Date: 2019-12-25 20:40:22 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 21168 rows and 61 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] 21168 61
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:kmeans | 3 | 1.000 | 0.967 | 0.982 | ** | |
| SD:skmeans | 2 | 1.000 | 0.982 | 0.993 | ** | |
| SD:pam | 4 | 1.000 | 0.963 | 0.987 | ** | 2,3 |
| CV:kmeans | 3 | 1.000 | 0.970 | 0.986 | ** | |
| CV:pam | 4 | 1.000 | 0.974 | 0.990 | ** | 3 |
| MAD:skmeans | 2 | 1.000 | 0.976 | 0.991 | ** | |
| MAD:NMF | 2 | 1.000 | 0.972 | 0.988 | ** | |
| ATC:pam | 4 | 1.000 | 0.972 | 0.989 | ** | 2,3 |
| ATC:NMF | 2 | 1.000 | 0.961 | 0.986 | ** | |
| MAD:pam | 4 | 0.987 | 0.944 | 0.978 | ** | 2,3 |
| MAD:kmeans | 4 | 0.986 | 0.967 | 0.967 | ** | |
| ATC:hclust | 4 | 0.962 | 0.934 | 0.974 | ** | |
| MAD:mclust | 6 | 0.952 | 0.934 | 0.960 | ** | 4 |
| CV:mclust | 4 | 0.941 | 0.917 | 0.966 | * | |
| SD:hclust | 4 | 0.935 | 0.924 | 0.963 | * | 3 |
| CV:skmeans | 3 | 0.924 | 0.939 | 0.968 | * | 2 |
| MAD:hclust | 4 | 0.918 | 0.883 | 0.944 | * | 3 |
| SD:NMF | 4 | 0.912 | 0.885 | 0.954 | * | |
| ATC:skmeans | 3 | 0.900 | 0.932 | 0.962 | * | 2 |
| CV:hclust | 3 | 0.891 | 0.897 | 0.954 | ||
| CV:NMF | 3 | 0.874 | 0.895 | 0.956 | ||
| ATC:kmeans | 2 | 0.847 | 0.943 | 0.973 | ||
| SD:mclust | 3 | 0.840 | 0.889 | 0.950 | ||
| ATC:mclust | 2 | 0.642 | 0.778 | 0.913 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 0.806 0.892 0.956 0.500 0.498 0.498
#> CV:NMF 2 0.774 0.870 0.947 0.501 0.492 0.492
#> MAD:NMF 2 1.000 0.972 0.988 0.494 0.503 0.503
#> ATC:NMF 2 1.000 0.961 0.986 0.491 0.508 0.508
#> SD:skmeans 2 1.000 0.982 0.993 0.490 0.508 0.508
#> CV:skmeans 2 1.000 0.988 0.995 0.496 0.503 0.503
#> MAD:skmeans 2 1.000 0.976 0.991 0.489 0.515 0.515
#> ATC:skmeans 2 1.000 0.991 0.996 0.496 0.503 0.503
#> SD:mclust 2 0.272 0.658 0.799 0.457 0.493 0.493
#> CV:mclust 2 0.494 0.772 0.885 0.495 0.503 0.503
#> MAD:mclust 2 0.446 0.215 0.581 0.487 0.721 0.721
#> ATC:mclust 2 0.642 0.778 0.913 0.456 0.552 0.552
#> SD:kmeans 2 0.368 0.728 0.773 0.411 0.541 0.541
#> CV:kmeans 2 0.323 0.687 0.700 0.406 0.552 0.552
#> MAD:kmeans 2 0.495 0.920 0.898 0.443 0.515 0.515
#> ATC:kmeans 2 0.847 0.943 0.973 0.469 0.515 0.515
#> SD:pam 2 1.000 0.972 0.987 0.456 0.552 0.552
#> CV:pam 2 0.788 0.887 0.947 0.473 0.541 0.541
#> MAD:pam 2 0.966 0.948 0.965 0.455 0.552 0.552
#> ATC:pam 2 0.932 0.953 0.978 0.450 0.564 0.564
#> SD:hclust 2 0.607 0.915 0.946 0.303 0.744 0.744
#> CV:hclust 2 0.368 0.566 0.712 0.379 0.541 0.541
#> MAD:hclust 2 0.432 0.579 0.718 0.338 0.531 0.531
#> ATC:hclust 2 0.508 0.926 0.909 0.369 0.607 0.607
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.845 0.874 0.947 0.319 0.697 0.466
#> CV:NMF 3 0.874 0.895 0.956 0.301 0.661 0.424
#> MAD:NMF 3 0.814 0.851 0.939 0.345 0.708 0.481
#> ATC:NMF 3 0.869 0.865 0.947 0.334 0.751 0.549
#> SD:skmeans 3 0.869 0.894 0.951 0.375 0.722 0.500
#> CV:skmeans 3 0.924 0.939 0.968 0.359 0.711 0.483
#> MAD:skmeans 3 0.722 0.853 0.930 0.372 0.733 0.517
#> ATC:skmeans 3 0.900 0.932 0.962 0.280 0.803 0.624
#> SD:mclust 3 0.840 0.889 0.950 0.435 0.727 0.511
#> CV:mclust 3 0.842 0.865 0.939 0.314 0.733 0.522
#> MAD:mclust 3 0.818 0.882 0.943 0.335 0.560 0.418
#> ATC:mclust 3 0.668 0.814 0.898 0.374 0.727 0.537
#> SD:kmeans 3 1.000 0.967 0.982 0.459 0.820 0.677
#> CV:kmeans 3 1.000 0.970 0.986 0.477 0.815 0.675
#> MAD:kmeans 3 0.780 0.915 0.944 0.385 0.757 0.579
#> ATC:kmeans 3 0.659 0.782 0.841 0.316 0.734 0.550
#> SD:pam 3 1.000 0.999 1.000 0.328 0.843 0.715
#> CV:pam 3 1.000 0.987 0.994 0.289 0.845 0.715
#> MAD:pam 3 1.000 0.989 0.995 0.338 0.843 0.715
#> ATC:pam 3 1.000 0.971 0.987 0.342 0.838 0.712
#> SD:hclust 3 0.917 0.937 0.974 0.906 0.685 0.577
#> CV:hclust 3 0.891 0.897 0.954 0.548 0.767 0.607
#> MAD:hclust 3 0.915 0.913 0.965 0.723 0.702 0.526
#> ATC:hclust 3 0.725 0.935 0.933 0.565 0.823 0.708
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.912 0.885 0.954 0.0900 0.816 0.543
#> CV:NMF 4 0.885 0.892 0.950 0.1035 0.830 0.579
#> MAD:NMF 4 0.894 0.900 0.953 0.0853 0.804 0.513
#> ATC:NMF 4 0.675 0.653 0.825 0.1239 0.797 0.489
#> SD:skmeans 4 0.858 0.872 0.944 0.1049 0.786 0.463
#> CV:skmeans 4 0.754 0.812 0.911 0.1074 0.797 0.480
#> MAD:skmeans 4 0.835 0.854 0.936 0.1015 0.784 0.464
#> ATC:skmeans 4 0.754 0.800 0.906 0.1530 0.839 0.581
#> SD:mclust 4 0.898 0.857 0.944 0.1089 0.889 0.699
#> CV:mclust 4 0.941 0.917 0.966 0.0982 0.918 0.774
#> MAD:mclust 4 0.918 0.878 0.951 0.1176 0.907 0.744
#> ATC:mclust 4 0.707 0.758 0.881 0.1159 0.946 0.851
#> SD:kmeans 4 0.889 0.900 0.948 0.1583 0.889 0.722
#> CV:kmeans 4 0.848 0.893 0.902 0.1593 0.874 0.693
#> MAD:kmeans 4 0.986 0.967 0.967 0.1480 0.867 0.673
#> ATC:kmeans 4 0.679 0.899 0.896 0.1203 0.863 0.668
#> SD:pam 4 1.000 0.963 0.987 0.1144 0.926 0.814
#> CV:pam 4 1.000 0.974 0.990 0.1074 0.926 0.814
#> MAD:pam 4 0.987 0.944 0.978 0.1157 0.926 0.814
#> ATC:pam 4 1.000 0.972 0.989 0.1370 0.911 0.780
#> SD:hclust 4 0.935 0.924 0.963 0.2386 0.850 0.650
#> CV:hclust 4 0.754 0.827 0.896 0.1977 0.877 0.700
#> MAD:hclust 4 0.918 0.883 0.944 0.2066 0.850 0.650
#> ATC:hclust 4 0.962 0.934 0.974 0.2409 0.843 0.634
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.727 0.706 0.850 0.0625 0.979 0.929
#> CV:NMF 5 0.835 0.800 0.907 0.0507 0.966 0.885
#> MAD:NMF 5 0.770 0.759 0.885 0.0485 0.978 0.921
#> ATC:NMF 5 0.763 0.701 0.858 0.0554 0.954 0.820
#> SD:skmeans 5 0.791 0.680 0.852 0.0707 0.884 0.595
#> CV:skmeans 5 0.744 0.612 0.802 0.0677 0.877 0.574
#> MAD:skmeans 5 0.784 0.688 0.847 0.0769 0.893 0.632
#> ATC:skmeans 5 0.750 0.720 0.853 0.0636 0.925 0.718
#> SD:mclust 5 0.738 0.759 0.806 0.0552 1.000 1.000
#> CV:mclust 5 0.786 0.586 0.803 0.0628 0.923 0.740
#> MAD:mclust 5 0.842 0.872 0.907 0.0369 0.986 0.952
#> ATC:mclust 5 0.778 0.701 0.850 0.0991 0.938 0.808
#> SD:kmeans 5 0.756 0.799 0.862 0.0723 1.000 1.000
#> CV:kmeans 5 0.765 0.786 0.859 0.0739 0.992 0.974
#> MAD:kmeans 5 0.805 0.871 0.888 0.0705 1.000 1.000
#> ATC:kmeans 5 0.791 0.854 0.878 0.0811 1.000 1.000
#> SD:pam 5 0.858 0.811 0.914 0.1411 0.907 0.713
#> CV:pam 5 0.833 0.818 0.905 0.1156 0.928 0.778
#> MAD:pam 5 0.854 0.847 0.923 0.1271 0.920 0.753
#> ATC:pam 5 0.850 0.839 0.918 0.1094 0.920 0.747
#> SD:hclust 5 0.942 0.897 0.958 0.0198 0.987 0.953
#> CV:hclust 5 0.789 0.834 0.908 0.0335 0.990 0.966
#> MAD:hclust 5 0.927 0.910 0.954 0.0306 0.987 0.953
#> ATC:hclust 5 0.904 0.820 0.936 0.0272 0.989 0.960
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.748 0.634 0.784 0.0481 0.951 0.830
#> CV:NMF 6 0.735 0.597 0.792 0.0610 0.961 0.855
#> MAD:NMF 6 0.759 0.667 0.811 0.0493 0.952 0.827
#> ATC:NMF 6 0.745 0.583 0.799 0.0306 0.975 0.889
#> SD:skmeans 6 0.799 0.660 0.799 0.0333 0.918 0.641
#> CV:skmeans 6 0.776 0.579 0.777 0.0353 0.949 0.761
#> MAD:skmeans 6 0.794 0.625 0.792 0.0345 0.954 0.787
#> ATC:skmeans 6 0.762 0.652 0.796 0.0348 0.943 0.743
#> SD:mclust 6 0.783 0.836 0.876 0.0578 0.889 0.611
#> CV:mclust 6 0.805 0.680 0.838 0.0613 0.905 0.621
#> MAD:mclust 6 0.952 0.934 0.960 0.0720 0.916 0.695
#> ATC:mclust 6 0.838 0.774 0.861 0.0271 0.936 0.759
#> SD:kmeans 6 0.743 0.595 0.754 0.0527 0.919 0.732
#> CV:kmeans 6 0.741 0.632 0.782 0.0457 0.962 0.867
#> MAD:kmeans 6 0.776 0.661 0.822 0.0456 0.940 0.794
#> ATC:kmeans 6 0.785 0.772 0.830 0.0496 0.943 0.800
#> SD:pam 6 0.839 0.726 0.877 0.0178 0.979 0.912
#> CV:pam 6 0.854 0.798 0.887 0.0343 0.974 0.899
#> MAD:pam 6 0.882 0.872 0.924 0.0432 0.939 0.756
#> ATC:pam 6 0.819 0.691 0.882 0.0365 0.975 0.896
#> SD:hclust 6 0.919 0.842 0.936 0.0135 0.996 0.984
#> CV:hclust 6 0.765 0.709 0.871 0.0370 0.975 0.909
#> MAD:hclust 6 0.865 0.867 0.926 0.0282 0.996 0.984
#> ATC:hclust 6 0.892 0.803 0.916 0.0244 0.961 0.863
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n disease.state(p) k
#> SD:NMF 58 1.05e-11 2
#> CV:NMF 56 1.75e-09 2
#> MAD:NMF 60 6.78e-13 2
#> ATC:NMF 59 1.54e-13 2
#> SD:skmeans 60 9.36e-14 2
#> CV:skmeans 61 2.53e-12 2
#> MAD:skmeans 60 9.36e-14 2
#> ATC:skmeans 61 2.53e-12 2
#> SD:mclust 51 8.42e-12 2
#> CV:mclust 55 7.58e-12 2
#> MAD:mclust 9 NA 2
#> ATC:mclust 51 8.42e-12 2
#> SD:kmeans 58 2.54e-13 2
#> CV:kmeans 48 3.33e-11 2
#> MAD:kmeans 61 5.68e-14 2
#> ATC:kmeans 61 5.68e-14 2
#> SD:pam 61 1.09e-10 2
#> CV:pam 57 6.32e-10 2
#> MAD:pam 60 1.69e-10 2
#> ATC:pam 61 5.78e-10 2
#> SD:hclust 61 5.68e-14 2
#> CV:hclust 47 1.47e-08 2
#> MAD:hclust 46 2.27e-08 2
#> ATC:hclust 61 5.49e-08 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) k
#> SD:NMF 58 3.82e-14 3
#> CV:NMF 59 3.53e-15 3
#> MAD:NMF 56 2.12e-13 3
#> ATC:NMF 56 1.21e-09 3
#> SD:skmeans 58 1.47e-12 3
#> CV:skmeans 61 1.51e-13 3
#> MAD:skmeans 58 1.47e-12 3
#> ATC:skmeans 59 2.62e-10 3
#> SD:mclust 60 2.13e-19 3
#> CV:mclust 59 4.76e-19 3
#> MAD:mclust 60 2.13e-19 3
#> ATC:mclust 57 2.32e-15 3
#> SD:kmeans 60 1.88e-21 3
#> CV:kmeans 60 1.88e-21 3
#> MAD:kmeans 60 1.88e-21 3
#> ATC:kmeans 61 3.74e-21 3
#> SD:pam 61 6.70e-22 3
#> CV:pam 61 6.70e-22 3
#> MAD:pam 61 6.70e-22 3
#> ATC:pam 61 3.74e-21 3
#> SD:hclust 58 4.67e-19 3
#> CV:hclust 59 1.58e-19 3
#> MAD:hclust 58 8.94e-20 3
#> ATC:hclust 61 3.64e-19 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) k
#> SD:NMF 58 2.45e-19 4
#> CV:NMF 58 8.53e-21 4
#> MAD:NMF 58 2.45e-19 4
#> ATC:NMF 46 7.13e-12 4
#> SD:skmeans 58 5.27e-17 4
#> CV:skmeans 57 6.33e-18 4
#> MAD:skmeans 57 7.66e-18 4
#> ATC:skmeans 56 9.11e-12 4
#> SD:mclust 56 3.11e-20 4
#> CV:mclust 58 8.78e-22 4
#> MAD:mclust 58 4.42e-21 4
#> ATC:mclust 54 9.16e-20 4
#> SD:kmeans 58 3.15e-21 4
#> CV:kmeans 59 1.37e-21 4
#> MAD:kmeans 61 2.38e-22 4
#> ATC:kmeans 61 2.38e-22 4
#> SD:pam 60 1.47e-22 4
#> CV:pam 61 3.47e-22 4
#> MAD:pam 60 9.09e-22 4
#> ATC:pam 60 3.16e-21 4
#> SD:hclust 59 6.37e-21 4
#> CV:hclust 58 1.14e-20 4
#> MAD:hclust 57 2.14e-21 4
#> ATC:hclust 58 8.60e-22 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) k
#> SD:NMF 50 2.51e-19 5
#> CV:NMF 54 6.25e-19 5
#> MAD:NMF 54 1.53e-18 5
#> ATC:NMF 48 1.53e-12 5
#> SD:skmeans 45 1.46e-14 5
#> CV:skmeans 36 1.83e-11 5
#> MAD:skmeans 45 1.62e-14 5
#> ATC:skmeans 49 3.43e-16 5
#> SD:mclust 53 2.63e-19 5
#> CV:mclust 35 4.09e-13 5
#> MAD:mclust 58 3.46e-20 5
#> ATC:mclust 47 7.65e-17 5
#> SD:kmeans 57 6.85e-21 5
#> CV:kmeans 53 2.52e-19 5
#> MAD:kmeans 61 2.38e-22 5
#> ATC:kmeans 61 2.38e-22 5
#> SD:pam 55 3.18e-19 5
#> CV:pam 57 4.82e-20 5
#> MAD:pam 59 7.23e-21 5
#> ATC:pam 58 3.75e-19 5
#> SD:hclust 58 2.22e-21 5
#> CV:hclust 58 2.22e-21 5
#> MAD:hclust 57 5.72e-21 5
#> ATC:hclust 49 2.62e-20 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) k
#> SD:NMF 46 1.82e-16 6
#> CV:NMF 43 3.31e-14 6
#> MAD:NMF 46 1.16e-17 6
#> ATC:NMF 39 5.47e-11 6
#> SD:skmeans 40 5.02e-13 6
#> CV:skmeans 34 1.23e-11 6
#> MAD:skmeans 38 3.11e-13 6
#> ATC:skmeans 42 2.63e-13 6
#> SD:mclust 60 7.11e-20 6
#> CV:mclust 50 8.71e-16 6
#> MAD:mclust 60 7.11e-20 6
#> ATC:mclust 53 4.93e-17 6
#> SD:kmeans 41 1.93e-14 6
#> CV:kmeans 48 3.43e-16 6
#> MAD:kmeans 46 1.82e-16 6
#> ATC:kmeans 57 5.72e-21 6
#> SD:pam 49 1.15e-15 6
#> CV:pam 56 1.70e-18 6
#> MAD:pam 59 5.78e-19 6
#> ATC:pam 47 7.15e-17 6
#> SD:hclust 57 5.72e-21 6
#> CV:hclust 54 1.35e-18 6
#> MAD:hclust 58 2.22e-21 6
#> ATC:hclust 52 3.67e-20 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 21168 rows and 61 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 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 0.607 0.915 0.946 0.3032 0.744 0.744
#> 3 3 0.917 0.937 0.974 0.9059 0.685 0.577
#> 4 4 0.935 0.924 0.963 0.2386 0.850 0.650
#> 5 5 0.942 0.897 0.958 0.0198 0.987 0.953
#> 6 6 0.919 0.842 0.936 0.0135 0.996 0.984
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 3
There is also optional best \(k\) = 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
#> GSM246087 1 0.000 1.000 1.000 0.000
#> GSM246088 1 0.000 1.000 1.000 0.000
#> GSM246089 1 0.000 1.000 1.000 0.000
#> GSM246090 1 0.000 1.000 1.000 0.000
#> GSM246119 1 0.000 1.000 1.000 0.000
#> GSM246120 1 0.000 1.000 1.000 0.000
#> GSM246121 1 0.000 1.000 1.000 0.000
#> GSM246122 1 0.000 1.000 1.000 0.000
#> GSM246123 1 0.000 1.000 1.000 0.000
#> GSM246422 2 0.000 0.930 0.000 1.000
#> GSM246423 2 0.000 0.930 0.000 1.000
#> GSM246484 2 0.000 0.930 0.000 1.000
#> GSM246485 2 0.416 0.895 0.084 0.916
#> GSM246486 2 0.000 0.930 0.000 1.000
#> GSM246487 2 0.000 0.930 0.000 1.000
#> GSM246488 2 0.000 0.930 0.000 1.000
#> GSM246489 2 0.714 0.835 0.196 0.804
#> GSM246490 2 0.706 0.838 0.192 0.808
#> GSM246491 2 0.706 0.838 0.192 0.808
#> GSM247162 2 0.714 0.835 0.196 0.804
#> GSM247163 2 0.706 0.838 0.192 0.808
#> GSM247164 2 0.706 0.838 0.192 0.808
#> GSM247165 2 0.706 0.838 0.192 0.808
#> GSM247166 2 0.714 0.835 0.196 0.804
#> GSM247168 2 0.714 0.835 0.196 0.804
#> GSM247169 2 0.714 0.835 0.196 0.804
#> GSM247171 2 0.714 0.835 0.196 0.804
#> GSM247173 2 0.714 0.835 0.196 0.804
#> GSM247174 2 0.714 0.835 0.196 0.804
#> GSM247175 2 0.714 0.835 0.196 0.804
#> GSM247188 2 0.714 0.835 0.196 0.804
#> GSM247189 2 0.416 0.895 0.084 0.916
#> GSM247190 2 0.714 0.835 0.196 0.804
#> GSM247650 2 0.000 0.930 0.000 1.000
#> GSM247651 2 0.000 0.930 0.000 1.000
#> GSM247652 2 0.000 0.930 0.000 1.000
#> GSM247653 2 0.000 0.930 0.000 1.000
#> GSM247654 2 0.000 0.930 0.000 1.000
#> GSM247655 2 0.000 0.930 0.000 1.000
#> GSM247656 2 0.000 0.930 0.000 1.000
#> GSM247657 2 0.000 0.930 0.000 1.000
#> GSM247658 2 0.000 0.930 0.000 1.000
#> GSM247659 2 0.000 0.930 0.000 1.000
#> GSM247660 2 0.000 0.930 0.000 1.000
#> GSM247661 2 0.000 0.930 0.000 1.000
#> GSM247662 2 0.000 0.930 0.000 1.000
#> GSM247663 2 0.000 0.930 0.000 1.000
#> GSM247856 2 0.000 0.930 0.000 1.000
#> GSM247857 2 0.000 0.930 0.000 1.000
#> GSM247859 2 0.000 0.930 0.000 1.000
#> GSM247860 2 0.000 0.930 0.000 1.000
#> GSM247862 2 0.000 0.930 0.000 1.000
#> GSM247864 2 0.000 0.930 0.000 1.000
#> GSM247865 2 0.000 0.930 0.000 1.000
#> GSM247866 2 0.000 0.930 0.000 1.000
#> GSM247876 2 0.000 0.930 0.000 1.000
#> GSM247877 2 0.000 0.930 0.000 1.000
#> GSM247878 2 0.000 0.930 0.000 1.000
#> GSM247879 2 0.000 0.930 0.000 1.000
#> GSM247881 2 0.000 0.930 0.000 1.000
#> GSM247883 2 0.000 0.930 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 1.000 0.000 0.000 1
#> GSM246088 3 0.0000 1.000 0.000 0.000 1
#> GSM246089 3 0.0000 1.000 0.000 0.000 1
#> GSM246090 3 0.0000 1.000 0.000 0.000 1
#> GSM246119 3 0.0000 1.000 0.000 0.000 1
#> GSM246120 3 0.0000 1.000 0.000 0.000 1
#> GSM246121 3 0.0000 1.000 0.000 0.000 1
#> GSM246122 3 0.0000 1.000 0.000 0.000 1
#> GSM246123 3 0.0000 1.000 0.000 0.000 1
#> GSM246422 1 0.0000 0.962 1.000 0.000 0
#> GSM246423 1 0.0000 0.962 1.000 0.000 0
#> GSM246484 1 0.0000 0.962 1.000 0.000 0
#> GSM246485 1 0.5968 0.460 0.636 0.364 0
#> GSM246486 1 0.3816 0.824 0.852 0.148 0
#> GSM246487 1 0.3816 0.824 0.852 0.148 0
#> GSM246488 1 0.4291 0.785 0.820 0.180 0
#> GSM246489 2 0.0000 0.968 0.000 1.000 0
#> GSM246490 2 0.0237 0.965 0.004 0.996 0
#> GSM246491 2 0.0237 0.965 0.004 0.996 0
#> GSM247162 2 0.0000 0.968 0.000 1.000 0
#> GSM247163 2 0.0237 0.965 0.004 0.996 0
#> GSM247164 2 0.0237 0.965 0.004 0.996 0
#> GSM247165 2 0.5706 0.486 0.320 0.680 0
#> GSM247166 2 0.0000 0.968 0.000 1.000 0
#> GSM247168 2 0.0000 0.968 0.000 1.000 0
#> GSM247169 2 0.0000 0.968 0.000 1.000 0
#> GSM247171 2 0.0000 0.968 0.000 1.000 0
#> GSM247173 2 0.0000 0.968 0.000 1.000 0
#> GSM247174 2 0.0000 0.968 0.000 1.000 0
#> GSM247175 2 0.0000 0.968 0.000 1.000 0
#> GSM247188 2 0.0000 0.968 0.000 1.000 0
#> GSM247189 1 0.5968 0.460 0.636 0.364 0
#> GSM247190 2 0.0000 0.968 0.000 1.000 0
#> GSM247650 1 0.0000 0.962 1.000 0.000 0
#> GSM247651 1 0.0000 0.962 1.000 0.000 0
#> GSM247652 1 0.0000 0.962 1.000 0.000 0
#> GSM247653 1 0.0000 0.962 1.000 0.000 0
#> GSM247654 1 0.0000 0.962 1.000 0.000 0
#> GSM247655 1 0.0000 0.962 1.000 0.000 0
#> GSM247656 1 0.0000 0.962 1.000 0.000 0
#> GSM247657 1 0.0000 0.962 1.000 0.000 0
#> GSM247658 1 0.0000 0.962 1.000 0.000 0
#> GSM247659 1 0.0000 0.962 1.000 0.000 0
#> GSM247660 1 0.0000 0.962 1.000 0.000 0
#> GSM247661 1 0.0000 0.962 1.000 0.000 0
#> GSM247662 1 0.0000 0.962 1.000 0.000 0
#> GSM247663 1 0.0000 0.962 1.000 0.000 0
#> GSM247856 1 0.0000 0.962 1.000 0.000 0
#> GSM247857 1 0.0000 0.962 1.000 0.000 0
#> GSM247859 1 0.0000 0.962 1.000 0.000 0
#> GSM247860 1 0.0000 0.962 1.000 0.000 0
#> GSM247862 1 0.0000 0.962 1.000 0.000 0
#> GSM247864 1 0.0000 0.962 1.000 0.000 0
#> GSM247865 1 0.1411 0.933 0.964 0.036 0
#> GSM247866 1 0.0000 0.962 1.000 0.000 0
#> GSM247876 1 0.0000 0.962 1.000 0.000 0
#> GSM247877 1 0.0000 0.962 1.000 0.000 0
#> GSM247878 1 0.0000 0.962 1.000 0.000 0
#> GSM247879 1 0.0000 0.962 1.000 0.000 0
#> GSM247881 1 0.0000 0.962 1.000 0.000 0
#> GSM247883 1 0.0000 0.962 1.000 0.000 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246422 4 0.0921 0.848 0.028 0.000 0 0.972
#> GSM246423 4 0.0921 0.848 0.028 0.000 0 0.972
#> GSM246484 4 0.0921 0.848 0.028 0.000 0 0.972
#> GSM246485 4 0.5371 0.559 0.020 0.364 0 0.616
#> GSM246486 4 0.3913 0.827 0.028 0.148 0 0.824
#> GSM246487 4 0.3913 0.827 0.028 0.148 0 0.824
#> GSM246488 4 0.4281 0.804 0.028 0.180 0 0.792
#> GSM246489 2 0.0000 0.972 0.000 1.000 0 0.000
#> GSM246490 2 0.0188 0.969 0.004 0.996 0 0.000
#> GSM246491 2 0.0188 0.969 0.004 0.996 0 0.000
#> GSM247162 2 0.0000 0.972 0.000 1.000 0 0.000
#> GSM247163 2 0.0188 0.969 0.004 0.996 0 0.000
#> GSM247164 2 0.0188 0.969 0.004 0.996 0 0.000
#> GSM247165 2 0.4677 0.393 0.004 0.680 0 0.316
#> GSM247166 2 0.0000 0.972 0.000 1.000 0 0.000
#> GSM247168 2 0.0000 0.972 0.000 1.000 0 0.000
#> GSM247169 2 0.0000 0.972 0.000 1.000 0 0.000
#> GSM247171 2 0.0000 0.972 0.000 1.000 0 0.000
#> GSM247173 2 0.0000 0.972 0.000 1.000 0 0.000
#> GSM247174 2 0.0000 0.972 0.000 1.000 0 0.000
#> GSM247175 2 0.0000 0.972 0.000 1.000 0 0.000
#> GSM247188 2 0.0000 0.972 0.000 1.000 0 0.000
#> GSM247189 4 0.5371 0.559 0.020 0.364 0 0.616
#> GSM247190 2 0.0000 0.972 0.000 1.000 0 0.000
#> GSM247650 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247651 1 0.0336 0.976 0.992 0.000 0 0.008
#> GSM247652 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247653 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247654 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247655 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247656 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247657 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247658 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247659 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247660 1 0.0336 0.976 0.992 0.000 0 0.008
#> GSM247661 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247662 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247663 1 0.0469 0.973 0.988 0.000 0 0.012
#> GSM247856 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247857 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247859 1 0.0336 0.976 0.992 0.000 0 0.008
#> GSM247860 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247862 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247864 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247865 1 0.5742 0.286 0.596 0.036 0 0.368
#> GSM247866 1 0.0000 0.979 1.000 0.000 0 0.000
#> GSM247876 1 0.0707 0.966 0.980 0.000 0 0.020
#> GSM247877 4 0.0921 0.840 0.028 0.000 0 0.972
#> GSM247878 4 0.0000 0.835 0.000 0.000 0 1.000
#> GSM247879 4 0.0921 0.840 0.028 0.000 0 0.972
#> GSM247881 1 0.0336 0.976 0.992 0.000 0 0.008
#> GSM247883 1 0.0336 0.976 0.992 0.000 0 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246422 4 0.0000 0.664 0.000 0.000 0 1.000 0.000
#> GSM246423 4 0.0000 0.664 0.000 0.000 0 1.000 0.000
#> GSM246484 4 0.0000 0.664 0.000 0.000 0 1.000 0.000
#> GSM246485 4 0.4074 0.591 0.000 0.364 0 0.636 0.000
#> GSM246486 4 0.2605 0.756 0.000 0.148 0 0.852 0.000
#> GSM246487 4 0.2605 0.756 0.000 0.148 0 0.852 0.000
#> GSM246488 4 0.2929 0.742 0.000 0.180 0 0.820 0.000
#> GSM246489 2 0.0000 0.971 0.000 1.000 0 0.000 0.000
#> GSM246490 2 0.0162 0.969 0.000 0.996 0 0.004 0.000
#> GSM246491 2 0.0162 0.969 0.000 0.996 0 0.004 0.000
#> GSM247162 2 0.0000 0.971 0.000 1.000 0 0.000 0.000
#> GSM247163 2 0.0162 0.969 0.000 0.996 0 0.004 0.000
#> GSM247164 2 0.0162 0.969 0.000 0.996 0 0.004 0.000
#> GSM247165 2 0.3895 0.338 0.000 0.680 0 0.320 0.000
#> GSM247166 2 0.0000 0.971 0.000 1.000 0 0.000 0.000
#> GSM247168 2 0.0000 0.971 0.000 1.000 0 0.000 0.000
#> GSM247169 2 0.0000 0.971 0.000 1.000 0 0.000 0.000
#> GSM247171 2 0.0000 0.971 0.000 1.000 0 0.000 0.000
#> GSM247173 2 0.0000 0.971 0.000 1.000 0 0.000 0.000
#> GSM247174 2 0.0000 0.971 0.000 1.000 0 0.000 0.000
#> GSM247175 2 0.0000 0.971 0.000 1.000 0 0.000 0.000
#> GSM247188 2 0.0000 0.971 0.000 1.000 0 0.000 0.000
#> GSM247189 4 0.4074 0.591 0.000 0.364 0 0.636 0.000
#> GSM247190 2 0.0000 0.971 0.000 1.000 0 0.000 0.000
#> GSM247650 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247651 1 0.0404 0.971 0.988 0.000 0 0.012 0.000
#> GSM247652 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247653 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247654 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247655 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247656 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247657 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247658 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247659 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247660 1 0.0404 0.971 0.988 0.000 0 0.012 0.000
#> GSM247661 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247662 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247663 1 0.0404 0.970 0.988 0.000 0 0.000 0.012
#> GSM247856 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247857 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247859 1 0.0404 0.971 0.988 0.000 0 0.012 0.000
#> GSM247860 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247862 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247864 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247865 1 0.4958 0.305 0.592 0.036 0 0.372 0.000
#> GSM247866 1 0.0000 0.977 1.000 0.000 0 0.000 0.000
#> GSM247876 1 0.0609 0.964 0.980 0.000 0 0.000 0.020
#> GSM247877 5 0.0000 0.749 0.000 0.000 0 0.000 1.000
#> GSM247878 5 0.4307 0.182 0.000 0.000 0 0.496 0.504
#> GSM247879 5 0.0000 0.749 0.000 0.000 0 0.000 1.000
#> GSM247881 1 0.0404 0.971 0.988 0.000 0 0.012 0.000
#> GSM247883 1 0.0404 0.971 0.988 0.000 0 0.012 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0000 0.854 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246088 3 0.0000 0.854 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246089 6 0.1141 0.000 0.000 0.000 0.052 0.000 0.000 0.948
#> GSM246090 3 0.0000 0.854 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246119 3 0.3244 0.732 0.000 0.000 0.732 0.000 0.000 0.268
#> GSM246120 3 0.3244 0.732 0.000 0.000 0.732 0.000 0.000 0.268
#> GSM246121 3 0.0865 0.848 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM246122 3 0.0000 0.854 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246123 3 0.3244 0.732 0.000 0.000 0.732 0.000 0.000 0.268
#> GSM246422 4 0.0146 0.668 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM246423 4 0.0146 0.668 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM246484 4 0.0146 0.668 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM246485 4 0.3647 0.592 0.000 0.360 0.000 0.640 0.000 0.000
#> GSM246486 4 0.2300 0.757 0.000 0.144 0.000 0.856 0.000 0.000
#> GSM246487 4 0.2300 0.757 0.000 0.144 0.000 0.856 0.000 0.000
#> GSM246488 4 0.2597 0.743 0.000 0.176 0.000 0.824 0.000 0.000
#> GSM246489 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246490 2 0.0146 0.969 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM246491 2 0.0146 0.969 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM247162 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247163 2 0.0146 0.969 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM247164 2 0.0146 0.969 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM247165 2 0.3515 0.330 0.000 0.676 0.000 0.324 0.000 0.000
#> GSM247166 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247168 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247169 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247171 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247174 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247175 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247189 4 0.3647 0.592 0.000 0.360 0.000 0.640 0.000 0.000
#> GSM247190 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247650 1 0.0000 0.958 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247651 1 0.0363 0.955 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM247652 1 0.0000 0.958 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247653 1 0.1007 0.953 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM247654 1 0.1007 0.953 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM247655 1 0.0000 0.958 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247656 1 0.1007 0.953 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM247657 1 0.1075 0.953 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM247658 1 0.0000 0.958 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247659 1 0.1075 0.953 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM247660 1 0.0363 0.955 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM247661 1 0.1007 0.953 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM247662 1 0.1075 0.953 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM247663 1 0.0363 0.954 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM247856 1 0.0000 0.958 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247857 1 0.1075 0.953 0.952 0.000 0.000 0.000 0.000 0.048
#> GSM247859 1 0.0363 0.955 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM247860 1 0.1007 0.953 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM247862 1 0.0458 0.958 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM247864 1 0.0000 0.958 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247865 1 0.4400 0.290 0.592 0.032 0.000 0.376 0.000 0.000
#> GSM247866 1 0.1007 0.953 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM247876 1 0.0547 0.952 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM247877 5 0.0000 0.605 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM247878 5 0.3998 0.180 0.000 0.000 0.000 0.492 0.504 0.004
#> GSM247879 5 0.0000 0.605 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM247881 1 0.0363 0.955 0.988 0.000 0.000 0.012 0.000 0.000
#> GSM247883 1 0.0363 0.955 0.988 0.000 0.000 0.012 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:hclust 61 5.68e-14 2
#> SD:hclust 58 4.67e-19 3
#> SD:hclust 59 6.37e-21 4
#> SD:hclust 58 2.22e-21 5
#> SD:hclust 57 5.72e-21 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 21168 rows and 61 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 0.368 0.728 0.773 0.4111 0.541 0.541
#> 3 3 1.000 0.967 0.982 0.4589 0.820 0.677
#> 4 4 0.889 0.900 0.948 0.1583 0.889 0.722
#> 5 5 0.756 0.799 0.862 0.0723 1.000 1.000
#> 6 6 0.743 0.595 0.754 0.0527 0.919 0.732
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
#> GSM246087 1 0.9795 0.525 0.584 0.416
#> GSM246088 1 0.9795 0.525 0.584 0.416
#> GSM246089 1 0.9795 0.525 0.584 0.416
#> GSM246090 1 0.9795 0.525 0.584 0.416
#> GSM246119 1 0.9795 0.525 0.584 0.416
#> GSM246120 1 0.9795 0.525 0.584 0.416
#> GSM246121 1 0.9795 0.525 0.584 0.416
#> GSM246122 1 0.9795 0.525 0.584 0.416
#> GSM246123 1 0.9795 0.525 0.584 0.416
#> GSM246422 1 0.9977 -0.623 0.528 0.472
#> GSM246423 1 0.9977 -0.623 0.528 0.472
#> GSM246484 1 0.9977 -0.623 0.528 0.472
#> GSM246485 2 0.9710 0.868 0.400 0.600
#> GSM246486 2 0.9795 0.838 0.416 0.584
#> GSM246487 2 0.9909 0.795 0.444 0.556
#> GSM246488 2 0.9795 0.838 0.416 0.584
#> GSM246489 2 0.9000 0.967 0.316 0.684
#> GSM246490 2 0.9000 0.967 0.316 0.684
#> GSM246491 2 0.9000 0.967 0.316 0.684
#> GSM247162 2 0.9000 0.967 0.316 0.684
#> GSM247163 2 0.9000 0.967 0.316 0.684
#> GSM247164 2 0.9000 0.967 0.316 0.684
#> GSM247165 2 0.9000 0.967 0.316 0.684
#> GSM247166 2 0.9000 0.967 0.316 0.684
#> GSM247168 2 0.9000 0.967 0.316 0.684
#> GSM247169 2 0.9000 0.967 0.316 0.684
#> GSM247171 2 0.9000 0.967 0.316 0.684
#> GSM247173 2 0.9000 0.967 0.316 0.684
#> GSM247174 2 0.9000 0.967 0.316 0.684
#> GSM247175 2 0.9000 0.967 0.316 0.684
#> GSM247188 2 0.9000 0.967 0.316 0.684
#> GSM247189 2 0.9000 0.967 0.316 0.684
#> GSM247190 2 0.9000 0.967 0.316 0.684
#> GSM247650 1 0.0376 0.780 0.996 0.004
#> GSM247651 1 0.1633 0.779 0.976 0.024
#> GSM247652 1 0.1633 0.779 0.976 0.024
#> GSM247653 1 0.0376 0.780 0.996 0.004
#> GSM247654 1 0.1633 0.779 0.976 0.024
#> GSM247655 1 0.1633 0.779 0.976 0.024
#> GSM247656 1 0.0376 0.780 0.996 0.004
#> GSM247657 1 0.1633 0.779 0.976 0.024
#> GSM247658 1 0.1633 0.779 0.976 0.024
#> GSM247659 1 0.0376 0.780 0.996 0.004
#> GSM247660 1 0.1633 0.779 0.976 0.024
#> GSM247661 1 0.0376 0.780 0.996 0.004
#> GSM247662 1 0.0376 0.780 0.996 0.004
#> GSM247663 1 0.0376 0.780 0.996 0.004
#> GSM247856 1 0.1414 0.780 0.980 0.020
#> GSM247857 1 0.1633 0.779 0.976 0.024
#> GSM247859 1 0.1633 0.779 0.976 0.024
#> GSM247860 1 0.0000 0.781 1.000 0.000
#> GSM247862 1 0.1633 0.779 0.976 0.024
#> GSM247864 1 0.1633 0.779 0.976 0.024
#> GSM247865 1 0.3431 0.725 0.936 0.064
#> GSM247866 1 0.1633 0.779 0.976 0.024
#> GSM247876 1 0.0000 0.781 1.000 0.000
#> GSM247877 1 0.0000 0.781 1.000 0.000
#> GSM247878 1 0.1633 0.779 0.976 0.024
#> GSM247879 1 0.0376 0.780 0.996 0.004
#> GSM247881 1 0.1633 0.779 0.976 0.024
#> GSM247883 1 0.1633 0.779 0.976 0.024
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0424 0.997 0.000 0.008 0.992
#> GSM246088 3 0.0424 0.997 0.000 0.008 0.992
#> GSM246089 3 0.0892 0.996 0.000 0.020 0.980
#> GSM246090 3 0.0424 0.997 0.000 0.008 0.992
#> GSM246119 3 0.0892 0.996 0.000 0.020 0.980
#> GSM246120 3 0.0892 0.996 0.000 0.020 0.980
#> GSM246121 3 0.0424 0.997 0.000 0.008 0.992
#> GSM246122 3 0.0424 0.997 0.000 0.008 0.992
#> GSM246123 3 0.0892 0.996 0.000 0.020 0.980
#> GSM246422 1 0.1832 0.957 0.956 0.036 0.008
#> GSM246423 1 0.1832 0.957 0.956 0.036 0.008
#> GSM246484 1 0.1832 0.957 0.956 0.036 0.008
#> GSM246485 2 0.6295 0.114 0.472 0.528 0.000
#> GSM246486 2 0.1170 0.956 0.016 0.976 0.008
#> GSM246487 1 0.1765 0.955 0.956 0.040 0.004
#> GSM246488 2 0.1170 0.956 0.016 0.976 0.008
#> GSM246489 2 0.0592 0.965 0.012 0.988 0.000
#> GSM246490 2 0.0592 0.965 0.012 0.988 0.000
#> GSM246491 2 0.0592 0.965 0.012 0.988 0.000
#> GSM247162 2 0.0592 0.965 0.012 0.988 0.000
#> GSM247163 2 0.0592 0.965 0.012 0.988 0.000
#> GSM247164 2 0.0592 0.965 0.012 0.988 0.000
#> GSM247165 2 0.0592 0.965 0.012 0.988 0.000
#> GSM247166 2 0.0592 0.965 0.012 0.988 0.000
#> GSM247168 2 0.0592 0.965 0.012 0.988 0.000
#> GSM247169 2 0.0592 0.965 0.012 0.988 0.000
#> GSM247171 2 0.0592 0.965 0.012 0.988 0.000
#> GSM247173 2 0.0592 0.965 0.012 0.988 0.000
#> GSM247174 2 0.0592 0.965 0.012 0.988 0.000
#> GSM247175 2 0.0592 0.965 0.012 0.988 0.000
#> GSM247188 2 0.0592 0.965 0.012 0.988 0.000
#> GSM247189 2 0.0829 0.962 0.012 0.984 0.004
#> GSM247190 2 0.0592 0.965 0.012 0.988 0.000
#> GSM247650 1 0.0237 0.992 0.996 0.000 0.004
#> GSM247651 1 0.0000 0.992 1.000 0.000 0.000
#> GSM247652 1 0.0237 0.992 0.996 0.000 0.004
#> GSM247653 1 0.0237 0.992 0.996 0.000 0.004
#> GSM247654 1 0.0237 0.992 0.996 0.000 0.004
#> GSM247655 1 0.0000 0.992 1.000 0.000 0.000
#> GSM247656 1 0.0237 0.992 0.996 0.000 0.004
#> GSM247657 1 0.0237 0.992 0.996 0.000 0.004
#> GSM247658 1 0.0000 0.992 1.000 0.000 0.000
#> GSM247659 1 0.0237 0.992 0.996 0.000 0.004
#> GSM247660 1 0.0000 0.992 1.000 0.000 0.000
#> GSM247661 1 0.0237 0.992 0.996 0.000 0.004
#> GSM247662 1 0.0237 0.992 0.996 0.000 0.004
#> GSM247663 1 0.0237 0.992 0.996 0.000 0.004
#> GSM247856 1 0.0237 0.992 0.996 0.000 0.004
#> GSM247857 1 0.0237 0.992 0.996 0.000 0.004
#> GSM247859 1 0.0000 0.992 1.000 0.000 0.000
#> GSM247860 1 0.0237 0.992 0.996 0.000 0.004
#> GSM247862 1 0.0000 0.992 1.000 0.000 0.000
#> GSM247864 1 0.0000 0.992 1.000 0.000 0.000
#> GSM247865 1 0.0000 0.992 1.000 0.000 0.000
#> GSM247866 1 0.0000 0.992 1.000 0.000 0.000
#> GSM247876 1 0.0237 0.992 0.996 0.000 0.004
#> GSM247877 1 0.0424 0.988 0.992 0.000 0.008
#> GSM247878 1 0.0424 0.988 0.992 0.000 0.008
#> GSM247879 1 0.0237 0.992 0.996 0.000 0.004
#> GSM247881 1 0.0000 0.992 1.000 0.000 0.000
#> GSM247883 1 0.0000 0.992 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 0.981 0.000 0.000 1.000 0.000
#> GSM246088 3 0.0000 0.981 0.000 0.000 1.000 0.000
#> GSM246089 3 0.1867 0.964 0.000 0.000 0.928 0.072
#> GSM246090 3 0.0000 0.981 0.000 0.000 1.000 0.000
#> GSM246119 3 0.1389 0.975 0.000 0.000 0.952 0.048
#> GSM246120 3 0.1389 0.975 0.000 0.000 0.952 0.048
#> GSM246121 3 0.0000 0.981 0.000 0.000 1.000 0.000
#> GSM246122 3 0.0000 0.981 0.000 0.000 1.000 0.000
#> GSM246123 3 0.1389 0.975 0.000 0.000 0.952 0.048
#> GSM246422 4 0.2859 0.842 0.112 0.008 0.000 0.880
#> GSM246423 4 0.2859 0.842 0.112 0.008 0.000 0.880
#> GSM246484 4 0.2859 0.842 0.112 0.008 0.000 0.880
#> GSM246485 2 0.7483 -0.160 0.184 0.456 0.000 0.360
#> GSM246486 4 0.4624 0.441 0.000 0.340 0.000 0.660
#> GSM246487 4 0.5331 0.618 0.332 0.024 0.000 0.644
#> GSM246488 4 0.2921 0.724 0.000 0.140 0.000 0.860
#> GSM246489 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM246490 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM246491 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM247162 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM247163 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM247164 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM247165 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM247166 2 0.1211 0.910 0.000 0.960 0.000 0.040
#> GSM247168 2 0.1211 0.910 0.000 0.960 0.000 0.040
#> GSM247169 2 0.1211 0.910 0.000 0.960 0.000 0.040
#> GSM247171 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM247173 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM247174 2 0.1211 0.910 0.000 0.960 0.000 0.040
#> GSM247175 2 0.0000 0.926 0.000 1.000 0.000 0.000
#> GSM247188 2 0.0592 0.920 0.000 0.984 0.000 0.016
#> GSM247189 2 0.4925 0.166 0.000 0.572 0.000 0.428
#> GSM247190 2 0.0188 0.925 0.000 0.996 0.000 0.004
#> GSM247650 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247651 1 0.2081 0.906 0.916 0.000 0.000 0.084
#> GSM247652 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247653 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247654 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247655 1 0.0188 0.984 0.996 0.000 0.000 0.004
#> GSM247656 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247657 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247658 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247659 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247660 1 0.1716 0.929 0.936 0.000 0.000 0.064
#> GSM247661 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247662 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247663 1 0.0336 0.981 0.992 0.000 0.000 0.008
#> GSM247856 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247857 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247859 1 0.1211 0.953 0.960 0.000 0.000 0.040
#> GSM247860 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247862 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247864 1 0.0188 0.984 0.996 0.000 0.000 0.004
#> GSM247865 1 0.1867 0.921 0.928 0.000 0.000 0.072
#> GSM247866 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247876 1 0.0336 0.981 0.992 0.000 0.000 0.008
#> GSM247877 4 0.3172 0.824 0.160 0.000 0.000 0.840
#> GSM247878 4 0.3123 0.826 0.156 0.000 0.000 0.844
#> GSM247879 1 0.0707 0.972 0.980 0.000 0.000 0.020
#> GSM247881 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247883 1 0.0188 0.984 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 0.9534 0.000 0.000 1.000 0.000 NA
#> GSM246088 3 0.0000 0.9534 0.000 0.000 1.000 0.000 NA
#> GSM246089 3 0.2964 0.9214 0.000 0.000 0.856 0.024 NA
#> GSM246090 3 0.0000 0.9534 0.000 0.000 1.000 0.000 NA
#> GSM246119 3 0.2304 0.9395 0.000 0.000 0.892 0.008 NA
#> GSM246120 3 0.2304 0.9395 0.000 0.000 0.892 0.008 NA
#> GSM246121 3 0.0000 0.9534 0.000 0.000 1.000 0.000 NA
#> GSM246122 3 0.0000 0.9534 0.000 0.000 1.000 0.000 NA
#> GSM246123 3 0.2304 0.9395 0.000 0.000 0.892 0.008 NA
#> GSM246422 4 0.0963 0.7390 0.036 0.000 0.000 0.964 NA
#> GSM246423 4 0.0963 0.7390 0.036 0.000 0.000 0.964 NA
#> GSM246484 4 0.0963 0.7390 0.036 0.000 0.000 0.964 NA
#> GSM246485 2 0.8456 -0.3225 0.164 0.312 0.000 0.276 NA
#> GSM246486 4 0.6538 0.3815 0.000 0.272 0.000 0.480 NA
#> GSM246487 4 0.6755 0.4646 0.296 0.004 0.000 0.452 NA
#> GSM246488 4 0.4693 0.6551 0.000 0.056 0.000 0.700 NA
#> GSM246489 2 0.0000 0.8805 0.000 1.000 0.000 0.000 NA
#> GSM246490 2 0.0609 0.8766 0.000 0.980 0.000 0.000 NA
#> GSM246491 2 0.0609 0.8766 0.000 0.980 0.000 0.000 NA
#> GSM247162 2 0.0000 0.8805 0.000 1.000 0.000 0.000 NA
#> GSM247163 2 0.1121 0.8665 0.000 0.956 0.000 0.000 NA
#> GSM247164 2 0.0880 0.8721 0.000 0.968 0.000 0.000 NA
#> GSM247165 2 0.2377 0.8009 0.000 0.872 0.000 0.000 NA
#> GSM247166 2 0.2377 0.8292 0.000 0.872 0.000 0.000 NA
#> GSM247168 2 0.2377 0.8292 0.000 0.872 0.000 0.000 NA
#> GSM247169 2 0.2377 0.8292 0.000 0.872 0.000 0.000 NA
#> GSM247171 2 0.0000 0.8805 0.000 1.000 0.000 0.000 NA
#> GSM247173 2 0.0000 0.8805 0.000 1.000 0.000 0.000 NA
#> GSM247174 2 0.2127 0.8389 0.000 0.892 0.000 0.000 NA
#> GSM247175 2 0.0000 0.8805 0.000 1.000 0.000 0.000 NA
#> GSM247188 2 0.0510 0.8780 0.000 0.984 0.000 0.000 NA
#> GSM247189 2 0.6458 0.0988 0.000 0.496 0.000 0.280 NA
#> GSM247190 2 0.0609 0.8772 0.000 0.980 0.000 0.000 NA
#> GSM247650 1 0.2230 0.8544 0.884 0.000 0.000 0.000 NA
#> GSM247651 1 0.3601 0.8132 0.820 0.000 0.000 0.052 NA
#> GSM247652 1 0.1341 0.8734 0.944 0.000 0.000 0.000 NA
#> GSM247653 1 0.3210 0.8173 0.788 0.000 0.000 0.000 NA
#> GSM247654 1 0.2732 0.8414 0.840 0.000 0.000 0.000 NA
#> GSM247655 1 0.2513 0.8455 0.876 0.000 0.000 0.008 NA
#> GSM247656 1 0.2179 0.8618 0.888 0.000 0.000 0.000 NA
#> GSM247657 1 0.2127 0.8593 0.892 0.000 0.000 0.000 NA
#> GSM247658 1 0.1851 0.8665 0.912 0.000 0.000 0.000 NA
#> GSM247659 1 0.2127 0.8623 0.892 0.000 0.000 0.000 NA
#> GSM247660 1 0.3229 0.8264 0.840 0.000 0.000 0.032 NA
#> GSM247661 1 0.3210 0.8173 0.788 0.000 0.000 0.000 NA
#> GSM247662 1 0.2074 0.8625 0.896 0.000 0.000 0.000 NA
#> GSM247663 1 0.3835 0.7670 0.744 0.000 0.000 0.012 NA
#> GSM247856 1 0.0703 0.8736 0.976 0.000 0.000 0.000 NA
#> GSM247857 1 0.2020 0.8631 0.900 0.000 0.000 0.000 NA
#> GSM247859 1 0.1836 0.8592 0.932 0.000 0.000 0.032 NA
#> GSM247860 1 0.3210 0.8173 0.788 0.000 0.000 0.000 NA
#> GSM247862 1 0.1478 0.8736 0.936 0.000 0.000 0.000 NA
#> GSM247864 1 0.2612 0.8431 0.868 0.000 0.000 0.008 NA
#> GSM247865 1 0.2304 0.8515 0.908 0.000 0.000 0.044 NA
#> GSM247866 1 0.3242 0.8257 0.784 0.000 0.000 0.000 NA
#> GSM247876 1 0.3807 0.7665 0.748 0.000 0.000 0.012 NA
#> GSM247877 4 0.4924 0.6337 0.060 0.000 0.000 0.668 NA
#> GSM247878 4 0.4901 0.6357 0.060 0.000 0.000 0.672 NA
#> GSM247879 1 0.4787 0.6226 0.640 0.000 0.000 0.036 NA
#> GSM247881 1 0.0703 0.8716 0.976 0.000 0.000 0.000 NA
#> GSM247883 1 0.1124 0.8665 0.960 0.000 0.000 0.004 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0000 0.9185 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246088 3 0.0000 0.9185 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246089 3 0.4645 0.8544 0.000 0.000 0.752 0.080 0.080 0.088
