Date: 2019-12-25 21:54:24 CET, cola version: 1.3.2
Document is loading...
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 | ||
|---|---|---|---|---|---|---|
| SD:skmeans | 2 | 1.000 | 0.958 | 0.983 | ** | |
| CV:skmeans | 2 | 1.000 | 0.951 | 0.980 | ** | |
| MAD:skmeans | 2 | 1.000 | 0.959 | 0.984 | ** | |
| ATC:skmeans | 3 | 1.000 | 0.953 | 0.982 | ** | 2 |
| ATC:mclust | 3 | 0.971 | 0.927 | 0.973 | ** | |
| SD:kmeans | 2 | 0.961 | 0.916 | 0.957 | ** | |
| MAD:kmeans | 2 | 0.961 | 0.919 | 0.962 | ** | |
| CV:NMF | 2 | 0.957 | 0.952 | 0.977 | ** | |
| CV:pam | 3 | 0.937 | 0.894 | 0.942 | * | 2 |
| CV:kmeans | 2 | 0.930 | 0.923 | 0.946 | * | |
| SD:NMF | 2 | 0.917 | 0.951 | 0.977 | * | |
| SD:pam | 6 | 0.912 | 0.850 | 0.936 | * | 4 |
| MAD:pam | 4 | 0.911 | 0.902 | 0.957 | * | |
| ATC:kmeans | 3 | 0.889 | 0.893 | 0.956 | ||
| ATC:NMF | 2 | 0.885 | 0.931 | 0.969 | ||
| MAD:NMF | 2 | 0.884 | 0.927 | 0.969 | ||
| SD:mclust | 4 | 0.853 | 0.851 | 0.928 | ||
| ATC:pam | 3 | 0.828 | 0.910 | 0.961 | ||
| CV:mclust | 4 | 0.820 | 0.836 | 0.926 | ||
| MAD:mclust | 4 | 0.570 | 0.698 | 0.832 | ||
| ATC:hclust | 2 | 0.439 | 0.700 | 0.864 | ||
| SD:hclust | 3 | 0.279 | 0.688 | 0.807 | ||
| MAD:hclust | 3 | 0.235 | 0.676 | 0.807 | ||
| CV:hclust | 3 | 0.216 | 0.614 | 0.774 |
**: 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 0.9169 0.951 0.977 0.497 0.502 0.502
#> CV:NMF 2 0.9569 0.952 0.977 0.495 0.502 0.502
#> MAD:NMF 2 0.8839 0.927 0.969 0.503 0.497 0.497
#> ATC:NMF 2 0.8855 0.931 0.969 0.477 0.516 0.516
#> SD:skmeans 2 1.0000 0.958 0.983 0.507 0.493 0.493
#> CV:skmeans 2 1.0000 0.951 0.980 0.507 0.493 0.493
#> MAD:skmeans 2 1.0000 0.959 0.984 0.509 0.491 0.491
#> ATC:skmeans 2 1.0000 0.989 0.995 0.509 0.491 0.491
#> SD:mclust 2 0.3487 0.215 0.780 0.304 0.860 0.860
#> CV:mclust 2 0.4675 0.857 0.869 0.344 0.591 0.591
#> MAD:mclust 2 0.3608 0.840 0.833 0.376 0.508 0.508
#> ATC:mclust 2 0.4934 0.000 0.824 0.295 1.000 1.000
#> SD:kmeans 2 0.9608 0.916 0.957 0.503 0.497 0.497
#> CV:kmeans 2 0.9302 0.923 0.946 0.500 0.502 0.502
#> MAD:kmeans 2 0.9608 0.919 0.962 0.507 0.493 0.493
#> ATC:kmeans 2 0.7264 0.888 0.955 0.458 0.535 0.535
#> SD:pam 2 0.8486 0.893 0.960 0.508 0.491 0.491
#> CV:pam 2 0.9208 0.899 0.962 0.508 0.493 0.493
#> MAD:pam 2 0.8494 0.903 0.960 0.506 0.491 0.491
#> ATC:pam 2 0.8259 0.878 0.940 0.461 0.525 0.525
#> SD:hclust 2 0.1124 0.530 0.757 0.393 0.560 0.560
#> CV:hclust 2 0.1702 0.670 0.768 0.390 0.591 0.591
#> MAD:hclust 2 0.0935 0.624 0.780 0.424 0.502 0.502
#> ATC:hclust 2 0.4392 0.700 0.864 0.453 0.493 0.493
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.435 0.591 0.788 0.344 0.756 0.544
#> CV:NMF 3 0.521 0.713 0.849 0.350 0.757 0.546
#> MAD:NMF 3 0.568 0.754 0.858 0.329 0.766 0.559
#> ATC:NMF 3 0.826 0.870 0.941 0.410 0.764 0.562
#> SD:skmeans 3 0.887 0.915 0.936 0.321 0.778 0.575
#> CV:skmeans 3 0.710 0.913 0.925 0.324 0.755 0.541
#> MAD:skmeans 3 0.878 0.893 0.936 0.315 0.747 0.529
#> ATC:skmeans 3 1.000 0.953 0.982 0.280 0.830 0.666
#> SD:mclust 3 0.155 0.413 0.656 0.750 0.635 0.584
#> CV:mclust 3 0.399 0.588 0.756 0.664 0.672 0.490
#> MAD:mclust 3 0.239 0.618 0.683 0.469 0.857 0.742
#> ATC:mclust 3 0.971 0.927 0.973 1.232 0.342 0.342
#> SD:kmeans 3 0.400 0.601 0.701 0.301 0.820 0.647
#> CV:kmeans 3 0.436 0.588 0.718 0.310 0.785 0.593
#> MAD:kmeans 3 0.467 0.426 0.624 0.291 0.829 0.675
#> ATC:kmeans 3 0.889 0.893 0.956 0.440 0.660 0.440
#> SD:pam 3 0.583 0.421 0.694 0.315 0.681 0.436
#> CV:pam 3 0.937 0.894 0.942 0.296 0.802 0.615
#> MAD:pam 3 0.472 0.512 0.789 0.309 0.737 0.513
#> ATC:pam 3 0.828 0.910 0.961 0.359 0.720 0.528
#> SD:hclust 3 0.279 0.688 0.807 0.458 0.706 0.542
#> CV:hclust 3 0.216 0.614 0.774 0.479 0.659 0.475
#> MAD:hclust 3 0.235 0.676 0.807 0.383 0.862 0.724
#> ATC:hclust 3 0.550 0.680 0.862 0.396 0.713 0.499
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.649 0.692 0.838 0.1349 0.798 0.474
#> CV:NMF 4 0.642 0.695 0.839 0.1354 0.853 0.588
#> MAD:NMF 4 0.539 0.568 0.764 0.1329 0.834 0.548
#> ATC:NMF 4 0.666 0.738 0.874 0.0816 0.936 0.806
#> SD:skmeans 4 0.863 0.894 0.934 0.1344 0.862 0.608
#> CV:skmeans 4 0.887 0.916 0.938 0.1330 0.853 0.587
#> MAD:skmeans 4 0.754 0.822 0.888 0.1348 0.846 0.572
#> ATC:skmeans 4 0.851 0.790 0.918 0.0989 0.932 0.809
#> SD:mclust 4 0.853 0.851 0.928 0.3837 0.670 0.417
#> CV:mclust 4 0.820 0.836 0.926 0.2631 0.841 0.606
#> MAD:mclust 4 0.570 0.698 0.832 0.3135 0.725 0.439
#> ATC:mclust 4 0.758 0.630 0.755 0.1113 0.823 0.532
#> SD:kmeans 4 0.623 0.789 0.830 0.1447 0.849 0.589
#> CV:kmeans 4 0.591 0.761 0.824 0.1410 0.808 0.502
#> MAD:kmeans 4 0.621 0.716 0.792 0.1429 0.771 0.463
#> ATC:kmeans 4 0.648 0.658 0.794 0.1238 0.855 0.597
#> SD:pam 4 0.921 0.855 0.940 0.1357 0.846 0.570
#> CV:pam 4 0.856 0.896 0.945 0.1364 0.875 0.650
#> MAD:pam 4 0.911 0.902 0.957 0.1473 0.751 0.389
#> ATC:pam 4 0.724 0.844 0.866 0.1669 0.869 0.656
#> SD:hclust 4 0.443 0.473 0.657 0.1577 0.771 0.518
#> CV:hclust 4 0.359 0.653 0.712 0.1712 0.886 0.705
#> MAD:hclust 4 0.370 0.498 0.664 0.1842 0.941 0.837
#> ATC:hclust 4 0.608 0.534 0.736 0.1305 0.913 0.764
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.591 0.550 0.755 0.0640 0.832 0.438
#> CV:NMF 5 0.604 0.644 0.764 0.0652 0.845 0.466
#> MAD:NMF 5 0.576 0.353 0.650 0.0638 0.850 0.519
#> ATC:NMF 5 0.627 0.612 0.799 0.0715 0.843 0.508
#> SD:skmeans 5 0.872 0.851 0.920 0.0650 0.899 0.615
#> CV:skmeans 5 0.785 0.792 0.882 0.0627 0.915 0.668
#> MAD:skmeans 5 0.856 0.835 0.916 0.0674 0.883 0.567
#> ATC:skmeans 5 0.773 0.687 0.845 0.0509 0.958 0.859
#> SD:mclust 5 0.703 0.781 0.844 0.0631 0.834 0.486
#> CV:mclust 5 0.670 0.557 0.764 0.0735 0.899 0.663
#> MAD:mclust 5 0.682 0.632 0.786 0.0879 0.865 0.540
#> ATC:mclust 5 0.789 0.832 0.914 0.0146 0.808 0.448
#> SD:kmeans 5 0.721 0.725 0.809 0.0685 0.904 0.636
#> CV:kmeans 5 0.675 0.659 0.767 0.0674 0.934 0.735
#> MAD:kmeans 5 0.733 0.752 0.831 0.0729 0.883 0.570
#> ATC:kmeans 5 0.667 0.592 0.777 0.0715 0.890 0.601
#> SD:pam 5 0.817 0.728 0.857 0.0593 0.935 0.745
#> CV:pam 5 0.813 0.833 0.874 0.0680 0.945 0.783
#> MAD:pam 5 0.821 0.790 0.896 0.0569 0.921 0.690
#> ATC:pam 5 0.744 0.805 0.885 0.0716 0.958 0.831
#> SD:hclust 5 0.510 0.527 0.706 0.1160 0.782 0.454
#> CV:hclust 5 0.452 0.459 0.657 0.0920 0.813 0.474
#> MAD:hclust 5 0.513 0.440 0.693 0.1056 0.766 0.400
#> ATC:hclust 5 0.604 0.620 0.749 0.0486 0.832 0.511
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.642 0.553 0.748 0.0369 0.866 0.453
#> CV:NMF 6 0.681 0.589 0.753 0.0374 0.902 0.557
#> MAD:NMF 6 0.660 0.536 0.736 0.0395 0.814 0.367
#> ATC:NMF 6 0.647 0.545 0.759 0.0437 0.929 0.695
#> SD:skmeans 6 0.789 0.630 0.808 0.0372 0.956 0.778
#> CV:skmeans 6 0.771 0.634 0.804 0.0386 0.969 0.841
#> MAD:skmeans 6 0.806 0.668 0.810 0.0372 0.953 0.761
#> ATC:skmeans 6 0.720 0.663 0.826 0.0382 0.959 0.849
#> SD:mclust 6 0.764 0.655 0.797 0.0457 0.971 0.861
#> CV:mclust 6 0.673 0.515 0.707 0.0449 0.899 0.605
#> MAD:mclust 6 0.750 0.658 0.822 0.0433 0.932 0.690
#> ATC:mclust 6 0.774 0.735 0.870 0.0727 0.902 0.667
#> SD:kmeans 6 0.727 0.621 0.752 0.0396 0.943 0.739
#> CV:kmeans 6 0.725 0.614 0.766 0.0419 0.936 0.699
#> MAD:kmeans 6 0.751 0.658 0.808 0.0408 0.966 0.825
#> ATC:kmeans 6 0.675 0.508 0.734 0.0396 0.925 0.677
#> SD:pam 6 0.912 0.850 0.936 0.0452 0.947 0.742
#> CV:pam 6 0.851 0.781 0.900 0.0472 0.948 0.745
#> MAD:pam 6 0.871 0.745 0.891 0.0468 0.899 0.552
#> ATC:pam 6 0.718 0.730 0.861 0.0220 0.989 0.946
#> SD:hclust 6 0.576 0.517 0.723 0.0595 0.797 0.412
#> CV:hclust 6 0.569 0.609 0.726 0.0765 0.922 0.685
#> MAD:hclust 6 0.588 0.468 0.632 0.0557 0.790 0.321
#> ATC:hclust 6 0.685 0.630 0.769 0.0549 0.962 0.835
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> SD:NMF 54 0.2071 0.826 1.07e-05 0.686 2
#> CV:NMF 54 0.2071 0.826 1.07e-05 0.686 2
#> MAD:NMF 52 0.2912 0.892 2.38e-06 0.803 2
#> ATC:NMF 53 0.5690 0.591 1.12e-03 0.617 2
#> SD:skmeans 53 0.5145 0.996 1.76e-08 0.446 2
#> CV:skmeans 52 0.4271 0.992 2.92e-08 0.493 2
#> MAD:skmeans 52 0.5924 0.992 2.84e-08 0.592 2
#> ATC:skmeans 54 0.6047 0.465 5.66e-02 0.856 2
#> SD:mclust 31 0.0113 0.335 3.18e-02 0.515 2
#> CV:mclust 52 0.9241 0.776 1.17e-04 1.000 2
#> MAD:mclust 52 0.1277 0.934 1.26e-06 0.610 2
#> ATC:mclust 0 NA NA NA NA 2
#> SD:kmeans 52 0.2912 0.979 1.31e-07 0.592 2
#> CV:kmeans 53 0.2457 0.968 3.22e-07 0.639 2
#> MAD:kmeans 52 0.5924 0.992 2.84e-08 0.592 2
#> ATC:kmeans 50 0.3483 0.344 3.92e-02 0.299 2
#> SD:pam 51 0.4676 0.634 1.26e-03 0.151 2
#> CV:pam 50 0.7394 0.578 1.85e-03 0.404 2
#> MAD:pam 52 0.3789 0.529 2.21e-03 0.183 2
#> ATC:pam 51 0.3408 0.728 8.77e-04 0.382 2
#> SD:hclust 39 0.3474 0.657 2.31e-04 1.000 2
#> CV:hclust 50 0.1689 0.957 6.51e-06 0.551 2
#> MAD:hclust 43 0.2744 0.520 4.54e-04 0.929 2
#> ATC:hclust 47 0.4727 0.410 2.84e-02 0.543 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> SD:NMF 42 1.11e-01 0.3641 4.12e-05 0.71220 3
#> CV:NMF 46 1.53e-01 0.4872 7.42e-06 0.70705 3
#> MAD:NMF 51 5.84e-02 0.3490 8.43e-06 0.65483 3
#> ATC:NMF 51 3.73e-01 0.4199 3.80e-04 0.10927 3
#> SD:skmeans 54 1.42e-01 0.8084 1.84e-07 0.47590 3
#> CV:skmeans 54 9.36e-02 0.8155 5.54e-07 0.39917 3
#> MAD:skmeans 51 2.02e-01 0.7105 6.43e-07 0.30021 3
#> ATC:skmeans 52 1.65e-01 0.5003 3.09e-03 0.04214 3
#> SD:mclust 34 1.29e-02 0.4791 1.92e-04 0.50207 3
#> CV:mclust 41 1.35e-01 0.3797 2.17e-05 0.49450 3
#> MAD:mclust 40 3.32e-05 0.4734 2.19e-06 0.07649 3
#> ATC:mclust 51 4.54e-01 0.4275 4.20e-03 0.16901 3
#> SD:kmeans 47 2.25e-01 0.5509 1.38e-06 0.36256 3
#> CV:kmeans 48 1.62e-01 0.6369 2.92e-06 0.67059 3
#> MAD:kmeans 28 1.67e-01 0.6397 3.09e-04 1.00000 3
#> ATC:kmeans 49 2.57e-01 0.3962 3.64e-03 0.17809 3
#> SD:pam 17 NA NA NA NA 3
#> CV:pam 52 4.35e-01 0.0936 1.18e-03 0.00941 3
#> MAD:pam 34 3.80e-02 0.3851 1.83e-04 0.24468 3
#> ATC:pam 53 2.29e-01 0.3835 5.52e-04 0.09660 3
#> SD:hclust 46 2.01e-04 0.2743 2.81e-03 0.14790 3
#> CV:hclust 45 1.04e-04 0.2603 9.45e-05 0.19017 3
#> MAD:hclust 50 2.06e-04 0.3780 2.62e-04 0.35781 3
#> ATC:hclust 42 1.51e-01 0.2602 3.13e-03 0.16388 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> SD:NMF 46 0.000552 0.3713 8.12e-05 0.0221 4
#> CV:NMF 48 0.004563 0.3205 2.80e-05 0.0937 4
#> MAD:NMF 36 0.000955 0.2071 9.66e-04 0.1239 4
#> ATC:NMF 46 0.154812 0.7067 9.82e-04 0.1208 4
#> SD:skmeans 52 0.000141 0.7098 1.49e-07 0.2016 4
#> CV:skmeans 54 0.000591 0.7511 2.60e-07 0.1678 4
#> MAD:skmeans 52 0.000141 0.7098 1.49e-07 0.2016 4
#> ATC:skmeans 46 0.025302 0.1798 2.30e-03 0.0240 4
#> SD:mclust 49 0.000201 0.3027 8.73e-05 0.1409 4
#> CV:mclust 50 0.001368 0.4592 1.77e-04 0.2552 4
#> MAD:mclust 46 0.000124 0.3518 3.43e-05 0.2156 4
#> ATC:mclust 44 0.094504 0.3769 9.75e-04 0.0356 4
#> SD:kmeans 52 0.000304 0.5982 2.38e-06 0.1479 4
#> CV:kmeans 52 0.000304 0.5982 2.38e-06 0.1479 4
#> MAD:kmeans 50 0.000587 0.6547 1.41e-06 0.1687 4
#> ATC:kmeans 48 0.194094 0.1898 3.17e-02 0.0715 4
#> SD:pam 47 0.104982 0.2781 5.48e-05 0.0368 4
#> CV:pam 53 0.468660 0.3829 3.69e-05 0.0302 4
#> MAD:pam 52 0.072421 0.2879 1.23e-04 0.0383 4
#> ATC:pam 53 0.051116 0.2469 1.13e-04 0.0137 4
#> SD:hclust 34 0.001140 0.6746 3.01e-05 0.1568 4
#> CV:hclust 46 0.000209 0.0218 3.30e-04 0.0198 4
#> MAD:hclust 31 0.001706 0.3980 9.86e-05 0.0531 4
#> ATC:hclust 37 0.143567 0.3661 1.53e-02 0.0888 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> SD:NMF 36 9.51e-03 0.3528 3.57e-03 0.36632 5
#> CV:NMF 45 1.16e-03 0.4018 1.25e-04 0.18451 5
#> MAD:NMF 23 2.65e-03 0.2685 7.78e-01 0.40697 5
#> ATC:NMF 37 6.00e-02 0.7074 2.24e-05 0.08693 5
#> SD:skmeans 51 3.95e-05 0.1910 7.61e-06 0.07089 5
#> CV:skmeans 49 9.02e-05 0.3295 7.61e-06 0.09783 5
#> MAD:skmeans 50 1.76e-05 0.1896 1.17e-05 0.05464 5
#> ATC:skmeans 43 4.05e-02 0.0715 1.65e-03 0.03452 5
#> SD:mclust 50 4.56e-05 0.4263 5.02e-05 0.23931 5
#> CV:mclust 29 3.98e-04 0.3123 6.51e-04 0.16276 5
#> MAD:mclust 41 9.93e-06 0.3335 2.00e-04 0.07270 5
#> ATC:mclust 51 2.02e-01 0.6311 2.23e-05 0.22670 5
#> SD:kmeans 46 6.53e-05 0.4170 3.05e-05 0.08302 5
#> CV:kmeans 45 2.08e-04 0.4103 2.88e-05 0.12558 5
#> MAD:kmeans 51 2.54e-04 0.2499 1.56e-05 0.18695 5
#> ATC:kmeans 40 4.04e-02 0.5451 1.60e-03 0.00976 5
#> SD:pam 44 7.85e-02 0.4106 8.10e-05 0.09554 5
#> CV:pam 52 1.67e-01 0.2525 1.73e-04 0.00216 5
#> MAD:pam 48 1.14e-02 0.3662 1.74e-04 0.01031 5
#> ATC:pam 50 1.44e-01 0.2386 2.51e-04 0.04781 5
#> SD:hclust 24 2.50e-05 0.0871 3.83e-02 0.13734 5
#> CV:hclust 27 4.04e-04 0.7112 1.79e-04 0.18535 5
#> MAD:hclust 17 5.43e-03 0.1350 6.50e-02 0.13567 5
#> ATC:hclust 38 7.94e-02 0.4254 2.21e-02 0.11562 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> SD:NMF 37 2.62e-03 0.5171 6.83e-04 6.83e-02 6
#> CV:NMF 42 5.27e-04 0.1871 2.06e-03 2.68e-02 6
#> MAD:NMF 37 2.06e-04 0.4434 3.29e-04 2.11e-01 6
#> ATC:NMF 35 1.06e-01 0.4374 1.74e-04 1.05e-01 6
#> SD:skmeans 41 4.67e-05 0.4206 2.29e-04 3.17e-02 6
#> CV:skmeans 41 7.20e-05 0.6225 9.13e-05 3.17e-02 6
#> MAD:skmeans 40 1.13e-05 0.3937 3.79e-04 1.85e-02 6
#> ATC:skmeans 43 1.20e-01 0.3257 3.44e-04 2.30e-02 6
#> SD:mclust 36 1.22e-04 0.5370 8.84e-04 1.60e-01 6
#> CV:mclust 34 1.16e-04 0.2505 6.43e-03 3.56e-02 6
#> MAD:mclust 43 3.84e-05 0.4787 1.90e-04 1.94e-02 6
#> ATC:mclust 49 3.88e-01 0.6404 4.37e-05 1.21e-01 6
#> SD:kmeans 46 3.48e-04 0.2419 1.06e-04 5.24e-02 6
#> CV:kmeans 42 2.81e-04 0.4343 1.69e-04 1.35e-03 6
#> MAD:kmeans 43 4.00e-04 0.5472 3.61e-04 2.86e-02 6
#> ATC:kmeans 35 1.01e-01 0.5023 8.11e-04 1.24e-02 6
#> SD:pam 49 3.77e-02 0.2642 1.94e-05 1.20e-02 6
#> CV:pam 47 4.25e-02 0.2707 3.60e-04 8.25e-05 6
#> MAD:pam 46 3.42e-02 0.3032 1.61e-05 2.04e-03 6
#> ATC:pam 48 7.44e-02 0.1650 3.25e-04 2.04e-02 6
#> SD:hclust 38 9.48e-05 0.0171 5.55e-04 1.60e-02 6
#> CV:hclust 43 7.70e-05 0.0664 4.69e-04 2.74e-02 6
#> MAD:hclust 29 4.47e-04 0.0180 1.89e-02 4.66e-02 6
#> ATC:hclust 39 1.28e-01 0.3463 3.99e-02 7.44e-02 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 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 0.112 0.530 0.757 0.3930 0.560 0.560
#> 3 3 0.279 0.688 0.807 0.4585 0.706 0.542
#> 4 4 0.443 0.473 0.657 0.1577 0.771 0.518
#> 5 5 0.510 0.527 0.706 0.1160 0.782 0.454
#> 6 6 0.576 0.517 0.723 0.0595 0.797 0.412
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
#> GSM680053 2 0.886 0.258 0.304 0.696
#> GSM680062 2 0.886 0.258 0.304 0.696
#> GSM680054 2 0.886 0.258 0.304 0.696
#> GSM680063 2 0.886 0.258 0.304 0.696
#> GSM680055 2 0.886 0.258 0.304 0.696
#> GSM680064 1 0.936 0.665 0.648 0.352
#> GSM680056 2 0.991 -0.233 0.444 0.556
#> GSM680065 2 0.991 -0.233 0.444 0.556
#> GSM680057 2 0.373 0.693 0.072 0.928
#> GSM680066 1 0.943 0.663 0.640 0.360
#> GSM680058 2 0.295 0.667 0.052 0.948
#> GSM680067 2 0.833 0.559 0.264 0.736
#> GSM680059 2 0.295 0.667 0.052 0.948
#> GSM680068 1 0.943 0.663 0.640 0.360
#> GSM680060 1 0.995 0.530 0.540 0.460
#> GSM680069 1 0.995 0.530 0.540 0.460
#> GSM680061 2 0.833 0.559 0.264 0.736
#> GSM680070 1 0.943 0.663 0.640 0.360
#> GSM680071 1 0.994 0.538 0.544 0.456
#> GSM680077 1 0.983 0.580 0.576 0.424
#> GSM680072 2 0.295 0.667 0.052 0.948
#> GSM680078 1 0.958 0.639 0.620 0.380
#> GSM680073 2 0.295 0.667 0.052 0.948
#> GSM680079 1 0.936 0.665 0.648 0.352
#> GSM680074 2 0.295 0.667 0.052 0.948
#> GSM680080 2 0.295 0.667 0.052 0.948
#> GSM680075 2 0.605 0.658 0.148 0.852
#> GSM680081 2 0.574 0.653 0.136 0.864
#> GSM680076 1 1.000 0.468 0.512 0.488
#> GSM680082 1 1.000 0.468 0.512 0.488
#> GSM680029 2 0.373 0.688 0.072 0.928
#> GSM680041 1 0.295 0.509 0.948 0.052
#> GSM680035 2 0.295 0.691 0.052 0.948
#> GSM680047 1 0.443 0.503 0.908 0.092
#> GSM680036 2 0.402 0.683 0.080 0.920
#> GSM680048 2 0.952 0.430 0.372 0.628
#> GSM680037 2 0.295 0.691 0.052 0.948
#> GSM680049 1 0.295 0.509 0.948 0.052
#> GSM680038 2 0.430 0.690 0.088 0.912
#> GSM680050 1 0.981 0.582 0.580 0.420
#> GSM680039 2 0.343 0.697 0.064 0.936
#> GSM680051 2 0.876 0.536 0.296 0.704
#> GSM680040 2 0.295 0.691 0.052 0.948
#> GSM680052 2 0.952 0.430 0.372 0.628
#> GSM680030 2 0.373 0.693 0.072 0.928
#> GSM680042 1 0.295 0.509 0.948 0.052
#> GSM680031 2 0.814 0.579 0.252 0.748
#> GSM680043 2 0.814 0.579 0.252 0.748
#> GSM680032 2 0.917 0.289 0.332 0.668
#> GSM680044 2 0.917 0.289 0.332 0.668
#> GSM680033 2 0.295 0.691 0.052 0.948
#> GSM680045 2 0.925 0.473 0.340 0.660
#> GSM680034 2 0.373 0.693 0.072 0.928
#> GSM680046 2 0.925 0.473 0.340 0.660
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 1 0.6291 0.395 0.532 0.468 0.000
#> GSM680062 1 0.6291 0.395 0.532 0.468 0.000
#> GSM680054 1 0.6291 0.395 0.532 0.468 0.000
#> GSM680063 1 0.6291 0.395 0.532 0.468 0.000
#> GSM680055 1 0.6291 0.395 0.532 0.468 0.000
#> GSM680064 1 0.4892 0.692 0.840 0.048 0.112
#> GSM680056 1 0.5147 0.716 0.800 0.180 0.020
#> GSM680065 1 0.5147 0.716 0.800 0.180 0.020
#> GSM680057 2 0.3472 0.797 0.040 0.904 0.056
#> GSM680066 1 0.5094 0.695 0.832 0.056 0.112
#> GSM680058 2 0.2096 0.779 0.052 0.944 0.004
#> GSM680067 2 0.6854 0.666 0.068 0.716 0.216
#> GSM680059 2 0.2096 0.779 0.052 0.944 0.004
#> GSM680068 1 0.5191 0.695 0.828 0.060 0.112
#> GSM680060 1 0.2772 0.705 0.916 0.080 0.004
#> GSM680069 1 0.2682 0.705 0.920 0.076 0.004
#> GSM680061 2 0.6854 0.666 0.068 0.716 0.216
#> GSM680070 1 0.5094 0.695 0.832 0.056 0.112
#> GSM680071 1 0.2590 0.703 0.924 0.072 0.004
#> GSM680077 1 0.0829 0.689 0.984 0.012 0.004
#> GSM680072 2 0.2096 0.779 0.052 0.944 0.004
#> GSM680078 1 0.5722 0.701 0.804 0.084 0.112
#> GSM680073 2 0.2096 0.779 0.052 0.944 0.004
#> GSM680079 1 0.4892 0.692 0.840 0.048 0.112
#> GSM680074 2 0.2096 0.779 0.052 0.944 0.004
#> GSM680080 2 0.2096 0.779 0.052 0.944 0.004
#> GSM680075 2 0.5623 0.506 0.280 0.716 0.004
#> GSM680081 2 0.5497 0.495 0.292 0.708 0.000
#> GSM680076 1 0.3193 0.695 0.896 0.100 0.004
#> GSM680082 1 0.3193 0.695 0.896 0.100 0.004
#> GSM680029 2 0.3030 0.770 0.092 0.904 0.004
#> GSM680041 3 0.0237 0.975 0.000 0.004 0.996
#> GSM680035 2 0.2537 0.777 0.080 0.920 0.000
#> GSM680047 3 0.2414 0.921 0.020 0.040 0.940
#> GSM680036 2 0.3425 0.751 0.112 0.884 0.004
#> GSM680048 2 0.7992 0.583 0.080 0.592 0.328
#> GSM680037 2 0.2537 0.777 0.080 0.920 0.000
#> GSM680049 3 0.0237 0.975 0.000 0.004 0.996
#> GSM680038 2 0.3888 0.797 0.064 0.888 0.048
#> GSM680050 1 0.1877 0.684 0.956 0.012 0.032
#> GSM680039 2 0.3112 0.793 0.056 0.916 0.028
#> GSM680051 2 0.7411 0.672 0.076 0.668 0.256
#> GSM680040 2 0.2448 0.779 0.076 0.924 0.000
#> GSM680052 2 0.7992 0.583 0.080 0.592 0.328
#> GSM680030 2 0.3797 0.795 0.052 0.892 0.056
#> GSM680042 3 0.0237 0.975 0.000 0.004 0.996
#> GSM680031 2 0.7047 0.711 0.084 0.712 0.204
#> GSM680043 2 0.7047 0.711 0.084 0.712 0.204
#> GSM680032 1 0.8056 0.384 0.532 0.400 0.068
#> GSM680044 1 0.8056 0.384 0.532 0.400 0.068
#> GSM680033 2 0.2448 0.779 0.076 0.924 0.000
#> GSM680045 2 0.8285 0.604 0.112 0.600 0.288
#> GSM680034 2 0.3472 0.797 0.040 0.904 0.056
#> GSM680046 2 0.8285 0.604 0.112 0.600 0.288
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 3 0.5994 0.3610 0.068 0.296 0.636 0.000
#> GSM680062 3 0.5994 0.3610 0.068 0.296 0.636 0.000
#> GSM680054 3 0.5994 0.3610 0.068 0.296 0.636 0.000
#> GSM680063 3 0.5994 0.3610 0.068 0.296 0.636 0.000
#> GSM680055 3 0.5994 0.3610 0.068 0.296 0.636 0.000
#> GSM680064 1 0.4244 0.6937 0.804 0.000 0.160 0.036
#> GSM680056 3 0.5175 -0.2227 0.328 0.012 0.656 0.004
#> GSM680065 3 0.5175 -0.2227 0.328 0.012 0.656 0.004
#> GSM680057 2 0.4012 0.6376 0.000 0.800 0.184 0.016
#> GSM680066 1 0.4613 0.6922 0.792 0.008 0.164 0.036
#> GSM680058 2 0.0524 0.6525 0.004 0.988 0.008 0.000
#> GSM680067 2 0.4831 0.3102 0.000 0.704 0.280 0.016
#> GSM680059 2 0.1109 0.6592 0.004 0.968 0.028 0.000
#> GSM680068 1 0.4739 0.6899 0.788 0.012 0.164 0.036
#> GSM680060 1 0.6044 0.5810 0.528 0.044 0.428 0.000
#> GSM680069 1 0.5971 0.5807 0.532 0.040 0.428 0.000
#> GSM680061 2 0.4831 0.3102 0.000 0.704 0.280 0.016
#> GSM680070 1 0.4613 0.6922 0.792 0.008 0.164 0.036
#> GSM680071 1 0.5964 0.5855 0.536 0.040 0.424 0.000
#> GSM680077 1 0.2281 0.6570 0.904 0.000 0.096 0.000
#> GSM680072 2 0.0524 0.6525 0.004 0.988 0.008 0.000
#> GSM680078 1 0.5036 0.6706 0.760 0.012 0.192 0.036
#> GSM680073 2 0.1305 0.6560 0.004 0.960 0.036 0.000
#> GSM680079 1 0.4244 0.6937 0.804 0.000 0.160 0.036
#> GSM680074 2 0.0524 0.6525 0.004 0.988 0.008 0.000
#> GSM680080 2 0.0524 0.6525 0.004 0.988 0.008 0.000
#> GSM680075 2 0.6396 0.2420 0.076 0.564 0.360 0.000
#> GSM680081 2 0.6451 0.2103 0.072 0.524 0.404 0.000
#> GSM680076 1 0.5756 0.5763 0.568 0.032 0.400 0.000
#> GSM680082 1 0.5756 0.5763 0.568 0.032 0.400 0.000
#> GSM680029 2 0.4690 0.5941 0.012 0.712 0.276 0.000
#> GSM680041 4 0.0000 0.9711 0.000 0.000 0.000 1.000
#> GSM680035 2 0.4222 0.5985 0.000 0.728 0.272 0.000
#> GSM680047 4 0.1824 0.9106 0.004 0.000 0.060 0.936
#> GSM680036 2 0.4844 0.5638 0.012 0.688 0.300 0.000
#> GSM680048 3 0.7280 0.0409 0.004 0.384 0.480 0.132
#> GSM680037 2 0.4222 0.5985 0.000 0.728 0.272 0.000
#> GSM680049 4 0.0000 0.9711 0.000 0.000 0.000 1.000
#> GSM680038 2 0.3925 0.6450 0.000 0.808 0.176 0.016
#> GSM680050 1 0.3182 0.6462 0.876 0.000 0.096 0.028
#> GSM680039 2 0.4485 0.6280 0.000 0.740 0.248 0.012
#> GSM680051 3 0.6561 -0.1094 0.004 0.460 0.472 0.064
#> GSM680040 2 0.4193 0.6018 0.000 0.732 0.268 0.000
#> GSM680052 3 0.7280 0.0409 0.004 0.384 0.480 0.132
#> GSM680030 2 0.4356 0.6290 0.004 0.780 0.200 0.016
#> GSM680042 4 0.0000 0.9711 0.000 0.000 0.000 1.000
#> GSM680031 3 0.5464 -0.1606 0.004 0.492 0.496 0.008
#> GSM680043 3 0.5464 -0.1606 0.004 0.492 0.496 0.008
#> GSM680032 3 0.7984 0.2653 0.264 0.232 0.488 0.016
#> GSM680044 3 0.7984 0.2653 0.264 0.232 0.488 0.016
#> GSM680033 2 0.4193 0.6018 0.000 0.732 0.268 0.000
#> GSM680045 3 0.7547 0.0514 0.056 0.392 0.492 0.060
#> GSM680034 2 0.4012 0.6376 0.000 0.800 0.184 0.016
#> GSM680046 3 0.7547 0.0514 0.056 0.392 0.492 0.060
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 3 0.6380 0.1927 0.136 0.324 0.528 0.012 0.000
#> GSM680062 3 0.6380 0.1927 0.136 0.324 0.528 0.012 0.000
#> GSM680054 3 0.6380 0.1927 0.136 0.324 0.528 0.012 0.000
#> GSM680063 3 0.6380 0.1927 0.136 0.324 0.528 0.012 0.000
#> GSM680055 3 0.6380 0.1927 0.136 0.324 0.528 0.012 0.000
#> GSM680064 1 0.0162 0.8453 0.996 0.000 0.004 0.000 0.000
#> GSM680056 2 0.6276 0.5122 0.176 0.584 0.228 0.012 0.000
#> GSM680065 2 0.6276 0.5122 0.176 0.584 0.228 0.012 0.000
#> GSM680057 3 0.4593 0.0924 0.000 0.004 0.512 0.480 0.004
#> GSM680066 1 0.0798 0.8479 0.976 0.008 0.016 0.000 0.000
#> GSM680058 3 0.4367 0.3901 0.004 0.000 0.580 0.416 0.000
#> GSM680067 4 0.2351 0.4819 0.000 0.016 0.088 0.896 0.000
#> GSM680059 3 0.3949 0.4181 0.004 0.000 0.696 0.300 0.000
#> GSM680068 1 0.0898 0.8461 0.972 0.008 0.020 0.000 0.000
#> GSM680060 2 0.2344 0.7562 0.064 0.904 0.000 0.032 0.000
#> GSM680069 2 0.2331 0.7580 0.064 0.908 0.004 0.024 0.000
#> GSM680061 4 0.2351 0.4819 0.000 0.016 0.088 0.896 0.000
#> GSM680070 1 0.0798 0.8479 0.976 0.008 0.016 0.000 0.000
#> GSM680071 2 0.2171 0.7573 0.064 0.912 0.000 0.024 0.000
#> GSM680077 1 0.4331 0.4506 0.596 0.400 0.000 0.004 0.000
#> GSM680072 3 0.4367 0.3901 0.004 0.000 0.580 0.416 0.000
#> GSM680078 1 0.1282 0.8218 0.952 0.004 0.044 0.000 0.000
#> GSM680073 3 0.4009 0.4187 0.004 0.000 0.684 0.312 0.000
#> GSM680079 1 0.0162 0.8453 0.996 0.000 0.004 0.000 0.000
#> GSM680074 3 0.4375 0.3881 0.004 0.000 0.576 0.420 0.000
#> GSM680080 3 0.4375 0.3881 0.004 0.000 0.576 0.420 0.000
#> GSM680075 3 0.5778 0.4528 0.068 0.164 0.692 0.076 0.000
#> GSM680081 3 0.4665 0.4310 0.056 0.168 0.756 0.020 0.000
#> GSM680076 2 0.1851 0.6921 0.000 0.912 0.000 0.088 0.000
#> GSM680082 2 0.1851 0.6921 0.000 0.912 0.000 0.088 0.000
#> GSM680029 3 0.1538 0.4792 0.008 0.008 0.948 0.036 0.000
#> GSM680041 5 0.0000 0.9701 0.000 0.000 0.000 0.000 1.000
#> GSM680035 3 0.0794 0.4586 0.000 0.000 0.972 0.028 0.000
#> GSM680047 5 0.1717 0.9083 0.008 0.000 0.052 0.004 0.936
#> GSM680036 3 0.2467 0.4914 0.016 0.024 0.908 0.052 0.000
#> GSM680048 4 0.6658 0.7504 0.008 0.016 0.336 0.516 0.124
#> GSM680037 3 0.0794 0.4586 0.000 0.000 0.972 0.028 0.000
#> GSM680049 5 0.0000 0.9701 0.000 0.000 0.000 0.000 1.000
#> GSM680038 3 0.4835 0.1627 0.004 0.008 0.528 0.456 0.004
#> GSM680050 1 0.5033 0.4283 0.568 0.400 0.000 0.004 0.028
#> GSM680039 3 0.3039 0.3635 0.000 0.000 0.808 0.192 0.000
#> GSM680051 4 0.5870 0.7060 0.008 0.016 0.372 0.556 0.048
#> GSM680040 3 0.0510 0.4648 0.000 0.000 0.984 0.016 0.000
#> GSM680052 4 0.6658 0.7504 0.008 0.016 0.336 0.516 0.124
#> GSM680030 3 0.4595 0.0954 0.000 0.004 0.504 0.488 0.004
#> GSM680042 5 0.0000 0.9701 0.000 0.000 0.000 0.000 1.000
#> GSM680031 4 0.4997 0.6980 0.008 0.016 0.468 0.508 0.000
#> GSM680043 4 0.4997 0.6980 0.008 0.016 0.468 0.508 0.000
#> GSM680032 3 0.7872 0.0474 0.328 0.192 0.400 0.076 0.004
#> GSM680044 3 0.7872 0.0474 0.328 0.192 0.400 0.076 0.004
#> GSM680033 3 0.0510 0.4648 0.000 0.000 0.984 0.016 0.000
#> GSM680045 4 0.6896 0.7502 0.084 0.016 0.340 0.520 0.040
#> GSM680034 3 0.4593 0.0924 0.000 0.004 0.512 0.480 0.004
#> GSM680046 4 0.6896 0.7502 0.084 0.016 0.340 0.520 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.6061 0.5386 0.072 0.064 0.388 0.000 0.476 0.000
#> GSM680062 5 0.6061 0.5386 0.072 0.064 0.388 0.000 0.476 0.000
#> GSM680054 5 0.6061 0.5386 0.072 0.064 0.388 0.000 0.476 0.000
#> GSM680063 5 0.6061 0.5386 0.072 0.064 0.388 0.000 0.476 0.000
#> GSM680055 5 0.6061 0.5386 0.072 0.064 0.388 0.000 0.476 0.000
#> GSM680064 1 0.0000 0.6862 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM680056 5 0.5950 0.5176 0.112 0.044 0.108 0.000 0.672 0.064
#> GSM680065 5 0.5950 0.5176 0.112 0.044 0.108 0.000 0.672 0.064
#> GSM680057 2 0.3881 0.3009 0.000 0.600 0.396 0.000 0.004 0.000
#> GSM680066 1 0.0696 0.6922 0.980 0.008 0.004 0.000 0.004 0.004
#> GSM680058 3 0.4344 0.5051 0.000 0.060 0.720 0.004 0.212 0.004
#> GSM680067 2 0.4576 0.4524 0.000 0.716 0.208 0.004 0.052 0.020
#> GSM680059 3 0.4186 0.5450 0.000 0.080 0.728 0.000 0.192 0.000
#> GSM680068 1 0.0810 0.6914 0.976 0.008 0.008 0.000 0.004 0.004
#> GSM680060 5 0.4420 0.0736 0.008 0.012 0.008 0.000 0.624 0.348
#> GSM680069 5 0.4223 0.0795 0.008 0.008 0.004 0.000 0.632 0.348
#> GSM680061 2 0.4576 0.4524 0.000 0.716 0.208 0.004 0.052 0.020
#> GSM680070 1 0.0696 0.6922 0.980 0.008 0.004 0.000 0.004 0.004
#> GSM680071 5 0.4236 0.0721 0.008 0.008 0.004 0.000 0.628 0.352
#> GSM680077 1 0.4975 0.2482 0.596 0.000 0.000 0.000 0.092 0.312
#> GSM680072 3 0.4344 0.5051 0.000 0.060 0.720 0.004 0.212 0.004
#> GSM680078 1 0.1312 0.6794 0.956 0.008 0.020 0.000 0.012 0.004
#> GSM680073 3 0.4008 0.5469 0.000 0.064 0.740 0.000 0.196 0.000
#> GSM680079 1 0.0000 0.6862 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM680074 3 0.4399 0.5044 0.000 0.064 0.716 0.004 0.212 0.004
#> GSM680080 3 0.4399 0.5044 0.000 0.064 0.716 0.004 0.212 0.004
#> GSM680075 3 0.6196 0.3050 0.048 0.064 0.556 0.000 0.304 0.028
#> GSM680081 3 0.6829 0.3041 0.048 0.184 0.536 0.000 0.200 0.032
#> GSM680076 6 0.0777 1.0000 0.000 0.000 0.004 0.000 0.024 0.972
#> GSM680082 6 0.0777 1.0000 0.000 0.000 0.004 0.000 0.024 0.972
#> GSM680029 3 0.4030 0.5592 0.000 0.172 0.748 0.000 0.080 0.000
#> GSM680041 4 0.0146 0.9652 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM680035 3 0.3468 0.5165 0.000 0.284 0.712 0.000 0.004 0.000
#> GSM680047 4 0.1644 0.8942 0.012 0.052 0.004 0.932 0.000 0.000
#> GSM680036 3 0.4371 0.5380 0.008 0.132 0.740 0.000 0.120 0.000
#> GSM680048 2 0.3702 0.6285 0.012 0.808 0.056 0.120 0.004 0.000
#> GSM680037 3 0.3468 0.5165 0.000 0.284 0.712 0.000 0.004 0.000
#> GSM680049 4 0.0146 0.9652 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM680038 2 0.4620 0.1873 0.000 0.532 0.428 0.000 0.040 0.000
#> GSM680050 1 0.5605 0.2205 0.568 0.000 0.000 0.028 0.092 0.312
#> GSM680039 3 0.3937 0.2292 0.000 0.424 0.572 0.000 0.004 0.000
#> GSM680051 2 0.3493 0.6313 0.012 0.828 0.108 0.044 0.008 0.000
#> GSM680040 3 0.3405 0.5286 0.000 0.272 0.724 0.000 0.004 0.000
#> GSM680052 2 0.3702 0.6285 0.012 0.808 0.056 0.120 0.004 0.000
#> GSM680030 2 0.4411 0.2740 0.000 0.576 0.400 0.000 0.012 0.012
#> GSM680042 4 0.0146 0.9652 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM680031 2 0.3053 0.5947 0.012 0.812 0.172 0.000 0.004 0.000
#> GSM680043 2 0.3053 0.5947 0.012 0.812 0.172 0.000 0.004 0.000
#> GSM680032 1 0.8424 0.0549 0.332 0.144 0.244 0.000 0.076 0.204
#> GSM680044 1 0.8424 0.0549 0.332 0.144 0.244 0.000 0.076 0.204
#> GSM680033 3 0.3405 0.5286 0.000 0.272 0.724 0.000 0.004 0.000
#> GSM680045 2 0.3871 0.6299 0.088 0.812 0.060 0.036 0.004 0.000
#> GSM680034 2 0.3881 0.3009 0.000 0.600 0.396 0.000 0.004 0.000
#> GSM680046 2 0.3871 0.6299 0.088 0.812 0.060 0.036 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> SD:hclust 39 3.47e-01 0.6569 2.31e-04 1.000 2
#> SD:hclust 46 2.01e-04 0.2743 2.81e-03 0.148 3
#> SD:hclust 34 1.14e-03 0.6746 3.01e-05 0.157 4
#> SD:hclust 24 2.50e-05 0.0871 3.83e-02 0.137 5
#> SD:hclust 38 9.48e-05 0.0171 5.55e-04 0.016 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 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 0.916 0.957 0.5028 0.497 0.497
#> 3 3 0.400 0.601 0.701 0.3014 0.820 0.647
#> 4 4 0.623 0.789 0.830 0.1447 0.849 0.589
#> 5 5 0.721 0.725 0.809 0.0685 0.904 0.636
#> 6 6 0.727 0.621 0.752 0.0396 0.943 0.739
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
#> GSM680053 2 0.0672 0.9537 0.008 0.992
#> GSM680062 1 0.9977 0.0176 0.528 0.472
#> GSM680054 2 0.0000 0.9548 0.000 1.000
#> GSM680063 2 0.9909 0.1832 0.444 0.556
#> GSM680055 2 0.0672 0.9537 0.008 0.992
#> GSM680064 1 0.2043 0.9598 0.968 0.032
#> GSM680056 1 0.2603 0.9550 0.956 0.044
#> GSM680065 1 0.2236 0.9593 0.964 0.036
#> GSM680057 2 0.2043 0.9500 0.032 0.968
#> GSM680066 1 0.1843 0.9605 0.972 0.028
#> GSM680058 2 0.0938 0.9534 0.012 0.988
#> GSM680067 2 0.2236 0.9480 0.036 0.964
#> GSM680059 2 0.1184 0.9549 0.016 0.984
#> GSM680068 1 0.1843 0.9605 0.972 0.028
#> GSM680060 2 0.0938 0.9534 0.012 0.988
#> GSM680069 2 0.7139 0.7488 0.196 0.804
#> GSM680061 2 0.2236 0.9480 0.036 0.964
#> GSM680070 1 0.2236 0.9593 0.964 0.036
#> GSM680071 2 0.7219 0.7504 0.200 0.800
#> GSM680077 1 0.2236 0.9593 0.964 0.036
#> GSM680072 2 0.0000 0.9548 0.000 1.000
#> GSM680078 1 0.2236 0.9593 0.964 0.036
#> GSM680073 2 0.0672 0.9537 0.008 0.992
#> GSM680079 1 0.2236 0.9593 0.964 0.036
#> GSM680074 2 0.0938 0.9534 0.012 0.988
#> GSM680080 2 0.0000 0.9548 0.000 1.000
#> GSM680075 2 0.0672 0.9537 0.008 0.992
#> GSM680081 2 0.0672 0.9537 0.008 0.992
#> GSM680076 2 0.0376 0.9546 0.004 0.996
#> GSM680082 1 0.2043 0.9599 0.968 0.032
#> GSM680029 2 0.0938 0.9546 0.012 0.988
#> GSM680041 1 0.0672 0.9570 0.992 0.008
#> GSM680035 2 0.1843 0.9541 0.028 0.972
#> GSM680047 1 0.0376 0.9584 0.996 0.004
#> GSM680036 2 0.0672 0.9537 0.008 0.992
#> GSM680048 1 0.0672 0.9570 0.992 0.008
#> GSM680037 2 0.1843 0.9541 0.028 0.972
#> GSM680049 1 0.0672 0.9570 0.992 0.008
#> GSM680038 2 0.2043 0.9500 0.032 0.968
#> GSM680050 1 0.1414 0.9594 0.980 0.020
#> GSM680039 2 0.1843 0.9514 0.028 0.972
#> GSM680051 1 0.0672 0.9570 0.992 0.008
#> GSM680040 2 0.1843 0.9541 0.028 0.972
#> GSM680052 1 0.0672 0.9570 0.992 0.008
#> GSM680030 2 0.2043 0.9500 0.032 0.968
#> GSM680042 1 0.0376 0.9584 0.996 0.004
#> GSM680031 2 0.1843 0.9541 0.028 0.972
#> GSM680043 1 0.0376 0.9592 0.996 0.004
#> GSM680032 1 0.2236 0.9593 0.964 0.036
#> GSM680044 1 0.1184 0.9590 0.984 0.016
#> GSM680033 2 0.1843 0.9541 0.028 0.972
#> GSM680045 1 0.0000 0.9588 1.000 0.000
#> GSM680034 2 0.2236 0.9480 0.036 0.964
#> GSM680046 1 0.0376 0.9584 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 3 0.6271 0.614 0.088 0.140 0.772
#> GSM680062 3 0.6808 0.543 0.084 0.184 0.732
#> GSM680054 3 0.5926 -0.193 0.000 0.356 0.644
#> GSM680063 3 0.6625 0.565 0.080 0.176 0.744
#> GSM680055 3 0.6271 0.614 0.088 0.140 0.772
#> GSM680064 1 0.2959 0.747 0.900 0.100 0.000
#> GSM680056 1 0.8937 0.230 0.540 0.152 0.308
#> GSM680065 1 0.4677 0.718 0.840 0.132 0.028
#> GSM680057 3 0.6308 -0.742 0.000 0.492 0.508
#> GSM680066 1 0.4128 0.719 0.856 0.012 0.132
#> GSM680058 2 0.6244 0.759 0.000 0.560 0.440
#> GSM680067 2 0.5733 0.659 0.000 0.676 0.324
#> GSM680059 3 0.3482 0.529 0.000 0.128 0.872
#> GSM680068 1 0.2636 0.747 0.932 0.020 0.048
#> GSM680060 2 0.6235 0.758 0.000 0.564 0.436
#> GSM680069 3 0.8474 0.436 0.252 0.144 0.604
#> GSM680061 2 0.5785 0.667 0.000 0.668 0.332
#> GSM680070 1 0.1525 0.740 0.964 0.004 0.032
#> GSM680071 2 0.7642 0.322 0.248 0.660 0.092
#> GSM680077 1 0.2031 0.736 0.952 0.016 0.032
#> GSM680072 2 0.6286 0.739 0.000 0.536 0.464
#> GSM680078 1 0.5115 0.631 0.796 0.016 0.188
#> GSM680073 3 0.4399 0.465 0.000 0.188 0.812
#> GSM680079 1 0.1289 0.741 0.968 0.000 0.032
#> GSM680074 2 0.6286 0.752 0.000 0.536 0.464
#> GSM680080 2 0.6291 0.749 0.000 0.532 0.468
#> GSM680075 3 0.4369 0.641 0.040 0.096 0.864
#> GSM680081 3 0.3459 0.649 0.096 0.012 0.892
#> GSM680076 2 0.8314 0.690 0.092 0.556 0.352
#> GSM680082 1 0.1877 0.737 0.956 0.012 0.032
#> GSM680029 3 0.1163 0.674 0.028 0.000 0.972
#> GSM680041 1 0.6735 0.729 0.564 0.424 0.012
#> GSM680035 3 0.0424 0.668 0.000 0.008 0.992
#> GSM680047 1 0.8570 0.705 0.476 0.428 0.096
#> GSM680036 3 0.3550 0.657 0.024 0.080 0.896
#> GSM680048 1 0.8608 0.709 0.488 0.412 0.100
#> GSM680037 3 0.0475 0.671 0.004 0.004 0.992
#> GSM680049 1 0.6490 0.737 0.628 0.360 0.012
#> GSM680038 2 0.6295 0.735 0.000 0.528 0.472
#> GSM680050 1 0.2165 0.752 0.936 0.064 0.000
#> GSM680039 3 0.6252 -0.668 0.000 0.444 0.556
#> GSM680051 1 0.8608 0.709 0.488 0.412 0.100
#> GSM680040 3 0.0424 0.668 0.000 0.008 0.992
#> GSM680052 1 0.8608 0.709 0.488 0.412 0.100
#> GSM680030 2 0.6309 0.719 0.000 0.504 0.496
#> GSM680042 1 0.6701 0.733 0.576 0.412 0.012
#> GSM680031 3 0.0237 0.670 0.000 0.004 0.996
#> GSM680043 1 0.8394 0.722 0.576 0.316 0.108
#> GSM680032 1 0.3148 0.734 0.916 0.048 0.036
#> GSM680044 1 0.8464 0.731 0.596 0.272 0.132
#> GSM680033 3 0.0592 0.664 0.000 0.012 0.988
#> GSM680045 1 0.8394 0.722 0.576 0.316 0.108
#> GSM680034 2 0.6126 0.592 0.000 0.600 0.400
#> GSM680046 1 0.7533 0.738 0.600 0.348 0.052
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 3 0.562 0.739 0.044 0.072 0.768 0.116
#> GSM680062 3 0.590 0.732 0.048 0.060 0.744 0.148
#> GSM680054 2 0.706 0.369 0.016 0.544 0.352 0.088
#> GSM680063 3 0.587 0.731 0.048 0.064 0.748 0.140
#> GSM680055 3 0.577 0.736 0.048 0.076 0.760 0.116
#> GSM680064 1 0.380 0.810 0.832 0.012 0.008 0.148
#> GSM680056 1 0.776 0.536 0.612 0.076 0.148 0.164
#> GSM680065 1 0.596 0.673 0.724 0.020 0.088 0.168
#> GSM680057 2 0.336 0.817 0.000 0.824 0.176 0.000
#> GSM680066 1 0.329 0.838 0.884 0.016 0.020 0.080
#> GSM680058 2 0.149 0.844 0.000 0.952 0.044 0.004
#> GSM680067 2 0.323 0.811 0.000 0.880 0.048 0.072
#> GSM680059 3 0.464 0.691 0.004 0.208 0.764 0.024
#> GSM680068 1 0.252 0.852 0.908 0.016 0.000 0.076
#> GSM680060 2 0.121 0.843 0.000 0.964 0.032 0.004
#> GSM680069 3 0.848 0.381 0.288 0.084 0.500 0.128
#> GSM680061 2 0.324 0.812 0.000 0.880 0.052 0.068
#> GSM680070 1 0.182 0.862 0.936 0.004 0.000 0.060
#> GSM680071 2 0.638 0.637 0.060 0.720 0.084 0.136
#> GSM680077 1 0.198 0.864 0.940 0.016 0.004 0.040
#> GSM680072 2 0.293 0.827 0.004 0.896 0.076 0.024
#> GSM680078 1 0.192 0.852 0.944 0.004 0.024 0.028
#> GSM680073 3 0.600 0.661 0.032 0.284 0.660 0.024
#> GSM680079 1 0.166 0.864 0.944 0.004 0.000 0.052
#> GSM680074 2 0.236 0.840 0.000 0.920 0.056 0.024
#> GSM680080 2 0.236 0.840 0.000 0.920 0.056 0.024
#> GSM680075 3 0.578 0.738 0.044 0.208 0.720 0.028
#> GSM680081 3 0.320 0.791 0.036 0.060 0.892 0.012
#> GSM680076 2 0.274 0.821 0.052 0.912 0.012 0.024
#> GSM680082 1 0.168 0.866 0.948 0.012 0.000 0.040
#> GSM680029 3 0.267 0.798 0.020 0.060 0.912 0.008
#> GSM680041 4 0.326 0.857 0.108 0.008 0.012 0.872
#> GSM680035 3 0.280 0.798 0.020 0.060 0.908 0.012
#> GSM680047 4 0.299 0.892 0.100 0.004 0.012 0.884
#> GSM680036 3 0.517 0.756 0.036 0.088 0.796 0.080
#> GSM680048 4 0.368 0.907 0.120 0.016 0.012 0.852
#> GSM680037 3 0.280 0.798 0.020 0.060 0.908 0.012
#> GSM680049 4 0.363 0.885 0.184 0.004 0.000 0.812
#> GSM680038 2 0.292 0.827 0.000 0.860 0.140 0.000
#> GSM680050 1 0.345 0.829 0.864 0.012 0.012 0.112
#> GSM680039 2 0.472 0.661 0.004 0.672 0.324 0.000
#> GSM680051 4 0.410 0.906 0.112 0.016 0.032 0.840
#> GSM680040 3 0.280 0.798 0.020 0.060 0.908 0.012
#> GSM680052 4 0.410 0.906 0.112 0.016 0.032 0.840
#> GSM680030 2 0.340 0.822 0.004 0.832 0.164 0.000
#> GSM680042 4 0.363 0.883 0.144 0.008 0.008 0.840
#> GSM680031 3 0.280 0.798 0.020 0.060 0.908 0.012
#> GSM680043 4 0.556 0.843 0.228 0.016 0.040 0.716
#> GSM680032 1 0.194 0.857 0.944 0.008 0.016 0.032
#> GSM680044 4 0.551 0.792 0.284 0.020 0.016 0.680
#> GSM680033 3 0.280 0.798 0.020 0.060 0.908 0.012
#> GSM680045 4 0.544 0.861 0.196 0.016 0.048 0.740
#> GSM680034 2 0.500 0.770 0.000 0.768 0.148 0.084
#> GSM680046 4 0.433 0.895 0.172 0.016 0.012 0.800
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.4783 0.6885 0.008 0.008 0.372 0.004 0.608
#> GSM680062 5 0.5413 0.7126 0.012 0.008 0.340 0.032 0.608
#> GSM680054 5 0.6458 0.4598 0.000 0.280 0.224 0.000 0.496
#> GSM680063 5 0.5413 0.7126 0.012 0.008 0.340 0.032 0.608
#> GSM680055 5 0.5041 0.7164 0.012 0.008 0.328 0.016 0.636
#> GSM680064 1 0.4113 0.8200 0.804 0.004 0.004 0.108 0.080
#> GSM680056 5 0.4812 0.6098 0.172 0.004 0.048 0.024 0.752
#> GSM680065 5 0.4268 0.4504 0.268 0.000 0.000 0.024 0.708
#> GSM680057 2 0.3280 0.7707 0.000 0.824 0.160 0.004 0.012
#> GSM680066 1 0.2056 0.8932 0.928 0.008 0.008 0.048 0.008
#> GSM680058 2 0.2011 0.8181 0.000 0.928 0.020 0.008 0.044
#> GSM680067 2 0.1467 0.8133 0.004 0.956 0.016 0.016 0.008
#> GSM680059 3 0.5746 0.5962 0.000 0.148 0.692 0.044 0.116
#> GSM680068 1 0.1877 0.8940 0.932 0.004 0.004 0.052 0.008
#> GSM680060 2 0.1549 0.8193 0.000 0.944 0.016 0.000 0.040
#> GSM680069 5 0.5120 0.6866 0.068 0.012 0.156 0.020 0.744
#> GSM680061 2 0.1340 0.8137 0.004 0.960 0.016 0.016 0.004
#> GSM680070 1 0.0833 0.9104 0.976 0.000 0.004 0.016 0.004
#> GSM680071 2 0.4841 0.2329 0.004 0.520 0.004 0.008 0.464
#> GSM680077 1 0.3106 0.8757 0.856 0.008 0.020 0.000 0.116
#> GSM680072 2 0.5232 0.7076 0.000 0.704 0.040 0.044 0.212
#> GSM680078 1 0.1369 0.9097 0.956 0.000 0.008 0.008 0.028
#> GSM680073 3 0.6987 0.4252 0.000 0.168 0.528 0.044 0.260
#> GSM680079 1 0.2290 0.9067 0.920 0.004 0.016 0.016 0.044
#> GSM680074 2 0.4038 0.7777 0.000 0.808 0.032 0.028 0.132
#> GSM680080 2 0.4038 0.7777 0.000 0.808 0.032 0.028 0.132
#> GSM680075 3 0.6461 0.4392 0.000 0.104 0.584 0.044 0.268
#> GSM680081 3 0.1404 0.7418 0.028 0.004 0.956 0.004 0.008
#> GSM680076 2 0.4795 0.7477 0.036 0.764 0.012 0.028 0.160
#> GSM680082 1 0.1717 0.9029 0.936 0.008 0.004 0.000 0.052
#> GSM680029 3 0.1685 0.7572 0.004 0.016 0.948 0.016 0.016
#> GSM680041 4 0.2694 0.8344 0.032 0.000 0.004 0.888 0.076
#> GSM680035 3 0.1093 0.7677 0.004 0.020 0.968 0.004 0.004
#> GSM680047 4 0.2308 0.8465 0.036 0.000 0.004 0.912 0.048
#> GSM680036 5 0.4994 0.4937 0.000 0.008 0.464 0.016 0.512
#> GSM680048 4 0.2291 0.8548 0.048 0.012 0.000 0.916 0.024
#> GSM680037 3 0.1093 0.7677 0.004 0.020 0.968 0.004 0.004
#> GSM680049 4 0.3002 0.8418 0.076 0.000 0.004 0.872 0.048
#> GSM680038 2 0.3435 0.7718 0.000 0.820 0.156 0.004 0.020
#> GSM680050 1 0.4184 0.8528 0.808 0.008 0.016 0.044 0.124
#> GSM680039 3 0.4437 -0.0106 0.000 0.464 0.532 0.004 0.000
#> GSM680051 4 0.2309 0.8507 0.036 0.028 0.012 0.920 0.004
#> GSM680040 3 0.0932 0.7683 0.004 0.020 0.972 0.004 0.000
#> GSM680052 4 0.2246 0.8530 0.048 0.020 0.008 0.920 0.004
#> GSM680030 2 0.3674 0.7679 0.008 0.816 0.152 0.004 0.020
#> GSM680042 4 0.2740 0.8396 0.044 0.000 0.004 0.888 0.064
#> GSM680031 3 0.1093 0.7677 0.004 0.020 0.968 0.004 0.004
#> GSM680043 4 0.6082 0.5087 0.352 0.024 0.048 0.564 0.012
#> GSM680032 1 0.2359 0.8946 0.912 0.008 0.004 0.016 0.060
#> GSM680044 4 0.6154 0.3881 0.408 0.028 0.012 0.512 0.040
#> GSM680033 3 0.0932 0.7683 0.004 0.020 0.972 0.004 0.000
#> GSM680045 4 0.5178 0.7505 0.180 0.024 0.052 0.732 0.012
#> GSM680034 2 0.3820 0.7553 0.004 0.816 0.132 0.044 0.004
#> GSM680046 4 0.3153 0.8412 0.076 0.024 0.012 0.876 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.3536 0.7254 0.000 0.008 0.252 0.000 0.736 NA
#> GSM680062 5 0.3944 0.7347 0.004 0.008 0.240 0.012 0.732 NA
#> GSM680054 5 0.5792 0.6294 0.000 0.180 0.136 0.004 0.632 NA
#> GSM680063 5 0.3944 0.7347 0.004 0.008 0.240 0.012 0.732 NA
#> GSM680055 5 0.3357 0.7400 0.000 0.008 0.224 0.000 0.764 NA
#> GSM680064 1 0.6618 0.4926 0.540 0.000 0.000 0.192 0.116 NA
#> GSM680056 5 0.2495 0.6772 0.052 0.000 0.012 0.004 0.896 NA
#> GSM680065 5 0.2651 0.6430 0.088 0.000 0.000 0.004 0.872 NA
#> GSM680057 2 0.5484 0.6783 0.000 0.568 0.148 0.004 0.000 NA
#> GSM680066 1 0.2044 0.7022 0.920 0.000 0.008 0.028 0.004 NA
#> GSM680058 2 0.3328 0.7154 0.000 0.788 0.008 0.000 0.012 NA
#> GSM680067 2 0.4618 0.7165 0.000 0.652 0.008 0.032 0.008 NA
#> GSM680059 3 0.5555 0.5037 0.004 0.280 0.592 0.000 0.016 NA
#> GSM680068 1 0.1755 0.7052 0.932 0.000 0.008 0.028 0.000 NA
#> GSM680060 2 0.3766 0.7179 0.000 0.684 0.000 0.000 0.012 NA
#> GSM680069 5 0.3492 0.7265 0.028 0.004 0.084 0.000 0.836 NA
#> GSM680061 2 0.4159 0.7209 0.000 0.672 0.008 0.020 0.000 NA
#> GSM680070 1 0.1857 0.7240 0.928 0.000 0.000 0.012 0.032 NA
#> GSM680071 5 0.5911 0.0576 0.000 0.280 0.000 0.000 0.468 NA
#> GSM680077 1 0.5594 0.6001 0.548 0.000 0.000 0.008 0.136 NA
#> GSM680072 2 0.4024 0.5097 0.000 0.784 0.020 0.000 0.080 NA
#> GSM680078 1 0.2084 0.7188 0.916 0.000 0.016 0.000 0.044 NA
#> GSM680073 2 0.7093 -0.3573 0.004 0.380 0.372 0.000 0.120 NA
#> GSM680079 1 0.5148 0.6504 0.636 0.000 0.000 0.016 0.092 NA
#> GSM680074 2 0.0363 0.6592 0.000 0.988 0.012 0.000 0.000 NA
#> GSM680080 2 0.0363 0.6592 0.000 0.988 0.012 0.000 0.000 NA
#> GSM680075 3 0.7177 0.3112 0.008 0.284 0.448 0.000 0.136 NA
#> GSM680081 3 0.0622 0.7863 0.012 0.000 0.980 0.000 0.000 NA
#> GSM680076 2 0.2786 0.6002 0.024 0.864 0.000 0.000 0.012 NA
#> GSM680082 1 0.3465 0.7151 0.812 0.000 0.000 0.008 0.048 NA
#> GSM680029 3 0.1707 0.7587 0.004 0.000 0.928 0.000 0.012 NA
#> GSM680041 4 0.2795 0.8061 0.000 0.000 0.000 0.856 0.044 NA
#> GSM680035 3 0.0000 0.7950 0.000 0.000 1.000 0.000 0.000 NA
#> GSM680047 4 0.2653 0.8136 0.004 0.000 0.000 0.868 0.028 NA
#> GSM680036 5 0.5434 0.5340 0.004 0.012 0.324 0.000 0.572 NA
#> GSM680048 4 0.0291 0.8157 0.004 0.000 0.000 0.992 0.004 NA
#> GSM680037 3 0.0000 0.7950 0.000 0.000 1.000 0.000 0.000 NA
#> GSM680049 4 0.2492 0.8127 0.004 0.000 0.000 0.876 0.020 NA
#> GSM680038 2 0.5907 0.6805 0.000 0.556 0.140 0.004 0.020 NA
#> GSM680050 1 0.6091 0.5820 0.500 0.000 0.000 0.028 0.144 NA
#> GSM680039 3 0.5828 -0.0572 0.000 0.272 0.516 0.004 0.000 NA
#> GSM680051 4 0.1679 0.8035 0.028 0.008 0.000 0.936 0.000 NA
#> GSM680040 3 0.0000 0.7950 0.000 0.000 1.000 0.000 0.000 NA
#> GSM680052 4 0.1743 0.8038 0.028 0.008 0.000 0.936 0.004 NA
#> GSM680030 2 0.5732 0.6716 0.004 0.524 0.144 0.004 0.000 NA
#> GSM680042 4 0.2795 0.8061 0.000 0.000 0.000 0.856 0.044 NA
#> GSM680031 3 0.0291 0.7908 0.000 0.004 0.992 0.000 0.004 NA
#> GSM680043 1 0.5943 0.1481 0.524 0.012 0.048 0.368 0.004 NA
#> GSM680032 1 0.3249 0.7078 0.836 0.000 0.000 0.008 0.060 NA
#> GSM680044 1 0.5647 0.2747 0.556 0.000 0.004 0.328 0.020 NA
#> GSM680033 3 0.0000 0.7950 0.000 0.000 1.000 0.000 0.000 NA
#> GSM680045 4 0.6101 0.0662 0.408 0.012 0.056 0.476 0.004 NA
#> GSM680034 2 0.6476 0.6596 0.012 0.516 0.124 0.048 0.000 NA
#> GSM680046 4 0.3414 0.7034 0.140 0.008 0.000 0.812 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> SD:kmeans 52 2.91e-01 0.979 1.31e-07 0.5925 2
#> SD:kmeans 47 2.25e-01 0.551 1.38e-06 0.3626 3
#> SD:kmeans 52 3.04e-04 0.598 2.38e-06 0.1479 4
#> SD:kmeans 46 6.53e-05 0.417 3.05e-05 0.0830 5
#> SD:kmeans 46 3.48e-04 0.242 1.06e-04 0.0524 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 1.000 0.958 0.983 0.5074 0.493 0.493
#> 3 3 0.887 0.915 0.936 0.3205 0.778 0.575
#> 4 4 0.863 0.894 0.934 0.1344 0.862 0.608
#> 5 5 0.872 0.851 0.920 0.0650 0.899 0.615
#> 6 6 0.789 0.630 0.808 0.0372 0.956 0.778
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
#> GSM680053 2 0.0000 0.974 0.000 1.000
#> GSM680062 1 0.0376 0.987 0.996 0.004
#> GSM680054 2 0.0000 0.974 0.000 1.000
#> GSM680063 1 0.7219 0.738 0.800 0.200
#> GSM680055 2 0.0000 0.974 0.000 1.000
#> GSM680064 1 0.0000 0.991 1.000 0.000
#> GSM680056 1 0.0000 0.991 1.000 0.000
#> GSM680065 1 0.0000 0.991 1.000 0.000
#> GSM680057 2 0.0000 0.974 0.000 1.000
#> GSM680066 1 0.0000 0.991 1.000 0.000
#> GSM680058 2 0.0000 0.974 0.000 1.000
#> GSM680067 2 0.0000 0.974 0.000 1.000
#> GSM680059 2 0.0000 0.974 0.000 1.000
#> GSM680068 1 0.0000 0.991 1.000 0.000
#> GSM680060 2 0.0000 0.974 0.000 1.000
#> GSM680069 2 0.9552 0.406 0.376 0.624
#> GSM680061 2 0.0000 0.974 0.000 1.000
#> GSM680070 1 0.0000 0.991 1.000 0.000
#> GSM680071 2 0.9087 0.524 0.324 0.676
#> GSM680077 1 0.0000 0.991 1.000 0.000
#> GSM680072 2 0.0000 0.974 0.000 1.000
#> GSM680078 1 0.0000 0.991 1.000 0.000
#> GSM680073 2 0.0000 0.974 0.000 1.000
#> GSM680079 1 0.0000 0.991 1.000 0.000
#> GSM680074 2 0.0000 0.974 0.000 1.000
#> GSM680080 2 0.0000 0.974 0.000 1.000
#> GSM680075 2 0.0000 0.974 0.000 1.000
#> GSM680081 2 0.0000 0.974 0.000 1.000
#> GSM680076 2 0.0000 0.974 0.000 1.000
#> GSM680082 1 0.0000 0.991 1.000 0.000
#> GSM680029 2 0.0000 0.974 0.000 1.000
#> GSM680041 1 0.0000 0.991 1.000 0.000
#> GSM680035 2 0.0000 0.974 0.000 1.000
#> GSM680047 1 0.0000 0.991 1.000 0.000
#> GSM680036 2 0.0000 0.974 0.000 1.000
#> GSM680048 1 0.0000 0.991 1.000 0.000
#> GSM680037 2 0.0000 0.974 0.000 1.000
#> GSM680049 1 0.0000 0.991 1.000 0.000
#> GSM680038 2 0.0000 0.974 0.000 1.000
#> GSM680050 1 0.0000 0.991 1.000 0.000
#> GSM680039 2 0.0000 0.974 0.000 1.000
#> GSM680051 1 0.0000 0.991 1.000 0.000
#> GSM680040 2 0.0000 0.974 0.000 1.000
#> GSM680052 1 0.0000 0.991 1.000 0.000
#> GSM680030 2 0.0000 0.974 0.000 1.000
#> GSM680042 1 0.0000 0.991 1.000 0.000
#> GSM680031 2 0.0000 0.974 0.000 1.000
#> GSM680043 1 0.0000 0.991 1.000 0.000
#> GSM680032 1 0.0000 0.991 1.000 0.000
#> GSM680044 1 0.0000 0.991 1.000 0.000
#> GSM680033 2 0.0000 0.974 0.000 1.000
#> GSM680045 1 0.0000 0.991 1.000 0.000
#> GSM680034 2 0.0000 0.974 0.000 1.000
#> GSM680046 1 0.0000 0.991 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 3 0.2066 0.919 0.000 0.060 0.940
#> GSM680062 3 0.2448 0.883 0.076 0.000 0.924
#> GSM680054 2 0.5431 0.586 0.000 0.716 0.284
#> GSM680063 3 0.2651 0.893 0.060 0.012 0.928
#> GSM680055 3 0.1860 0.917 0.000 0.052 0.948
#> GSM680064 1 0.2356 0.951 0.928 0.000 0.072
#> GSM680056 3 0.1964 0.847 0.056 0.000 0.944
#> GSM680065 1 0.3192 0.929 0.888 0.000 0.112
#> GSM680057 2 0.0424 0.950 0.000 0.992 0.008
#> GSM680066 1 0.2261 0.951 0.932 0.000 0.068
#> GSM680058 2 0.1031 0.946 0.000 0.976 0.024
#> GSM680067 2 0.2165 0.903 0.064 0.936 0.000
#> GSM680059 3 0.5733 0.661 0.000 0.324 0.676
#> GSM680068 1 0.2066 0.953 0.940 0.000 0.060
#> GSM680060 2 0.0592 0.950 0.000 0.988 0.012
#> GSM680069 3 0.0424 0.882 0.008 0.000 0.992
#> GSM680061 2 0.0592 0.944 0.012 0.988 0.000
