Date: 2019-12-25 22:21:46 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 21586 rows and 54 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 21586 54
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:hclust | 2 | 1.000 | 0.980 | 0.982 | ** | |
| SD:pam | 2 | 1.000 | 0.966 | 0.987 | ** | |
| CV:hclust | 2 | 1.000 | 0.988 | 0.986 | ** | |
| MAD:hclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:kmeans | 3 | 1.000 | 0.983 | 0.980 | ** | |
| MAD:pam | 3 | 1.000 | 0.968 | 0.986 | ** | 2 |
| ATC:kmeans | 3 | 1.000 | 0.976 | 0.967 | ** | |
| ATC:skmeans | 3 | 1.000 | 0.988 | 0.995 | ** | |
| ATC:pam | 3 | 1.000 | 0.973 | 0.991 | ** | 2 |
| MAD:mclust | 3 | 0.995 | 0.953 | 0.975 | ** | |
| CV:NMF | 3 | 0.970 | 0.941 | 0.974 | ** | 2 |
| ATC:NMF | 3 | 0.970 | 0.935 | 0.975 | ** | |
| MAD:NMF | 3 | 0.969 | 0.947 | 0.981 | ** | 2 |
| SD:NMF | 5 | 0.959 | 0.920 | 0.960 | ** | 2,3 |
| CV:kmeans | 3 | 0.955 | 0.963 | 0.956 | ** | |
| CV:mclust | 4 | 0.949 | 0.927 | 0.962 | * | |
| CV:skmeans | 3 | 0.944 | 0.935 | 0.974 | * | |
| MAD:skmeans | 3 | 0.941 | 0.919 | 0.968 | * | 2 |
| SD:skmeans | 3 | 0.940 | 0.902 | 0.966 | * | 2 |
| CV:pam | 6 | 0.928 | 0.905 | 0.946 | * | 2,3,4 |
| ATC:hclust | 5 | 0.922 | 0.964 | 0.971 | * | 2,3,4 |
| SD:mclust | 2 | 0.849 | 0.901 | 0.942 | ||
| ATC:mclust | 3 | 0.764 | 0.884 | 0.942 | ||
| SD:kmeans | 3 | 0.750 | 0.968 | 0.950 |
**: 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 1.000 0.972 0.988 0.383 0.628 0.628
#> CV:NMF 2 1.000 0.973 0.988 0.384 0.628 0.628
#> MAD:NMF 2 0.962 0.959 0.982 0.383 0.628 0.628
#> ATC:NMF 2 0.851 0.900 0.956 0.411 0.609 0.609
#> SD:skmeans 2 1.000 1.000 1.000 0.485 0.516 0.516
#> CV:skmeans 2 0.730 0.918 0.955 0.475 0.516 0.516
#> MAD:skmeans 2 1.000 0.969 0.982 0.486 0.516 0.516
#> ATC:skmeans 2 0.739 0.857 0.930 0.458 0.508 0.508
#> SD:mclust 2 0.849 0.901 0.942 0.479 0.525 0.525
#> CV:mclust 2 0.476 0.849 0.912 0.467 0.525 0.525
#> MAD:mclust 2 0.851 0.925 0.958 0.412 0.560 0.560
#> ATC:mclust 2 0.704 0.887 0.943 0.421 0.591 0.591
#> SD:kmeans 2 0.437 0.730 0.832 0.347 0.535 0.535
#> CV:kmeans 2 0.443 0.830 0.861 0.342 0.669 0.669
#> MAD:kmeans 2 0.399 0.798 0.852 0.366 0.669 0.669
#> ATC:kmeans 2 0.500 0.815 0.847 0.348 0.648 0.648
#> SD:pam 2 1.000 0.966 0.987 0.346 0.669 0.669
#> CV:pam 2 1.000 0.984 0.994 0.339 0.669 0.669
#> MAD:pam 2 1.000 0.955 0.982 0.352 0.669 0.669
#> ATC:pam 2 1.000 1.000 1.000 0.331 0.669 0.669
#> SD:hclust 2 1.000 0.980 0.982 0.337 0.669 0.669
#> CV:hclust 2 1.000 0.988 0.986 0.334 0.669 0.669
#> MAD:hclust 2 1.000 1.000 1.000 0.331 0.669 0.669
#> ATC:hclust 2 0.961 0.922 0.972 0.374 0.648 0.648
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 1.000 0.978 0.990 0.536 0.740 0.599
#> CV:NMF 3 0.970 0.941 0.974 0.570 0.740 0.599
#> MAD:NMF 3 0.969 0.947 0.981 0.562 0.728 0.580
#> ATC:NMF 3 0.970 0.935 0.975 0.468 0.720 0.568
#> SD:skmeans 3 0.940 0.902 0.966 0.278 0.787 0.613
#> CV:skmeans 3 0.944 0.935 0.974 0.340 0.764 0.576
#> MAD:skmeans 3 0.941 0.919 0.968 0.303 0.764 0.576
#> ATC:skmeans 3 1.000 0.988 0.995 0.363 0.810 0.645
#> SD:mclust 3 0.757 0.881 0.933 0.326 0.735 0.539
#> CV:mclust 3 0.744 0.906 0.946 0.358 0.717 0.513
#> MAD:mclust 3 0.995 0.953 0.975 0.523 0.723 0.541
#> ATC:mclust 3 0.764 0.884 0.942 0.462 0.797 0.657
#> SD:kmeans 3 0.750 0.968 0.950 0.578 0.881 0.783
#> CV:kmeans 3 0.955 0.963 0.956 0.624 0.769 0.656
#> MAD:kmeans 3 1.000 0.983 0.980 0.529 0.769 0.656
#> ATC:kmeans 3 1.000 0.976 0.967 0.523 0.762 0.645
#> SD:pam 3 0.887 0.939 0.975 0.581 0.786 0.681
#> CV:pam 3 0.968 0.971 0.987 0.639 0.786 0.681
#> MAD:pam 3 1.000 0.968 0.986 0.574 0.786 0.681
#> ATC:pam 3 1.000 0.973 0.991 0.619 0.786 0.681
#> SD:hclust 3 0.835 0.929 0.966 0.745 0.727 0.593
#> CV:hclust 3 0.863 0.912 0.951 0.666 0.786 0.681
#> MAD:hclust 3 0.841 0.894 0.950 0.744 0.716 0.576
#> ATC:hclust 3 0.937 0.912 0.968 0.496 0.810 0.707
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.779 0.796 0.885 0.1837 0.859 0.660
#> CV:NMF 4 0.700 0.761 0.871 0.2014 0.839 0.614
#> MAD:NMF 4 0.753 0.790 0.892 0.1742 0.883 0.717
#> ATC:NMF 4 0.737 0.773 0.884 0.1750 0.848 0.638
#> SD:skmeans 4 0.800 0.693 0.871 0.2143 0.827 0.564
#> CV:skmeans 4 0.707 0.682 0.861 0.1839 0.822 0.544
#> MAD:skmeans 4 0.858 0.841 0.931 0.1905 0.834 0.569
#> ATC:skmeans 4 0.747 0.775 0.849 0.1681 0.827 0.561
#> SD:mclust 4 0.847 0.923 0.947 0.0438 0.888 0.731
#> CV:mclust 4 0.949 0.927 0.962 0.0228 0.863 0.678
#> MAD:mclust 4 0.649 0.702 0.785 0.1369 0.762 0.452
#> ATC:mclust 4 0.687 0.580 0.793 0.1721 0.828 0.591
#> SD:kmeans 4 0.715 0.766 0.868 0.2145 0.919 0.815
#> CV:kmeans 4 0.715 0.736 0.861 0.2103 0.919 0.815
#> MAD:kmeans 4 0.682 0.712 0.795 0.2510 0.811 0.570
#> ATC:kmeans 4 0.707 0.717 0.861 0.2532 0.935 0.857
#> SD:pam 4 0.727 0.720 0.877 0.3041 0.809 0.581
#> CV:pam 4 0.938 0.925 0.967 0.3303 0.801 0.563
#> MAD:pam 4 0.768 0.794 0.834 0.2047 0.816 0.595
#> ATC:pam 4 0.711 0.822 0.801 0.1611 1.000 1.000
#> SD:hclust 4 0.838 0.927 0.959 0.0755 0.975 0.937
#> CV:hclust 4 0.767 0.871 0.892 0.1742 0.855 0.681
#> MAD:hclust 4 0.782 0.820 0.912 0.1627 0.969 0.918
#> ATC:hclust 4 1.000 0.973 0.987 0.0986 0.935 0.858
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.959 0.920 0.960 0.0866 0.943 0.804
#> CV:NMF 5 0.777 0.744 0.880 0.0795 0.899 0.650
#> MAD:NMF 5 0.811 0.807 0.896 0.1168 0.878 0.625
#> ATC:NMF 5 0.700 0.723 0.839 0.0851 0.874 0.604
#> SD:skmeans 5 0.827 0.808 0.884 0.0718 0.898 0.621
#> CV:skmeans 5 0.796 0.796 0.886 0.0707 0.936 0.744
#> MAD:skmeans 5 0.743 0.670 0.820 0.0659 0.915 0.673
#> ATC:skmeans 5 0.734 0.577 0.759 0.0647 0.906 0.657
#> SD:mclust 5 0.775 0.751 0.877 0.1397 0.857 0.602
#> CV:mclust 5 0.803 0.849 0.918 0.1825 0.839 0.565
#> MAD:mclust 5 0.731 0.543 0.737 0.0693 0.783 0.439
#> ATC:mclust 5 0.716 0.738 0.827 0.0279 0.955 0.847
#> SD:kmeans 5 0.676 0.569 0.716 0.1225 0.971 0.921
#> CV:kmeans 5 0.707 0.794 0.832 0.1168 0.843 0.571
#> MAD:kmeans 5 0.656 0.657 0.766 0.0832 0.919 0.722
#> ATC:kmeans 5 0.657 0.803 0.861 0.0951 0.867 0.664
#> SD:pam 5 0.700 0.582 0.790 0.0607 0.893 0.646
#> CV:pam 5 0.868 0.877 0.930 0.0550 0.947 0.796
#> MAD:pam 5 0.755 0.742 0.877 0.1404 0.913 0.703
#> ATC:pam 5 0.671 0.752 0.853 0.1351 0.846 0.666
#> SD:hclust 5 0.771 0.916 0.935 0.1064 0.927 0.805
#> CV:hclust 5 0.799 0.873 0.912 0.0671 0.980 0.938
#> MAD:hclust 5 0.835 0.847 0.915 0.0695 0.930 0.803
#> ATC:hclust 5 0.922 0.964 0.971 0.1482 0.895 0.733
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.805 0.787 0.868 0.0844 0.916 0.661
#> CV:NMF 6 0.745 0.570 0.753 0.0527 0.905 0.595
#> MAD:NMF 6 0.767 0.671 0.822 0.0526 0.886 0.537
#> ATC:NMF 6 0.714 0.670 0.812 0.0452 0.958 0.823
#> SD:skmeans 6 0.816 0.731 0.841 0.0381 0.950 0.751
#> CV:skmeans 6 0.805 0.734 0.838 0.0380 0.960 0.798
#> MAD:skmeans 6 0.770 0.609 0.784 0.0398 0.930 0.671
#> ATC:skmeans 6 0.787 0.832 0.889 0.0516 0.916 0.651
#> SD:mclust 6 0.795 0.802 0.886 0.0540 0.962 0.824
#> CV:mclust 6 0.853 0.861 0.917 0.0533 0.961 0.823
#> MAD:mclust 6 0.842 0.857 0.922 0.0478 0.832 0.493
#> ATC:mclust 6 0.729 0.780 0.822 0.0276 0.878 0.592
#> SD:kmeans 6 0.677 0.707 0.761 0.0630 0.828 0.515
#> CV:kmeans 6 0.695 0.668 0.792 0.0593 0.974 0.886
#> MAD:kmeans 6 0.726 0.679 0.788 0.0651 0.910 0.669
#> ATC:kmeans 6 0.734 0.717 0.803 0.0640 0.998 0.992
#> SD:pam 6 0.810 0.773 0.901 0.0422 0.881 0.573
#> CV:pam 6 0.928 0.905 0.946 0.0331 0.986 0.934
#> MAD:pam 6 0.752 0.573 0.757 0.0580 0.874 0.525
#> ATC:pam 6 0.770 0.777 0.895 0.0874 0.954 0.853
#> SD:hclust 6 0.877 0.939 0.963 0.0473 0.986 0.953
#> CV:hclust 6 0.789 0.704 0.750 0.0866 0.957 0.867
#> MAD:hclust 6 0.891 0.912 0.959 0.0281 0.986 0.951
#> ATC:hclust 6 0.951 0.954 0.949 0.0208 0.989 0.961
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 tissue(p) k
#> SD:NMF 54 0.398 2
#> CV:NMF 54 0.398 2
#> MAD:NMF 53 0.397 2
#> ATC:NMF 52 0.396 2
#> SD:skmeans 54 0.398 2
#> CV:skmeans 54 0.398 2
#> MAD:skmeans 54 0.398 2
#> ATC:skmeans 53 0.397 2
#> SD:mclust 52 0.396 2
#> CV:mclust 54 0.398 2
#> MAD:mclust 54 0.398 2
#> ATC:mclust 54 0.398 2
#> SD:kmeans 44 0.387 2
#> CV:kmeans 54 0.398 2
#> MAD:kmeans 46 0.389 2
#> ATC:kmeans 46 0.389 2
#> SD:pam 53 0.397 2
#> CV:pam 53 0.397 2
#> MAD:pam 53 0.397 2
#> ATC:pam 54 0.398 2
#> SD:hclust 54 0.398 2
#> CV:hclust 54 0.398 2
#> MAD:hclust 54 0.398 2
#> ATC:hclust 51 0.395 2
test_to_known_factors(res_list, k = 3)
#> n tissue(p) k
#> SD:NMF 54 0.374 3
#> CV:NMF 53 0.373 3
#> MAD:NMF 53 0.373 3
#> ATC:NMF 52 0.372 3
#> SD:skmeans 51 0.371 3
#> CV:skmeans 53 0.373 3
#> MAD:skmeans 52 0.372 3
#> ATC:skmeans 54 0.374 3
#> SD:mclust 53 0.443 3
#> CV:mclust 53 0.443 3
#> MAD:mclust 53 0.373 3
#> ATC:mclust 54 0.374 3
#> SD:kmeans 54 0.374 3
#> CV:kmeans 54 0.374 3
#> MAD:kmeans 54 0.374 3
#> ATC:kmeans 54 0.374 3
#> SD:pam 53 0.373 3
#> CV:pam 54 0.374 3
#> MAD:pam 53 0.373 3
#> ATC:pam 53 0.373 3
#> SD:hclust 54 0.374 3
#> CV:hclust 53 0.373 3
#> MAD:hclust 49 0.368 3
#> ATC:hclust 51 0.371 3
test_to_known_factors(res_list, k = 4)
#> n tissue(p) k
#> SD:NMF 48 0.510 4
#> CV:NMF 45 0.504 4
#> MAD:NMF 49 0.348 4
#> ATC:NMF 47 0.344 4
#> SD:skmeans 41 0.407 4
#> CV:skmeans 40 0.406 4
#> MAD:skmeans 50 0.432 4
#> ATC:skmeans 50 0.416 4
#> SD:mclust 54 0.523 4
#> CV:mclust 53 0.520 4
#> MAD:mclust 46 0.427 4
#> ATC:mclust 36 0.411 4
#> SD:kmeans 51 0.516 4
#> CV:kmeans 48 0.508 4
#> MAD:kmeans 46 0.428 4
#> ATC:kmeans 48 0.346 4
#> SD:pam 47 0.422 4
#> CV:pam 52 0.425 4
#> MAD:pam 50 0.426 4
#> ATC:pam 53 0.373 4
#> SD:hclust 54 0.355 4
#> CV:hclust 53 0.447 4
#> MAD:hclust 49 0.348 4
#> ATC:hclust 54 0.355 4
test_to_known_factors(res_list, k = 5)
#> n tissue(p) k
#> SD:NMF 53 0.440 5
#> CV:NMF 45 0.441 5
#> MAD:NMF 49 0.413 5
#> ATC:NMF 46 0.467 5
#> SD:skmeans 50 0.439 5
#> CV:skmeans 50 0.443 5
#> MAD:skmeans 36 0.411 5
#> ATC:skmeans 42 0.399 5
#> SD:mclust 47 0.404 5
#> CV:mclust 52 0.409 5
#> MAD:mclust 28 0.388 5
#> ATC:mclust 48 0.405 5
#> SD:kmeans 37 0.402 5
#> CV:kmeans 51 0.497 5
#> MAD:kmeans 42 0.408 5
#> ATC:kmeans 52 0.334 5
#> SD:pam 37 0.393 5
#> CV:pam 53 0.481 5
#> MAD:pam 46 0.393 5
#> ATC:pam 50 0.331 5
#> SD:hclust 54 0.483 5
#> CV:hclust 53 0.480 5
#> MAD:hclust 53 0.481 5
#> ATC:hclust 54 0.337 5
test_to_known_factors(res_list, k = 6)
#> n tissue(p) k
#> SD:NMF 52 0.430 6
#> CV:NMF 34 0.430 6
#> MAD:NMF 40 0.410 6
#> ATC:NMF 42 0.457 6
#> SD:skmeans 42 0.408 6
#> CV:skmeans 45 0.419 6
#> MAD:skmeans 38 0.442 6
#> ATC:skmeans 52 0.391 6
#> SD:mclust 50 0.400 6
#> CV:mclust 52 0.402 6
#> MAD:mclust 50 0.400 6
#> ATC:mclust 48 0.438 6
#> SD:kmeans 46 0.450 6
#> CV:kmeans 46 0.479 6
#> MAD:kmeans 48 0.485 6
#> ATC:kmeans 50 0.407 6
#> SD:pam 48 0.458 6
#> CV:pam 53 0.448 6
#> MAD:pam 32 0.395 6
#> ATC:pam 49 0.314 6
#> SD:hclust 54 0.450 6
#> CV:hclust 44 0.410 6
#> MAD:hclust 53 0.448 6
#> ATC:hclust 54 0.322 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.980 0.982 0.3369 0.669 0.669
#> 3 3 0.835 0.929 0.966 0.7449 0.727 0.593
#> 4 4 0.838 0.927 0.959 0.0755 0.975 0.937
#> 5 5 0.771 0.916 0.935 0.1064 0.927 0.805
#> 6 6 0.877 0.939 0.963 0.0473 0.986 0.953
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
#> GSM28762 2 0.000 0.985 0.000 1.000
#> GSM28763 2 0.000 0.985 0.000 1.000
#> GSM28764 2 0.000 0.985 0.000 1.000
#> GSM11274 2 0.204 0.972 0.032 0.968
#> GSM28772 1 0.204 1.000 0.968 0.032
#> GSM11269 1 0.204 1.000 0.968 0.032
#> GSM28775 1 0.204 1.000 0.968 0.032
#> GSM11293 1 0.204 1.000 0.968 0.032
#> GSM28755 1 0.204 1.000 0.968 0.032
#> GSM11279 1 0.204 1.000 0.968 0.032
#> GSM28758 1 0.204 1.000 0.968 0.032
#> GSM11281 1 0.204 1.000 0.968 0.032
#> GSM11287 1 0.204 1.000 0.968 0.032
#> GSM28759 1 0.204 1.000 0.968 0.032
#> GSM11292 2 0.000 0.985 0.000 1.000
#> GSM28766 2 0.000 0.985 0.000 1.000
#> GSM11268 2 0.204 0.972 0.032 0.968
#> GSM28767 2 0.000 0.985 0.000 1.000
#> GSM11286 2 0.000 0.985 0.000 1.000
#> GSM28751 2 0.000 0.985 0.000 1.000
#> GSM28770 2 0.000 0.985 0.000 1.000
#> GSM11283 2 0.000 0.985 0.000 1.000
#> GSM11289 2 0.000 0.985 0.000 1.000
#> GSM11280 2 0.000 0.985 0.000 1.000
#> GSM28749 2 0.000 0.985 0.000 1.000
#> GSM28750 2 0.204 0.972 0.032 0.968
#> GSM11290 2 0.204 0.972 0.032 0.968
#> GSM11294 2 0.204 0.972 0.032 0.968
#> GSM28771 2 0.000 0.985 0.000 1.000
#> GSM28760 2 0.000 0.985 0.000 1.000
#> GSM28774 2 0.000 0.985 0.000 1.000
#> GSM11284 2 0.000 0.985 0.000 1.000
#> GSM28761 2 0.204 0.972 0.032 0.968
#> GSM11278 2 0.204 0.972 0.032 0.968
#> GSM11291 2 0.204 0.972 0.032 0.968
#> GSM11277 2 0.204 0.972 0.032 0.968
#> GSM11272 2 0.204 0.972 0.032 0.968
#> GSM11285 2 0.000 0.985 0.000 1.000
#> GSM28753 2 0.000 0.985 0.000 1.000
#> GSM28773 2 0.000 0.985 0.000 1.000
#> GSM28765 2 0.000 0.985 0.000 1.000
#> GSM28768 2 0.730 0.733 0.204 0.796
#> GSM28754 2 0.000 0.985 0.000 1.000
#> GSM28769 2 0.000 0.985 0.000 1.000
#> GSM11275 1 0.204 1.000 0.968 0.032
#> GSM11270 2 0.204 0.972 0.032 0.968
#> GSM11271 2 0.000 0.985 0.000 1.000
#> GSM11288 2 0.000 0.985 0.000 1.000
#> GSM11273 2 0.204 0.972 0.032 0.968
#> GSM28757 2 0.000 0.985 0.000 1.000
#> GSM11282 2 0.204 0.972 0.032 0.968
#> GSM28756 2 0.000 0.985 0.000 1.000
#> GSM11276 2 0.000 0.985 0.000 1.000
#> GSM28752 2 0.000 0.985 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.000 0.983 0.000 1.000 0.000
#> GSM28763 2 0.000 0.983 0.000 1.000 0.000
#> GSM28764 2 0.000 0.983 0.000 1.000 0.000
#> GSM11274 3 0.455 0.767 0.000 0.200 0.800
#> GSM28772 1 0.000 1.000 1.000 0.000 0.000
#> GSM11269 1 0.000 1.000 1.000 0.000 0.000
#> GSM28775 1 0.000 1.000 1.000 0.000 0.000
#> GSM11293 1 0.000 1.000 1.000 0.000 0.000
#> GSM28755 1 0.000 1.000 1.000 0.000 0.000
#> GSM11279 1 0.000 1.000 1.000 0.000 0.000
#> GSM28758 1 0.000 1.000 1.000 0.000 0.000
#> GSM11281 1 0.000 1.000 1.000 0.000 0.000
#> GSM11287 1 0.000 1.000 1.000 0.000 0.000
#> GSM28759 1 0.000 1.000 1.000 0.000 0.000
#> GSM11292 2 0.000 0.983 0.000 1.000 0.000
#> GSM28766 2 0.000 0.983 0.000 1.000 0.000
#> GSM11268 3 0.000 0.839 0.000 0.000 1.000
#> GSM28767 2 0.000 0.983 0.000 1.000 0.000
#> GSM11286 2 0.000 0.983 0.000 1.000 0.000
#> GSM28751 2 0.000 0.983 0.000 1.000 0.000
#> GSM28770 2 0.000 0.983 0.000 1.000 0.000
#> GSM11283 2 0.000 0.983 0.000 1.000 0.000
#> GSM11289 2 0.000 0.983 0.000 1.000 0.000
#> GSM11280 2 0.000 0.983 0.000 1.000 0.000
#> GSM28749 2 0.000 0.983 0.000 1.000 0.000
#> GSM28750 3 0.000 0.839 0.000 0.000 1.000
#> GSM11290 3 0.000 0.839 0.000 0.000 1.000
#> GSM11294 3 0.000 0.839 0.000 0.000 1.000
#> GSM28771 2 0.000 0.983 0.000 1.000 0.000
#> GSM28760 2 0.000 0.983 0.000 1.000 0.000
#> GSM28774 2 0.000 0.983 0.000 1.000 0.000
#> GSM11284 2 0.000 0.983 0.000 1.000 0.000
#> GSM28761 3 0.000 0.839 0.000 0.000 1.000
#> GSM11278 3 0.556 0.701 0.000 0.300 0.700
#> GSM11291 3 0.000 0.839 0.000 0.000 1.000
#> GSM11277 3 0.000 0.839 0.000 0.000 1.000
#> GSM11272 3 0.000 0.839 0.000 0.000 1.000
#> GSM11285 2 0.000 0.983 0.000 1.000 0.000
#> GSM28753 2 0.000 0.983 0.000 1.000 0.000
#> GSM28773 2 0.000 0.983 0.000 1.000 0.000
#> GSM28765 2 0.000 0.983 0.000 1.000 0.000
#> GSM28768 2 0.460 0.721 0.204 0.796 0.000
#> GSM28754 2 0.000 0.983 0.000 1.000 0.000
#> GSM28769 2 0.000 0.983 0.000 1.000 0.000
#> GSM11275 1 0.000 1.000 1.000 0.000 0.000
#> GSM11270 3 0.556 0.701 0.000 0.300 0.700
#> GSM11271 2 0.000 0.983 0.000 1.000 0.000
#> GSM11288 2 0.475 0.666 0.000 0.784 0.216
#> GSM11273 3 0.556 0.701 0.000 0.300 0.700
#> GSM28757 2 0.000 0.983 0.000 1.000 0.000
#> GSM11282 3 0.556 0.701 0.000 0.300 0.700
#> GSM28756 2 0.000 0.983 0.000 1.000 0.000
#> GSM11276 2 0.000 0.983 0.000 1.000 0.000
#> GSM28752 2 0.000 0.983 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM28763 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM28764 2 0.0336 0.972 0.000 0.992 0.008 0.000
#> GSM11274 3 0.0000 0.728 0.000 0.000 1.000 0.000
#> GSM28772 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11292 2 0.0921 0.963 0.000 0.972 0.028 0.000
#> GSM28766 2 0.0921 0.963 0.000 0.972 0.028 0.000
#> GSM11268 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM28767 2 0.0921 0.963 0.000 0.972 0.028 0.000
#> GSM11286 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM28751 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM28770 2 0.0921 0.963 0.000 0.972 0.028 0.000
#> GSM11283 2 0.0707 0.965 0.000 0.980 0.020 0.000
#> GSM11289 2 0.0921 0.963 0.000 0.972 0.028 0.000
#> GSM11280 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM28749 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM28750 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM11290 3 0.4277 0.676 0.000 0.000 0.720 0.280
#> GSM11294 3 0.4277 0.676 0.000 0.000 0.720 0.280
#> GSM28771 2 0.0707 0.965 0.000 0.980 0.020 0.000
#> GSM28760 2 0.0707 0.965 0.000 0.980 0.020 0.000
#> GSM28774 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM11284 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM28761 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM11278 3 0.2345 0.755 0.000 0.100 0.900 0.000
#> GSM11291 3 0.4277 0.676 0.000 0.000 0.720 0.280
#> GSM11277 3 0.4277 0.676 0.000 0.000 0.720 0.280
#> GSM11272 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM11285 2 0.0707 0.965 0.000 0.980 0.020 0.000
#> GSM28753 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM28773 2 0.0336 0.972 0.000 0.992 0.008 0.000
#> GSM28765 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM28768 2 0.3649 0.740 0.204 0.796 0.000 0.000
#> GSM28754 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM28769 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM11275 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11270 3 0.2345 0.755 0.000 0.100 0.900 0.000
#> GSM11271 2 0.0921 0.963 0.000 0.972 0.028 0.000
#> GSM11288 2 0.4635 0.709 0.000 0.756 0.028 0.216
#> GSM11273 3 0.2345 0.755 0.000 0.100 0.900 0.000
#> GSM28757 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM11282 3 0.2345 0.755 0.000 0.100 0.900 0.000
#> GSM28756 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM11276 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM28752 2 0.0000 0.975 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
#> GSM28762 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM28763 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM28764 2 0.0290 0.962 0.000 0.992 0.000 0.000 0.008
#> GSM11274 5 0.0404 0.701 0.000 0.000 0.000 0.012 0.988
#> GSM28772 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM11292 2 0.0794 0.953 0.000 0.972 0.000 0.000 0.028
#> GSM28766 2 0.0794 0.953 0.000 0.972 0.000 0.000 0.028
#> GSM11268 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM28767 2 0.0794 0.953 0.000 0.972 0.000 0.000 0.028
#> GSM11286 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM28751 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM28770 2 0.0794 0.953 0.000 0.972 0.000 0.000 0.028
#> GSM11283 4 0.2020 1.000 0.000 0.100 0.000 0.900 0.000
#> GSM11289 2 0.0794 0.953 0.000 0.972 0.000 0.000 0.028
#> GSM11280 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM28749 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM28750 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM11290 5 0.5312 0.633 0.000 0.000 0.248 0.100 0.652
#> GSM11294 5 0.5312 0.633 0.000 0.000 0.248 0.100 0.652
#> GSM28771 4 0.2020 1.000 0.000 0.100 0.000 0.900 0.000
#> GSM28760 4 0.2020 1.000 0.000 0.100 0.000 0.900 0.000
#> GSM28774 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM11284 2 0.2813 0.785 0.000 0.832 0.000 0.168 0.000
#> GSM28761 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM11278 5 0.2416 0.728 0.000 0.100 0.000 0.012 0.888
#> GSM11291 5 0.5312 0.633 0.000 0.000 0.248 0.100 0.652
#> GSM11277 5 0.5312 0.633 0.000 0.000 0.248 0.100 0.652
#> GSM11272 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM11285 4 0.2020 1.000 0.000 0.100 0.000 0.900 0.000
#> GSM28753 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM28773 2 0.0290 0.962 0.000 0.992 0.000 0.000 0.008
#> GSM28765 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM28768 2 0.3143 0.712 0.204 0.796 0.000 0.000 0.000
#> GSM28754 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM28769 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM11275 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM11270 5 0.2416 0.728 0.000 0.100 0.000 0.012 0.888
#> GSM11271 2 0.0794 0.953 0.000 0.972 0.000 0.000 0.028
#> GSM11288 2 0.3993 0.689 0.000 0.756 0.216 0.000 0.028
#> GSM11273 5 0.2416 0.728 0.000 0.100 0.000 0.012 0.888
#> GSM28757 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM11282 5 0.2416 0.728 0.000 0.100 0.000 0.012 0.888
#> GSM28756 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM11276 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM28752 2 0.0000 0.964 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
#> GSM28762 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28763 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28764 2 0.1910 0.902 0.000 0.892 0.000 0.000 0.108 0.000
#> GSM11274 5 0.1814 0.840 0.000 0.000 0.100 0.000 0.900 0.000
#> GSM28772 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11292 2 0.2135 0.894 0.000 0.872 0.000 0.000 0.128 0.000
#> GSM28766 2 0.2135 0.894 0.000 0.872 0.000 0.000 0.128 0.000
#> GSM11268 6 0.0000 0.965 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM28767 2 0.2135 0.894 0.000 0.872 0.000 0.000 0.128 0.000
#> GSM11286 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28751 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28770 2 0.2135 0.894 0.000 0.872 0.000 0.000 0.128 0.000
#> GSM11283 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11289 2 0.2135 0.894 0.000 0.872 0.000 0.000 0.128 0.000
#> GSM11280 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28749 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28750 6 0.0000 0.965 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM11290 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11294 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM28771 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM28760 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM28774 2 0.1814 0.904 0.000 0.900 0.000 0.000 0.100 0.000
#> GSM11284 2 0.4232 0.760 0.000 0.732 0.000 0.168 0.100 0.000
#> GSM28761 6 0.0000 0.965 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM11278 5 0.0000 0.963 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11291 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11277 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11272 6 0.1863 0.884 0.000 0.000 0.104 0.000 0.000 0.896
#> GSM11285 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM28753 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28773 2 0.1714 0.908 0.000 0.908 0.000 0.000 0.092 0.000
#> GSM28765 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28768 2 0.2823 0.726 0.204 0.796 0.000 0.000 0.000 0.000
#> GSM28754 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28769 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11275 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11270 5 0.0000 0.963 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11271 2 0.2135 0.894 0.000 0.872 0.000 0.000 0.128 0.000
#> GSM11288 2 0.3586 0.690 0.000 0.756 0.000 0.000 0.028 0.216
#> GSM11273 5 0.0000 0.963 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28757 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11282 5 0.0000 0.963 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28756 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11276 2 0.0713 0.923 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM28752 2 0.0000 0.927 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 tissue(p) k
#> SD:hclust 54 0.398 2
#> SD:hclust 54 0.374 3
#> SD:hclust 54 0.355 4
#> SD:hclust 54 0.483 5
#> SD:hclust 54 0.450 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.437 0.730 0.832 0.347 0.535 0.535
#> 3 3 0.750 0.968 0.950 0.578 0.881 0.783
#> 4 4 0.715 0.766 0.868 0.215 0.919 0.815
#> 5 5 0.676 0.569 0.716 0.123 0.971 0.921
#> 6 6 0.677 0.707 0.761 0.063 0.828 0.515
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
#> GSM28762 2 0.0000 0.944 0.000 1.000
#> GSM28763 2 0.0000 0.944 0.000 1.000
#> GSM28764 2 0.0000 0.944 0.000 1.000
#> GSM11274 2 0.9552 0.119 0.376 0.624
#> GSM28772 1 0.9552 0.589 0.624 0.376
#> GSM11269 1 0.9552 0.589 0.624 0.376
#> GSM28775 1 0.9552 0.589 0.624 0.376
#> GSM11293 1 0.9552 0.589 0.624 0.376
#> GSM28755 1 0.9552 0.589 0.624 0.376
#> GSM11279 1 0.9552 0.589 0.624 0.376
#> GSM28758 1 0.9552 0.589 0.624 0.376
#> GSM11281 1 0.9552 0.589 0.624 0.376
#> GSM11287 1 0.9552 0.589 0.624 0.376
#> GSM28759 1 0.9552 0.589 0.624 0.376
#> GSM11292 2 0.0000 0.944 0.000 1.000
#> GSM28766 2 0.0672 0.939 0.008 0.992
#> GSM11268 1 0.9993 0.242 0.516 0.484
#> GSM28767 2 0.0000 0.944 0.000 1.000
#> GSM11286 2 0.0000 0.944 0.000 1.000
#> GSM28751 2 0.0000 0.944 0.000 1.000
#> GSM28770 2 0.0000 0.944 0.000 1.000
#> GSM11283 2 0.0376 0.940 0.004 0.996
#> GSM11289 2 0.0000 0.944 0.000 1.000
#> GSM11280 2 0.0000 0.944 0.000 1.000
#> GSM28749 2 0.0672 0.939 0.008 0.992
#> GSM28750 1 0.9993 0.242 0.516 0.484
#> GSM11290 1 0.9988 0.250 0.520 0.480
#> GSM11294 1 0.9988 0.250 0.520 0.480
#> GSM28771 2 0.0938 0.937 0.012 0.988
#> GSM28760 2 0.1184 0.933 0.016 0.984
#> GSM28774 2 0.0000 0.944 0.000 1.000
#> GSM11284 2 0.0938 0.937 0.012 0.988
#> GSM28761 1 0.9993 0.242 0.516 0.484
#> GSM11278 2 0.1184 0.931 0.016 0.984
#> GSM11291 1 0.9988 0.250 0.520 0.480
#> GSM11277 1 0.9988 0.250 0.520 0.480
#> GSM11272 1 0.9988 0.250 0.520 0.480
#> GSM11285 2 0.0938 0.937 0.012 0.988
#> GSM28753 2 0.0000 0.944 0.000 1.000
#> GSM28773 2 0.0672 0.939 0.008 0.992
#> GSM28765 2 0.0000 0.944 0.000 1.000
#> GSM28768 2 0.5737 0.672 0.136 0.864
#> GSM28754 2 0.0000 0.944 0.000 1.000
#> GSM28769 2 0.0000 0.944 0.000 1.000
#> GSM11275 1 0.9552 0.589 0.624 0.376
#> GSM11270 2 0.1184 0.931 0.016 0.984
#> GSM11271 2 0.0000 0.944 0.000 1.000
#> GSM11288 2 0.2236 0.900 0.036 0.964
#> GSM11273 2 0.9522 0.124 0.372 0.628
#> GSM28757 2 0.0000 0.944 0.000 1.000
#> GSM11282 2 0.1184 0.931 0.016 0.984
#> GSM28756 2 0.0000 0.944 0.000 1.000
#> GSM11276 2 0.0000 0.944 0.000 1.000
#> GSM28752 2 0.0000 0.944 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28763 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28764 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11274 3 0.1163 0.968 0.000 0.028 0.972
#> GSM28772 1 0.3038 1.000 0.896 0.104 0.000
#> GSM11269 1 0.3038 1.000 0.896 0.104 0.000
#> GSM28775 1 0.3038 1.000 0.896 0.104 0.000
#> GSM11293 1 0.3038 1.000 0.896 0.104 0.000
#> GSM28755 1 0.3038 1.000 0.896 0.104 0.000
#> GSM11279 1 0.3038 1.000 0.896 0.104 0.000
#> GSM28758 1 0.3038 1.000 0.896 0.104 0.000
#> GSM11281 1 0.3038 1.000 0.896 0.104 0.000
#> GSM11287 1 0.3038 1.000 0.896 0.104 0.000
#> GSM28759 1 0.3038 1.000 0.896 0.104 0.000
#> GSM11292 2 0.0747 0.970 0.000 0.984 0.016
#> GSM28766 2 0.0747 0.970 0.000 0.984 0.016
#> GSM11268 3 0.3310 0.978 0.064 0.028 0.908
#> GSM28767 2 0.0747 0.970 0.000 0.984 0.016
#> GSM11286 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28751 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28770 2 0.0747 0.970 0.000 0.984 0.016
#> GSM11283 2 0.3888 0.902 0.064 0.888 0.048
#> GSM11289 2 0.0892 0.969 0.000 0.980 0.020
#> GSM11280 2 0.1337 0.958 0.012 0.972 0.016
#> GSM28749 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28750 3 0.3310 0.978 0.064 0.028 0.908
#> GSM11290 3 0.2187 0.981 0.024 0.028 0.948
#> GSM11294 3 0.2187 0.981 0.024 0.028 0.948
#> GSM28771 2 0.3888 0.902 0.064 0.888 0.048
#> GSM28760 2 0.3888 0.902 0.064 0.888 0.048
#> GSM28774 2 0.0592 0.970 0.000 0.988 0.012
#> GSM11284 2 0.2903 0.930 0.048 0.924 0.028
#> GSM28761 3 0.3310 0.978 0.064 0.028 0.908
#> GSM11278 2 0.1031 0.966 0.000 0.976 0.024
#> GSM11291 3 0.2187 0.981 0.024 0.028 0.948
#> GSM11277 3 0.2187 0.981 0.024 0.028 0.948
#> GSM11272 3 0.3310 0.978 0.064 0.028 0.908
#> GSM11285 2 0.3993 0.901 0.064 0.884 0.052
#> GSM28753 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28773 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28765 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28768 2 0.4178 0.764 0.172 0.828 0.000
#> GSM28754 2 0.0237 0.971 0.000 0.996 0.004
#> GSM28769 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11275 1 0.3038 1.000 0.896 0.104 0.000
#> GSM11270 2 0.1031 0.966 0.000 0.976 0.024
#> GSM11271 2 0.0747 0.970 0.000 0.984 0.016
#> GSM11288 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11273 3 0.1411 0.965 0.000 0.036 0.964
#> GSM28757 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11282 2 0.1031 0.966 0.000 0.976 0.024
#> GSM28756 2 0.0237 0.971 0.000 0.996 0.004
#> GSM11276 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28752 2 0.0000 0.972 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.2345 0.696 0.000 0.900 0.000 0.100
#> GSM28763 2 0.2345 0.696 0.000 0.900 0.000 0.100
#> GSM28764 2 0.1978 0.729 0.000 0.928 0.004 0.068
#> GSM11274 3 0.1867 0.846 0.000 0.000 0.928 0.072
#> GSM28772 1 0.0469 0.985 0.988 0.012 0.000 0.000
#> GSM11269 1 0.0469 0.985 0.988 0.012 0.000 0.000
#> GSM28775 1 0.0657 0.984 0.984 0.012 0.000 0.004
#> GSM11293 1 0.1174 0.980 0.968 0.012 0.000 0.020
#> GSM28755 1 0.0657 0.984 0.984 0.012 0.000 0.004
#> GSM11279 1 0.0469 0.985 0.988 0.012 0.000 0.000
#> GSM28758 1 0.2402 0.950 0.912 0.012 0.000 0.076
#> GSM11281 1 0.0469 0.985 0.988 0.012 0.000 0.000
#> GSM11287 1 0.0469 0.985 0.988 0.012 0.000 0.000
#> GSM28759 1 0.1174 0.980 0.968 0.012 0.000 0.020
#> GSM11292 2 0.3751 0.635 0.000 0.800 0.004 0.196
#> GSM28766 2 0.3751 0.635 0.000 0.800 0.004 0.196
#> GSM11268 3 0.4327 0.858 0.016 0.000 0.768 0.216
#> GSM28767 2 0.3751 0.635 0.000 0.800 0.004 0.196
#> GSM11286 2 0.1211 0.727 0.000 0.960 0.000 0.040
#> GSM28751 2 0.2345 0.696 0.000 0.900 0.000 0.100
#> GSM28770 2 0.3751 0.635 0.000 0.800 0.004 0.196
#> GSM11283 4 0.4679 0.919 0.000 0.352 0.000 0.648
#> GSM11289 2 0.3751 0.635 0.000 0.800 0.004 0.196
#> GSM11280 2 0.3172 0.617 0.000 0.840 0.000 0.160
#> GSM28749 2 0.3024 0.636 0.000 0.852 0.000 0.148
#> GSM28750 3 0.4327 0.858 0.016 0.000 0.768 0.216
#> GSM11290 3 0.0188 0.881 0.004 0.000 0.996 0.000
#> GSM11294 3 0.0188 0.881 0.004 0.000 0.996 0.000
#> GSM28771 4 0.4564 0.952 0.000 0.328 0.000 0.672
#> GSM28760 4 0.4564 0.952 0.000 0.328 0.000 0.672
#> GSM28774 2 0.2466 0.715 0.000 0.900 0.004 0.096
#> GSM11284 2 0.4819 0.304 0.000 0.652 0.004 0.344
#> GSM28761 3 0.4327 0.858 0.016 0.000 0.768 0.216
#> GSM11278 2 0.4295 0.554 0.000 0.752 0.008 0.240
#> GSM11291 3 0.0188 0.881 0.004 0.000 0.996 0.000
#> GSM11277 3 0.0188 0.881 0.004 0.000 0.996 0.000
#> GSM11272 3 0.4327 0.858 0.016 0.000 0.768 0.216
#> GSM11285 4 0.4605 0.900 0.000 0.336 0.000 0.664
#> GSM28753 2 0.2408 0.693 0.000 0.896 0.000 0.104
#> GSM28773 2 0.2408 0.693 0.000 0.896 0.000 0.104
#> GSM28765 2 0.0188 0.736 0.000 0.996 0.000 0.004
#> GSM28768 2 0.5220 0.462 0.092 0.752 0.000 0.156
#> GSM28754 2 0.1489 0.734 0.000 0.952 0.004 0.044
#> GSM28769 2 0.2345 0.696 0.000 0.900 0.000 0.100
#> GSM11275 1 0.2402 0.950 0.912 0.012 0.000 0.076
#> GSM11270 2 0.4295 0.554 0.000 0.752 0.008 0.240
#> GSM11271 2 0.3626 0.649 0.000 0.812 0.004 0.184
#> GSM11288 2 0.5127 0.229 0.012 0.632 0.000 0.356
#> GSM11273 3 0.4502 0.629 0.000 0.016 0.748 0.236
#> GSM28757 2 0.0707 0.733 0.000 0.980 0.000 0.020
#> GSM11282 2 0.4360 0.540 0.000 0.744 0.008 0.248
#> GSM28756 2 0.2125 0.726 0.000 0.920 0.004 0.076
#> GSM11276 2 0.0336 0.737 0.000 0.992 0.000 0.008
#> GSM28752 2 0.0188 0.737 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
#> GSM28762 2 0.4288 0.5327 0.000 0.612 0.000 0.384 0.004
#> GSM28763 2 0.4288 0.5327 0.000 0.612 0.000 0.384 0.004
#> GSM28764 2 0.1281 0.5270 0.000 0.956 0.000 0.032 0.012
#> GSM11274 3 0.5114 0.5811 0.000 0.000 0.488 0.036 0.476
#> GSM28772 1 0.0000 0.9674 1.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.9674 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0566 0.9626 0.984 0.000 0.000 0.004 0.012
#> GSM11293 1 0.1430 0.9524 0.944 0.000 0.000 0.004 0.052
#> GSM28755 1 0.0566 0.9626 0.984 0.000 0.000 0.004 0.012
#> GSM11279 1 0.0000 0.9674 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.2795 0.9128 0.872 0.000 0.000 0.028 0.100
#> GSM11281 1 0.0000 0.9674 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.9674 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.1430 0.9524 0.944 0.000 0.000 0.004 0.052
#> GSM11292 2 0.4199 0.3509 0.000 0.772 0.000 0.160 0.068
#> GSM28766 2 0.4238 0.3466 0.000 0.768 0.000 0.164 0.068
#> GSM11268 3 0.0000 0.7100 0.000 0.000 1.000 0.000 0.000
#> GSM28767 2 0.4199 0.3509 0.000 0.772 0.000 0.160 0.068
#> GSM11286 2 0.4009 0.5609 0.000 0.684 0.000 0.312 0.004
#> GSM28751 2 0.4415 0.5292 0.000 0.604 0.000 0.388 0.008
#> GSM28770 2 0.4199 0.3509 0.000 0.772 0.000 0.160 0.068
#> GSM11283 4 0.5215 0.6702 0.000 0.096 0.000 0.664 0.240
#> GSM11289 2 0.4238 0.3466 0.000 0.768 0.000 0.164 0.068
#> GSM11280 2 0.4473 0.5004 0.000 0.580 0.000 0.412 0.008
#> GSM28749 2 0.4375 0.4998 0.000 0.576 0.000 0.420 0.004
#> GSM28750 3 0.0000 0.7100 0.000 0.000 1.000 0.000 0.000
#> GSM11290 3 0.4171 0.7308 0.000 0.000 0.604 0.000 0.396
#> GSM11294 3 0.4171 0.7308 0.000 0.000 0.604 0.000 0.396
#> GSM28771 4 0.5066 0.6751 0.000 0.084 0.000 0.676 0.240
#> GSM28760 4 0.5035 0.6706 0.000 0.076 0.000 0.672 0.252
#> GSM28774 2 0.2450 0.4604 0.000 0.896 0.000 0.028 0.076
#> GSM11284 2 0.5094 0.1679 0.000 0.600 0.000 0.352 0.048
#> GSM28761 3 0.0000 0.7100 0.000 0.000 1.000 0.000 0.000
#> GSM11278 2 0.5824 -0.0897 0.000 0.608 0.000 0.168 0.224
#> GSM11291 3 0.4171 0.7308 0.000 0.000 0.604 0.000 0.396
#> GSM11277 3 0.4171 0.7308 0.000 0.000 0.604 0.000 0.396
#> GSM11272 3 0.0000 0.7100 0.000 0.000 1.000 0.000 0.000
#> GSM11285 4 0.5595 0.5908 0.000 0.124 0.000 0.624 0.252
#> GSM28753 2 0.4276 0.5323 0.000 0.616 0.000 0.380 0.004
#> GSM28773 2 0.4517 0.5274 0.000 0.600 0.000 0.388 0.012
#> GSM28765 2 0.3766 0.5728 0.000 0.728 0.000 0.268 0.004
#> GSM28768 2 0.5799 0.4646 0.020 0.536 0.000 0.392 0.052
#> GSM28754 2 0.2974 0.4956 0.000 0.868 0.000 0.052 0.080
#> GSM28769 2 0.4415 0.5292 0.000 0.604 0.000 0.388 0.008
#> GSM11275 1 0.2795 0.9128 0.872 0.000 0.000 0.028 0.100
#> GSM11270 2 0.5824 -0.0897 0.000 0.608 0.000 0.168 0.224
#> GSM11271 2 0.3898 0.3805 0.000 0.804 0.000 0.116 0.080
#> GSM11288 4 0.6547 -0.2074 0.000 0.296 0.232 0.472 0.000
#> GSM11273 5 0.7551 0.0000 0.000 0.276 0.096 0.148 0.480
#> GSM28757 2 0.4902 0.5581 0.000 0.648 0.000 0.304 0.048
#> GSM11282 2 0.5880 -0.1018 0.000 0.600 0.000 0.172 0.228
#> GSM28756 2 0.2233 0.4750 0.000 0.904 0.000 0.016 0.080
#> GSM11276 2 0.2629 0.5799 0.000 0.860 0.000 0.136 0.004
#> GSM28752 2 0.3715 0.5744 0.000 0.736 0.000 0.260 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 2 0.0436 0.829 0.000 0.988 0.000 0.004 0.004 0.004
#> GSM28763 2 0.0436 0.829 0.000 0.988 0.000 0.004 0.004 0.004
#> GSM28764 5 0.4913 0.418 0.000 0.428 0.000 0.020 0.524 0.028
#> GSM11274 3 0.4410 0.400 0.000 0.000 0.744 0.016 0.144 0.096
#> GSM28772 1 0.0000 0.925 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.925 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.1605 0.907 0.936 0.000 0.000 0.044 0.004 0.016
#> GSM11293 1 0.2152 0.903 0.912 0.000 0.000 0.036 0.012 0.040
#> GSM28755 1 0.1605 0.907 0.936 0.000 0.000 0.044 0.004 0.016
#> GSM11279 1 0.0146 0.925 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM28758 1 0.4901 0.772 0.708 0.000 0.000 0.100 0.032 0.160
#> GSM11281 1 0.0000 0.925 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.925 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.2152 0.903 0.912 0.000 0.000 0.036 0.012 0.040
#> GSM11292 5 0.4095 0.701 0.000 0.208 0.000 0.064 0.728 0.000
#> GSM28766 5 0.4095 0.701 0.000 0.208 0.000 0.064 0.728 0.000
#> GSM11268 6 0.3868 0.996 0.000 0.000 0.496 0.000 0.000 0.504
#> GSM28767 5 0.4095 0.701 0.000 0.208 0.000 0.064 0.728 0.000
#> GSM11286 2 0.2883 0.803 0.000 0.860 0.000 0.008 0.040 0.092
#> GSM28751 2 0.0748 0.828 0.000 0.976 0.000 0.004 0.004 0.016
#> GSM28770 5 0.4066 0.701 0.000 0.204 0.000 0.064 0.732 0.000
#> GSM11283 4 0.3424 0.934 0.000 0.092 0.000 0.812 0.096 0.000
#> GSM11289 5 0.4066 0.701 0.000 0.204 0.000 0.064 0.732 0.000
#> GSM11280 2 0.3265 0.792 0.000 0.836 0.000 0.068 0.008 0.088
#> GSM28749 2 0.3306 0.793 0.000 0.840 0.000 0.052 0.020 0.088
#> GSM28750 6 0.3999 0.993 0.000 0.000 0.496 0.000 0.004 0.500
#> GSM11290 3 0.0000 0.688 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11294 3 0.0000 0.688 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM28771 4 0.3413 0.944 0.000 0.080 0.000 0.812 0.108 0.000
#> GSM28760 4 0.4203 0.941 0.000 0.072 0.000 0.768 0.136 0.024
#> GSM28774 5 0.5785 0.514 0.000 0.332 0.000 0.024 0.532 0.112
#> GSM11284 5 0.7044 0.429 0.000 0.228 0.000 0.224 0.448 0.100
#> GSM28761 6 0.3868 0.996 0.000 0.000 0.496 0.000 0.000 0.504
#> GSM11278 5 0.4498 0.561 0.000 0.072 0.000 0.032 0.744 0.152
#> GSM11291 3 0.0000 0.688 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11277 3 0.0000 0.688 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11272 3 0.4185 -0.983 0.000 0.000 0.496 0.012 0.000 0.492
#> GSM11285 4 0.3912 0.902 0.000 0.028 0.000 0.768 0.180 0.024
#> GSM28753 2 0.1010 0.830 0.000 0.960 0.000 0.004 0.000 0.036
#> GSM28773 2 0.2764 0.811 0.000 0.864 0.000 0.008 0.028 0.100
#> GSM28765 2 0.3318 0.764 0.000 0.828 0.000 0.004 0.084 0.084
#> GSM28768 2 0.3988 0.710 0.012 0.804 0.000 0.068 0.020 0.096
#> GSM28754 5 0.6001 0.331 0.000 0.416 0.000 0.024 0.436 0.124
#> GSM28769 2 0.0748 0.828 0.000 0.976 0.000 0.004 0.004 0.016
#> GSM11275 1 0.4901 0.772 0.708 0.000 0.000 0.100 0.032 0.160
#> GSM11270 5 0.4498 0.561 0.000 0.072 0.000 0.032 0.744 0.152
#> GSM11271 5 0.3586 0.705 0.000 0.216 0.000 0.028 0.756 0.000
#> GSM11288 2 0.4877 0.606 0.000 0.700 0.000 0.064 0.040 0.196
#> GSM11273 5 0.5193 0.374 0.000 0.000 0.148 0.032 0.680 0.140
#> GSM28757 2 0.3710 0.772 0.000 0.812 0.000 0.024 0.064 0.100
#> GSM11282 5 0.4283 0.560 0.000 0.064 0.000 0.028 0.760 0.148
#> GSM28756 5 0.5832 0.481 0.000 0.352 0.000 0.024 0.512 0.112
#> GSM11276 2 0.4705 0.186 0.000 0.612 0.000 0.008 0.336 0.044
#> GSM28752 2 0.3280 0.695 0.000 0.812 0.000 0.004 0.152 0.032
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 tissue(p) k
#> SD:kmeans 44 0.387 2
#> SD:kmeans 54 0.374 3
#> SD:kmeans 51 0.516 4
#> SD:kmeans 37 0.402 5
#> SD:kmeans 46 0.450 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 1.000 1.000 0.4848 0.516 0.516
#> 3 3 0.940 0.902 0.966 0.2776 0.787 0.613
#> 4 4 0.800 0.693 0.871 0.2143 0.827 0.564
#> 5 5 0.827 0.808 0.884 0.0718 0.898 0.621
#> 6 6 0.816 0.731 0.841 0.0381 0.950 0.751
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
#> GSM28762 2 0 1 0 1
#> GSM28763 2 0 1 0 1
#> GSM28764 2 0 1 0 1
#> GSM11274 2 0 1 0 1
#> GSM28772 1 0 1 1 0
#> GSM11269 1 0 1 1 0
#> GSM28775 1 0 1 1 0
#> GSM11293 1 0 1 1 0
#> GSM28755 1 0 1 1 0
#> GSM11279 1 0 1 1 0
#> GSM28758 1 0 1 1 0
#> GSM11281 1 0 1 1 0
#> GSM11287 1 0 1 1 0
#> GSM28759 1 0 1 1 0
#> GSM11292 2 0 1 0 1
#> GSM28766 2 0 1 0 1
#> GSM11268 1 0 1 1 0
#> GSM28767 2 0 1 0 1
#> GSM11286 2 0 1 0 1
#> GSM28751 2 0 1 0 1
#> GSM28770 2 0 1 0 1
#> GSM11283 2 0 1 0 1
#> GSM11289 2 0 1 0 1
#> GSM11280 2 0 1 0 1
#> GSM28749 2 0 1 0 1
#> GSM28750 1 0 1 1 0
#> GSM11290 1 0 1 1 0
#> GSM11294 1 0 1 1 0
#> GSM28771 2 0 1 0 1
#> GSM28760 2 0 1 0 1
#> GSM28774 2 0 1 0 1
#> GSM11284 2 0 1 0 1
#> GSM28761 1 0 1 1 0
#> GSM11278 2 0 1 0 1
#> GSM11291 1 0 1 1 0
#> GSM11277 1 0 1 1 0
#> GSM11272 1 0 1 1 0
#> GSM11285 2 0 1 0 1
#> GSM28753 2 0 1 0 1
#> GSM28773 2 0 1 0 1
#> GSM28765 2 0 1 0 1
#> GSM28768 1 0 1 1 0
#> GSM28754 2 0 1 0 1
#> GSM28769 2 0 1 0 1
#> GSM11275 1 0 1 1 0
#> GSM11270 2 0 1 0 1
#> GSM11271 2 0 1 0 1
#> GSM11288 1 0 1 1 0
#> GSM11273 2 0 1 0 1
#> GSM28757 2 0 1 0 1
#> GSM11282 2 0 1 0 1
#> GSM28756 2 0 1 0 1
#> GSM11276 2 0 1 0 1
#> GSM28752 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM28763 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM28764 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM11274 3 0.0000 0.9420 0.000 0.000 1.000
#> GSM28772 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM11269 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM28775 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM11293 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM28755 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM11279 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM28758 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM11281 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM11287 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM28759 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM11292 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM28766 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM11268 3 0.0000 0.9420 0.000 0.000 1.000
#> GSM28767 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM11286 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM28751 1 0.5529 0.5933 0.704 0.296 0.000
#> GSM28770 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM11283 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM11289 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM11280 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM28749 2 0.3267 0.8505 0.000 0.884 0.116
#> GSM28750 3 0.0000 0.9420 0.000 0.000 1.000
#> GSM11290 3 0.0000 0.9420 0.000 0.000 1.000
#> GSM11294 3 0.0000 0.9420 0.000 0.000 1.000
#> GSM28771 2 0.6252 0.1338 0.000 0.556 0.444
#> GSM28760 3 0.6305 0.0192 0.000 0.484 0.516
#> GSM28774 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM11284 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM28761 3 0.0000 0.9420 0.000 0.000 1.000
#> GSM11278 2 0.0592 0.9672 0.000 0.988 0.012
#> GSM11291 3 0.0000 0.9420 0.000 0.000 1.000
#> GSM11277 3 0.0000 0.9420 0.000 0.000 1.000
#> GSM11272 3 0.0000 0.9420 0.000 0.000 1.000
#> GSM11285 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM28753 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM28773 2 0.0424 0.9701 0.000 0.992 0.008
#> GSM28765 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM28768 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM28754 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM28769 1 0.6244 0.2665 0.560 0.440 0.000
#> GSM11275 1 0.0000 0.9271 1.000 0.000 0.000