#> GSM246090 3 0.0000 0.9185 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246119 3 0.3695 0.8937 0.000 0.000 0.820 0.044 0.052 0.084
#> GSM246120 3 0.3695 0.8937 0.000 0.000 0.820 0.044 0.052 0.084
#> GSM246121 3 0.0146 0.9183 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM246122 3 0.0146 0.9183 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM246123 3 0.3695 0.8937 0.000 0.000 0.820 0.044 0.052 0.084
#> GSM246422 4 0.4726 0.3519 0.000 0.000 0.000 0.528 0.424 0.048
#> GSM246423 4 0.4726 0.3519 0.000 0.000 0.000 0.528 0.424 0.048
#> GSM246484 4 0.4726 0.3519 0.000 0.000 0.000 0.528 0.424 0.048
#> GSM246485 4 0.5272 0.4209 0.104 0.256 0.000 0.624 0.000 0.016
#> GSM246486 4 0.2920 0.5177 0.008 0.168 0.000 0.820 0.000 0.004
#> GSM246487 4 0.3441 0.3429 0.216 0.004 0.000 0.768 0.004 0.008
#> GSM246488 4 0.2637 0.5022 0.000 0.024 0.000 0.872 0.096 0.008
#> GSM246489 2 0.0000 0.8905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246490 2 0.1257 0.8770 0.000 0.952 0.000 0.028 0.000 0.020
#> GSM246491 2 0.1257 0.8770 0.000 0.952 0.000 0.028 0.000 0.020
#> GSM247162 2 0.0000 0.8905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247163 2 0.1549 0.8682 0.000 0.936 0.000 0.044 0.000 0.020
#> GSM247164 2 0.1549 0.8682 0.000 0.936 0.000 0.044 0.000 0.020
#> GSM247165 2 0.2536 0.8013 0.000 0.864 0.000 0.116 0.000 0.020
#> GSM247166 2 0.4394 0.6894 0.000 0.688 0.000 0.028 0.020 0.264
#> GSM247168 2 0.4394 0.6894 0.000 0.688 0.000 0.028 0.020 0.264
#> GSM247169 2 0.4394 0.6894 0.000 0.688 0.000 0.028 0.020 0.264
#> GSM247171 2 0.0000 0.8905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.8905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247174 2 0.3090 0.8012 0.000 0.828 0.000 0.028 0.004 0.140
#> GSM247175 2 0.0000 0.8905 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247188 2 0.0508 0.8872 0.000 0.984 0.000 0.012 0.000 0.004
#> GSM247189 4 0.4172 0.0899 0.000 0.460 0.000 0.528 0.000 0.012
#> GSM247190 2 0.1124 0.8776 0.000 0.956 0.000 0.008 0.000 0.036
#> GSM247650 1 0.2094 0.6019 0.900 0.000 0.000 0.000 0.080 0.020
#> GSM247651 1 0.3346 0.5862 0.840 0.000 0.000 0.056 0.080 0.024
#> GSM247652 1 0.3050 0.2317 0.764 0.000 0.000 0.000 0.000 0.236
#> GSM247653 6 0.3851 0.9749 0.460 0.000 0.000 0.000 0.000 0.540
#> GSM247654 1 0.3923 -0.5746 0.580 0.000 0.000 0.000 0.004 0.416
#> GSM247655 1 0.2755 0.6049 0.876 0.000 0.000 0.040 0.068 0.016
#> GSM247656 1 0.3679 0.1499 0.724 0.000 0.000 0.004 0.012 0.260
#> GSM247657 1 0.3702 0.1148 0.720 0.000 0.000 0.004 0.012 0.264
#> GSM247658 1 0.3244 0.0933 0.732 0.000 0.000 0.000 0.000 0.268
#> GSM247659 1 0.3680 0.2363 0.744 0.000 0.000 0.004 0.020 0.232
#> GSM247660 1 0.3238 0.5906 0.848 0.000 0.000 0.056 0.072 0.024
#> GSM247661 6 0.4076 0.9599 0.452 0.000 0.000 0.000 0.008 0.540
#> GSM247662 1 0.3329 0.3598 0.792 0.000 0.000 0.004 0.020 0.184
#> GSM247663 1 0.4198 0.4200 0.708 0.000 0.000 0.000 0.232 0.060
#> GSM247856 1 0.2001 0.5396 0.900 0.000 0.000 0.004 0.004 0.092
#> GSM247857 1 0.3329 0.3598 0.792 0.000 0.000 0.004 0.020 0.184
#> GSM247859 1 0.1984 0.6068 0.912 0.000 0.000 0.056 0.000 0.032
#> GSM247860 6 0.3854 0.9726 0.464 0.000 0.000 0.000 0.000 0.536
#> GSM247862 1 0.1908 0.5540 0.900 0.000 0.000 0.004 0.000 0.096
#> GSM247864 1 0.2911 0.6040 0.868 0.000 0.000 0.036 0.072 0.024
#> GSM247865 1 0.2288 0.5962 0.896 0.000 0.000 0.072 0.004 0.028
#> GSM247866 1 0.4659 -0.0635 0.624 0.000 0.000 0.004 0.052 0.320
#> GSM247876 1 0.4075 0.4200 0.712 0.000 0.000 0.000 0.240 0.048
#> GSM247877 5 0.2412 0.4355 0.028 0.000 0.000 0.092 0.880 0.000
#> GSM247878 5 0.2412 0.4355 0.028 0.000 0.000 0.092 0.880 0.000
#> GSM247879 5 0.4650 -0.1819 0.472 0.000 0.000 0.000 0.488 0.040
#> GSM247881 1 0.0767 0.5977 0.976 0.000 0.000 0.004 0.012 0.008
#> GSM247883 1 0.1633 0.6086 0.932 0.000 0.000 0.044 0.000 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:kmeans 58 2.54e-13 2
#> SD:kmeans 60 1.88e-21 3
#> SD:kmeans 58 3.15e-21 4
#> SD:kmeans 57 6.85e-21 5
#> SD:kmeans 41 1.93e-14 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 21168 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.982 0.993 0.4901 0.508 0.508
#> 3 3 0.869 0.894 0.951 0.3748 0.722 0.500
#> 4 4 0.858 0.872 0.944 0.1049 0.786 0.463
#> 5 5 0.791 0.680 0.852 0.0707 0.884 0.595
#> 6 6 0.799 0.660 0.799 0.0333 0.918 0.641
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
#> GSM246087 1 0.000 0.999 1.000 0.000
#> GSM246088 1 0.000 0.999 1.000 0.000
#> GSM246089 1 0.000 0.999 1.000 0.000
#> GSM246090 1 0.000 0.999 1.000 0.000
#> GSM246119 1 0.000 0.999 1.000 0.000
#> GSM246120 1 0.000 0.999 1.000 0.000
#> GSM246121 1 0.000 0.999 1.000 0.000
#> GSM246122 1 0.000 0.999 1.000 0.000
#> GSM246123 1 0.000 0.999 1.000 0.000
#> GSM246422 2 0.000 0.984 0.000 1.000
#> GSM246423 2 0.000 0.984 0.000 1.000
#> GSM246484 2 0.000 0.984 0.000 1.000
#> GSM246485 2 0.000 0.984 0.000 1.000
#> GSM246486 2 0.000 0.984 0.000 1.000
#> GSM246487 2 0.000 0.984 0.000 1.000
#> GSM246488 2 0.000 0.984 0.000 1.000
#> GSM246489 2 0.000 0.984 0.000 1.000
#> GSM246490 2 0.000 0.984 0.000 1.000
#> GSM246491 2 0.000 0.984 0.000 1.000
#> GSM247162 2 0.000 0.984 0.000 1.000
#> GSM247163 2 0.000 0.984 0.000 1.000
#> GSM247164 2 0.000 0.984 0.000 1.000
#> GSM247165 2 0.000 0.984 0.000 1.000
#> GSM247166 2 0.000 0.984 0.000 1.000
#> GSM247168 2 0.000 0.984 0.000 1.000
#> GSM247169 2 0.000 0.984 0.000 1.000
#> GSM247171 2 0.000 0.984 0.000 1.000
#> GSM247173 2 0.000 0.984 0.000 1.000
#> GSM247174 2 0.000 0.984 0.000 1.000
#> GSM247175 2 0.000 0.984 0.000 1.000
#> GSM247188 2 0.000 0.984 0.000 1.000
#> GSM247189 2 0.000 0.984 0.000 1.000
#> GSM247190 2 0.000 0.984 0.000 1.000
#> GSM247650 1 0.000 0.999 1.000 0.000
#> GSM247651 1 0.000 0.999 1.000 0.000
#> GSM247652 1 0.000 0.999 1.000 0.000
#> GSM247653 1 0.000 0.999 1.000 0.000
#> GSM247654 1 0.000 0.999 1.000 0.000
#> GSM247655 1 0.000 0.999 1.000 0.000
#> GSM247656 1 0.000 0.999 1.000 0.000
#> GSM247657 1 0.000 0.999 1.000 0.000
#> GSM247658 1 0.000 0.999 1.000 0.000
#> GSM247659 1 0.000 0.999 1.000 0.000
#> GSM247660 1 0.000 0.999 1.000 0.000
#> GSM247661 1 0.000 0.999 1.000 0.000
#> GSM247662 1 0.000 0.999 1.000 0.000
#> GSM247663 1 0.000 0.999 1.000 0.000
#> GSM247856 1 0.000 0.999 1.000 0.000
#> GSM247857 1 0.000 0.999 1.000 0.000
#> GSM247859 1 0.000 0.999 1.000 0.000
#> GSM247860 1 0.000 0.999 1.000 0.000
#> GSM247862 1 0.000 0.999 1.000 0.000
#> GSM247864 1 0.000 0.999 1.000 0.000
#> GSM247865 2 0.952 0.405 0.372 0.628
#> GSM247866 1 0.000 0.999 1.000 0.000
#> GSM247876 1 0.000 0.999 1.000 0.000
#> GSM247877 1 0.000 0.999 1.000 0.000
#> GSM247878 1 0.000 0.999 1.000 0.000
#> GSM247879 1 0.000 0.999 1.000 0.000
#> GSM247881 1 0.000 0.999 1.000 0.000
#> GSM247883 1 0.278 0.948 0.952 0.048
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 0.910 0.000 0.000 1.000
#> GSM246088 3 0.0000 0.910 0.000 0.000 1.000
#> GSM246089 3 0.0000 0.910 0.000 0.000 1.000
#> GSM246090 3 0.0000 0.910 0.000 0.000 1.000
#> GSM246119 3 0.0000 0.910 0.000 0.000 1.000
#> GSM246120 3 0.0000 0.910 0.000 0.000 1.000
#> GSM246121 3 0.0000 0.910 0.000 0.000 1.000
#> GSM246122 3 0.0000 0.910 0.000 0.000 1.000
#> GSM246123 3 0.0000 0.910 0.000 0.000 1.000
#> GSM246422 1 0.0747 0.917 0.984 0.016 0.000
#> GSM246423 1 0.0747 0.917 0.984 0.016 0.000
#> GSM246484 1 0.0747 0.917 0.984 0.016 0.000
#> GSM246485 2 0.0424 0.990 0.008 0.992 0.000
#> GSM246486 2 0.1031 0.977 0.024 0.976 0.000
#> GSM246487 1 0.3267 0.825 0.884 0.116 0.000
#> GSM246488 2 0.1643 0.958 0.044 0.956 0.000
#> GSM246489 2 0.0000 0.996 0.000 1.000 0.000
#> GSM246490 2 0.0000 0.996 0.000 1.000 0.000
#> GSM246491 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247162 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247163 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247164 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247165 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247166 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247168 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247169 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247171 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247173 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247174 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247175 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247188 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247189 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247190 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247650 1 0.2878 0.860 0.904 0.000 0.096
#> GSM247651 1 0.0000 0.924 1.000 0.000 0.000
#> GSM247652 1 0.6026 0.320 0.624 0.000 0.376
#> GSM247653 3 0.0747 0.906 0.016 0.000 0.984
#> GSM247654 3 0.4654 0.766 0.208 0.000 0.792
#> GSM247655 1 0.0000 0.924 1.000 0.000 0.000
#> GSM247656 3 0.2711 0.866 0.088 0.000 0.912
#> GSM247657 3 0.4750 0.757 0.216 0.000 0.784
#> GSM247658 1 0.1964 0.894 0.944 0.000 0.056
#> GSM247659 3 0.0000 0.910 0.000 0.000 1.000
#> GSM247660 1 0.0000 0.924 1.000 0.000 0.000
#> GSM247661 3 0.0747 0.906 0.016 0.000 0.984
#> GSM247662 3 0.4504 0.779 0.196 0.000 0.804
#> GSM247663 1 0.2625 0.872 0.916 0.000 0.084
#> GSM247856 3 0.6267 0.256 0.452 0.000 0.548
#> GSM247857 3 0.5327 0.680 0.272 0.000 0.728
#> GSM247859 1 0.0000 0.924 1.000 0.000 0.000
#> GSM247860 3 0.0892 0.905 0.020 0.000 0.980
#> GSM247862 1 0.0000 0.924 1.000 0.000 0.000
#> GSM247864 1 0.0000 0.924 1.000 0.000 0.000
#> GSM247865 1 0.0000 0.924 1.000 0.000 0.000
#> GSM247866 1 0.0000 0.924 1.000 0.000 0.000
#> GSM247876 1 0.2261 0.890 0.932 0.000 0.068
#> GSM247877 1 0.4291 0.761 0.820 0.000 0.180
#> GSM247878 1 0.0000 0.924 1.000 0.000 0.000
#> GSM247879 1 0.6045 0.445 0.620 0.000 0.380
#> GSM247881 1 0.0237 0.923 0.996 0.000 0.004
#> GSM247883 1 0.0000 0.924 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 0.986 0.000 0.000 1.000 0.000
#> GSM246088 3 0.0000 0.986 0.000 0.000 1.000 0.000
#> GSM246089 3 0.0000 0.986 0.000 0.000 1.000 0.000
#> GSM246090 3 0.0000 0.986 0.000 0.000 1.000 0.000
#> GSM246119 3 0.0000 0.986 0.000 0.000 1.000 0.000
#> GSM246120 3 0.0000 0.986 0.000 0.000 1.000 0.000
#> GSM246121 3 0.0000 0.986 0.000 0.000 1.000 0.000
#> GSM246122 3 0.0000 0.986 0.000 0.000 1.000 0.000
#> GSM246123 3 0.0000 0.986 0.000 0.000 1.000 0.000
#> GSM246422 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM246423 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM246484 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM246485 2 0.4790 0.441 0.000 0.620 0.000 0.380
#> GSM246486 4 0.1302 0.838 0.000 0.044 0.000 0.956
#> GSM246487 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM246488 4 0.0707 0.855 0.000 0.020 0.000 0.980
#> GSM246489 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM246490 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM246491 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM247162 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM247163 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM247164 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM247165 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM247166 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM247168 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM247169 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM247171 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM247173 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM247174 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM247175 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM247188 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM247189 2 0.3610 0.757 0.000 0.800 0.000 0.200
#> GSM247190 2 0.0000 0.966 0.000 1.000 0.000 0.000
#> GSM247650 1 0.0336 0.909 0.992 0.000 0.000 0.008
#> GSM247651 4 0.4522 0.543 0.320 0.000 0.000 0.680
#> GSM247652 1 0.0000 0.909 1.000 0.000 0.000 0.000
#> GSM247653 1 0.0469 0.906 0.988 0.000 0.012 0.000
#> GSM247654 1 0.0188 0.908 0.996 0.000 0.004 0.000
#> GSM247655 1 0.2647 0.825 0.880 0.000 0.000 0.120
#> GSM247656 1 0.4916 0.250 0.576 0.000 0.424 0.000
#> GSM247657 1 0.0000 0.909 1.000 0.000 0.000 0.000
#> GSM247658 1 0.0000 0.909 1.000 0.000 0.000 0.000
#> GSM247659 3 0.0921 0.962 0.028 0.000 0.972 0.000
#> GSM247660 4 0.4624 0.501 0.340 0.000 0.000 0.660
#> GSM247661 1 0.1022 0.896 0.968 0.000 0.032 0.000
#> GSM247662 1 0.2469 0.831 0.892 0.000 0.108 0.000
#> GSM247663 1 0.0469 0.907 0.988 0.000 0.000 0.012
#> GSM247856 1 0.0707 0.904 0.980 0.000 0.020 0.000
#> GSM247857 1 0.0000 0.909 1.000 0.000 0.000 0.000
#> GSM247859 1 0.4643 0.456 0.656 0.000 0.000 0.344
#> GSM247860 1 0.0817 0.900 0.976 0.000 0.024 0.000
#> GSM247862 1 0.0188 0.909 0.996 0.000 0.000 0.004
#> GSM247864 1 0.3528 0.743 0.808 0.000 0.000 0.192
#> GSM247865 4 0.3764 0.700 0.216 0.000 0.000 0.784
#> GSM247866 1 0.0336 0.908 0.992 0.000 0.000 0.008
#> GSM247876 1 0.1042 0.903 0.972 0.000 0.008 0.020
#> GSM247877 4 0.3219 0.711 0.000 0.000 0.164 0.836
#> GSM247878 4 0.0000 0.865 0.000 0.000 0.000 1.000
#> GSM247879 3 0.2919 0.889 0.044 0.000 0.896 0.060
#> GSM247881 1 0.0336 0.909 0.992 0.000 0.000 0.008
#> GSM247883 1 0.4008 0.658 0.756 0.000 0.000 0.244
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM246088 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM246089 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM246090 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM246119 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM246120 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM246121 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM246122 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM246123 3 0.0000 0.967 0.000 0.000 1.000 0.000 0.000
#> GSM246422 4 0.0162 0.772 0.004 0.000 0.000 0.996 0.000
#> GSM246423 4 0.0162 0.772 0.004 0.000 0.000 0.996 0.000
#> GSM246484 4 0.0162 0.772 0.004 0.000 0.000 0.996 0.000
#> GSM246485 4 0.4455 0.231 0.000 0.404 0.000 0.588 0.008
#> GSM246486 4 0.0794 0.763 0.000 0.028 0.000 0.972 0.000
#> GSM246487 4 0.0566 0.769 0.012 0.004 0.000 0.984 0.000
#> GSM246488 4 0.0510 0.769 0.000 0.016 0.000 0.984 0.000
#> GSM246489 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
#> GSM246490 2 0.0162 0.970 0.004 0.996 0.000 0.000 0.000
#> GSM246491 2 0.0162 0.970 0.004 0.996 0.000 0.000 0.000
#> GSM247162 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
#> GSM247163 2 0.0162 0.970 0.004 0.996 0.000 0.000 0.000
#> GSM247164 2 0.0162 0.970 0.004 0.996 0.000 0.000 0.000
#> GSM247165 2 0.0162 0.970 0.004 0.996 0.000 0.000 0.000
#> GSM247166 2 0.0162 0.970 0.000 0.996 0.000 0.000 0.004
#> GSM247168 2 0.0162 0.970 0.000 0.996 0.000 0.000 0.004
#> GSM247169 2 0.0162 0.970 0.000 0.996 0.000 0.000 0.004
#> GSM247171 2 0.0162 0.970 0.004 0.996 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
#> GSM247174 2 0.0162 0.970 0.000 0.996 0.000 0.000 0.004
#> GSM247175 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
#> GSM247189 2 0.4310 0.305 0.004 0.604 0.000 0.392 0.000
#> GSM247190 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
#> GSM247650 1 0.2170 0.588 0.904 0.000 0.004 0.004 0.088
#> GSM247651 1 0.4083 0.579 0.744 0.000 0.000 0.228 0.028
#> GSM247652 5 0.3366 0.570 0.232 0.000 0.000 0.000 0.768
#> GSM247653 5 0.1408 0.685 0.044 0.000 0.008 0.000 0.948
#> GSM247654 5 0.0963 0.688 0.036 0.000 0.000 0.000 0.964
#> GSM247655 1 0.3427 0.587 0.836 0.000 0.000 0.056 0.108
#> GSM247656 5 0.5091 0.499 0.084 0.000 0.244 0.000 0.672
#> GSM247657 5 0.2280 0.667 0.120 0.000 0.000 0.000 0.880
#> GSM247658 5 0.3876 0.440 0.316 0.000 0.000 0.000 0.684
#> GSM247659 3 0.4575 0.603 0.052 0.000 0.712 0.000 0.236
#> GSM247660 1 0.3929 0.593 0.764 0.000 0.000 0.208 0.028
#> GSM247661 5 0.1893 0.682 0.048 0.000 0.024 0.000 0.928
#> GSM247662 5 0.5652 0.388 0.344 0.000 0.092 0.000 0.564
#> GSM247663 1 0.3421 0.516 0.788 0.000 0.000 0.008 0.204
#> GSM247856 5 0.5071 0.182 0.424 0.000 0.036 0.000 0.540
#> GSM247857 5 0.4470 0.402 0.372 0.000 0.012 0.000 0.616
#> GSM247859 1 0.6111 0.362 0.560 0.000 0.000 0.180 0.260
#> GSM247860 5 0.2110 0.678 0.072 0.000 0.016 0.000 0.912
#> GSM247862 1 0.4449 0.044 0.512 0.000 0.000 0.004 0.484
#> GSM247864 1 0.2983 0.605 0.868 0.000 0.000 0.056 0.076
#> GSM247865 4 0.5044 -0.122 0.464 0.000 0.000 0.504 0.032
#> GSM247866 1 0.4510 0.226 0.560 0.000 0.000 0.008 0.432
#> GSM247876 1 0.3541 0.561 0.824 0.000 0.012 0.020 0.144
#> GSM247877 4 0.5714 0.153 0.412 0.000 0.072 0.512 0.004
#> GSM247878 1 0.4227 0.126 0.580 0.000 0.000 0.420 0.000
#> GSM247879 1 0.5439 0.312 0.596 0.000 0.348 0.032 0.024
#> GSM247881 1 0.4126 0.168 0.620 0.000 0.000 0.000 0.380
#> GSM247883 1 0.5325 0.326 0.616 0.000 0.000 0.076 0.308
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0000 0.94453 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246088 3 0.0000 0.94453 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246089 3 0.0146 0.94486 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM246090 3 0.0000 0.94453 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246119 3 0.0146 0.94486 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM246120 3 0.0146 0.94486 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM246121 3 0.0146 0.94486 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM246122 3 0.0000 0.94453 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246123 3 0.0146 0.94486 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM246422 4 0.1141 0.84551 0.000 0.000 0.000 0.948 0.052 0.000
#> GSM246423 4 0.1141 0.84551 0.000 0.000 0.000 0.948 0.052 0.000
#> GSM246484 4 0.1141 0.84551 0.000 0.000 0.000 0.948 0.052 0.000
#> GSM246485 4 0.4662 0.41066 0.004 0.332 0.000 0.620 0.040 0.004
#> GSM246486 4 0.1261 0.83093 0.000 0.024 0.000 0.952 0.024 0.000
#> GSM246487 4 0.2001 0.80238 0.048 0.000 0.000 0.912 0.040 0.000
#> GSM246488 4 0.0291 0.84298 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM246489 2 0.0146 0.95928 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM246490 2 0.0551 0.95621 0.004 0.984 0.000 0.008 0.000 0.004
#> GSM246491 2 0.0146 0.95875 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM247162 2 0.0146 0.95927 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM247163 2 0.0291 0.95770 0.004 0.992 0.000 0.004 0.000 0.000
#> GSM247164 2 0.0520 0.95438 0.008 0.984 0.000 0.008 0.000 0.000
#> GSM247165 2 0.0717 0.94920 0.008 0.976 0.000 0.016 0.000 0.000
#> GSM247166 2 0.0767 0.95308 0.008 0.976 0.000 0.000 0.012 0.004
#> GSM247168 2 0.0767 0.95308 0.008 0.976 0.000 0.000 0.012 0.004
#> GSM247169 2 0.0767 0.95308 0.008 0.976 0.000 0.000 0.012 0.004
#> GSM247171 2 0.0000 0.95924 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247173 2 0.0146 0.95924 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM247174 2 0.0405 0.95754 0.008 0.988 0.000 0.000 0.004 0.000
#> GSM247175 2 0.0000 0.95924 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247188 2 0.0291 0.95849 0.004 0.992 0.000 0.000 0.004 0.000
#> GSM247189 2 0.4886 0.04426 0.012 0.520 0.000 0.432 0.036 0.000
#> GSM247190 2 0.0000 0.95924 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247650 1 0.4971 0.16501 0.508 0.000 0.000 0.000 0.424 0.068
#> GSM247651 1 0.6050 0.35464 0.512 0.000 0.000 0.172 0.296 0.020
#> GSM247652 6 0.4932 0.36761 0.372 0.000 0.000 0.000 0.072 0.556
#> GSM247653 6 0.0820 0.61817 0.012 0.000 0.000 0.000 0.016 0.972
#> GSM247654 6 0.1643 0.61172 0.068 0.000 0.000 0.000 0.008 0.924
#> GSM247655 1 0.4430 0.49533 0.708 0.000 0.000 0.032 0.232 0.028
#> GSM247656 6 0.6882 0.25616 0.284 0.000 0.180 0.000 0.084 0.452
#> GSM247657 6 0.4674 0.37124 0.332 0.000 0.000 0.000 0.060 0.608
#> GSM247658 6 0.4827 0.41658 0.276 0.000 0.000 0.000 0.092 0.632
#> GSM247659 3 0.6604 0.31715 0.220 0.000 0.532 0.000 0.104 0.144
#> GSM247660 1 0.5798 0.41401 0.568 0.000 0.000 0.140 0.268 0.024
#> GSM247661 6 0.1515 0.61006 0.028 0.000 0.008 0.000 0.020 0.944
#> GSM247662 1 0.6202 0.13141 0.560 0.000 0.060 0.000 0.140 0.240
#> GSM247663 5 0.5037 0.44665 0.172 0.000 0.000 0.000 0.640 0.188
#> GSM247856 1 0.6714 -0.12353 0.432 0.000 0.048 0.004 0.176 0.340
#> GSM247857 1 0.5250 0.16678 0.612 0.000 0.008 0.000 0.116 0.264
#> GSM247859 1 0.5374 0.49042 0.688 0.000 0.000 0.112 0.096 0.104
#> GSM247860 6 0.1564 0.61379 0.024 0.000 0.000 0.000 0.040 0.936
#> GSM247862 6 0.5384 0.00606 0.428 0.000 0.000 0.004 0.096 0.472
#> GSM247864 1 0.4511 0.45599 0.672 0.000 0.000 0.036 0.276 0.016
#> GSM247865 1 0.5912 0.27484 0.488 0.000 0.000 0.364 0.128 0.020
#> GSM247866 6 0.5839 0.15544 0.276 0.000 0.000 0.000 0.236 0.488
#> GSM247876 5 0.4162 0.58517 0.144 0.000 0.000 0.004 0.752 0.100
#> GSM247877 5 0.3812 0.61277 0.012 0.000 0.012 0.248 0.728 0.000
#> GSM247878 5 0.4294 0.59826 0.060 0.000 0.000 0.248 0.692 0.000
#> GSM247879 5 0.4624 0.60605 0.068 0.000 0.124 0.020 0.760 0.028
#> GSM247881 1 0.3962 0.45783 0.764 0.000 0.000 0.000 0.116 0.120
#> GSM247883 1 0.3225 0.51860 0.852 0.000 0.000 0.036 0.064 0.048
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:skmeans 60 9.36e-14 2
#> SD:skmeans 58 1.47e-12 3
#> SD:skmeans 58 5.27e-17 4
#> SD:skmeans 45 1.46e-14 5
#> SD:skmeans 40 5.02e-13 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 21168 rows and 61 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 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 1.000 0.972 0.987 0.4560 0.552 0.552
#> 3 3 1.000 0.999 1.000 0.3283 0.843 0.715
#> 4 4 1.000 0.963 0.987 0.1144 0.926 0.814
#> 5 5 0.858 0.811 0.914 0.1411 0.907 0.713
#> 6 6 0.839 0.726 0.877 0.0178 0.979 0.912
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> 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
#> GSM246087 1 0.8207 0.676 0.744 0.256
#> GSM246088 1 0.0938 0.971 0.988 0.012
#> GSM246089 1 0.0000 0.981 1.000 0.000
#> GSM246090 1 0.2778 0.939 0.952 0.048
#> GSM246119 1 0.0000 0.981 1.000 0.000
#> GSM246120 1 0.0000 0.981 1.000 0.000
#> GSM246121 1 0.6712 0.794 0.824 0.176
#> GSM246122 1 0.8443 0.649 0.728 0.272
#> GSM246123 1 0.0000 0.981 1.000 0.000
#> GSM246422 1 0.0000 0.981 1.000 0.000
#> GSM246423 1 0.0000 0.981 1.000 0.000
#> GSM246484 1 0.0376 0.978 0.996 0.004
#> GSM246485 2 0.0672 0.992 0.008 0.992
#> GSM246486 2 0.0000 0.999 0.000 1.000
#> GSM246487 1 0.0376 0.978 0.996 0.004
#> GSM246488 2 0.0000 0.999 0.000 1.000
#> GSM246489 2 0.0000 0.999 0.000 1.000
#> GSM246490 2 0.0000 0.999 0.000 1.000
#> GSM246491 2 0.0000 0.999 0.000 1.000
#> GSM247162 2 0.0000 0.999 0.000 1.000
#> GSM247163 2 0.0000 0.999 0.000 1.000
#> GSM247164 2 0.0000 0.999 0.000 1.000
#> GSM247165 2 0.0000 0.999 0.000 1.000
#> GSM247166 2 0.0000 0.999 0.000 1.000
#> GSM247168 2 0.0000 0.999 0.000 1.000
#> GSM247169 2 0.0000 0.999 0.000 1.000
#> GSM247171 2 0.0000 0.999 0.000 1.000
#> GSM247173 2 0.0000 0.999 0.000 1.000
#> GSM247174 2 0.0000 0.999 0.000 1.000
#> GSM247175 2 0.0000 0.999 0.000 1.000
#> GSM247188 2 0.0000 0.999 0.000 1.000
#> GSM247189 2 0.0376 0.996 0.004 0.996
#> GSM247190 2 0.0000 0.999 0.000 1.000
#> GSM247650 1 0.0000 0.981 1.000 0.000
#> GSM247651 1 0.0000 0.981 1.000 0.000
#> GSM247652 1 0.0000 0.981 1.000 0.000
#> GSM247653 1 0.0000 0.981 1.000 0.000
#> GSM247654 1 0.0000 0.981 1.000 0.000
#> GSM247655 1 0.0000 0.981 1.000 0.000
#> GSM247656 1 0.0000 0.981 1.000 0.000
#> GSM247657 1 0.0000 0.981 1.000 0.000
#> GSM247658 1 0.0000 0.981 1.000 0.000
#> GSM247659 1 0.0000 0.981 1.000 0.000
#> GSM247660 1 0.0000 0.981 1.000 0.000
#> GSM247661 1 0.0000 0.981 1.000 0.000
#> GSM247662 1 0.0000 0.981 1.000 0.000
#> GSM247663 1 0.0000 0.981 1.000 0.000
#> GSM247856 1 0.0000 0.981 1.000 0.000
#> GSM247857 1 0.0000 0.981 1.000 0.000
#> GSM247859 1 0.0000 0.981 1.000 0.000
#> GSM247860 1 0.0000 0.981 1.000 0.000
#> GSM247862 1 0.0000 0.981 1.000 0.000
#> GSM247864 1 0.0000 0.981 1.000 0.000
#> GSM247865 1 0.0000 0.981 1.000 0.000
#> GSM247866 1 0.0000 0.981 1.000 0.000
#> GSM247876 1 0.0000 0.981 1.000 0.000
#> GSM247877 1 0.0000 0.981 1.000 0.000
#> GSM247878 1 0.0000 0.981 1.000 0.000
#> GSM247879 1 0.0000 0.981 1.000 0.000
#> GSM247881 1 0.0000 0.981 1.000 0.000
#> GSM247883 1 0.0000 0.981 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 1.000 0.000 0.000 1
#> GSM246088 3 0.0000 1.000 0.000 0.000 1
#> GSM246089 3 0.0000 1.000 0.000 0.000 1
#> GSM246090 3 0.0000 1.000 0.000 0.000 1
#> GSM246119 3 0.0000 1.000 0.000 0.000 1
#> GSM246120 3 0.0000 1.000 0.000 0.000 1
#> GSM246121 3 0.0000 1.000 0.000 0.000 1
#> GSM246122 3 0.0000 1.000 0.000 0.000 1
#> GSM246123 3 0.0000 1.000 0.000 0.000 1
#> GSM246422 1 0.0000 1.000 1.000 0.000 0
#> GSM246423 1 0.0000 1.000 1.000 0.000 0
#> GSM246484 1 0.0000 1.000 1.000 0.000 0
#> GSM246485 2 0.0592 0.984 0.012 0.988 0
#> GSM246486 2 0.0000 0.999 0.000 1.000 0
#> GSM246487 1 0.0000 1.000 1.000 0.000 0
#> GSM246488 2 0.0000 0.999 0.000 1.000 0
#> GSM246489 2 0.0000 0.999 0.000 1.000 0
#> GSM246490 2 0.0000 0.999 0.000 1.000 0
#> GSM246491 2 0.0000 0.999 0.000 1.000 0
#> GSM247162 2 0.0000 0.999 0.000 1.000 0
#> GSM247163 2 0.0000 0.999 0.000 1.000 0
#> GSM247164 2 0.0000 0.999 0.000 1.000 0
#> GSM247165 2 0.0000 0.999 0.000 1.000 0
#> GSM247166 2 0.0000 0.999 0.000 1.000 0
#> GSM247168 2 0.0000 0.999 0.000 1.000 0
#> GSM247169 2 0.0000 0.999 0.000 1.000 0
#> GSM247171 2 0.0000 0.999 0.000 1.000 0
#> GSM247173 2 0.0000 0.999 0.000 1.000 0
#> GSM247174 2 0.0000 0.999 0.000 1.000 0
#> GSM247175 2 0.0000 0.999 0.000 1.000 0
#> GSM247188 2 0.0000 0.999 0.000 1.000 0
#> GSM247189 2 0.0237 0.994 0.004 0.996 0
#> GSM247190 2 0.0000 0.999 0.000 1.000 0
#> GSM247650 1 0.0000 1.000 1.000 0.000 0
#> GSM247651 1 0.0000 1.000 1.000 0.000 0
#> GSM247652 1 0.0000 1.000 1.000 0.000 0
#> GSM247653 1 0.0000 1.000 1.000 0.000 0
#> GSM247654 1 0.0000 1.000 1.000 0.000 0
#> GSM247655 1 0.0000 1.000 1.000 0.000 0
#> GSM247656 1 0.0000 1.000 1.000 0.000 0
#> GSM247657 1 0.0000 1.000 1.000 0.000 0
#> GSM247658 1 0.0000 1.000 1.000 0.000 0
#> GSM247659 1 0.0000 1.000 1.000 0.000 0
#> GSM247660 1 0.0000 1.000 1.000 0.000 0
#> GSM247661 1 0.0000 1.000 1.000 0.000 0
#> GSM247662 1 0.0000 1.000 1.000 0.000 0
#> GSM247663 1 0.0000 1.000 1.000 0.000 0
#> GSM247856 1 0.0000 1.000 1.000 0.000 0
#> GSM247857 1 0.0000 1.000 1.000 0.000 0
#> GSM247859 1 0.0000 1.000 1.000 0.000 0
#> GSM247860 1 0.0000 1.000 1.000 0.000 0
#> GSM247862 1 0.0000 1.000 1.000 0.000 0
#> GSM247864 1 0.0000 1.000 1.000 0.000 0
#> GSM247865 1 0.0000 1.000 1.000 0.000 0
#> GSM247866 1 0.0000 1.000 1.000 0.000 0
#> GSM247876 1 0.0000 1.000 1.000 0.000 0
#> GSM247877 1 0.0000 1.000 1.000 0.000 0
#> GSM247878 1 0.0000 1.000 1.000 0.000 0
#> GSM247879 1 0.0000 1.000 1.000 0.000 0
#> GSM247881 1 0.0000 1.000 1.000 0.000 0
#> GSM247883 1 0.0000 1.000 1.000 0.000 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246422 4 0.0000 0.863 0.000 0.000 0 1.000
#> GSM246423 4 0.0000 0.863 0.000 0.000 0 1.000
#> GSM246484 4 0.0000 0.863 0.000 0.000 0 1.000
#> GSM246485 2 0.0336 0.979 0.008 0.992 0 0.000
#> GSM246486 2 0.3569 0.758 0.000 0.804 0 0.196
#> GSM246487 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM246488 4 0.0000 0.863 0.000 0.000 0 1.000
#> GSM246489 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM246490 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM246491 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM247162 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM247163 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM247164 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM247165 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM247166 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM247168 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM247169 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM247171 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM247173 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM247174 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM247175 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM247188 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM247189 2 0.0188 0.984 0.004 0.996 0 0.000
#> GSM247190 2 0.0000 0.988 0.000 1.000 0 0.000
#> GSM247650 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247651 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247652 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247653 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247654 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247655 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247656 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247657 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247658 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247659 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247660 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247661 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247662 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247663 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247856 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247857 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247859 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247860 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247862 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247864 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247865 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247866 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247876 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247877 4 0.4679 0.443 0.352 0.000 0 0.648
#> GSM247878 1 0.4134 0.609 0.740 0.000 0 0.260
#> GSM247879 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247881 1 0.0000 0.989 1.000 0.000 0 0.000
#> GSM247883 1 0.0000 0.989 1.000 0.000 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000
#> GSM246088 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000
#> GSM246089 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000
#> GSM246090 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000
#> GSM246119 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000
#> GSM246120 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000
#> GSM246121 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000
#> GSM246122 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000
#> GSM246123 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000
#> GSM246422 4 0.0000 0.8766 0.000 0.000 0 1.000 0.000
#> GSM246423 4 0.0000 0.8766 0.000 0.000 0 1.000 0.000
#> GSM246484 4 0.0000 0.8766 0.000 0.000 0 1.000 0.000
#> GSM246485 2 0.0579 0.9731 0.008 0.984 0 0.000 0.008
#> GSM246486 2 0.3074 0.7545 0.000 0.804 0 0.196 0.000
#> GSM246487 1 0.0510 0.7607 0.984 0.000 0 0.000 0.016
#> GSM246488 4 0.0000 0.8766 0.000 0.000 0 1.000 0.000
#> GSM246489 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM246490 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM246491 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM247162 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM247163 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM247164 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM247165 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM247166 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM247168 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM247169 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM247171 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM247173 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM247174 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM247175 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM247188 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM247189 2 0.0162 0.9837 0.004 0.996 0 0.000 0.000
#> GSM247190 2 0.0000 0.9876 0.000 1.000 0 0.000 0.000
#> GSM247650 1 0.1270 0.7625 0.948 0.000 0 0.000 0.052
#> GSM247651 1 0.0510 0.7607 0.984 0.000 0 0.000 0.016
#> GSM247652 5 0.4030 0.4153 0.352 0.000 0 0.000 0.648
#> GSM247653 5 0.3508 0.5882 0.252 0.000 0 0.000 0.748
#> GSM247654 5 0.3074 0.6768 0.196 0.000 0 0.000 0.804
#> GSM247655 1 0.0290 0.7627 0.992 0.000 0 0.000 0.008
#> GSM247656 5 0.1121 0.7457 0.044 0.000 0 0.000 0.956
#> GSM247657 5 0.0609 0.7742 0.020 0.000 0 0.000 0.980
#> GSM247658 1 0.3003 0.6831 0.812 0.000 0 0.000 0.188
#> GSM247659 5 0.1270 0.7783 0.052 0.000 0 0.000 0.948
#> GSM247660 1 0.1121 0.7644 0.956 0.000 0 0.000 0.044
#> GSM247661 5 0.3876 0.4514 0.316 0.000 0 0.000 0.684
#> GSM247662 5 0.2471 0.7315 0.136 0.000 0 0.000 0.864
#> GSM247663 1 0.1608 0.7596 0.928 0.000 0 0.000 0.072
#> GSM247856 1 0.4192 0.4219 0.596 0.000 0 0.000 0.404
#> GSM247857 5 0.1270 0.7783 0.052 0.000 0 0.000 0.948
#> GSM247859 1 0.3876 0.5470 0.684 0.000 0 0.000 0.316
#> GSM247860 1 0.4201 0.0758 0.592 0.000 0 0.000 0.408
#> GSM247862 1 0.1121 0.7644 0.956 0.000 0 0.000 0.044
#> GSM247864 1 0.1121 0.7644 0.956 0.000 0 0.000 0.044
#> GSM247865 1 0.3876 0.5470 0.684 0.000 0 0.000 0.316
#> GSM247866 1 0.1121 0.7644 0.956 0.000 0 0.000 0.044
#> GSM247876 1 0.3999 0.5520 0.656 0.000 0 0.000 0.344
#> GSM247877 4 0.4101 0.3464 0.372 0.000 0 0.628 0.000
#> GSM247878 1 0.1908 0.7255 0.908 0.000 0 0.092 0.000
#> GSM247879 1 0.1908 0.7320 0.908 0.000 0 0.000 0.092
#> GSM247881 1 0.3913 0.5681 0.676 0.000 0 0.000 0.324
#> GSM247883 1 0.4182 0.4193 0.600 0.000 0 0.000 0.400
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.1387 0.9211 0.000 0.000 0.932 0.000 0.000 0.068
#> GSM246088 3 0.1387 0.9211 0.000 0.000 0.932 0.000 0.000 0.068
#> GSM246089 3 0.3789 0.5625 0.000 0.000 0.584 0.000 0.000 0.416
#> GSM246090 3 0.1387 0.9211 0.000 0.000 0.932 0.000 0.000 0.068
#> GSM246119 3 0.0458 0.9203 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM246120 3 0.0458 0.9203 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM246121 3 0.0000 0.9220 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246122 3 0.1387 0.9211 0.000 0.000 0.932 0.000 0.000 0.068
#> GSM246123 3 0.0458 0.9203 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM246422 4 0.0000 0.8655 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM246423 4 0.0000 0.8655 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM246484 4 0.0000 0.8655 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM246485 2 0.0520 0.9731 0.008 0.984 0.000 0.000 0.008 0.000
#> GSM246486 2 0.2762 0.7551 0.000 0.804 0.000 0.196 0.000 0.000
#> GSM246487 1 0.0000 0.6817 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM246488 4 0.0000 0.8655 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM246489 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246490 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246491 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247162 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247163 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247164 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247165 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247166 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247168 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247169 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247171 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247174 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247175 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247189 2 0.0146 0.9837 0.004 0.996 0.000 0.000 0.000 0.000
#> GSM247190 2 0.0000 0.9876 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247650 1 0.1267 0.6813 0.940 0.000 0.000 0.000 0.060 0.000
#> GSM247651 1 0.0000 0.6817 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247652 1 0.5731 0.0598 0.516 0.000 0.000 0.000 0.260 0.224
#> GSM247653 6 0.5634 0.7787 0.164 0.000 0.000 0.000 0.336 0.500
#> GSM247654 6 0.5486 0.7559 0.132 0.000 0.000 0.000 0.372 0.496
#> GSM247655 1 0.0260 0.6834 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM247656 5 0.4291 -0.0128 0.052 0.000 0.000 0.000 0.680 0.268
#> GSM247657 5 0.0260 0.6971 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM247658 1 0.4582 0.4210 0.684 0.000 0.000 0.000 0.100 0.216
#> GSM247659 5 0.0146 0.7005 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM247660 1 0.1219 0.6833 0.948 0.000 0.000 0.000 0.048 0.004
#> GSM247661 5 0.5461 0.2169 0.248 0.000 0.000 0.000 0.568 0.184
#> GSM247662 5 0.1444 0.6483 0.072 0.000 0.000 0.000 0.928 0.000
#> GSM247663 1 0.3651 0.5508 0.772 0.000 0.000 0.000 0.048 0.180
#> GSM247856 1 0.5520 0.1184 0.532 0.000 0.000 0.000 0.312 0.156
#> GSM247857 5 0.0146 0.7005 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM247859 1 0.4181 0.4496 0.700 0.000 0.000 0.000 0.248 0.052
#> GSM247860 1 0.5190 -0.1859 0.464 0.000 0.000 0.000 0.088 0.448
#> GSM247862 1 0.1219 0.6833 0.948 0.000 0.000 0.000 0.048 0.004
#> GSM247864 1 0.1219 0.6833 0.948 0.000 0.000 0.000 0.048 0.004
#> GSM247865 1 0.4181 0.4496 0.700 0.000 0.000 0.000 0.248 0.052
#> GSM247866 1 0.1219 0.6833 0.948 0.000 0.000 0.000 0.048 0.004
#> GSM247876 1 0.4481 0.4582 0.648 0.000 0.000 0.000 0.296 0.056
#> GSM247877 4 0.4099 0.3451 0.372 0.000 0.000 0.612 0.000 0.016
#> GSM247878 1 0.1610 0.6534 0.916 0.000 0.000 0.084 0.000 0.000
#> GSM247879 1 0.2581 0.6099 0.856 0.000 0.000 0.000 0.128 0.016
#> GSM247881 1 0.4809 0.4111 0.652 0.000 0.000 0.000 0.240 0.108
#> GSM247883 1 0.5610 0.1153 0.536 0.000 0.000 0.000 0.272 0.192
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:pam 61 1.09e-10 2
#> SD:pam 61 6.70e-22 3
#> SD:pam 60 1.47e-22 4
#> SD:pam 55 3.18e-19 5
#> SD:pam 49 1.15e-15 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 21168 rows and 61 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 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 0.272 0.658 0.799 0.4568 0.493 0.493
#> 3 3 0.840 0.889 0.950 0.4347 0.727 0.511
#> 4 4 0.898 0.857 0.944 0.1089 0.889 0.699
#> 5 5 0.738 0.759 0.806 0.0552 1.000 1.000
#> 6 6 0.783 0.836 0.876 0.0578 0.889 0.611
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
#> GSM246087 2 0.6623 0.584 0.172 0.828
#> GSM246088 2 0.6623 0.584 0.172 0.828
#> GSM246089 2 0.6623 0.584 0.172 0.828
#> GSM246090 2 0.6623 0.584 0.172 0.828
#> GSM246119 2 0.6623 0.584 0.172 0.828
#> GSM246120 2 0.6623 0.584 0.172 0.828
#> GSM246121 2 0.6623 0.584 0.172 0.828
#> GSM246122 2 0.6623 0.584 0.172 0.828
#> GSM246123 2 0.6623 0.584 0.172 0.828
#> GSM246422 2 0.7453 0.499 0.212 0.788
#> GSM246423 2 0.7453 0.499 0.212 0.788
#> GSM246484 2 0.7453 0.499 0.212 0.788
#> GSM246485 1 0.9944 -0.144 0.544 0.456
#> GSM246486 1 0.9944 -0.144 0.544 0.456
#> GSM246487 1 0.8327 0.496 0.736 0.264
#> GSM246488 1 0.9944 -0.144 0.544 0.456
#> GSM246489 2 0.9170 0.630 0.332 0.668
#> GSM246490 2 0.9170 0.630 0.332 0.668
#> GSM246491 2 0.9170 0.630 0.332 0.668
#> GSM247162 2 0.9170 0.630 0.332 0.668
#> GSM247163 2 0.9170 0.630 0.332 0.668
#> GSM247164 2 0.9170 0.630 0.332 0.668
#> GSM247165 2 0.9170 0.630 0.332 0.668
#> GSM247166 2 0.9170 0.630 0.332 0.668
#> GSM247168 2 0.9170 0.630 0.332 0.668
#> GSM247169 2 0.9170 0.630 0.332 0.668
#> GSM247171 2 0.9170 0.630 0.332 0.668
#> GSM247173 2 0.9170 0.630 0.332 0.668
#> GSM247174 2 0.9170 0.630 0.332 0.668
#> GSM247175 2 0.9170 0.630 0.332 0.668
#> GSM247188 2 0.9170 0.630 0.332 0.668
#> GSM247189 2 0.9635 0.537 0.388 0.612
#> GSM247190 2 0.9170 0.630 0.332 0.668
#> GSM247650 1 0.0376 0.883 0.996 0.004
#> GSM247651 1 0.0000 0.886 1.000 0.000
#> GSM247652 1 0.0000 0.886 1.000 0.000