#> GSM680070 1 0.2261 0.951 0.932 0.000 0.068
#> GSM680071 2 0.3349 0.873 0.004 0.888 0.108
#> GSM680077 1 0.2448 0.949 0.924 0.000 0.076
#> GSM680072 2 0.1163 0.944 0.000 0.972 0.028
#> GSM680078 1 0.4842 0.793 0.776 0.000 0.224
#> GSM680073 3 0.5621 0.670 0.000 0.308 0.692
#> GSM680079 1 0.2356 0.950 0.928 0.000 0.072
#> GSM680074 2 0.0424 0.950 0.000 0.992 0.008
#> GSM680080 2 0.0424 0.950 0.000 0.992 0.008
#> GSM680075 3 0.2356 0.921 0.000 0.072 0.928
#> GSM680081 3 0.1711 0.893 0.008 0.032 0.960
#> GSM680076 2 0.1315 0.941 0.008 0.972 0.020
#> GSM680082 1 0.2448 0.949 0.924 0.000 0.076
#> GSM680029 3 0.2711 0.921 0.000 0.088 0.912
#> GSM680041 1 0.0661 0.955 0.988 0.008 0.004
#> GSM680035 3 0.3116 0.917 0.000 0.108 0.892
#> GSM680047 1 0.0661 0.955 0.988 0.008 0.004
#> GSM680036 3 0.2165 0.920 0.000 0.064 0.936
#> GSM680048 1 0.0424 0.956 0.992 0.008 0.000
#> GSM680037 3 0.3038 0.918 0.000 0.104 0.896
#> GSM680049 1 0.0424 0.956 0.992 0.008 0.000
#> GSM680038 2 0.0592 0.950 0.000 0.988 0.012
#> GSM680050 1 0.2165 0.953 0.936 0.000 0.064
#> GSM680039 2 0.0424 0.950 0.000 0.992 0.008
#> GSM680051 1 0.0424 0.956 0.992 0.008 0.000
#> GSM680040 3 0.3116 0.917 0.000 0.108 0.892
#> GSM680052 1 0.0424 0.956 0.992 0.008 0.000
#> GSM680030 2 0.0000 0.949 0.000 1.000 0.000
#> GSM680042 1 0.0661 0.955 0.988 0.008 0.004
#> GSM680031 3 0.3038 0.918 0.000 0.104 0.896
#> GSM680043 1 0.0424 0.956 0.992 0.008 0.000
#> GSM680032 1 0.2537 0.947 0.920 0.000 0.080
#> GSM680044 1 0.0237 0.956 0.996 0.004 0.000
#> GSM680033 3 0.3192 0.915 0.000 0.112 0.888
#> GSM680045 1 0.0424 0.956 0.992 0.008 0.000
#> GSM680034 2 0.1753 0.918 0.048 0.952 0.000
#> GSM680046 1 0.0424 0.956 0.992 0.008 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 3 0.2281 0.8863 0.096 0.000 0.904 0.000
#> GSM680062 4 0.6792 -0.0156 0.096 0.000 0.428 0.476
#> GSM680054 2 0.4444 0.8085 0.072 0.808 0.120 0.000
#> GSM680063 3 0.6415 0.4719 0.100 0.000 0.612 0.288
#> GSM680055 3 0.2530 0.8778 0.112 0.000 0.888 0.000
#> GSM680064 1 0.2973 0.9090 0.856 0.000 0.000 0.144
#> GSM680056 1 0.1733 0.8817 0.948 0.000 0.024 0.028
#> GSM680065 1 0.1510 0.8859 0.956 0.000 0.016 0.028
#> GSM680057 2 0.0336 0.9573 0.000 0.992 0.008 0.000
#> GSM680066 1 0.2844 0.9134 0.900 0.000 0.052 0.048
#> GSM680058 2 0.0000 0.9591 0.000 1.000 0.000 0.000
#> GSM680067 2 0.0336 0.9564 0.000 0.992 0.000 0.008
#> GSM680059 3 0.1867 0.8997 0.000 0.072 0.928 0.000
#> GSM680068 1 0.2345 0.9298 0.900 0.000 0.000 0.100
#> GSM680060 2 0.0000 0.9591 0.000 1.000 0.000 0.000
#> GSM680069 1 0.2715 0.8247 0.892 0.004 0.100 0.004
#> GSM680061 2 0.0000 0.9591 0.000 1.000 0.000 0.000
#> GSM680070 1 0.2149 0.9353 0.912 0.000 0.000 0.088
#> GSM680071 2 0.2923 0.8968 0.080 0.896 0.016 0.008
#> GSM680077 1 0.2011 0.9356 0.920 0.000 0.000 0.080
#> GSM680072 2 0.1022 0.9452 0.000 0.968 0.032 0.000
#> GSM680078 1 0.2282 0.9276 0.924 0.000 0.024 0.052
#> GSM680073 3 0.2408 0.8729 0.000 0.104 0.896 0.000
#> GSM680079 1 0.2149 0.9353 0.912 0.000 0.000 0.088
#> GSM680074 2 0.0000 0.9591 0.000 1.000 0.000 0.000
#> GSM680080 2 0.0000 0.9591 0.000 1.000 0.000 0.000
#> GSM680075 3 0.1174 0.9254 0.012 0.020 0.968 0.000
#> GSM680081 3 0.1637 0.9019 0.060 0.000 0.940 0.000
#> GSM680076 2 0.0336 0.9562 0.008 0.992 0.000 0.000
#> GSM680082 1 0.2149 0.9353 0.912 0.000 0.000 0.088
#> GSM680029 3 0.0524 0.9257 0.008 0.004 0.988 0.000
#> GSM680041 4 0.0188 0.9332 0.004 0.000 0.000 0.996
#> GSM680035 3 0.0592 0.9286 0.000 0.016 0.984 0.000
#> GSM680047 4 0.0188 0.9332 0.004 0.000 0.000 0.996
#> GSM680036 3 0.1940 0.8967 0.076 0.000 0.924 0.000
#> GSM680048 4 0.0000 0.9346 0.000 0.000 0.000 1.000
#> GSM680037 3 0.0592 0.9286 0.000 0.016 0.984 0.000
#> GSM680049 4 0.0000 0.9346 0.000 0.000 0.000 1.000
#> GSM680038 2 0.0188 0.9583 0.000 0.996 0.004 0.000
#> GSM680050 1 0.3610 0.8526 0.800 0.000 0.000 0.200
#> GSM680039 2 0.3074 0.8304 0.000 0.848 0.152 0.000
#> GSM680051 4 0.0000 0.9346 0.000 0.000 0.000 1.000
#> GSM680040 3 0.0592 0.9286 0.000 0.016 0.984 0.000
#> GSM680052 4 0.0000 0.9346 0.000 0.000 0.000 1.000
#> GSM680030 2 0.0188 0.9584 0.000 0.996 0.004 0.000
#> GSM680042 4 0.0188 0.9332 0.004 0.000 0.000 0.996
#> GSM680031 3 0.0592 0.9286 0.000 0.016 0.984 0.000
#> GSM680043 4 0.1118 0.9166 0.036 0.000 0.000 0.964
#> GSM680032 1 0.2266 0.9352 0.912 0.004 0.000 0.084
#> GSM680044 4 0.1557 0.9011 0.056 0.000 0.000 0.944
#> GSM680033 3 0.0592 0.9286 0.000 0.016 0.984 0.000
#> GSM680045 4 0.0817 0.9242 0.024 0.000 0.000 0.976
#> GSM680034 2 0.2266 0.8986 0.000 0.912 0.004 0.084
#> GSM680046 4 0.0469 0.9306 0.012 0.000 0.000 0.988
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.1544 0.841 0.000 0.000 0.068 0.000 0.932
#> GSM680062 5 0.1918 0.839 0.000 0.000 0.036 0.036 0.928
#> GSM680054 5 0.4169 0.609 0.000 0.240 0.028 0.000 0.732
#> GSM680063 5 0.1809 0.842 0.000 0.000 0.060 0.012 0.928
#> GSM680055 5 0.1478 0.842 0.000 0.000 0.064 0.000 0.936
#> GSM680064 1 0.3412 0.820 0.820 0.000 0.000 0.152 0.028
#> GSM680056 5 0.1430 0.832 0.052 0.000 0.000 0.004 0.944
#> GSM680065 5 0.3689 0.610 0.256 0.000 0.000 0.004 0.740
#> GSM680057 2 0.1710 0.909 0.004 0.940 0.040 0.000 0.016
#> GSM680066 1 0.0867 0.939 0.976 0.000 0.008 0.008 0.008
#> GSM680058 2 0.0404 0.926 0.000 0.988 0.000 0.000 0.012
#> GSM680067 2 0.1267 0.917 0.004 0.960 0.000 0.024 0.012
#> GSM680059 3 0.1764 0.874 0.000 0.064 0.928 0.000 0.008
#> GSM680068 1 0.0579 0.942 0.984 0.000 0.000 0.008 0.008
#> GSM680060 2 0.0510 0.925 0.000 0.984 0.000 0.000 0.016
#> GSM680069 5 0.1502 0.832 0.056 0.000 0.004 0.000 0.940
#> GSM680061 2 0.0727 0.923 0.004 0.980 0.000 0.004 0.012
#> GSM680070 1 0.0290 0.943 0.992 0.000 0.000 0.008 0.000
#> GSM680071 2 0.4270 0.484 0.004 0.656 0.000 0.004 0.336
#> GSM680077 1 0.0727 0.940 0.980 0.004 0.000 0.004 0.012
#> GSM680072 2 0.1757 0.903 0.004 0.936 0.012 0.000 0.048
#> GSM680078 1 0.0324 0.942 0.992 0.000 0.004 0.004 0.000
#> GSM680073 3 0.4522 0.723 0.004 0.192 0.744 0.000 0.060
#> GSM680079 1 0.0451 0.943 0.988 0.000 0.000 0.008 0.004
#> GSM680074 2 0.0510 0.925 0.000 0.984 0.000 0.000 0.016
#> GSM680080 2 0.0510 0.925 0.000 0.984 0.000 0.000 0.016
#> GSM680075 3 0.3397 0.827 0.004 0.068 0.848 0.000 0.080
#> GSM680081 3 0.1205 0.877 0.040 0.000 0.956 0.000 0.004
#> GSM680076 2 0.0703 0.924 0.000 0.976 0.000 0.000 0.024
#> GSM680082 1 0.0579 0.943 0.984 0.000 0.000 0.008 0.008
#> GSM680029 3 0.0162 0.900 0.004 0.000 0.996 0.000 0.000
#> GSM680041 4 0.0162 0.942 0.000 0.000 0.000 0.996 0.004
#> GSM680035 3 0.0162 0.902 0.000 0.000 0.996 0.000 0.004
#> GSM680047 4 0.0000 0.944 0.000 0.000 0.000 1.000 0.000
#> GSM680036 5 0.4551 0.228 0.004 0.004 0.436 0.000 0.556
#> GSM680048 4 0.0000 0.944 0.000 0.000 0.000 1.000 0.000
#> GSM680037 3 0.0162 0.902 0.000 0.000 0.996 0.000 0.004
#> GSM680049 4 0.0000 0.944 0.000 0.000 0.000 1.000 0.000
#> GSM680038 2 0.1403 0.919 0.000 0.952 0.024 0.000 0.024
#> GSM680050 1 0.4240 0.718 0.736 0.000 0.000 0.228 0.036
#> GSM680039 3 0.4553 0.489 0.004 0.328 0.652 0.000 0.016
#> GSM680051 4 0.0324 0.940 0.000 0.004 0.000 0.992 0.004
#> GSM680040 3 0.0162 0.902 0.000 0.000 0.996 0.000 0.004
#> GSM680052 4 0.0000 0.944 0.000 0.000 0.000 1.000 0.000
#> GSM680030 2 0.1547 0.913 0.004 0.948 0.032 0.000 0.016
#> GSM680042 4 0.0000 0.944 0.000 0.000 0.000 1.000 0.000
#> GSM680031 3 0.0162 0.902 0.000 0.000 0.996 0.000 0.004
#> GSM680043 4 0.3289 0.797 0.172 0.000 0.004 0.816 0.008
#> GSM680032 1 0.0566 0.938 0.984 0.000 0.000 0.004 0.012
#> GSM680044 4 0.4156 0.616 0.288 0.000 0.004 0.700 0.008
#> GSM680033 3 0.0162 0.902 0.000 0.000 0.996 0.000 0.004
#> GSM680045 4 0.1492 0.918 0.040 0.000 0.004 0.948 0.008
#> GSM680034 2 0.4465 0.766 0.004 0.780 0.052 0.148 0.016
#> GSM680046 4 0.0324 0.942 0.004 0.000 0.000 0.992 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.1219 0.8150 0.000 0.000 0.048 0.000 0.948 0.004
#> GSM680062 5 0.2112 0.8086 0.000 0.000 0.036 0.020 0.916 0.028
#> GSM680054 5 0.4350 0.6227 0.000 0.188 0.020 0.000 0.736 0.056
#> GSM680063 5 0.1572 0.8157 0.000 0.000 0.036 0.000 0.936 0.028
#> GSM680055 5 0.0891 0.8187 0.000 0.000 0.024 0.000 0.968 0.008
#> GSM680064 1 0.4438 0.6630 0.712 0.000 0.000 0.224 0.024 0.040
#> GSM680056 5 0.1745 0.8031 0.012 0.000 0.000 0.000 0.920 0.068
#> GSM680065 5 0.4255 0.6067 0.224 0.000 0.000 0.000 0.708 0.068
#> GSM680057 2 0.1088 0.5828 0.000 0.960 0.024 0.000 0.000 0.016
#> GSM680066 1 0.2003 0.8527 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM680058 2 0.3810 0.1494 0.000 0.572 0.000 0.000 0.000 0.428
#> GSM680067 2 0.1082 0.5870 0.000 0.956 0.000 0.004 0.000 0.040
#> GSM680059 3 0.3888 0.3705 0.000 0.016 0.672 0.000 0.000 0.312
#> GSM680068 1 0.2003 0.8491 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM680060 2 0.3371 0.3957 0.000 0.708 0.000 0.000 0.000 0.292
#> GSM680069 5 0.2009 0.7993 0.008 0.004 0.000 0.000 0.904 0.084
#> GSM680061 2 0.0632 0.5877 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM680070 1 0.0935 0.8725 0.964 0.000 0.000 0.000 0.004 0.032
#> GSM680071 2 0.6554 0.1324 0.016 0.416 0.000 0.008 0.328 0.232
#> GSM680077 1 0.1572 0.8619 0.936 0.000 0.000 0.000 0.028 0.036
#> GSM680072 6 0.4780 0.0847 0.000 0.364 0.016 0.000 0.032 0.588
#> GSM680078 1 0.1732 0.8703 0.920 0.000 0.004 0.000 0.004 0.072
#> GSM680073 6 0.5531 0.3699 0.000 0.060 0.344 0.000 0.040 0.556
#> GSM680079 1 0.0820 0.8700 0.972 0.000 0.000 0.000 0.012 0.016
#> GSM680074 2 0.3857 0.0528 0.000 0.532 0.000 0.000 0.000 0.468
#> GSM680080 2 0.3860 0.0399 0.000 0.528 0.000 0.000 0.000 0.472
#> GSM680075 6 0.5259 0.0519 0.008 0.008 0.452 0.000 0.052 0.480
#> GSM680081 3 0.1401 0.8836 0.020 0.004 0.948 0.000 0.000 0.028
#> GSM680076 6 0.4205 -0.1442 0.016 0.420 0.000 0.000 0.000 0.564
#> GSM680082 1 0.1588 0.8665 0.924 0.000 0.000 0.000 0.004 0.072
#> GSM680029 3 0.1267 0.8732 0.000 0.000 0.940 0.000 0.000 0.060
#> GSM680041 4 0.0547 0.8671 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM680035 3 0.0291 0.9092 0.000 0.004 0.992 0.000 0.004 0.000
#> GSM680047 4 0.0260 0.8698 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM680036 5 0.5896 0.1722 0.000 0.000 0.324 0.000 0.456 0.220
#> GSM680048 4 0.0260 0.8704 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM680037 3 0.0260 0.9093 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM680049 4 0.0260 0.8697 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM680038 2 0.2544 0.5531 0.000 0.864 0.012 0.000 0.004 0.120
#> GSM680050 1 0.5113 0.5457 0.628 0.000 0.000 0.288 0.036 0.048
#> GSM680039 2 0.4184 -0.0548 0.000 0.504 0.484 0.000 0.000 0.012
#> GSM680051 4 0.0993 0.8656 0.000 0.012 0.000 0.964 0.000 0.024
#> GSM680040 3 0.0000 0.9092 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680052 4 0.0632 0.8679 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM680030 2 0.2069 0.5719 0.004 0.908 0.020 0.000 0.000 0.068
#> GSM680042 4 0.0458 0.8686 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM680031 3 0.1124 0.8868 0.000 0.000 0.956 0.000 0.008 0.036
#> GSM680043 4 0.6047 0.5267 0.220 0.000 0.016 0.544 0.004 0.216
#> GSM680032 1 0.2405 0.8511 0.880 0.004 0.000 0.000 0.016 0.100
#> GSM680044 4 0.6108 0.3731 0.272 0.000 0.000 0.488 0.012 0.228
#> GSM680033 3 0.0291 0.9091 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM680045 4 0.4427 0.7501 0.044 0.000 0.020 0.728 0.004 0.204
#> GSM680034 2 0.3224 0.5056 0.000 0.848 0.036 0.084 0.000 0.032
#> GSM680046 4 0.2357 0.8324 0.012 0.000 0.000 0.872 0.000 0.116
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> SD:skmeans 53 5.14e-01 0.996 1.76e-08 0.4455 2
#> SD:skmeans 54 1.42e-01 0.808 1.84e-07 0.4759 3
#> SD:skmeans 52 1.41e-04 0.710 1.49e-07 0.2016 4
#> SD:skmeans 51 3.95e-05 0.191 7.61e-06 0.0709 5
#> SD:skmeans 41 4.67e-05 0.421 2.29e-04 0.0317 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.849 0.893 0.960 0.5084 0.491 0.491
#> 3 3 0.583 0.421 0.694 0.3152 0.681 0.436
#> 4 4 0.921 0.855 0.940 0.1357 0.846 0.570
#> 5 5 0.817 0.728 0.857 0.0593 0.935 0.745
#> 6 6 0.912 0.850 0.936 0.0452 0.947 0.742
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 4
There is also optional best \(k\) = 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM680053 1 0.0000 0.9561 1.000 0.000
#> GSM680062 1 0.0000 0.9561 1.000 0.000
#> GSM680054 2 0.0000 0.9555 0.000 1.000
#> GSM680063 1 0.0000 0.9561 1.000 0.000
#> GSM680055 1 0.0000 0.9561 1.000 0.000
#> GSM680064 1 0.0000 0.9561 1.000 0.000
#> GSM680056 1 0.0000 0.9561 1.000 0.000
#> GSM680065 1 0.0000 0.9561 1.000 0.000
#> GSM680057 2 0.0000 0.9555 0.000 1.000
#> GSM680066 2 0.0000 0.9555 0.000 1.000
#> GSM680058 2 0.0000 0.9555 0.000 1.000
#> GSM680067 2 0.0000 0.9555 0.000 1.000
#> GSM680059 2 0.0672 0.9492 0.008 0.992
#> GSM680068 1 0.0000 0.9561 1.000 0.000
#> GSM680060 2 0.0000 0.9555 0.000 1.000
#> GSM680069 1 0.0000 0.9561 1.000 0.000
#> GSM680061 2 0.0000 0.9555 0.000 1.000
#> GSM680070 1 0.0000 0.9561 1.000 0.000
#> GSM680071 2 0.6438 0.7879 0.164 0.836
#> GSM680077 1 0.9944 0.1414 0.544 0.456
#> GSM680072 2 0.0000 0.9555 0.000 1.000
#> GSM680078 1 0.0000 0.9561 1.000 0.000
#> GSM680073 2 0.8443 0.6124 0.272 0.728
#> GSM680079 1 0.0000 0.9561 1.000 0.000
#> GSM680074 2 0.0000 0.9555 0.000 1.000
#> GSM680080 2 0.0000 0.9555 0.000 1.000
#> GSM680075 1 0.0000 0.9561 1.000 0.000
#> GSM680081 2 0.0000 0.9555 0.000 1.000
#> GSM680076 2 0.0000 0.9555 0.000 1.000
#> GSM680082 2 0.0000 0.9555 0.000 1.000
#> GSM680029 1 0.7453 0.7086 0.788 0.212
#> GSM680041 1 0.0000 0.9561 1.000 0.000
#> GSM680035 2 0.0000 0.9555 0.000 1.000
#> GSM680047 1 0.0000 0.9561 1.000 0.000
#> GSM680036 2 0.9996 0.0265 0.488 0.512
#> GSM680048 1 0.0000 0.9561 1.000 0.000
#> GSM680037 1 0.0000 0.9561 1.000 0.000
#> GSM680049 1 0.9909 0.1624 0.556 0.444
#> GSM680038 2 0.0000 0.9555 0.000 1.000
#> GSM680050 1 0.0000 0.9561 1.000 0.000
#> GSM680039 2 0.0000 0.9555 0.000 1.000
#> GSM680051 2 0.5059 0.8511 0.112 0.888
#> GSM680040 2 0.0000 0.9555 0.000 1.000
#> GSM680052 1 0.0000 0.9561 1.000 0.000
#> GSM680030 2 0.0000 0.9555 0.000 1.000
#> GSM680042 1 0.0000 0.9561 1.000 0.000
#> GSM680031 1 0.0000 0.9561 1.000 0.000
#> GSM680043 1 0.0000 0.9561 1.000 0.000
#> GSM680032 2 0.0000 0.9555 0.000 1.000
#> GSM680044 1 0.0000 0.9561 1.000 0.000
#> GSM680033 2 0.0000 0.9555 0.000 1.000
#> GSM680045 1 0.0000 0.9561 1.000 0.000
#> GSM680034 2 0.0000 0.9555 0.000 1.000
#> GSM680046 1 0.0000 0.9561 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 3 0.1031 0.4805 0.000 0.024 0.976
#> GSM680062 3 0.3276 0.4329 0.068 0.024 0.908
#> GSM680054 2 0.1163 0.9151 0.000 0.972 0.028
#> GSM680063 3 0.1411 0.4754 0.000 0.036 0.964
#> GSM680055 3 0.1031 0.4805 0.000 0.024 0.976
#> GSM680064 1 0.6286 0.1772 0.536 0.000 0.464
#> GSM680056 3 0.2165 0.4552 0.000 0.064 0.936
#> GSM680065 3 0.0892 0.4805 0.000 0.020 0.980
#> GSM680057 2 0.0000 0.9292 0.000 1.000 0.000
#> GSM680066 2 0.2945 0.8710 0.004 0.908 0.088
#> GSM680058 2 0.0000 0.9292 0.000 1.000 0.000
#> GSM680067 2 0.0000 0.9292 0.000 1.000 0.000
#> GSM680059 1 0.9615 -0.0505 0.456 0.220 0.324
#> GSM680068 1 0.0000 0.0826 1.000 0.000 0.000
#> GSM680060 2 0.0000 0.9292 0.000 1.000 0.000
#> GSM680069 3 0.0747 0.4798 0.000 0.016 0.984
#> GSM680061 2 0.0000 0.9292 0.000 1.000 0.000
#> GSM680070 1 0.6154 0.1582 0.592 0.000 0.408
#> GSM680071 2 0.3619 0.7867 0.000 0.864 0.136
#> GSM680077 2 0.6062 0.3234 0.000 0.616 0.384
#> GSM680072 2 0.1781 0.9096 0.020 0.960 0.020
#> GSM680078 3 0.6274 0.3121 0.456 0.000 0.544
#> GSM680073 1 0.9136 -0.1647 0.456 0.144 0.400
#> GSM680079 3 0.6307 0.2978 0.488 0.000 0.512
#> GSM680074 2 0.0000 0.9292 0.000 1.000 0.000
#> GSM680080 2 0.0000 0.9292 0.000 1.000 0.000
#> GSM680075 3 0.6274 0.3121 0.456 0.000 0.544
#> GSM680081 1 0.9615 -0.0505 0.456 0.220 0.324
#> GSM680076 2 0.0000 0.9292 0.000 1.000 0.000
#> GSM680082 1 0.6274 -0.0594 0.544 0.456 0.000
#> GSM680029 3 0.7169 0.2864 0.456 0.024 0.520
#> GSM680041 3 0.6008 0.0691 0.372 0.000 0.628
#> GSM680035 1 0.9615 -0.0505 0.456 0.220 0.324
#> GSM680047 3 0.5926 0.0982 0.356 0.000 0.644
#> GSM680036 3 0.6931 0.2976 0.456 0.016 0.528
#> GSM680048 3 0.5926 0.0982 0.356 0.000 0.644
#> GSM680037 3 0.6654 0.3064 0.456 0.008 0.536
#> GSM680049 1 0.9151 0.2158 0.544 0.228 0.228
#> GSM680038 2 0.0000 0.9292 0.000 1.000 0.000
#> GSM680050 3 0.8067 0.1489 0.188 0.160 0.652
#> GSM680039 2 0.2711 0.8723 0.000 0.912 0.088
#> GSM680051 1 0.6641 -0.0408 0.544 0.448 0.008
#> GSM680040 1 0.9568 -0.0648 0.456 0.208 0.336
#> GSM680052 1 0.6274 0.1867 0.544 0.000 0.456
#> GSM680030 2 0.0000 0.9292 0.000 1.000 0.000
#> GSM680042 1 0.6274 0.1867 0.544 0.000 0.456
#> GSM680031 3 0.6527 0.3281 0.404 0.008 0.588
#> GSM680043 1 0.6274 0.1867 0.544 0.000 0.456
#> GSM680032 2 0.3120 0.8744 0.012 0.908 0.080
#> GSM680044 3 0.5760 0.1327 0.328 0.000 0.672
#> GSM680033 1 0.9615 -0.0505 0.456 0.220 0.324
#> GSM680045 1 0.6274 0.1867 0.544 0.000 0.456
#> GSM680034 2 0.2796 0.8551 0.092 0.908 0.000
#> GSM680046 1 0.6274 0.1867 0.544 0.000 0.456
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 1 0.0000 0.924 1.000 0.000 0.000 0.000
#> GSM680062 1 0.0000 0.924 1.000 0.000 0.000 0.000
#> GSM680054 2 0.4843 0.330 0.396 0.604 0.000 0.000
#> GSM680063 1 0.0000 0.924 1.000 0.000 0.000 0.000
#> GSM680055 1 0.0000 0.924 1.000 0.000 0.000 0.000
#> GSM680064 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM680056 1 0.0000 0.924 1.000 0.000 0.000 0.000
#> GSM680065 1 0.0000 0.924 1.000 0.000 0.000 0.000
#> GSM680057 2 0.0000 0.852 0.000 1.000 0.000 0.000
#> GSM680066 2 0.5827 0.294 0.000 0.532 0.436 0.032
#> GSM680058 2 0.0000 0.852 0.000 1.000 0.000 0.000
#> GSM680067 2 0.0000 0.852 0.000 1.000 0.000 0.000
#> GSM680059 3 0.0000 0.991 0.000 0.000 1.000 0.000
#> GSM680068 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM680060 2 0.0000 0.852 0.000 1.000 0.000 0.000
#> GSM680069 1 0.0524 0.918 0.988 0.008 0.004 0.000
#> GSM680061 2 0.0000 0.852 0.000 1.000 0.000 0.000
#> GSM680070 4 0.0707 0.979 0.020 0.000 0.000 0.980
#> GSM680071 2 0.0188 0.849 0.004 0.996 0.000 0.000
#> GSM680077 1 0.4985 0.126 0.532 0.468 0.000 0.000
#> GSM680072 2 0.0000 0.852 0.000 1.000 0.000 0.000
#> GSM680078 3 0.0000 0.991 0.000 0.000 1.000 0.000
#> GSM680073 3 0.0000 0.991 0.000 0.000 1.000 0.000
#> GSM680079 3 0.0188 0.988 0.004 0.000 0.996 0.000
#> GSM680074 2 0.0000 0.852 0.000 1.000 0.000 0.000
#> GSM680080 2 0.0000 0.852 0.000 1.000 0.000 0.000
#> GSM680075 3 0.0000 0.991 0.000 0.000 1.000 0.000
#> GSM680081 3 0.0000 0.991 0.000 0.000 1.000 0.000
#> GSM680076 2 0.0000 0.852 0.000 1.000 0.000 0.000
#> GSM680082 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM680029 3 0.0000 0.991 0.000 0.000 1.000 0.000
#> GSM680041 1 0.4713 0.422 0.640 0.000 0.000 0.360
#> GSM680035 3 0.0000 0.991 0.000 0.000 1.000 0.000
#> GSM680047 1 0.0336 0.922 0.992 0.000 0.000 0.008
#> GSM680036 3 0.0000 0.991 0.000 0.000 1.000 0.000
#> GSM680048 1 0.0336 0.922 0.992 0.000 0.000 0.008
#> GSM680037 3 0.0000 0.991 0.000 0.000 1.000 0.000
#> GSM680049 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM680038 2 0.0000 0.852 0.000 1.000 0.000 0.000
#> GSM680050 1 0.0336 0.922 0.992 0.000 0.000 0.008
#> GSM680039 2 0.4985 0.247 0.000 0.532 0.468 0.000
#> GSM680051 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM680040 3 0.0000 0.991 0.000 0.000 1.000 0.000
#> GSM680052 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM680030 2 0.0000 0.852 0.000 1.000 0.000 0.000
#> GSM680042 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM680031 3 0.2281 0.891 0.096 0.000 0.904 0.000
#> GSM680043 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM680032 2 0.6644 0.435 0.008 0.572 0.344 0.076
#> GSM680044 1 0.0000 0.924 1.000 0.000 0.000 0.000
#> GSM680033 3 0.0000 0.991 0.000 0.000 1.000 0.000
#> GSM680045 4 0.0000 0.998 0.000 0.000 0.000 1.000
#> GSM680034 2 0.4985 0.191 0.000 0.532 0.000 0.468
#> GSM680046 4 0.0000 0.998 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.0000 0.867856 0.000 0.000 0.000 0.000 1.000
#> GSM680062 5 0.0000 0.867856 0.000 0.000 0.000 0.000 1.000
#> GSM680054 2 0.2020 0.701478 0.000 0.900 0.000 0.000 0.100
#> GSM680063 5 0.0000 0.867856 0.000 0.000 0.000 0.000 1.000
#> GSM680055 5 0.0000 0.867856 0.000 0.000 0.000 0.000 1.000
#> GSM680064 1 0.1671 0.134810 0.924 0.000 0.000 0.076 0.000
#> GSM680056 1 0.4305 0.000699 0.512 0.000 0.000 0.000 0.488
#> GSM680065 1 0.4305 0.000699 0.512 0.000 0.000 0.000 0.488
#> GSM680057 2 0.0000 0.752657 0.000 1.000 0.000 0.000 0.000
#> GSM680066 2 0.3635 0.665154 0.040 0.836 0.108 0.016 0.000
#> GSM680058 2 0.4138 0.656576 0.000 0.616 0.000 0.384 0.000
#> GSM680067 2 0.3949 0.670966 0.000 0.668 0.000 0.332 0.000
#> GSM680059 3 0.0162 0.985365 0.000 0.000 0.996 0.004 0.000
#> GSM680068 4 0.4201 0.960804 0.408 0.000 0.000 0.592 0.000
#> GSM680060 2 0.4074 0.663637 0.000 0.636 0.000 0.364 0.000
#> GSM680069 5 0.1731 0.811332 0.060 0.004 0.004 0.000 0.932
#> GSM680061 2 0.0000 0.752657 0.000 1.000 0.000 0.000 0.000
#> GSM680070 4 0.4561 0.850298 0.488 0.000 0.000 0.504 0.008
#> GSM680071 1 0.6787 -0.003602 0.380 0.288 0.000 0.332 0.000
#> GSM680077 1 0.6503 0.434484 0.616 0.132 0.000 0.196 0.056
#> GSM680072 2 0.4138 0.656576 0.000 0.616 0.000 0.384 0.000
#> GSM680078 3 0.0000 0.988941 0.000 0.000 1.000 0.000 0.000
#> GSM680073 3 0.0000 0.988941 0.000 0.000 1.000 0.000 0.000
#> GSM680079 1 0.4415 0.102211 0.552 0.000 0.444 0.000 0.004
#> GSM680074 2 0.4138 0.656576 0.000 0.616 0.000 0.384 0.000
#> GSM680080 2 0.1270 0.749080 0.000 0.948 0.000 0.052 0.000
#> GSM680075 3 0.0000 0.988941 0.000 0.000 1.000 0.000 0.000
#> GSM680081 3 0.0000 0.988941 0.000 0.000 1.000 0.000 0.000
#> GSM680076 2 0.5360 0.619053 0.060 0.556 0.000 0.384 0.000
#> GSM680082 1 0.0000 0.256828 1.000 0.000 0.000 0.000 0.000
#> GSM680029 3 0.0000 0.988941 0.000 0.000 1.000 0.000 0.000
#> GSM680041 5 0.4840 0.400179 0.040 0.000 0.000 0.320 0.640
#> GSM680035 3 0.0000 0.988941 0.000 0.000 1.000 0.000 0.000
#> GSM680047 5 0.0290 0.864583 0.000 0.000 0.000 0.008 0.992
#> GSM680036 3 0.0000 0.988941 0.000 0.000 1.000 0.000 0.000
#> GSM680048 5 0.0290 0.864583 0.000 0.000 0.000 0.008 0.992
#> GSM680037 3 0.0000 0.988941 0.000 0.000 1.000 0.000 0.000
#> GSM680049 4 0.4138 0.978621 0.384 0.000 0.000 0.616 0.000
#> GSM680038 2 0.0000 0.752657 0.000 1.000 0.000 0.000 0.000
#> GSM680050 5 0.4425 -0.026756 0.452 0.000 0.000 0.004 0.544
#> GSM680039 2 0.2773 0.646241 0.000 0.836 0.164 0.000 0.000
#> GSM680051 4 0.4138 0.978621 0.384 0.000 0.000 0.616 0.000
#> GSM680040 3 0.0000 0.988941 0.000 0.000 1.000 0.000 0.000
#> GSM680052 4 0.4138 0.978621 0.384 0.000 0.000 0.616 0.000
#> GSM680030 2 0.0000 0.752657 0.000 1.000 0.000 0.000 0.000
#> GSM680042 4 0.4138 0.978621 0.384 0.000 0.000 0.616 0.000
#> GSM680031 3 0.1965 0.873759 0.000 0.000 0.904 0.000 0.096
#> GSM680043 4 0.4288 0.975551 0.384 0.000 0.000 0.612 0.004
#> GSM680032 2 0.4451 0.357275 0.340 0.644 0.016 0.000 0.000
#> GSM680044 5 0.0000 0.867856 0.000 0.000 0.000 0.000 1.000
#> GSM680033 3 0.0000 0.988941 0.000 0.000 1.000 0.000 0.000
#> GSM680045 4 0.4138 0.978621 0.384 0.000 0.000 0.616 0.000
#> GSM680034 2 0.2773 0.647384 0.000 0.836 0.000 0.164 0.000
#> GSM680046 4 0.4138 0.978621 0.384 0.000 0.000 0.616 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.0000 0.917 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680062 5 0.0000 0.917 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680054 2 0.0000 0.895 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680063 5 0.0000 0.917 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680055 5 0.0000 0.917 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680064 1 0.1204 0.800 0.944 0.000 0.000 0.056 0.000 0.000
#> GSM680056 1 0.2969 0.718 0.776 0.000 0.000 0.000 0.224 0.000
#> GSM680065 1 0.2969 0.718 0.776 0.000 0.000 0.000 0.224 0.000
#> GSM680057 2 0.0000 0.895 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680066 2 0.1003 0.875 0.028 0.964 0.004 0.004 0.000 0.000
#> GSM680058 6 0.0260 0.872 0.000 0.008 0.000 0.000 0.000 0.992
#> GSM680067 2 0.3695 0.305 0.000 0.624 0.000 0.000 0.000 0.376
#> GSM680059 3 0.0146 0.987 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM680068 4 0.0865 0.948 0.036 0.000 0.000 0.964 0.000 0.000
#> GSM680060 6 0.2135 0.791 0.000 0.128 0.000 0.000 0.000 0.872
#> GSM680069 5 0.2703 0.713 0.172 0.000 0.004 0.000 0.824 0.000
#> GSM680061 2 0.0000 0.895 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680070 4 0.2772 0.782 0.180 0.000 0.000 0.816 0.004 0.000
#> GSM680071 1 0.5653 0.135 0.468 0.156 0.000 0.000 0.000 0.376
#> GSM680077 1 0.0146 0.810 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM680072 6 0.0260 0.872 0.000 0.008 0.000 0.000 0.000 0.992
#> GSM680078 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680073 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680079 1 0.0713 0.805 0.972 0.000 0.028 0.000 0.000 0.000
#> GSM680074 6 0.0260 0.872 0.000 0.008 0.000 0.000 0.000 0.992
#> GSM680080 6 0.3659 0.396 0.000 0.364 0.000 0.000 0.000 0.636
#> GSM680075 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680081 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680076 6 0.0632 0.857 0.024 0.000 0.000 0.000 0.000 0.976
#> GSM680082 1 0.0260 0.810 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM680029 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680041 5 0.3647 0.438 0.000 0.000 0.000 0.360 0.640 0.000
#> GSM680035 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680047 5 0.0146 0.915 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM680036 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680048 5 0.0146 0.915 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM680037 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680049 4 0.0000 0.972 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680038 2 0.0000 0.895 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680050 1 0.2668 0.751 0.828 0.000 0.000 0.004 0.168 0.000
#> GSM680039 2 0.0260 0.890 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM680051 4 0.0000 0.972 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680040 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680052 4 0.0000 0.972 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680030 2 0.0000 0.895 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680042 4 0.0000 0.972 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680031 3 0.1765 0.890 0.000 0.000 0.904 0.000 0.096 0.000
#> GSM680043 4 0.0146 0.969 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM680032 2 0.3874 0.410 0.356 0.636 0.000 0.000 0.000 0.008
#> GSM680044 5 0.0000 0.917 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680033 3 0.0000 0.990 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680045 4 0.0000 0.972 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680034 2 0.0260 0.891 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM680046 4 0.0000 0.972 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> SD:pam 51 0.4676 0.634 1.26e-03 0.1511 2
#> SD:pam 17 NA NA NA NA 3
#> SD:pam 47 0.1050 0.278 5.48e-05 0.0368 4
#> SD:pam 44 0.0785 0.411 8.10e-05 0.0955 5
#> SD:pam 49 0.0377 0.264 1.94e-05 0.0120 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 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 0.349 0.215 0.780 0.3044 0.860 0.860
#> 3 3 0.155 0.413 0.656 0.7497 0.635 0.584
#> 4 4 0.853 0.851 0.928 0.3837 0.670 0.417
#> 5 5 0.703 0.781 0.844 0.0631 0.834 0.486
#> 6 6 0.764 0.655 0.797 0.0457 0.971 0.861
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
#> GSM680053 2 0.0000 0.616 0.000 1.000
#> GSM680062 2 0.0000 0.616 0.000 1.000
#> GSM680054 2 0.0000 0.616 0.000 1.000
#> GSM680063 2 0.0000 0.616 0.000 1.000
#> GSM680055 2 0.0000 0.616 0.000 1.000
#> GSM680064 2 0.9963 -0.760 0.464 0.536
#> GSM680056 2 0.9922 -0.734 0.448 0.552
#> GSM680065 2 0.9963 -0.760 0.464 0.536
#> GSM680057 2 0.0000 0.616 0.000 1.000
#> GSM680066 2 0.0000 0.616 0.000 1.000
#> GSM680058 2 0.0000 0.616 0.000 1.000
#> GSM680067 2 0.0000 0.616 0.000 1.000
#> GSM680059 2 0.0000 0.616 0.000 1.000
#> GSM680068 2 0.9963 -0.760 0.464 0.536
#> GSM680060 2 0.0000 0.616 0.000 1.000
#> GSM680069 2 0.0000 0.616 0.000 1.000
#> GSM680061 2 0.0000 0.616 0.000 1.000
#> GSM680070 2 0.9963 -0.760 0.464 0.536
#> GSM680071 2 0.4431 0.489 0.092 0.908
#> GSM680077 2 0.9963 -0.760 0.464 0.536
#> GSM680072 2 0.0938 0.605 0.012 0.988
#> GSM680078 2 0.2948 0.553 0.052 0.948
#> GSM680073 2 0.0000 0.616 0.000 1.000
#> GSM680079 2 0.9963 -0.760 0.464 0.536
#> GSM680074 2 0.0000 0.616 0.000 1.000
#> GSM680080 2 0.0938 0.605 0.012 0.988
#> GSM680075 2 0.0000 0.616 0.000 1.000
#> GSM680081 2 0.0000 0.616 0.000 1.000
#> GSM680076 2 0.0000 0.616 0.000 1.000
#> GSM680082 2 0.9963 -0.760 0.464 0.536
#> GSM680029 2 0.0000 0.616 0.000 1.000
#> GSM680041 2 0.9963 -0.760 0.464 0.536
#> GSM680035 2 0.9754 0.240 0.408 0.592
#> GSM680047 1 0.9998 0.849 0.508 0.492
#> GSM680036 2 0.0000 0.616 0.000 1.000
#> GSM680048 1 0.9815 0.821 0.580 0.420
#> GSM680037 2 0.9393 0.274 0.356 0.644
#> GSM680049 2 0.9963 -0.760 0.464 0.536
#> GSM680038 2 0.0000 0.616 0.000 1.000
#> GSM680050 2 0.9963 -0.760 0.464 0.536
#> GSM680039 2 0.0000 0.616 0.000 1.000
#> GSM680051 2 0.9754 -0.503 0.408 0.592
#> GSM680040 2 0.9754 0.240 0.408 0.592
#> GSM680052 1 0.9996 0.777 0.512 0.488
#> GSM680030 2 0.0000 0.616 0.000 1.000
#> GSM680042 2 0.9963 -0.760 0.464 0.536
#> GSM680031 2 0.9754 0.240 0.408 0.592
#> GSM680043 2 0.9922 -0.704 0.448 0.552
#> GSM680032 2 0.9087 -0.354 0.324 0.676
#> GSM680044 2 0.6048 0.368 0.148 0.852
#> GSM680033 2 0.9754 0.240 0.408 0.592
#> GSM680045 2 0.7299 0.323 0.204 0.796
#> GSM680034 2 0.0000 0.616 0.000 1.000
#> GSM680046 1 0.9996 0.855 0.512 0.488
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 2 0.0592 0.6107 0.012 0.988 0.000
#> GSM680062 2 0.2796 0.5785 0.092 0.908 0.000
#> GSM680054 2 0.4139 0.6186 0.016 0.860 0.124
#> GSM680063 2 0.1411 0.6074 0.036 0.964 0.000
#> GSM680055 2 0.0237 0.6113 0.004 0.996 0.000
#> GSM680064 1 0.5560 0.6289 0.700 0.300 0.000
#> GSM680056 1 0.5905 0.6100 0.648 0.352 0.000
#> GSM680065 1 0.5560 0.6289 0.700 0.300 0.000
#> GSM680057 2 0.6931 0.5643 0.032 0.640 0.328
#> GSM680066 2 0.4931 0.3799 0.232 0.768 0.000
#> GSM680058 2 0.7291 0.5394 0.040 0.604 0.356
#> GSM680067 2 0.8157 0.4928 0.076 0.540 0.384
#> GSM680059 2 0.1031 0.6093 0.024 0.976 0.000
#> GSM680068 1 0.6079 0.5745 0.612 0.388 0.000
#> GSM680060 2 0.8058 0.5028 0.072 0.552 0.376
#> GSM680069 2 0.4346 0.4704 0.184 0.816 0.000
#> GSM680061 2 0.8180 0.4910 0.076 0.532 0.392
#> GSM680070 1 0.5560 0.6289 0.700 0.300 0.000
#> GSM680071 2 0.9450 0.3383 0.212 0.492 0.296
#> GSM680077 1 0.6172 0.6275 0.680 0.308 0.012
#> GSM680072 2 0.5254 0.5952 0.000 0.736 0.264
#> GSM680078 2 0.6045 -0.1105 0.380 0.620 0.000
#> GSM680073 2 0.0000 0.6124 0.000 1.000 0.000
#> GSM680079 1 0.5560 0.6289 0.700 0.300 0.000
#> GSM680074 2 0.8071 0.5005 0.072 0.548 0.380
#> GSM680080 2 0.7567 0.5213 0.048 0.576 0.376
#> GSM680075 2 0.0424 0.6102 0.008 0.992 0.000
#> GSM680081 2 0.0237 0.6113 0.004 0.996 0.000
#> GSM680076 2 0.8037 0.5047 0.076 0.572 0.352
#> GSM680082 1 0.6019 0.6210 0.700 0.288 0.012
#> GSM680029 2 0.0892 0.6093 0.020 0.980 0.000
#> GSM680041 1 0.9247 -0.5946 0.452 0.156 0.392
#> GSM680035 2 0.7657 0.4311 0.208 0.676 0.116
#> GSM680047 1 0.9256 -0.6278 0.444 0.156 0.400
#> GSM680036 2 0.0237 0.6120 0.004 0.996 0.000
#> GSM680048 3 0.8848 1.0000 0.372 0.124 0.504
#> GSM680037 2 0.7613 0.4340 0.204 0.680 0.116
#> GSM680049 1 0.9724 -0.0822 0.448 0.252 0.300
#> GSM680038 2 0.6452 0.5948 0.036 0.712 0.252
#> GSM680050 1 0.6313 0.5408 0.676 0.308 0.016
#> GSM680039 2 0.3889 0.6178 0.032 0.884 0.084
#> GSM680051 3 0.8848 1.0000 0.372 0.124 0.504
#> GSM680040 2 0.7657 0.4311 0.208 0.676 0.116
#> GSM680052 3 0.8848 1.0000 0.372 0.124 0.504
#> GSM680030 2 0.7107 0.5585 0.036 0.624 0.340
#> GSM680042 1 0.9560 -0.3646 0.452 0.204 0.344
#> GSM680031 2 0.7657 0.4311 0.208 0.676 0.116
#> GSM680043 2 0.9889 -0.3951 0.296 0.408 0.296
#> GSM680032 2 0.6079 -0.0359 0.388 0.612 0.000
#> GSM680044 2 0.6008 0.0616 0.372 0.628 0.000
#> GSM680033 2 0.7657 0.4311 0.208 0.676 0.116
#> GSM680045 2 0.9962 -0.4633 0.304 0.376 0.320
#> GSM680034 2 0.8000 0.5193 0.076 0.580 0.344
#> GSM680046 1 0.9256 -0.6278 0.444 0.156 0.400
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 3 0.0817 0.879 0.024 0.000 0.976 0.000
#> GSM680062 3 0.1297 0.881 0.020 0.016 0.964 0.000
#> GSM680054 3 0.4431 0.584 0.000 0.304 0.696 0.000
#> GSM680063 3 0.1406 0.881 0.024 0.016 0.960 0.000
#> GSM680055 3 0.1867 0.856 0.072 0.000 0.928 0.000
#> GSM680064 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM680056 1 0.0592 0.978 0.984 0.000 0.016 0.000
#> GSM680065 1 0.0592 0.978 0.984 0.000 0.016 0.000
#> GSM680057 2 0.0895 0.888 0.000 0.976 0.020 0.004
#> GSM680066 3 0.6883 0.484 0.260 0.156 0.584 0.000
#> GSM680058 2 0.0592 0.890 0.000 0.984 0.016 0.000
#> GSM680067 2 0.0707 0.889 0.000 0.980 0.000 0.020
#> GSM680059 3 0.1118 0.875 0.000 0.036 0.964 0.000
#> GSM680068 1 0.0188 0.984 0.996 0.000 0.004 0.000
#> GSM680060 2 0.0000 0.895 0.000 1.000 0.000 0.000
#> GSM680069 3 0.4500 0.586 0.316 0.000 0.684 0.000
#> GSM680061 2 0.0707 0.889 0.000 0.980 0.000 0.020
#> GSM680070 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM680071 2 0.4866 0.354 0.404 0.596 0.000 0.000
#> GSM680077 1 0.0707 0.974 0.980 0.020 0.000 0.000
#> GSM680072 3 0.4977 0.177 0.000 0.460 0.540 0.000
#> GSM680078 1 0.0469 0.978 0.988 0.000 0.012 0.000
#> GSM680073 3 0.0895 0.880 0.020 0.004 0.976 0.000
#> GSM680079 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM680074 2 0.0000 0.895 0.000 1.000 0.000 0.000
#> GSM680080 2 0.0000 0.895 0.000 1.000 0.000 0.000
#> GSM680075 3 0.0817 0.879 0.024 0.000 0.976 0.000
#> GSM680081 3 0.1406 0.881 0.024 0.016 0.960 0.000
#> GSM680076 2 0.0592 0.889 0.016 0.984 0.000 0.000
#> GSM680082 1 0.0707 0.974 0.980 0.020 0.000 0.000
#> GSM680029 3 0.0707 0.880 0.020 0.000 0.980 0.000
#> GSM680041 4 0.0927 0.967 0.008 0.016 0.000 0.976
#> GSM680035 3 0.0592 0.879 0.000 0.016 0.984 0.000
#> GSM680047 4 0.0336 0.971 0.008 0.000 0.000 0.992
#> GSM680036 3 0.0817 0.879 0.024 0.000 0.976 0.000
#> GSM680048 4 0.0000 0.971 0.000 0.000 0.000 1.000
#> GSM680037 3 0.0592 0.879 0.000 0.016 0.984 0.000
#> GSM680049 4 0.1042 0.964 0.008 0.020 0.000 0.972
#> GSM680038 3 0.5165 0.135 0.000 0.484 0.512 0.004
#> GSM680050 1 0.0707 0.974 0.980 0.020 0.000 0.000
#> GSM680039 3 0.1305 0.874 0.000 0.036 0.960 0.004
#> GSM680051 4 0.0000 0.971 0.000 0.000 0.000 1.000
#> GSM680040 3 0.0592 0.879 0.000 0.016 0.984 0.000
#> GSM680052 4 0.0000 0.971 0.000 0.000 0.000 1.000
#> GSM680030 2 0.4382 0.485 0.000 0.704 0.296 0.000
#> GSM680042 4 0.0927 0.967 0.008 0.016 0.000 0.976
#> GSM680031 3 0.0592 0.879 0.000 0.016 0.984 0.000
#> GSM680043 4 0.0921 0.956 0.000 0.000 0.028 0.972
#> GSM680032 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM680044 3 0.3280 0.822 0.124 0.016 0.860 0.000
#> GSM680033 3 0.0592 0.879 0.000 0.016 0.984 0.000
#> GSM680045 4 0.2469 0.868 0.000 0.000 0.108 0.892
#> GSM680034 2 0.3088 0.789 0.000 0.864 0.008 0.128
#> GSM680046 4 0.0336 0.971 0.008 0.000 0.000 0.992
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.0162 0.811 0.004 0.000 0.000 0.000 0.996
#> GSM680062 5 0.1517 0.806 0.004 0.012 0.028 0.004 0.952
#> GSM680054 2 0.5575 0.571 0.000 0.612 0.108 0.000 0.280
#> GSM680063 5 0.1267 0.807 0.004 0.012 0.024 0.000 0.960
#> GSM680055 5 0.0290 0.812 0.008 0.000 0.000 0.000 0.992
#> GSM680064 1 0.0510 0.940 0.984 0.000 0.000 0.000 0.016
#> GSM680056 1 0.2329 0.864 0.876 0.000 0.000 0.000 0.124
#> GSM680065 1 0.1043 0.930 0.960 0.000 0.000 0.000 0.040
#> GSM680057 2 0.4879 0.673 0.000 0.720 0.124 0.000 0.156
#> GSM680066 5 0.5754 0.505 0.260 0.136 0.000 0.000 0.604
#> GSM680058 2 0.0798 0.719 0.008 0.976 0.016 0.000 0.000
#> GSM680067 2 0.3810 0.697 0.000 0.788 0.176 0.036 0.000
#> GSM680059 2 0.6170 0.356 0.000 0.524 0.320 0.000 0.156
#> GSM680068 1 0.2970 0.798 0.828 0.004 0.000 0.000 0.168
#> GSM680060 2 0.0290 0.716 0.008 0.992 0.000 0.000 0.000
#> GSM680069 5 0.1671 0.781 0.076 0.000 0.000 0.000 0.924
#> GSM680061 2 0.3810 0.697 0.000 0.788 0.176 0.036 0.000
#> GSM680070 1 0.0510 0.940 0.984 0.000 0.000 0.000 0.016
#> GSM680071 2 0.4359 0.361 0.412 0.584 0.000 0.000 0.004
#> GSM680077 1 0.0162 0.933 0.996 0.000 0.004 0.000 0.000
#> GSM680072 2 0.4793 0.674 0.000 0.708 0.076 0.000 0.216
#> GSM680078 5 0.3707 0.536 0.284 0.000 0.000 0.000 0.716
#> GSM680073 2 0.5341 0.326 0.000 0.504 0.052 0.000 0.444
#> GSM680079 1 0.0510 0.940 0.984 0.000 0.000 0.000 0.016
#> GSM680074 2 0.0290 0.716 0.008 0.992 0.000 0.000 0.000
#> GSM680080 2 0.0798 0.715 0.000 0.976 0.016 0.000 0.008
#> GSM680075 5 0.2964 0.706 0.000 0.120 0.024 0.000 0.856
#> GSM680081 5 0.2102 0.776 0.004 0.012 0.068 0.000 0.916
#> GSM680076 2 0.1121 0.712 0.044 0.956 0.000 0.000 0.000
#> GSM680082 1 0.0162 0.933 0.996 0.000 0.004 0.000 0.000
#> GSM680029 5 0.3366 0.534 0.000 0.004 0.212 0.000 0.784
#> GSM680041 4 0.1924 0.950 0.064 0.000 0.008 0.924 0.004
#> GSM680035 3 0.3039 0.993 0.000 0.000 0.808 0.000 0.192
#> GSM680047 4 0.1638 0.951 0.064 0.000 0.004 0.932 0.000
#> GSM680036 5 0.0566 0.807 0.000 0.004 0.012 0.000 0.984
#> GSM680048 4 0.0000 0.947 0.000 0.000 0.000 1.000 0.000
#> GSM680037 3 0.3177 0.980 0.000 0.000 0.792 0.000 0.208
#> GSM680049 4 0.2084 0.949 0.064 0.004 0.008 0.920 0.004
#> GSM680038 2 0.5059 0.655 0.000 0.700 0.124 0.000 0.176
#> GSM680050 1 0.0451 0.938 0.988 0.004 0.000 0.000 0.008
#> GSM680039 2 0.6425 0.297 0.000 0.476 0.336 0.000 0.188
#> GSM680051 4 0.0000 0.947 0.000 0.000 0.000 1.000 0.000
#> GSM680040 3 0.3039 0.993 0.000 0.000 0.808 0.000 0.192
#> GSM680052 4 0.0000 0.947 0.000 0.000 0.000 1.000 0.000
#> GSM680030 2 0.4964 0.668 0.000 0.712 0.132 0.000 0.156
#> GSM680042 4 0.1924 0.950 0.064 0.000 0.008 0.924 0.004
#> GSM680031 3 0.3074 0.992 0.000 0.000 0.804 0.000 0.196
#> GSM680043 4 0.1124 0.929 0.000 0.000 0.004 0.960 0.036
#> GSM680032 1 0.2763 0.828 0.848 0.004 0.000 0.000 0.148
#> GSM680044 5 0.4700 0.692 0.076 0.012 0.024 0.100 0.788
#> GSM680033 3 0.3039 0.993 0.000 0.000 0.808 0.000 0.192
#> GSM680045 4 0.0865 0.937 0.000 0.000 0.004 0.972 0.024
#> GSM680034 2 0.5895 0.608 0.000 0.588 0.260 0.152 0.000
#> GSM680046 4 0.1638 0.951 0.064 0.000 0.004 0.932 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.0692 0.8497 0.000 0.000 0.004 0.000 0.976 0.020
#> GSM680062 5 0.1198 0.8496 0.004 0.004 0.020 0.000 0.960 0.012
#> GSM680054 2 0.6992 0.1990 0.000 0.440 0.288 0.000 0.172 0.100
#> GSM680063 5 0.0696 0.8526 0.004 0.004 0.008 0.000 0.980 0.004
#> GSM680055 5 0.0260 0.8527 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM680064 1 0.0767 0.9127 0.976 0.000 0.004 0.000 0.008 0.012
#> GSM680056 1 0.3650 0.6033 0.716 0.000 0.004 0.000 0.272 0.008
#> GSM680065 1 0.0951 0.9096 0.968 0.000 0.004 0.000 0.020 0.008
#> GSM680057 2 0.3867 0.3983 0.000 0.688 0.296 0.000 0.004 0.012
#> GSM680066 5 0.4756 0.4273 0.332 0.056 0.000 0.000 0.608 0.004
#> GSM680058 2 0.4351 0.1475 0.008 0.516 0.004 0.000 0.004 0.468
#> GSM680067 2 0.1461 0.3215 0.000 0.940 0.016 0.000 0.000 0.044
#> GSM680059 6 0.6550 0.2507 0.000 0.256 0.348 0.000 0.024 0.372
#> GSM680068 1 0.2320 0.8208 0.864 0.000 0.000 0.000 0.132 0.004
#> GSM680060 2 0.4222 0.1499 0.008 0.516 0.004 0.000 0.000 0.472
#> GSM680069 5 0.0458 0.8518 0.016 0.000 0.000 0.000 0.984 0.000
#> GSM680061 2 0.1461 0.3215 0.000 0.940 0.016 0.000 0.000 0.044
#> GSM680070 1 0.0260 0.9142 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM680071 2 0.5921 0.0682 0.400 0.432 0.000 0.000 0.008 0.160
#> GSM680077 1 0.0547 0.9097 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM680072 6 0.4582 0.1349 0.000 0.356 0.008 0.000 0.032 0.604
#> GSM680078 5 0.2178 0.7887 0.132 0.000 0.000 0.000 0.868 0.000
#> GSM680073 6 0.6137 0.3682 0.000 0.252 0.008 0.000 0.280 0.460
#> GSM680079 1 0.0260 0.9142 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM680074 2 0.4091 0.1428 0.008 0.520 0.000 0.000 0.000 0.472
#> GSM680080 2 0.4097 0.0934 0.008 0.500 0.000 0.000 0.000 0.492
#> GSM680075 5 0.3976 0.6437 0.000 0.052 0.004 0.000 0.748 0.196
#> GSM680081 5 0.1759 0.8274 0.004 0.004 0.064 0.000 0.924 0.004
#> GSM680076 2 0.4093 0.1382 0.008 0.516 0.000 0.000 0.000 0.476
#> GSM680082 1 0.0547 0.9097 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM680029 5 0.2706 0.7318 0.000 0.000 0.160 0.000 0.832 0.008
#> GSM680041 4 0.4291 0.7896 0.052 0.000 0.000 0.680 0.000 0.268
#> GSM680035 3 0.0547 0.9987 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM680047 4 0.1682 0.8769 0.052 0.000 0.000 0.928 0.000 0.020
#> GSM680036 5 0.0692 0.8497 0.000 0.000 0.004 0.000 0.976 0.020
#> GSM680048 4 0.0000 0.8812 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680037 3 0.0632 0.9947 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM680049 4 0.4469 0.7814 0.052 0.004 0.000 0.668 0.000 0.276
#> GSM680038 2 0.4113 0.3872 0.000 0.668 0.308 0.000 0.016 0.008
#> GSM680050 1 0.0436 0.9118 0.988 0.004 0.000 0.004 0.000 0.004
#> GSM680039 2 0.4072 0.2599 0.000 0.544 0.448 0.000 0.008 0.000
#> GSM680051 4 0.0000 0.8812 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680040 3 0.0547 0.9987 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM680052 4 0.0000 0.8812 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680030 2 0.3772 0.3980 0.000 0.692 0.296 0.000 0.008 0.004
#> GSM680042 4 0.4291 0.7896 0.052 0.000 0.000 0.680 0.000 0.268
#> GSM680031 3 0.0547 0.9987 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM680043 4 0.1225 0.8653 0.000 0.000 0.000 0.952 0.036 0.012
#> GSM680032 1 0.2562 0.7800 0.828 0.000 0.000 0.000 0.172 0.000
#> GSM680044 5 0.4951 0.6680 0.092 0.004 0.016 0.156 0.720 0.012
#> GSM680033 3 0.0547 0.9987 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM680045 4 0.1297 0.8627 0.000 0.000 0.000 0.948 0.040 0.012
#> GSM680034 2 0.2728 0.3591 0.000 0.864 0.100 0.032 0.000 0.004
#> GSM680046 4 0.1682 0.8769 0.052 0.000 0.000 0.928 0.000 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> SD:mclust 31 1.13e-02 0.335 3.18e-02 0.515 2
#> SD:mclust 34 1.29e-02 0.479 1.92e-04 0.502 3
#> SD:mclust 49 2.01e-04 0.303 8.73e-05 0.141 4
#> SD:mclust 50 4.56e-05 0.426 5.02e-05 0.239 5
#> SD:mclust 36 1.22e-04 0.537 8.84e-04 0.160 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 0.917 0.951 0.977 0.4973 0.502 0.502
#> 3 3 0.435 0.591 0.788 0.3444 0.756 0.544
#> 4 4 0.649 0.692 0.838 0.1349 0.798 0.474
#> 5 5 0.591 0.550 0.755 0.0640 0.832 0.438
#> 6 6 0.642 0.553 0.748 0.0369 0.866 0.453
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
#> GSM680053 2 0.0000 0.978 0.000 1.000
#> GSM680062 1 0.8955 0.557 0.688 0.312
#> GSM680054 2 0.0000 0.978 0.000 1.000
#> GSM680063 2 0.7528 0.728 0.216 0.784
#> GSM680055 2 0.0000 0.978 0.000 1.000
#> GSM680064 1 0.0000 0.971 1.000 0.000
#> GSM680056 1 0.2236 0.948 0.964 0.036
#> GSM680065 1 0.0000 0.971 1.000 0.000
#> GSM680057 2 0.0000 0.978 0.000 1.000
#> GSM680066 2 0.3431 0.925 0.064 0.936
#> GSM680058 2 0.0000 0.978 0.000 1.000
#> GSM680067 2 0.6343 0.814 0.160 0.840
#> GSM680059 2 0.0000 0.978 0.000 1.000
#> GSM680068 1 0.0000 0.971 1.000 0.000
#> GSM680060 2 0.0000 0.978 0.000 1.000
#> GSM680069 2 0.4939 0.879 0.108 0.892
#> GSM680061 2 0.0000 0.978 0.000 1.000
#> GSM680070 1 0.0000 0.971 1.000 0.000
#> GSM680071 1 0.2603 0.942 0.956 0.044
#> GSM680077 1 0.0000 0.971 1.000 0.000
#> GSM680072 2 0.0000 0.978 0.000 1.000
#> GSM680078 2 0.4161 0.905 0.084 0.916
#> GSM680073 2 0.0000 0.978 0.000 1.000
#> GSM680079 1 0.0000 0.971 1.000 0.000
#> GSM680074 2 0.0000 0.978 0.000 1.000
#> GSM680080 2 0.0000 0.978 0.000 1.000
#> GSM680075 2 0.0000 0.978 0.000 1.000
#> GSM680081 2 0.0000 0.978 0.000 1.000
#> GSM680076 2 0.0000 0.978 0.000 1.000
#> GSM680082 1 0.0000 0.971 1.000 0.000
#> GSM680029 2 0.0000 0.978 0.000 1.000
#> GSM680041 1 0.0000 0.971 1.000 0.000
#> GSM680035 2 0.0000 0.978 0.000 1.000
#> GSM680047 1 0.0000 0.971 1.000 0.000
#> GSM680036 2 0.0000 0.978 0.000 1.000
#> GSM680048 1 0.0000 0.971 1.000 0.000
#> GSM680037 2 0.0000 0.978 0.000 1.000
#> GSM680049 1 0.0000 0.971 1.000 0.000
#> GSM680038 2 0.0000 0.978 0.000 1.000
#> GSM680050 1 0.0000 0.971 1.000 0.000
#> GSM680039 2 0.0000 0.978 0.000 1.000
#> GSM680051 1 0.0000 0.971 1.000 0.000
#> GSM680040 2 0.0000 0.978 0.000 1.000
#> GSM680052 1 0.0000 0.971 1.000 0.000
#> GSM680030 2 0.0000 0.978 0.000 1.000
#> GSM680042 1 0.0000 0.971 1.000 0.000
#> GSM680031 2 0.0000 0.978 0.000 1.000
#> GSM680043 1 0.0000 0.971 1.000 0.000
#> GSM680032 1 0.4431 0.894 0.908 0.092
#> GSM680044 1 0.0938 0.964 0.988 0.012
#> GSM680033 2 0.0000 0.978 0.000 1.000
#> GSM680045 1 0.5059 0.873 0.888 0.112
#> GSM680034 2 0.0000 0.978 0.000 1.000
#> GSM680046 1 0.0000 0.971 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 3 0.3941 0.62175 0.000 0.156 0.844
#> GSM680062 3 0.5726 0.57927 0.216 0.024 0.760
#> GSM680054 2 0.6062 0.16951 0.000 0.616 0.384
#> GSM680063 3 0.5944 0.64416 0.120 0.088 0.792
#> GSM680055 3 0.3551 0.56827 0.000 0.132 0.868
#> GSM680064 1 0.2878 0.81574 0.904 0.000 0.096
#> GSM680056 3 0.8675 -0.13490 0.388 0.108 0.504
#> GSM680065 1 0.6195 0.71102 0.704 0.020 0.276
#> GSM680057 2 0.3551 0.64032 0.000 0.868 0.132
#> GSM680066 3 0.8454 0.13203 0.088 0.432 0.480
#> GSM680058 2 0.1753 0.67138 0.000 0.952 0.048
#> GSM680067 2 0.5538 0.62141 0.116 0.812 0.072
#> GSM680059 3 0.6079 0.45792 0.000 0.388 0.612
#> GSM680068 1 0.2625 0.81853 0.916 0.000 0.084
#> GSM680060 2 0.2959 0.64332 0.000 0.900 0.100
#> GSM680069 3 0.7851 0.24622 0.100 0.256 0.644
#> GSM680061 2 0.2796 0.66662 0.000 0.908 0.092
#> GSM680070 1 0.3941 0.79789 0.844 0.000 0.156
#> GSM680071 2 0.9178 0.23871 0.240 0.540 0.220
#> GSM680077 1 0.8799 0.58390 0.584 0.196 0.220
#> GSM680072 2 0.5058 0.49638 0.000 0.756 0.244
#> GSM680078 3 0.4056 0.56576 0.032 0.092 0.876
#> GSM680073 2 0.6215 0.00216 0.000 0.572 0.428
#> GSM680079 1 0.4834 0.77242 0.792 0.004 0.204
#> GSM680074 2 0.0424 0.68362 0.000 0.992 0.008
#> GSM680080 2 0.0424 0.68353 0.000 0.992 0.008
#> GSM680075 3 0.4555 0.55186 0.000 0.200 0.800
#> GSM680081 3 0.4702 0.67012 0.000 0.212 0.788
#> GSM680076 2 0.4291 0.57733 0.000 0.820 0.180
#> GSM680082 1 0.7344 0.70893 0.696 0.100 0.204
#> GSM680029 3 0.4887 0.66686 0.000 0.228 0.772
#> GSM680041 1 0.0000 0.82470 1.000 0.000 0.000
#> GSM680035 3 0.4796 0.66671 0.000 0.220 0.780
#> GSM680047 1 0.0592 0.82372 0.988 0.000 0.012
#> GSM680036 3 0.4974 0.62372 0.000 0.236 0.764
#> GSM680048 1 0.0592 0.82372 0.988 0.000 0.012
#> GSM680037 3 0.4750 0.66882 0.000 0.216 0.784
#> GSM680049 1 0.0000 0.82470 1.000 0.000 0.000
#> GSM680038 2 0.5016 0.53178 0.000 0.760 0.240
#> GSM680050 1 0.4121 0.79309 0.832 0.000 0.168
#> GSM680039 2 0.6204 0.08896 0.000 0.576 0.424
#> GSM680051 1 0.2400 0.80596 0.932 0.004 0.064
#> GSM680040 3 0.4796 0.66671 0.000 0.220 0.780
#> GSM680052 1 0.2066 0.80851 0.940 0.000 0.060
#> GSM680030 2 0.2711 0.66917 0.000 0.912 0.088