#> GSM11270 2 0.0592 0.9672 0.000 0.988 0.012
#> GSM11271 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM11288 3 0.0592 0.9308 0.012 0.000 0.988
#> GSM11273 3 0.0000 0.9420 0.000 0.000 1.000
#> GSM28757 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM11282 2 0.0592 0.9672 0.000 0.988 0.012
#> GSM28756 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM11276 2 0.0000 0.9759 0.000 1.000 0.000
#> GSM28752 2 0.0000 0.9759 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 4 0.2814 0.6061 0.000 0.132 0.000 0.868
#> GSM28763 4 0.2814 0.6061 0.000 0.132 0.000 0.868
#> GSM28764 2 0.3219 0.6080 0.000 0.836 0.000 0.164
#> GSM11274 3 0.0188 0.9900 0.000 0.000 0.996 0.004
#> GSM28772 1 0.0000 0.9973 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.9973 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.9973 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.9973 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.9973 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.9973 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.9973 1.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.9973 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.9973 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.9973 1.000 0.000 0.000 0.000
#> GSM11292 2 0.0000 0.7025 0.000 1.000 0.000 0.000
#> GSM28766 2 0.0000 0.7025 0.000 1.000 0.000 0.000
#> GSM11268 3 0.0000 0.9922 0.000 0.000 1.000 0.000
#> GSM28767 2 0.0000 0.7025 0.000 1.000 0.000 0.000
#> GSM11286 4 0.4989 -0.1470 0.000 0.472 0.000 0.528
#> GSM28751 4 0.3392 0.6251 0.072 0.056 0.000 0.872
#> GSM28770 2 0.0000 0.7025 0.000 1.000 0.000 0.000
#> GSM11283 4 0.4730 0.3328 0.000 0.364 0.000 0.636
#> GSM11289 2 0.0000 0.7025 0.000 1.000 0.000 0.000
#> GSM11280 4 0.0188 0.6472 0.000 0.004 0.000 0.996
#> GSM28749 4 0.4168 0.5749 0.000 0.092 0.080 0.828
#> GSM28750 3 0.0000 0.9922 0.000 0.000 1.000 0.000
#> GSM11290 3 0.0000 0.9922 0.000 0.000 1.000 0.000
#> GSM11294 3 0.0000 0.9922 0.000 0.000 1.000 0.000
#> GSM28771 4 0.5105 0.2489 0.000 0.432 0.004 0.564
#> GSM28760 4 0.5126 0.2286 0.000 0.444 0.004 0.552
#> GSM28774 2 0.4454 0.4747 0.000 0.692 0.000 0.308
#> GSM11284 2 0.4040 0.3779 0.000 0.752 0.000 0.248
#> GSM28761 3 0.0000 0.9922 0.000 0.000 1.000 0.000
#> GSM11278 2 0.0188 0.7005 0.000 0.996 0.000 0.004
#> GSM11291 3 0.0000 0.9922 0.000 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.9922 0.000 0.000 1.000 0.000
#> GSM11272 3 0.0000 0.9922 0.000 0.000 1.000 0.000
#> GSM11285 2 0.4907 -0.0279 0.000 0.580 0.000 0.420
#> GSM28753 4 0.0188 0.6472 0.000 0.004 0.000 0.996
#> GSM28773 4 0.0592 0.6472 0.000 0.016 0.000 0.984
#> GSM28765 2 0.4994 0.1788 0.000 0.520 0.000 0.480
#> GSM28768 1 0.0921 0.9692 0.972 0.000 0.000 0.028
#> GSM28754 2 0.4916 0.3078 0.000 0.576 0.000 0.424
#> GSM28769 4 0.3266 0.6283 0.040 0.084 0.000 0.876
#> GSM11275 1 0.0000 0.9973 1.000 0.000 0.000 0.000
#> GSM11270 2 0.0188 0.7005 0.000 0.996 0.000 0.004
#> GSM11271 2 0.0000 0.7025 0.000 1.000 0.000 0.000
#> GSM11288 3 0.1978 0.9263 0.004 0.000 0.928 0.068
#> GSM11273 3 0.0188 0.9900 0.000 0.000 0.996 0.004
#> GSM28757 4 0.4994 -0.1699 0.000 0.480 0.000 0.520
#> GSM11282 2 0.0188 0.7005 0.000 0.996 0.000 0.004
#> GSM28756 2 0.4697 0.4149 0.000 0.644 0.000 0.356
#> GSM11276 2 0.4955 0.2701 0.000 0.556 0.000 0.444
#> GSM28752 2 0.4961 0.2615 0.000 0.552 0.000 0.448
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28762 2 0.1952 0.768 0.000 0.912 0.000 0.084 0.004
#> GSM28763 2 0.1952 0.768 0.000 0.912 0.000 0.084 0.004
#> GSM28764 5 0.3455 0.676 0.000 0.208 0.000 0.008 0.784
#> GSM11274 3 0.1059 0.948 0.000 0.020 0.968 0.008 0.004
#> GSM28772 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.1012 0.830 0.000 0.020 0.000 0.012 0.968
#> GSM28766 5 0.1012 0.830 0.000 0.020 0.000 0.012 0.968
#> GSM11268 3 0.0162 0.965 0.000 0.000 0.996 0.004 0.000
#> GSM28767 5 0.1012 0.830 0.000 0.020 0.000 0.012 0.968
#> GSM11286 2 0.2632 0.777 0.000 0.888 0.000 0.040 0.072
#> GSM28751 2 0.2929 0.774 0.008 0.880 0.000 0.068 0.044
#> GSM28770 5 0.1012 0.830 0.000 0.020 0.000 0.012 0.968
#> GSM11283 4 0.0566 0.820 0.000 0.012 0.000 0.984 0.004
#> GSM11289 5 0.1012 0.830 0.000 0.020 0.000 0.012 0.968
#> GSM11280 4 0.3274 0.715 0.000 0.220 0.000 0.780 0.000
#> GSM28749 4 0.3554 0.720 0.000 0.216 0.004 0.776 0.004
#> GSM28750 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM11290 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM11294 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM28771 4 0.0613 0.819 0.000 0.008 0.004 0.984 0.004
#> GSM28760 4 0.0727 0.819 0.000 0.004 0.004 0.980 0.012
#> GSM28774 5 0.4437 0.570 0.000 0.316 0.000 0.020 0.664
#> GSM11284 4 0.3085 0.747 0.000 0.032 0.000 0.852 0.116
#> GSM28761 3 0.0162 0.965 0.000 0.000 0.996 0.004 0.000
#> GSM11278 5 0.2844 0.789 0.000 0.092 0.004 0.028 0.876
#> GSM11291 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM11277 3 0.0000 0.966 0.000 0.000 1.000 0.000 0.000
#> GSM11272 3 0.0162 0.965 0.000 0.000 0.996 0.004 0.000
#> GSM11285 4 0.1704 0.798 0.000 0.004 0.000 0.928 0.068
#> GSM28753 2 0.4138 0.288 0.000 0.616 0.000 0.384 0.000
#> GSM28773 4 0.4883 0.244 0.000 0.464 0.004 0.516 0.016
#> GSM28765 2 0.2970 0.725 0.000 0.828 0.000 0.004 0.168
#> GSM28768 1 0.3074 0.761 0.804 0.196 0.000 0.000 0.000
#> GSM28754 5 0.4538 0.249 0.000 0.452 0.000 0.008 0.540
#> GSM28769 2 0.2867 0.774 0.004 0.880 0.000 0.072 0.044
#> GSM11275 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000
#> GSM11270 5 0.2928 0.787 0.000 0.092 0.004 0.032 0.872
#> GSM11271 5 0.1012 0.830 0.000 0.020 0.000 0.012 0.968
#> GSM11288 3 0.3421 0.733 0.000 0.008 0.788 0.204 0.000
#> GSM11273 3 0.2267 0.908 0.000 0.028 0.916 0.008 0.048
#> GSM28757 2 0.3370 0.733 0.000 0.824 0.000 0.028 0.148
#> GSM11282 5 0.2408 0.795 0.000 0.092 0.000 0.016 0.892
#> GSM28756 5 0.4151 0.530 0.000 0.344 0.000 0.004 0.652
#> GSM11276 2 0.4150 0.407 0.000 0.612 0.000 0.000 0.388
#> GSM28752 2 0.3395 0.690 0.000 0.764 0.000 0.000 0.236
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 2 0.0862 0.661 0.000 0.972 0.000 0.016 0.004 0.008
#> GSM28763 2 0.0951 0.660 0.000 0.968 0.000 0.020 0.004 0.008
#> GSM28764 5 0.1970 0.868 0.000 0.060 0.000 0.000 0.912 0.028
#> GSM11274 3 0.3398 0.748 0.000 0.000 0.740 0.008 0.000 0.252
#> GSM28772 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.0000 0.978 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28766 5 0.0000 0.978 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11268 3 0.0692 0.861 0.000 0.004 0.976 0.000 0.000 0.020
#> GSM28767 5 0.0000 0.978 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11286 2 0.4773 0.362 0.000 0.572 0.000 0.004 0.048 0.376
#> GSM28751 2 0.0909 0.660 0.000 0.968 0.000 0.020 0.012 0.000
#> GSM28770 5 0.0000 0.978 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11283 4 0.0291 0.838 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM11289 5 0.0000 0.978 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11280 4 0.5005 0.608 0.000 0.164 0.000 0.644 0.000 0.192
#> GSM28749 4 0.5694 0.584 0.000 0.160 0.028 0.608 0.000 0.204
#> GSM28750 3 0.0146 0.865 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM11290 3 0.1663 0.870 0.000 0.000 0.912 0.000 0.000 0.088
#> GSM11294 3 0.1663 0.870 0.000 0.000 0.912 0.000 0.000 0.088
#> GSM28771 4 0.0291 0.838 0.000 0.000 0.000 0.992 0.004 0.004
#> GSM28760 4 0.0146 0.837 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM28774 6 0.5440 0.499 0.000 0.140 0.000 0.000 0.324 0.536
#> GSM11284 4 0.2937 0.745 0.000 0.000 0.000 0.848 0.056 0.096
#> GSM28761 3 0.0692 0.861 0.000 0.004 0.976 0.000 0.000 0.020
#> GSM11278 6 0.3997 0.526 0.000 0.004 0.012 0.012 0.256 0.716
#> GSM11291 3 0.1663 0.870 0.000 0.000 0.912 0.000 0.000 0.088
#> GSM11277 3 0.1663 0.870 0.000 0.000 0.912 0.000 0.000 0.088
#> GSM11272 3 0.0692 0.861 0.000 0.004 0.976 0.000 0.000 0.020
#> GSM11285 4 0.0790 0.827 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM28753 2 0.5327 0.358 0.000 0.588 0.000 0.248 0.000 0.164
#> GSM28773 6 0.6773 -0.195 0.000 0.284 0.028 0.340 0.004 0.344
#> GSM28765 2 0.5592 0.275 0.000 0.516 0.000 0.004 0.136 0.344
#> GSM28768 1 0.3373 0.669 0.744 0.248 0.000 0.000 0.000 0.008
#> GSM28754 6 0.5053 0.451 0.000 0.204 0.000 0.000 0.160 0.636
#> GSM28769 2 0.0909 0.660 0.000 0.968 0.000 0.020 0.012 0.000
#> GSM11275 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11270 6 0.4121 0.528 0.000 0.004 0.012 0.020 0.248 0.716
#> GSM11271 5 0.0146 0.973 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM11288 3 0.4634 0.637 0.008 0.024 0.740 0.156 0.000 0.072
#> GSM11273 3 0.4604 0.443 0.000 0.000 0.536 0.008 0.024 0.432
#> GSM28757 6 0.4339 0.190 0.000 0.316 0.000 0.004 0.032 0.648
#> GSM11282 6 0.3819 0.490 0.000 0.000 0.000 0.012 0.316 0.672
#> GSM28756 6 0.5237 0.484 0.000 0.172 0.000 0.000 0.220 0.608
#> GSM11276 2 0.5187 0.228 0.000 0.472 0.000 0.000 0.440 0.088
#> GSM28752 2 0.4456 0.484 0.000 0.668 0.000 0.000 0.268 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 tissue(p) k
#> SD:skmeans 54 0.398 2
#> SD:skmeans 51 0.371 3
#> SD:skmeans 41 0.407 4
#> SD:skmeans 50 0.439 5
#> SD:skmeans 42 0.408 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.966 0.987 0.3463 0.669 0.669
#> 3 3 0.887 0.939 0.975 0.5808 0.786 0.681
#> 4 4 0.727 0.720 0.877 0.3041 0.809 0.581
#> 5 5 0.700 0.582 0.790 0.0607 0.893 0.646
#> 6 6 0.810 0.773 0.901 0.0422 0.881 0.573
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
#> GSM28762 2 0.0000 0.983 0.000 1.000
#> GSM28763 2 0.0000 0.983 0.000 1.000
#> GSM28764 2 0.0000 0.983 0.000 1.000
#> GSM11274 2 0.0000 0.983 0.000 1.000
#> GSM28772 1 0.0000 1.000 1.000 0.000
#> GSM11269 1 0.0000 1.000 1.000 0.000
#> GSM28775 1 0.0000 1.000 1.000 0.000
#> GSM11293 1 0.0000 1.000 1.000 0.000
#> GSM28755 1 0.0000 1.000 1.000 0.000
#> GSM11279 1 0.0000 1.000 1.000 0.000
#> GSM28758 1 0.0000 1.000 1.000 0.000
#> GSM11281 1 0.0000 1.000 1.000 0.000
#> GSM11287 1 0.0000 1.000 1.000 0.000
#> GSM28759 1 0.0000 1.000 1.000 0.000
#> GSM11292 2 0.0000 0.983 0.000 1.000
#> GSM28766 2 0.0000 0.983 0.000 1.000
#> GSM11268 2 0.0000 0.983 0.000 1.000
#> GSM28767 2 0.0000 0.983 0.000 1.000
#> GSM11286 2 0.0000 0.983 0.000 1.000
#> GSM28751 2 0.0000 0.983 0.000 1.000
#> GSM28770 2 0.0000 0.983 0.000 1.000
#> GSM11283 2 0.0000 0.983 0.000 1.000
#> GSM11289 2 0.0000 0.983 0.000 1.000
#> GSM11280 2 0.0000 0.983 0.000 1.000
#> GSM28749 2 0.0000 0.983 0.000 1.000
#> GSM28750 2 0.0000 0.983 0.000 1.000
#> GSM11290 2 0.2423 0.945 0.040 0.960
#> GSM11294 2 0.0000 0.983 0.000 1.000
#> GSM28771 2 0.0000 0.983 0.000 1.000
#> GSM28760 2 0.0000 0.983 0.000 1.000
#> GSM28774 2 0.0000 0.983 0.000 1.000
#> GSM11284 2 0.0000 0.983 0.000 1.000
#> GSM28761 2 0.0000 0.983 0.000 1.000
#> GSM11278 2 0.0000 0.983 0.000 1.000
#> GSM11291 2 0.0000 0.983 0.000 1.000
#> GSM11277 2 0.0376 0.979 0.004 0.996
#> GSM11272 2 0.9933 0.194 0.452 0.548
#> GSM11285 2 0.0000 0.983 0.000 1.000
#> GSM28753 2 0.0000 0.983 0.000 1.000
#> GSM28773 2 0.0000 0.983 0.000 1.000
#> GSM28765 2 0.0000 0.983 0.000 1.000
#> GSM28768 2 0.7528 0.724 0.216 0.784
#> GSM28754 2 0.0000 0.983 0.000 1.000
#> GSM28769 2 0.0000 0.983 0.000 1.000
#> GSM11275 1 0.0000 1.000 1.000 0.000
#> GSM11270 2 0.0000 0.983 0.000 1.000
#> GSM11271 2 0.0000 0.983 0.000 1.000
#> GSM11288 2 0.0000 0.983 0.000 1.000
#> GSM11273 2 0.0000 0.983 0.000 1.000
#> GSM28757 2 0.0000 0.983 0.000 1.000
#> GSM11282 2 0.0000 0.983 0.000 1.000
#> GSM28756 2 0.0000 0.983 0.000 1.000
#> GSM11276 2 0.0000 0.983 0.000 1.000
#> GSM28752 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
#> GSM28762 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28763 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28764 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11274 3 0.0000 0.905 0.000 0.000 1.000
#> GSM28772 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11292 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28766 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11268 3 0.2959 0.813 0.000 0.100 0.900
#> GSM28767 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11286 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28751 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28770 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11283 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11289 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11280 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28749 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28750 3 0.0000 0.905 0.000 0.000 1.000
#> GSM11290 3 0.0000 0.905 0.000 0.000 1.000
#> GSM11294 3 0.0000 0.905 0.000 0.000 1.000
#> GSM28771 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28760 2 0.3686 0.842 0.000 0.860 0.140
#> GSM28774 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11284 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28761 3 0.6126 0.309 0.000 0.400 0.600
#> GSM11278 2 0.3686 0.842 0.000 0.860 0.140
#> GSM11291 3 0.0000 0.905 0.000 0.000 1.000
#> GSM11277 3 0.0000 0.905 0.000 0.000 1.000
#> GSM11272 3 0.0592 0.898 0.000 0.012 0.988
#> GSM11285 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28753 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28773 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28765 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28768 2 0.2878 0.875 0.096 0.904 0.000
#> GSM28754 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28769 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11275 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11270 2 0.3686 0.842 0.000 0.860 0.140
#> GSM11271 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11288 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11273 2 0.4346 0.785 0.000 0.816 0.184
#> GSM28757 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11282 2 0.3686 0.842 0.000 0.860 0.140
#> GSM28756 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11276 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28752 2 0.0000 0.972 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.0000 0.804 0 1.000 0.000 0.000
#> GSM28763 2 0.0000 0.804 0 1.000 0.000 0.000
#> GSM28764 2 0.4477 0.365 0 0.688 0.000 0.312
#> GSM11274 3 0.4776 0.562 0 0.000 0.624 0.376
#> GSM28772 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11292 4 0.4877 0.562 0 0.408 0.000 0.592
#> GSM28766 4 0.4817 0.567 0 0.388 0.000 0.612
#> GSM11268 3 0.0657 0.889 0 0.004 0.984 0.012
#> GSM28767 4 0.4877 0.562 0 0.408 0.000 0.592
#> GSM11286 2 0.0000 0.804 0 1.000 0.000 0.000
#> GSM28751 2 0.0000 0.804 0 1.000 0.000 0.000
#> GSM28770 4 0.4877 0.562 0 0.408 0.000 0.592
#> GSM11283 2 0.0921 0.785 0 0.972 0.000 0.028
#> GSM11289 4 0.4877 0.562 0 0.408 0.000 0.592
#> GSM11280 2 0.0188 0.802 0 0.996 0.000 0.004
#> GSM28749 2 0.4948 -0.148 0 0.560 0.000 0.440
#> GSM28750 3 0.0336 0.891 0 0.000 0.992 0.008
#> GSM11290 3 0.0000 0.892 0 0.000 1.000 0.000
#> GSM11294 3 0.0000 0.892 0 0.000 1.000 0.000
#> GSM28771 2 0.0921 0.785 0 0.972 0.000 0.028
#> GSM28760 4 0.2530 0.528 0 0.112 0.000 0.888
#> GSM28774 4 0.2530 0.629 0 0.112 0.000 0.888
#> GSM11284 4 0.4989 0.345 0 0.472 0.000 0.528
#> GSM28761 3 0.6494 0.457 0 0.340 0.572 0.088
#> GSM11278 4 0.1022 0.634 0 0.032 0.000 0.968
#> GSM11291 3 0.0000 0.892 0 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.892 0 0.000 1.000 0.000
#> GSM11272 3 0.2214 0.858 0 0.044 0.928 0.028
#> GSM11285 4 0.4790 0.566 0 0.380 0.000 0.620
#> GSM28753 2 0.0000 0.804 0 1.000 0.000 0.000
#> GSM28773 2 0.0188 0.802 0 0.996 0.000 0.004
#> GSM28765 2 0.0000 0.804 0 1.000 0.000 0.000
#> GSM28768 2 0.0000 0.804 0 1.000 0.000 0.000
#> GSM28754 2 0.3528 0.574 0 0.808 0.000 0.192
#> GSM28769 2 0.0000 0.804 0 1.000 0.000 0.000
#> GSM11275 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11270 4 0.1022 0.634 0 0.032 0.000 0.968
#> GSM11271 2 0.4661 0.262 0 0.652 0.000 0.348
#> GSM11288 2 0.1302 0.775 0 0.956 0.000 0.044
#> GSM11273 4 0.0469 0.618 0 0.012 0.000 0.988
#> GSM28757 2 0.4761 0.273 0 0.628 0.000 0.372
#> GSM11282 4 0.1022 0.634 0 0.032 0.000 0.968
#> GSM28756 2 0.3907 0.541 0 0.768 0.000 0.232
#> GSM11276 2 0.4277 0.442 0 0.720 0.000 0.280
#> GSM28752 2 0.3873 0.548 0 0.772 0.000 0.228
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28762 2 0.4074 0.759 0 0.636 0.000 0.000 0.364
#> GSM28763 2 0.4074 0.759 0 0.636 0.000 0.000 0.364
#> GSM28764 5 0.4138 -0.354 0 0.384 0.000 0.000 0.616
#> GSM11274 4 0.6300 0.262 0 0.336 0.168 0.496 0.000
#> GSM28772 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11292 5 0.0000 0.565 0 0.000 0.000 0.000 1.000
#> GSM28766 5 0.0703 0.566 0 0.024 0.000 0.000 0.976
#> GSM11268 3 0.0000 0.795 0 0.000 1.000 0.000 0.000
#> GSM28767 5 0.0000 0.565 0 0.000 0.000 0.000 1.000
#> GSM11286 2 0.4211 0.758 0 0.636 0.004 0.000 0.360
#> GSM28751 2 0.4074 0.759 0 0.636 0.000 0.000 0.364
#> GSM28770 5 0.0000 0.565 0 0.000 0.000 0.000 1.000
#> GSM11283 2 0.6025 0.373 0 0.496 0.000 0.384 0.120
#> GSM11289 5 0.0000 0.565 0 0.000 0.000 0.000 1.000
#> GSM11280 2 0.6912 0.593 0 0.508 0.220 0.024 0.248
#> GSM28749 5 0.5862 0.133 0 0.176 0.220 0.000 0.604
#> GSM28750 3 0.3274 0.411 0 0.000 0.780 0.220 0.000
#> GSM11290 4 0.4138 0.508 0 0.000 0.384 0.616 0.000
#> GSM11294 4 0.4138 0.508 0 0.000 0.384 0.616 0.000
#> GSM28771 2 0.6025 0.373 0 0.496 0.000 0.384 0.120
#> GSM28760 4 0.8162 -0.164 0 0.124 0.220 0.384 0.272
#> GSM28774 5 0.4161 0.485 0 0.392 0.000 0.000 0.608
#> GSM11284 5 0.6615 0.262 0 0.116 0.080 0.188 0.616
#> GSM28761 3 0.1671 0.704 0 0.076 0.924 0.000 0.000
#> GSM11278 5 0.3966 0.470 0 0.336 0.000 0.000 0.664
#> GSM11291 4 0.4138 0.508 0 0.000 0.384 0.616 0.000
#> GSM11277 4 0.4138 0.508 0 0.000 0.384 0.616 0.000
#> GSM11272 3 0.0000 0.795 0 0.000 1.000 0.000 0.000
#> GSM11285 5 0.4835 0.351 0 0.028 0.000 0.380 0.592
#> GSM28753 2 0.4555 0.753 0 0.636 0.020 0.000 0.344
#> GSM28773 2 0.6408 0.606 0 0.508 0.220 0.000 0.272
#> GSM28765 2 0.4074 0.759 0 0.636 0.000 0.000 0.364
#> GSM28768 2 0.4074 0.759 0 0.636 0.000 0.000 0.364
#> GSM28754 2 0.2852 0.584 0 0.828 0.000 0.000 0.172
#> GSM28769 2 0.4074 0.759 0 0.636 0.000 0.000 0.364
#> GSM11275 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11270 5 0.3966 0.470 0 0.336 0.000 0.000 0.664
#> GSM11271 5 0.3966 -0.239 0 0.336 0.000 0.000 0.664
#> GSM11288 2 0.6465 0.592 0 0.492 0.220 0.000 0.288
#> GSM11273 5 0.4060 0.445 0 0.360 0.000 0.000 0.640
#> GSM28757 2 0.0794 0.390 0 0.972 0.000 0.000 0.028
#> GSM11282 5 0.3966 0.470 0 0.336 0.000 0.000 0.664
#> GSM28756 2 0.4306 0.577 0 0.508 0.000 0.000 0.492
#> GSM11276 5 0.4227 -0.437 0 0.420 0.000 0.000 0.580
#> GSM28752 2 0.4307 0.570 0 0.504 0.000 0.000 0.496
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 2 0.0000 0.813 0 1.000 0.00 0.000 0.000 0.000
#> GSM28763 2 0.0000 0.813 0 1.000 0.00 0.000 0.000 0.000
#> GSM28764 2 0.3515 0.346 0 0.676 0.00 0.000 0.324 0.000
#> GSM11274 3 0.3578 0.549 0 0.000 0.66 0.000 0.340 0.000
#> GSM28772 1 0.0000 1.000 1 0.000 0.00 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1 0.000 0.00 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1 0.000 0.00 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1 0.000 0.00 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1 0.000 0.00 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1 0.000 0.00 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1 0.000 0.00 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1 0.000 0.00 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1 0.000 0.00 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1 0.000 0.00 0.000 0.000 0.000
#> GSM11292 5 0.3578 0.661 0 0.340 0.00 0.000 0.660 0.000
#> GSM28766 5 0.3578 0.661 0 0.340 0.00 0.000 0.660 0.000
#> GSM11268 6 0.0000 0.905 0 0.000 0.00 0.000 0.000 1.000
#> GSM28767 5 0.3578 0.661 0 0.340 0.00 0.000 0.660 0.000
#> GSM11286 2 0.0146 0.812 0 0.996 0.00 0.000 0.000 0.004
#> GSM28751 2 0.0000 0.813 0 1.000 0.00 0.000 0.000 0.000
#> GSM28770 5 0.3578 0.661 0 0.340 0.00 0.000 0.660 0.000
#> GSM11283 4 0.0000 0.825 0 0.000 0.00 1.000 0.000 0.000
#> GSM11289 5 0.3578 0.661 0 0.340 0.00 0.000 0.660 0.000
#> GSM11280 2 0.3422 0.700 0 0.788 0.00 0.036 0.000 0.176
#> GSM28749 2 0.5093 0.472 0 0.632 0.00 0.000 0.192 0.176
#> GSM28750 6 0.2793 0.713 0 0.000 0.20 0.000 0.000 0.800
#> GSM11290 3 0.0000 0.892 0 0.000 1.00 0.000 0.000 0.000
#> GSM11294 3 0.0000 0.892 0 0.000 1.00 0.000 0.000 0.000
#> GSM28771 4 0.0000 0.825 0 0.000 0.00 1.000 0.000 0.000
#> GSM28760 4 0.0000 0.825 0 0.000 0.00 1.000 0.000 0.000
#> GSM28774 5 0.1663 0.667 0 0.088 0.00 0.000 0.912 0.000
#> GSM11284 4 0.4660 0.444 0 0.304 0.00 0.644 0.024 0.028
#> GSM28761 6 0.0000 0.905 0 0.000 0.00 0.000 0.000 1.000
#> GSM11278 5 0.0000 0.683 0 0.000 0.00 0.000 1.000 0.000
#> GSM11291 3 0.0000 0.892 0 0.000 1.00 0.000 0.000 0.000
#> GSM11277 3 0.0000 0.892 0 0.000 1.00 0.000 0.000 0.000
#> GSM11272 6 0.0937 0.893 0 0.000 0.04 0.000 0.000 0.960
#> GSM11285 4 0.1995 0.785 0 0.036 0.00 0.912 0.052 0.000
#> GSM28753 2 0.0260 0.811 0 0.992 0.00 0.000 0.000 0.008
#> GSM28773 2 0.2597 0.725 0 0.824 0.00 0.000 0.000 0.176
#> GSM28765 2 0.0000 0.813 0 1.000 0.00 0.000 0.000 0.000
#> GSM28768 2 0.0000 0.813 0 1.000 0.00 0.000 0.000 0.000
#> GSM28754 2 0.2730 0.640 0 0.808 0.00 0.000 0.192 0.000
#> GSM28769 2 0.0000 0.813 0 1.000 0.00 0.000 0.000 0.000
#> GSM11275 1 0.0000 1.000 1 0.000 0.00 0.000 0.000 0.000
#> GSM11270 5 0.0000 0.683 0 0.000 0.00 0.000 1.000 0.000
#> GSM11271 2 0.3647 0.255 0 0.640 0.00 0.000 0.360 0.000
#> GSM11288 2 0.2597 0.725 0 0.824 0.00 0.000 0.000 0.176
#> GSM11273 5 0.0000 0.683 0 0.000 0.00 0.000 1.000 0.000
#> GSM28757 2 0.3578 0.437 0 0.660 0.00 0.000 0.340 0.000
#> GSM11282 5 0.0000 0.683 0 0.000 0.00 0.000 1.000 0.000
#> GSM28756 2 0.0000 0.813 0 1.000 0.00 0.000 0.000 0.000
#> GSM11276 2 0.3351 0.423 0 0.712 0.00 0.000 0.288 0.000
#> GSM28752 2 0.1556 0.756 0 0.920 0.00 0.000 0.080 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 tissue(p) k
#> SD:pam 53 0.397 2
#> SD:pam 53 0.373 3
#> SD:pam 47 0.422 4
#> SD:pam 37 0.393 5
#> SD:pam 48 0.458 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.849 0.901 0.942 0.4788 0.525 0.525
#> 3 3 0.757 0.881 0.933 0.3258 0.735 0.539
#> 4 4 0.847 0.923 0.947 0.0438 0.888 0.731
#> 5 5 0.775 0.751 0.877 0.1397 0.857 0.602
#> 6 6 0.795 0.802 0.886 0.0540 0.962 0.824
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
#> GSM28762 2 0.0376 0.941 0.004 0.996
#> GSM28763 2 0.0672 0.940 0.008 0.992
#> GSM28764 2 0.0000 0.942 0.000 1.000
#> GSM11274 1 0.8955 0.537 0.688 0.312
#> GSM28772 1 0.2603 0.954 0.956 0.044
#> GSM11269 1 0.2603 0.954 0.956 0.044
#> GSM28775 1 0.2603 0.954 0.956 0.044
#> GSM11293 1 0.2603 0.954 0.956 0.044
#> GSM28755 1 0.2603 0.954 0.956 0.044
#> GSM11279 1 0.2603 0.954 0.956 0.044
#> GSM28758 1 0.2603 0.954 0.956 0.044
#> GSM11281 1 0.2603 0.954 0.956 0.044
#> GSM11287 1 0.2603 0.954 0.956 0.044
#> GSM28759 1 0.2603 0.954 0.956 0.044
#> GSM11292 2 0.0000 0.942 0.000 1.000
#> GSM28766 2 0.0000 0.942 0.000 1.000
#> GSM11268 1 0.2423 0.944 0.960 0.040
#> GSM28767 2 0.0000 0.942 0.000 1.000
#> GSM11286 2 0.0000 0.942 0.000 1.000
#> GSM28751 2 0.3431 0.917 0.064 0.936
#> GSM28770 2 0.0000 0.942 0.000 1.000
#> GSM11283 2 0.5842 0.879 0.140 0.860
#> GSM11289 2 0.0376 0.941 0.004 0.996
#> GSM11280 2 0.4562 0.907 0.096 0.904
#> GSM28749 2 0.3274 0.925 0.060 0.940
#> GSM28750 1 0.2423 0.944 0.960 0.040
#> GSM11290 1 0.2423 0.944 0.960 0.040
#> GSM11294 1 0.2423 0.944 0.960 0.040
#> GSM28771 2 0.5842 0.879 0.140 0.860
#> GSM28760 2 0.5842 0.879 0.140 0.860
#> GSM28774 2 0.0000 0.942 0.000 1.000
#> GSM11284 2 0.4298 0.910 0.088 0.912
#> GSM28761 1 0.2423 0.944 0.960 0.040
#> GSM11278 2 0.0376 0.941 0.004 0.996
#> GSM11291 1 0.2423 0.944 0.960 0.040
#> GSM11277 1 0.2423 0.944 0.960 0.040
#> GSM11272 1 0.2423 0.944 0.960 0.040
#> GSM11285 2 0.5842 0.879 0.140 0.860
#> GSM28753 2 0.3114 0.924 0.056 0.944
#> GSM28773 2 0.1414 0.937 0.020 0.980
#> GSM28765 2 0.0000 0.942 0.000 1.000
#> GSM28768 2 0.5408 0.875 0.124 0.876
#> GSM28754 2 0.0000 0.942 0.000 1.000
#> GSM28769 2 0.2423 0.926 0.040 0.960
#> GSM11275 1 0.2603 0.954 0.956 0.044
#> GSM11270 2 0.0376 0.941 0.004 0.996
#> GSM11271 2 0.0000 0.942 0.000 1.000
#> GSM11288 2 0.9909 0.219 0.444 0.556
#> GSM11273 2 0.9933 0.205 0.452 0.548
#> GSM28757 2 0.0000 0.942 0.000 1.000
#> GSM11282 2 0.0376 0.941 0.004 0.996
#> GSM28756 2 0.0000 0.942 0.000 1.000
#> GSM11276 2 0.0000 0.942 0.000 1.000
#> GSM28752 2 0.0000 0.942 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.3619 0.831 0.000 0.864 0.136
#> GSM28763 2 0.3686 0.828 0.000 0.860 0.140
#> GSM28764 2 0.0000 0.880 0.000 1.000 0.000
#> GSM11274 3 0.0000 0.953 0.000 0.000 1.000
#> GSM28772 1 0.0000 0.980 1.000 0.000 0.000
#> GSM11269 1 0.0000 0.980 1.000 0.000 0.000
#> GSM28775 1 0.1964 0.944 0.944 0.000 0.056
#> GSM11293 1 0.0000 0.980 1.000 0.000 0.000
#> GSM28755 1 0.0000 0.980 1.000 0.000 0.000
#> GSM11279 1 0.0000 0.980 1.000 0.000 0.000
#> GSM28758 1 0.1964 0.944 0.944 0.000 0.056
#> GSM11281 1 0.0000 0.980 1.000 0.000 0.000
#> GSM11287 1 0.0000 0.980 1.000 0.000 0.000
#> GSM28759 1 0.0000 0.980 1.000 0.000 0.000
#> GSM11292 2 0.0000 0.880 0.000 1.000 0.000
#> GSM28766 2 0.0000 0.880 0.000 1.000 0.000
#> GSM11268 3 0.0000 0.953 0.000 0.000 1.000
#> GSM28767 2 0.0000 0.880 0.000 1.000 0.000
#> GSM11286 2 0.0000 0.880 0.000 1.000 0.000
#> GSM28751 2 0.4099 0.828 0.008 0.852 0.140
#> GSM28770 2 0.0000 0.880 0.000 1.000 0.000
#> GSM11283 3 0.2537 0.929 0.000 0.080 0.920
#> GSM11289 2 0.1163 0.873 0.000 0.972 0.028
#> GSM11280 3 0.3340 0.885 0.000 0.120 0.880
#> GSM28749 2 0.6192 0.411 0.000 0.580 0.420
#> GSM28750 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11290 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11294 3 0.0000 0.953 0.000 0.000 1.000
#> GSM28771 3 0.2537 0.929 0.000 0.080 0.920
#> GSM28760 3 0.2537 0.929 0.000 0.080 0.920
#> GSM28774 2 0.0000 0.880 0.000 1.000 0.000
#> GSM11284 3 0.2878 0.915 0.000 0.096 0.904
#> GSM28761 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11278 2 0.5431 0.692 0.000 0.716 0.284
#> GSM11291 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11277 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11272 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11285 3 0.2537 0.929 0.000 0.080 0.920
#> GSM28753 2 0.5926 0.568 0.000 0.644 0.356
#> GSM28773 2 0.5650 0.653 0.000 0.688 0.312
#> GSM28765 2 0.0000 0.880 0.000 1.000 0.000
#> GSM28768 2 0.6407 0.778 0.080 0.760 0.160
#> GSM28754 2 0.0000 0.880 0.000 1.000 0.000
#> GSM28769 2 0.3752 0.826 0.000 0.856 0.144
#> GSM11275 1 0.1964 0.944 0.944 0.000 0.056
#> GSM11270 2 0.5650 0.654 0.000 0.688 0.312
#> GSM11271 2 0.0000 0.880 0.000 1.000 0.000
#> GSM11288 3 0.2356 0.933 0.000 0.072 0.928
#> GSM11273 3 0.0424 0.952 0.000 0.008 0.992
#> GSM28757 2 0.0000 0.880 0.000 1.000 0.000
#> GSM11282 2 0.5678 0.648 0.000 0.684 0.316
#> GSM28756 2 0.0000 0.880 0.000 1.000 0.000
#> GSM11276 2 0.0000 0.880 0.000 1.000 0.000
#> GSM28752 2 0.0592 0.878 0.000 0.988 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.2081 0.913 0.000 0.916 0.000 0.084
#> GSM28763 2 0.2011 0.914 0.000 0.920 0.000 0.080
#> GSM28764 2 0.0707 0.922 0.000 0.980 0.000 0.020
#> GSM11274 3 0.2739 0.851 0.000 0.036 0.904 0.060
#> GSM28772 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM11292 2 0.0188 0.918 0.000 0.996 0.000 0.004
#> GSM28766 2 0.0707 0.920 0.000 0.980 0.000 0.020
#> GSM11268 3 0.0188 0.945 0.000 0.000 0.996 0.004
#> GSM28767 2 0.0188 0.918 0.000 0.996 0.000 0.004
#> GSM11286 2 0.1211 0.921 0.000 0.960 0.000 0.040
#> GSM28751 2 0.3074 0.888 0.000 0.848 0.000 0.152
#> GSM28770 2 0.0188 0.918 0.000 0.996 0.000 0.004
#> GSM11283 4 0.0188 0.994 0.000 0.000 0.004 0.996
#> GSM11289 2 0.1211 0.924 0.000 0.960 0.000 0.040
#> GSM11280 2 0.4331 0.753 0.000 0.712 0.000 0.288
#> GSM28749 2 0.3569 0.857 0.000 0.804 0.000 0.196
#> GSM28750 3 0.0188 0.945 0.000 0.000 0.996 0.004
#> GSM11290 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM11294 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM28771 4 0.0188 0.994 0.000 0.000 0.004 0.996
#> GSM28760 4 0.0188 0.994 0.000 0.000 0.004 0.996
#> GSM28774 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM11284 2 0.4277 0.764 0.000 0.720 0.000 0.280
#> GSM28761 3 0.0188 0.945 0.000 0.000 0.996 0.004
#> GSM11278 2 0.2224 0.908 0.000 0.928 0.032 0.040
#> GSM11291 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.945 0.000 0.000 1.000 0.000
#> GSM11272 3 0.0188 0.945 0.000 0.000 0.996 0.004
#> GSM11285 4 0.0657 0.981 0.000 0.012 0.004 0.984
#> GSM28753 2 0.3583 0.867 0.000 0.816 0.004 0.180
#> GSM28773 2 0.3208 0.887 0.000 0.848 0.004 0.148
#> GSM28765 2 0.0921 0.922 0.000 0.972 0.000 0.028
#> GSM28768 2 0.3577 0.882 0.012 0.832 0.000 0.156
#> GSM28754 2 0.0000 0.919 0.000 1.000 0.000 0.000
#> GSM28769 2 0.3157 0.890 0.000 0.852 0.004 0.144
#> GSM11275 1 0.1022 0.957 0.968 0.000 0.000 0.032
#> GSM11270 2 0.2644 0.901 0.000 0.908 0.032 0.060
#> GSM11271 2 0.0188 0.918 0.000 0.996 0.000 0.004
#> GSM11288 2 0.4514 0.847 0.000 0.796 0.056 0.148
#> GSM11273 3 0.5240 0.611 0.000 0.188 0.740 0.072
#> GSM28757 2 0.0592 0.921 0.000 0.984 0.000 0.016
#> GSM11282 2 0.2644 0.901 0.000 0.908 0.032 0.060
#> GSM28756 2 0.0188 0.918 0.000 0.996 0.000 0.004
#> GSM11276 2 0.0336 0.920 0.000 0.992 0.000 0.008
#> GSM28752 2 0.1474 0.919 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
#> GSM28762 5 0.4074 0.7222 0.000 0.364 0.000 0.000 0.636
#> GSM28763 5 0.4126 0.6997 0.000 0.380 0.000 0.000 0.620
#> GSM28764 2 0.0404 0.8695 0.000 0.988 0.000 0.000 0.012
#> GSM11274 3 0.3551 0.7163 0.000 0.000 0.772 0.008 0.220
#> GSM28772 1 0.0000 0.9499 1.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.9499 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0162 0.9455 0.996 0.000 0.000 0.000 0.004
#> GSM11293 1 0.0000 0.9499 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.9499 1.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.9499 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.9499 1.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.9499 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.9499 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.9499 1.000 0.000 0.000 0.000 0.000
#> GSM11292 2 0.0000 0.8681 0.000 1.000 0.000 0.000 0.000
#> GSM28766 2 0.0162 0.8659 0.000 0.996 0.000 0.000 0.004
#> GSM11268 3 0.0162 0.8949 0.000 0.000 0.996 0.000 0.004
#> GSM28767 2 0.0000 0.8681 0.000 1.000 0.000 0.000 0.000
#> GSM11286 2 0.1908 0.7879 0.000 0.908 0.000 0.000 0.092
#> GSM28751 5 0.4074 0.7222 0.000 0.364 0.000 0.000 0.636
#> GSM28770 2 0.0000 0.8681 0.000 1.000 0.000 0.000 0.000
#> GSM11283 4 0.0703 0.8401 0.000 0.000 0.000 0.976 0.024
#> GSM11289 2 0.3999 0.2779 0.000 0.656 0.000 0.000 0.344
#> GSM11280 5 0.3442 0.6991 0.000 0.104 0.000 0.060 0.836
#> GSM28749 5 0.3276 0.7283 0.000 0.132 0.000 0.032 0.836
#> GSM28750 3 0.0162 0.8949 0.000 0.000 0.996 0.000 0.004
#> GSM11290 3 0.0000 0.8946 0.000 0.000 1.000 0.000 0.000
#> GSM11294 3 0.0000 0.8946 0.000 0.000 1.000 0.000 0.000
#> GSM28771 4 0.0703 0.8401 0.000 0.000 0.000 0.976 0.024
#> GSM28760 4 0.0703 0.8401 0.000 0.000 0.000 0.976 0.024
#> GSM28774 2 0.0404 0.8695 0.000 0.988 0.000 0.000 0.012
#> GSM11284 5 0.3427 0.7053 0.000 0.108 0.000 0.056 0.836
#> GSM28761 3 0.0162 0.8949 0.000 0.000 0.996 0.000 0.004
#> GSM11278 2 0.5029 -0.2537 0.000 0.528 0.004 0.024 0.444
#> GSM11291 3 0.0000 0.8946 0.000 0.000 1.000 0.000 0.000
#> GSM11277 3 0.0000 0.8946 0.000 0.000 1.000 0.000 0.000
#> GSM11272 3 0.0162 0.8949 0.000 0.000 0.996 0.000 0.004
#> GSM11285 4 0.4182 0.2800 0.000 0.000 0.000 0.600 0.400
#> GSM28753 5 0.3229 0.7282 0.000 0.128 0.000 0.032 0.840
#> GSM28773 5 0.4360 0.7507 0.000 0.300 0.000 0.020 0.680
#> GSM28765 2 0.0510 0.8688 0.000 0.984 0.000 0.000 0.016
#> GSM28768 5 0.4891 0.7368 0.044 0.316 0.000 0.000 0.640
#> GSM28754 2 0.0703 0.8629 0.000 0.976 0.000 0.000 0.024
#> GSM28769 5 0.4015 0.7361 0.000 0.348 0.000 0.000 0.652
#> GSM11275 1 0.4074 0.3720 0.636 0.000 0.000 0.000 0.364
#> GSM11270 2 0.5050 -0.2954 0.000 0.496 0.004 0.024 0.476
#> GSM11271 2 0.0000 0.8681 0.000 1.000 0.000 0.000 0.000
#> GSM11288 5 0.3317 0.7172 0.000 0.116 0.000 0.044 0.840
#> GSM11273 3 0.7032 0.0702 0.000 0.384 0.400 0.020 0.196
#> GSM28757 2 0.0609 0.8660 0.000 0.980 0.000 0.000 0.020
#> GSM11282 5 0.5045 0.1912 0.000 0.464 0.004 0.024 0.508
#> GSM28756 2 0.0000 0.8681 0.000 1.000 0.000 0.000 0.000
#> GSM11276 2 0.0404 0.8695 0.000 0.988 0.000 0.000 0.012
#> GSM28752 2 0.0609 0.8671 0.000 0.980 0.000 0.000 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 2 0.3245 0.745 0.000 0.764 0.000 0.000 0.228 0.008
#> GSM28763 2 0.3373 0.719 0.000 0.744 0.000 0.000 0.248 0.008
#> GSM28764 5 0.0858 0.899 0.000 0.028 0.000 0.000 0.968 0.004
#> GSM11274 3 0.3795 0.471 0.000 0.004 0.632 0.000 0.000 0.364
#> GSM28772 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0363 0.967 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM11293 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0363 0.967 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM11281 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.973 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.0000 0.910 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28766 5 0.0000 0.910 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11268 3 0.0777 0.863 0.000 0.000 0.972 0.004 0.000 0.024
#> GSM28767 5 0.0000 0.910 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11286 5 0.3265 0.574 0.000 0.248 0.000 0.000 0.748 0.004
#> GSM28751 2 0.3171 0.758 0.000 0.784 0.000 0.000 0.204 0.012
#> GSM28770 5 0.0000 0.910 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11283 4 0.0146 0.845 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM11289 5 0.3756 0.291 0.000 0.400 0.000 0.000 0.600 0.000
#> GSM11280 2 0.1226 0.746 0.000 0.952 0.000 0.040 0.004 0.004
#> GSM28749 2 0.1138 0.754 0.000 0.960 0.000 0.024 0.012 0.004
#> GSM28750 3 0.0405 0.864 0.000 0.000 0.988 0.004 0.000 0.008
#> GSM11290 3 0.2340 0.859 0.000 0.000 0.852 0.000 0.000 0.148
#> GSM11294 3 0.2378 0.859 0.000 0.000 0.848 0.000 0.000 0.152
#> GSM28771 4 0.0146 0.845 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM28760 4 0.0146 0.845 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM28774 5 0.0260 0.909 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM11284 2 0.1857 0.744 0.000 0.924 0.000 0.044 0.028 0.004
#> GSM28761 3 0.0777 0.863 0.000 0.000 0.972 0.004 0.000 0.024
#> GSM11278 6 0.5702 0.658 0.000 0.180 0.000 0.000 0.324 0.496
#> GSM11291 3 0.2378 0.859 0.000 0.000 0.848 0.000 0.000 0.152
#> GSM11277 3 0.2378 0.859 0.000 0.000 0.848 0.000 0.000 0.152
#> GSM11272 3 0.0777 0.863 0.000 0.000 0.972 0.004 0.000 0.024
#> GSM11285 4 0.3714 0.439 0.000 0.340 0.004 0.656 0.000 0.000
#> GSM28753 2 0.1138 0.754 0.000 0.960 0.000 0.024 0.012 0.004
#> GSM28773 2 0.4014 0.651 0.000 0.696 0.000 0.024 0.276 0.004
#> GSM28765 5 0.1007 0.889 0.000 0.044 0.000 0.000 0.956 0.000
#> GSM28768 2 0.3470 0.759 0.020 0.792 0.000 0.000 0.176 0.012
#> GSM28754 5 0.0937 0.883 0.000 0.040 0.000 0.000 0.960 0.000
#> GSM28769 2 0.3201 0.760 0.000 0.780 0.000 0.000 0.208 0.012
#> GSM11275 1 0.3121 0.718 0.804 0.180 0.004 0.000 0.000 0.012
#> GSM11270 6 0.5624 0.688 0.000 0.180 0.000 0.000 0.296 0.524
#> GSM11271 5 0.0000 0.910 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11288 2 0.1553 0.743 0.000 0.944 0.004 0.032 0.008 0.012
#> GSM11273 6 0.4569 -0.199 0.000 0.016 0.396 0.000 0.016 0.572
#> GSM28757 5 0.0363 0.908 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM11282 6 0.5731 0.689 0.000 0.176 0.004 0.000 0.296 0.524
#> GSM28756 5 0.0000 0.910 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11276 5 0.0260 0.909 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM28752 5 0.1663 0.840 0.000 0.088 0.000 0.000 0.912 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> SD:mclust 52 0.396 2
#> SD:mclust 53 0.443 3
#> SD:mclust 54 0.523 4
#> SD:mclust 47 0.404 5
#> SD:mclust 50 0.400 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.972 0.988 0.3830 0.628 0.628
#> 3 3 1.000 0.978 0.990 0.5362 0.740 0.599
#> 4 4 0.779 0.796 0.885 0.1837 0.859 0.660
#> 5 5 0.959 0.920 0.960 0.0866 0.943 0.804
#> 6 6 0.805 0.787 0.868 0.0844 0.916 0.661
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM28762 2 0.0000 0.985 0.000 1.000
#> GSM28763 2 0.2423 0.948 0.040 0.960
#> GSM28764 2 0.0000 0.985 0.000 1.000
#> GSM11274 2 0.0000 0.985 0.000 1.000
#> GSM28772 1 0.0000 0.996 1.000 0.000
#> GSM11269 1 0.0000 0.996 1.000 0.000
#> GSM28775 1 0.0000 0.996 1.000 0.000
#> GSM11293 1 0.0000 0.996 1.000 0.000
#> GSM28755 1 0.0000 0.996 1.000 0.000
#> GSM11279 1 0.0000 0.996 1.000 0.000
#> GSM28758 1 0.0000 0.996 1.000 0.000
#> GSM11281 1 0.0000 0.996 1.000 0.000
#> GSM11287 1 0.0000 0.996 1.000 0.000
#> GSM28759 1 0.0000 0.996 1.000 0.000
#> GSM11292 2 0.0000 0.985 0.000 1.000
#> GSM28766 2 0.0000 0.985 0.000 1.000
#> GSM11268 2 0.0000 0.985 0.000 1.000
#> GSM28767 2 0.0000 0.985 0.000 1.000
#> GSM11286 2 0.0000 0.985 0.000 1.000
#> GSM28751 1 0.2948 0.943 0.948 0.052
#> GSM28770 2 0.0000 0.985 0.000 1.000
#> GSM11283 2 0.0000 0.985 0.000 1.000
#> GSM11289 2 0.0000 0.985 0.000 1.000
#> GSM11280 2 0.0000 0.985 0.000 1.000
#> GSM28749 2 0.0000 0.985 0.000 1.000
#> GSM28750 2 0.0000 0.985 0.000 1.000
#> GSM11290 2 0.0000 0.985 0.000 1.000
#> GSM11294 2 0.0000 0.985 0.000 1.000
#> GSM28771 2 0.0000 0.985 0.000 1.000
#> GSM28760 2 0.0000 0.985 0.000 1.000
#> GSM28774 2 0.0000 0.985 0.000 1.000
#> GSM11284 2 0.0000 0.985 0.000 1.000
#> GSM28761 2 0.0000 0.985 0.000 1.000
#> GSM11278 2 0.0000 0.985 0.000 1.000
#> GSM11291 2 0.0000 0.985 0.000 1.000
#> GSM11277 2 0.0000 0.985 0.000 1.000
#> GSM11272 2 0.7815 0.703 0.232 0.768
#> GSM11285 2 0.0000 0.985 0.000 1.000
#> GSM28753 2 0.0000 0.985 0.000 1.000
#> GSM28773 2 0.0000 0.985 0.000 1.000
#> GSM28765 2 0.0000 0.985 0.000 1.000
#> GSM28768 1 0.0000 0.996 1.000 0.000
#> GSM28754 2 0.0000 0.985 0.000 1.000
#> GSM28769 2 0.9087 0.532 0.324 0.676
#> GSM11275 1 0.0000 0.996 1.000 0.000
#> GSM11270 2 0.0000 0.985 0.000 1.000
#> GSM11271 2 0.0000 0.985 0.000 1.000
#> GSM11288 2 0.0672 0.978 0.008 0.992
#> GSM11273 2 0.0000 0.985 0.000 1.000
#> GSM28757 2 0.0000 0.985 0.000 1.000
#> GSM11282 2 0.0000 0.985 0.000 1.000
#> GSM28756 2 0.0000 0.985 0.000 1.000
#> GSM11276 2 0.0000 0.985 0.000 1.000
#> GSM28752 2 0.0000 0.985 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.0000 0.996 0.000 1.000 0.000
#> GSM28763 2 0.0000 0.996 0.000 1.000 0.000
#> GSM28764 2 0.0000 0.996 0.000 1.000 0.000
#> GSM11274 3 0.0000 0.966 0.000 0.000 1.000
#> GSM28772 1 0.0000 0.990 1.000 0.000 0.000
#> GSM11269 1 0.0000 0.990 1.000 0.000 0.000
#> GSM28775 1 0.0000 0.990 1.000 0.000 0.000
#> GSM11293 1 0.0000 0.990 1.000 0.000 0.000
#> GSM28755 1 0.0000 0.990 1.000 0.000 0.000
#> GSM11279 1 0.0000 0.990 1.000 0.000 0.000
#> GSM28758 1 0.0000 0.990 1.000 0.000 0.000
#> GSM11281 1 0.0000 0.990 1.000 0.000 0.000
#> GSM11287 1 0.0000 0.990 1.000 0.000 0.000
#> GSM28759 1 0.0000 0.990 1.000 0.000 0.000
#> GSM11292 2 0.0000 0.996 0.000 1.000 0.000
#> GSM28766 2 0.0000 0.996 0.000 1.000 0.000
#> GSM11268 3 0.0000 0.966 0.000 0.000 1.000
#> GSM28767 2 0.0000 0.996 0.000 1.000 0.000
#> GSM11286 2 0.0000 0.996 0.000 1.000 0.000
#> GSM28751 2 0.1753 0.948 0.048 0.952 0.000
#> GSM28770 2 0.0000 0.996 0.000 1.000 0.000
#> GSM11283 2 0.0000 0.996 0.000 1.000 0.000
#> GSM11289 2 0.0000 0.996 0.000 1.000 0.000
#> GSM11280 2 0.0000 0.996 0.000 1.000 0.000
#> GSM28749 2 0.0000 0.996 0.000 1.000 0.000
#> GSM28750 3 0.0000 0.966 0.000 0.000 1.000
#> GSM11290 3 0.0000 0.966 0.000 0.000 1.000
#> GSM11294 3 0.0000 0.966 0.000 0.000 1.000
#> GSM28771 2 0.0000 0.996 0.000 1.000 0.000
#> GSM28760 2 0.1964 0.939 0.000 0.944 0.056
#> GSM28774 2 0.0000 0.996 0.000 1.000 0.000
#> GSM11284 2 0.0000 0.996 0.000 1.000 0.000
#> GSM28761 3 0.0000 0.966 0.000 0.000 1.000
#> GSM11278 2 0.0000 0.996 0.000 1.000 0.000
#> GSM11291 3 0.0000 0.966 0.000 0.000 1.000
#> GSM11277 3 0.0000 0.966 0.000 0.000 1.000
#> GSM11272 3 0.0237 0.963 0.004 0.000 0.996
#> GSM11285 2 0.0000 0.996 0.000 1.000 0.000
#> GSM28753 2 0.0000 0.996 0.000 1.000 0.000
#> GSM28773 2 0.0000 0.996 0.000 1.000 0.000
#> GSM28765 2 0.0000 0.996 0.000 1.000 0.000
#> GSM28768 1 0.2537 0.882 0.920 0.080 0.000
#> GSM28754 2 0.0000 0.996 0.000 1.000 0.000
#> GSM28769 2 0.0000 0.996 0.000 1.000 0.000
#> GSM11275 1 0.0000 0.990 1.000 0.000 0.000
#> GSM11270 2 0.0000 0.996 0.000 1.000 0.000
#> GSM11271 2 0.0000 0.996 0.000 1.000 0.000
#> GSM11288 3 0.7930 0.578 0.172 0.164 0.664
#> GSM11273 3 0.0000 0.966 0.000 0.000 1.000
#> GSM28757 2 0.0000 0.996 0.000 1.000 0.000
#> GSM11282 2 0.0000 0.996 0.000 1.000 0.000
#> GSM28756 2 0.0000 0.996 0.000 1.000 0.000
#> GSM11276 2 0.0000 0.996 0.000 1.000 0.000
#> GSM28752 2 0.0000 0.996 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.0188 0.932 0.000 0.996 0.000 0.004
#> GSM28763 2 0.0707 0.924 0.000 0.980 0.000 0.020
#> GSM28764 2 0.0188 0.933 0.000 0.996 0.000 0.004
#> GSM11274 3 0.0469 0.785 0.000 0.000 0.988 0.012
#> GSM28772 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM11292 2 0.1211 0.909 0.000 0.960 0.000 0.040
#> GSM28766 2 0.1389 0.900 0.000 0.952 0.000 0.048
#> GSM11268 3 0.4992 0.588 0.000 0.000 0.524 0.476
#> GSM28767 2 0.0336 0.932 0.000 0.992 0.000 0.008
#> GSM11286 2 0.0336 0.932 0.000 0.992 0.000 0.008
#> GSM28751 2 0.2924 0.792 0.100 0.884 0.000 0.016
#> GSM28770 2 0.0188 0.933 0.000 0.996 0.000 0.004
#> GSM11283 4 0.4843 0.559 0.000 0.396 0.000 0.604
#> GSM11289 2 0.1211 0.904 0.000 0.960 0.000 0.040
#> GSM11280 4 0.4564 0.619 0.000 0.328 0.000 0.672
#> GSM28749 4 0.4804 0.394 0.000 0.384 0.000 0.616
#> GSM28750 3 0.4866 0.638 0.000 0.000 0.596 0.404
#> GSM11290 3 0.0000 0.790 0.000 0.000 1.000 0.000
#> GSM11294 3 0.0000 0.790 0.000 0.000 1.000 0.000
#> GSM28771 4 0.4313 0.614 0.000 0.260 0.004 0.736
#> GSM28760 4 0.5229 0.356 0.000 0.084 0.168 0.748
#> GSM28774 2 0.0188 0.932 0.000 0.996 0.000 0.004
#> GSM11284 2 0.4331 0.350 0.000 0.712 0.000 0.288
#> GSM28761 3 0.5165 0.573 0.000 0.004 0.512 0.484
#> GSM11278 2 0.1059 0.920 0.000 0.972 0.012 0.016
#> GSM11291 3 0.0000 0.790 0.000 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.790 0.000 0.000 1.000 0.000
#> GSM11272 3 0.4955 0.616 0.000 0.000 0.556 0.444
#> GSM11285 4 0.4916 0.517 0.000 0.424 0.000 0.576
