Date: 2019-12-25 20:17:15 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 17209 rows and 59 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] 17209 59
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 | ||
|---|---|---|---|---|---|
| ATC:kmeans | 2 | 1.000 | 0.956 | 0.983 | ** |
| ATC:pam | 2 | 1.000 | 0.959 | 0.985 | ** |
| CV:mclust | 3 | 0.954 | 0.924 | 0.947 | ** |
| ATC:mclust | 5 | 0.917 | 0.860 | 0.943 | * |
| ATC:skmeans | 2 | 0.897 | 0.929 | 0.970 | |
| MAD:pam | 5 | 0.849 | 0.833 | 0.930 | |
| CV:skmeans | 3 | 0.846 | 0.903 | 0.954 | |
| MAD:mclust | 5 | 0.829 | 0.817 | 0.901 | |
| CV:pam | 2 | 0.802 | 0.905 | 0.962 | |
| CV:kmeans | 3 | 0.794 | 0.884 | 0.931 | |
| SD:pam | 5 | 0.786 | 0.781 | 0.910 | |
| MAD:skmeans | 3 | 0.747 | 0.819 | 0.919 | |
| SD:mclust | 5 | 0.720 | 0.697 | 0.856 | |
| SD:skmeans | 4 | 0.710 | 0.785 | 0.893 | |
| ATC:hclust | 2 | 0.628 | 0.693 | 0.886 | |
| ATC:NMF | 3 | 0.626 | 0.701 | 0.886 | |
| SD:NMF | 4 | 0.608 | 0.735 | 0.830 | |
| MAD:kmeans | 2 | 0.574 | 0.784 | 0.897 | |
| CV:hclust | 2 | 0.504 | 0.814 | 0.903 | |
| SD:kmeans | 2 | 0.488 | 0.662 | 0.865 | |
| MAD:NMF | 2 | 0.486 | 0.864 | 0.896 | |
| CV:NMF | 2 | 0.453 | 0.695 | 0.870 | |
| MAD:hclust | 2 | 0.395 | 0.798 | 0.883 | |
| SD:hclust | 2 | 0.231 | 0.719 | 0.834 |
**: 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 0.367 0.710 0.819 0.487 0.492 0.492
#> CV:NMF 2 0.453 0.695 0.870 0.488 0.492 0.492
#> MAD:NMF 2 0.486 0.864 0.896 0.494 0.493 0.493
#> ATC:NMF 2 0.711 0.863 0.934 0.381 0.583 0.583
#> SD:skmeans 2 0.537 0.650 0.874 0.507 0.492 0.492
#> CV:skmeans 2 0.633 0.820 0.923 0.503 0.495 0.495
#> MAD:skmeans 2 0.578 0.741 0.887 0.507 0.493 0.493
#> ATC:skmeans 2 0.897 0.929 0.970 0.500 0.503 0.503
#> SD:mclust 2 0.251 0.648 0.801 0.407 0.614 0.614
#> CV:mclust 2 0.349 0.610 0.832 0.405 0.583 0.583
#> MAD:mclust 2 0.219 0.678 0.769 0.457 0.544 0.544
#> ATC:mclust 2 0.569 0.823 0.929 0.235 0.842 0.842
#> SD:kmeans 2 0.488 0.662 0.865 0.501 0.493 0.493
#> CV:kmeans 2 0.635 0.783 0.900 0.486 0.499 0.499
#> MAD:kmeans 2 0.574 0.784 0.897 0.502 0.503 0.503
#> ATC:kmeans 2 1.000 0.956 0.983 0.488 0.516 0.516
#> SD:pam 2 0.311 0.521 0.816 0.403 0.614 0.614
#> CV:pam 2 0.802 0.905 0.962 0.462 0.544 0.544
#> MAD:pam 2 0.224 0.183 0.628 0.433 0.534 0.534
#> ATC:pam 2 1.000 0.959 0.985 0.490 0.509 0.509
#> SD:hclust 2 0.231 0.719 0.834 0.454 0.516 0.516
#> CV:hclust 2 0.504 0.814 0.903 0.454 0.534 0.534
#> MAD:hclust 2 0.395 0.798 0.883 0.455 0.544 0.544
#> ATC:hclust 2 0.628 0.693 0.886 0.470 0.524 0.524
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.427 0.619 0.770 0.371 0.681 0.438
#> CV:NMF 3 0.489 0.725 0.860 0.307 0.749 0.537
#> MAD:NMF 3 0.492 0.733 0.839 0.356 0.695 0.456
#> ATC:NMF 3 0.626 0.701 0.886 0.529 0.786 0.643
#> SD:skmeans 3 0.593 0.503 0.781 0.319 0.739 0.543
#> CV:skmeans 3 0.846 0.903 0.954 0.304 0.696 0.466
#> MAD:skmeans 3 0.747 0.819 0.919 0.327 0.750 0.532
#> ATC:skmeans 3 0.743 0.800 0.875 0.251 0.811 0.637
#> SD:mclust 3 0.473 0.590 0.817 0.516 0.663 0.482
#> CV:mclust 3 0.954 0.924 0.947 0.586 0.684 0.496
#> MAD:mclust 3 0.384 0.610 0.769 0.344 0.821 0.685
#> ATC:mclust 3 0.286 0.245 0.628 1.508 0.476 0.426
#> SD:kmeans 3 0.458 0.593 0.794 0.307 0.704 0.476
#> CV:kmeans 3 0.794 0.884 0.931 0.338 0.730 0.518
#> MAD:kmeans 3 0.461 0.626 0.806 0.322 0.658 0.419
#> ATC:kmeans 3 0.707 0.844 0.905 0.362 0.711 0.489
#> SD:pam 3 0.619 0.625 0.847 0.415 0.783 0.662
#> CV:pam 3 0.682 0.813 0.901 0.359 0.820 0.669
#> MAD:pam 3 0.626 0.714 0.849 0.391 0.609 0.410
#> ATC:pam 3 0.864 0.861 0.948 0.304 0.695 0.483
#> SD:hclust 3 0.386 0.671 0.775 0.388 0.743 0.533
#> CV:hclust 3 0.662 0.809 0.895 0.409 0.741 0.552
#> MAD:hclust 3 0.499 0.776 0.849 0.431 0.745 0.548
#> ATC:hclust 3 0.546 0.755 0.828 0.359 0.707 0.487
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.608 0.735 0.830 0.1185 0.812 0.505
#> CV:NMF 4 0.401 0.516 0.691 0.1387 0.824 0.550
#> MAD:NMF 4 0.600 0.720 0.806 0.1167 0.833 0.553
#> ATC:NMF 4 0.473 0.560 0.785 0.1738 0.841 0.638
#> SD:skmeans 4 0.710 0.785 0.893 0.1168 0.819 0.559
#> CV:skmeans 4 0.852 0.871 0.939 0.1303 0.857 0.616
#> MAD:skmeans 4 0.692 0.712 0.865 0.1124 0.848 0.581
#> ATC:skmeans 4 0.813 0.819 0.924 0.1045 0.822 0.572
#> SD:mclust 4 0.469 0.503 0.778 0.1481 0.742 0.420
#> CV:mclust 4 0.745 0.818 0.848 0.1033 0.889 0.708
#> MAD:mclust 4 0.527 0.637 0.807 0.1668 0.679 0.370
#> ATC:mclust 4 0.700 0.760 0.868 0.2643 0.732 0.447
#> SD:kmeans 4 0.607 0.681 0.823 0.1292 0.798 0.490
#> CV:kmeans 4 0.690 0.662 0.780 0.1294 0.850 0.597
#> MAD:kmeans 4 0.582 0.633 0.813 0.1212 0.843 0.580
#> ATC:kmeans 4 0.654 0.719 0.788 0.1178 0.880 0.654
#> SD:pam 4 0.708 0.787 0.892 0.2358 0.802 0.583
#> CV:pam 4 0.662 0.700 0.855 0.0809 0.879 0.707
#> MAD:pam 4 0.718 0.832 0.900 0.2104 0.827 0.587
#> ATC:pam 4 0.647 0.669 0.840 0.1212 0.899 0.730
#> SD:hclust 4 0.519 0.573 0.752 0.1361 0.957 0.873
#> CV:hclust 4 0.641 0.741 0.814 0.1162 0.910 0.754
#> MAD:hclust 4 0.579 0.711 0.800 0.0981 0.964 0.895
#> ATC:hclust 4 0.580 0.695 0.804 0.1224 0.936 0.802
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.658 0.639 0.805 0.0599 0.933 0.746
#> CV:NMF 5 0.452 0.439 0.678 0.0737 0.821 0.461
#> MAD:NMF 5 0.664 0.670 0.811 0.0562 0.950 0.810
#> ATC:NMF 5 0.442 0.373 0.694 0.0871 0.937 0.818
#> SD:skmeans 5 0.657 0.555 0.767 0.0728 0.876 0.561
#> CV:skmeans 5 0.758 0.683 0.802 0.0595 0.959 0.850
#> MAD:skmeans 5 0.674 0.605 0.766 0.0703 0.859 0.522
#> ATC:skmeans 5 0.791 0.852 0.887 0.0429 0.926 0.763
#> SD:mclust 5 0.720 0.697 0.856 0.0803 0.842 0.526
#> CV:mclust 5 0.775 0.752 0.851 0.0876 0.935 0.785
#> MAD:mclust 5 0.829 0.817 0.901 0.0874 0.883 0.625
#> ATC:mclust 5 0.917 0.860 0.943 0.0766 0.870 0.545
#> SD:kmeans 5 0.641 0.481 0.691 0.0721 0.901 0.638
#> CV:kmeans 5 0.703 0.573 0.750 0.0755 0.910 0.680
#> MAD:kmeans 5 0.644 0.450 0.652 0.0713 0.907 0.669
#> ATC:kmeans 5 0.658 0.579 0.692 0.0629 1.000 1.000
#> SD:pam 5 0.786 0.781 0.910 0.1146 0.888 0.639
#> CV:pam 5 0.636 0.623 0.762 0.1228 0.845 0.572
#> MAD:pam 5 0.849 0.833 0.930 0.0867 0.901 0.651
#> ATC:pam 5 0.860 0.807 0.924 0.0808 0.886 0.628
#> SD:hclust 5 0.572 0.509 0.730 0.0775 0.904 0.697
#> CV:hclust 5 0.679 0.710 0.820 0.0664 0.955 0.838
#> MAD:hclust 5 0.617 0.619 0.757 0.0779 0.905 0.703
#> ATC:hclust 5 0.632 0.603 0.764 0.0630 0.901 0.671
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.655 0.482 0.716 0.0393 0.896 0.598
#> CV:NMF 6 0.521 0.395 0.623 0.0408 0.888 0.553
#> MAD:NMF 6 0.649 0.507 0.740 0.0391 0.944 0.768
#> ATC:NMF 6 0.479 0.435 0.636 0.0424 0.944 0.823
#> SD:skmeans 6 0.678 0.509 0.725 0.0448 0.935 0.688
#> CV:skmeans 6 0.739 0.534 0.720 0.0392 0.899 0.635
#> MAD:skmeans 6 0.700 0.542 0.759 0.0446 0.904 0.576
#> ATC:skmeans 6 0.831 0.842 0.896 0.0337 0.991 0.965
#> SD:mclust 6 0.705 0.559 0.785 0.0769 0.859 0.476
#> CV:mclust 6 0.806 0.699 0.846 0.0748 0.884 0.564
#> MAD:mclust 6 0.788 0.716 0.816 0.0606 0.944 0.745
#> ATC:mclust 6 0.843 0.804 0.912 0.0224 0.950 0.768
#> SD:kmeans 6 0.667 0.558 0.749 0.0418 0.915 0.632
#> CV:kmeans 6 0.683 0.563 0.712 0.0463 0.875 0.532
#> MAD:kmeans 6 0.683 0.554 0.696 0.0407 0.892 0.563
#> ATC:kmeans 6 0.706 0.598 0.738 0.0427 0.828 0.419
#> SD:pam 6 0.784 0.785 0.887 0.0368 0.961 0.820
#> CV:pam 6 0.702 0.760 0.845 0.0600 0.926 0.689
#> MAD:pam 6 0.846 0.815 0.902 0.0316 0.965 0.834
#> ATC:pam 6 0.873 0.856 0.927 0.0609 0.853 0.463
#> SD:hclust 6 0.627 0.532 0.699 0.0534 0.885 0.570
#> CV:hclust 6 0.712 0.611 0.788 0.0446 0.924 0.707
#> MAD:hclust 6 0.673 0.685 0.788 0.0611 0.932 0.712
#> ATC:hclust 6 0.676 0.654 0.759 0.0483 0.905 0.637
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) specimen(p) k
#> SD:NMF 58 0.7783 0.299 2
#> CV:NMF 48 1.0000 1.000 2
#> MAD:NMF 58 0.7783 0.299 2
#> ATC:NMF 56 1.0000 0.854 2
#> SD:skmeans 42 0.1959 0.129 2
#> CV:skmeans 49 0.8363 0.468 2
#> MAD:skmeans 45 0.1683 0.145 2
#> ATC:skmeans 56 0.5626 0.318 2
#> SD:mclust 53 0.1752 1.000 2
#> CV:mclust 41 0.0692 0.617 2
#> MAD:mclust 58 0.4573 1.000 2
#> ATC:mclust 53 0.3249 0.738 2
#> SD:kmeans 43 0.1502 0.146 2
#> CV:kmeans 52 0.9132 0.567 2
#> MAD:kmeans 54 0.1755 0.246 2
#> ATC:kmeans 57 0.6664 0.402 2
#> SD:pam 32 0.5032 1.000 2
#> CV:pam 57 1.0000 0.700 2
#> MAD:pam 0 NA NA 2
#> ATC:pam 57 0.6664 0.402 2
#> SD:hclust 54 1.0000 0.713 2
#> CV:hclust 54 1.0000 0.699 2
#> MAD:hclust 54 1.0000 0.610 2
#> ATC:hclust 45 1.0000 0.675 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) specimen(p) k
#> SD:NMF 49 0.20082 0.126 3
#> CV:NMF 53 0.12288 0.217 3
#> MAD:NMF 54 0.31690 0.188 3
#> ATC:NMF 47 0.04984 0.220 3
#> SD:skmeans 43 0.00283 0.302 3
#> CV:skmeans 57 0.06974 0.262 3
#> MAD:skmeans 53 0.23331 0.171 3
#> ATC:skmeans 53 0.25971 0.419 3
#> SD:mclust 41 0.08799 0.431 3
#> CV:mclust 58 0.10430 0.355 3
#> MAD:mclust 47 0.07645 0.575 3
#> ATC:mclust 29 1.00000 1.000 3
#> SD:kmeans 41 0.01581 0.263 3
#> CV:kmeans 56 0.10325 0.405 3
#> MAD:kmeans 51 0.16779 0.252 3
#> ATC:kmeans 57 0.93000 0.516 3
#> SD:pam 44 0.01500 0.827 3
#> CV:pam 56 0.23776 0.411 3
#> MAD:pam 54 0.00286 0.677 3
#> ATC:pam 53 0.42471 0.157 3
#> SD:hclust 47 0.11161 0.194 3
#> CV:hclust 54 0.16428 0.333 3
#> MAD:hclust 56 0.15106 0.177 3
#> ATC:hclust 51 0.76150 0.392 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) specimen(p) k
#> SD:NMF 53 0.01395 0.306 4
#> CV:NMF 44 0.24887 0.992 4
#> MAD:NMF 51 0.00239 0.320 4
#> ATC:NMF 43 0.33043 0.665 4
#> SD:skmeans 56 0.00530 0.249 4
#> CV:skmeans 56 0.14766 0.697 4
#> MAD:skmeans 53 0.01834 0.285 4
#> ATC:skmeans 51 0.20447 0.421 4
#> SD:mclust 39 0.00689 0.187 4
#> CV:mclust 56 0.20813 0.373 4
#> MAD:mclust 47 0.02422 0.446 4
#> ATC:mclust 51 0.13970 0.425 4
#> SD:kmeans 49 0.02034 0.353 4
#> CV:kmeans 48 0.20824 0.586 4
#> MAD:kmeans 49 0.06572 0.127 4
#> ATC:kmeans 53 0.55553 0.588 4
#> SD:pam 54 0.00831 0.419 4
#> CV:pam 51 0.27543 0.801 4
#> MAD:pam 56 0.03049 0.332 4
#> ATC:pam 49 0.26909 0.311 4
#> SD:hclust 44 0.17095 0.429 4
#> CV:hclust 54 0.23142 0.215 4
#> MAD:hclust 53 0.27719 0.378 4
#> ATC:hclust 45 0.70405 0.435 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) specimen(p) k
#> SD:NMF 49 0.04613 0.2670 5
#> CV:NMF 29 0.00535 0.4177 5
#> MAD:NMF 50 0.01015 0.2645 5
#> ATC:NMF 23 0.15132 0.8113 5
#> SD:skmeans 39 0.01905 0.4615 5
#> CV:skmeans 51 0.25312 0.6276 5
#> MAD:skmeans 45 0.00669 0.5665 5
#> ATC:skmeans 55 0.41176 0.6884 5
#> SD:mclust 49 0.14885 0.6020 5
#> CV:mclust 53 0.08373 0.6348 5
#> MAD:mclust 56 0.15770 0.5686 5
#> ATC:mclust 54 0.14289 0.1676 5
#> SD:kmeans 32 0.01414 0.4465 5
#> CV:kmeans 43 0.23882 0.4138 5
#> MAD:kmeans 35 0.08006 0.0218 5
#> ATC:kmeans 49 0.40417 0.3665 5
#> SD:pam 52 0.04739 0.3046 5
#> CV:pam 47 0.07121 0.7144 5
#> MAD:pam 53 0.15548 0.5616 5
#> ATC:pam 53 0.05764 0.2668 5
#> SD:hclust 38 0.31665 0.5597 5
#> CV:hclust 53 0.16880 0.0750 5
#> MAD:hclust 42 0.48669 0.1636 5
#> ATC:hclust 41 0.79051 0.6650 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) specimen(p) k
#> SD:NMF 38 0.06174 0.1286 6
#> CV:NMF 23 0.00638 0.0558 6
#> MAD:NMF 38 0.01317 0.1085 6
#> ATC:NMF 21 0.35464 0.8858 6
#> SD:skmeans 34 0.02061 0.0168 6
#> CV:skmeans 39 0.38588 0.6324 6
#> MAD:skmeans 38 0.01668 0.0942 6
#> ATC:skmeans 55 0.52037 0.6252 6
#> SD:mclust 39 0.03389 0.6479 6
#> CV:mclust 48 0.08709 0.2328 6
#> MAD:mclust 54 0.17980 0.1101 6
#> ATC:mclust 52 0.08807 0.2008 6
#> SD:kmeans 42 0.01870 0.0895 6
#> CV:kmeans 37 0.08576 0.2991 6
#> MAD:kmeans 40 0.01184 0.0595 6
#> ATC:kmeans 46 0.16994 0.5912 6
#> SD:pam 54 0.11488 0.3386 6
#> CV:pam 55 0.04053 0.5000 6
#> MAD:pam 55 0.19700 0.6693 6
#> ATC:pam 58 0.13827 0.5340 6
#> SD:hclust 39 0.10269 0.5210 6
#> CV:hclust 39 0.11504 0.3458 6
#> MAD:hclust 51 0.03818 0.5755 6
#> ATC:hclust 47 0.18081 0.7447 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 17209 rows and 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.231 0.719 0.834 0.4541 0.516 0.516
#> 3 3 0.386 0.671 0.775 0.3881 0.743 0.533
#> 4 4 0.519 0.573 0.752 0.1361 0.957 0.873
#> 5 5 0.572 0.509 0.730 0.0775 0.904 0.697
#> 6 6 0.627 0.532 0.699 0.0534 0.885 0.570
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
#> GSM110395 2 0.5946 0.8232 0.144 0.856
#> GSM110396 1 0.5519 0.7827 0.872 0.128
#> GSM110397 1 0.4939 0.7775 0.892 0.108
#> GSM110398 2 0.1184 0.8501 0.016 0.984
#> GSM110399 2 0.2236 0.8484 0.036 0.964
#> GSM110400 2 0.6247 0.8132 0.156 0.844
#> GSM110401 1 0.4431 0.7762 0.908 0.092
#> GSM110406 2 0.2236 0.8484 0.036 0.964
#> GSM110407 1 0.5178 0.7798 0.884 0.116
#> GSM110409 1 0.9522 0.6408 0.628 0.372
#> GSM110410 2 0.0000 0.8517 0.000 1.000
#> GSM110413 2 0.0000 0.8517 0.000 1.000
#> GSM110414 2 0.4431 0.8212 0.092 0.908
#> GSM110415 2 0.6438 0.8101 0.164 0.836
#> GSM110416 2 0.8555 0.7068 0.280 0.720
#> GSM110418 2 0.8555 0.7068 0.280 0.720
#> GSM110419 2 0.8207 0.7230 0.256 0.744
#> GSM110420 1 0.9988 -0.0500 0.520 0.480
#> GSM110421 2 0.0000 0.8517 0.000 1.000
#> GSM110423 2 0.6247 0.8132 0.156 0.844
#> GSM110424 2 0.0000 0.8517 0.000 1.000
#> GSM110425 2 0.8207 0.7230 0.256 0.744
#> GSM110427 2 0.6048 0.8212 0.148 0.852
#> GSM110428 1 0.7219 0.7120 0.800 0.200
#> GSM110430 1 0.4431 0.7762 0.908 0.092
#> GSM110431 1 0.6887 0.7341 0.816 0.184
#> GSM110432 2 0.8207 0.7230 0.256 0.744
#> GSM110434 2 0.1414 0.8516 0.020 0.980
#> GSM110435 1 0.5842 0.7313 0.860 0.140
#> GSM110437 1 0.4431 0.7762 0.908 0.092
#> GSM110438 1 0.8608 0.5787 0.716 0.284
#> GSM110388 1 0.9963 0.4970 0.536 0.464
#> GSM110392 2 0.9963 -0.1146 0.464 0.536
#> GSM110394 1 0.5294 0.7796 0.880 0.120
#> GSM110402 2 0.8499 0.7120 0.276 0.724
#> GSM110411 1 0.9954 0.5028 0.540 0.460
#> GSM110412 2 0.1414 0.8407 0.020 0.980
#> GSM110417 1 0.5737 0.7736 0.864 0.136
#> GSM110422 2 0.1843 0.8512 0.028 0.972
#> GSM110426 1 0.5178 0.7765 0.884 0.116
#> GSM110429 2 0.1843 0.8512 0.028 0.972
#> GSM110433 2 0.0000 0.8517 0.000 1.000
#> GSM110436 2 0.6048 0.8188 0.148 0.852
#> GSM110440 1 0.5519 0.7521 0.872 0.128
#> GSM110441 2 0.0000 0.8517 0.000 1.000
#> GSM110444 1 0.9954 0.5028 0.540 0.460
#> GSM110445 1 0.7674 0.7530 0.776 0.224
#> GSM110446 1 1.0000 0.0675 0.500 0.500
#> GSM110449 2 0.0000 0.8517 0.000 1.000
#> GSM110451 2 0.8144 0.7275 0.252 0.748
#> GSM110391 2 0.0000 0.8517 0.000 1.000
#> GSM110439 2 0.0672 0.8517 0.008 0.992
#> GSM110442 2 0.0376 0.8522 0.004 0.996
#> GSM110443 2 0.9635 0.2558 0.388 0.612
#> GSM110447 2 0.8661 0.6866 0.288 0.712
#> GSM110448 1 0.9954 0.5028 0.540 0.460
#> GSM110450 1 0.5059 0.7825 0.888 0.112
#> GSM110452 2 0.0000 0.8517 0.000 1.000
#> GSM110453 2 0.1843 0.8512 0.028 0.972
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 3 0.6102 0.6195 0.008 0.320 0.672
#> GSM110396 1 0.4256 0.7138 0.868 0.036 0.096
#> GSM110397 1 0.2261 0.7059 0.932 0.000 0.068
#> GSM110398 2 0.1182 0.8453 0.012 0.976 0.012
#> GSM110399 2 0.2550 0.8410 0.024 0.936 0.040
#> GSM110400 3 0.4842 0.7418 0.000 0.224 0.776
#> GSM110401 1 0.2537 0.7127 0.920 0.000 0.080
#> GSM110406 2 0.2550 0.8410 0.024 0.936 0.040
#> GSM110407 1 0.4002 0.6805 0.840 0.000 0.160
#> GSM110409 1 0.6975 0.5184 0.616 0.356 0.028
#> GSM110410 2 0.3340 0.8377 0.000 0.880 0.120
#> GSM110413 2 0.1015 0.8419 0.012 0.980 0.008
#> GSM110414 3 0.5797 0.6510 0.008 0.280 0.712
#> GSM110415 3 0.5360 0.7539 0.012 0.220 0.768
#> GSM110416 3 0.7297 0.8110 0.108 0.188 0.704
#> GSM110418 3 0.7297 0.8110 0.108 0.188 0.704
#> GSM110419 3 0.7899 0.8055 0.144 0.192 0.664
#> GSM110420 3 0.4002 0.5184 0.160 0.000 0.840
#> GSM110421 2 0.1482 0.8401 0.012 0.968 0.020
#> GSM110423 3 0.4842 0.7418 0.000 0.224 0.776
#> GSM110424 2 0.3340 0.8377 0.000 0.880 0.120
#> GSM110425 3 0.7899 0.8055 0.144 0.192 0.664
#> GSM110427 2 0.6483 0.3662 0.008 0.600 0.392
#> GSM110428 1 0.6745 0.3605 0.560 0.012 0.428
#> GSM110430 1 0.2537 0.7127 0.920 0.000 0.080
#> GSM110431 1 0.6095 0.4263 0.608 0.000 0.392
#> GSM110432 3 0.8113 0.8018 0.144 0.212 0.644
#> GSM110434 2 0.2955 0.8468 0.008 0.912 0.080
#> GSM110435 1 0.5650 0.5420 0.688 0.000 0.312
#> GSM110437 1 0.2537 0.7127 0.920 0.000 0.080
#> GSM110438 3 0.6168 -0.0115 0.412 0.000 0.588
#> GSM110388 1 0.7015 0.4369 0.584 0.392 0.024
#> GSM110392 1 0.9724 0.0392 0.436 0.328 0.236
#> GSM110394 1 0.4062 0.6781 0.836 0.000 0.164
#> GSM110402 3 0.7228 0.8115 0.104 0.188 0.708
#> GSM110411 1 0.7001 0.4423 0.588 0.388 0.024
#> GSM110412 2 0.2564 0.8315 0.028 0.936 0.036
#> GSM110417 1 0.1905 0.7031 0.956 0.016 0.028
#> GSM110422 2 0.4602 0.8175 0.016 0.832 0.152
#> GSM110426 1 0.1964 0.7033 0.944 0.000 0.056
#> GSM110429 2 0.4602 0.8175 0.016 0.832 0.152
#> GSM110433 2 0.1482 0.8401 0.012 0.968 0.020
#> GSM110436 2 0.6386 0.3128 0.004 0.584 0.412
#> GSM110440 1 0.5580 0.5991 0.736 0.008 0.256
#> GSM110441 2 0.1860 0.8507 0.000 0.948 0.052
#> GSM110444 1 0.7001 0.4423 0.588 0.388 0.024
#> GSM110445 1 0.5285 0.6822 0.812 0.148 0.040
#> GSM110446 3 0.6180 0.4256 0.260 0.024 0.716
#> GSM110449 2 0.0747 0.8506 0.000 0.984 0.016
#> GSM110451 3 0.8058 0.8023 0.140 0.212 0.648
#> GSM110391 2 0.1482 0.8401 0.012 0.968 0.020
#> GSM110439 2 0.3826 0.8349 0.008 0.868 0.124
#> GSM110442 2 0.3573 0.8383 0.004 0.876 0.120
#> GSM110443 2 0.8817 0.1103 0.380 0.500 0.120
#> GSM110447 3 0.8052 0.7937 0.152 0.196 0.652
#> GSM110448 1 0.7001 0.4423 0.588 0.388 0.024
#> GSM110450 1 0.3752 0.7130 0.884 0.020 0.096
#> GSM110452 2 0.0747 0.8506 0.000 0.984 0.016
#> GSM110453 2 0.4602 0.8175 0.016 0.832 0.152
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 3 0.4764 0.5813 0.008 0.136 0.796 0.060
#> GSM110396 1 0.2923 0.5947 0.908 0.020 0.036 0.036
#> GSM110397 1 0.3581 0.5909 0.852 0.000 0.032 0.116
#> GSM110398 2 0.1297 0.7966 0.016 0.964 0.000 0.020
#> GSM110399 2 0.2936 0.7962 0.032 0.908 0.024 0.036
#> GSM110400 3 0.2142 0.7010 0.000 0.016 0.928 0.056
#> GSM110401 1 0.0817 0.5983 0.976 0.000 0.024 0.000
#> GSM110406 2 0.2936 0.7962 0.032 0.908 0.024 0.036
#> GSM110407 1 0.3157 0.5306 0.852 0.000 0.144 0.004
#> GSM110409 1 0.5797 0.4193 0.624 0.340 0.012 0.024
#> GSM110410 2 0.3828 0.7960 0.000 0.848 0.084 0.068
#> GSM110413 2 0.2334 0.7700 0.000 0.908 0.004 0.088
#> GSM110414 3 0.3542 0.6456 0.000 0.060 0.864 0.076
#> GSM110415 3 0.2563 0.7092 0.012 0.012 0.916 0.060
#> GSM110416 3 0.2300 0.7024 0.048 0.000 0.924 0.028
#> GSM110418 3 0.2300 0.7024 0.048 0.000 0.924 0.028
#> GSM110419 3 0.2654 0.6853 0.108 0.000 0.888 0.004
#> GSM110420 4 0.6148 0.4950 0.048 0.000 0.468 0.484
#> GSM110421 2 0.4262 0.6758 0.000 0.756 0.008 0.236
#> GSM110423 3 0.2142 0.7010 0.000 0.016 0.928 0.056
#> GSM110424 2 0.3894 0.7951 0.000 0.844 0.088 0.068
#> GSM110425 3 0.2654 0.6853 0.108 0.000 0.888 0.004
#> GSM110427 2 0.6848 0.1695 0.008 0.472 0.444 0.076
#> GSM110428 1 0.7708 -0.1596 0.508 0.008 0.256 0.228
#> GSM110430 1 0.0817 0.5983 0.976 0.000 0.024 0.000
#> GSM110431 1 0.7028 -0.0228 0.576 0.000 0.196 0.228
#> GSM110432 3 0.3917 0.6722 0.108 0.044 0.844 0.004
#> GSM110434 2 0.3705 0.8035 0.016 0.868 0.076 0.040
#> GSM110435 1 0.5773 0.2265 0.620 0.000 0.336 0.044
#> GSM110437 1 0.0817 0.5983 0.976 0.000 0.024 0.000
#> GSM110438 4 0.7884 0.4861 0.356 0.000 0.284 0.360
#> GSM110388 1 0.7463 0.3964 0.440 0.176 0.000 0.384
#> GSM110392 1 0.9222 -0.0254 0.404 0.288 0.096 0.212
#> GSM110394 1 0.3208 0.5266 0.848 0.000 0.148 0.004
#> GSM110402 3 0.2197 0.7050 0.048 0.000 0.928 0.024
#> GSM110411 1 0.7436 0.3989 0.444 0.172 0.000 0.384
#> GSM110412 2 0.5010 0.6412 0.000 0.700 0.024 0.276
#> GSM110417 1 0.3672 0.5848 0.824 0.000 0.012 0.164
#> GSM110422 2 0.5500 0.7699 0.024 0.768 0.112 0.096
#> GSM110426 1 0.3760 0.5857 0.836 0.000 0.028 0.136
#> GSM110429 2 0.5608 0.7639 0.024 0.760 0.120 0.096
#> GSM110433 2 0.4262 0.6758 0.000 0.756 0.008 0.236
#> GSM110436 3 0.6725 -0.2131 0.004 0.456 0.464 0.076
#> GSM110440 1 0.5378 0.3571 0.696 0.004 0.264 0.036
#> GSM110441 2 0.1929 0.8072 0.000 0.940 0.024 0.036
#> GSM110444 1 0.7436 0.3989 0.444 0.172 0.000 0.384
#> GSM110445 1 0.3560 0.5641 0.844 0.140 0.004 0.012
#> GSM110446 4 0.7670 0.6318 0.192 0.008 0.300 0.500
#> GSM110449 2 0.0779 0.8028 0.000 0.980 0.016 0.004
#> GSM110451 3 0.3857 0.6757 0.104 0.044 0.848 0.004
#> GSM110391 2 0.4262 0.6758 0.000 0.756 0.008 0.236
#> GSM110439 2 0.4425 0.7929 0.008 0.824 0.092 0.076
#> GSM110442 2 0.4131 0.7941 0.004 0.836 0.096 0.064
#> GSM110443 2 0.7623 0.1686 0.420 0.460 0.072 0.048
#> GSM110447 3 0.3519 0.6493 0.120 0.004 0.856 0.020
#> GSM110448 1 0.7436 0.3989 0.444 0.172 0.000 0.384
#> GSM110450 1 0.2392 0.5912 0.924 0.016 0.052 0.008
#> GSM110452 2 0.0779 0.8028 0.000 0.980 0.016 0.004
#> GSM110453 2 0.5386 0.7742 0.024 0.776 0.104 0.096
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 3 0.334 0.61760 0.000 0.172 0.812 0.016 0.000
#> GSM110396 1 0.275 0.59382 0.900 0.032 0.012 0.008 0.048
#> GSM110397 1 0.554 0.39874 0.604 0.000 0.004 0.312 0.080
#> GSM110398 2 0.493 0.52157 0.000 0.652 0.000 0.296 0.052
#> GSM110399 2 0.596 0.54727 0.012 0.628 0.024 0.276 0.060
#> GSM110400 3 0.104 0.73057 0.000 0.040 0.960 0.000 0.000
#> GSM110401 1 0.000 0.60883 1.000 0.000 0.000 0.000 0.000
#> GSM110406 2 0.596 0.54727 0.012 0.628 0.024 0.276 0.060
#> GSM110407 1 0.306 0.55774 0.864 0.000 0.068 0.000 0.068
#> GSM110409 1 0.595 0.34923 0.612 0.300 0.012 0.024 0.052
#> GSM110410 2 0.209 0.68884 0.000 0.924 0.048 0.020 0.008
#> GSM110413 2 0.559 0.33149 0.000 0.548 0.000 0.372 0.080
#> GSM110414 3 0.261 0.69256 0.000 0.056 0.896 0.004 0.044
#> GSM110415 3 0.157 0.73889 0.008 0.032 0.948 0.000 0.012
#> GSM110416 3 0.426 0.71764 0.044 0.000 0.744 0.000 0.212
#> GSM110418 3 0.426 0.71764 0.044 0.000 0.744 0.000 0.212
#> GSM110419 3 0.427 0.74827 0.116 0.000 0.776 0.000 0.108
#> GSM110420 5 0.341 0.62033 0.024 0.000 0.160 0.000 0.816
#> GSM110421 4 0.541 0.08864 0.000 0.408 0.000 0.532 0.060
#> GSM110423 3 0.104 0.73057 0.000 0.040 0.960 0.000 0.000
#> GSM110424 2 0.196 0.68915 0.000 0.928 0.048 0.020 0.004
#> GSM110425 3 0.427 0.74827 0.116 0.000 0.776 0.000 0.108
#> GSM110427 2 0.419 0.37340 0.000 0.596 0.404 0.000 0.000
#> GSM110428 1 0.657 -0.13303 0.508 0.008 0.152 0.004 0.328
#> GSM110430 1 0.000 0.60883 1.000 0.000 0.000 0.000 0.000
#> GSM110431 1 0.537 -0.00327 0.584 0.000 0.068 0.000 0.348
#> GSM110432 3 0.539 0.73296 0.116 0.048 0.728 0.000 0.108
#> GSM110434 2 0.241 0.68447 0.004 0.912 0.008 0.024 0.052
#> GSM110435 1 0.573 0.28144 0.616 0.000 0.148 0.000 0.236
#> GSM110437 1 0.000 0.60883 1.000 0.000 0.000 0.000 0.000
#> GSM110438 5 0.570 0.42762 0.352 0.000 0.072 0.008 0.568
#> GSM110388 4 0.385 0.50014 0.220 0.020 0.000 0.760 0.000
#> GSM110392 1 0.859 -0.07623 0.352 0.316 0.020 0.124 0.188
#> GSM110394 1 0.312 0.55499 0.860 0.000 0.068 0.000 0.072
#> GSM110402 3 0.423 0.71993 0.044 0.000 0.748 0.000 0.208
#> GSM110411 4 0.376 0.49991 0.220 0.016 0.000 0.764 0.000
#> GSM110412 2 0.569 0.02462 0.000 0.504 0.008 0.428 0.060
#> GSM110417 1 0.550 0.32890 0.556 0.000 0.004 0.380 0.060
#> GSM110422 2 0.266 0.68834 0.004 0.892 0.064 0.000 0.040
#> GSM110426 1 0.563 0.37284 0.580 0.000 0.004 0.336 0.080
#> GSM110429 2 0.279 0.68573 0.004 0.884 0.072 0.000 0.040
#> GSM110433 4 0.541 0.08864 0.000 0.408 0.000 0.532 0.060
#> GSM110436 2 0.423 0.33521 0.000 0.576 0.424 0.000 0.000
#> GSM110440 1 0.525 0.40137 0.696 0.008 0.108 0.000 0.188
#> GSM110441 2 0.458 0.57178 0.000 0.696 0.032 0.268 0.004
#> GSM110444 4 0.376 0.49991 0.220 0.016 0.000 0.764 0.000
#> GSM110445 1 0.345 0.54508 0.836 0.120 0.000 0.040 0.004
#> GSM110446 5 0.446 0.64355 0.176 0.020 0.040 0.000 0.764
#> GSM110449 2 0.344 0.64731 0.000 0.828 0.004 0.140 0.028
#> GSM110451 3 0.534 0.73527 0.112 0.048 0.732 0.000 0.108
#> GSM110391 4 0.541 0.08864 0.000 0.408 0.000 0.532 0.060
#> GSM110439 2 0.136 0.69411 0.000 0.948 0.048 0.004 0.000
#> GSM110442 2 0.191 0.69457 0.000 0.932 0.036 0.028 0.004
#> GSM110443 2 0.670 0.09406 0.408 0.476 0.012 0.060 0.044
#> GSM110447 3 0.518 0.68403 0.120 0.008 0.708 0.000 0.164
#> GSM110448 4 0.376 0.49991 0.220 0.016 0.000 0.764 0.000
#> GSM110450 1 0.190 0.60172 0.940 0.008 0.016 0.024 0.012
#> GSM110452 2 0.344 0.64731 0.000 0.828 0.004 0.140 0.028
#> GSM110453 2 0.253 0.68945 0.004 0.900 0.056 0.000 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 3 0.5132 0.6134 0.000 0.184 0.684 0.000 0.040 0.092
#> GSM110396 1 0.2720 0.6037 0.892 0.056 0.012 0.008 0.016 0.016
#> GSM110397 4 0.5464 0.5646 0.232 0.000 0.008 0.636 0.020 0.104
#> GSM110398 5 0.4366 0.5070 0.000 0.324 0.004 0.024 0.644 0.004
#> GSM110399 5 0.4499 0.4992 0.008 0.344 0.012 0.000 0.624 0.012
#> GSM110400 3 0.3576 0.7138 0.000 0.084 0.812 0.000 0.008 0.096
#> GSM110401 1 0.0146 0.6219 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM110406 5 0.4499 0.4992 0.008 0.344 0.012 0.000 0.624 0.012
#> GSM110407 1 0.2812 0.5866 0.860 0.000 0.108 0.004 0.004 0.024
#> GSM110409 1 0.5393 0.3569 0.604 0.280 0.012 0.004 0.100 0.000
#> GSM110410 2 0.2009 0.6583 0.000 0.904 0.000 0.004 0.084 0.008
#> GSM110413 5 0.3381 0.4859 0.000 0.148 0.000 0.040 0.808 0.004
#> GSM110414 3 0.4682 0.6770 0.000 0.088 0.748 0.000 0.068 0.096
#> GSM110415 3 0.3707 0.7210 0.008 0.076 0.808 0.000 0.004 0.104
#> GSM110416 3 0.2909 0.6898 0.028 0.000 0.836 0.000 0.000 0.136
#> GSM110418 3 0.2909 0.6898 0.028 0.000 0.836 0.000 0.000 0.136
#> GSM110419 3 0.2212 0.7347 0.112 0.008 0.880 0.000 0.000 0.000
#> GSM110420 6 0.2883 0.6379 0.000 0.000 0.212 0.000 0.000 0.788
#> GSM110421 5 0.5633 0.2593 0.000 0.272 0.000 0.196 0.532 0.000
#> GSM110423 3 0.3576 0.7138 0.000 0.084 0.812 0.000 0.008 0.096
#> GSM110424 2 0.1897 0.6601 0.000 0.908 0.000 0.004 0.084 0.004
#> GSM110425 3 0.2212 0.7347 0.112 0.008 0.880 0.000 0.000 0.000
#> GSM110427 2 0.5225 0.4353 0.000 0.620 0.272 0.000 0.016 0.092
#> GSM110428 1 0.5921 0.0526 0.508 0.004 0.184 0.004 0.000 0.300
#> GSM110430 1 0.0146 0.6219 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM110431 1 0.5240 0.1752 0.584 0.000 0.132 0.000 0.000 0.284
#> GSM110432 3 0.3123 0.7207 0.112 0.056 0.832 0.000 0.000 0.000
#> GSM110434 2 0.2170 0.5837 0.000 0.888 0.012 0.000 0.100 0.000
#> GSM110435 1 0.5259 0.2909 0.600 0.000 0.240 0.000 0.000 0.160
#> GSM110437 1 0.0291 0.6214 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM110438 6 0.6162 0.3670 0.336 0.000 0.188 0.016 0.000 0.460
#> GSM110388 4 0.3025 0.7414 0.024 0.000 0.000 0.820 0.156 0.000
#> GSM110392 1 0.8296 -0.0509 0.340 0.308 0.020 0.140 0.032 0.160
#> GSM110394 1 0.2890 0.5842 0.856 0.000 0.108 0.004 0.004 0.028
#> GSM110402 3 0.3050 0.6922 0.028 0.004 0.832 0.000 0.000 0.136
#> GSM110411 4 0.2988 0.7447 0.024 0.000 0.000 0.824 0.152 0.000
#> GSM110412 2 0.6267 -0.1203 0.000 0.380 0.008 0.256 0.356 0.000
#> GSM110417 4 0.4789 0.6136 0.184 0.000 0.004 0.708 0.016 0.088
#> GSM110422 2 0.0951 0.6804 0.000 0.968 0.020 0.000 0.004 0.008
#> GSM110426 4 0.5319 0.5882 0.208 0.000 0.008 0.660 0.020 0.104
#> GSM110429 2 0.1116 0.6791 0.000 0.960 0.028 0.000 0.004 0.008
#> GSM110433 5 0.5633 0.2593 0.000 0.272 0.000 0.196 0.532 0.000
#> GSM110436 2 0.5311 0.4190 0.000 0.600 0.292 0.000 0.016 0.092
#> GSM110440 1 0.4956 0.4269 0.684 0.008 0.180 0.000 0.004 0.124
#> GSM110441 5 0.3942 0.4552 0.000 0.368 0.000 0.004 0.624 0.004
#> GSM110444 4 0.2988 0.7447 0.024 0.000 0.000 0.824 0.152 0.000
#> GSM110445 1 0.3362 0.5521 0.840 0.088 0.004 0.016 0.052 0.000
#> GSM110446 6 0.5304 0.6264 0.156 0.048 0.104 0.000 0.004 0.688
#> GSM110449 5 0.4428 0.3154 0.000 0.452 0.004 0.012 0.528 0.004
#> GSM110451 3 0.3078 0.7237 0.108 0.056 0.836 0.000 0.000 0.000
#> GSM110391 5 0.5633 0.2593 0.000 0.272 0.000 0.196 0.532 0.000
#> GSM110439 2 0.1340 0.6759 0.000 0.948 0.008 0.004 0.040 0.000
#> GSM110442 2 0.3194 0.5520 0.000 0.808 0.000 0.020 0.168 0.004
#> GSM110443 1 0.7014 0.0790 0.404 0.352 0.012 0.028 0.192 0.012
#> GSM110447 3 0.4144 0.6703 0.108 0.012 0.776 0.000 0.004 0.100
#> GSM110448 4 0.2988 0.7447 0.024 0.000 0.000 0.824 0.152 0.000
#> GSM110450 1 0.1590 0.6215 0.944 0.008 0.028 0.012 0.008 0.000
#> GSM110452 5 0.4428 0.3154 0.000 0.452 0.004 0.012 0.528 0.004
#> GSM110453 2 0.0881 0.6763 0.000 0.972 0.012 0.000 0.008 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) specimen(p) k
#> SD:hclust 54 1.000 0.713 2
#> SD:hclust 47 0.112 0.194 3
#> SD:hclust 44 0.171 0.429 4
#> SD:hclust 38 0.317 0.560 5
#> SD:hclust 39 0.103 0.521 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 17209 rows and 59 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 0.488 0.662 0.865 0.5014 0.493 0.493
#> 3 3 0.458 0.593 0.794 0.3071 0.704 0.476
#> 4 4 0.607 0.681 0.823 0.1292 0.798 0.490
#> 5 5 0.641 0.481 0.691 0.0721 0.901 0.638
#> 6 6 0.667 0.558 0.749 0.0418 0.915 0.632
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
#> GSM110395 2 0.8763 0.592 0.296 0.704
#> GSM110396 1 0.1184 0.820 0.984 0.016
#> GSM110397 1 0.1184 0.820 0.984 0.016
#> GSM110398 2 0.8327 0.488 0.264 0.736
#> GSM110399 2 0.1633 0.823 0.024 0.976
#> GSM110400 2 0.9635 0.458 0.388 0.612
#> GSM110401 1 0.1184 0.820 0.984 0.016
#> GSM110406 2 0.1633 0.823 0.024 0.976
#> GSM110407 1 0.0376 0.822 0.996 0.004
#> GSM110409 1 0.0376 0.822 0.996 0.004
#> GSM110410 2 0.0000 0.823 0.000 1.000
#> GSM110413 2 0.0000 0.823 0.000 1.000
#> GSM110414 2 0.1184 0.821 0.016 0.984
#> GSM110415 1 0.9996 -0.213 0.512 0.488
#> GSM110416 1 0.0376 0.822 0.996 0.004
#> GSM110418 1 0.0376 0.822 0.996 0.004
#> GSM110419 1 0.9996 -0.213 0.512 0.488
#> GSM110420 1 0.0376 0.822 0.996 0.004
#> GSM110421 2 0.0376 0.821 0.004 0.996
#> GSM110423 2 1.0000 0.209 0.496 0.504
#> GSM110424 2 0.0000 0.823 0.000 1.000
#> GSM110425 2 1.0000 0.209 0.496 0.504
#> GSM110427 2 0.2423 0.818 0.040 0.960
#> GSM110428 1 0.0376 0.822 0.996 0.004
#> GSM110430 1 0.1184 0.820 0.984 0.016
#> GSM110431 1 0.0376 0.822 0.996 0.004
#> GSM110432 2 0.9661 0.450 0.392 0.608
#> GSM110434 2 0.1633 0.823 0.024 0.976
#> GSM110435 1 0.0376 0.822 0.996 0.004
#> GSM110437 1 0.1184 0.820 0.984 0.016
#> GSM110438 1 0.0376 0.822 0.996 0.004
#> GSM110388 1 0.9732 0.386 0.596 0.404
#> GSM110392 1 0.9209 0.500 0.664 0.336
#> GSM110394 1 0.0376 0.822 0.996 0.004
#> GSM110402 2 1.0000 0.209 0.496 0.504
#> GSM110411 1 0.9795 0.363 0.584 0.416
#> GSM110412 2 0.0000 0.823 0.000 1.000
#> GSM110417 1 0.6623 0.695 0.828 0.172
#> GSM110422 2 0.2423 0.818 0.040 0.960
#> GSM110426 1 0.2423 0.806 0.960 0.040
#> GSM110429 2 0.5946 0.751 0.144 0.856
#> GSM110433 2 0.0000 0.823 0.000 1.000
#> GSM110436 2 0.9608 0.464 0.384 0.616
#> GSM110440 1 0.0000 0.821 1.000 0.000
#> GSM110441 2 0.0000 0.823 0.000 1.000
#> GSM110444 2 0.5946 0.700 0.144 0.856
#> GSM110445 1 0.9635 0.395 0.612 0.388
#> GSM110446 1 0.0376 0.822 0.996 0.004
#> GSM110449 2 0.0376 0.821 0.004 0.996
#> GSM110451 2 0.9635 0.458 0.388 0.612
#> GSM110391 2 0.0000 0.823 0.000 1.000
#> GSM110439 2 0.0938 0.824 0.012 0.988
#> GSM110442 2 0.0000 0.823 0.000 1.000
#> GSM110443 2 0.5294 0.766 0.120 0.880
#> GSM110447 1 0.9996 -0.213 0.512 0.488
#> GSM110448 1 0.9661 0.406 0.608 0.392
#> GSM110450 1 0.1184 0.820 0.984 0.016
#> GSM110452 2 0.0938 0.824 0.012 0.988
#> GSM110453 2 0.0938 0.824 0.012 0.988
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.3619 0.7328 0.000 0.864 0.136
#> GSM110396 1 0.6779 0.4706 0.544 0.012 0.444
#> GSM110397 1 0.6154 0.4927 0.592 0.000 0.408
#> GSM110398 2 0.4805 0.7660 0.176 0.812 0.012
#> GSM110399 2 0.1860 0.8448 0.052 0.948 0.000
#> GSM110400 3 0.4887 0.6376 0.000 0.228 0.772
#> GSM110401 1 0.6483 0.4672 0.544 0.004 0.452
#> GSM110406 2 0.1989 0.8466 0.048 0.948 0.004
#> GSM110407 3 0.6529 0.0152 0.368 0.012 0.620
#> GSM110409 3 0.8619 -0.1402 0.368 0.108 0.524
#> GSM110410 2 0.0747 0.8527 0.016 0.984 0.000
#> GSM110413 2 0.3340 0.8178 0.120 0.880 0.000
#> GSM110414 2 0.9032 0.2300 0.148 0.512 0.340
#> GSM110415 3 0.4128 0.6858 0.012 0.132 0.856
#> GSM110416 3 0.0747 0.6614 0.016 0.000 0.984
#> GSM110418 3 0.0747 0.6614 0.016 0.000 0.984
#> GSM110419 3 0.3816 0.6868 0.000 0.148 0.852
#> GSM110420 3 0.0892 0.6598 0.020 0.000 0.980
#> GSM110421 2 0.6079 0.6023 0.388 0.612 0.000
#> GSM110423 3 0.3879 0.6854 0.000 0.152 0.848
#> GSM110424 2 0.0747 0.8527 0.016 0.984 0.000
#> GSM110425 3 0.3879 0.6854 0.000 0.152 0.848
#> GSM110427 2 0.0892 0.8415 0.000 0.980 0.020
#> GSM110428 3 0.0000 0.6616 0.000 0.000 1.000
#> GSM110430 1 0.6483 0.4672 0.544 0.004 0.452
#> GSM110431 3 0.5254 0.3197 0.264 0.000 0.736
#> GSM110432 3 0.4796 0.6444 0.000 0.220 0.780
#> GSM110434 2 0.0000 0.8507 0.000 1.000 0.000
#> GSM110435 3 0.5254 0.3197 0.264 0.000 0.736
#> GSM110437 1 0.6274 0.4624 0.544 0.000 0.456
#> GSM110438 3 0.1753 0.6441 0.048 0.000 0.952
#> GSM110388 1 0.2066 0.5770 0.940 0.060 0.000
#> GSM110392 3 0.9760 0.1905 0.276 0.280 0.444
#> GSM110394 3 0.5098 0.3472 0.248 0.000 0.752
#> GSM110402 3 0.4047 0.6874 0.004 0.148 0.848
#> GSM110411 1 0.2066 0.5770 0.940 0.060 0.000
#> GSM110412 2 0.8637 0.4017 0.448 0.452 0.100
#> GSM110417 1 0.3425 0.6006 0.884 0.004 0.112
#> GSM110422 2 0.0237 0.8492 0.000 0.996 0.004
#> GSM110426 1 0.4291 0.5960 0.820 0.000 0.180
#> GSM110429 2 0.2165 0.8095 0.000 0.936 0.064
#> GSM110433 2 0.5968 0.6287 0.364 0.636 0.000
#> GSM110436 3 0.6204 0.3379 0.000 0.424 0.576
#> GSM110440 3 0.6274 -0.2825 0.456 0.000 0.544
#> GSM110441 2 0.3116 0.8245 0.108 0.892 0.000
#> GSM110444 1 0.4452 0.3577 0.808 0.192 0.000
#> GSM110445 1 0.8173 0.4481 0.600 0.300 0.100
#> GSM110446 3 0.1860 0.6413 0.052 0.000 0.948
#> GSM110449 2 0.3482 0.8129 0.128 0.872 0.000
#> GSM110451 3 0.5497 0.5774 0.000 0.292 0.708
#> GSM110391 2 0.6079 0.6023 0.388 0.612 0.000
#> GSM110439 2 0.0424 0.8526 0.008 0.992 0.000
#> GSM110442 2 0.0424 0.8526 0.008 0.992 0.000
#> GSM110443 2 0.3349 0.8173 0.108 0.888 0.004
#> GSM110447 3 0.3752 0.6870 0.000 0.144 0.856
#> GSM110448 1 0.2066 0.5770 0.940 0.060 0.000
#> GSM110450 1 0.6483 0.4672 0.544 0.004 0.452
#> GSM110452 2 0.0424 0.8526 0.008 0.992 0.000
#> GSM110453 2 0.0000 0.8507 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.4747 0.7107 0.024 0.780 0.180 0.016
#> GSM110396 1 0.3888 0.7460 0.860 0.016 0.052 0.072
#> GSM110397 1 0.4224 0.6730 0.812 0.000 0.044 0.144
#> GSM110398 2 0.4127 0.7617 0.052 0.824 0.000 0.124
#> GSM110399 2 0.1543 0.8702 0.008 0.956 0.004 0.032
#> GSM110400 3 0.2297 0.8404 0.024 0.032 0.932 0.012
#> GSM110401 1 0.3721 0.7493 0.864 0.008 0.056 0.072
#> GSM110406 2 0.2432 0.8659 0.024 0.928 0.020 0.028
#> GSM110407 1 0.4835 0.6801 0.756 0.004 0.208 0.032
#> GSM110409 1 0.5197 0.6638 0.780 0.144 0.044 0.032
#> GSM110410 2 0.2924 0.8478 0.036 0.900 0.004 0.060
#> GSM110413 2 0.5358 0.6510 0.052 0.724 0.004 0.220
#> GSM110414 3 0.5942 0.6241 0.048 0.060 0.740 0.152
#> GSM110415 3 0.0564 0.8557 0.004 0.004 0.988 0.004
#> GSM110416 3 0.3279 0.8073 0.096 0.000 0.872 0.032
#> GSM110418 3 0.3464 0.7997 0.108 0.000 0.860 0.032
#> GSM110419 3 0.1722 0.8563 0.048 0.008 0.944 0.000
#> GSM110420 3 0.3464 0.7997 0.108 0.000 0.860 0.032
#> GSM110421 4 0.6079 0.2079 0.048 0.408 0.000 0.544
#> GSM110423 3 0.1059 0.8557 0.016 0.012 0.972 0.000
#> GSM110424 2 0.3104 0.8434 0.044 0.892 0.004 0.060
#> GSM110425 3 0.1284 0.8541 0.024 0.012 0.964 0.000
#> GSM110427 2 0.3238 0.8199 0.020 0.880 0.092 0.008
#> GSM110428 3 0.1576 0.8539 0.048 0.000 0.948 0.004
#> GSM110430 1 0.3721 0.7493 0.864 0.008 0.056 0.072
#> GSM110431 1 0.5269 0.4818 0.620 0.000 0.364 0.016
#> GSM110432 3 0.2613 0.8314 0.024 0.052 0.916 0.008
#> GSM110434 2 0.0524 0.8749 0.000 0.988 0.008 0.004
#> GSM110435 1 0.5599 0.4815 0.616 0.000 0.352 0.032
#> GSM110437 1 0.3877 0.7453 0.852 0.004 0.072 0.072
#> GSM110438 3 0.4964 0.6224 0.244 0.000 0.724 0.032
#> GSM110388 4 0.3113 0.5865 0.108 0.012 0.004 0.876
#> GSM110392 4 0.9453 -0.0273 0.252 0.104 0.296 0.348
#> GSM110394 1 0.5203 0.4843 0.636 0.000 0.348 0.016
#> GSM110402 3 0.1767 0.8515 0.044 0.012 0.944 0.000
#> GSM110411 4 0.2730 0.5957 0.088 0.016 0.000 0.896
#> GSM110412 4 0.4694 0.5988 0.044 0.084 0.048 0.824
#> GSM110417 4 0.4964 0.1305 0.380 0.000 0.004 0.616
#> GSM110422 2 0.0895 0.8741 0.000 0.976 0.020 0.004
#> GSM110426 1 0.5859 0.0659 0.496 0.000 0.032 0.472
#> GSM110429 2 0.3854 0.7596 0.012 0.828 0.152 0.008
#> GSM110433 4 0.6120 0.1389 0.048 0.432 0.000 0.520
#> GSM110436 3 0.4260 0.7224 0.020 0.180 0.796 0.004
#> GSM110440 1 0.2918 0.7345 0.876 0.000 0.116 0.008
#> GSM110441 2 0.3266 0.8301 0.040 0.876 0.000 0.084
#> GSM110444 4 0.2214 0.6093 0.044 0.028 0.000 0.928
#> GSM110445 1 0.5200 0.5950 0.744 0.184 0.000 0.072
#> GSM110446 3 0.5511 0.4579 0.332 0.000 0.636 0.032
#> GSM110449 2 0.2976 0.8108 0.008 0.872 0.000 0.120
#> GSM110451 3 0.4265 0.7478 0.024 0.148 0.816 0.012
#> GSM110391 4 0.6079 0.2079 0.048 0.408 0.000 0.544
#> GSM110439 2 0.0376 0.8766 0.000 0.992 0.004 0.004
#> GSM110442 2 0.0564 0.8769 0.004 0.988 0.004 0.004
#> GSM110443 2 0.4218 0.7089 0.184 0.796 0.008 0.012
#> GSM110447 3 0.0657 0.8561 0.004 0.012 0.984 0.000
#> GSM110448 4 0.3102 0.5755 0.116 0.008 0.004 0.872
#> GSM110450 1 0.3948 0.7452 0.852 0.008 0.068 0.072
#> GSM110452 2 0.0376 0.8766 0.000 0.992 0.004 0.004
#> GSM110453 2 0.0524 0.8769 0.000 0.988 0.004 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 5 0.6077 0.0309 0.032 0.436 0.052 0.000 0.480
#> GSM110396 1 0.0566 0.7748 0.984 0.000 0.000 0.004 0.012
#> GSM110397 1 0.6635 0.5215 0.608 0.000 0.188 0.140 0.064
#> GSM110398 2 0.4927 0.6778 0.060 0.756 0.000 0.044 0.140
#> GSM110399 2 0.4230 0.6969 0.008 0.764 0.000 0.036 0.192
#> GSM110400 5 0.5000 -0.0584 0.016 0.008 0.476 0.000 0.500
#> GSM110401 1 0.0613 0.7797 0.984 0.000 0.008 0.004 0.004
#> GSM110406 2 0.5138 0.6508 0.028 0.684 0.000 0.036 0.252
#> GSM110407 1 0.4036 0.7165 0.788 0.000 0.144 0.000 0.068
#> GSM110409 1 0.4156 0.7345 0.820 0.056 0.060 0.000 0.064
#> GSM110410 2 0.3421 0.6601 0.000 0.788 0.000 0.008 0.204
#> GSM110413 5 0.5922 -0.4881 0.000 0.420 0.000 0.104 0.476
#> GSM110414 5 0.4799 0.2256 0.000 0.008 0.260 0.040 0.692
#> GSM110415 3 0.4313 0.3939 0.008 0.000 0.636 0.000 0.356
#> GSM110416 3 0.0510 0.5279 0.000 0.000 0.984 0.000 0.016
#> GSM110418 3 0.0000 0.5279 0.000 0.000 1.000 0.000 0.000
#> GSM110419 3 0.4774 0.3796 0.028 0.000 0.612 0.000 0.360
#> GSM110420 3 0.0162 0.5270 0.000 0.000 0.996 0.000 0.004
#> GSM110421 4 0.6468 0.3837 0.000 0.188 0.000 0.452 0.360
#> GSM110423 3 0.4367 0.3686 0.008 0.000 0.620 0.000 0.372
#> GSM110424 2 0.3612 0.6481 0.000 0.764 0.000 0.008 0.228
#> GSM110425 3 0.4494 0.3490 0.012 0.000 0.608 0.000 0.380
#> GSM110427 2 0.4668 0.2019 0.008 0.600 0.008 0.000 0.384
#> GSM110428 3 0.4787 0.3736 0.028 0.000 0.608 0.000 0.364
#> GSM110430 1 0.0613 0.7797 0.984 0.000 0.008 0.004 0.004
#> GSM110431 1 0.4648 0.3819 0.524 0.000 0.464 0.000 0.012
#> GSM110432 5 0.6323 0.1729 0.028 0.080 0.400 0.000 0.492
#> GSM110434 2 0.0566 0.7469 0.004 0.984 0.000 0.000 0.012
#> GSM110435 3 0.4252 -0.1033 0.340 0.000 0.652 0.000 0.008
#> GSM110437 1 0.1153 0.7764 0.964 0.000 0.024 0.004 0.008
#> GSM110438 3 0.1764 0.5029 0.064 0.000 0.928 0.000 0.008
#> GSM110388 4 0.1502 0.6507 0.056 0.000 0.000 0.940 0.004
#> GSM110392 3 0.8574 -0.1079 0.140 0.064 0.428 0.284 0.084
#> GSM110394 1 0.4723 0.4006 0.536 0.000 0.448 0.000 0.016
#> GSM110402 3 0.4201 0.4191 0.008 0.000 0.664 0.000 0.328
#> GSM110411 4 0.1557 0.6771 0.008 0.000 0.000 0.940 0.052
#> GSM110412 4 0.3462 0.6406 0.000 0.012 0.000 0.792 0.196
#> GSM110417 4 0.4846 0.4370 0.244 0.000 0.004 0.696 0.056
#> GSM110422 2 0.2286 0.7068 0.004 0.888 0.000 0.000 0.108
#> GSM110426 4 0.6760 0.2665 0.272 0.000 0.108 0.560 0.060
#> GSM110429 2 0.4651 0.0470 0.004 0.560 0.008 0.000 0.428
#> GSM110433 4 0.6715 0.2647 0.000 0.248 0.000 0.392 0.360
#> GSM110436 5 0.6844 0.3812 0.016 0.216 0.276 0.000 0.492
#> GSM110440 1 0.3618 0.7300 0.788 0.000 0.196 0.004 0.012
#> GSM110441 2 0.4990 0.5541 0.000 0.628 0.000 0.048 0.324
#> GSM110444 4 0.1628 0.6772 0.008 0.000 0.000 0.936 0.056
#> GSM110445 1 0.4326 0.6145 0.772 0.164 0.000 0.008 0.056
#> GSM110446 3 0.2879 0.4633 0.100 0.000 0.868 0.000 0.032
#> GSM110449 2 0.3914 0.6896 0.000 0.788 0.000 0.048 0.164
#> GSM110451 5 0.6801 0.3562 0.020 0.176 0.308 0.000 0.496
#> GSM110391 4 0.6468 0.3837 0.000 0.188 0.000 0.452 0.360
#> GSM110439 2 0.0000 0.7487 0.000 1.000 0.000 0.000 0.000
#> GSM110442 2 0.0290 0.7482 0.000 0.992 0.000 0.000 0.008
#> GSM110443 2 0.5551 0.4753 0.284 0.612 0.000 0.000 0.104
#> GSM110447 3 0.4354 0.3779 0.008 0.000 0.624 0.000 0.368
#> GSM110448 4 0.1478 0.6456 0.064 0.000 0.000 0.936 0.000
#> GSM110450 1 0.0451 0.7759 0.988 0.000 0.000 0.004 0.008
#> GSM110452 2 0.0000 0.7487 0.000 1.000 0.000 0.000 0.000
#> GSM110453 2 0.0404 0.7484 0.000 0.988 0.000 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 3 0.4724 0.2717 0.004 0.328 0.628 0.004 0.020 0.016
#> GSM110396 1 0.0972 0.7518 0.964 0.000 0.000 0.008 0.000 0.028
#> GSM110397 1 0.5893 0.1696 0.424 0.000 0.000 0.372 0.000 0.204
#> GSM110398 2 0.6252 0.4926 0.052 0.640 0.012 0.028 0.172 0.096
#> GSM110399 2 0.5407 0.5557 0.000 0.688 0.068 0.012 0.168 0.064
#> GSM110400 3 0.0551 0.7270 0.000 0.004 0.984 0.000 0.004 0.008
#> GSM110401 1 0.0551 0.7538 0.984 0.000 0.000 0.008 0.004 0.004
#> GSM110406 2 0.6778 0.4969 0.016 0.568 0.180 0.012 0.164 0.060
#> GSM110407 1 0.3687 0.6937 0.812 0.000 0.108 0.012 0.004 0.064
#> GSM110409 1 0.3893 0.7074 0.824 0.072 0.036 0.012 0.004 0.052
#> GSM110410 2 0.4659 0.3549 0.000 0.644 0.008 0.004 0.304 0.040
#> GSM110413 5 0.3953 0.4677 0.000 0.160 0.040 0.000 0.776 0.024
#> GSM110414 3 0.4284 0.5913 0.000 0.008 0.720 0.000 0.216 0.056
#> GSM110415 3 0.2631 0.6999 0.000 0.000 0.820 0.000 0.000 0.180
#> GSM110416 6 0.3309 0.7257 0.000 0.000 0.280 0.000 0.000 0.720
#> GSM110418 6 0.3221 0.7431 0.000 0.000 0.264 0.000 0.000 0.736
#> GSM110419 3 0.3204 0.6937 0.032 0.000 0.820 0.004 0.000 0.144
#> GSM110420 6 0.3398 0.7515 0.000 0.000 0.252 0.008 0.000 0.740
#> GSM110421 5 0.2558 0.6000 0.000 0.028 0.000 0.104 0.868 0.000
#> GSM110423 3 0.2378 0.7213 0.000 0.000 0.848 0.000 0.000 0.152
#> GSM110424 2 0.4872 0.3015 0.000 0.608 0.012 0.004 0.336 0.040
#> GSM110425 3 0.2219 0.7278 0.000 0.000 0.864 0.000 0.000 0.136
#> GSM110427 2 0.4381 0.1454 0.000 0.524 0.456 0.000 0.016 0.004
#> GSM110428 3 0.3242 0.7048 0.032 0.000 0.816 0.004 0.000 0.148
#> GSM110430 1 0.0665 0.7537 0.980 0.000 0.000 0.008 0.004 0.008
#> GSM110431 1 0.4932 0.3203 0.556 0.000 0.072 0.000 0.000 0.372
#> GSM110432 3 0.2296 0.6998 0.004 0.084 0.896 0.004 0.004 0.008
#> GSM110434 2 0.0665 0.6726 0.000 0.980 0.004 0.000 0.008 0.008
#> GSM110435 6 0.4278 0.5457 0.212 0.000 0.076 0.000 0.000 0.712
#> GSM110437 1 0.1138 0.7509 0.960 0.000 0.000 0.012 0.004 0.024
#> GSM110438 6 0.4397 0.7619 0.072 0.000 0.188 0.012 0.000 0.728
#> GSM110388 4 0.3245 0.7197 0.016 0.000 0.000 0.796 0.184 0.004
#> GSM110392 6 0.7720 0.0733 0.084 0.052 0.084 0.372 0.020 0.388
#> GSM110394 1 0.5249 0.3486 0.556 0.000 0.096 0.004 0.000 0.344
#> GSM110402 3 0.3351 0.5382 0.000 0.000 0.712 0.000 0.000 0.288
#> GSM110411 4 0.3652 0.6153 0.000 0.000 0.000 0.672 0.324 0.004
#> GSM110412 5 0.4662 -0.2331 0.000 0.004 0.016 0.420 0.548 0.012
#> GSM110417 4 0.3062 0.6130 0.112 0.000 0.000 0.836 0.000 0.052
#> GSM110422 2 0.2214 0.6486 0.000 0.892 0.092 0.000 0.012 0.004
#> GSM110426 4 0.3595 0.5853 0.120 0.000 0.000 0.796 0.000 0.084
#> GSM110429 2 0.4195 0.1742 0.000 0.548 0.440 0.000 0.008 0.004
#> GSM110433 5 0.2609 0.6038 0.000 0.036 0.000 0.096 0.868 0.000
#> GSM110436 3 0.3469 0.6397 0.004 0.180 0.792 0.000 0.012 0.012
#> GSM110440 1 0.3459 0.6334 0.768 0.000 0.016 0.004 0.000 0.212
#> GSM110441 5 0.5200 -0.2205 0.000 0.444 0.004 0.000 0.476 0.076
#> GSM110444 4 0.3652 0.6154 0.000 0.000 0.000 0.672 0.324 0.004
#> GSM110445 1 0.6299 0.4299 0.616 0.196 0.000 0.044 0.052 0.092
#> GSM110446 6 0.4238 0.7622 0.072 0.000 0.168 0.012 0.000 0.748
#> GSM110449 2 0.5317 0.4860 0.000 0.648 0.000 0.028 0.216 0.108
#> GSM110451 3 0.3018 0.6653 0.004 0.148 0.832 0.004 0.004 0.008
#> GSM110391 5 0.2701 0.5981 0.000 0.028 0.000 0.104 0.864 0.004
#> GSM110439 2 0.0870 0.6701 0.000 0.972 0.004 0.000 0.012 0.012
#> GSM110442 2 0.2308 0.6578 0.000 0.904 0.008 0.004 0.056 0.028
#> GSM110443 2 0.7168 0.4422 0.220 0.560 0.044 0.036 0.056 0.084
#> GSM110447 3 0.2879 0.7093 0.004 0.000 0.816 0.000 0.004 0.176
#> GSM110448 4 0.3104 0.7204 0.016 0.000 0.000 0.800 0.184 0.000
#> GSM110450 1 0.1078 0.7507 0.964 0.000 0.000 0.016 0.012 0.008
#> GSM110452 2 0.1390 0.6672 0.000 0.948 0.004 0.000 0.016 0.032
#> GSM110453 2 0.0767 0.6724 0.000 0.976 0.004 0.000 0.012 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) specimen(p) k
#> SD:kmeans 43 0.1502 0.1459 2
#> SD:kmeans 41 0.0158 0.2626 3
#> SD:kmeans 49 0.0203 0.3533 4
#> SD:kmeans 32 0.0141 0.4465 5
#> SD:kmeans 42 0.0187 0.0895 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 17209 rows and 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.537 0.650 0.874 0.5075 0.492 0.492
#> 3 3 0.593 0.503 0.781 0.3187 0.739 0.543
#> 4 4 0.710 0.785 0.893 0.1168 0.819 0.559
#> 5 5 0.657 0.555 0.767 0.0728 0.876 0.561
#> 6 6 0.678 0.509 0.725 0.0448 0.935 0.688
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
#> GSM110395 2 0.753 0.594 0.216 0.784
#> GSM110396 1 0.000 0.816 1.000 0.000
#> GSM110397 1 0.000 0.816 1.000 0.000
#> GSM110398 2 0.975 0.244 0.408 0.592
#> GSM110399 2 0.000 0.837 0.000 1.000
#> GSM110400 2 0.973 0.228 0.404 0.596
#> GSM110401 1 0.000 0.816 1.000 0.000
#> GSM110406 2 0.000 0.837 0.000 1.000
#> GSM110407 1 0.000 0.816 1.000 0.000
#> GSM110409 1 0.000 0.816 1.000 0.000
#> GSM110410 2 0.000 0.837 0.000 1.000
#> GSM110413 2 0.000 0.837 0.000 1.000
#> GSM110414 2 0.000 0.837 0.000 1.000
#> GSM110415 1 0.975 0.298 0.592 0.408
#> GSM110416 1 0.000 0.816 1.000 0.000
#> GSM110418 1 0.000 0.816 1.000 0.000
#> GSM110419 1 0.971 0.313 0.600 0.400
#> GSM110420 1 0.000 0.816 1.000 0.000
#> GSM110421 2 0.000 0.837 0.000 1.000
#> GSM110423 1 0.983 0.262 0.576 0.424
#> GSM110424 2 0.000 0.837 0.000 1.000
#> GSM110425 1 0.983 0.262 0.576 0.424
#> GSM110427 2 0.000 0.837 0.000 1.000
#> GSM110428 1 0.000 0.816 1.000 0.000
#> GSM110430 1 0.000 0.816 1.000 0.000
#> GSM110431 1 0.000 0.816 1.000 0.000
#> GSM110432 2 0.988 0.135 0.436 0.564
#> GSM110434 2 0.000 0.837 0.000 1.000
#> GSM110435 1 0.000 0.816 1.000 0.000
#> GSM110437 1 0.000 0.816 1.000 0.000
#> GSM110438 1 0.000 0.816 1.000 0.000
#> GSM110388 1 0.990 0.138 0.560 0.440
#> GSM110392 1 0.966 0.257 0.608 0.392
#> GSM110394 1 0.000 0.816 1.000 0.000
#> GSM110402 1 0.983 0.262 0.576 0.424
#> GSM110411 2 0.983 0.209 0.424 0.576
#> GSM110412 2 0.000 0.837 0.000 1.000
#> GSM110417 1 0.662 0.642 0.828 0.172
#> GSM110422 2 0.000 0.837 0.000 1.000
#> GSM110426 1 0.000 0.816 1.000 0.000
#> GSM110429 2 0.000 0.837 0.000 1.000
#> GSM110433 2 0.000 0.837 0.000 1.000
#> GSM110436 2 0.969 0.248 0.396 0.604
#> GSM110440 1 0.000 0.816 1.000 0.000
#> GSM110441 2 0.000 0.837 0.000 1.000
#> GSM110444 2 0.983 0.209 0.424 0.576
#> GSM110445 2 0.987 0.190 0.432 0.568
#> GSM110446 1 0.000 0.816 1.000 0.000
#> GSM110449 2 0.000 0.837 0.000 1.000
#> GSM110451 2 0.971 0.238 0.400 0.600
#> GSM110391 2 0.000 0.837 0.000 1.000
#> GSM110439 2 0.000 0.837 0.000 1.000
#> GSM110442 2 0.000 0.837 0.000 1.000
#> GSM110443 2 0.000 0.837 0.000 1.000
#> GSM110447 1 0.975 0.298 0.592 0.408
#> GSM110448 1 0.980 0.201 0.584 0.416
#> GSM110450 1 0.000 0.816 1.000 0.000
#> GSM110452 2 0.000 0.837 0.000 1.000
#> GSM110453 2 0.000 0.837 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.1337 0.889 0.016 0.972 0.012
#> GSM110396 3 0.5948 -0.465 0.360 0.000 0.640
#> GSM110397 3 0.5785 -0.396 0.332 0.000 0.668
#> GSM110398 2 0.6128 0.654 0.084 0.780 0.136
#> GSM110399 2 0.0000 0.904 0.000 1.000 0.000
#> GSM110400 3 0.6295 0.575 0.472 0.000 0.528
#> GSM110401 3 0.5785 -0.396 0.332 0.000 0.668
#> GSM110406 2 0.0000 0.904 0.000 1.000 0.000
#> GSM110407 3 0.2165 0.148 0.064 0.000 0.936
#> GSM110409 3 0.7999 -0.313 0.148 0.196 0.656
#> GSM110410 2 0.0000 0.904 0.000 1.000 0.000
#> GSM110413 2 0.4399 0.804 0.188 0.812 0.000
#> GSM110414 1 0.7533 -0.208 0.668 0.244 0.088
#> GSM110415 3 0.6295 0.575 0.472 0.000 0.528
#> GSM110416 3 0.6295 0.575 0.472 0.000 0.528
#> GSM110418 3 0.6295 0.575 0.472 0.000 0.528
#> GSM110419 3 0.6295 0.575 0.472 0.000 0.528
#> GSM110420 3 0.6295 0.575 0.472 0.000 0.528
#> GSM110421 2 0.4504 0.798 0.196 0.804 0.000
#> GSM110423 3 0.6295 0.575 0.472 0.000 0.528
#> GSM110424 2 0.4504 0.798 0.196 0.804 0.000
#> GSM110425 3 0.6295 0.575 0.472 0.000 0.528
#> GSM110427 2 0.0592 0.898 0.012 0.988 0.000
#> GSM110428 3 0.6295 0.575 0.472 0.000 0.528
#> GSM110430 3 0.5785 -0.396 0.332 0.000 0.668
#> GSM110431 3 0.0000 0.255 0.000 0.000 1.000
#> GSM110432 3 0.6804 0.570 0.460 0.012 0.528
#> GSM110434 2 0.0000 0.904 0.000 1.000 0.000
#> GSM110435 3 0.0000 0.255 0.000 0.000 1.000
#> GSM110437 3 0.5785 -0.396 0.332 0.000 0.668
#> GSM110438 3 0.5621 0.507 0.308 0.000 0.692
#> GSM110388 1 0.6931 0.770 0.528 0.016 0.456
#> GSM110392 1 0.5553 0.507 0.724 0.004 0.272
#> GSM110394 3 0.0592 0.269 0.012 0.000 0.988
#> GSM110402 3 0.6295 0.575 0.472 0.000 0.528
#> GSM110411 1 0.6931 0.770 0.528 0.016 0.456
#> GSM110412 2 0.6095 0.559 0.392 0.608 0.000
#> GSM110417 1 0.6295 0.758 0.528 0.000 0.472
#> GSM110422 2 0.0000 0.904 0.000 1.000 0.000
#> GSM110426 1 0.6295 0.758 0.528 0.000 0.472
#> GSM110429 2 0.1289 0.887 0.032 0.968 0.000
#> GSM110433 2 0.4504 0.798 0.196 0.804 0.000
#> GSM110436 3 0.9147 0.474 0.412 0.144 0.444
#> GSM110440 3 0.4974 -0.226 0.236 0.000 0.764
#> GSM110441 2 0.0000 0.904 0.000 1.000 0.000
#> GSM110444 1 0.7627 0.746 0.528 0.044 0.428
#> GSM110445 3 0.9497 -0.557 0.332 0.200 0.468
#> GSM110446 3 0.4555 0.434 0.200 0.000 0.800
#> GSM110449 2 0.0000 0.904 0.000 1.000 0.000
#> GSM110451 3 0.7940 0.544 0.416 0.060 0.524
#> GSM110391 2 0.4504 0.798 0.196 0.804 0.000
#> GSM110439 2 0.0000 0.904 0.000 1.000 0.000
#> GSM110442 2 0.0000 0.904 0.000 1.000 0.000
#> GSM110443 2 0.4645 0.738 0.176 0.816 0.008
#> GSM110447 3 0.6295 0.575 0.472 0.000 0.528
#> GSM110448 1 0.6931 0.770 0.528 0.016 0.456
#> GSM110450 3 0.5785 -0.396 0.332 0.000 0.668
#> GSM110452 2 0.0000 0.904 0.000 1.000 0.000
#> GSM110453 2 0.0000 0.904 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.2216 0.832 0.000 0.908 0.092 0.000
#> GSM110396 1 0.0469 0.847 0.988 0.000 0.000 0.012
#> GSM110397 1 0.0817 0.845 0.976 0.000 0.000 0.024
#> GSM110398 2 0.4849 0.727 0.064 0.772 0.000 0.164
#> GSM110399 2 0.0921 0.876 0.000 0.972 0.000 0.028
#> GSM110400 3 0.0188 0.920 0.000 0.004 0.996 0.000
#> GSM110401 1 0.0469 0.847 0.988 0.000 0.000 0.012
#> GSM110406 2 0.1284 0.878 0.000 0.964 0.012 0.024
#> GSM110407 1 0.3219 0.806 0.836 0.000 0.164 0.000
#> GSM110409 1 0.2647 0.782 0.880 0.120 0.000 0.000
#> GSM110410 2 0.0817 0.878 0.000 0.976 0.000 0.024
#> GSM110413 2 0.4103 0.681 0.000 0.744 0.000 0.256
#> GSM110414 3 0.3893 0.704 0.000 0.008 0.796 0.196
#> GSM110415 3 0.0592 0.922 0.016 0.000 0.984 0.000