#> GSM680042 1 0.0000 0.82470 1.000 0.000 0.000
#> GSM680031 3 0.4750 0.66882 0.000 0.216 0.784
#> GSM680043 1 0.6448 0.40808 0.636 0.012 0.352
#> GSM680032 1 0.7576 0.65962 0.648 0.076 0.276
#> GSM680044 1 0.3192 0.77355 0.888 0.000 0.112
#> GSM680033 3 0.4842 0.66369 0.000 0.224 0.776
#> GSM680045 1 0.7534 0.15423 0.532 0.040 0.428
#> GSM680034 2 0.6229 0.45193 0.020 0.700 0.280
#> GSM680046 1 0.1163 0.82018 0.972 0.000 0.028
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 3 0.4252 0.6182 0.252 0.004 0.744 0.000
#> GSM680062 3 0.1936 0.7716 0.032 0.000 0.940 0.028
#> GSM680054 3 0.7618 0.3529 0.284 0.244 0.472 0.000
#> GSM680063 3 0.2142 0.7665 0.056 0.000 0.928 0.016
#> GSM680055 1 0.4401 0.4769 0.724 0.004 0.272 0.000
#> GSM680064 1 0.4933 0.3523 0.568 0.000 0.000 0.432
#> GSM680056 1 0.1209 0.7732 0.964 0.000 0.032 0.004
#> GSM680065 1 0.1356 0.7877 0.960 0.000 0.008 0.032
#> GSM680057 2 0.1297 0.8419 0.000 0.964 0.020 0.016
#> GSM680066 3 0.9022 0.0802 0.060 0.300 0.372 0.268
#> GSM680058 2 0.1970 0.8389 0.060 0.932 0.008 0.000
#> GSM680067 2 0.2654 0.7919 0.000 0.888 0.004 0.108
#> GSM680059 3 0.2048 0.7638 0.008 0.064 0.928 0.000
#> GSM680068 4 0.3560 0.7974 0.140 0.004 0.012 0.844
#> GSM680060 2 0.1022 0.8458 0.032 0.968 0.000 0.000
#> GSM680069 1 0.1890 0.7542 0.936 0.008 0.056 0.000
#> GSM680061 2 0.1398 0.8347 0.000 0.956 0.004 0.040
#> GSM680070 1 0.4761 0.5541 0.664 0.004 0.000 0.332
#> GSM680071 1 0.2999 0.6993 0.864 0.132 0.000 0.004
#> GSM680077 1 0.1510 0.7845 0.956 0.016 0.000 0.028
#> GSM680072 2 0.5879 0.5994 0.248 0.672 0.080 0.000
#> GSM680078 1 0.3982 0.5779 0.776 0.000 0.220 0.004
#> GSM680073 3 0.7645 0.3390 0.264 0.268 0.468 0.000
#> GSM680079 1 0.3610 0.7209 0.800 0.000 0.000 0.200
#> GSM680074 2 0.0804 0.8464 0.012 0.980 0.008 0.000
#> GSM680080 2 0.1767 0.8448 0.044 0.944 0.012 0.000
#> GSM680075 3 0.5512 0.1597 0.488 0.016 0.496 0.000
#> GSM680081 3 0.0376 0.7841 0.000 0.004 0.992 0.004
#> GSM680076 2 0.3311 0.7587 0.172 0.828 0.000 0.000
#> GSM680082 1 0.3351 0.7559 0.844 0.008 0.000 0.148
#> GSM680029 3 0.0336 0.7823 0.008 0.000 0.992 0.000
#> GSM680041 4 0.2868 0.8036 0.136 0.000 0.000 0.864
#> GSM680035 3 0.0524 0.7843 0.000 0.004 0.988 0.008
#> GSM680047 4 0.1411 0.8715 0.020 0.000 0.020 0.960
#> GSM680036 3 0.4372 0.6075 0.268 0.004 0.728 0.000
#> GSM680048 4 0.0672 0.8701 0.008 0.000 0.008 0.984
#> GSM680037 3 0.0524 0.7843 0.000 0.004 0.988 0.008
#> GSM680049 4 0.1824 0.8516 0.060 0.004 0.000 0.936
#> GSM680038 2 0.5120 0.6628 0.044 0.752 0.196 0.008
#> GSM680050 1 0.4277 0.6344 0.720 0.000 0.000 0.280
#> GSM680039 3 0.6976 0.2994 0.000 0.320 0.544 0.136
#> GSM680051 4 0.1575 0.8638 0.004 0.012 0.028 0.956
#> GSM680040 3 0.0804 0.7839 0.000 0.012 0.980 0.008
#> GSM680052 4 0.0921 0.8677 0.000 0.000 0.028 0.972
#> GSM680030 2 0.1377 0.8451 0.008 0.964 0.020 0.008
#> GSM680042 4 0.3074 0.7803 0.152 0.000 0.000 0.848
#> GSM680031 3 0.0804 0.7834 0.000 0.008 0.980 0.012
#> GSM680043 4 0.3870 0.7176 0.000 0.004 0.208 0.788
#> GSM680032 1 0.1978 0.7877 0.928 0.004 0.000 0.068
#> GSM680044 4 0.3828 0.8343 0.068 0.000 0.084 0.848
#> GSM680033 3 0.0804 0.7839 0.000 0.012 0.980 0.008
#> GSM680045 4 0.4594 0.6075 0.000 0.008 0.280 0.712
#> GSM680034 2 0.5938 0.0316 0.000 0.488 0.036 0.476
#> GSM680046 4 0.0524 0.8691 0.004 0.000 0.008 0.988
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.3262 0.7329 0.000 0.000 0.124 0.036 0.840
#> GSM680062 5 0.5649 0.4929 0.000 0.000 0.108 0.296 0.596
#> GSM680054 5 0.3649 0.7547 0.000 0.064 0.032 0.056 0.848
#> GSM680063 5 0.5592 0.5879 0.000 0.000 0.144 0.220 0.636
#> GSM680055 5 0.2586 0.7555 0.012 0.000 0.084 0.012 0.892
#> GSM680064 1 0.4088 0.4980 0.776 0.000 0.000 0.168 0.056
#> GSM680056 5 0.1857 0.7499 0.060 0.000 0.004 0.008 0.928
#> GSM680065 5 0.4594 0.4989 0.284 0.000 0.000 0.036 0.680
#> GSM680057 2 0.1732 0.7632 0.000 0.920 0.000 0.080 0.000
#> GSM680066 1 0.5158 0.4670 0.632 0.008 0.316 0.044 0.000
#> GSM680058 2 0.2648 0.7113 0.000 0.848 0.000 0.000 0.152
#> GSM680067 2 0.2020 0.7534 0.000 0.900 0.000 0.100 0.000
#> GSM680059 3 0.0775 0.6831 0.004 0.008 0.980 0.004 0.004
#> GSM680068 1 0.3130 0.6516 0.856 0.000 0.096 0.048 0.000
#> GSM680060 2 0.1671 0.7576 0.000 0.924 0.000 0.000 0.076
#> GSM680069 5 0.3188 0.7319 0.100 0.000 0.012 0.028 0.860
#> GSM680061 2 0.1478 0.7663 0.000 0.936 0.000 0.064 0.000
#> GSM680070 1 0.0865 0.6840 0.972 0.000 0.024 0.004 0.000
#> GSM680071 5 0.4945 0.6707 0.056 0.148 0.000 0.044 0.752
#> GSM680077 1 0.3384 0.6586 0.864 0.012 0.012 0.032 0.080
#> GSM680072 2 0.4900 0.2542 0.004 0.564 0.000 0.020 0.412
#> GSM680078 1 0.6529 0.2687 0.468 0.000 0.408 0.032 0.092
#> GSM680073 3 0.7912 -0.0280 0.016 0.280 0.356 0.036 0.312
#> GSM680079 1 0.0510 0.6856 0.984 0.000 0.016 0.000 0.000
#> GSM680074 2 0.0609 0.7685 0.000 0.980 0.000 0.000 0.020
#> GSM680080 2 0.0794 0.7683 0.000 0.972 0.000 0.000 0.028
#> GSM680075 3 0.6005 0.3154 0.060 0.016 0.652 0.032 0.240
#> GSM680081 3 0.1885 0.6895 0.020 0.000 0.932 0.044 0.004
#> GSM680076 2 0.3769 0.7075 0.100 0.828 0.004 0.004 0.064
#> GSM680082 1 0.1603 0.6828 0.948 0.012 0.004 0.004 0.032
#> GSM680029 3 0.1251 0.6916 0.000 0.000 0.956 0.008 0.036
#> GSM680041 4 0.5748 0.3998 0.116 0.000 0.000 0.584 0.300
#> GSM680035 3 0.5026 0.6423 0.000 0.000 0.656 0.280 0.064
#> GSM680047 4 0.4132 0.4653 0.020 0.000 0.000 0.720 0.260
#> GSM680036 5 0.3090 0.7454 0.000 0.000 0.104 0.040 0.856
#> GSM680048 4 0.4297 0.6077 0.164 0.000 0.000 0.764 0.072
#> GSM680037 3 0.4536 0.6800 0.000 0.000 0.712 0.240 0.048
#> GSM680049 1 0.5283 -0.1811 0.508 0.000 0.000 0.444 0.048
#> GSM680038 5 0.5430 0.5982 0.000 0.192 0.000 0.148 0.660
#> GSM680050 1 0.0898 0.6791 0.972 0.000 0.000 0.008 0.020
#> GSM680039 2 0.6725 -0.0125 0.000 0.400 0.256 0.344 0.000
#> GSM680051 4 0.1618 0.6214 0.008 0.000 0.008 0.944 0.040
#> GSM680040 3 0.4248 0.6873 0.000 0.000 0.728 0.240 0.032
#> GSM680052 4 0.2850 0.6290 0.092 0.000 0.036 0.872 0.000
#> GSM680030 2 0.3806 0.6901 0.000 0.804 0.004 0.040 0.152
#> GSM680042 4 0.5752 0.2207 0.412 0.000 0.000 0.500 0.088
#> GSM680031 3 0.3109 0.6893 0.000 0.000 0.800 0.200 0.000
#> GSM680043 4 0.6036 0.3085 0.144 0.000 0.308 0.548 0.000
#> GSM680032 1 0.4408 0.5589 0.752 0.008 0.004 0.032 0.204
#> GSM680044 1 0.6803 -0.2277 0.412 0.004 0.172 0.404 0.008
#> GSM680033 3 0.4250 0.6811 0.000 0.000 0.720 0.252 0.028
#> GSM680045 4 0.5455 0.3615 0.036 0.040 0.268 0.656 0.000
#> GSM680034 2 0.4655 0.2161 0.000 0.512 0.012 0.476 0.000
#> GSM680046 4 0.4108 0.4747 0.308 0.000 0.008 0.684 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.3898 0.6132 0.004 0.000 0.048 0.004 0.768 0.176
#> GSM680062 4 0.7068 -0.0103 0.008 0.000 0.056 0.400 0.308 0.228
#> GSM680054 5 0.2856 0.6935 0.004 0.032 0.036 0.004 0.884 0.040
#> GSM680063 5 0.6716 0.1829 0.000 0.000 0.072 0.164 0.464 0.300
#> GSM680055 5 0.3482 0.6887 0.032 0.004 0.024 0.004 0.836 0.100
#> GSM680064 4 0.3281 0.6694 0.200 0.000 0.000 0.784 0.012 0.004
#> GSM680056 5 0.3248 0.6946 0.144 0.000 0.008 0.008 0.824 0.016
#> GSM680065 5 0.4416 0.4485 0.372 0.000 0.000 0.008 0.600 0.020
#> GSM680057 3 0.5110 0.3362 0.004 0.324 0.600 0.000 0.012 0.060
#> GSM680066 1 0.5855 0.3905 0.576 0.012 0.288 0.024 0.000 0.100
#> GSM680058 2 0.2679 0.6600 0.000 0.864 0.000 0.000 0.096 0.040
#> GSM680067 2 0.4287 0.5425 0.008 0.748 0.188 0.008 0.004 0.044
#> GSM680059 6 0.4707 0.4584 0.004 0.040 0.308 0.004 0.004 0.640
#> GSM680068 1 0.6171 0.5121 0.600 0.000 0.164 0.132 0.000 0.104
#> GSM680060 2 0.3352 0.6428 0.032 0.836 0.004 0.000 0.108 0.020
#> GSM680069 5 0.3627 0.6735 0.224 0.000 0.000 0.004 0.752 0.020
#> GSM680061 2 0.4333 0.4808 0.008 0.708 0.240 0.004 0.000 0.040
#> GSM680070 1 0.2173 0.7451 0.904 0.000 0.000 0.064 0.004 0.028
#> GSM680071 5 0.4848 0.5725 0.300 0.032 0.000 0.004 0.640 0.024
#> GSM680077 1 0.2077 0.7161 0.920 0.008 0.000 0.008 0.040 0.024
#> GSM680072 2 0.5386 0.4231 0.004 0.604 0.000 0.000 0.204 0.188
#> GSM680078 6 0.6177 0.4488 0.224 0.036 0.040 0.012 0.064 0.624
#> GSM680073 2 0.6165 0.0260 0.004 0.428 0.020 0.000 0.140 0.408
#> GSM680079 1 0.3253 0.7282 0.832 0.000 0.000 0.096 0.004 0.068
#> GSM680074 2 0.1168 0.6700 0.000 0.956 0.000 0.000 0.016 0.028
#> GSM680080 2 0.1408 0.6696 0.000 0.944 0.000 0.000 0.020 0.036
#> GSM680075 6 0.4978 0.6228 0.024 0.036 0.092 0.000 0.108 0.740
#> GSM680081 3 0.4470 0.5260 0.076 0.000 0.752 0.004 0.024 0.144
#> GSM680076 2 0.3754 0.6115 0.076 0.812 0.004 0.000 0.016 0.092
#> GSM680082 1 0.3129 0.7108 0.868 0.048 0.000 0.040 0.012 0.032
#> GSM680029 3 0.4472 -0.0676 0.000 0.000 0.496 0.000 0.028 0.476
#> GSM680041 4 0.1542 0.7928 0.000 0.000 0.008 0.936 0.052 0.004
#> GSM680035 3 0.3566 0.5772 0.000 0.000 0.812 0.008 0.076 0.104
#> GSM680047 4 0.2479 0.7746 0.000 0.000 0.028 0.892 0.064 0.016
#> GSM680036 5 0.3242 0.6580 0.000 0.004 0.032 0.000 0.816 0.148
#> GSM680048 4 0.0551 0.8004 0.004 0.000 0.004 0.984 0.008 0.000
#> GSM680037 3 0.3946 0.4987 0.000 0.000 0.748 0.012 0.032 0.208
#> GSM680049 4 0.1686 0.7914 0.064 0.000 0.012 0.924 0.000 0.000
#> GSM680038 5 0.4408 0.6405 0.004 0.048 0.056 0.024 0.796 0.072
#> GSM680050 1 0.2925 0.7205 0.856 0.000 0.000 0.104 0.024 0.016
#> GSM680039 3 0.4007 0.5352 0.000 0.176 0.764 0.008 0.004 0.048
#> GSM680051 3 0.5034 0.3067 0.000 0.000 0.580 0.356 0.024 0.040
#> GSM680040 3 0.3159 0.5704 0.000 0.000 0.820 0.008 0.020 0.152
#> GSM680052 4 0.1845 0.7894 0.008 0.000 0.072 0.916 0.000 0.004
#> GSM680030 2 0.7895 0.1604 0.028 0.360 0.272 0.008 0.248 0.084
#> GSM680042 4 0.1340 0.7986 0.040 0.000 0.000 0.948 0.008 0.004
#> GSM680031 3 0.3686 0.5251 0.004 0.000 0.772 0.012 0.016 0.196
#> GSM680043 3 0.5271 0.4048 0.024 0.008 0.648 0.248 0.000 0.072
#> GSM680032 1 0.6109 0.5534 0.676 0.120 0.012 0.044 0.068 0.080
#> GSM680044 4 0.4703 0.7098 0.080 0.048 0.028 0.776 0.004 0.064
#> GSM680033 3 0.2476 0.5872 0.000 0.000 0.880 0.004 0.024 0.092
#> GSM680045 4 0.4364 0.4091 0.004 0.000 0.364 0.608 0.000 0.024
#> GSM680034 3 0.5480 0.4255 0.004 0.260 0.636 0.044 0.008 0.048
#> GSM680046 4 0.2848 0.7684 0.036 0.000 0.104 0.856 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> SD:NMF 54 0.207125 0.826 1.07e-05 0.6858 2
#> SD:NMF 42 0.110602 0.364 4.12e-05 0.7122 3
#> SD:NMF 46 0.000552 0.371 8.12e-05 0.0221 4
#> SD:NMF 36 0.009513 0.353 3.57e-03 0.3663 5
#> SD:NMF 37 0.002622 0.517 6.83e-04 0.0683 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 0.170 0.670 0.768 0.3902 0.591 0.591
#> 3 3 0.216 0.614 0.774 0.4792 0.659 0.475
#> 4 4 0.359 0.653 0.712 0.1712 0.886 0.705
#> 5 5 0.452 0.459 0.657 0.0920 0.813 0.474
#> 6 6 0.569 0.609 0.726 0.0765 0.922 0.685
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
#> GSM680053 2 0.8713 0.672 0.292 0.708
#> GSM680062 2 0.8713 0.672 0.292 0.708
#> GSM680054 2 0.8499 0.685 0.276 0.724
#> GSM680063 2 0.8713 0.672 0.292 0.708
#> GSM680055 2 0.8713 0.672 0.292 0.708
#> GSM680064 1 0.6712 0.656 0.824 0.176
#> GSM680056 2 0.8813 0.663 0.300 0.700
#> GSM680065 2 0.8813 0.663 0.300 0.700
#> GSM680057 2 0.2778 0.766 0.048 0.952
#> GSM680066 1 0.9323 0.583 0.652 0.348
#> GSM680058 2 0.1184 0.760 0.016 0.984
#> GSM680067 2 0.1414 0.758 0.020 0.980
#> GSM680059 2 0.0000 0.764 0.000 1.000
#> GSM680068 1 0.9286 0.591 0.656 0.344
#> GSM680060 2 0.7745 0.685 0.228 0.772
#> GSM680069 2 0.7745 0.685 0.228 0.772
#> GSM680061 2 0.1414 0.758 0.020 0.980
#> GSM680070 1 0.9286 0.591 0.656 0.344
#> GSM680071 2 0.7745 0.685 0.228 0.772
#> GSM680077 2 0.9522 0.422 0.372 0.628
#> GSM680072 2 0.0376 0.764 0.004 0.996
#> GSM680078 1 0.9248 0.575 0.660 0.340
#> GSM680073 2 0.4690 0.759 0.100 0.900
#> GSM680079 1 0.6973 0.651 0.812 0.188
#> GSM680074 2 0.0376 0.764 0.004 0.996
#> GSM680080 2 0.0376 0.764 0.004 0.996
#> GSM680075 2 0.4939 0.758 0.108 0.892
#> GSM680081 2 0.5629 0.740 0.132 0.868
#> GSM680076 2 0.9209 0.505 0.336 0.664
#> GSM680082 2 0.9209 0.505 0.336 0.664
#> GSM680029 2 0.6623 0.751 0.172 0.828
#> GSM680041 1 0.3114 0.664 0.944 0.056
#> GSM680035 2 0.5408 0.740 0.124 0.876
#> GSM680047 1 0.6247 0.693 0.844 0.156
#> GSM680036 2 0.6623 0.753 0.172 0.828
#> GSM680048 1 0.9427 0.648 0.640 0.360
#> GSM680037 2 0.5408 0.740 0.124 0.876
#> GSM680049 1 0.2778 0.658 0.952 0.048
#> GSM680038 2 0.2778 0.773 0.048 0.952
#> GSM680050 2 0.9661 0.379 0.392 0.608
#> GSM680039 2 0.4161 0.765 0.084 0.916
#> GSM680051 1 0.9815 0.572 0.580 0.420
#> GSM680040 2 0.3879 0.764 0.076 0.924
#> GSM680052 1 0.9661 0.619 0.608 0.392
#> GSM680030 2 0.3114 0.770 0.056 0.944
#> GSM680042 1 0.3114 0.664 0.944 0.056
#> GSM680031 2 0.3584 0.764 0.068 0.932
#> GSM680043 2 0.3584 0.764 0.068 0.932
#> GSM680032 2 0.9427 0.376 0.360 0.640
#> GSM680044 2 0.9427 0.376 0.360 0.640
#> GSM680033 2 0.3879 0.764 0.076 0.924
#> GSM680045 1 0.9732 0.606 0.596 0.404
#> GSM680034 2 0.2778 0.766 0.048 0.952
#> GSM680046 1 0.9710 0.612 0.600 0.400
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 3 0.5397 0.615 0.000 0.280 0.720
#> GSM680062 3 0.5397 0.615 0.000 0.280 0.720
#> GSM680054 3 0.5988 0.467 0.000 0.368 0.632
#> GSM680063 3 0.5397 0.615 0.000 0.280 0.720
#> GSM680055 3 0.5397 0.615 0.000 0.280 0.720
#> GSM680064 3 0.6675 0.205 0.404 0.012 0.584
#> GSM680056 3 0.5618 0.628 0.008 0.260 0.732
#> GSM680065 3 0.5618 0.628 0.008 0.260 0.732
#> GSM680057 2 0.3009 0.803 0.028 0.920 0.052
#> GSM680066 3 0.9389 0.335 0.352 0.180 0.468
#> GSM680058 2 0.2414 0.796 0.020 0.940 0.040
#> GSM680067 2 0.2443 0.794 0.028 0.940 0.032
#> GSM680059 2 0.1031 0.807 0.000 0.976 0.024
#> GSM680068 3 0.9328 0.330 0.356 0.172 0.472
#> GSM680060 3 0.6698 0.590 0.036 0.280 0.684
#> GSM680069 3 0.6698 0.590 0.036 0.280 0.684
#> GSM680061 2 0.2443 0.794 0.028 0.940 0.032
#> GSM680070 3 0.9328 0.330 0.356 0.172 0.472
#> GSM680071 3 0.6698 0.590 0.036 0.280 0.684
#> GSM680077 3 0.3412 0.550 0.000 0.124 0.876
#> GSM680072 2 0.1529 0.803 0.000 0.960 0.040
#> GSM680078 3 0.9447 0.342 0.348 0.188 0.464
#> GSM680073 2 0.3752 0.732 0.000 0.856 0.144
#> GSM680079 3 0.6566 0.232 0.376 0.012 0.612
#> GSM680074 2 0.1411 0.804 0.000 0.964 0.036
#> GSM680080 2 0.1411 0.804 0.000 0.964 0.036
#> GSM680075 2 0.3941 0.718 0.000 0.844 0.156
#> GSM680081 2 0.4002 0.752 0.000 0.840 0.160
#> GSM680076 3 0.4473 0.573 0.008 0.164 0.828
#> GSM680082 3 0.4413 0.573 0.008 0.160 0.832
#> GSM680029 2 0.4452 0.705 0.000 0.808 0.192
#> GSM680041 1 0.0000 0.630 1.000 0.000 0.000
#> GSM680035 2 0.3816 0.759 0.000 0.852 0.148
#> GSM680047 1 0.3532 0.668 0.884 0.108 0.008
#> GSM680036 2 0.5016 0.622 0.000 0.760 0.240
#> GSM680048 1 0.7218 0.681 0.652 0.296 0.052
#> GSM680037 2 0.3816 0.759 0.000 0.852 0.148
#> GSM680049 1 0.0424 0.625 0.992 0.000 0.008
#> GSM680038 2 0.5223 0.706 0.024 0.800 0.176
#> GSM680050 3 0.5138 0.545 0.052 0.120 0.828
#> GSM680039 2 0.2955 0.798 0.008 0.912 0.080
#> GSM680051 1 0.7658 0.640 0.588 0.356 0.056
#> GSM680040 2 0.2537 0.795 0.000 0.920 0.080
#> GSM680052 1 0.7425 0.677 0.620 0.328 0.052
#> GSM680030 2 0.4683 0.753 0.024 0.836 0.140
#> GSM680042 1 0.0000 0.630 1.000 0.000 0.000
#> GSM680031 2 0.3045 0.802 0.020 0.916 0.064
#> GSM680043 2 0.3045 0.802 0.020 0.916 0.064
#> GSM680032 2 0.9247 -0.199 0.156 0.452 0.392
#> GSM680044 2 0.9247 -0.199 0.156 0.452 0.392
#> GSM680033 2 0.2537 0.795 0.000 0.920 0.080
#> GSM680045 1 0.7492 0.664 0.608 0.340 0.052
#> GSM680034 2 0.3009 0.803 0.028 0.920 0.052
#> GSM680046 1 0.7470 0.670 0.612 0.336 0.052
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 1 0.7456 0.563 0.488 0.316 0.196 0.000
#> GSM680062 1 0.7456 0.563 0.488 0.316 0.196 0.000
#> GSM680054 1 0.7688 0.534 0.456 0.260 0.284 0.000
#> GSM680063 1 0.7456 0.563 0.488 0.316 0.196 0.000
#> GSM680055 1 0.7456 0.563 0.488 0.316 0.196 0.000
#> GSM680064 1 0.5953 0.312 0.692 0.092 0.004 0.212
#> GSM680056 1 0.7629 0.549 0.488 0.332 0.172 0.008
#> GSM680065 1 0.7629 0.549 0.488 0.332 0.172 0.008
#> GSM680057 3 0.4401 0.736 0.068 0.084 0.832 0.016
#> GSM680066 1 0.6720 0.494 0.684 0.040 0.116 0.160
#> GSM680058 3 0.4294 0.748 0.052 0.104 0.832 0.012
#> GSM680067 3 0.3935 0.738 0.060 0.060 0.860 0.020
#> GSM680059 3 0.3229 0.771 0.072 0.048 0.880 0.000
#> GSM680068 1 0.6616 0.492 0.692 0.040 0.108 0.160
#> GSM680060 2 0.3319 0.811 0.036 0.888 0.060 0.016
#> GSM680069 2 0.3319 0.811 0.036 0.888 0.060 0.016
#> GSM680061 3 0.3935 0.738 0.060 0.060 0.860 0.020
#> GSM680070 1 0.6616 0.492 0.692 0.040 0.108 0.160
#> GSM680071 2 0.3319 0.811 0.036 0.888 0.060 0.016
#> GSM680077 2 0.3764 0.756 0.216 0.784 0.000 0.000
#> GSM680072 3 0.3978 0.750 0.056 0.108 0.836 0.000
#> GSM680078 1 0.6942 0.493 0.672 0.048 0.128 0.152
#> GSM680073 3 0.5165 0.684 0.168 0.080 0.752 0.000
#> GSM680079 1 0.5674 0.309 0.724 0.096 0.004 0.176
#> GSM680074 3 0.4072 0.739 0.052 0.120 0.828 0.000
#> GSM680080 3 0.4072 0.739 0.052 0.120 0.828 0.000
#> GSM680075 3 0.5314 0.671 0.176 0.084 0.740 0.000
#> GSM680081 3 0.3870 0.696 0.208 0.004 0.788 0.000
#> GSM680076 2 0.2401 0.823 0.092 0.904 0.004 0.000
#> GSM680082 2 0.2216 0.822 0.092 0.908 0.000 0.000
#> GSM680029 3 0.4818 0.629 0.216 0.036 0.748 0.000
#> GSM680041 4 0.0188 0.641 0.004 0.000 0.000 0.996
#> GSM680035 3 0.3610 0.708 0.200 0.000 0.800 0.000
#> GSM680047 4 0.2899 0.693 0.004 0.004 0.112 0.880
#> GSM680036 3 0.5716 0.526 0.252 0.068 0.680 0.000
#> GSM680048 4 0.6217 0.717 0.052 0.016 0.288 0.644
#> GSM680037 3 0.3610 0.708 0.200 0.000 0.800 0.000
#> GSM680049 4 0.0469 0.635 0.012 0.000 0.000 0.988
#> GSM680038 3 0.6499 0.626 0.156 0.148 0.680 0.016
#> GSM680050 2 0.4994 0.740 0.208 0.744 0.000 0.048
#> GSM680039 3 0.3160 0.760 0.120 0.004 0.868 0.008
#> GSM680051 4 0.6656 0.682 0.056 0.020 0.344 0.580
#> GSM680040 3 0.2760 0.753 0.128 0.000 0.872 0.000
#> GSM680052 4 0.6467 0.713 0.052 0.020 0.316 0.612
#> GSM680030 3 0.5926 0.664 0.144 0.112 0.728 0.016
#> GSM680042 4 0.0188 0.641 0.004 0.000 0.000 0.996
#> GSM680031 3 0.3255 0.755 0.092 0.016 0.880 0.012
#> GSM680043 3 0.3255 0.755 0.092 0.016 0.880 0.012
#> GSM680032 1 0.7437 0.353 0.516 0.080 0.368 0.036
#> GSM680044 1 0.7437 0.353 0.516 0.080 0.368 0.036
#> GSM680033 3 0.2760 0.753 0.128 0.000 0.872 0.000
#> GSM680045 4 0.6734 0.698 0.068 0.020 0.316 0.596
#> GSM680034 3 0.4401 0.736 0.068 0.084 0.832 0.016
#> GSM680046 4 0.6670 0.706 0.064 0.020 0.316 0.600
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.8490 0.2996 0.276 0.168 0.268 0.000 0.288
#> GSM680062 5 0.8490 0.2996 0.276 0.168 0.268 0.000 0.288
#> GSM680054 3 0.8461 -0.2705 0.244 0.180 0.336 0.000 0.240
#> GSM680063 5 0.8490 0.2996 0.276 0.168 0.268 0.000 0.288
#> GSM680055 5 0.8490 0.2996 0.276 0.168 0.268 0.000 0.288
#> GSM680064 1 0.1788 0.7460 0.932 0.004 0.000 0.056 0.008
#> GSM680056 5 0.8601 0.2983 0.280 0.168 0.244 0.004 0.304
#> GSM680065 5 0.8601 0.2983 0.280 0.168 0.244 0.004 0.304
#> GSM680057 2 0.4108 0.7211 0.000 0.684 0.308 0.008 0.000
#> GSM680066 1 0.3516 0.8513 0.812 0.004 0.164 0.020 0.000
#> GSM680058 3 0.4736 -0.1948 0.000 0.404 0.576 0.000 0.020
#> GSM680067 2 0.3700 0.6891 0.000 0.752 0.240 0.008 0.000
#> GSM680059 3 0.1728 0.4767 0.000 0.036 0.940 0.004 0.020
#> GSM680068 1 0.3435 0.8575 0.820 0.004 0.156 0.020 0.000
#> GSM680060 5 0.3786 0.4384 0.016 0.204 0.000 0.004 0.776
#> GSM680069 5 0.3786 0.4384 0.016 0.204 0.000 0.004 0.776
#> GSM680061 2 0.3700 0.6891 0.000 0.752 0.240 0.008 0.000
#> GSM680070 1 0.3435 0.8575 0.820 0.004 0.156 0.020 0.000
#> GSM680071 5 0.3786 0.4384 0.016 0.204 0.000 0.004 0.776
#> GSM680077 5 0.3607 0.3146 0.244 0.004 0.000 0.000 0.752
#> GSM680072 3 0.4675 -0.1125 0.000 0.380 0.600 0.000 0.020
#> GSM680078 1 0.3461 0.8248 0.812 0.000 0.168 0.016 0.004
#> GSM680073 3 0.4338 0.4924 0.068 0.072 0.808 0.000 0.052
#> GSM680079 1 0.1377 0.7466 0.956 0.004 0.000 0.020 0.020
#> GSM680074 3 0.4752 -0.1863 0.000 0.412 0.568 0.000 0.020
#> GSM680080 3 0.4752 -0.1863 0.000 0.412 0.568 0.000 0.020
#> GSM680075 3 0.4531 0.4909 0.072 0.072 0.796 0.000 0.060
#> GSM680081 3 0.3210 0.5315 0.092 0.040 0.860 0.000 0.008
#> GSM680076 5 0.0932 0.4355 0.020 0.004 0.004 0.000 0.972
#> GSM680082 5 0.0865 0.4343 0.024 0.004 0.000 0.000 0.972
#> GSM680029 3 0.4060 0.5288 0.120 0.032 0.812 0.000 0.036
#> GSM680041 4 0.0162 0.6792 0.004 0.000 0.000 0.996 0.000
#> GSM680035 3 0.2871 0.5336 0.088 0.040 0.872 0.000 0.000
#> GSM680047 4 0.3073 0.7133 0.004 0.052 0.076 0.868 0.000
#> GSM680036 3 0.5022 0.4879 0.136 0.060 0.752 0.000 0.052
#> GSM680048 4 0.6050 0.7237 0.024 0.216 0.128 0.632 0.000
#> GSM680037 3 0.2871 0.5336 0.088 0.040 0.872 0.000 0.000
#> GSM680049 4 0.0794 0.6696 0.028 0.000 0.000 0.972 0.000
#> GSM680038 2 0.6299 0.3575 0.044 0.464 0.444 0.004 0.044
#> GSM680050 5 0.4608 0.2997 0.260 0.004 0.000 0.036 0.700
#> GSM680039 3 0.2885 0.5033 0.052 0.064 0.880 0.004 0.000
#> GSM680051 4 0.6370 0.6787 0.020 0.260 0.144 0.576 0.000
#> GSM680040 3 0.1591 0.5382 0.052 0.004 0.940 0.004 0.000
#> GSM680052 4 0.6155 0.7138 0.020 0.240 0.132 0.608 0.000
#> GSM680030 2 0.5202 0.5976 0.012 0.636 0.316 0.004 0.032
#> GSM680042 4 0.0162 0.6792 0.004 0.000 0.000 0.996 0.000
#> GSM680031 3 0.4245 0.3067 0.024 0.224 0.744 0.008 0.000
#> GSM680043 3 0.4245 0.3067 0.024 0.224 0.744 0.008 0.000
#> GSM680032 3 0.7923 -0.0179 0.352 0.176 0.388 0.008 0.076
#> GSM680044 3 0.7923 -0.0179 0.352 0.176 0.388 0.008 0.076
#> GSM680033 3 0.1830 0.5362 0.052 0.012 0.932 0.004 0.000
#> GSM680045 4 0.6436 0.7006 0.028 0.236 0.148 0.588 0.000
#> GSM680034 2 0.4108 0.7211 0.000 0.684 0.308 0.008 0.000
#> GSM680046 4 0.6389 0.7069 0.028 0.240 0.140 0.592 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.2277 0.8290 0.032 0.000 0.076 0.000 0.892 0.000
#> GSM680062 5 0.2277 0.8290 0.032 0.000 0.076 0.000 0.892 0.000
#> GSM680054 5 0.3399 0.7495 0.020 0.024 0.140 0.000 0.816 0.000
#> GSM680063 5 0.2277 0.8290 0.032 0.000 0.076 0.000 0.892 0.000
#> GSM680055 5 0.2277 0.8290 0.032 0.000 0.076 0.000 0.892 0.000
#> GSM680064 1 0.1382 0.7875 0.948 0.000 0.000 0.036 0.008 0.008
#> GSM680056 5 0.1930 0.8180 0.036 0.000 0.048 0.000 0.916 0.000
#> GSM680065 5 0.1930 0.8180 0.036 0.000 0.048 0.000 0.916 0.000
#> GSM680057 2 0.3841 0.7011 0.000 0.764 0.168 0.000 0.068 0.000
#> GSM680066 1 0.3462 0.8678 0.816 0.004 0.080 0.000 0.100 0.000
#> GSM680058 3 0.4962 0.0802 0.004 0.412 0.536 0.000 0.040 0.008
#> GSM680067 2 0.1901 0.6214 0.000 0.912 0.076 0.004 0.008 0.000
#> GSM680059 3 0.0976 0.5795 0.000 0.008 0.968 0.000 0.016 0.008
#> GSM680068 1 0.3324 0.8763 0.824 0.004 0.060 0.000 0.112 0.000
#> GSM680060 6 0.5463 0.6453 0.000 0.148 0.000 0.000 0.312 0.540
#> GSM680069 6 0.5463 0.6453 0.000 0.148 0.000 0.000 0.312 0.540
#> GSM680061 2 0.1901 0.6214 0.000 0.912 0.076 0.004 0.008 0.000
#> GSM680070 1 0.3324 0.8763 0.824 0.004 0.060 0.000 0.112 0.000
#> GSM680071 6 0.5463 0.6453 0.000 0.148 0.000 0.000 0.312 0.540
#> GSM680077 6 0.3641 0.5986 0.248 0.000 0.000 0.000 0.020 0.732
#> GSM680072 3 0.5025 0.1501 0.004 0.384 0.556 0.000 0.048 0.008
#> GSM680078 1 0.3370 0.8404 0.812 0.000 0.064 0.000 0.124 0.000
#> GSM680073 3 0.3806 0.5104 0.004 0.008 0.724 0.000 0.256 0.008
#> GSM680079 1 0.0717 0.7884 0.976 0.000 0.000 0.000 0.008 0.016
#> GSM680074 3 0.4863 0.0848 0.004 0.428 0.528 0.000 0.032 0.008
#> GSM680080 3 0.4863 0.0848 0.004 0.428 0.528 0.000 0.032 0.008
#> GSM680075 3 0.4087 0.4569 0.004 0.008 0.668 0.000 0.312 0.008
#> GSM680081 3 0.3490 0.5423 0.000 0.008 0.724 0.000 0.268 0.000
#> GSM680076 6 0.1176 0.6786 0.020 0.000 0.000 0.000 0.024 0.956
#> GSM680082 6 0.1261 0.6783 0.024 0.000 0.000 0.000 0.024 0.952
#> GSM680029 3 0.3758 0.5206 0.008 0.000 0.668 0.000 0.324 0.000
#> GSM680041 4 0.0146 0.6747 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM680035 3 0.3073 0.5981 0.000 0.008 0.788 0.000 0.204 0.000
#> GSM680047 4 0.2891 0.7148 0.000 0.036 0.060 0.872 0.032 0.000
#> GSM680036 3 0.4063 0.3519 0.004 0.004 0.572 0.000 0.420 0.000
#> GSM680048 4 0.5847 0.7312 0.000 0.172 0.104 0.632 0.092 0.000
#> GSM680037 3 0.3073 0.5981 0.000 0.008 0.788 0.000 0.204 0.000
#> GSM680049 4 0.0777 0.6621 0.024 0.000 0.000 0.972 0.004 0.000
#> GSM680038 2 0.6078 0.2815 0.000 0.420 0.352 0.000 0.224 0.004
#> GSM680050 6 0.4268 0.5840 0.264 0.000 0.000 0.036 0.008 0.692
#> GSM680039 3 0.3384 0.5965 0.000 0.068 0.812 0.000 0.120 0.000
#> GSM680051 4 0.6323 0.6944 0.000 0.216 0.112 0.568 0.104 0.000
#> GSM680040 3 0.2191 0.6192 0.000 0.004 0.876 0.000 0.120 0.000
#> GSM680052 4 0.6090 0.7228 0.000 0.196 0.108 0.600 0.096 0.000
#> GSM680030 2 0.5276 0.5790 0.000 0.604 0.188 0.000 0.208 0.000
#> GSM680042 4 0.0146 0.6747 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM680031 3 0.4383 0.4096 0.000 0.176 0.716 0.000 0.108 0.000
#> GSM680043 3 0.4383 0.4096 0.000 0.176 0.716 0.000 0.108 0.000
#> GSM680032 5 0.7071 0.3320 0.264 0.056 0.212 0.000 0.452 0.016
#> GSM680044 5 0.7071 0.3320 0.264 0.056 0.212 0.000 0.452 0.016
#> GSM680033 3 0.2489 0.6194 0.000 0.012 0.860 0.000 0.128 0.000
#> GSM680045 4 0.6615 0.7088 0.016 0.196 0.116 0.572 0.100 0.000
#> GSM680034 2 0.3841 0.7011 0.000 0.764 0.168 0.000 0.068 0.000
#> GSM680046 4 0.6581 0.7149 0.016 0.196 0.108 0.576 0.104 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> CV:hclust 50 0.168948 0.9565 6.51e-06 0.5512 2
#> CV:hclust 45 0.000104 0.2603 9.45e-05 0.1902 3
#> CV:hclust 46 0.000209 0.0218 3.30e-04 0.0198 4
#> CV:hclust 27 0.000404 0.7112 1.79e-04 0.1853 5
#> CV:hclust 43 0.000077 0.0664 4.69e-04 0.0274 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 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 0.930 0.923 0.946 0.5003 0.502 0.502
#> 3 3 0.436 0.588 0.718 0.3099 0.785 0.593
#> 4 4 0.591 0.761 0.824 0.1410 0.808 0.502
#> 5 5 0.675 0.659 0.767 0.0674 0.934 0.735
#> 6 6 0.725 0.614 0.766 0.0419 0.936 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
#> GSM680053 2 0.1184 0.938 0.016 0.984
#> GSM680062 2 0.9944 0.262 0.456 0.544
#> GSM680054 2 0.1414 0.941 0.020 0.980
#> GSM680063 2 0.8207 0.708 0.256 0.744
#> GSM680055 2 0.1184 0.938 0.016 0.984
#> GSM680064 1 0.2043 0.965 0.968 0.032
#> GSM680056 1 0.5294 0.908 0.880 0.120
#> GSM680065 1 0.3114 0.957 0.944 0.056
#> GSM680057 2 0.3274 0.934 0.060 0.940
#> GSM680066 1 0.3274 0.957 0.940 0.060
#> GSM680058 2 0.1184 0.938 0.016 0.984
#> GSM680067 2 0.3114 0.935 0.056 0.944
#> GSM680059 2 0.0938 0.941 0.012 0.988
#> GSM680068 1 0.1843 0.965 0.972 0.028
#> GSM680060 2 0.1414 0.937 0.020 0.980
#> GSM680069 2 0.6343 0.810 0.160 0.840
#> GSM680061 2 0.3114 0.935 0.056 0.944
#> GSM680070 1 0.2043 0.964 0.968 0.032
#> GSM680071 2 0.7602 0.747 0.220 0.780
#> GSM680077 1 0.3114 0.956 0.944 0.056
#> GSM680072 2 0.0672 0.938 0.008 0.992
#> GSM680078 1 0.4022 0.953 0.920 0.080
#> GSM680073 2 0.0938 0.937 0.012 0.988
#> GSM680079 1 0.3114 0.956 0.944 0.056
#> GSM680074 2 0.1184 0.938 0.016 0.984
#> GSM680080 2 0.0938 0.937 0.012 0.988
#> GSM680075 2 0.0938 0.937 0.012 0.988
#> GSM680081 2 0.2778 0.939 0.048 0.952
#> GSM680076 2 0.1184 0.935 0.016 0.984
#> GSM680082 1 0.3114 0.956 0.944 0.056
#> GSM680029 2 0.1184 0.940 0.016 0.984
#> GSM680041 1 0.0938 0.964 0.988 0.012
#> GSM680035 2 0.2948 0.937 0.052 0.948
#> GSM680047 1 0.1184 0.964 0.984 0.016
#> GSM680036 2 0.1184 0.938 0.016 0.984
#> GSM680048 1 0.1633 0.964 0.976 0.024
#> GSM680037 2 0.2948 0.937 0.052 0.948
#> GSM680049 1 0.0672 0.963 0.992 0.008
#> GSM680038 2 0.2236 0.939 0.036 0.964
#> GSM680050 1 0.2778 0.957 0.952 0.048
#> GSM680039 2 0.3114 0.934 0.056 0.944
#> GSM680051 1 0.2043 0.961 0.968 0.032
#> GSM680040 2 0.2948 0.937 0.052 0.948
#> GSM680052 1 0.2043 0.961 0.968 0.032
#> GSM680030 2 0.3114 0.937 0.056 0.944
#> GSM680042 1 0.0672 0.964 0.992 0.008
#> GSM680031 2 0.2948 0.937 0.052 0.948
#> GSM680043 1 0.1843 0.962 0.972 0.028
#> GSM680032 1 0.3274 0.957 0.940 0.060
#> GSM680044 1 0.2043 0.963 0.968 0.032
#> GSM680033 2 0.2948 0.937 0.052 0.948
#> GSM680045 1 0.2778 0.950 0.952 0.048
#> GSM680034 2 0.3274 0.934 0.060 0.940
#> GSM680046 1 0.0938 0.964 0.988 0.012
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 3 0.280 0.6413 0.016 0.060 0.924
#> GSM680062 3 0.683 0.5365 0.148 0.112 0.740
#> GSM680054 3 0.571 -0.1798 0.000 0.320 0.680
#> GSM680063 3 0.453 0.6318 0.052 0.088 0.860
#> GSM680055 3 0.280 0.6413 0.016 0.060 0.924
#> GSM680064 1 0.572 0.7529 0.704 0.292 0.004
#> GSM680056 3 0.958 0.0784 0.216 0.320 0.464
#> GSM680065 1 0.774 0.7243 0.608 0.324 0.068
#> GSM680057 2 0.615 0.6479 0.000 0.592 0.408
#> GSM680066 1 0.910 0.6559 0.456 0.404 0.140
#> GSM680058 2 0.631 0.6609 0.000 0.508 0.492
#> GSM680067 2 0.848 0.5732 0.224 0.612 0.164
#> GSM680059 3 0.319 0.6309 0.000 0.112 0.888
#> GSM680068 1 0.742 0.7473 0.632 0.312 0.056
#> GSM680060 2 0.630 0.6687 0.000 0.520 0.480
#> GSM680069 3 0.576 0.5131 0.028 0.208 0.764
#> GSM680061 2 0.852 0.5940 0.208 0.612 0.180
#> GSM680070 1 0.749 0.7433 0.620 0.324 0.056
#> GSM680071 2 0.680 0.4183 0.072 0.724 0.204
#> GSM680077 1 0.762 0.7363 0.596 0.348 0.056
#> GSM680072 3 0.581 -0.2843 0.000 0.336 0.664
#> GSM680078 3 0.952 0.0482 0.212 0.312 0.476
#> GSM680073 3 0.141 0.6204 0.000 0.036 0.964
#> GSM680079 1 0.754 0.7424 0.612 0.332 0.056
#> GSM680074 2 0.631 0.6606 0.000 0.512 0.488
#> GSM680080 2 0.631 0.6573 0.000 0.508 0.492
#> GSM680075 3 0.153 0.6362 0.000 0.040 0.960
#> GSM680081 3 0.348 0.6514 0.000 0.128 0.872
#> GSM680076 2 0.632 0.6015 0.008 0.636 0.356
#> GSM680082 1 0.749 0.7412 0.608 0.340 0.052
#> GSM680029 3 0.263 0.6612 0.000 0.084 0.916
#> GSM680041 1 0.175 0.7546 0.952 0.048 0.000
#> GSM680035 3 0.364 0.6447 0.004 0.124 0.872
#> GSM680047 1 0.389 0.7339 0.880 0.096 0.024
#> GSM680036 3 0.164 0.6421 0.000 0.044 0.956
#> GSM680048 1 0.380 0.7349 0.884 0.092 0.024
#> GSM680037 3 0.364 0.6447 0.004 0.124 0.872
#> GSM680049 1 0.103 0.7615 0.976 0.024 0.000
#> GSM680038 3 0.631 -0.6949 0.000 0.492 0.508
#> GSM680050 1 0.607 0.7470 0.676 0.316 0.008
#> GSM680039 2 0.623 0.6142 0.000 0.564 0.436
#> GSM680051 1 0.432 0.7215 0.860 0.112 0.028
#> GSM680040 3 0.364 0.6447 0.004 0.124 0.872
#> GSM680052 1 0.432 0.7215 0.860 0.112 0.028
#> GSM680030 2 0.624 0.6674 0.000 0.560 0.440
#> GSM680042 1 0.153 0.7566 0.960 0.040 0.000
#> GSM680031 3 0.364 0.6447 0.004 0.124 0.872
#> GSM680043 1 0.668 0.6927 0.748 0.152 0.100
#> GSM680032 1 0.772 0.7363 0.612 0.320 0.068
#> GSM680044 1 0.492 0.7519 0.844 0.080 0.076
#> GSM680033 3 0.364 0.6447 0.004 0.124 0.872
#> GSM680045 1 0.669 0.6896 0.748 0.148 0.104
#> GSM680034 2 0.873 0.5824 0.208 0.592 0.200
#> GSM680046 1 0.303 0.7472 0.912 0.076 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 3 0.5789 0.745 0.116 0.120 0.744 0.020
#> GSM680062 3 0.6237 0.742 0.116 0.096 0.732 0.056
#> GSM680054 2 0.6566 0.295 0.056 0.552 0.380 0.012
#> GSM680063 3 0.6027 0.743 0.116 0.116 0.736 0.032
#> GSM680055 3 0.5789 0.745 0.116 0.120 0.744 0.020
#> GSM680064 1 0.4408 0.756 0.756 0.008 0.004 0.232
#> GSM680056 1 0.6659 0.585 0.696 0.116 0.140 0.048
#> GSM680065 1 0.5101 0.721 0.800 0.036 0.072 0.092
#> GSM680057 2 0.4364 0.798 0.004 0.792 0.180 0.024
#> GSM680066 1 0.5199 0.753 0.764 0.004 0.088 0.144
#> GSM680058 2 0.1767 0.813 0.000 0.944 0.044 0.012
#> GSM680067 2 0.4535 0.792 0.000 0.804 0.112 0.084
#> GSM680059 3 0.4333 0.752 0.032 0.148 0.812 0.008
#> GSM680068 1 0.3538 0.804 0.832 0.004 0.004 0.160
#> GSM680060 2 0.0804 0.814 0.000 0.980 0.012 0.008
#> GSM680069 1 0.7790 -0.141 0.436 0.128 0.412 0.024
#> GSM680061 2 0.4469 0.794 0.000 0.808 0.112 0.080
#> GSM680070 1 0.3355 0.805 0.836 0.004 0.000 0.160
#> GSM680071 2 0.4484 0.731 0.052 0.836 0.072 0.040
#> GSM680077 1 0.3519 0.812 0.852 0.016 0.004 0.128
#> GSM680072 2 0.5679 0.573 0.068 0.716 0.208 0.008
#> GSM680078 1 0.3558 0.761 0.872 0.008 0.072 0.048
#> GSM680073 3 0.6624 0.728 0.128 0.220 0.644 0.008
#> GSM680079 1 0.3105 0.811 0.856 0.000 0.004 0.140
#> GSM680074 2 0.2923 0.816 0.016 0.896 0.080 0.008
#> GSM680080 2 0.2923 0.816 0.016 0.896 0.080 0.008
#> GSM680075 3 0.6574 0.735 0.132 0.208 0.652 0.008
#> GSM680081 3 0.2563 0.805 0.012 0.060 0.916 0.012
#> GSM680076 2 0.2790 0.789 0.072 0.904 0.012 0.012
#> GSM680082 1 0.3606 0.811 0.840 0.020 0.000 0.140
#> GSM680029 3 0.2652 0.804 0.028 0.056 0.912 0.004
#> GSM680041 4 0.1786 0.878 0.036 0.008 0.008 0.948
#> GSM680035 3 0.2515 0.806 0.004 0.072 0.912 0.012
#> GSM680047 4 0.1151 0.892 0.000 0.008 0.024 0.968
#> GSM680036 3 0.5620 0.759 0.120 0.120 0.748 0.012
#> GSM680048 4 0.1174 0.896 0.012 0.000 0.020 0.968
#> GSM680037 3 0.2515 0.806 0.004 0.072 0.912 0.012
#> GSM680049 4 0.2053 0.873 0.072 0.004 0.000 0.924
#> GSM680038 2 0.3599 0.801 0.020 0.868 0.092 0.020
#> GSM680050 1 0.4527 0.786 0.780 0.020 0.008 0.192
#> GSM680039 2 0.5085 0.707 0.004 0.688 0.292 0.016
#> GSM680051 4 0.1821 0.889 0.008 0.012 0.032 0.948
#> GSM680040 3 0.2515 0.806 0.004 0.072 0.912 0.012
#> GSM680052 4 0.1398 0.893 0.004 0.000 0.040 0.956
#> GSM680030 2 0.3855 0.808 0.004 0.820 0.164 0.012
#> GSM680042 4 0.2221 0.874 0.044 0.016 0.008 0.932
#> GSM680031 3 0.2515 0.806 0.004 0.072 0.912 0.012
#> GSM680043 4 0.5632 0.742 0.084 0.008 0.176 0.732
#> GSM680032 1 0.3823 0.802 0.852 0.028 0.012 0.108
#> GSM680044 4 0.5165 0.734 0.180 0.012 0.048 0.760
#> GSM680033 3 0.2515 0.806 0.004 0.072 0.912 0.012
#> GSM680045 4 0.4698 0.772 0.032 0.008 0.180 0.780
#> GSM680034 2 0.5257 0.780 0.004 0.756 0.160 0.080
#> GSM680046 4 0.1488 0.894 0.032 0.000 0.012 0.956
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.5554 0.558 0.004 0.028 0.452 0.016 0.500
#> GSM680062 5 0.5922 0.556 0.004 0.028 0.452 0.036 0.480
#> GSM680054 2 0.6685 -0.124 0.000 0.388 0.236 0.000 0.376
#> GSM680063 5 0.5718 0.554 0.004 0.028 0.464 0.024 0.480
#> GSM680055 5 0.5756 0.568 0.012 0.028 0.444 0.016 0.500
#> GSM680064 1 0.3806 0.822 0.812 0.000 0.000 0.104 0.084
#> GSM680056 5 0.5805 0.349 0.304 0.008 0.048 0.024 0.616
#> GSM680065 5 0.4907 -0.156 0.488 0.000 0.000 0.024 0.488
#> GSM680057 2 0.3373 0.732 0.000 0.816 0.168 0.008 0.008
#> GSM680066 1 0.3171 0.850 0.872 0.004 0.060 0.056 0.008
#> GSM680058 2 0.2125 0.747 0.000 0.920 0.024 0.004 0.052
#> GSM680067 2 0.3893 0.736 0.004 0.820 0.100 0.072 0.004
#> GSM680059 3 0.5888 0.523 0.020 0.144 0.652 0.000 0.184
#> GSM680068 1 0.2213 0.869 0.912 0.004 0.008 0.072 0.004
#> GSM680060 2 0.1831 0.748 0.000 0.920 0.004 0.000 0.076
#> GSM680069 5 0.6703 0.550 0.176 0.016 0.208 0.016 0.584
#> GSM680061 2 0.3705 0.740 0.004 0.832 0.100 0.060 0.004
#> GSM680070 1 0.0955 0.880 0.968 0.000 0.000 0.028 0.004
#> GSM680071 2 0.4551 0.422 0.004 0.556 0.000 0.004 0.436
#> GSM680077 1 0.3559 0.861 0.844 0.012 0.012 0.020 0.112
#> GSM680072 2 0.6300 0.426 0.020 0.552 0.092 0.004 0.332
#> GSM680078 1 0.3294 0.824 0.868 0.012 0.036 0.008 0.076
#> GSM680073 3 0.6878 0.242 0.020 0.168 0.440 0.000 0.372
#> GSM680079 1 0.2978 0.872 0.880 0.004 0.012 0.024 0.080
#> GSM680074 2 0.3680 0.714 0.004 0.820 0.032 0.004 0.140
#> GSM680080 2 0.3680 0.714 0.004 0.820 0.032 0.004 0.140
#> GSM680075 3 0.6812 0.256 0.024 0.148 0.464 0.000 0.364
#> GSM680081 3 0.0798 0.741 0.016 0.008 0.976 0.000 0.000
#> GSM680076 2 0.4019 0.679 0.028 0.768 0.000 0.004 0.200
#> GSM680082 1 0.3068 0.870 0.876 0.032 0.000 0.020 0.072
#> GSM680029 3 0.2889 0.702 0.016 0.020 0.880 0.000 0.084
#> GSM680041 4 0.2077 0.831 0.008 0.000 0.000 0.908 0.084
#> GSM680035 3 0.0671 0.759 0.000 0.016 0.980 0.004 0.000
#> GSM680047 4 0.1502 0.839 0.004 0.000 0.000 0.940 0.056
#> GSM680036 5 0.5481 0.355 0.016 0.032 0.456 0.000 0.496
#> GSM680048 4 0.1205 0.841 0.004 0.000 0.000 0.956 0.040
#> GSM680037 3 0.0671 0.759 0.000 0.016 0.980 0.004 0.000
#> GSM680049 4 0.2694 0.820 0.040 0.000 0.000 0.884 0.076
#> GSM680038 2 0.3731 0.725 0.000 0.816 0.072 0.000 0.112
#> GSM680050 1 0.4240 0.838 0.792 0.008 0.012 0.036 0.152
#> GSM680039 2 0.4523 0.554 0.000 0.640 0.344 0.012 0.004
#> GSM680051 4 0.1018 0.837 0.000 0.016 0.016 0.968 0.000
#> GSM680040 3 0.0671 0.759 0.000 0.016 0.980 0.004 0.000
#> GSM680052 4 0.0912 0.838 0.000 0.016 0.012 0.972 0.000
#> GSM680030 2 0.3815 0.736 0.000 0.804 0.156 0.008 0.032
#> GSM680042 4 0.2189 0.831 0.012 0.000 0.000 0.904 0.084
#> GSM680031 3 0.0960 0.753 0.000 0.016 0.972 0.004 0.008
#> GSM680043 4 0.6523 0.557 0.128 0.016 0.264 0.580 0.012
#> GSM680032 1 0.3806 0.834 0.824 0.020 0.004 0.024 0.128
#> GSM680044 4 0.6553 0.368 0.328 0.004 0.056 0.548 0.064
#> GSM680033 3 0.0671 0.759 0.000 0.016 0.980 0.004 0.000
#> GSM680045 4 0.5599 0.611 0.052 0.016 0.264 0.656 0.012
#> GSM680034 2 0.4384 0.723 0.004 0.784 0.136 0.068 0.008
#> GSM680046 4 0.1686 0.831 0.036 0.012 0.004 0.944 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.4470 0.6332 0.000 0.012 0.300 0.000 0.656 0.032
#> GSM680062 5 0.4813 0.6418 0.000 0.008 0.284 0.028 0.656 0.024
#> GSM680054 5 0.6517 0.4073 0.000 0.280 0.188 0.000 0.484 0.048
#> GSM680063 5 0.4759 0.6415 0.000 0.008 0.288 0.024 0.656 0.024
#> GSM680055 5 0.4416 0.6392 0.000 0.012 0.288 0.000 0.668 0.032
#> GSM680064 1 0.5873 0.4927 0.612 0.000 0.000 0.216 0.076 0.096
#> GSM680056 5 0.3209 0.5772 0.124 0.004 0.028 0.004 0.836 0.004
#> GSM680065 5 0.3183 0.5203 0.196 0.000 0.004 0.004 0.792 0.004
#> GSM680057 2 0.2039 0.7655 0.000 0.908 0.072 0.000 0.016 0.004
#> GSM680066 1 0.2432 0.7262 0.908 0.024 0.020 0.036 0.004 0.008
#> GSM680058 2 0.2450 0.7301 0.000 0.868 0.000 0.000 0.016 0.116
#> GSM680067 2 0.1225 0.7693 0.000 0.952 0.012 0.036 0.000 0.000
#> GSM680059 3 0.5090 -0.2971 0.004 0.028 0.528 0.004 0.016 0.420
#> GSM680068 1 0.1585 0.7307 0.940 0.004 0.004 0.044 0.004 0.004
#> GSM680060 2 0.2201 0.7483 0.000 0.896 0.000 0.000 0.028 0.076
#> GSM680069 5 0.3607 0.6057 0.100 0.008 0.072 0.000 0.816 0.004
#> GSM680061 2 0.1151 0.7707 0.000 0.956 0.012 0.032 0.000 0.000
#> GSM680070 1 0.0146 0.7403 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM680071 5 0.5453 0.0695 0.004 0.376 0.000 0.004 0.520 0.096
#> GSM680077 1 0.5198 0.6180 0.608 0.000 0.000 0.000 0.152 0.240
#> GSM680072 6 0.5933 0.2178 0.000 0.320 0.040 0.000 0.104 0.536
#> GSM680078 1 0.3748 0.6784 0.824 0.000 0.036 0.008 0.048 0.084
#> GSM680073 6 0.6495 0.5889 0.008 0.040 0.320 0.004 0.128 0.500
#> GSM680079 1 0.4431 0.6642 0.704 0.000 0.000 0.000 0.096 0.200
#> GSM680074 2 0.4089 0.4667 0.000 0.632 0.004 0.000 0.012 0.352
#> GSM680080 2 0.4089 0.4667 0.000 0.632 0.004 0.000 0.012 0.352
#> GSM680075 6 0.6397 0.5340 0.008 0.028 0.360 0.004 0.128 0.472
#> GSM680081 3 0.0146 0.8590 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM680076 2 0.4841 0.2773 0.012 0.504 0.000 0.000 0.032 0.452
#> GSM680082 1 0.3253 0.7228 0.832 0.004 0.000 0.000 0.068 0.096
#> GSM680029 3 0.3178 0.6245 0.004 0.000 0.816 0.004 0.016 0.160
#> GSM680041 4 0.2917 0.7661 0.004 0.000 0.000 0.852 0.040 0.104
#> GSM680035 3 0.0146 0.8590 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM680047 4 0.2094 0.7832 0.000 0.000 0.000 0.900 0.020 0.080
#> GSM680036 5 0.6191 0.2523 0.000 0.012 0.348 0.004 0.456 0.180
#> GSM680048 4 0.0291 0.7931 0.004 0.000 0.000 0.992 0.000 0.004
#> GSM680037 3 0.0146 0.8590 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM680049 4 0.3198 0.7612 0.032 0.000 0.000 0.844 0.024 0.100
#> GSM680038 2 0.2918 0.7559 0.000 0.868 0.064 0.000 0.048 0.020
#> GSM680050 1 0.6034 0.5591 0.500 0.000 0.000 0.016 0.176 0.308
#> GSM680039 2 0.3323 0.6086 0.000 0.752 0.240 0.000 0.008 0.000
#> GSM680051 4 0.1390 0.7882 0.016 0.032 0.000 0.948 0.004 0.000
#> GSM680040 3 0.0146 0.8590 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM680052 4 0.1401 0.7883 0.020 0.028 0.000 0.948 0.004 0.000
#> GSM680030 2 0.2520 0.7674 0.000 0.888 0.068 0.000 0.012 0.032
#> GSM680042 4 0.3281 0.7592 0.008 0.004 0.000 0.832 0.036 0.120
#> GSM680031 3 0.0779 0.8392 0.000 0.008 0.976 0.000 0.008 0.008
#> GSM680043 4 0.7123 0.3035 0.244 0.044 0.220 0.468 0.012 0.012
#> GSM680032 1 0.4279 0.6967 0.768 0.016 0.000 0.004 0.108 0.104
#> GSM680044 1 0.6477 -0.0238 0.452 0.020 0.024 0.416 0.028 0.060
#> GSM680033 3 0.0146 0.8590 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM680045 4 0.6985 0.3689 0.204 0.044 0.228 0.500 0.012 0.012
#> GSM680034 2 0.2457 0.7615 0.000 0.896 0.056 0.036 0.008 0.004
#> GSM680046 4 0.2065 0.7725 0.052 0.032 0.000 0.912 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> CV:kmeans 53 0.245708 0.968 3.22e-07 0.63939 2
#> CV:kmeans 48 0.162335 0.637 2.92e-06 0.67059 3
#> CV:kmeans 52 0.000304 0.598 2.38e-06 0.14785 4
#> CV:kmeans 45 0.000208 0.410 2.88e-05 0.12558 5
#> CV:kmeans 42 0.000281 0.434 1.69e-04 0.00135 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 1.000 0.951 0.980 0.5070 0.493 0.493
#> 3 3 0.710 0.913 0.925 0.3244 0.755 0.541
#> 4 4 0.887 0.916 0.938 0.1330 0.853 0.587
#> 5 5 0.785 0.792 0.882 0.0627 0.915 0.668
#> 6 6 0.771 0.634 0.804 0.0386 0.969 0.841
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
#> GSM680053 2 0.0000 0.975 0.000 1.000
#> GSM680062 1 0.1843 0.957 0.972 0.028
#> GSM680054 2 0.0000 0.975 0.000 1.000
#> GSM680063 1 0.9393 0.427 0.644 0.356
#> GSM680055 2 0.0000 0.975 0.000 1.000
#> GSM680064 1 0.0000 0.983 1.000 0.000
#> GSM680056 1 0.0376 0.980 0.996 0.004
#> GSM680065 1 0.0000 0.983 1.000 0.000
#> GSM680057 2 0.0000 0.975 0.000 1.000
#> GSM680066 1 0.0000 0.983 1.000 0.000
#> GSM680058 2 0.0000 0.975 0.000 1.000
#> GSM680067 2 0.0938 0.965 0.012 0.988
#> GSM680059 2 0.0000 0.975 0.000 1.000
#> GSM680068 1 0.0000 0.983 1.000 0.000
#> GSM680060 2 0.0000 0.975 0.000 1.000
#> GSM680069 2 0.9460 0.433 0.364 0.636
#> GSM680061 2 0.0000 0.975 0.000 1.000
#> GSM680070 1 0.0000 0.983 1.000 0.000
#> GSM680071 2 0.8763 0.579 0.296 0.704
#> GSM680077 1 0.0000 0.983 1.000 0.000
#> GSM680072 2 0.0000 0.975 0.000 1.000
#> GSM680078 1 0.0000 0.983 1.000 0.000
#> GSM680073 2 0.0000 0.975 0.000 1.000
#> GSM680079 1 0.0000 0.983 1.000 0.000
#> GSM680074 2 0.0000 0.975 0.000 1.000
#> GSM680080 2 0.0000 0.975 0.000 1.000
#> GSM680075 2 0.0000 0.975 0.000 1.000
#> GSM680081 2 0.0000 0.975 0.000 1.000
#> GSM680076 2 0.0000 0.975 0.000 1.000
#> GSM680082 1 0.0000 0.983 1.000 0.000
#> GSM680029 2 0.0000 0.975 0.000 1.000
#> GSM680041 1 0.0000 0.983 1.000 0.000
#> GSM680035 2 0.0000 0.975 0.000 1.000
#> GSM680047 1 0.0000 0.983 1.000 0.000
#> GSM680036 2 0.0000 0.975 0.000 1.000
#> GSM680048 1 0.0000 0.983 1.000 0.000
#> GSM680037 2 0.0000 0.975 0.000 1.000
#> GSM680049 1 0.0000 0.983 1.000 0.000
#> GSM680038 2 0.0000 0.975 0.000 1.000
#> GSM680050 1 0.0000 0.983 1.000 0.000
#> GSM680039 2 0.0000 0.975 0.000 1.000
#> GSM680051 1 0.0000 0.983 1.000 0.000
#> GSM680040 2 0.0000 0.975 0.000 1.000
#> GSM680052 1 0.0000 0.983 1.000 0.000
#> GSM680030 2 0.0000 0.975 0.000 1.000
#> GSM680042 1 0.0000 0.983 1.000 0.000
#> GSM680031 2 0.0000 0.975 0.000 1.000
#> GSM680043 1 0.0000 0.983 1.000 0.000
#> GSM680032 1 0.0000 0.983 1.000 0.000
#> GSM680044 1 0.0000 0.983 1.000 0.000
#> GSM680033 2 0.0000 0.975 0.000 1.000
#> GSM680045 1 0.0000 0.983 1.000 0.000
#> GSM680034 2 0.0000 0.975 0.000 1.000
#> GSM680046 1 0.0000 0.983 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 3 0.0592 0.931 0.000 0.012 0.988
#> GSM680062 3 0.3539 0.862 0.012 0.100 0.888
#> GSM680054 2 0.4702 0.849 0.000 0.788 0.212
#> GSM680063 3 0.1832 0.921 0.008 0.036 0.956
#> GSM680055 3 0.0829 0.931 0.004 0.012 0.984
#> GSM680064 1 0.0237 0.932 0.996 0.000 0.004
#> GSM680056 3 0.4692 0.809 0.168 0.012 0.820
#> GSM680065 1 0.1031 0.925 0.976 0.000 0.024
#> GSM680057 2 0.3267 0.928 0.000 0.884 0.116
#> GSM680066 1 0.1399 0.922 0.968 0.004 0.028
#> GSM680058 2 0.3192 0.930 0.000 0.888 0.112
#> GSM680067 2 0.0829 0.880 0.004 0.984 0.012
#> GSM680059 3 0.1163 0.931 0.000 0.028 0.972
#> GSM680068 1 0.0424 0.932 0.992 0.000 0.008
#> GSM680060 2 0.3530 0.923 0.032 0.900 0.068
#> GSM680069 3 0.3845 0.850 0.116 0.012 0.872
#> GSM680061 2 0.1129 0.885 0.004 0.976 0.020
#> GSM680070 1 0.0592 0.931 0.988 0.000 0.012
#> GSM680071 2 0.3752 0.872 0.096 0.884 0.020
#> GSM680077 1 0.0592 0.931 0.988 0.000 0.012
#> GSM680072 2 0.4178 0.890 0.000 0.828 0.172
#> GSM680078 3 0.5982 0.589 0.328 0.004 0.668
#> GSM680073 3 0.1411 0.928 0.000 0.036 0.964
#> GSM680079 1 0.0592 0.931 0.988 0.000 0.012
#> GSM680074 2 0.3267 0.926 0.000 0.884 0.116
#> GSM680080 2 0.3267 0.926 0.000 0.884 0.116
#> GSM680075 3 0.0747 0.931 0.000 0.016 0.984
#> GSM680081 3 0.2031 0.922 0.032 0.016 0.952
#> GSM680076 2 0.3618 0.880 0.104 0.884 0.012
#> GSM680082 1 0.0592 0.931 0.988 0.000 0.012
#> GSM680029 3 0.0747 0.933 0.000 0.016 0.984
#> GSM680041 1 0.3267 0.936 0.884 0.116 0.000
#> GSM680035 3 0.1031 0.933 0.000 0.024 0.976
#> GSM680047 1 0.3267 0.936 0.884 0.116 0.000
#> GSM680036 3 0.0747 0.931 0.000 0.016 0.984
#> GSM680048 1 0.3267 0.936 0.884 0.116 0.000
#> GSM680037 3 0.1031 0.933 0.000 0.024 0.976
#> GSM680049 1 0.3192 0.937 0.888 0.112 0.000
#> GSM680038 2 0.3192 0.930 0.000 0.888 0.112
#> GSM680050 1 0.0237 0.932 0.996 0.000 0.004
#> GSM680039 2 0.3412 0.927 0.000 0.876 0.124
#> GSM680051 1 0.3682 0.934 0.876 0.116 0.008
#> GSM680040 3 0.1031 0.933 0.000 0.024 0.976
#> GSM680052 1 0.3682 0.934 0.876 0.116 0.008
#> GSM680030 2 0.2959 0.930 0.000 0.900 0.100
#> GSM680042 1 0.3116 0.937 0.892 0.108 0.000
#> GSM680031 3 0.1031 0.933 0.000 0.024 0.976
#> GSM680043 1 0.3682 0.934 0.876 0.116 0.008
#> GSM680032 1 0.0829 0.930 0.984 0.004 0.012
#> GSM680044 1 0.2878 0.938 0.904 0.096 0.000
#> GSM680033 3 0.1031 0.933 0.000 0.024 0.976
#> GSM680045 1 0.3682 0.934 0.876 0.116 0.008
#> GSM680034 2 0.0829 0.880 0.004 0.984 0.012
#> GSM680046 1 0.3267 0.936 0.884 0.116 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 3 0.3067 0.905 0.084 0.024 0.888 0.004
#> GSM680062 4 0.5967 0.564 0.080 0.004 0.236 0.680
#> GSM680054 2 0.4944 0.750 0.072 0.768 0.160 0.000
#> GSM680063 3 0.5648 0.745 0.088 0.012 0.740 0.160
#> GSM680055 3 0.3264 0.898 0.096 0.024 0.876 0.004
#> GSM680064 1 0.3311 0.880 0.828 0.000 0.000 0.172
#> GSM680056 1 0.2715 0.869 0.916 0.016 0.032 0.036
#> GSM680065 1 0.1492 0.895 0.956 0.004 0.004 0.036
#> GSM680057 2 0.0707 0.954 0.000 0.980 0.020 0.000
#> GSM680066 1 0.2751 0.916 0.904 0.000 0.040 0.056
#> GSM680058 2 0.0336 0.951 0.000 0.992 0.008 0.000
#> GSM680067 2 0.1174 0.951 0.000 0.968 0.020 0.012
#> GSM680059 3 0.1118 0.942 0.000 0.036 0.964 0.000
#> GSM680068 1 0.2281 0.921 0.904 0.000 0.000 0.096
#> GSM680060 2 0.0188 0.953 0.000 0.996 0.004 0.000
#> GSM680069 1 0.3663 0.818 0.864 0.020 0.096 0.020
#> GSM680061 2 0.0895 0.953 0.000 0.976 0.020 0.004
#> GSM680070 1 0.1940 0.929 0.924 0.000 0.000 0.076
#> GSM680071 2 0.2231 0.920 0.044 0.932 0.012 0.012
#> GSM680077 1 0.1792 0.929 0.932 0.000 0.000 0.068
#> GSM680072 2 0.3441 0.848 0.024 0.856 0.120 0.000
#> GSM680078 1 0.2174 0.907 0.928 0.000 0.052 0.020
#> GSM680073 3 0.2032 0.937 0.028 0.036 0.936 0.000
#> GSM680079 1 0.1940 0.929 0.924 0.000 0.000 0.076
#> GSM680074 2 0.0336 0.955 0.000 0.992 0.008 0.000
#> GSM680080 2 0.0336 0.955 0.000 0.992 0.008 0.000
#> GSM680075 3 0.1677 0.938 0.040 0.012 0.948 0.000
#> GSM680081 3 0.1452 0.934 0.036 0.008 0.956 0.000
#> GSM680076 2 0.0707 0.948 0.020 0.980 0.000 0.000
#> GSM680082 1 0.1940 0.929 0.924 0.000 0.000 0.076
#> GSM680029 3 0.0937 0.946 0.012 0.012 0.976 0.000