#> GSM28753 4 0.4985 0.446 0.000 0.468 0.000 0.532
#> GSM28773 4 0.4981 0.247 0.000 0.464 0.000 0.536
#> GSM28765 2 0.0817 0.924 0.000 0.976 0.000 0.024
#> GSM28768 1 0.0336 0.989 0.992 0.008 0.000 0.000
#> GSM28754 2 0.0188 0.932 0.000 0.996 0.000 0.004
#> GSM28769 2 0.2814 0.781 0.000 0.868 0.000 0.132
#> GSM11275 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM11270 2 0.3335 0.746 0.000 0.856 0.128 0.016
#> GSM11271 2 0.0336 0.932 0.000 0.992 0.000 0.008
#> GSM11288 4 0.6091 -0.126 0.124 0.004 0.180 0.692
#> GSM11273 3 0.0469 0.785 0.000 0.000 0.988 0.012
#> GSM28757 2 0.0336 0.932 0.000 0.992 0.000 0.008
#> GSM11282 2 0.0937 0.923 0.000 0.976 0.012 0.012
#> GSM28756 2 0.0188 0.932 0.000 0.996 0.000 0.004
#> GSM11276 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM28752 2 0.0707 0.926 0.000 0.980 0.000 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28762 2 0.0898 0.938 0.000 0.972 0.000 0.020 0.008
#> GSM28763 2 0.0880 0.934 0.000 0.968 0.000 0.032 0.000
#> GSM28764 2 0.0671 0.939 0.000 0.980 0.000 0.004 0.016
#> GSM11274 3 0.0162 0.978 0.000 0.000 0.996 0.000 0.004
#> GSM28772 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM11292 2 0.0955 0.936 0.000 0.968 0.000 0.004 0.028
#> GSM28766 2 0.1430 0.925 0.000 0.944 0.000 0.004 0.052
#> GSM11268 5 0.0290 0.967 0.000 0.000 0.008 0.000 0.992
#> GSM28767 2 0.0451 0.940 0.000 0.988 0.000 0.004 0.008
#> GSM11286 2 0.1043 0.936 0.000 0.960 0.000 0.000 0.040
#> GSM28751 2 0.3458 0.817 0.120 0.840 0.000 0.016 0.024
#> GSM28770 2 0.0162 0.939 0.000 0.996 0.000 0.004 0.000
#> GSM11283 4 0.0000 0.865 0.000 0.000 0.000 1.000 0.000
#> GSM11289 2 0.1544 0.901 0.000 0.932 0.000 0.068 0.000
#> GSM11280 4 0.0898 0.858 0.000 0.008 0.000 0.972 0.020
#> GSM28749 5 0.0880 0.947 0.000 0.032 0.000 0.000 0.968
#> GSM28750 5 0.1478 0.925 0.000 0.000 0.064 0.000 0.936
#> GSM11290 3 0.1043 0.974 0.000 0.000 0.960 0.000 0.040
#> GSM11294 3 0.0703 0.986 0.000 0.000 0.976 0.000 0.024
#> GSM28771 4 0.0000 0.865 0.000 0.000 0.000 1.000 0.000
#> GSM28760 4 0.0000 0.865 0.000 0.000 0.000 1.000 0.000
#> GSM28774 2 0.0451 0.938 0.000 0.988 0.008 0.000 0.004
#> GSM11284 4 0.4415 0.162 0.000 0.444 0.000 0.552 0.004
#> GSM28761 5 0.0290 0.967 0.000 0.000 0.008 0.000 0.992
#> GSM11278 2 0.2017 0.894 0.000 0.912 0.080 0.000 0.008
#> GSM11291 3 0.0703 0.986 0.000 0.000 0.976 0.000 0.024
#> GSM11277 3 0.0703 0.986 0.000 0.000 0.976 0.000 0.024
#> GSM11272 5 0.0609 0.963 0.000 0.000 0.020 0.000 0.980
#> GSM11285 4 0.0162 0.865 0.000 0.004 0.000 0.996 0.000
#> GSM28753 4 0.2069 0.809 0.000 0.076 0.000 0.912 0.012
#> GSM28773 5 0.0880 0.947 0.000 0.032 0.000 0.000 0.968
#> GSM28765 2 0.0963 0.937 0.000 0.964 0.000 0.000 0.036
#> GSM28768 1 0.0404 0.983 0.988 0.012 0.000 0.000 0.000
#> GSM28754 2 0.0693 0.937 0.000 0.980 0.008 0.000 0.012
#> GSM28769 2 0.4734 0.672 0.000 0.724 0.000 0.088 0.188
#> GSM11275 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM11270 2 0.3980 0.636 0.000 0.708 0.284 0.000 0.008
#> GSM11271 2 0.0162 0.939 0.000 0.996 0.000 0.004 0.000
#> GSM11288 5 0.0740 0.965 0.000 0.008 0.004 0.008 0.980
#> GSM11273 3 0.0162 0.973 0.000 0.004 0.996 0.000 0.000
#> GSM28757 2 0.0880 0.936 0.000 0.968 0.000 0.000 0.032
#> GSM11282 2 0.1408 0.921 0.000 0.948 0.044 0.000 0.008
#> GSM28756 2 0.0290 0.938 0.000 0.992 0.000 0.000 0.008
#> GSM11276 2 0.0162 0.939 0.000 0.996 0.000 0.004 0.000
#> GSM28752 2 0.0510 0.939 0.000 0.984 0.000 0.000 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 5 0.3995 -0.2367 0.000 0.480 0.000 0.000 0.516 0.004
#> GSM28763 2 0.4058 0.5827 0.000 0.616 0.000 0.008 0.372 0.004
#> GSM28764 5 0.1007 0.8001 0.000 0.044 0.000 0.000 0.956 0.000
#> GSM11274 3 0.0547 0.9653 0.000 0.020 0.980 0.000 0.000 0.000
#> GSM28772 1 0.0000 0.9789 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0146 0.9785 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.9789 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0146 0.9785 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.9789 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.9789 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0146 0.9785 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.9789 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.9789 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0146 0.9785 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM11292 5 0.0777 0.7901 0.000 0.004 0.000 0.000 0.972 0.024
#> GSM28766 5 0.2743 0.6653 0.000 0.008 0.000 0.000 0.828 0.164
#> GSM11268 6 0.0713 0.8836 0.000 0.028 0.000 0.000 0.000 0.972
#> GSM28767 5 0.0547 0.8040 0.000 0.020 0.000 0.000 0.980 0.000
#> GSM11286 2 0.2744 0.7344 0.000 0.840 0.000 0.000 0.144 0.016
#> GSM28751 5 0.4594 0.6265 0.056 0.236 0.000 0.000 0.692 0.016
#> GSM28770 5 0.0547 0.8033 0.000 0.020 0.000 0.000 0.980 0.000
#> GSM11283 4 0.0000 0.7860 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11289 5 0.0692 0.7902 0.000 0.004 0.000 0.020 0.976 0.000
#> GSM11280 4 0.3717 0.6505 0.000 0.276 0.000 0.708 0.000 0.016
#> GSM28749 6 0.3161 0.7797 0.000 0.216 0.000 0.000 0.008 0.776
#> GSM28750 6 0.1321 0.8735 0.000 0.024 0.020 0.000 0.004 0.952
#> GSM11290 3 0.0865 0.9698 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM11294 3 0.0547 0.9789 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM28771 4 0.0000 0.7860 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM28760 4 0.0000 0.7860 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM28774 2 0.3547 0.7617 0.000 0.668 0.000 0.000 0.332 0.000
#> GSM11284 4 0.5167 0.0635 0.000 0.412 0.000 0.500 0.088 0.000
#> GSM28761 6 0.0547 0.8847 0.000 0.020 0.000 0.000 0.000 0.980
#> GSM11278 2 0.4764 0.7485 0.000 0.640 0.088 0.000 0.272 0.000
#> GSM11291 3 0.0547 0.9789 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM11277 3 0.0458 0.9788 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM11272 6 0.1321 0.8719 0.000 0.024 0.004 0.000 0.020 0.952
#> GSM11285 4 0.0146 0.7849 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM28753 4 0.5643 0.5382 0.000 0.140 0.000 0.624 0.200 0.036
#> GSM28773 6 0.4178 0.6082 0.000 0.372 0.000 0.000 0.020 0.608
#> GSM28765 2 0.4252 0.6108 0.000 0.604 0.000 0.000 0.372 0.024
#> GSM28768 1 0.3088 0.7541 0.808 0.172 0.000 0.000 0.020 0.000
#> GSM28754 2 0.3290 0.7765 0.000 0.744 0.000 0.000 0.252 0.004
#> GSM28769 5 0.5100 0.5949 0.008 0.220 0.000 0.012 0.668 0.092
#> GSM11275 1 0.0146 0.9785 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM11270 2 0.4845 0.5847 0.000 0.628 0.280 0.000 0.092 0.000
#> GSM11271 5 0.1075 0.7984 0.000 0.048 0.000 0.000 0.952 0.000
#> GSM11288 6 0.1138 0.8832 0.000 0.024 0.004 0.000 0.012 0.960
#> GSM11273 3 0.0777 0.9604 0.000 0.024 0.972 0.000 0.004 0.000
#> GSM28757 2 0.2432 0.7046 0.000 0.876 0.000 0.000 0.100 0.024
#> GSM11282 2 0.4670 0.7558 0.000 0.636 0.072 0.000 0.292 0.000
#> GSM28756 2 0.3714 0.7568 0.000 0.656 0.000 0.000 0.340 0.004
#> GSM11276 5 0.1444 0.7870 0.000 0.072 0.000 0.000 0.928 0.000
#> GSM28752 5 0.2340 0.7292 0.000 0.148 0.000 0.000 0.852 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 tissue(p) k
#> SD:NMF 54 0.398 2
#> SD:NMF 54 0.374 3
#> SD:NMF 48 0.510 4
#> SD:NMF 53 0.440 5
#> SD:NMF 52 0.430 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.988 0.986 0.3343 0.669 0.669
#> 3 3 0.863 0.912 0.951 0.6661 0.786 0.681
#> 4 4 0.767 0.871 0.892 0.1742 0.855 0.681
#> 5 5 0.799 0.873 0.912 0.0671 0.980 0.938
#> 6 6 0.789 0.704 0.750 0.0866 0.957 0.867
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
#> GSM28762 2 0.1843 0.988 0.028 0.972
#> GSM28763 2 0.1843 0.988 0.028 0.972
#> GSM28764 2 0.1843 0.988 0.028 0.972
#> GSM11274 2 0.0000 0.982 0.000 1.000
#> GSM28772 1 0.0000 0.999 1.000 0.000
#> GSM11269 1 0.0000 0.999 1.000 0.000
#> GSM28775 1 0.0000 0.999 1.000 0.000
#> GSM11293 1 0.0000 0.999 1.000 0.000
#> GSM28755 1 0.0000 0.999 1.000 0.000
#> GSM11279 1 0.0000 0.999 1.000 0.000
#> GSM28758 1 0.0376 0.996 0.996 0.004
#> GSM11281 1 0.0000 0.999 1.000 0.000
#> GSM11287 1 0.0000 0.999 1.000 0.000
#> GSM28759 1 0.0000 0.999 1.000 0.000
#> GSM11292 2 0.1843 0.988 0.028 0.972
#> GSM28766 2 0.1843 0.988 0.028 0.972
#> GSM11268 2 0.0000 0.982 0.000 1.000
#> GSM28767 2 0.1843 0.988 0.028 0.972
#> GSM11286 2 0.1843 0.988 0.028 0.972
#> GSM28751 2 0.1843 0.988 0.028 0.972
#> GSM28770 2 0.1843 0.988 0.028 0.972
#> GSM11283 2 0.0000 0.982 0.000 1.000
#> GSM11289 2 0.1843 0.988 0.028 0.972
#> GSM11280 2 0.1843 0.988 0.028 0.972
#> GSM28749 2 0.1843 0.988 0.028 0.972
#> GSM28750 2 0.0000 0.982 0.000 1.000
#> GSM11290 2 0.0000 0.982 0.000 1.000
#> GSM11294 2 0.0000 0.982 0.000 1.000
#> GSM28771 2 0.0000 0.982 0.000 1.000
#> GSM28760 2 0.0000 0.982 0.000 1.000
#> GSM28774 2 0.1843 0.988 0.028 0.972
#> GSM11284 2 0.1843 0.988 0.028 0.972
#> GSM28761 2 0.0000 0.982 0.000 1.000
#> GSM11278 2 0.0000 0.982 0.000 1.000
#> GSM11291 2 0.0000 0.982 0.000 1.000
#> GSM11277 2 0.0000 0.982 0.000 1.000
#> GSM11272 2 0.0000 0.982 0.000 1.000
#> GSM11285 2 0.0000 0.982 0.000 1.000
#> GSM28753 2 0.1843 0.988 0.028 0.972
#> GSM28773 2 0.1843 0.988 0.028 0.972
#> GSM28765 2 0.1843 0.988 0.028 0.972
#> GSM28768 2 0.2603 0.976 0.044 0.956
#> GSM28754 2 0.1843 0.988 0.028 0.972
#> GSM28769 2 0.1843 0.988 0.028 0.972
#> GSM11275 1 0.0376 0.996 0.996 0.004
#> GSM11270 2 0.0000 0.982 0.000 1.000
#> GSM11271 2 0.1843 0.988 0.028 0.972
#> GSM11288 2 0.1843 0.988 0.028 0.972
#> GSM11273 2 0.0000 0.982 0.000 1.000
#> GSM28757 2 0.1843 0.988 0.028 0.972
#> GSM11282 2 0.0000 0.982 0.000 1.000
#> GSM28756 2 0.1843 0.988 0.028 0.972
#> GSM11276 2 0.1843 0.988 0.028 0.972
#> GSM28752 2 0.1843 0.988 0.028 0.972
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.0237 0.941 0.000 0.996 0.004
#> GSM28763 2 0.0237 0.941 0.000 0.996 0.004
#> GSM28764 2 0.0424 0.941 0.000 0.992 0.008
#> GSM11274 3 0.7050 0.292 0.028 0.372 0.600
#> GSM28772 1 0.1163 0.999 0.972 0.028 0.000
#> GSM11269 1 0.1163 0.999 0.972 0.028 0.000
#> GSM28775 1 0.1163 0.999 0.972 0.028 0.000
#> GSM11293 1 0.1163 0.999 0.972 0.028 0.000
#> GSM28755 1 0.1163 0.999 0.972 0.028 0.000
#> GSM11279 1 0.1163 0.999 0.972 0.028 0.000
#> GSM28758 1 0.1289 0.995 0.968 0.032 0.000
#> GSM11281 1 0.1163 0.999 0.972 0.028 0.000
#> GSM11287 1 0.1163 0.999 0.972 0.028 0.000
#> GSM28759 1 0.1163 0.999 0.972 0.028 0.000
#> GSM11292 2 0.1643 0.926 0.000 0.956 0.044
#> GSM28766 2 0.1643 0.926 0.000 0.956 0.044
#> GSM11268 3 0.0237 0.931 0.000 0.004 0.996
#> GSM28767 2 0.1529 0.928 0.000 0.960 0.040
#> GSM11286 2 0.0237 0.941 0.000 0.996 0.004
#> GSM28751 2 0.0237 0.941 0.000 0.996 0.004
#> GSM28770 2 0.1643 0.926 0.000 0.956 0.044
#> GSM11283 2 0.1399 0.928 0.028 0.968 0.004
#> GSM11289 2 0.1643 0.926 0.000 0.956 0.044
#> GSM11280 2 0.0237 0.941 0.000 0.996 0.004
#> GSM28749 2 0.0237 0.941 0.000 0.996 0.004
#> GSM28750 3 0.0237 0.931 0.000 0.004 0.996
#> GSM11290 3 0.0237 0.931 0.000 0.004 0.996
#> GSM11294 3 0.0237 0.931 0.000 0.004 0.996
#> GSM28771 2 0.1399 0.928 0.028 0.968 0.004
#> GSM28760 2 0.1399 0.928 0.028 0.968 0.004
#> GSM28774 2 0.0000 0.940 0.000 1.000 0.000
#> GSM11284 2 0.0000 0.940 0.000 1.000 0.000
#> GSM28761 3 0.0237 0.931 0.000 0.004 0.996
#> GSM11278 2 0.6337 0.655 0.028 0.708 0.264
#> GSM11291 3 0.0237 0.931 0.000 0.004 0.996
#> GSM11277 3 0.0237 0.931 0.000 0.004 0.996
#> GSM11272 3 0.0237 0.931 0.000 0.004 0.996
#> GSM11285 2 0.1399 0.928 0.028 0.968 0.004
#> GSM28753 2 0.0237 0.941 0.000 0.996 0.004
#> GSM28773 2 0.2066 0.916 0.000 0.940 0.060
#> GSM28765 2 0.0237 0.941 0.000 0.996 0.004
#> GSM28768 2 0.0983 0.933 0.016 0.980 0.004
#> GSM28754 2 0.0237 0.941 0.000 0.996 0.004
#> GSM28769 2 0.0237 0.941 0.000 0.996 0.004
#> GSM11275 1 0.1289 0.995 0.968 0.032 0.000
#> GSM11270 2 0.6337 0.655 0.028 0.708 0.264
#> GSM11271 2 0.1411 0.930 0.000 0.964 0.036
#> GSM11288 2 0.4750 0.761 0.000 0.784 0.216
#> GSM11273 2 0.6337 0.655 0.028 0.708 0.264
#> GSM28757 2 0.0237 0.941 0.000 0.996 0.004
#> GSM11282 2 0.6108 0.692 0.028 0.732 0.240
#> GSM28756 2 0.0237 0.941 0.000 0.996 0.004
#> GSM11276 2 0.0237 0.941 0.000 0.996 0.004
#> GSM28752 2 0.0237 0.941 0.000 0.996 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.0000 0.935 0.000 1.000 0.000 0.000
#> GSM28763 2 0.0000 0.935 0.000 1.000 0.000 0.000
#> GSM28764 2 0.0524 0.931 0.000 0.988 0.004 0.008
#> GSM11274 3 0.5861 0.149 0.000 0.032 0.488 0.480
#> GSM28772 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0188 0.996 0.996 0.004 0.000 0.000
#> GSM11281 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM11292 2 0.2996 0.860 0.000 0.892 0.044 0.064
#> GSM28766 2 0.2996 0.860 0.000 0.892 0.044 0.064
#> GSM11268 3 0.3172 0.826 0.000 0.000 0.840 0.160
#> GSM28767 2 0.2586 0.881 0.000 0.912 0.040 0.048
#> GSM11286 2 0.0000 0.935 0.000 1.000 0.000 0.000
#> GSM28751 2 0.0000 0.935 0.000 1.000 0.000 0.000
#> GSM28770 2 0.2996 0.860 0.000 0.892 0.044 0.064
#> GSM11283 4 0.4406 0.748 0.000 0.300 0.000 0.700
#> GSM11289 2 0.2996 0.860 0.000 0.892 0.044 0.064
#> GSM11280 2 0.0000 0.935 0.000 1.000 0.000 0.000
#> GSM28749 2 0.0000 0.935 0.000 1.000 0.000 0.000
#> GSM28750 3 0.3123 0.827 0.000 0.000 0.844 0.156
#> GSM11290 3 0.1940 0.833 0.000 0.000 0.924 0.076
#> GSM11294 3 0.1940 0.833 0.000 0.000 0.924 0.076
#> GSM28771 4 0.4406 0.748 0.000 0.300 0.000 0.700
#> GSM28760 4 0.4406 0.748 0.000 0.300 0.000 0.700
#> GSM28774 2 0.1716 0.899 0.000 0.936 0.000 0.064
#> GSM11284 2 0.1716 0.899 0.000 0.936 0.000 0.064
#> GSM28761 3 0.3172 0.826 0.000 0.000 0.840 0.160
#> GSM11278 4 0.7205 0.716 0.000 0.344 0.152 0.504
#> GSM11291 3 0.1940 0.833 0.000 0.000 0.924 0.076
#> GSM11277 3 0.1940 0.833 0.000 0.000 0.924 0.076
#> GSM11272 3 0.3172 0.826 0.000 0.000 0.840 0.160
#> GSM11285 4 0.4406 0.748 0.000 0.300 0.000 0.700
#> GSM28753 2 0.0000 0.935 0.000 1.000 0.000 0.000
#> GSM28773 2 0.2466 0.859 0.000 0.916 0.056 0.028
#> GSM28765 2 0.0000 0.935 0.000 1.000 0.000 0.000
#> GSM28768 2 0.0592 0.921 0.016 0.984 0.000 0.000
#> GSM28754 2 0.0000 0.935 0.000 1.000 0.000 0.000
#> GSM28769 2 0.0000 0.935 0.000 1.000 0.000 0.000
#> GSM11275 1 0.0188 0.996 0.996 0.004 0.000 0.000
#> GSM11270 4 0.7205 0.716 0.000 0.344 0.152 0.504
#> GSM11271 2 0.2319 0.892 0.000 0.924 0.036 0.040
#> GSM11288 2 0.4086 0.591 0.000 0.776 0.216 0.008
#> GSM11273 4 0.7205 0.716 0.000 0.344 0.152 0.504
#> GSM28757 2 0.0000 0.935 0.000 1.000 0.000 0.000
#> GSM11282 4 0.7012 0.697 0.000 0.372 0.124 0.504
#> GSM28756 2 0.0000 0.935 0.000 1.000 0.000 0.000
#> GSM11276 2 0.0188 0.934 0.000 0.996 0.000 0.004
#> GSM28752 2 0.0000 0.935 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
#> GSM28762 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000
#> GSM28763 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000
#> GSM28764 2 0.0807 0.915 0.000 0.976 0.000 0.012 0.012
#> GSM11274 5 0.0000 0.149 0.000 0.000 0.000 0.000 1.000
#> GSM28772 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0162 0.995 0.996 0.004 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11292 2 0.3165 0.821 0.000 0.848 0.000 0.036 0.116
#> GSM28766 2 0.3165 0.821 0.000 0.848 0.000 0.036 0.116
#> GSM11268 3 0.0000 0.719 0.000 0.000 1.000 0.000 0.000
#> GSM28767 2 0.2574 0.850 0.000 0.876 0.000 0.012 0.112
#> GSM11286 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000
#> GSM28751 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000
#> GSM28770 2 0.3165 0.821 0.000 0.848 0.000 0.036 0.116
#> GSM11283 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM11289 2 0.3165 0.821 0.000 0.848 0.000 0.036 0.116
#> GSM11280 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000
#> GSM28749 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000
#> GSM28750 3 0.0162 0.719 0.000 0.000 0.996 0.000 0.004
#> GSM11290 3 0.4302 0.709 0.000 0.000 0.520 0.000 0.480
#> GSM11294 3 0.4305 0.706 0.000 0.000 0.512 0.000 0.488
#> GSM28771 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM28760 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM28774 2 0.2554 0.864 0.000 0.892 0.000 0.036 0.072
#> GSM11284 2 0.2554 0.864 0.000 0.892 0.000 0.036 0.072
#> GSM28761 3 0.0000 0.719 0.000 0.000 1.000 0.000 0.000
#> GSM11278 5 0.4677 0.845 0.000 0.300 0.000 0.036 0.664
#> GSM11291 3 0.4305 0.706 0.000 0.000 0.512 0.000 0.488
#> GSM11277 3 0.4305 0.706 0.000 0.000 0.512 0.000 0.488
#> GSM11272 3 0.0000 0.719 0.000 0.000 1.000 0.000 0.000
#> GSM11285 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM28753 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000
#> GSM28773 2 0.2313 0.858 0.000 0.912 0.044 0.004 0.040
#> GSM28765 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000
#> GSM28768 2 0.0510 0.911 0.016 0.984 0.000 0.000 0.000
#> GSM28754 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000
#> GSM28769 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000
#> GSM11275 1 0.0162 0.995 0.996 0.004 0.000 0.000 0.000
#> GSM11270 5 0.4677 0.845 0.000 0.300 0.000 0.036 0.664
#> GSM11271 2 0.2361 0.865 0.000 0.892 0.000 0.012 0.096
#> GSM11288 2 0.3628 0.639 0.000 0.772 0.216 0.000 0.012
#> GSM11273 5 0.4677 0.845 0.000 0.300 0.000 0.036 0.664
#> GSM28757 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000
#> GSM11282 5 0.4804 0.804 0.000 0.328 0.000 0.036 0.636
#> GSM28756 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000
#> GSM11276 2 0.0162 0.922 0.000 0.996 0.000 0.004 0.000
#> GSM28752 2 0.0000 0.923 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
#> GSM28762 5 0.4141 0.737 0.000 NA 0.000 0.000 0.556 0.012
#> GSM28763 5 0.4141 0.737 0.000 NA 0.000 0.000 0.556 0.012
#> GSM28764 5 0.2595 0.685 0.000 NA 0.000 0.000 0.836 0.004
#> GSM11274 4 0.5581 -0.126 0.000 NA 0.424 0.460 0.108 0.008
#> GSM28772 1 0.0000 0.999 1.000 NA 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.999 1.000 NA 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.999 1.000 NA 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.999 1.000 NA 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.999 1.000 NA 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.999 1.000 NA 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0146 0.995 0.996 NA 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.999 1.000 NA 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.999 1.000 NA 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.999 1.000 NA 0.000 0.000 0.000 0.000
#> GSM11292 5 0.0260 0.598 0.000 NA 0.000 0.008 0.992 0.000
#> GSM28766 5 0.0260 0.598 0.000 NA 0.000 0.008 0.992 0.000
#> GSM11268 6 0.3706 0.998 0.000 NA 0.380 0.000 0.000 0.620
#> GSM28767 5 0.0777 0.620 0.000 NA 0.000 0.004 0.972 0.000
#> GSM11286 5 0.4513 0.728 0.000 NA 0.000 0.000 0.528 0.032
#> GSM28751 5 0.4294 0.736 0.000 NA 0.000 0.000 0.552 0.020
#> GSM28770 5 0.0260 0.598 0.000 NA 0.000 0.008 0.992 0.000
#> GSM11283 4 0.3851 0.401 0.000 NA 0.000 0.540 0.000 0.000
#> GSM11289 5 0.0260 0.598 0.000 NA 0.000 0.008 0.992 0.000
#> GSM11280 5 0.4685 0.724 0.000 NA 0.000 0.000 0.520 0.044
#> GSM28749 5 0.4685 0.724 0.000 NA 0.000 0.000 0.520 0.044
#> GSM28750 6 0.3717 0.994 0.000 NA 0.384 0.000 0.000 0.616
#> GSM11290 3 0.0260 0.983 0.000 NA 0.992 0.000 0.000 0.008
#> GSM11294 3 0.0000 0.994 0.000 NA 1.000 0.000 0.000 0.000
#> GSM28771 4 0.3851 0.401 0.000 NA 0.000 0.540 0.000 0.000
#> GSM28760 4 0.3851 0.401 0.000 NA 0.000 0.540 0.000 0.000
#> GSM28774 5 0.0935 0.627 0.000 NA 0.000 0.000 0.964 0.004
#> GSM11284 5 0.0935 0.627 0.000 NA 0.000 0.000 0.964 0.004
#> GSM28761 6 0.3706 0.998 0.000 NA 0.380 0.000 0.000 0.620
#> GSM11278 4 0.5415 0.325 0.000 NA 0.088 0.460 0.444 0.008
#> GSM11291 3 0.0000 0.994 0.000 NA 1.000 0.000 0.000 0.000
#> GSM11277 3 0.0000 0.994 0.000 NA 1.000 0.000 0.000 0.000
#> GSM11272 6 0.3706 0.998 0.000 NA 0.380 0.000 0.000 0.620
#> GSM11285 4 0.3851 0.401 0.000 NA 0.000 0.540 0.000 0.000
#> GSM28753 5 0.4218 0.737 0.000 NA 0.000 0.000 0.556 0.016
#> GSM28773 5 0.5718 0.046 0.000 NA 0.000 0.000 0.440 0.396
#> GSM28765 5 0.3409 0.732 0.000 NA 0.000 0.000 0.700 0.000
#> GSM28768 5 0.5182 0.713 0.016 NA 0.000 0.000 0.504 0.052
#> GSM28754 5 0.3409 0.732 0.000 NA 0.000 0.000 0.700 0.000
#> GSM28769 5 0.4294 0.736 0.000 NA 0.000 0.000 0.552 0.020
#> GSM11275 1 0.0146 0.995 0.996 NA 0.000 0.000 0.000 0.000
#> GSM11270 4 0.5415 0.325 0.000 NA 0.088 0.460 0.444 0.008
#> GSM11271 5 0.0865 0.630 0.000 NA 0.000 0.000 0.964 0.000
#> GSM11288 5 0.7215 0.513 0.000 NA 0.120 0.000 0.400 0.184
#> GSM11273 4 0.5415 0.325 0.000 NA 0.088 0.460 0.444 0.008
#> GSM28757 5 0.4685 0.724 0.000 NA 0.000 0.000 0.520 0.044
#> GSM11282 5 0.5129 -0.471 0.000 NA 0.060 0.460 0.472 0.008
#> GSM28756 5 0.3409 0.732 0.000 NA 0.000 0.000 0.700 0.000
#> GSM11276 5 0.3923 0.741 0.000 NA 0.000 0.000 0.580 0.004
#> GSM28752 5 0.3950 0.738 0.000 NA 0.000 0.000 0.564 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 tissue(p) k
#> CV:hclust 54 0.398 2
#> CV:hclust 53 0.373 3
#> CV:hclust 53 0.447 4
#> CV:hclust 53 0.480 5
#> CV:hclust 44 0.410 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.443 0.830 0.861 0.3419 0.669 0.669
#> 3 3 0.955 0.963 0.956 0.6241 0.769 0.656
#> 4 4 0.715 0.736 0.861 0.2103 0.919 0.815
#> 5 5 0.707 0.794 0.832 0.1168 0.843 0.571
#> 6 6 0.695 0.668 0.792 0.0593 0.974 0.886
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
#> GSM28762 2 0.891 0.867 0.308 0.692
#> GSM28763 2 0.891 0.867 0.308 0.692
#> GSM28764 2 0.891 0.867 0.308 0.692
#> GSM11274 2 0.000 0.610 0.000 1.000
#> GSM28772 1 0.000 1.000 1.000 0.000
#> GSM11269 1 0.000 1.000 1.000 0.000
#> GSM28775 1 0.000 1.000 1.000 0.000
#> GSM11293 1 0.000 1.000 1.000 0.000
#> GSM28755 1 0.000 1.000 1.000 0.000
#> GSM11279 1 0.000 1.000 1.000 0.000
#> GSM28758 1 0.000 1.000 1.000 0.000
#> GSM11281 1 0.000 1.000 1.000 0.000
#> GSM11287 1 0.000 1.000 1.000 0.000
#> GSM28759 1 0.000 1.000 1.000 0.000
#> GSM11292 2 0.891 0.867 0.308 0.692
#> GSM28766 2 0.891 0.867 0.308 0.692
#> GSM11268 2 0.494 0.513 0.108 0.892
#> GSM28767 2 0.891 0.867 0.308 0.692
#> GSM11286 2 0.891 0.867 0.308 0.692
#> GSM28751 2 0.891 0.867 0.308 0.692
#> GSM28770 2 0.891 0.867 0.308 0.692
#> GSM11283 2 0.891 0.867 0.308 0.692
#> GSM11289 2 0.891 0.867 0.308 0.692
#> GSM11280 2 0.891 0.867 0.308 0.692
#> GSM28749 2 0.891 0.867 0.308 0.692
#> GSM28750 2 0.494 0.513 0.108 0.892
#> GSM11290 2 0.494 0.513 0.108 0.892
#> GSM11294 2 0.494 0.513 0.108 0.892
#> GSM28771 2 0.881 0.863 0.300 0.700
#> GSM28760 2 0.844 0.846 0.272 0.728
#> GSM28774 2 0.891 0.867 0.308 0.692
#> GSM11284 2 0.891 0.867 0.308 0.692
#> GSM28761 2 0.494 0.513 0.108 0.892
#> GSM11278 2 0.844 0.846 0.272 0.728
#> GSM11291 2 0.494 0.513 0.108 0.892
#> GSM11277 2 0.494 0.513 0.108 0.892
#> GSM11272 2 0.494 0.513 0.108 0.892
#> GSM11285 2 0.881 0.863 0.300 0.700
#> GSM28753 2 0.891 0.867 0.308 0.692
#> GSM28773 2 0.886 0.865 0.304 0.696
#> GSM28765 2 0.891 0.867 0.308 0.692
#> GSM28768 2 0.891 0.867 0.308 0.692
#> GSM28754 2 0.891 0.867 0.308 0.692
#> GSM28769 2 0.891 0.867 0.308 0.692
#> GSM11275 1 0.000 1.000 1.000 0.000
#> GSM11270 2 0.844 0.846 0.272 0.728
#> GSM11271 2 0.891 0.867 0.308 0.692
#> GSM11288 2 0.891 0.867 0.308 0.692
#> GSM11273 2 0.000 0.610 0.000 1.000
#> GSM28757 2 0.891 0.867 0.308 0.692
#> GSM11282 2 0.844 0.846 0.272 0.728
#> GSM28756 2 0.891 0.867 0.308 0.692
#> GSM11276 2 0.891 0.867 0.308 0.692
#> GSM28752 2 0.891 0.867 0.308 0.692
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.0000 0.970 0.000 1.000 0.000
#> GSM28763 2 0.0000 0.970 0.000 1.000 0.000
#> GSM28764 2 0.0000 0.970 0.000 1.000 0.000
#> GSM11274 3 0.1860 0.975 0.000 0.052 0.948
#> GSM28772 1 0.1964 1.000 0.944 0.056 0.000
#> GSM11269 1 0.1964 1.000 0.944 0.056 0.000
#> GSM28775 1 0.1964 1.000 0.944 0.056 0.000
#> GSM11293 1 0.1964 1.000 0.944 0.056 0.000
#> GSM28755 1 0.1964 1.000 0.944 0.056 0.000
#> GSM11279 1 0.1964 1.000 0.944 0.056 0.000
#> GSM28758 1 0.1964 1.000 0.944 0.056 0.000
#> GSM11281 1 0.1964 1.000 0.944 0.056 0.000
#> GSM11287 1 0.1964 1.000 0.944 0.056 0.000
#> GSM28759 1 0.1964 1.000 0.944 0.056 0.000
#> GSM11292 2 0.0237 0.969 0.000 0.996 0.004
#> GSM28766 2 0.0237 0.969 0.000 0.996 0.004
#> GSM11268 3 0.3009 0.988 0.028 0.052 0.920
#> GSM28767 2 0.0237 0.969 0.000 0.996 0.004
#> GSM11286 2 0.0000 0.970 0.000 1.000 0.000
#> GSM28751 2 0.0000 0.970 0.000 1.000 0.000
#> GSM28770 2 0.0237 0.969 0.000 0.996 0.004
#> GSM11283 2 0.3983 0.885 0.048 0.884 0.068
#> GSM11289 2 0.0237 0.969 0.000 0.996 0.004
#> GSM11280 2 0.0424 0.965 0.000 0.992 0.008
#> GSM28749 2 0.0000 0.970 0.000 1.000 0.000
#> GSM28750 3 0.3009 0.988 0.028 0.052 0.920
#> GSM11290 3 0.2743 0.988 0.020 0.052 0.928
#> GSM11294 3 0.2743 0.988 0.020 0.052 0.928
#> GSM28771 2 0.4165 0.879 0.048 0.876 0.076
#> GSM28760 2 0.6606 0.689 0.048 0.716 0.236
#> GSM28774 2 0.0237 0.969 0.000 0.996 0.004
#> GSM11284 2 0.2564 0.926 0.036 0.936 0.028
#> GSM28761 3 0.3009 0.988 0.028 0.052 0.920
#> GSM11278 2 0.0747 0.963 0.000 0.984 0.016
#> GSM11291 3 0.2743 0.988 0.020 0.052 0.928
#> GSM11277 3 0.2743 0.988 0.020 0.052 0.928
#> GSM11272 3 0.3009 0.988 0.028 0.052 0.920
#> GSM11285 2 0.4165 0.882 0.048 0.876 0.076
#> GSM28753 2 0.0000 0.970 0.000 1.000 0.000
#> GSM28773 2 0.0237 0.968 0.004 0.996 0.000
#> GSM28765 2 0.0000 0.970 0.000 1.000 0.000
#> GSM28768 2 0.0000 0.970 0.000 1.000 0.000
#> GSM28754 2 0.0237 0.969 0.000 0.996 0.004
#> GSM28769 2 0.0000 0.970 0.000 1.000 0.000
#> GSM11275 1 0.1964 1.000 0.944 0.056 0.000
#> GSM11270 2 0.0747 0.963 0.000 0.984 0.016
#> GSM11271 2 0.0237 0.969 0.000 0.996 0.004
#> GSM11288 2 0.4629 0.753 0.004 0.808 0.188
#> GSM11273 3 0.2711 0.945 0.000 0.088 0.912
#> GSM28757 2 0.0000 0.970 0.000 1.000 0.000
#> GSM11282 2 0.0747 0.963 0.000 0.984 0.016
#> GSM28756 2 0.0237 0.969 0.000 0.996 0.004
#> GSM11276 2 0.0000 0.970 0.000 1.000 0.000
#> GSM28752 2 0.0000 0.970 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.2011 0.684 0.000 0.920 0.000 0.080
#> GSM28763 2 0.2011 0.684 0.000 0.920 0.000 0.080
#> GSM28764 2 0.2345 0.698 0.000 0.900 0.000 0.100
#> GSM11274 3 0.2081 0.838 0.000 0.000 0.916 0.084
#> GSM28772 1 0.0592 0.983 0.984 0.016 0.000 0.000
#> GSM11269 1 0.0592 0.983 0.984 0.016 0.000 0.000
#> GSM28775 1 0.0927 0.981 0.976 0.016 0.000 0.008
#> GSM11293 1 0.1406 0.978 0.960 0.016 0.000 0.024
#> GSM28755 1 0.1182 0.978 0.968 0.016 0.000 0.016
#> GSM11279 1 0.0927 0.981 0.976 0.016 0.000 0.008
#> GSM28758 1 0.2522 0.951 0.908 0.016 0.000 0.076
#> GSM11281 1 0.0592 0.983 0.984 0.016 0.000 0.000
#> GSM11287 1 0.0592 0.983 0.984 0.016 0.000 0.000
#> GSM28759 1 0.1406 0.978 0.960 0.016 0.000 0.024
#> GSM11292 2 0.4431 0.546 0.000 0.696 0.000 0.304
#> GSM28766 2 0.4431 0.546 0.000 0.696 0.000 0.304
#> GSM11268 3 0.2987 0.877 0.016 0.000 0.880 0.104
#> GSM28767 2 0.4431 0.546 0.000 0.696 0.000 0.304
#> GSM11286 2 0.1022 0.705 0.000 0.968 0.000 0.032
#> GSM28751 2 0.2011 0.684 0.000 0.920 0.000 0.080
#> GSM28770 2 0.4431 0.546 0.000 0.696 0.000 0.304
#> GSM11283 4 0.4713 0.781 0.000 0.360 0.000 0.640
#> GSM11289 2 0.4431 0.546 0.000 0.696 0.000 0.304
#> GSM11280 2 0.2216 0.676 0.000 0.908 0.000 0.092
#> GSM28749 2 0.2149 0.680 0.000 0.912 0.000 0.088
#> GSM28750 3 0.2987 0.877 0.016 0.000 0.880 0.104
#> GSM11290 3 0.0000 0.883 0.000 0.000 1.000 0.000
#> GSM11294 3 0.0592 0.883 0.000 0.000 0.984 0.016
#> GSM28771 4 0.4585 0.823 0.000 0.332 0.000 0.668
#> GSM28760 4 0.4574 0.820 0.000 0.220 0.024 0.756
#> GSM28774 2 0.3266 0.665 0.000 0.832 0.000 0.168
#> GSM11284 2 0.4790 0.328 0.000 0.620 0.000 0.380
#> GSM28761 3 0.2987 0.877 0.016 0.000 0.880 0.104
#> GSM11278 2 0.4781 0.489 0.000 0.660 0.004 0.336
#> GSM11291 3 0.0592 0.883 0.000 0.000 0.984 0.016
#> GSM11277 3 0.0592 0.883 0.000 0.000 0.984 0.016
#> GSM11272 3 0.2987 0.877 0.016 0.000 0.880 0.104
#> GSM11285 4 0.3837 0.780 0.000 0.224 0.000 0.776
#> GSM28753 2 0.2011 0.684 0.000 0.920 0.000 0.080
#> GSM28773 2 0.2922 0.658 0.004 0.884 0.008 0.104
#> GSM28765 2 0.0188 0.712 0.000 0.996 0.000 0.004
#> GSM28768 2 0.2814 0.632 0.000 0.868 0.000 0.132
#> GSM28754 2 0.2345 0.698 0.000 0.900 0.000 0.100
#> GSM28769 2 0.2011 0.684 0.000 0.920 0.000 0.080
#> GSM11275 1 0.2522 0.951 0.908 0.016 0.000 0.076
#> GSM11270 2 0.4781 0.489 0.000 0.660 0.004 0.336
#> GSM11271 2 0.4277 0.572 0.000 0.720 0.000 0.280
#> GSM11288 2 0.5962 0.342 0.004 0.696 0.200 0.100
#> GSM11273 3 0.7054 0.120 0.000 0.144 0.536 0.320
#> GSM28757 2 0.0336 0.712 0.000 0.992 0.000 0.008
#> GSM11282 2 0.4781 0.489 0.000 0.660 0.004 0.336
#> GSM28756 2 0.2760 0.687 0.000 0.872 0.000 0.128
#> GSM11276 2 0.0921 0.711 0.000 0.972 0.000 0.028
#> GSM28752 2 0.0188 0.712 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
#> GSM28762 2 0.0324 0.8608 0.000 0.992 0.000 0.004 0.004
#> GSM28763 2 0.0324 0.8608 0.000 0.992 0.000 0.004 0.004
#> GSM28764 2 0.4734 0.0195 0.000 0.652 0.000 0.036 0.312
#> GSM11274 3 0.5423 0.7771 0.000 0.000 0.644 0.112 0.244
#> GSM28772 1 0.0162 0.9585 0.996 0.000 0.000 0.004 0.000
#> GSM11269 1 0.0162 0.9585 0.996 0.000 0.000 0.004 0.000
#> GSM28775 1 0.1012 0.9503 0.968 0.000 0.000 0.012 0.020
#> GSM11293 1 0.1818 0.9427 0.932 0.000 0.000 0.044 0.024
#> GSM28755 1 0.1117 0.9489 0.964 0.000 0.000 0.016 0.020
#> GSM11279 1 0.0451 0.9579 0.988 0.000 0.000 0.008 0.004
#> GSM28758 1 0.3169 0.9026 0.856 0.000 0.000 0.084 0.060
#> GSM11281 1 0.0324 0.9584 0.992 0.000 0.000 0.004 0.004
#> GSM11287 1 0.0162 0.9585 0.996 0.000 0.000 0.004 0.000
#> GSM28759 1 0.1818 0.9427 0.932 0.000 0.000 0.044 0.024
#> GSM11292 5 0.5268 0.8051 0.000 0.320 0.000 0.068 0.612
#> GSM28766 5 0.5268 0.8051 0.000 0.320 0.000 0.068 0.612
#> GSM11268 3 0.0000 0.8645 0.000 0.000 1.000 0.000 0.000
#> GSM28767 5 0.5268 0.8051 0.000 0.320 0.000 0.068 0.612
#> GSM11286 2 0.1211 0.8556 0.000 0.960 0.000 0.016 0.024
#> GSM28751 2 0.0162 0.8603 0.000 0.996 0.000 0.004 0.000
#> GSM28770 5 0.5268 0.8051 0.000 0.320 0.000 0.068 0.612
#> GSM11283 4 0.4591 0.9264 0.000 0.132 0.000 0.748 0.120
#> GSM11289 5 0.5268 0.8051 0.000 0.320 0.000 0.068 0.612
#> GSM11280 2 0.1041 0.8517 0.000 0.964 0.000 0.032 0.004
#> GSM28749 2 0.1026 0.8532 0.000 0.968 0.004 0.024 0.004
#> GSM28750 3 0.0000 0.8645 0.000 0.000 1.000 0.000 0.000
#> GSM11290 3 0.4020 0.8761 0.000 0.000 0.796 0.108 0.096
#> GSM11294 3 0.4406 0.8747 0.000 0.000 0.764 0.108 0.128
#> GSM28771 4 0.4593 0.9352 0.000 0.124 0.000 0.748 0.128
#> GSM28760 4 0.4718 0.9316 0.000 0.092 0.000 0.728 0.180
#> GSM28774 5 0.4415 0.5715 0.000 0.444 0.000 0.004 0.552
#> GSM11284 5 0.6569 0.5222 0.000 0.272 0.000 0.256 0.472
#> GSM28761 3 0.0000 0.8645 0.000 0.000 1.000 0.000 0.000
#> GSM11278 5 0.3231 0.7358 0.000 0.196 0.000 0.004 0.800
#> GSM11291 3 0.4406 0.8747 0.000 0.000 0.764 0.108 0.128
#> GSM11277 3 0.4406 0.8747 0.000 0.000 0.764 0.108 0.128
#> GSM11272 3 0.0000 0.8645 0.000 0.000 1.000 0.000 0.000
#> GSM11285 4 0.4555 0.9066 0.000 0.068 0.000 0.732 0.200
#> GSM28753 2 0.0290 0.8601 0.000 0.992 0.000 0.008 0.000
#> GSM28773 2 0.2430 0.8186 0.000 0.912 0.020 0.040 0.028
#> GSM28765 2 0.0955 0.8512 0.000 0.968 0.000 0.004 0.028
#> GSM28768 2 0.2438 0.8052 0.000 0.900 0.000 0.060 0.040
#> GSM28754 2 0.4446 -0.4303 0.000 0.520 0.000 0.004 0.476
#> GSM28769 2 0.0162 0.8603 0.000 0.996 0.000 0.004 0.000
#> GSM11275 1 0.3169 0.9026 0.856 0.000 0.000 0.084 0.060
#> GSM11270 5 0.3231 0.7358 0.000 0.196 0.000 0.004 0.800
#> GSM11271 5 0.4787 0.7961 0.000 0.324 0.000 0.036 0.640
#> GSM11288 2 0.3720 0.5966 0.000 0.760 0.228 0.012 0.000
#> GSM11273 5 0.3183 0.4061 0.000 0.028 0.108 0.008 0.856
#> GSM28757 2 0.1914 0.8347 0.000 0.924 0.000 0.016 0.060
#> GSM11282 5 0.3231 0.7358 0.000 0.196 0.000 0.004 0.800
#> GSM28756 5 0.4443 0.5028 0.000 0.472 0.000 0.004 0.524
#> GSM11276 2 0.1704 0.8065 0.000 0.928 0.000 0.004 0.068
#> GSM28752 2 0.0609 0.8550 0.000 0.980 0.000 0.000 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 2 0.0881 0.8372 0.000 0.972 0.012 0.008 0.008 0.000
#> GSM28763 2 0.0881 0.8372 0.000 0.972 0.012 0.008 0.008 0.000
#> GSM28764 2 0.4591 -0.1799 0.000 0.552 0.000 0.040 0.408 0.000
#> GSM11274 3 0.5614 0.0000 0.000 0.000 0.488 0.008 0.116 0.388
#> GSM28772 1 0.0000 0.9231 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.9231 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.2328 0.8953 0.904 0.000 0.020 0.044 0.032 0.000
#> GSM11293 1 0.2454 0.8986 0.884 0.000 0.088 0.008 0.020 0.000
#> GSM28755 1 0.2538 0.8919 0.892 0.000 0.020 0.048 0.040 0.000
#> GSM11279 1 0.0405 0.9216 0.988 0.000 0.000 0.004 0.008 0.000
#> GSM28758 1 0.4109 0.8250 0.748 0.000 0.196 0.032 0.024 0.000
#> GSM11281 1 0.0000 0.9231 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.9231 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.2454 0.8986 0.884 0.000 0.088 0.008 0.020 0.000
#> GSM11292 5 0.3971 0.7281 0.000 0.184 0.000 0.068 0.748 0.000
#> GSM28766 5 0.3971 0.7281 0.000 0.184 0.000 0.068 0.748 0.000
#> GSM11268 6 0.0000 0.5226 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM28767 5 0.3971 0.7281 0.000 0.184 0.000 0.068 0.748 0.000
#> GSM11286 2 0.2274 0.8288 0.000 0.892 0.088 0.012 0.008 0.000
#> GSM28751 2 0.1624 0.8354 0.000 0.936 0.044 0.012 0.008 0.000
#> GSM28770 5 0.3939 0.7279 0.000 0.180 0.000 0.068 0.752 0.000
#> GSM11283 4 0.2507 0.9330 0.000 0.072 0.004 0.884 0.040 0.000
#> GSM11289 5 0.3939 0.7279 0.000 0.180 0.000 0.068 0.752 0.000
#> GSM11280 2 0.2748 0.8149 0.000 0.848 0.128 0.024 0.000 0.000
#> GSM28749 2 0.3056 0.8112 0.000 0.832 0.140 0.016 0.000 0.012
#> GSM28750 6 0.0000 0.5226 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM11290 6 0.3915 0.0399 0.000 0.000 0.412 0.000 0.004 0.584
#> GSM11294 6 0.4136 -0.0365 0.000 0.000 0.428 0.000 0.012 0.560
#> GSM28771 4 0.2519 0.9376 0.000 0.068 0.004 0.884 0.044 0.000
#> GSM28760 4 0.2630 0.9356 0.000 0.032 0.004 0.872 0.092 0.000
#> GSM28774 5 0.5317 0.5697 0.000 0.332 0.096 0.008 0.564 0.000
#> GSM11284 5 0.6853 0.5110 0.000 0.164 0.100 0.256 0.480 0.000
#> GSM28761 6 0.0000 0.5226 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM11278 5 0.4553 0.6285 0.000 0.064 0.180 0.028 0.728 0.000
#> GSM11291 6 0.4136 -0.0365 0.000 0.000 0.428 0.000 0.012 0.560
#> GSM11277 6 0.4136 -0.0365 0.000 0.000 0.428 0.000 0.012 0.560
#> GSM11272 6 0.0000 0.5226 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM11285 4 0.2540 0.9224 0.000 0.020 0.004 0.872 0.104 0.000
#> GSM28753 2 0.1657 0.8402 0.000 0.928 0.056 0.016 0.000 0.000
#> GSM28773 2 0.4731 0.7526 0.000 0.732 0.176 0.020 0.024 0.048
#> GSM28765 2 0.1230 0.8273 0.000 0.956 0.008 0.008 0.028 0.000
#> GSM28768 2 0.2892 0.7919 0.000 0.840 0.136 0.020 0.004 0.000
#> GSM28754 5 0.5450 0.3518 0.000 0.440 0.092 0.008 0.460 0.000
#> GSM28769 2 0.1624 0.8354 0.000 0.936 0.044 0.012 0.008 0.000
#> GSM11275 1 0.4109 0.8250 0.748 0.000 0.196 0.032 0.024 0.000
#> GSM11270 5 0.4584 0.6267 0.000 0.064 0.184 0.028 0.724 0.000
#> GSM11271 5 0.3529 0.7281 0.000 0.208 0.000 0.028 0.764 0.000
#> GSM11288 2 0.5194 0.6029 0.000 0.632 0.128 0.008 0.000 0.232
#> GSM11273 5 0.4794 0.4735 0.000 0.004 0.248 0.028 0.680 0.040
#> GSM28757 2 0.3299 0.7921 0.000 0.836 0.092 0.012 0.060 0.000
#> GSM11282 5 0.4553 0.6285 0.000 0.064 0.180 0.028 0.728 0.000
#> GSM28756 5 0.5359 0.5218 0.000 0.364 0.092 0.008 0.536 0.000
#> GSM11276 2 0.2431 0.7300 0.000 0.860 0.000 0.008 0.132 0.000
#> GSM28752 2 0.1500 0.8197 0.000 0.936 0.012 0.000 0.052 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 tissue(p) k
#> CV:kmeans 54 0.398 2
#> CV:kmeans 54 0.374 3
#> CV:kmeans 48 0.508 4
#> CV:kmeans 51 0.497 5
#> CV:kmeans 46 0.479 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.730 0.918 0.955 0.4748 0.516 0.516
#> 3 3 0.944 0.935 0.974 0.3402 0.764 0.576
#> 4 4 0.707 0.682 0.861 0.1839 0.822 0.544
#> 5 5 0.796 0.796 0.886 0.0707 0.936 0.744
#> 6 6 0.805 0.734 0.838 0.0380 0.960 0.798
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
#> GSM28762 2 0.0000 0.972 0.000 1.000
#> GSM28763 2 0.6887 0.762 0.184 0.816
#> GSM28764 2 0.0000 0.972 0.000 1.000
#> GSM11274 2 0.0000 0.972 0.000 1.000
#> GSM28772 1 0.0000 0.913 1.000 0.000
#> GSM11269 1 0.0000 0.913 1.000 0.000
#> GSM28775 1 0.0000 0.913 1.000 0.000
#> GSM11293 1 0.0000 0.913 1.000 0.000
#> GSM28755 1 0.0000 0.913 1.000 0.000
#> GSM11279 1 0.0000 0.913 1.000 0.000
#> GSM28758 1 0.0000 0.913 1.000 0.000
#> GSM11281 1 0.0000 0.913 1.000 0.000
#> GSM11287 1 0.0000 0.913 1.000 0.000
#> GSM28759 1 0.0000 0.913 1.000 0.000
#> GSM11292 2 0.0000 0.972 0.000 1.000
#> GSM28766 2 0.0000 0.972 0.000 1.000
#> GSM11268 1 0.7219 0.832 0.800 0.200
#> GSM28767 2 0.0000 0.972 0.000 1.000
#> GSM11286 2 0.0000 0.972 0.000 1.000
#> GSM28751 2 0.9170 0.541 0.332 0.668
#> GSM28770 2 0.0000 0.972 0.000 1.000
#> GSM11283 2 0.0000 0.972 0.000 1.000
#> GSM11289 2 0.0000 0.972 0.000 1.000
#> GSM11280 2 0.0000 0.972 0.000 1.000
#> GSM28749 2 0.0000 0.972 0.000 1.000
#> GSM28750 1 0.7219 0.832 0.800 0.200
#> GSM11290 1 0.7056 0.838 0.808 0.192
#> GSM11294 1 0.7219 0.832 0.800 0.200
#> GSM28771 2 0.0000 0.972 0.000 1.000
#> GSM28760 2 0.0000 0.972 0.000 1.000
#> GSM28774 2 0.0000 0.972 0.000 1.000
#> GSM11284 2 0.0000 0.972 0.000 1.000
#> GSM28761 1 0.7056 0.838 0.808 0.192
#> GSM11278 2 0.0000 0.972 0.000 1.000
#> GSM11291 1 0.7219 0.832 0.800 0.200
#> GSM11277 1 0.7219 0.832 0.800 0.200
#> GSM11272 1 0.0000 0.913 1.000 0.000
#> GSM11285 2 0.0000 0.972 0.000 1.000
#> GSM28753 2 0.0000 0.972 0.000 1.000
#> GSM28773 2 0.0000 0.972 0.000 1.000
#> GSM28765 2 0.0000 0.972 0.000 1.000
#> GSM28768 1 0.0376 0.911 0.996 0.004
#> GSM28754 2 0.0000 0.972 0.000 1.000
#> GSM28769 2 0.9087 0.557 0.324 0.676
#> GSM11275 1 0.0000 0.913 1.000 0.000
#> GSM11270 2 0.0000 0.972 0.000 1.000
#> GSM11271 2 0.0000 0.972 0.000 1.000
#> GSM11288 1 0.7139 0.835 0.804 0.196
#> GSM11273 2 0.0000 0.972 0.000 1.000
#> GSM28757 2 0.0000 0.972 0.000 1.000
#> GSM11282 2 0.0000 0.972 0.000 1.000
#> GSM28756 2 0.0000 0.972 0.000 1.000
#> GSM11276 2 0.0000 0.972 0.000 1.000
#> GSM28752 2 0.0000 0.972 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28763 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28764 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11274 3 0.0000 0.964 0.000 0.000 1.000
#> GSM28772 1 0.0000 0.966 1.000 0.000 0.000
#> GSM11269 1 0.0000 0.966 1.000 0.000 0.000
#> GSM28775 1 0.0000 0.966 1.000 0.000 0.000
#> GSM11293 1 0.0000 0.966 1.000 0.000 0.000
#> GSM28755 1 0.0000 0.966 1.000 0.000 0.000
#> GSM11279 1 0.0000 0.966 1.000 0.000 0.000
#> GSM28758 1 0.0000 0.966 1.000 0.000 0.000
#> GSM11281 1 0.0000 0.966 1.000 0.000 0.000
#> GSM11287 1 0.0000 0.966 1.000 0.000 0.000
#> GSM28759 1 0.0000 0.966 1.000 0.000 0.000
#> GSM11292 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28766 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11268 3 0.0000 0.964 0.000 0.000 1.000
#> GSM28767 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11286 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28751 1 0.2796 0.873 0.908 0.092 0.000
#> GSM28770 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11283 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11289 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11280 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28749 2 0.4555 0.742 0.000 0.800 0.200
#> GSM28750 3 0.0000 0.964 0.000 0.000 1.000
#> GSM11290 3 0.0000 0.964 0.000 0.000 1.000
#> GSM11294 3 0.0000 0.964 0.000 0.000 1.000
#> GSM28771 2 0.5926 0.424 0.000 0.644 0.356
#> GSM28760 3 0.5678 0.509 0.000 0.316 0.684
#> GSM28774 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11284 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28761 3 0.0000 0.964 0.000 0.000 1.000
#> GSM11278 2 0.0424 0.965 0.000 0.992 0.008
#> GSM11291 3 0.0000 0.964 0.000 0.000 1.000
#> GSM11277 3 0.0000 0.964 0.000 0.000 1.000
#> GSM11272 3 0.0000 0.964 0.000 0.000 1.000
#> GSM11285 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28753 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28773 3 0.0892 0.946 0.000 0.020 0.980
#> GSM28765 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28768 1 0.0000 0.966 1.000 0.000 0.000
#> GSM28754 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28769 1 0.5291 0.650 0.732 0.268 0.000
#> GSM11275 1 0.0000 0.966 1.000 0.000 0.000
#> GSM11270 2 0.3482 0.841 0.000 0.872 0.128
#> GSM11271 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11288 3 0.0424 0.958 0.008 0.000 0.992
#> GSM11273 3 0.0000 0.964 0.000 0.000 1.000
#> GSM28757 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11282 2 0.0237 0.968 0.000 0.996 0.004
#> GSM28756 2 0.0000 0.972 0.000 1.000 0.000
#> GSM11276 2 0.0000 0.972 0.000 1.000 0.000
#> GSM28752 2 0.0000 0.972 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.2589 0.6220 0.000 0.884 0.000 0.116
#> GSM28763 2 0.2589 0.6220 0.000 0.884 0.000 0.116
#> GSM28764 4 0.4406 0.3623 0.000 0.300 0.000 0.700
#> GSM11274 3 0.2814 0.8164 0.000 0.000 0.868 0.132
#> GSM28772 1 0.0000 0.9893 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.9893 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.9893 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.9893 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.9893 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.9893 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.9893 1.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.9893 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.9893 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.9893 1.000 0.000 0.000 0.000
#> GSM11292 4 0.0188 0.7621 0.000 0.004 0.000 0.996
#> GSM28766 4 0.0188 0.7621 0.000 0.004 0.000 0.996
#> GSM11268 3 0.0000 0.9135 0.000 0.000 1.000 0.000
#> GSM28767 4 0.0188 0.7621 0.000 0.004 0.000 0.996
#> GSM11286 2 0.4804 0.4373 0.000 0.616 0.000 0.384
#> GSM28751 2 0.3335 0.5947 0.128 0.856 0.000 0.016
#> GSM28770 4 0.0188 0.7621 0.000 0.004 0.000 0.996
#> GSM11283 2 0.4585 0.2152 0.000 0.668 0.000 0.332
#> GSM11289 4 0.0188 0.7621 0.000 0.004 0.000 0.996
#> GSM11280 2 0.0592 0.5997 0.000 0.984 0.000 0.016
#> GSM28749 2 0.5484 0.4620 0.000 0.732 0.164 0.104
#> GSM28750 3 0.0000 0.9135 0.000 0.000 1.000 0.000
#> GSM11290 3 0.0000 0.9135 0.000 0.000 1.000 0.000
#> GSM11294 3 0.0000 0.9135 0.000 0.000 1.000 0.000
#> GSM28771 2 0.5493 -0.0738 0.000 0.528 0.016 0.456
#> GSM28760 4 0.6125 0.1062 0.000 0.436 0.048 0.516
#> GSM28774 4 0.3726 0.5262 0.000 0.212 0.000 0.788
#> GSM11284 4 0.3266 0.6032 0.000 0.168 0.000 0.832
#> GSM28761 3 0.0000 0.9135 0.000 0.000 1.000 0.000
#> GSM11278 4 0.0336 0.7586 0.000 0.000 0.008 0.992