#> GSM110416 3 0.1452 0.913 0.036 0.000 0.956 0.008
#> GSM110418 3 0.1706 0.909 0.036 0.000 0.948 0.016
#> GSM110419 3 0.0376 0.922 0.004 0.000 0.992 0.004
#> GSM110420 3 0.2060 0.898 0.052 0.000 0.932 0.016
#> GSM110421 4 0.4830 0.212 0.000 0.392 0.000 0.608
#> GSM110423 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM110424 2 0.3356 0.756 0.000 0.824 0.000 0.176
#> GSM110425 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM110427 2 0.1389 0.864 0.000 0.952 0.048 0.000
#> GSM110428 3 0.3810 0.730 0.188 0.000 0.804 0.008
#> GSM110430 1 0.0469 0.847 0.988 0.000 0.000 0.012
#> GSM110431 1 0.4630 0.715 0.732 0.000 0.252 0.016
#> GSM110432 3 0.1557 0.894 0.000 0.056 0.944 0.000
#> GSM110434 2 0.0000 0.880 0.000 1.000 0.000 0.000
#> GSM110435 1 0.4364 0.751 0.764 0.000 0.220 0.016
#> GSM110437 1 0.0469 0.847 0.988 0.000 0.000 0.012
#> GSM110438 1 0.5298 0.524 0.612 0.000 0.372 0.016
#> GSM110388 4 0.0592 0.802 0.016 0.000 0.000 0.984
#> GSM110392 4 0.5533 0.677 0.140 0.032 0.064 0.764
#> GSM110394 1 0.4690 0.705 0.724 0.000 0.260 0.016
#> GSM110402 3 0.0817 0.920 0.024 0.000 0.976 0.000
#> GSM110411 4 0.0592 0.802 0.016 0.000 0.000 0.984
#> GSM110412 4 0.1004 0.792 0.000 0.024 0.004 0.972
#> GSM110417 4 0.3266 0.705 0.168 0.000 0.000 0.832
#> GSM110422 2 0.0000 0.880 0.000 1.000 0.000 0.000
#> GSM110426 4 0.4193 0.591 0.268 0.000 0.000 0.732
#> GSM110429 2 0.1867 0.846 0.000 0.928 0.072 0.000
#> GSM110433 2 0.4989 0.159 0.000 0.528 0.000 0.472
#> GSM110436 3 0.2973 0.822 0.000 0.144 0.856 0.000
#> GSM110440 1 0.0804 0.847 0.980 0.000 0.012 0.008
#> GSM110441 2 0.1792 0.863 0.000 0.932 0.000 0.068
#> GSM110444 4 0.0672 0.802 0.008 0.008 0.000 0.984
#> GSM110445 1 0.2179 0.809 0.924 0.064 0.000 0.012
#> GSM110446 1 0.3695 0.791 0.828 0.000 0.156 0.016
#> GSM110449 2 0.2704 0.818 0.000 0.876 0.000 0.124
#> GSM110451 3 0.2868 0.830 0.000 0.136 0.864 0.000
#> GSM110391 4 0.4898 0.135 0.000 0.416 0.000 0.584
#> GSM110439 2 0.0188 0.880 0.000 0.996 0.000 0.004
#> GSM110442 2 0.0188 0.880 0.000 0.996 0.000 0.004
#> GSM110443 2 0.4773 0.596 0.280 0.708 0.008 0.004
#> GSM110447 3 0.0592 0.922 0.016 0.000 0.984 0.000
#> GSM110448 4 0.0921 0.798 0.028 0.000 0.000 0.972
#> GSM110450 1 0.1059 0.842 0.972 0.000 0.016 0.012
#> GSM110452 2 0.0000 0.880 0.000 1.000 0.000 0.000
#> GSM110453 2 0.0000 0.880 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 5 0.4060 0.2504 0.000 0.360 0.000 0.000 0.640
#> GSM110396 1 0.0162 0.8424 0.996 0.000 0.000 0.000 0.004
#> GSM110397 1 0.5508 0.3777 0.604 0.000 0.316 0.076 0.004
#> GSM110398 2 0.6207 0.6127 0.132 0.656 0.000 0.060 0.152
#> GSM110399 2 0.3462 0.7457 0.000 0.792 0.000 0.012 0.196
#> GSM110400 5 0.3452 0.5743 0.000 0.000 0.244 0.000 0.756
#> GSM110401 1 0.0000 0.8424 1.000 0.000 0.000 0.000 0.000
#> GSM110406 2 0.4876 0.5419 0.012 0.544 0.000 0.008 0.436
#> GSM110407 1 0.3169 0.7377 0.856 0.000 0.060 0.000 0.084
#> GSM110409 1 0.1970 0.8055 0.924 0.060 0.004 0.000 0.012
#> GSM110410 2 0.1597 0.7618 0.000 0.940 0.000 0.012 0.048
#> GSM110413 2 0.5956 0.5608 0.000 0.592 0.000 0.196 0.212
#> GSM110414 5 0.6037 0.4746 0.000 0.012 0.232 0.144 0.612
#> GSM110415 3 0.3561 0.3561 0.000 0.000 0.740 0.000 0.260
#> GSM110416 3 0.1121 0.5750 0.000 0.000 0.956 0.000 0.044
#> GSM110418 3 0.0000 0.5924 0.000 0.000 1.000 0.000 0.000
#> GSM110419 5 0.4561 0.2277 0.008 0.000 0.488 0.000 0.504
#> GSM110420 3 0.0000 0.5924 0.000 0.000 1.000 0.000 0.000
#> GSM110421 4 0.6343 0.0449 0.000 0.332 0.000 0.492 0.176
#> GSM110423 5 0.4291 0.3143 0.000 0.000 0.464 0.000 0.536
#> GSM110424 2 0.3593 0.7114 0.000 0.824 0.000 0.116 0.060
#> GSM110425 5 0.4219 0.3980 0.000 0.000 0.416 0.000 0.584
#> GSM110427 5 0.4182 0.2420 0.000 0.400 0.000 0.000 0.600
#> GSM110428 3 0.6645 0.2413 0.244 0.000 0.440 0.000 0.316
#> GSM110430 1 0.0000 0.8424 1.000 0.000 0.000 0.000 0.000
#> GSM110431 3 0.4559 0.0885 0.480 0.000 0.512 0.000 0.008
#> GSM110432 5 0.3760 0.6029 0.000 0.028 0.188 0.000 0.784
#> GSM110434 2 0.1270 0.7524 0.000 0.948 0.000 0.000 0.052
#> GSM110435 3 0.4264 0.2916 0.376 0.000 0.620 0.000 0.004
#> GSM110437 1 0.0162 0.8418 0.996 0.000 0.004 0.000 0.000
#> GSM110438 3 0.3010 0.5783 0.172 0.000 0.824 0.000 0.004
#> GSM110388 4 0.0451 0.7962 0.008 0.000 0.004 0.988 0.000
#> GSM110392 4 0.5745 0.6150 0.084 0.024 0.180 0.696 0.016
#> GSM110394 3 0.4979 0.0641 0.480 0.000 0.492 0.000 0.028
#> GSM110402 3 0.3424 0.3855 0.000 0.000 0.760 0.000 0.240
#> GSM110411 4 0.0000 0.7968 0.000 0.000 0.000 1.000 0.000
#> GSM110412 4 0.0000 0.7968 0.000 0.000 0.000 1.000 0.000
#> GSM110417 4 0.2017 0.7613 0.080 0.000 0.008 0.912 0.000
#> GSM110422 2 0.3305 0.5828 0.000 0.776 0.000 0.000 0.224
#> GSM110426 4 0.4320 0.6755 0.096 0.000 0.120 0.780 0.004
#> GSM110429 5 0.4341 0.3219 0.000 0.404 0.004 0.000 0.592
#> GSM110433 2 0.6383 0.3223 0.000 0.488 0.000 0.328 0.184
#> GSM110436 5 0.4226 0.6181 0.000 0.140 0.084 0.000 0.776
#> GSM110440 1 0.4251 0.2525 0.624 0.000 0.372 0.000 0.004
#> GSM110441 2 0.3513 0.7340 0.000 0.800 0.000 0.020 0.180
#> GSM110444 4 0.0000 0.7968 0.000 0.000 0.000 1.000 0.000
#> GSM110445 1 0.2707 0.7501 0.876 0.100 0.000 0.000 0.024
#> GSM110446 3 0.3333 0.5351 0.208 0.000 0.788 0.000 0.004
#> GSM110449 2 0.3454 0.7345 0.000 0.816 0.000 0.028 0.156
#> GSM110451 5 0.4247 0.6186 0.000 0.132 0.092 0.000 0.776
#> GSM110391 4 0.6445 -0.0658 0.000 0.360 0.000 0.456 0.184
#> GSM110439 2 0.0703 0.7618 0.000 0.976 0.000 0.000 0.024
#> GSM110442 2 0.0880 0.7638 0.000 0.968 0.000 0.000 0.032
#> GSM110443 2 0.5365 0.2760 0.416 0.528 0.000 0.000 0.056
#> GSM110447 3 0.3796 0.2841 0.000 0.000 0.700 0.000 0.300
#> GSM110448 4 0.0566 0.7955 0.012 0.000 0.004 0.984 0.000
#> GSM110450 1 0.0162 0.8424 0.996 0.000 0.000 0.000 0.004
#> GSM110452 2 0.0703 0.7618 0.000 0.976 0.000 0.000 0.024
#> GSM110453 2 0.1043 0.7590 0.000 0.960 0.000 0.000 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 6 0.5383 0.3213 0.000 0.184 0.000 0.000 0.232 0.584
#> GSM110396 1 0.1524 0.7367 0.932 0.000 0.000 0.008 0.060 0.000
#> GSM110397 1 0.6795 0.4053 0.500 0.000 0.236 0.156 0.108 0.000
#> GSM110398 2 0.5763 0.2396 0.072 0.552 0.000 0.008 0.336 0.032
#> GSM110399 2 0.4776 0.2692 0.004 0.588 0.000 0.000 0.356 0.052
#> GSM110400 6 0.3020 0.5170 0.000 0.000 0.076 0.000 0.080 0.844
#> GSM110401 1 0.0146 0.7396 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM110406 5 0.6447 0.0565 0.024 0.240 0.000 0.000 0.436 0.300
#> GSM110407 1 0.3852 0.6659 0.804 0.000 0.048 0.000 0.040 0.108
#> GSM110409 1 0.3331 0.7045 0.852 0.064 0.028 0.000 0.048 0.008
#> GSM110410 2 0.3126 0.4489 0.000 0.752 0.000 0.000 0.248 0.000
#> GSM110413 5 0.5165 0.6184 0.000 0.204 0.000 0.144 0.644 0.008
#> GSM110414 6 0.6230 0.3313 0.000 0.000 0.100 0.076 0.284 0.540
#> GSM110415 3 0.5320 0.2964 0.000 0.000 0.532 0.000 0.116 0.352
#> GSM110416 3 0.1970 0.6459 0.000 0.000 0.912 0.000 0.028 0.060
#> GSM110418 3 0.0713 0.6592 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM110419 6 0.5195 0.0805 0.016 0.000 0.352 0.000 0.064 0.568
#> GSM110420 3 0.0632 0.6589 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM110421 5 0.5160 0.6584 0.000 0.108 0.000 0.320 0.572 0.000
#> GSM110423 6 0.5004 0.1375 0.000 0.000 0.348 0.000 0.084 0.568
#> GSM110424 2 0.4593 0.1707 0.000 0.604 0.000 0.040 0.352 0.004
#> GSM110425 6 0.4681 0.2949 0.004 0.000 0.256 0.000 0.076 0.664
#> GSM110427 6 0.4938 0.2836 0.000 0.356 0.000 0.000 0.076 0.568
#> GSM110428 3 0.6850 0.2048 0.252 0.000 0.364 0.000 0.048 0.336
#> GSM110430 1 0.0260 0.7396 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM110431 1 0.5309 0.1870 0.476 0.000 0.452 0.000 0.032 0.040
#> GSM110432 6 0.2326 0.5646 0.004 0.028 0.020 0.000 0.040 0.908
#> GSM110434 2 0.2201 0.6238 0.000 0.900 0.000 0.000 0.052 0.048
#> GSM110435 3 0.3629 0.2977 0.276 0.000 0.712 0.000 0.012 0.000
#> GSM110437 1 0.1138 0.7374 0.960 0.000 0.004 0.012 0.024 0.000
#> GSM110438 3 0.2958 0.6001 0.088 0.000 0.864 0.004 0.024 0.020
#> GSM110388 4 0.0291 0.8568 0.004 0.000 0.000 0.992 0.004 0.000
#> GSM110392 4 0.6004 0.6491 0.032 0.020 0.180 0.640 0.120 0.008
#> GSM110394 1 0.5479 0.2724 0.508 0.000 0.404 0.000 0.032 0.056
#> GSM110402 3 0.4481 0.4309 0.000 0.000 0.648 0.000 0.056 0.296
#> GSM110411 4 0.0632 0.8503 0.000 0.000 0.000 0.976 0.024 0.000
#> GSM110412 4 0.2006 0.7752 0.000 0.000 0.000 0.892 0.104 0.004
#> GSM110417 4 0.2742 0.8140 0.044 0.000 0.008 0.872 0.076 0.000
#> GSM110422 2 0.4033 0.4704 0.000 0.724 0.000 0.000 0.052 0.224
#> GSM110426 4 0.4244 0.7632 0.048 0.000 0.076 0.780 0.096 0.000
#> GSM110429 6 0.4783 0.1803 0.000 0.428 0.000 0.000 0.052 0.520
#> GSM110433 5 0.5283 0.6805 0.000 0.148 0.000 0.264 0.588 0.000
#> GSM110436 6 0.4000 0.5582 0.000 0.184 0.004 0.000 0.060 0.752
#> GSM110440 1 0.4847 0.5176 0.636 0.000 0.280 0.004 0.080 0.000
#> GSM110441 5 0.4256 0.2099 0.000 0.420 0.000 0.012 0.564 0.004
#> GSM110444 4 0.0790 0.8461 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM110445 1 0.5431 0.4898 0.688 0.184 0.016 0.008 0.072 0.032
#> GSM110446 3 0.2650 0.5991 0.072 0.000 0.880 0.004 0.040 0.004
#> GSM110449 2 0.4359 0.3198 0.000 0.652 0.000 0.008 0.312 0.028
#> GSM110451 6 0.2904 0.5791 0.000 0.112 0.008 0.000 0.028 0.852
#> GSM110391 5 0.5199 0.6759 0.000 0.120 0.000 0.300 0.580 0.000
#> GSM110439 2 0.0692 0.6450 0.000 0.976 0.000 0.000 0.020 0.004
#> GSM110442 2 0.1686 0.6326 0.000 0.924 0.000 0.000 0.064 0.012
#> GSM110443 2 0.6700 0.2628 0.324 0.480 0.020 0.000 0.132 0.044
#> GSM110447 3 0.5624 0.1780 0.000 0.000 0.456 0.000 0.148 0.396
#> GSM110448 4 0.0146 0.8568 0.004 0.000 0.000 0.996 0.000 0.000
#> GSM110450 1 0.1644 0.7366 0.932 0.000 0.004 0.012 0.052 0.000
#> GSM110452 2 0.1003 0.6464 0.000 0.964 0.000 0.000 0.016 0.020
#> GSM110453 2 0.1320 0.6427 0.000 0.948 0.000 0.000 0.036 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) specimen(p) k
#> SD:skmeans 42 0.19593 0.1285 2
#> SD:skmeans 43 0.00283 0.3024 3
#> SD:skmeans 56 0.00530 0.2489 4
#> SD:skmeans 39 0.01905 0.4615 5
#> SD:skmeans 34 0.02061 0.0168 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 17209 rows and 59 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.311 0.521 0.816 0.4031 0.614 0.614
#> 3 3 0.619 0.625 0.847 0.4153 0.783 0.662
#> 4 4 0.708 0.787 0.892 0.2358 0.802 0.583
#> 5 5 0.786 0.781 0.910 0.1146 0.888 0.639
#> 6 6 0.784 0.785 0.887 0.0368 0.961 0.820
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM110395 2 0.0000 0.7602 0.000 1.000
#> GSM110396 1 0.9983 0.4382 0.524 0.476
#> GSM110397 1 0.0000 0.5326 1.000 0.000
#> GSM110398 2 0.9044 0.0636 0.320 0.680
#> GSM110399 2 0.0000 0.7602 0.000 1.000
#> GSM110400 2 0.0000 0.7602 0.000 1.000
#> GSM110401 1 0.9983 0.4382 0.524 0.476
#> GSM110406 2 0.0000 0.7602 0.000 1.000
#> GSM110407 2 0.9977 -0.3804 0.472 0.528
#> GSM110409 2 0.9248 -0.0132 0.340 0.660
#> GSM110410 2 0.0000 0.7602 0.000 1.000
#> GSM110413 2 0.0000 0.7602 0.000 1.000
#> GSM110414 2 0.0000 0.7602 0.000 1.000
#> GSM110415 2 0.4562 0.6819 0.096 0.904
#> GSM110416 2 0.8081 0.4927 0.248 0.752
#> GSM110418 2 0.8081 0.4927 0.248 0.752
#> GSM110419 2 0.0000 0.7602 0.000 1.000
#> GSM110420 2 0.8081 0.4927 0.248 0.752
#> GSM110421 2 0.9775 0.1741 0.412 0.588
#> GSM110423 2 0.4562 0.6819 0.096 0.904
#> GSM110424 2 0.6438 0.5768 0.164 0.836
#> GSM110425 2 0.0000 0.7602 0.000 1.000
#> GSM110427 2 0.0000 0.7602 0.000 1.000
#> GSM110428 2 0.6148 0.5904 0.152 0.848
#> GSM110430 1 0.9983 0.4382 0.524 0.476
#> GSM110431 1 0.9775 0.4574 0.588 0.412
#> GSM110432 2 0.0000 0.7602 0.000 1.000
#> GSM110434 2 0.0000 0.7602 0.000 1.000
#> GSM110435 1 0.9970 0.3475 0.532 0.468
#> GSM110437 1 0.9754 0.4618 0.592 0.408
#> GSM110438 2 0.8081 0.4927 0.248 0.752
#> GSM110388 1 0.8081 0.4541 0.752 0.248
#> GSM110392 2 0.9522 0.3107 0.372 0.628
#> GSM110394 2 0.8861 0.2400 0.304 0.696
#> GSM110402 2 0.1414 0.7481 0.020 0.980
#> GSM110411 1 0.8081 0.4541 0.752 0.248
#> GSM110412 2 0.9998 0.0814 0.492 0.508
#> GSM110417 1 0.4022 0.5417 0.920 0.080
#> GSM110422 2 0.0000 0.7602 0.000 1.000
#> GSM110426 1 0.0000 0.5326 1.000 0.000
#> GSM110429 2 0.0000 0.7602 0.000 1.000
#> GSM110433 2 0.9775 0.1741 0.412 0.588
#> GSM110436 2 0.0000 0.7602 0.000 1.000
#> GSM110440 1 0.9775 0.4574 0.588 0.412
#> GSM110441 2 0.0000 0.7602 0.000 1.000
#> GSM110444 2 0.9775 0.1741 0.412 0.588
#> GSM110445 2 0.9286 -0.0255 0.344 0.656
#> GSM110446 2 0.8081 0.4927 0.248 0.752
#> GSM110449 1 0.9963 0.0851 0.536 0.464
#> GSM110451 2 0.0000 0.7602 0.000 1.000
#> GSM110391 2 0.9775 0.1741 0.412 0.588
#> GSM110439 2 0.0000 0.7602 0.000 1.000
#> GSM110442 2 0.0672 0.7547 0.008 0.992
#> GSM110443 2 0.0000 0.7602 0.000 1.000
#> GSM110447 2 0.1414 0.7481 0.020 0.980
#> GSM110448 1 0.4690 0.5278 0.900 0.100
#> GSM110450 1 0.9998 0.4089 0.508 0.492
#> GSM110452 2 0.0000 0.7602 0.000 1.000
#> GSM110453 2 0.0000 0.7602 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110396 1 0.6307 0.4932 0.512 0.488 0.000
#> GSM110397 1 0.0237 0.5282 0.996 0.000 0.004
#> GSM110398 2 0.6295 -0.4578 0.472 0.528 0.000
#> GSM110399 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110400 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110401 1 0.6260 0.5641 0.552 0.448 0.000
#> GSM110406 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110407 2 0.6286 -0.4387 0.464 0.536 0.000
#> GSM110409 1 0.6267 0.5593 0.548 0.452 0.000
#> GSM110410 2 0.0237 0.7705 0.004 0.996 0.000
#> GSM110413 2 0.0237 0.7705 0.004 0.996 0.000
#> GSM110414 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110415 2 0.7152 0.3191 0.444 0.532 0.024
#> GSM110416 2 0.7159 0.3146 0.448 0.528 0.024
#> GSM110418 2 0.7164 0.3093 0.452 0.524 0.024
#> GSM110419 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110420 2 0.7164 0.3093 0.452 0.524 0.024
#> GSM110421 3 0.1031 0.9172 0.000 0.024 0.976
#> GSM110423 2 0.6180 0.5220 0.260 0.716 0.024
#> GSM110424 2 0.0237 0.7705 0.004 0.996 0.000
#> GSM110425 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110427 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110428 2 0.0237 0.7695 0.004 0.996 0.000
#> GSM110430 1 0.6260 0.5641 0.552 0.448 0.000
#> GSM110431 1 0.1753 0.5404 0.952 0.048 0.000
#> GSM110432 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110434 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110435 1 0.5053 0.4471 0.812 0.164 0.024
#> GSM110437 1 0.0424 0.5356 0.992 0.008 0.000
#> GSM110438 2 0.7164 0.3093 0.452 0.524 0.024
#> GSM110388 3 0.1031 0.9104 0.024 0.000 0.976
#> GSM110392 2 0.7849 0.4550 0.248 0.648 0.104
#> GSM110394 2 0.5331 0.4568 0.184 0.792 0.024
#> GSM110402 2 0.6126 0.4407 0.352 0.644 0.004
#> GSM110411 3 0.1170 0.9142 0.016 0.008 0.976
#> GSM110412 3 0.1031 0.9172 0.000 0.024 0.976
#> GSM110417 3 0.1031 0.9104 0.024 0.000 0.976
#> GSM110422 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110426 3 0.1031 0.8901 0.024 0.000 0.976
#> GSM110429 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110433 3 0.1031 0.9172 0.000 0.024 0.976
#> GSM110436 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110440 1 0.0237 0.5324 0.996 0.004 0.000
#> GSM110441 2 0.0661 0.7638 0.004 0.988 0.008
#> GSM110444 3 0.1031 0.9172 0.000 0.024 0.976
#> GSM110445 1 0.6476 0.5567 0.548 0.448 0.004
#> GSM110446 2 0.7164 0.3093 0.452 0.524 0.024
#> GSM110449 3 0.6809 0.0429 0.012 0.464 0.524
#> GSM110451 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110391 3 0.1031 0.9172 0.000 0.024 0.976
#> GSM110439 2 0.0237 0.7705 0.004 0.996 0.000
#> GSM110442 2 0.0237 0.7705 0.004 0.996 0.000
#> GSM110443 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110447 2 0.5760 0.4697 0.328 0.672 0.000
#> GSM110448 3 0.1031 0.9104 0.024 0.000 0.976
#> GSM110450 1 0.6260 0.5641 0.552 0.448 0.000
#> GSM110452 2 0.0000 0.7723 0.000 1.000 0.000
#> GSM110453 2 0.0237 0.7705 0.004 0.996 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.0188 0.885 0.004 0.996 0.000 0.000
#> GSM110396 1 0.4585 0.670 0.668 0.332 0.000 0.000
#> GSM110397 1 0.4989 0.159 0.528 0.000 0.472 0.000
#> GSM110398 1 0.4456 0.581 0.716 0.280 0.004 0.000
#> GSM110399 2 0.0188 0.885 0.004 0.996 0.000 0.000
#> GSM110400 2 0.0188 0.885 0.004 0.996 0.000 0.000
#> GSM110401 1 0.2973 0.763 0.856 0.144 0.000 0.000
#> GSM110406 2 0.0188 0.885 0.004 0.996 0.000 0.000
#> GSM110407 1 0.4933 0.501 0.568 0.432 0.000 0.000
#> GSM110409 1 0.3801 0.749 0.780 0.220 0.000 0.000
#> GSM110410 2 0.3208 0.823 0.148 0.848 0.004 0.000
#> GSM110413 2 0.2773 0.841 0.116 0.880 0.004 0.000
#> GSM110414 2 0.1978 0.864 0.068 0.928 0.004 0.000
#> GSM110415 3 0.2125 0.859 0.004 0.076 0.920 0.000
#> GSM110416 3 0.0188 0.923 0.000 0.004 0.996 0.000
#> GSM110418 3 0.0188 0.923 0.000 0.004 0.996 0.000
#> GSM110419 2 0.0188 0.885 0.004 0.996 0.000 0.000
#> GSM110420 3 0.0188 0.923 0.000 0.004 0.996 0.000
#> GSM110421 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM110423 3 0.2011 0.860 0.000 0.080 0.920 0.000
#> GSM110424 2 0.2958 0.839 0.116 0.876 0.004 0.004
#> GSM110425 2 0.0188 0.885 0.004 0.996 0.000 0.000
#> GSM110427 2 0.0000 0.885 0.000 1.000 0.000 0.000
#> GSM110428 2 0.0469 0.881 0.012 0.988 0.000 0.000
#> GSM110430 1 0.3024 0.764 0.852 0.148 0.000 0.000
#> GSM110431 3 0.3764 0.716 0.172 0.012 0.816 0.000
#> GSM110432 2 0.0188 0.885 0.004 0.996 0.000 0.000
#> GSM110434 2 0.0469 0.885 0.012 0.988 0.000 0.000
#> GSM110435 3 0.0188 0.923 0.000 0.004 0.996 0.000
#> GSM110437 1 0.3074 0.657 0.848 0.000 0.152 0.000
#> GSM110438 3 0.0188 0.923 0.000 0.004 0.996 0.000
#> GSM110388 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM110392 3 0.4622 0.758 0.004 0.060 0.800 0.136
#> GSM110394 2 0.5028 0.276 0.004 0.596 0.400 0.000
#> GSM110402 2 0.4967 0.249 0.000 0.548 0.452 0.000
#> GSM110411 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM110412 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM110417 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM110422 2 0.0469 0.885 0.012 0.988 0.000 0.000
#> GSM110426 4 0.4967 0.137 0.000 0.000 0.452 0.548
#> GSM110429 2 0.0469 0.885 0.012 0.988 0.000 0.000
#> GSM110433 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM110436 2 0.0188 0.885 0.004 0.996 0.000 0.000
#> GSM110440 1 0.4399 0.619 0.768 0.020 0.212 0.000
#> GSM110441 2 0.3216 0.834 0.124 0.864 0.004 0.008
#> GSM110444 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM110445 1 0.0592 0.698 0.984 0.016 0.000 0.000
#> GSM110446 3 0.0188 0.923 0.000 0.004 0.996 0.000
#> GSM110449 4 0.5589 0.631 0.192 0.080 0.004 0.724
#> GSM110451 2 0.0188 0.885 0.004 0.996 0.000 0.000
#> GSM110391 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM110439 2 0.3257 0.821 0.152 0.844 0.004 0.000
#> GSM110442 2 0.3257 0.821 0.152 0.844 0.004 0.000
#> GSM110443 2 0.0336 0.885 0.008 0.992 0.000 0.000
#> GSM110447 2 0.4855 0.378 0.000 0.600 0.400 0.000
#> GSM110448 4 0.0000 0.922 0.000 0.000 0.000 1.000
#> GSM110450 1 0.3024 0.764 0.852 0.148 0.000 0.000
#> GSM110452 2 0.1118 0.877 0.036 0.964 0.000 0.000
#> GSM110453 2 0.3208 0.823 0.148 0.848 0.004 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.0703 0.8931 0.000 0.976 0.000 0.000 0.024
#> GSM110396 1 0.3508 0.6619 0.748 0.252 0.000 0.000 0.000
#> GSM110397 1 0.4300 0.1398 0.524 0.000 0.476 0.000 0.000
#> GSM110398 5 0.3019 0.7815 0.088 0.048 0.000 0.000 0.864
#> GSM110399 2 0.0000 0.9036 0.000 1.000 0.000 0.000 0.000
#> GSM110400 2 0.0404 0.8995 0.000 0.988 0.000 0.000 0.012
#> GSM110401 1 0.0000 0.8173 1.000 0.000 0.000 0.000 0.000
#> GSM110406 2 0.1121 0.8837 0.000 0.956 0.000 0.000 0.044
#> GSM110407 1 0.4060 0.4794 0.640 0.360 0.000 0.000 0.000
#> GSM110409 1 0.2424 0.7500 0.868 0.132 0.000 0.000 0.000
#> GSM110410 5 0.0880 0.8589 0.000 0.032 0.000 0.000 0.968
#> GSM110413 5 0.0404 0.8558 0.000 0.012 0.000 0.000 0.988
#> GSM110414 2 0.2377 0.8005 0.000 0.872 0.000 0.000 0.128
#> GSM110415 3 0.2329 0.8019 0.000 0.124 0.876 0.000 0.000
#> GSM110416 3 0.0000 0.9282 0.000 0.000 1.000 0.000 0.000
#> GSM110418 3 0.0000 0.9282 0.000 0.000 1.000 0.000 0.000
#> GSM110419 2 0.0000 0.9036 0.000 1.000 0.000 0.000 0.000
#> GSM110420 3 0.0000 0.9282 0.000 0.000 1.000 0.000 0.000
#> GSM110421 4 0.0000 0.9026 0.000 0.000 0.000 1.000 0.000
#> GSM110423 3 0.0290 0.9229 0.000 0.008 0.992 0.000 0.000
#> GSM110424 5 0.0955 0.8602 0.000 0.028 0.000 0.004 0.968
#> GSM110425 2 0.0000 0.9036 0.000 1.000 0.000 0.000 0.000
#> GSM110427 2 0.0000 0.9036 0.000 1.000 0.000 0.000 0.000
#> GSM110428 2 0.0162 0.9024 0.004 0.996 0.000 0.000 0.000
#> GSM110430 1 0.0000 0.8173 1.000 0.000 0.000 0.000 0.000
#> GSM110431 3 0.3343 0.7173 0.172 0.016 0.812 0.000 0.000
#> GSM110432 2 0.0000 0.9036 0.000 1.000 0.000 0.000 0.000
#> GSM110434 2 0.0162 0.9030 0.000 0.996 0.000 0.000 0.004
#> GSM110435 3 0.0000 0.9282 0.000 0.000 1.000 0.000 0.000
#> GSM110437 1 0.0000 0.8173 1.000 0.000 0.000 0.000 0.000
#> GSM110438 3 0.0000 0.9282 0.000 0.000 1.000 0.000 0.000
#> GSM110388 4 0.0000 0.9026 0.000 0.000 0.000 1.000 0.000
#> GSM110392 3 0.3318 0.7053 0.000 0.008 0.800 0.192 0.000
#> GSM110394 2 0.4182 0.3177 0.000 0.600 0.400 0.000 0.000
#> GSM110402 2 0.4542 0.2133 0.000 0.536 0.456 0.000 0.008
#> GSM110411 4 0.0000 0.9026 0.000 0.000 0.000 1.000 0.000
#> GSM110412 4 0.0000 0.9026 0.000 0.000 0.000 1.000 0.000
#> GSM110417 4 0.0000 0.9026 0.000 0.000 0.000 1.000 0.000
#> GSM110422 2 0.0162 0.9028 0.000 0.996 0.000 0.000 0.004
#> GSM110426 4 0.4278 0.1775 0.000 0.000 0.452 0.548 0.000
#> GSM110429 2 0.0162 0.9030 0.000 0.996 0.000 0.000 0.004
#> GSM110433 5 0.4300 -0.0429 0.000 0.000 0.000 0.476 0.524
#> GSM110436 2 0.0000 0.9036 0.000 1.000 0.000 0.000 0.000
#> GSM110440 1 0.2674 0.7370 0.856 0.004 0.140 0.000 0.000
#> GSM110441 5 0.0290 0.8552 0.000 0.008 0.000 0.000 0.992
#> GSM110444 4 0.0000 0.9026 0.000 0.000 0.000 1.000 0.000
#> GSM110445 1 0.0000 0.8173 1.000 0.000 0.000 0.000 0.000
#> GSM110446 3 0.0000 0.9282 0.000 0.000 1.000 0.000 0.000
#> GSM110449 5 0.0609 0.8495 0.000 0.000 0.000 0.020 0.980
#> GSM110451 2 0.0000 0.9036 0.000 1.000 0.000 0.000 0.000
#> GSM110391 4 0.3424 0.6412 0.000 0.000 0.000 0.760 0.240
#> GSM110439 5 0.0703 0.8599 0.000 0.024 0.000 0.000 0.976
#> GSM110442 5 0.3143 0.7186 0.000 0.204 0.000 0.000 0.796
#> GSM110443 2 0.2171 0.8474 0.064 0.912 0.000 0.000 0.024
#> GSM110447 2 0.4350 0.3374 0.000 0.588 0.408 0.000 0.004
#> GSM110448 4 0.0000 0.9026 0.000 0.000 0.000 1.000 0.000
#> GSM110450 1 0.0162 0.8170 0.996 0.004 0.000 0.000 0.000
#> GSM110452 2 0.0404 0.8997 0.000 0.988 0.000 0.000 0.012
#> GSM110453 5 0.3003 0.7408 0.000 0.188 0.000 0.000 0.812
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.0993 0.890 0.000 0.964 0.000 0.000 0.024 0.012
#> GSM110396 6 0.3862 0.783 0.132 0.096 0.000 0.000 0.000 0.772
#> GSM110397 1 0.3991 0.111 0.524 0.000 0.472 0.000 0.000 0.004
#> GSM110398 5 0.4640 0.715 0.088 0.020 0.000 0.000 0.720 0.172
#> GSM110399 2 0.0260 0.898 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM110400 2 0.0508 0.898 0.000 0.984 0.000 0.000 0.012 0.004
#> GSM110401 1 0.0000 0.860 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110406 2 0.1367 0.883 0.000 0.944 0.000 0.000 0.044 0.012
#> GSM110407 6 0.3878 0.785 0.116 0.112 0.000 0.000 0.000 0.772
#> GSM110409 1 0.3396 0.696 0.812 0.116 0.000 0.000 0.000 0.072
#> GSM110410 5 0.0858 0.816 0.000 0.028 0.000 0.000 0.968 0.004
#> GSM110413 5 0.1492 0.809 0.000 0.036 0.000 0.000 0.940 0.024
#> GSM110414 2 0.2651 0.832 0.000 0.860 0.000 0.000 0.112 0.028
#> GSM110415 3 0.2527 0.797 0.000 0.108 0.868 0.000 0.000 0.024
#> GSM110416 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110418 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110419 2 0.0146 0.900 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM110420 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110421 4 0.0458 0.891 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM110423 3 0.0622 0.918 0.000 0.008 0.980 0.000 0.000 0.012
#> GSM110424 5 0.1418 0.815 0.000 0.024 0.000 0.000 0.944 0.032
#> GSM110425 2 0.0146 0.900 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM110427 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110428 2 0.0260 0.899 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM110430 1 0.0000 0.860 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110431 6 0.3348 0.743 0.000 0.016 0.216 0.000 0.000 0.768
#> GSM110432 2 0.0146 0.900 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM110434 2 0.1863 0.859 0.000 0.896 0.000 0.000 0.000 0.104
#> GSM110435 6 0.3244 0.683 0.000 0.000 0.268 0.000 0.000 0.732
#> GSM110437 1 0.0000 0.860 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110438 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110388 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110392 3 0.3231 0.713 0.000 0.008 0.800 0.180 0.000 0.012
#> GSM110394 6 0.2996 0.711 0.000 0.228 0.000 0.000 0.000 0.772
#> GSM110402 2 0.4080 0.260 0.000 0.536 0.456 0.000 0.008 0.000
#> GSM110411 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110412 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110417 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110422 2 0.0291 0.899 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM110426 4 0.3843 0.183 0.000 0.000 0.452 0.548 0.000 0.000
#> GSM110429 2 0.1814 0.861 0.000 0.900 0.000 0.000 0.000 0.100
#> GSM110433 5 0.4250 0.047 0.000 0.000 0.000 0.456 0.528 0.016
#> GSM110436 2 0.0547 0.896 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM110440 6 0.3530 0.756 0.152 0.000 0.056 0.000 0.000 0.792
#> GSM110441 5 0.0622 0.812 0.000 0.008 0.000 0.000 0.980 0.012
#> GSM110444 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110445 1 0.0000 0.860 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110446 3 0.0000 0.930 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110449 5 0.2199 0.796 0.000 0.000 0.000 0.020 0.892 0.088
#> GSM110451 2 0.0146 0.900 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM110391 4 0.3534 0.612 0.000 0.000 0.000 0.740 0.244 0.016
#> GSM110439 5 0.2199 0.805 0.000 0.020 0.000 0.000 0.892 0.088
#> GSM110442 5 0.3043 0.679 0.000 0.200 0.000 0.000 0.792 0.008
#> GSM110443 2 0.2510 0.857 0.060 0.892 0.000 0.000 0.024 0.024
#> GSM110447 2 0.4417 0.407 0.000 0.588 0.384 0.000 0.004 0.024
#> GSM110448 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110450 1 0.0146 0.857 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM110452 2 0.3422 0.769 0.000 0.788 0.000 0.000 0.036 0.176
#> GSM110453 5 0.4269 0.677 0.000 0.184 0.000 0.000 0.724 0.092
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) specimen(p) k
#> SD:pam 32 0.50320 1.000 2
#> SD:pam 44 0.01500 0.827 3
#> SD:pam 54 0.00831 0.419 4
#> SD:pam 52 0.04739 0.305 5
#> SD:pam 54 0.11488 0.339 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 17209 rows and 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.251 0.648 0.801 0.4072 0.614 0.614
#> 3 3 0.473 0.590 0.817 0.5157 0.663 0.482
#> 4 4 0.469 0.503 0.778 0.1481 0.742 0.420
#> 5 5 0.720 0.697 0.856 0.0803 0.842 0.526
#> 6 6 0.705 0.559 0.785 0.0769 0.859 0.476
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM110395 2 0.0672 0.7577 0.008 0.992
#> GSM110396 2 0.4298 0.7485 0.088 0.912
#> GSM110397 1 0.8386 0.8005 0.732 0.268
#> GSM110398 2 0.0672 0.7554 0.008 0.992
#> GSM110399 2 0.3733 0.7422 0.072 0.928
#> GSM110400 2 0.3274 0.7703 0.060 0.940
#> GSM110401 2 0.4298 0.7485 0.088 0.912
#> GSM110406 2 0.3584 0.7444 0.068 0.932
#> GSM110407 2 0.8386 0.7080 0.268 0.732
#> GSM110409 2 0.4298 0.7485 0.088 0.912
#> GSM110410 2 0.9552 -0.2487 0.376 0.624
#> GSM110413 2 0.3733 0.7415 0.072 0.928
#> GSM110414 1 0.9983 0.6320 0.524 0.476
#> GSM110415 1 0.9933 0.6013 0.548 0.452
#> GSM110416 2 0.9248 0.6431 0.340 0.660
#> GSM110418 1 0.9795 -0.0466 0.584 0.416
#> GSM110419 2 0.6973 0.7349 0.188 0.812
#> GSM110420 1 0.9686 0.0323 0.604 0.396
#> GSM110421 1 0.9087 0.7998 0.676 0.324
#> GSM110423 2 0.7674 0.7121 0.224 0.776
#> GSM110424 2 1.0000 -0.5921 0.496 0.504
#> GSM110425 2 0.6801 0.7355 0.180 0.820
#> GSM110427 2 0.0938 0.7557 0.012 0.988
#> GSM110428 2 0.8386 0.7080 0.268 0.732
#> GSM110430 2 0.4298 0.7485 0.088 0.912
#> GSM110431 2 0.8386 0.7080 0.268 0.732
#> GSM110432 2 0.6801 0.7355 0.180 0.820
#> GSM110434 2 0.3733 0.7422 0.072 0.928
#> GSM110435 2 0.8386 0.7080 0.268 0.732
#> GSM110437 2 0.4298 0.7485 0.088 0.912
#> GSM110438 2 0.8386 0.7080 0.268 0.732
#> GSM110388 1 0.8016 0.8086 0.756 0.244
#> GSM110392 2 0.9833 -0.4164 0.424 0.576
#> GSM110394 2 0.8386 0.7080 0.268 0.732
#> GSM110402 2 0.6801 0.7355 0.180 0.820
#> GSM110411 1 0.8144 0.8101 0.748 0.252
#> GSM110412 1 0.9170 0.8027 0.668 0.332
#> GSM110417 1 0.8016 0.8086 0.756 0.244
#> GSM110422 2 0.0672 0.7577 0.008 0.992
#> GSM110426 1 0.8144 0.8054 0.748 0.252
#> GSM110429 2 0.0672 0.7577 0.008 0.992
#> GSM110433 1 0.9087 0.7998 0.676 0.324
#> GSM110436 2 0.3431 0.7704 0.064 0.936
#> GSM110440 2 0.8267 0.7133 0.260 0.740
#> GSM110441 2 0.3733 0.7422 0.072 0.928
#> GSM110444 1 0.9170 0.8027 0.668 0.332
#> GSM110445 2 0.4431 0.7474 0.092 0.908
#> GSM110446 2 0.8207 0.7156 0.256 0.744
#> GSM110449 2 0.1184 0.7536 0.016 0.984
#> GSM110451 2 0.6247 0.7474 0.156 0.844
#> GSM110391 1 0.9087 0.7998 0.676 0.324
#> GSM110439 2 0.3733 0.7422 0.072 0.928
#> GSM110442 2 0.3733 0.7422 0.072 0.928
#> GSM110443 2 0.0000 0.7578 0.000 1.000
#> GSM110447 2 0.9977 -0.0240 0.472 0.528
#> GSM110448 1 0.8016 0.8086 0.756 0.244
#> GSM110450 2 0.7219 0.7400 0.200 0.800
#> GSM110452 2 0.3733 0.7422 0.072 0.928
#> GSM110453 2 0.3733 0.7422 0.072 0.928
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.7353 0.08481 0.032 0.532 0.436
#> GSM110396 2 0.6936 0.62308 0.064 0.704 0.232
#> GSM110397 1 0.6326 0.53327 0.688 0.020 0.292
#> GSM110398 2 0.2384 0.75576 0.056 0.936 0.008
#> GSM110399 2 0.0237 0.75838 0.000 0.996 0.004
#> GSM110400 3 0.0661 0.63723 0.004 0.008 0.988
#> GSM110401 2 0.6283 0.66994 0.064 0.760 0.176
#> GSM110406 2 0.0424 0.76022 0.000 0.992 0.008
#> GSM110407 2 0.6927 0.59310 0.060 0.700 0.240
#> GSM110409 2 0.6297 0.67026 0.060 0.756 0.184
#> GSM110410 3 0.7670 0.28768 0.068 0.312 0.620
#> GSM110413 2 0.3038 0.71566 0.000 0.896 0.104
#> GSM110414 1 0.6936 0.17928 0.524 0.016 0.460
#> GSM110415 3 0.4887 0.45898 0.228 0.000 0.772
#> GSM110416 3 0.0661 0.63682 0.008 0.004 0.988
#> GSM110418 3 0.0661 0.63682 0.008 0.004 0.988
#> GSM110419 3 0.6180 0.31453 0.000 0.416 0.584
#> GSM110420 3 0.0661 0.63682 0.008 0.004 0.988
#> GSM110421 1 0.1170 0.90922 0.976 0.016 0.008
#> GSM110423 3 0.0475 0.63728 0.004 0.004 0.992
#> GSM110424 3 0.8868 0.26951 0.172 0.260 0.568
#> GSM110425 3 0.0475 0.63728 0.004 0.004 0.992
#> GSM110427 2 0.7099 0.21637 0.028 0.588 0.384
#> GSM110428 3 0.6204 0.29205 0.000 0.424 0.576
#> GSM110430 2 0.6283 0.66994 0.064 0.760 0.176
#> GSM110431 3 0.6421 0.28718 0.004 0.424 0.572
#> GSM110432 3 0.6267 0.24787 0.000 0.452 0.548
#> GSM110434 2 0.0424 0.76022 0.000 0.992 0.008
#> GSM110435 3 0.6516 0.17207 0.004 0.480 0.516
#> GSM110437 2 0.6283 0.66994 0.064 0.760 0.176
#> GSM110438 3 0.6168 0.33304 0.000 0.412 0.588
#> GSM110388 1 0.0000 0.91396 1.000 0.000 0.000
#> GSM110392 3 0.5096 0.54024 0.080 0.084 0.836
#> GSM110394 3 0.6513 0.18260 0.004 0.476 0.520
#> GSM110402 3 0.0661 0.63729 0.004 0.008 0.988
#> GSM110411 1 0.0000 0.91396 1.000 0.000 0.000
#> GSM110412 1 0.0848 0.91175 0.984 0.008 0.008
#> GSM110417 1 0.0000 0.91396 1.000 0.000 0.000
#> GSM110422 2 0.6570 0.37845 0.028 0.680 0.292
#> GSM110426 1 0.0000 0.91396 1.000 0.000 0.000
#> GSM110429 2 0.6381 0.28037 0.012 0.648 0.340
#> GSM110433 1 0.1315 0.90681 0.972 0.020 0.008
#> GSM110436 3 0.5621 0.44879 0.000 0.308 0.692
#> GSM110440 3 0.7489 -0.00518 0.036 0.468 0.496
#> GSM110441 2 0.3038 0.71566 0.000 0.896 0.104
#> GSM110444 1 0.0237 0.91352 0.996 0.004 0.000
#> GSM110445 2 0.2902 0.75517 0.064 0.920 0.016
#> GSM110446 3 0.4121 0.57871 0.000 0.168 0.832
#> GSM110449 2 0.3896 0.74222 0.060 0.888 0.052
#> GSM110451 3 0.6225 0.28364 0.000 0.432 0.568
#> GSM110391 1 0.1170 0.90922 0.976 0.016 0.008
#> GSM110439 2 0.0424 0.75910 0.000 0.992 0.008
#> GSM110442 2 0.2448 0.73290 0.000 0.924 0.076
#> GSM110443 2 0.2703 0.75744 0.056 0.928 0.016
#> GSM110447 3 0.0892 0.62822 0.020 0.000 0.980
#> GSM110448 1 0.0000 0.91396 1.000 0.000 0.000
#> GSM110450 2 0.6976 0.62198 0.064 0.700 0.236
#> GSM110452 2 0.0424 0.75910 0.000 0.992 0.008
#> GSM110453 2 0.0747 0.76102 0.000 0.984 0.016
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.3610 0.4708 0.000 0.800 0.200 0.000
#> GSM110396 1 0.4963 0.4669 0.696 0.284 0.020 0.000
#> GSM110397 1 0.6997 0.2641 0.572 0.008 0.116 0.304
#> GSM110398 2 0.4454 0.4066 0.308 0.692 0.000 0.000
#> GSM110399 2 0.2973 0.5966 0.144 0.856 0.000 0.000
#> GSM110400 3 0.3486 0.6607 0.000 0.188 0.812 0.000
#> GSM110401 1 0.0000 0.7227 1.000 0.000 0.000 0.000
#> GSM110406 2 0.4819 0.3231 0.344 0.652 0.004 0.000
#> GSM110407 1 0.3852 0.6092 0.800 0.008 0.192 0.000
#> GSM110409 1 0.3610 0.6361 0.800 0.200 0.000 0.000
#> GSM110410 2 0.4382 0.3631 0.000 0.704 0.296 0.000
#> GSM110413 2 0.2149 0.6259 0.088 0.912 0.000 0.000
#> GSM110414 3 0.7498 0.0585 0.000 0.216 0.492 0.292
#> GSM110415 3 0.2675 0.6672 0.000 0.008 0.892 0.100
#> GSM110416 3 0.0000 0.7166 0.000 0.000 1.000 0.000
#> GSM110418 3 0.0000 0.7166 0.000 0.000 1.000 0.000
#> GSM110419 3 0.4843 0.4190 0.000 0.396 0.604 0.000
#> GSM110420 3 0.0000 0.7166 0.000 0.000 1.000 0.000
#> GSM110421 4 0.4804 0.5554 0.000 0.384 0.000 0.616
#> GSM110423 3 0.0000 0.7166 0.000 0.000 1.000 0.000
#> GSM110424 2 0.6446 0.2479 0.000 0.584 0.328 0.088
#> GSM110425 3 0.0000 0.7166 0.000 0.000 1.000 0.000
#> GSM110427 2 0.1022 0.6212 0.000 0.968 0.032 0.000
#> GSM110428 3 0.4843 0.4190 0.000 0.396 0.604 0.000
#> GSM110430 1 0.0000 0.7227 1.000 0.000 0.000 0.000
#> GSM110431 2 0.7684 -0.1844 0.216 0.396 0.388 0.000
#> GSM110432 2 0.5060 0.0511 0.004 0.584 0.412 0.000
#> GSM110434 2 0.2868 0.6050 0.136 0.864 0.000 0.000
#> GSM110435 2 0.7700 -0.1811 0.220 0.396 0.384 0.000
#> GSM110437 1 0.0000 0.7227 1.000 0.000 0.000 0.000
#> GSM110438 3 0.6600 0.3807 0.084 0.396 0.520 0.000
#> GSM110388 4 0.0000 0.7713 0.000 0.000 0.000 1.000
#> GSM110392 3 0.6574 0.5085 0.092 0.196 0.680 0.032
#> GSM110394 2 0.7684 -0.1839 0.216 0.396 0.388 0.000
#> GSM110402 3 0.4103 0.6054 0.000 0.256 0.744 0.000
#> GSM110411 4 0.0000 0.7713 0.000 0.000 0.000 1.000
#> GSM110412 4 0.3873 0.6812 0.000 0.228 0.000 0.772
#> GSM110417 4 0.0000 0.7713 0.000 0.000 0.000 1.000
#> GSM110422 2 0.0672 0.6233 0.008 0.984 0.008 0.000
#> GSM110426 4 0.1637 0.7269 0.060 0.000 0.000 0.940
#> GSM110429 2 0.2675 0.5814 0.008 0.892 0.100 0.000
#> GSM110433 4 0.5112 0.5489 0.000 0.384 0.008 0.608
#> GSM110436 2 0.4898 0.0655 0.000 0.584 0.416 0.000
#> GSM110440 2 0.7743 -0.1083 0.368 0.400 0.232 0.000
#> GSM110441 2 0.2011 0.6287 0.080 0.920 0.000 0.000
#> GSM110444 4 0.0000 0.7713 0.000 0.000 0.000 1.000
#> GSM110445 1 0.3311 0.6527 0.828 0.172 0.000 0.000
#> GSM110446 3 0.7349 0.3704 0.164 0.364 0.472 0.000
#> GSM110449 2 0.2469 0.6202 0.108 0.892 0.000 0.000
#> GSM110451 2 0.4843 0.1040 0.000 0.604 0.396 0.000
#> GSM110391 4 0.4804 0.5554 0.000 0.384 0.000 0.616
#> GSM110439 2 0.1716 0.6319 0.064 0.936 0.000 0.000
#> GSM110442 2 0.1716 0.6318 0.064 0.936 0.000 0.000
#> GSM110443 2 0.3486 0.5618 0.188 0.812 0.000 0.000
#> GSM110447 3 0.0469 0.7142 0.000 0.012 0.988 0.000
#> GSM110448 4 0.0000 0.7713 0.000 0.000 0.000 1.000
#> GSM110450 1 0.7212 0.2320 0.516 0.324 0.160 0.000
#> GSM110452 2 0.2149 0.6279 0.088 0.912 0.000 0.000
#> GSM110453 2 0.2408 0.6229 0.104 0.896 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.3916 0.62864 0.000 0.732 0.256 0.000 0.012
#> GSM110396 1 0.1357 0.79230 0.948 0.048 0.004 0.000 0.000
#> GSM110397 4 0.4929 0.55233 0.312 0.008 0.032 0.648 0.000
#> GSM110398 2 0.3305 0.68657 0.224 0.776 0.000 0.000 0.000
#> GSM110399 2 0.0451 0.87539 0.004 0.988 0.008 0.000 0.000
#> GSM110400 3 0.1444 0.69740 0.000 0.040 0.948 0.000 0.012
#> GSM110401 1 0.0000 0.79257 1.000 0.000 0.000 0.000 0.000
#> GSM110406 2 0.0579 0.87455 0.008 0.984 0.008 0.000 0.000
#> GSM110407 1 0.4364 0.59380 0.736 0.048 0.216 0.000 0.000
#> GSM110409 1 0.3456 0.73252 0.800 0.184 0.016 0.000 0.000
#> GSM110410 5 0.5470 0.59993 0.000 0.272 0.080 0.008 0.640
#> GSM110413 2 0.2852 0.73828 0.000 0.828 0.000 0.000 0.172
#> GSM110414 5 0.2642 0.82092 0.000 0.008 0.104 0.008 0.880
#> GSM110415 3 0.1369 0.70435 0.000 0.008 0.956 0.008 0.028
#> GSM110416 3 0.0794 0.71000 0.000 0.000 0.972 0.000 0.028
#> GSM110418 3 0.0794 0.71000 0.000 0.000 0.972 0.000 0.028
#> GSM110419 3 0.4489 0.21127 0.008 0.420 0.572 0.000 0.000
#> GSM110420 3 0.0955 0.70938 0.000 0.000 0.968 0.004 0.028
#> GSM110421 5 0.1341 0.86974 0.000 0.000 0.000 0.056 0.944
#> GSM110423 3 0.0794 0.71000 0.000 0.000 0.972 0.000 0.028
#> GSM110424 5 0.2824 0.84479 0.000 0.024 0.088 0.008 0.880
#> GSM110425 3 0.0794 0.71000 0.000 0.000 0.972 0.000 0.028
#> GSM110427 2 0.2046 0.85324 0.000 0.916 0.068 0.000 0.016
#> GSM110428 3 0.5467 0.27744 0.384 0.068 0.548 0.000 0.000
#> GSM110430 1 0.0000 0.79257 1.000 0.000 0.000 0.000 0.000
#> GSM110431 3 0.5467 0.27744 0.384 0.068 0.548 0.000 0.000
#> GSM110432 2 0.4310 0.34953 0.000 0.604 0.392 0.000 0.004
#> GSM110434 2 0.0290 0.87560 0.000 0.992 0.008 0.000 0.000
#> GSM110435 3 0.5527 0.26149 0.388 0.072 0.540 0.000 0.000
#> GSM110437 1 0.0000 0.79257 1.000 0.000 0.000 0.000 0.000
#> GSM110438 3 0.5357 0.38738 0.344 0.068 0.588 0.000 0.000
#> GSM110388 4 0.0000 0.93657 0.000 0.000 0.000 1.000 0.000
#> GSM110392 3 0.5101 0.52812 0.172 0.072 0.732 0.004 0.020
#> GSM110394 3 0.5535 0.25090 0.392 0.072 0.536 0.000 0.000
#> GSM110402 3 0.1197 0.69413 0.000 0.048 0.952 0.000 0.000
#> GSM110411 4 0.0000 0.93657 0.000 0.000 0.000 1.000 0.000
#> GSM110412 5 0.2597 0.85836 0.000 0.000 0.024 0.092 0.884
#> GSM110417 4 0.0000 0.93657 0.000 0.000 0.000 1.000 0.000
#> GSM110422 2 0.1704 0.85620 0.000 0.928 0.068 0.000 0.004
#> GSM110426 4 0.0162 0.93396 0.004 0.000 0.000 0.996 0.000
#> GSM110429 2 0.1942 0.85444 0.000 0.920 0.068 0.000 0.012
#> GSM110433 5 0.1341 0.86974 0.000 0.000 0.000 0.056 0.944
#> GSM110436 3 0.4582 0.17312 0.000 0.416 0.572 0.000 0.012
#> GSM110440 1 0.5622 0.00767 0.508 0.076 0.416 0.000 0.000
#> GSM110441 2 0.0290 0.87042 0.000 0.992 0.000 0.000 0.008
#> GSM110444 4 0.0000 0.93657 0.000 0.000 0.000 1.000 0.000
#> GSM110445 1 0.2690 0.73013 0.844 0.156 0.000 0.000 0.000
#> GSM110446 3 0.4923 0.50073 0.252 0.068 0.680 0.000 0.000
#> GSM110449 2 0.1894 0.83151 0.072 0.920 0.000 0.000 0.008
#> GSM110451 2 0.4588 0.36423 0.000 0.604 0.380 0.000 0.016
#> GSM110391 5 0.1341 0.86974 0.000 0.000 0.000 0.056 0.944
#> GSM110439 2 0.0290 0.87560 0.000 0.992 0.008 0.000 0.000
#> GSM110442 2 0.0000 0.87211 0.000 1.000 0.000 0.000 0.000
#> GSM110443 2 0.1211 0.86990 0.024 0.960 0.016 0.000 0.000
#> GSM110447 3 0.1082 0.70608 0.000 0.008 0.964 0.000 0.028
#> GSM110448 4 0.0000 0.93657 0.000 0.000 0.000 1.000 0.000
#> GSM110450 1 0.3442 0.75230 0.836 0.104 0.060 0.000 0.000
#> GSM110452 2 0.0290 0.87560 0.000 0.992 0.008 0.000 0.000
#> GSM110453 2 0.0290 0.87560 0.000 0.992 0.008 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.1682 0.5656 0.000 0.928 0.020 0.000 0.000 0.052
#> GSM110396 1 0.3136 0.5474 0.768 0.004 0.000 0.000 0.000 0.228
#> GSM110397 4 0.3724 0.7254 0.188 0.000 0.028 0.772 0.000 0.012
#> GSM110398 6 0.3658 0.4512 0.216 0.032 0.000 0.000 0.000 0.752
#> GSM110399 6 0.3717 0.2696 0.000 0.384 0.000 0.000 0.000 0.616
#> GSM110400 3 0.3789 0.4570 0.000 0.416 0.584 0.000 0.000 0.000
#> GSM110401 1 0.2762 0.5600 0.804 0.000 0.000 0.000 0.000 0.196
#> GSM110406 2 0.4086 -0.1078 0.008 0.528 0.000 0.000 0.000 0.464
#> GSM110407 1 0.4244 0.5685 0.720 0.000 0.200 0.000 0.000 0.080
#> GSM110409 1 0.1806 0.5918 0.908 0.004 0.000 0.000 0.000 0.088
#> GSM110410 5 0.5144 0.3952 0.000 0.192 0.012 0.000 0.656 0.140
#> GSM110413 6 0.5279 0.4596 0.000 0.200 0.000 0.000 0.196 0.604
#> GSM110414 5 0.3955 0.3948 0.000 0.008 0.384 0.000 0.608 0.000
#> GSM110415 3 0.1124 0.8109 0.000 0.008 0.956 0.000 0.036 0.000
#> GSM110416 3 0.0000 0.8346 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110418 3 0.0000 0.8346 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110419 2 0.4887 0.2022 0.088 0.612 0.300 0.000 0.000 0.000
#> GSM110420 3 0.0000 0.8346 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110421 5 0.0000 0.8431 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM110423 3 0.0260 0.8352 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM110424 5 0.0508 0.8393 0.000 0.004 0.012 0.000 0.984 0.000
#> GSM110425 3 0.0260 0.8352 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM110427 2 0.0820 0.5723 0.000 0.972 0.012 0.000 0.000 0.016
#> GSM110428 1 0.5465 0.5093 0.572 0.208 0.220 0.000 0.000 0.000
#> GSM110430 1 0.2762 0.5600 0.804 0.000 0.000 0.000 0.000 0.196
#> GSM110431 1 0.5395 0.5178 0.584 0.196 0.220 0.000 0.000 0.000
#> GSM110432 2 0.1075 0.5606 0.000 0.952 0.048 0.000 0.000 0.000
#> GSM110434 2 0.3828 0.1669 0.000 0.560 0.000 0.000 0.000 0.440
#> GSM110435 1 0.5303 0.5306 0.600 0.196 0.204 0.000 0.000 0.000
#> GSM110437 1 0.2854 0.5569 0.792 0.000 0.000 0.000 0.000 0.208
#> GSM110438 1 0.5815 0.1128 0.472 0.200 0.328 0.000 0.000 0.000
#> GSM110388 4 0.0000 0.9582 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110392 3 0.6239 0.1469 0.368 0.016 0.420 0.000 0.196 0.000
#> GSM110394 1 0.5373 0.5214 0.588 0.196 0.216 0.000 0.000 0.000
#> GSM110402 3 0.3342 0.6057 0.012 0.228 0.760 0.000 0.000 0.000
#> GSM110411 4 0.0000 0.9582 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110412 5 0.1471 0.8112 0.000 0.000 0.004 0.064 0.932 0.000
#> GSM110417 4 0.0000 0.9582 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110422 2 0.1196 0.5676 0.000 0.952 0.008 0.000 0.000 0.040
#> GSM110426 4 0.0000 0.9582 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110429 2 0.0260 0.5704 0.000 0.992 0.008 0.000 0.000 0.000
#> GSM110433 5 0.0000 0.8431 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM110436 2 0.2941 0.4038 0.000 0.780 0.220 0.000 0.000 0.000
#> GSM110440 1 0.4613 0.5653 0.688 0.196 0.116 0.000 0.000 0.000
#> GSM110441 6 0.2996 0.5347 0.000 0.228 0.000 0.000 0.000 0.772
#> GSM110444 4 0.0000 0.9582 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110445 1 0.3923 0.3709 0.620 0.008 0.000 0.000 0.000 0.372
#> GSM110446 1 0.5852 0.0123 0.440 0.196 0.364 0.000 0.000 0.000
#> GSM110449 6 0.1334 0.5938 0.020 0.032 0.000 0.000 0.000 0.948
#> GSM110451 2 0.0937 0.5623 0.000 0.960 0.040 0.000 0.000 0.000
#> GSM110391 5 0.0000 0.8431 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM110439 2 0.3828 0.1669 0.000 0.560 0.000 0.000 0.000 0.440
#> GSM110442 2 0.3838 0.1435 0.000 0.552 0.000 0.000 0.000 0.448
#> GSM110443 6 0.4455 0.4862 0.080 0.232 0.000 0.000 0.000 0.688
#> GSM110447 3 0.0260 0.8352 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM110448 4 0.0000 0.9582 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110450 1 0.3023 0.4845 0.784 0.004 0.000 0.000 0.000 0.212
#> GSM110452 2 0.3828 0.1669 0.000 0.560 0.000 0.000 0.000 0.440
#> GSM110453 2 0.3828 0.1669 0.000 0.560 0.000 0.000 0.000 0.440
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) specimen(p) k
#> SD:mclust 53 0.17524 1.000 2
#> SD:mclust 41 0.08799 0.431 3
#> SD:mclust 39 0.00689 0.187 4
#> SD:mclust 49 0.14885 0.602 5
#> SD:mclust 39 0.03389 0.648 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 17209 rows and 59 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 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 0.367 0.710 0.819 0.4870 0.492 0.492
#> 3 3 0.427 0.619 0.770 0.3712 0.681 0.438
#> 4 4 0.608 0.735 0.830 0.1185 0.812 0.505
#> 5 5 0.658 0.639 0.805 0.0599 0.933 0.746
#> 6 6 0.655 0.482 0.716 0.0393 0.896 0.598
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
#> GSM110395 2 0.9710 0.8050 0.400 0.600
#> GSM110396 1 0.8081 0.7142 0.752 0.248
#> GSM110397 1 0.9710 0.6312 0.600 0.400
#> GSM110398 1 0.7219 0.7332 0.800 0.200
#> GSM110399 2 0.9732 0.8013 0.404 0.596
#> GSM110400 2 0.9710 0.8050 0.400 0.600
#> GSM110401 1 0.6973 0.7370 0.812 0.188
#> GSM110406 2 0.9710 0.8050 0.400 0.600
#> GSM110407 1 0.0000 0.7498 1.000 0.000
#> GSM110409 1 0.0000 0.7498 1.000 0.000
#> GSM110410 2 0.6887 0.7084 0.184 0.816
#> GSM110413 2 0.0000 0.5857 0.000 1.000
#> GSM110414 2 0.7299 0.7194 0.204 0.796
#> GSM110415 2 0.9427 0.7745 0.360 0.640
#> GSM110416 1 0.0938 0.7373 0.988 0.012
#> GSM110418 1 0.0000 0.7498 1.000 0.000
#> GSM110419 1 0.3274 0.6732 0.940 0.060
#> GSM110420 1 0.0000 0.7498 1.000 0.000
#> GSM110421 2 0.0000 0.5857 0.000 1.000
#> GSM110423 2 0.9710 0.8050 0.400 0.600
#> GSM110424 2 0.3733 0.6374 0.072 0.928
#> GSM110425 2 0.9710 0.8050 0.400 0.600
#> GSM110427 2 0.9710 0.8050 0.400 0.600
#> GSM110428 1 0.0000 0.7498 1.000 0.000
#> GSM110430 1 0.5059 0.7508 0.888 0.112
#> GSM110431 1 0.0000 0.7498 1.000 0.000
#> GSM110432 2 0.9732 0.8013 0.404 0.596
#> GSM110434 2 0.9710 0.8050 0.400 0.600
#> GSM110435 1 0.0000 0.7498 1.000 0.000
#> GSM110437 1 0.5737 0.7480 0.864 0.136
#> GSM110438 1 0.0000 0.7498 1.000 0.000
#> GSM110388 1 0.9710 0.6312 0.600 0.400
#> GSM110392 1 0.9491 0.6405 0.632 0.368
#> GSM110394 1 0.0000 0.7498 1.000 0.000
#> GSM110402 2 0.9732 0.8013 0.404 0.596
#> GSM110411 1 0.9710 0.6312 0.600 0.400
#> GSM110412 2 0.0000 0.5857 0.000 1.000
#> GSM110417 1 0.9710 0.6312 0.600 0.400
#> GSM110422 2 0.9710 0.8050 0.400 0.600
#> GSM110426 1 0.9710 0.6312 0.600 0.400
#> GSM110429 2 0.9710 0.8050 0.400 0.600
#> GSM110433 2 0.0000 0.5857 0.000 1.000
#> GSM110436 2 0.9710 0.8050 0.400 0.600
#> GSM110440 1 0.0938 0.7521 0.988 0.012
#> GSM110441 2 0.0000 0.5857 0.000 1.000
#> GSM110444 1 0.9977 0.5705 0.528 0.472
#> GSM110445 1 0.7139 0.7348 0.804 0.196
#> GSM110446 1 0.0000 0.7498 1.000 0.000
#> GSM110449 2 0.2423 0.5402 0.040 0.960
#> GSM110451 2 0.9710 0.8050 0.400 0.600
#> GSM110391 2 0.0000 0.5857 0.000 1.000
#> GSM110439 2 0.9710 0.8050 0.400 0.600
#> GSM110442 2 0.8144 0.7464 0.252 0.748
#> GSM110443 1 0.8813 -0.0561 0.700 0.300
#> GSM110447 2 0.9427 0.7915 0.360 0.640
#> GSM110448 1 0.9710 0.6312 0.600 0.400
#> GSM110450 1 0.0672 0.7516 0.992 0.008
#> GSM110452 2 0.9710 0.8050 0.400 0.600
#> GSM110453 2 0.9710 0.8050 0.400 0.600
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.6724 0.499 0.012 0.568 0.420
#> GSM110396 1 0.0661 0.717 0.988 0.004 0.008
#> GSM110397 1 0.4291 0.709 0.840 0.152 0.008
#> GSM110398 1 0.0424 0.715 0.992 0.008 0.000
#> GSM110399 2 0.7785 0.434 0.420 0.528 0.052
#> GSM110400 3 0.5216 0.456 0.000 0.260 0.740
#> GSM110401 1 0.1411 0.711 0.964 0.000 0.036
#> GSM110406 2 0.8760 0.548 0.176 0.584 0.240
#> GSM110407 1 0.6215 0.184 0.572 0.000 0.428
#> GSM110409 1 0.4654 0.553 0.792 0.000 0.208
#> GSM110410 2 0.5111 0.712 0.036 0.820 0.144
#> GSM110413 2 0.2165 0.685 0.000 0.936 0.064
#> GSM110414 2 0.6215 0.460 0.000 0.572 0.428
#> GSM110415 3 0.1753 0.757 0.000 0.048 0.952
#> GSM110416 3 0.0475 0.781 0.004 0.004 0.992
#> GSM110418 3 0.0475 0.781 0.004 0.004 0.992
#> GSM110419 3 0.1860 0.774 0.052 0.000 0.948
#> GSM110420 3 0.1031 0.781 0.024 0.000 0.976
#> GSM110421 2 0.1163 0.634 0.028 0.972 0.000
#> GSM110423 3 0.1163 0.770 0.000 0.028 0.972
#> GSM110424 2 0.2537 0.700 0.000 0.920 0.080
#> GSM110425 3 0.0747 0.776 0.000 0.016 0.984
#> GSM110427 2 0.6111 0.518 0.000 0.604 0.396
#> GSM110428 3 0.2066 0.770 0.060 0.000 0.940
#> GSM110430 1 0.1529 0.708 0.960 0.000 0.040
#> GSM110431 3 0.5327 0.569 0.272 0.000 0.728
#> GSM110432 3 0.1031 0.781 0.024 0.000 0.976
#> GSM110434 2 0.9588 0.518 0.240 0.476 0.284
#> GSM110435 3 0.5810 0.544 0.336 0.000 0.664
#> GSM110437 1 0.1529 0.708 0.960 0.000 0.040
#> GSM110438 3 0.5859 0.533 0.344 0.000 0.656
#> GSM110388 1 0.5926 0.639 0.644 0.356 0.000
#> GSM110392 3 0.8918 0.306 0.160 0.288 0.552
#> GSM110394 3 0.4235 0.692 0.176 0.000 0.824
#> GSM110402 3 0.0000 0.780 0.000 0.000 1.000
#> GSM110411 1 0.5968 0.633 0.636 0.364 0.000
#> GSM110412 2 0.0661 0.653 0.008 0.988 0.004
#> GSM110417 1 0.5905 0.642 0.648 0.352 0.000
#> GSM110422 2 0.8907 0.623 0.168 0.560 0.272
#> GSM110426 1 0.6104 0.645 0.648 0.348 0.004
#> GSM110429 3 0.7622 0.144 0.060 0.332 0.608
#> GSM110433 2 0.0000 0.656 0.000 1.000 0.000
#> GSM110436 3 0.5859 0.219 0.000 0.344 0.656
#> GSM110440 1 0.5621 0.497 0.692 0.000 0.308
#> GSM110441 2 0.2063 0.674 0.044 0.948 0.008
#> GSM110444 1 0.6008 0.626 0.628 0.372 0.000
#> GSM110445 1 0.0424 0.715 0.992 0.000 0.008
#> GSM110446 3 0.5968 0.501 0.364 0.000 0.636
#> GSM110449 1 0.5397 0.598 0.720 0.280 0.000
#> GSM110451 3 0.3038 0.702 0.000 0.104 0.896
#> GSM110391 2 0.1129 0.644 0.020 0.976 0.004
#> GSM110439 2 0.8600 0.674 0.212 0.604 0.184
#> GSM110442 2 0.7944 0.697 0.196 0.660 0.144
#> GSM110443 1 0.7485 0.419 0.696 0.172 0.132
#> GSM110447 3 0.1289 0.768 0.000 0.032 0.968
#> GSM110448 1 0.5926 0.639 0.644 0.356 0.000
#> GSM110450 1 0.5098 0.575 0.752 0.000 0.248
#> GSM110452 2 0.8647 0.673 0.208 0.600 0.192
#> GSM110453 2 0.8148 0.691 0.200 0.644 0.156
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.5798 0.6291 0.112 0.704 0.184 0.000
#> GSM110396 1 0.2002 0.8300 0.936 0.020 0.000 0.044
#> GSM110397 4 0.5138 0.4050 0.392 0.008 0.000 0.600
#> GSM110398 1 0.2480 0.8136 0.904 0.088 0.000 0.008
#> GSM110399 1 0.4605 0.5876 0.664 0.336 0.000 0.000
#> GSM110400 3 0.2441 0.8349 0.004 0.020 0.920 0.056
#> GSM110401 1 0.1443 0.8533 0.960 0.008 0.028 0.004
#> GSM110406 1 0.5593 0.7070 0.708 0.212 0.080 0.000
#> GSM110407 1 0.3450 0.7977 0.836 0.008 0.156 0.000
#> GSM110409 1 0.1975 0.8581 0.936 0.048 0.016 0.000
#> GSM110410 2 0.0927 0.7900 0.016 0.976 0.000 0.008
#> GSM110413 2 0.6245 0.5028 0.012 0.632 0.056 0.300
#> GSM110414 3 0.7019 0.4046 0.004 0.184 0.596 0.216
#> GSM110415 3 0.2452 0.8168 0.004 0.004 0.908 0.084
#> GSM110416 3 0.0564 0.8623 0.004 0.004 0.988 0.004
#> GSM110418 3 0.0564 0.8623 0.004 0.004 0.988 0.004
#> GSM110419 3 0.2216 0.8514 0.092 0.000 0.908 0.000
#> GSM110420 3 0.1576 0.8629 0.048 0.000 0.948 0.004
#> GSM110421 4 0.3751 0.6311 0.004 0.196 0.000 0.800
#> GSM110423 3 0.0188 0.8618 0.000 0.004 0.996 0.000
#> GSM110424 2 0.4568 0.6648 0.004 0.772 0.024 0.200
#> GSM110425 3 0.0336 0.8638 0.008 0.000 0.992 0.000
#> GSM110427 2 0.4175 0.6995 0.008 0.792 0.192 0.008
#> GSM110428 3 0.2266 0.8545 0.084 0.004 0.912 0.000
#> GSM110430 1 0.1082 0.8539 0.972 0.004 0.020 0.004
#> GSM110431 3 0.2868 0.8306 0.136 0.000 0.864 0.000
#> GSM110432 3 0.4477 0.8114 0.108 0.084 0.808 0.000
#> GSM110434 2 0.3577 0.7017 0.156 0.832 0.012 0.000
#> GSM110435 3 0.3157 0.8291 0.144 0.004 0.852 0.000
#> GSM110437 1 0.1114 0.8523 0.972 0.008 0.016 0.004
#> GSM110438 3 0.3172 0.8201 0.160 0.000 0.840 0.000
#> GSM110388 4 0.2345 0.8072 0.100 0.000 0.000 0.900
#> GSM110392 4 0.7863 0.0998 0.040 0.104 0.412 0.444
#> GSM110394 3 0.4331 0.6382 0.288 0.000 0.712 0.000