#> GSM247653 1 0.0000 0.886 1.000 0.000
#> GSM247654 1 0.0000 0.886 1.000 0.000
#> GSM247655 1 0.0000 0.886 1.000 0.000
#> GSM247656 1 0.0938 0.874 0.988 0.012
#> GSM247657 1 0.0000 0.886 1.000 0.000
#> GSM247658 1 0.0000 0.886 1.000 0.000
#> GSM247659 1 0.5737 0.723 0.864 0.136
#> GSM247660 1 0.0000 0.886 1.000 0.000
#> GSM247661 1 0.0000 0.886 1.000 0.000
#> GSM247662 1 0.0672 0.878 0.992 0.008
#> GSM247663 1 0.0376 0.883 0.996 0.004
#> GSM247856 1 0.0376 0.883 0.996 0.004
#> GSM247857 1 0.0000 0.886 1.000 0.000
#> GSM247859 1 0.0000 0.886 1.000 0.000
#> GSM247860 1 0.0000 0.886 1.000 0.000
#> GSM247862 1 0.0000 0.886 1.000 0.000
#> GSM247864 1 0.0000 0.886 1.000 0.000
#> GSM247865 1 0.5842 0.701 0.860 0.140
#> GSM247866 1 0.0000 0.886 1.000 0.000
#> GSM247876 1 0.4161 0.784 0.916 0.084
#> GSM247877 2 0.9358 0.376 0.352 0.648
#> GSM247878 2 0.9170 0.399 0.332 0.668
#> GSM247879 2 0.9608 0.330 0.384 0.616
#> GSM247881 1 0.0000 0.886 1.000 0.000
#> GSM247883 1 0.2948 0.829 0.948 0.052
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 0.947 0.000 0.000 1.000
#> GSM246088 3 0.0000 0.947 0.000 0.000 1.000
#> GSM246089 3 0.0000 0.947 0.000 0.000 1.000
#> GSM246090 3 0.0000 0.947 0.000 0.000 1.000
#> GSM246119 3 0.0000 0.947 0.000 0.000 1.000
#> GSM246120 3 0.0000 0.947 0.000 0.000 1.000
#> GSM246121 3 0.0000 0.947 0.000 0.000 1.000
#> GSM246122 3 0.0000 0.947 0.000 0.000 1.000
#> GSM246123 3 0.0000 0.947 0.000 0.000 1.000
#> GSM246422 3 0.4346 0.785 0.000 0.184 0.816
#> GSM246423 3 0.4346 0.785 0.000 0.184 0.816
#> GSM246484 3 0.4346 0.785 0.000 0.184 0.816
#> GSM246485 2 0.4750 0.752 0.000 0.784 0.216
#> GSM246486 2 0.4504 0.775 0.000 0.804 0.196
#> GSM246487 2 0.4750 0.752 0.000 0.784 0.216
#> GSM246488 2 0.4654 0.762 0.000 0.792 0.208
#> GSM246489 2 0.0000 0.933 0.000 1.000 0.000
#> GSM246490 2 0.0000 0.933 0.000 1.000 0.000
#> GSM246491 2 0.1163 0.919 0.000 0.972 0.028
#> GSM247162 2 0.0000 0.933 0.000 1.000 0.000
#> GSM247163 2 0.1289 0.916 0.000 0.968 0.032
#> GSM247164 2 0.0000 0.933 0.000 1.000 0.000
#> GSM247165 2 0.0000 0.933 0.000 1.000 0.000
#> GSM247166 2 0.0000 0.933 0.000 1.000 0.000
#> GSM247168 2 0.0000 0.933 0.000 1.000 0.000
#> GSM247169 2 0.0000 0.933 0.000 1.000 0.000
#> GSM247171 2 0.0000 0.933 0.000 1.000 0.000
#> GSM247173 2 0.0000 0.933 0.000 1.000 0.000
#> GSM247174 2 0.0000 0.933 0.000 1.000 0.000
#> GSM247175 2 0.0000 0.933 0.000 1.000 0.000
#> GSM247188 2 0.0000 0.933 0.000 1.000 0.000
#> GSM247189 2 0.5216 0.681 0.000 0.740 0.260
#> GSM247190 2 0.0000 0.933 0.000 1.000 0.000
#> GSM247650 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247651 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247652 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247653 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247654 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247655 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247656 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247657 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247658 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247659 1 0.5706 0.557 0.680 0.000 0.320
#> GSM247660 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247661 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247662 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247663 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247856 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247857 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247859 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247860 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247862 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247864 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247865 1 0.1950 0.908 0.952 0.008 0.040
#> GSM247866 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247876 1 0.4605 0.732 0.796 0.000 0.204
#> GSM247877 3 0.0000 0.947 0.000 0.000 1.000
#> GSM247878 1 0.5650 0.571 0.688 0.000 0.312
#> GSM247879 1 0.6295 0.212 0.528 0.000 0.472
#> GSM247881 1 0.0000 0.945 1.000 0.000 0.000
#> GSM247883 1 0.0237 0.942 0.996 0.004 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 1.00000 0.000 0.000 1 0.000
#> GSM246088 3 0.0000 1.00000 0.000 0.000 1 0.000
#> GSM246089 3 0.0000 1.00000 0.000 0.000 1 0.000
#> GSM246090 3 0.0000 1.00000 0.000 0.000 1 0.000
#> GSM246119 3 0.0000 1.00000 0.000 0.000 1 0.000
#> GSM246120 3 0.0000 1.00000 0.000 0.000 1 0.000
#> GSM246121 3 0.0000 1.00000 0.000 0.000 1 0.000
#> GSM246122 3 0.0000 1.00000 0.000 0.000 1 0.000
#> GSM246123 3 0.0000 1.00000 0.000 0.000 1 0.000
#> GSM246422 4 0.0000 0.90435 0.000 0.000 0 1.000
#> GSM246423 4 0.0000 0.90435 0.000 0.000 0 1.000
#> GSM246484 4 0.0000 0.90435 0.000 0.000 0 1.000
#> GSM246485 4 0.1940 0.89810 0.000 0.076 0 0.924
#> GSM246486 4 0.1940 0.89810 0.000 0.076 0 0.924
#> GSM246487 4 0.1940 0.89810 0.000 0.076 0 0.924
#> GSM246488 4 0.1940 0.89810 0.000 0.076 0 0.924
#> GSM246489 2 0.0000 0.89358 0.000 1.000 0 0.000
#> GSM246490 2 0.0000 0.89358 0.000 1.000 0 0.000
#> GSM246491 2 0.4661 0.43616 0.000 0.652 0 0.348
#> GSM247162 2 0.0000 0.89358 0.000 1.000 0 0.000
#> GSM247163 2 0.4999 -0.00421 0.000 0.508 0 0.492
#> GSM247164 2 0.4304 0.59072 0.000 0.716 0 0.284
#> GSM247165 2 0.4304 0.59072 0.000 0.716 0 0.284
#> GSM247166 2 0.0000 0.89358 0.000 1.000 0 0.000
#> GSM247168 2 0.0000 0.89358 0.000 1.000 0 0.000
#> GSM247169 2 0.0000 0.89358 0.000 1.000 0 0.000
#> GSM247171 2 0.0000 0.89358 0.000 1.000 0 0.000
#> GSM247173 2 0.0000 0.89358 0.000 1.000 0 0.000
#> GSM247174 2 0.0000 0.89358 0.000 1.000 0 0.000
#> GSM247175 2 0.0000 0.89358 0.000 1.000 0 0.000
#> GSM247188 2 0.0000 0.89358 0.000 1.000 0 0.000
#> GSM247189 4 0.1940 0.89810 0.000 0.076 0 0.924
#> GSM247190 2 0.0000 0.89358 0.000 1.000 0 0.000
#> GSM247650 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247651 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247652 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247653 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247654 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247655 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247656 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247657 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247658 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247659 1 0.4985 0.06186 0.532 0.000 0 0.468
#> GSM247660 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247661 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247662 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247663 1 0.0188 0.93651 0.996 0.000 0 0.004
#> GSM247856 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247857 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247859 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247860 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247862 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247864 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247865 1 0.4624 0.47944 0.660 0.000 0 0.340
#> GSM247866 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247876 1 0.3486 0.73098 0.812 0.000 0 0.188
#> GSM247877 4 0.0188 0.90351 0.004 0.000 0 0.996
#> GSM247878 4 0.0188 0.90351 0.004 0.000 0 0.996
#> GSM247879 4 0.4643 0.40698 0.344 0.000 0 0.656
#> GSM247881 1 0.0000 0.93973 1.000 0.000 0 0.000
#> GSM247883 1 0.4431 0.54541 0.696 0.000 0 0.304
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 1.000 0.000 0.000 1 0.000 NA
#> GSM246088 3 0.0000 1.000 0.000 0.000 1 0.000 NA
#> GSM246089 3 0.0000 1.000 0.000 0.000 1 0.000 NA
#> GSM246090 3 0.0000 1.000 0.000 0.000 1 0.000 NA
#> GSM246119 3 0.0000 1.000 0.000 0.000 1 0.000 NA
#> GSM246120 3 0.0000 1.000 0.000 0.000 1 0.000 NA
#> GSM246121 3 0.0000 1.000 0.000 0.000 1 0.000 NA
#> GSM246122 3 0.0000 1.000 0.000 0.000 1 0.000 NA
#> GSM246123 3 0.0000 1.000 0.000 0.000 1 0.000 NA
#> GSM246422 4 0.4210 0.655 0.000 0.000 0 0.588 NA
#> GSM246423 4 0.4210 0.655 0.000 0.000 0 0.588 NA
#> GSM246484 4 0.4210 0.655 0.000 0.000 0 0.588 NA
#> GSM246485 4 0.6770 0.440 0.132 0.104 0 0.612 NA
#> GSM246486 4 0.3424 0.409 0.000 0.240 0 0.760 NA
#> GSM246487 4 0.6280 0.361 0.164 0.004 0 0.540 NA
#> GSM246488 4 0.3395 0.416 0.000 0.236 0 0.764 NA
#> GSM246489 2 0.0000 0.913 0.000 1.000 0 0.000 NA
#> GSM246490 2 0.0609 0.901 0.000 0.980 0 0.020 NA
#> GSM246491 2 0.4812 0.415 0.000 0.600 0 0.372 NA
#> GSM247162 2 0.0000 0.913 0.000 1.000 0 0.000 NA
#> GSM247163 2 0.4824 0.405 0.000 0.596 0 0.376 NA
#> GSM247164 2 0.2813 0.782 0.000 0.832 0 0.168 NA
#> GSM247165 2 0.2813 0.782 0.000 0.832 0 0.168 NA
#> GSM247166 2 0.0000 0.913 0.000 1.000 0 0.000 NA
#> GSM247168 2 0.0000 0.913 0.000 1.000 0 0.000 NA
#> GSM247169 2 0.0000 0.913 0.000 1.000 0 0.000 NA
#> GSM247171 2 0.0000 0.913 0.000 1.000 0 0.000 NA
#> GSM247173 2 0.0000 0.913 0.000 1.000 0 0.000 NA
#> GSM247174 2 0.0000 0.913 0.000 1.000 0 0.000 NA
#> GSM247175 2 0.0000 0.913 0.000 1.000 0 0.000 NA
#> GSM247188 2 0.0000 0.913 0.000 1.000 0 0.000 NA
#> GSM247189 4 0.3395 0.416 0.000 0.236 0 0.764 NA
#> GSM247190 2 0.0000 0.913 0.000 1.000 0 0.000 NA
#> GSM247650 1 0.3636 0.740 0.728 0.000 0 0.000 NA
#> GSM247651 1 0.1357 0.806 0.948 0.000 0 0.004 NA
#> GSM247652 1 0.0609 0.802 0.980 0.000 0 0.000 NA
#> GSM247653 1 0.3730 0.658 0.712 0.000 0 0.000 NA
#> GSM247654 1 0.3242 0.707 0.784 0.000 0 0.000 NA
#> GSM247655 1 0.1205 0.804 0.956 0.000 0 0.004 NA
#> GSM247656 1 0.3837 0.755 0.692 0.000 0 0.000 NA
#> GSM247657 1 0.3039 0.718 0.808 0.000 0 0.000 NA
#> GSM247658 1 0.0671 0.802 0.980 0.000 0 0.004 NA
#> GSM247659 1 0.6076 0.508 0.536 0.000 0 0.144 NA
#> GSM247660 1 0.1357 0.806 0.948 0.000 0 0.004 NA
#> GSM247661 1 0.3730 0.658 0.712 0.000 0 0.000 NA
#> GSM247662 1 0.3210 0.777 0.788 0.000 0 0.000 NA
#> GSM247663 1 0.3636 0.740 0.728 0.000 0 0.000 NA
#> GSM247856 1 0.3039 0.776 0.808 0.000 0 0.000 NA
#> GSM247857 1 0.2020 0.804 0.900 0.000 0 0.000 NA
#> GSM247859 1 0.4563 0.727 0.708 0.000 0 0.048 NA
#> GSM247860 1 0.3730 0.658 0.712 0.000 0 0.000 NA
#> GSM247862 1 0.0865 0.802 0.972 0.000 0 0.004 NA
#> GSM247864 1 0.1357 0.806 0.948 0.000 0 0.004 NA
#> GSM247865 1 0.6155 0.517 0.556 0.000 0 0.192 NA
#> GSM247866 1 0.0955 0.802 0.968 0.000 0 0.004 NA
#> GSM247876 1 0.5213 0.675 0.640 0.000 0 0.076 NA
#> GSM247877 4 0.4249 0.650 0.000 0.000 0 0.568 NA
#> GSM247878 4 0.4397 0.649 0.004 0.000 0 0.564 NA
#> GSM247879 4 0.6674 0.457 0.248 0.000 0 0.428 NA
#> GSM247881 1 0.2439 0.796 0.876 0.000 0 0.004 NA
#> GSM247883 1 0.5763 0.585 0.620 0.000 0 0.192 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0363 0.948 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM246088 3 0.0363 0.948 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM246089 3 0.1957 0.937 0.000 0.000 0.888 0.112 0.000 0.000
#> GSM246090 3 0.0363 0.948 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM246119 3 0.1957 0.937 0.000 0.000 0.888 0.112 0.000 0.000
#> GSM246120 3 0.1957 0.937 0.000 0.000 0.888 0.112 0.000 0.000
#> GSM246121 3 0.0000 0.948 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246122 3 0.0363 0.948 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM246123 3 0.1957 0.937 0.000 0.000 0.888 0.112 0.000 0.000
#> GSM246422 5 0.1075 0.966 0.000 0.000 0.000 0.048 0.952 0.000
#> GSM246423 5 0.1075 0.966 0.000 0.000 0.000 0.048 0.952 0.000
#> GSM246484 5 0.1075 0.966 0.000 0.000 0.000 0.048 0.952 0.000
#> GSM246485 4 0.3001 0.927 0.008 0.024 0.000 0.840 0.128 0.000
#> GSM246486 4 0.2389 0.943 0.000 0.008 0.000 0.864 0.128 0.000
#> GSM246487 4 0.4820 0.823 0.100 0.020 0.000 0.724 0.148 0.008
#> GSM246488 4 0.2278 0.943 0.000 0.004 0.000 0.868 0.128 0.000
#> GSM246489 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246490 2 0.1765 0.880 0.000 0.904 0.000 0.096 0.000 0.000
#> GSM246491 2 0.3777 0.718 0.004 0.788 0.000 0.084 0.124 0.000
#> GSM247162 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247163 2 0.4742 0.605 0.004 0.688 0.000 0.184 0.124 0.000
#> GSM247164 2 0.2260 0.851 0.000 0.860 0.000 0.140 0.000 0.000
#> GSM247165 2 0.2300 0.847 0.000 0.856 0.000 0.144 0.000 0.000
#> GSM247166 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247168 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247169 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247171 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247174 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247175 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247189 4 0.2278 0.943 0.000 0.004 0.000 0.868 0.128 0.000
#> GSM247190 2 0.0000 0.936 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247650 1 0.2520 0.713 0.844 0.000 0.000 0.004 0.000 0.152
#> GSM247651 1 0.2003 0.814 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM247652 6 0.3309 0.752 0.280 0.000 0.000 0.000 0.000 0.720
#> GSM247653 6 0.1007 0.781 0.044 0.000 0.000 0.000 0.000 0.956
#> GSM247654 6 0.1957 0.801 0.112 0.000 0.000 0.000 0.000 0.888
#> GSM247655 1 0.2092 0.812 0.876 0.000 0.000 0.000 0.000 0.124
#> GSM247656 6 0.2362 0.790 0.136 0.000 0.000 0.004 0.000 0.860
#> GSM247657 6 0.2378 0.800 0.152 0.000 0.000 0.000 0.000 0.848
#> GSM247658 6 0.3266 0.762 0.272 0.000 0.000 0.000 0.000 0.728
#> GSM247659 6 0.5193 0.606 0.200 0.000 0.000 0.004 0.164 0.632
#> GSM247660 1 0.2003 0.814 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM247661 6 0.0547 0.771 0.020 0.000 0.000 0.000 0.000 0.980
#> GSM247662 6 0.3508 0.743 0.292 0.000 0.000 0.004 0.000 0.704
#> GSM247663 1 0.1908 0.758 0.900 0.000 0.000 0.004 0.000 0.096
#> GSM247856 6 0.3547 0.733 0.300 0.000 0.000 0.004 0.000 0.696
#> GSM247857 6 0.3151 0.780 0.252 0.000 0.000 0.000 0.000 0.748
#> GSM247859 1 0.0865 0.806 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM247860 6 0.0865 0.773 0.036 0.000 0.000 0.000 0.000 0.964
#> GSM247862 1 0.2416 0.794 0.844 0.000 0.000 0.000 0.000 0.156
#> GSM247864 1 0.2003 0.814 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM247865 1 0.1346 0.797 0.952 0.000 0.000 0.016 0.008 0.024
#> GSM247866 1 0.2135 0.810 0.872 0.000 0.000 0.000 0.000 0.128
#> GSM247876 1 0.4153 0.629 0.752 0.000 0.000 0.004 0.148 0.096
#> GSM247877 5 0.0000 0.951 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM247878 5 0.0000 0.951 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM247879 1 0.4751 0.530 0.624 0.000 0.000 0.000 0.300 0.076
#> GSM247881 1 0.3851 -0.079 0.540 0.000 0.000 0.000 0.000 0.460
#> GSM247883 1 0.1700 0.806 0.928 0.000 0.000 0.024 0.000 0.048
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:mclust 51 8.42e-12 2
#> SD:mclust 60 2.13e-19 3
#> SD:mclust 56 3.11e-20 4
#> SD:mclust 53 2.63e-19 5
#> SD:mclust 60 7.11e-20 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 21168 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.806 0.892 0.956 0.4996 0.498 0.498
#> 3 3 0.845 0.874 0.947 0.3189 0.697 0.466
#> 4 4 0.912 0.885 0.954 0.0900 0.816 0.543
#> 5 5 0.727 0.706 0.850 0.0625 0.979 0.929
#> 6 6 0.748 0.634 0.784 0.0481 0.951 0.830
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
#> GSM246087 1 0.0000 0.94094 1.000 0.000
#> GSM246088 1 0.0000 0.94094 1.000 0.000
#> GSM246089 1 0.0000 0.94094 1.000 0.000
#> GSM246090 1 0.0000 0.94094 1.000 0.000
#> GSM246119 1 0.0000 0.94094 1.000 0.000
#> GSM246120 1 0.0000 0.94094 1.000 0.000
#> GSM246121 1 0.0000 0.94094 1.000 0.000
#> GSM246122 1 0.0000 0.94094 1.000 0.000
#> GSM246123 1 0.0000 0.94094 1.000 0.000
#> GSM246422 2 0.0376 0.96136 0.004 0.996
#> GSM246423 2 0.3274 0.91007 0.060 0.940
#> GSM246484 2 0.0000 0.96448 0.000 1.000
#> GSM246485 2 0.0000 0.96448 0.000 1.000
#> GSM246486 2 0.0000 0.96448 0.000 1.000
#> GSM246487 2 0.0000 0.96448 0.000 1.000
#> GSM246488 2 0.0000 0.96448 0.000 1.000
#> GSM246489 2 0.0000 0.96448 0.000 1.000
#> GSM246490 2 0.0000 0.96448 0.000 1.000
#> GSM246491 2 0.0000 0.96448 0.000 1.000
#> GSM247162 2 0.0000 0.96448 0.000 1.000
#> GSM247163 2 0.0000 0.96448 0.000 1.000
#> GSM247164 2 0.0000 0.96448 0.000 1.000
#> GSM247165 2 0.0000 0.96448 0.000 1.000
#> GSM247166 2 0.0000 0.96448 0.000 1.000
#> GSM247168 2 0.0000 0.96448 0.000 1.000
#> GSM247169 2 0.0000 0.96448 0.000 1.000
#> GSM247171 2 0.0000 0.96448 0.000 1.000
#> GSM247173 2 0.0000 0.96448 0.000 1.000
#> GSM247174 2 0.0000 0.96448 0.000 1.000
#> GSM247175 2 0.0000 0.96448 0.000 1.000
#> GSM247188 2 0.0000 0.96448 0.000 1.000
#> GSM247189 2 0.0000 0.96448 0.000 1.000
#> GSM247190 2 0.0000 0.96448 0.000 1.000
#> GSM247650 1 0.0000 0.94094 1.000 0.000
#> GSM247651 2 0.9977 0.00698 0.472 0.528
#> GSM247652 1 0.0000 0.94094 1.000 0.000
#> GSM247653 1 0.0000 0.94094 1.000 0.000
#> GSM247654 1 0.0000 0.94094 1.000 0.000
#> GSM247655 1 0.6247 0.81369 0.844 0.156
#> GSM247656 1 0.0000 0.94094 1.000 0.000
#> GSM247657 1 0.0000 0.94094 1.000 0.000
#> GSM247658 1 0.0938 0.93484 0.988 0.012
#> GSM247659 1 0.0000 0.94094 1.000 0.000
#> GSM247660 1 0.9996 0.09283 0.512 0.488
#> GSM247661 1 0.0000 0.94094 1.000 0.000
#> GSM247662 1 0.0000 0.94094 1.000 0.000
#> GSM247663 1 0.0000 0.94094 1.000 0.000
#> GSM247856 1 0.0000 0.94094 1.000 0.000
#> GSM247857 1 0.0000 0.94094 1.000 0.000
#> GSM247859 1 0.9815 0.31846 0.580 0.420
#> GSM247860 1 0.0376 0.93899 0.996 0.004
#> GSM247862 1 0.4562 0.87289 0.904 0.096
#> GSM247864 1 0.2043 0.92239 0.968 0.032
#> GSM247865 2 0.5946 0.81328 0.144 0.856
#> GSM247866 1 0.8713 0.61221 0.708 0.292
#> GSM247876 1 0.0000 0.94094 1.000 0.000
#> GSM247877 1 0.2603 0.91423 0.956 0.044
#> GSM247878 1 0.6343 0.80915 0.840 0.160
#> GSM247879 1 0.0000 0.94094 1.000 0.000
#> GSM247881 1 0.5946 0.82686 0.856 0.144
#> GSM247883 2 0.6247 0.79680 0.156 0.844
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 0.906 0.000 0.000 1.000
#> GSM246088 3 0.0000 0.906 0.000 0.000 1.000
#> GSM246089 3 0.0000 0.906 0.000 0.000 1.000
#> GSM246090 3 0.0000 0.906 0.000 0.000 1.000
#> GSM246119 3 0.0000 0.906 0.000 0.000 1.000
#> GSM246120 3 0.0000 0.906 0.000 0.000 1.000
#> GSM246121 3 0.0000 0.906 0.000 0.000 1.000
#> GSM246122 3 0.0000 0.906 0.000 0.000 1.000
#> GSM246123 3 0.0000 0.906 0.000 0.000 1.000
#> GSM246422 1 0.0000 0.948 1.000 0.000 0.000
#> GSM246423 1 0.0000 0.948 1.000 0.000 0.000
#> GSM246484 1 0.0000 0.948 1.000 0.000 0.000
#> GSM246485 2 0.2448 0.889 0.076 0.924 0.000
#> GSM246486 2 0.5678 0.569 0.316 0.684 0.000
#> GSM246487 1 0.1031 0.926 0.976 0.024 0.000
#> GSM246488 2 0.6095 0.410 0.392 0.608 0.000
#> GSM246489 2 0.0000 0.951 0.000 1.000 0.000
#> GSM246490 2 0.0000 0.951 0.000 1.000 0.000
#> GSM246491 2 0.0000 0.951 0.000 1.000 0.000
#> GSM247162 2 0.0000 0.951 0.000 1.000 0.000
#> GSM247163 2 0.0000 0.951 0.000 1.000 0.000
#> GSM247164 2 0.0000 0.951 0.000 1.000 0.000
#> GSM247165 2 0.0000 0.951 0.000 1.000 0.000
#> GSM247166 2 0.0000 0.951 0.000 1.000 0.000
#> GSM247168 2 0.0000 0.951 0.000 1.000 0.000
#> GSM247169 2 0.0000 0.951 0.000 1.000 0.000
#> GSM247171 2 0.0000 0.951 0.000 1.000 0.000
#> GSM247173 2 0.0000 0.951 0.000 1.000 0.000
#> GSM247174 2 0.0000 0.951 0.000 1.000 0.000
#> GSM247175 2 0.0000 0.951 0.000 1.000 0.000
#> GSM247188 2 0.0000 0.951 0.000 1.000 0.000
#> GSM247189 2 0.1643 0.916 0.044 0.956 0.000
#> GSM247190 2 0.0000 0.951 0.000 1.000 0.000
#> GSM247650 1 0.5216 0.629 0.740 0.000 0.260
#> GSM247651 1 0.0000 0.948 1.000 0.000 0.000
#> GSM247652 1 0.2448 0.884 0.924 0.000 0.076
#> GSM247653 3 0.6274 0.201 0.456 0.000 0.544
#> GSM247654 1 0.6079 0.310 0.612 0.000 0.388
#> GSM247655 1 0.0000 0.948 1.000 0.000 0.000
#> GSM247656 3 0.2959 0.848 0.100 0.000 0.900
#> GSM247657 3 0.5138 0.681 0.252 0.000 0.748
#> GSM247658 1 0.0000 0.948 1.000 0.000 0.000
#> GSM247659 3 0.0000 0.906 0.000 0.000 1.000
#> GSM247660 1 0.0000 0.948 1.000 0.000 0.000
#> GSM247661 3 0.3752 0.810 0.144 0.000 0.856
#> GSM247662 3 0.1411 0.890 0.036 0.000 0.964
#> GSM247663 1 0.2066 0.900 0.940 0.000 0.060
#> GSM247856 1 0.5178 0.634 0.744 0.000 0.256
#> GSM247857 3 0.5650 0.575 0.312 0.000 0.688
#> GSM247859 1 0.0000 0.948 1.000 0.000 0.000
#> GSM247860 1 0.0000 0.948 1.000 0.000 0.000
#> GSM247862 1 0.0000 0.948 1.000 0.000 0.000
#> GSM247864 1 0.0000 0.948 1.000 0.000 0.000
#> GSM247865 1 0.0000 0.948 1.000 0.000 0.000
#> GSM247866 1 0.0000 0.948 1.000 0.000 0.000
#> GSM247876 1 0.0000 0.948 1.000 0.000 0.000
#> GSM247877 1 0.0000 0.948 1.000 0.000 0.000
#> GSM247878 1 0.0000 0.948 1.000 0.000 0.000
#> GSM247879 1 0.0892 0.934 0.980 0.000 0.020
#> GSM247881 1 0.0000 0.948 1.000 0.000 0.000
#> GSM247883 1 0.0000 0.948 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 0.9618 0.000 0.000 1.000 0.000
#> GSM246088 3 0.0000 0.9618 0.000 0.000 1.000 0.000
#> GSM246089 3 0.0000 0.9618 0.000 0.000 1.000 0.000
#> GSM246090 3 0.0000 0.9618 0.000 0.000 1.000 0.000
#> GSM246119 3 0.0000 0.9618 0.000 0.000 1.000 0.000
#> GSM246120 3 0.0000 0.9618 0.000 0.000 1.000 0.000
#> GSM246121 3 0.0000 0.9618 0.000 0.000 1.000 0.000
#> GSM246122 3 0.0000 0.9618 0.000 0.000 1.000 0.000
#> GSM246123 3 0.0000 0.9618 0.000 0.000 1.000 0.000
#> GSM246422 4 0.0000 0.8757 0.000 0.000 0.000 1.000
#> GSM246423 4 0.0000 0.8757 0.000 0.000 0.000 1.000
#> GSM246484 4 0.0000 0.8757 0.000 0.000 0.000 1.000
#> GSM246485 2 0.0188 0.9695 0.000 0.996 0.000 0.004
#> GSM246486 2 0.4817 0.2418 0.000 0.612 0.000 0.388
#> GSM246487 1 0.7660 -0.0421 0.428 0.216 0.000 0.356
#> GSM246488 4 0.3688 0.7018 0.000 0.208 0.000 0.792
#> GSM246489 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM246490 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM246491 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247162 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247163 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247164 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247165 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247166 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247168 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247169 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247171 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247173 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247174 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247175 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247188 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247189 4 0.4999 0.0504 0.000 0.492 0.000 0.508
#> GSM247190 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247650 1 0.0804 0.9365 0.980 0.000 0.008 0.012
#> GSM247651 1 0.3726 0.7609 0.788 0.000 0.000 0.212
#> GSM247652 1 0.0000 0.9410 1.000 0.000 0.000 0.000
#> GSM247653 1 0.0000 0.9410 1.000 0.000 0.000 0.000
#> GSM247654 1 0.0000 0.9410 1.000 0.000 0.000 0.000
#> GSM247655 1 0.0336 0.9395 0.992 0.000 0.000 0.008
#> GSM247656 1 0.1557 0.9041 0.944 0.000 0.056 0.000
#> GSM247657 1 0.0000 0.9410 1.000 0.000 0.000 0.000
#> GSM247658 1 0.0000 0.9410 1.000 0.000 0.000 0.000
#> GSM247659 3 0.4040 0.6309 0.248 0.000 0.752 0.000
#> GSM247660 1 0.1940 0.9010 0.924 0.000 0.000 0.076
#> GSM247661 1 0.0000 0.9410 1.000 0.000 0.000 0.000
#> GSM247662 1 0.2921 0.8157 0.860 0.000 0.140 0.000
#> GSM247663 1 0.1557 0.9152 0.944 0.000 0.000 0.056
#> GSM247856 1 0.0000 0.9410 1.000 0.000 0.000 0.000
#> GSM247857 1 0.0000 0.9410 1.000 0.000 0.000 0.000
#> GSM247859 1 0.0188 0.9404 0.996 0.000 0.000 0.004
#> GSM247860 1 0.0000 0.9410 1.000 0.000 0.000 0.000
#> GSM247862 1 0.0000 0.9410 1.000 0.000 0.000 0.000
#> GSM247864 1 0.1022 0.9299 0.968 0.000 0.000 0.032
#> GSM247865 1 0.1022 0.9300 0.968 0.000 0.000 0.032
#> GSM247866 1 0.0336 0.9395 0.992 0.000 0.000 0.008
#> GSM247876 1 0.3801 0.7493 0.780 0.000 0.000 0.220
#> GSM247877 4 0.0000 0.8757 0.000 0.000 0.000 1.000
#> GSM247878 4 0.0000 0.8757 0.000 0.000 0.000 1.000
#> GSM247879 4 0.0000 0.8757 0.000 0.000 0.000 1.000
#> GSM247881 1 0.0000 0.9410 1.000 0.000 0.000 0.000
#> GSM247883 1 0.0188 0.9404 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0703 0.8530 0.000 0.000 0.976 0.000 0.024
#> GSM246088 3 0.0290 0.8586 0.000 0.000 0.992 0.000 0.008
#> GSM246089 3 0.3752 0.6278 0.000 0.000 0.708 0.000 0.292
#> GSM246090 3 0.0000 0.8601 0.000 0.000 1.000 0.000 0.000
#> GSM246119 3 0.1608 0.8600 0.000 0.000 0.928 0.000 0.072
#> GSM246120 3 0.1608 0.8600 0.000 0.000 0.928 0.000 0.072
#> GSM246121 3 0.1792 0.8558 0.000 0.000 0.916 0.000 0.084
#> GSM246122 3 0.0794 0.8508 0.000 0.000 0.972 0.000 0.028
#> GSM246123 3 0.1732 0.8573 0.000 0.000 0.920 0.000 0.080
#> GSM246422 4 0.0000 0.5499 0.000 0.000 0.000 1.000 0.000
#> GSM246423 4 0.0290 0.5488 0.000 0.000 0.000 0.992 0.008
#> GSM246484 4 0.0404 0.5456 0.000 0.000 0.000 0.988 0.012
#> GSM246485 2 0.4690 0.6641 0.004 0.748 0.000 0.140 0.108
#> GSM246486 2 0.5103 0.0195 0.004 0.524 0.000 0.444 0.028
#> GSM246487 4 0.7224 0.1701 0.216 0.212 0.000 0.516 0.056
#> GSM246488 4 0.3327 0.4758 0.000 0.144 0.000 0.828 0.028
#> GSM246489 2 0.0162 0.9477 0.000 0.996 0.000 0.000 0.004
#> GSM246490 2 0.0000 0.9481 0.000 1.000 0.000 0.000 0.000
#> GSM246491 2 0.0162 0.9477 0.000 0.996 0.000 0.000 0.004
#> GSM247162 2 0.0162 0.9476 0.000 0.996 0.000 0.000 0.004
#> GSM247163 2 0.0290 0.9462 0.000 0.992 0.000 0.000 0.008
#> GSM247164 2 0.0324 0.9462 0.000 0.992 0.000 0.004 0.004
#> GSM247165 2 0.0693 0.9381 0.000 0.980 0.000 0.008 0.012
#> GSM247166 2 0.0162 0.9481 0.000 0.996 0.000 0.000 0.004
#> GSM247168 2 0.0162 0.9481 0.000 0.996 0.000 0.000 0.004
#> GSM247169 2 0.0162 0.9481 0.000 0.996 0.000 0.000 0.004
#> GSM247171 2 0.0162 0.9476 0.000 0.996 0.000 0.000 0.004
#> GSM247173 2 0.0162 0.9481 0.000 0.996 0.000 0.000 0.004
#> GSM247174 2 0.0162 0.9481 0.000 0.996 0.000 0.000 0.004
#> GSM247175 2 0.0000 0.9481 0.000 1.000 0.000 0.000 0.000
#> GSM247188 2 0.0290 0.9459 0.000 0.992 0.000 0.000 0.008
#> GSM247189 4 0.5591 0.1272 0.000 0.432 0.000 0.496 0.072
#> GSM247190 2 0.0162 0.9476 0.000 0.996 0.000 0.000 0.004
#> GSM247650 1 0.3337 0.7898 0.856 0.000 0.064 0.008 0.072
#> GSM247651 1 0.4777 0.5696 0.664 0.000 0.000 0.292 0.044
#> GSM247652 1 0.2127 0.7900 0.892 0.000 0.000 0.000 0.108
#> GSM247653 1 0.2377 0.7846 0.872 0.000 0.000 0.000 0.128
#> GSM247654 1 0.2020 0.8040 0.900 0.000 0.000 0.000 0.100
#> GSM247655 1 0.0912 0.8022 0.972 0.000 0.000 0.016 0.012
#> GSM247656 1 0.5974 0.4401 0.564 0.000 0.292 0.000 0.144
#> GSM247657 1 0.2280 0.7845 0.880 0.000 0.000 0.000 0.120
#> GSM247658 1 0.2020 0.7907 0.900 0.000 0.000 0.000 0.100
#> GSM247659 3 0.6203 0.2633 0.188 0.000 0.544 0.000 0.268
#> GSM247660 1 0.3309 0.7583 0.836 0.000 0.000 0.128 0.036
#> GSM247661 1 0.2690 0.7732 0.844 0.000 0.000 0.000 0.156
#> GSM247662 1 0.6761 0.0637 0.380 0.000 0.352 0.000 0.268
#> GSM247663 1 0.3399 0.7701 0.812 0.000 0.004 0.012 0.172
#> GSM247856 1 0.3336 0.7821 0.832 0.000 0.008 0.016 0.144
#> GSM247857 1 0.4481 0.6786 0.720 0.000 0.048 0.000 0.232
#> GSM247859 1 0.3764 0.7751 0.800 0.000 0.000 0.044 0.156
#> GSM247860 1 0.2516 0.7679 0.860 0.000 0.000 0.000 0.140
#> GSM247862 1 0.2074 0.7885 0.896 0.000 0.000 0.000 0.104
#> GSM247864 1 0.3535 0.7727 0.832 0.000 0.000 0.088 0.080
#> GSM247865 1 0.5399 0.6430 0.664 0.000 0.000 0.188 0.148
#> GSM247866 1 0.2813 0.7402 0.832 0.000 0.000 0.000 0.168
#> GSM247876 1 0.5696 0.3309 0.560 0.000 0.000 0.096 0.344
#> GSM247877 4 0.4313 -0.1482 0.008 0.000 0.000 0.636 0.356
#> GSM247878 4 0.2304 0.4567 0.008 0.000 0.000 0.892 0.100
#> GSM247879 5 0.5789 0.0000 0.076 0.000 0.024 0.272 0.628
#> GSM247881 1 0.0703 0.8017 0.976 0.000 0.000 0.000 0.024
#> GSM247883 1 0.2976 0.7844 0.852 0.004 0.000 0.012 0.132
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.1152 0.75261 0.000 0.000 0.952 0.000 0.004 NA
#> GSM246088 3 0.0692 0.75908 0.000 0.000 0.976 0.000 0.004 NA
#> GSM246089 3 0.5928 0.36126 0.000 0.000 0.464 0.000 0.268 NA
#> GSM246090 3 0.0146 0.76260 0.000 0.000 0.996 0.000 0.004 NA
#> GSM246119 3 0.3103 0.74981 0.000 0.000 0.836 0.000 0.100 NA
#> GSM246120 3 0.2897 0.75461 0.000 0.000 0.852 0.000 0.088 NA
#> GSM246121 3 0.3321 0.74232 0.000 0.000 0.820 0.000 0.100 NA
#> GSM246122 3 0.1349 0.75005 0.000 0.000 0.940 0.000 0.004 NA
#> GSM246123 3 0.2923 0.75532 0.000 0.000 0.848 0.000 0.100 NA
#> GSM246422 4 0.0000 0.63300 0.000 0.000 0.000 1.000 0.000 NA
#> GSM246423 4 0.0000 0.63300 0.000 0.000 0.000 1.000 0.000 NA
#> GSM246484 4 0.0146 0.63135 0.000 0.000 0.000 0.996 0.004 NA
#> GSM246485 2 0.6949 -0.27737 0.016 0.372 0.000 0.340 0.028 NA
#> GSM246486 4 0.4370 0.39899 0.000 0.356 0.000 0.616 0.008 NA
#> GSM246487 4 0.6136 0.34317 0.236 0.184 0.000 0.552 0.012 NA
#> GSM246488 4 0.1411 0.63340 0.000 0.060 0.000 0.936 0.004 NA
#> GSM246489 2 0.0603 0.93482 0.000 0.980 0.000 0.000 0.004 NA
#> GSM246490 2 0.0458 0.93473 0.000 0.984 0.000 0.000 0.000 NA
#> GSM246491 2 0.0363 0.93604 0.000 0.988 0.000 0.000 0.000 NA
#> GSM247162 2 0.0000 0.93600 0.000 1.000 0.000 0.000 0.000 NA
#> GSM247163 2 0.0520 0.93306 0.000 0.984 0.000 0.000 0.008 NA
#> GSM247164 2 0.0000 0.93600 0.000 1.000 0.000 0.000 0.000 NA
#> GSM247165 2 0.0976 0.92915 0.000 0.968 0.000 0.008 0.008 NA
#> GSM247166 2 0.1802 0.90141 0.000 0.916 0.000 0.000 0.012 NA
#> GSM247168 2 0.1745 0.90275 0.000 0.920 0.000 0.000 0.012 NA
#> GSM247169 2 0.1802 0.90034 0.000 0.916 0.000 0.000 0.012 NA
#> GSM247171 2 0.0405 0.93383 0.000 0.988 0.000 0.000 0.004 NA
#> GSM247173 2 0.0260 0.93642 0.000 0.992 0.000 0.000 0.000 NA
#> GSM247174 2 0.0790 0.93000 0.000 0.968 0.000 0.000 0.000 NA
#> GSM247175 2 0.0291 0.93478 0.000 0.992 0.000 0.000 0.004 NA
#> GSM247188 2 0.0291 0.93596 0.000 0.992 0.000 0.000 0.004 NA
#> GSM247189 4 0.4668 0.39540 0.000 0.276 0.000 0.660 0.052 NA
#> GSM247190 2 0.0000 0.93600 0.000 1.000 0.000 0.000 0.000 NA
#> GSM247650 1 0.5648 0.32046 0.604 0.000 0.224 0.000 0.148 NA
#> GSM247651 1 0.5092 0.43765 0.604 0.000 0.000 0.320 0.024 NA
#> GSM247652 1 0.1152 0.66096 0.952 0.000 0.004 0.000 0.000 NA
#> GSM247653 1 0.4703 0.56422 0.492 0.000 0.000 0.000 0.044 NA
#> GSM247654 1 0.3888 0.64683 0.672 0.000 0.000 0.000 0.016 NA
#> GSM247655 1 0.2573 0.67070 0.872 0.000 0.000 0.012 0.012 NA
#> GSM247656 1 0.5940 -0.00253 0.428 0.000 0.412 0.000 0.012 NA
#> GSM247657 1 0.4051 0.61540 0.560 0.000 0.000 0.000 0.008 NA
#> GSM247658 1 0.1806 0.66205 0.908 0.000 0.000 0.000 0.004 NA
#> GSM247659 3 0.6539 0.32464 0.048 0.004 0.512 0.000 0.192 NA
#> GSM247660 1 0.6112 0.54976 0.548 0.000 0.000 0.216 0.032 NA
#> GSM247661 1 0.4264 0.57867 0.500 0.000 0.000 0.000 0.016 NA
#> GSM247662 3 0.6782 0.22473 0.120 0.000 0.448 0.000 0.104 NA
#> GSM247663 1 0.2039 0.62641 0.904 0.000 0.000 0.000 0.076 NA
#> GSM247856 1 0.1621 0.64722 0.944 0.000 0.016 0.008 0.012 NA
#> GSM247857 1 0.6613 0.36808 0.408 0.000 0.148 0.000 0.060 NA
#> GSM247859 1 0.1794 0.65720 0.924 0.000 0.000 0.036 0.000 NA
#> GSM247860 1 0.5106 0.56602 0.520 0.000 0.000 0.000 0.084 NA
#> GSM247862 1 0.4184 0.62152 0.576 0.000 0.000 0.000 0.016 NA
#> GSM247864 1 0.5811 0.58996 0.644 0.000 0.008 0.096 0.068 NA
#> GSM247865 1 0.3946 0.44526 0.736 0.000 0.000 0.228 0.020 NA
#> GSM247866 1 0.5186 0.61752 0.612 0.000 0.000 0.000 0.156 NA
#> GSM247876 5 0.4910 0.33880 0.312 0.000 0.000 0.052 0.620 NA
#> GSM247877 5 0.3923 0.26910 0.000 0.000 0.000 0.416 0.580 NA
#> GSM247878 4 0.3841 0.25555 0.028 0.000 0.000 0.716 0.256 NA
#> GSM247879 5 0.2908 0.55019 0.020 0.004 0.000 0.124 0.848 NA
#> GSM247881 1 0.4807 0.58833 0.692 0.000 0.008 0.000 0.164 NA
#> GSM247883 1 0.1930 0.63176 0.916 0.000 0.000 0.000 0.048 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> SD:NMF 58 1.05e-11 2
#> SD:NMF 58 3.82e-14 3
#> SD:NMF 58 2.45e-19 4
#> SD:NMF 50 2.51e-19 5
#> SD:NMF 46 1.82e-16 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 21168 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.368 0.566 0.712 0.3790 0.541 0.541
#> 3 3 0.891 0.897 0.954 0.5475 0.767 0.607
#> 4 4 0.754 0.827 0.896 0.1977 0.877 0.700
#> 5 5 0.789 0.834 0.908 0.0335 0.990 0.966
#> 6 6 0.765 0.709 0.871 0.0370 0.975 0.909
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
#> GSM246087 1 0.866 0.0371 0.712 0.288
#> GSM246088 1 0.866 0.0371 0.712 0.288
#> GSM246089 1 0.866 0.0371 0.712 0.288
#> GSM246090 1 0.866 0.0371 0.712 0.288
#> GSM246119 1 0.866 0.0371 0.712 0.288
#> GSM246120 1 0.866 0.0371 0.712 0.288
#> GSM246121 1 0.866 0.0371 0.712 0.288
#> GSM246122 1 0.866 0.0371 0.712 0.288
#> GSM246123 1 0.866 0.0371 0.712 0.288
#> GSM246422 1 0.963 0.7004 0.612 0.388
#> GSM246423 1 0.963 0.7004 0.612 0.388
#> GSM246484 1 0.963 0.7004 0.612 0.388
#> GSM246485 2 0.808 0.4082 0.248 0.752
#> GSM246486 2 0.992 -0.2991 0.448 0.552
#> GSM246487 2 0.992 -0.2991 0.448 0.552
#> GSM246488 2 0.998 -0.3691 0.472 0.528
#> GSM246489 2 0.000 0.8195 0.000 1.000
#> GSM246490 2 0.000 0.8195 0.000 1.000
#> GSM246491 2 0.000 0.8195 0.000 1.000
#> GSM247162 2 0.000 0.8195 0.000 1.000
#> GSM247163 2 0.000 0.8195 0.000 1.000
#> GSM247164 2 0.000 0.8195 0.000 1.000
#> GSM247165 2 0.689 0.5496 0.184 0.816
#> GSM247166 2 0.000 0.8195 0.000 1.000
#> GSM247168 2 0.000 0.8195 0.000 1.000
#> GSM247169 2 0.000 0.8195 0.000 1.000
#> GSM247171 2 0.000 0.8195 0.000 1.000
#> GSM247173 2 0.000 0.8195 0.000 1.000
#> GSM247174 2 0.000 0.8195 0.000 1.000
#> GSM247175 2 0.000 0.8195 0.000 1.000
#> GSM247188 2 0.000 0.8195 0.000 1.000
#> GSM247189 2 0.808 0.4082 0.248 0.752
#> GSM247190 2 0.000 0.8195 0.000 1.000
#> GSM247650 1 0.963 0.7004 0.612 0.388
#> GSM247651 1 0.963 0.7004 0.612 0.388
#> GSM247652 1 0.963 0.7004 0.612 0.388
#> GSM247653 1 0.978 0.6646 0.588 0.412
#> GSM247654 1 0.969 0.6911 0.604 0.396
#> GSM247655 1 0.963 0.7004 0.612 0.388
#> GSM247656 1 0.963 0.7004 0.612 0.388
#> GSM247657 1 0.969 0.6911 0.604 0.396
#> GSM247658 1 0.969 0.6911 0.604 0.396
#> GSM247659 1 0.963 0.7004 0.612 0.388
#> GSM247660 1 0.963 0.7004 0.612 0.388
#> GSM247661 1 0.978 0.6646 0.588 0.412
#> GSM247662 1 0.963 0.7004 0.612 0.388
#> GSM247663 1 0.963 0.7004 0.612 0.388
#> GSM247856 1 0.963 0.7004 0.612 0.388
#> GSM247857 1 0.963 0.7004 0.612 0.388
#> GSM247859 1 0.963 0.7004 0.612 0.388
#> GSM247860 1 0.978 0.6646 0.588 0.412
#> GSM247862 1 0.975 0.6716 0.592 0.408
#> GSM247864 1 0.963 0.7004 0.612 0.388
#> GSM247865 1 0.966 0.6950 0.608 0.392
#> GSM247866 1 0.975 0.6716 0.592 0.408
#> GSM247876 1 0.963 0.7004 0.612 0.388
#> GSM247877 1 0.963 0.7004 0.612 0.388
#> GSM247878 1 0.963 0.7004 0.612 0.388
#> GSM247879 1 0.963 0.7004 0.612 0.388
#> GSM247881 1 0.963 0.7004 0.612 0.388
#> GSM247883 1 0.963 0.7004 0.612 0.388
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246422 1 0.0592 0.945 0.988 0.012 0.000
#> GSM246423 1 0.0592 0.945 0.988 0.012 0.000
#> GSM246484 1 0.0592 0.945 0.988 0.012 0.000
#> GSM246485 2 0.6291 0.120 0.468 0.532 0.000
#> GSM246486 1 0.5760 0.509 0.672 0.328 0.000
#> GSM246487 1 0.5760 0.509 0.672 0.328 0.000
#> GSM246488 1 0.5621 0.553 0.692 0.308 0.000
#> GSM246489 2 0.0592 0.913 0.012 0.988 0.000
#> GSM246490 2 0.0592 0.913 0.012 0.988 0.000
#> GSM246491 2 0.0592 0.913 0.012 0.988 0.000
#> GSM247162 2 0.0592 0.913 0.012 0.988 0.000
#> GSM247163 2 0.0592 0.913 0.012 0.988 0.000
#> GSM247164 2 0.0592 0.913 0.012 0.988 0.000
#> GSM247165 2 0.5254 0.630 0.264 0.736 0.000
#> GSM247166 2 0.0592 0.913 0.012 0.988 0.000
#> GSM247168 2 0.0592 0.913 0.012 0.988 0.000
#> GSM247169 2 0.0592 0.913 0.012 0.988 0.000
#> GSM247171 2 0.0592 0.913 0.012 0.988 0.000
#> GSM247173 2 0.0592 0.913 0.012 0.988 0.000
#> GSM247174 2 0.0592 0.913 0.012 0.988 0.000
#> GSM247175 2 0.0592 0.913 0.012 0.988 0.000
#> GSM247188 2 0.0592 0.913 0.012 0.988 0.000
#> GSM247189 2 0.5905 0.455 0.352 0.648 0.000
#> GSM247190 2 0.0592 0.913 0.012 0.988 0.000
#> GSM247650 1 0.0424 0.952 0.992 0.008 0.000
#> GSM247651 1 0.0424 0.952 0.992 0.008 0.000
#> GSM247652 1 0.0237 0.952 0.996 0.004 0.000
#> GSM247653 1 0.2590 0.909 0.924 0.072 0.004
#> GSM247654 1 0.0747 0.949 0.984 0.016 0.000
#> GSM247655 1 0.0424 0.952 0.992 0.008 0.000
#> GSM247656 1 0.0237 0.952 0.996 0.004 0.000
#> GSM247657 1 0.0747 0.949 0.984 0.016 0.000
#> GSM247658 1 0.0892 0.947 0.980 0.020 0.000
#> GSM247659 1 0.0237 0.952 0.996 0.004 0.000
#> GSM247660 1 0.0424 0.952 0.992 0.008 0.000
#> GSM247661 1 0.2261 0.915 0.932 0.068 0.000
#> GSM247662 1 0.0237 0.952 0.996 0.004 0.000
#> GSM247663 1 0.0424 0.952 0.992 0.008 0.000
#> GSM247856 1 0.0424 0.952 0.992 0.008 0.000
#> GSM247857 1 0.0237 0.952 0.996 0.004 0.000
#> GSM247859 1 0.0424 0.952 0.992 0.008 0.000
#> GSM247860 1 0.2590 0.909 0.924 0.072 0.004
#> GSM247862 1 0.2066 0.921 0.940 0.060 0.000
#> GSM247864 1 0.0424 0.952 0.992 0.008 0.000
#> GSM247865 1 0.0592 0.947 0.988 0.012 0.000
#> GSM247866 1 0.2165 0.918 0.936 0.064 0.000
#> GSM247876 1 0.0237 0.952 0.996 0.004 0.000
#> GSM247877 1 0.0592 0.945 0.988 0.012 0.000
#> GSM247878 1 0.0592 0.945 0.988 0.012 0.000
#> GSM247879 1 0.0592 0.945 0.988 0.012 0.000
#> GSM247881 1 0.0237 0.952 0.996 0.004 0.000
#> GSM247883 1 0.0237 0.952 0.996 0.004 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246088 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246089 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246090 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246119 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246120 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246121 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246122 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246123 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246422 4 0.3764 0.7410 0.216 0.000 0 0.784
#> GSM246423 4 0.3764 0.7410 0.216 0.000 0 0.784
#> GSM246484 4 0.3764 0.7410 0.216 0.000 0 0.784
#> GSM246485 2 0.6979 -0.0452 0.128 0.528 0 0.344
#> GSM246486 4 0.7031 0.5152 0.140 0.324 0 0.536
#> GSM246487 4 0.7031 0.5152 0.140 0.324 0 0.536
#> GSM246488 4 0.6783 0.5304 0.124 0.304 0 0.572
#> GSM246489 2 0.0000 0.9239 0.000 1.000 0 0.000
#> GSM246490 2 0.0000 0.9239 0.000 1.000 0 0.000
#> GSM246491 2 0.0000 0.9239 0.000 1.000 0 0.000
#> GSM247162 2 0.0000 0.9239 0.000 1.000 0 0.000
#> GSM247163 2 0.0000 0.9239 0.000 1.000 0 0.000
#> GSM247164 2 0.0000 0.9239 0.000 1.000 0 0.000
#> GSM247165 2 0.4642 0.5962 0.020 0.740 0 0.240
#> GSM247166 2 0.0000 0.9239 0.000 1.000 0 0.000
#> GSM247168 2 0.0000 0.9239 0.000 1.000 0 0.000
#> GSM247169 2 0.0000 0.9239 0.000 1.000 0 0.000
#> GSM247171 2 0.0000 0.9239 0.000 1.000 0 0.000
#> GSM247173 2 0.0000 0.9239 0.000 1.000 0 0.000
#> GSM247174 2 0.0000 0.9239 0.000 1.000 0 0.000
#> GSM247175 2 0.0000 0.9239 0.000 1.000 0 0.000
#> GSM247188 2 0.0000 0.9239 0.000 1.000 0 0.000
#> GSM247189 2 0.5614 0.4142 0.044 0.652 0 0.304
#> GSM247190 2 0.0000 0.9239 0.000 1.000 0 0.000
#> GSM247650 1 0.0188 0.8967 0.996 0.000 0 0.004
#> GSM247651 1 0.2281 0.8320 0.904 0.000 0 0.096
#> GSM247652 1 0.0469 0.8945 0.988 0.000 0 0.012
#> GSM247653 1 0.3764 0.7382 0.784 0.000 0 0.216
#> GSM247654 1 0.0817 0.8919 0.976 0.000 0 0.024
#> GSM247655 1 0.0336 0.8959 0.992 0.000 0 0.008
#> GSM247656 1 0.0469 0.8945 0.988 0.000 0 0.012
#> GSM247657 1 0.0817 0.8922 0.976 0.000 0 0.024
#> GSM247658 1 0.1118 0.8864 0.964 0.000 0 0.036
#> GSM247659 1 0.0592 0.8951 0.984 0.000 0 0.016
#> GSM247660 1 0.2281 0.8320 0.904 0.000 0 0.096
#> GSM247661 1 0.3610 0.7547 0.800 0.000 0 0.200
#> GSM247662 1 0.0592 0.8951 0.984 0.000 0 0.016
#> GSM247663 1 0.0336 0.8961 0.992 0.000 0 0.008
#> GSM247856 1 0.0188 0.8967 0.996 0.000 0 0.004
#> GSM247857 1 0.0592 0.8951 0.984 0.000 0 0.016
#> GSM247859 1 0.2149 0.8401 0.912 0.000 0 0.088
#> GSM247860 1 0.3764 0.7382 0.784 0.000 0 0.216
#> GSM247862 1 0.3172 0.7959 0.840 0.000 0 0.160
#> GSM247864 1 0.0336 0.8970 0.992 0.000 0 0.008
#> GSM247865 1 0.4608 0.4272 0.692 0.004 0 0.304