#> GSM11291 3 0.0000 0.9135 0.000 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.9135 0.000 0.000 1.000 0.000
#> GSM11272 3 0.0000 0.9135 0.000 0.000 1.000 0.000
#> GSM11285 4 0.4679 0.3272 0.000 0.352 0.000 0.648
#> GSM28753 2 0.0188 0.6061 0.000 0.996 0.000 0.004
#> GSM28773 3 0.5294 0.1792 0.000 0.484 0.508 0.008
#> GSM28765 2 0.4898 0.3971 0.000 0.584 0.000 0.416
#> GSM28768 1 0.2469 0.8698 0.892 0.108 0.000 0.000
#> GSM28754 4 0.4955 -0.0995 0.000 0.444 0.000 0.556
#> GSM28769 2 0.3080 0.6103 0.096 0.880 0.000 0.024
#> GSM11275 1 0.0000 0.9893 1.000 0.000 0.000 0.000
#> GSM11270 4 0.0524 0.7572 0.000 0.004 0.008 0.988
#> GSM11271 4 0.0188 0.7621 0.000 0.004 0.000 0.996
#> GSM11288 3 0.2773 0.8332 0.004 0.116 0.880 0.000
#> GSM11273 3 0.3074 0.7979 0.000 0.000 0.848 0.152
#> GSM28757 2 0.4888 0.4035 0.000 0.588 0.000 0.412
#> GSM11282 4 0.0336 0.7586 0.000 0.000 0.008 0.992
#> GSM28756 4 0.4585 0.2750 0.000 0.332 0.000 0.668
#> GSM11276 2 0.4967 0.3230 0.000 0.548 0.000 0.452
#> GSM28752 2 0.4933 0.3678 0.000 0.568 0.000 0.432
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28762 2 0.1952 0.8145 0.000 0.912 0.000 0.084 0.004
#> GSM28763 2 0.2011 0.8136 0.000 0.908 0.000 0.088 0.004
#> GSM28764 5 0.4794 0.4712 0.000 0.344 0.000 0.032 0.624
#> GSM11274 3 0.0740 0.8802 0.000 0.004 0.980 0.008 0.008
#> GSM28772 1 0.0000 0.9642 1.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.9642 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.9642 1.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.9642 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.9642 1.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.9642 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.9642 1.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.9642 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.9642 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.9642 1.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.1918 0.8313 0.000 0.036 0.000 0.036 0.928
#> GSM28766 5 0.1918 0.8313 0.000 0.036 0.000 0.036 0.928
#> GSM11268 3 0.0451 0.8893 0.000 0.004 0.988 0.008 0.000
#> GSM28767 5 0.1918 0.8313 0.000 0.036 0.000 0.036 0.928
#> GSM11286 2 0.2871 0.8056 0.000 0.872 0.000 0.040 0.088
#> GSM28751 2 0.2981 0.8029 0.024 0.876 0.000 0.084 0.016
#> GSM28770 5 0.1918 0.8313 0.000 0.036 0.000 0.036 0.928
#> GSM11283 4 0.1281 0.8593 0.000 0.032 0.000 0.956 0.012
#> GSM11289 5 0.1918 0.8313 0.000 0.036 0.000 0.036 0.928
#> GSM11280 4 0.3496 0.7319 0.000 0.200 0.000 0.788 0.012
#> GSM28749 4 0.4150 0.7264 0.000 0.216 0.000 0.748 0.036
#> GSM28750 3 0.0451 0.8893 0.000 0.004 0.988 0.008 0.000
#> GSM11290 3 0.0000 0.8900 0.000 0.000 1.000 0.000 0.000
#> GSM11294 3 0.0000 0.8900 0.000 0.000 1.000 0.000 0.000
#> GSM28771 4 0.1300 0.8606 0.000 0.028 0.000 0.956 0.016
#> GSM28760 4 0.1285 0.8598 0.000 0.004 0.004 0.956 0.036
#> GSM28774 5 0.3527 0.7197 0.000 0.192 0.000 0.016 0.792
#> GSM11284 4 0.3950 0.7751 0.000 0.068 0.000 0.796 0.136
#> GSM28761 3 0.0451 0.8893 0.000 0.004 0.988 0.008 0.000
#> GSM11278 5 0.2656 0.8002 0.000 0.064 0.012 0.028 0.896
#> GSM11291 3 0.0000 0.8900 0.000 0.000 1.000 0.000 0.000
#> GSM11277 3 0.0000 0.8900 0.000 0.000 1.000 0.000 0.000
#> GSM11272 3 0.0451 0.8893 0.000 0.004 0.988 0.008 0.000
#> GSM11285 4 0.2233 0.8417 0.000 0.016 0.000 0.904 0.080
#> GSM28753 2 0.4029 0.5255 0.000 0.680 0.000 0.316 0.004
#> GSM28773 3 0.7113 -0.0484 0.000 0.304 0.380 0.304 0.012
#> GSM28765 2 0.3106 0.7790 0.000 0.840 0.000 0.020 0.140
#> GSM28768 1 0.4416 0.4338 0.632 0.356 0.000 0.012 0.000
#> GSM28754 5 0.5036 0.3213 0.000 0.404 0.000 0.036 0.560
#> GSM28769 2 0.2518 0.8129 0.008 0.896 0.000 0.080 0.016
#> GSM11275 1 0.0000 0.9642 1.000 0.000 0.000 0.000 0.000
#> GSM11270 5 0.2693 0.7995 0.000 0.060 0.016 0.028 0.896
#> GSM11271 5 0.1568 0.8304 0.000 0.036 0.000 0.020 0.944
#> GSM11288 3 0.5176 0.5108 0.020 0.036 0.656 0.288 0.000
#> GSM11273 3 0.3463 0.7428 0.000 0.008 0.820 0.016 0.156
#> GSM28757 2 0.3883 0.7307 0.000 0.780 0.000 0.036 0.184
#> GSM11282 5 0.2409 0.8032 0.000 0.060 0.012 0.020 0.908
#> GSM28756 5 0.4268 0.6183 0.000 0.268 0.000 0.024 0.708
#> GSM11276 2 0.3508 0.6705 0.000 0.748 0.000 0.000 0.252
#> GSM28752 2 0.2377 0.8028 0.000 0.872 0.000 0.000 0.128
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 2 0.0993 0.710 0.000 0.964 0.000 0.012 0.000 0.024
#> GSM28763 2 0.0993 0.710 0.000 0.964 0.000 0.012 0.000 0.024
#> GSM28764 5 0.3190 0.713 0.000 0.136 0.000 0.000 0.820 0.044
#> GSM11274 3 0.3053 0.772 0.000 0.000 0.812 0.020 0.000 0.168
#> GSM28772 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28766 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11268 3 0.0146 0.814 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM28767 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11286 2 0.5462 0.368 0.000 0.472 0.000 0.032 0.052 0.444
#> GSM28751 2 0.0912 0.711 0.004 0.972 0.000 0.008 0.012 0.004
#> GSM28770 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11283 4 0.0858 0.806 0.000 0.028 0.000 0.968 0.004 0.000
#> GSM11289 5 0.0000 0.953 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11280 4 0.5011 0.571 0.000 0.116 0.000 0.620 0.000 0.264
#> GSM28749 4 0.6081 0.543 0.000 0.112 0.020 0.568 0.024 0.276
#> GSM28750 3 0.0000 0.814 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11290 3 0.1471 0.818 0.000 0.000 0.932 0.004 0.000 0.064
#> GSM11294 3 0.2100 0.812 0.000 0.000 0.884 0.004 0.000 0.112
#> GSM28771 4 0.0858 0.806 0.000 0.028 0.000 0.968 0.004 0.000
#> GSM28760 4 0.0806 0.806 0.000 0.020 0.000 0.972 0.008 0.000
#> GSM28774 6 0.5521 0.647 0.000 0.112 0.000 0.012 0.320 0.556
#> GSM11284 4 0.3929 0.669 0.000 0.008 0.000 0.776 0.072 0.144
#> GSM28761 3 0.0146 0.814 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM11278 6 0.4170 0.616 0.000 0.004 0.000 0.020 0.328 0.648
#> GSM11291 3 0.2100 0.812 0.000 0.000 0.884 0.004 0.000 0.112
#> GSM11277 3 0.2100 0.812 0.000 0.000 0.884 0.004 0.000 0.112
#> GSM11272 3 0.0146 0.814 0.000 0.004 0.996 0.000 0.000 0.000
#> GSM11285 4 0.1444 0.782 0.000 0.000 0.000 0.928 0.072 0.000
#> GSM28753 2 0.5927 0.343 0.000 0.540 0.000 0.256 0.016 0.188
#> GSM28773 3 0.7503 -0.129 0.000 0.316 0.324 0.160 0.000 0.200
#> GSM28765 2 0.5497 0.438 0.000 0.556 0.000 0.020 0.088 0.336
#> GSM28768 1 0.4609 0.496 0.648 0.296 0.000 0.008 0.000 0.048
#> GSM28754 6 0.4988 0.628 0.000 0.136 0.000 0.008 0.188 0.668
#> GSM28769 2 0.0767 0.711 0.000 0.976 0.000 0.008 0.012 0.004
#> GSM11275 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11270 6 0.4290 0.617 0.000 0.004 0.004 0.020 0.324 0.648
#> GSM11271 5 0.0146 0.949 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM11288 3 0.5533 0.462 0.008 0.052 0.656 0.208 0.000 0.076
#> GSM11273 3 0.5028 0.375 0.000 0.000 0.524 0.020 0.036 0.420
#> GSM28757 6 0.4178 0.358 0.000 0.184 0.000 0.016 0.052 0.748
#> GSM11282 6 0.4290 0.599 0.000 0.004 0.000 0.020 0.364 0.612
#> GSM28756 6 0.5204 0.641 0.000 0.112 0.000 0.012 0.244 0.632
#> GSM11276 2 0.5243 0.367 0.000 0.532 0.000 0.004 0.376 0.088
#> GSM28752 2 0.3992 0.621 0.000 0.756 0.000 0.008 0.184 0.052
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 tissue(p) k
#> CV:skmeans 54 0.398 2
#> CV:skmeans 53 0.373 3
#> CV:skmeans 40 0.406 4
#> CV:skmeans 50 0.443 5
#> CV:skmeans 45 0.419 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.984 0.994 0.3387 0.669 0.669
#> 3 3 0.968 0.971 0.987 0.6385 0.786 0.681
#> 4 4 0.938 0.925 0.967 0.3303 0.801 0.563
#> 5 5 0.868 0.877 0.930 0.0550 0.947 0.796
#> 6 6 0.928 0.905 0.946 0.0331 0.986 0.934
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM28762 2 0.0000 0.992 0.000 1.000
#> GSM28763 2 0.0000 0.992 0.000 1.000
#> GSM28764 2 0.0000 0.992 0.000 1.000
#> GSM11274 2 0.0000 0.992 0.000 1.000
#> GSM28772 1 0.0000 1.000 1.000 0.000
#> GSM11269 1 0.0000 1.000 1.000 0.000
#> GSM28775 1 0.0000 1.000 1.000 0.000
#> GSM11293 1 0.0000 1.000 1.000 0.000
#> GSM28755 1 0.0000 1.000 1.000 0.000
#> GSM11279 1 0.0000 1.000 1.000 0.000
#> GSM28758 1 0.0000 1.000 1.000 0.000
#> GSM11281 1 0.0000 1.000 1.000 0.000
#> GSM11287 1 0.0000 1.000 1.000 0.000
#> GSM28759 1 0.0000 1.000 1.000 0.000
#> GSM11292 2 0.0000 0.992 0.000 1.000
#> GSM28766 2 0.0000 0.992 0.000 1.000
#> GSM11268 2 0.0000 0.992 0.000 1.000
#> GSM28767 2 0.0000 0.992 0.000 1.000
#> GSM11286 2 0.0000 0.992 0.000 1.000
#> GSM28751 2 0.0000 0.992 0.000 1.000
#> GSM28770 2 0.0000 0.992 0.000 1.000
#> GSM11283 2 0.0000 0.992 0.000 1.000
#> GSM11289 2 0.0000 0.992 0.000 1.000
#> GSM11280 2 0.0000 0.992 0.000 1.000
#> GSM28749 2 0.0000 0.992 0.000 1.000
#> GSM28750 2 0.0000 0.992 0.000 1.000
#> GSM11290 2 0.0000 0.992 0.000 1.000
#> GSM11294 2 0.0000 0.992 0.000 1.000
#> GSM28771 2 0.0000 0.992 0.000 1.000
#> GSM28760 2 0.0000 0.992 0.000 1.000
#> GSM28774 2 0.0000 0.992 0.000 1.000
#> GSM11284 2 0.0000 0.992 0.000 1.000
#> GSM28761 2 0.0000 0.992 0.000 1.000
#> GSM11278 2 0.0000 0.992 0.000 1.000
#> GSM11291 2 0.0000 0.992 0.000 1.000
#> GSM11277 2 0.0000 0.992 0.000 1.000
#> GSM11272 2 0.0376 0.988 0.004 0.996
#> GSM11285 2 0.0000 0.992 0.000 1.000
#> GSM28753 2 0.0000 0.992 0.000 1.000
#> GSM28773 2 0.0000 0.992 0.000 1.000
#> GSM28765 2 0.0000 0.992 0.000 1.000
#> GSM28768 2 0.9286 0.476 0.344 0.656
#> GSM28754 2 0.0000 0.992 0.000 1.000
#> GSM28769 2 0.0000 0.992 0.000 1.000
#> GSM11275 1 0.0000 1.000 1.000 0.000
#> GSM11270 2 0.0000 0.992 0.000 1.000
#> GSM11271 2 0.0000 0.992 0.000 1.000
#> GSM11288 2 0.0000 0.992 0.000 1.000
#> GSM11273 2 0.0000 0.992 0.000 1.000
#> GSM28757 2 0.0000 0.992 0.000 1.000
#> GSM11282 2 0.0000 0.992 0.000 1.000
#> GSM28756 2 0.0000 0.992 0.000 1.000
#> GSM11276 2 0.0000 0.992 0.000 1.000
#> GSM28752 2 0.0000 0.992 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.0000 0.979 0.000 1.000 0.000
#> GSM28763 2 0.0000 0.979 0.000 1.000 0.000
#> GSM28764 2 0.0000 0.979 0.000 1.000 0.000
#> GSM11274 3 0.0000 0.995 0.000 0.000 1.000
#> GSM28772 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11292 2 0.0000 0.979 0.000 1.000 0.000
#> GSM28766 2 0.0000 0.979 0.000 1.000 0.000
#> GSM11268 3 0.0000 0.995 0.000 0.000 1.000
#> GSM28767 2 0.0000 0.979 0.000 1.000 0.000
#> GSM11286 2 0.0000 0.979 0.000 1.000 0.000
#> GSM28751 2 0.0000 0.979 0.000 1.000 0.000
#> GSM28770 2 0.0000 0.979 0.000 1.000 0.000
#> GSM11283 2 0.0000 0.979 0.000 1.000 0.000
#> GSM11289 2 0.0000 0.979 0.000 1.000 0.000
#> GSM11280 2 0.0000 0.979 0.000 1.000 0.000
#> GSM28749 2 0.0000 0.979 0.000 1.000 0.000
#> GSM28750 3 0.0000 0.995 0.000 0.000 1.000
#> GSM11290 3 0.0000 0.995 0.000 0.000 1.000
#> GSM11294 3 0.0000 0.995 0.000 0.000 1.000
#> GSM28771 2 0.0000 0.979 0.000 1.000 0.000
#> GSM28760 2 0.4121 0.808 0.000 0.832 0.168
#> GSM28774 2 0.0000 0.979 0.000 1.000 0.000
#> GSM11284 2 0.0000 0.979 0.000 1.000 0.000
#> GSM28761 3 0.1163 0.959 0.000 0.028 0.972
#> GSM11278 2 0.0237 0.976 0.000 0.996 0.004
#> GSM11291 3 0.0000 0.995 0.000 0.000 1.000
#> GSM11277 3 0.0000 0.995 0.000 0.000 1.000
#> GSM11272 3 0.0000 0.995 0.000 0.000 1.000
#> GSM11285 2 0.0000 0.979 0.000 1.000 0.000
#> GSM28753 2 0.0000 0.979 0.000 1.000 0.000
#> GSM28773 2 0.0000 0.979 0.000 1.000 0.000
#> GSM28765 2 0.0000 0.979 0.000 1.000 0.000
#> GSM28768 2 0.3038 0.877 0.104 0.896 0.000
#> GSM28754 2 0.0000 0.979 0.000 1.000 0.000
#> GSM28769 2 0.0000 0.979 0.000 1.000 0.000
#> GSM11275 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11270 2 0.4178 0.802 0.000 0.828 0.172
#> GSM11271 2 0.0000 0.979 0.000 1.000 0.000
#> GSM11288 2 0.0000 0.979 0.000 1.000 0.000
#> GSM11273 2 0.5016 0.704 0.000 0.760 0.240
#> GSM28757 2 0.0000 0.979 0.000 1.000 0.000
#> GSM11282 2 0.0237 0.976 0.000 0.996 0.004
#> GSM28756 2 0.0000 0.979 0.000 1.000 0.000
#> GSM11276 2 0.0000 0.979 0.000 1.000 0.000
#> GSM28752 2 0.0000 0.979 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.0000 0.982 0 1.000 0.000 0.000
#> GSM28763 2 0.0000 0.982 0 1.000 0.000 0.000
#> GSM28764 2 0.1716 0.924 0 0.936 0.000 0.064
#> GSM11274 3 0.0000 0.996 0 0.000 1.000 0.000
#> GSM28772 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11292 4 0.0188 0.878 0 0.004 0.000 0.996
#> GSM28766 4 0.0000 0.875 0 0.000 0.000 1.000
#> GSM11268 3 0.0000 0.996 0 0.000 1.000 0.000
#> GSM28767 4 0.0188 0.878 0 0.004 0.000 0.996
#> GSM11286 2 0.0000 0.982 0 1.000 0.000 0.000
#> GSM28751 2 0.0000 0.982 0 1.000 0.000 0.000
#> GSM28770 4 0.0188 0.878 0 0.004 0.000 0.996
#> GSM11283 2 0.0188 0.979 0 0.996 0.000 0.004
#> GSM11289 4 0.0188 0.878 0 0.004 0.000 0.996
#> GSM11280 2 0.0000 0.982 0 1.000 0.000 0.000
#> GSM28749 4 0.4072 0.695 0 0.252 0.000 0.748
#> GSM28750 3 0.0000 0.996 0 0.000 1.000 0.000
#> GSM11290 3 0.0000 0.996 0 0.000 1.000 0.000
#> GSM11294 3 0.0000 0.996 0 0.000 1.000 0.000
#> GSM28771 2 0.0592 0.972 0 0.984 0.000 0.016
#> GSM28760 4 0.3962 0.774 0 0.044 0.124 0.832
#> GSM28774 4 0.3024 0.795 0 0.148 0.000 0.852
#> GSM11284 4 0.4925 0.338 0 0.428 0.000 0.572
#> GSM28761 3 0.1004 0.968 0 0.024 0.972 0.004
#> GSM11278 4 0.0188 0.878 0 0.004 0.000 0.996
#> GSM11291 3 0.0000 0.996 0 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.996 0 0.000 1.000 0.000
#> GSM11272 3 0.0000 0.996 0 0.000 1.000 0.000
#> GSM11285 4 0.0817 0.870 0 0.024 0.000 0.976
#> GSM28753 2 0.0000 0.982 0 1.000 0.000 0.000
#> GSM28773 2 0.0000 0.982 0 1.000 0.000 0.000
#> GSM28765 2 0.0000 0.982 0 1.000 0.000 0.000
#> GSM28768 2 0.0000 0.982 0 1.000 0.000 0.000
#> GSM28754 2 0.0000 0.982 0 1.000 0.000 0.000
#> GSM28769 2 0.0000 0.982 0 1.000 0.000 0.000
#> GSM11275 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11270 4 0.0188 0.878 0 0.004 0.000 0.996
#> GSM11271 4 0.4933 0.262 0 0.432 0.000 0.568
#> GSM11288 2 0.3074 0.795 0 0.848 0.000 0.152
#> GSM11273 4 0.0657 0.873 0 0.004 0.012 0.984
#> GSM28757 2 0.0000 0.982 0 1.000 0.000 0.000
#> GSM11282 4 0.0188 0.878 0 0.004 0.000 0.996
#> GSM28756 2 0.0000 0.982 0 1.000 0.000 0.000
#> GSM11276 2 0.1302 0.944 0 0.956 0.000 0.044
#> GSM28752 2 0.0000 0.982 0 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
#> GSM28762 2 0.0566 0.942 0 0.984 0.000 0.004 0.012
#> GSM28763 2 0.0000 0.951 0 1.000 0.000 0.000 0.000
#> GSM28764 2 0.3368 0.745 0 0.820 0.000 0.024 0.156
#> GSM11274 3 0.0798 0.889 0 0.000 0.976 0.008 0.016
#> GSM28772 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11292 5 0.0865 0.864 0 0.004 0.000 0.024 0.972
#> GSM28766 5 0.0794 0.861 0 0.000 0.000 0.028 0.972
#> GSM11268 3 0.3366 0.876 0 0.000 0.784 0.212 0.004
#> GSM28767 5 0.0865 0.864 0 0.004 0.000 0.024 0.972
#> GSM11286 2 0.0000 0.951 0 1.000 0.000 0.000 0.000
#> GSM28751 2 0.0000 0.951 0 1.000 0.000 0.000 0.000
#> GSM28770 5 0.0865 0.864 0 0.004 0.000 0.024 0.972
#> GSM11283 4 0.3561 0.740 0 0.260 0.000 0.740 0.000
#> GSM11289 5 0.0865 0.864 0 0.004 0.000 0.024 0.972
#> GSM11280 2 0.0290 0.947 0 0.992 0.000 0.008 0.000
#> GSM28749 5 0.4063 0.530 0 0.280 0.000 0.012 0.708
#> GSM28750 3 0.3366 0.876 0 0.000 0.784 0.212 0.004
#> GSM11290 3 0.0000 0.902 0 0.000 1.000 0.000 0.000
#> GSM11294 3 0.0000 0.902 0 0.000 1.000 0.000 0.000
#> GSM28771 4 0.3274 0.779 0 0.220 0.000 0.780 0.000
#> GSM28760 4 0.3210 0.685 0 0.000 0.000 0.788 0.212
#> GSM28774 5 0.3242 0.686 0 0.172 0.000 0.012 0.816
#> GSM11284 4 0.4495 0.788 0 0.200 0.000 0.736 0.064
#> GSM28761 3 0.4033 0.859 0 0.024 0.760 0.212 0.004
#> GSM11278 5 0.0451 0.862 0 0.004 0.000 0.008 0.988
#> GSM11291 3 0.0000 0.902 0 0.000 1.000 0.000 0.000
#> GSM11277 3 0.0000 0.902 0 0.000 1.000 0.000 0.000
#> GSM11272 3 0.3366 0.876 0 0.000 0.784 0.212 0.004
#> GSM11285 4 0.3274 0.685 0 0.000 0.000 0.780 0.220
#> GSM28753 2 0.0000 0.951 0 1.000 0.000 0.000 0.000
#> GSM28773 2 0.0162 0.949 0 0.996 0.000 0.004 0.000
#> GSM28765 2 0.0000 0.951 0 1.000 0.000 0.000 0.000
#> GSM28768 2 0.0000 0.951 0 1.000 0.000 0.000 0.000
#> GSM28754 2 0.0162 0.950 0 0.996 0.000 0.004 0.000
#> GSM28769 2 0.0000 0.951 0 1.000 0.000 0.000 0.000
#> GSM11275 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11270 5 0.0451 0.862 0 0.004 0.000 0.008 0.988
#> GSM11271 5 0.4649 0.246 0 0.404 0.000 0.016 0.580
#> GSM11288 2 0.4567 0.647 0 0.760 0.004 0.116 0.120
#> GSM11273 5 0.0740 0.859 0 0.004 0.008 0.008 0.980
#> GSM28757 2 0.0290 0.947 0 0.992 0.000 0.008 0.000
#> GSM11282 5 0.0451 0.862 0 0.004 0.000 0.008 0.988
#> GSM28756 2 0.0162 0.950 0 0.996 0.000 0.000 0.004
#> GSM11276 2 0.2873 0.790 0 0.856 0.000 0.016 0.128
#> GSM28752 2 0.0000 0.951 0 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
#> GSM28762 2 0.1096 0.927 0 0.964 0.020 0.004 0.008 0.004
#> GSM28763 2 0.0000 0.938 0 1.000 0.000 0.000 0.000 0.000
#> GSM28764 2 0.3351 0.753 0 0.800 0.000 0.040 0.160 0.000
#> GSM11274 3 0.0146 0.889 0 0.000 0.996 0.000 0.004 0.000
#> GSM28772 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.0937 0.852 0 0.000 0.000 0.040 0.960 0.000
#> GSM28766 5 0.0937 0.852 0 0.000 0.000 0.040 0.960 0.000
#> GSM11268 6 0.0547 1.000 0 0.000 0.020 0.000 0.000 0.980
#> GSM28767 5 0.0937 0.852 0 0.000 0.000 0.040 0.960 0.000
#> GSM11286 2 0.0146 0.938 0 0.996 0.000 0.000 0.000 0.004
#> GSM28751 2 0.0000 0.938 0 1.000 0.000 0.000 0.000 0.000
#> GSM28770 5 0.0937 0.852 0 0.000 0.000 0.040 0.960 0.000
#> GSM11283 4 0.1007 0.934 0 0.044 0.000 0.956 0.000 0.000
#> GSM11289 5 0.0937 0.852 0 0.000 0.000 0.040 0.960 0.000
#> GSM11280 2 0.0914 0.931 0 0.968 0.000 0.016 0.000 0.016
#> GSM28749 5 0.4080 0.614 0 0.264 0.000 0.016 0.704 0.016
#> GSM28750 6 0.0547 1.000 0 0.000 0.020 0.000 0.000 0.980
#> GSM11290 3 0.1501 0.972 0 0.000 0.924 0.000 0.000 0.076
#> GSM11294 3 0.1501 0.972 0 0.000 0.924 0.000 0.000 0.076
#> GSM28771 4 0.0000 0.961 0 0.000 0.000 1.000 0.000 0.000
#> GSM28760 4 0.0000 0.961 0 0.000 0.000 1.000 0.000 0.000
#> GSM28774 5 0.3590 0.765 0 0.116 0.076 0.000 0.804 0.004
#> GSM11284 4 0.1844 0.921 0 0.040 0.016 0.928 0.000 0.016
#> GSM28761 6 0.0547 1.000 0 0.000 0.020 0.000 0.000 0.980
#> GSM11278 5 0.1644 0.847 0 0.000 0.076 0.000 0.920 0.004
#> GSM11291 3 0.1501 0.972 0 0.000 0.924 0.000 0.000 0.076
#> GSM11277 3 0.1501 0.972 0 0.000 0.924 0.000 0.000 0.076
#> GSM11272 6 0.0547 1.000 0 0.000 0.020 0.000 0.000 0.980
#> GSM11285 4 0.0146 0.960 0 0.000 0.000 0.996 0.004 0.000
#> GSM28753 2 0.0000 0.938 0 1.000 0.000 0.000 0.000 0.000
#> GSM28773 2 0.0458 0.935 0 0.984 0.000 0.000 0.000 0.016
#> GSM28765 2 0.0000 0.938 0 1.000 0.000 0.000 0.000 0.000
#> GSM28768 2 0.0458 0.935 0 0.984 0.000 0.000 0.000 0.016
#> GSM28754 2 0.0935 0.926 0 0.964 0.032 0.000 0.000 0.004
#> GSM28769 2 0.0146 0.938 0 0.996 0.000 0.004 0.000 0.000
#> GSM11275 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM11270 5 0.1644 0.847 0 0.000 0.076 0.000 0.920 0.004
#> GSM11271 5 0.4326 0.232 0 0.404 0.000 0.024 0.572 0.000
#> GSM11288 2 0.4375 0.507 0 0.648 0.000 0.028 0.008 0.316
#> GSM11273 5 0.1644 0.847 0 0.000 0.076 0.000 0.920 0.004
#> GSM28757 2 0.1858 0.893 0 0.912 0.076 0.000 0.000 0.012
#> GSM11282 5 0.1644 0.847 0 0.000 0.076 0.000 0.920 0.004
#> GSM28756 2 0.0458 0.935 0 0.984 0.016 0.000 0.000 0.000
#> GSM11276 2 0.2706 0.808 0 0.852 0.000 0.024 0.124 0.000
#> GSM28752 2 0.0000 0.938 0 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 tissue(p) k
#> CV:pam 53 0.397 2
#> CV:pam 54 0.374 3
#> CV:pam 52 0.425 4
#> CV:pam 53 0.481 5
#> CV:pam 53 0.448 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.476 0.849 0.912 0.4670 0.525 0.525
#> 3 3 0.744 0.906 0.946 0.3585 0.717 0.513
#> 4 4 0.949 0.927 0.962 0.0228 0.863 0.678
#> 5 5 0.803 0.849 0.918 0.1825 0.839 0.565
#> 6 6 0.853 0.861 0.917 0.0533 0.961 0.823
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
#> GSM28762 2 0.0376 0.914 0.004 0.996
#> GSM28763 2 0.0938 0.911 0.012 0.988
#> GSM28764 2 0.0000 0.914 0.000 1.000
#> GSM11274 1 0.8144 0.801 0.748 0.252
#> GSM28772 1 0.0672 0.868 0.992 0.008
#> GSM11269 1 0.0672 0.868 0.992 0.008
#> GSM28775 1 0.0672 0.868 0.992 0.008
#> GSM11293 1 0.0672 0.868 0.992 0.008
#> GSM28755 1 0.0672 0.868 0.992 0.008
#> GSM11279 1 0.0672 0.868 0.992 0.008
#> GSM28758 1 0.0672 0.868 0.992 0.008
#> GSM11281 1 0.0672 0.868 0.992 0.008
#> GSM11287 1 0.0672 0.868 0.992 0.008
#> GSM28759 1 0.0672 0.868 0.992 0.008
#> GSM11292 2 0.0000 0.914 0.000 1.000
#> GSM28766 2 0.0000 0.914 0.000 1.000
#> GSM11268 1 0.8081 0.807 0.752 0.248
#> GSM28767 2 0.0000 0.914 0.000 1.000
#> GSM11286 2 0.0000 0.914 0.000 1.000
#> GSM28751 2 0.8555 0.657 0.280 0.720
#> GSM28770 2 0.0000 0.914 0.000 1.000
#> GSM11283 2 0.6148 0.829 0.152 0.848
#> GSM11289 2 0.1633 0.906 0.024 0.976
#> GSM11280 2 0.5842 0.832 0.140 0.860
#> GSM28749 2 0.1633 0.906 0.024 0.976
#> GSM28750 1 0.8081 0.807 0.752 0.248
#> GSM11290 1 0.8081 0.807 0.752 0.248
#> GSM11294 1 0.8081 0.807 0.752 0.248
#> GSM28771 2 0.6148 0.829 0.152 0.848
#> GSM28760 2 0.6148 0.829 0.152 0.848
#> GSM28774 2 0.0000 0.914 0.000 1.000
#> GSM11284 2 0.4562 0.866 0.096 0.904
#> GSM28761 1 0.8081 0.807 0.752 0.248
#> GSM11278 2 0.0000 0.914 0.000 1.000
#> GSM11291 1 0.8081 0.807 0.752 0.248
#> GSM11277 1 0.8081 0.807 0.752 0.248
#> GSM11272 1 0.8081 0.807 0.752 0.248
#> GSM11285 2 0.6148 0.829 0.152 0.848
#> GSM28753 2 0.4022 0.876 0.080 0.920
#> GSM28773 2 0.7602 0.674 0.220 0.780
#> GSM28765 2 0.0000 0.914 0.000 1.000
#> GSM28768 2 0.9286 0.549 0.344 0.656
#> GSM28754 2 0.0000 0.914 0.000 1.000
#> GSM28769 2 0.7674 0.699 0.224 0.776
#> GSM11275 1 0.0672 0.868 0.992 0.008
#> GSM11270 2 0.0000 0.914 0.000 1.000
#> GSM11271 2 0.0000 0.914 0.000 1.000
#> GSM11288 2 0.7674 0.661 0.224 0.776
#> GSM11273 2 0.6438 0.762 0.164 0.836
#> GSM28757 2 0.0000 0.914 0.000 1.000
#> GSM11282 2 0.0000 0.914 0.000 1.000
#> GSM28756 2 0.0000 0.914 0.000 1.000
#> GSM11276 2 0.0000 0.914 0.000 1.000
#> GSM28752 2 0.0000 0.914 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.3192 0.880 0 0.888 0.112
#> GSM28763 2 0.3192 0.880 0 0.888 0.112
#> GSM28764 2 0.0000 0.926 0 1.000 0.000
#> GSM11274 3 0.2625 0.918 0 0.084 0.916
#> GSM28772 1 0.0000 1.000 1 0.000 0.000
#> GSM11269 1 0.0000 1.000 1 0.000 0.000
#> GSM28775 1 0.0000 1.000 1 0.000 0.000
#> GSM11293 1 0.0000 1.000 1 0.000 0.000
#> GSM28755 1 0.0000 1.000 1 0.000 0.000
#> GSM11279 1 0.0000 1.000 1 0.000 0.000
#> GSM28758 1 0.0000 1.000 1 0.000 0.000
#> GSM11281 1 0.0000 1.000 1 0.000 0.000
#> GSM11287 1 0.0000 1.000 1 0.000 0.000
#> GSM28759 1 0.0000 1.000 1 0.000 0.000
#> GSM11292 2 0.0000 0.926 0 1.000 0.000
#> GSM28766 2 0.0424 0.924 0 0.992 0.008
#> GSM11268 3 0.0000 0.910 0 0.000 1.000
#> GSM28767 2 0.0000 0.926 0 1.000 0.000
#> GSM11286 2 0.0000 0.926 0 1.000 0.000
#> GSM28751 2 0.3686 0.861 0 0.860 0.140
#> GSM28770 2 0.0000 0.926 0 1.000 0.000
#> GSM11283 3 0.2625 0.918 0 0.084 0.916
#> GSM11289 2 0.1031 0.919 0 0.976 0.024
#> GSM11280 3 0.3941 0.848 0 0.156 0.844
#> GSM28749 2 0.4002 0.844 0 0.840 0.160
#> GSM28750 3 0.0000 0.910 0 0.000 1.000
#> GSM11290 3 0.0000 0.910 0 0.000 1.000
#> GSM11294 3 0.0000 0.910 0 0.000 1.000
#> GSM28771 3 0.2625 0.918 0 0.084 0.916
#> GSM28760 3 0.2625 0.918 0 0.084 0.916
#> GSM28774 2 0.0000 0.926 0 1.000 0.000
#> GSM11284 3 0.2878 0.911 0 0.096 0.904
#> GSM28761 3 0.0000 0.910 0 0.000 1.000
#> GSM11278 2 0.3116 0.879 0 0.892 0.108
#> GSM11291 3 0.0000 0.910 0 0.000 1.000
#> GSM11277 3 0.0000 0.910 0 0.000 1.000
#> GSM11272 3 0.0000 0.910 0 0.000 1.000
#> GSM11285 3 0.2625 0.918 0 0.084 0.916
#> GSM28753 2 0.5058 0.723 0 0.756 0.244
#> GSM28773 3 0.6192 0.274 0 0.420 0.580
#> GSM28765 2 0.0000 0.926 0 1.000 0.000
#> GSM28768 2 0.4605 0.796 0 0.796 0.204
#> GSM28754 2 0.0000 0.926 0 1.000 0.000
#> GSM28769 2 0.3340 0.874 0 0.880 0.120
#> GSM11275 1 0.0000 1.000 1 0.000 0.000
#> GSM11270 2 0.4555 0.784 0 0.800 0.200
#> GSM11271 2 0.0000 0.926 0 1.000 0.000
#> GSM11288 3 0.2796 0.913 0 0.092 0.908
#> GSM11273 3 0.2878 0.912 0 0.096 0.904
#> GSM28757 2 0.0000 0.926 0 1.000 0.000
#> GSM11282 2 0.4555 0.784 0 0.800 0.200
#> GSM28756 2 0.0000 0.926 0 1.000 0.000
#> GSM11276 2 0.0000 0.926 0 1.000 0.000
#> GSM28752 2 0.0000 0.926 0 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.1118 0.952 0.000 0.964 0.000 0.036
#> GSM28763 2 0.1118 0.952 0.000 0.964 0.000 0.036
#> GSM28764 2 0.0707 0.956 0.000 0.980 0.000 0.020
#> GSM11274 3 0.3962 0.674 0.000 0.152 0.820 0.028
#> GSM28772 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11292 2 0.0592 0.953 0.000 0.984 0.000 0.016
#> GSM28766 2 0.0592 0.953 0.000 0.984 0.000 0.016
#> GSM11268 3 0.0000 0.887 0.000 0.000 1.000 0.000
#> GSM28767 2 0.0592 0.953 0.000 0.984 0.000 0.016
#> GSM11286 2 0.0817 0.955 0.000 0.976 0.000 0.024
#> GSM28751 2 0.1211 0.951 0.000 0.960 0.000 0.040
#> GSM28770 2 0.0592 0.953 0.000 0.984 0.000 0.016
#> GSM11283 4 0.0592 1.000 0.000 0.016 0.000 0.984
#> GSM11289 2 0.0592 0.956 0.000 0.984 0.000 0.016
#> GSM11280 2 0.3907 0.746 0.000 0.768 0.000 0.232
#> GSM28749 2 0.1211 0.951 0.000 0.960 0.000 0.040
#> GSM28750 3 0.0000 0.887 0.000 0.000 1.000 0.000
#> GSM11290 3 0.0000 0.887 0.000 0.000 1.000 0.000
#> GSM11294 3 0.0000 0.887 0.000 0.000 1.000 0.000
#> GSM28771 4 0.0592 1.000 0.000 0.016 0.000 0.984
#> GSM28760 4 0.0592 1.000 0.000 0.016 0.000 0.984
#> GSM28774 2 0.0592 0.953 0.000 0.984 0.000 0.016
#> GSM11284 2 0.3873 0.752 0.000 0.772 0.000 0.228
#> GSM28761 3 0.0000 0.887 0.000 0.000 1.000 0.000
#> GSM11278 2 0.0895 0.951 0.000 0.976 0.004 0.020
#> GSM11291 3 0.0000 0.887 0.000 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.887 0.000 0.000 1.000 0.000
#> GSM11272 3 0.0000 0.887 0.000 0.000 1.000 0.000
#> GSM11285 4 0.0592 1.000 0.000 0.016 0.000 0.984
#> GSM28753 2 0.1211 0.951 0.000 0.960 0.000 0.040
#> GSM28773 2 0.1833 0.948 0.000 0.944 0.024 0.032
#> GSM28765 2 0.0707 0.956 0.000 0.980 0.000 0.020
#> GSM28768 2 0.1890 0.938 0.008 0.936 0.000 0.056
#> GSM28754 2 0.0000 0.955 0.000 1.000 0.000 0.000
#> GSM28769 2 0.1211 0.951 0.000 0.960 0.000 0.040
#> GSM11275 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11270 2 0.0895 0.951 0.000 0.976 0.004 0.020
#> GSM11271 2 0.0592 0.953 0.000 0.984 0.000 0.016
#> GSM11288 2 0.4356 0.795 0.000 0.804 0.148 0.048
#> GSM11273 3 0.5576 0.216 0.000 0.444 0.536 0.020
#> GSM28757 2 0.0592 0.956 0.000 0.984 0.000 0.016
#> GSM11282 2 0.0895 0.951 0.000 0.976 0.004 0.020
#> GSM28756 2 0.0592 0.953 0.000 0.984 0.000 0.016
#> GSM11276 2 0.0000 0.955 0.000 1.000 0.000 0.000
#> GSM28752 2 0.1118 0.952 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
#> GSM28762 5 0.3274 0.8212 0.00 0.220 0.000 0.000 0.780
#> GSM28763 5 0.3274 0.8212 0.00 0.220 0.000 0.000 0.780
#> GSM28764 2 0.4235 0.0179 0.00 0.576 0.000 0.000 0.424
#> GSM11274 3 0.3280 0.7908 0.00 0.004 0.808 0.004 0.184
#> GSM28772 1 0.0000 0.9837 1.00 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.9837 1.00 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.9837 1.00 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.9837 1.00 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.9837 1.00 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.9837 1.00 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.9837 1.00 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.9837 1.00 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.9837 1.00 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.9837 1.00 0.000 0.000 0.000 0.000
#> GSM11292 2 0.0162 0.8755 0.00 0.996 0.000 0.000 0.004
#> GSM28766 2 0.0609 0.8621 0.00 0.980 0.000 0.000 0.020
#> GSM11268 3 0.0000 0.9765 0.00 0.000 1.000 0.000 0.000
#> GSM28767 2 0.0162 0.8755 0.00 0.996 0.000 0.000 0.004
#> GSM11286 2 0.2179 0.8215 0.00 0.888 0.000 0.000 0.112
#> GSM28751 5 0.3109 0.8368 0.00 0.200 0.000 0.000 0.800
#> GSM28770 2 0.0162 0.8755 0.00 0.996 0.000 0.000 0.004
#> GSM11283 4 0.0290 0.9293 0.00 0.000 0.000 0.992 0.008
#> GSM11289 5 0.4307 0.0149 0.00 0.496 0.000 0.000 0.504
#> GSM11280 5 0.1197 0.7998 0.00 0.048 0.000 0.000 0.952
#> GSM28749 5 0.1410 0.8102 0.00 0.060 0.000 0.000 0.940
#> GSM28750 3 0.0000 0.9765 0.00 0.000 1.000 0.000 0.000
#> GSM11290 3 0.0000 0.9765 0.00 0.000 1.000 0.000 0.000
#> GSM11294 3 0.0000 0.9765 0.00 0.000 1.000 0.000 0.000
#> GSM28771 4 0.0290 0.9293 0.00 0.000 0.000 0.992 0.008
#> GSM28760 4 0.0290 0.9293 0.00 0.000 0.000 0.992 0.008
#> GSM28774 2 0.0794 0.8780 0.00 0.972 0.000 0.000 0.028
#> GSM11284 5 0.1270 0.8024 0.00 0.052 0.000 0.000 0.948
#> GSM28761 3 0.0000 0.9765 0.00 0.000 1.000 0.000 0.000
#> GSM11278 2 0.3756 0.6975 0.00 0.744 0.000 0.008 0.248
#> GSM11291 3 0.0000 0.9765 0.00 0.000 1.000 0.000 0.000
#> GSM11277 3 0.0000 0.9765 0.00 0.000 1.000 0.000 0.000
#> GSM11272 3 0.0000 0.9765 0.00 0.000 1.000 0.000 0.000
#> GSM11285 4 0.3086 0.7610 0.00 0.004 0.000 0.816 0.180
#> GSM28753 5 0.1478 0.8123 0.00 0.064 0.000 0.000 0.936
#> GSM28773 5 0.3160 0.8396 0.00 0.188 0.004 0.000 0.808
#> GSM28765 2 0.0963 0.8777 0.00 0.964 0.000 0.000 0.036
#> GSM28768 5 0.3143 0.8330 0.00 0.204 0.000 0.000 0.796
#> GSM28754 2 0.0963 0.8777 0.00 0.964 0.000 0.000 0.036
#> GSM28769 5 0.3074 0.8378 0.00 0.196 0.000 0.000 0.804
#> GSM11275 1 0.2280 0.8233 0.88 0.000 0.000 0.000 0.120
#> GSM11270 2 0.3756 0.6975 0.00 0.744 0.000 0.008 0.248
#> GSM11271 2 0.0000 0.8740 0.00 1.000 0.000 0.000 0.000
#> GSM11288 5 0.1638 0.7344 0.00 0.004 0.064 0.000 0.932
#> GSM11273 2 0.5282 0.6445 0.00 0.700 0.144 0.008 0.148
#> GSM28757 2 0.0963 0.8777 0.00 0.964 0.000 0.000 0.036
#> GSM11282 2 0.3756 0.6975 0.00 0.744 0.000 0.008 0.248
#> GSM28756 2 0.0162 0.8755 0.00 0.996 0.000 0.000 0.004
#> GSM11276 2 0.0963 0.8777 0.00 0.964 0.000 0.000 0.036
#> GSM28752 2 0.0963 0.8777 0.00 0.964 0.000 0.000 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 2 0.2260 0.8521 0.000 0.860 0.000 0.000 0.140 0.000
#> GSM28763 2 0.2558 0.8362 0.000 0.840 0.000 0.000 0.156 0.004
#> GSM28764 5 0.3864 0.0326 0.000 0.480 0.000 0.000 0.520 0.000
#> GSM11274 3 0.2772 0.8103 0.000 0.004 0.816 0.000 0.000 0.180
#> GSM28772 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.9995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.0865 0.8091 0.000 0.000 0.000 0.000 0.964 0.036
#> GSM28766 5 0.1444 0.7722 0.000 0.000 0.000 0.000 0.928 0.072
#> GSM11268 3 0.0146 0.9760 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM28767 5 0.0713 0.8138 0.000 0.000 0.000 0.000 0.972 0.028
#> GSM11286 5 0.3351 0.6181 0.000 0.288 0.000 0.000 0.712 0.000
#> GSM28751 2 0.1910 0.8662 0.000 0.892 0.000 0.000 0.108 0.000
#> GSM28770 5 0.0790 0.8117 0.000 0.000 0.000 0.000 0.968 0.032
#> GSM11283 4 0.0146 0.9570 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM11289 2 0.4141 0.2074 0.000 0.596 0.000 0.000 0.388 0.016
#> GSM11280 2 0.1152 0.8360 0.000 0.952 0.000 0.004 0.000 0.044
#> GSM28749 2 0.1794 0.8490 0.000 0.924 0.000 0.000 0.040 0.036
#> GSM28750 3 0.0146 0.9760 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM11290 3 0.0000 0.9757 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11294 3 0.0146 0.9750 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM28771 4 0.0146 0.9570 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM28760 4 0.0146 0.9570 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM28774 5 0.0790 0.8251 0.000 0.032 0.000 0.000 0.968 0.000
#> GSM11284 2 0.1410 0.8370 0.000 0.944 0.000 0.008 0.004 0.044
#> GSM28761 3 0.0146 0.9760 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM11278 6 0.3012 0.8830 0.000 0.008 0.000 0.000 0.196 0.796
#> GSM11291 3 0.0146 0.9750 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM11277 3 0.0146 0.9750 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM11272 3 0.0146 0.9760 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM11285 4 0.1714 0.8682 0.000 0.092 0.000 0.908 0.000 0.000
#> GSM28753 2 0.0806 0.8488 0.000 0.972 0.000 0.000 0.008 0.020
#> GSM28773 2 0.2357 0.8622 0.000 0.872 0.000 0.000 0.116 0.012
#> GSM28765 5 0.2520 0.7917 0.000 0.152 0.000 0.000 0.844 0.004
#> GSM28768 2 0.1814 0.8667 0.000 0.900 0.000 0.000 0.100 0.000
#> GSM28754 5 0.2006 0.8240 0.000 0.080 0.000 0.000 0.904 0.016
#> GSM28769 2 0.2402 0.8492 0.000 0.856 0.000 0.000 0.140 0.004
#> GSM11275 1 0.0146 0.9948 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM11270 6 0.2948 0.8809 0.000 0.008 0.000 0.000 0.188 0.804
#> GSM11271 5 0.0790 0.8117 0.000 0.000 0.000 0.000 0.968 0.032
#> GSM11288 2 0.1657 0.8344 0.000 0.928 0.016 0.000 0.000 0.056
#> GSM11273 6 0.3409 0.6367 0.000 0.004 0.144 0.000 0.044 0.808
#> GSM28757 5 0.2146 0.8125 0.000 0.116 0.000 0.000 0.880 0.004
#> GSM11282 6 0.3012 0.8830 0.000 0.008 0.000 0.000 0.196 0.796
#> GSM28756 5 0.0713 0.8138 0.000 0.000 0.000 0.000 0.972 0.028
#> GSM11276 5 0.2135 0.8076 0.000 0.128 0.000 0.000 0.872 0.000
#> GSM28752 5 0.2520 0.7917 0.000 0.152 0.000 0.000 0.844 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 tissue(p) k
#> CV:mclust 54 0.398 2
#> CV:mclust 53 0.443 3
#> CV:mclust 53 0.520 4
#> CV:mclust 52 0.409 5
#> CV:mclust 52 0.402 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.973 0.988 0.3838 0.628 0.628
#> 3 3 0.970 0.941 0.974 0.5704 0.740 0.599
#> 4 4 0.700 0.761 0.871 0.2014 0.839 0.614
#> 5 5 0.777 0.744 0.880 0.0795 0.899 0.650
#> 6 6 0.745 0.570 0.753 0.0527 0.905 0.595
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
#> GSM28762 2 0.0000 0.984 0.000 1.000
#> GSM28763 2 0.6531 0.804 0.168 0.832
#> GSM28764 2 0.0000 0.984 0.000 1.000
#> GSM11274 2 0.0000 0.984 0.000 1.000
#> GSM28772 1 0.0000 0.998 1.000 0.000
#> GSM11269 1 0.0000 0.998 1.000 0.000
#> GSM28775 1 0.0000 0.998 1.000 0.000
#> GSM11293 1 0.0000 0.998 1.000 0.000
#> GSM28755 1 0.0000 0.998 1.000 0.000
#> GSM11279 1 0.0000 0.998 1.000 0.000
#> GSM28758 1 0.0000 0.998 1.000 0.000
#> GSM11281 1 0.0000 0.998 1.000 0.000
#> GSM11287 1 0.0000 0.998 1.000 0.000
#> GSM28759 1 0.0000 0.998 1.000 0.000
#> GSM11292 2 0.0000 0.984 0.000 1.000
#> GSM28766 2 0.0000 0.984 0.000 1.000
#> GSM11268 2 0.0000 0.984 0.000 1.000
#> GSM28767 2 0.0000 0.984 0.000 1.000
#> GSM11286 2 0.0938 0.974 0.012 0.988
#> GSM28751 1 0.1843 0.970 0.972 0.028
#> GSM28770 2 0.0000 0.984 0.000 1.000
#> GSM11283 2 0.0000 0.984 0.000 1.000
#> GSM11289 2 0.0000 0.984 0.000 1.000
#> GSM11280 2 0.0000 0.984 0.000 1.000
#> GSM28749 2 0.0000 0.984 0.000 1.000
#> GSM28750 2 0.0000 0.984 0.000 1.000
#> GSM11290 2 0.0000 0.984 0.000 1.000
#> GSM11294 2 0.0000 0.984 0.000 1.000
#> GSM28771 2 0.0000 0.984 0.000 1.000
#> GSM28760 2 0.0000 0.984 0.000 1.000
#> GSM28774 2 0.0000 0.984 0.000 1.000
#> GSM11284 2 0.0000 0.984 0.000 1.000
#> GSM28761 2 0.0000 0.984 0.000 1.000
#> GSM11278 2 0.0000 0.984 0.000 1.000
#> GSM11291 2 0.0000 0.984 0.000 1.000
#> GSM11277 2 0.0000 0.984 0.000 1.000
#> GSM11272 2 0.5408 0.859 0.124 0.876
#> GSM11285 2 0.0000 0.984 0.000 1.000
#> GSM28753 2 0.0000 0.984 0.000 1.000
#> GSM28773 2 0.0000 0.984 0.000 1.000
#> GSM28765 2 0.0938 0.974 0.012 0.988
#> GSM28768 1 0.0000 0.998 1.000 0.000
#> GSM28754 2 0.0000 0.984 0.000 1.000
#> GSM28769 2 0.9044 0.549 0.320 0.680
#> GSM11275 1 0.0000 0.998 1.000 0.000
#> GSM11270 2 0.0000 0.984 0.000 1.000
#> GSM11271 2 0.0000 0.984 0.000 1.000
#> GSM11288 2 0.0000 0.984 0.000 1.000
#> GSM11273 2 0.0000 0.984 0.000 1.000
#> GSM28757 2 0.0000 0.984 0.000 1.000
#> GSM11282 2 0.0000 0.984 0.000 1.000
#> GSM28756 2 0.0000 0.984 0.000 1.000
#> GSM11276 2 0.0000 0.984 0.000 1.000
#> GSM28752 2 0.0376 0.981 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.0000 0.959 0.000 1.000 0.000
#> GSM28763 2 0.0000 0.959 0.000 1.000 0.000
#> GSM28764 2 0.0000 0.959 0.000 1.000 0.000
#> GSM11274 3 0.0000 0.989 0.000 0.000 1.000
#> GSM28772 1 0.0000 0.989 1.000 0.000 0.000
#> GSM11269 1 0.0000 0.989 1.000 0.000 0.000
#> GSM28775 1 0.0000 0.989 1.000 0.000 0.000
#> GSM11293 1 0.0000 0.989 1.000 0.000 0.000
#> GSM28755 1 0.0000 0.989 1.000 0.000 0.000
#> GSM11279 1 0.0000 0.989 1.000 0.000 0.000
#> GSM28758 1 0.0000 0.989 1.000 0.000 0.000
#> GSM11281 1 0.0000 0.989 1.000 0.000 0.000
#> GSM11287 1 0.0000 0.989 1.000 0.000 0.000
#> GSM28759 1 0.0000 0.989 1.000 0.000 0.000
#> GSM11292 2 0.0000 0.959 0.000 1.000 0.000
#> GSM28766 2 0.0237 0.957 0.000 0.996 0.004
#> GSM11268 3 0.0000 0.989 0.000 0.000 1.000
#> GSM28767 2 0.0000 0.959 0.000 1.000 0.000
#> GSM11286 2 0.0000 0.959 0.000 1.000 0.000
#> GSM28751 2 0.5882 0.484 0.348 0.652 0.000
#> GSM28770 2 0.0000 0.959 0.000 1.000 0.000
#> GSM11283 2 0.0000 0.959 0.000 1.000 0.000
#> GSM11289 2 0.0000 0.959 0.000 1.000 0.000
#> GSM11280 2 0.0000 0.959 0.000 1.000 0.000
#> GSM28749 2 0.0592 0.952 0.000 0.988 0.012
#> GSM28750 3 0.0000 0.989 0.000 0.000 1.000
#> GSM11290 3 0.0000 0.989 0.000 0.000 1.000
#> GSM11294 3 0.0000 0.989 0.000 0.000 1.000
#> GSM28771 2 0.0000 0.959 0.000 1.000 0.000
#> GSM28760 2 0.5529 0.608 0.000 0.704 0.296
#> GSM28774 2 0.0000 0.959 0.000 1.000 0.000
#> GSM11284 2 0.0000 0.959 0.000 1.000 0.000
#> GSM28761 3 0.0000 0.989 0.000 0.000 1.000
#> GSM11278 2 0.0424 0.954 0.000 0.992 0.008
#> GSM11291 3 0.0000 0.989 0.000 0.000 1.000
#> GSM11277 3 0.0000 0.989 0.000 0.000 1.000
#> GSM11272 3 0.0000 0.989 0.000 0.000 1.000
#> GSM11285 2 0.0000 0.959 0.000 1.000 0.000
#> GSM28753 2 0.0000 0.959 0.000 1.000 0.000
#> GSM28773 2 0.5810 0.529 0.000 0.664 0.336
#> GSM28765 2 0.0000 0.959 0.000 1.000 0.000
#> GSM28768 1 0.2796 0.869 0.908 0.092 0.000
#> GSM28754 2 0.0000 0.959 0.000 1.000 0.000
#> GSM28769 2 0.0237 0.957 0.004 0.996 0.000
#> GSM11275 1 0.0000 0.989 1.000 0.000 0.000
#> GSM11270 2 0.4291 0.781 0.000 0.820 0.180
#> GSM11271 2 0.0000 0.959 0.000 1.000 0.000
#> GSM11288 3 0.3406 0.889 0.028 0.068 0.904
#> GSM11273 3 0.0000 0.989 0.000 0.000 1.000
#> GSM28757 2 0.0000 0.959 0.000 1.000 0.000
#> GSM11282 2 0.0747 0.949 0.000 0.984 0.016
#> GSM28756 2 0.0000 0.959 0.000 1.000 0.000
#> GSM11276 2 0.0000 0.959 0.000 1.000 0.000
#> GSM28752 2 0.0000 0.959 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.2704 0.770 0.000 0.876 0.000 0.124
#> GSM28763 2 0.2814 0.757 0.000 0.868 0.000 0.132
#> GSM28764 2 0.0592 0.873 0.000 0.984 0.000 0.016
#> GSM11274 3 0.0707 0.862 0.000 0.000 0.980 0.020
#> GSM28772 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM11292 2 0.0921 0.873 0.000 0.972 0.000 0.028
#> GSM28766 2 0.0921 0.873 0.000 0.972 0.000 0.028
#> GSM11268 3 0.4543 0.694 0.000 0.000 0.676 0.324
#> GSM28767 2 0.0707 0.873 0.000 0.980 0.000 0.020
#> GSM11286 2 0.3356 0.747 0.000 0.824 0.000 0.176
#> GSM28751 4 0.7566 0.480 0.292 0.228 0.000 0.480
#> GSM28770 2 0.0592 0.873 0.000 0.984 0.000 0.016
#> GSM11283 4 0.4304 0.609 0.000 0.284 0.000 0.716
#> GSM11289 2 0.0469 0.872 0.000 0.988 0.000 0.012
#> GSM11280 4 0.3764 0.647 0.000 0.216 0.000 0.784
#> GSM28749 4 0.5386 0.423 0.000 0.344 0.024 0.632
#> GSM28750 3 0.3219 0.814 0.000 0.000 0.836 0.164
#> GSM11290 3 0.0188 0.867 0.000 0.000 0.996 0.004
#> GSM11294 3 0.0000 0.867 0.000 0.000 1.000 0.000
#> GSM28771 4 0.4808 0.634 0.000 0.236 0.028 0.736
#> GSM28760 4 0.5292 0.471 0.000 0.064 0.208 0.728
#> GSM28774 2 0.0469 0.872 0.000 0.988 0.000 0.012
#> GSM11284 2 0.4730 0.220 0.000 0.636 0.000 0.364
#> GSM28761 3 0.4564 0.687 0.000 0.000 0.672 0.328
#> GSM11278 2 0.2882 0.786 0.000 0.892 0.084 0.024
#> GSM11291 3 0.0000 0.867 0.000 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.867 0.000 0.000 1.000 0.000
#> GSM11272 3 0.4040 0.763 0.000 0.000 0.752 0.248
#> GSM11285 4 0.5183 0.421 0.000 0.408 0.008 0.584
#> GSM28753 4 0.4331 0.620 0.000 0.288 0.000 0.712
#> GSM28773 4 0.6546 0.370 0.000 0.172 0.192 0.636
#> GSM28765 2 0.2868 0.779 0.000 0.864 0.000 0.136
#> GSM28768 1 0.1936 0.927 0.940 0.032 0.000 0.028
#> GSM28754 2 0.0707 0.873 0.000 0.980 0.000 0.020
#> GSM28769 4 0.5244 0.428 0.012 0.388 0.000 0.600
#> GSM11275 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM11270 2 0.5560 0.222 0.000 0.584 0.392 0.024
#> GSM11271 2 0.0336 0.874 0.000 0.992 0.000 0.008
#> GSM11288 4 0.6316 -0.387 0.048 0.004 0.472 0.476
#> GSM11273 3 0.1042 0.851 0.000 0.008 0.972 0.020
#> GSM28757 2 0.2647 0.810 0.000 0.880 0.000 0.120
#> GSM11282 2 0.2174 0.829 0.000 0.928 0.052 0.020
#> GSM28756 2 0.0592 0.873 0.000 0.984 0.000 0.016
#> GSM11276 2 0.0336 0.873 0.000 0.992 0.000 0.008
#> GSM28752 2 0.1389 0.859 0.000 0.952 0.000 0.048
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28762 2 0.1965 0.87311 0.000 0.924 0.000 0.052 0.024
#> GSM28763 2 0.2685 0.84776 0.000 0.880 0.000 0.092 0.028
#> GSM28764 2 0.0771 0.88884 0.000 0.976 0.000 0.004 0.020
#> GSM11274 3 0.0451 0.80760 0.000 0.000 0.988 0.004 0.008
#> GSM28772 1 0.0000 0.97837 1.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.97837 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.97837 1.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.97837 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.97837 1.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.97837 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.97837 1.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.97837 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.97837 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.97837 1.000 0.000 0.000 0.000 0.000
#> GSM11292 2 0.1651 0.88386 0.000 0.944 0.012 0.008 0.036
#> GSM28766 2 0.2158 0.87440 0.000 0.920 0.020 0.008 0.052
#> GSM11268 5 0.3109 0.61573 0.000 0.000 0.200 0.000 0.800
#> GSM28767 2 0.1280 0.88675 0.000 0.960 0.008 0.008 0.024
#> GSM11286 2 0.4299 0.45958 0.000 0.608 0.000 0.004 0.388
#> GSM28751 5 0.6743 0.44395 0.148 0.124 0.000 0.112 0.616
#> GSM28770 2 0.1299 0.88567 0.000 0.960 0.012 0.008 0.020
#> GSM11283 4 0.0290 0.78889 0.000 0.008 0.000 0.992 0.000
#> GSM11289 2 0.1413 0.88545 0.000 0.956 0.012 0.012 0.020
#> GSM11280 4 0.2516 0.70507 0.000 0.000 0.000 0.860 0.140
#> GSM28749 5 0.1357 0.65216 0.000 0.048 0.004 0.000 0.948
#> GSM28750 3 0.4273 0.03682 0.000 0.000 0.552 0.000 0.448
#> GSM11290 3 0.1121 0.81189 0.000 0.000 0.956 0.000 0.044
#> GSM11294 3 0.0963 0.81648 0.000 0.000 0.964 0.000 0.036
#> GSM28771 4 0.0290 0.78889 0.000 0.008 0.000 0.992 0.000
#> GSM28760 4 0.0290 0.78889 0.000 0.008 0.000 0.992 0.000
#> GSM28774 2 0.1197 0.88347 0.000 0.952 0.000 0.000 0.048
#> GSM11284 4 0.4798 0.10095 0.000 0.440 0.000 0.540 0.020
#> GSM28761 5 0.3305 0.59954 0.000 0.000 0.224 0.000 0.776
#> GSM11278 2 0.3399 0.75686 0.000 0.812 0.168 0.000 0.020
#> GSM11291 3 0.0963 0.81648 0.000 0.000 0.964 0.000 0.036
#> GSM11277 3 0.0963 0.81648 0.000 0.000 0.964 0.000 0.036
#> GSM11272 5 0.4030 0.40571 0.000 0.000 0.352 0.000 0.648
#> GSM11285 4 0.0404 0.78781 0.000 0.012 0.000 0.988 0.000
#> GSM28753 4 0.4969 0.26424 0.000 0.036 0.000 0.588 0.376
#> GSM28773 5 0.1498 0.65935 0.000 0.016 0.024 0.008 0.952
#> GSM28765 5 0.4446 0.00679 0.000 0.476 0.000 0.004 0.520
#> GSM28768 1 0.4231 0.70627 0.776 0.060 0.000 0.004 0.160