#> GSM110402 3 0.1109 0.8646 0.028 0.004 0.968 0.000
#> GSM110411 4 0.0592 0.8114 0.016 0.000 0.000 0.984
#> GSM110412 4 0.0992 0.7989 0.004 0.008 0.012 0.976
#> GSM110417 4 0.2345 0.8064 0.100 0.000 0.000 0.900
#> GSM110422 2 0.2342 0.7730 0.008 0.912 0.080 0.000
#> GSM110426 4 0.2949 0.8061 0.088 0.000 0.024 0.888
#> GSM110429 2 0.4485 0.5792 0.012 0.740 0.248 0.000
#> GSM110433 2 0.5666 0.1974 0.004 0.520 0.016 0.460
#> GSM110436 3 0.5112 0.4451 0.008 0.340 0.648 0.004
#> GSM110440 1 0.4980 0.7337 0.756 0.004 0.196 0.044
#> GSM110441 2 0.1488 0.7853 0.012 0.956 0.000 0.032
#> GSM110444 4 0.0524 0.8082 0.008 0.004 0.000 0.988
#> GSM110445 1 0.1807 0.8481 0.940 0.052 0.000 0.008
#> GSM110446 3 0.3972 0.7776 0.204 0.008 0.788 0.000
#> GSM110449 2 0.6887 0.3501 0.308 0.560 0.000 0.132
#> GSM110451 3 0.4057 0.7578 0.028 0.160 0.812 0.000
#> GSM110391 4 0.3289 0.7036 0.004 0.140 0.004 0.852
#> GSM110439 2 0.1211 0.7895 0.040 0.960 0.000 0.000
#> GSM110442 2 0.0592 0.7908 0.016 0.984 0.000 0.000
#> GSM110443 1 0.3881 0.7911 0.812 0.172 0.016 0.000
#> GSM110447 3 0.1575 0.8484 0.004 0.012 0.956 0.028
#> GSM110448 4 0.1792 0.8144 0.068 0.000 0.000 0.932
#> GSM110450 1 0.3350 0.8231 0.864 0.016 0.116 0.004
#> GSM110452 2 0.1302 0.7888 0.044 0.956 0.000 0.000
#> GSM110453 2 0.0469 0.7905 0.012 0.988 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 5 0.7348 0.11776 0.316 0.224 0.036 0.000 0.424
#> GSM110396 1 0.3152 0.73561 0.840 0.000 0.000 0.024 0.136
#> GSM110397 4 0.3485 0.60744 0.124 0.000 0.000 0.828 0.048
#> GSM110398 1 0.5519 0.63134 0.712 0.128 0.000 0.120 0.040
#> GSM110399 1 0.4078 0.70660 0.784 0.148 0.000 0.000 0.068
#> GSM110400 3 0.4585 0.39263 0.020 0.000 0.628 0.000 0.352
#> GSM110401 1 0.2124 0.74341 0.900 0.000 0.004 0.000 0.096
#> GSM110406 1 0.3975 0.67998 0.744 0.008 0.008 0.000 0.240
#> GSM110407 1 0.3803 0.71685 0.804 0.000 0.056 0.000 0.140
#> GSM110409 1 0.2769 0.74197 0.888 0.076 0.004 0.004 0.028
#> GSM110410 2 0.0955 0.81522 0.000 0.968 0.000 0.004 0.028
#> GSM110413 5 0.2270 0.50452 0.076 0.000 0.000 0.020 0.904
#> GSM110414 5 0.5247 0.24124 0.000 0.012 0.400 0.028 0.560
#> GSM110415 3 0.0693 0.85244 0.000 0.000 0.980 0.012 0.008
#> GSM110416 3 0.0000 0.85799 0.000 0.000 1.000 0.000 0.000
#> GSM110418 3 0.0000 0.85799 0.000 0.000 1.000 0.000 0.000
#> GSM110419 3 0.1444 0.85059 0.040 0.000 0.948 0.000 0.012
#> GSM110420 3 0.0162 0.85814 0.000 0.000 0.996 0.004 0.000
#> GSM110421 5 0.5104 0.52442 0.000 0.116 0.000 0.192 0.692
#> GSM110423 3 0.0162 0.85797 0.000 0.004 0.996 0.000 0.000
#> GSM110424 2 0.5106 0.61677 0.000 0.736 0.024 0.136 0.104
#> GSM110425 3 0.0404 0.85804 0.012 0.000 0.988 0.000 0.000
#> GSM110427 2 0.5462 0.59502 0.024 0.704 0.140 0.000 0.132
#> GSM110428 3 0.3319 0.77106 0.160 0.000 0.820 0.000 0.020
#> GSM110430 1 0.1012 0.74755 0.968 0.000 0.000 0.020 0.012
#> GSM110431 3 0.3081 0.78344 0.156 0.000 0.832 0.000 0.012
#> GSM110432 3 0.4652 0.69605 0.188 0.012 0.744 0.000 0.056
#> GSM110434 2 0.2389 0.75265 0.116 0.880 0.000 0.000 0.004
#> GSM110435 3 0.1082 0.85656 0.028 0.000 0.964 0.000 0.008
#> GSM110437 1 0.4415 0.67932 0.776 0.020 0.000 0.156 0.048
#> GSM110438 3 0.3150 0.80812 0.096 0.000 0.864 0.024 0.016
#> GSM110388 4 0.0451 0.72880 0.004 0.000 0.000 0.988 0.008
#> GSM110392 4 0.5008 0.48902 0.016 0.248 0.020 0.700 0.016
#> GSM110394 1 0.4549 0.07105 0.528 0.000 0.464 0.000 0.008
#> GSM110402 3 0.0290 0.85831 0.000 0.000 0.992 0.000 0.008
#> GSM110411 4 0.3424 0.58967 0.000 0.000 0.000 0.760 0.240
#> GSM110412 4 0.4449 0.13215 0.000 0.000 0.004 0.512 0.484
#> GSM110417 4 0.1469 0.73055 0.016 0.000 0.000 0.948 0.036
#> GSM110422 2 0.1492 0.81178 0.008 0.948 0.040 0.000 0.004
#> GSM110426 4 0.0960 0.72974 0.008 0.000 0.004 0.972 0.016
#> GSM110429 2 0.2623 0.76354 0.004 0.884 0.096 0.000 0.016
#> GSM110433 5 0.5115 0.53426 0.000 0.136 0.000 0.168 0.696
#> GSM110436 3 0.5594 -0.00378 0.004 0.444 0.492 0.000 0.060
#> GSM110440 1 0.5267 0.64599 0.716 0.000 0.108 0.156 0.020
#> GSM110441 2 0.4452 -0.08843 0.004 0.500 0.000 0.000 0.496
#> GSM110444 4 0.4268 0.25541 0.000 0.000 0.000 0.556 0.444
#> GSM110445 1 0.3738 0.72215 0.844 0.052 0.000 0.064 0.040
#> GSM110446 3 0.4775 0.74303 0.100 0.024 0.788 0.068 0.020
#> GSM110449 2 0.4665 0.65466 0.056 0.756 0.000 0.168 0.020
#> GSM110451 3 0.3344 0.79037 0.028 0.104 0.852 0.000 0.016
#> GSM110391 5 0.4028 0.50284 0.000 0.040 0.000 0.192 0.768
#> GSM110439 2 0.0510 0.81912 0.016 0.984 0.000 0.000 0.000
#> GSM110442 2 0.0404 0.81938 0.000 0.988 0.000 0.000 0.012
#> GSM110443 1 0.6252 -0.02026 0.444 0.436 0.000 0.008 0.112
#> GSM110447 3 0.1569 0.84148 0.000 0.008 0.948 0.012 0.032
#> GSM110448 4 0.1197 0.72475 0.000 0.000 0.000 0.952 0.048
#> GSM110450 1 0.2681 0.73762 0.876 0.000 0.012 0.004 0.108
#> GSM110452 2 0.0609 0.81836 0.020 0.980 0.000 0.000 0.000
#> GSM110453 2 0.0671 0.81932 0.004 0.980 0.000 0.000 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 1 0.8079 -0.2306 0.348 0.144 0.036 0.000 0.236 0.236
#> GSM110396 1 0.2974 0.6416 0.872 0.004 0.000 0.052 0.028 0.044
#> GSM110397 4 0.1913 0.6560 0.012 0.000 0.000 0.908 0.000 0.080
#> GSM110398 2 0.7500 0.0415 0.252 0.388 0.000 0.100 0.012 0.248
#> GSM110399 1 0.5326 0.1700 0.500 0.404 0.000 0.000 0.004 0.092
#> GSM110400 3 0.3598 0.6536 0.004 0.000 0.804 0.000 0.112 0.080
#> GSM110401 1 0.0405 0.6453 0.988 0.000 0.000 0.008 0.000 0.004
#> GSM110406 1 0.3307 0.6089 0.808 0.000 0.000 0.000 0.044 0.148
#> GSM110407 1 0.1926 0.6394 0.912 0.000 0.020 0.000 0.000 0.068
#> GSM110409 1 0.6077 0.5208 0.608 0.144 0.016 0.020 0.008 0.204
#> GSM110410 2 0.3220 0.5217 0.000 0.840 0.004 0.004 0.056 0.096
#> GSM110413 5 0.4313 0.4124 0.116 0.016 0.000 0.000 0.756 0.112
#> GSM110414 3 0.6126 -0.0817 0.000 0.008 0.456 0.004 0.348 0.184
#> GSM110415 3 0.1065 0.7353 0.000 0.000 0.964 0.008 0.008 0.020
#> GSM110416 3 0.0260 0.7377 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM110418 3 0.0777 0.7373 0.000 0.000 0.972 0.004 0.000 0.024
#> GSM110419 3 0.1644 0.7344 0.040 0.000 0.932 0.000 0.000 0.028
#> GSM110420 3 0.1088 0.7368 0.000 0.000 0.960 0.016 0.000 0.024
#> GSM110421 5 0.2604 0.6355 0.000 0.024 0.000 0.056 0.888 0.032
#> GSM110423 3 0.0858 0.7349 0.000 0.004 0.968 0.000 0.000 0.028
#> GSM110424 6 0.7262 0.3610 0.000 0.344 0.008 0.096 0.172 0.380
#> GSM110425 3 0.1668 0.7241 0.004 0.000 0.928 0.000 0.008 0.060
#> GSM110427 2 0.7999 -0.6540 0.024 0.352 0.188 0.000 0.196 0.240
#> GSM110428 1 0.6298 0.1384 0.428 0.000 0.328 0.004 0.008 0.232
#> GSM110430 1 0.2499 0.6427 0.880 0.000 0.000 0.072 0.000 0.048
#> GSM110431 3 0.4292 0.4566 0.340 0.000 0.628 0.000 0.000 0.032
#> GSM110432 3 0.6856 0.2792 0.296 0.020 0.468 0.000 0.040 0.176
#> GSM110434 2 0.2222 0.6224 0.012 0.896 0.008 0.000 0.000 0.084
#> GSM110435 3 0.3255 0.6892 0.036 0.004 0.828 0.004 0.000 0.128
#> GSM110437 1 0.5862 0.4576 0.508 0.004 0.000 0.276 0.000 0.212
#> GSM110438 3 0.5333 0.6029 0.056 0.028 0.704 0.052 0.000 0.160
#> GSM110388 4 0.3936 0.5344 0.000 0.000 0.004 0.700 0.276 0.020
#> GSM110392 4 0.4875 0.5024 0.004 0.224 0.004 0.684 0.008 0.076
#> GSM110394 3 0.4254 0.3547 0.404 0.000 0.576 0.000 0.000 0.020
#> GSM110402 3 0.0551 0.7391 0.004 0.000 0.984 0.000 0.004 0.008
#> GSM110411 5 0.3915 0.2930 0.000 0.000 0.000 0.412 0.584 0.004
#> GSM110412 5 0.3647 0.4060 0.000 0.000 0.000 0.360 0.640 0.000
#> GSM110417 4 0.2998 0.7031 0.008 0.000 0.000 0.856 0.072 0.064
#> GSM110422 2 0.2089 0.6141 0.000 0.916 0.044 0.000 0.020 0.020
#> GSM110426 4 0.2162 0.7123 0.000 0.000 0.004 0.896 0.088 0.012
#> GSM110429 2 0.1500 0.6114 0.000 0.936 0.052 0.000 0.000 0.012
#> GSM110433 5 0.1719 0.6152 0.000 0.056 0.000 0.008 0.928 0.008
#> GSM110436 6 0.7986 0.4805 0.008 0.276 0.252 0.008 0.156 0.300
#> GSM110440 1 0.5883 0.5152 0.580 0.000 0.064 0.272 0.000 0.084
#> GSM110441 2 0.6651 -0.2833 0.004 0.444 0.000 0.032 0.280 0.240
#> GSM110444 5 0.3804 0.2800 0.000 0.000 0.000 0.424 0.576 0.000
#> GSM110445 1 0.6203 0.5301 0.552 0.044 0.000 0.196 0.000 0.208
#> GSM110446 3 0.5429 0.5753 0.028 0.032 0.676 0.064 0.000 0.200
#> GSM110449 2 0.5381 0.4386 0.004 0.632 0.000 0.192 0.008 0.164
#> GSM110451 3 0.5722 0.5197 0.024 0.092 0.684 0.000 0.080 0.120
#> GSM110391 5 0.1218 0.6350 0.000 0.004 0.000 0.012 0.956 0.028
#> GSM110439 2 0.1728 0.6314 0.000 0.924 0.000 0.008 0.004 0.064
#> GSM110442 2 0.4057 0.4733 0.004 0.788 0.000 0.060 0.024 0.124
#> GSM110443 1 0.7012 0.3446 0.476 0.224 0.000 0.164 0.000 0.136
#> GSM110447 3 0.5728 0.2801 0.004 0.004 0.576 0.020 0.096 0.300
#> GSM110448 4 0.3266 0.5571 0.000 0.000 0.000 0.728 0.272 0.000
#> GSM110450 1 0.5267 0.5649 0.648 0.008 0.004 0.160 0.000 0.180
#> GSM110452 2 0.1434 0.6338 0.000 0.940 0.000 0.000 0.012 0.048
#> GSM110453 2 0.0291 0.6210 0.000 0.992 0.000 0.000 0.004 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) specimen(p) k
#> SD:NMF 58 0.7783 0.299 2
#> SD:NMF 49 0.2008 0.126 3
#> SD:NMF 53 0.0140 0.306 4
#> SD:NMF 49 0.0461 0.267 5
#> SD:NMF 38 0.0617 0.129 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 17209 rows and 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.504 0.814 0.903 0.4542 0.534 0.534
#> 3 3 0.662 0.809 0.895 0.4093 0.741 0.552
#> 4 4 0.641 0.741 0.814 0.1162 0.910 0.754
#> 5 5 0.679 0.710 0.820 0.0664 0.955 0.838
#> 6 6 0.712 0.611 0.788 0.0446 0.924 0.707
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
#> GSM110395 2 0.469 0.8902 0.100 0.900
#> GSM110396 1 0.000 0.9029 1.000 0.000
#> GSM110397 1 0.000 0.9029 1.000 0.000
#> GSM110398 2 0.994 0.1030 0.456 0.544
#> GSM110399 2 0.388 0.8919 0.076 0.924
#> GSM110400 2 0.574 0.8745 0.136 0.864
#> GSM110401 1 0.000 0.9029 1.000 0.000
#> GSM110406 2 0.388 0.8919 0.076 0.924
#> GSM110407 1 0.000 0.9029 1.000 0.000
#> GSM110409 1 0.000 0.9029 1.000 0.000
#> GSM110410 2 0.000 0.8804 0.000 1.000
#> GSM110413 2 0.141 0.8834 0.020 0.980
#> GSM110414 2 0.000 0.8804 0.000 1.000
#> GSM110415 2 0.697 0.8390 0.188 0.812
#> GSM110416 2 0.697 0.8390 0.188 0.812
#> GSM110418 2 0.697 0.8390 0.188 0.812
#> GSM110419 2 0.634 0.8616 0.160 0.840
#> GSM110420 2 0.753 0.8101 0.216 0.784
#> GSM110421 2 0.343 0.8923 0.064 0.936
#> GSM110423 2 0.574 0.8745 0.136 0.864
#> GSM110424 2 0.000 0.8804 0.000 1.000
#> GSM110425 2 0.574 0.8745 0.136 0.864
#> GSM110427 2 0.141 0.8834 0.020 0.980
#> GSM110428 1 0.327 0.8717 0.940 0.060
#> GSM110430 1 0.000 0.9029 1.000 0.000
#> GSM110431 1 0.000 0.9029 1.000 0.000
#> GSM110432 2 0.541 0.8833 0.124 0.876
#> GSM110434 2 0.506 0.8876 0.112 0.888
#> GSM110435 1 0.000 0.9029 1.000 0.000
#> GSM110437 1 0.000 0.9029 1.000 0.000
#> GSM110438 1 0.988 0.1040 0.564 0.436
#> GSM110388 1 0.295 0.8791 0.948 0.052
#> GSM110392 2 1.000 0.0734 0.492 0.508
#> GSM110394 1 0.000 0.9029 1.000 0.000
#> GSM110402 2 0.615 0.8668 0.152 0.848
#> GSM110411 1 0.990 0.1140 0.560 0.440
#> GSM110412 2 0.697 0.8328 0.188 0.812
#> GSM110417 1 0.000 0.9029 1.000 0.000
#> GSM110422 2 0.141 0.8834 0.020 0.980
#> GSM110426 1 0.000 0.9029 1.000 0.000
#> GSM110429 2 0.541 0.8833 0.124 0.876
#> GSM110433 2 0.000 0.8804 0.000 1.000
#> GSM110436 2 0.141 0.8834 0.020 0.980
#> GSM110440 1 0.000 0.9029 1.000 0.000
#> GSM110441 2 0.000 0.8804 0.000 1.000
#> GSM110444 1 0.990 0.1140 0.560 0.440
#> GSM110445 1 0.388 0.8605 0.924 0.076
#> GSM110446 2 0.714 0.8314 0.196 0.804
#> GSM110449 2 0.388 0.8919 0.076 0.924
#> GSM110451 2 0.541 0.8833 0.124 0.876
#> GSM110391 2 0.000 0.8804 0.000 1.000
#> GSM110439 2 0.000 0.8804 0.000 1.000
#> GSM110442 2 0.358 0.8920 0.068 0.932
#> GSM110443 2 0.358 0.8920 0.068 0.932
#> GSM110447 2 0.615 0.8668 0.152 0.848
#> GSM110448 1 0.260 0.8839 0.956 0.044
#> GSM110450 1 0.388 0.8605 0.924 0.076
#> GSM110452 2 0.141 0.8834 0.020 0.980
#> GSM110453 2 0.000 0.8804 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.2625 0.835 0.000 0.916 0.084
#> GSM110396 1 0.0000 0.914 1.000 0.000 0.000
#> GSM110397 1 0.0000 0.914 1.000 0.000 0.000
#> GSM110398 2 0.8157 0.316 0.384 0.540 0.076
#> GSM110399 2 0.2682 0.841 0.004 0.920 0.076
#> GSM110400 3 0.1753 0.934 0.000 0.048 0.952
#> GSM110401 1 0.0000 0.914 1.000 0.000 0.000
#> GSM110406 2 0.2682 0.841 0.004 0.920 0.076
#> GSM110407 1 0.2537 0.895 0.920 0.000 0.080
#> GSM110409 1 0.2537 0.895 0.920 0.000 0.080
#> GSM110410 2 0.1031 0.839 0.000 0.976 0.024
#> GSM110413 2 0.0000 0.843 0.000 1.000 0.000
#> GSM110414 3 0.5016 0.742 0.000 0.240 0.760
#> GSM110415 3 0.0424 0.930 0.008 0.000 0.992
#> GSM110416 3 0.0424 0.930 0.008 0.000 0.992
#> GSM110418 3 0.0424 0.930 0.008 0.000 0.992
#> GSM110419 3 0.1031 0.938 0.000 0.024 0.976
#> GSM110420 3 0.4002 0.792 0.160 0.000 0.840
#> GSM110421 2 0.1964 0.845 0.000 0.944 0.056
#> GSM110423 3 0.1753 0.934 0.000 0.048 0.952
#> GSM110424 2 0.1031 0.839 0.000 0.976 0.024
#> GSM110425 3 0.1753 0.934 0.000 0.048 0.952
#> GSM110427 2 0.0000 0.843 0.000 1.000 0.000
#> GSM110428 1 0.6119 0.804 0.772 0.064 0.164
#> GSM110430 1 0.0000 0.914 1.000 0.000 0.000
#> GSM110431 1 0.0892 0.911 0.980 0.020 0.000
#> GSM110432 2 0.3551 0.809 0.000 0.868 0.132
#> GSM110434 2 0.3193 0.827 0.004 0.896 0.100
#> GSM110435 1 0.1482 0.913 0.968 0.020 0.012
#> GSM110437 1 0.0000 0.914 1.000 0.000 0.000
#> GSM110438 2 0.9485 0.127 0.388 0.428 0.184
#> GSM110388 1 0.5692 0.812 0.784 0.040 0.176
#> GSM110392 2 0.8973 0.297 0.364 0.500 0.136
#> GSM110394 1 0.1482 0.913 0.968 0.020 0.012
#> GSM110402 3 0.1289 0.938 0.000 0.032 0.968
#> GSM110411 2 0.9481 0.138 0.384 0.432 0.184
#> GSM110412 2 0.5564 0.770 0.064 0.808 0.128
#> GSM110417 1 0.0000 0.914 1.000 0.000 0.000
#> GSM110422 2 0.0000 0.843 0.000 1.000 0.000
#> GSM110426 1 0.0000 0.914 1.000 0.000 0.000
#> GSM110429 2 0.3482 0.811 0.000 0.872 0.128
#> GSM110433 2 0.1031 0.839 0.000 0.976 0.024
#> GSM110436 2 0.0000 0.843 0.000 1.000 0.000
#> GSM110440 1 0.1482 0.913 0.968 0.020 0.012
#> GSM110441 2 0.0892 0.840 0.000 0.980 0.020
#> GSM110444 2 0.9481 0.138 0.384 0.432 0.184
#> GSM110445 1 0.6203 0.788 0.760 0.056 0.184
#> GSM110446 3 0.1031 0.922 0.024 0.000 0.976
#> GSM110449 2 0.2682 0.841 0.004 0.920 0.076
#> GSM110451 2 0.3551 0.809 0.000 0.868 0.132
#> GSM110391 2 0.0892 0.840 0.000 0.980 0.020
#> GSM110439 2 0.0892 0.840 0.000 0.980 0.020
#> GSM110442 2 0.2301 0.845 0.004 0.936 0.060
#> GSM110443 2 0.2301 0.845 0.004 0.936 0.060
#> GSM110447 3 0.1289 0.938 0.000 0.032 0.968
#> GSM110448 1 0.5470 0.821 0.796 0.036 0.168
#> GSM110450 1 0.6203 0.788 0.760 0.056 0.184
#> GSM110452 2 0.0424 0.845 0.000 0.992 0.008
#> GSM110453 2 0.1031 0.839 0.000 0.976 0.024
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.6108 0.651 0.000 0.528 0.048 0.424
#> GSM110396 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> GSM110397 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> GSM110398 2 0.3024 0.392 0.072 0.896 0.012 0.020
#> GSM110399 2 0.5174 0.668 0.000 0.620 0.012 0.368
#> GSM110400 3 0.1913 0.927 0.000 0.040 0.940 0.020
#> GSM110401 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> GSM110406 2 0.5174 0.668 0.000 0.620 0.012 0.368
#> GSM110407 1 0.2623 0.855 0.908 0.028 0.064 0.000
#> GSM110409 1 0.2623 0.855 0.908 0.028 0.064 0.000
#> GSM110410 4 0.0336 0.862 0.000 0.008 0.000 0.992
#> GSM110413 2 0.4985 0.585 0.000 0.532 0.000 0.468
#> GSM110414 3 0.4008 0.741 0.000 0.000 0.756 0.244
#> GSM110415 3 0.0469 0.927 0.000 0.012 0.988 0.000
#> GSM110416 3 0.0469 0.927 0.000 0.012 0.988 0.000
#> GSM110418 3 0.0469 0.927 0.000 0.012 0.988 0.000
#> GSM110419 3 0.1356 0.932 0.000 0.032 0.960 0.008
#> GSM110420 3 0.4530 0.785 0.124 0.056 0.812 0.008
#> GSM110421 2 0.5050 0.650 0.000 0.588 0.004 0.408
#> GSM110423 3 0.1913 0.927 0.000 0.040 0.940 0.020
#> GSM110424 4 0.0592 0.866 0.000 0.016 0.000 0.984
#> GSM110425 3 0.1913 0.927 0.000 0.040 0.940 0.020
#> GSM110427 2 0.4994 0.573 0.000 0.520 0.000 0.480
#> GSM110428 1 0.6353 0.731 0.652 0.208 0.140 0.000
#> GSM110430 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> GSM110431 1 0.2281 0.856 0.904 0.096 0.000 0.000
#> GSM110432 2 0.6758 0.637 0.000 0.504 0.096 0.400
#> GSM110434 2 0.6270 0.658 0.000 0.536 0.060 0.404
#> GSM110435 1 0.3037 0.857 0.880 0.100 0.020 0.000
#> GSM110437 1 0.0000 0.868 1.000 0.000 0.000 0.000
#> GSM110438 2 0.4656 0.337 0.056 0.784 0.160 0.000
#> GSM110388 1 0.7175 0.526 0.460 0.404 0.136 0.000
#> GSM110392 2 0.4461 0.400 0.048 0.832 0.092 0.028
#> GSM110394 1 0.3037 0.857 0.880 0.100 0.020 0.000
#> GSM110402 3 0.1488 0.933 0.000 0.032 0.956 0.012
#> GSM110411 2 0.5054 0.347 0.072 0.784 0.132 0.012
#> GSM110412 2 0.6563 0.613 0.004 0.584 0.084 0.328
#> GSM110417 1 0.0707 0.869 0.980 0.020 0.000 0.000
#> GSM110422 2 0.4994 0.573 0.000 0.520 0.000 0.480
#> GSM110426 1 0.0469 0.869 0.988 0.012 0.000 0.000
#> GSM110429 2 0.6775 0.628 0.000 0.492 0.096 0.412
#> GSM110433 4 0.0469 0.866 0.000 0.012 0.000 0.988
#> GSM110436 2 0.4994 0.573 0.000 0.520 0.000 0.480
#> GSM110440 1 0.3037 0.857 0.880 0.100 0.020 0.000
#> GSM110441 4 0.3528 0.720 0.000 0.192 0.000 0.808
#> GSM110444 2 0.5054 0.347 0.072 0.784 0.132 0.012
#> GSM110445 1 0.5770 0.734 0.712 0.148 0.140 0.000
#> GSM110446 3 0.2602 0.895 0.008 0.076 0.908 0.008
#> GSM110449 2 0.5174 0.668 0.000 0.620 0.012 0.368
#> GSM110451 2 0.6758 0.637 0.000 0.504 0.096 0.400
#> GSM110391 4 0.3266 0.768 0.000 0.168 0.000 0.832
#> GSM110439 4 0.2921 0.804 0.000 0.140 0.000 0.860
#> GSM110442 2 0.4978 0.663 0.000 0.612 0.004 0.384
#> GSM110443 2 0.4978 0.663 0.000 0.612 0.004 0.384
#> GSM110447 3 0.1488 0.933 0.000 0.032 0.956 0.012
#> GSM110448 1 0.6432 0.698 0.636 0.236 0.128 0.000
#> GSM110450 1 0.5770 0.734 0.712 0.148 0.140 0.000
#> GSM110452 2 0.4961 0.613 0.000 0.552 0.000 0.448
#> GSM110453 4 0.0469 0.866 0.000 0.012 0.000 0.988
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.2304 0.818 0.000 0.908 0.048 0.000 0.044
#> GSM110396 1 0.0510 0.794 0.984 0.000 0.000 0.016 0.000
#> GSM110397 1 0.0404 0.792 0.988 0.000 0.000 0.012 0.000
#> GSM110398 2 0.4986 -0.437 0.012 0.532 0.012 0.444 0.000
#> GSM110399 2 0.1012 0.814 0.000 0.968 0.012 0.020 0.000
#> GSM110400 3 0.1628 0.879 0.000 0.056 0.936 0.000 0.008
#> GSM110401 1 0.2813 0.737 0.832 0.000 0.000 0.168 0.000
#> GSM110406 2 0.1012 0.814 0.000 0.968 0.012 0.020 0.000
#> GSM110407 1 0.2782 0.781 0.880 0.000 0.048 0.072 0.000
#> GSM110409 1 0.2782 0.781 0.880 0.000 0.048 0.072 0.000
#> GSM110410 5 0.2179 0.869 0.000 0.112 0.000 0.000 0.888
#> GSM110413 2 0.1792 0.805 0.000 0.916 0.000 0.000 0.084
#> GSM110414 3 0.3452 0.697 0.000 0.000 0.756 0.000 0.244
#> GSM110415 3 0.0404 0.879 0.000 0.012 0.988 0.000 0.000
#> GSM110416 3 0.0404 0.879 0.000 0.012 0.988 0.000 0.000
#> GSM110418 3 0.0404 0.879 0.000 0.012 0.988 0.000 0.000
#> GSM110419 3 0.1043 0.885 0.000 0.040 0.960 0.000 0.000
#> GSM110420 3 0.6764 0.559 0.060 0.000 0.564 0.264 0.112
#> GSM110421 2 0.0609 0.824 0.000 0.980 0.000 0.000 0.020
#> GSM110423 3 0.1628 0.879 0.000 0.056 0.936 0.000 0.008
#> GSM110424 5 0.2280 0.873 0.000 0.120 0.000 0.000 0.880
#> GSM110425 3 0.1628 0.879 0.000 0.056 0.936 0.000 0.008
#> GSM110427 2 0.1908 0.803 0.000 0.908 0.000 0.000 0.092
#> GSM110428 1 0.6100 0.550 0.628 0.028 0.120 0.224 0.000
#> GSM110430 1 0.2813 0.737 0.832 0.000 0.000 0.168 0.000
#> GSM110431 1 0.2127 0.773 0.892 0.000 0.000 0.108 0.000
#> GSM110432 2 0.2685 0.787 0.000 0.880 0.092 0.000 0.028
#> GSM110434 2 0.2390 0.810 0.000 0.908 0.060 0.008 0.024
#> GSM110435 1 0.2921 0.769 0.856 0.000 0.020 0.124 0.000
#> GSM110437 1 0.2813 0.737 0.832 0.000 0.000 0.168 0.000
#> GSM110438 4 0.6171 0.585 0.000 0.372 0.140 0.488 0.000
#> GSM110388 4 0.5978 -0.155 0.400 0.020 0.064 0.516 0.000
#> GSM110392 2 0.6018 -0.454 0.000 0.480 0.088 0.424 0.008
#> GSM110394 1 0.2921 0.769 0.856 0.000 0.020 0.124 0.000
#> GSM110402 3 0.1197 0.885 0.000 0.048 0.952 0.000 0.000
#> GSM110411 4 0.5736 0.640 0.012 0.392 0.060 0.536 0.000
#> GSM110412 2 0.4034 0.654 0.000 0.812 0.080 0.096 0.012
#> GSM110417 1 0.0963 0.793 0.964 0.000 0.000 0.036 0.000
#> GSM110422 2 0.1908 0.803 0.000 0.908 0.000 0.000 0.092
#> GSM110426 1 0.0703 0.794 0.976 0.000 0.000 0.024 0.000
#> GSM110429 2 0.2927 0.785 0.000 0.868 0.092 0.000 0.040
#> GSM110433 5 0.2230 0.873 0.000 0.116 0.000 0.000 0.884
#> GSM110436 2 0.1908 0.803 0.000 0.908 0.000 0.000 0.092
#> GSM110440 1 0.2921 0.769 0.856 0.000 0.020 0.124 0.000
#> GSM110441 5 0.3983 0.754 0.000 0.340 0.000 0.000 0.660
#> GSM110444 4 0.5736 0.640 0.012 0.392 0.060 0.536 0.000
#> GSM110445 1 0.6107 0.425 0.508 0.024 0.068 0.400 0.000
#> GSM110446 3 0.5447 0.619 0.000 0.000 0.640 0.248 0.112
#> GSM110449 2 0.0912 0.817 0.000 0.972 0.012 0.016 0.000
#> GSM110451 2 0.2685 0.787 0.000 0.880 0.092 0.000 0.028
#> GSM110391 5 0.3837 0.800 0.000 0.308 0.000 0.000 0.692
#> GSM110439 5 0.3661 0.828 0.000 0.276 0.000 0.000 0.724
#> GSM110442 2 0.0162 0.823 0.000 0.996 0.000 0.004 0.000
#> GSM110443 2 0.0162 0.823 0.000 0.996 0.000 0.004 0.000
#> GSM110447 3 0.1197 0.885 0.000 0.048 0.952 0.000 0.000
#> GSM110448 1 0.5717 0.378 0.576 0.016 0.060 0.348 0.000
#> GSM110450 1 0.6107 0.425 0.508 0.024 0.068 0.400 0.000
#> GSM110452 2 0.1410 0.815 0.000 0.940 0.000 0.000 0.060
#> GSM110453 5 0.2230 0.873 0.000 0.116 0.000 0.000 0.884
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.2675 0.830 0.000 0.876 0.076 0.000 0.040 0.008
#> GSM110396 1 0.3843 -0.369 0.548 0.000 0.000 0.452 0.000 0.000
#> GSM110397 4 0.5449 0.312 0.436 0.000 0.000 0.464 0.008 0.092
#> GSM110398 2 0.5590 0.284 0.000 0.512 0.000 0.328 0.000 0.160
#> GSM110399 2 0.0777 0.838 0.000 0.972 0.000 0.024 0.000 0.004
#> GSM110400 3 0.0603 0.913 0.000 0.016 0.980 0.000 0.000 0.004
#> GSM110401 1 0.0000 0.618 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110406 2 0.0858 0.838 0.000 0.968 0.000 0.028 0.000 0.004
#> GSM110407 4 0.4184 0.265 0.432 0.000 0.008 0.556 0.000 0.004
#> GSM110409 4 0.4184 0.265 0.432 0.000 0.008 0.556 0.000 0.004
#> GSM110410 5 0.0260 0.816 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM110413 2 0.1858 0.818 0.000 0.904 0.000 0.004 0.092 0.000
#> GSM110414 3 0.3276 0.537 0.000 0.000 0.764 0.004 0.228 0.004
#> GSM110415 3 0.0993 0.903 0.000 0.000 0.964 0.024 0.000 0.012
#> GSM110416 3 0.0993 0.903 0.000 0.000 0.964 0.024 0.000 0.012
#> GSM110418 3 0.0993 0.903 0.000 0.000 0.964 0.024 0.000 0.012
#> GSM110419 3 0.0665 0.919 0.000 0.008 0.980 0.008 0.000 0.004
#> GSM110420 6 0.3841 0.808 0.000 0.000 0.256 0.028 0.000 0.716
#> GSM110421 2 0.0922 0.843 0.000 0.968 0.000 0.004 0.024 0.004
#> GSM110423 3 0.0603 0.913 0.000 0.016 0.980 0.000 0.000 0.004
#> GSM110424 5 0.0458 0.821 0.000 0.016 0.000 0.000 0.984 0.000
#> GSM110425 3 0.0603 0.913 0.000 0.016 0.980 0.000 0.000 0.004
#> GSM110427 2 0.2051 0.819 0.000 0.896 0.000 0.004 0.096 0.004
#> GSM110428 4 0.4483 0.331 0.160 0.008 0.064 0.748 0.000 0.020
#> GSM110430 1 0.0000 0.618 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110431 4 0.3930 0.378 0.420 0.000 0.000 0.576 0.004 0.000
#> GSM110432 2 0.3043 0.805 0.000 0.836 0.132 0.000 0.024 0.008
#> GSM110434 2 0.2709 0.827 0.000 0.876 0.088 0.008 0.020 0.008
#> GSM110435 4 0.3976 0.399 0.380 0.000 0.004 0.612 0.004 0.000
#> GSM110437 1 0.0000 0.618 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110438 4 0.6933 -0.155 0.000 0.332 0.084 0.412 0.000 0.172
#> GSM110388 4 0.3872 0.181 0.032 0.004 0.012 0.772 0.000 0.180
#> GSM110392 2 0.7092 0.255 0.000 0.416 0.116 0.308 0.000 0.160
#> GSM110394 4 0.3996 0.395 0.388 0.000 0.004 0.604 0.004 0.000
#> GSM110402 3 0.0622 0.921 0.000 0.012 0.980 0.008 0.000 0.000
#> GSM110411 4 0.5890 -0.142 0.000 0.372 0.004 0.448 0.000 0.176
#> GSM110412 2 0.4470 0.733 0.000 0.752 0.108 0.120 0.008 0.012
#> GSM110417 4 0.5548 0.329 0.424 0.000 0.000 0.464 0.008 0.104
#> GSM110422 2 0.2051 0.819 0.000 0.896 0.000 0.004 0.096 0.004
#> GSM110426 4 0.5443 0.328 0.424 0.000 0.000 0.476 0.008 0.092
#> GSM110429 2 0.3266 0.802 0.000 0.824 0.132 0.000 0.036 0.008
#> GSM110433 5 0.0363 0.821 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM110436 2 0.2051 0.819 0.000 0.896 0.000 0.004 0.096 0.004
#> GSM110440 4 0.3976 0.399 0.380 0.000 0.004 0.612 0.004 0.000
#> GSM110441 5 0.3601 0.654 0.000 0.312 0.000 0.004 0.684 0.000
#> GSM110444 4 0.5890 -0.142 0.000 0.372 0.004 0.448 0.000 0.176
#> GSM110445 1 0.4639 0.455 0.664 0.012 0.008 0.284 0.000 0.032
#> GSM110446 6 0.5147 0.791 0.000 0.000 0.328 0.104 0.000 0.568
#> GSM110449 2 0.0717 0.840 0.000 0.976 0.000 0.016 0.000 0.008
#> GSM110451 2 0.3043 0.805 0.000 0.836 0.132 0.000 0.024 0.008
#> GSM110391 5 0.3265 0.728 0.000 0.248 0.000 0.004 0.748 0.000
#> GSM110439 5 0.2703 0.779 0.000 0.172 0.000 0.004 0.824 0.000
#> GSM110442 2 0.0000 0.844 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110443 2 0.0000 0.844 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110447 3 0.0622 0.921 0.000 0.012 0.980 0.008 0.000 0.000
#> GSM110448 4 0.3458 0.244 0.044 0.000 0.012 0.816 0.000 0.128
#> GSM110450 1 0.4639 0.455 0.664 0.012 0.008 0.284 0.000 0.032
#> GSM110452 2 0.1471 0.831 0.000 0.932 0.000 0.004 0.064 0.000
#> GSM110453 5 0.0363 0.821 0.000 0.012 0.000 0.000 0.988 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) specimen(p) k
#> CV:hclust 54 1.000 0.699 2
#> CV:hclust 54 0.164 0.333 3
#> CV:hclust 54 0.231 0.215 4
#> CV:hclust 53 0.169 0.075 5
#> CV:hclust 39 0.115 0.346 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 17209 rows and 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.635 0.783 0.900 0.4864 0.499 0.499
#> 3 3 0.794 0.884 0.931 0.3376 0.730 0.518
#> 4 4 0.690 0.662 0.780 0.1294 0.850 0.597
#> 5 5 0.703 0.573 0.750 0.0755 0.910 0.680
#> 6 6 0.683 0.563 0.712 0.0463 0.875 0.532
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
#> GSM110395 2 0.3431 0.892 0.064 0.936
#> GSM110396 1 0.0376 0.869 0.996 0.004
#> GSM110397 1 0.0000 0.868 1.000 0.000
#> GSM110398 1 0.9286 0.507 0.656 0.344
#> GSM110399 1 0.9732 0.396 0.596 0.404
#> GSM110400 2 0.0376 0.876 0.004 0.996
#> GSM110401 1 0.0376 0.869 0.996 0.004
#> GSM110406 1 0.9710 0.405 0.600 0.400
#> GSM110407 1 0.0376 0.869 0.996 0.004
#> GSM110409 1 0.0376 0.869 0.996 0.004
#> GSM110410 2 0.0000 0.876 0.000 1.000
#> GSM110413 2 0.5629 0.836 0.132 0.868
#> GSM110414 2 0.0376 0.876 0.004 0.996
#> GSM110415 2 0.0376 0.876 0.004 0.996
#> GSM110416 2 0.8608 0.553 0.284 0.716
#> GSM110418 2 0.8909 0.511 0.308 0.692
#> GSM110419 2 0.0376 0.876 0.004 0.996
#> GSM110420 2 0.9686 0.321 0.396 0.604
#> GSM110421 2 0.3431 0.892 0.064 0.936
#> GSM110423 2 0.0376 0.876 0.004 0.996
#> GSM110424 2 0.3431 0.892 0.064 0.936
#> GSM110425 2 0.0376 0.876 0.004 0.996
#> GSM110427 2 0.3431 0.892 0.064 0.936
#> GSM110428 1 0.0376 0.869 0.996 0.004
#> GSM110430 1 0.0376 0.869 0.996 0.004
#> GSM110431 1 0.0000 0.868 1.000 0.000
#> GSM110432 2 0.3431 0.892 0.064 0.936
#> GSM110434 2 0.5629 0.836 0.132 0.868
#> GSM110435 1 0.0000 0.868 1.000 0.000
#> GSM110437 1 0.0376 0.869 0.996 0.004
#> GSM110438 1 0.3274 0.823 0.940 0.060
#> GSM110388 1 0.0376 0.869 0.996 0.004
#> GSM110392 2 0.9866 0.148 0.432 0.568
#> GSM110394 1 0.0000 0.868 1.000 0.000
#> GSM110402 2 0.0376 0.876 0.004 0.996
#> GSM110411 1 0.8016 0.647 0.756 0.244
#> GSM110412 2 0.3431 0.892 0.064 0.936
#> GSM110417 1 0.0000 0.868 1.000 0.000
#> GSM110422 2 0.3431 0.892 0.064 0.936
#> GSM110426 1 0.0000 0.868 1.000 0.000
#> GSM110429 2 0.3431 0.892 0.064 0.936
#> GSM110433 2 0.0000 0.876 0.000 1.000
#> GSM110436 2 0.3431 0.892 0.064 0.936
#> GSM110440 1 0.0000 0.868 1.000 0.000
#> GSM110441 2 0.3431 0.892 0.064 0.936
#> GSM110444 1 0.9833 0.344 0.576 0.424
#> GSM110445 1 0.0376 0.869 0.996 0.004
#> GSM110446 2 0.8909 0.511 0.308 0.692
#> GSM110449 1 0.9732 0.396 0.596 0.404
#> GSM110451 2 0.3431 0.892 0.064 0.936
#> GSM110391 2 0.3431 0.892 0.064 0.936
#> GSM110439 2 0.3431 0.892 0.064 0.936
#> GSM110442 2 0.5629 0.836 0.132 0.868
#> GSM110443 1 0.9710 0.405 0.600 0.400
#> GSM110447 2 0.0376 0.876 0.004 0.996
#> GSM110448 1 0.0376 0.869 0.996 0.004
#> GSM110450 1 0.0376 0.869 0.996 0.004
#> GSM110452 2 0.5629 0.836 0.132 0.868
#> GSM110453 2 0.3431 0.892 0.064 0.936
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.2356 0.926 0.000 0.928 0.072
#> GSM110396 1 0.0747 0.911 0.984 0.000 0.016
#> GSM110397 1 0.0000 0.913 1.000 0.000 0.000
#> GSM110398 1 0.8828 0.464 0.580 0.228 0.192
#> GSM110399 2 0.4164 0.889 0.008 0.848 0.144
#> GSM110400 3 0.0892 0.932 0.000 0.020 0.980
#> GSM110401 1 0.0747 0.911 0.984 0.000 0.016
#> GSM110406 2 0.3454 0.916 0.008 0.888 0.104
#> GSM110407 1 0.0747 0.911 0.984 0.000 0.016
#> GSM110409 1 0.0424 0.912 0.992 0.000 0.008
#> GSM110410 2 0.0000 0.932 0.000 1.000 0.000
#> GSM110413 2 0.0237 0.930 0.000 0.996 0.004
#> GSM110414 3 0.4750 0.775 0.000 0.216 0.784
#> GSM110415 3 0.0747 0.934 0.000 0.016 0.984
#> GSM110416 3 0.2998 0.905 0.068 0.016 0.916
#> GSM110418 3 0.2998 0.905 0.068 0.016 0.916
#> GSM110419 3 0.0747 0.934 0.000 0.016 0.984
#> GSM110420 3 0.5115 0.771 0.188 0.016 0.796
#> GSM110421 2 0.2356 0.926 0.000 0.928 0.072
#> GSM110423 3 0.0747 0.934 0.000 0.016 0.984
#> GSM110424 2 0.0000 0.932 0.000 1.000 0.000
#> GSM110425 3 0.0747 0.934 0.000 0.016 0.984
#> GSM110427 2 0.0000 0.932 0.000 1.000 0.000
#> GSM110428 1 0.3551 0.807 0.868 0.000 0.132
#> GSM110430 1 0.0747 0.911 0.984 0.000 0.016
#> GSM110431 1 0.0000 0.913 1.000 0.000 0.000
#> GSM110432 2 0.4399 0.847 0.000 0.812 0.188
#> GSM110434 2 0.2537 0.924 0.000 0.920 0.080
#> GSM110435 1 0.0000 0.913 1.000 0.000 0.000
#> GSM110437 1 0.0747 0.911 0.984 0.000 0.016
#> GSM110438 1 0.6379 0.476 0.624 0.008 0.368
#> GSM110388 1 0.0000 0.913 1.000 0.000 0.000
#> GSM110392 2 0.4915 0.847 0.012 0.804 0.184
#> GSM110394 1 0.0000 0.913 1.000 0.000 0.000
#> GSM110402 3 0.0747 0.934 0.000 0.016 0.984
#> GSM110411 1 0.8794 0.470 0.584 0.224 0.192
#> GSM110412 2 0.4346 0.850 0.000 0.816 0.184
#> GSM110417 1 0.0000 0.913 1.000 0.000 0.000
#> GSM110422 2 0.0000 0.932 0.000 1.000 0.000
#> GSM110426 1 0.0000 0.913 1.000 0.000 0.000
#> GSM110429 2 0.2878 0.918 0.000 0.904 0.096
#> GSM110433 2 0.0000 0.932 0.000 1.000 0.000
#> GSM110436 2 0.0000 0.932 0.000 1.000 0.000
#> GSM110440 1 0.0000 0.913 1.000 0.000 0.000
#> GSM110441 2 0.0000 0.932 0.000 1.000 0.000
#> GSM110444 2 0.4915 0.847 0.012 0.804 0.184
#> GSM110445 1 0.4235 0.778 0.824 0.000 0.176
#> GSM110446 3 0.3183 0.898 0.076 0.016 0.908
#> GSM110449 2 0.3532 0.914 0.008 0.884 0.108
#> GSM110451 2 0.2796 0.920 0.000 0.908 0.092
#> GSM110391 2 0.0000 0.932 0.000 1.000 0.000
#> GSM110439 2 0.0000 0.932 0.000 1.000 0.000
#> GSM110442 2 0.0000 0.932 0.000 1.000 0.000
#> GSM110443 2 0.3454 0.916 0.008 0.888 0.104
#> GSM110447 3 0.0747 0.934 0.000 0.016 0.984
#> GSM110448 1 0.0000 0.913 1.000 0.000 0.000
#> GSM110450 1 0.0747 0.911 0.984 0.000 0.016
#> GSM110452 2 0.0000 0.932 0.000 1.000 0.000
#> GSM110453 2 0.0000 0.932 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.4941 0.1673 0.000 0.564 0.000 0.436
#> GSM110396 1 0.3486 0.8605 0.812 0.000 0.000 0.188
#> GSM110397 1 0.0000 0.8826 1.000 0.000 0.000 0.000
#> GSM110398 4 0.3429 0.5035 0.064 0.056 0.004 0.876
#> GSM110399 4 0.4356 0.5764 0.000 0.292 0.000 0.708
#> GSM110400 3 0.1557 0.9192 0.000 0.000 0.944 0.056
#> GSM110401 1 0.3486 0.8605 0.812 0.000 0.000 0.188
#> GSM110406 4 0.4356 0.5764 0.000 0.292 0.000 0.708
#> GSM110407 1 0.4579 0.8615 0.768 0.000 0.032 0.200
#> GSM110409 1 0.4540 0.8629 0.772 0.000 0.032 0.196
#> GSM110410 2 0.0000 0.7034 0.000 1.000 0.000 0.000
#> GSM110413 2 0.4304 0.5116 0.000 0.716 0.000 0.284
#> GSM110414 3 0.3528 0.7744 0.000 0.192 0.808 0.000
#> GSM110415 3 0.1022 0.9368 0.000 0.000 0.968 0.032
#> GSM110416 3 0.1637 0.9129 0.000 0.000 0.940 0.060
#> GSM110418 3 0.1637 0.9129 0.000 0.000 0.940 0.060
#> GSM110419 3 0.1022 0.9368 0.000 0.000 0.968 0.032
#> GSM110420 3 0.4673 0.7804 0.132 0.000 0.792 0.076
#> GSM110421 2 0.4933 0.1808 0.000 0.568 0.000 0.432
#> GSM110423 3 0.1022 0.9368 0.000 0.000 0.968 0.032
#> GSM110424 2 0.0000 0.7034 0.000 1.000 0.000 0.000
#> GSM110425 3 0.1022 0.9368 0.000 0.000 0.968 0.032
#> GSM110427 2 0.1867 0.6933 0.000 0.928 0.000 0.072
#> GSM110428 1 0.4996 0.7122 0.752 0.000 0.192 0.056
#> GSM110430 1 0.3486 0.8605 0.812 0.000 0.000 0.188
#> GSM110431 1 0.0188 0.8826 0.996 0.000 0.000 0.004
#> GSM110432 2 0.6130 0.0340 0.000 0.512 0.048 0.440
#> GSM110434 4 0.4972 0.1576 0.000 0.456 0.000 0.544
#> GSM110435 1 0.1488 0.8816 0.956 0.000 0.032 0.012
#> GSM110437 1 0.3486 0.8605 0.812 0.000 0.000 0.188
#> GSM110438 4 0.7347 0.2879 0.244 0.000 0.228 0.528
#> GSM110388 1 0.4244 0.7712 0.800 0.000 0.032 0.168
#> GSM110392 4 0.5172 0.5757 0.000 0.260 0.036 0.704
#> GSM110394 1 0.1488 0.8816 0.956 0.000 0.032 0.012
#> GSM110402 3 0.1022 0.9368 0.000 0.000 0.968 0.032
#> GSM110411 4 0.4026 0.5064 0.092 0.048 0.012 0.848
#> GSM110412 4 0.6120 0.2016 0.000 0.432 0.048 0.520
#> GSM110417 1 0.0592 0.8800 0.984 0.000 0.000 0.016
#> GSM110422 2 0.4103 0.5559 0.000 0.744 0.000 0.256
#> GSM110426 1 0.0592 0.8800 0.984 0.000 0.000 0.016
#> GSM110429 2 0.5182 0.4547 0.000 0.684 0.028 0.288
#> GSM110433 2 0.0000 0.7034 0.000 1.000 0.000 0.000
#> GSM110436 2 0.1867 0.6933 0.000 0.928 0.000 0.072
#> GSM110440 1 0.1488 0.8816 0.956 0.000 0.032 0.012
#> GSM110441 2 0.0000 0.7034 0.000 1.000 0.000 0.000
#> GSM110444 4 0.4606 0.5875 0.000 0.264 0.012 0.724
#> GSM110445 4 0.5576 -0.4347 0.444 0.000 0.020 0.536
#> GSM110446 3 0.1940 0.9074 0.000 0.000 0.924 0.076
#> GSM110449 4 0.4304 0.5833 0.000 0.284 0.000 0.716
#> GSM110451 2 0.5691 0.2133 0.000 0.564 0.028 0.408
#> GSM110391 2 0.0000 0.7034 0.000 1.000 0.000 0.000
#> GSM110439 2 0.0000 0.7034 0.000 1.000 0.000 0.000
#> GSM110442 4 0.4994 0.0877 0.000 0.480 0.000 0.520
#> GSM110443 4 0.4277 0.5851 0.000 0.280 0.000 0.720
#> GSM110447 3 0.1022 0.9368 0.000 0.000 0.968 0.032
#> GSM110448 1 0.1833 0.8783 0.944 0.000 0.032 0.024
#> GSM110450 1 0.4764 0.8520 0.748 0.000 0.032 0.220
#> GSM110452 2 0.4564 0.4485 0.000 0.672 0.000 0.328
#> GSM110453 2 0.0000 0.7034 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.6080 0.4362 0.000 0.560 0.000 0.168 0.272
#> GSM110396 1 0.4287 0.5448 0.540 0.000 0.000 0.460 0.000
#> GSM110397 1 0.2136 0.6462 0.904 0.008 0.000 0.088 0.000
#> GSM110398 2 0.3402 0.4036 0.008 0.804 0.000 0.184 0.004
#> GSM110399 2 0.2520 0.5618 0.000 0.896 0.000 0.056 0.048
#> GSM110400 3 0.1106 0.8515 0.000 0.024 0.964 0.012 0.000
#> GSM110401 1 0.4297 0.5437 0.528 0.000 0.000 0.472 0.000
#> GSM110406 2 0.1197 0.5810 0.000 0.952 0.000 0.000 0.048
#> GSM110407 1 0.4438 0.5449 0.608 0.004 0.004 0.384 0.000
#> GSM110409 1 0.4438 0.5451 0.608 0.004 0.004 0.384 0.000
#> GSM110410 5 0.0000 0.7744 0.000 0.000 0.000 0.000 1.000
#> GSM110413 2 0.4980 0.2997 0.000 0.584 0.000 0.036 0.380
#> GSM110414 3 0.3462 0.7080 0.000 0.000 0.792 0.012 0.196
#> GSM110415 3 0.0290 0.8730 0.000 0.008 0.992 0.000 0.000
#> GSM110416 3 0.4596 0.7831 0.044 0.028 0.764 0.164 0.000
#> GSM110418 3 0.4596 0.7831 0.044 0.028 0.764 0.164 0.000
#> GSM110419 3 0.0290 0.8730 0.000 0.008 0.992 0.000 0.000
#> GSM110420 3 0.5604 0.7314 0.084 0.036 0.688 0.192 0.000
#> GSM110421 2 0.5087 0.4810 0.000 0.644 0.000 0.064 0.292
#> GSM110423 3 0.0290 0.8730 0.000 0.008 0.992 0.000 0.000
#> GSM110424 5 0.0000 0.7744 0.000 0.000 0.000 0.000 1.000
#> GSM110425 3 0.0290 0.8730 0.000 0.008 0.992 0.000 0.000
#> GSM110427 5 0.5379 0.5168 0.000 0.168 0.000 0.164 0.668
#> GSM110428 1 0.5497 0.2910 0.720 0.084 0.060 0.136 0.000
#> GSM110430 1 0.4297 0.5437 0.528 0.000 0.000 0.472 0.000
#> GSM110431 1 0.1908 0.6502 0.908 0.000 0.000 0.092 0.000
#> GSM110432 2 0.8008 0.3134 0.000 0.428 0.136 0.172 0.264
#> GSM110434 2 0.4946 0.5932 0.000 0.712 0.000 0.168 0.120
#> GSM110435 1 0.0451 0.6396 0.988 0.004 0.008 0.000 0.000
#> GSM110437 1 0.4297 0.5437 0.528 0.000 0.000 0.472 0.000
#> GSM110438 4 0.7791 0.1595 0.344 0.184 0.084 0.388 0.000
#> GSM110388 1 0.4010 0.3634 0.784 0.056 0.000 0.160 0.000
#> GSM110392 2 0.6461 0.4668 0.000 0.584 0.104 0.268 0.044
#> GSM110394 1 0.0833 0.6451 0.976 0.004 0.004 0.016 0.000
#> GSM110402 3 0.0290 0.8730 0.000 0.008 0.992 0.000 0.000
#> GSM110411 2 0.3399 0.4259 0.020 0.812 0.000 0.168 0.000
#> GSM110412 2 0.8064 0.4171 0.000 0.424 0.136 0.248 0.192
#> GSM110417 1 0.2130 0.6437 0.908 0.012 0.000 0.080 0.000
#> GSM110422 5 0.6269 0.1128 0.000 0.324 0.000 0.168 0.508
#> GSM110426 1 0.2189 0.6431 0.904 0.012 0.000 0.084 0.000
#> GSM110429 5 0.7926 0.0762 0.000 0.264 0.128 0.168 0.440
#> GSM110433 5 0.0000 0.7744 0.000 0.000 0.000 0.000 1.000
#> GSM110436 5 0.5379 0.5168 0.000 0.168 0.000 0.164 0.668
#> GSM110440 1 0.0451 0.6396 0.988 0.004 0.008 0.000 0.000
#> GSM110441 5 0.1251 0.7468 0.000 0.036 0.000 0.008 0.956
#> GSM110444 2 0.3681 0.5135 0.000 0.808 0.000 0.148 0.044
#> GSM110445 4 0.6495 0.0539 0.204 0.328 0.000 0.468 0.000
#> GSM110446 3 0.5292 0.7513 0.064 0.036 0.712 0.188 0.000
#> GSM110449 2 0.3130 0.5370 0.000 0.856 0.000 0.096 0.048
#> GSM110451 2 0.8057 0.1650 0.000 0.372 0.128 0.168 0.332
#> GSM110391 5 0.0290 0.7724 0.000 0.000 0.000 0.008 0.992
#> GSM110439 5 0.0000 0.7744 0.000 0.000 0.000 0.000 1.000
#> GSM110442 2 0.3409 0.5999 0.000 0.824 0.000 0.032 0.144
#> GSM110443 2 0.2782 0.5532 0.000 0.880 0.000 0.072 0.048
#> GSM110447 3 0.0290 0.8730 0.000 0.008 0.992 0.000 0.000
#> GSM110448 1 0.1195 0.6366 0.960 0.012 0.000 0.028 0.000
#> GSM110450 1 0.4507 0.5295 0.580 0.004 0.004 0.412 0.000
#> GSM110452 2 0.6282 0.2120 0.000 0.476 0.000 0.156 0.368
#> GSM110453 5 0.0000 0.7744 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.2135 0.46716 0.000 0.872 0.000 0.000 0.128 0.000
#> GSM110396 1 0.0146 0.80291 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM110397 6 0.3620 0.71103 0.352 0.000 0.000 0.000 0.000 0.648
#> GSM110398 4 0.4323 0.59675 0.004 0.376 0.000 0.600 0.000 0.020
#> GSM110399 2 0.4051 -0.39996 0.000 0.560 0.000 0.432 0.008 0.000
#> GSM110400 3 0.0725 0.85686 0.000 0.012 0.976 0.012 0.000 0.000
#> GSM110401 1 0.0547 0.80338 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM110406 2 0.3955 -0.28768 0.000 0.608 0.000 0.384 0.008 0.000
#> GSM110407 1 0.2985 0.72057 0.844 0.000 0.000 0.100 0.000 0.056
#> GSM110409 1 0.3183 0.70383 0.828 0.000 0.000 0.112 0.000 0.060
#> GSM110410 5 0.0363 0.95398 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM110413 2 0.6095 0.21021 0.000 0.508 0.000 0.256 0.220 0.016
#> GSM110414 3 0.4169 0.71409 0.000 0.000 0.756 0.032 0.176 0.036
#> GSM110415 3 0.0520 0.86378 0.000 0.008 0.984 0.008 0.000 0.000
#> GSM110416 3 0.4601 0.77480 0.000 0.008 0.716 0.140 0.000 0.136
#> GSM110418 3 0.4638 0.77276 0.000 0.008 0.712 0.140 0.000 0.140
#> GSM110419 3 0.0146 0.86501 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM110420 3 0.5461 0.70112 0.004 0.000 0.592 0.196 0.000 0.208
#> GSM110421 2 0.5808 0.32748 0.000 0.568 0.000 0.212 0.204 0.016
#> GSM110423 3 0.0146 0.86472 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM110424 5 0.0363 0.95398 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM110425 3 0.0146 0.86472 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM110427 2 0.4181 0.10067 0.000 0.512 0.000 0.000 0.476 0.012
#> GSM110428 6 0.7631 0.36396 0.244 0.108 0.016 0.256 0.000 0.376
#> GSM110430 1 0.0547 0.80338 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM110431 6 0.5181 0.65546 0.428 0.000 0.000 0.088 0.000 0.484
#> GSM110432 2 0.5715 0.45731 0.000 0.628 0.152 0.012 0.188 0.020
#> GSM110434 2 0.1794 0.37388 0.000 0.924 0.000 0.040 0.036 0.000
#> GSM110435 6 0.5279 0.70552 0.324 0.000 0.000 0.120 0.000 0.556
#> GSM110437 1 0.0547 0.80338 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM110438 4 0.6488 -0.01505 0.000 0.168 0.044 0.452 0.000 0.336
#> GSM110388 6 0.5155 0.42568 0.124 0.000 0.000 0.280 0.000 0.596
#> GSM110392 2 0.6185 -0.16950 0.000 0.532 0.104 0.300 0.000 0.064
#> GSM110394 6 0.5300 0.67452 0.376 0.000 0.000 0.108 0.000 0.516
#> GSM110402 3 0.0146 0.86501 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM110411 4 0.4809 0.61422 0.000 0.328 0.000 0.600 0.000 0.072
#> GSM110412 2 0.7811 0.15648 0.000 0.452 0.148 0.228 0.096 0.076
#> GSM110417 6 0.3699 0.71593 0.336 0.000 0.000 0.004 0.000 0.660
#> GSM110422 2 0.4044 0.42120 0.000 0.668 0.000 0.008 0.312 0.012
#> GSM110426 6 0.3699 0.71593 0.336 0.000 0.000 0.004 0.000 0.660
#> GSM110429 2 0.5956 0.37444 0.000 0.556 0.128 0.012 0.288 0.016
#> GSM110433 5 0.0291 0.94431 0.000 0.000 0.000 0.004 0.992 0.004
#> GSM110436 2 0.4551 0.17973 0.000 0.536 0.000 0.012 0.436 0.016
#> GSM110440 6 0.5291 0.70622 0.328 0.000 0.000 0.120 0.000 0.552
#> GSM110441 5 0.2631 0.82112 0.000 0.128 0.000 0.004 0.856 0.012
#> GSM110444 4 0.4913 0.60603 0.000 0.364 0.000 0.564 0.000 0.072
#> GSM110445 1 0.5304 0.44166 0.632 0.096 0.000 0.248 0.000 0.024
#> GSM110446 3 0.5327 0.70360 0.000 0.000 0.596 0.208 0.000 0.196
#> GSM110449 4 0.4097 0.40253 0.000 0.492 0.000 0.500 0.008 0.000
#> GSM110451 2 0.5117 0.48094 0.000 0.672 0.088 0.008 0.216 0.016
#> GSM110391 5 0.1605 0.91223 0.000 0.044 0.000 0.004 0.936 0.016
#> GSM110439 5 0.0363 0.95398 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM110442 2 0.4098 -0.00931 0.000 0.676 0.000 0.292 0.032 0.000
#> GSM110443 2 0.3868 -0.52560 0.000 0.508 0.000 0.492 0.000 0.000
#> GSM110447 3 0.0146 0.86472 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM110448 6 0.4020 0.70673 0.276 0.000 0.000 0.032 0.000 0.692
#> GSM110450 1 0.2647 0.75503 0.868 0.000 0.000 0.088 0.000 0.044
#> GSM110452 2 0.3825 0.43921 0.000 0.768 0.000 0.072 0.160 0.000
#> GSM110453 5 0.0363 0.95398 0.000 0.012 0.000 0.000 0.988 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) specimen(p) k
#> CV:kmeans 52 0.9132 0.567 2
#> CV:kmeans 56 0.1033 0.405 3
#> CV:kmeans 48 0.2082 0.586 4
#> CV:kmeans 43 0.2388 0.414 5
#> CV:kmeans 37 0.0858 0.299 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 17209 rows and 59 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 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.633 0.820 0.923 0.5030 0.495 0.495
#> 3 3 0.846 0.903 0.954 0.3037 0.696 0.466
#> 4 4 0.852 0.871 0.939 0.1303 0.857 0.616
#> 5 5 0.758 0.683 0.802 0.0595 0.959 0.850
#> 6 6 0.739 0.534 0.720 0.0392 0.899 0.635
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM110395 2 0.000 0.925 0.000 1.000
#> GSM110396 1 0.000 0.885 1.000 0.000
#> GSM110397 1 0.000 0.885 1.000 0.000
#> GSM110398 1 0.722 0.720 0.800 0.200
#> GSM110399 1 0.971 0.468 0.600 0.400
#> GSM110400 2 0.000 0.925 0.000 1.000
#> GSM110401 1 0.000 0.885 1.000 0.000
#> GSM110406 1 0.971 0.468 0.600 0.400
#> GSM110407 1 0.000 0.885 1.000 0.000
#> GSM110409 1 0.000 0.885 1.000 0.000
#> GSM110410 2 0.000 0.925 0.000 1.000
#> GSM110413 2 0.000 0.925 0.000 1.000
#> GSM110414 2 0.000 0.925 0.000 1.000
#> GSM110415 2 0.722 0.719 0.200 0.800
#> GSM110416 2 0.971 0.399 0.400 0.600
#> GSM110418 2 0.971 0.399 0.400 0.600
#> GSM110419 2 0.644 0.763 0.164 0.836
#> GSM110420 2 0.971 0.399 0.400 0.600
#> GSM110421 2 0.000 0.925 0.000 1.000
#> GSM110423 2 0.000 0.925 0.000 1.000
#> GSM110424 2 0.000 0.925 0.000 1.000
#> GSM110425 2 0.000 0.925 0.000 1.000
#> GSM110427 2 0.000 0.925 0.000 1.000
#> GSM110428 1 0.000 0.885 1.000 0.000
#> GSM110430 1 0.000 0.885 1.000 0.000
#> GSM110431 1 0.000 0.885 1.000 0.000
#> GSM110432 2 0.000 0.925 0.000 1.000
#> GSM110434 2 0.000 0.925 0.000 1.000
#> GSM110435 1 0.000 0.885 1.000 0.000
#> GSM110437 1 0.000 0.885 1.000 0.000
#> GSM110438 1 0.000 0.885 1.000 0.000
#> GSM110388 1 0.000 0.885 1.000 0.000
#> GSM110392 1 0.971 0.468 0.600 0.400
#> GSM110394 1 0.000 0.885 1.000 0.000
#> GSM110402 2 0.000 0.925 0.000 1.000
#> GSM110411 1 0.000 0.885 1.000 0.000
#> GSM110412 2 0.000 0.925 0.000 1.000
#> GSM110417 1 0.000 0.885 1.000 0.000
#> GSM110422 2 0.000 0.925 0.000 1.000
#> GSM110426 1 0.000 0.885 1.000 0.000
#> GSM110429 2 0.000 0.925 0.000 1.000
#> GSM110433 2 0.000 0.925 0.000 1.000
#> GSM110436 2 0.000 0.925 0.000 1.000
#> GSM110440 1 0.000 0.885 1.000 0.000
#> GSM110441 2 0.000 0.925 0.000 1.000
#> GSM110444 1 0.971 0.468 0.600 0.400
#> GSM110445 1 0.000 0.885 1.000 0.000
#> GSM110446 2 0.971 0.399 0.400 0.600
#> GSM110449 1 0.971 0.468 0.600 0.400
#> GSM110451 2 0.000 0.925 0.000 1.000
#> GSM110391 2 0.000 0.925 0.000 1.000
#> GSM110439 2 0.000 0.925 0.000 1.000
#> GSM110442 2 0.000 0.925 0.000 1.000
#> GSM110443 1 0.971 0.468 0.600 0.400
#> GSM110447 2 0.000 0.925 0.000 1.000
#> GSM110448 1 0.000 0.885 1.000 0.000
#> GSM110450 1 0.000 0.885 1.000 0.000
#> GSM110452 2 0.000 0.925 0.000 1.000
#> GSM110453 2 0.000 0.925 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110396 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110397 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110398 1 0.4834 0.710 0.792 0.204 0.004
#> GSM110399 2 0.4784 0.762 0.200 0.796 0.004
#> GSM110400 3 0.0237 0.902 0.000 0.004 0.996
#> GSM110401 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110406 2 0.0237 0.944 0.000 0.996 0.004
#> GSM110407 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110409 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110410 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110413 2 0.0237 0.944 0.000 0.996 0.004
#> GSM110414 3 0.0592 0.899 0.000 0.012 0.988
#> GSM110415 3 0.0237 0.901 0.004 0.000 0.996
#> GSM110416 3 0.1529 0.888 0.040 0.000 0.960
#> GSM110418 3 0.4399 0.796 0.188 0.000 0.812
#> GSM110419 3 0.0237 0.902 0.000 0.004 0.996
#> GSM110420 3 0.4555 0.786 0.200 0.000 0.800
#> GSM110421 2 0.0237 0.944 0.000 0.996 0.004
#> GSM110423 3 0.0237 0.902 0.000 0.004 0.996
#> GSM110424 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110425 3 0.0237 0.902 0.000 0.004 0.996
#> GSM110427 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110428 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110430 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110431 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110432 3 0.3752 0.788 0.000 0.144 0.856
#> GSM110434 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110435 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110437 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110438 3 0.6291 0.252 0.468 0.000 0.532
#> GSM110388 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110392 2 0.1170 0.935 0.016 0.976 0.008
#> GSM110394 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110402 3 0.0237 0.902 0.000 0.004 0.996
#> GSM110411 1 0.2301 0.909 0.936 0.060 0.004
#> GSM110412 2 0.1529 0.922 0.000 0.960 0.040
#> GSM110417 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110422 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110426 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110429 2 0.1411 0.925 0.000 0.964 0.036
#> GSM110433 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110436 2 0.1411 0.925 0.000 0.964 0.036
#> GSM110440 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110441 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110444 2 0.6228 0.446 0.372 0.624 0.004
#> GSM110445 1 0.0237 0.977 0.996 0.000 0.004
#> GSM110446 3 0.4555 0.786 0.200 0.000 0.800
#> GSM110449 2 0.4733 0.767 0.196 0.800 0.004
#> GSM110451 2 0.1411 0.925 0.000 0.964 0.036
#> GSM110391 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110439 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110442 2 0.0237 0.944 0.000 0.996 0.004
#> GSM110443 2 0.4931 0.747 0.212 0.784 0.004
#> GSM110447 3 0.0237 0.902 0.000 0.004 0.996
#> GSM110448 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110450 1 0.0000 0.981 1.000 0.000 0.000
#> GSM110452 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110453 2 0.0000 0.945 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.0188 0.9036 0.000 0.996 0.000 0.004
#> GSM110396 1 0.0336 0.9719 0.992 0.000 0.000 0.008
#> GSM110397 1 0.0000 0.9728 1.000 0.000 0.000 0.000
#> GSM110398 4 0.1004 0.9134 0.004 0.024 0.000 0.972
#> GSM110399 4 0.1118 0.9177 0.000 0.036 0.000 0.964
#> GSM110400 3 0.1452 0.9038 0.000 0.036 0.956 0.008
#> GSM110401 1 0.0336 0.9719 0.992 0.000 0.000 0.008
#> GSM110406 4 0.1118 0.9177 0.000 0.036 0.000 0.964
#> GSM110407 1 0.0336 0.9719 0.992 0.000 0.000 0.008
#> GSM110409 1 0.0336 0.9719 0.992 0.000 0.000 0.008
#> GSM110410 2 0.0000 0.9039 0.000 1.000 0.000 0.000
#> GSM110413 2 0.4522 0.5345 0.000 0.680 0.000 0.320
#> GSM110414 3 0.2737 0.8416 0.000 0.104 0.888 0.008
#> GSM110415 3 0.0000 0.9242 0.000 0.000 1.000 0.000
#> GSM110416 3 0.0657 0.9209 0.004 0.000 0.984 0.012
#> GSM110418 3 0.3105 0.8504 0.120 0.000 0.868 0.012
#> GSM110419 3 0.0188 0.9233 0.000 0.000 0.996 0.004
#> GSM110420 3 0.3852 0.8022 0.180 0.000 0.808 0.012
#> GSM110421 2 0.0921 0.8933 0.000 0.972 0.000 0.028
#> GSM110423 3 0.0336 0.9249 0.000 0.000 0.992 0.008
#> GSM110424 2 0.0000 0.9039 0.000 1.000 0.000 0.000
#> GSM110425 3 0.0336 0.9249 0.000 0.000 0.992 0.008
#> GSM110427 2 0.0188 0.9036 0.000 0.996 0.000 0.004
#> GSM110428 1 0.0779 0.9622 0.980 0.000 0.004 0.016
#> GSM110430 1 0.0336 0.9719 0.992 0.000 0.000 0.008
#> GSM110431 1 0.0000 0.9728 1.000 0.000 0.000 0.000
#> GSM110432 2 0.5268 0.3176 0.000 0.592 0.396 0.012
#> GSM110434 2 0.3266 0.7700 0.000 0.832 0.000 0.168
#> GSM110435 1 0.0000 0.9728 1.000 0.000 0.000 0.000
#> GSM110437 1 0.0336 0.9719 0.992 0.000 0.000 0.008
#> GSM110438 1 0.5075 0.4178 0.644 0.000 0.344 0.012
#> GSM110388 1 0.0188 0.9714 0.996 0.000 0.000 0.004
#> GSM110392 4 0.4250 0.6156 0.000 0.276 0.000 0.724
#> GSM110394 1 0.0000 0.9728 1.000 0.000 0.000 0.000
#> GSM110402 3 0.0336 0.9249 0.000 0.000 0.992 0.008
#> GSM110411 4 0.1118 0.8913 0.036 0.000 0.000 0.964
#> GSM110412 2 0.0779 0.8967 0.000 0.980 0.004 0.016
#> GSM110417 1 0.0000 0.9728 1.000 0.000 0.000 0.000
#> GSM110422 2 0.0188 0.9036 0.000 0.996 0.000 0.004
#> GSM110426 1 0.0000 0.9728 1.000 0.000 0.000 0.000
#> GSM110429 2 0.0657 0.9001 0.000 0.984 0.004 0.012
#> GSM110433 2 0.0000 0.9039 0.000 1.000 0.000 0.000
#> GSM110436 2 0.0657 0.9001 0.000 0.984 0.004 0.012
#> GSM110440 1 0.0000 0.9728 1.000 0.000 0.000 0.000
#> GSM110441 2 0.1211 0.8862 0.000 0.960 0.000 0.040
#> GSM110444 4 0.2466 0.8811 0.004 0.096 0.000 0.900
#> GSM110445 4 0.2973 0.7944 0.144 0.000 0.000 0.856
#> GSM110446 3 0.3852 0.8022 0.180 0.000 0.808 0.012
#> GSM110449 4 0.1118 0.9166 0.000 0.036 0.000 0.964
#> GSM110451 2 0.0657 0.9001 0.000 0.984 0.004 0.012
#> GSM110391 2 0.0336 0.9016 0.000 0.992 0.000 0.008
#> GSM110439 2 0.0000 0.9039 0.000 1.000 0.000 0.000
#> GSM110442 2 0.4989 0.0872 0.000 0.528 0.000 0.472
#> GSM110443 4 0.1637 0.9091 0.000 0.060 0.000 0.940
#> GSM110447 3 0.0336 0.9249 0.000 0.000 0.992 0.008
#> GSM110448 1 0.0000 0.9728 1.000 0.000 0.000 0.000
#> GSM110450 1 0.0592 0.9665 0.984 0.000 0.000 0.016
#> GSM110452 2 0.2814 0.8081 0.000 0.868 0.000 0.132
#> GSM110453 2 0.0000 0.9039 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.4125 0.686 0.000 0.772 0.000 0.172 0.056
#> GSM110396 1 0.1544 0.833 0.932 0.000 0.000 0.000 0.068
#> GSM110397 1 0.2389 0.812 0.880 0.000 0.000 0.116 0.004
