Date: 2019-12-25 21:12:22 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 21167 rows and 52 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 21167 52
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:kmeans | 3 | 1.000 | 0.981 | 0.986 | ** | |
| SD:skmeans | 3 | 1.000 | 0.982 | 0.993 | ** | |
| SD:pam | 3 | 1.000 | 0.958 | 0.985 | ** | 2 |
| SD:mclust | 2 | 1.000 | 0.981 | 0.987 | ** | |
| CV:kmeans | 3 | 1.000 | 0.975 | 0.981 | ** | |
| CV:skmeans | 3 | 1.000 | 0.969 | 0.989 | ** | |
| CV:mclust | 2 | 1.000 | 0.976 | 0.986 | ** | |
| CV:NMF | 3 | 1.000 | 0.973 | 0.988 | ** | |
| MAD:kmeans | 3 | 1.000 | 0.969 | 0.978 | ** | |
| MAD:skmeans | 3 | 1.000 | 0.960 | 0.985 | ** | |
| ATC:kmeans | 3 | 1.000 | 0.998 | 0.995 | ** | |
| ATC:skmeans | 3 | 1.000 | 0.993 | 0.996 | ** | 2 |
| CV:pam | 3 | 0.999 | 0.962 | 0.985 | ** | 2 |
| SD:NMF | 3 | 0.998 | 0.948 | 0.978 | ** | |
| MAD:mclust | 3 | 0.979 | 0.962 | 0.977 | ** | 2 |
| MAD:NMF | 3 | 0.969 | 0.917 | 0.968 | ** | |
| MAD:pam | 3 | 0.967 | 0.927 | 0.973 | ** | |
| ATC:NMF | 3 | 0.922 | 0.925 | 0.968 | * | 2 |
| ATC:pam | 3 | 0.772 | 0.924 | 0.967 | ||
| ATC:mclust | 4 | 0.765 | 0.789 | 0.900 | ||
| ATC:hclust | 3 | 0.684 | 0.818 | 0.904 | ||
| CV:hclust | 3 | 0.662 | 0.830 | 0.897 | ||
| MAD:hclust | 3 | 0.385 | 0.617 | 0.801 | ||
| SD:hclust | 2 | 0.381 | 0.750 | 0.848 |
**: 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 0.422 0.782 0.858 0.452 0.527 0.527
#> CV:NMF 2 0.418 0.820 0.861 0.450 0.527 0.527
#> MAD:NMF 2 0.880 0.944 0.973 0.479 0.527 0.527
#> ATC:NMF 2 1.000 0.958 0.982 0.405 0.599 0.599
#> SD:skmeans 2 0.571 0.918 0.933 0.481 0.517 0.517
#> CV:skmeans 2 0.524 0.899 0.912 0.476 0.517 0.517
#> MAD:skmeans 2 0.847 0.945 0.976 0.486 0.517 0.517
#> ATC:skmeans 2 1.000 0.969 0.987 0.500 0.497 0.497
#> SD:mclust 2 1.000 0.981 0.987 0.328 0.683 0.683
#> CV:mclust 2 1.000 0.976 0.986 0.331 0.683 0.683
#> MAD:mclust 2 1.000 0.978 0.974 0.324 0.683 0.683
#> ATC:mclust 2 0.451 0.781 0.770 0.369 0.517 0.517
#> SD:kmeans 2 0.482 0.606 0.774 0.375 0.502 0.502
#> CV:kmeans 2 0.497 0.756 0.795 0.376 0.581 0.581
#> MAD:kmeans 2 0.491 0.786 0.850 0.414 0.538 0.538
#> ATC:kmeans 2 0.479 0.832 0.843 0.419 0.566 0.566
#> SD:pam 2 1.000 0.966 0.973 0.327 0.683 0.683
#> CV:pam 2 1.000 0.975 0.974 0.320 0.683 0.683
#> MAD:pam 2 0.473 0.747 0.840 0.372 0.599 0.599
#> ATC:pam 2 0.501 0.769 0.861 0.329 0.735 0.735
#> SD:hclust 2 0.381 0.750 0.848 0.397 0.527 0.527
#> CV:hclust 2 0.409 0.807 0.871 0.375 0.618 0.618
#> MAD:hclust 2 0.685 0.833 0.931 0.364 0.638 0.638
#> ATC:hclust 2 0.788 0.961 0.973 0.417 0.566 0.566
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.998 0.948 0.978 0.376 0.687 0.490
#> CV:NMF 3 1.000 0.973 0.988 0.367 0.702 0.509
#> MAD:NMF 3 0.969 0.917 0.968 0.342 0.775 0.593
#> ATC:NMF 3 0.922 0.925 0.968 0.658 0.660 0.463
#> SD:skmeans 3 1.000 0.982 0.993 0.344 0.773 0.586
#> CV:skmeans 3 1.000 0.969 0.989 0.355 0.773 0.586
#> MAD:skmeans 3 1.000 0.960 0.985 0.339 0.773 0.586
#> ATC:skmeans 3 1.000 0.993 0.996 0.357 0.738 0.515
#> SD:mclust 3 0.687 0.819 0.911 0.896 0.704 0.567
#> CV:mclust 3 0.628 0.842 0.908 0.855 0.716 0.584
#> MAD:mclust 3 0.979 0.962 0.977 0.903 0.704 0.567
#> ATC:mclust 3 0.509 0.822 0.850 0.704 0.756 0.556
#> SD:kmeans 3 1.000 0.981 0.986 0.620 0.849 0.710
#> CV:kmeans 3 1.000 0.975 0.981 0.618 0.793 0.647
#> MAD:kmeans 3 1.000 0.969 0.978 0.472 0.740 0.563
#> ATC:kmeans 3 1.000 0.998 0.995 0.569 0.775 0.601
#> SD:pam 3 1.000 0.958 0.985 0.786 0.729 0.603
#> CV:pam 3 0.999 0.962 0.985 0.783 0.743 0.624
#> MAD:pam 3 0.967 0.927 0.973 0.630 0.633 0.463
#> ATC:pam 3 0.772 0.924 0.967 0.756 0.667 0.551
#> SD:hclust 3 0.642 0.695 0.855 0.392 0.621 0.431
#> CV:hclust 3 0.662 0.830 0.897 0.448 0.781 0.646
#> MAD:hclust 3 0.385 0.617 0.801 0.530 0.743 0.603
#> ATC:hclust 3 0.684 0.818 0.904 0.572 0.759 0.573
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.730 0.769 0.885 0.1802 0.855 0.638
#> CV:NMF 4 0.707 0.703 0.854 0.1689 0.867 0.665
#> MAD:NMF 4 0.680 0.625 0.834 0.1157 0.825 0.570
#> ATC:NMF 4 0.619 0.606 0.789 0.0956 0.900 0.715
#> SD:skmeans 4 0.866 0.932 0.954 0.1661 0.851 0.600
#> CV:skmeans 4 0.847 0.907 0.931 0.1694 0.851 0.600
#> MAD:skmeans 4 0.844 0.852 0.908 0.1514 0.851 0.600
#> ATC:skmeans 4 0.898 0.901 0.926 0.0867 0.926 0.776
#> SD:mclust 4 0.703 0.562 0.820 0.1283 0.873 0.695
#> CV:mclust 4 0.699 0.548 0.805 0.1460 0.925 0.811
#> MAD:mclust 4 0.770 0.819 0.871 0.1028 0.988 0.969
#> ATC:mclust 4 0.765 0.789 0.900 0.1436 0.888 0.682
#> SD:kmeans 4 0.704 0.629 0.814 0.1622 0.931 0.824
#> CV:kmeans 4 0.677 0.706 0.824 0.1463 0.931 0.825
#> MAD:kmeans 4 0.681 0.616 0.814 0.1623 0.876 0.696
#> ATC:kmeans 4 0.694 0.741 0.776 0.1151 0.889 0.680
#> SD:pam 4 0.855 0.932 0.947 0.2300 0.853 0.652
#> CV:pam 4 0.832 0.895 0.944 0.2335 0.860 0.677
#> MAD:pam 4 0.816 0.878 0.934 0.2014 0.843 0.625
#> ATC:pam 4 0.734 0.855 0.928 0.2663 0.791 0.524
#> SD:hclust 4 0.514 0.586 0.773 0.1931 0.848 0.668
#> CV:hclust 4 0.530 0.787 0.828 0.1909 0.957 0.895
#> MAD:hclust 4 0.408 0.609 0.741 0.1979 0.928 0.830
#> ATC:hclust 4 0.713 0.682 0.827 0.0640 0.989 0.965
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.700 0.638 0.793 0.0693 0.922 0.729
#> CV:NMF 5 0.702 0.637 0.817 0.0822 0.845 0.524
#> MAD:NMF 5 0.654 0.671 0.795 0.0905 0.839 0.516
#> ATC:NMF 5 0.672 0.699 0.828 0.0743 0.881 0.595
#> SD:skmeans 5 0.804 0.698 0.839 0.0574 0.907 0.658
#> CV:skmeans 5 0.771 0.690 0.843 0.0574 0.913 0.674
#> MAD:skmeans 5 0.801 0.688 0.830 0.0582 0.857 0.526
#> ATC:skmeans 5 0.857 0.894 0.909 0.0712 0.942 0.781
#> SD:mclust 5 0.707 0.772 0.808 0.0624 0.910 0.715
#> CV:mclust 5 0.683 0.670 0.801 0.0472 0.851 0.607
#> MAD:mclust 5 0.736 0.771 0.802 0.0905 0.834 0.572
#> ATC:mclust 5 0.697 0.788 0.856 0.0478 0.920 0.709
#> SD:kmeans 5 0.657 0.589 0.722 0.0834 0.923 0.776
#> CV:kmeans 5 0.659 0.592 0.743 0.0882 0.923 0.777
#> MAD:kmeans 5 0.665 0.640 0.770 0.0882 0.910 0.720
#> ATC:kmeans 5 0.770 0.675 0.784 0.0658 0.804 0.413
#> SD:pam 5 0.823 0.902 0.929 0.0234 0.988 0.958
#> CV:pam 5 0.825 0.886 0.934 0.0233 0.988 0.959
#> MAD:pam 5 0.829 0.881 0.931 0.0240 0.986 0.948
#> ATC:pam 5 0.725 0.614 0.794 0.0791 0.864 0.551
#> SD:hclust 5 0.645 0.677 0.800 0.0745 0.950 0.868
#> CV:hclust 5 0.658 0.654 0.807 0.1100 0.969 0.918
#> MAD:hclust 5 0.577 0.615 0.756 0.1158 0.836 0.597
#> ATC:hclust 5 0.736 0.660 0.781 0.0917 0.891 0.671
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.716 0.631 0.786 0.0509 0.847 0.451
#> CV:NMF 6 0.740 0.657 0.799 0.0565 0.870 0.514
#> MAD:NMF 6 0.671 0.633 0.771 0.0556 0.916 0.654
#> ATC:NMF 6 0.629 0.511 0.711 0.0380 0.956 0.801
#> SD:skmeans 6 0.781 0.547 0.789 0.0331 0.965 0.844
#> CV:skmeans 6 0.759 0.539 0.765 0.0349 0.956 0.797
#> MAD:skmeans 6 0.772 0.549 0.783 0.0341 0.990 0.955
#> ATC:skmeans 6 0.846 0.798 0.853 0.0391 0.973 0.869
#> SD:mclust 6 0.715 0.707 0.818 0.0400 0.955 0.820
#> CV:mclust 6 0.730 0.633 0.787 0.0484 0.948 0.830
#> MAD:mclust 6 0.858 0.864 0.921 0.0715 0.952 0.800
#> ATC:mclust 6 0.749 0.710 0.813 0.0653 0.925 0.685
#> SD:kmeans 6 0.669 0.577 0.705 0.0493 0.848 0.513
#> CV:kmeans 6 0.674 0.544 0.702 0.0667 0.836 0.485
#> MAD:kmeans 6 0.694 0.578 0.737 0.0555 0.851 0.504
#> ATC:kmeans 6 0.764 0.789 0.839 0.0379 0.941 0.751
#> SD:pam 6 0.758 0.794 0.871 0.0325 0.981 0.932
#> CV:pam 6 0.850 0.830 0.917 0.0230 0.993 0.976
#> MAD:pam 6 0.719 0.629 0.830 0.0523 0.946 0.803
#> ATC:pam 6 0.782 0.781 0.888 0.0447 0.834 0.396
#> SD:hclust 6 0.651 0.642 0.749 0.0507 0.905 0.744
#> CV:hclust 6 0.643 0.445 0.776 0.0479 0.947 0.852
#> MAD:hclust 6 0.642 0.567 0.755 0.0481 0.876 0.564
#> ATC:hclust 6 0.773 0.710 0.855 0.0338 0.958 0.826
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n disease.state(p) k
#> SD:NMF 49 1.10e-01 2
#> CV:NMF 50 1.22e-01 2
#> MAD:NMF 52 2.84e-01 2
#> ATC:NMF 52 7.24e-01 2
#> SD:skmeans 52 6.10e-01 2
#> CV:skmeans 52 6.10e-01 2
#> MAD:skmeans 52 6.10e-01 2
#> ATC:skmeans 51 3.92e-01 2
#> SD:mclust 52 1.99e-10 2
#> CV:mclust 52 1.99e-10 2
#> MAD:mclust 52 1.99e-10 2
#> ATC:mclust 45 1.00e+00 2
#> SD:kmeans 28 NA 2
#> CV:kmeans 42 7.20e-01 2
#> MAD:kmeans 49 5.19e-01 2
#> ATC:kmeans 52 5.15e-01 2
#> SD:pam 52 1.99e-10 2
#> CV:pam 52 1.99e-10 2
#> MAD:pam 48 1.09e-09 2
#> ATC:pam 50 1.00e+00 2
#> SD:hclust 47 1.81e-01 2
#> CV:hclust 50 2.90e-01 2
#> MAD:hclust 48 5.03e-01 2
#> ATC:hclust 52 5.15e-01 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) k
#> SD:NMF 51 1.31e-10 3
#> CV:NMF 52 8.27e-11 3
#> MAD:NMF 49 4.55e-09 3
#> ATC:NMF 51 3.28e-02 3
#> SD:skmeans 52 1.31e-09 3
#> CV:skmeans 51 1.98e-09 3
#> MAD:skmeans 51 2.00e-09 3
#> ATC:skmeans 52 4.76e-02 3
#> SD:mclust 49 3.24e-10 3
#> CV:mclust 49 3.24e-10 3
#> MAD:mclust 52 8.27e-11 3
#> ATC:mclust 51 2.34e-02 3
#> SD:kmeans 52 8.27e-11 3
#> CV:kmeans 52 8.27e-11 3
#> MAD:kmeans 52 9.23e-10 3
#> ATC:kmeans 52 3.39e-01 3
#> SD:pam 51 1.24e-10 3
#> CV:pam 52 7.80e-11 3
#> MAD:pam 50 2.49e-10 3
#> ATC:pam 51 8.17e-01 3
#> SD:hclust 41 2.26e-08 3
#> CV:hclust 50 2.05e-10 3
#> MAD:hclust 38 8.40e-08 3
#> ATC:hclust 50 1.16e-02 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) k
#> SD:NMF 44 3.12e-08 4
#> CV:NMF 45 1.58e-08 4
#> MAD:NMF 36 7.39e-07 4
#> ATC:NMF 41 8.42e-04 4
#> SD:skmeans 52 6.69e-09 4
#> CV:skmeans 51 1.01e-08 4
#> MAD:skmeans 50 2.17e-08 4
#> ATC:skmeans 52 3.19e-02 4
#> SD:mclust 27 9.27e-06 4
#> CV:mclust 38 5.20e-08 4
#> MAD:mclust 50 1.37e-09 4
#> ATC:mclust 47 7.96e-05 4
#> SD:kmeans 36 1.30e-07 4
#> CV:kmeans 45 1.93e-09 4
#> MAD:kmeans 39 3.60e-08 4
#> ATC:kmeans 49 2.18e-02 4
#> SD:pam 51 6.63e-10 4
#> CV:pam 51 6.63e-10 4
#> MAD:pam 50 1.26e-09 4
#> ATC:pam 51 1.49e-02 4
#> SD:hclust 46 6.53e-09 4
#> CV:hclust 50 1.11e-09 4
#> MAD:hclust 40 9.62e-08 4
#> ATC:hclust 49 1.36e-02 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) k
#> SD:NMF 44 7.87e-08 5
#> CV:NMF 41 1.10e-07 5
#> MAD:NMF 46 2.74e-07 5
#> ATC:NMF 47 5.90e-05 5
#> SD:skmeans 40 3.95e-07 5
#> CV:skmeans 42 1.66e-07 5
#> MAD:skmeans 38 2.79e-06 5
#> ATC:skmeans 52 4.66e-02 5
#> SD:mclust 50 4.77e-09 5
#> CV:mclust 45 1.55e-08 5
#> MAD:mclust 48 1.40e-08 5
#> ATC:mclust 48 2.46e-05 5
#> SD:kmeans 34 3.24e-07 5
#> CV:kmeans 40 1.97e-08 5
#> MAD:kmeans 39 5.73e-07 5
#> ATC:kmeans 39 3.49e-03 5
#> SD:pam 51 2.87e-09 5
#> CV:pam 51 2.87e-09 5
#> MAD:pam 51 2.87e-09 5
#> ATC:pam 34 9.04e-04 5
#> SD:hclust 43 2.96e-08 5
#> CV:hclust 38 8.67e-07 5
#> MAD:hclust 35 3.15e-06 5
#> ATC:hclust 48 1.63e-02 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) k
#> SD:NMF 41 9.38e-08 6
#> CV:NMF 42 5.89e-08 6
#> MAD:NMF 38 9.49e-07 6
#> ATC:NMF 32 1.64e-04 6
#> SD:skmeans 32 3.80e-06 6
#> CV:skmeans 33 8.40e-06 6
#> MAD:skmeans 31 1.82e-04 6
#> ATC:skmeans 49 6.23e-02 6
#> SD:mclust 45 1.75e-07 6
#> CV:mclust 38 3.39e-07 6
#> MAD:mclust 51 1.14e-08 6
#> ATC:mclust 45 2.69e-07 6
#> SD:kmeans 36 6.48e-06 6
#> CV:kmeans 34 1.26e-05 6
#> MAD:kmeans 29 4.63e-05 6
#> ATC:kmeans 49 1.47e-02 6
#> SD:pam 46 2.54e-08 6
#> CV:pam 49 6.75e-09 6
#> MAD:pam 38 8.67e-07 6
#> ATC:pam 49 4.81e-04 6
#> SD:hclust 44 2.32e-08 6
#> CV:hclust 25 8.49e-05 6
#> MAD:hclust 32 3.76e-05 6
#> ATC:hclust 47 4.08e-02 6
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.381 0.750 0.848 0.3974 0.527 0.527
#> 3 3 0.642 0.695 0.855 0.3922 0.621 0.431
#> 4 4 0.514 0.586 0.773 0.1931 0.848 0.668
#> 5 5 0.645 0.677 0.800 0.0745 0.950 0.868
#> 6 6 0.651 0.642 0.749 0.0507 0.905 0.744
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
#> GSM559383 1 0.000 0.7741 1.000 0.000
#> GSM559387 1 0.000 0.7741 1.000 0.000
#> GSM559391 1 0.000 0.7741 1.000 0.000
#> GSM559395 1 0.000 0.7741 1.000 0.000
#> GSM559397 1 0.000 0.7741 1.000 0.000
#> GSM559401 1 0.000 0.7741 1.000 0.000
#> GSM559414 1 0.000 0.7741 1.000 0.000
#> GSM559422 1 0.118 0.7646 0.984 0.016
#> GSM559424 1 0.000 0.7741 1.000 0.000
#> GSM559431 2 0.000 0.7794 0.000 1.000
#> GSM559432 1 0.118 0.7646 0.984 0.016
#> GSM559381 1 0.850 0.7711 0.724 0.276
#> GSM559382 2 0.891 0.5178 0.308 0.692
#> GSM559384 1 0.714 0.8893 0.804 0.196
#> GSM559385 1 0.714 0.8893 0.804 0.196
#> GSM559386 2 0.932 0.4443 0.348 0.652
#> GSM559388 2 0.861 0.5551 0.284 0.716
#> GSM559389 1 0.788 0.8385 0.764 0.236
#> GSM559390 1 0.767 0.8569 0.776 0.224
#> GSM559392 2 0.000 0.7794 0.000 1.000
#> GSM559393 1 0.714 0.8893 0.804 0.196
#> GSM559394 1 0.714 0.8893 0.804 0.196
#> GSM559396 1 0.714 0.8893 0.804 0.196
#> GSM559398 2 0.000 0.7794 0.000 1.000
#> GSM559399 1 0.714 0.8893 0.804 0.196
#> GSM559400 2 0.662 0.6778 0.172 0.828
#> GSM559402 1 0.714 0.8893 0.804 0.196
#> GSM559403 1 0.714 0.8893 0.804 0.196
#> GSM559404 1 0.714 0.8893 0.804 0.196
#> GSM559405 1 0.730 0.8806 0.796 0.204
#> GSM559406 1 0.714 0.8893 0.804 0.196
#> GSM559407 1 0.714 0.8893 0.804 0.196
#> GSM559408 1 0.714 0.8893 0.804 0.196
#> GSM559409 1 0.714 0.8893 0.804 0.196
#> GSM559410 1 0.714 0.8893 0.804 0.196
#> GSM559411 1 0.714 0.8893 0.804 0.196
#> GSM559412 1 0.714 0.8893 0.804 0.196
#> GSM559413 1 0.714 0.8893 0.804 0.196
#> GSM559415 2 1.000 -0.0703 0.500 0.500
#> GSM559416 2 0.988 0.2114 0.436 0.564
#> GSM559417 2 0.988 0.2114 0.436 0.564
#> GSM559418 2 1.000 -0.0703 0.500 0.500
#> GSM559419 1 0.714 0.8893 0.804 0.196
#> GSM559420 1 0.714 0.8893 0.804 0.196
#> GSM559421 2 0.000 0.7794 0.000 1.000
#> GSM559423 2 0.000 0.7794 0.000 1.000
#> GSM559425 2 0.000 0.7794 0.000 1.000
#> GSM559426 2 0.118 0.7775 0.016 0.984
#> GSM559427 2 0.000 0.7794 0.000 1.000
#> GSM559428 2 0.118 0.7775 0.016 0.984
#> GSM559429 2 0.118 0.7775 0.016 0.984
#> GSM559430 2 0.000 0.7794 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.000 0.7043 0.000 0.000 1.000
#> GSM559387 3 0.000 0.7043 0.000 0.000 1.000
#> GSM559391 3 0.000 0.7043 0.000 0.000 1.000
#> GSM559395 3 0.000 0.7043 0.000 0.000 1.000
#> GSM559397 3 0.000 0.7043 0.000 0.000 1.000
#> GSM559401 3 0.650 0.4915 0.004 0.460 0.536
#> GSM559414 3 0.000 0.7043 0.000 0.000 1.000
#> GSM559422 3 0.652 0.4736 0.004 0.480 0.516
#> GSM559424 3 0.000 0.7043 0.000 0.000 1.000
#> GSM559431 2 0.630 0.9917 0.480 0.520 0.000
#> GSM559432 3 0.652 0.4736 0.004 0.480 0.516
#> GSM559381 1 0.740 0.6944 0.552 0.036 0.412
#> GSM559382 1 0.968 -0.0715 0.448 0.320 0.232
#> GSM559384 1 0.630 0.7744 0.516 0.000 0.484
#> GSM559385 1 0.630 0.7749 0.520 0.000 0.480
#> GSM559386 1 0.978 0.1042 0.436 0.304 0.260
#> GSM559388 1 0.950 -0.1486 0.476 0.316 0.208
#> GSM559389 1 0.748 0.7296 0.512 0.036 0.452
#> GSM559390 1 0.628 0.7541 0.540 0.000 0.460
#> GSM559392 2 0.630 0.9917 0.480 0.520 0.000
#> GSM559393 1 0.652 0.7736 0.516 0.004 0.480
#> GSM559394 1 0.630 0.7749 0.520 0.000 0.480
#> GSM559396 1 0.630 0.7744 0.516 0.000 0.484
#> GSM559398 2 0.630 0.9917 0.480 0.520 0.000
#> GSM559399 1 0.630 0.7749 0.520 0.000 0.480
#> GSM559400 1 0.618 -0.4865 0.732 0.236 0.032
#> GSM559402 1 0.630 0.7744 0.516 0.000 0.484
#> GSM559403 1 0.630 0.7749 0.520 0.000 0.480
#> GSM559404 1 0.630 0.7744 0.516 0.000 0.484
#> GSM559405 1 0.630 0.7716 0.528 0.000 0.472
#> GSM559406 1 0.631 0.7679 0.508 0.000 0.492
#> GSM559407 1 0.630 0.7744 0.516 0.000 0.484
#> GSM559408 1 0.630 0.7744 0.516 0.000 0.484
#> GSM559409 1 0.630 0.7744 0.516 0.000 0.484
#> GSM559410 1 0.630 0.7749 0.520 0.000 0.480
#> GSM559411 1 0.630 0.7744 0.516 0.000 0.484
#> GSM559412 1 0.630 0.7744 0.516 0.000 0.484
#> GSM559413 1 0.630 0.7744 0.516 0.000 0.484
#> GSM559415 1 0.781 0.4986 0.640 0.092 0.268
#> GSM559416 1 0.872 0.4239 0.576 0.152 0.272
#> GSM559417 1 0.872 0.4239 0.576 0.152 0.272
#> GSM559418 1 0.781 0.4986 0.640 0.092 0.268
#> GSM559419 1 0.630 0.7749 0.520 0.000 0.480
#> GSM559420 1 0.630 0.7749 0.520 0.000 0.480
#> GSM559421 2 0.630 0.9917 0.480 0.520 0.000
#> GSM559423 2 0.630 0.9917 0.480 0.520 0.000
#> GSM559425 2 0.630 0.9917 0.480 0.520 0.000
#> GSM559426 2 0.682 0.9798 0.472 0.516 0.012
#> GSM559427 2 0.630 0.9917 0.480 0.520 0.000
#> GSM559428 2 0.682 0.9668 0.484 0.504 0.012
#> GSM559429 2 0.682 0.9798 0.472 0.516 0.012
#> GSM559430 2 0.630 0.9917 0.480 0.520 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.4164 0.809 0.264 0.000 0.736 0.000
#> GSM559387 3 0.4164 0.809 0.264 0.000 0.736 0.000
#> GSM559391 3 0.4164 0.809 0.264 0.000 0.736 0.000
#> GSM559395 3 0.4164 0.809 0.264 0.000 0.736 0.000
#> GSM559397 3 0.4164 0.809 0.264 0.000 0.736 0.000
#> GSM559401 3 0.4086 0.563 0.008 0.000 0.776 0.216
#> GSM559414 3 0.4164 0.809 0.264 0.000 0.736 0.000
#> GSM559422 3 0.3975 0.546 0.000 0.000 0.760 0.240
#> GSM559424 3 0.4164 0.809 0.264 0.000 0.736 0.000
#> GSM559431 2 0.3311 0.620 0.000 0.828 0.000 0.172
#> GSM559432 3 0.3975 0.546 0.000 0.000 0.760 0.240
#> GSM559381 1 0.4361 0.548 0.772 0.020 0.000 0.208
#> GSM559382 2 0.7863 -0.482 0.276 0.380 0.000 0.344
#> GSM559384 1 0.1297 0.768 0.964 0.000 0.016 0.020
#> GSM559385 1 0.3166 0.743 0.868 0.000 0.016 0.116
#> GSM559386 2 0.7924 -0.591 0.328 0.340 0.000 0.332
#> GSM559388 2 0.7812 -0.421 0.264 0.408 0.000 0.328
#> GSM559389 1 0.3900 0.647 0.816 0.020 0.000 0.164
#> GSM559390 1 0.3726 0.572 0.788 0.000 0.000 0.212
#> GSM559392 2 0.2408 0.689 0.000 0.896 0.000 0.104
#> GSM559393 1 0.3408 0.738 0.860 0.004 0.016 0.120
#> GSM559394 1 0.3166 0.743 0.868 0.000 0.016 0.116
#> GSM559396 1 0.1297 0.768 0.964 0.000 0.016 0.020
#> GSM559398 2 0.2408 0.689 0.000 0.896 0.000 0.104
#> GSM559399 1 0.2216 0.754 0.908 0.000 0.000 0.092
#> GSM559400 2 0.6200 0.173 0.052 0.504 0.000 0.444
#> GSM559402 1 0.0657 0.770 0.984 0.000 0.012 0.004
#> GSM559403 1 0.2281 0.753 0.904 0.000 0.000 0.096
#> GSM559404 1 0.5179 0.514 0.728 0.000 0.220 0.052
#> GSM559405 1 0.2281 0.751 0.904 0.000 0.000 0.096
#> GSM559406 1 0.4163 0.619 0.792 0.000 0.020 0.188
#> GSM559407 1 0.0657 0.770 0.984 0.000 0.012 0.004
#> GSM559408 1 0.1042 0.767 0.972 0.000 0.020 0.008
#> GSM559409 1 0.1042 0.767 0.972 0.000 0.020 0.008
#> GSM559410 1 0.2546 0.757 0.900 0.000 0.008 0.092
#> GSM559411 1 0.1059 0.767 0.972 0.000 0.012 0.016
#> GSM559412 1 0.4562 0.545 0.764 0.000 0.208 0.028
#> GSM559413 1 0.4562 0.545 0.764 0.000 0.208 0.028
#> GSM559415 1 0.6987 -0.447 0.568 0.160 0.000 0.272
#> GSM559416 4 0.7344 0.958 0.380 0.160 0.000 0.460
#> GSM559417 4 0.7301 0.959 0.356 0.160 0.000 0.484
#> GSM559418 1 0.6987 -0.447 0.568 0.160 0.000 0.272
#> GSM559419 1 0.0469 0.771 0.988 0.000 0.000 0.012
#> GSM559420 1 0.0469 0.771 0.988 0.000 0.000 0.012
#> GSM559421 2 0.2216 0.691 0.000 0.908 0.000 0.092
#> GSM559423 2 0.2281 0.691 0.000 0.904 0.000 0.096
#> GSM559425 2 0.3311 0.620 0.000 0.828 0.000 0.172
#> GSM559426 2 0.2473 0.670 0.012 0.908 0.000 0.080
#> GSM559427 2 0.3311 0.620 0.000 0.828 0.000 0.172
#> GSM559428 2 0.2796 0.663 0.016 0.892 0.000 0.092
#> GSM559429 2 0.2542 0.669 0.012 0.904 0.000 0.084
#> GSM559430 2 0.2149 0.692 0.000 0.912 0.000 0.088
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559383 3 0.0000 0.9174 0.000 0.000 1.000 0.000 NA
#> GSM559387 3 0.0000 0.9174 0.000 0.000 1.000 0.000 NA
#> GSM559391 3 0.0000 0.9174 0.000 0.000 1.000 0.000 NA
#> GSM559395 3 0.0000 0.9174 0.000 0.000 1.000 0.000 NA
#> GSM559397 3 0.0000 0.9174 0.000 0.000 1.000 0.000 NA
#> GSM559401 3 0.4307 -0.1779 0.000 0.000 0.500 0.500 NA
#> GSM559414 3 0.0000 0.9174 0.000 0.000 1.000 0.000 NA
#> GSM559422 4 0.1851 1.0000 0.000 0.000 0.088 0.912 NA
#> GSM559424 3 0.0000 0.9174 0.000 0.000 1.000 0.000 NA
#> GSM559431 2 0.3942 0.5637 0.000 0.728 0.000 0.012 NA
#> GSM559432 4 0.1851 1.0000 0.000 0.000 0.088 0.912 NA
#> GSM559381 1 0.3085 0.7344 0.852 0.032 0.000 0.000 NA
#> GSM559382 2 0.6613 0.2946 0.352 0.468 0.000 0.008 NA
#> GSM559384 1 0.3194 0.7958 0.832 0.000 0.020 0.000 NA
#> GSM559385 1 0.1502 0.7966 0.940 0.000 0.000 0.004 NA
#> GSM559386 2 0.6594 0.1771 0.404 0.428 0.000 0.008 NA
#> GSM559388 2 0.6481 0.3382 0.340 0.496 0.000 0.008 NA
#> GSM559389 1 0.2473 0.7645 0.896 0.032 0.000 0.000 NA
#> GSM559390 1 0.3805 0.7498 0.784 0.000 0.000 0.032 NA
#> GSM559392 2 0.0404 0.6979 0.000 0.988 0.000 0.000 NA
#> GSM559393 1 0.1731 0.7949 0.932 0.004 0.000 0.004 NA
#> GSM559394 1 0.1502 0.7966 0.940 0.000 0.000 0.004 NA
#> GSM559396 1 0.3351 0.7948 0.828 0.000 0.020 0.004 NA
#> GSM559398 2 0.0404 0.6979 0.000 0.988 0.000 0.000 NA
#> GSM559399 1 0.0451 0.8015 0.988 0.000 0.000 0.004 NA
#> GSM559400 2 0.6420 0.4171 0.100 0.596 0.000 0.048 NA
#> GSM559402 1 0.2471 0.7980 0.864 0.000 0.000 0.000 NA
#> GSM559403 1 0.0727 0.8016 0.980 0.000 0.004 0.004 NA
#> GSM559404 1 0.5755 0.5550 0.604 0.000 0.060 0.024 NA
#> GSM559405 1 0.0566 0.8014 0.984 0.000 0.000 0.004 NA
#> GSM559406 1 0.3925 0.7557 0.784 0.000 0.004 0.032 NA
#> GSM559407 1 0.2471 0.7980 0.864 0.000 0.000 0.000 NA
#> GSM559408 1 0.2763 0.7949 0.848 0.000 0.004 0.000 NA
#> GSM559409 1 0.2763 0.7949 0.848 0.000 0.004 0.000 NA
#> GSM559410 1 0.0671 0.8028 0.980 0.000 0.000 0.004 NA
#> GSM559411 1 0.2719 0.7966 0.852 0.000 0.004 0.000 NA
#> GSM559412 1 0.5049 0.6225 0.644 0.000 0.060 0.000 NA
#> GSM559413 1 0.5049 0.6225 0.644 0.000 0.060 0.000 NA
#> GSM559415 1 0.5691 0.4065 0.632 0.236 0.000 0.004 NA
#> GSM559416 1 0.7343 0.1016 0.408 0.236 0.000 0.032 NA
#> GSM559417 1 0.7362 0.0554 0.392 0.236 0.000 0.032 NA
#> GSM559418 1 0.5691 0.4065 0.632 0.236 0.000 0.004 NA
#> GSM559419 1 0.2329 0.8020 0.876 0.000 0.000 0.000 NA
#> GSM559420 1 0.2329 0.8020 0.876 0.000 0.000 0.000 NA
#> GSM559421 2 0.0000 0.6991 0.000 1.000 0.000 0.000 NA
#> GSM559423 2 0.0162 0.6995 0.000 0.996 0.000 0.000 NA
#> GSM559425 2 0.3942 0.5637 0.000 0.728 0.000 0.012 NA
#> GSM559426 2 0.3783 0.6641 0.012 0.768 0.000 0.004 NA
#> GSM559427 2 0.3942 0.5637 0.000 0.728 0.000 0.012 NA
#> GSM559428 2 0.4054 0.6565 0.012 0.744 0.000 0.008 NA
#> GSM559429 2 0.3875 0.6596 0.012 0.756 0.000 0.004 NA
#> GSM559430 2 0.0404 0.6986 0.000 0.988 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
#> GSM559383 3 0.0000 0.92470 0.000 0.000 1.00 0.000 0.0 0.000
#> GSM559387 3 0.0000 0.92470 0.000 0.000 1.00 0.000 0.0 0.000
#> GSM559391 3 0.0000 0.92470 0.000 0.000 1.00 0.000 0.0 0.000
#> GSM559395 3 0.0000 0.92470 0.000 0.000 1.00 0.000 0.0 0.000
#> GSM559397 3 0.0000 0.92470 0.000 0.000 1.00 0.000 0.0 0.000
#> GSM559401 3 0.3869 -0.00016 0.000 0.000 0.50 0.000 0.5 0.000
#> GSM559414 3 0.0000 0.92470 0.000 0.000 1.00 0.000 0.0 0.000
#> GSM559422 5 0.0000 1.00000 0.000 0.000 0.00 0.000 1.0 0.000
#> GSM559424 3 0.0000 0.92470 0.000 0.000 1.00 0.000 0.0 0.000
#> GSM559431 2 0.0790 0.49872 0.000 0.968 0.00 0.000 0.0 0.032
#> GSM559432 5 0.0000 1.00000 0.000 0.000 0.00 0.000 1.0 0.000
#> GSM559381 1 0.4580 0.57283 0.708 0.004 0.00 0.120 0.0 0.168
#> GSM559382 4 0.7415 0.59937 0.204 0.208 0.00 0.404 0.0 0.184
#> GSM559384 1 0.2332 0.70666 0.904 0.000 0.02 0.036 0.0 0.040
#> GSM559385 1 0.3834 0.64219 0.708 0.000 0.00 0.024 0.0 0.268
#> GSM559386 4 0.7414 0.60832 0.252 0.168 0.00 0.392 0.0 0.188
#> GSM559388 4 0.7443 0.56865 0.188 0.236 0.00 0.392 0.0 0.184
#> GSM559389 1 0.4102 0.62655 0.752 0.004 0.00 0.080 0.0 0.164
#> GSM559390 1 0.3404 0.58588 0.760 0.000 0.00 0.224 0.0 0.016
#> GSM559392 2 0.3288 0.73816 0.000 0.724 0.00 0.276 0.0 0.000
#> GSM559393 1 0.4045 0.63614 0.700 0.004 0.00 0.028 0.0 0.268
#> GSM559394 1 0.3834 0.64219 0.708 0.000 0.00 0.024 0.0 0.268
#> GSM559396 1 0.2401 0.70535 0.900 0.000 0.02 0.036 0.0 0.044
#> GSM559398 2 0.3288 0.73816 0.000 0.724 0.00 0.276 0.0 0.000
#> GSM559399 1 0.3240 0.66202 0.752 0.000 0.00 0.004 0.0 0.244
#> GSM559400 4 0.4289 -0.17813 0.020 0.332 0.00 0.640 0.0 0.008
#> GSM559402 1 0.0508 0.71641 0.984 0.000 0.00 0.012 0.0 0.004
#> GSM559403 1 0.3373 0.66112 0.744 0.000 0.00 0.008 0.0 0.248
#> GSM559404 1 0.5208 0.39745 0.604 0.000 0.00 0.248 0.0 0.148
#> GSM559405 1 0.2968 0.68499 0.816 0.000 0.00 0.016 0.0 0.168
#> GSM559406 1 0.3431 0.60388 0.756 0.000 0.00 0.228 0.0 0.016
#> GSM559407 1 0.0508 0.71641 0.984 0.000 0.00 0.012 0.0 0.004
#> GSM559408 1 0.0935 0.71279 0.964 0.000 0.00 0.032 0.0 0.004
#> GSM559409 1 0.0935 0.71279 0.964 0.000 0.00 0.032 0.0 0.004
#> GSM559410 1 0.3445 0.66410 0.744 0.000 0.00 0.012 0.0 0.244
#> GSM559411 1 0.1713 0.70035 0.928 0.000 0.00 0.028 0.0 0.044
#> GSM559412 1 0.4025 0.52077 0.720 0.000 0.00 0.232 0.0 0.048
#> GSM559413 1 0.4025 0.52077 0.720 0.000 0.00 0.232 0.0 0.048
#> GSM559415 1 0.6051 -0.27548 0.396 0.000 0.00 0.344 0.0 0.260
#> GSM559416 4 0.3578 0.51342 0.340 0.000 0.00 0.660 0.0 0.000
#> GSM559417 4 0.3482 0.53826 0.316 0.000 0.00 0.684 0.0 0.000
#> GSM559418 1 0.6051 -0.27548 0.396 0.000 0.00 0.344 0.0 0.260
#> GSM559419 1 0.0260 0.71888 0.992 0.000 0.00 0.000 0.0 0.008
#> GSM559420 1 0.0260 0.71888 0.992 0.000 0.00 0.000 0.0 0.008
#> GSM559421 2 0.3221 0.74239 0.000 0.736 0.00 0.264 0.0 0.000
#> GSM559423 2 0.3360 0.74015 0.000 0.732 0.00 0.264 0.0 0.004
#> GSM559425 2 0.0790 0.49872 0.000 0.968 0.00 0.000 0.0 0.032
#> GSM559426 6 0.4238 0.90251 0.000 0.444 0.00 0.016 0.0 0.540
#> GSM559427 2 0.0790 0.49872 0.000 0.968 0.00 0.000 0.0 0.032
#> GSM559428 6 0.4228 0.94043 0.000 0.392 0.00 0.020 0.0 0.588
#> GSM559429 6 0.4168 0.94678 0.000 0.400 0.00 0.016 0.0 0.584
#> GSM559430 2 0.3151 0.73925 0.000 0.748 0.00 0.252 0.0 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:hclust 47 1.81e-01 2
#> SD:hclust 41 2.26e-08 3
#> SD:hclust 46 6.53e-09 4
#> SD:hclust 43 2.96e-08 5
#> SD:hclust 44 2.32e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.482 0.606 0.774 0.3753 0.502 0.502
#> 3 3 1.000 0.981 0.986 0.6200 0.849 0.710
#> 4 4 0.704 0.629 0.814 0.1622 0.931 0.824
#> 5 5 0.657 0.589 0.722 0.0834 0.923 0.776
#> 6 6 0.669 0.577 0.705 0.0493 0.848 0.513
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
#> GSM559383 2 0.9983 0.242 0.476 0.524
#> GSM559387 2 0.9983 0.242 0.476 0.524
#> GSM559391 2 0.9983 0.242 0.476 0.524
#> GSM559395 2 0.9983 0.242 0.476 0.524
#> GSM559397 2 0.9983 0.242 0.476 0.524
#> GSM559401 2 0.9983 0.242 0.476 0.524
#> GSM559414 2 0.9983 0.242 0.476 0.524
#> GSM559422 2 0.9983 0.242 0.476 0.524
#> GSM559424 2 0.9983 0.242 0.476 0.524
#> GSM559431 2 0.9996 0.347 0.488 0.512
#> GSM559432 2 0.0000 0.331 0.000 1.000
#> GSM559381 1 0.0000 0.923 1.000 0.000
#> GSM559382 2 0.9996 0.347 0.488 0.512
#> GSM559384 1 0.0000 0.923 1.000 0.000
#> GSM559385 1 0.0000 0.923 1.000 0.000
#> GSM559386 1 0.4939 0.731 0.892 0.108
#> GSM559388 1 0.9996 -0.349 0.512 0.488
#> GSM559389 1 0.0000 0.923 1.000 0.000
#> GSM559390 1 0.0000 0.923 1.000 0.000
#> GSM559392 2 0.9998 0.339 0.492 0.508
#> GSM559393 1 0.1633 0.889 0.976 0.024
#> GSM559394 1 0.0000 0.923 1.000 0.000
#> GSM559396 1 0.0000 0.923 1.000 0.000
#> GSM559398 2 0.9996 0.347 0.488 0.512
#> GSM559399 1 0.0000 0.923 1.000 0.000
#> GSM559400 1 0.9970 -0.312 0.532 0.468
#> GSM559402 1 0.0000 0.923 1.000 0.000
#> GSM559403 1 0.0000 0.923 1.000 0.000
#> GSM559404 1 0.0672 0.914 0.992 0.008
#> GSM559405 1 0.0000 0.923 1.000 0.000
#> GSM559406 1 0.0672 0.914 0.992 0.008
#> GSM559407 1 0.0000 0.923 1.000 0.000
#> GSM559408 1 0.0000 0.923 1.000 0.000
#> GSM559409 1 0.0000 0.923 1.000 0.000
#> GSM559410 1 0.0000 0.923 1.000 0.000
#> GSM559411 1 0.0672 0.914 0.992 0.008
#> GSM559412 1 0.0672 0.914 0.992 0.008
#> GSM559413 1 0.0672 0.914 0.992 0.008
#> GSM559415 1 0.0000 0.923 1.000 0.000
#> GSM559416 1 0.0000 0.923 1.000 0.000
#> GSM559417 1 0.0000 0.923 1.000 0.000
#> GSM559418 1 0.2603 0.856 0.956 0.044
#> GSM559419 1 0.0000 0.923 1.000 0.000
#> GSM559420 1 0.0000 0.923 1.000 0.000
#> GSM559421 2 0.9996 0.347 0.488 0.512
#> GSM559423 2 0.9996 0.347 0.488 0.512
#> GSM559425 2 0.9996 0.347 0.488 0.512
#> GSM559426 2 0.9996 0.347 0.488 0.512
#> GSM559427 2 0.9996 0.347 0.488 0.512
#> GSM559428 2 0.9996 0.347 0.488 0.512
#> GSM559429 2 0.9996 0.347 0.488 0.512
#> GSM559430 2 0.9996 0.347 0.488 0.512
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.1163 0.992 0.028 0.000 0.972
#> GSM559387 3 0.1163 0.992 0.028 0.000 0.972
#> GSM559391 3 0.1163 0.992 0.028 0.000 0.972
#> GSM559395 3 0.1163 0.992 0.028 0.000 0.972
#> GSM559397 3 0.1163 0.992 0.028 0.000 0.972
#> GSM559401 3 0.1399 0.991 0.028 0.004 0.968
#> GSM559414 3 0.1163 0.992 0.028 0.000 0.972
#> GSM559422 3 0.0661 0.974 0.008 0.004 0.988
#> GSM559424 3 0.1163 0.992 0.028 0.000 0.972
#> GSM559431 2 0.0661 0.971 0.004 0.988 0.008
#> GSM559432 3 0.0237 0.966 0.000 0.004 0.996
#> GSM559381 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559382 2 0.1129 0.968 0.004 0.976 0.020
#> GSM559384 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559385 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559386 1 0.1315 0.973 0.972 0.008 0.020
#> GSM559388 2 0.1129 0.968 0.004 0.976 0.020
#> GSM559389 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559390 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559392 2 0.0237 0.972 0.004 0.996 0.000
#> GSM559393 1 0.1315 0.973 0.972 0.008 0.020
#> GSM559394 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559396 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559398 2 0.0661 0.971 0.004 0.988 0.008
#> GSM559399 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559400 2 0.5200 0.734 0.184 0.796 0.020
#> GSM559402 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559403 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559404 1 0.0237 0.992 0.996 0.000 0.004
#> GSM559405 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559406 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559407 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559408 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559409 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559410 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559411 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559412 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559413 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559415 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559416 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559417 1 0.0983 0.980 0.980 0.004 0.016
#> GSM559418 1 0.1170 0.976 0.976 0.008 0.016
#> GSM559419 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559420 1 0.0000 0.996 1.000 0.000 0.000
#> GSM559421 2 0.0237 0.972 0.004 0.996 0.000
#> GSM559423 2 0.0983 0.969 0.004 0.980 0.016
#> GSM559425 2 0.0661 0.971 0.004 0.988 0.008
#> GSM559426 2 0.0237 0.972 0.004 0.996 0.000
#> GSM559427 2 0.0661 0.971 0.004 0.988 0.008
#> GSM559428 2 0.1129 0.968 0.004 0.976 0.020
#> GSM559429 2 0.0983 0.969 0.004 0.980 0.016
#> GSM559430 2 0.0661 0.971 0.004 0.988 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.0188 0.9647 0.000 0.000 0.996 0.004
#> GSM559387 3 0.0000 0.9654 0.000 0.000 1.000 0.000
#> GSM559391 3 0.0188 0.9647 0.000 0.000 0.996 0.004
#> GSM559395 3 0.0000 0.9654 0.000 0.000 1.000 0.000
#> GSM559397 3 0.0000 0.9654 0.000 0.000 1.000 0.000
#> GSM559401 3 0.0000 0.9654 0.000 0.000 1.000 0.000
#> GSM559414 3 0.0000 0.9654 0.000 0.000 1.000 0.000
#> GSM559422 3 0.3649 0.8581 0.000 0.000 0.796 0.204
#> GSM559424 3 0.0188 0.9647 0.000 0.000 0.996 0.004
#> GSM559431 2 0.0336 0.8567 0.000 0.992 0.000 0.008
#> GSM559432 3 0.3726 0.8528 0.000 0.000 0.788 0.212
#> GSM559381 1 0.1792 0.6394 0.932 0.000 0.000 0.068
#> GSM559382 2 0.5771 0.4645 0.028 0.512 0.000 0.460
#> GSM559384 1 0.2216 0.6468 0.908 0.000 0.000 0.092
#> GSM559385 1 0.1792 0.6321 0.932 0.000 0.000 0.068
#> GSM559386 1 0.4907 -0.0738 0.580 0.000 0.000 0.420
#> GSM559388 2 0.4907 0.5400 0.000 0.580 0.000 0.420
#> GSM559389 1 0.2081 0.6182 0.916 0.000 0.000 0.084
#> GSM559390 4 0.4843 0.4317 0.396 0.000 0.000 0.604
#> GSM559392 2 0.1867 0.8612 0.000 0.928 0.000 0.072
#> GSM559393 1 0.4948 -0.0473 0.560 0.000 0.000 0.440
#> GSM559394 1 0.1792 0.6321 0.932 0.000 0.000 0.068
#> GSM559396 1 0.4222 0.5020 0.728 0.000 0.000 0.272
#> GSM559398 2 0.0336 0.8589 0.000 0.992 0.000 0.008
#> GSM559399 1 0.2408 0.5873 0.896 0.000 0.000 0.104
#> GSM559400 4 0.5947 -0.3058 0.044 0.384 0.000 0.572
#> GSM559402 1 0.2868 0.6303 0.864 0.000 0.000 0.136
#> GSM559403 1 0.1792 0.6321 0.932 0.000 0.000 0.068
#> GSM559404 1 0.2081 0.6371 0.916 0.000 0.000 0.084
#> GSM559405 1 0.0000 0.6533 1.000 0.000 0.000 0.000
#> GSM559406 1 0.4356 0.4772 0.708 0.000 0.000 0.292
#> GSM559407 1 0.2921 0.6288 0.860 0.000 0.000 0.140
#> GSM559408 1 0.4277 0.4927 0.720 0.000 0.000 0.280
#> GSM559409 1 0.4277 0.4927 0.720 0.000 0.000 0.280
#> GSM559410 1 0.0336 0.6537 0.992 0.000 0.000 0.008
#> GSM559411 1 0.4356 0.4871 0.708 0.000 0.000 0.292
#> GSM559412 1 0.4356 0.4871 0.708 0.000 0.000 0.292
#> GSM559413 1 0.4356 0.4871 0.708 0.000 0.000 0.292
#> GSM559415 1 0.2345 0.5923 0.900 0.000 0.000 0.100
#> GSM559416 4 0.4961 0.4070 0.448 0.000 0.000 0.552
#> GSM559417 4 0.4961 0.4070 0.448 0.000 0.000 0.552
#> GSM559418 1 0.4477 0.1311 0.688 0.000 0.000 0.312
#> GSM559419 1 0.4888 0.0463 0.588 0.000 0.000 0.412
#> GSM559420 1 0.2868 0.6303 0.864 0.000 0.000 0.136
#> GSM559421 2 0.1792 0.8616 0.000 0.932 0.000 0.068
#> GSM559423 2 0.2011 0.8592 0.000 0.920 0.000 0.080
#> GSM559425 2 0.0000 0.8582 0.000 1.000 0.000 0.000
#> GSM559426 2 0.2011 0.8598 0.000 0.920 0.000 0.080
#> GSM559427 2 0.0000 0.8582 0.000 1.000 0.000 0.000
#> GSM559428 2 0.5774 0.4681 0.028 0.508 0.000 0.464
#> GSM559429 2 0.2345 0.8551 0.000 0.900 0.000 0.100
#> GSM559430 2 0.0000 0.8582 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
#> GSM559383 3 0.0898 0.9102 0.000 0.000 0.972 0.020 NA
#> GSM559387 3 0.0000 0.9145 0.000 0.000 1.000 0.000 NA
#> GSM559391 3 0.0898 0.9102 0.000 0.000 0.972 0.020 NA
#> GSM559395 3 0.0000 0.9145 0.000 0.000 1.000 0.000 NA
#> GSM559397 3 0.0000 0.9145 0.000 0.000 1.000 0.000 NA
#> GSM559401 3 0.0000 0.9145 0.000 0.000 1.000 0.000 NA
#> GSM559414 3 0.0000 0.9145 0.000 0.000 1.000 0.000 NA
#> GSM559422 3 0.4256 0.6363 0.000 0.000 0.564 0.000 NA
#> GSM559424 3 0.0898 0.9102 0.000 0.000 0.972 0.020 NA
#> GSM559431 2 0.0324 0.9059 0.000 0.992 0.000 0.004 NA
#> GSM559432 3 0.4268 0.6293 0.000 0.000 0.556 0.000 NA
#> GSM559381 1 0.3532 0.5857 0.832 0.000 0.000 0.092 NA
#> GSM559382 4 0.7126 0.2497 0.032 0.304 0.000 0.468 NA
#> GSM559384 1 0.3543 0.6114 0.828 0.000 0.000 0.112 NA
#> GSM559385 1 0.3565 0.5580 0.816 0.000 0.000 0.040 NA
#> GSM559386 4 0.6372 0.2367 0.376 0.000 0.000 0.456 NA
#> GSM559388 4 0.6553 0.1365 0.004 0.368 0.000 0.452 NA
#> GSM559389 1 0.3242 0.5672 0.852 0.000 0.000 0.076 NA
#> GSM559390 4 0.3532 0.3905 0.128 0.000 0.000 0.824 NA
#> GSM559392 2 0.3184 0.8779 0.000 0.852 0.000 0.048 NA
#> GSM559393 1 0.6361 0.0439 0.484 0.000 0.000 0.340 NA
#> GSM559394 1 0.3803 0.5557 0.804 0.000 0.000 0.056 NA
#> GSM559396 1 0.5727 0.4091 0.560 0.000 0.000 0.340 NA
#> GSM559398 2 0.1549 0.9009 0.000 0.944 0.000 0.016 NA
#> GSM559399 1 0.3639 0.5319 0.812 0.000 0.000 0.144 NA
#> GSM559400 4 0.5605 0.4411 0.012 0.172 0.000 0.672 NA
#> GSM559402 1 0.3930 0.5978 0.792 0.000 0.000 0.152 NA
#> GSM559403 1 0.3262 0.5685 0.840 0.000 0.000 0.036 NA
#> GSM559404 1 0.4303 0.5598 0.752 0.000 0.000 0.056 NA
#> GSM559405 1 0.0451 0.6184 0.988 0.000 0.000 0.004 NA
#> GSM559406 1 0.5447 0.3723 0.500 0.000 0.000 0.440 NA
#> GSM559407 1 0.4049 0.5947 0.780 0.000 0.000 0.164 NA
#> GSM559408 1 0.5622 0.3926 0.508 0.000 0.000 0.416 NA
#> GSM559409 1 0.5703 0.3967 0.508 0.000 0.000 0.408 NA
#> GSM559410 1 0.1403 0.6188 0.952 0.000 0.000 0.024 NA
#> GSM559411 1 0.5928 0.4046 0.500 0.000 0.000 0.392 NA
#> GSM559412 1 0.5826 0.3915 0.500 0.000 0.000 0.404 NA
#> GSM559413 1 0.6019 0.4019 0.500 0.000 0.000 0.380 NA
#> GSM559415 1 0.3595 0.5388 0.816 0.000 0.000 0.140 NA
#> GSM559416 4 0.3231 0.3031 0.196 0.000 0.000 0.800 NA
#> GSM559417 4 0.3003 0.3194 0.188 0.000 0.000 0.812 NA
#> GSM559418 1 0.5145 0.1985 0.612 0.000 0.000 0.332 NA
#> GSM559419 4 0.4686 -0.1650 0.384 0.000 0.000 0.596 NA
#> GSM559420 1 0.4190 0.5938 0.768 0.000 0.000 0.172 NA
#> GSM559421 2 0.2735 0.8927 0.000 0.880 0.000 0.036 NA
#> GSM559423 2 0.3390 0.8749 0.000 0.840 0.000 0.060 NA
#> GSM559425 2 0.0000 0.9077 0.000 1.000 0.000 0.000 NA
#> GSM559426 2 0.3276 0.8659 0.000 0.836 0.000 0.032 NA
#> GSM559427 2 0.0000 0.9077 0.000 1.000 0.000 0.000 NA
#> GSM559428 4 0.7328 0.1986 0.028 0.292 0.000 0.408 NA
#> GSM559429 2 0.4252 0.8074 0.000 0.764 0.000 0.064 NA
#> GSM559430 2 0.0000 0.9077 0.000 1.000 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
#> GSM559383 3 0.1151 0.9487 0.012 0.000 0.956 0.000 0.000 0.032
#> GSM559387 3 0.0000 0.9679 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559391 3 0.1151 0.9487 0.012 0.000 0.956 0.000 0.000 0.032
#> GSM559395 3 0.0000 0.9679 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559397 3 0.0000 0.9679 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559401 3 0.0291 0.9614 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM559414 3 0.0000 0.9679 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559422 5 0.3817 0.9749 0.000 0.000 0.432 0.000 0.568 0.000
#> GSM559424 3 0.1151 0.9487 0.012 0.000 0.956 0.000 0.000 0.032
#> GSM559431 2 0.1232 0.7825 0.024 0.956 0.000 0.000 0.016 0.004
#> GSM559432 5 0.4032 0.9753 0.000 0.000 0.420 0.000 0.572 0.008
#> GSM559381 1 0.6238 0.1789 0.452 0.000 0.000 0.392 0.056 0.100
#> GSM559382 6 0.3837 0.5939 0.068 0.140 0.000 0.000 0.008 0.784
#> GSM559384 4 0.5351 0.0571 0.388 0.000 0.000 0.528 0.064 0.020
#> GSM559385 1 0.5380 0.5903 0.660 0.000 0.000 0.192 0.104 0.044
#> GSM559386 6 0.3826 0.5436 0.236 0.000 0.000 0.012 0.016 0.736
#> GSM559388 6 0.3727 0.5380 0.040 0.188 0.000 0.000 0.004 0.768
#> GSM559389 1 0.4378 0.6229 0.704 0.000 0.000 0.240 0.016 0.040
#> GSM559390 6 0.6037 0.0252 0.068 0.000 0.000 0.408 0.064 0.460
#> GSM559392 2 0.3314 0.7102 0.000 0.740 0.000 0.000 0.004 0.256
#> GSM559393 1 0.4754 0.4537 0.692 0.000 0.000 0.016 0.080 0.212
#> GSM559394 1 0.4702 0.6190 0.724 0.000 0.000 0.164 0.080 0.032
#> GSM559396 4 0.6695 0.2695 0.256 0.000 0.000 0.504 0.100 0.140
#> GSM559398 2 0.1908 0.7695 0.000 0.900 0.000 0.000 0.004 0.096
#> GSM559399 1 0.4740 0.6034 0.696 0.000 0.000 0.220 0.032 0.052
#> GSM559400 6 0.5131 0.5924 0.052 0.060 0.000 0.084 0.060 0.744
#> GSM559402 4 0.5017 0.2282 0.312 0.000 0.000 0.612 0.060 0.016
#> GSM559403 1 0.4837 0.6116 0.692 0.000 0.000 0.208 0.076 0.024
#> GSM559404 4 0.5828 -0.1455 0.356 0.000 0.000 0.516 0.096 0.032
#> GSM559405 1 0.4010 0.4571 0.584 0.000 0.000 0.408 0.008 0.000
#> GSM559406 4 0.2924 0.5319 0.024 0.000 0.000 0.868 0.040 0.068
#> GSM559407 4 0.4986 0.2411 0.304 0.000 0.000 0.620 0.060 0.016
#> GSM559408 4 0.1464 0.5577 0.016 0.000 0.000 0.944 0.004 0.036
#> GSM559409 4 0.1148 0.5601 0.016 0.000 0.000 0.960 0.004 0.020
#> GSM559410 1 0.4200 0.4994 0.592 0.000 0.000 0.392 0.012 0.004
#> GSM559411 4 0.1307 0.5543 0.008 0.000 0.000 0.952 0.032 0.008
#> GSM559412 4 0.0914 0.5591 0.000 0.000 0.000 0.968 0.016 0.016
#> GSM559413 4 0.0777 0.5579 0.000 0.000 0.000 0.972 0.024 0.004
#> GSM559415 1 0.4700 0.6053 0.704 0.000 0.000 0.212 0.040 0.044
#> GSM559416 4 0.6855 0.1138 0.152 0.000 0.000 0.448 0.092 0.308
#> GSM559417 4 0.6830 0.0855 0.144 0.000 0.000 0.444 0.092 0.320
#> GSM559418 1 0.4922 0.5507 0.712 0.000 0.000 0.096 0.040 0.152
#> GSM559419 4 0.6340 0.3407 0.236 0.000 0.000 0.548 0.068 0.148
#> GSM559420 4 0.5407 0.2150 0.340 0.000 0.000 0.564 0.072 0.024
#> GSM559421 2 0.3189 0.7244 0.000 0.760 0.000 0.000 0.004 0.236
#> GSM559423 2 0.4525 0.6596 0.020 0.672 0.000 0.000 0.032 0.276
#> GSM559425 2 0.0820 0.7859 0.016 0.972 0.000 0.000 0.012 0.000
#> GSM559426 2 0.5434 0.6489 0.052 0.664 0.000 0.000 0.112 0.172
#> GSM559427 2 0.0820 0.7859 0.016 0.972 0.000 0.000 0.012 0.000
#> GSM559428 6 0.6158 0.4450 0.112 0.132 0.000 0.000 0.152 0.604
#> GSM559429 2 0.6369 0.4752 0.068 0.536 0.000 0.000 0.140 0.256
#> GSM559430 2 0.0000 0.7875 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:kmeans 28 NA 2
#> SD:kmeans 52 8.27e-11 3
#> SD:kmeans 36 1.30e-07 4
#> SD:kmeans 34 3.24e-07 5
#> SD:kmeans 36 6.48e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "skmeans"]
# you can also extract it by
# res = res_list["SD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.571 0.918 0.933 0.4814 0.517 0.517
#> 3 3 1.000 0.982 0.993 0.3439 0.773 0.586
#> 4 4 0.866 0.932 0.954 0.1661 0.851 0.600
#> 5 5 0.804 0.698 0.839 0.0574 0.907 0.658
#> 6 6 0.781 0.547 0.789 0.0331 0.965 0.844
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
#> GSM559383 1 0.184 0.923 0.972 0.028
#> GSM559387 1 0.184 0.923 0.972 0.028
#> GSM559391 1 0.184 0.923 0.972 0.028
#> GSM559395 1 0.184 0.923 0.972 0.028
#> GSM559397 1 0.184 0.923 0.972 0.028
#> GSM559401 1 0.184 0.923 0.972 0.028
#> GSM559414 1 0.184 0.923 0.972 0.028
#> GSM559422 2 0.871 0.656 0.292 0.708
#> GSM559424 1 0.184 0.923 0.972 0.028
#> GSM559431 2 0.000 0.946 0.000 1.000
#> GSM559432 2 0.518 0.857 0.116 0.884
#> GSM559381 1 0.662 0.863 0.828 0.172
#> GSM559382 2 0.118 0.954 0.016 0.984
#> GSM559384 1 0.518 0.914 0.884 0.116
#> GSM559385 1 0.518 0.914 0.884 0.116
#> GSM559386 2 0.184 0.947 0.028 0.972
#> GSM559388 2 0.118 0.954 0.016 0.984
#> GSM559389 1 0.662 0.863 0.828 0.172
#> GSM559390 1 0.000 0.930 1.000 0.000
#> GSM559392 2 0.118 0.954 0.016 0.984
#> GSM559393 2 0.184 0.947 0.028 0.972
#> GSM559394 1 0.518 0.914 0.884 0.116
#> GSM559396 1 0.118 0.924 0.984 0.016
#> GSM559398 2 0.118 0.954 0.016 0.984
#> GSM559399 1 0.518 0.914 0.884 0.116
#> GSM559400 2 0.518 0.857 0.116 0.884
#> GSM559402 1 0.518 0.914 0.884 0.116
#> GSM559403 1 0.518 0.914 0.884 0.116
#> GSM559404 1 0.000 0.930 1.000 0.000
#> GSM559405 1 0.518 0.914 0.884 0.116
#> GSM559406 1 0.000 0.930 1.000 0.000
#> GSM559407 1 0.518 0.914 0.884 0.116
#> GSM559408 1 0.163 0.931 0.976 0.024
#> GSM559409 1 0.118 0.931 0.984 0.016
#> GSM559410 1 0.518 0.914 0.884 0.116
#> GSM559411 1 0.000 0.930 1.000 0.000
#> GSM559412 1 0.000 0.930 1.000 0.000
#> GSM559413 1 0.000 0.930 1.000 0.000
#> GSM559415 1 0.518 0.914 0.884 0.116
#> GSM559416 1 0.260 0.927 0.956 0.044
#> GSM559417 2 0.795 0.746 0.240 0.760
#> GSM559418 2 0.184 0.947 0.028 0.972
#> GSM559419 1 0.469 0.919 0.900 0.100
#> GSM559420 1 0.469 0.919 0.900 0.100
#> GSM559421 2 0.118 0.954 0.016 0.984
#> GSM559423 2 0.118 0.954 0.016 0.984
#> GSM559425 2 0.118 0.954 0.016 0.984
#> GSM559426 2 0.118 0.954 0.016 0.984
#> GSM559427 2 0.118 0.954 0.016 0.984
#> GSM559428 2 0.000 0.946 0.000 1.000
#> GSM559429 2 0.000 0.946 0.000 1.000
#> GSM559430 2 0.118 0.954 0.016 0.984
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559387 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559391 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559395 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559397 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559401 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559414 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559422 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559424 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559431 2 0.0000 0.980 0.000 1.000 0.000
#> GSM559432 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559381 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559382 2 0.0000 0.980 0.000 1.000 0.000
#> GSM559384 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559385 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559386 2 0.0000 0.980 0.000 1.000 0.000
#> GSM559388 2 0.0000 0.980 0.000 1.000 0.000
#> GSM559389 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559390 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559392 2 0.0000 0.980 0.000 1.000 0.000
#> GSM559393 2 0.0592 0.967 0.012 0.988 0.000
#> GSM559394 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559396 3 0.0237 0.995 0.004 0.000 0.996
#> GSM559398 2 0.0000 0.980 0.000 1.000 0.000
#> GSM559399 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559400 2 0.0000 0.980 0.000 1.000 0.000
#> GSM559402 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559403 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559404 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559405 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559406 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559407 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559408 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559409 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559410 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559411 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559412 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559413 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559415 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559416 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559417 1 0.3038 0.880 0.896 0.104 0.000
#> GSM559418 2 0.5178 0.654 0.256 0.744 0.000
#> GSM559419 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559420 1 0.0000 0.995 1.000 0.000 0.000
#> GSM559421 2 0.0000 0.980 0.000 1.000 0.000
#> GSM559423 2 0.0000 0.980 0.000 1.000 0.000
#> GSM559425 2 0.0000 0.980 0.000 1.000 0.000
#> GSM559426 2 0.0000 0.980 0.000 1.000 0.000
#> GSM559427 2 0.0000 0.980 0.000 1.000 0.000
#> GSM559428 2 0.0000 0.980 0.000 1.000 0.000
#> GSM559429 2 0.0000 0.980 0.000 1.000 0.000
