116 0.600 0.052 0.108
#> GSM213124 2 0.9507 -0.11262 0.064 0.276 0.104 0.192 0.176 0.188
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 development.stage(p) disease.state(p) k
#> CV:skmeans 47 0.923 0.891 2
#> CV:skmeans 39 0.356 0.978 3
#> CV:skmeans 19 0.495 0.976 4
#> CV:skmeans 15 NA NA 5
#> CV:skmeans 14 NA NA 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.571 0.826 0.919 0.4577 0.560 0.560
#> 3 3 0.460 0.694 0.825 0.4020 0.743 0.550
#> 4 4 0.431 0.624 0.805 0.0574 0.964 0.892
#> 5 5 0.429 0.605 0.789 0.0228 0.979 0.933
#> 6 6 0.489 0.583 0.790 0.0245 0.990 0.966
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
#> GSM213078 1 0.2236 0.892 0.964 0.036
#> GSM213082 2 0.0000 0.920 0.000 1.000
#> GSM213085 1 0.0938 0.899 0.988 0.012
#> GSM213088 1 0.8386 0.657 0.732 0.268
#> GSM213091 1 0.0938 0.899 0.988 0.012
#> GSM213092 1 0.0000 0.898 1.000 0.000
#> GSM213096 1 0.0376 0.899 0.996 0.004
#> GSM213100 1 0.0000 0.898 1.000 0.000
#> GSM213111 2 0.0000 0.920 0.000 1.000
#> GSM213117 1 0.4690 0.858 0.900 0.100
#> GSM213118 1 0.0000 0.898 1.000 0.000
#> GSM213120 2 0.5519 0.823 0.128 0.872
#> GSM213122 2 0.0000 0.920 0.000 1.000
#> GSM213074 1 0.0000 0.898 1.000 0.000
#> GSM213077 1 0.0000 0.898 1.000 0.000
#> GSM213083 1 0.0376 0.899 0.996 0.004
#> GSM213094 1 0.7883 0.696 0.764 0.236
#> GSM213095 2 0.5519 0.820 0.128 0.872
#> GSM213102 1 0.0672 0.899 0.992 0.008
#> GSM213103 2 0.8207 0.624 0.256 0.744
#> GSM213104 1 0.9988 0.148 0.520 0.480
#> GSM213107 2 0.0000 0.920 0.000 1.000
#> GSM213108 2 0.1843 0.910 0.028 0.972
#> GSM213112 1 0.2236 0.891 0.964 0.036
#> GSM213114 1 0.0376 0.899 0.996 0.004
#> GSM213115 2 0.0000 0.920 0.000 1.000
#> GSM213116 1 0.8327 0.683 0.736 0.264
#> GSM213119 2 0.0000 0.920 0.000 1.000
#> GSM213072 1 0.7883 0.695 0.764 0.236
#> GSM213075 1 0.7950 0.706 0.760 0.240
#> GSM213076 2 0.9833 0.165 0.424 0.576
#> GSM213079 1 0.8267 0.682 0.740 0.260
#> GSM213080 1 0.8608 0.631 0.716 0.284
#> GSM213081 1 0.4161 0.864 0.916 0.084
#> GSM213084 1 0.3431 0.877 0.936 0.064
#> GSM213087 2 0.0000 0.920 0.000 1.000
#> GSM213089 1 0.0376 0.899 0.996 0.004
#> GSM213090 1 0.9522 0.433 0.628 0.372
#> GSM213093 1 0.2948 0.880 0.948 0.052
#> GSM213097 1 0.0000 0.898 1.000 0.000
#> GSM213099 1 0.1633 0.896 0.976 0.024
#> GSM213101 1 0.0672 0.899 0.992 0.008
#> GSM213105 2 0.0000 0.920 0.000 1.000
#> GSM213109 1 0.0000 0.898 1.000 0.000
#> GSM213110 2 0.2236 0.905 0.036 0.964
#> GSM213113 1 0.0938 0.899 0.988 0.012
#> GSM213121 2 0.0000 0.920 0.000 1.000
#> GSM213123 1 0.1184 0.899 0.984 0.016
#> GSM213125 2 0.0000 0.920 0.000 1.000
#> GSM213073 1 0.6343 0.807 0.840 0.160
#> GSM213086 1 0.0000 0.898 1.000 0.000
#> GSM213098 1 0.1633 0.896 0.976 0.024
#> GSM213106 1 0.0000 0.898 1.000 0.000
#> GSM213124 2 0.3879 0.876 0.076 0.924
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.0000 0.769 1.000 0.000 0.000
#> GSM213082 2 0.1031 0.903 0.000 0.976 0.024
#> GSM213085 3 0.4399 0.728 0.188 0.000 0.812
#> GSM213088 1 0.1529 0.749 0.960 0.040 0.000
#> GSM213091 1 0.6483 0.164 0.544 0.004 0.452
#> GSM213092 3 0.4504 0.726 0.196 0.000 0.804
#> GSM213096 1 0.1411 0.775 0.964 0.000 0.036
#> GSM213100 1 0.4796 0.700 0.780 0.000 0.220
#> GSM213111 2 0.1482 0.904 0.012 0.968 0.020
#> GSM213117 1 0.5514 0.724 0.800 0.044 0.156
#> GSM213118 3 0.5560 0.633 0.300 0.000 0.700
#> GSM213120 2 0.5111 0.779 0.144 0.820 0.036
#> GSM213122 2 0.1163 0.902 0.000 0.972 0.028
#> GSM213074 3 0.5810 0.643 0.336 0.000 0.664
#> GSM213077 1 0.4121 0.755 0.832 0.000 0.168
#> GSM213083 1 0.3879 0.766 0.848 0.000 0.152
#> GSM213094 3 0.1765 0.690 0.040 0.004 0.956
#> GSM213095 3 0.6577 0.248 0.008 0.420 0.572
#> GSM213102 1 0.4047 0.765 0.848 0.004 0.148
#> GSM213103 2 0.5848 0.633 0.268 0.720 0.012
#> GSM213104 3 0.9517 0.361 0.208 0.320 0.472
#> GSM213107 2 0.0000 0.905 0.000 1.000 0.000
#> GSM213108 2 0.1774 0.896 0.024 0.960 0.016
#> GSM213112 3 0.5008 0.731 0.180 0.016 0.804
#> GSM213114 1 0.2448 0.782 0.924 0.000 0.076
#> GSM213115 2 0.0237 0.905 0.004 0.996 0.000
#> GSM213116 1 0.9151 0.237 0.528 0.180 0.292
#> GSM213119 2 0.0747 0.904 0.000 0.984 0.016
#> GSM213072 3 0.6684 0.574 0.292 0.032 0.676
#> GSM213075 1 0.3039 0.773 0.920 0.044 0.036
#> GSM213076 2 0.7819 0.141 0.440 0.508 0.052
#> GSM213079 3 0.3993 0.652 0.064 0.052 0.884
#> GSM213080 1 0.1411 0.756 0.964 0.036 0.000
#> GSM213081 1 0.3587 0.778 0.892 0.020 0.088
#> GSM213084 1 0.5202 0.601 0.772 0.008 0.220
#> GSM213087 2 0.0747 0.904 0.000 0.984 0.016
#> GSM213089 3 0.5706 0.618 0.320 0.000 0.680
#> GSM213090 3 0.1950 0.690 0.040 0.008 0.952
#> GSM213093 3 0.7699 0.233 0.420 0.048 0.532
#> GSM213097 1 0.3686 0.769 0.860 0.000 0.140
#> GSM213099 3 0.5728 0.692 0.272 0.008 0.720
#> GSM213101 1 0.0747 0.775 0.984 0.000 0.016
#> GSM213105 2 0.1031 0.903 0.000 0.976 0.024
#> GSM213109 1 0.6008 0.356 0.628 0.000 0.372
#> GSM213110 2 0.2261 0.880 0.068 0.932 0.000
#> GSM213113 3 0.5553 0.670 0.272 0.004 0.724
#> GSM213121 2 0.0829 0.905 0.004 0.984 0.012
#> GSM213123 1 0.5268 0.670 0.776 0.012 0.212
#> GSM213125 2 0.0983 0.905 0.004 0.980 0.016
#> GSM213073 3 0.3572 0.675 0.060 0.040 0.900
#> GSM213086 3 0.4399 0.728 0.188 0.000 0.812
#> GSM213098 1 0.4682 0.704 0.804 0.004 0.192
#> GSM213106 1 0.5560 0.596 0.700 0.000 0.300
#> GSM213124 2 0.3587 0.850 0.088 0.892 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.0188 0.7684 0.996 0.000 0.000 0.004
#> GSM213082 2 0.2530 0.8450 0.000 0.888 0.112 0.000
#> GSM213085 4 0.2149 0.6578 0.088 0.000 0.000 0.912
#> GSM213088 1 0.0817 0.7621 0.976 0.024 0.000 0.000
#> GSM213091 4 0.4985 -0.0585 0.468 0.000 0.000 0.532
#> GSM213092 4 0.2530 0.6604 0.112 0.000 0.000 0.888
#> GSM213096 1 0.1970 0.7659 0.932 0.000 0.008 0.060
#> GSM213100 1 0.4539 0.6427 0.720 0.000 0.008 0.272
#> GSM213111 2 0.1151 0.8538 0.008 0.968 0.024 0.000
#> GSM213117 1 0.5208 0.6649 0.736 0.032 0.012 0.220
#> GSM213118 4 0.3908 0.6388 0.212 0.000 0.004 0.784
#> GSM213120 2 0.4078 0.7274 0.132 0.828 0.004 0.036
#> GSM213122 2 0.2704 0.8409 0.000 0.876 0.124 0.000
#> GSM213074 4 0.4655 0.5949 0.312 0.000 0.004 0.684
#> GSM213077 1 0.3610 0.7386 0.800 0.000 0.000 0.200
#> GSM213083 1 0.3448 0.7583 0.828 0.000 0.004 0.168
#> GSM213094 3 0.3945 0.0000 0.004 0.000 0.780 0.216
#> GSM213095 4 0.5884 0.1618 0.004 0.384 0.032 0.580
#> GSM213102 1 0.3819 0.7526 0.816 0.004 0.008 0.172
#> GSM213103 2 0.5366 0.5631 0.240 0.712 0.004 0.044
#> GSM213104 4 0.7373 0.2384 0.184 0.316 0.000 0.500
#> GSM213107 2 0.1211 0.8570 0.000 0.960 0.040 0.000
#> GSM213108 2 0.1394 0.8511 0.016 0.964 0.012 0.008
#> GSM213112 4 0.2530 0.6605 0.100 0.000 0.004 0.896
#> GSM213114 1 0.2216 0.7797 0.908 0.000 0.000 0.092
#> GSM213115 2 0.0188 0.8534 0.000 0.996 0.004 0.000
#> GSM213116 1 0.7816 0.1331 0.476 0.184 0.012 0.328
#> GSM213119 2 0.2345 0.8460 0.000 0.900 0.100 0.000
#> GSM213072 4 0.4639 0.5898 0.228 0.008 0.012 0.752
#> GSM213075 1 0.2408 0.7721 0.920 0.044 0.000 0.036
#> GSM213076 2 0.7068 0.1843 0.396 0.516 0.032 0.056
#> GSM213079 4 0.6278 0.1224 0.040 0.024 0.304 0.632
#> GSM213080 1 0.0895 0.7660 0.976 0.020 0.000 0.004
#> GSM213081 1 0.2741 0.7771 0.892 0.012 0.000 0.096
#> GSM213084 1 0.4123 0.5848 0.772 0.008 0.000 0.220
#> GSM213087 2 0.2345 0.8460 0.000 0.900 0.100 0.000
#> GSM213089 4 0.4511 0.6056 0.268 0.000 0.008 0.724
#> GSM213090 4 0.2924 0.5055 0.016 0.000 0.100 0.884
#> GSM213093 4 0.5453 0.2630 0.388 0.020 0.000 0.592
#> GSM213097 1 0.3266 0.7568 0.832 0.000 0.000 0.168
#> GSM213099 4 0.3852 0.6554 0.192 0.000 0.008 0.800
#> GSM213101 1 0.0707 0.7739 0.980 0.000 0.000 0.020
#> GSM213105 2 0.2589 0.8431 0.000 0.884 0.116 0.000
#> GSM213109 1 0.5039 0.3163 0.592 0.000 0.004 0.404
#> GSM213110 2 0.1716 0.8325 0.064 0.936 0.000 0.000
#> GSM213113 4 0.3400 0.6590 0.180 0.000 0.000 0.820
#> GSM213121 2 0.1022 0.8555 0.000 0.968 0.032 0.000
#> GSM213123 1 0.4122 0.6448 0.760 0.004 0.000 0.236
#> GSM213125 2 0.2011 0.8538 0.000 0.920 0.080 0.000
#> GSM213073 4 0.5642 0.1955 0.020 0.020 0.288 0.672
#> GSM213086 4 0.2149 0.6578 0.088 0.000 0.000 0.912
#> GSM213098 1 0.3870 0.6797 0.788 0.000 0.004 0.208
#> GSM213106 1 0.4836 0.5693 0.672 0.000 0.008 0.320
#> GSM213124 2 0.2730 0.8014 0.088 0.896 0.000 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.0000 0.7466 1.000 0.000 0.000 0.000 0.000
#> GSM213082 2 0.2966 0.7931 0.000 0.816 0.000 0.000 0.184
#> GSM213085 4 0.1965 0.6563 0.096 0.000 0.000 0.904 0.000
#> GSM213088 1 0.0290 0.7462 0.992 0.008 0.000 0.000 0.000
#> GSM213091 4 0.4294 0.0331 0.468 0.000 0.000 0.532 0.000
#> GSM213092 4 0.2424 0.6631 0.132 0.000 0.000 0.868 0.000
#> GSM213096 1 0.2248 0.7333 0.900 0.000 0.012 0.088 0.000
#> GSM213100 1 0.4173 0.5770 0.688 0.000 0.012 0.300 0.000
#> GSM213111 2 0.1331 0.8146 0.008 0.952 0.000 0.000 0.040
#> GSM213117 1 0.5053 0.5913 0.700 0.028 0.016 0.244 0.012
#> GSM213118 4 0.3398 0.6486 0.216 0.000 0.004 0.780 0.000
#> GSM213120 2 0.3011 0.7084 0.140 0.844 0.000 0.016 0.000
#> GSM213122 2 0.3242 0.7817 0.000 0.784 0.000 0.000 0.216
#> GSM213074 4 0.4135 0.5671 0.340 0.000 0.004 0.656 0.000
#> GSM213077 1 0.3177 0.7086 0.792 0.000 0.000 0.208 0.000
#> GSM213083 1 0.3123 0.7256 0.812 0.000 0.004 0.184 0.000
#> GSM213094 5 0.4678 0.0000 0.000 0.000 0.224 0.064 0.712
#> GSM213095 4 0.5460 -0.0479 0.004 0.420 0.000 0.524 0.052
#> GSM213102 1 0.3575 0.7185 0.800 0.004 0.016 0.180 0.000
#> GSM213103 2 0.4976 0.5147 0.228 0.696 0.004 0.072 0.000
#> GSM213104 4 0.6358 0.2174 0.180 0.328 0.000 0.492 0.000
#> GSM213107 2 0.1270 0.8192 0.000 0.948 0.000 0.000 0.052
#> GSM213108 2 0.1673 0.8166 0.016 0.944 0.000 0.008 0.032
#> GSM213112 4 0.2286 0.6603 0.108 0.000 0.004 0.888 0.000
#> GSM213114 1 0.2020 0.7568 0.900 0.000 0.000 0.100 0.000
#> GSM213115 2 0.0162 0.8139 0.000 0.996 0.000 0.000 0.004
#> GSM213116 1 0.6859 0.0211 0.452 0.184 0.016 0.348 0.000
#> GSM213119 2 0.2852 0.7942 0.000 0.828 0.000 0.000 0.172
#> GSM213072 4 0.4257 0.6176 0.212 0.008 0.012 0.756 0.012
#> GSM213075 1 0.2074 0.7513 0.920 0.044 0.000 0.036 0.000
#> GSM213076 2 0.6571 0.1716 0.376 0.500 0.000 0.072 0.052
#> GSM213079 3 0.3837 0.6453 0.000 0.000 0.692 0.308 0.000
#> GSM213080 1 0.0404 0.7464 0.988 0.012 0.000 0.000 0.000
#> GSM213081 1 0.2248 0.7548 0.900 0.012 0.000 0.088 0.000
#> GSM213084 1 0.3388 0.5983 0.792 0.008 0.000 0.200 0.000
#> GSM213087 2 0.2773 0.7972 0.000 0.836 0.000 0.000 0.164
#> GSM213089 4 0.4380 0.5851 0.288 0.000 0.008 0.692 0.012
#> GSM213090 4 0.5018 -0.0234 0.004 0.000 0.252 0.680 0.064
#> GSM213093 4 0.4640 0.2671 0.400 0.016 0.000 0.584 0.000
#> GSM213097 1 0.2891 0.7292 0.824 0.000 0.000 0.176 0.000
#> GSM213099 4 0.3778 0.6653 0.188 0.000 0.012 0.788 0.012
#> GSM213101 1 0.0404 0.7515 0.988 0.000 0.000 0.012 0.000
#> GSM213105 2 0.3143 0.7864 0.000 0.796 0.000 0.000 0.204
#> GSM213109 1 0.4321 0.2953 0.600 0.000 0.004 0.396 0.000
#> GSM213110 2 0.1341 0.8015 0.056 0.944 0.000 0.000 0.000
#> GSM213113 4 0.2891 0.6786 0.176 0.000 0.000 0.824 0.000
#> GSM213121 2 0.1478 0.8162 0.000 0.936 0.000 0.000 0.064
#> GSM213123 1 0.3521 0.6344 0.764 0.004 0.000 0.232 0.000
#> GSM213125 2 0.2732 0.8061 0.000 0.840 0.000 0.000 0.160
#> GSM213073 3 0.3366 0.6013 0.000 0.004 0.784 0.212 0.000
#> GSM213086 4 0.2020 0.6589 0.100 0.000 0.000 0.900 0.000
#> GSM213098 1 0.3461 0.6330 0.772 0.000 0.004 0.224 0.000
#> GSM213106 1 0.4453 0.5187 0.660 0.000 0.008 0.324 0.008
#> GSM213124 2 0.2130 0.7763 0.080 0.908 0.000 0.012 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.0000 0.7269 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213082 2 0.2854 0.7782 0.000 0.792 0.000 0.000 0.000 0.208
#> GSM213085 4 0.1327 0.6526 0.064 0.000 0.000 0.936 0.000 0.000
#> GSM213088 1 0.0551 0.7272 0.984 0.008 0.000 0.004 0.000 0.004
#> GSM213091 4 0.3937 0.1613 0.424 0.000 0.000 0.572 0.004 0.000
#> GSM213092 4 0.2219 0.6599 0.136 0.000 0.000 0.864 0.000 0.000
#> GSM213096 1 0.2624 0.6758 0.844 0.000 0.004 0.148 0.004 0.000
#> GSM213100 1 0.4022 0.4561 0.628 0.000 0.008 0.360 0.004 0.000
#> GSM213111 2 0.1554 0.8047 0.008 0.940 0.000 0.004 0.004 0.044
#> GSM213117 1 0.4926 0.4747 0.636 0.024 0.000 0.292 0.048 0.000
#> GSM213118 4 0.2772 0.6619 0.180 0.000 0.004 0.816 0.000 0.000
#> GSM213120 2 0.2933 0.7146 0.124 0.848 0.000 0.016 0.008 0.004
#> GSM213122 2 0.3076 0.7666 0.000 0.760 0.000 0.000 0.000 0.240
#> GSM213074 4 0.3861 0.5189 0.352 0.000 0.000 0.640 0.008 0.000
#> GSM213077 1 0.2854 0.6894 0.792 0.000 0.000 0.208 0.000 0.000
#> GSM213083 1 0.2838 0.7046 0.808 0.000 0.004 0.188 0.000 0.000
#> GSM213094 5 0.2462 0.0000 0.000 0.000 0.096 0.028 0.876 0.000
#> GSM213095 4 0.5058 -0.0296 0.004 0.444 0.000 0.496 0.004 0.052
#> GSM213102 1 0.3437 0.6939 0.788 0.004 0.008 0.188 0.012 0.000
#> GSM213103 2 0.5107 0.4428 0.212 0.652 0.004 0.128 0.004 0.000
#> GSM213104 4 0.5487 0.2287 0.148 0.320 0.000 0.532 0.000 0.000
#> GSM213107 2 0.1285 0.8105 0.000 0.944 0.000 0.004 0.000 0.052
#> GSM213108 2 0.1628 0.8094 0.012 0.940 0.000 0.008 0.004 0.036
#> GSM213112 4 0.1444 0.6537 0.072 0.000 0.000 0.928 0.000 0.000
#> GSM213114 1 0.1863 0.7363 0.896 0.000 0.000 0.104 0.000 0.000
#> GSM213115 2 0.0405 0.8057 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM213116 1 0.6303 -0.0687 0.420 0.176 0.008 0.384 0.012 0.000
#> GSM213119 2 0.2730 0.7802 0.000 0.808 0.000 0.000 0.000 0.192
#> GSM213072 4 0.3502 0.6174 0.192 0.000 0.008 0.780 0.020 0.000
#> GSM213075 1 0.2009 0.7312 0.916 0.040 0.000 0.040 0.004 0.000
#> GSM213076 2 0.6344 0.1912 0.340 0.492 0.000 0.112 0.004 0.052
#> GSM213079 3 0.5131 0.5371 0.000 0.000 0.648 0.204 0.008 0.140
#> GSM213080 1 0.0508 0.7260 0.984 0.012 0.000 0.004 0.000 0.000
#> GSM213081 1 0.2070 0.7323 0.896 0.012 0.000 0.092 0.000 0.000
#> GSM213084 1 0.3073 0.5678 0.788 0.008 0.000 0.204 0.000 0.000
#> GSM213087 2 0.2631 0.7852 0.000 0.820 0.000 0.000 0.000 0.180
#> GSM213089 4 0.4309 0.5406 0.296 0.000 0.000 0.660 0.044 0.000
#> GSM213090 6 0.5465 0.0000 0.000 0.000 0.028 0.228 0.116 0.628
#> GSM213093 4 0.4045 0.1600 0.428 0.008 0.000 0.564 0.000 0.000
#> GSM213097 1 0.2597 0.7091 0.824 0.000 0.000 0.176 0.000 0.000
#> GSM213099 4 0.3542 0.6528 0.160 0.000 0.000 0.788 0.052 0.000
#> GSM213101 1 0.0547 0.7326 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM213105 2 0.2969 0.7729 0.000 0.776 0.000 0.000 0.000 0.224
#> GSM213109 1 0.3890 0.2968 0.596 0.000 0.004 0.400 0.000 0.000
#> GSM213110 2 0.1349 0.7944 0.056 0.940 0.000 0.000 0.004 0.000
#> GSM213113 4 0.2491 0.6786 0.164 0.000 0.000 0.836 0.000 0.000
#> GSM213121 2 0.1732 0.8067 0.000 0.920 0.000 0.004 0.004 0.072
#> GSM213123 1 0.3136 0.6222 0.768 0.004 0.000 0.228 0.000 0.000
#> GSM213125 2 0.2632 0.7959 0.000 0.832 0.000 0.000 0.004 0.164
#> GSM213073 3 0.1700 0.5185 0.000 0.004 0.916 0.080 0.000 0.000
#> GSM213086 4 0.1444 0.6546 0.072 0.000 0.000 0.928 0.000 0.000
#> GSM213098 1 0.3198 0.5694 0.740 0.000 0.000 0.260 0.000 0.000
#> GSM213106 1 0.4018 0.5040 0.656 0.000 0.000 0.324 0.020 0.000
#> GSM213124 2 0.2182 0.7708 0.072 0.904 0.004 0.016 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 development.stage(p) disease.state(p) k
#> CV:pam 51 0.534 0.736 2
#> CV:pam 47 0.649 0.923 3
#> CV:pam 44 0.740 0.792 4
#> CV:pam 45 0.461 0.922 5
#> CV:pam 42 0.485 0.952 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.507 0.795 0.903 0.4555 0.560 0.560
#> 3 3 0.697 0.883 0.922 0.1579 0.874 0.783
#> 4 4 0.442 0.434 0.725 0.3161 0.744 0.481
#> 5 5 0.534 0.475 0.692 0.0548 0.841 0.505
#> 6 6 0.580 0.494 0.716 0.0442 0.820 0.438
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
#> GSM213078 1 0.2236 0.871 0.964 0.036
#> GSM213082 2 0.0000 0.910 0.000 1.000
#> GSM213085 1 0.0000 0.876 1.000 0.000
#> GSM213088 1 0.5519 0.824 0.872 0.128
#> GSM213091 1 0.6712 0.790 0.824 0.176
#> GSM213092 1 0.0000 0.876 1.000 0.000
#> GSM213096 1 0.2236 0.871 0.964 0.036
#> GSM213100 1 0.0376 0.876 0.996 0.004
#> GSM213111 2 0.0000 0.910 0.000 1.000
#> GSM213117 1 0.0376 0.876 0.996 0.004
#> GSM213118 1 0.0000 0.876 1.000 0.000
#> GSM213120 2 0.8207 0.641 0.256 0.744
#> GSM213122 2 0.0000 0.910 0.000 1.000
#> GSM213074 1 0.6438 0.801 0.836 0.164
#> GSM213077 1 0.0000 0.876 1.000 0.000
#> GSM213083 1 0.0000 0.876 1.000 0.000
#> GSM213094 1 0.9954 0.345 0.540 0.460
#> GSM213095 2 0.0000 0.910 0.000 1.000
#> GSM213102 1 0.0000 0.876 1.000 0.000
#> GSM213103 2 0.8813 0.565 0.300 0.700
#> GSM213104 1 0.9993 0.122 0.516 0.484
#> GSM213107 2 0.0000 0.910 0.000 1.000
#> GSM213108 2 0.0000 0.910 0.000 1.000
#> GSM213112 1 0.0000 0.876 1.000 0.000
#> GSM213114 1 0.6343 0.804 0.840 0.160
#> GSM213115 2 0.1414 0.898 0.020 0.980
#> GSM213116 1 0.0000 0.876 1.000 0.000
#> GSM213119 2 0.0000 0.910 0.000 1.000
#> GSM213072 1 0.4298 0.849 0.912 0.088
#> GSM213075 1 0.3733 0.858 0.928 0.072
#> GSM213076 2 0.0672 0.906 0.008 0.992
#> GSM213079 1 0.9954 0.345 0.540 0.460
#> GSM213080 1 0.8443 0.674 0.728 0.272
#> GSM213081 1 0.4022 0.855 0.920 0.080
#> GSM213084 1 0.1184 0.874 0.984 0.016
#> GSM213087 2 0.0000 0.910 0.000 1.000
#> GSM213089 1 0.0000 0.876 1.000 0.000
#> GSM213090 1 0.9954 0.345 0.540 0.460
#> GSM213093 1 0.0000 0.876 1.000 0.000
#> GSM213097 1 0.0000 0.876 1.000 0.000
#> GSM213099 1 0.5737 0.819 0.864 0.136
#> GSM213101 1 0.1414 0.874 0.980 0.020
#> GSM213105 2 0.0000 0.910 0.000 1.000
#> GSM213109 1 0.0000 0.876 1.000 0.000
#> GSM213110 2 0.8386 0.621 0.268 0.732
#> GSM213113 1 0.6887 0.783 0.816 0.184
#> GSM213121 2 0.0000 0.910 0.000 1.000
#> GSM213123 1 0.0376 0.876 0.996 0.004
#> GSM213125 2 0.0000 0.910 0.000 1.000
#> GSM213073 1 0.9954 0.345 0.540 0.460
#> GSM213086 1 0.0000 0.876 1.000 0.000
#> GSM213098 1 0.6887 0.783 0.816 0.184
#> GSM213106 1 0.0000 0.876 1.000 0.000
#> GSM213124 2 0.8713 0.579 0.292 0.708
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.2564 0.927 0.936 0.028 0.036
#> GSM213082 2 0.1289 0.847 0.000 0.968 0.032
#> GSM213085 1 0.1482 0.932 0.968 0.020 0.012
#> GSM213088 1 0.2918 0.922 0.924 0.032 0.044
#> GSM213091 1 0.5470 0.837 0.796 0.036 0.168
#> GSM213092 1 0.1031 0.928 0.976 0.000 0.024
#> GSM213096 1 0.2165 0.928 0.936 0.000 0.064
#> GSM213100 1 0.1163 0.928 0.972 0.000 0.028
#> GSM213111 2 0.3482 0.850 0.000 0.872 0.128
#> GSM213117 1 0.0592 0.930 0.988 0.000 0.012
#> GSM213118 1 0.1182 0.931 0.976 0.012 0.012
#> GSM213120 2 0.4731 0.819 0.032 0.840 0.128
#> GSM213122 2 0.0000 0.839 0.000 1.000 0.000
#> GSM213074 1 0.4059 0.880 0.860 0.012 0.128
#> GSM213077 1 0.1031 0.928 0.976 0.000 0.024
#> GSM213083 1 0.1031 0.928 0.976 0.000 0.024
#> GSM213094 3 0.1411 1.000 0.000 0.036 0.964
#> GSM213095 2 0.3482 0.850 0.000 0.872 0.128
#> GSM213102 1 0.0000 0.929 1.000 0.000 0.000
#> GSM213103 2 0.8963 0.144 0.404 0.468 0.128
#> GSM213104 1 0.4848 0.870 0.836 0.036 0.128
#> GSM213107 2 0.3482 0.850 0.000 0.872 0.128
#> GSM213108 2 0.3482 0.850 0.000 0.872 0.128
#> GSM213112 1 0.1482 0.932 0.968 0.020 0.012
#> GSM213114 1 0.4731 0.875 0.840 0.032 0.128
#> GSM213115 2 0.0237 0.841 0.000 0.996 0.004
#> GSM213116 1 0.0424 0.929 0.992 0.000 0.008
#> GSM213119 2 0.0000 0.839 0.000 1.000 0.000
#> GSM213072 1 0.3359 0.907 0.900 0.016 0.084
#> GSM213075 1 0.2651 0.920 0.928 0.012 0.060
#> GSM213076 2 0.3482 0.850 0.000 0.872 0.128
#> GSM213079 3 0.1411 1.000 0.000 0.036 0.964
#> GSM213080 1 0.4799 0.872 0.836 0.032 0.132
#> GSM213081 1 0.3377 0.917 0.896 0.012 0.092
#> GSM213084 1 0.1289 0.929 0.968 0.000 0.032
#> GSM213087 2 0.0000 0.839 0.000 1.000 0.000
#> GSM213089 1 0.0424 0.929 0.992 0.000 0.008
#> GSM213090 3 0.1411 1.000 0.000 0.036 0.964
#> GSM213093 1 0.0424 0.929 0.992 0.000 0.008
#> GSM213097 1 0.0000 0.929 1.000 0.000 0.000
#> GSM213099 1 0.4662 0.877 0.844 0.032 0.124
#> GSM213101 1 0.2056 0.930 0.952 0.024 0.024
#> GSM213105 2 0.0000 0.839 0.000 1.000 0.000
#> GSM213109 1 0.0000 0.929 1.000 0.000 0.000
#> GSM213110 2 0.5656 0.768 0.068 0.804 0.128
#> GSM213113 1 0.4915 0.868 0.832 0.036 0.132
#> GSM213121 2 0.3192 0.852 0.000 0.888 0.112
#> GSM213123 1 0.0424 0.931 0.992 0.000 0.008
#> GSM213125 2 0.0000 0.839 0.000 1.000 0.000
#> GSM213073 3 0.1411 1.000 0.000 0.036 0.964
#> GSM213086 1 0.1031 0.928 0.976 0.000 0.024
#> GSM213098 1 0.4779 0.873 0.840 0.036 0.124
#> GSM213106 1 0.0237 0.929 0.996 0.000 0.004
#> GSM213124 1 0.5174 0.860 0.824 0.048 0.128
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.4245 0.6047 0.832 0.008 0.056 0.104
#> GSM213082 2 0.1867 0.6820 0.000 0.928 0.072 0.000
#> GSM213085 4 0.6171 -0.1740 0.456 0.004 0.040 0.500
#> GSM213088 1 0.8021 0.1368 0.448 0.012 0.224 0.316
#> GSM213091 4 0.4277 0.3514 0.000 0.000 0.280 0.720
#> GSM213092 1 0.4222 0.5615 0.728 0.000 0.000 0.272
#> GSM213096 1 0.2334 0.6022 0.908 0.004 0.000 0.088
#> GSM213100 1 0.3123 0.6086 0.844 0.000 0.000 0.156
#> GSM213111 2 0.6189 0.5628 0.048 0.600 0.344 0.008
#> GSM213117 4 0.2714 0.5980 0.112 0.004 0.000 0.884
#> GSM213118 1 0.6293 0.1505 0.504 0.008 0.040 0.448
#> GSM213120 2 0.6678 0.5196 0.060 0.564 0.360 0.016
#> GSM213122 2 0.0000 0.6866 0.000 1.000 0.000 0.000
#> GSM213074 4 0.3718 0.5337 0.012 0.000 0.168 0.820
#> GSM213077 1 0.4304 0.5514 0.716 0.000 0.000 0.284
#> GSM213083 1 0.4304 0.5507 0.716 0.000 0.000 0.284
#> GSM213094 3 0.0895 0.5623 0.000 0.004 0.976 0.020
#> GSM213095 2 0.6742 0.4736 0.072 0.520 0.400 0.008
#> GSM213102 4 0.4907 -0.0652 0.420 0.000 0.000 0.580
#> GSM213103 3 0.9808 0.3215 0.212 0.204 0.352 0.232
#> GSM213104 1 0.8288 -0.1710 0.412 0.032 0.380 0.176
#> GSM213107 2 0.6382 0.5208 0.052 0.560 0.380 0.008
#> GSM213108 2 0.5936 0.5632 0.040 0.604 0.352 0.004
#> GSM213112 4 0.6177 -0.1887 0.468 0.004 0.040 0.488
#> GSM213114 1 0.6607 0.2992 0.612 0.012 0.296 0.080
#> GSM213115 2 0.0336 0.6887 0.000 0.992 0.008 0.000
#> GSM213116 4 0.2149 0.6119 0.088 0.000 0.000 0.912
#> GSM213119 2 0.0000 0.6866 0.000 1.000 0.000 0.000
#> GSM213072 4 0.2480 0.6060 0.008 0.000 0.088 0.904
#> GSM213075 4 0.5282 0.5721 0.100 0.004 0.136 0.760
#> GSM213076 2 0.6345 0.5547 0.056 0.588 0.348 0.008
#> GSM213079 3 0.0000 0.5654 0.000 0.000 1.000 0.000
#> GSM213080 1 0.7083 0.1669 0.576 0.032 0.320 0.072
#> GSM213081 1 0.4469 0.5791 0.808 0.000 0.080 0.112
#> GSM213084 1 0.2408 0.6072 0.896 0.000 0.000 0.104
#> GSM213087 2 0.0336 0.6890 0.000 0.992 0.008 0.000
#> GSM213089 4 0.1867 0.6118 0.072 0.000 0.000 0.928
#> GSM213090 3 0.0000 0.5654 0.000 0.000 1.000 0.000
#> GSM213093 4 0.2704 0.5916 0.124 0.000 0.000 0.876
#> GSM213097 1 0.4961 0.3282 0.552 0.000 0.000 0.448
#> GSM213099 4 0.3494 0.5451 0.004 0.000 0.172 0.824
#> GSM213101 1 0.4597 0.5972 0.800 0.008 0.044 0.148
#> GSM213105 2 0.0000 0.6866 0.000 1.000 0.000 0.000
#> GSM213109 1 0.4992 0.2689 0.524 0.000 0.000 0.476
#> GSM213110 3 0.9090 -0.0165 0.076 0.356 0.356 0.212
#> GSM213113 3 0.8004 0.1485 0.168 0.020 0.416 0.396
#> GSM213121 2 0.5832 0.5847 0.044 0.640 0.312 0.004
#> GSM213123 4 0.5132 0.0785 0.448 0.000 0.004 0.548
#> GSM213125 2 0.0188 0.6882 0.000 0.996 0.004 0.000
#> GSM213073 3 0.0000 0.5654 0.000 0.000 1.000 0.000
#> GSM213086 1 0.4382 0.5398 0.704 0.000 0.000 0.296
#> GSM213098 3 0.8355 0.0944 0.340 0.016 0.360 0.284
#> GSM213106 4 0.2281 0.6100 0.096 0.000 0.000 0.904
#> GSM213124 4 0.8028 -0.2132 0.076 0.076 0.372 0.476
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.5130 0.64678 0.656 0.000 0.012 0.288 0.044
#> GSM213082 2 0.0963 0.75135 0.000 0.964 0.000 0.000 0.036
#> GSM213085 4 0.5010 -0.18165 0.376 0.000 0.008 0.592 0.024
#> GSM213088 4 0.6541 0.25817 0.244 0.012 0.004 0.560 0.180
#> GSM213091 4 0.6273 0.48330 0.164 0.000 0.060 0.648 0.128
#> GSM213092 1 0.4499 0.53831 0.584 0.000 0.004 0.408 0.004
#> GSM213096 1 0.4535 0.65287 0.684 0.000 0.004 0.288 0.024
#> GSM213100 1 0.3857 0.63601 0.688 0.000 0.000 0.312 0.000
#> GSM213111 2 0.4273 -0.24552 0.000 0.552 0.000 0.000 0.448
#> GSM213117 4 0.0740 0.61317 0.008 0.000 0.004 0.980 0.008
#> GSM213118 4 0.4822 -0.22230 0.416 0.000 0.004 0.564 0.016
#> GSM213120 5 0.4446 0.41748 0.008 0.400 0.000 0.000 0.592
#> GSM213122 2 0.0162 0.76512 0.000 0.996 0.000 0.000 0.004
#> GSM213074 4 0.4871 0.54856 0.128 0.000 0.032 0.760 0.080
#> GSM213077 1 0.4516 0.52421 0.576 0.000 0.004 0.416 0.004
#> GSM213083 1 0.4367 0.52379 0.580 0.000 0.000 0.416 0.004
#> GSM213094 3 0.1990 0.95039 0.008 0.000 0.920 0.004 0.068
#> GSM213095 5 0.3536 0.47299 0.000 0.156 0.032 0.000 0.812
#> GSM213102 4 0.2806 0.52044 0.152 0.000 0.000 0.844 0.004
#> GSM213103 5 0.7255 0.45611 0.204 0.220 0.000 0.060 0.516
#> GSM213104 1 0.5889 0.29529 0.560 0.000 0.016 0.072 0.352
#> GSM213107 5 0.4418 0.27865 0.000 0.332 0.016 0.000 0.652
#> GSM213108 2 0.4714 -0.09634 0.004 0.576 0.012 0.000 0.408
#> GSM213112 4 0.5138 -0.24794 0.396 0.000 0.008 0.568 0.028
#> GSM213114 1 0.5882 0.51771 0.644 0.000 0.016 0.140 0.200
#> GSM213115 2 0.0880 0.75604 0.000 0.968 0.000 0.000 0.032
#> GSM213116 4 0.0404 0.61018 0.012 0.000 0.000 0.988 0.000
#> GSM213119 2 0.0162 0.76512 0.000 0.996 0.000 0.000 0.004
#> GSM213072 4 0.4534 0.54634 0.164 0.000 0.016 0.764 0.056
#> GSM213075 4 0.3570 0.56831 0.048 0.008 0.004 0.844 0.096
#> GSM213076 5 0.4249 0.35807 0.000 0.432 0.000 0.000 0.568
#> GSM213079 3 0.0880 0.97381 0.000 0.000 0.968 0.000 0.032
#> GSM213080 1 0.5519 0.37231 0.624 0.000 0.020 0.052 0.304
#> GSM213081 1 0.5559 0.61303 0.600 0.000 0.004 0.316 0.080
#> GSM213084 1 0.4253 0.64985 0.700 0.000 0.008 0.284 0.008
#> GSM213087 2 0.0290 0.76435 0.000 0.992 0.000 0.000 0.008
#> GSM213089 4 0.0451 0.61284 0.004 0.000 0.000 0.988 0.008
#> GSM213090 3 0.0703 0.97187 0.000 0.000 0.976 0.000 0.024
#> GSM213093 4 0.0609 0.61056 0.020 0.000 0.000 0.980 0.000
#> GSM213097 4 0.4118 0.17067 0.336 0.000 0.000 0.660 0.004
#> GSM213099 4 0.5130 0.52886 0.168 0.000 0.020 0.724 0.088
#> GSM213101 1 0.4726 0.62737 0.644 0.000 0.004 0.328 0.024
#> GSM213105 2 0.0162 0.76512 0.000 0.996 0.000 0.000 0.004
#> GSM213109 4 0.3949 0.28011 0.300 0.000 0.000 0.696 0.004
#> GSM213110 5 0.6121 0.43896 0.060 0.384 0.000 0.032 0.524
#> GSM213113 4 0.7514 0.09588 0.228 0.004 0.040 0.436 0.292
#> GSM213121 2 0.4278 -0.00555 0.000 0.548 0.000 0.000 0.452
#> GSM213123 4 0.4218 0.22720 0.324 0.000 0.004 0.668 0.004
#> GSM213125 2 0.0404 0.76279 0.000 0.988 0.000 0.000 0.012
#> GSM213073 3 0.1341 0.96632 0.000 0.000 0.944 0.000 0.056
#> GSM213086 1 0.4383 0.50548 0.572 0.000 0.000 0.424 0.004
#> GSM213098 1 0.6628 0.42849 0.520 0.000 0.012 0.196 0.272
#> GSM213106 4 0.0566 0.61128 0.012 0.000 0.000 0.984 0.004
#> GSM213124 5 0.6178 0.22271 0.040 0.044 0.004 0.388 0.524
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.2490 0.58577 0.892 0.000 0.000 0.012 0.044 0.052
#> GSM213082 2 0.0935 0.67112 0.000 0.964 0.000 0.000 0.032 0.004
#> GSM213085 1 0.4661 0.44044 0.620 0.000 0.000 0.332 0.036 0.012
#> GSM213088 1 0.6913 0.00792 0.436 0.028 0.000 0.308 0.204 0.024
#> GSM213091 4 0.4829 0.55502 0.044 0.000 0.012 0.744 0.076 0.124
#> GSM213092 1 0.2356 0.63959 0.884 0.000 0.000 0.096 0.004 0.016
#> GSM213096 1 0.1737 0.59608 0.932 0.000 0.000 0.008 0.020 0.040
#> GSM213100 1 0.1370 0.62887 0.948 0.000 0.000 0.036 0.004 0.012
#> GSM213111 2 0.5272 0.38448 0.000 0.596 0.000 0.004 0.276 0.124
#> GSM213117 4 0.2871 0.76384 0.192 0.004 0.000 0.804 0.000 0.000
#> GSM213118 1 0.4370 0.43628 0.640 0.000 0.000 0.324 0.032 0.004
#> GSM213120 2 0.6119 0.08412 0.004 0.432 0.004 0.000 0.360 0.200
#> GSM213122 2 0.0363 0.67246 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM213074 4 0.4093 0.67896 0.076 0.000 0.016 0.804 0.028 0.076
#> GSM213077 1 0.2445 0.63844 0.868 0.000 0.000 0.120 0.004 0.008
#> GSM213083 1 0.2517 0.63901 0.876 0.000 0.000 0.100 0.008 0.016
#> GSM213094 3 0.4920 0.76340 0.004 0.000 0.696 0.024 0.200 0.076
#> GSM213095 6 0.4820 0.67506 0.000 0.088 0.004 0.000 0.256 0.652
#> GSM213102 4 0.4389 0.17749 0.468 0.000 0.000 0.512 0.004 0.016
#> GSM213103 5 0.6879 -0.03520 0.200 0.280 0.000 0.036 0.464 0.020
#> GSM213104 5 0.6293 0.11840 0.348 0.000 0.000 0.080 0.488 0.084
#> GSM213107 6 0.5203 0.73932 0.000 0.184 0.004 0.000 0.180 0.632
#> GSM213108 2 0.4959 0.43568 0.000 0.616 0.000 0.008 0.304 0.072
#> GSM213112 1 0.4661 0.44618 0.620 0.000 0.000 0.332 0.036 0.012
#> GSM213114 1 0.5478 0.14840 0.600 0.000 0.000 0.024 0.276 0.100
#> GSM213115 2 0.1341 0.66742 0.000 0.948 0.000 0.000 0.028 0.024
#> GSM213116 4 0.3073 0.75680 0.204 0.000 0.000 0.788 0.000 0.008
#> GSM213119 2 0.0260 0.67198 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM213072 4 0.3300 0.69602 0.076 0.000 0.000 0.840 0.016 0.068