#> GSM680041 4 0.0188 0.950 0.004 0.000 0.000 0.996
#> GSM680035 3 0.0469 0.948 0.000 0.012 0.988 0.000
#> GSM680047 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM680036 3 0.2174 0.926 0.052 0.020 0.928 0.000
#> GSM680048 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM680037 3 0.0469 0.948 0.000 0.012 0.988 0.000
#> GSM680049 4 0.0188 0.952 0.004 0.000 0.000 0.996
#> GSM680038 2 0.0188 0.953 0.000 0.996 0.004 0.000
#> GSM680050 1 0.3764 0.824 0.784 0.000 0.000 0.216
#> GSM680039 2 0.1867 0.927 0.000 0.928 0.072 0.000
#> GSM680051 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM680040 3 0.0469 0.948 0.000 0.012 0.988 0.000
#> GSM680052 4 0.0000 0.952 0.000 0.000 0.000 1.000
#> GSM680030 2 0.0707 0.954 0.000 0.980 0.020 0.000
#> GSM680042 4 0.0188 0.952 0.004 0.000 0.000 0.996
#> GSM680031 3 0.0469 0.948 0.000 0.012 0.988 0.000
#> GSM680043 4 0.1798 0.932 0.040 0.000 0.016 0.944
#> GSM680032 1 0.2088 0.929 0.928 0.004 0.004 0.064
#> GSM680044 4 0.1302 0.933 0.044 0.000 0.000 0.956
#> GSM680033 3 0.0469 0.948 0.000 0.012 0.988 0.000
#> GSM680045 4 0.1624 0.935 0.028 0.000 0.020 0.952
#> GSM680034 2 0.1297 0.950 0.000 0.964 0.020 0.016
#> GSM680046 4 0.0817 0.944 0.024 0.000 0.000 0.976
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.2690 0.700 0.000 0.000 0.156 0.000 0.844
#> GSM680062 5 0.4469 0.667 0.000 0.000 0.096 0.148 0.756
#> GSM680054 5 0.5500 0.247 0.000 0.376 0.072 0.000 0.552
#> GSM680063 5 0.3681 0.706 0.000 0.000 0.148 0.044 0.808
#> GSM680055 5 0.2488 0.713 0.004 0.000 0.124 0.000 0.872
#> GSM680064 1 0.3574 0.781 0.804 0.000 0.000 0.168 0.028
#> GSM680056 5 0.3053 0.682 0.164 0.000 0.008 0.000 0.828
#> GSM680065 5 0.4278 0.162 0.452 0.000 0.000 0.000 0.548
#> GSM680057 2 0.1357 0.861 0.000 0.948 0.048 0.000 0.004
#> GSM680066 1 0.1710 0.903 0.944 0.000 0.020 0.024 0.012
#> GSM680058 2 0.1410 0.869 0.000 0.940 0.000 0.000 0.060
#> GSM680067 2 0.1883 0.856 0.000 0.932 0.012 0.048 0.008
#> GSM680059 3 0.3037 0.823 0.000 0.040 0.860 0.000 0.100
#> GSM680068 1 0.1205 0.903 0.956 0.000 0.000 0.040 0.004
#> GSM680060 2 0.0963 0.872 0.000 0.964 0.000 0.000 0.036
#> GSM680069 5 0.3111 0.698 0.144 0.004 0.012 0.000 0.840
#> GSM680061 2 0.1356 0.865 0.000 0.956 0.012 0.028 0.004
#> GSM680070 1 0.0579 0.911 0.984 0.000 0.000 0.008 0.008
#> GSM680071 2 0.4642 0.499 0.020 0.648 0.000 0.004 0.328
#> GSM680077 1 0.0510 0.909 0.984 0.000 0.000 0.000 0.016
#> GSM680072 2 0.4114 0.688 0.000 0.732 0.024 0.000 0.244
#> GSM680078 1 0.2228 0.864 0.912 0.000 0.040 0.000 0.048
#> GSM680073 3 0.5807 0.596 0.008 0.128 0.628 0.000 0.236
#> GSM680079 1 0.0566 0.910 0.984 0.000 0.000 0.004 0.012
#> GSM680074 2 0.1341 0.869 0.000 0.944 0.000 0.000 0.056
#> GSM680080 2 0.1478 0.867 0.000 0.936 0.000 0.000 0.064
#> GSM680075 3 0.5241 0.650 0.012 0.064 0.672 0.000 0.252
#> GSM680081 3 0.1012 0.877 0.020 0.000 0.968 0.000 0.012
#> GSM680076 2 0.2616 0.851 0.036 0.888 0.000 0.000 0.076
#> GSM680082 1 0.0290 0.909 0.992 0.000 0.000 0.000 0.008
#> GSM680029 3 0.1571 0.866 0.000 0.004 0.936 0.000 0.060
#> GSM680041 4 0.0451 0.944 0.004 0.000 0.000 0.988 0.008
#> GSM680035 3 0.0404 0.886 0.000 0.000 0.988 0.000 0.012
#> GSM680047 4 0.0324 0.945 0.004 0.000 0.000 0.992 0.004
#> GSM680036 5 0.4726 0.191 0.000 0.020 0.400 0.000 0.580
#> GSM680048 4 0.0162 0.945 0.004 0.000 0.000 0.996 0.000
#> GSM680037 3 0.0404 0.886 0.000 0.000 0.988 0.000 0.012
#> GSM680049 4 0.1041 0.933 0.032 0.000 0.000 0.964 0.004
#> GSM680038 2 0.1205 0.869 0.000 0.956 0.004 0.000 0.040
#> GSM680050 1 0.4404 0.669 0.712 0.000 0.000 0.252 0.036
#> GSM680039 2 0.4327 0.450 0.000 0.632 0.360 0.000 0.008
#> GSM680051 4 0.0324 0.944 0.000 0.004 0.000 0.992 0.004
#> GSM680040 3 0.0162 0.886 0.000 0.000 0.996 0.000 0.004
#> GSM680052 4 0.0000 0.945 0.000 0.000 0.000 1.000 0.000
#> GSM680030 2 0.1369 0.867 0.008 0.956 0.028 0.000 0.008
#> GSM680042 4 0.0693 0.943 0.012 0.000 0.000 0.980 0.008
#> GSM680031 3 0.0794 0.879 0.000 0.000 0.972 0.000 0.028
#> GSM680043 4 0.3950 0.834 0.076 0.000 0.080 0.824 0.020
#> GSM680032 1 0.1041 0.902 0.964 0.000 0.000 0.004 0.032
#> GSM680044 4 0.3985 0.741 0.196 0.000 0.004 0.772 0.028
#> GSM680033 3 0.0404 0.886 0.000 0.000 0.988 0.000 0.012
#> GSM680045 4 0.2131 0.905 0.008 0.000 0.056 0.920 0.016
#> GSM680034 2 0.2992 0.826 0.000 0.876 0.044 0.072 0.008
#> GSM680046 4 0.0324 0.943 0.004 0.000 0.000 0.992 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.1549 0.7626 0.000 0.000 0.044 0.000 0.936 0.020
#> GSM680062 5 0.2669 0.7402 0.000 0.000 0.032 0.072 0.880 0.016
#> GSM680054 5 0.5157 0.4145 0.000 0.284 0.024 0.000 0.624 0.068
#> GSM680063 5 0.1838 0.7622 0.000 0.000 0.040 0.020 0.928 0.012
#> GSM680055 5 0.1370 0.7652 0.004 0.000 0.036 0.000 0.948 0.012
#> GSM680064 1 0.4563 0.6483 0.700 0.000 0.000 0.232 0.028 0.040
#> GSM680056 5 0.2461 0.7488 0.044 0.000 0.000 0.004 0.888 0.064
#> GSM680065 5 0.4822 0.4242 0.308 0.000 0.000 0.004 0.620 0.068
#> GSM680057 2 0.1049 0.6379 0.000 0.960 0.032 0.000 0.000 0.008
#> GSM680066 1 0.2669 0.8192 0.864 0.000 0.024 0.004 0.000 0.108
#> GSM680058 2 0.3742 0.4080 0.000 0.648 0.000 0.000 0.004 0.348
#> GSM680067 2 0.1708 0.6374 0.000 0.932 0.004 0.024 0.000 0.040
#> GSM680059 3 0.3903 0.4527 0.000 0.012 0.680 0.000 0.004 0.304
#> GSM680068 1 0.2009 0.8334 0.904 0.000 0.000 0.008 0.004 0.084
#> GSM680060 2 0.3330 0.5029 0.000 0.716 0.000 0.000 0.000 0.284
#> GSM680069 5 0.2772 0.7457 0.040 0.000 0.000 0.004 0.864 0.092
#> GSM680061 2 0.1232 0.6422 0.000 0.956 0.004 0.016 0.000 0.024
#> GSM680070 1 0.1285 0.8393 0.944 0.000 0.000 0.004 0.000 0.052
#> GSM680071 2 0.6633 0.1265 0.016 0.396 0.000 0.008 0.308 0.272
#> GSM680077 1 0.1644 0.8303 0.932 0.000 0.000 0.000 0.028 0.040
#> GSM680072 6 0.5678 0.2037 0.000 0.296 0.036 0.000 0.092 0.576
#> GSM680078 1 0.3461 0.7566 0.804 0.000 0.036 0.000 0.008 0.152
#> GSM680073 6 0.5746 0.3432 0.004 0.036 0.344 0.000 0.072 0.544
#> GSM680079 1 0.0748 0.8377 0.976 0.000 0.000 0.004 0.004 0.016
#> GSM680074 2 0.3727 0.3286 0.000 0.612 0.000 0.000 0.000 0.388
#> GSM680080 2 0.3890 0.2931 0.000 0.596 0.000 0.000 0.004 0.400
#> GSM680075 6 0.5581 0.1854 0.008 0.016 0.408 0.000 0.068 0.500
#> GSM680081 3 0.1080 0.8739 0.004 0.004 0.960 0.000 0.000 0.032
#> GSM680076 6 0.4820 -0.3154 0.036 0.464 0.000 0.000 0.008 0.492
#> GSM680082 1 0.1895 0.8289 0.912 0.000 0.000 0.000 0.016 0.072
#> GSM680029 3 0.2810 0.7457 0.000 0.004 0.832 0.000 0.008 0.156
#> GSM680041 4 0.0520 0.8641 0.000 0.000 0.000 0.984 0.008 0.008
#> GSM680035 3 0.0964 0.8823 0.000 0.012 0.968 0.000 0.016 0.004
#> GSM680047 4 0.0291 0.8653 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM680036 5 0.6140 0.0702 0.000 0.008 0.260 0.000 0.460 0.272
#> GSM680048 4 0.0260 0.8666 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM680037 3 0.0603 0.8857 0.000 0.000 0.980 0.000 0.016 0.004
#> GSM680049 4 0.1151 0.8555 0.032 0.000 0.000 0.956 0.000 0.012
#> GSM680038 2 0.3240 0.5926 0.000 0.820 0.008 0.000 0.028 0.144
#> GSM680050 1 0.5481 0.5116 0.596 0.000 0.000 0.296 0.044 0.064
#> GSM680039 2 0.4206 0.2447 0.000 0.620 0.356 0.000 0.000 0.024
#> GSM680051 4 0.1003 0.8639 0.000 0.016 0.000 0.964 0.000 0.020
#> GSM680040 3 0.0520 0.8834 0.000 0.000 0.984 0.000 0.008 0.008
#> GSM680052 4 0.0790 0.8642 0.000 0.000 0.000 0.968 0.000 0.032
#> GSM680030 2 0.2150 0.6241 0.004 0.912 0.016 0.004 0.004 0.060
#> GSM680042 4 0.1332 0.8553 0.012 0.000 0.000 0.952 0.008 0.028
#> GSM680031 3 0.1624 0.8557 0.000 0.004 0.936 0.000 0.020 0.040
#> GSM680043 4 0.7279 0.5055 0.172 0.008 0.124 0.516 0.016 0.164
#> GSM680032 1 0.4380 0.7631 0.764 0.020 0.000 0.012 0.060 0.144
#> GSM680044 4 0.6120 0.5028 0.224 0.000 0.016 0.580 0.024 0.156
#> GSM680033 3 0.0458 0.8858 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM680045 4 0.5464 0.7301 0.036 0.012 0.088 0.704 0.016 0.144
#> GSM680034 2 0.2919 0.5973 0.000 0.872 0.044 0.044 0.000 0.040
#> GSM680046 4 0.2527 0.8363 0.032 0.000 0.000 0.880 0.004 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 disease.state(p) individual(p) protocol(p) other(p) k
#> CV:skmeans 52 4.27e-01 0.992 2.92e-08 0.4929 2
#> CV:skmeans 54 9.36e-02 0.816 5.54e-07 0.3992 3
#> CV:skmeans 54 5.91e-04 0.751 2.60e-07 0.1678 4
#> CV:skmeans 49 9.02e-05 0.330 7.61e-06 0.0978 5
#> CV:skmeans 41 7.20e-05 0.623 9.13e-05 0.0317 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 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 0.921 0.899 0.962 0.5077 0.493 0.493
#> 3 3 0.937 0.894 0.942 0.2961 0.802 0.615
#> 4 4 0.856 0.896 0.945 0.1364 0.875 0.650
#> 5 5 0.813 0.833 0.874 0.0680 0.945 0.783
#> 6 6 0.851 0.781 0.900 0.0472 0.948 0.745
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
#> GSM680053 1 0.0000 0.9514 1.000 0.000
#> GSM680062 1 0.0000 0.9514 1.000 0.000
#> GSM680054 2 0.0000 0.9673 0.000 1.000
#> GSM680063 1 0.0000 0.9514 1.000 0.000
#> GSM680055 1 0.0000 0.9514 1.000 0.000
#> GSM680064 1 0.0000 0.9514 1.000 0.000
#> GSM680056 1 0.0000 0.9514 1.000 0.000
#> GSM680065 1 0.0000 0.9514 1.000 0.000
#> GSM680057 2 0.0000 0.9673 0.000 1.000
#> GSM680066 2 0.0000 0.9673 0.000 1.000
#> GSM680058 2 0.0000 0.9673 0.000 1.000
#> GSM680067 2 0.0000 0.9673 0.000 1.000
#> GSM680059 2 0.4939 0.8624 0.108 0.892
#> GSM680068 1 0.0000 0.9514 1.000 0.000
#> GSM680060 2 0.0000 0.9673 0.000 1.000
#> GSM680069 1 0.0000 0.9514 1.000 0.000
#> GSM680061 2 0.0000 0.9673 0.000 1.000
#> GSM680070 1 0.0000 0.9514 1.000 0.000
#> GSM680071 2 0.4562 0.8755 0.096 0.904
#> GSM680077 2 0.9963 0.0986 0.464 0.536
#> GSM680072 2 0.2603 0.9322 0.044 0.956
#> GSM680078 1 0.0000 0.9514 1.000 0.000
#> GSM680073 1 0.2423 0.9167 0.960 0.040
#> GSM680079 1 0.0000 0.9514 1.000 0.000
#> GSM680074 2 0.0000 0.9673 0.000 1.000
#> GSM680080 2 0.0000 0.9673 0.000 1.000
#> GSM680075 1 0.0000 0.9514 1.000 0.000
#> GSM680081 2 0.0000 0.9673 0.000 1.000
#> GSM680076 2 0.0000 0.9673 0.000 1.000
#> GSM680082 2 0.0000 0.9673 0.000 1.000
#> GSM680029 1 0.9866 0.2349 0.568 0.432
#> GSM680041 1 0.0000 0.9514 1.000 0.000
#> GSM680035 2 0.0000 0.9673 0.000 1.000
#> GSM680047 1 0.0000 0.9514 1.000 0.000
#> GSM680036 1 0.9248 0.4860 0.660 0.340
#> GSM680048 1 0.0000 0.9514 1.000 0.000
#> GSM680037 1 0.0376 0.9482 0.996 0.004
#> GSM680049 1 0.9996 0.0583 0.512 0.488
#> GSM680038 2 0.0000 0.9673 0.000 1.000
#> GSM680050 1 0.0000 0.9514 1.000 0.000
#> GSM680039 2 0.0000 0.9673 0.000 1.000
#> GSM680051 2 0.1633 0.9491 0.024 0.976
#> GSM680040 2 0.0000 0.9673 0.000 1.000
#> GSM680052 1 0.0000 0.9514 1.000 0.000
#> GSM680030 2 0.0000 0.9673 0.000 1.000
#> GSM680042 1 0.0000 0.9514 1.000 0.000
#> GSM680031 1 0.0000 0.9514 1.000 0.000
#> GSM680043 1 0.0000 0.9514 1.000 0.000
#> GSM680032 2 0.0000 0.9673 0.000 1.000
#> GSM680044 1 0.0000 0.9514 1.000 0.000
#> GSM680033 2 0.0000 0.9673 0.000 1.000
#> GSM680045 1 0.0000 0.9514 1.000 0.000
#> GSM680034 2 0.0000 0.9673 0.000 1.000
#> GSM680046 1 0.0000 0.9514 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 1 0.1267 0.9439 0.972 0.004 0.024
#> GSM680062 1 0.1267 0.9439 0.972 0.004 0.024
#> GSM680054 2 0.0592 0.9424 0.000 0.988 0.012
#> GSM680063 1 0.1267 0.9439 0.972 0.004 0.024
#> GSM680055 1 0.1267 0.9439 0.972 0.004 0.024
#> GSM680064 1 0.2165 0.9153 0.936 0.000 0.064
#> GSM680056 1 0.1399 0.9438 0.968 0.004 0.028
#> GSM680065 1 0.1399 0.9438 0.968 0.004 0.028
#> GSM680057 2 0.0000 0.9485 0.000 1.000 0.000
#> GSM680066 2 0.0237 0.9468 0.000 0.996 0.004
#> GSM680058 2 0.0000 0.9485 0.000 1.000 0.000
#> GSM680067 2 0.0237 0.9471 0.004 0.996 0.000
#> GSM680059 3 0.3045 0.9181 0.020 0.064 0.916
#> GSM680068 3 0.4062 0.7781 0.164 0.000 0.836
#> GSM680060 2 0.0000 0.9485 0.000 1.000 0.000
#> GSM680069 1 0.1163 0.9431 0.972 0.000 0.028
#> GSM680061 2 0.0000 0.9485 0.000 1.000 0.000
#> GSM680070 1 0.2796 0.8989 0.908 0.000 0.092
#> GSM680071 2 0.2878 0.8657 0.096 0.904 0.000
#> GSM680077 2 0.7969 0.2024 0.396 0.540 0.064
#> GSM680072 2 0.3623 0.8749 0.032 0.896 0.072
#> GSM680078 3 0.1031 0.9153 0.024 0.000 0.976
#> GSM680073 3 0.2165 0.9148 0.064 0.000 0.936
#> GSM680079 3 0.1643 0.9120 0.044 0.000 0.956
#> GSM680074 2 0.0000 0.9485 0.000 1.000 0.000
#> GSM680080 2 0.0000 0.9485 0.000 1.000 0.000
#> GSM680075 3 0.2165 0.9148 0.064 0.000 0.936
#> GSM680081 3 0.2711 0.9028 0.000 0.088 0.912
#> GSM680076 2 0.0000 0.9485 0.000 1.000 0.000
#> GSM680082 2 0.3310 0.8890 0.028 0.908 0.064
#> GSM680029 3 0.2681 0.9234 0.028 0.040 0.932
#> GSM680041 1 0.0000 0.9441 1.000 0.000 0.000
#> GSM680035 2 0.0747 0.9400 0.000 0.984 0.016
#> GSM680047 1 0.0000 0.9441 1.000 0.000 0.000
#> GSM680036 3 0.2879 0.9207 0.024 0.052 0.924
#> GSM680048 1 0.0592 0.9452 0.988 0.000 0.012
#> GSM680037 3 0.2165 0.9148 0.064 0.000 0.936
#> GSM680049 1 0.8045 0.0905 0.504 0.432 0.064
#> GSM680038 2 0.0000 0.9485 0.000 1.000 0.000
#> GSM680050 1 0.1860 0.9361 0.948 0.000 0.052
#> GSM680039 2 0.0000 0.9485 0.000 1.000 0.000
#> GSM680051 2 0.2879 0.9008 0.052 0.924 0.024
#> GSM680040 3 0.2537 0.9080 0.000 0.080 0.920
#> GSM680052 1 0.1031 0.9379 0.976 0.000 0.024
#> GSM680030 2 0.0000 0.9485 0.000 1.000 0.000
#> GSM680042 1 0.1289 0.9350 0.968 0.000 0.032
#> GSM680031 1 0.1163 0.9431 0.972 0.000 0.028
#> GSM680043 1 0.1031 0.9379 0.976 0.000 0.024
#> GSM680032 2 0.2096 0.9184 0.004 0.944 0.052
#> GSM680044 1 0.0747 0.9453 0.984 0.000 0.016
#> GSM680033 3 0.5465 0.6564 0.000 0.288 0.712
#> GSM680045 1 0.1031 0.9379 0.976 0.000 0.024
#> GSM680034 2 0.0237 0.9471 0.004 0.996 0.000
#> GSM680046 1 0.1031 0.9379 0.976 0.000 0.024
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM680062 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM680054 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM680063 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM680055 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM680064 4 0.0000 0.857 0.000 0.000 0.000 1.000
#> GSM680056 1 0.0336 0.957 0.992 0.000 0.000 0.008
#> GSM680065 1 0.0592 0.953 0.984 0.000 0.000 0.016
#> GSM680057 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM680066 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM680058 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM680067 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM680059 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM680068 4 0.0336 0.854 0.000 0.000 0.008 0.992
#> GSM680060 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM680069 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM680061 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM680070 4 0.0000 0.857 0.000 0.000 0.000 1.000
#> GSM680071 2 0.2281 0.867 0.096 0.904 0.000 0.000
#> GSM680077 2 0.7417 0.326 0.284 0.508 0.000 0.208
#> GSM680072 2 0.2830 0.878 0.040 0.900 0.060 0.000
#> GSM680078 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM680073 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM680079 3 0.3649 0.763 0.000 0.000 0.796 0.204
#> GSM680074 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM680080 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM680075 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM680081 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM680076 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM680082 4 0.0000 0.857 0.000 0.000 0.000 1.000
#> GSM680029 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM680041 1 0.3610 0.716 0.800 0.000 0.000 0.200
#> GSM680035 2 0.0469 0.944 0.000 0.988 0.012 0.000
#> GSM680047 1 0.1637 0.909 0.940 0.000 0.000 0.060
#> GSM680036 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM680048 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM680037 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM680049 4 0.0000 0.857 0.000 0.000 0.000 1.000
#> GSM680038 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM680050 1 0.2469 0.856 0.892 0.000 0.000 0.108
#> GSM680039 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM680051 4 0.3688 0.728 0.000 0.208 0.000 0.792
#> GSM680040 3 0.0000 0.952 0.000 0.000 1.000 0.000
#> GSM680052 4 0.3688 0.828 0.208 0.000 0.000 0.792
#> GSM680030 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM680042 4 0.3528 0.833 0.192 0.000 0.000 0.808
#> GSM680031 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM680043 4 0.3688 0.828 0.208 0.000 0.000 0.792
#> GSM680032 2 0.3444 0.781 0.000 0.816 0.000 0.184
#> GSM680044 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM680033 3 0.3873 0.694 0.000 0.228 0.772 0.000
#> GSM680045 4 0.3688 0.828 0.208 0.000 0.000 0.792
#> GSM680034 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM680046 4 0.3688 0.828 0.208 0.000 0.000 0.792
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000
#> GSM680062 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000
#> GSM680054 1 0.0162 0.837 0.996 0.000 0.000 0.000 0.004
#> GSM680063 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000
#> GSM680055 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000
#> GSM680064 4 0.3039 0.800 0.000 0.192 0.000 0.808 0.000
#> GSM680056 5 0.2280 0.866 0.000 0.120 0.000 0.000 0.880
#> GSM680065 5 0.2439 0.864 0.000 0.120 0.000 0.004 0.876
#> GSM680057 1 0.0000 0.839 1.000 0.000 0.000 0.000 0.000
#> GSM680066 1 0.0324 0.835 0.992 0.000 0.004 0.004 0.000
#> GSM680058 2 0.4015 0.914 0.348 0.652 0.000 0.000 0.000
#> GSM680067 1 0.1851 0.739 0.912 0.088 0.000 0.000 0.000
#> GSM680059 3 0.0000 0.945 0.000 0.000 1.000 0.000 0.000
#> GSM680068 4 0.2233 0.846 0.000 0.104 0.004 0.892 0.000
#> GSM680060 2 0.3999 0.916 0.344 0.656 0.000 0.000 0.000
#> GSM680069 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000
#> GSM680061 1 0.0000 0.839 1.000 0.000 0.000 0.000 0.000
#> GSM680070 4 0.2389 0.841 0.000 0.116 0.000 0.880 0.004
#> GSM680071 1 0.4457 0.553 0.756 0.152 0.000 0.000 0.092
#> GSM680077 1 0.7529 0.215 0.428 0.348 0.000 0.080 0.144
#> GSM680072 2 0.4736 0.895 0.312 0.656 0.004 0.000 0.028
#> GSM680078 3 0.0000 0.945 0.000 0.000 1.000 0.000 0.000
#> GSM680073 3 0.0000 0.945 0.000 0.000 1.000 0.000 0.000
#> GSM680079 3 0.4847 0.664 0.000 0.216 0.704 0.080 0.000
#> GSM680074 2 0.3999 0.916 0.344 0.656 0.000 0.000 0.000
#> GSM680080 2 0.4242 0.815 0.428 0.572 0.000 0.000 0.000
#> GSM680075 3 0.0000 0.945 0.000 0.000 1.000 0.000 0.000
#> GSM680081 3 0.0000 0.945 0.000 0.000 1.000 0.000 0.000
#> GSM680076 2 0.3242 0.788 0.216 0.784 0.000 0.000 0.000
#> GSM680082 4 0.3999 0.680 0.000 0.344 0.000 0.656 0.000
#> GSM680029 3 0.0000 0.945 0.000 0.000 1.000 0.000 0.000
#> GSM680041 5 0.3913 0.595 0.000 0.000 0.000 0.324 0.676
#> GSM680035 1 0.0609 0.824 0.980 0.000 0.020 0.000 0.000
#> GSM680047 5 0.2966 0.807 0.000 0.000 0.000 0.184 0.816
#> GSM680036 3 0.0000 0.945 0.000 0.000 1.000 0.000 0.000
#> GSM680048 5 0.1908 0.874 0.000 0.000 0.000 0.092 0.908
#> GSM680037 3 0.0000 0.945 0.000 0.000 1.000 0.000 0.000
#> GSM680049 4 0.0162 0.860 0.004 0.000 0.000 0.996 0.000
#> GSM680038 1 0.0510 0.827 0.984 0.016 0.000 0.000 0.000
#> GSM680050 5 0.3012 0.849 0.000 0.104 0.000 0.036 0.860
#> GSM680039 1 0.0000 0.839 1.000 0.000 0.000 0.000 0.000
#> GSM680051 4 0.1908 0.827 0.092 0.000 0.000 0.908 0.000
#> GSM680040 3 0.0000 0.945 0.000 0.000 1.000 0.000 0.000
#> GSM680052 4 0.2077 0.860 0.008 0.000 0.000 0.908 0.084
#> GSM680030 1 0.0000 0.839 1.000 0.000 0.000 0.000 0.000
#> GSM680042 4 0.1544 0.863 0.000 0.000 0.000 0.932 0.068
#> GSM680031 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000
#> GSM680043 4 0.2966 0.819 0.000 0.000 0.000 0.816 0.184
#> GSM680032 1 0.5004 0.478 0.672 0.256 0.000 0.072 0.000
#> GSM680044 5 0.0000 0.919 0.000 0.000 0.000 0.000 1.000
#> GSM680033 3 0.3336 0.684 0.228 0.000 0.772 0.000 0.000
#> GSM680045 4 0.3093 0.829 0.008 0.000 0.000 0.824 0.168
#> GSM680034 1 0.0000 0.839 1.000 0.000 0.000 0.000 0.000
#> GSM680046 4 0.2077 0.860 0.008 0.000 0.000 0.908 0.084
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.0000 0.831 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680062 5 0.0000 0.831 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680054 2 0.0260 0.898 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM680063 5 0.0000 0.831 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680055 5 0.0000 0.831 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680064 1 0.3634 0.329 0.644 0.000 0.000 0.356 0.000 0.000
#> GSM680056 1 0.3868 0.248 0.504 0.000 0.000 0.000 0.496 0.000
#> GSM680065 1 0.3868 0.248 0.504 0.000 0.000 0.000 0.496 0.000
#> GSM680057 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680066 2 0.0260 0.898 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM680058 6 0.1327 0.922 0.000 0.064 0.000 0.000 0.000 0.936
#> GSM680067 2 0.2048 0.807 0.000 0.880 0.000 0.000 0.000 0.120
#> GSM680059 3 0.0000 0.969 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680068 4 0.2941 0.739 0.220 0.000 0.000 0.780 0.000 0.000
#> GSM680060 6 0.0865 0.939 0.000 0.036 0.000 0.000 0.000 0.964
#> GSM680069 5 0.0000 0.831 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680061 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680070 4 0.3189 0.718 0.236 0.000 0.000 0.760 0.004 0.000
#> GSM680071 2 0.6597 0.128 0.324 0.472 0.000 0.000 0.084 0.120
#> GSM680077 1 0.0000 0.653 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM680072 6 0.0806 0.935 0.000 0.020 0.000 0.000 0.008 0.972
#> GSM680078 3 0.0000 0.969 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680073 3 0.0000 0.969 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680079 1 0.1610 0.634 0.916 0.000 0.084 0.000 0.000 0.000
#> GSM680074 6 0.0713 0.938 0.000 0.028 0.000 0.000 0.000 0.972
#> GSM680080 6 0.2300 0.850 0.000 0.144 0.000 0.000 0.000 0.856
#> GSM680075 3 0.0000 0.969 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680081 3 0.0000 0.969 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680076 6 0.1267 0.888 0.060 0.000 0.000 0.000 0.000 0.940
#> GSM680082 1 0.1257 0.652 0.952 0.000 0.000 0.020 0.000 0.028
#> GSM680029 3 0.0000 0.969 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680041 5 0.3774 0.472 0.000 0.000 0.000 0.408 0.592 0.000
#> GSM680035 2 0.0458 0.893 0.000 0.984 0.016 0.000 0.000 0.000
#> GSM680047 5 0.3351 0.626 0.000 0.000 0.000 0.288 0.712 0.000
#> GSM680036 3 0.0000 0.969 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680048 5 0.2697 0.702 0.000 0.000 0.000 0.188 0.812 0.000
#> GSM680037 3 0.0000 0.969 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680049 4 0.0458 0.849 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM680038 2 0.0363 0.896 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM680050 5 0.3930 0.214 0.420 0.000 0.000 0.004 0.576 0.000
#> GSM680039 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680051 4 0.0713 0.848 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM680040 3 0.0000 0.969 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680052 4 0.0806 0.856 0.000 0.008 0.000 0.972 0.020 0.000
#> GSM680030 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680042 4 0.0000 0.849 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680031 5 0.0146 0.828 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM680043 4 0.2912 0.728 0.000 0.000 0.000 0.784 0.216 0.000
#> GSM680032 2 0.4196 0.486 0.332 0.640 0.000 0.000 0.000 0.028
#> GSM680044 5 0.0000 0.831 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680033 3 0.2996 0.687 0.000 0.228 0.772 0.000 0.000 0.000
#> GSM680045 4 0.2933 0.745 0.000 0.004 0.000 0.796 0.200 0.000
#> GSM680034 2 0.0000 0.901 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680046 4 0.0891 0.856 0.000 0.008 0.000 0.968 0.024 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5)
get_signatures(res, k = 6)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> CV:pam 50 0.7394 0.5783 1.85e-03 4.04e-01 2
#> CV:pam 52 0.4354 0.0936 1.18e-03 9.41e-03 3
#> CV:pam 53 0.4687 0.3829 3.69e-05 3.02e-02 4
#> CV:pam 52 0.1666 0.2525 1.73e-04 2.16e-03 5
#> CV:pam 47 0.0425 0.2707 3.60e-04 8.25e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 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 0.467 0.857 0.869 0.3444 0.591 0.591
#> 3 3 0.399 0.588 0.756 0.6639 0.672 0.490
#> 4 4 0.820 0.836 0.926 0.2631 0.841 0.606
#> 5 5 0.670 0.557 0.764 0.0735 0.899 0.663
#> 6 6 0.673 0.515 0.707 0.0449 0.899 0.605
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
#> GSM680053 2 0.0938 0.906 0.012 0.988
#> GSM680062 2 0.0000 0.909 0.000 1.000
#> GSM680054 2 0.2423 0.898 0.040 0.960
#> GSM680063 2 0.0000 0.909 0.000 1.000
#> GSM680055 2 0.0000 0.909 0.000 1.000
#> GSM680064 1 0.8661 0.935 0.712 0.288
#> GSM680056 1 0.9833 0.803 0.576 0.424
#> GSM680065 1 0.8763 0.937 0.704 0.296
#> GSM680057 2 0.1843 0.904 0.028 0.972
#> GSM680066 2 0.0000 0.909 0.000 1.000
#> GSM680058 2 0.1843 0.904 0.028 0.972
#> GSM680067 2 0.1414 0.907 0.020 0.980
#> GSM680059 2 0.1843 0.895 0.028 0.972
#> GSM680068 1 0.9460 0.895 0.636 0.364
#> GSM680060 2 0.1414 0.907 0.020 0.980
#> GSM680069 2 0.0000 0.909 0.000 1.000
#> GSM680061 2 0.1414 0.907 0.020 0.980
#> GSM680070 1 0.8763 0.937 0.704 0.296
#> GSM680071 2 0.1414 0.907 0.020 0.980
#> GSM680077 1 0.8499 0.931 0.724 0.276
#> GSM680072 2 0.1633 0.907 0.024 0.976
#> GSM680078 2 0.0000 0.909 0.000 1.000
#> GSM680073 2 0.0000 0.909 0.000 1.000
#> GSM680079 1 0.8763 0.937 0.704 0.296
#> GSM680074 2 0.1414 0.907 0.020 0.980
#> GSM680080 2 0.1633 0.907 0.024 0.976
#> GSM680075 2 0.0000 0.909 0.000 1.000
#> GSM680081 2 0.0000 0.909 0.000 1.000
#> GSM680076 2 0.1414 0.907 0.020 0.980
#> GSM680082 1 0.8499 0.931 0.724 0.276
#> GSM680029 2 0.0938 0.906 0.012 0.988
#> GSM680041 1 0.8661 0.935 0.712 0.288
#> GSM680035 2 0.8207 0.637 0.256 0.744
#> GSM680047 1 0.9522 0.885 0.628 0.372
#> GSM680036 2 0.0938 0.906 0.012 0.988
#> GSM680048 1 0.9815 0.815 0.580 0.420
#> GSM680037 2 0.6801 0.729 0.180 0.820
#> GSM680049 1 0.8443 0.929 0.728 0.272
#> GSM680038 2 0.1843 0.904 0.028 0.972
#> GSM680050 1 0.8499 0.931 0.724 0.276
#> GSM680039 2 0.0000 0.909 0.000 1.000
#> GSM680051 2 0.8443 0.310 0.272 0.728
#> GSM680040 2 0.8207 0.637 0.256 0.744
#> GSM680052 2 0.8499 0.295 0.276 0.724
#> GSM680030 2 0.1843 0.904 0.028 0.972
#> GSM680042 1 0.8661 0.935 0.712 0.288
#> GSM680031 2 0.7528 0.686 0.216 0.784
#> GSM680043 2 0.0000 0.909 0.000 1.000
#> GSM680032 2 0.6623 0.631 0.172 0.828
#> GSM680044 2 0.0376 0.907 0.004 0.996
#> GSM680033 2 0.8207 0.637 0.256 0.744
#> GSM680045 2 0.0000 0.909 0.000 1.000
#> GSM680034 2 0.0938 0.909 0.012 0.988
#> GSM680046 1 0.9522 0.885 0.628 0.372
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 3 0.1643 0.739 0.044 0.000 0.956
#> GSM680062 3 0.2200 0.732 0.056 0.004 0.940
#> GSM680054 3 0.5247 0.400 0.008 0.224 0.768
#> GSM680063 3 0.2096 0.735 0.052 0.004 0.944
#> GSM680055 3 0.2096 0.734 0.052 0.004 0.944
#> GSM680064 1 0.6381 0.727 0.648 0.340 0.012
#> GSM680056 1 0.7238 0.727 0.628 0.328 0.044
#> GSM680065 1 0.6651 0.729 0.640 0.340 0.020
#> GSM680057 3 0.7578 -0.637 0.040 0.460 0.500
#> GSM680066 3 0.5480 0.426 0.264 0.004 0.732
#> GSM680058 2 0.6822 0.669 0.012 0.508 0.480
#> GSM680067 2 0.7442 0.830 0.048 0.604 0.348
#> GSM680059 3 0.1163 0.734 0.028 0.000 0.972
#> GSM680068 1 0.6890 0.729 0.632 0.340 0.028
#> GSM680060 2 0.6427 0.814 0.012 0.640 0.348
#> GSM680069 3 0.5292 0.490 0.228 0.008 0.764
#> GSM680061 2 0.7328 0.832 0.044 0.612 0.344
#> GSM680070 1 0.6651 0.729 0.640 0.340 0.020
#> GSM680071 2 0.9962 0.456 0.292 0.364 0.344
#> GSM680077 1 0.6104 0.724 0.648 0.348 0.004
#> GSM680072 3 0.5024 0.398 0.004 0.220 0.776
#> GSM680078 3 0.8171 0.328 0.172 0.184 0.644
#> GSM680073 3 0.1878 0.738 0.044 0.004 0.952
#> GSM680079 1 0.6381 0.727 0.648 0.340 0.012
#> GSM680074 2 0.6104 0.803 0.004 0.648 0.348
#> GSM680080 2 0.6521 0.644 0.004 0.504 0.492
#> GSM680075 3 0.1878 0.738 0.044 0.004 0.952
#> GSM680081 3 0.1643 0.739 0.044 0.000 0.956
#> GSM680076 2 0.7442 0.832 0.048 0.604 0.348
#> GSM680082 1 0.6104 0.724 0.648 0.348 0.004
#> GSM680029 3 0.1529 0.739 0.040 0.000 0.960
#> GSM680041 1 0.2866 0.709 0.916 0.008 0.076
#> GSM680035 3 0.0661 0.711 0.004 0.008 0.988
#> GSM680047 1 0.3412 0.696 0.876 0.000 0.124
#> GSM680036 3 0.1643 0.739 0.044 0.000 0.956
#> GSM680048 1 0.3826 0.693 0.868 0.008 0.124
#> GSM680037 3 0.0661 0.711 0.004 0.008 0.988
#> GSM680049 1 0.2749 0.708 0.924 0.012 0.064
#> GSM680038 3 0.7065 -0.235 0.032 0.352 0.616
#> GSM680050 1 0.7847 0.732 0.588 0.344 0.068
#> GSM680039 3 0.5069 0.570 0.044 0.128 0.828
#> GSM680051 1 0.4755 0.664 0.808 0.008 0.184
#> GSM680040 3 0.0661 0.711 0.004 0.008 0.988
#> GSM680052 1 0.4164 0.688 0.848 0.008 0.144
#> GSM680030 3 0.6905 -0.540 0.016 0.440 0.544
#> GSM680042 1 0.2680 0.709 0.924 0.008 0.068
#> GSM680031 3 0.0848 0.714 0.008 0.008 0.984
#> GSM680043 1 0.6678 0.158 0.512 0.008 0.480
#> GSM680032 1 0.6498 0.236 0.596 0.008 0.396
#> GSM680044 1 0.6513 0.178 0.520 0.004 0.476
#> GSM680033 3 0.0661 0.711 0.004 0.008 0.988
#> GSM680045 3 0.6189 0.248 0.364 0.004 0.632
#> GSM680034 2 0.7582 0.811 0.048 0.572 0.380
#> GSM680046 1 0.3644 0.694 0.872 0.004 0.124
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 3 0.0921 0.8902 0.028 0.000 0.972 0.000
#> GSM680062 3 0.1388 0.8872 0.028 0.000 0.960 0.012
#> GSM680054 3 0.4304 0.6278 0.000 0.284 0.716 0.000
#> GSM680063 3 0.1388 0.8872 0.028 0.000 0.960 0.012
#> GSM680055 3 0.1388 0.8872 0.028 0.000 0.960 0.012
#> GSM680064 1 0.0000 0.9406 1.000 0.000 0.000 0.000
#> GSM680056 1 0.2867 0.8619 0.884 0.000 0.104 0.012
#> GSM680065 1 0.0469 0.9384 0.988 0.000 0.000 0.012
#> GSM680057 2 0.0336 0.9382 0.000 0.992 0.008 0.000
#> GSM680066 3 0.6270 0.5992 0.212 0.096 0.680 0.012
#> GSM680058 2 0.0469 0.9357 0.000 0.988 0.012 0.000
#> GSM680067 2 0.0000 0.9406 0.000 1.000 0.000 0.000
#> GSM680059 3 0.0336 0.8877 0.008 0.000 0.992 0.000
#> GSM680068 1 0.0804 0.9367 0.980 0.000 0.008 0.012
#> GSM680060 2 0.0000 0.9406 0.000 1.000 0.000 0.000
#> GSM680069 3 0.2805 0.8436 0.100 0.000 0.888 0.012
#> GSM680061 2 0.0000 0.9406 0.000 1.000 0.000 0.000
#> GSM680070 1 0.0188 0.9412 0.996 0.000 0.000 0.004
#> GSM680071 2 0.5028 0.3536 0.400 0.596 0.004 0.000
#> GSM680077 1 0.0188 0.9396 0.996 0.004 0.000 0.000
#> GSM680072 3 0.4647 0.6165 0.008 0.288 0.704 0.000
#> GSM680078 1 0.3625 0.7940 0.828 0.000 0.160 0.012
#> GSM680073 3 0.0921 0.8902 0.028 0.000 0.972 0.000
#> GSM680079 1 0.0188 0.9412 0.996 0.000 0.000 0.004
#> GSM680074 2 0.0000 0.9406 0.000 1.000 0.000 0.000
#> GSM680080 2 0.0188 0.9394 0.004 0.996 0.000 0.000
#> GSM680075 3 0.0921 0.8902 0.028 0.000 0.972 0.000
#> GSM680081 3 0.0921 0.8902 0.028 0.000 0.972 0.000
#> GSM680076 2 0.0921 0.9193 0.028 0.972 0.000 0.000
#> GSM680082 1 0.0188 0.9396 0.996 0.004 0.000 0.000
#> GSM680029 3 0.0817 0.8902 0.024 0.000 0.976 0.000
#> GSM680041 4 0.1398 0.8985 0.040 0.004 0.000 0.956
#> GSM680035 3 0.0000 0.8860 0.000 0.000 1.000 0.000
#> GSM680047 4 0.0000 0.9109 0.000 0.000 0.000 1.000
#> GSM680036 3 0.0921 0.8902 0.028 0.000 0.972 0.000
#> GSM680048 4 0.0000 0.9109 0.000 0.000 0.000 1.000
#> GSM680037 3 0.0000 0.8860 0.000 0.000 1.000 0.000
#> GSM680049 4 0.1398 0.8985 0.040 0.004 0.000 0.956
#> GSM680038 3 0.4989 0.1865 0.000 0.472 0.528 0.000
#> GSM680050 1 0.0188 0.9396 0.996 0.004 0.000 0.000
#> GSM680039 3 0.1716 0.8651 0.000 0.064 0.936 0.000
#> GSM680051 4 0.0000 0.9109 0.000 0.000 0.000 1.000
#> GSM680040 3 0.0000 0.8860 0.000 0.000 1.000 0.000
#> GSM680052 4 0.0000 0.9109 0.000 0.000 0.000 1.000
#> GSM680030 2 0.1940 0.8715 0.000 0.924 0.076 0.000
#> GSM680042 4 0.1398 0.8985 0.040 0.004 0.000 0.956
#> GSM680031 3 0.0000 0.8860 0.000 0.000 1.000 0.000
#> GSM680043 4 0.5119 0.0819 0.004 0.000 0.440 0.556
#> GSM680032 1 0.3217 0.8339 0.860 0.000 0.128 0.012
#> GSM680044 3 0.3308 0.8316 0.036 0.000 0.872 0.092
#> GSM680033 3 0.0000 0.8860 0.000 0.000 1.000 0.000
#> GSM680045 3 0.5212 0.2537 0.008 0.000 0.572 0.420
#> GSM680034 2 0.0000 0.9406 0.000 1.000 0.000 0.000
#> GSM680046 4 0.0000 0.9109 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.4225 0.2987 0.004 0.000 0.364 0.000 0.632
#> GSM680062 5 0.5781 0.3574 0.008 0.000 0.260 0.112 0.620
#> GSM680054 5 0.4497 0.0642 0.000 0.352 0.016 0.000 0.632
#> GSM680063 5 0.4102 0.3824 0.004 0.000 0.300 0.004 0.692
#> GSM680055 5 0.4375 0.3029 0.004 0.000 0.364 0.004 0.628
#> GSM680064 1 0.1591 0.8736 0.940 0.004 0.052 0.004 0.000
#> GSM680056 1 0.3812 0.7508 0.796 0.000 0.168 0.004 0.032
#> GSM680065 1 0.0955 0.8724 0.968 0.000 0.028 0.004 0.000
#> GSM680057 2 0.3408 0.7519 0.004 0.840 0.008 0.020 0.128
#> GSM680066 1 0.7339 0.0798 0.484 0.036 0.188 0.008 0.284
#> GSM680058 2 0.3478 0.7734 0.032 0.844 0.016 0.000 0.108
#> GSM680067 2 0.2142 0.7812 0.000 0.920 0.028 0.048 0.004
#> GSM680059 5 0.4270 -0.1408 0.004 0.004 0.336 0.000 0.656
#> GSM680068 1 0.1798 0.8736 0.928 0.004 0.064 0.004 0.000
#> GSM680060 2 0.3193 0.7791 0.032 0.852 0.112 0.000 0.004
#> GSM680069 5 0.6346 0.1802 0.160 0.000 0.320 0.004 0.516
#> GSM680061 2 0.1828 0.7837 0.000 0.936 0.028 0.032 0.004
#> GSM680070 1 0.1518 0.8741 0.944 0.004 0.048 0.004 0.000
#> GSM680071 2 0.5051 0.3934 0.392 0.576 0.024 0.008 0.000
#> GSM680077 1 0.0671 0.8717 0.980 0.004 0.016 0.000 0.000
#> GSM680072 3 0.6811 0.0867 0.000 0.336 0.360 0.000 0.304
#> GSM680078 1 0.4382 0.6905 0.700 0.000 0.276 0.004 0.020
#> GSM680073 3 0.4507 0.3259 0.004 0.004 0.580 0.000 0.412
#> GSM680079 1 0.1571 0.8744 0.936 0.004 0.060 0.000 0.000
#> GSM680074 2 0.3276 0.7717 0.032 0.836 0.132 0.000 0.000
#> GSM680080 2 0.3396 0.7726 0.028 0.832 0.136 0.000 0.004
#> GSM680075 3 0.4490 0.3244 0.004 0.004 0.588 0.000 0.404
#> GSM680081 5 0.4044 0.4033 0.012 0.004 0.252 0.000 0.732
#> GSM680076 2 0.3759 0.7548 0.056 0.808 0.136 0.000 0.000
#> GSM680082 1 0.0671 0.8717 0.980 0.004 0.016 0.000 0.000
#> GSM680029 5 0.4264 0.2602 0.004 0.000 0.376 0.000 0.620
#> GSM680041 4 0.4734 0.7330 0.108 0.000 0.160 0.732 0.000
#> GSM680035 5 0.0510 0.4475 0.000 0.000 0.016 0.000 0.984
#> GSM680047 4 0.0609 0.8082 0.000 0.000 0.020 0.980 0.000
#> GSM680036 5 0.4321 0.2219 0.004 0.000 0.396 0.000 0.600
#> GSM680048 4 0.0162 0.8084 0.000 0.000 0.004 0.996 0.000
#> GSM680037 5 0.0963 0.4538 0.000 0.000 0.036 0.000 0.964
#> GSM680049 4 0.4888 0.7315 0.108 0.004 0.160 0.728 0.000
#> GSM680038 2 0.5065 0.2267 0.000 0.524 0.008 0.020 0.448
#> GSM680050 1 0.0613 0.8731 0.984 0.004 0.004 0.008 0.000
#> GSM680039 5 0.5282 -0.0359 0.004 0.440 0.024 0.008 0.524
#> GSM680051 4 0.0324 0.8078 0.000 0.004 0.004 0.992 0.000
#> GSM680040 5 0.0510 0.4505 0.000 0.000 0.016 0.000 0.984
#> GSM680052 4 0.0324 0.8078 0.000 0.004 0.004 0.992 0.000
#> GSM680030 2 0.3674 0.7318 0.004 0.816 0.008 0.020 0.152
#> GSM680042 4 0.4734 0.7330 0.108 0.000 0.160 0.732 0.000
#> GSM680031 5 0.0162 0.4527 0.000 0.000 0.004 0.000 0.996
#> GSM680043 4 0.4835 0.4104 0.000 0.016 0.016 0.648 0.320
#> GSM680032 1 0.2234 0.8545 0.916 0.004 0.060 0.004 0.016
#> GSM680044 5 0.7439 0.2518 0.104 0.004 0.172 0.176 0.544
#> GSM680033 5 0.0609 0.4444 0.000 0.000 0.020 0.000 0.980
#> GSM680045 4 0.4882 0.2520 0.000 0.012 0.012 0.588 0.388
#> GSM680034 2 0.3857 0.7648 0.000 0.832 0.028 0.052 0.088
#> GSM680046 4 0.0771 0.8081 0.000 0.004 0.020 0.976 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.1350 0.6555 0.020 0.000 0.020 0.000 0.952 NA
#> GSM680062 5 0.5189 0.5300 0.012 0.000 0.108 0.144 0.704 NA
#> GSM680054 5 0.6125 -0.3490 0.000 0.312 0.340 0.000 0.348 NA
#> GSM680063 5 0.3088 0.6213 0.004 0.004 0.064 0.028 0.868 NA
#> GSM680055 5 0.1036 0.6570 0.024 0.000 0.008 0.004 0.964 NA
#> GSM680064 1 0.3067 0.8152 0.868 0.016 0.024 0.012 0.004 NA
#> GSM680056 1 0.5598 0.6155 0.648 0.004 0.044 0.028 0.240 NA
#> GSM680065 1 0.2543 0.8245 0.904 0.004 0.024 0.012 0.024 NA
#> GSM680057 3 0.4810 -0.3420 0.000 0.420 0.536 0.000 0.032 NA
#> GSM680066 1 0.6013 0.2426 0.496 0.028 0.028 0.032 0.404 NA
#> GSM680058 2 0.4130 0.4926 0.000 0.672 0.300 0.000 0.024 NA
#> GSM680067 2 0.5754 0.4902 0.000 0.476 0.380 0.008 0.000 NA
#> GSM680059 5 0.6633 0.2539 0.004 0.020 0.224 0.004 0.416 NA
#> GSM680068 1 0.2015 0.8257 0.916 0.012 0.000 0.000 0.056 NA
#> GSM680060 2 0.1349 0.6291 0.000 0.940 0.056 0.000 0.004 NA
#> GSM680069 5 0.4318 0.5479 0.180 0.004 0.020 0.028 0.756 NA
#> GSM680061 2 0.5694 0.4948 0.000 0.484 0.368 0.004 0.000 NA
#> GSM680070 1 0.0964 0.8304 0.968 0.012 0.000 0.000 0.004 NA
#> GSM680071 2 0.6479 0.3992 0.316 0.500 0.136 0.024 0.024 NA
#> GSM680077 1 0.0767 0.8313 0.976 0.012 0.004 0.000 0.000 NA
#> GSM680072 2 0.7233 0.1785 0.000 0.444 0.136 0.004 0.160 NA
#> GSM680078 1 0.5385 0.2354 0.480 0.004 0.016 0.028 0.456 NA
#> GSM680073 5 0.5205 0.5359 0.024 0.020 0.036 0.004 0.660 NA
#> GSM680079 1 0.1390 0.8274 0.948 0.004 0.016 0.000 0.000 NA
#> GSM680074 2 0.0692 0.6238 0.000 0.976 0.020 0.000 0.000 NA
#> GSM680080 2 0.1485 0.6127 0.000 0.944 0.024 0.000 0.004 NA
#> GSM680075 5 0.4997 0.5419 0.024 0.020 0.024 0.004 0.672 NA
#> GSM680081 5 0.2573 0.5582 0.008 0.000 0.132 0.004 0.856 NA
#> GSM680076 2 0.0146 0.6267 0.004 0.996 0.000 0.000 0.000 NA
#> GSM680082 1 0.0837 0.8311 0.972 0.020 0.004 0.000 0.000 NA
#> GSM680029 5 0.1857 0.6423 0.004 0.000 0.028 0.000 0.924 NA
#> GSM680041 4 0.4786 0.6237 0.044 0.004 0.000 0.540 0.000 NA
#> GSM680035 3 0.5182 0.3704 0.000 0.000 0.532 0.000 0.372 NA
#> GSM680047 4 0.0790 0.7816 0.000 0.000 0.000 0.968 0.000 NA
#> GSM680036 5 0.1718 0.6561 0.020 0.000 0.020 0.000 0.936 NA
#> GSM680048 4 0.0146 0.7834 0.000 0.000 0.000 0.996 0.004 NA
#> GSM680037 3 0.5187 0.2866 0.000 0.000 0.472 0.000 0.440 NA
#> GSM680049 4 0.4903 0.6126 0.044 0.008 0.000 0.524 0.000 NA
#> GSM680038 3 0.5943 0.0534 0.000 0.304 0.508 0.000 0.176 NA
#> GSM680050 1 0.0837 0.8320 0.972 0.020 0.004 0.000 0.004 NA
#> GSM680039 3 0.5434 0.0277 0.000 0.312 0.544 0.000 0.144 NA
#> GSM680051 4 0.0405 0.7822 0.000 0.000 0.004 0.988 0.008 NA
#> GSM680040 3 0.5212 0.3687 0.000 0.000 0.532 0.000 0.368 NA
#> GSM680052 4 0.0405 0.7822 0.000 0.000 0.004 0.988 0.008 NA
#> GSM680030 3 0.5157 -0.3367 0.000 0.416 0.524 0.012 0.040 NA
#> GSM680042 4 0.4780 0.6243 0.044 0.004 0.000 0.544 0.000 NA
#> GSM680031 3 0.5175 0.3155 0.000 0.000 0.492 0.000 0.420 NA
#> GSM680043 4 0.4832 0.5814 0.000 0.004 0.088 0.728 0.144 NA
#> GSM680032 1 0.3121 0.8007 0.868 0.012 0.020 0.028 0.068 NA
#> GSM680044 5 0.6981 0.4194 0.088 0.004 0.136 0.180 0.560 NA
#> GSM680033 3 0.5182 0.3704 0.000 0.000 0.532 0.000 0.372 NA
#> GSM680045 4 0.4753 0.5633 0.000 0.000 0.096 0.724 0.148 NA
#> GSM680034 2 0.5807 0.4430 0.000 0.440 0.428 0.016 0.000 NA
#> GSM680046 4 0.0865 0.7815 0.000 0.000 0.000 0.964 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> CV:mclust 52 0.924063 0.776 1.17e-04 1.0000 2
#> CV:mclust 41 0.134749 0.380 2.17e-05 0.4945 3
#> CV:mclust 50 0.001368 0.459 1.77e-04 0.2552 4
#> CV:mclust 29 0.000398 0.312 6.51e-04 0.1628 5
#> CV:mclust 34 0.000116 0.250 6.43e-03 0.0356 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 0.957 0.952 0.977 0.4952 0.502 0.502
#> 3 3 0.521 0.713 0.849 0.3499 0.757 0.546
#> 4 4 0.642 0.695 0.839 0.1354 0.853 0.588
#> 5 5 0.604 0.644 0.764 0.0652 0.845 0.466
#> 6 6 0.681 0.589 0.753 0.0374 0.902 0.557
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
#> GSM680053 2 0.0000 0.986 0.000 1.000
#> GSM680062 1 0.8955 0.578 0.688 0.312
#> GSM680054 2 0.0000 0.986 0.000 1.000
#> GSM680063 2 0.5059 0.868 0.112 0.888
#> GSM680055 2 0.0000 0.986 0.000 1.000
#> GSM680064 1 0.0000 0.963 1.000 0.000
#> GSM680056 1 0.3879 0.907 0.924 0.076
#> GSM680065 1 0.0000 0.963 1.000 0.000
#> GSM680057 2 0.0000 0.986 0.000 1.000
#> GSM680066 2 0.0938 0.976 0.012 0.988
#> GSM680058 2 0.0000 0.986 0.000 1.000
#> GSM680067 2 0.7528 0.724 0.216 0.784
#> GSM680059 2 0.0000 0.986 0.000 1.000
#> GSM680068 1 0.0000 0.963 1.000 0.000
#> GSM680060 2 0.0000 0.986 0.000 1.000
#> GSM680069 2 0.3584 0.921 0.068 0.932
#> GSM680061 2 0.0000 0.986 0.000 1.000
#> GSM680070 1 0.0000 0.963 1.000 0.000
#> GSM680071 1 0.3879 0.908 0.924 0.076
#> GSM680077 1 0.0000 0.963 1.000 0.000
#> GSM680072 2 0.0000 0.986 0.000 1.000
#> GSM680078 2 0.0376 0.982 0.004 0.996
#> GSM680073 2 0.0000 0.986 0.000 1.000
#> GSM680079 1 0.0000 0.963 1.000 0.000
#> GSM680074 2 0.0000 0.986 0.000 1.000
#> GSM680080 2 0.0000 0.986 0.000 1.000
#> GSM680075 2 0.0000 0.986 0.000 1.000
#> GSM680081 2 0.0000 0.986 0.000 1.000
#> GSM680076 2 0.0000 0.986 0.000 1.000
#> GSM680082 1 0.0000 0.963 1.000 0.000
#> GSM680029 2 0.0000 0.986 0.000 1.000
#> GSM680041 1 0.0000 0.963 1.000 0.000
#> GSM680035 2 0.0000 0.986 0.000 1.000
#> GSM680047 1 0.0000 0.963 1.000 0.000
#> GSM680036 2 0.0000 0.986 0.000 1.000
#> GSM680048 1 0.0000 0.963 1.000 0.000
#> GSM680037 2 0.0000 0.986 0.000 1.000
#> GSM680049 1 0.0000 0.963 1.000 0.000
#> GSM680038 2 0.0000 0.986 0.000 1.000
#> GSM680050 1 0.0000 0.963 1.000 0.000
#> GSM680039 2 0.0000 0.986 0.000 1.000
#> GSM680051 1 0.0000 0.963 1.000 0.000
#> GSM680040 2 0.0000 0.986 0.000 1.000
#> GSM680052 1 0.0000 0.963 1.000 0.000
#> GSM680030 2 0.0000 0.986 0.000 1.000
#> GSM680042 1 0.0000 0.963 1.000 0.000
#> GSM680031 2 0.0000 0.986 0.000 1.000
#> GSM680043 1 0.0376 0.961 0.996 0.004
#> GSM680032 1 0.3431 0.916 0.936 0.064
#> GSM680044 1 0.0672 0.958 0.992 0.008
#> GSM680033 2 0.0000 0.986 0.000 1.000
#> GSM680045 1 0.8386 0.658 0.732 0.268
#> GSM680034 2 0.0000 0.986 0.000 1.000
#> GSM680046 1 0.0000 0.963 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 3 0.2878 0.756 0.000 0.096 0.904
#> GSM680062 3 0.4047 0.733 0.148 0.004 0.848
#> GSM680054 3 0.6204 0.356 0.000 0.424 0.576
#> GSM680063 3 0.3583 0.803 0.044 0.056 0.900
#> GSM680055 3 0.2448 0.753 0.000 0.076 0.924
#> GSM680064 1 0.0892 0.880 0.980 0.000 0.020
#> GSM680056 3 0.9375 0.190 0.308 0.196 0.496
#> GSM680065 1 0.4662 0.829 0.844 0.032 0.124
#> GSM680057 2 0.3551 0.716 0.000 0.868 0.132
#> GSM680066 2 0.7555 0.150 0.040 0.520 0.440
#> GSM680058 2 0.1753 0.746 0.000 0.952 0.048
#> GSM680067 2 0.4921 0.680 0.164 0.816 0.020
#> GSM680059 3 0.3551 0.803 0.000 0.132 0.868
#> GSM680068 1 0.1289 0.876 0.968 0.000 0.032
#> GSM680060 2 0.2537 0.731 0.000 0.920 0.080
#> GSM680069 3 0.7457 0.478 0.104 0.208 0.688
#> GSM680061 2 0.2590 0.745 0.004 0.924 0.072
#> GSM680070 1 0.2860 0.862 0.912 0.004 0.084
#> GSM680071 2 0.8790 0.179 0.328 0.540 0.132
#> GSM680077 1 0.7680 0.670 0.680 0.188 0.132
#> GSM680072 2 0.6225 0.036 0.000 0.568 0.432
#> GSM680078 3 0.1031 0.779 0.000 0.024 0.976
#> GSM680073 3 0.4291 0.771 0.000 0.180 0.820
#> GSM680079 1 0.3771 0.846 0.876 0.012 0.112
#> GSM680074 2 0.1289 0.756 0.000 0.968 0.032
#> GSM680080 2 0.1643 0.754 0.000 0.956 0.044
#> GSM680075 3 0.2448 0.770 0.000 0.076 0.924
#> GSM680081 3 0.3619 0.805 0.000 0.136 0.864
#> GSM680076 2 0.3551 0.692 0.000 0.868 0.132
#> GSM680082 1 0.6460 0.762 0.764 0.124 0.112
#> GSM680029 3 0.3267 0.807 0.000 0.116 0.884
#> GSM680041 1 0.0000 0.880 1.000 0.000 0.000
#> GSM680035 3 0.3619 0.805 0.000 0.136 0.864
#> GSM680047 1 0.0000 0.880 1.000 0.000 0.000
#> GSM680036 3 0.2878 0.799 0.000 0.096 0.904
#> GSM680048 1 0.0000 0.880 1.000 0.000 0.000
#> GSM680037 3 0.3619 0.805 0.000 0.136 0.864
#> GSM680049 1 0.0000 0.880 1.000 0.000 0.000
#> GSM680038 2 0.4399 0.667 0.000 0.812 0.188
#> GSM680050 1 0.3030 0.859 0.904 0.004 0.092
#> GSM680039 2 0.5678 0.491 0.000 0.684 0.316
#> GSM680051 1 0.1774 0.869 0.960 0.024 0.016
#> GSM680040 3 0.3619 0.805 0.000 0.136 0.864
#> GSM680052 1 0.1482 0.872 0.968 0.020 0.012
#> GSM680030 2 0.1031 0.755 0.000 0.976 0.024
#> GSM680042 1 0.0237 0.880 0.996 0.000 0.004
#> GSM680031 3 0.3784 0.803 0.004 0.132 0.864
#> GSM680043 1 0.6897 0.615 0.712 0.068 0.220
#> GSM680032 1 0.6783 0.748 0.744 0.116 0.140
#> GSM680044 1 0.0747 0.879 0.984 0.000 0.016
#> GSM680033 3 0.3752 0.799 0.000 0.144 0.856
#> GSM680045 1 0.8117 0.282 0.552 0.076 0.372
#> GSM680034 2 0.4963 0.658 0.008 0.792 0.200
#> GSM680046 1 0.0747 0.877 0.984 0.016 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 3 0.4331 0.6436 0.288 0.000 0.712 0.000
#> GSM680062 3 0.2335 0.8016 0.020 0.000 0.920 0.060
#> GSM680054 3 0.7846 0.1885 0.300 0.296 0.404 0.000
#> GSM680063 3 0.1722 0.8173 0.048 0.000 0.944 0.008
#> GSM680055 1 0.4643 0.2789 0.656 0.000 0.344 0.000
#> GSM680064 4 0.4933 0.2197 0.432 0.000 0.000 0.568
#> GSM680056 1 0.1847 0.7729 0.940 0.004 0.052 0.004
#> GSM680065 1 0.1824 0.7809 0.936 0.000 0.004 0.060
#> GSM680057 2 0.2329 0.8294 0.000 0.916 0.012 0.072
#> GSM680066 4 0.8792 0.1371 0.048 0.236 0.324 0.392
#> GSM680058 2 0.1389 0.8333 0.048 0.952 0.000 0.000
#> GSM680067 2 0.3219 0.7772 0.000 0.836 0.000 0.164
#> GSM680059 3 0.0927 0.8276 0.008 0.016 0.976 0.000
#> GSM680068 4 0.4035 0.7258 0.176 0.000 0.020 0.804
#> GSM680060 2 0.0921 0.8380 0.028 0.972 0.000 0.000
#> GSM680069 1 0.2466 0.7525 0.916 0.028 0.056 0.000
#> GSM680061 2 0.2589 0.8109 0.000 0.884 0.000 0.116
#> GSM680070 1 0.5126 0.0893 0.552 0.004 0.000 0.444
#> GSM680071 1 0.4235 0.6485 0.792 0.188 0.004 0.016
#> GSM680077 1 0.1767 0.7778 0.944 0.044 0.000 0.012
#> GSM680072 2 0.6273 0.5318 0.248 0.644 0.108 0.000
#> GSM680078 3 0.4776 0.4934 0.376 0.000 0.624 0.000
#> GSM680073 3 0.5532 0.6645 0.228 0.068 0.704 0.000
#> GSM680079 1 0.3668 0.6837 0.808 0.000 0.004 0.188
#> GSM680074 2 0.0921 0.8380 0.028 0.972 0.000 0.000
#> GSM680080 2 0.1109 0.8380 0.028 0.968 0.004 0.000
#> GSM680075 3 0.5055 0.5274 0.368 0.008 0.624 0.000
#> GSM680081 3 0.0967 0.8292 0.004 0.004 0.976 0.016
#> GSM680076 2 0.3873 0.6745 0.228 0.772 0.000 0.000
#> GSM680082 1 0.2546 0.7655 0.900 0.008 0.000 0.092
#> GSM680029 3 0.0376 0.8284 0.004 0.004 0.992 0.000
#> GSM680041 4 0.3311 0.7303 0.172 0.000 0.000 0.828
#> GSM680035 3 0.0779 0.8295 0.000 0.004 0.980 0.016
#> GSM680047 4 0.2125 0.7804 0.076 0.000 0.004 0.920
#> GSM680036 3 0.3975 0.6966 0.240 0.000 0.760 0.000
#> GSM680048 4 0.0895 0.7818 0.020 0.004 0.000 0.976
#> GSM680037 3 0.0779 0.8295 0.000 0.004 0.980 0.016
#> GSM680049 4 0.2814 0.7600 0.132 0.000 0.000 0.868
#> GSM680038 2 0.3938 0.7879 0.080 0.852 0.060 0.008
#> GSM680050 1 0.3873 0.6278 0.772 0.000 0.000 0.228
#> GSM680039 2 0.6871 0.5608 0.000 0.592 0.240 0.168
#> GSM680051 4 0.1471 0.7714 0.004 0.024 0.012 0.960
#> GSM680040 3 0.0779 0.8295 0.000 0.004 0.980 0.016
#> GSM680052 4 0.1520 0.7692 0.000 0.020 0.024 0.956
#> GSM680030 2 0.1139 0.8396 0.008 0.972 0.008 0.012
#> GSM680042 4 0.3444 0.7193 0.184 0.000 0.000 0.816
#> GSM680031 3 0.1209 0.8226 0.000 0.004 0.964 0.032
#> GSM680043 4 0.3901 0.6802 0.004 0.012 0.168 0.816
#> GSM680032 1 0.1576 0.7848 0.948 0.000 0.004 0.048
#> GSM680044 4 0.2928 0.7734 0.108 0.000 0.012 0.880
#> GSM680033 3 0.0927 0.8285 0.000 0.008 0.976 0.016
#> GSM680045 4 0.4741 0.6156 0.000 0.028 0.228 0.744
#> GSM680034 2 0.4485 0.6868 0.000 0.740 0.012 0.248
#> GSM680046 4 0.0000 0.7801 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.3132 0.6811 0.000 0.000 0.172 0.008 0.820
#> GSM680062 5 0.6358 0.2742 0.000 0.000 0.180 0.328 0.492
#> GSM680054 5 0.3122 0.7238 0.000 0.120 0.024 0.004 0.852
#> GSM680063 5 0.5565 0.5336 0.000 0.000 0.216 0.144 0.640
#> GSM680055 5 0.3086 0.7277 0.040 0.000 0.092 0.004 0.864
#> GSM680064 1 0.5131 0.1936 0.588 0.000 0.000 0.364 0.048