#> GSM28754 2 0.1732 0.86906 0.000 0.920 0.000 0.000 0.080
#> GSM28769 5 0.4010 0.58059 0.000 0.160 0.000 0.056 0.784
#> GSM11275 1 0.0000 0.97837 1.000 0.000 0.000 0.000 0.000
#> GSM11270 3 0.4746 0.27248 0.000 0.376 0.600 0.000 0.024
#> GSM11271 2 0.0510 0.88861 0.000 0.984 0.000 0.000 0.016
#> GSM11288 5 0.3715 0.55620 0.000 0.000 0.260 0.004 0.736
#> GSM11273 3 0.0579 0.79259 0.000 0.008 0.984 0.000 0.008
#> GSM28757 2 0.4288 0.46739 0.000 0.612 0.000 0.004 0.384
#> GSM11282 2 0.1907 0.87073 0.000 0.928 0.044 0.000 0.028
#> GSM28756 2 0.1197 0.88086 0.000 0.952 0.000 0.000 0.048
#> GSM11276 2 0.0290 0.88799 0.000 0.992 0.000 0.000 0.008
#> GSM28752 2 0.3123 0.78580 0.000 0.812 0.000 0.004 0.184
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 2 0.4614 0.24162 0.000 0.568 0.008 0.004 0.400 0.020
#> GSM28763 2 0.4399 0.25999 0.000 0.604 0.008 0.008 0.372 0.008
#> GSM28764 5 0.0363 0.64487 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM11274 3 0.0692 0.75482 0.000 0.004 0.976 0.000 0.000 0.020
#> GSM28772 1 0.0000 0.95916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.95916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.95916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0146 0.95806 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.95916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.95916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0260 0.95601 0.992 0.008 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.95916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.95916 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0146 0.95806 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM11292 5 0.1897 0.58505 0.000 0.004 0.004 0.000 0.908 0.084
#> GSM28766 5 0.3411 0.42580 0.000 0.004 0.008 0.000 0.756 0.232
#> GSM11268 6 0.1500 0.81511 0.000 0.052 0.012 0.000 0.000 0.936
#> GSM28767 5 0.0146 0.64497 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM11286 2 0.4176 0.45903 0.000 0.720 0.000 0.000 0.212 0.068
#> GSM28751 2 0.7040 0.29367 0.088 0.536 0.000 0.032 0.152 0.192
#> GSM28770 5 0.0291 0.64583 0.000 0.004 0.004 0.000 0.992 0.000
#> GSM11283 4 0.0000 0.73743 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11289 5 0.0291 0.64403 0.000 0.000 0.004 0.000 0.992 0.004
#> GSM11280 4 0.4193 0.55858 0.000 0.272 0.000 0.684 0.000 0.044
#> GSM28749 6 0.4687 0.45861 0.000 0.336 0.000 0.000 0.060 0.604
#> GSM28750 6 0.3014 0.71619 0.000 0.012 0.184 0.000 0.000 0.804
#> GSM11290 3 0.2520 0.70267 0.000 0.004 0.844 0.000 0.000 0.152
#> GSM11294 3 0.1970 0.75602 0.000 0.008 0.900 0.000 0.000 0.092
#> GSM28771 4 0.0000 0.73743 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM28760 4 0.0000 0.73743 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM28774 5 0.4473 -0.02940 0.000 0.480 0.028 0.000 0.492 0.000
#> GSM11284 4 0.5711 0.07402 0.000 0.380 0.000 0.472 0.144 0.004
#> GSM28761 6 0.1059 0.82474 0.000 0.016 0.016 0.000 0.004 0.964
#> GSM11278 3 0.5852 0.08329 0.000 0.328 0.464 0.000 0.208 0.000
#> GSM11291 3 0.1918 0.75820 0.000 0.008 0.904 0.000 0.000 0.088
#> GSM11277 3 0.1753 0.75994 0.000 0.004 0.912 0.000 0.000 0.084
#> GSM11272 6 0.2997 0.82058 0.000 0.060 0.096 0.000 0.000 0.844
#> GSM11285 4 0.1219 0.72104 0.000 0.004 0.000 0.948 0.048 0.000
#> GSM28753 4 0.7060 0.25520 0.000 0.264 0.000 0.440 0.104 0.192
#> GSM28773 2 0.3864 -0.25239 0.000 0.520 0.000 0.000 0.000 0.480
#> GSM28765 2 0.5595 0.43523 0.000 0.540 0.000 0.000 0.268 0.192
#> GSM28768 1 0.4511 0.37526 0.620 0.332 0.000 0.000 0.048 0.000
#> GSM28754 2 0.4385 0.00275 0.000 0.532 0.024 0.000 0.444 0.000
#> GSM28769 2 0.5483 0.20987 0.008 0.584 0.000 0.012 0.088 0.308
#> GSM11275 1 0.0260 0.95601 0.992 0.008 0.000 0.000 0.000 0.000
#> GSM11270 3 0.4406 0.40225 0.000 0.336 0.624 0.000 0.040 0.000
#> GSM11271 5 0.0547 0.64325 0.000 0.020 0.000 0.000 0.980 0.000
#> GSM11288 6 0.2326 0.82873 0.000 0.028 0.060 0.000 0.012 0.900
#> GSM11273 3 0.0458 0.74684 0.000 0.016 0.984 0.000 0.000 0.000
#> GSM28757 2 0.3766 0.44260 0.000 0.748 0.000 0.000 0.212 0.040
#> GSM11282 5 0.5997 0.03651 0.000 0.344 0.240 0.000 0.416 0.000
#> GSM28756 5 0.4262 -0.01974 0.000 0.476 0.016 0.000 0.508 0.000
#> GSM11276 5 0.2668 0.51211 0.000 0.168 0.000 0.000 0.828 0.004
#> GSM28752 5 0.4535 -0.19083 0.000 0.480 0.000 0.000 0.488 0.032
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 tissue(p) k
#> CV:NMF 54 0.398 2
#> CV:NMF 53 0.373 3
#> CV:NMF 45 0.504 4
#> CV:NMF 45 0.441 5
#> CV:NMF 34 0.430 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.3313 0.669 0.669
#> 3 3 0.841 0.894 0.950 0.7438 0.716 0.576
#> 4 4 0.782 0.820 0.912 0.1627 0.969 0.918
#> 5 5 0.835 0.847 0.915 0.0695 0.930 0.803
#> 6 6 0.891 0.912 0.959 0.0281 0.986 0.951
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
#> GSM28762 2 0.0000 1.000 0.000 1.000
#> GSM28763 2 0.0000 1.000 0.000 1.000
#> GSM28764 2 0.0000 1.000 0.000 1.000
#> GSM11274 2 0.0000 1.000 0.000 1.000
#> GSM28772 1 0.0000 1.000 1.000 0.000
#> GSM11269 1 0.0000 1.000 1.000 0.000
#> GSM28775 1 0.0000 1.000 1.000 0.000
#> GSM11293 1 0.0000 1.000 1.000 0.000
#> GSM28755 1 0.0000 1.000 1.000 0.000
#> GSM11279 1 0.0000 1.000 1.000 0.000
#> GSM28758 1 0.0000 1.000 1.000 0.000
#> GSM11281 1 0.0000 1.000 1.000 0.000
#> GSM11287 1 0.0000 1.000 1.000 0.000
#> GSM28759 1 0.0000 1.000 1.000 0.000
#> GSM11292 2 0.0000 1.000 0.000 1.000
#> GSM28766 2 0.0000 1.000 0.000 1.000
#> GSM11268 2 0.0000 1.000 0.000 1.000
#> GSM28767 2 0.0000 1.000 0.000 1.000
#> GSM11286 2 0.0000 1.000 0.000 1.000
#> GSM28751 2 0.0000 1.000 0.000 1.000
#> GSM28770 2 0.0000 1.000 0.000 1.000
#> GSM11283 2 0.0000 1.000 0.000 1.000
#> GSM11289 2 0.0000 1.000 0.000 1.000
#> GSM11280 2 0.0000 1.000 0.000 1.000
#> GSM28749 2 0.0000 1.000 0.000 1.000
#> GSM28750 2 0.0000 1.000 0.000 1.000
#> GSM11290 2 0.0000 1.000 0.000 1.000
#> GSM11294 2 0.0000 1.000 0.000 1.000
#> GSM28771 2 0.0000 1.000 0.000 1.000
#> GSM28760 2 0.0000 1.000 0.000 1.000
#> GSM28774 2 0.0000 1.000 0.000 1.000
#> GSM11284 2 0.0000 1.000 0.000 1.000
#> GSM28761 2 0.0000 1.000 0.000 1.000
#> GSM11278 2 0.0000 1.000 0.000 1.000
#> GSM11291 2 0.0000 1.000 0.000 1.000
#> GSM11277 2 0.0000 1.000 0.000 1.000
#> GSM11272 2 0.0000 1.000 0.000 1.000
#> GSM11285 2 0.0000 1.000 0.000 1.000
#> GSM28753 2 0.0000 1.000 0.000 1.000
#> GSM28773 2 0.0000 1.000 0.000 1.000
#> GSM28765 2 0.0000 1.000 0.000 1.000
#> GSM28768 2 0.0376 0.996 0.004 0.996
#> GSM28754 2 0.0000 1.000 0.000 1.000
#> GSM28769 2 0.0000 1.000 0.000 1.000
#> GSM11275 1 0.0000 1.000 1.000 0.000
#> GSM11270 2 0.0000 1.000 0.000 1.000
#> GSM11271 2 0.0000 1.000 0.000 1.000
#> GSM11288 2 0.0000 1.000 0.000 1.000
#> GSM11273 2 0.0000 1.000 0.000 1.000
#> GSM28757 2 0.0000 1.000 0.000 1.000
#> GSM11282 2 0.0000 1.000 0.000 1.000
#> GSM28756 2 0.0000 1.000 0.000 1.000
#> GSM11276 2 0.0000 1.000 0.000 1.000
#> GSM28752 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.6291 0.998 0.000 0.532 0.468
#> GSM28763 2 0.6291 0.998 0.000 0.532 0.468
#> GSM28764 2 0.6291 0.998 0.000 0.532 0.468
#> GSM11274 3 0.0424 0.436 0.008 0.000 0.992
#> GSM28772 1 0.6291 1.000 0.532 0.468 0.000
#> GSM11269 1 0.6291 1.000 0.532 0.468 0.000
#> GSM28775 1 0.6291 1.000 0.532 0.468 0.000
#> GSM11293 1 0.6291 1.000 0.532 0.468 0.000
#> GSM28755 1 0.6291 1.000 0.532 0.468 0.000
#> GSM11279 1 0.6291 1.000 0.532 0.468 0.000
#> GSM28758 1 0.6291 1.000 0.532 0.468 0.000
#> GSM11281 1 0.6291 1.000 0.532 0.468 0.000
#> GSM11287 1 0.6291 1.000 0.532 0.468 0.000
#> GSM28759 1 0.6291 1.000 0.532 0.468 0.000
#> GSM11292 2 0.6299 0.991 0.000 0.524 0.476
#> GSM28766 2 0.6299 0.991 0.000 0.524 0.476
#> GSM11268 3 0.6291 0.712 0.468 0.000 0.532
#> GSM28767 2 0.6299 0.991 0.000 0.524 0.476
#> GSM11286 2 0.6291 0.998 0.000 0.532 0.468
#> GSM28751 2 0.6291 0.998 0.000 0.532 0.468
#> GSM28770 2 0.6299 0.991 0.000 0.524 0.476
#> GSM11283 2 0.6291 0.998 0.000 0.532 0.468
#> GSM11289 2 0.6299 0.991 0.000 0.524 0.476
#> GSM11280 2 0.6291 0.998 0.000 0.532 0.468
#> GSM28749 2 0.6291 0.998 0.000 0.532 0.468
#> GSM28750 3 0.6291 0.712 0.468 0.000 0.532
#> GSM11290 3 0.6291 0.712 0.468 0.000 0.532
#> GSM11294 3 0.6291 0.712 0.468 0.000 0.532
#> GSM28771 2 0.6291 0.998 0.000 0.532 0.468
#> GSM28760 2 0.6291 0.998 0.000 0.532 0.468
#> GSM28774 2 0.6291 0.998 0.000 0.532 0.468
#> GSM11284 2 0.6291 0.998 0.000 0.532 0.468
#> GSM28761 3 0.6291 0.712 0.468 0.000 0.532
#> GSM11278 3 0.0000 0.423 0.000 0.000 1.000
#> GSM11291 3 0.6291 0.712 0.468 0.000 0.532
#> GSM11277 3 0.6291 0.712 0.468 0.000 0.532
#> GSM11272 3 0.6291 0.712 0.468 0.000 0.532
#> GSM11285 2 0.6291 0.998 0.000 0.532 0.468
#> GSM28753 2 0.6291 0.998 0.000 0.532 0.468
#> GSM28773 2 0.6291 0.998 0.000 0.532 0.468
#> GSM28765 2 0.6291 0.998 0.000 0.532 0.468
#> GSM28768 2 0.6286 0.993 0.000 0.536 0.464
#> GSM28754 2 0.6291 0.998 0.000 0.532 0.468
#> GSM28769 2 0.6291 0.998 0.000 0.532 0.468
#> GSM11275 1 0.6291 1.000 0.532 0.468 0.000
#> GSM11270 3 0.0000 0.423 0.000 0.000 1.000
#> GSM11271 2 0.6299 0.991 0.000 0.524 0.476
#> GSM11288 3 0.8894 0.578 0.300 0.152 0.548
#> GSM11273 3 0.0000 0.423 0.000 0.000 1.000
#> GSM28757 2 0.6291 0.998 0.000 0.532 0.468
#> GSM11282 3 0.0000 0.423 0.000 0.000 1.000
#> GSM28756 2 0.6291 0.998 0.000 0.532 0.468
#> GSM11276 2 0.6291 0.998 0.000 0.532 0.468
#> GSM28752 2 0.6291 0.998 0.000 0.532 0.468
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM28763 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM28764 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM11274 3 0.0000 0.688 0.000 0.000 1.000 0.000
#> GSM28772 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11292 2 0.3688 0.791 0.000 0.792 0.208 0.000
#> GSM28766 2 0.3688 0.791 0.000 0.792 0.208 0.000
#> GSM11268 4 0.0000 0.817 0.000 0.000 0.000 1.000
#> GSM28767 2 0.3688 0.791 0.000 0.792 0.208 0.000
#> GSM11286 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM28751 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM28770 2 0.3688 0.791 0.000 0.792 0.208 0.000
#> GSM11283 2 0.4454 0.648 0.000 0.692 0.308 0.000
#> GSM11289 2 0.3688 0.791 0.000 0.792 0.208 0.000
#> GSM11280 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM28749 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM28750 4 0.1022 0.788 0.000 0.000 0.032 0.968
#> GSM11290 3 0.4989 0.407 0.000 0.000 0.528 0.472
#> GSM11294 3 0.4989 0.407 0.000 0.000 0.528 0.472
#> GSM28771 2 0.4454 0.648 0.000 0.692 0.308 0.000
#> GSM28760 2 0.4454 0.648 0.000 0.692 0.308 0.000
#> GSM28774 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM11284 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM28761 4 0.0000 0.817 0.000 0.000 0.000 1.000
#> GSM11278 3 0.0336 0.691 0.000 0.008 0.992 0.000
#> GSM11291 3 0.4989 0.407 0.000 0.000 0.528 0.472
#> GSM11277 3 0.4989 0.407 0.000 0.000 0.528 0.472
#> GSM11272 4 0.0000 0.817 0.000 0.000 0.000 1.000
#> GSM11285 2 0.4134 0.712 0.000 0.740 0.260 0.000
#> GSM28753 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM28773 2 0.1118 0.890 0.000 0.964 0.036 0.000
#> GSM28765 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM28768 2 0.0188 0.903 0.004 0.996 0.000 0.000
#> GSM28754 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM28769 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM11275 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11270 3 0.0336 0.691 0.000 0.008 0.992 0.000
#> GSM11271 2 0.3688 0.791 0.000 0.792 0.208 0.000
#> GSM11288 4 0.4792 0.373 0.000 0.312 0.008 0.680
#> GSM11273 3 0.0336 0.691 0.000 0.008 0.992 0.000
#> GSM28757 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM11282 3 0.0336 0.691 0.000 0.008 0.992 0.000
#> GSM28756 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM11276 2 0.0000 0.905 0.000 1.000 0.000 0.000
#> GSM28752 2 0.0000 0.905 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
#> GSM28762 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM28763 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM28764 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM11274 3 0.3895 0.630 0.000 0.000 0.680 0.320 0.000
#> GSM28772 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM11292 2 0.4159 0.766 0.000 0.776 0.156 0.068 0.000
#> GSM28766 2 0.4159 0.766 0.000 0.776 0.156 0.068 0.000
#> GSM11268 5 0.0000 0.832 0.000 0.000 0.000 0.000 1.000
#> GSM28767 2 0.4159 0.766 0.000 0.776 0.156 0.068 0.000
#> GSM11286 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM28751 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM28770 2 0.4159 0.766 0.000 0.776 0.156 0.068 0.000
#> GSM11283 4 0.1478 0.901 0.000 0.064 0.000 0.936 0.000
#> GSM11289 2 0.4159 0.766 0.000 0.776 0.156 0.068 0.000
#> GSM11280 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM28749 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM28750 5 0.1732 0.782 0.000 0.000 0.080 0.000 0.920
#> GSM11290 3 0.3074 0.563 0.000 0.000 0.804 0.000 0.196
#> GSM11294 3 0.3074 0.563 0.000 0.000 0.804 0.000 0.196
#> GSM28771 4 0.1478 0.901 0.000 0.064 0.000 0.936 0.000
#> GSM28760 4 0.1478 0.901 0.000 0.064 0.000 0.936 0.000
#> GSM28774 2 0.0162 0.931 0.000 0.996 0.000 0.004 0.000
#> GSM11284 2 0.0162 0.931 0.000 0.996 0.000 0.004 0.000
#> GSM28761 5 0.0000 0.832 0.000 0.000 0.000 0.000 1.000
#> GSM11278 3 0.4165 0.632 0.000 0.008 0.672 0.320 0.000
#> GSM11291 3 0.3074 0.563 0.000 0.000 0.804 0.000 0.196
#> GSM11277 3 0.3074 0.563 0.000 0.000 0.804 0.000 0.196
#> GSM11272 5 0.0000 0.832 0.000 0.000 0.000 0.000 1.000
#> GSM11285 4 0.3143 0.714 0.000 0.204 0.000 0.796 0.000
#> GSM28753 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM28773 2 0.1041 0.911 0.000 0.964 0.032 0.004 0.000
#> GSM28765 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM28768 2 0.0162 0.930 0.004 0.996 0.000 0.000 0.000
#> GSM28754 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM28769 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM11275 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM11270 3 0.4165 0.632 0.000 0.008 0.672 0.320 0.000
#> GSM11271 2 0.4159 0.766 0.000 0.776 0.156 0.068 0.000
#> GSM11288 5 0.4213 0.377 0.000 0.308 0.000 0.012 0.680
#> GSM11273 3 0.4165 0.632 0.000 0.008 0.672 0.320 0.000
#> GSM28757 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM11282 3 0.4165 0.632 0.000 0.008 0.672 0.320 0.000
#> GSM28756 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM11276 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000
#> GSM28752 2 0.0000 0.932 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
#> GSM28762 2 0.0146 0.928 0.000 0.996 0.004 0.000 0.000 0.00
#> GSM28763 2 0.0146 0.928 0.000 0.996 0.004 0.000 0.000 0.00
#> GSM28764 2 0.0260 0.926 0.000 0.992 0.000 0.000 0.008 0.00
#> GSM11274 5 0.0260 0.988 0.000 0.000 0.008 0.000 0.992 0.00
#> GSM28772 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM11269 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM28775 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM11293 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM28755 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM11279 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM28758 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM11281 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM11287 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM28759 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM11292 2 0.3892 0.761 0.000 0.752 0.000 0.060 0.188 0.00
#> GSM28766 2 0.3892 0.761 0.000 0.752 0.000 0.060 0.188 0.00
#> GSM11268 6 0.0000 0.832 0.000 0.000 0.000 0.000 0.000 1.00
#> GSM28767 2 0.3892 0.761 0.000 0.752 0.000 0.060 0.188 0.00
#> GSM11286 2 0.0146 0.928 0.000 0.996 0.004 0.000 0.000 0.00
#> GSM28751 2 0.0146 0.928 0.000 0.996 0.004 0.000 0.000 0.00
#> GSM28770 2 0.3892 0.761 0.000 0.752 0.000 0.060 0.188 0.00
#> GSM11283 4 0.0000 0.906 0.000 0.000 0.000 1.000 0.000 0.00
#> GSM11289 2 0.3892 0.761 0.000 0.752 0.000 0.060 0.188 0.00
#> GSM11280 2 0.0146 0.928 0.000 0.996 0.004 0.000 0.000 0.00
#> GSM28749 2 0.0146 0.928 0.000 0.996 0.004 0.000 0.000 0.00
#> GSM28750 6 0.1556 0.782 0.000 0.000 0.080 0.000 0.000 0.92
#> GSM11290 3 0.0146 1.000 0.000 0.000 0.996 0.000 0.004 0.00
#> GSM11294 3 0.0146 1.000 0.000 0.000 0.996 0.000 0.004 0.00
#> GSM28771 4 0.0000 0.906 0.000 0.000 0.000 1.000 0.000 0.00
#> GSM28760 4 0.0000 0.906 0.000 0.000 0.000 1.000 0.000 0.00
#> GSM28774 2 0.0405 0.924 0.000 0.988 0.000 0.004 0.008 0.00
#> GSM11284 2 0.0405 0.924 0.000 0.988 0.000 0.004 0.008 0.00
#> GSM28761 6 0.0000 0.832 0.000 0.000 0.000 0.000 0.000 1.00
#> GSM11278 5 0.0000 0.997 0.000 0.000 0.000 0.000 1.000 0.00
#> GSM11291 3 0.0146 1.000 0.000 0.000 0.996 0.000 0.004 0.00
#> GSM11277 3 0.0146 1.000 0.000 0.000 0.996 0.000 0.004 0.00
#> GSM11272 6 0.0000 0.832 0.000 0.000 0.000 0.000 0.000 1.00
#> GSM11285 4 0.2442 0.713 0.000 0.144 0.000 0.852 0.004 0.00
#> GSM28753 2 0.0146 0.928 0.000 0.996 0.004 0.000 0.000 0.00
#> GSM28773 2 0.1152 0.907 0.000 0.952 0.004 0.000 0.044 0.00
#> GSM28765 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000 0.00
#> GSM28768 2 0.0291 0.926 0.004 0.992 0.004 0.000 0.000 0.00
#> GSM28754 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000 0.00
#> GSM28769 2 0.0146 0.928 0.000 0.996 0.004 0.000 0.000 0.00
#> GSM11275 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.00
#> GSM11270 5 0.0000 0.997 0.000 0.000 0.000 0.000 1.000 0.00
#> GSM11271 2 0.3892 0.761 0.000 0.752 0.000 0.060 0.188 0.00
#> GSM11288 6 0.3853 0.400 0.000 0.304 0.000 0.016 0.000 0.68
#> GSM11273 5 0.0000 0.997 0.000 0.000 0.000 0.000 1.000 0.00
#> GSM28757 2 0.0146 0.928 0.000 0.996 0.004 0.000 0.000 0.00
#> GSM11282 5 0.0000 0.997 0.000 0.000 0.000 0.000 1.000 0.00
#> GSM28756 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000 0.00
#> GSM11276 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000 0.00
#> GSM28752 2 0.0000 0.928 0.000 1.000 0.000 0.000 0.000 0.00
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:hclust 54 0.398 2
#> MAD:hclust 49 0.368 3
#> MAD:hclust 49 0.348 4
#> MAD:hclust 53 0.481 5
#> MAD:hclust 53 0.448 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.399 0.798 0.852 0.3659 0.669 0.669
#> 3 3 1.000 0.983 0.980 0.5290 0.769 0.656
#> 4 4 0.682 0.712 0.795 0.2510 0.811 0.570
#> 5 5 0.656 0.657 0.766 0.0832 0.919 0.722
#> 6 6 0.726 0.679 0.788 0.0651 0.910 0.669
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
#> GSM28762 2 0.1843 0.837 0.028 0.972
#> GSM28763 2 0.1843 0.837 0.028 0.972
#> GSM28764 2 0.1843 0.837 0.028 0.972
#> GSM11274 2 0.8207 0.646 0.256 0.744
#> GSM28772 1 0.8207 1.000 0.744 0.256
#> GSM11269 1 0.8207 1.000 0.744 0.256
#> GSM28775 1 0.8207 1.000 0.744 0.256
#> GSM11293 1 0.8207 1.000 0.744 0.256
#> GSM28755 1 0.8207 1.000 0.744 0.256
#> GSM11279 1 0.8207 1.000 0.744 0.256
#> GSM28758 1 0.8207 1.000 0.744 0.256
#> GSM11281 1 0.8207 1.000 0.744 0.256
#> GSM11287 1 0.8207 1.000 0.744 0.256
#> GSM28759 1 0.8207 1.000 0.744 0.256
#> GSM11292 2 0.0000 0.840 0.000 1.000
#> GSM28766 2 0.0376 0.838 0.004 0.996
#> GSM11268 2 0.9933 0.449 0.452 0.548
#> GSM28767 2 0.0000 0.840 0.000 1.000
#> GSM11286 2 0.1843 0.837 0.028 0.972
#> GSM28751 2 0.1843 0.837 0.028 0.972
#> GSM28770 2 0.0000 0.840 0.000 1.000
#> GSM11283 2 0.1843 0.837 0.028 0.972
#> GSM11289 2 0.0000 0.840 0.000 1.000
#> GSM11280 2 0.1843 0.837 0.028 0.972
#> GSM28749 2 0.0000 0.840 0.000 1.000
#> GSM28750 2 0.9933 0.449 0.452 0.548
#> GSM11290 2 0.9933 0.449 0.452 0.548
#> GSM11294 2 0.9933 0.449 0.452 0.548
#> GSM28771 2 0.0000 0.840 0.000 1.000
#> GSM28760 2 0.4298 0.791 0.088 0.912
#> GSM28774 2 0.1843 0.837 0.028 0.972
#> GSM11284 2 0.0000 0.840 0.000 1.000
#> GSM28761 2 0.9933 0.449 0.452 0.548
#> GSM11278 2 0.3114 0.814 0.056 0.944
#> GSM11291 2 0.9933 0.449 0.452 0.548
#> GSM11277 2 0.9933 0.449 0.452 0.548
#> GSM11272 2 0.9933 0.449 0.452 0.548
#> GSM11285 2 0.0672 0.837 0.008 0.992
#> GSM28753 2 0.1843 0.837 0.028 0.972
#> GSM28773 2 0.0000 0.840 0.000 1.000
#> GSM28765 2 0.1843 0.837 0.028 0.972
#> GSM28768 2 0.5059 0.744 0.112 0.888
#> GSM28754 2 0.1843 0.837 0.028 0.972
#> GSM28769 2 0.1843 0.837 0.028 0.972
#> GSM11275 1 0.8207 1.000 0.744 0.256
#> GSM11270 2 0.3114 0.814 0.056 0.944
#> GSM11271 2 0.0000 0.840 0.000 1.000
#> GSM11288 2 0.7299 0.611 0.204 0.796
#> GSM11273 2 0.8207 0.646 0.256 0.744
#> GSM28757 2 0.1843 0.837 0.028 0.972
#> GSM11282 2 0.3114 0.814 0.056 0.944
#> GSM28756 2 0.1843 0.837 0.028 0.972
#> GSM11276 2 0.1843 0.837 0.028 0.972
#> GSM28752 2 0.1843 0.837 0.028 0.972
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28763 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28764 2 0.0000 0.987 0.000 1.000 0.000
#> GSM11274 3 0.0424 0.983 0.000 0.008 0.992
#> GSM28772 1 0.1289 0.999 0.968 0.032 0.000
#> GSM11269 1 0.1289 0.999 0.968 0.032 0.000
#> GSM28775 1 0.1289 0.999 0.968 0.032 0.000
#> GSM11293 1 0.1525 0.998 0.964 0.032 0.004
#> GSM28755 1 0.1289 0.999 0.968 0.032 0.000
#> GSM11279 1 0.1289 0.999 0.968 0.032 0.000
#> GSM28758 1 0.1525 0.998 0.964 0.032 0.004
#> GSM11281 1 0.1289 0.999 0.968 0.032 0.000
#> GSM11287 1 0.1289 0.999 0.968 0.032 0.000
#> GSM28759 1 0.1525 0.998 0.964 0.032 0.004
#> GSM11292 2 0.0592 0.984 0.000 0.988 0.012
#> GSM28766 2 0.0592 0.984 0.000 0.988 0.012
#> GSM11268 3 0.1711 0.988 0.032 0.008 0.960
#> GSM28767 2 0.0592 0.984 0.000 0.988 0.012
#> GSM11286 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28751 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28770 2 0.0592 0.984 0.000 0.988 0.012
#> GSM11283 2 0.0829 0.978 0.012 0.984 0.004
#> GSM11289 2 0.0592 0.984 0.000 0.988 0.012
#> GSM11280 2 0.0237 0.985 0.000 0.996 0.004
#> GSM28749 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28750 3 0.1711 0.988 0.032 0.008 0.960
#> GSM11290 3 0.1015 0.990 0.012 0.008 0.980
#> GSM11294 3 0.1015 0.990 0.012 0.008 0.980
#> GSM28771 2 0.0829 0.978 0.012 0.984 0.004
#> GSM28760 2 0.1999 0.961 0.012 0.952 0.036
#> GSM28774 2 0.0237 0.986 0.000 0.996 0.004
#> GSM11284 2 0.0237 0.986 0.000 0.996 0.004
#> GSM28761 3 0.1711 0.988 0.032 0.008 0.960
#> GSM11278 2 0.0892 0.980 0.000 0.980 0.020
#> GSM11291 3 0.1015 0.990 0.012 0.008 0.980
#> GSM11277 3 0.1015 0.990 0.012 0.008 0.980
#> GSM11272 3 0.1711 0.988 0.032 0.008 0.960
#> GSM11285 2 0.1337 0.976 0.012 0.972 0.016
#> GSM28753 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28773 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28765 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28768 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28754 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28769 2 0.0000 0.987 0.000 1.000 0.000
#> GSM11275 1 0.1525 0.998 0.964 0.032 0.004
#> GSM11270 2 0.0892 0.980 0.000 0.980 0.020
#> GSM11271 2 0.0592 0.984 0.000 0.988 0.012
#> GSM11288 2 0.5122 0.736 0.012 0.788 0.200
#> GSM11273 3 0.0424 0.983 0.000 0.008 0.992
#> GSM28757 2 0.0000 0.987 0.000 1.000 0.000
#> GSM11282 2 0.0892 0.980 0.000 0.980 0.020
#> GSM28756 2 0.0237 0.986 0.000 0.996 0.004
#> GSM11276 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28752 2 0.0000 0.987 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 4 0.4790 0.7701 0.000 0.380 0.000 0.620
#> GSM28763 4 0.4790 0.7701 0.000 0.380 0.000 0.620
#> GSM28764 2 0.4500 0.3237 0.000 0.684 0.000 0.316
#> GSM11274 3 0.2647 0.8298 0.000 0.120 0.880 0.000
#> GSM28772 1 0.0000 0.9933 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.9933 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.9933 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0707 0.9884 0.980 0.000 0.000 0.020
#> GSM28755 1 0.0000 0.9933 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.9933 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0817 0.9869 0.976 0.000 0.000 0.024
#> GSM11281 1 0.0000 0.9933 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.9933 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0707 0.9884 0.980 0.000 0.000 0.020
#> GSM11292 2 0.2149 0.7177 0.000 0.912 0.000 0.088
#> GSM28766 2 0.2149 0.7177 0.000 0.912 0.000 0.088
#> GSM11268 3 0.3486 0.8701 0.000 0.000 0.812 0.188
#> GSM28767 2 0.2149 0.7177 0.000 0.912 0.000 0.088
#> GSM11286 4 0.4804 0.7647 0.000 0.384 0.000 0.616
#> GSM28751 4 0.4790 0.7701 0.000 0.380 0.000 0.620
#> GSM28770 2 0.2149 0.7177 0.000 0.912 0.000 0.088
#> GSM11283 4 0.4605 0.5233 0.000 0.336 0.000 0.664
#> GSM11289 2 0.2149 0.7177 0.000 0.912 0.000 0.088
#> GSM11280 4 0.4304 0.7448 0.000 0.284 0.000 0.716
#> GSM28749 4 0.4008 0.7170 0.000 0.244 0.000 0.756
#> GSM28750 3 0.3486 0.8701 0.000 0.000 0.812 0.188
#> GSM11290 3 0.0000 0.8857 0.000 0.000 1.000 0.000
#> GSM11294 3 0.0000 0.8857 0.000 0.000 1.000 0.000
#> GSM28771 4 0.4643 0.5107 0.000 0.344 0.000 0.656
#> GSM28760 2 0.5039 0.0690 0.000 0.592 0.004 0.404
#> GSM28774 2 0.3801 0.5668 0.000 0.780 0.000 0.220
#> GSM11284 2 0.3172 0.6833 0.000 0.840 0.000 0.160
#> GSM28761 3 0.3486 0.8701 0.000 0.000 0.812 0.188
#> GSM11278 2 0.0376 0.6667 0.000 0.992 0.004 0.004
#> GSM11291 3 0.0000 0.8857 0.000 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.8857 0.000 0.000 1.000 0.000
#> GSM11272 3 0.3486 0.8701 0.000 0.000 0.812 0.188
#> GSM11285 2 0.3400 0.4985 0.000 0.820 0.000 0.180
#> GSM28753 4 0.4454 0.7584 0.000 0.308 0.000 0.692
#> GSM28773 4 0.4222 0.7391 0.000 0.272 0.000 0.728
#> GSM28765 4 0.4996 0.4901 0.000 0.484 0.000 0.516
#> GSM28768 4 0.4776 0.7698 0.000 0.376 0.000 0.624
#> GSM28754 2 0.4941 -0.2585 0.000 0.564 0.000 0.436
#> GSM28769 4 0.4790 0.7701 0.000 0.380 0.000 0.620
#> GSM11275 1 0.0817 0.9869 0.976 0.000 0.000 0.024
#> GSM11270 2 0.0376 0.6667 0.000 0.992 0.004 0.004
#> GSM11271 2 0.2149 0.7177 0.000 0.912 0.000 0.088
#> GSM11288 4 0.4888 0.3704 0.000 0.096 0.124 0.780
#> GSM11273 3 0.4624 0.6031 0.000 0.340 0.660 0.000
#> GSM28757 4 0.4817 0.7634 0.000 0.388 0.000 0.612
#> GSM11282 2 0.0376 0.6667 0.000 0.992 0.004 0.004
#> GSM28756 2 0.3837 0.5595 0.000 0.776 0.000 0.224
#> GSM11276 2 0.4790 0.0920 0.000 0.620 0.000 0.380
#> GSM28752 2 0.4843 0.0132 0.000 0.604 0.000 0.396
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28762 2 0.112 0.7014 0.000 0.964 0.000 NA 0.016
#> GSM28763 2 0.112 0.7014 0.000 0.964 0.000 NA 0.016
#> GSM28764 2 0.464 -0.2226 0.000 0.528 0.000 NA 0.460
#> GSM11274 3 0.410 0.6808 0.000 0.000 0.788 NA 0.124
#> GSM28772 1 0.000 0.9701 1.000 0.000 0.000 NA 0.000
#> GSM11269 1 0.000 0.9701 1.000 0.000 0.000 NA 0.000
#> GSM28775 1 0.051 0.9654 0.984 0.000 0.000 NA 0.000
#> GSM11293 1 0.128 0.9587 0.956 0.000 0.000 NA 0.012
#> GSM28755 1 0.051 0.9654 0.984 0.000 0.000 NA 0.000
#> GSM11279 1 0.000 0.9701 1.000 0.000 0.000 NA 0.000
#> GSM28758 1 0.285 0.9122 0.872 0.000 0.000 NA 0.036
#> GSM11281 1 0.000 0.9701 1.000 0.000 0.000 NA 0.000
#> GSM11287 1 0.000 0.9701 1.000 0.000 0.000 NA 0.000
#> GSM28759 1 0.128 0.9587 0.956 0.000 0.000 NA 0.012
#> GSM11292 5 0.356 0.7284 0.000 0.260 0.000 NA 0.740
#> GSM28766 5 0.356 0.7284 0.000 0.260 0.000 NA 0.740
#> GSM11268 3 0.429 0.7309 0.000 0.000 0.540 NA 0.000
#> GSM28767 5 0.356 0.7284 0.000 0.260 0.000 NA 0.740
#> GSM11286 2 0.194 0.6798 0.000 0.920 0.000 NA 0.068
#> GSM28751 2 0.140 0.7003 0.000 0.952 0.000 NA 0.024
#> GSM28770 5 0.356 0.7284 0.000 0.260 0.000 NA 0.740
#> GSM11283 2 0.626 0.3324 0.000 0.512 0.000 NA 0.168
#> GSM11289 5 0.356 0.7284 0.000 0.260 0.000 NA 0.740
#> GSM11280 2 0.257 0.6657 0.000 0.880 0.000 NA 0.016
#> GSM28749 2 0.311 0.6540 0.000 0.840 0.000 NA 0.020
#> GSM28750 3 0.429 0.7309 0.000 0.000 0.540 NA 0.000
#> GSM11290 3 0.000 0.7764 0.000 0.000 1.000 NA 0.000
#> GSM11294 3 0.000 0.7764 0.000 0.000 1.000 NA 0.000
#> GSM28771 2 0.634 0.3149 0.000 0.500 0.000 NA 0.180
#> GSM28760 5 0.674 0.0480 0.000 0.256 0.000 NA 0.380
#> GSM28774 5 0.514 0.4341 0.000 0.424 0.000 NA 0.536
#> GSM11284 5 0.535 0.6333 0.000 0.280 0.000 NA 0.632
#> GSM28761 3 0.429 0.7309 0.000 0.000 0.540 NA 0.000
#> GSM11278 5 0.468 0.6484 0.000 0.140 0.000 NA 0.740
#> GSM11291 3 0.000 0.7764 0.000 0.000 1.000 NA 0.000
#> GSM11277 3 0.000 0.7764 0.000 0.000 1.000 NA 0.000
#> GSM11272 3 0.429 0.7309 0.000 0.000 0.540 NA 0.000
#> GSM11285 5 0.484 0.4655 0.000 0.084 0.000 NA 0.708
#> GSM28753 2 0.112 0.6941 0.000 0.960 0.000 NA 0.004
#> GSM28773 2 0.297 0.6574 0.000 0.852 0.000 NA 0.020
#> GSM28765 2 0.258 0.6193 0.000 0.864 0.000 NA 0.132
#> GSM28768 2 0.284 0.6723 0.000 0.876 0.000 NA 0.048
#> GSM28754 2 0.450 0.4024 0.000 0.704 0.000 NA 0.256
#> GSM28769 2 0.140 0.7003 0.000 0.952 0.000 NA 0.024
#> GSM11275 1 0.285 0.9122 0.872 0.000 0.000 NA 0.036
#> GSM11270 5 0.468 0.6484 0.000 0.140 0.000 NA 0.740
#> GSM11271 5 0.356 0.7284 0.000 0.260 0.000 NA 0.740
#> GSM11288 2 0.555 0.1817 0.000 0.496 0.068 NA 0.000
#> GSM11273 3 0.607 0.4117 0.000 0.008 0.560 NA 0.316
#> GSM28757 2 0.271 0.6664 0.000 0.880 0.000 NA 0.088
#> GSM11282 5 0.455 0.6509 0.000 0.132 0.000 NA 0.752
#> GSM28756 5 0.515 0.4061 0.000 0.436 0.000 NA 0.524
#> GSM11276 2 0.447 0.0912 0.000 0.616 0.000 NA 0.372
#> GSM28752 2 0.411 0.3423 0.000 0.700 0.000 NA 0.288
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 2 0.1737 0.714 0.000 0.932 0.020 0.008 0.040 0.000
#> GSM28763 2 0.1737 0.714 0.000 0.932 0.020 0.008 0.040 0.000
#> GSM28764 5 0.4193 0.532 0.000 0.272 0.044 0.000 0.684 0.000
#> GSM11274 3 0.5512 0.552 0.000 0.000 0.604 0.084 0.036 0.276
#> GSM28772 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0725 0.935 0.976 0.000 0.012 0.012 0.000 0.000
#> GSM11293 1 0.1864 0.919 0.924 0.000 0.032 0.040 0.004 0.000
#> GSM28755 1 0.0725 0.935 0.976 0.000 0.012 0.012 0.000 0.000
#> GSM11279 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.4414 0.805 0.752 0.012 0.072 0.156 0.004 0.004
#> GSM11281 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.941 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.1864 0.919 0.924 0.000 0.032 0.040 0.004 0.000
#> GSM11292 5 0.1204 0.700 0.000 0.056 0.000 0.000 0.944 0.000
#> GSM28766 5 0.1204 0.700 0.000 0.056 0.000 0.000 0.944 0.000
#> GSM11268 6 0.0146 0.997 0.000 0.004 0.000 0.000 0.000 0.996
#> GSM28767 5 0.1204 0.700 0.000 0.056 0.000 0.000 0.944 0.000
#> GSM11286 2 0.3306 0.700 0.000 0.848 0.044 0.052 0.056 0.000
#> GSM28751 2 0.2415 0.708 0.000 0.900 0.040 0.024 0.036 0.000
#> GSM28770 5 0.1204 0.700 0.000 0.056 0.000 0.000 0.944 0.000
#> GSM11283 4 0.4227 0.862 0.000 0.256 0.000 0.692 0.052 0.000
#> GSM11289 5 0.1204 0.700 0.000 0.056 0.000 0.000 0.944 0.000
#> GSM11280 2 0.4037 0.574 0.000 0.752 0.028 0.196 0.024 0.000
#> GSM28749 2 0.4723 0.571 0.000 0.732 0.028 0.180 0.024 0.036
#> GSM28750 6 0.0146 0.992 0.000 0.000 0.004 0.000 0.000 0.996
#> GSM11290 3 0.3789 0.714 0.000 0.000 0.584 0.000 0.000 0.416
#> GSM11294 3 0.3789 0.714 0.000 0.000 0.584 0.000 0.000 0.416
#> GSM28771 4 0.4261 0.867 0.000 0.252 0.000 0.692 0.056 0.000
#> GSM28760 4 0.5097 0.766 0.000 0.124 0.044 0.700 0.132 0.000
#> GSM28774 5 0.6304 0.567 0.000 0.200 0.120 0.104 0.576 0.000
#> GSM11284 5 0.5630 0.584 0.000 0.084 0.084 0.184 0.648 0.000
#> GSM28761 6 0.0146 0.997 0.000 0.004 0.000 0.000 0.000 0.996
#> GSM11278 5 0.5648 0.513 0.000 0.020 0.232 0.152 0.596 0.000
#> GSM11291 3 0.3789 0.714 0.000 0.000 0.584 0.000 0.000 0.416
#> GSM11277 3 0.3789 0.714 0.000 0.000 0.584 0.000 0.000 0.416
#> GSM11272 6 0.0146 0.997 0.000 0.004 0.000 0.000 0.000 0.996
#> GSM11285 5 0.3971 -0.104 0.000 0.004 0.000 0.448 0.548 0.000
#> GSM28753 2 0.2668 0.694 0.000 0.884 0.028 0.060 0.028 0.000
#> GSM28773 2 0.4924 0.550 0.000 0.716 0.036 0.188 0.024 0.036
#> GSM28765 2 0.3918 0.668 0.000 0.800 0.044 0.048 0.108 0.000
#> GSM28768 2 0.3916 0.605 0.000 0.792 0.056 0.132 0.016 0.004
#> GSM28754 2 0.6726 0.129 0.000 0.488 0.128 0.104 0.280 0.000
#> GSM28769 2 0.2342 0.708 0.000 0.904 0.040 0.024 0.032 0.000
#> GSM11275 1 0.4414 0.805 0.752 0.012 0.072 0.156 0.004 0.004
#> GSM11270 5 0.5648 0.513 0.000 0.020 0.232 0.152 0.596 0.000
#> GSM11271 5 0.1411 0.700 0.000 0.060 0.000 0.004 0.936 0.000
#> GSM11288 2 0.5969 0.219 0.000 0.536 0.032 0.128 0.000 0.304
#> GSM11273 3 0.5792 0.337 0.000 0.000 0.632 0.108 0.184 0.076
#> GSM28757 2 0.4065 0.676 0.000 0.796 0.076 0.072 0.056 0.000
#> GSM11282 5 0.5564 0.519 0.000 0.020 0.228 0.144 0.608 0.000
#> GSM28756 5 0.6540 0.522 0.000 0.232 0.128 0.104 0.536 0.000
#> GSM11276 5 0.5238 0.108 0.000 0.460 0.044 0.024 0.472 0.000
#> GSM28752 2 0.5210 0.244 0.000 0.576 0.040 0.036 0.348 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 tissue(p) k
#> MAD:kmeans 46 0.389 2
#> MAD:kmeans 54 0.374 3
#> MAD:kmeans 46 0.428 4
#> MAD:kmeans 42 0.408 5
#> MAD:kmeans 48 0.485 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.982 0.4865 0.516 0.516
#> 3 3 0.941 0.919 0.968 0.3033 0.764 0.576
#> 4 4 0.858 0.841 0.931 0.1905 0.834 0.569
#> 5 5 0.743 0.670 0.820 0.0659 0.915 0.673
#> 6 6 0.770 0.609 0.784 0.0398 0.930 0.671
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
#> GSM28762 2 0.242 0.956 0.040 0.960
#> GSM28763 2 0.242 0.956 0.040 0.960
#> GSM28764 2 0.000 0.981 0.000 1.000
#> GSM11274 2 0.000 0.981 0.000 1.000
#> GSM28772 1 0.000 0.981 1.000 0.000
#> GSM11269 1 0.000 0.981 1.000 0.000
#> GSM28775 1 0.000 0.981 1.000 0.000
#> GSM11293 1 0.000 0.981 1.000 0.000
#> GSM28755 1 0.000 0.981 1.000 0.000
#> GSM11279 1 0.000 0.981 1.000 0.000
#> GSM28758 1 0.000 0.981 1.000 0.000
#> GSM11281 1 0.000 0.981 1.000 0.000
#> GSM11287 1 0.000 0.981 1.000 0.000
#> GSM28759 1 0.000 0.981 1.000 0.000
#> GSM11292 2 0.000 0.981 0.000 1.000
#> GSM28766 2 0.000 0.981 0.000 1.000
#> GSM11268 1 0.242 0.972 0.960 0.040
#> GSM28767 2 0.000 0.981 0.000 1.000
#> GSM11286 2 0.204 0.962 0.032 0.968
#> GSM28751 2 0.730 0.774 0.204 0.796
#> GSM28770 2 0.000 0.981 0.000 1.000
#> GSM11283 2 0.000 0.981 0.000 1.000
#> GSM11289 2 0.000 0.981 0.000 1.000
#> GSM11280 2 0.000 0.981 0.000 1.000
#> GSM28749 2 0.000 0.981 0.000 1.000
#> GSM28750 1 0.242 0.972 0.960 0.040
#> GSM11290 1 0.242 0.972 0.960 0.040
#> GSM11294 1 0.242 0.972 0.960 0.040
#> GSM28771 2 0.000 0.981 0.000 1.000
#> GSM28760 2 0.000 0.981 0.000 1.000
#> GSM28774 2 0.000 0.981 0.000 1.000
#> GSM11284 2 0.000 0.981 0.000 1.000
#> GSM28761 1 0.242 0.972 0.960 0.040
#> GSM11278 2 0.000 0.981 0.000 1.000
#> GSM11291 1 0.242 0.972 0.960 0.040
#> GSM11277 1 0.242 0.972 0.960 0.040
#> GSM11272 1 0.000 0.981 1.000 0.000
#> GSM11285 2 0.000 0.981 0.000 1.000
#> GSM28753 2 0.204 0.962 0.032 0.968
#> GSM28773 2 0.000 0.981 0.000 1.000
#> GSM28765 2 0.204 0.962 0.032 0.968
#> GSM28768 1 0.260 0.951 0.956 0.044
#> GSM28754 2 0.000 0.981 0.000 1.000
#> GSM28769 2 0.730 0.774 0.204 0.796
#> GSM11275 1 0.000 0.981 1.000 0.000
#> GSM11270 2 0.000 0.981 0.000 1.000
#> GSM11271 2 0.000 0.981 0.000 1.000
#> GSM11288 1 0.242 0.972 0.960 0.040
#> GSM11273 2 0.000 0.981 0.000 1.000
#> GSM28757 2 0.000 0.981 0.000 1.000
#> GSM11282 2 0.000 0.981 0.000 1.000
#> GSM28756 2 0.000 0.981 0.000 1.000
#> GSM11276 2 0.000 0.981 0.000 1.000
#> GSM28752 2 0.242 0.956 0.040 0.960
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.0000 0.971 0.000 1.000 0.000
#> GSM28763 2 0.0000 0.971 0.000 1.000 0.000
#> GSM28764 2 0.0000 0.971 0.000 1.000 0.000
#> GSM11274 3 0.0000 0.953 0.000 0.000 1.000
#> GSM28772 1 0.0000 0.948 1.000 0.000 0.000
#> GSM11269 1 0.0000 0.948 1.000 0.000 0.000
#> GSM28775 1 0.0000 0.948 1.000 0.000 0.000
#> GSM11293 1 0.0000 0.948 1.000 0.000 0.000
#> GSM28755 1 0.0000 0.948 1.000 0.000 0.000
#> GSM11279 1 0.0000 0.948 1.000 0.000 0.000
#> GSM28758 1 0.0000 0.948 1.000 0.000 0.000
#> GSM11281 1 0.0000 0.948 1.000 0.000 0.000
#> GSM11287 1 0.0000 0.948 1.000 0.000 0.000
#> GSM28759 1 0.0000 0.948 1.000 0.000 0.000
#> GSM11292 2 0.0000 0.971 0.000 1.000 0.000
#> GSM28766 2 0.0000 0.971 0.000 1.000 0.000
#> GSM11268 3 0.0000 0.953 0.000 0.000 1.000
#> GSM28767 2 0.0000 0.971 0.000 1.000 0.000
#> GSM11286 2 0.0000 0.971 0.000 1.000 0.000
#> GSM28751 1 0.5465 0.616 0.712 0.288 0.000
#> GSM28770 2 0.0000 0.971 0.000 1.000 0.000
#> GSM11283 2 0.0000 0.971 0.000 1.000 0.000
#> GSM11289 2 0.0000 0.971 0.000 1.000 0.000
#> GSM11280 2 0.0000 0.971 0.000 1.000 0.000
#> GSM28749 2 0.5098 0.662 0.000 0.752 0.248
#> GSM28750 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11290 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11294 3 0.0000 0.953 0.000 0.000 1.000
#> GSM28771 3 0.6168 0.287 0.000 0.412 0.588
#> GSM28760 3 0.0424 0.946 0.000 0.008 0.992
#> GSM28774 2 0.0000 0.971 0.000 1.000 0.000
#> GSM11284 2 0.0000 0.971 0.000 1.000 0.000
#> GSM28761 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11278 2 0.1163 0.949 0.000 0.972 0.028
#> GSM11291 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11277 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11272 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11285 2 0.0000 0.971 0.000 1.000 0.000
#> GSM28753 2 0.0000 0.971 0.000 1.000 0.000
#> GSM28773 2 0.5905 0.456 0.000 0.648 0.352
#> GSM28765 2 0.0000 0.971 0.000 1.000 0.000
#> GSM28768 1 0.0000 0.948 1.000 0.000 0.000
#> GSM28754 2 0.0000 0.971 0.000 1.000 0.000
#> GSM28769 1 0.5098 0.683 0.752 0.248 0.000
#> GSM11275 1 0.0000 0.948 1.000 0.000 0.000
#> GSM11270 2 0.2066 0.918 0.000 0.940 0.060
#> GSM11271 2 0.0000 0.971 0.000 1.000 0.000
#> GSM11288 3 0.1643 0.914 0.044 0.000 0.956
#> GSM11273 3 0.0000 0.953 0.000 0.000 1.000
#> GSM28757 2 0.0000 0.971 0.000 1.000 0.000
#> GSM11282 2 0.1031 0.952 0.000 0.976 0.024
#> GSM28756 2 0.0000 0.971 0.000 1.000 0.000
#> GSM11276 2 0.0000 0.971 0.000 1.000 0.000
#> GSM28752 2 0.0000 0.971 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 4 0.0188 0.846 0.000 0.004 0.000 0.996
#> GSM28763 4 0.0188 0.846 0.000 0.004 0.000 0.996
#> GSM28764 2 0.2149 0.846 0.000 0.912 0.000 0.088
#> GSM11274 3 0.0188 0.947 0.000 0.000 0.996 0.004
#> GSM28772 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM11292 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM28766 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM11268 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM28767 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM11286 4 0.4477 0.506 0.000 0.312 0.000 0.688
#> GSM28751 4 0.0336 0.845 0.000 0.008 0.000 0.992
#> GSM28770 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM11283 4 0.1022 0.832 0.000 0.032 0.000 0.968
#> GSM11289 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM11280 4 0.0188 0.846 0.000 0.004 0.000 0.996
#> GSM28749 4 0.4214 0.658 0.000 0.016 0.204 0.780
#> GSM28750 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM11290 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM11294 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM28771 4 0.2589 0.777 0.000 0.116 0.000 0.884
#> GSM28760 3 0.7264 0.117 0.000 0.148 0.460 0.392
#> GSM28774 2 0.2216 0.843 0.000 0.908 0.000 0.092
#> GSM11284 2 0.0188 0.892 0.000 0.996 0.000 0.004
#> GSM28761 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM11278 2 0.0336 0.891 0.000 0.992 0.000 0.008
#> GSM11291 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM11272 3 0.0000 0.949 0.000 0.000 1.000 0.000
#> GSM11285 2 0.0336 0.891 0.000 0.992 0.000 0.008
#> GSM28753 4 0.0188 0.846 0.000 0.004 0.000 0.996
#> GSM28773 4 0.4225 0.686 0.000 0.024 0.184 0.792
#> GSM28765 4 0.4746 0.367 0.000 0.368 0.000 0.632
#> GSM28768 1 0.1716 0.930 0.936 0.000 0.000 0.064
#> GSM28754 2 0.4925 0.275 0.000 0.572 0.000 0.428
#> GSM28769 4 0.0336 0.845 0.000 0.008 0.000 0.992
#> GSM11275 1 0.0000 0.994 1.000 0.000 0.000 0.000
#> GSM11270 2 0.0336 0.891 0.000 0.992 0.000 0.008
#> GSM11271 2 0.0000 0.893 0.000 1.000 0.000 0.000
#> GSM11288 3 0.1209 0.920 0.032 0.000 0.964 0.004
#> GSM11273 3 0.0376 0.944 0.000 0.004 0.992 0.004
#> GSM28757 4 0.4331 0.548 0.000 0.288 0.000 0.712
#> GSM11282 2 0.0336 0.891 0.000 0.992 0.000 0.008
#> GSM28756 2 0.2814 0.810 0.000 0.868 0.000 0.132
#> GSM11276 2 0.4564 0.542 0.000 0.672 0.000 0.328
#> GSM28752 2 0.4776 0.437 0.000 0.624 0.000 0.376
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28762 2 0.0451 0.4812 0.000 0.988 0.000 0.008 0.004
#> GSM28763 2 0.0451 0.4812 0.000 0.988 0.000 0.008 0.004
#> GSM28764 5 0.3495 0.6042 0.000 0.160 0.000 0.028 0.812
#> GSM11274 3 0.2230 0.8265 0.000 0.000 0.884 0.116 0.000
#> GSM28772 1 0.0000 0.9706 1.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.9706 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.9706 1.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.9706 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.9706 1.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.9706 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.9706 1.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.9706 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.9706 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.9706 1.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.0000 0.7765 0.000 0.000 0.000 0.000 1.000
#> GSM28766 5 0.0000 0.7765 0.000 0.000 0.000 0.000 1.000
#> GSM11268 3 0.2074 0.8990 0.000 0.000 0.896 0.104 0.000
#> GSM28767 5 0.0000 0.7765 0.000 0.000 0.000 0.000 1.000
#> GSM11286 2 0.5538 0.4765 0.000 0.644 0.000 0.212 0.144
#> GSM28751 2 0.0898 0.4903 0.008 0.972 0.000 0.000 0.020
#> GSM28770 5 0.0000 0.7765 0.000 0.000 0.000 0.000 1.000
#> GSM11283 4 0.4415 0.4819 0.000 0.444 0.000 0.552 0.004
#> GSM11289 5 0.0000 0.7765 0.000 0.000 0.000 0.000 1.000
#> GSM11280 4 0.4306 0.3389 0.000 0.492 0.000 0.508 0.000
#> GSM28749 4 0.6127 0.4114 0.000 0.292 0.040 0.596 0.072
#> GSM28750 3 0.2074 0.8990 0.000 0.000 0.896 0.104 0.000
#> GSM11290 3 0.0000 0.9061 0.000 0.000 1.000 0.000 0.000
#> GSM11294 3 0.0000 0.9061 0.000 0.000 1.000 0.000 0.000
#> GSM28771 4 0.4397 0.4862 0.000 0.432 0.000 0.564 0.004
#> GSM28760 4 0.6719 0.4325 0.000 0.224 0.184 0.560 0.032
#> GSM28774 5 0.5408 0.5996 0.000 0.120 0.000 0.228 0.652
#> GSM11284 5 0.4269 0.6143 0.000 0.016 0.000 0.300 0.684
#> GSM28761 3 0.2074 0.8990 0.000 0.000 0.896 0.104 0.000
#> GSM11278 5 0.5836 0.5734 0.000 0.004 0.104 0.316 0.576
#> GSM11291 3 0.0000 0.9061 0.000 0.000 1.000 0.000 0.000
#> GSM11277 3 0.0000 0.9061 0.000 0.000 1.000 0.000 0.000
#> GSM11272 3 0.2074 0.8990 0.000 0.000 0.896 0.104 0.000
#> GSM11285 5 0.2890 0.6795 0.000 0.004 0.000 0.160 0.836
#> GSM28753 2 0.3895 -0.0884 0.000 0.680 0.000 0.320 0.000
#> GSM28773 4 0.5430 0.3456 0.000 0.372 0.032 0.576 0.020
#> GSM28765 2 0.5844 0.4653 0.000 0.608 0.000 0.208 0.184
#> GSM28768 1 0.4252 0.5791 0.700 0.280 0.000 0.020 0.000
#> GSM28754 4 0.6818 -0.2610 0.000 0.336 0.000 0.352 0.312
#> GSM28769 2 0.0671 0.4914 0.004 0.980 0.000 0.000 0.016
#> GSM11275 1 0.0000 0.9706 1.000 0.000 0.000 0.000 0.000