#> GSM213075 4 0.4924 0.65490 0.184 0.016 0.000 0.696 0.100 0.004
#> GSM213076 2 0.6048 0.08193 0.000 0.460 0.004 0.000 0.288 0.248
#> GSM213079 3 0.0405 0.90710 0.000 0.000 0.988 0.004 0.008 0.000
#> GSM213080 1 0.5652 -0.06334 0.516 0.000 0.000 0.024 0.372 0.088
#> GSM213081 1 0.3947 0.54590 0.788 0.000 0.000 0.084 0.112 0.016
#> GSM213084 1 0.0551 0.61452 0.984 0.000 0.000 0.004 0.004 0.008
#> GSM213087 2 0.0405 0.67281 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM213089 4 0.2915 0.76694 0.184 0.000 0.000 0.808 0.000 0.008
#> GSM213090 3 0.1036 0.90204 0.000 0.000 0.964 0.004 0.008 0.024
#> GSM213093 4 0.3329 0.73718 0.220 0.000 0.000 0.768 0.004 0.008
#> GSM213097 1 0.4187 0.28567 0.624 0.000 0.000 0.356 0.004 0.016
#> GSM213099 4 0.4244 0.61061 0.048 0.000 0.004 0.784 0.056 0.108
#> GSM213101 1 0.3044 0.59111 0.864 0.000 0.000 0.048 0.036 0.052
#> GSM213105 2 0.0260 0.67198 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM213109 1 0.4138 0.22440 0.616 0.000 0.000 0.368 0.004 0.012
#> GSM213110 2 0.6140 0.15896 0.048 0.444 0.000 0.020 0.436 0.052
#> GSM213113 5 0.7426 0.09206 0.292 0.000 0.052 0.308 0.324 0.024
#> GSM213121 6 0.5376 0.49159 0.000 0.408 0.000 0.000 0.112 0.480
#> GSM213123 1 0.4393 0.01178 0.532 0.000 0.000 0.448 0.012 0.008
#> GSM213125 2 0.0603 0.67103 0.000 0.980 0.000 0.000 0.016 0.004
#> GSM213073 3 0.0692 0.90387 0.000 0.000 0.976 0.004 0.020 0.000
#> GSM213086 1 0.2592 0.63634 0.864 0.000 0.000 0.116 0.004 0.016
#> GSM213098 1 0.6094 -0.05458 0.488 0.000 0.000 0.112 0.360 0.040
#> GSM213106 4 0.2933 0.76207 0.200 0.000 0.000 0.796 0.004 0.000
#> GSM213124 5 0.6029 0.13939 0.024 0.052 0.000 0.404 0.484 0.036
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 development.stage(p) disease.state(p) k
#> CV:mclust 49 0.773 0.704 2
#> CV:mclust 53 0.453 0.821 3
#> CV:mclust 36 0.378 0.899 4
#> CV:mclust 32 0.501 0.911 5
#> CV:mclust 33 0.417 0.360 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "NMF"]
# you can also extract it by
# res = res_list["CV:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.922 0.944 0.977 0.4427 0.560 0.560
#> 3 3 0.551 0.736 0.870 0.4869 0.743 0.553
#> 4 4 0.502 0.580 0.774 0.1258 0.817 0.527
#> 5 5 0.524 0.466 0.699 0.0698 0.888 0.620
#> 6 6 0.560 0.397 0.630 0.0429 0.920 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
#> GSM213078 1 0.0000 0.978 1.000 0.000
#> GSM213082 2 0.0000 0.969 0.000 1.000
#> GSM213085 1 0.0000 0.978 1.000 0.000
#> GSM213088 1 0.6148 0.815 0.848 0.152
#> GSM213091 1 0.0000 0.978 1.000 0.000
#> GSM213092 1 0.0000 0.978 1.000 0.000
#> GSM213096 1 0.0000 0.978 1.000 0.000
#> GSM213100 1 0.0000 0.978 1.000 0.000
#> GSM213111 2 0.0000 0.969 0.000 1.000
#> GSM213117 1 0.0000 0.978 1.000 0.000
#> GSM213118 1 0.0000 0.978 1.000 0.000
#> GSM213120 2 0.0000 0.969 0.000 1.000
#> GSM213122 2 0.0000 0.969 0.000 1.000
#> GSM213074 1 0.0000 0.978 1.000 0.000
#> GSM213077 1 0.0000 0.978 1.000 0.000
#> GSM213083 1 0.0000 0.978 1.000 0.000
#> GSM213094 1 0.0000 0.978 1.000 0.000
#> GSM213095 2 0.0000 0.969 0.000 1.000
#> GSM213102 1 0.0000 0.978 1.000 0.000
#> GSM213103 2 0.4815 0.866 0.104 0.896
#> GSM213104 1 0.9393 0.435 0.644 0.356
#> GSM213107 2 0.0000 0.969 0.000 1.000
#> GSM213108 2 0.0000 0.969 0.000 1.000
#> GSM213112 1 0.0000 0.978 1.000 0.000
#> GSM213114 1 0.0000 0.978 1.000 0.000
#> GSM213115 2 0.0000 0.969 0.000 1.000
#> GSM213116 1 0.0000 0.978 1.000 0.000
#> GSM213119 2 0.0000 0.969 0.000 1.000
#> GSM213072 1 0.0000 0.978 1.000 0.000
#> GSM213075 1 0.0000 0.978 1.000 0.000
#> GSM213076 2 0.0000 0.969 0.000 1.000
#> GSM213079 1 0.0000 0.978 1.000 0.000
#> GSM213080 2 0.9522 0.394 0.372 0.628
#> GSM213081 1 0.0000 0.978 1.000 0.000
#> GSM213084 1 0.0000 0.978 1.000 0.000
#> GSM213087 2 0.0000 0.969 0.000 1.000
#> GSM213089 1 0.0000 0.978 1.000 0.000
#> GSM213090 1 0.0000 0.978 1.000 0.000
#> GSM213093 1 0.0000 0.978 1.000 0.000
#> GSM213097 1 0.0000 0.978 1.000 0.000
#> GSM213099 1 0.0000 0.978 1.000 0.000
#> GSM213101 1 0.0000 0.978 1.000 0.000
#> GSM213105 2 0.0000 0.969 0.000 1.000
#> GSM213109 1 0.0000 0.978 1.000 0.000
#> GSM213110 2 0.0000 0.969 0.000 1.000
#> GSM213113 1 0.0000 0.978 1.000 0.000
#> GSM213121 2 0.0000 0.969 0.000 1.000
#> GSM213123 1 0.0000 0.978 1.000 0.000
#> GSM213125 2 0.0000 0.969 0.000 1.000
#> GSM213073 1 0.0000 0.978 1.000 0.000
#> GSM213086 1 0.0000 0.978 1.000 0.000
#> GSM213098 1 0.0376 0.975 0.996 0.004
#> GSM213106 1 0.0000 0.978 1.000 0.000
#> GSM213124 1 0.7950 0.679 0.760 0.240
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.0000 0.8198 1.000 0.000 0.000
#> GSM213082 2 0.0000 0.9228 0.000 1.000 0.000
#> GSM213085 1 0.3340 0.7873 0.880 0.000 0.120
#> GSM213088 1 0.5576 0.7395 0.812 0.084 0.104
#> GSM213091 3 0.0237 0.7901 0.004 0.000 0.996
#> GSM213092 1 0.2356 0.8099 0.928 0.000 0.072
#> GSM213096 1 0.0000 0.8198 1.000 0.000 0.000
#> GSM213100 1 0.0237 0.8207 0.996 0.000 0.004
#> GSM213111 2 0.1860 0.9010 0.000 0.948 0.052
#> GSM213117 1 0.6008 0.5045 0.628 0.000 0.372
#> GSM213118 1 0.1964 0.8203 0.944 0.000 0.056
#> GSM213120 2 0.0661 0.9195 0.004 0.988 0.008
#> GSM213122 2 0.0000 0.9228 0.000 1.000 0.000
#> GSM213074 3 0.3941 0.7576 0.156 0.000 0.844
#> GSM213077 1 0.3879 0.7650 0.848 0.000 0.152
#> GSM213083 1 0.0592 0.8219 0.988 0.000 0.012
#> GSM213094 3 0.0000 0.7893 0.000 0.000 1.000
#> GSM213095 2 0.3340 0.8447 0.000 0.880 0.120
#> GSM213102 1 0.4654 0.7239 0.792 0.000 0.208
#> GSM213103 2 0.4750 0.7286 0.216 0.784 0.000
#> GSM213104 1 0.5200 0.6450 0.796 0.184 0.020
#> GSM213107 2 0.0237 0.9216 0.000 0.996 0.004
#> GSM213108 2 0.6295 0.2379 0.000 0.528 0.472
#> GSM213112 1 0.6045 0.3841 0.620 0.000 0.380
#> GSM213114 1 0.0000 0.8198 1.000 0.000 0.000
#> GSM213115 2 0.0000 0.9228 0.000 1.000 0.000
#> GSM213116 3 0.6295 -0.0441 0.472 0.000 0.528
#> GSM213119 2 0.0000 0.9228 0.000 1.000 0.000
#> GSM213072 3 0.5785 0.6149 0.332 0.000 0.668
#> GSM213075 3 0.5560 0.6557 0.300 0.000 0.700
#> GSM213076 2 0.2165 0.8947 0.000 0.936 0.064
#> GSM213079 3 0.1031 0.7901 0.024 0.000 0.976
#> GSM213080 1 0.1015 0.8185 0.980 0.008 0.012
#> GSM213081 1 0.3116 0.7849 0.892 0.000 0.108
#> GSM213084 1 0.0237 0.8206 0.996 0.000 0.004
#> GSM213087 2 0.0000 0.9228 0.000 1.000 0.000
#> GSM213089 3 0.3267 0.7685 0.116 0.000 0.884
#> GSM213090 3 0.0000 0.7893 0.000 0.000 1.000
#> GSM213093 3 0.4178 0.7496 0.172 0.000 0.828
#> GSM213097 1 0.6026 0.4985 0.624 0.000 0.376
#> GSM213099 3 0.0237 0.7901 0.004 0.000 0.996
#> GSM213101 1 0.0000 0.8198 1.000 0.000 0.000
#> GSM213105 2 0.0000 0.9228 0.000 1.000 0.000
#> GSM213109 1 0.3116 0.8032 0.892 0.000 0.108
#> GSM213110 2 0.4452 0.7611 0.192 0.808 0.000
#> GSM213113 3 0.4178 0.7352 0.172 0.000 0.828
#> GSM213121 2 0.0000 0.9228 0.000 1.000 0.000
#> GSM213123 3 0.6274 0.2193 0.456 0.000 0.544
#> GSM213125 2 0.0000 0.9228 0.000 1.000 0.000
#> GSM213073 3 0.1860 0.7855 0.052 0.000 0.948
#> GSM213086 1 0.1643 0.8205 0.956 0.000 0.044
#> GSM213098 3 0.4887 0.7094 0.228 0.000 0.772
#> GSM213106 1 0.6026 0.4962 0.624 0.000 0.376
#> GSM213124 1 0.9820 0.1291 0.428 0.296 0.276
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.1975 0.8025 0.936 0.000 0.016 0.048
#> GSM213082 2 0.0779 0.8648 0.000 0.980 0.004 0.016
#> GSM213085 1 0.4700 0.7562 0.792 0.000 0.124 0.084
#> GSM213088 1 0.6625 0.3787 0.588 0.036 0.036 0.340
#> GSM213091 4 0.3907 0.3348 0.000 0.000 0.232 0.768
#> GSM213092 1 0.3697 0.7883 0.852 0.000 0.100 0.048
#> GSM213096 1 0.1824 0.7926 0.936 0.000 0.060 0.004
#> GSM213100 1 0.2342 0.7999 0.912 0.000 0.008 0.080
#> GSM213111 2 0.1488 0.8616 0.000 0.956 0.032 0.012
#> GSM213117 4 0.4853 0.5577 0.220 0.000 0.036 0.744
#> GSM213118 1 0.4831 0.6978 0.752 0.000 0.040 0.208
#> GSM213120 2 0.2867 0.8349 0.000 0.884 0.104 0.012
#> GSM213122 2 0.0524 0.8673 0.000 0.988 0.004 0.008
#> GSM213074 4 0.3647 0.5400 0.040 0.000 0.108 0.852
#> GSM213077 1 0.3307 0.7807 0.868 0.000 0.028 0.104
#> GSM213083 1 0.2402 0.8002 0.912 0.000 0.012 0.076
#> GSM213094 4 0.4713 0.0598 0.000 0.000 0.360 0.640
#> GSM213095 3 0.5441 0.1329 0.008 0.332 0.644 0.016
#> GSM213102 4 0.5781 -0.1280 0.484 0.000 0.028 0.488
#> GSM213103 2 0.8501 0.3197 0.220 0.480 0.252 0.048
#> GSM213104 3 0.5139 0.1487 0.380 0.004 0.612 0.004
#> GSM213107 2 0.4677 0.6455 0.004 0.680 0.316 0.000
#> GSM213108 4 0.6885 0.0634 0.000 0.436 0.104 0.460
#> GSM213112 1 0.7508 0.3406 0.496 0.000 0.272 0.232
#> GSM213114 1 0.1940 0.7815 0.924 0.000 0.076 0.000
#> GSM213115 2 0.0376 0.8684 0.004 0.992 0.004 0.000
#> GSM213116 4 0.4079 0.5792 0.180 0.000 0.020 0.800
#> GSM213119 2 0.0188 0.8685 0.000 0.996 0.000 0.004
#> GSM213072 4 0.5272 0.5032 0.172 0.000 0.084 0.744
#> GSM213075 4 0.5653 0.4372 0.096 0.000 0.192 0.712
#> GSM213076 2 0.4922 0.7119 0.000 0.736 0.228 0.036
#> GSM213079 3 0.5039 0.3842 0.004 0.000 0.592 0.404
#> GSM213080 1 0.3743 0.7097 0.824 0.000 0.160 0.016
#> GSM213081 1 0.4464 0.6692 0.768 0.000 0.208 0.024
#> GSM213084 1 0.1489 0.7945 0.952 0.000 0.044 0.004
#> GSM213087 2 0.0469 0.8674 0.000 0.988 0.012 0.000
#> GSM213089 4 0.2282 0.5411 0.024 0.000 0.052 0.924
#> GSM213090 3 0.4948 0.3014 0.000 0.000 0.560 0.440
#> GSM213093 4 0.4931 0.5467 0.092 0.000 0.132 0.776
#> GSM213097 4 0.5793 0.2208 0.384 0.000 0.036 0.580
#> GSM213099 4 0.4103 0.2873 0.000 0.000 0.256 0.744
#> GSM213101 1 0.2675 0.7853 0.892 0.000 0.008 0.100
#> GSM213105 2 0.0188 0.8683 0.000 0.996 0.004 0.000
#> GSM213109 1 0.5168 0.6294 0.712 0.000 0.040 0.248
#> GSM213110 2 0.4333 0.6789 0.208 0.776 0.008 0.008
#> GSM213113 3 0.6548 0.4589 0.104 0.000 0.592 0.304
#> GSM213121 2 0.3024 0.8060 0.000 0.852 0.148 0.000
#> GSM213123 4 0.6746 0.3998 0.316 0.000 0.116 0.568
#> GSM213125 2 0.0188 0.8685 0.000 0.996 0.000 0.004
#> GSM213073 3 0.4877 0.4719 0.008 0.000 0.664 0.328
#> GSM213086 1 0.3895 0.7665 0.832 0.000 0.036 0.132
#> GSM213098 3 0.4532 0.4858 0.156 0.000 0.792 0.052
#> GSM213106 4 0.4574 0.5639 0.220 0.000 0.024 0.756
#> GSM213124 4 0.7654 0.4460 0.128 0.176 0.076 0.620
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.1644 0.7143 0.940 0.000 0.008 0.048 0.004
#> GSM213082 2 0.0798 0.7999 0.000 0.976 0.000 0.016 0.008
#> GSM213085 1 0.7355 0.2527 0.452 0.000 0.248 0.040 0.260
#> GSM213088 4 0.5548 -0.0194 0.456 0.016 0.000 0.492 0.036
#> GSM213091 4 0.4823 0.4496 0.000 0.000 0.276 0.672 0.052
#> GSM213092 1 0.5971 0.5492 0.644 0.000 0.168 0.020 0.168
#> GSM213096 1 0.3975 0.6945 0.816 0.000 0.020 0.048 0.116
#> GSM213100 1 0.3495 0.7121 0.852 0.000 0.020 0.048 0.080
#> GSM213111 2 0.2452 0.7698 0.000 0.908 0.012 0.028 0.052
#> GSM213117 4 0.2894 0.5786 0.084 0.000 0.004 0.876 0.036
#> GSM213118 1 0.6044 0.5773 0.624 0.000 0.020 0.128 0.228
#> GSM213120 2 0.5489 0.5636 0.000 0.700 0.024 0.120 0.156
#> GSM213122 2 0.0671 0.8026 0.000 0.980 0.000 0.004 0.016
#> GSM213074 4 0.7392 0.2184 0.040 0.000 0.220 0.424 0.316
#> GSM213077 1 0.4043 0.6405 0.788 0.000 0.012 0.168 0.032
#> GSM213083 1 0.1885 0.7229 0.936 0.000 0.012 0.020 0.032
#> GSM213094 4 0.5215 0.3061 0.000 0.000 0.372 0.576 0.052
#> GSM213095 3 0.6171 0.1206 0.008 0.156 0.580 0.000 0.256
#> GSM213102 1 0.5372 0.1116 0.504 0.000 0.004 0.448 0.044
#> GSM213103 5 0.8615 0.2386 0.188 0.224 0.048 0.100 0.440
#> GSM213104 5 0.6848 0.0364 0.232 0.008 0.316 0.000 0.444
#> GSM213107 5 0.6247 -0.0558 0.000 0.424 0.144 0.000 0.432
#> GSM213108 2 0.7372 0.1827 0.000 0.524 0.092 0.160 0.224
#> GSM213112 3 0.7477 0.1077 0.268 0.000 0.412 0.040 0.280
#> GSM213114 1 0.2959 0.6814 0.864 0.000 0.016 0.008 0.112
#> GSM213115 2 0.0404 0.8030 0.000 0.988 0.000 0.000 0.012
#> GSM213116 4 0.3670 0.5766 0.080 0.000 0.016 0.840 0.064
#> GSM213119 2 0.0451 0.8034 0.000 0.988 0.000 0.004 0.008
#> GSM213072 4 0.7819 0.2837 0.132 0.000 0.168 0.472 0.228
#> GSM213075 4 0.7481 0.3133 0.092 0.000 0.276 0.488 0.144
#> GSM213076 2 0.6793 0.3868 0.000 0.596 0.100 0.100 0.204
#> GSM213079 3 0.2629 0.4871 0.000 0.000 0.860 0.136 0.004
#> GSM213080 1 0.5272 0.4227 0.624 0.004 0.000 0.060 0.312
#> GSM213081 1 0.7412 0.3875 0.540 0.000 0.168 0.160 0.132
#> GSM213084 1 0.2040 0.7130 0.928 0.000 0.032 0.008 0.032
#> GSM213087 2 0.0290 0.8015 0.000 0.992 0.000 0.000 0.008
#> GSM213089 4 0.2769 0.5681 0.024 0.000 0.064 0.892 0.020
#> GSM213090 3 0.4218 0.4453 0.004 0.000 0.760 0.040 0.196
#> GSM213093 4 0.6582 0.4634 0.068 0.000 0.212 0.608 0.112
#> GSM213097 4 0.5813 0.2890 0.344 0.000 0.016 0.572 0.068
#> GSM213099 4 0.4431 0.4753 0.000 0.000 0.216 0.732 0.052
#> GSM213101 1 0.1956 0.7131 0.916 0.000 0.000 0.076 0.008
#> GSM213105 2 0.0000 0.8024 0.000 1.000 0.000 0.000 0.000
#> GSM213109 1 0.5467 0.6467 0.692 0.000 0.020 0.104 0.184
#> GSM213110 2 0.3628 0.5476 0.216 0.772 0.000 0.000 0.012
#> GSM213113 3 0.6981 0.2530 0.032 0.000 0.512 0.256 0.200
#> GSM213121 2 0.4178 0.5067 0.000 0.696 0.008 0.004 0.292
#> GSM213123 4 0.7089 0.4271 0.196 0.000 0.140 0.568 0.096
#> GSM213125 2 0.0324 0.8030 0.000 0.992 0.000 0.004 0.004
#> GSM213073 3 0.4022 0.4542 0.000 0.000 0.796 0.104 0.100
#> GSM213086 1 0.4319 0.6914 0.784 0.000 0.012 0.064 0.140
#> GSM213098 5 0.6735 -0.1330 0.048 0.000 0.412 0.088 0.452
#> GSM213106 4 0.3467 0.5656 0.128 0.000 0.004 0.832 0.036
#> GSM213124 5 0.9113 -0.1050 0.088 0.236 0.072 0.288 0.316
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.3518 0.6015 0.840 0.000 0.008 0.072 0.048 0.032
#> GSM213082 2 0.2082 0.7567 0.000 0.924 0.016 0.024 0.016 0.020
#> GSM213085 6 0.6818 -0.0653 0.360 0.000 0.224 0.004 0.040 0.372
#> GSM213088 4 0.6192 0.2670 0.340 0.008 0.012 0.532 0.052 0.056
#> GSM213091 4 0.5718 0.3387 0.000 0.000 0.276 0.556 0.012 0.156
#> GSM213092 1 0.6780 0.3126 0.540 0.000 0.192 0.024 0.056 0.188
#> GSM213096 1 0.4994 0.4418 0.648 0.000 0.004 0.000 0.120 0.228
#> GSM213100 1 0.4751 0.4703 0.684 0.000 0.020 0.008 0.040 0.248
#> GSM213111 2 0.3938 0.7022 0.000 0.812 0.012 0.052 0.092 0.032
#> GSM213117 4 0.5464 0.4036 0.092 0.000 0.016 0.612 0.008 0.272
#> GSM213118 6 0.6805 0.2060 0.292 0.000 0.004 0.068 0.168 0.468
#> GSM213120 2 0.6988 0.2730 0.008 0.496 0.032 0.212 0.228 0.024
#> GSM213122 2 0.0405 0.7727 0.000 0.988 0.000 0.008 0.000 0.004
#> GSM213074 6 0.5077 0.4085 0.048 0.000 0.128 0.088 0.012 0.724
#> GSM213077 1 0.3682 0.5742 0.796 0.000 0.028 0.156 0.004 0.016
#> GSM213083 1 0.3182 0.6239 0.868 0.000 0.024 0.032 0.032 0.044
#> GSM213094 4 0.6645 0.1385 0.000 0.000 0.364 0.388 0.040 0.208
#> GSM213095 3 0.6495 0.1043 0.024 0.124 0.528 0.000 0.288 0.036
#> GSM213102 4 0.6073 0.1921 0.372 0.000 0.012 0.484 0.016 0.116
#> GSM213103 6 0.7171 0.1737 0.108 0.076 0.016 0.012 0.352 0.436
#> GSM213104 5 0.5579 0.2160 0.256 0.000 0.176 0.000 0.564 0.004
#> GSM213107 5 0.4710 0.2540 0.000 0.276 0.052 0.008 0.660 0.004
#> GSM213108 2 0.6858 0.3686 0.000 0.548 0.136 0.100 0.020 0.196
#> GSM213112 3 0.7468 -0.1762 0.296 0.000 0.312 0.024 0.056 0.312
#> GSM213114 1 0.3469 0.5737 0.792 0.000 0.004 0.012 0.180 0.012
#> GSM213115 2 0.1391 0.7683 0.000 0.944 0.000 0.000 0.016 0.040
#> GSM213116 4 0.5993 0.2446 0.080 0.000 0.020 0.496 0.020 0.384
#> GSM213119 2 0.0810 0.7725 0.000 0.976 0.004 0.004 0.008 0.008
#> GSM213072 6 0.6009 0.4169 0.096 0.000 0.056 0.108 0.068 0.672
#> GSM213075 6 0.7665 0.0792 0.056 0.004 0.236 0.188 0.064 0.452
#> GSM213076 2 0.7145 0.2181 0.004 0.488 0.116 0.140 0.244 0.008
#> GSM213079 3 0.3931 0.3799 0.000 0.000 0.800 0.100 0.064 0.036
#> GSM213080 1 0.5757 0.3181 0.548 0.004 0.008 0.076 0.344 0.020
#> GSM213081 1 0.7759 0.0942 0.436 0.000 0.108 0.240 0.168 0.048
#> GSM213084 1 0.2908 0.6175 0.872 0.000 0.064 0.004 0.044 0.016
#> GSM213087 2 0.1340 0.7652 0.000 0.948 0.000 0.008 0.040 0.004
#> GSM213089 4 0.3523 0.4835 0.016 0.000 0.020 0.812 0.008 0.144
#> GSM213090 3 0.4235 0.4018 0.012 0.000 0.776 0.032 0.036 0.144
#> GSM213093 4 0.7653 0.2635 0.084 0.000 0.196 0.452 0.052 0.216
#> GSM213097 4 0.5355 0.4307 0.240 0.000 0.024 0.656 0.024 0.056
#> GSM213099 4 0.5410 0.4068 0.000 0.000 0.192 0.636 0.020 0.152
#> GSM213101 1 0.3324 0.6091 0.832 0.000 0.000 0.084 0.008 0.076
#> GSM213105 2 0.0405 0.7716 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM213109 1 0.5831 0.3551 0.572 0.000 0.040 0.076 0.008 0.304
#> GSM213110 2 0.4013 0.6108 0.176 0.768 0.000 0.004 0.020 0.032
#> GSM213113 5 0.7803 0.0650 0.032 0.000 0.296 0.196 0.368 0.108
#> GSM213121 2 0.4127 0.3671 0.000 0.588 0.000 0.008 0.400 0.004
#> GSM213123 4 0.7259 0.3459 0.164 0.000 0.104 0.540 0.132 0.060
#> GSM213125 2 0.0291 0.7716 0.000 0.992 0.004 0.000 0.004 0.000
#> GSM213073 3 0.4779 0.2817 0.000 0.000 0.704 0.092 0.184 0.020
#> GSM213086 1 0.5486 0.3849 0.604 0.000 0.024 0.044 0.024 0.304
#> GSM213098 5 0.5626 0.3559 0.004 0.000 0.144 0.104 0.668 0.080
#> GSM213106 4 0.4057 0.5027 0.132 0.000 0.004 0.776 0.008 0.080
#> GSM213124 6 0.5748 0.4297 0.080 0.076 0.060 0.048 0.020 0.716
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 development.stage(p) disease.state(p) k
#> CV:NMF 52 0.4734 1.000 2
#> CV:NMF 47 0.0336 0.989 3
#> CV:NMF 35 0.7532 0.632 4
#> CV:NMF 27 0.7726 0.457 5
#> CV:NMF 16 0.4602 0.227 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "hclust"]
# you can also extract it by
# res = res_list["MAD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.358 0.797 0.870 0.4059 0.591 0.591
#> 3 3 0.399 0.750 0.857 0.3050 0.902 0.835
#> 4 4 0.464 0.712 0.866 0.0819 0.973 0.946
#> 5 5 0.413 0.627 0.786 0.1177 1.000 1.000
#> 6 6 0.476 0.226 0.683 0.0743 0.930 0.851
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
#> GSM213078 1 0.2423 0.872 0.960 0.040
#> GSM213082 2 0.5294 0.903 0.120 0.880
#> GSM213085 1 0.4022 0.864 0.920 0.080
#> GSM213088 1 0.2236 0.872 0.964 0.036
#> GSM213091 1 0.3584 0.829 0.932 0.068
#> GSM213092 1 0.3879 0.865 0.924 0.076
#> GSM213096 1 0.3879 0.866 0.924 0.076
#> GSM213100 1 0.3879 0.866 0.924 0.076
#> GSM213111 2 0.6531 0.882 0.168 0.832
#> GSM213117 1 0.2423 0.871 0.960 0.040
#> GSM213118 1 0.6438 0.793 0.836 0.164
#> GSM213120 2 0.9552 0.526 0.376 0.624
#> GSM213122 2 0.4815 0.904 0.104 0.896
#> GSM213074 1 0.3584 0.829 0.932 0.068
#> GSM213077 1 0.3879 0.866 0.924 0.076
#> GSM213083 1 0.3879 0.866 0.924 0.076
#> GSM213094 1 0.4690 0.803 0.900 0.100
#> GSM213095 2 0.9944 0.299 0.456 0.544
#> GSM213102 1 0.0376 0.866 0.996 0.004
#> GSM213103 1 0.9795 0.220 0.584 0.416
#> GSM213104 1 0.9686 0.327 0.604 0.396
#> GSM213107 2 0.4690 0.903 0.100 0.900
#> GSM213108 2 0.6048 0.892 0.148 0.852
#> GSM213112 1 0.4022 0.864 0.920 0.080
#> GSM213114 1 0.8813 0.582 0.700 0.300
#> GSM213115 2 0.6712 0.875 0.176 0.824
#> GSM213116 1 0.2423 0.871 0.960 0.040
#> GSM213119 2 0.4815 0.904 0.104 0.896
#> GSM213072 1 0.3733 0.831 0.928 0.072
#> GSM213075 1 0.3584 0.851 0.932 0.068
#> GSM213076 2 0.7674 0.812 0.224 0.776
#> GSM213079 1 0.4690 0.803 0.900 0.100
#> GSM213080 1 0.8813 0.582 0.700 0.300
#> GSM213081 1 0.3879 0.869 0.924 0.076
#> GSM213084 1 0.3733 0.867 0.928 0.072
#> GSM213087 2 0.4690 0.903 0.100 0.900
#> GSM213089 1 0.0672 0.868 0.992 0.008
#> GSM213090 1 0.4690 0.803 0.900 0.100
#> GSM213093 1 0.0376 0.866 0.996 0.004
#> GSM213097 1 0.0376 0.866 0.996 0.004
#> GSM213099 1 0.4161 0.817 0.916 0.084
#> GSM213101 1 0.2236 0.872 0.964 0.036
#> GSM213105 2 0.4815 0.904 0.104 0.896
#> GSM213109 1 0.2948 0.871 0.948 0.052
#> GSM213110 2 0.6801 0.872 0.180 0.820
#> GSM213113 1 0.6148 0.813 0.848 0.152
#> GSM213121 2 0.4690 0.903 0.100 0.900
#> GSM213123 1 0.4022 0.868 0.920 0.080
#> GSM213125 2 0.4815 0.904 0.104 0.896
#> GSM213073 1 0.4690 0.803 0.900 0.100
#> GSM213086 1 0.5519 0.830 0.872 0.128
#> GSM213098 1 0.9323 0.469 0.652 0.348
#> GSM213106 1 0.2043 0.871 0.968 0.032
#> GSM213124 1 0.9170 0.455 0.668 0.332
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.165 0.8143 0.960 0.004 0.036
#> GSM213082 2 0.240 0.8882 0.064 0.932 0.004
#> GSM213085 1 0.195 0.8179 0.952 0.040 0.008
#> GSM213088 1 0.176 0.8132 0.956 0.004 0.040
#> GSM213091 1 0.546 0.6718 0.788 0.028 0.184
#> GSM213092 1 0.183 0.8185 0.956 0.036 0.008
#> GSM213096 1 0.188 0.8173 0.956 0.032 0.012
#> GSM213100 1 0.188 0.8173 0.956 0.032 0.012
#> GSM213111 2 0.377 0.8661 0.104 0.880 0.016
#> GSM213117 1 0.343 0.8067 0.904 0.032 0.064
#> GSM213118 1 0.434 0.7539 0.856 0.120 0.024
#> GSM213120 2 0.663 0.5143 0.336 0.644 0.020
#> GSM213122 2 0.207 0.8897 0.060 0.940 0.000
#> GSM213074 1 0.512 0.6978 0.812 0.028 0.160
#> GSM213077 1 0.153 0.8182 0.964 0.032 0.004
#> GSM213083 1 0.153 0.8182 0.964 0.032 0.004
#> GSM213094 3 0.547 0.7744 0.168 0.036 0.796
#> GSM213095 2 0.816 0.3712 0.084 0.568 0.348
#> GSM213102 1 0.303 0.7896 0.904 0.004 0.092
#> GSM213103 1 0.640 0.2987 0.580 0.416 0.004
#> GSM213104 1 0.731 0.3263 0.580 0.384 0.036
#> GSM213107 2 0.141 0.8762 0.036 0.964 0.000
#> GSM213108 2 0.362 0.8765 0.072 0.896 0.032
#> GSM213112 1 0.212 0.8169 0.948 0.040 0.012
#> GSM213114 1 0.663 0.5583 0.692 0.272 0.036
#> GSM213115 2 0.410 0.8404 0.140 0.852 0.008
#> GSM213116 1 0.337 0.8039 0.904 0.024 0.072
#> GSM213119 2 0.207 0.8897 0.060 0.940 0.000
#> GSM213072 1 0.474 0.7242 0.836 0.028 0.136
#> GSM213075 1 0.421 0.7590 0.856 0.016 0.128
#> GSM213076 2 0.463 0.7874 0.164 0.824 0.012
#> GSM213079 3 0.455 0.9181 0.200 0.000 0.800
#> GSM213080 1 0.663 0.5583 0.692 0.272 0.036
#> GSM213081 1 0.231 0.8137 0.944 0.024 0.032
#> GSM213084 1 0.158 0.8191 0.964 0.028 0.008
#> GSM213087 2 0.153 0.8803 0.040 0.960 0.000
#> GSM213089 1 0.312 0.7851 0.892 0.000 0.108
#> GSM213090 3 0.445 0.9161 0.192 0.000 0.808
#> GSM213093 1 0.295 0.7922 0.908 0.004 0.088
#> GSM213097 1 0.295 0.7908 0.908 0.004 0.088
#> GSM213099 1 0.726 -0.0462 0.528 0.028 0.444
#> GSM213101 1 0.176 0.8132 0.956 0.004 0.040
#> GSM213105 2 0.207 0.8897 0.060 0.940 0.000
#> GSM213109 1 0.164 0.8194 0.964 0.016 0.020
#> GSM213110 2 0.426 0.8390 0.140 0.848 0.012
#> GSM213113 1 0.489 0.7586 0.840 0.112 0.048
#> GSM213121 2 0.153 0.8803 0.040 0.960 0.000
#> GSM213123 1 0.243 0.8199 0.940 0.036 0.024
#> GSM213125 2 0.196 0.8886 0.056 0.944 0.000
#> GSM213073 3 0.465 0.9130 0.208 0.000 0.792
#> GSM213086 1 0.295 0.7911 0.908 0.088 0.004
#> GSM213098 1 0.698 0.4672 0.632 0.336 0.032
#> GSM213106 1 0.116 0.8142 0.972 0.000 0.028
#> GSM213124 1 0.682 0.4590 0.644 0.328 0.028
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.1940 0.7833 0.924 0.000 0.000 0.076
#> GSM213082 2 0.1398 0.8779 0.040 0.956 0.000 0.004
#> GSM213085 1 0.1284 0.7928 0.964 0.024 0.000 0.012
#> GSM213088 1 0.2011 0.7817 0.920 0.000 0.000 0.080
#> GSM213091 1 0.4599 0.5785 0.736 0.000 0.016 0.248
#> GSM213092 1 0.1174 0.7931 0.968 0.020 0.000 0.012
#> GSM213096 1 0.1174 0.7924 0.968 0.020 0.000 0.012
#> GSM213100 1 0.1174 0.7924 0.968 0.020 0.000 0.012
#> GSM213111 2 0.2522 0.8587 0.076 0.908 0.000 0.016
#> GSM213117 1 0.3221 0.7706 0.876 0.020 0.004 0.100
#> GSM213118 1 0.3706 0.7238 0.848 0.112 0.000 0.040
#> GSM213120 2 0.5453 0.4626 0.320 0.648 0.000 0.032
#> GSM213122 2 0.1118 0.8791 0.036 0.964 0.000 0.000
#> GSM213074 1 0.4122 0.6193 0.760 0.000 0.004 0.236
#> GSM213077 1 0.1174 0.7938 0.968 0.020 0.000 0.012
#> GSM213083 1 0.1174 0.7938 0.968 0.020 0.000 0.012
#> GSM213094 4 0.2685 -0.0346 0.044 0.004 0.040 0.912
#> GSM213095 2 0.5467 0.3273 0.008 0.584 0.400 0.008
#> GSM213102 1 0.2814 0.7503 0.868 0.000 0.000 0.132
#> GSM213103 1 0.5435 0.2702 0.564 0.420 0.000 0.016
#> GSM213104 1 0.6153 0.3148 0.576 0.376 0.008 0.040
#> GSM213107 2 0.0524 0.8572 0.004 0.988 0.000 0.008
#> GSM213108 2 0.2497 0.8692 0.040 0.924 0.016 0.020
#> GSM213112 1 0.1406 0.7916 0.960 0.024 0.000 0.016
#> GSM213114 1 0.5543 0.5143 0.696 0.256 0.008 0.040
#> GSM213115 2 0.3142 0.8162 0.132 0.860 0.000 0.008
#> GSM213116 1 0.3113 0.7677 0.876 0.012 0.004 0.108
#> GSM213119 2 0.1118 0.8791 0.036 0.964 0.000 0.000
#> GSM213072 1 0.3908 0.6551 0.784 0.000 0.004 0.212
#> GSM213075 1 0.3852 0.6999 0.808 0.012 0.000 0.180
#> GSM213076 2 0.3730 0.7670 0.144 0.836 0.004 0.016
#> GSM213079 3 0.0336 0.9857 0.008 0.000 0.992 0.000
#> GSM213080 1 0.5543 0.5143 0.696 0.256 0.008 0.040
#> GSM213081 1 0.1675 0.7856 0.948 0.004 0.004 0.044
#> GSM213084 1 0.1182 0.7943 0.968 0.016 0.000 0.016
#> GSM213087 2 0.0524 0.8639 0.008 0.988 0.000 0.004
#> GSM213089 1 0.3249 0.7395 0.852 0.000 0.008 0.140
#> GSM213090 3 0.0000 0.9838 0.000 0.000 1.000 0.000
#> GSM213093 1 0.2921 0.7472 0.860 0.000 0.000 0.140
#> GSM213097 1 0.2868 0.7484 0.864 0.000 0.000 0.136
#> GSM213099 4 0.5236 0.0916 0.432 0.000 0.008 0.560
#> GSM213101 1 0.2011 0.7817 0.920 0.000 0.000 0.080
#> GSM213105 2 0.1118 0.8791 0.036 0.964 0.000 0.000
#> GSM213109 1 0.1256 0.7940 0.964 0.008 0.000 0.028
#> GSM213110 2 0.3271 0.8147 0.132 0.856 0.000 0.012
#> GSM213113 1 0.4208 0.7238 0.840 0.096 0.016 0.048
#> GSM213121 2 0.0672 0.8617 0.008 0.984 0.000 0.008
#> GSM213123 1 0.1936 0.7944 0.940 0.032 0.000 0.028
#> GSM213125 2 0.1022 0.8780 0.032 0.968 0.000 0.000
#> GSM213073 3 0.0804 0.9829 0.008 0.000 0.980 0.012
#> GSM213086 1 0.2198 0.7659 0.920 0.072 0.000 0.008
#> GSM213098 1 0.5929 0.3977 0.620 0.332 0.004 0.044
#> GSM213106 1 0.1716 0.7846 0.936 0.000 0.000 0.064
#> GSM213124 1 0.5755 0.3723 0.624 0.332 0.000 0.044
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.3333 0.6734 0.788 0.004 0.000 0.000 NA
#> GSM213082 2 0.1934 0.8205 0.020 0.932 0.000 0.008 NA
#> GSM213085 1 0.1725 0.6975 0.936 0.020 0.000 0.000 NA
#> GSM213088 1 0.3366 0.6713 0.784 0.004 0.000 0.000 NA
#> GSM213091 1 0.6143 0.4322 0.584 0.000 0.012 0.132 NA
#> GSM213092 1 0.1386 0.7025 0.952 0.016 0.000 0.000 NA
#> GSM213096 1 0.1300 0.7027 0.956 0.016 0.000 0.000 NA
#> GSM213100 1 0.1300 0.7027 0.956 0.016 0.000 0.000 NA
#> GSM213111 2 0.3787 0.8057 0.048 0.836 0.000 0.028 NA
#> GSM213117 1 0.4204 0.6681 0.768 0.016 0.004 0.016 NA
#> GSM213118 1 0.4714 0.6398 0.744 0.100 0.000 0.004 NA
#> GSM213120 2 0.5699 0.4799 0.264 0.608 0.000 0.000 NA
#> GSM213122 2 0.0566 0.8220 0.012 0.984 0.000 0.000 NA
#> GSM213074 1 0.5849 0.4603 0.596 0.000 0.004 0.120 NA
#> GSM213077 1 0.1386 0.7029 0.952 0.016 0.000 0.000 NA
#> GSM213083 1 0.1386 0.7029 0.952 0.016 0.000 0.000 NA
#> GSM213094 4 0.1651 -0.0468 0.008 0.000 0.012 0.944 NA
#> GSM213095 2 0.7328 0.1638 0.004 0.432 0.292 0.024 NA
#> GSM213102 1 0.4015 0.6304 0.724 0.004 0.000 0.008 NA
#> GSM213103 1 0.6336 0.2620 0.488 0.376 0.000 0.008 NA
#> GSM213104 1 0.6582 0.2696 0.496 0.280 0.000 0.004 NA
#> GSM213107 2 0.3779 0.7332 0.000 0.752 0.000 0.012 NA
#> GSM213108 2 0.3006 0.8106 0.020 0.888 0.008 0.028 NA
#> GSM213112 1 0.1800 0.6961 0.932 0.020 0.000 0.000 NA
#> GSM213114 1 0.5853 0.4565 0.624 0.184 0.000 0.004 NA
#> GSM213115 2 0.3150 0.7822 0.096 0.864 0.000 0.016 NA
#> GSM213116 1 0.4104 0.6683 0.772 0.012 0.004 0.016 NA
#> GSM213119 2 0.0727 0.8218 0.012 0.980 0.000 0.004 NA
#> GSM213072 1 0.5476 0.5181 0.632 0.000 0.004 0.088 NA
#> GSM213075 1 0.5348 0.5684 0.660 0.016 0.000 0.060 NA
#> GSM213076 2 0.4914 0.7019 0.108 0.712 0.000 0.000 NA
#> GSM213079 3 0.0324 0.9099 0.004 0.000 0.992 0.004 NA
#> GSM213080 1 0.5853 0.4565 0.624 0.184 0.000 0.004 NA
#> GSM213081 1 0.3522 0.6106 0.780 0.004 0.000 0.004 NA
#> GSM213084 1 0.1522 0.7061 0.944 0.012 0.000 0.000 NA
#> GSM213087 2 0.3234 0.7898 0.008 0.836 0.000 0.012 NA
#> GSM213089 1 0.4732 0.6281 0.720 0.004 0.004 0.048 NA
#> GSM213090 3 0.2561 0.8774 0.000 0.000 0.884 0.020 NA
#> GSM213093 1 0.4170 0.6213 0.712 0.004 0.000 0.012 NA
#> GSM213097 1 0.4064 0.6245 0.716 0.004 0.000 0.008 NA
#> GSM213099 4 0.6724 0.2020 0.296 0.000 0.004 0.460 NA
#> GSM213101 1 0.3366 0.6713 0.784 0.004 0.000 0.000 NA
#> GSM213105 2 0.0727 0.8218 0.012 0.980 0.000 0.004 NA
#> GSM213109 1 0.1740 0.7062 0.932 0.012 0.000 0.000 NA
#> GSM213110 2 0.3246 0.7808 0.096 0.860 0.000 0.020 NA
#> GSM213113 1 0.5160 0.5614 0.712 0.072 0.008 0.008 NA
#> GSM213121 2 0.3690 0.7414 0.000 0.764 0.000 0.012 NA
#> GSM213123 1 0.3370 0.6948 0.824 0.028 0.000 0.000 NA
#> GSM213125 2 0.0727 0.8225 0.012 0.980 0.000 0.004 NA
#> GSM213073 3 0.2570 0.8848 0.008 0.000 0.880 0.004 NA
#> GSM213086 1 0.2859 0.6690 0.876 0.056 0.000 0.000 NA
#> GSM213098 1 0.6607 0.3191 0.516 0.236 0.000 0.008 NA
#> GSM213106 1 0.3365 0.6781 0.808 0.004 0.000 0.008 NA
#> GSM213124 1 0.6524 0.3406 0.544 0.312 0.000 0.032 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.3894 -0.1888 0.664 0.004 0.000 0.324 0.008 0.000
#> GSM213082 2 0.3106 0.6317 0.024 0.852 0.000 0.020 0.100 0.004
#> GSM213085 1 0.1180 0.4161 0.960 0.012 0.000 0.016 0.012 0.000