#> GSM680056 5 0.2006 0.7291 0.072 0.000 0.000 0.012 0.916
#> GSM680065 5 0.4193 0.5620 0.256 0.000 0.000 0.024 0.720
#> GSM680057 2 0.2536 0.7889 0.000 0.868 0.004 0.128 0.000
#> GSM680066 1 0.5751 0.4200 0.568 0.008 0.356 0.064 0.004
#> GSM680058 2 0.3961 0.5600 0.016 0.736 0.000 0.000 0.248
#> GSM680067 2 0.2773 0.7721 0.000 0.836 0.000 0.164 0.000
#> GSM680059 3 0.0566 0.7922 0.004 0.000 0.984 0.000 0.012
#> GSM680068 1 0.4859 0.6420 0.732 0.000 0.112 0.152 0.004
#> GSM680060 2 0.1608 0.7825 0.000 0.928 0.000 0.000 0.072
#> GSM680069 5 0.2462 0.7229 0.112 0.000 0.008 0.000 0.880
#> GSM680061 2 0.1851 0.7976 0.000 0.912 0.000 0.088 0.000
#> GSM680070 1 0.2758 0.7331 0.888 0.000 0.024 0.076 0.012
#> GSM680071 5 0.5077 0.6743 0.156 0.108 0.000 0.012 0.724
#> GSM680077 1 0.1731 0.7391 0.932 0.004 0.004 0.000 0.060
#> GSM680072 5 0.5166 0.3987 0.044 0.348 0.004 0.000 0.604
#> GSM680078 1 0.5109 0.2456 0.504 0.000 0.460 0.000 0.036
#> GSM680073 3 0.6750 0.0251 0.068 0.068 0.476 0.000 0.388
#> GSM680079 1 0.2444 0.7465 0.912 0.000 0.028 0.036 0.024
#> GSM680074 2 0.1741 0.7874 0.040 0.936 0.000 0.000 0.024
#> GSM680080 2 0.2304 0.7816 0.048 0.908 0.000 0.000 0.044
#> GSM680075 3 0.4675 0.4887 0.044 0.004 0.704 0.000 0.248
#> GSM680081 3 0.1808 0.8079 0.012 0.000 0.936 0.044 0.008
#> GSM680076 2 0.5039 0.6388 0.184 0.700 0.000 0.000 0.116
#> GSM680082 1 0.1983 0.7312 0.924 0.008 0.000 0.008 0.060
#> GSM680029 3 0.0609 0.7996 0.000 0.000 0.980 0.000 0.020
#> GSM680041 4 0.4637 0.6535 0.100 0.000 0.000 0.740 0.160
#> GSM680035 3 0.3595 0.8041 0.000 0.000 0.816 0.140 0.044
#> GSM680047 4 0.3612 0.6723 0.028 0.000 0.000 0.800 0.172
#> GSM680036 5 0.2891 0.6811 0.000 0.000 0.176 0.000 0.824
#> GSM680048 4 0.3209 0.7215 0.068 0.008 0.000 0.864 0.060
#> GSM680037 3 0.2813 0.8219 0.000 0.000 0.876 0.084 0.040
#> GSM680049 4 0.4687 0.5706 0.288 0.000 0.000 0.672 0.040
#> GSM680038 5 0.4517 0.6373 0.008 0.208 0.004 0.036 0.744
#> GSM680050 1 0.2153 0.7397 0.916 0.000 0.000 0.044 0.040
#> GSM680039 2 0.5190 0.6457 0.000 0.680 0.088 0.228 0.004
#> GSM680051 4 0.2217 0.7017 0.000 0.044 0.012 0.920 0.024
#> GSM680040 3 0.3115 0.8181 0.000 0.000 0.852 0.112 0.036
#> GSM680052 4 0.1569 0.7027 0.004 0.044 0.008 0.944 0.000
#> GSM680030 2 0.4108 0.7568 0.044 0.808 0.004 0.016 0.128
#> GSM680042 4 0.4617 0.6249 0.224 0.000 0.000 0.716 0.060
#> GSM680031 3 0.2964 0.7797 0.000 0.004 0.840 0.152 0.004
#> GSM680043 4 0.5679 0.2775 0.028 0.032 0.352 0.584 0.004
#> GSM680032 1 0.3289 0.6633 0.816 0.004 0.000 0.008 0.172
#> GSM680044 4 0.5732 0.6158 0.236 0.000 0.052 0.660 0.052
#> GSM680033 3 0.3432 0.8081 0.000 0.000 0.828 0.132 0.040
#> GSM680045 4 0.5169 0.4245 0.004 0.052 0.284 0.656 0.004
#> GSM680034 2 0.4065 0.6779 0.000 0.720 0.016 0.264 0.000
#> GSM680046 4 0.2904 0.7006 0.112 0.008 0.008 0.868 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.3548 0.7619 0.004 0.000 0.048 0.000 0.796 0.152
#> GSM680062 4 0.6359 0.2873 0.004 0.000 0.072 0.528 0.296 0.100
#> GSM680054 5 0.3371 0.7886 0.004 0.040 0.044 0.000 0.848 0.064
#> GSM680063 5 0.5138 0.6506 0.000 0.000 0.068 0.052 0.680 0.200
#> GSM680055 5 0.3590 0.7835 0.024 0.000 0.032 0.000 0.808 0.136
#> GSM680064 4 0.2809 0.6727 0.168 0.000 0.000 0.824 0.004 0.004
#> GSM680056 5 0.2658 0.7878 0.080 0.000 0.000 0.008 0.876 0.036
#> GSM680065 5 0.4023 0.6468 0.240 0.000 0.000 0.004 0.720 0.036
#> GSM680057 3 0.4850 0.1574 0.004 0.456 0.508 0.012 0.012 0.008
#> GSM680066 1 0.6121 0.5150 0.596 0.032 0.252 0.040 0.000 0.080
#> GSM680058 2 0.4636 0.5080 0.000 0.692 0.000 0.000 0.160 0.148
#> GSM680067 2 0.3013 0.5531 0.004 0.848 0.116 0.024 0.000 0.008
#> GSM680059 6 0.4034 0.4801 0.000 0.020 0.328 0.000 0.000 0.652
#> GSM680068 1 0.5455 0.6534 0.660 0.000 0.100 0.184 0.000 0.056
#> GSM680060 2 0.2948 0.6009 0.012 0.860 0.000 0.000 0.084 0.044
#> GSM680069 5 0.1957 0.7938 0.112 0.000 0.000 0.000 0.888 0.000
#> GSM680061 2 0.2485 0.5789 0.004 0.884 0.088 0.020 0.000 0.004
#> GSM680070 1 0.1707 0.7908 0.928 0.000 0.004 0.056 0.000 0.012
#> GSM680071 5 0.4044 0.7267 0.200 0.028 0.000 0.004 0.752 0.016
#> GSM680077 1 0.2001 0.7705 0.924 0.012 0.000 0.004 0.032 0.028
#> GSM680072 6 0.5939 -0.1367 0.000 0.372 0.000 0.000 0.216 0.412
#> GSM680078 6 0.4667 0.5273 0.132 0.000 0.108 0.000 0.028 0.732
#> GSM680073 6 0.4668 0.4663 0.004 0.120 0.040 0.000 0.088 0.748
#> GSM680079 1 0.2944 0.7770 0.856 0.000 0.000 0.068 0.004 0.072
#> GSM680074 2 0.3073 0.5851 0.000 0.788 0.000 0.000 0.008 0.204
#> GSM680080 2 0.3533 0.5610 0.004 0.748 0.000 0.000 0.012 0.236
#> GSM680075 6 0.4494 0.6092 0.016 0.016 0.156 0.000 0.060 0.752
#> GSM680081 3 0.2222 0.6931 0.040 0.000 0.908 0.000 0.012 0.040
#> GSM680076 2 0.4762 0.5208 0.060 0.668 0.000 0.000 0.016 0.256
#> GSM680082 1 0.3508 0.7368 0.828 0.008 0.000 0.020 0.032 0.112
#> GSM680029 6 0.4096 0.1900 0.000 0.000 0.484 0.000 0.008 0.508
#> GSM680041 4 0.1003 0.7899 0.016 0.000 0.000 0.964 0.020 0.000
#> GSM680035 3 0.1562 0.7116 0.000 0.000 0.940 0.004 0.024 0.032
#> GSM680047 4 0.1251 0.7893 0.000 0.000 0.012 0.956 0.024 0.008
#> GSM680036 5 0.3293 0.7717 0.008 0.000 0.040 0.000 0.824 0.128
#> GSM680048 4 0.0622 0.7910 0.012 0.000 0.000 0.980 0.008 0.000
#> GSM680037 3 0.2070 0.6578 0.000 0.000 0.892 0.000 0.008 0.100
#> GSM680049 4 0.1387 0.7763 0.068 0.000 0.000 0.932 0.000 0.000
#> GSM680038 5 0.3181 0.7721 0.012 0.052 0.024 0.004 0.868 0.040
#> GSM680050 1 0.2602 0.7803 0.884 0.000 0.000 0.072 0.024 0.020
#> GSM680039 3 0.4917 0.4187 0.000 0.328 0.616 0.028 0.008 0.020
#> GSM680051 4 0.6209 -0.0907 0.000 0.092 0.432 0.432 0.020 0.024
#> GSM680040 3 0.1700 0.6874 0.000 0.000 0.916 0.000 0.004 0.080
#> GSM680052 4 0.2806 0.7548 0.000 0.056 0.060 0.872 0.000 0.012
#> GSM680030 2 0.8050 0.2612 0.040 0.380 0.180 0.000 0.236 0.164
#> GSM680042 4 0.0935 0.7869 0.032 0.000 0.000 0.964 0.004 0.000
#> GSM680031 3 0.2202 0.6961 0.000 0.012 0.904 0.008 0.004 0.072
#> GSM680043 3 0.6212 0.3503 0.020 0.100 0.556 0.288 0.000 0.036
#> GSM680032 1 0.5373 0.6224 0.680 0.016 0.000 0.024 0.112 0.168
#> GSM680044 4 0.3626 0.7251 0.060 0.004 0.004 0.820 0.008 0.104
#> GSM680033 3 0.1338 0.7144 0.000 0.004 0.952 0.004 0.008 0.032
#> GSM680045 4 0.5359 0.4871 0.012 0.076 0.268 0.628 0.000 0.016
#> GSM680034 2 0.4915 -0.2482 0.004 0.488 0.468 0.028 0.000 0.012
#> GSM680046 4 0.2044 0.7827 0.028 0.004 0.040 0.920 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> CV:NMF 54 0.207125 0.826 1.07e-05 0.6858 2
#> CV:NMF 46 0.152692 0.487 7.42e-06 0.7071 3
#> CV:NMF 48 0.004563 0.321 2.80e-05 0.0937 4
#> CV:NMF 45 0.001156 0.402 1.25e-04 0.1845 5
#> CV:NMF 42 0.000527 0.187 2.06e-03 0.0268 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 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 0.0935 0.624 0.780 0.4238 0.502 0.502
#> 3 3 0.2345 0.676 0.807 0.3833 0.862 0.724
#> 4 4 0.3695 0.498 0.664 0.1842 0.941 0.837
#> 5 5 0.5128 0.440 0.693 0.1056 0.766 0.400
#> 6 6 0.5878 0.468 0.632 0.0557 0.790 0.321
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
#> GSM680053 1 0.9850 0.475 0.572 0.428
#> GSM680062 1 0.9833 0.482 0.576 0.424
#> GSM680054 1 0.9866 0.466 0.568 0.432
#> GSM680063 1 0.9833 0.482 0.576 0.424
#> GSM680055 1 0.9850 0.475 0.572 0.428
#> GSM680064 1 0.4690 0.716 0.900 0.100
#> GSM680056 1 0.6887 0.716 0.816 0.184
#> GSM680065 1 0.6887 0.716 0.816 0.184
#> GSM680057 2 0.8081 0.708 0.248 0.752
#> GSM680066 1 0.4815 0.718 0.896 0.104
#> GSM680058 2 0.0000 0.726 0.000 1.000
#> GSM680067 2 0.6048 0.704 0.148 0.852
#> GSM680059 2 0.0938 0.732 0.012 0.988
#> GSM680068 1 0.4815 0.718 0.896 0.104
#> GSM680060 1 0.9552 0.566 0.624 0.376
#> GSM680069 1 0.9552 0.566 0.624 0.376
#> GSM680061 2 0.6048 0.704 0.148 0.852
#> GSM680070 1 0.4815 0.718 0.896 0.104
#> GSM680071 1 0.9170 0.623 0.668 0.332
#> GSM680077 1 0.7883 0.703 0.764 0.236
#> GSM680072 2 0.0000 0.726 0.000 1.000
#> GSM680078 1 0.4815 0.718 0.896 0.104
#> GSM680073 2 0.4690 0.718 0.100 0.900
#> GSM680079 1 0.4690 0.716 0.900 0.100
#> GSM680074 2 0.0000 0.726 0.000 1.000
#> GSM680080 2 0.0000 0.726 0.000 1.000
#> GSM680075 2 0.9710 0.308 0.400 0.600
#> GSM680081 2 0.8909 0.608 0.308 0.692
#> GSM680076 1 0.9552 0.587 0.624 0.376
#> GSM680082 1 0.9552 0.587 0.624 0.376
#> GSM680029 2 0.8763 0.532 0.296 0.704
#> GSM680041 1 0.0000 0.649 1.000 0.000
#> GSM680035 2 0.6623 0.735 0.172 0.828
#> GSM680047 1 0.0000 0.649 1.000 0.000
#> GSM680036 2 0.8813 0.523 0.300 0.700
#> GSM680048 1 0.9552 0.395 0.624 0.376
#> GSM680037 2 0.6623 0.735 0.172 0.828
#> GSM680049 1 0.0000 0.649 1.000 0.000
#> GSM680038 2 0.7056 0.739 0.192 0.808
#> GSM680050 1 0.7883 0.703 0.764 0.236
#> GSM680039 2 0.6438 0.763 0.164 0.836
#> GSM680051 1 0.9983 0.113 0.524 0.476
#> GSM680040 2 0.5519 0.759 0.128 0.872
#> GSM680052 1 0.9552 0.395 0.624 0.376
#> GSM680030 2 0.8081 0.708 0.248 0.752
#> GSM680042 1 0.0000 0.649 1.000 0.000
#> GSM680031 2 0.8909 0.607 0.308 0.692
#> GSM680043 2 0.8955 0.606 0.312 0.688
#> GSM680032 1 0.7219 0.708 0.800 0.200
#> GSM680044 1 0.7219 0.708 0.800 0.200
#> GSM680033 2 0.5629 0.761 0.132 0.868
#> GSM680045 1 0.9686 0.389 0.604 0.396
#> GSM680034 2 0.8081 0.708 0.248 0.752
#> GSM680046 1 0.9686 0.389 0.604 0.396
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 3 0.5591 0.611 0.000 0.304 0.696
#> GSM680062 3 0.5560 0.617 0.000 0.300 0.700
#> GSM680054 3 0.5905 0.522 0.000 0.352 0.648
#> GSM680063 3 0.5560 0.617 0.000 0.300 0.700
#> GSM680055 3 0.5591 0.611 0.000 0.304 0.696
#> GSM680064 3 0.2537 0.791 0.080 0.000 0.920
#> GSM680056 3 0.0983 0.801 0.004 0.016 0.980
#> GSM680065 3 0.0983 0.801 0.004 0.016 0.980
#> GSM680057 2 0.6834 0.716 0.112 0.740 0.148
#> GSM680066 3 0.2772 0.793 0.080 0.004 0.916
#> GSM680058 2 0.0747 0.725 0.000 0.984 0.016
#> GSM680067 2 0.4291 0.597 0.152 0.840 0.008
#> GSM680059 2 0.0892 0.732 0.000 0.980 0.020
#> GSM680068 3 0.2955 0.793 0.080 0.008 0.912
#> GSM680060 3 0.4887 0.701 0.000 0.228 0.772
#> GSM680069 3 0.4887 0.701 0.000 0.228 0.772
#> GSM680061 2 0.4291 0.597 0.152 0.840 0.008
#> GSM680070 3 0.2772 0.793 0.080 0.004 0.916
#> GSM680071 3 0.4346 0.742 0.000 0.184 0.816
#> GSM680077 3 0.2400 0.788 0.004 0.064 0.932
#> GSM680072 2 0.0747 0.725 0.000 0.984 0.016
#> GSM680078 3 0.2772 0.793 0.080 0.004 0.916
#> GSM680073 2 0.3340 0.714 0.000 0.880 0.120
#> GSM680079 3 0.2537 0.791 0.080 0.000 0.920
#> GSM680074 2 0.0237 0.723 0.000 0.996 0.004
#> GSM680080 2 0.0237 0.723 0.000 0.996 0.004
#> GSM680075 2 0.6244 0.344 0.000 0.560 0.440
#> GSM680081 2 0.6008 0.618 0.004 0.664 0.332
#> GSM680076 3 0.5024 0.716 0.004 0.220 0.776
#> GSM680082 3 0.5024 0.716 0.004 0.220 0.776
#> GSM680029 2 0.5810 0.547 0.000 0.664 0.336
#> GSM680041 1 0.0237 0.657 0.996 0.000 0.004
#> GSM680035 2 0.4346 0.746 0.000 0.816 0.184
#> GSM680047 1 0.0237 0.657 0.996 0.000 0.004
#> GSM680036 2 0.5859 0.532 0.000 0.656 0.344
#> GSM680048 1 0.7710 0.526 0.576 0.368 0.056
#> GSM680037 2 0.4346 0.746 0.000 0.816 0.184
#> GSM680049 1 0.0237 0.657 0.996 0.000 0.004
#> GSM680038 2 0.5883 0.723 0.092 0.796 0.112
#> GSM680050 3 0.2400 0.788 0.004 0.064 0.932
#> GSM680039 2 0.5094 0.765 0.040 0.824 0.136
#> GSM680051 1 0.7752 0.272 0.496 0.456 0.048
#> GSM680040 2 0.3851 0.764 0.004 0.860 0.136
#> GSM680052 1 0.7710 0.526 0.576 0.368 0.056
#> GSM680030 2 0.6834 0.716 0.112 0.740 0.148
#> GSM680042 1 0.0237 0.657 0.996 0.000 0.004
#> GSM680031 2 0.7731 0.650 0.108 0.664 0.228
#> GSM680043 2 0.7796 0.644 0.112 0.660 0.228
#> GSM680032 3 0.5304 0.782 0.068 0.108 0.824
#> GSM680044 3 0.5304 0.782 0.068 0.108 0.824
#> GSM680033 2 0.4033 0.764 0.008 0.856 0.136
#> GSM680045 1 0.8586 0.488 0.520 0.376 0.104
#> GSM680034 2 0.6834 0.716 0.112 0.740 0.148
#> GSM680046 1 0.8586 0.488 0.520 0.376 0.104
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 1 0.7599 0.3136 0.424 0.200 0.376 0.000
#> GSM680062 1 0.7595 0.3158 0.428 0.200 0.372 0.000
#> GSM680054 1 0.7953 0.2797 0.416 0.192 0.380 0.012
#> GSM680063 1 0.7595 0.3158 0.428 0.200 0.372 0.000
#> GSM680055 1 0.7599 0.3136 0.424 0.200 0.376 0.000
#> GSM680064 1 0.0188 0.4802 0.996 0.000 0.000 0.004
#> GSM680056 1 0.4957 0.0626 0.656 0.336 0.004 0.004
#> GSM680065 1 0.4957 0.0626 0.656 0.336 0.004 0.004
#> GSM680057 3 0.6914 0.6094 0.076 0.200 0.664 0.060
#> GSM680066 1 0.0376 0.4840 0.992 0.000 0.004 0.004
#> GSM680058 3 0.4012 0.6475 0.000 0.184 0.800 0.016
#> GSM680067 3 0.6737 0.4018 0.004 0.408 0.508 0.080
#> GSM680059 3 0.1716 0.6844 0.000 0.064 0.936 0.000
#> GSM680068 1 0.0524 0.4833 0.988 0.000 0.008 0.004
#> GSM680060 2 0.5936 0.8305 0.324 0.620 0.056 0.000
#> GSM680069 2 0.5936 0.8305 0.324 0.620 0.056 0.000
#> GSM680061 3 0.6737 0.4018 0.004 0.408 0.508 0.080
#> GSM680070 1 0.0376 0.4840 0.992 0.000 0.004 0.004
#> GSM680071 2 0.5560 0.7308 0.392 0.584 0.024 0.000
#> GSM680077 1 0.4985 -0.4508 0.532 0.468 0.000 0.000
#> GSM680072 3 0.4012 0.6475 0.000 0.184 0.800 0.016
#> GSM680078 1 0.0376 0.4840 0.992 0.000 0.004 0.004
#> GSM680073 3 0.4155 0.6634 0.072 0.100 0.828 0.000
#> GSM680079 1 0.0188 0.4802 0.996 0.000 0.000 0.004
#> GSM680074 3 0.3881 0.6511 0.000 0.172 0.812 0.016
#> GSM680080 3 0.3881 0.6511 0.000 0.172 0.812 0.016
#> GSM680075 3 0.6429 0.3654 0.324 0.088 0.588 0.000
#> GSM680081 3 0.5489 0.5745 0.240 0.060 0.700 0.000
#> GSM680076 2 0.5339 0.8281 0.272 0.688 0.040 0.000
#> GSM680082 2 0.5339 0.8281 0.272 0.688 0.040 0.000
#> GSM680029 3 0.5318 0.5239 0.196 0.072 0.732 0.000
#> GSM680041 4 0.1302 0.5768 0.044 0.000 0.000 0.956
#> GSM680035 3 0.2983 0.6835 0.068 0.040 0.892 0.000
#> GSM680047 4 0.1302 0.5768 0.044 0.000 0.000 0.956
#> GSM680036 3 0.5421 0.5135 0.200 0.076 0.724 0.000
#> GSM680048 4 0.8936 0.5494 0.076 0.236 0.240 0.448
#> GSM680037 3 0.2983 0.6835 0.068 0.040 0.892 0.000
#> GSM680049 4 0.1302 0.5768 0.044 0.000 0.000 0.956
#> GSM680038 3 0.6578 0.6223 0.056 0.200 0.684 0.060
#> GSM680050 1 0.4985 -0.4508 0.532 0.468 0.000 0.000
#> GSM680039 3 0.4273 0.6901 0.052 0.044 0.848 0.056
#> GSM680051 4 0.8598 0.3822 0.036 0.244 0.308 0.412
#> GSM680040 3 0.1854 0.6947 0.048 0.012 0.940 0.000
#> GSM680052 4 0.8936 0.5494 0.076 0.236 0.240 0.448
#> GSM680030 3 0.6914 0.6094 0.076 0.200 0.664 0.060
#> GSM680042 4 0.1302 0.5768 0.044 0.000 0.000 0.956
#> GSM680031 3 0.7946 0.4316 0.192 0.252 0.528 0.028
#> GSM680043 3 0.7987 0.4172 0.192 0.260 0.520 0.028
#> GSM680032 1 0.3372 0.4373 0.868 0.036 0.096 0.000
#> GSM680044 1 0.3372 0.4373 0.868 0.036 0.096 0.000
#> GSM680033 3 0.1975 0.6953 0.048 0.016 0.936 0.000
#> GSM680045 4 0.9646 0.5139 0.148 0.236 0.248 0.368
#> GSM680034 3 0.6914 0.6094 0.076 0.200 0.664 0.060
#> GSM680046 4 0.9646 0.5139 0.148 0.236 0.248 0.368
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 3 0.6956 0.2871 0.240 0.012 0.440 0.000 0.308
#> GSM680062 3 0.6971 0.2829 0.244 0.012 0.436 0.000 0.308
#> GSM680054 3 0.8025 0.2716 0.232 0.100 0.392 0.000 0.276
#> GSM680063 3 0.6971 0.2829 0.244 0.012 0.436 0.000 0.308
#> GSM680055 3 0.6956 0.2871 0.240 0.012 0.440 0.000 0.308
#> GSM680064 1 0.0000 0.9204 1.000 0.000 0.000 0.000 0.000
#> GSM680056 5 0.5059 0.2657 0.400 0.012 0.012 0.004 0.572
#> GSM680065 5 0.5059 0.2657 0.400 0.012 0.012 0.004 0.572
#> GSM680057 2 0.5232 0.4189 0.008 0.492 0.472 0.000 0.028
#> GSM680066 1 0.0162 0.9239 0.996 0.000 0.004 0.000 0.000
#> GSM680058 3 0.4736 0.2759 0.000 0.404 0.576 0.000 0.020
#> GSM680067 2 0.2674 0.4276 0.000 0.868 0.120 0.000 0.012
#> GSM680059 3 0.2471 0.4044 0.000 0.136 0.864 0.000 0.000
#> GSM680068 1 0.0324 0.9214 0.992 0.004 0.004 0.000 0.000
#> GSM680060 5 0.5275 0.6754 0.108 0.132 0.032 0.000 0.728
#> GSM680069 5 0.5275 0.6754 0.108 0.132 0.032 0.000 0.728
#> GSM680061 2 0.2674 0.4276 0.000 0.868 0.120 0.000 0.012
#> GSM680070 1 0.0162 0.9239 0.996 0.000 0.004 0.000 0.000
#> GSM680071 5 0.2804 0.6695 0.068 0.044 0.004 0.000 0.884
#> GSM680077 5 0.5672 0.4519 0.368 0.088 0.000 0.000 0.544
#> GSM680072 3 0.4736 0.2759 0.000 0.404 0.576 0.000 0.020
#> GSM680078 1 0.0162 0.9239 0.996 0.000 0.004 0.000 0.000
#> GSM680073 3 0.4394 0.4529 0.000 0.136 0.764 0.000 0.100
#> GSM680079 1 0.0000 0.9204 1.000 0.000 0.000 0.000 0.000
#> GSM680074 3 0.4464 0.2741 0.000 0.408 0.584 0.000 0.008
#> GSM680080 3 0.4464 0.2741 0.000 0.408 0.584 0.000 0.008
#> GSM680075 3 0.6151 0.3943 0.120 0.028 0.620 0.000 0.232
#> GSM680081 3 0.5386 0.3584 0.116 0.040 0.724 0.000 0.120
#> GSM680076 5 0.3239 0.6759 0.012 0.156 0.004 0.000 0.828
#> GSM680082 5 0.3239 0.6759 0.012 0.156 0.004 0.000 0.828
#> GSM680029 3 0.4147 0.4878 0.056 0.012 0.796 0.000 0.136
#> GSM680041 4 0.0000 0.7241 0.000 0.000 0.000 1.000 0.000
#> GSM680035 3 0.1623 0.4651 0.016 0.016 0.948 0.000 0.020
#> GSM680047 4 0.0000 0.7241 0.000 0.000 0.000 1.000 0.000
#> GSM680036 3 0.4255 0.4872 0.060 0.012 0.788 0.000 0.140
#> GSM680048 4 0.7211 0.0407 0.044 0.356 0.140 0.456 0.004
#> GSM680037 3 0.1623 0.4651 0.016 0.016 0.948 0.000 0.020
#> GSM680049 4 0.0162 0.7230 0.000 0.004 0.000 0.996 0.000
#> GSM680038 2 0.5222 0.3820 0.008 0.512 0.452 0.000 0.028
#> GSM680050 5 0.5672 0.4519 0.368 0.088 0.000 0.000 0.544
#> GSM680039 3 0.2891 0.2556 0.000 0.176 0.824 0.000 0.000
#> GSM680051 2 0.7070 0.0629 0.024 0.436 0.196 0.344 0.000
#> GSM680040 3 0.0404 0.4511 0.000 0.012 0.988 0.000 0.000
#> GSM680052 4 0.7211 0.0407 0.044 0.356 0.140 0.456 0.004
#> GSM680030 2 0.5232 0.4189 0.008 0.492 0.472 0.000 0.028
#> GSM680042 4 0.0000 0.7241 0.000 0.000 0.000 1.000 0.000
#> GSM680031 3 0.7026 -0.3393 0.168 0.376 0.428 0.000 0.028
#> GSM680043 3 0.7031 -0.3488 0.168 0.384 0.420 0.000 0.028
#> GSM680032 1 0.4074 0.7655 0.820 0.036 0.092 0.000 0.052
#> GSM680044 1 0.4074 0.7655 0.820 0.036 0.092 0.000 0.052
#> GSM680033 3 0.0510 0.4480 0.000 0.016 0.984 0.000 0.000
#> GSM680045 2 0.8173 -0.0724 0.144 0.360 0.144 0.348 0.004
#> GSM680034 2 0.5232 0.4189 0.008 0.492 0.472 0.000 0.028
#> GSM680046 2 0.8173 -0.0724 0.144 0.360 0.144 0.348 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.4488 0.5905 0.016 0.004 0.432 0.000 0.544 0.004
#> GSM680062 5 0.4559 0.5930 0.020 0.004 0.428 0.000 0.544 0.004
#> GSM680054 5 0.5495 0.5112 0.012 0.096 0.368 0.000 0.524 0.000
#> GSM680063 5 0.4559 0.5930 0.020 0.004 0.428 0.000 0.544 0.004
#> GSM680055 5 0.4488 0.5905 0.016 0.004 0.432 0.000 0.544 0.004
#> GSM680064 1 0.0458 0.9107 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM680056 5 0.3844 0.3561 0.108 0.000 0.004 0.004 0.792 0.092
#> GSM680065 5 0.3844 0.3561 0.108 0.000 0.004 0.004 0.792 0.092
#> GSM680057 3 0.7467 -0.1225 0.000 0.316 0.328 0.272 0.064 0.020
#> GSM680066 1 0.0260 0.9162 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM680058 2 0.4531 0.5428 0.000 0.608 0.352 0.000 0.036 0.004
#> GSM680067 2 0.3969 0.3612 0.000 0.644 0.008 0.344 0.004 0.000
#> GSM680059 3 0.3583 0.2510 0.000 0.260 0.728 0.004 0.008 0.000
#> GSM680068 1 0.0146 0.9140 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM680060 6 0.5519 0.5323 0.084 0.012 0.012 0.004 0.272 0.616
#> GSM680069 6 0.5519 0.5323 0.084 0.012 0.012 0.004 0.272 0.616
#> GSM680061 2 0.3969 0.3612 0.000 0.644 0.008 0.344 0.004 0.000
#> GSM680070 1 0.0260 0.9162 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM680071 5 0.4122 -0.3928 0.000 0.004 0.000 0.004 0.520 0.472
#> GSM680077 6 0.3912 0.4768 0.340 0.000 0.000 0.000 0.012 0.648
#> GSM680072 2 0.4531 0.5428 0.000 0.608 0.352 0.000 0.036 0.004
#> GSM680078 1 0.0146 0.9164 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM680073 3 0.5165 0.2480 0.000 0.256 0.628 0.004 0.108 0.004
#> GSM680079 1 0.0458 0.9107 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM680074 2 0.4353 0.5418 0.000 0.612 0.360 0.000 0.024 0.004
#> GSM680080 2 0.4353 0.5418 0.000 0.612 0.360 0.000 0.024 0.004
#> GSM680075 3 0.6275 0.2587 0.052 0.012 0.592 0.004 0.224 0.116
#> GSM680081 3 0.5119 0.4206 0.056 0.000 0.720 0.008 0.104 0.112
#> GSM680076 6 0.1152 0.6663 0.004 0.000 0.000 0.000 0.044 0.952
#> GSM680082 6 0.1152 0.6663 0.004 0.000 0.000 0.000 0.044 0.952
#> GSM680029 3 0.3561 0.3642 0.004 0.012 0.776 0.004 0.200 0.004
#> GSM680041 4 0.5239 0.4428 0.000 0.248 0.000 0.600 0.152 0.000
#> GSM680035 3 0.1082 0.5386 0.000 0.000 0.956 0.004 0.040 0.000
#> GSM680047 4 0.5239 0.4428 0.000 0.248 0.000 0.600 0.152 0.000
#> GSM680036 3 0.3620 0.3513 0.004 0.012 0.768 0.004 0.208 0.004
#> GSM680048 4 0.2963 0.5504 0.036 0.000 0.096 0.856 0.012 0.000
#> GSM680037 3 0.1082 0.5386 0.000 0.000 0.956 0.004 0.040 0.000
#> GSM680049 4 0.5208 0.4435 0.000 0.248 0.000 0.604 0.148 0.000
#> GSM680038 2 0.7395 0.0608 0.000 0.384 0.284 0.248 0.064 0.020
#> GSM680050 6 0.3912 0.4768 0.340 0.000 0.000 0.000 0.012 0.648
#> GSM680039 3 0.4378 0.4017 0.000 0.108 0.760 0.104 0.028 0.000
#> GSM680051 4 0.5031 0.4733 0.016 0.068 0.132 0.736 0.044 0.004
#> GSM680040 3 0.0405 0.5577 0.000 0.008 0.988 0.004 0.000 0.000
#> GSM680052 4 0.2963 0.5504 0.036 0.000 0.096 0.856 0.012 0.000
#> GSM680030 3 0.7467 -0.1225 0.000 0.316 0.328 0.272 0.064 0.020
#> GSM680042 4 0.5239 0.4428 0.000 0.248 0.000 0.600 0.152 0.000
#> GSM680031 4 0.7599 0.1167 0.152 0.036 0.368 0.376 0.052 0.016
#> GSM680043 4 0.7597 0.1350 0.152 0.036 0.360 0.384 0.052 0.016
#> GSM680032 1 0.4328 0.7585 0.800 0.004 0.072 0.020 0.056 0.048
#> GSM680044 1 0.4328 0.7585 0.800 0.004 0.072 0.020 0.056 0.048
#> GSM680033 3 0.0520 0.5579 0.000 0.008 0.984 0.008 0.000 0.000
#> GSM680045 4 0.4423 0.5292 0.140 0.000 0.096 0.748 0.012 0.004
#> GSM680034 3 0.7467 -0.1225 0.000 0.316 0.328 0.272 0.064 0.020
#> GSM680046 4 0.4423 0.5292 0.140 0.000 0.096 0.748 0.012 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> MAD:hclust 43 0.274425 0.520 4.54e-04 0.9287 2
#> MAD:hclust 50 0.000206 0.378 2.62e-04 0.3578 3
#> MAD:hclust 31 0.001706 0.398 9.86e-05 0.0531 4
#> MAD:hclust 17 0.005429 0.135 6.50e-02 0.1357 5
#> MAD:hclust 29 0.000447 0.018 1.89e-02 0.0466 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 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 0.919 0.962 0.5072 0.493 0.493
#> 3 3 0.467 0.426 0.624 0.2911 0.829 0.675
#> 4 4 0.621 0.716 0.792 0.1429 0.771 0.463
#> 5 5 0.733 0.752 0.831 0.0729 0.883 0.570
#> 6 6 0.751 0.658 0.808 0.0408 0.966 0.825
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
#> GSM680053 2 0.0376 0.9508 0.004 0.996
#> GSM680062 1 0.5408 0.8670 0.876 0.124
#> GSM680054 2 0.0376 0.9508 0.004 0.996
#> GSM680063 1 0.7376 0.7566 0.792 0.208
#> GSM680055 2 0.0376 0.9508 0.004 0.996
#> GSM680064 1 0.1633 0.9736 0.976 0.024
#> GSM680056 1 0.1843 0.9729 0.972 0.028
#> GSM680065 1 0.1843 0.9729 0.972 0.028
#> GSM680057 2 0.1633 0.9491 0.024 0.976
#> GSM680066 1 0.1184 0.9753 0.984 0.016
#> GSM680058 2 0.0938 0.9507 0.012 0.988
#> GSM680067 2 0.1843 0.9479 0.028 0.972
#> GSM680059 2 0.0938 0.9512 0.012 0.988
#> GSM680068 1 0.1184 0.9753 0.984 0.016
#> GSM680060 2 0.0938 0.9507 0.012 0.988
#> GSM680069 2 0.9998 -0.0145 0.492 0.508
#> GSM680061 2 0.1843 0.9479 0.028 0.972
#> GSM680070 1 0.1414 0.9747 0.980 0.020
#> GSM680071 2 1.0000 -0.0159 0.496 0.504
#> GSM680077 1 0.1633 0.9736 0.976 0.024
#> GSM680072 2 0.0376 0.9508 0.004 0.996
#> GSM680078 1 0.1843 0.9729 0.972 0.028
#> GSM680073 2 0.0376 0.9508 0.004 0.996
#> GSM680079 1 0.1843 0.9729 0.972 0.028
#> GSM680074 2 0.0938 0.9507 0.012 0.988
#> GSM680080 2 0.0672 0.9506 0.008 0.992
#> GSM680075 2 0.0376 0.9508 0.004 0.996
#> GSM680081 2 0.0672 0.9509 0.008 0.992
#> GSM680076 2 0.0672 0.9506 0.008 0.992
#> GSM680082 1 0.1633 0.9736 0.976 0.024
#> GSM680029 2 0.0376 0.9508 0.004 0.996
#> GSM680041 1 0.0672 0.9745 0.992 0.008
#> GSM680035 2 0.1414 0.9504 0.020 0.980
#> GSM680047 1 0.0672 0.9745 0.992 0.008
#> GSM680036 2 0.0376 0.9508 0.004 0.996
#> GSM680048 1 0.0000 0.9748 1.000 0.000
#> GSM680037 2 0.1414 0.9504 0.020 0.980
#> GSM680049 1 0.0376 0.9737 0.996 0.004
#> GSM680038 2 0.1414 0.9505 0.020 0.980
#> GSM680050 1 0.1414 0.9745 0.980 0.020
#> GSM680039 2 0.1843 0.9479 0.028 0.972
#> GSM680051 1 0.0000 0.9748 1.000 0.000
#> GSM680040 2 0.1414 0.9504 0.020 0.980
#> GSM680052 1 0.0000 0.9748 1.000 0.000
#> GSM680030 2 0.1633 0.9491 0.024 0.976
#> GSM680042 1 0.0672 0.9745 0.992 0.008
#> GSM680031 2 0.1414 0.9504 0.020 0.980
#> GSM680043 1 0.0376 0.9737 0.996 0.004
#> GSM680032 1 0.1843 0.9729 0.972 0.028
#> GSM680044 1 0.0376 0.9754 0.996 0.004
#> GSM680033 2 0.1843 0.9499 0.028 0.972
#> GSM680045 1 0.0376 0.9737 0.996 0.004
#> GSM680034 2 0.1843 0.9479 0.028 0.972
#> GSM680046 1 0.0376 0.9737 0.996 0.004
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 3 0.6940 0.3940 0.068 0.224 0.708
#> GSM680062 3 0.8784 0.2859 0.124 0.352 0.524
#> GSM680054 3 0.5431 0.2552 0.000 0.284 0.716
#> GSM680063 3 0.8784 0.2859 0.124 0.352 0.524
#> GSM680055 3 0.7339 0.3850 0.088 0.224 0.688
#> GSM680064 1 0.4233 0.7648 0.836 0.160 0.004
#> GSM680056 1 0.9776 0.1622 0.440 0.284 0.276
#> GSM680065 1 0.5681 0.7054 0.748 0.236 0.016
#> GSM680057 3 0.6225 -0.5823 0.000 0.432 0.568
#> GSM680066 1 0.2550 0.7839 0.932 0.012 0.056
#> GSM680058 2 0.6521 0.5724 0.004 0.500 0.496
#> GSM680067 2 0.6260 0.6215 0.000 0.552 0.448
#> GSM680059 3 0.4291 0.2572 0.008 0.152 0.840
#> GSM680068 1 0.2050 0.7934 0.952 0.028 0.020
#> GSM680060 2 0.6521 0.5724 0.004 0.500 0.496
#> GSM680069 3 0.9429 0.2638 0.264 0.232 0.504
#> GSM680061 2 0.6274 0.6227 0.000 0.544 0.456
#> GSM680070 1 0.0829 0.7890 0.984 0.004 0.012
#> GSM680071 2 0.7381 0.0901 0.244 0.676 0.080
#> GSM680077 1 0.1337 0.7868 0.972 0.016 0.012
#> GSM680072 3 0.6513 -0.5698 0.004 0.476 0.520
#> GSM680078 1 0.2446 0.7809 0.936 0.012 0.052
#> GSM680073 3 0.4883 0.2680 0.004 0.208 0.788
#> GSM680079 1 0.0983 0.7889 0.980 0.004 0.016
#> GSM680074 3 0.6521 -0.6421 0.004 0.492 0.504
#> GSM680080 3 0.6521 -0.6421 0.004 0.492 0.504
#> GSM680075 3 0.4768 0.4407 0.052 0.100 0.848
#> GSM680081 3 0.4409 0.3962 0.172 0.004 0.824
#> GSM680076 2 0.6825 0.5754 0.012 0.496 0.492
#> GSM680082 1 0.1015 0.7890 0.980 0.008 0.012
#> GSM680029 3 0.1585 0.4634 0.028 0.008 0.964
#> GSM680041 1 0.6260 0.7499 0.552 0.448 0.000
#> GSM680035 3 0.0661 0.4576 0.008 0.004 0.988
#> GSM680047 1 0.7722 0.7447 0.520 0.432 0.048
#> GSM680036 3 0.4485 0.4439 0.020 0.136 0.844
#> GSM680048 1 0.7517 0.7673 0.588 0.364 0.048
#> GSM680037 3 0.0661 0.4576 0.008 0.004 0.988
#> GSM680049 1 0.5760 0.7845 0.672 0.328 0.000
#> GSM680038 3 0.6295 -0.6141 0.000 0.472 0.528
#> GSM680050 1 0.4121 0.7819 0.832 0.168 0.000
#> GSM680039 3 0.6398 -0.5616 0.004 0.416 0.580
#> GSM680051 1 0.7676 0.7654 0.584 0.360 0.056
#> GSM680040 3 0.0661 0.4576 0.008 0.004 0.988
#> GSM680052 1 0.7676 0.7654 0.584 0.360 0.056
#> GSM680030 3 0.6225 -0.5823 0.000 0.432 0.568
#> GSM680042 1 0.6192 0.7621 0.580 0.420 0.000
#> GSM680031 3 0.0661 0.4576 0.008 0.004 0.988
#> GSM680043 1 0.7180 0.7689 0.672 0.268 0.060
#> GSM680032 1 0.1015 0.7881 0.980 0.008 0.012
#> GSM680044 1 0.6542 0.7870 0.736 0.204 0.060
#> GSM680033 3 0.0848 0.4541 0.008 0.008 0.984
#> GSM680045 1 0.7246 0.7692 0.664 0.276 0.060
#> GSM680034 2 0.6676 0.5872 0.008 0.516 0.476
#> GSM680046 1 0.6062 0.7799 0.708 0.276 0.016
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 3 0.5466 0.6400 0.220 0.068 0.712 0.000
#> GSM680062 3 0.6392 0.6083 0.232 0.052 0.676 0.040
#> GSM680054 3 0.7332 0.2121 0.164 0.356 0.480 0.000
#> GSM680063 3 0.6317 0.6116 0.232 0.048 0.680 0.040
#> GSM680055 3 0.5565 0.6327 0.232 0.068 0.700 0.000
#> GSM680064 1 0.5038 0.6573 0.684 0.000 0.020 0.296
#> GSM680056 1 0.6367 0.4174 0.692 0.032 0.200 0.076
#> GSM680065 1 0.5113 0.5036 0.760 0.000 0.152 0.088
#> GSM680057 2 0.3402 0.8214 0.000 0.832 0.164 0.004
#> GSM680066 1 0.5185 0.7564 0.728 0.032 0.008 0.232
#> GSM680058 2 0.1356 0.8424 0.008 0.960 0.032 0.000
#> GSM680067 2 0.3353 0.8191 0.004 0.880 0.060 0.056
#> GSM680059 3 0.4804 0.6174 0.016 0.276 0.708 0.000
#> GSM680068 1 0.5126 0.7550 0.728 0.028 0.008 0.236
#> GSM680060 2 0.0657 0.8413 0.004 0.984 0.012 0.000
#> GSM680069 1 0.6461 -0.0158 0.564 0.068 0.364 0.004
#> GSM680061 2 0.3241 0.8255 0.004 0.884 0.072 0.040
#> GSM680070 1 0.4895 0.7628 0.740 0.020 0.008 0.232
#> GSM680071 2 0.7912 0.3132 0.296 0.520 0.152 0.032
#> GSM680077 1 0.4192 0.7607 0.780 0.008 0.004 0.208
#> GSM680072 2 0.3803 0.7268 0.032 0.836 0.132 0.000
#> GSM680078 1 0.4514 0.7662 0.756 0.008 0.008 0.228
#> GSM680073 3 0.5548 0.5967 0.032 0.340 0.628 0.000
#> GSM680079 1 0.4088 0.7639 0.764 0.000 0.004 0.232
#> GSM680074 2 0.1798 0.8423 0.016 0.944 0.040 0.000
#> GSM680080 2 0.1798 0.8423 0.016 0.944 0.040 0.000
#> GSM680075 3 0.5170 0.6949 0.048 0.228 0.724 0.000
#> GSM680081 3 0.4162 0.6979 0.088 0.052 0.844 0.016
#> GSM680076 2 0.1151 0.8352 0.024 0.968 0.008 0.000
#> GSM680082 1 0.4788 0.7640 0.744 0.016 0.008 0.232
#> GSM680029 3 0.3680 0.7302 0.012 0.120 0.852 0.016
#> GSM680041 4 0.3342 0.7684 0.100 0.000 0.032 0.868
#> GSM680035 3 0.3575 0.7279 0.004 0.124 0.852 0.020
#> GSM680047 4 0.1545 0.8592 0.040 0.000 0.008 0.952
#> GSM680036 3 0.5361 0.6702 0.148 0.108 0.744 0.000
#> GSM680048 4 0.0376 0.8861 0.004 0.004 0.000 0.992
#> GSM680037 3 0.3519 0.7291 0.004 0.120 0.856 0.020
#> GSM680049 4 0.0817 0.8813 0.024 0.000 0.000 0.976
#> GSM680038 2 0.2773 0.8347 0.000 0.880 0.116 0.004
#> GSM680050 1 0.5339 0.6303 0.624 0.000 0.020 0.356
#> GSM680039 2 0.4372 0.7208 0.000 0.728 0.268 0.004
#> GSM680051 4 0.0376 0.8839 0.000 0.004 0.004 0.992
#> GSM680040 3 0.3575 0.7279 0.004 0.124 0.852 0.020
#> GSM680052 4 0.0564 0.8856 0.004 0.004 0.004 0.988
#> GSM680030 2 0.3355 0.8237 0.000 0.836 0.160 0.004
#> GSM680042 4 0.2222 0.8543 0.060 0.000 0.016 0.924
#> GSM680031 3 0.3575 0.7279 0.004 0.124 0.852 0.020
#> GSM680043 4 0.4374 0.7427 0.168 0.024 0.008 0.800
#> GSM680032 1 0.4879 0.7651 0.744 0.016 0.012 0.228
#> GSM680044 4 0.4709 0.6922 0.200 0.024 0.008 0.768
#> GSM680033 3 0.3575 0.7279 0.004 0.124 0.852 0.020
#> GSM680045 4 0.3341 0.8313 0.084 0.024 0.012 0.880
#> GSM680034 2 0.4565 0.7918 0.000 0.796 0.140 0.064
#> GSM680046 4 0.2125 0.8714 0.052 0.012 0.004 0.932
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.3949 0.706 0.000 0.004 0.300 0.000 0.696
#> GSM680062 5 0.4395 0.731 0.012 0.000 0.272 0.012 0.704
#> GSM680054 5 0.5590 0.663 0.000 0.156 0.204 0.000 0.640
#> GSM680063 5 0.4395 0.731 0.012 0.000 0.272 0.012 0.704
#> GSM680055 5 0.3511 0.756 0.012 0.004 0.184 0.000 0.800
#> GSM680064 1 0.4599 0.739 0.768 0.004 0.012 0.064 0.152
#> GSM680056 5 0.3497 0.706 0.140 0.000 0.012 0.020 0.828
#> GSM680065 5 0.3516 0.675 0.164 0.004 0.000 0.020 0.812
#> GSM680057 2 0.3554 0.757 0.000 0.776 0.216 0.004 0.004
#> GSM680066 1 0.1412 0.830 0.952 0.004 0.000 0.008 0.036
#> GSM680058 2 0.2980 0.798 0.000 0.884 0.024 0.036 0.056
#> GSM680067 2 0.1757 0.799 0.000 0.936 0.048 0.012 0.004
#> GSM680059 3 0.5617 0.669 0.000 0.180 0.696 0.052 0.072
#> GSM680068 1 0.1412 0.830 0.952 0.004 0.000 0.008 0.036
#> GSM680060 2 0.1725 0.805 0.000 0.936 0.020 0.000 0.044
#> GSM680069 5 0.3222 0.736 0.108 0.004 0.036 0.000 0.852
#> GSM680061 2 0.1764 0.802 0.000 0.928 0.064 0.008 0.000
#> GSM680070 1 0.0867 0.841 0.976 0.008 0.000 0.008 0.008
#> GSM680071 5 0.4505 0.551 0.020 0.244 0.000 0.016 0.720
#> GSM680077 1 0.1924 0.832 0.924 0.004 0.008 0.000 0.064
#> GSM680072 2 0.5007 0.723 0.004 0.748 0.036 0.052 0.160
#> GSM680078 1 0.0703 0.845 0.976 0.000 0.000 0.000 0.024
#> GSM680073 3 0.6906 0.554 0.004 0.228 0.572 0.052 0.144
#> GSM680079 1 0.1616 0.845 0.948 0.004 0.008 0.008 0.032
#> GSM680074 2 0.3908 0.783 0.004 0.832 0.028 0.040 0.096
#> GSM680080 2 0.3908 0.783 0.004 0.832 0.028 0.040 0.096
#> GSM680075 3 0.6564 0.534 0.000 0.128 0.600 0.052 0.220
#> GSM680081 3 0.1408 0.806 0.044 0.000 0.948 0.000 0.008
#> GSM680076 2 0.3964 0.781 0.012 0.832 0.020 0.040 0.096
#> GSM680082 1 0.1041 0.845 0.964 0.000 0.000 0.004 0.032
#> GSM680029 3 0.1503 0.840 0.000 0.020 0.952 0.008 0.020
#> GSM680041 4 0.2139 0.889 0.012 0.000 0.012 0.920 0.056
#> GSM680035 3 0.0609 0.849 0.000 0.020 0.980 0.000 0.000
#> GSM680047 4 0.2253 0.910 0.036 0.000 0.016 0.920 0.028
#> GSM680036 5 0.4852 0.548 0.000 0.008 0.380 0.016 0.596
#> GSM680048 4 0.2285 0.919 0.052 0.024 0.004 0.916 0.004
#> GSM680037 3 0.0609 0.849 0.000 0.020 0.980 0.000 0.000
#> GSM680049 4 0.2026 0.915 0.056 0.000 0.012 0.924 0.008
#> GSM680038 2 0.3719 0.762 0.000 0.776 0.208 0.004 0.012
#> GSM680050 1 0.5549 0.699 0.700 0.004 0.020 0.116 0.160
#> GSM680039 2 0.4446 0.279 0.000 0.520 0.476 0.004 0.000
#> GSM680051 4 0.2301 0.917 0.048 0.028 0.004 0.916 0.004
#> GSM680040 3 0.0609 0.849 0.000 0.020 0.980 0.000 0.000
#> GSM680052 4 0.2374 0.918 0.052 0.028 0.004 0.912 0.004
#> GSM680030 2 0.3554 0.757 0.000 0.776 0.216 0.004 0.004
#> GSM680042 4 0.2228 0.910 0.040 0.000 0.012 0.920 0.028
#> GSM680031 3 0.0771 0.847 0.000 0.020 0.976 0.000 0.004
#> GSM680043 1 0.5989 0.237 0.556 0.032 0.004 0.364 0.044
#> GSM680032 1 0.0880 0.845 0.968 0.000 0.000 0.000 0.032
#> GSM680044 1 0.5757 0.269 0.568 0.028 0.000 0.360 0.044
#> GSM680033 3 0.0609 0.849 0.000 0.020 0.980 0.000 0.000
#> GSM680045 4 0.5353 0.690 0.228 0.032 0.004 0.692 0.044
#> GSM680034 2 0.3427 0.747 0.000 0.796 0.192 0.012 0.000
#> GSM680046 4 0.3938 0.863 0.104 0.032 0.000 0.824 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.2378 0.7975 0.000 0.000 0.152 0.000 0.848 0.000
#> GSM680062 5 0.2520 0.7971 0.000 0.000 0.152 0.000 0.844 0.004
#> GSM680054 5 0.3960 0.7556 0.000 0.072 0.128 0.000 0.784 0.016
#> GSM680063 5 0.2520 0.7971 0.000 0.000 0.152 0.000 0.844 0.004
#> GSM680055 5 0.1765 0.8039 0.000 0.000 0.096 0.000 0.904 0.000
#> GSM680064 1 0.5583 0.6547 0.660 0.000 0.000 0.156 0.076 0.108
#> GSM680056 5 0.2721 0.7542 0.040 0.004 0.000 0.000 0.868 0.088
#> GSM680065 5 0.3079 0.7386 0.056 0.004 0.000 0.000 0.844 0.096
#> GSM680057 2 0.3020 0.6620 0.000 0.812 0.176 0.004 0.004 0.004
#> GSM680066 1 0.2056 0.7729 0.904 0.000 0.000 0.004 0.012 0.080
#> GSM680058 2 0.4107 0.4906 0.000 0.688 0.000 0.004 0.028 0.280
#> GSM680067 2 0.1312 0.6871 0.000 0.956 0.020 0.004 0.012 0.008
#> GSM680059 3 0.5308 -0.3379 0.000 0.068 0.516 0.004 0.008 0.404
#> GSM680068 1 0.2056 0.7729 0.904 0.000 0.000 0.004 0.012 0.080
#> GSM680060 2 0.1844 0.6720 0.000 0.924 0.000 0.004 0.024 0.048
#> GSM680069 5 0.2344 0.7722 0.028 0.000 0.008 0.000 0.896 0.068
#> GSM680061 2 0.0777 0.6903 0.000 0.972 0.024 0.004 0.000 0.000
#> GSM680070 1 0.0935 0.7959 0.964 0.000 0.000 0.004 0.000 0.032
#> GSM680071 5 0.4871 0.5200 0.000 0.224 0.000 0.000 0.652 0.124
#> GSM680077 1 0.3500 0.7239 0.768 0.000 0.000 0.000 0.028 0.204
#> GSM680072 6 0.5952 0.2334 0.000 0.332 0.028 0.000 0.124 0.516
#> GSM680078 1 0.0653 0.7957 0.980 0.000 0.004 0.004 0.000 0.012
#> GSM680073 6 0.6587 0.6116 0.000 0.096 0.280 0.004 0.104 0.516
#> GSM680079 1 0.3178 0.7463 0.804 0.000 0.000 0.004 0.016 0.176
#> GSM680074 2 0.4365 0.3853 0.004 0.612 0.012 0.000 0.008 0.364
#> GSM680080 2 0.4365 0.3853 0.004 0.612 0.012 0.000 0.008 0.364
#> GSM680075 6 0.6397 0.4660 0.000 0.032 0.364 0.004 0.152 0.448
#> GSM680081 3 0.1053 0.7731 0.020 0.000 0.964 0.000 0.004 0.012
#> GSM680076 2 0.4418 0.3531 0.012 0.592 0.004 0.000 0.008 0.384
#> GSM680082 1 0.1364 0.7909 0.944 0.000 0.004 0.004 0.000 0.048
#> GSM680029 3 0.2099 0.7092 0.000 0.004 0.904 0.004 0.008 0.080
#> GSM680041 4 0.0547 0.8637 0.000 0.000 0.000 0.980 0.020 0.000
#> GSM680035 3 0.0291 0.8007 0.000 0.004 0.992 0.000 0.004 0.000
#> GSM680047 4 0.0520 0.8696 0.008 0.000 0.000 0.984 0.008 0.000
#> GSM680036 5 0.5020 0.5530 0.000 0.000 0.220 0.004 0.648 0.128
#> GSM680048 4 0.2375 0.8688 0.012 0.012 0.000 0.888 0.000 0.088
#> GSM680037 3 0.0291 0.8007 0.000 0.004 0.992 0.000 0.004 0.000
#> GSM680049 4 0.0508 0.8698 0.012 0.000 0.000 0.984 0.004 0.000
#> GSM680038 2 0.3387 0.6612 0.000 0.808 0.160 0.004 0.016 0.012
#> GSM680050 1 0.6350 0.5900 0.548 0.000 0.000 0.152 0.068 0.232
#> GSM680039 3 0.3989 0.0431 0.000 0.468 0.528 0.004 0.000 0.000
#> GSM680051 4 0.2056 0.8700 0.004 0.012 0.000 0.904 0.000 0.080
#> GSM680040 3 0.0291 0.8007 0.000 0.004 0.992 0.000 0.004 0.000
#> GSM680052 4 0.2426 0.8676 0.012 0.012 0.000 0.884 0.000 0.092
#> GSM680030 2 0.3020 0.6620 0.000 0.812 0.176 0.004 0.004 0.004
#> GSM680042 4 0.0622 0.8680 0.008 0.000 0.000 0.980 0.012 0.000
#> GSM680031 3 0.0291 0.8007 0.000 0.004 0.992 0.000 0.004 0.000
#> GSM680043 1 0.6314 0.3292 0.544 0.028 0.000 0.244 0.012 0.172
#> GSM680032 1 0.0862 0.7950 0.972 0.000 0.004 0.008 0.000 0.016
#> GSM680044 1 0.5860 0.3828 0.576 0.008 0.000 0.236 0.012 0.168
#> GSM680033 3 0.0291 0.8007 0.000 0.004 0.992 0.000 0.004 0.000
#> GSM680045 4 0.6412 0.4370 0.268 0.028 0.000 0.520 0.012 0.172
#> GSM680034 2 0.3048 0.6577 0.000 0.824 0.152 0.004 0.000 0.020
#> GSM680046 4 0.4988 0.7451 0.076 0.028 0.000 0.712 0.012 0.172
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> MAD:kmeans 52 0.592410 0.992 2.84e-08 0.5921 2
#> MAD:kmeans 28 0.167064 0.640 3.09e-04 1.0000 3
#> MAD:kmeans 50 0.000587 0.655 1.41e-06 0.1687 4
#> MAD:kmeans 51 0.000254 0.250 1.56e-05 0.1870 5
#> MAD:kmeans 43 0.000400 0.547 3.61e-04 0.0286 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 1.000 0.959 0.984 0.5088 0.491 0.491
#> 3 3 0.878 0.893 0.936 0.3146 0.747 0.529
#> 4 4 0.754 0.822 0.888 0.1348 0.846 0.572
#> 5 5 0.856 0.835 0.916 0.0674 0.883 0.567
#> 6 6 0.806 0.668 0.810 0.0372 0.953 0.761
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
#> GSM680053 2 0.000 1.000 0.000 1.000
#> GSM680062 1 0.000 0.967 1.000 0.000
#> GSM680054 2 0.000 1.000 0.000 1.000
#> GSM680063 1 0.000 0.967 1.000 0.000
#> GSM680055 2 0.000 1.000 0.000 1.000
#> GSM680064 1 0.000 0.967 1.000 0.000
#> GSM680056 1 0.000 0.967 1.000 0.000
#> GSM680065 1 0.000 0.967 1.000 0.000
#> GSM680057 2 0.000 1.000 0.000 1.000
#> GSM680066 1 0.000 0.967 1.000 0.000
#> GSM680058 2 0.000 1.000 0.000 1.000
#> GSM680067 2 0.000 1.000 0.000 1.000
#> GSM680059 2 0.000 1.000 0.000 1.000
#> GSM680068 1 0.000 0.967 1.000 0.000
#> GSM680060 2 0.000 1.000 0.000 1.000
#> GSM680069 1 0.978 0.324 0.588 0.412
#> GSM680061 2 0.000 1.000 0.000 1.000
#> GSM680070 1 0.000 0.967 1.000 0.000
#> GSM680071 1 0.987 0.269 0.568 0.432
#> GSM680077 1 0.000 0.967 1.000 0.000
#> GSM680072 2 0.000 1.000 0.000 1.000
#> GSM680078 1 0.000 0.967 1.000 0.000
#> GSM680073 2 0.000 1.000 0.000 1.000
#> GSM680079 1 0.000 0.967 1.000 0.000
#> GSM680074 2 0.000 1.000 0.000 1.000
#> GSM680080 2 0.000 1.000 0.000 1.000
#> GSM680075 2 0.000 1.000 0.000 1.000
#> GSM680081 2 0.000 1.000 0.000 1.000
#> GSM680076 2 0.000 1.000 0.000 1.000
#> GSM680082 1 0.000 0.967 1.000 0.000
#> GSM680029 2 0.000 1.000 0.000 1.000
#> GSM680041 1 0.000 0.967 1.000 0.000
#> GSM680035 2 0.000 1.000 0.000 1.000
#> GSM680047 1 0.000 0.967 1.000 0.000
#> GSM680036 2 0.000 1.000 0.000 1.000
#> GSM680048 1 0.000 0.967 1.000 0.000
#> GSM680037 2 0.000 1.000 0.000 1.000
#> GSM680049 1 0.000 0.967 1.000 0.000
#> GSM680038 2 0.000 1.000 0.000 1.000
#> GSM680050 1 0.000 0.967 1.000 0.000
#> GSM680039 2 0.000 1.000 0.000 1.000
#> GSM680051 1 0.000 0.967 1.000 0.000
#> GSM680040 2 0.000 1.000 0.000 1.000
#> GSM680052 1 0.000 0.967 1.000 0.000
#> GSM680030 2 0.000 1.000 0.000 1.000
#> GSM680042 1 0.000 0.967 1.000 0.000
#> GSM680031 2 0.000 1.000 0.000 1.000
#> GSM680043 1 0.000 0.967 1.000 0.000
#> GSM680032 1 0.000 0.967 1.000 0.000
#> GSM680044 1 0.000 0.967 1.000 0.000
#> GSM680033 2 0.000 1.000 0.000 1.000
#> GSM680045 1 0.000 0.967 1.000 0.000
#> GSM680034 2 0.000 1.000 0.000 1.000
#> GSM680046 1 0.000 0.967 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 3 0.1031 0.8838 0.000 0.024 0.976
#> GSM680062 3 0.1905 0.8644 0.028 0.016 0.956
#> GSM680054 2 0.6307 0.0464 0.000 0.512 0.488
#> GSM680063 3 0.1163 0.8743 0.028 0.000 0.972
#> GSM680055 3 0.0892 0.8827 0.000 0.020 0.980
#> GSM680064 1 0.1289 0.9712 0.968 0.000 0.032
#> GSM680056 3 0.3482 0.7640 0.128 0.000 0.872
#> GSM680065 1 0.3412 0.8995 0.876 0.000 0.124
#> GSM680057 2 0.0747 0.9408 0.000 0.984 0.016
#> GSM680066 1 0.1163 0.9713 0.972 0.000 0.028
#> GSM680058 2 0.0747 0.9408 0.000 0.984 0.016
#> GSM680067 2 0.1163 0.9105 0.028 0.972 0.000
#> GSM680059 3 0.6180 0.4223 0.000 0.416 0.584
#> GSM680068 1 0.1031 0.9718 0.976 0.000 0.024
#> GSM680060 2 0.0747 0.9408 0.000 0.984 0.016
#> GSM680069 3 0.0747 0.8626 0.016 0.000 0.984
#> GSM680061 2 0.0000 0.9328 0.000 1.000 0.000
#> GSM680070 1 0.1163 0.9713 0.972 0.000 0.028
#> GSM680071 2 0.4068 0.8300 0.016 0.864 0.120
#> GSM680077 1 0.1289 0.9704 0.968 0.000 0.032
#> GSM680072 2 0.1163 0.9349 0.000 0.972 0.028
#> GSM680078 1 0.1860 0.9599 0.948 0.000 0.052
#> GSM680073 3 0.6180 0.4173 0.000 0.416 0.584
#> GSM680079 1 0.1289 0.9704 0.968 0.000 0.032
#> GSM680074 2 0.0747 0.9408 0.000 0.984 0.016
#> GSM680080 2 0.0747 0.9408 0.000 0.984 0.016
#> GSM680075 3 0.2261 0.8911 0.000 0.068 0.932
#> GSM680081 3 0.2804 0.8843 0.016 0.060 0.924
#> GSM680076 2 0.0747 0.9318 0.016 0.984 0.000
#> GSM680082 1 0.1289 0.9704 0.968 0.000 0.032
#> GSM680029 3 0.2711 0.8898 0.000 0.088 0.912
#> GSM680041 1 0.2152 0.9558 0.948 0.016 0.036
#> GSM680035 3 0.3116 0.8844 0.000 0.108 0.892
#> GSM680047 1 0.1170 0.9709 0.976 0.016 0.008
#> GSM680036 3 0.1289 0.8857 0.000 0.032 0.968
#> GSM680048 1 0.0747 0.9729 0.984 0.016 0.000
#> GSM680037 3 0.2959 0.8871 0.000 0.100 0.900
#> GSM680049 1 0.0747 0.9729 0.984 0.016 0.000
#> GSM680038 2 0.0747 0.9408 0.000 0.984 0.016
#> GSM680050 1 0.1289 0.9712 0.968 0.000 0.032
#> GSM680039 2 0.0747 0.9408 0.000 0.984 0.016
#> GSM680051 1 0.0747 0.9729 0.984 0.016 0.000
#> GSM680040 3 0.3267 0.8797 0.000 0.116 0.884
#> GSM680052 1 0.0747 0.9729 0.984 0.016 0.000
#> GSM680030 2 0.0747 0.9408 0.000 0.984 0.016
#> GSM680042 1 0.0983 0.9720 0.980 0.016 0.004
#> GSM680031 3 0.3116 0.8844 0.000 0.108 0.892
#> GSM680043 1 0.0747 0.9729 0.984 0.016 0.000
#> GSM680032 1 0.1411 0.9692 0.964 0.000 0.036
#> GSM680044 1 0.0747 0.9729 0.984 0.016 0.000
#> GSM680033 3 0.3340 0.8768 0.000 0.120 0.880
#> GSM680045 1 0.0747 0.9729 0.984 0.016 0.000
#> GSM680034 2 0.0892 0.9177 0.020 0.980 0.000
#> GSM680046 1 0.0747 0.9729 0.984 0.016 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 3 0.4447 0.799 0.044 0.008 0.812 0.136
#> GSM680062 4 0.5807 0.221 0.044 0.000 0.344 0.612
#> GSM680054 2 0.6627 0.574 0.016 0.644 0.244 0.096
#> GSM680063 4 0.6074 -0.130 0.044 0.000 0.456 0.500
#> GSM680055 3 0.4447 0.799 0.044 0.008 0.812 0.136
#> GSM680064 1 0.3123 0.830 0.844 0.000 0.000 0.156
#> GSM680056 1 0.4679 0.748 0.772 0.000 0.044 0.184
#> GSM680065 1 0.4323 0.759 0.788 0.000 0.028 0.184
#> GSM680057 2 0.0921 0.923 0.000 0.972 0.028 0.000
#> GSM680066 1 0.1624 0.875 0.952 0.000 0.020 0.028
#> GSM680058 2 0.0188 0.929 0.000 0.996 0.004 0.000
#> GSM680067 2 0.0672 0.928 0.000 0.984 0.008 0.008
#> GSM680059 3 0.3123 0.834 0.000 0.156 0.844 0.000
#> GSM680068 1 0.1474 0.872 0.948 0.000 0.000 0.052
#> GSM680060 2 0.0188 0.929 0.000 0.996 0.004 0.000
#> GSM680069 1 0.5631 0.707 0.732 0.004 0.108 0.156
#> GSM680061 2 0.0336 0.928 0.000 0.992 0.008 0.000
#> GSM680070 1 0.1118 0.882 0.964 0.000 0.000 0.036
#> GSM680071 2 0.6130 0.702 0.092 0.724 0.032 0.152
#> GSM680077 1 0.0707 0.882 0.980 0.000 0.000 0.020
#> GSM680072 2 0.2053 0.886 0.000 0.924 0.072 0.004
#> GSM680078 1 0.0817 0.883 0.976 0.000 0.000 0.024
#> GSM680073 3 0.3583 0.811 0.000 0.180 0.816 0.004
#> GSM680079 1 0.1118 0.882 0.964 0.000 0.000 0.036
#> GSM680074 2 0.0000 0.929 0.000 1.000 0.000 0.000
#> GSM680080 2 0.0000 0.929 0.000 1.000 0.000 0.000
#> GSM680075 3 0.2896 0.888 0.056 0.032 0.904 0.008
#> GSM680081 3 0.2831 0.840 0.120 0.004 0.876 0.000
#> GSM680076 2 0.0592 0.923 0.016 0.984 0.000 0.000
#> GSM680082 1 0.1118 0.882 0.964 0.000 0.000 0.036
#> GSM680029 3 0.1284 0.907 0.012 0.024 0.964 0.000
#> GSM680041 4 0.1022 0.778 0.032 0.000 0.000 0.968
#> GSM680035 3 0.1022 0.910 0.000 0.032 0.968 0.000
#> GSM680047 4 0.2281 0.827 0.096 0.000 0.000 0.904
#> GSM680036 3 0.2940 0.855 0.012 0.008 0.892 0.088
#> GSM680048 4 0.2868 0.843 0.136 0.000 0.000 0.864
#> GSM680037 3 0.1022 0.910 0.000 0.032 0.968 0.000
#> GSM680049 4 0.2973 0.842 0.144 0.000 0.000 0.856
#> GSM680038 2 0.0336 0.929 0.000 0.992 0.008 0.000
#> GSM680050 1 0.4356 0.662 0.708 0.000 0.000 0.292
#> GSM680039 2 0.3266 0.804 0.000 0.832 0.168 0.000
#> GSM680051 4 0.2868 0.843 0.136 0.000 0.000 0.864
#> GSM680040 3 0.1022 0.910 0.000 0.032 0.968 0.000
#> GSM680052 4 0.2868 0.843 0.136 0.000 0.000 0.864
#> GSM680030 2 0.0921 0.923 0.000 0.972 0.028 0.000
#> GSM680042 4 0.2281 0.827 0.096 0.000 0.000 0.904
#> GSM680031 3 0.1022 0.910 0.000 0.032 0.968 0.000
#> GSM680043 4 0.3528 0.821 0.192 0.000 0.000 0.808
#> GSM680032 1 0.0921 0.884 0.972 0.000 0.000 0.028
#> GSM680044 4 0.3649 0.812 0.204 0.000 0.000 0.796
#> GSM680033 3 0.1022 0.910 0.000 0.032 0.968 0.000
#> GSM680045 4 0.3400 0.829 0.180 0.000 0.000 0.820
#> GSM680034 2 0.1624 0.917 0.000 0.952 0.028 0.020
#> GSM680046 4 0.3400 0.829 0.180 0.000 0.000 0.820
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.0963 0.8436 0.000 0.000 0.036 0.000 0.964
#> GSM680062 5 0.0992 0.8446 0.000 0.000 0.008 0.024 0.968
#> GSM680054 5 0.3821 0.6908 0.000 0.216 0.020 0.000 0.764
#> GSM680063 5 0.0807 0.8479 0.000 0.000 0.012 0.012 0.976
#> GSM680055 5 0.0794 0.8464 0.000 0.000 0.028 0.000 0.972
#> GSM680064 1 0.4264 0.7087 0.744 0.000 0.000 0.212 0.044
#> GSM680056 5 0.1041 0.8457 0.032 0.000 0.000 0.004 0.964
#> GSM680065 5 0.2338 0.7895 0.112 0.000 0.000 0.004 0.884
#> GSM680057 2 0.2455 0.9033 0.008 0.896 0.088 0.004 0.004
#> GSM680066 1 0.0451 0.9263 0.988 0.000 0.004 0.008 0.000
#> GSM680058 2 0.0451 0.9472 0.000 0.988 0.004 0.000 0.008
#> GSM680067 2 0.0889 0.9447 0.004 0.976 0.004 0.012 0.004
#> GSM680059 3 0.2249 0.8265 0.000 0.096 0.896 0.000 0.008
#> GSM680068 1 0.0290 0.9271 0.992 0.000 0.000 0.008 0.000
#> GSM680060 2 0.0290 0.9472 0.000 0.992 0.000 0.000 0.008
#> GSM680069 5 0.0794 0.8471 0.028 0.000 0.000 0.000 0.972
#> GSM680061 2 0.0902 0.9451 0.004 0.976 0.008 0.008 0.004
#> GSM680070 1 0.0290 0.9271 0.992 0.000 0.000 0.008 0.000
#> GSM680071 5 0.4664 0.2426 0.004 0.436 0.000 0.008 0.552
#> GSM680077 1 0.0486 0.9243 0.988 0.004 0.000 0.004 0.004
#> GSM680072 2 0.2104 0.8985 0.000 0.916 0.024 0.000 0.060
#> GSM680078 1 0.0451 0.9263 0.988 0.000 0.004 0.008 0.000
#> GSM680073 3 0.4563 0.6827 0.000 0.244 0.708 0.000 0.048
#> GSM680079 1 0.0451 0.9261 0.988 0.000 0.000 0.008 0.004
#> GSM680074 2 0.0451 0.9472 0.000 0.988 0.004 0.000 0.008
#> GSM680080 2 0.0451 0.9472 0.000 0.988 0.004 0.000 0.008
#> GSM680075 3 0.4279 0.7440 0.004 0.108 0.784 0.000 0.104
#> GSM680081 3 0.1608 0.8321 0.072 0.000 0.928 0.000 0.000
#> GSM680076 2 0.0451 0.9472 0.000 0.988 0.004 0.000 0.008
#> GSM680082 1 0.0290 0.9271 0.992 0.000 0.000 0.008 0.000
#> GSM680029 3 0.0290 0.8700 0.000 0.000 0.992 0.000 0.008
#> GSM680041 4 0.0510 0.9271 0.000 0.000 0.000 0.984 0.016
#> GSM680035 3 0.0451 0.8707 0.004 0.000 0.988 0.000 0.008
#> GSM680047 4 0.0290 0.9315 0.000 0.000 0.000 0.992 0.008
#> GSM680036 5 0.4235 0.4629 0.000 0.008 0.336 0.000 0.656
#> GSM680048 4 0.0162 0.9331 0.004 0.000 0.000 0.996 0.000
#> GSM680037 3 0.0451 0.8707 0.004 0.000 0.988 0.000 0.008
#> GSM680049 4 0.0290 0.9325 0.008 0.000 0.000 0.992 0.000