#> GSM11270 5 0.5836 0.5734 0.000 0.004 0.104 0.316 0.576
#> GSM11271 5 0.0000 0.7765 0.000 0.000 0.000 0.000 1.000
#> GSM11288 3 0.3394 0.8537 0.020 0.004 0.824 0.152 0.000
#> GSM11273 3 0.3123 0.7562 0.000 0.000 0.812 0.184 0.004
#> GSM28757 2 0.5297 0.3493 0.000 0.580 0.000 0.360 0.060
#> GSM11282 5 0.5351 0.6109 0.000 0.004 0.068 0.304 0.624
#> GSM28756 5 0.6203 0.4202 0.000 0.188 0.000 0.268 0.544
#> GSM11276 2 0.5406 0.2008 0.000 0.480 0.000 0.056 0.464
#> GSM28752 2 0.5401 0.3483 0.000 0.536 0.000 0.060 0.404
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 2 0.1434 0.5917 0.000 0.940 0.000 0.048 0.000 0.012
#> GSM28763 2 0.1434 0.5917 0.000 0.940 0.000 0.048 0.000 0.012
#> GSM28764 5 0.2197 0.7298 0.000 0.056 0.000 0.000 0.900 0.044
#> GSM11274 3 0.5150 0.5268 0.000 0.000 0.608 0.136 0.000 0.256
#> GSM28772 1 0.0000 0.9640 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.9640 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.9640 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.9640 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.9640 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.9640 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.9640 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.9640 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.9640 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.9640 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.0000 0.7976 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28766 5 0.0000 0.7976 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11268 3 0.2170 0.7879 0.000 0.000 0.888 0.100 0.000 0.012
#> GSM28767 5 0.0000 0.7976 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11286 6 0.6453 -0.1931 0.000 0.396 0.000 0.076 0.100 0.428
#> GSM28751 2 0.0405 0.6003 0.000 0.988 0.000 0.008 0.004 0.000
#> GSM28770 5 0.0000 0.7976 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11283 4 0.4091 0.6151 0.000 0.212 0.000 0.732 0.004 0.052
#> GSM11289 5 0.0000 0.7976 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11280 4 0.5438 0.5154 0.000 0.172 0.000 0.568 0.000 0.260
#> GSM28749 4 0.5873 0.5117 0.000 0.100 0.044 0.620 0.012 0.224
#> GSM28750 3 0.1663 0.7925 0.000 0.000 0.912 0.088 0.000 0.000
#> GSM11290 3 0.1531 0.8041 0.000 0.000 0.928 0.004 0.000 0.068
#> GSM11294 3 0.1812 0.8025 0.000 0.000 0.912 0.008 0.000 0.080
#> GSM28771 4 0.3839 0.6113 0.000 0.212 0.000 0.748 0.004 0.036
#> GSM28760 4 0.4020 0.5608 0.000 0.080 0.072 0.808 0.020 0.020
#> GSM28774 6 0.5319 0.3068 0.000 0.072 0.000 0.016 0.364 0.548
#> GSM11284 5 0.6361 -0.0993 0.000 0.012 0.000 0.280 0.396 0.312
#> GSM28761 3 0.2170 0.7879 0.000 0.000 0.888 0.100 0.000 0.012
#> GSM11278 6 0.6109 0.4122 0.000 0.000 0.080 0.152 0.168 0.600
#> GSM11291 3 0.1812 0.8025 0.000 0.000 0.912 0.008 0.000 0.080
#> GSM11277 3 0.1812 0.8025 0.000 0.000 0.912 0.008 0.000 0.080
#> GSM11272 3 0.2170 0.7879 0.000 0.000 0.888 0.100 0.000 0.012
#> GSM11285 5 0.3309 0.5367 0.000 0.000 0.000 0.280 0.720 0.000
#> GSM28753 2 0.5779 -0.1778 0.000 0.452 0.000 0.368 0.000 0.180
#> GSM28773 4 0.6873 0.3741 0.000 0.248 0.044 0.464 0.012 0.232
#> GSM28765 2 0.6358 -0.0209 0.000 0.424 0.000 0.048 0.128 0.400
#> GSM28768 1 0.4767 0.4260 0.616 0.332 0.000 0.024 0.000 0.028
#> GSM28754 6 0.4808 0.4081 0.000 0.156 0.000 0.024 0.108 0.712
#> GSM28769 2 0.0508 0.5999 0.000 0.984 0.000 0.012 0.004 0.000
#> GSM11275 1 0.0000 0.9640 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11270 6 0.6168 0.4069 0.000 0.000 0.088 0.152 0.164 0.596
#> GSM11271 5 0.0260 0.7932 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM11288 3 0.4249 0.7006 0.044 0.012 0.768 0.156 0.000 0.020
#> GSM11273 3 0.5667 0.3198 0.000 0.000 0.488 0.140 0.004 0.368
#> GSM28757 6 0.4974 0.3249 0.000 0.200 0.000 0.048 0.060 0.692
#> GSM11282 6 0.6098 0.4139 0.000 0.000 0.056 0.152 0.212 0.580
#> GSM28756 6 0.4941 0.4427 0.000 0.104 0.000 0.008 0.228 0.660
#> GSM11276 5 0.5509 0.0719 0.000 0.364 0.000 0.004 0.512 0.120
#> GSM28752 2 0.5387 0.0503 0.000 0.500 0.000 0.008 0.404 0.088
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
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 tissue(p) k
#> MAD:skmeans 54 0.398 2
#> MAD:skmeans 52 0.372 3
#> MAD:skmeans 50 0.432 4
#> MAD:skmeans 36 0.411 5
#> MAD:skmeans 38 0.442 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.955 0.982 0.352 0.669 0.669
#> 3 3 1.000 0.968 0.986 0.574 0.786 0.681
#> 4 4 0.768 0.794 0.834 0.205 0.816 0.595
#> 5 5 0.755 0.742 0.877 0.140 0.913 0.703
#> 6 6 0.752 0.573 0.757 0.058 0.874 0.525
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
#> GSM28762 2 0.000 0.976 0.000 1.000
#> GSM28763 2 0.000 0.976 0.000 1.000
#> GSM28764 2 0.000 0.976 0.000 1.000
#> GSM11274 2 0.000 0.976 0.000 1.000
#> GSM28772 1 0.000 1.000 1.000 0.000
#> GSM11269 1 0.000 1.000 1.000 0.000
#> GSM28775 1 0.000 1.000 1.000 0.000
#> GSM11293 1 0.000 1.000 1.000 0.000
#> GSM28755 1 0.000 1.000 1.000 0.000
#> GSM11279 1 0.000 1.000 1.000 0.000
#> GSM28758 1 0.000 1.000 1.000 0.000
#> GSM11281 1 0.000 1.000 1.000 0.000
#> GSM11287 1 0.000 1.000 1.000 0.000
#> GSM28759 1 0.000 1.000 1.000 0.000
#> GSM11292 2 0.000 0.976 0.000 1.000
#> GSM28766 2 0.000 0.976 0.000 1.000
#> GSM11268 2 0.000 0.976 0.000 1.000
#> GSM28767 2 0.000 0.976 0.000 1.000
#> GSM11286 2 0.000 0.976 0.000 1.000
#> GSM28751 2 0.706 0.760 0.192 0.808
#> GSM28770 2 0.000 0.976 0.000 1.000
#> GSM11283 2 0.000 0.976 0.000 1.000
#> GSM11289 2 0.000 0.976 0.000 1.000
#> GSM11280 2 0.000 0.976 0.000 1.000
#> GSM28749 2 0.000 0.976 0.000 1.000
#> GSM28750 2 0.000 0.976 0.000 1.000
#> GSM11290 2 0.204 0.947 0.032 0.968
#> GSM11294 2 0.000 0.976 0.000 1.000
#> GSM28771 2 0.000 0.976 0.000 1.000
#> GSM28760 2 0.000 0.976 0.000 1.000
#> GSM28774 2 0.000 0.976 0.000 1.000
#> GSM11284 2 0.000 0.976 0.000 1.000
#> GSM28761 2 0.000 0.976 0.000 1.000
#> GSM11278 2 0.000 0.976 0.000 1.000
#> GSM11291 2 0.000 0.976 0.000 1.000
#> GSM11277 2 0.000 0.976 0.000 1.000
#> GSM11272 2 0.993 0.212 0.452 0.548
#> GSM11285 2 0.000 0.976 0.000 1.000
#> GSM28753 2 0.000 0.976 0.000 1.000
#> GSM28773 2 0.000 0.976 0.000 1.000
#> GSM28765 2 0.000 0.976 0.000 1.000
#> GSM28768 2 0.900 0.555 0.316 0.684
#> GSM28754 2 0.000 0.976 0.000 1.000
#> GSM28769 2 0.000 0.976 0.000 1.000
#> GSM11275 1 0.000 1.000 1.000 0.000
#> GSM11270 2 0.000 0.976 0.000 1.000
#> GSM11271 2 0.000 0.976 0.000 1.000
#> GSM11288 2 0.000 0.976 0.000 1.000
#> GSM11273 2 0.000 0.976 0.000 1.000
#> GSM28757 2 0.000 0.976 0.000 1.000
#> GSM11282 2 0.000 0.976 0.000 1.000
#> GSM28756 2 0.000 0.976 0.000 1.000
#> GSM11276 2 0.000 0.976 0.000 1.000
#> GSM28752 2 0.000 0.976 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.0000 0.980 0.000 1.000 0.000
#> GSM28763 2 0.0000 0.980 0.000 1.000 0.000
#> GSM28764 2 0.0000 0.980 0.000 1.000 0.000
#> GSM11274 3 0.0000 0.985 0.000 0.000 1.000
#> GSM28772 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11292 2 0.0000 0.980 0.000 1.000 0.000
#> GSM28766 2 0.0000 0.980 0.000 1.000 0.000
#> GSM11268 3 0.1860 0.926 0.000 0.052 0.948
#> GSM28767 2 0.0000 0.980 0.000 1.000 0.000
#> GSM11286 2 0.0000 0.980 0.000 1.000 0.000
#> GSM28751 2 0.3412 0.855 0.124 0.876 0.000
#> GSM28770 2 0.0000 0.980 0.000 1.000 0.000
#> GSM11283 2 0.0000 0.980 0.000 1.000 0.000
#> GSM11289 2 0.0000 0.980 0.000 1.000 0.000
#> GSM11280 2 0.0000 0.980 0.000 1.000 0.000
#> GSM28749 2 0.0000 0.980 0.000 1.000 0.000
#> GSM28750 3 0.0000 0.985 0.000 0.000 1.000
#> GSM11290 3 0.0000 0.985 0.000 0.000 1.000
#> GSM11294 3 0.0000 0.985 0.000 0.000 1.000
#> GSM28771 2 0.0000 0.980 0.000 1.000 0.000
#> GSM28760 2 0.0892 0.966 0.000 0.980 0.020
#> GSM28774 2 0.0000 0.980 0.000 1.000 0.000
#> GSM11284 2 0.0000 0.980 0.000 1.000 0.000
#> GSM28761 3 0.0747 0.972 0.000 0.016 0.984
#> GSM11278 2 0.0892 0.966 0.000 0.980 0.020
#> GSM11291 3 0.0000 0.985 0.000 0.000 1.000
#> GSM11277 3 0.0000 0.985 0.000 0.000 1.000
#> GSM11272 3 0.0892 0.969 0.020 0.000 0.980
#> GSM11285 2 0.0000 0.980 0.000 1.000 0.000
#> GSM28753 2 0.0000 0.980 0.000 1.000 0.000
#> GSM28773 2 0.0000 0.980 0.000 1.000 0.000
#> GSM28765 2 0.0000 0.980 0.000 1.000 0.000
#> GSM28768 2 0.6026 0.412 0.376 0.624 0.000
#> GSM28754 2 0.0000 0.980 0.000 1.000 0.000
#> GSM28769 2 0.0000 0.980 0.000 1.000 0.000
#> GSM11275 1 0.0000 1.000 1.000 0.000 0.000
#> GSM11270 2 0.0892 0.966 0.000 0.980 0.020
#> GSM11271 2 0.0000 0.980 0.000 1.000 0.000
#> GSM11288 2 0.0000 0.980 0.000 1.000 0.000
#> GSM11273 2 0.2448 0.914 0.000 0.924 0.076
#> GSM28757 2 0.0000 0.980 0.000 1.000 0.000
#> GSM11282 2 0.0892 0.966 0.000 0.980 0.020
#> GSM28756 2 0.0000 0.980 0.000 1.000 0.000
#> GSM11276 2 0.0000 0.980 0.000 1.000 0.000
#> GSM28752 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
#> GSM28762 2 0.0000 0.823 0.000 1.000 0.000 0.000
#> GSM28763 2 0.0000 0.823 0.000 1.000 0.000 0.000
#> GSM28764 2 0.2589 0.696 0.000 0.884 0.000 0.116
#> GSM11274 3 0.0000 0.850 0.000 0.000 1.000 0.000
#> GSM28772 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11292 4 0.4916 0.983 0.000 0.424 0.000 0.576
#> GSM28766 4 0.4916 0.983 0.000 0.424 0.000 0.576
#> GSM11268 3 0.4916 0.805 0.000 0.000 0.576 0.424
#> GSM28767 4 0.4916 0.983 0.000 0.424 0.000 0.576
#> GSM11286 2 0.0469 0.822 0.000 0.988 0.000 0.012
#> GSM28751 2 0.0779 0.809 0.004 0.980 0.000 0.016
#> GSM28770 4 0.4916 0.983 0.000 0.424 0.000 0.576
#> GSM11283 2 0.0000 0.823 0.000 1.000 0.000 0.000
#> GSM11289 4 0.4916 0.983 0.000 0.424 0.000 0.576
#> GSM11280 2 0.0921 0.812 0.000 0.972 0.000 0.028
#> GSM28749 2 0.4972 -0.623 0.000 0.544 0.000 0.456
#> GSM28750 3 0.4866 0.808 0.000 0.000 0.596 0.404
#> GSM11290 3 0.0000 0.850 0.000 0.000 1.000 0.000
#> GSM11294 3 0.0000 0.850 0.000 0.000 1.000 0.000
#> GSM28771 2 0.0000 0.823 0.000 1.000 0.000 0.000
#> GSM28760 4 0.4866 0.947 0.000 0.404 0.000 0.596
#> GSM28774 2 0.4925 -0.595 0.000 0.572 0.000 0.428
#> GSM11284 4 0.4992 0.871 0.000 0.476 0.000 0.524
#> GSM28761 3 0.4916 0.805 0.000 0.000 0.576 0.424
#> GSM11278 4 0.4916 0.983 0.000 0.424 0.000 0.576
#> GSM11291 3 0.0000 0.850 0.000 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.850 0.000 0.000 1.000 0.000
#> GSM11272 3 0.4916 0.805 0.000 0.000 0.576 0.424
#> GSM11285 4 0.4916 0.983 0.000 0.424 0.000 0.576
#> GSM28753 2 0.0000 0.823 0.000 1.000 0.000 0.000
#> GSM28773 2 0.0921 0.812 0.000 0.972 0.000 0.028
#> GSM28765 2 0.0336 0.822 0.000 0.992 0.000 0.008
#> GSM28768 2 0.2335 0.753 0.060 0.920 0.000 0.020
#> GSM28754 2 0.0336 0.822 0.000 0.992 0.000 0.008
#> GSM28769 2 0.0000 0.823 0.000 1.000 0.000 0.000
#> GSM11275 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM11270 4 0.4916 0.983 0.000 0.424 0.000 0.576
#> GSM11271 2 0.4992 -0.743 0.000 0.524 0.000 0.476
#> GSM11288 2 0.4008 0.364 0.000 0.756 0.000 0.244
#> GSM11273 4 0.5337 0.967 0.000 0.424 0.012 0.564
#> GSM28757 2 0.0336 0.822 0.000 0.992 0.000 0.008
#> GSM11282 4 0.4916 0.983 0.000 0.424 0.000 0.576
#> GSM28756 2 0.1940 0.757 0.000 0.924 0.000 0.076
#> GSM11276 2 0.2589 0.696 0.000 0.884 0.000 0.116
#> GSM28752 2 0.1302 0.791 0.000 0.956 0.000 0.044
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28762 2 0.0000 0.797 0.00 1.000 0.000 0.000 0.000
#> GSM28763 2 0.0000 0.797 0.00 1.000 0.000 0.000 0.000
#> GSM28764 2 0.3480 0.648 0.00 0.752 0.000 0.000 0.248
#> GSM11274 3 0.0162 0.908 0.00 0.000 0.996 0.000 0.004
#> GSM28772 1 0.0000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM11292 5 0.1952 0.862 0.00 0.084 0.000 0.004 0.912
#> GSM28766 5 0.1952 0.862 0.00 0.084 0.000 0.004 0.912
#> GSM11268 4 0.0290 0.639 0.00 0.000 0.008 0.992 0.000
#> GSM28767 5 0.1908 0.862 0.00 0.092 0.000 0.000 0.908
#> GSM11286 2 0.2249 0.812 0.00 0.896 0.000 0.008 0.096
#> GSM28751 2 0.0000 0.797 0.00 1.000 0.000 0.000 0.000
#> GSM28770 5 0.1908 0.862 0.00 0.092 0.000 0.000 0.908
#> GSM11283 2 0.2136 0.717 0.00 0.904 0.000 0.008 0.088
#> GSM11289 5 0.1908 0.862 0.00 0.092 0.000 0.000 0.908
#> GSM11280 2 0.4818 -0.192 0.00 0.520 0.000 0.460 0.020
#> GSM28749 4 0.6564 0.133 0.00 0.224 0.000 0.460 0.316
#> GSM28750 3 0.4294 0.378 0.00 0.000 0.532 0.468 0.000
#> GSM11290 3 0.0000 0.911 0.00 0.000 1.000 0.000 0.000
#> GSM11294 3 0.0000 0.911 0.00 0.000 1.000 0.000 0.000
#> GSM28771 2 0.2136 0.717 0.00 0.904 0.000 0.008 0.088
#> GSM28760 5 0.4294 -0.162 0.00 0.000 0.000 0.468 0.532
#> GSM28774 5 0.3305 0.728 0.00 0.224 0.000 0.000 0.776
#> GSM11284 5 0.6004 0.229 0.00 0.120 0.000 0.372 0.508
#> GSM28761 4 0.0290 0.639 0.00 0.000 0.008 0.992 0.000
#> GSM11278 5 0.1851 0.863 0.00 0.088 0.000 0.000 0.912
#> GSM11291 3 0.0000 0.911 0.00 0.000 1.000 0.000 0.000
#> GSM11277 3 0.0000 0.911 0.00 0.000 1.000 0.000 0.000
#> GSM11272 4 0.0290 0.639 0.00 0.000 0.008 0.992 0.000
#> GSM11285 5 0.1952 0.862 0.00 0.084 0.000 0.004 0.912
#> GSM28753 2 0.1908 0.814 0.00 0.908 0.000 0.000 0.092
#> GSM28773 2 0.4897 -0.167 0.00 0.516 0.000 0.460 0.024
#> GSM28765 2 0.1965 0.814 0.00 0.904 0.000 0.000 0.096
#> GSM28768 2 0.1809 0.756 0.06 0.928 0.000 0.012 0.000
#> GSM28754 2 0.1965 0.814 0.00 0.904 0.000 0.000 0.096
#> GSM28769 2 0.0000 0.797 0.00 1.000 0.000 0.000 0.000
#> GSM11275 1 0.0000 1.000 1.00 0.000 0.000 0.000 0.000
#> GSM11270 5 0.1851 0.863 0.00 0.088 0.000 0.000 0.912
#> GSM11271 5 0.3999 0.479 0.00 0.344 0.000 0.000 0.656
#> GSM11288 4 0.4989 0.258 0.00 0.416 0.000 0.552 0.032
#> GSM11273 5 0.2077 0.859 0.00 0.084 0.008 0.000 0.908
#> GSM28757 2 0.2124 0.813 0.00 0.900 0.000 0.004 0.096
#> GSM11282 5 0.1792 0.862 0.00 0.084 0.000 0.000 0.916
#> GSM28756 2 0.2424 0.793 0.00 0.868 0.000 0.000 0.132
#> GSM11276 2 0.3480 0.648 0.00 0.752 0.000 0.000 0.248
#> GSM28752 2 0.2471 0.790 0.00 0.864 0.000 0.000 0.136
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 2 0.3531 0.50311 0.00 0.672 0.000 0.000 0.328 0.000
#> GSM28763 2 0.3531 0.50311 0.00 0.672 0.000 0.000 0.328 0.000
#> GSM28764 2 0.2454 0.23214 0.00 0.840 0.000 0.000 0.160 0.000
#> GSM11274 4 0.3828 -0.16204 0.00 0.000 0.440 0.560 0.000 0.000
#> GSM28772 1 0.0000 1.00000 1.00 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.00000 1.00 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.00000 1.00 0.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.00000 1.00 0.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.00000 1.00 0.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.00000 1.00 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.00000 1.00 0.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.00000 1.00 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.00000 1.00 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.00000 1.00 0.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.3592 0.87498 0.00 0.344 0.000 0.000 0.656 0.000
#> GSM28766 5 0.3592 0.87498 0.00 0.344 0.000 0.000 0.656 0.000
#> GSM11268 6 0.0000 0.48248 0.00 0.000 0.000 0.000 0.000 1.000
#> GSM28767 5 0.3804 0.90139 0.00 0.424 0.000 0.000 0.576 0.000
#> GSM11286 2 0.0790 0.54194 0.00 0.968 0.000 0.000 0.000 0.032
#> GSM28751 2 0.3531 0.50311 0.00 0.672 0.000 0.000 0.328 0.000
#> GSM28770 5 0.3804 0.90139 0.00 0.424 0.000 0.000 0.576 0.000
#> GSM11283 4 0.5656 -0.13353 0.00 0.152 0.000 0.440 0.408 0.000
#> GSM11289 5 0.3804 0.90139 0.00 0.424 0.000 0.000 0.576 0.000
#> GSM11280 6 0.6825 0.33639 0.00 0.248 0.000 0.048 0.316 0.388
#> GSM28749 2 0.4666 0.00541 0.00 0.564 0.000 0.000 0.048 0.388
#> GSM28750 3 0.3868 0.36569 0.00 0.000 0.504 0.000 0.000 0.496
#> GSM11290 3 0.0000 0.88082 0.00 0.000 1.000 0.000 0.000 0.000
#> GSM11294 3 0.0000 0.88082 0.00 0.000 1.000 0.000 0.000 0.000
#> GSM28771 4 0.5561 -0.12817 0.00 0.136 0.000 0.440 0.424 0.000
#> GSM28760 4 0.6871 -0.11230 0.00 0.292 0.000 0.460 0.104 0.144
#> GSM28774 4 0.4855 0.37622 0.00 0.064 0.000 0.556 0.380 0.000
#> GSM11284 2 0.6117 -0.43636 0.00 0.352 0.000 0.000 0.300 0.348
#> GSM28761 6 0.0000 0.48248 0.00 0.000 0.000 0.000 0.000 1.000
#> GSM11278 4 0.4212 0.39426 0.00 0.016 0.000 0.560 0.424 0.000
#> GSM11291 3 0.0000 0.88082 0.00 0.000 1.000 0.000 0.000 0.000
#> GSM11277 3 0.0000 0.88082 0.00 0.000 1.000 0.000 0.000 0.000
#> GSM11272 6 0.0000 0.48248 0.00 0.000 0.000 0.000 0.000 1.000
#> GSM11285 5 0.3592 0.87498 0.00 0.344 0.000 0.000 0.656 0.000
#> GSM28753 2 0.3428 0.51586 0.00 0.696 0.000 0.000 0.304 0.000
#> GSM28773 6 0.6093 0.26225 0.00 0.296 0.000 0.000 0.316 0.388
#> GSM28765 2 0.0000 0.54637 0.00 1.000 0.000 0.000 0.000 0.000
#> GSM28768 2 0.5152 0.43189 0.06 0.592 0.000 0.000 0.328 0.020
#> GSM28754 2 0.0777 0.53238 0.00 0.972 0.000 0.024 0.004 0.000
#> GSM28769 2 0.3531 0.50311 0.00 0.672 0.000 0.000 0.328 0.000
#> GSM11275 1 0.0000 1.00000 1.00 0.000 0.000 0.000 0.000 0.000
#> GSM11270 4 0.4212 0.39426 0.00 0.016 0.000 0.560 0.424 0.000
#> GSM11271 5 0.3862 0.82726 0.00 0.476 0.000 0.000 0.524 0.000
#> GSM11288 6 0.5902 0.38037 0.00 0.204 0.000 0.000 0.392 0.404
#> GSM11273 4 0.4433 0.39700 0.00 0.016 0.008 0.560 0.416 0.000
#> GSM28757 2 0.5524 0.38407 0.00 0.560 0.000 0.204 0.236 0.000
#> GSM11282 4 0.4212 0.39426 0.00 0.016 0.000 0.560 0.424 0.000
#> GSM28756 2 0.1007 0.50613 0.00 0.956 0.000 0.000 0.044 0.000
#> GSM11276 2 0.2454 0.23214 0.00 0.840 0.000 0.000 0.160 0.000
#> GSM28752 2 0.0547 0.54969 0.00 0.980 0.000 0.000 0.020 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 tissue(p) k
#> MAD:pam 53 0.397 2
#> MAD:pam 53 0.373 3
#> MAD:pam 50 0.426 4
#> MAD:pam 46 0.393 5
#> MAD:pam 32 0.395 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.851 0.925 0.958 0.4123 0.560 0.560
#> 3 3 0.995 0.953 0.975 0.5234 0.723 0.541
#> 4 4 0.649 0.702 0.785 0.1369 0.762 0.452
#> 5 5 0.731 0.543 0.737 0.0693 0.783 0.439
#> 6 6 0.842 0.857 0.922 0.0478 0.832 0.493
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
#> GSM28762 2 0.0000 0.984 0.000 1.000
#> GSM28763 2 0.0000 0.984 0.000 1.000
#> GSM28764 2 0.0000 0.984 0.000 1.000
#> GSM11274 1 0.9522 0.544 0.628 0.372
#> GSM28772 1 0.0000 0.884 1.000 0.000
#> GSM11269 1 0.0000 0.884 1.000 0.000
#> GSM28775 1 0.2948 0.868 0.948 0.052
#> GSM11293 1 0.0000 0.884 1.000 0.000
#> GSM28755 1 0.0000 0.884 1.000 0.000
#> GSM11279 1 0.0000 0.884 1.000 0.000
#> GSM28758 1 0.0000 0.884 1.000 0.000
#> GSM11281 1 0.0000 0.884 1.000 0.000
#> GSM11287 1 0.0000 0.884 1.000 0.000
#> GSM28759 1 0.0000 0.884 1.000 0.000
#> GSM11292 2 0.0000 0.984 0.000 1.000
#> GSM28766 2 0.0000 0.984 0.000 1.000
#> GSM11268 2 0.2948 0.955 0.052 0.948
#> GSM28767 2 0.0000 0.984 0.000 1.000
#> GSM11286 2 0.0000 0.984 0.000 1.000
#> GSM28751 2 0.0000 0.984 0.000 1.000
#> GSM28770 2 0.0000 0.984 0.000 1.000
#> GSM11283 2 0.0000 0.984 0.000 1.000
#> GSM11289 2 0.0000 0.984 0.000 1.000
#> GSM11280 2 0.1184 0.977 0.016 0.984
#> GSM28749 2 0.2236 0.967 0.036 0.964
#> GSM28750 2 0.2948 0.955 0.052 0.948
#> GSM11290 1 0.7883 0.761 0.764 0.236
#> GSM11294 1 0.7883 0.761 0.764 0.236
#> GSM28771 2 0.0000 0.984 0.000 1.000
#> GSM28760 2 0.2236 0.967 0.036 0.964
#> GSM28774 2 0.0000 0.984 0.000 1.000
#> GSM11284 2 0.0000 0.984 0.000 1.000
#> GSM28761 2 0.2948 0.955 0.052 0.948
#> GSM11278 2 0.2778 0.958 0.048 0.952
#> GSM11291 1 0.7883 0.761 0.764 0.236
#> GSM11277 1 0.7883 0.761 0.764 0.236
#> GSM11272 2 0.2948 0.955 0.052 0.948
#> GSM11285 2 0.0000 0.984 0.000 1.000
#> GSM28753 2 0.0000 0.984 0.000 1.000
#> GSM28773 2 0.2236 0.967 0.036 0.964
#> GSM28765 2 0.0000 0.984 0.000 1.000
#> GSM28768 2 0.0672 0.980 0.008 0.992
#> GSM28754 2 0.0000 0.984 0.000 1.000
#> GSM28769 2 0.0000 0.984 0.000 1.000
#> GSM11275 1 0.1184 0.880 0.984 0.016
#> GSM11270 2 0.2778 0.958 0.048 0.952
#> GSM11271 2 0.0000 0.984 0.000 1.000
#> GSM11288 2 0.2603 0.961 0.044 0.956
#> GSM11273 1 0.9580 0.526 0.620 0.380
#> GSM28757 2 0.0000 0.984 0.000 1.000
#> GSM11282 2 0.2423 0.964 0.040 0.960
#> GSM28756 2 0.0000 0.984 0.000 1.000
#> GSM11276 2 0.0000 0.984 0.000 1.000
#> GSM28752 2 0.0000 0.984 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.1289 0.972 0.032 0.968 0.000
#> GSM28763 2 0.1289 0.972 0.032 0.968 0.000
#> GSM28764 2 0.0000 0.983 0.000 1.000 0.000
#> GSM11274 3 0.1289 0.930 0.000 0.032 0.968
#> GSM28772 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11269 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28775 1 0.1753 0.948 0.952 0.000 0.048
#> GSM11293 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28755 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11279 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28758 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11281 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11287 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28759 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11292 2 0.0000 0.983 0.000 1.000 0.000
#> GSM28766 2 0.0000 0.983 0.000 1.000 0.000
#> GSM11268 3 0.0424 0.934 0.008 0.000 0.992
#> GSM28767 2 0.0000 0.983 0.000 1.000 0.000
#> GSM11286 2 0.1031 0.975 0.024 0.976 0.000
#> GSM28751 2 0.1289 0.972 0.032 0.968 0.000
#> GSM28770 2 0.0000 0.983 0.000 1.000 0.000
#> GSM11283 2 0.0424 0.978 0.000 0.992 0.008
#> GSM11289 2 0.0000 0.983 0.000 1.000 0.000
#> GSM11280 2 0.0237 0.981 0.000 0.996 0.004
#> GSM28749 2 0.2384 0.935 0.008 0.936 0.056
#> GSM28750 3 0.0000 0.934 0.000 0.000 1.000
#> GSM11290 3 0.0000 0.934 0.000 0.000 1.000
#> GSM11294 3 0.0000 0.934 0.000 0.000 1.000
#> GSM28771 3 0.6168 0.372 0.000 0.412 0.588
#> GSM28760 3 0.1964 0.921 0.000 0.056 0.944
#> GSM28774 2 0.0000 0.983 0.000 1.000 0.000
#> GSM11284 2 0.0000 0.983 0.000 1.000 0.000
#> GSM28761 3 0.0424 0.934 0.008 0.000 0.992
#> GSM11278 3 0.2796 0.894 0.000 0.092 0.908
#> GSM11291 3 0.0000 0.934 0.000 0.000 1.000
#> GSM11277 3 0.0000 0.934 0.000 0.000 1.000
#> GSM11272 3 0.0424 0.934 0.008 0.000 0.992
#> GSM11285 2 0.0000 0.983 0.000 1.000 0.000
#> GSM28753 2 0.1289 0.972 0.032 0.968 0.000
#> GSM28773 2 0.2774 0.917 0.008 0.920 0.072
#> GSM28765 2 0.1163 0.974 0.028 0.972 0.000
#> GSM28768 2 0.1289 0.972 0.032 0.968 0.000
#> GSM28754 2 0.0000 0.983 0.000 1.000 0.000
#> GSM28769 2 0.1289 0.972 0.032 0.968 0.000
#> GSM11275 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11270 3 0.2537 0.905 0.000 0.080 0.920
#> GSM11271 2 0.0000 0.983 0.000 1.000 0.000
#> GSM11288 3 0.1170 0.931 0.016 0.008 0.976
#> GSM11273 3 0.1529 0.928 0.000 0.040 0.960
#> GSM28757 2 0.0000 0.983 0.000 1.000 0.000
#> GSM11282 3 0.2625 0.902 0.000 0.084 0.916
#> GSM28756 2 0.0000 0.983 0.000 1.000 0.000
#> GSM11276 2 0.0000 0.983 0.000 1.000 0.000
#> GSM28752 2 0.1289 0.972 0.032 0.968 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.0000 0.8034 0.000 1.000 0.000 0.000
#> GSM28763 2 0.0188 0.8039 0.000 0.996 0.000 0.004
#> GSM28764 2 0.3873 0.5925 0.000 0.772 0.000 0.228
#> GSM11274 4 0.4967 0.0921 0.000 0.000 0.452 0.548
#> GSM28772 1 0.0000 0.9985 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.9985 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0336 0.9908 0.992 0.000 0.000 0.008
#> GSM11293 1 0.0000 0.9985 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.9985 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.9985 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.9985 1.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.9985 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.9985 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.9985 1.000 0.000 0.000 0.000
#> GSM11292 4 0.4907 0.5324 0.000 0.420 0.000 0.580
#> GSM28766 4 0.5070 0.5374 0.000 0.416 0.004 0.580
#> GSM11268 3 0.4228 0.8674 0.000 0.008 0.760 0.232
#> GSM28767 4 0.4830 0.5743 0.000 0.392 0.000 0.608
#> GSM11286 2 0.0188 0.8044 0.000 0.996 0.000 0.004
#> GSM28751 2 0.0336 0.8040 0.000 0.992 0.000 0.008
#> GSM28770 4 0.4730 0.5821 0.000 0.364 0.000 0.636
#> GSM11283 2 0.4008 0.5913 0.000 0.756 0.000 0.244
#> GSM11289 4 0.4830 0.5739 0.000 0.392 0.000 0.608
#> GSM11280 2 0.2589 0.7452 0.000 0.884 0.000 0.116
#> GSM28749 2 0.3266 0.6983 0.000 0.832 0.000 0.168
#> GSM28750 3 0.4228 0.8674 0.000 0.008 0.760 0.232
#> GSM11290 3 0.0188 0.8643 0.000 0.000 0.996 0.004
#> GSM11294 3 0.0000 0.8644 0.000 0.000 1.000 0.000
#> GSM28771 2 0.4784 0.6671 0.000 0.788 0.112 0.100
#> GSM28760 4 0.6850 0.3526 0.000 0.188 0.212 0.600
#> GSM28774 4 0.4713 0.5819 0.000 0.360 0.000 0.640
#> GSM11284 4 0.4925 0.5196 0.000 0.428 0.000 0.572
#> GSM28761 3 0.4228 0.8674 0.000 0.008 0.760 0.232
#> GSM11278 4 0.6315 0.2485 0.000 0.064 0.396 0.540
#> GSM11291 3 0.0000 0.8644 0.000 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.8644 0.000 0.000 1.000 0.000
#> GSM11272 3 0.4228 0.8674 0.000 0.008 0.760 0.232
#> GSM11285 4 0.4843 0.5649 0.000 0.396 0.000 0.604
#> GSM28753 2 0.1474 0.7888 0.000 0.948 0.000 0.052
#> GSM28773 2 0.3266 0.6996 0.000 0.832 0.000 0.168
#> GSM28765 2 0.0000 0.8034 0.000 1.000 0.000 0.000
#> GSM28768 2 0.0804 0.8023 0.008 0.980 0.000 0.012
#> GSM28754 2 0.4661 0.2711 0.000 0.652 0.000 0.348
#> GSM28769 2 0.0817 0.8007 0.000 0.976 0.000 0.024
#> GSM11275 1 0.0188 0.9951 0.996 0.000 0.000 0.004
#> GSM11270 4 0.6315 0.2485 0.000 0.064 0.396 0.540
#> GSM11271 4 0.4830 0.5743 0.000 0.392 0.000 0.608
#> GSM11288 2 0.6889 0.4358 0.000 0.592 0.176 0.232
#> GSM11273 4 0.4967 0.0921 0.000 0.000 0.452 0.548
#> GSM28757 2 0.3486 0.6459 0.000 0.812 0.000 0.188
#> GSM11282 4 0.6367 0.2550 0.000 0.068 0.392 0.540
#> GSM28756 4 0.4843 0.5700 0.000 0.396 0.000 0.604
#> GSM11276 2 0.4103 0.5430 0.000 0.744 0.000 0.256
#> GSM28752 2 0.0469 0.7993 0.000 0.988 0.000 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28762 2 0.2966 0.485 0 0.816 0.000 0.184 0.000
#> GSM28763 2 0.4126 0.236 0 0.620 0.000 0.380 0.000
#> GSM28764 2 0.2719 0.601 0 0.852 0.000 0.004 0.144
#> GSM11274 5 0.4305 0.316 0 0.000 0.000 0.488 0.512
#> GSM28772 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11292 2 0.4300 0.477 0 0.524 0.000 0.000 0.476
#> GSM28766 2 0.4304 0.467 0 0.516 0.000 0.000 0.484
#> GSM11268 3 0.0000 0.968 0 0.000 1.000 0.000 0.000
#> GSM28767 2 0.4300 0.477 0 0.524 0.000 0.000 0.476
#> GSM11286 2 0.0162 0.603 0 0.996 0.000 0.004 0.000
#> GSM28751 2 0.1792 0.568 0 0.916 0.000 0.084 0.000
#> GSM28770 2 0.4446 0.477 0 0.520 0.000 0.004 0.476
#> GSM11283 2 0.2416 0.609 0 0.888 0.000 0.012 0.100
#> GSM11289 2 0.4446 0.477 0 0.520 0.000 0.004 0.476
#> GSM11280 2 0.1041 0.592 0 0.964 0.004 0.032 0.000
#> GSM28749 2 0.2011 0.560 0 0.908 0.004 0.088 0.000
#> GSM28750 3 0.1341 0.900 0 0.000 0.944 0.056 0.000
#> GSM11290 4 0.4798 0.106 0 0.000 0.440 0.540 0.020
#> GSM11294 4 0.4942 0.122 0 0.000 0.432 0.540 0.028
#> GSM28771 4 0.5434 -0.150 0 0.452 0.004 0.496 0.048
#> GSM28760 4 0.6035 -0.144 0 0.092 0.012 0.544 0.352
#> GSM28774 2 0.4440 0.483 0 0.528 0.000 0.004 0.468
#> GSM11284 2 0.4249 0.493 0 0.568 0.000 0.000 0.432
#> GSM28761 3 0.0000 0.968 0 0.000 1.000 0.000 0.000
#> GSM11278 5 0.3003 0.581 0 0.000 0.000 0.188 0.812
#> GSM11291 4 0.4942 0.122 0 0.000 0.432 0.540 0.028
#> GSM11277 4 0.4942 0.122 0 0.000 0.432 0.540 0.028
#> GSM11272 3 0.0000 0.968 0 0.000 1.000 0.000 0.000
#> GSM11285 2 0.4446 0.468 0 0.520 0.004 0.000 0.476
#> GSM28753 2 0.4242 0.172 0 0.572 0.000 0.428 0.000
#> GSM28773 2 0.2970 0.493 0 0.828 0.004 0.168 0.000
#> GSM28765 2 0.0162 0.603 0 0.996 0.000 0.004 0.000
#> GSM28768 2 0.4161 0.219 0 0.608 0.000 0.392 0.000
#> GSM28754 5 0.6676 -0.397 0 0.344 0.000 0.240 0.416
#> GSM28769 2 0.4227 0.179 0 0.580 0.000 0.420 0.000
#> GSM11275 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM11270 5 0.3003 0.581 0 0.000 0.000 0.188 0.812
#> GSM11271 2 0.4300 0.477 0 0.524 0.000 0.000 0.476
#> GSM11288 4 0.6240 -0.036 0 0.152 0.360 0.488 0.000
#> GSM11273 5 0.4297 0.331 0 0.000 0.000 0.472 0.528
#> GSM28757 2 0.5270 0.502 0 0.672 0.000 0.208 0.120
#> GSM11282 5 0.3039 0.579 0 0.000 0.000 0.192 0.808
#> GSM28756 2 0.4287 0.487 0 0.540 0.000 0.000 0.460
#> GSM11276 2 0.2848 0.599 0 0.840 0.000 0.004 0.156
#> GSM28752 2 0.0451 0.605 0 0.988 0.000 0.004 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 2 0.1610 0.8363 0 0.916 0.000 0.000 0.084 0.000
#> GSM28763 2 0.1501 0.8299 0 0.924 0.000 0.000 0.076 0.000
#> GSM28764 5 0.2260 0.7967 0 0.140 0.000 0.000 0.860 0.000
#> GSM11274 4 0.2340 0.8392 0 0.000 0.148 0.852 0.000 0.000
#> GSM28772 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.0000 0.8952 0 0.000 0.000 0.000 1.000 0.000
#> GSM28766 5 0.0000 0.8952 0 0.000 0.000 0.000 1.000 0.000
#> GSM11268 6 0.0146 0.9969 0 0.000 0.004 0.000 0.000 0.996
#> GSM28767 5 0.0000 0.8952 0 0.000 0.000 0.000 1.000 0.000
#> GSM11286 2 0.2092 0.8341 0 0.876 0.000 0.000 0.124 0.000
#> GSM28751 2 0.1957 0.8374 0 0.888 0.000 0.000 0.112 0.000
#> GSM28770 5 0.0000 0.8952 0 0.000 0.000 0.000 1.000 0.000
#> GSM11283 2 0.4184 0.1094 0 0.500 0.000 0.012 0.488 0.000
#> GSM11289 5 0.0000 0.8952 0 0.000 0.000 0.000 1.000 0.000
#> GSM11280 2 0.2095 0.8314 0 0.904 0.000 0.016 0.076 0.004
#> GSM28749 2 0.2998 0.8126 0 0.856 0.000 0.064 0.072 0.008
#> GSM28750 6 0.0260 0.9969 0 0.000 0.008 0.000 0.000 0.992
#> GSM11290 3 0.0000 1.0000 0 0.000 1.000 0.000 0.000 0.000
#> GSM11294 3 0.0000 1.0000 0 0.000 1.000 0.000 0.000 0.000
#> GSM28771 2 0.5025 0.4163 0 0.608 0.000 0.108 0.284 0.000
#> GSM28760 5 0.6058 0.0876 0 0.260 0.000 0.356 0.384 0.000
#> GSM28774 5 0.0000 0.8952 0 0.000 0.000 0.000 1.000 0.000
#> GSM11284 5 0.0363 0.8921 0 0.012 0.000 0.000 0.988 0.000
#> GSM28761 6 0.0146 0.9969 0 0.000 0.004 0.000 0.000 0.996
#> GSM11278 4 0.1327 0.9352 0 0.000 0.000 0.936 0.064 0.000
#> GSM11291 3 0.0000 1.0000 0 0.000 1.000 0.000 0.000 0.000
#> GSM11277 3 0.0000 1.0000 0 0.000 1.000 0.000 0.000 0.000
#> GSM11272 6 0.0260 0.9969 0 0.000 0.008 0.000 0.000 0.992
#> GSM11285 5 0.0405 0.8893 0 0.004 0.000 0.008 0.988 0.000
#> GSM28753 2 0.0551 0.8118 0 0.984 0.000 0.008 0.004 0.004
#> GSM28773 2 0.2765 0.8102 0 0.872 0.000 0.064 0.056 0.008
#> GSM28765 2 0.2048 0.8354 0 0.880 0.000 0.000 0.120 0.000
#> GSM28768 2 0.1007 0.8298 0 0.956 0.000 0.000 0.044 0.000
#> GSM28754 5 0.2823 0.7370 0 0.204 0.000 0.000 0.796 0.000
#> GSM28769 2 0.0260 0.8157 0 0.992 0.000 0.000 0.008 0.000
#> GSM11275 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000 0.000
#> GSM11270 4 0.1327 0.9352 0 0.000 0.000 0.936 0.064 0.000
#> GSM11271 5 0.0000 0.8952 0 0.000 0.000 0.000 1.000 0.000
#> GSM11288 2 0.4575 0.3057 0 0.600 0.000 0.048 0.000 0.352
#> GSM11273 4 0.1327 0.9007 0 0.000 0.064 0.936 0.000 0.000
#> GSM28757 5 0.3288 0.6467 0 0.276 0.000 0.000 0.724 0.000
#> GSM11282 4 0.1327 0.9352 0 0.000 0.000 0.936 0.064 0.000
#> GSM28756 5 0.0000 0.8952 0 0.000 0.000 0.000 1.000 0.000
#> GSM11276 5 0.2219 0.8000 0 0.136 0.000 0.000 0.864 0.000
#> GSM28752 2 0.2454 0.8125 0 0.840 0.000 0.000 0.160 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 tissue(p) k
#> MAD:mclust 54 0.398 2
#> MAD:mclust 53 0.373 3
#> MAD:mclust 46 0.427 4
#> MAD:mclust 28 0.388 5
#> MAD:mclust 50 0.400 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.962 0.959 0.982 0.3825 0.628 0.628
#> 3 3 0.969 0.947 0.981 0.5617 0.728 0.580
#> 4 4 0.753 0.790 0.892 0.1742 0.883 0.717
#> 5 5 0.811 0.807 0.896 0.1168 0.878 0.625
#> 6 6 0.767 0.671 0.822 0.0526 0.886 0.537
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
#> GSM28762 2 0.0376 0.978 0.004 0.996
#> GSM28763 2 0.3733 0.916 0.072 0.928
#> GSM28764 2 0.0000 0.980 0.000 1.000
#> GSM11274 2 0.0000 0.980 0.000 1.000
#> GSM28772 1 0.0000 0.982 1.000 0.000
#> GSM11269 1 0.0000 0.982 1.000 0.000
#> GSM28775 1 0.0000 0.982 1.000 0.000
#> GSM11293 1 0.0000 0.982 1.000 0.000
#> GSM28755 1 0.0000 0.982 1.000 0.000
#> GSM11279 1 0.0000 0.982 1.000 0.000
#> GSM28758 1 0.0000 0.982 1.000 0.000
#> GSM11281 1 0.0000 0.982 1.000 0.000
#> GSM11287 1 0.0000 0.982 1.000 0.000
#> GSM28759 1 0.0000 0.982 1.000 0.000
#> GSM11292 2 0.0000 0.980 0.000 1.000
#> GSM28766 2 0.0000 0.980 0.000 1.000
#> GSM11268 2 0.0000 0.980 0.000 1.000
#> GSM28767 2 0.0000 0.980 0.000 1.000
#> GSM11286 2 0.1184 0.968 0.016 0.984
#> GSM28751 1 0.7376 0.726 0.792 0.208
#> GSM28770 2 0.0000 0.980 0.000 1.000
#> GSM11283 2 0.0000 0.980 0.000 1.000
#> GSM11289 2 0.0000 0.980 0.000 1.000
#> GSM11280 2 0.0000 0.980 0.000 1.000
#> GSM28749 2 0.0000 0.980 0.000 1.000
#> GSM28750 2 0.0000 0.980 0.000 1.000
#> GSM11290 2 0.0000 0.980 0.000 1.000
#> GSM11294 2 0.0000 0.980 0.000 1.000
#> GSM28771 2 0.0000 0.980 0.000 1.000
#> GSM28760 2 0.0000 0.980 0.000 1.000
#> GSM28774 2 0.0000 0.980 0.000 1.000
#> GSM11284 2 0.0000 0.980 0.000 1.000
#> GSM28761 2 0.0000 0.980 0.000 1.000
#> GSM11278 2 0.0000 0.980 0.000 1.000
#> GSM11291 2 0.0000 0.980 0.000 1.000
#> GSM11277 2 0.0000 0.980 0.000 1.000
#> GSM11272 2 0.5737 0.843 0.136 0.864
#> GSM11285 2 0.0000 0.980 0.000 1.000
#> GSM28753 2 0.0000 0.980 0.000 1.000
#> GSM28773 2 0.0000 0.980 0.000 1.000
#> GSM28765 2 0.0376 0.978 0.004 0.996
#> GSM28768 1 0.0000 0.982 1.000 0.000
#> GSM28754 2 0.0000 0.980 0.000 1.000
#> GSM28769 2 0.9427 0.444 0.360 0.640
#> GSM11275 1 0.0000 0.982 1.000 0.000
#> GSM11270 2 0.0000 0.980 0.000 1.000
#> GSM11271 2 0.0000 0.980 0.000 1.000
#> GSM11288 2 0.6148 0.819 0.152 0.848
#> GSM11273 2 0.0000 0.980 0.000 1.000
#> GSM28757 2 0.0000 0.980 0.000 1.000
#> GSM11282 2 0.0000 0.980 0.000 1.000
#> GSM28756 2 0.0000 0.980 0.000 1.000
#> GSM11276 2 0.0000 0.980 0.000 1.000
#> GSM28752 2 0.1414 0.965 0.020 0.980
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.000 0.9953 0.000 1.000 0.000
#> GSM28763 2 0.000 0.9953 0.000 1.000 0.000
#> GSM28764 2 0.000 0.9953 0.000 1.000 0.000
#> GSM11274 3 0.000 0.9142 0.000 0.000 1.000
#> GSM28772 1 0.000 0.9846 1.000 0.000 0.000
#> GSM11269 1 0.000 0.9846 1.000 0.000 0.000
#> GSM28775 1 0.000 0.9846 1.000 0.000 0.000
#> GSM11293 1 0.000 0.9846 1.000 0.000 0.000
#> GSM28755 1 0.000 0.9846 1.000 0.000 0.000
#> GSM11279 1 0.000 0.9846 1.000 0.000 0.000
#> GSM28758 1 0.000 0.9846 1.000 0.000 0.000
#> GSM11281 1 0.000 0.9846 1.000 0.000 0.000
#> GSM11287 1 0.000 0.9846 1.000 0.000 0.000
#> GSM28759 1 0.000 0.9846 1.000 0.000 0.000
#> GSM11292 2 0.000 0.9953 0.000 1.000 0.000
#> GSM28766 2 0.000 0.9953 0.000 1.000 0.000
#> GSM11268 3 0.000 0.9142 0.000 0.000 1.000
#> GSM28767 2 0.000 0.9953 0.000 1.000 0.000
#> GSM11286 2 0.000 0.9953 0.000 1.000 0.000
#> GSM28751 2 0.296 0.8858 0.100 0.900 0.000
#> GSM28770 2 0.000 0.9953 0.000 1.000 0.000
#> GSM11283 2 0.000 0.9953 0.000 1.000 0.000
#> GSM11289 2 0.000 0.9953 0.000 1.000 0.000
#> GSM11280 2 0.000 0.9953 0.000 1.000 0.000
#> GSM28749 2 0.000 0.9953 0.000 1.000 0.000
#> GSM28750 3 0.000 0.9142 0.000 0.000 1.000
#> GSM11290 3 0.000 0.9142 0.000 0.000 1.000
#> GSM11294 3 0.000 0.9142 0.000 0.000 1.000
#> GSM28771 2 0.000 0.9953 0.000 1.000 0.000
#> GSM28760 3 0.630 0.0897 0.000 0.476 0.524
#> GSM28774 2 0.000 0.9953 0.000 1.000 0.000
#> GSM11284 2 0.000 0.9953 0.000 1.000 0.000
#> GSM28761 3 0.000 0.9142 0.000 0.000 1.000
#> GSM11278 2 0.000 0.9953 0.000 1.000 0.000
#> GSM11291 3 0.000 0.9142 0.000 0.000 1.000
#> GSM11277 3 0.000 0.9142 0.000 0.000 1.000
#> GSM11272 3 0.000 0.9142 0.000 0.000 1.000
#> GSM11285 2 0.000 0.9953 0.000 1.000 0.000
#> GSM28753 2 0.000 0.9953 0.000 1.000 0.000
#> GSM28773 2 0.000 0.9953 0.000 1.000 0.000
#> GSM28765 2 0.000 0.9953 0.000 1.000 0.000
#> GSM28768 1 0.334 0.8219 0.880 0.120 0.000
#> GSM28754 2 0.000 0.9953 0.000 1.000 0.000
#> GSM28769 2 0.000 0.9953 0.000 1.000 0.000
#> GSM11275 1 0.000 0.9846 1.000 0.000 0.000
#> GSM11270 2 0.116 0.9672 0.000 0.972 0.028
#> GSM11271 2 0.000 0.9953 0.000 1.000 0.000
#> GSM11288 3 0.546 0.5544 0.288 0.000 0.712
#> GSM11273 3 0.000 0.9142 0.000 0.000 1.000
#> GSM28757 2 0.000 0.9953 0.000 1.000 0.000
#> GSM11282 2 0.000 0.9953 0.000 1.000 0.000
#> GSM28756 2 0.000 0.9953 0.000 1.000 0.000
#> GSM11276 2 0.000 0.9953 0.000 1.000 0.000
#> GSM28752 2 0.000 0.9953 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.2760 0.830 0.000 0.872 0.000 0.128
#> GSM28763 2 0.2589 0.839 0.000 0.884 0.000 0.116
#> GSM28764 2 0.0817 0.871 0.000 0.976 0.000 0.024
#> GSM11274 3 0.0000 0.892 0.000 0.000 1.000 0.000
#> GSM28772 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM11292 2 0.1474 0.866 0.000 0.948 0.000 0.052
#> GSM28766 2 0.1637 0.864 0.000 0.940 0.000 0.060
#> GSM11268 4 0.3569 0.629 0.000 0.000 0.196 0.804
#> GSM28767 2 0.1389 0.867 0.000 0.952 0.000 0.048
#> GSM11286 2 0.2647 0.858 0.000 0.880 0.000 0.120
#> GSM28751 2 0.5434 0.718 0.084 0.728 0.000 0.188
#> GSM28770 2 0.0817 0.871 0.000 0.976 0.000 0.024
#> GSM11283 2 0.4088 0.733 0.000 0.764 0.004 0.232
#> GSM11289 2 0.0469 0.871 0.000 0.988 0.000 0.012
#> GSM11280 4 0.4989 -0.196 0.000 0.472 0.000 0.528
#> GSM28749 4 0.2342 0.648 0.000 0.080 0.008 0.912
#> GSM28750 4 0.4564 0.476 0.000 0.000 0.328 0.672
#> GSM11290 3 0.0921 0.889 0.000 0.000 0.972 0.028
#> GSM11294 3 0.0707 0.896 0.000 0.000 0.980 0.020
#> GSM28771 2 0.5368 0.538 0.000 0.636 0.024 0.340
#> GSM28760 4 0.7553 0.231 0.000 0.324 0.208 0.468
#> GSM28774 2 0.1022 0.866 0.000 0.968 0.000 0.032
#> GSM11284 2 0.2345 0.854 0.000 0.900 0.000 0.100
#> GSM28761 4 0.3444 0.635 0.000 0.000 0.184 0.816
#> GSM11278 2 0.4244 0.720 0.000 0.800 0.168 0.032
#> GSM11291 3 0.0707 0.896 0.000 0.000 0.980 0.020
#> GSM11277 3 0.0592 0.896 0.000 0.000 0.984 0.016
#> GSM11272 4 0.4072 0.580 0.000 0.000 0.252 0.748
#> GSM11285 2 0.1792 0.862 0.000 0.932 0.000 0.068
#> GSM28753 2 0.4996 0.235 0.000 0.516 0.000 0.484
#> GSM28773 4 0.1211 0.646 0.000 0.040 0.000 0.960
#> GSM28765 2 0.2081 0.867 0.000 0.916 0.000 0.084
#> GSM28768 1 0.1209 0.949 0.964 0.032 0.000 0.004
#> GSM28754 2 0.1022 0.866 0.000 0.968 0.000 0.032
#> GSM28769 2 0.4697 0.521 0.000 0.644 0.000 0.356
#> GSM11275 1 0.0000 0.996 1.000 0.000 0.000 0.000
#> GSM11270 3 0.5411 0.414 0.000 0.312 0.656 0.032
#> GSM11271 2 0.1118 0.869 0.000 0.964 0.000 0.036
#> GSM11288 4 0.3016 0.653 0.040 0.004 0.060 0.896
#> GSM11273 3 0.0188 0.889 0.000 0.000 0.996 0.004
#> GSM28757 2 0.2281 0.857 0.000 0.904 0.000 0.096
#> GSM11282 2 0.3149 0.812 0.000 0.880 0.088 0.032
#> GSM28756 2 0.0817 0.868 0.000 0.976 0.000 0.024
#> GSM11276 2 0.0469 0.871 0.000 0.988 0.000 0.012
#> GSM28752 2 0.1474 0.867 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
#> GSM28762 4 0.3561 0.695 0.000 0.260 0.000 0.740 0.000
#> GSM28763 4 0.3857 0.652 0.000 0.312 0.000 0.688 0.000
#> GSM28764 2 0.1628 0.839 0.000 0.936 0.000 0.056 0.008
#> GSM11274 3 0.0290 0.944 0.000 0.000 0.992 0.000 0.008
#> GSM28772 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11292 2 0.2284 0.831 0.000 0.912 0.004 0.056 0.028
#> GSM28766 2 0.3493 0.774 0.000 0.832 0.000 0.060 0.108
#> GSM11268 5 0.0566 0.864 0.000 0.000 0.004 0.012 0.984
#> GSM28767 2 0.1697 0.836 0.000 0.932 0.000 0.060 0.008
#> GSM11286 2 0.3508 0.612 0.000 0.748 0.000 0.252 0.000
#> GSM28751 4 0.5435 0.633 0.188 0.152 0.000 0.660 0.000
#> GSM28770 2 0.1518 0.841 0.000 0.944 0.004 0.048 0.004
#> GSM11283 4 0.0510 0.762 0.000 0.016 0.000 0.984 0.000
#> GSM11289 2 0.1764 0.835 0.000 0.928 0.000 0.064 0.008
#> GSM11280 4 0.1661 0.720 0.000 0.024 0.000 0.940 0.036
#> GSM28749 5 0.3355 0.775 0.000 0.036 0.000 0.132 0.832
#> GSM28750 5 0.2077 0.812 0.000 0.000 0.084 0.008 0.908
#> GSM11290 3 0.1671 0.924 0.000 0.000 0.924 0.000 0.076
#> GSM11294 3 0.1043 0.952 0.000 0.000 0.960 0.000 0.040
#> GSM28771 4 0.0609 0.764 0.000 0.020 0.000 0.980 0.000
#> GSM28760 4 0.0992 0.742 0.000 0.000 0.008 0.968 0.024
#> GSM28774 2 0.1331 0.825 0.000 0.952 0.008 0.040 0.000
#> GSM11284 2 0.4210 0.315 0.000 0.588 0.000 0.412 0.000
#> GSM28761 5 0.0162 0.861 0.000 0.004 0.000 0.000 0.996
#> GSM11278 2 0.4268 0.498 0.000 0.648 0.344 0.008 0.000
#> GSM11291 3 0.1043 0.952 0.000 0.000 0.960 0.000 0.040
#> GSM11277 3 0.1043 0.952 0.000 0.000 0.960 0.000 0.040
#> GSM11272 5 0.0404 0.862 0.000 0.000 0.012 0.000 0.988
#> GSM11285 4 0.4653 0.138 0.000 0.472 0.000 0.516 0.012
#> GSM28753 4 0.1364 0.766 0.000 0.036 0.000 0.952 0.012
#> GSM28773 5 0.4300 0.205 0.000 0.000 0.000 0.476 0.524
#> GSM28765 2 0.0912 0.838 0.000 0.972 0.000 0.012 0.016
#> GSM28768 1 0.0324 0.991 0.992 0.004 0.000 0.004 0.000
#> GSM28754 2 0.1830 0.811 0.000 0.924 0.008 0.068 0.000
#> GSM28769 4 0.4342 0.711 0.000 0.232 0.000 0.728 0.040
#> GSM11275 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11270 3 0.2411 0.834 0.000 0.108 0.884 0.008 0.000
#> GSM11271 2 0.1408 0.841 0.000 0.948 0.000 0.044 0.008
#> GSM11288 5 0.0609 0.863 0.000 0.000 0.000 0.020 0.980
#> GSM11273 3 0.0000 0.941 0.000 0.000 1.000 0.000 0.000
#> GSM28757 2 0.4276 0.357 0.000 0.616 0.004 0.380 0.000
#> GSM11282 2 0.3300 0.693 0.000 0.792 0.204 0.004 0.000
#> GSM28756 2 0.0693 0.832 0.000 0.980 0.008 0.012 0.000
#> GSM11276 2 0.1270 0.841 0.000 0.948 0.000 0.052 0.000
#> GSM28752 2 0.0798 0.839 0.000 0.976 0.000 0.016 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 2 0.5926 0.4373 0.000 0.460 0.000 0.296 0.244 0.000
#> GSM28763 2 0.5676 0.4850 0.000 0.528 0.000 0.256 0.216 0.000
#> GSM28764 5 0.0790 0.7954 0.000 0.032 0.000 0.000 0.968 0.000
#> GSM11274 3 0.0260 0.7996 0.000 0.008 0.992 0.000 0.000 0.000
#> GSM28772 1 0.0000 0.9809 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.9809 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.9809 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.9809 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.9809 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.9809 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.9809 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.9809 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.9809 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.9809 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.1471 0.7417 0.000 0.004 0.000 0.000 0.932 0.064
#> GSM28766 5 0.3189 0.5170 0.000 0.004 0.000 0.000 0.760 0.236
#> GSM11268 6 0.2003 0.8646 0.000 0.116 0.000 0.000 0.000 0.884
#> GSM28767 5 0.0260 0.7932 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM11286 2 0.3372 0.5361 0.000 0.796 0.000 0.008 0.176 0.020
#> GSM28751 2 0.7386 0.1669 0.192 0.392 0.000 0.124 0.288 0.004
#> GSM28770 5 0.0547 0.7982 0.000 0.020 0.000 0.000 0.980 0.000
#> GSM11283 4 0.0146 0.8148 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM11289 5 0.0291 0.7945 0.000 0.004 0.000 0.000 0.992 0.004
#> GSM11280 4 0.3445 0.6485 0.000 0.260 0.000 0.732 0.000 0.008
#> GSM28749 6 0.3954 0.6301 0.000 0.352 0.000 0.000 0.012 0.636
#> GSM28750 6 0.1931 0.8286 0.000 0.004 0.068 0.008 0.004 0.916
#> GSM11290 3 0.1765 0.7704 0.000 0.000 0.904 0.000 0.000 0.096
#> GSM11294 3 0.1219 0.8026 0.000 0.004 0.948 0.000 0.000 0.048