#> GSM559430 2 0.0000 0.980 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM559387 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM559391 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM559395 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM559397 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM559401 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM559414 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM559422 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM559424 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM559431 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559432 3 0.0469 0.985 0.000 0.012 0.988 0.000
#> GSM559381 1 0.1389 0.898 0.952 0.000 0.000 0.048
#> GSM559382 2 0.0188 0.979 0.000 0.996 0.000 0.004
#> GSM559384 1 0.2149 0.878 0.912 0.000 0.000 0.088
#> GSM559385 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> GSM559386 2 0.3164 0.884 0.064 0.884 0.000 0.052
#> GSM559388 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559389 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> GSM559390 4 0.0921 0.923 0.028 0.000 0.000 0.972
#> GSM559392 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559393 1 0.2053 0.856 0.924 0.072 0.000 0.004
#> GSM559394 1 0.0469 0.898 0.988 0.000 0.000 0.012
#> GSM559396 3 0.0817 0.974 0.000 0.000 0.976 0.024
#> GSM559398 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559399 1 0.2589 0.859 0.884 0.000 0.000 0.116
#> GSM559400 2 0.2921 0.839 0.000 0.860 0.000 0.140
#> GSM559402 1 0.3649 0.772 0.796 0.000 0.000 0.204
#> GSM559403 1 0.0000 0.900 1.000 0.000 0.000 0.000
#> GSM559404 1 0.1022 0.901 0.968 0.000 0.000 0.032
#> GSM559405 1 0.1022 0.901 0.968 0.000 0.000 0.032
#> GSM559406 4 0.2345 0.943 0.100 0.000 0.000 0.900
#> GSM559407 1 0.3837 0.747 0.776 0.000 0.000 0.224
#> GSM559408 4 0.2469 0.943 0.108 0.000 0.000 0.892
#> GSM559409 4 0.2530 0.943 0.112 0.000 0.000 0.888
#> GSM559410 1 0.1557 0.897 0.944 0.000 0.000 0.056
#> GSM559411 4 0.2530 0.943 0.112 0.000 0.000 0.888
#> GSM559412 4 0.2530 0.943 0.112 0.000 0.000 0.888
#> GSM559413 4 0.2530 0.943 0.112 0.000 0.000 0.888
#> GSM559415 1 0.2704 0.858 0.876 0.000 0.000 0.124
#> GSM559416 4 0.0000 0.912 0.000 0.000 0.000 1.000
#> GSM559417 4 0.0000 0.912 0.000 0.000 0.000 1.000
#> GSM559418 1 0.3497 0.839 0.860 0.036 0.000 0.104
#> GSM559419 4 0.0336 0.916 0.008 0.000 0.000 0.992
#> GSM559420 1 0.4164 0.709 0.736 0.000 0.000 0.264
#> GSM559421 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559423 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559425 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559426 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559427 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559428 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559429 2 0.0000 0.982 0.000 1.000 0.000 0.000
#> GSM559430 2 0.0000 0.982 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
#> GSM559383 3 0.0000 0.9529 0.000 0.000 1.000 0.000 0.000
#> GSM559387 3 0.0000 0.9529 0.000 0.000 1.000 0.000 0.000
#> GSM559391 3 0.0000 0.9529 0.000 0.000 1.000 0.000 0.000
#> GSM559395 3 0.0000 0.9529 0.000 0.000 1.000 0.000 0.000
#> GSM559397 3 0.0000 0.9529 0.000 0.000 1.000 0.000 0.000
#> GSM559401 3 0.0000 0.9529 0.000 0.000 1.000 0.000 0.000
#> GSM559414 3 0.0000 0.9529 0.000 0.000 1.000 0.000 0.000
#> GSM559422 3 0.0579 0.9440 0.008 0.000 0.984 0.008 0.000
#> GSM559424 3 0.0000 0.9529 0.000 0.000 1.000 0.000 0.000
#> GSM559431 2 0.0000 0.9382 0.000 1.000 0.000 0.000 0.000
#> GSM559432 3 0.1770 0.8974 0.008 0.048 0.936 0.008 0.000
#> GSM559381 1 0.4306 0.3818 0.660 0.000 0.000 0.012 0.328
#> GSM559382 2 0.1828 0.9066 0.028 0.936 0.000 0.004 0.032
#> GSM559384 1 0.2930 0.5626 0.832 0.000 0.000 0.004 0.164
#> GSM559385 5 0.1341 0.7783 0.056 0.000 0.000 0.000 0.944
#> GSM559386 2 0.6358 0.5633 0.064 0.632 0.000 0.104 0.200
#> GSM559388 2 0.1372 0.9188 0.024 0.956 0.000 0.004 0.016
#> GSM559389 5 0.2719 0.7417 0.144 0.000 0.000 0.004 0.852
#> GSM559390 4 0.3495 0.6639 0.152 0.000 0.000 0.816 0.032
#> GSM559392 2 0.0000 0.9382 0.000 1.000 0.000 0.000 0.000
#> GSM559393 5 0.1082 0.7513 0.028 0.008 0.000 0.000 0.964
#> GSM559394 5 0.1197 0.7786 0.048 0.000 0.000 0.000 0.952
#> GSM559396 3 0.4478 0.4816 0.360 0.000 0.628 0.004 0.008
#> GSM559398 2 0.0000 0.9382 0.000 1.000 0.000 0.000 0.000
#> GSM559399 5 0.5405 0.7064 0.136 0.000 0.000 0.204 0.660
#> GSM559400 2 0.4387 0.4867 0.012 0.640 0.000 0.348 0.000
#> GSM559402 1 0.2020 0.5849 0.900 0.000 0.000 0.000 0.100
#> GSM559403 5 0.2020 0.7713 0.100 0.000 0.000 0.000 0.900
#> GSM559404 1 0.4470 0.3447 0.616 0.000 0.000 0.012 0.372
#> GSM559405 1 0.4287 -0.0388 0.540 0.000 0.000 0.000 0.460
#> GSM559406 4 0.4225 0.2894 0.364 0.000 0.000 0.632 0.004
#> GSM559407 1 0.2193 0.5848 0.900 0.000 0.000 0.008 0.092
#> GSM559408 1 0.4450 -0.0351 0.508 0.000 0.000 0.488 0.004
#> GSM559409 1 0.4464 0.1714 0.584 0.000 0.000 0.408 0.008
#> GSM559410 5 0.4872 0.2309 0.436 0.000 0.000 0.024 0.540
#> GSM559411 1 0.3534 0.4101 0.744 0.000 0.000 0.256 0.000
#> GSM559412 1 0.4350 0.2057 0.588 0.000 0.000 0.408 0.004
#> GSM559413 1 0.4084 0.3389 0.668 0.000 0.000 0.328 0.004
#> GSM559415 5 0.5164 0.7098 0.096 0.000 0.000 0.232 0.672
#> GSM559416 4 0.0794 0.7313 0.028 0.000 0.000 0.972 0.000
#> GSM559417 4 0.0865 0.7307 0.024 0.004 0.000 0.972 0.000
#> GSM559418 5 0.5324 0.6988 0.072 0.016 0.000 0.232 0.680
#> GSM559419 4 0.3882 0.5705 0.224 0.000 0.000 0.756 0.020
#> GSM559420 1 0.3906 0.5014 0.800 0.000 0.000 0.132 0.068
#> GSM559421 2 0.0000 0.9382 0.000 1.000 0.000 0.000 0.000
#> GSM559423 2 0.0000 0.9382 0.000 1.000 0.000 0.000 0.000
#> GSM559425 2 0.0000 0.9382 0.000 1.000 0.000 0.000 0.000
#> GSM559426 2 0.0162 0.9370 0.004 0.996 0.000 0.000 0.000
#> GSM559427 2 0.0000 0.9382 0.000 1.000 0.000 0.000 0.000
#> GSM559428 2 0.1483 0.9192 0.028 0.952 0.000 0.012 0.008
#> GSM559429 2 0.0833 0.9288 0.016 0.976 0.000 0.004 0.004
#> GSM559430 2 0.0000 0.9382 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
#> GSM559383 3 0.0146 0.914801 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM559387 3 0.0000 0.915374 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559391 3 0.0146 0.914801 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM559395 3 0.0000 0.915374 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559397 3 0.0000 0.915374 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559401 3 0.0146 0.914136 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM559414 3 0.0000 0.915374 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559422 3 0.2145 0.859434 0.012 0.000 0.904 0.004 0.004 0.076
#> GSM559424 3 0.0146 0.914801 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM559431 2 0.0000 0.875174 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559432 3 0.3331 0.803246 0.008 0.060 0.844 0.004 0.004 0.080
#> GSM559381 6 0.6042 0.000000 0.212 0.004 0.000 0.360 0.000 0.424
#> GSM559382 2 0.3264 0.788116 0.012 0.796 0.000 0.000 0.008 0.184
#> GSM559384 4 0.5269 -0.247684 0.088 0.000 0.000 0.604 0.016 0.292
#> GSM559385 1 0.1168 0.628381 0.956 0.000 0.000 0.016 0.000 0.028
#> GSM559386 2 0.6950 0.195084 0.136 0.412 0.000 0.008 0.080 0.364
#> GSM559388 2 0.2333 0.828547 0.004 0.872 0.000 0.000 0.004 0.120
#> GSM559389 1 0.4300 0.384322 0.712 0.000 0.000 0.080 0.000 0.208
#> GSM559390 5 0.4730 0.532472 0.008 0.000 0.000 0.184 0.696 0.112
#> GSM559392 2 0.0790 0.871559 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM559393 1 0.1765 0.582994 0.904 0.000 0.000 0.000 0.000 0.096
#> GSM559394 1 0.0748 0.640108 0.976 0.000 0.000 0.016 0.004 0.004
#> GSM559396 3 0.6332 -0.076423 0.000 0.000 0.408 0.264 0.012 0.316
#> GSM559398 2 0.0632 0.873444 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM559399 1 0.6681 0.461879 0.508 0.000 0.000 0.080 0.204 0.208
#> GSM559400 2 0.5653 0.216136 0.000 0.496 0.000 0.004 0.360 0.140
#> GSM559402 4 0.3351 0.076968 0.040 0.000 0.000 0.800 0.000 0.160
#> GSM559403 1 0.1950 0.613654 0.912 0.000 0.000 0.064 0.000 0.024
#> GSM559404 4 0.5027 -0.049062 0.324 0.000 0.000 0.600 0.012 0.064
#> GSM559405 4 0.5681 -0.337238 0.416 0.000 0.000 0.428 0.000 0.156
#> GSM559406 4 0.4472 -0.000703 0.000 0.000 0.000 0.496 0.476 0.028
#> GSM559407 4 0.3457 0.125477 0.052 0.000 0.000 0.808 0.004 0.136
#> GSM559408 4 0.4254 0.311889 0.004 0.000 0.000 0.624 0.352 0.020
#> GSM559409 4 0.4255 0.408131 0.012 0.000 0.000 0.680 0.284 0.024
#> GSM559410 4 0.5816 -0.183573 0.428 0.000 0.000 0.432 0.012 0.128
#> GSM559411 4 0.3381 0.399554 0.000 0.000 0.000 0.800 0.156 0.044
#> GSM559412 4 0.3650 0.424069 0.004 0.000 0.000 0.716 0.272 0.008
#> GSM559413 4 0.2902 0.425151 0.000 0.000 0.000 0.800 0.196 0.004
#> GSM559415 1 0.6152 0.523638 0.548 0.000 0.000 0.044 0.256 0.152
#> GSM559416 5 0.0806 0.766677 0.000 0.000 0.000 0.020 0.972 0.008
#> GSM559417 5 0.0993 0.766864 0.000 0.000 0.000 0.024 0.964 0.012
#> GSM559418 1 0.6701 0.487105 0.496 0.020 0.000 0.040 0.292 0.152
#> GSM559419 5 0.5041 0.551543 0.024 0.000 0.000 0.128 0.688 0.160
#> GSM559420 4 0.5766 -0.211403 0.036 0.000 0.000 0.572 0.104 0.288
#> GSM559421 2 0.0632 0.873954 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM559423 2 0.0260 0.874955 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM559425 2 0.0000 0.875174 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559426 2 0.0790 0.867898 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM559427 2 0.0000 0.875174 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559428 2 0.3240 0.732849 0.000 0.752 0.000 0.000 0.004 0.244
#> GSM559429 2 0.2092 0.823455 0.000 0.876 0.000 0.000 0.000 0.124
#> GSM559430 2 0.0000 0.875174 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:skmeans 52 6.10e-01 2
#> SD:skmeans 52 1.31e-09 3
#> SD:skmeans 52 6.69e-09 4
#> SD:skmeans 40 3.95e-07 5
#> SD:skmeans 32 3.80e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "pam"]
# you can also extract it by
# res = res_list["SD:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.966 0.973 0.3268 0.683 0.683
#> 3 3 1.000 0.958 0.985 0.7857 0.729 0.603
#> 4 4 0.855 0.932 0.947 0.2300 0.853 0.652
#> 5 5 0.823 0.902 0.929 0.0234 0.988 0.958
#> 6 6 0.758 0.794 0.871 0.0325 0.981 0.932
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM559383 2 0.3114 0.993 0.056 0.944
#> GSM559387 2 0.3114 0.993 0.056 0.944
#> GSM559391 2 0.3114 0.993 0.056 0.944
#> GSM559395 2 0.3114 0.993 0.056 0.944
#> GSM559397 2 0.3114 0.993 0.056 0.944
#> GSM559401 2 0.3114 0.993 0.056 0.944
#> GSM559414 2 0.3114 0.993 0.056 0.944
#> GSM559422 2 0.3114 0.993 0.056 0.944
#> GSM559424 2 0.3114 0.993 0.056 0.944
#> GSM559431 1 0.3114 0.950 0.944 0.056
#> GSM559432 2 0.0000 0.940 0.000 1.000
#> GSM559381 1 0.0000 0.976 1.000 0.000
#> GSM559382 1 0.0000 0.976 1.000 0.000
#> GSM559384 1 0.0000 0.976 1.000 0.000
#> GSM559385 1 0.0000 0.976 1.000 0.000
#> GSM559386 1 0.0000 0.976 1.000 0.000
#> GSM559388 1 0.0376 0.974 0.996 0.004
#> GSM559389 1 0.0000 0.976 1.000 0.000
#> GSM559390 1 0.0000 0.976 1.000 0.000
#> GSM559392 1 0.3114 0.950 0.944 0.056
#> GSM559393 1 0.0000 0.976 1.000 0.000
#> GSM559394 1 0.0000 0.976 1.000 0.000
#> GSM559396 1 0.0000 0.976 1.000 0.000
#> GSM559398 1 0.3114 0.950 0.944 0.056
#> GSM559399 1 0.0000 0.976 1.000 0.000
#> GSM559400 1 0.3114 0.950 0.944 0.056
#> GSM559402 1 0.0000 0.976 1.000 0.000
#> GSM559403 1 0.0000 0.976 1.000 0.000
#> GSM559404 1 0.6801 0.771 0.820 0.180
#> GSM559405 1 0.0000 0.976 1.000 0.000
#> GSM559406 1 0.0672 0.971 0.992 0.008
#> GSM559407 1 0.0000 0.976 1.000 0.000
#> GSM559408 1 0.0000 0.976 1.000 0.000
#> GSM559409 1 0.0000 0.976 1.000 0.000
#> GSM559410 1 0.0000 0.976 1.000 0.000
#> GSM559411 1 0.0000 0.976 1.000 0.000
#> GSM559412 1 0.0000 0.976 1.000 0.000
#> GSM559413 1 0.5178 0.860 0.884 0.116
#> GSM559415 1 0.0000 0.976 1.000 0.000
#> GSM559416 1 0.0000 0.976 1.000 0.000
#> GSM559417 1 0.0000 0.976 1.000 0.000
#> GSM559418 1 0.0000 0.976 1.000 0.000
#> GSM559419 1 0.0000 0.976 1.000 0.000
#> GSM559420 1 0.0000 0.976 1.000 0.000
#> GSM559421 1 0.3114 0.950 0.944 0.056
#> GSM559423 1 0.3114 0.950 0.944 0.056
#> GSM559425 1 0.3114 0.950 0.944 0.056
#> GSM559426 1 0.3114 0.950 0.944 0.056
#> GSM559427 1 0.3114 0.950 0.944 0.056
#> GSM559428 1 0.0000 0.976 1.000 0.000
#> GSM559429 1 0.3114 0.950 0.944 0.056
#> GSM559430 1 0.3114 0.950 0.944 0.056
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.000 1.000 0.000 0.000 1
#> GSM559387 3 0.000 1.000 0.000 0.000 1
#> GSM559391 3 0.000 1.000 0.000 0.000 1
#> GSM559395 3 0.000 1.000 0.000 0.000 1
#> GSM559397 3 0.000 1.000 0.000 0.000 1
#> GSM559401 3 0.000 1.000 0.000 0.000 1
#> GSM559414 3 0.000 1.000 0.000 0.000 1
#> GSM559422 3 0.000 1.000 0.000 0.000 1
#> GSM559424 3 0.000 1.000 0.000 0.000 1
#> GSM559431 2 0.000 0.931 0.000 1.000 0
#> GSM559432 3 0.000 1.000 0.000 0.000 1
#> GSM559381 1 0.000 0.991 1.000 0.000 0
#> GSM559382 1 0.460 0.726 0.796 0.204 0
#> GSM559384 1 0.000 0.991 1.000 0.000 0
#> GSM559385 1 0.000 0.991 1.000 0.000 0
#> GSM559386 1 0.000 0.991 1.000 0.000 0
#> GSM559388 2 0.619 0.284 0.420 0.580 0
#> GSM559389 1 0.000 0.991 1.000 0.000 0
#> GSM559390 1 0.000 0.991 1.000 0.000 0
#> GSM559392 2 0.000 0.931 0.000 1.000 0
#> GSM559393 1 0.000 0.991 1.000 0.000 0
#> GSM559394 1 0.000 0.991 1.000 0.000 0
#> GSM559396 1 0.000 0.991 1.000 0.000 0
#> GSM559398 2 0.000 0.931 0.000 1.000 0
#> GSM559399 1 0.000 0.991 1.000 0.000 0
#> GSM559400 2 0.341 0.796 0.124 0.876 0
#> GSM559402 1 0.000 0.991 1.000 0.000 0
#> GSM559403 1 0.000 0.991 1.000 0.000 0
#> GSM559404 1 0.000 0.991 1.000 0.000 0
#> GSM559405 1 0.000 0.991 1.000 0.000 0
#> GSM559406 1 0.000 0.991 1.000 0.000 0
#> GSM559407 1 0.000 0.991 1.000 0.000 0
#> GSM559408 1 0.000 0.991 1.000 0.000 0
#> GSM559409 1 0.000 0.991 1.000 0.000 0
#> GSM559410 1 0.000 0.991 1.000 0.000 0
#> GSM559411 1 0.000 0.991 1.000 0.000 0
#> GSM559412 1 0.000 0.991 1.000 0.000 0
#> GSM559413 1 0.000 0.991 1.000 0.000 0
#> GSM559415 1 0.000 0.991 1.000 0.000 0
#> GSM559416 1 0.000 0.991 1.000 0.000 0
#> GSM559417 1 0.000 0.991 1.000 0.000 0
#> GSM559418 1 0.000 0.991 1.000 0.000 0
#> GSM559419 1 0.000 0.991 1.000 0.000 0
#> GSM559420 1 0.000 0.991 1.000 0.000 0
#> GSM559421 2 0.000 0.931 0.000 1.000 0
#> GSM559423 2 0.000 0.931 0.000 1.000 0
#> GSM559425 2 0.000 0.931 0.000 1.000 0
#> GSM559426 2 0.000 0.931 0.000 1.000 0
#> GSM559427 2 0.000 0.931 0.000 1.000 0
#> GSM559428 1 0.116 0.964 0.972 0.028 0
#> GSM559429 2 0.000 0.931 0.000 1.000 0
#> GSM559430 2 0.000 0.931 0.000 1.000 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM559387 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM559391 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM559395 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM559397 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM559401 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM559414 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM559422 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM559424 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM559431 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM559432 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM559381 1 0.000 0.946 1.000 0.000 0 0.000
#> GSM559382 4 0.422 0.859 0.100 0.076 0 0.824
#> GSM559384 1 0.000 0.946 1.000 0.000 0 0.000
#> GSM559385 1 0.000 0.946 1.000 0.000 0 0.000
#> GSM559386 4 0.241 0.884 0.104 0.000 0 0.896
#> GSM559388 4 0.518 0.817 0.120 0.120 0 0.760
#> GSM559389 1 0.000 0.946 1.000 0.000 0 0.000
#> GSM559390 4 0.000 0.887 0.000 0.000 0 1.000
#> GSM559392 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM559393 1 0.000 0.946 1.000 0.000 0 0.000
#> GSM559394 1 0.000 0.946 1.000 0.000 0 0.000
#> GSM559396 1 0.000 0.946 1.000 0.000 0 0.000
#> GSM559398 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM559399 1 0.000 0.946 1.000 0.000 0 0.000
#> GSM559400 4 0.234 0.884 0.100 0.000 0 0.900
#> GSM559402 1 0.000 0.946 1.000 0.000 0 0.000
#> GSM559403 1 0.000 0.946 1.000 0.000 0 0.000
#> GSM559404 1 0.000 0.946 1.000 0.000 0 0.000
#> GSM559405 1 0.000 0.946 1.000 0.000 0 0.000
#> GSM559406 4 0.000 0.887 0.000 0.000 0 1.000
#> GSM559407 1 0.121 0.929 0.960 0.000 0 0.040
#> GSM559408 1 0.234 0.898 0.900 0.000 0 0.100
#> GSM559409 1 0.234 0.898 0.900 0.000 0 0.100
#> GSM559410 1 0.234 0.898 0.900 0.000 0 0.100
#> GSM559411 1 0.234 0.898 0.900 0.000 0 0.100
#> GSM559412 1 0.234 0.898 0.900 0.000 0 0.100
#> GSM559413 1 0.234 0.898 0.900 0.000 0 0.100
#> GSM559415 1 0.000 0.946 1.000 0.000 0 0.000
#> GSM559416 4 0.000 0.887 0.000 0.000 0 1.000
#> GSM559417 4 0.000 0.887 0.000 0.000 0 1.000
#> GSM559418 1 0.000 0.946 1.000 0.000 0 0.000
#> GSM559419 1 0.496 0.215 0.552 0.000 0 0.448
#> GSM559420 1 0.000 0.946 1.000 0.000 0 0.000
#> GSM559421 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM559423 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM559425 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM559426 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM559427 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM559428 4 0.433 0.767 0.244 0.008 0 0.748
#> GSM559429 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM559430 2 0.000 1.000 0.000 1.000 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559383 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559387 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559391 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559395 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559397 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559401 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559414 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559422 5 0.3452 1.000 0.000 0.000 0.244 0.000 0.756
#> GSM559424 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559431 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000
#> GSM559432 5 0.3452 1.000 0.000 0.000 0.244 0.000 0.756
#> GSM559381 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000
#> GSM559382 4 0.5148 0.787 0.100 0.084 0.000 0.752 0.064
#> GSM559384 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000
#> GSM559385 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000
#> GSM559386 4 0.2669 0.826 0.104 0.000 0.000 0.876 0.020
#> GSM559388 4 0.6123 0.717 0.100 0.156 0.000 0.668 0.076
#> GSM559389 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000
#> GSM559390 4 0.0000 0.832 0.000 0.000 0.000 1.000 0.000
#> GSM559392 2 0.1270 0.922 0.000 0.948 0.000 0.000 0.052
#> GSM559393 1 0.0609 0.931 0.980 0.000 0.000 0.000 0.020
#> GSM559394 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000
#> GSM559396 1 0.0162 0.940 0.996 0.000 0.000 0.000 0.004
#> GSM559398 2 0.0162 0.941 0.000 0.996 0.000 0.000 0.004
#> GSM559399 1 0.0162 0.940 0.996 0.000 0.000 0.004 0.000
#> GSM559400 4 0.2707 0.827 0.100 0.000 0.000 0.876 0.024
#> GSM559402 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000
#> GSM559403 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000
#> GSM559404 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000
#> GSM559405 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000
#> GSM559406 4 0.0162 0.831 0.004 0.000 0.000 0.996 0.000
#> GSM559407 1 0.1043 0.925 0.960 0.000 0.000 0.040 0.000
#> GSM559408 1 0.2280 0.882 0.880 0.000 0.000 0.120 0.000
#> GSM559409 1 0.2329 0.880 0.876 0.000 0.000 0.124 0.000
#> GSM559410 1 0.2020 0.893 0.900 0.000 0.000 0.100 0.000
#> GSM559411 1 0.2020 0.893 0.900 0.000 0.000 0.100 0.000
#> GSM559412 1 0.2280 0.882 0.880 0.000 0.000 0.120 0.000
#> GSM559413 1 0.2280 0.882 0.880 0.000 0.000 0.120 0.000
#> GSM559415 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000
#> GSM559416 4 0.0000 0.832 0.000 0.000 0.000 1.000 0.000
#> GSM559417 4 0.0000 0.832 0.000 0.000 0.000 1.000 0.000
#> GSM559418 1 0.0162 0.940 0.996 0.000 0.000 0.004 0.000
#> GSM559419 1 0.4278 0.240 0.548 0.000 0.000 0.452 0.000
#> GSM559420 1 0.0162 0.940 0.996 0.000 0.000 0.004 0.000
#> GSM559421 2 0.1270 0.922 0.000 0.948 0.000 0.000 0.052
#> GSM559423 2 0.1851 0.910 0.000 0.912 0.000 0.000 0.088
#> GSM559425 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000
#> GSM559426 2 0.2690 0.855 0.000 0.844 0.000 0.000 0.156
#> GSM559427 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000
#> GSM559428 4 0.5525 0.702 0.124 0.000 0.000 0.636 0.240
#> GSM559429 2 0.3039 0.829 0.000 0.808 0.000 0.000 0.192
#> GSM559430 2 0.0000 0.942 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
#> GSM559383 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559387 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559391 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559395 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559397 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559401 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559414 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559422 5 0.1610 1.0000 0.000 0.000 0.084 0.000 0.916 0.000
#> GSM559424 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559431 2 0.0547 0.8849 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM559432 5 0.1610 1.0000 0.000 0.000 0.084 0.000 0.916 0.000
#> GSM559381 1 0.0000 0.8950 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559382 4 0.5855 0.2364 0.072 0.080 0.000 0.616 0.004 0.228
#> GSM559384 1 0.0000 0.8950 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559385 1 0.0000 0.8950 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559386 4 0.3315 0.5821 0.076 0.000 0.000 0.820 0.000 0.104
#> GSM559388 6 0.6823 0.0976 0.064 0.156 0.000 0.384 0.004 0.392
#> GSM559389 1 0.0000 0.8950 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559390 4 0.0000 0.7120 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM559392 2 0.2964 0.7827 0.000 0.792 0.000 0.000 0.004 0.204
#> GSM559393 1 0.2631 0.7720 0.820 0.000 0.000 0.000 0.000 0.180
#> GSM559394 1 0.0000 0.8950 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559396 1 0.2389 0.8608 0.888 0.000 0.000 0.052 0.060 0.000
#> GSM559398 2 0.1411 0.8677 0.000 0.936 0.000 0.000 0.004 0.060
#> GSM559399 1 0.1957 0.8479 0.888 0.000 0.000 0.112 0.000 0.000
#> GSM559400 4 0.4176 0.4789 0.064 0.000 0.000 0.716 0.000 0.220
#> GSM559402 1 0.0937 0.8854 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM559403 1 0.0000 0.8950 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559404 1 0.0000 0.8950 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559405 1 0.0000 0.8950 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559406 4 0.1957 0.5864 0.112 0.000 0.000 0.888 0.000 0.000
#> GSM559407 1 0.0713 0.8901 0.972 0.000 0.000 0.028 0.000 0.000
#> GSM559408 1 0.2562 0.8207 0.828 0.000 0.000 0.172 0.000 0.000
#> GSM559409 1 0.2793 0.8113 0.800 0.000 0.000 0.200 0.000 0.000
#> GSM559410 1 0.2048 0.8531 0.880 0.000 0.000 0.120 0.000 0.000
#> GSM559411 1 0.2997 0.8489 0.844 0.000 0.000 0.096 0.060 0.000
#> GSM559412 1 0.2562 0.8207 0.828 0.000 0.000 0.172 0.000 0.000
#> GSM559413 1 0.3763 0.7865 0.768 0.000 0.000 0.172 0.060 0.000
#> GSM559415 1 0.0146 0.8944 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM559416 4 0.0000 0.7120 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM559417 4 0.0146 0.7105 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM559418 1 0.1957 0.8479 0.888 0.000 0.000 0.112 0.000 0.000
#> GSM559419 1 0.4471 0.2798 0.500 0.000 0.000 0.472 0.028 0.000
#> GSM559420 1 0.1957 0.8479 0.888 0.000 0.000 0.112 0.000 0.000
#> GSM559421 2 0.2738 0.8042 0.000 0.820 0.000 0.000 0.004 0.176
#> GSM559423 2 0.2838 0.8176 0.000 0.808 0.000 0.000 0.004 0.188
#> GSM559425 2 0.0547 0.8849 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM559426 2 0.2454 0.7685 0.000 0.840 0.000 0.000 0.000 0.160
#> GSM559427 2 0.0547 0.8849 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM559428 6 0.4972 0.2069 0.080 0.000 0.000 0.352 0.000 0.568
#> GSM559429 6 0.2823 0.1437 0.000 0.204 0.000 0.000 0.000 0.796
#> GSM559430 2 0.0000 0.8844 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:pam 52 1.99e-10 2
#> SD:pam 51 1.24e-10 3
#> SD:pam 51 6.63e-10 4
#> SD:pam 51 2.87e-09 5
#> SD:pam 46 2.54e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.981 0.987 0.3279 0.683 0.683
#> 3 3 0.687 0.819 0.911 0.8960 0.704 0.567
#> 4 4 0.703 0.562 0.820 0.1283 0.873 0.695
#> 5 5 0.707 0.772 0.808 0.0624 0.910 0.715
#> 6 6 0.715 0.707 0.818 0.0400 0.955 0.820
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 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
#> GSM559383 2 0.0000 1.000 0.000 1.000
#> GSM559387 2 0.0000 1.000 0.000 1.000
#> GSM559391 2 0.0000 1.000 0.000 1.000
#> GSM559395 2 0.0000 1.000 0.000 1.000
#> GSM559397 2 0.0000 1.000 0.000 1.000
#> GSM559401 2 0.0000 1.000 0.000 1.000
#> GSM559414 2 0.0000 1.000 0.000 1.000
#> GSM559422 2 0.0000 1.000 0.000 1.000
#> GSM559424 2 0.0000 1.000 0.000 1.000
#> GSM559431 1 0.4815 0.908 0.896 0.104
#> GSM559432 2 0.0000 1.000 0.000 1.000
#> GSM559381 1 0.0000 0.984 1.000 0.000
#> GSM559382 1 0.1843 0.976 0.972 0.028
#> GSM559384 1 0.0000 0.984 1.000 0.000
#> GSM559385 1 0.0000 0.984 1.000 0.000
#> GSM559386 1 0.1184 0.980 0.984 0.016
#> GSM559388 1 0.1843 0.976 0.972 0.028
#> GSM559389 1 0.0000 0.984 1.000 0.000
#> GSM559390 1 0.0000 0.984 1.000 0.000
#> GSM559392 1 0.1843 0.976 0.972 0.028
#> GSM559393 1 0.0000 0.984 1.000 0.000
#> GSM559394 1 0.0000 0.984 1.000 0.000
#> GSM559396 1 0.2236 0.970 0.964 0.036
#> GSM559398 1 0.1843 0.976 0.972 0.028
#> GSM559399 1 0.0000 0.984 1.000 0.000
#> GSM559400 1 0.1843 0.976 0.972 0.028
#> GSM559402 1 0.0000 0.984 1.000 0.000
#> GSM559403 1 0.0000 0.984 1.000 0.000
#> GSM559404 1 0.0000 0.984 1.000 0.000
#> GSM559405 1 0.0000 0.984 1.000 0.000
#> GSM559406 1 0.0000 0.984 1.000 0.000
#> GSM559407 1 0.0000 0.984 1.000 0.000
#> GSM559408 1 0.0000 0.984 1.000 0.000
#> GSM559409 1 0.0000 0.984 1.000 0.000
#> GSM559410 1 0.0000 0.984 1.000 0.000
#> GSM559411 1 0.0000 0.984 1.000 0.000
#> GSM559412 1 0.0000 0.984 1.000 0.000
#> GSM559413 1 0.0000 0.984 1.000 0.000
#> GSM559415 1 0.0000 0.984 1.000 0.000
#> GSM559416 1 0.0000 0.984 1.000 0.000
#> GSM559417 1 0.0000 0.984 1.000 0.000
#> GSM559418 1 0.0672 0.982 0.992 0.008
#> GSM559419 1 0.0000 0.984 1.000 0.000
#> GSM559420 1 0.0000 0.984 1.000 0.000
#> GSM559421 1 0.1843 0.976 0.972 0.028
#> GSM559423 1 0.1843 0.976 0.972 0.028
#> GSM559425 1 0.1843 0.976 0.972 0.028
#> GSM559426 1 0.1843 0.976 0.972 0.028
#> GSM559427 1 0.1843 0.976 0.972 0.028
#> GSM559428 1 0.4815 0.908 0.896 0.104
#> GSM559429 1 0.4815 0.908 0.896 0.104
#> GSM559430 1 0.1843 0.976 0.972 0.028
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.0000 0.994 0.000 0.000 1.000
#> GSM559387 3 0.0000 0.994 0.000 0.000 1.000
#> GSM559391 3 0.0000 0.994 0.000 0.000 1.000
#> GSM559395 3 0.0000 0.994 0.000 0.000 1.000
#> GSM559397 3 0.0000 0.994 0.000 0.000 1.000
#> GSM559401 3 0.0000 0.994 0.000 0.000 1.000
#> GSM559414 3 0.0000 0.994 0.000 0.000 1.000
#> GSM559422 3 0.0000 0.994 0.000 0.000 1.000
#> GSM559424 3 0.0000 0.994 0.000 0.000 1.000
#> GSM559431 2 0.0000 0.910 0.000 1.000 0.000
#> GSM559432 3 0.1860 0.944 0.000 0.052 0.948
#> GSM559381 1 0.1529 0.849 0.960 0.040 0.000
#> GSM559382 2 0.0424 0.905 0.008 0.992 0.000
#> GSM559384 1 0.2537 0.843 0.920 0.080 0.000
#> GSM559385 1 0.5016 0.622 0.760 0.240 0.000
#> GSM559386 2 0.6154 0.200 0.408 0.592 0.000
#> GSM559388 2 0.0000 0.910 0.000 1.000 0.000
#> GSM559389 1 0.0000 0.843 1.000 0.000 0.000
#> GSM559390 1 0.4842 0.750 0.776 0.224 0.000
#> GSM559392 2 0.0000 0.910 0.000 1.000 0.000
#> GSM559393 1 0.5016 0.622 0.760 0.240 0.000
#> GSM559394 1 0.5016 0.622 0.760 0.240 0.000
#> GSM559396 1 0.6180 0.589 0.660 0.332 0.008
#> GSM559398 2 0.0000 0.910 0.000 1.000 0.000
#> GSM559399 1 0.2261 0.846 0.932 0.068 0.000
#> GSM559400 1 0.6280 0.266 0.540 0.460 0.000
#> GSM559402 1 0.0237 0.845 0.996 0.004 0.000
#> GSM559403 1 0.0000 0.843 1.000 0.000 0.000
#> GSM559404 1 0.2261 0.829 0.932 0.068 0.000
#> GSM559405 1 0.0000 0.843 1.000 0.000 0.000
#> GSM559406 1 0.4842 0.750 0.776 0.224 0.000
#> GSM559407 1 0.0237 0.845 0.996 0.004 0.000
#> GSM559408 1 0.0592 0.846 0.988 0.012 0.000
#> GSM559409 1 0.1643 0.850 0.956 0.044 0.000
#> GSM559410 1 0.0000 0.843 1.000 0.000 0.000
#> GSM559411 1 0.4842 0.750 0.776 0.224 0.000
#> GSM559412 1 0.3116 0.833 0.892 0.108 0.000
#> GSM559413 1 0.4842 0.750 0.776 0.224 0.000
#> GSM559415 1 0.0000 0.843 1.000 0.000 0.000
#> GSM559416 1 0.0747 0.847 0.984 0.016 0.000
#> GSM559417 1 0.2796 0.840 0.908 0.092 0.000
#> GSM559418 1 0.6180 0.376 0.584 0.416 0.000
#> GSM559419 1 0.2261 0.847 0.932 0.068 0.000
#> GSM559420 1 0.4452 0.778 0.808 0.192 0.000
#> GSM559421 2 0.0000 0.910 0.000 1.000 0.000
#> GSM559423 2 0.0000 0.910 0.000 1.000 0.000
#> GSM559425 2 0.0000 0.910 0.000 1.000 0.000
#> GSM559426 2 0.0000 0.910 0.000 1.000 0.000
#> GSM559427 2 0.0000 0.910 0.000 1.000 0.000
#> GSM559428 2 0.5016 0.626 0.240 0.760 0.000
#> GSM559429 2 0.5016 0.626 0.240 0.760 0.000
#> GSM559430 2 0.0000 0.910 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.0000 0.9252 0.000 0.000 1.000 0.000
#> GSM559387 3 0.0000 0.9252 0.000 0.000 1.000 0.000
#> GSM559391 3 0.0000 0.9252 0.000 0.000 1.000 0.000
#> GSM559395 3 0.0000 0.9252 0.000 0.000 1.000 0.000
#> GSM559397 3 0.0000 0.9252 0.000 0.000 1.000 0.000
#> GSM559401 3 0.3610 0.8603 0.000 0.000 0.800 0.200
#> GSM559414 3 0.0000 0.9252 0.000 0.000 1.000 0.000
#> GSM559422 3 0.4454 0.8099 0.000 0.000 0.692 0.308
#> GSM559424 3 0.2053 0.8779 0.072 0.000 0.924 0.004
#> GSM559431 2 0.0188 0.9558 0.004 0.996 0.000 0.000
#> GSM559432 3 0.4855 0.7529 0.000 0.000 0.600 0.400
#> GSM559381 1 0.4981 -0.1815 0.536 0.000 0.000 0.464
#> GSM559382 2 0.0817 0.9444 0.024 0.976 0.000 0.000
#> GSM559384 1 0.4866 0.0398 0.596 0.000 0.000 0.404
#> GSM559385 4 0.4477 0.9014 0.312 0.000 0.000 0.688
#> GSM559386 1 0.7654 -0.2054 0.464 0.252 0.000 0.284
#> GSM559388 2 0.0188 0.9553 0.000 0.996 0.000 0.004
#> GSM559389 1 0.4992 -0.2295 0.524 0.000 0.000 0.476
#> GSM559390 1 0.1305 0.4545 0.960 0.036 0.000 0.004
#> GSM559392 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM559393 4 0.4477 0.9014 0.312 0.000 0.000 0.688
#> GSM559394 4 0.4477 0.9014 0.312 0.000 0.000 0.688
#> GSM559396 1 0.3765 0.2958 0.812 0.180 0.004 0.004
#> GSM559398 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM559399 1 0.4624 0.1768 0.660 0.000 0.000 0.340
#> GSM559400 2 0.5088 0.4712 0.424 0.572 0.000 0.004
#> GSM559402 1 0.4624 0.1783 0.660 0.000 0.000 0.340
#> GSM559403 1 0.5000 -0.3227 0.504 0.000 0.000 0.496
#> GSM559404 4 0.4877 0.6389 0.408 0.000 0.000 0.592
#> GSM559405 1 0.4992 -0.2295 0.524 0.000 0.000 0.476
#> GSM559406 1 0.1305 0.4545 0.960 0.036 0.000 0.004
#> GSM559407 1 0.4564 0.2043 0.672 0.000 0.000 0.328
#> GSM559408 1 0.2704 0.4453 0.876 0.000 0.000 0.124
#> GSM559409 1 0.3764 0.3834 0.784 0.000 0.000 0.216
#> GSM559410 1 0.4661 0.1535 0.652 0.000 0.000 0.348
#> GSM559411 1 0.1305 0.4567 0.960 0.036 0.000 0.004
#> GSM559412 1 0.1211 0.4682 0.960 0.000 0.000 0.040
#> GSM559413 1 0.0469 0.4634 0.988 0.000 0.000 0.012
#> GSM559415 1 0.4981 -0.2024 0.536 0.000 0.000 0.464
#> GSM559416 1 0.3243 0.4390 0.876 0.036 0.000 0.088
#> GSM559417 1 0.3243 0.4390 0.876 0.036 0.000 0.088
#> GSM559418 1 0.6709 -0.2617 0.508 0.092 0.000 0.400
#> GSM559419 1 0.3731 0.4387 0.844 0.036 0.000 0.120
#> GSM559420 1 0.4546 0.3284 0.732 0.012 0.000 0.256
#> GSM559421 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM559423 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM559425 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM559426 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM559427 2 0.0000 0.9573 0.000 1.000 0.000 0.000
#> GSM559428 2 0.1792 0.9075 0.068 0.932 0.000 0.000
#> GSM559429 2 0.0469 0.9522 0.012 0.988 0.000 0.000
#> GSM559430 2 0.0000 0.9573 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
#> GSM559383 3 0.0000 0.880 0.000 0.000 1.000 0.000 0.000
#> GSM559387 3 0.0000 0.880 0.000 0.000 1.000 0.000 0.000
#> GSM559391 3 0.0404 0.877 0.000 0.000 0.988 0.012 0.000
#> GSM559395 3 0.0000 0.880 0.000 0.000 1.000 0.000 0.000
#> GSM559397 3 0.0000 0.880 0.000 0.000 1.000 0.000 0.000
#> GSM559401 3 0.5484 0.716 0.000 0.000 0.640 0.240 0.120
#> GSM559414 3 0.0000 0.880 0.000 0.000 1.000 0.000 0.000
#> GSM559422 3 0.5888 0.678 0.000 0.000 0.576 0.288 0.136
#> GSM559424 3 0.1043 0.865 0.000 0.000 0.960 0.040 0.000
#> GSM559431 2 0.1671 0.882 0.000 0.924 0.000 0.000 0.076
#> GSM559432 3 0.6309 0.628 0.000 0.000 0.520 0.288 0.192
#> GSM559381 1 0.0324 0.815 0.992 0.004 0.000 0.000 0.004
#> GSM559382 2 0.3130 0.785 0.096 0.856 0.000 0.048 0.000
#> GSM559384 1 0.0566 0.812 0.984 0.000 0.000 0.012 0.004
#> GSM559385 5 0.4114 0.968 0.376 0.000 0.000 0.000 0.624
#> GSM559386 1 0.3132 0.587 0.820 0.172 0.000 0.000 0.008
#> GSM559388 2 0.0510 0.886 0.016 0.984 0.000 0.000 0.000
#> GSM559389 1 0.0451 0.811 0.988 0.004 0.000 0.000 0.008
#> GSM559390 4 0.5971 0.804 0.396 0.000 0.000 0.492 0.112
#> GSM559392 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM559393 5 0.4251 0.964 0.372 0.004 0.000 0.000 0.624
#> GSM559394 5 0.4114 0.968 0.376 0.000 0.000 0.000 0.624
#> GSM559396 4 0.5161 0.697 0.260 0.044 0.000 0.676 0.020
#> GSM559398 2 0.1410 0.884 0.000 0.940 0.000 0.000 0.060
#> GSM559399 1 0.0451 0.814 0.988 0.000 0.000 0.008 0.004
#> GSM559400 2 0.6230 0.328 0.008 0.480 0.000 0.400 0.112
#> GSM559402 1 0.1195 0.807 0.960 0.000 0.000 0.012 0.028
#> GSM559403 1 0.1792 0.720 0.916 0.000 0.000 0.000 0.084
#> GSM559404 5 0.4557 0.905 0.404 0.000 0.000 0.012 0.584
#> GSM559405 1 0.0162 0.813 0.996 0.000 0.000 0.000 0.004
#> GSM559406 4 0.4138 0.812 0.384 0.000 0.000 0.616 0.000
#> GSM559407 1 0.1195 0.807 0.960 0.000 0.000 0.012 0.028
#> GSM559408 1 0.3695 0.597 0.800 0.000 0.000 0.164 0.036
#> GSM559409 1 0.3772 0.597 0.792 0.000 0.000 0.172 0.036
#> GSM559410 1 0.0451 0.814 0.988 0.000 0.000 0.008 0.004
#> GSM559411 4 0.4242 0.796 0.428 0.000 0.000 0.572 0.000
#> GSM559412 1 0.3724 0.535 0.776 0.000 0.000 0.204 0.020
#> GSM559413 1 0.4390 -0.457 0.568 0.000 0.000 0.428 0.004
#> GSM559415 1 0.0486 0.814 0.988 0.004 0.000 0.004 0.004
#> GSM559416 4 0.5338 0.839 0.400 0.000 0.000 0.544 0.056
#> GSM559417 4 0.5345 0.839 0.404 0.000 0.000 0.540 0.056
#> GSM559418 1 0.0992 0.799 0.968 0.024 0.000 0.000 0.008
#> GSM559419 4 0.5106 0.729 0.456 0.000 0.000 0.508 0.036
#> GSM559420 1 0.3922 0.569 0.780 0.000 0.000 0.180 0.040
#> GSM559421 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM559423 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000
#> GSM559425 2 0.1410 0.884 0.000 0.940 0.000 0.000 0.060
#> GSM559426 2 0.0162 0.889 0.004 0.996 0.000 0.000 0.000
#> GSM559427 2 0.1410 0.884 0.000 0.940 0.000 0.000 0.060
#> GSM559428 2 0.4735 0.639 0.012 0.668 0.000 0.300 0.020
#> GSM559429 2 0.3357 0.811 0.012 0.836 0.000 0.136 0.016
#> GSM559430 2 0.1270 0.886 0.000 0.948 0.000 0.000 0.052
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559383 3 0.0547 0.836783 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM559387 3 0.0000 0.843048 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559391 3 0.3023 0.748649 0.000 0.000 0.828 0.140 0.032 0.000
#> GSM559395 3 0.0363 0.836157 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM559397 3 0.0000 0.843048 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559401 3 0.3797 -0.222702 0.000 0.000 0.580 0.000 0.420 0.000
#> GSM559414 3 0.0000 0.843048 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559422 5 0.3288 1.000000 0.000 0.000 0.276 0.000 0.724 0.000
#> GSM559424 3 0.3023 0.748649 0.000 0.000 0.828 0.140 0.032 0.000
#> GSM559431 2 0.4462 0.797170 0.000 0.712 0.000 0.152 0.136 0.000
#> GSM559432 5 0.3288 1.000000 0.000 0.000 0.276 0.000 0.724 0.000
#> GSM559381 1 0.0000 0.742473 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559382 2 0.1082 0.868721 0.000 0.956 0.000 0.040 0.000 0.004
#> GSM559384 1 0.1644 0.736078 0.932 0.000 0.000 0.000 0.040 0.028
#> GSM559385 6 0.2491 0.984436 0.164 0.000 0.000 0.000 0.000 0.836
#> GSM559386 1 0.2320 0.622842 0.864 0.132 0.000 0.000 0.000 0.004
#> GSM559388 2 0.0000 0.878280 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559389 1 0.0363 0.742446 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM559390 4 0.5510 0.732402 0.292 0.000 0.000 0.584 0.020 0.104
#> GSM559392 2 0.0000 0.878280 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559393 6 0.2664 0.975428 0.184 0.000 0.000 0.000 0.000 0.816
#> GSM559394 6 0.2562 0.985542 0.172 0.000 0.000 0.000 0.000 0.828
#> GSM559396 4 0.3699 0.624829 0.160 0.000 0.000 0.788 0.040 0.012
#> GSM559398 2 0.2300 0.851415 0.000 0.856 0.000 0.144 0.000 0.000
#> GSM559399 1 0.0260 0.742631 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM559400 2 0.5990 0.463123 0.000 0.576 0.000 0.252 0.052 0.120
#> GSM559402 1 0.0551 0.741108 0.984 0.000 0.000 0.004 0.004 0.008
#> GSM559403 1 0.2416 0.610173 0.844 0.000 0.000 0.000 0.000 0.156
#> GSM559404 6 0.2527 0.983803 0.168 0.000 0.000 0.000 0.000 0.832
#> GSM559405 1 0.0547 0.741421 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM559406 1 0.4468 0.000782 0.560 0.000 0.000 0.408 0.032 0.000
#> GSM559407 1 0.1622 0.727065 0.940 0.000 0.000 0.028 0.016 0.016
#> GSM559408 1 0.5073 0.502179 0.692 0.000 0.000 0.180 0.084 0.044
#> GSM559409 1 0.4915 0.530966 0.712 0.000 0.000 0.160 0.084 0.044
#> GSM559410 1 0.0632 0.740726 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM559411 4 0.4532 0.270860 0.468 0.000 0.000 0.500 0.032 0.000
#> GSM559412 1 0.5330 0.414606 0.648 0.000 0.000 0.228 0.084 0.040
#> GSM559413 1 0.4709 0.178045 0.596 0.000 0.000 0.352 0.048 0.004
#> GSM559415 1 0.0632 0.740726 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM559416 4 0.4096 0.751258 0.304 0.000 0.000 0.672 0.008 0.016
#> GSM559417 4 0.4717 0.759303 0.308 0.000 0.000 0.632 0.008 0.052
#> GSM559418 1 0.0993 0.735942 0.964 0.012 0.000 0.000 0.000 0.024
#> GSM559419 1 0.5535 -0.158291 0.516 0.000 0.000 0.392 0.048 0.044
#> GSM559420 1 0.4739 0.553571 0.732 0.000 0.000 0.140 0.084 0.044
#> GSM559421 2 0.0000 0.878280 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559423 2 0.0000 0.878280 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559425 2 0.2553 0.848100 0.000 0.848 0.000 0.144 0.008 0.000
#> GSM559426 2 0.0820 0.871008 0.016 0.972 0.000 0.000 0.000 0.012
#> GSM559427 2 0.2553 0.848100 0.000 0.848 0.000 0.144 0.008 0.000
#> GSM559428 2 0.2890 0.822456 0.004 0.844 0.000 0.024 0.128 0.000
#> GSM559429 2 0.2667 0.826717 0.000 0.852 0.000 0.020 0.128 0.000
#> GSM559430 2 0.2300 0.851415 0.000 0.856 0.000 0.144 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:mclust 52 1.99e-10 2
#> SD:mclust 49 3.24e-10 3
#> SD:mclust 27 9.27e-06 4
#> SD:mclust 50 4.77e-09 5
#> SD:mclust 45 1.75e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.422 0.782 0.858 0.4516 0.527 0.527
#> 3 3 0.998 0.948 0.978 0.3760 0.687 0.490
#> 4 4 0.730 0.769 0.885 0.1802 0.855 0.638
#> 5 5 0.700 0.638 0.793 0.0693 0.922 0.729
#> 6 6 0.716 0.631 0.786 0.0509 0.847 0.451
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
#> GSM559383 1 0.000 0.752 1.000 0.000
#> GSM559387 1 0.000 0.752 1.000 0.000
#> GSM559391 1 0.000 0.752 1.000 0.000
#> GSM559395 1 0.000 0.752 1.000 0.000
#> GSM559397 1 0.000 0.752 1.000 0.000
#> GSM559401 1 0.000 0.752 1.000 0.000
#> GSM559414 1 0.000 0.752 1.000 0.000
#> GSM559422 1 0.000 0.752 1.000 0.000
#> GSM559424 1 0.000 0.752 1.000 0.000
#> GSM559431 2 0.327 0.883 0.060 0.940
#> GSM559432 1 0.999 -0.205 0.516 0.484
#> GSM559381 1 0.999 0.459 0.516 0.484
#> GSM559382 2 0.000 0.947 0.000 1.000
#> GSM559384 1 0.738 0.832 0.792 0.208
#> GSM559385 1 0.760 0.828 0.780 0.220
#> GSM559386 2 0.000 0.947 0.000 1.000
#> GSM559388 2 0.000 0.947 0.000 1.000
#> GSM559389 1 0.981 0.602 0.580 0.420
#> GSM559390 1 0.808 0.813 0.752 0.248
#> GSM559392 2 0.000 0.947 0.000 1.000
#> GSM559393 2 0.118 0.931 0.016 0.984
#> GSM559394 1 0.971 0.637 0.600 0.400
#> GSM559396 1 0.697 0.829 0.812 0.188
#> GSM559398 2 0.000 0.947 0.000 1.000
#> GSM559399 1 0.997 0.500 0.532 0.468
#> GSM559400 2 0.000 0.947 0.000 1.000
#> GSM559402 1 0.909 0.747 0.676 0.324
#> GSM559403 1 0.855 0.790 0.720 0.280
#> GSM559404 1 0.697 0.829 0.812 0.188
#> GSM559405 1 0.760 0.828 0.780 0.220
#> GSM559406 1 0.730 0.831 0.796 0.204
#> GSM559407 1 0.753 0.830 0.784 0.216
#> GSM559408 1 0.738 0.832 0.792 0.208
#> GSM559409 1 0.738 0.832 0.792 0.208
#> GSM559410 1 0.876 0.776 0.704 0.296
#> GSM559411 1 0.738 0.832 0.792 0.208
#> GSM559412 1 0.738 0.832 0.792 0.208
#> GSM559413 1 0.730 0.831 0.796 0.204
#> GSM559415 2 0.992 -0.305 0.448 0.552
#> GSM559416 1 0.921 0.737 0.664 0.336
#> GSM559417 2 0.402 0.847 0.080 0.920
#> GSM559418 2 0.000 0.947 0.000 1.000
#> GSM559419 1 0.861 0.788 0.716 0.284
#> GSM559420 1 0.745 0.831 0.788 0.212
#> GSM559421 2 0.000 0.947 0.000 1.000
#> GSM559423 2 0.000 0.947 0.000 1.000
#> GSM559425 2 0.000 0.947 0.000 1.000
#> GSM559426 2 0.000 0.947 0.000 1.000
#> GSM559427 2 0.000 0.947 0.000 1.000
#> GSM559428 2 0.388 0.863 0.076 0.924
#> GSM559429 2 0.000 0.947 0.000 1.000
#> GSM559430 2 0.000 0.947 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.000 1.000 0.000 0.000 1.000
#> GSM559387 3 0.000 1.000 0.000 0.000 1.000
#> GSM559391 3 0.000 1.000 0.000 0.000 1.000
#> GSM559395 3 0.000 1.000 0.000 0.000 1.000
#> GSM559397 3 0.000 1.000 0.000 0.000 1.000
#> GSM559401 3 0.000 1.000 0.000 0.000 1.000
#> GSM559414 3 0.000 1.000 0.000 0.000 1.000
#> GSM559422 3 0.000 1.000 0.000 0.000 1.000
#> GSM559424 3 0.000 1.000 0.000 0.000 1.000
#> GSM559431 2 0.000 0.991 0.000 1.000 0.000
#> GSM559432 3 0.000 1.000 0.000 0.000 1.000
#> GSM559381 1 0.000 0.961 1.000 0.000 0.000
#> GSM559382 2 0.000 0.991 0.000 1.000 0.000
#> GSM559384 1 0.000 0.961 1.000 0.000 0.000
#> GSM559385 1 0.000 0.961 1.000 0.000 0.000
#> GSM559386 1 0.522 0.664 0.740 0.260 0.000
#> GSM559388 2 0.000 0.991 0.000 1.000 0.000
#> GSM559389 1 0.000 0.961 1.000 0.000 0.000
#> GSM559390 1 0.000 0.961 1.000 0.000 0.000
#> GSM559392 2 0.000 0.991 0.000 1.000 0.000
#> GSM559393 1 0.382 0.821 0.852 0.148 0.000
#> GSM559394 1 0.000 0.961 1.000 0.000 0.000
#> GSM559396 1 0.288 0.875 0.904 0.000 0.096
#> GSM559398 2 0.000 0.991 0.000 1.000 0.000
#> GSM559399 1 0.000 0.961 1.000 0.000 0.000
#> GSM559400 2 0.210 0.927 0.052 0.944 0.004
#> GSM559402 1 0.000 0.961 1.000 0.000 0.000
#> GSM559403 1 0.000 0.961 1.000 0.000 0.000
#> GSM559404 1 0.000 0.961 1.000 0.000 0.000
#> GSM559405 1 0.000 0.961 1.000 0.000 0.000
#> GSM559406 1 0.000 0.961 1.000 0.000 0.000
#> GSM559407 1 0.000 0.961 1.000 0.000 0.000
#> GSM559408 1 0.000 0.961 1.000 0.000 0.000
#> GSM559409 1 0.000 0.961 1.000 0.000 0.000
#> GSM559410 1 0.000 0.961 1.000 0.000 0.000
#> GSM559411 1 0.000 0.961 1.000 0.000 0.000
#> GSM559412 1 0.000 0.961 1.000 0.000 0.000
#> GSM559413 1 0.000 0.961 1.000 0.000 0.000
#> GSM559415 1 0.000 0.961 1.000 0.000 0.000
#> GSM559416 1 0.000 0.961 1.000 0.000 0.000
#> GSM559417 1 0.153 0.929 0.960 0.040 0.000
#> GSM559418 1 0.630 0.154 0.528 0.472 0.000
#> GSM559419 1 0.000 0.961 1.000 0.000 0.000
#> GSM559420 1 0.000 0.961 1.000 0.000 0.000
#> GSM559421 2 0.000 0.991 0.000 1.000 0.000
#> GSM559423 2 0.000 0.991 0.000 1.000 0.000
#> GSM559425 2 0.000 0.991 0.000 1.000 0.000
#> GSM559426 2 0.000 0.991 0.000 1.000 0.000
#> GSM559427 2 0.000 0.991 0.000 1.000 0.000
#> GSM559428 2 0.175 0.947 0.000 0.952 0.048
#> GSM559429 2 0.000 0.991 0.000 1.000 0.000
#> GSM559430 2 0.000 0.991 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.4730 0.4682 0.000 0.000 0.636 0.364
#> GSM559387 3 0.1792 0.9102 0.000 0.000 0.932 0.068
#> GSM559391 4 0.4713 0.2554 0.000 0.000 0.360 0.640
#> GSM559395 3 0.1302 0.9196 0.000 0.000 0.956 0.044
#> GSM559397 3 0.1557 0.9163 0.000 0.000 0.944 0.056
#> GSM559401 3 0.0000 0.9131 0.000 0.000 1.000 0.000
#> GSM559414 3 0.1302 0.9197 0.000 0.000 0.956 0.044
#> GSM559422 3 0.0592 0.9061 0.000 0.000 0.984 0.016
#> GSM559424 4 0.4304 0.4330 0.000 0.000 0.284 0.716
#> GSM559431 2 0.0817 0.9365 0.000 0.976 0.000 0.024
#> GSM559432 3 0.0336 0.9103 0.000 0.000 0.992 0.008
#> GSM559381 1 0.0336 0.8559 0.992 0.000 0.000 0.008
#> GSM559382 2 0.2342 0.8916 0.008 0.912 0.000 0.080
#> GSM559384 1 0.1940 0.8240 0.924 0.000 0.000 0.076
#> GSM559385 1 0.0469 0.8554 0.988 0.000 0.000 0.012
#> GSM559386 1 0.5894 0.3452 0.568 0.392 0.000 0.040
#> GSM559388 2 0.1151 0.9298 0.008 0.968 0.000 0.024
#> GSM559389 1 0.0336 0.8549 0.992 0.000 0.000 0.008
#> GSM559390 4 0.2466 0.7734 0.096 0.000 0.004 0.900
#> GSM559392 2 0.0707 0.9338 0.000 0.980 0.000 0.020
#> GSM559393 1 0.2845 0.7992 0.896 0.076 0.000 0.028
#> GSM559394 1 0.0895 0.8504 0.976 0.004 0.000 0.020
#> GSM559396 4 0.3820 0.6937 0.100 0.016 0.028 0.856
#> GSM559398 2 0.0707 0.9338 0.000 0.980 0.000 0.020
#> GSM559399 1 0.0188 0.8571 0.996 0.000 0.000 0.004
#> GSM559400 2 0.5214 0.4514 0.008 0.624 0.004 0.364
#> GSM559402 1 0.1474 0.8446 0.948 0.000 0.000 0.052
#> GSM559403 1 0.0188 0.8571 0.996 0.000 0.000 0.004