#> GSM110398 5 0.2756 0.671 0.060 0.012 0.000 0.036 0.892
#> GSM110399 5 0.1862 0.710 0.004 0.048 0.000 0.016 0.932
#> GSM110400 3 0.0566 0.891 0.000 0.004 0.984 0.012 0.000
#> GSM110401 1 0.1544 0.833 0.932 0.000 0.000 0.000 0.068
#> GSM110406 5 0.2349 0.706 0.004 0.084 0.000 0.012 0.900
#> GSM110407 1 0.1704 0.834 0.928 0.000 0.000 0.004 0.068
#> GSM110409 1 0.1704 0.834 0.928 0.000 0.000 0.004 0.068
#> GSM110410 2 0.3913 0.696 0.000 0.676 0.000 0.324 0.000
#> GSM110413 2 0.6674 0.417 0.000 0.436 0.000 0.260 0.304
#> GSM110414 3 0.1012 0.880 0.000 0.020 0.968 0.012 0.000
#> GSM110415 3 0.1410 0.892 0.000 0.000 0.940 0.060 0.000
#> GSM110416 3 0.3010 0.834 0.004 0.000 0.824 0.172 0.000
#> GSM110418 3 0.3527 0.820 0.024 0.000 0.804 0.172 0.000
#> GSM110419 3 0.1410 0.892 0.000 0.000 0.940 0.060 0.000
#> GSM110420 3 0.3810 0.806 0.040 0.000 0.792 0.168 0.000
#> GSM110421 2 0.5434 0.652 0.000 0.588 0.000 0.336 0.076
#> GSM110423 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> GSM110424 2 0.3932 0.694 0.000 0.672 0.000 0.328 0.000
#> GSM110425 3 0.0000 0.898 0.000 0.000 1.000 0.000 0.000
#> GSM110427 2 0.0000 0.675 0.000 1.000 0.000 0.000 0.000
#> GSM110428 1 0.3317 0.720 0.840 0.000 0.000 0.116 0.044
#> GSM110430 1 0.1478 0.836 0.936 0.000 0.000 0.000 0.064
#> GSM110431 1 0.1908 0.827 0.908 0.000 0.000 0.092 0.000
#> GSM110432 2 0.4552 0.430 0.000 0.696 0.264 0.040 0.000
#> GSM110434 2 0.4024 0.522 0.000 0.752 0.000 0.028 0.220
#> GSM110435 1 0.2127 0.820 0.892 0.000 0.000 0.108 0.000
#> GSM110437 1 0.1478 0.836 0.936 0.000 0.000 0.000 0.064
#> GSM110438 4 0.6794 0.000 0.336 0.000 0.164 0.480 0.020
#> GSM110388 1 0.3764 0.728 0.800 0.000 0.000 0.156 0.044
#> GSM110392 2 0.7645 -0.189 0.008 0.340 0.028 0.336 0.288
#> GSM110394 1 0.1502 0.835 0.940 0.000 0.000 0.056 0.004
#> GSM110402 3 0.0162 0.898 0.000 0.000 0.996 0.004 0.000
#> GSM110411 5 0.4756 0.508 0.044 0.000 0.000 0.288 0.668
#> GSM110412 2 0.6092 0.395 0.000 0.480 0.044 0.436 0.040
#> GSM110417 1 0.2674 0.792 0.856 0.000 0.000 0.140 0.004
#> GSM110422 2 0.0609 0.670 0.000 0.980 0.000 0.020 0.000
#> GSM110426 1 0.2629 0.795 0.860 0.000 0.000 0.136 0.004
#> GSM110429 2 0.1981 0.651 0.000 0.924 0.048 0.028 0.000
#> GSM110433 2 0.3999 0.690 0.000 0.656 0.000 0.344 0.000
#> GSM110436 2 0.1907 0.653 0.000 0.928 0.044 0.028 0.000
#> GSM110440 1 0.2074 0.822 0.896 0.000 0.000 0.104 0.000
#> GSM110441 2 0.5815 0.631 0.000 0.540 0.000 0.356 0.104
#> GSM110444 5 0.6203 0.463 0.032 0.072 0.000 0.352 0.544
#> GSM110445 5 0.4118 0.276 0.336 0.000 0.000 0.004 0.660
#> GSM110446 3 0.3944 0.795 0.052 0.000 0.788 0.160 0.000
#> GSM110449 5 0.1626 0.705 0.000 0.016 0.000 0.044 0.940
#> GSM110451 2 0.1915 0.654 0.000 0.928 0.040 0.032 0.000
#> GSM110391 2 0.4030 0.688 0.000 0.648 0.000 0.352 0.000
#> GSM110439 2 0.3857 0.699 0.000 0.688 0.000 0.312 0.000
#> GSM110442 5 0.6267 -0.168 0.000 0.404 0.000 0.148 0.448
#> GSM110443 5 0.2784 0.701 0.004 0.108 0.000 0.016 0.872
#> GSM110447 3 0.0162 0.896 0.000 0.000 0.996 0.004 0.000
#> GSM110448 1 0.2964 0.801 0.856 0.000 0.000 0.120 0.024
#> GSM110450 1 0.1608 0.830 0.928 0.000 0.000 0.000 0.072
#> GSM110452 2 0.4210 0.527 0.000 0.740 0.000 0.036 0.224
#> GSM110453 2 0.3895 0.697 0.000 0.680 0.000 0.320 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.4927 0.2919 0.000 0.648 0.000 0.104 0.244 0.004
#> GSM110396 1 0.0146 0.7186 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM110397 1 0.3986 0.6123 0.608 0.000 0.000 0.004 0.004 0.384
#> GSM110398 4 0.4597 0.4772 0.168 0.000 0.000 0.732 0.036 0.064
#> GSM110399 4 0.1816 0.6725 0.048 0.004 0.000 0.928 0.016 0.004
#> GSM110400 3 0.1219 0.8667 0.000 0.048 0.948 0.000 0.000 0.004
#> GSM110401 1 0.0405 0.7175 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM110406 4 0.3250 0.6853 0.052 0.048 0.000 0.860 0.028 0.012
#> GSM110407 1 0.0405 0.7175 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM110409 1 0.0405 0.7175 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM110410 5 0.4456 0.3253 0.000 0.448 0.000 0.028 0.524 0.000
#> GSM110413 4 0.6330 -0.0459 0.000 0.252 0.000 0.440 0.292 0.016
#> GSM110414 3 0.1141 0.8584 0.000 0.052 0.948 0.000 0.000 0.000
#> GSM110415 3 0.1267 0.8754 0.000 0.000 0.940 0.000 0.000 0.060
#> GSM110416 3 0.3109 0.7941 0.000 0.000 0.772 0.000 0.004 0.224
#> GSM110418 3 0.3276 0.7880 0.004 0.000 0.764 0.000 0.004 0.228
#> GSM110419 3 0.0858 0.8806 0.000 0.000 0.968 0.000 0.004 0.028
#> GSM110420 3 0.3384 0.7854 0.008 0.000 0.760 0.000 0.004 0.228
#> GSM110421 5 0.6116 0.2769 0.000 0.312 0.000 0.136 0.516 0.036
#> GSM110423 3 0.0146 0.8811 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM110424 5 0.4509 0.3374 0.000 0.436 0.000 0.032 0.532 0.000
#> GSM110425 3 0.0260 0.8810 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM110427 2 0.1461 0.6837 0.000 0.940 0.000 0.016 0.044 0.000
#> GSM110428 1 0.2378 0.6437 0.848 0.000 0.000 0.000 0.000 0.152
#> GSM110430 1 0.0291 0.7185 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM110431 1 0.3390 0.6677 0.704 0.000 0.000 0.000 0.000 0.296
#> GSM110432 2 0.3002 0.5873 0.000 0.836 0.136 0.000 0.008 0.020
#> GSM110434 2 0.5218 0.4264 0.000 0.592 0.000 0.312 0.084 0.012
#> GSM110435 1 0.3819 0.6259 0.624 0.000 0.000 0.000 0.004 0.372
#> GSM110437 1 0.0405 0.7175 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM110438 6 0.5303 0.0000 0.076 0.004 0.080 0.016 0.100 0.724
#> GSM110388 1 0.4876 0.5471 0.596 0.000 0.000 0.036 0.020 0.348
#> GSM110392 5 0.7670 -0.2741 0.004 0.164 0.012 0.136 0.372 0.312
#> GSM110394 1 0.2823 0.6963 0.796 0.000 0.000 0.000 0.000 0.204
#> GSM110402 3 0.0291 0.8819 0.000 0.004 0.992 0.000 0.000 0.004
#> GSM110411 5 0.7010 -0.3168 0.068 0.000 0.000 0.320 0.376 0.236
#> GSM110412 5 0.6474 -0.1394 0.000 0.236 0.008 0.028 0.504 0.224
#> GSM110417 1 0.4006 0.6026 0.600 0.000 0.000 0.004 0.004 0.392
#> GSM110422 2 0.0862 0.7079 0.000 0.972 0.000 0.016 0.008 0.004
#> GSM110426 1 0.4006 0.6034 0.600 0.000 0.000 0.004 0.004 0.392
#> GSM110429 2 0.1003 0.7156 0.000 0.964 0.028 0.000 0.004 0.004
#> GSM110433 5 0.4830 0.3521 0.000 0.412 0.000 0.040 0.540 0.008
#> GSM110436 2 0.1116 0.7161 0.000 0.960 0.028 0.000 0.008 0.004
#> GSM110440 1 0.3782 0.6350 0.636 0.000 0.000 0.000 0.004 0.360
#> GSM110441 5 0.5313 0.3354 0.000 0.324 0.000 0.124 0.552 0.000
#> GSM110444 5 0.6432 -0.2784 0.016 0.004 0.000 0.268 0.448 0.264
#> GSM110445 1 0.4962 -0.1212 0.488 0.000 0.000 0.460 0.012 0.040
#> GSM110446 3 0.3599 0.7800 0.020 0.000 0.756 0.000 0.004 0.220
#> GSM110449 4 0.1757 0.6667 0.008 0.000 0.000 0.928 0.052 0.012
#> GSM110451 2 0.0993 0.7148 0.000 0.964 0.024 0.000 0.000 0.012
#> GSM110391 5 0.5072 0.3597 0.000 0.372 0.000 0.064 0.556 0.008
#> GSM110439 5 0.4591 0.2954 0.000 0.464 0.000 0.036 0.500 0.000
#> GSM110442 4 0.6119 0.2255 0.000 0.256 0.000 0.524 0.196 0.024
#> GSM110443 4 0.3704 0.6786 0.064 0.036 0.000 0.836 0.040 0.024
#> GSM110447 3 0.0260 0.8810 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM110448 1 0.4153 0.6249 0.640 0.000 0.000 0.012 0.008 0.340
#> GSM110450 1 0.0508 0.7155 0.984 0.000 0.000 0.004 0.000 0.012
#> GSM110452 2 0.5223 0.3949 0.000 0.576 0.000 0.328 0.088 0.008
#> GSM110453 5 0.4589 0.3028 0.000 0.460 0.000 0.036 0.504 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) specimen(p) k
#> CV:skmeans 49 0.8363 0.468 2
#> CV:skmeans 57 0.0697 0.262 3
#> CV:skmeans 56 0.1477 0.697 4
#> CV:skmeans 51 0.2531 0.628 5
#> CV:skmeans 39 0.3859 0.632 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 17209 rows and 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.802 0.905 0.962 0.4621 0.544 0.544
#> 3 3 0.682 0.813 0.901 0.3590 0.820 0.669
#> 4 4 0.662 0.700 0.855 0.0809 0.879 0.707
#> 5 5 0.636 0.623 0.762 0.1228 0.845 0.572
#> 6 6 0.702 0.760 0.845 0.0600 0.926 0.689
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
#> GSM110395 2 0.000 0.9593 0.000 1.000
#> GSM110396 1 0.000 0.9524 1.000 0.000
#> GSM110397 1 0.000 0.9524 1.000 0.000
#> GSM110398 1 0.714 0.7465 0.804 0.196
#> GSM110399 2 0.000 0.9593 0.000 1.000
#> GSM110400 2 0.000 0.9593 0.000 1.000
#> GSM110401 1 0.000 0.9524 1.000 0.000
#> GSM110406 2 0.204 0.9324 0.032 0.968
#> GSM110407 1 0.000 0.9524 1.000 0.000
#> GSM110409 1 0.000 0.9524 1.000 0.000
#> GSM110410 2 0.000 0.9593 0.000 1.000
#> GSM110413 2 0.000 0.9593 0.000 1.000
#> GSM110414 2 0.000 0.9593 0.000 1.000
#> GSM110415 2 0.000 0.9593 0.000 1.000
#> GSM110416 2 0.722 0.7518 0.200 0.800
#> GSM110418 2 0.722 0.7518 0.200 0.800
#> GSM110419 2 0.000 0.9593 0.000 1.000
#> GSM110420 2 0.753 0.7303 0.216 0.784
#> GSM110421 2 0.000 0.9593 0.000 1.000
#> GSM110423 2 0.000 0.9593 0.000 1.000
#> GSM110424 2 0.000 0.9593 0.000 1.000
#> GSM110425 2 0.000 0.9593 0.000 1.000
#> GSM110427 2 0.000 0.9593 0.000 1.000
#> GSM110428 1 0.985 0.1904 0.572 0.428
#> GSM110430 1 0.000 0.9524 1.000 0.000
#> GSM110431 1 0.000 0.9524 1.000 0.000
#> GSM110432 2 0.000 0.9593 0.000 1.000
#> GSM110434 2 0.000 0.9593 0.000 1.000
#> GSM110435 1 0.000 0.9524 1.000 0.000
#> GSM110437 1 0.000 0.9524 1.000 0.000
#> GSM110438 2 0.494 0.8580 0.108 0.892
#> GSM110388 1 0.000 0.9524 1.000 0.000
#> GSM110392 2 0.000 0.9593 0.000 1.000
#> GSM110394 1 0.000 0.9524 1.000 0.000
#> GSM110402 2 0.000 0.9593 0.000 1.000
#> GSM110411 1 0.738 0.7302 0.792 0.208
#> GSM110412 2 0.000 0.9593 0.000 1.000
#> GSM110417 1 0.000 0.9524 1.000 0.000
#> GSM110422 2 0.000 0.9593 0.000 1.000
#> GSM110426 1 0.000 0.9524 1.000 0.000
#> GSM110429 2 0.000 0.9593 0.000 1.000
#> GSM110433 2 0.000 0.9593 0.000 1.000
#> GSM110436 2 0.000 0.9593 0.000 1.000
#> GSM110440 1 0.000 0.9524 1.000 0.000
#> GSM110441 2 0.000 0.9593 0.000 1.000
#> GSM110444 2 0.000 0.9593 0.000 1.000
#> GSM110445 1 0.000 0.9524 1.000 0.000
#> GSM110446 2 0.722 0.7518 0.200 0.800
#> GSM110449 2 0.995 0.0761 0.460 0.540
#> GSM110451 2 0.000 0.9593 0.000 1.000
#> GSM110391 2 0.000 0.9593 0.000 1.000
#> GSM110439 2 0.000 0.9593 0.000 1.000
#> GSM110442 2 0.000 0.9593 0.000 1.000
#> GSM110443 2 0.000 0.9593 0.000 1.000
#> GSM110447 2 0.000 0.9593 0.000 1.000
#> GSM110448 1 0.000 0.9524 1.000 0.000
#> GSM110450 1 0.000 0.9524 1.000 0.000
#> GSM110452 2 0.000 0.9593 0.000 1.000
#> GSM110453 2 0.000 0.9593 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.1031 0.9048 0.000 0.976 0.024
#> GSM110396 1 0.0237 0.9140 0.996 0.000 0.004
#> GSM110397 1 0.1031 0.9124 0.976 0.000 0.024
#> GSM110398 1 0.5277 0.6893 0.796 0.180 0.024
#> GSM110399 2 0.1031 0.9048 0.000 0.976 0.024
#> GSM110400 2 0.6308 -0.2419 0.000 0.508 0.492
#> GSM110401 1 0.0237 0.9136 0.996 0.000 0.004
#> GSM110406 2 0.2313 0.8825 0.032 0.944 0.024
#> GSM110407 1 0.0237 0.9140 0.996 0.000 0.004
#> GSM110409 1 0.0000 0.9136 1.000 0.000 0.000
#> GSM110410 2 0.3116 0.8439 0.000 0.892 0.108
#> GSM110413 2 0.0424 0.9017 0.000 0.992 0.008
#> GSM110414 3 0.6008 0.5570 0.000 0.372 0.628
#> GSM110415 3 0.3619 0.8362 0.000 0.136 0.864
#> GSM110416 3 0.3619 0.7641 0.136 0.000 0.864
#> GSM110418 3 0.3619 0.7641 0.136 0.000 0.864
#> GSM110419 3 0.3941 0.8370 0.000 0.156 0.844
#> GSM110420 3 0.3551 0.7634 0.132 0.000 0.868
#> GSM110421 2 0.0000 0.9042 0.000 1.000 0.000
#> GSM110423 3 0.4121 0.8329 0.000 0.168 0.832
#> GSM110424 2 0.3116 0.8439 0.000 0.892 0.108
#> GSM110425 3 0.4235 0.8268 0.000 0.176 0.824
#> GSM110427 2 0.0000 0.9042 0.000 1.000 0.000
#> GSM110428 1 0.8138 0.0361 0.480 0.452 0.068
#> GSM110430 1 0.0000 0.9136 1.000 0.000 0.000
#> GSM110431 1 0.1031 0.9124 0.976 0.000 0.024
#> GSM110432 2 0.1031 0.9048 0.000 0.976 0.024
#> GSM110434 2 0.1031 0.9048 0.000 0.976 0.024
#> GSM110435 1 0.2878 0.8744 0.904 0.000 0.096
#> GSM110437 1 0.0237 0.9136 0.996 0.000 0.004
#> GSM110438 2 0.5625 0.7324 0.116 0.808 0.076
#> GSM110388 1 0.1643 0.9014 0.956 0.000 0.044
#> GSM110392 2 0.1031 0.9048 0.000 0.976 0.024
#> GSM110394 1 0.1163 0.9121 0.972 0.000 0.028
#> GSM110402 3 0.4062 0.8351 0.000 0.164 0.836
#> GSM110411 1 0.5633 0.6511 0.768 0.208 0.024
#> GSM110412 2 0.1031 0.9048 0.000 0.976 0.024
#> GSM110417 1 0.1031 0.9124 0.976 0.000 0.024
#> GSM110422 2 0.0000 0.9042 0.000 1.000 0.000
#> GSM110426 1 0.1643 0.9088 0.956 0.000 0.044
#> GSM110429 2 0.1031 0.9048 0.000 0.976 0.024
#> GSM110433 2 0.3116 0.8439 0.000 0.892 0.108
#> GSM110436 2 0.0000 0.9042 0.000 1.000 0.000
#> GSM110440 1 0.2356 0.8951 0.928 0.000 0.072
#> GSM110441 2 0.1860 0.8807 0.000 0.948 0.052
#> GSM110444 2 0.1031 0.9048 0.000 0.976 0.024
#> GSM110445 1 0.1031 0.9011 0.976 0.000 0.024
#> GSM110446 3 0.3619 0.7641 0.136 0.000 0.864
#> GSM110449 2 0.7174 0.0507 0.460 0.516 0.024
#> GSM110451 2 0.1031 0.9048 0.000 0.976 0.024
#> GSM110391 2 0.1289 0.8912 0.000 0.968 0.032
#> GSM110439 2 0.3116 0.8439 0.000 0.892 0.108
#> GSM110442 2 0.0892 0.9050 0.000 0.980 0.020
#> GSM110443 2 0.1031 0.9048 0.000 0.976 0.024
#> GSM110447 3 0.5882 0.6055 0.000 0.348 0.652
#> GSM110448 1 0.1753 0.9057 0.952 0.000 0.048
#> GSM110450 1 0.0592 0.9093 0.988 0.000 0.012
#> GSM110452 2 0.0000 0.9042 0.000 1.000 0.000
#> GSM110453 2 0.3116 0.8439 0.000 0.892 0.108
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.0469 0.8601 0.000 0.988 0.012 0.000
#> GSM110396 4 0.5000 0.2839 0.496 0.000 0.000 0.504
#> GSM110397 1 0.4585 0.4230 0.668 0.000 0.000 0.332
#> GSM110398 2 0.6014 0.0460 0.020 0.488 0.012 0.480
#> GSM110399 2 0.0657 0.8602 0.004 0.984 0.012 0.000
#> GSM110400 2 0.4994 -0.1714 0.000 0.520 0.480 0.000
#> GSM110401 1 0.0188 0.7997 0.996 0.000 0.000 0.004
#> GSM110406 2 0.1488 0.8450 0.000 0.956 0.012 0.032
#> GSM110407 4 0.4998 0.3018 0.488 0.000 0.000 0.512
#> GSM110409 1 0.4996 -0.4025 0.516 0.000 0.000 0.484
#> GSM110410 2 0.4057 0.7651 0.000 0.812 0.028 0.160
#> GSM110413 2 0.0469 0.8585 0.000 0.988 0.000 0.012
#> GSM110414 3 0.5543 0.5250 0.000 0.360 0.612 0.028
#> GSM110415 3 0.0921 0.7996 0.000 0.028 0.972 0.000
#> GSM110416 3 0.1211 0.7834 0.000 0.000 0.960 0.040
#> GSM110418 3 0.1211 0.7834 0.000 0.000 0.960 0.040
#> GSM110419 3 0.2149 0.8090 0.000 0.088 0.912 0.000
#> GSM110420 3 0.1211 0.7834 0.000 0.000 0.960 0.040
#> GSM110421 2 0.0188 0.8600 0.000 0.996 0.000 0.004
#> GSM110423 3 0.3356 0.7758 0.000 0.176 0.824 0.000
#> GSM110424 2 0.4057 0.7651 0.000 0.812 0.028 0.160
#> GSM110425 3 0.3486 0.7670 0.000 0.188 0.812 0.000
#> GSM110427 2 0.0000 0.8602 0.000 1.000 0.000 0.000
#> GSM110428 2 0.5941 0.6409 0.008 0.712 0.172 0.108
#> GSM110430 1 0.0188 0.7997 0.996 0.000 0.000 0.004
#> GSM110431 4 0.3486 0.7167 0.188 0.000 0.000 0.812
#> GSM110432 2 0.0469 0.8601 0.000 0.988 0.012 0.000
#> GSM110434 2 0.0469 0.8601 0.000 0.988 0.012 0.000
#> GSM110435 4 0.3450 0.7506 0.008 0.000 0.156 0.836
#> GSM110437 1 0.0188 0.7997 0.996 0.000 0.000 0.004
#> GSM110438 2 0.4088 0.7371 0.008 0.808 0.172 0.012
#> GSM110388 4 0.4663 0.7532 0.064 0.000 0.148 0.788
#> GSM110392 2 0.0657 0.8598 0.000 0.984 0.012 0.004
#> GSM110394 4 0.3597 0.7520 0.148 0.000 0.016 0.836
#> GSM110402 3 0.2530 0.8052 0.000 0.112 0.888 0.000
#> GSM110411 2 0.5576 0.0825 0.004 0.500 0.012 0.484
#> GSM110412 2 0.0657 0.8598 0.000 0.984 0.012 0.004
#> GSM110417 1 0.3024 0.6945 0.852 0.000 0.000 0.148
#> GSM110422 2 0.0000 0.8602 0.000 1.000 0.000 0.000
#> GSM110426 4 0.3996 0.7745 0.104 0.000 0.060 0.836
#> GSM110429 2 0.0469 0.8601 0.000 0.988 0.012 0.000
#> GSM110433 2 0.4057 0.7651 0.000 0.812 0.028 0.160
#> GSM110436 2 0.0000 0.8602 0.000 1.000 0.000 0.000
#> GSM110440 4 0.3450 0.7506 0.008 0.000 0.156 0.836
#> GSM110441 2 0.2179 0.8330 0.000 0.924 0.012 0.064
#> GSM110444 2 0.0657 0.8598 0.000 0.984 0.012 0.004
#> GSM110445 1 0.0804 0.7916 0.980 0.000 0.008 0.012
#> GSM110446 3 0.1211 0.7834 0.000 0.000 0.960 0.040
#> GSM110449 2 0.5482 0.2878 0.004 0.572 0.012 0.412
#> GSM110451 2 0.0469 0.8601 0.000 0.988 0.012 0.000
#> GSM110391 2 0.1767 0.8417 0.000 0.944 0.012 0.044
#> GSM110439 2 0.4057 0.7651 0.000 0.812 0.028 0.160
#> GSM110442 2 0.0336 0.8606 0.000 0.992 0.008 0.000
#> GSM110443 2 0.0657 0.8598 0.000 0.984 0.012 0.004
#> GSM110447 3 0.4761 0.5348 0.000 0.372 0.628 0.000
#> GSM110448 4 0.3972 0.7777 0.080 0.000 0.080 0.840
#> GSM110450 1 0.0469 0.7956 0.988 0.000 0.000 0.012
#> GSM110452 2 0.0000 0.8602 0.000 1.000 0.000 0.000
#> GSM110453 2 0.4057 0.7651 0.000 0.812 0.028 0.160
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.0290 0.7379 0.000 0.992 0.008 0.000 0.000
#> GSM110396 1 0.3274 0.6274 0.780 0.000 0.000 0.000 0.220
#> GSM110397 5 0.4138 0.5639 0.384 0.000 0.000 0.000 0.616
#> GSM110398 4 0.5883 0.5636 0.000 0.108 0.000 0.524 0.368
#> GSM110399 2 0.1830 0.6966 0.000 0.924 0.008 0.000 0.068
#> GSM110400 2 0.4305 -0.2291 0.000 0.512 0.488 0.000 0.000
#> GSM110401 1 0.0000 0.7228 1.000 0.000 0.000 0.000 0.000
#> GSM110406 2 0.0693 0.7338 0.000 0.980 0.008 0.000 0.012
#> GSM110407 1 0.3491 0.6173 0.768 0.000 0.004 0.000 0.228
#> GSM110409 1 0.3857 0.6256 0.688 0.000 0.000 0.000 0.312
#> GSM110410 2 0.4235 0.4932 0.000 0.576 0.000 0.424 0.000
#> GSM110413 2 0.1544 0.6743 0.000 0.932 0.000 0.068 0.000
#> GSM110414 3 0.4941 0.5683 0.000 0.328 0.628 0.044 0.000
#> GSM110415 3 0.1282 0.8017 0.000 0.004 0.952 0.044 0.000
#> GSM110416 3 0.1408 0.7991 0.000 0.000 0.948 0.044 0.008
#> GSM110418 3 0.1408 0.7991 0.000 0.000 0.948 0.044 0.008
#> GSM110419 3 0.1732 0.8112 0.000 0.080 0.920 0.000 0.000
#> GSM110420 3 0.1408 0.7991 0.000 0.000 0.948 0.044 0.008
#> GSM110421 2 0.3837 0.0363 0.000 0.692 0.000 0.308 0.000
#> GSM110423 3 0.2929 0.7725 0.000 0.180 0.820 0.000 0.000
#> GSM110424 2 0.4235 0.4932 0.000 0.576 0.000 0.424 0.000
#> GSM110425 3 0.3039 0.7621 0.000 0.192 0.808 0.000 0.000
#> GSM110427 2 0.0000 0.7381 0.000 1.000 0.000 0.000 0.000
#> GSM110428 2 0.4800 0.5256 0.000 0.716 0.196 0.000 0.088
#> GSM110430 1 0.0000 0.7228 1.000 0.000 0.000 0.000 0.000
#> GSM110431 5 0.3231 0.8254 0.196 0.000 0.004 0.000 0.800
#> GSM110432 2 0.0290 0.7379 0.000 0.992 0.008 0.000 0.000
#> GSM110434 2 0.0290 0.7379 0.000 0.992 0.008 0.000 0.000
#> GSM110435 5 0.3098 0.7578 0.016 0.000 0.148 0.000 0.836
#> GSM110437 1 0.0000 0.7228 1.000 0.000 0.000 0.000 0.000
#> GSM110438 2 0.5597 0.4352 0.000 0.668 0.196 0.124 0.012
#> GSM110388 4 0.4731 0.3820 0.016 0.000 0.000 0.528 0.456
#> GSM110392 4 0.4294 0.5611 0.000 0.468 0.000 0.532 0.000
#> GSM110394 5 0.3039 0.8429 0.152 0.000 0.012 0.000 0.836
#> GSM110402 3 0.2127 0.8072 0.000 0.108 0.892 0.000 0.000
#> GSM110411 4 0.5949 0.5833 0.000 0.120 0.000 0.532 0.348
#> GSM110412 4 0.4294 0.5611 0.000 0.468 0.000 0.532 0.000
#> GSM110417 1 0.6106 0.1662 0.564 0.000 0.004 0.288 0.144
#> GSM110422 2 0.0000 0.7381 0.000 1.000 0.000 0.000 0.000
#> GSM110426 5 0.3912 0.8436 0.144 0.000 0.028 0.020 0.808
#> GSM110429 2 0.0290 0.7379 0.000 0.992 0.008 0.000 0.000
#> GSM110433 2 0.4235 0.4932 0.000 0.576 0.000 0.424 0.000
#> GSM110436 2 0.0000 0.7381 0.000 1.000 0.000 0.000 0.000
#> GSM110440 5 0.3464 0.8364 0.096 0.000 0.068 0.000 0.836
#> GSM110441 4 0.4088 0.1318 0.000 0.368 0.000 0.632 0.000
#> GSM110444 4 0.4294 0.5611 0.000 0.468 0.000 0.532 0.000
#> GSM110445 1 0.3282 0.6987 0.804 0.000 0.000 0.008 0.188
#> GSM110446 3 0.1408 0.7991 0.000 0.000 0.948 0.044 0.008
#> GSM110449 4 0.6253 0.6337 0.000 0.188 0.000 0.532 0.280
#> GSM110451 2 0.0290 0.7379 0.000 0.992 0.008 0.000 0.000
#> GSM110391 4 0.4219 0.5506 0.000 0.416 0.000 0.584 0.000
#> GSM110439 2 0.4235 0.4932 0.000 0.576 0.000 0.424 0.000
#> GSM110442 2 0.0290 0.7353 0.000 0.992 0.000 0.008 0.000
#> GSM110443 4 0.5670 0.6167 0.000 0.388 0.000 0.528 0.084
#> GSM110447 3 0.4015 0.5748 0.000 0.348 0.652 0.000 0.000
#> GSM110448 4 0.4589 0.3566 0.004 0.000 0.004 0.520 0.472
#> GSM110450 1 0.3282 0.6987 0.804 0.000 0.000 0.008 0.188
#> GSM110452 2 0.0000 0.7381 0.000 1.000 0.000 0.000 0.000
#> GSM110453 2 0.4235 0.4932 0.000 0.576 0.000 0.424 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.0000 0.9019 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110396 1 0.2454 0.7423 0.840 0.000 0.000 0.000 0.000 0.160
#> GSM110397 6 0.3076 0.7324 0.240 0.000 0.000 0.000 0.000 0.760
#> GSM110398 4 0.2420 0.7363 0.000 0.040 0.000 0.884 0.000 0.076
#> GSM110399 2 0.1444 0.8360 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM110400 3 0.6126 0.4107 0.000 0.428 0.432 0.076 0.064 0.000
#> GSM110401 1 0.0000 0.7826 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110406 2 0.0000 0.9019 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110407 1 0.3266 0.6505 0.728 0.000 0.000 0.000 0.000 0.272
#> GSM110409 1 0.2474 0.7743 0.880 0.000 0.000 0.040 0.000 0.080
#> GSM110410 5 0.1814 0.9603 0.000 0.100 0.000 0.000 0.900 0.000
#> GSM110413 2 0.1524 0.8409 0.000 0.932 0.000 0.060 0.008 0.000
#> GSM110414 3 0.6861 0.6383 0.000 0.268 0.476 0.108 0.148 0.000
#> GSM110415 3 0.0000 0.7135 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110416 3 0.0000 0.7135 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110418 3 0.0000 0.7135 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110419 3 0.5152 0.7395 0.000 0.084 0.708 0.108 0.100 0.000
#> GSM110420 3 0.0000 0.7135 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110421 2 0.3659 0.1561 0.000 0.636 0.000 0.364 0.000 0.000
#> GSM110423 3 0.6080 0.7202 0.000 0.188 0.604 0.108 0.100 0.000
#> GSM110424 5 0.1814 0.9603 0.000 0.100 0.000 0.000 0.900 0.000
#> GSM110425 3 0.6155 0.7138 0.000 0.200 0.592 0.108 0.100 0.000
#> GSM110427 2 0.0000 0.9019 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110428 2 0.3925 0.6169 0.000 0.744 0.200 0.000 0.000 0.056
#> GSM110430 1 0.0000 0.7826 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110431 6 0.2730 0.7821 0.192 0.000 0.000 0.000 0.000 0.808
#> GSM110432 2 0.0000 0.9019 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110434 2 0.0000 0.9019 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110435 6 0.0000 0.8973 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM110437 1 0.0000 0.7826 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110438 2 0.5100 0.4335 0.000 0.600 0.284 0.116 0.000 0.000
#> GSM110388 4 0.2070 0.6966 0.008 0.000 0.000 0.892 0.000 0.100
#> GSM110392 4 0.3446 0.7302 0.000 0.308 0.000 0.692 0.000 0.000
#> GSM110394 6 0.0000 0.8973 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM110402 3 0.5201 0.7429 0.000 0.108 0.704 0.096 0.092 0.000
#> GSM110411 4 0.2308 0.7393 0.000 0.040 0.000 0.892 0.000 0.068
#> GSM110412 4 0.3482 0.7210 0.000 0.316 0.000 0.684 0.000 0.000
#> GSM110417 1 0.5779 0.0511 0.452 0.000 0.000 0.368 0.000 0.180
#> GSM110422 2 0.0000 0.9019 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110426 6 0.0547 0.8844 0.000 0.000 0.000 0.020 0.000 0.980
#> GSM110429 2 0.0000 0.9019 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110433 5 0.1814 0.9603 0.000 0.100 0.000 0.000 0.900 0.000
#> GSM110436 2 0.0000 0.9019 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110440 6 0.0000 0.8973 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM110441 5 0.3161 0.7987 0.000 0.216 0.000 0.008 0.776 0.000
#> GSM110444 4 0.3446 0.7302 0.000 0.308 0.000 0.692 0.000 0.000
#> GSM110445 1 0.2933 0.7432 0.796 0.000 0.000 0.200 0.000 0.004
#> GSM110446 3 0.0000 0.7135 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110449 4 0.2199 0.7580 0.000 0.088 0.000 0.892 0.000 0.020
#> GSM110451 2 0.0000 0.9019 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110391 4 0.4517 0.7071 0.000 0.292 0.000 0.648 0.060 0.000
#> GSM110439 5 0.1814 0.9603 0.000 0.100 0.000 0.000 0.900 0.000
#> GSM110442 2 0.0000 0.9019 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110443 4 0.2883 0.7817 0.000 0.212 0.000 0.788 0.000 0.000
#> GSM110447 3 0.6590 0.6279 0.000 0.300 0.492 0.108 0.100 0.000
#> GSM110448 4 0.3482 0.5511 0.000 0.000 0.000 0.684 0.000 0.316
#> GSM110450 1 0.2933 0.7432 0.796 0.000 0.000 0.200 0.000 0.004
#> GSM110452 2 0.0000 0.9019 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110453 5 0.1814 0.9603 0.000 0.100 0.000 0.000 0.900 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) specimen(p) k
#> CV:pam 57 1.0000 0.700 2
#> CV:pam 56 0.2378 0.411 3
#> CV:pam 51 0.2754 0.801 4
#> CV:pam 47 0.0712 0.714 5
#> CV:pam 55 0.0405 0.500 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 17209 rows and 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.349 0.610 0.832 0.4048 0.583 0.583
#> 3 3 0.954 0.924 0.947 0.5863 0.684 0.496
#> 4 4 0.745 0.818 0.848 0.1033 0.889 0.708
#> 5 5 0.775 0.752 0.851 0.0876 0.935 0.785
#> 6 6 0.806 0.699 0.846 0.0748 0.884 0.564
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
#> GSM110395 2 0.0000 0.79185 0.000 1.000
#> GSM110396 2 0.9732 0.41526 0.404 0.596
#> GSM110397 1 0.9933 -0.00676 0.548 0.452
#> GSM110398 2 0.0376 0.79166 0.004 0.996
#> GSM110399 2 0.0000 0.79185 0.000 1.000
#> GSM110400 1 0.7602 0.68480 0.780 0.220
#> GSM110401 2 0.9732 0.41526 0.404 0.596
#> GSM110406 2 0.0376 0.79166 0.004 0.996
#> GSM110407 2 0.9732 0.41526 0.404 0.596
#> GSM110409 2 0.9732 0.41526 0.404 0.596
#> GSM110410 2 0.0938 0.78999 0.012 0.988
#> GSM110413 2 0.0000 0.79185 0.000 1.000
#> GSM110414 1 0.6712 0.70124 0.824 0.176
#> GSM110415 1 0.6887 0.70512 0.816 0.184
#> GSM110416 1 0.1414 0.67531 0.980 0.020
#> GSM110418 1 0.1414 0.67531 0.980 0.020
#> GSM110419 1 0.7219 0.69853 0.800 0.200
#> GSM110420 1 0.1414 0.67531 0.980 0.020
#> GSM110421 2 0.0376 0.79166 0.004 0.996
#> GSM110423 1 0.6887 0.70512 0.816 0.184
#> GSM110424 2 0.0938 0.78999 0.012 0.988
#> GSM110425 1 0.6887 0.70512 0.816 0.184
#> GSM110427 2 0.0672 0.79144 0.008 0.992
#> GSM110428 2 0.9732 0.41526 0.404 0.596
#> GSM110430 2 0.9732 0.41526 0.404 0.596
#> GSM110431 1 0.9963 -0.01067 0.536 0.464
#> GSM110432 2 0.7950 0.55564 0.240 0.760
#> GSM110434 2 0.0000 0.79185 0.000 1.000
#> GSM110435 1 0.9963 -0.01067 0.536 0.464
#> GSM110437 2 0.9732 0.41526 0.404 0.596
#> GSM110438 1 0.9996 -0.11121 0.512 0.488
#> GSM110388 2 0.9815 0.40474 0.420 0.580
#> GSM110392 2 0.2778 0.77049 0.048 0.952
#> GSM110394 2 0.9795 0.38591 0.416 0.584
#> GSM110402 1 0.6887 0.70512 0.816 0.184
#> GSM110411 2 0.0938 0.78999 0.012 0.988
#> GSM110412 2 0.1184 0.78982 0.016 0.984
#> GSM110417 2 0.9850 0.38583 0.428 0.572
#> GSM110422 2 0.0376 0.78924 0.004 0.996
#> GSM110426 2 0.9815 0.40474 0.420 0.580
#> GSM110429 2 0.0672 0.79144 0.008 0.992
#> GSM110433 2 0.0938 0.78999 0.012 0.988
#> GSM110436 2 0.0672 0.79144 0.008 0.992
#> GSM110440 1 0.9963 -0.01067 0.536 0.464
#> GSM110441 2 0.0000 0.79185 0.000 1.000
#> GSM110444 2 0.1414 0.78837 0.020 0.980
#> GSM110445 2 0.7376 0.64326 0.208 0.792
#> GSM110446 1 0.2236 0.67423 0.964 0.036
#> GSM110449 2 0.0938 0.78999 0.012 0.988
#> GSM110451 2 0.0672 0.79144 0.008 0.992
#> GSM110391 2 0.0938 0.78999 0.012 0.988
#> GSM110439 2 0.0000 0.79185 0.000 1.000
#> GSM110442 2 0.0000 0.79185 0.000 1.000
#> GSM110443 2 0.0000 0.79185 0.000 1.000
#> GSM110447 1 0.6887 0.70512 0.816 0.184
#> GSM110448 2 0.9815 0.40474 0.420 0.580
#> GSM110450 2 0.9686 0.42770 0.396 0.604
#> GSM110452 2 0.0000 0.79185 0.000 1.000
#> GSM110453 2 0.0000 0.79185 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.0475 0.957 0.004 0.992 0.004
#> GSM110396 1 0.2165 0.927 0.936 0.064 0.000
#> GSM110397 1 0.1964 0.910 0.944 0.000 0.056
#> GSM110398 2 0.6140 0.206 0.404 0.596 0.000
#> GSM110399 2 0.0000 0.958 0.000 1.000 0.000
#> GSM110400 3 0.2280 0.953 0.008 0.052 0.940
#> GSM110401 1 0.2165 0.927 0.936 0.064 0.000
#> GSM110406 2 0.0000 0.958 0.000 1.000 0.000
#> GSM110407 1 0.2165 0.927 0.936 0.064 0.000
#> GSM110409 1 0.2165 0.927 0.936 0.064 0.000
#> GSM110410 2 0.2297 0.941 0.036 0.944 0.020
#> GSM110413 2 0.0237 0.958 0.000 0.996 0.004
#> GSM110414 3 0.1267 0.983 0.004 0.024 0.972
#> GSM110415 3 0.1267 0.983 0.004 0.024 0.972
#> GSM110416 3 0.1163 0.970 0.028 0.000 0.972
#> GSM110418 3 0.1267 0.974 0.024 0.004 0.972
#> GSM110419 3 0.1267 0.983 0.004 0.024 0.972
#> GSM110420 3 0.1753 0.960 0.048 0.000 0.952
#> GSM110421 2 0.1289 0.953 0.032 0.968 0.000
#> GSM110423 3 0.1267 0.983 0.004 0.024 0.972
#> GSM110424 2 0.2297 0.941 0.036 0.944 0.020
#> GSM110425 3 0.1267 0.983 0.004 0.024 0.972
#> GSM110427 2 0.0829 0.956 0.004 0.984 0.012
#> GSM110428 1 0.5507 0.834 0.808 0.056 0.136
#> GSM110430 1 0.2165 0.927 0.936 0.064 0.000
#> GSM110431 1 0.2173 0.915 0.944 0.008 0.048
#> GSM110432 2 0.0829 0.956 0.004 0.984 0.012
#> GSM110434 2 0.0475 0.957 0.004 0.992 0.004
#> GSM110435 1 0.2066 0.908 0.940 0.000 0.060
#> GSM110437 1 0.2165 0.927 0.936 0.064 0.000
#> GSM110438 1 0.5536 0.772 0.776 0.024 0.200
#> GSM110388 1 0.1267 0.911 0.972 0.004 0.024
#> GSM110392 2 0.2550 0.939 0.040 0.936 0.024
#> GSM110394 1 0.1964 0.925 0.944 0.056 0.000
#> GSM110402 3 0.1267 0.983 0.004 0.024 0.972
#> GSM110411 1 0.5551 0.727 0.768 0.212 0.020
#> GSM110412 2 0.2550 0.939 0.040 0.936 0.024
#> GSM110417 1 0.1163 0.911 0.972 0.000 0.028
#> GSM110422 2 0.0829 0.956 0.004 0.984 0.012
#> GSM110426 1 0.1163 0.911 0.972 0.000 0.028
#> GSM110429 2 0.0829 0.956 0.004 0.984 0.012
#> GSM110433 2 0.1411 0.951 0.036 0.964 0.000
#> GSM110436 2 0.0829 0.956 0.004 0.984 0.012
#> GSM110440 1 0.2066 0.908 0.940 0.000 0.060
#> GSM110441 2 0.1163 0.954 0.028 0.972 0.000
#> GSM110444 2 0.2414 0.941 0.040 0.940 0.020
#> GSM110445 1 0.4452 0.818 0.808 0.192 0.000
#> GSM110446 3 0.1163 0.970 0.028 0.000 0.972
#> GSM110449 2 0.1411 0.951 0.036 0.964 0.000
#> GSM110451 2 0.0829 0.956 0.004 0.984 0.012
#> GSM110391 2 0.2297 0.941 0.036 0.944 0.020
#> GSM110439 2 0.1411 0.951 0.036 0.964 0.000
#> GSM110442 2 0.0000 0.958 0.000 1.000 0.000
#> GSM110443 2 0.0000 0.958 0.000 1.000 0.000
#> GSM110447 3 0.1267 0.983 0.004 0.024 0.972
#> GSM110448 1 0.1267 0.911 0.972 0.004 0.024
#> GSM110450 1 0.2165 0.927 0.936 0.064 0.000
#> GSM110452 2 0.0237 0.958 0.000 0.996 0.004
#> GSM110453 2 0.0000 0.958 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.4417 0.734 0.044 0.796 0.000 0.160
#> GSM110396 1 0.0376 0.896 0.992 0.004 0.000 0.004
#> GSM110397 1 0.3726 0.853 0.788 0.000 0.000 0.212
#> GSM110398 2 0.4134 0.357 0.260 0.740 0.000 0.000
#> GSM110399 2 0.1297 0.763 0.020 0.964 0.000 0.016
#> GSM110400 3 0.2632 0.900 0.048 0.008 0.916 0.028
#> GSM110401 1 0.0376 0.896 0.992 0.004 0.000 0.004
#> GSM110406 2 0.2814 0.695 0.132 0.868 0.000 0.000
#> GSM110407 1 0.0895 0.892 0.976 0.004 0.000 0.020
#> GSM110409 1 0.0895 0.892 0.976 0.004 0.000 0.020
#> GSM110410 4 0.4936 0.988 0.000 0.372 0.004 0.624
#> GSM110413 2 0.0000 0.756 0.000 1.000 0.000 0.000
#> GSM110414 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM110415 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM110416 3 0.0188 0.983 0.000 0.000 0.996 0.004
#> GSM110418 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM110419 3 0.0188 0.982 0.004 0.000 0.996 0.000
#> GSM110420 3 0.1576 0.943 0.004 0.000 0.948 0.048
#> GSM110421 2 0.0376 0.755 0.000 0.992 0.004 0.004
#> GSM110423 3 0.0188 0.983 0.000 0.000 0.996 0.004
#> GSM110424 4 0.4936 0.988 0.000 0.372 0.004 0.624
#> GSM110425 3 0.0188 0.983 0.000 0.000 0.996 0.004
#> GSM110427 2 0.4589 0.729 0.048 0.784 0.000 0.168
#> GSM110428 1 0.3027 0.865 0.888 0.004 0.088 0.020
#> GSM110430 1 0.0376 0.896 0.992 0.004 0.000 0.004
#> GSM110431 1 0.1890 0.885 0.936 0.000 0.056 0.008
#> GSM110432 2 0.6431 0.658 0.048 0.704 0.076 0.172
#> GSM110434 2 0.4017 0.744 0.044 0.828 0.000 0.128
#> GSM110435 1 0.3768 0.815 0.808 0.000 0.184 0.008
#> GSM110437 1 0.0188 0.896 0.996 0.004 0.000 0.000
#> GSM110438 2 0.7491 0.280 0.268 0.500 0.232 0.000
#> GSM110388 1 0.4323 0.847 0.776 0.020 0.000 0.204
#> GSM110392 2 0.2053 0.739 0.000 0.924 0.072 0.004
#> GSM110394 1 0.1722 0.887 0.944 0.000 0.048 0.008
#> GSM110402 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM110411 2 0.5683 0.115 0.452 0.528 0.008 0.012
#> GSM110412 2 0.2311 0.737 0.004 0.916 0.076 0.004
#> GSM110417 1 0.3726 0.853 0.788 0.000 0.000 0.212
#> GSM110422 2 0.4589 0.729 0.048 0.784 0.000 0.168
#> GSM110426 1 0.3726 0.853 0.788 0.000 0.000 0.212
#> GSM110429 2 0.6086 0.681 0.048 0.724 0.056 0.172
#> GSM110433 4 0.4936 0.988 0.000 0.372 0.004 0.624
#> GSM110436 2 0.5686 0.701 0.048 0.744 0.036 0.172
#> GSM110440 1 0.2976 0.860 0.872 0.000 0.120 0.008
#> GSM110441 2 0.0376 0.755 0.000 0.992 0.004 0.004
#> GSM110444 2 0.0895 0.753 0.000 0.976 0.020 0.004
#> GSM110445 1 0.3907 0.677 0.768 0.232 0.000 0.000
#> GSM110446 3 0.0336 0.980 0.008 0.000 0.992 0.000
#> GSM110449 2 0.0188 0.754 0.000 0.996 0.004 0.000
#> GSM110451 2 0.4814 0.725 0.048 0.776 0.004 0.172
#> GSM110391 4 0.5138 0.962 0.000 0.392 0.008 0.600
#> GSM110439 2 0.0376 0.755 0.000 0.992 0.004 0.004
#> GSM110442 2 0.0000 0.756 0.000 1.000 0.000 0.000
#> GSM110443 2 0.0000 0.756 0.000 1.000 0.000 0.000
#> GSM110447 3 0.0000 0.984 0.000 0.000 1.000 0.000
#> GSM110448 1 0.3726 0.853 0.788 0.000 0.000 0.212
#> GSM110450 1 0.1042 0.891 0.972 0.008 0.000 0.020
#> GSM110452 2 0.0707 0.761 0.000 0.980 0.000 0.020
#> GSM110453 4 0.4790 0.981 0.000 0.380 0.000 0.620
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.0000 0.722 0.000 1.000 0.000 0.000 0.000
#> GSM110396 1 0.0000 0.897 1.000 0.000 0.000 0.000 0.000
#> GSM110397 4 0.0000 0.695 0.000 0.000 0.000 1.000 0.000
#> GSM110398 2 0.4321 0.633 0.004 0.600 0.000 0.000 0.396
#> GSM110399 2 0.2439 0.724 0.004 0.876 0.000 0.000 0.120
#> GSM110400 3 0.3109 0.721 0.000 0.200 0.800 0.000 0.000
#> GSM110401 1 0.0794 0.895 0.972 0.028 0.000 0.000 0.000
#> GSM110406 2 0.1041 0.725 0.004 0.964 0.000 0.000 0.032
#> GSM110407 1 0.1469 0.880 0.948 0.036 0.000 0.016 0.000
#> GSM110409 4 0.4958 0.496 0.400 0.032 0.000 0.568 0.000
#> GSM110410 5 0.0000 0.967 0.000 0.000 0.000 0.000 1.000
#> GSM110413 2 0.3048 0.715 0.004 0.820 0.000 0.000 0.176
#> GSM110414 3 0.0162 0.969 0.000 0.000 0.996 0.000 0.004
#> GSM110415 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000
#> GSM110416 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000
#> GSM110418 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000
#> GSM110419 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000
#> GSM110420 3 0.0880 0.943 0.000 0.000 0.968 0.032 0.000
#> GSM110421 2 0.4256 0.606 0.000 0.564 0.000 0.000 0.436
#> GSM110423 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000
#> GSM110424 5 0.0000 0.967 0.000 0.000 0.000 0.000 1.000
#> GSM110425 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000
#> GSM110427 2 0.0404 0.722 0.000 0.988 0.000 0.000 0.012
#> GSM110428 4 0.6202 0.424 0.356 0.148 0.000 0.496 0.000
#> GSM110430 1 0.0000 0.897 1.000 0.000 0.000 0.000 0.000
#> GSM110431 4 0.4390 0.500 0.428 0.004 0.000 0.568 0.000
#> GSM110432 2 0.0290 0.722 0.000 0.992 0.000 0.000 0.008
#> GSM110434 2 0.0000 0.722 0.000 1.000 0.000 0.000 0.000
#> GSM110435 4 0.5835 0.580 0.120 0.000 0.312 0.568 0.000
#> GSM110437 1 0.0000 0.897 1.000 0.000 0.000 0.000 0.000
#> GSM110438 4 0.4958 0.458 0.032 0.000 0.400 0.568 0.000
#> GSM110388 4 0.0000 0.695 0.000 0.000 0.000 1.000 0.000
#> GSM110392 2 0.4958 0.606 0.000 0.568 0.032 0.000 0.400
#> GSM110394 4 0.4390 0.500 0.428 0.004 0.000 0.568 0.000
#> GSM110402 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000
#> GSM110411 2 0.4497 0.610 0.000 0.568 0.000 0.008 0.424
#> GSM110412 2 0.4958 0.606 0.000 0.568 0.032 0.000 0.400
#> GSM110417 4 0.0000 0.695 0.000 0.000 0.000 1.000 0.000
#> GSM110422 2 0.0404 0.722 0.000 0.988 0.000 0.000 0.012
#> GSM110426 4 0.0000 0.695 0.000 0.000 0.000 1.000 0.000
#> GSM110429 2 0.0404 0.722 0.000 0.988 0.000 0.000 0.012
#> GSM110433 5 0.0000 0.967 0.000 0.000 0.000 0.000 1.000
#> GSM110436 2 0.0404 0.722 0.000 0.988 0.000 0.000 0.012
#> GSM110440 4 0.5785 0.575 0.112 0.000 0.320 0.568 0.000
#> GSM110441 2 0.4268 0.602 0.000 0.556 0.000 0.000 0.444
#> GSM110444 2 0.4893 0.607 0.000 0.568 0.028 0.000 0.404
#> GSM110445 1 0.4229 0.409 0.704 0.020 0.000 0.000 0.276
#> GSM110446 3 0.0162 0.969 0.004 0.000 0.996 0.000 0.000
#> GSM110449 2 0.4249 0.607 0.000 0.568 0.000 0.000 0.432
#> GSM110451 2 0.0404 0.722 0.000 0.988 0.000 0.000 0.012
#> GSM110391 5 0.0000 0.967 0.000 0.000 0.000 0.000 1.000
#> GSM110439 2 0.4268 0.602 0.000 0.556 0.000 0.000 0.444
#> GSM110442 2 0.4196 0.654 0.004 0.640 0.000 0.000 0.356
#> GSM110443 2 0.3766 0.689 0.004 0.728 0.000 0.000 0.268
#> GSM110447 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000
#> GSM110448 4 0.0000 0.695 0.000 0.000 0.000 1.000 0.000
#> GSM110450 1 0.0880 0.892 0.968 0.032 0.000 0.000 0.000
#> GSM110452 2 0.1041 0.725 0.004 0.964 0.000 0.000 0.032
#> GSM110453 5 0.1851 0.860 0.000 0.088 0.000 0.000 0.912
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.2527 0.8388 0.000 0.832 0.000 0.168 0.000 0.000
#> GSM110396 1 0.0146 0.7556 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM110397 6 0.0000 0.6662 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM110398 4 0.0146 0.6838 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM110399 4 0.0632 0.6800 0.000 0.024 0.000 0.976 0.000 0.000
#> GSM110400 3 0.2793 0.7325 0.000 0.200 0.800 0.000 0.000 0.000
#> GSM110401 1 0.0000 0.7549 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110406 4 0.3563 0.3802 0.000 0.336 0.000 0.664 0.000 0.000
#> GSM110407 1 0.0146 0.7556 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM110409 1 0.4603 0.1879 0.544 0.040 0.000 0.000 0.000 0.416
#> GSM110410 5 0.0713 0.9028 0.000 0.000 0.000 0.028 0.972 0.000
#> GSM110413 4 0.1444 0.6653 0.000 0.072 0.000 0.928 0.000 0.000
#> GSM110414 3 0.0000 0.9775 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110415 3 0.0000 0.9775 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110416 3 0.0000 0.9775 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110418 3 0.0000 0.9775 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110419 3 0.0000 0.9775 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110420 3 0.0000 0.9775 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110421 4 0.3298 0.6542 0.000 0.008 0.000 0.756 0.236 0.000
#> GSM110423 3 0.0000 0.9775 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110424 5 0.0713 0.9028 0.000 0.000 0.000 0.028 0.972 0.000
#> GSM110425 3 0.0000 0.9775 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110427 2 0.0937 0.9652 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM110428 6 0.6564 0.1714 0.264 0.292 0.000 0.000 0.028 0.416
#> GSM110430 1 0.0000 0.7549 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110431 1 0.5219 0.1473 0.516 0.040 0.000 0.000 0.028 0.416
#> GSM110432 2 0.0937 0.9652 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM110434 4 0.3843 0.0945 0.000 0.452 0.000 0.548 0.000 0.000
#> GSM110435 6 0.7215 0.3089 0.264 0.040 0.252 0.000 0.028 0.416
#> GSM110437 1 0.0000 0.7549 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110438 6 0.6924 0.3618 0.144 0.040 0.372 0.000 0.028 0.416
#> GSM110388 6 0.0000 0.6662 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM110392 4 0.3426 0.6355 0.000 0.004 0.000 0.720 0.276 0.000
#> GSM110394 1 0.5219 0.1473 0.516 0.040 0.000 0.000 0.028 0.416
#> GSM110402 3 0.0000 0.9775 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110411 4 0.3586 0.6351 0.000 0.000 0.000 0.720 0.268 0.012
#> GSM110412 4 0.3629 0.6334 0.000 0.012 0.000 0.712 0.276 0.000
#> GSM110417 6 0.0000 0.6662 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM110422 2 0.1610 0.9348 0.000 0.916 0.000 0.084 0.000 0.000
#> GSM110426 6 0.0000 0.6662 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM110429 2 0.0937 0.9652 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM110433 5 0.0713 0.9028 0.000 0.000 0.000 0.028 0.972 0.000
#> GSM110436 2 0.0937 0.9652 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM110440 6 0.7162 0.3483 0.232 0.040 0.268 0.000 0.028 0.432
#> GSM110441 4 0.3847 0.5297 0.000 0.008 0.000 0.644 0.348 0.000
#> GSM110444 4 0.3288 0.6350 0.000 0.000 0.000 0.724 0.276 0.000
#> GSM110445 4 0.3995 0.0236 0.480 0.000 0.000 0.516 0.000 0.004
#> GSM110446 3 0.0146 0.9735 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM110449 4 0.3244 0.6390 0.000 0.000 0.000 0.732 0.268 0.000
#> GSM110451 2 0.0937 0.9652 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM110391 5 0.0713 0.9028 0.000 0.000 0.000 0.028 0.972 0.000
#> GSM110439 5 0.2794 0.8078 0.000 0.060 0.000 0.080 0.860 0.000
#> GSM110442 4 0.0146 0.6840 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM110443 4 0.0146 0.6830 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM110447 3 0.0000 0.9775 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110448 6 0.0000 0.6662 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM110450 1 0.0146 0.7556 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM110452 4 0.3620 0.3114 0.000 0.352 0.000 0.648 0.000 0.000
#> GSM110453 5 0.3405 0.6136 0.000 0.004 0.000 0.272 0.724 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) specimen(p) k
#> CV:mclust 41 0.0692 0.617 2
#> CV:mclust 58 0.1043 0.355 3
#> CV:mclust 56 0.2081 0.373 4
#> CV:mclust 53 0.0837 0.635 5
#> CV:mclust 48 0.0871 0.233 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 17209 rows and 59 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 0.453 0.695 0.870 0.4881 0.492 0.492
#> 3 3 0.489 0.725 0.860 0.3073 0.749 0.537
#> 4 4 0.401 0.516 0.691 0.1387 0.824 0.550
#> 5 5 0.452 0.439 0.678 0.0737 0.821 0.461
#> 6 6 0.521 0.395 0.623 0.0408 0.888 0.553
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
#> GSM110395 2 0.9491 0.268 0.368 0.632
#> GSM110396 1 0.0000 0.806 1.000 0.000
#> GSM110397 1 0.0000 0.806 1.000 0.000
#> GSM110398 1 0.7376 0.707 0.792 0.208
#> GSM110399 1 0.9686 0.498 0.604 0.396
#> GSM110400 2 0.0000 0.846 0.000 1.000
#> GSM110401 1 0.0000 0.806 1.000 0.000
#> GSM110406 1 0.9710 0.491 0.600 0.400
#> GSM110407 1 0.0000 0.806 1.000 0.000
#> GSM110409 1 0.0376 0.805 0.996 0.004
#> GSM110410 2 0.0000 0.846 0.000 1.000
#> GSM110413 1 0.9896 0.398 0.560 0.440
#> GSM110414 2 0.0000 0.846 0.000 1.000
#> GSM110415 2 0.0672 0.841 0.008 0.992
#> GSM110416 2 0.7219 0.658 0.200 0.800
#> GSM110418 2 0.8955 0.509 0.312 0.688
#> GSM110419 2 0.0000 0.846 0.000 1.000
#> GSM110420 2 0.9710 0.351 0.400 0.600
#> GSM110421 2 0.9491 0.268 0.368 0.632
#> GSM110423 2 0.0000 0.846 0.000 1.000
#> GSM110424 2 0.0000 0.846 0.000 1.000
#> GSM110425 2 0.0000 0.846 0.000 1.000
#> GSM110427 2 0.0000 0.846 0.000 1.000
#> GSM110428 1 0.0000 0.806 1.000 0.000
#> GSM110430 1 0.0000 0.806 1.000 0.000
#> GSM110431 1 0.0000 0.806 1.000 0.000
#> GSM110432 2 0.7139 0.651 0.196 0.804
#> GSM110434 1 0.9866 0.419 0.568 0.432
#> GSM110435 1 0.0000 0.806 1.000 0.000
#> GSM110437 1 0.0000 0.806 1.000 0.000
#> GSM110438 1 0.1633 0.799 0.976 0.024
#> GSM110388 1 0.0376 0.805 0.996 0.004
#> GSM110392 1 0.9710 0.491 0.600 0.400
#> GSM110394 1 0.0000 0.806 1.000 0.000
#> GSM110402 2 0.0000 0.846 0.000 1.000
#> GSM110411 1 0.7219 0.713 0.800 0.200
#> GSM110412 2 0.9209 0.361 0.336 0.664
#> GSM110417 1 0.0000 0.806 1.000 0.000
#> GSM110422 2 0.3431 0.802 0.064 0.936
#> GSM110426 1 0.0000 0.806 1.000 0.000
#> GSM110429 2 0.0000 0.846 0.000 1.000
#> GSM110433 2 0.0000 0.846 0.000 1.000
#> GSM110436 2 0.0000 0.846 0.000 1.000
#> GSM110440 1 0.0000 0.806 1.000 0.000
#> GSM110441 2 0.7299 0.638 0.204 0.796
#> GSM110444 1 0.9608 0.517 0.616 0.384
#> GSM110445 1 0.7219 0.713 0.800 0.200
#> GSM110446 2 0.8327 0.580 0.264 0.736
#> GSM110449 1 0.9661 0.505 0.608 0.392
#> GSM110451 2 0.2236 0.824 0.036 0.964
#> GSM110391 2 0.0000 0.846 0.000 1.000
#> GSM110439 2 0.0000 0.846 0.000 1.000
#> GSM110442 1 0.9815 0.448 0.580 0.420
#> GSM110443 1 0.9491 0.539 0.632 0.368
#> GSM110447 2 0.0000 0.846 0.000 1.000
#> GSM110448 1 0.0000 0.806 1.000 0.000
#> GSM110450 1 0.5842 0.749 0.860 0.140
#> GSM110452 2 0.9983 -0.165 0.476 0.524
#> GSM110453 2 0.0000 0.846 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.1643 0.870 0.044 0.956 0.000
#> GSM110396 1 0.1964 0.786 0.944 0.000 0.056
#> GSM110397 3 0.6079 0.439 0.388 0.000 0.612
#> GSM110398 1 0.4178 0.784 0.828 0.172 0.000
#> GSM110399 1 0.5397 0.706 0.720 0.280 0.000
#> GSM110400 2 0.4796 0.659 0.000 0.780 0.220
#> GSM110401 1 0.1753 0.786 0.952 0.000 0.048
#> GSM110406 1 0.5291 0.721 0.732 0.268 0.000
#> GSM110407 1 0.4504 0.755 0.804 0.000 0.196
#> GSM110409 1 0.4733 0.756 0.800 0.004 0.196
#> GSM110410 2 0.0000 0.889 0.000 1.000 0.000
#> GSM110413 2 0.5024 0.662 0.220 0.776 0.004
#> GSM110414 2 0.5397 0.565 0.000 0.720 0.280
#> GSM110415 3 0.1525 0.782 0.004 0.032 0.964
#> GSM110416 3 0.0237 0.775 0.004 0.000 0.996
#> GSM110418 3 0.0000 0.776 0.000 0.000 1.000
#> GSM110419 3 0.3412 0.757 0.000 0.124 0.876
#> GSM110420 3 0.0237 0.775 0.004 0.000 0.996
#> GSM110421 2 0.0475 0.889 0.004 0.992 0.004
#> GSM110423 3 0.2537 0.777 0.000 0.080 0.920
#> GSM110424 2 0.0237 0.889 0.000 0.996 0.004
#> GSM110425 3 0.4452 0.700 0.000 0.192 0.808
#> GSM110427 2 0.0237 0.889 0.000 0.996 0.004
#> GSM110428 1 0.4555 0.753 0.800 0.000 0.200
#> GSM110430 1 0.1411 0.788 0.964 0.000 0.036
#> GSM110431 1 0.6180 0.172 0.584 0.000 0.416
#> GSM110432 2 0.3590 0.831 0.028 0.896 0.076
#> GSM110434 2 0.6168 0.135 0.412 0.588 0.000
#> GSM110435 3 0.5058 0.542 0.244 0.000 0.756
#> GSM110437 1 0.1643 0.786 0.956 0.000 0.044
#> GSM110438 3 0.7293 0.134 0.476 0.028 0.496
#> GSM110388 1 0.0237 0.788 0.996 0.000 0.004
#> GSM110392 1 0.6168 0.449 0.588 0.412 0.000
#> GSM110394 1 0.4654 0.750 0.792 0.000 0.208
#> GSM110402 3 0.3686 0.745 0.000 0.140 0.860
#> GSM110411 1 0.4110 0.787 0.844 0.152 0.004
#> GSM110412 2 0.2200 0.865 0.056 0.940 0.004
#> GSM110417 1 0.1289 0.782 0.968 0.000 0.032
#> GSM110422 2 0.0000 0.889 0.000 1.000 0.000
#> GSM110426 1 0.1289 0.783 0.968 0.000 0.032
#> GSM110429 2 0.0424 0.887 0.000 0.992 0.008
#> GSM110433 2 0.0237 0.889 0.000 0.996 0.004
#> GSM110436 2 0.0592 0.886 0.000 0.988 0.012
#> GSM110440 1 0.5835 0.546 0.660 0.000 0.340
#> GSM110441 2 0.0237 0.889 0.004 0.996 0.000
#> GSM110444 1 0.5722 0.663 0.704 0.292 0.004
#> GSM110445 1 0.4178 0.784 0.828 0.172 0.000
#> GSM110446 3 0.3879 0.719 0.152 0.000 0.848
#> GSM110449 1 0.4702 0.761 0.788 0.212 0.000
#> GSM110451 2 0.1643 0.863 0.000 0.956 0.044
#> GSM110391 2 0.0983 0.883 0.016 0.980 0.004
#> GSM110439 2 0.0000 0.889 0.000 1.000 0.000
#> GSM110442 2 0.5327 0.558 0.272 0.728 0.000
#> GSM110443 1 0.4654 0.767 0.792 0.208 0.000
#> GSM110447 3 0.6286 0.119 0.000 0.464 0.536
#> GSM110448 1 0.0000 0.787 1.000 0.000 0.000
#> GSM110450 1 0.4209 0.798 0.860 0.120 0.020
#> GSM110452 2 0.2878 0.827 0.096 0.904 0.000
#> GSM110453 2 0.0000 0.889 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.4548 0.5704 0.044 0.804 0.008 0.144
#> GSM110396 1 0.1936 0.6852 0.940 0.028 0.032 0.000
#> GSM110397 1 0.5613 0.5752 0.724 0.000 0.156 0.120
#> GSM110398 1 0.4900 0.5983 0.732 0.236 0.000 0.032
#> GSM110399 1 0.5597 0.2187 0.516 0.464 0.000 0.020
#> GSM110400 3 0.7844 -0.1268 0.000 0.288 0.404 0.308
#> GSM110401 1 0.2466 0.6719 0.900 0.096 0.004 0.000
#> GSM110406 2 0.4163 0.5198 0.220 0.772 0.004 0.004
#> GSM110407 1 0.6648 0.5242 0.612 0.248 0.140 0.000
#> GSM110409 1 0.6219 0.5293 0.640 0.264 0.096 0.000
#> GSM110410 4 0.4948 0.6062 0.000 0.440 0.000 0.560
#> GSM110413 2 0.6583 -0.2506 0.084 0.528 0.000 0.388
#> GSM110414 4 0.7088 0.4746 0.000 0.228 0.204 0.568
#> GSM110415 3 0.4761 0.5764 0.000 0.000 0.628 0.372
#> GSM110416 3 0.0000 0.7153 0.000 0.000 1.000 0.000
#> GSM110418 3 0.0336 0.7150 0.000 0.000 0.992 0.008
#> GSM110419 3 0.6346 0.5614 0.000 0.152 0.656 0.192
#> GSM110420 3 0.1576 0.7036 0.004 0.000 0.948 0.048
#> GSM110421 4 0.5576 0.5005 0.020 0.444 0.000 0.536
#> GSM110423 3 0.2300 0.7120 0.000 0.064 0.920 0.016
#> GSM110424 4 0.4500 0.7365 0.000 0.316 0.000 0.684
#> GSM110425 3 0.3243 0.7044 0.000 0.088 0.876 0.036
#> GSM110427 2 0.4049 0.4087 0.000 0.780 0.008 0.212
#> GSM110428 2 0.7847 -0.0377 0.316 0.464 0.212 0.008
#> GSM110430 1 0.0524 0.6859 0.988 0.008 0.004 0.000
#> GSM110431 1 0.7754 0.0600 0.428 0.176 0.388 0.008
#> GSM110432 2 0.3158 0.5942 0.020 0.880 0.096 0.004
#> GSM110434 2 0.1940 0.6177 0.076 0.924 0.000 0.000
#> GSM110435 3 0.3908 0.5203 0.212 0.000 0.784 0.004
#> GSM110437 1 0.1191 0.6874 0.968 0.004 0.004 0.024
#> GSM110438 3 0.7818 0.4265 0.212 0.276 0.500 0.012
#> GSM110388 1 0.4699 0.6544 0.676 0.000 0.004 0.320
#> GSM110392 2 0.4071 0.6080 0.064 0.832 0.000 0.104
#> GSM110394 1 0.7474 0.4345 0.500 0.280 0.220 0.000
#> GSM110402 3 0.7020 0.3984 0.000 0.136 0.532 0.332
#> GSM110411 1 0.5624 0.6507 0.668 0.052 0.000 0.280
#> GSM110412 4 0.5449 0.5321 0.032 0.288 0.004 0.676
#> GSM110417 1 0.4770 0.6531 0.700 0.000 0.012 0.288
#> GSM110422 2 0.0927 0.6258 0.000 0.976 0.008 0.016
#> GSM110426 1 0.4720 0.6629 0.720 0.000 0.016 0.264
#> GSM110429 2 0.3088 0.6059 0.000 0.888 0.060 0.052
#> GSM110433 4 0.4304 0.7391 0.000 0.284 0.000 0.716
#> GSM110436 2 0.4046 0.5543 0.000 0.828 0.048 0.124
#> GSM110440 1 0.5642 0.6193 0.704 0.004 0.228 0.064
#> GSM110441 4 0.5384 0.7158 0.028 0.324 0.000 0.648
#> GSM110444 1 0.6785 0.5002 0.540 0.108 0.000 0.352
#> GSM110445 1 0.4018 0.6214 0.772 0.224 0.000 0.004
#> GSM110446 3 0.5138 0.6407 0.180 0.020 0.764 0.036
#> GSM110449 1 0.6970 0.4834 0.576 0.256 0.000 0.168
#> GSM110451 2 0.2761 0.6090 0.012 0.908 0.064 0.016
#> GSM110391 4 0.3688 0.7018 0.000 0.208 0.000 0.792
#> GSM110439 2 0.4790 -0.1459 0.000 0.620 0.000 0.380
#> GSM110442 2 0.4808 0.3587 0.028 0.736 0.000 0.236
#> GSM110443 2 0.4328 0.4780 0.244 0.748 0.000 0.008
#> GSM110447 3 0.6320 0.5236 0.000 0.180 0.660 0.160
#> GSM110448 1 0.4746 0.6521 0.688 0.000 0.008 0.304
#> GSM110450 1 0.4283 0.5852 0.740 0.256 0.000 0.004
#> GSM110452 2 0.2214 0.6231 0.028 0.928 0.000 0.044
#> GSM110453 2 0.4776 -0.1213 0.000 0.624 0.000 0.376
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.578 0.5223 0.084 0.640 0.004 0.016 0.256
#> GSM110396 1 0.338 0.6137 0.864 0.004 0.052 0.064 0.016
#> GSM110397 4 0.614 0.4375 0.272 0.000 0.132 0.584 0.012
#> GSM110398 1 0.715 0.3320 0.460 0.324 0.000 0.180 0.036
#> GSM110399 1 0.535 0.5711 0.688 0.228 0.000 0.040 0.044
#> GSM110400 3 0.611 0.1881 0.000 0.108 0.444 0.004 0.444
#> GSM110401 1 0.249 0.6074 0.896 0.020 0.004 0.080 0.000
#> GSM110406 1 0.592 0.4238 0.600 0.256 0.000 0.004 0.140
#> GSM110407 1 0.304 0.6309 0.888 0.032 0.052 0.012 0.016
#> GSM110409 1 0.325 0.6420 0.864 0.092 0.028 0.008 0.008
#> GSM110410 2 0.468 0.3796 0.000 0.620 0.000 0.024 0.356
#> GSM110413 5 0.709 0.0540 0.340 0.240 0.000 0.016 0.404
#> GSM110414 5 0.411 0.4136 0.000 0.068 0.116 0.012 0.804
#> GSM110415 3 0.482 0.3884 0.000 0.000 0.632 0.036 0.332
#> GSM110416 3 0.215 0.5897 0.004 0.004 0.916 0.008 0.068
#> GSM110418 3 0.141 0.5868 0.000 0.008 0.948 0.044 0.000
#> GSM110419 5 0.487 -0.1692 0.000 0.024 0.436 0.000 0.540
#> GSM110420 3 0.157 0.5809 0.000 0.000 0.936 0.060 0.004
#> GSM110421 2 0.681 0.2017 0.004 0.412 0.000 0.236 0.348
#> GSM110423 3 0.428 0.5663 0.000 0.084 0.788 0.008 0.120
#> GSM110424 2 0.514 0.3971 0.000 0.624 0.000 0.060 0.316
#> GSM110425 3 0.563 0.4018 0.000 0.060 0.600 0.016 0.324
#> GSM110427 2 0.450 0.5328 0.012 0.708 0.004 0.012 0.264