#> GSM213088 1 0.3805 -0.1935 0.664 0.004 0.000 0.328 0.004 0.000
#> GSM213091 4 0.5060 0.8559 0.448 0.000 0.004 0.492 0.004 0.052
#> GSM213092 1 0.1332 0.4130 0.952 0.008 0.000 0.028 0.012 0.000
#> GSM213096 1 0.0972 0.4099 0.964 0.008 0.000 0.028 0.000 0.000
#> GSM213100 1 0.0972 0.4099 0.964 0.008 0.000 0.028 0.000 0.000
#> GSM213111 2 0.4775 0.5312 0.048 0.708 0.000 0.028 0.208 0.008
#> GSM213117 1 0.4286 -0.1862 0.660 0.012 0.000 0.312 0.008 0.008
#> GSM213118 1 0.5531 0.3062 0.684 0.064 0.000 0.160 0.076 0.016
#> GSM213120 2 0.6675 0.1313 0.228 0.500 0.000 0.056 0.212 0.004
#> GSM213122 2 0.1168 0.6570 0.016 0.956 0.000 0.000 0.028 0.000
#> GSM213074 4 0.5147 0.8511 0.464 0.000 0.004 0.476 0.012 0.044
#> GSM213077 1 0.0806 0.4095 0.972 0.008 0.000 0.020 0.000 0.000
#> GSM213083 1 0.0806 0.4095 0.972 0.008 0.000 0.020 0.000 0.000
#> GSM213094 6 0.1700 -0.0793 0.000 0.000 0.004 0.080 0.000 0.916
#> GSM213095 5 0.7696 0.2128 0.008 0.220 0.216 0.104 0.432 0.020
#> GSM213102 1 0.3872 -0.4296 0.604 0.004 0.000 0.392 0.000 0.000
#> GSM213103 1 0.7319 0.0301 0.412 0.288 0.000 0.144 0.152 0.004
#> GSM213104 1 0.6784 0.1262 0.472 0.116 0.000 0.084 0.320 0.008
#> GSM213107 5 0.3706 0.5904 0.000 0.380 0.000 0.000 0.620 0.000
#> GSM213108 2 0.4065 0.5938 0.028 0.784 0.000 0.036 0.144 0.008
#> GSM213112 1 0.1269 0.4163 0.956 0.012 0.000 0.020 0.012 0.000
#> GSM213114 1 0.6021 0.2908 0.604 0.068 0.000 0.088 0.232 0.008
#> GSM213115 2 0.2990 0.6171 0.084 0.860 0.000 0.036 0.020 0.000
#> GSM213116 1 0.4077 -0.1982 0.660 0.012 0.000 0.320 0.000 0.008
#> GSM213119 2 0.1088 0.6548 0.016 0.960 0.000 0.000 0.024 0.000
#> GSM213072 1 0.4492 -0.8452 0.496 0.000 0.000 0.480 0.008 0.016
#> GSM213075 1 0.4691 -0.7056 0.524 0.016 0.000 0.444 0.012 0.004
#> GSM213076 2 0.5852 -0.0320 0.076 0.496 0.000 0.044 0.384 0.000
#> GSM213079 3 0.0146 0.8170 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM213080 1 0.6021 0.2908 0.604 0.068 0.000 0.088 0.232 0.008
#> GSM213081 1 0.5052 0.2888 0.672 0.020 0.000 0.244 0.044 0.020
#> GSM213084 1 0.1588 0.3679 0.924 0.004 0.000 0.072 0.000 0.000
#> GSM213087 2 0.4184 -0.2244 0.016 0.576 0.000 0.000 0.408 0.000
#> GSM213089 1 0.4510 -0.4470 0.600 0.004 0.000 0.368 0.004 0.024
#> GSM213090 3 0.4140 0.7566 0.000 0.000 0.784 0.104 0.076 0.036
#> GSM213093 1 0.4033 -0.4874 0.588 0.004 0.000 0.404 0.000 0.004
#> GSM213097 1 0.3890 -0.4415 0.596 0.004 0.000 0.400 0.000 0.000
#> GSM213099 6 0.6054 -0.1721 0.212 0.000 0.000 0.380 0.004 0.404
#> GSM213101 1 0.3805 -0.1935 0.664 0.004 0.000 0.328 0.004 0.000
#> GSM213105 2 0.1088 0.6548 0.016 0.960 0.000 0.000 0.024 0.000
#> GSM213109 1 0.2377 0.3045 0.868 0.004 0.000 0.124 0.004 0.000
#> GSM213110 2 0.3059 0.6155 0.084 0.856 0.000 0.040 0.020 0.000
#> GSM213113 1 0.5543 0.3158 0.676 0.048 0.000 0.172 0.088 0.016
#> GSM213121 5 0.3890 0.5653 0.004 0.400 0.000 0.000 0.596 0.000
#> GSM213123 1 0.4098 0.2812 0.760 0.016 0.000 0.180 0.040 0.004
#> GSM213125 2 0.1503 0.6600 0.016 0.944 0.000 0.008 0.032 0.000
#> GSM213073 3 0.4576 0.7534 0.004 0.004 0.756 0.096 0.116 0.024
#> GSM213086 1 0.2843 0.4038 0.876 0.032 0.000 0.044 0.048 0.000
#> GSM213098 1 0.6998 0.1914 0.456 0.084 0.000 0.136 0.312 0.012
#> GSM213106 1 0.3684 -0.1508 0.692 0.004 0.000 0.300 0.004 0.000
#> GSM213124 1 0.6817 -0.0436 0.460 0.296 0.000 0.184 0.052 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n development.stage(p) disease.state(p) k
#> MAD:hclust 49 0.821 1.000 2
#> MAD:hclust 48 0.512 0.697 3
#> MAD:hclust 46 0.201 0.992 4
#> MAD:hclust 42 0.224 0.952 5
#> MAD:hclust 16 0.120 0.949 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "kmeans"]
# you can also extract it by
# res = res_list["MAD:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.500 0.924 0.913 0.4128 0.560 0.560
#> 3 3 0.700 0.835 0.903 0.4648 0.824 0.686
#> 4 4 0.600 0.606 0.756 0.1553 0.810 0.554
#> 5 5 0.577 0.568 0.735 0.0901 0.876 0.609
#> 6 6 0.605 0.484 0.715 0.0549 0.949 0.792
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
#> GSM213078 1 0.0672 0.944 0.992 0.008
#> GSM213082 2 0.6148 0.973 0.152 0.848
#> GSM213085 1 0.0672 0.944 0.992 0.008
#> GSM213088 1 0.1184 0.942 0.984 0.016
#> GSM213091 1 0.5842 0.865 0.860 0.140
#> GSM213092 1 0.0672 0.944 0.992 0.008
#> GSM213096 1 0.0672 0.944 0.992 0.008
#> GSM213100 1 0.0672 0.944 0.992 0.008
#> GSM213111 2 0.6148 0.973 0.152 0.848
#> GSM213117 1 0.0938 0.941 0.988 0.012
#> GSM213118 1 0.0938 0.943 0.988 0.012
#> GSM213120 2 0.6148 0.973 0.152 0.848
#> GSM213122 2 0.6247 0.974 0.156 0.844
#> GSM213074 1 0.5737 0.868 0.864 0.136
#> GSM213077 1 0.0672 0.944 0.992 0.008
#> GSM213083 1 0.0672 0.944 0.992 0.008
#> GSM213094 1 0.6438 0.845 0.836 0.164
#> GSM213095 2 0.5737 0.946 0.136 0.864
#> GSM213102 1 0.0672 0.942 0.992 0.008
#> GSM213103 2 0.6247 0.974 0.156 0.844
#> GSM213104 1 0.5519 0.809 0.872 0.128
#> GSM213107 2 0.6148 0.972 0.152 0.848
#> GSM213108 2 0.6247 0.964 0.156 0.844
#> GSM213112 1 0.0672 0.944 0.992 0.008
#> GSM213114 1 0.0672 0.944 0.992 0.008
#> GSM213115 2 0.6247 0.974 0.156 0.844
#> GSM213116 1 0.0672 0.942 0.992 0.008
#> GSM213119 2 0.6148 0.973 0.152 0.848
#> GSM213072 1 0.5737 0.868 0.864 0.136
#> GSM213075 1 0.4562 0.895 0.904 0.096
#> GSM213076 2 0.6148 0.973 0.152 0.848
#> GSM213079 1 0.6247 0.845 0.844 0.156
#> GSM213080 1 0.5408 0.815 0.876 0.124
#> GSM213081 1 0.0672 0.944 0.992 0.008
#> GSM213084 1 0.0672 0.944 0.992 0.008
#> GSM213087 2 0.6247 0.974 0.156 0.844
#> GSM213089 1 0.1843 0.935 0.972 0.028
#> GSM213090 1 0.6247 0.845 0.844 0.156
#> GSM213093 1 0.0672 0.942 0.992 0.008
#> GSM213097 1 0.0672 0.942 0.992 0.008
#> GSM213099 1 0.5946 0.862 0.856 0.144
#> GSM213101 1 0.0672 0.944 0.992 0.008
#> GSM213105 2 0.6247 0.974 0.156 0.844
#> GSM213109 1 0.0000 0.943 1.000 0.000
#> GSM213110 2 0.6247 0.974 0.156 0.844
#> GSM213113 1 0.1184 0.942 0.984 0.016
#> GSM213121 2 0.6247 0.974 0.156 0.844
#> GSM213123 1 0.0672 0.942 0.992 0.008
#> GSM213125 2 0.6247 0.974 0.156 0.844
#> GSM213073 1 0.6247 0.845 0.844 0.156
#> GSM213086 1 0.0672 0.944 0.992 0.008
#> GSM213098 1 0.1184 0.942 0.984 0.016
#> GSM213106 1 0.1184 0.940 0.984 0.016
#> GSM213124 2 0.9866 0.506 0.432 0.568
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.0237 0.880 0.996 0.000 0.004
#> GSM213082 2 0.0000 0.967 0.000 1.000 0.000
#> GSM213085 1 0.1411 0.878 0.964 0.000 0.036
#> GSM213088 1 0.1964 0.867 0.944 0.000 0.056
#> GSM213091 3 0.5859 0.694 0.344 0.000 0.656
#> GSM213092 1 0.1411 0.878 0.964 0.000 0.036
#> GSM213096 1 0.0747 0.878 0.984 0.000 0.016
#> GSM213100 1 0.0237 0.881 0.996 0.000 0.004
#> GSM213111 2 0.0000 0.967 0.000 1.000 0.000
#> GSM213117 1 0.4887 0.683 0.772 0.000 0.228
#> GSM213118 1 0.1753 0.878 0.952 0.000 0.048
#> GSM213120 2 0.1163 0.960 0.000 0.972 0.028
#> GSM213122 2 0.0000 0.967 0.000 1.000 0.000
#> GSM213074 3 0.6008 0.661 0.372 0.000 0.628
#> GSM213077 1 0.0592 0.879 0.988 0.000 0.012
#> GSM213083 1 0.0592 0.881 0.988 0.000 0.012
#> GSM213094 3 0.2796 0.725 0.092 0.000 0.908
#> GSM213095 2 0.3030 0.914 0.004 0.904 0.092
#> GSM213102 1 0.4002 0.782 0.840 0.000 0.160
#> GSM213103 2 0.1529 0.956 0.000 0.960 0.040
#> GSM213104 1 0.3377 0.808 0.896 0.012 0.092
#> GSM213107 2 0.2165 0.943 0.000 0.936 0.064
#> GSM213108 2 0.0747 0.960 0.000 0.984 0.016
#> GSM213112 1 0.1643 0.875 0.956 0.000 0.044
#> GSM213114 1 0.2261 0.845 0.932 0.000 0.068
#> GSM213115 2 0.0000 0.967 0.000 1.000 0.000
#> GSM213116 1 0.4750 0.702 0.784 0.000 0.216
#> GSM213119 2 0.0000 0.967 0.000 1.000 0.000
#> GSM213072 3 0.6095 0.636 0.392 0.000 0.608
#> GSM213075 3 0.6235 0.520 0.436 0.000 0.564
#> GSM213076 2 0.1163 0.960 0.000 0.972 0.028
#> GSM213079 3 0.2448 0.723 0.076 0.000 0.924
#> GSM213080 1 0.3213 0.813 0.900 0.008 0.092
#> GSM213081 1 0.1643 0.881 0.956 0.000 0.044
#> GSM213084 1 0.0237 0.881 0.996 0.000 0.004
#> GSM213087 2 0.0000 0.967 0.000 1.000 0.000
#> GSM213089 1 0.5810 0.405 0.664 0.000 0.336
#> GSM213090 3 0.2356 0.719 0.072 0.000 0.928
#> GSM213093 1 0.4399 0.752 0.812 0.000 0.188
#> GSM213097 1 0.3619 0.809 0.864 0.000 0.136
#> GSM213099 3 0.5835 0.697 0.340 0.000 0.660
#> GSM213101 1 0.0424 0.880 0.992 0.000 0.008
#> GSM213105 2 0.0000 0.967 0.000 1.000 0.000
#> GSM213109 1 0.1411 0.877 0.964 0.000 0.036
#> GSM213110 2 0.0000 0.967 0.000 1.000 0.000
#> GSM213113 1 0.3879 0.835 0.848 0.000 0.152
#> GSM213121 2 0.1753 0.952 0.000 0.952 0.048
#> GSM213123 1 0.2796 0.847 0.908 0.000 0.092
#> GSM213125 2 0.0000 0.967 0.000 1.000 0.000
#> GSM213073 3 0.1860 0.698 0.052 0.000 0.948
#> GSM213086 1 0.0892 0.877 0.980 0.000 0.020
#> GSM213098 1 0.4121 0.818 0.832 0.000 0.168
#> GSM213106 1 0.4702 0.715 0.788 0.000 0.212
#> GSM213124 2 0.6144 0.683 0.132 0.780 0.088
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.5132 0.6546 0.548 0.004 0.000 0.448
#> GSM213082 2 0.0707 0.8500 0.020 0.980 0.000 0.000
#> GSM213085 1 0.5645 0.7213 0.604 0.000 0.032 0.364
#> GSM213088 4 0.3751 0.4693 0.196 0.004 0.000 0.800
#> GSM213091 4 0.3942 0.4776 0.000 0.000 0.236 0.764
#> GSM213092 1 0.5510 0.7229 0.600 0.000 0.024 0.376
#> GSM213096 1 0.5371 0.7218 0.616 0.000 0.020 0.364
#> GSM213100 1 0.5453 0.7215 0.592 0.000 0.020 0.388
#> GSM213111 2 0.2179 0.8424 0.064 0.924 0.012 0.000
#> GSM213117 4 0.2053 0.6224 0.072 0.004 0.000 0.924
#> GSM213118 1 0.5408 0.4719 0.556 0.004 0.008 0.432
#> GSM213120 2 0.4136 0.7936 0.196 0.788 0.016 0.000
#> GSM213122 2 0.0376 0.8536 0.004 0.992 0.004 0.000
#> GSM213074 4 0.4049 0.5105 0.008 0.000 0.212 0.780
#> GSM213077 1 0.5476 0.7125 0.584 0.000 0.020 0.396
#> GSM213083 1 0.5643 0.6824 0.548 0.000 0.024 0.428
#> GSM213094 3 0.4331 0.6714 0.000 0.000 0.712 0.288
#> GSM213095 2 0.7458 0.4821 0.252 0.508 0.240 0.000
#> GSM213102 4 0.2944 0.5825 0.128 0.004 0.000 0.868
#> GSM213103 2 0.4687 0.7679 0.224 0.752 0.020 0.004
#> GSM213104 1 0.1821 0.4426 0.948 0.008 0.012 0.032
#> GSM213107 2 0.5404 0.6861 0.328 0.644 0.028 0.000
#> GSM213108 2 0.1443 0.8470 0.028 0.960 0.008 0.004
#> GSM213112 1 0.5645 0.7222 0.604 0.000 0.032 0.364
#> GSM213114 1 0.3306 0.5621 0.840 0.000 0.004 0.156
#> GSM213115 2 0.0000 0.8534 0.000 1.000 0.000 0.000
#> GSM213116 4 0.1792 0.6233 0.068 0.000 0.000 0.932
#> GSM213119 2 0.0376 0.8536 0.004 0.992 0.004 0.000
#> GSM213072 4 0.3583 0.5551 0.004 0.000 0.180 0.816
#> GSM213075 4 0.3583 0.5550 0.004 0.000 0.180 0.816
#> GSM213076 2 0.4910 0.7417 0.276 0.704 0.020 0.000
#> GSM213079 3 0.1256 0.8976 0.008 0.000 0.964 0.028
#> GSM213080 1 0.2665 0.5019 0.900 0.008 0.004 0.088
#> GSM213081 4 0.5155 -0.4407 0.468 0.004 0.000 0.528
#> GSM213084 1 0.5564 0.6762 0.544 0.000 0.020 0.436
#> GSM213087 2 0.0524 0.8530 0.008 0.988 0.004 0.000
#> GSM213089 4 0.1661 0.6188 0.004 0.000 0.052 0.944
#> GSM213090 3 0.0927 0.8984 0.008 0.000 0.976 0.016
#> GSM213093 4 0.2714 0.5966 0.112 0.004 0.000 0.884
#> GSM213097 4 0.2944 0.5841 0.128 0.004 0.000 0.868
#> GSM213099 4 0.4283 0.4219 0.004 0.000 0.256 0.740
#> GSM213101 1 0.5147 0.6346 0.536 0.004 0.000 0.460
#> GSM213105 2 0.0376 0.8536 0.004 0.992 0.004 0.000
#> GSM213109 4 0.5682 -0.5427 0.456 0.000 0.024 0.520
#> GSM213110 2 0.0000 0.8534 0.000 1.000 0.000 0.000
#> GSM213113 4 0.6152 -0.0132 0.464 0.008 0.032 0.496
#> GSM213121 2 0.4908 0.7251 0.292 0.692 0.016 0.000
#> GSM213123 4 0.4428 0.2426 0.276 0.004 0.000 0.720
#> GSM213125 2 0.0188 0.8536 0.000 0.996 0.004 0.000
#> GSM213073 3 0.0927 0.8917 0.016 0.000 0.976 0.008
#> GSM213086 1 0.5326 0.7228 0.604 0.000 0.016 0.380
#> GSM213098 1 0.4910 0.0734 0.704 0.000 0.020 0.276
#> GSM213106 4 0.1978 0.6229 0.068 0.004 0.000 0.928
#> GSM213124 2 0.5923 0.4506 0.040 0.652 0.012 0.296
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.3517 0.7327 0.840 0.000 0.004 0.084 0.072
#> GSM213082 2 0.3265 0.6557 0.004 0.848 0.016 0.008 0.124
#> GSM213085 1 0.2790 0.7783 0.892 0.000 0.028 0.020 0.060
#> GSM213088 4 0.5583 0.5584 0.336 0.000 0.004 0.584 0.076
#> GSM213091 4 0.4549 0.5992 0.052 0.000 0.060 0.792 0.096
#> GSM213092 1 0.2634 0.7801 0.900 0.000 0.024 0.020 0.056
#> GSM213096 1 0.2005 0.7863 0.924 0.000 0.004 0.016 0.056
#> GSM213100 1 0.1904 0.7854 0.936 0.000 0.020 0.028 0.016
#> GSM213111 2 0.5243 0.3399 0.004 0.644 0.016 0.032 0.304
#> GSM213117 4 0.4241 0.6805 0.264 0.000 0.008 0.716 0.012
#> GSM213118 1 0.5363 0.6208 0.676 0.000 0.004 0.120 0.200
#> GSM213120 5 0.5739 0.0849 0.008 0.468 0.016 0.032 0.476
#> GSM213122 2 0.0486 0.7637 0.004 0.988 0.004 0.000 0.004
#> GSM213074 4 0.4932 0.5959 0.080 0.000 0.048 0.764 0.108
#> GSM213077 1 0.1787 0.7848 0.940 0.000 0.012 0.032 0.016
#> GSM213083 1 0.2522 0.7692 0.904 0.000 0.012 0.056 0.028
#> GSM213094 4 0.6361 -0.3437 0.000 0.004 0.428 0.428 0.140
#> GSM213095 5 0.7237 0.2726 0.008 0.200 0.296 0.024 0.472
#> GSM213102 4 0.4921 0.6245 0.320 0.000 0.004 0.640 0.036
#> GSM213103 2 0.5238 0.0543 0.012 0.576 0.016 0.008 0.388
#> GSM213104 1 0.5387 0.3531 0.524 0.004 0.020 0.016 0.436
#> GSM213107 5 0.4874 0.1994 0.000 0.452 0.016 0.004 0.528
#> GSM213108 2 0.5487 0.4686 0.004 0.676 0.028 0.052 0.240
#> GSM213112 1 0.2790 0.7783 0.892 0.000 0.028 0.020 0.060
#> GSM213114 1 0.4629 0.6427 0.708 0.000 0.012 0.028 0.252
#> GSM213115 2 0.1016 0.7603 0.004 0.972 0.004 0.008 0.012
#> GSM213116 4 0.4434 0.6834 0.248 0.000 0.012 0.720 0.020
#> GSM213119 2 0.0486 0.7637 0.004 0.988 0.004 0.000 0.004
#> GSM213072 4 0.4889 0.6154 0.084 0.000 0.048 0.768 0.100
#> GSM213075 4 0.4146 0.6419 0.072 0.000 0.056 0.820 0.052
#> GSM213076 5 0.5399 0.1723 0.000 0.440 0.016 0.028 0.516
#> GSM213079 3 0.1697 0.9699 0.008 0.000 0.932 0.060 0.000
#> GSM213080 1 0.5527 0.4982 0.592 0.004 0.024 0.028 0.352
#> GSM213081 1 0.6384 0.1631 0.528 0.000 0.020 0.340 0.112
#> GSM213084 1 0.2502 0.7634 0.904 0.000 0.012 0.060 0.024
#> GSM213087 2 0.2095 0.7227 0.000 0.920 0.012 0.008 0.060
#> GSM213089 4 0.3053 0.6938 0.128 0.000 0.008 0.852 0.012
#> GSM213090 3 0.2390 0.9680 0.008 0.000 0.908 0.060 0.024
#> GSM213093 4 0.4956 0.6261 0.312 0.000 0.004 0.644 0.040
#> GSM213097 4 0.5186 0.6086 0.320 0.000 0.004 0.624 0.052
#> GSM213099 4 0.4803 0.5621 0.048 0.000 0.056 0.768 0.128
#> GSM213101 1 0.4044 0.6921 0.800 0.000 0.004 0.120 0.076
#> GSM213105 2 0.0486 0.7637 0.004 0.988 0.004 0.000 0.004
#> GSM213109 1 0.3573 0.7095 0.832 0.000 0.012 0.124 0.032
#> GSM213110 2 0.1016 0.7603 0.004 0.972 0.004 0.008 0.012
#> GSM213113 5 0.7321 -0.0199 0.276 0.000 0.032 0.260 0.432
#> GSM213121 5 0.4891 0.1498 0.000 0.480 0.016 0.004 0.500
#> GSM213123 4 0.6105 0.3977 0.392 0.000 0.008 0.500 0.100
#> GSM213125 2 0.0613 0.7623 0.004 0.984 0.004 0.000 0.008
#> GSM213073 3 0.2026 0.9675 0.012 0.000 0.928 0.044 0.016
#> GSM213086 1 0.2228 0.7832 0.916 0.000 0.008 0.020 0.056
#> GSM213098 5 0.6090 0.2349 0.132 0.000 0.016 0.244 0.608
#> GSM213106 4 0.4775 0.6662 0.268 0.000 0.008 0.688 0.036
#> GSM213124 2 0.6791 0.2515 0.044 0.584 0.016 0.260 0.096
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.3599 0.6781 0.756 0.000 0.000 0.220 0.004 0.020
#> GSM213082 2 0.3514 0.5354 0.000 0.752 0.000 0.000 0.228 0.020
#> GSM213085 1 0.1874 0.7684 0.928 0.000 0.000 0.028 0.016 0.028
#> GSM213088 4 0.3284 0.5748 0.196 0.000 0.000 0.784 0.000 0.020
#> GSM213091 4 0.4903 -0.3557 0.012 0.000 0.032 0.556 0.004 0.396
#> GSM213092 1 0.1930 0.7704 0.924 0.000 0.000 0.036 0.012 0.028
#> GSM213096 1 0.1078 0.7690 0.964 0.000 0.000 0.008 0.012 0.016
#> GSM213100 1 0.1644 0.7710 0.932 0.000 0.000 0.052 0.004 0.012
#> GSM213111 5 0.4784 -0.0329 0.000 0.452 0.008 0.008 0.512 0.020
#> GSM213117 4 0.4222 0.5261 0.100 0.000 0.000 0.764 0.016 0.120
#> GSM213118 1 0.6202 0.4893 0.600 0.000 0.000 0.136 0.120 0.144
#> GSM213120 5 0.4650 0.4548 0.000 0.232 0.004 0.016 0.696 0.052
#> GSM213122 2 0.0291 0.7387 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM213074 4 0.5523 -0.3751 0.040 0.000 0.028 0.516 0.012 0.404
#> GSM213077 1 0.1967 0.7669 0.904 0.000 0.000 0.084 0.000 0.012
#> GSM213083 1 0.2734 0.7407 0.840 0.000 0.000 0.148 0.004 0.008
#> GSM213094 6 0.5958 0.2964 0.000 0.000 0.316 0.160 0.016 0.508
#> GSM213095 5 0.5773 0.3530 0.000 0.108 0.212 0.000 0.620 0.060
#> GSM213102 4 0.2632 0.5933 0.164 0.000 0.000 0.832 0.000 0.004
#> GSM213103 2 0.6789 -0.1535 0.028 0.440 0.004 0.016 0.344 0.168
#> GSM213104 1 0.6204 0.1577 0.436 0.000 0.000 0.008 0.264 0.292
#> GSM213107 5 0.6077 0.3939 0.004 0.248 0.004 0.000 0.488 0.256
#> GSM213108 2 0.5417 0.0707 0.000 0.488 0.008 0.016 0.436 0.052
#> GSM213112 1 0.2102 0.7661 0.920 0.000 0.004 0.020 0.024 0.032
#> GSM213114 1 0.4875 0.5467 0.668 0.000 0.000 0.008 0.100 0.224
#> GSM213115 2 0.1049 0.7353 0.000 0.960 0.000 0.008 0.032 0.000
#> GSM213116 4 0.4301 0.5268 0.120 0.000 0.000 0.740 0.004 0.136
#> GSM213119 2 0.0508 0.7379 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM213072 4 0.5641 -0.3427 0.060 0.000 0.016 0.512 0.016 0.396
#> GSM213075 4 0.4369 0.1398 0.016 0.000 0.016 0.712 0.016 0.240
#> GSM213076 5 0.3559 0.4507 0.000 0.240 0.004 0.000 0.744 0.012
#> GSM213079 3 0.0458 0.9571 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM213080 1 0.5851 0.3630 0.536 0.000 0.000 0.012 0.176 0.276
#> GSM213081 4 0.5952 0.2661 0.320 0.000 0.000 0.528 0.032 0.120
#> GSM213084 1 0.2558 0.7368 0.840 0.000 0.000 0.156 0.000 0.004
#> GSM213087 2 0.2573 0.6701 0.000 0.884 0.000 0.008 0.064 0.044
#> GSM213089 4 0.3713 0.2723 0.032 0.000 0.000 0.744 0.000 0.224
#> GSM213090 3 0.1003 0.9524 0.004 0.000 0.964 0.000 0.028 0.004
#> GSM213093 4 0.2704 0.5960 0.140 0.000 0.000 0.844 0.000 0.016
#> GSM213097 4 0.2768 0.5933 0.156 0.000 0.000 0.832 0.000 0.012
#> GSM213099 6 0.4949 0.1605 0.012 0.000 0.024 0.468 0.008 0.488
#> GSM213101 1 0.3872 0.6171 0.712 0.000 0.000 0.264 0.004 0.020
#> GSM213105 2 0.0508 0.7379 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM213109 1 0.3503 0.7178 0.788 0.000 0.000 0.180 0.012 0.020
#> GSM213110 2 0.0806 0.7345 0.000 0.972 0.000 0.008 0.020 0.000
#> GSM213113 5 0.7085 0.2442 0.132 0.000 0.012 0.264 0.480 0.112
#> GSM213121 5 0.6186 0.3441 0.004 0.304 0.004 0.000 0.448 0.240
#> GSM213123 4 0.5453 0.4787 0.200 0.000 0.000 0.656 0.068 0.076
#> GSM213125 2 0.0806 0.7347 0.000 0.972 0.000 0.000 0.020 0.008
#> GSM213073 3 0.1092 0.9534 0.000 0.000 0.960 0.000 0.020 0.020
#> GSM213086 1 0.2183 0.7672 0.912 0.000 0.000 0.028 0.020 0.040
#> GSM213098 5 0.6557 0.3666 0.108 0.000 0.000 0.128 0.536 0.228
#> GSM213106 4 0.2776 0.5823 0.104 0.000 0.000 0.860 0.004 0.032
#> GSM213124 2 0.7392 0.2203 0.052 0.500 0.004 0.244 0.116 0.084
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 development.stage(p) disease.state(p) k
#> MAD:kmeans 54 0.688 0.902 2
#> MAD:kmeans 53 0.428 0.921 3
#> MAD:kmeans 42 0.311 0.940 4
#> MAD:kmeans 38 0.135 0.964 5
#> MAD:kmeans 31 0.185 0.895 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "skmeans"]
# you can also extract it by
# res = res_list["MAD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.483 0.808 0.905 0.4975 0.525 0.525
#> 3 3 0.329 0.565 0.764 0.3544 0.725 0.511
#> 4 4 0.340 0.380 0.627 0.1182 0.933 0.796
#> 5 5 0.420 0.362 0.585 0.0616 0.902 0.665
#> 6 6 0.481 0.297 0.532 0.0416 0.925 0.687
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
#> GSM213078 1 0.0000 0.868 1.000 0.000
#> GSM213082 2 0.0000 0.940 0.000 1.000
#> GSM213085 1 0.3584 0.865 0.932 0.068
#> GSM213088 1 0.9044 0.576 0.680 0.320
#> GSM213091 1 0.1414 0.873 0.980 0.020
#> GSM213092 1 0.0000 0.868 1.000 0.000
#> GSM213096 1 0.4815 0.846 0.896 0.104
#> GSM213100 1 0.0000 0.868 1.000 0.000
#> GSM213111 2 0.0000 0.940 0.000 1.000
#> GSM213117 1 0.6623 0.802 0.828 0.172
#> GSM213118 1 0.9580 0.479 0.620 0.380
#> GSM213120 2 0.0376 0.938 0.004 0.996
#> GSM213122 2 0.0000 0.940 0.000 1.000
#> GSM213074 1 0.1184 0.872 0.984 0.016
#> GSM213077 1 0.0000 0.868 1.000 0.000
#> GSM213083 1 0.0000 0.868 1.000 0.000
#> GSM213094 1 0.6438 0.807 0.836 0.164
#> GSM213095 2 0.0672 0.936 0.008 0.992
#> GSM213102 1 0.1414 0.872 0.980 0.020
#> GSM213103 2 0.2236 0.921 0.036 0.964
#> GSM213104 2 0.6148 0.813 0.152 0.848
#> GSM213107 2 0.0000 0.940 0.000 1.000
#> GSM213108 2 0.2043 0.921 0.032 0.968
#> GSM213112 1 0.5178 0.838 0.884 0.116
#> GSM213114 1 0.8861 0.617 0.696 0.304
#> GSM213115 2 0.0000 0.940 0.000 1.000
#> GSM213116 1 0.1414 0.873 0.980 0.020
#> GSM213119 2 0.0000 0.940 0.000 1.000
#> GSM213072 1 0.2603 0.872 0.956 0.044
#> GSM213075 1 0.9087 0.599 0.676 0.324
#> GSM213076 2 0.0000 0.940 0.000 1.000
#> GSM213079 1 0.4690 0.848 0.900 0.100
#> GSM213080 2 0.6887 0.766 0.184 0.816
#> GSM213081 1 0.4161 0.860 0.916 0.084
#> GSM213084 1 0.0000 0.868 1.000 0.000
#> GSM213087 2 0.0000 0.940 0.000 1.000
#> GSM213089 1 0.4690 0.854 0.900 0.100
#> GSM213090 1 0.9988 0.194 0.520 0.480
#> GSM213093 1 0.2236 0.873 0.964 0.036
#> GSM213097 1 0.1184 0.872 0.984 0.016
#> GSM213099 1 0.2423 0.873 0.960 0.040
#> GSM213101 1 0.2043 0.872 0.968 0.032
#> GSM213105 2 0.0000 0.940 0.000 1.000
#> GSM213109 1 0.0000 0.868 1.000 0.000
#> GSM213110 2 0.1184 0.933 0.016 0.984
#> GSM213113 1 1.0000 0.143 0.504 0.496
#> GSM213121 2 0.0000 0.940 0.000 1.000
#> GSM213123 1 0.5629 0.834 0.868 0.132
#> GSM213125 2 0.0000 0.940 0.000 1.000
#> GSM213073 1 0.9944 0.278 0.544 0.456
#> GSM213086 1 0.1843 0.873 0.972 0.028
#> GSM213098 2 0.9795 0.161 0.416 0.584
#> GSM213106 1 0.3431 0.869 0.936 0.064
#> GSM213124 2 0.6531 0.777 0.168 0.832
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.3340 0.5917 0.880 0.000 0.120
#> GSM213082 2 0.1289 0.9062 0.000 0.968 0.032
#> GSM213085 1 0.6082 0.4496 0.692 0.012 0.296
#> GSM213088 1 0.9269 0.1556 0.508 0.184 0.308
#> GSM213091 3 0.2448 0.5897 0.076 0.000 0.924
#> GSM213092 1 0.5058 0.5385 0.756 0.000 0.244
#> GSM213096 1 0.4324 0.6000 0.860 0.028 0.112
#> GSM213100 1 0.4702 0.5815 0.788 0.000 0.212
#> GSM213111 2 0.1832 0.9036 0.008 0.956 0.036
#> GSM213117 3 0.8677 0.3930 0.280 0.144 0.576
#> GSM213118 1 0.9133 0.2147 0.528 0.176 0.296
#> GSM213120 2 0.3690 0.8649 0.016 0.884 0.100
#> GSM213122 2 0.0237 0.9098 0.004 0.996 0.000
#> GSM213074 3 0.4861 0.5747 0.180 0.012 0.808
#> GSM213077 1 0.3816 0.6068 0.852 0.000 0.148
#> GSM213083 1 0.4291 0.6006 0.820 0.000 0.180
#> GSM213094 3 0.2496 0.5874 0.068 0.004 0.928
#> GSM213095 2 0.4891 0.8279 0.040 0.836 0.124
#> GSM213102 1 0.7080 0.2321 0.564 0.024 0.412
#> GSM213103 2 0.5010 0.8238 0.084 0.840 0.076
#> GSM213104 1 0.8798 0.1954 0.520 0.356 0.124
#> GSM213107 2 0.1170 0.9072 0.016 0.976 0.008
#> GSM213108 2 0.5167 0.7789 0.024 0.804 0.172
#> GSM213112 1 0.7481 0.2958 0.596 0.048 0.356
#> GSM213114 1 0.4194 0.5797 0.876 0.064 0.060
#> GSM213115 2 0.0237 0.9095 0.004 0.996 0.000
#> GSM213116 3 0.6169 0.3413 0.360 0.004 0.636
#> GSM213119 2 0.0237 0.9096 0.000 0.996 0.004
#> GSM213072 3 0.5020 0.5756 0.192 0.012 0.796
#> GSM213075 3 0.8148 0.4905 0.200 0.156 0.644
#> GSM213076 2 0.4256 0.8618 0.036 0.868 0.096
#> GSM213079 3 0.4575 0.5645 0.160 0.012 0.828
#> GSM213080 1 0.6927 0.3592 0.664 0.296 0.040
#> GSM213081 1 0.7337 0.4301 0.644 0.056 0.300
#> GSM213084 1 0.4504 0.5925 0.804 0.000 0.196
#> GSM213087 2 0.0237 0.9096 0.004 0.996 0.000
#> GSM213089 3 0.6756 0.5181 0.232 0.056 0.712
#> GSM213090 3 0.7535 0.4954 0.176 0.132 0.692
#> GSM213093 3 0.6865 0.2777 0.384 0.020 0.596
#> GSM213097 1 0.6682 0.0316 0.504 0.008 0.488
#> GSM213099 3 0.3682 0.5920 0.116 0.008 0.876
#> GSM213101 1 0.5277 0.5703 0.796 0.024 0.180
#> GSM213105 2 0.0000 0.9093 0.000 1.000 0.000
#> GSM213109 1 0.5905 0.4096 0.648 0.000 0.352
#> GSM213110 2 0.4206 0.8461 0.088 0.872 0.040
#> GSM213113 3 0.9916 0.2114 0.316 0.288 0.396
#> GSM213121 2 0.0475 0.9091 0.004 0.992 0.004
#> GSM213123 3 0.8740 0.0578 0.432 0.108 0.460
#> GSM213125 2 0.0000 0.9093 0.000 1.000 0.000
#> GSM213073 3 0.8195 0.4537 0.232 0.136 0.632
#> GSM213086 1 0.4555 0.5861 0.800 0.000 0.200
#> GSM213098 3 0.9721 0.2415 0.284 0.264 0.452
#> GSM213106 3 0.7660 0.3608 0.324 0.064 0.612
#> GSM213124 2 0.8231 0.4553 0.136 0.628 0.236
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.5364 0.3686 0.724 0.012 0.228 0.036
#> GSM213082 2 0.2809 0.8046 0.004 0.904 0.064 0.028
#> GSM213085 1 0.7553 0.2984 0.548 0.012 0.240 0.200
#> GSM213088 3 0.9402 0.1071 0.340 0.128 0.356 0.176
#> GSM213091 4 0.5380 0.4045 0.072 0.004 0.184 0.740
#> GSM213092 1 0.6133 0.3954 0.672 0.000 0.204 0.124
#> GSM213096 1 0.5474 0.4229 0.756 0.020 0.160 0.064
#> GSM213100 1 0.5945 0.4013 0.716 0.008 0.132 0.144
#> GSM213111 2 0.4556 0.7631 0.008 0.816 0.096 0.080
#> GSM213117 3 0.8631 -0.1555 0.152 0.064 0.392 0.392
#> GSM213118 3 0.9121 0.0374 0.332 0.104 0.400 0.164
#> GSM213120 2 0.6222 0.6732 0.024 0.692 0.212 0.072
#> GSM213122 2 0.1256 0.8109 0.000 0.964 0.028 0.008
#> GSM213074 4 0.5906 0.4071 0.148 0.000 0.152 0.700
#> GSM213077 1 0.4483 0.4483 0.808 0.000 0.088 0.104
#> GSM213083 1 0.4669 0.4180 0.796 0.000 0.104 0.100
#> GSM213094 4 0.3417 0.4341 0.060 0.008 0.052 0.880
#> GSM213095 2 0.7712 0.5087 0.040 0.584 0.168 0.208
#> GSM213102 1 0.8431 -0.0889 0.412 0.024 0.280 0.284
#> GSM213103 2 0.7541 0.5371 0.084 0.608 0.232 0.076
#> GSM213104 1 0.8895 -0.0225 0.408 0.184 0.336 0.072
#> GSM213107 2 0.4348 0.7761 0.012 0.820 0.132 0.036
#> GSM213108 2 0.6977 0.5517 0.040 0.640 0.088 0.232
#> GSM213112 1 0.7469 0.2657 0.532 0.004 0.240 0.224
#> GSM213114 1 0.6613 0.3131 0.604 0.044 0.320 0.032
#> GSM213115 2 0.0592 0.8091 0.000 0.984 0.016 0.000
#> GSM213116 4 0.8095 0.1107 0.236 0.012 0.324 0.428
#> GSM213119 2 0.0921 0.8106 0.000 0.972 0.028 0.000
#> GSM213072 4 0.6320 0.3819 0.180 0.000 0.160 0.660
#> GSM213075 4 0.8647 0.1735 0.136 0.112 0.236 0.516
#> GSM213076 2 0.5981 0.7188 0.028 0.724 0.176 0.072
#> GSM213079 4 0.5487 0.3914 0.108 0.008 0.132 0.752
#> GSM213080 1 0.8127 0.0693 0.452 0.204 0.324 0.020
#> GSM213081 1 0.8150 0.0159 0.420 0.020 0.364 0.196
#> GSM213084 1 0.5171 0.4358 0.760 0.000 0.128 0.112
#> GSM213087 2 0.1302 0.8092 0.000 0.956 0.044 0.000
#> GSM213089 4 0.7646 0.3047 0.128 0.036 0.272 0.564
#> GSM213090 4 0.7534 0.2525 0.124 0.076 0.168 0.632
#> GSM213093 4 0.8503 0.0335 0.300 0.024 0.296 0.380
#> GSM213097 1 0.8120 -0.0926 0.404 0.012 0.352 0.232
#> GSM213099 4 0.5339 0.4130 0.100 0.000 0.156 0.744
#> GSM213101 1 0.6291 0.3105 0.640 0.012 0.284 0.064
#> GSM213105 2 0.0817 0.8104 0.000 0.976 0.024 0.000
#> GSM213109 1 0.6792 0.2573 0.588 0.000 0.140 0.272
#> GSM213110 2 0.4371 0.7547 0.064 0.836 0.080 0.020
#> GSM213113 3 0.9335 0.1180 0.144 0.156 0.408 0.292
#> GSM213121 2 0.2124 0.8068 0.000 0.924 0.068 0.008
#> GSM213123 3 0.8692 0.1456 0.300 0.040 0.404 0.256
#> GSM213125 2 0.0657 0.8103 0.000 0.984 0.012 0.004
#> GSM213073 4 0.7999 0.1635 0.140 0.052 0.260 0.548
#> GSM213086 1 0.6991 0.3549 0.592 0.008 0.268 0.132
#> GSM213098 3 0.9586 0.1893 0.204 0.148 0.376 0.272
#> GSM213106 4 0.8465 0.0265 0.232 0.028 0.348 0.392
#> GSM213124 2 0.8650 0.2734 0.088 0.512 0.216 0.184
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.6017 0.2574 0.552 0.000 0.008 0.336 0.104
#> GSM213082 2 0.3735 0.7202 0.000 0.836 0.016 0.072 0.076
#> GSM213085 1 0.6738 0.3359 0.616 0.008 0.112 0.068 0.196
#> GSM213088 4 0.7425 0.2784 0.188 0.128 0.016 0.568 0.100
#> GSM213091 3 0.6216 0.3703 0.036 0.004 0.608 0.272 0.080
#> GSM213092 1 0.6578 0.3667 0.628 0.004 0.092 0.084 0.192
#> GSM213096 1 0.7354 0.2983 0.544 0.024 0.064 0.104 0.264
#> GSM213100 1 0.6809 0.3982 0.608 0.000 0.104 0.148 0.140
#> GSM213111 2 0.4337 0.7041 0.004 0.784 0.048 0.012 0.152
#> GSM213117 4 0.8524 0.1801 0.100 0.044 0.188 0.452 0.216
#> GSM213118 5 0.9243 0.1595 0.236 0.072 0.140 0.188 0.364
#> GSM213120 2 0.5879 0.6308 0.020 0.688 0.044 0.052 0.196
#> GSM213122 2 0.1525 0.7468 0.000 0.948 0.004 0.012 0.036
#> GSM213074 3 0.7342 0.3058 0.116 0.004 0.524 0.264 0.092
#> GSM213077 1 0.4617 0.4645 0.784 0.000 0.048 0.112 0.056
#> GSM213083 1 0.6175 0.4041 0.648 0.000 0.068 0.200 0.084
#> GSM213094 3 0.4012 0.4868 0.044 0.000 0.820 0.104 0.032
#> GSM213095 2 0.8177 0.1964 0.084 0.444 0.252 0.020 0.200
#> GSM213102 4 0.7305 0.3415 0.200 0.012 0.160 0.560 0.068
#> GSM213103 2 0.7073 0.3833 0.036 0.540 0.052 0.060 0.312
#> GSM213104 5 0.8466 0.0850 0.304 0.132 0.084 0.056 0.424
#> GSM213107 2 0.5175 0.6039 0.012 0.664 0.052 0.000 0.272
#> GSM213108 2 0.7697 0.4179 0.040 0.548 0.220 0.080 0.112
#> GSM213112 1 0.7541 0.2669 0.556 0.024 0.180 0.072 0.168
#> GSM213114 1 0.6858 0.1864 0.528 0.032 0.008 0.120 0.312
#> GSM213115 2 0.1885 0.7464 0.000 0.932 0.004 0.020 0.044