#> GSM559404 1 0.0188 0.8571 0.996 0.000 0.000 0.004
#> GSM559405 1 0.0188 0.8571 0.996 0.000 0.000 0.004
#> GSM559406 4 0.3311 0.7515 0.172 0.000 0.000 0.828
#> GSM559407 1 0.2469 0.8008 0.892 0.000 0.000 0.108
#> GSM559408 1 0.4406 0.5468 0.700 0.000 0.000 0.300
#> GSM559409 1 0.2760 0.7828 0.872 0.000 0.000 0.128
#> GSM559410 1 0.0188 0.8571 0.996 0.000 0.000 0.004
#> GSM559411 4 0.2530 0.7763 0.112 0.000 0.000 0.888
#> GSM559412 1 0.4804 0.3479 0.616 0.000 0.000 0.384
#> GSM559413 4 0.4977 0.1198 0.460 0.000 0.000 0.540
#> GSM559415 1 0.0336 0.8549 0.992 0.000 0.000 0.008
#> GSM559416 4 0.2741 0.7742 0.096 0.012 0.000 0.892
#> GSM559417 4 0.5417 0.6582 0.088 0.180 0.000 0.732
#> GSM559418 1 0.3695 0.7314 0.828 0.156 0.000 0.016
#> GSM559419 4 0.3123 0.7642 0.156 0.000 0.000 0.844
#> GSM559420 1 0.4961 0.0751 0.552 0.000 0.000 0.448
#> GSM559421 2 0.1576 0.9240 0.004 0.948 0.000 0.048
#> GSM559423 2 0.1209 0.9341 0.004 0.964 0.000 0.032
#> GSM559425 2 0.0592 0.9373 0.000 0.984 0.000 0.016
#> GSM559426 2 0.1398 0.9318 0.004 0.956 0.000 0.040
#> GSM559427 2 0.0336 0.9357 0.000 0.992 0.000 0.008
#> GSM559428 2 0.3292 0.8785 0.004 0.880 0.080 0.036
#> GSM559429 2 0.1398 0.9318 0.004 0.956 0.000 0.040
#> GSM559430 2 0.0657 0.9375 0.004 0.984 0.000 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559383 5 0.5953 -0.18051 0.000 0.000 0.384 0.112 0.504
#> GSM559387 3 0.4617 0.52827 0.000 0.000 0.552 0.012 0.436
#> GSM559391 5 0.5756 0.55620 0.000 0.000 0.112 0.312 0.576
#> GSM559395 3 0.4582 0.56805 0.000 0.000 0.572 0.012 0.416
#> GSM559397 3 0.4425 0.59967 0.000 0.000 0.600 0.008 0.392
#> GSM559401 3 0.2074 0.59567 0.000 0.000 0.896 0.000 0.104
#> GSM559414 3 0.4436 0.59732 0.000 0.000 0.596 0.008 0.396
#> GSM559422 3 0.0000 0.55617 0.000 0.000 1.000 0.000 0.000
#> GSM559424 5 0.5498 0.55841 0.000 0.000 0.080 0.340 0.580
#> GSM559431 2 0.3845 0.78982 0.000 0.760 0.012 0.004 0.224
#> GSM559432 3 0.0162 0.55923 0.000 0.000 0.996 0.000 0.004
#> GSM559381 1 0.1469 0.79731 0.948 0.000 0.000 0.016 0.036
#> GSM559382 2 0.3852 0.60294 0.000 0.760 0.000 0.220 0.020
#> GSM559384 1 0.4206 0.63305 0.708 0.000 0.000 0.020 0.272
#> GSM559385 1 0.0000 0.80366 1.000 0.000 0.000 0.000 0.000
#> GSM559386 1 0.6105 0.25413 0.512 0.368 0.000 0.116 0.004
#> GSM559388 2 0.2824 0.75240 0.008 0.880 0.000 0.088 0.024
#> GSM559389 1 0.0451 0.80378 0.988 0.000 0.000 0.004 0.008
#> GSM559390 4 0.1179 0.73371 0.016 0.004 0.000 0.964 0.016
#> GSM559392 2 0.0898 0.80764 0.000 0.972 0.000 0.008 0.020
#> GSM559393 1 0.1130 0.79865 0.968 0.004 0.004 0.012 0.012
#> GSM559394 1 0.0404 0.80298 0.988 0.000 0.000 0.000 0.012
#> GSM559396 5 0.2775 0.33289 0.036 0.008 0.000 0.068 0.888
#> GSM559398 2 0.0992 0.80622 0.000 0.968 0.000 0.008 0.024
#> GSM559399 1 0.0566 0.80234 0.984 0.004 0.000 0.000 0.012
#> GSM559400 4 0.5319 0.40531 0.000 0.360 0.008 0.588 0.044
#> GSM559402 1 0.5074 0.61653 0.700 0.000 0.000 0.168 0.132
#> GSM559403 1 0.0000 0.80366 1.000 0.000 0.000 0.000 0.000
#> GSM559404 1 0.0880 0.79676 0.968 0.000 0.000 0.032 0.000
#> GSM559405 1 0.0162 0.80369 0.996 0.000 0.000 0.004 0.000
#> GSM559406 4 0.1484 0.74695 0.048 0.000 0.000 0.944 0.008
#> GSM559407 1 0.5309 0.47662 0.644 0.000 0.000 0.264 0.092
#> GSM559408 4 0.3561 0.63257 0.260 0.000 0.000 0.740 0.000
#> GSM559409 1 0.4440 0.00967 0.528 0.000 0.000 0.468 0.004
#> GSM559410 1 0.1282 0.79187 0.952 0.000 0.000 0.044 0.004
#> GSM559411 4 0.4029 0.52624 0.024 0.000 0.000 0.744 0.232
#> GSM559412 4 0.4575 0.66254 0.236 0.000 0.000 0.712 0.052
#> GSM559413 4 0.5137 0.65732 0.208 0.000 0.000 0.684 0.108
#> GSM559415 1 0.1041 0.80073 0.964 0.000 0.000 0.004 0.032
#> GSM559416 4 0.1095 0.73346 0.008 0.012 0.000 0.968 0.012
#> GSM559417 4 0.2959 0.70077 0.008 0.112 0.000 0.864 0.016
#> GSM559418 1 0.4914 0.44972 0.628 0.336 0.000 0.004 0.032
#> GSM559419 4 0.2153 0.73538 0.040 0.000 0.000 0.916 0.044
#> GSM559420 1 0.6674 0.19578 0.436 0.000 0.000 0.260 0.304
#> GSM559421 2 0.1106 0.81897 0.000 0.964 0.000 0.012 0.024
#> GSM559423 2 0.4152 0.76163 0.000 0.692 0.000 0.012 0.296
#> GSM559425 2 0.2377 0.81861 0.000 0.872 0.000 0.000 0.128
#> GSM559426 2 0.4108 0.75516 0.000 0.684 0.000 0.008 0.308
#> GSM559427 2 0.0566 0.81747 0.000 0.984 0.000 0.004 0.012
#> GSM559428 2 0.6359 0.62822 0.000 0.532 0.152 0.008 0.308
#> GSM559429 2 0.4165 0.74780 0.000 0.672 0.000 0.008 0.320
#> GSM559430 2 0.1732 0.82389 0.000 0.920 0.000 0.000 0.080
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559383 3 0.1082 0.8372 0.000 0.000 0.956 0.004 0.040 0.000
#> GSM559387 3 0.2260 0.8532 0.000 0.000 0.860 0.000 0.140 0.000
#> GSM559391 3 0.0935 0.7977 0.000 0.000 0.964 0.032 0.004 0.000
#> GSM559395 3 0.2340 0.8508 0.000 0.000 0.852 0.000 0.148 0.000
#> GSM559397 3 0.2762 0.8171 0.000 0.000 0.804 0.000 0.196 0.000
#> GSM559401 5 0.3175 0.7193 0.000 0.000 0.256 0.000 0.744 0.000
#> GSM559414 3 0.2854 0.8040 0.000 0.000 0.792 0.000 0.208 0.000
#> GSM559422 5 0.1714 0.8806 0.000 0.000 0.092 0.000 0.908 0.000
#> GSM559424 3 0.0935 0.7980 0.000 0.000 0.964 0.032 0.004 0.000
#> GSM559431 6 0.4853 0.1414 0.000 0.456 0.000 0.000 0.056 0.488
#> GSM559432 5 0.1765 0.8826 0.000 0.000 0.096 0.000 0.904 0.000
#> GSM559381 1 0.3698 0.7749 0.788 0.000 0.000 0.028 0.020 0.164
#> GSM559382 2 0.4768 0.5343 0.040 0.728 0.000 0.164 0.004 0.064
#> GSM559384 1 0.5691 0.5154 0.564 0.000 0.032 0.028 0.036 0.340
#> GSM559385 1 0.0862 0.8294 0.972 0.004 0.000 0.000 0.008 0.016
#> GSM559386 1 0.6542 0.2830 0.504 0.312 0.000 0.104 0.008 0.072
#> GSM559388 2 0.2699 0.6050 0.068 0.880 0.000 0.020 0.000 0.032
#> GSM559389 1 0.1667 0.8296 0.936 0.004 0.000 0.008 0.008 0.044
#> GSM559390 4 0.1830 0.7744 0.004 0.016 0.016 0.936 0.004 0.024
#> GSM559392 2 0.0603 0.6428 0.000 0.980 0.000 0.000 0.004 0.016
#> GSM559393 1 0.2716 0.7861 0.868 0.096 0.000 0.000 0.008 0.028
#> GSM559394 1 0.1908 0.8176 0.924 0.044 0.000 0.000 0.012 0.020
#> GSM559396 6 0.5377 -0.1154 0.004 0.000 0.460 0.028 0.040 0.468
#> GSM559398 2 0.0291 0.6426 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM559399 1 0.2019 0.8289 0.924 0.032 0.000 0.004 0.020 0.020
#> GSM559400 2 0.4537 0.1104 0.000 0.488 0.000 0.484 0.004 0.024
#> GSM559402 4 0.7086 0.2198 0.276 0.008 0.008 0.384 0.032 0.292
#> GSM559403 1 0.0405 0.8310 0.988 0.008 0.000 0.000 0.004 0.000
#> GSM559404 1 0.3243 0.8027 0.844 0.000 0.000 0.064 0.016 0.076
#> GSM559405 1 0.1914 0.8302 0.920 0.000 0.000 0.016 0.008 0.056
#> GSM559406 4 0.1381 0.7841 0.020 0.004 0.000 0.952 0.004 0.020
#> GSM559407 4 0.6659 0.5581 0.172 0.008 0.016 0.552 0.040 0.212
#> GSM559408 4 0.1854 0.7962 0.020 0.004 0.000 0.932 0.016 0.028
#> GSM559409 4 0.4543 0.6117 0.256 0.000 0.004 0.688 0.016 0.036
#> GSM559410 1 0.2763 0.8079 0.868 0.000 0.000 0.088 0.008 0.036
#> GSM559411 4 0.5354 0.7066 0.012 0.004 0.092 0.692 0.032 0.168
#> GSM559412 4 0.2556 0.7879 0.008 0.000 0.000 0.864 0.008 0.120
#> GSM559413 4 0.3526 0.7705 0.008 0.000 0.004 0.808 0.036 0.144
#> GSM559415 1 0.3995 0.7401 0.768 0.000 0.000 0.032 0.028 0.172
#> GSM559416 4 0.0914 0.7822 0.000 0.016 0.016 0.968 0.000 0.000
#> GSM559417 4 0.1059 0.7866 0.000 0.016 0.000 0.964 0.016 0.004
#> GSM559418 2 0.6200 0.0894 0.376 0.488 0.000 0.024 0.024 0.088
#> GSM559419 4 0.2238 0.7976 0.004 0.004 0.016 0.900 0.000 0.076
#> GSM559420 6 0.8152 -0.1809 0.248 0.008 0.128 0.224 0.032 0.360
#> GSM559421 2 0.2778 0.5889 0.000 0.824 0.000 0.000 0.008 0.168
#> GSM559423 6 0.3935 0.4447 0.004 0.292 0.000 0.000 0.016 0.688
#> GSM559425 2 0.3288 0.4151 0.000 0.724 0.000 0.000 0.000 0.276
#> GSM559426 6 0.3468 0.4892 0.004 0.284 0.000 0.000 0.000 0.712
#> GSM559427 2 0.2135 0.6029 0.000 0.872 0.000 0.000 0.000 0.128
#> GSM559428 6 0.4830 0.4743 0.000 0.172 0.000 0.000 0.160 0.668
#> GSM559429 6 0.3652 0.5014 0.000 0.264 0.000 0.000 0.016 0.720
#> GSM559430 2 0.3161 0.5085 0.000 0.776 0.000 0.000 0.008 0.216
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:NMF 49 1.10e-01 2
#> SD:NMF 51 1.31e-10 3
#> SD:NMF 44 3.12e-08 4
#> SD:NMF 44 7.87e-08 5
#> SD:NMF 41 9.38e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.409 0.807 0.871 0.3753 0.618 0.618
#> 3 3 0.662 0.830 0.897 0.4484 0.781 0.646
#> 4 4 0.530 0.787 0.828 0.1909 0.957 0.895
#> 5 5 0.658 0.654 0.807 0.1100 0.969 0.918
#> 6 6 0.643 0.445 0.776 0.0479 0.947 0.852
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
#> GSM559383 1 0.6973 0.766 0.812 0.188
#> GSM559387 1 0.6973 0.766 0.812 0.188
#> GSM559391 1 0.6973 0.766 0.812 0.188
#> GSM559395 1 0.6973 0.766 0.812 0.188
#> GSM559397 1 0.6973 0.766 0.812 0.188
#> GSM559401 1 0.6973 0.766 0.812 0.188
#> GSM559414 1 0.6973 0.766 0.812 0.188
#> GSM559422 1 0.8763 0.676 0.704 0.296
#> GSM559424 1 0.6973 0.766 0.812 0.188
#> GSM559431 2 0.6973 0.904 0.188 0.812
#> GSM559432 1 0.8763 0.676 0.704 0.296
#> GSM559381 1 0.2948 0.849 0.948 0.052
#> GSM559382 1 0.9815 -0.190 0.580 0.420
#> GSM559384 1 0.0000 0.882 1.000 0.000
#> GSM559385 1 0.0000 0.882 1.000 0.000
#> GSM559386 1 0.9000 0.279 0.684 0.316
#> GSM559388 2 0.9460 0.745 0.364 0.636
#> GSM559389 1 0.2948 0.849 0.948 0.052
#> GSM559390 1 0.2948 0.850 0.948 0.052
#> GSM559392 2 0.6973 0.904 0.188 0.812
#> GSM559393 1 0.0376 0.881 0.996 0.004
#> GSM559394 1 0.0000 0.882 1.000 0.000
#> GSM559396 1 0.0000 0.882 1.000 0.000
#> GSM559398 2 0.6973 0.904 0.188 0.812
#> GSM559399 1 0.0000 0.882 1.000 0.000
#> GSM559400 2 0.9522 0.734 0.372 0.628
#> GSM559402 1 0.0000 0.882 1.000 0.000
#> GSM559403 1 0.0000 0.882 1.000 0.000
#> GSM559404 1 0.0000 0.882 1.000 0.000
#> GSM559405 1 0.2948 0.849 0.948 0.052
#> GSM559406 1 0.0376 0.881 0.996 0.004
#> GSM559407 1 0.0000 0.882 1.000 0.000
#> GSM559408 1 0.0000 0.882 1.000 0.000
#> GSM559409 1 0.0000 0.882 1.000 0.000
#> GSM559410 1 0.0000 0.882 1.000 0.000
#> GSM559411 1 0.0000 0.882 1.000 0.000
#> GSM559412 1 0.0000 0.882 1.000 0.000
#> GSM559413 1 0.0000 0.882 1.000 0.000
#> GSM559415 1 0.2778 0.852 0.952 0.048
#> GSM559416 1 0.3733 0.828 0.928 0.072
#> GSM559417 1 0.3733 0.828 0.928 0.072
#> GSM559418 1 0.2778 0.852 0.952 0.048
#> GSM559419 1 0.0000 0.882 1.000 0.000
#> GSM559420 1 0.0000 0.882 1.000 0.000
#> GSM559421 2 0.6973 0.904 0.188 0.812
#> GSM559423 2 0.7219 0.901 0.200 0.800
#> GSM559425 2 0.6973 0.904 0.188 0.812
#> GSM559426 2 0.7674 0.888 0.224 0.776
#> GSM559427 2 0.6973 0.904 0.188 0.812
#> GSM559428 2 0.9970 0.513 0.468 0.532
#> GSM559429 2 0.9358 0.756 0.352 0.648
#> GSM559430 2 0.6973 0.904 0.188 0.812
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.5810 0.8648 0.336 0.000 0.664
#> GSM559387 3 0.5810 0.8648 0.336 0.000 0.664
#> GSM559391 3 0.5810 0.8648 0.336 0.000 0.664
#> GSM559395 3 0.5810 0.8648 0.336 0.000 0.664
#> GSM559397 3 0.5810 0.8648 0.336 0.000 0.664
#> GSM559401 3 0.4750 0.7886 0.216 0.000 0.784
#> GSM559414 3 0.5810 0.8648 0.336 0.000 0.664
#> GSM559422 3 0.0747 0.5675 0.000 0.016 0.984
#> GSM559424 3 0.5810 0.8648 0.336 0.000 0.664
#> GSM559431 2 0.0237 0.8463 0.000 0.996 0.004
#> GSM559432 3 0.0747 0.5675 0.000 0.016 0.984
#> GSM559381 1 0.2537 0.8707 0.920 0.080 0.000
#> GSM559382 1 0.6520 -0.0811 0.508 0.488 0.004
#> GSM559384 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559385 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559386 1 0.6148 0.3953 0.640 0.356 0.004
#> GSM559388 2 0.5656 0.6357 0.284 0.712 0.004
#> GSM559389 1 0.2537 0.8707 0.920 0.080 0.000
#> GSM559390 1 0.1989 0.8981 0.948 0.048 0.004
#> GSM559392 2 0.1289 0.8635 0.032 0.968 0.000
#> GSM559393 1 0.1163 0.9129 0.972 0.028 0.000
#> GSM559394 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559396 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559398 2 0.1289 0.8635 0.032 0.968 0.000
#> GSM559399 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559400 2 0.5815 0.6102 0.304 0.692 0.004
#> GSM559402 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559403 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559404 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559405 1 0.2537 0.8707 0.920 0.080 0.000
#> GSM559406 1 0.0237 0.9263 0.996 0.000 0.004
#> GSM559407 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559408 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559409 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559410 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559411 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559412 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559413 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559415 1 0.1878 0.8980 0.952 0.044 0.004
#> GSM559416 1 0.2496 0.8776 0.928 0.068 0.004
#> GSM559417 1 0.2496 0.8776 0.928 0.068 0.004
#> GSM559418 1 0.1878 0.8980 0.952 0.044 0.004
#> GSM559419 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559420 1 0.0000 0.9285 1.000 0.000 0.000
#> GSM559421 2 0.1289 0.8635 0.032 0.968 0.000
#> GSM559423 2 0.1765 0.8603 0.040 0.956 0.004
#> GSM559425 2 0.0424 0.8551 0.008 0.992 0.000
#> GSM559426 2 0.1753 0.8509 0.048 0.952 0.000
#> GSM559427 2 0.0424 0.8551 0.008 0.992 0.000
#> GSM559428 2 0.5785 0.5123 0.332 0.668 0.000
#> GSM559429 2 0.4235 0.7204 0.176 0.824 0.000
#> GSM559430 2 0.0424 0.8551 0.008 0.992 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.3486 0.9672 0.188 0.000 0.812 0.000
#> GSM559387 3 0.3486 0.9672 0.188 0.000 0.812 0.000
#> GSM559391 3 0.3486 0.9672 0.188 0.000 0.812 0.000
#> GSM559395 3 0.3486 0.9672 0.188 0.000 0.812 0.000
#> GSM559397 3 0.3486 0.9672 0.188 0.000 0.812 0.000
#> GSM559401 3 0.3978 0.7200 0.108 0.000 0.836 0.056
#> GSM559414 3 0.3486 0.9672 0.188 0.000 0.812 0.000
#> GSM559422 4 0.4941 1.0000 0.000 0.000 0.436 0.564
#> GSM559424 3 0.3486 0.9672 0.188 0.000 0.812 0.000
#> GSM559431 2 0.2329 0.7593 0.000 0.916 0.012 0.072
#> GSM559432 4 0.4941 1.0000 0.000 0.000 0.436 0.564
#> GSM559381 1 0.5021 0.7200 0.724 0.036 0.000 0.240
#> GSM559382 2 0.7968 0.3611 0.264 0.408 0.004 0.324
#> GSM559384 1 0.0895 0.8408 0.976 0.000 0.004 0.020
#> GSM559385 1 0.4646 0.7853 0.796 0.000 0.120 0.084
#> GSM559386 1 0.7977 0.0417 0.412 0.280 0.004 0.304
#> GSM559388 2 0.5988 0.6302 0.100 0.676 0.000 0.224
#> GSM559389 1 0.5021 0.7200 0.724 0.036 0.000 0.240
#> GSM559390 1 0.4126 0.7660 0.776 0.004 0.004 0.216
#> GSM559392 2 0.1022 0.7942 0.000 0.968 0.000 0.032
#> GSM559393 1 0.5680 0.7618 0.752 0.020 0.120 0.108
#> GSM559394 1 0.4646 0.7853 0.796 0.000 0.120 0.084
#> GSM559396 1 0.0895 0.8408 0.976 0.000 0.004 0.020
#> GSM559398 2 0.1022 0.7942 0.000 0.968 0.000 0.032
#> GSM559399 1 0.1022 0.8415 0.968 0.000 0.000 0.032
#> GSM559400 2 0.6175 0.6233 0.092 0.664 0.004 0.240
#> GSM559402 1 0.2149 0.8118 0.912 0.000 0.088 0.000
#> GSM559403 1 0.1724 0.8426 0.948 0.000 0.020 0.032
#> GSM559404 1 0.3658 0.7505 0.836 0.000 0.144 0.020
#> GSM559405 1 0.5021 0.7200 0.724 0.036 0.000 0.240
#> GSM559406 1 0.2773 0.8240 0.880 0.000 0.004 0.116
#> GSM559407 1 0.2149 0.8118 0.912 0.000 0.088 0.000
#> GSM559408 1 0.0336 0.8405 0.992 0.000 0.008 0.000
#> GSM559409 1 0.0336 0.8405 0.992 0.000 0.008 0.000
#> GSM559410 1 0.3082 0.8198 0.884 0.000 0.084 0.032
#> GSM559411 1 0.0336 0.8405 0.992 0.000 0.008 0.000
#> GSM559412 1 0.2216 0.8093 0.908 0.000 0.092 0.000
#> GSM559413 1 0.2216 0.8093 0.908 0.000 0.092 0.000
#> GSM559415 1 0.3501 0.8082 0.848 0.020 0.000 0.132
#> GSM559416 1 0.4854 0.7365 0.732 0.020 0.004 0.244
#> GSM559417 1 0.4854 0.7365 0.732 0.020 0.004 0.244
#> GSM559418 1 0.3501 0.8082 0.848 0.020 0.000 0.132
#> GSM559419 1 0.0376 0.8416 0.992 0.000 0.004 0.004
#> GSM559420 1 0.0376 0.8416 0.992 0.000 0.004 0.004
#> GSM559421 2 0.1022 0.7942 0.000 0.968 0.000 0.032
#> GSM559423 2 0.1389 0.7932 0.000 0.952 0.000 0.048
#> GSM559425 2 0.1767 0.7732 0.000 0.944 0.012 0.044
#> GSM559426 2 0.3047 0.7629 0.012 0.872 0.000 0.116
#> GSM559427 2 0.1767 0.7732 0.000 0.944 0.012 0.044
#> GSM559428 2 0.7117 0.5360 0.196 0.584 0.004 0.216
#> GSM559429 2 0.5574 0.6709 0.092 0.732 0.004 0.172
#> GSM559430 2 0.0188 0.7895 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
#> GSM559383 3 0.1043 0.981 0.040 0.000 0.960 0.000 0.000
#> GSM559387 3 0.1043 0.981 0.040 0.000 0.960 0.000 0.000
#> GSM559391 3 0.1043 0.981 0.040 0.000 0.960 0.000 0.000
#> GSM559395 3 0.1043 0.981 0.040 0.000 0.960 0.000 0.000
#> GSM559397 3 0.1043 0.981 0.040 0.000 0.960 0.000 0.000
#> GSM559401 3 0.2077 0.849 0.000 0.000 0.920 0.040 0.040
#> GSM559414 3 0.1043 0.981 0.040 0.000 0.960 0.000 0.000
#> GSM559422 5 0.4666 1.000 0.000 0.000 0.040 0.284 0.676
#> GSM559424 3 0.1043 0.981 0.040 0.000 0.960 0.000 0.000
#> GSM559431 2 0.2293 0.734 0.000 0.900 0.000 0.084 0.016
#> GSM559432 5 0.4666 1.000 0.000 0.000 0.040 0.284 0.676
#> GSM559381 1 0.4761 0.299 0.616 0.028 0.000 0.356 0.000
#> GSM559382 4 0.6272 0.579 0.152 0.380 0.000 0.468 0.000
#> GSM559384 1 0.1430 0.713 0.944 0.000 0.000 0.052 0.004
#> GSM559385 1 0.6448 0.494 0.560 0.000 0.052 0.076 0.312
#> GSM559386 4 0.6641 0.681 0.296 0.256 0.000 0.448 0.000
#> GSM559388 2 0.4522 0.280 0.024 0.660 0.000 0.316 0.000
#> GSM559389 1 0.4761 0.299 0.616 0.028 0.000 0.356 0.000
#> GSM559390 1 0.3857 0.472 0.688 0.000 0.000 0.312 0.000
#> GSM559392 2 0.1197 0.763 0.000 0.952 0.000 0.048 0.000
#> GSM559393 1 0.7285 0.422 0.508 0.016 0.052 0.112 0.312
#> GSM559394 1 0.6448 0.494 0.560 0.000 0.052 0.076 0.312
#> GSM559396 1 0.1410 0.710 0.940 0.000 0.000 0.060 0.000
#> GSM559398 2 0.1197 0.763 0.000 0.952 0.000 0.048 0.000
#> GSM559399 1 0.1469 0.721 0.948 0.000 0.000 0.036 0.016
#> GSM559400 2 0.4467 0.277 0.016 0.640 0.000 0.344 0.000
#> GSM559402 1 0.2389 0.701 0.880 0.000 0.004 0.000 0.116
#> GSM559403 1 0.2157 0.724 0.920 0.000 0.004 0.036 0.040
#> GSM559404 1 0.5654 0.474 0.592 0.000 0.076 0.008 0.324
#> GSM559405 1 0.4761 0.299 0.616 0.028 0.000 0.356 0.000
#> GSM559406 1 0.3048 0.639 0.820 0.000 0.000 0.176 0.004
#> GSM559407 1 0.2389 0.701 0.880 0.000 0.004 0.000 0.116
#> GSM559408 1 0.0451 0.724 0.988 0.000 0.000 0.008 0.004
#> GSM559409 1 0.0451 0.724 0.988 0.000 0.000 0.008 0.004
#> GSM559410 1 0.3222 0.707 0.852 0.000 0.004 0.036 0.108
#> GSM559411 1 0.0609 0.724 0.980 0.000 0.000 0.000 0.020
#> GSM559412 1 0.2970 0.677 0.828 0.000 0.004 0.000 0.168
#> GSM559413 1 0.2970 0.677 0.828 0.000 0.004 0.000 0.168
#> GSM559415 1 0.3779 0.583 0.752 0.012 0.000 0.236 0.000
#> GSM559416 1 0.4565 0.276 0.580 0.012 0.000 0.408 0.000
#> GSM559417 1 0.4565 0.276 0.580 0.012 0.000 0.408 0.000
#> GSM559418 1 0.3779 0.583 0.752 0.012 0.000 0.236 0.000
#> GSM559419 1 0.0290 0.724 0.992 0.000 0.000 0.008 0.000
#> GSM559420 1 0.0290 0.724 0.992 0.000 0.000 0.008 0.000
#> GSM559421 2 0.1341 0.763 0.000 0.944 0.000 0.056 0.000
#> GSM559423 2 0.1544 0.760 0.000 0.932 0.000 0.068 0.000
#> GSM559425 2 0.1478 0.748 0.000 0.936 0.000 0.064 0.000
#> GSM559426 2 0.2864 0.684 0.012 0.852 0.000 0.136 0.000
#> GSM559427 2 0.1478 0.748 0.000 0.936 0.000 0.064 0.000
#> GSM559428 2 0.6054 -0.226 0.148 0.548 0.000 0.304 0.000
#> GSM559429 2 0.4873 0.403 0.068 0.688 0.000 0.244 0.000
#> GSM559430 2 0.0794 0.764 0.000 0.972 0.000 0.028 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559383 3 0.0000 0.9824 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM559387 3 0.0000 0.9824 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM559391 3 0.0000 0.9824 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM559395 3 0.0000 0.9824 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM559397 3 0.0000 0.9824 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM559401 3 0.2048 0.8632 0.000 0.000 0.880 0.000 0.12 0.000
#> GSM559414 3 0.0000 0.9824 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM559422 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.00 0.000
#> GSM559424 3 0.0000 0.9824 0.000 0.000 1.000 0.000 0.00 0.000
#> GSM559431 2 0.4626 0.5726 0.000 0.692 0.000 0.172 0.00 0.136
#> GSM559432 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.00 0.000
#> GSM559381 1 0.5975 0.2058 0.580 0.028 0.012 0.116 0.00 0.264
#> GSM559382 2 0.7510 -0.1912 0.116 0.396 0.012 0.196 0.00 0.280
#> GSM559384 1 0.1682 0.5251 0.928 0.000 0.000 0.052 0.00 0.020
#> GSM559385 1 0.3868 -0.8547 0.504 0.000 0.000 0.496 0.00 0.000
#> GSM559386 6 0.7941 0.0887 0.260 0.264 0.012 0.184 0.00 0.280
#> GSM559388 2 0.4838 0.4160 0.004 0.676 0.000 0.192 0.00 0.128
#> GSM559389 1 0.5975 0.2058 0.580 0.028 0.012 0.116 0.00 0.264
#> GSM559390 1 0.4785 0.3210 0.660 0.004 0.012 0.052 0.00 0.272
#> GSM559392 2 0.0000 0.6803 0.000 1.000 0.000 0.000 0.00 0.000
#> GSM559393 4 0.4869 0.0000 0.456 0.024 0.000 0.500 0.00 0.020
#> GSM559394 1 0.3868 -0.8547 0.504 0.000 0.000 0.496 0.00 0.000
#> GSM559396 1 0.1845 0.5251 0.920 0.000 0.000 0.052 0.00 0.028
#> GSM559398 2 0.0260 0.6804 0.000 0.992 0.000 0.000 0.00 0.008
#> GSM559399 1 0.1501 0.4968 0.924 0.000 0.000 0.076 0.00 0.000
#> GSM559400 2 0.4949 0.4253 0.004 0.644 0.000 0.104 0.00 0.248
#> GSM559402 1 0.2135 0.3783 0.872 0.000 0.000 0.128 0.00 0.000
#> GSM559403 1 0.1814 0.4735 0.900 0.000 0.000 0.100 0.00 0.000
#> GSM559404 1 0.3862 -0.6616 0.524 0.000 0.000 0.476 0.00 0.000
#> GSM559405 1 0.5975 0.2058 0.580 0.028 0.012 0.116 0.00 0.264
#> GSM559406 1 0.3477 0.4549 0.808 0.004 0.000 0.056 0.00 0.132
#> GSM559407 1 0.2135 0.3783 0.872 0.000 0.000 0.128 0.00 0.000
#> GSM559408 1 0.0520 0.5303 0.984 0.000 0.000 0.008 0.00 0.008
#> GSM559409 1 0.0520 0.5303 0.984 0.000 0.000 0.008 0.00 0.008
#> GSM559410 1 0.2562 0.3537 0.828 0.000 0.000 0.172 0.00 0.000
#> GSM559411 1 0.1010 0.5186 0.960 0.000 0.000 0.036 0.00 0.004
#> GSM559412 1 0.2838 0.2601 0.808 0.000 0.000 0.188 0.00 0.004
#> GSM559413 1 0.2871 0.2505 0.804 0.000 0.000 0.192 0.00 0.004
#> GSM559415 1 0.4295 0.3905 0.720 0.020 0.000 0.224 0.00 0.036
#> GSM559416 1 0.5930 0.2681 0.564 0.024 0.000 0.192 0.00 0.220
#> GSM559417 1 0.5930 0.2681 0.564 0.024 0.000 0.192 0.00 0.220
#> GSM559418 1 0.4295 0.3905 0.720 0.020 0.000 0.224 0.00 0.036
#> GSM559419 1 0.0405 0.5299 0.988 0.000 0.000 0.008 0.00 0.004
#> GSM559420 1 0.0405 0.5299 0.988 0.000 0.000 0.008 0.00 0.004
#> GSM559421 2 0.0937 0.6677 0.000 0.960 0.000 0.000 0.00 0.040
#> GSM559423 2 0.2747 0.6127 0.000 0.860 0.000 0.044 0.00 0.096
#> GSM559425 2 0.3901 0.6236 0.000 0.768 0.000 0.136 0.00 0.096
#> GSM559426 6 0.4833 0.1237 0.000 0.428 0.000 0.056 0.00 0.516
#> GSM559427 2 0.3901 0.6236 0.000 0.768 0.000 0.136 0.00 0.096
#> GSM559428 6 0.5183 0.4180 0.120 0.176 0.012 0.012 0.00 0.680
#> GSM559429 6 0.4332 0.3735 0.000 0.228 0.000 0.072 0.00 0.700
#> GSM559430 2 0.2106 0.6670 0.000 0.904 0.000 0.032 0.00 0.064
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:hclust 50 2.90e-01 2
#> CV:hclust 50 2.05e-10 3
#> CV:hclust 50 1.11e-09 4
#> CV:hclust 38 8.67e-07 5
#> CV:hclust 25 8.49e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.497 0.756 0.795 0.3757 0.581 0.581
#> 3 3 1.000 0.975 0.981 0.6180 0.793 0.647
#> 4 4 0.677 0.706 0.824 0.1463 0.931 0.825
#> 5 5 0.659 0.592 0.743 0.0882 0.923 0.777
#> 6 6 0.674 0.544 0.702 0.0667 0.836 0.485
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
#> GSM559383 1 0.118 0.445 0.984 0.016
#> GSM559387 1 0.118 0.445 0.984 0.016
#> GSM559391 1 0.118 0.445 0.984 0.016
#> GSM559395 1 0.118 0.445 0.984 0.016
#> GSM559397 1 0.118 0.445 0.984 0.016
#> GSM559401 1 0.118 0.445 0.984 0.016
#> GSM559414 1 0.118 0.445 0.984 0.016
#> GSM559422 1 0.343 0.387 0.936 0.064
#> GSM559424 1 0.118 0.445 0.984 0.016
#> GSM559431 2 0.000 0.936 0.000 1.000
#> GSM559432 2 0.993 0.347 0.452 0.548
#> GSM559381 1 0.993 0.787 0.548 0.452
#> GSM559382 2 0.141 0.911 0.020 0.980
#> GSM559384 1 0.993 0.787 0.548 0.452
#> GSM559385 1 0.993 0.787 0.548 0.452
#> GSM559386 1 0.995 0.776 0.540 0.460
#> GSM559388 2 0.000 0.936 0.000 1.000
#> GSM559389 1 0.993 0.787 0.548 0.452
#> GSM559390 1 0.993 0.787 0.548 0.452
#> GSM559392 2 0.000 0.936 0.000 1.000
#> GSM559393 1 0.994 0.782 0.544 0.456
#> GSM559394 1 0.993 0.787 0.548 0.452
#> GSM559396 1 0.993 0.787 0.548 0.452
#> GSM559398 2 0.000 0.936 0.000 1.000
#> GSM559399 1 0.993 0.787 0.548 0.452
#> GSM559400 2 0.141 0.909 0.020 0.980
#> GSM559402 1 0.993 0.787 0.548 0.452
#> GSM559403 1 0.993 0.787 0.548 0.452
#> GSM559404 1 0.990 0.781 0.560 0.440
#> GSM559405 1 0.993 0.787 0.548 0.452
#> GSM559406 1 0.990 0.781 0.560 0.440
#> GSM559407 1 0.993 0.787 0.548 0.452
#> GSM559408 1 0.993 0.787 0.548 0.452
#> GSM559409 1 0.993 0.787 0.548 0.452
#> GSM559410 1 0.993 0.787 0.548 0.452
#> GSM559411 1 0.990 0.781 0.560 0.440
#> GSM559412 1 0.990 0.781 0.560 0.440
#> GSM559413 1 0.990 0.781 0.560 0.440
#> GSM559415 1 0.993 0.787 0.548 0.452
#> GSM559416 1 0.993 0.787 0.548 0.452
#> GSM559417 1 0.993 0.787 0.548 0.452
#> GSM559418 1 0.994 0.782 0.544 0.456
#> GSM559419 1 0.993 0.787 0.548 0.452
#> GSM559420 1 0.993 0.787 0.548 0.452
#> GSM559421 2 0.000 0.936 0.000 1.000
#> GSM559423 2 0.000 0.936 0.000 1.000
#> GSM559425 2 0.000 0.936 0.000 1.000
#> GSM559426 2 0.000 0.936 0.000 1.000
#> GSM559427 2 0.000 0.936 0.000 1.000
#> GSM559428 2 0.141 0.911 0.020 0.980
#> GSM559429 2 0.000 0.936 0.000 1.000
#> GSM559430 2 0.000 0.936 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.1643 0.988 0.044 0.000 0.956
#> GSM559387 3 0.1643 0.988 0.044 0.000 0.956
#> GSM559391 3 0.1643 0.988 0.044 0.000 0.956
#> GSM559395 3 0.1643 0.988 0.044 0.000 0.956
#> GSM559397 3 0.1643 0.988 0.044 0.000 0.956
#> GSM559401 3 0.1643 0.988 0.044 0.000 0.956
#> GSM559414 3 0.1643 0.988 0.044 0.000 0.956
#> GSM559422 3 0.0424 0.954 0.008 0.000 0.992
#> GSM559424 3 0.1643 0.988 0.044 0.000 0.956
#> GSM559431 2 0.0424 0.964 0.000 0.992 0.008
#> GSM559432 3 0.0237 0.944 0.000 0.004 0.996
#> GSM559381 1 0.0237 0.990 0.996 0.004 0.000
#> GSM559382 2 0.3039 0.923 0.044 0.920 0.036
#> GSM559384 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559385 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559386 1 0.1832 0.958 0.956 0.008 0.036
#> GSM559388 2 0.1411 0.953 0.000 0.964 0.036
#> GSM559389 1 0.0237 0.990 0.996 0.004 0.000
#> GSM559390 1 0.0592 0.984 0.988 0.000 0.012
#> GSM559392 2 0.0000 0.964 0.000 1.000 0.000
#> GSM559393 1 0.1832 0.958 0.956 0.008 0.036
#> GSM559394 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559396 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559398 2 0.0424 0.964 0.000 0.992 0.008
#> GSM559399 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559400 2 0.4915 0.806 0.132 0.832 0.036
#> GSM559402 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559403 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559404 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559405 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559406 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559407 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559408 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559409 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559410 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559411 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559412 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559413 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559415 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559416 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559417 1 0.1647 0.961 0.960 0.004 0.036
#> GSM559418 1 0.1832 0.958 0.956 0.008 0.036
#> GSM559419 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559420 1 0.0000 0.992 1.000 0.000 0.000
#> GSM559421 2 0.0000 0.964 0.000 1.000 0.000
#> GSM559423 2 0.1031 0.959 0.000 0.976 0.024
#> GSM559425 2 0.0424 0.964 0.000 0.992 0.008
#> GSM559426 2 0.0000 0.964 0.000 1.000 0.000
#> GSM559427 2 0.0424 0.964 0.000 0.992 0.008
#> GSM559428 2 0.3039 0.923 0.044 0.920 0.036
#> GSM559429 2 0.1031 0.959 0.000 0.976 0.024
#> GSM559430 2 0.0424 0.964 0.000 0.992 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.0188 0.95679 0.000 0.000 0.996 0.004
#> GSM559387 3 0.0000 0.95751 0.000 0.000 1.000 0.000
#> GSM559391 3 0.0188 0.95679 0.000 0.000 0.996 0.004
#> GSM559395 3 0.0000 0.95751 0.000 0.000 1.000 0.000
#> GSM559397 3 0.0000 0.95751 0.000 0.000 1.000 0.000
#> GSM559401 3 0.0000 0.95751 0.000 0.000 1.000 0.000
#> GSM559414 3 0.0000 0.95751 0.000 0.000 1.000 0.000
#> GSM559422 3 0.4008 0.81993 0.000 0.000 0.756 0.244
#> GSM559424 3 0.0188 0.95679 0.000 0.000 0.996 0.004
#> GSM559431 2 0.0336 0.84863 0.000 0.992 0.000 0.008
#> GSM559432 3 0.4008 0.81993 0.000 0.000 0.756 0.244
#> GSM559381 1 0.4454 0.74220 0.692 0.000 0.000 0.308
#> GSM559382 4 0.5508 -0.03453 0.016 0.476 0.000 0.508
#> GSM559384 1 0.3356 0.79573 0.824 0.000 0.000 0.176
#> GSM559385 1 0.4356 0.75152 0.708 0.000 0.000 0.292
#> GSM559386 4 0.4543 -0.00163 0.324 0.000 0.000 0.676
#> GSM559388 2 0.4925 0.16550 0.000 0.572 0.000 0.428
#> GSM559389 1 0.4624 0.71270 0.660 0.000 0.000 0.340
#> GSM559390 1 0.4250 0.42975 0.724 0.000 0.000 0.276
#> GSM559392 2 0.3123 0.82103 0.000 0.844 0.000 0.156
#> GSM559393 4 0.4564 -0.04922 0.328 0.000 0.000 0.672
#> GSM559394 1 0.4382 0.75035 0.704 0.000 0.000 0.296
#> GSM559396 1 0.3610 0.79439 0.800 0.000 0.000 0.200
#> GSM559398 2 0.0817 0.85204 0.000 0.976 0.000 0.024
#> GSM559399 1 0.4522 0.74240 0.680 0.000 0.000 0.320
#> GSM559400 4 0.7412 0.12340 0.168 0.388 0.000 0.444
#> GSM559402 1 0.3219 0.79590 0.836 0.000 0.000 0.164
#> GSM559403 1 0.4331 0.75364 0.712 0.000 0.000 0.288
#> GSM559404 1 0.4040 0.78065 0.752 0.000 0.000 0.248
#> GSM559405 1 0.3907 0.77854 0.768 0.000 0.000 0.232
#> GSM559406 1 0.0592 0.75015 0.984 0.000 0.000 0.016
#> GSM559407 1 0.3074 0.79496 0.848 0.000 0.000 0.152
#> GSM559408 1 0.0000 0.75891 1.000 0.000 0.000 0.000
#> GSM559409 1 0.0000 0.75891 1.000 0.000 0.000 0.000
#> GSM559410 1 0.3764 0.78504 0.784 0.000 0.000 0.216
#> GSM559411 1 0.0707 0.75466 0.980 0.000 0.000 0.020
#> GSM559412 1 0.0707 0.75466 0.980 0.000 0.000 0.020
#> GSM559413 1 0.0707 0.75466 0.980 0.000 0.000 0.020
#> GSM559415 1 0.4522 0.74170 0.680 0.000 0.000 0.320
#> GSM559416 1 0.3444 0.59305 0.816 0.000 0.000 0.184
#> GSM559417 1 0.3688 0.55254 0.792 0.000 0.000 0.208
#> GSM559418 1 0.4989 0.51813 0.528 0.000 0.000 0.472
#> GSM559419 1 0.2281 0.72587 0.904 0.000 0.000 0.096
#> GSM559420 1 0.3219 0.79601 0.836 0.000 0.000 0.164
#> GSM559421 2 0.2345 0.85013 0.000 0.900 0.000 0.100
#> GSM559423 2 0.3266 0.80943 0.000 0.832 0.000 0.168
#> GSM559425 2 0.0000 0.85143 0.000 1.000 0.000 0.000
#> GSM559426 2 0.2469 0.84723 0.000 0.892 0.000 0.108
#> GSM559427 2 0.0000 0.85143 0.000 1.000 0.000 0.000
#> GSM559428 4 0.5510 -0.06143 0.016 0.480 0.000 0.504
#> GSM559429 2 0.3266 0.81293 0.000 0.832 0.000 0.168
#> GSM559430 2 0.0000 0.85143 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
#> GSM559383 3 0.0609 0.90963 0.000 0.000 0.980 0.020 NA
#> GSM559387 3 0.0000 0.91239 0.000 0.000 1.000 0.000 NA
#> GSM559391 3 0.0609 0.90963 0.000 0.000 0.980 0.020 NA
#> GSM559395 3 0.0000 0.91239 0.000 0.000 1.000 0.000 NA
#> GSM559397 3 0.0000 0.91239 0.000 0.000 1.000 0.000 NA
#> GSM559401 3 0.0000 0.91239 0.000 0.000 1.000 0.000 NA
#> GSM559414 3 0.0000 0.91239 0.000 0.000 1.000 0.000 NA
#> GSM559422 3 0.4425 0.61454 0.000 0.000 0.544 0.004 NA
#> GSM559424 3 0.0609 0.90963 0.000 0.000 0.980 0.020 NA
#> GSM559431 2 0.0671 0.81506 0.000 0.980 0.000 0.004 NA
#> GSM559432 3 0.4641 0.60324 0.000 0.000 0.532 0.012 NA
#> GSM559381 1 0.3779 0.58047 0.804 0.000 0.000 0.144 NA
#> GSM559382 4 0.6165 0.27890 0.040 0.220 0.000 0.632 NA
#> GSM559384 1 0.1568 0.66097 0.944 0.000 0.000 0.036 NA
#> GSM559385 1 0.4890 0.54902 0.680 0.000 0.000 0.064 NA
#> GSM559386 4 0.5839 0.43850 0.248 0.004 0.000 0.612 NA
#> GSM559388 4 0.5825 0.06219 0.000 0.320 0.000 0.564 NA
#> GSM559389 1 0.4934 0.55929 0.708 0.000 0.000 0.104 NA
#> GSM559390 4 0.3957 0.19026 0.280 0.000 0.000 0.712 NA
#> GSM559392 2 0.5305 0.72280 0.000 0.672 0.000 0.196 NA
#> GSM559393 4 0.6796 0.02692 0.328 0.000 0.000 0.376 NA
#> GSM559394 1 0.5059 0.54006 0.668 0.000 0.000 0.076 NA
#> GSM559396 1 0.3002 0.63416 0.856 0.000 0.000 0.116 NA
#> GSM559398 2 0.1661 0.81446 0.000 0.940 0.000 0.036 NA
#> GSM559399 1 0.4836 0.56873 0.716 0.000 0.000 0.096 NA
#> GSM559400 4 0.4733 0.35025 0.008 0.152 0.000 0.748 NA
#> GSM559402 1 0.1670 0.65783 0.936 0.000 0.000 0.052 NA
#> GSM559403 1 0.4890 0.54902 0.680 0.000 0.000 0.064 NA
#> GSM559404 1 0.4298 0.60158 0.756 0.000 0.000 0.060 NA
#> GSM559405 1 0.2573 0.64534 0.880 0.000 0.000 0.016 NA
#> GSM559406 1 0.5027 0.49735 0.640 0.000 0.000 0.304 NA
#> GSM559407 1 0.1764 0.65655 0.928 0.000 0.000 0.064 NA
#> GSM559408 1 0.4967 0.51980 0.660 0.000 0.000 0.280 NA
#> GSM559409 1 0.4878 0.52737 0.676 0.000 0.000 0.264 NA
#> GSM559410 1 0.3565 0.63029 0.800 0.000 0.000 0.024 NA
#> GSM559411 1 0.4890 0.52760 0.680 0.000 0.000 0.256 NA
#> GSM559412 1 0.4937 0.52620 0.672 0.000 0.000 0.264 NA
#> GSM559413 1 0.4914 0.52756 0.676 0.000 0.000 0.260 NA
#> GSM559415 1 0.4998 0.55713 0.700 0.000 0.000 0.104 NA
#> GSM559416 4 0.4930 -0.03626 0.388 0.000 0.000 0.580 NA
#> GSM559417 4 0.4898 0.00102 0.376 0.000 0.000 0.592 NA
#> GSM559418 1 0.6102 0.33691 0.568 0.000 0.000 0.232 NA
#> GSM559419 1 0.4966 0.36040 0.564 0.000 0.000 0.404 NA
#> GSM559420 1 0.2325 0.65256 0.904 0.000 0.000 0.068 NA
#> GSM559421 2 0.4351 0.79447 0.000 0.768 0.000 0.132 NA
#> GSM559423 2 0.5367 0.74616 0.000 0.668 0.000 0.184 NA
#> GSM559425 2 0.0404 0.81718 0.000 0.988 0.000 0.000 NA
#> GSM559426 2 0.4764 0.78151 0.000 0.732 0.000 0.140 NA
#> GSM559427 2 0.0404 0.81718 0.000 0.988 0.000 0.000 NA
#> GSM559428 4 0.6867 0.21261 0.048 0.224 0.000 0.560 NA
#> GSM559429 2 0.5109 0.75723 0.000 0.696 0.000 0.172 NA
#> GSM559430 2 0.0510 0.81793 0.000 0.984 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
#> GSM559383 3 0.0622 0.9766 0.012 0.000 0.980 0.000 0.000 0.008
#> GSM559387 3 0.0000 0.9829 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559391 3 0.0622 0.9766 0.012 0.000 0.980 0.000 0.000 0.008
#> GSM559395 3 0.0146 0.9829 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM559397 3 0.0000 0.9829 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559401 3 0.0260 0.9759 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM559414 3 0.0000 0.9829 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559422 5 0.3862 0.9826 0.000 0.000 0.476 0.000 0.524 0.000
#> GSM559424 3 0.0622 0.9766 0.012 0.000 0.980 0.000 0.000 0.008
#> GSM559431 2 0.1003 0.6895 0.000 0.964 0.000 0.000 0.016 0.020
#> GSM559432 5 0.3857 0.9828 0.000 0.000 0.468 0.000 0.532 0.000
#> GSM559381 1 0.6917 0.1100 0.376 0.000 0.000 0.364 0.072 0.188
#> GSM559382 6 0.3150 0.5791 0.104 0.064 0.000 0.000 0.000 0.832
#> GSM559384 4 0.5310 0.1550 0.332 0.000 0.000 0.576 0.072 0.020
#> GSM559385 1 0.4606 0.6579 0.708 0.000 0.000 0.208 0.064 0.020
#> GSM559386 6 0.3192 0.5573 0.216 0.000 0.000 0.004 0.004 0.776
#> GSM559388 6 0.3852 0.5272 0.064 0.120 0.000 0.000 0.020 0.796
#> GSM559389 1 0.5606 0.5907 0.644 0.000 0.000 0.192 0.060 0.104
#> GSM559390 6 0.7139 0.0615 0.116 0.000 0.000 0.328 0.164 0.392
#> GSM559392 2 0.4636 0.3915 0.004 0.532 0.000 0.000 0.032 0.432
#> GSM559393 1 0.4317 0.5117 0.740 0.000 0.000 0.016 0.064 0.180
#> GSM559394 1 0.4170 0.6653 0.740 0.000 0.000 0.192 0.060 0.008
#> GSM559396 4 0.6266 0.2096 0.292 0.000 0.000 0.532 0.084 0.092
#> GSM559398 2 0.2750 0.6509 0.000 0.844 0.000 0.000 0.020 0.136
#> GSM559399 1 0.3753 0.6446 0.788 0.000 0.000 0.156 0.040 0.016
#> GSM559400 6 0.5523 0.5190 0.060 0.032 0.000 0.052 0.168 0.688
#> GSM559402 4 0.4978 0.2780 0.268 0.000 0.000 0.644 0.072 0.016
#> GSM559403 1 0.4213 0.6519 0.708 0.000 0.000 0.240 0.048 0.004
#> GSM559404 4 0.5282 0.1470 0.244 0.000 0.000 0.636 0.096 0.024
#> GSM559405 1 0.5285 0.2695 0.488 0.000 0.000 0.436 0.060 0.016
#> GSM559406 4 0.2870 0.5362 0.004 0.000 0.000 0.856 0.100 0.040
#> GSM559407 4 0.4729 0.3004 0.256 0.000 0.000 0.668 0.064 0.012
#> GSM559408 4 0.1923 0.5595 0.004 0.000 0.000 0.916 0.064 0.016
#> GSM559409 4 0.1196 0.5678 0.000 0.000 0.000 0.952 0.040 0.008
#> GSM559410 1 0.3706 0.5353 0.620 0.000 0.000 0.380 0.000 0.000
#> GSM559411 4 0.0508 0.5653 0.012 0.000 0.000 0.984 0.004 0.000
#> GSM559412 4 0.1010 0.5670 0.004 0.000 0.000 0.960 0.036 0.000
#> GSM559413 4 0.0260 0.5642 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM559415 1 0.3473 0.6443 0.812 0.000 0.000 0.136 0.040 0.012
#> GSM559416 4 0.7386 0.1414 0.200 0.000 0.000 0.412 0.188 0.200
#> GSM559417 4 0.7396 0.1085 0.188 0.000 0.000 0.408 0.188 0.216
#> GSM559418 1 0.3236 0.6061 0.852 0.000 0.000 0.060 0.040 0.048
#> GSM559419 4 0.7074 0.2656 0.268 0.000 0.000 0.444 0.168 0.120
#> GSM559420 4 0.5356 0.1955 0.348 0.000 0.000 0.560 0.072 0.020
#> GSM559421 2 0.4446 0.4902 0.004 0.600 0.000 0.000 0.028 0.368
#> GSM559423 6 0.5503 -0.4437 0.016 0.448 0.000 0.000 0.080 0.456
#> GSM559425 2 0.0146 0.7032 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM559426 2 0.5504 0.4573 0.024 0.564 0.000 0.000 0.084 0.328
#> GSM559427 2 0.0146 0.7032 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM559428 6 0.4167 0.4969 0.072 0.056 0.000 0.000 0.084 0.788
#> GSM559429 2 0.5992 0.3351 0.032 0.464 0.000 0.000 0.108 0.396
#> GSM559430 2 0.0291 0.7036 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) k
#> CV:kmeans 42 7.20e-01 2
#> CV:kmeans 52 8.27e-11 3
#> CV:kmeans 45 1.93e-09 4
#> CV:kmeans 40 1.97e-08 5
#> CV:kmeans 34 1.26e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.524 0.899 0.912 0.4755 0.517 0.517
#> 3 3 1.000 0.969 0.989 0.3554 0.773 0.586
#> 4 4 0.847 0.907 0.931 0.1694 0.851 0.600
#> 5 5 0.771 0.690 0.843 0.0574 0.913 0.674
#> 6 6 0.759 0.539 0.765 0.0349 0.956 0.797
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
#> GSM559383 1 0.6801 0.845 0.820 0.180
#> GSM559387 1 0.6801 0.845 0.820 0.180
#> GSM559391 1 0.6801 0.845 0.820 0.180
#> GSM559395 1 0.6801 0.845 0.820 0.180
#> GSM559397 1 0.6801 0.845 0.820 0.180
#> GSM559401 1 0.6801 0.845 0.820 0.180
#> GSM559414 1 0.6801 0.845 0.820 0.180
#> GSM559422 2 0.1414 0.858 0.020 0.980
#> GSM559424 1 0.6801 0.845 0.820 0.180
#> GSM559431 2 0.0000 0.871 0.000 1.000
#> GSM559432 2 0.1414 0.858 0.020 0.980
#> GSM559381 1 0.1414 0.931 0.980 0.020
#> GSM559382 2 0.5408 0.928 0.124 0.876
#> GSM559384 1 0.1414 0.931 0.980 0.020
#> GSM559385 1 0.1414 0.931 0.980 0.020
#> GSM559386 2 0.6801 0.889 0.180 0.820
#> GSM559388 2 0.5842 0.919 0.140 0.860
#> GSM559389 1 0.1414 0.931 0.980 0.020
#> GSM559390 1 0.0000 0.930 1.000 0.000
#> GSM559392 2 0.5408 0.928 0.124 0.876
#> GSM559393 2 0.6801 0.889 0.180 0.820
#> GSM559394 1 0.1414 0.931 0.980 0.020
#> GSM559396 1 0.5519 0.867 0.872 0.128
#> GSM559398 2 0.5408 0.928 0.124 0.876
#> GSM559399 1 0.1414 0.931 0.980 0.020
#> GSM559400 2 0.3584 0.889 0.068 0.932
#> GSM559402 1 0.1414 0.931 0.980 0.020
#> GSM559403 1 0.1414 0.931 0.980 0.020
#> GSM559404 1 0.3274 0.906 0.940 0.060
#> GSM559405 1 0.1414 0.931 0.980 0.020
#> GSM559406 1 0.0000 0.930 1.000 0.000
#> GSM559407 1 0.1414 0.931 0.980 0.020
#> GSM559408 1 0.0672 0.931 0.992 0.008
#> GSM559409 1 0.0672 0.931 0.992 0.008
#> GSM559410 1 0.1414 0.931 0.980 0.020
#> GSM559411 1 0.0000 0.930 1.000 0.000
#> GSM559412 1 0.0000 0.930 1.000 0.000
#> GSM559413 1 0.2603 0.913 0.956 0.044
#> GSM559415 1 0.1414 0.931 0.980 0.020
#> GSM559416 1 0.0672 0.931 0.992 0.008
#> GSM559417 2 0.9552 0.607 0.376 0.624
#> GSM559418 2 0.6801 0.889 0.180 0.820
#> GSM559419 1 0.1414 0.931 0.980 0.020
#> GSM559420 1 0.1414 0.931 0.980 0.020
#> GSM559421 2 0.5408 0.928 0.124 0.876
#> GSM559423 2 0.5408 0.928 0.124 0.876
#> GSM559425 2 0.5408 0.928 0.124 0.876
#> GSM559426 2 0.5408 0.928 0.124 0.876
#> GSM559427 2 0.5408 0.928 0.124 0.876
#> GSM559428 2 0.0000 0.871 0.000 1.000
#> GSM559429 2 0.0000 0.871 0.000 1.000
#> GSM559430 2 0.5408 0.928 0.124 0.876
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.000 1.000 0.000 0.000 1
#> GSM559387 3 0.000 1.000 0.000 0.000 1
#> GSM559391 3 0.000 1.000 0.000 0.000 1
#> GSM559395 3 0.000 1.000 0.000 0.000 1
#> GSM559397 3 0.000 1.000 0.000 0.000 1
#> GSM559401 3 0.000 1.000 0.000 0.000 1
#> GSM559414 3 0.000 1.000 0.000 0.000 1
#> GSM559422 3 0.000 1.000 0.000 0.000 1
#> GSM559424 3 0.000 1.000 0.000 0.000 1
#> GSM559431 2 0.000 0.956 0.000 1.000 0
#> GSM559432 3 0.000 1.000 0.000 0.000 1
#> GSM559381 1 0.000 1.000 1.000 0.000 0
#> GSM559382 2 0.000 0.956 0.000 1.000 0
#> GSM559384 1 0.000 1.000 1.000 0.000 0
#> GSM559385 1 0.000 1.000 1.000 0.000 0
#> GSM559386 2 0.000 0.956 0.000 1.000 0
#> GSM559388 2 0.000 0.956 0.000 1.000 0
#> GSM559389 1 0.000 1.000 1.000 0.000 0
#> GSM559390 1 0.000 1.000 1.000 0.000 0
#> GSM559392 2 0.000 0.956 0.000 1.000 0
#> GSM559393 2 0.362 0.809 0.136 0.864 0
#> GSM559394 1 0.000 1.000 1.000 0.000 0
#> GSM559396 3 0.000 1.000 0.000 0.000 1
#> GSM559398 2 0.000 0.956 0.000 1.000 0
#> GSM559399 1 0.000 1.000 1.000 0.000 0
#> GSM559400 2 0.000 0.956 0.000 1.000 0
#> GSM559402 1 0.000 1.000 1.000 0.000 0
#> GSM559403 1 0.000 1.000 1.000 0.000 0
#> GSM559404 1 0.000 1.000 1.000 0.000 0
#> GSM559405 1 0.000 1.000 1.000 0.000 0
#> GSM559406 1 0.000 1.000 1.000 0.000 0
#> GSM559407 1 0.000 1.000 1.000 0.000 0
#> GSM559408 1 0.000 1.000 1.000 0.000 0
#> GSM559409 1 0.000 1.000 1.000 0.000 0
#> GSM559410 1 0.000 1.000 1.000 0.000 0
#> GSM559411 1 0.000 1.000 1.000 0.000 0
#> GSM559412 1 0.000 1.000 1.000 0.000 0
#> GSM559413 1 0.000 1.000 1.000 0.000 0
#> GSM559415 1 0.000 1.000 1.000 0.000 0
#> GSM559416 1 0.000 1.000 1.000 0.000 0
#> GSM559417 1 0.000 1.000 1.000 0.000 0
#> GSM559418 2 0.623 0.250 0.436 0.564 0
#> GSM559419 1 0.000 1.000 1.000 0.000 0
#> GSM559420 1 0.000 1.000 1.000 0.000 0
#> GSM559421 2 0.000 0.956 0.000 1.000 0
#> GSM559423 2 0.000 0.956 0.000 1.000 0
#> GSM559425 2 0.000 0.956 0.000 1.000 0
#> GSM559426 2 0.000 0.956 0.000 1.000 0
#> GSM559427 2 0.000 0.956 0.000 1.000 0
#> GSM559428 2 0.000 0.956 0.000 1.000 0
#> GSM559429 2 0.000 0.956 0.000 1.000 0
#> GSM559430 2 0.000 0.956 0.000 1.000 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.0000 0.989 0.000 0.000 1.00 0.000
#> GSM559387 3 0.0000 0.989 0.000 0.000 1.00 0.000
#> GSM559391 3 0.0000 0.989 0.000 0.000 1.00 0.000
#> GSM559395 3 0.0000 0.989 0.000 0.000 1.00 0.000
#> GSM559397 3 0.0000 0.989 0.000 0.000 1.00 0.000
#> GSM559401 3 0.0000 0.989 0.000 0.000 1.00 0.000
#> GSM559414 3 0.0000 0.989 0.000 0.000 1.00 0.000
#> GSM559422 3 0.0000 0.989 0.000 0.000 1.00 0.000
#> GSM559424 3 0.0000 0.989 0.000 0.000 1.00 0.000
#> GSM559431 2 0.0000 0.986 0.000 1.000 0.00 0.000
#> GSM559432 3 0.1637 0.932 0.000 0.060 0.94 0.000
#> GSM559381 1 0.2921 0.830 0.860 0.000 0.00 0.140
#> GSM559382 2 0.0000 0.986 0.000 1.000 0.00 0.000
#> GSM559384 1 0.3311 0.806 0.828 0.000 0.00 0.172
#> GSM559385 1 0.0000 0.848 1.000 0.000 0.00 0.000
#> GSM559386 2 0.2775 0.894 0.084 0.896 0.00 0.020
#> GSM559388 2 0.0000 0.986 0.000 1.000 0.00 0.000
#> GSM559389 1 0.0707 0.851 0.980 0.000 0.00 0.020
#> GSM559390 4 0.0707 0.917 0.020 0.000 0.00 0.980
#> GSM559392 2 0.0000 0.986 0.000 1.000 0.00 0.000
#> GSM559393 1 0.1389 0.826 0.952 0.048 0.00 0.000
#> GSM559394 1 0.0336 0.847 0.992 0.000 0.00 0.008
#> GSM559396 3 0.1211 0.954 0.000 0.000 0.96 0.040
#> GSM559398 2 0.0000 0.986 0.000 1.000 0.00 0.000
#> GSM559399 1 0.2345 0.827 0.900 0.000 0.00 0.100
#> GSM559400 2 0.2345 0.891 0.000 0.900 0.00 0.100
#> GSM559402 1 0.4382 0.665 0.704 0.000 0.00 0.296
#> GSM559403 1 0.0188 0.849 0.996 0.000 0.00 0.004
#> GSM559404 1 0.2760 0.837 0.872 0.000 0.00 0.128
#> GSM559405 1 0.2530 0.842 0.888 0.000 0.00 0.112
#> GSM559406 4 0.2216 0.936 0.092 0.000 0.00 0.908
#> GSM559407 1 0.4585 0.605 0.668 0.000 0.00 0.332
#> GSM559408 4 0.2345 0.937 0.100 0.000 0.00 0.900
#> GSM559409 4 0.2469 0.933 0.108 0.000 0.00 0.892
#> GSM559410 1 0.2345 0.847 0.900 0.000 0.00 0.100
#> GSM559411 4 0.2408 0.937 0.104 0.000 0.00 0.896
#> GSM559412 4 0.2408 0.937 0.104 0.000 0.00 0.896
#> GSM559413 4 0.2408 0.937 0.104 0.000 0.00 0.896
#> GSM559415 1 0.2345 0.810 0.900 0.000 0.00 0.100
#> GSM559416 4 0.0592 0.901 0.016 0.000 0.00 0.984
#> GSM559417 4 0.0779 0.898 0.016 0.004 0.00 0.980
#> GSM559418 1 0.2924 0.801 0.884 0.016 0.00 0.100
#> GSM559419 4 0.0817 0.903 0.024 0.000 0.00 0.976
#> GSM559420 1 0.4907 0.458 0.580 0.000 0.00 0.420
#> GSM559421 2 0.0000 0.986 0.000 1.000 0.00 0.000
#> GSM559423 2 0.0000 0.986 0.000 1.000 0.00 0.000
#> GSM559425 2 0.0000 0.986 0.000 1.000 0.00 0.000
#> GSM559426 2 0.0000 0.986 0.000 1.000 0.00 0.000
#> GSM559427 2 0.0000 0.986 0.000 1.000 0.00 0.000
#> GSM559428 2 0.0000 0.986 0.000 1.000 0.00 0.000
#> GSM559429 2 0.0000 0.986 0.000 1.000 0.00 0.000
#> GSM559430 2 0.0000 0.986 0.000 1.000 0.00 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559383 3 0.0000 0.93187 0.000 0.000 1.000 0.000 0.000
#> GSM559387 3 0.0000 0.93187 0.000 0.000 1.000 0.000 0.000
#> GSM559391 3 0.0000 0.93187 0.000 0.000 1.000 0.000 0.000
#> GSM559395 3 0.0000 0.93187 0.000 0.000 1.000 0.000 0.000
#> GSM559397 3 0.0000 0.93187 0.000 0.000 1.000 0.000 0.000
#> GSM559401 3 0.0000 0.93187 0.000 0.000 1.000 0.000 0.000
#> GSM559414 3 0.0000 0.93187 0.000 0.000 1.000 0.000 0.000
#> GSM559422 3 0.0898 0.91630 0.020 0.000 0.972 0.008 0.000
#> GSM559424 3 0.0000 0.93187 0.000 0.000 1.000 0.000 0.000