#> GSM110428 1 0.827 0.3235 0.504 0.208 0.084 0.064 0.140
#> GSM110430 1 0.284 0.5800 0.868 0.000 0.004 0.112 0.016
#> GSM110431 1 0.622 0.4011 0.628 0.048 0.256 0.056 0.012
#> GSM110432 2 0.713 0.4206 0.076 0.600 0.048 0.060 0.216
#> GSM110434 2 0.540 0.4181 0.224 0.692 0.004 0.040 0.040
#> GSM110435 3 0.549 -0.2569 0.476 0.000 0.476 0.032 0.016
#> GSM110437 1 0.475 0.1645 0.636 0.004 0.004 0.340 0.016
#> GSM110438 2 0.845 -0.0412 0.052 0.376 0.212 0.312 0.048
#> GSM110388 4 0.329 0.7695 0.140 0.000 0.008 0.836 0.016
#> GSM110392 2 0.365 0.5524 0.000 0.808 0.000 0.152 0.040
#> GSM110394 1 0.510 0.5905 0.724 0.032 0.204 0.028 0.012
#> GSM110402 5 0.601 0.0257 0.000 0.092 0.384 0.008 0.516
#> GSM110411 4 0.613 0.6749 0.160 0.060 0.004 0.672 0.104
#> GSM110412 2 0.702 0.1868 0.008 0.404 0.004 0.360 0.224
#> GSM110417 4 0.293 0.7687 0.152 0.000 0.008 0.840 0.000
#> GSM110422 2 0.194 0.5953 0.020 0.924 0.000 0.000 0.056
#> GSM110426 4 0.352 0.7471 0.116 0.008 0.032 0.840 0.004
#> GSM110429 2 0.405 0.5746 0.020 0.816 0.016 0.020 0.128
#> GSM110433 5 0.413 0.3707 0.000 0.180 0.000 0.052 0.768
#> GSM110436 2 0.414 0.5461 0.008 0.776 0.008 0.020 0.188
#> GSM110440 1 0.607 0.5036 0.612 0.000 0.264 0.096 0.028
#> GSM110441 5 0.642 0.3167 0.104 0.248 0.000 0.048 0.600
#> GSM110444 4 0.655 0.5413 0.112 0.072 0.000 0.616 0.200
#> GSM110445 1 0.553 0.5841 0.696 0.180 0.000 0.092 0.032
#> GSM110446 3 0.583 0.4709 0.116 0.060 0.704 0.116 0.004
#> GSM110449 1 0.849 0.0821 0.336 0.244 0.000 0.208 0.212
#> GSM110451 2 0.643 0.4822 0.072 0.648 0.020 0.056 0.204
#> GSM110391 5 0.500 0.4200 0.004 0.092 0.000 0.196 0.708
#> GSM110439 2 0.413 0.4829 0.008 0.720 0.000 0.008 0.264
#> GSM110442 2 0.331 0.5644 0.012 0.844 0.000 0.020 0.124
#> GSM110443 2 0.398 0.5147 0.160 0.796 0.000 0.016 0.028
#> GSM110447 3 0.546 0.3152 0.000 0.048 0.552 0.008 0.392
#> GSM110448 4 0.384 0.7421 0.196 0.000 0.008 0.780 0.016
#> GSM110450 1 0.545 0.5789 0.724 0.088 0.000 0.056 0.132
#> GSM110452 2 0.271 0.5851 0.036 0.892 0.000 0.008 0.064
#> GSM110453 2 0.440 0.4082 0.004 0.648 0.000 0.008 0.340
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.6713 -0.34532 0.116 0.404 0.000 0.000 0.092 0.388
#> GSM110396 1 0.4060 0.73201 0.820 0.004 0.036 0.056 0.056 0.028
#> GSM110397 4 0.7566 0.34974 0.136 0.000 0.128 0.500 0.060 0.176
#> GSM110398 1 0.6472 0.20108 0.424 0.424 0.000 0.084 0.020 0.048
#> GSM110399 1 0.5126 0.63801 0.700 0.188 0.000 0.016 0.060 0.036
#> GSM110400 5 0.6470 -0.21521 0.000 0.028 0.376 0.000 0.392 0.204
#> GSM110401 1 0.1624 0.72501 0.936 0.000 0.000 0.044 0.012 0.008
#> GSM110406 1 0.5388 0.52168 0.664 0.104 0.000 0.008 0.028 0.196
#> GSM110407 1 0.1793 0.72158 0.932 0.000 0.016 0.004 0.008 0.040
#> GSM110409 1 0.2484 0.72618 0.904 0.044 0.016 0.004 0.008 0.024
#> GSM110410 2 0.3351 0.47819 0.000 0.800 0.000 0.000 0.160 0.040
#> GSM110413 5 0.8456 0.23025 0.144 0.212 0.000 0.076 0.316 0.252
#> GSM110414 5 0.4426 0.38499 0.000 0.096 0.044 0.000 0.764 0.096
#> GSM110415 3 0.4446 0.38772 0.000 0.000 0.588 0.020 0.384 0.008
#> GSM110416 3 0.2056 0.59820 0.000 0.000 0.904 0.004 0.080 0.012
#> GSM110418 3 0.0551 0.59539 0.000 0.000 0.984 0.004 0.004 0.008
#> GSM110419 5 0.6121 -0.00861 0.000 0.036 0.312 0.004 0.528 0.120
#> GSM110420 3 0.1096 0.58500 0.000 0.004 0.964 0.004 0.008 0.020
#> GSM110421 4 0.7323 0.11782 0.004 0.172 0.000 0.380 0.120 0.324
#> GSM110423 3 0.5262 0.52137 0.000 0.032 0.672 0.000 0.148 0.148
#> GSM110424 2 0.4632 0.38105 0.000 0.668 0.000 0.004 0.256 0.072
#> GSM110425 3 0.6600 0.23345 0.004 0.032 0.452 0.000 0.296 0.216
#> GSM110427 6 0.4883 0.24754 0.004 0.456 0.000 0.000 0.048 0.492
#> GSM110428 6 0.5761 -0.11272 0.416 0.016 0.064 0.004 0.012 0.488
#> GSM110430 1 0.2282 0.72057 0.900 0.000 0.000 0.068 0.012 0.020
#> GSM110431 1 0.5802 0.51175 0.604 0.000 0.220 0.016 0.012 0.148
#> GSM110432 6 0.6177 0.42669 0.104 0.252 0.028 0.004 0.024 0.588
#> GSM110434 2 0.4212 0.33578 0.264 0.688 0.000 0.000 0.000 0.048
#> GSM110435 1 0.5530 0.39829 0.496 0.000 0.412 0.004 0.016 0.072
#> GSM110437 1 0.5412 0.49938 0.644 0.004 0.000 0.240 0.048 0.064
#> GSM110438 6 0.8479 0.05769 0.020 0.284 0.152 0.204 0.032 0.308
#> GSM110388 4 0.3041 0.66450 0.040 0.004 0.000 0.864 0.072 0.020
#> GSM110392 2 0.5524 0.15258 0.004 0.616 0.000 0.112 0.020 0.248
#> GSM110394 1 0.4351 0.69168 0.748 0.000 0.184 0.012 0.020 0.036
#> GSM110402 5 0.4976 0.12912 0.000 0.072 0.252 0.000 0.656 0.020
#> GSM110411 4 0.4421 0.63565 0.028 0.028 0.000 0.768 0.032 0.144
#> GSM110412 4 0.5907 0.31106 0.000 0.112 0.000 0.504 0.028 0.356
#> GSM110417 4 0.2151 0.66419 0.032 0.000 0.004 0.916 0.036 0.012
#> GSM110422 2 0.4015 0.11169 0.008 0.656 0.000 0.008 0.000 0.328
#> GSM110426 4 0.2332 0.66630 0.020 0.000 0.004 0.908 0.036 0.032
#> GSM110429 2 0.4009 0.04133 0.008 0.632 0.000 0.004 0.000 0.356
#> GSM110433 5 0.6784 0.40943 0.000 0.248 0.000 0.088 0.488 0.176
#> GSM110436 6 0.4428 0.30446 0.000 0.440 0.004 0.008 0.008 0.540
#> GSM110440 1 0.6811 0.63802 0.596 0.008 0.168 0.044 0.108 0.076
#> GSM110441 5 0.6132 0.20202 0.116 0.308 0.004 0.012 0.540 0.020
#> GSM110444 4 0.4880 0.59313 0.024 0.028 0.000 0.716 0.040 0.192
#> GSM110445 1 0.5437 0.65479 0.696 0.160 0.000 0.028 0.068 0.048
#> GSM110446 3 0.7029 0.33253 0.040 0.144 0.584 0.044 0.032 0.156
#> GSM110449 2 0.7909 -0.01899 0.264 0.356 0.000 0.040 0.244 0.096
#> GSM110451 6 0.4856 0.41977 0.052 0.348 0.000 0.000 0.008 0.592
#> GSM110391 5 0.7085 0.34130 0.000 0.156 0.000 0.216 0.468 0.160
#> GSM110439 2 0.2772 0.50573 0.004 0.868 0.000 0.004 0.092 0.032
#> GSM110442 2 0.2528 0.49769 0.012 0.900 0.000 0.016 0.032 0.040
#> GSM110443 2 0.4639 0.35932 0.240 0.696 0.000 0.008 0.020 0.036
#> GSM110447 3 0.6787 0.11102 0.000 0.064 0.400 0.000 0.360 0.176
#> GSM110448 4 0.3225 0.66258 0.064 0.000 0.000 0.852 0.048 0.036
#> GSM110450 1 0.4414 0.63957 0.736 0.028 0.000 0.052 0.000 0.184
#> GSM110452 2 0.2994 0.46342 0.064 0.852 0.000 0.000 0.004 0.080
#> GSM110453 2 0.2714 0.49863 0.004 0.848 0.000 0.000 0.136 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) specimen(p) k
#> CV:NMF 48 1.00000 1.0000 2
#> CV:NMF 53 0.12288 0.2167 3
#> CV:NMF 44 0.24887 0.9920 4
#> CV:NMF 29 0.00535 0.4177 5
#> CV:NMF 23 0.00638 0.0558 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 17209 rows and 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.395 0.798 0.883 0.4553 0.544 0.544
#> 3 3 0.499 0.776 0.849 0.4312 0.745 0.548
#> 4 4 0.579 0.711 0.800 0.0981 0.964 0.895
#> 5 5 0.617 0.619 0.757 0.0779 0.905 0.703
#> 6 6 0.673 0.685 0.788 0.0611 0.932 0.712
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
#> GSM110395 2 0.5294 0.86431 0.120 0.880
#> GSM110396 1 0.4939 0.85350 0.892 0.108
#> GSM110397 1 0.2423 0.86082 0.960 0.040
#> GSM110398 2 0.0376 0.88028 0.004 0.996
#> GSM110399 2 0.1843 0.87700 0.028 0.972
#> GSM110400 2 0.5408 0.86134 0.124 0.876
#> GSM110401 1 0.1843 0.85762 0.972 0.028
#> GSM110406 2 0.1843 0.87700 0.028 0.972
#> GSM110407 1 0.2043 0.85223 0.968 0.032
#> GSM110409 1 0.7139 0.81029 0.804 0.196
#> GSM110410 2 0.0000 0.87955 0.000 1.000
#> GSM110413 2 0.0376 0.88036 0.004 0.996
#> GSM110414 2 0.1843 0.87490 0.028 0.972
#> GSM110415 2 0.5519 0.86028 0.128 0.872
#> GSM110416 2 0.6887 0.82342 0.184 0.816
#> GSM110418 2 0.6887 0.82342 0.184 0.816
#> GSM110419 2 0.6048 0.85026 0.148 0.852
#> GSM110420 2 0.9686 0.48397 0.396 0.604
#> GSM110421 2 0.0000 0.87955 0.000 1.000
#> GSM110423 2 0.5519 0.86028 0.128 0.872
#> GSM110424 2 0.0000 0.87955 0.000 1.000
#> GSM110425 2 0.6148 0.84777 0.152 0.848
#> GSM110427 2 0.5178 0.86402 0.116 0.884
#> GSM110428 1 0.6148 0.79873 0.848 0.152
#> GSM110430 1 0.1843 0.85762 0.972 0.028
#> GSM110431 1 0.5408 0.80748 0.876 0.124
#> GSM110432 2 0.6048 0.85026 0.148 0.852
#> GSM110434 2 0.0376 0.88028 0.004 0.996
#> GSM110435 1 0.4298 0.83704 0.912 0.088
#> GSM110437 1 0.1843 0.85762 0.972 0.028
#> GSM110438 1 0.9686 0.23091 0.604 0.396
#> GSM110388 1 0.9248 0.66361 0.660 0.340
#> GSM110392 2 0.9993 -0.00977 0.484 0.516
#> GSM110394 1 0.2236 0.85173 0.964 0.036
#> GSM110402 2 0.6247 0.84524 0.156 0.844
#> GSM110411 1 0.8555 0.72455 0.720 0.280
#> GSM110412 2 0.2043 0.86576 0.032 0.968
#> GSM110417 1 0.4298 0.84844 0.912 0.088
#> GSM110422 2 0.0938 0.88107 0.012 0.988
#> GSM110426 1 0.4022 0.85698 0.920 0.080
#> GSM110429 2 0.0938 0.88107 0.012 0.988
#> GSM110433 2 0.0000 0.87955 0.000 1.000
#> GSM110436 2 0.5408 0.86134 0.124 0.876
#> GSM110440 1 0.4022 0.85548 0.920 0.080
#> GSM110441 2 0.0000 0.87955 0.000 1.000
#> GSM110444 1 0.8555 0.72455 0.720 0.280
#> GSM110445 2 0.9710 0.33490 0.400 0.600
#> GSM110446 2 0.9686 0.48397 0.396 0.604
#> GSM110449 2 0.0000 0.87955 0.000 1.000
#> GSM110451 2 0.6048 0.85026 0.148 0.852
#> GSM110391 2 0.0000 0.87955 0.000 1.000
#> GSM110439 2 0.0000 0.87955 0.000 1.000
#> GSM110442 2 0.0000 0.87955 0.000 1.000
#> GSM110443 2 0.8763 0.57913 0.296 0.704
#> GSM110447 2 0.6247 0.84382 0.156 0.844
#> GSM110448 1 0.8555 0.72455 0.720 0.280
#> GSM110450 1 0.3274 0.86149 0.940 0.060
#> GSM110452 2 0.0000 0.87955 0.000 1.000
#> GSM110453 2 0.0938 0.88107 0.012 0.988
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 3 0.5585 0.78409 0.024 0.204 0.772
#> GSM110396 1 0.3590 0.79769 0.896 0.076 0.028
#> GSM110397 1 0.3619 0.80592 0.864 0.000 0.136
#> GSM110398 2 0.0424 0.89010 0.000 0.992 0.008
#> GSM110399 2 0.1315 0.88656 0.020 0.972 0.008
#> GSM110400 3 0.4209 0.87112 0.020 0.120 0.860
#> GSM110401 1 0.2537 0.80883 0.920 0.000 0.080
#> GSM110406 2 0.1315 0.88656 0.020 0.972 0.008
#> GSM110407 1 0.4002 0.78213 0.840 0.000 0.160
#> GSM110409 1 0.4733 0.72999 0.800 0.196 0.004
#> GSM110410 2 0.2261 0.89095 0.000 0.932 0.068
#> GSM110413 2 0.0829 0.89236 0.012 0.984 0.004
#> GSM110414 3 0.5366 0.77404 0.016 0.208 0.776
#> GSM110415 3 0.4136 0.87307 0.020 0.116 0.864
#> GSM110416 3 0.4137 0.86347 0.032 0.096 0.872
#> GSM110418 3 0.4137 0.86347 0.032 0.096 0.872
#> GSM110419 3 0.3618 0.87950 0.012 0.104 0.884
#> GSM110420 3 0.4452 0.61836 0.192 0.000 0.808
#> GSM110421 2 0.1877 0.89434 0.012 0.956 0.032
#> GSM110423 3 0.4136 0.87307 0.020 0.116 0.864
#> GSM110424 2 0.2261 0.89095 0.000 0.932 0.068
#> GSM110425 3 0.3539 0.87877 0.012 0.100 0.888
#> GSM110427 2 0.6195 0.61385 0.020 0.704 0.276
#> GSM110428 1 0.6096 0.66960 0.704 0.016 0.280
#> GSM110430 1 0.2537 0.80883 0.920 0.000 0.080
#> GSM110431 1 0.5497 0.67404 0.708 0.000 0.292
#> GSM110432 3 0.3618 0.87950 0.012 0.104 0.884
#> GSM110434 2 0.2261 0.89167 0.000 0.932 0.068
#> GSM110435 1 0.5138 0.72448 0.748 0.000 0.252
#> GSM110437 1 0.2796 0.80802 0.908 0.000 0.092
#> GSM110438 3 0.6421 0.00609 0.424 0.004 0.572
#> GSM110388 1 0.6964 0.63229 0.684 0.264 0.052
#> GSM110392 1 0.9100 0.24070 0.516 0.160 0.324
#> GSM110394 1 0.4121 0.77874 0.832 0.000 0.168
#> GSM110402 3 0.3112 0.87421 0.004 0.096 0.900
#> GSM110411 1 0.6258 0.69329 0.752 0.196 0.052
#> GSM110412 2 0.2564 0.86398 0.036 0.936 0.028
#> GSM110417 1 0.2229 0.78995 0.944 0.012 0.044
#> GSM110422 2 0.2860 0.88257 0.004 0.912 0.084
#> GSM110426 1 0.2590 0.80034 0.924 0.004 0.072
#> GSM110429 2 0.3030 0.87644 0.004 0.904 0.092
#> GSM110433 2 0.1877 0.89434 0.012 0.956 0.032
#> GSM110436 2 0.6294 0.59159 0.020 0.692 0.288
#> GSM110440 1 0.4399 0.77155 0.812 0.000 0.188
#> GSM110441 2 0.0424 0.89373 0.000 0.992 0.008
#> GSM110444 1 0.6258 0.69329 0.752 0.196 0.052
#> GSM110445 2 0.7263 0.25681 0.400 0.568 0.032
#> GSM110446 3 0.4452 0.61836 0.192 0.000 0.808
#> GSM110449 2 0.0592 0.89180 0.000 0.988 0.012
#> GSM110451 3 0.3618 0.87950 0.012 0.104 0.884
#> GSM110391 2 0.2031 0.89359 0.016 0.952 0.032
#> GSM110439 2 0.2261 0.89095 0.000 0.932 0.068
#> GSM110442 2 0.2261 0.89095 0.000 0.932 0.068
#> GSM110443 2 0.6852 0.51557 0.300 0.664 0.036
#> GSM110447 3 0.4887 0.85484 0.060 0.096 0.844
#> GSM110448 1 0.6258 0.69329 0.752 0.196 0.052
#> GSM110450 1 0.3850 0.80984 0.884 0.028 0.088
#> GSM110452 2 0.0747 0.89537 0.000 0.984 0.016
#> GSM110453 2 0.2682 0.88691 0.004 0.920 0.076
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 3 0.3200 0.77865 0.012 0.096 0.880 0.012
#> GSM110396 1 0.3081 0.69590 0.900 0.044 0.016 0.040
#> GSM110397 1 0.3427 0.69206 0.860 0.000 0.028 0.112
#> GSM110398 2 0.3610 0.79892 0.000 0.800 0.000 0.200
#> GSM110399 2 0.4458 0.79389 0.016 0.780 0.008 0.196
#> GSM110400 3 0.0804 0.90954 0.008 0.012 0.980 0.000
#> GSM110401 1 0.0921 0.70996 0.972 0.000 0.028 0.000
#> GSM110406 2 0.4458 0.79389 0.016 0.780 0.008 0.196
#> GSM110407 1 0.2704 0.67720 0.876 0.000 0.124 0.000
#> GSM110409 1 0.4332 0.62503 0.800 0.160 0.000 0.040
#> GSM110410 2 0.2222 0.80321 0.000 0.924 0.060 0.016
#> GSM110413 2 0.3668 0.79758 0.000 0.808 0.004 0.188
#> GSM110414 3 0.2965 0.78331 0.000 0.072 0.892 0.036
#> GSM110415 3 0.0672 0.91140 0.008 0.008 0.984 0.000
#> GSM110416 3 0.2529 0.87131 0.048 0.008 0.920 0.024
#> GSM110418 3 0.2529 0.87131 0.048 0.008 0.920 0.024
#> GSM110419 3 0.1488 0.91931 0.032 0.012 0.956 0.000
#> GSM110420 4 0.7239 1.00000 0.156 0.000 0.344 0.500
#> GSM110421 2 0.3545 0.80040 0.000 0.828 0.008 0.164
#> GSM110423 3 0.0672 0.91140 0.008 0.008 0.984 0.000
#> GSM110424 2 0.2222 0.80321 0.000 0.924 0.060 0.016
#> GSM110425 3 0.1356 0.91785 0.032 0.008 0.960 0.000
#> GSM110427 2 0.5695 0.48439 0.008 0.624 0.344 0.024
#> GSM110428 1 0.6075 0.51753 0.680 0.000 0.192 0.128
#> GSM110430 1 0.0921 0.70996 0.972 0.000 0.028 0.000
#> GSM110431 1 0.5719 0.54799 0.716 0.000 0.152 0.132
#> GSM110432 3 0.1488 0.91931 0.032 0.012 0.956 0.000
#> GSM110434 2 0.2840 0.80344 0.000 0.900 0.056 0.044
#> GSM110435 1 0.5050 0.57379 0.756 0.000 0.176 0.068
#> GSM110437 1 0.0895 0.70687 0.976 0.000 0.020 0.004
#> GSM110438 1 0.7845 -0.48258 0.400 0.000 0.280 0.320
#> GSM110388 1 0.6564 0.52311 0.536 0.084 0.000 0.380
#> GSM110392 1 0.8759 0.00997 0.432 0.080 0.148 0.340
#> GSM110394 1 0.2944 0.67343 0.868 0.000 0.128 0.004
#> GSM110402 3 0.1635 0.90112 0.044 0.008 0.948 0.000
#> GSM110411 1 0.6205 0.56675 0.596 0.048 0.008 0.348
#> GSM110412 2 0.5085 0.75603 0.008 0.716 0.020 0.256
#> GSM110417 1 0.3937 0.68330 0.800 0.000 0.012 0.188
#> GSM110422 2 0.3542 0.79439 0.000 0.864 0.076 0.060
#> GSM110426 1 0.3757 0.69053 0.828 0.000 0.020 0.152
#> GSM110429 2 0.3996 0.78089 0.000 0.836 0.104 0.060
#> GSM110433 2 0.3545 0.80040 0.000 0.828 0.008 0.164
#> GSM110436 2 0.5546 0.46720 0.008 0.620 0.356 0.016
#> GSM110440 1 0.3758 0.66523 0.848 0.000 0.104 0.048
#> GSM110441 2 0.3355 0.80478 0.000 0.836 0.004 0.160
#> GSM110444 1 0.6205 0.56675 0.596 0.048 0.008 0.348
#> GSM110445 2 0.7614 0.25214 0.412 0.436 0.012 0.140
#> GSM110446 4 0.7239 1.00000 0.156 0.000 0.344 0.500
#> GSM110449 2 0.3757 0.80761 0.000 0.828 0.020 0.152
#> GSM110451 3 0.1488 0.91931 0.032 0.012 0.956 0.000
#> GSM110391 2 0.3591 0.79890 0.000 0.824 0.008 0.168
#> GSM110439 2 0.1824 0.80617 0.000 0.936 0.060 0.004
#> GSM110442 2 0.1902 0.80658 0.000 0.932 0.064 0.004
#> GSM110443 2 0.7950 0.49021 0.304 0.516 0.036 0.144
#> GSM110447 3 0.2860 0.84784 0.100 0.008 0.888 0.004
#> GSM110448 1 0.6205 0.56675 0.596 0.048 0.008 0.348
#> GSM110450 1 0.2165 0.71220 0.936 0.008 0.032 0.024
#> GSM110452 2 0.3552 0.81406 0.000 0.848 0.024 0.128
#> GSM110453 2 0.3071 0.79984 0.000 0.888 0.068 0.044
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 3 0.2452 0.807 0.004 0.084 0.896 0.000 0.016
#> GSM110396 1 0.2797 0.673 0.896 0.020 0.016 0.008 0.060
#> GSM110397 1 0.4375 0.630 0.768 0.004 0.000 0.156 0.072
#> GSM110398 5 0.3774 0.695 0.000 0.296 0.000 0.000 0.704
#> GSM110399 5 0.4382 0.703 0.020 0.276 0.004 0.000 0.700
#> GSM110400 3 0.0162 0.893 0.000 0.004 0.996 0.000 0.000
#> GSM110401 1 0.0703 0.689 0.976 0.000 0.024 0.000 0.000
#> GSM110406 5 0.4382 0.703 0.020 0.276 0.004 0.000 0.700
#> GSM110407 1 0.2927 0.668 0.872 0.000 0.060 0.068 0.000
#> GSM110409 1 0.3906 0.602 0.800 0.132 0.000 0.000 0.068
#> GSM110410 2 0.0865 0.669 0.000 0.972 0.024 0.000 0.004
#> GSM110413 5 0.4009 0.647 0.004 0.312 0.000 0.000 0.684
#> GSM110414 3 0.2446 0.815 0.000 0.056 0.900 0.000 0.044
#> GSM110415 3 0.0000 0.895 0.000 0.000 1.000 0.000 0.000
#> GSM110416 3 0.3016 0.860 0.020 0.000 0.848 0.132 0.000
#> GSM110418 3 0.3016 0.860 0.020 0.000 0.848 0.132 0.000
#> GSM110419 3 0.1862 0.913 0.016 0.004 0.932 0.048 0.000
#> GSM110420 4 0.2707 0.667 0.024 0.000 0.100 0.876 0.000
#> GSM110421 2 0.4029 0.420 0.000 0.680 0.000 0.004 0.316
#> GSM110423 3 0.0000 0.895 0.000 0.000 1.000 0.000 0.000
#> GSM110424 2 0.0865 0.669 0.000 0.972 0.024 0.000 0.004
#> GSM110425 3 0.1701 0.912 0.016 0.000 0.936 0.048 0.000
#> GSM110427 2 0.4147 0.469 0.000 0.676 0.316 0.000 0.008
#> GSM110428 1 0.5605 0.449 0.640 0.000 0.168 0.192 0.000
#> GSM110430 1 0.0703 0.689 0.976 0.000 0.024 0.000 0.000
#> GSM110431 1 0.4890 0.488 0.680 0.000 0.064 0.256 0.000
#> GSM110432 3 0.1862 0.913 0.016 0.004 0.932 0.048 0.000
#> GSM110434 2 0.3326 0.602 0.000 0.824 0.024 0.000 0.152
#> GSM110435 1 0.4757 0.551 0.716 0.000 0.080 0.204 0.000
#> GSM110437 1 0.0880 0.687 0.968 0.000 0.000 0.032 0.000
#> GSM110438 4 0.5863 0.435 0.316 0.000 0.096 0.580 0.008
#> GSM110388 1 0.6644 0.420 0.488 0.060 0.000 0.068 0.384
#> GSM110392 4 0.8199 0.176 0.352 0.080 0.028 0.392 0.148
#> GSM110394 1 0.3051 0.666 0.864 0.000 0.060 0.076 0.000
#> GSM110402 3 0.2616 0.886 0.020 0.000 0.880 0.100 0.000
#> GSM110411 1 0.6530 0.449 0.508 0.024 0.000 0.116 0.352
#> GSM110412 2 0.4387 0.382 0.000 0.640 0.000 0.012 0.348
#> GSM110417 1 0.4994 0.623 0.720 0.004 0.000 0.124 0.152
#> GSM110422 2 0.2632 0.650 0.000 0.888 0.040 0.000 0.072
#> GSM110426 1 0.4677 0.613 0.740 0.004 0.000 0.176 0.080
#> GSM110429 2 0.3119 0.642 0.000 0.860 0.068 0.000 0.072
#> GSM110433 2 0.4029 0.420 0.000 0.680 0.000 0.004 0.316
#> GSM110436 2 0.3932 0.461 0.000 0.672 0.328 0.000 0.000
#> GSM110440 1 0.3779 0.645 0.804 0.000 0.052 0.144 0.000
#> GSM110441 5 0.4196 0.642 0.000 0.356 0.004 0.000 0.640
#> GSM110444 1 0.6530 0.449 0.508 0.024 0.000 0.116 0.352
#> GSM110445 5 0.6498 0.347 0.408 0.132 0.012 0.000 0.448
#> GSM110446 4 0.2707 0.667 0.024 0.000 0.100 0.876 0.000
#> GSM110449 5 0.4249 0.588 0.000 0.432 0.000 0.000 0.568
#> GSM110451 3 0.1862 0.913 0.016 0.004 0.932 0.048 0.000
#> GSM110391 2 0.4232 0.419 0.000 0.676 0.000 0.012 0.312
#> GSM110439 2 0.1893 0.661 0.000 0.928 0.024 0.000 0.048
#> GSM110442 2 0.2036 0.656 0.000 0.920 0.024 0.000 0.056
#> GSM110443 5 0.6920 0.464 0.300 0.216 0.016 0.000 0.468
#> GSM110447 3 0.3055 0.870 0.064 0.000 0.864 0.072 0.000
#> GSM110448 1 0.6530 0.449 0.508 0.024 0.000 0.116 0.352
#> GSM110450 1 0.1668 0.689 0.940 0.000 0.028 0.000 0.032
#> GSM110452 2 0.4307 -0.514 0.000 0.504 0.000 0.000 0.496
#> GSM110453 2 0.3085 0.639 0.000 0.852 0.032 0.000 0.116
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 3 0.2263 0.805 0.004 0.060 0.900 0.000 0.036 0.000
#> GSM110396 1 0.2222 0.781 0.896 0.000 0.008 0.012 0.084 0.000
#> GSM110397 4 0.6191 0.365 0.420 0.024 0.000 0.436 0.012 0.108
#> GSM110398 5 0.1958 0.751 0.000 0.100 0.000 0.004 0.896 0.000
#> GSM110399 5 0.2006 0.753 0.016 0.080 0.000 0.000 0.904 0.000
#> GSM110400 3 0.0000 0.880 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110401 1 0.0547 0.807 0.980 0.000 0.020 0.000 0.000 0.000
#> GSM110406 5 0.2006 0.753 0.016 0.080 0.000 0.000 0.904 0.000
#> GSM110407 1 0.2728 0.806 0.860 0.000 0.040 0.000 0.000 0.100
#> GSM110409 1 0.3563 0.701 0.800 0.092 0.000 0.000 0.108 0.000
#> GSM110410 2 0.0891 0.701 0.000 0.968 0.024 0.000 0.008 0.000
#> GSM110413 5 0.3061 0.662 0.004 0.168 0.000 0.008 0.816 0.004
#> GSM110414 3 0.2288 0.825 0.000 0.048 0.904 0.004 0.040 0.004
#> GSM110415 3 0.0146 0.881 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM110416 3 0.2762 0.826 0.000 0.000 0.804 0.000 0.000 0.196
#> GSM110418 3 0.2762 0.826 0.000 0.000 0.804 0.000 0.000 0.196
#> GSM110419 3 0.1444 0.901 0.000 0.000 0.928 0.000 0.000 0.072
#> GSM110420 6 0.0865 0.838 0.000 0.000 0.036 0.000 0.000 0.964
#> GSM110421 2 0.5203 0.444 0.000 0.580 0.000 0.100 0.316 0.004
#> GSM110423 3 0.0146 0.881 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM110424 2 0.0993 0.701 0.000 0.964 0.024 0.000 0.012 0.000
#> GSM110425 3 0.1501 0.900 0.000 0.000 0.924 0.000 0.000 0.076
#> GSM110427 2 0.3741 0.546 0.000 0.672 0.320 0.000 0.008 0.000
#> GSM110428 1 0.5390 0.594 0.624 0.000 0.164 0.012 0.000 0.200
#> GSM110430 1 0.0547 0.807 0.980 0.000 0.020 0.000 0.000 0.000
#> GSM110431 1 0.4229 0.657 0.668 0.000 0.040 0.000 0.000 0.292
#> GSM110432 3 0.1444 0.901 0.000 0.000 0.928 0.000 0.000 0.072
#> GSM110434 2 0.3539 0.628 0.000 0.756 0.024 0.000 0.220 0.000
#> GSM110435 1 0.4089 0.677 0.696 0.000 0.040 0.000 0.000 0.264
#> GSM110437 1 0.1074 0.798 0.960 0.000 0.000 0.000 0.012 0.028
#> GSM110438 6 0.5721 0.623 0.136 0.000 0.044 0.164 0.008 0.648
#> GSM110388 4 0.2622 0.604 0.040 0.024 0.000 0.896 0.012 0.028
#> GSM110392 4 0.7326 -0.160 0.152 0.072 0.008 0.412 0.016 0.340
#> GSM110394 1 0.2822 0.803 0.852 0.000 0.040 0.000 0.000 0.108
#> GSM110402 3 0.2491 0.855 0.000 0.000 0.836 0.000 0.000 0.164
#> GSM110411 4 0.0858 0.641 0.028 0.000 0.000 0.968 0.004 0.000
#> GSM110412 2 0.6342 0.442 0.012 0.544 0.000 0.224 0.192 0.028
#> GSM110417 4 0.4575 0.515 0.324 0.024 0.000 0.636 0.008 0.008
#> GSM110422 2 0.2930 0.682 0.000 0.840 0.036 0.000 0.124 0.000
#> GSM110426 4 0.5882 0.454 0.368 0.024 0.000 0.516 0.012 0.080
#> GSM110429 2 0.3384 0.675 0.000 0.812 0.068 0.000 0.120 0.000
#> GSM110433 2 0.5203 0.444 0.000 0.580 0.000 0.100 0.316 0.004
#> GSM110436 2 0.3547 0.534 0.000 0.668 0.332 0.000 0.000 0.000
#> GSM110440 1 0.3806 0.772 0.780 0.000 0.032 0.020 0.000 0.168
#> GSM110441 5 0.3567 0.680 0.000 0.252 0.004 0.004 0.736 0.004
#> GSM110444 4 0.0858 0.641 0.028 0.000 0.000 0.968 0.004 0.000
#> GSM110445 5 0.5047 0.438 0.332 0.000 0.004 0.080 0.584 0.000
#> GSM110446 6 0.0865 0.838 0.000 0.000 0.036 0.000 0.000 0.964
#> GSM110449 5 0.3383 0.704 0.000 0.268 0.000 0.004 0.728 0.000
#> GSM110451 3 0.1444 0.901 0.000 0.000 0.928 0.000 0.000 0.072
#> GSM110391 2 0.5992 0.445 0.012 0.560 0.000 0.104 0.296 0.028
#> GSM110439 2 0.2383 0.684 0.000 0.880 0.024 0.000 0.096 0.000
#> GSM110442 2 0.2669 0.675 0.000 0.864 0.024 0.004 0.108 0.000
#> GSM110443 5 0.5883 0.540 0.224 0.064 0.008 0.084 0.620 0.000
#> GSM110447 3 0.3258 0.855 0.040 0.000 0.840 0.020 0.000 0.100
#> GSM110448 4 0.0858 0.641 0.028 0.000 0.000 0.968 0.004 0.000
#> GSM110450 1 0.2042 0.793 0.920 0.000 0.024 0.024 0.032 0.000
#> GSM110452 5 0.3714 0.619 0.000 0.340 0.000 0.004 0.656 0.000
#> GSM110453 2 0.3409 0.665 0.000 0.780 0.028 0.000 0.192 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) specimen(p) k
#> MAD:hclust 54 1.0000 0.610 2
#> MAD:hclust 56 0.1511 0.177 3
#> MAD:hclust 53 0.2772 0.378 4
#> MAD:hclust 42 0.4867 0.164 5
#> MAD:hclust 51 0.0382 0.575 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 17209 rows and 59 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 0.574 0.784 0.897 0.5018 0.503 0.503
#> 3 3 0.461 0.626 0.806 0.3216 0.658 0.419
#> 4 4 0.582 0.633 0.813 0.1212 0.843 0.580
#> 5 5 0.644 0.450 0.652 0.0713 0.907 0.669
#> 6 6 0.683 0.554 0.696 0.0407 0.892 0.563
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
#> GSM110395 2 0.7299 0.737 0.204 0.796
#> GSM110396 1 0.0376 0.897 0.996 0.004
#> GSM110397 1 0.0376 0.897 0.996 0.004
#> GSM110398 1 0.9963 0.273 0.536 0.464
#> GSM110399 2 0.0672 0.858 0.008 0.992
#> GSM110400 2 0.8499 0.667 0.276 0.724
#> GSM110401 1 0.0376 0.897 0.996 0.004
#> GSM110406 2 0.0376 0.859 0.004 0.996
#> GSM110407 1 0.0376 0.897 0.996 0.004
#> GSM110409 1 0.0672 0.897 0.992 0.008
#> GSM110410 2 0.0000 0.859 0.000 1.000
#> GSM110413 2 0.0672 0.858 0.008 0.992
#> GSM110414 2 0.0376 0.858 0.004 0.996
#> GSM110415 2 0.9580 0.538 0.380 0.620
#> GSM110416 1 0.0672 0.896 0.992 0.008
#> GSM110418 1 0.0672 0.896 0.992 0.008
#> GSM110419 2 0.9710 0.502 0.400 0.600
#> GSM110420 1 0.0672 0.896 0.992 0.008
#> GSM110421 2 0.0672 0.858 0.008 0.992
#> GSM110423 2 0.9552 0.545 0.376 0.624
#> GSM110424 2 0.0376 0.859 0.004 0.996
#> GSM110425 2 0.9552 0.545 0.376 0.624
#> GSM110427 2 0.0376 0.858 0.004 0.996
#> GSM110428 1 0.0672 0.896 0.992 0.008
#> GSM110430 1 0.0376 0.897 0.996 0.004
#> GSM110431 1 0.0672 0.896 0.992 0.008
#> GSM110432 2 0.9460 0.560 0.364 0.636
#> GSM110434 2 0.0000 0.859 0.000 1.000
#> GSM110435 1 0.0672 0.896 0.992 0.008
#> GSM110437 1 0.0376 0.897 0.996 0.004
#> GSM110438 1 0.0672 0.896 0.992 0.008
#> GSM110388 1 0.9460 0.492 0.636 0.364
#> GSM110392 2 0.8386 0.561 0.268 0.732
#> GSM110394 1 0.0672 0.896 0.992 0.008
#> GSM110402 2 0.9552 0.545 0.376 0.624
#> GSM110411 1 0.9552 0.471 0.624 0.376
#> GSM110412 2 0.0672 0.858 0.008 0.992
#> GSM110417 1 0.0672 0.895 0.992 0.008
#> GSM110422 2 0.0376 0.858 0.004 0.996
#> GSM110426 1 0.0376 0.897 0.996 0.004
#> GSM110429 2 0.0672 0.857 0.008 0.992
#> GSM110433 2 0.0672 0.858 0.008 0.992
#> GSM110436 2 0.7299 0.737 0.204 0.796
#> GSM110440 1 0.0000 0.897 1.000 0.000
#> GSM110441 2 0.0672 0.858 0.008 0.992
#> GSM110444 2 0.0672 0.858 0.008 0.992
#> GSM110445 1 0.9460 0.492 0.636 0.364
#> GSM110446 1 0.0672 0.896 0.992 0.008
#> GSM110449 2 0.0672 0.858 0.008 0.992
#> GSM110451 2 0.7299 0.737 0.204 0.796
#> GSM110391 2 0.0672 0.858 0.008 0.992
#> GSM110439 2 0.0000 0.859 0.000 1.000
#> GSM110442 2 0.0672 0.858 0.008 0.992
#> GSM110443 2 0.0672 0.858 0.008 0.992
#> GSM110447 2 0.9552 0.545 0.376 0.624
#> GSM110448 1 0.9460 0.492 0.636 0.364
#> GSM110450 1 0.0376 0.897 0.996 0.004
#> GSM110452 2 0.0000 0.859 0.000 1.000
#> GSM110453 2 0.0000 0.859 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.3551 0.7320 0.000 0.868 0.132
#> GSM110396 1 0.5958 0.7271 0.692 0.008 0.300
#> GSM110397 1 0.5497 0.7302 0.708 0.000 0.292
#> GSM110398 2 0.5905 0.5816 0.352 0.648 0.000
#> GSM110399 2 0.3551 0.8287 0.132 0.868 0.000
#> GSM110400 3 0.4796 0.6903 0.000 0.220 0.780
#> GSM110401 1 0.5621 0.7268 0.692 0.000 0.308
#> GSM110406 2 0.3454 0.8408 0.104 0.888 0.008
#> GSM110407 3 0.6308 -0.3943 0.492 0.000 0.508
#> GSM110409 1 0.6950 0.5469 0.572 0.020 0.408
#> GSM110410 2 0.0592 0.8493 0.012 0.988 0.000
#> GSM110413 2 0.4178 0.8177 0.172 0.828 0.000
#> GSM110414 2 0.8384 0.0885 0.088 0.520 0.392
#> GSM110415 3 0.4235 0.7064 0.000 0.176 0.824
#> GSM110416 3 0.0000 0.6547 0.000 0.000 1.000
#> GSM110418 3 0.0424 0.6513 0.008 0.000 0.992
#> GSM110419 3 0.4291 0.7078 0.000 0.180 0.820
#> GSM110420 3 0.0424 0.6513 0.008 0.000 0.992
#> GSM110421 2 0.5138 0.7804 0.252 0.748 0.000
#> GSM110423 3 0.4399 0.7069 0.000 0.188 0.812
#> GSM110424 2 0.1031 0.8484 0.024 0.976 0.000
#> GSM110425 3 0.4399 0.7069 0.000 0.188 0.812
#> GSM110427 2 0.1163 0.8320 0.000 0.972 0.028
#> GSM110428 3 0.0592 0.6528 0.012 0.000 0.988
#> GSM110430 1 0.5621 0.7268 0.692 0.000 0.308
#> GSM110431 3 0.6192 -0.1935 0.420 0.000 0.580
#> GSM110432 3 0.4750 0.6930 0.000 0.216 0.784
#> GSM110434 2 0.0000 0.8487 0.000 1.000 0.000
#> GSM110435 3 0.6111 -0.1226 0.396 0.000 0.604
#> GSM110437 1 0.5621 0.7268 0.692 0.000 0.308
#> GSM110438 3 0.1411 0.6303 0.036 0.000 0.964
#> GSM110388 1 0.2845 0.6224 0.920 0.068 0.012
#> GSM110392 3 0.9659 0.3459 0.284 0.252 0.464
#> GSM110394 3 0.6154 -0.1566 0.408 0.000 0.592
#> GSM110402 3 0.4399 0.7069 0.000 0.188 0.812
#> GSM110411 1 0.2845 0.6224 0.920 0.068 0.012
#> GSM110412 2 0.8192 0.6555 0.220 0.636 0.144
#> GSM110417 1 0.3941 0.7056 0.844 0.000 0.156
#> GSM110422 2 0.0237 0.8469 0.000 0.996 0.004
#> GSM110426 1 0.5016 0.7265 0.760 0.000 0.240
#> GSM110429 2 0.3340 0.7446 0.000 0.880 0.120
#> GSM110433 2 0.5098 0.7828 0.248 0.752 0.000
#> GSM110436 3 0.6299 0.2363 0.000 0.476 0.524
#> GSM110440 1 0.5882 0.6756 0.652 0.000 0.348
#> GSM110441 2 0.3941 0.8206 0.156 0.844 0.000
#> GSM110444 1 0.6470 -0.0634 0.632 0.356 0.012
#> GSM110445 1 0.4228 0.6229 0.844 0.148 0.008
#> GSM110446 3 0.1411 0.6303 0.036 0.000 0.964
#> GSM110449 2 0.4399 0.8016 0.188 0.812 0.000
#> GSM110451 3 0.5760 0.5729 0.000 0.328 0.672
#> GSM110391 2 0.5138 0.7804 0.252 0.748 0.000
#> GSM110439 2 0.0000 0.8487 0.000 1.000 0.000
#> GSM110442 2 0.0000 0.8487 0.000 1.000 0.000
#> GSM110443 2 0.3752 0.8278 0.144 0.856 0.000
#> GSM110447 3 0.4291 0.7070 0.000 0.180 0.820
#> GSM110448 1 0.2804 0.6294 0.924 0.060 0.016
#> GSM110450 1 0.5621 0.7268 0.692 0.000 0.308
#> GSM110452 2 0.0000 0.8487 0.000 1.000 0.000
#> GSM110453 2 0.0000 0.8487 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.4548 0.625 0.008 0.752 0.232 0.008
#> GSM110396 1 0.2773 0.783 0.880 0.004 0.000 0.116
#> GSM110397 1 0.2796 0.774 0.892 0.000 0.016 0.092
#> GSM110398 2 0.5898 0.446 0.056 0.628 0.000 0.316
#> GSM110399 2 0.3932 0.731 0.008 0.832 0.020 0.140
#> GSM110400 3 0.2302 0.792 0.008 0.060 0.924 0.008
#> GSM110401 1 0.2773 0.785 0.880 0.000 0.004 0.116
#> GSM110406 2 0.4360 0.731 0.012 0.816 0.032 0.140
#> GSM110407 1 0.3978 0.744 0.836 0.000 0.108 0.056
#> GSM110409 1 0.3648 0.751 0.868 0.068 0.008 0.056
#> GSM110410 2 0.2174 0.778 0.000 0.928 0.020 0.052
#> GSM110413 2 0.5130 0.499 0.000 0.652 0.016 0.332
#> GSM110414 3 0.4784 0.676 0.000 0.100 0.788 0.112
#> GSM110415 3 0.0469 0.817 0.012 0.000 0.988 0.000
#> GSM110416 3 0.4104 0.745 0.164 0.000 0.808 0.028
#> GSM110418 3 0.4104 0.745 0.164 0.000 0.808 0.028
#> GSM110419 3 0.1209 0.818 0.032 0.004 0.964 0.000
#> GSM110420 3 0.4149 0.741 0.168 0.000 0.804 0.028
#> GSM110421 4 0.5296 -0.195 0.000 0.492 0.008 0.500
#> GSM110423 3 0.1174 0.817 0.012 0.020 0.968 0.000
#> GSM110424 2 0.2563 0.770 0.000 0.908 0.020 0.072
#> GSM110425 3 0.1174 0.817 0.012 0.020 0.968 0.000
#> GSM110427 2 0.3391 0.713 0.004 0.844 0.148 0.004
#> GSM110428 3 0.2542 0.795 0.084 0.000 0.904 0.012
#> GSM110430 1 0.2773 0.785 0.880 0.000 0.004 0.116
#> GSM110431 1 0.4485 0.652 0.772 0.000 0.200 0.028
#> GSM110432 3 0.2456 0.788 0.008 0.068 0.916 0.008
#> GSM110434 2 0.0817 0.790 0.000 0.976 0.024 0.000
#> GSM110435 1 0.4840 0.595 0.732 0.000 0.240 0.028
#> GSM110437 1 0.2918 0.786 0.876 0.000 0.008 0.116
#> GSM110438 3 0.4993 0.637 0.260 0.000 0.712 0.028
#> GSM110388 4 0.2988 0.575 0.112 0.012 0.000 0.876
#> GSM110392 3 0.8677 0.277 0.136 0.096 0.488 0.280
#> GSM110394 1 0.4485 0.649 0.772 0.000 0.200 0.028
#> GSM110402 3 0.1109 0.817 0.028 0.004 0.968 0.000
#> GSM110411 4 0.2198 0.596 0.072 0.008 0.000 0.920
#> GSM110412 4 0.6260 0.412 0.000 0.144 0.192 0.664
#> GSM110417 4 0.5143 -0.179 0.456 0.000 0.004 0.540
#> GSM110422 2 0.1902 0.775 0.000 0.932 0.064 0.004
#> GSM110426 1 0.5366 0.209 0.548 0.000 0.012 0.440
#> GSM110429 2 0.4368 0.606 0.004 0.748 0.244 0.004
#> GSM110433 2 0.5290 0.118 0.000 0.516 0.008 0.476
#> GSM110436 3 0.4923 0.542 0.008 0.304 0.684 0.004
#> GSM110440 1 0.1109 0.770 0.968 0.000 0.028 0.004
#> GSM110441 2 0.3725 0.695 0.000 0.812 0.008 0.180
#> GSM110444 4 0.1677 0.603 0.040 0.012 0.000 0.948
#> GSM110445 1 0.5495 0.656 0.728 0.096 0.000 0.176
#> GSM110446 3 0.5442 0.524 0.336 0.000 0.636 0.028
#> GSM110449 2 0.4277 0.590 0.000 0.720 0.000 0.280
#> GSM110451 3 0.4856 0.587 0.008 0.272 0.712 0.008
#> GSM110391 4 0.5296 -0.195 0.000 0.492 0.008 0.500
#> GSM110439 2 0.1004 0.790 0.000 0.972 0.024 0.004
#> GSM110442 2 0.1004 0.790 0.000 0.972 0.024 0.004
#> GSM110443 2 0.4298 0.732 0.092 0.840 0.036 0.032
#> GSM110447 3 0.1174 0.817 0.012 0.020 0.968 0.000
#> GSM110448 4 0.3626 0.480 0.184 0.004 0.000 0.812
#> GSM110450 1 0.2918 0.784 0.876 0.000 0.008 0.116
#> GSM110452 2 0.1004 0.790 0.000 0.972 0.024 0.004
#> GSM110453 2 0.0817 0.790 0.000 0.976 0.024 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.6109 0.1831 0.004 0.480 0.044 0.032 0.440
#> GSM110396 1 0.0324 0.8238 0.992 0.004 0.000 0.000 0.004
#> GSM110397 1 0.4500 0.7400 0.784 0.000 0.100 0.020 0.096
#> GSM110398 2 0.6810 0.3359 0.072 0.556 0.000 0.276 0.096
#> GSM110399 2 0.5925 0.4822 0.012 0.624 0.000 0.232 0.132
#> GSM110400 3 0.4838 0.2814 0.004 0.008 0.524 0.004 0.460
#> GSM110401 1 0.0162 0.8275 0.996 0.000 0.004 0.000 0.000
#> GSM110406 2 0.6657 0.4486 0.012 0.520 0.000 0.252 0.216
#> GSM110407 1 0.2964 0.7941 0.856 0.000 0.120 0.000 0.024
#> GSM110409 1 0.2609 0.8132 0.896 0.008 0.068 0.000 0.028
#> GSM110410 2 0.3530 0.5541 0.000 0.784 0.000 0.204 0.012
#> GSM110413 4 0.5233 0.0814 0.000 0.288 0.000 0.636 0.076
#> GSM110414 5 0.6876 -0.1481 0.000 0.012 0.336 0.208 0.444
#> GSM110415 3 0.3999 0.5300 0.000 0.000 0.656 0.000 0.344
#> GSM110416 3 0.0324 0.5627 0.004 0.000 0.992 0.000 0.004
#> GSM110418 3 0.0324 0.5627 0.004 0.000 0.992 0.000 0.004
#> GSM110419 3 0.3928 0.5665 0.004 0.000 0.700 0.000 0.296
#> GSM110420 3 0.0671 0.5548 0.016 0.000 0.980 0.000 0.004
#> GSM110421 4 0.2966 0.4048 0.000 0.184 0.000 0.816 0.000
#> GSM110423 3 0.4045 0.5172 0.000 0.000 0.644 0.000 0.356
#> GSM110424 2 0.3563 0.5519 0.000 0.780 0.000 0.208 0.012
#> GSM110425 3 0.4060 0.5143 0.000 0.000 0.640 0.000 0.360
#> GSM110427 2 0.4927 0.3423 0.004 0.616 0.016 0.008 0.356
#> GSM110428 3 0.3928 0.5641 0.004 0.000 0.700 0.000 0.296
#> GSM110430 1 0.0162 0.8275 0.996 0.000 0.004 0.000 0.000
#> GSM110431 1 0.4640 0.5492 0.584 0.000 0.400 0.000 0.016
#> GSM110432 5 0.5843 -0.2943 0.004 0.068 0.456 0.004 0.468
#> GSM110434 2 0.0510 0.6695 0.000 0.984 0.000 0.000 0.016
#> GSM110435 3 0.4811 -0.4043 0.452 0.000 0.528 0.000 0.020
#> GSM110437 1 0.0693 0.8271 0.980 0.000 0.008 0.000 0.012
#> GSM110438 3 0.1981 0.5224 0.064 0.000 0.920 0.000 0.016
#> GSM110388 4 0.5583 0.4815 0.072 0.000 0.000 0.504 0.424
#> GSM110392 3 0.8995 -0.0606 0.096 0.092 0.360 0.136 0.316
#> GSM110394 1 0.4658 0.5361 0.576 0.000 0.408 0.000 0.016
#> GSM110402 3 0.3838 0.5691 0.004 0.000 0.716 0.000 0.280
#> GSM110411 4 0.4930 0.5248 0.032 0.000 0.000 0.580 0.388
#> GSM110412 4 0.5460 0.4547 0.000 0.024 0.040 0.620 0.316
#> GSM110417 5 0.6691 -0.2591 0.360 0.000 0.000 0.240 0.400
#> GSM110422 2 0.2843 0.6339 0.000 0.848 0.000 0.008 0.144
#> GSM110426 5 0.7332 -0.2313 0.352 0.000 0.036 0.208 0.404
#> GSM110429 2 0.5097 0.1866 0.004 0.548 0.016 0.008 0.424
#> GSM110433 4 0.3366 0.3354 0.000 0.232 0.000 0.768 0.000
#> GSM110436 5 0.6797 0.1784 0.004 0.348 0.180 0.008 0.460
#> GSM110440 1 0.3513 0.7706 0.800 0.000 0.180 0.000 0.020
#> GSM110441 2 0.5296 0.1961 0.000 0.480 0.000 0.472 0.048
#> GSM110444 4 0.4757 0.5300 0.024 0.000 0.000 0.596 0.380
#> GSM110445 1 0.4594 0.6341 0.764 0.116 0.000 0.008 0.112
#> GSM110446 3 0.2300 0.5120 0.072 0.000 0.904 0.000 0.024
#> GSM110449 2 0.5394 0.4041 0.000 0.628 0.000 0.280 0.092
#> GSM110451 5 0.6855 0.1408 0.004 0.292 0.240 0.004 0.460
#> GSM110391 4 0.2966 0.4048 0.000 0.184 0.000 0.816 0.000
#> GSM110439 2 0.0000 0.6694 0.000 1.000 0.000 0.000 0.000
#> GSM110442 2 0.0000 0.6694 0.000 1.000 0.000 0.000 0.000
#> GSM110443 2 0.5386 0.5343 0.168 0.680 0.000 0.004 0.148
#> GSM110447 3 0.4030 0.5230 0.000 0.000 0.648 0.000 0.352
#> GSM110448 4 0.5673 0.4741 0.080 0.000 0.000 0.500 0.420
#> GSM110450 1 0.0324 0.8272 0.992 0.000 0.004 0.000 0.004
#> GSM110452 2 0.0000 0.6694 0.000 1.000 0.000 0.000 0.000
#> GSM110453 2 0.0566 0.6694 0.000 0.984 0.000 0.004 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 3 0.6868 0.2806 0.000 0.304 0.476 0.028 0.040 0.152
#> GSM110396 1 0.1251 0.7821 0.956 0.000 0.000 0.012 0.008 0.024
#> GSM110397 1 0.6278 0.4197 0.520 0.000 0.000 0.248 0.036 0.196
#> GSM110398 2 0.7267 0.1276 0.056 0.436 0.000 0.048 0.328 0.132
#> GSM110399 2 0.6717 0.2376 0.016 0.452 0.000 0.028 0.316 0.188
#> GSM110400 3 0.2946 0.6661 0.000 0.024 0.848 0.004 0.004 0.120
#> GSM110401 1 0.0520 0.7830 0.984 0.000 0.000 0.008 0.008 0.000
#> GSM110406 2 0.7950 0.1684 0.020 0.344 0.068 0.028 0.324 0.216
#> GSM110407 1 0.2596 0.7668 0.892 0.000 0.024 0.016 0.008 0.060
#> GSM110409 1 0.2512 0.7745 0.900 0.020 0.000 0.012 0.020 0.048
#> GSM110410 2 0.4273 0.4003 0.000 0.696 0.000 0.012 0.260 0.032
#> GSM110413 5 0.3305 0.6239 0.000 0.108 0.000 0.012 0.832 0.048
#> GSM110414 3 0.4657 0.5513 0.000 0.004 0.684 0.000 0.220 0.092
#> GSM110415 3 0.1075 0.6369 0.000 0.000 0.952 0.000 0.000 0.048
#> GSM110416 6 0.3833 0.8205 0.000 0.000 0.444 0.000 0.000 0.556
#> GSM110418 6 0.3804 0.8447 0.000 0.000 0.424 0.000 0.000 0.576
#> GSM110419 3 0.2718 0.5738 0.020 0.000 0.880 0.020 0.004 0.076
#> GSM110420 6 0.3782 0.8509 0.000 0.000 0.412 0.000 0.000 0.588
#> GSM110421 5 0.2672 0.7023 0.000 0.052 0.000 0.080 0.868 0.000
#> GSM110423 3 0.0146 0.6629 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM110424 2 0.4678 0.3253 0.000 0.640 0.000 0.012 0.304 0.044
#> GSM110425 3 0.0000 0.6643 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110427 2 0.5716 0.3541 0.000 0.612 0.228 0.016 0.012 0.132
#> GSM110428 3 0.2978 0.5715 0.032 0.000 0.868 0.016 0.008 0.076
#> GSM110430 1 0.0767 0.7826 0.976 0.000 0.000 0.008 0.012 0.004
#> GSM110431 1 0.5623 0.3830 0.568 0.000 0.116 0.004 0.012 0.300
#> GSM110432 3 0.4536 0.6472 0.004 0.064 0.768 0.028 0.012 0.124
#> GSM110434 2 0.1448 0.6165 0.000 0.948 0.000 0.012 0.016 0.024
#> GSM110435 6 0.5645 0.4594 0.252 0.000 0.160 0.000 0.012 0.576
#> GSM110437 1 0.1173 0.7827 0.960 0.000 0.000 0.008 0.016 0.016
#> GSM110438 6 0.4333 0.8514 0.028 0.000 0.376 0.000 0.000 0.596
#> GSM110388 4 0.2942 0.6926 0.032 0.000 0.000 0.836 0.132 0.000
#> GSM110392 4 0.7333 0.0659 0.016 0.052 0.164 0.416 0.016 0.336
#> GSM110394 1 0.5728 0.4010 0.576 0.000 0.112 0.008 0.016 0.288
#> GSM110402 3 0.1957 0.5331 0.000 0.000 0.888 0.000 0.000 0.112
#> GSM110411 4 0.3411 0.6329 0.004 0.000 0.000 0.756 0.232 0.008
#> GSM110412 5 0.6548 -0.1973 0.000 0.008 0.148 0.396 0.412 0.036
#> GSM110417 4 0.3917 0.6307 0.124 0.000 0.000 0.792 0.024 0.060
#> GSM110422 2 0.3110 0.5781 0.000 0.848 0.012 0.016 0.012 0.112
#> GSM110426 4 0.4160 0.6233 0.112 0.000 0.000 0.776 0.024 0.088
#> GSM110429 2 0.5893 0.2717 0.000 0.576 0.264 0.016 0.012 0.132
#> GSM110433 5 0.2912 0.7077 0.000 0.076 0.000 0.072 0.852 0.000
#> GSM110436 3 0.5801 0.4492 0.000 0.268 0.572 0.012 0.008 0.140
#> GSM110440 1 0.3939 0.6716 0.756 0.000 0.020 0.008 0.012 0.204
#> GSM110441 5 0.5156 0.2043 0.000 0.320 0.000 0.012 0.592 0.076
#> GSM110444 4 0.3512 0.6152 0.004 0.000 0.000 0.740 0.248 0.008
#> GSM110445 1 0.6316 0.4453 0.620 0.128 0.000 0.032 0.060 0.160
#> GSM110446 6 0.4238 0.8344 0.028 0.000 0.344 0.000 0.000 0.628
#> GSM110449 2 0.6198 0.1633 0.000 0.496 0.000 0.044 0.336 0.124
#> GSM110451 3 0.5728 0.5597 0.000 0.204 0.632 0.028 0.012 0.124
#> GSM110391 5 0.2724 0.7003 0.000 0.052 0.000 0.084 0.864 0.000
#> GSM110439 2 0.1003 0.6138 0.000 0.964 0.000 0.004 0.028 0.004
#> GSM110442 2 0.1257 0.6147 0.000 0.952 0.000 0.000 0.028 0.020
#> GSM110443 2 0.7080 0.3978 0.160 0.512 0.000 0.036 0.064 0.228
#> GSM110447 3 0.1204 0.6400 0.000 0.000 0.944 0.000 0.000 0.056
#> GSM110448 4 0.2930 0.6949 0.036 0.000 0.000 0.840 0.124 0.000
#> GSM110450 1 0.0862 0.7812 0.972 0.000 0.000 0.004 0.008 0.016
#> GSM110452 2 0.0777 0.6159 0.000 0.972 0.000 0.000 0.024 0.004
#> GSM110453 2 0.1138 0.6173 0.000 0.960 0.000 0.004 0.024 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) specimen(p) k
#> MAD:kmeans 54 0.1755 0.2458 2
#> MAD:kmeans 51 0.1678 0.2521 3
#> MAD:kmeans 49 0.0657 0.1270 4
#> MAD:kmeans 35 0.0801 0.0218 5
#> MAD:kmeans 40 0.0118 0.0595 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 17209 rows and 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.578 0.741 0.887 0.5070 0.493 0.493
#> 3 3 0.747 0.819 0.919 0.3274 0.750 0.532
#> 4 4 0.692 0.712 0.865 0.1124 0.848 0.581
#> 5 5 0.674 0.605 0.766 0.0703 0.859 0.522
#> 6 6 0.700 0.542 0.759 0.0446 0.904 0.576
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
#> GSM110395 2 0.7219 0.7132 0.200 0.800
#> GSM110396 1 0.0000 0.8521 1.000 0.000
#> GSM110397 1 0.0000 0.8521 1.000 0.000
#> GSM110398 1 0.9732 0.4622 0.596 0.404
#> GSM110399 2 0.0000 0.8529 0.000 1.000
#> GSM110400 2 0.9710 0.4872 0.400 0.600
#> GSM110401 1 0.0000 0.8521 1.000 0.000
#> GSM110406 2 0.0000 0.8529 0.000 1.000
#> GSM110407 1 0.0000 0.8521 1.000 0.000
#> GSM110409 1 0.0000 0.8521 1.000 0.000
#> GSM110410 2 0.0000 0.8529 0.000 1.000
#> GSM110413 2 0.0000 0.8529 0.000 1.000
#> GSM110414 2 0.0000 0.8529 0.000 1.000
#> GSM110415 2 0.9775 0.4653 0.412 0.588
#> GSM110416 1 0.0000 0.8521 1.000 0.000
#> GSM110418 1 0.0000 0.8521 1.000 0.000
#> GSM110419 1 0.9710 0.0544 0.600 0.400
#> GSM110420 1 0.0000 0.8521 1.000 0.000
#> GSM110421 2 0.0000 0.8529 0.000 1.000
#> GSM110423 2 0.9710 0.4872 0.400 0.600
#> GSM110424 2 0.0000 0.8529 0.000 1.000
#> GSM110425 2 0.9710 0.4872 0.400 0.600
#> GSM110427 2 0.0000 0.8529 0.000 1.000
#> GSM110428 1 0.0000 0.8521 1.000 0.000
#> GSM110430 1 0.0000 0.8521 1.000 0.000
#> GSM110431 1 0.0000 0.8521 1.000 0.000
#> GSM110432 2 0.9710 0.4872 0.400 0.600
#> GSM110434 2 0.0000 0.8529 0.000 1.000
#> GSM110435 1 0.0000 0.8521 1.000 0.000
#> GSM110437 1 0.0000 0.8521 1.000 0.000
#> GSM110438 1 0.0000 0.8521 1.000 0.000
#> GSM110388 1 0.9710 0.4690 0.600 0.400
#> GSM110392 1 0.9323 0.5333 0.652 0.348
#> GSM110394 1 0.0000 0.8521 1.000 0.000
#> GSM110402 2 0.9732 0.4805 0.404 0.596
#> GSM110411 1 0.9710 0.4690 0.600 0.400
#> GSM110412 2 0.0000 0.8529 0.000 1.000
#> GSM110417 1 0.0938 0.8443 0.988 0.012
#> GSM110422 2 0.0000 0.8529 0.000 1.000
#> GSM110426 1 0.0000 0.8521 1.000 0.000
#> GSM110429 2 0.0000 0.8529 0.000 1.000
#> GSM110433 2 0.0000 0.8529 0.000 1.000
#> GSM110436 2 0.7219 0.7132 0.200 0.800
#> GSM110440 1 0.0000 0.8521 1.000 0.000
#> GSM110441 2 0.0000 0.8529 0.000 1.000
#> GSM110444 1 0.9833 0.4251 0.576 0.424
#> GSM110445 1 0.9710 0.4690 0.600 0.400
#> GSM110446 1 0.0000 0.8521 1.000 0.000
#> GSM110449 2 0.0000 0.8529 0.000 1.000
#> GSM110451 2 0.8608 0.6290 0.284 0.716
#> GSM110391 2 0.0000 0.8529 0.000 1.000
#> GSM110439 2 0.0000 0.8529 0.000 1.000
#> GSM110442 2 0.0000 0.8529 0.000 1.000
#> GSM110443 2 0.0000 0.8529 0.000 1.000
#> GSM110447 2 0.9732 0.4805 0.404 0.596
#> GSM110448 1 0.9710 0.4690 0.600 0.400
#> GSM110450 1 0.0000 0.8521 1.000 0.000
#> GSM110452 2 0.0000 0.8529 0.000 1.000
#> GSM110453 2 0.0000 0.8529 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.3412 0.840 0.000 0.876 0.124
#> GSM110396 1 0.0000 0.826 1.000 0.000 0.000
#> GSM110397 1 0.1163 0.828 0.972 0.000 0.028
#> GSM110398 1 0.6302 0.123 0.520 0.480 0.000
#> GSM110399 2 0.0000 0.970 0.000 1.000 0.000
#> GSM110400 3 0.0000 0.919 0.000 0.000 1.000
#> GSM110401 1 0.1163 0.828 0.972 0.000 0.028
#> GSM110406 2 0.0000 0.970 0.000 1.000 0.000
#> GSM110407 1 0.5497 0.613 0.708 0.000 0.292
#> GSM110409 1 0.4748 0.754 0.832 0.024 0.144
#> GSM110410 2 0.0000 0.970 0.000 1.000 0.000
#> GSM110413 2 0.0592 0.966 0.012 0.988 0.000
#> GSM110414 3 0.7129 0.309 0.028 0.392 0.580
#> GSM110415 3 0.0000 0.919 0.000 0.000 1.000
#> GSM110416 3 0.0000 0.919 0.000 0.000 1.000
#> GSM110418 3 0.0000 0.919 0.000 0.000 1.000
#> GSM110419 3 0.0000 0.919 0.000 0.000 1.000
#> GSM110420 3 0.0000 0.919 0.000 0.000 1.000
#> GSM110421 2 0.1163 0.959 0.028 0.972 0.000
#> GSM110423 3 0.0000 0.919 0.000 0.000 1.000
#> GSM110424 2 0.1031 0.961 0.024 0.976 0.000
#> GSM110425 3 0.0000 0.919 0.000 0.000 1.000
#> GSM110427 2 0.0237 0.968 0.000 0.996 0.004
#> GSM110428 3 0.0000 0.919 0.000 0.000 1.000
#> GSM110430 1 0.1163 0.828 0.972 0.000 0.028
#> GSM110431 1 0.6295 0.290 0.528 0.000 0.472
#> GSM110432 3 0.0237 0.917 0.000 0.004 0.996
#> GSM110434 2 0.0000 0.970 0.000 1.000 0.000
#> GSM110435 1 0.6295 0.290 0.528 0.000 0.472
#> GSM110437 1 0.1163 0.828 0.972 0.000 0.028
#> GSM110438 3 0.0747 0.906 0.016 0.000 0.984
#> GSM110388 1 0.0892 0.823 0.980 0.020 0.000
#> GSM110392 1 0.6421 0.212 0.572 0.004 0.424
#> GSM110394 1 0.6295 0.290 0.528 0.000 0.472
#> GSM110402 3 0.0000 0.919 0.000 0.000 1.000
#> GSM110411 1 0.0747 0.824 0.984 0.016 0.000
#> GSM110412 2 0.3983 0.893 0.068 0.884 0.048
#> GSM110417 1 0.0000 0.826 1.000 0.000 0.000
#> GSM110422 2 0.0000 0.970 0.000 1.000 0.000
#> GSM110426 1 0.0000 0.826 1.000 0.000 0.000
#> GSM110429 2 0.1163 0.952 0.000 0.972 0.028
#> GSM110433 2 0.1163 0.959 0.028 0.972 0.000
#> GSM110436 3 0.5431 0.615 0.000 0.284 0.716
#> GSM110440 1 0.3941 0.755 0.844 0.000 0.156
#> GSM110441 2 0.0000 0.970 0.000 1.000 0.000
#> GSM110444 1 0.1529 0.811 0.960 0.040 0.000
#> GSM110445 1 0.1163 0.822 0.972 0.028 0.000
#> GSM110446 3 0.3412 0.775 0.124 0.000 0.876
#> GSM110449 2 0.0000 0.970 0.000 1.000 0.000
#> GSM110451 3 0.4121 0.763 0.000 0.168 0.832
#> GSM110391 2 0.1163 0.959 0.028 0.972 0.000
#> GSM110439 2 0.0000 0.970 0.000 1.000 0.000
#> GSM110442 2 0.0000 0.970 0.000 1.000 0.000
#> GSM110443 2 0.4504 0.763 0.196 0.804 0.000
#> GSM110447 3 0.0000 0.919 0.000 0.000 1.000
#> GSM110448 1 0.0592 0.825 0.988 0.012 0.000
#> GSM110450 1 0.1163 0.828 0.972 0.000 0.028
#> GSM110452 2 0.0000 0.970 0.000 1.000 0.000
#> GSM110453 2 0.0000 0.970 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.3292 0.738 0.004 0.868 0.112 0.016
#> GSM110396 1 0.1118 0.859 0.964 0.000 0.000 0.036
#> GSM110397 1 0.0921 0.864 0.972 0.000 0.000 0.028
#> GSM110398 2 0.5659 0.527 0.032 0.600 0.000 0.368
#> GSM110399 2 0.3801 0.716 0.000 0.780 0.000 0.220
#> GSM110400 3 0.0592 0.894 0.000 0.016 0.984 0.000
#> GSM110401 1 0.0921 0.864 0.972 0.000 0.000 0.028
#> GSM110406 2 0.3973 0.730 0.004 0.792 0.004 0.200
#> GSM110407 1 0.1305 0.856 0.960 0.000 0.036 0.004
#> GSM110409 1 0.0657 0.862 0.984 0.012 0.000 0.004
#> GSM110410 2 0.0592 0.810 0.000 0.984 0.000 0.016
#> GSM110413 2 0.4679 0.593 0.000 0.648 0.000 0.352
#> GSM110414 3 0.3787 0.765 0.000 0.036 0.840 0.124
#> GSM110415 3 0.0000 0.899 0.000 0.000 1.000 0.000
#> GSM110416 3 0.1302 0.894 0.044 0.000 0.956 0.000
#> GSM110418 3 0.1302 0.894 0.044 0.000 0.956 0.000
#> GSM110419 3 0.1118 0.897 0.036 0.000 0.964 0.000
#> GSM110420 3 0.1389 0.892 0.048 0.000 0.952 0.000
#> GSM110421 4 0.4972 -0.269 0.000 0.456 0.000 0.544
#> GSM110423 3 0.0000 0.899 0.000 0.000 1.000 0.000
#> GSM110424 2 0.2216 0.777 0.000 0.908 0.000 0.092
#> GSM110425 3 0.0000 0.899 0.000 0.000 1.000 0.000
#> GSM110427 2 0.1118 0.794 0.000 0.964 0.036 0.000
#> GSM110428 3 0.3649 0.723 0.204 0.000 0.796 0.000
#> GSM110430 1 0.0921 0.864 0.972 0.000 0.000 0.028
#> GSM110431 1 0.3024 0.795 0.852 0.000 0.148 0.000
#> GSM110432 3 0.2011 0.857 0.000 0.080 0.920 0.000
#> GSM110434 2 0.0000 0.809 0.000 1.000 0.000 0.000
#> GSM110435 1 0.3024 0.795 0.852 0.000 0.148 0.000
#> GSM110437 1 0.0921 0.864 0.972 0.000 0.000 0.028
#> GSM110438 1 0.4989 0.200 0.528 0.000 0.472 0.000
#> GSM110388 4 0.2469 0.668 0.108 0.000 0.000 0.892
#> GSM110392 4 0.6901 0.547 0.056 0.180 0.092 0.672
#> GSM110394 1 0.3024 0.795 0.852 0.000 0.148 0.000
#> GSM110402 3 0.0921 0.898 0.028 0.000 0.972 0.000
#> GSM110411 4 0.0188 0.660 0.004 0.000 0.000 0.996
#> GSM110412 4 0.2329 0.642 0.000 0.072 0.012 0.916
#> GSM110417 4 0.4661 0.407 0.348 0.000 0.000 0.652
#> GSM110422 2 0.0000 0.809 0.000 1.000 0.000 0.000
#> GSM110426 4 0.4804 0.349 0.384 0.000 0.000 0.616
#> GSM110429 2 0.2408 0.737 0.000 0.896 0.104 0.000
#> GSM110433 2 0.4996 0.328 0.000 0.516 0.000 0.484
#> GSM110436 3 0.4382 0.634 0.000 0.296 0.704 0.000
#> GSM110440 1 0.0524 0.864 0.988 0.000 0.008 0.004
#> GSM110441 2 0.4250 0.675 0.000 0.724 0.000 0.276
#> GSM110444 4 0.0000 0.658 0.000 0.000 0.000 1.000
#> GSM110445 1 0.2131 0.835 0.932 0.032 0.000 0.036
#> GSM110446 1 0.4277 0.628 0.720 0.000 0.280 0.000
#> GSM110449 2 0.4624 0.605 0.000 0.660 0.000 0.340
#> GSM110451 3 0.4277 0.655 0.000 0.280 0.720 0.000
#> GSM110391 4 0.4977 -0.280 0.000 0.460 0.000 0.540
#> GSM110439 2 0.0188 0.810 0.000 0.996 0.000 0.004
#> GSM110442 2 0.0469 0.810 0.000 0.988 0.000 0.012
#> GSM110443 2 0.3300 0.700 0.144 0.848 0.000 0.008
#> GSM110447 3 0.0336 0.900 0.008 0.000 0.992 0.000
#> GSM110448 4 0.3444 0.616 0.184 0.000 0.000 0.816
#> GSM110450 1 0.0921 0.864 0.972 0.000 0.000 0.028
#> GSM110452 2 0.0336 0.810 0.000 0.992 0.000 0.008
#> GSM110453 2 0.0000 0.809 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 5 0.3807 0.467 0.000 0.240 0.012 0.000 0.748
#> GSM110396 1 0.0162 0.860 0.996 0.000 0.000 0.004 0.000
#> GSM110397 1 0.3983 0.751 0.784 0.000 0.164 0.052 0.000
#> GSM110398 2 0.3847 0.621 0.088 0.828 0.000 0.068 0.016
#> GSM110399 2 0.1774 0.669 0.000 0.932 0.000 0.016 0.052
#> GSM110400 5 0.4608 0.233 0.000 0.008 0.336 0.012 0.644
#> GSM110401 1 0.0000 0.862 1.000 0.000 0.000 0.000 0.000
#> GSM110406 2 0.4467 0.501 0.016 0.716 0.000 0.016 0.252
#> GSM110407 1 0.1082 0.854 0.964 0.000 0.028 0.000 0.008
#> GSM110409 1 0.0798 0.858 0.976 0.008 0.016 0.000 0.000
#> GSM110410 2 0.4422 0.618 0.000 0.664 0.004 0.012 0.320
#> GSM110413 2 0.3170 0.648 0.000 0.856 0.004 0.104 0.036
#> GSM110414 5 0.6254 0.269 0.000 0.076 0.280 0.048 0.596
#> GSM110415 3 0.3391 0.612 0.000 0.000 0.800 0.012 0.188
#> GSM110416 3 0.0486 0.657 0.004 0.000 0.988 0.004 0.004
#> GSM110418 3 0.0324 0.657 0.004 0.000 0.992 0.004 0.000
#> GSM110419 3 0.4194 0.547 0.004 0.000 0.708 0.012 0.276
#> GSM110420 3 0.0324 0.657 0.004 0.000 0.992 0.004 0.000
#> GSM110421 2 0.4768 0.493 0.000 0.672 0.004 0.288 0.036
#> GSM110423 3 0.4655 0.166 0.000 0.000 0.512 0.012 0.476
#> GSM110424 2 0.5059 0.624 0.000 0.652 0.004 0.052 0.292
#> GSM110425 3 0.4656 0.162 0.000 0.000 0.508 0.012 0.480
#> GSM110427 5 0.2848 0.490 0.000 0.156 0.004 0.000 0.840
#> GSM110428 3 0.5960 0.485 0.264 0.000 0.592 0.004 0.140
#> GSM110430 1 0.0000 0.862 1.000 0.000 0.000 0.000 0.000
#> GSM110431 1 0.4196 0.523 0.640 0.000 0.356 0.004 0.000
#> GSM110432 5 0.4070 0.412 0.000 0.004 0.256 0.012 0.728
#> GSM110434 2 0.4045 0.570 0.000 0.644 0.000 0.000 0.356
#> GSM110435 3 0.4440 -0.229 0.468 0.000 0.528 0.004 0.000
#> GSM110437 1 0.0000 0.862 1.000 0.000 0.000 0.000 0.000
#> GSM110438 3 0.2848 0.566 0.156 0.000 0.840 0.004 0.000
#> GSM110388 4 0.1041 0.911 0.032 0.004 0.000 0.964 0.000
#> GSM110392 4 0.4518 0.790 0.024 0.016 0.164 0.776 0.020
#> GSM110394 1 0.3999 0.547 0.656 0.000 0.344 0.000 0.000
#> GSM110402 3 0.3399 0.623 0.004 0.000 0.812 0.012 0.172
#> GSM110411 4 0.0703 0.904 0.000 0.024 0.000 0.976 0.000
#> GSM110412 4 0.1202 0.896 0.000 0.032 0.004 0.960 0.004
#> GSM110417 4 0.2561 0.848 0.144 0.000 0.000 0.856 0.000
#> GSM110422 5 0.4262 -0.236 0.000 0.440 0.000 0.000 0.560
#> GSM110426 4 0.3601 0.831 0.128 0.000 0.052 0.820 0.000
#> GSM110429 5 0.1965 0.597 0.000 0.096 0.000 0.000 0.904
#> GSM110433 2 0.3764 0.630 0.000 0.808 0.004 0.148 0.040
#> GSM110436 5 0.1571 0.632 0.000 0.004 0.060 0.000 0.936
#> GSM110440 1 0.3274 0.722 0.780 0.000 0.220 0.000 0.000
#> GSM110441 2 0.1996 0.668 0.000 0.928 0.004 0.032 0.036
#> GSM110444 4 0.0703 0.904 0.000 0.024 0.000 0.976 0.000
#> GSM110445 1 0.2570 0.771 0.880 0.108 0.000 0.008 0.004
#> GSM110446 3 0.3671 0.430 0.236 0.000 0.756 0.008 0.000
#> GSM110449 2 0.1408 0.671 0.000 0.948 0.000 0.044 0.008
#> GSM110451 5 0.1792 0.621 0.000 0.000 0.084 0.000 0.916
#> GSM110391 2 0.4747 0.499 0.000 0.676 0.004 0.284 0.036
#> GSM110439 2 0.3895 0.608 0.000 0.680 0.000 0.000 0.320
#> GSM110442 2 0.3895 0.608 0.000 0.680 0.000 0.000 0.320