#> GSM247866 1 0.3610 0.7545 0.800 0.000 0 0.200
#> GSM247876 1 0.1716 0.8594 0.936 0.000 0 0.064
#> GSM247877 4 0.4888 0.6109 0.412 0.000 0 0.588
#> GSM247878 4 0.4877 0.6208 0.408 0.000 0 0.592
#> GSM247879 4 0.4888 0.6109 0.412 0.000 0 0.588
#> GSM247881 1 0.1022 0.8882 0.968 0.000 0 0.032
#> GSM247883 1 0.1022 0.8882 0.968 0.000 0 0.032
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246422 4 0.3318 0.615 0.192 0.000 0 0.800 0.008
#> GSM246423 4 0.3318 0.615 0.192 0.000 0 0.800 0.008
#> GSM246484 4 0.3318 0.615 0.192 0.000 0 0.800 0.008
#> GSM246485 2 0.6021 -0.177 0.128 0.524 0 0.348 0.000
#> GSM246486 4 0.6043 0.656 0.140 0.320 0 0.540 0.000
#> GSM246487 4 0.6043 0.656 0.140 0.320 0 0.540 0.000
#> GSM246488 4 0.5827 0.664 0.124 0.300 0 0.576 0.000
#> GSM246489 2 0.0000 0.919 0.000 1.000 0 0.000 0.000
#> GSM246490 2 0.0000 0.919 0.000 1.000 0 0.000 0.000
#> GSM246491 2 0.0000 0.919 0.000 1.000 0 0.000 0.000
#> GSM247162 2 0.0000 0.919 0.000 1.000 0 0.000 0.000
#> GSM247163 2 0.0000 0.919 0.000 1.000 0 0.000 0.000
#> GSM247164 2 0.0000 0.919 0.000 1.000 0 0.000 0.000
#> GSM247165 2 0.4026 0.553 0.020 0.736 0 0.244 0.000
#> GSM247166 2 0.0000 0.919 0.000 1.000 0 0.000 0.000
#> GSM247168 2 0.0000 0.919 0.000 1.000 0 0.000 0.000
#> GSM247169 2 0.0000 0.919 0.000 1.000 0 0.000 0.000
#> GSM247171 2 0.0000 0.919 0.000 1.000 0 0.000 0.000
#> GSM247173 2 0.0000 0.919 0.000 1.000 0 0.000 0.000
#> GSM247174 2 0.0000 0.919 0.000 1.000 0 0.000 0.000
#> GSM247175 2 0.0000 0.919 0.000 1.000 0 0.000 0.000
#> GSM247188 2 0.0000 0.919 0.000 1.000 0 0.000 0.000
#> GSM247189 2 0.4854 0.340 0.044 0.648 0 0.308 0.000
#> GSM247190 2 0.0000 0.919 0.000 1.000 0 0.000 0.000
#> GSM247650 1 0.0162 0.905 0.996 0.000 0 0.000 0.004
#> GSM247651 1 0.1965 0.848 0.904 0.000 0 0.096 0.000
#> GSM247652 1 0.0404 0.904 0.988 0.000 0 0.012 0.000
#> GSM247653 1 0.3745 0.768 0.780 0.000 0 0.196 0.024
#> GSM247654 1 0.0798 0.902 0.976 0.000 0 0.016 0.008
#> GSM247655 1 0.0290 0.904 0.992 0.000 0 0.008 0.000
#> GSM247656 1 0.0404 0.904 0.988 0.000 0 0.012 0.000
#> GSM247657 1 0.0771 0.902 0.976 0.000 0 0.020 0.004
#> GSM247658 1 0.1106 0.898 0.964 0.000 0 0.024 0.012
#> GSM247659 1 0.0510 0.905 0.984 0.000 0 0.016 0.000
#> GSM247660 1 0.1965 0.848 0.904 0.000 0 0.096 0.000
#> GSM247661 1 0.3318 0.785 0.800 0.000 0 0.192 0.008
#> GSM247662 1 0.0510 0.905 0.984 0.000 0 0.016 0.000
#> GSM247663 1 0.0955 0.901 0.968 0.000 0 0.004 0.028
#> GSM247856 1 0.0162 0.905 0.996 0.000 0 0.000 0.004
#> GSM247857 1 0.0510 0.905 0.984 0.000 0 0.016 0.000
#> GSM247859 1 0.1851 0.855 0.912 0.000 0 0.088 0.000
#> GSM247860 1 0.3745 0.768 0.780 0.000 0 0.196 0.024
#> GSM247862 1 0.2997 0.824 0.840 0.000 0 0.148 0.012
#> GSM247864 1 0.0324 0.905 0.992 0.000 0 0.004 0.004
#> GSM247865 1 0.3837 0.493 0.692 0.000 0 0.308 0.000
#> GSM247866 1 0.3456 0.786 0.800 0.000 0 0.184 0.016
#> GSM247876 1 0.2806 0.811 0.844 0.000 0 0.004 0.152
#> GSM247877 5 0.0703 0.830 0.024 0.000 0 0.000 0.976
#> GSM247878 5 0.5472 0.569 0.108 0.000 0 0.260 0.632
#> GSM247879 5 0.0703 0.830 0.024 0.000 0 0.000 0.976
#> GSM247881 1 0.0880 0.897 0.968 0.000 0 0.032 0.000
#> GSM247883 1 0.0880 0.897 0.968 0.000 0 0.032 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246088 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246089 3 0.5030 0.544 0.000 0.000 0.616 0.116 0.000 0.268
#> GSM246090 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246119 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246120 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246121 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246122 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246123 3 0.0000 0.956 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246422 4 0.2003 0.598 0.116 0.000 0.000 0.884 0.000 0.000
#> GSM246423 4 0.2003 0.598 0.116 0.000 0.000 0.884 0.000 0.000
#> GSM246484 4 0.2003 0.598 0.116 0.000 0.000 0.884 0.000 0.000
#> GSM246485 2 0.5771 -0.169 0.128 0.524 0.000 0.332 0.000 0.016
#> GSM246486 4 0.5947 0.646 0.136 0.320 0.000 0.520 0.000 0.024
#> GSM246487 4 0.5947 0.646 0.136 0.320 0.000 0.520 0.000 0.024
#> GSM246488 4 0.5642 0.664 0.124 0.300 0.000 0.560 0.000 0.016
#> GSM246489 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246490 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246491 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247162 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247163 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247164 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247165 2 0.3946 0.553 0.020 0.736 0.000 0.228 0.000 0.016
#> GSM247166 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247168 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247169 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247171 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247174 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247175 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247189 2 0.4712 0.340 0.044 0.648 0.000 0.292 0.000 0.016
#> GSM247190 2 0.0000 0.919 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247650 1 0.0547 0.759 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM247651 1 0.2163 0.704 0.892 0.000 0.000 0.092 0.000 0.016
#> GSM247652 1 0.0725 0.761 0.976 0.000 0.000 0.012 0.000 0.012
#> GSM247653 6 0.3847 0.980 0.456 0.000 0.000 0.000 0.000 0.544
#> GSM247654 1 0.1556 0.720 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM247655 1 0.0622 0.761 0.980 0.000 0.000 0.008 0.000 0.012
#> GSM247656 1 0.1563 0.743 0.932 0.000 0.000 0.012 0.000 0.056
#> GSM247657 1 0.1444 0.725 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM247658 1 0.1267 0.735 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM247659 1 0.1745 0.739 0.920 0.000 0.000 0.012 0.000 0.068
#> GSM247660 1 0.2163 0.704 0.892 0.000 0.000 0.092 0.000 0.016
#> GSM247661 1 0.3851 -0.792 0.540 0.000 0.000 0.000 0.000 0.460
#> GSM247662 1 0.1625 0.743 0.928 0.000 0.000 0.012 0.000 0.060
#> GSM247663 1 0.2814 0.607 0.820 0.000 0.000 0.000 0.008 0.172
#> GSM247856 1 0.0632 0.757 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM247857 1 0.1625 0.743 0.928 0.000 0.000 0.012 0.000 0.060
#> GSM247859 1 0.2147 0.713 0.896 0.000 0.000 0.084 0.000 0.020
#> GSM247860 6 0.3851 0.981 0.460 0.000 0.000 0.000 0.000 0.540
#> GSM247862 1 0.3349 0.161 0.748 0.000 0.000 0.008 0.000 0.244
#> GSM247864 1 0.0603 0.759 0.980 0.000 0.000 0.004 0.000 0.016
#> GSM247865 1 0.4079 0.381 0.680 0.000 0.000 0.288 0.000 0.032
#> GSM247866 1 0.3823 -0.727 0.564 0.000 0.000 0.000 0.000 0.436
#> GSM247876 1 0.4631 0.351 0.692 0.000 0.000 0.000 0.140 0.168
#> GSM247877 5 0.0000 0.837 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM247878 5 0.4306 0.599 0.032 0.000 0.000 0.344 0.624 0.000
#> GSM247879 5 0.0000 0.837 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM247881 1 0.1168 0.760 0.956 0.000 0.000 0.028 0.000 0.016
#> GSM247883 1 0.1074 0.759 0.960 0.000 0.000 0.028 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:hclust 47 1.47e-08 2
#> CV:hclust 59 1.58e-19 3
#> CV:hclust 58 1.14e-20 4
#> CV:hclust 58 2.22e-21 5
#> CV:hclust 54 1.35e-18 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 21168 rows and 61 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 0.323 0.687 0.700 0.4056 0.552 0.552
#> 3 3 1.000 0.970 0.986 0.4773 0.815 0.675
#> 4 4 0.848 0.893 0.902 0.1593 0.874 0.693
#> 5 5 0.765 0.786 0.859 0.0739 0.992 0.974
#> 6 6 0.741 0.632 0.782 0.0457 0.962 0.867
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
#> GSM246087 1 0.9993 0.428 0.516 0.484
#> GSM246088 1 0.9993 0.428 0.516 0.484
#> GSM246089 1 0.9993 0.428 0.516 0.484
#> GSM246090 1 0.9993 0.428 0.516 0.484
#> GSM246119 1 0.9993 0.428 0.516 0.484
#> GSM246120 1 0.9993 0.428 0.516 0.484
#> GSM246121 1 0.9993 0.428 0.516 0.484
#> GSM246122 1 0.9993 0.428 0.516 0.484
#> GSM246123 1 0.9993 0.428 0.516 0.484
#> GSM246422 1 0.9129 -0.158 0.672 0.328
#> GSM246423 1 0.9129 -0.158 0.672 0.328
#> GSM246484 1 0.9129 -0.158 0.672 0.328
#> GSM246485 2 0.9998 0.703 0.492 0.508
#> GSM246486 2 0.9993 0.718 0.484 0.516
#> GSM246487 1 0.9933 -0.600 0.548 0.452
#> GSM246488 2 0.9993 0.718 0.484 0.516
#> GSM246489 2 0.9209 0.958 0.336 0.664
#> GSM246490 2 0.9209 0.958 0.336 0.664
#> GSM246491 2 0.9209 0.958 0.336 0.664
#> GSM247162 2 0.9209 0.958 0.336 0.664
#> GSM247163 2 0.9209 0.958 0.336 0.664
#> GSM247164 2 0.9209 0.958 0.336 0.664
#> GSM247165 2 0.9209 0.958 0.336 0.664
#> GSM247166 2 0.9209 0.958 0.336 0.664
#> GSM247168 2 0.9209 0.958 0.336 0.664
#> GSM247169 2 0.9209 0.958 0.336 0.664
#> GSM247171 2 0.9209 0.958 0.336 0.664
#> GSM247173 2 0.9209 0.958 0.336 0.664
#> GSM247174 2 0.9209 0.958 0.336 0.664
#> GSM247175 2 0.9209 0.958 0.336 0.664
#> GSM247188 2 0.9209 0.958 0.336 0.664
#> GSM247189 2 0.9209 0.958 0.336 0.664
#> GSM247190 2 0.9209 0.958 0.336 0.664
#> GSM247650 1 0.0376 0.749 0.996 0.004
#> GSM247651 1 0.2043 0.735 0.968 0.032
#> GSM247652 1 0.0000 0.749 1.000 0.000
#> GSM247653 1 0.0000 0.749 1.000 0.000
#> GSM247654 1 0.0000 0.749 1.000 0.000
#> GSM247655 1 0.2043 0.735 0.968 0.032
#> GSM247656 1 0.0376 0.749 0.996 0.004
#> GSM247657 1 0.0000 0.749 1.000 0.000
#> GSM247658 1 0.0000 0.749 1.000 0.000
#> GSM247659 1 0.3431 0.695 0.936 0.064
#> GSM247660 1 0.2043 0.735 0.968 0.032
#> GSM247661 1 0.0376 0.749 0.996 0.004
#> GSM247662 1 0.0376 0.749 0.996 0.004
#> GSM247663 1 0.0376 0.749 0.996 0.004
#> GSM247856 1 0.0000 0.749 1.000 0.000
#> GSM247857 1 0.0000 0.749 1.000 0.000
#> GSM247859 1 0.2043 0.735 0.968 0.032
#> GSM247860 1 0.0000 0.749 1.000 0.000
#> GSM247862 1 0.2043 0.735 0.968 0.032
#> GSM247864 1 0.2043 0.735 0.968 0.032
#> GSM247865 1 0.3733 0.678 0.928 0.072
#> GSM247866 1 0.2043 0.735 0.968 0.032
#> GSM247876 1 0.0376 0.749 0.996 0.004
#> GSM247877 1 0.2236 0.737 0.964 0.036
#> GSM247878 1 0.2043 0.735 0.968 0.032
#> GSM247879 1 0.0376 0.749 0.996 0.004
#> GSM247881 1 0.2043 0.735 0.968 0.032
#> GSM247883 1 0.2043 0.735 0.968 0.032
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0237 0.9984 0.000 0.004 0.996
#> GSM246088 3 0.0237 0.9984 0.000 0.004 0.996
#> GSM246089 3 0.0237 0.9972 0.000 0.004 0.996
#> GSM246090 3 0.0237 0.9984 0.000 0.004 0.996
#> GSM246119 3 0.0000 0.9986 0.000 0.000 1.000
#> GSM246120 3 0.0000 0.9986 0.000 0.000 1.000
#> GSM246121 3 0.0000 0.9986 0.000 0.000 1.000
#> GSM246122 3 0.0237 0.9984 0.000 0.004 0.996
#> GSM246123 3 0.0000 0.9986 0.000 0.000 1.000
#> GSM246422 1 0.0424 0.9742 0.992 0.008 0.000
#> GSM246423 1 0.0424 0.9742 0.992 0.008 0.000
#> GSM246484 1 0.0424 0.9742 0.992 0.008 0.000
#> GSM246485 1 0.6299 0.0706 0.524 0.476 0.000
#> GSM246486 2 0.0592 0.9893 0.012 0.988 0.000
#> GSM246487 1 0.0424 0.9742 0.992 0.008 0.000
#> GSM246488 2 0.2959 0.8712 0.100 0.900 0.000
#> GSM246489 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM246490 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM246491 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM247162 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM247163 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM247164 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM247165 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM247166 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM247168 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM247169 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM247171 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM247173 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM247174 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM247175 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM247188 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM247189 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM247190 2 0.0424 0.9929 0.008 0.992 0.000
#> GSM247650 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247651 1 0.0000 0.9796 1.000 0.000 0.000
#> GSM247652 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247653 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247654 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247655 1 0.0000 0.9796 1.000 0.000 0.000
#> GSM247656 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247657 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247658 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247659 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247660 1 0.0000 0.9796 1.000 0.000 0.000
#> GSM247661 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247662 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247663 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247856 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247857 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247859 1 0.0000 0.9796 1.000 0.000 0.000
#> GSM247860 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247862 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247864 1 0.0000 0.9796 1.000 0.000 0.000
#> GSM247865 1 0.0000 0.9796 1.000 0.000 0.000
#> GSM247866 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247876 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247877 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247878 1 0.0000 0.9796 1.000 0.000 0.000
#> GSM247879 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247881 1 0.0237 0.9809 0.996 0.000 0.004
#> GSM247883 1 0.0000 0.9796 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0817 0.986 0.000 0.000 0.976 0.024
#> GSM246088 3 0.0817 0.986 0.000 0.000 0.976 0.024
#> GSM246089 3 0.1635 0.961 0.000 0.008 0.948 0.044
#> GSM246090 3 0.0817 0.986 0.000 0.000 0.976 0.024
#> GSM246119 3 0.0000 0.987 0.000 0.000 1.000 0.000
#> GSM246120 3 0.0000 0.987 0.000 0.000 1.000 0.000
#> GSM246121 3 0.0000 0.987 0.000 0.000 1.000 0.000
#> GSM246122 3 0.0817 0.986 0.000 0.000 0.976 0.024
#> GSM246123 3 0.0000 0.987 0.000 0.000 1.000 0.000
#> GSM246422 4 0.2760 0.804 0.128 0.000 0.000 0.872
#> GSM246423 4 0.2760 0.804 0.128 0.000 0.000 0.872
#> GSM246484 4 0.2760 0.804 0.128 0.000 0.000 0.872
#> GSM246485 4 0.7841 0.416 0.276 0.324 0.000 0.400
#> GSM246486 4 0.4295 0.604 0.008 0.240 0.000 0.752
#> GSM246487 4 0.4468 0.771 0.232 0.016 0.000 0.752
#> GSM246488 4 0.3108 0.710 0.016 0.112 0.000 0.872
#> GSM246489 2 0.0336 0.957 0.008 0.992 0.000 0.000
#> GSM246490 2 0.0336 0.957 0.008 0.992 0.000 0.000
#> GSM246491 2 0.0336 0.957 0.008 0.992 0.000 0.000
#> GSM247162 2 0.0336 0.957 0.008 0.992 0.000 0.000
#> GSM247163 2 0.0336 0.957 0.008 0.992 0.000 0.000
#> GSM247164 2 0.0336 0.957 0.008 0.992 0.000 0.000
#> GSM247165 2 0.0336 0.957 0.008 0.992 0.000 0.000
#> GSM247166 2 0.1970 0.929 0.008 0.932 0.000 0.060
#> GSM247168 2 0.1970 0.929 0.008 0.932 0.000 0.060
#> GSM247169 2 0.1970 0.929 0.008 0.932 0.000 0.060
#> GSM247171 2 0.0336 0.957 0.008 0.992 0.000 0.000
#> GSM247173 2 0.0336 0.957 0.008 0.992 0.000 0.000
#> GSM247174 2 0.1807 0.933 0.008 0.940 0.000 0.052
#> GSM247175 2 0.0524 0.956 0.008 0.988 0.000 0.004
#> GSM247188 2 0.0672 0.955 0.008 0.984 0.000 0.008
#> GSM247189 2 0.5138 0.257 0.008 0.600 0.000 0.392
#> GSM247190 2 0.0672 0.955 0.008 0.984 0.000 0.008
#> GSM247650 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247651 1 0.4277 0.526 0.720 0.000 0.000 0.280
#> GSM247652 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247653 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247654 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247655 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247656 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247657 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247658 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247659 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247660 1 0.4193 0.553 0.732 0.000 0.000 0.268
#> GSM247661 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247662 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247663 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247856 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247857 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247859 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247860 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247862 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247864 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247865 1 0.4008 0.611 0.756 0.000 0.000 0.244
#> GSM247866 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247876 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247877 4 0.4277 0.727 0.280 0.000 0.000 0.720
#> GSM247878 4 0.4222 0.735 0.272 0.000 0.000 0.728
#> GSM247879 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247881 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM247883 1 0.0000 0.960 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.1571 0.965 0.000 0.000 0.936 0.004 0.060
#> GSM246088 3 0.1571 0.965 0.000 0.000 0.936 0.004 0.060
#> GSM246089 3 0.0865 0.960 0.000 0.000 0.972 0.004 0.024
#> GSM246090 3 0.1571 0.965 0.000 0.000 0.936 0.004 0.060
#> GSM246119 3 0.0162 0.969 0.000 0.000 0.996 0.000 0.004
#> GSM246120 3 0.0000 0.970 0.000 0.000 1.000 0.000 0.000
#> GSM246121 3 0.0162 0.969 0.000 0.000 0.996 0.000 0.004
#> GSM246122 3 0.1571 0.965 0.000 0.000 0.936 0.004 0.060
#> GSM246123 3 0.0162 0.969 0.000 0.000 0.996 0.000 0.004
#> GSM246422 4 0.2997 0.458 0.012 0.000 0.000 0.840 0.148
#> GSM246423 4 0.2997 0.458 0.012 0.000 0.000 0.840 0.148
#> GSM246484 4 0.2997 0.458 0.012 0.000 0.000 0.840 0.148
#> GSM246485 4 0.6904 0.196 0.184 0.300 0.000 0.492 0.024
#> GSM246486 4 0.3942 0.420 0.000 0.232 0.000 0.748 0.020
#> GSM246487 4 0.4415 0.238 0.184 0.012 0.000 0.760 0.044
#> GSM246488 4 0.0794 0.504 0.000 0.028 0.000 0.972 0.000
#> GSM246489 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> GSM246490 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> GSM246491 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> GSM247162 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> GSM247163 2 0.0794 0.894 0.000 0.972 0.000 0.028 0.000
#> GSM247164 2 0.0794 0.894 0.000 0.972 0.000 0.028 0.000
#> GSM247165 2 0.1908 0.845 0.000 0.908 0.000 0.092 0.000
#> GSM247166 2 0.3550 0.771 0.000 0.760 0.000 0.004 0.236
#> GSM247168 2 0.3550 0.771 0.000 0.760 0.000 0.004 0.236
#> GSM247169 2 0.3550 0.771 0.000 0.760 0.000 0.004 0.236
#> GSM247171 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000
#> GSM247173 2 0.0162 0.906 0.000 0.996 0.000 0.000 0.004
#> GSM247174 2 0.1571 0.889 0.000 0.936 0.000 0.004 0.060
#> GSM247175 2 0.0566 0.904 0.000 0.984 0.000 0.004 0.012
#> GSM247188 2 0.1502 0.891 0.000 0.940 0.000 0.004 0.056
#> GSM247189 2 0.4415 0.278 0.000 0.604 0.000 0.388 0.008
#> GSM247190 2 0.1124 0.898 0.000 0.960 0.000 0.004 0.036
#> GSM247650 1 0.1965 0.828 0.904 0.000 0.000 0.000 0.096
#> GSM247651 1 0.4808 0.640 0.728 0.000 0.000 0.136 0.136
#> GSM247652 1 0.1270 0.844 0.948 0.000 0.000 0.000 0.052
#> GSM247653 1 0.3039 0.779 0.808 0.000 0.000 0.000 0.192
#> GSM247654 1 0.1851 0.835 0.912 0.000 0.000 0.000 0.088
#> GSM247655 1 0.2574 0.812 0.876 0.000 0.000 0.012 0.112
#> GSM247656 1 0.1671 0.838 0.924 0.000 0.000 0.000 0.076
#> GSM247657 1 0.1792 0.837 0.916 0.000 0.000 0.000 0.084
#> GSM247658 1 0.2230 0.819 0.884 0.000 0.000 0.000 0.116
#> GSM247659 1 0.2127 0.832 0.892 0.000 0.000 0.000 0.108
#> GSM247660 1 0.4588 0.672 0.748 0.000 0.000 0.136 0.116
#> GSM247661 1 0.3039 0.780 0.808 0.000 0.000 0.000 0.192
#> GSM247662 1 0.1197 0.847 0.952 0.000 0.000 0.000 0.048
#> GSM247663 1 0.2471 0.820 0.864 0.000 0.000 0.000 0.136
#> GSM247856 1 0.0703 0.848 0.976 0.000 0.000 0.000 0.024
#> GSM247857 1 0.1197 0.847 0.952 0.000 0.000 0.000 0.048
#> GSM247859 1 0.1809 0.842 0.928 0.000 0.000 0.012 0.060
#> GSM247860 1 0.3039 0.780 0.808 0.000 0.000 0.000 0.192
#> GSM247862 1 0.1608 0.844 0.928 0.000 0.000 0.000 0.072
#> GSM247864 1 0.2389 0.815 0.880 0.000 0.000 0.004 0.116
#> GSM247865 1 0.4390 0.684 0.760 0.000 0.000 0.156 0.084
#> GSM247866 1 0.3074 0.802 0.804 0.000 0.000 0.000 0.196
#> GSM247876 1 0.3949 0.581 0.668 0.000 0.000 0.000 0.332
#> GSM247877 5 0.6117 0.931 0.136 0.000 0.000 0.360 0.504
#> GSM247878 5 0.6248 0.930 0.148 0.000 0.000 0.384 0.468
#> GSM247879 1 0.4126 0.487 0.620 0.000 0.000 0.000 0.380
#> GSM247881 1 0.1341 0.844 0.944 0.000 0.000 0.000 0.056
#> GSM247883 1 0.1628 0.842 0.936 0.000 0.000 0.008 0.056
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.1720 0.945 0.000 0.000 0.928 0.000 0.032 0.040
#> GSM246088 3 0.1720 0.945 0.000 0.000 0.928 0.000 0.032 0.040
#> GSM246089 3 0.2733 0.873 0.000 0.000 0.864 0.000 0.080 0.056
#> GSM246090 3 0.1720 0.945 0.000 0.000 0.928 0.000 0.032 0.040
#> GSM246119 3 0.0725 0.945 0.000 0.000 0.976 0.000 0.012 0.012
#> GSM246120 3 0.0725 0.945 0.000 0.000 0.976 0.000 0.012 0.012
#> GSM246121 3 0.0000 0.947 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246122 3 0.1720 0.945 0.000 0.000 0.928 0.000 0.032 0.040
#> GSM246123 3 0.0725 0.945 0.000 0.000 0.976 0.000 0.012 0.012
#> GSM246422 4 0.4168 0.506 0.000 0.000 0.000 0.696 0.256 0.048
#> GSM246423 4 0.4168 0.506 0.000 0.000 0.000 0.696 0.256 0.048
#> GSM246484 4 0.4168 0.506 0.000 0.000 0.000 0.696 0.256 0.048
#> GSM246485 4 0.5771 0.365 0.124 0.240 0.000 0.604 0.024 0.008
#> GSM246486 4 0.3352 0.514 0.004 0.180 0.000 0.796 0.016 0.004
#> GSM246487 4 0.3462 0.434 0.180 0.008 0.000 0.792 0.016 0.004
#> GSM246488 4 0.0291 0.570 0.000 0.004 0.000 0.992 0.004 0.000
#> GSM246489 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246490 2 0.0405 0.865 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM246491 2 0.0622 0.864 0.000 0.980 0.000 0.000 0.012 0.008
#> GSM247162 2 0.0000 0.866 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247163 2 0.1078 0.857 0.000 0.964 0.000 0.016 0.012 0.008
#> GSM247164 2 0.0976 0.858 0.000 0.968 0.000 0.016 0.008 0.008
#> GSM247165 2 0.2982 0.744 0.000 0.828 0.000 0.152 0.012 0.008
#> GSM247166 2 0.5084 0.601 0.000 0.612 0.000 0.000 0.124 0.264
#> GSM247168 2 0.5084 0.601 0.000 0.612 0.000 0.000 0.124 0.264
#> GSM247169 2 0.5100 0.601 0.000 0.612 0.000 0.000 0.128 0.260
#> GSM247171 2 0.0146 0.866 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM247173 2 0.0146 0.866 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM247174 2 0.1934 0.838 0.000 0.916 0.000 0.000 0.040 0.044
#> GSM247175 2 0.0260 0.865 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM247188 2 0.1498 0.849 0.000 0.940 0.000 0.000 0.028 0.032
#> GSM247189 2 0.4617 0.129 0.000 0.524 0.000 0.444 0.024 0.008
#> GSM247190 2 0.0820 0.861 0.000 0.972 0.000 0.000 0.012 0.016
#> GSM247650 1 0.1461 0.627 0.940 0.000 0.000 0.000 0.044 0.016
#> GSM247651 1 0.2822 0.581 0.864 0.000 0.000 0.056 0.076 0.004
#> GSM247652 1 0.2482 0.504 0.848 0.000 0.000 0.000 0.004 0.148
#> GSM247653 6 0.4045 0.973 0.428 0.000 0.000 0.000 0.008 0.564
#> GSM247654 1 0.3547 0.132 0.696 0.000 0.000 0.000 0.004 0.300
#> GSM247655 1 0.1434 0.625 0.940 0.000 0.000 0.012 0.048 0.000
#> GSM247656 1 0.3349 0.337 0.748 0.000 0.000 0.000 0.008 0.244
#> GSM247657 1 0.3690 0.143 0.700 0.000 0.000 0.000 0.012 0.288
#> GSM247658 1 0.3795 -0.357 0.632 0.000 0.000 0.000 0.004 0.364
#> GSM247659 1 0.3756 0.225 0.712 0.000 0.000 0.000 0.020 0.268
#> GSM247660 1 0.2325 0.599 0.892 0.000 0.000 0.048 0.060 0.000
#> GSM247661 6 0.4141 0.946 0.432 0.000 0.000 0.000 0.012 0.556
#> GSM247662 1 0.2946 0.460 0.812 0.000 0.000 0.000 0.012 0.176
#> GSM247663 1 0.3013 0.588 0.844 0.000 0.000 0.000 0.088 0.068
#> GSM247856 1 0.2146 0.544 0.880 0.000 0.000 0.000 0.004 0.116
#> GSM247857 1 0.2946 0.460 0.812 0.000 0.000 0.000 0.012 0.176
#> GSM247859 1 0.0984 0.627 0.968 0.000 0.000 0.012 0.008 0.012
#> GSM247860 6 0.4045 0.973 0.428 0.000 0.000 0.000 0.008 0.564
#> GSM247862 1 0.1957 0.587 0.912 0.000 0.000 0.008 0.008 0.072
#> GSM247864 1 0.1398 0.624 0.940 0.000 0.000 0.008 0.052 0.000
#> GSM247865 1 0.2505 0.577 0.880 0.000 0.000 0.092 0.020 0.008
#> GSM247866 1 0.4139 -0.273 0.640 0.000 0.000 0.000 0.024 0.336
#> GSM247876 1 0.4675 0.177 0.560 0.000 0.000 0.000 0.392 0.048
#> GSM247877 5 0.5045 0.950 0.156 0.000 0.000 0.132 0.688 0.024
#> GSM247878 5 0.4666 0.949 0.168 0.000 0.000 0.144 0.688 0.000
#> GSM247879 1 0.4808 -0.124 0.476 0.000 0.000 0.000 0.472 0.052
#> GSM247881 1 0.0972 0.622 0.964 0.000 0.000 0.000 0.008 0.028
#> GSM247883 1 0.0870 0.627 0.972 0.000 0.000 0.012 0.004 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:kmeans 48 3.33e-11 2
#> CV:kmeans 60 1.88e-21 3
#> CV:kmeans 59 1.37e-21 4
#> CV:kmeans 53 2.52e-19 5
#> CV:kmeans 48 3.43e-16 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 21168 rows and 61 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 1.000 0.988 0.995 0.4961 0.503 0.503
#> 3 3 0.924 0.939 0.968 0.3588 0.711 0.483
#> 4 4 0.754 0.812 0.911 0.1074 0.797 0.480
#> 5 5 0.744 0.612 0.802 0.0677 0.877 0.574
#> 6 6 0.776 0.579 0.777 0.0353 0.949 0.761
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
#> GSM246087 1 0.000 1.000 1.000 0.000
#> GSM246088 1 0.000 1.000 1.000 0.000
#> GSM246089 1 0.000 1.000 1.000 0.000
#> GSM246090 1 0.000 1.000 1.000 0.000
#> GSM246119 1 0.000 1.000 1.000 0.000
#> GSM246120 1 0.000 1.000 1.000 0.000
#> GSM246121 1 0.000 1.000 1.000 0.000
#> GSM246122 1 0.000 1.000 1.000 0.000
#> GSM246123 1 0.000 1.000 1.000 0.000
#> GSM246422 2 0.000 0.988 0.000 1.000
#> GSM246423 2 0.000 0.988 0.000 1.000
#> GSM246484 2 0.000 0.988 0.000 1.000
#> GSM246485 2 0.000 0.988 0.000 1.000
#> GSM246486 2 0.000 0.988 0.000 1.000
#> GSM246487 2 0.000 0.988 0.000 1.000
#> GSM246488 2 0.000 0.988 0.000 1.000
#> GSM246489 2 0.000 0.988 0.000 1.000
#> GSM246490 2 0.000 0.988 0.000 1.000
#> GSM246491 2 0.000 0.988 0.000 1.000
#> GSM247162 2 0.000 0.988 0.000 1.000
#> GSM247163 2 0.000 0.988 0.000 1.000
#> GSM247164 2 0.000 0.988 0.000 1.000
#> GSM247165 2 0.000 0.988 0.000 1.000
#> GSM247166 2 0.000 0.988 0.000 1.000
#> GSM247168 2 0.000 0.988 0.000 1.000
#> GSM247169 2 0.000 0.988 0.000 1.000
#> GSM247171 2 0.000 0.988 0.000 1.000
#> GSM247173 2 0.000 0.988 0.000 1.000
#> GSM247174 2 0.000 0.988 0.000 1.000
#> GSM247175 2 0.000 0.988 0.000 1.000
#> GSM247188 2 0.000 0.988 0.000 1.000
#> GSM247189 2 0.000 0.988 0.000 1.000
#> GSM247190 2 0.000 0.988 0.000 1.000
#> GSM247650 1 0.000 1.000 1.000 0.000
#> GSM247651 1 0.000 1.000 1.000 0.000
#> GSM247652 1 0.000 1.000 1.000 0.000
#> GSM247653 1 0.000 1.000 1.000 0.000
#> GSM247654 1 0.000 1.000 1.000 0.000
#> GSM247655 1 0.000 1.000 1.000 0.000
#> GSM247656 1 0.000 1.000 1.000 0.000
#> GSM247657 1 0.000 1.000 1.000 0.000
#> GSM247658 1 0.000 1.000 1.000 0.000
#> GSM247659 1 0.000 1.000 1.000 0.000
#> GSM247660 1 0.000 1.000 1.000 0.000
#> GSM247661 1 0.000 1.000 1.000 0.000
#> GSM247662 1 0.000 1.000 1.000 0.000
#> GSM247663 1 0.000 1.000 1.000 0.000
#> GSM247856 1 0.000 1.000 1.000 0.000
#> GSM247857 1 0.000 1.000 1.000 0.000
#> GSM247859 1 0.000 1.000 1.000 0.000
#> GSM247860 1 0.000 1.000 1.000 0.000
#> GSM247862 1 0.000 1.000 1.000 0.000
#> GSM247864 1 0.000 1.000 1.000 0.000
#> GSM247865 2 0.000 0.988 0.000 1.000
#> GSM247866 1 0.000 1.000 1.000 0.000
#> GSM247876 1 0.000 1.000 1.000 0.000
#> GSM247877 1 0.000 1.000 1.000 0.000
#> GSM247878 1 0.000 1.000 1.000 0.000
#> GSM247879 1 0.000 1.000 1.000 0.000
#> GSM247881 1 0.000 1.000 1.000 0.000
#> GSM247883 2 0.886 0.563 0.304 0.696
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 0.957 0.000 0.000 1.000
#> GSM246088 3 0.0000 0.957 0.000 0.000 1.000
#> GSM246089 3 0.0000 0.957 0.000 0.000 1.000
#> GSM246090 3 0.0000 0.957 0.000 0.000 1.000
#> GSM246119 3 0.0000 0.957 0.000 0.000 1.000
#> GSM246120 3 0.0000 0.957 0.000 0.000 1.000
#> GSM246121 3 0.0000 0.957 0.000 0.000 1.000
#> GSM246122 3 0.0000 0.957 0.000 0.000 1.000
#> GSM246123 3 0.0000 0.957 0.000 0.000 1.000
#> GSM246422 1 0.0892 0.935 0.980 0.020 0.000
#> GSM246423 1 0.0892 0.935 0.980 0.020 0.000
#> GSM246484 1 0.0892 0.935 0.980 0.020 0.000
#> GSM246485 2 0.0237 0.993 0.004 0.996 0.000
#> GSM246486 2 0.0592 0.986 0.012 0.988 0.000
#> GSM246487 1 0.2356 0.896 0.928 0.072 0.000
#> GSM246488 2 0.2066 0.938 0.060 0.940 0.000
#> GSM246489 2 0.0000 0.996 0.000 1.000 0.000
#> GSM246490 2 0.0000 0.996 0.000 1.000 0.000
#> GSM246491 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247162 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247163 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247164 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247165 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247166 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247168 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247169 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247171 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247173 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247174 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247175 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247188 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247189 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247190 2 0.0000 0.996 0.000 1.000 0.000
#> GSM247650 1 0.2066 0.917 0.940 0.000 0.060
#> GSM247651 1 0.0000 0.943 1.000 0.000 0.000
#> GSM247652 1 0.3412 0.858 0.876 0.000 0.124
#> GSM247653 3 0.1031 0.951 0.024 0.000 0.976
#> GSM247654 3 0.4178 0.816 0.172 0.000 0.828
#> GSM247655 1 0.0000 0.943 1.000 0.000 0.000
#> GSM247656 3 0.1411 0.945 0.036 0.000 0.964
#> GSM247657 3 0.3192 0.885 0.112 0.000 0.888
#> GSM247658 1 0.2066 0.916 0.940 0.000 0.060
#> GSM247659 3 0.0000 0.957 0.000 0.000 1.000
#> GSM247660 1 0.0000 0.943 1.000 0.000 0.000
#> GSM247661 3 0.0892 0.951 0.020 0.000 0.980
#> GSM247662 3 0.2066 0.931 0.060 0.000 0.940
#> GSM247663 1 0.2165 0.913 0.936 0.000 0.064
#> GSM247856 1 0.5178 0.668 0.744 0.000 0.256
#> GSM247857 3 0.5098 0.703 0.248 0.000 0.752
#> GSM247859 1 0.0000 0.943 1.000 0.000 0.000
#> GSM247860 3 0.1964 0.933 0.056 0.000 0.944
#> GSM247862 1 0.0000 0.943 1.000 0.000 0.000
#> GSM247864 1 0.0000 0.943 1.000 0.000 0.000
#> GSM247865 1 0.0000 0.943 1.000 0.000 0.000
#> GSM247866 1 0.0000 0.943 1.000 0.000 0.000
#> GSM247876 1 0.2796 0.893 0.908 0.000 0.092
#> GSM247877 1 0.2796 0.891 0.908 0.000 0.092
#> GSM247878 1 0.0000 0.943 1.000 0.000 0.000
#> GSM247879 1 0.5529 0.617 0.704 0.000 0.296
#> GSM247881 1 0.0000 0.943 1.000 0.000 0.000
#> GSM247883 1 0.0000 0.943 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 0.9037 0.000 0.000 1.000 0.000
#> GSM246088 3 0.0000 0.9037 0.000 0.000 1.000 0.000
#> GSM246089 3 0.0000 0.9037 0.000 0.000 1.000 0.000
#> GSM246090 3 0.0000 0.9037 0.000 0.000 1.000 0.000
#> GSM246119 3 0.0000 0.9037 0.000 0.000 1.000 0.000
#> GSM246120 3 0.0000 0.9037 0.000 0.000 1.000 0.000
#> GSM246121 3 0.0000 0.9037 0.000 0.000 1.000 0.000
#> GSM246122 3 0.0000 0.9037 0.000 0.000 1.000 0.000
#> GSM246123 3 0.0000 0.9037 0.000 0.000 1.000 0.000
#> GSM246422 4 0.0000 0.8501 0.000 0.000 0.000 1.000
#> GSM246423 4 0.0000 0.8501 0.000 0.000 0.000 1.000
#> GSM246484 4 0.0000 0.8501 0.000 0.000 0.000 1.000
#> GSM246485 2 0.4999 0.0941 0.000 0.508 0.000 0.492
#> GSM246486 4 0.2868 0.7549 0.000 0.136 0.000 0.864
#> GSM246487 4 0.0469 0.8473 0.000 0.012 0.000 0.988
#> GSM246488 4 0.1389 0.8286 0.000 0.048 0.000 0.952
#> GSM246489 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM246490 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM246491 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM247162 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM247163 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM247164 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM247165 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM247166 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM247168 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM247169 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM247171 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM247173 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM247174 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM247175 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM247188 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM247189 2 0.4193 0.6417 0.000 0.732 0.000 0.268
#> GSM247190 2 0.0000 0.9542 0.000 1.000 0.000 0.000
#> GSM247650 1 0.1767 0.8582 0.944 0.000 0.012 0.044
#> GSM247651 4 0.4500 0.5659 0.316 0.000 0.000 0.684
#> GSM247652 1 0.0336 0.8608 0.992 0.000 0.008 0.000
#> GSM247653 1 0.3024 0.7970 0.852 0.000 0.148 0.000
#> GSM247654 1 0.1940 0.8489 0.924 0.000 0.076 0.000
#> GSM247655 1 0.3649 0.7327 0.796 0.000 0.000 0.204
#> GSM247656 3 0.4961 0.1215 0.448 0.000 0.552 0.000
#> GSM247657 1 0.1792 0.8514 0.932 0.000 0.068 0.000
#> GSM247658 1 0.0188 0.8604 0.996 0.000 0.004 0.000
#> GSM247659 3 0.2408 0.8264 0.104 0.000 0.896 0.000
#> GSM247660 4 0.4564 0.5355 0.328 0.000 0.000 0.672
#> GSM247661 1 0.3400 0.7643 0.820 0.000 0.180 0.000
#> GSM247662 1 0.3978 0.7621 0.796 0.000 0.192 0.012
#> GSM247663 1 0.0524 0.8615 0.988 0.000 0.004 0.008
#> GSM247856 1 0.2342 0.8549 0.912 0.000 0.080 0.008
#> GSM247857 1 0.1305 0.8639 0.960 0.000 0.036 0.004
#> GSM247859 1 0.4989 0.0698 0.528 0.000 0.000 0.472
#> GSM247860 1 0.2011 0.8503 0.920 0.000 0.080 0.000
#> GSM247862 1 0.0592 0.8603 0.984 0.000 0.000 0.016
#> GSM247864 1 0.3074 0.7869 0.848 0.000 0.000 0.152
#> GSM247865 4 0.3074 0.7789 0.152 0.000 0.000 0.848
#> GSM247866 1 0.1389 0.8566 0.952 0.000 0.000 0.048
#> GSM247876 1 0.4953 0.7459 0.776 0.000 0.104 0.120
#> GSM247877 4 0.3850 0.7752 0.044 0.000 0.116 0.840
#> GSM247878 4 0.2868 0.7995 0.136 0.000 0.000 0.864
#> GSM247879 3 0.6883 0.4302 0.212 0.000 0.596 0.192
#> GSM247881 1 0.1792 0.8483 0.932 0.000 0.000 0.068
#> GSM247883 1 0.4193 0.6324 0.732 0.000 0.000 0.268
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 0.96575 0.000 0.000 1.000 0.000 0.000
#> GSM246088 3 0.0000 0.96575 0.000 0.000 1.000 0.000 0.000
#> GSM246089 3 0.0000 0.96575 0.000 0.000 1.000 0.000 0.000
#> GSM246090 3 0.0000 0.96575 0.000 0.000 1.000 0.000 0.000
#> GSM246119 3 0.0000 0.96575 0.000 0.000 1.000 0.000 0.000
#> GSM246120 3 0.0000 0.96575 0.000 0.000 1.000 0.000 0.000
#> GSM246121 3 0.0000 0.96575 0.000 0.000 1.000 0.000 0.000
#> GSM246122 3 0.0000 0.96575 0.000 0.000 1.000 0.000 0.000
#> GSM246123 3 0.0000 0.96575 0.000 0.000 1.000 0.000 0.000
#> GSM246422 4 0.0510 0.74835 0.016 0.000 0.000 0.984 0.000
#> GSM246423 4 0.0510 0.74835 0.016 0.000 0.000 0.984 0.000
#> GSM246484 4 0.0510 0.74835 0.016 0.000 0.000 0.984 0.000
#> GSM246485 4 0.4919 0.36076 0.016 0.368 0.000 0.604 0.012
#> GSM246486 4 0.2997 0.64947 0.012 0.148 0.000 0.840 0.000
#> GSM246487 4 0.1043 0.73691 0.040 0.000 0.000 0.960 0.000
#> GSM246488 4 0.0671 0.74536 0.004 0.016 0.000 0.980 0.000
#> GSM246489 2 0.0000 0.96960 0.000 1.000 0.000 0.000 0.000
#> GSM246490 2 0.0451 0.96709 0.004 0.988 0.000 0.008 0.000
#> GSM246491 2 0.0451 0.96730 0.008 0.988 0.000 0.004 0.000
#> GSM247162 2 0.0000 0.96960 0.000 1.000 0.000 0.000 0.000
#> GSM247163 2 0.0579 0.96407 0.008 0.984 0.000 0.008 0.000
#> GSM247164 2 0.0579 0.96407 0.008 0.984 0.000 0.008 0.000
#> GSM247165 2 0.0992 0.95122 0.008 0.968 0.000 0.024 0.000
#> GSM247166 2 0.0162 0.96860 0.000 0.996 0.000 0.004 0.000
#> GSM247168 2 0.0162 0.96860 0.000 0.996 0.000 0.004 0.000
#> GSM247169 2 0.0162 0.96860 0.000 0.996 0.000 0.004 0.000
#> GSM247171 2 0.0162 0.96896 0.004 0.996 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.96960 0.000 1.000 0.000 0.000 0.000
#> GSM247174 2 0.0000 0.96960 0.000 1.000 0.000 0.000 0.000
#> GSM247175 2 0.0162 0.96896 0.004 0.996 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.96960 0.000 1.000 0.000 0.000 0.000
#> GSM247189 2 0.4478 0.39518 0.008 0.628 0.000 0.360 0.004
#> GSM247190 2 0.0000 0.96960 0.000 1.000 0.000 0.000 0.000
#> GSM247650 1 0.3631 0.36484 0.788 0.000 0.008 0.008 0.196
#> GSM247651 1 0.5153 0.17878 0.524 0.000 0.000 0.436 0.040
#> GSM247652 5 0.4138 0.36306 0.384 0.000 0.000 0.000 0.616
#> GSM247653 5 0.2221 0.55233 0.052 0.000 0.036 0.000 0.912
#> GSM247654 5 0.2843 0.55355 0.144 0.000 0.008 0.000 0.848
#> GSM247655 1 0.4509 0.42791 0.752 0.000 0.000 0.096 0.152
#> GSM247656 5 0.6424 0.22198 0.176 0.000 0.380 0.000 0.444
#> GSM247657 5 0.3582 0.48300 0.224 0.000 0.008 0.000 0.768
#> GSM247658 5 0.3913 0.45847 0.324 0.000 0.000 0.000 0.676
#> GSM247659 3 0.4964 0.58611 0.096 0.000 0.700 0.000 0.204
#> GSM247660 1 0.5394 0.28286 0.540 0.000 0.000 0.400 0.060
#> GSM247661 5 0.3593 0.52269 0.088 0.000 0.084 0.000 0.828
#> GSM247662 1 0.6299 -0.00702 0.504 0.000 0.144 0.004 0.348
#> GSM247663 1 0.4327 0.12764 0.632 0.000 0.000 0.008 0.360
#> GSM247856 5 0.5457 0.21413 0.460 0.000 0.060 0.000 0.480
#> GSM247857 1 0.5116 -0.05621 0.508 0.000 0.028 0.004 0.460
#> GSM247859 1 0.6442 0.29914 0.504 0.000 0.000 0.252 0.244
#> GSM247860 5 0.3085 0.51912 0.116 0.000 0.032 0.000 0.852
#> GSM247862 1 0.4830 -0.02522 0.492 0.000 0.000 0.020 0.488
#> GSM247864 1 0.3966 0.43844 0.796 0.000 0.000 0.072 0.132
#> GSM247865 4 0.5323 0.27588 0.296 0.000 0.000 0.624 0.080
#> GSM247866 5 0.4522 0.06789 0.440 0.000 0.000 0.008 0.552
#> GSM247876 1 0.5674 0.29685 0.640 0.000 0.036 0.052 0.272
#> GSM247877 4 0.6135 -0.03362 0.444 0.000 0.032 0.468 0.056
#> GSM247878 1 0.4803 0.05279 0.536 0.000 0.000 0.444 0.020
#> GSM247879 1 0.7540 0.23694 0.512 0.000 0.216 0.116 0.156
#> GSM247881 1 0.4080 0.32064 0.728 0.000 0.000 0.020 0.252
#> GSM247883 1 0.5357 0.30309 0.640 0.000 0.000 0.096 0.264
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0146 0.9469 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM246088 3 0.0146 0.9469 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM246089 3 0.0000 0.9474 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246090 3 0.0146 0.9469 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM246119 3 0.0000 0.9474 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246120 3 0.0000 0.9474 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246121 3 0.0000 0.9474 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246122 3 0.0146 0.9469 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM246123 3 0.0000 0.9474 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246422 4 0.1074 0.7956 0.012 0.000 0.000 0.960 0.028 0.000
#> GSM246423 4 0.1074 0.7956 0.012 0.000 0.000 0.960 0.028 0.000
#> GSM246484 4 0.1074 0.7956 0.012 0.000 0.000 0.960 0.028 0.000
#> GSM246485 4 0.4899 0.4637 0.016 0.252 0.000 0.676 0.032 0.024
#> GSM246486 4 0.2214 0.7254 0.004 0.092 0.000 0.892 0.012 0.000
#> GSM246487 4 0.1477 0.7761 0.048 0.004 0.000 0.940 0.008 0.000
#> GSM246488 4 0.0405 0.7905 0.000 0.004 0.000 0.988 0.008 0.000
#> GSM246489 2 0.0291 0.9466 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM246490 2 0.0767 0.9446 0.004 0.976 0.000 0.008 0.012 0.000
#> GSM246491 2 0.0603 0.9459 0.000 0.980 0.000 0.004 0.016 0.000
#> GSM247162 2 0.0508 0.9471 0.000 0.984 0.000 0.004 0.012 0.000
#> GSM247163 2 0.1346 0.9379 0.008 0.952 0.000 0.016 0.024 0.000
#> GSM247164 2 0.1078 0.9391 0.008 0.964 0.000 0.016 0.012 0.000
#> GSM247165 2 0.1913 0.9058 0.004 0.920 0.000 0.060 0.012 0.004
#> GSM247166 2 0.1268 0.9359 0.000 0.952 0.000 0.004 0.036 0.008
#> GSM247168 2 0.1124 0.9371 0.000 0.956 0.000 0.000 0.036 0.008
#> GSM247169 2 0.1124 0.9371 0.000 0.956 0.000 0.000 0.036 0.008
#> GSM247171 2 0.0436 0.9465 0.004 0.988 0.000 0.004 0.004 0.000
#> GSM247173 2 0.0665 0.9457 0.004 0.980 0.000 0.008 0.008 0.000