#> GSM559431 2 0.0404 0.93341 0.012 0.988 0.000 0.000 0.000
#> GSM559432 3 0.2899 0.81573 0.020 0.100 0.872 0.008 0.000
#> GSM559381 1 0.4138 0.43833 0.708 0.000 0.000 0.016 0.276
#> GSM559382 2 0.2599 0.89530 0.044 0.904 0.000 0.024 0.028
#> GSM559384 1 0.3452 0.59517 0.820 0.000 0.000 0.032 0.148
#> GSM559385 5 0.0880 0.77085 0.032 0.000 0.000 0.000 0.968
#> GSM559386 2 0.6471 0.54140 0.084 0.612 0.000 0.076 0.228
#> GSM559388 2 0.1173 0.92553 0.020 0.964 0.000 0.012 0.004
#> GSM559389 5 0.4063 0.53087 0.280 0.000 0.000 0.012 0.708
#> GSM559390 4 0.3848 0.60543 0.172 0.000 0.000 0.788 0.040
#> GSM559392 2 0.0324 0.93570 0.004 0.992 0.000 0.004 0.000
#> GSM559393 5 0.1041 0.75024 0.032 0.004 0.000 0.000 0.964
#> GSM559394 5 0.0963 0.77309 0.036 0.000 0.000 0.000 0.964
#> GSM559396 3 0.5328 0.16023 0.468 0.000 0.492 0.028 0.012
#> GSM559398 2 0.0324 0.93570 0.004 0.992 0.000 0.004 0.000
#> GSM559399 5 0.5166 0.69407 0.108 0.000 0.000 0.212 0.680
#> GSM559400 2 0.4674 0.59481 0.024 0.676 0.000 0.292 0.008
#> GSM559402 1 0.3192 0.61203 0.848 0.000 0.000 0.040 0.112
#> GSM559403 5 0.1608 0.76137 0.072 0.000 0.000 0.000 0.928
#> GSM559404 1 0.4622 0.56231 0.684 0.000 0.000 0.040 0.276
#> GSM559405 1 0.4256 0.17987 0.564 0.000 0.000 0.000 0.436
#> GSM559406 4 0.4626 0.37314 0.364 0.000 0.000 0.616 0.020
#> GSM559407 1 0.3705 0.60676 0.816 0.000 0.000 0.064 0.120
#> GSM559408 4 0.4829 0.04987 0.480 0.000 0.000 0.500 0.020
#> GSM559409 1 0.4848 0.00951 0.556 0.000 0.000 0.420 0.024
#> GSM559410 5 0.5043 0.29642 0.356 0.000 0.000 0.044 0.600
#> GSM559411 1 0.3992 0.39913 0.720 0.000 0.000 0.268 0.012
#> GSM559412 1 0.4744 0.08718 0.572 0.000 0.000 0.408 0.020
#> GSM559413 1 0.4437 0.32171 0.664 0.000 0.000 0.316 0.020
#> GSM559415 5 0.4342 0.71817 0.040 0.000 0.000 0.232 0.728
#> GSM559416 4 0.0963 0.66264 0.036 0.000 0.000 0.964 0.000
#> GSM559417 4 0.0963 0.66264 0.036 0.000 0.000 0.964 0.000
#> GSM559418 5 0.4587 0.71954 0.040 0.008 0.000 0.228 0.724
#> GSM559419 4 0.3409 0.60079 0.144 0.000 0.000 0.824 0.032
#> GSM559420 1 0.4277 0.52844 0.768 0.000 0.000 0.156 0.076
#> GSM559421 2 0.0162 0.93632 0.000 0.996 0.000 0.004 0.000
#> GSM559423 2 0.0000 0.93655 0.000 1.000 0.000 0.000 0.000
#> GSM559425 2 0.0000 0.93655 0.000 1.000 0.000 0.000 0.000
#> GSM559426 2 0.0162 0.93625 0.004 0.996 0.000 0.000 0.000
#> GSM559427 2 0.0000 0.93655 0.000 1.000 0.000 0.000 0.000
#> GSM559428 2 0.2312 0.89764 0.060 0.912 0.000 0.012 0.016
#> GSM559429 2 0.0703 0.93037 0.024 0.976 0.000 0.000 0.000
#> GSM559430 2 0.0000 0.93655 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
#> GSM559383 3 0.0000 0.9008 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559387 3 0.0000 0.9008 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559391 3 0.0000 0.9008 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559395 3 0.0000 0.9008 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559397 3 0.0146 0.9002 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM559401 3 0.0603 0.8939 0.000 0.000 0.980 0.000 0.004 0.016
#> GSM559414 3 0.0146 0.9002 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM559422 3 0.2331 0.8394 0.000 0.000 0.888 0.000 0.032 0.080
#> GSM559424 3 0.0000 0.9008 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559431 2 0.0777 0.8650 0.000 0.972 0.000 0.000 0.004 0.024
#> GSM559432 3 0.4357 0.7202 0.000 0.104 0.768 0.000 0.040 0.088
#> GSM559381 6 0.6162 0.4505 0.208 0.008 0.000 0.216 0.020 0.548
#> GSM559382 2 0.4776 0.7254 0.036 0.712 0.000 0.000 0.068 0.184
#> GSM559384 6 0.6296 0.3114 0.112 0.000 0.000 0.416 0.052 0.420
#> GSM559385 1 0.1245 0.5486 0.952 0.000 0.000 0.032 0.000 0.016
#> GSM559386 2 0.7442 0.2179 0.156 0.376 0.000 0.020 0.100 0.348
#> GSM559388 2 0.2803 0.8225 0.004 0.864 0.000 0.000 0.048 0.084
#> GSM559389 1 0.5171 -0.0855 0.512 0.000 0.000 0.076 0.004 0.408
#> GSM559390 5 0.6290 0.3795 0.032 0.000 0.000 0.332 0.472 0.164
#> GSM559392 2 0.1088 0.8641 0.000 0.960 0.000 0.000 0.024 0.016
#> GSM559393 1 0.2122 0.5059 0.900 0.000 0.000 0.000 0.024 0.076
#> GSM559394 1 0.1218 0.5573 0.956 0.000 0.000 0.028 0.012 0.004
#> GSM559396 3 0.7120 -0.2563 0.008 0.000 0.352 0.236 0.056 0.348
#> GSM559398 2 0.0914 0.8661 0.000 0.968 0.000 0.000 0.016 0.016
#> GSM559399 1 0.6584 0.3921 0.460 0.000 0.000 0.056 0.320 0.164
#> GSM559400 2 0.5827 0.4348 0.008 0.552 0.000 0.012 0.300 0.128
#> GSM559402 4 0.5516 -0.3115 0.080 0.000 0.000 0.584 0.032 0.304
#> GSM559403 1 0.2309 0.5359 0.888 0.000 0.000 0.084 0.000 0.028
#> GSM559404 4 0.5438 -0.0924 0.284 0.000 0.000 0.572 0.004 0.140
#> GSM559405 1 0.6572 -0.3497 0.372 0.000 0.000 0.332 0.024 0.272
#> GSM559406 4 0.4527 0.1761 0.012 0.000 0.000 0.664 0.284 0.040
#> GSM559407 4 0.5421 -0.1219 0.088 0.000 0.000 0.636 0.040 0.236
#> GSM559408 4 0.3420 0.3876 0.008 0.000 0.000 0.776 0.204 0.012
#> GSM559409 4 0.3033 0.5010 0.012 0.000 0.000 0.848 0.108 0.032
#> GSM559410 1 0.6041 0.1823 0.512 0.000 0.000 0.348 0.068 0.072
#> GSM559411 4 0.1297 0.4896 0.000 0.000 0.000 0.948 0.012 0.040
#> GSM559412 4 0.2400 0.5153 0.004 0.000 0.000 0.872 0.116 0.008
#> GSM559413 4 0.0692 0.5237 0.000 0.000 0.000 0.976 0.020 0.004
#> GSM559415 1 0.5218 0.4308 0.544 0.000 0.000 0.012 0.376 0.068
#> GSM559416 5 0.3329 0.7382 0.004 0.000 0.000 0.236 0.756 0.004
#> GSM559417 5 0.3543 0.7394 0.004 0.000 0.000 0.212 0.764 0.020
#> GSM559418 1 0.5269 0.4174 0.532 0.008 0.000 0.000 0.380 0.080
#> GSM559419 5 0.4988 0.6208 0.024 0.000 0.000 0.224 0.672 0.080
#> GSM559420 4 0.6570 -0.4708 0.052 0.000 0.000 0.400 0.156 0.392
#> GSM559421 2 0.0508 0.8688 0.000 0.984 0.000 0.000 0.004 0.012
#> GSM559423 2 0.0260 0.8696 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM559425 2 0.0146 0.8693 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM559426 2 0.0806 0.8668 0.000 0.972 0.000 0.000 0.008 0.020
#> GSM559427 2 0.0000 0.8697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559428 2 0.4312 0.7237 0.008 0.724 0.000 0.000 0.064 0.204
#> GSM559429 2 0.2679 0.8178 0.000 0.864 0.000 0.000 0.040 0.096
#> GSM559430 2 0.0000 0.8697 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:skmeans 52 6.10e-01 2
#> CV:skmeans 51 1.98e-09 3
#> CV:skmeans 51 1.01e-08 4
#> CV:skmeans 42 1.66e-07 5
#> CV:skmeans 33 8.40e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "pam"]
# you can also extract it by
# res = res_list["CV:pam"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.975 0.974 0.3202 0.683 0.683
#> 3 3 0.999 0.962 0.985 0.7828 0.743 0.624
#> 4 4 0.832 0.895 0.944 0.2335 0.860 0.677
#> 5 5 0.825 0.886 0.934 0.0233 0.988 0.959
#> 6 6 0.850 0.830 0.917 0.0230 0.993 0.976
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM559383 2 0.358 0.992 0.068 0.932
#> GSM559387 2 0.358 0.992 0.068 0.932
#> GSM559391 2 0.358 0.992 0.068 0.932
#> GSM559395 2 0.358 0.992 0.068 0.932
#> GSM559397 2 0.358 0.992 0.068 0.932
#> GSM559401 2 0.358 0.992 0.068 0.932
#> GSM559414 2 0.358 0.992 0.068 0.932
#> GSM559422 2 0.358 0.992 0.068 0.932
#> GSM559424 2 0.358 0.992 0.068 0.932
#> GSM559431 1 0.358 0.945 0.932 0.068
#> GSM559432 2 0.000 0.929 0.000 1.000
#> GSM559381 1 0.000 0.981 1.000 0.000
#> GSM559382 1 0.000 0.981 1.000 0.000
#> GSM559384 1 0.000 0.981 1.000 0.000
#> GSM559385 1 0.000 0.981 1.000 0.000
#> GSM559386 1 0.000 0.981 1.000 0.000
#> GSM559388 1 0.118 0.973 0.984 0.016
#> GSM559389 1 0.000 0.981 1.000 0.000
#> GSM559390 1 0.000 0.981 1.000 0.000
#> GSM559392 1 0.358 0.945 0.932 0.068
#> GSM559393 1 0.000 0.981 1.000 0.000
#> GSM559394 1 0.000 0.981 1.000 0.000
#> GSM559396 1 0.000 0.981 1.000 0.000
#> GSM559398 1 0.358 0.945 0.932 0.068
#> GSM559399 1 0.000 0.981 1.000 0.000
#> GSM559400 1 0.311 0.952 0.944 0.056
#> GSM559402 1 0.000 0.981 1.000 0.000
#> GSM559403 1 0.000 0.981 1.000 0.000
#> GSM559404 1 0.000 0.981 1.000 0.000
#> GSM559405 1 0.000 0.981 1.000 0.000
#> GSM559406 1 0.000 0.981 1.000 0.000
#> GSM559407 1 0.000 0.981 1.000 0.000
#> GSM559408 1 0.000 0.981 1.000 0.000
#> GSM559409 1 0.000 0.981 1.000 0.000
#> GSM559410 1 0.000 0.981 1.000 0.000
#> GSM559411 1 0.000 0.981 1.000 0.000
#> GSM559412 1 0.000 0.981 1.000 0.000
#> GSM559413 1 0.000 0.981 1.000 0.000
#> GSM559415 1 0.000 0.981 1.000 0.000
#> GSM559416 1 0.000 0.981 1.000 0.000
#> GSM559417 1 0.000 0.981 1.000 0.000
#> GSM559418 1 0.000 0.981 1.000 0.000
#> GSM559419 1 0.000 0.981 1.000 0.000
#> GSM559420 1 0.000 0.981 1.000 0.000
#> GSM559421 1 0.358 0.945 0.932 0.068
#> GSM559423 1 0.358 0.945 0.932 0.068
#> GSM559425 1 0.358 0.945 0.932 0.068
#> GSM559426 1 0.358 0.945 0.932 0.068
#> GSM559427 1 0.358 0.945 0.932 0.068
#> GSM559428 1 0.000 0.981 1.000 0.000
#> GSM559429 1 0.295 0.954 0.948 0.052
#> GSM559430 1 0.358 0.945 0.932 0.068
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.0000 0.979 0.000 0.000 1.00
#> GSM559387 3 0.0000 0.979 0.000 0.000 1.00
#> GSM559391 3 0.0000 0.979 0.000 0.000 1.00
#> GSM559395 3 0.0000 0.979 0.000 0.000 1.00
#> GSM559397 3 0.0000 0.979 0.000 0.000 1.00
#> GSM559401 3 0.0000 0.979 0.000 0.000 1.00
#> GSM559414 3 0.0000 0.979 0.000 0.000 1.00
#> GSM559422 3 0.0000 0.979 0.000 0.000 1.00
#> GSM559424 3 0.0000 0.979 0.000 0.000 1.00
#> GSM559431 2 0.0000 0.942 0.000 1.000 0.00
#> GSM559432 3 0.4291 0.775 0.000 0.180 0.82
#> GSM559381 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559382 1 0.0747 0.977 0.984 0.016 0.00
#> GSM559384 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559385 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559386 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559388 1 0.4399 0.760 0.812 0.188 0.00
#> GSM559389 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559390 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559392 2 0.1529 0.909 0.040 0.960 0.00
#> GSM559393 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559394 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559396 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559398 2 0.0000 0.942 0.000 1.000 0.00
#> GSM559399 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559400 2 0.5431 0.578 0.284 0.716 0.00
#> GSM559402 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559403 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559404 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559405 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559406 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559407 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559408 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559409 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559410 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559411 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559412 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559413 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559415 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559416 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559417 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559418 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559419 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559420 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559421 2 0.0000 0.942 0.000 1.000 0.00
#> GSM559423 2 0.0000 0.942 0.000 1.000 0.00
#> GSM559425 2 0.0000 0.942 0.000 1.000 0.00
#> GSM559426 2 0.0000 0.942 0.000 1.000 0.00
#> GSM559427 2 0.0000 0.942 0.000 1.000 0.00
#> GSM559428 1 0.0000 0.993 1.000 0.000 0.00
#> GSM559429 2 0.2261 0.876 0.068 0.932 0.00
#> GSM559430 2 0.0000 0.942 0.000 1.000 0.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.0000 0.978 0.000 0.000 1.00 0.000
#> GSM559387 3 0.0000 0.978 0.000 0.000 1.00 0.000
#> GSM559391 3 0.0000 0.978 0.000 0.000 1.00 0.000
#> GSM559395 3 0.0000 0.978 0.000 0.000 1.00 0.000
#> GSM559397 3 0.0000 0.978 0.000 0.000 1.00 0.000
#> GSM559401 3 0.0000 0.978 0.000 0.000 1.00 0.000
#> GSM559414 3 0.0000 0.978 0.000 0.000 1.00 0.000
#> GSM559422 3 0.0000 0.978 0.000 0.000 1.00 0.000
#> GSM559424 3 0.0000 0.978 0.000 0.000 1.00 0.000
#> GSM559431 2 0.0000 0.977 0.000 1.000 0.00 0.000
#> GSM559432 3 0.3400 0.778 0.000 0.180 0.82 0.000
#> GSM559381 1 0.0000 0.924 1.000 0.000 0.00 0.000
#> GSM559382 4 0.3311 0.811 0.172 0.000 0.00 0.828
#> GSM559384 1 0.0000 0.924 1.000 0.000 0.00 0.000
#> GSM559385 1 0.0000 0.924 1.000 0.000 0.00 0.000
#> GSM559386 4 0.4543 0.695 0.324 0.000 0.00 0.676
#> GSM559388 4 0.5321 0.716 0.296 0.032 0.00 0.672
#> GSM559389 1 0.0000 0.924 1.000 0.000 0.00 0.000
#> GSM559390 4 0.0336 0.808 0.008 0.000 0.00 0.992
#> GSM559392 2 0.2892 0.878 0.068 0.896 0.00 0.036
#> GSM559393 1 0.0000 0.924 1.000 0.000 0.00 0.000
#> GSM559394 1 0.0000 0.924 1.000 0.000 0.00 0.000
#> GSM559396 1 0.0000 0.924 1.000 0.000 0.00 0.000
#> GSM559398 2 0.0336 0.975 0.000 0.992 0.00 0.008
#> GSM559399 1 0.0000 0.924 1.000 0.000 0.00 0.000
#> GSM559400 4 0.3219 0.809 0.164 0.000 0.00 0.836
#> GSM559402 1 0.0000 0.924 1.000 0.000 0.00 0.000
#> GSM559403 1 0.0000 0.924 1.000 0.000 0.00 0.000
#> GSM559404 1 0.0000 0.924 1.000 0.000 0.00 0.000
#> GSM559405 1 0.0000 0.924 1.000 0.000 0.00 0.000
#> GSM559406 4 0.1302 0.822 0.044 0.000 0.00 0.956
#> GSM559407 1 0.1637 0.893 0.940 0.000 0.00 0.060
#> GSM559408 1 0.3219 0.823 0.836 0.000 0.00 0.164
#> GSM559409 1 0.3219 0.823 0.836 0.000 0.00 0.164
#> GSM559410 1 0.3219 0.823 0.836 0.000 0.00 0.164
#> GSM559411 1 0.3219 0.823 0.836 0.000 0.00 0.164
#> GSM559412 1 0.3219 0.823 0.836 0.000 0.00 0.164
#> GSM559413 1 0.3219 0.823 0.836 0.000 0.00 0.164
#> GSM559415 1 0.0000 0.924 1.000 0.000 0.00 0.000
#> GSM559416 4 0.1118 0.822 0.036 0.000 0.00 0.964
#> GSM559417 4 0.1302 0.825 0.044 0.000 0.00 0.956
#> GSM559418 1 0.0000 0.924 1.000 0.000 0.00 0.000
#> GSM559419 1 0.1716 0.875 0.936 0.000 0.00 0.064
#> GSM559420 1 0.0000 0.924 1.000 0.000 0.00 0.000
#> GSM559421 2 0.1118 0.960 0.000 0.964 0.00 0.036
#> GSM559423 2 0.1042 0.960 0.020 0.972 0.00 0.008
#> GSM559425 2 0.0000 0.977 0.000 1.000 0.00 0.000
#> GSM559426 2 0.0000 0.977 0.000 1.000 0.00 0.000
#> GSM559427 2 0.0000 0.977 0.000 1.000 0.00 0.000
#> GSM559428 1 0.4382 0.444 0.704 0.000 0.00 0.296
#> GSM559429 2 0.0336 0.974 0.008 0.992 0.00 0.000
#> GSM559430 2 0.0000 0.977 0.000 1.000 0.00 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559383 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM559387 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM559391 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM559395 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM559397 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM559401 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM559414 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM559422 5 0.2732 1.000 0.000 0.000 0.16 0.000 0.840
#> GSM559424 3 0.0000 1.000 0.000 0.000 1.00 0.000 0.000
#> GSM559431 2 0.0000 0.942 0.000 1.000 0.00 0.000 0.000
#> GSM559432 5 0.2732 1.000 0.000 0.000 0.16 0.000 0.840
#> GSM559381 1 0.0000 0.925 1.000 0.000 0.00 0.000 0.000
#> GSM559382 4 0.3093 0.756 0.168 0.000 0.00 0.824 0.008
#> GSM559384 1 0.0000 0.925 1.000 0.000 0.00 0.000 0.000
#> GSM559385 1 0.0000 0.925 1.000 0.000 0.00 0.000 0.000
#> GSM559386 4 0.4366 0.615 0.320 0.000 0.00 0.664 0.016
#> GSM559388 4 0.5996 0.657 0.192 0.024 0.00 0.644 0.140
#> GSM559389 1 0.0000 0.925 1.000 0.000 0.00 0.000 0.000
#> GSM559390 4 0.0162 0.757 0.004 0.000 0.00 0.996 0.000
#> GSM559392 2 0.3521 0.856 0.008 0.824 0.00 0.024 0.144
#> GSM559393 1 0.0000 0.925 1.000 0.000 0.00 0.000 0.000
#> GSM559394 1 0.0000 0.925 1.000 0.000 0.00 0.000 0.000
#> GSM559396 1 0.0000 0.925 1.000 0.000 0.00 0.000 0.000
#> GSM559398 2 0.2439 0.888 0.000 0.876 0.00 0.004 0.120
#> GSM559399 1 0.0000 0.925 1.000 0.000 0.00 0.000 0.000
#> GSM559400 4 0.2773 0.756 0.164 0.000 0.00 0.836 0.000
#> GSM559402 1 0.0000 0.925 1.000 0.000 0.00 0.000 0.000
#> GSM559403 1 0.0000 0.925 1.000 0.000 0.00 0.000 0.000
#> GSM559404 1 0.0000 0.925 1.000 0.000 0.00 0.000 0.000
#> GSM559405 1 0.0000 0.925 1.000 0.000 0.00 0.000 0.000
#> GSM559406 4 0.0880 0.768 0.032 0.000 0.00 0.968 0.000
#> GSM559407 1 0.1410 0.895 0.940 0.000 0.00 0.060 0.000
#> GSM559408 1 0.2773 0.827 0.836 0.000 0.00 0.164 0.000
#> GSM559409 1 0.2773 0.827 0.836 0.000 0.00 0.164 0.000
#> GSM559410 1 0.2773 0.827 0.836 0.000 0.00 0.164 0.000
#> GSM559411 1 0.2773 0.827 0.836 0.000 0.00 0.164 0.000
#> GSM559412 1 0.2773 0.827 0.836 0.000 0.00 0.164 0.000
#> GSM559413 1 0.2773 0.827 0.836 0.000 0.00 0.164 0.000
#> GSM559415 1 0.0000 0.925 1.000 0.000 0.00 0.000 0.000
#> GSM559416 4 0.0703 0.769 0.024 0.000 0.00 0.976 0.000
#> GSM559417 4 0.0880 0.773 0.032 0.000 0.00 0.968 0.000
#> GSM559418 1 0.0000 0.925 1.000 0.000 0.00 0.000 0.000
#> GSM559419 1 0.1845 0.870 0.928 0.000 0.00 0.056 0.016
#> GSM559420 1 0.0000 0.925 1.000 0.000 0.00 0.000 0.000
#> GSM559421 2 0.3241 0.863 0.000 0.832 0.00 0.024 0.144
#> GSM559423 2 0.1082 0.934 0.008 0.964 0.00 0.000 0.028
#> GSM559425 2 0.0000 0.942 0.000 1.000 0.00 0.000 0.000
#> GSM559426 2 0.0510 0.938 0.000 0.984 0.00 0.000 0.016
#> GSM559427 2 0.0000 0.942 0.000 1.000 0.00 0.000 0.000
#> GSM559428 1 0.4206 0.444 0.696 0.000 0.00 0.288 0.016
#> GSM559429 2 0.0798 0.935 0.008 0.976 0.00 0.000 0.016
#> GSM559430 2 0.0290 0.941 0.000 0.992 0.00 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559383 3 0.0000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM559387 3 0.0000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM559391 3 0.0000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM559395 3 0.0000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM559397 3 0.0000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM559401 3 0.0000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM559414 3 0.0000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM559422 5 0.0000 1.000 0.000 0.000 0 0.000 1 0.000
#> GSM559424 3 0.0000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM559431 2 0.0146 0.796 0.000 0.996 0 0.000 0 0.004
#> GSM559432 5 0.0000 1.000 0.000 0.000 0 0.000 1 0.000
#> GSM559381 1 0.0000 0.929 1.000 0.000 0 0.000 0 0.000
#> GSM559382 4 0.3469 0.716 0.088 0.000 0 0.808 0 0.104
#> GSM559384 1 0.0000 0.929 1.000 0.000 0 0.000 0 0.000
#> GSM559385 1 0.0000 0.929 1.000 0.000 0 0.000 0 0.000
#> GSM559386 4 0.4892 0.548 0.248 0.000 0 0.640 0 0.112
#> GSM559388 4 0.5712 0.388 0.096 0.020 0 0.468 0 0.416
#> GSM559389 1 0.0000 0.929 1.000 0.000 0 0.000 0 0.000
#> GSM559390 4 0.0000 0.757 0.000 0.000 0 1.000 0 0.000
#> GSM559392 2 0.3684 0.603 0.000 0.628 0 0.000 0 0.372
#> GSM559393 1 0.1204 0.898 0.944 0.000 0 0.000 0 0.056
#> GSM559394 1 0.0000 0.929 1.000 0.000 0 0.000 0 0.000
#> GSM559396 1 0.0000 0.929 1.000 0.000 0 0.000 0 0.000
#> GSM559398 2 0.2730 0.722 0.000 0.808 0 0.000 0 0.192
#> GSM559399 1 0.0000 0.929 1.000 0.000 0 0.000 0 0.000
#> GSM559400 4 0.3327 0.719 0.088 0.000 0 0.820 0 0.092
#> GSM559402 1 0.0000 0.929 1.000 0.000 0 0.000 0 0.000
#> GSM559403 1 0.0000 0.929 1.000 0.000 0 0.000 0 0.000
#> GSM559404 1 0.0000 0.929 1.000 0.000 0 0.000 0 0.000
#> GSM559405 1 0.0000 0.929 1.000 0.000 0 0.000 0 0.000
#> GSM559406 4 0.0260 0.757 0.008 0.000 0 0.992 0 0.000
#> GSM559407 1 0.0632 0.919 0.976 0.000 0 0.024 0 0.000
#> GSM559408 1 0.2631 0.822 0.820 0.000 0 0.180 0 0.000
#> GSM559409 1 0.2631 0.822 0.820 0.000 0 0.180 0 0.000
#> GSM559410 1 0.2454 0.838 0.840 0.000 0 0.160 0 0.000
#> GSM559411 1 0.1765 0.878 0.904 0.000 0 0.096 0 0.000
#> GSM559412 1 0.2631 0.822 0.820 0.000 0 0.180 0 0.000
#> GSM559413 1 0.2631 0.822 0.820 0.000 0 0.180 0 0.000
#> GSM559415 1 0.0000 0.929 1.000 0.000 0 0.000 0 0.000
#> GSM559416 4 0.0000 0.757 0.000 0.000 0 1.000 0 0.000
#> GSM559417 4 0.0632 0.754 0.024 0.000 0 0.976 0 0.000
#> GSM559418 1 0.0000 0.929 1.000 0.000 0 0.000 0 0.000
#> GSM559419 1 0.1549 0.891 0.936 0.000 0 0.044 0 0.020
#> GSM559420 1 0.0000 0.929 1.000 0.000 0 0.000 0 0.000
#> GSM559421 2 0.3547 0.649 0.000 0.668 0 0.000 0 0.332
#> GSM559423 2 0.2416 0.763 0.000 0.844 0 0.000 0 0.156
#> GSM559425 2 0.0000 0.798 0.000 1.000 0 0.000 0 0.000
#> GSM559426 2 0.1610 0.779 0.000 0.916 0 0.000 0 0.084
#> GSM559427 2 0.0000 0.798 0.000 1.000 0 0.000 0 0.000
#> GSM559428 1 0.5048 0.344 0.616 0.000 0 0.264 0 0.120
#> GSM559429 6 0.3547 0.000 0.000 0.332 0 0.000 0 0.668
#> GSM559430 2 0.0547 0.802 0.000 0.980 0 0.000 0 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) k
#> CV:pam 52 1.99e-10 2
#> CV:pam 52 7.80e-11 3
#> CV:pam 51 6.63e-10 4
#> CV:pam 51 2.87e-09 5
#> CV:pam 49 6.75e-09 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.976 0.986 0.3306 0.683 0.683
#> 3 3 0.628 0.842 0.908 0.8546 0.716 0.584
#> 4 4 0.699 0.548 0.805 0.1460 0.925 0.811
#> 5 5 0.683 0.670 0.801 0.0472 0.851 0.607
#> 6 6 0.730 0.633 0.787 0.0484 0.948 0.830
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
#> GSM559383 2 0.0000 1.000 0.000 1.000
#> GSM559387 2 0.0000 1.000 0.000 1.000
#> GSM559391 2 0.0000 1.000 0.000 1.000
#> GSM559395 2 0.0000 1.000 0.000 1.000
#> GSM559397 2 0.0000 1.000 0.000 1.000
#> GSM559401 2 0.0000 1.000 0.000 1.000
#> GSM559414 2 0.0000 1.000 0.000 1.000
#> GSM559422 2 0.0000 1.000 0.000 1.000
#> GSM559424 2 0.0000 1.000 0.000 1.000
#> GSM559431 1 0.6148 0.844 0.848 0.152
#> GSM559432 2 0.0000 1.000 0.000 1.000
#> GSM559381 1 0.0000 0.982 1.000 0.000
#> GSM559382 1 0.1414 0.976 0.980 0.020
#> GSM559384 1 0.0000 0.982 1.000 0.000
#> GSM559385 1 0.0376 0.981 0.996 0.004
#> GSM559386 1 0.0000 0.982 1.000 0.000
#> GSM559388 1 0.1414 0.976 0.980 0.020
#> GSM559389 1 0.0000 0.982 1.000 0.000
#> GSM559390 1 0.0000 0.982 1.000 0.000
#> GSM559392 1 0.1414 0.976 0.980 0.020
#> GSM559393 1 0.0376 0.981 0.996 0.004
#> GSM559394 1 0.0376 0.981 0.996 0.004
#> GSM559396 1 0.2778 0.956 0.952 0.048
#> GSM559398 1 0.1414 0.976 0.980 0.020
#> GSM559399 1 0.0000 0.982 1.000 0.000
#> GSM559400 1 0.1414 0.976 0.980 0.020
#> GSM559402 1 0.0000 0.982 1.000 0.000
#> GSM559403 1 0.0376 0.981 0.996 0.004
#> GSM559404 1 0.0376 0.981 0.996 0.004
#> GSM559405 1 0.0000 0.982 1.000 0.000
#> GSM559406 1 0.0000 0.982 1.000 0.000
#> GSM559407 1 0.0000 0.982 1.000 0.000
#> GSM559408 1 0.0000 0.982 1.000 0.000
#> GSM559409 1 0.0000 0.982 1.000 0.000
#> GSM559410 1 0.0000 0.982 1.000 0.000
#> GSM559411 1 0.0000 0.982 1.000 0.000
#> GSM559412 1 0.0000 0.982 1.000 0.000
#> GSM559413 1 0.0000 0.982 1.000 0.000
#> GSM559415 1 0.0000 0.982 1.000 0.000
#> GSM559416 1 0.0376 0.981 0.996 0.004
#> GSM559417 1 0.0000 0.982 1.000 0.000
#> GSM559418 1 0.0000 0.982 1.000 0.000
#> GSM559419 1 0.0000 0.982 1.000 0.000
#> GSM559420 1 0.0000 0.982 1.000 0.000
#> GSM559421 1 0.1414 0.976 0.980 0.020
#> GSM559423 1 0.1414 0.976 0.980 0.020
#> GSM559425 1 0.1414 0.976 0.980 0.020
#> GSM559426 1 0.1414 0.976 0.980 0.020
#> GSM559427 1 0.1414 0.976 0.980 0.020
#> GSM559428 1 0.6148 0.844 0.848 0.152
#> GSM559429 1 0.6148 0.844 0.848 0.152
#> GSM559430 1 0.1414 0.976 0.980 0.020
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.0000 0.998 0.000 0.000 1.00
#> GSM559387 3 0.0000 0.998 0.000 0.000 1.00
#> GSM559391 3 0.0000 0.998 0.000 0.000 1.00
#> GSM559395 3 0.0000 0.998 0.000 0.000 1.00
#> GSM559397 3 0.0000 0.998 0.000 0.000 1.00
#> GSM559401 3 0.0000 0.998 0.000 0.000 1.00
#> GSM559414 3 0.0000 0.998 0.000 0.000 1.00
#> GSM559422 3 0.0000 0.998 0.000 0.000 1.00
#> GSM559424 3 0.0000 0.998 0.000 0.000 1.00
#> GSM559431 2 0.0424 0.908 0.008 0.992 0.00
#> GSM559432 3 0.0892 0.979 0.000 0.020 0.98
#> GSM559381 1 0.2796 0.846 0.908 0.092 0.00
#> GSM559382 2 0.3192 0.866 0.112 0.888 0.00
#> GSM559384 1 0.2878 0.847 0.904 0.096 0.00
#> GSM559385 1 0.4504 0.690 0.804 0.196 0.00
#> GSM559386 1 0.6095 0.468 0.608 0.392 0.00
#> GSM559388 2 0.1529 0.934 0.040 0.960 0.00
#> GSM559389 1 0.0237 0.845 0.996 0.004 0.00
#> GSM559390 1 0.4399 0.805 0.812 0.188 0.00
#> GSM559392 2 0.1411 0.936 0.036 0.964 0.00
#> GSM559393 1 0.4452 0.691 0.808 0.192 0.00
#> GSM559394 1 0.4504 0.690 0.804 0.196 0.00
#> GSM559396 1 0.5785 0.646 0.668 0.332 0.00
#> GSM559398 2 0.1411 0.936 0.036 0.964 0.00
#> GSM559399 1 0.2711 0.847 0.912 0.088 0.00
#> GSM559400 1 0.6225 0.403 0.568 0.432 0.00
#> GSM559402 1 0.0747 0.848 0.984 0.016 0.00
#> GSM559403 1 0.0424 0.844 0.992 0.008 0.00
#> GSM559404 1 0.3340 0.801 0.880 0.120 0.00
#> GSM559405 1 0.0237 0.845 0.996 0.004 0.00
#> GSM559406 1 0.4555 0.796 0.800 0.200 0.00
#> GSM559407 1 0.0237 0.845 0.996 0.004 0.00
#> GSM559408 1 0.0424 0.848 0.992 0.008 0.00
#> GSM559409 1 0.1964 0.851 0.944 0.056 0.00
#> GSM559410 1 0.0237 0.845 0.996 0.004 0.00
#> GSM559411 1 0.4452 0.802 0.808 0.192 0.00
#> GSM559412 1 0.4002 0.812 0.840 0.160 0.00
#> GSM559413 1 0.4605 0.795 0.796 0.204 0.00
#> GSM559415 1 0.1031 0.845 0.976 0.024 0.00
#> GSM559416 1 0.0000 0.845 1.000 0.000 0.00
#> GSM559417 1 0.2878 0.846 0.904 0.096 0.00
#> GSM559418 1 0.6140 0.436 0.596 0.404 0.00
#> GSM559419 1 0.0424 0.848 0.992 0.008 0.00
#> GSM559420 1 0.3816 0.820 0.852 0.148 0.00
#> GSM559421 2 0.1411 0.936 0.036 0.964 0.00
#> GSM559423 2 0.1411 0.936 0.036 0.964 0.00
#> GSM559425 2 0.1411 0.936 0.036 0.964 0.00
#> GSM559426 2 0.1289 0.933 0.032 0.968 0.00
#> GSM559427 2 0.1411 0.936 0.036 0.964 0.00
#> GSM559428 2 0.5016 0.626 0.240 0.760 0.00
#> GSM559429 2 0.4750 0.664 0.216 0.784 0.00
#> GSM559430 2 0.1411 0.936 0.036 0.964 0.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.0000 0.941 0.000 0.000 1.000 0.000
#> GSM559387 3 0.0000 0.941 0.000 0.000 1.000 0.000
#> GSM559391 3 0.0469 0.936 0.000 0.000 0.988 0.012
#> GSM559395 3 0.0000 0.941 0.000 0.000 1.000 0.000
#> GSM559397 3 0.0000 0.941 0.000 0.000 1.000 0.000
#> GSM559401 3 0.0707 0.936 0.000 0.000 0.980 0.020
#> GSM559414 3 0.0000 0.941 0.000 0.000 1.000 0.000
#> GSM559422 3 0.4431 0.798 0.000 0.000 0.696 0.304
#> GSM559424 3 0.2011 0.885 0.000 0.000 0.920 0.080
#> GSM559431 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM559432 3 0.4431 0.798 0.000 0.000 0.696 0.304
#> GSM559381 1 0.0469 0.616 0.988 0.000 0.000 0.012
#> GSM559382 2 0.2125 0.875 0.004 0.920 0.000 0.076
#> GSM559384 1 0.1022 0.616 0.968 0.000 0.000 0.032
#> GSM559385 1 0.3266 0.552 0.832 0.000 0.000 0.168
#> GSM559386 1 0.2197 0.589 0.916 0.080 0.000 0.004
#> GSM559388 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM559389 1 0.0779 0.615 0.980 0.004 0.000 0.016
#> GSM559390 4 0.4998 0.438 0.488 0.000 0.000 0.512
#> GSM559392 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM559393 1 0.3266 0.552 0.832 0.000 0.000 0.168
#> GSM559394 1 0.3266 0.552 0.832 0.000 0.000 0.168
#> GSM559396 1 0.7100 -0.149 0.512 0.084 0.016 0.388
#> GSM559398 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM559399 1 0.2081 0.602 0.916 0.000 0.000 0.084
#> GSM559400 4 0.5764 -0.181 0.028 0.452 0.000 0.520
#> GSM559402 1 0.2011 0.604 0.920 0.000 0.000 0.080
#> GSM559403 1 0.2281 0.592 0.904 0.000 0.000 0.096
#> GSM559404 1 0.3486 0.539 0.812 0.000 0.000 0.188
#> GSM559405 1 0.0779 0.615 0.980 0.004 0.000 0.016
#> GSM559406 4 0.4998 0.438 0.488 0.000 0.000 0.512
#> GSM559407 1 0.2149 0.600 0.912 0.000 0.000 0.088
#> GSM559408 1 0.4955 -0.367 0.556 0.000 0.000 0.444
#> GSM559409 1 0.4790 -0.210 0.620 0.000 0.000 0.380
#> GSM559410 1 0.2266 0.602 0.912 0.004 0.000 0.084
#> GSM559411 4 0.4998 0.438 0.488 0.000 0.000 0.512
#> GSM559412 1 0.4961 -0.389 0.552 0.000 0.000 0.448
#> GSM559413 1 0.4994 -0.505 0.520 0.000 0.000 0.480
#> GSM559415 1 0.1978 0.609 0.928 0.004 0.000 0.068
#> GSM559416 1 0.4955 -0.337 0.556 0.000 0.000 0.444
#> GSM559417 1 0.4955 -0.337 0.556 0.000 0.000 0.444
#> GSM559418 1 0.2542 0.585 0.904 0.084 0.000 0.012
#> GSM559419 1 0.4955 -0.337 0.556 0.000 0.000 0.444
#> GSM559420 1 0.4477 0.160 0.688 0.000 0.000 0.312
#> GSM559421 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM559423 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM559425 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM559426 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM559427 2 0.0000 0.938 0.000 1.000 0.000 0.000
#> GSM559428 2 0.7002 0.339 0.164 0.568 0.000 0.268
#> GSM559429 2 0.4370 0.739 0.156 0.800 0.000 0.044
#> GSM559430 2 0.0000 0.938 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
#> GSM559383 3 0.0000 0.9764 0.000 0.000 1.000 0.000 0.000
#> GSM559387 3 0.0000 0.9764 0.000 0.000 1.000 0.000 0.000
#> GSM559391 3 0.0000 0.9764 0.000 0.000 1.000 0.000 0.000
#> GSM559395 3 0.0000 0.9764 0.000 0.000 1.000 0.000 0.000
#> GSM559397 3 0.0000 0.9764 0.000 0.000 1.000 0.000 0.000
#> GSM559401 3 0.2561 0.8196 0.000 0.000 0.856 0.000 0.144
#> GSM559414 3 0.0000 0.9764 0.000 0.000 1.000 0.000 0.000
#> GSM559422 5 0.5645 -0.0982 0.000 0.000 0.376 0.084 0.540
#> GSM559424 3 0.0162 0.9738 0.000 0.000 0.996 0.004 0.000
#> GSM559431 2 0.3174 0.8610 0.004 0.844 0.020 0.132 0.000
#> GSM559432 5 0.5645 -0.0982 0.000 0.000 0.376 0.084 0.540
#> GSM559381 1 0.4403 0.5500 0.560 0.004 0.000 0.000 0.436
#> GSM559382 2 0.4078 0.8050 0.096 0.816 0.000 0.064 0.024
#> GSM559384 1 0.4415 0.5466 0.552 0.004 0.000 0.000 0.444
#> GSM559385 4 0.6172 0.9703 0.176 0.000 0.000 0.544 0.280
#> GSM559386 1 0.6932 0.3911 0.480 0.064 0.000 0.092 0.364
#> GSM559388 2 0.0000 0.8913 0.000 1.000 0.000 0.000 0.000
#> GSM559389 1 0.6038 0.3341 0.448 0.004 0.000 0.100 0.448
#> GSM559390 1 0.2753 0.5558 0.856 0.000 0.000 0.136 0.008
#> GSM559392 2 0.0000 0.8913 0.000 1.000 0.000 0.000 0.000
#> GSM559393 4 0.6248 0.9518 0.176 0.000 0.000 0.524 0.300
#> GSM559394 4 0.6172 0.9703 0.176 0.000 0.000 0.544 0.280
#> GSM559396 1 0.4610 0.4931 0.760 0.008 0.000 0.140 0.092
#> GSM559398 2 0.1544 0.8853 0.000 0.932 0.000 0.068 0.000
#> GSM559399 1 0.4273 0.5452 0.552 0.000 0.000 0.000 0.448
#> GSM559400 2 0.6488 0.4816 0.272 0.516 0.000 0.208 0.004
#> GSM559402 1 0.4403 0.5500 0.560 0.004 0.000 0.000 0.436
#> GSM559403 5 0.6145 -0.6789 0.436 0.004 0.000 0.112 0.448
#> GSM559404 4 0.6066 0.9338 0.188 0.000 0.000 0.572 0.240
#> GSM559405 1 0.4425 0.5393 0.544 0.004 0.000 0.000 0.452
#> GSM559406 1 0.1341 0.5634 0.944 0.000 0.000 0.056 0.000
#> GSM559407 1 0.4201 0.5618 0.592 0.000 0.000 0.000 0.408
#> GSM559408 1 0.1544 0.6212 0.932 0.000 0.000 0.000 0.068
#> GSM559409 1 0.1792 0.6228 0.916 0.000 0.000 0.000 0.084
#> GSM559410 1 0.4273 0.5452 0.552 0.000 0.000 0.000 0.448
#> GSM559411 1 0.0451 0.5942 0.988 0.000 0.000 0.008 0.004
#> GSM559412 1 0.1571 0.6192 0.936 0.000 0.000 0.004 0.060
#> GSM559413 1 0.1106 0.6069 0.964 0.000 0.000 0.012 0.024
#> GSM559415 1 0.4425 0.5393 0.544 0.004 0.000 0.000 0.452
#> GSM559416 1 0.2798 0.5032 0.852 0.000 0.000 0.140 0.008
#> GSM559417 1 0.2136 0.5691 0.904 0.000 0.000 0.088 0.008
#> GSM559418 1 0.4425 0.5393 0.544 0.004 0.000 0.000 0.452
#> GSM559419 1 0.0290 0.5985 0.992 0.000 0.000 0.000 0.008
#> GSM559420 1 0.3109 0.5941 0.800 0.000 0.000 0.000 0.200
#> GSM559421 2 0.0404 0.8916 0.000 0.988 0.000 0.012 0.000
#> GSM559423 2 0.0000 0.8913 0.000 1.000 0.000 0.000 0.000
#> GSM559425 2 0.1544 0.8853 0.000 0.932 0.000 0.068 0.000
#> GSM559426 2 0.0566 0.8891 0.000 0.984 0.000 0.012 0.004
#> GSM559427 2 0.1544 0.8853 0.000 0.932 0.000 0.068 0.000
#> GSM559428 2 0.5887 0.6786 0.164 0.668 0.000 0.136 0.032
#> GSM559429 2 0.3351 0.8308 0.028 0.836 0.000 0.132 0.004
#> GSM559430 2 0.1544 0.8853 0.000 0.932 0.000 0.068 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559383 3 0.0000 0.933 0.000 0.000 1.000 0.000 0.000 NA
#> GSM559387 3 0.0000 0.933 0.000 0.000 1.000 0.000 0.000 NA
#> GSM559391 3 0.1556 0.902 0.000 0.000 0.920 0.000 0.000 NA
#> GSM559395 3 0.0000 0.933 0.000 0.000 1.000 0.000 0.000 NA
#> GSM559397 3 0.0000 0.933 0.000 0.000 1.000 0.000 0.000 NA
#> GSM559401 3 0.4614 0.617 0.000 0.000 0.684 0.000 0.208 NA
#> GSM559414 3 0.0000 0.933 0.000 0.000 1.000 0.000 0.000 NA
#> GSM559422 5 0.6212 -0.129 0.000 0.000 0.292 0.012 0.456 NA
#> GSM559424 3 0.1556 0.902 0.000 0.000 0.920 0.000 0.000 NA
#> GSM559431 2 0.4110 0.737 0.000 0.608 0.000 0.016 0.000 NA
#> GSM559432 5 0.6216 -0.124 0.000 0.000 0.288 0.012 0.456 NA
#> GSM559381 1 0.0000 0.695 1.000 0.000 0.000 0.000 0.000 NA
#> GSM559382 2 0.1554 0.823 0.004 0.940 0.000 0.004 0.044 NA
#> GSM559384 1 0.0551 0.694 0.984 0.000 0.000 0.004 0.004 NA
#> GSM559385 4 0.2793 0.983 0.200 0.000 0.000 0.800 0.000 NA
#> GSM559386 1 0.2402 0.603 0.856 0.140 0.000 0.000 0.004 NA
#> GSM559388 2 0.0000 0.836 0.000 1.000 0.000 0.000 0.000 NA
#> GSM559389 1 0.0000 0.695 1.000 0.000 0.000 0.000 0.000 NA
#> GSM559390 1 0.7260 0.166 0.404 0.000 0.000 0.116 0.248 NA
#> GSM559392 2 0.0000 0.836 0.000 1.000 0.000 0.000 0.000 NA
#> GSM559393 4 0.2823 0.980 0.204 0.000 0.000 0.796 0.000 NA
#> GSM559394 4 0.2793 0.983 0.200 0.000 0.000 0.800 0.000 NA
#> GSM559396 5 0.6564 -0.200 0.320 0.000 0.000 0.032 0.420 NA
#> GSM559398 2 0.3198 0.782 0.000 0.740 0.000 0.000 0.000 NA
#> GSM559399 1 0.0405 0.694 0.988 0.000 0.000 0.004 0.008 NA
#> GSM559400 2 0.6225 0.472 0.000 0.576 0.000 0.152 0.072 NA
#> GSM559402 1 0.0363 0.695 0.988 0.000 0.000 0.000 0.012 NA
#> GSM559403 1 0.2048 0.602 0.880 0.000 0.000 0.120 0.000 NA
#> GSM559404 4 0.2562 0.952 0.172 0.000 0.000 0.828 0.000 NA
#> GSM559405 1 0.0146 0.694 0.996 0.000 0.000 0.004 0.000 NA
#> GSM559406 1 0.4165 0.412 0.536 0.000 0.000 0.000 0.452 NA
#> GSM559407 1 0.1267 0.684 0.940 0.000 0.000 0.000 0.060 NA
#> GSM559408 1 0.4118 0.487 0.592 0.000 0.000 0.004 0.396 NA
#> GSM559409 1 0.4100 0.489 0.600 0.000 0.000 0.004 0.388 NA
#> GSM559410 1 0.0405 0.694 0.988 0.000 0.000 0.004 0.008 NA
#> GSM559411 5 0.3998 -0.519 0.492 0.000 0.000 0.000 0.504 NA
#> GSM559412 1 0.4127 0.486 0.588 0.000 0.000 0.004 0.400 NA
#> GSM559413 1 0.3789 0.473 0.584 0.000 0.000 0.000 0.416 NA
#> GSM559415 1 0.0146 0.694 0.996 0.000 0.000 0.004 0.000 NA
#> GSM559416 1 0.6139 0.171 0.384 0.000 0.000 0.004 0.372 NA
#> GSM559417 1 0.6208 0.223 0.416 0.000 0.000 0.012 0.364 NA
#> GSM559418 1 0.0260 0.694 0.992 0.000 0.000 0.008 0.000 NA
#> GSM559419 1 0.4124 0.369 0.516 0.000 0.000 0.004 0.476 NA
#> GSM559420 1 0.3290 0.589 0.744 0.000 0.000 0.004 0.252 NA
#> GSM559421 2 0.0632 0.838 0.000 0.976 0.000 0.000 0.000 NA
#> GSM559423 2 0.0000 0.836 0.000 1.000 0.000 0.000 0.000 NA
#> GSM559425 2 0.3330 0.774 0.000 0.716 0.000 0.000 0.000 NA
#> GSM559426 2 0.1003 0.833 0.020 0.964 0.000 0.000 0.000 NA
#> GSM559427 2 0.3330 0.774 0.000 0.716 0.000 0.000 0.000 NA
#> GSM559428 2 0.3277 0.782 0.008 0.836 0.000 0.020 0.016 NA
#> GSM559429 2 0.2745 0.799 0.000 0.860 0.000 0.020 0.008 NA
#> GSM559430 2 0.3266 0.780 0.000 0.728 0.000 0.000 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:mclust 52 1.99e-10 2
#> CV:mclust 49 3.24e-10 3
#> CV:mclust 38 5.20e-08 4
#> CV:mclust 45 1.55e-08 5
#> CV:mclust 38 3.39e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.418 0.820 0.861 0.4504 0.527 0.527
#> 3 3 1.000 0.973 0.988 0.3671 0.702 0.509
#> 4 4 0.707 0.703 0.854 0.1689 0.867 0.665
#> 5 5 0.702 0.637 0.817 0.0822 0.845 0.524
#> 6 6 0.740 0.657 0.799 0.0565 0.870 0.514
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
#> GSM559383 1 0.7815 0.756 0.768 0.232
#> GSM559387 1 0.7815 0.756 0.768 0.232
#> GSM559391 1 0.7815 0.756 0.768 0.232
#> GSM559395 1 0.7815 0.756 0.768 0.232
#> GSM559397 1 0.7815 0.756 0.768 0.232
#> GSM559401 1 0.7815 0.756 0.768 0.232
#> GSM559414 1 0.7815 0.756 0.768 0.232
#> GSM559422 1 0.7815 0.756 0.768 0.232
#> GSM559424 1 0.7815 0.756 0.768 0.232
#> GSM559431 2 0.3114 0.757 0.056 0.944
#> GSM559432 2 0.7376 0.449 0.208 0.792
#> GSM559381 1 0.7139 0.617 0.804 0.196
#> GSM559382 2 0.7815 0.928 0.232 0.768
#> GSM559384 1 0.0000 0.865 1.000 0.000
#> GSM559385 1 0.0000 0.865 1.000 0.000
#> GSM559386 2 0.7815 0.928 0.232 0.768
#> GSM559388 2 0.7815 0.928 0.232 0.768
#> GSM559389 1 0.6148 0.695 0.848 0.152
#> GSM559390 1 0.0672 0.860 0.992 0.008
#> GSM559392 2 0.7815 0.928 0.232 0.768
#> GSM559393 2 0.8016 0.916 0.244 0.756
#> GSM559394 1 0.5946 0.707 0.856 0.144
#> GSM559396 1 0.1633 0.858 0.976 0.024
#> GSM559398 2 0.7815 0.928 0.232 0.768
#> GSM559399 1 0.6247 0.688 0.844 0.156
#> GSM559400 2 0.7815 0.928 0.232 0.768
#> GSM559402 1 0.0000 0.865 1.000 0.000
#> GSM559403 1 0.0672 0.860 0.992 0.008
#> GSM559404 1 0.3274 0.844 0.940 0.060
#> GSM559405 1 0.0000 0.865 1.000 0.000
#> GSM559406 1 0.0000 0.865 1.000 0.000
#> GSM559407 1 0.0000 0.865 1.000 0.000
#> GSM559408 1 0.0000 0.865 1.000 0.000
#> GSM559409 1 0.0000 0.865 1.000 0.000
#> GSM559410 1 0.0376 0.863 0.996 0.004
#> GSM559411 1 0.0000 0.865 1.000 0.000
#> GSM559412 1 0.0000 0.865 1.000 0.000
#> GSM559413 1 0.1414 0.859 0.980 0.020
#> GSM559415 1 0.8713 0.373 0.708 0.292
#> GSM559416 1 0.0672 0.861 0.992 0.008
#> GSM559417 2 0.9963 0.524 0.464 0.536
#> GSM559418 2 0.7815 0.928 0.232 0.768
#> GSM559419 1 0.0672 0.860 0.992 0.008
#> GSM559420 1 0.0000 0.865 1.000 0.000
#> GSM559421 2 0.7815 0.928 0.232 0.768
#> GSM559423 2 0.7815 0.928 0.232 0.768
#> GSM559425 2 0.7815 0.928 0.232 0.768
#> GSM559426 2 0.7815 0.928 0.232 0.768
#> GSM559427 2 0.7815 0.928 0.232 0.768
#> GSM559428 2 0.2778 0.749 0.048 0.952
#> GSM559429 2 0.7815 0.928 0.232 0.768
#> GSM559430 2 0.7815 0.928 0.232 0.768
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559387 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559391 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559395 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559397 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559401 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559414 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559422 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559424 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559431 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559432 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559381 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559382 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559384 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559385 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559386 1 0.5178 0.664 0.744 0.256 0.000
#> GSM559388 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559389 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559390 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559392 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559393 1 0.1031 0.961 0.976 0.024 0.000
#> GSM559394 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559396 1 0.0592 0.972 0.988 0.000 0.012
#> GSM559398 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559399 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559400 2 0.3340 0.834 0.120 0.880 0.000
#> GSM559402 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559403 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559404 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559405 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559406 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559407 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559408 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559409 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559410 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559411 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559412 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559413 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559415 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559416 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559417 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559418 1 0.4235 0.790 0.824 0.176 0.000
#> GSM559419 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559420 1 0.0000 0.982 1.000 0.000 0.000
#> GSM559421 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559423 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559425 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559426 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559427 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559428 2 0.1163 0.962 0.000 0.972 0.028
#> GSM559429 2 0.0000 0.986 0.000 1.000 0.000
#> GSM559430 2 0.0000 0.986 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.4898 0.5533 0.000 0.000 0.584 0.416
#> GSM559387 3 0.3610 0.8426 0.000 0.000 0.800 0.200
#> GSM559391 4 0.4916 -0.2863 0.000 0.000 0.424 0.576
#> GSM559395 3 0.3528 0.8466 0.000 0.000 0.808 0.192
#> GSM559397 3 0.3266 0.8532 0.000 0.000 0.832 0.168
#> GSM559401 3 0.0000 0.8207 0.000 0.000 1.000 0.000
#> GSM559414 3 0.3074 0.8540 0.000 0.000 0.848 0.152
#> GSM559422 3 0.1792 0.7935 0.000 0.000 0.932 0.068
#> GSM559424 4 0.4605 -0.0161 0.000 0.000 0.336 0.664
#> GSM559431 2 0.2216 0.9130 0.000 0.908 0.000 0.092
#> GSM559432 3 0.1792 0.7935 0.000 0.000 0.932 0.068
#> GSM559381 1 0.0817 0.8122 0.976 0.000 0.000 0.024
#> GSM559382 2 0.1211 0.9229 0.000 0.960 0.000 0.040
#> GSM559384 1 0.1792 0.7837 0.932 0.000 0.000 0.068
#> GSM559385 1 0.0188 0.8168 0.996 0.000 0.000 0.004
#> GSM559386 1 0.5856 0.0931 0.504 0.464 0.000 0.032
#> GSM559388 2 0.0188 0.9411 0.000 0.996 0.000 0.004
#> GSM559389 1 0.0000 0.8183 1.000 0.000 0.000 0.000
#> GSM559390 4 0.3764 0.6726 0.172 0.000 0.012 0.816
#> GSM559392 2 0.0188 0.9411 0.000 0.996 0.000 0.004
#> GSM559393 1 0.1677 0.7830 0.948 0.040 0.000 0.012
#> GSM559394 1 0.0336 0.8149 0.992 0.000 0.000 0.008
#> GSM559396 4 0.4004 0.5641 0.164 0.000 0.024 0.812
#> GSM559398 2 0.0188 0.9411 0.000 0.996 0.000 0.004
#> GSM559399 1 0.0188 0.8177 0.996 0.000 0.000 0.004
#> GSM559400 2 0.5393 0.6034 0.000 0.688 0.044 0.268
#> GSM559402 1 0.1557 0.7961 0.944 0.000 0.000 0.056
#> GSM559403 1 0.0000 0.8183 1.000 0.000 0.000 0.000
#> GSM559404 1 0.0000 0.8183 1.000 0.000 0.000 0.000
#> GSM559405 1 0.0000 0.8183 1.000 0.000 0.000 0.000
#> GSM559406 4 0.4564 0.5831 0.328 0.000 0.000 0.672
#> GSM559407 1 0.2149 0.7738 0.912 0.000 0.000 0.088
#> GSM559408 1 0.4730 0.3549 0.636 0.000 0.000 0.364
#> GSM559409 1 0.3486 0.6669 0.812 0.000 0.000 0.188
#> GSM559410 1 0.0000 0.8183 1.000 0.000 0.000 0.000
#> GSM559411 4 0.4103 0.6607 0.256 0.000 0.000 0.744
#> GSM559412 1 0.4804 0.2988 0.616 0.000 0.000 0.384
#> GSM559413 1 0.4916 0.1617 0.576 0.000 0.000 0.424
#> GSM559415 1 0.0000 0.8183 1.000 0.000 0.000 0.000
#> GSM559416 4 0.4331 0.6372 0.288 0.000 0.000 0.712
#> GSM559417 4 0.6966 0.5239 0.268 0.160 0.000 0.572
#> GSM559418 1 0.1940 0.7662 0.924 0.076 0.000 0.000
#> GSM559419 4 0.4522 0.5953 0.320 0.000 0.000 0.680
#> GSM559420 1 0.4941 -0.0347 0.564 0.000 0.000 0.436
#> GSM559421 2 0.0000 0.9415 0.000 1.000 0.000 0.000
#> GSM559423 2 0.1389 0.9324 0.000 0.952 0.000 0.048
#> GSM559425 2 0.0592 0.9398 0.000 0.984 0.000 0.016
#> GSM559426 2 0.1389 0.9324 0.000 0.952 0.000 0.048
#> GSM559427 2 0.0000 0.9415 0.000 1.000 0.000 0.000
#> GSM559428 2 0.4662 0.8272 0.000 0.796 0.092 0.112
#> GSM559429 2 0.2149 0.9169 0.000 0.912 0.000 0.088
#> GSM559430 2 0.0000 0.9415 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
#> GSM559383 3 0.2653 0.665 0.000 0.000 0.880 0.096 0.024
#> GSM559387 3 0.0404 0.679 0.000 0.000 0.988 0.012 0.000
#> GSM559391 3 0.4615 0.577 0.000 0.000 0.700 0.252 0.048
#> GSM559395 3 0.0671 0.673 0.000 0.000 0.980 0.004 0.016
#> GSM559397 3 0.0798 0.675 0.000 0.000 0.976 0.008 0.016
#> GSM559401 3 0.4950 -0.011 0.000 0.000 0.612 0.040 0.348
#> GSM559414 3 0.0794 0.662 0.000 0.000 0.972 0.000 0.028
#> GSM559422 5 0.5058 0.316 0.000 0.000 0.384 0.040 0.576
#> GSM559424 3 0.4866 0.548 0.000 0.000 0.664 0.284 0.052
#> GSM559431 2 0.3983 0.545 0.000 0.660 0.000 0.000 0.340
#> GSM559432 5 0.5058 0.317 0.000 0.000 0.384 0.040 0.576
#> GSM559381 1 0.1915 0.855 0.928 0.000 0.000 0.040 0.032
#> GSM559382 2 0.2477 0.708 0.008 0.892 0.000 0.092 0.008
#> GSM559384 1 0.3804 0.767 0.812 0.000 0.004 0.052 0.132
#> GSM559385 1 0.0324 0.867 0.992 0.000 0.000 0.004 0.004
#> GSM559386 2 0.5688 0.289 0.372 0.548 0.000 0.076 0.004
#> GSM559388 2 0.1731 0.747 0.008 0.940 0.000 0.040 0.012
#> GSM559389 1 0.0579 0.865 0.984 0.000 0.000 0.008 0.008
#> GSM559390 4 0.1834 0.771 0.032 0.008 0.016 0.940 0.004
#> GSM559392 2 0.0451 0.773 0.000 0.988 0.000 0.004 0.008
#> GSM559393 1 0.1173 0.856 0.964 0.012 0.000 0.004 0.020
#> GSM559394 1 0.0671 0.865 0.980 0.000 0.000 0.004 0.016
#> GSM559396 3 0.7380 0.194 0.100 0.000 0.408 0.096 0.396
#> GSM559398 2 0.0324 0.772 0.000 0.992 0.000 0.004 0.004
#> GSM559399 1 0.0566 0.869 0.984 0.000 0.000 0.012 0.004
#> GSM559400 4 0.5161 0.343 0.000 0.396 0.012 0.568 0.024
#> GSM559402 1 0.3863 0.729 0.796 0.000 0.000 0.152 0.052
#> GSM559403 1 0.0324 0.867 0.992 0.000 0.000 0.004 0.004
#> GSM559404 1 0.0880 0.865 0.968 0.000 0.000 0.032 0.000
#> GSM559405 1 0.0404 0.869 0.988 0.000 0.000 0.012 0.000
#> GSM559406 4 0.1928 0.796 0.072 0.004 0.000 0.920 0.004
#> GSM559407 1 0.5114 0.337 0.608 0.000 0.000 0.340 0.052
#> GSM559408 4 0.3662 0.702 0.252 0.000 0.000 0.744 0.004
#> GSM559409 4 0.4359 0.391 0.412 0.000 0.000 0.584 0.004
#> GSM559410 1 0.0963 0.863 0.964 0.000 0.000 0.036 0.000
#> GSM559411 4 0.3823 0.736 0.064 0.000 0.028 0.836 0.072
#> GSM559412 4 0.3696 0.746 0.212 0.000 0.000 0.772 0.016
#> GSM559413 4 0.4302 0.734 0.208 0.000 0.000 0.744 0.048
#> GSM559415 1 0.0671 0.869 0.980 0.000 0.000 0.016 0.004