#> GSM110443 2 0.6815 0.337 0.280 0.436 0.000 0.004 0.280
#> GSM110447 3 0.4217 0.545 0.004 0.000 0.704 0.012 0.280
#> GSM110448 4 0.1041 0.911 0.032 0.004 0.000 0.964 0.000
#> GSM110450 1 0.0000 0.862 1.000 0.000 0.000 0.000 0.000
#> GSM110452 2 0.3932 0.601 0.000 0.672 0.000 0.000 0.328
#> GSM110453 2 0.3895 0.608 0.000 0.680 0.000 0.000 0.320
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 6 0.5781 0.12263 0.000 0.232 0.000 0.000 0.264 0.504
#> GSM110396 1 0.0363 0.82000 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM110397 1 0.4902 0.63008 0.672 0.000 0.172 0.152 0.004 0.000
#> GSM110398 5 0.6253 0.42897 0.056 0.372 0.000 0.024 0.496 0.052
#> GSM110399 5 0.5042 0.41768 0.000 0.412 0.000 0.004 0.520 0.064
#> GSM110400 6 0.2604 0.57396 0.000 0.008 0.076 0.000 0.036 0.880
#> GSM110401 1 0.0291 0.82044 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM110406 5 0.5747 0.43667 0.012 0.204 0.000 0.000 0.568 0.216
#> GSM110407 1 0.2172 0.79675 0.912 0.000 0.024 0.000 0.020 0.044
#> GSM110409 1 0.1198 0.81579 0.960 0.012 0.004 0.000 0.020 0.004
#> GSM110410 2 0.2969 0.50328 0.000 0.776 0.000 0.000 0.224 0.000
#> GSM110413 5 0.3027 0.69431 0.000 0.148 0.000 0.028 0.824 0.000
#> GSM110414 6 0.5884 0.40287 0.000 0.008 0.100 0.032 0.284 0.576
#> GSM110415 3 0.4818 0.25441 0.000 0.000 0.572 0.004 0.052 0.372
#> GSM110416 3 0.1682 0.63595 0.000 0.000 0.928 0.000 0.020 0.052
#> GSM110418 3 0.0603 0.64920 0.000 0.000 0.980 0.000 0.004 0.016
#> GSM110419 6 0.4857 0.00118 0.004 0.000 0.424 0.000 0.048 0.524
#> GSM110420 3 0.0363 0.64960 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM110421 5 0.4010 0.67094 0.000 0.084 0.000 0.148 0.764 0.004
#> GSM110423 6 0.4424 0.31816 0.000 0.000 0.324 0.000 0.044 0.632
#> GSM110424 2 0.3684 0.34177 0.000 0.664 0.000 0.004 0.332 0.000
#> GSM110425 6 0.4146 0.37270 0.000 0.000 0.288 0.000 0.036 0.676
#> GSM110427 2 0.4620 0.17632 0.000 0.532 0.000 0.000 0.040 0.428
#> GSM110428 3 0.6767 0.29146 0.256 0.000 0.448 0.000 0.056 0.240
#> GSM110430 1 0.0291 0.82044 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM110431 1 0.4649 0.48856 0.616 0.000 0.340 0.000 0.020 0.024
#> GSM110432 6 0.3154 0.58252 0.000 0.072 0.068 0.000 0.012 0.848
#> GSM110434 2 0.0993 0.63297 0.000 0.964 0.000 0.000 0.024 0.012
#> GSM110435 3 0.3833 0.19174 0.344 0.000 0.648 0.000 0.008 0.000
#> GSM110437 1 0.0436 0.82083 0.988 0.000 0.000 0.004 0.004 0.004
#> GSM110438 3 0.2377 0.62925 0.084 0.000 0.892 0.008 0.008 0.008
#> GSM110388 4 0.1204 0.87058 0.000 0.000 0.000 0.944 0.056 0.000
#> GSM110392 4 0.6011 0.60489 0.016 0.060 0.212 0.644 0.032 0.036
#> GSM110394 1 0.4686 0.52898 0.636 0.000 0.312 0.000 0.020 0.032
#> GSM110402 3 0.4344 0.38690 0.000 0.000 0.652 0.000 0.044 0.304
#> GSM110411 4 0.1327 0.86926 0.000 0.000 0.000 0.936 0.064 0.000
#> GSM110412 4 0.3110 0.74780 0.000 0.000 0.000 0.792 0.196 0.012
#> GSM110417 4 0.1327 0.83285 0.064 0.000 0.000 0.936 0.000 0.000
#> GSM110422 2 0.3470 0.55938 0.000 0.772 0.000 0.000 0.028 0.200
#> GSM110426 4 0.2680 0.79898 0.076 0.000 0.056 0.868 0.000 0.000
#> GSM110429 2 0.4517 0.12954 0.000 0.524 0.000 0.000 0.032 0.444
#> GSM110433 5 0.3867 0.69483 0.000 0.128 0.000 0.088 0.780 0.004
#> GSM110436 6 0.3993 0.36049 0.000 0.300 0.000 0.000 0.024 0.676
#> GSM110440 1 0.3679 0.70124 0.772 0.000 0.192 0.024 0.012 0.000
#> GSM110441 5 0.3390 0.60077 0.000 0.296 0.000 0.000 0.704 0.000
#> GSM110444 4 0.1444 0.86656 0.000 0.000 0.000 0.928 0.072 0.000
#> GSM110445 1 0.5941 0.53608 0.668 0.124 0.008 0.012 0.092 0.096
#> GSM110446 3 0.2401 0.62410 0.060 0.000 0.900 0.004 0.016 0.020
#> GSM110449 2 0.5188 -0.40859 0.000 0.496 0.000 0.016 0.436 0.052
#> GSM110451 6 0.3633 0.45013 0.000 0.252 0.004 0.000 0.012 0.732
#> GSM110391 5 0.3867 0.68332 0.000 0.088 0.000 0.128 0.780 0.004
#> GSM110439 2 0.0790 0.63225 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM110442 2 0.1411 0.62813 0.000 0.936 0.000 0.000 0.060 0.004
#> GSM110443 2 0.6803 0.29888 0.200 0.548 0.008 0.004 0.136 0.104
#> GSM110447 3 0.5116 0.04220 0.000 0.000 0.488 0.012 0.052 0.448
#> GSM110448 4 0.1075 0.87045 0.000 0.000 0.000 0.952 0.048 0.000
#> GSM110450 1 0.1346 0.81102 0.952 0.000 0.000 0.008 0.016 0.024
#> GSM110452 2 0.0858 0.63686 0.000 0.968 0.000 0.000 0.028 0.004
#> GSM110453 2 0.1152 0.63392 0.000 0.952 0.000 0.000 0.044 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) specimen(p) k
#> MAD:skmeans 45 0.16833 0.1452 2
#> MAD:skmeans 53 0.23331 0.1707 3
#> MAD:skmeans 53 0.01834 0.2847 4
#> MAD:skmeans 45 0.00669 0.5665 5
#> MAD:skmeans 38 0.01668 0.0942 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 17209 rows and 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.224 0.183 0.628 0.4330 0.534 0.534
#> 3 3 0.626 0.714 0.849 0.3910 0.609 0.410
#> 4 4 0.718 0.832 0.900 0.2104 0.827 0.587
#> 5 5 0.849 0.833 0.930 0.0867 0.901 0.651
#> 6 6 0.846 0.815 0.902 0.0316 0.965 0.834
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM110395 2 0.925 0.13402 0.340 0.660
#> GSM110396 2 0.871 0.14503 0.292 0.708
#> GSM110397 1 0.925 -0.05485 0.660 0.340
#> GSM110398 1 0.969 0.13485 0.604 0.396
#> GSM110399 2 0.925 0.13402 0.340 0.660
#> GSM110400 2 0.925 0.13402 0.340 0.660
#> GSM110401 2 0.850 0.15778 0.276 0.724
#> GSM110406 2 0.925 0.13402 0.340 0.660
#> GSM110407 2 0.833 0.16231 0.264 0.736
#> GSM110409 1 0.969 0.13485 0.604 0.396
#> GSM110410 2 0.925 0.13402 0.340 0.660
#> GSM110413 2 0.961 -0.02011 0.384 0.616
#> GSM110414 2 0.925 0.13402 0.340 0.660
#> GSM110415 1 0.998 0.02593 0.524 0.476
#> GSM110416 2 0.689 0.19559 0.184 0.816
#> GSM110418 2 0.689 0.19559 0.184 0.816
#> GSM110419 2 0.925 0.13402 0.340 0.660
#> GSM110420 2 0.689 0.19559 0.184 0.816
#> GSM110421 1 0.992 0.44010 0.552 0.448
#> GSM110423 1 0.998 0.02593 0.524 0.476
#> GSM110424 1 0.994 0.43017 0.544 0.456
#> GSM110425 2 0.925 0.13402 0.340 0.660
#> GSM110427 2 0.925 0.13402 0.340 0.660
#> GSM110428 2 0.000 0.14062 0.000 1.000
#> GSM110430 2 0.850 0.15778 0.276 0.724
#> GSM110431 2 0.992 0.16771 0.448 0.552
#> GSM110432 2 0.925 0.13402 0.340 0.660
#> GSM110434 2 0.925 0.13402 0.340 0.660
#> GSM110435 2 0.990 0.17000 0.440 0.560
#> GSM110437 2 0.994 0.16388 0.456 0.544
#> GSM110438 2 0.689 0.19559 0.184 0.816
#> GSM110388 1 0.689 0.33279 0.816 0.184
#> GSM110392 1 0.833 0.30435 0.736 0.264
#> GSM110394 2 0.952 0.17964 0.372 0.628
#> GSM110402 1 0.999 0.02404 0.520 0.480
#> GSM110411 1 0.689 0.33279 0.816 0.184
#> GSM110412 1 0.981 0.42869 0.580 0.420
#> GSM110417 2 0.998 -0.03855 0.476 0.524
#> GSM110422 2 0.925 0.13402 0.340 0.660
#> GSM110426 1 0.925 -0.05485 0.660 0.340
#> GSM110429 2 0.925 0.13402 0.340 0.660
#> GSM110433 1 0.992 0.44010 0.552 0.448
#> GSM110436 2 0.925 0.13402 0.340 0.660
#> GSM110440 2 0.993 0.16602 0.452 0.548
#> GSM110441 1 0.992 0.44010 0.552 0.448
#> GSM110444 1 0.992 0.44010 0.552 0.448
#> GSM110445 1 0.881 0.25802 0.700 0.300
#> GSM110446 2 0.689 0.19559 0.184 0.816
#> GSM110449 1 0.990 0.44001 0.560 0.440
#> GSM110451 2 0.925 0.13402 0.340 0.660
#> GSM110391 1 0.992 0.44010 0.552 0.448
#> GSM110439 2 0.925 0.13402 0.340 0.660
#> GSM110442 1 0.995 0.42403 0.540 0.460
#> GSM110443 2 0.925 0.13402 0.340 0.660
#> GSM110447 2 0.985 0.00103 0.428 0.572
#> GSM110448 1 0.881 0.20484 0.700 0.300
#> GSM110450 2 0.855 0.15507 0.280 0.720
#> GSM110452 2 0.925 0.13402 0.340 0.660
#> GSM110453 2 0.925 0.13402 0.340 0.660
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 3 0.0000 0.817 0.000 0.000 1.000
#> GSM110396 1 0.8231 0.668 0.636 0.156 0.208
#> GSM110397 1 0.1031 0.625 0.976 0.024 0.000
#> GSM110398 1 0.7656 0.648 0.572 0.052 0.376
#> GSM110399 3 0.0000 0.817 0.000 0.000 1.000
#> GSM110400 3 0.0000 0.817 0.000 0.000 1.000
#> GSM110401 1 0.6553 0.737 0.656 0.020 0.324
#> GSM110406 3 0.0000 0.817 0.000 0.000 1.000
#> GSM110407 1 0.6026 0.701 0.624 0.000 0.376
#> GSM110409 1 0.5882 0.725 0.652 0.000 0.348
#> GSM110410 3 0.1031 0.804 0.024 0.000 0.976
#> GSM110413 2 0.7145 0.266 0.024 0.536 0.440
#> GSM110414 3 0.1031 0.804 0.024 0.000 0.976
#> GSM110415 3 0.7190 0.560 0.320 0.044 0.636
#> GSM110416 3 0.7190 0.560 0.320 0.044 0.636
#> GSM110418 3 0.7214 0.556 0.324 0.044 0.632
#> GSM110419 3 0.0000 0.817 0.000 0.000 1.000
#> GSM110420 3 0.7284 0.542 0.336 0.044 0.620
#> GSM110421 2 0.1643 0.883 0.000 0.956 0.044
#> GSM110423 3 0.6699 0.615 0.256 0.044 0.700
#> GSM110424 3 0.2663 0.770 0.024 0.044 0.932
#> GSM110425 3 0.0000 0.817 0.000 0.000 1.000
#> GSM110427 3 0.0000 0.817 0.000 0.000 1.000
#> GSM110428 3 0.0424 0.813 0.000 0.008 0.992
#> GSM110430 1 0.5859 0.727 0.656 0.000 0.344
#> GSM110431 1 0.1643 0.651 0.956 0.000 0.044
#> GSM110432 3 0.0000 0.817 0.000 0.000 1.000
#> GSM110434 3 0.0000 0.817 0.000 0.000 1.000
#> GSM110435 1 0.6585 0.395 0.712 0.044 0.244
#> GSM110437 1 0.1031 0.646 0.976 0.000 0.024
#> GSM110438 3 0.7284 0.542 0.336 0.044 0.620
#> GSM110388 2 0.1643 0.862 0.044 0.956 0.000
#> GSM110392 3 0.8690 0.436 0.132 0.308 0.560
#> GSM110394 3 0.7657 -0.166 0.448 0.044 0.508
#> GSM110402 3 0.6962 0.571 0.316 0.036 0.648
#> GSM110411 2 0.1919 0.877 0.020 0.956 0.024
#> GSM110412 2 0.1643 0.883 0.000 0.956 0.044
#> GSM110417 2 0.1643 0.862 0.044 0.956 0.000
#> GSM110422 3 0.0000 0.817 0.000 0.000 1.000
#> GSM110426 2 0.0747 0.846 0.016 0.984 0.000
#> GSM110429 3 0.0000 0.817 0.000 0.000 1.000
#> GSM110433 2 0.1643 0.883 0.000 0.956 0.044
#> GSM110436 3 0.0000 0.817 0.000 0.000 1.000
#> GSM110440 1 0.1529 0.650 0.960 0.000 0.040
#> GSM110441 2 0.6994 0.403 0.028 0.612 0.360
#> GSM110444 2 0.1643 0.883 0.000 0.956 0.044
#> GSM110445 1 0.6501 0.721 0.664 0.020 0.316
#> GSM110446 3 0.7284 0.542 0.336 0.044 0.620
#> GSM110449 2 0.2903 0.868 0.028 0.924 0.048
#> GSM110451 3 0.0000 0.817 0.000 0.000 1.000
#> GSM110391 2 0.1643 0.883 0.000 0.956 0.044
#> GSM110439 3 0.1163 0.801 0.028 0.000 0.972
#> GSM110442 3 0.2050 0.788 0.028 0.020 0.952
#> GSM110443 3 0.0237 0.815 0.004 0.000 0.996
#> GSM110447 3 0.4842 0.669 0.224 0.000 0.776
#> GSM110448 2 0.1643 0.862 0.044 0.956 0.000
#> GSM110450 1 0.7590 0.725 0.652 0.080 0.268
#> GSM110452 3 0.0000 0.817 0.000 0.000 1.000
#> GSM110453 3 0.1031 0.804 0.024 0.000 0.976
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.0188 0.931 0.000 0.996 0.004 0.000
#> GSM110396 1 0.3508 0.867 0.848 0.136 0.004 0.012
#> GSM110397 1 0.3726 0.737 0.788 0.000 0.212 0.000
#> GSM110398 1 0.4692 0.722 0.816 0.112 0.036 0.036
#> GSM110399 2 0.0188 0.930 0.004 0.996 0.000 0.000
#> GSM110400 2 0.0188 0.931 0.000 0.996 0.004 0.000
#> GSM110401 1 0.2530 0.876 0.888 0.112 0.000 0.000
#> GSM110406 2 0.0188 0.931 0.000 0.996 0.004 0.000
#> GSM110407 1 0.3831 0.819 0.792 0.204 0.004 0.000
#> GSM110409 1 0.3311 0.849 0.828 0.172 0.000 0.000
#> GSM110410 2 0.3616 0.854 0.112 0.852 0.036 0.000
#> GSM110413 4 0.7022 0.584 0.100 0.216 0.040 0.644
#> GSM110414 2 0.2722 0.889 0.064 0.904 0.032 0.000
#> GSM110415 3 0.2081 0.811 0.000 0.084 0.916 0.000
#> GSM110416 3 0.1118 0.837 0.000 0.036 0.964 0.000
#> GSM110418 3 0.1118 0.837 0.000 0.036 0.964 0.000
#> GSM110419 2 0.0188 0.931 0.000 0.996 0.004 0.000
#> GSM110420 3 0.1118 0.837 0.000 0.036 0.964 0.000
#> GSM110421 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM110423 3 0.1389 0.833 0.000 0.048 0.952 0.000
#> GSM110424 2 0.5669 0.774 0.100 0.764 0.036 0.100
#> GSM110425 2 0.0188 0.931 0.000 0.996 0.004 0.000
#> GSM110427 2 0.0188 0.931 0.000 0.996 0.004 0.000
#> GSM110428 2 0.0188 0.931 0.000 0.996 0.004 0.000
#> GSM110430 1 0.2530 0.876 0.888 0.112 0.000 0.000
#> GSM110431 3 0.5673 0.251 0.372 0.032 0.596 0.000
#> GSM110432 2 0.0188 0.931 0.000 0.996 0.004 0.000
#> GSM110434 2 0.0592 0.927 0.016 0.984 0.000 0.000
#> GSM110435 3 0.1118 0.837 0.000 0.036 0.964 0.000
#> GSM110437 1 0.2530 0.819 0.888 0.000 0.112 0.000
#> GSM110438 3 0.1118 0.837 0.000 0.036 0.964 0.000
#> GSM110388 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM110392 3 0.4188 0.639 0.000 0.004 0.752 0.244
#> GSM110394 3 0.4072 0.649 0.000 0.252 0.748 0.000
#> GSM110402 3 0.4304 0.588 0.000 0.284 0.716 0.000
#> GSM110411 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM110412 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM110417 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM110422 2 0.0376 0.931 0.004 0.992 0.004 0.000
#> GSM110426 3 0.4916 0.301 0.000 0.000 0.576 0.424
#> GSM110429 2 0.0188 0.930 0.004 0.996 0.000 0.000
#> GSM110433 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM110436 2 0.0188 0.931 0.000 0.996 0.004 0.000
#> GSM110440 1 0.3441 0.819 0.856 0.024 0.120 0.000
#> GSM110441 4 0.5292 0.771 0.120 0.060 0.036 0.784
#> GSM110444 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM110445 1 0.0000 0.821 1.000 0.000 0.000 0.000
#> GSM110446 3 0.1118 0.837 0.000 0.036 0.964 0.000
#> GSM110449 4 0.4057 0.820 0.120 0.008 0.036 0.836
#> GSM110451 2 0.0188 0.931 0.000 0.996 0.004 0.000
#> GSM110391 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM110439 2 0.3731 0.849 0.120 0.844 0.036 0.000
#> GSM110442 2 0.3731 0.849 0.120 0.844 0.036 0.000
#> GSM110443 2 0.0469 0.928 0.012 0.988 0.000 0.000
#> GSM110447 2 0.4661 0.451 0.000 0.652 0.348 0.000
#> GSM110448 4 0.0000 0.927 0.000 0.000 0.000 1.000
#> GSM110450 1 0.2714 0.876 0.884 0.112 0.000 0.004
#> GSM110452 2 0.1452 0.916 0.036 0.956 0.008 0.000
#> GSM110453 2 0.3616 0.854 0.112 0.852 0.036 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000
#> GSM110396 1 0.1628 0.900 0.936 0.056 0.000 0.008 0.000
#> GSM110397 1 0.3508 0.678 0.748 0.000 0.252 0.000 0.000
#> GSM110398 5 0.0000 0.849 0.000 0.000 0.000 0.000 1.000
#> GSM110399 2 0.0290 0.958 0.000 0.992 0.000 0.000 0.008
#> GSM110400 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000
#> GSM110401 1 0.0000 0.922 1.000 0.000 0.000 0.000 0.000
#> GSM110406 2 0.0162 0.958 0.000 0.996 0.000 0.000 0.004
#> GSM110407 1 0.2179 0.858 0.888 0.112 0.000 0.000 0.000
#> GSM110409 1 0.2471 0.822 0.864 0.136 0.000 0.000 0.000
#> GSM110410 5 0.0162 0.849 0.000 0.004 0.000 0.000 0.996
#> GSM110413 5 0.0609 0.842 0.000 0.020 0.000 0.000 0.980
#> GSM110414 2 0.2280 0.841 0.000 0.880 0.000 0.000 0.120
#> GSM110415 3 0.1851 0.795 0.000 0.088 0.912 0.000 0.000
#> GSM110416 3 0.0000 0.839 0.000 0.000 1.000 0.000 0.000
#> GSM110418 3 0.0000 0.839 0.000 0.000 1.000 0.000 0.000
#> GSM110419 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000
#> GSM110420 3 0.0000 0.839 0.000 0.000 1.000 0.000 0.000
#> GSM110421 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM110423 3 0.0000 0.839 0.000 0.000 1.000 0.000 0.000
#> GSM110424 5 0.0771 0.842 0.000 0.004 0.000 0.020 0.976
#> GSM110425 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000
#> GSM110427 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000
#> GSM110428 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000
#> GSM110430 1 0.0000 0.922 1.000 0.000 0.000 0.000 0.000
#> GSM110431 3 0.4088 0.299 0.368 0.000 0.632 0.000 0.000
#> GSM110432 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000
#> GSM110434 2 0.0703 0.947 0.000 0.976 0.000 0.000 0.024
#> GSM110435 3 0.0000 0.839 0.000 0.000 1.000 0.000 0.000
#> GSM110437 1 0.0000 0.922 1.000 0.000 0.000 0.000 0.000
#> GSM110438 3 0.0000 0.839 0.000 0.000 1.000 0.000 0.000
#> GSM110388 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM110392 3 0.3700 0.618 0.000 0.008 0.752 0.240 0.000
#> GSM110394 3 0.3534 0.643 0.000 0.256 0.744 0.000 0.000
#> GSM110402 3 0.3480 0.618 0.000 0.248 0.752 0.000 0.000
#> GSM110411 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM110412 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM110417 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM110422 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000
#> GSM110426 3 0.4235 0.253 0.000 0.000 0.576 0.424 0.000
#> GSM110429 2 0.0290 0.958 0.000 0.992 0.000 0.000 0.008
#> GSM110433 5 0.4045 0.427 0.000 0.000 0.000 0.356 0.644
#> GSM110436 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000
#> GSM110440 1 0.1410 0.895 0.940 0.000 0.060 0.000 0.000
#> GSM110441 5 0.0000 0.849 0.000 0.000 0.000 0.000 1.000
#> GSM110444 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM110445 1 0.0000 0.922 1.000 0.000 0.000 0.000 0.000
#> GSM110446 3 0.0000 0.839 0.000 0.000 1.000 0.000 0.000
#> GSM110449 5 0.0162 0.848 0.000 0.000 0.000 0.004 0.996
#> GSM110451 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000
#> GSM110391 5 0.4262 0.228 0.000 0.000 0.000 0.440 0.560
#> GSM110439 5 0.0162 0.849 0.000 0.004 0.000 0.000 0.996
#> GSM110442 5 0.3983 0.430 0.000 0.340 0.000 0.000 0.660
#> GSM110443 2 0.0290 0.958 0.000 0.992 0.000 0.000 0.008
#> GSM110447 2 0.4171 0.332 0.000 0.604 0.396 0.000 0.000
#> GSM110448 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM110450 1 0.0000 0.922 1.000 0.000 0.000 0.000 0.000
#> GSM110452 2 0.1270 0.924 0.000 0.948 0.000 0.000 0.052
#> GSM110453 5 0.1851 0.791 0.000 0.088 0.000 0.000 0.912
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110396 6 0.3627 0.815 0.136 0.056 0.000 0.008 0.000 0.800
#> GSM110397 1 0.3151 0.624 0.748 0.000 0.252 0.000 0.000 0.000
#> GSM110398 5 0.2219 0.786 0.000 0.000 0.000 0.000 0.864 0.136
#> GSM110399 2 0.0935 0.925 0.000 0.964 0.000 0.000 0.004 0.032
#> GSM110400 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110401 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110406 2 0.0146 0.936 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM110407 6 0.3435 0.815 0.136 0.060 0.000 0.000 0.000 0.804
#> GSM110409 1 0.4745 0.528 0.644 0.088 0.000 0.000 0.000 0.268
#> GSM110410 5 0.0692 0.811 0.000 0.004 0.000 0.000 0.976 0.020
#> GSM110413 5 0.1605 0.806 0.000 0.016 0.000 0.012 0.940 0.032
#> GSM110414 2 0.2398 0.855 0.000 0.876 0.000 0.000 0.104 0.020
#> GSM110415 3 0.1806 0.778 0.000 0.088 0.908 0.000 0.000 0.004
#> GSM110416 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110418 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110419 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110420 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110421 4 0.0632 0.975 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM110423 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110424 5 0.1485 0.807 0.000 0.004 0.000 0.028 0.944 0.024
#> GSM110425 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110427 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110428 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110430 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110431 6 0.2762 0.783 0.000 0.000 0.196 0.000 0.000 0.804
#> GSM110432 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110434 2 0.2923 0.847 0.000 0.848 0.000 0.000 0.052 0.100
#> GSM110435 6 0.2793 0.780 0.000 0.000 0.200 0.000 0.000 0.800
#> GSM110437 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110438 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110388 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110392 3 0.3323 0.630 0.000 0.008 0.752 0.240 0.000 0.000
#> GSM110394 6 0.2762 0.724 0.000 0.196 0.000 0.000 0.000 0.804
#> GSM110402 3 0.3126 0.547 0.000 0.248 0.752 0.000 0.000 0.000
#> GSM110411 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110412 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110417 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110422 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110426 3 0.3804 0.262 0.000 0.000 0.576 0.424 0.000 0.000
#> GSM110429 2 0.1285 0.915 0.000 0.944 0.000 0.000 0.004 0.052
#> GSM110433 5 0.4234 0.500 0.000 0.000 0.000 0.324 0.644 0.032
#> GSM110436 2 0.0146 0.937 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM110440 6 0.3356 0.807 0.140 0.000 0.052 0.000 0.000 0.808
#> GSM110441 5 0.0632 0.810 0.000 0.000 0.000 0.000 0.976 0.024
#> GSM110444 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110445 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110446 3 0.0000 0.846 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110449 5 0.1152 0.808 0.000 0.000 0.000 0.004 0.952 0.044
#> GSM110451 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM110391 5 0.4468 0.321 0.000 0.000 0.000 0.408 0.560 0.032
#> GSM110439 5 0.1531 0.804 0.000 0.004 0.000 0.000 0.928 0.068
#> GSM110442 5 0.4224 0.382 0.000 0.340 0.000 0.000 0.632 0.028
#> GSM110443 2 0.1219 0.918 0.000 0.948 0.000 0.000 0.004 0.048
#> GSM110447 2 0.3872 0.378 0.000 0.604 0.392 0.000 0.000 0.004
#> GSM110448 4 0.0000 0.996 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110450 1 0.0000 0.885 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110452 2 0.3394 0.809 0.000 0.804 0.000 0.000 0.052 0.144
#> GSM110453 5 0.3423 0.739 0.000 0.088 0.000 0.000 0.812 0.100
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) specimen(p) k
#> MAD:pam 0 NA NA 2
#> MAD:pam 54 0.00286 0.677 3
#> MAD:pam 56 0.03049 0.332 4
#> MAD:pam 53 0.15548 0.562 5
#> MAD:pam 55 0.19700 0.669 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 17209 rows and 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.219 0.678 0.769 0.4566 0.544 0.544
#> 3 3 0.384 0.610 0.769 0.3442 0.821 0.685
#> 4 4 0.527 0.637 0.807 0.1668 0.679 0.370
#> 5 5 0.829 0.817 0.901 0.0874 0.883 0.625
#> 6 6 0.788 0.716 0.816 0.0606 0.944 0.745
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM110395 2 0.2043 0.729 0.032 0.968
#> GSM110396 2 0.7950 0.673 0.240 0.760
#> GSM110397 1 0.7453 0.715 0.788 0.212
#> GSM110398 2 0.1843 0.726 0.028 0.972
#> GSM110399 2 0.0000 0.721 0.000 1.000
#> GSM110400 2 0.5408 0.722 0.124 0.876
#> GSM110401 2 0.7950 0.673 0.240 0.760
#> GSM110406 2 0.0672 0.724 0.008 0.992
#> GSM110407 2 0.9775 0.618 0.412 0.588
#> GSM110409 2 0.7950 0.673 0.240 0.760
#> GSM110410 1 0.9983 0.707 0.524 0.476
#> GSM110413 2 0.2603 0.673 0.044 0.956
#> GSM110414 1 0.9815 0.730 0.580 0.420
#> GSM110415 1 0.8763 0.648 0.704 0.296
#> GSM110416 1 0.5178 0.462 0.884 0.116
#> GSM110418 1 0.4022 0.512 0.920 0.080
#> GSM110419 2 0.8499 0.670 0.276 0.724
#> GSM110420 1 0.4022 0.512 0.920 0.080
#> GSM110421 1 0.9909 0.732 0.556 0.444
#> GSM110423 2 0.9608 0.514 0.384 0.616
#> GSM110424 1 0.9922 0.731 0.552 0.448
#> GSM110425 2 0.8955 0.628 0.312 0.688
#> GSM110427 2 0.1414 0.725 0.020 0.980
#> GSM110428 2 0.9909 0.605 0.444 0.556
#> GSM110430 2 0.7950 0.673 0.240 0.760
#> GSM110431 2 0.9909 0.605 0.444 0.556
#> GSM110432 2 0.8144 0.671 0.252 0.748
#> GSM110434 2 0.0000 0.721 0.000 1.000
#> GSM110435 2 0.9909 0.605 0.444 0.556
#> GSM110437 2 0.7950 0.673 0.240 0.760
#> GSM110438 2 0.9909 0.605 0.444 0.556
#> GSM110388 1 0.7815 0.727 0.768 0.232
#> GSM110392 1 0.9795 0.738 0.584 0.416
#> GSM110394 2 0.9909 0.605 0.444 0.556
#> GSM110402 2 0.8267 0.670 0.260 0.740
#> GSM110411 1 0.7815 0.727 0.768 0.232
#> GSM110412 1 0.9795 0.743 0.584 0.416
#> GSM110417 1 0.7299 0.718 0.796 0.204
#> GSM110422 2 0.1414 0.725 0.020 0.980
#> GSM110426 1 0.7299 0.718 0.796 0.204
#> GSM110429 2 0.2603 0.731 0.044 0.956
#> GSM110433 1 0.9909 0.732 0.556 0.444
#> GSM110436 2 0.3114 0.732 0.056 0.944
#> GSM110440 2 0.9635 0.630 0.388 0.612
#> GSM110441 2 0.2603 0.673 0.044 0.956
#> GSM110444 1 0.9795 0.743 0.584 0.416
#> GSM110445 2 0.7453 0.672 0.212 0.788
#> GSM110446 2 0.9909 0.605 0.444 0.556
#> GSM110449 2 0.2778 0.668 0.048 0.952
#> GSM110451 2 0.6148 0.714 0.152 0.848
#> GSM110391 1 0.9909 0.732 0.556 0.444
#> GSM110439 2 0.0000 0.721 0.000 1.000
#> GSM110442 2 0.0376 0.718 0.004 0.996
#> GSM110443 2 0.1414 0.725 0.020 0.980
#> GSM110447 1 0.9286 0.639 0.656 0.344
#> GSM110448 1 0.7674 0.725 0.776 0.224
#> GSM110450 2 0.8016 0.673 0.244 0.756
#> GSM110452 2 0.0000 0.721 0.000 1.000
#> GSM110453 2 0.0000 0.721 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.6405 0.6230 0.172 0.756 0.072
#> GSM110396 2 0.1129 0.5897 0.004 0.976 0.020
#> GSM110397 1 0.6738 0.5146 0.624 0.356 0.020
#> GSM110398 2 0.8734 0.6408 0.168 0.584 0.248
#> GSM110399 2 0.8748 0.6441 0.172 0.584 0.244
#> GSM110400 3 0.6452 0.7853 0.036 0.252 0.712
#> GSM110401 2 0.0237 0.5932 0.000 0.996 0.004
#> GSM110406 2 0.8683 0.6505 0.172 0.592 0.236
#> GSM110407 2 0.1647 0.5907 0.004 0.960 0.036
#> GSM110409 2 0.0892 0.5933 0.000 0.980 0.020
#> GSM110410 3 0.4784 0.2584 0.200 0.004 0.796
#> GSM110413 2 0.8976 0.6427 0.172 0.552 0.276
#> GSM110414 1 0.5948 0.4302 0.640 0.000 0.360
#> GSM110415 3 0.9151 0.5208 0.292 0.180 0.528
#> GSM110416 3 0.5541 0.8076 0.008 0.252 0.740
#> GSM110418 3 0.5659 0.8074 0.012 0.248 0.740
#> GSM110419 2 0.5591 0.3922 0.000 0.696 0.304
#> GSM110420 3 0.5541 0.8076 0.008 0.252 0.740
#> GSM110421 1 0.4235 0.6736 0.824 0.000 0.176
#> GSM110423 3 0.5365 0.8063 0.004 0.252 0.744
#> GSM110424 3 0.5882 -0.0146 0.348 0.000 0.652
#> GSM110425 3 0.5138 0.8039 0.000 0.252 0.748
#> GSM110427 2 0.9153 0.6230 0.172 0.520 0.308
#> GSM110428 2 0.5560 0.3998 0.000 0.700 0.300
#> GSM110430 2 0.0237 0.5932 0.000 0.996 0.004
#> GSM110431 2 0.4842 0.4595 0.000 0.776 0.224
#> GSM110432 2 0.6264 0.4585 0.028 0.716 0.256
#> GSM110434 2 0.8748 0.6488 0.172 0.584 0.244
#> GSM110435 2 0.5363 0.4306 0.000 0.724 0.276
#> GSM110437 2 0.0237 0.5932 0.000 0.996 0.004
#> GSM110438 2 0.5706 0.3391 0.000 0.680 0.320
#> GSM110388 1 0.4178 0.7470 0.828 0.172 0.000
#> GSM110392 3 0.6372 0.7422 0.084 0.152 0.764
#> GSM110394 2 0.5098 0.4561 0.000 0.752 0.248
#> GSM110402 3 0.5138 0.8039 0.000 0.252 0.748
#> GSM110411 1 0.4178 0.7470 0.828 0.172 0.000
#> GSM110412 1 0.0237 0.7373 0.996 0.000 0.004
#> GSM110417 1 0.4178 0.7470 0.828 0.172 0.000
#> GSM110422 2 0.9025 0.6346 0.172 0.544 0.284
#> GSM110426 1 0.4654 0.7217 0.792 0.208 0.000
#> GSM110429 2 0.9048 0.6321 0.172 0.540 0.288
#> GSM110433 1 0.4750 0.6434 0.784 0.000 0.216
#> GSM110436 2 0.8334 0.4213 0.136 0.616 0.248
#> GSM110440 2 0.4808 0.3945 0.008 0.804 0.188
#> GSM110441 2 0.8976 0.6427 0.172 0.552 0.276
#> GSM110444 1 0.0237 0.7373 0.996 0.000 0.004
#> GSM110445 2 0.5016 0.6042 0.000 0.760 0.240
#> GSM110446 3 0.6062 0.6181 0.000 0.384 0.616
#> GSM110449 2 0.8883 0.6434 0.176 0.568 0.256
#> GSM110451 2 0.7333 0.5567 0.136 0.708 0.156
#> GSM110391 1 0.4452 0.6629 0.808 0.000 0.192
#> GSM110439 2 0.8868 0.6454 0.172 0.568 0.260
#> GSM110442 2 0.8976 0.6438 0.172 0.552 0.276
#> GSM110443 2 0.8171 0.6669 0.172 0.644 0.184
#> GSM110447 3 0.6511 0.7714 0.072 0.180 0.748
#> GSM110448 1 0.4178 0.7470 0.828 0.172 0.000
#> GSM110450 2 0.1031 0.5891 0.000 0.976 0.024
#> GSM110452 2 0.8748 0.6484 0.172 0.584 0.244
#> GSM110453 2 0.8386 0.6643 0.172 0.624 0.204
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.3831 0.522 0.004 0.792 0.204 0.000
#> GSM110396 1 0.1792 0.728 0.932 0.068 0.000 0.000
#> GSM110397 1 0.4769 0.395 0.684 0.000 0.008 0.308
#> GSM110398 2 0.4356 0.651 0.292 0.708 0.000 0.000
#> GSM110399 2 0.4040 0.680 0.248 0.752 0.000 0.000
#> GSM110400 3 0.4040 0.719 0.000 0.248 0.752 0.000
#> GSM110401 1 0.0000 0.724 1.000 0.000 0.000 0.000
#> GSM110406 2 0.4040 0.684 0.248 0.752 0.000 0.000
#> GSM110407 1 0.3486 0.655 0.812 0.000 0.188 0.000
#> GSM110409 1 0.0592 0.726 0.984 0.000 0.016 0.000
#> GSM110410 2 0.4121 0.665 0.000 0.796 0.184 0.020
#> GSM110413 2 0.2011 0.731 0.080 0.920 0.000 0.000
#> GSM110414 2 0.6729 0.367 0.012 0.492 0.436 0.060
#> GSM110415 3 0.1411 0.782 0.020 0.000 0.960 0.020
#> GSM110416 3 0.0336 0.804 0.000 0.008 0.992 0.000
#> GSM110418 3 0.0336 0.804 0.000 0.008 0.992 0.000
#> GSM110419 3 0.4483 0.694 0.004 0.284 0.712 0.000
#> GSM110420 3 0.0336 0.804 0.000 0.008 0.992 0.000
#> GSM110421 2 0.5466 0.253 0.000 0.548 0.016 0.436
#> GSM110423 3 0.0336 0.804 0.000 0.008 0.992 0.000
#> GSM110424 2 0.6123 0.574 0.000 0.676 0.192 0.132
#> GSM110425 3 0.0336 0.804 0.000 0.008 0.992 0.000
#> GSM110427 2 0.0921 0.714 0.000 0.972 0.028 0.000
#> GSM110428 3 0.4621 0.691 0.008 0.284 0.708 0.000
#> GSM110430 1 0.0000 0.724 1.000 0.000 0.000 0.000
#> GSM110431 1 0.7503 0.431 0.496 0.276 0.228 0.000
#> GSM110432 2 0.4950 0.127 0.004 0.620 0.376 0.000
#> GSM110434 2 0.4054 0.716 0.188 0.796 0.016 0.000
#> GSM110435 1 0.7676 0.359 0.460 0.276 0.264 0.000
#> GSM110437 1 0.0000 0.724 1.000 0.000 0.000 0.000
#> GSM110438 3 0.6444 0.636 0.104 0.284 0.612 0.000
#> GSM110388 4 0.0000 0.877 0.000 0.000 0.000 1.000
#> GSM110392 3 0.6374 0.584 0.052 0.128 0.720 0.100
#> GSM110394 1 0.7547 0.418 0.488 0.276 0.236 0.000
#> GSM110402 3 0.3942 0.734 0.000 0.236 0.764 0.000
#> GSM110411 4 0.0000 0.877 0.000 0.000 0.000 1.000
#> GSM110412 4 0.5510 -0.222 0.000 0.480 0.016 0.504
#> GSM110417 4 0.0000 0.877 0.000 0.000 0.000 1.000
#> GSM110422 2 0.1004 0.714 0.004 0.972 0.024 0.000
#> GSM110426 4 0.1209 0.848 0.032 0.000 0.004 0.964
#> GSM110429 2 0.1209 0.711 0.004 0.964 0.032 0.000
#> GSM110433 2 0.5069 0.465 0.000 0.664 0.016 0.320
#> GSM110436 2 0.4605 0.291 0.000 0.664 0.336 0.000
#> GSM110440 1 0.6971 0.509 0.568 0.276 0.156 0.000
#> GSM110441 2 0.1637 0.731 0.060 0.940 0.000 0.000
#> GSM110444 4 0.0000 0.877 0.000 0.000 0.000 1.000
#> GSM110445 1 0.0707 0.718 0.980 0.020 0.000 0.000
#> GSM110446 3 0.6262 0.652 0.092 0.280 0.628 0.000
#> GSM110449 2 0.3972 0.705 0.204 0.788 0.008 0.000
#> GSM110451 2 0.4741 0.277 0.004 0.668 0.328 0.000
#> GSM110391 2 0.5427 0.299 0.000 0.568 0.016 0.416
#> GSM110439 2 0.0469 0.724 0.012 0.988 0.000 0.000
#> GSM110442 2 0.0921 0.728 0.028 0.972 0.000 0.000
#> GSM110443 2 0.4193 0.669 0.268 0.732 0.000 0.000
#> GSM110447 3 0.1042 0.794 0.020 0.008 0.972 0.000
#> GSM110448 4 0.0000 0.877 0.000 0.000 0.000 1.000
#> GSM110450 1 0.3219 0.702 0.836 0.164 0.000 0.000
#> GSM110452 2 0.2973 0.725 0.144 0.856 0.000 0.000
#> GSM110453 2 0.4012 0.716 0.184 0.800 0.016 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.3196 0.773 0.004 0.804 0.192 0.000 0.000
#> GSM110396 1 0.1124 0.776 0.960 0.036 0.000 0.004 0.000
#> GSM110397 4 0.3496 0.753 0.200 0.000 0.012 0.788 0.000
#> GSM110398 2 0.2011 0.845 0.088 0.908 0.000 0.004 0.000
#> GSM110399 2 0.0324 0.890 0.004 0.992 0.000 0.004 0.000
#> GSM110400 3 0.1547 0.864 0.004 0.032 0.948 0.000 0.016
#> GSM110401 1 0.0162 0.778 0.996 0.004 0.000 0.000 0.000
#> GSM110406 2 0.0451 0.888 0.008 0.988 0.000 0.004 0.000
#> GSM110407 1 0.2929 0.732 0.840 0.008 0.152 0.000 0.000
#> GSM110409 1 0.0609 0.778 0.980 0.020 0.000 0.000 0.000
#> GSM110410 5 0.1117 0.951 0.000 0.020 0.016 0.000 0.964
#> GSM110413 2 0.2011 0.842 0.004 0.908 0.000 0.000 0.088
#> GSM110414 5 0.0566 0.956 0.004 0.000 0.012 0.000 0.984
#> GSM110415 3 0.1124 0.896 0.004 0.000 0.960 0.000 0.036
#> GSM110416 3 0.0880 0.898 0.000 0.000 0.968 0.000 0.032
#> GSM110418 3 0.0880 0.898 0.000 0.000 0.968 0.000 0.032
#> GSM110419 2 0.4973 0.190 0.020 0.496 0.480 0.004 0.000
#> GSM110420 3 0.0880 0.898 0.000 0.000 0.968 0.000 0.032
#> GSM110421 5 0.0880 0.974 0.000 0.000 0.000 0.032 0.968
#> GSM110423 3 0.0880 0.898 0.000 0.000 0.968 0.000 0.032
#> GSM110424 5 0.0693 0.968 0.000 0.000 0.008 0.012 0.980
#> GSM110425 3 0.0880 0.898 0.000 0.000 0.968 0.000 0.032
#> GSM110427 2 0.1124 0.881 0.004 0.960 0.036 0.000 0.000
#> GSM110428 1 0.4689 0.554 0.592 0.008 0.392 0.008 0.000
#> GSM110430 1 0.0162 0.778 0.996 0.004 0.000 0.000 0.000
#> GSM110431 1 0.4679 0.560 0.596 0.008 0.388 0.008 0.000
#> GSM110432 2 0.3826 0.720 0.004 0.752 0.236 0.008 0.000
#> GSM110434 2 0.0324 0.890 0.004 0.992 0.000 0.004 0.000
#> GSM110435 1 0.4709 0.541 0.584 0.008 0.400 0.008 0.000
#> GSM110437 1 0.0162 0.778 0.996 0.004 0.000 0.000 0.000
#> GSM110438 3 0.4416 0.492 0.316 0.008 0.668 0.008 0.000
#> GSM110388 4 0.0290 0.960 0.000 0.000 0.000 0.992 0.008
#> GSM110392 3 0.5020 0.705 0.140 0.044 0.764 0.024 0.028
#> GSM110394 1 0.4620 0.583 0.616 0.008 0.368 0.008 0.000
#> GSM110402 3 0.0324 0.872 0.004 0.004 0.992 0.000 0.000
#> GSM110411 4 0.0290 0.960 0.000 0.000 0.000 0.992 0.008
#> GSM110412 5 0.1205 0.971 0.000 0.000 0.004 0.040 0.956
#> GSM110417 4 0.0290 0.960 0.000 0.000 0.000 0.992 0.008
#> GSM110422 2 0.1124 0.881 0.004 0.960 0.036 0.000 0.000
#> GSM110426 4 0.0451 0.957 0.000 0.000 0.004 0.988 0.008
#> GSM110429 2 0.1124 0.881 0.004 0.960 0.036 0.000 0.000
#> GSM110433 5 0.0880 0.974 0.000 0.000 0.000 0.032 0.968
#> GSM110436 2 0.4331 0.448 0.004 0.596 0.400 0.000 0.000
#> GSM110440 1 0.4434 0.577 0.640 0.008 0.348 0.004 0.000
#> GSM110441 2 0.0162 0.890 0.004 0.996 0.000 0.000 0.000
#> GSM110444 4 0.0290 0.960 0.000 0.000 0.000 0.992 0.008
#> GSM110445 1 0.0963 0.770 0.964 0.036 0.000 0.000 0.000
#> GSM110446 3 0.4057 0.626 0.252 0.008 0.732 0.008 0.000
#> GSM110449 2 0.0162 0.890 0.004 0.996 0.000 0.000 0.000
#> GSM110451 2 0.3797 0.725 0.004 0.756 0.232 0.008 0.000
#> GSM110391 5 0.0880 0.974 0.000 0.000 0.000 0.032 0.968
#> GSM110439 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM110442 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM110443 2 0.0324 0.890 0.004 0.992 0.000 0.004 0.000
#> GSM110447 3 0.1041 0.897 0.004 0.000 0.964 0.000 0.032
#> GSM110448 4 0.0290 0.960 0.000 0.000 0.000 0.992 0.008
#> GSM110450 1 0.1205 0.775 0.956 0.040 0.000 0.004 0.000
#> GSM110452 2 0.0162 0.890 0.004 0.996 0.000 0.000 0.000
#> GSM110453 2 0.0324 0.890 0.004 0.992 0.004 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.3348 0.723 0.000 0.768 0.016 0.000 0.000 0.216
#> GSM110396 1 0.1663 0.776 0.912 0.088 0.000 0.000 0.000 0.000
#> GSM110397 4 0.3499 0.739 0.196 0.008 0.012 0.780 0.000 0.004
#> GSM110398 6 0.2362 0.516 0.136 0.004 0.000 0.000 0.000 0.860
#> GSM110399 6 0.3136 0.655 0.004 0.228 0.000 0.000 0.000 0.768
#> GSM110400 3 0.4155 0.415 0.000 0.364 0.616 0.000 0.000 0.020
#> GSM110401 1 0.0405 0.773 0.988 0.008 0.000 0.000 0.000 0.004
#> GSM110406 6 0.3512 0.639 0.008 0.272 0.000 0.000 0.000 0.720
#> GSM110407 1 0.0937 0.775 0.960 0.000 0.040 0.000 0.000 0.000
#> GSM110409 1 0.0000 0.774 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110410 5 0.0767 0.979 0.000 0.004 0.012 0.000 0.976 0.008
#> GSM110413 6 0.2632 0.452 0.000 0.004 0.000 0.000 0.164 0.832
#> GSM110414 5 0.1536 0.950 0.000 0.016 0.040 0.004 0.940 0.000
#> GSM110415 3 0.1549 0.805 0.000 0.020 0.936 0.000 0.044 0.000
#> GSM110416 3 0.0000 0.825 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110418 3 0.0000 0.825 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110419 2 0.3797 -0.175 0.000 0.580 0.420 0.000 0.000 0.000
#> GSM110420 3 0.0000 0.825 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110421 5 0.0000 0.982 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM110423 3 0.0547 0.825 0.000 0.020 0.980 0.000 0.000 0.000
#> GSM110424 5 0.0508 0.981 0.000 0.000 0.012 0.000 0.984 0.004
#> GSM110425 3 0.0547 0.825 0.000 0.020 0.980 0.000 0.000 0.000
#> GSM110427 2 0.2964 0.738 0.000 0.792 0.004 0.000 0.000 0.204
#> GSM110428 1 0.5781 0.574 0.504 0.232 0.264 0.000 0.000 0.000
#> GSM110430 1 0.0405 0.773 0.988 0.008 0.000 0.000 0.000 0.004
#> GSM110431 1 0.5614 0.610 0.540 0.204 0.256 0.000 0.000 0.000
#> GSM110432 2 0.3352 0.741 0.000 0.792 0.032 0.000 0.000 0.176
#> GSM110434 6 0.4056 0.545 0.004 0.416 0.000 0.000 0.004 0.576
#> GSM110435 1 0.5327 0.661 0.596 0.208 0.196 0.000 0.000 0.000
#> GSM110437 1 0.0520 0.772 0.984 0.008 0.000 0.000 0.000 0.008
#> GSM110438 3 0.5817 0.208 0.312 0.208 0.480 0.000 0.000 0.000
#> GSM110388 4 0.0000 0.959 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110392 3 0.4427 0.685 0.152 0.012 0.768 0.036 0.020 0.012
#> GSM110394 1 0.5601 0.618 0.544 0.208 0.248 0.000 0.000 0.000
#> GSM110402 3 0.1814 0.796 0.000 0.100 0.900 0.000 0.000 0.000
#> GSM110411 4 0.0000 0.959 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110412 5 0.0520 0.981 0.000 0.000 0.008 0.008 0.984 0.000
#> GSM110417 4 0.0000 0.959 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110422 2 0.2912 0.713 0.000 0.784 0.000 0.000 0.000 0.216
#> GSM110426 4 0.0260 0.952 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM110429 2 0.2762 0.741 0.000 0.804 0.000 0.000 0.000 0.196
#> GSM110433 5 0.0000 0.982 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM110436 2 0.3588 0.612 0.000 0.788 0.152 0.000 0.000 0.060
#> GSM110440 1 0.5022 0.669 0.640 0.204 0.156 0.000 0.000 0.000
#> GSM110441 6 0.0520 0.584 0.000 0.008 0.000 0.000 0.008 0.984
#> GSM110444 4 0.0146 0.957 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM110445 1 0.2912 0.606 0.784 0.000 0.000 0.000 0.000 0.216
#> GSM110446 3 0.5817 0.224 0.312 0.208 0.480 0.000 0.000 0.000
#> GSM110449 6 0.0000 0.581 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM110451 2 0.3189 0.748 0.000 0.796 0.020 0.000 0.000 0.184
#> GSM110391 5 0.0000 0.982 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM110439 6 0.3797 0.545 0.000 0.420 0.000 0.000 0.000 0.580
#> GSM110442 6 0.3899 0.560 0.000 0.404 0.000 0.000 0.004 0.592
#> GSM110443 6 0.3314 0.653 0.004 0.256 0.000 0.000 0.000 0.740
#> GSM110447 3 0.0692 0.825 0.004 0.020 0.976 0.000 0.000 0.000
#> GSM110448 4 0.0000 0.959 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110450 1 0.2743 0.759 0.828 0.164 0.000 0.000 0.000 0.008
#> GSM110452 6 0.3923 0.551 0.004 0.416 0.000 0.000 0.000 0.580
#> GSM110453 6 0.4041 0.558 0.004 0.408 0.000 0.000 0.004 0.584
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) specimen(p) k
#> MAD:mclust 58 0.4573 1.000 2
#> MAD:mclust 47 0.0765 0.575 3
#> MAD:mclust 47 0.0242 0.446 4
#> MAD:mclust 56 0.1577 0.569 5
#> MAD:mclust 54 0.1798 0.110 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 17209 rows and 59 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 0.486 0.864 0.896 0.4937 0.493 0.493
#> 3 3 0.492 0.733 0.839 0.3564 0.695 0.456
#> 4 4 0.600 0.720 0.806 0.1167 0.833 0.553
#> 5 5 0.664 0.670 0.811 0.0562 0.950 0.810
#> 6 6 0.649 0.507 0.740 0.0391 0.944 0.768
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
#> GSM110395 2 0.0000 0.914 0.000 1.000
#> GSM110396 1 0.3274 0.861 0.940 0.060
#> GSM110397 1 0.0000 0.831 1.000 0.000
#> GSM110398 1 0.2603 0.854 0.956 0.044
#> GSM110399 2 0.0000 0.914 0.000 1.000
#> GSM110400 2 0.0000 0.914 0.000 1.000
#> GSM110401 1 0.7139 0.896 0.804 0.196
#> GSM110406 2 0.0000 0.914 0.000 1.000
#> GSM110407 1 0.7219 0.896 0.800 0.200
#> GSM110409 1 0.7219 0.896 0.800 0.200
#> GSM110410 2 0.5946 0.845 0.144 0.856
#> GSM110413 2 0.5408 0.857 0.124 0.876
#> GSM110414 2 0.0376 0.912 0.004 0.996
#> GSM110415 2 0.2603 0.876 0.044 0.956
#> GSM110416 1 0.8661 0.809 0.712 0.288
#> GSM110418 1 0.7376 0.891 0.792 0.208
#> GSM110419 1 0.9044 0.768 0.680 0.320
#> GSM110420 1 0.7219 0.896 0.800 0.200
#> GSM110421 2 0.7219 0.805 0.200 0.800
#> GSM110423 2 0.0000 0.914 0.000 1.000
#> GSM110424 2 0.7219 0.805 0.200 0.800
#> GSM110425 2 0.0000 0.914 0.000 1.000
#> GSM110427 2 0.0000 0.914 0.000 1.000
#> GSM110428 1 0.7219 0.896 0.800 0.200
#> GSM110430 1 0.7219 0.896 0.800 0.200
#> GSM110431 1 0.7219 0.896 0.800 0.200
#> GSM110432 2 0.0000 0.914 0.000 1.000
#> GSM110434 2 0.0000 0.914 0.000 1.000
#> GSM110435 1 0.7219 0.896 0.800 0.200
#> GSM110437 1 0.7056 0.896 0.808 0.192
#> GSM110438 1 0.7219 0.896 0.800 0.200
#> GSM110388 1 0.0000 0.831 1.000 0.000
#> GSM110392 1 0.4298 0.779 0.912 0.088
#> GSM110394 1 0.7219 0.896 0.800 0.200
#> GSM110402 2 0.0376 0.911 0.004 0.996
#> GSM110411 1 0.0000 0.831 1.000 0.000
#> GSM110412 2 0.7219 0.805 0.200 0.800
#> GSM110417 1 0.0000 0.831 1.000 0.000
#> GSM110422 2 0.0000 0.914 0.000 1.000
#> GSM110426 1 0.0000 0.831 1.000 0.000
#> GSM110429 2 0.0000 0.914 0.000 1.000
#> GSM110433 2 0.7219 0.805 0.200 0.800
#> GSM110436 2 0.0000 0.914 0.000 1.000
#> GSM110440 1 0.6887 0.895 0.816 0.184
#> GSM110441 2 0.6712 0.823 0.176 0.824
#> GSM110444 1 0.3584 0.796 0.932 0.068
#> GSM110445 1 0.4815 0.876 0.896 0.104
#> GSM110446 1 0.7219 0.896 0.800 0.200
#> GSM110449 2 0.9170 0.674 0.332 0.668
#> GSM110451 2 0.0000 0.914 0.000 1.000
#> GSM110391 2 0.7219 0.805 0.200 0.800
#> GSM110439 2 0.0000 0.914 0.000 1.000
#> GSM110442 2 0.4022 0.880 0.080 0.920
#> GSM110443 2 0.8555 0.462 0.280 0.720
#> GSM110447 2 0.0938 0.909 0.012 0.988
#> GSM110448 1 0.0000 0.831 1.000 0.000
#> GSM110450 1 0.7219 0.896 0.800 0.200
#> GSM110452 2 0.0000 0.914 0.000 1.000
#> GSM110453 2 0.0000 0.914 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.4842 0.751 0.000 0.776 0.224
#> GSM110396 1 0.4811 0.834 0.828 0.148 0.024
#> GSM110397 1 0.1636 0.822 0.964 0.016 0.020
#> GSM110398 1 0.4645 0.829 0.816 0.176 0.008
#> GSM110399 2 0.4679 0.631 0.148 0.832 0.020
#> GSM110400 3 0.5760 0.344 0.000 0.328 0.672
#> GSM110401 1 0.5412 0.827 0.796 0.172 0.032
#> GSM110406 2 0.3148 0.771 0.036 0.916 0.048
#> GSM110407 1 0.9183 0.370 0.484 0.156 0.360
#> GSM110409 1 0.8392 0.668 0.624 0.176 0.200
#> GSM110410 2 0.5047 0.790 0.036 0.824 0.140
#> GSM110413 2 0.5173 0.789 0.036 0.816 0.148
#> GSM110414 2 0.5178 0.719 0.000 0.744 0.256
#> GSM110415 3 0.1031 0.832 0.000 0.024 0.976
#> GSM110416 3 0.0424 0.837 0.000 0.008 0.992
#> GSM110418 3 0.0424 0.837 0.000 0.008 0.992
#> GSM110419 3 0.2625 0.821 0.000 0.084 0.916
#> GSM110420 3 0.1163 0.840 0.000 0.028 0.972
#> GSM110421 2 0.4399 0.778 0.188 0.812 0.000
#> GSM110423 3 0.0747 0.835 0.000 0.016 0.984
#> GSM110424 2 0.5344 0.800 0.092 0.824 0.084
#> GSM110425 3 0.0747 0.835 0.000 0.016 0.984
#> GSM110427 2 0.4931 0.744 0.000 0.768 0.232
#> GSM110428 3 0.1031 0.840 0.000 0.024 0.976
#> GSM110430 1 0.5348 0.827 0.796 0.176 0.028
#> GSM110431 3 0.7104 0.630 0.136 0.140 0.724
#> GSM110432 3 0.2165 0.834 0.000 0.064 0.936
#> GSM110434 2 0.3644 0.718 0.004 0.872 0.124
#> GSM110435 3 0.4749 0.763 0.012 0.172 0.816
#> GSM110437 1 0.5467 0.826 0.792 0.176 0.032
#> GSM110438 3 0.4409 0.768 0.004 0.172 0.824
#> GSM110388 1 0.0237 0.815 0.996 0.004 0.000
#> GSM110392 3 0.5536 0.663 0.236 0.012 0.752
#> GSM110394 3 0.5558 0.742 0.048 0.152 0.800
#> GSM110402 3 0.0892 0.839 0.000 0.020 0.980
#> GSM110411 1 0.0592 0.813 0.988 0.012 0.000
#> GSM110412 2 0.4399 0.778 0.188 0.812 0.000
#> GSM110417 1 0.0592 0.813 0.988 0.012 0.000
#> GSM110422 2 0.4504 0.757 0.000 0.804 0.196
#> GSM110426 1 0.1182 0.812 0.976 0.012 0.012
#> GSM110429 2 0.6302 0.261 0.000 0.520 0.480
#> GSM110433 2 0.5053 0.790 0.164 0.812 0.024
#> GSM110436 3 0.6286 -0.156 0.000 0.464 0.536
#> GSM110440 1 0.7447 0.751 0.700 0.140 0.160
#> GSM110441 2 0.5119 0.796 0.152 0.816 0.032
#> GSM110444 1 0.0747 0.811 0.984 0.016 0.000
#> GSM110445 1 0.4953 0.829 0.808 0.176 0.016
#> GSM110446 3 0.4645 0.763 0.008 0.176 0.816
#> GSM110449 1 0.3941 0.685 0.844 0.156 0.000
#> GSM110451 3 0.3816 0.721 0.000 0.148 0.852
#> GSM110391 2 0.4452 0.776 0.192 0.808 0.000
#> GSM110439 2 0.1170 0.775 0.008 0.976 0.016
#> GSM110442 2 0.4121 0.807 0.108 0.868 0.024
#> GSM110443 2 0.8938 0.102 0.284 0.552 0.164
#> GSM110447 3 0.0892 0.834 0.000 0.020 0.980
#> GSM110448 1 0.0424 0.814 0.992 0.008 0.000
#> GSM110450 1 0.6809 0.793 0.740 0.156 0.104
#> GSM110452 2 0.1182 0.775 0.012 0.976 0.012
#> GSM110453 2 0.1525 0.785 0.004 0.964 0.032
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.4499 0.721 0.072 0.804 0.124 0.000
#> GSM110396 1 0.2466 0.819 0.900 0.000 0.004 0.096
#> GSM110397 4 0.5064 0.432 0.360 0.004 0.004 0.632
#> GSM110398 1 0.3497 0.793 0.860 0.104 0.000 0.036
#> GSM110399 1 0.4103 0.694 0.744 0.256 0.000 0.000
#> GSM110400 3 0.4233 0.709 0.008 0.044 0.828 0.120
#> GSM110401 1 0.1510 0.863 0.956 0.000 0.028 0.016
#> GSM110406 1 0.4797 0.689 0.720 0.260 0.020 0.000
#> GSM110407 1 0.2647 0.821 0.880 0.000 0.120 0.000
#> GSM110409 1 0.0927 0.864 0.976 0.008 0.016 0.000
#> GSM110410 2 0.0188 0.815 0.000 0.996 0.004 0.000
#> GSM110413 2 0.6543 0.564 0.012 0.640 0.092 0.256
#> GSM110414 3 0.7635 0.173 0.008 0.272 0.516 0.204
#> GSM110415 3 0.2010 0.781 0.008 0.012 0.940 0.040
#> GSM110416 3 0.1847 0.816 0.052 0.004 0.940 0.004
#> GSM110418 3 0.1492 0.815 0.036 0.004 0.956 0.004
#> GSM110419 3 0.2345 0.805 0.100 0.000 0.900 0.000
#> GSM110420 3 0.2480 0.809 0.088 0.000 0.904 0.008
#> GSM110421 4 0.5420 0.468 0.008 0.276 0.028 0.688
#> GSM110423 3 0.0817 0.803 0.000 0.024 0.976 0.000
#> GSM110424 2 0.5485 0.683 0.008 0.744 0.080 0.168
#> GSM110425 3 0.0592 0.812 0.016 0.000 0.984 0.000
#> GSM110427 2 0.2796 0.785 0.008 0.892 0.096 0.004
#> GSM110428 3 0.2647 0.802 0.120 0.000 0.880 0.000
#> GSM110430 1 0.1598 0.861 0.956 0.004 0.020 0.020
#> GSM110431 3 0.2973 0.789 0.144 0.000 0.856 0.000
#> GSM110432 3 0.6115 0.679 0.172 0.148 0.680 0.000
#> GSM110434 2 0.2867 0.770 0.104 0.884 0.012 0.000
#> GSM110435 3 0.2973 0.794 0.144 0.000 0.856 0.000
#> GSM110437 1 0.1339 0.863 0.964 0.004 0.024 0.008
#> GSM110438 3 0.3355 0.784 0.160 0.004 0.836 0.000
#> GSM110388 4 0.1716 0.828 0.064 0.000 0.000 0.936
#> GSM110392 3 0.6063 0.470 0.008 0.048 0.628 0.316
#> GSM110394 3 0.4925 0.319 0.428 0.000 0.572 0.000
#> GSM110402 3 0.1743 0.815 0.056 0.004 0.940 0.000
#> GSM110411 4 0.0336 0.823 0.008 0.000 0.000 0.992
#> GSM110412 4 0.3344 0.761 0.008 0.024 0.092 0.876
#> GSM110417 4 0.2868 0.781 0.136 0.000 0.000 0.864
#> GSM110422 2 0.1059 0.815 0.016 0.972 0.012 0.000
#> GSM110426 4 0.3745 0.791 0.088 0.000 0.060 0.852
#> GSM110429 2 0.3768 0.663 0.008 0.808 0.184 0.000
#> GSM110433 2 0.6751 0.440 0.008 0.576 0.088 0.328
#> GSM110436 3 0.5400 0.217 0.008 0.428 0.560 0.004
#> GSM110440 1 0.5376 0.723 0.736 0.000 0.176 0.088
#> GSM110441 2 0.2530 0.771 0.000 0.888 0.000 0.112
#> GSM110444 4 0.0188 0.822 0.004 0.000 0.000 0.996
#> GSM110445 1 0.1706 0.847 0.948 0.016 0.000 0.036
#> GSM110446 3 0.3583 0.775 0.180 0.004 0.816 0.000
#> GSM110449 2 0.7464 0.204 0.328 0.480 0.000 0.192
#> GSM110451 3 0.5599 0.507 0.040 0.316 0.644 0.000
#> GSM110391 4 0.4712 0.683 0.008 0.132 0.060 0.800
#> GSM110439 2 0.0895 0.814 0.020 0.976 0.004 0.000
#> GSM110442 2 0.0376 0.815 0.004 0.992 0.004 0.000
#> GSM110443 1 0.3105 0.817 0.868 0.120 0.012 0.000
#> GSM110447 3 0.1139 0.796 0.008 0.012 0.972 0.008
#> GSM110448 4 0.1792 0.828 0.068 0.000 0.000 0.932
#> GSM110450 1 0.2401 0.841 0.904 0.000 0.092 0.004
#> GSM110452 2 0.0707 0.813 0.020 0.980 0.000 0.000
#> GSM110453 2 0.0779 0.815 0.016 0.980 0.004 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 5 0.6650 0.3866 0.144 0.336 0.020 0.000 0.500
#> GSM110396 1 0.4221 0.7385 0.732 0.000 0.000 0.032 0.236
#> GSM110397 4 0.3421 0.6774 0.152 0.000 0.008 0.824 0.016
#> GSM110398 1 0.4775 0.6609 0.768 0.104 0.000 0.100 0.028
#> GSM110399 1 0.3875 0.7398 0.804 0.124 0.000 0.000 0.072
#> GSM110400 3 0.4516 0.3347 0.004 0.004 0.576 0.000 0.416
#> GSM110401 1 0.2338 0.7766 0.884 0.000 0.004 0.000 0.112
#> GSM110406 1 0.4585 0.6038 0.592 0.008 0.004 0.000 0.396
#> GSM110407 1 0.3863 0.7309 0.740 0.000 0.012 0.000 0.248
#> GSM110409 1 0.1314 0.7765 0.960 0.012 0.012 0.000 0.016
#> GSM110410 2 0.0162 0.8093 0.000 0.996 0.000 0.000 0.004
#> GSM110413 5 0.1372 0.5551 0.024 0.016 0.000 0.004 0.956
#> GSM110414 3 0.5411 0.1016 0.004 0.020 0.492 0.016 0.468
#> GSM110415 3 0.0960 0.8325 0.004 0.000 0.972 0.016 0.008
#> GSM110416 3 0.0162 0.8353 0.000 0.000 0.996 0.004 0.000
#> GSM110418 3 0.0324 0.8349 0.004 0.000 0.992 0.004 0.000
#> GSM110419 3 0.1195 0.8314 0.028 0.000 0.960 0.000 0.012
#> GSM110420 3 0.0290 0.8354 0.000 0.000 0.992 0.008 0.000
#> GSM110421 5 0.6139 0.6381 0.000 0.260 0.000 0.184 0.556
#> GSM110423 3 0.0854 0.8334 0.004 0.012 0.976 0.000 0.008
#> GSM110424 2 0.4652 0.5726 0.004 0.768 0.008 0.116 0.104
#> GSM110425 3 0.0290 0.8352 0.000 0.000 0.992 0.000 0.008
#> GSM110427 2 0.3033 0.7202 0.000 0.864 0.052 0.000 0.084
#> GSM110428 3 0.2561 0.8024 0.096 0.000 0.884 0.000 0.020
#> GSM110430 1 0.0867 0.7778 0.976 0.000 0.008 0.008 0.008
#> GSM110431 3 0.2707 0.7848 0.132 0.000 0.860 0.000 0.008
#> GSM110432 3 0.4373 0.7016 0.176 0.008 0.764 0.000 0.052
#> GSM110434 2 0.2929 0.6876 0.152 0.840 0.000 0.000 0.008
#> GSM110435 3 0.1059 0.8341 0.020 0.004 0.968 0.000 0.008
#> GSM110437 1 0.3077 0.7405 0.864 0.000 0.008 0.100 0.028
#> GSM110438 3 0.2172 0.8067 0.076 0.000 0.908 0.000 0.016
#> GSM110388 4 0.0162 0.8154 0.000 0.000 0.000 0.996 0.004
#> GSM110392 4 0.4430 0.6597 0.020 0.132 0.036 0.796 0.016
#> GSM110394 3 0.4473 0.3171 0.412 0.000 0.580 0.000 0.008
#> GSM110402 3 0.0162 0.8353 0.000 0.000 0.996 0.004 0.000
#> GSM110411 4 0.2377 0.7559 0.000 0.000 0.000 0.872 0.128
#> GSM110412 4 0.4262 0.5543 0.004 0.000 0.012 0.696 0.288
#> GSM110417 4 0.0404 0.8152 0.000 0.000 0.000 0.988 0.012
#> GSM110422 2 0.0510 0.8070 0.000 0.984 0.016 0.000 0.000
#> GSM110426 4 0.0162 0.8137 0.000 0.000 0.004 0.996 0.000
#> GSM110429 2 0.2338 0.7090 0.000 0.884 0.112 0.000 0.004
#> GSM110433 5 0.5987 0.6134 0.000 0.304 0.000 0.140 0.556
#> GSM110436 3 0.5111 0.0881 0.000 0.464 0.500 0.000 0.036
#> GSM110440 1 0.6027 0.4712 0.600 0.000 0.124 0.264 0.012
#> GSM110441 2 0.4403 -0.2237 0.000 0.560 0.000 0.004 0.436
#> GSM110444 4 0.4074 0.4067 0.000 0.000 0.000 0.636 0.364
#> GSM110445 1 0.1872 0.7694 0.928 0.000 0.000 0.052 0.020
#> GSM110446 3 0.3216 0.7743 0.116 0.000 0.852 0.012 0.020
#> GSM110449 2 0.5361 0.5096 0.104 0.680 0.000 0.208 0.008
#> GSM110451 3 0.3842 0.7251 0.028 0.156 0.804 0.000 0.012
#> GSM110391 5 0.4281 0.5646 0.000 0.056 0.004 0.172 0.768
#> GSM110439 2 0.0000 0.8099 0.000 1.000 0.000 0.000 0.000
#> GSM110442 2 0.0290 0.8097 0.000 0.992 0.000 0.000 0.008
#> GSM110443 1 0.6204 0.3116 0.524 0.336 0.000 0.004 0.136
#> GSM110447 3 0.0902 0.8337 0.004 0.004 0.976 0.008 0.008
#> GSM110448 4 0.0290 0.8158 0.000 0.000 0.000 0.992 0.008
#> GSM110450 1 0.3205 0.7609 0.816 0.000 0.004 0.004 0.176
#> GSM110452 2 0.0898 0.8032 0.020 0.972 0.000 0.000 0.008
#> GSM110453 2 0.0000 0.8099 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 5 0.7695 0.2624 0.264 0.184 0.028 0.000 0.408 0.116
#> GSM110396 1 0.3185 0.4876 0.848 0.000 0.000 0.016 0.060 0.076
#> GSM110397 4 0.2838 0.6881 0.028 0.000 0.000 0.852 0.004 0.116
#> GSM110398 6 0.7632 0.0000 0.264 0.260 0.000 0.092 0.020 0.364
#> GSM110399 1 0.5753 -0.2560 0.512 0.376 0.000 0.000 0.044 0.068
#> GSM110400 3 0.4420 0.5660 0.008 0.004 0.700 0.000 0.244 0.044
#> GSM110401 1 0.1218 0.5151 0.956 0.000 0.000 0.012 0.004 0.028
#> GSM110406 1 0.5033 0.4207 0.684 0.020 0.000 0.000 0.164 0.132
#> GSM110407 1 0.1838 0.5206 0.928 0.000 0.012 0.000 0.020 0.040
#> GSM110409 1 0.4668 0.2402 0.668 0.040 0.008 0.004 0.004 0.276
#> GSM110410 2 0.2058 0.6532 0.000 0.908 0.000 0.000 0.056 0.036
#> GSM110413 5 0.3555 0.5828 0.104 0.016 0.000 0.004 0.824 0.052
#> GSM110414 5 0.5199 -0.0753 0.000 0.016 0.464 0.000 0.468 0.052
#> GSM110415 3 0.1078 0.7732 0.000 0.000 0.964 0.012 0.016 0.008
#> GSM110416 3 0.0000 0.7744 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110418 3 0.0622 0.7748 0.000 0.000 0.980 0.008 0.000 0.012
#> GSM110419 3 0.1932 0.7727 0.040 0.000 0.924 0.000 0.016 0.020
#> GSM110420 3 0.1053 0.7747 0.004 0.000 0.964 0.012 0.000 0.020
#> GSM110421 5 0.4007 0.5877 0.000 0.068 0.000 0.108 0.792 0.032
#> GSM110423 3 0.0717 0.7727 0.000 0.000 0.976 0.000 0.008 0.016
#> GSM110424 2 0.6407 0.3763 0.000 0.520 0.016 0.032 0.296 0.136
#> GSM110425 3 0.1801 0.7608 0.004 0.000 0.924 0.000 0.016 0.056
#> GSM110427 2 0.6243 0.2799 0.000 0.524 0.060 0.000 0.300 0.116