#> GSM28771 4 0.0000 0.8156 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM28760 4 0.0000 0.8156 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM28774 2 0.4310 0.2855 0.000 0.512 0.012 0.004 0.472 0.000
#> GSM11284 2 0.5521 0.4308 0.000 0.536 0.000 0.132 0.328 0.004
#> GSM28761 6 0.1349 0.8801 0.000 0.056 0.000 0.000 0.004 0.940
#> GSM11278 3 0.5898 -0.0585 0.000 0.380 0.416 0.000 0.204 0.000
#> GSM11291 3 0.1007 0.8040 0.000 0.000 0.956 0.000 0.000 0.044
#> GSM11277 3 0.1152 0.8040 0.000 0.004 0.952 0.000 0.000 0.044
#> GSM11272 6 0.1493 0.8783 0.000 0.056 0.004 0.000 0.004 0.936
#> GSM11285 4 0.4452 0.4741 0.000 0.004 0.000 0.644 0.312 0.040
#> GSM28753 4 0.3194 0.7304 0.000 0.168 0.000 0.808 0.004 0.020
#> GSM28773 2 0.4218 -0.3237 0.000 0.584 0.000 0.012 0.004 0.400
#> GSM28765 2 0.4736 0.3850 0.000 0.552 0.000 0.000 0.396 0.052
#> GSM28768 1 0.2915 0.7558 0.808 0.184 0.000 0.000 0.008 0.000
#> GSM28754 2 0.3727 0.4177 0.000 0.612 0.000 0.000 0.388 0.000
#> GSM28769 2 0.6323 0.1855 0.000 0.376 0.000 0.244 0.368 0.012
#> GSM11275 1 0.0000 0.9809 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11270 3 0.4026 0.4463 0.000 0.348 0.636 0.000 0.016 0.000
#> GSM11271 5 0.1007 0.7902 0.000 0.044 0.000 0.000 0.956 0.000
#> GSM11288 6 0.0520 0.8728 0.000 0.008 0.000 0.008 0.000 0.984
#> GSM11273 3 0.0713 0.7957 0.000 0.028 0.972 0.000 0.000 0.000
#> GSM28757 2 0.2612 0.5326 0.000 0.868 0.000 0.016 0.108 0.008
#> GSM11282 5 0.6024 -0.2928 0.000 0.368 0.244 0.000 0.388 0.000
#> GSM28756 2 0.3868 0.2800 0.000 0.508 0.000 0.000 0.492 0.000
#> GSM11276 5 0.1141 0.7829 0.000 0.052 0.000 0.000 0.948 0.000
#> GSM28752 5 0.1910 0.7239 0.000 0.108 0.000 0.000 0.892 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 tissue(p) k
#> MAD:NMF 53 0.397 2
#> MAD:NMF 53 0.373 3
#> MAD:NMF 49 0.348 4
#> MAD:NMF 49 0.413 5
#> MAD:NMF 40 0.410 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.961 0.922 0.972 0.3741 0.648 0.648
#> 3 3 0.937 0.912 0.968 0.4959 0.810 0.707
#> 4 4 1.000 0.973 0.987 0.0986 0.935 0.858
#> 5 5 0.922 0.964 0.971 0.1482 0.895 0.733
#> 6 6 0.951 0.954 0.949 0.0208 0.989 0.961
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM28762 2 0.000 0.966 0.000 1.000
#> GSM28763 2 0.000 0.966 0.000 1.000
#> GSM28764 2 0.000 0.966 0.000 1.000
#> GSM11274 2 0.000 0.966 0.000 1.000
#> GSM28772 1 0.000 0.982 1.000 0.000
#> GSM11269 1 0.000 0.982 1.000 0.000
#> GSM28775 1 0.000 0.982 1.000 0.000
#> GSM11293 1 0.000 0.982 1.000 0.000
#> GSM28755 1 0.000 0.982 1.000 0.000
#> GSM11279 1 0.000 0.982 1.000 0.000
#> GSM28758 1 0.000 0.982 1.000 0.000
#> GSM11281 1 0.000 0.982 1.000 0.000
#> GSM11287 1 0.000 0.982 1.000 0.000
#> GSM28759 1 0.000 0.982 1.000 0.000
#> GSM11292 2 0.000 0.966 0.000 1.000
#> GSM28766 2 0.000 0.966 0.000 1.000
#> GSM11268 2 0.000 0.966 0.000 1.000
#> GSM28767 2 0.000 0.966 0.000 1.000
#> GSM11286 2 0.000 0.966 0.000 1.000
#> GSM28751 2 0.992 0.199 0.448 0.552
#> GSM28770 2 0.000 0.966 0.000 1.000
#> GSM11283 2 0.000 0.966 0.000 1.000
#> GSM11289 2 0.000 0.966 0.000 1.000
#> GSM11280 2 0.000 0.966 0.000 1.000
#> GSM28749 2 0.000 0.966 0.000 1.000
#> GSM28750 2 0.000 0.966 0.000 1.000
#> GSM11290 2 0.000 0.966 0.000 1.000
#> GSM11294 2 0.000 0.966 0.000 1.000
#> GSM28771 2 0.000 0.966 0.000 1.000
#> GSM28760 2 0.000 0.966 0.000 1.000
#> GSM28774 2 0.000 0.966 0.000 1.000
#> GSM11284 2 0.000 0.966 0.000 1.000
#> GSM28761 2 0.000 0.966 0.000 1.000
#> GSM11278 2 0.000 0.966 0.000 1.000
#> GSM11291 2 0.000 0.966 0.000 1.000
#> GSM11277 2 0.000 0.966 0.000 1.000
#> GSM11272 2 0.000 0.966 0.000 1.000
#> GSM11285 2 0.000 0.966 0.000 1.000
#> GSM28753 2 0.000 0.966 0.000 1.000
#> GSM28773 2 0.000 0.966 0.000 1.000
#> GSM28765 2 0.000 0.966 0.000 1.000
#> GSM28768 1 0.697 0.752 0.812 0.188
#> GSM28754 2 0.000 0.966 0.000 1.000
#> GSM28769 2 0.992 0.199 0.448 0.552
#> GSM11275 1 0.000 0.982 1.000 0.000
#> GSM11270 2 0.000 0.966 0.000 1.000
#> GSM11271 2 0.000 0.966 0.000 1.000
#> GSM11288 2 0.992 0.199 0.448 0.552
#> GSM11273 2 0.000 0.966 0.000 1.000
#> GSM28757 2 0.000 0.966 0.000 1.000
#> GSM11282 2 0.000 0.966 0.000 1.000
#> GSM28756 2 0.000 0.966 0.000 1.000
#> GSM11276 2 0.000 0.966 0.000 1.000
#> GSM28752 2 0.000 0.966 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28763 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28764 2 0.0000 0.951 0.000 1.000 0.000
#> GSM11274 2 0.3686 0.803 0.000 0.860 0.140
#> GSM28772 1 0.0000 0.974 1.000 0.000 0.000
#> GSM11269 1 0.0000 0.974 1.000 0.000 0.000
#> GSM28775 1 0.0000 0.974 1.000 0.000 0.000
#> GSM11293 1 0.0000 0.974 1.000 0.000 0.000
#> GSM28755 1 0.0000 0.974 1.000 0.000 0.000
#> GSM11279 1 0.0000 0.974 1.000 0.000 0.000
#> GSM28758 1 0.0000 0.974 1.000 0.000 0.000
#> GSM11281 1 0.0000 0.974 1.000 0.000 0.000
#> GSM11287 1 0.0000 0.974 1.000 0.000 0.000
#> GSM28759 1 0.0000 0.974 1.000 0.000 0.000
#> GSM11292 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28766 2 0.0000 0.951 0.000 1.000 0.000
#> GSM11268 3 0.0000 0.993 0.000 0.000 1.000
#> GSM28767 2 0.0000 0.951 0.000 1.000 0.000
#> GSM11286 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28751 2 0.6260 0.208 0.448 0.552 0.000
#> GSM28770 2 0.0000 0.951 0.000 1.000 0.000
#> GSM11283 2 0.0000 0.951 0.000 1.000 0.000
#> GSM11289 2 0.0000 0.951 0.000 1.000 0.000
#> GSM11280 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28749 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28750 3 0.0000 0.993 0.000 0.000 1.000
#> GSM11290 3 0.0000 0.993 0.000 0.000 1.000
#> GSM11294 3 0.0000 0.993 0.000 0.000 1.000
#> GSM28771 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28760 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28774 2 0.0000 0.951 0.000 1.000 0.000
#> GSM11284 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28761 3 0.0000 0.993 0.000 0.000 1.000
#> GSM11278 2 0.0000 0.951 0.000 1.000 0.000
#> GSM11291 3 0.0000 0.993 0.000 0.000 1.000
#> GSM11277 3 0.0000 0.993 0.000 0.000 1.000
#> GSM11272 3 0.1411 0.947 0.000 0.036 0.964
#> GSM11285 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28753 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28773 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28765 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28768 1 0.4399 0.705 0.812 0.188 0.000
#> GSM28754 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28769 2 0.6260 0.208 0.448 0.552 0.000
#> GSM11275 1 0.0000 0.974 1.000 0.000 0.000
#> GSM11270 2 0.0000 0.951 0.000 1.000 0.000
#> GSM11271 2 0.0000 0.951 0.000 1.000 0.000
#> GSM11288 2 0.6260 0.208 0.448 0.552 0.000
#> GSM11273 2 0.0747 0.937 0.000 0.984 0.016
#> GSM28757 2 0.0000 0.951 0.000 1.000 0.000
#> GSM11282 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28756 2 0.0000 0.951 0.000 1.000 0.000
#> GSM11276 2 0.0000 0.951 0.000 1.000 0.000
#> GSM28752 2 0.0000 0.951 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM28763 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM28764 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM11274 2 0.400 0.800 0.00 0.824 0.140 0.036
#> GSM28772 1 0.000 0.974 1.00 0.000 0.000 0.000
#> GSM11269 1 0.000 0.974 1.00 0.000 0.000 0.000
#> GSM28775 1 0.000 0.974 1.00 0.000 0.000 0.000
#> GSM11293 1 0.000 0.974 1.00 0.000 0.000 0.000
#> GSM28755 1 0.000 0.974 1.00 0.000 0.000 0.000
#> GSM11279 1 0.000 0.974 1.00 0.000 0.000 0.000
#> GSM28758 1 0.000 0.974 1.00 0.000 0.000 0.000
#> GSM11281 1 0.000 0.974 1.00 0.000 0.000 0.000
#> GSM11287 1 0.000 0.974 1.00 0.000 0.000 0.000
#> GSM28759 1 0.000 0.974 1.00 0.000 0.000 0.000
#> GSM11292 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM28766 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM11268 3 0.000 0.994 0.00 0.000 1.000 0.000
#> GSM28767 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM11286 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM28751 4 0.000 1.000 0.00 0.000 0.000 1.000
#> GSM28770 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM11283 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM11289 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM11280 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM28749 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM28750 3 0.000 0.994 0.00 0.000 1.000 0.000
#> GSM11290 3 0.000 0.994 0.00 0.000 1.000 0.000
#> GSM11294 3 0.000 0.994 0.00 0.000 1.000 0.000
#> GSM28771 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM28760 2 0.112 0.963 0.00 0.964 0.000 0.036
#> GSM28774 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM11284 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM28761 3 0.000 0.994 0.00 0.000 1.000 0.000
#> GSM11278 2 0.112 0.963 0.00 0.964 0.000 0.036
#> GSM11291 3 0.000 0.994 0.00 0.000 1.000 0.000
#> GSM11277 3 0.000 0.994 0.00 0.000 1.000 0.000
#> GSM11272 3 0.112 0.954 0.00 0.000 0.964 0.036
#> GSM11285 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM28753 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM28773 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM28765 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM28768 1 0.428 0.611 0.72 0.000 0.000 0.280
#> GSM28754 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM28769 4 0.000 1.000 0.00 0.000 0.000 1.000
#> GSM11275 1 0.000 0.974 1.00 0.000 0.000 0.000
#> GSM11270 2 0.112 0.963 0.00 0.964 0.000 0.036
#> GSM11271 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM11288 4 0.000 1.000 0.00 0.000 0.000 1.000
#> GSM11273 2 0.171 0.949 0.00 0.948 0.016 0.036
#> GSM28757 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM11282 2 0.112 0.963 0.00 0.964 0.000 0.036
#> GSM28756 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM11276 2 0.000 0.988 0.00 1.000 0.000 0.000
#> GSM28752 2 0.000 0.988 0.00 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
#> GSM28762 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM28763 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM28764 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM11274 5 0.2377 0.722 0.000 0.000 0.128 0.000 0.872
#> GSM28772 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.1270 0.942 0.948 0.000 0.000 0.000 0.052
#> GSM11293 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.1270 0.942 0.948 0.000 0.000 0.000 0.052
#> GSM11279 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.1197 0.944 0.952 0.000 0.000 0.000 0.048
#> GSM11281 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.955 1.000 0.000 0.000 0.000 0.000
#> GSM11292 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM28766 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM11268 3 0.0880 0.973 0.000 0.000 0.968 0.000 0.032
#> GSM28767 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM11286 2 0.0290 0.992 0.000 0.992 0.000 0.000 0.008
#> GSM28751 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM28770 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM11283 2 0.0510 0.983 0.000 0.984 0.000 0.000 0.016
#> GSM11289 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM11280 2 0.0290 0.992 0.000 0.992 0.000 0.000 0.008
#> GSM28749 2 0.0162 0.994 0.000 0.996 0.000 0.000 0.004
#> GSM28750 3 0.0000 0.984 0.000 0.000 1.000 0.000 0.000
#> GSM11290 3 0.0000 0.984 0.000 0.000 1.000 0.000 0.000
#> GSM11294 3 0.0000 0.984 0.000 0.000 1.000 0.000 0.000
#> GSM28771 2 0.0703 0.979 0.000 0.976 0.000 0.000 0.024
#> GSM28760 5 0.2377 0.936 0.000 0.128 0.000 0.000 0.872
#> GSM28774 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM11284 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM28761 3 0.0880 0.973 0.000 0.000 0.968 0.000 0.032
#> GSM11278 5 0.2377 0.940 0.000 0.128 0.000 0.000 0.872
#> GSM11291 3 0.0000 0.984 0.000 0.000 1.000 0.000 0.000
#> GSM11277 3 0.0000 0.984 0.000 0.000 1.000 0.000 0.000
#> GSM11272 3 0.1544 0.947 0.000 0.000 0.932 0.000 0.068
#> GSM11285 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM28753 2 0.0404 0.990 0.000 0.988 0.000 0.000 0.012
#> GSM28773 2 0.0162 0.993 0.000 0.996 0.000 0.000 0.004
#> GSM28765 2 0.0290 0.992 0.000 0.992 0.000 0.000 0.008
#> GSM28768 1 0.4995 0.587 0.668 0.000 0.000 0.264 0.068
#> GSM28754 2 0.0404 0.990 0.000 0.988 0.000 0.000 0.012
#> GSM28769 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM11275 1 0.1197 0.944 0.952 0.000 0.000 0.000 0.048
#> GSM11270 5 0.2377 0.940 0.000 0.128 0.000 0.000 0.872
#> GSM11271 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM11288 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM11273 5 0.2462 0.928 0.000 0.112 0.008 0.000 0.880
#> GSM28757 2 0.0404 0.990 0.000 0.988 0.000 0.000 0.012
#> GSM11282 5 0.2377 0.940 0.000 0.128 0.000 0.000 0.872
#> GSM28756 2 0.0290 0.992 0.000 0.992 0.000 0.000 0.008
#> GSM11276 2 0.0000 0.995 0.000 1.000 0.000 0.000 0.000
#> GSM28752 2 0.0000 0.995 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
#> GSM28762 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28763 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28764 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11274 4 0.2048 0.769 0.000 0.000 0.120 0.880 0.000 0.000
#> GSM28772 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.1564 0.936 0.936 0.000 0.000 0.024 0.000 0.040
#> GSM11293 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.1564 0.936 0.936 0.000 0.000 0.024 0.000 0.040
#> GSM11279 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.1564 0.936 0.936 0.000 0.000 0.024 0.000 0.040
#> GSM11281 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.951 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28766 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11268 6 0.2762 0.912 0.000 0.000 0.196 0.000 0.000 0.804
#> GSM28767 5 0.0146 0.988 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM11286 5 0.0363 0.985 0.000 0.000 0.000 0.012 0.988 0.000
#> GSM28751 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28770 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11283 5 0.0972 0.962 0.000 0.000 0.000 0.028 0.964 0.008
#> GSM11289 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11280 5 0.0363 0.985 0.000 0.000 0.000 0.012 0.988 0.000
#> GSM28749 5 0.0363 0.985 0.000 0.000 0.000 0.012 0.988 0.000
#> GSM28750 6 0.3499 0.787 0.000 0.000 0.320 0.000 0.000 0.680
#> GSM11290 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11294 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM28771 5 0.1124 0.959 0.000 0.000 0.000 0.036 0.956 0.008
#> GSM28760 4 0.1863 0.929 0.000 0.000 0.000 0.896 0.104 0.000
#> GSM28774 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11284 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28761 6 0.2730 0.912 0.000 0.000 0.192 0.000 0.000 0.808
#> GSM11278 4 0.1714 0.946 0.000 0.000 0.000 0.908 0.092 0.000
#> GSM11291 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11277 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11272 6 0.2048 0.866 0.000 0.000 0.120 0.000 0.000 0.880
#> GSM11285 5 0.0000 0.989 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28753 5 0.0713 0.976 0.000 0.000 0.000 0.028 0.972 0.000
#> GSM28773 5 0.0146 0.987 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM28765 5 0.0363 0.985 0.000 0.000 0.000 0.012 0.988 0.000
#> GSM28768 1 0.5460 0.604 0.652 0.192 0.000 0.044 0.000 0.112
#> GSM28754 5 0.0790 0.973 0.000 0.000 0.000 0.032 0.968 0.000
#> GSM28769 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11275 1 0.1564 0.936 0.936 0.000 0.000 0.024 0.000 0.040
#> GSM11270 4 0.1714 0.946 0.000 0.000 0.000 0.908 0.092 0.000
#> GSM11271 5 0.0146 0.988 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM11288 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11273 4 0.1501 0.933 0.000 0.000 0.000 0.924 0.076 0.000
#> GSM28757 5 0.1075 0.959 0.000 0.000 0.000 0.048 0.952 0.000
#> GSM11282 4 0.1714 0.946 0.000 0.000 0.000 0.908 0.092 0.000
#> GSM28756 5 0.0632 0.978 0.000 0.000 0.000 0.024 0.976 0.000
#> GSM11276 5 0.0146 0.988 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM28752 5 0.0000 0.989 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 tissue(p) k
#> ATC:hclust 51 0.395 2
#> ATC:hclust 51 0.371 3
#> ATC:hclust 54 0.355 4
#> ATC:hclust 54 0.337 5
#> ATC:hclust 54 0.322 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.500 0.815 0.847 0.3484 0.648 0.648
#> 3 3 1.000 0.976 0.967 0.5232 0.762 0.645
#> 4 4 0.707 0.717 0.861 0.2532 0.935 0.857
#> 5 5 0.657 0.803 0.861 0.0951 0.867 0.664
#> 6 6 0.734 0.717 0.803 0.0640 0.998 0.992
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
#> GSM28762 2 0.000 0.852 0.000 1.000
#> GSM28763 2 0.000 0.852 0.000 1.000
#> GSM28764 2 0.000 0.852 0.000 1.000
#> GSM11274 2 0.921 0.566 0.336 0.664
#> GSM28772 1 0.921 0.988 0.664 0.336
#> GSM11269 1 0.921 0.988 0.664 0.336
#> GSM28775 1 0.921 0.988 0.664 0.336
#> GSM11293 1 0.921 0.988 0.664 0.336
#> GSM28755 1 0.921 0.988 0.664 0.336
#> GSM11279 1 0.921 0.988 0.664 0.336
#> GSM28758 1 0.921 0.988 0.664 0.336
#> GSM11281 1 0.921 0.988 0.664 0.336
#> GSM11287 1 0.921 0.988 0.664 0.336
#> GSM28759 1 0.921 0.988 0.664 0.336
#> GSM11292 2 0.000 0.852 0.000 1.000
#> GSM28766 2 0.000 0.852 0.000 1.000
#> GSM11268 2 0.985 0.495 0.428 0.572
#> GSM28767 2 0.000 0.852 0.000 1.000
#> GSM11286 2 0.000 0.852 0.000 1.000
#> GSM28751 2 0.000 0.852 0.000 1.000
#> GSM28770 2 0.000 0.852 0.000 1.000
#> GSM11283 2 0.000 0.852 0.000 1.000
#> GSM11289 2 0.000 0.852 0.000 1.000
#> GSM11280 2 0.000 0.852 0.000 1.000
#> GSM28749 2 0.000 0.852 0.000 1.000
#> GSM28750 2 0.985 0.495 0.428 0.572
#> GSM11290 2 0.985 0.495 0.428 0.572
#> GSM11294 2 0.985 0.495 0.428 0.572
#> GSM28771 2 0.000 0.852 0.000 1.000
#> GSM28760 2 0.184 0.832 0.028 0.972
#> GSM28774 2 0.000 0.852 0.000 1.000
#> GSM11284 2 0.000 0.852 0.000 1.000
#> GSM28761 2 0.985 0.495 0.428 0.572
#> GSM11278 2 0.000 0.852 0.000 1.000
#> GSM11291 2 0.985 0.495 0.428 0.572
#> GSM11277 2 0.985 0.495 0.428 0.572
#> GSM11272 2 0.985 0.495 0.428 0.572
#> GSM11285 2 0.000 0.852 0.000 1.000
#> GSM28753 2 0.000 0.852 0.000 1.000
#> GSM28773 2 0.000 0.852 0.000 1.000
#> GSM28765 2 0.000 0.852 0.000 1.000
#> GSM28768 1 0.983 0.851 0.576 0.424
#> GSM28754 2 0.000 0.852 0.000 1.000
#> GSM28769 2 0.000 0.852 0.000 1.000
#> GSM11275 1 0.921 0.988 0.664 0.336
#> GSM11270 2 0.000 0.852 0.000 1.000
#> GSM11271 2 0.000 0.852 0.000 1.000
#> GSM11288 2 0.443 0.742 0.092 0.908
#> GSM11273 2 0.821 0.635 0.256 0.744
#> GSM28757 2 0.000 0.852 0.000 1.000
#> GSM11282 2 0.184 0.832 0.028 0.972
#> GSM28756 2 0.000 0.852 0.000 1.000
#> GSM11276 2 0.000 0.852 0.000 1.000
#> GSM28752 2 0.000 0.852 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28763 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28764 2 0.0000 0.987 0.000 1.000 0.000
#> GSM11274 3 0.2625 0.991 0.000 0.084 0.916
#> GSM28772 1 0.1031 0.980 0.976 0.024 0.000
#> GSM11269 1 0.1031 0.980 0.976 0.024 0.000
#> GSM28775 1 0.3181 0.965 0.912 0.024 0.064
#> GSM11293 1 0.1031 0.980 0.976 0.024 0.000
#> GSM28755 1 0.3181 0.965 0.912 0.024 0.064
#> GSM11279 1 0.1031 0.980 0.976 0.024 0.000
#> GSM28758 1 0.3181 0.965 0.912 0.024 0.064
#> GSM11281 1 0.1031 0.980 0.976 0.024 0.000
#> GSM11287 1 0.1031 0.980 0.976 0.024 0.000
#> GSM28759 1 0.1031 0.980 0.976 0.024 0.000
#> GSM11292 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28766 2 0.0000 0.987 0.000 1.000 0.000
#> GSM11268 3 0.2625 0.991 0.000 0.084 0.916
#> GSM28767 2 0.0000 0.987 0.000 1.000 0.000
#> GSM11286 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28751 2 0.0892 0.971 0.000 0.980 0.020
#> GSM28770 2 0.0000 0.987 0.000 1.000 0.000
#> GSM11283 2 0.0000 0.987 0.000 1.000 0.000
#> GSM11289 2 0.0000 0.987 0.000 1.000 0.000
#> GSM11280 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28749 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28750 3 0.2625 0.991 0.000 0.084 0.916
#> GSM11290 3 0.3637 0.989 0.024 0.084 0.892
#> GSM11294 3 0.3637 0.989 0.024 0.084 0.892
#> GSM28771 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28760 2 0.1031 0.963 0.000 0.976 0.024
#> GSM28774 2 0.0000 0.987 0.000 1.000 0.000
#> GSM11284 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28761 3 0.2625 0.991 0.000 0.084 0.916
#> GSM11278 2 0.0000 0.987 0.000 1.000 0.000
#> GSM11291 3 0.3637 0.989 0.024 0.084 0.892
#> GSM11277 3 0.3637 0.989 0.024 0.084 0.892
#> GSM11272 3 0.2625 0.991 0.000 0.084 0.916
#> GSM11285 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28753 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28773 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28765 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28768 2 0.7001 0.617 0.200 0.716 0.084
#> GSM28754 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28769 2 0.0892 0.971 0.000 0.980 0.020
#> GSM11275 1 0.3181 0.965 0.912 0.024 0.064
#> GSM11270 2 0.0000 0.987 0.000 1.000 0.000
#> GSM11271 2 0.0000 0.987 0.000 1.000 0.000
#> GSM11288 2 0.0892 0.971 0.000 0.980 0.020
#> GSM11273 2 0.1031 0.963 0.000 0.976 0.024
#> GSM28757 2 0.0000 0.987 0.000 1.000 0.000
#> GSM11282 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28756 2 0.0000 0.987 0.000 1.000 0.000
#> GSM11276 2 0.0000 0.987 0.000 1.000 0.000
#> GSM28752 2 0.0000 0.987 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.3610 0.541 0.000 0.800 0.000 0.200
#> GSM28763 2 0.3444 0.547 0.000 0.816 0.000 0.184
#> GSM28764 2 0.0921 0.716 0.000 0.972 0.000 0.028
#> GSM11274 3 0.4746 0.641 0.000 0.000 0.632 0.368
#> GSM28772 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM28775 1 0.1867 0.958 0.928 0.000 0.000 0.072
#> GSM11293 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM28755 1 0.1792 0.959 0.932 0.000 0.000 0.068
#> GSM11279 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM28758 1 0.1867 0.958 0.928 0.000 0.000 0.072
#> GSM11281 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.977 1.000 0.000 0.000 0.000
#> GSM11292 2 0.1940 0.715 0.000 0.924 0.000 0.076
#> GSM28766 2 0.2011 0.715 0.000 0.920 0.000 0.080
#> GSM11268 3 0.1302 0.934 0.000 0.000 0.956 0.044
#> GSM28767 2 0.1022 0.724 0.000 0.968 0.000 0.032
#> GSM11286 2 0.3074 0.625 0.000 0.848 0.000 0.152
#> GSM28751 2 0.5000 -0.664 0.000 0.500 0.000 0.500
#> GSM28770 2 0.1022 0.724 0.000 0.968 0.000 0.032
#> GSM11283 2 0.3074 0.636 0.000 0.848 0.000 0.152
#> GSM11289 2 0.0469 0.722 0.000 0.988 0.000 0.012
#> GSM11280 2 0.3219 0.626 0.000 0.836 0.000 0.164
#> GSM28749 2 0.3726 0.622 0.000 0.788 0.000 0.212
#> GSM28750 3 0.1302 0.934 0.000 0.000 0.956 0.044
#> GSM11290 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM11294 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM28771 2 0.3688 0.592 0.000 0.792 0.000 0.208
#> GSM28760 2 0.4898 0.354 0.000 0.584 0.000 0.416
#> GSM28774 2 0.0921 0.725 0.000 0.972 0.000 0.028
#> GSM11284 2 0.1637 0.722 0.000 0.940 0.000 0.060
#> GSM28761 3 0.2081 0.922 0.000 0.000 0.916 0.084
#> GSM11278 2 0.4790 0.416 0.000 0.620 0.000 0.380
#> GSM11291 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.935 0.000 0.000 1.000 0.000
#> GSM11272 3 0.2081 0.922 0.000 0.000 0.916 0.084
#> GSM11285 2 0.3569 0.616 0.000 0.804 0.000 0.196
#> GSM28753 2 0.2647 0.672 0.000 0.880 0.000 0.120
#> GSM28773 2 0.2530 0.699 0.000 0.888 0.000 0.112
#> GSM28765 2 0.2345 0.665 0.000 0.900 0.000 0.100
#> GSM28768 4 0.5671 0.705 0.028 0.400 0.000 0.572
#> GSM28754 2 0.2149 0.696 0.000 0.912 0.000 0.088
#> GSM28769 4 0.4933 0.688 0.000 0.432 0.000 0.568
#> GSM11275 1 0.1867 0.958 0.928 0.000 0.000 0.072
#> GSM11270 2 0.4790 0.416 0.000 0.620 0.000 0.380
#> GSM11271 2 0.1022 0.724 0.000 0.968 0.000 0.032
#> GSM11288 4 0.3975 0.662 0.000 0.240 0.000 0.760
#> GSM11273 2 0.4981 0.258 0.000 0.536 0.000 0.464
#> GSM28757 2 0.3311 0.622 0.000 0.828 0.000 0.172
#> GSM11282 2 0.4817 0.404 0.000 0.612 0.000 0.388
#> GSM28756 2 0.0469 0.724 0.000 0.988 0.000 0.012
#> GSM11276 2 0.0817 0.717 0.000 0.976 0.000 0.024
#> GSM28752 2 0.2814 0.648 0.000 0.868 0.000 0.132
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28762 2 0.4114 0.634 0.000 0.732 0.000 0.244 0.024
#> GSM28763 2 0.3942 0.651 0.000 0.748 0.000 0.232 0.020
#> GSM28764 2 0.0162 0.824 0.000 0.996 0.000 0.004 0.000
#> GSM11274 5 0.4734 0.277 0.000 0.000 0.232 0.064 0.704
#> GSM28772 1 0.0000 0.954 1.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.954 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.2654 0.917 0.884 0.000 0.000 0.032 0.084
#> GSM11293 1 0.0000 0.954 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.2654 0.917 0.884 0.000 0.000 0.032 0.084
#> GSM11279 1 0.0000 0.954 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.3289 0.895 0.844 0.000 0.000 0.048 0.108
#> GSM11281 1 0.0000 0.954 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.954 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.954 1.000 0.000 0.000 0.000 0.000
#> GSM11292 2 0.2338 0.792 0.000 0.884 0.000 0.004 0.112
#> GSM28766 2 0.2338 0.792 0.000 0.884 0.000 0.004 0.112
#> GSM11268 3 0.3620 0.895 0.000 0.000 0.824 0.108 0.068
#> GSM28767 2 0.1121 0.824 0.000 0.956 0.000 0.000 0.044
#> GSM11286 2 0.3530 0.703 0.000 0.784 0.000 0.204 0.012
#> GSM28751 4 0.4315 0.773 0.000 0.276 0.000 0.700 0.024
#> GSM28770 2 0.1121 0.824 0.000 0.956 0.000 0.000 0.044
#> GSM11283 2 0.3702 0.690 0.000 0.820 0.000 0.096 0.084
#> GSM11289 2 0.0404 0.825 0.000 0.988 0.000 0.000 0.012
#> GSM11280 2 0.3993 0.681 0.000 0.756 0.000 0.216 0.028
#> GSM28749 2 0.5341 0.647 0.000 0.664 0.000 0.212 0.124
#> GSM28750 3 0.3493 0.897 0.000 0.000 0.832 0.108 0.060
#> GSM11290 3 0.0000 0.904 0.000 0.000 1.000 0.000 0.000
#> GSM11294 3 0.0000 0.904 0.000 0.000 1.000 0.000 0.000
#> GSM28771 5 0.5821 0.472 0.000 0.400 0.000 0.096 0.504
#> GSM28760 5 0.3123 0.789 0.000 0.184 0.000 0.004 0.812
#> GSM28774 2 0.1282 0.824 0.000 0.952 0.000 0.004 0.044
#> GSM11284 2 0.2338 0.791 0.000 0.884 0.000 0.004 0.112
#> GSM28761 3 0.4428 0.870 0.000 0.000 0.756 0.160 0.084
#> GSM11278 5 0.3461 0.800 0.000 0.224 0.000 0.004 0.772
#> GSM11291 3 0.0000 0.904 0.000 0.000 1.000 0.000 0.000
#> GSM11277 3 0.0000 0.904 0.000 0.000 1.000 0.000 0.000
#> GSM11272 3 0.4428 0.870 0.000 0.000 0.756 0.160 0.084
#> GSM11285 2 0.2763 0.749 0.000 0.848 0.000 0.004 0.148
#> GSM28753 2 0.3409 0.742 0.000 0.816 0.000 0.160 0.024
#> GSM28773 2 0.2563 0.783 0.000 0.872 0.000 0.008 0.120
#> GSM28765 2 0.2612 0.774 0.000 0.868 0.000 0.124 0.008
#> GSM28768 4 0.5711 0.758 0.012 0.224 0.000 0.648 0.116
#> GSM28754 2 0.3012 0.771 0.000 0.852 0.000 0.124 0.024
#> GSM28769 4 0.4708 0.798 0.000 0.220 0.000 0.712 0.068
#> GSM11275 1 0.3289 0.895 0.844 0.000 0.000 0.048 0.108
#> GSM11270 5 0.3461 0.800 0.000 0.224 0.000 0.004 0.772
#> GSM11271 2 0.1121 0.824 0.000 0.956 0.000 0.000 0.044
#> GSM11288 4 0.4234 0.594 0.000 0.056 0.000 0.760 0.184
#> GSM11273 5 0.3399 0.761 0.000 0.168 0.000 0.020 0.812
#> GSM28757 2 0.4224 0.675 0.000 0.744 0.000 0.216 0.040
#> GSM11282 5 0.3461 0.800 0.000 0.224 0.000 0.004 0.772
#> GSM28756 2 0.0693 0.823 0.000 0.980 0.000 0.008 0.012
#> GSM11276 2 0.0162 0.824 0.000 0.996 0.000 0.004 0.000
#> GSM28752 2 0.1648 0.821 0.000 0.940 0.000 0.040 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 5 0.3817 0.568 0.000 0.432 0.000 0.000 0.568 0.000
#> GSM28763 5 0.3823 0.568 0.000 0.436 0.000 0.000 0.564 0.000
#> GSM28764 5 0.0713 0.759 0.000 0.028 0.000 0.000 0.972 0.000
#> GSM11274 4 0.3073 0.596 0.000 0.004 0.164 0.816 0.000 0.016
#> GSM28772 1 0.0000 0.880 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.880 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.3641 0.755 0.732 0.000 0.000 0.020 0.000 0.248
#> GSM11293 1 0.0000 0.880 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.3641 0.755 0.732 0.000 0.000 0.020 0.000 0.248
#> GSM11279 1 0.0000 0.880 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.4078 0.701 0.676 0.016 0.000 0.008 0.000 0.300
#> GSM11281 1 0.0000 0.880 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.880 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.880 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.2006 0.724 0.000 0.004 0.000 0.104 0.892 0.000
#> GSM28766 5 0.2006 0.724 0.000 0.004 0.000 0.104 0.892 0.000
#> GSM11268 3 0.1088 0.833 0.000 0.000 0.960 0.024 0.000 0.016
#> GSM28767 5 0.1124 0.756 0.000 0.008 0.000 0.036 0.956 0.000
#> GSM11286 5 0.3659 0.632 0.000 0.364 0.000 0.000 0.636 0.000
#> GSM28751 2 0.4947 0.621 0.000 0.596 0.000 0.000 0.088 0.316
#> GSM28770 5 0.1572 0.752 0.000 0.028 0.000 0.036 0.936 0.000
#> GSM11283 5 0.5673 0.464 0.000 0.344 0.000 0.040 0.544 0.072
#> GSM11289 5 0.0935 0.756 0.000 0.032 0.000 0.004 0.964 0.000
#> GSM11280 5 0.3923 0.589 0.000 0.416 0.000 0.004 0.580 0.000
#> GSM28749 5 0.4746 0.645 0.000 0.236 0.000 0.104 0.660 0.000
#> GSM28750 3 0.0458 0.838 0.000 0.000 0.984 0.016 0.000 0.000
#> GSM11290 3 0.3809 0.844 0.000 0.016 0.756 0.020 0.000 0.208
#> GSM11294 3 0.3809 0.844 0.000 0.016 0.756 0.020 0.000 0.208
#> GSM28771 4 0.7018 0.234 0.000 0.344 0.000 0.364 0.220 0.072
#> GSM28760 4 0.2013 0.809 0.000 0.008 0.000 0.908 0.076 0.008
#> GSM28774 5 0.1196 0.756 0.000 0.008 0.000 0.040 0.952 0.000
#> GSM11284 5 0.1970 0.732 0.000 0.008 0.000 0.092 0.900 0.000
#> GSM28761 3 0.1867 0.819 0.000 0.004 0.924 0.036 0.000 0.036
#> GSM11278 4 0.2053 0.816 0.000 0.004 0.000 0.888 0.108 0.000
#> GSM11291 3 0.3809 0.844 0.000 0.016 0.756 0.020 0.000 0.208
#> GSM11277 3 0.3809 0.844 0.000 0.016 0.756 0.020 0.000 0.208
#> GSM11272 3 0.1867 0.819 0.000 0.004 0.924 0.036 0.000 0.036
#> GSM11285 5 0.2513 0.693 0.000 0.008 0.000 0.140 0.852 0.000
#> GSM28753 5 0.3881 0.611 0.000 0.396 0.000 0.004 0.600 0.000
#> GSM28773 5 0.2302 0.713 0.000 0.008 0.000 0.120 0.872 0.000
#> GSM28765 5 0.3547 0.656 0.000 0.332 0.000 0.000 0.668 0.000
#> GSM28768 6 0.4278 0.000 0.000 0.336 0.000 0.000 0.032 0.632
#> GSM28754 5 0.3819 0.631 0.000 0.372 0.000 0.004 0.624 0.000
#> GSM28769 2 0.5212 0.679 0.000 0.592 0.000 0.024 0.060 0.324
#> GSM11275 1 0.4078 0.701 0.676 0.016 0.000 0.008 0.000 0.300
#> GSM11270 4 0.2053 0.816 0.000 0.004 0.000 0.888 0.108 0.000
#> GSM11271 5 0.0937 0.756 0.000 0.000 0.000 0.040 0.960 0.000
#> GSM11288 2 0.5568 0.424 0.000 0.524 0.000 0.096 0.016 0.364
#> GSM11273 4 0.1801 0.786 0.000 0.004 0.000 0.924 0.056 0.016
#> GSM28757 5 0.3945 0.615 0.000 0.380 0.000 0.008 0.612 0.000
#> GSM11282 4 0.2053 0.816 0.000 0.004 0.000 0.888 0.108 0.000
#> GSM28756 5 0.2772 0.725 0.000 0.180 0.000 0.004 0.816 0.000
#> GSM11276 5 0.0865 0.759 0.000 0.036 0.000 0.000 0.964 0.000
#> GSM28752 5 0.1204 0.756 0.000 0.056 0.000 0.000 0.944 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 tissue(p) k
#> ATC:kmeans 46 0.389 2
#> ATC:kmeans 54 0.374 3
#> ATC:kmeans 48 0.346 4
#> ATC:kmeans 52 0.334 5
#> ATC:kmeans 50 0.407 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.739 0.857 0.930 0.4576 0.508 0.508
#> 3 3 1.000 0.988 0.995 0.3627 0.810 0.645
#> 4 4 0.747 0.775 0.849 0.1681 0.827 0.561
#> 5 5 0.734 0.577 0.759 0.0647 0.906 0.657
#> 6 6 0.787 0.832 0.889 0.0516 0.916 0.651
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
#> GSM28762 2 0.000 0.983 0.00 1.00
#> GSM28763 2 0.000 0.983 0.00 1.00
#> GSM28764 2 0.000 0.983 0.00 1.00
#> GSM11274 2 0.000 0.983 0.00 1.00
#> GSM28772 1 0.000 0.823 1.00 0.00
#> GSM11269 1 0.000 0.823 1.00 0.00
#> GSM28775 1 0.000 0.823 1.00 0.00
#> GSM11293 1 0.000 0.823 1.00 0.00
#> GSM28755 1 0.000 0.823 1.00 0.00
#> GSM11279 1 0.000 0.823 1.00 0.00
#> GSM28758 1 0.000 0.823 1.00 0.00
#> GSM11281 1 0.000 0.823 1.00 0.00
#> GSM11287 1 0.000 0.823 1.00 0.00
#> GSM28759 1 0.000 0.823 1.00 0.00
#> GSM11292 2 0.000 0.983 0.00 1.00
#> GSM28766 2 0.000 0.983 0.00 1.00
#> GSM11268 1 0.981 0.513 0.58 0.42
#> GSM28767 2 0.000 0.983 0.00 1.00
#> GSM11286 2 0.000 0.983 0.00 1.00
#> GSM28751 2 0.981 0.203 0.42 0.58
#> GSM28770 2 0.000 0.983 0.00 1.00
#> GSM11283 2 0.000 0.983 0.00 1.00
#> GSM11289 2 0.000 0.983 0.00 1.00
#> GSM11280 2 0.000 0.983 0.00 1.00
#> GSM28749 2 0.000 0.983 0.00 1.00
#> GSM28750 1 0.981 0.513 0.58 0.42
#> GSM11290 1 0.981 0.513 0.58 0.42
#> GSM11294 1 0.981 0.513 0.58 0.42
#> GSM28771 2 0.000 0.983 0.00 1.00
#> GSM28760 2 0.000 0.983 0.00 1.00
#> GSM28774 2 0.000 0.983 0.00 1.00
#> GSM11284 2 0.000 0.983 0.00 1.00
#> GSM28761 1 0.981 0.513 0.58 0.42
#> GSM11278 2 0.000 0.983 0.00 1.00
#> GSM11291 1 0.981 0.513 0.58 0.42
#> GSM11277 1 0.981 0.513 0.58 0.42
#> GSM11272 1 0.981 0.513 0.58 0.42
#> GSM11285 2 0.000 0.983 0.00 1.00
#> GSM28753 2 0.000 0.983 0.00 1.00
#> GSM28773 2 0.000 0.983 0.00 1.00
#> GSM28765 2 0.000 0.983 0.00 1.00
#> GSM28768 1 0.000 0.823 1.00 0.00
#> GSM28754 2 0.000 0.983 0.00 1.00
#> GSM28769 1 0.000 0.823 1.00 0.00
#> GSM11275 1 0.000 0.823 1.00 0.00
#> GSM11270 2 0.000 0.983 0.00 1.00
#> GSM11271 2 0.000 0.983 0.00 1.00
#> GSM11288 1 0.000 0.823 1.00 0.00
#> GSM11273 2 0.000 0.983 0.00 1.00
#> GSM28757 2 0.000 0.983 0.00 1.00
#> GSM11282 2 0.000 0.983 0.00 1.00
#> GSM28756 2 0.000 0.983 0.00 1.00
#> GSM11276 2 0.000 0.983 0.00 1.00
#> GSM28752 2 0.000 0.983 0.00 1.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.000 1.000 0.000 1.000 0.000
#> GSM28763 2 0.000 1.000 0.000 1.000 0.000
#> GSM28764 2 0.000 1.000 0.000 1.000 0.000
#> GSM11274 3 0.000 0.979 0.000 0.000 1.000
#> GSM28772 1 0.000 0.994 1.000 0.000 0.000
#> GSM11269 1 0.000 0.994 1.000 0.000 0.000
#> GSM28775 1 0.000 0.994 1.000 0.000 0.000
#> GSM11293 1 0.000 0.994 1.000 0.000 0.000
#> GSM28755 1 0.000 0.994 1.000 0.000 0.000
#> GSM11279 1 0.000 0.994 1.000 0.000 0.000
#> GSM28758 1 0.000 0.994 1.000 0.000 0.000
#> GSM11281 1 0.000 0.994 1.000 0.000 0.000
#> GSM11287 1 0.000 0.994 1.000 0.000 0.000
#> GSM28759 1 0.000 0.994 1.000 0.000 0.000
#> GSM11292 2 0.000 1.000 0.000 1.000 0.000
#> GSM28766 2 0.000 1.000 0.000 1.000 0.000
#> GSM11268 3 0.000 0.979 0.000 0.000 1.000
#> GSM28767 2 0.000 1.000 0.000 1.000 0.000
#> GSM11286 2 0.000 1.000 0.000 1.000 0.000
#> GSM28751 1 0.000 0.994 1.000 0.000 0.000
#> GSM28770 2 0.000 1.000 0.000 1.000 0.000
#> GSM11283 2 0.000 1.000 0.000 1.000 0.000
#> GSM11289 2 0.000 1.000 0.000 1.000 0.000
#> GSM11280 2 0.000 1.000 0.000 1.000 0.000
#> GSM28749 2 0.000 1.000 0.000 1.000 0.000
#> GSM28750 3 0.000 0.979 0.000 0.000 1.000
#> GSM11290 3 0.000 0.979 0.000 0.000 1.000
#> GSM11294 3 0.000 0.979 0.000 0.000 1.000
#> GSM28771 2 0.000 1.000 0.000 1.000 0.000
#> GSM28760 3 0.440 0.751 0.000 0.188 0.812
#> GSM28774 2 0.000 1.000 0.000 1.000 0.000
#> GSM11284 2 0.000 1.000 0.000 1.000 0.000
#> GSM28761 3 0.000 0.979 0.000 0.000 1.000
#> GSM11278 2 0.000 1.000 0.000 1.000 0.000
#> GSM11291 3 0.000 0.979 0.000 0.000 1.000
#> GSM11277 3 0.000 0.979 0.000 0.000 1.000
#> GSM11272 3 0.000 0.979 0.000 0.000 1.000
#> GSM11285 2 0.000 1.000 0.000 1.000 0.000
#> GSM28753 2 0.000 1.000 0.000 1.000 0.000
#> GSM28773 2 0.000 1.000 0.000 1.000 0.000
#> GSM28765 2 0.000 1.000 0.000 1.000 0.000
#> GSM28768 1 0.000 0.994 1.000 0.000 0.000
#> GSM28754 2 0.000 1.000 0.000 1.000 0.000
#> GSM28769 1 0.216 0.914 0.936 0.064 0.000
#> GSM11275 1 0.000 0.994 1.000 0.000 0.000
#> GSM11270 2 0.000 1.000 0.000 1.000 0.000
#> GSM11271 2 0.000 1.000 0.000 1.000 0.000
#> GSM11288 3 0.000 0.979 0.000 0.000 1.000
#> GSM11273 3 0.000 0.979 0.000 0.000 1.000
#> GSM28757 2 0.000 1.000 0.000 1.000 0.000
#> GSM11282 2 0.000 1.000 0.000 1.000 0.000
#> GSM28756 2 0.000 1.000 0.000 1.000 0.000
#> GSM11276 2 0.000 1.000 0.000 1.000 0.000
#> GSM28752 2 0.000 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
#> GSM28762 2 0.1940 0.727 0.000 0.924 0.000 0.076
#> GSM28763 2 0.1940 0.727 0.000 0.924 0.000 0.076
#> GSM28764 2 0.2704 0.672 0.000 0.876 0.000 0.124
#> GSM11274 3 0.3486 0.844 0.000 0.000 0.812 0.188
#> GSM28772 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM11292 4 0.4746 0.812 0.000 0.368 0.000 0.632
#> GSM28766 4 0.4746 0.812 0.000 0.368 0.000 0.632
#> GSM11268 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM28767 4 0.4961 0.732 0.000 0.448 0.000 0.552
#> GSM11286 2 0.0592 0.780 0.000 0.984 0.000 0.016
#> GSM28751 2 0.6826 0.378 0.228 0.600 0.000 0.172
#> GSM28770 4 0.4948 0.745 0.000 0.440 0.000 0.560
#> GSM11283 2 0.3444 0.546 0.000 0.816 0.000 0.184
#> GSM11289 2 0.4817 -0.294 0.000 0.612 0.000 0.388
#> GSM11280 2 0.0336 0.780 0.000 0.992 0.000 0.008
#> GSM28749 4 0.4761 0.811 0.000 0.372 0.000 0.628
#> GSM28750 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM11290 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM11294 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM28771 2 0.4866 0.205 0.000 0.596 0.000 0.404
#> GSM28760 4 0.5199 0.573 0.000 0.144 0.100 0.756
#> GSM28774 4 0.4998 0.628 0.000 0.488 0.000 0.512
#> GSM11284 4 0.4776 0.808 0.000 0.376 0.000 0.624
#> GSM28761 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM11278 4 0.3311 0.689 0.000 0.172 0.000 0.828
#> GSM11291 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM11272 3 0.0000 0.959 0.000 0.000 1.000 0.000
#> GSM11285 4 0.4730 0.812 0.000 0.364 0.000 0.636
#> GSM28753 2 0.0469 0.780 0.000 0.988 0.000 0.012
#> GSM28773 4 0.4746 0.812 0.000 0.368 0.000 0.632
#> GSM28765 2 0.0592 0.780 0.000 0.984 0.000 0.016
#> GSM28768 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM28754 2 0.0469 0.781 0.000 0.988 0.000 0.012
#> GSM28769 1 0.9637 0.144 0.356 0.296 0.164 0.184
#> GSM11275 1 0.0000 0.953 1.000 0.000 0.000 0.000
#> GSM11270 4 0.3311 0.689 0.000 0.172 0.000 0.828
#> GSM11271 4 0.4955 0.739 0.000 0.444 0.000 0.556
#> GSM11288 3 0.2281 0.903 0.000 0.000 0.904 0.096
#> GSM11273 3 0.3569 0.838 0.000 0.000 0.804 0.196
#> GSM28757 2 0.0592 0.781 0.000 0.984 0.000 0.016
#> GSM11282 4 0.3311 0.689 0.000 0.172 0.000 0.828
#> GSM28756 2 0.1474 0.765 0.000 0.948 0.000 0.052
#> GSM11276 2 0.1940 0.736 0.000 0.924 0.000 0.076
#> GSM28752 2 0.3569 0.521 0.000 0.804 0.000 0.196
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28762 4 0.324 0.6121 0.000 0.136 0.000 0.836 0.028
#> GSM28763 4 0.315 0.6163 0.000 0.136 0.000 0.840 0.024
#> GSM28764 4 0.445 -0.1856 0.000 0.476 0.000 0.520 0.004
#> GSM11274 3 0.187 0.2482 0.000 0.052 0.928 0.000 0.020
#> GSM28772 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM11292 2 0.311 0.6506 0.000 0.800 0.000 0.200 0.000
#> GSM28766 2 0.311 0.6506 0.000 0.800 0.000 0.200 0.000
#> GSM11268 3 0.430 0.5999 0.000 0.000 0.528 0.000 0.472
#> GSM28767 2 0.398 0.5796 0.000 0.660 0.000 0.340 0.000
#> GSM11286 4 0.312 0.6134 0.000 0.184 0.000 0.812 0.004
#> GSM28751 5 0.707 0.5462 0.060 0.136 0.000 0.284 0.520
#> GSM28770 2 0.395 0.5913 0.000 0.668 0.000 0.332 0.000
#> GSM11283 4 0.392 0.5571 0.000 0.180 0.032 0.784 0.004
#> GSM11289 2 0.429 0.3046 0.000 0.536 0.000 0.464 0.000
#> GSM11280 4 0.096 0.6822 0.000 0.016 0.004 0.972 0.008
#> GSM28749 2 0.450 0.6045 0.000 0.664 0.024 0.312 0.000
#> GSM28750 3 0.430 0.5999 0.000 0.000 0.528 0.000 0.472
#> GSM11290 3 0.430 0.5999 0.000 0.000 0.528 0.000 0.472
#> GSM11294 3 0.430 0.5999 0.000 0.000 0.528 0.000 0.472
#> GSM28771 4 0.646 0.1767 0.000 0.212 0.260 0.524 0.004
#> GSM28760 3 0.542 -0.1146 0.000 0.416 0.524 0.060 0.000
#> GSM28774 2 0.421 0.5774 0.000 0.636 0.004 0.360 0.000
#> GSM11284 2 0.376 0.6481 0.000 0.744 0.008 0.248 0.000
#> GSM28761 3 0.430 0.5999 0.000 0.000 0.528 0.000 0.472
#> GSM11278 2 0.541 0.0865 0.000 0.472 0.472 0.056 0.000
#> GSM11291 3 0.430 0.5999 0.000 0.000 0.528 0.000 0.472
#> GSM11277 3 0.430 0.5999 0.000 0.000 0.528 0.000 0.472
#> GSM11272 3 0.430 0.5999 0.000 0.000 0.528 0.000 0.472
#> GSM11285 2 0.352 0.6373 0.000 0.776 0.008 0.216 0.000
#> GSM28753 4 0.154 0.6876 0.000 0.036 0.008 0.948 0.008
#> GSM28773 2 0.386 0.6376 0.000 0.728 0.008 0.264 0.000
#> GSM28765 4 0.273 0.6403 0.000 0.160 0.000 0.840 0.000
#> GSM28768 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM28754 4 0.172 0.6889 0.000 0.052 0.004 0.936 0.008
#> GSM28769 5 0.666 0.6099 0.056 0.132 0.000 0.220 0.592
#> GSM11275 1 0.000 1.0000 1.000 0.000 0.000 0.000 0.000
#> GSM11270 2 0.541 0.0865 0.000 0.472 0.472 0.056 0.000
#> GSM11271 2 0.402 0.5716 0.000 0.652 0.000 0.348 0.000
#> GSM11288 5 0.269 -0.1801 0.000 0.000 0.156 0.000 0.844
#> GSM11273 3 0.207 0.2280 0.000 0.076 0.912 0.000 0.012
#> GSM28757 4 0.205 0.6827 0.000 0.072 0.004 0.916 0.008
#> GSM11282 3 0.541 -0.2224 0.000 0.472 0.472 0.056 0.000
#> GSM28756 4 0.349 0.5523 0.000 0.228 0.000 0.768 0.004
#> GSM11276 4 0.440 -0.0144 0.000 0.432 0.000 0.564 0.004
#> GSM28752 2 0.444 0.3057 0.000 0.532 0.000 0.464 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 2 0.3147 0.733 0.000 0.844 0.012 0.100 0.044 0.000
#> GSM28763 2 0.2951 0.737 0.000 0.856 0.008 0.092 0.044 0.000
#> GSM28764 5 0.2946 0.767 0.000 0.176 0.000 0.012 0.812 0.000
#> GSM11274 3 0.3547 0.564 0.000 0.000 0.668 0.000 0.000 0.332
#> GSM28772 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.1970 0.812 0.000 0.000 0.092 0.008 0.900 0.000
#> GSM28766 5 0.2020 0.810 0.000 0.000 0.096 0.008 0.896 0.000
#> GSM11268 6 0.0000 0.950 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM28767 5 0.1950 0.837 0.000 0.064 0.024 0.000 0.912 0.000
#> GSM11286 2 0.3927 0.648 0.000 0.712 0.004 0.024 0.260 0.000
#> GSM28751 4 0.0508 0.974 0.000 0.012 0.000 0.984 0.004 0.000
#> GSM28770 5 0.1982 0.835 0.000 0.068 0.016 0.004 0.912 0.000
#> GSM11283 2 0.4697 0.682 0.000 0.712 0.136 0.012 0.140 0.000
#> GSM11289 5 0.2101 0.820 0.000 0.100 0.004 0.004 0.892 0.000
#> GSM11280 2 0.2394 0.760 0.000 0.900 0.048 0.020 0.032 0.000
#> GSM28749 5 0.5028 0.644 0.000 0.196 0.124 0.012 0.668 0.000
#> GSM28750 6 0.0000 0.950 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM11290 6 0.0000 0.950 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM11294 6 0.0000 0.950 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM28771 2 0.4780 0.375 0.000 0.580 0.372 0.012 0.036 0.000
#> GSM28760 3 0.2395 0.785 0.000 0.012 0.896 0.016 0.072 0.004
#> GSM28774 5 0.3135 0.816 0.000 0.124 0.028 0.012 0.836 0.000
#> GSM11284 5 0.3257 0.816 0.000 0.064 0.084 0.012 0.840 0.000
#> GSM28761 6 0.0000 0.950 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM11278 3 0.1075 0.817 0.000 0.000 0.952 0.000 0.048 0.000
#> GSM11291 6 0.0000 0.950 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM11277 6 0.0000 0.950 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM11272 6 0.0000 0.950 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM11285 5 0.2389 0.798 0.000 0.000 0.128 0.008 0.864 0.000
#> GSM28753 2 0.2407 0.770 0.000 0.892 0.048 0.004 0.056 0.000
#> GSM28773 5 0.4493 0.751 0.000 0.096 0.144 0.020 0.740 0.000
#> GSM28765 2 0.3541 0.712 0.000 0.748 0.000 0.020 0.232 0.000
#> GSM28768 1 0.0146 0.996 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM28754 2 0.2513 0.775 0.000 0.888 0.044 0.008 0.060 0.000
#> GSM28769 4 0.0717 0.974 0.000 0.008 0.000 0.976 0.000 0.016