#> GSM559416 4 0.1444 0.785 0.040 0.012 0.000 0.948 0.000
#> GSM559417 4 0.3209 0.763 0.032 0.088 0.000 0.864 0.016
#> GSM559418 1 0.4190 0.595 0.724 0.256 0.000 0.012 0.008
#> GSM559419 4 0.2052 0.798 0.080 0.004 0.000 0.912 0.004
#> GSM559420 1 0.6656 0.176 0.492 0.000 0.028 0.360 0.120
#> GSM559421 2 0.0566 0.776 0.000 0.984 0.000 0.004 0.012
#> GSM559423 2 0.4162 0.602 0.004 0.680 0.000 0.004 0.312
#> GSM559425 2 0.1851 0.758 0.000 0.912 0.000 0.000 0.088
#> GSM559426 2 0.4181 0.595 0.004 0.676 0.000 0.004 0.316
#> GSM559427 2 0.0510 0.775 0.000 0.984 0.000 0.000 0.016
#> GSM559428 5 0.4604 -0.424 0.000 0.428 0.012 0.000 0.560
#> GSM559429 2 0.4524 0.453 0.004 0.572 0.000 0.004 0.420
#> GSM559430 2 0.0880 0.775 0.000 0.968 0.000 0.000 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559383 3 0.0000 0.9230 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559387 3 0.1387 0.9367 0.000 0.000 0.932 0.000 0.068 0.000
#> GSM559391 3 0.0363 0.9162 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM559395 3 0.1444 0.9359 0.000 0.000 0.928 0.000 0.072 0.000
#> GSM559397 3 0.1556 0.9316 0.000 0.000 0.920 0.000 0.080 0.000
#> GSM559401 5 0.3695 0.3809 0.000 0.000 0.376 0.000 0.624 0.000
#> GSM559414 3 0.1714 0.9215 0.000 0.000 0.908 0.000 0.092 0.000
#> GSM559422 5 0.1007 0.7780 0.000 0.000 0.044 0.000 0.956 0.000
#> GSM559424 3 0.0508 0.9124 0.000 0.000 0.984 0.004 0.012 0.000
#> GSM559431 6 0.5659 -0.3020 0.000 0.420 0.000 0.000 0.152 0.428
#> GSM559432 5 0.1007 0.7780 0.000 0.000 0.044 0.000 0.956 0.000
#> GSM559381 1 0.5660 0.5278 0.576 0.008 0.000 0.292 0.012 0.112
#> GSM559382 2 0.2500 0.5032 0.036 0.896 0.000 0.036 0.000 0.032
#> GSM559384 1 0.6234 0.4530 0.520 0.004 0.012 0.320 0.020 0.124
#> GSM559385 1 0.0748 0.7759 0.976 0.016 0.000 0.004 0.004 0.000
#> GSM559386 1 0.5898 0.3156 0.536 0.328 0.000 0.092 0.000 0.044
#> GSM559388 2 0.4203 0.7071 0.056 0.720 0.000 0.004 0.000 0.220
#> GSM559389 1 0.1546 0.7828 0.944 0.004 0.000 0.020 0.004 0.028
#> GSM559390 4 0.4204 0.7212 0.004 0.272 0.036 0.688 0.000 0.000
#> GSM559392 2 0.3547 0.7592 0.004 0.696 0.000 0.000 0.000 0.300
#> GSM559393 1 0.1471 0.7623 0.932 0.064 0.000 0.004 0.000 0.000
#> GSM559394 1 0.1074 0.7761 0.960 0.028 0.000 0.012 0.000 0.000
#> GSM559396 6 0.6183 0.2397 0.008 0.000 0.208 0.220 0.020 0.544
#> GSM559398 2 0.3371 0.7586 0.000 0.708 0.000 0.000 0.000 0.292
#> GSM559399 1 0.2002 0.7831 0.908 0.012 0.000 0.076 0.004 0.000
#> GSM559400 2 0.2848 0.3237 0.000 0.816 0.000 0.176 0.008 0.000
#> GSM559402 4 0.5150 0.2951 0.280 0.004 0.008 0.640 0.016 0.052
#> GSM559403 1 0.0508 0.7778 0.984 0.012 0.000 0.004 0.000 0.000
#> GSM559404 1 0.2615 0.7701 0.872 0.004 0.000 0.104 0.012 0.008
#> GSM559405 1 0.2113 0.7808 0.896 0.004 0.000 0.092 0.000 0.008
#> GSM559406 4 0.4115 0.7228 0.004 0.268 0.032 0.696 0.000 0.000
#> GSM559407 4 0.3722 0.5827 0.160 0.004 0.008 0.796 0.012 0.020
#> GSM559408 4 0.3215 0.7410 0.004 0.240 0.000 0.756 0.000 0.000
#> GSM559409 4 0.4853 0.6819 0.172 0.124 0.000 0.692 0.012 0.000
#> GSM559410 1 0.2320 0.7665 0.864 0.004 0.000 0.132 0.000 0.000
#> GSM559411 4 0.3023 0.6834 0.012 0.000 0.072 0.868 0.032 0.016
#> GSM559412 4 0.1682 0.7337 0.020 0.052 0.000 0.928 0.000 0.000
#> GSM559413 4 0.1967 0.7034 0.028 0.004 0.004 0.928 0.028 0.008
#> GSM559415 1 0.3564 0.7031 0.768 0.004 0.000 0.204 0.000 0.024
#> GSM559416 4 0.4032 0.7280 0.004 0.268 0.020 0.704 0.004 0.000
#> GSM559417 4 0.3788 0.7287 0.004 0.272 0.008 0.712 0.004 0.000
#> GSM559418 1 0.6737 -0.0452 0.424 0.348 0.000 0.068 0.000 0.160
#> GSM559419 4 0.3483 0.7470 0.004 0.176 0.024 0.792 0.004 0.000
#> GSM559420 4 0.6037 0.4411 0.096 0.008 0.044 0.640 0.020 0.192
#> GSM559421 2 0.3659 0.7517 0.000 0.636 0.000 0.000 0.000 0.364
#> GSM559423 6 0.1082 0.6229 0.000 0.040 0.000 0.004 0.000 0.956
#> GSM559425 2 0.3747 0.7239 0.000 0.604 0.000 0.000 0.000 0.396
#> GSM559426 6 0.1075 0.6129 0.000 0.048 0.000 0.000 0.000 0.952
#> GSM559427 2 0.3634 0.7551 0.000 0.644 0.000 0.000 0.000 0.356
#> GSM559428 6 0.3518 0.4793 0.000 0.012 0.000 0.000 0.256 0.732
#> GSM559429 6 0.1168 0.6402 0.000 0.016 0.000 0.000 0.028 0.956
#> GSM559430 2 0.3727 0.7356 0.000 0.612 0.000 0.000 0.000 0.388
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:NMF 50 1.22e-01 2
#> CV:NMF 52 8.27e-11 3
#> CV:NMF 45 1.58e-08 4
#> CV:NMF 41 1.10e-07 5
#> CV:NMF 42 5.89e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.685 0.833 0.931 0.3644 0.638 0.638
#> 3 3 0.385 0.617 0.801 0.5297 0.743 0.603
#> 4 4 0.408 0.609 0.741 0.1979 0.928 0.830
#> 5 5 0.577 0.615 0.756 0.1158 0.836 0.597
#> 6 6 0.642 0.567 0.755 0.0481 0.876 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
#> GSM559383 1 0.0000 0.9370 1.000 0.000
#> GSM559387 1 0.0000 0.9370 1.000 0.000
#> GSM559391 1 0.0000 0.9370 1.000 0.000
#> GSM559395 1 0.0000 0.9370 1.000 0.000
#> GSM559397 1 0.0000 0.9370 1.000 0.000
#> GSM559401 1 0.0000 0.9370 1.000 0.000
#> GSM559414 1 0.0000 0.9370 1.000 0.000
#> GSM559422 1 0.4298 0.8723 0.912 0.088
#> GSM559424 1 0.0000 0.9370 1.000 0.000
#> GSM559431 2 0.0000 0.8495 0.000 1.000
#> GSM559432 1 0.4562 0.8644 0.904 0.096
#> GSM559381 1 0.6712 0.7686 0.824 0.176
#> GSM559382 1 0.9393 0.4054 0.644 0.356
#> GSM559384 1 0.0000 0.9370 1.000 0.000
#> GSM559385 1 0.0672 0.9357 0.992 0.008
#> GSM559386 1 0.8813 0.5456 0.700 0.300
#> GSM559388 2 0.9954 0.2011 0.460 0.540
#> GSM559389 1 0.3274 0.8995 0.940 0.060
#> GSM559390 1 0.5294 0.8346 0.880 0.120
#> GSM559392 2 0.0000 0.8495 0.000 1.000
#> GSM559393 1 0.0672 0.9357 0.992 0.008
#> GSM559394 1 0.0672 0.9357 0.992 0.008
#> GSM559396 1 0.0000 0.9370 1.000 0.000
#> GSM559398 2 0.0000 0.8495 0.000 1.000
#> GSM559399 1 0.0376 0.9367 0.996 0.004
#> GSM559400 1 0.9996 -0.0374 0.512 0.488
#> GSM559402 1 0.0376 0.9367 0.996 0.004
#> GSM559403 1 0.0672 0.9357 0.992 0.008
#> GSM559404 1 0.0000 0.9370 1.000 0.000
#> GSM559405 1 0.0672 0.9358 0.992 0.008
#> GSM559406 1 0.0376 0.9362 0.996 0.004
#> GSM559407 1 0.0376 0.9367 0.996 0.004
#> GSM559408 1 0.0000 0.9370 1.000 0.000
#> GSM559409 1 0.0000 0.9370 1.000 0.000
#> GSM559410 1 0.0672 0.9357 0.992 0.008
#> GSM559411 1 0.0000 0.9370 1.000 0.000
#> GSM559412 1 0.0000 0.9370 1.000 0.000
#> GSM559413 1 0.0000 0.9370 1.000 0.000
#> GSM559415 1 0.2043 0.9219 0.968 0.032
#> GSM559416 1 0.6048 0.8083 0.852 0.148
#> GSM559417 1 0.6148 0.8032 0.848 0.152
#> GSM559418 1 0.2423 0.9162 0.960 0.040
#> GSM559419 1 0.0376 0.9367 0.996 0.004
#> GSM559420 1 0.0376 0.9367 0.996 0.004
#> GSM559421 2 0.0000 0.8495 0.000 1.000
#> GSM559423 2 0.4431 0.8109 0.092 0.908
#> GSM559425 2 0.0000 0.8495 0.000 1.000
#> GSM559426 2 0.7528 0.7130 0.216 0.784
#> GSM559427 2 0.0000 0.8495 0.000 1.000
#> GSM559428 2 0.9996 0.1038 0.488 0.512
#> GSM559429 2 0.7674 0.7036 0.224 0.776
#> GSM559430 2 0.0000 0.8495 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.6192 0.740 0.420 0.000 0.580
#> GSM559387 3 0.6192 0.740 0.420 0.000 0.580
#> GSM559391 3 0.6192 0.740 0.420 0.000 0.580
#> GSM559395 3 0.6192 0.740 0.420 0.000 0.580
#> GSM559397 3 0.6192 0.740 0.420 0.000 0.580
#> GSM559401 3 0.6008 0.491 0.372 0.000 0.628
#> GSM559414 3 0.6192 0.740 0.420 0.000 0.580
#> GSM559422 3 0.5845 0.464 0.308 0.004 0.688
#> GSM559424 3 0.6192 0.740 0.420 0.000 0.580
#> GSM559431 2 0.0000 0.793 0.000 1.000 0.000
#> GSM559432 3 0.6172 0.461 0.308 0.012 0.680
#> GSM559381 1 0.6044 0.510 0.772 0.172 0.056
#> GSM559382 1 0.7150 0.260 0.616 0.348 0.036
#> GSM559384 1 0.2625 0.688 0.916 0.000 0.084
#> GSM559385 1 0.0424 0.725 0.992 0.000 0.008
#> GSM559386 1 0.7616 0.299 0.636 0.292 0.072
#> GSM559388 2 0.7446 0.271 0.432 0.532 0.036
#> GSM559389 1 0.4095 0.646 0.880 0.056 0.064
#> GSM559390 1 0.5695 0.572 0.804 0.120 0.076
#> GSM559392 2 0.0000 0.793 0.000 1.000 0.000
#> GSM559393 1 0.0424 0.725 0.992 0.000 0.008
#> GSM559394 1 0.0424 0.725 0.992 0.000 0.008
#> GSM559396 1 0.2625 0.688 0.916 0.000 0.084
#> GSM559398 2 0.0000 0.793 0.000 1.000 0.000
#> GSM559399 1 0.0592 0.725 0.988 0.000 0.012
#> GSM559400 2 0.9059 0.127 0.380 0.480 0.140
#> GSM559402 1 0.2165 0.714 0.936 0.000 0.064
#> GSM559403 1 0.0747 0.725 0.984 0.000 0.016
#> GSM559404 1 0.5678 0.411 0.684 0.000 0.316
#> GSM559405 1 0.2301 0.717 0.936 0.004 0.060
#> GSM559406 1 0.5785 0.469 0.696 0.004 0.300
#> GSM559407 1 0.2165 0.714 0.936 0.000 0.064
#> GSM559408 1 0.5016 0.533 0.760 0.000 0.240
#> GSM559409 1 0.5016 0.533 0.760 0.000 0.240
#> GSM559410 1 0.2261 0.717 0.932 0.000 0.068
#> GSM559411 1 0.4931 0.561 0.768 0.000 0.232
#> GSM559412 1 0.5678 0.411 0.684 0.000 0.316
#> GSM559413 1 0.5678 0.411 0.684 0.000 0.316
#> GSM559415 1 0.2056 0.707 0.952 0.024 0.024
#> GSM559416 1 0.7104 0.419 0.724 0.140 0.136
#> GSM559417 1 0.7163 0.412 0.720 0.144 0.136
#> GSM559418 1 0.2313 0.702 0.944 0.032 0.024
#> GSM559419 1 0.0000 0.726 1.000 0.000 0.000
#> GSM559420 1 0.0000 0.726 1.000 0.000 0.000
#> GSM559421 2 0.0000 0.793 0.000 1.000 0.000
#> GSM559423 2 0.2945 0.763 0.088 0.908 0.004
#> GSM559425 2 0.0000 0.793 0.000 1.000 0.000
#> GSM559426 2 0.4931 0.685 0.212 0.784 0.004
#> GSM559427 2 0.0000 0.793 0.000 1.000 0.000
#> GSM559428 2 0.7974 0.246 0.436 0.504 0.060
#> GSM559429 2 0.5024 0.677 0.220 0.776 0.004
#> GSM559430 2 0.0000 0.793 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.3400 0.880 0.180 0.000 0.820 0.000
#> GSM559387 3 0.3400 0.880 0.180 0.000 0.820 0.000
#> GSM559391 3 0.3400 0.880 0.180 0.000 0.820 0.000
#> GSM559395 3 0.3400 0.880 0.180 0.000 0.820 0.000
#> GSM559397 3 0.3539 0.876 0.176 0.000 0.820 0.004
#> GSM559401 4 0.4985 0.833 0.000 0.000 0.468 0.532
#> GSM559414 3 0.3539 0.876 0.176 0.000 0.820 0.004
#> GSM559422 4 0.4697 0.921 0.000 0.000 0.356 0.644
#> GSM559424 3 0.3400 0.880 0.180 0.000 0.820 0.000
#> GSM559431 2 0.0000 0.778 0.000 1.000 0.000 0.000
#> GSM559432 4 0.5007 0.920 0.000 0.008 0.356 0.636
#> GSM559381 1 0.5652 0.577 0.736 0.080 0.012 0.172
#> GSM559382 1 0.6805 0.281 0.592 0.260 0.000 0.148
#> GSM559384 1 0.5175 0.608 0.760 0.000 0.120 0.120
#> GSM559385 1 0.0188 0.689 0.996 0.000 0.000 0.004
#> GSM559386 1 0.6756 0.360 0.612 0.188 0.000 0.200
#> GSM559388 2 0.7182 0.189 0.412 0.452 0.000 0.136
#> GSM559389 1 0.3896 0.651 0.844 0.012 0.024 0.120
#> GSM559390 1 0.5834 0.616 0.744 0.076 0.032 0.148
#> GSM559392 2 0.0000 0.778 0.000 1.000 0.000 0.000
#> GSM559393 1 0.0188 0.689 0.996 0.000 0.000 0.004
#> GSM559394 1 0.0188 0.689 0.996 0.000 0.000 0.004
#> GSM559396 1 0.5175 0.608 0.760 0.000 0.120 0.120
#> GSM559398 2 0.0000 0.778 0.000 1.000 0.000 0.000
#> GSM559399 1 0.1151 0.687 0.968 0.000 0.024 0.008
#> GSM559400 2 0.8780 0.110 0.368 0.396 0.068 0.168
#> GSM559402 1 0.4956 0.624 0.776 0.000 0.108 0.116
#> GSM559403 1 0.0779 0.688 0.980 0.000 0.016 0.004
#> GSM559404 3 0.6833 0.261 0.272 0.000 0.584 0.144
#> GSM559405 1 0.2593 0.678 0.892 0.000 0.104 0.004
#> GSM559406 1 0.6665 0.343 0.544 0.000 0.360 0.096
#> GSM559407 1 0.4956 0.624 0.776 0.000 0.108 0.116
#> GSM559408 1 0.6887 0.305 0.528 0.000 0.356 0.116
#> GSM559409 1 0.6887 0.305 0.528 0.000 0.356 0.116
#> GSM559410 1 0.2675 0.679 0.892 0.000 0.100 0.008
#> GSM559411 1 0.6774 0.389 0.568 0.000 0.312 0.120
#> GSM559412 1 0.7047 0.105 0.440 0.000 0.440 0.120
#> GSM559413 1 0.7047 0.105 0.440 0.000 0.440 0.120
#> GSM559415 1 0.1902 0.679 0.932 0.000 0.004 0.064
#> GSM559416 1 0.6488 0.535 0.688 0.044 0.068 0.200
#> GSM559417 1 0.6523 0.532 0.684 0.044 0.068 0.204
#> GSM559418 1 0.1940 0.675 0.924 0.000 0.000 0.076
#> GSM559419 1 0.3278 0.662 0.864 0.000 0.020 0.116
#> GSM559420 1 0.3278 0.662 0.864 0.000 0.020 0.116
#> GSM559421 2 0.0336 0.776 0.000 0.992 0.000 0.008
#> GSM559423 2 0.3601 0.731 0.084 0.860 0.000 0.056
#> GSM559425 2 0.0000 0.778 0.000 1.000 0.000 0.000
#> GSM559426 2 0.5530 0.642 0.212 0.712 0.000 0.076
#> GSM559427 2 0.0000 0.778 0.000 1.000 0.000 0.000
#> GSM559428 1 0.7546 -0.197 0.412 0.400 0.000 0.188
#> GSM559429 2 0.5598 0.635 0.220 0.704 0.000 0.076
#> GSM559430 2 0.0000 0.778 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
#> GSM559383 3 0.0404 0.9979 0.012 0.000 0.988 0.000 0.000
#> GSM559387 3 0.0404 0.9979 0.012 0.000 0.988 0.000 0.000
#> GSM559391 3 0.0404 0.9979 0.012 0.000 0.988 0.000 0.000
#> GSM559395 3 0.0404 0.9979 0.012 0.000 0.988 0.000 0.000
#> GSM559397 3 0.0566 0.9947 0.012 0.000 0.984 0.000 0.004
#> GSM559401 5 0.4161 0.6549 0.000 0.000 0.392 0.000 0.608
#> GSM559414 3 0.0566 0.9947 0.012 0.000 0.984 0.000 0.004
#> GSM559422 5 0.2813 0.8604 0.000 0.000 0.168 0.000 0.832
#> GSM559424 3 0.0404 0.9979 0.012 0.000 0.988 0.000 0.000
#> GSM559431 2 0.0000 0.8637 0.000 1.000 0.000 0.000 0.000
#> GSM559432 5 0.3093 0.8598 0.000 0.008 0.168 0.000 0.824
#> GSM559381 4 0.4060 0.4837 0.360 0.000 0.000 0.640 0.000
#> GSM559382 4 0.5565 0.5904 0.216 0.144 0.000 0.640 0.000
#> GSM559384 1 0.4982 0.5059 0.708 0.000 0.228 0.032 0.032
#> GSM559385 1 0.4417 0.5672 0.760 0.000 0.000 0.092 0.148
#> GSM559386 4 0.4736 0.6144 0.216 0.072 0.000 0.712 0.000
#> GSM559388 4 0.5908 0.2619 0.108 0.380 0.000 0.512 0.000
#> GSM559389 1 0.4546 0.3031 0.668 0.000 0.028 0.304 0.000
#> GSM559390 4 0.5061 0.3298 0.432 0.000 0.012 0.540 0.016
#> GSM559392 2 0.0000 0.8637 0.000 1.000 0.000 0.000 0.000
#> GSM559393 1 0.4417 0.5672 0.760 0.000 0.000 0.092 0.148
#> GSM559394 1 0.4417 0.5672 0.760 0.000 0.000 0.092 0.148
#> GSM559396 1 0.4982 0.5059 0.708 0.000 0.228 0.032 0.032
#> GSM559398 2 0.0000 0.8637 0.000 1.000 0.000 0.000 0.000
#> GSM559399 1 0.5001 0.5792 0.744 0.000 0.028 0.080 0.148
#> GSM559400 4 0.8046 0.2707 0.084 0.352 0.152 0.396 0.016
#> GSM559402 1 0.1597 0.6052 0.940 0.000 0.048 0.012 0.000
#> GSM559403 1 0.5189 0.5764 0.732 0.000 0.032 0.088 0.148
#> GSM559404 1 0.7058 -0.0308 0.376 0.000 0.360 0.252 0.012
#> GSM559405 1 0.4839 0.5993 0.760 0.000 0.044 0.052 0.144
#> GSM559406 1 0.6845 0.3644 0.496 0.000 0.232 0.256 0.016
#> GSM559407 1 0.1597 0.6052 0.940 0.000 0.048 0.012 0.000
#> GSM559408 1 0.5384 0.4849 0.664 0.000 0.228 0.104 0.004
#> GSM559409 1 0.5384 0.4849 0.664 0.000 0.228 0.104 0.004
#> GSM559410 1 0.4945 0.5976 0.752 0.000 0.044 0.056 0.148
#> GSM559411 1 0.5007 0.5223 0.720 0.000 0.176 0.096 0.008
#> GSM559412 1 0.6022 0.4279 0.592 0.000 0.268 0.132 0.008
#> GSM559413 1 0.6022 0.4279 0.592 0.000 0.268 0.132 0.008
#> GSM559415 1 0.5202 0.5069 0.700 0.000 0.004 0.148 0.148
#> GSM559416 4 0.6606 0.3103 0.384 0.000 0.164 0.444 0.008
#> GSM559417 4 0.6602 0.3178 0.380 0.000 0.164 0.448 0.008
#> GSM559418 1 0.5198 0.4868 0.688 0.000 0.000 0.164 0.148
#> GSM559419 1 0.1331 0.6030 0.952 0.000 0.008 0.040 0.000
#> GSM559420 1 0.1331 0.6030 0.952 0.000 0.008 0.040 0.000
#> GSM559421 2 0.0609 0.8542 0.000 0.980 0.000 0.020 0.000
#> GSM559423 2 0.3074 0.7121 0.000 0.804 0.000 0.196 0.000
#> GSM559425 2 0.0000 0.8637 0.000 1.000 0.000 0.000 0.000
#> GSM559426 2 0.4210 0.4423 0.000 0.588 0.000 0.412 0.000
#> GSM559427 2 0.0000 0.8637 0.000 1.000 0.000 0.000 0.000
#> GSM559428 4 0.4983 0.3662 0.064 0.272 0.000 0.664 0.000
#> GSM559429 2 0.4235 0.4204 0.000 0.576 0.000 0.424 0.000
#> GSM559430 2 0.0000 0.8637 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
#> GSM559383 3 0.0260 0.9981 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM559387 3 0.0260 0.9981 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM559391 3 0.0260 0.9981 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM559395 3 0.0260 0.9981 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM559397 3 0.0405 0.9951 0.000 0.000 0.988 0.008 0.004 0.000
#> GSM559401 5 0.3737 0.3645 0.000 0.000 0.392 0.000 0.608 0.000
#> GSM559414 3 0.0405 0.9951 0.000 0.000 0.988 0.008 0.004 0.000
#> GSM559422 5 0.0000 0.7732 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM559424 3 0.0260 0.9981 0.000 0.000 0.992 0.008 0.000 0.000
#> GSM559431 2 0.0000 0.9543 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559432 5 0.0260 0.7719 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM559381 6 0.5102 0.3858 0.212 0.000 0.000 0.160 0.000 0.628
#> GSM559382 6 0.4896 0.5527 0.212 0.120 0.000 0.004 0.000 0.664
#> GSM559384 4 0.6007 0.0586 0.324 0.000 0.216 0.456 0.000 0.004
#> GSM559385 1 0.3446 0.8113 0.692 0.000 0.000 0.308 0.000 0.000
#> GSM559386 6 0.4031 0.5478 0.212 0.048 0.000 0.004 0.000 0.736
#> GSM559388 6 0.4938 0.3286 0.076 0.356 0.000 0.000 0.000 0.568
#> GSM559389 1 0.6488 0.3305 0.440 0.000 0.028 0.236 0.000 0.296
#> GSM559390 6 0.5751 0.1718 0.208 0.000 0.000 0.288 0.000 0.504
#> GSM559392 2 0.0000 0.9543 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559393 1 0.3446 0.8113 0.692 0.000 0.000 0.308 0.000 0.000
#> GSM559394 1 0.3446 0.8113 0.692 0.000 0.000 0.308 0.000 0.000
#> GSM559396 4 0.6007 0.0586 0.324 0.000 0.216 0.456 0.000 0.004
#> GSM559398 2 0.0000 0.9543 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559399 1 0.4134 0.7910 0.656 0.000 0.028 0.316 0.000 0.000
#> GSM559400 6 0.6346 0.2193 0.028 0.348 0.124 0.004 0.008 0.488
#> GSM559402 4 0.3695 0.0099 0.376 0.000 0.000 0.624 0.000 0.000
#> GSM559403 1 0.4118 0.7921 0.660 0.000 0.028 0.312 0.000 0.000
#> GSM559404 4 0.3620 0.2104 0.248 0.000 0.008 0.736 0.000 0.008
#> GSM559405 1 0.4039 0.6359 0.568 0.000 0.000 0.424 0.000 0.008
#> GSM559406 4 0.4521 0.3770 0.072 0.000 0.024 0.732 0.000 0.172
#> GSM559407 4 0.3695 0.0099 0.376 0.000 0.000 0.624 0.000 0.000
#> GSM559408 4 0.2122 0.5171 0.076 0.000 0.024 0.900 0.000 0.000
#> GSM559409 4 0.2122 0.5171 0.076 0.000 0.024 0.900 0.000 0.000
#> GSM559410 1 0.3789 0.6501 0.584 0.000 0.000 0.416 0.000 0.000
#> GSM559411 4 0.2135 0.4754 0.128 0.000 0.000 0.872 0.000 0.000
#> GSM559412 4 0.0000 0.5104 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM559413 4 0.0000 0.5104 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM559415 1 0.3780 0.7721 0.728 0.000 0.004 0.248 0.000 0.020
#> GSM559416 6 0.6518 0.2896 0.296 0.000 0.124 0.080 0.000 0.500
#> GSM559417 6 0.6476 0.2969 0.296 0.000 0.124 0.076 0.000 0.504
#> GSM559418 1 0.3791 0.7549 0.732 0.000 0.000 0.236 0.000 0.032
#> GSM559419 4 0.3993 -0.3012 0.476 0.000 0.004 0.520 0.000 0.000
#> GSM559420 4 0.3993 -0.3012 0.476 0.000 0.004 0.520 0.000 0.000
#> GSM559421 2 0.0603 0.9383 0.004 0.980 0.000 0.000 0.000 0.016
#> GSM559423 2 0.3245 0.6323 0.008 0.764 0.000 0.000 0.000 0.228
#> GSM559425 2 0.0000 0.9543 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559426 6 0.4121 0.1108 0.016 0.380 0.000 0.000 0.000 0.604
#> GSM559427 2 0.0000 0.9543 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559428 6 0.1327 0.4678 0.000 0.064 0.000 0.000 0.000 0.936
#> GSM559429 6 0.4088 0.1366 0.016 0.368 0.000 0.000 0.000 0.616
#> GSM559430 2 0.0000 0.9543 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:hclust 48 5.03e-01 2
#> MAD:hclust 38 8.40e-08 3
#> MAD:hclust 40 9.62e-08 4
#> MAD:hclust 35 3.15e-06 5
#> MAD:hclust 32 3.76e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.491 0.786 0.850 0.4141 0.538 0.538
#> 3 3 1.000 0.969 0.978 0.4717 0.740 0.563
#> 4 4 0.681 0.616 0.814 0.1623 0.876 0.696
#> 5 5 0.665 0.640 0.770 0.0882 0.910 0.720
#> 6 6 0.694 0.578 0.737 0.0555 0.851 0.504
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
#> GSM559383 1 0.0938 0.733 0.988 0.012
#> GSM559387 1 0.0938 0.733 0.988 0.012
#> GSM559391 1 0.0938 0.733 0.988 0.012
#> GSM559395 1 0.0938 0.733 0.988 0.012
#> GSM559397 1 0.0938 0.733 0.988 0.012
#> GSM559401 1 0.0938 0.733 0.988 0.012
#> GSM559414 1 0.0938 0.733 0.988 0.012
#> GSM559422 1 0.0938 0.733 0.988 0.012
#> GSM559424 1 0.0938 0.733 0.988 0.012
#> GSM559431 2 0.0000 0.875 0.000 1.000
#> GSM559432 2 0.8267 0.604 0.260 0.740
#> GSM559381 1 0.8267 0.876 0.740 0.260
#> GSM559382 2 0.0000 0.875 0.000 1.000
#> GSM559384 1 0.8267 0.876 0.740 0.260
#> GSM559385 1 0.8267 0.876 0.740 0.260
#> GSM559386 2 0.9850 -0.105 0.428 0.572
#> GSM559388 2 0.0000 0.875 0.000 1.000
#> GSM559389 1 0.8267 0.876 0.740 0.260
#> GSM559390 1 0.8267 0.876 0.740 0.260
#> GSM559392 2 0.0000 0.875 0.000 1.000
#> GSM559393 2 0.9896 -0.154 0.440 0.560
#> GSM559394 1 0.8267 0.876 0.740 0.260
#> GSM559396 1 0.7528 0.860 0.784 0.216
#> GSM559398 2 0.0000 0.875 0.000 1.000
#> GSM559399 1 0.8267 0.876 0.740 0.260
#> GSM559400 2 0.0000 0.875 0.000 1.000
#> GSM559402 1 0.8267 0.876 0.740 0.260
#> GSM559403 1 0.8267 0.876 0.740 0.260
#> GSM559404 1 0.7139 0.861 0.804 0.196
#> GSM559405 1 0.8267 0.876 0.740 0.260
#> GSM559406 1 0.7219 0.863 0.800 0.200
#> GSM559407 1 0.8267 0.876 0.740 0.260
#> GSM559408 1 0.8267 0.876 0.740 0.260
#> GSM559409 1 0.8207 0.876 0.744 0.256
#> GSM559410 1 0.8267 0.876 0.740 0.260
#> GSM559411 1 0.7219 0.863 0.800 0.200
#> GSM559412 1 0.7299 0.864 0.796 0.204
#> GSM559413 1 0.7139 0.861 0.804 0.196
#> GSM559415 1 0.8267 0.876 0.740 0.260
#> GSM559416 1 0.8267 0.876 0.740 0.260
#> GSM559417 1 0.8267 0.876 0.740 0.260
#> GSM559418 2 0.9881 -0.137 0.436 0.564
#> GSM559419 1 0.8267 0.876 0.740 0.260
#> GSM559420 1 0.8267 0.876 0.740 0.260
#> GSM559421 2 0.0000 0.875 0.000 1.000
#> GSM559423 2 0.0000 0.875 0.000 1.000
#> GSM559425 2 0.0000 0.875 0.000 1.000
#> GSM559426 2 0.0000 0.875 0.000 1.000
#> GSM559427 2 0.0000 0.875 0.000 1.000
#> GSM559428 2 0.0000 0.875 0.000 1.000
#> GSM559429 2 0.0000 0.875 0.000 1.000
#> GSM559430 2 0.0000 0.875 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.1643 0.993 0.044 0.000 0.956
#> GSM559387 3 0.1643 0.993 0.044 0.000 0.956
#> GSM559391 3 0.1643 0.993 0.044 0.000 0.956
#> GSM559395 3 0.1643 0.993 0.044 0.000 0.956
#> GSM559397 3 0.1643 0.993 0.044 0.000 0.956
#> GSM559401 3 0.1643 0.993 0.044 0.000 0.956
#> GSM559414 3 0.1643 0.993 0.044 0.000 0.956
#> GSM559422 3 0.0000 0.940 0.000 0.000 1.000
#> GSM559424 3 0.1643 0.993 0.044 0.000 0.956
#> GSM559431 2 0.0000 0.966 0.000 1.000 0.000
#> GSM559432 2 0.5785 0.559 0.000 0.668 0.332
#> GSM559381 1 0.0424 0.984 0.992 0.000 0.008
#> GSM559382 2 0.1643 0.948 0.000 0.956 0.044
#> GSM559384 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559385 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559386 1 0.2793 0.936 0.928 0.028 0.044
#> GSM559388 2 0.1529 0.949 0.000 0.960 0.040
#> GSM559389 1 0.0424 0.984 0.992 0.000 0.008
#> GSM559390 1 0.1529 0.962 0.960 0.000 0.040
#> GSM559392 2 0.0000 0.966 0.000 1.000 0.000
#> GSM559393 1 0.2063 0.954 0.948 0.008 0.044
#> GSM559394 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559396 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559398 2 0.0000 0.966 0.000 1.000 0.000
#> GSM559399 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559400 2 0.1643 0.948 0.000 0.956 0.044
#> GSM559402 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559403 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559404 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559405 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559406 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559407 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559408 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559409 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559410 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559411 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559412 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559413 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559415 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559416 1 0.1163 0.971 0.972 0.000 0.028
#> GSM559417 1 0.1529 0.962 0.960 0.000 0.040
#> GSM559418 1 0.1950 0.957 0.952 0.008 0.040
#> GSM559419 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559420 1 0.0000 0.989 1.000 0.000 0.000
#> GSM559421 2 0.0000 0.966 0.000 1.000 0.000
#> GSM559423 2 0.0000 0.966 0.000 1.000 0.000
#> GSM559425 2 0.0000 0.966 0.000 1.000 0.000
#> GSM559426 2 0.0000 0.966 0.000 1.000 0.000
#> GSM559427 2 0.0000 0.966 0.000 1.000 0.000
#> GSM559428 2 0.1643 0.948 0.000 0.956 0.044
#> GSM559429 2 0.0000 0.966 0.000 1.000 0.000
#> GSM559430 2 0.0000 0.966 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.0000 0.9157 0.000 0.000 1.000 0.000
#> GSM559387 3 0.0000 0.9157 0.000 0.000 1.000 0.000
#> GSM559391 3 0.0000 0.9157 0.000 0.000 1.000 0.000
#> GSM559395 3 0.0000 0.9157 0.000 0.000 1.000 0.000
#> GSM559397 3 0.0000 0.9157 0.000 0.000 1.000 0.000
#> GSM559401 3 0.1474 0.8938 0.000 0.000 0.948 0.052
#> GSM559414 3 0.0000 0.9157 0.000 0.000 1.000 0.000
#> GSM559422 3 0.4624 0.7026 0.000 0.000 0.660 0.340
#> GSM559424 3 0.0000 0.9157 0.000 0.000 1.000 0.000
#> GSM559431 2 0.0000 0.9447 0.000 1.000 0.000 0.000
#> GSM559432 3 0.7694 0.3845 0.000 0.244 0.448 0.308
#> GSM559381 1 0.2647 0.6881 0.880 0.000 0.000 0.120
#> GSM559382 4 0.5294 -0.1328 0.008 0.484 0.000 0.508
#> GSM559384 1 0.1940 0.7387 0.924 0.000 0.000 0.076
#> GSM559385 1 0.2281 0.6941 0.904 0.000 0.000 0.096
#> GSM559386 1 0.5755 -0.0431 0.528 0.028 0.000 0.444
#> GSM559388 2 0.4790 0.2828 0.000 0.620 0.000 0.380
#> GSM559389 1 0.3219 0.6554 0.836 0.000 0.000 0.164
#> GSM559390 4 0.4888 -0.0429 0.412 0.000 0.000 0.588
#> GSM559392 2 0.0188 0.9443 0.000 0.996 0.000 0.004
#> GSM559393 4 0.4941 0.0383 0.436 0.000 0.000 0.564
#> GSM559394 1 0.3024 0.6785 0.852 0.000 0.000 0.148
#> GSM559396 1 0.5510 0.4188 0.600 0.000 0.024 0.376
#> GSM559398 2 0.0000 0.9447 0.000 1.000 0.000 0.000
#> GSM559399 1 0.3975 0.5264 0.760 0.000 0.000 0.240
#> GSM559400 4 0.4746 0.0170 0.000 0.368 0.000 0.632
#> GSM559402 1 0.1557 0.7357 0.944 0.000 0.000 0.056
#> GSM559403 1 0.2011 0.7045 0.920 0.000 0.000 0.080
#> GSM559404 1 0.1940 0.7103 0.924 0.000 0.000 0.076
#> GSM559405 1 0.0336 0.7303 0.992 0.000 0.000 0.008
#> GSM559406 1 0.3649 0.6747 0.796 0.000 0.000 0.204
#> GSM559407 1 0.1637 0.7350 0.940 0.000 0.000 0.060
#> GSM559408 1 0.3569 0.6818 0.804 0.000 0.000 0.196
#> GSM559409 1 0.3569 0.6818 0.804 0.000 0.000 0.196
#> GSM559410 1 0.0707 0.7309 0.980 0.000 0.000 0.020
#> GSM559411 1 0.3569 0.6818 0.804 0.000 0.000 0.196
#> GSM559412 1 0.3569 0.6818 0.804 0.000 0.000 0.196
#> GSM559413 1 0.3569 0.6818 0.804 0.000 0.000 0.196
#> GSM559415 1 0.3837 0.5547 0.776 0.000 0.000 0.224
#> GSM559416 4 0.4994 -0.1831 0.480 0.000 0.000 0.520
#> GSM559417 4 0.4977 -0.1271 0.460 0.000 0.000 0.540
#> GSM559418 1 0.4866 0.1421 0.596 0.000 0.000 0.404
#> GSM559419 1 0.4961 0.2785 0.552 0.000 0.000 0.448
#> GSM559420 1 0.2408 0.7333 0.896 0.000 0.000 0.104
#> GSM559421 2 0.0188 0.9443 0.000 0.996 0.000 0.004
#> GSM559423 2 0.0469 0.9413 0.000 0.988 0.000 0.012
#> GSM559425 2 0.0000 0.9447 0.000 1.000 0.000 0.000
#> GSM559426 2 0.0921 0.9313 0.000 0.972 0.000 0.028
#> GSM559427 2 0.0000 0.9447 0.000 1.000 0.000 0.000
#> GSM559428 4 0.5288 -0.1008 0.008 0.472 0.000 0.520
#> GSM559429 2 0.1022 0.9281 0.000 0.968 0.000 0.032
#> GSM559430 2 0.0000 0.9447 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
#> GSM559383 3 0.0162 0.9678 0.000 0.000 0.996 0.004 0.000
#> GSM559387 3 0.0000 0.9671 0.000 0.000 1.000 0.000 0.000
#> GSM559391 3 0.0162 0.9678 0.000 0.000 0.996 0.004 0.000
#> GSM559395 3 0.0162 0.9678 0.000 0.000 0.996 0.004 0.000
#> GSM559397 3 0.0000 0.9671 0.000 0.000 1.000 0.000 0.000
#> GSM559401 3 0.2424 0.7513 0.000 0.000 0.868 0.000 0.132
#> GSM559414 3 0.0000 0.9671 0.000 0.000 1.000 0.000 0.000
#> GSM559422 5 0.4588 0.6890 0.000 0.000 0.380 0.016 0.604
#> GSM559424 3 0.0162 0.9678 0.000 0.000 0.996 0.004 0.000
#> GSM559431 2 0.0000 0.9628 0.000 1.000 0.000 0.000 0.000
#> GSM559432 5 0.6318 0.7320 0.000 0.124 0.288 0.020 0.568
#> GSM559381 1 0.4431 0.5385 0.732 0.000 0.000 0.216 0.052
#> GSM559382 4 0.5781 0.4396 0.004 0.200 0.000 0.632 0.164
#> GSM559384 1 0.1725 0.6585 0.936 0.000 0.000 0.020 0.044
#> GSM559385 1 0.4933 0.5464 0.692 0.000 0.000 0.080 0.228
#> GSM559386 4 0.5269 0.5294 0.180 0.024 0.000 0.712 0.084
#> GSM559388 4 0.5313 0.2877 0.000 0.388 0.000 0.556 0.056
#> GSM559389 1 0.5490 0.4570 0.644 0.000 0.000 0.228 0.128
#> GSM559390 4 0.3039 0.5064 0.152 0.000 0.000 0.836 0.012
#> GSM559392 2 0.1041 0.9507 0.000 0.964 0.000 0.004 0.032
#> GSM559393 4 0.6599 0.2986 0.268 0.000 0.000 0.464 0.268
#> GSM559394 1 0.5464 0.5020 0.648 0.000 0.000 0.128 0.224
#> GSM559396 1 0.6602 -0.0816 0.444 0.000 0.044 0.432 0.080
#> GSM559398 2 0.0955 0.9503 0.000 0.968 0.000 0.004 0.028
#> GSM559399 1 0.5652 0.1379 0.552 0.000 0.000 0.360 0.088
#> GSM559400 4 0.5904 0.3405 0.000 0.172 0.000 0.596 0.232
#> GSM559402 1 0.0693 0.6617 0.980 0.000 0.000 0.008 0.012
#> GSM559403 1 0.4212 0.5972 0.776 0.000 0.000 0.080 0.144
#> GSM559404 1 0.4676 0.6121 0.720 0.000 0.000 0.072 0.208
#> GSM559405 1 0.2304 0.6496 0.908 0.000 0.000 0.044 0.048
#> GSM559406 1 0.5149 0.5512 0.680 0.000 0.000 0.216 0.104
#> GSM559407 1 0.0807 0.6620 0.976 0.000 0.000 0.012 0.012
#> GSM559408 1 0.4934 0.5718 0.708 0.000 0.000 0.188 0.104
#> GSM559409 1 0.4934 0.5718 0.708 0.000 0.000 0.188 0.104
#> GSM559410 1 0.2370 0.6542 0.904 0.000 0.000 0.040 0.056
#> GSM559411 1 0.5006 0.5738 0.704 0.000 0.000 0.180 0.116
#> GSM559412 1 0.5006 0.5715 0.704 0.000 0.000 0.180 0.116
#> GSM559413 1 0.5006 0.5715 0.704 0.000 0.000 0.180 0.116
#> GSM559415 1 0.5652 0.1751 0.564 0.000 0.000 0.344 0.092
#> GSM559416 4 0.4479 0.4056 0.264 0.000 0.000 0.700 0.036
#> GSM559417 4 0.4297 0.4457 0.236 0.000 0.000 0.728 0.036
#> GSM559418 4 0.5708 0.2482 0.384 0.000 0.000 0.528 0.088
#> GSM559419 4 0.4966 0.1507 0.404 0.000 0.000 0.564 0.032
#> GSM559420 1 0.2676 0.6276 0.884 0.000 0.000 0.080 0.036
#> GSM559421 2 0.0451 0.9615 0.000 0.988 0.000 0.008 0.004
#> GSM559423 2 0.0898 0.9561 0.000 0.972 0.000 0.020 0.008
#> GSM559425 2 0.0000 0.9628 0.000 1.000 0.000 0.000 0.000
#> GSM559426 2 0.2446 0.9045 0.000 0.900 0.000 0.056 0.044
#> GSM559427 2 0.0000 0.9628 0.000 1.000 0.000 0.000 0.000
#> GSM559428 4 0.5604 0.4448 0.008 0.180 0.000 0.664 0.148
#> GSM559429 2 0.2992 0.8769 0.000 0.868 0.000 0.068 0.064
#> GSM559430 2 0.0000 0.9628 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
#> GSM559383 3 0.1074 0.9420 0.012 0.000 0.960 0.000 0.000 0.028
#> GSM559387 3 0.0000 0.9413 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559391 3 0.1168 0.9406 0.016 0.000 0.956 0.000 0.000 0.028
#> GSM559395 3 0.0820 0.9434 0.012 0.000 0.972 0.000 0.000 0.016
#> GSM559397 3 0.0000 0.9413 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559401 3 0.2597 0.7054 0.000 0.000 0.824 0.000 0.176 0.000
#> GSM559414 3 0.0000 0.9413 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559422 5 0.3500 0.8496 0.000 0.000 0.204 0.000 0.768 0.028
#> GSM559424 3 0.1168 0.9406 0.016 0.000 0.956 0.000 0.000 0.028
#> GSM559431 2 0.0000 0.9278 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559432 5 0.5310 0.8481 0.000 0.056 0.176 0.000 0.676 0.092
#> GSM559381 1 0.6487 0.3282 0.504 0.000 0.000 0.268 0.056 0.172
#> GSM559382 6 0.4387 0.6393 0.104 0.152 0.000 0.000 0.008 0.736
#> GSM559384 1 0.5406 0.2337 0.556 0.000 0.000 0.356 0.048 0.040
#> GSM559385 1 0.6484 0.3629 0.536 0.000 0.000 0.208 0.184 0.072
#> GSM559386 6 0.3578 0.4893 0.340 0.000 0.000 0.000 0.000 0.660
#> GSM559388 6 0.4859 0.5653 0.084 0.304 0.000 0.000 0.000 0.612
#> GSM559389 1 0.4633 0.4738 0.736 0.000 0.000 0.148 0.036 0.080
#> GSM559390 6 0.6323 0.3789 0.156 0.000 0.000 0.296 0.044 0.504
#> GSM559392 2 0.1296 0.9092 0.004 0.948 0.000 0.000 0.004 0.044
#> GSM559393 1 0.5625 0.1902 0.548 0.000 0.000 0.004 0.168 0.280
#> GSM559394 1 0.5904 0.4228 0.620 0.000 0.000 0.144 0.168 0.068
#> GSM559396 1 0.7484 0.1754 0.416 0.000 0.044 0.300 0.060 0.180
#> GSM559398 2 0.1155 0.9091 0.004 0.956 0.000 0.000 0.004 0.036
#> GSM559399 1 0.2579 0.4975 0.876 0.000 0.000 0.088 0.004 0.032
#> GSM559400 6 0.6004 0.4453 0.088 0.080 0.000 0.000 0.248 0.584
#> GSM559402 4 0.5496 -0.0263 0.404 0.000 0.000 0.508 0.048 0.040
#> GSM559403 1 0.5523 0.3497 0.604 0.000 0.000 0.280 0.068 0.048
#> GSM559404 4 0.5474 0.3677 0.196 0.000 0.000 0.656 0.080 0.068
#> GSM559405 1 0.5089 0.1665 0.532 0.000 0.000 0.408 0.032 0.028
#> GSM559406 4 0.2224 0.6695 0.020 0.000 0.000 0.904 0.012 0.064
#> GSM559407 4 0.5434 0.0742 0.368 0.000 0.000 0.544 0.048 0.040
#> GSM559408 4 0.0993 0.7196 0.012 0.000 0.000 0.964 0.000 0.024
#> GSM559409 4 0.0806 0.7232 0.008 0.000 0.000 0.972 0.000 0.020
#> GSM559410 1 0.4080 0.1365 0.536 0.000 0.000 0.456 0.008 0.000
#> GSM559411 4 0.1180 0.7140 0.012 0.000 0.000 0.960 0.012 0.016
#> GSM559412 4 0.0146 0.7255 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM559413 4 0.0146 0.7255 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM559415 1 0.3101 0.4991 0.852 0.000 0.000 0.092 0.024 0.032
#> GSM559416 1 0.6986 -0.1507 0.328 0.000 0.000 0.324 0.056 0.292
#> GSM559417 1 0.6950 -0.1737 0.328 0.000 0.000 0.320 0.052 0.300
#> GSM559418 1 0.2793 0.4593 0.872 0.000 0.000 0.024 0.024 0.080
#> GSM559419 1 0.6144 0.2030 0.492 0.000 0.000 0.336 0.032 0.140
#> GSM559420 1 0.5475 0.2497 0.564 0.000 0.000 0.340 0.052 0.044
#> GSM559421 2 0.0508 0.9257 0.004 0.984 0.000 0.000 0.000 0.012
#> GSM559423 2 0.1036 0.9191 0.008 0.964 0.000 0.000 0.004 0.024
#> GSM559425 2 0.0000 0.9278 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559426 2 0.3280 0.7892 0.004 0.808 0.000 0.000 0.028 0.160
#> GSM559427 2 0.0000 0.9278 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559428 6 0.4560 0.5951 0.080 0.140 0.000 0.000 0.036 0.744
#> GSM559429 2 0.4133 0.6617 0.008 0.708 0.000 0.000 0.032 0.252
#> GSM559430 2 0.0000 0.9278 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:kmeans 49 5.19e-01 2
#> MAD:kmeans 52 9.23e-10 3
#> MAD:kmeans 39 3.60e-08 4
#> MAD:kmeans 39 5.73e-07 5
#> MAD:kmeans 29 4.63e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "skmeans"]
# you can also extract it by
# res = res_list["MAD:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.847 0.945 0.976 0.4862 0.517 0.517
#> 3 3 1.000 0.960 0.985 0.3389 0.773 0.586
#> 4 4 0.844 0.852 0.908 0.1514 0.851 0.600
#> 5 5 0.801 0.688 0.830 0.0582 0.857 0.526
#> 6 6 0.772 0.549 0.783 0.0341 0.990 0.955
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
#> GSM559383 1 0.000 0.972 1.000 0.000
#> GSM559387 1 0.000 0.972 1.000 0.000
#> GSM559391 1 0.000 0.972 1.000 0.000
#> GSM559395 1 0.000 0.972 1.000 0.000
#> GSM559397 1 0.000 0.972 1.000 0.000
#> GSM559401 1 0.000 0.972 1.000 0.000
#> GSM559414 1 0.000 0.972 1.000 0.000
#> GSM559422 2 0.839 0.625 0.268 0.732
#> GSM559424 1 0.000 0.972 1.000 0.000
#> GSM559431 2 0.000 0.975 0.000 1.000
#> GSM559432 2 0.000 0.975 0.000 1.000
#> GSM559381 1 0.722 0.752 0.800 0.200
#> GSM559382 2 0.000 0.975 0.000 1.000
#> GSM559384 1 0.000 0.972 1.000 0.000
#> GSM559385 1 0.000 0.972 1.000 0.000
#> GSM559386 2 0.000 0.975 0.000 1.000
#> GSM559388 2 0.000 0.975 0.000 1.000
#> GSM559389 1 0.722 0.752 0.800 0.200
#> GSM559390 1 0.605 0.821 0.852 0.148
#> GSM559392 2 0.000 0.975 0.000 1.000
#> GSM559393 2 0.000 0.975 0.000 1.000
#> GSM559394 1 0.000 0.972 1.000 0.000
#> GSM559396 1 0.000 0.972 1.000 0.000
#> GSM559398 2 0.000 0.975 0.000 1.000
#> GSM559399 1 0.000 0.972 1.000 0.000
#> GSM559400 2 0.000 0.975 0.000 1.000
#> GSM559402 1 0.000 0.972 1.000 0.000
#> GSM559403 1 0.000 0.972 1.000 0.000
#> GSM559404 1 0.000 0.972 1.000 0.000
#> GSM559405 1 0.000 0.972 1.000 0.000
#> GSM559406 1 0.000 0.972 1.000 0.000
#> GSM559407 1 0.000 0.972 1.000 0.000
#> GSM559408 1 0.000 0.972 1.000 0.000
#> GSM559409 1 0.000 0.972 1.000 0.000
#> GSM559410 1 0.000 0.972 1.000 0.000
#> GSM559411 1 0.000 0.972 1.000 0.000
#> GSM559412 1 0.000 0.972 1.000 0.000
#> GSM559413 1 0.000 0.972 1.000 0.000
#> GSM559415 1 0.000 0.972 1.000 0.000
#> GSM559416 1 0.833 0.643 0.736 0.264
#> GSM559417 2 0.671 0.775 0.176 0.824
#> GSM559418 2 0.000 0.975 0.000 1.000
#> GSM559419 1 0.000 0.972 1.000 0.000
#> GSM559420 1 0.000 0.972 1.000 0.000
#> GSM559421 2 0.000 0.975 0.000 1.000
#> GSM559423 2 0.000 0.975 0.000 1.000
#> GSM559425 2 0.000 0.975 0.000 1.000
#> GSM559426 2 0.000 0.975 0.000 1.000
#> GSM559427 2 0.000 0.975 0.000 1.000
#> GSM559428 2 0.000 0.975 0.000 1.000
#> GSM559429 2 0.000 0.975 0.000 1.000
#> GSM559430 2 0.000 0.975 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.0000 0.9882 0.000 0.000 1.000
#> GSM559387 3 0.0000 0.9882 0.000 0.000 1.000
#> GSM559391 3 0.0000 0.9882 0.000 0.000 1.000
#> GSM559395 3 0.0000 0.9882 0.000 0.000 1.000
#> GSM559397 3 0.0000 0.9882 0.000 0.000 1.000
#> GSM559401 3 0.0000 0.9882 0.000 0.000 1.000
#> GSM559414 3 0.0000 0.9882 0.000 0.000 1.000
#> GSM559422 3 0.0000 0.9882 0.000 0.000 1.000
#> GSM559424 3 0.0000 0.9882 0.000 0.000 1.000
#> GSM559431 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM559432 3 0.3267 0.8680 0.000 0.116 0.884
#> GSM559381 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559382 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM559384 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559385 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559386 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM559388 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM559389 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559390 1 0.3340 0.8460 0.880 0.000 0.120
#> GSM559392 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM559393 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM559394 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559396 3 0.0000 0.9882 0.000 0.000 1.000
#> GSM559398 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM559399 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559400 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM559402 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559403 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559404 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559405 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559406 1 0.1163 0.9461 0.972 0.000 0.028
#> GSM559407 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559408 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559409 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559410 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559411 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559412 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559413 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559415 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559416 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559417 1 0.6308 0.0302 0.508 0.492 0.000
#> GSM559418 2 0.0747 0.9806 0.016 0.984 0.000
#> GSM559419 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559420 1 0.0000 0.9698 1.000 0.000 0.000
#> GSM559421 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM559423 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM559425 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM559426 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM559427 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM559428 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM559429 2 0.0000 0.9988 0.000 1.000 0.000
#> GSM559430 2 0.0000 0.9988 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM559387 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM559391 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM559395 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM559397 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM559401 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM559414 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM559422 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM559424 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM559431 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM559432 3 0.4898 0.286 0.000 0.416 0.584 0.000
#> GSM559381 1 0.4431 0.816 0.696 0.000 0.000 0.304
#> GSM559382 2 0.0188 0.989 0.004 0.996 0.000 0.000
#> GSM559384 1 0.4382 0.817 0.704 0.000 0.000 0.296
#> GSM559385 1 0.4040 0.819 0.752 0.000 0.000 0.248
#> GSM559386 2 0.2737 0.886 0.104 0.888 0.000 0.008
#> GSM559388 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM559389 1 0.4008 0.819 0.756 0.000 0.000 0.244
#> GSM559390 4 0.3486 0.777 0.188 0.000 0.000 0.812
#> GSM559392 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM559393 1 0.4804 0.355 0.616 0.384 0.000 0.000
#> GSM559394 1 0.3801 0.814 0.780 0.000 0.000 0.220
#> GSM559396 3 0.0000 0.951 0.000 0.000 1.000 0.000
#> GSM559398 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM559399 1 0.0469 0.664 0.988 0.000 0.000 0.012
#> GSM559400 2 0.0469 0.982 0.000 0.988 0.000 0.012
#> GSM559402 1 0.4804 0.753 0.616 0.000 0.000 0.384
#> GSM559403 1 0.4072 0.819 0.748 0.000 0.000 0.252
#> GSM559404 1 0.4431 0.817 0.696 0.000 0.000 0.304
#> GSM559405 1 0.4356 0.819 0.708 0.000 0.000 0.292
#> GSM559406 4 0.1610 0.813 0.016 0.000 0.032 0.952
#> GSM559407 1 0.4877 0.722 0.592 0.000 0.000 0.408
#> GSM559408 4 0.1022 0.819 0.032 0.000 0.000 0.968
#> GSM559409 4 0.1118 0.818 0.036 0.000 0.000 0.964
#> GSM559410 1 0.4543 0.808 0.676 0.000 0.000 0.324
#> GSM559411 4 0.1118 0.818 0.036 0.000 0.000 0.964
#> GSM559412 4 0.1118 0.818 0.036 0.000 0.000 0.964
#> GSM559413 4 0.1118 0.818 0.036 0.000 0.000 0.964
#> GSM559415 1 0.1022 0.647 0.968 0.000 0.000 0.032
#> GSM559416 4 0.4220 0.750 0.248 0.004 0.000 0.748
#> GSM559417 4 0.4220 0.750 0.248 0.004 0.000 0.748
#> GSM559418 1 0.2596 0.596 0.908 0.068 0.000 0.024
#> GSM559419 4 0.4040 0.752 0.248 0.000 0.000 0.752
#> GSM559420 1 0.4277 0.724 0.720 0.000 0.000 0.280
#> GSM559421 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM559423 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM559425 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM559426 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM559427 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM559428 2 0.0188 0.989 0.004 0.996 0.000 0.000
#> GSM559429 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM559430 2 0.0000 0.991 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
#> GSM559383 3 0.0000 0.98311 0.000 0.000 1.000 0.000 0.000
#> GSM559387 3 0.0000 0.98311 0.000 0.000 1.000 0.000 0.000
#> GSM559391 3 0.0000 0.98311 0.000 0.000 1.000 0.000 0.000
#> GSM559395 3 0.0000 0.98311 0.000 0.000 1.000 0.000 0.000
#> GSM559397 3 0.0000 0.98311 0.000 0.000 1.000 0.000 0.000
#> GSM559401 3 0.0000 0.98311 0.000 0.000 1.000 0.000 0.000
#> GSM559414 3 0.0000 0.98311 0.000 0.000 1.000 0.000 0.000
#> GSM559422 3 0.2983 0.86648 0.000 0.000 0.864 0.040 0.096
#> GSM559424 3 0.0000 0.98311 0.000 0.000 1.000 0.000 0.000
#> GSM559431 2 0.0000 0.92782 0.000 1.000 0.000 0.000 0.000
#> GSM559432 2 0.5318 0.05860 0.000 0.496 0.460 0.040 0.004
#> GSM559381 1 0.6545 0.40954 0.464 0.000 0.000 0.220 0.316
#> GSM559382 2 0.1281 0.90450 0.000 0.956 0.000 0.012 0.032
#> GSM559384 1 0.6528 0.44998 0.480 0.000 0.000 0.236 0.284
#> GSM559385 5 0.0955 0.86656 0.028 0.000 0.000 0.004 0.968
#> GSM559386 2 0.5648 0.60395 0.020 0.680 0.000 0.160 0.140
#> GSM559388 2 0.0579 0.92136 0.000 0.984 0.000 0.008 0.008
#> GSM559389 5 0.3037 0.80959 0.040 0.000 0.000 0.100 0.860
#> GSM559390 1 0.4886 -0.00479 0.596 0.000 0.000 0.372 0.032
#> GSM559392 2 0.0000 0.92782 0.000 1.000 0.000 0.000 0.000
#> GSM559393 5 0.2588 0.76212 0.000 0.048 0.000 0.060 0.892
#> GSM559394 5 0.1106 0.86151 0.024 0.000 0.000 0.012 0.964
#> GSM559396 3 0.0912 0.96124 0.012 0.000 0.972 0.016 0.000
#> GSM559398 2 0.0000 0.92782 0.000 1.000 0.000 0.000 0.000
#> GSM559399 4 0.4708 0.19633 0.016 0.000 0.000 0.548 0.436
#> GSM559400 2 0.2674 0.81854 0.000 0.856 0.000 0.140 0.004
#> GSM559402 1 0.5984 0.54385 0.588 0.000 0.000 0.208 0.204
#> GSM559403 5 0.2329 0.79003 0.124 0.000 0.000 0.000 0.876
#> GSM559404 1 0.5512 0.53573 0.620 0.000 0.000 0.104 0.276
#> GSM559405 1 0.6218 0.41019 0.488 0.000 0.000 0.148 0.364
#> GSM559406 1 0.3002 0.47664 0.856 0.000 0.028 0.116 0.000
#> GSM559407 1 0.5904 0.54937 0.600 0.000 0.000 0.196 0.204
#> GSM559408 1 0.0880 0.57464 0.968 0.000 0.000 0.032 0.000
#> GSM559409 1 0.0703 0.57883 0.976 0.000 0.000 0.024 0.000
#> GSM559410 1 0.5968 0.36864 0.512 0.000 0.000 0.116 0.372
#> GSM559411 1 0.0880 0.59265 0.968 0.000 0.000 0.032 0.000
#> GSM559412 1 0.0290 0.58820 0.992 0.000 0.000 0.008 0.000
#> GSM559413 1 0.0000 0.58982 1.000 0.000 0.000 0.000 0.000
#> GSM559415 4 0.4294 0.21349 0.000 0.000 0.000 0.532 0.468
#> GSM559416 4 0.3837 0.45739 0.308 0.000 0.000 0.692 0.000
#> GSM559417 4 0.4047 0.44280 0.320 0.000 0.000 0.676 0.004
#> GSM559418 4 0.4590 0.26485 0.000 0.012 0.000 0.568 0.420
#> GSM559419 4 0.3990 0.46208 0.308 0.000 0.000 0.688 0.004
#> GSM559420 4 0.6169 -0.21410 0.392 0.000 0.000 0.472 0.136
#> GSM559421 2 0.0000 0.92782 0.000 1.000 0.000 0.000 0.000
#> GSM559423 2 0.0000 0.92782 0.000 1.000 0.000 0.000 0.000
#> GSM559425 2 0.0000 0.92782 0.000 1.000 0.000 0.000 0.000
#> GSM559426 2 0.0000 0.92782 0.000 1.000 0.000 0.000 0.000
#> GSM559427 2 0.0000 0.92782 0.000 1.000 0.000 0.000 0.000
#> GSM559428 2 0.1012 0.91337 0.000 0.968 0.000 0.020 0.012
#> GSM559429 2 0.0000 0.92782 0.000 1.000 0.000 0.000 0.000
#> GSM559430 2 0.0000 0.92782 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