#> GSM110428 1 0.6934 0.1393 0.408 0.000 0.328 0.008 0.048 0.208
#> GSM110430 1 0.2709 0.4647 0.848 0.000 0.000 0.020 0.000 0.132
#> GSM110431 3 0.4587 0.5019 0.316 0.000 0.632 0.000 0.004 0.048
#> GSM110432 3 0.7828 0.2363 0.256 0.040 0.412 0.000 0.164 0.128
#> GSM110434 2 0.2565 0.5729 0.016 0.872 0.008 0.000 0.000 0.104
#> GSM110435 3 0.3302 0.7283 0.028 0.008 0.824 0.004 0.000 0.136
#> GSM110437 1 0.5375 0.1409 0.564 0.004 0.004 0.100 0.000 0.328
#> GSM110438 3 0.4303 0.6833 0.052 0.012 0.756 0.012 0.000 0.168
#> GSM110388 4 0.2201 0.7927 0.000 0.000 0.000 0.900 0.052 0.048
#> GSM110392 4 0.4327 0.6116 0.000 0.152 0.004 0.760 0.024 0.060
#> GSM110394 3 0.3684 0.5167 0.332 0.000 0.664 0.000 0.000 0.004
#> GSM110402 3 0.0405 0.7759 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM110411 4 0.3956 0.6936 0.000 0.000 0.000 0.712 0.252 0.036
#> GSM110412 4 0.4490 0.5044 0.000 0.000 0.008 0.596 0.372 0.024
#> GSM110417 4 0.1562 0.7874 0.004 0.000 0.000 0.940 0.024 0.032
#> GSM110422 2 0.1894 0.6480 0.004 0.928 0.040 0.000 0.012 0.016
#> GSM110426 4 0.0935 0.7844 0.000 0.000 0.004 0.964 0.000 0.032
#> GSM110429 2 0.2239 0.6404 0.000 0.908 0.048 0.000 0.020 0.024
#> GSM110433 5 0.3572 0.6137 0.000 0.100 0.000 0.060 0.820 0.020
#> GSM110436 2 0.7414 0.0504 0.000 0.384 0.204 0.000 0.260 0.152
#> GSM110440 1 0.5982 0.3407 0.612 0.000 0.120 0.216 0.016 0.036
#> GSM110441 2 0.5788 0.1764 0.000 0.464 0.004 0.012 0.412 0.108
#> GSM110444 4 0.3758 0.6711 0.000 0.000 0.000 0.700 0.284 0.016
#> GSM110445 1 0.5059 0.2724 0.652 0.028 0.000 0.052 0.004 0.264
#> GSM110446 3 0.5157 0.6039 0.036 0.020 0.680 0.040 0.000 0.224
#> GSM110449 2 0.5785 0.2295 0.020 0.632 0.000 0.096 0.032 0.220
#> GSM110451 3 0.7291 0.3251 0.036 0.176 0.512 0.000 0.172 0.104
#> GSM110391 5 0.3840 0.5703 0.000 0.028 0.004 0.088 0.812 0.068
#> GSM110439 2 0.1010 0.6469 0.000 0.960 0.000 0.000 0.004 0.036
#> GSM110442 2 0.3497 0.6322 0.004 0.832 0.000 0.016 0.076 0.072
#> GSM110443 1 0.7026 0.1849 0.484 0.240 0.000 0.052 0.024 0.200
#> GSM110447 3 0.4917 0.5643 0.000 0.004 0.700 0.016 0.172 0.108
#> GSM110448 4 0.1285 0.7974 0.000 0.000 0.000 0.944 0.052 0.004
#> GSM110450 1 0.4601 0.4764 0.720 0.004 0.000 0.068 0.016 0.192
#> GSM110452 2 0.1606 0.6335 0.004 0.932 0.000 0.000 0.008 0.056
#> GSM110453 2 0.0260 0.6577 0.000 0.992 0.000 0.000 0.008 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) specimen(p) k
#> MAD:NMF 58 0.77828 0.299 2
#> MAD:NMF 54 0.31690 0.188 3
#> MAD:NMF 51 0.00239 0.320 4
#> MAD:NMF 50 0.01015 0.264 5
#> MAD:NMF 38 0.01317 0.108 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 17209 rows and 59 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 0.628 0.693 0.886 0.4695 0.524 0.524
#> 3 3 0.546 0.755 0.828 0.3594 0.707 0.487
#> 4 4 0.580 0.695 0.804 0.1224 0.936 0.802
#> 5 5 0.632 0.603 0.764 0.0630 0.901 0.671
#> 6 6 0.676 0.654 0.759 0.0483 0.905 0.637
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
#> GSM110395 2 0.0000 0.8496 0.000 1.000
#> GSM110396 1 0.0000 0.8665 1.000 0.000
#> GSM110397 1 0.0000 0.8665 1.000 0.000
#> GSM110398 1 0.9833 0.2123 0.576 0.424
#> GSM110399 2 0.9922 0.2168 0.448 0.552
#> GSM110400 2 0.0000 0.8496 0.000 1.000
#> GSM110401 1 0.0000 0.8665 1.000 0.000
#> GSM110406 2 0.9922 0.2168 0.448 0.552
#> GSM110407 1 0.0376 0.8671 0.996 0.004
#> GSM110409 1 0.0376 0.8671 0.996 0.004
#> GSM110410 2 0.0000 0.8496 0.000 1.000
#> GSM110413 2 0.0000 0.8496 0.000 1.000
#> GSM110414 2 0.0000 0.8496 0.000 1.000
#> GSM110415 2 0.4161 0.8009 0.084 0.916
#> GSM110416 2 0.9988 0.0848 0.480 0.520
#> GSM110418 2 0.9988 0.0848 0.480 0.520
#> GSM110419 2 0.4161 0.8009 0.084 0.916
#> GSM110420 1 0.9754 0.2444 0.592 0.408
#> GSM110421 2 0.0000 0.8496 0.000 1.000
#> GSM110423 2 0.0000 0.8496 0.000 1.000
#> GSM110424 2 0.0000 0.8496 0.000 1.000
#> GSM110425 2 0.0000 0.8496 0.000 1.000
#> GSM110427 2 0.0000 0.8496 0.000 1.000
#> GSM110428 1 0.9775 0.2486 0.588 0.412
#> GSM110430 1 0.0000 0.8665 1.000 0.000
#> GSM110431 1 0.0000 0.8665 1.000 0.000
#> GSM110432 2 0.3431 0.8160 0.064 0.936
#> GSM110434 2 0.0000 0.8496 0.000 1.000
#> GSM110435 1 0.0376 0.8671 0.996 0.004
#> GSM110437 1 0.0000 0.8665 1.000 0.000
#> GSM110438 1 0.9775 0.2486 0.588 0.412
#> GSM110388 1 0.0376 0.8671 0.996 0.004
#> GSM110392 2 0.9922 0.2168 0.448 0.552
#> GSM110394 1 0.0376 0.8671 0.996 0.004
#> GSM110402 2 0.2603 0.8289 0.044 0.956
#> GSM110411 1 0.9833 0.2123 0.576 0.424
#> GSM110412 2 0.2778 0.8267 0.048 0.952
#> GSM110417 1 0.0000 0.8665 1.000 0.000
#> GSM110422 2 0.0000 0.8496 0.000 1.000
#> GSM110426 1 0.0000 0.8665 1.000 0.000
#> GSM110429 2 0.0000 0.8496 0.000 1.000
#> GSM110433 2 0.0000 0.8496 0.000 1.000
#> GSM110436 2 0.0000 0.8496 0.000 1.000
#> GSM110440 1 0.0376 0.8671 0.996 0.004
#> GSM110441 2 0.0000 0.8496 0.000 1.000
#> GSM110444 2 0.9922 0.2168 0.448 0.552
#> GSM110445 1 0.5294 0.7629 0.880 0.120
#> GSM110446 2 0.9996 0.0550 0.488 0.512
#> GSM110449 2 0.9922 0.2168 0.448 0.552
#> GSM110451 2 0.0000 0.8496 0.000 1.000
#> GSM110391 2 0.0000 0.8496 0.000 1.000
#> GSM110439 2 0.0000 0.8496 0.000 1.000
#> GSM110442 2 0.0000 0.8496 0.000 1.000
#> GSM110443 2 0.9922 0.2168 0.448 0.552
#> GSM110447 2 0.2603 0.8290 0.044 0.956
#> GSM110448 1 0.0376 0.8671 0.996 0.004
#> GSM110450 1 0.0672 0.8646 0.992 0.008
#> GSM110452 2 0.0000 0.8496 0.000 1.000
#> GSM110453 2 0.0000 0.8496 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.196 0.931 0.000 0.944 0.056
#> GSM110396 1 0.000 0.919 1.000 0.000 0.000
#> GSM110397 1 0.216 0.896 0.936 0.000 0.064
#> GSM110398 3 0.665 0.591 0.240 0.048 0.712
#> GSM110399 3 0.803 0.680 0.172 0.172 0.656
#> GSM110400 3 0.631 0.117 0.000 0.496 0.504
#> GSM110401 1 0.216 0.896 0.936 0.000 0.064
#> GSM110406 3 0.803 0.680 0.172 0.172 0.656
#> GSM110407 1 0.216 0.919 0.936 0.000 0.064
#> GSM110409 1 0.216 0.919 0.936 0.000 0.064
#> GSM110410 2 0.000 0.924 0.000 1.000 0.000
#> GSM110413 2 0.175 0.936 0.000 0.952 0.048
#> GSM110414 2 0.000 0.924 0.000 1.000 0.000
#> GSM110415 3 0.581 0.470 0.000 0.336 0.664
#> GSM110416 3 0.341 0.578 0.124 0.000 0.876
#> GSM110418 3 0.341 0.578 0.124 0.000 0.876
#> GSM110419 3 0.581 0.470 0.000 0.336 0.664
#> GSM110420 3 0.546 0.357 0.288 0.000 0.712
#> GSM110421 2 0.196 0.931 0.000 0.944 0.056
#> GSM110423 3 0.631 0.117 0.000 0.496 0.504
#> GSM110424 2 0.000 0.924 0.000 1.000 0.000
#> GSM110425 3 0.631 0.117 0.000 0.496 0.504
#> GSM110427 2 0.000 0.924 0.000 1.000 0.000
#> GSM110428 3 0.676 0.578 0.252 0.048 0.700
#> GSM110430 1 0.216 0.896 0.936 0.000 0.064
#> GSM110431 1 0.216 0.896 0.936 0.000 0.064
#> GSM110432 2 0.525 0.596 0.000 0.736 0.264
#> GSM110434 2 0.196 0.931 0.000 0.944 0.056
#> GSM110435 1 0.207 0.921 0.940 0.000 0.060
#> GSM110437 1 0.216 0.896 0.936 0.000 0.064
#> GSM110438 3 0.676 0.578 0.252 0.048 0.700
#> GSM110388 1 0.288 0.897 0.904 0.000 0.096
#> GSM110392 3 0.803 0.680 0.172 0.172 0.656
#> GSM110394 1 0.207 0.921 0.940 0.000 0.060
#> GSM110402 3 0.610 0.377 0.000 0.392 0.608
#> GSM110411 3 0.665 0.591 0.240 0.048 0.712
#> GSM110412 2 0.502 0.649 0.000 0.760 0.240
#> GSM110417 1 0.000 0.919 1.000 0.000 0.000
#> GSM110422 2 0.175 0.936 0.000 0.952 0.048
#> GSM110426 1 0.000 0.919 1.000 0.000 0.000
#> GSM110429 2 0.296 0.882 0.000 0.900 0.100
#> GSM110433 2 0.000 0.924 0.000 1.000 0.000
#> GSM110436 2 0.000 0.924 0.000 1.000 0.000
#> GSM110440 1 0.207 0.921 0.940 0.000 0.060
#> GSM110441 2 0.175 0.936 0.000 0.952 0.048
#> GSM110444 3 0.803 0.680 0.172 0.172 0.656
#> GSM110445 1 0.522 0.652 0.740 0.000 0.260
#> GSM110446 3 0.355 0.571 0.132 0.000 0.868
#> GSM110449 3 0.803 0.680 0.172 0.172 0.656
#> GSM110451 2 0.175 0.936 0.000 0.952 0.048
#> GSM110391 2 0.175 0.936 0.000 0.952 0.048
#> GSM110439 2 0.000 0.924 0.000 1.000 0.000
#> GSM110442 2 0.175 0.936 0.000 0.952 0.048
#> GSM110443 3 0.803 0.680 0.172 0.172 0.656
#> GSM110447 3 0.624 0.281 0.000 0.440 0.560
#> GSM110448 1 0.226 0.917 0.932 0.000 0.068
#> GSM110450 1 0.296 0.893 0.900 0.000 0.100
#> GSM110452 2 0.175 0.936 0.000 0.952 0.048
#> GSM110453 2 0.000 0.924 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.3172 0.833 0.000 0.840 0.000 0.160
#> GSM110396 1 0.2530 0.857 0.888 0.000 0.112 0.000
#> GSM110397 1 0.4040 0.813 0.752 0.000 0.248 0.000
#> GSM110398 4 0.4591 0.689 0.116 0.000 0.084 0.800
#> GSM110399 4 0.0000 0.764 0.000 0.000 0.000 1.000
#> GSM110400 3 0.7859 0.447 0.000 0.352 0.376 0.272
#> GSM110401 1 0.4040 0.813 0.752 0.000 0.248 0.000
#> GSM110406 4 0.0000 0.764 0.000 0.000 0.000 1.000
#> GSM110407 1 0.0376 0.858 0.992 0.000 0.004 0.004
#> GSM110409 1 0.0376 0.858 0.992 0.000 0.004 0.004
#> GSM110410 2 0.1118 0.805 0.000 0.964 0.036 0.000
#> GSM110413 2 0.2973 0.842 0.000 0.856 0.000 0.144
#> GSM110414 2 0.1118 0.805 0.000 0.964 0.036 0.000
#> GSM110415 3 0.7589 0.463 0.000 0.196 0.404 0.400
#> GSM110416 3 0.5948 0.380 0.144 0.000 0.696 0.160
#> GSM110418 3 0.5948 0.380 0.144 0.000 0.696 0.160
#> GSM110419 3 0.7589 0.463 0.000 0.196 0.404 0.400
#> GSM110420 3 0.4605 0.312 0.336 0.000 0.664 0.000
#> GSM110421 2 0.3172 0.833 0.000 0.840 0.000 0.160
#> GSM110423 3 0.7859 0.447 0.000 0.352 0.376 0.272
#> GSM110424 2 0.1118 0.805 0.000 0.964 0.036 0.000
#> GSM110425 3 0.7859 0.447 0.000 0.352 0.376 0.272
#> GSM110427 2 0.1118 0.805 0.000 0.964 0.036 0.000
#> GSM110428 4 0.4992 0.665 0.132 0.000 0.096 0.772
#> GSM110430 1 0.4040 0.813 0.752 0.000 0.248 0.000
#> GSM110431 1 0.4040 0.813 0.752 0.000 0.248 0.000
#> GSM110432 2 0.4941 0.378 0.000 0.564 0.000 0.436
#> GSM110434 2 0.3172 0.833 0.000 0.840 0.000 0.160
#> GSM110435 1 0.0188 0.859 0.996 0.000 0.000 0.004
#> GSM110437 1 0.4040 0.813 0.752 0.000 0.248 0.000
#> GSM110438 4 0.4992 0.665 0.132 0.000 0.096 0.772
#> GSM110388 1 0.1388 0.842 0.960 0.000 0.028 0.012
#> GSM110392 4 0.0000 0.764 0.000 0.000 0.000 1.000
#> GSM110394 1 0.0188 0.859 0.996 0.000 0.000 0.004
#> GSM110402 3 0.7800 0.480 0.000 0.248 0.376 0.376
#> GSM110411 4 0.4591 0.689 0.116 0.000 0.084 0.800
#> GSM110412 2 0.4888 0.416 0.000 0.588 0.000 0.412
#> GSM110417 1 0.2530 0.857 0.888 0.000 0.112 0.000
#> GSM110422 2 0.2469 0.839 0.000 0.892 0.000 0.108
#> GSM110426 1 0.2469 0.857 0.892 0.000 0.108 0.000
#> GSM110429 2 0.3726 0.751 0.000 0.788 0.000 0.212
#> GSM110433 2 0.1118 0.805 0.000 0.964 0.036 0.000
#> GSM110436 2 0.1004 0.809 0.000 0.972 0.024 0.004
#> GSM110440 1 0.0188 0.859 0.996 0.000 0.000 0.004
#> GSM110441 2 0.3105 0.842 0.000 0.856 0.004 0.140
#> GSM110444 4 0.0000 0.764 0.000 0.000 0.000 1.000
#> GSM110445 1 0.6180 0.406 0.624 0.000 0.080 0.296
#> GSM110446 3 0.5650 0.361 0.180 0.000 0.716 0.104
#> GSM110449 4 0.0000 0.764 0.000 0.000 0.000 1.000
#> GSM110451 2 0.2973 0.842 0.000 0.856 0.000 0.144
#> GSM110391 2 0.2973 0.842 0.000 0.856 0.000 0.144
#> GSM110439 2 0.1305 0.807 0.000 0.960 0.036 0.004
#> GSM110442 2 0.3074 0.838 0.000 0.848 0.000 0.152
#> GSM110443 4 0.0000 0.764 0.000 0.000 0.000 1.000
#> GSM110447 4 0.7871 -0.541 0.000 0.284 0.332 0.384
#> GSM110448 1 0.0469 0.856 0.988 0.000 0.000 0.012
#> GSM110450 1 0.4365 0.664 0.784 0.000 0.028 0.188
#> GSM110452 2 0.2973 0.842 0.000 0.856 0.000 0.144
#> GSM110453 2 0.1118 0.805 0.000 0.964 0.036 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.0963 0.656 0.000 0.964 0.000 0.036 0.000
#> GSM110396 1 0.0000 0.826 1.000 0.000 0.000 0.000 0.000
#> GSM110397 1 0.3653 0.774 0.828 0.000 0.036 0.012 0.124
#> GSM110398 4 0.3115 0.779 0.000 0.012 0.108 0.860 0.020
#> GSM110399 4 0.1792 0.851 0.000 0.084 0.000 0.916 0.000
#> GSM110400 2 0.6952 -0.135 0.000 0.456 0.364 0.148 0.032
#> GSM110401 1 0.3653 0.774 0.828 0.000 0.036 0.012 0.124
#> GSM110406 4 0.1792 0.851 0.000 0.084 0.000 0.916 0.000
#> GSM110407 1 0.3044 0.828 0.840 0.000 0.148 0.004 0.008
#> GSM110409 1 0.3044 0.828 0.840 0.000 0.148 0.004 0.008
#> GSM110410 5 0.3999 0.987 0.000 0.344 0.000 0.000 0.656
#> GSM110413 2 0.1082 0.653 0.000 0.964 0.000 0.028 0.008
#> GSM110414 5 0.3913 0.962 0.000 0.324 0.000 0.000 0.676
#> GSM110415 3 0.7442 0.379 0.000 0.272 0.368 0.328 0.032
#> GSM110416 3 0.4871 0.496 0.000 0.000 0.704 0.212 0.084
#> GSM110418 3 0.4871 0.496 0.000 0.000 0.704 0.212 0.084
#> GSM110419 3 0.7442 0.379 0.000 0.272 0.368 0.328 0.032
#> GSM110420 3 0.5032 0.359 0.128 0.000 0.704 0.000 0.168
#> GSM110421 2 0.0963 0.656 0.000 0.964 0.000 0.036 0.000
#> GSM110423 2 0.6952 -0.135 0.000 0.456 0.364 0.148 0.032
#> GSM110424 2 0.4138 -0.285 0.000 0.616 0.000 0.000 0.384
#> GSM110425 2 0.6952 -0.135 0.000 0.456 0.364 0.148 0.032
#> GSM110427 2 0.3612 0.131 0.000 0.732 0.000 0.000 0.268
#> GSM110428 4 0.3431 0.751 0.000 0.008 0.144 0.828 0.020
#> GSM110430 1 0.3653 0.774 0.828 0.000 0.036 0.012 0.124
#> GSM110431 1 0.3653 0.774 0.828 0.000 0.036 0.012 0.124
#> GSM110432 2 0.3876 0.463 0.000 0.684 0.000 0.316 0.000
#> GSM110434 2 0.0963 0.656 0.000 0.964 0.000 0.036 0.000
#> GSM110435 1 0.2921 0.828 0.844 0.000 0.148 0.004 0.004
#> GSM110437 1 0.3653 0.774 0.828 0.000 0.036 0.012 0.124
#> GSM110438 4 0.3431 0.751 0.000 0.008 0.144 0.828 0.020
#> GSM110388 1 0.3437 0.813 0.808 0.000 0.176 0.004 0.012
#> GSM110392 4 0.1792 0.851 0.000 0.084 0.000 0.916 0.000
#> GSM110394 1 0.2921 0.828 0.844 0.000 0.148 0.004 0.004
#> GSM110402 3 0.7420 0.235 0.000 0.348 0.364 0.256 0.032
#> GSM110411 4 0.3115 0.779 0.000 0.012 0.108 0.860 0.020
#> GSM110412 2 0.3752 0.492 0.000 0.708 0.000 0.292 0.000
#> GSM110417 1 0.0000 0.826 1.000 0.000 0.000 0.000 0.000
#> GSM110422 2 0.0609 0.619 0.000 0.980 0.000 0.000 0.020
#> GSM110426 1 0.0162 0.826 0.996 0.000 0.004 0.000 0.000
#> GSM110429 2 0.1851 0.620 0.000 0.912 0.000 0.088 0.000
#> GSM110433 5 0.3999 0.987 0.000 0.344 0.000 0.000 0.656
#> GSM110436 2 0.3177 0.286 0.000 0.792 0.000 0.000 0.208
#> GSM110440 1 0.2921 0.828 0.844 0.000 0.148 0.004 0.004
#> GSM110441 2 0.1668 0.637 0.000 0.940 0.000 0.028 0.032
#> GSM110444 4 0.1792 0.851 0.000 0.084 0.000 0.916 0.000
#> GSM110445 1 0.6532 0.303 0.500 0.000 0.124 0.356 0.020
#> GSM110446 3 0.5271 0.440 0.000 0.000 0.680 0.152 0.168
#> GSM110449 4 0.1792 0.851 0.000 0.084 0.000 0.916 0.000
#> GSM110451 2 0.1082 0.653 0.000 0.964 0.000 0.028 0.008
#> GSM110391 2 0.1082 0.653 0.000 0.964 0.000 0.028 0.008
#> GSM110439 2 0.3586 0.145 0.000 0.736 0.000 0.000 0.264
#> GSM110442 2 0.1251 0.655 0.000 0.956 0.000 0.036 0.008
#> GSM110443 4 0.1792 0.851 0.000 0.084 0.000 0.916 0.000
#> GSM110447 2 0.7229 -0.277 0.000 0.384 0.332 0.264 0.020
#> GSM110448 1 0.3006 0.826 0.836 0.000 0.156 0.004 0.004
#> GSM110450 1 0.5949 0.644 0.632 0.000 0.176 0.180 0.012
#> GSM110452 2 0.1195 0.651 0.000 0.960 0.000 0.028 0.012
#> GSM110453 5 0.3999 0.987 0.000 0.344 0.000 0.000 0.656
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.1124 0.7980 0.000 0.956 0.008 0.036 0.000 0.000
#> GSM110396 1 0.3515 0.1165 0.676 0.000 0.000 0.000 0.000 0.324
#> GSM110397 6 0.3547 1.0000 0.332 0.000 0.000 0.000 0.000 0.668
#> GSM110398 4 0.3499 0.7386 0.004 0.000 0.264 0.728 0.004 0.000
#> GSM110399 4 0.0713 0.8153 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM110400 3 0.5353 0.4929 0.000 0.420 0.472 0.108 0.000 0.000
#> GSM110401 6 0.3547 1.0000 0.332 0.000 0.000 0.000 0.000 0.668
#> GSM110406 4 0.0713 0.8153 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM110407 1 0.0146 0.7783 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM110409 1 0.0146 0.7783 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM110410 5 0.5720 0.7767 0.000 0.180 0.000 0.000 0.488 0.332
#> GSM110413 2 0.0713 0.8024 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM110414 5 0.6070 0.7623 0.000 0.160 0.020 0.000 0.488 0.332
#> GSM110415 3 0.5784 0.5992 0.000 0.236 0.504 0.260 0.000 0.000
#> GSM110416 3 0.5002 0.2615 0.000 0.000 0.636 0.136 0.228 0.000
#> GSM110418 3 0.5002 0.2615 0.000 0.000 0.636 0.136 0.228 0.000
#> GSM110419 3 0.5784 0.5992 0.000 0.236 0.504 0.260 0.000 0.000
#> GSM110420 5 0.5764 -0.0813 0.228 0.000 0.264 0.000 0.508 0.000
#> GSM110421 2 0.1124 0.7980 0.000 0.956 0.008 0.036 0.000 0.000
#> GSM110423 3 0.5353 0.4929 0.000 0.420 0.472 0.108 0.000 0.000
#> GSM110424 2 0.5779 -0.1052 0.000 0.488 0.000 0.000 0.312 0.200
#> GSM110425 3 0.5353 0.4929 0.000 0.420 0.472 0.108 0.000 0.000
#> GSM110427 2 0.3221 0.5603 0.000 0.736 0.000 0.000 0.264 0.000
#> GSM110428 4 0.3997 0.7165 0.004 0.000 0.288 0.688 0.020 0.000
#> GSM110430 6 0.3547 1.0000 0.332 0.000 0.000 0.000 0.000 0.668
#> GSM110431 6 0.3547 1.0000 0.332 0.000 0.000 0.000 0.000 0.668
#> GSM110432 2 0.3923 0.3384 0.000 0.620 0.008 0.372 0.000 0.000
#> GSM110434 2 0.1124 0.7980 0.000 0.956 0.008 0.036 0.000 0.000
#> GSM110435 1 0.0291 0.7780 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM110437 6 0.3547 1.0000 0.332 0.000 0.000 0.000 0.000 0.668
#> GSM110438 4 0.3997 0.7165 0.004 0.000 0.288 0.688 0.020 0.000
#> GSM110388 1 0.1668 0.7462 0.928 0.000 0.060 0.008 0.004 0.000
#> GSM110392 4 0.0713 0.8153 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM110394 1 0.0291 0.7780 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM110402 3 0.5886 0.5790 0.000 0.292 0.472 0.236 0.000 0.000
#> GSM110411 4 0.3499 0.7386 0.004 0.000 0.264 0.728 0.004 0.000
#> GSM110412 2 0.3847 0.3735 0.000 0.644 0.008 0.348 0.000 0.000
#> GSM110417 1 0.2697 0.5641 0.812 0.000 0.000 0.000 0.000 0.188
#> GSM110422 2 0.0363 0.7852 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM110426 1 0.2697 0.5646 0.812 0.000 0.000 0.000 0.000 0.188
#> GSM110429 2 0.2134 0.7143 0.000 0.904 0.052 0.044 0.000 0.000
#> GSM110433 5 0.5720 0.7767 0.000 0.180 0.000 0.000 0.488 0.332
#> GSM110436 2 0.2793 0.6435 0.000 0.800 0.000 0.000 0.200 0.000
#> GSM110440 1 0.0291 0.7780 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM110441 2 0.1341 0.7984 0.000 0.948 0.000 0.028 0.024 0.000
#> GSM110444 4 0.0713 0.8153 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM110445 1 0.5900 0.2756 0.500 0.000 0.276 0.220 0.004 0.000
#> GSM110446 3 0.4089 -0.0728 0.000 0.000 0.524 0.008 0.468 0.000
#> GSM110449 4 0.0713 0.8153 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM110451 2 0.0713 0.8024 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM110391 2 0.0713 0.8024 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM110439 2 0.3198 0.5676 0.000 0.740 0.000 0.000 0.260 0.000
#> GSM110442 2 0.1204 0.7924 0.000 0.944 0.000 0.056 0.000 0.000
#> GSM110443 4 0.0713 0.8153 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM110447 3 0.6112 0.5045 0.000 0.320 0.372 0.308 0.000 0.000
#> GSM110448 1 0.0665 0.7753 0.980 0.000 0.008 0.008 0.000 0.004
#> GSM110450 1 0.3628 0.5643 0.776 0.000 0.036 0.184 0.004 0.000
#> GSM110452 2 0.0858 0.8026 0.000 0.968 0.000 0.028 0.004 0.000
#> GSM110453 5 0.5720 0.7767 0.000 0.180 0.000 0.000 0.488 0.332
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) specimen(p) k
#> ATC:hclust 45 1.000 0.675 2
#> ATC:hclust 51 0.762 0.392 3
#> ATC:hclust 45 0.704 0.435 4
#> ATC:hclust 41 0.791 0.665 5
#> ATC:hclust 47 0.181 0.745 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 17209 rows and 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.956 0.983 0.4879 0.516 0.516
#> 3 3 0.707 0.844 0.905 0.3619 0.711 0.489
#> 4 4 0.654 0.719 0.788 0.1178 0.880 0.654
#> 5 5 0.658 0.579 0.692 0.0629 1.000 1.000
#> 6 6 0.706 0.598 0.738 0.0427 0.828 0.419
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
#> GSM110395 2 0.000 0.976 0.000 1.000
#> GSM110396 1 0.000 0.990 1.000 0.000
#> GSM110397 1 0.000 0.990 1.000 0.000
#> GSM110398 1 0.000 0.990 1.000 0.000
#> GSM110399 2 0.000 0.976 0.000 1.000
#> GSM110400 2 0.000 0.976 0.000 1.000
#> GSM110401 1 0.000 0.990 1.000 0.000
#> GSM110406 2 0.000 0.976 0.000 1.000
#> GSM110407 1 0.000 0.990 1.000 0.000
#> GSM110409 1 0.000 0.990 1.000 0.000
#> GSM110410 2 0.000 0.976 0.000 1.000
#> GSM110413 2 0.000 0.976 0.000 1.000
#> GSM110414 2 0.000 0.976 0.000 1.000
#> GSM110415 2 0.000 0.976 0.000 1.000
#> GSM110416 2 0.971 0.338 0.400 0.600
#> GSM110418 2 0.971 0.338 0.400 0.600
#> GSM110419 2 0.000 0.976 0.000 1.000
#> GSM110420 1 0.000 0.990 1.000 0.000
#> GSM110421 2 0.000 0.976 0.000 1.000
#> GSM110423 2 0.000 0.976 0.000 1.000
#> GSM110424 2 0.000 0.976 0.000 1.000
#> GSM110425 2 0.000 0.976 0.000 1.000
#> GSM110427 2 0.000 0.976 0.000 1.000
#> GSM110428 1 0.000 0.990 1.000 0.000
#> GSM110430 1 0.000 0.990 1.000 0.000
#> GSM110431 1 0.000 0.990 1.000 0.000
#> GSM110432 2 0.000 0.976 0.000 1.000
#> GSM110434 2 0.000 0.976 0.000 1.000
#> GSM110435 1 0.000 0.990 1.000 0.000
#> GSM110437 1 0.000 0.990 1.000 0.000
#> GSM110438 1 0.000 0.990 1.000 0.000
#> GSM110388 1 0.000 0.990 1.000 0.000
#> GSM110392 2 0.000 0.976 0.000 1.000
#> GSM110394 1 0.000 0.990 1.000 0.000
#> GSM110402 2 0.000 0.976 0.000 1.000
#> GSM110411 1 0.000 0.990 1.000 0.000
#> GSM110412 2 0.000 0.976 0.000 1.000
#> GSM110417 1 0.000 0.990 1.000 0.000
#> GSM110422 2 0.000 0.976 0.000 1.000
#> GSM110426 1 0.000 0.990 1.000 0.000
#> GSM110429 2 0.000 0.976 0.000 1.000
#> GSM110433 2 0.000 0.976 0.000 1.000
#> GSM110436 2 0.000 0.976 0.000 1.000
#> GSM110440 1 0.000 0.990 1.000 0.000
#> GSM110441 2 0.000 0.976 0.000 1.000
#> GSM110444 2 0.000 0.976 0.000 1.000
#> GSM110445 1 0.000 0.990 1.000 0.000
#> GSM110446 1 0.730 0.732 0.796 0.204
#> GSM110449 2 0.000 0.976 0.000 1.000
#> GSM110451 2 0.000 0.976 0.000 1.000
#> GSM110391 2 0.000 0.976 0.000 1.000
#> GSM110439 2 0.000 0.976 0.000 1.000
#> GSM110442 2 0.000 0.976 0.000 1.000
#> GSM110443 2 0.000 0.976 0.000 1.000
#> GSM110447 2 0.000 0.976 0.000 1.000
#> GSM110448 1 0.000 0.990 1.000 0.000
#> GSM110450 1 0.000 0.990 1.000 0.000
#> GSM110452 2 0.000 0.976 0.000 1.000
#> GSM110453 2 0.000 0.976 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.0237 0.944 0.000 0.996 0.004
#> GSM110396 1 0.0000 0.954 1.000 0.000 0.000
#> GSM110397 1 0.0000 0.954 1.000 0.000 0.000
#> GSM110398 3 0.4974 0.660 0.236 0.000 0.764
#> GSM110399 3 0.5178 0.768 0.000 0.256 0.744
#> GSM110400 2 0.4974 0.727 0.000 0.764 0.236
#> GSM110401 1 0.0000 0.954 1.000 0.000 0.000
#> GSM110406 3 0.5291 0.764 0.000 0.268 0.732
#> GSM110407 1 0.1411 0.954 0.964 0.000 0.036
#> GSM110409 1 0.1411 0.954 0.964 0.000 0.036
#> GSM110410 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110413 2 0.0424 0.940 0.000 0.992 0.008
#> GSM110414 2 0.4750 0.745 0.000 0.784 0.216
#> GSM110415 3 0.1643 0.781 0.000 0.044 0.956
#> GSM110416 3 0.0424 0.772 0.000 0.008 0.992
#> GSM110418 3 0.0424 0.772 0.000 0.008 0.992
#> GSM110419 3 0.1643 0.781 0.000 0.044 0.956
#> GSM110420 3 0.6359 0.224 0.364 0.008 0.628
#> GSM110421 2 0.0237 0.944 0.000 0.996 0.004
#> GSM110423 2 0.4974 0.727 0.000 0.764 0.236
#> GSM110424 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110425 2 0.4974 0.727 0.000 0.764 0.236
#> GSM110427 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110428 3 0.4931 0.665 0.232 0.000 0.768
#> GSM110430 1 0.0000 0.954 1.000 0.000 0.000
#> GSM110431 1 0.0000 0.954 1.000 0.000 0.000
#> GSM110432 3 0.5327 0.762 0.000 0.272 0.728
#> GSM110434 2 0.0237 0.944 0.000 0.996 0.004
#> GSM110435 1 0.1411 0.954 0.964 0.000 0.036
#> GSM110437 1 0.0000 0.954 1.000 0.000 0.000
#> GSM110438 3 0.4702 0.681 0.212 0.000 0.788
#> GSM110388 1 0.1411 0.954 0.964 0.000 0.036
#> GSM110392 3 0.5291 0.764 0.000 0.268 0.732
#> GSM110394 1 0.1411 0.954 0.964 0.000 0.036
#> GSM110402 3 0.3551 0.735 0.000 0.132 0.868
#> GSM110411 3 0.4974 0.660 0.236 0.000 0.764
#> GSM110412 3 0.5327 0.762 0.000 0.272 0.728
#> GSM110417 1 0.0000 0.954 1.000 0.000 0.000
#> GSM110422 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110426 1 0.0000 0.954 1.000 0.000 0.000
#> GSM110429 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110433 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110436 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110440 1 0.1411 0.954 0.964 0.000 0.036
#> GSM110441 2 0.0237 0.944 0.000 0.996 0.004
#> GSM110444 3 0.5178 0.768 0.000 0.256 0.744
#> GSM110445 1 0.6140 0.254 0.596 0.000 0.404
#> GSM110446 3 0.0424 0.772 0.000 0.008 0.992
#> GSM110449 3 0.5291 0.764 0.000 0.268 0.732
#> GSM110451 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110391 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110439 2 0.0000 0.945 0.000 1.000 0.000
#> GSM110442 2 0.0237 0.944 0.000 0.996 0.004
#> GSM110443 3 0.5291 0.764 0.000 0.268 0.732
#> GSM110447 3 0.3752 0.733 0.000 0.144 0.856
#> GSM110448 1 0.1411 0.954 0.964 0.000 0.036
#> GSM110450 1 0.1411 0.954 0.964 0.000 0.036
#> GSM110452 2 0.0237 0.944 0.000 0.996 0.004
#> GSM110453 2 0.0000 0.945 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.4955 0.702 0.000 0.648 0.344 0.008
#> GSM110396 1 0.1398 0.878 0.956 0.000 0.040 0.004
#> GSM110397 1 0.1302 0.877 0.956 0.000 0.044 0.000
#> GSM110398 4 0.1042 0.698 0.020 0.000 0.008 0.972
#> GSM110399 4 0.4139 0.764 0.000 0.024 0.176 0.800
#> GSM110400 3 0.3311 0.539 0.000 0.172 0.828 0.000
#> GSM110401 1 0.1398 0.878 0.956 0.000 0.040 0.004
#> GSM110406 4 0.4139 0.764 0.000 0.024 0.176 0.800
#> GSM110407 1 0.3734 0.879 0.848 0.000 0.044 0.108
#> GSM110409 1 0.4798 0.842 0.768 0.000 0.052 0.180
#> GSM110410 2 0.0000 0.789 0.000 1.000 0.000 0.000
#> GSM110413 2 0.3831 0.793 0.000 0.792 0.204 0.004
#> GSM110414 2 0.3726 0.534 0.000 0.788 0.212 0.000
#> GSM110415 3 0.4175 0.556 0.000 0.012 0.776 0.212
#> GSM110416 3 0.4955 0.433 0.000 0.000 0.556 0.444
#> GSM110418 3 0.4972 0.429 0.000 0.000 0.544 0.456
#> GSM110419 3 0.4262 0.535 0.000 0.008 0.756 0.236
#> GSM110420 3 0.7085 0.361 0.232 0.000 0.568 0.200
#> GSM110421 2 0.4819 0.704 0.000 0.652 0.344 0.004
#> GSM110423 3 0.3400 0.527 0.000 0.180 0.820 0.000
#> GSM110424 2 0.0000 0.789 0.000 1.000 0.000 0.000
#> GSM110425 3 0.3400 0.527 0.000 0.180 0.820 0.000
#> GSM110427 2 0.0000 0.789 0.000 1.000 0.000 0.000
#> GSM110428 4 0.1833 0.669 0.024 0.000 0.032 0.944
#> GSM110430 1 0.1398 0.878 0.956 0.000 0.040 0.004
#> GSM110431 1 0.1302 0.877 0.956 0.000 0.044 0.000
#> GSM110432 4 0.6668 0.393 0.000 0.092 0.380 0.528
#> GSM110434 2 0.4955 0.702 0.000 0.648 0.344 0.008
#> GSM110435 1 0.3978 0.877 0.836 0.000 0.056 0.108
#> GSM110437 1 0.1398 0.878 0.956 0.000 0.040 0.004
#> GSM110438 4 0.1109 0.682 0.004 0.000 0.028 0.968
#> GSM110388 1 0.4756 0.842 0.772 0.000 0.052 0.176
#> GSM110392 4 0.4139 0.764 0.000 0.024 0.176 0.800
#> GSM110394 1 0.3978 0.877 0.836 0.000 0.056 0.108
#> GSM110402 3 0.2871 0.612 0.000 0.032 0.896 0.072
#> GSM110411 4 0.1042 0.698 0.020 0.000 0.008 0.972
#> GSM110412 4 0.6668 0.393 0.000 0.092 0.380 0.528
#> GSM110417 1 0.0000 0.883 1.000 0.000 0.000 0.000
#> GSM110422 2 0.3074 0.805 0.000 0.848 0.152 0.000
#> GSM110426 1 0.0188 0.883 0.996 0.000 0.004 0.000
#> GSM110429 2 0.4585 0.715 0.000 0.668 0.332 0.000
#> GSM110433 2 0.0000 0.789 0.000 1.000 0.000 0.000
#> GSM110436 2 0.0000 0.789 0.000 1.000 0.000 0.000
#> GSM110440 1 0.3978 0.877 0.836 0.000 0.056 0.108
#> GSM110441 2 0.3668 0.798 0.000 0.808 0.188 0.004
#> GSM110444 4 0.4139 0.764 0.000 0.024 0.176 0.800
#> GSM110445 4 0.3758 0.567 0.104 0.000 0.048 0.848
#> GSM110446 3 0.4933 0.408 0.000 0.000 0.568 0.432
#> GSM110449 4 0.4139 0.764 0.000 0.024 0.176 0.800
#> GSM110451 2 0.4643 0.707 0.000 0.656 0.344 0.000
#> GSM110391 2 0.3074 0.805 0.000 0.848 0.152 0.000
#> GSM110439 2 0.0000 0.789 0.000 1.000 0.000 0.000
#> GSM110442 2 0.4955 0.702 0.000 0.648 0.344 0.008
#> GSM110443 4 0.4139 0.764 0.000 0.024 0.176 0.800
#> GSM110447 3 0.4100 0.601 0.000 0.092 0.832 0.076
#> GSM110448 1 0.4532 0.855 0.792 0.000 0.052 0.156
#> GSM110450 1 0.4798 0.842 0.768 0.000 0.052 0.180
#> GSM110452 2 0.3123 0.805 0.000 0.844 0.156 0.000
#> GSM110453 2 0.0000 0.789 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.5819 0.500500 0.000 0.612 0.188 0.200 NA
#> GSM110396 1 0.4410 0.718262 0.556 0.000 0.004 0.000 NA
#> GSM110397 1 0.4278 0.715391 0.548 0.000 0.000 0.000 NA
#> GSM110398 4 0.5104 0.616132 0.128 0.000 0.104 0.740 NA
#> GSM110399 4 0.0290 0.686431 0.000 0.000 0.008 0.992 NA
#> GSM110400 3 0.5051 0.477153 0.000 0.248 0.684 0.060 NA
#> GSM110401 1 0.4278 0.715391 0.548 0.000 0.000 0.000 NA
#> GSM110406 4 0.0510 0.682115 0.000 0.000 0.016 0.984 NA
#> GSM110407 1 0.0000 0.757307 1.000 0.000 0.000 0.000 NA
#> GSM110409 1 0.2344 0.709699 0.904 0.000 0.064 0.000 NA
#> GSM110410 2 0.4161 0.514485 0.000 0.608 0.000 0.000 NA
#> GSM110413 2 0.4662 0.565287 0.000 0.736 0.096 0.168 NA
#> GSM110414 2 0.6363 0.308811 0.000 0.444 0.164 0.000 NA
#> GSM110415 3 0.3607 0.576390 0.000 0.000 0.752 0.244 NA
#> GSM110416 3 0.5144 0.502876 0.000 0.000 0.692 0.176 NA
#> GSM110418 3 0.5451 0.500260 0.012 0.000 0.688 0.168 NA
#> GSM110419 3 0.3741 0.561900 0.000 0.000 0.732 0.264 NA
#> GSM110420 3 0.6320 0.379683 0.316 0.000 0.540 0.012 NA
#> GSM110421 2 0.5763 0.506425 0.000 0.620 0.188 0.192 NA
#> GSM110423 3 0.5051 0.477153 0.000 0.248 0.684 0.060 NA
#> GSM110424 2 0.4161 0.514485 0.000 0.608 0.000 0.000 NA
#> GSM110425 3 0.5051 0.477153 0.000 0.248 0.684 0.060 NA
#> GSM110427 2 0.3752 0.548746 0.000 0.708 0.000 0.000 NA
#> GSM110428 4 0.5692 0.586994 0.156 0.000 0.124 0.688 NA
#> GSM110430 1 0.4278 0.715391 0.548 0.000 0.000 0.000 NA
#> GSM110431 1 0.4410 0.718262 0.556 0.000 0.004 0.000 NA
#> GSM110432 4 0.6333 0.064758 0.000 0.288 0.196 0.516 NA
#> GSM110434 2 0.5817 0.500789 0.000 0.612 0.184 0.204 NA
#> GSM110435 1 0.0000 0.757307 1.000 0.000 0.000 0.000 NA
#> GSM110437 1 0.4278 0.715391 0.548 0.000 0.000 0.000 NA
#> GSM110438 4 0.5655 0.589718 0.152 0.000 0.124 0.692 NA
#> GSM110388 1 0.2344 0.709699 0.904 0.000 0.064 0.000 NA
#> GSM110392 4 0.0290 0.686431 0.000 0.000 0.008 0.992 NA
#> GSM110394 1 0.0000 0.757307 1.000 0.000 0.000 0.000 NA
#> GSM110402 3 0.3445 0.605041 0.000 0.036 0.824 0.140 NA
#> GSM110411 4 0.5104 0.616132 0.128 0.000 0.104 0.740 NA
#> GSM110412 4 0.6410 -0.000943 0.000 0.304 0.200 0.496 NA
#> GSM110417 1 0.3689 0.752595 0.740 0.000 0.004 0.000 NA
#> GSM110422 2 0.1851 0.587772 0.000 0.912 0.088 0.000 NA
#> GSM110426 1 0.3635 0.753678 0.748 0.000 0.004 0.000 NA
#> GSM110429 2 0.4571 0.535349 0.000 0.736 0.188 0.076 NA
#> GSM110433 2 0.4161 0.514485 0.000 0.608 0.000 0.000 NA
#> GSM110436 2 0.3586 0.554728 0.000 0.736 0.000 0.000 NA
#> GSM110440 1 0.0000 0.757307 1.000 0.000 0.000 0.000 NA
#> GSM110441 2 0.4573 0.568711 0.000 0.744 0.092 0.164 NA
#> GSM110444 4 0.0162 0.684749 0.000 0.000 0.004 0.996 NA
#> GSM110445 4 0.6480 0.420702 0.348 0.000 0.104 0.520 NA
#> GSM110446 3 0.6448 0.465087 0.080 0.000 0.640 0.148 NA
#> GSM110449 4 0.0290 0.686431 0.000 0.000 0.008 0.992 NA
#> GSM110451 2 0.5640 0.513966 0.000 0.636 0.188 0.176 NA
#> GSM110391 2 0.1851 0.587772 0.000 0.912 0.088 0.000 NA
#> GSM110439 2 0.3586 0.552779 0.000 0.736 0.000 0.000 NA
#> GSM110442 2 0.5731 0.511235 0.000 0.624 0.180 0.196 NA
#> GSM110443 4 0.0609 0.679321 0.000 0.000 0.020 0.980 NA
#> GSM110447 3 0.5847 0.458498 0.000 0.172 0.624 0.200 NA
#> GSM110448 1 0.1571 0.728218 0.936 0.000 0.060 0.000 NA
#> GSM110450 1 0.2344 0.709699 0.904 0.000 0.064 0.000 NA
#> GSM110452 2 0.4010 0.583178 0.000 0.796 0.088 0.116 NA
#> GSM110453 2 0.4161 0.514485 0.000 0.608 0.000 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.0458 0.661 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM110396 6 0.1865 0.785 0.040 0.000 0.040 0.000 0.000 0.920
#> GSM110397 6 0.0717 0.805 0.008 0.000 0.000 0.000 0.016 0.976
#> GSM110398 4 0.3842 0.701 0.156 0.000 0.076 0.768 0.000 0.000
#> GSM110399 4 0.2135 0.809 0.000 0.128 0.000 0.872 0.000 0.000
#> GSM110400 2 0.7575 -0.191 0.152 0.368 0.360 0.048 0.072 0.000
#> GSM110401 6 0.0000 0.807 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM110406 4 0.2178 0.806 0.000 0.132 0.000 0.868 0.000 0.000
#> GSM110407 1 0.4206 0.704 0.624 0.000 0.012 0.008 0.000 0.356
#> GSM110409 1 0.3566 0.725 0.744 0.000 0.000 0.020 0.000 0.236
#> GSM110410 5 0.1753 0.874 0.000 0.084 0.004 0.000 0.912 0.000
#> GSM110413 2 0.3801 0.590 0.028 0.828 0.040 0.028 0.076 0.000
#> GSM110414 5 0.3748 0.644 0.120 0.016 0.012 0.040 0.812 0.000
#> GSM110415 3 0.7273 0.573 0.152 0.076 0.520 0.196 0.056 0.000
#> GSM110416 3 0.2875 0.645 0.052 0.000 0.852 0.096 0.000 0.000
#> GSM110418 3 0.2888 0.646 0.056 0.000 0.852 0.092 0.000 0.000
#> GSM110419 3 0.7392 0.575 0.152 0.076 0.496 0.220 0.056 0.000
#> GSM110420 3 0.4186 0.495 0.192 0.000 0.728 0.000 0.000 0.080
#> GSM110421 2 0.0363 0.661 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM110423 2 0.7575 -0.191 0.152 0.368 0.360 0.048 0.072 0.000
#> GSM110424 5 0.1610 0.873 0.000 0.084 0.000 0.000 0.916 0.000
#> GSM110425 2 0.7575 -0.191 0.152 0.368 0.360 0.048 0.072 0.000
#> GSM110427 5 0.4125 0.803 0.024 0.208 0.028 0.000 0.740 0.000
#> GSM110428 4 0.4729 0.639 0.196 0.000 0.128 0.676 0.000 0.000
#> GSM110430 6 0.0000 0.807 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM110431 6 0.1528 0.796 0.048 0.000 0.000 0.000 0.016 0.936
#> GSM110432 2 0.5083 0.421 0.024 0.640 0.068 0.268 0.000 0.000
#> GSM110434 2 0.0547 0.660 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM110435 1 0.4102 0.699 0.628 0.000 0.012 0.000 0.004 0.356
#> GSM110437 6 0.0000 0.807 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM110438 4 0.4701 0.643 0.192 0.000 0.128 0.680 0.000 0.000
#> GSM110388 1 0.3860 0.718 0.728 0.000 0.000 0.036 0.000 0.236
#> GSM110392 4 0.2278 0.808 0.004 0.128 0.000 0.868 0.000 0.000
#> GSM110394 1 0.4102 0.699 0.628 0.000 0.012 0.000 0.004 0.356
#> GSM110402 3 0.7963 0.399 0.152 0.192 0.440 0.152 0.064 0.000
#> GSM110411 4 0.3946 0.694 0.168 0.000 0.076 0.756 0.000 0.000
#> GSM110412 2 0.4661 0.474 0.024 0.688 0.048 0.240 0.000 0.000
#> GSM110417 6 0.4938 0.172 0.348 0.000 0.040 0.000 0.020 0.592
#> GSM110422 2 0.4186 0.483 0.024 0.752 0.044 0.000 0.180 0.000
#> GSM110426 6 0.4949 0.156 0.352 0.000 0.040 0.000 0.020 0.588
#> GSM110429 2 0.2356 0.601 0.016 0.884 0.000 0.004 0.096 0.000
#> GSM110433 5 0.1753 0.874 0.000 0.084 0.004 0.000 0.912 0.000
#> GSM110436 5 0.4527 0.774 0.024 0.228 0.044 0.000 0.704 0.000
#> GSM110440 1 0.4102 0.699 0.628 0.000 0.012 0.000 0.004 0.356
#> GSM110441 2 0.3782 0.589 0.036 0.828 0.032 0.024 0.080 0.000
#> GSM110444 4 0.2135 0.809 0.000 0.128 0.000 0.872 0.000 0.000
#> GSM110445 1 0.5071 -0.228 0.480 0.000 0.076 0.444 0.000 0.000
#> GSM110446 3 0.3534 0.621 0.124 0.000 0.800 0.076 0.000 0.000
#> GSM110449 4 0.2135 0.809 0.000 0.128 0.000 0.872 0.000 0.000
#> GSM110451 2 0.0622 0.657 0.012 0.980 0.000 0.000 0.008 0.000
#> GSM110391 2 0.4348 0.470 0.028 0.732 0.040 0.000 0.200 0.000
#> GSM110439 5 0.4364 0.809 0.044 0.184 0.032 0.000 0.740 0.000
#> GSM110442 2 0.0717 0.660 0.000 0.976 0.008 0.016 0.000 0.000
#> GSM110443 4 0.2135 0.809 0.000 0.128 0.000 0.872 0.000 0.000
#> GSM110447 2 0.8150 -0.263 0.152 0.328 0.324 0.132 0.064 0.000
#> GSM110448 1 0.3528 0.728 0.700 0.000 0.000 0.000 0.004 0.296
#> GSM110450 1 0.3925 0.715 0.724 0.000 0.000 0.040 0.000 0.236
#> GSM110452 2 0.3794 0.566 0.024 0.812 0.044 0.008 0.112 0.000
#> GSM110453 5 0.1753 0.874 0.000 0.084 0.004 0.000 0.912 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) specimen(p) k
#> ATC:kmeans 57 0.666 0.402 2
#> ATC:kmeans 57 0.930 0.516 3
#> ATC:kmeans 53 0.556 0.588 4
#> ATC:kmeans 49 0.404 0.366 5
#> ATC:kmeans 46 0.170 0.591 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 17209 rows and 59 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 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 0.897 0.929 0.970 0.4998 0.503 0.503
#> 3 3 0.743 0.800 0.875 0.2512 0.811 0.637
#> 4 4 0.813 0.819 0.924 0.1045 0.822 0.572
#> 5 5 0.791 0.852 0.887 0.0429 0.926 0.763
#> 6 6 0.831 0.842 0.896 0.0337 0.991 0.965
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
#> GSM110395 2 0.0000 0.963 0.000 1.000
#> GSM110396 1 0.0000 0.974 1.000 0.000
#> GSM110397 1 0.0000 0.974 1.000 0.000
#> GSM110398 1 0.0000 0.974 1.000 0.000
#> GSM110399 2 0.9358 0.488 0.352 0.648
#> GSM110400 2 0.0000 0.963 0.000 1.000
#> GSM110401 1 0.0000 0.974 1.000 0.000
#> GSM110406 2 0.0000 0.963 0.000 1.000
#> GSM110407 1 0.0000 0.974 1.000 0.000
#> GSM110409 1 0.0000 0.974 1.000 0.000
#> GSM110410 2 0.0000 0.963 0.000 1.000
#> GSM110413 2 0.0000 0.963 0.000 1.000
#> GSM110414 2 0.0000 0.963 0.000 1.000
#> GSM110415 2 0.0000 0.963 0.000 1.000
#> GSM110416 1 0.9552 0.403 0.624 0.376
#> GSM110418 1 0.7299 0.732 0.796 0.204
#> GSM110419 2 0.0000 0.963 0.000 1.000
#> GSM110420 1 0.0000 0.974 1.000 0.000
#> GSM110421 2 0.0000 0.963 0.000 1.000
#> GSM110423 2 0.0000 0.963 0.000 1.000
#> GSM110424 2 0.0000 0.963 0.000 1.000
#> GSM110425 2 0.0000 0.963 0.000 1.000
#> GSM110427 2 0.0000 0.963 0.000 1.000
#> GSM110428 1 0.0000 0.974 1.000 0.000
#> GSM110430 1 0.0000 0.974 1.000 0.000
#> GSM110431 1 0.0000 0.974 1.000 0.000
#> GSM110432 2 0.0000 0.963 0.000 1.000
#> GSM110434 2 0.0000 0.963 0.000 1.000
#> GSM110435 1 0.0000 0.974 1.000 0.000
#> GSM110437 1 0.0000 0.974 1.000 0.000
#> GSM110438 1 0.0000 0.974 1.000 0.000
#> GSM110388 1 0.0000 0.974 1.000 0.000
#> GSM110392 2 0.0672 0.956 0.008 0.992
#> GSM110394 1 0.0000 0.974 1.000 0.000
#> GSM110402 2 0.0000 0.963 0.000 1.000
#> GSM110411 1 0.0000 0.974 1.000 0.000
#> GSM110412 2 0.0000 0.963 0.000 1.000
#> GSM110417 1 0.0000 0.974 1.000 0.000
#> GSM110422 2 0.0000 0.963 0.000 1.000
#> GSM110426 1 0.0000 0.974 1.000 0.000
#> GSM110429 2 0.0000 0.963 0.000 1.000
#> GSM110433 2 0.0000 0.963 0.000 1.000
#> GSM110436 2 0.0000 0.963 0.000 1.000
#> GSM110440 1 0.0000 0.974 1.000 0.000
#> GSM110441 2 0.0000 0.963 0.000 1.000
#> GSM110444 2 0.9710 0.375 0.400 0.600
#> GSM110445 1 0.0000 0.974 1.000 0.000
#> GSM110446 1 0.0000 0.974 1.000 0.000
#> GSM110449 2 0.7299 0.744 0.204 0.796
#> GSM110451 2 0.0000 0.963 0.000 1.000
#> GSM110391 2 0.0000 0.963 0.000 1.000
#> GSM110439 2 0.0000 0.963 0.000 1.000
#> GSM110442 2 0.0000 0.963 0.000 1.000
#> GSM110443 2 0.7299 0.744 0.204 0.796
#> GSM110447 2 0.0000 0.963 0.000 1.000
#> GSM110448 1 0.0000 0.974 1.000 0.000
#> GSM110450 1 0.0000 0.974 1.000 0.000
#> GSM110452 2 0.0000 0.963 0.000 1.000
#> GSM110453 2 0.0000 0.963 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110396 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110397 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110398 1 0.4465 0.788 0.820 0.176 0.004
#> GSM110399 2 0.1031 0.591 0.000 0.976 0.024
#> GSM110400 3 0.2165 0.669 0.000 0.064 0.936
#> GSM110401 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110406 2 0.3116 0.674 0.000 0.892 0.108
#> GSM110407 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110409 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110410 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110413 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110414 3 0.5254 0.168 0.000 0.264 0.736
#> GSM110415 3 0.0237 0.679 0.000 0.004 0.996
#> GSM110416 3 0.5859 0.441 0.344 0.000 0.656
#> GSM110418 3 0.6026 0.410 0.376 0.000 0.624
#> GSM110419 3 0.0237 0.679 0.000 0.004 0.996
#> GSM110420 3 0.6026 0.410 0.376 0.000 0.624
#> GSM110421 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110423 3 0.2165 0.669 0.000 0.064 0.936
#> GSM110424 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110425 3 0.2165 0.669 0.000 0.064 0.936
#> GSM110427 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110428 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110430 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110431 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110432 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110434 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110435 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110437 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110438 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110388 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110392 2 0.0237 0.569 0.000 0.996 0.004
#> GSM110394 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110402 3 0.2165 0.669 0.000 0.064 0.936
#> GSM110411 1 0.3193 0.879 0.896 0.100 0.004
#> GSM110412 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110417 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110422 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110426 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110429 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110433 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110436 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110440 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110441 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110444 2 0.6345 -0.139 0.400 0.596 0.004
#> GSM110445 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110446 3 0.6026 0.410 0.376 0.000 0.624
#> GSM110449 2 0.0747 0.583 0.000 0.984 0.016
#> GSM110451 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110391 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110439 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110442 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110443 2 0.0000 0.574 0.000 1.000 0.000
#> GSM110447 3 0.2625 0.641 0.000 0.084 0.916
#> GSM110448 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110450 1 0.0000 0.984 1.000 0.000 0.000
#> GSM110452 2 0.5810 0.875 0.000 0.664 0.336
#> GSM110453 2 0.5810 0.875 0.000 0.664 0.336
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110396 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110397 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110398 4 0.4936 0.467 0.372 0.000 0.004 0.624
#> GSM110399 4 0.2983 0.762 0.000 0.068 0.040 0.892
#> GSM110400 2 0.4855 0.362 0.000 0.600 0.400 0.000
#> GSM110401 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110406 4 0.3681 0.647 0.000 0.176 0.008 0.816
#> GSM110407 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110409 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110410 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110413 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110414 2 0.4855 0.362 0.000 0.600 0.400 0.000
#> GSM110415 3 0.1118 0.739 0.000 0.036 0.964 0.000
#> GSM110416 3 0.1389 0.748 0.048 0.000 0.952 0.000
#> GSM110418 3 0.3610 0.742 0.200 0.000 0.800 0.000
#> GSM110419 3 0.1118 0.739 0.000 0.036 0.964 0.000
#> GSM110420 3 0.3610 0.742 0.200 0.000 0.800 0.000
#> GSM110421 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110423 2 0.4855 0.362 0.000 0.600 0.400 0.000
#> GSM110424 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110425 2 0.4855 0.362 0.000 0.600 0.400 0.000
#> GSM110427 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110428 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110430 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110431 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110432 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110434 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110435 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110437 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110438 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110388 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110392 4 0.0336 0.776 0.000 0.008 0.000 0.992
#> GSM110394 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110402 3 0.4855 0.193 0.000 0.400 0.600 0.000
#> GSM110411 4 0.5004 0.425 0.392 0.000 0.004 0.604
#> GSM110412 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110417 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110422 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110426 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110429 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110433 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110436 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110440 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110441 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110444 4 0.0376 0.773 0.000 0.004 0.004 0.992
#> GSM110445 1 0.3569 0.711 0.804 0.000 0.000 0.196
#> GSM110446 3 0.3610 0.742 0.200 0.000 0.800 0.000
#> GSM110449 4 0.2565 0.769 0.000 0.056 0.032 0.912
#> GSM110451 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110391 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110439 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110442 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110443 4 0.0336 0.776 0.000 0.008 0.000 0.992
#> GSM110447 2 0.4855 0.362 0.000 0.600 0.400 0.000
#> GSM110448 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110450 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM110452 2 0.0000 0.900 0.000 1.000 0.000 0.000
#> GSM110453 2 0.0000 0.900 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110396 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110397 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110398 4 0.4873 0.5261 0.244 0.000 0.000 0.688 0.068
#> GSM110399 4 0.4735 0.6654 0.000 0.008 0.012 0.608 0.372
#> GSM110400 3 0.4030 0.7733 0.000 0.352 0.648 0.000 0.000
#> GSM110401 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110406 4 0.6618 0.4409 0.000 0.264 0.004 0.492 0.240
#> GSM110407 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110409 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110410 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110413 2 0.0566 0.9788 0.000 0.984 0.000 0.004 0.012
#> GSM110414 3 0.4297 0.6016 0.000 0.472 0.528 0.000 0.000
#> GSM110415 3 0.0404 0.2348 0.000 0.012 0.988 0.000 0.000
#> GSM110416 5 0.5103 0.7414 0.036 0.000 0.452 0.000 0.512
#> GSM110418 5 0.6245 0.9129 0.168 0.000 0.316 0.000 0.516
#> GSM110419 3 0.0566 0.2289 0.000 0.012 0.984 0.000 0.004
#> GSM110420 5 0.6275 0.9133 0.176 0.000 0.308 0.000 0.516
#> GSM110421 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110423 3 0.4045 0.7742 0.000 0.356 0.644 0.000 0.000
#> GSM110424 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110425 3 0.4045 0.7742 0.000 0.356 0.644 0.000 0.000
#> GSM110427 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110428 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110430 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110431 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110432 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110434 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110435 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110437 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110438 1 0.4434 -0.0242 0.536 0.000 0.000 0.004 0.460
#> GSM110388 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110392 4 0.3257 0.6697 0.000 0.028 0.004 0.844 0.124
#> GSM110394 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110402 3 0.3707 0.7164 0.000 0.284 0.716 0.000 0.000
#> GSM110411 4 0.4354 0.5079 0.256 0.000 0.000 0.712 0.032
#> GSM110412 2 0.0324 0.9891 0.000 0.992 0.000 0.004 0.004
#> GSM110417 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110422 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110426 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110429 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110433 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110436 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110440 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110441 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110444 4 0.0290 0.6855 0.000 0.000 0.000 0.992 0.008
#> GSM110445 1 0.2462 0.8196 0.880 0.000 0.000 0.112 0.008
#> GSM110446 5 0.6275 0.9133 0.176 0.000 0.308 0.000 0.516
#> GSM110449 4 0.4804 0.6677 0.000 0.016 0.008 0.612 0.364
#> GSM110451 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110391 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110439 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110442 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110443 4 0.2853 0.7023 0.000 0.040 0.004 0.880 0.076
#> GSM110447 3 0.4182 0.7392 0.000 0.400 0.600 0.000 0.000
#> GSM110448 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110450 1 0.0000 0.9623 1.000 0.000 0.000 0.000 0.000
#> GSM110452 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
#> GSM110453 2 0.0000 0.9983 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.0363 0.9670 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM110396 1 0.0000 0.9615 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110397 1 0.0146 0.9613 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM110398 4 0.4879 0.5317 0.096 0.000 0.000 0.732 0.096 0.076
#> GSM110399 6 0.3215 0.6068 0.000 0.004 0.000 0.240 0.000 0.756
#> GSM110400 3 0.2941 0.7978 0.000 0.220 0.780 0.000 0.000 0.000
#> GSM110401 1 0.0000 0.9615 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110406 6 0.6172 0.3080 0.000 0.232 0.000 0.328 0.008 0.432
#> GSM110407 1 0.0000 0.9615 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110409 1 0.0000 0.9615 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110410 2 0.0547 0.9631 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM110413 2 0.1663 0.9071 0.000 0.912 0.000 0.000 0.000 0.088
#> GSM110414 3 0.3756 0.6211 0.000 0.400 0.600 0.000 0.000 0.000
#> GSM110415 3 0.1007 0.5473 0.000 0.000 0.956 0.000 0.044 0.000
#> GSM110416 5 0.2872 0.8346 0.024 0.000 0.140 0.000 0.836 0.000
#> GSM110418 5 0.3045 0.9322 0.100 0.000 0.060 0.000 0.840 0.000
#> GSM110419 3 0.1007 0.5473 0.000 0.000 0.956 0.000 0.044 0.000
#> GSM110420 5 0.3227 0.9321 0.116 0.000 0.060 0.000 0.824 0.000
#> GSM110421 2 0.0458 0.9669 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM110423 3 0.2969 0.7980 0.000 0.224 0.776 0.000 0.000 0.000
#> GSM110424 2 0.0547 0.9631 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM110425 3 0.2996 0.7965 0.000 0.228 0.772 0.000 0.000 0.000
#> GSM110427 2 0.0713 0.9651 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM110428 1 0.0146 0.9613 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM110430 1 0.0000 0.9615 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110431 1 0.0146 0.9613 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM110432 2 0.1124 0.9587 0.000 0.956 0.008 0.000 0.000 0.036
#> GSM110434 2 0.0713 0.9650 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM110435 1 0.0146 0.9613 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM110437 1 0.0000 0.9615 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110438 1 0.5852 -0.0689 0.484 0.000 0.004 0.012 0.380 0.120
#> GSM110388 1 0.0000 0.9615 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110392 4 0.5456 0.4413 0.000 0.012 0.024 0.612 0.064 0.288
#> GSM110394 1 0.0146 0.9613 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM110402 3 0.2902 0.7851 0.000 0.196 0.800 0.000 0.004 0.000
#> GSM110411 4 0.3860 0.5732 0.108 0.000 0.000 0.788 0.096 0.008
#> GSM110412 2 0.1462 0.9440 0.000 0.936 0.000 0.000 0.008 0.056