#> GSM247174 2 0.0777 0.9418 0.000 0.972 0.000 0.000 0.024 0.004
#> GSM247175 2 0.0000 0.9467 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247188 2 0.0363 0.9456 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM247189 2 0.5266 0.0617 0.004 0.492 0.000 0.420 0.084 0.000
#> GSM247190 2 0.0000 0.9467 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247650 1 0.5592 0.1328 0.536 0.000 0.012 0.004 0.352 0.096
#> GSM247651 1 0.6550 -0.0250 0.372 0.000 0.000 0.348 0.256 0.024
#> GSM247652 1 0.4704 -0.1858 0.488 0.000 0.000 0.000 0.044 0.468
#> GSM247653 6 0.3455 0.5193 0.052 0.000 0.036 0.000 0.076 0.836
#> GSM247654 6 0.4263 0.3981 0.276 0.000 0.008 0.000 0.032 0.684
#> GSM247655 1 0.4892 0.3345 0.720 0.000 0.000 0.056 0.148 0.076
#> GSM247656 6 0.7042 0.1703 0.280 0.000 0.256 0.000 0.072 0.392
#> GSM247657 6 0.4917 0.3431 0.300 0.000 0.016 0.000 0.056 0.628
#> GSM247658 6 0.4694 0.2071 0.376 0.000 0.000 0.000 0.052 0.572
#> GSM247659 3 0.6526 0.2980 0.100 0.000 0.544 0.000 0.144 0.212
#> GSM247660 1 0.6813 0.0794 0.424 0.000 0.000 0.296 0.224 0.056
#> GSM247661 6 0.4201 0.4767 0.084 0.000 0.048 0.000 0.084 0.784
#> GSM247662 1 0.6893 0.0609 0.464 0.000 0.100 0.000 0.160 0.276
#> GSM247663 5 0.6240 -0.1069 0.368 0.000 0.004 0.004 0.392 0.232
#> GSM247856 1 0.5999 -0.0138 0.504 0.000 0.052 0.000 0.084 0.360
#> GSM247857 1 0.6267 0.0330 0.464 0.000 0.028 0.000 0.168 0.340
#> GSM247859 1 0.6376 0.2865 0.576 0.000 0.000 0.160 0.112 0.152
#> GSM247860 6 0.4060 0.4801 0.060 0.000 0.016 0.000 0.156 0.768
#> GSM247862 1 0.6095 0.0800 0.432 0.000 0.000 0.012 0.180 0.376
#> GSM247864 1 0.5517 0.2283 0.612 0.000 0.000 0.048 0.268 0.072
#> GSM247865 4 0.6219 0.0294 0.360 0.000 0.000 0.480 0.108 0.052
#> GSM247866 6 0.6182 0.0125 0.264 0.000 0.000 0.004 0.340 0.392
#> GSM247876 5 0.4648 0.4813 0.148 0.000 0.012 0.016 0.740 0.084
#> GSM247877 5 0.4481 0.5229 0.048 0.000 0.008 0.212 0.720 0.012
#> GSM247878 5 0.5454 0.4505 0.160 0.000 0.000 0.232 0.600 0.008
#> GSM247879 5 0.4090 0.5334 0.072 0.000 0.068 0.020 0.808 0.032
#> GSM247881 1 0.4990 0.3203 0.660 0.000 0.000 0.004 0.184 0.152
#> GSM247883 1 0.4824 0.3715 0.736 0.000 0.000 0.072 0.088 0.104
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:skmeans 61 2.53e-12 2
#> CV:skmeans 61 1.51e-13 3
#> CV:skmeans 57 6.33e-18 4
#> CV:skmeans 36 1.83e-11 5
#> CV:skmeans 34 1.23e-11 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 21168 rows and 61 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 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 0.788 0.887 0.947 0.4733 0.541 0.541
#> 3 3 1.000 0.987 0.994 0.2889 0.845 0.715
#> 4 4 1.000 0.974 0.990 0.1074 0.926 0.814
#> 5 5 0.833 0.818 0.905 0.1156 0.928 0.778
#> 6 6 0.854 0.798 0.887 0.0343 0.974 0.899
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 3
There is also optional best \(k\) = 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
#> GSM246087 1 0.9998 0.142 0.508 0.492
#> GSM246088 1 0.7815 0.727 0.768 0.232
#> GSM246089 1 0.9491 0.481 0.632 0.368
#> GSM246090 1 0.9933 0.268 0.548 0.452
#> GSM246119 1 0.5946 0.827 0.856 0.144
#> GSM246120 1 0.8499 0.662 0.724 0.276
#> GSM246121 1 0.6801 0.789 0.820 0.180
#> GSM246122 2 0.9661 0.230 0.392 0.608
#> GSM246123 1 0.7745 0.729 0.772 0.228
#> GSM246422 1 0.0672 0.928 0.992 0.008
#> GSM246423 1 0.0376 0.930 0.996 0.004
#> GSM246484 1 0.2603 0.903 0.956 0.044
#> GSM246485 2 0.0938 0.977 0.012 0.988
#> GSM246486 2 0.0938 0.977 0.012 0.988
#> GSM246487 1 0.4562 0.858 0.904 0.096
#> GSM246488 2 0.1184 0.973 0.016 0.984
#> GSM246489 2 0.0938 0.977 0.012 0.988
#> GSM246490 2 0.0938 0.977 0.012 0.988
#> GSM246491 2 0.0938 0.977 0.012 0.988
#> GSM247162 2 0.0938 0.977 0.012 0.988
#> GSM247163 2 0.0938 0.977 0.012 0.988
#> GSM247164 2 0.0938 0.977 0.012 0.988
#> GSM247165 2 0.0938 0.977 0.012 0.988
#> GSM247166 2 0.0938 0.977 0.012 0.988
#> GSM247168 2 0.0938 0.977 0.012 0.988
#> GSM247169 2 0.0938 0.977 0.012 0.988
#> GSM247171 2 0.0938 0.977 0.012 0.988
#> GSM247173 2 0.0938 0.977 0.012 0.988
#> GSM247174 2 0.0938 0.977 0.012 0.988
#> GSM247175 2 0.0938 0.977 0.012 0.988
#> GSM247188 2 0.0938 0.977 0.012 0.988
#> GSM247189 2 0.0938 0.977 0.012 0.988
#> GSM247190 2 0.0938 0.977 0.012 0.988
#> GSM247650 1 0.0000 0.932 1.000 0.000
#> GSM247651 1 0.0000 0.932 1.000 0.000
#> GSM247652 1 0.0000 0.932 1.000 0.000
#> GSM247653 1 0.0000 0.932 1.000 0.000
#> GSM247654 1 0.0000 0.932 1.000 0.000
#> GSM247655 1 0.0000 0.932 1.000 0.000
#> GSM247656 1 0.0000 0.932 1.000 0.000
#> GSM247657 1 0.0000 0.932 1.000 0.000
#> GSM247658 1 0.0000 0.932 1.000 0.000
#> GSM247659 1 0.2603 0.911 0.956 0.044
#> GSM247660 1 0.0000 0.932 1.000 0.000
#> GSM247661 1 0.0938 0.924 0.988 0.012
#> GSM247662 1 0.0376 0.930 0.996 0.004
#> GSM247663 1 0.0000 0.932 1.000 0.000
#> GSM247856 1 0.0000 0.932 1.000 0.000
#> GSM247857 1 0.0000 0.932 1.000 0.000
#> GSM247859 1 0.0000 0.932 1.000 0.000
#> GSM247860 1 0.0000 0.932 1.000 0.000
#> GSM247862 1 0.0000 0.932 1.000 0.000
#> GSM247864 1 0.0000 0.932 1.000 0.000
#> GSM247865 1 0.0000 0.932 1.000 0.000
#> GSM247866 1 0.0000 0.932 1.000 0.000
#> GSM247876 1 0.0000 0.932 1.000 0.000
#> GSM247877 1 0.0000 0.932 1.000 0.000
#> GSM247878 1 0.0000 0.932 1.000 0.000
#> GSM247879 1 0.0376 0.930 0.996 0.004
#> GSM247881 1 0.0000 0.932 1.000 0.000
#> GSM247883 1 0.0000 0.932 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246422 1 0.0000 0.988 1.000 0.000 0.000
#> GSM246423 1 0.0000 0.988 1.000 0.000 0.000
#> GSM246484 1 0.0000 0.988 1.000 0.000 0.000
#> GSM246485 2 0.0000 1.000 0.000 1.000 0.000
#> GSM246486 2 0.0000 1.000 0.000 1.000 0.000
#> GSM246487 1 0.0000 0.988 1.000 0.000 0.000
#> GSM246488 2 0.0237 0.995 0.004 0.996 0.000
#> GSM246489 2 0.0000 1.000 0.000 1.000 0.000
#> GSM246490 2 0.0000 1.000 0.000 1.000 0.000
#> GSM246491 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247162 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247163 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247164 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247165 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247166 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247168 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247169 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247171 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247173 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247174 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247175 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247188 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247189 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247190 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247650 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247651 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247652 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247653 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247654 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247655 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247656 1 0.4796 0.720 0.780 0.000 0.220
#> GSM247657 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247658 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247659 1 0.4742 0.829 0.848 0.048 0.104
#> GSM247660 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247661 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247662 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247663 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247856 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247857 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247859 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247860 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247862 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247864 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247865 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247866 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247876 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247877 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247878 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247879 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247881 1 0.0000 0.988 1.000 0.000 0.000
#> GSM247883 1 0.0000 0.988 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM246422 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> GSM246423 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> GSM246484 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> GSM246485 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM246486 2 0.1118 0.963 0.000 0.964 0.000 0.036
#> GSM246487 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM246488 4 0.0000 0.911 0.000 0.000 0.000 1.000
#> GSM246489 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM246490 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM246491 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM247162 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM247163 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM247164 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM247165 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM247166 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM247168 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM247169 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM247171 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM247173 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM247174 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM247175 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM247188 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM247189 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM247190 2 0.0000 0.998 0.000 1.000 0.000 0.000
#> GSM247650 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247651 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247652 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247653 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247654 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247655 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247656 1 0.0592 0.970 0.984 0.000 0.016 0.000
#> GSM247657 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247658 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247659 1 0.4956 0.702 0.776 0.116 0.108 0.000
#> GSM247660 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247661 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247662 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247663 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247856 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247857 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247859 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247860 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247862 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247864 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247865 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247866 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247876 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247877 4 0.3907 0.647 0.232 0.000 0.000 0.768
#> GSM247878 1 0.2530 0.862 0.888 0.000 0.000 0.112
#> GSM247879 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247881 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM247883 1 0.0000 0.986 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246089 3 0.0162 0.997 0.000 0.000 0.996 0.000 0.004
#> GSM246090 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246422 4 0.0000 0.865 0.000 0.000 0.000 1.000 0.000
#> GSM246423 4 0.0000 0.865 0.000 0.000 0.000 1.000 0.000
#> GSM246484 4 0.0000 0.865 0.000 0.000 0.000 1.000 0.000
#> GSM246485 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM246486 2 0.0963 0.963 0.000 0.964 0.000 0.036 0.000
#> GSM246487 1 0.0000 0.767 1.000 0.000 0.000 0.000 0.000
#> GSM246488 4 0.0000 0.865 0.000 0.000 0.000 1.000 0.000
#> GSM246489 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM246490 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM246491 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM247162 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM247163 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM247164 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM247165 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM247166 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM247168 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM247169 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM247171 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM247174 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM247175 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM247189 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM247190 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM247650 1 0.1478 0.715 0.936 0.000 0.000 0.000 0.064
#> GSM247651 1 0.0290 0.767 0.992 0.000 0.000 0.000 0.008
#> GSM247652 1 0.3730 0.643 0.712 0.000 0.000 0.000 0.288
#> GSM247653 1 0.4305 0.327 0.512 0.000 0.000 0.000 0.488
#> GSM247654 1 0.4101 0.551 0.628 0.000 0.000 0.000 0.372
#> GSM247655 1 0.0000 0.767 1.000 0.000 0.000 0.000 0.000
#> GSM247656 5 0.3074 0.649 0.196 0.000 0.000 0.000 0.804
#> GSM247657 5 0.3661 0.666 0.276 0.000 0.000 0.000 0.724
#> GSM247658 1 0.3210 0.705 0.788 0.000 0.000 0.000 0.212
#> GSM247659 5 0.4738 0.631 0.164 0.012 0.076 0.000 0.748
#> GSM247660 1 0.0000 0.767 1.000 0.000 0.000 0.000 0.000
#> GSM247661 5 0.3143 0.576 0.204 0.000 0.000 0.000 0.796
#> GSM247662 5 0.4305 0.583 0.488 0.000 0.000 0.000 0.512
#> GSM247663 1 0.2852 0.720 0.828 0.000 0.000 0.000 0.172
#> GSM247856 1 0.4161 0.502 0.608 0.000 0.000 0.000 0.392
#> GSM247857 5 0.4256 0.628 0.436 0.000 0.000 0.000 0.564
#> GSM247859 1 0.2852 0.729 0.828 0.000 0.000 0.000 0.172
#> GSM247860 1 0.3949 0.445 0.668 0.000 0.000 0.000 0.332
#> GSM247862 1 0.0000 0.767 1.000 0.000 0.000 0.000 0.000
#> GSM247864 1 0.0000 0.767 1.000 0.000 0.000 0.000 0.000
#> GSM247865 1 0.2732 0.737 0.840 0.000 0.000 0.000 0.160
#> GSM247866 1 0.0162 0.766 0.996 0.000 0.000 0.000 0.004
#> GSM247876 1 0.2424 0.745 0.868 0.000 0.000 0.000 0.132
#> GSM247877 4 0.4161 0.262 0.392 0.000 0.000 0.608 0.000
#> GSM247878 1 0.1608 0.717 0.928 0.000 0.000 0.072 0.000
#> GSM247879 1 0.3932 0.105 0.672 0.000 0.000 0.000 0.328
#> GSM247881 1 0.2377 0.756 0.872 0.000 0.000 0.000 0.128
#> GSM247883 1 0.2891 0.738 0.824 0.000 0.000 0.000 0.176
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246088 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246089 3 0.3953 0.741 0.000 0.000 0.744 0.000 0.060 0.196
#> GSM246090 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246119 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246120 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246121 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246122 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246123 3 0.0000 0.972 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246422 4 0.0000 0.844 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM246423 4 0.0000 0.844 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM246484 4 0.0000 0.844 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM246485 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246486 2 0.0865 0.962 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM246487 1 0.0146 0.768 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM246488 4 0.0000 0.844 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM246489 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246490 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246491 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247162 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247163 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247164 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247165 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247166 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247168 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247169 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247171 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247174 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247175 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247189 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247190 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247650 1 0.2558 0.676 0.840 0.000 0.000 0.000 0.004 0.156
#> GSM247651 1 0.0291 0.768 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM247652 1 0.3684 0.584 0.628 0.000 0.000 0.000 0.372 0.000
#> GSM247653 6 0.5663 0.537 0.248 0.000 0.000 0.000 0.220 0.532
#> GSM247654 1 0.3823 0.506 0.564 0.000 0.000 0.000 0.436 0.000
#> GSM247655 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247656 5 0.1444 0.426 0.072 0.000 0.000 0.000 0.928 0.000
#> GSM247657 5 0.4487 0.788 0.068 0.000 0.000 0.000 0.668 0.264
#> GSM247658 1 0.3409 0.648 0.700 0.000 0.000 0.000 0.300 0.000
#> GSM247659 5 0.5005 0.758 0.072 0.004 0.004 0.000 0.612 0.308
#> GSM247660 1 0.0146 0.768 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM247661 6 0.4176 -0.144 0.064 0.000 0.000 0.000 0.220 0.716
#> GSM247662 5 0.5287 0.767 0.144 0.000 0.000 0.000 0.584 0.272
#> GSM247663 1 0.3151 0.672 0.748 0.000 0.000 0.000 0.252 0.000
#> GSM247856 1 0.3838 0.482 0.552 0.000 0.000 0.000 0.448 0.000
#> GSM247857 5 0.4972 0.800 0.108 0.000 0.000 0.000 0.620 0.272
#> GSM247859 1 0.2597 0.745 0.824 0.000 0.000 0.000 0.176 0.000
#> GSM247860 6 0.5575 0.555 0.296 0.000 0.000 0.000 0.172 0.532
#> GSM247862 1 0.0146 0.768 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM247864 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247865 1 0.2632 0.751 0.832 0.000 0.000 0.000 0.164 0.004
#> GSM247866 1 0.0363 0.765 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM247876 1 0.2006 0.763 0.892 0.000 0.000 0.000 0.104 0.004
#> GSM247877 4 0.4144 0.179 0.408 0.000 0.000 0.580 0.008 0.004
#> GSM247878 1 0.1644 0.708 0.920 0.000 0.000 0.076 0.000 0.004
#> GSM247879 1 0.5438 -0.178 0.496 0.000 0.000 0.000 0.380 0.124
#> GSM247881 1 0.2482 0.755 0.848 0.000 0.000 0.000 0.148 0.004
#> GSM247883 1 0.2996 0.718 0.772 0.000 0.000 0.000 0.228 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:pam 57 6.32e-10 2
#> CV:pam 61 6.70e-22 3
#> CV:pam 61 3.47e-22 4
#> CV:pam 57 4.82e-20 5
#> CV:pam 56 1.70e-18 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 21168 rows and 61 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 0.494 0.772 0.885 0.4954 0.503 0.503
#> 3 3 0.842 0.865 0.939 0.3144 0.733 0.522
#> 4 4 0.941 0.917 0.966 0.0982 0.918 0.774
#> 5 5 0.786 0.586 0.803 0.0628 0.923 0.740
#> 6 6 0.805 0.680 0.838 0.0613 0.905 0.621
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
#> GSM246087 2 0.8555 0.698 0.280 0.720
#> GSM246088 2 0.8555 0.698 0.280 0.720
#> GSM246089 2 0.8555 0.698 0.280 0.720
#> GSM246090 2 0.8555 0.698 0.280 0.720
#> GSM246119 2 0.8555 0.698 0.280 0.720
#> GSM246120 2 0.8555 0.698 0.280 0.720
#> GSM246121 2 0.8555 0.698 0.280 0.720
#> GSM246122 2 0.8555 0.698 0.280 0.720
#> GSM246123 2 0.8555 0.698 0.280 0.720
#> GSM246422 1 0.9983 0.373 0.524 0.476
#> GSM246423 1 0.9983 0.373 0.524 0.476
#> GSM246484 1 0.9983 0.373 0.524 0.476
#> GSM246485 1 0.9933 0.401 0.548 0.452
#> GSM246486 1 0.9970 0.368 0.532 0.468
#> GSM246487 1 0.9286 0.563 0.656 0.344
#> GSM246488 1 0.9963 0.377 0.536 0.464
#> GSM246489 2 0.0938 0.867 0.012 0.988
#> GSM246490 2 0.0938 0.867 0.012 0.988
#> GSM246491 2 0.0938 0.867 0.012 0.988
#> GSM247162 2 0.0938 0.867 0.012 0.988
#> GSM247163 2 0.1184 0.865 0.016 0.984
#> GSM247164 2 0.0938 0.867 0.012 0.988
#> GSM247165 2 0.0938 0.867 0.012 0.988
#> GSM247166 2 0.0938 0.867 0.012 0.988
#> GSM247168 2 0.0938 0.867 0.012 0.988
#> GSM247169 2 0.0938 0.867 0.012 0.988
#> GSM247171 2 0.0938 0.867 0.012 0.988
#> GSM247173 2 0.0938 0.867 0.012 0.988
#> GSM247174 2 0.0938 0.867 0.012 0.988
#> GSM247175 2 0.0938 0.867 0.012 0.988
#> GSM247188 2 0.0938 0.867 0.012 0.988
#> GSM247189 2 0.2948 0.833 0.052 0.948
#> GSM247190 2 0.0938 0.867 0.012 0.988
#> GSM247650 1 0.0000 0.859 1.000 0.000
#> GSM247651 1 0.0000 0.859 1.000 0.000
#> GSM247652 1 0.0000 0.859 1.000 0.000
#> GSM247653 1 0.0000 0.859 1.000 0.000
#> GSM247654 1 0.0000 0.859 1.000 0.000
#> GSM247655 1 0.0000 0.859 1.000 0.000
#> GSM247656 1 0.0376 0.856 0.996 0.004
#> GSM247657 1 0.0000 0.859 1.000 0.000
#> GSM247658 1 0.0000 0.859 1.000 0.000
#> GSM247659 1 0.4161 0.806 0.916 0.084
#> GSM247660 1 0.0000 0.859 1.000 0.000
#> GSM247661 1 0.0000 0.859 1.000 0.000
#> GSM247662 1 0.0672 0.854 0.992 0.008
#> GSM247663 1 0.0000 0.859 1.000 0.000
#> GSM247856 1 0.0000 0.859 1.000 0.000
#> GSM247857 1 0.0000 0.859 1.000 0.000
#> GSM247859 1 0.0000 0.859 1.000 0.000
#> GSM247860 1 0.0000 0.859 1.000 0.000
#> GSM247862 1 0.0000 0.859 1.000 0.000
#> GSM247864 1 0.0000 0.859 1.000 0.000
#> GSM247865 1 0.5519 0.775 0.872 0.128
#> GSM247866 1 0.0000 0.859 1.000 0.000
#> GSM247876 1 0.2948 0.830 0.948 0.052
#> GSM247877 1 0.9248 0.562 0.660 0.340
#> GSM247878 1 0.8555 0.657 0.720 0.280
#> GSM247879 1 0.5519 0.773 0.872 0.128
#> GSM247881 1 0.0000 0.859 1.000 0.000
#> GSM247883 1 0.2423 0.839 0.960 0.040
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 0.948 0.000 0.000 1.000
#> GSM246088 3 0.0000 0.948 0.000 0.000 1.000
#> GSM246089 3 0.0000 0.948 0.000 0.000 1.000
#> GSM246090 3 0.0000 0.948 0.000 0.000 1.000
#> GSM246119 3 0.0000 0.948 0.000 0.000 1.000
#> GSM246120 3 0.0000 0.948 0.000 0.000 1.000
#> GSM246121 3 0.0000 0.948 0.000 0.000 1.000
#> GSM246122 3 0.0000 0.948 0.000 0.000 1.000
#> GSM246123 3 0.0000 0.948 0.000 0.000 1.000
#> GSM246422 3 0.3589 0.897 0.052 0.048 0.900
#> GSM246423 3 0.3589 0.897 0.052 0.048 0.900
#> GSM246484 3 0.3589 0.897 0.052 0.048 0.900
#> GSM246485 2 0.7425 0.509 0.052 0.620 0.328
#> GSM246486 2 0.6579 0.549 0.020 0.652 0.328
#> GSM246487 2 0.7514 0.504 0.056 0.616 0.328
#> GSM246488 2 0.6819 0.539 0.028 0.644 0.328
#> GSM246489 2 0.0000 0.892 0.000 1.000 0.000
#> GSM246490 2 0.0000 0.892 0.000 1.000 0.000
#> GSM246491 2 0.1289 0.875 0.000 0.968 0.032
#> GSM247162 2 0.0000 0.892 0.000 1.000 0.000
#> GSM247163 2 0.2448 0.845 0.000 0.924 0.076
#> GSM247164 2 0.0237 0.890 0.000 0.996 0.004
#> GSM247165 2 0.0475 0.888 0.004 0.992 0.004
#> GSM247166 2 0.0000 0.892 0.000 1.000 0.000
#> GSM247168 2 0.0000 0.892 0.000 1.000 0.000
#> GSM247169 2 0.0000 0.892 0.000 1.000 0.000
#> GSM247171 2 0.0000 0.892 0.000 1.000 0.000
#> GSM247173 2 0.0000 0.892 0.000 1.000 0.000
#> GSM247174 2 0.0000 0.892 0.000 1.000 0.000
#> GSM247175 2 0.0000 0.892 0.000 1.000 0.000
#> GSM247188 2 0.0000 0.892 0.000 1.000 0.000
#> GSM247189 2 0.6579 0.549 0.020 0.652 0.328
#> GSM247190 2 0.0000 0.892 0.000 1.000 0.000
#> GSM247650 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247651 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247652 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247653 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247654 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247655 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247656 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247657 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247658 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247659 1 0.5810 0.490 0.664 0.000 0.336
#> GSM247660 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247661 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247662 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247663 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247856 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247857 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247859 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247860 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247862 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247864 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247865 1 0.0237 0.943 0.996 0.000 0.004
#> GSM247866 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247876 1 0.5397 0.601 0.720 0.000 0.280
#> GSM247877 3 0.5619 0.668 0.244 0.012 0.744
#> GSM247878 1 0.5178 0.641 0.744 0.000 0.256
#> GSM247879 1 0.5810 0.490 0.664 0.000 0.336
#> GSM247881 1 0.0000 0.947 1.000 0.000 0.000
#> GSM247883 1 0.0000 0.947 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246422 4 0.0000 0.944 0.000 0.000 0 1.000
#> GSM246423 4 0.0000 0.944 0.000 0.000 0 1.000
#> GSM246484 4 0.0000 0.944 0.000 0.000 0 1.000
#> GSM246485 4 0.0000 0.944 0.000 0.000 0 1.000
#> GSM246486 4 0.0000 0.944 0.000 0.000 0 1.000
#> GSM246487 4 0.0188 0.940 0.004 0.000 0 0.996
#> GSM246488 4 0.0000 0.944 0.000 0.000 0 1.000
#> GSM246489 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM246490 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM246491 2 0.4564 0.459 0.000 0.672 0 0.328
#> GSM247162 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247163 4 0.4925 0.221 0.000 0.428 0 0.572
#> GSM247164 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247165 2 0.0336 0.966 0.000 0.992 0 0.008
#> GSM247166 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247168 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247169 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247171 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247173 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247174 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247175 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247188 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247189 4 0.0000 0.944 0.000 0.000 0 1.000
#> GSM247190 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247650 1 0.0469 0.944 0.988 0.000 0 0.012
#> GSM247651 1 0.0469 0.944 0.988 0.000 0 0.012
#> GSM247652 1 0.0000 0.947 1.000 0.000 0 0.000
#> GSM247653 1 0.0000 0.947 1.000 0.000 0 0.000
#> GSM247654 1 0.0000 0.947 1.000 0.000 0 0.000
#> GSM247655 1 0.0188 0.947 0.996 0.000 0 0.004
#> GSM247656 1 0.0336 0.945 0.992 0.000 0 0.008
#> GSM247657 1 0.0000 0.947 1.000 0.000 0 0.000
#> GSM247658 1 0.0000 0.947 1.000 0.000 0 0.000
#> GSM247659 1 0.4564 0.565 0.672 0.000 0 0.328
#> GSM247660 1 0.0188 0.947 0.996 0.000 0 0.004
#> GSM247661 1 0.0000 0.947 1.000 0.000 0 0.000
#> GSM247662 1 0.0336 0.945 0.992 0.000 0 0.008
#> GSM247663 1 0.0469 0.944 0.988 0.000 0 0.012
#> GSM247856 1 0.0188 0.947 0.996 0.000 0 0.004
#> GSM247857 1 0.0000 0.947 1.000 0.000 0 0.000
#> GSM247859 1 0.0188 0.947 0.996 0.000 0 0.004
#> GSM247860 1 0.0000 0.947 1.000 0.000 0 0.000
#> GSM247862 1 0.0000 0.947 1.000 0.000 0 0.000
#> GSM247864 1 0.0188 0.947 0.996 0.000 0 0.004
#> GSM247865 1 0.1118 0.926 0.964 0.000 0 0.036
#> GSM247866 1 0.0000 0.947 1.000 0.000 0 0.000
#> GSM247876 1 0.3311 0.792 0.828 0.000 0 0.172
#> GSM247877 4 0.0188 0.940 0.004 0.000 0 0.996
#> GSM247878 1 0.4790 0.464 0.620 0.000 0 0.380
#> GSM247879 1 0.4624 0.544 0.660 0.000 0 0.340
#> GSM247881 1 0.0000 0.947 1.000 0.000 0 0.000
#> GSM247883 1 0.0188 0.947 0.996 0.000 0 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM246088 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM246089 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM246090 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM246119 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM246120 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM246121 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM246122 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM246123 3 0.0000 1.00000 0.000 0.000 1 0.000 0.000
#> GSM246422 4 0.4249 0.68785 0.000 0.000 0 0.568 0.432
#> GSM246423 4 0.4249 0.68785 0.000 0.000 0 0.568 0.432
#> GSM246484 4 0.4249 0.68785 0.000 0.000 0 0.568 0.432
#> GSM246485 4 0.1757 0.77432 0.012 0.004 0 0.936 0.048
#> GSM246486 4 0.1124 0.78774 0.000 0.004 0 0.960 0.036
#> GSM246487 4 0.2052 0.78127 0.004 0.004 0 0.912 0.080
#> GSM246488 4 0.0963 0.78846 0.000 0.000 0 0.964 0.036
#> GSM246489 2 0.0000 0.96145 0.000 1.000 0 0.000 0.000
#> GSM246490 2 0.0000 0.96145 0.000 1.000 0 0.000 0.000
#> GSM246491 2 0.3966 0.46339 0.000 0.664 0 0.336 0.000
#> GSM247162 2 0.0000 0.96145 0.000 1.000 0 0.000 0.000
#> GSM247163 4 0.4291 0.00574 0.000 0.464 0 0.536 0.000
#> GSM247164 2 0.1043 0.93325 0.000 0.960 0 0.040 0.000
#> GSM247165 2 0.1851 0.88544 0.000 0.912 0 0.088 0.000
#> GSM247166 2 0.0162 0.96116 0.000 0.996 0 0.000 0.004
#> GSM247168 2 0.0162 0.96116 0.000 0.996 0 0.000 0.004
#> GSM247169 2 0.0162 0.96116 0.000 0.996 0 0.000 0.004
#> GSM247171 2 0.0404 0.95471 0.000 0.988 0 0.012 0.000
#> GSM247173 2 0.0000 0.96145 0.000 1.000 0 0.000 0.000
#> GSM247174 2 0.0162 0.96116 0.000 0.996 0 0.000 0.004
#> GSM247175 2 0.0000 0.96145 0.000 1.000 0 0.000 0.000
#> GSM247188 2 0.0000 0.96145 0.000 1.000 0 0.000 0.000
#> GSM247189 4 0.0963 0.78846 0.000 0.000 0 0.964 0.036
#> GSM247190 2 0.0162 0.96116 0.000 0.996 0 0.000 0.004
#> GSM247650 1 0.4331 0.27343 0.596 0.000 0 0.004 0.400
#> GSM247651 5 0.4555 0.14467 0.472 0.000 0 0.008 0.520
#> GSM247652 1 0.3752 0.46048 0.708 0.000 0 0.000 0.292
#> GSM247653 1 0.1043 0.44886 0.960 0.000 0 0.000 0.040
#> GSM247654 1 0.0510 0.45866 0.984 0.000 0 0.000 0.016
#> GSM247655 5 0.4446 0.13576 0.476 0.000 0 0.004 0.520
#> GSM247656 1 0.3480 0.50164 0.752 0.000 0 0.000 0.248
#> GSM247657 1 0.0510 0.45866 0.984 0.000 0 0.000 0.016
#> GSM247658 1 0.3143 0.50598 0.796 0.000 0 0.000 0.204
#> GSM247659 1 0.5579 0.21167 0.552 0.000 0 0.080 0.368
#> GSM247660 5 0.4555 0.14467 0.472 0.000 0 0.008 0.520
#> GSM247661 1 0.1608 0.45652 0.928 0.000 0 0.000 0.072
#> GSM247662 1 0.3949 0.42266 0.668 0.000 0 0.000 0.332
#> GSM247663 1 0.4331 0.27343 0.596 0.000 0 0.004 0.400
#> GSM247856 1 0.3109 0.51487 0.800 0.000 0 0.000 0.200
#> GSM247857 1 0.2377 0.51026 0.872 0.000 0 0.000 0.128
#> GSM247859 1 0.4449 -0.11743 0.512 0.000 0 0.004 0.484
#> GSM247860 1 0.0794 0.45481 0.972 0.000 0 0.000 0.028
#> GSM247862 1 0.4114 0.28083 0.624 0.000 0 0.000 0.376
#> GSM247864 5 0.4302 0.11600 0.480 0.000 0 0.000 0.520
#> GSM247865 5 0.5114 0.07558 0.476 0.000 0 0.036 0.488
#> GSM247866 1 0.3983 0.34775 0.660 0.000 0 0.000 0.340
#> GSM247876 1 0.4590 0.24471 0.568 0.000 0 0.012 0.420
#> GSM247877 5 0.5594 -0.57579 0.072 0.000 0 0.436 0.492
#> GSM247878 5 0.6429 0.06379 0.296 0.000 0 0.208 0.496
#> GSM247879 1 0.6000 0.03230 0.460 0.000 0 0.112 0.428
#> GSM247881 1 0.4425 0.24517 0.600 0.000 0 0.008 0.392
#> GSM247883 1 0.4656 -0.12766 0.508 0.000 0 0.012 0.480
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246088 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246089 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246090 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246119 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246120 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246121 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246122 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246123 3 0.0000 1.0000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246422 6 0.0632 0.8122 0.000 0.000 0 0.024 0.000 0.976
#> GSM246423 6 0.0632 0.8122 0.000 0.000 0 0.024 0.000 0.976
#> GSM246484 6 0.0632 0.8122 0.000 0.000 0 0.024 0.000 0.976
#> GSM246485 4 0.1411 0.9089 0.000 0.004 0 0.936 0.060 0.000
#> GSM246486 4 0.0000 0.9366 0.000 0.000 0 1.000 0.000 0.000
#> GSM246487 4 0.3004 0.8375 0.008 0.004 0 0.860 0.080 0.048
#> GSM246488 4 0.0000 0.9366 0.000 0.000 0 1.000 0.000 0.000
#> GSM246489 2 0.0000 0.9441 0.000 1.000 0 0.000 0.000 0.000
#> GSM246490 2 0.0692 0.9362 0.000 0.976 0 0.020 0.000 0.004
#> GSM246491 2 0.1814 0.8800 0.000 0.900 0 0.100 0.000 0.000
#> GSM247162 2 0.0260 0.9444 0.000 0.992 0 0.000 0.000 0.008
#> GSM247163 2 0.3101 0.7339 0.000 0.756 0 0.244 0.000 0.000
#> GSM247164 2 0.2320 0.8494 0.000 0.864 0 0.132 0.000 0.004
#> GSM247165 2 0.3383 0.6838 0.000 0.728 0 0.268 0.000 0.004
#> GSM247166 2 0.0260 0.9444 0.000 0.992 0 0.000 0.000 0.008
#> GSM247168 2 0.0260 0.9444 0.000 0.992 0 0.000 0.000 0.008
#> GSM247169 2 0.0260 0.9444 0.000 0.992 0 0.000 0.000 0.008
#> GSM247171 2 0.0603 0.9387 0.000 0.980 0 0.016 0.000 0.004
#> GSM247173 2 0.0146 0.9433 0.000 0.996 0 0.000 0.000 0.004
#> GSM247174 2 0.0260 0.9444 0.000 0.992 0 0.000 0.000 0.008
#> GSM247175 2 0.0000 0.9441 0.000 1.000 0 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.9441 0.000 1.000 0 0.000 0.000 0.000
#> GSM247189 4 0.0146 0.9347 0.000 0.004 0 0.996 0.000 0.000
#> GSM247190 2 0.0260 0.9444 0.000 0.992 0 0.000 0.000 0.008
#> GSM247650 5 0.4062 -0.1954 0.440 0.000 0 0.000 0.552 0.008
#> GSM247651 5 0.3565 0.5203 0.304 0.000 0 0.004 0.692 0.000
#> GSM247652 1 0.2340 0.5754 0.852 0.000 0 0.000 0.148 0.000
#> GSM247653 1 0.0458 0.6456 0.984 0.000 0 0.000 0.016 0.000
#> GSM247654 1 0.0000 0.6431 1.000 0.000 0 0.000 0.000 0.000
#> GSM247655 5 0.3428 0.5225 0.304 0.000 0 0.000 0.696 0.000
#> GSM247656 1 0.3695 0.3653 0.624 0.000 0 0.000 0.376 0.000
#> GSM247657 1 0.0000 0.6431 1.000 0.000 0 0.000 0.000 0.000
#> GSM247658 1 0.2597 0.5451 0.824 0.000 0 0.000 0.176 0.000
#> GSM247659 1 0.5206 0.1550 0.492 0.000 0 0.012 0.436 0.060
#> GSM247660 5 0.3428 0.5225 0.304 0.000 0 0.000 0.696 0.000
#> GSM247661 1 0.1010 0.6400 0.960 0.000 0 0.000 0.036 0.004
#> GSM247662 1 0.4032 0.3100 0.572 0.000 0 0.000 0.420 0.008
#> GSM247663 5 0.4057 -0.1894 0.436 0.000 0 0.000 0.556 0.008
#> GSM247856 1 0.3101 0.5075 0.756 0.000 0 0.000 0.244 0.000
#> GSM247857 1 0.0937 0.6411 0.960 0.000 0 0.000 0.040 0.000
#> GSM247859 5 0.3578 0.4994 0.340 0.000 0 0.000 0.660 0.000
#> GSM247860 1 0.0260 0.6458 0.992 0.000 0 0.000 0.008 0.000
#> GSM247862 1 0.3607 0.1987 0.652 0.000 0 0.000 0.348 0.000
#> GSM247864 5 0.3428 0.5225 0.304 0.000 0 0.000 0.696 0.000
#> GSM247865 5 0.4124 0.5049 0.332 0.000 0 0.008 0.648 0.012
#> GSM247866 1 0.3774 0.0227 0.592 0.000 0 0.000 0.408 0.000
#> GSM247876 5 0.4760 -0.1874 0.436 0.000 0 0.004 0.520 0.040
#> GSM247877 6 0.3649 0.7204 0.000 0.000 0 0.040 0.196 0.764
#> GSM247878 6 0.4565 0.5385 0.000 0.000 0 0.036 0.432 0.532
#> GSM247879 5 0.5407 -0.0553 0.340 0.000 0 0.024 0.564 0.072
#> GSM247881 1 0.3563 0.2412 0.664 0.000 0 0.000 0.336 0.000
#> GSM247883 5 0.3699 0.5038 0.336 0.000 0 0.004 0.660 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:mclust 55 7.58e-12 2
#> CV:mclust 59 4.76e-19 3
#> CV:mclust 58 8.78e-22 4
#> CV:mclust 35 4.09e-13 5
#> CV:mclust 50 8.71e-16 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 21168 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.774 0.870 0.947 0.5008 0.492 0.492
#> 3 3 0.874 0.895 0.956 0.3011 0.661 0.424
#> 4 4 0.885 0.892 0.950 0.1035 0.830 0.579
#> 5 5 0.835 0.800 0.907 0.0507 0.966 0.885
#> 6 6 0.735 0.597 0.792 0.0610 0.961 0.855
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
#> GSM246087 1 0.0000 0.939 1.000 0.000
#> GSM246088 1 0.0000 0.939 1.000 0.000
#> GSM246089 1 0.0000 0.939 1.000 0.000
#> GSM246090 1 0.0000 0.939 1.000 0.000
#> GSM246119 1 0.0000 0.939 1.000 0.000
#> GSM246120 1 0.0000 0.939 1.000 0.000
#> GSM246121 1 0.0000 0.939 1.000 0.000
#> GSM246122 1 0.0000 0.939 1.000 0.000
#> GSM246123 1 0.0000 0.939 1.000 0.000
#> GSM246422 2 0.0000 0.940 0.000 1.000
#> GSM246423 2 0.0000 0.940 0.000 1.000
#> GSM246484 2 0.0000 0.940 0.000 1.000
#> GSM246485 2 0.0000 0.940 0.000 1.000
#> GSM246486 2 0.0000 0.940 0.000 1.000
#> GSM246487 2 0.0000 0.940 0.000 1.000
#> GSM246488 2 0.0000 0.940 0.000 1.000
#> GSM246489 2 0.0000 0.940 0.000 1.000
#> GSM246490 2 0.0000 0.940 0.000 1.000
#> GSM246491 2 0.0000 0.940 0.000 1.000
#> GSM247162 2 0.0000 0.940 0.000 1.000
#> GSM247163 2 0.0000 0.940 0.000 1.000
#> GSM247164 2 0.0000 0.940 0.000 1.000
#> GSM247165 2 0.0000 0.940 0.000 1.000
#> GSM247166 2 0.0000 0.940 0.000 1.000
#> GSM247168 2 0.0000 0.940 0.000 1.000
#> GSM247169 2 0.0000 0.940 0.000 1.000
#> GSM247171 2 0.0000 0.940 0.000 1.000
#> GSM247173 2 0.0000 0.940 0.000 1.000
#> GSM247174 2 0.0000 0.940 0.000 1.000
#> GSM247175 2 0.0000 0.940 0.000 1.000
#> GSM247188 2 0.0000 0.940 0.000 1.000
#> GSM247189 2 0.0000 0.940 0.000 1.000
#> GSM247190 2 0.0000 0.940 0.000 1.000
#> GSM247650 1 0.0000 0.939 1.000 0.000
#> GSM247651 2 0.7883 0.688 0.236 0.764
#> GSM247652 1 0.0000 0.939 1.000 0.000
#> GSM247653 1 0.0000 0.939 1.000 0.000
#> GSM247654 1 0.0000 0.939 1.000 0.000
#> GSM247655 1 0.9944 0.142 0.544 0.456
#> GSM247656 1 0.0000 0.939 1.000 0.000
#> GSM247657 1 0.0000 0.939 1.000 0.000
#> GSM247658 1 0.3114 0.895 0.944 0.056
#> GSM247659 1 0.0000 0.939 1.000 0.000
#> GSM247660 2 0.8608 0.609 0.284 0.716
#> GSM247661 1 0.0000 0.939 1.000 0.000
#> GSM247662 1 0.0000 0.939 1.000 0.000
#> GSM247663 1 0.0000 0.939 1.000 0.000
#> GSM247856 1 0.0000 0.939 1.000 0.000
#> GSM247857 1 0.0000 0.939 1.000 0.000
#> GSM247859 2 0.8327 0.644 0.264 0.736
#> GSM247860 1 0.0938 0.930 0.988 0.012
#> GSM247862 1 0.9248 0.481 0.660 0.340
#> GSM247864 1 0.6438 0.780 0.836 0.164
#> GSM247865 2 0.1633 0.922 0.024 0.976
#> GSM247866 2 0.9635 0.374 0.388 0.612
#> GSM247876 1 0.0000 0.939 1.000 0.000
#> GSM247877 1 0.7299 0.726 0.796 0.204
#> GSM247878 1 0.9580 0.380 0.620 0.380
#> GSM247879 1 0.0000 0.939 1.000 0.000
#> GSM247881 2 0.9393 0.457 0.356 0.644
#> GSM247883 2 0.3733 0.881 0.072 0.928
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 0.9197 0.000 0.000 1.000
#> GSM246088 3 0.0000 0.9197 0.000 0.000 1.000
#> GSM246089 3 0.0000 0.9197 0.000 0.000 1.000
#> GSM246090 3 0.0000 0.9197 0.000 0.000 1.000
#> GSM246119 3 0.0000 0.9197 0.000 0.000 1.000
#> GSM246120 3 0.0000 0.9197 0.000 0.000 1.000
#> GSM246121 3 0.0000 0.9197 0.000 0.000 1.000
#> GSM246122 3 0.0000 0.9197 0.000 0.000 1.000
#> GSM246123 3 0.0000 0.9197 0.000 0.000 1.000
#> GSM246422 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM246423 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM246484 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM246485 2 0.2625 0.8872 0.084 0.916 0.000
#> GSM246486 2 0.2537 0.8914 0.080 0.920 0.000
#> GSM246487 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM246488 2 0.6026 0.4174 0.376 0.624 0.000
#> GSM246489 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM246490 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM246491 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM247162 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM247163 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM247164 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM247165 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM247166 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM247168 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM247169 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM247171 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM247173 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM247174 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM247175 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM247188 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM247189 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM247190 2 0.0000 0.9666 0.000 1.000 0.000
#> GSM247650 1 0.2356 0.8969 0.928 0.000 0.072
#> GSM247651 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM247652 1 0.0237 0.9476 0.996 0.000 0.004
#> GSM247653 3 0.5529 0.6190 0.296 0.000 0.704
#> GSM247654 1 0.4291 0.7652 0.820 0.000 0.180