#> GSM559383 3 0.0000 0.93756 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559387 3 0.0000 0.93756 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559391 3 0.0000 0.93756 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559395 3 0.0000 0.93756 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559397 3 0.0000 0.93756 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559401 3 0.0858 0.91986 0.004 0.000 0.968 0.000 0.000 0.028
#> GSM559414 3 0.0000 0.93756 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559422 3 0.5698 0.45415 0.176 0.000 0.556 0.000 0.008 0.260
#> GSM559424 3 0.0000 0.93756 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559431 2 0.0000 0.85963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559432 2 0.6579 0.07712 0.012 0.388 0.312 0.000 0.008 0.280
#> GSM559381 6 0.7076 0.00000 0.196 0.000 0.000 0.308 0.092 0.404
#> GSM559382 2 0.3499 0.76579 0.032 0.796 0.000 0.000 0.008 0.164
#> GSM559384 4 0.7481 -0.41494 0.168 0.000 0.000 0.376 0.212 0.244
#> GSM559385 1 0.1708 0.78967 0.932 0.000 0.000 0.040 0.004 0.024
#> GSM559386 2 0.7019 0.24612 0.100 0.428 0.000 0.016 0.100 0.356
#> GSM559388 2 0.1781 0.83569 0.008 0.924 0.000 0.000 0.008 0.060
#> GSM559389 1 0.5169 0.49319 0.672 0.000 0.000 0.056 0.060 0.212
#> GSM559390 4 0.6526 -0.17084 0.020 0.000 0.000 0.360 0.340 0.280
#> GSM559392 2 0.0260 0.85841 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM559393 1 0.2317 0.72101 0.900 0.016 0.000 0.000 0.020 0.064
#> GSM559394 1 0.1218 0.78556 0.956 0.000 0.000 0.028 0.012 0.004
#> GSM559396 3 0.2661 0.83310 0.000 0.000 0.872 0.016 0.016 0.096
#> GSM559398 2 0.0260 0.85841 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM559399 5 0.5232 0.38517 0.316 0.000 0.000 0.012 0.588 0.084
#> GSM559400 2 0.5282 0.49113 0.004 0.584 0.000 0.000 0.116 0.296
#> GSM559402 4 0.6445 -0.07341 0.108 0.000 0.000 0.564 0.148 0.180
#> GSM559403 1 0.3351 0.66181 0.820 0.000 0.000 0.136 0.016 0.028
#> GSM559404 4 0.4484 0.24049 0.160 0.000 0.000 0.744 0.056 0.040
#> GSM559405 4 0.6716 -0.23296 0.252 0.000 0.000 0.504 0.104 0.140
#> GSM559406 4 0.3627 0.39693 0.004 0.000 0.052 0.824 0.096 0.024
#> GSM559407 4 0.6043 0.03652 0.100 0.000 0.000 0.616 0.136 0.148
#> GSM559408 4 0.1082 0.49525 0.000 0.000 0.000 0.956 0.040 0.004
#> GSM559409 4 0.0692 0.50274 0.000 0.000 0.000 0.976 0.020 0.004
#> GSM559410 4 0.6094 -0.00339 0.268 0.000 0.000 0.556 0.124 0.052
#> GSM559411 4 0.1245 0.48480 0.000 0.000 0.000 0.952 0.016 0.032
#> GSM559412 4 0.0547 0.50336 0.000 0.000 0.000 0.980 0.020 0.000
#> GSM559413 4 0.0260 0.50200 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM559415 5 0.4486 0.36872 0.384 0.000 0.000 0.004 0.584 0.028
#> GSM559416 5 0.3551 0.50541 0.000 0.000 0.000 0.168 0.784 0.048
#> GSM559417 5 0.4314 0.47037 0.000 0.000 0.000 0.184 0.720 0.096
#> GSM559418 5 0.4774 0.40543 0.336 0.020 0.000 0.000 0.612 0.032
#> GSM559419 5 0.3377 0.50783 0.000 0.000 0.000 0.188 0.784 0.028
#> GSM559420 5 0.7102 -0.30176 0.100 0.000 0.000 0.236 0.432 0.232
#> GSM559421 2 0.0000 0.85963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559423 2 0.0363 0.85805 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM559425 2 0.0000 0.85963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559426 2 0.1411 0.84402 0.000 0.936 0.000 0.000 0.004 0.060
#> GSM559427 2 0.0000 0.85963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559428 2 0.3089 0.77139 0.004 0.800 0.000 0.000 0.008 0.188
#> GSM559429 2 0.1908 0.83012 0.000 0.900 0.000 0.000 0.004 0.096
#> GSM559430 2 0.0000 0.85963 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:skmeans 52 6.10e-01 2
#> MAD:skmeans 51 2.00e-09 3
#> MAD:skmeans 50 2.17e-08 4
#> MAD:skmeans 38 2.79e-06 5
#> MAD:skmeans 31 1.82e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.473 0.747 0.840 0.3720 0.599 0.599
#> 3 3 0.967 0.927 0.973 0.6302 0.633 0.463
#> 4 4 0.816 0.878 0.934 0.2014 0.843 0.625
#> 5 5 0.829 0.881 0.931 0.0240 0.986 0.948
#> 6 6 0.719 0.629 0.830 0.0523 0.946 0.803
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
#> GSM559383 2 0.000 0.8100 0.000 1.000
#> GSM559387 2 0.000 0.8100 0.000 1.000
#> GSM559391 2 0.000 0.8100 0.000 1.000
#> GSM559395 2 0.000 0.8100 0.000 1.000
#> GSM559397 2 0.000 0.8100 0.000 1.000
#> GSM559401 2 0.000 0.8100 0.000 1.000
#> GSM559414 2 0.000 0.8100 0.000 1.000
#> GSM559422 2 0.000 0.8100 0.000 1.000
#> GSM559424 2 0.000 0.8100 0.000 1.000
#> GSM559431 1 0.000 0.7287 1.000 0.000
#> GSM559432 2 0.821 0.5685 0.256 0.744
#> GSM559381 1 0.821 0.8521 0.744 0.256
#> GSM559382 1 0.821 0.8521 0.744 0.256
#> GSM559384 1 0.821 0.8521 0.744 0.256
#> GSM559385 1 0.821 0.8521 0.744 0.256
#> GSM559386 1 0.821 0.8521 0.744 0.256
#> GSM559388 1 0.000 0.7287 1.000 0.000
#> GSM559389 1 0.821 0.8521 0.744 0.256
#> GSM559390 1 0.821 0.8521 0.744 0.256
#> GSM559392 1 0.000 0.7287 1.000 0.000
#> GSM559393 1 0.821 0.8521 0.744 0.256
#> GSM559394 1 0.821 0.8521 0.744 0.256
#> GSM559396 2 0.985 -0.0779 0.428 0.572
#> GSM559398 1 0.000 0.7287 1.000 0.000
#> GSM559399 1 0.821 0.8521 0.744 0.256
#> GSM559400 1 0.295 0.6696 0.948 0.052
#> GSM559402 1 0.821 0.8521 0.744 0.256
#> GSM559403 1 0.821 0.8521 0.744 0.256
#> GSM559404 2 0.997 -0.2184 0.468 0.532
#> GSM559405 1 0.821 0.8521 0.744 0.256
#> GSM559406 2 0.861 0.4397 0.284 0.716
#> GSM559407 1 0.821 0.8521 0.744 0.256
#> GSM559408 1 0.821 0.8521 0.744 0.256
#> GSM559409 1 0.821 0.8521 0.744 0.256
#> GSM559410 1 0.821 0.8521 0.744 0.256
#> GSM559411 1 0.881 0.7922 0.700 0.300
#> GSM559412 1 0.821 0.8521 0.744 0.256
#> GSM559413 2 0.958 0.1588 0.380 0.620
#> GSM559415 1 0.821 0.8521 0.744 0.256
#> GSM559416 1 0.821 0.8521 0.744 0.256
#> GSM559417 1 0.821 0.8521 0.744 0.256
#> GSM559418 1 0.821 0.8521 0.744 0.256
#> GSM559419 1 0.821 0.8521 0.744 0.256
#> GSM559420 1 0.821 0.8521 0.744 0.256
#> GSM559421 1 0.000 0.7287 1.000 0.000
#> GSM559423 1 0.000 0.7287 1.000 0.000
#> GSM559425 1 0.000 0.7287 1.000 0.000
#> GSM559426 1 0.000 0.7287 1.000 0.000
#> GSM559427 1 0.000 0.7287 1.000 0.000
#> GSM559428 1 0.163 0.7399 0.976 0.024
#> GSM559429 1 0.000 0.7287 1.000 0.000
#> GSM559430 1 0.000 0.7287 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559387 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559391 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559395 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559397 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559401 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559414 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559422 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559424 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559431 2 0.0000 0.939 0.000 1.000 0.000
#> GSM559432 2 0.6295 0.120 0.000 0.528 0.472
#> GSM559381 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559382 1 0.5760 0.506 0.672 0.328 0.000
#> GSM559384 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559385 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559386 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559388 2 0.0592 0.927 0.012 0.988 0.000
#> GSM559389 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559390 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559392 2 0.0000 0.939 0.000 1.000 0.000
#> GSM559393 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559394 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559396 1 0.6062 0.380 0.616 0.000 0.384
#> GSM559398 2 0.0000 0.939 0.000 1.000 0.000
#> GSM559399 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559400 2 0.0000 0.939 0.000 1.000 0.000
#> GSM559402 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559403 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559404 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559405 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559406 1 0.0237 0.970 0.996 0.000 0.004
#> GSM559407 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559408 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559409 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559410 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559411 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559412 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559413 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559415 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559416 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559417 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559418 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559419 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559420 1 0.0000 0.974 1.000 0.000 0.000
#> GSM559421 2 0.0000 0.939 0.000 1.000 0.000
#> GSM559423 2 0.0000 0.939 0.000 1.000 0.000
#> GSM559425 2 0.0000 0.939 0.000 1.000 0.000
#> GSM559426 2 0.0000 0.939 0.000 1.000 0.000
#> GSM559427 2 0.0000 0.939 0.000 1.000 0.000
#> GSM559428 2 0.4750 0.668 0.216 0.784 0.000
#> GSM559429 2 0.0000 0.939 0.000 1.000 0.000
#> GSM559430 2 0.0000 0.939 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM559387 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM559391 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM559395 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM559397 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM559401 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM559414 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM559422 3 0.0188 0.995 0.004 0.000 0.996 0.000
#> GSM559424 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM559431 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM559432 2 0.4985 0.129 0.000 0.532 0.468 0.000
#> GSM559381 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM559382 4 0.3688 0.845 0.208 0.000 0.000 0.792
#> GSM559384 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM559385 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM559386 4 0.3688 0.845 0.208 0.000 0.000 0.792
#> GSM559388 4 0.3870 0.844 0.208 0.004 0.000 0.788
#> GSM559389 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM559390 4 0.0000 0.835 0.000 0.000 0.000 1.000
#> GSM559392 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM559393 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM559394 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM559396 1 0.4790 0.443 0.620 0.000 0.380 0.000
#> GSM559398 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM559399 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM559400 4 0.4499 0.835 0.160 0.048 0.000 0.792
#> GSM559402 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM559403 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM559404 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM559405 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM559406 4 0.0000 0.835 0.000 0.000 0.000 1.000
#> GSM559407 1 0.2814 0.842 0.868 0.000 0.000 0.132
#> GSM559408 1 0.3688 0.800 0.792 0.000 0.000 0.208
#> GSM559409 1 0.3688 0.800 0.792 0.000 0.000 0.208
#> GSM559410 1 0.3688 0.800 0.792 0.000 0.000 0.208
#> GSM559411 1 0.3688 0.800 0.792 0.000 0.000 0.208
#> GSM559412 1 0.3688 0.800 0.792 0.000 0.000 0.208
#> GSM559413 1 0.3688 0.800 0.792 0.000 0.000 0.208
#> GSM559415 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM559416 4 0.0000 0.835 0.000 0.000 0.000 1.000
#> GSM559417 4 0.0000 0.835 0.000 0.000 0.000 1.000
#> GSM559418 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM559419 4 0.2921 0.773 0.140 0.000 0.000 0.860
#> GSM559420 1 0.0000 0.901 1.000 0.000 0.000 0.000
#> GSM559421 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM559423 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM559425 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM559426 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM559427 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM559428 4 0.3688 0.845 0.208 0.000 0.000 0.792
#> GSM559429 2 0.0000 0.951 0.000 1.000 0.000 0.000
#> GSM559430 2 0.0000 0.951 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
#> GSM559383 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559387 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559391 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559395 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559397 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559401 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559414 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559422 5 0.1908 1.000 0.000 0.000 0.092 0.000 0.908
#> GSM559424 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM559431 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM559432 5 0.1908 1.000 0.000 0.000 0.092 0.000 0.908
#> GSM559381 1 0.0000 0.897 1.000 0.000 0.000 0.000 0.000
#> GSM559382 4 0.4205 0.750 0.208 0.008 0.000 0.756 0.028
#> GSM559384 1 0.0000 0.897 1.000 0.000 0.000 0.000 0.000
#> GSM559385 1 0.0000 0.897 1.000 0.000 0.000 0.000 0.000
#> GSM559386 4 0.3333 0.754 0.208 0.000 0.000 0.788 0.004
#> GSM559388 4 0.4592 0.743 0.208 0.024 0.000 0.740 0.028
#> GSM559389 1 0.0000 0.897 1.000 0.000 0.000 0.000 0.000
#> GSM559390 4 0.0000 0.780 0.000 0.000 0.000 1.000 0.000
#> GSM559392 2 0.0609 0.979 0.000 0.980 0.000 0.000 0.020
#> GSM559393 1 0.0162 0.895 0.996 0.000 0.000 0.000 0.004
#> GSM559394 1 0.0000 0.897 1.000 0.000 0.000 0.000 0.000
#> GSM559396 1 0.5113 0.448 0.604 0.000 0.352 0.004 0.040
#> GSM559398 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM559399 1 0.0000 0.897 1.000 0.000 0.000 0.000 0.000
#> GSM559400 4 0.3455 0.668 0.008 0.000 0.000 0.784 0.208
#> GSM559402 1 0.0000 0.897 1.000 0.000 0.000 0.000 0.000
#> GSM559403 1 0.0000 0.897 1.000 0.000 0.000 0.000 0.000
#> GSM559404 1 0.0000 0.897 1.000 0.000 0.000 0.000 0.000
#> GSM559405 1 0.0000 0.897 1.000 0.000 0.000 0.000 0.000
#> GSM559406 4 0.0162 0.779 0.004 0.000 0.000 0.996 0.000
#> GSM559407 1 0.2424 0.837 0.868 0.000 0.000 0.132 0.000
#> GSM559408 1 0.3210 0.790 0.788 0.000 0.000 0.212 0.000
#> GSM559409 1 0.4224 0.763 0.744 0.000 0.000 0.216 0.040
#> GSM559410 1 0.3177 0.793 0.792 0.000 0.000 0.208 0.000
#> GSM559411 1 0.4224 0.763 0.744 0.000 0.000 0.216 0.040
#> GSM559412 1 0.3210 0.790 0.788 0.000 0.000 0.212 0.000
#> GSM559413 1 0.4193 0.765 0.748 0.000 0.000 0.212 0.040
#> GSM559415 1 0.0000 0.897 1.000 0.000 0.000 0.000 0.000
#> GSM559416 4 0.0000 0.780 0.000 0.000 0.000 1.000 0.000
#> GSM559417 4 0.0000 0.780 0.000 0.000 0.000 1.000 0.000
#> GSM559418 1 0.0162 0.895 0.996 0.000 0.000 0.004 0.000
#> GSM559419 4 0.3262 0.682 0.124 0.000 0.000 0.840 0.036
#> GSM559420 1 0.0162 0.895 0.996 0.000 0.000 0.004 0.000
#> GSM559421 2 0.0609 0.979 0.000 0.980 0.000 0.000 0.020
#> GSM559423 2 0.0404 0.984 0.000 0.988 0.000 0.000 0.012
#> GSM559425 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM559426 2 0.0703 0.978 0.000 0.976 0.000 0.000 0.024
#> GSM559427 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000
#> GSM559428 4 0.4369 0.744 0.208 0.000 0.000 0.740 0.052
#> GSM559429 2 0.0880 0.974 0.000 0.968 0.000 0.000 0.032
#> GSM559430 2 0.0000 0.988 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
#> GSM559383 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559387 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559391 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559395 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559397 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559401 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559414 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559422 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM559424 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559431 2 0.0000 0.8931 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559432 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM559381 1 0.0000 0.7956 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559382 6 0.5655 0.9203 0.132 0.004 0.000 0.408 0.000 0.456
#> GSM559384 1 0.2092 0.7708 0.876 0.000 0.000 0.124 0.000 0.000
#> GSM559385 1 0.0000 0.7956 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559386 4 0.4558 -0.3085 0.132 0.000 0.000 0.700 0.000 0.168
#> GSM559388 6 0.5767 0.9202 0.124 0.012 0.000 0.392 0.000 0.472
#> GSM559389 1 0.0000 0.7956 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559390 4 0.2340 0.1941 0.000 0.000 0.000 0.852 0.000 0.148
#> GSM559392 2 0.2996 0.7434 0.000 0.772 0.000 0.000 0.000 0.228
#> GSM559393 1 0.3954 0.3439 0.636 0.000 0.000 0.012 0.000 0.352
#> GSM559394 1 0.0000 0.7956 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559396 4 0.6319 0.0728 0.308 0.000 0.036 0.488 0.000 0.168
#> GSM559398 2 0.2597 0.7815 0.000 0.824 0.000 0.000 0.000 0.176
#> GSM559399 1 0.4088 0.2623 0.616 0.000 0.000 0.368 0.000 0.016
#> GSM559400 4 0.5466 -0.6624 0.000 0.000 0.000 0.472 0.124 0.404
#> GSM559402 1 0.2092 0.7708 0.876 0.000 0.000 0.124 0.000 0.000
#> GSM559403 1 0.0000 0.7956 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559404 1 0.0000 0.7956 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559405 1 0.0000 0.7956 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559406 4 0.5571 -0.0130 0.356 0.000 0.000 0.496 0.000 0.148
#> GSM559407 1 0.2053 0.7769 0.888 0.000 0.000 0.108 0.000 0.004
#> GSM559408 1 0.2706 0.7583 0.852 0.000 0.000 0.024 0.000 0.124
#> GSM559409 1 0.4037 0.6897 0.736 0.000 0.000 0.064 0.000 0.200
#> GSM559410 1 0.2346 0.7657 0.868 0.000 0.000 0.008 0.000 0.124
#> GSM559411 1 0.4494 0.6398 0.692 0.000 0.000 0.092 0.000 0.216
#> GSM559412 1 0.2790 0.7557 0.844 0.000 0.000 0.024 0.000 0.132
#> GSM559413 1 0.3876 0.6382 0.700 0.000 0.000 0.024 0.000 0.276
#> GSM559415 1 0.3778 0.5556 0.696 0.000 0.000 0.288 0.000 0.016
#> GSM559416 4 0.0458 0.2138 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM559417 4 0.2219 0.2054 0.000 0.000 0.000 0.864 0.000 0.136
#> GSM559418 1 0.4121 0.2362 0.604 0.000 0.000 0.380 0.000 0.016
#> GSM559419 4 0.3717 0.2784 0.072 0.000 0.000 0.780 0.000 0.148
#> GSM559420 4 0.3868 -0.2749 0.496 0.000 0.000 0.504 0.000 0.000
#> GSM559421 2 0.1141 0.8725 0.000 0.948 0.000 0.000 0.000 0.052
#> GSM559423 2 0.0363 0.8897 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM559425 2 0.0000 0.8931 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559426 2 0.0790 0.8819 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM559427 2 0.0000 0.8931 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559428 4 0.5390 -0.5519 0.132 0.000 0.000 0.540 0.000 0.328
#> GSM559429 2 0.3797 0.4527 0.000 0.580 0.000 0.000 0.000 0.420
#> GSM559430 2 0.0000 0.8931 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:pam 48 1.09e-09 2
#> MAD:pam 50 2.49e-10 3
#> MAD:pam 50 1.26e-09 4
#> MAD:pam 51 2.87e-09 5
#> MAD:pam 38 8.67e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.978 0.974 0.3244 0.683 0.683
#> 3 3 0.979 0.962 0.977 0.9025 0.704 0.567
#> 4 4 0.770 0.819 0.871 0.1028 0.988 0.969
#> 5 5 0.736 0.771 0.802 0.0905 0.834 0.572
#> 6 6 0.858 0.864 0.921 0.0715 0.952 0.800
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM559383 2 0.2778 1.000 0.048 0.952
#> GSM559387 2 0.2778 1.000 0.048 0.952
#> GSM559391 2 0.2778 1.000 0.048 0.952
#> GSM559395 2 0.2778 1.000 0.048 0.952
#> GSM559397 2 0.2778 1.000 0.048 0.952
#> GSM559401 2 0.2778 1.000 0.048 0.952
#> GSM559414 2 0.2778 1.000 0.048 0.952
#> GSM559422 2 0.2778 1.000 0.048 0.952
#> GSM559424 2 0.2778 1.000 0.048 0.952
#> GSM559431 1 0.3114 0.961 0.944 0.056
#> GSM559432 2 0.2778 1.000 0.048 0.952
#> GSM559381 1 0.0376 0.979 0.996 0.004
#> GSM559382 1 0.2778 0.964 0.952 0.048
#> GSM559384 1 0.0000 0.979 1.000 0.000
#> GSM559385 1 0.0000 0.979 1.000 0.000
#> GSM559386 1 0.0376 0.979 0.996 0.004
#> GSM559388 1 0.3114 0.961 0.944 0.056
#> GSM559389 1 0.0000 0.979 1.000 0.000
#> GSM559390 1 0.0938 0.975 0.988 0.012
#> GSM559392 1 0.3114 0.961 0.944 0.056
#> GSM559393 1 0.0000 0.979 1.000 0.000
#> GSM559394 1 0.0000 0.979 1.000 0.000
#> GSM559396 1 0.1414 0.973 0.980 0.020
#> GSM559398 1 0.3114 0.961 0.944 0.056
#> GSM559399 1 0.0376 0.979 0.996 0.004
#> GSM559400 1 0.2236 0.972 0.964 0.036
#> GSM559402 1 0.0376 0.979 0.996 0.004
#> GSM559403 1 0.0000 0.979 1.000 0.000
#> GSM559404 1 0.0000 0.979 1.000 0.000
#> GSM559405 1 0.0000 0.979 1.000 0.000
#> GSM559406 1 0.0938 0.975 0.988 0.012
#> GSM559407 1 0.0376 0.979 0.996 0.004
#> GSM559408 1 0.0938 0.975 0.988 0.012
#> GSM559409 1 0.0000 0.979 1.000 0.000
#> GSM559410 1 0.0000 0.979 1.000 0.000
#> GSM559411 1 0.0938 0.975 0.988 0.012
#> GSM559412 1 0.0938 0.975 0.988 0.012
#> GSM559413 1 0.0938 0.975 0.988 0.012
#> GSM559415 1 0.0376 0.979 0.996 0.004
#> GSM559416 1 0.0938 0.975 0.988 0.012
#> GSM559417 1 0.0938 0.975 0.988 0.012
#> GSM559418 1 0.0000 0.979 1.000 0.000
#> GSM559419 1 0.0672 0.976 0.992 0.008
#> GSM559420 1 0.0000 0.979 1.000 0.000
#> GSM559421 1 0.3114 0.961 0.944 0.056
#> GSM559423 1 0.3114 0.961 0.944 0.056
#> GSM559425 1 0.3114 0.961 0.944 0.056
#> GSM559426 1 0.3114 0.961 0.944 0.056
#> GSM559427 1 0.3114 0.961 0.944 0.056
#> GSM559428 1 0.2948 0.962 0.948 0.052
#> GSM559429 1 0.2948 0.962 0.948 0.052
#> GSM559430 1 0.3114 0.961 0.944 0.056
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.0000 0.986 0.000 0.000 1.000
#> GSM559387 3 0.0000 0.986 0.000 0.000 1.000
#> GSM559391 3 0.0000 0.986 0.000 0.000 1.000
#> GSM559395 3 0.0000 0.986 0.000 0.000 1.000
#> GSM559397 3 0.0000 0.986 0.000 0.000 1.000
#> GSM559401 3 0.0000 0.986 0.000 0.000 1.000
#> GSM559414 3 0.0000 0.986 0.000 0.000 1.000
#> GSM559422 3 0.0000 0.986 0.000 0.000 1.000
#> GSM559424 3 0.0000 0.986 0.000 0.000 1.000
#> GSM559431 2 0.0000 0.984 0.000 1.000 0.000
#> GSM559432 3 0.3412 0.857 0.000 0.124 0.876
#> GSM559381 1 0.0000 0.967 1.000 0.000 0.000
#> GSM559382 2 0.0747 0.974 0.016 0.984 0.000
#> GSM559384 1 0.0000 0.967 1.000 0.000 0.000
#> GSM559385 1 0.1620 0.958 0.964 0.024 0.012
#> GSM559386 1 0.2537 0.927 0.920 0.080 0.000
#> GSM559388 2 0.0237 0.983 0.004 0.996 0.000
#> GSM559389 1 0.1289 0.959 0.968 0.032 0.000
#> GSM559390 1 0.2537 0.927 0.920 0.080 0.000
#> GSM559392 2 0.0000 0.984 0.000 1.000 0.000
#> GSM559393 1 0.1620 0.958 0.964 0.024 0.012
#> GSM559394 1 0.1620 0.958 0.964 0.024 0.012
#> GSM559396 1 0.5268 0.756 0.776 0.212 0.012
#> GSM559398 2 0.0000 0.984 0.000 1.000 0.000
#> GSM559399 1 0.0000 0.967 1.000 0.000 0.000
#> GSM559400 2 0.2229 0.948 0.044 0.944 0.012
#> GSM559402 1 0.0000 0.967 1.000 0.000 0.000
#> GSM559403 1 0.1289 0.959 0.968 0.032 0.000
#> GSM559404 1 0.1289 0.959 0.968 0.032 0.000
#> GSM559405 1 0.0000 0.967 1.000 0.000 0.000
#> GSM559406 1 0.3459 0.908 0.892 0.096 0.012
#> GSM559407 1 0.0000 0.967 1.000 0.000 0.000
#> GSM559408 1 0.0000 0.967 1.000 0.000 0.000
#> GSM559409 1 0.0000 0.967 1.000 0.000 0.000
#> GSM559410 1 0.0000 0.967 1.000 0.000 0.000
#> GSM559411 1 0.2066 0.942 0.940 0.060 0.000
#> GSM559412 1 0.0237 0.967 0.996 0.004 0.000
#> GSM559413 1 0.2066 0.942 0.940 0.060 0.000
#> GSM559415 1 0.0000 0.967 1.000 0.000 0.000
#> GSM559416 1 0.0892 0.964 0.980 0.020 0.000
#> GSM559417 1 0.1031 0.963 0.976 0.024 0.000
#> GSM559418 1 0.1031 0.963 0.976 0.024 0.000
#> GSM559419 1 0.0424 0.966 0.992 0.008 0.000
#> GSM559420 1 0.0747 0.965 0.984 0.016 0.000
#> GSM559421 2 0.0000 0.984 0.000 1.000 0.000
#> GSM559423 2 0.0000 0.984 0.000 1.000 0.000
#> GSM559425 2 0.0000 0.984 0.000 1.000 0.000
#> GSM559426 2 0.0237 0.983 0.004 0.996 0.000
#> GSM559427 2 0.0000 0.984 0.000 1.000 0.000
#> GSM559428 2 0.2116 0.952 0.040 0.948 0.012
#> GSM559429 2 0.2063 0.951 0.044 0.948 0.008
#> GSM559430 2 0.0000 0.984 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.0000 0.892 0.000 0.000 1.000 0.000
#> GSM559387 3 0.0000 0.892 0.000 0.000 1.000 0.000
#> GSM559391 3 0.0000 0.892 0.000 0.000 1.000 0.000
#> GSM559395 3 0.0000 0.892 0.000 0.000 1.000 0.000
#> GSM559397 3 0.0000 0.892 0.000 0.000 1.000 0.000
#> GSM559401 3 0.4933 -0.626 0.000 0.000 0.568 0.432
#> GSM559414 3 0.0000 0.892 0.000 0.000 1.000 0.000
#> GSM559422 4 0.4877 0.991 0.000 0.000 0.408 0.592
#> GSM559424 3 0.0000 0.892 0.000 0.000 1.000 0.000
#> GSM559431 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM559432 4 0.4866 0.991 0.000 0.000 0.404 0.596
#> GSM559381 1 0.2973 0.800 0.856 0.000 0.000 0.144
#> GSM559382 2 0.0336 0.971 0.000 0.992 0.000 0.008
#> GSM559384 1 0.0000 0.816 1.000 0.000 0.000 0.000
#> GSM559385 1 0.3486 0.786 0.812 0.000 0.000 0.188
#> GSM559386 1 0.5674 0.743 0.720 0.148 0.000 0.132
#> GSM559388 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM559389 1 0.2973 0.800 0.856 0.000 0.000 0.144
#> GSM559390 1 0.4853 0.754 0.744 0.036 0.000 0.220
#> GSM559392 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM559393 1 0.4163 0.773 0.792 0.020 0.000 0.188
#> GSM559394 1 0.3486 0.786 0.812 0.000 0.000 0.188
#> GSM559396 1 0.7882 0.401 0.488 0.280 0.012 0.220
#> GSM559398 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM559399 1 0.2408 0.809 0.896 0.000 0.000 0.104
#> GSM559400 2 0.3688 0.731 0.000 0.792 0.000 0.208
#> GSM559402 1 0.1211 0.816 0.960 0.000 0.000 0.040
#> GSM559403 1 0.3311 0.793 0.828 0.000 0.000 0.172
#> GSM559404 1 0.3444 0.788 0.816 0.000 0.000 0.184
#> GSM559405 1 0.2973 0.800 0.856 0.000 0.000 0.144
#> GSM559406 1 0.5179 0.740 0.728 0.052 0.000 0.220
#> GSM559407 1 0.0000 0.816 1.000 0.000 0.000 0.000
#> GSM559408 1 0.3649 0.777 0.796 0.000 0.000 0.204
#> GSM559409 1 0.3569 0.780 0.804 0.000 0.000 0.196
#> GSM559410 1 0.0000 0.816 1.000 0.000 0.000 0.000
#> GSM559411 1 0.4364 0.766 0.764 0.016 0.000 0.220
#> GSM559412 1 0.3726 0.774 0.788 0.000 0.000 0.212
#> GSM559413 1 0.3801 0.771 0.780 0.000 0.000 0.220
#> GSM559415 1 0.2973 0.800 0.856 0.000 0.000 0.144
#> GSM559416 1 0.4574 0.763 0.756 0.024 0.000 0.220
#> GSM559417 1 0.4574 0.763 0.756 0.024 0.000 0.220
#> GSM559418 1 0.3441 0.800 0.856 0.024 0.000 0.120
#> GSM559419 1 0.4290 0.770 0.772 0.016 0.000 0.212
#> GSM559420 1 0.1970 0.810 0.932 0.008 0.000 0.060
#> GSM559421 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM559423 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM559425 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM559426 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM559427 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM559428 2 0.1389 0.933 0.000 0.952 0.000 0.048
#> GSM559429 2 0.0336 0.971 0.000 0.992 0.000 0.008
#> GSM559430 2 0.0000 0.976 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
#> GSM559383 3 0.0000 0.854 0.000 0.000 1.000 0.000 0.000
#> GSM559387 3 0.0000 0.854 0.000 0.000 1.000 0.000 0.000
#> GSM559391 3 0.0404 0.851 0.000 0.000 0.988 0.012 0.000
#> GSM559395 3 0.0000 0.854 0.000 0.000 1.000 0.000 0.000
#> GSM559397 3 0.0000 0.854 0.000 0.000 1.000 0.000 0.000
#> GSM559401 3 0.5426 0.680 0.000 0.000 0.640 0.252 0.108
#> GSM559414 3 0.0000 0.854 0.000 0.000 1.000 0.000 0.000
#> GSM559422 3 0.6725 0.527 0.000 0.000 0.420 0.288 0.292
#> GSM559424 3 0.0703 0.848 0.000 0.000 0.976 0.024 0.000
#> GSM559431 2 0.0000 0.911 0.000 1.000 0.000 0.000 0.000
#> GSM559432 3 0.6779 0.489 0.000 0.000 0.384 0.284 0.332
#> GSM559381 1 0.0000 0.816 1.000 0.000 0.000 0.000 0.000
#> GSM559382 2 0.3687 0.821 0.028 0.792 0.000 0.180 0.000
#> GSM559384 1 0.1484 0.792 0.944 0.000 0.000 0.008 0.048
#> GSM559385 5 0.3752 0.935 0.292 0.000 0.000 0.000 0.708
#> GSM559386 1 0.2535 0.713 0.892 0.076 0.000 0.032 0.000
#> GSM559388 2 0.1544 0.893 0.000 0.932 0.000 0.068 0.000
#> GSM559389 1 0.0955 0.794 0.968 0.004 0.000 0.000 0.028
#> GSM559390 4 0.4446 0.909 0.400 0.008 0.000 0.592 0.000
#> GSM559392 2 0.0404 0.909 0.000 0.988 0.000 0.012 0.000
#> GSM559393 5 0.4890 0.866 0.224 0.008 0.000 0.060 0.708
#> GSM559394 5 0.3796 0.936 0.300 0.000 0.000 0.000 0.700
#> GSM559396 4 0.5158 0.793 0.308 0.040 0.012 0.640 0.000
#> GSM559398 2 0.0000 0.911 0.000 1.000 0.000 0.000 0.000
#> GSM559399 1 0.0000 0.816 1.000 0.000 0.000 0.000 0.000
#> GSM559400 2 0.4455 0.555 0.008 0.588 0.000 0.404 0.000
#> GSM559402 1 0.0000 0.816 1.000 0.000 0.000 0.000 0.000
#> GSM559403 1 0.4166 0.180 0.648 0.004 0.000 0.000 0.348
#> GSM559404 5 0.4270 0.909 0.320 0.000 0.000 0.012 0.668
#> GSM559405 1 0.0000 0.816 1.000 0.000 0.000 0.000 0.000
#> GSM559406 4 0.4575 0.903 0.392 0.008 0.000 0.596 0.004
#> GSM559407 1 0.0000 0.816 1.000 0.000 0.000 0.000 0.000
#> GSM559408 1 0.3039 0.559 0.808 0.000 0.000 0.192 0.000
#> GSM559409 1 0.1608 0.768 0.928 0.000 0.000 0.072 0.000
#> GSM559410 1 0.0000 0.816 1.000 0.000 0.000 0.000 0.000
#> GSM559411 4 0.4273 0.838 0.448 0.000 0.000 0.552 0.000
#> GSM559412 1 0.3177 0.530 0.792 0.000 0.000 0.208 0.000
#> GSM559413 1 0.3990 0.151 0.688 0.000 0.000 0.308 0.004
#> GSM559415 1 0.0000 0.816 1.000 0.000 0.000 0.000 0.000
#> GSM559416 4 0.4201 0.907 0.408 0.000 0.000 0.592 0.000
#> GSM559417 4 0.4235 0.892 0.424 0.000 0.000 0.576 0.000
#> GSM559418 1 0.1331 0.775 0.952 0.008 0.000 0.040 0.000
#> GSM559419 1 0.4114 -0.232 0.624 0.000 0.000 0.376 0.000
#> GSM559420 1 0.1410 0.766 0.940 0.000 0.000 0.060 0.000
#> GSM559421 2 0.0000 0.911 0.000 1.000 0.000 0.000 0.000
#> GSM559423 2 0.1478 0.894 0.000 0.936 0.000 0.064 0.000
#> GSM559425 2 0.0000 0.911 0.000 1.000 0.000 0.000 0.000
#> GSM559426 2 0.0000 0.911 0.000 1.000 0.000 0.000 0.000
#> GSM559427 2 0.0000 0.911 0.000 1.000 0.000 0.000 0.000
#> GSM559428 2 0.4150 0.789 0.036 0.748 0.000 0.216 0.000
#> GSM559429 2 0.4054 0.798 0.036 0.760 0.000 0.204 0.000
#> GSM559430 2 0.0000 0.911 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
#> GSM559383 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559387 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559391 3 0.0865 0.965 0.000 0.000 0.964 0.036 0.000 0.000
#> GSM559395 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559397 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559401 5 0.3309 0.859 0.000 0.000 0.280 0.000 0.720 0.000
#> GSM559414 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559422 5 0.2631 0.937 0.000 0.000 0.180 0.000 0.820 0.000
#> GSM559424 3 0.0865 0.965 0.000 0.000 0.964 0.036 0.000 0.000
#> GSM559431 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559432 5 0.2631 0.937 0.000 0.000 0.180 0.000 0.820 0.000
#> GSM559381 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559382 2 0.2384 0.898 0.000 0.884 0.000 0.032 0.084 0.000
#> GSM559384 1 0.2066 0.867 0.904 0.000 0.000 0.000 0.024 0.072
#> GSM559385 6 0.0000 0.854 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559386 1 0.1625 0.867 0.928 0.060 0.000 0.012 0.000 0.000
#> GSM559388 2 0.0260 0.952 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM559389 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559390 4 0.2384 0.785 0.048 0.000 0.000 0.888 0.064 0.000
#> GSM559392 2 0.0260 0.952 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM559393 6 0.0000 0.854 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559394 6 0.0000 0.854 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559396 4 0.1812 0.715 0.008 0.000 0.000 0.912 0.080 0.000
#> GSM559398 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559399 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559400 2 0.4200 0.743 0.000 0.740 0.000 0.120 0.140 0.000
#> GSM559402 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559403 6 0.3428 0.531 0.304 0.000 0.000 0.000 0.000 0.696
#> GSM559404 6 0.1267 0.828 0.060 0.000 0.000 0.000 0.000 0.940
#> GSM559405 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559406 4 0.2136 0.769 0.048 0.000 0.000 0.904 0.048 0.000
#> GSM559407 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559408 1 0.3364 0.761 0.780 0.000 0.000 0.196 0.024 0.000
#> GSM559409 1 0.2988 0.810 0.824 0.000 0.000 0.152 0.024 0.000
#> GSM559410 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559411 4 0.3309 0.591 0.280 0.000 0.000 0.720 0.000 0.000
#> GSM559412 1 0.3364 0.761 0.780 0.000 0.000 0.196 0.024 0.000
#> GSM559413 1 0.3266 0.675 0.728 0.000 0.000 0.272 0.000 0.000
#> GSM559415 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559416 4 0.2258 0.785 0.044 0.000 0.000 0.896 0.060 0.000
#> GSM559417 4 0.2258 0.785 0.044 0.000 0.000 0.896 0.060 0.000
#> GSM559418 1 0.0622 0.903 0.980 0.000 0.000 0.008 0.000 0.012
#> GSM559419 4 0.3774 0.278 0.408 0.000 0.000 0.592 0.000 0.000
#> GSM559420 1 0.2165 0.853 0.884 0.000 0.000 0.108 0.008 0.000
#> GSM559421 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559423 2 0.0260 0.952 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM559425 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559426 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559427 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559428 2 0.2537 0.891 0.000 0.872 0.000 0.032 0.096 0.000
#> GSM559429 2 0.2487 0.893 0.000 0.876 0.000 0.032 0.092 0.000
#> GSM559430 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:mclust 52 1.99e-10 2
#> MAD:mclust 52 8.27e-11 3
#> MAD:mclust 50 1.37e-09 4
#> MAD:mclust 48 1.40e-08 5
#> MAD:mclust 51 1.14e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.880 0.944 0.973 0.4788 0.527 0.527
#> 3 3 0.969 0.917 0.968 0.3424 0.775 0.593
#> 4 4 0.680 0.625 0.834 0.1157 0.825 0.570
#> 5 5 0.654 0.671 0.795 0.0905 0.839 0.516
#> 6 6 0.671 0.633 0.771 0.0556 0.916 0.654
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
#> GSM559383 1 0.0000 0.964 1.000 0.000
#> GSM559387 1 0.0000 0.964 1.000 0.000
#> GSM559391 1 0.0000 0.964 1.000 0.000
#> GSM559395 1 0.0000 0.964 1.000 0.000
#> GSM559397 1 0.0000 0.964 1.000 0.000
#> GSM559401 1 0.0000 0.964 1.000 0.000
#> GSM559414 1 0.0000 0.964 1.000 0.000
#> GSM559422 1 0.0000 0.964 1.000 0.000
#> GSM559424 1 0.0000 0.964 1.000 0.000
#> GSM559431 2 0.0000 0.983 0.000 1.000
#> GSM559432 2 0.3431 0.922 0.064 0.936
#> GSM559381 1 0.7950 0.721 0.760 0.240
#> GSM559382 2 0.0000 0.983 0.000 1.000
#> GSM559384 1 0.0000 0.964 1.000 0.000
#> GSM559385 1 0.0000 0.964 1.000 0.000
#> GSM559386 2 0.0000 0.983 0.000 1.000
#> GSM559388 2 0.0000 0.983 0.000 1.000
#> GSM559389 1 0.7883 0.727 0.764 0.236
#> GSM559390 1 0.0376 0.963 0.996 0.004
#> GSM559392 2 0.0000 0.983 0.000 1.000
#> GSM559393 2 0.0000 0.983 0.000 1.000
#> GSM559394 1 0.5408 0.864 0.876 0.124
#> GSM559396 1 0.0000 0.964 1.000 0.000
#> GSM559398 2 0.0000 0.983 0.000 1.000
#> GSM559399 1 0.3879 0.909 0.924 0.076
#> GSM559400 2 0.0000 0.983 0.000 1.000
#> GSM559402 1 0.1633 0.950 0.976 0.024
#> GSM559403 1 0.0672 0.961 0.992 0.008
#> GSM559404 1 0.0000 0.964 1.000 0.000
#> GSM559405 1 0.0376 0.963 0.996 0.004
#> GSM559406 1 0.0000 0.964 1.000 0.000
#> GSM559407 1 0.0000 0.964 1.000 0.000
#> GSM559408 1 0.0000 0.964 1.000 0.000
#> GSM559409 1 0.0000 0.964 1.000 0.000
#> GSM559410 1 0.0672 0.961 0.992 0.008
#> GSM559411 1 0.0000 0.964 1.000 0.000
#> GSM559412 1 0.0000 0.964 1.000 0.000
#> GSM559413 1 0.0000 0.964 1.000 0.000
#> GSM559415 1 0.8443 0.668 0.728 0.272
#> GSM559416 1 0.5408 0.858 0.876 0.124
#> GSM559417 2 0.7815 0.687 0.232 0.768
#> GSM559418 2 0.0000 0.983 0.000 1.000
#> GSM559419 1 0.0672 0.961 0.992 0.008
#> GSM559420 1 0.0000 0.964 1.000 0.000
#> GSM559421 2 0.0000 0.983 0.000 1.000
#> GSM559423 2 0.0000 0.983 0.000 1.000
#> GSM559425 2 0.0000 0.983 0.000 1.000
#> GSM559426 2 0.0000 0.983 0.000 1.000
#> GSM559427 2 0.0000 0.983 0.000 1.000
#> GSM559428 2 0.0000 0.983 0.000 1.000
#> GSM559429 2 0.0000 0.983 0.000 1.000
#> GSM559430 2 0.0000 0.983 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.0000 0.996 0.000 0.000 1.000
#> GSM559387 3 0.0000 0.996 0.000 0.000 1.000
#> GSM559391 3 0.0000 0.996 0.000 0.000 1.000
#> GSM559395 3 0.0000 0.996 0.000 0.000 1.000
#> GSM559397 3 0.0000 0.996 0.000 0.000 1.000
#> GSM559401 3 0.0000 0.996 0.000 0.000 1.000
#> GSM559414 3 0.0000 0.996 0.000 0.000 1.000
#> GSM559422 3 0.0000 0.996 0.000 0.000 1.000
#> GSM559424 3 0.0000 0.996 0.000 0.000 1.000
#> GSM559431 2 0.0000 0.915 0.000 1.000 0.000
#> GSM559432 3 0.0000 0.996 0.000 0.000 1.000
#> GSM559381 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559382 2 0.0000 0.915 0.000 1.000 0.000
#> GSM559384 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559385 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559386 2 0.6126 0.380 0.400 0.600 0.000
#> GSM559388 2 0.0000 0.915 0.000 1.000 0.000
#> GSM559389 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559390 1 0.1411 0.944 0.964 0.000 0.036
#> GSM559392 2 0.0000 0.915 0.000 1.000 0.000
#> GSM559393 2 0.6062 0.420 0.384 0.616 0.000
#> GSM559394 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559396 3 0.1411 0.958 0.036 0.000 0.964
#> GSM559398 2 0.0000 0.915 0.000 1.000 0.000
#> GSM559399 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559400 2 0.1753 0.876 0.000 0.952 0.048
#> GSM559402 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559403 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559404 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559405 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559406 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559407 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559408 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559409 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559410 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559411 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559412 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559413 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559415 1 0.0237 0.974 0.996 0.004 0.000
#> GSM559416 1 0.1411 0.942 0.964 0.036 0.000
#> GSM559417 1 0.6168 0.202 0.588 0.412 0.000
#> GSM559418 2 0.5465 0.608 0.288 0.712 0.000
#> GSM559419 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559420 1 0.0000 0.976 1.000 0.000 0.000
#> GSM559421 2 0.0000 0.915 0.000 1.000 0.000
#> GSM559423 2 0.0000 0.915 0.000 1.000 0.000
#> GSM559425 2 0.0000 0.915 0.000 1.000 0.000
#> GSM559426 2 0.0000 0.915 0.000 1.000 0.000
#> GSM559427 2 0.0000 0.915 0.000 1.000 0.000
#> GSM559428 2 0.0000 0.915 0.000 1.000 0.000
#> GSM559429 2 0.0000 0.915 0.000 1.000 0.000
#> GSM559430 2 0.0000 0.915 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 4 0.4543 -0.1049 0.000 0.000 0.324 0.676
#> GSM559387 4 0.4994 -0.5326 0.000 0.000 0.480 0.520
#> GSM559391 4 0.3907 0.1696 0.000 0.000 0.232 0.768
#> GSM559395 3 0.5000 0.4407 0.000 0.000 0.504 0.496
#> GSM559397 3 0.4817 0.5811 0.000 0.000 0.612 0.388
#> GSM559401 3 0.2281 0.6571 0.000 0.000 0.904 0.096
#> GSM559414 3 0.4985 0.4956 0.000 0.000 0.532 0.468
#> GSM559422 3 0.0469 0.6366 0.000 0.000 0.988 0.012
#> GSM559424 4 0.3764 0.2012 0.000 0.000 0.216 0.784
#> GSM559431 2 0.0188 0.9101 0.000 0.996 0.000 0.004
#> GSM559432 3 0.0188 0.6251 0.000 0.004 0.996 0.000
#> GSM559381 1 0.0921 0.8235 0.972 0.000 0.000 0.028
#> GSM559382 2 0.1305 0.9010 0.000 0.960 0.036 0.004
#> GSM559384 1 0.2216 0.7984 0.908 0.000 0.000 0.092
#> GSM559385 1 0.0672 0.8183 0.984 0.000 0.008 0.008
#> GSM559386 2 0.5987 0.0351 0.440 0.520 0.000 0.040
#> GSM559388 2 0.0927 0.9078 0.000 0.976 0.016 0.008
#> GSM559389 1 0.0707 0.8234 0.980 0.000 0.000 0.020
#> GSM559390 4 0.5309 0.3285 0.280 0.028 0.004 0.688
#> GSM559392 2 0.0895 0.9081 0.000 0.976 0.020 0.004
#> GSM559393 1 0.5422 0.6116 0.740 0.040 0.200 0.020
#> GSM559394 1 0.3737 0.7086 0.840 0.004 0.136 0.020
#> GSM559396 4 0.3552 0.2957 0.024 0.000 0.128 0.848
#> GSM559398 2 0.0817 0.9069 0.000 0.976 0.024 0.000
#> GSM559399 1 0.1302 0.8216 0.956 0.000 0.000 0.044
#> GSM559400 2 0.3691 0.8257 0.000 0.856 0.076 0.068
#> GSM559402 1 0.1940 0.8137 0.924 0.000 0.000 0.076
#> GSM559403 1 0.0469 0.8199 0.988 0.000 0.000 0.012
#> GSM559404 1 0.0188 0.8219 0.996 0.000 0.000 0.004
#> GSM559405 1 0.0000 0.8226 1.000 0.000 0.000 0.000
#> GSM559406 1 0.5000 0.2189 0.504 0.000 0.000 0.496
#> GSM559407 1 0.2530 0.8003 0.888 0.000 0.000 0.112
#> GSM559408 1 0.4164 0.6734 0.736 0.000 0.000 0.264
#> GSM559409 1 0.2589 0.7976 0.884 0.000 0.000 0.116
#> GSM559410 1 0.0336 0.8238 0.992 0.000 0.000 0.008
#> GSM559411 4 0.4008 0.4195 0.244 0.000 0.000 0.756
#> GSM559412 1 0.4356 0.6411 0.708 0.000 0.000 0.292
#> GSM559413 1 0.4605 0.5807 0.664 0.000 0.000 0.336
#> GSM559415 1 0.0376 0.8222 0.992 0.004 0.000 0.004
#> GSM559416 4 0.6054 0.3292 0.088 0.256 0.000 0.656
#> GSM559417 2 0.6570 0.3317 0.080 0.572 0.004 0.344
#> GSM559418 1 0.5143 0.4221 0.628 0.360 0.000 0.012
#> GSM559419 4 0.5125 0.0407 0.388 0.008 0.000 0.604
#> GSM559420 1 0.4713 0.4319 0.640 0.000 0.000 0.360
#> GSM559421 2 0.0336 0.9095 0.000 0.992 0.000 0.008
#> GSM559423 2 0.1059 0.9075 0.000 0.972 0.016 0.012
#> GSM559425 2 0.0000 0.9104 0.000 1.000 0.000 0.000
#> GSM559426 2 0.0592 0.9086 0.000 0.984 0.000 0.016
#> GSM559427 2 0.0188 0.9101 0.000 0.996 0.000 0.004
#> GSM559428 2 0.0592 0.9089 0.000 0.984 0.000 0.016
#> GSM559429 2 0.0592 0.9086 0.000 0.984 0.000 0.016
#> GSM559430 2 0.0188 0.9103 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
#> GSM559383 3 0.1571 0.7932 0.000 0.000 0.936 0.060 0.004
#> GSM559387 3 0.1282 0.7911 0.000 0.000 0.952 0.004 0.044
#> GSM559391 3 0.3152 0.7530 0.000 0.000 0.840 0.136 0.024
#> GSM559395 3 0.1282 0.7915 0.000 0.000 0.952 0.004 0.044
#> GSM559397 3 0.2329 0.7073 0.000 0.000 0.876 0.000 0.124
#> GSM559401 5 0.4074 0.5844 0.000 0.000 0.364 0.000 0.636
#> GSM559414 3 0.1908 0.7491 0.000 0.000 0.908 0.000 0.092
#> GSM559422 5 0.3796 0.6613 0.000 0.000 0.300 0.000 0.700
#> GSM559424 3 0.2997 0.7498 0.000 0.000 0.840 0.148 0.012
#> GSM559431 2 0.1741 0.8024 0.000 0.936 0.000 0.024 0.040
#> GSM559432 5 0.3752 0.6629 0.000 0.000 0.292 0.000 0.708
#> GSM559381 1 0.2060 0.7921 0.924 0.008 0.000 0.052 0.016
#> GSM559382 2 0.3003 0.7822 0.000 0.864 0.000 0.044 0.092
#> GSM559384 1 0.5055 0.6769 0.760 0.004 0.068 0.048 0.120
#> GSM559385 1 0.0324 0.7970 0.992 0.000 0.000 0.004 0.004
#> GSM559386 2 0.7233 0.0753 0.384 0.424 0.000 0.136 0.056
#> GSM559388 2 0.4562 0.7337 0.004 0.760 0.000 0.108 0.128
#> GSM559389 1 0.0671 0.7966 0.980 0.004 0.000 0.000 0.016
#> GSM559390 4 0.3947 0.6880 0.036 0.028 0.068 0.844 0.024
#> GSM559392 2 0.3651 0.7721 0.004 0.828 0.000 0.060 0.108
#> GSM559393 1 0.4937 0.6337 0.740 0.060 0.000 0.028 0.172
#> GSM559394 1 0.2612 0.7479 0.868 0.000 0.000 0.008 0.124
#> GSM559396 3 0.5912 0.6020 0.004 0.076 0.700 0.096 0.124
#> GSM559398 2 0.4025 0.7545 0.000 0.792 0.000 0.076 0.132
#> GSM559399 1 0.2554 0.7831 0.896 0.008 0.000 0.076 0.020
#> GSM559400 5 0.6649 0.1903 0.000 0.216 0.004 0.308 0.472
#> GSM559402 1 0.3787 0.7359 0.824 0.008 0.000 0.104 0.064
#> GSM559403 1 0.0162 0.7975 0.996 0.000 0.000 0.000 0.004
#> GSM559404 1 0.1478 0.7820 0.936 0.000 0.000 0.064 0.000
#> GSM559405 1 0.0671 0.7973 0.980 0.000 0.000 0.016 0.004
#> GSM559406 4 0.4668 0.7520 0.168 0.000 0.076 0.748 0.008
#> GSM559407 1 0.5111 -0.2755 0.500 0.000 0.000 0.464 0.036
#> GSM559408 4 0.4152 0.6783 0.296 0.000 0.000 0.692 0.012
#> GSM559409 4 0.4641 0.3795 0.456 0.000 0.000 0.532 0.012
#> GSM559410 1 0.2488 0.7395 0.872 0.000 0.000 0.124 0.004
#> GSM559411 4 0.5974 0.6815 0.108 0.000 0.176 0.668 0.048
#> GSM559412 4 0.4403 0.6707 0.316 0.000 0.004 0.668 0.012
#> GSM559413 4 0.4839 0.6789 0.304 0.000 0.012 0.660 0.024
#> GSM559415 1 0.4204 0.7324 0.808 0.028 0.000 0.104 0.060
#> GSM559416 4 0.2735 0.6522 0.004 0.036 0.056 0.896 0.008
#> GSM559417 4 0.2894 0.6006 0.004 0.084 0.000 0.876 0.036
#> GSM559418 2 0.6571 0.3517 0.348 0.524 0.000 0.068 0.060
#> GSM559419 4 0.5127 0.7435 0.132 0.000 0.096 0.740 0.032
#> GSM559420 1 0.8029 0.2187 0.448 0.004 0.248 0.176 0.124
#> GSM559421 2 0.1915 0.8060 0.000 0.928 0.000 0.032 0.040
#> GSM559423 2 0.3008 0.7726 0.004 0.868 0.000 0.036 0.092
#> GSM559425 2 0.1386 0.8060 0.000 0.952 0.000 0.032 0.016
#> GSM559426 2 0.3030 0.7699 0.004 0.868 0.000 0.040 0.088
#> GSM559427 2 0.3159 0.7842 0.000 0.856 0.000 0.056 0.088
#> GSM559428 2 0.2927 0.7701 0.000 0.868 0.000 0.040 0.092
#> GSM559429 2 0.3161 0.7661 0.004 0.860 0.000 0.044 0.092
#> GSM559430 2 0.1117 0.8056 0.000 0.964 0.000 0.016 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559383 3 0.1010 0.8801 0.000 0.000 0.960 0.000 0.036 0.004
#> GSM559387 3 0.1910 0.8738 0.000 0.000 0.892 0.000 0.108 0.000
#> GSM559391 3 0.1053 0.8511 0.000 0.000 0.964 0.004 0.020 0.012
#> GSM559395 3 0.1714 0.8789 0.000 0.000 0.908 0.000 0.092 0.000
#> GSM559397 3 0.2838 0.8140 0.000 0.000 0.808 0.000 0.188 0.004
#> GSM559401 5 0.2003 0.9500 0.000 0.000 0.116 0.000 0.884 0.000
#> GSM559414 3 0.2882 0.8193 0.000 0.000 0.812 0.000 0.180 0.008
#> GSM559422 5 0.1444 0.9648 0.000 0.000 0.072 0.000 0.928 0.000
#> GSM559424 3 0.0881 0.8682 0.000 0.000 0.972 0.008 0.012 0.008
#> GSM559431 6 0.3975 0.4363 0.000 0.452 0.000 0.004 0.000 0.544
#> GSM559432 5 0.1753 0.9699 0.000 0.000 0.084 0.000 0.912 0.004
#> GSM559381 1 0.4903 0.6717 0.740 0.036 0.004 0.072 0.012 0.136
#> GSM559382 2 0.5766 0.0416 0.040 0.584 0.000 0.064 0.012 0.300
#> GSM559384 1 0.5888 0.6085 0.636 0.004 0.100 0.044 0.012 0.204
#> GSM559385 1 0.1452 0.7283 0.948 0.020 0.000 0.012 0.000 0.020
#> GSM559386 1 0.7840 0.1044 0.340 0.212 0.000 0.176 0.012 0.260
#> GSM559388 2 0.1691 0.4677 0.028 0.940 0.000 0.012 0.008 0.012
#> GSM559389 1 0.2159 0.7281 0.916 0.040 0.000 0.016 0.004 0.024
#> GSM559390 4 0.3172 0.8163 0.008 0.104 0.008 0.852 0.016 0.012
#> GSM559392 2 0.2051 0.4600 0.004 0.896 0.000 0.000 0.004 0.096
#> GSM559393 1 0.4224 0.5688 0.700 0.256 0.000 0.000 0.036 0.008