#> GSM213116 4 0.8328 0.0262 0.160 0.004 0.316 0.360 0.160
#> GSM213119 2 0.0960 0.7454 0.000 0.972 0.004 0.008 0.016
#> GSM213072 3 0.7661 0.2676 0.124 0.004 0.516 0.204 0.152
#> GSM213075 4 0.8588 -0.0661 0.092 0.068 0.344 0.384 0.112
#> GSM213076 2 0.6655 0.5385 0.008 0.592 0.092 0.052 0.256
#> GSM213079 3 0.4413 0.4613 0.100 0.004 0.804 0.040 0.052
#> GSM213080 1 0.8033 -0.1344 0.372 0.168 0.000 0.124 0.336
#> GSM213081 4 0.8479 0.0413 0.296 0.020 0.084 0.336 0.264
#> GSM213084 1 0.5063 0.4476 0.740 0.000 0.056 0.160 0.044
#> GSM213087 2 0.1857 0.7448 0.000 0.928 0.008 0.004 0.060
#> GSM213089 3 0.7855 0.1260 0.088 0.016 0.396 0.384 0.116
#> GSM213090 3 0.6514 0.3366 0.132 0.044 0.668 0.036 0.120
#> GSM213093 4 0.7324 0.2813 0.144 0.008 0.216 0.552 0.080
#> GSM213097 4 0.6601 0.3525 0.212 0.004 0.100 0.616 0.068
#> GSM213099 3 0.7199 0.3385 0.056 0.016 0.548 0.264 0.116
#> GSM213101 1 0.7460 0.0307 0.408 0.028 0.032 0.408 0.124
#> GSM213105 2 0.0510 0.7435 0.000 0.984 0.000 0.000 0.016
#> GSM213109 1 0.6896 0.3195 0.588 0.000 0.156 0.176 0.080
#> GSM213110 2 0.4641 0.6853 0.052 0.804 0.020 0.044 0.080
#> GSM213113 5 0.9646 0.0654 0.164 0.092 0.252 0.232 0.260
#> GSM213121 2 0.2674 0.7279 0.000 0.856 0.004 0.000 0.140
#> GSM213123 4 0.8812 0.2105 0.240 0.036 0.156 0.400 0.168
#> GSM213125 2 0.0932 0.7462 0.004 0.972 0.000 0.004 0.020
#> GSM213073 3 0.7643 0.2247 0.116 0.036 0.560 0.088 0.200
#> GSM213086 1 0.7427 0.3035 0.528 0.008 0.100 0.108 0.256
#> GSM213098 5 0.8866 0.2543 0.096 0.080 0.228 0.168 0.428
#> GSM213106 4 0.7204 0.2924 0.104 0.016 0.204 0.584 0.092
#> GSM213124 2 0.8982 0.0966 0.104 0.436 0.132 0.120 0.208
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 4 0.651 -0.03959 0.336 0.000 0.008 0.472 0.144 0.040
#> GSM213082 2 0.406 0.66158 0.004 0.812 0.060 0.008 0.048 0.068
#> GSM213085 1 0.565 0.39770 0.692 0.000 0.132 0.040 0.052 0.084
#> GSM213088 4 0.669 0.31828 0.076 0.068 0.016 0.636 0.104 0.100
#> GSM213091 3 0.722 0.01449 0.036 0.004 0.440 0.200 0.032 0.288
#> GSM213092 1 0.549 0.43553 0.724 0.004 0.084 0.056 0.060 0.072
#> GSM213096 1 0.757 0.24395 0.476 0.008 0.032 0.148 0.236 0.100
#> GSM213100 1 0.743 0.33790 0.528 0.008 0.084 0.204 0.068 0.108
#> GSM213111 2 0.570 0.64430 0.020 0.700 0.056 0.016 0.128 0.080
#> GSM213117 6 0.895 0.22701 0.080 0.072 0.136 0.228 0.104 0.380
#> GSM213118 5 0.862 0.14855 0.212 0.032 0.036 0.140 0.336 0.244
#> GSM213120 2 0.721 0.52737 0.024 0.556 0.056 0.048 0.204 0.112
#> GSM213122 2 0.231 0.68560 0.004 0.908 0.000 0.016 0.032 0.040
#> GSM213074 6 0.783 -0.01440 0.136 0.008 0.312 0.148 0.020 0.376
#> GSM213077 1 0.624 0.43159 0.644 0.000 0.048 0.144 0.076 0.088
#> GSM213083 1 0.622 0.32731 0.560 0.004 0.028 0.304 0.044 0.060
#> GSM213094 3 0.553 0.26753 0.032 0.008 0.604 0.044 0.008 0.304
#> GSM213095 2 0.827 0.15461 0.084 0.340 0.320 0.008 0.164 0.084
#> GSM213102 4 0.666 0.21308 0.132 0.008 0.088 0.620 0.044 0.108
#> GSM213103 2 0.778 0.20624 0.032 0.372 0.032 0.048 0.356 0.160
#> GSM213104 5 0.767 0.26682 0.240 0.064 0.088 0.040 0.508 0.060
#> GSM213107 2 0.583 0.47563 0.004 0.528 0.064 0.004 0.364 0.036
#> GSM213108 2 0.738 0.33219 0.032 0.452 0.272 0.012 0.040 0.192
#> GSM213112 1 0.602 0.35818 0.668 0.004 0.128 0.044 0.108 0.048
#> GSM213114 5 0.677 -0.00223 0.400 0.016 0.028 0.128 0.416 0.012
#> GSM213115 2 0.229 0.68557 0.000 0.896 0.000 0.004 0.072 0.028
#> GSM213116 6 0.841 0.19679 0.128 0.004 0.160 0.296 0.080 0.332
#> GSM213119 2 0.146 0.68468 0.000 0.948 0.004 0.004 0.016 0.028
#> GSM213072 3 0.797 -0.05905 0.132 0.004 0.360 0.104 0.060 0.340
#> GSM213075 6 0.876 0.13136 0.060 0.060 0.268 0.264 0.060 0.288
#> GSM213076 2 0.753 0.43324 0.008 0.472 0.132 0.024 0.244 0.120
#> GSM213079 3 0.396 0.37141 0.060 0.004 0.824 0.028 0.024 0.060
#> GSM213080 5 0.654 0.28158 0.228 0.092 0.000 0.116 0.556 0.008
#> GSM213081 4 0.867 0.07899 0.172 0.012 0.108 0.340 0.260 0.108
#> GSM213084 1 0.689 0.34652 0.520 0.000 0.036 0.272 0.076 0.096
#> GSM213087 2 0.280 0.67958 0.000 0.860 0.008 0.004 0.112 0.016
#> GSM213089 6 0.796 0.16491 0.064 0.012 0.264 0.256 0.040 0.364
#> GSM213090 3 0.482 0.33919 0.116 0.008 0.760 0.036 0.020 0.060
#> GSM213093 4 0.756 0.07169 0.116 0.004 0.168 0.512 0.056 0.144
#> GSM213097 4 0.545 0.25695 0.088 0.000 0.076 0.712 0.028 0.096
#> GSM213099 3 0.677 0.00442 0.044 0.000 0.420 0.156 0.012 0.368
#> GSM213101 4 0.711 0.09050 0.296 0.016 0.016 0.488 0.120 0.064
#> GSM213105 2 0.160 0.68670 0.000 0.944 0.008 0.008 0.016 0.024
#> GSM213109 1 0.722 0.27902 0.492 0.000 0.056 0.252 0.052 0.148
#> GSM213110 2 0.495 0.62362 0.040 0.768 0.016 0.040 0.088 0.048
#> GSM213113 5 0.952 -0.02692 0.104 0.064 0.176 0.204 0.268 0.184
#> GSM213121 2 0.473 0.60854 0.008 0.672 0.020 0.000 0.268 0.032
#> GSM213123 4 0.851 0.10973 0.120 0.016 0.116 0.420 0.188 0.140
#> GSM213125 2 0.164 0.68792 0.004 0.944 0.012 0.004 0.012 0.024
#> GSM213073 3 0.557 0.30278 0.052 0.012 0.704 0.036 0.152 0.044
#> GSM213086 1 0.754 0.14381 0.496 0.008 0.044 0.104 0.228 0.120
#> GSM213098 5 0.846 0.20366 0.056 0.052 0.168 0.128 0.452 0.144
#> GSM213106 4 0.775 -0.03134 0.052 0.024 0.124 0.472 0.068 0.260
#> GSM213124 2 0.908 0.09763 0.108 0.344 0.076 0.068 0.168 0.236
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 development.stage(p) disease.state(p) k
#> MAD:skmeans 49 0.986 0.752 2
#> MAD:skmeans 33 0.518 0.883 3
#> MAD:skmeans 16 NA NA 4
#> MAD:skmeans 13 NA NA 5
#> MAD:skmeans 11 NA NA 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "pam"]
# you can also extract it by
# res = res_list["MAD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.315 0.733 0.850 0.4137 0.575 0.575
#> 3 3 0.260 0.631 0.777 0.4972 0.774 0.613
#> 4 4 0.379 0.572 0.756 0.1067 0.891 0.720
#> 5 5 0.384 0.532 0.760 0.0235 0.944 0.835
#> 6 6 0.373 0.470 0.723 0.0370 0.989 0.965
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
#> GSM213078 1 0.2043 0.8396 0.968 0.032
#> GSM213082 2 0.9044 0.7886 0.320 0.680
#> GSM213085 1 0.4815 0.8122 0.896 0.104
#> GSM213088 1 0.2603 0.8328 0.956 0.044
#> GSM213091 1 0.3733 0.8285 0.928 0.072
#> GSM213092 1 0.1843 0.8465 0.972 0.028
#> GSM213096 1 0.1184 0.8490 0.984 0.016
#> GSM213100 1 0.0938 0.8495 0.988 0.012
#> GSM213111 2 0.6801 0.7740 0.180 0.820
#> GSM213117 1 0.0376 0.8495 0.996 0.004
#> GSM213118 1 0.6623 0.7325 0.828 0.172
#> GSM213120 2 0.9795 0.6471 0.416 0.584
#> GSM213122 2 0.8909 0.7931 0.308 0.692
#> GSM213074 1 0.0938 0.8506 0.988 0.012
#> GSM213077 1 0.1843 0.8485 0.972 0.028
#> GSM213083 1 0.0672 0.8494 0.992 0.008
#> GSM213094 1 0.9044 0.3751 0.680 0.320
#> GSM213095 2 0.8955 0.7313 0.312 0.688
#> GSM213102 1 0.0376 0.8493 0.996 0.004
#> GSM213103 2 0.9552 0.7284 0.376 0.624
#> GSM213104 1 0.9988 0.2862 0.520 0.480
#> GSM213107 2 0.0000 0.6816 0.000 1.000
#> GSM213108 2 0.9393 0.7527 0.356 0.644
#> GSM213112 1 0.2603 0.8453 0.956 0.044
#> GSM213114 1 0.8386 0.5860 0.732 0.268
#> GSM213115 2 0.3114 0.7119 0.056 0.944
#> GSM213116 1 0.3431 0.8257 0.936 0.064
#> GSM213119 2 0.8763 0.7947 0.296 0.704
#> GSM213072 1 0.4562 0.7901 0.904 0.096
#> GSM213075 1 0.6438 0.6992 0.836 0.164
#> GSM213076 1 0.9710 -0.0224 0.600 0.400
#> GSM213079 1 0.5946 0.7610 0.856 0.144
#> GSM213080 1 0.8713 0.5692 0.708 0.292
#> GSM213081 1 0.8327 0.5950 0.736 0.264
#> GSM213084 1 0.4562 0.8112 0.904 0.096
#> GSM213087 2 0.1633 0.6899 0.024 0.976
#> GSM213089 1 0.1843 0.8495 0.972 0.028
#> GSM213090 1 0.9775 0.0371 0.588 0.412
#> GSM213093 1 0.1414 0.8467 0.980 0.020
#> GSM213097 1 0.0000 0.8490 1.000 0.000
#> GSM213099 1 0.4815 0.7855 0.896 0.104
#> GSM213101 1 0.0000 0.8490 1.000 0.000
#> GSM213105 2 0.8713 0.7961 0.292 0.708
#> GSM213109 1 0.1633 0.8452 0.976 0.024
#> GSM213110 2 0.9248 0.7736 0.340 0.660
#> GSM213113 1 0.0938 0.8512 0.988 0.012
#> GSM213121 2 0.1843 0.6908 0.028 0.972
#> GSM213123 1 0.0376 0.8500 0.996 0.004
#> GSM213125 2 0.7602 0.7918 0.220 0.780
#> GSM213073 1 0.5059 0.8171 0.888 0.112
#> GSM213086 1 0.8713 0.5771 0.708 0.292
#> GSM213098 1 0.1184 0.8516 0.984 0.016
#> GSM213106 1 0.0000 0.8490 1.000 0.000
#> GSM213124 2 0.9815 0.6214 0.420 0.580
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.0000 0.741 1.000 0.000 0.000
#> GSM213082 2 0.4291 0.781 0.180 0.820 0.000
#> GSM213085 3 0.3879 0.783 0.152 0.000 0.848
#> GSM213088 1 0.0000 0.741 1.000 0.000 0.000
#> GSM213091 1 0.6057 0.392 0.656 0.004 0.340
#> GSM213092 3 0.4504 0.762 0.196 0.000 0.804
#> GSM213096 1 0.2261 0.737 0.932 0.000 0.068
#> GSM213100 1 0.2066 0.737 0.940 0.000 0.060
#> GSM213111 2 0.5961 0.762 0.136 0.788 0.076
#> GSM213117 1 0.3192 0.726 0.888 0.000 0.112
#> GSM213118 3 0.6307 0.460 0.328 0.012 0.660
#> GSM213120 2 0.7400 0.510 0.412 0.552 0.036
#> GSM213122 2 0.4346 0.779 0.184 0.816 0.000
#> GSM213074 1 0.5291 0.553 0.732 0.000 0.268
#> GSM213077 1 0.6225 0.139 0.568 0.000 0.432
#> GSM213083 1 0.4702 0.639 0.788 0.000 0.212
#> GSM213094 3 0.5466 0.773 0.160 0.040 0.800
#> GSM213095 3 0.5200 0.682 0.020 0.184 0.796
#> GSM213102 1 0.0000 0.741 1.000 0.000 0.000
#> GSM213103 2 0.7726 0.564 0.372 0.572 0.056
#> GSM213104 3 0.8231 0.447 0.136 0.236 0.628
#> GSM213107 2 0.3752 0.648 0.000 0.856 0.144
#> GSM213108 2 0.6228 0.680 0.316 0.672 0.012
#> GSM213112 3 0.3879 0.783 0.152 0.000 0.848
#> GSM213114 1 0.7930 0.445 0.664 0.164 0.172
#> GSM213115 2 0.1267 0.718 0.024 0.972 0.004
#> GSM213116 1 0.3888 0.724 0.888 0.048 0.064
#> GSM213119 2 0.4062 0.781 0.164 0.836 0.000
#> GSM213072 1 0.6422 0.451 0.660 0.016 0.324
#> GSM213075 1 0.3826 0.689 0.868 0.124 0.008
#> GSM213076 1 0.7916 0.282 0.620 0.292 0.088
#> GSM213079 3 0.4099 0.785 0.140 0.008 0.852
#> GSM213080 1 0.7615 0.460 0.688 0.164 0.148
#> GSM213081 1 0.7441 0.479 0.700 0.164 0.136
#> GSM213084 1 0.4799 0.681 0.836 0.032 0.132
#> GSM213087 2 0.1031 0.690 0.000 0.976 0.024
#> GSM213089 1 0.6252 0.128 0.556 0.000 0.444
#> GSM213090 3 0.4779 0.782 0.124 0.036 0.840
#> GSM213093 1 0.5497 0.499 0.708 0.000 0.292
#> GSM213097 1 0.0000 0.741 1.000 0.000 0.000
#> GSM213099 1 0.5371 0.678 0.812 0.048 0.140
#> GSM213101 1 0.0000 0.741 1.000 0.000 0.000
#> GSM213105 2 0.4002 0.782 0.160 0.840 0.000
#> GSM213109 3 0.5810 0.565 0.336 0.000 0.664
#> GSM213110 2 0.5882 0.645 0.348 0.652 0.000
#> GSM213113 1 0.5760 0.450 0.672 0.000 0.328
#> GSM213121 2 0.3983 0.648 0.004 0.852 0.144
#> GSM213123 1 0.2959 0.724 0.900 0.000 0.100
#> GSM213125 2 0.4628 0.751 0.088 0.856 0.056
#> GSM213073 3 0.5216 0.696 0.260 0.000 0.740
#> GSM213086 3 0.5631 0.620 0.064 0.132 0.804
#> GSM213098 1 0.3267 0.726 0.884 0.000 0.116
#> GSM213106 1 0.0592 0.742 0.988 0.000 0.012
#> GSM213124 2 0.8310 0.405 0.420 0.500 0.080
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.0707 0.7236 0.980 0.000 0.000 0.020
#> GSM213082 2 0.1256 0.6902 0.028 0.964 0.000 0.008
#> GSM213085 3 0.2976 0.7572 0.120 0.000 0.872 0.008
#> GSM213088 1 0.0469 0.7250 0.988 0.000 0.000 0.012
#> GSM213091 1 0.6106 0.4047 0.604 0.000 0.332 0.064
#> GSM213092 3 0.3583 0.7244 0.180 0.000 0.816 0.004
#> GSM213096 1 0.4824 0.6986 0.780 0.000 0.076 0.144
#> GSM213100 1 0.4586 0.6995 0.796 0.000 0.068 0.136
#> GSM213111 2 0.7080 0.4539 0.100 0.648 0.048 0.204
#> GSM213117 1 0.3182 0.7327 0.876 0.000 0.096 0.028
#> GSM213118 3 0.7171 0.4716 0.212 0.000 0.556 0.232
#> GSM213120 2 0.7136 0.1487 0.444 0.468 0.036 0.052
#> GSM213122 2 0.1004 0.6944 0.024 0.972 0.000 0.004
#> GSM213074 1 0.5339 0.5603 0.688 0.000 0.272 0.040
#> GSM213077 1 0.5292 0.0231 0.512 0.000 0.480 0.008
#> GSM213083 1 0.3982 0.6649 0.776 0.000 0.220 0.004
#> GSM213094 3 0.6415 0.7150 0.116 0.036 0.708 0.140
#> GSM213095 3 0.3870 0.6846 0.008 0.164 0.820 0.008
#> GSM213102 1 0.0000 0.7246 1.000 0.000 0.000 0.000
#> GSM213103 1 0.8939 -0.0113 0.400 0.328 0.068 0.204
#> GSM213104 4 0.6360 0.4421 0.064 0.036 0.212 0.688
#> GSM213107 4 0.4605 0.3430 0.000 0.336 0.000 0.664
#> GSM213108 2 0.4828 0.5406 0.268 0.716 0.008 0.008
#> GSM213112 3 0.3105 0.7573 0.120 0.000 0.868 0.012
#> GSM213114 4 0.5127 0.6044 0.356 0.000 0.012 0.632
#> GSM213115 2 0.0779 0.6912 0.004 0.980 0.000 0.016
#> GSM213116 1 0.3599 0.7265 0.876 0.020 0.040 0.064
#> GSM213119 2 0.0524 0.6912 0.004 0.988 0.000 0.008
#> GSM213072 1 0.6090 0.6123 0.696 0.020 0.216 0.068
#> GSM213075 1 0.4329 0.7067 0.824 0.040 0.012 0.124
#> GSM213076 1 0.6674 0.4079 0.636 0.272 0.044 0.048
#> GSM213079 3 0.2593 0.7000 0.004 0.000 0.892 0.104
#> GSM213080 4 0.4855 0.5942 0.400 0.000 0.000 0.600
#> GSM213081 4 0.4992 0.4486 0.476 0.000 0.000 0.524
#> GSM213084 1 0.5128 0.6499 0.760 0.000 0.148 0.092
#> GSM213087 2 0.1867 0.6413 0.000 0.928 0.000 0.072
#> GSM213089 1 0.4925 0.2757 0.572 0.000 0.428 0.000
#> GSM213090 3 0.1109 0.7186 0.004 0.000 0.968 0.028
#> GSM213093 1 0.5300 0.4866 0.664 0.000 0.308 0.028
#> GSM213097 1 0.0592 0.7240 0.984 0.000 0.000 0.016
#> GSM213099 1 0.4336 0.7154 0.828 0.040 0.116 0.016
#> GSM213101 1 0.0000 0.7246 1.000 0.000 0.000 0.000
#> GSM213105 2 0.0376 0.6914 0.004 0.992 0.000 0.004
#> GSM213109 3 0.4605 0.4739 0.336 0.000 0.664 0.000
#> GSM213110 2 0.5099 0.4061 0.380 0.612 0.000 0.008
#> GSM213113 1 0.4304 0.6049 0.716 0.000 0.284 0.000
#> GSM213121 4 0.4624 0.3363 0.000 0.340 0.000 0.660
#> GSM213123 1 0.2843 0.7297 0.892 0.000 0.088 0.020
#> GSM213125 2 0.1151 0.6844 0.000 0.968 0.008 0.024
#> GSM213073 3 0.3606 0.6872 0.132 0.000 0.844 0.024
#> GSM213086 3 0.6232 0.4161 0.072 0.000 0.596 0.332
#> GSM213098 1 0.5787 0.5899 0.680 0.000 0.076 0.244
#> GSM213106 1 0.0779 0.7295 0.980 0.000 0.016 0.004
#> GSM213124 2 0.7177 0.0537 0.444 0.444 0.104 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 4 0.0798 0.6993 0.008 0.000 0.000 0.976 0.016
#> GSM213082 2 0.1646 0.7832 0.004 0.944 0.000 0.020 0.032
#> GSM213085 3 0.3039 0.6007 0.012 0.000 0.836 0.152 0.000
#> GSM213088 4 0.0451 0.7008 0.004 0.000 0.000 0.988 0.008
#> GSM213091 4 0.5866 0.3399 0.032 0.000 0.332 0.584 0.052
#> GSM213092 3 0.3395 0.5686 0.000 0.000 0.764 0.236 0.000
#> GSM213096 4 0.5591 0.6346 0.120 0.000 0.100 0.716 0.064
#> GSM213100 4 0.5204 0.6447 0.096 0.000 0.092 0.748 0.064
#> GSM213111 2 0.6438 0.4812 0.212 0.632 0.052 0.096 0.008
#> GSM213117 4 0.3506 0.6958 0.020 0.004 0.080 0.856 0.040
#> GSM213118 3 0.7246 0.3452 0.216 0.000 0.512 0.216 0.056
#> GSM213120 4 0.6530 0.0412 0.044 0.448 0.040 0.452 0.016
#> GSM213122 2 0.1630 0.7873 0.004 0.944 0.000 0.016 0.036
#> GSM213074 4 0.4695 0.5326 0.016 0.000 0.260 0.700 0.024
#> GSM213077 4 0.4546 0.0747 0.008 0.000 0.460 0.532 0.000
#> GSM213083 4 0.3398 0.6262 0.004 0.000 0.216 0.780 0.000
#> GSM213094 5 0.3366 0.0000 0.000 0.000 0.212 0.004 0.784
#> GSM213095 3 0.3948 0.4370 0.012 0.196 0.776 0.016 0.000
#> GSM213102 4 0.0000 0.7008 0.000 0.000 0.000 1.000 0.000
#> GSM213103 4 0.8706 0.2363 0.204 0.268 0.092 0.392 0.044
#> GSM213104 1 0.5252 0.4777 0.740 0.024 0.160 0.056 0.020
#> GSM213107 1 0.3210 0.4907 0.788 0.212 0.000 0.000 0.000
#> GSM213108 2 0.4619 0.5270 0.012 0.704 0.012 0.264 0.008
#> GSM213112 3 0.3141 0.6004 0.016 0.000 0.832 0.152 0.000
#> GSM213114 1 0.4604 0.6085 0.680 0.000 0.012 0.292 0.016
#> GSM213115 2 0.0898 0.7836 0.020 0.972 0.000 0.000 0.008
#> GSM213116 4 0.3789 0.6926 0.048 0.012 0.040 0.852 0.048
#> GSM213119 2 0.0880 0.7861 0.000 0.968 0.000 0.000 0.032
#> GSM213072 4 0.5910 0.5753 0.048 0.016 0.212 0.676 0.048
#> GSM213075 4 0.3966 0.6911 0.068 0.032 0.012 0.840 0.048
#> GSM213076 4 0.6248 0.5212 0.092 0.220 0.040 0.640 0.008
#> GSM213079 3 0.4210 0.3703 0.096 0.000 0.780 0.000 0.124
#> GSM213080 1 0.3983 0.6091 0.660 0.000 0.000 0.340 0.000
#> GSM213081 1 0.4572 0.4783 0.540 0.000 0.004 0.452 0.004
#> GSM213084 4 0.4507 0.6361 0.044 0.000 0.120 0.788 0.048
#> GSM213087 2 0.1830 0.7511 0.068 0.924 0.000 0.000 0.008
#> GSM213089 4 0.4367 0.2654 0.000 0.000 0.416 0.580 0.004
#> GSM213090 3 0.2871 0.4145 0.088 0.000 0.872 0.000 0.040
#> GSM213093 4 0.4568 0.4777 0.008 0.000 0.288 0.684 0.020
#> GSM213097 4 0.0693 0.7000 0.008 0.000 0.000 0.980 0.012
#> GSM213099 4 0.4362 0.6822 0.004 0.032 0.084 0.808 0.072
#> GSM213101 4 0.0000 0.7008 0.000 0.000 0.000 1.000 0.000
#> GSM213105 2 0.0963 0.7856 0.000 0.964 0.000 0.000 0.036
#> GSM213109 3 0.4074 0.3802 0.000 0.000 0.636 0.364 0.000
#> GSM213110 2 0.4791 0.2054 0.008 0.588 0.000 0.392 0.012
#> GSM213113 4 0.3884 0.5693 0.004 0.000 0.288 0.708 0.000
#> GSM213121 1 0.3366 0.4885 0.784 0.212 0.000 0.000 0.004
#> GSM213123 4 0.2354 0.6933 0.008 0.000 0.076 0.904 0.012
#> GSM213125 2 0.1026 0.7822 0.024 0.968 0.004 0.000 0.004
#> GSM213073 3 0.4637 0.4244 0.032 0.000 0.780 0.108 0.080
#> GSM213086 3 0.5657 0.2459 0.360 0.000 0.560 0.076 0.004
#> GSM213098 4 0.6096 0.5453 0.220 0.000 0.096 0.640 0.044
#> GSM213106 4 0.0671 0.7032 0.000 0.000 0.016 0.980 0.004
#> GSM213124 4 0.6466 0.1155 0.016 0.428 0.100 0.452 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 4 0.1261 0.6589 0.008 0.000 0.028 0.956 0.004 0.004
#> GSM213082 2 0.2055 0.7617 0.000 0.924 0.020 0.020 0.008 0.028
#> GSM213085 1 0.1814 0.4054 0.900 0.000 0.000 0.100 0.000 0.000
#> GSM213088 4 0.0806 0.6616 0.008 0.000 0.020 0.972 0.000 0.000
#> GSM213091 4 0.5921 0.3376 0.316 0.000 0.076 0.560 0.016 0.032
#> GSM213092 1 0.3023 0.3804 0.768 0.000 0.000 0.232 0.000 0.000
#> GSM213096 4 0.6032 0.5253 0.160 0.000 0.132 0.628 0.072 0.008
#> GSM213100 4 0.5864 0.5328 0.160 0.000 0.132 0.644 0.052 0.012
#> GSM213111 2 0.6565 0.4542 0.096 0.584 0.012 0.068 0.224 0.016
#> GSM213117 4 0.3438 0.6502 0.096 0.000 0.020 0.840 0.016 0.028
#> GSM213118 1 0.6682 0.1289 0.560 0.000 0.120 0.160 0.152 0.008
#> GSM213120 4 0.6561 0.0636 0.068 0.412 0.016 0.440 0.056 0.008
#> GSM213122 2 0.1950 0.7655 0.000 0.928 0.020 0.012 0.008 0.032
#> GSM213074 4 0.4405 0.4977 0.260 0.000 0.040 0.688 0.012 0.000
#> GSM213077 4 0.4217 0.0535 0.464 0.000 0.008 0.524 0.004 0.000
#> GSM213083 4 0.3109 0.5839 0.224 0.000 0.000 0.772 0.004 0.000
#> GSM213094 6 0.1444 0.0000 0.072 0.000 0.000 0.000 0.000 0.928
#> GSM213095 1 0.3492 0.1189 0.796 0.172 0.004 0.016 0.012 0.000
#> GSM213102 4 0.0000 0.6634 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM213103 4 0.8715 0.1736 0.160 0.248 0.096 0.328 0.160 0.008
#> GSM213104 5 0.4689 0.5578 0.120 0.020 0.056 0.044 0.760 0.000
#> GSM213107 5 0.2135 0.5524 0.000 0.128 0.000 0.000 0.872 0.000
#> GSM213108 2 0.4638 0.5264 0.004 0.684 0.016 0.264 0.020 0.012
#> GSM213112 1 0.1958 0.4053 0.896 0.000 0.004 0.100 0.000 0.000
#> GSM213114 5 0.4070 0.6463 0.004 0.000 0.028 0.248 0.716 0.004
#> GSM213115 2 0.1528 0.7565 0.000 0.944 0.012 0.000 0.028 0.016
#> GSM213116 4 0.3634 0.6509 0.052 0.004 0.052 0.844 0.020 0.028
#> GSM213119 2 0.1257 0.7649 0.000 0.952 0.020 0.000 0.000 0.028
#> GSM213072 4 0.6190 0.4780 0.248 0.020 0.068 0.608 0.032 0.024
#> GSM213075 4 0.4328 0.6430 0.040 0.020 0.088 0.800 0.044 0.008
#> GSM213076 4 0.5830 0.4798 0.048 0.196 0.000 0.624 0.128 0.004
#> GSM213079 3 0.4301 0.4368 0.400 0.000 0.580 0.000 0.004 0.016
#> GSM213080 5 0.3575 0.6473 0.000 0.000 0.008 0.284 0.708 0.000
#> GSM213081 5 0.4776 0.4179 0.012 0.000 0.028 0.448 0.512 0.000
#> GSM213084 4 0.5022 0.5521 0.168 0.000 0.096 0.704 0.024 0.008
#> GSM213087 2 0.1556 0.7252 0.000 0.920 0.000 0.000 0.080 0.000
#> GSM213089 4 0.3944 0.2244 0.428 0.000 0.000 0.568 0.000 0.004
#> GSM213090 3 0.4853 0.4091 0.456 0.000 0.488 0.000 0.056 0.000
#> GSM213093 4 0.4579 0.4238 0.316 0.000 0.032 0.640 0.008 0.004
#> GSM213097 4 0.1180 0.6597 0.008 0.000 0.024 0.960 0.004 0.004
#> GSM213099 4 0.4976 0.6160 0.084 0.032 0.008 0.740 0.012 0.124
#> GSM213101 4 0.0000 0.6634 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM213105 2 0.1334 0.7641 0.000 0.948 0.020 0.000 0.000 0.032
#> GSM213109 1 0.3634 0.3235 0.644 0.000 0.000 0.356 0.000 0.000
#> GSM213110 2 0.4969 0.1809 0.000 0.560 0.016 0.392 0.016 0.016
#> GSM213113 4 0.3428 0.5194 0.304 0.000 0.000 0.696 0.000 0.000
#> GSM213121 5 0.2219 0.5463 0.000 0.136 0.000 0.000 0.864 0.000
#> GSM213123 4 0.2485 0.6506 0.084 0.000 0.024 0.884 0.008 0.000
#> GSM213125 2 0.1729 0.7564 0.004 0.936 0.012 0.000 0.036 0.012
#> GSM213073 1 0.5529 -0.2166 0.616 0.000 0.268 0.084 0.020 0.012
#> GSM213086 1 0.5194 -0.0393 0.544 0.000 0.020 0.052 0.384 0.000
#> GSM213098 4 0.5940 0.4811 0.096 0.000 0.076 0.600 0.228 0.000
#> GSM213106 4 0.0692 0.6645 0.020 0.000 0.004 0.976 0.000 0.000
#> GSM213124 4 0.6457 0.1213 0.124 0.396 0.008 0.440 0.020 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 development.stage(p) disease.state(p) k
#> MAD:pam 50 0.474 0.640 2
#> MAD:pam 41 0.740 0.715 3
#> MAD:pam 37 0.846 0.814 4
#> MAD:pam 33 0.327 0.938 5
#> MAD:pam 29 0.821 0.348 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "mclust"]
# you can also extract it by
# res = res_list["MAD:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.599 0.807 0.905 0.4511 0.525 0.525
#> 3 3 0.383 0.478 0.724 0.1924 0.617 0.424
#> 4 4 0.421 0.574 0.746 0.2786 0.611 0.285
#> 5 5 0.549 0.680 0.790 0.0721 0.864 0.596
#> 6 6 0.625 0.532 0.773 0.0636 0.936 0.772
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
#> GSM213078 1 0.1843 0.9245 0.972 0.028
#> GSM213082 2 0.0938 0.8503 0.012 0.988
#> GSM213085 1 0.1843 0.9244 0.972 0.028
#> GSM213088 1 0.5629 0.8622 0.868 0.132
#> GSM213091 1 0.4298 0.8950 0.912 0.088
#> GSM213092 1 0.1843 0.9238 0.972 0.028
#> GSM213096 1 0.1633 0.9243 0.976 0.024
#> GSM213100 1 0.1843 0.9238 0.972 0.028
#> GSM213111 2 0.0938 0.8503 0.012 0.988
#> GSM213117 1 0.1184 0.9198 0.984 0.016
#> GSM213118 1 0.1843 0.9245 0.972 0.028
#> GSM213120 2 0.3274 0.8206 0.060 0.940
#> GSM213122 2 0.0376 0.8486 0.004 0.996
#> GSM213074 1 0.5842 0.8451 0.860 0.140
#> GSM213077 1 0.1843 0.9238 0.972 0.028
#> GSM213083 1 0.1843 0.9245 0.972 0.028
#> GSM213094 2 0.9323 0.4942 0.348 0.652
#> GSM213095 2 0.0938 0.8503 0.012 0.988
#> GSM213102 1 0.0376 0.9166 0.996 0.004
#> GSM213103 2 0.9970 0.0135 0.468 0.532
#> GSM213104 1 0.8909 0.6116 0.692 0.308
#> GSM213107 2 0.0938 0.8503 0.012 0.988
#> GSM213108 2 0.2043 0.8411 0.032 0.968
#> GSM213112 1 0.3879 0.9024 0.924 0.076
#> GSM213114 1 0.6887 0.8011 0.816 0.184
#> GSM213115 2 0.0376 0.8486 0.004 0.996
#> GSM213116 1 0.0376 0.9166 0.996 0.004
#> GSM213119 2 0.0376 0.8486 0.004 0.996
#> GSM213072 1 0.1414 0.9228 0.980 0.020
#> GSM213075 1 0.1633 0.9229 0.976 0.024
#> GSM213076 2 0.0938 0.8503 0.012 0.988
#> GSM213079 2 0.9248 0.5111 0.340 0.660
#> GSM213080 1 0.8813 0.6269 0.700 0.300
#> GSM213081 1 0.1843 0.9247 0.972 0.028
#> GSM213084 1 0.1843 0.9238 0.972 0.028
#> GSM213087 2 0.0376 0.8486 0.004 0.996
#> GSM213089 1 0.2236 0.9150 0.964 0.036
#> GSM213090 2 0.9248 0.5111 0.340 0.660
#> GSM213093 1 0.0376 0.9166 0.996 0.004
#> GSM213097 1 0.0376 0.9166 0.996 0.004
#> GSM213099 1 0.5408 0.8686 0.876 0.124
#> GSM213101 1 0.1843 0.9245 0.972 0.028
#> GSM213105 2 0.0376 0.8486 0.004 0.996
#> GSM213109 1 0.0938 0.9208 0.988 0.012
#> GSM213110 2 0.9970 0.0135 0.468 0.532
#> GSM213113 1 0.5629 0.8607 0.868 0.132
#> GSM213121 2 0.0938 0.8503 0.012 0.988
#> GSM213123 1 0.1414 0.9239 0.980 0.020
#> GSM213125 2 0.0376 0.8486 0.004 0.996
#> GSM213073 2 0.9248 0.5111 0.340 0.660
#> GSM213086 1 0.1843 0.9238 0.972 0.028
#> GSM213098 1 0.7056 0.7937 0.808 0.192
#> GSM213106 1 0.0376 0.9166 0.996 0.004
#> GSM213124 1 0.9710 0.3756 0.600 0.400
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 2 0.6509 0.0856 0.472 0.524 0.004
#> GSM213082 2 0.1289 0.7195 0.000 0.968 0.032
#> GSM213085 1 0.9338 -0.4673 0.468 0.172 0.360
#> GSM213088 2 0.6295 0.0936 0.472 0.528 0.000
#> GSM213091 1 0.7158 0.3107 0.596 0.372 0.032
#> GSM213092 3 0.7841 0.8483 0.472 0.052 0.476
#> GSM213096 1 0.8142 -0.8321 0.468 0.068 0.464
#> GSM213100 3 0.6295 0.9382 0.472 0.000 0.528
#> GSM213111 2 0.0237 0.7242 0.000 0.996 0.004
#> GSM213117 1 0.0592 0.4562 0.988 0.012 0.000
#> GSM213118 1 0.8826 0.1505 0.472 0.412 0.116
#> GSM213120 2 0.0237 0.7242 0.000 0.996 0.004
#> GSM213122 2 0.2625 0.7029 0.000 0.916 0.084
#> GSM213074 1 0.6180 0.3506 0.660 0.332 0.008
#> GSM213077 3 0.6295 0.9382 0.472 0.000 0.528
#> GSM213083 1 0.9571 -0.2785 0.472 0.224 0.304
#> GSM213094 2 0.6566 0.5463 0.012 0.612 0.376
#> GSM213095 2 0.1289 0.7195 0.000 0.968 0.032
#> GSM213102 1 0.0000 0.4462 1.000 0.000 0.000
#> GSM213103 2 0.0000 0.7243 0.000 1.000 0.000
#> GSM213104 2 0.6529 0.3389 0.368 0.620 0.012
#> GSM213107 2 0.0237 0.7240 0.000 0.996 0.004
#> GSM213108 2 0.0000 0.7243 0.000 1.000 0.000
#> GSM213112 1 0.9102 0.1321 0.452 0.408 0.140
#> GSM213114 2 0.6566 0.3227 0.376 0.612 0.012
#> GSM213115 2 0.2625 0.7029 0.000 0.916 0.084
#> GSM213116 1 0.0237 0.4518 0.996 0.004 0.000
#> GSM213119 2 0.2625 0.7029 0.000 0.916 0.084
#> GSM213072 1 0.5420 0.3791 0.752 0.240 0.008
#> GSM213075 1 0.2066 0.4611 0.940 0.060 0.000
#> GSM213076 2 0.0000 0.7243 0.000 1.000 0.000
#> GSM213079 2 0.6282 0.5475 0.004 0.612 0.384
#> GSM213080 2 0.6548 0.3312 0.372 0.616 0.012
#> GSM213081 3 0.7841 0.8534 0.468 0.052 0.480
#> GSM213084 3 0.6295 0.9382 0.472 0.000 0.528
#> GSM213087 2 0.2165 0.7090 0.000 0.936 0.064
#> GSM213089 1 0.1411 0.4627 0.964 0.036 0.000
#> GSM213090 2 0.6079 0.5477 0.000 0.612 0.388
#> GSM213093 1 0.0000 0.4462 1.000 0.000 0.000
#> GSM213097 1 0.0592 0.4532 0.988 0.012 0.000
#> GSM213099 2 0.8097 0.2268 0.388 0.540 0.072
#> GSM213101 2 0.6513 0.0723 0.476 0.520 0.004
#> GSM213105 2 0.2625 0.7029 0.000 0.916 0.084
#> GSM213109 1 0.3551 0.4295 0.868 0.132 0.000
#> GSM213110 2 0.0237 0.7242 0.000 0.996 0.004
#> GSM213113 2 0.6540 0.2463 0.408 0.584 0.008
#> GSM213121 2 0.0000 0.7243 0.000 1.000 0.000
#> GSM213123 1 0.3481 0.3754 0.904 0.044 0.052
#> GSM213125 2 0.2625 0.7029 0.000 0.916 0.084
#> GSM213073 2 0.6282 0.5482 0.004 0.612 0.384
#> GSM213086 3 0.6295 0.9382 0.472 0.000 0.528
#> GSM213098 2 0.6451 0.3047 0.384 0.608 0.008
#> GSM213106 1 0.0237 0.4518 0.996 0.004 0.000
#> GSM213124 2 0.5291 0.5081 0.268 0.732 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.5679 0.6228 0.608 0.008 0.020 0.364
#> GSM213082 2 0.4188 0.6192 0.000 0.752 0.004 0.244
#> GSM213085 1 0.5352 0.5995 0.596 0.000 0.016 0.388
#> GSM213088 4 0.3105 0.4744 0.084 0.008 0.020 0.888
#> GSM213091 4 0.4408 0.6792 0.008 0.004 0.232 0.756
#> GSM213092 1 0.3443 0.7041 0.848 0.000 0.016 0.136
#> GSM213096 1 0.3072 0.7039 0.868 0.004 0.004 0.124
#> GSM213100 1 0.1978 0.6877 0.928 0.000 0.004 0.068
#> GSM213111 2 0.5220 0.5635 0.000 0.632 0.016 0.352
#> GSM213117 4 0.5271 0.6812 0.020 0.000 0.340 0.640
#> GSM213118 4 0.5540 0.2060 0.352 0.012 0.012 0.624
#> GSM213120 2 0.5641 0.5464 0.004 0.608 0.024 0.364
#> GSM213122 2 0.0000 0.6365 0.000 1.000 0.000 0.000
#> GSM213074 4 0.4408 0.6817 0.008 0.004 0.232 0.756
#> GSM213077 1 0.1792 0.6868 0.932 0.000 0.000 0.068
#> GSM213083 1 0.5105 0.6758 0.696 0.000 0.028 0.276
#> GSM213094 3 0.4991 0.8992 0.000 0.004 0.608 0.388
#> GSM213095 3 0.7859 0.5324 0.004 0.220 0.400 0.376
#> GSM213102 4 0.6398 0.6525 0.080 0.000 0.344 0.576
#> GSM213103 4 0.5346 -0.1148 0.004 0.272 0.032 0.692
#> GSM213104 1 0.6432 0.3490 0.556 0.020 0.036 0.388
#> GSM213107 2 0.6239 0.4914 0.004 0.568 0.052 0.376
#> GSM213108 2 0.5613 0.5243 0.000 0.592 0.028 0.380
#> GSM213112 1 0.5648 0.5233 0.536 0.004 0.016 0.444
#> GSM213114 1 0.6041 0.4377 0.600 0.012 0.032 0.356
#> GSM213115 2 0.0000 0.6365 0.000 1.000 0.000 0.000
#> GSM213116 4 0.6570 0.6531 0.100 0.000 0.320 0.580
#> GSM213119 2 0.0000 0.6365 0.000 1.000 0.000 0.000
#> GSM213072 4 0.5519 0.6879 0.028 0.004 0.316 0.652
#> GSM213075 4 0.5254 0.6923 0.028 0.000 0.300 0.672
#> GSM213076 2 0.5941 0.5184 0.004 0.584 0.036 0.376
#> GSM213079 3 0.5070 0.9039 0.008 0.000 0.620 0.372
#> GSM213080 1 0.6386 0.3644 0.572 0.020 0.036 0.372
#> GSM213081 1 0.2918 0.6847 0.876 0.008 0.000 0.116
#> GSM213084 1 0.1978 0.6875 0.928 0.000 0.004 0.068
#> GSM213087 2 0.3196 0.6398 0.000 0.856 0.008 0.136
#> GSM213089 4 0.5069 0.6886 0.016 0.000 0.320 0.664
#> GSM213090 3 0.4790 0.9021 0.000 0.000 0.620 0.380
#> GSM213093 4 0.6069 0.6599 0.056 0.000 0.356 0.588
#> GSM213097 4 0.7686 0.4711 0.228 0.000 0.336 0.436
#> GSM213099 4 0.3400 0.5960 0.012 0.004 0.128 0.856
#> GSM213101 1 0.5670 0.6080 0.584 0.008 0.016 0.392
#> GSM213105 2 0.0000 0.6365 0.000 1.000 0.000 0.000
#> GSM213109 1 0.7581 0.1491 0.440 0.000 0.360 0.200
#> GSM213110 4 0.4675 0.0013 0.000 0.244 0.020 0.736
#> GSM213113 4 0.2497 0.4180 0.040 0.016 0.020 0.924
#> GSM213121 2 0.6007 0.5197 0.004 0.584 0.040 0.372
#> GSM213123 4 0.6565 0.5810 0.224 0.000 0.148 0.628