#> GSM247655 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM247656 3 0.4291 0.7856 0.180 0.000 0.820
#> GSM247657 1 0.6299 0.0164 0.524 0.000 0.476
#> GSM247658 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM247659 3 0.0000 0.9197 0.000 0.000 1.000
#> GSM247660 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM247661 3 0.4504 0.7692 0.196 0.000 0.804
#> GSM247662 3 0.5363 0.6305 0.276 0.000 0.724
#> GSM247663 1 0.0424 0.9453 0.992 0.000 0.008
#> GSM247856 1 0.2356 0.8954 0.928 0.000 0.072
#> GSM247857 1 0.5363 0.6175 0.724 0.000 0.276
#> GSM247859 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM247860 1 0.2959 0.8680 0.900 0.000 0.100
#> GSM247862 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM247864 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM247865 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM247866 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM247876 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM247877 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM247878 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM247879 1 0.0424 0.9453 0.992 0.000 0.008
#> GSM247881 1 0.0000 0.9497 1.000 0.000 0.000
#> GSM247883 1 0.0000 0.9497 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM246088 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM246089 3 0.0336 0.991 0.000 0.000 0.992 0.008
#> GSM246090 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM246119 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM246120 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM246121 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM246122 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM246123 3 0.0000 0.999 0.000 0.000 1.000 0.000
#> GSM246422 4 0.0336 0.905 0.008 0.000 0.000 0.992
#> GSM246423 4 0.0336 0.905 0.008 0.000 0.000 0.992
#> GSM246484 4 0.0336 0.905 0.008 0.000 0.000 0.992
#> GSM246485 2 0.2408 0.859 0.000 0.896 0.000 0.104
#> GSM246486 2 0.4855 0.361 0.000 0.600 0.000 0.400
#> GSM246487 4 0.5395 0.724 0.092 0.172 0.000 0.736
#> GSM246488 4 0.1576 0.878 0.004 0.048 0.000 0.948
#> GSM246489 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM246490 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM246491 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM247162 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM247163 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM247164 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM247165 2 0.0592 0.938 0.000 0.984 0.000 0.016
#> GSM247166 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM247168 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM247169 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM247171 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM247173 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM247174 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM247175 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM247188 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM247189 2 0.4661 0.490 0.000 0.652 0.000 0.348
#> GSM247190 2 0.0000 0.950 0.000 1.000 0.000 0.000
#> GSM247650 1 0.0469 0.932 0.988 0.000 0.012 0.000
#> GSM247651 1 0.4072 0.675 0.748 0.000 0.000 0.252
#> GSM247652 1 0.0188 0.932 0.996 0.000 0.004 0.000
#> GSM247653 1 0.0672 0.931 0.984 0.000 0.008 0.008
#> GSM247654 1 0.0469 0.931 0.988 0.000 0.012 0.000
#> GSM247655 1 0.0707 0.927 0.980 0.000 0.000 0.020
#> GSM247656 1 0.3764 0.735 0.784 0.000 0.216 0.000
#> GSM247657 1 0.0592 0.930 0.984 0.000 0.016 0.000
#> GSM247658 1 0.0188 0.932 0.996 0.000 0.000 0.004
#> GSM247659 1 0.5143 0.212 0.540 0.000 0.456 0.004
#> GSM247660 1 0.2408 0.862 0.896 0.000 0.000 0.104
#> GSM247661 1 0.0672 0.931 0.984 0.000 0.008 0.008
#> GSM247662 1 0.1302 0.915 0.956 0.000 0.044 0.000
#> GSM247663 1 0.1042 0.927 0.972 0.000 0.008 0.020
#> GSM247856 1 0.0188 0.932 0.996 0.000 0.004 0.000
#> GSM247857 1 0.0336 0.932 0.992 0.000 0.008 0.000
#> GSM247859 1 0.0592 0.929 0.984 0.000 0.000 0.016
#> GSM247860 1 0.0524 0.932 0.988 0.000 0.004 0.008
#> GSM247862 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM247864 1 0.0592 0.929 0.984 0.000 0.000 0.016
#> GSM247865 1 0.1022 0.921 0.968 0.000 0.000 0.032
#> GSM247866 1 0.0336 0.932 0.992 0.000 0.000 0.008
#> GSM247876 1 0.3975 0.691 0.760 0.000 0.000 0.240
#> GSM247877 4 0.0188 0.902 0.004 0.000 0.000 0.996
#> GSM247878 4 0.0817 0.900 0.024 0.000 0.000 0.976
#> GSM247879 4 0.4228 0.675 0.232 0.000 0.008 0.760
#> GSM247881 1 0.0000 0.932 1.000 0.000 0.000 0.000
#> GSM247883 1 0.0592 0.929 0.984 0.000 0.000 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0510 0.915 0.000 0.000 0.984 0.000 0.016
#> GSM246088 3 0.0404 0.916 0.000 0.000 0.988 0.000 0.012
#> GSM246089 3 0.4291 0.289 0.000 0.000 0.536 0.000 0.464
#> GSM246090 3 0.0000 0.918 0.000 0.000 1.000 0.000 0.000
#> GSM246119 3 0.0703 0.917 0.000 0.000 0.976 0.000 0.024
#> GSM246120 3 0.0510 0.918 0.000 0.000 0.984 0.000 0.016
#> GSM246121 3 0.1341 0.904 0.000 0.000 0.944 0.000 0.056
#> GSM246122 3 0.0609 0.913 0.000 0.000 0.980 0.000 0.020
#> GSM246123 3 0.1410 0.902 0.000 0.000 0.940 0.000 0.060
#> GSM246422 4 0.0162 0.885 0.000 0.000 0.000 0.996 0.004
#> GSM246423 4 0.0000 0.884 0.000 0.000 0.000 1.000 0.000
#> GSM246484 4 0.0162 0.885 0.000 0.000 0.000 0.996 0.004
#> GSM246485 2 0.3063 0.839 0.012 0.864 0.000 0.104 0.020
#> GSM246486 2 0.3928 0.593 0.000 0.700 0.000 0.296 0.004
#> GSM246487 4 0.4454 0.705 0.092 0.108 0.000 0.784 0.016
#> GSM246488 4 0.1571 0.846 0.000 0.060 0.000 0.936 0.004
#> GSM246489 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000
#> GSM246490 2 0.0162 0.954 0.000 0.996 0.000 0.000 0.004
#> GSM246491 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000
#> GSM247162 2 0.0290 0.954 0.000 0.992 0.000 0.000 0.008
#> GSM247163 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000
#> GSM247164 2 0.0566 0.952 0.000 0.984 0.000 0.004 0.012
#> GSM247165 2 0.0162 0.953 0.000 0.996 0.000 0.004 0.000
#> GSM247166 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000
#> GSM247168 2 0.0000 0.954 0.000 1.000 0.000 0.000 0.000
#> GSM247169 2 0.0162 0.954 0.000 0.996 0.000 0.000 0.004
#> GSM247171 2 0.0404 0.953 0.000 0.988 0.000 0.000 0.012
#> GSM247173 2 0.0162 0.954 0.000 0.996 0.000 0.000 0.004
#> GSM247174 2 0.0290 0.954 0.000 0.992 0.000 0.000 0.008
#> GSM247175 2 0.0162 0.954 0.000 0.996 0.000 0.000 0.004
#> GSM247188 2 0.0404 0.953 0.000 0.988 0.000 0.000 0.012
#> GSM247189 2 0.4622 0.591 0.000 0.692 0.000 0.264 0.044
#> GSM247190 2 0.0404 0.953 0.000 0.988 0.000 0.000 0.012
#> GSM247650 1 0.1300 0.859 0.956 0.000 0.016 0.000 0.028
#> GSM247651 1 0.4651 0.379 0.608 0.000 0.000 0.372 0.020
#> GSM247652 1 0.0609 0.856 0.980 0.000 0.000 0.000 0.020
#> GSM247653 1 0.2852 0.750 0.828 0.000 0.000 0.000 0.172
#> GSM247654 1 0.0671 0.858 0.980 0.000 0.004 0.000 0.016
#> GSM247655 1 0.0693 0.860 0.980 0.000 0.000 0.008 0.012
#> GSM247656 1 0.4804 0.413 0.636 0.000 0.328 0.000 0.036
#> GSM247657 1 0.0955 0.856 0.968 0.000 0.004 0.000 0.028
#> GSM247658 1 0.0880 0.858 0.968 0.000 0.000 0.000 0.032
#> GSM247659 1 0.6176 0.219 0.540 0.000 0.172 0.000 0.288
#> GSM247660 1 0.2900 0.797 0.864 0.000 0.000 0.108 0.028
#> GSM247661 1 0.1965 0.824 0.904 0.000 0.000 0.000 0.096
#> GSM247662 1 0.3437 0.750 0.832 0.000 0.120 0.000 0.048
#> GSM247663 1 0.1626 0.855 0.940 0.000 0.000 0.016 0.044
#> GSM247856 1 0.0771 0.856 0.976 0.000 0.000 0.004 0.020
#> GSM247857 1 0.1282 0.854 0.952 0.000 0.004 0.000 0.044
#> GSM247859 1 0.0898 0.855 0.972 0.000 0.000 0.008 0.020
#> GSM247860 5 0.4256 0.155 0.436 0.000 0.000 0.000 0.564
#> GSM247862 1 0.1197 0.852 0.952 0.000 0.000 0.000 0.048
#> GSM247864 1 0.1364 0.855 0.952 0.000 0.000 0.012 0.036
#> GSM247865 1 0.2293 0.819 0.900 0.000 0.000 0.084 0.016
#> GSM247866 1 0.4219 0.233 0.584 0.000 0.000 0.000 0.416
#> GSM247876 5 0.3351 0.634 0.148 0.000 0.004 0.020 0.828
#> GSM247877 5 0.3756 0.409 0.000 0.000 0.008 0.248 0.744
#> GSM247878 4 0.3081 0.747 0.012 0.000 0.000 0.832 0.156
#> GSM247879 5 0.2151 0.589 0.016 0.000 0.020 0.040 0.924
#> GSM247881 1 0.0963 0.855 0.964 0.000 0.000 0.000 0.036
#> GSM247883 1 0.0566 0.858 0.984 0.000 0.000 0.004 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0632 0.7827 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM246088 3 0.0458 0.7877 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM246089 3 0.6217 0.0499 0.000 0.000 0.384 0.004 0.316 0.296
#> GSM246090 3 0.0260 0.7886 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM246119 3 0.1461 0.7842 0.000 0.000 0.940 0.000 0.016 0.044
#> GSM246120 3 0.0909 0.7901 0.000 0.000 0.968 0.000 0.012 0.020
#> GSM246121 3 0.2527 0.7443 0.000 0.000 0.868 0.000 0.024 0.108
#> GSM246122 3 0.1219 0.7676 0.000 0.000 0.948 0.000 0.004 0.048
#> GSM246123 3 0.1408 0.7864 0.000 0.000 0.944 0.000 0.020 0.036
#> GSM246422 4 0.0146 0.8114 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM246423 4 0.0508 0.8098 0.000 0.000 0.000 0.984 0.012 0.004
#> GSM246484 4 0.0405 0.8118 0.000 0.000 0.000 0.988 0.008 0.004
#> GSM246485 2 0.6160 0.0436 0.008 0.428 0.000 0.340 0.000 0.224
#> GSM246486 2 0.4263 0.0831 0.000 0.504 0.000 0.480 0.000 0.016
#> GSM246487 4 0.5361 0.5547 0.128 0.144 0.000 0.676 0.000 0.052
#> GSM246488 4 0.1461 0.7851 0.000 0.044 0.000 0.940 0.000 0.016
#> GSM246489 2 0.0622 0.8756 0.000 0.980 0.000 0.008 0.000 0.012
#> GSM246490 2 0.0692 0.8742 0.000 0.976 0.000 0.000 0.004 0.020
#> GSM246491 2 0.0458 0.8757 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM247162 2 0.0653 0.8747 0.000 0.980 0.000 0.012 0.004 0.004
#> GSM247163 2 0.0909 0.8749 0.000 0.968 0.000 0.012 0.000 0.020
#> GSM247164 2 0.0964 0.8726 0.000 0.968 0.000 0.016 0.004 0.012
#> GSM247165 2 0.1003 0.8718 0.000 0.964 0.000 0.016 0.000 0.020
#> GSM247166 2 0.2048 0.8301 0.000 0.880 0.000 0.000 0.000 0.120
#> GSM247168 2 0.2048 0.8301 0.000 0.880 0.000 0.000 0.000 0.120
#> GSM247169 2 0.2053 0.8330 0.000 0.888 0.000 0.000 0.004 0.108
#> GSM247171 2 0.1269 0.8692 0.000 0.956 0.000 0.012 0.020 0.012
#> GSM247173 2 0.0508 0.8762 0.000 0.984 0.000 0.012 0.000 0.004
#> GSM247174 2 0.1082 0.8659 0.000 0.956 0.000 0.000 0.004 0.040
#> GSM247175 2 0.0260 0.8761 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM247188 2 0.0725 0.8739 0.000 0.976 0.000 0.000 0.012 0.012
#> GSM247189 2 0.5978 -0.0877 0.000 0.432 0.000 0.428 0.112 0.028
#> GSM247190 2 0.0622 0.8738 0.000 0.980 0.000 0.000 0.008 0.012
#> GSM247650 1 0.4153 0.5372 0.792 0.000 0.100 0.004 0.048 0.056
#> GSM247651 1 0.3972 0.3746 0.664 0.000 0.000 0.320 0.012 0.004
#> GSM247652 1 0.1219 0.6389 0.948 0.000 0.000 0.000 0.004 0.048
#> GSM247653 1 0.5658 0.2398 0.432 0.000 0.000 0.000 0.152 0.416
#> GSM247654 1 0.3534 0.5958 0.740 0.000 0.000 0.000 0.016 0.244
#> GSM247655 1 0.2902 0.6095 0.800 0.000 0.000 0.004 0.000 0.196
#> GSM247656 3 0.5635 -0.3245 0.408 0.000 0.468 0.000 0.008 0.116
#> GSM247657 1 0.3923 0.4753 0.580 0.000 0.004 0.000 0.000 0.416
#> GSM247658 1 0.2163 0.6333 0.892 0.000 0.000 0.000 0.016 0.092
#> GSM247659 6 0.7497 0.4686 0.148 0.004 0.180 0.000 0.304 0.364
#> GSM247660 1 0.5726 0.4630 0.580 0.000 0.000 0.224 0.016 0.180
#> GSM247661 1 0.5132 0.4000 0.500 0.000 0.000 0.000 0.084 0.416
#> GSM247662 6 0.6664 0.5499 0.236 0.000 0.336 0.000 0.036 0.392
#> GSM247663 1 0.1341 0.6360 0.948 0.000 0.000 0.000 0.028 0.024
#> GSM247856 1 0.0862 0.6323 0.972 0.000 0.016 0.000 0.008 0.004
#> GSM247857 1 0.5473 0.2500 0.520 0.000 0.052 0.000 0.036 0.392
#> GSM247859 1 0.1889 0.6350 0.920 0.000 0.000 0.020 0.004 0.056
#> GSM247860 5 0.6099 -0.0261 0.300 0.000 0.000 0.000 0.384 0.316
#> GSM247862 1 0.4252 0.5475 0.652 0.000 0.000 0.000 0.036 0.312
#> GSM247864 1 0.4306 0.5573 0.700 0.000 0.000 0.008 0.044 0.248
#> GSM247865 1 0.3598 0.5264 0.804 0.000 0.000 0.112 0.004 0.080
#> GSM247866 1 0.5575 0.2061 0.460 0.000 0.000 0.000 0.400 0.140
#> GSM247876 5 0.3339 0.4528 0.188 0.000 0.004 0.008 0.792 0.008
#> GSM247877 5 0.3133 0.4612 0.000 0.000 0.008 0.180 0.804 0.008
#> GSM247878 4 0.4771 0.3612 0.056 0.000 0.000 0.628 0.308 0.008
#> GSM247879 5 0.1639 0.5341 0.020 0.004 0.004 0.008 0.944 0.020
#> GSM247881 1 0.5005 0.4443 0.628 0.000 0.000 0.000 0.124 0.248
#> GSM247883 1 0.1624 0.6173 0.936 0.004 0.000 0.000 0.020 0.040
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> CV:NMF 56 1.75e-09 2
#> CV:NMF 59 3.53e-15 3
#> CV:NMF 58 8.53e-21 4
#> CV:NMF 54 6.25e-19 5
#> CV:NMF 43 3.31e-14 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 21168 rows and 61 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 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 0.432 0.579 0.718 0.3381 0.531 0.531
#> 3 3 0.915 0.913 0.965 0.7230 0.702 0.526
#> 4 4 0.918 0.883 0.944 0.2066 0.850 0.650
#> 5 5 0.927 0.910 0.954 0.0306 0.987 0.953
#> 6 6 0.865 0.867 0.926 0.0282 0.996 0.984
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 3
There is also optional best \(k\) = 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
#> GSM246087 1 0.1633 0.3361 0.976 0.024
#> GSM246088 1 0.1633 0.3361 0.976 0.024
#> GSM246089 1 0.1633 0.3361 0.976 0.024
#> GSM246090 1 0.1633 0.3361 0.976 0.024
#> GSM246119 1 0.1633 0.3361 0.976 0.024
#> GSM246120 1 0.1633 0.3361 0.976 0.024
#> GSM246121 1 0.1633 0.3361 0.976 0.024
#> GSM246122 1 0.1633 0.3361 0.976 0.024
#> GSM246123 1 0.1633 0.3361 0.976 0.024
#> GSM246422 1 0.9993 0.6938 0.516 0.484
#> GSM246423 1 0.9993 0.6938 0.516 0.484
#> GSM246484 1 0.9993 0.6938 0.516 0.484
#> GSM246485 2 0.9170 0.0331 0.332 0.668
#> GSM246486 2 0.9552 -0.1875 0.376 0.624
#> GSM246487 2 0.9552 -0.1875 0.376 0.624
#> GSM246488 2 0.9323 -0.0429 0.348 0.652
#> GSM246489 2 0.0000 0.7864 0.000 1.000
#> GSM246490 2 0.0672 0.7832 0.008 0.992
#> GSM246491 2 0.0672 0.7832 0.008 0.992
#> GSM247162 2 0.0000 0.7864 0.000 1.000
#> GSM247163 2 0.0672 0.7832 0.008 0.992
#> GSM247164 2 0.0672 0.7832 0.008 0.992
#> GSM247165 2 0.6048 0.5817 0.148 0.852
#> GSM247166 2 0.0000 0.7864 0.000 1.000
#> GSM247168 2 0.0000 0.7864 0.000 1.000
#> GSM247169 2 0.0000 0.7864 0.000 1.000
#> GSM247171 2 0.0000 0.7864 0.000 1.000
#> GSM247173 2 0.0000 0.7864 0.000 1.000
#> GSM247174 2 0.0000 0.7864 0.000 1.000
#> GSM247175 2 0.0000 0.7864 0.000 1.000
#> GSM247188 2 0.0000 0.7864 0.000 1.000
#> GSM247189 2 0.9209 0.0134 0.336 0.664
#> GSM247190 2 0.0000 0.7864 0.000 1.000
#> GSM247650 1 0.9993 0.6938 0.516 0.484
#> GSM247651 1 0.9993 0.6938 0.516 0.484
#> GSM247652 1 0.9993 0.6938 0.516 0.484
#> GSM247653 1 0.9993 0.6938 0.516 0.484
#> GSM247654 1 0.9993 0.6938 0.516 0.484
#> GSM247655 1 0.9993 0.6938 0.516 0.484
#> GSM247656 1 0.9993 0.6938 0.516 0.484
#> GSM247657 1 0.9993 0.6938 0.516 0.484
#> GSM247658 1 0.9993 0.6938 0.516 0.484
#> GSM247659 1 0.9993 0.6938 0.516 0.484
#> GSM247660 1 0.9993 0.6938 0.516 0.484
#> GSM247661 1 0.9993 0.6938 0.516 0.484
#> GSM247662 1 0.9993 0.6938 0.516 0.484
#> GSM247663 1 0.9993 0.6938 0.516 0.484
#> GSM247856 1 0.9993 0.6938 0.516 0.484
#> GSM247857 1 0.9993 0.6938 0.516 0.484
#> GSM247859 1 0.9993 0.6938 0.516 0.484
#> GSM247860 1 0.9993 0.6938 0.516 0.484
#> GSM247862 1 0.9993 0.6938 0.516 0.484
#> GSM247864 1 0.9993 0.6938 0.516 0.484
#> GSM247865 2 0.9933 -0.5178 0.452 0.548
#> GSM247866 1 0.9993 0.6938 0.516 0.484
#> GSM247876 1 0.9993 0.6938 0.516 0.484
#> GSM247877 1 0.9993 0.6938 0.516 0.484
#> GSM247878 1 0.9993 0.6938 0.516 0.484
#> GSM247879 1 0.9993 0.6938 0.516 0.484
#> GSM247881 1 0.9993 0.6938 0.516 0.484
#> GSM247883 1 0.9993 0.6938 0.516 0.484
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 1.000 0.000 0.000 1
#> GSM246088 3 0.0000 1.000 0.000 0.000 1
#> GSM246089 3 0.0000 1.000 0.000 0.000 1
#> GSM246090 3 0.0000 1.000 0.000 0.000 1
#> GSM246119 3 0.0000 1.000 0.000 0.000 1
#> GSM246120 3 0.0000 1.000 0.000 0.000 1
#> GSM246121 3 0.0000 1.000 0.000 0.000 1
#> GSM246122 3 0.0000 1.000 0.000 0.000 1
#> GSM246123 3 0.0000 1.000 0.000 0.000 1
#> GSM246422 1 0.0000 0.942 1.000 0.000 0
#> GSM246423 1 0.0000 0.942 1.000 0.000 0
#> GSM246484 1 0.0000 0.942 1.000 0.000 0
#> GSM246485 1 0.6111 0.400 0.604 0.396 0
#> GSM246486 1 0.5650 0.574 0.688 0.312 0
#> GSM246487 1 0.5650 0.574 0.688 0.312 0
#> GSM246488 1 0.5988 0.464 0.632 0.368 0
#> GSM246489 2 0.0000 0.971 0.000 1.000 0
#> GSM246490 2 0.0424 0.966 0.008 0.992 0
#> GSM246491 2 0.0424 0.966 0.008 0.992 0
#> GSM247162 2 0.0000 0.971 0.000 1.000 0
#> GSM247163 2 0.0424 0.966 0.008 0.992 0
#> GSM247164 2 0.0424 0.966 0.008 0.992 0
#> GSM247165 2 0.5327 0.582 0.272 0.728 0
#> GSM247166 2 0.0000 0.971 0.000 1.000 0
#> GSM247168 2 0.0000 0.971 0.000 1.000 0
#> GSM247169 2 0.0000 0.971 0.000 1.000 0
#> GSM247171 2 0.0000 0.971 0.000 1.000 0
#> GSM247173 2 0.0000 0.971 0.000 1.000 0
#> GSM247174 2 0.0000 0.971 0.000 1.000 0
#> GSM247175 2 0.0000 0.971 0.000 1.000 0
#> GSM247188 2 0.0000 0.971 0.000 1.000 0
#> GSM247189 1 0.6095 0.410 0.608 0.392 0
#> GSM247190 2 0.0000 0.971 0.000 1.000 0
#> GSM247650 1 0.0000 0.942 1.000 0.000 0
#> GSM247651 1 0.0000 0.942 1.000 0.000 0
#> GSM247652 1 0.0000 0.942 1.000 0.000 0
#> GSM247653 1 0.0000 0.942 1.000 0.000 0
#> GSM247654 1 0.0000 0.942 1.000 0.000 0
#> GSM247655 1 0.0000 0.942 1.000 0.000 0
#> GSM247656 1 0.0000 0.942 1.000 0.000 0
#> GSM247657 1 0.0000 0.942 1.000 0.000 0
#> GSM247658 1 0.0000 0.942 1.000 0.000 0
#> GSM247659 1 0.0000 0.942 1.000 0.000 0
#> GSM247660 1 0.0000 0.942 1.000 0.000 0
#> GSM247661 1 0.0000 0.942 1.000 0.000 0
#> GSM247662 1 0.0000 0.942 1.000 0.000 0
#> GSM247663 1 0.0000 0.942 1.000 0.000 0
#> GSM247856 1 0.0000 0.942 1.000 0.000 0
#> GSM247857 1 0.0000 0.942 1.000 0.000 0
#> GSM247859 1 0.0000 0.942 1.000 0.000 0
#> GSM247860 1 0.0000 0.942 1.000 0.000 0
#> GSM247862 1 0.0000 0.942 1.000 0.000 0
#> GSM247864 1 0.0000 0.942 1.000 0.000 0
#> GSM247865 1 0.2165 0.889 0.936 0.064 0
#> GSM247866 1 0.0000 0.942 1.000 0.000 0
#> GSM247876 1 0.0000 0.942 1.000 0.000 0
#> GSM247877 1 0.0000 0.942 1.000 0.000 0
#> GSM247878 1 0.0000 0.942 1.000 0.000 0
#> GSM247879 1 0.0000 0.942 1.000 0.000 0
#> GSM247881 1 0.0000 0.942 1.000 0.000 0
#> GSM247883 1 0.0000 0.942 1.000 0.000 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1 0.000
#> GSM246422 4 0.0000 0.628 0.000 0.000 0 1.000
#> GSM246423 4 0.0000 0.628 0.000 0.000 0 1.000
#> GSM246484 4 0.0000 0.628 0.000 0.000 0 1.000
#> GSM246485 4 0.4843 0.480 0.000 0.396 0 0.604
#> GSM246486 4 0.4477 0.582 0.000 0.312 0 0.688
#> GSM246487 4 0.4477 0.582 0.000 0.312 0 0.688
#> GSM246488 4 0.4746 0.523 0.000 0.368 0 0.632
#> GSM246489 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM246490 2 0.0336 0.970 0.000 0.992 0 0.008
#> GSM246491 2 0.0336 0.970 0.000 0.992 0 0.008
#> GSM247162 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247163 2 0.0336 0.970 0.000 0.992 0 0.008
#> GSM247164 2 0.0336 0.970 0.000 0.992 0 0.008
#> GSM247165 2 0.4222 0.502 0.000 0.728 0 0.272
#> GSM247166 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247168 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247169 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247171 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247173 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247174 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247175 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247188 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247189 4 0.4830 0.487 0.000 0.392 0 0.608
#> GSM247190 2 0.0000 0.974 0.000 1.000 0 0.000
#> GSM247650 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247651 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247652 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247653 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247654 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247655 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247656 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247657 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247658 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247659 1 0.0469 0.977 0.988 0.000 0 0.012
#> GSM247660 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247661 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247662 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247663 1 0.0188 0.984 0.996 0.000 0 0.004
#> GSM247856 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247857 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247859 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247860 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247862 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247864 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247865 1 0.4514 0.720 0.800 0.064 0 0.136
#> GSM247866 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247876 1 0.1389 0.936 0.952 0.000 0 0.048
#> GSM247877 4 0.4998 0.133 0.488 0.000 0 0.512
#> GSM247878 4 0.2281 0.601 0.096 0.000 0 0.904
#> GSM247879 4 0.4998 0.133 0.488 0.000 0 0.512
#> GSM247881 1 0.0000 0.987 1.000 0.000 0 0.000
#> GSM247883 1 0.0000 0.987 1.000 0.000 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246422 4 0.0000 0.484 0.000 0.000 0 1.000 0.000
#> GSM246423 4 0.0000 0.484 0.000 0.000 0 1.000 0.000
#> GSM246484 4 0.0000 0.484 0.000 0.000 0 1.000 0.000
#> GSM246485 4 0.4171 0.658 0.000 0.396 0 0.604 0.000
#> GSM246486 4 0.3857 0.725 0.000 0.312 0 0.688 0.000
#> GSM246487 4 0.3857 0.725 0.000 0.312 0 0.688 0.000
#> GSM246488 4 0.4088 0.695 0.000 0.368 0 0.632 0.000
#> GSM246489 2 0.0000 0.972 0.000 1.000 0 0.000 0.000
#> GSM246490 2 0.0290 0.967 0.000 0.992 0 0.008 0.000
#> GSM246491 2 0.0290 0.967 0.000 0.992 0 0.008 0.000
#> GSM247162 2 0.0000 0.972 0.000 1.000 0 0.000 0.000
#> GSM247163 2 0.0290 0.967 0.000 0.992 0 0.008 0.000
#> GSM247164 2 0.0290 0.967 0.000 0.992 0 0.008 0.000
#> GSM247165 2 0.3636 0.433 0.000 0.728 0 0.272 0.000
#> GSM247166 2 0.0000 0.972 0.000 1.000 0 0.000 0.000
#> GSM247168 2 0.0000 0.972 0.000 1.000 0 0.000 0.000
#> GSM247169 2 0.0000 0.972 0.000 1.000 0 0.000 0.000
#> GSM247171 2 0.0000 0.972 0.000 1.000 0 0.000 0.000
#> GSM247173 2 0.0000 0.972 0.000 1.000 0 0.000 0.000
#> GSM247174 2 0.0000 0.972 0.000 1.000 0 0.000 0.000
#> GSM247175 2 0.0000 0.972 0.000 1.000 0 0.000 0.000
#> GSM247188 2 0.0000 0.972 0.000 1.000 0 0.000 0.000
#> GSM247189 4 0.4161 0.665 0.000 0.392 0 0.608 0.000
#> GSM247190 2 0.0000 0.972 0.000 1.000 0 0.000 0.000
#> GSM247650 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247651 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247652 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247653 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247654 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247655 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247656 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247657 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247658 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247659 1 0.0451 0.978 0.988 0.000 0 0.004 0.008
#> GSM247660 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247661 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247662 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247663 1 0.0162 0.985 0.996 0.000 0 0.000 0.004
#> GSM247856 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247857 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247859 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247860 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247862 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247864 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247865 1 0.3888 0.737 0.800 0.064 0 0.136 0.000
#> GSM247866 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247876 1 0.1341 0.935 0.944 0.000 0 0.000 0.056
#> GSM247877 5 0.0000 0.820 0.000 0.000 0 0.000 1.000
#> GSM247878 5 0.4249 0.551 0.000 0.000 0 0.432 0.568
#> GSM247879 5 0.0000 0.820 0.000 0.000 0 0.000 1.000
#> GSM247881 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
#> GSM247883 1 0.0000 0.988 1.000 0.000 0 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246089 6 0.3482 0.000 0.000 0.000 0.316 0.000 0.000 0.684
#> GSM246090 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246422 4 0.1863 0.531 0.000 0.000 0.000 0.896 0.000 0.104
#> GSM246423 4 0.1863 0.531 0.000 0.000 0.000 0.896 0.000 0.104
#> GSM246484 4 0.1863 0.531 0.000 0.000 0.000 0.896 0.000 0.104
#> GSM246485 4 0.3784 0.710 0.000 0.308 0.000 0.680 0.000 0.012
#> GSM246486 4 0.3023 0.740 0.000 0.232 0.000 0.768 0.000 0.000
#> GSM246487 4 0.3023 0.740 0.000 0.232 0.000 0.768 0.000 0.000
#> GSM246488 4 0.3575 0.728 0.000 0.284 0.000 0.708 0.000 0.008
#> GSM246489 2 0.0146 0.955 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM246490 2 0.0972 0.937 0.000 0.964 0.000 0.028 0.000 0.008
#> GSM246491 2 0.0972 0.937 0.000 0.964 0.000 0.028 0.000 0.008
#> GSM247162 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247163 2 0.0972 0.937 0.000 0.964 0.000 0.028 0.000 0.008
#> GSM247164 2 0.0972 0.937 0.000 0.964 0.000 0.028 0.000 0.008
#> GSM247165 2 0.3927 0.283 0.000 0.644 0.000 0.344 0.000 0.012
#> GSM247166 2 0.0260 0.954 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM247168 2 0.0260 0.954 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM247169 2 0.0260 0.954 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM247171 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247174 2 0.0260 0.954 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM247175 2 0.0146 0.955 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM247188 2 0.0260 0.954 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM247189 4 0.3766 0.714 0.000 0.304 0.000 0.684 0.000 0.012
#> GSM247190 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247650 1 0.0146 0.948 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM247651 1 0.0000 0.947 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247652 1 0.0713 0.947 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM247653 1 0.1556 0.933 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM247654 1 0.1501 0.935 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM247655 1 0.0146 0.948 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM247656 1 0.1556 0.942 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM247657 1 0.1556 0.932 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM247658 1 0.0713 0.947 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM247659 1 0.2003 0.919 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM247660 1 0.0000 0.947 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247661 1 0.1910 0.922 0.892 0.000 0.000 0.000 0.000 0.108
#> GSM247662 1 0.1556 0.932 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM247663 1 0.1556 0.925 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM247856 1 0.0713 0.947 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM247857 1 0.1556 0.932 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM247859 1 0.0363 0.948 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM247860 1 0.1910 0.922 0.892 0.000 0.000 0.000 0.000 0.108
#> GSM247862 1 0.0713 0.949 0.972 0.000 0.000 0.000 0.000 0.028
#> GSM247864 1 0.0146 0.948 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM247865 1 0.3315 0.735 0.780 0.000 0.000 0.200 0.000 0.020
#> GSM247866 1 0.1863 0.924 0.896 0.000 0.000 0.000 0.000 0.104
#> GSM247876 1 0.2660 0.888 0.868 0.000 0.000 0.000 0.048 0.084
#> GSM247877 5 0.0000 0.731 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM247878 5 0.5147 0.464 0.000 0.000 0.000 0.328 0.568 0.104
#> GSM247879 5 0.0260 0.729 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM247881 1 0.0547 0.946 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM247883 1 0.0458 0.947 0.984 0.000 0.000 0.000 0.000 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:hclust 46 2.27e-08 2
#> MAD:hclust 58 8.94e-20 3
#> MAD:hclust 57 2.14e-21 4
#> MAD:hclust 57 5.72e-21 5
#> MAD:hclust 58 2.22e-21 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 21168 rows and 61 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 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 0.495 0.920 0.898 0.4427 0.515 0.515
#> 3 3 0.780 0.915 0.944 0.3854 0.757 0.579
#> 4 4 0.986 0.967 0.967 0.1480 0.867 0.673
#> 5 5 0.805 0.871 0.888 0.0705 1.000 1.000
#> 6 6 0.776 0.661 0.822 0.0456 0.940 0.794
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
#> GSM246087 1 0.311 0.787 0.944 0.056
#> GSM246088 1 0.311 0.787 0.944 0.056
#> GSM246089 1 0.311 0.787 0.944 0.056
#> GSM246090 1 0.311 0.787 0.944 0.056
#> GSM246119 1 0.311 0.787 0.944 0.056
#> GSM246120 1 0.311 0.787 0.944 0.056
#> GSM246121 1 0.311 0.787 0.944 0.056
#> GSM246122 1 0.311 0.787 0.944 0.056
#> GSM246123 1 0.311 0.787 0.944 0.056
#> GSM246422 2 0.456 0.905 0.096 0.904
#> GSM246423 2 0.456 0.905 0.096 0.904
#> GSM246484 2 0.456 0.905 0.096 0.904
#> GSM246485 2 0.327 0.934 0.060 0.940
#> GSM246486 2 0.295 0.939 0.052 0.948
#> GSM246487 2 0.443 0.909 0.092 0.908
#> GSM246488 2 0.295 0.939 0.052 0.948
#> GSM246489 2 0.000 0.972 0.000 1.000
#> GSM246490 2 0.000 0.972 0.000 1.000
#> GSM246491 2 0.000 0.972 0.000 1.000
#> GSM247162 2 0.000 0.972 0.000 1.000
#> GSM247163 2 0.000 0.972 0.000 1.000
#> GSM247164 2 0.000 0.972 0.000 1.000
#> GSM247165 2 0.000 0.972 0.000 1.000
#> GSM247166 2 0.000 0.972 0.000 1.000
#> GSM247168 2 0.000 0.972 0.000 1.000
#> GSM247169 2 0.000 0.972 0.000 1.000
#> GSM247171 2 0.000 0.972 0.000 1.000
#> GSM247173 2 0.000 0.972 0.000 1.000
#> GSM247174 2 0.000 0.972 0.000 1.000
#> GSM247175 2 0.000 0.972 0.000 1.000
#> GSM247188 2 0.000 0.972 0.000 1.000
#> GSM247189 2 0.000 0.972 0.000 1.000
#> GSM247190 2 0.000 0.972 0.000 1.000
#> GSM247650 1 0.689 0.931 0.816 0.184
#> GSM247651 1 0.689 0.931 0.816 0.184
#> GSM247652 1 0.689 0.931 0.816 0.184
#> GSM247653 1 0.689 0.931 0.816 0.184
#> GSM247654 1 0.689 0.931 0.816 0.184
#> GSM247655 1 0.689 0.931 0.816 0.184
#> GSM247656 1 0.689 0.931 0.816 0.184
#> GSM247657 1 0.689 0.931 0.816 0.184
#> GSM247658 1 0.689 0.931 0.816 0.184
#> GSM247659 1 0.689 0.931 0.816 0.184
#> GSM247660 1 0.689 0.931 0.816 0.184
#> GSM247661 1 0.689 0.931 0.816 0.184
#> GSM247662 1 0.689 0.931 0.816 0.184
#> GSM247663 1 0.689 0.931 0.816 0.184
#> GSM247856 1 0.689 0.931 0.816 0.184
#> GSM247857 1 0.689 0.931 0.816 0.184
#> GSM247859 1 0.689 0.931 0.816 0.184
#> GSM247860 1 0.689 0.931 0.816 0.184
#> GSM247862 1 0.689 0.931 0.816 0.184
#> GSM247864 1 0.689 0.931 0.816 0.184
#> GSM247865 1 0.689 0.931 0.816 0.184
#> GSM247866 1 0.689 0.931 0.816 0.184
#> GSM247876 1 0.689 0.931 0.816 0.184
#> GSM247877 1 0.689 0.931 0.816 0.184
#> GSM247878 1 0.689 0.931 0.816 0.184
#> GSM247879 1 0.689 0.931 0.816 0.184
#> GSM247881 1 0.689 0.931 0.816 0.184
#> GSM247883 1 0.689 0.931 0.816 0.184
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246422 1 0.2796 0.846 0.908 0.092 0.000
#> GSM246423 1 0.2796 0.846 0.908 0.092 0.000
#> GSM246484 1 0.2796 0.846 0.908 0.092 0.000
#> GSM246485 2 0.6244 0.320 0.440 0.560 0.000
#> GSM246486 2 0.3686 0.831 0.140 0.860 0.000
#> GSM246487 1 0.2625 0.849 0.916 0.084 0.000
#> GSM246488 2 0.3686 0.831 0.140 0.860 0.000
#> GSM246489 2 0.0424 0.950 0.008 0.992 0.000
#> GSM246490 2 0.0424 0.950 0.008 0.992 0.000
#> GSM246491 2 0.0424 0.950 0.008 0.992 0.000
#> GSM247162 2 0.0424 0.950 0.008 0.992 0.000
#> GSM247163 2 0.0424 0.950 0.008 0.992 0.000
#> GSM247164 2 0.0000 0.943 0.000 1.000 0.000
#> GSM247165 2 0.0000 0.943 0.000 1.000 0.000
#> GSM247166 2 0.0424 0.950 0.008 0.992 0.000
#> GSM247168 2 0.0424 0.950 0.008 0.992 0.000
#> GSM247169 2 0.0424 0.950 0.008 0.992 0.000
#> GSM247171 2 0.0424 0.950 0.008 0.992 0.000
#> GSM247173 2 0.0424 0.950 0.008 0.992 0.000
#> GSM247174 2 0.0424 0.950 0.008 0.992 0.000
#> GSM247175 2 0.0424 0.950 0.008 0.992 0.000
#> GSM247188 2 0.0424 0.950 0.008 0.992 0.000
#> GSM247189 2 0.2356 0.893 0.072 0.928 0.000
#> GSM247190 2 0.0424 0.950 0.008 0.992 0.000
#> GSM247650 1 0.3686 0.902 0.860 0.000 0.140
#> GSM247651 1 0.0000 0.909 1.000 0.000 0.000
#> GSM247652 1 0.3686 0.902 0.860 0.000 0.140
#> GSM247653 1 0.3686 0.902 0.860 0.000 0.140
#> GSM247654 1 0.3686 0.902 0.860 0.000 0.140
#> GSM247655 1 0.0000 0.909 1.000 0.000 0.000
#> GSM247656 1 0.3686 0.902 0.860 0.000 0.140
#> GSM247657 1 0.3686 0.902 0.860 0.000 0.140
#> GSM247658 1 0.2878 0.910 0.904 0.000 0.096
#> GSM247659 1 0.3686 0.902 0.860 0.000 0.140
#> GSM247660 1 0.0000 0.909 1.000 0.000 0.000
#> GSM247661 1 0.3686 0.902 0.860 0.000 0.140
#> GSM247662 1 0.3686 0.902 0.860 0.000 0.140
#> GSM247663 1 0.3686 0.902 0.860 0.000 0.140
#> GSM247856 1 0.3686 0.902 0.860 0.000 0.140
#> GSM247857 1 0.3686 0.902 0.860 0.000 0.140
#> GSM247859 1 0.0000 0.909 1.000 0.000 0.000
#> GSM247860 1 0.3686 0.902 0.860 0.000 0.140
#> GSM247862 1 0.0000 0.909 1.000 0.000 0.000
#> GSM247864 1 0.0000 0.909 1.000 0.000 0.000
#> GSM247865 1 0.0000 0.909 1.000 0.000 0.000
#> GSM247866 1 0.0000 0.909 1.000 0.000 0.000
#> GSM247876 1 0.2625 0.911 0.916 0.000 0.084
#> GSM247877 1 0.0424 0.905 0.992 0.008 0.000
#> GSM247878 1 0.0424 0.905 0.992 0.008 0.000
#> GSM247879 1 0.3116 0.908 0.892 0.000 0.108
#> GSM247881 1 0.0000 0.909 1.000 0.000 0.000
#> GSM247883 1 0.0000 0.909 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.1520 0.984 0.024 0.000 0.956 0.020
#> GSM246088 3 0.1520 0.984 0.024 0.000 0.956 0.020
#> GSM246089 3 0.1833 0.979 0.024 0.000 0.944 0.032
#> GSM246090 3 0.1520 0.984 0.024 0.000 0.956 0.020
#> GSM246119 3 0.1520 0.984 0.024 0.000 0.956 0.020
#> GSM246120 3 0.1520 0.984 0.024 0.000 0.956 0.020
#> GSM246121 3 0.0817 0.985 0.024 0.000 0.976 0.000
#> GSM246122 3 0.1520 0.984 0.024 0.000 0.956 0.020
#> GSM246123 3 0.1520 0.984 0.024 0.000 0.956 0.020
#> GSM246422 4 0.2142 0.918 0.056 0.016 0.000 0.928
#> GSM246423 4 0.2142 0.918 0.056 0.016 0.000 0.928
#> GSM246484 4 0.2142 0.918 0.056 0.016 0.000 0.928
#> GSM246485 4 0.3286 0.903 0.044 0.080 0.000 0.876
#> GSM246486 4 0.2530 0.881 0.004 0.100 0.000 0.896
#> GSM246487 4 0.2730 0.905 0.088 0.016 0.000 0.896
#> GSM246488 4 0.1978 0.892 0.004 0.068 0.000 0.928
#> GSM246489 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM246490 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM246491 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM247162 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM247163 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM247164 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM247165 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM247166 2 0.1520 0.969 0.000 0.956 0.024 0.020
#> GSM247168 2 0.1520 0.969 0.000 0.956 0.024 0.020
#> GSM247169 2 0.1520 0.969 0.000 0.956 0.024 0.020
#> GSM247171 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM247173 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM247174 2 0.1297 0.973 0.000 0.964 0.016 0.020
#> GSM247175 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM247188 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM247189 4 0.2973 0.841 0.000 0.144 0.000 0.856
#> GSM247190 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM247650 1 0.0188 0.983 0.996 0.000 0.004 0.000
#> GSM247651 1 0.1022 0.975 0.968 0.000 0.000 0.032
#> GSM247652 1 0.0188 0.983 0.996 0.000 0.004 0.000
#> GSM247653 1 0.0188 0.983 0.996 0.000 0.004 0.000
#> GSM247654 1 0.0188 0.983 0.996 0.000 0.004 0.000
#> GSM247655 1 0.1022 0.975 0.968 0.000 0.000 0.032
#> GSM247656 1 0.0188 0.983 0.996 0.000 0.004 0.000
#> GSM247657 1 0.0188 0.983 0.996 0.000 0.004 0.000
#> GSM247658 1 0.0188 0.983 0.996 0.000 0.000 0.004
#> GSM247659 1 0.0188 0.983 0.996 0.000 0.004 0.000
#> GSM247660 1 0.1022 0.975 0.968 0.000 0.000 0.032
#> GSM247661 1 0.0188 0.983 0.996 0.000 0.004 0.000
#> GSM247662 1 0.0188 0.983 0.996 0.000 0.004 0.000
#> GSM247663 1 0.0188 0.983 0.996 0.000 0.004 0.000
#> GSM247856 1 0.0188 0.983 0.996 0.000 0.004 0.000
#> GSM247857 1 0.0188 0.983 0.996 0.000 0.004 0.000
#> GSM247859 1 0.1022 0.975 0.968 0.000 0.000 0.032
#> GSM247860 1 0.0188 0.983 0.996 0.000 0.004 0.000
#> GSM247862 1 0.0817 0.978 0.976 0.000 0.000 0.024
#> GSM247864 1 0.1022 0.975 0.968 0.000 0.000 0.032
#> GSM247865 1 0.1022 0.975 0.968 0.000 0.000 0.032
#> GSM247866 1 0.0817 0.978 0.976 0.000 0.000 0.024
#> GSM247876 1 0.0469 0.981 0.988 0.000 0.000 0.012
#> GSM247877 4 0.3074 0.846 0.152 0.000 0.000 0.848
#> GSM247878 4 0.2973 0.852 0.144 0.000 0.000 0.856
#> GSM247879 1 0.0188 0.983 0.996 0.000 0.000 0.004
#> GSM247881 1 0.0817 0.978 0.976 0.000 0.000 0.024
#> GSM247883 1 0.1022 0.975 0.968 0.000 0.000 0.032
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.1270 0.966 0.000 0.000 0.948 0.000 0.052
#> GSM246088 3 0.1270 0.966 0.000 0.000 0.948 0.000 0.052
#> GSM246089 3 0.1768 0.939 0.000 0.000 0.924 0.004 0.072
#> GSM246090 3 0.1270 0.966 0.000 0.000 0.948 0.000 0.052
#> GSM246119 3 0.0671 0.966 0.000 0.000 0.980 0.004 0.016
#> GSM246120 3 0.0671 0.966 0.000 0.000 0.980 0.004 0.016
#> GSM246121 3 0.0000 0.968 0.000 0.000 1.000 0.000 0.000
#> GSM246122 3 0.1270 0.966 0.000 0.000 0.948 0.000 0.052
#> GSM246123 3 0.0671 0.966 0.000 0.000 0.980 0.004 0.016
#> GSM246422 4 0.2707 0.823 0.000 0.008 0.000 0.860 0.132
#> GSM246423 4 0.2707 0.823 0.000 0.008 0.000 0.860 0.132
#> GSM246484 4 0.2707 0.823 0.000 0.008 0.000 0.860 0.132
#> GSM246485 4 0.2956 0.803 0.020 0.096 0.000 0.872 0.012
#> GSM246486 4 0.2130 0.812 0.000 0.080 0.000 0.908 0.012
#> GSM246487 4 0.2633 0.799 0.068 0.012 0.000 0.896 0.024
#> GSM246488 4 0.0404 0.823 0.000 0.012 0.000 0.988 0.000
#> GSM246489 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000
#> GSM246490 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000
#> GSM246491 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000
#> GSM247162 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000
#> GSM247163 2 0.0510 0.947 0.000 0.984 0.000 0.016 0.000
#> GSM247164 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000
#> GSM247165 2 0.1544 0.908 0.000 0.932 0.000 0.068 0.000
#> GSM247166 2 0.2966 0.860 0.000 0.816 0.000 0.000 0.184
#> GSM247168 2 0.2966 0.860 0.000 0.816 0.000 0.000 0.184
#> GSM247169 2 0.2966 0.860 0.000 0.816 0.000 0.000 0.184
#> GSM247171 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.955 0.000 1.000 0.000 0.000 0.000
#> GSM247174 2 0.1671 0.926 0.000 0.924 0.000 0.000 0.076
#> GSM247175 2 0.0162 0.954 0.000 0.996 0.000 0.000 0.004
#> GSM247188 2 0.0609 0.950 0.000 0.980 0.000 0.000 0.020
#> GSM247189 4 0.2561 0.777 0.000 0.144 0.000 0.856 0.000
#> GSM247190 2 0.0703 0.949 0.000 0.976 0.000 0.000 0.024
#> GSM247650 1 0.2074 0.850 0.896 0.000 0.000 0.000 0.104
#> GSM247651 1 0.2763 0.834 0.848 0.000 0.000 0.004 0.148
#> GSM247652 1 0.2471 0.857 0.864 0.000 0.000 0.000 0.136
#> GSM247653 1 0.3816 0.783 0.696 0.000 0.000 0.000 0.304
#> GSM247654 1 0.2929 0.843 0.820 0.000 0.000 0.000 0.180
#> GSM247655 1 0.2674 0.838 0.856 0.000 0.000 0.004 0.140
#> GSM247656 1 0.2561 0.856 0.856 0.000 0.000 0.000 0.144
#> GSM247657 1 0.2648 0.853 0.848 0.000 0.000 0.000 0.152
#> GSM247658 1 0.2966 0.849 0.816 0.000 0.000 0.000 0.184
#> GSM247659 1 0.2179 0.866 0.888 0.000 0.000 0.000 0.112
#> GSM247660 1 0.2763 0.834 0.848 0.000 0.000 0.004 0.148
#> GSM247661 1 0.3816 0.783 0.696 0.000 0.000 0.000 0.304
#> GSM247662 1 0.1544 0.871 0.932 0.000 0.000 0.000 0.068
#> GSM247663 1 0.2648 0.855 0.848 0.000 0.000 0.000 0.152
#> GSM247856 1 0.1965 0.868 0.904 0.000 0.000 0.000 0.096
#> GSM247857 1 0.1544 0.871 0.932 0.000 0.000 0.000 0.068
#> GSM247859 1 0.1205 0.867 0.956 0.000 0.000 0.004 0.040