#> GSM680038 2 0.1492 0.9362 0.008 0.948 0.040 0.000 0.004
#> GSM680050 1 0.5022 0.4950 0.620 0.000 0.000 0.332 0.048
#> GSM680039 3 0.4719 0.0992 0.004 0.452 0.536 0.004 0.004
#> GSM680051 4 0.0162 0.9308 0.000 0.004 0.000 0.996 0.000
#> GSM680040 3 0.0290 0.8711 0.000 0.000 0.992 0.000 0.008
#> GSM680052 4 0.0162 0.9331 0.004 0.000 0.000 0.996 0.000
#> GSM680030 2 0.2396 0.9057 0.008 0.900 0.084 0.004 0.004
#> GSM680042 4 0.0290 0.9315 0.000 0.000 0.000 0.992 0.008
#> GSM680031 3 0.0404 0.8705 0.000 0.000 0.988 0.000 0.012
#> GSM680043 4 0.3863 0.6878 0.248 0.000 0.000 0.740 0.012
#> GSM680032 1 0.0613 0.9172 0.984 0.000 0.004 0.008 0.004
#> GSM680044 4 0.4040 0.6371 0.276 0.000 0.000 0.712 0.012
#> GSM680033 3 0.0290 0.8711 0.000 0.000 0.992 0.000 0.008
#> GSM680045 4 0.1281 0.9170 0.032 0.000 0.000 0.956 0.012
#> GSM680034 2 0.3586 0.8656 0.008 0.844 0.092 0.052 0.004
#> GSM680046 4 0.0510 0.9303 0.016 0.000 0.000 0.984 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.0622 0.8417 0.000 0.000 0.008 0.000 0.980 0.012
#> GSM680062 5 0.1307 0.8396 0.000 0.000 0.008 0.008 0.952 0.032
#> GSM680054 5 0.2917 0.7811 0.000 0.104 0.004 0.000 0.852 0.040
#> GSM680063 5 0.1307 0.8396 0.000 0.000 0.008 0.008 0.952 0.032
#> GSM680055 5 0.0260 0.8425 0.000 0.000 0.008 0.000 0.992 0.000
#> GSM680064 1 0.5327 0.5240 0.616 0.000 0.000 0.280 0.032 0.072
#> GSM680056 5 0.1843 0.8326 0.004 0.004 0.000 0.000 0.912 0.080
#> GSM680065 5 0.3317 0.7974 0.080 0.004 0.000 0.000 0.828 0.088
#> GSM680057 6 0.4332 0.9049 0.000 0.352 0.032 0.000 0.000 0.616
#> GSM680066 1 0.1588 0.8577 0.924 0.000 0.000 0.000 0.004 0.072
#> GSM680058 2 0.2562 0.4099 0.000 0.828 0.000 0.000 0.000 0.172
#> GSM680067 6 0.3727 0.8695 0.000 0.388 0.000 0.000 0.000 0.612
#> GSM680059 3 0.3967 0.4338 0.000 0.356 0.632 0.000 0.000 0.012
#> GSM680068 1 0.1700 0.8540 0.916 0.000 0.000 0.000 0.004 0.080
#> GSM680060 2 0.3647 -0.1175 0.000 0.640 0.000 0.000 0.000 0.360
#> GSM680069 5 0.2766 0.8246 0.012 0.028 0.000 0.000 0.868 0.092
#> GSM680061 6 0.3727 0.8793 0.000 0.388 0.000 0.000 0.000 0.612
#> GSM680070 1 0.0790 0.8727 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM680071 5 0.5688 0.4279 0.000 0.264 0.000 0.000 0.524 0.212
#> GSM680077 1 0.0790 0.8727 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM680072 2 0.1168 0.4506 0.000 0.956 0.016 0.000 0.028 0.000
#> GSM680078 1 0.0935 0.8738 0.964 0.004 0.000 0.000 0.000 0.032
#> GSM680073 2 0.4637 0.1587 0.000 0.636 0.316 0.000 0.024 0.024
#> GSM680079 1 0.0547 0.8744 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM680074 2 0.2378 0.4502 0.000 0.848 0.000 0.000 0.000 0.152
#> GSM680080 2 0.2340 0.4544 0.000 0.852 0.000 0.000 0.000 0.148
#> GSM680075 2 0.5778 -0.0643 0.008 0.528 0.368 0.000 0.048 0.048
#> GSM680081 3 0.2250 0.7864 0.064 0.000 0.896 0.000 0.000 0.040
#> GSM680076 2 0.2454 0.4573 0.000 0.840 0.000 0.000 0.000 0.160
#> GSM680082 1 0.0713 0.8748 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM680029 3 0.1686 0.8085 0.000 0.064 0.924 0.000 0.000 0.012
#> GSM680041 4 0.0858 0.8770 0.000 0.000 0.000 0.968 0.004 0.028
#> GSM680035 3 0.0000 0.8448 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680047 4 0.0458 0.8837 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM680036 5 0.6309 0.3461 0.000 0.252 0.224 0.000 0.496 0.028
#> GSM680048 4 0.0547 0.8850 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM680037 3 0.0146 0.8439 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM680049 4 0.0363 0.8854 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM680038 2 0.4098 -0.6900 0.000 0.496 0.008 0.000 0.000 0.496
#> GSM680050 1 0.5761 0.3728 0.536 0.000 0.000 0.344 0.040 0.080
#> GSM680039 3 0.5731 -0.1773 0.000 0.168 0.448 0.000 0.000 0.384
#> GSM680051 4 0.0260 0.8858 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM680040 3 0.0000 0.8448 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680052 4 0.0458 0.8856 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM680030 6 0.4344 0.9031 0.000 0.356 0.032 0.000 0.000 0.612
#> GSM680042 4 0.0547 0.8824 0.000 0.000 0.000 0.980 0.000 0.020
#> GSM680031 3 0.0405 0.8414 0.000 0.000 0.988 0.000 0.004 0.008
#> GSM680043 4 0.5420 0.5162 0.272 0.000 0.000 0.580 0.004 0.144
#> GSM680032 1 0.2122 0.8514 0.900 0.008 0.000 0.000 0.008 0.084
#> GSM680044 4 0.5586 0.5271 0.252 0.000 0.000 0.584 0.012 0.152
#> GSM680033 3 0.0000 0.8448 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680045 4 0.3275 0.8141 0.036 0.000 0.000 0.816 0.004 0.144
#> GSM680034 6 0.4685 0.8540 0.000 0.300 0.040 0.016 0.000 0.644
#> GSM680046 4 0.2149 0.8540 0.004 0.000 0.000 0.888 0.004 0.104
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> MAD:skmeans 52 5.92e-01 0.992 2.84e-08 0.5921 2
#> MAD:skmeans 51 2.02e-01 0.710 6.43e-07 0.3002 3
#> MAD:skmeans 52 1.41e-04 0.710 1.49e-07 0.2016 4
#> MAD:skmeans 50 1.76e-05 0.190 1.17e-05 0.0546 5
#> MAD:skmeans 40 1.13e-05 0.394 3.79e-04 0.0185 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 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 0.849 0.903 0.960 0.5063 0.491 0.491
#> 3 3 0.472 0.512 0.789 0.3090 0.737 0.513
#> 4 4 0.911 0.902 0.957 0.1473 0.751 0.389
#> 5 5 0.821 0.790 0.896 0.0569 0.921 0.690
#> 6 6 0.871 0.745 0.891 0.0468 0.899 0.552
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
#> GSM680053 1 0.0376 0.974 0.996 0.004
#> GSM680062 1 0.0376 0.974 0.996 0.004
#> GSM680054 2 0.2778 0.902 0.048 0.952
#> GSM680063 1 0.0376 0.974 0.996 0.004
#> GSM680055 1 0.0376 0.974 0.996 0.004
#> GSM680064 1 0.0000 0.975 1.000 0.000
#> GSM680056 1 0.0376 0.974 0.996 0.004
#> GSM680065 1 0.0000 0.975 1.000 0.000
#> GSM680057 2 0.0000 0.935 0.000 1.000
#> GSM680066 2 0.0000 0.935 0.000 1.000
#> GSM680058 2 0.0000 0.935 0.000 1.000
#> GSM680067 2 0.0000 0.935 0.000 1.000
#> GSM680059 2 0.1414 0.922 0.020 0.980
#> GSM680068 1 0.0000 0.975 1.000 0.000
#> GSM680060 2 0.0000 0.935 0.000 1.000
#> GSM680069 1 0.0376 0.974 0.996 0.004
#> GSM680061 2 0.0000 0.935 0.000 1.000
#> GSM680070 1 0.0000 0.975 1.000 0.000
#> GSM680071 2 0.9954 0.167 0.460 0.540
#> GSM680077 2 0.9933 0.221 0.452 0.548
#> GSM680072 2 0.0000 0.935 0.000 1.000
#> GSM680078 1 0.0000 0.975 1.000 0.000
#> GSM680073 2 0.7453 0.720 0.212 0.788
#> GSM680079 1 0.0000 0.975 1.000 0.000
#> GSM680074 2 0.0000 0.935 0.000 1.000
#> GSM680080 2 0.0000 0.935 0.000 1.000
#> GSM680075 1 0.0672 0.971 0.992 0.008
#> GSM680081 2 0.0000 0.935 0.000 1.000
#> GSM680076 2 0.0000 0.935 0.000 1.000
#> GSM680082 2 0.2948 0.900 0.052 0.948
#> GSM680029 1 0.5842 0.830 0.860 0.140
#> GSM680041 1 0.0000 0.975 1.000 0.000
#> GSM680035 2 0.0000 0.935 0.000 1.000
#> GSM680047 1 0.0000 0.975 1.000 0.000
#> GSM680036 1 0.6712 0.777 0.824 0.176
#> GSM680048 1 0.0000 0.975 1.000 0.000
#> GSM680037 1 0.0376 0.974 0.996 0.004
#> GSM680049 1 0.8267 0.629 0.740 0.260
#> GSM680038 2 0.0000 0.935 0.000 1.000
#> GSM680050 1 0.0000 0.975 1.000 0.000
#> GSM680039 2 0.0000 0.935 0.000 1.000
#> GSM680051 2 0.8813 0.567 0.300 0.700
#> GSM680040 2 0.0000 0.935 0.000 1.000
#> GSM680052 1 0.0000 0.975 1.000 0.000
#> GSM680030 2 0.0000 0.935 0.000 1.000
#> GSM680042 1 0.0000 0.975 1.000 0.000
#> GSM680031 1 0.1414 0.961 0.980 0.020
#> GSM680043 1 0.0000 0.975 1.000 0.000
#> GSM680032 2 0.0000 0.935 0.000 1.000
#> GSM680044 1 0.0000 0.975 1.000 0.000
#> GSM680033 2 0.0000 0.935 0.000 1.000
#> GSM680045 1 0.0000 0.975 1.000 0.000
#> GSM680034 2 0.0000 0.935 0.000 1.000
#> GSM680046 1 0.0000 0.975 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 3 0.2486 0.6594 0.060 0.008 0.932
#> GSM680062 3 0.4136 0.6065 0.116 0.020 0.864
#> GSM680054 2 0.4605 0.4980 0.000 0.796 0.204
#> GSM680063 3 0.6887 0.4847 0.060 0.236 0.704
#> GSM680055 3 0.2486 0.6594 0.060 0.008 0.932
#> GSM680064 1 0.4605 0.7082 0.796 0.000 0.204
#> GSM680056 3 0.4725 0.6296 0.060 0.088 0.852
#> GSM680065 3 0.2261 0.6548 0.068 0.000 0.932
#> GSM680057 2 0.0000 0.7157 0.000 1.000 0.000
#> GSM680066 3 0.9710 -0.0499 0.220 0.372 0.408
#> GSM680058 2 0.0000 0.7157 0.000 1.000 0.000
#> GSM680067 2 0.0000 0.7157 0.000 1.000 0.000
#> GSM680059 3 0.6308 -0.2117 0.000 0.492 0.508
#> GSM680068 1 0.2066 0.6874 0.940 0.000 0.060
#> GSM680060 2 0.0000 0.7157 0.000 1.000 0.000
#> GSM680069 3 0.7092 0.5173 0.084 0.208 0.708
#> GSM680061 2 0.0000 0.7157 0.000 1.000 0.000
#> GSM680070 1 0.0000 0.7230 1.000 0.000 0.000
#> GSM680071 2 0.6129 0.2785 0.008 0.668 0.324
#> GSM680077 2 0.9137 0.1874 0.276 0.536 0.188
#> GSM680072 2 0.0592 0.7079 0.000 0.988 0.012
#> GSM680078 3 0.4702 0.5657 0.212 0.000 0.788
#> GSM680073 3 0.6111 0.0787 0.000 0.396 0.604
#> GSM680079 3 0.5968 0.4049 0.364 0.000 0.636
#> GSM680074 2 0.0000 0.7157 0.000 1.000 0.000
#> GSM680080 2 0.0000 0.7157 0.000 1.000 0.000
#> GSM680075 3 0.0747 0.6760 0.000 0.016 0.984
#> GSM680081 2 0.6309 0.1588 0.000 0.504 0.496
#> GSM680076 2 0.0000 0.7157 0.000 1.000 0.000
#> GSM680082 1 0.2066 0.6932 0.940 0.060 0.000
#> GSM680029 3 0.4796 0.4830 0.000 0.220 0.780
#> GSM680041 1 0.6180 0.5314 0.584 0.000 0.416
#> GSM680035 2 0.6309 0.1588 0.000 0.504 0.496
#> GSM680047 1 0.6302 0.4429 0.520 0.000 0.480
#> GSM680036 3 0.1964 0.6754 0.000 0.056 0.944
#> GSM680048 1 0.6302 0.4429 0.520 0.000 0.480
#> GSM680037 3 0.1031 0.6766 0.000 0.024 0.976
#> GSM680049 1 0.1753 0.7021 0.952 0.048 0.000
#> GSM680038 2 0.0000 0.7157 0.000 1.000 0.000
#> GSM680050 3 0.8675 -0.2930 0.388 0.108 0.504
#> GSM680039 2 0.6126 0.3090 0.000 0.600 0.400
#> GSM680051 1 0.5803 0.5597 0.736 0.248 0.016
#> GSM680040 2 0.6309 0.1588 0.000 0.504 0.496
#> GSM680052 1 0.4702 0.7137 0.788 0.000 0.212
#> GSM680030 2 0.0000 0.7157 0.000 1.000 0.000
#> GSM680042 1 0.4702 0.7137 0.788 0.000 0.212
#> GSM680031 3 0.3043 0.6629 0.008 0.084 0.908
#> GSM680043 1 0.0000 0.7230 1.000 0.000 0.000
#> GSM680032 2 0.8102 0.2789 0.076 0.556 0.368
#> GSM680044 1 0.6302 0.4429 0.520 0.000 0.480
#> GSM680033 2 0.6309 0.1588 0.000 0.504 0.496
#> GSM680045 1 0.4702 0.7137 0.788 0.000 0.212
#> GSM680034 2 0.6180 0.2007 0.416 0.584 0.000
#> GSM680046 1 0.0000 0.7230 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 1 0.0592 0.9160 0.984 0.000 0.016 0.000
#> GSM680062 1 0.0000 0.9198 1.000 0.000 0.000 0.000
#> GSM680054 1 0.4877 0.3020 0.592 0.408 0.000 0.000
#> GSM680063 1 0.0000 0.9198 1.000 0.000 0.000 0.000
#> GSM680055 1 0.0592 0.9160 0.984 0.000 0.016 0.000
#> GSM680064 4 0.3649 0.7424 0.204 0.000 0.000 0.796
#> GSM680056 1 0.0000 0.9198 1.000 0.000 0.000 0.000
#> GSM680065 1 0.0000 0.9198 1.000 0.000 0.000 0.000
#> GSM680057 2 0.0188 0.9547 0.000 0.996 0.004 0.000
#> GSM680066 3 0.2949 0.8922 0.000 0.088 0.888 0.024
#> GSM680058 2 0.0000 0.9566 0.000 1.000 0.000 0.000
#> GSM680067 2 0.0000 0.9566 0.000 1.000 0.000 0.000
#> GSM680059 3 0.0000 0.9615 0.000 0.000 1.000 0.000
#> GSM680068 4 0.0000 0.9678 0.000 0.000 0.000 1.000
#> GSM680060 2 0.0000 0.9566 0.000 1.000 0.000 0.000
#> GSM680069 1 0.4771 0.7034 0.768 0.036 0.192 0.004
#> GSM680061 2 0.0188 0.9547 0.000 0.996 0.004 0.000
#> GSM680070 4 0.0188 0.9667 0.004 0.000 0.000 0.996
#> GSM680071 2 0.0188 0.9537 0.004 0.996 0.000 0.000
#> GSM680077 2 0.5285 0.0736 0.468 0.524 0.000 0.008
#> GSM680072 2 0.0000 0.9566 0.000 1.000 0.000 0.000
#> GSM680078 3 0.0188 0.9603 0.000 0.000 0.996 0.004
#> GSM680073 3 0.1022 0.9457 0.000 0.032 0.968 0.000
#> GSM680079 3 0.0779 0.9535 0.016 0.000 0.980 0.004
#> GSM680074 2 0.0000 0.9566 0.000 1.000 0.000 0.000
#> GSM680080 2 0.0000 0.9566 0.000 1.000 0.000 0.000
#> GSM680075 3 0.0000 0.9615 0.000 0.000 1.000 0.000
#> GSM680081 3 0.0000 0.9615 0.000 0.000 1.000 0.000
#> GSM680076 2 0.0000 0.9566 0.000 1.000 0.000 0.000
#> GSM680082 4 0.0592 0.9582 0.016 0.000 0.000 0.984
#> GSM680029 3 0.0000 0.9615 0.000 0.000 1.000 0.000
#> GSM680041 1 0.3486 0.7425 0.812 0.000 0.000 0.188
#> GSM680035 3 0.0000 0.9615 0.000 0.000 1.000 0.000
#> GSM680047 1 0.0707 0.9155 0.980 0.000 0.000 0.020
#> GSM680036 3 0.0188 0.9606 0.000 0.004 0.996 0.000
#> GSM680048 1 0.0707 0.9156 0.980 0.000 0.000 0.020
#> GSM680037 3 0.0188 0.9601 0.004 0.000 0.996 0.000
#> GSM680049 4 0.0000 0.9678 0.000 0.000 0.000 1.000
#> GSM680038 2 0.0000 0.9566 0.000 1.000 0.000 0.000
#> GSM680050 1 0.0000 0.9198 1.000 0.000 0.000 0.000
#> GSM680039 3 0.3074 0.8381 0.000 0.152 0.848 0.000
#> GSM680051 4 0.0188 0.9665 0.000 0.000 0.004 0.996
#> GSM680040 3 0.0000 0.9615 0.000 0.000 1.000 0.000
#> GSM680052 4 0.0188 0.9673 0.004 0.000 0.000 0.996
#> GSM680030 2 0.0188 0.9547 0.000 0.996 0.004 0.000
#> GSM680042 4 0.0188 0.9673 0.004 0.000 0.000 0.996
#> GSM680031 3 0.1557 0.9261 0.056 0.000 0.944 0.000
#> GSM680043 4 0.0000 0.9678 0.000 0.000 0.000 1.000
#> GSM680032 3 0.4999 0.8070 0.012 0.100 0.792 0.096
#> GSM680044 1 0.0592 0.9167 0.984 0.000 0.000 0.016
#> GSM680033 3 0.0188 0.9607 0.000 0.004 0.996 0.000
#> GSM680045 4 0.0188 0.9673 0.004 0.000 0.000 0.996
#> GSM680034 4 0.2334 0.8834 0.000 0.088 0.004 0.908
#> GSM680046 4 0.0000 0.9678 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.0000 0.813 0.000 0.000 0.000 0.000 1.000
#> GSM680062 5 0.0000 0.813 0.000 0.000 0.000 0.000 1.000
#> GSM680054 5 0.4949 0.306 0.032 0.396 0.000 0.000 0.572
#> GSM680063 5 0.0000 0.813 0.000 0.000 0.000 0.000 1.000
#> GSM680055 5 0.0000 0.813 0.000 0.000 0.000 0.000 1.000
#> GSM680064 1 0.3630 0.600 0.780 0.000 0.000 0.204 0.016
#> GSM680056 1 0.4300 0.312 0.524 0.000 0.000 0.000 0.476
#> GSM680065 1 0.4300 0.312 0.524 0.000 0.000 0.000 0.476
#> GSM680057 2 0.0880 0.927 0.032 0.968 0.000 0.000 0.000
#> GSM680066 3 0.5665 0.599 0.184 0.140 0.664 0.012 0.000
#> GSM680058 2 0.2074 0.923 0.104 0.896 0.000 0.000 0.000
#> GSM680067 2 0.0000 0.934 0.000 1.000 0.000 0.000 0.000
#> GSM680059 3 0.0000 0.938 0.000 0.000 1.000 0.000 0.000
#> GSM680068 4 0.2516 0.842 0.140 0.000 0.000 0.860 0.000
#> GSM680060 2 0.0703 0.936 0.024 0.976 0.000 0.000 0.000
#> GSM680069 5 0.7107 -0.327 0.376 0.036 0.160 0.000 0.428
#> GSM680061 2 0.0880 0.927 0.032 0.968 0.000 0.000 0.000
#> GSM680070 4 0.2966 0.798 0.184 0.000 0.000 0.816 0.000
#> GSM680071 2 0.0963 0.919 0.036 0.964 0.000 0.000 0.000
#> GSM680077 1 0.2513 0.638 0.876 0.008 0.000 0.000 0.116
#> GSM680072 2 0.2074 0.923 0.104 0.896 0.000 0.000 0.000
#> GSM680078 3 0.1608 0.888 0.072 0.000 0.928 0.000 0.000
#> GSM680073 3 0.1121 0.910 0.000 0.044 0.956 0.000 0.000
#> GSM680079 1 0.2605 0.617 0.852 0.000 0.148 0.000 0.000
#> GSM680074 2 0.2074 0.923 0.104 0.896 0.000 0.000 0.000
#> GSM680080 2 0.2230 0.924 0.116 0.884 0.000 0.000 0.000
#> GSM680075 3 0.0000 0.938 0.000 0.000 1.000 0.000 0.000
#> GSM680081 3 0.0000 0.938 0.000 0.000 1.000 0.000 0.000
#> GSM680076 2 0.2074 0.923 0.104 0.896 0.000 0.000 0.000
#> GSM680082 1 0.2471 0.625 0.864 0.000 0.000 0.136 0.000
#> GSM680029 3 0.0000 0.938 0.000 0.000 1.000 0.000 0.000
#> GSM680041 5 0.2891 0.627 0.000 0.000 0.000 0.176 0.824
#> GSM680035 3 0.0000 0.938 0.000 0.000 1.000 0.000 0.000
#> GSM680047 5 0.0510 0.807 0.000 0.000 0.000 0.016 0.984
#> GSM680036 3 0.0510 0.931 0.000 0.016 0.984 0.000 0.000
#> GSM680048 5 0.0510 0.807 0.000 0.000 0.000 0.016 0.984
#> GSM680037 3 0.0000 0.938 0.000 0.000 1.000 0.000 0.000
#> GSM680049 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000
#> GSM680038 2 0.1041 0.925 0.032 0.964 0.004 0.000 0.000
#> GSM680050 1 0.4489 0.375 0.572 0.000 0.000 0.008 0.420
#> GSM680039 3 0.3694 0.740 0.032 0.172 0.796 0.000 0.000
#> GSM680051 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000
#> GSM680040 3 0.0000 0.938 0.000 0.000 1.000 0.000 0.000
#> GSM680052 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000
#> GSM680030 2 0.0880 0.927 0.032 0.968 0.000 0.000 0.000
#> GSM680042 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000
#> GSM680031 3 0.1341 0.898 0.000 0.000 0.944 0.000 0.056
#> GSM680043 4 0.0404 0.931 0.000 0.000 0.000 0.988 0.012
#> GSM680032 1 0.5754 0.389 0.588 0.120 0.292 0.000 0.000
#> GSM680044 5 0.0000 0.813 0.000 0.000 0.000 0.000 1.000
#> GSM680033 3 0.0000 0.938 0.000 0.000 1.000 0.000 0.000
#> GSM680045 4 0.0162 0.935 0.000 0.000 0.000 0.996 0.004
#> GSM680034 4 0.3366 0.757 0.032 0.140 0.000 0.828 0.000
#> GSM680046 4 0.0000 0.936 0.000 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.0000 0.7702 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680062 5 0.0000 0.7702 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680054 2 0.0000 0.8607 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680063 5 0.0000 0.7702 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680055 5 0.0000 0.7702 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680064 1 0.3073 0.6637 0.840 0.000 0.000 0.080 0.080 0.000
#> GSM680056 1 0.3727 0.4177 0.612 0.000 0.000 0.000 0.388 0.000
#> GSM680065 1 0.3727 0.4177 0.612 0.000 0.000 0.000 0.388 0.000
#> GSM680057 2 0.0000 0.8607 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680066 2 0.4067 0.5908 0.260 0.700 0.040 0.000 0.000 0.000
#> GSM680058 6 0.0000 0.8658 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM680067 2 0.3833 0.1185 0.000 0.556 0.000 0.000 0.000 0.444
#> GSM680059 3 0.0000 0.9862 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680068 4 0.3175 0.7533 0.256 0.000 0.000 0.744 0.000 0.000
#> GSM680060 6 0.2340 0.7526 0.000 0.148 0.000 0.000 0.000 0.852
#> GSM680069 5 0.6120 -0.0287 0.364 0.000 0.172 0.000 0.448 0.016
#> GSM680061 2 0.0000 0.8607 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680070 4 0.3531 0.6756 0.328 0.000 0.000 0.672 0.000 0.000
#> GSM680071 1 0.5329 0.0215 0.452 0.104 0.000 0.000 0.000 0.444
#> GSM680077 1 0.0000 0.7071 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM680072 6 0.0000 0.8658 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM680078 3 0.1204 0.9405 0.056 0.000 0.944 0.000 0.000 0.000
#> GSM680073 3 0.0632 0.9697 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM680079 1 0.0547 0.6995 0.980 0.000 0.020 0.000 0.000 0.000
#> GSM680074 6 0.0000 0.8658 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM680080 6 0.3659 0.3657 0.000 0.364 0.000 0.000 0.000 0.636
#> GSM680075 3 0.0000 0.9862 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680081 3 0.0000 0.9862 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680076 6 0.0000 0.8658 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM680082 1 0.0000 0.7071 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM680029 3 0.0000 0.9862 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680041 5 0.3175 0.6093 0.000 0.000 0.000 0.256 0.744 0.000
#> GSM680035 3 0.0000 0.9862 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680047 5 0.3050 0.6552 0.000 0.000 0.000 0.236 0.764 0.000
#> GSM680036 3 0.0146 0.9843 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM680048 5 0.2527 0.6944 0.000 0.000 0.000 0.168 0.832 0.000
#> GSM680037 3 0.0000 0.9862 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680049 4 0.0000 0.8761 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680038 2 0.0146 0.8588 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM680050 5 0.4407 -0.1111 0.480 0.000 0.000 0.024 0.496 0.000
#> GSM680039 2 0.0146 0.8586 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM680051 4 0.0000 0.8761 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680040 3 0.0000 0.9862 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680052 4 0.1075 0.8607 0.000 0.000 0.000 0.952 0.048 0.000
#> GSM680030 2 0.0000 0.8607 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680042 4 0.0000 0.8761 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680031 3 0.1204 0.9376 0.000 0.000 0.944 0.000 0.056 0.000
#> GSM680043 4 0.3403 0.7769 0.212 0.000 0.000 0.768 0.020 0.000
#> GSM680032 2 0.3482 0.4995 0.316 0.684 0.000 0.000 0.000 0.000
#> GSM680044 5 0.0000 0.7702 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680033 3 0.0146 0.9840 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM680045 4 0.1444 0.8458 0.000 0.000 0.000 0.928 0.072 0.000
#> GSM680034 2 0.0000 0.8607 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680046 4 0.0000 0.8761 0.000 0.000 0.000 1.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> MAD:pam 52 0.3789 0.529 2.21e-03 0.18345 2
#> MAD:pam 34 0.0380 0.385 1.83e-04 0.24468 3
#> MAD:pam 52 0.0724 0.288 1.23e-04 0.03830 4
#> MAD:pam 48 0.0114 0.366 1.74e-04 0.01031 5
#> MAD:pam 46 0.0342 0.303 1.61e-05 0.00204 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 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 0.361 0.840 0.833 0.3762 0.508 0.508
#> 3 3 0.239 0.618 0.683 0.4691 0.857 0.742
#> 4 4 0.570 0.698 0.832 0.3135 0.725 0.439
#> 5 5 0.682 0.632 0.786 0.0879 0.865 0.540
#> 6 6 0.750 0.658 0.822 0.0433 0.932 0.690
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
#> GSM680053 2 0.7139 0.924 0.196 0.804
#> GSM680062 2 0.7299 0.915 0.204 0.796
#> GSM680054 2 0.7139 0.924 0.196 0.804
#> GSM680063 2 0.7139 0.924 0.196 0.804
#> GSM680055 2 0.7139 0.924 0.196 0.804
#> GSM680064 1 0.6887 0.874 0.816 0.184
#> GSM680056 1 0.6887 0.874 0.816 0.184
#> GSM680065 1 0.6887 0.874 0.816 0.184
#> GSM680057 2 0.7139 0.924 0.196 0.804
#> GSM680066 2 0.9248 0.660 0.340 0.660
#> GSM680058 2 0.7139 0.924 0.196 0.804
#> GSM680067 2 0.7139 0.924 0.196 0.804
#> GSM680059 2 0.7139 0.924 0.196 0.804
#> GSM680068 1 0.6887 0.874 0.816 0.184
#> GSM680060 2 0.7139 0.924 0.196 0.804
#> GSM680069 2 0.7139 0.924 0.196 0.804
#> GSM680061 2 0.7139 0.924 0.196 0.804
#> GSM680070 1 0.6887 0.874 0.816 0.184
#> GSM680071 2 0.9635 0.517 0.388 0.612
#> GSM680077 1 0.6887 0.874 0.816 0.184
#> GSM680072 2 0.7139 0.924 0.196 0.804
#> GSM680078 1 0.9732 0.394 0.596 0.404
#> GSM680073 2 0.7139 0.924 0.196 0.804
#> GSM680079 1 0.6887 0.874 0.816 0.184
#> GSM680074 2 0.7139 0.924 0.196 0.804
#> GSM680080 2 0.7139 0.924 0.196 0.804
#> GSM680075 2 0.7139 0.924 0.196 0.804
#> GSM680081 2 0.7139 0.924 0.196 0.804
#> GSM680076 2 0.7139 0.924 0.196 0.804
#> GSM680082 1 0.6887 0.874 0.816 0.184
#> GSM680029 2 0.7139 0.924 0.196 0.804
#> GSM680041 1 0.5629 0.862 0.868 0.132
#> GSM680035 2 0.0000 0.728 0.000 1.000
#> GSM680047 1 0.4562 0.846 0.904 0.096
#> GSM680036 2 0.7139 0.924 0.196 0.804
#> GSM680048 1 0.0000 0.773 1.000 0.000
#> GSM680037 2 0.0376 0.733 0.004 0.996
#> GSM680049 1 0.6712 0.873 0.824 0.176
#> GSM680038 2 0.6438 0.899 0.164 0.836
#> GSM680050 1 0.6887 0.874 0.816 0.184
#> GSM680039 2 0.6247 0.892 0.156 0.844
#> GSM680051 1 0.0000 0.773 1.000 0.000
#> GSM680040 2 0.0000 0.728 0.000 1.000
#> GSM680052 1 0.0000 0.773 1.000 0.000
#> GSM680030 2 0.6247 0.892 0.156 0.844
#> GSM680042 1 0.6148 0.869 0.848 0.152
#> GSM680031 2 0.0376 0.733 0.004 0.996
#> GSM680043 1 0.2948 0.810 0.948 0.052
#> GSM680032 1 0.9866 0.278 0.568 0.432
#> GSM680044 1 0.8144 0.779 0.748 0.252
#> GSM680033 2 0.0000 0.728 0.000 1.000
#> GSM680045 1 0.4161 0.806 0.916 0.084
#> GSM680034 2 0.7139 0.924 0.196 0.804
#> GSM680046 1 0.4431 0.844 0.908 0.092
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 2 0.6518 0.5633 0.004 0.512 0.484
#> GSM680062 2 0.7835 0.4961 0.052 0.492 0.456
#> GSM680054 2 0.6823 0.6036 0.036 0.668 0.296
#> GSM680063 2 0.7075 0.5313 0.020 0.492 0.488
#> GSM680055 2 0.6678 0.5607 0.008 0.512 0.480
#> GSM680064 3 0.7821 0.9490 0.176 0.152 0.672
#> GSM680056 3 0.7766 0.9502 0.176 0.148 0.676
#> GSM680065 3 0.7766 0.9502 0.176 0.148 0.676
#> GSM680057 2 0.3764 0.5578 0.040 0.892 0.068
#> GSM680066 2 0.9041 0.3070 0.140 0.488 0.372
#> GSM680058 2 0.5581 0.5649 0.040 0.792 0.168
#> GSM680067 2 0.5414 0.4658 0.212 0.772 0.016
#> GSM680059 2 0.6267 0.5739 0.000 0.548 0.452
#> GSM680068 3 0.7869 0.9456 0.180 0.152 0.668
#> GSM680060 2 0.5798 0.5541 0.040 0.776 0.184
#> GSM680069 2 0.7757 0.4952 0.048 0.488 0.464
#> GSM680061 2 0.5414 0.4658 0.212 0.772 0.016
#> GSM680070 3 0.7772 0.9500 0.172 0.152 0.676
#> GSM680071 2 0.8515 -0.2148 0.092 0.476 0.432
#> GSM680077 3 0.7766 0.9502 0.176 0.148 0.676
#> GSM680072 2 0.6698 0.6014 0.036 0.684 0.280
#> GSM680078 3 0.7059 0.8359 0.112 0.164 0.724
#> GSM680073 2 0.6302 0.5697 0.000 0.520 0.480
#> GSM680079 3 0.7772 0.9500 0.172 0.152 0.676
#> GSM680074 2 0.5798 0.5541 0.040 0.776 0.184
#> GSM680080 2 0.5635 0.5601 0.036 0.784 0.180
#> GSM680075 2 0.6302 0.5697 0.000 0.520 0.480
#> GSM680081 2 0.6516 0.5672 0.004 0.516 0.480
#> GSM680076 2 0.5741 0.5539 0.036 0.776 0.188
#> GSM680082 3 0.7759 0.9486 0.180 0.144 0.676
#> GSM680029 2 0.6302 0.5697 0.000 0.520 0.480
#> GSM680041 1 0.3921 0.8612 0.884 0.036 0.080
#> GSM680035 2 0.6225 0.4394 0.000 0.568 0.432
#> GSM680047 1 0.3921 0.8612 0.884 0.036 0.080
#> GSM680036 2 0.6302 0.5697 0.000 0.520 0.480
#> GSM680048 1 0.0424 0.8442 0.992 0.008 0.000
#> GSM680037 2 0.6225 0.4394 0.000 0.568 0.432
#> GSM680049 1 0.6291 0.6700 0.768 0.152 0.080
#> GSM680038 2 0.5407 0.5946 0.040 0.804 0.156
#> GSM680050 3 0.8849 0.7485 0.292 0.152 0.556
#> GSM680039 2 0.5466 0.5719 0.040 0.800 0.160
#> GSM680051 1 0.0424 0.8442 0.992 0.008 0.000
#> GSM680040 2 0.6225 0.4394 0.000 0.568 0.432
#> GSM680052 1 0.0424 0.8442 0.992 0.008 0.000
#> GSM680030 2 0.1950 0.5331 0.040 0.952 0.008
#> GSM680042 1 0.4745 0.8305 0.852 0.068 0.080
#> GSM680031 2 0.6225 0.4394 0.000 0.568 0.432
#> GSM680043 1 0.5566 0.7053 0.812 0.080 0.108
#> GSM680032 2 0.9367 -0.0311 0.168 0.428 0.404
#> GSM680044 2 0.9433 0.1417 0.184 0.460 0.356
#> GSM680033 2 0.6225 0.4394 0.000 0.568 0.432
#> GSM680045 1 0.4477 0.7780 0.864 0.068 0.068
#> GSM680034 2 0.5414 0.4658 0.212 0.772 0.016
#> GSM680046 1 0.3921 0.8612 0.884 0.036 0.080
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 3 0.4540 0.734 0.196 0.032 0.772 0.000
#> GSM680062 3 0.5250 0.609 0.316 0.024 0.660 0.000
#> GSM680054 3 0.6748 0.439 0.112 0.328 0.560 0.000
#> GSM680063 3 0.5206 0.621 0.308 0.024 0.668 0.000
#> GSM680055 3 0.5816 0.497 0.392 0.036 0.572 0.000
#> GSM680064 1 0.1284 0.826 0.964 0.024 0.012 0.000
#> GSM680056 1 0.2036 0.799 0.936 0.032 0.032 0.000
#> GSM680065 1 0.0707 0.823 0.980 0.000 0.020 0.000
#> GSM680057 2 0.3853 0.769 0.020 0.820 0.160 0.000
#> GSM680066 1 0.5721 0.539 0.660 0.284 0.056 0.000
#> GSM680058 2 0.3533 0.768 0.056 0.864 0.080 0.000
#> GSM680067 2 0.4918 0.771 0.044 0.812 0.088 0.056
#> GSM680059 3 0.6098 0.564 0.068 0.316 0.616 0.000
#> GSM680068 1 0.1871 0.823 0.948 0.024 0.012 0.016
#> GSM680060 2 0.1824 0.794 0.060 0.936 0.004 0.000
#> GSM680069 1 0.4737 0.488 0.728 0.020 0.252 0.000
#> GSM680061 2 0.4457 0.781 0.024 0.832 0.088 0.056
#> GSM680070 1 0.0921 0.827 0.972 0.028 0.000 0.000
#> GSM680071 1 0.4950 0.276 0.620 0.376 0.004 0.000
#> GSM680077 1 0.2149 0.787 0.912 0.088 0.000 0.000
#> GSM680072 2 0.6265 -0.270 0.056 0.500 0.444 0.000
#> GSM680078 1 0.0524 0.826 0.988 0.004 0.008 0.000
#> GSM680073 3 0.6205 0.698 0.136 0.196 0.668 0.000
#> GSM680079 1 0.0000 0.826 1.000 0.000 0.000 0.000
#> GSM680074 2 0.1576 0.795 0.048 0.948 0.004 0.000
#> GSM680080 2 0.1824 0.791 0.060 0.936 0.004 0.000
#> GSM680075 3 0.5994 0.704 0.152 0.156 0.692 0.000
#> GSM680081 3 0.4996 0.735 0.192 0.056 0.752 0.000
#> GSM680076 2 0.2149 0.792 0.088 0.912 0.000 0.000
#> GSM680082 1 0.2011 0.791 0.920 0.080 0.000 0.000
#> GSM680029 3 0.5122 0.739 0.164 0.080 0.756 0.000
#> GSM680041 4 0.3088 0.909 0.060 0.052 0.000 0.888
#> GSM680035 3 0.1022 0.708 0.000 0.032 0.968 0.000
#> GSM680047 4 0.1637 0.932 0.060 0.000 0.000 0.940
#> GSM680036 3 0.4881 0.732 0.196 0.048 0.756 0.000
#> GSM680048 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM680037 3 0.1022 0.708 0.000 0.032 0.968 0.000
#> GSM680049 4 0.3810 0.871 0.060 0.092 0.000 0.848
#> GSM680038 3 0.5550 0.119 0.020 0.428 0.552 0.000
#> GSM680050 1 0.2530 0.787 0.896 0.100 0.000 0.004
#> GSM680039 3 0.4008 0.570 0.000 0.244 0.756 0.000
#> GSM680051 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM680040 3 0.1022 0.708 0.000 0.032 0.968 0.000
#> GSM680052 4 0.0000 0.929 0.000 0.000 0.000 1.000
#> GSM680030 2 0.4991 0.450 0.004 0.608 0.388 0.000
#> GSM680042 4 0.3398 0.895 0.060 0.068 0.000 0.872
#> GSM680031 3 0.1022 0.708 0.000 0.032 0.968 0.000
#> GSM680043 4 0.1305 0.936 0.036 0.000 0.004 0.960
#> GSM680032 1 0.1004 0.826 0.972 0.024 0.004 0.000
#> GSM680044 1 0.8064 -0.244 0.408 0.024 0.404 0.164
#> GSM680033 3 0.1022 0.708 0.000 0.032 0.968 0.000
#> GSM680045 4 0.0469 0.933 0.012 0.000 0.000 0.988
#> GSM680034 2 0.5180 0.770 0.040 0.796 0.096 0.068
#> GSM680046 4 0.1637 0.932 0.060 0.000 0.000 0.940
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.4171 0.7790 0.052 0.028 0.112 0.000 0.808
#> GSM680062 5 0.5394 0.7334 0.136 0.008 0.152 0.004 0.700
#> GSM680054 2 0.6695 0.2214 0.000 0.428 0.308 0.000 0.264
#> GSM680063 5 0.5237 0.7337 0.156 0.008 0.132 0.000 0.704
#> GSM680055 5 0.4410 0.7400 0.160 0.028 0.036 0.000 0.776
#> GSM680064 1 0.0486 0.7902 0.988 0.000 0.004 0.004 0.004
#> GSM680056 1 0.4101 0.4400 0.664 0.004 0.000 0.000 0.332
#> GSM680065 1 0.2852 0.6859 0.828 0.000 0.000 0.000 0.172
#> GSM680057 2 0.6021 0.3935 0.000 0.476 0.408 0.000 0.116
#> GSM680066 1 0.7640 0.0934 0.400 0.320 0.044 0.004 0.232
#> GSM680058 2 0.3044 0.6088 0.004 0.840 0.148 0.000 0.008
#> GSM680067 2 0.6272 0.5507 0.000 0.652 0.088 0.088 0.172
#> GSM680059 2 0.4494 0.3964 0.000 0.608 0.380 0.000 0.012
#> GSM680068 1 0.2284 0.7580 0.912 0.000 0.028 0.056 0.004
#> GSM680060 2 0.0992 0.6169 0.024 0.968 0.000 0.000 0.008
#> GSM680069 5 0.3430 0.6637 0.220 0.004 0.000 0.000 0.776
#> GSM680061 2 0.6272 0.5507 0.000 0.652 0.088 0.088 0.172
#> GSM680070 1 0.0613 0.7900 0.984 0.000 0.004 0.004 0.008
#> GSM680071 1 0.5708 0.2412 0.528 0.384 0.000 0.000 0.088
#> GSM680077 1 0.0162 0.7885 0.996 0.000 0.000 0.000 0.004
#> GSM680072 2 0.5004 0.5633 0.000 0.692 0.216 0.000 0.092
#> GSM680078 1 0.3837 0.4482 0.692 0.000 0.000 0.000 0.308
#> GSM680073 2 0.6996 0.4011 0.044 0.532 0.244 0.000 0.180
#> GSM680079 1 0.0486 0.7902 0.988 0.000 0.004 0.004 0.004
#> GSM680074 2 0.0324 0.6184 0.004 0.992 0.000 0.000 0.004
#> GSM680080 2 0.0324 0.6184 0.004 0.992 0.000 0.000 0.004
#> GSM680075 5 0.5723 0.7059 0.048 0.148 0.108 0.000 0.696
#> GSM680081 5 0.6220 0.5142 0.076 0.028 0.368 0.000 0.528
#> GSM680076 2 0.1732 0.6035 0.080 0.920 0.000 0.000 0.000
#> GSM680082 1 0.0162 0.7885 0.996 0.000 0.000 0.000 0.004
#> GSM680029 5 0.5382 0.5461 0.016 0.040 0.340 0.000 0.604
#> GSM680041 4 0.1956 0.8824 0.076 0.000 0.000 0.916 0.008
#> GSM680035 3 0.0162 0.8508 0.000 0.000 0.996 0.000 0.004
#> GSM680047 4 0.1671 0.8836 0.076 0.000 0.000 0.924 0.000
#> GSM680036 5 0.4184 0.7790 0.048 0.032 0.112 0.000 0.808
#> GSM680048 4 0.0000 0.8828 0.000 0.000 0.000 1.000 0.000
#> GSM680037 3 0.0162 0.8508 0.000 0.000 0.996 0.000 0.004
#> GSM680049 4 0.2295 0.8743 0.088 0.004 0.000 0.900 0.008
#> GSM680038 2 0.5803 0.3808 0.000 0.488 0.420 0.000 0.092
#> GSM680050 1 0.0968 0.7879 0.972 0.000 0.012 0.012 0.004
#> GSM680039 3 0.5574 -0.3682 0.000 0.416 0.512 0.000 0.072
#> GSM680051 4 0.0000 0.8828 0.000 0.000 0.000 1.000 0.000
#> GSM680040 3 0.0162 0.8508 0.000 0.000 0.996 0.000 0.004
#> GSM680052 4 0.0000 0.8828 0.000 0.000 0.000 1.000 0.000
#> GSM680030 2 0.5998 0.3757 0.000 0.464 0.424 0.000 0.112
#> GSM680042 4 0.2249 0.8709 0.096 0.000 0.000 0.896 0.008
#> GSM680031 3 0.0162 0.8508 0.000 0.000 0.996 0.000 0.004
#> GSM680043 4 0.0566 0.8796 0.004 0.000 0.012 0.984 0.000
#> GSM680032 1 0.3001 0.7050 0.844 0.000 0.008 0.004 0.144
#> GSM680044 4 0.8567 -0.2164 0.276 0.008 0.132 0.312 0.272
#> GSM680033 3 0.0162 0.8508 0.000 0.000 0.996 0.000 0.004
#> GSM680045 4 0.0404 0.8795 0.000 0.000 0.012 0.988 0.000
#> GSM680034 2 0.7672 0.4679 0.000 0.456 0.284 0.092 0.168
#> GSM680046 4 0.1671 0.8836 0.076 0.000 0.000 0.924 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.1096 0.7975 0.004 0.020 0.008 0.000 0.964 0.004
#> GSM680062 5 0.2476 0.7828 0.036 0.004 0.020 0.000 0.900 0.040
#> GSM680054 5 0.6276 0.1542 0.008 0.288 0.300 0.000 0.404 0.000
#> GSM680063 5 0.2476 0.7828 0.036 0.004 0.020 0.000 0.900 0.040
#> GSM680055 5 0.0806 0.7958 0.008 0.020 0.000 0.000 0.972 0.000
#> GSM680064 1 0.2266 0.7649 0.880 0.000 0.000 0.000 0.012 0.108
#> GSM680056 1 0.5220 0.3541 0.528 0.000 0.000 0.000 0.372 0.100
#> GSM680065 1 0.3657 0.7217 0.792 0.000 0.000 0.000 0.108 0.100
#> GSM680057 3 0.5779 0.1007 0.000 0.188 0.472 0.000 0.000 0.340
#> GSM680066 1 0.5445 0.4105 0.592 0.036 0.008 0.004 0.324 0.036
#> GSM680058 2 0.0622 0.7680 0.012 0.980 0.000 0.000 0.008 0.000
#> GSM680067 6 0.4520 0.8504 0.000 0.228 0.076 0.004 0.000 0.692
#> GSM680059 2 0.4919 0.2254 0.008 0.528 0.424 0.000 0.036 0.004
#> GSM680068 1 0.2535 0.7679 0.892 0.004 0.000 0.048 0.048 0.008
#> GSM680060 2 0.0717 0.7673 0.016 0.976 0.000 0.000 0.008 0.000
#> GSM680069 5 0.2531 0.7076 0.128 0.004 0.000 0.000 0.860 0.008
#> GSM680061 6 0.4520 0.8504 0.000 0.228 0.076 0.004 0.000 0.692
#> GSM680070 1 0.0806 0.7816 0.972 0.000 0.000 0.000 0.020 0.008
#> GSM680071 1 0.5011 0.3979 0.580 0.348 0.000 0.000 0.064 0.008
#> GSM680077 1 0.2554 0.7578 0.876 0.004 0.000 0.000 0.028 0.092
#> GSM680072 2 0.2288 0.6900 0.000 0.876 0.004 0.000 0.116 0.004
#> GSM680078 1 0.4136 0.3005 0.560 0.000 0.000 0.000 0.428 0.012
#> GSM680073 2 0.4227 -0.0866 0.004 0.500 0.000 0.000 0.488 0.008
#> GSM680079 1 0.0622 0.7795 0.980 0.000 0.000 0.000 0.008 0.012
#> GSM680074 2 0.0363 0.7697 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM680080 2 0.0363 0.7697 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM680075 5 0.3626 0.5239 0.004 0.288 0.000 0.000 0.704 0.004
#> GSM680081 5 0.4734 0.7270 0.036 0.024 0.164 0.000 0.740 0.036
#> GSM680076 2 0.0363 0.7697 0.012 0.988 0.000 0.000 0.000 0.000
#> GSM680082 1 0.1633 0.7753 0.932 0.000 0.000 0.000 0.024 0.044
#> GSM680029 5 0.3691 0.7359 0.020 0.024 0.172 0.000 0.784 0.000
#> GSM680041 4 0.2000 0.8885 0.048 0.000 0.000 0.916 0.004 0.032
#> GSM680035 3 0.0000 0.7050 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680047 4 0.1434 0.8923 0.048 0.000 0.000 0.940 0.000 0.012
#> GSM680036 5 0.1413 0.7929 0.004 0.036 0.008 0.000 0.948 0.004
#> GSM680048 4 0.0000 0.8925 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680037 3 0.0000 0.7050 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680049 4 0.2895 0.8661 0.052 0.024 0.000 0.876 0.004 0.044
#> GSM680038 3 0.5911 0.2566 0.008 0.128 0.524 0.000 0.012 0.328
#> GSM680050 1 0.0912 0.7786 0.972 0.012 0.008 0.000 0.004 0.004
#> GSM680039 3 0.4575 0.5033 0.000 0.124 0.696 0.000 0.000 0.180
#> GSM680051 4 0.0000 0.8925 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680040 3 0.0000 0.7050 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680052 4 0.0146 0.8928 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM680030 3 0.5431 0.2383 0.000 0.132 0.524 0.000 0.000 0.344
#> GSM680042 4 0.2144 0.8872 0.048 0.004 0.000 0.912 0.004 0.032
#> GSM680031 3 0.0000 0.7050 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680043 4 0.0551 0.8895 0.000 0.000 0.008 0.984 0.004 0.004
#> GSM680032 1 0.3052 0.6907 0.780 0.000 0.000 0.000 0.216 0.004
#> GSM680044 4 0.6857 -0.0257 0.124 0.004 0.020 0.416 0.392 0.044
#> GSM680033 3 0.0000 0.7050 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680045 4 0.0551 0.8895 0.000 0.000 0.008 0.984 0.004 0.004
#> GSM680034 6 0.5524 0.6171 0.000 0.144 0.252 0.012 0.000 0.592
#> GSM680046 4 0.1594 0.8904 0.052 0.000 0.000 0.932 0.000 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> MAD:mclust 52 1.28e-01 0.934 1.26e-06 0.6100 2
#> MAD:mclust 40 3.32e-05 0.473 2.19e-06 0.0765 3
#> MAD:mclust 46 1.24e-04 0.352 3.43e-05 0.2156 4
#> MAD:mclust 41 9.93e-06 0.334 2.00e-04 0.0727 5
#> MAD:mclust 43 3.84e-05 0.479 1.90e-04 0.0194 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 0.884 0.927 0.969 0.5025 0.497 0.497
#> 3 3 0.568 0.754 0.858 0.3285 0.766 0.559
#> 4 4 0.539 0.568 0.764 0.1329 0.834 0.548
#> 5 5 0.576 0.353 0.650 0.0638 0.850 0.519
#> 6 6 0.660 0.536 0.736 0.0395 0.814 0.367
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
#> GSM680053 2 0.0000 0.966 0.000 1.000
#> GSM680062 1 0.6343 0.807 0.840 0.160
#> GSM680054 2 0.0000 0.966 0.000 1.000
#> GSM680063 1 0.9427 0.446 0.640 0.360
#> GSM680055 2 0.0000 0.966 0.000 1.000
#> GSM680064 1 0.0000 0.965 1.000 0.000
#> GSM680056 1 0.0000 0.965 1.000 0.000
#> GSM680065 1 0.0000 0.965 1.000 0.000
#> GSM680057 2 0.0000 0.966 0.000 1.000
#> GSM680066 2 0.3879 0.900 0.076 0.924
#> GSM680058 2 0.0000 0.966 0.000 1.000
#> GSM680067 2 0.7745 0.704 0.228 0.772
#> GSM680059 2 0.0000 0.966 0.000 1.000
#> GSM680068 1 0.0000 0.965 1.000 0.000
#> GSM680060 2 0.0000 0.966 0.000 1.000
#> GSM680069 2 0.7950 0.674 0.240 0.760
#> GSM680061 2 0.0000 0.966 0.000 1.000
#> GSM680070 1 0.0000 0.965 1.000 0.000
#> GSM680071 1 0.2948 0.924 0.948 0.052
#> GSM680077 1 0.0938 0.957 0.988 0.012
#> GSM680072 2 0.0000 0.966 0.000 1.000
#> GSM680078 2 0.9393 0.431 0.356 0.644
#> GSM680073 2 0.0000 0.966 0.000 1.000
#> GSM680079 1 0.0000 0.965 1.000 0.000
#> GSM680074 2 0.0000 0.966 0.000 1.000
#> GSM680080 2 0.0000 0.966 0.000 1.000
#> GSM680075 2 0.0000 0.966 0.000 1.000
#> GSM680081 2 0.0000 0.966 0.000 1.000
#> GSM680076 2 0.0000 0.966 0.000 1.000
#> GSM680082 1 0.0000 0.965 1.000 0.000
#> GSM680029 2 0.0000 0.966 0.000 1.000
#> GSM680041 1 0.0000 0.965 1.000 0.000
#> GSM680035 2 0.0000 0.966 0.000 1.000
#> GSM680047 1 0.0000 0.965 1.000 0.000
#> GSM680036 2 0.0000 0.966 0.000 1.000
#> GSM680048 1 0.0000 0.965 1.000 0.000
#> GSM680037 2 0.0000 0.966 0.000 1.000
#> GSM680049 1 0.0000 0.965 1.000 0.000
#> GSM680038 2 0.0000 0.966 0.000 1.000
#> GSM680050 1 0.0000 0.965 1.000 0.000
#> GSM680039 2 0.0000 0.966 0.000 1.000
#> GSM680051 1 0.0000 0.965 1.000 0.000
#> GSM680040 2 0.0000 0.966 0.000 1.000
#> GSM680052 1 0.0000 0.965 1.000 0.000
#> GSM680030 2 0.0000 0.966 0.000 1.000
#> GSM680042 1 0.0000 0.965 1.000 0.000
#> GSM680031 2 0.0000 0.966 0.000 1.000
#> GSM680043 1 0.0000 0.965 1.000 0.000
#> GSM680032 1 0.6712 0.781 0.824 0.176
#> GSM680044 1 0.0376 0.963 0.996 0.004
#> GSM680033 2 0.0000 0.966 0.000 1.000
#> GSM680045 1 0.0000 0.965 1.000 0.000
#> GSM680034 2 0.1414 0.950 0.020 0.980
#> GSM680046 1 0.0000 0.965 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 3 0.0592 0.7939 0.000 0.012 0.988
#> GSM680062 3 0.2860 0.7718 0.084 0.004 0.912
#> GSM680054 3 0.4931 0.6685 0.000 0.232 0.768
#> GSM680063 3 0.1860 0.7838 0.052 0.000 0.948
#> GSM680055 3 0.0592 0.7938 0.000 0.012 0.988
#> GSM680064 1 0.2356 0.8860 0.928 0.000 0.072
#> GSM680056 3 0.4842 0.6164 0.224 0.000 0.776
#> GSM680065 1 0.6026 0.5407 0.624 0.000 0.376
#> GSM680057 2 0.0592 0.8270 0.000 0.988 0.012
#> GSM680066 2 0.6882 0.6363 0.096 0.732 0.172
#> GSM680058 2 0.3192 0.7943 0.000 0.888 0.112
#> GSM680067 2 0.2301 0.8109 0.060 0.936 0.004
#> GSM680059 2 0.6252 0.0666 0.000 0.556 0.444
#> GSM680068 1 0.1636 0.8896 0.964 0.016 0.020
#> GSM680060 2 0.2711 0.8110 0.000 0.912 0.088
#> GSM680069 3 0.5331 0.6931 0.076 0.100 0.824
#> GSM680061 2 0.0424 0.8262 0.008 0.992 0.000
#> GSM680070 1 0.1585 0.8882 0.964 0.008 0.028
#> GSM680071 1 0.9561 0.2423 0.428 0.196 0.376
#> GSM680077 1 0.5526 0.7943 0.792 0.036 0.172
#> GSM680072 3 0.5621 0.5991 0.000 0.308 0.692
#> GSM680078 3 0.4589 0.6863 0.172 0.008 0.820
#> GSM680073 3 0.5291 0.6977 0.000 0.268 0.732
#> GSM680079 1 0.2860 0.8722 0.912 0.004 0.084
#> GSM680074 2 0.1753 0.8278 0.000 0.952 0.048
#> GSM680080 2 0.1964 0.8265 0.000 0.944 0.056
#> GSM680075 3 0.1643 0.7987 0.000 0.044 0.956
#> GSM680081 3 0.5058 0.7529 0.000 0.244 0.756
#> GSM680076 2 0.3769 0.7962 0.016 0.880 0.104
#> GSM680082 1 0.1765 0.8875 0.956 0.004 0.040
#> GSM680029 3 0.4346 0.7814 0.000 0.184 0.816
#> GSM680041 1 0.1411 0.8908 0.964 0.000 0.036
#> GSM680035 3 0.4750 0.7717 0.000 0.216 0.784
#> GSM680047 1 0.1832 0.8912 0.956 0.008 0.036
#> GSM680036 3 0.1860 0.7974 0.000 0.052 0.948
#> GSM680048 1 0.1877 0.8914 0.956 0.012 0.032
#> GSM680037 3 0.4702 0.7737 0.000 0.212 0.788
#> GSM680049 1 0.0424 0.8896 0.992 0.008 0.000
#> GSM680038 2 0.6235 -0.0822 0.000 0.564 0.436
#> GSM680050 1 0.1989 0.8883 0.948 0.004 0.048
#> GSM680039 2 0.2537 0.7867 0.000 0.920 0.080
#> GSM680051 1 0.2443 0.8891 0.940 0.028 0.032
#> GSM680040 3 0.5016 0.7556 0.000 0.240 0.760
#> GSM680052 1 0.2056 0.8910 0.952 0.024 0.024
#> GSM680030 2 0.1031 0.8252 0.000 0.976 0.024
#> GSM680042 1 0.1289 0.8910 0.968 0.000 0.032
#> GSM680031 3 0.4931 0.7621 0.000 0.232 0.768
#> GSM680043 1 0.3554 0.8499 0.900 0.064 0.036
#> GSM680032 1 0.5848 0.6917 0.720 0.012 0.268
#> GSM680044 1 0.1751 0.8925 0.960 0.012 0.028
#> GSM680033 3 0.5138 0.7433 0.000 0.252 0.748
#> GSM680045 1 0.6594 0.7009 0.756 0.128 0.116
#> GSM680034 2 0.3043 0.7879 0.084 0.908 0.008
#> GSM680046 1 0.0892 0.8880 0.980 0.020 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 3 0.4746 0.25471 0.368 0.000 0.632 0.000
#> GSM680062 3 0.2926 0.79607 0.056 0.000 0.896 0.048
#> GSM680054 1 0.6521 0.22896 0.512 0.076 0.412 0.000
#> GSM680063 3 0.4716 0.63411 0.196 0.000 0.764 0.040
#> GSM680055 1 0.4585 0.44104 0.668 0.000 0.332 0.000
#> GSM680064 4 0.5320 0.39517 0.416 0.000 0.012 0.572
#> GSM680056 1 0.3463 0.61492 0.864 0.000 0.096 0.040
#> GSM680065 1 0.3597 0.51295 0.836 0.000 0.016 0.148
#> GSM680057 2 0.0657 0.75310 0.004 0.984 0.012 0.000
#> GSM680066 2 0.9021 0.17040 0.140 0.444 0.120 0.296
#> GSM680058 2 0.4635 0.61098 0.268 0.720 0.012 0.000
#> GSM680067 2 0.0707 0.75121 0.000 0.980 0.000 0.020
#> GSM680059 3 0.5072 0.64788 0.052 0.208 0.740 0.000
#> GSM680068 4 0.4092 0.67121 0.184 0.008 0.008 0.800
#> GSM680060 2 0.2647 0.73580 0.120 0.880 0.000 0.000
#> GSM680069 1 0.3043 0.61214 0.876 0.004 0.112 0.008
#> GSM680061 2 0.0895 0.75068 0.000 0.976 0.004 0.020
#> GSM680070 4 0.5125 0.47052 0.388 0.008 0.000 0.604
#> GSM680071 1 0.3489 0.60023 0.884 0.048 0.028 0.040
#> GSM680077 1 0.2809 0.56390 0.904 0.028 0.004 0.064
#> GSM680072 1 0.7515 0.00714 0.448 0.364 0.188 0.000
#> GSM680078 1 0.5962 0.47744 0.660 0.000 0.260 0.080
#> GSM680073 1 0.7469 0.14807 0.432 0.176 0.392 0.000
#> GSM680079 4 0.5303 0.36474 0.448 0.004 0.004 0.544
#> GSM680074 2 0.2546 0.74259 0.092 0.900 0.008 0.000
#> GSM680080 2 0.3937 0.69673 0.188 0.800 0.012 0.000
#> GSM680075 1 0.5478 0.40403 0.628 0.028 0.344 0.000
#> GSM680081 3 0.2486 0.83961 0.048 0.028 0.920 0.004
#> GSM680076 2 0.3837 0.68139 0.224 0.776 0.000 0.000
#> GSM680082 1 0.5300 -0.14090 0.580 0.012 0.000 0.408
#> GSM680029 3 0.1488 0.82841 0.032 0.012 0.956 0.000
#> GSM680041 4 0.3108 0.71955 0.112 0.000 0.016 0.872
#> GSM680035 3 0.1004 0.85051 0.004 0.024 0.972 0.000
#> GSM680047 4 0.3497 0.70979 0.036 0.000 0.104 0.860
#> GSM680036 1 0.4996 0.13919 0.516 0.000 0.484 0.000
#> GSM680048 4 0.1911 0.73067 0.004 0.020 0.032 0.944
#> GSM680037 3 0.1151 0.85187 0.000 0.024 0.968 0.008
#> GSM680049 4 0.1209 0.73239 0.032 0.004 0.000 0.964
#> GSM680038 2 0.6809 0.36162 0.116 0.552 0.332 0.000
#> GSM680050 4 0.5151 0.34668 0.464 0.004 0.000 0.532
#> GSM680039 2 0.6307 0.45010 0.000 0.620 0.288 0.092
#> GSM680051 4 0.3862 0.69640 0.004 0.060 0.084 0.852
#> GSM680040 3 0.1452 0.85052 0.000 0.036 0.956 0.008
#> GSM680052 4 0.3004 0.71242 0.000 0.060 0.048 0.892
#> GSM680030 2 0.2467 0.74039 0.004 0.920 0.052 0.024
#> GSM680042 4 0.2737 0.71860 0.104 0.000 0.008 0.888
#> GSM680031 3 0.1706 0.84759 0.000 0.036 0.948 0.016
#> GSM680043 4 0.6437 0.57927 0.032 0.076 0.208 0.684
#> GSM680032 1 0.4431 0.20449 0.696 0.000 0.000 0.304
#> GSM680044 4 0.3505 0.72553 0.048 0.000 0.088 0.864
#> GSM680033 3 0.2174 0.83451 0.000 0.052 0.928 0.020
#> GSM680045 4 0.6707 0.37165 0.004 0.100 0.312 0.584
#> GSM680034 2 0.5312 0.53060 0.000 0.692 0.040 0.268
#> GSM680046 4 0.2186 0.72833 0.012 0.048 0.008 0.932
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.3667 0.6234 0.048 0.000 0.140 0.000 0.812
#> GSM680062 5 0.7350 0.3211 0.276 0.000 0.080 0.144 0.500
#> GSM680054 5 0.2845 0.6913 0.048 0.032 0.028 0.000 0.892
#> GSM680063 5 0.6464 0.4630 0.256 0.000 0.104 0.048 0.592
#> GSM680055 5 0.1579 0.6909 0.024 0.000 0.032 0.000 0.944
#> GSM680064 4 0.5287 0.2841 0.260 0.000 0.000 0.648 0.092
#> GSM680056 5 0.1608 0.6897 0.072 0.000 0.000 0.000 0.928
#> GSM680065 5 0.6016 0.2802 0.236 0.000 0.000 0.184 0.580
#> GSM680057 2 0.1430 0.7527 0.052 0.944 0.004 0.000 0.000
#> GSM680066 1 0.7785 -0.3694 0.380 0.064 0.252 0.304 0.000
#> GSM680058 2 0.3684 0.5210 0.000 0.720 0.000 0.000 0.280
#> GSM680067 2 0.1410 0.7510 0.060 0.940 0.000 0.000 0.000
#> GSM680059 3 0.1106 0.5797 0.012 0.024 0.964 0.000 0.000
#> GSM680068 4 0.5382 0.2354 0.336 0.000 0.072 0.592 0.000
#> GSM680060 2 0.2583 0.7009 0.004 0.864 0.000 0.000 0.132
#> GSM680069 5 0.2840 0.6697 0.108 0.012 0.004 0.004 0.872
#> GSM680061 2 0.1608 0.7480 0.072 0.928 0.000 0.000 0.000
#> GSM680070 4 0.4588 0.2797 0.380 0.000 0.016 0.604 0.000
#> GSM680071 5 0.4308 0.6266 0.072 0.128 0.000 0.012 0.788
#> GSM680077 4 0.6595 0.2194 0.416 0.032 0.004 0.464 0.084
#> GSM680072 5 0.5114 0.1157 0.024 0.424 0.008 0.000 0.544
#> GSM680078 3 0.7163 -0.1764 0.400 0.000 0.412 0.140 0.048
#> GSM680073 5 0.7704 0.1757 0.056 0.252 0.312 0.000 0.380
#> GSM680079 4 0.4917 0.2728 0.384 0.000 0.024 0.588 0.004
#> GSM680074 2 0.1041 0.7471 0.004 0.964 0.000 0.000 0.032
#> GSM680080 2 0.1697 0.7402 0.008 0.932 0.000 0.000 0.060
#> GSM680075 3 0.6915 0.1376 0.200 0.036 0.536 0.000 0.228
#> GSM680081 3 0.2006 0.5818 0.072 0.000 0.916 0.012 0.000
#> GSM680076 2 0.3215 0.6971 0.092 0.852 0.000 0.000 0.056
#> GSM680082 4 0.4985 0.2793 0.392 0.016 0.000 0.580 0.012
#> GSM680029 3 0.0609 0.5932 0.000 0.000 0.980 0.000 0.020
#> GSM680041 4 0.6448 -0.0483 0.228 0.000 0.000 0.500 0.272
#> GSM680035 3 0.5584 0.5427 0.324 0.000 0.584 0.000 0.092
#> GSM680047 4 0.6450 -0.1838 0.384 0.000 0.000 0.436 0.180
#> GSM680036 5 0.2388 0.6812 0.028 0.000 0.072 0.000 0.900
#> GSM680048 4 0.4905 -0.0827 0.336 0.000 0.000 0.624 0.040
#> GSM680037 3 0.4957 0.5737 0.332 0.000 0.624 0.000 0.044
#> GSM680049 4 0.1012 0.2370 0.020 0.000 0.000 0.968 0.012
#> GSM680038 5 0.5691 0.4997 0.144 0.196 0.008 0.000 0.652
#> GSM680050 4 0.4849 0.2930 0.360 0.000 0.000 0.608 0.032
#> GSM680039 2 0.6490 0.2672 0.344 0.492 0.156 0.008 0.000
#> GSM680051 1 0.5518 -0.2304 0.540 0.000 0.024 0.408 0.028
#> GSM680040 3 0.4540 0.5913 0.320 0.000 0.656 0.000 0.024
#> GSM680052 4 0.5106 -0.2679 0.456 0.000 0.036 0.508 0.000
#> GSM680030 2 0.5618 0.4363 0.136 0.628 0.000 0.000 0.236
#> GSM680042 4 0.3702 0.1905 0.084 0.000 0.000 0.820 0.096
#> GSM680031 3 0.3582 0.6113 0.224 0.000 0.768 0.000 0.008
#> GSM680043 4 0.6738 -0.1107 0.308 0.004 0.236 0.452 0.000
#> GSM680032 4 0.6451 0.2227 0.388 0.004 0.000 0.452 0.156
#> GSM680044 4 0.4430 0.1197 0.076 0.000 0.172 0.752 0.000
#> GSM680033 3 0.4639 0.5778 0.344 0.000 0.632 0.000 0.024
#> GSM680045 4 0.7446 -0.2317 0.340 0.036 0.244 0.380 0.000
#> GSM680034 2 0.6092 0.3223 0.380 0.524 0.020 0.076 0.000
#> GSM680046 4 0.2891 0.1149 0.176 0.000 0.000 0.824 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.4874 0.45075 0.000 0.000 0.084 0.004 0.636 0.276
#> GSM680062 4 0.6145 0.39803 0.000 0.004 0.036 0.568 0.184 0.208
#> GSM680054 5 0.3634 0.66353 0.000 0.060 0.048 0.004 0.832 0.056
#> GSM680063 4 0.7101 0.01678 0.000 0.004 0.060 0.372 0.292 0.272