#> GSM213125 2 0.0336 0.6383 0.000 0.992 0.000 0.008
#> GSM213073 3 0.5070 0.9039 0.008 0.000 0.620 0.372
#> GSM213086 1 0.2402 0.6852 0.912 0.000 0.012 0.076
#> GSM213098 4 0.3444 0.3766 0.104 0.012 0.016 0.868
#> GSM213106 4 0.5371 0.6668 0.020 0.000 0.364 0.616
#> GSM213124 4 0.2989 0.3499 0.004 0.100 0.012 0.884
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.6350 0.751 0.692 0.068 0.092 0.112 0.036
#> GSM213082 2 0.2648 0.643 0.000 0.848 0.000 0.000 0.152
#> GSM213085 1 0.5352 0.745 0.708 0.112 0.012 0.164 0.004
#> GSM213088 4 0.5950 0.703 0.088 0.132 0.052 0.708 0.020
#> GSM213091 4 0.4186 0.794 0.008 0.032 0.072 0.824 0.064
#> GSM213092 1 0.2464 0.795 0.892 0.012 0.004 0.092 0.000
#> GSM213096 1 0.2681 0.794 0.896 0.024 0.008 0.068 0.004
#> GSM213100 1 0.2228 0.785 0.912 0.000 0.008 0.068 0.012
#> GSM213111 2 0.0162 0.590 0.000 0.996 0.004 0.000 0.000
#> GSM213117 4 0.1278 0.849 0.020 0.016 0.004 0.960 0.000
#> GSM213118 1 0.5585 0.724 0.688 0.084 0.024 0.200 0.004
#> GSM213120 2 0.1041 0.570 0.000 0.964 0.004 0.000 0.032
#> GSM213122 2 0.3684 0.640 0.000 0.720 0.000 0.000 0.280
#> GSM213074 4 0.4061 0.786 0.000 0.040 0.072 0.824 0.064
#> GSM213077 1 0.1990 0.785 0.920 0.000 0.004 0.068 0.008
#> GSM213083 1 0.4748 0.780 0.784 0.036 0.040 0.124 0.016
#> GSM213094 3 0.4051 0.928 0.004 0.164 0.792 0.008 0.032
#> GSM213095 5 0.5901 0.900 0.000 0.344 0.116 0.000 0.540
#> GSM213102 4 0.2172 0.840 0.076 0.000 0.016 0.908 0.000
#> GSM213103 2 0.3223 0.486 0.012 0.880 0.020 0.044 0.044
#> GSM213104 1 0.6631 0.552 0.644 0.196 0.060 0.036 0.064
#> GSM213107 5 0.5541 0.905 0.000 0.372 0.076 0.000 0.552
#> GSM213108 2 0.2728 0.517 0.000 0.888 0.068 0.004 0.040
#> GSM213112 1 0.6074 0.712 0.656 0.144 0.028 0.168 0.004
#> GSM213114 1 0.5523 0.610 0.708 0.168 0.064 0.000 0.060
#> GSM213115 2 0.3684 0.640 0.000 0.720 0.000 0.000 0.280
#> GSM213116 4 0.2020 0.834 0.100 0.000 0.000 0.900 0.000
#> GSM213119 2 0.3684 0.640 0.000 0.720 0.000 0.000 0.280
#> GSM213072 4 0.3248 0.828 0.032 0.004 0.048 0.876 0.040
#> GSM213075 4 0.1646 0.848 0.020 0.032 0.004 0.944 0.000
#> GSM213076 2 0.1739 0.544 0.004 0.940 0.024 0.000 0.032
#> GSM213079 3 0.2773 0.953 0.000 0.164 0.836 0.000 0.000
#> GSM213080 1 0.5923 0.596 0.688 0.176 0.068 0.008 0.060
#> GSM213081 1 0.3094 0.791 0.868 0.012 0.012 0.100 0.008
#> GSM213084 1 0.2179 0.787 0.912 0.000 0.008 0.072 0.008
#> GSM213087 2 0.3177 0.648 0.000 0.792 0.000 0.000 0.208
#> GSM213089 4 0.1560 0.849 0.020 0.028 0.004 0.948 0.000
#> GSM213090 3 0.2930 0.953 0.000 0.164 0.832 0.000 0.004
#> GSM213093 4 0.1704 0.843 0.068 0.000 0.004 0.928 0.000
#> GSM213097 4 0.3446 0.809 0.116 0.000 0.036 0.840 0.008
#> GSM213099 4 0.5178 0.753 0.008 0.072 0.104 0.760 0.056
#> GSM213101 1 0.7687 0.249 0.452 0.068 0.084 0.360 0.036
#> GSM213105 2 0.3684 0.640 0.000 0.720 0.000 0.000 0.280
#> GSM213109 4 0.2629 0.806 0.136 0.000 0.004 0.860 0.000
#> GSM213110 2 0.2308 0.533 0.004 0.912 0.000 0.048 0.036
#> GSM213113 4 0.7222 0.239 0.248 0.180 0.048 0.520 0.004
#> GSM213121 2 0.5044 -0.559 0.000 0.504 0.032 0.000 0.464
#> GSM213123 4 0.4155 0.717 0.228 0.024 0.004 0.744 0.000
#> GSM213125 2 0.3684 0.640 0.000 0.720 0.000 0.000 0.280
#> GSM213073 3 0.3318 0.914 0.000 0.192 0.800 0.000 0.008
#> GSM213086 1 0.2532 0.785 0.892 0.000 0.008 0.088 0.012
#> GSM213098 1 0.6545 0.638 0.604 0.172 0.044 0.180 0.000
#> GSM213106 4 0.0703 0.846 0.024 0.000 0.000 0.976 0.000
#> GSM213124 2 0.6088 -0.232 0.028 0.480 0.024 0.448 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.7066 0.0604 0.404 0.004 0.008 0.352 0.060 0.172
#> GSM213082 2 0.1218 0.7745 0.000 0.956 0.012 0.000 0.028 0.004
#> GSM213085 1 0.3139 0.7284 0.852 0.000 0.024 0.100 0.012 0.012
#> GSM213088 4 0.6607 0.4310 0.132 0.016 0.024 0.600 0.048 0.180
#> GSM213091 4 0.4566 -0.9177 0.008 0.000 0.020 0.492 0.000 0.480
#> GSM213092 1 0.1850 0.7407 0.924 0.000 0.000 0.052 0.016 0.008
#> GSM213096 1 0.1536 0.7409 0.940 0.000 0.000 0.040 0.016 0.004
#> GSM213100 1 0.1820 0.7402 0.924 0.000 0.000 0.056 0.012 0.008
#> GSM213111 2 0.4177 0.7396 0.000 0.780 0.032 0.000 0.092 0.096
#> GSM213117 4 0.1251 0.5976 0.024 0.000 0.008 0.956 0.000 0.012
#> GSM213118 1 0.4653 0.6866 0.740 0.004 0.012 0.160 0.072 0.012
#> GSM213120 2 0.4833 0.7159 0.004 0.728 0.032 0.000 0.132 0.104
#> GSM213122 2 0.0146 0.7712 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM213074 4 0.4318 -0.8192 0.000 0.000 0.020 0.532 0.000 0.448
#> GSM213077 1 0.1370 0.7374 0.948 0.000 0.000 0.036 0.012 0.004
#> GSM213083 1 0.5276 0.4939 0.648 0.000 0.008 0.228 0.012 0.104
#> GSM213094 3 0.4087 0.5878 0.000 0.004 0.668 0.008 0.008 0.312
#> GSM213095 5 0.3786 0.6778 0.004 0.052 0.172 0.000 0.772 0.000
#> GSM213102 4 0.1686 0.6192 0.064 0.000 0.000 0.924 0.000 0.012
#> GSM213103 2 0.5573 0.6776 0.016 0.684 0.040 0.004 0.152 0.104
#> GSM213104 1 0.6696 0.4260 0.524 0.008 0.024 0.024 0.260 0.160
#> GSM213107 5 0.3953 0.7212 0.000 0.104 0.132 0.000 0.764 0.000
#> GSM213108 2 0.6290 0.5791 0.000 0.628 0.112 0.024 0.096 0.140
#> GSM213112 1 0.3743 0.7243 0.828 0.004 0.028 0.092 0.036 0.012
#> GSM213114 1 0.6224 0.4656 0.568 0.004 0.024 0.016 0.256 0.132
#> GSM213115 2 0.0291 0.7689 0.000 0.992 0.004 0.000 0.004 0.000
#> GSM213116 4 0.2135 0.6003 0.128 0.000 0.000 0.872 0.000 0.000
#> GSM213119 2 0.0146 0.7712 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM213072 4 0.4474 -0.7204 0.024 0.000 0.004 0.560 0.000 0.412
#> GSM213075 4 0.1659 0.5942 0.028 0.000 0.008 0.940 0.004 0.020
#> GSM213076 2 0.5094 0.6935 0.004 0.704 0.040 0.000 0.156 0.096
#> GSM213079 3 0.0146 0.8522 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM213080 1 0.6617 0.4175 0.520 0.008 0.024 0.016 0.264 0.168
#> GSM213081 1 0.3471 0.6547 0.784 0.000 0.000 0.188 0.008 0.020
#> GSM213084 1 0.2195 0.7382 0.904 0.000 0.000 0.068 0.012 0.016
#> GSM213087 2 0.0725 0.7721 0.000 0.976 0.012 0.000 0.012 0.000
#> GSM213089 4 0.1223 0.5739 0.008 0.000 0.012 0.960 0.004 0.016
#> GSM213090 3 0.0146 0.8522 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM213093 4 0.1411 0.6160 0.060 0.000 0.000 0.936 0.000 0.004
#> GSM213097 4 0.3068 0.5942 0.088 0.000 0.000 0.840 0.000 0.072
#> GSM213099 6 0.4982 0.0000 0.008 0.000 0.048 0.456 0.000 0.488
#> GSM213101 4 0.6706 0.3041 0.272 0.004 0.008 0.500 0.044 0.172
#> GSM213105 2 0.0291 0.7689 0.000 0.992 0.004 0.000 0.004 0.000
#> GSM213109 4 0.2800 0.5581 0.112 0.004 0.000 0.860 0.008 0.016
#> GSM213110 2 0.4862 0.7189 0.004 0.732 0.028 0.004 0.128 0.104
#> GSM213113 1 0.7503 0.1802 0.404 0.032 0.064 0.384 0.076 0.040
#> GSM213121 5 0.4809 0.5061 0.000 0.372 0.044 0.000 0.576 0.008
#> GSM213123 4 0.3591 0.4937 0.256 0.000 0.004 0.732 0.004 0.004
#> GSM213125 2 0.0146 0.7711 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM213073 3 0.1371 0.8250 0.000 0.004 0.948 0.004 0.040 0.004
#> GSM213086 1 0.1745 0.7418 0.920 0.000 0.000 0.068 0.012 0.000
#> GSM213098 1 0.6055 0.6486 0.672 0.020 0.036 0.140 0.096 0.036
#> GSM213106 4 0.0713 0.6016 0.028 0.000 0.000 0.972 0.000 0.000
#> GSM213124 2 0.7640 0.1436 0.008 0.412 0.040 0.332 0.096 0.112
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 development.stage(p) disease.state(p) k
#> MAD:mclust 50 1.000 1.000 2
#> MAD:mclust 27 1.000 1.000 3
#> MAD:mclust 41 0.574 0.585 4
#> MAD:mclust 49 0.220 0.244 5
#> MAD:mclust 40 0.440 0.794 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "NMF"]
# you can also extract it by
# res = res_list["MAD:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.922 0.943 0.977 0.4626 0.535 0.535
#> 3 3 0.504 0.710 0.829 0.4041 0.697 0.481
#> 4 4 0.510 0.499 0.703 0.1535 0.820 0.528
#> 5 5 0.582 0.528 0.727 0.0685 0.853 0.509
#> 6 6 0.620 0.430 0.668 0.0446 0.914 0.633
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
#> GSM213078 1 0.0000 0.9830 1.000 0.000
#> GSM213082 2 0.0000 0.9612 0.000 1.000
#> GSM213085 1 0.0000 0.9830 1.000 0.000
#> GSM213088 1 0.5737 0.8402 0.864 0.136
#> GSM213091 1 0.0000 0.9830 1.000 0.000
#> GSM213092 1 0.0000 0.9830 1.000 0.000
#> GSM213096 1 0.0000 0.9830 1.000 0.000
#> GSM213100 1 0.0000 0.9830 1.000 0.000
#> GSM213111 2 0.0000 0.9612 0.000 1.000
#> GSM213117 1 0.0000 0.9830 1.000 0.000
#> GSM213118 1 0.0672 0.9766 0.992 0.008
#> GSM213120 2 0.0000 0.9612 0.000 1.000
#> GSM213122 2 0.0000 0.9612 0.000 1.000
#> GSM213074 1 0.0000 0.9830 1.000 0.000
#> GSM213077 1 0.0000 0.9830 1.000 0.000
#> GSM213083 1 0.0000 0.9830 1.000 0.000
#> GSM213094 1 0.0000 0.9830 1.000 0.000
#> GSM213095 2 0.0000 0.9612 0.000 1.000
#> GSM213102 1 0.0000 0.9830 1.000 0.000
#> GSM213103 2 0.0000 0.9612 0.000 1.000
#> GSM213104 2 0.0672 0.9548 0.008 0.992
#> GSM213107 2 0.0000 0.9612 0.000 1.000
#> GSM213108 2 0.6801 0.7638 0.180 0.820
#> GSM213112 1 0.0000 0.9830 1.000 0.000
#> GSM213114 1 0.6531 0.7980 0.832 0.168
#> GSM213115 2 0.0000 0.9612 0.000 1.000
#> GSM213116 1 0.0000 0.9830 1.000 0.000
#> GSM213119 2 0.0000 0.9612 0.000 1.000
#> GSM213072 1 0.0000 0.9830 1.000 0.000
#> GSM213075 1 0.0000 0.9830 1.000 0.000
#> GSM213076 2 0.0000 0.9612 0.000 1.000
#> GSM213079 1 0.0000 0.9830 1.000 0.000
#> GSM213080 2 0.0000 0.9612 0.000 1.000
#> GSM213081 1 0.0000 0.9830 1.000 0.000
#> GSM213084 1 0.0000 0.9830 1.000 0.000
#> GSM213087 2 0.0000 0.9612 0.000 1.000
#> GSM213089 1 0.0000 0.9830 1.000 0.000
#> GSM213090 1 0.0000 0.9830 1.000 0.000
#> GSM213093 1 0.0000 0.9830 1.000 0.000
#> GSM213097 1 0.0000 0.9830 1.000 0.000
#> GSM213099 1 0.0000 0.9830 1.000 0.000
#> GSM213101 1 0.0000 0.9830 1.000 0.000
#> GSM213105 2 0.0000 0.9612 0.000 1.000
#> GSM213109 1 0.0000 0.9830 1.000 0.000
#> GSM213110 2 0.0000 0.9612 0.000 1.000
#> GSM213113 1 0.2043 0.9551 0.968 0.032
#> GSM213121 2 0.0000 0.9612 0.000 1.000
#> GSM213123 1 0.0000 0.9830 1.000 0.000
#> GSM213125 2 0.0000 0.9612 0.000 1.000
#> GSM213073 1 0.0000 0.9830 1.000 0.000
#> GSM213086 1 0.0000 0.9830 1.000 0.000
#> GSM213098 1 0.7376 0.7387 0.792 0.208
#> GSM213106 1 0.0000 0.9830 1.000 0.000
#> GSM213124 2 0.9996 0.0329 0.488 0.512
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.4346 0.756 0.816 0.000 0.184
#> GSM213082 2 0.1765 0.943 0.004 0.956 0.040
#> GSM213085 1 0.6079 0.603 0.612 0.000 0.388
#> GSM213088 1 0.9303 0.408 0.500 0.184 0.316
#> GSM213091 3 0.0747 0.744 0.016 0.000 0.984
#> GSM213092 1 0.5968 0.658 0.636 0.000 0.364
#> GSM213096 1 0.2878 0.722 0.904 0.000 0.096
#> GSM213100 1 0.5529 0.721 0.704 0.000 0.296
#> GSM213111 2 0.1751 0.950 0.012 0.960 0.028
#> GSM213117 3 0.4047 0.700 0.148 0.004 0.848
#> GSM213118 1 0.4346 0.752 0.816 0.000 0.184
#> GSM213120 2 0.1182 0.954 0.012 0.976 0.012
#> GSM213122 2 0.0829 0.953 0.004 0.984 0.012
#> GSM213074 3 0.1031 0.746 0.024 0.000 0.976
#> GSM213077 1 0.5327 0.743 0.728 0.000 0.272
#> GSM213083 1 0.5905 0.659 0.648 0.000 0.352
#> GSM213094 3 0.0747 0.740 0.016 0.000 0.984
#> GSM213095 2 0.5764 0.846 0.124 0.800 0.076
#> GSM213102 3 0.5588 0.541 0.276 0.004 0.720
#> GSM213103 2 0.2711 0.926 0.088 0.912 0.000
#> GSM213104 1 0.4589 0.527 0.820 0.172 0.008
#> GSM213107 2 0.4605 0.829 0.204 0.796 0.000
#> GSM213108 3 0.6587 0.132 0.008 0.424 0.568
#> GSM213112 1 0.6154 0.534 0.592 0.000 0.408
#> GSM213114 1 0.1337 0.665 0.972 0.012 0.016
#> GSM213115 2 0.0424 0.954 0.008 0.992 0.000
#> GSM213116 3 0.4235 0.681 0.176 0.000 0.824
#> GSM213119 2 0.0592 0.953 0.000 0.988 0.012
#> GSM213072 3 0.2066 0.744 0.060 0.000 0.940
#> GSM213075 3 0.2384 0.739 0.056 0.008 0.936
#> GSM213076 2 0.2313 0.947 0.032 0.944 0.024
#> GSM213079 3 0.2165 0.733 0.064 0.000 0.936
#> GSM213080 1 0.3192 0.591 0.888 0.112 0.000
#> GSM213081 1 0.4291 0.757 0.820 0.000 0.180
#> GSM213084 1 0.5882 0.675 0.652 0.000 0.348
#> GSM213087 2 0.0892 0.953 0.020 0.980 0.000
#> GSM213089 3 0.1643 0.746 0.044 0.000 0.956
#> GSM213090 3 0.2356 0.724 0.072 0.000 0.928
#> GSM213093 3 0.3192 0.726 0.112 0.000 0.888
#> GSM213097 3 0.5404 0.561 0.256 0.004 0.740
#> GSM213099 3 0.0592 0.742 0.012 0.000 0.988
#> GSM213101 1 0.5285 0.737 0.752 0.004 0.244
#> GSM213105 2 0.0237 0.954 0.004 0.996 0.000
#> GSM213109 3 0.5363 0.496 0.276 0.000 0.724
#> GSM213110 2 0.1643 0.945 0.044 0.956 0.000
#> GSM213113 3 0.5236 0.644 0.168 0.028 0.804
#> GSM213121 2 0.1964 0.941 0.056 0.944 0.000
#> GSM213123 3 0.5678 0.455 0.316 0.000 0.684
#> GSM213125 2 0.0424 0.954 0.000 0.992 0.008
#> GSM213073 3 0.5621 0.468 0.308 0.000 0.692
#> GSM213086 1 0.4887 0.757 0.772 0.000 0.228
#> GSM213098 3 0.7575 0.100 0.456 0.040 0.504
#> GSM213106 3 0.4465 0.681 0.176 0.004 0.820
#> GSM213124 3 0.7841 0.257 0.056 0.408 0.536
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.1674 0.5975 0.952 0.004 0.032 0.012
#> GSM213082 2 0.2635 0.7973 0.000 0.904 0.020 0.076
#> GSM213085 1 0.7283 0.0213 0.432 0.000 0.420 0.148
#> GSM213088 1 0.7538 0.3337 0.604 0.156 0.040 0.200
#> GSM213091 4 0.2089 0.7076 0.020 0.000 0.048 0.932
#> GSM213092 1 0.6951 0.2821 0.544 0.000 0.324 0.132
#> GSM213096 1 0.4018 0.4871 0.772 0.000 0.224 0.004
#> GSM213100 1 0.3143 0.5957 0.876 0.000 0.100 0.024
#> GSM213111 2 0.2256 0.8312 0.000 0.924 0.056 0.020
#> GSM213117 4 0.6049 0.5337 0.264 0.036 0.028 0.672
#> GSM213118 3 0.5696 -0.0613 0.484 0.000 0.492 0.024
#> GSM213120 2 0.3176 0.8202 0.000 0.880 0.084 0.036
#> GSM213122 2 0.1598 0.8364 0.004 0.956 0.020 0.020
#> GSM213074 4 0.1975 0.7112 0.048 0.000 0.016 0.936
#> GSM213077 1 0.3881 0.5464 0.812 0.000 0.172 0.016
#> GSM213083 1 0.2500 0.6044 0.916 0.000 0.044 0.040
#> GSM213094 4 0.3123 0.6502 0.000 0.000 0.156 0.844
#> GSM213095 3 0.5653 0.4564 0.000 0.192 0.712 0.096
#> GSM213102 1 0.5497 -0.0873 0.524 0.000 0.016 0.460
#> GSM213103 2 0.4957 0.5890 0.000 0.684 0.300 0.016
#> GSM213104 3 0.4716 0.4727 0.196 0.040 0.764 0.000
#> GSM213107 3 0.5105 -0.0381 0.004 0.432 0.564 0.000
#> GSM213108 4 0.6896 0.4160 0.020 0.300 0.084 0.596
#> GSM213112 3 0.6364 0.3624 0.204 0.000 0.652 0.144
#> GSM213114 1 0.4999 -0.1089 0.508 0.000 0.492 0.000
#> GSM213115 2 0.0657 0.8436 0.004 0.984 0.012 0.000
#> GSM213116 4 0.4720 0.5604 0.264 0.000 0.016 0.720
#> GSM213119 2 0.1510 0.8355 0.000 0.956 0.016 0.028
#> GSM213072 4 0.3679 0.7096 0.084 0.000 0.060 0.856
#> GSM213075 4 0.5144 0.6724 0.108 0.044 0.052 0.796
#> GSM213076 2 0.4387 0.7205 0.000 0.776 0.200 0.024
#> GSM213079 4 0.4606 0.5532 0.012 0.000 0.264 0.724
#> GSM213080 3 0.5517 0.2042 0.412 0.020 0.568 0.000
#> GSM213081 1 0.3279 0.5900 0.872 0.000 0.096 0.032
#> GSM213084 1 0.3778 0.5948 0.848 0.000 0.100 0.052
#> GSM213087 2 0.1118 0.8381 0.000 0.964 0.036 0.000
#> GSM213089 4 0.2021 0.7096 0.056 0.000 0.012 0.932
#> GSM213090 4 0.5003 0.4954 0.016 0.000 0.308 0.676
#> GSM213093 4 0.4869 0.5864 0.260 0.004 0.016 0.720
#> GSM213097 1 0.5760 -0.0315 0.524 0.000 0.028 0.448
#> GSM213099 4 0.2737 0.6842 0.008 0.000 0.104 0.888
#> GSM213101 1 0.2855 0.5850 0.904 0.004 0.040 0.052
#> GSM213105 2 0.0336 0.8436 0.000 0.992 0.008 0.000
#> GSM213109 1 0.6079 0.0753 0.544 0.000 0.048 0.408
#> GSM213110 2 0.1411 0.8392 0.020 0.960 0.020 0.000
#> GSM213113 4 0.6013 0.4060 0.044 0.004 0.352 0.600
#> GSM213121 2 0.3975 0.6859 0.000 0.760 0.240 0.000
#> GSM213123 4 0.6512 0.3786 0.344 0.004 0.076 0.576
#> GSM213125 2 0.0376 0.8438 0.000 0.992 0.004 0.004
#> GSM213073 3 0.5762 0.1647 0.040 0.000 0.608 0.352
#> GSM213086 1 0.4692 0.4894 0.756 0.000 0.212 0.032
#> GSM213098 3 0.4752 0.5186 0.068 0.008 0.800 0.124
#> GSM213106 4 0.6505 0.2549 0.416 0.024 0.032 0.528
#> GSM213124 2 0.8273 -0.0582 0.156 0.444 0.040 0.360
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.1522 0.64248 0.944 0.000 0.000 0.044 0.012
#> GSM213082 2 0.0451 0.76937 0.000 0.988 0.000 0.008 0.004
#> GSM213085 3 0.4842 0.42678 0.264 0.000 0.684 0.004 0.048
#> GSM213088 1 0.5707 -0.05463 0.524 0.052 0.004 0.412 0.008
#> GSM213091 4 0.2351 0.70374 0.000 0.000 0.088 0.896 0.016
#> GSM213092 3 0.5034 0.34606 0.308 0.000 0.648 0.016 0.028
#> GSM213096 1 0.5377 0.58119 0.700 0.000 0.168 0.016 0.116
#> GSM213100 1 0.5597 0.44820 0.616 0.000 0.312 0.032 0.040
#> GSM213111 2 0.2772 0.73262 0.000 0.892 0.012 0.044 0.052
#> GSM213117 4 0.4225 0.71052 0.124 0.008 0.032 0.808 0.028
#> GSM213118 5 0.5313 0.56702 0.200 0.000 0.032 0.064 0.704
#> GSM213120 2 0.6571 0.17691 0.000 0.456 0.012 0.388 0.144
#> GSM213122 2 0.0324 0.76915 0.004 0.992 0.000 0.004 0.000
#> GSM213074 4 0.5798 0.41373 0.032 0.000 0.404 0.528 0.036
#> GSM213077 1 0.4678 0.53611 0.712 0.000 0.224 0.000 0.064
#> GSM213083 1 0.2929 0.62936 0.840 0.000 0.152 0.000 0.008
#> GSM213094 4 0.4902 0.34413 0.000 0.000 0.408 0.564 0.028
#> GSM213095 3 0.5200 0.46871 0.004 0.052 0.668 0.008 0.268
#> GSM213102 4 0.4594 0.49956 0.364 0.000 0.012 0.620 0.004
#> GSM213103 5 0.6223 -0.01744 0.004 0.420 0.040 0.044 0.492
#> GSM213104 5 0.2995 0.60166 0.088 0.008 0.032 0.000 0.872
#> GSM213107 5 0.2890 0.56714 0.000 0.160 0.004 0.000 0.836
#> GSM213108 2 0.6633 0.40146 0.000 0.552 0.252 0.172 0.024
#> GSM213112 3 0.4359 0.55693 0.128 0.000 0.776 0.004 0.092
#> GSM213114 5 0.4494 0.39828 0.380 0.000 0.012 0.000 0.608
#> GSM213115 2 0.0324 0.76876 0.004 0.992 0.000 0.000 0.004
#> GSM213116 4 0.3635 0.72416 0.108 0.000 0.040 0.836 0.016
#> GSM213119 2 0.0740 0.76799 0.008 0.980 0.000 0.008 0.004
#> GSM213072 4 0.5997 0.48281 0.044 0.000 0.348 0.564 0.044
#> GSM213075 4 0.4266 0.70641 0.044 0.008 0.080 0.820 0.048
#> GSM213076 2 0.6370 0.29718 0.000 0.548 0.028 0.100 0.324
#> GSM213079 3 0.4593 0.52180 0.000 0.000 0.736 0.184 0.080
#> GSM213080 5 0.3730 0.55484 0.288 0.000 0.000 0.000 0.712
#> GSM213081 1 0.4748 0.52787 0.728 0.000 0.000 0.172 0.100
#> GSM213084 1 0.4420 0.51004 0.692 0.000 0.280 0.000 0.028
#> GSM213087 2 0.1282 0.75368 0.000 0.952 0.004 0.000 0.044
#> GSM213089 4 0.2748 0.71541 0.016 0.000 0.096 0.880 0.008
#> GSM213090 3 0.3334 0.60050 0.004 0.000 0.852 0.064 0.080
#> GSM213093 4 0.3739 0.71481 0.136 0.000 0.024 0.820 0.020
#> GSM213097 4 0.4275 0.60067 0.288 0.000 0.008 0.696 0.008
#> GSM213099 4 0.3323 0.68520 0.004 0.000 0.116 0.844 0.036
#> GSM213101 1 0.2054 0.63742 0.916 0.004 0.008 0.072 0.000
#> GSM213105 2 0.0324 0.76923 0.004 0.992 0.004 0.000 0.000
#> GSM213109 3 0.6115 0.00633 0.416 0.000 0.496 0.056 0.032
#> GSM213110 2 0.0865 0.76348 0.024 0.972 0.004 0.000 0.000
#> GSM213113 4 0.6507 0.29188 0.012 0.000 0.144 0.496 0.348
#> GSM213121 2 0.4403 0.19529 0.000 0.560 0.004 0.000 0.436
#> GSM213123 4 0.4620 0.66798 0.200 0.000 0.012 0.740 0.048
#> GSM213125 2 0.0451 0.76922 0.000 0.988 0.004 0.000 0.008
#> GSM213073 3 0.6041 0.33513 0.008 0.000 0.544 0.104 0.344
#> GSM213086 1 0.5380 0.57910 0.712 0.000 0.128 0.024 0.136
#> GSM213098 5 0.4735 0.41168 0.012 0.000 0.020 0.300 0.668
#> GSM213106 4 0.3764 0.67545 0.212 0.000 0.008 0.772 0.008
#> GSM213124 2 0.8115 0.24299 0.060 0.460 0.216 0.232 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.3336 0.5215 0.832 0.004 0.000 0.116 0.012 0.036
#> GSM213082 2 0.0964 0.8367 0.000 0.968 0.016 0.012 0.000 0.004
#> GSM213085 3 0.6734 0.2597 0.260 0.000 0.448 0.004 0.040 0.248
#> GSM213088 4 0.5323 0.1541 0.424 0.016 0.000 0.496 0.000 0.064
#> GSM213091 4 0.4893 0.3524 0.004 0.000 0.096 0.680 0.008 0.212
#> GSM213092 3 0.6413 0.2316 0.308 0.000 0.468 0.004 0.024 0.196
#> GSM213096 1 0.5971 0.4330 0.588 0.000 0.072 0.004 0.076 0.260
#> GSM213100 1 0.5789 0.3759 0.568 0.000 0.204 0.004 0.008 0.216
#> GSM213111 2 0.4435 0.7153 0.000 0.788 0.028 0.040 0.080 0.064
#> GSM213117 4 0.4260 0.2468 0.024 0.004 0.000 0.640 0.000 0.332
#> GSM213118 5 0.5759 0.5038 0.112 0.000 0.004 0.048 0.628 0.208
#> GSM213120 4 0.7171 0.1024 0.000 0.304 0.032 0.440 0.176 0.048
#> GSM213122 2 0.0146 0.8413 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM213074 6 0.4800 0.5155 0.012 0.000 0.104 0.192 0.000 0.692
#> GSM213077 1 0.4663 0.4309 0.692 0.000 0.244 0.008 0.020 0.036
#> GSM213083 1 0.2686 0.5500 0.868 0.000 0.100 0.024 0.000 0.008
#> GSM213094 4 0.6309 -0.0887 0.000 0.000 0.284 0.372 0.008 0.336
#> GSM213095 3 0.4773 0.5306 0.040 0.060 0.764 0.004 0.108 0.024
#> GSM213102 4 0.5505 0.3427 0.240 0.004 0.000 0.580 0.000 0.176
#> GSM213103 5 0.6890 0.3464 0.028 0.140 0.028 0.012 0.500 0.292
#> GSM213104 5 0.2639 0.6240 0.064 0.000 0.048 0.000 0.880 0.008
#> GSM213107 5 0.2339 0.6327 0.000 0.072 0.020 0.012 0.896 0.000
#> GSM213108 2 0.7076 0.1897 0.004 0.500 0.160 0.100 0.008 0.228
#> GSM213112 3 0.6244 0.4193 0.180 0.000 0.564 0.008 0.036 0.212
#> GSM213114 5 0.3976 0.3613 0.380 0.000 0.000 0.004 0.612 0.004
#> GSM213115 2 0.0993 0.8372 0.000 0.964 0.000 0.000 0.012 0.024
#> GSM213116 4 0.5059 0.1400 0.036 0.000 0.012 0.552 0.008 0.392
#> GSM213119 2 0.0405 0.8416 0.008 0.988 0.000 0.000 0.000 0.004
#> GSM213072 6 0.5390 0.4536 0.052 0.000 0.080 0.216 0.000 0.652
#> GSM213075 4 0.6309 0.0692 0.040 0.000 0.136 0.424 0.000 0.400
#> GSM213076 2 0.7995 -0.0828 0.004 0.372 0.140 0.168 0.284 0.032
#> GSM213079 3 0.3870 0.4790 0.008 0.000 0.808 0.060 0.020 0.104
#> GSM213080 5 0.3459 0.5832 0.212 0.000 0.000 0.016 0.768 0.004
#> GSM213081 1 0.6975 0.0844 0.476 0.000 0.032 0.320 0.080 0.092
#> GSM213084 1 0.4142 0.4476 0.704 0.000 0.264 0.008 0.008 0.016
#> GSM213087 2 0.1471 0.8126 0.000 0.932 0.000 0.000 0.064 0.004
#> GSM213089 4 0.4440 0.3336 0.004 0.000 0.032 0.672 0.008 0.284
#> GSM213090 3 0.1710 0.5630 0.012 0.000 0.940 0.020 0.008 0.020
#> GSM213093 4 0.5235 0.4358 0.124 0.000 0.044 0.696 0.004 0.132
#> GSM213097 4 0.4556 0.4209 0.232 0.004 0.004 0.700 0.004 0.056
#> GSM213099 4 0.4747 0.3557 0.000 0.000 0.108 0.692 0.008 0.192
#> GSM213101 1 0.3208 0.5409 0.832 0.000 0.000 0.120 0.008 0.040
#> GSM213105 2 0.0405 0.8415 0.004 0.988 0.000 0.000 0.000 0.008
#> GSM213109 1 0.6925 -0.0617 0.348 0.000 0.304 0.032 0.008 0.308
#> GSM213110 2 0.1074 0.8296 0.012 0.960 0.000 0.000 0.000 0.028
#> GSM213113 4 0.7213 0.1694 0.008 0.000 0.180 0.432 0.284 0.096
#> GSM213121 5 0.4234 0.2570 0.000 0.388 0.004 0.008 0.596 0.004
#> GSM213123 4 0.4755 0.4434 0.100 0.000 0.012 0.756 0.056 0.076
#> GSM213125 2 0.0405 0.8407 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM213073 3 0.5340 0.4053 0.004 0.000 0.684 0.072 0.172 0.068
#> GSM213086 1 0.6625 0.3932 0.564 0.000 0.068 0.032 0.100 0.236
#> GSM213098 5 0.4106 0.5096 0.000 0.000 0.024 0.216 0.736 0.024
#> GSM213106 4 0.4154 0.4416 0.164 0.000 0.000 0.740 0.000 0.096
#> GSM213124 6 0.6009 0.4285 0.028 0.252 0.040 0.076 0.000 0.604
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 development.stage(p) disease.state(p) k
#> MAD:NMF 53 0.565 0.977 2
#> MAD:NMF 47 0.187 0.930 3
#> MAD:NMF 32 0.727 0.436 4
#> MAD:NMF 34 0.568 0.783 5
#> MAD:NMF 20 0.927 0.454 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "hclust"]
# you can also extract it by
# res = res_list["ATC:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.693 0.897 0.938 0.3084 0.648 0.648
#> 3 3 0.795 0.826 0.932 0.3540 0.913 0.868
#> 4 4 0.588 0.685 0.842 0.2690 0.948 0.911
#> 5 5 0.535 0.609 0.741 0.0965 0.857 0.742
#> 6 6 0.520 0.588 0.706 0.1239 0.723 0.438
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
#> GSM213078 1 0.0000 0.970 1.000 0.000
#> GSM213082 2 0.8713 0.808 0.292 0.708
#> GSM213085 1 0.0000 0.970 1.000 0.000
#> GSM213088 1 0.0000 0.970 1.000 0.000
#> GSM213091 2 0.9552 0.692 0.376 0.624
#> GSM213092 1 0.0000 0.970 1.000 0.000
#> GSM213096 1 0.0000 0.970 1.000 0.000
#> GSM213100 1 0.0000 0.970 1.000 0.000
#> GSM213111 2 0.8713 0.808 0.292 0.708
#> GSM213117 1 0.0000 0.970 1.000 0.000
#> GSM213118 1 0.0000 0.970 1.000 0.000
#> GSM213120 1 0.0376 0.966 0.996 0.004
#> GSM213122 1 0.0000 0.970 1.000 0.000
#> GSM213074 1 0.0000 0.970 1.000 0.000
#> GSM213077 1 0.0000 0.970 1.000 0.000
#> GSM213083 1 0.0000 0.970 1.000 0.000
#> GSM213094 2 0.4815 0.804 0.104 0.896
#> GSM213095 2 0.0000 0.762 0.000 1.000
#> GSM213102 1 0.0000 0.970 1.000 0.000
#> GSM213103 1 0.0000 0.970 1.000 0.000
#> GSM213104 1 0.0000 0.970 1.000 0.000
#> GSM213107 1 0.9000 0.377 0.684 0.316
#> GSM213108 2 0.8713 0.808 0.292 0.708
#> GSM213112 1 0.0000 0.970 1.000 0.000
#> GSM213114 1 0.0000 0.970 1.000 0.000
#> GSM213115 1 0.0000 0.970 1.000 0.000
#> GSM213116 1 0.0000 0.970 1.000 0.000
#> GSM213119 1 0.0000 0.970 1.000 0.000
#> GSM213072 2 0.9427 0.720 0.360 0.640
#> GSM213075 1 0.0000 0.970 1.000 0.000
#> GSM213076 1 0.7883 0.592 0.764 0.236
#> GSM213079 2 0.0000 0.762 0.000 1.000
#> GSM213080 1 0.0000 0.970 1.000 0.000
#> GSM213081 1 0.0000 0.970 1.000 0.000
#> GSM213084 1 0.0000 0.970 1.000 0.000
#> GSM213087 1 0.0000 0.970 1.000 0.000
#> GSM213089 1 0.0000 0.970 1.000 0.000
#> GSM213090 2 0.4815 0.804 0.104 0.896
#> GSM213093 1 0.0000 0.970 1.000 0.000
#> GSM213097 1 0.0000 0.970 1.000 0.000
#> GSM213099 2 0.8763 0.802 0.296 0.704
#> GSM213101 1 0.0000 0.970 1.000 0.000
#> GSM213105 1 0.0000 0.970 1.000 0.000
#> GSM213109 1 0.0000 0.970 1.000 0.000
#> GSM213110 1 0.0000 0.970 1.000 0.000
#> GSM213113 1 0.1843 0.941 0.972 0.028
#> GSM213121 1 0.9000 0.377 0.684 0.316
#> GSM213123 1 0.1843 0.941 0.972 0.028
#> GSM213125 2 0.8713 0.808 0.292 0.708
#> GSM213073 2 0.0000 0.762 0.000 1.000
#> GSM213086 1 0.0000 0.970 1.000 0.000
#> GSM213098 1 0.1843 0.941 0.972 0.028
#> GSM213106 1 0.0000 0.970 1.000 0.000
#> GSM213124 1 0.0000 0.970 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.0000 0.955 1.000 0.000 0.000
#> GSM213082 2 0.0000 0.659 0.000 1.000 0.000
#> GSM213085 1 0.2448 0.930 0.924 0.076 0.000
#> GSM213088 1 0.0000 0.955 1.000 0.000 0.000
#> GSM213091 2 0.3112 0.615 0.096 0.900 0.004
#> GSM213092 1 0.2448 0.930 0.924 0.076 0.000
#> GSM213096 1 0.0000 0.955 1.000 0.000 0.000
#> GSM213100 1 0.0000 0.955 1.000 0.000 0.000
#> GSM213111 2 0.0000 0.659 0.000 1.000 0.000
#> GSM213117 1 0.2448 0.930 0.924 0.076 0.000
#> GSM213118 1 0.2448 0.930 0.924 0.076 0.000
#> GSM213120 1 0.1289 0.950 0.968 0.032 0.000
#> GSM213122 1 0.0592 0.952 0.988 0.012 0.000
#> GSM213074 1 0.1163 0.950 0.972 0.028 0.000
#> GSM213077 1 0.0000 0.955 1.000 0.000 0.000
#> GSM213083 1 0.0000 0.955 1.000 0.000 0.000
#> GSM213094 2 0.5706 0.179 0.000 0.680 0.320
#> GSM213095 3 0.5760 0.513 0.000 0.328 0.672
#> GSM213102 1 0.0000 0.955 1.000 0.000 0.000
#> GSM213103 1 0.0237 0.955 0.996 0.004 0.000
#> GSM213104 1 0.0892 0.951 0.980 0.020 0.000
#> GSM213107 2 0.6095 0.324 0.392 0.608 0.000
#> GSM213108 2 0.0000 0.659 0.000 1.000 0.000
#> GSM213112 1 0.2448 0.930 0.924 0.076 0.000
#> GSM213114 1 0.0000 0.955 1.000 0.000 0.000
#> GSM213115 1 0.0592 0.952 0.988 0.012 0.000
#> GSM213116 1 0.2448 0.930 0.924 0.076 0.000
#> GSM213119 1 0.0592 0.952 0.988 0.012 0.000
#> GSM213072 2 0.2772 0.630 0.080 0.916 0.004
#> GSM213075 1 0.0237 0.955 0.996 0.004 0.000
#> GSM213076 1 0.6008 0.400 0.628 0.372 0.000
#> GSM213079 3 0.0000 0.818 0.000 0.000 1.000
#> GSM213080 1 0.0000 0.955 1.000 0.000 0.000
#> GSM213081 1 0.0000 0.955 1.000 0.000 0.000
#> GSM213084 1 0.0000 0.955 1.000 0.000 0.000
#> GSM213087 1 0.0592 0.952 0.988 0.012 0.000
#> GSM213089 1 0.1163 0.950 0.972 0.028 0.000
#> GSM213090 2 0.6235 -0.114 0.000 0.564 0.436
#> GSM213093 1 0.2448 0.930 0.924 0.076 0.000
#> GSM213097 1 0.2448 0.930 0.924 0.076 0.000
#> GSM213099 2 0.1620 0.656 0.024 0.964 0.012
#> GSM213101 1 0.0000 0.955 1.000 0.000 0.000
#> GSM213105 1 0.0592 0.952 0.988 0.012 0.000
#> GSM213109 1 0.0000 0.955 1.000 0.000 0.000
#> GSM213110 1 0.0424 0.953 0.992 0.008 0.000
#> GSM213113 1 0.3116 0.903 0.892 0.108 0.000
#> GSM213121 2 0.6095 0.324 0.392 0.608 0.000
#> GSM213123 1 0.3116 0.903 0.892 0.108 0.000
#> GSM213125 2 0.0000 0.659 0.000 1.000 0.000
#> GSM213073 3 0.0000 0.818 0.000 0.000 1.000
#> GSM213086 1 0.2448 0.930 0.924 0.076 0.000
#> GSM213098 1 0.3116 0.903 0.892 0.108 0.000
#> GSM213106 1 0.0000 0.955 1.000 0.000 0.000
#> GSM213124 1 0.1163 0.950 0.972 0.028 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM213082 2 0.4877 0.312 0.000 0.592 0.000 0.408
#> GSM213085 1 0.3399 0.839 0.868 0.040 0.000 0.092
#> GSM213088 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM213091 4 0.5664 0.514 0.076 0.228 0.000 0.696
#> GSM213092 1 0.3399 0.839 0.868 0.040 0.000 0.092
#> GSM213096 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM213100 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM213111 2 0.4877 0.312 0.000 0.592 0.000 0.408
#> GSM213117 1 0.3399 0.839 0.868 0.040 0.000 0.092
#> GSM213118 1 0.3399 0.839 0.868 0.040 0.000 0.092
#> GSM213120 1 0.2174 0.857 0.928 0.020 0.000 0.052
#> GSM213122 1 0.4866 0.433 0.596 0.404 0.000 0.000
#> GSM213074 1 0.2060 0.857 0.932 0.016 0.000 0.052