#> GSM247860 1 0.3816 0.783 0.696 0.000 0.000 0.000 0.304
#> GSM247862 1 0.1608 0.875 0.928 0.000 0.000 0.000 0.072
#> GSM247864 1 0.2674 0.838 0.856 0.000 0.000 0.004 0.140
#> GSM247865 1 0.1357 0.866 0.948 0.000 0.000 0.004 0.048
#> GSM247866 1 0.3752 0.786 0.708 0.000 0.000 0.000 0.292
#> GSM247876 1 0.2929 0.823 0.820 0.000 0.000 0.000 0.180
#> GSM247877 4 0.5990 0.618 0.116 0.000 0.000 0.500 0.384
#> GSM247878 4 0.5996 0.624 0.120 0.000 0.000 0.512 0.368
#> GSM247879 1 0.3612 0.747 0.732 0.000 0.000 0.000 0.268
#> GSM247881 1 0.0609 0.872 0.980 0.000 0.000 0.000 0.020
#> GSM247883 1 0.1205 0.867 0.956 0.000 0.000 0.004 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.1867 0.9366 0.000 0.000 0.916 0.000 0.020 0.064
#> GSM246088 3 0.1867 0.9366 0.000 0.000 0.916 0.000 0.020 0.064
#> GSM246089 3 0.2688 0.8932 0.000 0.000 0.868 0.000 0.068 0.064
#> GSM246090 3 0.1867 0.9366 0.000 0.000 0.916 0.000 0.020 0.064
#> GSM246119 3 0.1168 0.9350 0.000 0.000 0.956 0.000 0.028 0.016
#> GSM246120 3 0.1168 0.9350 0.000 0.000 0.956 0.000 0.028 0.016
#> GSM246121 3 0.0000 0.9396 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246122 3 0.1867 0.9366 0.000 0.000 0.916 0.000 0.020 0.064
#> GSM246123 3 0.1168 0.9350 0.000 0.000 0.956 0.000 0.028 0.016
#> GSM246422 4 0.3852 0.6904 0.004 0.000 0.000 0.740 0.224 0.032
#> GSM246423 4 0.3852 0.6904 0.004 0.000 0.000 0.740 0.224 0.032
#> GSM246484 4 0.3852 0.6904 0.004 0.000 0.000 0.740 0.224 0.032
#> GSM246485 4 0.2508 0.7661 0.004 0.068 0.000 0.892 0.024 0.012
#> GSM246486 4 0.1863 0.7781 0.000 0.060 0.000 0.920 0.016 0.004
#> GSM246487 4 0.2082 0.7417 0.052 0.004 0.000 0.916 0.020 0.008
#> GSM246488 4 0.0603 0.7809 0.000 0.016 0.000 0.980 0.004 0.000
#> GSM246489 2 0.0551 0.9027 0.000 0.984 0.000 0.008 0.004 0.004
#> GSM246490 2 0.1511 0.8962 0.000 0.944 0.000 0.012 0.032 0.012
#> GSM246491 2 0.1605 0.8951 0.000 0.940 0.000 0.012 0.032 0.016
#> GSM247162 2 0.0260 0.9019 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM247163 2 0.2024 0.8863 0.000 0.920 0.000 0.028 0.036 0.016
#> GSM247164 2 0.1773 0.8922 0.000 0.932 0.000 0.016 0.036 0.016
#> GSM247165 2 0.2507 0.8681 0.000 0.892 0.000 0.056 0.036 0.016
#> GSM247166 2 0.4771 0.7041 0.000 0.652 0.000 0.000 0.100 0.248
#> GSM247168 2 0.4771 0.7041 0.000 0.652 0.000 0.000 0.100 0.248
#> GSM247169 2 0.4729 0.7040 0.000 0.656 0.000 0.000 0.096 0.248
#> GSM247171 2 0.0551 0.9015 0.000 0.984 0.000 0.008 0.004 0.004
#> GSM247173 2 0.0000 0.9021 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247174 2 0.2822 0.8405 0.000 0.852 0.000 0.000 0.040 0.108
#> GSM247175 2 0.0146 0.9016 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM247188 2 0.0993 0.8950 0.000 0.964 0.000 0.000 0.012 0.024
#> GSM247189 4 0.3313 0.6883 0.000 0.140 0.000 0.820 0.024 0.016
#> GSM247190 2 0.0935 0.8963 0.000 0.964 0.000 0.000 0.004 0.032
#> GSM247650 1 0.3044 0.5673 0.836 0.000 0.000 0.000 0.116 0.048
#> GSM247651 1 0.3719 0.5637 0.792 0.000 0.000 0.012 0.148 0.048
#> GSM247652 1 0.2738 0.3449 0.820 0.000 0.000 0.000 0.004 0.176
#> GSM247653 6 0.3851 0.9895 0.460 0.000 0.000 0.000 0.000 0.540
#> GSM247654 1 0.3769 -0.3755 0.640 0.000 0.000 0.000 0.004 0.356
#> GSM247655 1 0.3563 0.5728 0.808 0.000 0.000 0.012 0.132 0.048
#> GSM247656 1 0.3440 0.2936 0.776 0.000 0.000 0.000 0.028 0.196
#> GSM247657 1 0.3253 0.3284 0.788 0.000 0.000 0.000 0.020 0.192
#> GSM247658 1 0.3482 -0.1714 0.684 0.000 0.000 0.000 0.000 0.316
#> GSM247659 1 0.3417 0.3861 0.796 0.000 0.000 0.000 0.044 0.160
#> GSM247660 1 0.3719 0.5637 0.792 0.000 0.000 0.012 0.148 0.048
#> GSM247661 6 0.3847 0.9863 0.456 0.000 0.000 0.000 0.000 0.544
#> GSM247662 1 0.2889 0.4819 0.848 0.000 0.000 0.000 0.044 0.108
#> GSM247663 1 0.4121 0.4676 0.748 0.000 0.000 0.000 0.116 0.136
#> GSM247856 1 0.1806 0.5152 0.908 0.000 0.000 0.000 0.004 0.088
#> GSM247857 1 0.2889 0.4819 0.848 0.000 0.000 0.000 0.044 0.108
#> GSM247859 1 0.1434 0.5962 0.948 0.000 0.000 0.012 0.028 0.012
#> GSM247860 6 0.3854 0.9858 0.464 0.000 0.000 0.000 0.000 0.536
#> GSM247862 1 0.3725 0.4586 0.776 0.000 0.000 0.004 0.048 0.172
#> GSM247864 1 0.3583 0.5679 0.800 0.000 0.000 0.008 0.144 0.048
#> GSM247865 1 0.1787 0.5932 0.932 0.000 0.000 0.020 0.032 0.016
#> GSM247866 1 0.5270 -0.2221 0.548 0.000 0.000 0.004 0.096 0.352
#> GSM247876 1 0.4527 0.3784 0.660 0.000 0.000 0.000 0.272 0.068
#> GSM247877 5 0.4164 0.4721 0.040 0.000 0.000 0.220 0.728 0.012
#> GSM247878 5 0.4255 0.4688 0.068 0.000 0.000 0.224 0.708 0.000
#> GSM247879 5 0.5045 -0.0804 0.412 0.000 0.000 0.000 0.512 0.076
#> GSM247881 1 0.0891 0.5874 0.968 0.000 0.000 0.000 0.024 0.008
#> GSM247883 1 0.1622 0.5941 0.940 0.000 0.000 0.016 0.028 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:kmeans 61 5.68e-14 2
#> MAD:kmeans 60 1.88e-21 3
#> MAD:kmeans 61 2.38e-22 4
#> MAD:kmeans 61 2.38e-22 5
#> MAD:kmeans 46 1.82e-16 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 21168 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.976 0.991 0.4891 0.515 0.515
#> 3 3 0.722 0.853 0.930 0.3722 0.733 0.517
#> 4 4 0.835 0.854 0.936 0.1015 0.784 0.464
#> 5 5 0.784 0.688 0.847 0.0769 0.893 0.632
#> 6 6 0.794 0.625 0.792 0.0345 0.954 0.787
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
#> GSM246087 1 0.000 0.9853 1.000 0.000
#> GSM246088 1 0.000 0.9853 1.000 0.000
#> GSM246089 1 0.000 0.9853 1.000 0.000
#> GSM246090 1 0.000 0.9853 1.000 0.000
#> GSM246119 1 0.000 0.9853 1.000 0.000
#> GSM246120 1 0.000 0.9853 1.000 0.000
#> GSM246121 1 0.000 0.9853 1.000 0.000
#> GSM246122 1 0.000 0.9853 1.000 0.000
#> GSM246123 1 0.000 0.9853 1.000 0.000
#> GSM246422 2 0.000 1.0000 0.000 1.000
#> GSM246423 2 0.000 1.0000 0.000 1.000
#> GSM246484 2 0.000 1.0000 0.000 1.000
#> GSM246485 2 0.000 1.0000 0.000 1.000
#> GSM246486 2 0.000 1.0000 0.000 1.000
#> GSM246487 2 0.000 1.0000 0.000 1.000
#> GSM246488 2 0.000 1.0000 0.000 1.000
#> GSM246489 2 0.000 1.0000 0.000 1.000
#> GSM246490 2 0.000 1.0000 0.000 1.000
#> GSM246491 2 0.000 1.0000 0.000 1.000
#> GSM247162 2 0.000 1.0000 0.000 1.000
#> GSM247163 2 0.000 1.0000 0.000 1.000
#> GSM247164 2 0.000 1.0000 0.000 1.000
#> GSM247165 2 0.000 1.0000 0.000 1.000
#> GSM247166 2 0.000 1.0000 0.000 1.000
#> GSM247168 2 0.000 1.0000 0.000 1.000
#> GSM247169 2 0.000 1.0000 0.000 1.000
#> GSM247171 2 0.000 1.0000 0.000 1.000
#> GSM247173 2 0.000 1.0000 0.000 1.000
#> GSM247174 2 0.000 1.0000 0.000 1.000
#> GSM247175 2 0.000 1.0000 0.000 1.000
#> GSM247188 2 0.000 1.0000 0.000 1.000
#> GSM247189 2 0.000 1.0000 0.000 1.000
#> GSM247190 2 0.000 1.0000 0.000 1.000
#> GSM247650 1 0.000 0.9853 1.000 0.000
#> GSM247651 1 0.000 0.9853 1.000 0.000
#> GSM247652 1 0.000 0.9853 1.000 0.000
#> GSM247653 1 0.000 0.9853 1.000 0.000
#> GSM247654 1 0.000 0.9853 1.000 0.000
#> GSM247655 1 0.000 0.9853 1.000 0.000
#> GSM247656 1 0.000 0.9853 1.000 0.000
#> GSM247657 1 0.000 0.9853 1.000 0.000
#> GSM247658 1 0.000 0.9853 1.000 0.000
#> GSM247659 1 0.000 0.9853 1.000 0.000
#> GSM247660 1 0.000 0.9853 1.000 0.000
#> GSM247661 1 0.000 0.9853 1.000 0.000
#> GSM247662 1 0.000 0.9853 1.000 0.000
#> GSM247663 1 0.000 0.9853 1.000 0.000
#> GSM247856 1 0.000 0.9853 1.000 0.000
#> GSM247857 1 0.000 0.9853 1.000 0.000
#> GSM247859 1 0.000 0.9853 1.000 0.000
#> GSM247860 1 0.000 0.9853 1.000 0.000
#> GSM247862 1 0.000 0.9853 1.000 0.000
#> GSM247864 1 0.000 0.9853 1.000 0.000
#> GSM247865 1 0.999 0.0817 0.520 0.480
#> GSM247866 1 0.000 0.9853 1.000 0.000
#> GSM247876 1 0.000 0.9853 1.000 0.000
#> GSM247877 1 0.000 0.9853 1.000 0.000
#> GSM247878 1 0.000 0.9853 1.000 0.000
#> GSM247879 1 0.000 0.9853 1.000 0.000
#> GSM247881 1 0.000 0.9853 1.000 0.000
#> GSM247883 1 0.260 0.9421 0.956 0.044
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 0.859 0.000 0.000 1.000
#> GSM246088 3 0.0000 0.859 0.000 0.000 1.000
#> GSM246089 3 0.0000 0.859 0.000 0.000 1.000
#> GSM246090 3 0.0000 0.859 0.000 0.000 1.000
#> GSM246119 3 0.0000 0.859 0.000 0.000 1.000
#> GSM246120 3 0.0000 0.859 0.000 0.000 1.000
#> GSM246121 3 0.0000 0.859 0.000 0.000 1.000
#> GSM246122 3 0.0000 0.859 0.000 0.000 1.000
#> GSM246123 3 0.0000 0.859 0.000 0.000 1.000
#> GSM246422 1 0.3816 0.784 0.852 0.148 0.000
#> GSM246423 1 0.3752 0.788 0.856 0.144 0.000
#> GSM246484 1 0.3816 0.784 0.852 0.148 0.000
#> GSM246485 2 0.0424 0.991 0.008 0.992 0.000
#> GSM246486 2 0.0237 0.995 0.004 0.996 0.000
#> GSM246487 1 0.4235 0.756 0.824 0.176 0.000
#> GSM246488 2 0.1163 0.972 0.028 0.972 0.000
#> GSM246489 2 0.0000 0.998 0.000 1.000 0.000
#> GSM246490 2 0.0000 0.998 0.000 1.000 0.000
#> GSM246491 2 0.0000 0.998 0.000 1.000 0.000
#> GSM247162 2 0.0000 0.998 0.000 1.000 0.000
#> GSM247163 2 0.0000 0.998 0.000 1.000 0.000
#> GSM247164 2 0.0000 0.998 0.000 1.000 0.000
#> GSM247165 2 0.0000 0.998 0.000 1.000 0.000
#> GSM247166 2 0.0000 0.998 0.000 1.000 0.000
#> GSM247168 2 0.0000 0.998 0.000 1.000 0.000
#> GSM247169 2 0.0000 0.998 0.000 1.000 0.000
#> GSM247171 2 0.0000 0.998 0.000 1.000 0.000
#> GSM247173 2 0.0000 0.998 0.000 1.000 0.000
#> GSM247174 2 0.0000 0.998 0.000 1.000 0.000
#> GSM247175 2 0.0000 0.998 0.000 1.000 0.000
#> GSM247188 2 0.0000 0.998 0.000 1.000 0.000
#> GSM247189 2 0.0000 0.998 0.000 1.000 0.000
#> GSM247190 2 0.0000 0.998 0.000 1.000 0.000
#> GSM247650 1 0.4452 0.713 0.808 0.000 0.192
#> GSM247651 1 0.0000 0.882 1.000 0.000 0.000
#> GSM247652 1 0.5882 0.367 0.652 0.000 0.348
#> GSM247653 3 0.3752 0.825 0.144 0.000 0.856
#> GSM247654 3 0.4842 0.763 0.224 0.000 0.776
#> GSM247655 1 0.0000 0.882 1.000 0.000 0.000
#> GSM247656 3 0.3412 0.833 0.124 0.000 0.876
#> GSM247657 3 0.5465 0.681 0.288 0.000 0.712
#> GSM247658 1 0.4291 0.729 0.820 0.000 0.180
#> GSM247659 3 0.0000 0.859 0.000 0.000 1.000
#> GSM247660 1 0.0000 0.882 1.000 0.000 0.000
#> GSM247661 3 0.3551 0.831 0.132 0.000 0.868
#> GSM247662 3 0.4399 0.793 0.188 0.000 0.812
#> GSM247663 1 0.4399 0.719 0.812 0.000 0.188
#> GSM247856 3 0.6305 0.202 0.484 0.000 0.516
#> GSM247857 3 0.5327 0.709 0.272 0.000 0.728
#> GSM247859 1 0.0000 0.882 1.000 0.000 0.000
#> GSM247860 3 0.3686 0.828 0.140 0.000 0.860
#> GSM247862 1 0.0000 0.882 1.000 0.000 0.000
#> GSM247864 1 0.0000 0.882 1.000 0.000 0.000
#> GSM247865 1 0.0000 0.882 1.000 0.000 0.000
#> GSM247866 1 0.0000 0.882 1.000 0.000 0.000
#> GSM247876 1 0.2625 0.832 0.916 0.000 0.084
#> GSM247877 1 0.4399 0.733 0.812 0.000 0.188
#> GSM247878 1 0.0000 0.882 1.000 0.000 0.000
#> GSM247879 3 0.6192 0.185 0.420 0.000 0.580
#> GSM247881 1 0.1289 0.866 0.968 0.000 0.032
#> GSM247883 1 0.0000 0.882 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 0.9822 0.000 0.000 1.000 0.000
#> GSM246088 3 0.0000 0.9822 0.000 0.000 1.000 0.000
#> GSM246089 3 0.0000 0.9822 0.000 0.000 1.000 0.000
#> GSM246090 3 0.0000 0.9822 0.000 0.000 1.000 0.000
#> GSM246119 3 0.0000 0.9822 0.000 0.000 1.000 0.000
#> GSM246120 3 0.0000 0.9822 0.000 0.000 1.000 0.000
#> GSM246121 3 0.0000 0.9822 0.000 0.000 1.000 0.000
#> GSM246122 3 0.0000 0.9822 0.000 0.000 1.000 0.000
#> GSM246123 3 0.0000 0.9822 0.000 0.000 1.000 0.000
#> GSM246422 4 0.0000 0.8487 0.000 0.000 0.000 1.000
#> GSM246423 4 0.0000 0.8487 0.000 0.000 0.000 1.000
#> GSM246484 4 0.0000 0.8487 0.000 0.000 0.000 1.000
#> GSM246485 4 0.4877 0.2575 0.000 0.408 0.000 0.592
#> GSM246486 4 0.2081 0.8088 0.000 0.084 0.000 0.916
#> GSM246487 4 0.0000 0.8487 0.000 0.000 0.000 1.000
#> GSM246488 4 0.1211 0.8361 0.000 0.040 0.000 0.960
#> GSM246489 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM246490 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM246491 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247162 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247163 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247164 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247165 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247166 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247168 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247169 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247171 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247173 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247174 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247175 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247188 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247189 2 0.4817 0.3142 0.000 0.612 0.000 0.388
#> GSM247190 2 0.0000 0.9735 0.000 1.000 0.000 0.000
#> GSM247650 1 0.0000 0.8885 1.000 0.000 0.000 0.000
#> GSM247651 1 0.4331 0.6468 0.712 0.000 0.000 0.288
#> GSM247652 1 0.0000 0.8885 1.000 0.000 0.000 0.000
#> GSM247653 1 0.1022 0.8830 0.968 0.000 0.032 0.000
#> GSM247654 1 0.0817 0.8853 0.976 0.000 0.024 0.000
#> GSM247655 1 0.3024 0.8135 0.852 0.000 0.000 0.148
#> GSM247656 1 0.4972 0.2012 0.544 0.000 0.456 0.000
#> GSM247657 1 0.0817 0.8856 0.976 0.000 0.024 0.000
#> GSM247658 1 0.0000 0.8885 1.000 0.000 0.000 0.000
#> GSM247659 3 0.0469 0.9712 0.012 0.000 0.988 0.000
#> GSM247660 1 0.4193 0.6784 0.732 0.000 0.000 0.268
#> GSM247661 1 0.2760 0.8179 0.872 0.000 0.128 0.000
#> GSM247662 1 0.4072 0.6819 0.748 0.000 0.252 0.000
#> GSM247663 1 0.0000 0.8885 1.000 0.000 0.000 0.000
#> GSM247856 1 0.1118 0.8819 0.964 0.000 0.036 0.000
#> GSM247857 1 0.0921 0.8862 0.972 0.000 0.028 0.000
#> GSM247859 1 0.3356 0.7887 0.824 0.000 0.000 0.176
#> GSM247860 1 0.1302 0.8775 0.956 0.000 0.044 0.000
#> GSM247862 1 0.0000 0.8885 1.000 0.000 0.000 0.000
#> GSM247864 1 0.2814 0.8258 0.868 0.000 0.000 0.132
#> GSM247865 4 0.4916 0.0808 0.424 0.000 0.000 0.576
#> GSM247866 1 0.0188 0.8881 0.996 0.000 0.000 0.004
#> GSM247876 1 0.0524 0.8880 0.988 0.000 0.004 0.008
#> GSM247877 4 0.3142 0.7514 0.008 0.000 0.132 0.860
#> GSM247878 4 0.1389 0.8267 0.048 0.000 0.000 0.952
#> GSM247879 3 0.3217 0.8247 0.128 0.000 0.860 0.012
#> GSM247881 1 0.0000 0.8885 1.000 0.000 0.000 0.000
#> GSM247883 1 0.3486 0.7780 0.812 0.000 0.000 0.188
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM246088 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM246089 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM246090 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM246119 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM246120 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM246121 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM246122 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM246123 3 0.0000 0.9756 0.000 0.000 1.000 0.000 0.000
#> GSM246422 4 0.0162 0.8770 0.004 0.000 0.000 0.996 0.000
#> GSM246423 4 0.0162 0.8770 0.004 0.000 0.000 0.996 0.000
#> GSM246484 4 0.0162 0.8770 0.004 0.000 0.000 0.996 0.000
#> GSM246485 4 0.3462 0.6980 0.000 0.196 0.000 0.792 0.012
#> GSM246486 4 0.1364 0.8617 0.000 0.036 0.000 0.952 0.012
#> GSM246487 4 0.0579 0.8717 0.008 0.000 0.000 0.984 0.008
#> GSM246488 4 0.0865 0.8704 0.000 0.024 0.000 0.972 0.004
#> GSM246489 2 0.0000 0.9666 0.000 1.000 0.000 0.000 0.000
#> GSM246490 2 0.0162 0.9655 0.000 0.996 0.000 0.000 0.004
#> GSM246491 2 0.0162 0.9655 0.000 0.996 0.000 0.000 0.004
#> GSM247162 2 0.0000 0.9666 0.000 1.000 0.000 0.000 0.000
#> GSM247163 2 0.0162 0.9655 0.000 0.996 0.000 0.000 0.004
#> GSM247164 2 0.0162 0.9655 0.000 0.996 0.000 0.000 0.004
#> GSM247165 2 0.0451 0.9601 0.000 0.988 0.000 0.004 0.008
#> GSM247166 2 0.0162 0.9652 0.000 0.996 0.000 0.000 0.004
#> GSM247168 2 0.0162 0.9652 0.000 0.996 0.000 0.000 0.004
#> GSM247169 2 0.0162 0.9652 0.000 0.996 0.000 0.000 0.004
#> GSM247171 2 0.0000 0.9666 0.000 1.000 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.9666 0.000 1.000 0.000 0.000 0.000
#> GSM247174 2 0.0000 0.9666 0.000 1.000 0.000 0.000 0.000
#> GSM247175 2 0.0000 0.9666 0.000 1.000 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.9666 0.000 1.000 0.000 0.000 0.000
#> GSM247189 2 0.4546 0.0744 0.000 0.532 0.000 0.460 0.008
#> GSM247190 2 0.0000 0.9666 0.000 1.000 0.000 0.000 0.000
#> GSM247650 1 0.2329 0.5310 0.876 0.000 0.000 0.000 0.124
#> GSM247651 1 0.4010 0.5474 0.792 0.000 0.000 0.136 0.072
#> GSM247652 5 0.3983 0.5309 0.340 0.000 0.000 0.000 0.660
#> GSM247653 5 0.1956 0.6786 0.076 0.000 0.008 0.000 0.916
#> GSM247654 5 0.2660 0.6864 0.128 0.000 0.008 0.000 0.864
#> GSM247655 1 0.2654 0.5533 0.884 0.000 0.000 0.032 0.084
#> GSM247656 5 0.6206 0.3634 0.172 0.000 0.296 0.000 0.532
#> GSM247657 5 0.3534 0.5832 0.256 0.000 0.000 0.000 0.744
#> GSM247658 5 0.3932 0.5242 0.328 0.000 0.000 0.000 0.672
#> GSM247659 3 0.4194 0.7334 0.088 0.000 0.780 0.000 0.132
#> GSM247660 1 0.3705 0.5540 0.816 0.000 0.000 0.120 0.064
#> GSM247661 5 0.3527 0.6395 0.116 0.000 0.056 0.000 0.828
#> GSM247662 1 0.6084 0.0164 0.508 0.000 0.132 0.000 0.360
#> GSM247663 1 0.4088 0.1953 0.632 0.000 0.000 0.000 0.368
#> GSM247856 5 0.5325 0.3080 0.428 0.000 0.052 0.000 0.520
#> GSM247857 1 0.4590 0.0798 0.568 0.000 0.012 0.000 0.420
#> GSM247859 1 0.4451 0.4401 0.712 0.000 0.000 0.040 0.248
#> GSM247860 5 0.2389 0.6608 0.116 0.000 0.004 0.000 0.880
#> GSM247862 1 0.4249 0.1375 0.568 0.000 0.000 0.000 0.432
#> GSM247864 1 0.2344 0.5594 0.904 0.000 0.000 0.032 0.064
#> GSM247865 1 0.5441 0.3952 0.596 0.000 0.000 0.324 0.080
#> GSM247866 1 0.4533 0.1164 0.544 0.000 0.000 0.008 0.448
#> GSM247876 1 0.3790 0.4459 0.724 0.000 0.004 0.000 0.272
#> GSM247877 4 0.6615 0.3101 0.316 0.000 0.084 0.544 0.056
#> GSM247878 1 0.4989 0.1526 0.552 0.000 0.000 0.416 0.032
#> GSM247879 1 0.6487 0.0761 0.432 0.000 0.404 0.004 0.160
#> GSM247881 1 0.3274 0.4562 0.780 0.000 0.000 0.000 0.220
#> GSM247883 1 0.4462 0.4675 0.740 0.000 0.000 0.064 0.196
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0000 0.94359 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246088 3 0.0000 0.94359 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246089 3 0.0000 0.94359 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246090 3 0.0000 0.94359 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246119 3 0.0000 0.94359 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246120 3 0.0000 0.94359 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246121 3 0.0000 0.94359 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246122 3 0.0000 0.94359 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246123 3 0.0000 0.94359 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246422 4 0.1219 0.79486 0.004 0.000 0.000 0.948 0.048 0.000
#> GSM246423 4 0.1219 0.79486 0.004 0.000 0.000 0.948 0.048 0.000
#> GSM246484 4 0.1219 0.79486 0.004 0.000 0.000 0.948 0.048 0.000
#> GSM246485 4 0.3327 0.70303 0.004 0.116 0.000 0.828 0.048 0.004
#> GSM246486 4 0.2122 0.77663 0.008 0.040 0.000 0.912 0.040 0.000
#> GSM246487 4 0.2617 0.73665 0.080 0.004 0.000 0.876 0.040 0.000
#> GSM246488 4 0.0000 0.79435 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM246489 2 0.0146 0.98521 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM246490 2 0.0603 0.98308 0.000 0.980 0.000 0.004 0.016 0.000
#> GSM246491 2 0.0508 0.98426 0.000 0.984 0.000 0.004 0.012 0.000
#> GSM247162 2 0.0458 0.98405 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM247163 2 0.0603 0.98157 0.000 0.980 0.000 0.004 0.016 0.000
#> GSM247164 2 0.0405 0.98319 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM247165 2 0.1088 0.96304 0.000 0.960 0.000 0.024 0.016 0.000
#> GSM247166 2 0.0865 0.97455 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM247168 2 0.0865 0.97455 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM247169 2 0.0790 0.97677 0.000 0.968 0.000 0.000 0.032 0.000
#> GSM247171 2 0.0146 0.98529 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM247173 2 0.0260 0.98501 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM247174 2 0.0363 0.98388 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM247175 2 0.0146 0.98467 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM247188 2 0.0260 0.98486 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM247189 4 0.4712 0.17611 0.000 0.448 0.000 0.512 0.036 0.004
#> GSM247190 2 0.0547 0.98406 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM247650 1 0.4412 0.44560 0.732 0.000 0.008 0.000 0.160 0.100
#> GSM247651 1 0.3730 0.48316 0.812 0.000 0.000 0.052 0.104 0.032
#> GSM247652 6 0.5421 0.35964 0.308 0.000 0.000 0.000 0.144 0.548
#> GSM247653 6 0.1485 0.57135 0.028 0.000 0.004 0.000 0.024 0.944
#> GSM247654 6 0.3052 0.57872 0.068 0.000 0.004 0.000 0.080 0.848
#> GSM247655 1 0.2001 0.52816 0.912 0.000 0.000 0.000 0.040 0.048
#> GSM247656 6 0.6997 0.23443 0.088 0.000 0.224 0.000 0.244 0.444
#> GSM247657 6 0.5276 0.40737 0.188 0.000 0.000 0.000 0.208 0.604
#> GSM247658 6 0.4655 0.39596 0.300 0.000 0.000 0.000 0.068 0.632
#> GSM247659 3 0.6128 0.24468 0.044 0.000 0.544 0.000 0.272 0.140
#> GSM247660 1 0.3796 0.48946 0.812 0.000 0.000 0.048 0.092 0.048
#> GSM247661 6 0.3324 0.55110 0.080 0.000 0.020 0.000 0.060 0.840
#> GSM247662 5 0.7374 -0.21910 0.304 0.000 0.116 0.000 0.340 0.240
#> GSM247663 1 0.5461 0.23200 0.560 0.000 0.000 0.000 0.168 0.272
#> GSM247856 6 0.6838 0.19759 0.348 0.000 0.060 0.000 0.200 0.392
#> GSM247857 1 0.6242 0.00783 0.416 0.000 0.008 0.000 0.312 0.264
#> GSM247859 1 0.5093 0.43280 0.672 0.000 0.000 0.016 0.164 0.148
#> GSM247860 6 0.2442 0.55885 0.068 0.000 0.000 0.000 0.048 0.884
#> GSM247862 1 0.5387 0.01443 0.464 0.000 0.000 0.000 0.112 0.424
#> GSM247864 1 0.2294 0.51288 0.892 0.000 0.000 0.000 0.072 0.036
#> GSM247865 1 0.5785 0.34842 0.616 0.000 0.000 0.188 0.152 0.044
#> GSM247866 6 0.5782 -0.07517 0.400 0.000 0.000 0.000 0.176 0.424
#> GSM247876 1 0.5558 0.07491 0.448 0.000 0.000 0.000 0.416 0.136
#> GSM247877 5 0.6297 0.11347 0.208 0.000 0.012 0.332 0.444 0.004
#> GSM247878 1 0.5997 -0.17416 0.416 0.000 0.000 0.240 0.344 0.000
#> GSM247879 5 0.7037 0.13388 0.232 0.000 0.200 0.008 0.476 0.084
#> GSM247881 1 0.4963 0.43180 0.636 0.000 0.000 0.000 0.240 0.124
#> GSM247883 1 0.4675 0.45300 0.696 0.000 0.000 0.008 0.200 0.096
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:skmeans 60 9.36e-14 2
#> MAD:skmeans 58 1.47e-12 3
#> MAD:skmeans 57 7.66e-18 4
#> MAD:skmeans 45 1.62e-14 5
#> MAD:skmeans 38 3.11e-13 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 21168 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.966 0.948 0.965 0.4553 0.552 0.552
#> 3 3 1.000 0.989 0.995 0.3384 0.843 0.715
#> 4 4 0.987 0.944 0.978 0.1157 0.926 0.814
#> 5 5 0.854 0.847 0.923 0.1271 0.920 0.753
#> 6 6 0.882 0.872 0.924 0.0432 0.939 0.756
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> 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
#> GSM246087 1 0.0938 0.943 0.988 0.012
#> GSM246088 1 0.0000 0.947 1.000 0.000
#> GSM246089 1 0.0000 0.947 1.000 0.000
#> GSM246090 1 0.0000 0.947 1.000 0.000
#> GSM246119 1 0.0000 0.947 1.000 0.000
#> GSM246120 1 0.0000 0.947 1.000 0.000
#> GSM246121 1 0.0000 0.947 1.000 0.000
#> GSM246122 1 0.9170 0.485 0.668 0.332
#> GSM246123 1 0.0000 0.947 1.000 0.000
#> GSM246422 1 0.6438 0.835 0.836 0.164
#> GSM246423 1 0.2236 0.961 0.964 0.036
#> GSM246484 1 0.9170 0.574 0.668 0.332
#> GSM246485 2 0.1184 0.982 0.016 0.984
#> GSM246486 2 0.0000 0.999 0.000 1.000
#> GSM246487 1 0.9170 0.574 0.668 0.332
#> GSM246488 2 0.0000 0.999 0.000 1.000
#> GSM246489 2 0.0000 0.999 0.000 1.000
#> GSM246490 2 0.0000 0.999 0.000 1.000
#> GSM246491 2 0.0000 0.999 0.000 1.000
#> GSM247162 2 0.0000 0.999 0.000 1.000
#> GSM247163 2 0.0000 0.999 0.000 1.000
#> GSM247164 2 0.0000 0.999 0.000 1.000
#> GSM247165 2 0.0000 0.999 0.000 1.000
#> GSM247166 2 0.0000 0.999 0.000 1.000
#> GSM247168 2 0.0000 0.999 0.000 1.000
#> GSM247169 2 0.0000 0.999 0.000 1.000
#> GSM247171 2 0.0000 0.999 0.000 1.000
#> GSM247173 2 0.0000 0.999 0.000 1.000
#> GSM247174 2 0.0000 0.999 0.000 1.000
#> GSM247175 2 0.0000 0.999 0.000 1.000
#> GSM247188 2 0.0000 0.999 0.000 1.000
#> GSM247189 2 0.0000 0.999 0.000 1.000
#> GSM247190 2 0.0000 0.999 0.000 1.000
#> GSM247650 1 0.2236 0.961 0.964 0.036
#> GSM247651 1 0.2236 0.961 0.964 0.036
#> GSM247652 1 0.2236 0.961 0.964 0.036
#> GSM247653 1 0.2236 0.961 0.964 0.036
#> GSM247654 1 0.2236 0.961 0.964 0.036
#> GSM247655 1 0.2236 0.961 0.964 0.036
#> GSM247656 1 0.0938 0.953 0.988 0.012
#> GSM247657 1 0.2236 0.961 0.964 0.036
#> GSM247658 1 0.2236 0.961 0.964 0.036
#> GSM247659 1 0.0000 0.947 1.000 0.000
#> GSM247660 1 0.2236 0.961 0.964 0.036
#> GSM247661 1 0.0376 0.949 0.996 0.004
#> GSM247662 1 0.0376 0.949 0.996 0.004
#> GSM247663 1 0.2236 0.961 0.964 0.036
#> GSM247856 1 0.2236 0.961 0.964 0.036
#> GSM247857 1 0.2236 0.961 0.964 0.036
#> GSM247859 1 0.2236 0.961 0.964 0.036
#> GSM247860 1 0.2236 0.961 0.964 0.036
#> GSM247862 1 0.2236 0.961 0.964 0.036
#> GSM247864 1 0.2236 0.961 0.964 0.036
#> GSM247865 1 0.2236 0.961 0.964 0.036
#> GSM247866 1 0.2236 0.961 0.964 0.036
#> GSM247876 1 0.2236 0.961 0.964 0.036
#> GSM247877 1 0.2236 0.961 0.964 0.036
#> GSM247878 1 0.2236 0.961 0.964 0.036
#> GSM247879 1 0.2236 0.961 0.964 0.036
#> GSM247881 1 0.2236 0.961 0.964 0.036
#> GSM247883 1 0.2236 0.961 0.964 0.036
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246422 1 0.0000 0.990 1.000 0.000 0.000
#> GSM246423 1 0.0000 0.990 1.000 0.000 0.000
#> GSM246484 1 0.0000 0.990 1.000 0.000 0.000
#> GSM246485 2 0.0424 0.989 0.008 0.992 0.000
#> GSM246486 2 0.0000 0.999 0.000 1.000 0.000
#> GSM246487 1 0.0000 0.990 1.000 0.000 0.000
#> GSM246488 2 0.0000 0.999 0.000 1.000 0.000
#> GSM246489 2 0.0000 0.999 0.000 1.000 0.000
#> GSM246490 2 0.0000 0.999 0.000 1.000 0.000
#> GSM246491 2 0.0000 0.999 0.000 1.000 0.000
#> GSM247162 2 0.0000 0.999 0.000 1.000 0.000
#> GSM247163 2 0.0000 0.999 0.000 1.000 0.000
#> GSM247164 2 0.0000 0.999 0.000 1.000 0.000
#> GSM247165 2 0.0000 0.999 0.000 1.000 0.000
#> GSM247166 2 0.0000 0.999 0.000 1.000 0.000
#> GSM247168 2 0.0000 0.999 0.000 1.000 0.000
#> GSM247169 2 0.0000 0.999 0.000 1.000 0.000
#> GSM247171 2 0.0000 0.999 0.000 1.000 0.000
#> GSM247173 2 0.0000 0.999 0.000 1.000 0.000
#> GSM247174 2 0.0000 0.999 0.000 1.000 0.000
#> GSM247175 2 0.0000 0.999 0.000 1.000 0.000
#> GSM247188 2 0.0000 0.999 0.000 1.000 0.000
#> GSM247189 2 0.0000 0.999 0.000 1.000 0.000
#> GSM247190 2 0.0000 0.999 0.000 1.000 0.000
#> GSM247650 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247651 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247652 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247653 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247654 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247655 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247656 1 0.4974 0.692 0.764 0.000 0.236
#> GSM247657 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247658 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247659 1 0.2165 0.927 0.936 0.000 0.064
#> GSM247660 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247661 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247662 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247663 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247856 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247857 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247859 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247860 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247862 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247864 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247865 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247866 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247876 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247877 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247878 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247879 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247881 1 0.0000 0.990 1.000 0.000 0.000
#> GSM247883 1 0.0000 0.990 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM246088 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM246089 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM246090 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM246119 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM246120 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM246121 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM246122 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM246123 3 0.000 1.000 0.000 0.000 1.000 0.000
#> GSM246422 4 0.000 0.877 0.000 0.000 0.000 1.000
#> GSM246423 4 0.000 0.877 0.000 0.000 0.000 1.000
#> GSM246484 4 0.000 0.877 0.000 0.000 0.000 1.000
#> GSM246485 2 0.102 0.931 0.032 0.968 0.000 0.000
#> GSM246486 2 0.394 0.711 0.000 0.764 0.000 0.236
#> GSM246487 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM246488 4 0.000 0.877 0.000 0.000 0.000 1.000
#> GSM246489 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM246490 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM246491 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM247162 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM247163 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM247164 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM247165 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM247166 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM247168 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM247169 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM247171 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM247173 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM247174 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM247175 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM247188 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM247189 2 0.425 0.648 0.000 0.724 0.000 0.276
#> GSM247190 2 0.000 0.969 0.000 1.000 0.000 0.000
#> GSM247650 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247651 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247652 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247653 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247654 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247655 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247656 1 0.102 0.949 0.968 0.000 0.032 0.000
#> GSM247657 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247658 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247659 1 0.172 0.912 0.936 0.000 0.064 0.000
#> GSM247660 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247661 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247662 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247663 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247856 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247857 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247859 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247860 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247862 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247864 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247865 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247866 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247876 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247877 4 0.450 0.517 0.316 0.000 0.000 0.684
#> GSM247878 1 0.473 0.361 0.636 0.000 0.000 0.364
#> GSM247879 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247881 1 0.000 0.981 1.000 0.000 0.000 0.000
#> GSM247883 1 0.000 0.981 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM246422 4 0.0000 0.886 0.000 0.000 0.000 1.000 0.000
#> GSM246423 4 0.0000 0.886 0.000 0.000 0.000 1.000 0.000
#> GSM246484 4 0.0000 0.886 0.000 0.000 0.000 1.000 0.000
#> GSM246485 2 0.0794 0.939 0.028 0.972 0.000 0.000 0.000
#> GSM246486 2 0.3395 0.708 0.000 0.764 0.000 0.236 0.000
#> GSM246487 1 0.0162 0.834 0.996 0.000 0.000 0.000 0.004
#> GSM246488 4 0.0000 0.886 0.000 0.000 0.000 1.000 0.000
#> GSM246489 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM246490 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM246491 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM247162 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM247163 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM247164 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM247165 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM247166 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM247168 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM247169 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM247171 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM247174 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM247175 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM247189 2 0.3661 0.643 0.000 0.724 0.000 0.276 0.000
#> GSM247190 2 0.0000 0.969 0.000 1.000 0.000 0.000 0.000
#> GSM247650 1 0.0703 0.824 0.976 0.000 0.000 0.000 0.024
#> GSM247651 1 0.0000 0.834 1.000 0.000 0.000 0.000 0.000
#> GSM247652 1 0.3932 0.646 0.672 0.000 0.000 0.000 0.328
#> GSM247653 1 0.3837 0.672 0.692 0.000 0.000 0.000 0.308
#> GSM247654 1 0.4304 0.350 0.516 0.000 0.000 0.000 0.484
#> GSM247655 1 0.0162 0.833 0.996 0.000 0.000 0.000 0.004
#> GSM247656 5 0.0162 0.724 0.004 0.000 0.000 0.000 0.996
#> GSM247657 5 0.0162 0.724 0.004 0.000 0.000 0.000 0.996
#> GSM247658 1 0.3508 0.715 0.748 0.000 0.000 0.000 0.252
#> GSM247659 5 0.4087 0.757 0.208 0.000 0.036 0.000 0.756
#> GSM247660 1 0.0000 0.834 1.000 0.000 0.000 0.000 0.000
#> GSM247661 5 0.2329 0.781 0.124 0.000 0.000 0.000 0.876
#> GSM247662 5 0.3508 0.747 0.252 0.000 0.000 0.000 0.748
#> GSM247663 1 0.3534 0.716 0.744 0.000 0.000 0.000 0.256
#> GSM247856 5 0.3274 0.632 0.220 0.000 0.000 0.000 0.780
#> GSM247857 5 0.3452 0.753 0.244 0.000 0.000 0.000 0.756
#> GSM247859 1 0.0290 0.834 0.992 0.000 0.000 0.000 0.008
#> GSM247860 1 0.3730 0.690 0.712 0.000 0.000 0.000 0.288
#> GSM247862 1 0.0000 0.834 1.000 0.000 0.000 0.000 0.000
#> GSM247864 1 0.0162 0.833 0.996 0.000 0.000 0.000 0.004
#> GSM247865 1 0.0290 0.834 0.992 0.000 0.000 0.000 0.008
#> GSM247866 1 0.0162 0.833 0.996 0.000 0.000 0.000 0.004
#> GSM247876 1 0.0609 0.830 0.980 0.000 0.000 0.000 0.020
#> GSM247877 4 0.4029 0.456 0.316 0.000 0.000 0.680 0.004
#> GSM247878 1 0.3424 0.592 0.760 0.000 0.000 0.240 0.000
#> GSM247879 1 0.2891 0.653 0.824 0.000 0.000 0.000 0.176
#> GSM247881 1 0.1341 0.821 0.944 0.000 0.000 0.000 0.056
#> GSM247883 1 0.3534 0.715 0.744 0.000 0.000 0.000 0.256
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0000 0.9773 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM246088 3 0.0000 0.9773 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM246089 3 0.2941 0.7956 0.000 0.000 0.78 0.000 0.220 0.000
#> GSM246090 3 0.0000 0.9773 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM246119 3 0.0000 0.9773 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM246120 3 0.0000 0.9773 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM246121 3 0.0000 0.9773 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM246122 3 0.0000 0.9773 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM246123 3 0.0000 0.9773 0.000 0.000 1.00 0.000 0.000 0.000
#> GSM246422 4 0.0000 0.8904 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM246423 4 0.0000 0.8904 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM246484 4 0.0000 0.8904 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM246485 2 0.0713 0.9393 0.028 0.972 0.00 0.000 0.000 0.000
#> GSM246486 2 0.3050 0.7067 0.000 0.764 0.00 0.236 0.000 0.000
#> GSM246487 1 0.0000 0.9424 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM246488 4 0.0000 0.8904 0.000 0.000 0.00 1.000 0.000 0.000
#> GSM246489 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM246490 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM246491 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM247162 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM247163 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM247164 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM247165 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM247166 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM247168 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM247169 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM247171 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM247174 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM247175 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM247189 2 0.3288 0.6418 0.000 0.724 0.00 0.276 0.000 0.000
#> GSM247190 2 0.0000 0.9693 0.000 1.000 0.00 0.000 0.000 0.000
#> GSM247650 1 0.1444 0.8879 0.928 0.000 0.00 0.000 0.000 0.072
#> GSM247651 1 0.0000 0.9424 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM247652 5 0.3993 0.8250 0.300 0.000 0.00 0.000 0.676 0.024
#> GSM247653 5 0.2941 0.8170 0.220 0.000 0.00 0.000 0.780 0.000
#> GSM247654 5 0.3806 0.7437 0.152 0.000 0.00 0.000 0.772 0.076
#> GSM247655 1 0.0146 0.9415 0.996 0.000 0.00 0.000 0.000 0.004
#> GSM247656 5 0.3993 -0.0921 0.004 0.000 0.00 0.000 0.520 0.476
#> GSM247657 6 0.0146 0.8893 0.004 0.000 0.00 0.000 0.000 0.996
#> GSM247658 5 0.3515 0.8166 0.324 0.000 0.00 0.000 0.676 0.000
#> GSM247659 6 0.0000 0.8911 0.000 0.000 0.00 0.000 0.000 1.000
#> GSM247660 1 0.0000 0.9424 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM247661 6 0.0622 0.8824 0.008 0.000 0.00 0.000 0.012 0.980
#> GSM247662 6 0.0000 0.8911 0.000 0.000 0.00 0.000 0.000 1.000
#> GSM247663 5 0.3636 0.8167 0.320 0.000 0.00 0.000 0.676 0.004
#> GSM247856 6 0.5257 0.0990 0.104 0.000 0.00 0.000 0.372 0.524
#> GSM247857 6 0.0000 0.8911 0.000 0.000 0.00 0.000 0.000 1.000
#> GSM247859 1 0.0000 0.9424 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM247860 5 0.2969 0.8180 0.224 0.000 0.00 0.000 0.776 0.000
#> GSM247862 1 0.0000 0.9424 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM247864 1 0.0146 0.9415 0.996 0.000 0.00 0.000 0.000 0.004
#> GSM247865 1 0.0000 0.9424 1.000 0.000 0.00 0.000 0.000 0.000
#> GSM247866 1 0.0146 0.9415 0.996 0.000 0.00 0.000 0.000 0.004
#> GSM247876 1 0.0713 0.9276 0.972 0.000 0.00 0.000 0.000 0.028
#> GSM247877 4 0.3619 0.5134 0.316 0.000 0.00 0.680 0.000 0.004
#> GSM247878 1 0.2454 0.7649 0.840 0.000 0.00 0.160 0.000 0.000
#> GSM247879 1 0.2969 0.6854 0.776 0.000 0.00 0.000 0.000 0.224
#> GSM247881 1 0.1387 0.8688 0.932 0.000 0.00 0.000 0.068 0.000
#> GSM247883 5 0.3714 0.7991 0.340 0.000 0.00 0.000 0.656 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:pam 60 1.69e-10 2
#> MAD:pam 61 6.70e-22 3
#> MAD:pam 60 9.09e-22 4
#> MAD:pam 59 7.23e-21 5
#> MAD:pam 59 5.78e-19 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 21168 rows and 61 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.446 0.215 0.581 0.4869 0.721 0.721
#> 3 3 0.818 0.882 0.943 0.3350 0.560 0.418
#> 4 4 0.918 0.878 0.951 0.1176 0.907 0.744
#> 5 5 0.842 0.872 0.907 0.0369 0.986 0.952
#> 6 6 0.952 0.934 0.960 0.0720 0.916 0.695
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 4
There is also optional best \(k\) = 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM246087 1 0.7602 0.853 0.780 0.220
#> GSM246088 1 0.7602 0.853 0.780 0.220
#> GSM246089 1 0.7602 0.853 0.780 0.220
#> GSM246090 1 0.7602 0.853 0.780 0.220
#> GSM246119 1 0.7602 0.853 0.780 0.220
#> GSM246120 1 0.7602 0.853 0.780 0.220
#> GSM246121 1 0.7602 0.853 0.780 0.220
#> GSM246122 1 0.7602 0.853 0.780 0.220
#> GSM246123 1 0.7602 0.853 0.780 0.220
#> GSM246422 2 0.3733 0.104 0.072 0.928
#> GSM246423 2 0.3733 0.104 0.072 0.928
#> GSM246484 2 0.3733 0.104 0.072 0.928
#> GSM246485 2 0.0000 0.155 0.000 1.000
#> GSM246486 2 0.0000 0.155 0.000 1.000
#> GSM246487 2 0.7528 0.292 0.216 0.784
#> GSM246488 2 0.0938 0.149 0.012 0.988
#> GSM246489 2 0.9881 -0.294 0.436 0.564