#> GSM680055 5 0.4466 0.64925 0.016 0.008 0.064 0.008 0.764 0.140
#> GSM680064 4 0.4496 0.33065 0.408 0.000 0.000 0.564 0.020 0.008
#> GSM680056 5 0.3718 0.68033 0.136 0.000 0.020 0.016 0.808 0.020
#> GSM680065 5 0.4731 0.17939 0.472 0.000 0.000 0.016 0.492 0.020
#> GSM680057 3 0.5497 0.34947 0.000 0.336 0.556 0.000 0.020 0.088
#> GSM680066 1 0.5478 0.65109 0.696 0.028 0.120 0.024 0.004 0.128
#> GSM680058 2 0.3990 0.54953 0.000 0.688 0.000 0.000 0.284 0.028
#> GSM680067 2 0.4146 0.63899 0.008 0.800 0.052 0.036 0.004 0.100
#> GSM680059 6 0.5015 0.25526 0.000 0.092 0.288 0.004 0.000 0.616
#> GSM680068 1 0.4642 0.73497 0.748 0.000 0.076 0.060 0.000 0.116
#> GSM680060 2 0.3596 0.67604 0.012 0.792 0.000 0.000 0.164 0.032
#> GSM680069 5 0.3043 0.67994 0.140 0.008 0.000 0.000 0.832 0.020
#> GSM680061 2 0.5312 0.51997 0.008 0.688 0.156 0.024 0.004 0.120
#> GSM680070 1 0.2375 0.84121 0.896 0.000 0.000 0.036 0.008 0.060
#> GSM680071 5 0.3562 0.68073 0.112 0.040 0.000 0.016 0.824 0.008
#> GSM680077 1 0.2552 0.82853 0.900 0.024 0.000 0.012 0.036 0.028
#> GSM680072 2 0.5740 0.19569 0.000 0.512 0.004 0.000 0.316 0.168
#> GSM680078 6 0.5538 -0.06517 0.384 0.012 0.048 0.008 0.012 0.536
#> GSM680073 6 0.6475 0.09193 0.004 0.372 0.028 0.000 0.176 0.420
#> GSM680079 1 0.2483 0.84058 0.892 0.004 0.000 0.044 0.004 0.056
#> GSM680074 2 0.0653 0.71227 0.004 0.980 0.000 0.000 0.012 0.004
#> GSM680080 2 0.1511 0.71123 0.004 0.940 0.000 0.000 0.044 0.012
#> GSM680075 6 0.6408 0.47066 0.032 0.112 0.104 0.000 0.128 0.624
#> GSM680081 3 0.4005 0.55374 0.084 0.024 0.816 0.004 0.020 0.052
#> GSM680076 2 0.1555 0.70231 0.040 0.940 0.000 0.000 0.008 0.012
#> GSM680082 1 0.1148 0.83891 0.960 0.016 0.000 0.020 0.004 0.000
#> GSM680029 3 0.3984 0.28133 0.000 0.000 0.596 0.000 0.008 0.396
#> GSM680041 4 0.2389 0.72608 0.016 0.000 0.020 0.904 0.052 0.008
#> GSM680035 3 0.2917 0.58797 0.000 0.000 0.872 0.040 0.048 0.040
#> GSM680047 4 0.1245 0.72841 0.000 0.000 0.032 0.952 0.016 0.000
#> GSM680036 5 0.3855 0.65845 0.004 0.016 0.076 0.008 0.816 0.080
#> GSM680048 4 0.1370 0.73551 0.036 0.000 0.004 0.948 0.012 0.000
#> GSM680037 3 0.3473 0.55770 0.000 0.000 0.812 0.040 0.012 0.136
#> GSM680049 4 0.3293 0.68530 0.196 0.000 0.004 0.788 0.008 0.004
#> GSM680038 5 0.5670 0.52847 0.004 0.080 0.168 0.036 0.680 0.032
#> GSM680050 1 0.2154 0.82577 0.908 0.004 0.000 0.064 0.020 0.004
#> GSM680039 3 0.5252 0.53389 0.008 0.152 0.704 0.028 0.008 0.100
#> GSM680051 4 0.5022 0.00719 0.008 0.000 0.452 0.500 0.016 0.024
#> GSM680040 3 0.2748 0.58817 0.004 0.000 0.872 0.020 0.012 0.092
#> GSM680052 4 0.0632 0.73082 0.000 0.000 0.024 0.976 0.000 0.000
#> GSM680030 3 0.7484 0.15311 0.012 0.212 0.396 0.028 0.312 0.040
#> GSM680042 4 0.2306 0.72898 0.092 0.000 0.000 0.888 0.016 0.004
#> GSM680031 3 0.4528 0.39124 0.004 0.000 0.624 0.024 0.008 0.340
#> GSM680043 3 0.6569 0.02967 0.052 0.004 0.436 0.372 0.000 0.136
#> GSM680032 1 0.4189 0.72824 0.808 0.048 0.036 0.008 0.084 0.016
#> GSM680044 4 0.3465 0.71185 0.084 0.004 0.008 0.828 0.000 0.076
#> GSM680033 3 0.3144 0.57065 0.004 0.000 0.832 0.020 0.008 0.136
#> GSM680045 4 0.5014 0.56316 0.028 0.004 0.196 0.692 0.000 0.080
#> GSM680034 3 0.6507 0.37754 0.008 0.268 0.544 0.064 0.004 0.112
#> GSM680046 4 0.3676 0.70497 0.120 0.000 0.052 0.808 0.000 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> MAD:NMF 52 0.291172 0.892 2.38e-06 0.803 2
#> MAD:NMF 51 0.058420 0.349 8.43e-06 0.655 3
#> MAD:NMF 36 0.000955 0.207 9.66e-04 0.124 4
#> MAD:NMF 23 0.002650 0.268 7.78e-01 0.407 5
#> MAD:NMF 37 0.000206 0.443 3.29e-04 0.211 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 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 0.439 0.700 0.864 0.4526 0.493 0.493
#> 3 3 0.550 0.680 0.862 0.3955 0.713 0.499
#> 4 4 0.608 0.534 0.736 0.1305 0.913 0.764
#> 5 5 0.604 0.620 0.749 0.0486 0.832 0.511
#> 6 6 0.685 0.630 0.769 0.0549 0.962 0.835
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
#> GSM680053 2 0.925 0.615 0.340 0.660
#> GSM680062 2 0.991 0.367 0.444 0.556
#> GSM680054 2 0.000 0.766 0.000 1.000
#> GSM680063 2 0.163 0.768 0.024 0.976
#> GSM680055 1 0.506 0.806 0.888 0.112
#> GSM680064 1 0.000 0.854 1.000 0.000
#> GSM680056 1 0.952 0.319 0.628 0.372
#> GSM680065 1 0.000 0.854 1.000 0.000
#> GSM680057 2 0.000 0.766 0.000 1.000
#> GSM680066 1 0.278 0.843 0.952 0.048
#> GSM680058 1 0.925 0.426 0.660 0.340
#> GSM680067 2 0.163 0.768 0.024 0.976
#> GSM680059 2 0.932 0.605 0.348 0.652
#> GSM680068 1 0.000 0.854 1.000 0.000
#> GSM680060 1 0.000 0.854 1.000 0.000
#> GSM680069 1 0.311 0.840 0.944 0.056
#> GSM680061 2 0.000 0.766 0.000 1.000
#> GSM680070 1 0.000 0.854 1.000 0.000
#> GSM680071 1 0.000 0.854 1.000 0.000
#> GSM680077 1 0.000 0.854 1.000 0.000
#> GSM680072 2 0.932 0.605 0.348 0.652
#> GSM680078 1 0.000 0.854 1.000 0.000
#> GSM680073 1 0.839 0.591 0.732 0.268
#> GSM680079 1 0.000 0.854 1.000 0.000
#> GSM680074 2 0.932 0.605 0.348 0.652
#> GSM680080 2 0.932 0.605 0.348 0.652
#> GSM680075 1 0.000 0.854 1.000 0.000
#> GSM680081 2 0.260 0.765 0.044 0.956
#> GSM680076 1 0.909 0.473 0.676 0.324
#> GSM680082 1 0.000 0.854 1.000 0.000
#> GSM680029 1 0.552 0.792 0.872 0.128
#> GSM680041 1 0.443 0.820 0.908 0.092
#> GSM680035 2 0.000 0.766 0.000 1.000
#> GSM680047 1 0.000 0.854 1.000 0.000
#> GSM680036 1 0.343 0.836 0.936 0.064
#> GSM680048 1 0.998 -0.105 0.528 0.472
#> GSM680037 2 0.000 0.766 0.000 1.000
#> GSM680049 1 0.482 0.812 0.896 0.104
#> GSM680038 2 0.932 0.605 0.348 0.652
#> GSM680050 1 0.000 0.854 1.000 0.000
#> GSM680039 2 0.866 0.659 0.288 0.712
#> GSM680051 1 0.998 -0.105 0.528 0.472
#> GSM680040 2 0.753 0.701 0.216 0.784
#> GSM680052 2 0.929 0.610 0.344 0.656
#> GSM680030 2 0.163 0.768 0.024 0.976
#> GSM680042 1 0.184 0.848 0.972 0.028
#> GSM680031 2 0.000 0.766 0.000 1.000
#> GSM680043 2 0.000 0.766 0.000 1.000
#> GSM680032 1 0.706 0.718 0.808 0.192
#> GSM680044 2 0.991 0.367 0.444 0.556
#> GSM680033 2 0.000 0.766 0.000 1.000
#> GSM680045 2 0.913 0.627 0.328 0.672
#> GSM680034 2 0.000 0.766 0.000 1.000
#> GSM680046 1 0.000 0.854 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 2 0.0592 0.750 0.000 0.988 0.012
#> GSM680062 2 0.2796 0.710 0.092 0.908 0.000
#> GSM680054 3 0.0000 0.982 0.000 0.000 1.000
#> GSM680063 2 0.6204 0.199 0.000 0.576 0.424
#> GSM680055 1 0.6225 0.369 0.568 0.432 0.000
#> GSM680064 1 0.0000 0.829 1.000 0.000 0.000
#> GSM680056 2 0.5431 0.485 0.284 0.716 0.000
#> GSM680065 1 0.0000 0.829 1.000 0.000 0.000
#> GSM680057 3 0.3412 0.836 0.000 0.124 0.876
#> GSM680066 1 0.5138 0.674 0.748 0.252 0.000
#> GSM680058 2 0.5678 0.407 0.316 0.684 0.000
#> GSM680067 2 0.6204 0.199 0.000 0.576 0.424
#> GSM680059 2 0.0237 0.751 0.000 0.996 0.004
#> GSM680068 1 0.0000 0.829 1.000 0.000 0.000
#> GSM680060 1 0.1031 0.828 0.976 0.024 0.000
#> GSM680069 1 0.5291 0.656 0.732 0.268 0.000
#> GSM680061 3 0.0000 0.982 0.000 0.000 1.000
#> GSM680070 1 0.2165 0.819 0.936 0.064 0.000
#> GSM680071 1 0.0747 0.829 0.984 0.016 0.000
#> GSM680077 1 0.0000 0.829 1.000 0.000 0.000
#> GSM680072 2 0.0237 0.751 0.000 0.996 0.004
#> GSM680078 1 0.0000 0.829 1.000 0.000 0.000
#> GSM680073 2 0.6045 0.225 0.380 0.620 0.000
#> GSM680079 1 0.0000 0.829 1.000 0.000 0.000
#> GSM680074 2 0.0237 0.751 0.000 0.996 0.004
#> GSM680080 2 0.0237 0.751 0.000 0.996 0.004
#> GSM680075 1 0.0000 0.829 1.000 0.000 0.000
#> GSM680081 2 0.6192 0.240 0.000 0.580 0.420
#> GSM680076 2 0.5733 0.373 0.324 0.676 0.000
#> GSM680082 1 0.1964 0.822 0.944 0.056 0.000
#> GSM680029 1 0.6295 0.264 0.528 0.472 0.000
#> GSM680041 1 0.5968 0.512 0.636 0.364 0.000
#> GSM680035 3 0.0000 0.982 0.000 0.000 1.000
#> GSM680047 1 0.0000 0.829 1.000 0.000 0.000
#> GSM680036 1 0.5291 0.652 0.732 0.268 0.000
#> GSM680048 2 0.4654 0.614 0.208 0.792 0.000
#> GSM680037 3 0.0000 0.982 0.000 0.000 1.000
#> GSM680049 1 0.6180 0.410 0.584 0.416 0.000
#> GSM680038 2 0.0237 0.751 0.000 0.996 0.004
#> GSM680050 1 0.2356 0.816 0.928 0.072 0.000
#> GSM680039 2 0.2796 0.711 0.000 0.908 0.092
#> GSM680051 2 0.4654 0.614 0.208 0.792 0.000
#> GSM680040 2 0.4002 0.647 0.000 0.840 0.160
#> GSM680052 2 0.0424 0.751 0.000 0.992 0.008
#> GSM680030 2 0.6204 0.199 0.000 0.576 0.424
#> GSM680042 1 0.4654 0.722 0.792 0.208 0.000
#> GSM680031 3 0.0000 0.982 0.000 0.000 1.000
#> GSM680043 3 0.0000 0.982 0.000 0.000 1.000
#> GSM680032 2 0.6286 -0.118 0.464 0.536 0.000
#> GSM680044 2 0.2796 0.710 0.092 0.908 0.000
#> GSM680033 3 0.0000 0.982 0.000 0.000 1.000
#> GSM680045 2 0.1031 0.748 0.000 0.976 0.024
#> GSM680034 3 0.0000 0.982 0.000 0.000 1.000
#> GSM680046 1 0.0000 0.829 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 2 0.1792 0.6132 0.000 0.932 0.000 0.068
#> GSM680062 2 0.3024 0.5579 0.000 0.852 0.000 0.148
#> GSM680054 3 0.0000 0.8446 0.000 0.000 1.000 0.000
#> GSM680063 2 0.6722 0.1989 0.000 0.500 0.092 0.408
#> GSM680055 4 0.7408 0.5665 0.172 0.364 0.000 0.464
#> GSM680064 1 0.0000 0.8478 1.000 0.000 0.000 0.000
#> GSM680056 2 0.5599 0.1831 0.040 0.644 0.000 0.316
#> GSM680065 1 0.0000 0.8478 1.000 0.000 0.000 0.000
#> GSM680057 3 0.6607 0.6926 0.000 0.112 0.592 0.296
#> GSM680066 1 0.7681 -0.4880 0.404 0.216 0.000 0.380
#> GSM680058 2 0.5070 0.0719 0.008 0.620 0.000 0.372
#> GSM680067 2 0.6722 0.1989 0.000 0.500 0.092 0.408
#> GSM680059 2 0.0336 0.6213 0.000 0.992 0.000 0.008
#> GSM680068 1 0.0000 0.8478 1.000 0.000 0.000 0.000
#> GSM680060 1 0.0817 0.8340 0.976 0.024 0.000 0.000
#> GSM680069 4 0.7706 0.4673 0.364 0.224 0.000 0.412
#> GSM680061 3 0.0000 0.8446 0.000 0.000 1.000 0.000
#> GSM680070 1 0.4100 0.6997 0.824 0.048 0.000 0.128
#> GSM680071 1 0.0592 0.8394 0.984 0.016 0.000 0.000
#> GSM680077 1 0.0000 0.8478 1.000 0.000 0.000 0.000
#> GSM680072 2 0.0921 0.6165 0.000 0.972 0.000 0.028
#> GSM680078 1 0.0000 0.8478 1.000 0.000 0.000 0.000
#> GSM680073 2 0.4961 -0.1398 0.000 0.552 0.000 0.448
#> GSM680079 1 0.0000 0.8478 1.000 0.000 0.000 0.000
#> GSM680074 2 0.0336 0.6213 0.000 0.992 0.000 0.008
#> GSM680080 2 0.0336 0.6213 0.000 0.992 0.000 0.008
#> GSM680075 1 0.0000 0.8478 1.000 0.000 0.000 0.000
#> GSM680081 4 0.6633 -0.3625 0.000 0.416 0.084 0.500
#> GSM680076 2 0.4830 0.0177 0.000 0.608 0.000 0.392
#> GSM680082 1 0.3787 0.7182 0.840 0.036 0.000 0.124
#> GSM680029 4 0.7175 0.4963 0.136 0.404 0.000 0.460
#> GSM680041 4 0.7653 0.6055 0.240 0.300 0.000 0.460
#> GSM680035 3 0.4697 0.7892 0.000 0.000 0.644 0.356
#> GSM680047 1 0.0000 0.8478 1.000 0.000 0.000 0.000
#> GSM680036 4 0.7535 0.4958 0.336 0.200 0.000 0.464
#> GSM680048 2 0.5067 0.4295 0.048 0.736 0.000 0.216
#> GSM680037 3 0.4697 0.7892 0.000 0.000 0.644 0.356
#> GSM680049 4 0.7494 0.5824 0.188 0.352 0.000 0.460
#> GSM680038 2 0.1022 0.6159 0.000 0.968 0.000 0.032
#> GSM680050 1 0.4578 0.6446 0.788 0.052 0.000 0.160
#> GSM680039 2 0.3074 0.5562 0.000 0.848 0.000 0.152
#> GSM680051 2 0.5067 0.4295 0.048 0.736 0.000 0.216
#> GSM680040 2 0.4406 0.4592 0.000 0.700 0.000 0.300
#> GSM680052 2 0.1716 0.6172 0.000 0.936 0.000 0.064
#> GSM680030 2 0.6764 0.1973 0.000 0.500 0.096 0.404
#> GSM680042 1 0.7365 -0.3636 0.440 0.160 0.000 0.400
#> GSM680031 3 0.0000 0.8446 0.000 0.000 1.000 0.000
#> GSM680043 3 0.4697 0.7892 0.000 0.000 0.644 0.356
#> GSM680032 2 0.7135 -0.4610 0.132 0.468 0.000 0.400
#> GSM680044 2 0.3024 0.5579 0.000 0.852 0.000 0.148
#> GSM680033 3 0.0000 0.8446 0.000 0.000 1.000 0.000
#> GSM680045 2 0.2011 0.6110 0.000 0.920 0.000 0.080
#> GSM680034 3 0.0000 0.8446 0.000 0.000 1.000 0.000
#> GSM680046 1 0.0000 0.8478 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 2 0.4437 0.616 0.000 0.664 0.020 0.316 0.000
#> GSM680062 2 0.4262 0.412 0.000 0.560 0.000 0.440 0.000
#> GSM680054 5 0.0000 0.863 0.000 0.000 0.000 0.000 1.000
#> GSM680063 2 0.4457 0.280 0.000 0.656 0.328 0.012 0.004
#> GSM680055 4 0.2873 0.626 0.120 0.020 0.000 0.860 0.000
#> GSM680064 1 0.0451 0.923 0.988 0.008 0.004 0.000 0.000
#> GSM680056 4 0.4325 0.248 0.004 0.300 0.012 0.684 0.000
#> GSM680065 1 0.0324 0.924 0.992 0.004 0.004 0.000 0.000
#> GSM680057 5 0.6403 0.131 0.000 0.232 0.256 0.000 0.512
#> GSM680066 4 0.4283 0.458 0.348 0.000 0.008 0.644 0.000
#> GSM680058 4 0.2930 0.378 0.000 0.164 0.004 0.832 0.000
#> GSM680067 2 0.4457 0.280 0.000 0.656 0.328 0.012 0.004
#> GSM680059 2 0.4410 0.606 0.000 0.556 0.004 0.440 0.000
#> GSM680068 1 0.0000 0.925 1.000 0.000 0.000 0.000 0.000
#> GSM680060 1 0.1341 0.903 0.944 0.000 0.000 0.056 0.000
#> GSM680069 4 0.4108 0.523 0.308 0.000 0.008 0.684 0.000
#> GSM680061 5 0.1544 0.815 0.000 0.000 0.068 0.000 0.932
#> GSM680070 1 0.3388 0.748 0.792 0.000 0.008 0.200 0.000
#> GSM680071 1 0.1197 0.907 0.952 0.000 0.000 0.048 0.000
#> GSM680077 1 0.0510 0.921 0.984 0.000 0.000 0.016 0.000
#> GSM680072 2 0.4434 0.587 0.000 0.536 0.004 0.460 0.000
#> GSM680078 1 0.0451 0.923 0.988 0.008 0.004 0.000 0.000
#> GSM680073 4 0.1952 0.491 0.000 0.084 0.004 0.912 0.000
#> GSM680079 1 0.0451 0.923 0.988 0.008 0.004 0.000 0.000
#> GSM680074 2 0.4410 0.606 0.000 0.556 0.004 0.440 0.000
#> GSM680080 2 0.4410 0.606 0.000 0.556 0.004 0.440 0.000
#> GSM680075 1 0.0613 0.923 0.984 0.008 0.004 0.004 0.000
#> GSM680081 2 0.3932 0.158 0.000 0.672 0.328 0.000 0.000
#> GSM680076 4 0.2763 0.400 0.000 0.148 0.004 0.848 0.000
#> GSM680082 1 0.3246 0.766 0.808 0.000 0.008 0.184 0.000
#> GSM680029 4 0.3267 0.617 0.112 0.044 0.000 0.844 0.000
#> GSM680041 4 0.5011 0.618 0.176 0.088 0.012 0.724 0.000
#> GSM680035 3 0.1341 1.000 0.000 0.000 0.944 0.000 0.056
#> GSM680047 1 0.0000 0.925 1.000 0.000 0.000 0.000 0.000
#> GSM680036 4 0.3730 0.494 0.288 0.000 0.000 0.712 0.000
#> GSM680048 4 0.4989 -0.166 0.016 0.456 0.008 0.520 0.000
#> GSM680037 3 0.1341 1.000 0.000 0.000 0.944 0.000 0.056
#> GSM680049 4 0.5046 0.625 0.148 0.112 0.012 0.728 0.000
#> GSM680038 2 0.4437 0.582 0.000 0.532 0.004 0.464 0.000
#> GSM680050 1 0.3700 0.678 0.752 0.000 0.008 0.240 0.000
#> GSM680039 2 0.4948 0.596 0.000 0.676 0.068 0.256 0.000
#> GSM680051 4 0.4989 -0.166 0.016 0.456 0.008 0.520 0.000
#> GSM680040 2 0.4219 0.559 0.000 0.780 0.116 0.104 0.000
#> GSM680052 2 0.3990 0.595 0.000 0.688 0.004 0.308 0.000
#> GSM680030 2 0.4557 0.280 0.000 0.656 0.324 0.012 0.008
#> GSM680042 4 0.6048 0.282 0.376 0.088 0.012 0.524 0.000
#> GSM680031 5 0.0000 0.863 0.000 0.000 0.000 0.000 1.000
#> GSM680043 3 0.1341 1.000 0.000 0.000 0.944 0.000 0.056
#> GSM680032 4 0.4569 0.570 0.104 0.148 0.000 0.748 0.000
#> GSM680044 2 0.4262 0.412 0.000 0.560 0.000 0.440 0.000
#> GSM680033 5 0.0162 0.862 0.000 0.000 0.004 0.000 0.996
#> GSM680045 2 0.4318 0.612 0.000 0.688 0.020 0.292 0.000
#> GSM680034 5 0.0000 0.863 0.000 0.000 0.000 0.000 1.000
#> GSM680046 1 0.0000 0.925 1.000 0.000 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
#> GSM680053 2 0.5631 0.558 0.000 0.528 0.000 0.188 0.000 0.284
#> GSM680062 2 0.5900 0.412 0.000 0.448 0.000 0.336 0.000 0.216
#> GSM680054 5 0.0000 0.877 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680063 6 0.4635 0.698 0.000 0.336 0.056 0.000 0.000 0.608
#> GSM680055 4 0.2762 0.567 0.000 0.196 0.000 0.804 0.000 0.000
#> GSM680064 1 0.0405 0.910 0.988 0.004 0.000 0.008 0.000 0.000
#> GSM680056 4 0.5184 0.164 0.000 0.296 0.000 0.584 0.000 0.120
#> GSM680065 1 0.0508 0.911 0.984 0.004 0.000 0.012 0.000 0.000
#> GSM680057 5 0.5587 0.175 0.000 0.040 0.056 0.000 0.508 0.396
#> GSM680066 4 0.3622 0.516 0.212 0.024 0.000 0.760 0.000 0.004
#> GSM680058 4 0.3864 0.232 0.000 0.480 0.000 0.520 0.000 0.000
#> GSM680067 6 0.4635 0.698 0.000 0.336 0.056 0.000 0.000 0.608
#> GSM680059 2 0.2135 0.646 0.000 0.872 0.000 0.128 0.000 0.000
#> GSM680068 1 0.0713 0.915 0.972 0.000 0.000 0.028 0.000 0.000
#> GSM680060 1 0.1843 0.897 0.912 0.004 0.000 0.080 0.000 0.004
#> GSM680069 4 0.3492 0.541 0.176 0.032 0.000 0.788 0.000 0.004
#> GSM680061 5 0.1720 0.838 0.000 0.000 0.032 0.000 0.928 0.040
#> GSM680070 1 0.3050 0.759 0.764 0.000 0.000 0.236 0.000 0.000
#> GSM680071 1 0.1588 0.901 0.924 0.000 0.000 0.072 0.000 0.004
#> GSM680077 1 0.0865 0.913 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM680072 2 0.2340 0.637 0.000 0.852 0.000 0.148 0.000 0.000
#> GSM680078 1 0.0551 0.910 0.984 0.004 0.000 0.008 0.000 0.004
#> GSM680073 4 0.3756 0.394 0.000 0.400 0.000 0.600 0.000 0.000
#> GSM680079 1 0.0405 0.910 0.988 0.004 0.000 0.008 0.000 0.000
#> GSM680074 2 0.2135 0.646 0.000 0.872 0.000 0.128 0.000 0.000
#> GSM680080 2 0.2135 0.646 0.000 0.872 0.000 0.128 0.000 0.000
#> GSM680075 1 0.0603 0.911 0.980 0.000 0.000 0.016 0.000 0.004
#> GSM680081 6 0.2629 0.442 0.000 0.040 0.092 0.000 0.000 0.868
#> GSM680076 4 0.3854 0.260 0.000 0.464 0.000 0.536 0.000 0.000
#> GSM680082 1 0.2912 0.777 0.784 0.000 0.000 0.216 0.000 0.000
#> GSM680029 4 0.3265 0.542 0.000 0.248 0.000 0.748 0.000 0.004
#> GSM680041 4 0.0363 0.565 0.012 0.000 0.000 0.988 0.000 0.000
#> GSM680035 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680047 1 0.0858 0.915 0.968 0.000 0.000 0.028 0.000 0.004
#> GSM680036 4 0.4706 0.524 0.156 0.144 0.000 0.696 0.000 0.004
#> GSM680048 4 0.5783 -0.118 0.000 0.280 0.000 0.500 0.000 0.220
#> GSM680037 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680049 4 0.1471 0.564 0.004 0.064 0.000 0.932 0.000 0.000
#> GSM680038 2 0.2378 0.631 0.000 0.848 0.000 0.152 0.000 0.000
#> GSM680050 1 0.3266 0.703 0.728 0.000 0.000 0.272 0.000 0.000
#> GSM680039 2 0.4641 0.372 0.000 0.684 0.000 0.116 0.000 0.200
#> GSM680051 4 0.5783 -0.118 0.000 0.280 0.000 0.500 0.000 0.220
#> GSM680040 6 0.3578 0.186 0.000 0.340 0.000 0.000 0.000 0.660
#> GSM680052 2 0.5868 0.519 0.000 0.472 0.000 0.224 0.000 0.304
#> GSM680030 6 0.4769 0.696 0.000 0.336 0.056 0.000 0.004 0.604
#> GSM680042 4 0.2883 0.454 0.212 0.000 0.000 0.788 0.000 0.000
#> GSM680031 5 0.0000 0.877 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680043 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680032 4 0.3670 0.484 0.000 0.284 0.000 0.704 0.000 0.012
#> GSM680044 2 0.5900 0.412 0.000 0.448 0.000 0.336 0.000 0.216
#> GSM680033 5 0.0146 0.876 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM680045 2 0.5869 0.468 0.000 0.416 0.000 0.196 0.000 0.388
#> GSM680034 5 0.0000 0.877 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM680046 1 0.0858 0.915 0.968 0.000 0.000 0.028 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> ATC:hclust 47 0.4727 0.410 0.02837 0.5428 2
#> ATC:hclust 42 0.1512 0.260 0.00313 0.1639 3
#> ATC:hclust 37 0.1436 0.366 0.01531 0.0888 4
#> ATC:hclust 38 0.0794 0.425 0.02212 0.1156 5
#> ATC:hclust 39 0.1283 0.346 0.03993 0.0744 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 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 0.726 0.888 0.955 0.4576 0.535 0.535
#> 3 3 0.889 0.893 0.956 0.4399 0.660 0.440
#> 4 4 0.648 0.658 0.794 0.1238 0.855 0.597
#> 5 5 0.667 0.592 0.777 0.0715 0.890 0.601
#> 6 6 0.675 0.508 0.734 0.0396 0.925 0.677
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
#> GSM680053 2 0.6247 0.825 0.156 0.844
#> GSM680062 1 0.0938 0.952 0.988 0.012
#> GSM680054 2 0.0000 0.924 0.000 1.000
#> GSM680063 2 0.0000 0.924 0.000 1.000
#> GSM680055 1 0.0000 0.961 1.000 0.000
#> GSM680064 1 0.0000 0.961 1.000 0.000
#> GSM680056 1 0.0000 0.961 1.000 0.000
#> GSM680065 1 0.0000 0.961 1.000 0.000
#> GSM680057 2 0.0000 0.924 0.000 1.000
#> GSM680066 1 0.0000 0.961 1.000 0.000
#> GSM680058 1 0.0000 0.961 1.000 0.000
#> GSM680067 2 0.0000 0.924 0.000 1.000
#> GSM680059 1 0.9552 0.347 0.624 0.376
#> GSM680068 1 0.0000 0.961 1.000 0.000
#> GSM680060 1 0.0000 0.961 1.000 0.000
#> GSM680069 1 0.0000 0.961 1.000 0.000
#> GSM680061 2 0.0000 0.924 0.000 1.000
#> GSM680070 1 0.0000 0.961 1.000 0.000
#> GSM680071 1 0.0000 0.961 1.000 0.000
#> GSM680077 1 0.0000 0.961 1.000 0.000
#> GSM680072 1 0.1184 0.948 0.984 0.016
#> GSM680078 1 0.0000 0.961 1.000 0.000
#> GSM680073 1 0.0000 0.961 1.000 0.000
#> GSM680079 1 0.0000 0.961 1.000 0.000
#> GSM680074 2 0.7745 0.731 0.228 0.772
#> GSM680080 1 0.9552 0.347 0.624 0.376
#> GSM680075 1 0.0000 0.961 1.000 0.000
#> GSM680081 2 0.0000 0.924 0.000 1.000
#> GSM680076 1 0.0938 0.952 0.988 0.012
#> GSM680082 1 0.0000 0.961 1.000 0.000
#> GSM680029 1 0.0000 0.961 1.000 0.000
#> GSM680041 1 0.0000 0.961 1.000 0.000
#> GSM680035 2 0.0000 0.924 0.000 1.000
#> GSM680047 1 0.0000 0.961 1.000 0.000
#> GSM680036 1 0.0000 0.961 1.000 0.000
#> GSM680048 1 0.0000 0.961 1.000 0.000
#> GSM680037 2 0.0000 0.924 0.000 1.000
#> GSM680049 1 0.0000 0.961 1.000 0.000
#> GSM680038 1 0.9552 0.347 0.624 0.376
#> GSM680050 1 0.0000 0.961 1.000 0.000
#> GSM680039 2 0.5519 0.850 0.128 0.872
#> GSM680051 1 0.0000 0.961 1.000 0.000
#> GSM680040 2 0.5519 0.850 0.128 0.872
#> GSM680052 2 0.9977 0.143 0.472 0.528
#> GSM680030 2 0.0000 0.924 0.000 1.000
#> GSM680042 1 0.0000 0.961 1.000 0.000
#> GSM680031 2 0.0000 0.924 0.000 1.000
#> GSM680043 2 0.0000 0.924 0.000 1.000
#> GSM680032 1 0.0000 0.961 1.000 0.000
#> GSM680044 1 0.0938 0.952 0.988 0.012
#> GSM680033 2 0.0000 0.924 0.000 1.000
#> GSM680045 2 0.6343 0.821 0.160 0.840
#> GSM680034 2 0.0000 0.924 0.000 1.000
#> GSM680046 1 0.0000 0.961 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 2 0.0000 0.932 0.000 1.000 0.000
#> GSM680062 2 0.0424 0.936 0.008 0.992 0.000
#> GSM680054 3 0.0000 0.998 0.000 0.000 1.000
#> GSM680063 3 0.0000 0.998 0.000 0.000 1.000
#> GSM680055 2 0.0424 0.936 0.008 0.992 0.000
#> GSM680064 1 0.0000 0.936 1.000 0.000 0.000
#> GSM680056 2 0.3192 0.840 0.112 0.888 0.000
#> GSM680065 1 0.0000 0.936 1.000 0.000 0.000
#> GSM680057 3 0.0000 0.998 0.000 0.000 1.000
#> GSM680066 1 0.4555 0.712 0.800 0.200 0.000
#> GSM680058 2 0.0424 0.936 0.008 0.992 0.000
#> GSM680067 3 0.0000 0.998 0.000 0.000 1.000
#> GSM680059 2 0.0424 0.936 0.008 0.992 0.000
#> GSM680068 1 0.0000 0.936 1.000 0.000 0.000
#> GSM680060 1 0.0000 0.936 1.000 0.000 0.000
#> GSM680069 2 0.5948 0.451 0.360 0.640 0.000
#> GSM680061 3 0.0000 0.998 0.000 0.000 1.000
#> GSM680070 1 0.0000 0.936 1.000 0.000 0.000
#> GSM680071 1 0.0000 0.936 1.000 0.000 0.000
#> GSM680077 1 0.0000 0.936 1.000 0.000 0.000
#> GSM680072 2 0.0424 0.936 0.008 0.992 0.000
#> GSM680078 1 0.0000 0.936 1.000 0.000 0.000
#> GSM680073 2 0.0424 0.936 0.008 0.992 0.000
#> GSM680079 1 0.0000 0.936 1.000 0.000 0.000
#> GSM680074 2 0.0424 0.932 0.000 0.992 0.008
#> GSM680080 2 0.0424 0.936 0.008 0.992 0.000
#> GSM680075 1 0.0000 0.936 1.000 0.000 0.000
#> GSM680081 3 0.0424 0.995 0.000 0.008 0.992
#> GSM680076 2 0.0424 0.936 0.008 0.992 0.000
#> GSM680082 1 0.0000 0.936 1.000 0.000 0.000
#> GSM680029 2 0.0424 0.936 0.008 0.992 0.000
#> GSM680041 1 0.5988 0.382 0.632 0.368 0.000
#> GSM680035 3 0.0424 0.995 0.000 0.008 0.992
#> GSM680047 1 0.0000 0.936 1.000 0.000 0.000
#> GSM680036 1 0.6095 0.330 0.608 0.392 0.000
#> GSM680048 2 0.5882 0.478 0.348 0.652 0.000
#> GSM680037 3 0.0424 0.995 0.000 0.008 0.992
#> GSM680049 2 0.6192 0.292 0.420 0.580 0.000
#> GSM680038 2 0.0424 0.936 0.008 0.992 0.000
#> GSM680050 1 0.0000 0.936 1.000 0.000 0.000
#> GSM680039 2 0.0424 0.932 0.000 0.992 0.008
#> GSM680051 2 0.0424 0.936 0.008 0.992 0.000
#> GSM680040 2 0.0000 0.932 0.000 1.000 0.000
#> GSM680052 2 0.0000 0.932 0.000 1.000 0.000
#> GSM680030 3 0.0000 0.998 0.000 0.000 1.000
#> GSM680042 1 0.0000 0.936 1.000 0.000 0.000
#> GSM680031 3 0.0000 0.998 0.000 0.000 1.000
#> GSM680043 3 0.0424 0.995 0.000 0.008 0.992
#> GSM680032 2 0.0424 0.936 0.008 0.992 0.000
#> GSM680044 2 0.0424 0.936 0.008 0.992 0.000
#> GSM680033 3 0.0000 0.998 0.000 0.000 1.000
#> GSM680045 2 0.0000 0.932 0.000 1.000 0.000
#> GSM680034 3 0.0000 0.998 0.000 0.000 1.000
#> GSM680046 1 0.0000 0.936 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 2 0.2216 0.642 0.000 0.908 0.000 0.092
#> GSM680062 2 0.4955 0.650 0.000 0.556 0.000 0.444
#> GSM680054 3 0.0000 0.872 0.000 0.000 1.000 0.000
#> GSM680063 3 0.4454 0.763 0.000 0.308 0.692 0.000
#> GSM680055 4 0.4941 -0.313 0.000 0.436 0.000 0.564
#> GSM680064 1 0.0188 0.861 0.996 0.000 0.000 0.004
#> GSM680056 4 0.3653 0.536 0.028 0.128 0.000 0.844
#> GSM680065 1 0.0592 0.863 0.984 0.000 0.000 0.016
#> GSM680057 3 0.1940 0.864 0.000 0.076 0.924 0.000
#> GSM680066 4 0.4372 0.475 0.268 0.004 0.000 0.728
#> GSM680058 2 0.4933 0.615 0.000 0.568 0.000 0.432
#> GSM680067 3 0.4500 0.763 0.000 0.316 0.684 0.000
#> GSM680059 2 0.4543 0.744 0.000 0.676 0.000 0.324
#> GSM680068 1 0.0000 0.862 1.000 0.000 0.000 0.000
#> GSM680060 1 0.4990 0.527 0.640 0.008 0.000 0.352
#> GSM680069 4 0.3308 0.626 0.092 0.036 0.000 0.872
#> GSM680061 3 0.0000 0.872 0.000 0.000 1.000 0.000
#> GSM680070 1 0.4624 0.554 0.660 0.000 0.000 0.340
#> GSM680071 1 0.2081 0.853 0.916 0.000 0.000 0.084
#> GSM680077 1 0.1118 0.860 0.964 0.000 0.000 0.036
#> GSM680072 2 0.4585 0.740 0.000 0.668 0.000 0.332
#> GSM680078 1 0.1118 0.861 0.964 0.000 0.000 0.036
#> GSM680073 2 0.4907 0.636 0.000 0.580 0.000 0.420
#> GSM680079 1 0.0188 0.861 0.996 0.000 0.000 0.004
#> GSM680074 2 0.4431 0.742 0.000 0.696 0.000 0.304
#> GSM680080 2 0.4543 0.744 0.000 0.676 0.000 0.324
#> GSM680075 1 0.1302 0.860 0.956 0.000 0.000 0.044
#> GSM680081 3 0.6253 0.727 0.000 0.372 0.564 0.064
#> GSM680076 2 0.4776 0.696 0.000 0.624 0.000 0.376
#> GSM680082 1 0.4164 0.664 0.736 0.000 0.000 0.264
#> GSM680029 4 0.4989 -0.424 0.000 0.472 0.000 0.528
#> GSM680041 4 0.3400 0.610 0.180 0.000 0.000 0.820
#> GSM680035 3 0.3547 0.845 0.000 0.072 0.864 0.064
#> GSM680047 1 0.1474 0.860 0.948 0.000 0.000 0.052
#> GSM680036 4 0.5228 0.550 0.120 0.124 0.000 0.756
#> GSM680048 4 0.4037 0.637 0.136 0.040 0.000 0.824
#> GSM680037 3 0.3687 0.846 0.000 0.080 0.856 0.064
#> GSM680049 4 0.5070 0.627 0.192 0.060 0.000 0.748
#> GSM680038 2 0.4543 0.744 0.000 0.676 0.000 0.324
#> GSM680050 4 0.4996 -0.187 0.484 0.000 0.000 0.516
#> GSM680039 2 0.2149 0.643 0.000 0.912 0.000 0.088
#> GSM680051 4 0.3219 0.481 0.000 0.164 0.000 0.836
#> GSM680040 2 0.1302 0.604 0.000 0.956 0.000 0.044
#> GSM680052 2 0.3801 0.583 0.000 0.780 0.000 0.220
#> GSM680030 3 0.4431 0.767 0.000 0.304 0.696 0.000
#> GSM680042 1 0.4643 0.548 0.656 0.000 0.000 0.344
#> GSM680031 3 0.0000 0.872 0.000 0.000 1.000 0.000
#> GSM680043 3 0.3617 0.846 0.000 0.076 0.860 0.064
#> GSM680032 4 0.3688 0.357 0.000 0.208 0.000 0.792
#> GSM680044 2 0.4999 0.576 0.000 0.508 0.000 0.492
#> GSM680033 3 0.0000 0.872 0.000 0.000 1.000 0.000
#> GSM680045 2 0.3172 0.531 0.000 0.840 0.000 0.160
#> GSM680034 3 0.0000 0.872 0.000 0.000 1.000 0.000
#> GSM680046 1 0.1118 0.861 0.964 0.000 0.000 0.036
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 2 0.4552 -0.1565 0.000 0.524 0.000 0.008 0.468
#> GSM680062 2 0.4141 0.5532 0.000 0.736 0.000 0.236 0.028
#> GSM680054 3 0.0290 0.8518 0.000 0.000 0.992 0.008 0.000
#> GSM680063 5 0.4949 0.5332 0.000 0.032 0.396 0.000 0.572
#> GSM680055 2 0.4748 0.4697 0.000 0.660 0.000 0.300 0.040
#> GSM680064 1 0.1364 0.7977 0.952 0.000 0.000 0.012 0.036
#> GSM680056 4 0.3878 0.7626 0.012 0.144 0.000 0.808 0.036
#> GSM680065 1 0.2482 0.7940 0.892 0.000 0.000 0.024 0.084
#> GSM680057 3 0.3336 0.5587 0.000 0.000 0.772 0.000 0.228
#> GSM680066 4 0.4731 0.7430 0.088 0.048 0.000 0.780 0.084
#> GSM680058 2 0.3183 0.6474 0.000 0.828 0.000 0.156 0.016
#> GSM680067 5 0.4940 0.5346 0.000 0.032 0.392 0.000 0.576
#> GSM680059 2 0.0162 0.6876 0.000 0.996 0.000 0.000 0.004
#> GSM680068 1 0.0579 0.8025 0.984 0.000 0.000 0.008 0.008
#> GSM680060 1 0.7098 0.4978 0.532 0.052 0.000 0.216 0.200
#> GSM680069 4 0.4826 0.7676 0.048 0.104 0.000 0.772 0.076
#> GSM680061 3 0.0000 0.8520 0.000 0.000 1.000 0.000 0.000
#> GSM680070 1 0.5650 0.0336 0.468 0.000 0.000 0.456 0.076
#> GSM680071 1 0.4627 0.7411 0.732 0.000 0.000 0.080 0.188
#> GSM680077 1 0.2676 0.7852 0.884 0.000 0.000 0.036 0.080
#> GSM680072 2 0.0324 0.6899 0.000 0.992 0.000 0.004 0.004
#> GSM680078 1 0.2193 0.7947 0.900 0.000 0.000 0.008 0.092
#> GSM680073 2 0.3055 0.6559 0.000 0.840 0.000 0.144 0.016
#> GSM680079 1 0.1364 0.7977 0.952 0.000 0.000 0.012 0.036
#> GSM680074 2 0.0510 0.6794 0.000 0.984 0.000 0.000 0.016
#> GSM680080 2 0.0162 0.6876 0.000 0.996 0.000 0.000 0.004
#> GSM680075 1 0.3476 0.7744 0.804 0.000 0.000 0.020 0.176
#> GSM680081 5 0.4511 0.4598 0.000 0.012 0.260 0.020 0.708
#> GSM680076 2 0.1408 0.6925 0.000 0.948 0.000 0.044 0.008
#> GSM680082 1 0.5616 0.2515 0.536 0.000 0.000 0.384 0.080
#> GSM680029 2 0.3779 0.6008 0.000 0.776 0.000 0.200 0.024
#> GSM680041 4 0.2728 0.8029 0.040 0.068 0.000 0.888 0.004
#> GSM680035 3 0.4335 0.7629 0.000 0.000 0.760 0.072 0.168
#> GSM680047 1 0.2473 0.7991 0.896 0.000 0.000 0.032 0.072
#> GSM680036 2 0.7170 0.0886 0.040 0.468 0.000 0.316 0.176
#> GSM680048 4 0.2972 0.8026 0.040 0.084 0.000 0.872 0.004
#> GSM680037 3 0.4409 0.7591 0.000 0.000 0.752 0.072 0.176
#> GSM680049 4 0.4001 0.7919 0.048 0.104 0.000 0.820 0.028
#> GSM680038 2 0.0162 0.6876 0.000 0.996 0.000 0.000 0.004
#> GSM680050 4 0.5205 0.5808 0.200 0.008 0.000 0.696 0.096
#> GSM680039 2 0.4268 -0.0885 0.000 0.556 0.000 0.000 0.444
#> GSM680051 4 0.3309 0.7616 0.000 0.128 0.000 0.836 0.036
#> GSM680040 5 0.4559 0.0502 0.000 0.480 0.000 0.008 0.512
#> GSM680052 2 0.6647 -0.1326 0.000 0.392 0.000 0.224 0.384
#> GSM680030 5 0.4622 0.4608 0.000 0.012 0.440 0.000 0.548
#> GSM680042 4 0.5506 0.0821 0.404 0.000 0.000 0.528 0.068
#> GSM680031 3 0.0162 0.8523 0.000 0.000 0.996 0.004 0.000
#> GSM680043 3 0.4335 0.7629 0.000 0.000 0.760 0.072 0.168
#> GSM680032 4 0.3724 0.6841 0.000 0.204 0.000 0.776 0.020
#> GSM680044 2 0.4546 0.4726 0.000 0.668 0.000 0.304 0.028
#> GSM680033 3 0.0000 0.8520 0.000 0.000 1.000 0.000 0.000
#> GSM680045 5 0.6235 0.1614 0.000 0.344 0.000 0.156 0.500
#> GSM680034 3 0.0290 0.8518 0.000 0.000 0.992 0.008 0.000
#> GSM680046 1 0.1942 0.8008 0.920 0.000 0.000 0.012 0.068
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.5372 0.4881 0.000 0.324 0.000 0.044 0.584 0.048
#> GSM680062 2 0.5592 0.3944 0.000 0.568 0.000 0.304 0.108 0.020
#> GSM680054 3 0.5412 0.7953 0.000 0.000 0.580 0.016 0.096 0.308
#> GSM680063 5 0.3193 0.5105 0.000 0.008 0.112 0.004 0.840 0.036
#> GSM680055 2 0.5377 0.4666 0.000 0.596 0.000 0.288 0.016 0.100
#> GSM680064 1 0.0865 0.6084 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM680056 4 0.3063 0.6625 0.000 0.076 0.000 0.856 0.016 0.052
#> GSM680065 1 0.2556 0.5437 0.864 0.000 0.000 0.008 0.008 0.120
#> GSM680057 5 0.5999 -0.2660 0.000 0.000 0.276 0.004 0.476 0.244
#> GSM680066 4 0.4873 0.5583 0.020 0.048 0.000 0.676 0.008 0.248
#> GSM680058 2 0.2766 0.7108 0.000 0.868 0.000 0.092 0.012 0.028
#> GSM680067 5 0.3193 0.5105 0.000 0.008 0.112 0.004 0.840 0.036
#> GSM680059 2 0.0937 0.7297 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM680068 1 0.1625 0.6084 0.928 0.000 0.000 0.000 0.012 0.060
#> GSM680060 6 0.7097 0.0000 0.280 0.100 0.000 0.120 0.020 0.480
#> GSM680069 4 0.4569 0.5824 0.004 0.084 0.000 0.708 0.004 0.200
#> GSM680061 3 0.5133 0.7956 0.000 0.000 0.580 0.000 0.108 0.312
#> GSM680070 4 0.6341 -0.1512 0.364 0.000 0.000 0.372 0.012 0.252
#> GSM680071 1 0.4662 -0.1959 0.496 0.000 0.000 0.032 0.004 0.468
#> GSM680077 1 0.3359 0.4801 0.784 0.000 0.000 0.012 0.008 0.196
#> GSM680072 2 0.0291 0.7391 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM680078 1 0.2513 0.5700 0.852 0.000 0.000 0.000 0.008 0.140
#> GSM680073 2 0.2766 0.7108 0.000 0.868 0.000 0.092 0.012 0.028
#> GSM680079 1 0.0865 0.6084 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM680074 2 0.1204 0.7155 0.000 0.944 0.000 0.000 0.056 0.000
#> GSM680080 2 0.0937 0.7297 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM680075 1 0.3547 0.3530 0.696 0.000 0.000 0.000 0.004 0.300
#> GSM680081 5 0.4422 0.4482 0.000 0.000 0.284 0.020 0.672 0.024
#> GSM680076 2 0.0508 0.7408 0.000 0.984 0.000 0.012 0.000 0.004
#> GSM680082 1 0.6195 -0.1346 0.464 0.000 0.000 0.280 0.012 0.244
#> GSM680029 2 0.3800 0.6487 0.000 0.780 0.000 0.164 0.012 0.044
#> GSM680041 4 0.2789 0.6876 0.008 0.036 0.000 0.880 0.012 0.064
#> GSM680035 3 0.0458 0.6605 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM680047 1 0.5057 0.4502 0.692 0.000 0.000 0.088 0.040 0.180
#> GSM680036 2 0.6659 -0.0623 0.020 0.444 0.000 0.204 0.016 0.316
#> GSM680048 4 0.2402 0.6914 0.004 0.044 0.000 0.900 0.008 0.044
#> GSM680037 3 0.0692 0.6557 0.000 0.000 0.976 0.000 0.020 0.004
#> GSM680049 4 0.2630 0.6899 0.008 0.060 0.000 0.888 0.008 0.036
#> GSM680038 2 0.0937 0.7297 0.000 0.960 0.000 0.000 0.040 0.000
#> GSM680050 4 0.5251 0.4447 0.124 0.000 0.000 0.632 0.012 0.232
#> GSM680039 5 0.3975 0.3263 0.000 0.452 0.000 0.000 0.544 0.004
#> GSM680051 4 0.2317 0.6743 0.000 0.064 0.000 0.900 0.016 0.020
#> GSM680040 5 0.5889 0.5136 0.000 0.292 0.032 0.036 0.588 0.052
#> GSM680052 5 0.6720 0.3498 0.000 0.232 0.000 0.284 0.436 0.048
#> GSM680030 5 0.4433 0.3565 0.000 0.000 0.112 0.004 0.724 0.160
#> GSM680042 4 0.6034 0.1639 0.272 0.000 0.000 0.516 0.016 0.196
#> GSM680031 3 0.5044 0.7966 0.000 0.000 0.584 0.000 0.096 0.320
#> GSM680043 3 0.0603 0.6582 0.000 0.000 0.980 0.000 0.016 0.004
#> GSM680032 4 0.3092 0.6457 0.000 0.120 0.000 0.840 0.012 0.028
#> GSM680044 2 0.5488 0.3889 0.000 0.548 0.000 0.348 0.084 0.020
#> GSM680033 3 0.5133 0.7956 0.000 0.000 0.580 0.000 0.108 0.312
#> GSM680045 5 0.6419 0.5165 0.000 0.204 0.012 0.144 0.576 0.064
#> GSM680034 3 0.5412 0.7953 0.000 0.000 0.580 0.016 0.096 0.308
#> GSM680046 1 0.3976 0.5415 0.768 0.000 0.000 0.020 0.040 0.172
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> ATC:kmeans 50 0.3483 0.344 0.039170 0.29908 2
#> ATC:kmeans 49 0.2572 0.396 0.003640 0.17809 3
#> ATC:kmeans 48 0.1941 0.190 0.031670 0.07147 4
#> ATC:kmeans 40 0.0404 0.545 0.001600 0.00976 5
#> ATC:kmeans 35 0.1014 0.502 0.000811 0.01241 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 1.000 0.989 0.995 0.5087 0.491 0.491
#> 3 3 1.000 0.953 0.982 0.2795 0.830 0.666
#> 4 4 0.851 0.790 0.918 0.0989 0.932 0.809
#> 5 5 0.773 0.687 0.845 0.0509 0.958 0.859
#> 6 6 0.720 0.663 0.826 0.0382 0.959 0.849
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
#> GSM680053 2 0.000 0.990 0.000 1.000
#> GSM680062 2 0.000 0.990 0.000 1.000
#> GSM680054 2 0.000 0.990 0.000 1.000
#> GSM680063 2 0.000 0.990 0.000 1.000
#> GSM680055 1 0.000 1.000 1.000 0.000
#> GSM680064 1 0.000 1.000 1.000 0.000
#> GSM680056 1 0.000 1.000 1.000 0.000
#> GSM680065 1 0.000 1.000 1.000 0.000
#> GSM680057 2 0.000 0.990 0.000 1.000
#> GSM680066 1 0.000 1.000 1.000 0.000
#> GSM680058 1 0.000 1.000 1.000 0.000
#> GSM680067 2 0.000 0.990 0.000 1.000
#> GSM680059 2 0.000 0.990 0.000 1.000
#> GSM680068 1 0.000 1.000 1.000 0.000
#> GSM680060 1 0.000 1.000 1.000 0.000
#> GSM680069 1 0.000 1.000 1.000 0.000
#> GSM680061 2 0.000 0.990 0.000 1.000
#> GSM680070 1 0.000 1.000 1.000 0.000
#> GSM680071 1 0.000 1.000 1.000 0.000
#> GSM680077 1 0.000 1.000 1.000 0.000
#> GSM680072 2 0.000 0.990 0.000 1.000
#> GSM680078 1 0.000 1.000 1.000 0.000
#> GSM680073 1 0.000 1.000 1.000 0.000
#> GSM680079 1 0.000 1.000 1.000 0.000
#> GSM680074 2 0.000 0.990 0.000 1.000
#> GSM680080 2 0.000 0.990 0.000 1.000
#> GSM680075 1 0.000 1.000 1.000 0.000
#> GSM680081 2 0.000 0.990 0.000 1.000
#> GSM680076 2 0.802 0.677 0.244 0.756
#> GSM680082 1 0.000 1.000 1.000 0.000
#> GSM680029 1 0.000 1.000 1.000 0.000
#> GSM680041 1 0.000 1.000 1.000 0.000
#> GSM680035 2 0.000 0.990 0.000 1.000
#> GSM680047 1 0.000 1.000 1.000 0.000
#> GSM680036 1 0.000 1.000 1.000 0.000
#> GSM680048 1 0.000 1.000 1.000 0.000
#> GSM680037 2 0.000 0.990 0.000 1.000
#> GSM680049 1 0.000 1.000 1.000 0.000
#> GSM680038 2 0.000 0.990 0.000 1.000
#> GSM680050 1 0.000 1.000 1.000 0.000
#> GSM680039 2 0.000 0.990 0.000 1.000
#> GSM680051 1 0.000 1.000 1.000 0.000
#> GSM680040 2 0.000 0.990 0.000 1.000
#> GSM680052 2 0.000 0.990 0.000 1.000
#> GSM680030 2 0.000 0.990 0.000 1.000
#> GSM680042 1 0.000 1.000 1.000 0.000
#> GSM680031 2 0.000 0.990 0.000 1.000
#> GSM680043 2 0.000 0.990 0.000 1.000
#> GSM680032 1 0.000 1.000 1.000 0.000
#> GSM680044 2 0.000 0.990 0.000 1.000
#> GSM680033 2 0.000 0.990 0.000 1.000
#> GSM680045 2 0.000 0.990 0.000 1.000
#> GSM680034 2 0.000 0.990 0.000 1.000
#> GSM680046 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
#> GSM680053 3 0.000 1.000 0.000 0.000 1
#> GSM680062 2 0.000 0.983 0.000 1.000 0
#> GSM680054 3 0.000 1.000 0.000 0.000 1
#> GSM680063 3 0.000 1.000 0.000 0.000 1
#> GSM680055 1 0.611 0.351 0.604 0.396 0
#> GSM680064 1 0.000 0.963 1.000 0.000 0
#> GSM680056 1 0.000 0.963 1.000 0.000 0
#> GSM680065 1 0.000 0.963 1.000 0.000 0
#> GSM680057 3 0.000 1.000 0.000 0.000 1
#> GSM680066 1 0.000 0.963 1.000 0.000 0
#> GSM680058 2 0.000 0.983 0.000 1.000 0
#> GSM680067 3 0.000 1.000 0.000 0.000 1
#> GSM680059 2 0.000 0.983 0.000 1.000 0
#> GSM680068 1 0.000 0.963 1.000 0.000 0
#> GSM680060 1 0.000 0.963 1.000 0.000 0
#> GSM680069 1 0.000 0.963 1.000 0.000 0
#> GSM680061 3 0.000 1.000 0.000 0.000 1
#> GSM680070 1 0.000 0.963 1.000 0.000 0
#> GSM680071 1 0.000 0.963 1.000 0.000 0
#> GSM680077 1 0.000 0.963 1.000 0.000 0
#> GSM680072 2 0.000 0.983 0.000 1.000 0
#> GSM680078 1 0.000 0.963 1.000 0.000 0
#> GSM680073 2 0.000 0.983 0.000 1.000 0
#> GSM680079 1 0.000 0.963 1.000 0.000 0
#> GSM680074 2 0.000 0.983 0.000 1.000 0
#> GSM680080 2 0.000 0.983 0.000 1.000 0
#> GSM680075 1 0.000 0.963 1.000 0.000 0
#> GSM680081 3 0.000 1.000 0.000 0.000 1
#> GSM680076 2 0.000 0.983 0.000 1.000 0
#> GSM680082 1 0.000 0.963 1.000 0.000 0
#> GSM680029 2 0.388 0.811 0.152 0.848 0
#> GSM680041 1 0.000 0.963 1.000 0.000 0
#> GSM680035 3 0.000 1.000 0.000 0.000 1
#> GSM680047 1 0.000 0.963 1.000 0.000 0
#> GSM680036 1 0.610 0.361 0.608 0.392 0
#> GSM680048 1 0.000 0.963 1.000 0.000 0
#> GSM680037 3 0.000 1.000 0.000 0.000 1
#> GSM680049 1 0.000 0.963 1.000 0.000 0
#> GSM680038 2 0.000 0.983 0.000 1.000 0
#> GSM680050 1 0.000 0.963 1.000 0.000 0
#> GSM680039 3 0.000 1.000 0.000 0.000 1
#> GSM680051 1 0.000 0.963 1.000 0.000 0
#> GSM680040 3 0.000 1.000 0.000 0.000 1
#> GSM680052 3 0.000 1.000 0.000 0.000 1
#> GSM680030 3 0.000 1.000 0.000 0.000 1
#> GSM680042 1 0.000 0.963 1.000 0.000 0
#> GSM680031 3 0.000 1.000 0.000 0.000 1
#> GSM680043 3 0.000 1.000 0.000 0.000 1
#> GSM680032 1 0.186 0.915 0.948 0.052 0
#> GSM680044 2 0.000 0.983 0.000 1.000 0
#> GSM680033 3 0.000 1.000 0.000 0.000 1
#> GSM680045 3 0.000 1.000 0.000 0.000 1
#> GSM680034 3 0.000 1.000 0.000 0.000 1
#> GSM680046 1 0.000 0.963 1.000 0.000 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 3 0.0000 0.9770 0.000 0.000 1.000 0.000
#> GSM680062 2 0.4730 0.4045 0.000 0.636 0.000 0.364
#> GSM680054 3 0.0000 0.9770 0.000 0.000 1.000 0.000
#> GSM680063 3 0.0000 0.9770 0.000 0.000 1.000 0.000
#> GSM680055 1 0.5599 0.4505 0.672 0.276 0.000 0.052
#> GSM680064 1 0.0000 0.8624 1.000 0.000 0.000 0.000
#> GSM680056 4 0.4941 0.3206 0.436 0.000 0.000 0.564
#> GSM680065 1 0.0469 0.8602 0.988 0.000 0.000 0.012
#> GSM680057 3 0.0000 0.9770 0.000 0.000 1.000 0.000
#> GSM680066 1 0.0188 0.8620 0.996 0.000 0.000 0.004
#> GSM680058 2 0.0592 0.9103 0.000 0.984 0.000 0.016
#> GSM680067 3 0.0000 0.9770 0.000 0.000 1.000 0.000
#> GSM680059 2 0.0000 0.9162 0.000 1.000 0.000 0.000
#> GSM680068 1 0.0000 0.8624 1.000 0.000 0.000 0.000
#> GSM680060 1 0.1389 0.8353 0.952 0.000 0.000 0.048
#> GSM680069 1 0.0921 0.8531 0.972 0.000 0.000 0.028
#> GSM680061 3 0.0000 0.9770 0.000 0.000 1.000 0.000
#> GSM680070 1 0.0336 0.8608 0.992 0.000 0.000 0.008
#> GSM680071 1 0.0921 0.8502 0.972 0.000 0.000 0.028
#> GSM680077 1 0.0188 0.8620 0.996 0.000 0.000 0.004
#> GSM680072 2 0.0000 0.9162 0.000 1.000 0.000 0.000
#> GSM680078 1 0.0000 0.8624 1.000 0.000 0.000 0.000
#> GSM680073 2 0.0592 0.9103 0.000 0.984 0.000 0.016
#> GSM680079 1 0.0000 0.8624 1.000 0.000 0.000 0.000
#> GSM680074 2 0.0000 0.9162 0.000 1.000 0.000 0.000
#> GSM680080 2 0.0000 0.9162 0.000 1.000 0.000 0.000
#> GSM680075 1 0.1389 0.8353 0.952 0.000 0.000 0.048
#> GSM680081 3 0.0000 0.9770 0.000 0.000 1.000 0.000
#> GSM680076 2 0.0336 0.9141 0.000 0.992 0.000 0.008
#> GSM680082 1 0.0336 0.8608 0.992 0.000 0.000 0.008
#> GSM680029 2 0.4532 0.6360 0.156 0.792 0.000 0.052
#> GSM680041 1 0.5000 -0.2186 0.500 0.000 0.000 0.500
#> GSM680035 3 0.0000 0.9770 0.000 0.000 1.000 0.000
#> GSM680047 1 0.0188 0.8616 0.996 0.000 0.000 0.004
#> GSM680036 1 0.5434 0.4916 0.696 0.252 0.000 0.052
#> GSM680048 1 0.4977 -0.0935 0.540 0.000 0.000 0.460
#> GSM680037 3 0.0000 0.9770 0.000 0.000 1.000 0.000
#> GSM680049 4 0.2149 0.6178 0.088 0.000 0.000 0.912
#> GSM680038 2 0.0000 0.9162 0.000 1.000 0.000 0.000
#> GSM680050 1 0.0469 0.8587 0.988 0.000 0.000 0.012
#> GSM680039 3 0.0707 0.9595 0.000 0.020 0.980 0.000
#> GSM680051 4 0.4730 0.4095 0.364 0.000 0.000 0.636
#> GSM680040 3 0.0000 0.9770 0.000 0.000 1.000 0.000
#> GSM680052 3 0.4643 0.5084 0.000 0.000 0.656 0.344
#> GSM680030 3 0.0000 0.9770 0.000 0.000 1.000 0.000
#> GSM680042 1 0.3649 0.6054 0.796 0.000 0.000 0.204
#> GSM680031 3 0.0000 0.9770 0.000 0.000 1.000 0.000
#> GSM680043 3 0.0000 0.9770 0.000 0.000 1.000 0.000
#> GSM680032 4 0.4008 0.6259 0.244 0.000 0.000 0.756
#> GSM680044 4 0.4304 0.2899 0.000 0.284 0.000 0.716
#> GSM680033 3 0.0000 0.9770 0.000 0.000 1.000 0.000
#> GSM680045 3 0.0707 0.9615 0.000 0.000 0.980 0.020
#> GSM680034 3 0.0000 0.9770 0.000 0.000 1.000 0.000
#> GSM680046 1 0.0188 0.8616 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 3 0.2740 0.86664 0.000 0.004 0.888 0.044 0.064
#> GSM680062 4 0.5559 0.23965 0.000 0.344 0.000 0.572 0.084
#> GSM680054 3 0.0000 0.94536 0.000 0.000 1.000 0.000 0.000
#> GSM680063 3 0.0000 0.94536 0.000 0.000 1.000 0.000 0.000
#> GSM680055 5 0.6496 -0.11666 0.404 0.132 0.000 0.012 0.452
#> GSM680064 1 0.0162 0.80212 0.996 0.000 0.000 0.000 0.004
#> GSM680056 5 0.6328 0.49112 0.228 0.000 0.000 0.244 0.528
#> GSM680065 1 0.0000 0.80241 1.000 0.000 0.000 0.000 0.000
#> GSM680057 3 0.0000 0.94536 0.000 0.000 1.000 0.000 0.000
#> GSM680066 1 0.0000 0.80241 1.000 0.000 0.000 0.000 0.000
#> GSM680058 2 0.2852 0.80711 0.000 0.828 0.000 0.000 0.172
#> GSM680067 3 0.0000 0.94536 0.000 0.000 1.000 0.000 0.000
#> GSM680059 2 0.0290 0.87354 0.000 0.992 0.000 0.008 0.000
#> GSM680068 1 0.0162 0.80212 0.996 0.000 0.000 0.000 0.004
#> GSM680060 1 0.3508 0.59937 0.748 0.000 0.000 0.000 0.252
#> GSM680069 1 0.2179 0.74680 0.888 0.000 0.000 0.000 0.112
#> GSM680061 3 0.0000 0.94536 0.000 0.000 1.000 0.000 0.000
#> GSM680070 1 0.0404 0.80005 0.988 0.000 0.000 0.000 0.012
#> GSM680071 1 0.2230 0.74554 0.884 0.000 0.000 0.000 0.116
#> GSM680077 1 0.0000 0.80241 1.000 0.000 0.000 0.000 0.000
#> GSM680072 2 0.0162 0.87504 0.000 0.996 0.000 0.000 0.004
#> GSM680078 1 0.1043 0.79222 0.960 0.000 0.000 0.000 0.040
#> GSM680073 2 0.2813 0.80978 0.000 0.832 0.000 0.000 0.168
#> GSM680079 1 0.0000 0.80241 1.000 0.000 0.000 0.000 0.000
#> GSM680074 2 0.0609 0.87136 0.000 0.980 0.000 0.020 0.000
#> GSM680080 2 0.0451 0.87332 0.000 0.988 0.000 0.008 0.004
#> GSM680075 1 0.3452 0.60637 0.756 0.000 0.000 0.000 0.244
#> GSM680081 3 0.0703 0.93908 0.000 0.000 0.976 0.024 0.000
#> GSM680076 2 0.1981 0.86284 0.000 0.924 0.000 0.028 0.048
#> GSM680082 1 0.0703 0.79558 0.976 0.000 0.000 0.000 0.024
#> GSM680029 2 0.5284 0.50083 0.056 0.568 0.000 0.000 0.376
#> GSM680041 1 0.6175 0.01073 0.508 0.000 0.000 0.148 0.344
#> GSM680035 3 0.0703 0.93908 0.000 0.000 0.976 0.024 0.000
#> GSM680047 1 0.2351 0.76139 0.896 0.000 0.000 0.016 0.088
#> GSM680036 1 0.6248 -0.00805 0.468 0.148 0.000 0.000 0.384
#> GSM680048 1 0.6049 0.25886 0.576 0.000 0.000 0.192 0.232
#> GSM680037 3 0.0703 0.93908 0.000 0.000 0.976 0.024 0.000
#> GSM680049 5 0.6266 0.43704 0.152 0.000 0.000 0.376 0.472
#> GSM680038 2 0.0609 0.87136 0.000 0.980 0.000 0.020 0.000
#> GSM680050 1 0.1608 0.76007 0.928 0.000 0.000 0.000 0.072
#> GSM680039 3 0.3454 0.72792 0.000 0.156 0.816 0.028 0.000
#> GSM680051 4 0.6635 -0.30353 0.360 0.000 0.000 0.416 0.224
#> GSM680040 3 0.1831 0.90490 0.000 0.000 0.920 0.076 0.004
#> GSM680052 4 0.4464 0.06095 0.000 0.000 0.408 0.584 0.008
#> GSM680030 3 0.0000 0.94536 0.000 0.000 1.000 0.000 0.000
#> GSM680042 1 0.4806 0.41972 0.688 0.000 0.000 0.060 0.252
#> GSM680031 3 0.0000 0.94536 0.000 0.000 1.000 0.000 0.000
#> GSM680043 3 0.0703 0.93908 0.000 0.000 0.976 0.024 0.000
#> GSM680032 5 0.6422 0.50694 0.196 0.000 0.000 0.316 0.488
#> GSM680044 4 0.4424 0.28415 0.000 0.224 0.000 0.728 0.048
#> GSM680033 3 0.0000 0.94536 0.000 0.000 1.000 0.000 0.000
#> GSM680045 3 0.3966 0.50698 0.000 0.000 0.664 0.336 0.000
#> GSM680034 3 0.0000 0.94536 0.000 0.000 1.000 0.000 0.000
#> GSM680046 1 0.1877 0.78001 0.924 0.000 0.000 0.012 0.064
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 3 0.4196 0.7254 0.000 0.000 0.776 0.104 0.092 0.028
#> GSM680062 4 0.5774 0.3440 0.000 0.236 0.004 0.616 0.092 0.052
#> GSM680054 3 0.0000 0.8942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680063 3 0.0363 0.8881 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM680055 5 0.4404 0.5739 0.224 0.044 0.000 0.008 0.716 0.008
#> GSM680064 1 0.0000 0.8012 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM680056 6 0.5639 0.5710 0.180 0.000 0.000 0.036 0.156 0.628
#> GSM680065 1 0.0820 0.7983 0.972 0.000 0.000 0.000 0.012 0.016
#> GSM680057 3 0.0000 0.8942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680066 1 0.0458 0.8018 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM680058 2 0.3668 0.5920 0.000 0.668 0.000 0.004 0.328 0.000
#> GSM680067 3 0.0000 0.8942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680059 2 0.0146 0.8416 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM680068 1 0.0146 0.8012 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM680060 1 0.4138 0.4226 0.656 0.000 0.000 0.004 0.320 0.020
#> GSM680069 1 0.3014 0.7126 0.832 0.000 0.000 0.000 0.132 0.036
#> GSM680061 3 0.0000 0.8942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680070 1 0.0146 0.8013 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM680071 1 0.2544 0.7366 0.864 0.000 0.000 0.004 0.120 0.012
#> GSM680077 1 0.0260 0.8014 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM680072 2 0.1265 0.8371 0.000 0.948 0.000 0.008 0.044 0.000
#> GSM680078 1 0.1320 0.7922 0.948 0.000 0.000 0.000 0.036 0.016
#> GSM680073 2 0.3789 0.5969 0.000 0.668 0.000 0.004 0.324 0.004
#> GSM680079 1 0.0146 0.8012 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM680074 2 0.0622 0.8383 0.000 0.980 0.000 0.012 0.008 0.000
#> GSM680080 2 0.1088 0.8328 0.000 0.960 0.000 0.016 0.024 0.000
#> GSM680075 1 0.3903 0.4561 0.680 0.000 0.000 0.004 0.304 0.012
#> GSM680081 3 0.3141 0.8262 0.000 0.000 0.852 0.084 0.040 0.024
#> GSM680076 2 0.3310 0.7822 0.000 0.824 0.000 0.016 0.132 0.028
#> GSM680082 1 0.0458 0.7977 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM680029 5 0.4049 0.1512 0.020 0.332 0.000 0.000 0.648 0.000
#> GSM680041 1 0.5368 -0.0912 0.468 0.000 0.000 0.040 0.036 0.456
#> GSM680035 3 0.2402 0.8523 0.000 0.000 0.896 0.060 0.032 0.012
#> GSM680047 1 0.3795 0.6899 0.800 0.000 0.000 0.020 0.060 0.120
#> GSM680036 5 0.4735 0.5756 0.296 0.076 0.000 0.000 0.628 0.000
#> GSM680048 1 0.6228 0.1195 0.508 0.000 0.000 0.112 0.056 0.324
#> GSM680037 3 0.2918 0.8339 0.000 0.000 0.864 0.084 0.032 0.020
#> GSM680049 6 0.3101 0.6046 0.148 0.000 0.000 0.032 0.000 0.820