#> GSM213077 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM213083 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM213094 4 0.3528 0.451 0.000 0.000 0.192 0.808
#> GSM213095 3 0.5549 0.355 0.000 0.048 0.672 0.280
#> GSM213102 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM213103 1 0.4543 0.556 0.676 0.324 0.000 0.000
#> GSM213104 1 0.3975 0.666 0.760 0.240 0.000 0.000
#> GSM213107 2 0.0000 0.393 0.000 1.000 0.000 0.000
#> GSM213108 2 0.4888 0.303 0.000 0.588 0.000 0.412
#> GSM213112 1 0.3399 0.839 0.868 0.040 0.000 0.092
#> GSM213114 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM213115 1 0.4866 0.433 0.596 0.404 0.000 0.000
#> GSM213116 1 0.3399 0.839 0.868 0.040 0.000 0.092
#> GSM213119 1 0.4866 0.433 0.596 0.404 0.000 0.000
#> GSM213072 4 0.5559 0.526 0.064 0.240 0.000 0.696
#> GSM213075 1 0.0817 0.862 0.976 0.000 0.000 0.024
#> GSM213076 2 0.4193 0.168 0.268 0.732 0.000 0.000
#> GSM213079 3 0.0000 0.780 0.000 0.000 1.000 0.000
#> GSM213080 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM213081 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM213084 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM213087 1 0.4866 0.433 0.596 0.404 0.000 0.000
#> GSM213089 1 0.2060 0.857 0.932 0.016 0.000 0.052
#> GSM213090 4 0.3975 0.261 0.000 0.000 0.240 0.760
#> GSM213093 1 0.3399 0.839 0.868 0.040 0.000 0.092
#> GSM213097 1 0.3399 0.839 0.868 0.040 0.000 0.092
#> GSM213099 4 0.4228 0.528 0.008 0.232 0.000 0.760
#> GSM213101 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM213105 1 0.4866 0.433 0.596 0.404 0.000 0.000
#> GSM213109 1 0.0592 0.863 0.984 0.000 0.000 0.016
#> GSM213110 1 0.1767 0.845 0.944 0.044 0.000 0.012
#> GSM213113 1 0.4022 0.817 0.836 0.068 0.000 0.096
#> GSM213121 2 0.0000 0.393 0.000 1.000 0.000 0.000
#> GSM213123 1 0.4022 0.817 0.836 0.068 0.000 0.096
#> GSM213125 2 0.4877 0.312 0.000 0.592 0.000 0.408
#> GSM213073 3 0.0000 0.780 0.000 0.000 1.000 0.000
#> GSM213086 1 0.3399 0.839 0.868 0.040 0.000 0.092
#> GSM213098 1 0.4022 0.817 0.836 0.068 0.000 0.096
#> GSM213106 1 0.0469 0.863 0.988 0.000 0.000 0.012
#> GSM213124 1 0.2844 0.854 0.900 0.048 0.000 0.052
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.3305 0.737 0.776 0.224 0.000 0.000 0.000
#> GSM213082 5 0.6775 0.708 0.000 0.280 0.000 0.336 0.384
#> GSM213085 1 0.1608 0.729 0.928 0.000 0.000 0.072 0.000
#> GSM213088 1 0.3305 0.737 0.776 0.224 0.000 0.000 0.000
#> GSM213091 4 0.2179 0.741 0.100 0.004 0.000 0.896 0.000
#> GSM213092 1 0.1608 0.729 0.928 0.000 0.000 0.072 0.000
#> GSM213096 1 0.3305 0.737 0.776 0.224 0.000 0.000 0.000
#> GSM213100 1 0.3305 0.737 0.776 0.224 0.000 0.000 0.000
#> GSM213111 5 0.6775 0.708 0.000 0.280 0.000 0.336 0.384
#> GSM213117 1 0.1608 0.729 0.928 0.000 0.000 0.072 0.000
#> GSM213118 1 0.1608 0.729 0.928 0.000 0.000 0.072 0.000
#> GSM213120 1 0.0324 0.744 0.992 0.004 0.000 0.004 0.000
#> GSM213122 2 0.4262 0.536 0.440 0.560 0.000 0.000 0.000
#> GSM213074 1 0.0000 0.745 1.000 0.000 0.000 0.000 0.000
#> GSM213077 1 0.3305 0.737 0.776 0.224 0.000 0.000 0.000
#> GSM213083 1 0.3305 0.737 0.776 0.224 0.000 0.000 0.000
#> GSM213094 4 0.5002 0.489 0.000 0.000 0.132 0.708 0.160
#> GSM213095 3 0.4818 0.561 0.000 0.040 0.672 0.004 0.284
#> GSM213102 1 0.3305 0.737 0.776 0.224 0.000 0.000 0.000
#> GSM213103 1 0.4302 -0.334 0.520 0.480 0.000 0.000 0.000
#> GSM213104 1 0.4392 0.113 0.612 0.380 0.000 0.000 0.008
#> GSM213107 2 0.4266 -0.290 0.000 0.776 0.000 0.120 0.104
#> GSM213108 5 0.6770 0.704 0.000 0.276 0.000 0.340 0.384
#> GSM213112 1 0.1608 0.729 0.928 0.000 0.000 0.072 0.000
#> GSM213114 1 0.3305 0.737 0.776 0.224 0.000 0.000 0.000
#> GSM213115 2 0.4262 0.536 0.440 0.560 0.000 0.000 0.000
#> GSM213116 1 0.1608 0.729 0.928 0.000 0.000 0.072 0.000
#> GSM213119 2 0.4262 0.536 0.440 0.560 0.000 0.000 0.000
#> GSM213072 4 0.2011 0.752 0.088 0.004 0.000 0.908 0.000
#> GSM213075 1 0.2179 0.738 0.888 0.112 0.000 0.000 0.000
#> GSM213076 2 0.6874 0.330 0.268 0.556 0.000 0.096 0.080
#> GSM213079 3 0.0000 0.819 0.000 0.000 1.000 0.000 0.000
#> GSM213080 1 0.3305 0.737 0.776 0.224 0.000 0.000 0.000
#> GSM213081 1 0.3305 0.737 0.776 0.224 0.000 0.000 0.000
#> GSM213084 1 0.3305 0.737 0.776 0.224 0.000 0.000 0.000
#> GSM213087 2 0.4262 0.536 0.440 0.560 0.000 0.000 0.000
#> GSM213089 1 0.0000 0.745 1.000 0.000 0.000 0.000 0.000
#> GSM213090 5 0.4288 -0.420 0.000 0.000 0.004 0.384 0.612
#> GSM213093 1 0.1608 0.729 0.928 0.000 0.000 0.072 0.000
#> GSM213097 1 0.1608 0.729 0.928 0.000 0.000 0.072 0.000
#> GSM213099 4 0.0865 0.726 0.024 0.004 0.000 0.972 0.000
#> GSM213101 1 0.3305 0.737 0.776 0.224 0.000 0.000 0.000
#> GSM213105 2 0.4262 0.536 0.440 0.560 0.000 0.000 0.000
#> GSM213109 1 0.3274 0.738 0.780 0.220 0.000 0.000 0.000
#> GSM213110 1 0.3242 0.693 0.784 0.216 0.000 0.000 0.000
#> GSM213113 1 0.2179 0.697 0.896 0.004 0.000 0.100 0.000
#> GSM213121 2 0.4266 -0.290 0.000 0.776 0.000 0.120 0.104
#> GSM213123 1 0.2179 0.697 0.896 0.004 0.000 0.100 0.000
#> GSM213125 5 0.6775 0.708 0.000 0.280 0.000 0.336 0.384
#> GSM213073 3 0.0000 0.819 0.000 0.000 1.000 0.000 0.000
#> GSM213086 1 0.1608 0.729 0.928 0.000 0.000 0.072 0.000
#> GSM213098 1 0.2179 0.697 0.896 0.004 0.000 0.100 0.000
#> GSM213106 1 0.3305 0.737 0.776 0.224 0.000 0.000 0.000
#> GSM213124 1 0.0880 0.729 0.968 0.032 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
#> GSM213078 2 0.4460 0.595 0.452 0.520 0.000 0.000 0.000 0.028
#> GSM213082 6 0.5850 0.706 0.000 0.000 0.000 0.200 0.348 0.452
#> GSM213085 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213088 2 0.4460 0.595 0.452 0.520 0.000 0.000 0.000 0.028
#> GSM213091 4 0.3309 0.783 0.172 0.000 0.000 0.800 0.024 0.004
#> GSM213092 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213096 2 0.4460 0.595 0.452 0.520 0.000 0.000 0.000 0.028
#> GSM213100 2 0.4460 0.595 0.452 0.520 0.000 0.000 0.000 0.028
#> GSM213111 6 0.5850 0.706 0.000 0.000 0.000 0.200 0.348 0.452
#> GSM213117 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213118 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213120 1 0.2595 0.663 0.836 0.160 0.000 0.000 0.000 0.004
#> GSM213122 2 0.2750 0.313 0.136 0.844 0.000 0.000 0.020 0.000
#> GSM213074 1 0.2527 0.647 0.832 0.168 0.000 0.000 0.000 0.000
#> GSM213077 2 0.4460 0.595 0.452 0.520 0.000 0.000 0.000 0.028
#> GSM213083 2 0.4460 0.595 0.452 0.520 0.000 0.000 0.000 0.028
#> GSM213094 4 0.3860 0.516 0.000 0.024 0.096 0.808 0.004 0.068
#> GSM213095 3 0.3531 0.538 0.000 0.000 0.672 0.000 0.000 0.328
#> GSM213102 2 0.4460 0.595 0.452 0.520 0.000 0.000 0.000 0.028
#> GSM213103 2 0.3073 0.446 0.204 0.788 0.000 0.000 0.008 0.000
#> GSM213104 2 0.4199 0.256 0.416 0.568 0.000 0.000 0.016 0.000
#> GSM213107 5 0.3810 1.000 0.000 0.428 0.000 0.000 0.572 0.000
#> GSM213108 6 0.5868 0.703 0.000 0.000 0.000 0.204 0.348 0.448
#> GSM213112 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213114 2 0.4460 0.595 0.452 0.520 0.000 0.000 0.000 0.028
#> GSM213115 2 0.2750 0.313 0.136 0.844 0.000 0.000 0.020 0.000
#> GSM213116 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213119 2 0.2750 0.313 0.136 0.844 0.000 0.000 0.020 0.000
#> GSM213072 4 0.3025 0.794 0.156 0.000 0.000 0.820 0.024 0.000
#> GSM213075 1 0.3446 0.210 0.692 0.308 0.000 0.000 0.000 0.000
#> GSM213076 2 0.5976 -0.641 0.228 0.408 0.000 0.000 0.364 0.000
#> GSM213079 3 0.0000 0.815 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM213080 2 0.4460 0.595 0.452 0.520 0.000 0.000 0.000 0.028
#> GSM213081 2 0.4460 0.595 0.452 0.520 0.000 0.000 0.000 0.028
#> GSM213084 2 0.4460 0.595 0.452 0.520 0.000 0.000 0.000 0.028
#> GSM213087 2 0.2750 0.313 0.136 0.844 0.000 0.000 0.020 0.000
#> GSM213089 1 0.2527 0.647 0.832 0.168 0.000 0.000 0.000 0.000
#> GSM213090 6 0.4829 -0.215 0.000 0.000 0.000 0.056 0.424 0.520
#> GSM213093 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213097 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213099 4 0.2333 0.773 0.092 0.000 0.000 0.884 0.024 0.000
#> GSM213101 2 0.4460 0.595 0.452 0.520 0.000 0.000 0.000 0.028
#> GSM213105 2 0.2750 0.313 0.136 0.844 0.000 0.000 0.020 0.000
#> GSM213109 1 0.4277 -0.124 0.616 0.356 0.000 0.000 0.000 0.028
#> GSM213110 2 0.4262 0.474 0.476 0.508 0.000 0.000 0.016 0.000
#> GSM213113 1 0.0858 0.803 0.968 0.000 0.000 0.028 0.000 0.004
#> GSM213121 5 0.3810 1.000 0.000 0.428 0.000 0.000 0.572 0.000
#> GSM213123 1 0.0858 0.803 0.968 0.000 0.000 0.028 0.000 0.004
#> GSM213125 6 0.5850 0.706 0.000 0.000 0.000 0.200 0.348 0.452
#> GSM213073 3 0.0000 0.815 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM213086 1 0.0000 0.835 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213098 1 0.0858 0.803 0.968 0.000 0.000 0.028 0.000 0.004
#> GSM213106 2 0.4460 0.595 0.452 0.520 0.000 0.000 0.000 0.028
#> GSM213124 1 0.3672 0.284 0.688 0.304 0.000 0.000 0.008 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 development.stage(p) disease.state(p) k
#> ATC:hclust 52 1.000 1.000 2
#> ATC:hclust 49 0.769 0.256 3
#> ATC:hclust 39 0.297 0.380 4
#> ATC:hclust 47 0.764 0.525 5
#> ATC:hclust 41 0.912 0.866 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "kmeans"]
# you can also extract it by
# res = res_list["ATC:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.891 0.981 0.989 0.4447 0.547 0.547
#> 3 3 0.447 0.646 0.816 0.3428 0.704 0.525
#> 4 4 0.736 0.784 0.881 0.2037 0.764 0.477
#> 5 5 0.736 0.777 0.866 0.0786 0.909 0.688
#> 6 6 0.769 0.618 0.792 0.0448 0.928 0.699
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
#> GSM213078 1 0.000 1.000 1.000 0.000
#> GSM213082 2 0.000 0.966 0.000 1.000
#> GSM213085 1 0.000 1.000 1.000 0.000
#> GSM213088 1 0.000 1.000 1.000 0.000
#> GSM213091 2 0.574 0.868 0.136 0.864
#> GSM213092 1 0.000 1.000 1.000 0.000
#> GSM213096 1 0.000 1.000 1.000 0.000
#> GSM213100 1 0.000 1.000 1.000 0.000
#> GSM213111 2 0.000 0.966 0.000 1.000
#> GSM213117 1 0.000 1.000 1.000 0.000
#> GSM213118 1 0.000 1.000 1.000 0.000
#> GSM213120 1 0.000 1.000 1.000 0.000
#> GSM213122 1 0.000 1.000 1.000 0.000
#> GSM213074 1 0.000 1.000 1.000 0.000
#> GSM213077 1 0.000 1.000 1.000 0.000
#> GSM213083 1 0.000 1.000 1.000 0.000
#> GSM213094 2 0.000 0.966 0.000 1.000
#> GSM213095 2 0.000 0.966 0.000 1.000
#> GSM213102 1 0.000 1.000 1.000 0.000
#> GSM213103 1 0.000 1.000 1.000 0.000
#> GSM213104 1 0.000 1.000 1.000 0.000
#> GSM213107 2 0.000 0.966 0.000 1.000
#> GSM213108 2 0.000 0.966 0.000 1.000
#> GSM213112 1 0.000 1.000 1.000 0.000
#> GSM213114 1 0.000 1.000 1.000 0.000
#> GSM213115 1 0.000 1.000 1.000 0.000
#> GSM213116 1 0.000 1.000 1.000 0.000
#> GSM213119 1 0.000 1.000 1.000 0.000
#> GSM213072 2 0.000 0.966 0.000 1.000
#> GSM213075 1 0.000 1.000 1.000 0.000
#> GSM213076 2 0.000 0.966 0.000 1.000
#> GSM213079 2 0.000 0.966 0.000 1.000
#> GSM213080 1 0.000 1.000 1.000 0.000
#> GSM213081 1 0.000 1.000 1.000 0.000
#> GSM213084 1 0.000 1.000 1.000 0.000
#> GSM213087 1 0.000 1.000 1.000 0.000
#> GSM213089 1 0.000 1.000 1.000 0.000
#> GSM213090 2 0.000 0.966 0.000 1.000
#> GSM213093 1 0.000 1.000 1.000 0.000
#> GSM213097 1 0.000 1.000 1.000 0.000
#> GSM213099 2 0.000 0.966 0.000 1.000
#> GSM213101 1 0.000 1.000 1.000 0.000
#> GSM213105 1 0.000 1.000 1.000 0.000
#> GSM213109 1 0.000 1.000 1.000 0.000
#> GSM213110 1 0.000 1.000 1.000 0.000
#> GSM213113 2 0.574 0.868 0.136 0.864
#> GSM213121 2 0.000 0.966 0.000 1.000
#> GSM213123 2 0.644 0.835 0.164 0.836
#> GSM213125 2 0.000 0.966 0.000 1.000
#> GSM213073 2 0.000 0.966 0.000 1.000
#> GSM213086 1 0.000 1.000 1.000 0.000
#> GSM213098 2 0.574 0.868 0.136 0.864
#> GSM213106 1 0.000 1.000 1.000 0.000
#> GSM213124 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.0000 0.822 1.000 0.000 0.000
#> GSM213082 2 0.5363 0.496 0.000 0.724 0.276
#> GSM213085 1 0.6126 0.428 0.600 0.400 0.000
#> GSM213088 1 0.0000 0.822 1.000 0.000 0.000
#> GSM213091 2 0.8265 0.527 0.184 0.636 0.180
#> GSM213092 1 0.6140 0.422 0.596 0.404 0.000
#> GSM213096 1 0.0000 0.822 1.000 0.000 0.000
#> GSM213100 1 0.0000 0.822 1.000 0.000 0.000
#> GSM213111 2 0.5363 0.496 0.000 0.724 0.276
#> GSM213117 1 0.2878 0.777 0.904 0.096 0.000
#> GSM213118 1 0.6154 0.413 0.592 0.408 0.000
#> GSM213120 2 0.0000 0.603 0.000 1.000 0.000
#> GSM213122 2 0.5560 0.533 0.300 0.700 0.000
#> GSM213074 1 0.6180 0.395 0.584 0.416 0.000
#> GSM213077 1 0.0000 0.822 1.000 0.000 0.000
#> GSM213083 1 0.0000 0.822 1.000 0.000 0.000
#> GSM213094 3 0.0000 0.974 0.000 0.000 1.000
#> GSM213095 3 0.0000 0.974 0.000 0.000 1.000
#> GSM213102 1 0.0000 0.822 1.000 0.000 0.000
#> GSM213103 2 0.5810 0.491 0.336 0.664 0.000
#> GSM213104 1 0.6045 0.250 0.620 0.380 0.000
#> GSM213107 2 0.2878 0.583 0.000 0.904 0.096
#> GSM213108 3 0.3116 0.857 0.000 0.108 0.892
#> GSM213112 1 0.6140 0.422 0.596 0.404 0.000
#> GSM213114 1 0.0000 0.822 1.000 0.000 0.000
#> GSM213115 2 0.5810 0.491 0.336 0.664 0.000
#> GSM213116 1 0.3482 0.751 0.872 0.128 0.000
#> GSM213119 2 0.5760 0.503 0.328 0.672 0.000
#> GSM213072 2 0.8263 0.524 0.176 0.636 0.188
#> GSM213075 1 0.6008 0.258 0.628 0.372 0.000
#> GSM213076 2 0.2796 0.584 0.000 0.908 0.092
#> GSM213079 3 0.0000 0.974 0.000 0.000 1.000
#> GSM213080 1 0.0000 0.822 1.000 0.000 0.000
#> GSM213081 1 0.0000 0.822 1.000 0.000 0.000
#> GSM213084 1 0.0000 0.822 1.000 0.000 0.000
#> GSM213087 2 0.5760 0.503 0.328 0.672 0.000
#> GSM213089 2 0.4931 0.500 0.232 0.768 0.000
#> GSM213090 3 0.0000 0.974 0.000 0.000 1.000
#> GSM213093 1 0.1411 0.810 0.964 0.036 0.000
#> GSM213097 1 0.1411 0.810 0.964 0.036 0.000
#> GSM213099 2 0.6274 0.115 0.000 0.544 0.456
#> GSM213101 1 0.0000 0.822 1.000 0.000 0.000
#> GSM213105 2 0.5760 0.503 0.328 0.672 0.000
#> GSM213109 1 0.1289 0.812 0.968 0.032 0.000
#> GSM213110 1 0.0892 0.808 0.980 0.020 0.000
#> GSM213113 2 0.8265 0.527 0.184 0.636 0.180
#> GSM213121 2 0.2878 0.583 0.000 0.904 0.096
#> GSM213123 2 0.8265 0.527 0.184 0.636 0.180
#> GSM213125 2 0.5363 0.496 0.000 0.724 0.276
#> GSM213073 3 0.0000 0.974 0.000 0.000 1.000
#> GSM213086 1 0.6140 0.422 0.596 0.404 0.000
#> GSM213098 2 0.8265 0.527 0.184 0.636 0.180
#> GSM213106 1 0.0000 0.822 1.000 0.000 0.000
#> GSM213124 2 0.5216 0.564 0.260 0.740 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.0000 0.9576 1.000 0.000 0.000 0.000
#> GSM213082 2 0.4941 0.4939 0.000 0.564 0.000 0.436
#> GSM213085 4 0.4874 0.8100 0.180 0.056 0.000 0.764
#> GSM213088 1 0.0000 0.9576 1.000 0.000 0.000 0.000
#> GSM213091 4 0.0376 0.7720 0.004 0.004 0.000 0.992
#> GSM213092 4 0.4874 0.8100 0.180 0.056 0.000 0.764
#> GSM213096 1 0.0921 0.9354 0.972 0.028 0.000 0.000
#> GSM213100 1 0.0000 0.9576 1.000 0.000 0.000 0.000
#> GSM213111 2 0.4941 0.4939 0.000 0.564 0.000 0.436
#> GSM213117 4 0.6014 0.5555 0.360 0.052 0.000 0.588
#> GSM213118 4 0.4874 0.8100 0.180 0.056 0.000 0.764
#> GSM213120 2 0.4977 0.4056 0.000 0.540 0.000 0.460
#> GSM213122 2 0.1888 0.7471 0.044 0.940 0.000 0.016
#> GSM213074 4 0.4907 0.8088 0.176 0.060 0.000 0.764
#> GSM213077 1 0.0000 0.9576 1.000 0.000 0.000 0.000
#> GSM213083 1 0.0000 0.9576 1.000 0.000 0.000 0.000
#> GSM213094 3 0.0336 0.9425 0.000 0.008 0.992 0.000
#> GSM213095 3 0.0000 0.9432 0.000 0.000 1.000 0.000
#> GSM213102 1 0.0000 0.9576 1.000 0.000 0.000 0.000
#> GSM213103 2 0.1807 0.7485 0.052 0.940 0.000 0.008
#> GSM213104 2 0.5378 0.0504 0.448 0.540 0.000 0.012
#> GSM213107 2 0.1940 0.7160 0.000 0.924 0.000 0.076
#> GSM213108 3 0.5292 0.6864 0.000 0.060 0.724 0.216
#> GSM213112 4 0.4874 0.8100 0.180 0.056 0.000 0.764
#> GSM213114 1 0.0000 0.9576 1.000 0.000 0.000 0.000
#> GSM213115 2 0.1807 0.7485 0.052 0.940 0.000 0.008
#> GSM213116 4 0.5434 0.7410 0.252 0.052 0.000 0.696
#> GSM213119 2 0.1807 0.7485 0.052 0.940 0.000 0.008
#> GSM213072 4 0.1004 0.7589 0.004 0.024 0.000 0.972
#> GSM213075 1 0.5842 0.1228 0.520 0.448 0.000 0.032
#> GSM213076 2 0.4679 0.5891 0.000 0.648 0.000 0.352
#> GSM213079 3 0.0000 0.9432 0.000 0.000 1.000 0.000
#> GSM213080 1 0.0000 0.9576 1.000 0.000 0.000 0.000
#> GSM213081 1 0.0000 0.9576 1.000 0.000 0.000 0.000
#> GSM213084 1 0.0000 0.9576 1.000 0.000 0.000 0.000
#> GSM213087 2 0.1807 0.7485 0.052 0.940 0.000 0.008
#> GSM213089 4 0.1824 0.7717 0.004 0.060 0.000 0.936
#> GSM213090 3 0.0336 0.9425 0.000 0.008 0.992 0.000
#> GSM213093 1 0.2411 0.8852 0.920 0.040 0.000 0.040
#> GSM213097 1 0.0524 0.9491 0.988 0.004 0.000 0.008
#> GSM213099 4 0.1489 0.7448 0.000 0.044 0.004 0.952
#> GSM213101 1 0.0000 0.9576 1.000 0.000 0.000 0.000
#> GSM213105 2 0.1807 0.7485 0.052 0.940 0.000 0.008
#> GSM213109 1 0.0000 0.9576 1.000 0.000 0.000 0.000
#> GSM213110 1 0.1637 0.9114 0.940 0.060 0.000 0.000
#> GSM213113 4 0.0524 0.7703 0.004 0.008 0.000 0.988
#> GSM213121 2 0.1940 0.7160 0.000 0.924 0.000 0.076
#> GSM213123 4 0.0188 0.7731 0.004 0.000 0.000 0.996
#> GSM213125 2 0.4941 0.4939 0.000 0.564 0.000 0.436
#> GSM213073 3 0.0000 0.9432 0.000 0.000 1.000 0.000
#> GSM213086 4 0.4874 0.8100 0.180 0.056 0.000 0.764
#> GSM213098 4 0.0524 0.7703 0.004 0.008 0.000 0.988
#> GSM213106 1 0.0000 0.9576 1.000 0.000 0.000 0.000
#> GSM213124 2 0.1913 0.7404 0.020 0.940 0.000 0.040
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.0000 0.9183 1.000 0.000 0.000 0.000 0.000
#> GSM213082 5 0.4277 0.9250 0.000 0.156 0.000 0.076 0.768
#> GSM213085 4 0.2079 0.8134 0.064 0.000 0.000 0.916 0.020
#> GSM213088 1 0.0609 0.9172 0.980 0.000 0.000 0.000 0.020
#> GSM213091 4 0.3123 0.7582 0.000 0.004 0.000 0.812 0.184
#> GSM213092 4 0.1764 0.8178 0.064 0.000 0.000 0.928 0.008
#> GSM213096 1 0.2922 0.8647 0.872 0.000 0.000 0.072 0.056
#> GSM213100 1 0.1341 0.9027 0.944 0.000 0.000 0.000 0.056
#> GSM213111 5 0.4277 0.9250 0.000 0.156 0.000 0.076 0.768
#> GSM213117 4 0.3691 0.7439 0.076 0.000 0.000 0.820 0.104
#> GSM213118 4 0.1478 0.8178 0.064 0.000 0.000 0.936 0.000
#> GSM213120 4 0.4805 0.6367 0.000 0.144 0.000 0.728 0.128
#> GSM213122 2 0.0404 0.7547 0.012 0.988 0.000 0.000 0.000
#> GSM213074 4 0.2079 0.8144 0.064 0.000 0.000 0.916 0.020
#> GSM213077 1 0.1341 0.9027 0.944 0.000 0.000 0.000 0.056
#> GSM213083 1 0.0000 0.9183 1.000 0.000 0.000 0.000 0.000
#> GSM213094 3 0.1357 0.9682 0.000 0.004 0.948 0.000 0.048
#> GSM213095 3 0.0000 0.9780 0.000 0.000 1.000 0.000 0.000
#> GSM213102 1 0.1043 0.9118 0.960 0.000 0.000 0.000 0.040
#> GSM213103 2 0.0566 0.7540 0.012 0.984 0.000 0.000 0.004
#> GSM213104 2 0.4283 0.6486 0.136 0.780 0.000 0.004 0.080
#> GSM213107 2 0.4297 -0.0568 0.000 0.528 0.000 0.000 0.472
#> GSM213108 5 0.4515 0.6949 0.000 0.004 0.184 0.064 0.748
#> GSM213112 4 0.2079 0.8134 0.064 0.000 0.000 0.916 0.020
#> GSM213114 1 0.0000 0.9183 1.000 0.000 0.000 0.000 0.000
#> GSM213115 2 0.0404 0.7547 0.012 0.988 0.000 0.000 0.000
#> GSM213116 4 0.2859 0.7897 0.068 0.000 0.000 0.876 0.056
#> GSM213119 2 0.0404 0.7547 0.012 0.988 0.000 0.000 0.000
#> GSM213072 4 0.3550 0.7083 0.000 0.004 0.000 0.760 0.236
#> GSM213075 2 0.6097 0.5613 0.132 0.676 0.000 0.088 0.104
#> GSM213076 5 0.4372 0.9091 0.000 0.172 0.000 0.072 0.756
#> GSM213079 3 0.0290 0.9777 0.000 0.000 0.992 0.000 0.008
#> GSM213080 1 0.0162 0.9173 0.996 0.000 0.000 0.000 0.004
#> GSM213081 1 0.0000 0.9183 1.000 0.000 0.000 0.000 0.000
#> GSM213084 1 0.0000 0.9183 1.000 0.000 0.000 0.000 0.000
#> GSM213087 2 0.0566 0.7541 0.012 0.984 0.000 0.000 0.004
#> GSM213089 4 0.1768 0.7995 0.000 0.004 0.000 0.924 0.072
#> GSM213090 3 0.1430 0.9673 0.000 0.004 0.944 0.000 0.052
#> GSM213093 1 0.5606 0.5693 0.600 0.000 0.000 0.296 0.104
#> GSM213097 1 0.4734 0.7543 0.728 0.000 0.000 0.176 0.096
#> GSM213099 4 0.4025 0.6263 0.000 0.008 0.000 0.700 0.292
#> GSM213101 1 0.0609 0.9172 0.980 0.000 0.000 0.000 0.020
#> GSM213105 2 0.0566 0.7541 0.012 0.984 0.000 0.000 0.004
#> GSM213109 1 0.4262 0.8061 0.776 0.000 0.000 0.124 0.100
#> GSM213110 2 0.5431 0.1932 0.424 0.516 0.000 0.000 0.060
#> GSM213113 4 0.3123 0.7565 0.000 0.004 0.000 0.812 0.184
#> GSM213121 2 0.4297 -0.0568 0.000 0.528 0.000 0.000 0.472
#> GSM213123 4 0.3010 0.7634 0.000 0.004 0.000 0.824 0.172
#> GSM213125 5 0.4277 0.9250 0.000 0.156 0.000 0.076 0.768
#> GSM213073 3 0.0290 0.9777 0.000 0.000 0.992 0.000 0.008
#> GSM213086 4 0.1764 0.8178 0.064 0.000 0.000 0.928 0.008
#> GSM213098 4 0.3123 0.7565 0.000 0.004 0.000 0.812 0.184
#> GSM213106 1 0.1043 0.9118 0.960 0.000 0.000 0.000 0.040
#> GSM213124 2 0.2358 0.6836 0.000 0.888 0.000 0.104 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.0000 0.8748 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213082 5 0.3772 0.7857 0.000 0.068 0.000 0.160 0.772 0.000
#> GSM213085 6 0.5045 -0.0754 0.020 0.012 0.000 0.464 0.016 0.488
#> GSM213088 1 0.0909 0.8706 0.968 0.000 0.000 0.000 0.012 0.020
#> GSM213091 4 0.1196 0.6194 0.000 0.000 0.000 0.952 0.008 0.040
#> GSM213092 4 0.4533 0.1056 0.020 0.008 0.000 0.540 0.000 0.432
#> GSM213096 1 0.4956 0.2416 0.568 0.012 0.000 0.000 0.048 0.372
#> GSM213100 1 0.2812 0.7944 0.856 0.000 0.000 0.000 0.048 0.096
#> GSM213111 5 0.3772 0.7857 0.000 0.068 0.000 0.160 0.772 0.000
#> GSM213117 6 0.4696 0.2265 0.016 0.012 0.000 0.384 0.008 0.580
#> GSM213118 4 0.4523 0.1173 0.016 0.012 0.000 0.556 0.000 0.416
#> GSM213120 4 0.3763 0.5397 0.000 0.060 0.000 0.768 0.000 0.172
#> GSM213122 2 0.0508 0.8422 0.012 0.984 0.000 0.000 0.000 0.004
#> GSM213074 4 0.4791 0.0924 0.016 0.012 0.000 0.520 0.008 0.444
#> GSM213077 1 0.2629 0.8029 0.868 0.000 0.000 0.000 0.040 0.092
#> GSM213083 1 0.0000 0.8748 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213094 3 0.3660 0.8662 0.000 0.004 0.772 0.000 0.036 0.188
#> GSM213095 3 0.0458 0.9186 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM213102 1 0.1434 0.8597 0.940 0.000 0.000 0.000 0.012 0.048
#> GSM213103 2 0.1225 0.8361 0.012 0.952 0.000 0.000 0.000 0.036
#> GSM213104 2 0.4625 0.7424 0.056 0.744 0.000 0.000 0.064 0.136
#> GSM213107 5 0.5661 0.4218 0.000 0.356 0.000 0.016 0.520 0.108
#> GSM213108 5 0.4094 0.6830 0.000 0.000 0.076 0.120 0.780 0.024
#> GSM213112 4 0.5031 0.0254 0.020 0.012 0.000 0.512 0.016 0.440
#> GSM213114 1 0.0291 0.8732 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM213115 2 0.0363 0.8422 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM213116 6 0.4486 0.2007 0.016 0.012 0.000 0.396 0.000 0.576
#> GSM213119 2 0.0508 0.8417 0.012 0.984 0.000 0.000 0.004 0.000
#> GSM213072 4 0.1333 0.6153 0.000 0.000 0.000 0.944 0.008 0.048
#> GSM213075 2 0.6055 0.6131 0.052 0.620 0.000 0.072 0.032 0.224
#> GSM213076 5 0.5178 0.7663 0.000 0.076 0.000 0.176 0.688 0.060
#> GSM213079 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM213080 1 0.0891 0.8632 0.968 0.000 0.000 0.000 0.008 0.024
#> GSM213081 1 0.0520 0.8739 0.984 0.000 0.000 0.000 0.008 0.008
#> GSM213084 1 0.0000 0.8748 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213087 2 0.0870 0.8381 0.012 0.972 0.000 0.000 0.004 0.012
#> GSM213089 4 0.3493 0.5296 0.000 0.008 0.000 0.756 0.008 0.228
#> GSM213090 3 0.3601 0.8773 0.000 0.008 0.792 0.000 0.040 0.160
#> GSM213093 6 0.5279 0.3294 0.340 0.012 0.000 0.048 0.016 0.584
#> GSM213097 6 0.4397 0.0126 0.452 0.000 0.000 0.008 0.012 0.528
#> GSM213099 4 0.2145 0.5901 0.000 0.000 0.000 0.900 0.028 0.072
#> GSM213101 1 0.0909 0.8706 0.968 0.000 0.000 0.000 0.012 0.020
#> GSM213105 2 0.0870 0.8381 0.012 0.972 0.000 0.000 0.004 0.012
#> GSM213109 1 0.4463 0.0811 0.516 0.000 0.000 0.000 0.028 0.456
#> GSM213110 2 0.5721 0.5529 0.252 0.604 0.000 0.000 0.052 0.092
#> GSM213113 4 0.0146 0.6317 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM213121 5 0.5700 0.4250 0.000 0.356 0.000 0.020 0.520 0.104
#> GSM213123 4 0.0405 0.6317 0.000 0.000 0.000 0.988 0.004 0.008
#> GSM213125 5 0.3772 0.7857 0.000 0.068 0.000 0.160 0.772 0.000
#> GSM213073 3 0.0000 0.9183 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM213086 4 0.4533 0.1056 0.020 0.008 0.000 0.540 0.000 0.432
#> GSM213098 4 0.0000 0.6318 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM213106 1 0.1367 0.8605 0.944 0.000 0.000 0.000 0.012 0.044
#> GSM213124 2 0.2838 0.7367 0.000 0.808 0.000 0.004 0.000 0.188
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 development.stage(p) disease.state(p) k
#> ATC:kmeans 54 0.290 0.921 2
#> ATC:kmeans 40 0.514 0.202 3
#> ATC:kmeans 48 0.989 0.351 4
#> ATC:kmeans 51 0.965 0.474 5
#> ATC:kmeans 40 0.620 0.328 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "skmeans"]
# you can also extract it by
# res = res_list["ATC:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.717 0.837 0.927 0.4994 0.525 0.525
#> 3 3 1.000 0.953 0.979 0.3096 0.793 0.616
#> 4 4 0.896 0.905 0.959 0.1348 0.881 0.671
#> 5 5 0.813 0.732 0.851 0.0595 0.915 0.690
#> 6 6 0.778 0.641 0.811 0.0356 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] 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
#> GSM213078 1 0.0000 0.869 1.000 0.000
#> GSM213082 2 0.0000 1.000 0.000 1.000
#> GSM213085 1 0.0000 0.869 1.000 0.000
#> GSM213088 1 0.0000 0.869 1.000 0.000
#> GSM213091 2 0.0000 1.000 0.000 1.000
#> GSM213092 1 0.9922 0.245 0.552 0.448
#> GSM213096 1 0.0000 0.869 1.000 0.000
#> GSM213100 1 0.0000 0.869 1.000 0.000
#> GSM213111 2 0.0000 1.000 0.000 1.000
#> GSM213117 1 0.0000 0.869 1.000 0.000
#> GSM213118 1 0.5946 0.758 0.856 0.144
#> GSM213120 2 0.0000 1.000 0.000 1.000
#> GSM213122 1 0.9710 0.448 0.600 0.400
#> GSM213074 1 0.0376 0.866 0.996 0.004
#> GSM213077 1 0.0000 0.869 1.000 0.000
#> GSM213083 1 0.0000 0.869 1.000 0.000
#> GSM213094 2 0.0000 1.000 0.000 1.000
#> GSM213095 2 0.0000 1.000 0.000 1.000
#> GSM213102 1 0.0000 0.869 1.000 0.000
#> GSM213103 1 0.8499 0.636 0.724 0.276
#> GSM213104 1 0.0000 0.869 1.000 0.000
#> GSM213107 2 0.0000 1.000 0.000 1.000
#> GSM213108 2 0.0000 1.000 0.000 1.000
#> GSM213112 1 0.9427 0.451 0.640 0.360
#> GSM213114 1 0.0000 0.869 1.000 0.000
#> GSM213115 1 0.9209 0.556 0.664 0.336
#> GSM213116 1 0.0000 0.869 1.000 0.000
#> GSM213119 1 0.9635 0.473 0.612 0.388
#> GSM213072 2 0.0000 1.000 0.000 1.000
#> GSM213075 1 0.0000 0.869 1.000 0.000
#> GSM213076 2 0.0000 1.000 0.000 1.000
#> GSM213079 2 0.0000 1.000 0.000 1.000
#> GSM213080 1 0.0000 0.869 1.000 0.000
#> GSM213081 1 0.0000 0.869 1.000 0.000
#> GSM213084 1 0.0000 0.869 1.000 0.000
#> GSM213087 1 0.9635 0.473 0.612 0.388
#> GSM213089 2 0.0000 1.000 0.000 1.000
#> GSM213090 2 0.0000 1.000 0.000 1.000
#> GSM213093 1 0.0000 0.869 1.000 0.000
#> GSM213097 1 0.0000 0.869 1.000 0.000
#> GSM213099 2 0.0000 1.000 0.000 1.000
#> GSM213101 1 0.0000 0.869 1.000 0.000
#> GSM213105 1 0.9635 0.473 0.612 0.388
#> GSM213109 1 0.0000 0.869 1.000 0.000
#> GSM213110 1 0.0000 0.869 1.000 0.000
#> GSM213113 2 0.0000 1.000 0.000 1.000
#> GSM213121 2 0.0000 1.000 0.000 1.000
#> GSM213123 2 0.0000 1.000 0.000 1.000
#> GSM213125 2 0.0000 1.000 0.000 1.000
#> GSM213073 2 0.0000 1.000 0.000 1.000
#> GSM213086 1 0.9909 0.256 0.556 0.444
#> GSM213098 2 0.0000 1.000 0.000 1.000
#> GSM213106 1 0.0000 0.869 1.000 0.000
#> GSM213124 1 0.9635 0.473 0.612 0.388
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.0237 0.993 0.996 0.004 0.000
#> GSM213082 3 0.0892 0.957 0.000 0.020 0.980
#> GSM213085 1 0.0747 0.984 0.984 0.000 0.016
#> GSM213088 1 0.0237 0.993 0.996 0.004 0.000
#> GSM213091 3 0.0000 0.969 0.000 0.000 1.000
#> GSM213092 1 0.0892 0.982 0.980 0.000 0.020
#> GSM213096 1 0.0237 0.993 0.996 0.004 0.000
#> GSM213100 1 0.0237 0.993 0.996 0.004 0.000
#> GSM213111 3 0.0892 0.957 0.000 0.020 0.980
#> GSM213117 1 0.0000 0.992 1.000 0.000 0.000
#> GSM213118 1 0.0892 0.982 0.980 0.000 0.020
#> GSM213120 3 0.6168 0.257 0.000 0.412 0.588
#> GSM213122 2 0.0000 0.955 0.000 1.000 0.000
#> GSM213074 1 0.0892 0.982 0.980 0.000 0.020
#> GSM213077 1 0.0237 0.993 0.996 0.004 0.000
#> GSM213083 1 0.0237 0.993 0.996 0.004 0.000
#> GSM213094 3 0.0000 0.969 0.000 0.000 1.000
#> GSM213095 3 0.0000 0.969 0.000 0.000 1.000
#> GSM213102 1 0.0237 0.993 0.996 0.004 0.000
#> GSM213103 2 0.0000 0.955 0.000 1.000 0.000
#> GSM213104 2 0.0892 0.945 0.020 0.980 0.000
#> GSM213107 2 0.4555 0.758 0.000 0.800 0.200
#> GSM213108 3 0.0000 0.969 0.000 0.000 1.000
#> GSM213112 1 0.0892 0.982 0.980 0.000 0.020
#> GSM213114 1 0.0237 0.993 0.996 0.004 0.000
#> GSM213115 2 0.0000 0.955 0.000 1.000 0.000
#> GSM213116 1 0.0000 0.992 1.000 0.000 0.000
#> GSM213119 2 0.0000 0.955 0.000 1.000 0.000
#> GSM213072 3 0.0000 0.969 0.000 0.000 1.000
#> GSM213075 2 0.0892 0.945 0.020 0.980 0.000
#> GSM213076 3 0.1163 0.951 0.000 0.028 0.972
#> GSM213079 3 0.0000 0.969 0.000 0.000 1.000
#> GSM213080 1 0.0237 0.993 0.996 0.004 0.000
#> GSM213081 1 0.0237 0.993 0.996 0.004 0.000