#> GSM559394 1 0.2374 0.7192 0.904 0.028 0.000 0.004 0.048 0.016
#> GSM559396 3 0.2730 0.7822 0.004 0.000 0.864 0.004 0.020 0.108
#> GSM559398 2 0.1555 0.4741 0.004 0.932 0.000 0.000 0.004 0.060
#> GSM559399 1 0.5023 0.6150 0.700 0.208 0.008 0.020 0.012 0.052
#> GSM559400 2 0.5843 0.1186 0.000 0.516 0.000 0.220 0.260 0.004
#> GSM559402 1 0.5880 0.4868 0.572 0.000 0.020 0.284 0.012 0.112
#> GSM559403 1 0.0603 0.7269 0.980 0.000 0.000 0.016 0.000 0.004
#> GSM559404 1 0.3997 0.6790 0.776 0.000 0.000 0.108 0.008 0.108
#> GSM559405 1 0.1700 0.7293 0.928 0.000 0.000 0.048 0.000 0.024
#> GSM559406 4 0.3080 0.8467 0.032 0.036 0.020 0.880 0.012 0.020
#> GSM559407 4 0.4893 0.6372 0.204 0.004 0.020 0.712 0.028 0.032
#> GSM559408 4 0.1059 0.8706 0.016 0.016 0.004 0.964 0.000 0.000
#> GSM559409 4 0.3948 0.6888 0.208 0.020 0.000 0.752 0.004 0.016
#> GSM559410 1 0.3277 0.6739 0.792 0.000 0.000 0.188 0.004 0.016
#> GSM559411 4 0.4057 0.8175 0.020 0.000 0.116 0.800 0.032 0.032
#> GSM559412 4 0.1168 0.8662 0.028 0.000 0.000 0.956 0.000 0.016
#> GSM559413 4 0.1793 0.8628 0.036 0.000 0.000 0.928 0.004 0.032
#> GSM559415 1 0.5941 0.6035 0.632 0.040 0.000 0.152 0.016 0.160
#> GSM559416 4 0.2843 0.8474 0.004 0.060 0.040 0.880 0.008 0.008
#> GSM559417 4 0.2151 0.8615 0.004 0.040 0.016 0.920 0.012 0.008
#> GSM559418 2 0.6295 0.0879 0.332 0.456 0.000 0.024 0.000 0.188
#> GSM559419 4 0.3198 0.8497 0.024 0.000 0.060 0.864 0.020 0.032
#> GSM559420 1 0.7827 0.2136 0.320 0.012 0.304 0.092 0.012 0.260
#> GSM559421 2 0.3756 -0.1195 0.000 0.600 0.000 0.000 0.000 0.400
#> GSM559423 6 0.3420 0.7188 0.012 0.240 0.000 0.000 0.000 0.748
#> GSM559425 2 0.3899 -0.1841 0.000 0.592 0.000 0.004 0.000 0.404
#> GSM559426 6 0.3133 0.7615 0.008 0.212 0.000 0.000 0.000 0.780
#> GSM559427 2 0.3052 0.3323 0.000 0.780 0.000 0.004 0.000 0.216
#> GSM559428 6 0.3250 0.7546 0.004 0.196 0.012 0.000 0.000 0.788
#> GSM559429 6 0.3121 0.7475 0.004 0.180 0.012 0.000 0.000 0.804
#> GSM559430 6 0.3866 0.3651 0.000 0.484 0.000 0.000 0.000 0.516
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:NMF 52 2.84e-01 2
#> MAD:NMF 49 4.55e-09 3
#> MAD:NMF 36 7.39e-07 4
#> MAD:NMF 46 2.74e-07 5
#> MAD:NMF 38 9.49e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.788 0.961 0.973 0.4173 0.566 0.566
#> 3 3 0.684 0.818 0.904 0.5718 0.759 0.573
#> 4 4 0.713 0.682 0.827 0.0640 0.989 0.965
#> 5 5 0.736 0.660 0.781 0.0917 0.891 0.671
#> 6 6 0.773 0.710 0.855 0.0338 0.958 0.826
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
#> GSM559383 2 0.0000 0.990 0.000 1.000
#> GSM559387 2 0.0000 0.990 0.000 1.000
#> GSM559391 2 0.0000 0.990 0.000 1.000
#> GSM559395 2 0.0000 0.990 0.000 1.000
#> GSM559397 1 0.0000 0.929 1.000 0.000
#> GSM559401 2 0.0000 0.990 0.000 1.000
#> GSM559414 2 0.0000 0.990 0.000 1.000
#> GSM559422 1 0.6973 0.843 0.812 0.188
#> GSM559424 2 0.0000 0.990 0.000 1.000
#> GSM559431 2 0.0938 0.989 0.012 0.988
#> GSM559432 2 0.0938 0.989 0.012 0.988
#> GSM559381 1 0.0000 0.929 1.000 0.000
#> GSM559382 1 0.0000 0.929 1.000 0.000
#> GSM559384 1 0.0000 0.929 1.000 0.000
#> GSM559385 2 0.0376 0.990 0.004 0.996
#> GSM559386 1 0.0000 0.929 1.000 0.000
#> GSM559388 2 0.1184 0.989 0.016 0.984
#> GSM559389 1 0.0000 0.929 1.000 0.000
#> GSM559390 2 0.2778 0.955 0.048 0.952
#> GSM559392 2 0.1184 0.989 0.016 0.984
#> GSM559393 2 0.0376 0.990 0.004 0.996
#> GSM559394 2 0.0376 0.990 0.004 0.996
#> GSM559396 1 0.4690 0.906 0.900 0.100
#> GSM559398 2 0.0938 0.989 0.012 0.988
#> GSM559399 2 0.0672 0.990 0.008 0.992
#> GSM559400 2 0.1184 0.989 0.016 0.984
#> GSM559402 2 0.3114 0.942 0.056 0.944
#> GSM559403 2 0.0376 0.990 0.004 0.996
#> GSM559404 1 0.6973 0.847 0.812 0.188
#> GSM559405 1 0.0000 0.929 1.000 0.000
#> GSM559406 1 0.4690 0.906 0.900 0.100
#> GSM559407 2 0.0376 0.990 0.004 0.996
#> GSM559408 1 0.4690 0.906 0.900 0.100
#> GSM559409 2 0.0376 0.990 0.004 0.996
#> GSM559410 2 0.0000 0.990 0.000 1.000
#> GSM559411 2 0.0000 0.990 0.000 1.000
#> GSM559412 1 0.6973 0.847 0.812 0.188
#> GSM559413 1 0.6973 0.847 0.812 0.188
#> GSM559415 2 0.0672 0.990 0.008 0.992
#> GSM559416 2 0.0672 0.990 0.008 0.992
#> GSM559417 2 0.0672 0.990 0.008 0.992
#> GSM559418 2 0.0672 0.990 0.008 0.992
#> GSM559419 2 0.1843 0.976 0.028 0.972
#> GSM559420 1 0.0000 0.929 1.000 0.000
#> GSM559421 2 0.1184 0.989 0.016 0.984
#> GSM559423 2 0.1184 0.989 0.016 0.984
#> GSM559425 2 0.0938 0.989 0.012 0.988
#> GSM559426 2 0.0938 0.989 0.012 0.988
#> GSM559427 2 0.0938 0.989 0.012 0.988
#> GSM559428 1 0.0000 0.929 1.000 0.000
#> GSM559429 2 0.1184 0.989 0.016 0.984
#> GSM559430 2 0.0938 0.989 0.012 0.988
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.0237 0.925 0.000 0.004 0.996
#> GSM559387 3 0.0000 0.923 0.000 0.000 1.000
#> GSM559391 3 0.0237 0.925 0.000 0.004 0.996
#> GSM559395 3 0.0000 0.923 0.000 0.000 1.000
#> GSM559397 1 0.0000 0.927 1.000 0.000 0.000
#> GSM559401 3 0.0000 0.923 0.000 0.000 1.000
#> GSM559414 3 0.0000 0.923 0.000 0.000 1.000
#> GSM559422 1 0.4399 0.838 0.812 0.000 0.188
#> GSM559424 3 0.1529 0.900 0.000 0.040 0.960
#> GSM559431 2 0.0000 0.814 0.000 1.000 0.000
#> GSM559432 2 0.1964 0.812 0.000 0.944 0.056
#> GSM559381 1 0.0000 0.927 1.000 0.000 0.000
#> GSM559382 1 0.0000 0.927 1.000 0.000 0.000
#> GSM559384 1 0.0000 0.927 1.000 0.000 0.000
#> GSM559385 3 0.0661 0.923 0.004 0.008 0.988
#> GSM559386 1 0.0000 0.927 1.000 0.000 0.000
#> GSM559388 2 0.1267 0.820 0.004 0.972 0.024
#> GSM559389 1 0.0000 0.927 1.000 0.000 0.000
#> GSM559390 2 0.7442 0.535 0.044 0.588 0.368
#> GSM559392 2 0.1765 0.822 0.004 0.956 0.040
#> GSM559393 3 0.6033 0.354 0.004 0.336 0.660
#> GSM559394 3 0.6008 0.367 0.004 0.332 0.664
#> GSM559396 1 0.2959 0.903 0.900 0.000 0.100
#> GSM559398 2 0.0000 0.814 0.000 1.000 0.000
#> GSM559399 2 0.6247 0.569 0.004 0.620 0.376
#> GSM559400 2 0.2301 0.818 0.004 0.936 0.060
#> GSM559402 3 0.4458 0.818 0.056 0.080 0.864
#> GSM559403 3 0.0661 0.923 0.004 0.008 0.988
#> GSM559404 1 0.4399 0.839 0.812 0.000 0.188
#> GSM559405 1 0.0000 0.927 1.000 0.000 0.000
#> GSM559406 1 0.2959 0.903 0.900 0.000 0.100
#> GSM559407 3 0.0661 0.923 0.004 0.008 0.988
#> GSM559408 1 0.2959 0.903 0.900 0.000 0.100
#> GSM559409 3 0.0829 0.921 0.004 0.012 0.984
#> GSM559410 3 0.0000 0.923 0.000 0.000 1.000
#> GSM559411 3 0.0237 0.925 0.000 0.004 0.996
#> GSM559412 1 0.4399 0.839 0.812 0.000 0.188
#> GSM559413 1 0.4399 0.839 0.812 0.000 0.188
#> GSM559415 2 0.6247 0.569 0.004 0.620 0.376
#> GSM559416 2 0.6209 0.582 0.004 0.628 0.368
#> GSM559417 2 0.6081 0.612 0.004 0.652 0.344
#> GSM559418 2 0.6209 0.582 0.004 0.628 0.368
#> GSM559419 2 0.6899 0.569 0.024 0.612 0.364
#> GSM559420 1 0.0000 0.927 1.000 0.000 0.000
#> GSM559421 2 0.1765 0.822 0.004 0.956 0.040
#> GSM559423 2 0.1765 0.822 0.004 0.956 0.040
#> GSM559425 2 0.0000 0.814 0.000 1.000 0.000
#> GSM559426 2 0.0000 0.814 0.000 1.000 0.000
#> GSM559427 2 0.0000 0.814 0.000 1.000 0.000
#> GSM559428 1 0.0000 0.927 1.000 0.000 0.000
#> GSM559429 2 0.3112 0.803 0.004 0.900 0.096
#> GSM559430 2 0.0000 0.814 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.0895 0.872 0.020 0.004 0.976 0.000
#> GSM559387 3 0.2149 0.843 0.000 0.000 0.912 0.088
#> GSM559391 3 0.0188 0.876 0.000 0.004 0.996 0.000
#> GSM559395 3 0.2149 0.843 0.000 0.000 0.912 0.088
#> GSM559397 1 0.3942 0.576 0.764 0.000 0.000 0.236
#> GSM559401 3 0.2149 0.843 0.000 0.000 0.912 0.088
#> GSM559414 3 0.2149 0.843 0.000 0.000 0.912 0.088
#> GSM559422 1 0.2334 0.568 0.908 0.004 0.088 0.000
#> GSM559424 3 0.1302 0.861 0.000 0.044 0.956 0.000
#> GSM559431 2 0.1474 0.789 0.000 0.948 0.000 0.052
#> GSM559432 2 0.3009 0.792 0.000 0.892 0.056 0.052
#> GSM559381 1 0.4843 0.528 0.604 0.000 0.000 0.396
#> GSM559382 1 0.4843 0.528 0.604 0.000 0.000 0.396
#> GSM559384 1 0.4431 0.566 0.696 0.000 0.000 0.304
#> GSM559385 3 0.0524 0.877 0.004 0.008 0.988 0.000
#> GSM559386 1 0.4843 0.528 0.604 0.000 0.000 0.396
#> GSM559388 2 0.2383 0.799 0.004 0.924 0.024 0.048
#> GSM559389 1 0.4843 0.528 0.604 0.000 0.000 0.396
#> GSM559390 2 0.6022 0.562 0.048 0.612 0.336 0.004
#> GSM559392 2 0.0844 0.801 0.004 0.980 0.012 0.004
#> GSM559393 3 0.5064 0.304 0.004 0.360 0.632 0.004
#> GSM559394 3 0.5030 0.321 0.004 0.352 0.640 0.004
#> GSM559396 1 0.2401 0.607 0.904 0.004 0.000 0.092
#> GSM559398 2 0.1474 0.789 0.000 0.948 0.000 0.052
#> GSM559399 2 0.5013 0.590 0.004 0.644 0.348 0.004
#> GSM559400 2 0.1863 0.803 0.004 0.944 0.040 0.012
#> GSM559402 3 0.4535 0.758 0.080 0.104 0.812 0.004
#> GSM559403 3 0.0524 0.877 0.004 0.008 0.988 0.000
#> GSM559404 1 0.2216 0.569 0.908 0.000 0.092 0.000
#> GSM559405 1 0.4843 0.528 0.604 0.000 0.000 0.396
#> GSM559406 1 0.0188 0.604 0.996 0.004 0.000 0.000
#> GSM559407 3 0.0524 0.877 0.004 0.008 0.988 0.000
#> GSM559408 1 0.0188 0.604 0.996 0.004 0.000 0.000
#> GSM559409 3 0.1284 0.869 0.024 0.012 0.964 0.000
#> GSM559410 3 0.2149 0.843 0.000 0.000 0.912 0.088
#> GSM559411 3 0.0188 0.876 0.000 0.004 0.996 0.000
#> GSM559412 1 0.2216 0.569 0.908 0.000 0.092 0.000
#> GSM559413 1 0.2216 0.569 0.908 0.000 0.092 0.000
#> GSM559415 2 0.5030 0.585 0.004 0.640 0.352 0.004
#> GSM559416 2 0.4995 0.598 0.004 0.648 0.344 0.004
#> GSM559417 2 0.4854 0.629 0.004 0.676 0.316 0.004
#> GSM559418 2 0.4976 0.601 0.004 0.652 0.340 0.004
#> GSM559419 2 0.5525 0.590 0.024 0.636 0.336 0.004
#> GSM559420 1 0.4843 0.528 0.604 0.000 0.000 0.396
#> GSM559421 2 0.0844 0.801 0.004 0.980 0.012 0.004
#> GSM559423 2 0.0844 0.801 0.004 0.980 0.012 0.004
#> GSM559425 2 0.1474 0.789 0.000 0.948 0.000 0.052
#> GSM559426 2 0.1474 0.789 0.000 0.948 0.000 0.052
#> GSM559427 2 0.1474 0.789 0.000 0.948 0.000 0.052
#> GSM559428 4 0.2973 0.000 0.144 0.000 0.000 0.856
#> GSM559429 2 0.1978 0.794 0.004 0.928 0.068 0.000
#> GSM559430 2 0.1474 0.789 0.000 0.948 0.000 0.052
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559383 3 0.4181 0.8235 0.000 0.000 0.712 0.268 0.020
#> GSM559387 3 0.0771 0.7409 0.000 0.004 0.976 0.020 0.000
#> GSM559391 3 0.3612 0.8293 0.000 0.000 0.732 0.268 0.000
#> GSM559395 3 0.0771 0.7409 0.000 0.004 0.976 0.020 0.000
#> GSM559397 1 0.2732 0.5790 0.840 0.000 0.000 0.000 0.160
#> GSM559401 3 0.0771 0.7409 0.000 0.004 0.976 0.020 0.000
#> GSM559414 3 0.0162 0.7214 0.000 0.004 0.996 0.000 0.000
#> GSM559422 1 0.5818 0.5750 0.460 0.000 0.000 0.092 0.448
#> GSM559424 3 0.3857 0.7929 0.000 0.000 0.688 0.312 0.000
#> GSM559431 2 0.0162 0.9826 0.000 0.996 0.000 0.004 0.000
#> GSM559432 2 0.1628 0.8982 0.000 0.936 0.008 0.056 0.000
#> GSM559381 1 0.0000 0.5414 1.000 0.000 0.000 0.000 0.000
#> GSM559382 1 0.0000 0.5414 1.000 0.000 0.000 0.000 0.000
#> GSM559384 1 0.2329 0.5830 0.876 0.000 0.000 0.000 0.124
#> GSM559385 3 0.3661 0.8278 0.000 0.000 0.724 0.276 0.000
#> GSM559386 1 0.0000 0.5414 1.000 0.000 0.000 0.000 0.000
#> GSM559388 4 0.4283 0.2632 0.000 0.456 0.000 0.544 0.000
#> GSM559389 1 0.0000 0.5414 1.000 0.000 0.000 0.000 0.000
#> GSM559390 4 0.2760 0.6828 0.028 0.000 0.064 0.892 0.016
#> GSM559392 4 0.3586 0.5706 0.000 0.264 0.000 0.736 0.000
#> GSM559393 4 0.4045 0.0605 0.000 0.000 0.356 0.644 0.000
#> GSM559394 4 0.4074 0.0330 0.000 0.000 0.364 0.636 0.000
#> GSM559396 1 0.4298 0.6138 0.640 0.000 0.000 0.008 0.352
#> GSM559398 2 0.0290 0.9790 0.000 0.992 0.000 0.008 0.000
#> GSM559399 4 0.1608 0.7000 0.000 0.000 0.072 0.928 0.000
#> GSM559400 4 0.3814 0.5693 0.000 0.276 0.004 0.720 0.000
#> GSM559402 3 0.5879 0.6009 0.028 0.000 0.540 0.384 0.048
#> GSM559403 3 0.3661 0.8278 0.000 0.000 0.724 0.276 0.000
#> GSM559404 1 0.5921 0.5730 0.456 0.000 0.004 0.088 0.452
#> GSM559405 1 0.0000 0.5414 1.000 0.000 0.000 0.000 0.000
#> GSM559406 1 0.4528 0.6091 0.548 0.000 0.000 0.008 0.444
#> GSM559407 3 0.3661 0.8278 0.000 0.000 0.724 0.276 0.000
#> GSM559408 1 0.4528 0.6091 0.548 0.000 0.000 0.008 0.444
#> GSM559409 3 0.4252 0.8165 0.000 0.000 0.700 0.280 0.020
#> GSM559410 3 0.0162 0.7214 0.000 0.004 0.996 0.000 0.000
#> GSM559411 3 0.3612 0.8293 0.000 0.000 0.732 0.268 0.000
#> GSM559412 1 0.5921 0.5730 0.456 0.000 0.004 0.088 0.452
#> GSM559413 1 0.5921 0.5730 0.456 0.000 0.004 0.088 0.452
#> GSM559415 4 0.1671 0.6972 0.000 0.000 0.076 0.924 0.000
#> GSM559416 4 0.1544 0.7028 0.000 0.000 0.068 0.932 0.000
#> GSM559417 4 0.1043 0.7081 0.000 0.000 0.040 0.960 0.000
#> GSM559418 4 0.1478 0.7042 0.000 0.000 0.064 0.936 0.000
#> GSM559419 4 0.2141 0.6986 0.016 0.000 0.064 0.916 0.004
#> GSM559420 1 0.0000 0.5414 1.000 0.000 0.000 0.000 0.000
#> GSM559421 4 0.3586 0.5706 0.000 0.264 0.000 0.736 0.000
#> GSM559423 4 0.3586 0.5706 0.000 0.264 0.000 0.736 0.000
#> GSM559425 2 0.0162 0.9826 0.000 0.996 0.000 0.004 0.000
#> GSM559426 2 0.0162 0.9826 0.000 0.996 0.000 0.004 0.000
#> GSM559427 2 0.0162 0.9826 0.000 0.996 0.000 0.004 0.000
#> GSM559428 5 0.4278 0.0000 0.452 0.000 0.000 0.000 0.548
#> GSM559429 4 0.4167 0.6066 0.000 0.252 0.024 0.724 0.000
#> GSM559430 2 0.0162 0.9826 0.000 0.996 0.000 0.004 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559383 3 0.3834 0.8214 0.268 0.000 0.708 0.024 0.000 0.000
#> GSM559387 3 0.0951 0.7173 0.020 0.000 0.968 0.008 0.004 0.000
#> GSM559391 3 0.3383 0.8266 0.268 0.000 0.728 0.004 0.000 0.000
#> GSM559395 3 0.0951 0.7173 0.020 0.000 0.968 0.008 0.004 0.000
#> GSM559397 6 0.3126 0.5634 0.000 0.000 0.000 0.248 0.000 0.752
#> GSM559401 3 0.0951 0.7173 0.020 0.000 0.968 0.008 0.004 0.000
#> GSM559414 3 0.0405 0.6957 0.000 0.000 0.988 0.008 0.004 0.000
#> GSM559422 4 0.0508 0.7118 0.004 0.000 0.000 0.984 0.000 0.012
#> GSM559424 3 0.3601 0.7902 0.312 0.000 0.684 0.004 0.000 0.000
#> GSM559431 2 0.0000 0.9813 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559432 2 0.1434 0.8896 0.048 0.940 0.012 0.000 0.000 0.000
#> GSM559381 6 0.0000 0.9289 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559382 6 0.0000 0.9289 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559384 6 0.2092 0.7911 0.000 0.000 0.000 0.124 0.000 0.876
#> GSM559385 3 0.3426 0.8251 0.276 0.000 0.720 0.004 0.000 0.000
#> GSM559386 6 0.0000 0.9289 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559388 1 0.3847 0.2715 0.544 0.456 0.000 0.000 0.000 0.000
#> GSM559389 6 0.0000 0.9289 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559390 1 0.2258 0.6873 0.896 0.000 0.060 0.044 0.000 0.000
#> GSM559392 1 0.3360 0.5754 0.732 0.264 0.000 0.000 0.004 0.000
#> GSM559393 1 0.3756 0.0600 0.644 0.000 0.352 0.004 0.000 0.000
#> GSM559394 1 0.3782 0.0326 0.636 0.000 0.360 0.004 0.000 0.000
#> GSM559396 4 0.4072 0.3694 0.008 0.000 0.000 0.544 0.000 0.448
#> GSM559398 2 0.0146 0.9773 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM559399 1 0.1387 0.7019 0.932 0.000 0.068 0.000 0.000 0.000
#> GSM559400 1 0.3288 0.5738 0.724 0.276 0.000 0.000 0.000 0.000
#> GSM559402 3 0.5044 0.6018 0.384 0.000 0.536 0.080 0.000 0.000
#> GSM559403 3 0.3426 0.8251 0.276 0.000 0.720 0.004 0.000 0.000
#> GSM559404 4 0.0260 0.7120 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM559405 6 0.0000 0.9289 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559406 4 0.3861 0.5609 0.008 0.000 0.000 0.640 0.000 0.352
#> GSM559407 3 0.3426 0.8251 0.276 0.000 0.720 0.004 0.000 0.000
#> GSM559408 4 0.3861 0.5609 0.008 0.000 0.000 0.640 0.000 0.352
#> GSM559409 3 0.3897 0.8144 0.280 0.000 0.696 0.024 0.000 0.000
#> GSM559410 3 0.0405 0.6957 0.000 0.000 0.988 0.008 0.004 0.000
#> GSM559411 3 0.3383 0.8266 0.268 0.000 0.728 0.004 0.000 0.000
#> GSM559412 4 0.0260 0.7120 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM559413 4 0.0260 0.7120 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM559415 1 0.1444 0.6991 0.928 0.000 0.072 0.000 0.000 0.000
#> GSM559416 1 0.1327 0.7046 0.936 0.000 0.064 0.000 0.000 0.000
#> GSM559417 1 0.0865 0.7098 0.964 0.000 0.036 0.000 0.000 0.000
#> GSM559418 1 0.1267 0.7061 0.940 0.000 0.060 0.000 0.000 0.000
#> GSM559419 1 0.1807 0.7016 0.920 0.000 0.060 0.020 0.000 0.000
#> GSM559420 6 0.0000 0.9289 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559421 1 0.3360 0.5754 0.732 0.264 0.000 0.000 0.004 0.000
#> GSM559423 1 0.3360 0.5754 0.732 0.264 0.000 0.000 0.004 0.000
#> GSM559425 2 0.0000 0.9813 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559426 2 0.0000 0.9813 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559427 2 0.0000 0.9813 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559428 5 0.0260 0.0000 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM559429 1 0.3665 0.6109 0.728 0.252 0.020 0.000 0.000 0.000
#> GSM559430 2 0.0000 0.9813 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:hclust 52 0.5152 2
#> ATC:hclust 50 0.0116 3
#> ATC:hclust 49 0.0136 4
#> ATC:hclust 48 0.0163 5
#> ATC:hclust 47 0.0408 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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.479 0.832 0.843 0.4186 0.566 0.566
#> 3 3 1.000 0.998 0.995 0.5689 0.775 0.601
#> 4 4 0.694 0.741 0.776 0.1151 0.889 0.680
#> 5 5 0.770 0.675 0.784 0.0658 0.804 0.413
#> 6 6 0.764 0.789 0.839 0.0379 0.941 0.751
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
#> GSM559383 2 0.0000 0.791 0.000 1.000
#> GSM559387 2 0.0000 0.791 0.000 1.000
#> GSM559391 2 0.0000 0.791 0.000 1.000
#> GSM559395 2 0.0376 0.791 0.004 0.996
#> GSM559397 1 0.9358 0.999 0.648 0.352
#> GSM559401 2 0.0000 0.791 0.000 1.000
#> GSM559414 2 0.0000 0.791 0.000 1.000
#> GSM559422 1 0.9358 0.999 0.648 0.352
#> GSM559424 2 0.0000 0.791 0.000 1.000
#> GSM559431 2 0.9427 0.705 0.360 0.640
#> GSM559432 2 0.9358 0.702 0.352 0.648
#> GSM559381 1 0.9358 0.999 0.648 0.352
#> GSM559382 1 0.9358 0.999 0.648 0.352
#> GSM559384 1 0.9358 0.999 0.648 0.352
#> GSM559385 2 0.0000 0.791 0.000 1.000
#> GSM559386 1 0.9358 0.999 0.648 0.352
#> GSM559388 2 0.9427 0.705 0.360 0.640
#> GSM559389 1 0.9358 0.999 0.648 0.352
#> GSM559390 2 0.0672 0.788 0.008 0.992
#> GSM559392 2 0.9427 0.705 0.360 0.640
#> GSM559393 2 0.0672 0.788 0.008 0.992
#> GSM559394 2 0.0000 0.791 0.000 1.000
#> GSM559396 1 0.9358 0.999 0.648 0.352
#> GSM559398 2 0.9427 0.705 0.360 0.640
#> GSM559399 2 0.0672 0.788 0.008 0.992
#> GSM559400 2 0.9427 0.705 0.360 0.640
#> GSM559402 2 0.0672 0.788 0.008 0.992
#> GSM559403 2 0.0000 0.791 0.000 1.000
#> GSM559404 1 0.9427 0.988 0.640 0.360
#> GSM559405 1 0.9358 0.999 0.648 0.352
#> GSM559406 1 0.9358 0.999 0.648 0.352
#> GSM559407 2 0.0000 0.791 0.000 1.000
#> GSM559408 1 0.9358 0.999 0.648 0.352
#> GSM559409 2 0.0000 0.791 0.000 1.000
#> GSM559410 2 0.0000 0.791 0.000 1.000
#> GSM559411 2 0.0000 0.791 0.000 1.000
#> GSM559412 1 0.9358 0.999 0.648 0.352
#> GSM559413 1 0.9358 0.999 0.648 0.352
#> GSM559415 2 0.0938 0.789 0.012 0.988
#> GSM559416 2 0.4939 0.765 0.108 0.892
#> GSM559417 2 0.0938 0.789 0.012 0.988
#> GSM559418 2 0.0672 0.788 0.008 0.992
#> GSM559419 2 0.0672 0.788 0.008 0.992
#> GSM559420 1 0.9358 0.999 0.648 0.352
#> GSM559421 2 0.9427 0.705 0.360 0.640
#> GSM559423 2 0.9358 0.706 0.352 0.648
#> GSM559425 2 0.9427 0.705 0.360 0.640
#> GSM559426 2 0.9427 0.705 0.360 0.640
#> GSM559427 2 0.9427 0.705 0.360 0.640
#> GSM559428 1 0.9358 0.999 0.648 0.352
#> GSM559429 2 0.9427 0.705 0.360 0.640
#> GSM559430 2 0.9427 0.705 0.360 0.640
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559387 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559391 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559395 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559397 1 0.0000 0.999 1.000 0.000 0.000
#> GSM559401 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559414 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559422 1 0.0000 0.999 1.000 0.000 0.000
#> GSM559424 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559431 2 0.0747 0.997 0.000 0.984 0.016
#> GSM559432 2 0.0747 0.997 0.000 0.984 0.016
#> GSM559381 1 0.0000 0.999 1.000 0.000 0.000
#> GSM559382 1 0.0000 0.999 1.000 0.000 0.000
#> GSM559384 1 0.0000 0.999 1.000 0.000 0.000
#> GSM559385 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559386 1 0.0000 0.999 1.000 0.000 0.000
#> GSM559388 2 0.0747 0.997 0.000 0.984 0.016
#> GSM559389 1 0.0000 0.999 1.000 0.000 0.000
#> GSM559390 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559392 2 0.0747 0.997 0.000 0.984 0.016
#> GSM559393 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559394 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559396 1 0.0000 0.999 1.000 0.000 0.000
#> GSM559398 2 0.0747 0.997 0.000 0.984 0.016
#> GSM559399 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559400 2 0.0747 0.997 0.000 0.984 0.016
#> GSM559402 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559403 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559404 1 0.0000 0.999 1.000 0.000 0.000
#> GSM559405 1 0.0000 0.999 1.000 0.000 0.000
#> GSM559406 1 0.0000 0.999 1.000 0.000 0.000
#> GSM559407 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559408 1 0.0000 0.999 1.000 0.000 0.000
#> GSM559409 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559410 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559411 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559412 1 0.0000 0.999 1.000 0.000 0.000
#> GSM559413 1 0.0000 0.999 1.000 0.000 0.000
#> GSM559415 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559416 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559417 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559418 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559419 3 0.0000 1.000 0.000 0.000 1.000
#> GSM559420 1 0.0000 0.999 1.000 0.000 0.000
#> GSM559421 2 0.0747 0.997 0.000 0.984 0.016
#> GSM559423 2 0.0747 0.997 0.000 0.984 0.016
#> GSM559425 2 0.0747 0.997 0.000 0.984 0.016
#> GSM559426 2 0.0747 0.997 0.000 0.984 0.016
#> GSM559427 2 0.0747 0.997 0.000 0.984 0.016
#> GSM559428 1 0.0747 0.988 0.984 0.016 0.000
#> GSM559429 2 0.1860 0.959 0.000 0.948 0.052
#> GSM559430 2 0.0747 0.997 0.000 0.984 0.016
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.4331 0.649 0.000 0.000 0.712 0.288
#> GSM559387 3 0.0000 0.755 0.000 0.000 1.000 0.000
#> GSM559391 3 0.0000 0.755 0.000 0.000 1.000 0.000
#> GSM559395 3 0.0000 0.755 0.000 0.000 1.000 0.000
#> GSM559397 1 0.3311 0.836 0.828 0.000 0.000 0.172
#> GSM559401 3 0.0000 0.755 0.000 0.000 1.000 0.000
#> GSM559414 3 0.0000 0.755 0.000 0.000 1.000 0.000
#> GSM559422 1 0.4898 0.774 0.584 0.000 0.000 0.416
#> GSM559424 3 0.4222 0.671 0.000 0.000 0.728 0.272
#> GSM559431 2 0.0188 0.830 0.000 0.996 0.000 0.004
#> GSM559432 2 0.0188 0.830 0.000 0.996 0.000 0.004
#> GSM559381 1 0.0000 0.828 1.000 0.000 0.000 0.000
#> GSM559382 1 0.0000 0.828 1.000 0.000 0.000 0.000
#> GSM559384 1 0.3610 0.834 0.800 0.000 0.000 0.200
#> GSM559385 3 0.4250 0.666 0.000 0.000 0.724 0.276
#> GSM559386 1 0.0000 0.828 1.000 0.000 0.000 0.000
#> GSM559388 2 0.3444 0.756 0.000 0.816 0.000 0.184
#> GSM559389 1 0.0000 0.828 1.000 0.000 0.000 0.000
#> GSM559390 4 0.4164 0.797 0.000 0.000 0.264 0.736
#> GSM559392 2 0.4790 0.590 0.000 0.620 0.000 0.380
#> GSM559393 4 0.4624 0.780 0.000 0.000 0.340 0.660
#> GSM559394 3 0.4222 0.671 0.000 0.000 0.728 0.272
#> GSM559396 1 0.4585 0.813 0.668 0.000 0.000 0.332
#> GSM559398 2 0.0000 0.830 0.000 1.000 0.000 0.000
#> GSM559399 4 0.4730 0.753 0.000 0.000 0.364 0.636
#> GSM559400 2 0.4941 0.496 0.000 0.564 0.000 0.436
#> GSM559402 4 0.4250 0.789 0.000 0.000 0.276 0.724
#> GSM559403 3 0.4250 0.666 0.000 0.000 0.724 0.276
#> GSM559404 1 0.4697 0.811 0.644 0.000 0.000 0.356
#> GSM559405 1 0.0000 0.828 1.000 0.000 0.000 0.000
#> GSM559406 1 0.4898 0.774 0.584 0.000 0.000 0.416
#> GSM559407 3 0.4222 0.671 0.000 0.000 0.728 0.272
#> GSM559408 1 0.4916 0.767 0.576 0.000 0.000 0.424
#> GSM559409 3 0.4331 0.646 0.000 0.000 0.712 0.288
#> GSM559410 3 0.0000 0.755 0.000 0.000 1.000 0.000
#> GSM559411 3 0.0000 0.755 0.000 0.000 1.000 0.000
#> GSM559412 1 0.4697 0.811 0.644 0.000 0.000 0.356
#> GSM559413 1 0.4697 0.811 0.644 0.000 0.000 0.356
#> GSM559415 4 0.4761 0.743 0.000 0.000 0.372 0.628
#> GSM559416 4 0.4761 0.743 0.000 0.000 0.372 0.628
#> GSM559417 4 0.4222 0.807 0.000 0.000 0.272 0.728
#> GSM559418 4 0.4331 0.809 0.000 0.000 0.288 0.712
#> GSM559419 4 0.4277 0.809 0.000 0.000 0.280 0.720
#> GSM559420 1 0.0000 0.828 1.000 0.000 0.000 0.000
#> GSM559421 2 0.4356 0.681 0.000 0.708 0.000 0.292
#> GSM559423 2 0.4961 0.477 0.000 0.552 0.000 0.448
#> GSM559425 2 0.0000 0.830 0.000 1.000 0.000 0.000
#> GSM559426 2 0.0188 0.830 0.000 0.996 0.000 0.004
#> GSM559427 2 0.0000 0.830 0.000 1.000 0.000 0.000
#> GSM559428 1 0.1302 0.806 0.956 0.000 0.000 0.044
#> GSM559429 4 0.5112 -0.255 0.000 0.436 0.004 0.560
#> GSM559430 2 0.0188 0.830 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
#> GSM559383 1 0.5348 0.1736 0.492 0.000 0.456 0.052 0.000
#> GSM559387 3 0.1357 0.9873 0.048 0.000 0.948 0.000 0.004
#> GSM559391 3 0.1544 0.9727 0.068 0.000 0.932 0.000 0.000
#> GSM559395 3 0.1357 0.9873 0.048 0.000 0.948 0.000 0.004
#> GSM559397 4 0.3333 0.4681 0.000 0.000 0.004 0.788 0.208
#> GSM559401 3 0.1357 0.9873 0.048 0.000 0.948 0.000 0.004
#> GSM559414 3 0.1357 0.9873 0.048 0.000 0.948 0.000 0.004
#> GSM559422 4 0.1124 0.8759 0.036 0.000 0.004 0.960 0.000
#> GSM559424 1 0.4278 0.2448 0.548 0.000 0.452 0.000 0.000
#> GSM559431 2 0.0404 0.8401 0.000 0.988 0.012 0.000 0.000
#> GSM559432 2 0.0703 0.8365 0.000 0.976 0.024 0.000 0.000
#> GSM559381 5 0.4192 0.9536 0.000 0.000 0.000 0.404 0.596
#> GSM559382 5 0.4126 0.9435 0.000 0.000 0.000 0.380 0.620
#> GSM559384 4 0.2230 0.7478 0.000 0.000 0.000 0.884 0.116
#> GSM559385 1 0.4890 0.2267 0.524 0.000 0.452 0.024 0.000
#> GSM559386 5 0.4138 0.9457 0.000 0.000 0.000 0.384 0.616
#> GSM559388 2 0.6127 0.5723 0.220 0.584 0.004 0.000 0.192
#> GSM559389 5 0.4192 0.9536 0.000 0.000 0.000 0.404 0.596
#> GSM559390 1 0.0794 0.6495 0.972 0.000 0.000 0.028 0.000
#> GSM559392 1 0.6896 -0.1870 0.436 0.252 0.000 0.008 0.304
#> GSM559393 1 0.0451 0.6519 0.988 0.000 0.008 0.004 0.000
#> GSM559394 1 0.4262 0.2631 0.560 0.000 0.440 0.000 0.000
#> GSM559396 4 0.2450 0.8242 0.028 0.000 0.000 0.896 0.076
#> GSM559398 2 0.3662 0.7463 0.004 0.744 0.000 0.000 0.252
#> GSM559399 1 0.0566 0.6514 0.984 0.000 0.012 0.004 0.000
#> GSM559400 1 0.6408 0.0704 0.544 0.180 0.000 0.008 0.268
#> GSM559402 1 0.3969 0.4595 0.692 0.000 0.004 0.304 0.000
#> GSM559403 1 0.4890 0.2267 0.524 0.000 0.452 0.024 0.000
#> GSM559404 4 0.0854 0.8842 0.012 0.000 0.004 0.976 0.008
#> GSM559405 5 0.4192 0.9536 0.000 0.000 0.000 0.404 0.596
#> GSM559406 4 0.0963 0.8765 0.036 0.000 0.000 0.964 0.000
#> GSM559407 1 0.4890 0.2267 0.524 0.000 0.452 0.024 0.000
#> GSM559408 4 0.0963 0.8765 0.036 0.000 0.000 0.964 0.000
#> GSM559409 1 0.5161 0.2223 0.516 0.000 0.444 0.040 0.000
#> GSM559410 3 0.1981 0.9783 0.048 0.000 0.924 0.000 0.028
#> GSM559411 3 0.1764 0.9752 0.064 0.000 0.928 0.000 0.008
#> GSM559412 4 0.0854 0.8842 0.012 0.000 0.004 0.976 0.008
#> GSM559413 4 0.0854 0.8842 0.012 0.000 0.004 0.976 0.008
#> GSM559415 1 0.0609 0.6494 0.980 0.000 0.020 0.000 0.000
#> GSM559416 1 0.0771 0.6500 0.976 0.000 0.020 0.000 0.004
#> GSM559417 1 0.0771 0.6515 0.976 0.000 0.000 0.020 0.004
#> GSM559418 1 0.0771 0.6515 0.976 0.000 0.000 0.020 0.004
#> GSM559419 1 0.0771 0.6515 0.976 0.000 0.000 0.020 0.004
#> GSM559420 5 0.4192 0.9536 0.000 0.000 0.000 0.404 0.596
#> GSM559421 2 0.6791 0.2734 0.356 0.360 0.000 0.000 0.284
#> GSM559423 1 0.6462 0.0492 0.528 0.176 0.000 0.008 0.288
#> GSM559425 2 0.0865 0.8389 0.004 0.972 0.000 0.000 0.024
#> GSM559426 2 0.0510 0.8400 0.000 0.984 0.016 0.000 0.000
#> GSM559427 2 0.0865 0.8389 0.004 0.972 0.000 0.000 0.024
#> GSM559428 5 0.4773 0.8231 0.008 0.000 0.024 0.312 0.656
#> GSM559429 1 0.3488 0.5523 0.860 0.072 0.016 0.008 0.044
#> GSM559430 2 0.0404 0.8401 0.000 0.988 0.012 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559383 1 0.5238 0.578 0.588 0.020 0.324 0.068 0.000 0.000
#> GSM559387 3 0.0146 0.971 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM559391 3 0.1562 0.942 0.032 0.004 0.940 0.024 0.000 0.000
#> GSM559395 3 0.0146 0.971 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM559397 4 0.4958 0.659 0.000 0.076 0.000 0.560 0.000 0.364
#> GSM559401 3 0.0436 0.971 0.004 0.004 0.988 0.004 0.000 0.000
#> GSM559414 3 0.0436 0.971 0.004 0.004 0.988 0.004 0.000 0.000
#> GSM559422 4 0.5153 0.848 0.028 0.116 0.000 0.676 0.000 0.180
#> GSM559424 1 0.4373 0.615 0.624 0.004 0.344 0.028 0.000 0.000
#> GSM559431 5 0.0000 0.923 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM559432 5 0.1138 0.909 0.000 0.012 0.004 0.024 0.960 0.000
#> GSM559381 6 0.0363 0.951 0.000 0.000 0.000 0.012 0.000 0.988
#> GSM559382 6 0.0260 0.949 0.000 0.008 0.000 0.000 0.000 0.992
#> GSM559384 4 0.3592 0.769 0.000 0.000 0.000 0.656 0.000 0.344
#> GSM559385 1 0.4479 0.619 0.624 0.004 0.336 0.036 0.000 0.000
#> GSM559386 6 0.0260 0.949 0.000 0.008 0.000 0.000 0.000 0.992
#> GSM559388 2 0.6305 0.438 0.180 0.408 0.004 0.016 0.392 0.000
#> GSM559389 6 0.0363 0.951 0.000 0.000 0.000 0.012 0.000 0.988
#> GSM559390 1 0.1245 0.726 0.952 0.032 0.000 0.016 0.000 0.000
#> GSM559392 2 0.4382 0.767 0.200 0.716 0.000 0.000 0.080 0.004
#> GSM559393 1 0.0000 0.732 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559394 1 0.4093 0.659 0.680 0.004 0.292 0.024 0.000 0.000
#> GSM559396 4 0.4767 0.797 0.020 0.036 0.000 0.628 0.000 0.316
#> GSM559398 2 0.4508 0.243 0.000 0.568 0.000 0.036 0.396 0.000
#> GSM559399 1 0.0603 0.735 0.980 0.004 0.016 0.000 0.000 0.000
#> GSM559400 2 0.4601 0.729 0.312 0.628 0.000 0.000 0.060 0.000
#> GSM559402 1 0.3248 0.662 0.804 0.032 0.000 0.164 0.000 0.000
#> GSM559403 1 0.4479 0.619 0.624 0.004 0.336 0.036 0.000 0.000
#> GSM559404 4 0.3198 0.880 0.008 0.008 0.000 0.796 0.000 0.188
#> GSM559405 6 0.0713 0.939 0.000 0.000 0.000 0.028 0.000 0.972
#> GSM559406 4 0.4130 0.870 0.028 0.036 0.000 0.756 0.000 0.180
#> GSM559407 1 0.4479 0.619 0.624 0.004 0.336 0.036 0.000 0.000
#> GSM559408 4 0.4130 0.870 0.028 0.036 0.000 0.756 0.000 0.180
#> GSM559409 1 0.4809 0.635 0.640 0.020 0.296 0.044 0.000 0.000
#> GSM559410 3 0.1565 0.950 0.004 0.028 0.940 0.028 0.000 0.000
#> GSM559411 3 0.1485 0.949 0.024 0.004 0.944 0.028 0.000 0.000
#> GSM559412 4 0.3198 0.880 0.008 0.008 0.000 0.796 0.000 0.188
#> GSM559413 4 0.3198 0.880 0.008 0.008 0.000 0.796 0.000 0.188
#> GSM559415 1 0.0603 0.735 0.980 0.004 0.016 0.000 0.000 0.000
#> GSM559416 1 0.0820 0.729 0.972 0.016 0.012 0.000 0.000 0.000
#> GSM559417 1 0.0777 0.720 0.972 0.024 0.000 0.004 0.000 0.000
#> GSM559418 1 0.0458 0.726 0.984 0.016 0.000 0.000 0.000 0.000
#> GSM559419 1 0.0508 0.728 0.984 0.012 0.000 0.004 0.000 0.000
#> GSM559420 6 0.0260 0.951 0.000 0.000 0.000 0.008 0.000 0.992
#> GSM559421 2 0.4402 0.760 0.184 0.712 0.000 0.000 0.104 0.000
#> GSM559423 2 0.4465 0.753 0.260 0.684 0.000 0.004 0.048 0.004
#> GSM559425 5 0.2706 0.856 0.000 0.104 0.000 0.036 0.860 0.000
#> GSM559426 5 0.0725 0.917 0.000 0.012 0.000 0.012 0.976 0.000
#> GSM559427 5 0.2706 0.856 0.000 0.104 0.000 0.036 0.860 0.000
#> GSM559428 6 0.3449 0.778 0.000 0.116 0.000 0.076 0.000 0.808
#> GSM559429 1 0.3693 0.493 0.800 0.148 0.004 0.020 0.028 0.000
#> GSM559430 5 0.0000 0.923 0.000 0.000 0.000 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:kmeans 52 0.51516 2
#> ATC:kmeans 52 0.33864 3
#> ATC:kmeans 49 0.02175 4
#> ATC:kmeans 39 0.00349 5
#> ATC:kmeans 49 0.01469 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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.969 0.987 0.5002 0.497 0.497
#> 3 3 1.000 0.993 0.996 0.3567 0.738 0.515
#> 4 4 0.898 0.901 0.926 0.0867 0.926 0.776
#> 5 5 0.857 0.894 0.909 0.0712 0.942 0.781
#> 6 6 0.846 0.798 0.853 0.0391 0.973 0.869
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM559383 1 0.000 0.971 1.000 0.000
#> GSM559387 2 0.000 0.999 0.000 1.000
#> GSM559391 2 0.000 0.999 0.000 1.000
#> GSM559395 2 0.000 0.999 0.000 1.000
#> GSM559397 1 0.000 0.971 1.000 0.000
#> GSM559401 2 0.000 0.999 0.000 1.000
#> GSM559414 2 0.184 0.970 0.028 0.972
#> GSM559422 1 0.000 0.971 1.000 0.000
#> GSM559424 2 0.000 0.999 0.000 1.000
#> GSM559431 2 0.000 0.999 0.000 1.000
#> GSM559432 2 0.000 0.999 0.000 1.000
#> GSM559381 1 0.000 0.971 1.000 0.000
#> GSM559382 1 0.000 0.971 1.000 0.000
#> GSM559384 1 0.000 0.971 1.000 0.000
#> GSM559385 2 0.000 0.999 0.000 1.000
#> GSM559386 1 0.000 0.971 1.000 0.000
#> GSM559388 2 0.000 0.999 0.000 1.000
#> GSM559389 1 0.000 0.971 1.000 0.000
#> GSM559390 1 0.000 0.971 1.000 0.000
#> GSM559392 1 0.981 0.298 0.580 0.420
#> GSM559393 2 0.000 0.999 0.000 1.000
#> GSM559394 2 0.000 0.999 0.000 1.000
#> GSM559396 1 0.000 0.971 1.000 0.000
#> GSM559398 2 0.000 0.999 0.000 1.000
#> GSM559399 2 0.000 0.999 0.000 1.000
#> GSM559400 2 0.000 0.999 0.000 1.000
#> GSM559402 1 0.000 0.971 1.000 0.000
#> GSM559403 2 0.000 0.999 0.000 1.000
#> GSM559404 1 0.000 0.971 1.000 0.000
#> GSM559405 1 0.000 0.971 1.000 0.000
#> GSM559406 1 0.000 0.971 1.000 0.000
#> GSM559407 2 0.000 0.999 0.000 1.000
#> GSM559408 1 0.000 0.971 1.000 0.000
#> GSM559409 1 0.184 0.948 0.972 0.028
#> GSM559410 2 0.000 0.999 0.000 1.000
#> GSM559411 2 0.000 0.999 0.000 1.000
#> GSM559412 1 0.000 0.971 1.000 0.000
#> GSM559413 1 0.000 0.971 1.000 0.000
#> GSM559415 2 0.000 0.999 0.000 1.000
#> GSM559416 2 0.000 0.999 0.000 1.000
#> GSM559417 2 0.000 0.999 0.000 1.000
#> GSM559418 2 0.000 0.999 0.000 1.000
#> GSM559419 1 0.671 0.783 0.824 0.176
#> GSM559420 1 0.000 0.971 1.000 0.000
#> GSM559421 2 0.000 0.999 0.000 1.000
#> GSM559423 1 0.000 0.971 1.000 0.000
#> GSM559425 2 0.000 0.999 0.000 1.000
#> GSM559426 2 0.000 0.999 0.000 1.000
#> GSM559427 2 0.000 0.999 0.000 1.000
#> GSM559428 1 0.000 0.971 1.000 0.000
#> GSM559429 2 0.000 0.999 0.000 1.000
#> GSM559430 2 0.000 0.999 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559387 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559391 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559395 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559397 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559401 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559414 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559422 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559424 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559431 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559432 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559381 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559382 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559384 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559385 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559386 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559388 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559389 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559390 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559392 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559393 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559394 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559396 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559398 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559399 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559400 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559402 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559403 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559404 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559405 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559406 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559407 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559408 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559409 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559410 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559411 3 0.0000 0.999 0.000 0.000 1.000
#> GSM559412 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559413 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559415 3 0.0424 0.992 0.000 0.008 0.992
#> GSM559416 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559417 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559418 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559419 1 0.5449 0.808 0.816 0.116 0.068
#> GSM559420 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559421 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559423 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559425 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559426 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559427 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559428 1 0.0000 0.991 1.000 0.000 0.000
#> GSM559429 2 0.0000 1.000 0.000 1.000 0.000
#> GSM559430 2 0.0000 1.000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.1004 0.971 0.024 0.000 0.972 0.004
#> GSM559387 3 0.0188 0.992 0.000 0.000 0.996 0.004
#> GSM559391 3 0.0188 0.992 0.000 0.000 0.996 0.004
#> GSM559395 3 0.0188 0.992 0.000 0.000 0.996 0.004
#> GSM559397 1 0.3907 0.904 0.768 0.000 0.000 0.232
#> GSM559401 3 0.0188 0.992 0.000 0.000 0.996 0.004
#> GSM559414 3 0.0188 0.992 0.000 0.000 0.996 0.004
#> GSM559422 1 0.3873 0.904 0.772 0.000 0.000 0.228
#> GSM559424 3 0.0336 0.990 0.000 0.000 0.992 0.008
#> GSM559431 2 0.1118 0.956 0.000 0.964 0.000 0.036
#> GSM559432 2 0.1211 0.954 0.000 0.960 0.000 0.040
#> GSM559381 1 0.3942 0.904 0.764 0.000 0.000 0.236
#> GSM559382 1 0.3942 0.904 0.764 0.000 0.000 0.236
#> GSM559384 1 0.3907 0.904 0.768 0.000 0.000 0.232
#> GSM559385 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM559386 1 0.3942 0.904 0.764 0.000 0.000 0.236
#> GSM559388 2 0.1211 0.954 0.000 0.960 0.000 0.040
#> GSM559389 1 0.3942 0.904 0.764 0.000 0.000 0.236
#> GSM559390 1 0.0188 0.846 0.996 0.000 0.000 0.004
#> GSM559392 2 0.1118 0.950 0.000 0.964 0.000 0.036
#> GSM559393 3 0.0817 0.972 0.000 0.000 0.976 0.024
#> GSM559394 3 0.0336 0.988 0.000 0.000 0.992 0.008
#> GSM559396 1 0.3942 0.904 0.764 0.000 0.000 0.236
#> GSM559398 2 0.1118 0.950 0.000 0.964 0.000 0.036
#> GSM559399 4 0.4500 0.545 0.000 0.000 0.316 0.684
#> GSM559400 2 0.1118 0.950 0.000 0.964 0.000 0.036
#> GSM559402 1 0.0188 0.843 0.996 0.000 0.004 0.000
#> GSM559403 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM559404 1 0.0000 0.846 1.000 0.000 0.000 0.000
#> GSM559405 1 0.3907 0.904 0.768 0.000 0.000 0.232
#> GSM559406 1 0.0000 0.846 1.000 0.000 0.000 0.000
#> GSM559407 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM559408 1 0.0000 0.846 1.000 0.000 0.000 0.000
#> GSM559409 3 0.0707 0.976 0.020 0.000 0.980 0.000
#> GSM559410 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM559411 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM559412 1 0.0000 0.846 1.000 0.000 0.000 0.000
#> GSM559413 1 0.0000 0.846 1.000 0.000 0.000 0.000
#> GSM559415 4 0.5021 0.652 0.000 0.036 0.240 0.724
#> GSM559416 4 0.4250 0.679 0.000 0.276 0.000 0.724
#> GSM559417 4 0.4522 0.616 0.000 0.320 0.000 0.680
#> GSM559418 4 0.4331 0.668 0.000 0.288 0.000 0.712
#> GSM559419 4 0.2922 0.624 0.104 0.008 0.004 0.884
#> GSM559420 1 0.3942 0.904 0.764 0.000 0.000 0.236
#> GSM559421 2 0.1118 0.950 0.000 0.964 0.000 0.036
#> GSM559423 2 0.1302 0.944 0.000 0.956 0.000 0.044
#> GSM559425 2 0.0000 0.958 0.000 1.000 0.000 0.000
#> GSM559426 2 0.1211 0.954 0.000 0.960 0.000 0.040
#> GSM559427 2 0.0188 0.958 0.000 0.996 0.000 0.004
#> GSM559428 1 0.3942 0.904 0.764 0.000 0.000 0.236
#> GSM559429 2 0.1118 0.956 0.000 0.964 0.000 0.036
#> GSM559430 2 0.1118 0.956 0.000 0.964 0.000 0.036
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM559383 3 0.1341 0.919 0.000 0.000 0.944 0.000 0.056
#> GSM559387 3 0.0000 0.954 0.000 0.000 1.000 0.000 0.000
#> GSM559391 3 0.0000 0.954 0.000 0.000 1.000 0.000 0.000
#> GSM559395 3 0.0000 0.954 0.000 0.000 1.000 0.000 0.000
#> GSM559397 1 0.0880 0.960 0.968 0.000 0.000 0.000 0.032
#> GSM559401 3 0.0000 0.954 0.000 0.000 1.000 0.000 0.000
#> GSM559414 3 0.0000 0.954 0.000 0.000 1.000 0.000 0.000
#> GSM559422 1 0.1544 0.919 0.932 0.000 0.000 0.000 0.068
#> GSM559424 3 0.0000 0.954 0.000 0.000 1.000 0.000 0.000
#> GSM559431 2 0.3513 0.815 0.000 0.800 0.000 0.180 0.020
#> GSM559432 2 0.3513 0.815 0.000 0.800 0.000 0.180 0.020
#> GSM559381 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM559382 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM559384 1 0.0162 0.985 0.996 0.000 0.000 0.000 0.004
#> GSM559385 3 0.1965 0.951 0.000 0.000 0.924 0.024 0.052
#> GSM559386 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM559388 2 0.3419 0.815 0.000 0.804 0.000 0.180 0.016
#> GSM559389 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM559390 5 0.3003 0.959 0.188 0.000 0.000 0.000 0.812
#> GSM559392 2 0.2616 0.805 0.000 0.888 0.000 0.036 0.076
#> GSM559393 3 0.2795 0.925 0.000 0.000 0.880 0.064 0.056
#> GSM559394 3 0.2790 0.923 0.000 0.000 0.880 0.068 0.052
#> GSM559396 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM559398 2 0.2278 0.815 0.000 0.908 0.000 0.032 0.060
#> GSM559399 4 0.4141 0.588 0.000 0.000 0.236 0.736 0.028
#> GSM559400 2 0.2278 0.815 0.000 0.908 0.000 0.032 0.060
#> GSM559402 5 0.2329 0.932 0.124 0.000 0.000 0.000 0.876
#> GSM559403 3 0.1893 0.952 0.000 0.000 0.928 0.024 0.048
#> GSM559404 5 0.2813 0.984 0.168 0.000 0.000 0.000 0.832
#> GSM559405 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM559406 5 0.2813 0.984 0.168 0.000 0.000 0.000 0.832
#> GSM559407 3 0.1741 0.953 0.000 0.000 0.936 0.024 0.040
#> GSM559408 5 0.2813 0.984 0.168 0.000 0.000 0.000 0.832
#> GSM559409 3 0.2011 0.934 0.000 0.000 0.908 0.004 0.088
#> GSM559410 3 0.1661 0.954 0.000 0.000 0.940 0.024 0.036
#> GSM559411 3 0.1661 0.954 0.000 0.000 0.940 0.024 0.036
#> GSM559412 5 0.2813 0.984 0.168 0.000 0.000 0.000 0.832
#> GSM559413 5 0.2813 0.984 0.168 0.000 0.000 0.000 0.832
#> GSM559415 4 0.1682 0.780 0.000 0.032 0.012 0.944 0.012
#> GSM559416 4 0.1410 0.773 0.000 0.060 0.000 0.940 0.000
#> GSM559417 4 0.4420 0.602 0.000 0.280 0.000 0.692 0.028
#> GSM559418 4 0.2660 0.723 0.000 0.128 0.000 0.864 0.008
#> GSM559419 4 0.4469 0.682 0.120 0.020 0.000 0.784 0.076
#> GSM559420 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM559421 2 0.2491 0.810 0.000 0.896 0.000 0.036 0.068
#> GSM559423 2 0.3011 0.797 0.012 0.876 0.000 0.036 0.076
#> GSM559425 2 0.0000 0.832 0.000 1.000 0.000 0.000 0.000
#> GSM559426 2 0.3513 0.815 0.000 0.800 0.000 0.180 0.020
#> GSM559427 2 0.0162 0.832 0.000 0.996 0.000 0.000 0.004
#> GSM559428 1 0.0000 0.988 1.000 0.000 0.000 0.000 0.000
#> GSM559429 2 0.3513 0.815 0.000 0.800 0.000 0.180 0.020
#> GSM559430 2 0.3513 0.815 0.000 0.800 0.000 0.180 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM559383 3 0.1686 0.828 0.000 0.000 0.924 0.064 0.012 0.000
#> GSM559387 3 0.0146 0.856 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM559391 3 0.0146 0.856 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM559395 3 0.0363 0.856 0.012 0.000 0.988 0.000 0.000 0.000
#> GSM559397 6 0.1116 0.950 0.008 0.000 0.000 0.028 0.004 0.960
#> GSM559401 3 0.0146 0.856 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM559414 3 0.0405 0.856 0.000 0.000 0.988 0.004 0.008 0.000
#> GSM559422 6 0.2957 0.815 0.008 0.000 0.000 0.140 0.016 0.836
#> GSM559424 3 0.1285 0.847 0.052 0.000 0.944 0.000 0.004 0.000
#> GSM559431 2 0.0000 0.770 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559432 2 0.0146 0.767 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM559381 6 0.0000 0.978 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559382 6 0.0000 0.978 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559384 6 0.0260 0.973 0.000 0.000 0.000 0.008 0.000 0.992
#> GSM559385 3 0.4493 0.806 0.084 0.000 0.736 0.020 0.160 0.000
#> GSM559386 6 0.0000 0.978 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559388 2 0.1219 0.736 0.004 0.948 0.000 0.000 0.048 0.000
#> GSM559389 6 0.0000 0.978 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559390 4 0.3420 0.859 0.040 0.000 0.000 0.840 0.060 0.060
#> GSM559392 5 0.3782 0.915 0.000 0.412 0.000 0.000 0.588 0.000
#> GSM559393 3 0.6009 0.601 0.192 0.000 0.536 0.020 0.252 0.000
#> GSM559394 3 0.5543 0.623 0.248 0.000 0.572 0.004 0.176 0.000
#> GSM559396 6 0.0000 0.978 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559398 5 0.3854 0.873 0.000 0.464 0.000 0.000 0.536 0.000
#> GSM559399 1 0.3644 0.620 0.792 0.000 0.120 0.000 0.088 0.000
#> GSM559400 2 0.3868 -0.808 0.000 0.508 0.000 0.000 0.492 0.000
#> GSM559402 4 0.0862 0.927 0.008 0.000 0.000 0.972 0.004 0.016
#> GSM559403 3 0.4091 0.826 0.064 0.000 0.772 0.020 0.144 0.000
#> GSM559404 4 0.1204 0.968 0.000 0.000 0.000 0.944 0.000 0.056
#> GSM559405 6 0.0000 0.978 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559406 4 0.1204 0.968 0.000 0.000 0.000 0.944 0.000 0.056
#> GSM559407 3 0.3935 0.833 0.064 0.000 0.788 0.020 0.128 0.000
#> GSM559408 4 0.1204 0.968 0.000 0.000 0.000 0.944 0.000 0.056
#> GSM559409 3 0.3784 0.810 0.008 0.000 0.792 0.124 0.076 0.000
#> GSM559410 3 0.2870 0.852 0.040 0.000 0.856 0.004 0.100 0.000
#> GSM559411 3 0.2963 0.853 0.036 0.000 0.856 0.012 0.096 0.000
#> GSM559412 4 0.1204 0.968 0.000 0.000 0.000 0.944 0.000 0.056
#> GSM559413 4 0.1204 0.968 0.000 0.000 0.000 0.944 0.000 0.056