#> GSM110417 1 0.0146 0.9613 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM110422 2 0.0865 0.9627 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM110426 1 0.0146 0.9613 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM110429 2 0.0865 0.9627 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM110433 2 0.0632 0.9616 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM110436 2 0.0865 0.9627 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM110440 1 0.0146 0.9613 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM110441 2 0.1141 0.9434 0.000 0.948 0.000 0.000 0.000 0.052
#> GSM110444 4 0.0146 0.6043 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM110445 1 0.1908 0.8560 0.900 0.000 0.000 0.096 0.004 0.000
#> GSM110446 5 0.3227 0.9318 0.116 0.000 0.060 0.000 0.824 0.000
#> GSM110449 6 0.3215 0.6066 0.000 0.004 0.000 0.240 0.000 0.756
#> GSM110451 2 0.0865 0.9627 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM110391 2 0.0713 0.9600 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM110439 2 0.0547 0.9631 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM110442 2 0.0146 0.9665 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM110443 4 0.3997 0.4986 0.000 0.016 0.020 0.772 0.016 0.176
#> GSM110447 3 0.3620 0.6861 0.000 0.352 0.648 0.000 0.000 0.000
#> GSM110448 1 0.0000 0.9615 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110450 1 0.0000 0.9615 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM110452 2 0.0790 0.9639 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM110453 2 0.0547 0.9631 0.000 0.980 0.000 0.000 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) specimen(p) k
#> ATC:skmeans 56 0.563 0.318 2
#> ATC:skmeans 53 0.260 0.419 3
#> ATC:skmeans 51 0.204 0.421 4
#> ATC:skmeans 55 0.412 0.688 5
#> ATC:skmeans 55 0.520 0.625 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 17209 rows and 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.959 0.985 0.4905 0.509 0.509
#> 3 3 0.864 0.861 0.948 0.3036 0.695 0.483
#> 4 4 0.647 0.669 0.840 0.1212 0.899 0.730
#> 5 5 0.860 0.807 0.924 0.0808 0.886 0.628
#> 6 6 0.873 0.856 0.927 0.0609 0.853 0.463
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
#> GSM110395 2 0.0000 0.988 0.000 1.000
#> GSM110396 1 0.0000 0.979 1.000 0.000
#> GSM110397 1 0.0000 0.979 1.000 0.000
#> GSM110398 1 0.0376 0.977 0.996 0.004
#> GSM110399 2 0.0000 0.988 0.000 1.000
#> GSM110400 2 0.0000 0.988 0.000 1.000
#> GSM110401 1 0.0000 0.979 1.000 0.000
#> GSM110406 2 0.0000 0.988 0.000 1.000
#> GSM110407 1 0.0000 0.979 1.000 0.000
#> GSM110409 1 0.0000 0.979 1.000 0.000
#> GSM110410 2 0.0000 0.988 0.000 1.000
#> GSM110413 2 0.0000 0.988 0.000 1.000
#> GSM110414 2 0.0000 0.988 0.000 1.000
#> GSM110415 2 0.0000 0.988 0.000 1.000
#> GSM110416 2 0.9710 0.306 0.400 0.600
#> GSM110418 1 0.9896 0.196 0.560 0.440
#> GSM110419 2 0.0000 0.988 0.000 1.000
#> GSM110420 1 0.0376 0.977 0.996 0.004
#> GSM110421 2 0.0000 0.988 0.000 1.000
#> GSM110423 2 0.0000 0.988 0.000 1.000
#> GSM110424 2 0.0000 0.988 0.000 1.000
#> GSM110425 2 0.0000 0.988 0.000 1.000
#> GSM110427 2 0.0000 0.988 0.000 1.000
#> GSM110428 1 0.0376 0.977 0.996 0.004
#> GSM110430 1 0.0000 0.979 1.000 0.000
#> GSM110431 1 0.0000 0.979 1.000 0.000
#> GSM110432 2 0.0000 0.988 0.000 1.000
#> GSM110434 2 0.0000 0.988 0.000 1.000
#> GSM110435 1 0.0000 0.979 1.000 0.000
#> GSM110437 1 0.0000 0.979 1.000 0.000
#> GSM110438 1 0.0376 0.977 0.996 0.004
#> GSM110388 1 0.0000 0.979 1.000 0.000
#> GSM110392 2 0.0000 0.988 0.000 1.000
#> GSM110394 1 0.0000 0.979 1.000 0.000
#> GSM110402 2 0.0000 0.988 0.000 1.000
#> GSM110411 1 0.0376 0.977 0.996 0.004
#> GSM110412 2 0.0000 0.988 0.000 1.000
#> GSM110417 1 0.0000 0.979 1.000 0.000
#> GSM110422 2 0.0000 0.988 0.000 1.000
#> GSM110426 1 0.0000 0.979 1.000 0.000
#> GSM110429 2 0.0000 0.988 0.000 1.000
#> GSM110433 2 0.0000 0.988 0.000 1.000
#> GSM110436 2 0.0000 0.988 0.000 1.000
#> GSM110440 1 0.0000 0.979 1.000 0.000
#> GSM110441 2 0.0000 0.988 0.000 1.000
#> GSM110444 2 0.0000 0.988 0.000 1.000
#> GSM110445 1 0.0000 0.979 1.000 0.000
#> GSM110446 1 0.0672 0.974 0.992 0.008
#> GSM110449 2 0.0000 0.988 0.000 1.000
#> GSM110451 2 0.0000 0.988 0.000 1.000
#> GSM110391 2 0.0000 0.988 0.000 1.000
#> GSM110439 2 0.0000 0.988 0.000 1.000
#> GSM110442 2 0.0000 0.988 0.000 1.000
#> GSM110443 2 0.0000 0.988 0.000 1.000
#> GSM110447 2 0.0000 0.988 0.000 1.000
#> GSM110448 1 0.0000 0.979 1.000 0.000
#> GSM110450 1 0.0000 0.979 1.000 0.000
#> GSM110452 2 0.0000 0.988 0.000 1.000
#> GSM110453 2 0.0000 0.988 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 3 0.000 0.913 0.000 0.000 1.000
#> GSM110396 1 0.000 0.969 1.000 0.000 0.000
#> GSM110397 1 0.000 0.969 1.000 0.000 0.000
#> GSM110398 3 0.611 0.350 0.396 0.000 0.604
#> GSM110399 3 0.000 0.913 0.000 0.000 1.000
#> GSM110400 3 0.000 0.913 0.000 0.000 1.000
#> GSM110401 1 0.000 0.969 1.000 0.000 0.000
#> GSM110406 3 0.000 0.913 0.000 0.000 1.000
#> GSM110407 1 0.000 0.969 1.000 0.000 0.000
#> GSM110409 1 0.000 0.969 1.000 0.000 0.000
#> GSM110410 2 0.000 0.940 0.000 1.000 0.000
#> GSM110413 3 0.000 0.913 0.000 0.000 1.000
#> GSM110414 2 0.000 0.940 0.000 1.000 0.000
#> GSM110415 3 0.000 0.913 0.000 0.000 1.000
#> GSM110416 3 0.000 0.913 0.000 0.000 1.000
#> GSM110418 3 0.164 0.880 0.044 0.000 0.956
#> GSM110419 3 0.000 0.913 0.000 0.000 1.000
#> GSM110420 3 0.620 0.291 0.424 0.000 0.576
#> GSM110421 3 0.000 0.913 0.000 0.000 1.000
#> GSM110423 3 0.000 0.913 0.000 0.000 1.000
#> GSM110424 2 0.000 0.940 0.000 1.000 0.000
#> GSM110425 3 0.000 0.913 0.000 0.000 1.000
#> GSM110427 2 0.000 0.940 0.000 1.000 0.000
#> GSM110428 1 0.619 0.179 0.580 0.000 0.420
#> GSM110430 1 0.000 0.969 1.000 0.000 0.000
#> GSM110431 1 0.000 0.969 1.000 0.000 0.000
#> GSM110432 3 0.000 0.913 0.000 0.000 1.000
#> GSM110434 3 0.000 0.913 0.000 0.000 1.000
#> GSM110435 1 0.000 0.969 1.000 0.000 0.000
#> GSM110437 1 0.000 0.969 1.000 0.000 0.000
#> GSM110438 3 0.455 0.726 0.200 0.000 0.800
#> GSM110388 1 0.000 0.969 1.000 0.000 0.000
#> GSM110392 3 0.000 0.913 0.000 0.000 1.000
#> GSM110394 1 0.000 0.969 1.000 0.000 0.000
#> GSM110402 3 0.000 0.913 0.000 0.000 1.000
#> GSM110411 3 0.506 0.655 0.244 0.000 0.756
#> GSM110412 3 0.000 0.913 0.000 0.000 1.000
#> GSM110417 1 0.000 0.969 1.000 0.000 0.000
#> GSM110422 2 0.129 0.925 0.000 0.968 0.032
#> GSM110426 1 0.000 0.969 1.000 0.000 0.000
#> GSM110429 2 0.625 0.216 0.000 0.556 0.444
#> GSM110433 2 0.000 0.940 0.000 1.000 0.000
#> GSM110436 2 0.000 0.940 0.000 1.000 0.000
#> GSM110440 1 0.000 0.969 1.000 0.000 0.000
#> GSM110441 3 0.617 0.278 0.000 0.412 0.588
#> GSM110444 3 0.000 0.913 0.000 0.000 1.000
#> GSM110445 1 0.000 0.969 1.000 0.000 0.000
#> GSM110446 3 0.603 0.414 0.376 0.000 0.624
#> GSM110449 3 0.000 0.913 0.000 0.000 1.000
#> GSM110451 3 0.000 0.913 0.000 0.000 1.000
#> GSM110391 2 0.226 0.894 0.000 0.932 0.068
#> GSM110439 2 0.000 0.940 0.000 1.000 0.000
#> GSM110442 3 0.000 0.913 0.000 0.000 1.000
#> GSM110443 3 0.000 0.913 0.000 0.000 1.000
#> GSM110447 3 0.000 0.913 0.000 0.000 1.000
#> GSM110448 1 0.000 0.969 1.000 0.000 0.000
#> GSM110450 1 0.000 0.969 1.000 0.000 0.000
#> GSM110452 2 0.141 0.922 0.000 0.964 0.036
#> GSM110453 2 0.000 0.940 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 4 0.2469 0.80405 0.000 0.108 0.000 0.892
#> GSM110396 1 0.5028 0.64177 0.596 0.004 0.400 0.000
#> GSM110397 1 0.5028 0.64177 0.596 0.004 0.400 0.000
#> GSM110398 4 0.4624 0.23041 0.340 0.000 0.000 0.660
#> GSM110399 4 0.0000 0.76600 0.000 0.000 0.000 1.000
#> GSM110400 4 0.2593 0.80295 0.000 0.104 0.004 0.892
#> GSM110401 1 0.5028 0.64177 0.596 0.004 0.400 0.000
#> GSM110406 4 0.0000 0.76600 0.000 0.000 0.000 1.000
#> GSM110407 1 0.0000 0.79314 1.000 0.000 0.000 0.000
#> GSM110409 1 0.0000 0.79314 1.000 0.000 0.000 0.000
#> GSM110410 2 0.0188 0.89026 0.000 0.996 0.000 0.004
#> GSM110413 4 0.2469 0.80405 0.000 0.108 0.000 0.892
#> GSM110414 2 0.0376 0.88708 0.000 0.992 0.004 0.004
#> GSM110415 3 0.4855 0.51110 0.000 0.000 0.600 0.400
#> GSM110416 3 0.4855 0.51110 0.000 0.000 0.600 0.400
#> GSM110418 3 0.6855 0.61363 0.200 0.000 0.600 0.200
#> GSM110419 4 0.4907 -0.09425 0.000 0.000 0.420 0.580
#> GSM110420 3 0.4855 0.40850 0.400 0.000 0.600 0.000
#> GSM110421 4 0.2469 0.80405 0.000 0.108 0.000 0.892
#> GSM110423 4 0.4348 0.58851 0.000 0.024 0.196 0.780
#> GSM110424 2 0.0188 0.89026 0.000 0.996 0.000 0.004
#> GSM110425 4 0.2593 0.80295 0.000 0.104 0.004 0.892
#> GSM110427 2 0.0188 0.89026 0.000 0.996 0.000 0.004
#> GSM110428 1 0.4907 0.08376 0.580 0.000 0.000 0.420
#> GSM110430 1 0.5028 0.64177 0.596 0.004 0.400 0.000
#> GSM110431 1 0.5028 0.64177 0.596 0.004 0.400 0.000
#> GSM110432 4 0.2469 0.80405 0.000 0.108 0.000 0.892
#> GSM110434 4 0.2469 0.80405 0.000 0.108 0.000 0.892
#> GSM110435 1 0.0000 0.79314 1.000 0.000 0.000 0.000
#> GSM110437 1 0.5028 0.64177 0.596 0.004 0.400 0.000
#> GSM110438 4 0.7523 -0.27819 0.400 0.000 0.184 0.416
#> GSM110388 1 0.0188 0.79060 0.996 0.000 0.000 0.004
#> GSM110392 4 0.0000 0.76600 0.000 0.000 0.000 1.000
#> GSM110394 1 0.0000 0.79314 1.000 0.000 0.000 0.000
#> GSM110402 3 0.4967 0.39863 0.000 0.000 0.548 0.452
#> GSM110411 4 0.4679 0.23191 0.352 0.000 0.000 0.648
#> GSM110412 4 0.2469 0.80405 0.000 0.108 0.000 0.892
#> GSM110417 1 0.0188 0.79205 0.996 0.004 0.000 0.000
#> GSM110422 2 0.0592 0.88498 0.000 0.984 0.000 0.016
#> GSM110426 1 0.0000 0.79314 1.000 0.000 0.000 0.000
#> GSM110429 2 0.4925 0.10224 0.000 0.572 0.000 0.428
#> GSM110433 2 0.0188 0.89026 0.000 0.996 0.000 0.004
#> GSM110436 2 0.0188 0.89026 0.000 0.996 0.000 0.004
#> GSM110440 1 0.0000 0.79314 1.000 0.000 0.000 0.000
#> GSM110441 2 0.4994 0.00754 0.000 0.520 0.000 0.480
#> GSM110444 4 0.0000 0.76600 0.000 0.000 0.000 1.000
#> GSM110445 1 0.0188 0.79060 0.996 0.000 0.000 0.004
#> GSM110446 3 0.4855 0.40850 0.400 0.000 0.600 0.000
#> GSM110449 4 0.0000 0.76600 0.000 0.000 0.000 1.000
#> GSM110451 4 0.2469 0.80405 0.000 0.108 0.000 0.892
#> GSM110391 2 0.1302 0.86177 0.000 0.956 0.000 0.044
#> GSM110439 2 0.0188 0.89026 0.000 0.996 0.000 0.004
#> GSM110442 4 0.2469 0.80405 0.000 0.108 0.000 0.892
#> GSM110443 4 0.0000 0.76600 0.000 0.000 0.000 1.000
#> GSM110447 4 0.2469 0.80405 0.000 0.108 0.000 0.892
#> GSM110448 1 0.0000 0.79314 1.000 0.000 0.000 0.000
#> GSM110450 1 0.0000 0.79314 1.000 0.000 0.000 0.000
#> GSM110452 2 0.0707 0.88263 0.000 0.980 0.000 0.020
#> GSM110453 2 0.0188 0.89026 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000
#> GSM110396 1 0.2230 0.819 0.884 0.000 0.000 0.116 0.000
#> GSM110397 1 0.0000 0.898 1.000 0.000 0.000 0.000 0.000
#> GSM110398 4 0.5490 0.590 0.000 0.148 0.200 0.652 0.000
#> GSM110399 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000
#> GSM110400 2 0.0703 0.905 0.000 0.976 0.024 0.000 0.000
#> GSM110401 1 0.0000 0.898 1.000 0.000 0.000 0.000 0.000
#> GSM110406 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000
#> GSM110407 4 0.0000 0.910 0.000 0.000 0.000 1.000 0.000
#> GSM110409 4 0.0000 0.910 0.000 0.000 0.000 1.000 0.000
#> GSM110410 5 0.0000 0.921 0.000 0.000 0.000 0.000 1.000
#> GSM110413 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000
#> GSM110414 5 0.0703 0.907 0.000 0.000 0.024 0.000 0.976
#> GSM110415 3 0.3109 0.633 0.000 0.200 0.800 0.000 0.000
#> GSM110416 3 0.0000 0.686 0.000 0.000 1.000 0.000 0.000
#> GSM110418 3 0.0000 0.686 0.000 0.000 1.000 0.000 0.000
#> GSM110419 2 0.4182 0.155 0.000 0.600 0.400 0.000 0.000
#> GSM110420 3 0.3143 0.559 0.000 0.000 0.796 0.204 0.000
#> GSM110421 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000
#> GSM110423 2 0.3177 0.652 0.000 0.792 0.208 0.000 0.000
#> GSM110424 5 0.0000 0.921 0.000 0.000 0.000 0.000 1.000
#> GSM110425 2 0.0703 0.905 0.000 0.976 0.024 0.000 0.000
#> GSM110427 5 0.0000 0.921 0.000 0.000 0.000 0.000 1.000
#> GSM110428 4 0.3177 0.790 0.000 0.000 0.208 0.792 0.000
#> GSM110430 1 0.0000 0.898 1.000 0.000 0.000 0.000 0.000
#> GSM110431 1 0.0000 0.898 1.000 0.000 0.000 0.000 0.000
#> GSM110432 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000
#> GSM110434 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000
#> GSM110435 4 0.0000 0.910 0.000 0.000 0.000 1.000 0.000
#> GSM110437 1 0.0000 0.898 1.000 0.000 0.000 0.000 0.000
#> GSM110438 3 0.4779 0.337 0.000 0.388 0.588 0.024 0.000
#> GSM110388 4 0.0000 0.910 0.000 0.000 0.000 1.000 0.000
#> GSM110392 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000
#> GSM110394 4 0.0000 0.910 0.000 0.000 0.000 1.000 0.000
#> GSM110402 3 0.4278 0.195 0.000 0.452 0.548 0.000 0.000
#> GSM110411 4 0.3266 0.794 0.000 0.004 0.200 0.796 0.000
#> GSM110412 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000
#> GSM110417 1 0.4182 0.427 0.600 0.000 0.000 0.400 0.000
#> GSM110422 5 0.0880 0.913 0.000 0.032 0.000 0.000 0.968
#> GSM110426 4 0.0000 0.910 0.000 0.000 0.000 1.000 0.000
#> GSM110429 5 0.4268 0.171 0.000 0.444 0.000 0.000 0.556
#> GSM110433 5 0.0000 0.921 0.000 0.000 0.000 0.000 1.000
#> GSM110436 5 0.0880 0.913 0.000 0.032 0.000 0.000 0.968
#> GSM110440 4 0.0000 0.910 0.000 0.000 0.000 1.000 0.000
#> GSM110441 2 0.4210 0.215 0.000 0.588 0.000 0.000 0.412
#> GSM110444 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000
#> GSM110445 4 0.3109 0.797 0.000 0.000 0.200 0.800 0.000
#> GSM110446 3 0.0000 0.686 0.000 0.000 1.000 0.000 0.000
#> GSM110449 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000
#> GSM110451 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000
#> GSM110391 5 0.1544 0.878 0.000 0.068 0.000 0.000 0.932
#> GSM110439 5 0.0000 0.921 0.000 0.000 0.000 0.000 1.000
#> GSM110442 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000
#> GSM110443 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000
#> GSM110447 2 0.0000 0.925 0.000 1.000 0.000 0.000 0.000
#> GSM110448 4 0.0000 0.910 0.000 0.000 0.000 1.000 0.000
#> GSM110450 4 0.0794 0.900 0.000 0.000 0.028 0.972 0.000
#> GSM110452 5 0.0963 0.910 0.000 0.036 0.000 0.000 0.964
#> GSM110453 5 0.0000 0.921 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.0713 0.914 0.000 0.972 0.000 0.028 0.000 0.00
#> GSM110396 6 0.2048 0.815 0.120 0.000 0.000 0.000 0.000 0.88
#> GSM110397 6 0.0000 0.897 0.000 0.000 0.000 0.000 0.000 1.00
#> GSM110398 4 0.3470 0.748 0.028 0.000 0.200 0.772 0.000 0.00
#> GSM110399 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.00
#> GSM110400 2 0.0363 0.906 0.000 0.988 0.000 0.012 0.000 0.00
#> GSM110401 6 0.0000 0.897 0.000 0.000 0.000 0.000 0.000 1.00
#> GSM110406 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.00
#> GSM110407 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM110409 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM110410 5 0.0000 0.985 0.000 0.000 0.000 0.000 1.000 0.00
#> GSM110413 2 0.0713 0.914 0.000 0.972 0.000 0.028 0.000 0.00
#> GSM110414 5 0.0713 0.961 0.000 0.028 0.000 0.000 0.972 0.00
#> GSM110415 3 0.2933 0.735 0.000 0.004 0.796 0.200 0.000 0.00
#> GSM110416 3 0.0000 0.778 0.000 0.000 1.000 0.000 0.000 0.00
#> GSM110418 3 0.0000 0.778 0.000 0.000 1.000 0.000 0.000 0.00
#> GSM110419 3 0.3141 0.733 0.000 0.012 0.788 0.200 0.000 0.00
#> GSM110420 3 0.2996 0.647 0.228 0.000 0.772 0.000 0.000 0.00
#> GSM110421 2 0.0713 0.914 0.000 0.972 0.000 0.028 0.000 0.00
#> GSM110423 2 0.2454 0.748 0.000 0.840 0.160 0.000 0.000 0.00
#> GSM110424 5 0.0000 0.985 0.000 0.000 0.000 0.000 1.000 0.00
#> GSM110425 2 0.0000 0.907 0.000 1.000 0.000 0.000 0.000 0.00
#> GSM110427 5 0.0937 0.942 0.000 0.040 0.000 0.000 0.960 0.00
#> GSM110428 1 0.2996 0.733 0.772 0.000 0.228 0.000 0.000 0.00
#> GSM110430 6 0.0000 0.897 0.000 0.000 0.000 0.000 0.000 1.00
#> GSM110431 6 0.0000 0.897 0.000 0.000 0.000 0.000 0.000 1.00
#> GSM110432 2 0.3151 0.741 0.000 0.748 0.000 0.252 0.000 0.00
#> GSM110434 2 0.0713 0.914 0.000 0.972 0.000 0.028 0.000 0.00
#> GSM110435 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM110437 6 0.0000 0.897 0.000 0.000 0.000 0.000 0.000 1.00
#> GSM110438 4 0.3151 0.724 0.000 0.000 0.252 0.748 0.000 0.00
#> GSM110388 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM110392 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.00
#> GSM110394 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM110402 3 0.5461 0.538 0.000 0.228 0.572 0.200 0.000 0.00
#> GSM110411 4 0.3470 0.748 0.028 0.000 0.200 0.772 0.000 0.00
#> GSM110412 2 0.3446 0.673 0.000 0.692 0.000 0.308 0.000 0.00
#> GSM110417 6 0.3756 0.401 0.400 0.000 0.000 0.000 0.000 0.60
#> GSM110422 2 0.0713 0.909 0.000 0.972 0.000 0.000 0.028 0.00
#> GSM110426 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM110429 2 0.0713 0.909 0.000 0.972 0.000 0.000 0.028 0.00
#> GSM110433 5 0.0000 0.985 0.000 0.000 0.000 0.000 1.000 0.00
#> GSM110436 2 0.0713 0.909 0.000 0.972 0.000 0.000 0.028 0.00
#> GSM110440 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM110441 2 0.0713 0.914 0.000 0.972 0.000 0.028 0.000 0.00
#> GSM110444 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.00
#> GSM110445 1 0.3470 0.738 0.772 0.000 0.200 0.028 0.000 0.00
#> GSM110446 3 0.0000 0.778 0.000 0.000 1.000 0.000 0.000 0.00
#> GSM110449 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.00
#> GSM110451 2 0.0713 0.914 0.000 0.972 0.000 0.028 0.000 0.00
#> GSM110391 2 0.0713 0.909 0.000 0.972 0.000 0.000 0.028 0.00
#> GSM110439 5 0.0000 0.985 0.000 0.000 0.000 0.000 1.000 0.00
#> GSM110442 2 0.2996 0.763 0.000 0.772 0.000 0.228 0.000 0.00
#> GSM110443 4 0.0000 0.885 0.000 0.000 0.000 1.000 0.000 0.00
#> GSM110447 2 0.2823 0.763 0.000 0.796 0.000 0.204 0.000 0.00
#> GSM110448 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM110450 1 0.0713 0.927 0.972 0.000 0.028 0.000 0.000 0.00
#> GSM110452 2 0.0713 0.909 0.000 0.972 0.000 0.000 0.028 0.00
#> GSM110453 5 0.0000 0.985 0.000 0.000 0.000 0.000 1.000 0.00
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) specimen(p) k
#> ATC:pam 57 0.6664 0.402 2
#> ATC:pam 53 0.4247 0.157 3
#> ATC:pam 49 0.2691 0.311 4
#> ATC:pam 53 0.0576 0.267 5
#> ATC:pam 58 0.1383 0.534 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 17209 rows and 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.569 0.823 0.929 0.2346 0.842 0.842
#> 3 3 0.286 0.245 0.628 1.5081 0.476 0.426
#> 4 4 0.700 0.760 0.868 0.2643 0.732 0.447
#> 5 5 0.917 0.860 0.943 0.0766 0.870 0.545
#> 6 6 0.843 0.804 0.912 0.0224 0.950 0.768
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM110395 2 0.9996 -0.0756 0.488 0.512
#> GSM110396 2 0.4690 0.8379 0.100 0.900
#> GSM110397 2 0.4815 0.8355 0.104 0.896
#> GSM110398 2 0.0000 0.9194 0.000 1.000
#> GSM110399 2 0.0000 0.9194 0.000 1.000
#> GSM110400 2 0.0672 0.9165 0.008 0.992
#> GSM110401 2 0.4690 0.8379 0.100 0.900
#> GSM110406 2 0.0672 0.9145 0.008 0.992
#> GSM110407 2 0.0000 0.9194 0.000 1.000
#> GSM110409 2 0.0000 0.9194 0.000 1.000
#> GSM110410 2 0.0000 0.9194 0.000 1.000
#> GSM110413 2 0.0000 0.9194 0.000 1.000
#> GSM110414 2 0.0672 0.9165 0.008 0.992
#> GSM110415 2 0.0672 0.9165 0.008 0.992
#> GSM110416 2 0.0672 0.9165 0.008 0.992
#> GSM110418 2 0.0672 0.9165 0.008 0.992
#> GSM110419 2 0.0672 0.9165 0.008 0.992
#> GSM110420 2 0.0672 0.9165 0.008 0.992
#> GSM110421 2 0.9286 0.4030 0.344 0.656
#> GSM110423 2 0.0672 0.9165 0.008 0.992
#> GSM110424 2 0.0000 0.9194 0.000 1.000
#> GSM110425 2 0.0672 0.9165 0.008 0.992
#> GSM110427 1 0.4939 0.9861 0.892 0.108
#> GSM110428 2 0.0000 0.9194 0.000 1.000
#> GSM110430 2 0.4690 0.8379 0.100 0.900
#> GSM110431 2 0.0000 0.9194 0.000 1.000
#> GSM110432 2 1.0000 -0.1201 0.500 0.500
#> GSM110434 2 0.9248 0.4132 0.340 0.660
#> GSM110435 2 0.0000 0.9194 0.000 1.000
#> GSM110437 2 0.4690 0.8379 0.100 0.900
#> GSM110438 2 0.0000 0.9194 0.000 1.000
#> GSM110388 2 0.0000 0.9194 0.000 1.000
#> GSM110392 2 0.0000 0.9194 0.000 1.000
#> GSM110394 2 0.0000 0.9194 0.000 1.000
#> GSM110402 2 0.0672 0.9165 0.008 0.992
#> GSM110411 2 0.0000 0.9194 0.000 1.000
#> GSM110412 2 1.0000 -0.1201 0.500 0.500
#> GSM110417 2 0.4690 0.8379 0.100 0.900
#> GSM110422 1 0.4939 0.9861 0.892 0.108
#> GSM110426 2 0.0000 0.9194 0.000 1.000
#> GSM110429 1 0.6148 0.9414 0.848 0.152
#> GSM110433 2 0.0000 0.9194 0.000 1.000
#> GSM110436 1 0.4939 0.9861 0.892 0.108
#> GSM110440 2 0.0000 0.9194 0.000 1.000
#> GSM110441 2 0.0000 0.9194 0.000 1.000
#> GSM110444 2 0.0000 0.9194 0.000 1.000
#> GSM110445 2 0.0000 0.9194 0.000 1.000
#> GSM110446 2 0.0672 0.9165 0.008 0.992
#> GSM110449 2 0.0000 0.9194 0.000 1.000
#> GSM110451 1 0.4939 0.9861 0.892 0.108
#> GSM110391 2 0.0000 0.9194 0.000 1.000
#> GSM110439 2 0.0000 0.9194 0.000 1.000
#> GSM110442 2 0.8016 0.6167 0.244 0.756
#> GSM110443 2 0.0000 0.9194 0.000 1.000
#> GSM110447 2 0.0000 0.9194 0.000 1.000
#> GSM110448 2 0.0000 0.9194 0.000 1.000
#> GSM110450 2 0.0000 0.9194 0.000 1.000
#> GSM110452 2 1.0000 -0.1201 0.500 0.500
#> GSM110453 2 0.0000 0.9194 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.649 0.6265 0.004 0.540 0.456
#> GSM110396 1 0.746 -0.0500 0.524 0.036 0.440
#> GSM110397 1 0.703 -0.0445 0.540 0.020 0.440
#> GSM110398 2 0.314 0.5835 0.068 0.912 0.020
#> GSM110399 2 0.441 0.5628 0.140 0.844 0.016
#> GSM110400 1 0.618 0.1234 0.660 0.332 0.008
#> GSM110401 1 0.746 -0.0500 0.524 0.036 0.440
#> GSM110406 2 0.621 0.6104 0.048 0.752 0.200
#> GSM110407 1 0.893 -0.2543 0.456 0.124 0.420
#> GSM110409 1 0.893 -0.2543 0.456 0.124 0.420
#> GSM110410 2 0.752 0.2753 0.260 0.660 0.080
#> GSM110413 2 0.419 0.5900 0.060 0.876 0.064
#> GSM110414 1 0.711 0.0672 0.680 0.260 0.060
#> GSM110415 1 0.566 0.1194 0.740 0.248 0.012
#> GSM110416 1 0.470 0.1022 0.788 0.212 0.000
#> GSM110418 1 0.553 0.1174 0.704 0.296 0.000
#> GSM110419 1 0.556 0.1261 0.700 0.300 0.000
#> GSM110420 1 0.587 0.0894 0.760 0.208 0.032
#> GSM110421 2 0.809 0.6271 0.076 0.560 0.364
#> GSM110423 1 0.618 0.1234 0.660 0.332 0.008
#> GSM110424 2 0.446 0.5798 0.056 0.864 0.080
#> GSM110425 1 0.618 0.1234 0.660 0.332 0.008
#> GSM110427 2 0.630 0.6217 0.000 0.528 0.472
#> GSM110428 2 0.680 -0.0222 0.308 0.660 0.032
#> GSM110430 1 0.746 -0.0500 0.524 0.036 0.440
#> GSM110431 1 0.873 -0.2367 0.472 0.108 0.420
#> GSM110432 2 0.680 0.6232 0.012 0.528 0.460
#> GSM110434 2 0.613 0.6353 0.004 0.644 0.352
#> GSM110435 1 0.867 -0.3014 0.508 0.108 0.384
#> GSM110437 1 0.746 -0.0500 0.524 0.036 0.440
#> GSM110438 3 0.999 0.6916 0.316 0.336 0.348
#> GSM110388 1 0.995 -0.7690 0.368 0.284 0.348
#> GSM110392 2 0.220 0.6064 0.056 0.940 0.004
#> GSM110394 1 0.862 -0.3512 0.536 0.112 0.352
#> GSM110402 1 0.576 0.1267 0.716 0.276 0.008
#> GSM110411 2 0.406 0.5209 0.112 0.868 0.020
#> GSM110412 2 0.649 0.6265 0.004 0.540 0.456
#> GSM110417 1 0.726 -0.0471 0.532 0.028 0.440
#> GSM110422 2 0.630 0.6188 0.000 0.520 0.480
#> GSM110426 1 0.873 -0.2367 0.472 0.108 0.420
#> GSM110429 2 0.651 0.6191 0.004 0.520 0.476
#> GSM110433 2 0.526 0.5527 0.092 0.828 0.080
#> GSM110436 2 0.630 0.6205 0.000 0.524 0.476
#> GSM110440 1 0.972 -0.6850 0.424 0.228 0.348
#> GSM110441 2 0.598 0.5377 0.132 0.788 0.080
#> GSM110444 2 0.264 0.6003 0.048 0.932 0.020
#> GSM110445 3 0.997 0.6920 0.320 0.308 0.372
#> GSM110446 1 0.543 0.1124 0.716 0.284 0.000
#> GSM110449 2 0.355 0.5762 0.132 0.868 0.000
#> GSM110451 2 0.630 0.6188 0.000 0.520 0.480
#> GSM110391 2 0.409 0.5885 0.056 0.880 0.064
#> GSM110439 2 0.526 0.5527 0.092 0.828 0.080
#> GSM110442 2 0.640 0.6388 0.012 0.644 0.344
#> GSM110443 2 0.230 0.6011 0.060 0.936 0.004
#> GSM110447 1 0.643 0.0693 0.612 0.380 0.008
#> GSM110448 1 0.995 -0.7690 0.368 0.284 0.348
#> GSM110450 1 0.962 -0.4641 0.440 0.212 0.348
#> GSM110452 2 0.650 0.6250 0.004 0.536 0.460
#> GSM110453 2 0.475 0.5754 0.068 0.852 0.080
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM110396 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM110397 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM110398 4 0.6928 0.650 0.184 0.204 0.004 0.608
#> GSM110399 4 0.3519 0.679 0.016 0.128 0.004 0.852
#> GSM110400 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM110401 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM110406 4 0.6700 0.576 0.112 0.316 0.000 0.572
#> GSM110407 1 0.0188 0.932 0.996 0.000 0.004 0.000
#> GSM110409 1 0.0188 0.932 0.996 0.000 0.004 0.000
#> GSM110410 2 0.5105 0.198 0.000 0.564 0.004 0.432
#> GSM110413 4 0.5925 0.686 0.100 0.196 0.004 0.700
#> GSM110414 3 0.4933 0.399 0.000 0.000 0.568 0.432
#> GSM110415 3 0.0188 0.954 0.004 0.000 0.996 0.000
#> GSM110416 3 0.0188 0.954 0.004 0.000 0.996 0.000
#> GSM110418 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM110419 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM110420 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM110421 2 0.4579 0.384 0.004 0.720 0.004 0.272
#> GSM110423 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM110424 4 0.4279 0.559 0.012 0.204 0.004 0.780
#> GSM110425 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM110427 2 0.0188 0.839 0.000 0.996 0.004 0.000
#> GSM110428 2 0.5050 0.205 0.408 0.588 0.004 0.000
#> GSM110430 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM110431 1 0.1970 0.905 0.932 0.060 0.008 0.000
#> GSM110432 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM110434 2 0.0844 0.823 0.012 0.980 0.004 0.004
#> GSM110435 1 0.2216 0.887 0.908 0.000 0.092 0.000
#> GSM110437 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM110438 1 0.4632 0.550 0.688 0.308 0.004 0.000
#> GSM110388 1 0.2076 0.914 0.932 0.008 0.004 0.056
#> GSM110392 4 0.6969 0.347 0.112 0.436 0.000 0.452
#> GSM110394 1 0.2623 0.900 0.908 0.000 0.028 0.064
#> GSM110402 3 0.0188 0.954 0.004 0.000 0.996 0.000
#> GSM110411 4 0.7150 0.628 0.212 0.204 0.004 0.580
#> GSM110412 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM110417 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM110422 2 0.0188 0.839 0.000 0.996 0.004 0.000
#> GSM110426 1 0.2644 0.897 0.908 0.032 0.060 0.000
#> GSM110429 2 0.0592 0.832 0.000 0.984 0.016 0.000
#> GSM110433 4 0.3831 0.551 0.000 0.204 0.004 0.792
#> GSM110436 2 0.0188 0.839 0.000 0.996 0.004 0.000
#> GSM110440 1 0.2401 0.892 0.904 0.000 0.004 0.092
#> GSM110441 4 0.0188 0.631 0.000 0.000 0.004 0.996
#> GSM110444 4 0.6083 0.676 0.112 0.216 0.000 0.672
#> GSM110445 4 0.5345 0.403 0.404 0.008 0.004 0.584
#> GSM110446 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM110449 4 0.5099 0.684 0.048 0.200 0.004 0.748
#> GSM110451 2 0.0188 0.839 0.000 0.996 0.004 0.000
#> GSM110391 4 0.5750 0.566 0.052 0.272 0.004 0.672
#> GSM110439 4 0.3908 0.554 0.000 0.212 0.004 0.784
#> GSM110442 2 0.0000 0.838 0.000 1.000 0.000 0.000
#> GSM110443 4 0.6175 0.679 0.108 0.212 0.004 0.676
#> GSM110447 2 0.5028 0.326 0.000 0.596 0.400 0.004
#> GSM110448 1 0.2796 0.888 0.892 0.008 0.004 0.096
#> GSM110450 1 0.0895 0.921 0.976 0.020 0.004 0.000
#> GSM110452 2 0.0188 0.839 0.000 0.996 0.004 0.000
#> GSM110453 4 0.4220 0.497 0.000 0.248 0.004 0.748
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM110396 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM110397 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM110398 4 0.0579 0.829 0.008 0.008 0.000 0.984 0.000
#> GSM110399 4 0.1732 0.788 0.000 0.000 0.000 0.920 0.080
#> GSM110400 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM110401 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM110406 2 0.4210 0.266 0.000 0.588 0.000 0.412 0.000
#> GSM110407 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM110409 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM110410 5 0.0162 0.997 0.000 0.000 0.000 0.004 0.996
#> GSM110413 4 0.3487 0.653 0.000 0.008 0.000 0.780 0.212
#> GSM110414 5 0.0510 0.979 0.000 0.000 0.016 0.000 0.984
#> GSM110415 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM110416 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM110418 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM110419 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM110420 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM110421 2 0.0703 0.890 0.000 0.976 0.000 0.000 0.024
#> GSM110423 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM110424 5 0.0162 0.997 0.000 0.000 0.000 0.004 0.996
#> GSM110425 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM110427 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM110428 1 0.4235 0.229 0.576 0.424 0.000 0.000 0.000
#> GSM110430 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM110431 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM110432 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM110434 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM110435 1 0.0290 0.941 0.992 0.000 0.000 0.008 0.000
#> GSM110437 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM110438 2 0.4367 0.217 0.416 0.580 0.000 0.004 0.000
#> GSM110388 4 0.3774 0.577 0.296 0.000 0.000 0.704 0.000
#> GSM110392 4 0.4201 0.275 0.000 0.408 0.000 0.592 0.000
#> GSM110394 1 0.0290 0.941 0.992 0.000 0.000 0.008 0.000
#> GSM110402 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM110411 4 0.0579 0.829 0.008 0.008 0.000 0.984 0.000
#> GSM110412 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM110417 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM110422 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM110426 1 0.0000 0.945 1.000 0.000 0.000 0.000 0.000
#> GSM110429 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM110433 5 0.0162 0.997 0.000 0.000 0.000 0.004 0.996
#> GSM110436 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM110440 1 0.0510 0.935 0.984 0.000 0.000 0.016 0.000
#> GSM110441 5 0.0162 0.997 0.000 0.000 0.000 0.004 0.996
#> GSM110444 4 0.0290 0.827 0.000 0.008 0.000 0.992 0.000
#> GSM110445 4 0.0963 0.821 0.036 0.000 0.000 0.964 0.000
#> GSM110446 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM110449 4 0.0566 0.825 0.000 0.004 0.000 0.984 0.012
#> GSM110451 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM110391 5 0.0162 0.997 0.000 0.000 0.000 0.004 0.996
#> GSM110439 5 0.0162 0.997 0.000 0.000 0.000 0.004 0.996
#> GSM110442 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM110443 4 0.0613 0.828 0.004 0.008 0.000 0.984 0.004
#> GSM110447 2 0.3480 0.636 0.000 0.752 0.248 0.000 0.000
#> GSM110448 4 0.4268 0.273 0.444 0.000 0.000 0.556 0.000
#> GSM110450 1 0.2929 0.728 0.820 0.000 0.000 0.180 0.000
#> GSM110452 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM110453 5 0.0162 0.997 0.000 0.000 0.000 0.004 0.996
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.0363 0.894 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM110396 1 0.0790 0.836 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM110397 1 0.0260 0.835 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM110398 4 0.0000 0.855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110399 4 0.2664 0.641 0.000 0.000 0.000 0.816 0.184 0.000
#> GSM110400 3 0.0363 0.937 0.000 0.012 0.988 0.000 0.000 0.000
#> GSM110401 1 0.0790 0.836 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM110406 2 0.3789 0.233 0.000 0.584 0.000 0.416 0.000 0.000
#> GSM110407 1 0.0790 0.836 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM110409 1 0.0458 0.833 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM110410 5 0.0000 0.907 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM110413 5 0.3854 0.102 0.000 0.000 0.000 0.464 0.536 0.000
#> GSM110414 5 0.3013 0.774 0.000 0.000 0.088 0.000 0.844 0.068
#> GSM110415 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110416 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110418 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110419 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110420 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110421 2 0.3056 0.712 0.000 0.804 0.004 0.008 0.184 0.000
#> GSM110423 3 0.0363 0.937 0.000 0.012 0.988 0.000 0.000 0.000
#> GSM110424 5 0.0000 0.907 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM110425 3 0.0790 0.920 0.000 0.032 0.968 0.000 0.000 0.000
#> GSM110427 2 0.1714 0.889 0.000 0.908 0.000 0.000 0.000 0.092
#> GSM110428 1 0.3820 0.454 0.660 0.332 0.000 0.004 0.000 0.004
#> GSM110430 1 0.0790 0.836 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM110431 1 0.0146 0.836 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM110432 2 0.0405 0.893 0.000 0.988 0.008 0.004 0.000 0.000
#> GSM110434 2 0.0363 0.894 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM110435 1 0.2823 0.698 0.796 0.000 0.000 0.000 0.000 0.204
#> GSM110437 1 0.0790 0.836 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM110438 1 0.3850 0.440 0.652 0.340 0.000 0.004 0.000 0.004
#> GSM110388 6 0.3563 0.937 0.108 0.000 0.000 0.092 0.000 0.800
#> GSM110392 4 0.3695 0.400 0.000 0.376 0.000 0.624 0.000 0.000
#> GSM110394 1 0.2823 0.698 0.796 0.000 0.000 0.000 0.000 0.204
#> GSM110402 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110411 4 0.0000 0.855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110412 2 0.0363 0.894 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM110417 1 0.1141 0.823 0.948 0.000 0.000 0.000 0.000 0.052
#> GSM110422 2 0.1714 0.889 0.000 0.908 0.000 0.000 0.000 0.092
#> GSM110426 1 0.0146 0.836 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM110429 2 0.1714 0.889 0.000 0.908 0.000 0.000 0.000 0.092
#> GSM110433 5 0.0000 0.907 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM110436 2 0.1714 0.889 0.000 0.908 0.000 0.000 0.000 0.092
#> GSM110440 1 0.3922 0.486 0.664 0.000 0.000 0.016 0.000 0.320
#> GSM110441 5 0.0260 0.904 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM110444 4 0.0000 0.855 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM110445 4 0.2170 0.718 0.100 0.000 0.000 0.888 0.000 0.012
#> GSM110446 3 0.0000 0.943 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM110449 4 0.0146 0.853 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM110451 2 0.1714 0.889 0.000 0.908 0.000 0.000 0.000 0.092
#> GSM110391 5 0.0000 0.907 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM110439 5 0.0000 0.907 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM110442 2 0.0363 0.894 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM110443 4 0.0146 0.853 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM110447 3 0.3684 0.371 0.000 0.372 0.628 0.000 0.000 0.000
#> GSM110448 6 0.3416 0.939 0.140 0.000 0.000 0.056 0.000 0.804
#> GSM110450 1 0.3450 0.664 0.780 0.000 0.000 0.188 0.000 0.032
#> GSM110452 2 0.0713 0.896 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM110453 5 0.0000 0.907 0.000 0.000 0.000 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) specimen(p) k
#> ATC:mclust 53 0.3249 0.738 2
#> ATC:mclust 29 1.0000 1.000 3
#> ATC:mclust 51 0.1397 0.425 4
#> ATC:mclust 54 0.1429 0.168 5
#> ATC:mclust 52 0.0881 0.201 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 17209 rows and 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.711 0.863 0.934 0.3805 0.583 0.583
#> 3 3 0.626 0.701 0.886 0.5289 0.786 0.643
#> 4 4 0.473 0.560 0.785 0.1738 0.841 0.638
#> 5 5 0.442 0.373 0.694 0.0871 0.937 0.818
#> 6 6 0.479 0.435 0.636 0.0424 0.944 0.823
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
#> GSM110395 2 0.0000 0.963 0.000 1.000
#> GSM110396 1 0.0000 0.813 1.000 0.000
#> GSM110397 1 0.0000 0.813 1.000 0.000
#> GSM110398 2 0.9635 0.144 0.388 0.612
#> GSM110399 2 0.0000 0.963 0.000 1.000
#> GSM110400 2 0.0000 0.963 0.000 1.000
#> GSM110401 1 0.0000 0.813 1.000 0.000
#> GSM110406 2 0.0000 0.963 0.000 1.000
#> GSM110407 1 0.7219 0.794 0.800 0.200
#> GSM110409 1 0.9552 0.609 0.624 0.376
#> GSM110410 2 0.0000 0.963 0.000 1.000
#> GSM110413 2 0.0000 0.963 0.000 1.000
#> GSM110414 2 0.0000 0.963 0.000 1.000
#> GSM110415 2 0.0000 0.963 0.000 1.000
#> GSM110416 2 0.0000 0.963 0.000 1.000
#> GSM110418 2 0.0000 0.963 0.000 1.000
#> GSM110419 2 0.0000 0.963 0.000 1.000
#> GSM110420 2 0.0000 0.963 0.000 1.000
#> GSM110421 2 0.0000 0.963 0.000 1.000
#> GSM110423 2 0.0000 0.963 0.000 1.000
#> GSM110424 2 0.0000 0.963 0.000 1.000
#> GSM110425 2 0.0000 0.963 0.000 1.000
#> GSM110427 2 0.0000 0.963 0.000 1.000
#> GSM110428 2 0.9393 0.264 0.356 0.644
#> GSM110430 1 0.0000 0.813 1.000 0.000
#> GSM110431 1 0.0000 0.813 1.000 0.000
#> GSM110432 2 0.0000 0.963 0.000 1.000
#> GSM110434 2 0.0000 0.963 0.000 1.000
#> GSM110435 1 0.8267 0.755 0.740 0.260
#> GSM110437 1 0.0000 0.813 1.000 0.000
#> GSM110438 2 0.4562 0.843 0.096 0.904
#> GSM110388 1 0.9710 0.562 0.600 0.400
#> GSM110392 2 0.0000 0.963 0.000 1.000
#> GSM110394 1 0.7674 0.782 0.776 0.224
#> GSM110402 2 0.0000 0.963 0.000 1.000
#> GSM110411 2 0.9286 0.304 0.344 0.656
#> GSM110412 2 0.0000 0.963 0.000 1.000
#> GSM110417 1 0.0938 0.814 0.988 0.012
#> GSM110422 2 0.0000 0.963 0.000 1.000
#> GSM110426 1 0.2603 0.815 0.956 0.044
#> GSM110429 2 0.0000 0.963 0.000 1.000
#> GSM110433 2 0.0000 0.963 0.000 1.000
#> GSM110436 2 0.0000 0.963 0.000 1.000
#> GSM110440 1 0.7219 0.794 0.800 0.200
#> GSM110441 2 0.0000 0.963 0.000 1.000
#> GSM110444 2 0.0000 0.963 0.000 1.000
#> GSM110445 1 0.9710 0.562 0.600 0.400
#> GSM110446 2 0.0000 0.963 0.000 1.000
#> GSM110449 2 0.0000 0.963 0.000 1.000
#> GSM110451 2 0.0000 0.963 0.000 1.000
#> GSM110391 2 0.0000 0.963 0.000 1.000
#> GSM110439 2 0.0000 0.963 0.000 1.000
#> GSM110442 2 0.0000 0.963 0.000 1.000
#> GSM110443 2 0.0000 0.963 0.000 1.000
#> GSM110447 2 0.0000 0.963 0.000 1.000
#> GSM110448 1 0.7950 0.772 0.760 0.240
#> GSM110450 1 0.9552 0.609 0.624 0.376
#> GSM110452 2 0.0000 0.963 0.000 1.000
#> GSM110453 2 0.0000 0.963 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM110395 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110396 1 0.0237 0.7441 0.996 0.000 0.004
#> GSM110397 1 0.0237 0.7428 0.996 0.000 0.004
#> GSM110398 2 0.5882 0.3683 0.348 0.652 0.000
#> GSM110399 2 0.0424 0.9113 0.000 0.992 0.008
#> GSM110400 3 0.6252 0.2223 0.000 0.444 0.556
#> GSM110401 1 0.0000 0.7446 1.000 0.000 0.000
#> GSM110406 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110407 1 0.4452 0.6394 0.808 0.192 0.000
#> GSM110409 1 0.4931 0.5990 0.768 0.000 0.232
#> GSM110410 2 0.0592 0.9095 0.000 0.988 0.012
#> GSM110413 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110414 2 0.3619 0.7894 0.000 0.864 0.136
#> GSM110415 3 0.0237 0.7162 0.000 0.004 0.996
#> GSM110416 3 0.0000 0.7154 0.000 0.000 1.000
#> GSM110418 3 0.0000 0.7154 0.000 0.000 1.000
#> GSM110419 3 0.2878 0.6840 0.000 0.096 0.904
#> GSM110420 3 0.0000 0.7154 0.000 0.000 1.000
#> GSM110421 2 0.1031 0.8984 0.000 0.976 0.024
#> GSM110423 3 0.6291 0.1247 0.000 0.468 0.532
#> GSM110424 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110425 2 0.6079 0.3352 0.000 0.612 0.388
#> GSM110427 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110428 2 0.6520 -0.1174 0.488 0.508 0.004
#> GSM110430 1 0.0000 0.7446 1.000 0.000 0.000
#> GSM110431 1 0.2625 0.7074 0.916 0.000 0.084
#> GSM110432 2 0.0424 0.9122 0.000 0.992 0.008
#> GSM110434 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110435 3 0.2261 0.6746 0.068 0.000 0.932
#> GSM110437 1 0.0000 0.7446 1.000 0.000 0.000
#> GSM110438 2 0.7272 0.5829 0.096 0.700 0.204
#> GSM110388 1 0.6126 0.4060 0.600 0.400 0.000
#> GSM110392 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110394 3 0.6192 0.0516 0.420 0.000 0.580
#> GSM110402 3 0.4291 0.6167 0.000 0.180 0.820
#> GSM110411 2 0.5706 0.4409 0.320 0.680 0.000
#> GSM110412 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110417 1 0.0000 0.7446 1.000 0.000 0.000
#> GSM110422 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110426 3 0.6291 -0.1058 0.468 0.000 0.532
#> GSM110429 2 0.0747 0.9067 0.000 0.984 0.016
#> GSM110433 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110436 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110440 1 0.6079 0.3743 0.612 0.000 0.388
#> GSM110441 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110444 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110445 1 0.6204 0.3478 0.576 0.424 0.000
#> GSM110446 3 0.0892 0.7149 0.000 0.020 0.980
#> GSM110449 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110451 2 0.0237 0.9142 0.000 0.996 0.004
#> GSM110391 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110439 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110442 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110443 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110447 2 0.4654 0.6982 0.000 0.792 0.208
#> GSM110448 1 0.4555 0.6281 0.800 0.000 0.200
#> GSM110450 1 0.5948 0.4851 0.640 0.360 0.000
#> GSM110452 2 0.0000 0.9163 0.000 1.000 0.000
#> GSM110453 2 0.0000 0.9163 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM110395 2 0.1022 0.7427 0.000 0.968 0.000 0.032
#> GSM110396 1 0.1109 0.7439 0.968 0.000 0.004 0.028
#> GSM110397 1 0.0927 0.7387 0.976 0.000 0.008 0.016
#> GSM110398 2 0.6611 -0.0366 0.456 0.464 0.000 0.080
#> GSM110399 4 0.4919 0.5119 0.152 0.076 0.000 0.772
#> GSM110400 4 0.7834 0.2945 0.000 0.276 0.320 0.404
#> GSM110401 1 0.0188 0.7432 0.996 0.000 0.000 0.004
#> GSM110406 2 0.1256 0.7443 0.008 0.964 0.000 0.028
#> GSM110407 1 0.3710 0.6445 0.804 0.192 0.000 0.004
#> GSM110409 1 0.4837 0.7157 0.796 0.008 0.076 0.120
#> GSM110410 2 0.4898 0.1763 0.000 0.584 0.000 0.416
#> GSM110413 2 0.4431 0.5087 0.000 0.696 0.000 0.304
#> GSM110414 4 0.3123 0.7063 0.000 0.156 0.000 0.844
#> GSM110415 3 0.4889 0.4964 0.000 0.004 0.636 0.360
#> GSM110416 3 0.2402 0.7051 0.000 0.012 0.912 0.076
#> GSM110418 3 0.0469 0.7133 0.000 0.012 0.988 0.000
#> GSM110419 3 0.7414 -0.1975 0.000 0.172 0.460 0.368
#> GSM110420 3 0.0469 0.7156 0.000 0.000 0.988 0.012
#> GSM110421 2 0.3649 0.6369 0.000 0.796 0.000 0.204
#> GSM110423 2 0.6265 0.1318 0.000 0.500 0.444 0.056
#> GSM110424 2 0.3764 0.6203 0.000 0.784 0.000 0.216
#> GSM110425 2 0.5865 0.2271 0.000 0.552 0.412 0.036
#> GSM110427 2 0.0336 0.7431 0.000 0.992 0.000 0.008
#> GSM110428 2 0.2513 0.7029 0.036 0.924 0.024 0.016
#> GSM110430 1 0.0000 0.7436 1.000 0.000 0.000 0.000
#> GSM110431 1 0.3636 0.6831 0.820 0.000 0.172 0.008
#> GSM110432 2 0.0336 0.7429 0.000 0.992 0.000 0.008
#> GSM110434 2 0.1557 0.7373 0.000 0.944 0.000 0.056
#> GSM110435 3 0.6784 -0.0136 0.368 0.000 0.528 0.104
#> GSM110437 1 0.0000 0.7436 1.000 0.000 0.000 0.000
#> GSM110438 2 0.2883 0.7071 0.028 0.908 0.048 0.016
#> GSM110388 1 0.6071 0.4468 0.504 0.044 0.000 0.452
#> GSM110392 2 0.1940 0.7330 0.000 0.924 0.000 0.076
#> GSM110394 1 0.6936 0.4811 0.564 0.000 0.292 0.144
#> GSM110402 4 0.7216 0.5335 0.000 0.208 0.244 0.548
#> GSM110411 2 0.6170 0.1409 0.420 0.528 0.000 0.052
#> GSM110412 2 0.0707 0.7437 0.000 0.980 0.000 0.020
#> GSM110417 1 0.0336 0.7433 0.992 0.000 0.000 0.008
#> GSM110422 2 0.0000 0.7411 0.000 1.000 0.000 0.000
#> GSM110426 1 0.4933 0.4071 0.568 0.000 0.432 0.000
#> GSM110429 2 0.0927 0.7312 0.000 0.976 0.016 0.008
#> GSM110433 4 0.4406 0.6215 0.000 0.300 0.000 0.700
#> GSM110436 2 0.0000 0.7411 0.000 1.000 0.000 0.000
#> GSM110440 1 0.5745 0.6552 0.656 0.000 0.056 0.288
#> GSM110441 4 0.2814 0.7006 0.000 0.132 0.000 0.868
#> GSM110444 2 0.6969 0.2893 0.192 0.584 0.000 0.224
#> GSM110445 1 0.6531 0.5370 0.636 0.160 0.000 0.204
#> GSM110446 3 0.1042 0.7074 0.000 0.020 0.972 0.008
#> GSM110449 4 0.4507 0.7121 0.044 0.168 0.000 0.788
#> GSM110451 2 0.0336 0.7387 0.000 0.992 0.008 0.000
#> GSM110391 4 0.4564 0.5623 0.000 0.328 0.000 0.672
#> GSM110439 2 0.4961 0.0907 0.000 0.552 0.000 0.448
#> GSM110442 2 0.1302 0.7411 0.000 0.956 0.000 0.044
#> GSM110443 2 0.3401 0.6779 0.008 0.840 0.000 0.152
#> GSM110447 2 0.5700 0.0870 0.000 0.560 0.028 0.412
#> GSM110448 1 0.5334 0.6043 0.588 0.004 0.008 0.400
#> GSM110450 1 0.5038 0.4294 0.652 0.336 0.000 0.012
#> GSM110452 2 0.0469 0.7432 0.000 0.988 0.000 0.012
#> GSM110453 2 0.3649 0.6332 0.000 0.796 0.000 0.204
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM110395 2 0.2451 0.5050 0.000 0.904 0.004 0.036 0.056
#> GSM110396 1 0.3278 0.7007 0.860 0.000 0.020 0.092 0.028
#> GSM110397 1 0.1341 0.6931 0.944 0.000 0.000 0.056 0.000
#> GSM110398 2 0.8103 -0.4367 0.324 0.324 0.000 0.256 0.096
#> GSM110399 5 0.4752 0.4398 0.104 0.032 0.000 0.092 0.772
#> GSM110400 2 0.7773 -0.0180 0.000 0.444 0.124 0.136 0.296
#> GSM110401 1 0.0510 0.7143 0.984 0.000 0.000 0.016 0.000
#> GSM110406 2 0.4875 0.3578 0.064 0.760 0.000 0.136 0.040
#> GSM110407 1 0.3909 0.6957 0.760 0.024 0.000 0.216 0.000
#> GSM110409 1 0.5917 0.6683 0.680 0.000 0.104 0.160 0.056
#> GSM110410 2 0.5347 0.0444 0.000 0.528 0.004 0.044 0.424
#> GSM110413 2 0.6158 -0.0183 0.000 0.452 0.000 0.132 0.416
#> GSM110414 5 0.4113 0.5752 0.000 0.076 0.000 0.140 0.784
#> GSM110415 3 0.4866 0.3072 0.000 0.004 0.580 0.020 0.396
#> GSM110416 3 0.2299 0.7171 0.000 0.004 0.912 0.032 0.052
#> GSM110418 3 0.0451 0.7253 0.000 0.004 0.988 0.008 0.000
#> GSM110419 5 0.6929 0.3088 0.000 0.192 0.372 0.016 0.420
#> GSM110420 3 0.1522 0.7274 0.000 0.000 0.944 0.044 0.012
#> GSM110421 2 0.5555 0.4142 0.000 0.644 0.000 0.152 0.204
#> GSM110423 2 0.6915 0.2931 0.000 0.576 0.208 0.144 0.072
#> GSM110424 2 0.5572 0.2655 0.000 0.628 0.000 0.124 0.248
#> GSM110425 2 0.6430 0.3720 0.000 0.636 0.180 0.100 0.084
#> GSM110427 2 0.1560 0.5024 0.000 0.948 0.004 0.028 0.020
#> GSM110428 2 0.5122 0.2830 0.092 0.736 0.028 0.144 0.000
#> GSM110430 1 0.0404 0.7142 0.988 0.000 0.000 0.012 0.000
#> GSM110431 1 0.3890 0.6016 0.736 0.000 0.252 0.012 0.000
#> GSM110432 2 0.3614 0.4963 0.000 0.852 0.048 0.052 0.048
#> GSM110434 2 0.2221 0.4939 0.000 0.912 0.000 0.036 0.052
#> GSM110435 3 0.5700 -0.2834 0.456 0.000 0.472 0.004 0.068
#> GSM110437 1 0.0000 0.7126 1.000 0.000 0.000 0.000 0.000
#> GSM110438 2 0.6666 -0.5604 0.032 0.468 0.072 0.416 0.012
#> GSM110388 1 0.6768 0.5453 0.520 0.000 0.020 0.196 0.264
#> GSM110392 2 0.5365 -0.4502 0.000 0.528 0.000 0.416 0.056
#> GSM110394 1 0.7924 0.4634 0.468 0.000 0.184 0.172 0.176
#> GSM110402 5 0.7115 0.5271 0.000 0.140 0.200 0.096 0.564
#> GSM110411 4 0.7332 0.0000 0.144 0.376 0.000 0.420 0.060
#> GSM110412 2 0.3821 0.2800 0.000 0.764 0.000 0.216 0.020
#> GSM110417 1 0.4171 0.6962 0.764 0.004 0.012 0.204 0.016
#> GSM110422 2 0.1608 0.4830 0.000 0.928 0.000 0.072 0.000
#> GSM110426 1 0.4278 0.3085 0.548 0.000 0.452 0.000 0.000
#> GSM110429 2 0.3801 0.4702 0.000 0.820 0.036 0.128 0.016
#> GSM110433 5 0.4227 0.5170 0.000 0.292 0.000 0.016 0.692
#> GSM110436 2 0.1121 0.4753 0.000 0.956 0.000 0.044 0.000
#> GSM110440 1 0.5336 0.6292 0.632 0.000 0.052 0.012 0.304
#> GSM110441 5 0.2962 0.6078 0.000 0.084 0.000 0.048 0.868
#> GSM110444 2 0.7281 -0.5816 0.044 0.424 0.000 0.360 0.172
#> GSM110445 1 0.7187 0.4210 0.568 0.128 0.000 0.144 0.160
#> GSM110446 3 0.2787 0.6966 0.000 0.004 0.856 0.136 0.004
#> GSM110449 5 0.4232 0.6182 0.020 0.152 0.000 0.040 0.788
#> GSM110451 2 0.2227 0.4933 0.000 0.916 0.032 0.048 0.004
#> GSM110391 5 0.5029 0.4827 0.000 0.292 0.000 0.060 0.648
#> GSM110439 5 0.6173 0.1089 0.000 0.396 0.000 0.136 0.468
#> GSM110442 2 0.3804 0.4108 0.000 0.796 0.000 0.160 0.044
#> GSM110443 2 0.5572 -0.0737 0.004 0.612 0.000 0.296 0.088
#> GSM110447 2 0.6539 -0.0165 0.000 0.464 0.028 0.100 0.408
#> GSM110448 1 0.5173 0.5743 0.568 0.000 0.020 0.016 0.396
#> GSM110450 1 0.5305 0.4393 0.672 0.196 0.000 0.132 0.000
#> GSM110452 2 0.1965 0.4427 0.000 0.904 0.000 0.096 0.000
#> GSM110453 2 0.4800 0.3995 0.000 0.716 0.000 0.088 0.196
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM110395 2 0.3156 0.4506 0.000 0.852 0.000 0.080 0.024 NA
#> GSM110396 1 0.3452 0.7083 0.820 0.000 0.012 0.020 0.012 NA
#> GSM110397 1 0.2151 0.6926 0.912 0.000 0.016 0.024 0.000 NA
#> GSM110398 4 0.7707 0.3059 0.176 0.328 0.000 0.372 0.048 NA
#> GSM110399 5 0.4494 0.4695 0.024 0.020 0.000 0.064 0.768 NA
#> GSM110400 2 0.6825 0.1947 0.000 0.456 0.044 0.008 0.264 NA
#> GSM110401 1 0.0547 0.7094 0.980 0.000 0.000 0.000 0.000 NA
#> GSM110406 2 0.6416 0.2122 0.032 0.588 0.000 0.196 0.040 NA
#> GSM110407 1 0.4717 0.6779 0.728 0.036 0.000 0.152 0.000 NA
#> GSM110409 1 0.5814 0.6884 0.656 0.000 0.044 0.104 0.024 NA
#> GSM110410 2 0.5130 -0.0266 0.000 0.496 0.004 0.028 0.448 NA
#> GSM110413 2 0.7159 0.0305 0.000 0.388 0.000 0.252 0.272 NA
#> GSM110414 5 0.4738 0.5846 0.000 0.084 0.004 0.132 0.740 NA
#> GSM110415 3 0.6004 0.2544 0.000 0.020 0.488 0.020 0.392 NA
#> GSM110416 3 0.2542 0.8073 0.000 0.020 0.884 0.000 0.016 NA
#> GSM110418 3 0.2382 0.8087 0.000 0.024 0.904 0.020 0.004 NA
#> GSM110419 5 0.7060 0.3723 0.000 0.264 0.204 0.020 0.460 NA
#> GSM110420 3 0.0405 0.8151 0.000 0.000 0.988 0.004 0.000 NA
#> GSM110421 2 0.6507 0.3732 0.000 0.568 0.004 0.112 0.188 NA
#> GSM110423 2 0.6640 0.3301 0.000 0.512 0.072 0.016 0.100 NA
#> GSM110424 2 0.5223 0.2882 0.000 0.576 0.000 0.088 0.328 NA
#> GSM110425 2 0.6713 0.3836 0.000 0.584 0.080 0.036 0.168 NA
#> GSM110427 2 0.2675 0.4937 0.000 0.876 0.000 0.008 0.040 NA
#> GSM110428 2 0.6264 -0.0387 0.164 0.608 0.008 0.120 0.000 NA
#> GSM110430 1 0.1572 0.7115 0.936 0.000 0.000 0.028 0.000 NA
#> GSM110431 1 0.3916 0.6644 0.752 0.000 0.196 0.004 0.000 NA
#> GSM110432 2 0.4070 0.4771 0.000 0.764 0.000 0.020 0.048 NA
#> GSM110434 2 0.3396 0.4352 0.000 0.840 0.000 0.076 0.044 NA
#> GSM110435 1 0.6141 0.5427 0.568 0.000 0.280 0.012 0.056 NA
#> GSM110437 1 0.0777 0.7071 0.972 0.000 0.000 0.004 0.000 NA
#> GSM110438 4 0.6452 0.4845 0.016 0.372 0.116 0.468 0.008 NA
#> GSM110388 1 0.7042 0.3892 0.380 0.008 0.012 0.364 0.204 NA
#> GSM110392 4 0.4513 0.4605 0.004 0.440 0.000 0.532 0.024 NA
#> GSM110394 1 0.7513 0.5151 0.432 0.004 0.096 0.028 0.140 NA
#> GSM110402 5 0.7021 0.4517 0.000 0.144 0.208 0.104 0.524 NA
#> GSM110411 4 0.6029 0.5436 0.112 0.352 0.000 0.504 0.004 NA
#> GSM110412 2 0.3519 0.1680 0.000 0.744 0.004 0.244 0.004 NA
#> GSM110417 1 0.4849 0.6432 0.668 0.000 0.044 0.260 0.004 NA
#> GSM110422 2 0.2731 0.4592 0.000 0.876 0.000 0.044 0.012 NA
#> GSM110426 1 0.5369 0.4600 0.540 0.000 0.376 0.028 0.000 NA
#> GSM110429 2 0.4391 0.4361 0.000 0.700 0.004 0.024 0.020 NA
#> GSM110433 5 0.4008 0.4550 0.000 0.308 0.000 0.016 0.672 NA
#> GSM110436 2 0.1615 0.4353 0.000 0.928 0.000 0.064 0.004 NA
#> GSM110440 1 0.6172 0.6110 0.572 0.000 0.020 0.060 0.280 NA
#> GSM110441 5 0.2384 0.6030 0.000 0.040 0.000 0.056 0.896 NA
#> GSM110444 2 0.6269 -0.4297 0.036 0.448 0.000 0.408 0.096 NA
#> GSM110445 1 0.7204 0.4348 0.524 0.112 0.000 0.216 0.100 NA
#> GSM110446 3 0.1780 0.7984 0.000 0.000 0.924 0.048 0.000 NA
#> GSM110449 5 0.5039 0.5970 0.012 0.152 0.000 0.072 0.720 NA
#> GSM110451 2 0.3212 0.4558 0.000 0.844 0.008 0.036 0.008 NA
#> GSM110391 5 0.6178 0.2813 0.000 0.320 0.000 0.160 0.492 NA
#> GSM110439 5 0.5483 0.4729 0.000 0.276 0.000 0.108 0.596 NA
#> GSM110442 2 0.4789 0.3329 0.000 0.712 0.000 0.184 0.064 NA
#> GSM110443 2 0.5360 -0.1985 0.008 0.584 0.000 0.328 0.064 NA
#> GSM110447 2 0.6480 0.0108 0.000 0.456 0.016 0.124 0.372 NA
#> GSM110448 1 0.6090 0.5560 0.500 0.000 0.000 0.060 0.356 NA
#> GSM110450 1 0.5926 0.4771 0.604 0.152 0.004 0.208 0.004 NA
#> GSM110452 2 0.2288 0.3875 0.000 0.876 0.000 0.116 0.004 NA
#> GSM110453 2 0.4870 0.2560 0.000 0.584 0.000 0.060 0.352 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) specimen(p) k
#> ATC:NMF 56 1.0000 0.854 2
#> ATC:NMF 47 0.0498 0.220 3
#> ATC:NMF 43 0.3304 0.665 4
#> ATC:NMF 23 0.1513 0.811 5
#> ATC:NMF 21 0.3546 0.886 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