#> GSM213084 1 0.0237 0.993 0.996 0.004 0.000
#> GSM213087 2 0.0000 0.955 0.000 1.000 0.000
#> GSM213089 3 0.0000 0.969 0.000 0.000 1.000
#> GSM213090 3 0.0000 0.969 0.000 0.000 1.000
#> GSM213093 1 0.0000 0.992 1.000 0.000 0.000
#> GSM213097 1 0.0000 0.992 1.000 0.000 0.000
#> GSM213099 3 0.0000 0.969 0.000 0.000 1.000
#> GSM213101 1 0.0237 0.993 0.996 0.004 0.000
#> GSM213105 2 0.0000 0.955 0.000 1.000 0.000
#> GSM213109 1 0.0000 0.992 1.000 0.000 0.000
#> GSM213110 2 0.0892 0.945 0.020 0.980 0.000
#> GSM213113 3 0.0000 0.969 0.000 0.000 1.000
#> GSM213121 2 0.4555 0.758 0.000 0.800 0.200
#> GSM213123 3 0.0000 0.969 0.000 0.000 1.000
#> GSM213125 3 0.0892 0.957 0.000 0.020 0.980
#> GSM213073 3 0.0000 0.969 0.000 0.000 1.000
#> GSM213086 1 0.0892 0.982 0.980 0.000 0.020
#> GSM213098 3 0.0000 0.969 0.000 0.000 1.000
#> GSM213106 1 0.0237 0.993 0.996 0.004 0.000
#> GSM213124 2 0.0000 0.955 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213082 3 0.0336 0.922 0.000 0.008 0.992 0.000
#> GSM213085 4 0.0000 0.978 0.000 0.000 0.000 1.000
#> GSM213088 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213091 3 0.3610 0.776 0.000 0.000 0.800 0.200
#> GSM213092 4 0.0000 0.978 0.000 0.000 0.000 1.000
#> GSM213096 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213100 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213111 3 0.0336 0.922 0.000 0.008 0.992 0.000
#> GSM213117 1 0.1022 0.945 0.968 0.000 0.000 0.032
#> GSM213118 4 0.0000 0.978 0.000 0.000 0.000 1.000
#> GSM213120 3 0.4933 0.204 0.000 0.432 0.568 0.000
#> GSM213122 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM213074 4 0.0000 0.978 0.000 0.000 0.000 1.000
#> GSM213077 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213083 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213094 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM213095 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM213102 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213103 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM213104 2 0.0469 0.924 0.012 0.988 0.000 0.000
#> GSM213107 2 0.3688 0.736 0.000 0.792 0.208 0.000
#> GSM213108 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM213112 4 0.0000 0.978 0.000 0.000 0.000 1.000
#> GSM213114 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213115 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM213116 4 0.0469 0.968 0.012 0.000 0.000 0.988
#> GSM213119 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM213072 3 0.2011 0.884 0.000 0.000 0.920 0.080
#> GSM213075 2 0.2589 0.820 0.116 0.884 0.000 0.000
#> GSM213076 3 0.1302 0.900 0.000 0.044 0.956 0.000
#> GSM213079 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM213080 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213081 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213084 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213087 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM213089 3 0.0707 0.918 0.000 0.000 0.980 0.020
#> GSM213090 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM213093 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213097 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213099 3 0.0707 0.918 0.000 0.000 0.980 0.020
#> GSM213101 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213105 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM213109 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213110 1 0.4761 0.383 0.628 0.372 0.000 0.000
#> GSM213113 3 0.3486 0.793 0.000 0.000 0.812 0.188
#> GSM213121 2 0.3610 0.745 0.000 0.800 0.200 0.000
#> GSM213123 4 0.2589 0.853 0.000 0.000 0.116 0.884
#> GSM213125 3 0.0336 0.922 0.000 0.008 0.992 0.000
#> GSM213073 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM213086 4 0.0000 0.978 0.000 0.000 0.000 1.000
#> GSM213098 3 0.3219 0.816 0.000 0.000 0.836 0.164
#> GSM213106 1 0.0000 0.975 1.000 0.000 0.000 0.000
#> GSM213124 2 0.0000 0.933 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.0000 0.9771 1.000 0.000 0.000 0.000 0.000
#> GSM213082 2 0.3861 0.5382 0.000 0.728 0.264 0.000 0.008
#> GSM213085 4 0.0162 0.8616 0.004 0.000 0.000 0.996 0.000
#> GSM213088 1 0.0451 0.9752 0.988 0.008 0.000 0.004 0.000
#> GSM213091 3 0.1725 0.6069 0.000 0.020 0.936 0.044 0.000
#> GSM213092 4 0.0162 0.8632 0.000 0.000 0.004 0.996 0.000
#> GSM213096 1 0.0000 0.9771 1.000 0.000 0.000 0.000 0.000
#> GSM213100 1 0.0000 0.9771 1.000 0.000 0.000 0.000 0.000
#> GSM213111 2 0.3783 0.5565 0.000 0.740 0.252 0.000 0.008
#> GSM213117 1 0.3226 0.8680 0.852 0.088 0.000 0.060 0.000
#> GSM213118 4 0.1981 0.8490 0.000 0.048 0.028 0.924 0.000
#> GSM213120 2 0.4648 0.5122 0.000 0.740 0.104 0.000 0.156
#> GSM213122 5 0.0000 0.8910 0.000 0.000 0.000 0.000 1.000
#> GSM213074 4 0.6151 0.6081 0.008 0.156 0.252 0.584 0.000
#> GSM213077 1 0.0000 0.9771 1.000 0.000 0.000 0.000 0.000
#> GSM213083 1 0.0000 0.9771 1.000 0.000 0.000 0.000 0.000
#> GSM213094 3 0.3143 0.6205 0.000 0.204 0.796 0.000 0.000
#> GSM213095 3 0.4192 0.2367 0.000 0.404 0.596 0.000 0.000
#> GSM213102 1 0.0451 0.9752 0.988 0.008 0.000 0.004 0.000
#> GSM213103 5 0.0162 0.8897 0.000 0.004 0.000 0.000 0.996
#> GSM213104 5 0.2927 0.8209 0.060 0.068 0.000 0.000 0.872
#> GSM213107 2 0.5911 0.3676 0.000 0.488 0.104 0.000 0.408
#> GSM213108 2 0.4306 -0.0565 0.000 0.508 0.492 0.000 0.000
#> GSM213112 4 0.0162 0.8632 0.000 0.000 0.004 0.996 0.000
#> GSM213114 1 0.0000 0.9771 1.000 0.000 0.000 0.000 0.000
#> GSM213115 5 0.0000 0.8910 0.000 0.000 0.000 0.000 1.000
#> GSM213116 4 0.3110 0.7993 0.060 0.080 0.000 0.860 0.000
#> GSM213119 5 0.0000 0.8910 0.000 0.000 0.000 0.000 1.000
#> GSM213072 3 0.0771 0.6361 0.000 0.020 0.976 0.004 0.000
#> GSM213075 5 0.4180 0.7563 0.076 0.104 0.016 0.000 0.804
#> GSM213076 2 0.3906 0.5488 0.000 0.744 0.240 0.000 0.016
#> GSM213079 3 0.3395 0.6035 0.000 0.236 0.764 0.000 0.000
#> GSM213080 1 0.0404 0.9713 0.988 0.012 0.000 0.000 0.000
#> GSM213081 1 0.0000 0.9771 1.000 0.000 0.000 0.000 0.000
#> GSM213084 1 0.0000 0.9771 1.000 0.000 0.000 0.000 0.000
#> GSM213087 5 0.0000 0.8910 0.000 0.000 0.000 0.000 1.000
#> GSM213089 3 0.4510 0.1670 0.000 0.432 0.560 0.008 0.000
#> GSM213090 3 0.3424 0.5996 0.000 0.240 0.760 0.000 0.000
#> GSM213093 1 0.1704 0.9391 0.928 0.068 0.000 0.004 0.000
#> GSM213097 1 0.1704 0.9391 0.928 0.068 0.000 0.004 0.000
#> GSM213099 3 0.0404 0.6424 0.000 0.012 0.988 0.000 0.000
#> GSM213101 1 0.0451 0.9752 0.988 0.008 0.000 0.004 0.000
#> GSM213105 5 0.0000 0.8910 0.000 0.000 0.000 0.000 1.000
#> GSM213109 1 0.1430 0.9439 0.944 0.004 0.000 0.052 0.000
#> GSM213110 5 0.4760 0.3086 0.416 0.020 0.000 0.000 0.564
#> GSM213113 3 0.6332 0.2806 0.000 0.264 0.524 0.212 0.000
#> GSM213121 2 0.5431 0.3233 0.000 0.516 0.060 0.000 0.424
#> GSM213123 4 0.5838 0.3949 0.000 0.112 0.336 0.552 0.000
#> GSM213125 2 0.3756 0.5575 0.000 0.744 0.248 0.000 0.008
#> GSM213073 3 0.3395 0.6035 0.000 0.236 0.764 0.000 0.000
#> GSM213086 4 0.0162 0.8632 0.000 0.000 0.004 0.996 0.000
#> GSM213098 3 0.4069 0.5907 0.000 0.112 0.792 0.096 0.000
#> GSM213106 1 0.0451 0.9752 0.988 0.008 0.000 0.004 0.000
#> GSM213124 5 0.0703 0.8795 0.000 0.024 0.000 0.000 0.976
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 4 0.0000 0.908 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM213082 5 0.2442 0.584 0.000 0.004 0.144 0.000 0.852 0.000
#> GSM213085 1 0.0508 0.715 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM213088 4 0.1387 0.897 0.000 0.000 0.000 0.932 0.000 0.068
#> GSM213091 3 0.3093 0.470 0.012 0.000 0.816 0.000 0.008 0.164
#> GSM213092 1 0.0000 0.718 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213096 4 0.0146 0.907 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM213100 4 0.0000 0.908 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM213111 5 0.2553 0.595 0.000 0.008 0.144 0.000 0.848 0.000
#> GSM213117 4 0.4500 0.558 0.024 0.000 0.000 0.592 0.008 0.376
#> GSM213118 1 0.4130 0.534 0.716 0.000 0.036 0.000 0.008 0.240
#> GSM213120 5 0.3922 0.522 0.000 0.088 0.044 0.000 0.804 0.064
#> GSM213122 2 0.0291 0.815 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM213074 6 0.5844 0.205 0.252 0.000 0.144 0.016 0.008 0.580
#> GSM213077 4 0.0000 0.908 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM213083 4 0.0000 0.908 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM213094 3 0.2520 0.717 0.000 0.000 0.844 0.000 0.152 0.004
#> GSM213095 3 0.3592 0.532 0.000 0.000 0.656 0.000 0.344 0.000
#> GSM213102 4 0.1714 0.888 0.000 0.000 0.000 0.908 0.000 0.092
#> GSM213103 2 0.1082 0.806 0.000 0.956 0.000 0.000 0.004 0.040
#> GSM213104 2 0.6848 0.414 0.004 0.504 0.000 0.212 0.088 0.192
#> GSM213107 5 0.6056 0.422 0.000 0.272 0.048 0.000 0.556 0.124
#> GSM213108 3 0.3868 0.218 0.000 0.000 0.504 0.000 0.496 0.000
#> GSM213112 1 0.0405 0.717 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM213114 4 0.0260 0.905 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM213115 2 0.0000 0.818 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM213116 1 0.5268 0.292 0.564 0.000 0.008 0.064 0.008 0.356
#> GSM213119 2 0.0000 0.818 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM213072 3 0.2278 0.549 0.000 0.000 0.868 0.000 0.004 0.128
#> GSM213075 2 0.5015 0.516 0.000 0.616 0.000 0.092 0.004 0.288
#> GSM213076 5 0.3779 0.588 0.000 0.024 0.092 0.000 0.808 0.076
#> GSM213079 3 0.2631 0.717 0.000 0.000 0.820 0.000 0.180 0.000
#> GSM213080 4 0.0632 0.897 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM213081 4 0.0632 0.906 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM213084 4 0.0000 0.908 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM213087 2 0.0000 0.818 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM213089 6 0.6369 0.320 0.016 0.000 0.312 0.000 0.252 0.420
#> GSM213090 3 0.2793 0.708 0.000 0.000 0.800 0.000 0.200 0.000
#> GSM213093 4 0.3371 0.722 0.000 0.000 0.000 0.708 0.000 0.292
#> GSM213097 4 0.3351 0.726 0.000 0.000 0.000 0.712 0.000 0.288
#> GSM213099 3 0.2212 0.569 0.000 0.000 0.880 0.000 0.008 0.112
#> GSM213101 4 0.1387 0.897 0.000 0.000 0.000 0.932 0.000 0.068
#> GSM213105 2 0.0000 0.818 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM213109 4 0.3125 0.844 0.080 0.000 0.000 0.836 0.000 0.084
#> GSM213110 2 0.4620 0.315 0.000 0.532 0.000 0.428 0.000 0.040
#> GSM213113 5 0.7583 -0.264 0.260 0.000 0.284 0.000 0.300 0.156
#> GSM213121 5 0.5816 0.410 0.000 0.288 0.028 0.000 0.560 0.124
#> GSM213123 1 0.7378 -0.198 0.392 0.000 0.228 0.000 0.140 0.240
#> GSM213125 5 0.2431 0.599 0.000 0.008 0.132 0.000 0.860 0.000
#> GSM213073 3 0.2664 0.716 0.000 0.000 0.816 0.000 0.184 0.000
#> GSM213086 1 0.0000 0.718 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213098 3 0.5053 0.452 0.108 0.000 0.712 0.000 0.060 0.120
#> GSM213106 4 0.1714 0.888 0.000 0.000 0.000 0.908 0.000 0.092
#> GSM213124 2 0.1926 0.777 0.000 0.912 0.000 0.000 0.020 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 development.stage(p) disease.state(p) k
#> ATC:skmeans 46 0.249 0.776 2
#> ATC:skmeans 53 0.228 0.530 3
#> ATC:skmeans 52 0.380 0.459 4
#> ATC:skmeans 46 0.228 0.206 5
#> ATC:skmeans 42 0.516 0.406 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "pam"]
# you can also extract it by
# res = res_list["ATC:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.418 0.694 0.809 0.43424 0.609 0.609
#> 3 3 0.413 0.641 0.790 0.39914 0.704 0.546
#> 4 4 0.880 0.937 0.970 0.22599 0.806 0.538
#> 5 5 0.769 0.831 0.911 0.04317 0.975 0.900
#> 6 6 0.922 0.845 0.942 0.00142 0.997 0.988
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
#> GSM213078 1 0.9795 0.6882 0.584 0.416
#> GSM213082 2 0.9795 0.9985 0.416 0.584
#> GSM213085 1 0.6438 0.6791 0.836 0.164
#> GSM213088 1 0.9795 0.6882 0.584 0.416
#> GSM213091 1 0.2778 0.5510 0.952 0.048
#> GSM213092 1 0.5294 0.6692 0.880 0.120
#> GSM213096 1 0.9795 0.6882 0.584 0.416
#> GSM213100 1 0.9795 0.6882 0.584 0.416
#> GSM213111 2 0.9795 0.9985 0.416 0.584
#> GSM213117 1 0.0000 0.6172 1.000 0.000
#> GSM213118 1 0.0000 0.6172 1.000 0.000
#> GSM213120 1 0.6712 0.2393 0.824 0.176
#> GSM213122 1 0.0000 0.6172 1.000 0.000
#> GSM213074 1 0.0000 0.6172 1.000 0.000
#> GSM213077 1 0.9795 0.6882 0.584 0.416
#> GSM213083 1 0.9795 0.6882 0.584 0.416
#> GSM213094 2 0.9795 0.9985 0.416 0.584
#> GSM213095 2 0.9795 0.9985 0.416 0.584
#> GSM213102 1 0.9795 0.6882 0.584 0.416
#> GSM213103 1 0.0000 0.6172 1.000 0.000
#> GSM213104 1 0.7299 0.6829 0.796 0.204
#> GSM213107 2 0.9795 0.9985 0.416 0.584
#> GSM213108 2 0.9795 0.9985 0.416 0.584
#> GSM213112 1 0.6438 0.6791 0.836 0.164
#> GSM213114 1 0.9795 0.6882 0.584 0.416
#> GSM213115 1 0.0000 0.6172 1.000 0.000
#> GSM213116 1 0.0000 0.6172 1.000 0.000
#> GSM213119 1 0.0938 0.6028 0.988 0.012
#> GSM213072 1 0.6887 0.2119 0.816 0.184
#> GSM213075 1 0.0000 0.6172 1.000 0.000
#> GSM213076 2 0.9795 0.9985 0.416 0.584
#> GSM213079 2 0.9795 0.9985 0.416 0.584
#> GSM213080 1 0.9795 0.6882 0.584 0.416
#> GSM213081 1 0.9795 0.6882 0.584 0.416
#> GSM213084 1 0.9795 0.6882 0.584 0.416
#> GSM213087 1 0.7528 0.0724 0.784 0.216
#> GSM213089 1 0.0000 0.6172 1.000 0.000
#> GSM213090 2 0.9795 0.9985 0.416 0.584
#> GSM213093 1 0.5408 0.6709 0.876 0.124
#> GSM213097 1 0.9795 0.6882 0.584 0.416
#> GSM213099 2 0.9795 0.9985 0.416 0.584
#> GSM213101 1 0.9795 0.6882 0.584 0.416
#> GSM213105 1 0.7674 0.0356 0.776 0.224
#> GSM213109 1 0.9795 0.6882 0.584 0.416
#> GSM213110 1 0.9795 0.6882 0.584 0.416
#> GSM213113 2 0.9850 0.9804 0.428 0.572
#> GSM213121 2 0.9795 0.9985 0.416 0.584
#> GSM213123 1 0.3584 0.5163 0.932 0.068
#> GSM213125 2 0.9795 0.9985 0.416 0.584
#> GSM213073 2 0.9795 0.9985 0.416 0.584
#> GSM213086 1 0.2423 0.6387 0.960 0.040
#> GSM213098 1 0.7528 0.0836 0.784 0.216
#> GSM213106 1 0.9795 0.6882 0.584 0.416
#> GSM213124 1 0.0000 0.6172 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.3752 0.611 0.856 0.144 0.000
#> GSM213082 3 0.5905 0.573 0.000 0.352 0.648
#> GSM213085 1 0.8386 0.595 0.620 0.224 0.156
#> GSM213088 1 0.3752 0.611 0.856 0.144 0.000
#> GSM213091 1 0.8668 0.590 0.596 0.224 0.180
#> GSM213092 1 0.8436 0.595 0.616 0.224 0.160
#> GSM213096 1 0.3752 0.611 0.856 0.144 0.000
#> GSM213100 1 0.3752 0.611 0.856 0.144 0.000
#> GSM213111 3 0.6008 0.544 0.000 0.372 0.628
#> GSM213117 1 0.8668 0.590 0.596 0.224 0.180
#> GSM213118 1 0.8668 0.590 0.596 0.224 0.180
#> GSM213120 2 0.7759 0.405 0.144 0.676 0.180
#> GSM213122 2 0.0000 0.839 0.000 1.000 0.000
#> GSM213074 1 0.8668 0.590 0.596 0.224 0.180
#> GSM213077 1 0.3752 0.611 0.856 0.144 0.000
#> GSM213083 1 0.3752 0.611 0.856 0.144 0.000
#> GSM213094 3 0.0000 0.815 0.000 0.000 1.000
#> GSM213095 3 0.0000 0.815 0.000 0.000 1.000
#> GSM213102 1 0.3752 0.611 0.856 0.144 0.000
#> GSM213103 2 0.0000 0.839 0.000 1.000 0.000
#> GSM213104 2 0.6280 -0.132 0.460 0.540 0.000
#> GSM213107 2 0.2680 0.766 0.008 0.924 0.068
#> GSM213108 3 0.0000 0.815 0.000 0.000 1.000
#> GSM213112 1 0.8386 0.595 0.620 0.224 0.156
#> GSM213114 1 0.3752 0.611 0.856 0.144 0.000
#> GSM213115 2 0.0000 0.839 0.000 1.000 0.000
#> GSM213116 1 0.8668 0.590 0.596 0.224 0.180
#> GSM213119 2 0.0000 0.839 0.000 1.000 0.000
#> GSM213072 1 0.8984 0.554 0.564 0.224 0.212
#> GSM213075 2 0.2187 0.804 0.028 0.948 0.024
#> GSM213076 2 0.4874 0.647 0.144 0.828 0.028
#> GSM213079 3 0.0000 0.815 0.000 0.000 1.000
#> GSM213080 1 0.4702 0.526 0.788 0.212 0.000
#> GSM213081 1 0.3752 0.611 0.856 0.144 0.000
#> GSM213084 1 0.3752 0.611 0.856 0.144 0.000
#> GSM213087 2 0.0237 0.837 0.000 0.996 0.004
#> GSM213089 1 0.8803 0.570 0.580 0.240 0.180
#> GSM213090 3 0.0000 0.815 0.000 0.000 1.000
#> GSM213093 1 0.8466 0.597 0.616 0.212 0.172
#> GSM213097 1 0.0848 0.609 0.984 0.008 0.008
#> GSM213099 3 0.8063 0.466 0.132 0.224 0.644
#> GSM213101 1 0.3752 0.611 0.856 0.144 0.000
#> GSM213105 2 0.0237 0.837 0.000 0.996 0.004
#> GSM213109 1 0.2165 0.613 0.936 0.064 0.000
#> GSM213110 2 0.4842 0.534 0.224 0.776 0.000
#> GSM213113 1 0.8668 0.590 0.596 0.224 0.180
#> GSM213121 2 0.0829 0.834 0.012 0.984 0.004
#> GSM213123 1 0.8668 0.590 0.596 0.224 0.180
#> GSM213125 3 0.6045 0.537 0.000 0.380 0.620
#> GSM213073 3 0.0000 0.815 0.000 0.000 1.000
#> GSM213086 1 0.8623 0.591 0.600 0.224 0.176
#> GSM213098 1 0.8668 0.590 0.596 0.224 0.180
#> GSM213106 1 0.3752 0.611 0.856 0.144 0.000
#> GSM213124 2 0.0424 0.836 0.008 0.992 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM213082 3 0.2831 0.881 0.000 0.004 0.876 0.120
#> GSM213085 4 0.0000 0.993 0.000 0.000 0.000 1.000
#> GSM213088 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM213091 4 0.0000 0.993 0.000 0.000 0.000 1.000
#> GSM213092 4 0.0000 0.993 0.000 0.000 0.000 1.000
#> GSM213096 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM213100 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM213111 3 0.2831 0.881 0.000 0.004 0.876 0.120
#> GSM213117 4 0.0707 0.972 0.000 0.020 0.000 0.980
#> GSM213118 4 0.0000 0.993 0.000 0.000 0.000 1.000
#> GSM213120 4 0.0000 0.993 0.000 0.000 0.000 1.000
#> GSM213122 2 0.0188 0.914 0.004 0.996 0.000 0.000
#> GSM213074 4 0.0000 0.993 0.000 0.000 0.000 1.000
#> GSM213077 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM213083 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM213094 3 0.0000 0.942 0.000 0.000 1.000 0.000
#> GSM213095 3 0.0000 0.942 0.000 0.000 1.000 0.000
#> GSM213102 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM213103 2 0.0188 0.914 0.004 0.996 0.000 0.000
#> GSM213104 2 0.4304 0.583 0.284 0.716 0.000 0.000
#> GSM213107 2 0.2647 0.849 0.000 0.880 0.000 0.120
#> GSM213108 3 0.0188 0.941 0.000 0.004 0.996 0.000
#> GSM213112 4 0.0000 0.993 0.000 0.000 0.000 1.000
#> GSM213114 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM213115 2 0.0188 0.914 0.004 0.996 0.000 0.000
#> GSM213116 4 0.0000 0.993 0.000 0.000 0.000 1.000
#> GSM213119 2 0.0188 0.914 0.004 0.996 0.000 0.000
#> GSM213072 4 0.0000 0.993 0.000 0.000 0.000 1.000
#> GSM213075 2 0.0188 0.914 0.004 0.996 0.000 0.000
#> GSM213076 2 0.3569 0.770 0.000 0.804 0.000 0.196
#> GSM213079 3 0.0000 0.942 0.000 0.000 1.000 0.000
#> GSM213080 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM213081 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM213084 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM213087 2 0.0188 0.914 0.004 0.996 0.000 0.000
#> GSM213089 4 0.0000 0.993 0.000 0.000 0.000 1.000
#> GSM213090 3 0.0000 0.942 0.000 0.000 1.000 0.000
#> GSM213093 4 0.0000 0.993 0.000 0.000 0.000 1.000
#> GSM213097 1 0.4193 0.637 0.732 0.000 0.000 0.268
#> GSM213099 4 0.2125 0.906 0.000 0.004 0.076 0.920
#> GSM213101 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM213105 2 0.0188 0.914 0.004 0.996 0.000 0.000
#> GSM213109 1 0.0188 0.973 0.996 0.000 0.000 0.004
#> GSM213110 2 0.0188 0.914 0.004 0.996 0.000 0.000
#> GSM213113 4 0.0000 0.993 0.000 0.000 0.000 1.000
#> GSM213121 2 0.2647 0.849 0.000 0.880 0.000 0.120
#> GSM213123 4 0.0000 0.993 0.000 0.000 0.000 1.000
#> GSM213125 3 0.2888 0.878 0.000 0.004 0.872 0.124
#> GSM213073 3 0.0000 0.942 0.000 0.000 1.000 0.000
#> GSM213086 4 0.0000 0.993 0.000 0.000 0.000 1.000
#> GSM213098 4 0.0000 0.993 0.000 0.000 0.000 1.000
#> GSM213106 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM213124 2 0.2714 0.857 0.004 0.884 0.000 0.112
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM213082 5 0.0290 0.893 0.000 0.000 0.008 0.000 0.992
#> GSM213085 4 0.0000 0.872 0.000 0.000 0.000 1.000 0.000
#> GSM213088 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM213091 4 0.2605 0.893 0.000 0.000 0.000 0.852 0.148
#> GSM213092 4 0.0000 0.872 0.000 0.000 0.000 1.000 0.000
#> GSM213096 1 0.2561 0.839 0.856 0.000 0.000 0.144 0.000
#> GSM213100 1 0.2561 0.839 0.856 0.000 0.000 0.144 0.000
#> GSM213111 5 0.0000 0.893 0.000 0.000 0.000 0.000 1.000
#> GSM213117 4 0.0324 0.873 0.004 0.000 0.000 0.992 0.004
#> GSM213118 4 0.0000 0.872 0.000 0.000 0.000 1.000 0.000
#> GSM213120 4 0.2886 0.889 0.000 0.008 0.000 0.844 0.148
#> GSM213122 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000
#> GSM213074 4 0.2605 0.893 0.000 0.000 0.000 0.852 0.148
#> GSM213077 1 0.2561 0.839 0.856 0.000 0.000 0.144 0.000
#> GSM213083 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM213094 3 0.5158 0.540 0.000 0.000 0.676 0.100 0.224
#> GSM213095 3 0.0609 0.897 0.000 0.000 0.980 0.000 0.020
#> GSM213102 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM213103 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000
#> GSM213104 2 0.4889 0.588 0.136 0.720 0.000 0.144 0.000
#> GSM213107 2 0.4171 0.329 0.000 0.604 0.000 0.000 0.396
#> GSM213108 5 0.1851 0.844 0.000 0.000 0.088 0.000 0.912
#> GSM213112 4 0.0000 0.872 0.000 0.000 0.000 1.000 0.000
#> GSM213114 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM213115 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000
#> GSM213116 4 0.2329 0.835 0.124 0.000 0.000 0.876 0.000
#> GSM213119 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000
#> GSM213072 4 0.2605 0.893 0.000 0.000 0.000 0.852 0.148
#> GSM213075 2 0.2763 0.711 0.000 0.848 0.000 0.004 0.148
#> GSM213076 5 0.0703 0.887 0.000 0.024 0.000 0.000 0.976
#> GSM213079 3 0.0000 0.893 0.000 0.000 1.000 0.000 0.000
#> GSM213080 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM213081 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM213084 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM213087 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000
#> GSM213089 4 0.2605 0.893 0.000 0.000 0.000 0.852 0.148
#> GSM213090 3 0.0609 0.897 0.000 0.000 0.980 0.000 0.020
#> GSM213093 4 0.2561 0.821 0.144 0.000 0.000 0.856 0.000
#> GSM213097 1 0.4101 0.346 0.628 0.000 0.000 0.372 0.000
#> GSM213099 4 0.3999 0.648 0.000 0.000 0.000 0.656 0.344
#> GSM213101 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM213105 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000
#> GSM213109 1 0.2773 0.824 0.836 0.000 0.000 0.164 0.000
#> GSM213110 2 0.0000 0.868 0.000 1.000 0.000 0.000 0.000
#> GSM213113 4 0.2690 0.888 0.000 0.000 0.000 0.844 0.156
#> GSM213121 2 0.4138 0.358 0.000 0.616 0.000 0.000 0.384
#> GSM213123 4 0.2561 0.893 0.000 0.000 0.000 0.856 0.144
#> GSM213125 5 0.2843 0.761 0.000 0.144 0.008 0.000 0.848
#> GSM213073 3 0.0290 0.897 0.000 0.000 0.992 0.000 0.008
#> GSM213086 4 0.0000 0.872 0.000 0.000 0.000 1.000 0.000
#> GSM213098 4 0.2561 0.893 0.000 0.000 0.000 0.856 0.144
#> GSM213106 1 0.0000 0.916 1.000 0.000 0.000 0.000 0.000
#> GSM213124 2 0.0000 0.868 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
#> GSM213078 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213082 6 0.0260 0.968 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM213085 4 0.0865 0.948 0.000 0.000 0.000 0.964 0.036 0.000
#> GSM213088 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213091 4 0.0260 0.949 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM213092 4 0.0865 0.948 0.000 0.000 0.000 0.964 0.036 0.000
#> GSM213096 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213100 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213111 6 0.0146 0.962 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM213117 4 0.1204 0.940 0.000 0.000 0.000 0.944 0.056 0.000
#> GSM213118 4 0.0260 0.950 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM213120 4 0.1265 0.929 0.000 0.044 0.000 0.948 0.008 0.000
#> GSM213122 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM213074 4 0.1204 0.940 0.000 0.000 0.000 0.944 0.056 0.000
#> GSM213077 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213083 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213094 3 0.4791 0.387 0.000 0.000 0.664 0.248 0.008 0.080
#> GSM213095 3 0.3161 0.555 0.000 0.000 0.776 0.000 0.008 0.216
#> GSM213102 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213103 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM213104 2 0.3309 0.464 0.280 0.720 0.000 0.000 0.000 0.000
#> GSM213107 2 0.3737 0.382 0.000 0.608 0.000 0.000 0.000 0.392
#> GSM213108 6 0.0260 0.968 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM213112 4 0.0865 0.948 0.000 0.000 0.000 0.964 0.036 0.000
#> GSM213114 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213115 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM213116 4 0.1141 0.942 0.000 0.000 0.000 0.948 0.052 0.000
#> GSM213119 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM213072 4 0.0972 0.942 0.000 0.000 0.000 0.964 0.008 0.028
#> GSM213075 2 0.1049 0.837 0.000 0.960 0.000 0.032 0.008 0.000
#> GSM213076 6 0.1668 0.886 0.000 0.060 0.000 0.004 0.008 0.928
#> GSM213079 3 0.0000 0.666 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM213080 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213081 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213084 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213087 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM213089 4 0.1204 0.940 0.000 0.000 0.000 0.944 0.056 0.000
#> GSM213090 5 0.1806 0.000 0.000 0.000 0.088 0.000 0.908 0.004
#> GSM213093 4 0.1285 0.939 0.004 0.000 0.000 0.944 0.052 0.000
#> GSM213097 1 0.4482 0.377 0.628 0.000 0.000 0.324 0.048 0.000
#> GSM213099 4 0.2706 0.796 0.000 0.000 0.000 0.832 0.008 0.160
#> GSM213101 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213105 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM213109 1 0.2147 0.855 0.896 0.000 0.000 0.020 0.084 0.000
#> GSM213110 2 0.0000 0.869 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM213113 4 0.1010 0.947 0.000 0.000 0.000 0.960 0.036 0.004
#> GSM213121 2 0.3706 0.409 0.000 0.620 0.000 0.000 0.000 0.380
#> GSM213123 4 0.0865 0.948 0.000 0.000 0.000 0.964 0.036 0.000
#> GSM213125 6 0.0260 0.968 0.000 0.000 0.000 0.000 0.008 0.992
#> GSM213073 3 0.0146 0.669 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM213086 4 0.0865 0.948 0.000 0.000 0.000 0.964 0.036 0.000
#> GSM213098 4 0.0790 0.949 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM213106 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213124 2 0.0146 0.867 0.000 0.996 0.000 0.004 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 development.stage(p) disease.state(p) k
#> ATC:pam 49 0.440 1.000 2
#> ATC:pam 51 0.756 0.780 3
#> ATC:pam 54 0.971 0.756 4
#> ATC:pam 51 0.966 0.575 5
#> ATC:pam 48 0.924 0.665 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "mclust"]
# you can also extract it by
# res = res_list["ATC:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.971 0.986 0.5017 0.497 0.497
#> 3 3 0.557 0.733 0.848 0.1891 0.887 0.774
#> 4 4 0.853 0.847 0.918 0.1973 0.837 0.602
#> 5 5 0.896 0.843 0.935 0.0672 0.867 0.583
#> 6 6 0.800 0.705 0.843 0.0530 0.931 0.729
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
#> GSM213078 1 0.0000 0.992 1.000 0.000
#> GSM213082 2 0.0000 0.976 0.000 1.000
#> GSM213085 1 0.0000 0.992 1.000 0.000
#> GSM213088 1 0.0000 0.992 1.000 0.000
#> GSM213091 1 0.0000 0.992 1.000 0.000
#> GSM213092 1 0.0000 0.992 1.000 0.000
#> GSM213096 1 0.0000 0.992 1.000 0.000
#> GSM213100 1 0.0000 0.992 1.000 0.000
#> GSM213111 2 0.0000 0.976 0.000 1.000
#> GSM213117 1 0.0000 0.992 1.000 0.000
#> GSM213118 1 0.0000 0.992 1.000 0.000
#> GSM213120 2 0.3584 0.928 0.068 0.932
#> GSM213122 2 0.0000 0.976 0.000 1.000
#> GSM213074 1 0.0000 0.992 1.000 0.000
#> GSM213077 1 0.0000 0.992 1.000 0.000
#> GSM213083 1 0.0000 0.992 1.000 0.000
#> GSM213094 2 0.0000 0.976 0.000 1.000
#> GSM213095 2 0.0000 0.976 0.000 1.000
#> GSM213102 1 0.0000 0.992 1.000 0.000
#> GSM213103 2 0.0000 0.976 0.000 1.000
#> GSM213104 2 0.0000 0.976 0.000 1.000
#> GSM213107 2 0.0000 0.976 0.000 1.000
#> GSM213108 2 0.0000 0.976 0.000 1.000
#> GSM213112 1 0.0000 0.992 1.000 0.000
#> GSM213114 1 0.0000 0.992 1.000 0.000
#> GSM213115 2 0.0000 0.976 0.000 1.000
#> GSM213116 1 0.0000 0.992 1.000 0.000
#> GSM213119 2 0.0000 0.976 0.000 1.000
#> GSM213072 1 0.0000 0.992 1.000 0.000
#> GSM213075 2 0.3733 0.925 0.072 0.928
#> GSM213076 2 0.0000 0.976 0.000 1.000
#> GSM213079 2 0.0000 0.976 0.000 1.000
#> GSM213080 2 0.7815 0.722 0.232 0.768
#> GSM213081 1 0.0000 0.992 1.000 0.000
#> GSM213084 1 0.0000 0.992 1.000 0.000
#> GSM213087 2 0.0000 0.976 0.000 1.000
#> GSM213089 1 0.0376 0.988 0.996 0.004
#> GSM213090 2 0.0000 0.976 0.000 1.000
#> GSM213093 1 0.0000 0.992 1.000 0.000
#> GSM213097 1 0.0000 0.992 1.000 0.000
#> GSM213099 1 0.7745 0.707 0.772 0.228
#> GSM213101 1 0.0000 0.992 1.000 0.000
#> GSM213105 2 0.0000 0.976 0.000 1.000
#> GSM213109 1 0.0000 0.992 1.000 0.000
#> GSM213110 2 0.4939 0.888 0.108 0.892
#> GSM213113 1 0.0000 0.992 1.000 0.000