#> GSM559415 1 0.2604 0.737 0.880 0.076 0.008 0.000 0.036 0.000
#> GSM559416 1 0.2762 0.724 0.804 0.196 0.000 0.000 0.000 0.000
#> GSM559417 1 0.4954 0.503 0.552 0.052 0.000 0.008 0.388 0.000
#> GSM559418 1 0.4924 0.674 0.668 0.212 0.000 0.008 0.112 0.000
#> GSM559419 1 0.4546 0.695 0.724 0.000 0.000 0.032 0.192 0.052
#> GSM559420 6 0.0000 0.978 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559421 5 0.3828 0.912 0.000 0.440 0.000 0.000 0.560 0.000
#> GSM559423 5 0.3955 0.878 0.000 0.384 0.000 0.000 0.608 0.008
#> GSM559425 2 0.2823 0.463 0.000 0.796 0.000 0.000 0.204 0.000
#> GSM559426 2 0.0146 0.767 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM559427 2 0.2996 0.393 0.000 0.772 0.000 0.000 0.228 0.000
#> GSM559428 6 0.0000 0.978 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559429 2 0.0000 0.770 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559430 2 0.0000 0.770 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:skmeans 51 0.3921 2
#> ATC:skmeans 52 0.0476 3
#> ATC:skmeans 52 0.0319 4
#> ATC:skmeans 52 0.0466 5
#> ATC:skmeans 49 0.0623 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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.501 0.769 0.861 0.3287 0.735 0.735
#> 3 3 0.772 0.924 0.967 0.7559 0.667 0.551
#> 4 4 0.734 0.855 0.928 0.2663 0.791 0.524
#> 5 5 0.725 0.614 0.794 0.0791 0.864 0.551
#> 6 6 0.782 0.781 0.888 0.0447 0.834 0.396
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
#> GSM559383 1 0.0000 0.836 1.000 0.000
#> GSM559387 1 0.0000 0.836 1.000 0.000
#> GSM559391 1 0.0000 0.836 1.000 0.000
#> GSM559395 1 0.0000 0.836 1.000 0.000
#> GSM559397 1 0.8661 0.692 0.712 0.288
#> GSM559401 1 0.0000 0.836 1.000 0.000
#> GSM559414 1 0.0000 0.836 1.000 0.000
#> GSM559422 1 0.8207 0.708 0.744 0.256
#> GSM559424 1 0.0000 0.836 1.000 0.000
#> GSM559431 2 0.8661 1.000 0.288 0.712
#> GSM559432 2 0.8661 1.000 0.288 0.712
#> GSM559381 1 0.8661 0.692 0.712 0.288
#> GSM559382 1 0.8661 0.692 0.712 0.288
#> GSM559384 1 0.8661 0.692 0.712 0.288
#> GSM559385 1 0.0000 0.836 1.000 0.000
#> GSM559386 1 0.8661 0.692 0.712 0.288
#> GSM559388 1 0.9988 -0.510 0.520 0.480
#> GSM559389 1 0.8661 0.692 0.712 0.288
#> GSM559390 1 0.0000 0.836 1.000 0.000
#> GSM559392 1 0.9988 -0.510 0.520 0.480
#> GSM559393 1 0.0000 0.836 1.000 0.000
#> GSM559394 1 0.0000 0.836 1.000 0.000
#> GSM559396 1 0.0376 0.835 0.996 0.004
#> GSM559398 2 0.8661 1.000 0.288 0.712
#> GSM559399 1 0.0000 0.836 1.000 0.000
#> GSM559400 1 0.4562 0.724 0.904 0.096
#> GSM559402 1 0.0000 0.836 1.000 0.000
#> GSM559403 1 0.0000 0.836 1.000 0.000
#> GSM559404 1 0.8661 0.692 0.712 0.288
#> GSM559405 1 0.8661 0.692 0.712 0.288
#> GSM559406 1 0.0000 0.836 1.000 0.000
#> GSM559407 1 0.0000 0.836 1.000 0.000
#> GSM559408 1 0.0000 0.836 1.000 0.000
#> GSM559409 1 0.0000 0.836 1.000 0.000
#> GSM559410 1 0.0000 0.836 1.000 0.000
#> GSM559411 1 0.0000 0.836 1.000 0.000
#> GSM559412 1 0.8661 0.692 0.712 0.288
#> GSM559413 1 0.8661 0.692 0.712 0.288
#> GSM559415 1 0.0000 0.836 1.000 0.000
#> GSM559416 1 0.0000 0.836 1.000 0.000
#> GSM559417 1 0.0000 0.836 1.000 0.000
#> GSM559418 1 0.0000 0.836 1.000 0.000
#> GSM559419 1 0.0000 0.836 1.000 0.000
#> GSM559420 1 0.8661 0.692 0.712 0.288
#> GSM559421 2 0.8661 1.000 0.288 0.712
#> GSM559423 1 0.4562 0.724 0.904 0.096
#> GSM559425 2 0.8661 1.000 0.288 0.712
#> GSM559426 2 0.8661 1.000 0.288 0.712
#> GSM559427 2 0.8661 1.000 0.288 0.712
#> GSM559428 1 0.8661 0.692 0.712 0.288
#> GSM559429 1 0.2043 0.805 0.968 0.032
#> GSM559430 2 0.8661 1.000 0.288 0.712
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 1 0.000 0.977 1.000 0.000 0.000
#> GSM559387 1 0.000 0.977 1.000 0.000 0.000
#> GSM559391 1 0.000 0.977 1.000 0.000 0.000
#> GSM559395 1 0.000 0.977 1.000 0.000 0.000
#> GSM559397 3 0.000 0.942 0.000 0.000 1.000
#> GSM559401 1 0.000 0.977 1.000 0.000 0.000
#> GSM559414 1 0.000 0.977 1.000 0.000 0.000
#> GSM559422 3 0.388 0.825 0.152 0.000 0.848
#> GSM559424 1 0.000 0.977 1.000 0.000 0.000
#> GSM559431 2 0.000 0.893 0.000 1.000 0.000
#> GSM559432 2 0.288 0.834 0.096 0.904 0.000
#> GSM559381 3 0.000 0.942 0.000 0.000 1.000
#> GSM559382 3 0.000 0.942 0.000 0.000 1.000
#> GSM559384 3 0.000 0.942 0.000 0.000 1.000
#> GSM559385 1 0.000 0.977 1.000 0.000 0.000
#> GSM559386 3 0.000 0.942 0.000 0.000 1.000
#> GSM559388 1 0.327 0.866 0.884 0.116 0.000
#> GSM559389 3 0.000 0.942 0.000 0.000 1.000
#> GSM559390 1 0.000 0.977 1.000 0.000 0.000
#> GSM559392 2 0.604 0.408 0.380 0.620 0.000
#> GSM559393 1 0.000 0.977 1.000 0.000 0.000
#> GSM559394 1 0.000 0.977 1.000 0.000 0.000
#> GSM559396 1 0.341 0.854 0.876 0.000 0.124
#> GSM559398 2 0.000 0.893 0.000 1.000 0.000
#> GSM559399 1 0.000 0.977 1.000 0.000 0.000
#> GSM559400 1 0.327 0.866 0.884 0.116 0.000
#> GSM559402 1 0.000 0.977 1.000 0.000 0.000
#> GSM559403 1 0.000 0.977 1.000 0.000 0.000
#> GSM559404 3 0.327 0.870 0.116 0.000 0.884
#> GSM559405 3 0.000 0.942 0.000 0.000 1.000
#> GSM559406 1 0.000 0.977 1.000 0.000 0.000
#> GSM559407 1 0.000 0.977 1.000 0.000 0.000
#> GSM559408 1 0.000 0.977 1.000 0.000 0.000
#> GSM559409 1 0.000 0.977 1.000 0.000 0.000
#> GSM559410 1 0.000 0.977 1.000 0.000 0.000
#> GSM559411 1 0.000 0.977 1.000 0.000 0.000
#> GSM559412 3 0.327 0.870 0.116 0.000 0.884
#> GSM559413 3 0.327 0.870 0.116 0.000 0.884
#> GSM559415 1 0.000 0.977 1.000 0.000 0.000
#> GSM559416 1 0.000 0.977 1.000 0.000 0.000
#> GSM559417 1 0.000 0.977 1.000 0.000 0.000
#> GSM559418 1 0.000 0.977 1.000 0.000 0.000
#> GSM559419 1 0.000 0.977 1.000 0.000 0.000
#> GSM559420 3 0.000 0.942 0.000 0.000 1.000
#> GSM559421 2 0.369 0.794 0.140 0.860 0.000
#> GSM559423 1 0.327 0.866 0.884 0.116 0.000
#> GSM559425 2 0.000 0.893 0.000 1.000 0.000
#> GSM559426 2 0.000 0.893 0.000 1.000 0.000
#> GSM559427 2 0.000 0.893 0.000 1.000 0.000
#> GSM559428 3 0.000 0.942 0.000 0.000 1.000
#> GSM559429 1 0.327 0.866 0.884 0.116 0.000
#> GSM559430 2 0.000 0.893 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 3 0.1389 0.862 0.000 0.000 0.952 0.048
#> GSM559387 3 0.0000 0.854 0.000 0.000 1.000 0.000
#> GSM559391 3 0.0000 0.854 0.000 0.000 1.000 0.000
#> GSM559395 3 0.0000 0.854 0.000 0.000 1.000 0.000
#> GSM559397 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM559401 3 0.0000 0.854 0.000 0.000 1.000 0.000
#> GSM559414 3 0.0000 0.854 0.000 0.000 1.000 0.000
#> GSM559422 4 0.4088 0.744 0.140 0.000 0.040 0.820
#> GSM559424 3 0.3528 0.855 0.000 0.000 0.808 0.192
#> GSM559431 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM559432 2 0.3569 0.778 0.000 0.804 0.196 0.000
#> GSM559381 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM559382 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM559384 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM559385 3 0.3528 0.855 0.000 0.000 0.808 0.192
#> GSM559386 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM559388 4 0.4193 0.613 0.000 0.268 0.000 0.732
#> GSM559389 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM559390 4 0.0000 0.934 0.000 0.000 0.000 1.000
#> GSM559392 4 0.1211 0.904 0.000 0.040 0.000 0.960
#> GSM559393 4 0.2921 0.808 0.000 0.000 0.140 0.860
#> GSM559394 3 0.4103 0.782 0.000 0.000 0.744 0.256
#> GSM559396 4 0.0000 0.934 0.000 0.000 0.000 1.000
#> GSM559398 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM559399 4 0.0000 0.934 0.000 0.000 0.000 1.000
#> GSM559400 4 0.0000 0.934 0.000 0.000 0.000 1.000
#> GSM559402 4 0.2921 0.808 0.000 0.000 0.140 0.860
#> GSM559403 3 0.3569 0.852 0.000 0.000 0.804 0.196
#> GSM559404 1 0.3105 0.790 0.856 0.000 0.140 0.004
#> GSM559405 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM559406 4 0.0707 0.922 0.000 0.000 0.020 0.980
#> GSM559407 3 0.3528 0.855 0.000 0.000 0.808 0.192
#> GSM559408 4 0.2921 0.808 0.000 0.000 0.140 0.860
#> GSM559409 3 0.3942 0.812 0.000 0.000 0.764 0.236
#> GSM559410 3 0.0000 0.854 0.000 0.000 1.000 0.000
#> GSM559411 3 0.3219 0.863 0.000 0.000 0.836 0.164
#> GSM559412 1 0.7220 0.011 0.440 0.000 0.140 0.420
#> GSM559413 1 0.3377 0.784 0.848 0.000 0.140 0.012
#> GSM559415 4 0.0000 0.934 0.000 0.000 0.000 1.000
#> GSM559416 4 0.0000 0.934 0.000 0.000 0.000 1.000
#> GSM559417 4 0.0000 0.934 0.000 0.000 0.000 1.000
#> GSM559418 4 0.0000 0.934 0.000 0.000 0.000 1.000
#> GSM559419 4 0.0000 0.934 0.000 0.000 0.000 1.000
#> GSM559420 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM559421 2 0.4193 0.608 0.000 0.732 0.000 0.268
#> GSM559423 4 0.0000 0.934 0.000 0.000 0.000 1.000
#> GSM559425 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM559426 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM559427 2 0.0000 0.927 0.000 1.000 0.000 0.000
#> GSM559428 1 0.0000 0.908 1.000 0.000 0.000 0.000
#> GSM559429 4 0.0000 0.934 0.000 0.000 0.000 1.000
#> GSM559430 2 0.0000 0.927 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
#> GSM559383 1 0.2886 -0.1367 0.844 0.000 0.148 0.008 0.000
#> GSM559387 3 0.4268 1.0000 0.444 0.000 0.556 0.000 0.000
#> GSM559391 1 0.4114 -0.6216 0.624 0.000 0.376 0.000 0.000
#> GSM559395 3 0.4268 1.0000 0.444 0.000 0.556 0.000 0.000
#> GSM559397 5 0.0703 0.9741 0.024 0.000 0.000 0.000 0.976
#> GSM559401 3 0.4268 1.0000 0.444 0.000 0.556 0.000 0.000
#> GSM559414 3 0.4268 1.0000 0.444 0.000 0.556 0.000 0.000
#> GSM559422 4 0.5884 0.2740 0.352 0.000 0.112 0.536 0.000
#> GSM559424 1 0.5104 0.1325 0.648 0.000 0.068 0.284 0.000
#> GSM559431 2 0.0000 0.8740 0.000 1.000 0.000 0.000 0.000
#> GSM559432 2 0.4907 0.1664 0.000 0.488 0.488 0.024 0.000
#> GSM559381 5 0.0000 0.9968 0.000 0.000 0.000 0.000 1.000
#> GSM559382 5 0.0000 0.9968 0.000 0.000 0.000 0.000 1.000
#> GSM559384 5 0.0000 0.9968 0.000 0.000 0.000 0.000 1.000
#> GSM559385 1 0.4418 0.2130 0.652 0.000 0.016 0.332 0.000
#> GSM559386 5 0.0000 0.9968 0.000 0.000 0.000 0.000 1.000
#> GSM559388 4 0.4430 0.6375 0.000 0.172 0.076 0.752 0.000
#> GSM559389 5 0.0000 0.9968 0.000 0.000 0.000 0.000 1.000
#> GSM559390 4 0.1741 0.7812 0.024 0.000 0.040 0.936 0.000
#> GSM559392 4 0.4732 0.5818 0.000 0.208 0.076 0.716 0.000
#> GSM559393 4 0.3336 0.5207 0.228 0.000 0.000 0.772 0.000
#> GSM559394 1 0.4418 0.2130 0.652 0.000 0.016 0.332 0.000
#> GSM559396 4 0.5845 0.2803 0.352 0.000 0.108 0.540 0.000
#> GSM559398 2 0.1671 0.8381 0.000 0.924 0.076 0.000 0.000
#> GSM559399 4 0.0880 0.7998 0.032 0.000 0.000 0.968 0.000
#> GSM559400 4 0.1671 0.7792 0.000 0.000 0.076 0.924 0.000
#> GSM559402 1 0.5689 -0.0598 0.480 0.000 0.080 0.440 0.000
#> GSM559403 1 0.4138 0.2737 0.616 0.000 0.000 0.384 0.000
#> GSM559404 1 0.5825 0.4127 0.556 0.000 0.368 0.052 0.024
#> GSM559405 5 0.0000 0.9968 0.000 0.000 0.000 0.000 1.000
#> GSM559406 1 0.6695 0.1802 0.392 0.000 0.368 0.240 0.000
#> GSM559407 1 0.4329 0.2169 0.672 0.000 0.016 0.312 0.000
#> GSM559408 1 0.5530 0.4052 0.556 0.000 0.368 0.076 0.000
#> GSM559409 1 0.2852 0.3109 0.828 0.000 0.000 0.172 0.000
#> GSM559410 3 0.4268 1.0000 0.444 0.000 0.556 0.000 0.000
#> GSM559411 1 0.4435 -0.5321 0.648 0.000 0.336 0.016 0.000
#> GSM559412 1 0.5774 0.4123 0.556 0.000 0.368 0.060 0.016
#> GSM559413 1 0.5774 0.4123 0.556 0.000 0.368 0.060 0.016
#> GSM559415 4 0.0880 0.7998 0.032 0.000 0.000 0.968 0.000
#> GSM559416 4 0.1270 0.7766 0.052 0.000 0.000 0.948 0.000
#> GSM559417 4 0.0000 0.8004 0.000 0.000 0.000 1.000 0.000
#> GSM559418 4 0.0880 0.7998 0.032 0.000 0.000 0.968 0.000
#> GSM559419 4 0.0880 0.7998 0.032 0.000 0.000 0.968 0.000
#> GSM559420 5 0.0000 0.9968 0.000 0.000 0.000 0.000 1.000
#> GSM559421 2 0.4933 0.5823 0.000 0.688 0.076 0.236 0.000
#> GSM559423 4 0.1671 0.7792 0.000 0.000 0.076 0.924 0.000
#> GSM559425 2 0.0000 0.8740 0.000 1.000 0.000 0.000 0.000
#> GSM559426 2 0.0000 0.8740 0.000 1.000 0.000 0.000 0.000
#> GSM559427 2 0.0000 0.8740 0.000 1.000 0.000 0.000 0.000
#> GSM559428 5 0.0000 0.9968 0.000 0.000 0.000 0.000 1.000
#> GSM559429 4 0.1270 0.7887 0.000 0.000 0.052 0.948 0.000
#> GSM559430 2 0.0000 0.8740 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
#> GSM559383 3 0.2805 0.7858 0.000 0.004 0.812 0.184 0.000 0.000
#> GSM559387 3 0.0000 0.8852 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559391 3 0.0937 0.8739 0.000 0.000 0.960 0.040 0.000 0.000
#> GSM559395 3 0.0000 0.8852 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559397 6 0.1075 0.9436 0.000 0.000 0.000 0.048 0.000 0.952
#> GSM559401 3 0.0000 0.8852 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559414 3 0.0000 0.8852 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559422 4 0.2762 0.7617 0.196 0.000 0.000 0.804 0.000 0.000
#> GSM559424 3 0.4919 0.5988 0.204 0.004 0.664 0.128 0.000 0.000
#> GSM559431 5 0.0000 0.8040 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM559432 5 0.4035 0.5794 0.004 0.196 0.056 0.000 0.744 0.000
#> GSM559381 6 0.0000 0.9877 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559382 6 0.0000 0.9877 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559384 6 0.0000 0.9877 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559385 1 0.4264 0.7180 0.744 0.004 0.124 0.128 0.000 0.000
#> GSM559386 6 0.0000 0.9877 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559388 1 0.3547 0.4222 0.668 0.332 0.000 0.000 0.000 0.000
#> GSM559389 6 0.0000 0.9877 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559390 1 0.1007 0.8223 0.956 0.000 0.000 0.044 0.000 0.000
#> GSM559392 2 0.1349 0.6570 0.056 0.940 0.000 0.004 0.000 0.000
#> GSM559393 1 0.2278 0.7935 0.868 0.004 0.000 0.128 0.000 0.000
#> GSM559394 1 0.3608 0.7624 0.800 0.004 0.068 0.128 0.000 0.000
#> GSM559396 4 0.2793 0.7592 0.200 0.000 0.000 0.800 0.000 0.000
#> GSM559398 2 0.3175 0.3605 0.000 0.744 0.000 0.000 0.256 0.000
#> GSM559399 1 0.0000 0.8473 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559400 2 0.3868 0.0164 0.496 0.504 0.000 0.000 0.000 0.000
#> GSM559402 4 0.2631 0.7463 0.180 0.000 0.000 0.820 0.000 0.000
#> GSM559403 1 0.3663 0.7605 0.796 0.004 0.072 0.128 0.000 0.000
#> GSM559404 4 0.0146 0.8419 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM559405 6 0.0000 0.9877 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559406 4 0.2003 0.7924 0.116 0.000 0.000 0.884 0.000 0.000
#> GSM559407 1 0.5044 0.5856 0.644 0.004 0.224 0.128 0.000 0.000
#> GSM559408 4 0.0000 0.8417 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM559409 4 0.4509 0.5989 0.104 0.004 0.180 0.712 0.000 0.000
#> GSM559410 3 0.0000 0.8852 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559411 3 0.3716 0.7696 0.076 0.004 0.792 0.128 0.000 0.000
#> GSM559412 4 0.0146 0.8419 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM559413 4 0.0146 0.8419 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM559415 1 0.0000 0.8473 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559416 1 0.0000 0.8473 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559417 1 0.0146 0.8465 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM559418 1 0.0000 0.8473 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM559419 1 0.0146 0.8465 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM559420 6 0.0000 0.9877 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559421 2 0.1267 0.6133 0.000 0.940 0.000 0.000 0.060 0.000
#> GSM559423 2 0.2320 0.6387 0.132 0.864 0.000 0.004 0.000 0.000
#> GSM559425 5 0.3244 0.6554 0.000 0.268 0.000 0.000 0.732 0.000
#> GSM559426 5 0.0000 0.8040 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM559427 5 0.3428 0.6119 0.000 0.304 0.000 0.000 0.696 0.000
#> GSM559428 6 0.1141 0.9539 0.000 0.052 0.000 0.000 0.000 0.948
#> GSM559429 1 0.0146 0.8457 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM559430 5 0.0000 0.8040 0.000 0.000 0.000 0.000 1.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:pam 50 1.000000 2
#> ATC:pam 51 0.816772 3
#> ATC:pam 51 0.014854 4
#> ATC:pam 34 0.000904 5
#> ATC:pam 49 0.000481 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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.451 0.781 0.770 0.3695 0.517 0.517
#> 3 3 0.509 0.822 0.850 0.7038 0.756 0.556
#> 4 4 0.765 0.789 0.900 0.1436 0.888 0.682
#> 5 5 0.697 0.788 0.856 0.0478 0.920 0.709
#> 6 6 0.749 0.710 0.813 0.0653 0.925 0.685
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
#> GSM559383 2 0.998 -0.831 0.476 0.524
#> GSM559387 2 0.833 0.594 0.264 0.736
#> GSM559391 1 0.991 0.998 0.556 0.444
#> GSM559395 2 0.738 0.633 0.208 0.792
#> GSM559397 2 0.991 0.481 0.444 0.556
#> GSM559401 2 0.991 0.481 0.444 0.556
#> GSM559414 2 0.991 0.481 0.444 0.556
#> GSM559422 2 0.991 0.481 0.444 0.556
#> GSM559424 1 0.991 0.998 0.556 0.444
#> GSM559431 2 0.184 0.774 0.028 0.972
#> GSM559432 2 0.991 0.481 0.444 0.556
#> GSM559381 2 0.000 0.792 0.000 1.000
#> GSM559382 2 0.000 0.792 0.000 1.000
#> GSM559384 2 0.000 0.792 0.000 1.000
#> GSM559385 1 0.991 0.998 0.556 0.444
#> GSM559386 2 0.000 0.792 0.000 1.000
#> GSM559388 2 0.000 0.792 0.000 1.000
#> GSM559389 2 0.000 0.792 0.000 1.000
#> GSM559390 1 0.991 0.998 0.556 0.444
#> GSM559392 2 0.000 0.792 0.000 1.000
#> GSM559393 1 0.991 0.998 0.556 0.444
#> GSM559394 1 0.992 0.992 0.552 0.448
#> GSM559396 2 0.861 -0.175 0.284 0.716
#> GSM559398 2 0.000 0.792 0.000 1.000
#> GSM559399 1 0.991 0.998 0.556 0.444
#> GSM559400 2 0.000 0.792 0.000 1.000
#> GSM559402 1 0.991 0.998 0.556 0.444
#> GSM559403 1 0.991 0.998 0.556 0.444
#> GSM559404 2 0.000 0.792 0.000 1.000
#> GSM559405 2 0.000 0.792 0.000 1.000
#> GSM559406 1 0.991 0.998 0.556 0.444
#> GSM559407 1 0.991 0.998 0.556 0.444
#> GSM559408 1 0.991 0.998 0.556 0.444
#> GSM559409 1 0.991 0.998 0.556 0.444
#> GSM559410 2 0.000 0.792 0.000 1.000
#> GSM559411 1 0.995 0.971 0.540 0.460
#> GSM559412 1 0.991 0.998 0.556 0.444
#> GSM559413 2 0.373 0.664 0.072 0.928
#> GSM559415 1 0.991 0.998 0.556 0.444
#> GSM559416 1 0.991 0.998 0.556 0.444
#> GSM559417 1 0.991 0.998 0.556 0.444
#> GSM559418 1 0.991 0.998 0.556 0.444
#> GSM559419 1 0.991 0.998 0.556 0.444
#> GSM559420 2 0.000 0.792 0.000 1.000
#> GSM559421 2 0.000 0.792 0.000 1.000
#> GSM559423 2 0.000 0.792 0.000 1.000
#> GSM559425 2 0.000 0.792 0.000 1.000
#> GSM559426 2 0.000 0.792 0.000 1.000
#> GSM559427 2 0.000 0.792 0.000 1.000
#> GSM559428 2 0.000 0.792 0.000 1.000
#> GSM559429 2 0.163 0.776 0.024 0.976
#> GSM559430 2 0.000 0.792 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 1 0.6359 0.0677 0.592 0.404 0.004
#> GSM559387 2 0.8109 0.7907 0.116 0.628 0.256
#> GSM559391 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559395 2 0.8331 0.7739 0.164 0.628 0.208
#> GSM559397 2 0.6204 0.6752 0.000 0.576 0.424
#> GSM559401 2 0.8109 0.7907 0.116 0.628 0.256
#> GSM559414 2 0.8109 0.7907 0.116 0.628 0.256
#> GSM559422 2 0.6008 0.7322 0.000 0.628 0.372
#> GSM559424 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559431 2 0.3619 0.7896 0.000 0.864 0.136
#> GSM559432 2 0.5178 0.7817 0.000 0.744 0.256
#> GSM559381 3 0.2537 0.8366 0.080 0.000 0.920
#> GSM559382 2 0.7513 0.6593 0.052 0.604 0.344
#> GSM559384 3 0.4796 0.8397 0.220 0.000 0.780
#> GSM559385 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559386 3 0.2537 0.8366 0.080 0.000 0.920
#> GSM559388 2 0.3134 0.7831 0.032 0.916 0.052
#> GSM559389 3 0.2537 0.8366 0.080 0.000 0.920
#> GSM559390 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559392 2 0.4270 0.7829 0.116 0.860 0.024
#> GSM559393 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559394 1 0.0424 0.9535 0.992 0.008 0.000
#> GSM559396 3 0.5497 0.7910 0.292 0.000 0.708
#> GSM559398 2 0.0000 0.7632 0.000 1.000 0.000
#> GSM559399 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559400 2 0.5988 0.7772 0.168 0.776 0.056
#> GSM559402 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559403 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559404 3 0.5260 0.7516 0.080 0.092 0.828
#> GSM559405 3 0.2537 0.8366 0.080 0.000 0.920
#> GSM559406 3 0.5760 0.7409 0.328 0.000 0.672
#> GSM559407 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559408 3 0.5882 0.7049 0.348 0.000 0.652
#> GSM559409 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559410 2 0.8350 0.7485 0.196 0.628 0.176
#> GSM559411 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559412 3 0.5497 0.7910 0.292 0.000 0.708
#> GSM559413 3 0.4887 0.8367 0.228 0.000 0.772
#> GSM559415 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559416 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559417 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559418 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559419 1 0.0000 0.9636 1.000 0.000 0.000
#> GSM559420 3 0.2682 0.8325 0.076 0.004 0.920
#> GSM559421 2 0.3267 0.7738 0.116 0.884 0.000
#> GSM559423 2 0.8028 0.7747 0.168 0.656 0.176
#> GSM559425 2 0.0000 0.7632 0.000 1.000 0.000
#> GSM559426 2 0.0592 0.7644 0.012 0.988 0.000
#> GSM559427 2 0.0000 0.7632 0.000 1.000 0.000
#> GSM559428 2 0.7513 0.6593 0.052 0.604 0.344
#> GSM559429 2 0.8028 0.7747 0.168 0.656 0.176
#> GSM559430 2 0.0000 0.7632 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 4 0.3649 0.689 0.000 0.000 0.204 0.796
#> GSM559387 3 0.1716 0.756 0.000 0.000 0.936 0.064
#> GSM559391 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559395 3 0.7812 0.167 0.000 0.256 0.396 0.348
#> GSM559397 3 0.1022 0.781 0.032 0.000 0.968 0.000
#> GSM559401 3 0.0000 0.785 0.000 0.000 1.000 0.000
#> GSM559414 3 0.0000 0.785 0.000 0.000 1.000 0.000
#> GSM559422 3 0.0000 0.785 0.000 0.000 1.000 0.000
#> GSM559424 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559431 2 0.1557 0.851 0.000 0.944 0.056 0.000
#> GSM559432 3 0.0000 0.785 0.000 0.000 1.000 0.000
#> GSM559381 1 0.0000 0.751 1.000 0.000 0.000 0.000
#> GSM559382 3 0.4992 0.393 0.476 0.000 0.524 0.000
#> GSM559384 1 0.3907 0.824 0.768 0.000 0.000 0.232
#> GSM559385 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559386 1 0.0000 0.751 1.000 0.000 0.000 0.000
#> GSM559388 2 0.3942 0.574 0.000 0.764 0.000 0.236
#> GSM559389 1 0.0000 0.751 1.000 0.000 0.000 0.000
#> GSM559390 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559392 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM559393 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559394 4 0.0592 0.932 0.000 0.016 0.000 0.984
#> GSM559396 1 0.4008 0.819 0.756 0.000 0.000 0.244
#> GSM559398 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM559399 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559400 2 0.1302 0.860 0.000 0.956 0.000 0.044
#> GSM559402 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559403 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559404 1 0.3942 0.824 0.764 0.000 0.000 0.236
#> GSM559405 1 0.0000 0.751 1.000 0.000 0.000 0.000
#> GSM559406 1 0.4134 0.803 0.740 0.000 0.000 0.260
#> GSM559407 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559408 1 0.4222 0.791 0.728 0.000 0.000 0.272
#> GSM559409 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559410 4 0.7824 -0.187 0.000 0.264 0.336 0.400
#> GSM559411 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559412 1 0.3942 0.824 0.764 0.000 0.000 0.236
#> GSM559413 1 0.3942 0.824 0.764 0.000 0.000 0.236
#> GSM559415 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559416 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559417 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559418 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559419 4 0.0000 0.948 0.000 0.000 0.000 1.000
#> GSM559420 1 0.0000 0.751 1.000 0.000 0.000 0.000
#> GSM559421 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM559423 3 0.5592 0.477 0.000 0.300 0.656 0.044
#> GSM559425 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM559426 2 0.0336 0.890 0.000 0.992 0.000 0.008
#> GSM559427 2 0.0000 0.894 0.000 1.000 0.000 0.000
#> GSM559428 3 0.4713 0.581 0.360 0.000 0.640 0.000
#> GSM559429 2 0.6738 0.148 0.000 0.544 0.352 0.104
#> GSM559430 2 0.0000 0.894 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
#> GSM559383 1 0.4047 0.404 0.676 0.000 0.320 0.004 0.000
#> GSM559387 3 0.1478 0.737 0.064 0.000 0.936 0.000 0.000
#> GSM559391 1 0.0324 0.940 0.992 0.000 0.004 0.004 0.000
#> GSM559395 3 0.3219 0.702 0.136 0.020 0.840 0.004 0.000
#> GSM559397 3 0.5198 0.660 0.000 0.000 0.688 0.164 0.148
#> GSM559401 3 0.0000 0.731 0.000 0.000 1.000 0.000 0.000
#> GSM559414 3 0.0000 0.731 0.000 0.000 1.000 0.000 0.000
#> GSM559422 3 0.3242 0.709 0.000 0.000 0.784 0.216 0.000
#> GSM559424 1 0.0162 0.941 0.996 0.000 0.000 0.004 0.000
#> GSM559431 2 0.1732 0.834 0.000 0.920 0.080 0.000 0.000
#> GSM559432 3 0.3242 0.709 0.000 0.000 0.784 0.216 0.000
#> GSM559381 5 0.2280 0.837 0.000 0.000 0.000 0.120 0.880
#> GSM559382 5 0.3885 0.535 0.000 0.000 0.268 0.008 0.724
#> GSM559384 4 0.5079 0.707 0.136 0.000 0.000 0.700 0.164
#> GSM559385 1 0.0162 0.941 0.996 0.000 0.000 0.004 0.000
#> GSM559386 5 0.2280 0.837 0.000 0.000 0.000 0.120 0.880
#> GSM559388 2 0.4555 0.595 0.224 0.720 0.000 0.056 0.000
#> GSM559389 5 0.2280 0.837 0.000 0.000 0.000 0.120 0.880
#> GSM559390 1 0.1364 0.932 0.952 0.000 0.000 0.036 0.012
#> GSM559392 2 0.0510 0.899 0.016 0.984 0.000 0.000 0.000
#> GSM559393 1 0.0566 0.941 0.984 0.000 0.000 0.004 0.012
#> GSM559394 1 0.0451 0.939 0.988 0.000 0.008 0.004 0.000
#> GSM559396 4 0.4645 0.766 0.204 0.000 0.000 0.724 0.072
#> GSM559398 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM559399 1 0.1124 0.935 0.960 0.000 0.000 0.036 0.004
#> GSM559400 2 0.2179 0.814 0.112 0.888 0.000 0.000 0.000
#> GSM559402 1 0.0162 0.941 0.996 0.000 0.000 0.000 0.004
#> GSM559403 1 0.0162 0.941 0.996 0.000 0.000 0.004 0.000
#> GSM559404 4 0.7397 0.168 0.056 0.000 0.248 0.480 0.216
#> GSM559405 5 0.2329 0.834 0.000 0.000 0.000 0.124 0.876
#> GSM559406 4 0.4840 0.729 0.320 0.000 0.000 0.640 0.040
#> GSM559407 1 0.0162 0.942 0.996 0.000 0.004 0.000 0.000
#> GSM559408 4 0.4836 0.681 0.356 0.000 0.000 0.612 0.032
#> GSM559409 1 0.0162 0.941 0.996 0.000 0.000 0.004 0.000
#> GSM559410 3 0.4706 0.470 0.344 0.020 0.632 0.004 0.000
#> GSM559411 1 0.1124 0.916 0.960 0.000 0.036 0.004 0.000
#> GSM559412 4 0.4605 0.773 0.192 0.000 0.000 0.732 0.076
#> GSM559413 4 0.4698 0.761 0.172 0.000 0.000 0.732 0.096
#> GSM559415 1 0.0880 0.937 0.968 0.000 0.000 0.032 0.000
#> GSM559416 1 0.0963 0.936 0.964 0.000 0.000 0.036 0.000
#> GSM559417 1 0.1918 0.918 0.928 0.000 0.000 0.036 0.036
#> GSM559418 1 0.1836 0.921 0.932 0.000 0.000 0.036 0.032
#> GSM559419 1 0.1918 0.918 0.928 0.000 0.000 0.036 0.036
#> GSM559420 5 0.2280 0.837 0.000 0.000 0.000 0.120 0.880
#> GSM559421 2 0.0510 0.899 0.016 0.984 0.000 0.000 0.000
#> GSM559423 3 0.7026 0.614 0.112 0.224 0.580 0.008 0.076
#> GSM559425 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM559426 2 0.2488 0.788 0.124 0.872 0.000 0.004 0.000
#> GSM559427 2 0.0000 0.900 0.000 1.000 0.000 0.000 0.000
#> GSM559428 5 0.3885 0.535 0.000 0.000 0.268 0.008 0.724
#> GSM559429 3 0.6506 0.377 0.208 0.324 0.468 0.000 0.000
#> GSM559430 2 0.0000 0.900 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
#> GSM559383 4 0.6245 -0.305 0.284 0.000 0.008 0.420 0.288 0.000
#> GSM559387 3 0.4372 0.805 0.028 0.000 0.692 0.020 0.260 0.000
#> GSM559391 1 0.3499 0.425 0.680 0.000 0.000 0.000 0.320 0.000
#> GSM559395 3 0.6153 0.616 0.088 0.008 0.540 0.052 0.312 0.000
#> GSM559397 3 0.3133 0.740 0.000 0.000 0.780 0.212 0.000 0.008
#> GSM559401 3 0.2945 0.840 0.000 0.000 0.824 0.020 0.156 0.000
#> GSM559414 3 0.2945 0.840 0.000 0.000 0.824 0.020 0.156 0.000
#> GSM559422 3 0.0363 0.827 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM559424 1 0.3876 0.454 0.700 0.000 0.000 0.024 0.276 0.000
#> GSM559431 2 0.1180 0.872 0.004 0.960 0.008 0.024 0.000 0.004
#> GSM559432 3 0.0000 0.829 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM559381 6 0.0000 0.890 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM559382 6 0.3323 0.778 0.000 0.000 0.008 0.204 0.008 0.780
#> GSM559384 4 0.4230 0.615 0.024 0.000 0.000 0.612 0.000 0.364
#> GSM559385 1 0.3428 0.452 0.696 0.000 0.000 0.000 0.304 0.000
#> GSM559386 6 0.0146 0.892 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM559388 2 0.3933 0.646 0.216 0.740 0.040 0.004 0.000 0.000
#> GSM559389 6 0.0146 0.892 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM559390 1 0.0603 0.722 0.980 0.000 0.000 0.004 0.016 0.000
#> GSM559392 2 0.0508 0.879 0.004 0.984 0.000 0.000 0.012 0.000
#> GSM559393 1 0.1341 0.712 0.948 0.000 0.000 0.024 0.028 0.000
#> GSM559394 1 0.5137 0.294 0.604 0.004 0.000 0.104 0.288 0.000
#> GSM559396 4 0.6059 0.725 0.084 0.000 0.088 0.600 0.004 0.224
#> GSM559398 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559399 1 0.0547 0.726 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM559400 2 0.3441 0.770 0.140 0.816 0.000 0.012 0.028 0.004
#> GSM559402 1 0.0508 0.728 0.984 0.000 0.000 0.004 0.012 0.000
#> GSM559403 1 0.3371 0.470 0.708 0.000 0.000 0.000 0.292 0.000
#> GSM559404 4 0.4925 0.733 0.048 0.000 0.032 0.692 0.008 0.220
#> GSM559405 6 0.1471 0.851 0.004 0.000 0.064 0.000 0.000 0.932
#> GSM559406 4 0.4516 0.769 0.112 0.000 0.000 0.700 0.000 0.188
#> GSM559407 5 0.3765 0.708 0.404 0.000 0.000 0.000 0.596 0.000
#> GSM559408 4 0.4233 0.553 0.268 0.000 0.000 0.684 0.000 0.048
#> GSM559409 1 0.4371 0.400 0.664 0.000 0.000 0.052 0.284 0.000
#> GSM559410 5 0.4572 0.707 0.240 0.008 0.032 0.020 0.700 0.000
#> GSM559411 5 0.4105 0.784 0.348 0.000 0.000 0.020 0.632 0.000
#> GSM559412 4 0.4349 0.770 0.084 0.000 0.000 0.708 0.000 0.208
#> GSM559413 4 0.4255 0.762 0.068 0.000 0.000 0.708 0.000 0.224
#> GSM559415 1 0.0935 0.727 0.964 0.000 0.000 0.004 0.032 0.000
#> GSM559416 1 0.0692 0.728 0.976 0.000 0.000 0.000 0.020 0.004
#> GSM559417 1 0.1219 0.699 0.948 0.000 0.000 0.000 0.048 0.004
#> GSM559418 1 0.1152 0.707 0.952 0.000 0.000 0.004 0.044 0.000
#> GSM559419 1 0.1082 0.706 0.956 0.000 0.000 0.004 0.040 0.000
#> GSM559420 6 0.0146 0.892 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM559421 2 0.0508 0.879 0.004 0.984 0.000 0.000 0.012 0.000
#> GSM559423 2 0.6084 0.622 0.124 0.616 0.012 0.208 0.028 0.012
#> GSM559425 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559426 2 0.1152 0.865 0.044 0.952 0.000 0.004 0.000 0.000
#> GSM559427 2 0.0000 0.879 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM559428 6 0.3381 0.772 0.000 0.000 0.008 0.212 0.008 0.772
#> GSM559429 2 0.5827 0.645 0.172 0.660 0.032 0.044 0.092 0.000
#> GSM559430 2 0.0146 0.880 0.004 0.996 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:mclust 45 1.00e+00 2
#> ATC:mclust 51 2.34e-02 3
#> ATC:mclust 47 7.96e-05 4
#> ATC:mclust 48 2.46e-05 5
#> ATC:mclust 45 2.69e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 21167 rows and 52 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.958 0.982 0.4051 0.599 0.599
#> 3 3 0.922 0.925 0.968 0.6577 0.660 0.463
#> 4 4 0.619 0.606 0.789 0.0956 0.900 0.715
#> 5 5 0.672 0.699 0.828 0.0743 0.881 0.595
#> 6 6 0.629 0.511 0.711 0.0380 0.956 0.801
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM559383 1 0.0000 0.983 1.000 0.000
#> GSM559387 1 0.0000 0.983 1.000 0.000
#> GSM559391 1 0.0000 0.983 1.000 0.000
#> GSM559395 1 0.0000 0.983 1.000 0.000
#> GSM559397 1 0.0000 0.983 1.000 0.000
#> GSM559401 1 0.0000 0.983 1.000 0.000
#> GSM559414 1 0.0000 0.983 1.000 0.000
#> GSM559422 1 0.0000 0.983 1.000 0.000
#> GSM559424 1 0.0000 0.983 1.000 0.000
#> GSM559431 2 0.0000 0.973 0.000 1.000
#> GSM559432 2 0.0000 0.973 0.000 1.000
#> GSM559381 1 0.0000 0.983 1.000 0.000
#> GSM559382 1 0.0000 0.983 1.000 0.000
#> GSM559384 1 0.0000 0.983 1.000 0.000
#> GSM559385 1 0.0000 0.983 1.000 0.000
#> GSM559386 1 0.0000 0.983 1.000 0.000
#> GSM559388 2 0.0000 0.973 0.000 1.000
#> GSM559389 1 0.0000 0.983 1.000 0.000
#> GSM559390 1 0.0000 0.983 1.000 0.000
#> GSM559392 2 0.0000 0.973 0.000 1.000
#> GSM559393 1 0.0000 0.983 1.000 0.000
#> GSM559394 1 0.0000 0.983 1.000 0.000
#> GSM559396 1 0.0000 0.983 1.000 0.000
#> GSM559398 2 0.0000 0.973 0.000 1.000
#> GSM559399 1 0.0000 0.983 1.000 0.000
#> GSM559400 2 0.0000 0.973 0.000 1.000
#> GSM559402 1 0.0000 0.983 1.000 0.000
#> GSM559403 1 0.0000 0.983 1.000 0.000
#> GSM559404 1 0.0000 0.983 1.000 0.000
#> GSM559405 1 0.0000 0.983 1.000 0.000
#> GSM559406 1 0.0000 0.983 1.000 0.000
#> GSM559407 1 0.0000 0.983 1.000 0.000
#> GSM559408 1 0.0000 0.983 1.000 0.000
#> GSM559409 1 0.0000 0.983 1.000 0.000
#> GSM559410 1 0.0000 0.983 1.000 0.000
#> GSM559411 1 0.0000 0.983 1.000 0.000
#> GSM559412 1 0.0000 0.983 1.000 0.000
#> GSM559413 1 0.0000 0.983 1.000 0.000
#> GSM559415 1 0.1843 0.957 0.972 0.028
#> GSM559416 2 0.8713 0.577 0.292 0.708
#> GSM559417 1 0.8763 0.575 0.704 0.296
#> GSM559418 1 0.8267 0.643 0.740 0.260
#> GSM559419 1 0.0000 0.983 1.000 0.000
#> GSM559420 1 0.0000 0.983 1.000 0.000
#> GSM559421 2 0.0000 0.973 0.000 1.000
#> GSM559423 2 0.0938 0.965 0.012 0.988
#> GSM559425 2 0.0000 0.973 0.000 1.000
#> GSM559426 2 0.0000 0.973 0.000 1.000
#> GSM559427 2 0.0000 0.973 0.000 1.000
#> GSM559428 1 0.0000 0.983 1.000 0.000
#> GSM559429 2 0.2043 0.948 0.032 0.968
#> GSM559430 2 0.0000 0.973 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM559383 3 0.0000 0.978 0.000 0.000 1.000
#> GSM559387 3 0.0000 0.978 0.000 0.000 1.000
#> GSM559391 3 0.0000 0.978 0.000 0.000 1.000
#> GSM559395 3 0.0000 0.978 0.000 0.000 1.000
#> GSM559397 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559401 3 0.0000 0.978 0.000 0.000 1.000
#> GSM559414 3 0.0000 0.978 0.000 0.000 1.000
#> GSM559422 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559424 3 0.0000 0.978 0.000 0.000 1.000
#> GSM559431 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559432 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559381 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559382 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559384 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559385 3 0.0000 0.978 0.000 0.000 1.000
#> GSM559386 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559388 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559389 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559390 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559392 2 0.0424 0.952 0.008 0.992 0.000
#> GSM559393 1 0.7671 0.314 0.568 0.052 0.380
#> GSM559394 3 0.0000 0.978 0.000 0.000 1.000
#> GSM559396 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559398 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559399 3 0.0475 0.971 0.004 0.004 0.992
#> GSM559400 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559402 1 0.1289 0.933 0.968 0.000 0.032
#> GSM559403 3 0.0000 0.978 0.000 0.000 1.000
#> GSM559404 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559405 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559406 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559407 3 0.0000 0.978 0.000 0.000 1.000
#> GSM559408 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559409 3 0.0000 0.978 0.000 0.000 1.000
#> GSM559410 3 0.0000 0.978 0.000 0.000 1.000
#> GSM559411 3 0.0000 0.978 0.000 0.000 1.000
#> GSM559412 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559413 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559415 3 0.5621 0.532 0.000 0.308 0.692
#> GSM559416 2 0.3816 0.815 0.000 0.852 0.148
#> GSM559417 2 0.4974 0.702 0.236 0.764 0.000
#> GSM559418 2 0.4862 0.801 0.160 0.820 0.020
#> GSM559419 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559420 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559421 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559423 1 0.5397 0.581 0.720 0.280 0.000
#> GSM559425 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559426 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559427 2 0.0000 0.956 0.000 1.000 0.000
#> GSM559428 1 0.0000 0.961 1.000 0.000 0.000
#> GSM559429 2 0.0424 0.952 0.008 0.992 0.000
#> GSM559430 2 0.0000 0.956 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM559383 1 0.4999 -0.5177 0.508 0.000 0.492 0.000
#> GSM559387 3 0.4907 0.5639 0.420 0.000 0.580 0.000
#> GSM559391 1 0.1792 0.6407 0.932 0.000 0.068 0.000
#> GSM559395 3 0.4925 0.5567 0.428 0.000 0.572 0.000
#> GSM559397 4 0.1637 0.7835 0.000 0.000 0.060 0.940
#> GSM559401 3 0.4866 0.5729 0.404 0.000 0.596 0.000
#> GSM559414 3 0.6867 0.4833 0.384 0.000 0.508 0.108
#> GSM559422 3 0.4981 0.0414 0.000 0.000 0.536 0.464
#> GSM559424 1 0.2149 0.6458 0.912 0.000 0.088 0.000
#> GSM559431 2 0.0000 0.8099 0.000 1.000 0.000 0.000
#> GSM559432 2 0.4967 0.1901 0.000 0.548 0.452 0.000
#> GSM559381 4 0.0592 0.8016 0.000 0.000 0.016 0.984
#> GSM559382 4 0.2530 0.7997 0.000 0.000 0.112 0.888
#> GSM559384 4 0.2174 0.8121 0.052 0.000 0.020 0.928
#> GSM559385 1 0.0469 0.6733 0.988 0.000 0.012 0.000
#> GSM559386 4 0.0817 0.8094 0.000 0.000 0.024 0.976
#> GSM559388 2 0.0927 0.8050 0.016 0.976 0.008 0.000
#> GSM559389 4 0.0000 0.8064 0.000 0.000 0.000 1.000
#> GSM559390 4 0.7369 0.5325 0.196 0.000 0.292 0.512
#> GSM559392 2 0.2334 0.7799 0.000 0.908 0.088 0.004
#> GSM559393 1 0.7641 0.2751 0.592 0.120 0.052 0.236
#> GSM559394 1 0.2281 0.6328 0.904 0.000 0.096 0.000
#> GSM559396 4 0.5954 0.6582 0.052 0.000 0.344 0.604
#> GSM559398 2 0.0469 0.8084 0.000 0.988 0.012 0.000
#> GSM559399 1 0.3484 0.5704 0.844 0.004 0.144 0.008
#> GSM559400 2 0.4661 0.6772 0.016 0.728 0.256 0.000
#> GSM559402 1 0.6693 -0.0181 0.488 0.000 0.088 0.424
#> GSM559403 1 0.0188 0.6751 0.996 0.000 0.004 0.000
#> GSM559404 4 0.2578 0.8004 0.052 0.000 0.036 0.912
#> GSM559405 4 0.1109 0.7999 0.004 0.000 0.028 0.968
#> GSM559406 4 0.6351 0.6824 0.104 0.000 0.268 0.628
#> GSM559407 1 0.0592 0.6749 0.984 0.000 0.016 0.000
#> GSM559408 4 0.5897 0.7046 0.136 0.000 0.164 0.700
#> GSM559409 1 0.1182 0.6702 0.968 0.000 0.016 0.016
#> GSM559410 1 0.2704 0.5398 0.876 0.000 0.124 0.000
#> GSM559411 1 0.1637 0.6422 0.940 0.000 0.060 0.000
#> GSM559412 4 0.2363 0.8056 0.056 0.000 0.024 0.920
#> GSM559413 4 0.2385 0.8049 0.052 0.000 0.028 0.920
#> GSM559415 1 0.7085 0.2886 0.568 0.232 0.200 0.000
#> GSM559416 2 0.7001 0.0621 0.420 0.464 0.116 0.000
#> GSM559417 2 0.8869 0.3118 0.140 0.396 0.372 0.092
#> GSM559418 2 0.8311 0.3686 0.244 0.512 0.196 0.048
#> GSM559419 4 0.7216 0.5597 0.156 0.000 0.336 0.508
#> GSM559420 4 0.2654 0.8065 0.004 0.000 0.108 0.888
#> GSM559421 2 0.0000 0.8099 0.000 1.000 0.000 0.000
#> GSM559423 4 0.6508 0.4726 0.000 0.296 0.104 0.600
#> GSM559425 2 0.0000 0.8099 0.000 1.000 0.000 0.000
#> GSM559426 2 0.0000 0.8099 0.000 1.000 0.000 0.000
#> GSM559427 2 0.0000 0.8099 0.000 1.000 0.000 0.000
#> GSM559428 4 0.2408 0.8057 0.000 0.000 0.104 0.896
#> GSM559429 2 0.1743 0.7814 0.000 0.940 0.004 0.056
#> GSM559430 2 0.0000 0.8099 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
#> GSM559383 5 0.5813 0.2621 0.000 0.000 0.328 0.112 0.560
#> GSM559387 3 0.3305 0.7224 0.000 0.000 0.776 0.000 0.224
#> GSM559391 5 0.3241 0.7853 0.000 0.000 0.024 0.144 0.832
#> GSM559395 3 0.4588 0.6721 0.000 0.000 0.720 0.060 0.220
#> GSM559397 1 0.1831 0.8169 0.920 0.000 0.076 0.004 0.000
#> GSM559401 3 0.2329 0.7477 0.000 0.000 0.876 0.000 0.124
#> GSM559414 3 0.6077 0.3186 0.124 0.000 0.480 0.000 0.396
#> GSM559422 3 0.1502 0.6884 0.056 0.000 0.940 0.004 0.000
#> GSM559424 5 0.4341 0.5454 0.000 0.000 0.008 0.364 0.628
#> GSM559431 2 0.0000 0.9028 0.000 1.000 0.000 0.000 0.000
#> GSM559432 3 0.3282 0.6327 0.000 0.188 0.804 0.008 0.000
#> GSM559381 1 0.0451 0.8324 0.988 0.000 0.000 0.008 0.004
#> GSM559382 1 0.4002 0.7867 0.796 0.000 0.084 0.120 0.000
#> GSM559384 1 0.3265 0.8109 0.844 0.000 0.012 0.128 0.016
#> GSM559385 5 0.2719 0.7982 0.000 0.000 0.004 0.144 0.852
#> GSM559386 1 0.2069 0.8310 0.912 0.000 0.012 0.076 0.000
#> GSM559388 2 0.1851 0.8536 0.000 0.912 0.000 0.088 0.000
#> GSM559389 1 0.1430 0.8356 0.944 0.000 0.004 0.052 0.000
#> GSM559390 4 0.2863 0.7156 0.060 0.000 0.000 0.876 0.064
#> GSM559392 2 0.2570 0.8313 0.004 0.880 0.008 0.108 0.000
#> GSM559393 5 0.4058 0.7452 0.032 0.040 0.012 0.084 0.832
#> GSM559394 5 0.5002 0.5759 0.000 0.000 0.052 0.312 0.636
#> GSM559396 4 0.4042 0.6309 0.156 0.000 0.044 0.792 0.008
#> GSM559398 2 0.1124 0.8894 0.000 0.960 0.004 0.036 0.000
#> GSM559399 4 0.3336 0.5952 0.000 0.000 0.000 0.772 0.228
#> GSM559400 4 0.5868 0.1638 0.000 0.380 0.104 0.516 0.000
#> GSM559402 5 0.4520 0.6479 0.156 0.000 0.016 0.060 0.768
#> GSM559403 5 0.2806 0.7957 0.000 0.000 0.004 0.152 0.844
#> GSM559404 1 0.3068 0.7870 0.880 0.000 0.036 0.028 0.056
#> GSM559405 1 0.0960 0.8267 0.972 0.000 0.016 0.004 0.008
#> GSM559406 4 0.4125 0.5479 0.236 0.000 0.004 0.740 0.020
#> GSM559407 5 0.2136 0.7864 0.000 0.000 0.008 0.088 0.904
#> GSM559408 1 0.7048 -0.0233 0.388 0.000 0.016 0.220 0.376
#> GSM559409 5 0.3134 0.7838 0.028 0.000 0.012 0.096 0.864
#> GSM559410 5 0.0992 0.7416 0.000 0.000 0.024 0.008 0.968
#> GSM559411 5 0.1430 0.7891 0.000 0.000 0.004 0.052 0.944
#> GSM559412 1 0.2728 0.8046 0.896 0.000 0.016 0.040 0.048
#> GSM559413 1 0.2095 0.8179 0.928 0.000 0.020 0.028 0.024
#> GSM559415 4 0.3522 0.6100 0.000 0.004 0.004 0.780 0.212
#> GSM559416 4 0.3662 0.5540 0.000 0.004 0.000 0.744 0.252
#> GSM559417 4 0.2354 0.7195 0.000 0.020 0.032 0.916 0.032
#> GSM559418 2 0.7510 0.0136 0.044 0.452 0.012 0.332 0.160
#> GSM559419 4 0.1597 0.7219 0.012 0.000 0.000 0.940 0.048
#> GSM559420 1 0.3236 0.7999 0.828 0.000 0.020 0.152 0.000
#> GSM559421 2 0.0000 0.9028 0.000 1.000 0.000 0.000 0.000
#> GSM559423 1 0.6993 0.5034 0.556 0.248 0.084 0.112 0.000
#> GSM559425 2 0.0000 0.9028 0.000 1.000 0.000 0.000 0.000
#> GSM559426 2 0.0162 0.9012 0.000 0.996 0.000 0.004 0.000
#> GSM559427 2 0.0000 0.9028 0.000 1.000 0.000 0.000 0.000
#> GSM559428 1 0.3586 0.8044 0.828 0.000 0.076 0.096 0.000
#> GSM559429 2 0.2284 0.8263 0.096 0.896 0.000 0.004 0.004
#> GSM559430 2 0.0000 0.9028 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
#> GSM559383 1 0.8099 -0.02214 0.312 0.000 0.184 0.296 NA 0.032
#> GSM559387 3 0.3862 0.67916 0.100 0.000 0.796 0.016 NA 0.000
#> GSM559391 1 0.6137 -0.03583 0.464 0.000 0.048 0.388 NA 0.000
#> GSM559395 3 0.6059 0.44150 0.144 0.000 0.584 0.216 NA 0.000
#> GSM559397 6 0.3025 0.70902 0.000 0.000 0.024 0.000 NA 0.820
#> GSM559401 3 0.1010 0.70331 0.036 0.000 0.960 0.000 NA 0.000
#> GSM559414 3 0.6755 0.37283 0.208 0.000 0.416 0.000 NA 0.052
#> GSM559422 3 0.3140 0.66698 0.000 0.000 0.844 0.024 NA 0.024
#> GSM559424 4 0.5596 0.08709 0.400 0.000 0.028 0.500 NA 0.000
#> GSM559431 2 0.0547 0.86971 0.000 0.980 0.000 0.000 NA 0.000
#> GSM559432 3 0.2932 0.63255 0.000 0.164 0.820 0.000 NA 0.000
#> GSM559381 6 0.1814 0.71236 0.000 0.000 0.000 0.000 NA 0.900
#> GSM559382 6 0.3946 0.61805 0.000 0.000 0.004 0.052 NA 0.752
#> GSM559384 6 0.3331 0.70058 0.004 0.000 0.000 0.044 NA 0.816
#> GSM559385 1 0.2950 0.52229 0.828 0.000 0.000 0.148 NA 0.000
#> GSM559386 6 0.1434 0.70838 0.000 0.000 0.000 0.012 NA 0.940
#> GSM559388 2 0.4317 0.69434 0.012 0.732 0.012 0.212 NA 0.000
#> GSM559389 6 0.1152 0.70553 0.000 0.000 0.000 0.004 NA 0.952
#> GSM559390 4 0.4372 0.44607 0.128 0.000 0.000 0.764 NA 0.060
#> GSM559392 2 0.3807 0.78322 0.000 0.808 0.000 0.048 NA 0.040
#> GSM559393 1 0.6159 0.33500 0.604 0.016 0.008 0.128 NA 0.028
#> GSM559394 1 0.6312 0.32171 0.592 0.004 0.104 0.180 NA 0.000
#> GSM559396 4 0.5457 0.18191 0.000 0.000 0.004 0.544 NA 0.328
#> GSM559398 2 0.1867 0.84738 0.000 0.916 0.000 0.020 NA 0.000
#> GSM559399 4 0.4273 0.27385 0.380 0.000 0.000 0.596 NA 0.000
#> GSM559400 2 0.6916 0.35995 0.004 0.492 0.076 0.252 NA 0.004
#> GSM559402 1 0.6387 0.25743 0.576 0.000 0.000 0.120 NA 0.160
#> GSM559403 1 0.2531 0.51376 0.856 0.000 0.000 0.132 NA 0.000
#> GSM559404 6 0.4784 0.59867 0.032 0.000 0.004 0.012 NA 0.604
#> GSM559405 6 0.3081 0.68298 0.004 0.000 0.000 0.000 NA 0.776
#> GSM559406 4 0.6223 -0.02285 0.044 0.000 0.000 0.468 NA 0.368
#> GSM559407 1 0.1536 0.55510 0.940 0.000 0.000 0.040 NA 0.004
#> GSM559408 6 0.7386 0.06322 0.312 0.000 0.000 0.176 NA 0.360
#> GSM559409 1 0.3637 0.51280 0.820 0.000 0.000 0.096 NA 0.032
#> GSM559410 1 0.1592 0.55038 0.940 0.000 0.020 0.008 NA 0.000
#> GSM559411 1 0.2007 0.54555 0.920 0.000 0.012 0.036 NA 0.000
#> GSM559412 6 0.5869 0.54646 0.096 0.000 0.000 0.040 NA 0.540
#> GSM559413 6 0.5512 0.59081 0.064 0.000 0.000 0.044 NA 0.588
#> GSM559415 4 0.5662 0.01208 0.424 0.000 0.004 0.440 NA 0.000
#> GSM559416 4 0.4315 0.33719 0.328 0.000 0.000 0.636 NA 0.000
#> GSM559417 4 0.5911 0.42659 0.112 0.016 0.000 0.636 NA 0.048
#> GSM559418 1 0.8204 0.00974 0.312 0.300 0.000 0.192 NA 0.048
#> GSM559419 4 0.4673 0.46712 0.116 0.000 0.000 0.732 NA 0.028
#> GSM559420 6 0.3384 0.65874 0.000 0.000 0.000 0.068 NA 0.812
#> GSM559421 2 0.0363 0.87109 0.000 0.988 0.000 0.000 NA 0.000
#> GSM559423 6 0.7132 0.20586 0.000 0.212 0.004 0.076 NA 0.392
#> GSM559425 2 0.0146 0.87162 0.000 0.996 0.000 0.000 NA 0.000
#> GSM559426 2 0.1219 0.86045 0.000 0.948 0.000 0.004 NA 0.000
#> GSM559427 2 0.0000 0.87109 0.000 1.000 0.000 0.000 NA 0.000
#> GSM559428 6 0.3078 0.64135 0.000 0.000 0.000 0.012 NA 0.796
#> GSM559429 2 0.3317 0.77871 0.004 0.828 0.000 0.000 NA 0.088
#> GSM559430 2 0.0547 0.87054 0.000 0.980 0.000 0.000 NA 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:NMF 52 0.723848 2
#> ATC:NMF 51 0.032758 3
#> ATC:NMF 41 0.000842 4
#> ATC:NMF 47 0.000059 5
#> ATC:NMF 32 0.000164 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