#> GSM680038 2 0.0725 0.8380 0.000 0.976 0.000 0.012 0.012 0.000
#> GSM680050 1 0.1957 0.7331 0.888 0.000 0.000 0.000 0.000 0.112
#> GSM680039 3 0.4220 0.5225 0.000 0.228 0.724 0.032 0.012 0.004
#> GSM680051 6 0.7105 0.2393 0.312 0.000 0.000 0.268 0.072 0.348
#> GSM680040 3 0.5044 0.6518 0.000 0.008 0.692 0.204 0.064 0.032
#> GSM680052 4 0.3593 0.4232 0.000 0.000 0.208 0.764 0.004 0.024
#> GSM680030 3 0.0000 0.8942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680042 1 0.3758 0.4193 0.668 0.000 0.000 0.000 0.008 0.324
#> GSM680031 3 0.0000 0.8942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680043 3 0.2990 0.8313 0.000 0.000 0.860 0.084 0.036 0.020
#> GSM680032 6 0.4198 0.6003 0.128 0.000 0.000 0.020 0.084 0.768
#> GSM680044 4 0.6092 0.2716 0.000 0.168 0.000 0.568 0.044 0.220
#> GSM680033 3 0.0000 0.8942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680045 4 0.5238 -0.1562 0.000 0.000 0.464 0.468 0.044 0.024
#> GSM680034 3 0.0000 0.8942 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680046 1 0.2932 0.7407 0.860 0.000 0.000 0.012 0.040 0.088
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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5)
get_signatures(res, k = 6)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> ATC:skmeans 54 0.6047 0.4652 0.056590 0.8556 2
#> ATC:skmeans 52 0.1649 0.5003 0.003088 0.0421 3
#> ATC:skmeans 46 0.0253 0.1798 0.002295 0.0240 4
#> ATC:skmeans 43 0.0405 0.0715 0.001653 0.0345 5
#> ATC:skmeans 43 0.1199 0.3257 0.000344 0.0230 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 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 0.826 0.878 0.940 0.4606 0.525 0.525
#> 3 3 0.828 0.910 0.961 0.3592 0.720 0.528
#> 4 4 0.724 0.844 0.866 0.1669 0.869 0.656
#> 5 5 0.744 0.805 0.885 0.0716 0.958 0.831
#> 6 6 0.718 0.730 0.861 0.0220 0.989 0.946
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
#> GSM680053 2 0.295 0.950 0.052 0.948
#> GSM680062 2 0.295 0.950 0.052 0.948
#> GSM680054 2 0.000 0.940 0.000 1.000
#> GSM680063 2 0.000 0.940 0.000 1.000
#> GSM680055 2 0.430 0.922 0.088 0.912
#> GSM680064 1 0.000 0.917 1.000 0.000
#> GSM680056 1 0.850 0.611 0.724 0.276
#> GSM680065 1 0.000 0.917 1.000 0.000
#> GSM680057 2 0.000 0.940 0.000 1.000
#> GSM680066 1 0.000 0.917 1.000 0.000
#> GSM680058 2 0.295 0.950 0.052 0.948
#> GSM680067 2 0.000 0.940 0.000 1.000
#> GSM680059 2 0.295 0.950 0.052 0.948
#> GSM680068 1 0.000 0.917 1.000 0.000
#> GSM680060 1 0.985 0.200 0.572 0.428
#> GSM680069 1 1.000 -0.027 0.504 0.496
#> GSM680061 2 0.000 0.940 0.000 1.000
#> GSM680070 1 0.000 0.917 1.000 0.000
#> GSM680071 1 0.000 0.917 1.000 0.000
#> GSM680077 1 0.000 0.917 1.000 0.000
#> GSM680072 2 0.295 0.950 0.052 0.948
#> GSM680078 1 0.000 0.917 1.000 0.000
#> GSM680073 2 0.295 0.950 0.052 0.948
#> GSM680079 1 0.000 0.917 1.000 0.000
#> GSM680074 2 0.295 0.950 0.052 0.948
#> GSM680080 2 0.295 0.950 0.052 0.948
#> GSM680075 1 0.000 0.917 1.000 0.000
#> GSM680081 2 0.000 0.940 0.000 1.000
#> GSM680076 2 0.295 0.950 0.052 0.948
#> GSM680082 1 0.000 0.917 1.000 0.000
#> GSM680029 2 0.311 0.947 0.056 0.944
#> GSM680041 1 0.402 0.857 0.920 0.080
#> GSM680035 2 0.000 0.940 0.000 1.000
#> GSM680047 1 0.000 0.917 1.000 0.000
#> GSM680036 2 0.861 0.653 0.284 0.716
#> GSM680048 2 0.952 0.451 0.372 0.628
#> GSM680037 2 0.000 0.940 0.000 1.000
#> GSM680049 1 0.615 0.782 0.848 0.152
#> GSM680038 2 0.295 0.950 0.052 0.948
#> GSM680050 1 0.000 0.917 1.000 0.000
#> GSM680039 2 0.295 0.950 0.052 0.948
#> GSM680051 2 0.529 0.890 0.120 0.880
#> GSM680040 2 0.295 0.950 0.052 0.948
#> GSM680052 2 0.295 0.950 0.052 0.948
#> GSM680030 2 0.000 0.940 0.000 1.000
#> GSM680042 1 0.000 0.917 1.000 0.000
#> GSM680031 2 0.000 0.940 0.000 1.000
#> GSM680043 2 0.000 0.940 0.000 1.000
#> GSM680032 2 0.529 0.890 0.120 0.880
#> GSM680044 2 0.295 0.950 0.052 0.948
#> GSM680033 2 0.000 0.940 0.000 1.000
#> GSM680045 2 0.295 0.950 0.052 0.948
#> GSM680034 2 0.000 0.940 0.000 1.000
#> GSM680046 1 0.000 0.917 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 2 0.000 0.942 0.000 1.000 0.000
#> GSM680062 2 0.000 0.942 0.000 1.000 0.000
#> GSM680054 3 0.000 0.956 0.000 0.000 1.000
#> GSM680063 2 0.388 0.799 0.000 0.848 0.152
#> GSM680055 2 0.000 0.942 0.000 1.000 0.000
#> GSM680064 1 0.000 0.971 1.000 0.000 0.000
#> GSM680056 2 0.418 0.783 0.172 0.828 0.000
#> GSM680065 1 0.000 0.971 1.000 0.000 0.000
#> GSM680057 3 0.000 0.956 0.000 0.000 1.000
#> GSM680066 1 0.319 0.852 0.888 0.112 0.000
#> GSM680058 2 0.000 0.942 0.000 1.000 0.000
#> GSM680067 2 0.562 0.557 0.000 0.692 0.308
#> GSM680059 2 0.000 0.942 0.000 1.000 0.000
#> GSM680068 1 0.000 0.971 1.000 0.000 0.000
#> GSM680060 2 0.514 0.700 0.252 0.748 0.000
#> GSM680069 2 0.164 0.913 0.044 0.956 0.000
#> GSM680061 3 0.000 0.956 0.000 0.000 1.000
#> GSM680070 1 0.000 0.971 1.000 0.000 0.000
#> GSM680071 1 0.000 0.971 1.000 0.000 0.000
#> GSM680077 1 0.000 0.971 1.000 0.000 0.000
#> GSM680072 2 0.000 0.942 0.000 1.000 0.000
#> GSM680078 1 0.000 0.971 1.000 0.000 0.000
#> GSM680073 2 0.000 0.942 0.000 1.000 0.000
#> GSM680079 1 0.000 0.971 1.000 0.000 0.000
#> GSM680074 2 0.000 0.942 0.000 1.000 0.000
#> GSM680080 2 0.000 0.942 0.000 1.000 0.000
#> GSM680075 1 0.000 0.971 1.000 0.000 0.000
#> GSM680081 2 0.000 0.942 0.000 1.000 0.000
#> GSM680076 2 0.000 0.942 0.000 1.000 0.000
#> GSM680082 1 0.000 0.971 1.000 0.000 0.000
#> GSM680029 2 0.000 0.942 0.000 1.000 0.000
#> GSM680041 2 0.518 0.672 0.256 0.744 0.000
#> GSM680035 3 0.000 0.956 0.000 0.000 1.000
#> GSM680047 1 0.129 0.939 0.968 0.032 0.000
#> GSM680036 2 0.455 0.766 0.200 0.800 0.000
#> GSM680048 2 0.175 0.910 0.048 0.952 0.000
#> GSM680037 3 0.000 0.956 0.000 0.000 1.000
#> GSM680049 1 0.455 0.738 0.800 0.200 0.000
#> GSM680038 2 0.000 0.942 0.000 1.000 0.000
#> GSM680050 1 0.000 0.971 1.000 0.000 0.000
#> GSM680039 2 0.000 0.942 0.000 1.000 0.000
#> GSM680051 2 0.000 0.942 0.000 1.000 0.000
#> GSM680040 2 0.000 0.942 0.000 1.000 0.000
#> GSM680052 2 0.000 0.942 0.000 1.000 0.000
#> GSM680030 3 0.576 0.483 0.000 0.328 0.672
#> GSM680042 1 0.000 0.971 1.000 0.000 0.000
#> GSM680031 3 0.000 0.956 0.000 0.000 1.000
#> GSM680043 3 0.000 0.956 0.000 0.000 1.000
#> GSM680032 2 0.000 0.942 0.000 1.000 0.000
#> GSM680044 2 0.000 0.942 0.000 1.000 0.000
#> GSM680033 3 0.000 0.956 0.000 0.000 1.000
#> GSM680045 2 0.000 0.942 0.000 1.000 0.000
#> GSM680034 3 0.000 0.956 0.000 0.000 1.000
#> GSM680046 1 0.000 0.971 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 4 0.0000 0.900 0.000 0.000 0.000 1.000
#> GSM680062 4 0.0000 0.900 0.000 0.000 0.000 1.000
#> GSM680054 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM680063 4 0.3372 0.764 0.000 0.036 0.096 0.868
#> GSM680055 4 0.0469 0.896 0.000 0.012 0.000 0.988
#> GSM680064 1 0.4356 0.832 0.708 0.292 0.000 0.000
#> GSM680056 4 0.0524 0.896 0.004 0.008 0.000 0.988
#> GSM680065 1 0.0469 0.883 0.988 0.012 0.000 0.000
#> GSM680057 3 0.1022 0.948 0.000 0.032 0.968 0.000
#> GSM680066 1 0.1978 0.845 0.928 0.004 0.000 0.068
#> GSM680058 2 0.4585 0.876 0.000 0.668 0.000 0.332
#> GSM680067 4 0.5472 0.519 0.000 0.044 0.280 0.676
#> GSM680059 2 0.4605 0.876 0.000 0.664 0.000 0.336
#> GSM680068 1 0.2973 0.872 0.856 0.144 0.000 0.000
#> GSM680060 2 0.3893 0.502 0.196 0.796 0.000 0.008
#> GSM680069 2 0.5773 0.817 0.044 0.620 0.000 0.336
#> GSM680061 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM680070 1 0.0188 0.881 0.996 0.004 0.000 0.000
#> GSM680071 1 0.1211 0.882 0.960 0.040 0.000 0.000
#> GSM680077 1 0.0000 0.882 1.000 0.000 0.000 0.000
#> GSM680072 2 0.4605 0.876 0.000 0.664 0.000 0.336
#> GSM680078 1 0.4356 0.832 0.708 0.292 0.000 0.000
#> GSM680073 2 0.4585 0.876 0.000 0.668 0.000 0.332
#> GSM680079 1 0.4356 0.832 0.708 0.292 0.000 0.000
#> GSM680074 2 0.4605 0.876 0.000 0.664 0.000 0.336
#> GSM680080 2 0.4985 0.662 0.000 0.532 0.000 0.468
#> GSM680075 1 0.4713 0.784 0.640 0.360 0.000 0.000
#> GSM680081 4 0.1118 0.876 0.000 0.036 0.000 0.964
#> GSM680076 2 0.4605 0.876 0.000 0.664 0.000 0.336
#> GSM680082 1 0.0188 0.881 0.996 0.004 0.000 0.000
#> GSM680029 2 0.4564 0.874 0.000 0.672 0.000 0.328
#> GSM680041 4 0.3088 0.764 0.128 0.008 0.000 0.864
#> GSM680035 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM680047 1 0.4465 0.844 0.800 0.144 0.000 0.056
#> GSM680036 2 0.6147 0.690 0.200 0.672 0.000 0.128
#> GSM680048 4 0.2048 0.837 0.064 0.008 0.000 0.928
#> GSM680037 3 0.0707 0.954 0.000 0.020 0.980 0.000
#> GSM680049 1 0.3626 0.712 0.812 0.004 0.000 0.184
#> GSM680038 4 0.4250 0.276 0.000 0.276 0.000 0.724
#> GSM680050 1 0.0188 0.881 0.996 0.004 0.000 0.000
#> GSM680039 4 0.0336 0.895 0.000 0.008 0.000 0.992
#> GSM680051 4 0.0524 0.896 0.004 0.008 0.000 0.988
#> GSM680040 4 0.0336 0.895 0.000 0.008 0.000 0.992
#> GSM680052 4 0.0000 0.900 0.000 0.000 0.000 1.000
#> GSM680030 3 0.5219 0.637 0.000 0.044 0.712 0.244
#> GSM680042 1 0.0188 0.881 0.996 0.004 0.000 0.000
#> GSM680031 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM680043 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM680032 4 0.0000 0.900 0.000 0.000 0.000 1.000
#> GSM680044 4 0.0000 0.900 0.000 0.000 0.000 1.000
#> GSM680033 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM680045 4 0.0000 0.900 0.000 0.000 0.000 1.000
#> GSM680034 3 0.0000 0.962 0.000 0.000 1.000 0.000
#> GSM680046 1 0.4008 0.848 0.756 0.244 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 5 0.0162 0.868 0.000 0.004 0.000 0.000 0.996
#> GSM680062 5 0.0162 0.868 0.000 0.004 0.000 0.000 0.996
#> GSM680054 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000
#> GSM680063 5 0.2806 0.772 0.000 0.152 0.000 0.004 0.844
#> GSM680055 5 0.1410 0.854 0.000 0.060 0.000 0.000 0.940
#> GSM680064 4 0.0794 0.877 0.028 0.000 0.000 0.972 0.000
#> GSM680056 5 0.1341 0.855 0.000 0.056 0.000 0.000 0.944
#> GSM680065 1 0.1121 0.890 0.956 0.000 0.000 0.044 0.000
#> GSM680057 3 0.2536 0.841 0.000 0.128 0.868 0.004 0.000
#> GSM680066 1 0.2592 0.842 0.892 0.052 0.000 0.000 0.056
#> GSM680058 2 0.2813 0.845 0.000 0.832 0.000 0.000 0.168
#> GSM680067 5 0.6232 0.477 0.000 0.280 0.164 0.004 0.552
#> GSM680059 2 0.3109 0.854 0.000 0.800 0.000 0.000 0.200
#> GSM680068 1 0.3039 0.731 0.808 0.000 0.000 0.192 0.000
#> GSM680060 2 0.5008 0.522 0.152 0.708 0.000 0.140 0.000
#> GSM680069 2 0.5435 0.538 0.072 0.576 0.000 0.000 0.352
#> GSM680061 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000
#> GSM680070 1 0.0000 0.912 1.000 0.000 0.000 0.000 0.000
#> GSM680071 1 0.1410 0.877 0.940 0.000 0.000 0.060 0.000
#> GSM680077 1 0.0000 0.912 1.000 0.000 0.000 0.000 0.000
#> GSM680072 2 0.3109 0.854 0.000 0.800 0.000 0.000 0.200
#> GSM680078 4 0.0162 0.885 0.004 0.000 0.000 0.996 0.000
#> GSM680073 2 0.3109 0.854 0.000 0.800 0.000 0.000 0.200
#> GSM680079 4 0.0162 0.885 0.004 0.000 0.000 0.996 0.000
#> GSM680074 2 0.3109 0.854 0.000 0.800 0.000 0.000 0.200
#> GSM680080 2 0.4268 0.463 0.000 0.556 0.000 0.000 0.444
#> GSM680075 4 0.0162 0.885 0.004 0.000 0.000 0.996 0.000
#> GSM680081 5 0.2763 0.773 0.000 0.148 0.000 0.004 0.848
#> GSM680076 2 0.3109 0.854 0.000 0.800 0.000 0.000 0.200
#> GSM680082 1 0.0000 0.912 1.000 0.000 0.000 0.000 0.000
#> GSM680029 2 0.2690 0.839 0.000 0.844 0.000 0.000 0.156
#> GSM680041 5 0.3102 0.797 0.084 0.056 0.000 0.000 0.860
#> GSM680035 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000
#> GSM680047 4 0.4045 0.532 0.356 0.000 0.000 0.644 0.000
#> GSM680036 2 0.3098 0.683 0.148 0.836 0.000 0.000 0.016
#> GSM680048 5 0.1740 0.849 0.012 0.056 0.000 0.000 0.932
#> GSM680037 3 0.1124 0.907 0.000 0.036 0.960 0.004 0.000
#> GSM680049 1 0.3695 0.691 0.800 0.036 0.000 0.000 0.164
#> GSM680038 5 0.4060 0.206 0.000 0.360 0.000 0.000 0.640
#> GSM680050 1 0.0162 0.911 0.996 0.004 0.000 0.000 0.000
#> GSM680039 5 0.2516 0.739 0.000 0.140 0.000 0.000 0.860
#> GSM680051 5 0.1502 0.854 0.004 0.056 0.000 0.000 0.940
#> GSM680040 5 0.1043 0.849 0.000 0.040 0.000 0.000 0.960
#> GSM680052 5 0.0162 0.868 0.000 0.004 0.000 0.000 0.996
#> GSM680030 3 0.6488 0.428 0.000 0.284 0.512 0.004 0.200
#> GSM680042 1 0.0000 0.912 1.000 0.000 0.000 0.000 0.000
#> GSM680031 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000
#> GSM680043 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000
#> GSM680032 5 0.0404 0.865 0.000 0.012 0.000 0.000 0.988
#> GSM680044 5 0.0162 0.868 0.000 0.004 0.000 0.000 0.996
#> GSM680033 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000
#> GSM680045 5 0.0162 0.868 0.000 0.004 0.000 0.000 0.996
#> GSM680034 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000
#> GSM680046 4 0.2852 0.782 0.172 0.000 0.000 0.828 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 5 0.0146 0.817 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM680062 5 0.0146 0.817 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM680054 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680063 5 0.4377 0.439 0.000 0.120 0.000 0.000 0.720 0.160
#> GSM680055 5 0.1765 0.783 0.000 0.096 0.000 0.000 0.904 0.000
#> GSM680064 4 0.0777 0.833 0.024 0.000 0.000 0.972 0.000 0.004
#> GSM680056 5 0.1610 0.787 0.000 0.084 0.000 0.000 0.916 0.000
#> GSM680065 1 0.1225 0.889 0.952 0.000 0.000 0.036 0.000 0.012
#> GSM680057 3 0.3787 0.686 0.000 0.100 0.780 0.000 0.000 0.120
#> GSM680066 1 0.2786 0.802 0.860 0.084 0.000 0.000 0.056 0.000
#> GSM680058 2 0.2300 0.815 0.000 0.856 0.000 0.000 0.144 0.000
#> GSM680067 5 0.7440 -0.205 0.000 0.220 0.220 0.000 0.392 0.168
#> GSM680059 2 0.3043 0.833 0.000 0.792 0.000 0.000 0.200 0.008
#> GSM680068 1 0.2871 0.728 0.804 0.004 0.000 0.192 0.000 0.000
#> GSM680060 2 0.3961 0.561 0.124 0.764 0.000 0.112 0.000 0.000
#> GSM680069 2 0.4671 0.555 0.068 0.628 0.000 0.000 0.304 0.000
#> GSM680061 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680070 1 0.0000 0.907 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM680071 1 0.1204 0.879 0.944 0.000 0.000 0.056 0.000 0.000
#> GSM680077 1 0.0000 0.907 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM680072 2 0.3043 0.833 0.000 0.792 0.000 0.000 0.200 0.008
#> GSM680078 4 0.0000 0.843 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680073 2 0.2793 0.832 0.000 0.800 0.000 0.000 0.200 0.000
#> GSM680079 4 0.0000 0.843 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680074 2 0.3043 0.833 0.000 0.792 0.000 0.000 0.200 0.008
#> GSM680080 2 0.4067 0.472 0.000 0.548 0.000 0.000 0.444 0.008
#> GSM680075 4 0.0000 0.843 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680081 6 0.2664 0.000 0.000 0.000 0.000 0.000 0.184 0.816
#> GSM680076 2 0.3043 0.833 0.000 0.792 0.000 0.000 0.200 0.008
#> GSM680082 1 0.0000 0.907 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM680029 2 0.2135 0.805 0.000 0.872 0.000 0.000 0.128 0.000
#> GSM680041 5 0.3475 0.702 0.080 0.084 0.000 0.000 0.824 0.012
#> GSM680035 3 0.2219 0.808 0.000 0.000 0.864 0.000 0.000 0.136
#> GSM680047 4 0.3996 0.522 0.352 0.004 0.000 0.636 0.000 0.008
#> GSM680036 2 0.2494 0.669 0.120 0.864 0.000 0.000 0.016 0.000
#> GSM680048 5 0.1866 0.780 0.008 0.084 0.000 0.000 0.908 0.000
#> GSM680037 3 0.3053 0.795 0.000 0.020 0.812 0.000 0.000 0.168
#> GSM680049 1 0.3699 0.670 0.788 0.040 0.000 0.000 0.160 0.012
#> GSM680038 5 0.3861 0.177 0.000 0.352 0.000 0.000 0.640 0.008
#> GSM680050 1 0.0363 0.906 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM680039 5 0.2212 0.715 0.000 0.112 0.000 0.000 0.880 0.008
#> GSM680051 5 0.1610 0.787 0.000 0.084 0.000 0.000 0.916 0.000
#> GSM680040 5 0.0713 0.806 0.000 0.028 0.000 0.000 0.972 0.000
#> GSM680052 5 0.0146 0.817 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM680030 3 0.6711 0.203 0.000 0.224 0.512 0.000 0.096 0.168
#> GSM680042 1 0.0363 0.906 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM680031 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680043 3 0.2378 0.801 0.000 0.000 0.848 0.000 0.000 0.152
#> GSM680032 5 0.0547 0.813 0.000 0.020 0.000 0.000 0.980 0.000
#> GSM680044 5 0.0146 0.817 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM680033 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680045 5 0.0146 0.817 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM680034 3 0.0000 0.861 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM680046 4 0.2703 0.738 0.172 0.004 0.000 0.824 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 4)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> ATC:pam 51 0.3408 0.728 0.000877 0.3823 2
#> ATC:pam 53 0.2290 0.383 0.000552 0.0966 3
#> ATC:pam 53 0.0511 0.247 0.000113 0.0137 4
#> ATC:pam 50 0.1443 0.239 0.000251 0.0478 5
#> ATC:pam 48 0.0744 0.165 0.000325 0.0204 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 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 0.493 0.000 0.824 0.2947 1.000 1.000
#> 3 3 0.971 0.927 0.973 1.2322 0.342 0.342
#> 4 4 0.758 0.630 0.755 0.1113 0.823 0.532
#> 5 5 0.789 0.832 0.914 0.0146 0.808 0.448
#> 6 6 0.774 0.735 0.870 0.0727 0.902 0.667
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM680053 2 0.0000 0 0.000 1.000
#> GSM680062 2 0.0376 0 0.004 0.996
#> GSM680054 2 0.1843 0 0.028 0.972
#> GSM680063 2 0.1843 0 0.028 0.972
#> GSM680055 2 0.0000 0 0.000 1.000
#> GSM680064 2 0.9833 0 0.424 0.576
#> GSM680056 2 0.9988 0 0.480 0.520
#> GSM680065 2 0.9983 0 0.476 0.524
#> GSM680057 2 0.1843 0 0.028 0.972
#> GSM680066 2 0.0672 0 0.008 0.992
#> GSM680058 2 0.9983 0 0.476 0.524
#> GSM680067 2 0.1843 0 0.028 0.972
#> GSM680059 2 0.9983 0 0.476 0.524
#> GSM680068 2 0.0672 0 0.008 0.992
#> GSM680060 2 0.0000 0 0.000 1.000
#> GSM680069 2 0.0672 0 0.008 0.992
#> GSM680061 2 0.1843 0 0.028 0.972
#> GSM680070 2 0.9998 0 0.492 0.508
#> GSM680071 2 0.0376 0 0.004 0.996
#> GSM680077 2 0.9988 0 0.480 0.520
#> GSM680072 2 0.9983 0 0.476 0.524
#> GSM680078 2 0.0000 0 0.000 1.000
#> GSM680073 2 0.9944 0 0.456 0.544
#> GSM680079 2 0.9933 0 0.452 0.548
#> GSM680074 2 0.9983 0 0.476 0.524
#> GSM680080 2 0.6712 0 0.176 0.824
#> GSM680075 2 0.0000 0 0.000 1.000
#> GSM680081 2 0.1843 0 0.028 0.972
#> GSM680076 2 0.0000 0 0.000 1.000
#> GSM680082 2 1.0000 0 0.496 0.504
#> GSM680029 2 0.9983 0 0.476 0.524
#> GSM680041 2 1.0000 0 0.496 0.504
#> GSM680035 2 0.1843 0 0.028 0.972
#> GSM680047 2 0.0000 0 0.000 1.000
#> GSM680036 2 0.9983 0 0.476 0.524
#> GSM680048 2 0.0000 0 0.000 1.000
#> GSM680037 2 0.1843 0 0.028 0.972
#> GSM680049 2 0.0000 0 0.000 1.000
#> GSM680038 2 0.9983 0 0.476 0.524
#> GSM680050 2 1.0000 0 0.496 0.504
#> GSM680039 2 0.9248 0 0.340 0.660
#> GSM680051 2 0.0000 0 0.000 1.000
#> GSM680040 2 0.0000 0 0.000 1.000
#> GSM680052 2 0.0000 0 0.000 1.000
#> GSM680030 2 0.1843 0 0.028 0.972
#> GSM680042 2 1.0000 0 0.496 0.504
#> GSM680031 2 0.1843 0 0.028 0.972
#> GSM680043 2 0.1843 0 0.028 0.972
#> GSM680032 2 0.0000 0 0.000 1.000
#> GSM680044 2 0.0000 0 0.000 1.000
#> GSM680033 2 0.1843 0 0.028 0.972
#> GSM680045 2 0.0000 0 0.000 1.000
#> GSM680034 2 0.1843 0 0.028 0.972
#> GSM680046 2 0.0000 0 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 2 0.0237 0.955 0.000 0.996 0.004
#> GSM680062 2 0.0000 0.957 0.000 1.000 0.000
#> GSM680054 3 0.0000 1.000 0.000 0.000 1.000
#> GSM680063 3 0.0000 1.000 0.000 0.000 1.000
#> GSM680055 2 0.0000 0.957 0.000 1.000 0.000
#> GSM680064 1 0.0000 0.960 1.000 0.000 0.000
#> GSM680056 2 0.0237 0.955 0.004 0.996 0.000
#> GSM680065 1 0.0000 0.960 1.000 0.000 0.000
#> GSM680057 3 0.0000 1.000 0.000 0.000 1.000
#> GSM680066 1 0.5810 0.476 0.664 0.336 0.000
#> GSM680058 2 0.0000 0.957 0.000 1.000 0.000
#> GSM680067 3 0.0000 1.000 0.000 0.000 1.000
#> GSM680059 2 0.0000 0.957 0.000 1.000 0.000
#> GSM680068 1 0.0000 0.960 1.000 0.000 0.000
#> GSM680060 1 0.0892 0.942 0.980 0.020 0.000
#> GSM680069 2 0.1031 0.939 0.024 0.976 0.000
#> GSM680061 3 0.0000 1.000 0.000 0.000 1.000
#> GSM680070 1 0.0000 0.960 1.000 0.000 0.000
#> GSM680071 1 0.0000 0.960 1.000 0.000 0.000
#> GSM680077 1 0.0000 0.960 1.000 0.000 0.000
#> GSM680072 2 0.0000 0.957 0.000 1.000 0.000
#> GSM680078 1 0.0000 0.960 1.000 0.000 0.000
#> GSM680073 2 0.0000 0.957 0.000 1.000 0.000
#> GSM680079 1 0.0000 0.960 1.000 0.000 0.000
#> GSM680074 2 0.0000 0.957 0.000 1.000 0.000
#> GSM680080 2 0.0000 0.957 0.000 1.000 0.000
#> GSM680075 1 0.0000 0.960 1.000 0.000 0.000
#> GSM680081 3 0.0000 1.000 0.000 0.000 1.000
#> GSM680076 2 0.0000 0.957 0.000 1.000 0.000
#> GSM680082 1 0.0000 0.960 1.000 0.000 0.000
#> GSM680029 2 0.0000 0.957 0.000 1.000 0.000
#> GSM680041 1 0.4504 0.740 0.804 0.196 0.000
#> GSM680035 3 0.0000 1.000 0.000 0.000 1.000
#> GSM680047 1 0.0000 0.960 1.000 0.000 0.000
#> GSM680036 2 0.2066 0.903 0.060 0.940 0.000
#> GSM680048 2 0.5785 0.481 0.332 0.668 0.000
#> GSM680037 3 0.0000 1.000 0.000 0.000 1.000
#> GSM680049 2 0.6307 0.010 0.488 0.512 0.000
#> GSM680038 2 0.0000 0.957 0.000 1.000 0.000
#> GSM680050 1 0.0000 0.960 1.000 0.000 0.000
#> GSM680039 2 0.0000 0.957 0.000 1.000 0.000
#> GSM680051 2 0.0237 0.955 0.004 0.996 0.000
#> GSM680040 2 0.0237 0.955 0.000 0.996 0.004
#> GSM680052 2 0.0237 0.955 0.000 0.996 0.004
#> GSM680030 3 0.0000 1.000 0.000 0.000 1.000
#> GSM680042 1 0.0000 0.960 1.000 0.000 0.000
#> GSM680031 3 0.0000 1.000 0.000 0.000 1.000
#> GSM680043 3 0.0000 1.000 0.000 0.000 1.000
#> GSM680032 2 0.0237 0.955 0.004 0.996 0.000
#> GSM680044 2 0.0000 0.957 0.000 1.000 0.000
#> GSM680033 3 0.0000 1.000 0.000 0.000 1.000
#> GSM680045 2 0.0237 0.955 0.000 0.996 0.004
#> GSM680034 3 0.0000 1.000 0.000 0.000 1.000
#> GSM680046 1 0.0000 0.960 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 2 0.6946 0.8299 0.396 0.524 0.040 0.040
#> GSM680062 2 0.5643 0.8663 0.428 0.548 0.000 0.024
#> GSM680054 3 0.0000 0.8782 0.000 0.000 1.000 0.000
#> GSM680063 3 0.0000 0.8782 0.000 0.000 1.000 0.000
#> GSM680055 2 0.6330 0.8407 0.448 0.492 0.000 0.060
#> GSM680064 1 0.4967 0.5741 0.548 0.000 0.000 0.452
#> GSM680056 4 0.0000 0.7396 0.000 0.000 0.000 1.000
#> GSM680065 1 0.4972 0.5657 0.544 0.000 0.000 0.456
#> GSM680057 3 0.0000 0.8782 0.000 0.000 1.000 0.000
#> GSM680066 4 0.0188 0.7368 0.004 0.000 0.000 0.996
#> GSM680058 2 0.5378 0.8767 0.448 0.540 0.000 0.012
#> GSM680067 3 0.0000 0.8782 0.000 0.000 1.000 0.000
#> GSM680059 2 0.5132 0.8776 0.448 0.548 0.000 0.004
#> GSM680068 1 0.4967 0.5741 0.548 0.000 0.000 0.452
#> GSM680060 1 0.4485 -0.0791 0.772 0.028 0.000 0.200
#> GSM680069 4 0.0000 0.7396 0.000 0.000 0.000 1.000
#> GSM680061 3 0.0000 0.8782 0.000 0.000 1.000 0.000
#> GSM680070 4 0.3801 0.3966 0.220 0.000 0.000 0.780
#> GSM680071 1 0.4967 0.5741 0.548 0.000 0.000 0.452
#> GSM680077 1 0.4967 0.5741 0.548 0.000 0.000 0.452
#> GSM680072 2 0.5132 0.8776 0.448 0.548 0.000 0.004
#> GSM680078 1 0.4967 0.5741 0.548 0.000 0.000 0.452
#> GSM680073 2 0.5483 0.8752 0.448 0.536 0.000 0.016
#> GSM680079 1 0.4967 0.5741 0.548 0.000 0.000 0.452
#> GSM680074 2 0.5132 0.8776 0.448 0.548 0.000 0.004
#> GSM680080 2 0.5132 0.8776 0.448 0.548 0.000 0.004
#> GSM680075 1 0.0592 0.1276 0.984 0.000 0.000 0.016
#> GSM680081 3 0.4967 0.6983 0.000 0.452 0.548 0.000
#> GSM680076 2 0.5378 0.8767 0.448 0.540 0.000 0.012
#> GSM680082 4 0.4977 -0.4181 0.460 0.000 0.000 0.540
#> GSM680029 2 0.5483 0.8752 0.448 0.536 0.000 0.016
#> GSM680041 4 0.0000 0.7396 0.000 0.000 0.000 1.000
#> GSM680035 3 0.4967 0.6983 0.000 0.452 0.548 0.000
#> GSM680047 1 0.4961 0.5716 0.552 0.000 0.000 0.448
#> GSM680036 1 0.7117 -0.4125 0.448 0.128 0.000 0.424
#> GSM680048 4 0.0707 0.7299 0.000 0.020 0.000 0.980
#> GSM680037 3 0.4967 0.6983 0.000 0.452 0.548 0.000
#> GSM680049 4 0.0000 0.7396 0.000 0.000 0.000 1.000
#> GSM680038 2 0.5132 0.8776 0.448 0.548 0.000 0.004
#> GSM680050 4 0.0188 0.7368 0.004 0.000 0.000 0.996
#> GSM680039 2 0.5132 0.8776 0.448 0.548 0.000 0.004
#> GSM680051 4 0.3074 0.5774 0.000 0.152 0.000 0.848
#> GSM680040 2 0.2124 0.4235 0.000 0.932 0.040 0.028
#> GSM680052 4 0.5317 0.1443 0.004 0.460 0.004 0.532
#> GSM680030 3 0.0000 0.8782 0.000 0.000 1.000 0.000
#> GSM680042 4 0.4697 -0.0610 0.356 0.000 0.000 0.644
#> GSM680031 3 0.0000 0.8782 0.000 0.000 1.000 0.000
#> GSM680043 3 0.4967 0.6983 0.000 0.452 0.548 0.000
#> GSM680032 4 0.1452 0.7105 0.008 0.036 0.000 0.956
#> GSM680044 2 0.6077 -0.0740 0.044 0.496 0.000 0.460
#> GSM680033 3 0.0000 0.8782 0.000 0.000 1.000 0.000
#> GSM680045 2 0.3634 0.3765 0.000 0.856 0.048 0.096
#> GSM680034 3 0.0000 0.8782 0.000 0.000 1.000 0.000
#> GSM680046 1 0.4961 0.5716 0.552 0.000 0.000 0.448
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 2 0.5537 0.6027 0.200 0.692 0.000 0.048 0.060
#> GSM680062 2 0.4898 0.3347 0.376 0.592 0.000 0.032 0.000
#> GSM680054 5 0.0000 0.9994 0.000 0.000 0.000 0.000 1.000
#> GSM680063 5 0.0000 0.9994 0.000 0.000 0.000 0.000 1.000
#> GSM680055 2 0.2389 0.8136 0.116 0.880 0.000 0.004 0.000
#> GSM680064 1 0.4400 0.7371 0.736 0.000 0.052 0.212 0.000
#> GSM680056 1 0.0404 0.8924 0.988 0.012 0.000 0.000 0.000
#> GSM680065 1 0.1121 0.8886 0.956 0.000 0.000 0.044 0.000
#> GSM680057 5 0.0000 0.9994 0.000 0.000 0.000 0.000 1.000
#> GSM680066 1 0.0162 0.8920 0.996 0.000 0.004 0.000 0.000
#> GSM680058 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000
#> GSM680067 5 0.0162 0.9954 0.000 0.000 0.004 0.000 0.996
#> GSM680059 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000
#> GSM680068 1 0.4065 0.7136 0.720 0.000 0.016 0.264 0.000
#> GSM680060 2 0.4186 0.7555 0.128 0.796 0.012 0.064 0.000
#> GSM680069 1 0.0510 0.8884 0.984 0.000 0.000 0.016 0.000
#> GSM680061 5 0.0000 0.9994 0.000 0.000 0.000 0.000 1.000
#> GSM680070 1 0.0693 0.8923 0.980 0.000 0.008 0.012 0.000
#> GSM680071 1 0.2127 0.8622 0.892 0.000 0.000 0.108 0.000
#> GSM680077 1 0.2286 0.8538 0.888 0.000 0.004 0.108 0.000
#> GSM680072 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000
#> GSM680078 1 0.3636 0.7209 0.728 0.000 0.000 0.272 0.000
#> GSM680073 2 0.0162 0.8952 0.004 0.996 0.000 0.000 0.000
#> GSM680079 1 0.4400 0.7371 0.736 0.000 0.052 0.212 0.000
#> GSM680074 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000
#> GSM680080 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000
#> GSM680075 2 0.3863 0.7345 0.052 0.796 0.000 0.152 0.000
#> GSM680081 3 0.1544 0.8175 0.000 0.000 0.932 0.000 0.068
#> GSM680076 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000
#> GSM680082 1 0.1205 0.8872 0.956 0.000 0.004 0.040 0.000
#> GSM680029 2 0.0162 0.8952 0.004 0.996 0.000 0.000 0.000
#> GSM680041 1 0.0162 0.8920 0.996 0.000 0.004 0.000 0.000
#> GSM680035 3 0.1792 0.8291 0.000 0.000 0.916 0.000 0.084
#> GSM680047 4 0.2124 0.7522 0.096 0.000 0.004 0.900 0.000
#> GSM680036 2 0.1082 0.8778 0.028 0.964 0.008 0.000 0.000
#> GSM680048 1 0.0955 0.8870 0.968 0.028 0.000 0.004 0.000
#> GSM680037 3 0.1792 0.8291 0.000 0.000 0.916 0.000 0.084
#> GSM680049 1 0.0404 0.8924 0.988 0.012 0.000 0.000 0.000
#> GSM680038 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000
#> GSM680050 1 0.0162 0.8920 0.996 0.000 0.004 0.000 0.000
#> GSM680039 2 0.0000 0.8964 0.000 1.000 0.000 0.000 0.000
#> GSM680051 1 0.2344 0.8513 0.904 0.064 0.000 0.032 0.000
#> GSM680040 4 0.4778 0.3619 0.000 0.020 0.196 0.736 0.048
#> GSM680052 1 0.2735 0.8365 0.880 0.084 0.000 0.036 0.000
#> GSM680030 5 0.0000 0.9994 0.000 0.000 0.000 0.000 1.000
#> GSM680042 1 0.0451 0.8929 0.988 0.000 0.004 0.008 0.000
#> GSM680031 5 0.0000 0.9994 0.000 0.000 0.000 0.000 1.000
#> GSM680043 3 0.1792 0.8291 0.000 0.000 0.916 0.000 0.084
#> GSM680032 1 0.1579 0.8752 0.944 0.024 0.000 0.032 0.000
#> GSM680044 1 0.4248 0.6566 0.728 0.240 0.000 0.032 0.000
#> GSM680033 5 0.0000 0.9994 0.000 0.000 0.000 0.000 1.000
#> GSM680045 3 0.7855 0.0333 0.208 0.040 0.460 0.264 0.028
#> GSM680034 5 0.0000 0.9994 0.000 0.000 0.000 0.000 1.000
#> GSM680046 4 0.2127 0.7446 0.108 0.000 0.000 0.892 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 4 0.5336 0.18819 0.000 0.244 0.000 0.588 0.000 0.168
#> GSM680062 4 0.3672 0.32089 0.000 0.368 0.000 0.632 0.000 0.000
#> GSM680054 5 0.0858 0.96760 0.000 0.000 0.004 0.000 0.968 0.028
#> GSM680063 5 0.0777 0.97377 0.000 0.004 0.000 0.000 0.972 0.024
#> GSM680055 2 0.2838 0.74290 0.000 0.808 0.000 0.188 0.000 0.004
#> GSM680064 1 0.3634 0.78452 0.696 0.000 0.000 0.008 0.000 0.296
#> GSM680056 4 0.2806 0.73133 0.004 0.016 0.000 0.844 0.000 0.136
#> GSM680065 4 0.4795 0.61125 0.072 0.000 0.000 0.604 0.000 0.324
#> GSM680057 5 0.0547 0.97560 0.000 0.000 0.000 0.000 0.980 0.020
#> GSM680066 4 0.0632 0.71930 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM680058 2 0.0363 0.92715 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM680067 5 0.1075 0.95762 0.000 0.000 0.000 0.000 0.952 0.048
#> GSM680059 2 0.0000 0.93037 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680068 1 0.3575 0.78599 0.708 0.000 0.000 0.008 0.000 0.284
#> GSM680060 2 0.4244 0.72342 0.060 0.772 0.000 0.128 0.000 0.040
#> GSM680069 4 0.0000 0.70967 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM680061 5 0.0146 0.97813 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM680070 4 0.4018 0.64882 0.020 0.000 0.000 0.656 0.000 0.324
#> GSM680071 4 0.3806 0.62587 0.164 0.000 0.000 0.768 0.000 0.068
#> GSM680077 4 0.6130 -0.00977 0.336 0.000 0.000 0.340 0.000 0.324
#> GSM680072 2 0.0000 0.93037 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680078 1 0.3874 0.76374 0.732 0.000 0.000 0.040 0.000 0.228
#> GSM680073 2 0.0260 0.92866 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM680079 1 0.3867 0.76858 0.660 0.000 0.000 0.012 0.000 0.328
#> GSM680074 2 0.0000 0.93037 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680080 2 0.0000 0.93037 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680075 2 0.3769 0.69075 0.188 0.768 0.000 0.008 0.000 0.036
#> GSM680081 3 0.1245 0.78392 0.000 0.000 0.952 0.000 0.016 0.032
#> GSM680076 2 0.0000 0.93037 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680082 4 0.5057 0.57584 0.096 0.000 0.000 0.580 0.000 0.324
#> GSM680029 2 0.0713 0.91825 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM680041 4 0.2668 0.72296 0.004 0.000 0.000 0.828 0.000 0.168
#> GSM680035 3 0.0458 0.80739 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM680047 1 0.0146 0.55135 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM680036 2 0.1116 0.91037 0.004 0.960 0.000 0.028 0.000 0.008
#> GSM680048 4 0.0937 0.72353 0.000 0.000 0.000 0.960 0.000 0.040
#> GSM680037 3 0.0458 0.80739 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM680049 4 0.3895 0.67622 0.004 0.016 0.000 0.696 0.000 0.284
#> GSM680038 2 0.0000 0.93037 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM680050 4 0.3489 0.67472 0.004 0.000 0.000 0.708 0.000 0.288
#> GSM680039 2 0.0146 0.92861 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM680051 4 0.0363 0.70843 0.000 0.012 0.000 0.988 0.000 0.000
#> GSM680040 6 0.5192 0.00000 0.292 0.024 0.068 0.000 0.000 0.616
#> GSM680052 4 0.1720 0.68830 0.000 0.040 0.000 0.928 0.000 0.032
#> GSM680030 5 0.0632 0.97453 0.000 0.000 0.000 0.000 0.976 0.024
#> GSM680042 4 0.3938 0.65186 0.016 0.000 0.000 0.660 0.000 0.324
#> GSM680031 5 0.0146 0.97813 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM680043 3 0.0458 0.80739 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM680032 4 0.0458 0.70745 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM680044 4 0.2969 0.55664 0.000 0.224 0.000 0.776 0.000 0.000
#> GSM680033 5 0.0146 0.97813 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM680045 3 0.7182 -0.04064 0.048 0.028 0.448 0.216 0.000 0.260
#> GSM680034 5 0.0858 0.96760 0.000 0.000 0.004 0.000 0.968 0.028
#> GSM680046 1 0.0000 0.55900 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> ATC:mclust 0 NA NA NA NA 2
#> ATC:mclust 51 0.4544 0.428 4.20e-03 0.1690 3
#> ATC:mclust 44 0.0945 0.377 9.75e-04 0.0356 4
#> ATC:mclust 51 0.2023 0.631 2.23e-05 0.2267 5
#> ATC:mclust 49 0.3884 0.640 4.37e-05 0.1215 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 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 0.885 0.931 0.969 0.4774 0.516 0.516
#> 3 3 0.826 0.870 0.941 0.4101 0.764 0.562
#> 4 4 0.666 0.738 0.874 0.0816 0.936 0.806
#> 5 5 0.627 0.612 0.799 0.0715 0.843 0.508
#> 6 6 0.647 0.545 0.759 0.0437 0.929 0.695
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
#> GSM680053 2 0.0000 0.979 0.000 1.000
#> GSM680062 2 0.0000 0.979 0.000 1.000
#> GSM680054 2 0.0000 0.979 0.000 1.000
#> GSM680063 2 0.0000 0.979 0.000 1.000
#> GSM680055 2 0.0376 0.975 0.004 0.996
#> GSM680064 1 0.0000 0.946 1.000 0.000
#> GSM680056 2 0.9881 0.141 0.436 0.564
#> GSM680065 1 0.0000 0.946 1.000 0.000
#> GSM680057 2 0.0000 0.979 0.000 1.000
#> GSM680066 1 0.7376 0.772 0.792 0.208
#> GSM680058 2 0.0000 0.979 0.000 1.000
#> GSM680067 2 0.0000 0.979 0.000 1.000
#> GSM680059 2 0.0000 0.979 0.000 1.000
#> GSM680068 1 0.0000 0.946 1.000 0.000
#> GSM680060 1 0.1843 0.934 0.972 0.028
#> GSM680069 1 0.8327 0.689 0.736 0.264
#> GSM680061 2 0.0000 0.979 0.000 1.000
#> GSM680070 1 0.0000 0.946 1.000 0.000
#> GSM680071 1 0.0000 0.946 1.000 0.000
#> GSM680077 1 0.0000 0.946 1.000 0.000
#> GSM680072 2 0.0000 0.979 0.000 1.000
#> GSM680078 1 0.0000 0.946 1.000 0.000
#> GSM680073 2 0.0000 0.979 0.000 1.000
#> GSM680079 1 0.0000 0.946 1.000 0.000
#> GSM680074 2 0.0000 0.979 0.000 1.000
#> GSM680080 2 0.0000 0.979 0.000 1.000
#> GSM680075 1 0.0000 0.946 1.000 0.000
#> GSM680081 2 0.0000 0.979 0.000 1.000
#> GSM680076 2 0.0000 0.979 0.000 1.000
#> GSM680082 1 0.0000 0.946 1.000 0.000
#> GSM680029 2 0.0000 0.979 0.000 1.000
#> GSM680041 1 0.1184 0.940 0.984 0.016
#> GSM680035 2 0.0000 0.979 0.000 1.000
#> GSM680047 1 0.0000 0.946 1.000 0.000
#> GSM680036 1 0.3584 0.907 0.932 0.068
#> GSM680048 1 0.7950 0.728 0.760 0.240
#> GSM680037 2 0.0000 0.979 0.000 1.000
#> GSM680049 1 0.7056 0.791 0.808 0.192
#> GSM680038 2 0.0000 0.979 0.000 1.000
#> GSM680050 1 0.0938 0.942 0.988 0.012
#> GSM680039 2 0.0000 0.979 0.000 1.000
#> GSM680051 2 0.1414 0.960 0.020 0.980
#> GSM680040 2 0.0000 0.979 0.000 1.000
#> GSM680052 2 0.0000 0.979 0.000 1.000
#> GSM680030 2 0.0000 0.979 0.000 1.000
#> GSM680042 1 0.0000 0.946 1.000 0.000
#> GSM680031 2 0.0000 0.979 0.000 1.000
#> GSM680043 2 0.0000 0.979 0.000 1.000
#> GSM680032 2 0.6438 0.781 0.164 0.836
#> GSM680044 2 0.0000 0.979 0.000 1.000
#> GSM680033 2 0.0000 0.979 0.000 1.000
#> GSM680045 2 0.0000 0.979 0.000 1.000
#> GSM680034 2 0.0000 0.979 0.000 1.000
#> GSM680046 1 0.0000 0.946 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM680053 3 0.1289 0.921 0.000 0.032 0.968
#> GSM680062 2 0.1411 0.952 0.000 0.964 0.036
#> GSM680054 3 0.0237 0.936 0.000 0.004 0.996
#> GSM680063 3 0.4974 0.694 0.000 0.236 0.764
#> GSM680055 2 0.0237 0.978 0.000 0.996 0.004
#> GSM680064 1 0.0000 0.902 1.000 0.000 0.000
#> GSM680056 1 0.5706 0.536 0.680 0.000 0.320
#> GSM680065 1 0.0237 0.901 0.996 0.004 0.000
#> GSM680057 3 0.2066 0.900 0.000 0.060 0.940
#> GSM680066 1 0.2878 0.841 0.904 0.000 0.096
#> GSM680058 2 0.0000 0.977 0.000 1.000 0.000
#> GSM680067 3 0.0000 0.938 0.000 0.000 1.000
#> GSM680059 2 0.0237 0.978 0.000 0.996 0.004
#> GSM680068 1 0.0000 0.902 1.000 0.000 0.000
#> GSM680060 1 0.6180 0.300 0.584 0.416 0.000
#> GSM680069 1 0.6267 0.282 0.548 0.452 0.000
#> GSM680061 3 0.0000 0.938 0.000 0.000 1.000
#> GSM680070 1 0.0000 0.902 1.000 0.000 0.000
#> GSM680071 1 0.0237 0.901 0.996 0.004 0.000
#> GSM680077 1 0.0000 0.902 1.000 0.000 0.000
#> GSM680072 2 0.0237 0.978 0.000 0.996 0.004
#> GSM680078 1 0.0237 0.901 0.996 0.004 0.000
#> GSM680073 2 0.0000 0.977 0.000 1.000 0.000
#> GSM680079 1 0.0000 0.902 1.000 0.000 0.000
#> GSM680074 2 0.0237 0.978 0.000 0.996 0.004
#> GSM680080 2 0.0237 0.978 0.000 0.996 0.004
#> GSM680075 1 0.0592 0.898 0.988 0.012 0.000
#> GSM680081 3 0.0000 0.938 0.000 0.000 1.000
#> GSM680076 2 0.0000 0.977 0.000 1.000 0.000
#> GSM680082 1 0.0000 0.902 1.000 0.000 0.000
#> GSM680029 2 0.0000 0.977 0.000 1.000 0.000
#> GSM680041 1 0.4062 0.796 0.836 0.164 0.000
#> GSM680035 3 0.0000 0.938 0.000 0.000 1.000
#> GSM680047 1 0.0000 0.902 1.000 0.000 0.000
#> GSM680036 2 0.0000 0.977 0.000 1.000 0.000
#> GSM680048 1 0.3989 0.826 0.864 0.124 0.012
#> GSM680037 3 0.0000 0.938 0.000 0.000 1.000
#> GSM680049 1 0.4555 0.757 0.800 0.200 0.000
#> GSM680038 2 0.0237 0.978 0.000 0.996 0.004
#> GSM680050 1 0.2537 0.862 0.920 0.080 0.000
#> GSM680039 2 0.0747 0.970 0.000 0.984 0.016
#> GSM680051 3 0.7864 0.370 0.332 0.072 0.596
#> GSM680040 3 0.0000 0.938 0.000 0.000 1.000
#> GSM680052 3 0.0892 0.927 0.000 0.020 0.980
#> GSM680030 3 0.5397 0.631 0.000 0.280 0.720
#> GSM680042 1 0.0000 0.902 1.000 0.000 0.000
#> GSM680031 3 0.0000 0.938 0.000 0.000 1.000
#> GSM680043 3 0.0000 0.938 0.000 0.000 1.000
#> GSM680032 2 0.4784 0.711 0.200 0.796 0.004
#> GSM680044 2 0.0424 0.976 0.000 0.992 0.008
#> GSM680033 3 0.0000 0.938 0.000 0.000 1.000
#> GSM680045 3 0.0000 0.938 0.000 0.000 1.000
#> GSM680034 3 0.0000 0.938 0.000 0.000 1.000
#> GSM680046 1 0.0000 0.902 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM680053 3 0.2670 0.863 0.000 0.024 0.904 0.072
#> GSM680062 2 0.4388 0.774 0.000 0.808 0.060 0.132
#> GSM680054 3 0.0469 0.881 0.000 0.012 0.988 0.000
#> GSM680063 3 0.3074 0.764 0.000 0.152 0.848 0.000
#> GSM680055 2 0.2530 0.835 0.000 0.888 0.000 0.112
#> GSM680064 1 0.0000 0.808 1.000 0.000 0.000 0.000
#> GSM680056 1 0.5562 0.145 0.524 0.004 0.460 0.012
#> GSM680065 1 0.0000 0.808 1.000 0.000 0.000 0.000
#> GSM680057 3 0.1302 0.868 0.000 0.044 0.956 0.000
#> GSM680066 1 0.2197 0.793 0.936 0.024 0.028 0.012
#> GSM680058 2 0.0188 0.883 0.000 0.996 0.000 0.004
#> GSM680067 3 0.1452 0.869 0.000 0.036 0.956 0.008
#> GSM680059 2 0.0469 0.883 0.000 0.988 0.000 0.012
#> GSM680068 1 0.0336 0.806 0.992 0.000 0.000 0.008
#> GSM680060 4 0.5189 0.294 0.012 0.372 0.000 0.616
#> GSM680069 1 0.5183 0.366 0.584 0.408 0.000 0.008
#> GSM680061 3 0.0336 0.881 0.000 0.008 0.992 0.000
#> GSM680070 1 0.0336 0.807 0.992 0.000 0.000 0.008
#> GSM680071 1 0.1677 0.790 0.948 0.012 0.000 0.040
#> GSM680077 1 0.0000 0.808 1.000 0.000 0.000 0.000
#> GSM680072 2 0.0921 0.879 0.000 0.972 0.000 0.028
#> GSM680078 1 0.2216 0.768 0.908 0.000 0.000 0.092
#> GSM680073 2 0.1398 0.878 0.000 0.956 0.040 0.004
#> GSM680079 1 0.0000 0.808 1.000 0.000 0.000 0.000
#> GSM680074 2 0.1398 0.878 0.000 0.956 0.040 0.004
#> GSM680080 2 0.2081 0.855 0.000 0.916 0.000 0.084
#> GSM680075 1 0.5035 0.560 0.744 0.204 0.000 0.052
#> GSM680081 3 0.1792 0.870 0.000 0.000 0.932 0.068
#> GSM680076 2 0.2714 0.824 0.000 0.884 0.112 0.004
#> GSM680082 1 0.0000 0.808 1.000 0.000 0.000 0.000
#> GSM680029 2 0.1118 0.878 0.000 0.964 0.000 0.036
#> GSM680041 1 0.5070 0.632 0.748 0.192 0.000 0.060
#> GSM680035 3 0.1792 0.870 0.000 0.000 0.932 0.068
#> GSM680047 4 0.2530 0.652 0.112 0.000 0.000 0.888
#> GSM680036 2 0.1637 0.867 0.000 0.940 0.000 0.060
#> GSM680048 1 0.7250 0.140 0.504 0.160 0.000 0.336
#> GSM680037 3 0.2973 0.819 0.000 0.000 0.856 0.144
#> GSM680049 1 0.3933 0.665 0.792 0.200 0.000 0.008
#> GSM680038 2 0.1118 0.881 0.000 0.964 0.036 0.000
#> GSM680050 1 0.2859 0.752 0.880 0.112 0.000 0.008
#> GSM680039 2 0.1706 0.879 0.000 0.948 0.036 0.016
#> GSM680051 4 0.5182 0.661 0.024 0.112 0.076 0.788
#> GSM680040 4 0.4283 0.445 0.000 0.004 0.256 0.740
#> GSM680052 3 0.5148 0.599 0.000 0.208 0.736 0.056
#> GSM680030 3 0.2921 0.783 0.000 0.140 0.860 0.000
#> GSM680042 1 0.0817 0.805 0.976 0.024 0.000 0.000
#> GSM680031 3 0.0707 0.882 0.000 0.000 0.980 0.020
#> GSM680043 3 0.1940 0.870 0.000 0.000 0.924 0.076
#> GSM680032 2 0.6988 0.303 0.332 0.560 0.096 0.012
#> GSM680044 2 0.3052 0.796 0.000 0.860 0.136 0.004
#> GSM680033 3 0.0921 0.881 0.000 0.000 0.972 0.028
#> GSM680045 3 0.4830 0.484 0.000 0.000 0.608 0.392
#> GSM680034 3 0.0336 0.881 0.000 0.008 0.992 0.000
#> GSM680046 4 0.4790 0.343 0.380 0.000 0.000 0.620
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM680053 3 0.1285 0.918 0.000 0.004 0.956 0.004 0.036
#> GSM680062 2 0.5624 0.363 0.000 0.648 0.004 0.208 0.140
#> GSM680054 3 0.1012 0.920 0.000 0.020 0.968 0.000 0.012
#> GSM680063 2 0.4874 0.285 0.000 0.588 0.388 0.008 0.016
#> GSM680055 5 0.3837 0.569 0.020 0.156 0.008 0.008 0.808
#> GSM680064 1 0.0451 0.715 0.988 0.000 0.000 0.004 0.008
#> GSM680056 3 0.3897 0.705 0.204 0.000 0.768 0.000 0.028
#> GSM680065 1 0.0609 0.713 0.980 0.000 0.000 0.000 0.020
#> GSM680057 3 0.1630 0.912 0.000 0.036 0.944 0.004 0.016
#> GSM680066 1 0.6770 0.476 0.552 0.176 0.004 0.244 0.024
#> GSM680058 2 0.3766 0.280 0.000 0.728 0.004 0.000 0.268
#> GSM680067 2 0.5878 0.278 0.004 0.596 0.320 0.056 0.024
#> GSM680059 2 0.2471 0.550 0.000 0.864 0.000 0.000 0.136
#> GSM680068 1 0.3282 0.667 0.804 0.000 0.000 0.188 0.008
#> GSM680060 5 0.2104 0.506 0.000 0.060 0.000 0.024 0.916
#> GSM680069 1 0.5354 0.483 0.644 0.272 0.000 0.004 0.080
#> GSM680061 3 0.3815 0.699 0.000 0.220 0.764 0.004 0.012
#> GSM680070 1 0.4336 0.576 0.700 0.012 0.000 0.280 0.008
#> GSM680071 1 0.4588 0.417 0.668 0.012 0.000 0.012 0.308
#> GSM680077 1 0.1502 0.716 0.940 0.000 0.000 0.056 0.004
#> GSM680072 5 0.4307 0.390 0.000 0.496 0.000 0.000 0.504
#> GSM680078 1 0.5008 0.496 0.644 0.000 0.000 0.056 0.300
#> GSM680073 2 0.1484 0.630 0.000 0.944 0.008 0.000 0.048
#> GSM680079 1 0.0290 0.715 0.992 0.000 0.000 0.000 0.008
#> GSM680074 2 0.1205 0.632 0.000 0.956 0.004 0.000 0.040
#> GSM680080 5 0.4527 0.477 0.000 0.392 0.000 0.012 0.596
#> GSM680075 5 0.4707 0.179 0.392 0.020 0.000 0.000 0.588
#> GSM680081 3 0.0671 0.922 0.000 0.000 0.980 0.016 0.004
#> GSM680076 2 0.0162 0.633 0.000 0.996 0.000 0.000 0.004
#> GSM680082 1 0.1502 0.717 0.940 0.004 0.000 0.056 0.000
#> GSM680029 5 0.4452 0.371 0.000 0.496 0.004 0.000 0.500
#> GSM680041 1 0.7253 0.293 0.496 0.172 0.000 0.276 0.056
#> GSM680035 3 0.0771 0.922 0.000 0.000 0.976 0.020 0.004
#> GSM680047 4 0.2763 0.695 0.004 0.000 0.000 0.848 0.148
#> GSM680036 5 0.4651 0.540 0.020 0.372 0.000 0.000 0.608
#> GSM680048 4 0.4681 0.659 0.084 0.188 0.000 0.728 0.000
#> GSM680037 3 0.0771 0.922 0.000 0.000 0.976 0.020 0.004
#> GSM680049 1 0.6775 0.230 0.432 0.388 0.004 0.168 0.008
#> GSM680038 2 0.1557 0.629 0.000 0.940 0.008 0.000 0.052
#> GSM680050 1 0.3648 0.653 0.792 0.188 0.000 0.016 0.004
#> GSM680039 2 0.4407 0.410 0.000 0.724 0.012 0.020 0.244
#> GSM680051 4 0.2773 0.728 0.000 0.112 0.000 0.868 0.020
#> GSM680040 3 0.4057 0.777 0.000 0.000 0.792 0.120 0.088
#> GSM680052 4 0.5046 0.245 0.000 0.432 0.020 0.540 0.008
#> GSM680030 3 0.1597 0.909 0.000 0.048 0.940 0.000 0.012
#> GSM680042 1 0.3497 0.684 0.836 0.048 0.000 0.112 0.004
#> GSM680031 3 0.0324 0.924 0.000 0.004 0.992 0.004 0.000
#> GSM680043 3 0.1281 0.917 0.000 0.000 0.956 0.032 0.012
#> GSM680032 2 0.4460 0.180 0.392 0.600 0.004 0.000 0.004
#> GSM680044 2 0.1314 0.623 0.000 0.960 0.012 0.016 0.012
#> GSM680033 3 0.0854 0.924 0.000 0.012 0.976 0.008 0.004
#> GSM680045 4 0.1834 0.706 0.008 0.004 0.032 0.940 0.016
#> GSM680034 3 0.0671 0.924 0.000 0.016 0.980 0.000 0.004
#> GSM680046 4 0.3885 0.638 0.176 0.000 0.000 0.784 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM680053 3 0.2625 0.83699 0.000 0.000 0.872 0.000 0.056 0.072
#> GSM680062 4 0.5417 0.24150 0.000 0.428 0.004 0.496 0.028 0.044
#> GSM680054 3 0.1332 0.87366 0.000 0.012 0.952 0.000 0.008 0.028
#> GSM680063 2 0.5054 0.24146 0.000 0.628 0.296 0.012 0.008 0.056
#> GSM680055 5 0.4383 0.49221 0.004 0.052 0.052 0.020 0.796 0.076
#> GSM680064 1 0.0713 0.60210 0.972 0.000 0.000 0.028 0.000 0.000
#> GSM680056 3 0.5326 0.58675 0.160 0.000 0.664 0.000 0.032 0.144
#> GSM680065 1 0.0405 0.60418 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM680057 3 0.1218 0.87419 0.000 0.028 0.956 0.000 0.004 0.012
#> GSM680066 6 0.5019 0.41324 0.176 0.076 0.000 0.012 0.028 0.708
#> GSM680058 2 0.4881 0.24669 0.000 0.588 0.000 0.000 0.336 0.076
#> GSM680067 6 0.5059 0.50288 0.004 0.168 0.176 0.000 0.000 0.652
#> GSM680059 2 0.4854 0.52817 0.000 0.664 0.000 0.000 0.152 0.184
#> GSM680068 1 0.4289 0.43830 0.680 0.000 0.000 0.040 0.004 0.276
#> GSM680060 5 0.2551 0.52140 0.004 0.012 0.000 0.004 0.872 0.108
#> GSM680069 1 0.7190 0.00361 0.404 0.108 0.000 0.000 0.204 0.284
#> GSM680061 3 0.4140 0.64926 0.000 0.152 0.744 0.000 0.000 0.104
#> GSM680070 1 0.5112 0.28884 0.580 0.028 0.000 0.032 0.004 0.356
#> GSM680071 1 0.5691 0.21925 0.504 0.016 0.000 0.000 0.372 0.108
#> GSM680077 1 0.2814 0.54961 0.820 0.000 0.000 0.000 0.008 0.172
#> GSM680072 5 0.4443 0.39946 0.000 0.368 0.000 0.000 0.596 0.036
#> GSM680078 1 0.5932 0.21923 0.444 0.000 0.000 0.124 0.412 0.020
#> GSM680073 2 0.1391 0.70294 0.000 0.944 0.000 0.000 0.040 0.016
#> GSM680079 1 0.0260 0.60477 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM680074 2 0.3413 0.66607 0.000 0.812 0.000 0.000 0.080 0.108
#> GSM680080 5 0.5649 0.41938 0.000 0.232 0.000 0.000 0.536 0.232
#> GSM680075 5 0.3543 0.39722 0.248 0.004 0.000 0.004 0.740 0.004
#> GSM680081 3 0.2118 0.85611 0.000 0.000 0.888 0.000 0.008 0.104
#> GSM680076 2 0.1812 0.69734 0.000 0.912 0.000 0.000 0.008 0.080
#> GSM680082 1 0.1049 0.60222 0.960 0.000 0.000 0.008 0.000 0.032
#> GSM680029 5 0.4217 0.17476 0.000 0.464 0.000 0.004 0.524 0.008
#> GSM680041 4 0.6127 0.56220 0.216 0.108 0.000 0.604 0.012 0.060
#> GSM680035 3 0.1444 0.86878 0.000 0.000 0.928 0.000 0.000 0.072
#> GSM680047 4 0.1088 0.59422 0.000 0.000 0.000 0.960 0.024 0.016
#> GSM680036 5 0.4039 0.56182 0.016 0.248 0.000 0.004 0.720 0.012
#> GSM680048 4 0.4110 0.64123 0.052 0.148 0.000 0.772 0.000 0.028
#> GSM680037 3 0.1267 0.87141 0.000 0.000 0.940 0.000 0.000 0.060
#> GSM680049 4 0.6824 0.22439 0.324 0.312 0.008 0.332 0.000 0.024
#> GSM680038 2 0.1152 0.70138 0.000 0.952 0.000 0.000 0.044 0.004
#> GSM680050 1 0.4128 0.53091 0.780 0.140 0.000 0.040 0.004 0.036
#> GSM680039 2 0.4962 0.51961 0.000 0.684 0.020 0.032 0.236 0.028
#> GSM680051 4 0.1542 0.63068 0.000 0.052 0.004 0.936 0.000 0.008
#> GSM680040 3 0.4491 0.73719 0.000 0.000 0.744 0.048 0.048 0.160
#> GSM680052 4 0.4951 0.40755 0.000 0.384 0.016 0.560 0.000 0.040
#> GSM680030 3 0.2186 0.85806 0.000 0.048 0.908 0.000 0.008 0.036
#> GSM680042 1 0.4241 0.06995 0.608 0.024 0.000 0.368 0.000 0.000
#> GSM680031 3 0.0260 0.87716 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM680043 3 0.2300 0.83435 0.000 0.000 0.856 0.000 0.000 0.144
#> GSM680032 1 0.4671 0.02891 0.496 0.476 0.004 0.004 0.008 0.012
#> GSM680044 2 0.2288 0.66229 0.000 0.896 0.000 0.072 0.004 0.028
#> GSM680033 3 0.0260 0.87787 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM680045 4 0.4107 0.41764 0.004 0.000 0.028 0.688 0.000 0.280
#> GSM680034 3 0.0909 0.87630 0.000 0.020 0.968 0.000 0.000 0.012
#> GSM680046 4 0.3130 0.59661 0.144 0.000 0.000 0.824 0.004 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 3)
get_signatures(res, k = 4)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 5)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
get_signatures(res, k = 6)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) protocol(p) other(p) k
#> ATC:NMF 53 0.569 0.591 1.12e-03 0.6170 2
#> ATC:NMF 51 0.373 0.420 3.80e-04 0.1093 3
#> ATC:NMF 46 0.155 0.707 9.82e-04 0.1208 4
#> ATC:NMF 37 0.060 0.707 2.24e-05 0.0869 5
#> ATC:NMF 35 0.106 0.437 1.74e-04 0.1049 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