#> GSM11275 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11270 3 0.1075 0.817 0.000 0.000 0.952 0.000 0.048 0.000
#> GSM11271 5 0.2094 0.838 0.000 0.064 0.024 0.004 0.908 0.000
#> GSM11288 6 0.4426 0.377 0.008 0.004 0.016 0.356 0.000 0.616
#> GSM11273 3 0.3076 0.668 0.000 0.000 0.760 0.000 0.000 0.240
#> GSM28757 2 0.4309 0.740 0.000 0.768 0.044 0.060 0.128 0.000
#> GSM11282 3 0.1204 0.814 0.000 0.000 0.944 0.000 0.056 0.000
#> GSM28756 2 0.3634 0.635 0.000 0.696 0.008 0.000 0.296 0.000
#> GSM11276 5 0.3652 0.638 0.000 0.264 0.000 0.016 0.720 0.000
#> GSM28752 5 0.3232 0.785 0.000 0.160 0.008 0.020 0.812 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 tissue(p) k
#> ATC:skmeans 53 0.397 2
#> ATC:skmeans 54 0.374 3
#> ATC:skmeans 50 0.416 4
#> ATC:skmeans 42 0.399 5
#> ATC:skmeans 52 0.391 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.3312 0.669 0.669
#> 3 3 1.000 0.973 0.991 0.6192 0.786 0.681
#> 4 4 0.711 0.822 0.801 0.1611 1.000 1.000
#> 5 5 0.671 0.752 0.853 0.1351 0.846 0.666
#> 6 6 0.770 0.777 0.895 0.0874 0.954 0.853
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
#> GSM28762 2 0 1 0 1
#> GSM28763 2 0 1 0 1
#> GSM28764 2 0 1 0 1
#> GSM11274 2 0 1 0 1
#> GSM28772 1 0 1 1 0
#> GSM11269 1 0 1 1 0
#> GSM28775 1 0 1 1 0
#> GSM11293 1 0 1 1 0
#> GSM28755 1 0 1 1 0
#> GSM11279 1 0 1 1 0
#> GSM28758 1 0 1 1 0
#> GSM11281 1 0 1 1 0
#> GSM11287 1 0 1 1 0
#> GSM28759 1 0 1 1 0
#> GSM11292 2 0 1 0 1
#> GSM28766 2 0 1 0 1
#> GSM11268 2 0 1 0 1
#> GSM28767 2 0 1 0 1
#> GSM11286 2 0 1 0 1
#> GSM28751 2 0 1 0 1
#> GSM28770 2 0 1 0 1
#> GSM11283 2 0 1 0 1
#> GSM11289 2 0 1 0 1
#> GSM11280 2 0 1 0 1
#> GSM28749 2 0 1 0 1
#> GSM28750 2 0 1 0 1
#> GSM11290 2 0 1 0 1
#> GSM11294 2 0 1 0 1
#> GSM28771 2 0 1 0 1
#> GSM28760 2 0 1 0 1
#> GSM28774 2 0 1 0 1
#> GSM11284 2 0 1 0 1
#> GSM28761 2 0 1 0 1
#> GSM11278 2 0 1 0 1
#> GSM11291 2 0 1 0 1
#> GSM11277 2 0 1 0 1
#> GSM11272 2 0 1 0 1
#> GSM11285 2 0 1 0 1
#> GSM28753 2 0 1 0 1
#> GSM28773 2 0 1 0 1
#> GSM28765 2 0 1 0 1
#> GSM28768 2 0 1 0 1
#> GSM28754 2 0 1 0 1
#> GSM28769 2 0 1 0 1
#> GSM11275 1 0 1 1 0
#> GSM11270 2 0 1 0 1
#> GSM11271 2 0 1 0 1
#> GSM11288 2 0 1 0 1
#> GSM11273 2 0 1 0 1
#> GSM28757 2 0 1 0 1
#> GSM11282 2 0 1 0 1
#> GSM28756 2 0 1 0 1
#> GSM11276 2 0 1 0 1
#> GSM28752 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.000 1.000 0 1.000 0.000
#> GSM28763 2 0.000 1.000 0 1.000 0.000
#> GSM28764 2 0.000 1.000 0 1.000 0.000
#> GSM11274 3 0.621 0.263 0 0.428 0.572
#> GSM28772 1 0.000 1.000 1 0.000 0.000
#> GSM11269 1 0.000 1.000 1 0.000 0.000
#> GSM28775 1 0.000 1.000 1 0.000 0.000
#> GSM11293 1 0.000 1.000 1 0.000 0.000
#> GSM28755 1 0.000 1.000 1 0.000 0.000
#> GSM11279 1 0.000 1.000 1 0.000 0.000
#> GSM28758 1 0.000 1.000 1 0.000 0.000
#> GSM11281 1 0.000 1.000 1 0.000 0.000
#> GSM11287 1 0.000 1.000 1 0.000 0.000
#> GSM28759 1 0.000 1.000 1 0.000 0.000
#> GSM11292 2 0.000 1.000 0 1.000 0.000
#> GSM28766 2 0.000 1.000 0 1.000 0.000
#> GSM11268 3 0.000 0.913 0 0.000 1.000
#> GSM28767 2 0.000 1.000 0 1.000 0.000
#> GSM11286 2 0.000 1.000 0 1.000 0.000
#> GSM28751 2 0.000 1.000 0 1.000 0.000
#> GSM28770 2 0.000 1.000 0 1.000 0.000
#> GSM11283 2 0.000 1.000 0 1.000 0.000
#> GSM11289 2 0.000 1.000 0 1.000 0.000
#> GSM11280 2 0.000 1.000 0 1.000 0.000
#> GSM28749 2 0.000 1.000 0 1.000 0.000
#> GSM28750 3 0.000 0.913 0 0.000 1.000
#> GSM11290 3 0.000 0.913 0 0.000 1.000
#> GSM11294 3 0.000 0.913 0 0.000 1.000
#> GSM28771 2 0.000 1.000 0 1.000 0.000
#> GSM28760 2 0.000 1.000 0 1.000 0.000
#> GSM28774 2 0.000 1.000 0 1.000 0.000
#> GSM11284 2 0.000 1.000 0 1.000 0.000
#> GSM28761 3 0.000 0.913 0 0.000 1.000
#> GSM11278 2 0.000 1.000 0 1.000 0.000
#> GSM11291 3 0.000 0.913 0 0.000 1.000
#> GSM11277 3 0.000 0.913 0 0.000 1.000
#> GSM11272 3 0.153 0.874 0 0.040 0.960
#> GSM11285 2 0.000 1.000 0 1.000 0.000
#> GSM28753 2 0.000 1.000 0 1.000 0.000
#> GSM28773 2 0.000 1.000 0 1.000 0.000
#> GSM28765 2 0.000 1.000 0 1.000 0.000
#> GSM28768 2 0.000 1.000 0 1.000 0.000
#> GSM28754 2 0.000 1.000 0 1.000 0.000
#> GSM28769 2 0.000 1.000 0 1.000 0.000
#> GSM11275 1 0.000 1.000 1 0.000 0.000
#> GSM11270 2 0.000 1.000 0 1.000 0.000
#> GSM11271 2 0.000 1.000 0 1.000 0.000
#> GSM11288 2 0.000 1.000 0 1.000 0.000
#> GSM11273 2 0.000 1.000 0 1.000 0.000
#> GSM28757 2 0.000 1.000 0 1.000 0.000
#> GSM11282 2 0.000 1.000 0 1.000 0.000
#> GSM28756 2 0.000 1.000 0 1.000 0.000
#> GSM11276 2 0.000 1.000 0 1.000 0.000
#> GSM28752 2 0.000 1.000 0 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.0336 0.858 0 0.992 0.000 0.008
#> GSM28763 2 0.0336 0.858 0 0.992 0.000 0.008
#> GSM28764 2 0.0000 0.860 0 1.000 0.000 0.000
#> GSM11274 3 0.7500 0.246 0 0.180 0.416 0.404
#> GSM28772 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11269 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM28775 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11293 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM28755 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11279 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM28758 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11281 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11287 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM28759 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11292 2 0.3486 0.829 0 0.812 0.000 0.188
#> GSM28766 2 0.3837 0.815 0 0.776 0.000 0.224
#> GSM11268 3 0.0000 0.710 0 0.000 1.000 0.000
#> GSM28767 2 0.2408 0.854 0 0.896 0.000 0.104
#> GSM11286 2 0.0000 0.860 0 1.000 0.000 0.000
#> GSM28751 2 0.2345 0.805 0 0.900 0.000 0.100
#> GSM28770 2 0.2868 0.846 0 0.864 0.000 0.136
#> GSM11283 2 0.3400 0.832 0 0.820 0.000 0.180
#> GSM11289 2 0.0707 0.861 0 0.980 0.000 0.020
#> GSM11280 2 0.0336 0.858 0 0.992 0.000 0.008
#> GSM28749 2 0.2149 0.859 0 0.912 0.000 0.088
#> GSM28750 3 0.1637 0.719 0 0.000 0.940 0.060
#> GSM11290 3 0.5000 0.724 0 0.000 0.504 0.496
#> GSM11294 3 0.5000 0.724 0 0.000 0.504 0.496
#> GSM28771 2 0.3837 0.815 0 0.776 0.000 0.224
#> GSM28760 2 0.4866 0.679 0 0.596 0.000 0.404
#> GSM28774 2 0.0188 0.860 0 0.996 0.000 0.004
#> GSM11284 2 0.3400 0.832 0 0.820 0.000 0.180
#> GSM28761 3 0.0000 0.710 0 0.000 1.000 0.000
#> GSM11278 2 0.4866 0.679 0 0.596 0.000 0.404
#> GSM11291 3 0.5000 0.724 0 0.000 0.504 0.496
#> GSM11277 3 0.5000 0.724 0 0.000 0.504 0.496
#> GSM11272 3 0.4158 0.606 0 0.008 0.768 0.224
#> GSM11285 2 0.3801 0.817 0 0.780 0.000 0.220
#> GSM28753 2 0.0000 0.860 0 1.000 0.000 0.000
#> GSM28773 2 0.3400 0.832 0 0.820 0.000 0.180
#> GSM28765 2 0.0000 0.860 0 1.000 0.000 0.000
#> GSM28768 2 0.2345 0.805 0 0.900 0.000 0.100
#> GSM28754 2 0.1118 0.855 0 0.964 0.000 0.036
#> GSM28769 2 0.4522 0.649 0 0.680 0.000 0.320
#> GSM11275 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM11270 2 0.4877 0.677 0 0.592 0.000 0.408
#> GSM11271 2 0.2011 0.858 0 0.920 0.000 0.080
#> GSM11288 2 0.4830 0.637 0 0.608 0.000 0.392
#> GSM11273 2 0.4866 0.679 0 0.596 0.000 0.404
#> GSM28757 2 0.0469 0.858 0 0.988 0.000 0.012
#> GSM11282 2 0.4866 0.679 0 0.596 0.000 0.404
#> GSM28756 2 0.0000 0.860 0 1.000 0.000 0.000
#> GSM11276 2 0.0000 0.860 0 1.000 0.000 0.000
#> GSM28752 2 0.0000 0.860 0 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
#> GSM28762 2 0.3246 0.632 0.000 0.808 0.008 0.000 0.184
#> GSM28763 2 0.3246 0.632 0.000 0.808 0.008 0.000 0.184
#> GSM28764 2 0.0000 0.757 0.000 1.000 0.000 0.000 0.000
#> GSM11274 5 0.7511 0.599 0.000 0.156 0.172 0.144 0.528
#> GSM28772 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0162 0.997 0.996 0.000 0.000 0.004 0.000
#> GSM11281 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM11292 2 0.4636 0.602 0.000 0.744 0.000 0.124 0.132
#> GSM28766 2 0.4833 0.590 0.000 0.736 0.004 0.124 0.136
#> GSM11268 3 0.1121 0.904 0.000 0.000 0.956 0.044 0.000
#> GSM28767 2 0.2915 0.701 0.000 0.860 0.000 0.024 0.116
#> GSM11286 2 0.0703 0.752 0.000 0.976 0.000 0.000 0.024
#> GSM28751 2 0.4826 0.239 0.000 0.508 0.020 0.000 0.472
#> GSM28770 2 0.3780 0.667 0.000 0.812 0.000 0.072 0.116
#> GSM11283 2 0.4593 0.607 0.000 0.748 0.000 0.124 0.128
#> GSM11289 2 0.0880 0.750 0.000 0.968 0.000 0.000 0.032
#> GSM11280 2 0.3246 0.632 0.000 0.808 0.008 0.000 0.184
#> GSM28749 2 0.2773 0.723 0.000 0.836 0.000 0.000 0.164
#> GSM28750 3 0.3210 0.728 0.000 0.000 0.788 0.212 0.000
#> GSM11290 4 0.2424 1.000 0.000 0.000 0.132 0.868 0.000
#> GSM11294 4 0.2424 1.000 0.000 0.000 0.132 0.868 0.000
#> GSM28771 2 0.4833 0.590 0.000 0.736 0.004 0.124 0.136
#> GSM28760 5 0.6485 0.698 0.000 0.324 0.020 0.128 0.528
#> GSM28774 2 0.0955 0.754 0.000 0.968 0.004 0.000 0.028
#> GSM11284 2 0.4593 0.607 0.000 0.748 0.000 0.124 0.128
#> GSM28761 3 0.1121 0.904 0.000 0.000 0.956 0.044 0.000
#> GSM11278 5 0.6552 0.703 0.000 0.320 0.024 0.128 0.528
#> GSM11291 4 0.2424 1.000 0.000 0.000 0.132 0.868 0.000
#> GSM11277 4 0.2424 1.000 0.000 0.000 0.132 0.868 0.000
#> GSM11272 3 0.0609 0.870 0.000 0.000 0.980 0.000 0.020
#> GSM11285 2 0.4679 0.596 0.000 0.740 0.000 0.124 0.136
#> GSM28753 2 0.0000 0.757 0.000 1.000 0.000 0.000 0.000
#> GSM28773 2 0.4593 0.607 0.000 0.748 0.000 0.124 0.128
#> GSM28765 2 0.0703 0.752 0.000 0.976 0.000 0.000 0.024
#> GSM28768 2 0.4971 0.235 0.000 0.504 0.020 0.004 0.472
#> GSM28754 2 0.1671 0.725 0.000 0.924 0.000 0.000 0.076
#> GSM28769 5 0.2969 0.214 0.000 0.128 0.020 0.000 0.852
#> GSM11275 1 0.0162 0.997 0.996 0.000 0.000 0.004 0.000
#> GSM11270 5 0.6102 0.686 0.000 0.224 0.024 0.128 0.624
#> GSM11271 2 0.2127 0.719 0.000 0.892 0.000 0.000 0.108
#> GSM11288 5 0.1908 0.380 0.000 0.092 0.000 0.000 0.908
#> GSM11273 5 0.6552 0.703 0.000 0.320 0.024 0.128 0.528
#> GSM28757 2 0.3282 0.629 0.000 0.804 0.008 0.000 0.188
#> GSM11282 5 0.6552 0.703 0.000 0.320 0.024 0.128 0.528
#> GSM28756 2 0.0000 0.757 0.000 1.000 0.000 0.000 0.000
#> GSM11276 2 0.0000 0.757 0.000 1.000 0.000 0.000 0.000
#> GSM28752 2 0.0703 0.752 0.000 0.976 0.000 0.000 0.024
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 5 0.3864 0.169 0.000 0.480 0.000 0.000 0.520 0.000
#> GSM28763 5 0.3864 0.169 0.000 0.480 0.000 0.000 0.520 0.000
#> GSM28764 5 0.0000 0.773 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11274 4 0.0291 0.918 0.000 0.000 0.004 0.992 0.000 0.004
#> GSM28772 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0146 0.997 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.3023 0.680 0.000 0.000 0.000 0.232 0.768 0.000
#> GSM28766 5 0.3023 0.680 0.000 0.000 0.000 0.232 0.768 0.000
#> GSM11268 6 0.0000 0.890 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM28767 5 0.1501 0.761 0.000 0.000 0.000 0.076 0.924 0.000
#> GSM11286 5 0.1556 0.750 0.000 0.080 0.000 0.000 0.920 0.000
#> GSM28751 2 0.0146 0.813 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM28770 5 0.2491 0.723 0.000 0.000 0.000 0.164 0.836 0.000
#> GSM11283 5 0.3023 0.680 0.000 0.000 0.000 0.232 0.768 0.000
#> GSM11289 5 0.0000 0.773 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11280 5 0.3864 0.169 0.000 0.480 0.000 0.000 0.520 0.000
#> GSM28749 5 0.3588 0.718 0.000 0.152 0.000 0.060 0.788 0.000
#> GSM28750 6 0.3464 0.547 0.000 0.000 0.312 0.000 0.000 0.688
#> GSM11290 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11294 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM28771 5 0.3050 0.676 0.000 0.000 0.000 0.236 0.764 0.000
#> GSM28760 4 0.2793 0.642 0.000 0.000 0.000 0.800 0.200 0.000
#> GSM28774 5 0.4244 0.588 0.000 0.080 0.000 0.200 0.720 0.000
#> GSM11284 5 0.3023 0.680 0.000 0.000 0.000 0.232 0.768 0.000
#> GSM28761 6 0.0000 0.890 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM11278 4 0.0000 0.925 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11291 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11277 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11272 6 0.0000 0.890 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM11285 5 0.3023 0.680 0.000 0.000 0.000 0.232 0.768 0.000
#> GSM28753 5 0.0146 0.772 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM28773 5 0.3023 0.680 0.000 0.000 0.000 0.232 0.768 0.000
#> GSM28765 5 0.1556 0.750 0.000 0.080 0.000 0.000 0.920 0.000
#> GSM28768 2 0.0000 0.811 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28754 5 0.2094 0.744 0.000 0.080 0.000 0.020 0.900 0.000
#> GSM28769 2 0.0146 0.813 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM11275 1 0.0146 0.997 0.996 0.004 0.000 0.000 0.000 0.000
#> GSM11270 4 0.0000 0.925 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11271 5 0.1075 0.769 0.000 0.000 0.000 0.048 0.952 0.000
#> GSM11288 2 0.3986 0.193 0.000 0.532 0.000 0.464 0.004 0.000
#> GSM11273 4 0.0000 0.925 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM28757 5 0.3864 0.169 0.000 0.480 0.000 0.000 0.520 0.000
#> GSM11282 4 0.0000 0.925 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM28756 5 0.0000 0.773 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11276 5 0.0000 0.773 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28752 5 0.1556 0.750 0.000 0.080 0.000 0.000 0.920 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 tissue(p) k
#> ATC:pam 54 0.398 2
#> ATC:pam 53 0.373 3
#> ATC:pam 53 0.373 4
#> ATC:pam 50 0.331 5
#> ATC:pam 49 0.314 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.704 0.887 0.943 0.4214 0.591 0.591
#> 3 3 0.764 0.884 0.942 0.4623 0.797 0.657
#> 4 4 0.687 0.580 0.793 0.1721 0.828 0.591
#> 5 5 0.716 0.738 0.827 0.0279 0.955 0.847
#> 6 6 0.729 0.780 0.822 0.0276 0.878 0.592
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
#> GSM28762 2 0.3879 0.886 0.076 0.924
#> GSM28763 2 0.3879 0.886 0.076 0.924
#> GSM28764 2 0.0000 0.937 0.000 1.000
#> GSM11274 2 0.0000 0.937 0.000 1.000
#> GSM28772 1 0.0000 0.926 1.000 0.000
#> GSM11269 1 0.0000 0.926 1.000 0.000
#> GSM28775 1 0.0000 0.926 1.000 0.000
#> GSM11293 1 0.0000 0.926 1.000 0.000
#> GSM28755 1 0.0000 0.926 1.000 0.000
#> GSM11279 1 0.0000 0.926 1.000 0.000
#> GSM28758 1 0.0000 0.926 1.000 0.000
#> GSM11281 1 0.0000 0.926 1.000 0.000
#> GSM11287 1 0.0000 0.926 1.000 0.000
#> GSM28759 1 0.0000 0.926 1.000 0.000
#> GSM11292 2 0.0672 0.935 0.008 0.992
#> GSM28766 2 0.2236 0.919 0.036 0.964
#> GSM11268 2 0.7674 0.754 0.224 0.776
#> GSM28767 2 0.0672 0.935 0.008 0.992
#> GSM11286 2 0.2043 0.922 0.032 0.968
#> GSM28751 1 0.8207 0.705 0.744 0.256
#> GSM28770 2 0.0000 0.937 0.000 1.000
#> GSM11283 2 0.0000 0.937 0.000 1.000
#> GSM11289 2 0.0000 0.937 0.000 1.000
#> GSM11280 2 0.0672 0.935 0.008 0.992
#> GSM28749 2 0.1843 0.925 0.028 0.972
#> GSM28750 2 0.7674 0.754 0.224 0.776
#> GSM11290 2 0.7674 0.754 0.224 0.776
#> GSM11294 2 0.7674 0.754 0.224 0.776
#> GSM28771 2 0.0000 0.937 0.000 1.000
#> GSM28760 2 0.0000 0.937 0.000 1.000
#> GSM28774 2 0.0000 0.937 0.000 1.000
#> GSM11284 2 0.0672 0.935 0.008 0.992
#> GSM28761 2 0.7674 0.754 0.224 0.776
#> GSM11278 2 0.0000 0.937 0.000 1.000
#> GSM11291 2 0.7674 0.754 0.224 0.776
#> GSM11277 2 0.7674 0.754 0.224 0.776
#> GSM11272 2 0.7674 0.754 0.224 0.776
#> GSM11285 2 0.1414 0.929 0.020 0.980
#> GSM28753 2 0.0000 0.937 0.000 1.000
#> GSM28773 2 0.0000 0.937 0.000 1.000
#> GSM28765 2 0.1843 0.925 0.028 0.972
#> GSM28768 1 0.5946 0.818 0.856 0.144
#> GSM28754 2 0.0000 0.937 0.000 1.000
#> GSM28769 1 0.8861 0.629 0.696 0.304
#> GSM11275 1 0.0000 0.926 1.000 0.000
#> GSM11270 2 0.0000 0.937 0.000 1.000
#> GSM11271 2 0.0000 0.937 0.000 1.000
#> GSM11288 1 0.8386 0.676 0.732 0.268
#> GSM11273 2 0.0000 0.937 0.000 1.000
#> GSM28757 2 0.0672 0.935 0.008 0.992
#> GSM11282 2 0.0000 0.937 0.000 1.000
#> GSM28756 2 0.0000 0.937 0.000 1.000
#> GSM11276 2 0.0000 0.937 0.000 1.000
#> GSM28752 2 0.0000 0.937 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.1529 0.923 0.000 0.960 0.040
#> GSM28763 2 0.1529 0.923 0.000 0.960 0.040
#> GSM28764 2 0.0000 0.931 0.000 1.000 0.000
#> GSM11274 3 0.3879 0.802 0.000 0.152 0.848
#> GSM28772 1 0.0000 0.927 1.000 0.000 0.000
#> GSM11269 1 0.0000 0.927 1.000 0.000 0.000
#> GSM28775 1 0.0000 0.927 1.000 0.000 0.000
#> GSM11293 1 0.0000 0.927 1.000 0.000 0.000
#> GSM28755 1 0.0000 0.927 1.000 0.000 0.000
#> GSM11279 1 0.0000 0.927 1.000 0.000 0.000
#> GSM28758 1 0.0000 0.927 1.000 0.000 0.000
#> GSM11281 1 0.0000 0.927 1.000 0.000 0.000
#> GSM11287 1 0.0000 0.927 1.000 0.000 0.000
#> GSM28759 1 0.0000 0.927 1.000 0.000 0.000
#> GSM11292 2 0.1529 0.913 0.040 0.960 0.000
#> GSM28766 2 0.1289 0.918 0.032 0.968 0.000
#> GSM11268 3 0.0000 0.946 0.000 0.000 1.000
#> GSM28767 2 0.0000 0.931 0.000 1.000 0.000
#> GSM11286 2 0.0747 0.931 0.000 0.984 0.016
#> GSM28751 1 0.6722 0.640 0.720 0.220 0.060
#> GSM28770 2 0.0000 0.931 0.000 1.000 0.000
#> GSM11283 2 0.5431 0.678 0.000 0.716 0.284
#> GSM11289 2 0.0000 0.931 0.000 1.000 0.000
#> GSM11280 2 0.1031 0.929 0.000 0.976 0.024
#> GSM28749 2 0.4799 0.824 0.132 0.836 0.032
#> GSM28750 3 0.0000 0.946 0.000 0.000 1.000
#> GSM11290 3 0.0000 0.946 0.000 0.000 1.000
#> GSM11294 3 0.0000 0.946 0.000 0.000 1.000
#> GSM28771 2 0.5431 0.678 0.000 0.716 0.284
#> GSM28760 2 0.5529 0.657 0.000 0.704 0.296
#> GSM28774 2 0.0000 0.931 0.000 1.000 0.000
#> GSM11284 2 0.0000 0.931 0.000 1.000 0.000
#> GSM28761 3 0.0000 0.946 0.000 0.000 1.000
#> GSM11278 2 0.4002 0.833 0.000 0.840 0.160
#> GSM11291 3 0.0000 0.946 0.000 0.000 1.000
#> GSM11277 3 0.0000 0.946 0.000 0.000 1.000
#> GSM11272 3 0.0000 0.946 0.000 0.000 1.000
#> GSM11285 2 0.0000 0.931 0.000 1.000 0.000
#> GSM28753 2 0.1289 0.927 0.000 0.968 0.032
#> GSM28773 2 0.0237 0.931 0.000 0.996 0.004
#> GSM28765 2 0.1031 0.929 0.000 0.976 0.024
#> GSM28768 1 0.0747 0.915 0.984 0.016 0.000
#> GSM28754 2 0.1163 0.928 0.000 0.972 0.028
#> GSM28769 1 0.7739 0.605 0.672 0.204 0.124
#> GSM11275 1 0.0000 0.927 1.000 0.000 0.000
#> GSM11270 2 0.4178 0.821 0.000 0.828 0.172
#> GSM11271 2 0.0000 0.931 0.000 1.000 0.000
#> GSM11288 1 0.6684 0.584 0.676 0.032 0.292
#> GSM11273 3 0.4605 0.728 0.000 0.204 0.796
#> GSM28757 2 0.0892 0.930 0.000 0.980 0.020
#> GSM11282 2 0.4399 0.803 0.000 0.812 0.188
#> GSM28756 2 0.0000 0.931 0.000 1.000 0.000
#> GSM11276 2 0.0000 0.931 0.000 1.000 0.000
#> GSM28752 2 0.0000 0.931 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 2 0.1398 0.832463 0.000 0.956 0.004 0.040
#> GSM28763 2 0.1716 0.826046 0.000 0.936 0.000 0.064
#> GSM28764 2 0.1940 0.815352 0.000 0.924 0.000 0.076
#> GSM11274 4 0.5862 -0.222011 0.000 0.032 0.484 0.484
#> GSM28772 1 0.0000 0.997530 1.000 0.000 0.000 0.000
#> GSM11269 1 0.0188 0.996237 0.996 0.000 0.000 0.004
#> GSM28775 1 0.0000 0.997530 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.997530 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0000 0.997530 1.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.997530 1.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.997530 1.000 0.000 0.000 0.000
#> GSM11281 1 0.0336 0.993874 0.992 0.000 0.000 0.008
#> GSM11287 1 0.0188 0.996237 0.996 0.000 0.000 0.004
#> GSM28759 1 0.0000 0.997530 1.000 0.000 0.000 0.000
#> GSM11292 2 0.4907 0.383787 0.000 0.580 0.000 0.420
#> GSM28766 2 0.4916 0.380179 0.000 0.576 0.000 0.424
#> GSM11268 3 0.1557 0.555601 0.000 0.000 0.944 0.056
#> GSM28767 2 0.0188 0.840163 0.000 0.996 0.000 0.004
#> GSM11286 2 0.1389 0.828733 0.000 0.952 0.000 0.048
#> GSM28751 4 0.6343 0.106161 0.068 0.332 0.004 0.596
#> GSM28770 2 0.0592 0.839680 0.000 0.984 0.000 0.016
#> GSM11283 3 0.6506 -0.000593 0.000 0.072 0.468 0.460
#> GSM11289 2 0.1867 0.818503 0.000 0.928 0.000 0.072
#> GSM11280 2 0.1867 0.821052 0.000 0.928 0.000 0.072
#> GSM28749 2 0.5155 0.280574 0.000 0.528 0.004 0.468
#> GSM28750 3 0.0707 0.579434 0.000 0.000 0.980 0.020
#> GSM11290 3 0.0000 0.584828 0.000 0.000 1.000 0.000
#> GSM11294 3 0.0000 0.584828 0.000 0.000 1.000 0.000
#> GSM28771 4 0.6396 -0.194619 0.000 0.064 0.468 0.468
#> GSM28760 4 0.6826 -0.140021 0.000 0.100 0.416 0.484
#> GSM28774 2 0.0188 0.840163 0.000 0.996 0.000 0.004
#> GSM11284 2 0.0592 0.839115 0.000 0.984 0.000 0.016
#> GSM28761 3 0.4907 0.211987 0.000 0.000 0.580 0.420
#> GSM11278 3 0.7779 0.004912 0.000 0.244 0.400 0.356
#> GSM11291 3 0.0000 0.584828 0.000 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.584828 0.000 0.000 1.000 0.000
#> GSM11272 3 0.4907 0.211987 0.000 0.000 0.580 0.420
#> GSM11285 2 0.0817 0.839648 0.000 0.976 0.000 0.024
#> GSM28753 2 0.3024 0.743140 0.000 0.852 0.000 0.148
#> GSM28773 2 0.1302 0.832453 0.000 0.956 0.000 0.044
#> GSM28765 2 0.0188 0.840697 0.000 0.996 0.000 0.004
#> GSM28768 4 0.6055 0.035554 0.372 0.052 0.000 0.576
#> GSM28754 2 0.4158 0.639519 0.000 0.768 0.008 0.224
#> GSM28769 4 0.6605 0.151448 0.020 0.316 0.060 0.604
#> GSM11275 1 0.0469 0.991252 0.988 0.000 0.000 0.012
#> GSM11270 3 0.7629 -0.000801 0.000 0.204 0.400 0.396
#> GSM11271 2 0.0000 0.840312 0.000 1.000 0.000 0.000
#> GSM11288 4 0.7160 0.071964 0.020 0.104 0.300 0.576
#> GSM11273 3 0.5862 0.030039 0.000 0.032 0.484 0.484
#> GSM28757 2 0.3837 0.670370 0.000 0.776 0.000 0.224
#> GSM11282 4 0.7030 -0.131900 0.000 0.120 0.408 0.472
#> GSM28756 2 0.1118 0.837004 0.000 0.964 0.000 0.036
#> GSM11276 2 0.1118 0.835951 0.000 0.964 0.000 0.036
#> GSM28752 2 0.4999 0.320866 0.000 0.508 0.000 0.492
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28762 2 0.2358 0.811 0.000 0.888 0.000 0.008 0.104
#> GSM28763 2 0.1697 0.813 0.000 0.932 0.000 0.008 0.060
#> GSM28764 2 0.1205 0.807 0.000 0.956 0.000 0.040 0.004
#> GSM11274 4 0.2690 0.623 0.000 0.156 0.000 0.844 0.000
#> GSM28772 1 0.0162 0.980 0.996 0.000 0.000 0.000 0.004
#> GSM11269 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0510 0.970 0.984 0.000 0.000 0.000 0.016
#> GSM11293 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0162 0.980 0.996 0.000 0.000 0.000 0.004
#> GSM11279 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.982 1.000 0.000 0.000 0.000 0.000
#> GSM11292 2 0.5228 0.507 0.000 0.588 0.000 0.056 0.356
#> GSM28766 2 0.5228 0.499 0.000 0.588 0.000 0.056 0.356
#> GSM11268 3 0.3728 0.700 0.000 0.000 0.748 0.008 0.244
#> GSM28767 2 0.1041 0.820 0.000 0.964 0.000 0.004 0.032
#> GSM11286 2 0.3728 0.699 0.000 0.748 0.000 0.008 0.244
#> GSM28751 5 0.4452 0.639 0.040 0.100 0.000 0.064 0.796
#> GSM28770 2 0.1851 0.803 0.000 0.912 0.000 0.000 0.088
#> GSM11283 4 0.1725 0.452 0.000 0.044 0.000 0.936 0.020
#> GSM11289 2 0.1211 0.814 0.000 0.960 0.000 0.024 0.016
#> GSM11280 2 0.1701 0.810 0.000 0.936 0.000 0.016 0.048
#> GSM28749 2 0.5456 0.255 0.000 0.484 0.000 0.060 0.456
#> GSM28750 3 0.2612 0.751 0.000 0.000 0.868 0.008 0.124
#> GSM11290 3 0.1908 0.783 0.000 0.000 0.908 0.092 0.000
#> GSM11294 3 0.1965 0.783 0.000 0.000 0.904 0.096 0.000
#> GSM28771 4 0.0771 0.444 0.000 0.004 0.000 0.976 0.020
#> GSM28760 4 0.4015 0.677 0.000 0.348 0.000 0.652 0.000
#> GSM28774 2 0.1251 0.821 0.000 0.956 0.000 0.008 0.036
#> GSM11284 2 0.2605 0.768 0.000 0.852 0.000 0.000 0.148
#> GSM28761 3 0.4238 0.576 0.000 0.000 0.628 0.004 0.368
#> GSM11278 4 0.5088 0.596 0.000 0.436 0.000 0.528 0.036
#> GSM11291 3 0.1965 0.783 0.000 0.000 0.904 0.096 0.000
#> GSM11277 3 0.1965 0.783 0.000 0.000 0.904 0.096 0.000
#> GSM11272 3 0.4238 0.576 0.000 0.000 0.628 0.004 0.368
#> GSM11285 2 0.1493 0.806 0.000 0.948 0.000 0.028 0.024
#> GSM28753 2 0.2446 0.786 0.000 0.900 0.000 0.056 0.044
#> GSM28773 2 0.1750 0.801 0.000 0.936 0.000 0.028 0.036
#> GSM28765 2 0.1597 0.816 0.000 0.940 0.000 0.012 0.048
#> GSM28768 5 0.6128 0.293 0.388 0.032 0.000 0.060 0.520
#> GSM28754 2 0.2520 0.789 0.000 0.896 0.000 0.048 0.056
#> GSM28769 5 0.3223 0.634 0.000 0.052 0.016 0.064 0.868
#> GSM11275 1 0.2424 0.822 0.868 0.000 0.000 0.000 0.132
#> GSM11270 4 0.5077 0.609 0.000 0.428 0.000 0.536 0.036
#> GSM11271 2 0.1124 0.820 0.000 0.960 0.000 0.004 0.036
#> GSM11288 5 0.5428 0.268 0.000 0.024 0.248 0.060 0.668
#> GSM11273 4 0.3242 0.656 0.000 0.216 0.000 0.784 0.000
#> GSM28757 2 0.3910 0.684 0.000 0.720 0.000 0.008 0.272
#> GSM11282 4 0.5153 0.585 0.000 0.436 0.000 0.524 0.040
#> GSM28756 2 0.0693 0.816 0.000 0.980 0.000 0.012 0.008
#> GSM11276 2 0.1211 0.814 0.000 0.960 0.000 0.024 0.016
#> GSM28752 2 0.4109 0.662 0.000 0.700 0.000 0.012 0.288
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 5 0.3535 0.8178 0.000 0.040 0.000 0.060 0.832 0.068
#> GSM28763 5 0.3063 0.8381 0.000 0.024 0.000 0.064 0.860 0.052
#> GSM28764 5 0.0458 0.8658 0.000 0.000 0.000 0.016 0.984 0.000
#> GSM11274 4 0.1738 0.6446 0.000 0.000 0.004 0.928 0.052 0.016
#> GSM28772 1 0.0000 0.9789 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0000 0.9789 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0858 0.9574 0.968 0.028 0.000 0.000 0.000 0.004
#> GSM11293 1 0.0000 0.9789 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0260 0.9742 0.992 0.008 0.000 0.000 0.000 0.000
#> GSM11279 1 0.0000 0.9789 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28758 1 0.0000 0.9789 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.9789 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0000 0.9789 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM28759 1 0.0000 0.9789 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11292 2 0.4534 0.6750 0.000 0.612 0.000 0.020 0.352 0.016
#> GSM28766 2 0.4468 0.6728 0.000 0.612 0.000 0.016 0.356 0.016
#> GSM11268 6 0.3482 0.9403 0.000 0.000 0.316 0.000 0.000 0.684
#> GSM28767 5 0.0291 0.8637 0.000 0.004 0.000 0.004 0.992 0.000
#> GSM11286 5 0.4546 0.4176 0.000 0.240 0.000 0.028 0.696 0.036
#> GSM28751 2 0.3594 0.6334 0.000 0.796 0.000 0.008 0.152 0.044
#> GSM28770 5 0.0713 0.8538 0.000 0.028 0.000 0.000 0.972 0.000
#> GSM11283 4 0.4771 0.6223 0.000 0.044 0.000 0.712 0.056 0.188
#> GSM11289 5 0.0260 0.8648 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM11280 5 0.2602 0.8458 0.000 0.024 0.000 0.072 0.884 0.020
#> GSM28749 2 0.4042 0.6956 0.000 0.664 0.000 0.004 0.316 0.016
#> GSM28750 6 0.3531 0.9292 0.000 0.000 0.328 0.000 0.000 0.672
#> GSM11290 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11294 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM28771 4 0.4654 0.6201 0.000 0.044 0.000 0.720 0.048 0.188
#> GSM28760 5 0.4238 0.1135 0.000 0.000 0.000 0.444 0.540 0.016
#> GSM28774 5 0.0665 0.8628 0.000 0.004 0.000 0.008 0.980 0.008
#> GSM11284 5 0.2070 0.7689 0.000 0.092 0.000 0.000 0.896 0.012
#> GSM28761 6 0.3221 0.9438 0.000 0.000 0.264 0.000 0.000 0.736
#> GSM11278 4 0.4601 0.4294 0.000 0.020 0.000 0.588 0.376 0.016
#> GSM11291 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11277 3 0.0000 1.0000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11272 6 0.3221 0.9438 0.000 0.000 0.264 0.000 0.000 0.736
#> GSM11285 5 0.0748 0.8655 0.000 0.004 0.000 0.016 0.976 0.004
#> GSM28753 5 0.2575 0.8451 0.000 0.020 0.000 0.076 0.884 0.020
#> GSM28773 5 0.1882 0.8572 0.000 0.024 0.000 0.020 0.928 0.028
#> GSM28765 5 0.2684 0.8475 0.000 0.024 0.000 0.072 0.880 0.024
#> GSM28768 2 0.2726 0.5289 0.016 0.884 0.000 0.004 0.044 0.052
#> GSM28754 5 0.2784 0.8433 0.000 0.020 0.000 0.064 0.876 0.040
#> GSM28769 2 0.3646 0.6089 0.000 0.804 0.000 0.008 0.116 0.072
#> GSM11275 1 0.3065 0.8122 0.820 0.152 0.000 0.000 0.000 0.028
#> GSM11270 4 0.4601 0.4291 0.000 0.020 0.000 0.588 0.376 0.016
#> GSM11271 5 0.0000 0.8637 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM11288 2 0.5239 -0.0822 0.000 0.596 0.096 0.004 0.004 0.300
#> GSM11273 4 0.1866 0.6551 0.000 0.000 0.000 0.908 0.084 0.008
#> GSM28757 2 0.5003 0.4611 0.000 0.496 0.000 0.028 0.452 0.024
#> GSM11282 5 0.4194 0.5462 0.000 0.024 0.000 0.272 0.692 0.012
#> GSM28756 5 0.0508 0.8673 0.000 0.000 0.000 0.012 0.984 0.004
#> GSM11276 5 0.0260 0.8648 0.000 0.000 0.000 0.008 0.992 0.000
#> GSM28752 2 0.4710 0.6665 0.000 0.596 0.000 0.024 0.360 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 tissue(p) k
#> ATC:mclust 54 0.398 2
#> ATC:mclust 54 0.374 3
#> ATC:mclust 36 0.411 4
#> ATC:mclust 48 0.405 5
#> ATC:mclust 48 0.438 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 21586 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.851 0.900 0.956 0.4113 0.609 0.609
#> 3 3 0.970 0.935 0.975 0.4685 0.720 0.568
#> 4 4 0.737 0.773 0.884 0.1750 0.848 0.638
#> 5 5 0.700 0.723 0.839 0.0851 0.874 0.604
#> 6 6 0.714 0.670 0.812 0.0452 0.958 0.823
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM28762 2 0.8327 0.676 0.264 0.736
#> GSM28763 1 0.9686 0.242 0.604 0.396
#> GSM28764 2 0.9129 0.562 0.328 0.672
#> GSM11274 2 0.0000 0.948 0.000 1.000
#> GSM28772 1 0.0000 0.966 1.000 0.000
#> GSM11269 1 0.0000 0.966 1.000 0.000
#> GSM28775 1 0.0000 0.966 1.000 0.000
#> GSM11293 1 0.0000 0.966 1.000 0.000
#> GSM28755 1 0.0000 0.966 1.000 0.000
#> GSM11279 1 0.0000 0.966 1.000 0.000
#> GSM28758 1 0.0000 0.966 1.000 0.000
#> GSM11281 1 0.0000 0.966 1.000 0.000
#> GSM11287 1 0.0000 0.966 1.000 0.000
#> GSM28759 1 0.0000 0.966 1.000 0.000
#> GSM11292 2 0.0000 0.948 0.000 1.000
#> GSM28766 2 0.0000 0.948 0.000 1.000
#> GSM11268 2 0.0000 0.948 0.000 1.000
#> GSM28767 2 0.0000 0.948 0.000 1.000
#> GSM11286 2 0.4298 0.887 0.088 0.912
#> GSM28751 1 0.0376 0.962 0.996 0.004
#> GSM28770 2 0.0000 0.948 0.000 1.000
#> GSM11283 2 0.0376 0.946 0.004 0.996
#> GSM11289 2 0.8661 0.636 0.288 0.712
#> GSM11280 2 0.1633 0.934 0.024 0.976
#> GSM28749 2 0.0000 0.948 0.000 1.000
#> GSM28750 2 0.0000 0.948 0.000 1.000
#> GSM11290 2 0.0000 0.948 0.000 1.000
#> GSM11294 2 0.0000 0.948 0.000 1.000
#> GSM28771 2 0.0000 0.948 0.000 1.000
#> GSM28760 2 0.0000 0.948 0.000 1.000
#> GSM28774 2 0.0376 0.946 0.004 0.996
#> GSM11284 2 0.0000 0.948 0.000 1.000
#> GSM28761 2 0.0000 0.948 0.000 1.000
#> GSM11278 2 0.0000 0.948 0.000 1.000
#> GSM11291 2 0.0000 0.948 0.000 1.000
#> GSM11277 2 0.0000 0.948 0.000 1.000
#> GSM11272 2 0.0000 0.948 0.000 1.000
#> GSM11285 2 0.0000 0.948 0.000 1.000
#> GSM28753 2 0.0000 0.948 0.000 1.000
#> GSM28773 2 0.0000 0.948 0.000 1.000
#> GSM28765 2 0.6712 0.798 0.176 0.824
#> GSM28768 1 0.0000 0.966 1.000 0.000
#> GSM28754 2 0.2603 0.921 0.044 0.956
#> GSM28769 2 0.9881 0.296 0.436 0.564
#> GSM11275 1 0.0000 0.966 1.000 0.000
#> GSM11270 2 0.0000 0.948 0.000 1.000
#> GSM11271 2 0.0000 0.948 0.000 1.000
#> GSM11288 2 0.6531 0.811 0.168 0.832
#> GSM11273 2 0.0000 0.948 0.000 1.000
#> GSM28757 2 0.0000 0.948 0.000 1.000
#> GSM11282 2 0.0000 0.948 0.000 1.000
#> GSM28756 2 0.0000 0.948 0.000 1.000
#> GSM11276 2 0.3114 0.913 0.056 0.944
#> GSM28752 2 0.3879 0.897 0.076 0.924
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28762 2 0.000 0.962 0.000 1.000 0.00
#> GSM28763 2 0.000 0.962 0.000 1.000 0.00
#> GSM28764 2 0.000 0.962 0.000 1.000 0.00
#> GSM11274 3 0.000 0.973 0.000 0.000 1.00
#> GSM28772 1 0.000 1.000 1.000 0.000 0.00
#> GSM11269 1 0.000 1.000 1.000 0.000 0.00
#> GSM28775 1 0.000 1.000 1.000 0.000 0.00
#> GSM11293 1 0.000 1.000 1.000 0.000 0.00
#> GSM28755 1 0.000 1.000 1.000 0.000 0.00
#> GSM11279 1 0.000 1.000 1.000 0.000 0.00
#> GSM28758 1 0.000 1.000 1.000 0.000 0.00
#> GSM11281 1 0.000 1.000 1.000 0.000 0.00
#> GSM11287 1 0.000 1.000 1.000 0.000 0.00
#> GSM28759 1 0.000 1.000 1.000 0.000 0.00
#> GSM11292 2 0.000 0.962 0.000 1.000 0.00
#> GSM28766 2 0.000 0.962 0.000 1.000 0.00
#> GSM11268 3 0.000 0.973 0.000 0.000 1.00
#> GSM28767 2 0.000 0.962 0.000 1.000 0.00
#> GSM11286 2 0.000 0.962 0.000 1.000 0.00
#> GSM28751 2 0.608 0.386 0.388 0.612 0.00
#> GSM28770 2 0.000 0.962 0.000 1.000 0.00
#> GSM11283 2 0.000 0.962 0.000 1.000 0.00
#> GSM11289 2 0.000 0.962 0.000 1.000 0.00
#> GSM11280 2 0.000 0.962 0.000 1.000 0.00
#> GSM28749 2 0.000 0.962 0.000 1.000 0.00
#> GSM28750 3 0.000 0.973 0.000 0.000 1.00
#> GSM11290 3 0.000 0.973 0.000 0.000 1.00
#> GSM11294 3 0.000 0.973 0.000 0.000 1.00
#> GSM28771 2 0.000 0.962 0.000 1.000 0.00
#> GSM28760 2 0.502 0.676 0.000 0.760 0.24
#> GSM28774 2 0.000 0.962 0.000 1.000 0.00
#> GSM11284 2 0.000 0.962 0.000 1.000 0.00
#> GSM28761 3 0.000 0.973 0.000 0.000 1.00
#> GSM11278 2 0.000 0.962 0.000 1.000 0.00
#> GSM11291 3 0.000 0.973 0.000 0.000 1.00
#> GSM11277 3 0.000 0.973 0.000 0.000 1.00
#> GSM11272 3 0.000 0.973 0.000 0.000 1.00
#> GSM11285 2 0.000 0.962 0.000 1.000 0.00
#> GSM28753 2 0.000 0.962 0.000 1.000 0.00
#> GSM28773 2 0.000 0.962 0.000 1.000 0.00
#> GSM28765 2 0.000 0.962 0.000 1.000 0.00
#> GSM28768 1 0.000 1.000 1.000 0.000 0.00
#> GSM28754 2 0.000 0.962 0.000 1.000 0.00
#> GSM28769 2 0.706 0.122 0.464 0.516 0.02
#> GSM11275 1 0.000 1.000 1.000 0.000 0.00
#> GSM11270 2 0.000 0.962 0.000 1.000 0.00
#> GSM11271 2 0.000 0.962 0.000 1.000 0.00
#> GSM11288 3 0.522 0.647 0.260 0.000 0.74
#> GSM11273 3 0.000 0.973 0.000 0.000 1.00
#> GSM28757 2 0.000 0.962 0.000 1.000 0.00
#> GSM11282 2 0.000 0.962 0.000 1.000 0.00
#> GSM28756 2 0.000 0.962 0.000 1.000 0.00
#> GSM11276 2 0.000 0.962 0.000 1.000 0.00
#> GSM28752 2 0.000 0.962 0.000 1.000 0.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28762 4 0.4992 0.245 0.000 0.476 0.000 0.524
#> GSM28763 2 0.1557 0.867 0.000 0.944 0.000 0.056
#> GSM28764 2 0.0469 0.875 0.000 0.988 0.000 0.012
#> GSM11274 3 0.0336 0.920 0.000 0.000 0.992 0.008
#> GSM28772 1 0.0188 0.993 0.996 0.000 0.000 0.004
#> GSM11269 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM28755 1 0.0188 0.993 0.996 0.000 0.000 0.004
#> GSM11279 1 0.0336 0.991 0.992 0.000 0.000 0.008
#> GSM28758 1 0.0336 0.992 0.992 0.000 0.000 0.008
#> GSM11281 1 0.0000 0.993 1.000 0.000 0.000 0.000
#> GSM11287 1 0.0188 0.993 0.996 0.000 0.000 0.004
#> GSM28759 1 0.0188 0.992 0.996 0.000 0.000 0.004
#> GSM11292 2 0.3311 0.799 0.000 0.828 0.000 0.172
#> GSM28766 2 0.3123 0.810 0.000 0.844 0.000 0.156
#> GSM11268 3 0.2011 0.873 0.000 0.000 0.920 0.080
#> GSM28767 2 0.1557 0.873 0.000 0.944 0.000 0.056
#> GSM11286 4 0.4985 0.255 0.000 0.468 0.000 0.532
#> GSM28751 4 0.4036 0.598 0.076 0.088 0.000 0.836
#> GSM28770 2 0.1557 0.871 0.000 0.944 0.000 0.056
#> GSM11283 2 0.1867 0.838 0.000 0.928 0.000 0.072
#> GSM11289 2 0.1389 0.872 0.000 0.952 0.000 0.048
#> GSM11280 4 0.3837 0.647 0.000 0.224 0.000 0.776
#> GSM28749 4 0.4382 0.581 0.000 0.296 0.000 0.704
#> GSM28750 3 0.1118 0.906 0.000 0.000 0.964 0.036
#> GSM11290 3 0.0188 0.920 0.000 0.000 0.996 0.004
#> GSM11294 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM28771 2 0.1940 0.836 0.000 0.924 0.000 0.076
#> GSM28760 2 0.5927 0.405 0.000 0.660 0.264 0.076
#> GSM28774 2 0.1792 0.870 0.000 0.932 0.000 0.068
#> GSM11284 2 0.1302 0.875 0.000 0.956 0.000 0.044
#> GSM28761 4 0.4985 -0.257 0.000 0.000 0.468 0.532
#> GSM11278 2 0.1284 0.866 0.000 0.964 0.012 0.024
#> GSM11291 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM11277 3 0.0000 0.921 0.000 0.000 1.000 0.000
#> GSM11272 3 0.4994 0.226 0.000 0.000 0.520 0.480
#> GSM11285 2 0.0592 0.868 0.000 0.984 0.000 0.016
#> GSM28753 4 0.4998 0.189 0.000 0.488 0.000 0.512
#> GSM28773 2 0.0921 0.864 0.000 0.972 0.000 0.028
#> GSM28765 2 0.3907 0.700 0.000 0.768 0.000 0.232
#> GSM28768 1 0.1474 0.957 0.948 0.000 0.000 0.052
#> GSM28754 2 0.4250 0.568 0.000 0.724 0.000 0.276
#> GSM28769 4 0.3272 0.580 0.036 0.052 0.020 0.892
#> GSM11275 1 0.0469 0.988 0.988 0.000 0.000 0.012
#> GSM11270 2 0.1929 0.868 0.000 0.940 0.024 0.036
#> GSM11271 2 0.2408 0.849 0.000 0.896 0.000 0.104
#> GSM11288 4 0.5464 0.194 0.020 0.008 0.316 0.656
#> GSM11273 3 0.0188 0.919 0.000 0.000 0.996 0.004
#> GSM28757 4 0.3610 0.658 0.000 0.200 0.000 0.800
#> GSM11282 2 0.1297 0.872 0.000 0.964 0.016 0.020
#> GSM28756 2 0.2281 0.854 0.000 0.904 0.000 0.096
#> GSM11276 2 0.1792 0.868 0.000 0.932 0.000 0.068
#> GSM28752 2 0.3837 0.711 0.000 0.776 0.000 0.224
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28762 5 0.5136 0.5040 0.000 0.180 0.000 0.128 0.692
#> GSM28763 4 0.4760 0.6342 0.000 0.416 0.000 0.564 0.020
#> GSM28764 2 0.0703 0.7597 0.000 0.976 0.000 0.024 0.000
#> GSM11274 3 0.0290 0.9327 0.000 0.000 0.992 0.008 0.000
#> GSM28772 1 0.0162 0.9914 0.996 0.000 0.000 0.004 0.000
#> GSM11269 1 0.0000 0.9921 1.000 0.000 0.000 0.000 0.000
#> GSM28775 1 0.0000 0.9921 1.000 0.000 0.000 0.000 0.000
#> GSM11293 1 0.0000 0.9921 1.000 0.000 0.000 0.000 0.000
#> GSM28755 1 0.0162 0.9914 0.996 0.000 0.000 0.004 0.000
#> GSM11279 1 0.0290 0.9897 0.992 0.000 0.000 0.008 0.000
#> GSM28758 1 0.0000 0.9921 1.000 0.000 0.000 0.000 0.000
#> GSM11281 1 0.0000 0.9921 1.000 0.000 0.000 0.000 0.000
#> GSM11287 1 0.0162 0.9914 0.996 0.000 0.000 0.004 0.000
#> GSM28759 1 0.0000 0.9921 1.000 0.000 0.000 0.000 0.000
#> GSM11292 2 0.3165 0.7163 0.000 0.848 0.000 0.116 0.036
#> GSM28766 2 0.3930 0.6582 0.000 0.792 0.000 0.152 0.056
#> GSM11268 3 0.4469 0.7296 0.000 0.000 0.756 0.096 0.148
#> GSM28767 2 0.1670 0.7527 0.000 0.936 0.000 0.052 0.012
#> GSM11286 2 0.4590 0.3125 0.000 0.568 0.000 0.012 0.420
#> GSM28751 5 0.3454 0.6352 0.024 0.076 0.000 0.044 0.856
#> GSM28770 2 0.2351 0.7389 0.000 0.896 0.000 0.088 0.016
#> GSM11283 4 0.4270 0.7598 0.000 0.320 0.000 0.668 0.012
#> GSM11289 2 0.2561 0.7346 0.000 0.884 0.000 0.096 0.020
#> GSM11280 5 0.3307 0.6355 0.000 0.104 0.000 0.052 0.844
#> GSM28749 2 0.6100 0.1944 0.000 0.484 0.000 0.128 0.388
#> GSM28750 3 0.3043 0.8520 0.000 0.000 0.864 0.080 0.056
#> GSM11290 3 0.0290 0.9354 0.000 0.000 0.992 0.008 0.000
#> GSM11294 3 0.0290 0.9359 0.000 0.000 0.992 0.000 0.008
#> GSM28771 4 0.4329 0.7633 0.000 0.312 0.000 0.672 0.016
#> GSM28760 4 0.5788 0.6693 0.000 0.236 0.116 0.636 0.012
#> GSM28774 2 0.3239 0.7332 0.000 0.852 0.000 0.068 0.080
#> GSM11284 2 0.2519 0.7297 0.000 0.884 0.000 0.100 0.016
#> GSM28761 5 0.5739 0.3688 0.000 0.000 0.280 0.124 0.596
#> GSM11278 2 0.3267 0.7021 0.000 0.844 0.044 0.112 0.000
#> GSM11291 3 0.0162 0.9365 0.000 0.000 0.996 0.000 0.004
#> GSM11277 3 0.0162 0.9365 0.000 0.000 0.996 0.000 0.004
#> GSM11272 5 0.6347 -0.0115 0.000 0.000 0.408 0.160 0.432
#> GSM11285 2 0.1965 0.7285 0.000 0.904 0.000 0.096 0.000
#> GSM28753 4 0.6536 0.2754 0.000 0.216 0.000 0.464 0.320
#> GSM28773 2 0.3928 0.3935 0.000 0.700 0.000 0.296 0.004
#> GSM28765 2 0.4384 0.5850 0.000 0.728 0.000 0.044 0.228
#> GSM28768 1 0.1774 0.9422 0.932 0.000 0.000 0.052 0.016
#> GSM28754 5 0.6529 0.0858 0.000 0.228 0.000 0.296 0.476
#> GSM28769 5 0.2313 0.6393 0.008 0.040 0.008 0.024 0.920
#> GSM11275 1 0.0510 0.9833 0.984 0.000 0.000 0.016 0.000
#> GSM11270 2 0.4801 0.6579 0.000 0.768 0.076 0.120 0.036
#> GSM11271 2 0.1117 0.7617 0.000 0.964 0.000 0.016 0.020
#> GSM11288 5 0.6469 0.3615 0.016 0.016 0.284 0.104 0.580
#> GSM11273 3 0.0807 0.9222 0.000 0.012 0.976 0.012 0.000
#> GSM28757 5 0.2727 0.6323 0.000 0.116 0.000 0.016 0.868
#> GSM11282 2 0.3717 0.7122 0.000 0.836 0.040 0.100 0.024
#> GSM28756 2 0.2300 0.7420 0.000 0.904 0.000 0.072 0.024
#> GSM11276 2 0.1403 0.7611 0.000 0.952 0.000 0.024 0.024
#> GSM28752 2 0.2971 0.6928 0.000 0.836 0.000 0.008 0.156
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28762 2 0.5000 0.5687 0.000 0.704 0.000 0.156 0.100 0.040
#> GSM28763 4 0.4686 0.6364 0.000 0.088 0.000 0.676 0.232 0.004
#> GSM28764 5 0.0767 0.7388 0.000 0.012 0.000 0.008 0.976 0.004
#> GSM11274 3 0.1176 0.8318 0.000 0.000 0.956 0.020 0.000 0.024
#> GSM28772 1 0.0000 0.9881 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11269 1 0.0146 0.9882 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM28775 1 0.0260 0.9875 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM11293 1 0.0260 0.9875 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM28755 1 0.0260 0.9858 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM11279 1 0.0405 0.9839 0.988 0.000 0.000 0.008 0.000 0.004
#> GSM28758 1 0.0146 0.9881 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM11281 1 0.0146 0.9882 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM11287 1 0.0146 0.9872 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM28759 1 0.0000 0.9881 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM11292 5 0.2766 0.6935 0.000 0.004 0.000 0.020 0.852 0.124
#> GSM28766 5 0.4087 0.4879 0.000 0.000 0.000 0.036 0.688 0.276
#> GSM11268 3 0.4415 0.1871 0.000 0.020 0.556 0.004 0.000 0.420
#> GSM28767 5 0.1398 0.7252 0.000 0.000 0.000 0.008 0.940 0.052
#> GSM11286 2 0.4176 0.1196 0.000 0.580 0.000 0.000 0.404 0.016
#> GSM28751 2 0.2094 0.6070 0.004 0.908 0.000 0.000 0.024 0.064
#> GSM28770 5 0.2006 0.7110 0.000 0.000 0.000 0.016 0.904 0.080
#> GSM11283 4 0.2772 0.7475 0.000 0.004 0.000 0.816 0.180 0.000
#> GSM11289 5 0.2263 0.7042 0.000 0.000 0.000 0.016 0.884 0.100
#> GSM11280 2 0.4584 0.5533 0.000 0.732 0.000 0.056 0.040 0.172
#> GSM28749 6 0.5935 0.0170 0.000 0.244 0.000 0.000 0.300 0.456
#> GSM28750 3 0.3859 0.5741 0.000 0.012 0.720 0.012 0.000 0.256
#> GSM11290 3 0.1155 0.8304 0.000 0.004 0.956 0.004 0.000 0.036
#> GSM11294 3 0.0405 0.8403 0.000 0.004 0.988 0.000 0.000 0.008
#> GSM28771 4 0.2632 0.7468 0.000 0.004 0.000 0.832 0.164 0.000
#> GSM28760 4 0.4672 0.6832 0.000 0.000 0.092 0.728 0.152 0.028
#> GSM28774 5 0.4525 0.6612 0.000 0.220 0.000 0.072 0.700 0.008
#> GSM11284 5 0.3842 0.7050 0.000 0.100 0.000 0.112 0.784 0.004
#> GSM28761 6 0.5556 0.4171 0.000 0.148 0.252 0.012 0.000 0.588
#> GSM11278 5 0.5377 0.6403 0.000 0.048 0.096 0.132 0.704 0.020
#> GSM11291 3 0.0000 0.8408 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11277 3 0.0547 0.8365 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM11272 6 0.4295 0.4609 0.000 0.052 0.212 0.012 0.000 0.724
#> GSM11285 5 0.2182 0.7225 0.000 0.004 0.000 0.076 0.900 0.020
#> GSM28753 4 0.6534 0.0885 0.000 0.116 0.000 0.420 0.072 0.392
#> GSM28773 5 0.4581 0.3278 0.000 0.016 0.000 0.368 0.596 0.020
#> GSM28765 5 0.6507 0.3170 0.000 0.268 0.000 0.052 0.496 0.184
#> GSM28768 1 0.2137 0.9255 0.912 0.012 0.000 0.048 0.000 0.028
#> GSM28754 2 0.6815 0.1672 0.000 0.428 0.000 0.344 0.092 0.136
#> GSM28769 2 0.1644 0.5818 0.000 0.920 0.000 0.000 0.004 0.076
#> GSM11275 1 0.0547 0.9818 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM11270 5 0.7558 0.4110 0.000 0.176 0.172 0.116 0.488 0.048
#> GSM11271 5 0.1151 0.7421 0.000 0.032 0.000 0.012 0.956 0.000
#> GSM11288 2 0.4314 0.4211 0.004 0.716 0.036 0.012 0.000 0.232
#> GSM11273 3 0.1944 0.8010 0.000 0.000 0.924 0.024 0.016 0.036
#> GSM28757 2 0.3047 0.6148 0.000 0.848 0.000 0.004 0.064 0.084
#> GSM11282 5 0.5915 0.6369 0.000 0.100 0.096 0.120 0.664 0.020
#> GSM28756 5 0.3727 0.7036 0.000 0.128 0.000 0.088 0.784 0.000
#> GSM11276 5 0.1982 0.7413 0.000 0.068 0.000 0.016 0.912 0.004
#> GSM28752 5 0.4184 0.5544 0.000 0.296 0.000 0.004 0.672 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
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 tissue(p) k
#> ATC:NMF 52 0.396 2
#> ATC:NMF 52 0.372 3
#> ATC:NMF 47 0.344 4
#> ATC:NMF 46 0.467 5
#> ATC:NMF 42 0.457 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