#> GSM213121 2 0.0000 0.976 0.000 1.000
#> GSM213123 1 0.0000 0.992 1.000 0.000
#> GSM213125 2 0.0000 0.976 0.000 1.000
#> GSM213073 2 0.0000 0.976 0.000 1.000
#> GSM213086 1 0.0000 0.992 1.000 0.000
#> GSM213098 1 0.0000 0.992 1.000 0.000
#> GSM213106 1 0.0000 0.992 1.000 0.000
#> GSM213124 2 0.3274 0.935 0.060 0.940
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 3 0.5785 1.0000 0.332 0.000 0.668
#> GSM213082 2 0.0000 0.8830 0.000 1.000 0.000
#> GSM213085 1 0.0000 0.7506 1.000 0.000 0.000
#> GSM213088 1 0.5905 0.0534 0.648 0.000 0.352
#> GSM213091 1 0.0000 0.7506 1.000 0.000 0.000
#> GSM213092 1 0.0000 0.7506 1.000 0.000 0.000
#> GSM213096 1 0.7027 0.1896 0.660 0.044 0.296
#> GSM213100 3 0.5785 1.0000 0.332 0.000 0.668
#> GSM213111 2 0.0000 0.8830 0.000 1.000 0.000
#> GSM213117 1 0.0000 0.7506 1.000 0.000 0.000
#> GSM213118 1 0.0000 0.7506 1.000 0.000 0.000
#> GSM213120 2 0.0237 0.8822 0.004 0.996 0.000
#> GSM213122 2 0.0000 0.8830 0.000 1.000 0.000
#> GSM213074 1 0.0000 0.7506 1.000 0.000 0.000
#> GSM213077 3 0.5785 1.0000 0.332 0.000 0.668
#> GSM213083 3 0.5785 1.0000 0.332 0.000 0.668
#> GSM213094 2 0.5785 0.7639 0.000 0.668 0.332
#> GSM213095 2 0.4796 0.8229 0.000 0.780 0.220
#> GSM213102 1 0.4605 0.4954 0.796 0.000 0.204
#> GSM213103 2 0.0000 0.8830 0.000 1.000 0.000
#> GSM213104 2 0.6906 0.7079 0.192 0.724 0.084
#> GSM213107 2 0.2625 0.8733 0.000 0.916 0.084
#> GSM213108 2 0.1411 0.8837 0.000 0.964 0.036
#> GSM213112 1 0.0000 0.7506 1.000 0.000 0.000
#> GSM213114 3 0.5785 1.0000 0.332 0.000 0.668
#> GSM213115 2 0.0000 0.8830 0.000 1.000 0.000
#> GSM213116 1 0.0000 0.7506 1.000 0.000 0.000
#> GSM213119 2 0.1411 0.8837 0.000 0.964 0.036
#> GSM213072 1 0.0000 0.7506 1.000 0.000 0.000
#> GSM213075 2 0.5058 0.6479 0.244 0.756 0.000
#> GSM213076 2 0.1411 0.8837 0.000 0.964 0.036
#> GSM213079 2 0.5785 0.7639 0.000 0.668 0.332
#> GSM213080 2 0.5254 0.6114 0.264 0.736 0.000
#> GSM213081 3 0.5785 1.0000 0.332 0.000 0.668
#> GSM213084 3 0.5785 1.0000 0.332 0.000 0.668
#> GSM213087 2 0.1411 0.8837 0.000 0.964 0.036
#> GSM213089 1 0.4605 0.5165 0.796 0.204 0.000
#> GSM213090 2 0.5785 0.7639 0.000 0.668 0.332
#> GSM213093 1 0.0000 0.7506 1.000 0.000 0.000
#> GSM213097 1 0.1753 0.7124 0.952 0.000 0.048
#> GSM213099 1 0.6189 0.2860 0.632 0.364 0.004
#> GSM213101 1 0.5905 0.0534 0.648 0.000 0.352
#> GSM213105 2 0.1411 0.8837 0.000 0.964 0.036
#> GSM213109 1 0.1860 0.7084 0.948 0.000 0.052
#> GSM213110 2 0.5058 0.6476 0.244 0.756 0.000
#> GSM213113 1 0.6267 0.1626 0.548 0.452 0.000
#> GSM213121 2 0.1411 0.8837 0.000 0.964 0.036
#> GSM213123 1 0.6260 0.1737 0.552 0.448 0.000
#> GSM213125 2 0.0000 0.8830 0.000 1.000 0.000
#> GSM213073 2 0.5785 0.7639 0.000 0.668 0.332
#> GSM213086 1 0.0000 0.7506 1.000 0.000 0.000
#> GSM213098 1 0.0000 0.7506 1.000 0.000 0.000
#> GSM213106 1 0.4605 0.4954 0.796 0.000 0.204
#> GSM213124 2 0.0000 0.8830 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.1637 0.884 0.940 0.000 0.000 0.060
#> GSM213082 2 0.1396 0.926 0.004 0.960 0.032 0.004
#> GSM213085 4 0.0188 0.916 0.004 0.000 0.000 0.996
#> GSM213088 1 0.3907 0.834 0.768 0.000 0.000 0.232
#> GSM213091 4 0.0000 0.915 0.000 0.000 0.000 1.000
#> GSM213092 4 0.0188 0.916 0.004 0.000 0.000 0.996
#> GSM213096 1 0.3873 0.837 0.772 0.000 0.000 0.228
#> GSM213100 1 0.1557 0.884 0.944 0.000 0.000 0.056
#> GSM213111 2 0.1396 0.926 0.004 0.960 0.032 0.004
#> GSM213117 4 0.0469 0.912 0.012 0.000 0.000 0.988
#> GSM213118 4 0.0188 0.916 0.004 0.000 0.000 0.996
#> GSM213120 2 0.1209 0.924 0.000 0.964 0.004 0.032
#> GSM213122 2 0.0188 0.932 0.000 0.996 0.004 0.000
#> GSM213074 4 0.0188 0.916 0.004 0.000 0.000 0.996
#> GSM213077 1 0.1557 0.884 0.944 0.000 0.000 0.056
#> GSM213083 1 0.1022 0.870 0.968 0.000 0.000 0.032
#> GSM213094 3 0.1302 0.866 0.000 0.044 0.956 0.000
#> GSM213095 3 0.3718 0.787 0.012 0.168 0.820 0.000
#> GSM213102 1 0.3907 0.834 0.768 0.000 0.000 0.232
#> GSM213103 2 0.0000 0.932 0.000 1.000 0.000 0.000
#> GSM213104 2 0.1109 0.921 0.000 0.968 0.004 0.028
#> GSM213107 2 0.1936 0.923 0.028 0.940 0.032 0.000
#> GSM213108 3 0.5330 0.179 0.004 0.476 0.516 0.004
#> GSM213112 4 0.0188 0.916 0.004 0.000 0.000 0.996
#> GSM213114 1 0.1022 0.870 0.968 0.000 0.000 0.032
#> GSM213115 2 0.0336 0.931 0.000 0.992 0.008 0.000
#> GSM213116 4 0.0188 0.916 0.004 0.000 0.000 0.996
#> GSM213119 2 0.1302 0.910 0.000 0.956 0.044 0.000
#> GSM213072 4 0.0000 0.915 0.000 0.000 0.000 1.000
#> GSM213075 2 0.1109 0.919 0.004 0.968 0.000 0.028
#> GSM213076 2 0.1109 0.928 0.004 0.968 0.028 0.000
#> GSM213079 3 0.1302 0.866 0.000 0.044 0.956 0.000
#> GSM213080 2 0.5686 0.386 0.352 0.616 0.004 0.028
#> GSM213081 1 0.1474 0.883 0.948 0.000 0.000 0.052
#> GSM213084 1 0.1022 0.870 0.968 0.000 0.000 0.032
#> GSM213087 2 0.1767 0.907 0.012 0.944 0.044 0.000
#> GSM213089 4 0.1661 0.877 0.004 0.052 0.000 0.944
#> GSM213090 3 0.1302 0.866 0.000 0.044 0.956 0.000
#> GSM213093 4 0.0592 0.909 0.016 0.000 0.000 0.984
#> GSM213097 4 0.4643 0.351 0.344 0.000 0.000 0.656
#> GSM213099 4 0.4964 0.604 0.000 0.032 0.244 0.724
#> GSM213101 1 0.3907 0.834 0.768 0.000 0.000 0.232
#> GSM213105 2 0.1767 0.907 0.012 0.944 0.044 0.000
#> GSM213109 4 0.4697 0.316 0.356 0.000 0.000 0.644
#> GSM213110 2 0.1443 0.916 0.008 0.960 0.004 0.028
#> GSM213113 4 0.1489 0.879 0.000 0.044 0.004 0.952
#> GSM213121 2 0.1174 0.931 0.012 0.968 0.020 0.000
#> GSM213123 4 0.1489 0.879 0.000 0.044 0.004 0.952
#> GSM213125 2 0.1396 0.926 0.004 0.960 0.032 0.004
#> GSM213073 3 0.1302 0.866 0.000 0.044 0.956 0.000
#> GSM213086 4 0.0188 0.916 0.004 0.000 0.000 0.996
#> GSM213098 4 0.0000 0.915 0.000 0.000 0.000 1.000
#> GSM213106 1 0.3907 0.834 0.768 0.000 0.000 0.232
#> GSM213124 2 0.0188 0.933 0.004 0.996 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.0000 0.871 1.000 0.000 0.000 0.000 0.000
#> GSM213082 5 0.1197 0.886 0.000 0.048 0.000 0.000 0.952
#> GSM213085 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000
#> GSM213088 1 0.1041 0.865 0.964 0.000 0.000 0.004 0.032
#> GSM213091 4 0.0510 0.946 0.000 0.000 0.000 0.984 0.016
#> GSM213092 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000
#> GSM213096 1 0.0404 0.868 0.988 0.000 0.000 0.012 0.000
#> GSM213100 1 0.0000 0.871 1.000 0.000 0.000 0.000 0.000
#> GSM213111 5 0.1197 0.886 0.000 0.048 0.000 0.000 0.952
#> GSM213117 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000
#> GSM213118 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000
#> GSM213120 4 0.4151 0.440 0.000 0.344 0.000 0.652 0.004
#> GSM213122 2 0.0000 0.915 0.000 1.000 0.000 0.000 0.000
#> GSM213074 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000
#> GSM213077 1 0.0000 0.871 1.000 0.000 0.000 0.000 0.000
#> GSM213083 1 0.0000 0.871 1.000 0.000 0.000 0.000 0.000
#> GSM213094 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM213095 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM213102 1 0.1041 0.865 0.964 0.000 0.000 0.004 0.032
#> GSM213103 2 0.0000 0.915 0.000 1.000 0.000 0.000 0.000
#> GSM213104 2 0.2471 0.768 0.136 0.864 0.000 0.000 0.000
#> GSM213107 2 0.0162 0.914 0.000 0.996 0.000 0.000 0.004
#> GSM213108 5 0.4697 0.520 0.000 0.032 0.320 0.000 0.648
#> GSM213112 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000
#> GSM213114 1 0.0000 0.871 1.000 0.000 0.000 0.000 0.000
#> GSM213115 2 0.0000 0.915 0.000 1.000 0.000 0.000 0.000
#> GSM213116 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000
#> GSM213119 2 0.0162 0.915 0.000 0.996 0.000 0.000 0.004
#> GSM213072 4 0.0510 0.946 0.000 0.000 0.000 0.984 0.016
#> GSM213075 2 0.6202 0.136 0.372 0.484 0.000 0.144 0.000
#> GSM213076 2 0.0880 0.896 0.000 0.968 0.000 0.000 0.032
#> GSM213079 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM213080 1 0.3177 0.679 0.792 0.208 0.000 0.000 0.000
#> GSM213081 1 0.0000 0.871 1.000 0.000 0.000 0.000 0.000
#> GSM213084 1 0.0000 0.871 1.000 0.000 0.000 0.000 0.000
#> GSM213087 2 0.0162 0.915 0.000 0.996 0.000 0.000 0.004
#> GSM213089 4 0.0162 0.948 0.000 0.000 0.000 0.996 0.004
#> GSM213090 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM213093 4 0.1478 0.882 0.064 0.000 0.000 0.936 0.000
#> GSM213097 1 0.3837 0.555 0.692 0.000 0.000 0.308 0.000
#> GSM213099 4 0.3562 0.727 0.000 0.000 0.196 0.788 0.016
#> GSM213101 1 0.0880 0.865 0.968 0.000 0.000 0.000 0.032
#> GSM213105 2 0.0162 0.915 0.000 0.996 0.000 0.000 0.004
#> GSM213109 1 0.4283 0.239 0.544 0.000 0.000 0.456 0.000
#> GSM213110 1 0.4287 0.114 0.540 0.460 0.000 0.000 0.000
#> GSM213113 4 0.0510 0.946 0.000 0.000 0.000 0.984 0.016
#> GSM213121 2 0.0162 0.914 0.000 0.996 0.000 0.000 0.004
#> GSM213123 4 0.0510 0.946 0.000 0.000 0.000 0.984 0.016
#> GSM213125 5 0.1197 0.886 0.000 0.048 0.000 0.000 0.952
#> GSM213073 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM213086 4 0.0000 0.949 0.000 0.000 0.000 1.000 0.000
#> GSM213098 4 0.0510 0.946 0.000 0.000 0.000 0.984 0.016
#> GSM213106 1 0.1041 0.865 0.964 0.000 0.000 0.004 0.032
#> GSM213124 2 0.0703 0.895 0.000 0.976 0.000 0.024 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.0000 0.8498 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213082 6 0.0972 0.8629 0.000 0.008 0.000 0.028 0.000 0.964
#> GSM213085 4 0.3652 0.4407 0.004 0.000 0.000 0.672 0.324 0.000
#> GSM213088 1 0.2664 0.8091 0.816 0.000 0.000 0.000 0.184 0.000
#> GSM213091 4 0.0146 0.4937 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM213092 4 0.3515 0.4405 0.000 0.000 0.000 0.676 0.324 0.000
#> GSM213096 1 0.4743 0.6404 0.680 0.008 0.000 0.088 0.224 0.000
#> GSM213100 1 0.2178 0.8194 0.868 0.000 0.000 0.000 0.132 0.000
#> GSM213111 6 0.0972 0.8629 0.000 0.008 0.000 0.028 0.000 0.964
#> GSM213117 4 0.3996 -0.3369 0.004 0.000 0.000 0.512 0.484 0.000
#> GSM213118 4 0.3652 0.4407 0.004 0.000 0.000 0.672 0.324 0.000
#> GSM213120 2 0.4188 0.6272 0.000 0.712 0.000 0.236 0.004 0.048
#> GSM213122 2 0.0632 0.9096 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM213074 4 0.3652 0.4407 0.004 0.000 0.000 0.672 0.324 0.000
#> GSM213077 1 0.2178 0.8194 0.868 0.000 0.000 0.000 0.132 0.000
#> GSM213083 1 0.0000 0.8498 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213094 3 0.0146 0.9910 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM213095 3 0.0547 0.9757 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM213102 1 0.3563 0.7649 0.664 0.000 0.000 0.000 0.336 0.000
#> GSM213103 2 0.0146 0.9105 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM213104 2 0.0291 0.9102 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM213107 2 0.3009 0.8544 0.000 0.844 0.000 0.004 0.112 0.040
#> GSM213108 6 0.4486 0.3671 0.000 0.004 0.384 0.028 0.000 0.584
#> GSM213112 4 0.3652 0.4407 0.004 0.000 0.000 0.672 0.324 0.000
#> GSM213114 1 0.0146 0.8484 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM213115 2 0.1141 0.9063 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM213116 4 0.3797 0.0606 0.000 0.000 0.000 0.580 0.420 0.000
#> GSM213119 2 0.1984 0.8968 0.000 0.912 0.000 0.000 0.056 0.032
#> GSM213072 4 0.0547 0.4853 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM213075 2 0.0260 0.9101 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM213076 2 0.1644 0.8910 0.000 0.932 0.000 0.012 0.004 0.052
#> GSM213079 3 0.0000 0.9913 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM213080 1 0.3615 0.5734 0.700 0.292 0.000 0.000 0.008 0.000
#> GSM213081 1 0.0000 0.8498 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213084 1 0.0000 0.8498 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM213087 2 0.3094 0.8453 0.000 0.824 0.000 0.000 0.140 0.036
#> GSM213089 4 0.3733 0.4463 0.000 0.008 0.000 0.700 0.288 0.004
#> GSM213090 3 0.0000 0.9913 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM213093 5 0.4123 0.6153 0.012 0.000 0.000 0.420 0.568 0.000
#> GSM213097 5 0.5173 0.8040 0.108 0.000 0.000 0.324 0.568 0.000
#> GSM213099 4 0.3278 0.2863 0.000 0.000 0.152 0.808 0.000 0.040
#> GSM213101 1 0.2664 0.8091 0.816 0.000 0.000 0.000 0.184 0.000
#> GSM213105 2 0.3094 0.8453 0.000 0.824 0.000 0.000 0.140 0.036
#> GSM213109 5 0.5065 0.8218 0.092 0.000 0.000 0.340 0.568 0.000
#> GSM213110 2 0.0622 0.9085 0.012 0.980 0.000 0.000 0.008 0.000
#> GSM213113 4 0.1152 0.4715 0.004 0.000 0.000 0.952 0.000 0.044
#> GSM213121 2 0.3009 0.8544 0.000 0.844 0.000 0.004 0.112 0.040
#> GSM213123 4 0.1007 0.4719 0.000 0.000 0.000 0.956 0.000 0.044
#> GSM213125 6 0.0972 0.8629 0.000 0.008 0.000 0.028 0.000 0.964
#> GSM213073 3 0.0146 0.9910 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM213086 4 0.3515 0.4405 0.000 0.000 0.000 0.676 0.324 0.000
#> GSM213098 4 0.0291 0.4934 0.004 0.000 0.000 0.992 0.000 0.004
#> GSM213106 1 0.3371 0.7852 0.708 0.000 0.000 0.000 0.292 0.000
#> GSM213124 2 0.1155 0.9000 0.000 0.956 0.000 0.036 0.004 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
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 development.stage(p) disease.state(p) k
#> ATC:mclust 54 1.000 0.729 2
#> ATC:mclust 46 0.603 0.853 3
#> ATC:mclust 50 0.734 0.692 4
#> ATC:mclust 50 0.867 0.593 5
#> ATC:mclust 38 0.376 0.299 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "NMF"]
# you can also extract it by
# res = res_list["ATC:NMF"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.922 0.899 0.964 0.2744 0.743 0.743
#> 3 3 0.965 0.948 0.981 0.9881 0.662 0.562
#> 4 4 0.751 0.837 0.915 0.1304 0.940 0.870
#> 5 5 0.647 0.717 0.849 0.1645 0.829 0.602
#> 6 6 0.593 0.611 0.788 0.0481 0.944 0.820
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
#> GSM213078 1 0.000 0.9668 1.000 0.000
#> GSM213082 2 0.689 0.7476 0.184 0.816
#> GSM213085 1 0.000 0.9668 1.000 0.000
#> GSM213088 1 0.000 0.9668 1.000 0.000
#> GSM213091 1 0.000 0.9668 1.000 0.000
#> GSM213092 1 0.000 0.9668 1.000 0.000
#> GSM213096 1 0.000 0.9668 1.000 0.000
#> GSM213100 1 0.000 0.9668 1.000 0.000
#> GSM213111 1 0.995 0.0502 0.540 0.460
#> GSM213117 1 0.000 0.9668 1.000 0.000
#> GSM213118 1 0.000 0.9668 1.000 0.000
#> GSM213120 1 0.000 0.9668 1.000 0.000
#> GSM213122 1 0.000 0.9668 1.000 0.000
#> GSM213074 1 0.000 0.9668 1.000 0.000
#> GSM213077 1 0.000 0.9668 1.000 0.000
#> GSM213083 1 0.000 0.9668 1.000 0.000
#> GSM213094 2 0.000 0.9075 0.000 1.000
#> GSM213095 2 0.000 0.9075 0.000 1.000
#> GSM213102 1 0.000 0.9668 1.000 0.000
#> GSM213103 1 0.000 0.9668 1.000 0.000
#> GSM213104 1 0.000 0.9668 1.000 0.000
#> GSM213107 1 0.978 0.2248 0.588 0.412
#> GSM213108 2 0.000 0.9075 0.000 1.000
#> GSM213112 1 0.000 0.9668 1.000 0.000
#> GSM213114 1 0.000 0.9668 1.000 0.000
#> GSM213115 1 0.000 0.9668 1.000 0.000
#> GSM213116 1 0.000 0.9668 1.000 0.000
#> GSM213119 1 0.000 0.9668 1.000 0.000
#> GSM213072 1 0.000 0.9668 1.000 0.000
#> GSM213075 1 0.000 0.9668 1.000 0.000
#> GSM213076 1 0.295 0.9149 0.948 0.052
#> GSM213079 2 0.000 0.9075 0.000 1.000
#> GSM213080 1 0.000 0.9668 1.000 0.000
#> GSM213081 1 0.000 0.9668 1.000 0.000
#> GSM213084 1 0.000 0.9668 1.000 0.000
#> GSM213087 1 0.000 0.9668 1.000 0.000
#> GSM213089 1 0.000 0.9668 1.000 0.000
#> GSM213090 2 0.000 0.9075 0.000 1.000
#> GSM213093 1 0.000 0.9668 1.000 0.000
#> GSM213097 1 0.000 0.9668 1.000 0.000
#> GSM213099 1 0.949 0.3714 0.632 0.368
#> GSM213101 1 0.000 0.9668 1.000 0.000
#> GSM213105 1 0.000 0.9668 1.000 0.000
#> GSM213109 1 0.000 0.9668 1.000 0.000
#> GSM213110 1 0.000 0.9668 1.000 0.000
#> GSM213113 1 0.000 0.9668 1.000 0.000
#> GSM213121 1 0.327 0.9063 0.940 0.060
#> GSM213123 1 0.000 0.9668 1.000 0.000
#> GSM213125 2 0.983 0.2631 0.424 0.576
#> GSM213073 2 0.000 0.9075 0.000 1.000
#> GSM213086 1 0.000 0.9668 1.000 0.000
#> GSM213098 1 0.000 0.9668 1.000 0.000
#> GSM213106 1 0.000 0.9668 1.000 0.000
#> GSM213124 1 0.000 0.9668 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM213078 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213082 2 0.0000 0.961 0.000 1.000 0.000
#> GSM213085 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213088 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213091 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213092 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213096 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213100 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213111 2 0.0000 0.961 0.000 1.000 0.000
#> GSM213117 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213118 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213120 2 0.0000 0.961 0.000 1.000 0.000
#> GSM213122 2 0.0000 0.961 0.000 1.000 0.000
#> GSM213074 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213077 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213083 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213094 3 0.0000 0.997 0.000 0.000 1.000
#> GSM213095 3 0.0592 0.988 0.000 0.012 0.988
#> GSM213102 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213103 2 0.0000 0.961 0.000 1.000 0.000
#> GSM213104 2 0.6026 0.358 0.376 0.624 0.000
#> GSM213107 2 0.0000 0.961 0.000 1.000 0.000
#> GSM213108 2 0.0000 0.961 0.000 1.000 0.000
#> GSM213112 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213114 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213115 2 0.0000 0.961 0.000 1.000 0.000
#> GSM213116 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213119 2 0.0000 0.961 0.000 1.000 0.000
#> GSM213072 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213075 1 0.3192 0.857 0.888 0.112 0.000
#> GSM213076 2 0.0000 0.961 0.000 1.000 0.000
#> GSM213079 3 0.0000 0.997 0.000 0.000 1.000
#> GSM213080 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213081 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213084 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213087 2 0.0000 0.961 0.000 1.000 0.000
#> GSM213089 1 0.0747 0.963 0.984 0.016 0.000
#> GSM213090 3 0.0000 0.997 0.000 0.000 1.000
#> GSM213093 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213097 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213099 1 0.5678 0.547 0.684 0.000 0.316
#> GSM213101 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213105 2 0.0000 0.961 0.000 1.000 0.000
#> GSM213109 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213110 1 0.4750 0.711 0.784 0.216 0.000
#> GSM213113 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213121 2 0.0000 0.961 0.000 1.000 0.000
#> GSM213123 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213125 2 0.0000 0.961 0.000 1.000 0.000
#> GSM213073 3 0.0000 0.997 0.000 0.000 1.000
#> GSM213086 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213098 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213106 1 0.0000 0.978 1.000 0.000 0.000
#> GSM213124 2 0.0000 0.961 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM213078 1 0.0921 0.901 0.972 0.000 0.000 0.028
#> GSM213082 2 0.2944 0.867 0.004 0.868 0.000 0.128
#> GSM213085 1 0.0188 0.908 0.996 0.000 0.000 0.004
#> GSM213088 1 0.0336 0.908 0.992 0.000 0.000 0.008
#> GSM213091 1 0.2589 0.851 0.884 0.000 0.000 0.116
#> GSM213092 1 0.0707 0.906 0.980 0.000 0.000 0.020
#> GSM213096 1 0.0817 0.903 0.976 0.000 0.000 0.024
#> GSM213100 1 0.1022 0.899 0.968 0.000 0.000 0.032
#> GSM213111 2 0.1716 0.899 0.000 0.936 0.000 0.064
#> GSM213117 1 0.1867 0.883 0.928 0.000 0.000 0.072
#> GSM213118 1 0.1637 0.889 0.940 0.000 0.000 0.060
#> GSM213120 2 0.3052 0.861 0.004 0.860 0.000 0.136
#> GSM213122 2 0.0000 0.916 0.000 1.000 0.000 0.000
#> GSM213074 1 0.0592 0.907 0.984 0.000 0.000 0.016
#> GSM213077 1 0.1022 0.899 0.968 0.000 0.000 0.032
#> GSM213083 1 0.1022 0.899 0.968 0.000 0.000 0.032
#> GSM213094 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM213095 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM213102 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM213103 2 0.4543 0.573 0.000 0.676 0.000 0.324
#> GSM213104 4 0.4426 0.478 0.096 0.092 0.000 0.812
#> GSM213107 2 0.2921 0.827 0.000 0.860 0.000 0.140
#> GSM213108 2 0.3280 0.863 0.000 0.860 0.016 0.124
#> GSM213112 1 0.0336 0.908 0.992 0.000 0.000 0.008
#> GSM213114 1 0.2530 0.820 0.888 0.000 0.000 0.112
#> GSM213115 2 0.0469 0.916 0.000 0.988 0.000 0.012
#> GSM213116 1 0.1389 0.895 0.952 0.000 0.000 0.048
#> GSM213119 2 0.0592 0.914 0.000 0.984 0.000 0.016
#> GSM213072 1 0.2760 0.841 0.872 0.000 0.000 0.128
#> GSM213075 1 0.5565 0.157 0.624 0.032 0.000 0.344
#> GSM213076 2 0.0469 0.916 0.000 0.988 0.000 0.012
#> GSM213079 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM213080 4 0.4746 0.586 0.368 0.000 0.000 0.632
#> GSM213081 1 0.1557 0.882 0.944 0.000 0.000 0.056
#> GSM213084 1 0.1022 0.899 0.968 0.000 0.000 0.032
#> GSM213087 2 0.0469 0.915 0.000 0.988 0.000 0.012
#> GSM213089 1 0.2805 0.855 0.888 0.012 0.000 0.100
#> GSM213090 4 0.3870 0.209 0.000 0.004 0.208 0.788
#> GSM213093 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM213097 1 0.0469 0.907 0.988 0.000 0.000 0.012
#> GSM213099 1 0.5483 0.676 0.736 0.000 0.136 0.128
#> GSM213101 1 0.0469 0.907 0.988 0.000 0.000 0.012
#> GSM213105 2 0.0188 0.916 0.000 0.996 0.000 0.004
#> GSM213109 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM213110 4 0.6024 0.509 0.416 0.044 0.000 0.540
#> GSM213113 1 0.4511 0.739 0.784 0.040 0.000 0.176
#> GSM213121 2 0.0817 0.911 0.000 0.976 0.000 0.024
#> GSM213123 1 0.4035 0.766 0.804 0.020 0.000 0.176
#> GSM213125 2 0.2760 0.869 0.000 0.872 0.000 0.128
#> GSM213073 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM213086 1 0.0817 0.905 0.976 0.000 0.000 0.024
#> GSM213098 1 0.3266 0.800 0.832 0.000 0.000 0.168
#> GSM213106 1 0.0188 0.908 0.996 0.000 0.000 0.004
#> GSM213124 2 0.0336 0.915 0.000 0.992 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM213078 1 0.0404 0.8519 0.988 0.000 0.000 0.012 0.000
#> GSM213082 2 0.2448 0.8197 0.000 0.892 0.000 0.088 0.020
#> GSM213085 1 0.0955 0.8579 0.968 0.000 0.000 0.028 0.004
#> GSM213088 1 0.1251 0.8565 0.956 0.000 0.000 0.036 0.008
#> GSM213091 4 0.2561 0.8367 0.144 0.000 0.000 0.856 0.000
#> GSM213092 1 0.1704 0.8445 0.928 0.000 0.000 0.068 0.004
#> GSM213096 1 0.0703 0.8585 0.976 0.000 0.000 0.024 0.000
#> GSM213100 1 0.0579 0.8568 0.984 0.000 0.000 0.008 0.008
#> GSM213111 2 0.1485 0.8436 0.000 0.948 0.000 0.032 0.020
#> GSM213117 4 0.3734 0.7997 0.240 0.004 0.000 0.752 0.004
#> GSM213118 1 0.4403 0.3351 0.608 0.000 0.000 0.384 0.008
#> GSM213120 2 0.4747 0.1447 0.000 0.500 0.000 0.484 0.016
#> GSM213122 2 0.0324 0.8525 0.000 0.992 0.000 0.004 0.004
#> GSM213074 4 0.3398 0.8168 0.216 0.000 0.000 0.780 0.004
#> GSM213077 1 0.0451 0.8574 0.988 0.000 0.000 0.008 0.004
#> GSM213083 1 0.0693 0.8554 0.980 0.000 0.000 0.012 0.008
#> GSM213094 4 0.4354 0.2597 0.000 0.000 0.368 0.624 0.008
#> GSM213095 3 0.1560 0.9297 0.000 0.020 0.948 0.028 0.004
#> GSM213102 1 0.0963 0.8572 0.964 0.000 0.000 0.036 0.000
#> GSM213103 2 0.4323 0.5018 0.012 0.656 0.000 0.000 0.332
#> GSM213104 5 0.4846 0.4519 0.084 0.108 0.000 0.040 0.768
#> GSM213107 2 0.3099 0.7740 0.000 0.848 0.000 0.028 0.124
#> GSM213108 2 0.4338 0.7214 0.000 0.764 0.028 0.188 0.020
#> GSM213112 1 0.1557 0.8513 0.940 0.000 0.000 0.052 0.008
#> GSM213114 1 0.1106 0.8433 0.964 0.000 0.000 0.012 0.024
#> GSM213115 2 0.0609 0.8502 0.000 0.980 0.000 0.000 0.020
#> GSM213116 1 0.4383 0.1935 0.572 0.000 0.000 0.424 0.004
#> GSM213119 2 0.0566 0.8523 0.000 0.984 0.000 0.004 0.012
#> GSM213072 4 0.2886 0.8361 0.148 0.000 0.008 0.844 0.000
#> GSM213075 5 0.6055 0.3773 0.056 0.068 0.000 0.240 0.636
#> GSM213076 2 0.1282 0.8422 0.000 0.952 0.000 0.004 0.044
#> GSM213079 3 0.0000 0.9461 0.000 0.000 1.000 0.000 0.000
#> GSM213080 1 0.4962 -0.0496 0.544 0.016 0.000 0.008 0.432
#> GSM213081 1 0.3578 0.7547 0.820 0.000 0.000 0.048 0.132
#> GSM213084 1 0.0290 0.8551 0.992 0.000 0.000 0.000 0.008
#> GSM213087 2 0.0290 0.8518 0.000 0.992 0.000 0.000 0.008
#> GSM213089 4 0.3445 0.8200 0.140 0.036 0.000 0.824 0.000
#> GSM213090 5 0.4973 -0.1206 0.004 0.000 0.376 0.028 0.592
#> GSM213093 1 0.3123 0.7642 0.828 0.000 0.000 0.160 0.012
#> GSM213097 1 0.3461 0.6832 0.772 0.000 0.000 0.224 0.004
#> GSM213099 4 0.3401 0.7858 0.096 0.000 0.064 0.840 0.000
#> GSM213101 1 0.0566 0.8542 0.984 0.000 0.000 0.012 0.004
#> GSM213105 2 0.0798 0.8508 0.000 0.976 0.000 0.016 0.008
#> GSM213109 1 0.0880 0.8579 0.968 0.000 0.000 0.032 0.000
#> GSM213110 5 0.5995 0.3382 0.384 0.056 0.000 0.028 0.532
#> GSM213113 1 0.4985 0.5028 0.660 0.024 0.000 0.296 0.020
#> GSM213121 2 0.1740 0.8319 0.000 0.932 0.000 0.012 0.056
#> GSM213123 4 0.4141 0.8006 0.196 0.016 0.000 0.768 0.020
#> GSM213125 2 0.1943 0.8357 0.000 0.924 0.000 0.056 0.020
#> GSM213073 3 0.1444 0.9386 0.000 0.000 0.948 0.040 0.012
#> GSM213086 1 0.1544 0.8462 0.932 0.000 0.000 0.068 0.000
#> GSM213098 4 0.4096 0.7635 0.260 0.004 0.000 0.724 0.012
#> GSM213106 1 0.0703 0.8592 0.976 0.000 0.000 0.024 0.000
#> GSM213124 2 0.3916 0.7031 0.012 0.772 0.000 0.204 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM213078 1 0.0260 0.8052 0.992 0.000 0.000 0.000 0.000 NA
#> GSM213082 2 0.4237 0.6236 0.000 0.736 0.000 0.144 0.000 NA
#> GSM213085 1 0.2454 0.7893 0.876 0.004 0.000 0.016 0.000 NA
#> GSM213088 1 0.1690 0.8029 0.940 0.004 0.000 0.020 0.016 NA
#> GSM213091 4 0.1297 0.7285 0.040 0.000 0.000 0.948 0.000 NA
#> GSM213092 1 0.4177 0.6967 0.712 0.004 0.000 0.028 0.008 NA
#> GSM213096 1 0.1377 0.8077 0.952 0.004 0.000 0.016 0.004 NA
#> GSM213100 1 0.1053 0.8043 0.964 0.004 0.000 0.000 0.012 NA
#> GSM213111 2 0.2679 0.7060 0.000 0.864 0.000 0.040 0.000 NA
#> GSM213117 4 0.4635 0.6828 0.136 0.020 0.000 0.728 0.000 NA
#> GSM213118 1 0.5390 0.1787 0.500 0.004 0.000 0.396 0.000 NA
#> GSM213120 4 0.4955 0.4308 0.004 0.284 0.000 0.624 0.000 NA
#> GSM213122 2 0.0000 0.7272 0.000 1.000 0.000 0.000 0.000 NA
#> GSM213074 4 0.2362 0.7211 0.080 0.000 0.000 0.892 0.012 NA
#> GSM213077 1 0.0436 0.8062 0.988 0.000 0.000 0.004 0.004 NA
#> GSM213083 1 0.0862 0.8031 0.972 0.000 0.000 0.004 0.016 NA
#> GSM213094 4 0.4575 0.4616 0.000 0.000 0.196 0.720 0.032 NA
#> GSM213095 3 0.4691 0.5775 0.000 0.088 0.744 0.000 0.112 NA
#> GSM213102 1 0.1552 0.8059 0.940 0.004 0.000 0.020 0.000 NA
#> GSM213103 2 0.6978 0.1237 0.136 0.456 0.000 0.008 0.308 NA
#> GSM213104 5 0.4386 0.3687 0.108 0.112 0.012 0.000 0.760 NA
#> GSM213107 2 0.4583 0.4295 0.000 0.616 0.016 0.000 0.344 NA
#> GSM213108 2 0.5704 0.4831 0.000 0.592 0.036 0.264 0.000 NA
#> GSM213112 1 0.3627 0.7632 0.808 0.000 0.000 0.028 0.032 NA
#> GSM213114 1 0.0891 0.8041 0.968 0.000 0.000 0.000 0.024 NA
#> GSM213115 2 0.2849 0.6905 0.084 0.864 0.000 0.000 0.044 NA
#> GSM213116 1 0.5063 0.1297 0.500 0.004 0.000 0.432 0.000 NA
#> GSM213119 2 0.2051 0.7200 0.040 0.916 0.000 0.000 0.036 NA
#> GSM213072 4 0.1492 0.7267 0.036 0.000 0.000 0.940 0.000 NA
#> GSM213075 5 0.6852 0.3691 0.056 0.064 0.000 0.292 0.516 NA
#> GSM213076 2 0.4538 0.5651 0.000 0.696 0.000 0.060 0.232 NA
#> GSM213079 3 0.0725 0.7021 0.000 0.000 0.976 0.012 0.000 NA
#> GSM213080 1 0.5032 0.4198 0.648 0.028 0.000 0.000 0.264 NA
#> GSM213081 1 0.3925 0.7107 0.804 0.004 0.000 0.048 0.108 NA
#> GSM213084 1 0.0291 0.8056 0.992 0.000 0.000 0.000 0.004 NA
#> GSM213087 2 0.1251 0.7268 0.012 0.956 0.000 0.000 0.024 NA
#> GSM213089 4 0.2465 0.7218 0.024 0.024 0.000 0.900 0.004 NA
#> GSM213090 5 0.5661 -0.0601 0.000 0.004 0.320 0.004 0.536 NA
#> GSM213093 1 0.4650 0.6306 0.688 0.000 0.000 0.212 0.004 NA
#> GSM213097 1 0.4792 0.5508 0.644 0.000 0.000 0.260 0.000 NA
#> GSM213099 4 0.1994 0.7087 0.024 0.000 0.016 0.928 0.016 NA
#> GSM213101 1 0.0964 0.8021 0.968 0.004 0.000 0.000 0.012 NA
#> GSM213105 2 0.0964 0.7299 0.012 0.968 0.000 0.000 0.004 NA
#> GSM213109 1 0.2636 0.7841 0.860 0.004 0.000 0.016 0.000 NA
#> GSM213110 1 0.6653 0.1171 0.520 0.088 0.000 0.000 0.208 NA
#> GSM213113 4 0.6543 0.2170 0.336 0.024 0.000 0.384 0.000 NA
#> GSM213121 2 0.3680 0.5958 0.000 0.756 0.008 0.000 0.216 NA
#> GSM213123 4 0.4703 0.6820 0.088 0.020 0.000 0.712 0.000 NA
#> GSM213125 2 0.2979 0.6961 0.000 0.840 0.000 0.044 0.000 NA
#> GSM213073 3 0.3558 0.6345 0.000 0.000 0.736 0.016 0.000 NA
#> GSM213086 1 0.3966 0.7055 0.728 0.000 0.000 0.028 0.008 NA
#> GSM213098 4 0.4692 0.6679 0.152 0.008 0.000 0.716 0.004 NA
#> GSM213106 1 0.1442 0.8028 0.944 0.004 0.000 0.000 0.012 NA
#> GSM213124 2 0.6621 0.4898 0.136 0.604 0.000 0.140 0.048 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 development.stage(p) disease.state(p) k
#> ATC:NMF 50 1.000 0.481 2
#> ATC:NMF 53 0.666 0.402 3
#> ATC:NMF 51 0.464 0.276 4
#> ATC:NMF 45 0.730 0.606 5
#> ATC:NMF 40 0.727 0.444 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