#> GSM246490 2 0.9881 -0.294 0.436 0.564
#> GSM246491 2 0.9881 -0.294 0.436 0.564
#> GSM247162 2 0.9881 -0.294 0.436 0.564
#> GSM247163 2 0.9881 -0.294 0.436 0.564
#> GSM247164 2 0.9881 -0.294 0.436 0.564
#> GSM247165 2 0.9881 -0.294 0.436 0.564
#> GSM247166 2 0.9881 -0.294 0.436 0.564
#> GSM247168 2 0.9881 -0.294 0.436 0.564
#> GSM247169 2 0.9881 -0.294 0.436 0.564
#> GSM247171 2 0.9881 -0.294 0.436 0.564
#> GSM247173 2 0.9881 -0.294 0.436 0.564
#> GSM247174 2 0.9881 -0.294 0.436 0.564
#> GSM247175 2 0.9881 -0.294 0.436 0.564
#> GSM247188 2 0.9881 -0.294 0.436 0.564
#> GSM247189 2 0.6531 -0.114 0.168 0.832
#> GSM247190 2 0.9881 -0.294 0.436 0.564
#> GSM247650 2 0.9998 0.393 0.492 0.508
#> GSM247651 2 0.9998 0.393 0.492 0.508
#> GSM247652 2 0.9998 0.393 0.492 0.508
#> GSM247653 2 0.9998 0.393 0.492 0.508
#> GSM247654 2 0.9998 0.393 0.492 0.508
#> GSM247655 2 0.9998 0.393 0.492 0.508
#> GSM247656 1 1.0000 -0.454 0.504 0.496
#> GSM247657 2 0.9998 0.393 0.492 0.508
#> GSM247658 2 0.9998 0.393 0.492 0.508
#> GSM247659 2 0.9170 0.263 0.332 0.668
#> GSM247660 2 0.9998 0.393 0.492 0.508
#> GSM247661 2 0.9998 0.393 0.492 0.508
#> GSM247662 2 1.0000 0.389 0.496 0.504
#> GSM247663 2 0.9998 0.393 0.492 0.508
#> GSM247856 2 0.9998 0.393 0.492 0.508
#> GSM247857 2 0.9998 0.393 0.492 0.508
#> GSM247859 2 0.9998 0.393 0.492 0.508
#> GSM247860 2 0.9998 0.393 0.492 0.508
#> GSM247862 2 0.9998 0.393 0.492 0.508
#> GSM247864 2 0.9998 0.393 0.492 0.508
#> GSM247865 2 0.9775 0.365 0.412 0.588
#> GSM247866 2 0.9998 0.393 0.492 0.508
#> GSM247876 2 0.9983 0.383 0.476 0.524
#> GSM247877 2 0.6887 0.108 0.184 0.816
#> GSM247878 2 0.5059 0.106 0.112 0.888
#> GSM247879 2 0.9286 0.137 0.344 0.656
#> GSM247881 2 0.9998 0.393 0.492 0.508
#> GSM247883 2 0.9998 0.393 0.492 0.508
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 0.944 0.000 0.000 1.000
#> GSM246088 3 0.0000 0.944 0.000 0.000 1.000
#> GSM246089 3 0.0000 0.944 0.000 0.000 1.000
#> GSM246090 3 0.0000 0.944 0.000 0.000 1.000
#> GSM246119 3 0.0000 0.944 0.000 0.000 1.000
#> GSM246120 3 0.0000 0.944 0.000 0.000 1.000
#> GSM246121 3 0.0000 0.944 0.000 0.000 1.000
#> GSM246122 3 0.0000 0.944 0.000 0.000 1.000
#> GSM246123 3 0.0000 0.944 0.000 0.000 1.000
#> GSM246422 3 0.4982 0.830 0.036 0.136 0.828
#> GSM246423 3 0.4982 0.830 0.036 0.136 0.828
#> GSM246484 3 0.4982 0.830 0.036 0.136 0.828
#> GSM246485 2 0.6526 0.658 0.036 0.704 0.260
#> GSM246486 2 0.6526 0.658 0.036 0.704 0.260
#> GSM246487 2 0.7884 0.585 0.100 0.640 0.260
#> GSM246488 2 0.6526 0.658 0.036 0.704 0.260
#> GSM246489 2 0.0000 0.898 0.000 1.000 0.000
#> GSM246490 2 0.0000 0.898 0.000 1.000 0.000
#> GSM246491 2 0.3482 0.822 0.000 0.872 0.128
#> GSM247162 2 0.0000 0.898 0.000 1.000 0.000
#> GSM247163 2 0.3619 0.815 0.000 0.864 0.136
#> GSM247164 2 0.0000 0.898 0.000 1.000 0.000
#> GSM247165 2 0.0237 0.896 0.000 0.996 0.004
#> GSM247166 2 0.0000 0.898 0.000 1.000 0.000
#> GSM247168 2 0.0000 0.898 0.000 1.000 0.000
#> GSM247169 2 0.0000 0.898 0.000 1.000 0.000
#> GSM247171 2 0.0000 0.898 0.000 1.000 0.000
#> GSM247173 2 0.0000 0.898 0.000 1.000 0.000
#> GSM247174 2 0.0000 0.898 0.000 1.000 0.000
#> GSM247175 2 0.0000 0.898 0.000 1.000 0.000
#> GSM247188 2 0.0000 0.898 0.000 1.000 0.000
#> GSM247189 2 0.6526 0.658 0.036 0.704 0.260
#> GSM247190 2 0.0000 0.898 0.000 1.000 0.000
#> GSM247650 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247651 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247652 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247653 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247654 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247655 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247656 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247657 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247658 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247659 1 0.5815 0.558 0.692 0.004 0.304
#> GSM247660 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247661 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247662 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247663 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247856 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247857 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247859 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247860 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247862 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247864 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247865 1 0.0424 0.951 0.992 0.000 0.008
#> GSM247866 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247876 1 0.1529 0.921 0.960 0.000 0.040
#> GSM247877 3 0.3780 0.884 0.044 0.064 0.892
#> GSM247878 1 0.7267 0.521 0.668 0.064 0.268
#> GSM247879 1 0.6333 0.494 0.656 0.012 0.332
#> GSM247881 1 0.0000 0.957 1.000 0.000 0.000
#> GSM247883 1 0.0000 0.957 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246088 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246089 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246090 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246119 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246120 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246121 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246122 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246123 3 0.0000 1.0000 0.000 0.000 1 0.000
#> GSM246422 4 0.0000 0.9988 0.000 0.000 0 1.000
#> GSM246423 4 0.0000 0.9988 0.000 0.000 0 1.000
#> GSM246484 4 0.0000 0.9988 0.000 0.000 0 1.000
#> GSM246485 4 0.0000 0.9988 0.000 0.000 0 1.000
#> GSM246486 4 0.0000 0.9988 0.000 0.000 0 1.000
#> GSM246487 4 0.0000 0.9988 0.000 0.000 0 1.000
#> GSM246488 4 0.0000 0.9988 0.000 0.000 0 1.000
#> GSM246489 2 0.0000 0.8982 0.000 1.000 0 0.000
#> GSM246490 2 0.0000 0.8982 0.000 1.000 0 0.000
#> GSM246491 2 0.4382 0.5667 0.000 0.704 0 0.296
#> GSM247162 2 0.0000 0.8982 0.000 1.000 0 0.000
#> GSM247163 2 0.4967 0.2096 0.000 0.548 0 0.452
#> GSM247164 2 0.4522 0.5421 0.000 0.680 0 0.320
#> GSM247165 2 0.4522 0.5421 0.000 0.680 0 0.320
#> GSM247166 2 0.0000 0.8982 0.000 1.000 0 0.000
#> GSM247168 2 0.0000 0.8982 0.000 1.000 0 0.000
#> GSM247169 2 0.0000 0.8982 0.000 1.000 0 0.000
#> GSM247171 2 0.0000 0.8982 0.000 1.000 0 0.000
#> GSM247173 2 0.0000 0.8982 0.000 1.000 0 0.000
#> GSM247174 2 0.0000 0.8982 0.000 1.000 0 0.000
#> GSM247175 2 0.0000 0.8982 0.000 1.000 0 0.000
#> GSM247188 2 0.0000 0.8982 0.000 1.000 0 0.000
#> GSM247189 4 0.0000 0.9988 0.000 0.000 0 1.000
#> GSM247190 2 0.0000 0.8982 0.000 1.000 0 0.000
#> GSM247650 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247651 1 0.0707 0.9173 0.980 0.000 0 0.020
#> GSM247652 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247653 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247654 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247655 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247656 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247657 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247658 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247659 1 0.4933 0.2532 0.568 0.000 0 0.432
#> GSM247660 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247661 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247662 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247663 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247856 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247857 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247859 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247860 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247862 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247864 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247865 1 0.4500 0.5382 0.684 0.000 0 0.316
#> GSM247866 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247876 1 0.0188 0.9298 0.996 0.000 0 0.004
#> GSM247877 4 0.0000 0.9988 0.000 0.000 0 1.000
#> GSM247878 4 0.0336 0.9889 0.008 0.000 0 0.992
#> GSM247879 1 0.4998 0.0812 0.512 0.000 0 0.488
#> GSM247881 1 0.0000 0.9325 1.000 0.000 0 0.000
#> GSM247883 1 0.4477 0.5456 0.688 0.000 0 0.312
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246422 4 0.0703 0.972 0.000 0.000 0 0.976 0.024
#> GSM246423 4 0.0794 0.971 0.000 0.000 0 0.972 0.028
#> GSM246484 4 0.0703 0.972 0.000 0.000 0 0.976 0.024
#> GSM246485 5 0.4378 0.886 0.036 0.000 0 0.248 0.716
#> GSM246486 5 0.3612 0.905 0.000 0.000 0 0.268 0.732
#> GSM246487 5 0.4921 0.783 0.036 0.000 0 0.360 0.604
#> GSM246488 5 0.3636 0.907 0.000 0.000 0 0.272 0.728
#> GSM246489 2 0.0000 0.896 0.000 1.000 0 0.000 0.000
#> GSM246490 2 0.0963 0.874 0.000 0.964 0 0.000 0.036
#> GSM246491 2 0.3691 0.722 0.000 0.804 0 0.040 0.156
#> GSM247162 2 0.0000 0.896 0.000 1.000 0 0.000 0.000
#> GSM247163 2 0.5167 0.340 0.000 0.552 0 0.044 0.404
#> GSM247164 2 0.4192 0.403 0.000 0.596 0 0.000 0.404
#> GSM247165 2 0.4192 0.403 0.000 0.596 0 0.000 0.404
#> GSM247166 2 0.0000 0.896 0.000 1.000 0 0.000 0.000
#> GSM247168 2 0.0000 0.896 0.000 1.000 0 0.000 0.000
#> GSM247169 2 0.0000 0.896 0.000 1.000 0 0.000 0.000
#> GSM247171 2 0.0000 0.896 0.000 1.000 0 0.000 0.000
#> GSM247173 2 0.0000 0.896 0.000 1.000 0 0.000 0.000
#> GSM247174 2 0.0000 0.896 0.000 1.000 0 0.000 0.000
#> GSM247175 2 0.0000 0.896 0.000 1.000 0 0.000 0.000
#> GSM247188 2 0.0000 0.896 0.000 1.000 0 0.000 0.000
#> GSM247189 5 0.3857 0.896 0.000 0.000 0 0.312 0.688
#> GSM247190 2 0.0000 0.896 0.000 1.000 0 0.000 0.000
#> GSM247650 1 0.0000 0.904 1.000 0.000 0 0.000 0.000
#> GSM247651 1 0.1478 0.897 0.936 0.000 0 0.000 0.064
#> GSM247652 1 0.0794 0.903 0.972 0.000 0 0.000 0.028
#> GSM247653 1 0.3210 0.804 0.788 0.000 0 0.000 0.212
#> GSM247654 1 0.3177 0.807 0.792 0.000 0 0.000 0.208
#> GSM247655 1 0.1478 0.897 0.936 0.000 0 0.000 0.064
#> GSM247656 1 0.1410 0.892 0.940 0.000 0 0.000 0.060
#> GSM247657 1 0.3003 0.823 0.812 0.000 0 0.000 0.188
#> GSM247658 1 0.0609 0.905 0.980 0.000 0 0.000 0.020
#> GSM247659 1 0.3586 0.762 0.792 0.000 0 0.188 0.020
#> GSM247660 1 0.1478 0.897 0.936 0.000 0 0.000 0.064
#> GSM247661 1 0.3177 0.807 0.792 0.000 0 0.000 0.208
#> GSM247662 1 0.0404 0.904 0.988 0.000 0 0.000 0.012
#> GSM247663 1 0.0000 0.904 1.000 0.000 0 0.000 0.000
#> GSM247856 1 0.0404 0.904 0.988 0.000 0 0.000 0.012
#> GSM247857 1 0.0703 0.902 0.976 0.000 0 0.000 0.024
#> GSM247859 1 0.2424 0.854 0.868 0.000 0 0.000 0.132
#> GSM247860 1 0.3210 0.804 0.788 0.000 0 0.000 0.212
#> GSM247862 1 0.1043 0.902 0.960 0.000 0 0.000 0.040
#> GSM247864 1 0.1478 0.897 0.936 0.000 0 0.000 0.064
#> GSM247865 1 0.3519 0.763 0.776 0.000 0 0.008 0.216
#> GSM247866 1 0.1043 0.902 0.960 0.000 0 0.000 0.040
#> GSM247876 1 0.0162 0.904 0.996 0.000 0 0.000 0.004
#> GSM247877 4 0.0404 0.961 0.000 0.000 0 0.988 0.012
#> GSM247878 4 0.0671 0.951 0.004 0.000 0 0.980 0.016
#> GSM247879 1 0.3630 0.742 0.780 0.000 0 0.204 0.016
#> GSM247881 1 0.1043 0.902 0.960 0.000 0 0.000 0.040
#> GSM247883 1 0.3039 0.798 0.808 0.000 0 0.000 0.192
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM246422 5 0.0146 0.985 0.000 0.000 0 0.004 0.996 0.000
#> GSM246423 5 0.0146 0.985 0.000 0.000 0 0.004 0.996 0.000
#> GSM246484 5 0.0146 0.985 0.000 0.000 0 0.004 0.996 0.000
#> GSM246485 4 0.0000 0.993 0.000 0.000 0 1.000 0.000 0.000
#> GSM246486 4 0.0000 0.993 0.000 0.000 0 1.000 0.000 0.000
#> GSM246487 4 0.0862 0.971 0.000 0.004 0 0.972 0.008 0.016
#> GSM246488 4 0.0000 0.993 0.000 0.000 0 1.000 0.000 0.000
#> GSM246489 2 0.0000 0.977 0.000 1.000 0 0.000 0.000 0.000
#> GSM246490 2 0.0547 0.967 0.000 0.980 0 0.020 0.000 0.000
#> GSM246491 2 0.0632 0.964 0.000 0.976 0 0.024 0.000 0.000
#> GSM247162 2 0.0000 0.977 0.000 1.000 0 0.000 0.000 0.000
#> GSM247163 2 0.2597 0.814 0.000 0.824 0 0.176 0.000 0.000
#> GSM247164 2 0.1387 0.933 0.000 0.932 0 0.068 0.000 0.000
#> GSM247165 2 0.1387 0.933 0.000 0.932 0 0.068 0.000 0.000
#> GSM247166 2 0.0000 0.977 0.000 1.000 0 0.000 0.000 0.000
#> GSM247168 2 0.0000 0.977 0.000 1.000 0 0.000 0.000 0.000
#> GSM247169 2 0.0000 0.977 0.000 1.000 0 0.000 0.000 0.000
#> GSM247171 2 0.0000 0.977 0.000 1.000 0 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.977 0.000 1.000 0 0.000 0.000 0.000
#> GSM247174 2 0.0000 0.977 0.000 1.000 0 0.000 0.000 0.000
#> GSM247175 2 0.0000 0.977 0.000 1.000 0 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.977 0.000 1.000 0 0.000 0.000 0.000
#> GSM247189 4 0.0000 0.993 0.000 0.000 0 1.000 0.000 0.000
#> GSM247190 2 0.0000 0.977 0.000 1.000 0 0.000 0.000 0.000
#> GSM247650 1 0.2491 0.865 0.836 0.000 0 0.000 0.000 0.164
#> GSM247651 6 0.0458 0.896 0.016 0.000 0 0.000 0.000 0.984
#> GSM247652 1 0.1141 0.940 0.948 0.000 0 0.000 0.000 0.052
#> GSM247653 1 0.0260 0.926 0.992 0.000 0 0.000 0.000 0.008
#> GSM247654 1 0.0363 0.928 0.988 0.000 0 0.000 0.000 0.012
#> GSM247655 6 0.0458 0.896 0.016 0.000 0 0.000 0.000 0.984
#> GSM247656 1 0.0937 0.937 0.960 0.000 0 0.000 0.000 0.040
#> GSM247657 1 0.0547 0.932 0.980 0.000 0 0.000 0.000 0.020
#> GSM247658 1 0.1204 0.940 0.944 0.000 0 0.000 0.000 0.056
#> GSM247659 1 0.1802 0.929 0.916 0.000 0 0.000 0.012 0.072
#> GSM247660 6 0.0458 0.896 0.016 0.000 0 0.000 0.000 0.984
#> GSM247661 1 0.0260 0.922 0.992 0.000 0 0.000 0.000 0.008
#> GSM247662 1 0.1141 0.940 0.948 0.000 0 0.000 0.000 0.052
#> GSM247663 1 0.2562 0.860 0.828 0.000 0 0.000 0.000 0.172
#> GSM247856 1 0.1141 0.940 0.948 0.000 0 0.000 0.000 0.052
#> GSM247857 1 0.1075 0.940 0.952 0.000 0 0.000 0.000 0.048
#> GSM247859 6 0.0547 0.895 0.020 0.000 0 0.000 0.000 0.980
#> GSM247860 1 0.0146 0.924 0.996 0.000 0 0.000 0.000 0.004
#> GSM247862 6 0.3817 0.176 0.432 0.000 0 0.000 0.000 0.568
#> GSM247864 6 0.0458 0.896 0.016 0.000 0 0.000 0.000 0.984
#> GSM247865 6 0.0508 0.888 0.012 0.000 0 0.004 0.000 0.984
#> GSM247866 6 0.2527 0.762 0.168 0.000 0 0.000 0.000 0.832
#> GSM247876 1 0.2631 0.850 0.820 0.000 0 0.000 0.000 0.180
#> GSM247877 5 0.0632 0.977 0.000 0.000 0 0.000 0.976 0.024
#> GSM247878 5 0.0632 0.977 0.000 0.000 0 0.000 0.976 0.024
#> GSM247879 1 0.2980 0.847 0.808 0.000 0 0.000 0.012 0.180
#> GSM247881 1 0.1444 0.935 0.928 0.000 0 0.000 0.000 0.072
#> GSM247883 6 0.0692 0.894 0.020 0.000 0 0.004 0.000 0.976
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:mclust 9 NA 2
#> MAD:mclust 60 2.13e-19 3
#> MAD:mclust 58 4.42e-21 4
#> MAD:mclust 58 3.46e-20 5
#> MAD:mclust 60 7.11e-20 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 21168 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.972 0.988 0.4944 0.503 0.503
#> 3 3 0.814 0.851 0.939 0.3451 0.708 0.481
#> 4 4 0.894 0.900 0.953 0.0853 0.804 0.513
#> 5 5 0.770 0.759 0.885 0.0485 0.978 0.921
#> 6 6 0.759 0.667 0.811 0.0493 0.952 0.827
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
#> GSM246087 1 0.0000 0.996 1.000 0.000
#> GSM246088 1 0.0000 0.996 1.000 0.000
#> GSM246089 1 0.0000 0.996 1.000 0.000
#> GSM246090 1 0.0000 0.996 1.000 0.000
#> GSM246119 1 0.0000 0.996 1.000 0.000
#> GSM246120 1 0.0000 0.996 1.000 0.000
#> GSM246121 1 0.0000 0.996 1.000 0.000
#> GSM246122 1 0.0000 0.996 1.000 0.000
#> GSM246123 1 0.0000 0.996 1.000 0.000
#> GSM246422 2 0.0376 0.972 0.004 0.996
#> GSM246423 2 0.1633 0.955 0.024 0.976
#> GSM246484 2 0.0000 0.975 0.000 1.000
#> GSM246485 2 0.0000 0.975 0.000 1.000
#> GSM246486 2 0.0000 0.975 0.000 1.000
#> GSM246487 2 0.0000 0.975 0.000 1.000
#> GSM246488 2 0.0000 0.975 0.000 1.000
#> GSM246489 2 0.0000 0.975 0.000 1.000
#> GSM246490 2 0.0000 0.975 0.000 1.000
#> GSM246491 2 0.0000 0.975 0.000 1.000
#> GSM247162 2 0.0000 0.975 0.000 1.000
#> GSM247163 2 0.0000 0.975 0.000 1.000
#> GSM247164 2 0.0000 0.975 0.000 1.000
#> GSM247165 2 0.0000 0.975 0.000 1.000
#> GSM247166 2 0.0000 0.975 0.000 1.000
#> GSM247168 2 0.0000 0.975 0.000 1.000
#> GSM247169 2 0.0000 0.975 0.000 1.000
#> GSM247171 2 0.0000 0.975 0.000 1.000
#> GSM247173 2 0.0000 0.975 0.000 1.000
#> GSM247174 2 0.0000 0.975 0.000 1.000
#> GSM247175 2 0.0000 0.975 0.000 1.000
#> GSM247188 2 0.0000 0.975 0.000 1.000
#> GSM247189 2 0.0000 0.975 0.000 1.000
#> GSM247190 2 0.0000 0.975 0.000 1.000
#> GSM247650 1 0.0000 0.996 1.000 0.000
#> GSM247651 1 0.1633 0.978 0.976 0.024
#> GSM247652 1 0.0000 0.996 1.000 0.000
#> GSM247653 1 0.0000 0.996 1.000 0.000
#> GSM247654 1 0.0000 0.996 1.000 0.000
#> GSM247655 1 0.0000 0.996 1.000 0.000
#> GSM247656 1 0.0000 0.996 1.000 0.000
#> GSM247657 1 0.0000 0.996 1.000 0.000
#> GSM247658 1 0.0000 0.996 1.000 0.000
#> GSM247659 1 0.0000 0.996 1.000 0.000
#> GSM247660 1 0.1184 0.984 0.984 0.016
#> GSM247661 1 0.0000 0.996 1.000 0.000
#> GSM247662 1 0.0000 0.996 1.000 0.000
#> GSM247663 1 0.0000 0.996 1.000 0.000
#> GSM247856 1 0.0000 0.996 1.000 0.000
#> GSM247857 1 0.0000 0.996 1.000 0.000
#> GSM247859 1 0.2043 0.970 0.968 0.032
#> GSM247860 1 0.0000 0.996 1.000 0.000
#> GSM247862 1 0.0000 0.996 1.000 0.000
#> GSM247864 1 0.0000 0.996 1.000 0.000
#> GSM247865 2 0.7674 0.714 0.224 0.776
#> GSM247866 1 0.0376 0.993 0.996 0.004
#> GSM247876 1 0.0000 0.996 1.000 0.000
#> GSM247877 1 0.1633 0.978 0.976 0.024
#> GSM247878 1 0.1633 0.978 0.976 0.024
#> GSM247879 1 0.0000 0.996 1.000 0.000
#> GSM247881 1 0.0000 0.996 1.000 0.000
#> GSM247883 2 0.9460 0.443 0.364 0.636
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 0.8961 0.000 0.000 1.000
#> GSM246088 3 0.0000 0.8961 0.000 0.000 1.000
#> GSM246089 3 0.0000 0.8961 0.000 0.000 1.000
#> GSM246090 3 0.0000 0.8961 0.000 0.000 1.000
#> GSM246119 3 0.0000 0.8961 0.000 0.000 1.000
#> GSM246120 3 0.0000 0.8961 0.000 0.000 1.000
#> GSM246121 3 0.0000 0.8961 0.000 0.000 1.000
#> GSM246122 3 0.0000 0.8961 0.000 0.000 1.000
#> GSM246123 3 0.0000 0.8961 0.000 0.000 1.000
#> GSM246422 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM246423 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM246484 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM246485 2 0.2537 0.9150 0.080 0.920 0.000
#> GSM246486 2 0.3482 0.8660 0.128 0.872 0.000
#> GSM246487 1 0.0237 0.8987 0.996 0.004 0.000
#> GSM246488 2 0.4235 0.8136 0.176 0.824 0.000
#> GSM246489 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM246490 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM246491 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM247162 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM247163 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM247164 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM247165 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM247166 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM247168 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM247169 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM247171 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM247173 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM247174 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM247175 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM247188 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM247189 2 0.0424 0.9733 0.008 0.992 0.000
#> GSM247190 2 0.0000 0.9787 0.000 1.000 0.000
#> GSM247650 1 0.5678 0.5455 0.684 0.000 0.316
#> GSM247651 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM247652 1 0.4399 0.7424 0.812 0.000 0.188
#> GSM247653 3 0.5529 0.5630 0.296 0.000 0.704
#> GSM247654 3 0.6252 0.1621 0.444 0.000 0.556
#> GSM247655 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM247656 3 0.0592 0.8905 0.012 0.000 0.988
#> GSM247657 3 0.5835 0.4730 0.340 0.000 0.660
#> GSM247658 1 0.1289 0.8833 0.968 0.000 0.032
#> GSM247659 3 0.0000 0.8961 0.000 0.000 1.000
#> GSM247660 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM247661 3 0.1860 0.8631 0.052 0.000 0.948
#> GSM247662 3 0.0237 0.8946 0.004 0.000 0.996
#> GSM247663 1 0.3941 0.7793 0.844 0.000 0.156
#> GSM247856 1 0.6295 0.0924 0.528 0.000 0.472
#> GSM247857 3 0.5291 0.6131 0.268 0.000 0.732
#> GSM247859 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM247860 1 0.5882 0.4805 0.652 0.000 0.348
#> GSM247862 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM247864 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM247865 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM247866 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM247876 1 0.2261 0.8582 0.932 0.000 0.068
#> GSM247877 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM247878 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM247879 1 0.5905 0.4674 0.648 0.000 0.352
#> GSM247881 1 0.0000 0.9016 1.000 0.000 0.000
#> GSM247883 1 0.0000 0.9016 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0336 0.976 0.008 0.000 0.992 0.000
#> GSM246088 3 0.0336 0.976 0.008 0.000 0.992 0.000
#> GSM246089 3 0.0469 0.968 0.000 0.000 0.988 0.012
#> GSM246090 3 0.0336 0.976 0.008 0.000 0.992 0.000
#> GSM246119 3 0.0188 0.976 0.004 0.000 0.996 0.000
#> GSM246120 3 0.0336 0.972 0.000 0.000 0.992 0.008
#> GSM246121 3 0.0188 0.976 0.004 0.000 0.996 0.000
#> GSM246122 3 0.0336 0.976 0.008 0.000 0.992 0.000
#> GSM246123 3 0.0336 0.972 0.000 0.000 0.992 0.008
#> GSM246422 4 0.0188 0.830 0.000 0.000 0.004 0.996
#> GSM246423 4 0.0000 0.831 0.000 0.000 0.000 1.000
#> GSM246484 4 0.0000 0.831 0.000 0.000 0.000 1.000
#> GSM246485 2 0.1716 0.912 0.000 0.936 0.000 0.064
#> GSM246486 2 0.4500 0.498 0.000 0.684 0.000 0.316
#> GSM246487 4 0.7123 0.140 0.416 0.112 0.004 0.468
#> GSM246488 4 0.2469 0.779 0.000 0.108 0.000 0.892
#> GSM246489 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM246490 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM246491 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM247162 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM247163 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM247164 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM247165 2 0.0188 0.972 0.000 0.996 0.000 0.004
#> GSM247166 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM247168 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM247169 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM247171 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM247173 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM247174 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM247175 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM247188 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM247189 4 0.4543 0.484 0.000 0.324 0.000 0.676
#> GSM247190 2 0.0000 0.975 0.000 1.000 0.000 0.000
#> GSM247650 1 0.1004 0.946 0.972 0.000 0.024 0.004
#> GSM247651 1 0.4155 0.698 0.756 0.000 0.004 0.240
#> GSM247652 1 0.0469 0.951 0.988 0.000 0.012 0.000
#> GSM247653 1 0.0469 0.951 0.988 0.000 0.012 0.000
#> GSM247654 1 0.0469 0.951 0.988 0.000 0.012 0.000
#> GSM247655 1 0.1305 0.934 0.960 0.000 0.004 0.036
#> GSM247656 1 0.3172 0.814 0.840 0.000 0.160 0.000
#> GSM247657 1 0.0469 0.951 0.988 0.000 0.012 0.000
#> GSM247658 1 0.0469 0.951 0.988 0.000 0.012 0.000
#> GSM247659 3 0.2647 0.834 0.120 0.000 0.880 0.000
#> GSM247660 1 0.2593 0.879 0.892 0.000 0.004 0.104
#> GSM247661 1 0.0469 0.951 0.988 0.000 0.012 0.000
#> GSM247662 1 0.3975 0.706 0.760 0.000 0.240 0.000
#> GSM247663 1 0.1297 0.946 0.964 0.000 0.020 0.016
#> GSM247856 1 0.0469 0.951 0.988 0.000 0.012 0.000
#> GSM247857 1 0.0469 0.951 0.988 0.000 0.012 0.000
#> GSM247859 1 0.0524 0.947 0.988 0.000 0.004 0.008
#> GSM247860 1 0.0469 0.951 0.988 0.000 0.012 0.000
#> GSM247862 1 0.0000 0.949 1.000 0.000 0.000 0.000
#> GSM247864 1 0.1661 0.924 0.944 0.000 0.004 0.052
#> GSM247865 1 0.1209 0.936 0.964 0.000 0.004 0.032
#> GSM247866 1 0.0895 0.942 0.976 0.000 0.004 0.020
#> GSM247876 1 0.1388 0.944 0.960 0.000 0.012 0.028
#> GSM247877 4 0.0707 0.824 0.000 0.000 0.020 0.980
#> GSM247878 4 0.0469 0.828 0.012 0.000 0.000 0.988
#> GSM247879 4 0.3498 0.705 0.008 0.000 0.160 0.832
#> GSM247881 1 0.0188 0.950 0.996 0.000 0.004 0.000
#> GSM247883 1 0.0524 0.946 0.988 0.000 0.004 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0290 0.8062 0.000 0.000 0.992 0.000 0.008
#> GSM246088 3 0.0000 0.8080 0.000 0.000 1.000 0.000 0.000
#> GSM246089 3 0.4300 0.0892 0.000 0.000 0.524 0.000 0.476
#> GSM246090 3 0.0404 0.8079 0.000 0.000 0.988 0.000 0.012
#> GSM246119 3 0.1732 0.8004 0.000 0.000 0.920 0.000 0.080
#> GSM246120 3 0.1831 0.8005 0.000 0.000 0.920 0.004 0.076
#> GSM246121 3 0.2179 0.7818 0.000 0.000 0.888 0.000 0.112
#> GSM246122 3 0.0609 0.8011 0.000 0.000 0.980 0.000 0.020
#> GSM246123 3 0.2011 0.7973 0.000 0.000 0.908 0.004 0.088
#> GSM246422 4 0.0000 0.6497 0.000 0.000 0.000 1.000 0.000
#> GSM246423 4 0.0290 0.6484 0.000 0.000 0.000 0.992 0.008
#> GSM246484 4 0.0510 0.6465 0.000 0.000 0.000 0.984 0.016
#> GSM246485 2 0.3640 0.8114 0.008 0.836 0.000 0.084 0.072
#> GSM246486 2 0.3762 0.6477 0.004 0.748 0.000 0.244 0.004
#> GSM246487 4 0.6471 0.2540 0.256 0.124 0.000 0.584 0.036
#> GSM246488 4 0.2172 0.6134 0.000 0.076 0.000 0.908 0.016
#> GSM246489 2 0.0000 0.9687 0.000 1.000 0.000 0.000 0.000
#> GSM246490 2 0.0162 0.9691 0.000 0.996 0.000 0.000 0.004
#> GSM246491 2 0.0162 0.9679 0.000 0.996 0.000 0.000 0.004
#> GSM247162 2 0.0162 0.9691 0.000 0.996 0.000 0.000 0.004
#> GSM247163 2 0.0451 0.9634 0.000 0.988 0.000 0.008 0.004
#> GSM247164 2 0.0290 0.9682 0.000 0.992 0.000 0.000 0.008
#> GSM247165 2 0.0162 0.9681 0.000 0.996 0.000 0.000 0.004
#> GSM247166 2 0.0000 0.9687 0.000 1.000 0.000 0.000 0.000
#> GSM247168 2 0.0162 0.9682 0.000 0.996 0.000 0.000 0.004
#> GSM247169 2 0.0000 0.9687 0.000 1.000 0.000 0.000 0.000
#> GSM247171 2 0.0609 0.9633 0.000 0.980 0.000 0.000 0.020
#> GSM247173 2 0.0162 0.9691 0.000 0.996 0.000 0.000 0.004
#> GSM247174 2 0.0162 0.9691 0.000 0.996 0.000 0.000 0.004
#> GSM247175 2 0.0162 0.9691 0.000 0.996 0.000 0.000 0.004
#> GSM247188 2 0.0510 0.9647 0.000 0.984 0.000 0.000 0.016
#> GSM247189 4 0.5810 0.1490 0.000 0.428 0.000 0.480 0.092
#> GSM247190 2 0.0404 0.9666 0.000 0.988 0.000 0.000 0.012
#> GSM247650 1 0.2395 0.8641 0.912 0.000 0.036 0.012 0.040
#> GSM247651 1 0.3849 0.6858 0.752 0.000 0.000 0.232 0.016
#> GSM247652 1 0.1205 0.8668 0.956 0.000 0.004 0.000 0.040
#> GSM247653 1 0.2127 0.8582 0.892 0.000 0.000 0.000 0.108
#> GSM247654 1 0.1124 0.8729 0.960 0.000 0.004 0.000 0.036
#> GSM247655 1 0.1403 0.8733 0.952 0.000 0.000 0.024 0.024
#> GSM247656 1 0.5246 0.2840 0.564 0.000 0.384 0.000 0.052
#> GSM247657 1 0.1952 0.8684 0.912 0.000 0.004 0.000 0.084
#> GSM247658 1 0.1043 0.8694 0.960 0.000 0.000 0.000 0.040
#> GSM247659 3 0.4360 0.5915 0.064 0.000 0.752 0.000 0.184
#> GSM247660 1 0.3169 0.8481 0.856 0.000 0.000 0.084 0.060
#> GSM247661 1 0.2338 0.8602 0.884 0.000 0.004 0.000 0.112
#> GSM247662 3 0.6128 0.2552 0.252 0.000 0.560 0.000 0.188
#> GSM247663 1 0.1357 0.8696 0.948 0.000 0.000 0.004 0.048
#> GSM247856 1 0.1618 0.8673 0.944 0.000 0.008 0.008 0.040
#> GSM247857 1 0.3649 0.8079 0.808 0.000 0.040 0.000 0.152
#> GSM247859 1 0.1331 0.8665 0.952 0.000 0.000 0.008 0.040
#> GSM247860 1 0.4030 0.5729 0.648 0.000 0.000 0.000 0.352
#> GSM247862 1 0.1956 0.8668 0.916 0.000 0.000 0.008 0.076
#> GSM247864 1 0.2446 0.8661 0.900 0.000 0.000 0.044 0.056
#> GSM247865 1 0.3176 0.8219 0.856 0.000 0.000 0.080 0.064
#> GSM247866 1 0.3366 0.7548 0.768 0.000 0.000 0.000 0.232
#> GSM247876 1 0.4134 0.6587 0.704 0.000 0.008 0.004 0.284
#> GSM247877 4 0.4490 0.0121 0.004 0.000 0.004 0.588 0.404
#> GSM247878 4 0.2017 0.6069 0.008 0.000 0.000 0.912 0.080
#> GSM247879 5 0.4558 0.0000 0.028 0.000 0.056 0.140 0.776
#> GSM247881 1 0.1671 0.8691 0.924 0.000 0.000 0.000 0.076
#> GSM247883 1 0.1331 0.8671 0.952 0.000 0.000 0.008 0.040
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0891 0.7629 0.000 0.000 0.968 0.000 0.008 NA
#> GSM246088 3 0.0520 0.7664 0.000 0.000 0.984 0.000 0.008 NA
#> GSM246089 3 0.6109 0.0706 0.000 0.000 0.356 0.000 0.292 NA
#> GSM246090 3 0.0717 0.7651 0.000 0.000 0.976 0.000 0.008 NA
#> GSM246119 3 0.2134 0.7510 0.000 0.000 0.904 0.000 0.044 NA
#> GSM246120 3 0.2066 0.7520 0.000 0.000 0.908 0.000 0.040 NA
#> GSM246121 3 0.3663 0.6795 0.000 0.000 0.784 0.000 0.068 NA
#> GSM246122 3 0.0909 0.7669 0.000 0.000 0.968 0.000 0.012 NA
#> GSM246123 3 0.1418 0.7617 0.000 0.000 0.944 0.000 0.032 NA
#> GSM246422 4 0.0622 0.6584 0.000 0.000 0.000 0.980 0.012 NA
#> GSM246423 4 0.0551 0.6559 0.004 0.000 0.000 0.984 0.008 NA
#> GSM246484 4 0.0547 0.6561 0.000 0.000 0.000 0.980 0.020 NA
#> GSM246485 4 0.6991 0.2690 0.004 0.288 0.000 0.372 0.048 NA
#> GSM246486 2 0.4315 -0.1270 0.000 0.496 0.000 0.488 0.004 NA
#> GSM246487 4 0.5929 0.3952 0.216 0.084 0.000 0.624 0.012 NA
#> GSM246488 4 0.1398 0.6557 0.000 0.052 0.000 0.940 0.000 NA
#> GSM246489 2 0.0000 0.9438 0.000 1.000 0.000 0.000 0.000 NA
#> GSM246490 2 0.0260 0.9428 0.000 0.992 0.000 0.000 0.000 NA
#> GSM246491 2 0.0363 0.9419 0.000 0.988 0.000 0.000 0.000 NA
#> GSM247162 2 0.0000 0.9438 0.000 1.000 0.000 0.000 0.000 NA
#> GSM247163 2 0.0291 0.9432 0.000 0.992 0.000 0.004 0.000 NA
#> GSM247164 2 0.0260 0.9421 0.000 0.992 0.000 0.008 0.000 NA
#> GSM247165 2 0.0547 0.9353 0.000 0.980 0.000 0.020 0.000 NA
#> GSM247166 2 0.1444 0.9110 0.000 0.928 0.000 0.000 0.000 NA
#> GSM247168 2 0.1501 0.9083 0.000 0.924 0.000 0.000 0.000 NA
#> GSM247169 2 0.1444 0.9115 0.000 0.928 0.000 0.000 0.000 NA
#> GSM247171 2 0.0551 0.9394 0.000 0.984 0.000 0.008 0.004 NA
#> GSM247173 2 0.0405 0.9431 0.000 0.988 0.000 0.004 0.000 NA
#> GSM247174 2 0.0790 0.9335 0.000 0.968 0.000 0.000 0.000 NA
#> GSM247175 2 0.0000 0.9438 0.000 1.000 0.000 0.000 0.000 NA
#> GSM247188 2 0.0146 0.9438 0.000 0.996 0.000 0.000 0.000 NA
#> GSM247189 4 0.5650 0.3640 0.000 0.300 0.000 0.564 0.116 NA
#> GSM247190 2 0.0000 0.9438 0.000 1.000 0.000 0.000 0.000 NA
#> GSM247650 1 0.5939 0.3757 0.608 0.000 0.248 0.016 0.076 NA
#> GSM247651 1 0.4071 0.5603 0.716 0.000 0.000 0.248 0.020 NA
#> GSM247652 1 0.1858 0.7399 0.924 0.000 0.000 0.012 0.012 NA
#> GSM247653 1 0.4668 0.6433 0.620 0.000 0.000 0.000 0.064 NA
#> GSM247654 1 0.3374 0.7251 0.772 0.000 0.000 0.000 0.020 NA
#> GSM247655 1 0.1983 0.7434 0.916 0.000 0.000 0.012 0.012 NA
#> GSM247656 3 0.5201 0.2947 0.368 0.000 0.548 0.000 0.008 NA
#> GSM247657 1 0.4002 0.7141 0.704 0.000 0.000 0.000 0.036 NA
#> GSM247658 1 0.1958 0.7400 0.896 0.000 0.000 0.000 0.004 NA
#> GSM247659 3 0.5854 0.4650 0.020 0.004 0.588 0.000 0.192 NA
#> GSM247660 1 0.4805 0.6883 0.700 0.000 0.000 0.144 0.012 NA
#> GSM247661 1 0.4648 0.6438 0.604 0.000 0.000 0.000 0.056 NA
#> GSM247662 3 0.6045 0.4679 0.096 0.000 0.600 0.000 0.096 NA
#> GSM247663 1 0.1844 0.7299 0.932 0.000 0.012 0.004 0.028 NA
#> GSM247856 1 0.1722 0.7291 0.936 0.000 0.004 0.016 0.008 NA
#> GSM247857 1 0.6727 0.3863 0.500 0.000 0.152 0.000 0.096 NA
#> GSM247859 1 0.1577 0.7378 0.940 0.000 0.000 0.016 0.008 NA
#> GSM247860 1 0.5616 0.4569 0.492 0.000 0.000 0.000 0.156 NA
#> GSM247862 1 0.3909 0.7077 0.720 0.000 0.000 0.000 0.036 NA
#> GSM247864 1 0.4061 0.7110 0.792 0.000 0.000 0.052 0.052 NA
#> GSM247865 1 0.3465 0.6745 0.828 0.000 0.000 0.096 0.020 NA
#> GSM247866 1 0.5186 0.6106 0.616 0.000 0.000 0.000 0.216 NA
#> GSM247876 5 0.5249 0.0803 0.412 0.000 0.008 0.020 0.524 NA
#> GSM247877 5 0.4092 0.2170 0.000 0.000 0.000 0.344 0.636 NA
#> GSM247878 4 0.3658 0.4574 0.028 0.000 0.000 0.772 0.192 NA
#> GSM247879 5 0.2848 0.4650 0.016 0.000 0.024 0.064 0.880 NA
#> GSM247881 1 0.4525 0.6341 0.724 0.000 0.008 0.000 0.140 NA
#> GSM247883 1 0.1655 0.7259 0.932 0.000 0.000 0.008 0.008 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> MAD:NMF 60 6.78e-13 2
#> MAD:NMF 56 2.12e-13 3
#> MAD:NMF 58 2.45e-19 4
#> MAD:NMF 54 1.53e-18 5
#> MAD:NMF 46 1.16e-17 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 21168 rows and 61 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 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 0.508 0.926 0.909 0.3690 0.607 0.607
#> 3 3 0.725 0.935 0.933 0.5653 0.823 0.708
#> 4 4 0.962 0.934 0.974 0.2409 0.843 0.634
#> 5 5 0.904 0.820 0.936 0.0272 0.989 0.960
#> 6 6 0.892 0.803 0.916 0.0244 0.961 0.863
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
#> GSM246087 1 0.000 0.778 1.000 0.000
#> GSM246088 1 0.000 0.778 1.000 0.000
#> GSM246089 1 0.000 0.778 1.000 0.000
#> GSM246090 1 0.000 0.778 1.000 0.000
#> GSM246119 1 0.000 0.778 1.000 0.000
#> GSM246120 1 0.000 0.778 1.000 0.000
#> GSM246121 1 0.000 0.778 1.000 0.000
#> GSM246122 1 0.000 0.778 1.000 0.000
#> GSM246123 1 0.000 0.778 1.000 0.000
#> GSM246422 1 0.802 0.913 0.756 0.244
#> GSM246423 1 0.802 0.913 0.756 0.244
#> GSM246484 1 0.802 0.913 0.756 0.244
#> GSM246485 1 0.802 0.913 0.756 0.244
#> GSM246486 1 0.802 0.913 0.756 0.244
#> GSM246487 1 0.802 0.913 0.756 0.244
#> GSM246488 1 0.802 0.913 0.756 0.244
#> GSM246489 2 0.000 1.000 0.000 1.000
#> GSM246490 2 0.000 1.000 0.000 1.000
#> GSM246491 2 0.000 1.000 0.000 1.000
#> GSM247162 2 0.000 1.000 0.000 1.000
#> GSM247163 2 0.000 1.000 0.000 1.000
#> GSM247164 2 0.000 1.000 0.000 1.000
#> GSM247165 2 0.000 1.000 0.000 1.000
#> GSM247166 2 0.000 1.000 0.000 1.000
#> GSM247168 2 0.000 1.000 0.000 1.000
#> GSM247169 2 0.000 1.000 0.000 1.000
#> GSM247171 2 0.000 1.000 0.000 1.000
#> GSM247173 2 0.000 1.000 0.000 1.000
#> GSM247174 2 0.000 1.000 0.000 1.000
#> GSM247175 2 0.000 1.000 0.000 1.000
#> GSM247188 2 0.000 1.000 0.000 1.000
#> GSM247189 1 0.802 0.913 0.756 0.244
#> GSM247190 2 0.000 1.000 0.000 1.000
#> GSM247650 1 0.738 0.936 0.792 0.208
#> GSM247651 1 0.738 0.936 0.792 0.208
#> GSM247652 1 0.738 0.936 0.792 0.208
#> GSM247653 1 0.738 0.936 0.792 0.208
#> GSM247654 1 0.738 0.936 0.792 0.208
#> GSM247655 1 0.738 0.936 0.792 0.208
#> GSM247656 1 0.738 0.936 0.792 0.208
#> GSM247657 1 0.738 0.936 0.792 0.208
#> GSM247658 1 0.738 0.936 0.792 0.208
#> GSM247659 1 0.738 0.936 0.792 0.208
#> GSM247660 1 0.738 0.936 0.792 0.208
#> GSM247661 1 0.738 0.936 0.792 0.208
#> GSM247662 1 0.738 0.936 0.792 0.208
#> GSM247663 1 0.738 0.936 0.792 0.208
#> GSM247856 1 0.738 0.936 0.792 0.208
#> GSM247857 1 0.738 0.936 0.792 0.208
#> GSM247859 1 0.738 0.936 0.792 0.208
#> GSM247860 1 0.738 0.936 0.792 0.208
#> GSM247862 1 0.738 0.936 0.792 0.208
#> GSM247864 1 0.738 0.936 0.792 0.208
#> GSM247865 1 0.788 0.919 0.764 0.236
#> GSM247866 1 0.738 0.936 0.792 0.208
#> GSM247876 1 0.738 0.936 0.792 0.208
#> GSM247877 1 0.738 0.936 0.792 0.208
#> GSM247878 1 0.738 0.936 0.792 0.208
#> GSM247879 1 0.738 0.936 0.792 0.208
#> GSM247881 1 0.738 0.936 0.792 0.208
#> GSM247883 1 0.788 0.919 0.764 0.236
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.455 1.000 0.200 0 0.800
#> GSM246088 3 0.455 1.000 0.200 0 0.800
#> GSM246089 3 0.455 1.000 0.200 0 0.800
#> GSM246090 3 0.455 1.000 0.200 0 0.800
#> GSM246119 3 0.455 1.000 0.200 0 0.800
#> GSM246120 3 0.455 1.000 0.200 0 0.800
#> GSM246121 3 0.455 1.000 0.200 0 0.800
#> GSM246122 3 0.455 1.000 0.200 0 0.800
#> GSM246123 3 0.455 1.000 0.200 0 0.800
#> GSM246422 1 0.455 0.830 0.800 0 0.200
#> GSM246423 1 0.455 0.830 0.800 0 0.200
#> GSM246484 1 0.455 0.830 0.800 0 0.200
#> GSM246485 1 0.455 0.830 0.800 0 0.200
#> GSM246486 1 0.455 0.830 0.800 0 0.200
#> GSM246487 1 0.455 0.830 0.800 0 0.200
#> GSM246488 1 0.455 0.830 0.800 0 0.200
#> GSM246489 2 0.000 1.000 0.000 1 0.000
#> GSM246490 2 0.000 1.000 0.000 1 0.000
#> GSM246491 2 0.000 1.000 0.000 1 0.000
#> GSM247162 2 0.000 1.000 0.000 1 0.000
#> GSM247163 2 0.000 1.000 0.000 1 0.000
#> GSM247164 2 0.000 1.000 0.000 1 0.000
#> GSM247165 2 0.000 1.000 0.000 1 0.000
#> GSM247166 2 0.000 1.000 0.000 1 0.000
#> GSM247168 2 0.000 1.000 0.000 1 0.000
#> GSM247169 2 0.000 1.000 0.000 1 0.000
#> GSM247171 2 0.000 1.000 0.000 1 0.000
#> GSM247173 2 0.000 1.000 0.000 1 0.000
#> GSM247174 2 0.000 1.000 0.000 1 0.000
#> GSM247175 2 0.000 1.000 0.000 1 0.000
#> GSM247188 2 0.000 1.000 0.000 1 0.000
#> GSM247189 1 0.455 0.830 0.800 0 0.200
#> GSM247190 2 0.000 1.000 0.000 1 0.000
#> GSM247650 1 0.000 0.919 1.000 0 0.000
#> GSM247651 1 0.000 0.919 1.000 0 0.000
#> GSM247652 1 0.000 0.919 1.000 0 0.000
#> GSM247653 1 0.000 0.919 1.000 0 0.000
#> GSM247654 1 0.000 0.919 1.000 0 0.000
#> GSM247655 1 0.000 0.919 1.000 0 0.000
#> GSM247656 1 0.000 0.919 1.000 0 0.000
#> GSM247657 1 0.000 0.919 1.000 0 0.000
#> GSM247658 1 0.000 0.919 1.000 0 0.000
#> GSM247659 1 0.000 0.919 1.000 0 0.000
#> GSM247660 1 0.000 0.919 1.000 0 0.000
#> GSM247661 1 0.000 0.919 1.000 0 0.000
#> GSM247662 1 0.000 0.919 1.000 0 0.000
#> GSM247663 1 0.000 0.919 1.000 0 0.000
#> GSM247856 1 0.000 0.919 1.000 0 0.000
#> GSM247857 1 0.000 0.919 1.000 0 0.000
#> GSM247859 1 0.000 0.919 1.000 0 0.000
#> GSM247860 1 0.000 0.919 1.000 0 0.000
#> GSM247862 1 0.000 0.919 1.000 0 0.000
#> GSM247864 1 0.000 0.919 1.000 0 0.000
#> GSM247865 1 0.445 0.834 0.808 0 0.192
#> GSM247866 1 0.000 0.919 1.000 0 0.000
#> GSM247876 1 0.000 0.919 1.000 0 0.000
#> GSM247877 1 0.406 0.848 0.836 0 0.164
#> GSM247878 1 0.406 0.848 0.836 0 0.164
#> GSM247879 1 0.000 0.919 1.000 0 0.000
#> GSM247881 1 0.000 0.919 1.000 0 0.000
#> GSM247883 1 0.445 0.834 0.808 0 0.192
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.000 1.000 0.000 0 1 0.000
#> GSM246088 3 0.000 1.000 0.000 0 1 0.000
#> GSM246089 3 0.000 1.000 0.000 0 1 0.000
#> GSM246090 3 0.000 1.000 0.000 0 1 0.000
#> GSM246119 3 0.000 1.000 0.000 0 1 0.000
#> GSM246120 3 0.000 1.000 0.000 0 1 0.000
#> GSM246121 3 0.000 1.000 0.000 0 1 0.000
#> GSM246122 3 0.000 1.000 0.000 0 1 0.000
#> GSM246123 3 0.000 1.000 0.000 0 1 0.000
#> GSM246422 4 0.000 0.816 0.000 0 0 1.000
#> GSM246423 4 0.000 0.816 0.000 0 0 1.000
#> GSM246484 4 0.000 0.816 0.000 0 0 1.000
#> GSM246485 4 0.000 0.816 0.000 0 0 1.000
#> GSM246486 4 0.000 0.816 0.000 0 0 1.000
#> GSM246487 4 0.000 0.816 0.000 0 0 1.000
#> GSM246488 4 0.000 0.816 0.000 0 0 1.000
#> GSM246489 2 0.000 1.000 0.000 1 0 0.000
#> GSM246490 2 0.000 1.000 0.000 1 0 0.000
#> GSM246491 2 0.000 1.000 0.000 1 0 0.000
#> GSM247162 2 0.000 1.000 0.000 1 0 0.000
#> GSM247163 2 0.000 1.000 0.000 1 0 0.000
#> GSM247164 2 0.000 1.000 0.000 1 0 0.000
#> GSM247165 2 0.000 1.000 0.000 1 0 0.000
#> GSM247166 2 0.000 1.000 0.000 1 0 0.000
#> GSM247168 2 0.000 1.000 0.000 1 0 0.000
#> GSM247169 2 0.000 1.000 0.000 1 0 0.000
#> GSM247171 2 0.000 1.000 0.000 1 0 0.000
#> GSM247173 2 0.000 1.000 0.000 1 0 0.000
#> GSM247174 2 0.000 1.000 0.000 1 0 0.000
#> GSM247175 2 0.000 1.000 0.000 1 0 0.000
#> GSM247188 2 0.000 1.000 0.000 1 0 0.000
#> GSM247189 4 0.000 0.816 0.000 0 0 1.000
#> GSM247190 2 0.000 1.000 0.000 1 0 0.000
#> GSM247650 1 0.000 0.995 1.000 0 0 0.000
#> GSM247651 1 0.000 0.995 1.000 0 0 0.000
#> GSM247652 1 0.000 0.995 1.000 0 0 0.000
#> GSM247653 1 0.000 0.995 1.000 0 0 0.000
#> GSM247654 1 0.000 0.995 1.000 0 0 0.000
#> GSM247655 1 0.000 0.995 1.000 0 0 0.000
#> GSM247656 1 0.000 0.995 1.000 0 0 0.000
#> GSM247657 1 0.000 0.995 1.000 0 0 0.000
#> GSM247658 1 0.000 0.995 1.000 0 0 0.000
#> GSM247659 1 0.000 0.995 1.000 0 0 0.000
#> GSM247660 1 0.000 0.995 1.000 0 0 0.000
#> GSM247661 1 0.000 0.995 1.000 0 0 0.000
#> GSM247662 1 0.000 0.995 1.000 0 0 0.000
#> GSM247663 1 0.000 0.995 1.000 0 0 0.000
#> GSM247856 1 0.000 0.995 1.000 0 0 0.000
#> GSM247857 1 0.000 0.995 1.000 0 0 0.000
#> GSM247859 1 0.234 0.867 0.900 0 0 0.100
#> GSM247860 1 0.000 0.995 1.000 0 0 0.000
#> GSM247862 1 0.000 0.995 1.000 0 0 0.000
#> GSM247864 1 0.000 0.995 1.000 0 0 0.000
#> GSM247865 4 0.492 0.381 0.428 0 0 0.572
#> GSM247866 1 0.000 0.995 1.000 0 0 0.000
#> GSM247876 1 0.000 0.995 1.000 0 0 0.000
#> GSM247877 4 0.499 0.256 0.472 0 0 0.528
#> GSM247878 4 0.336 0.712 0.176 0 0 0.824
#> GSM247879 1 0.000 0.995 1.000 0 0 0.000
#> GSM247881 1 0.000 0.995 1.000 0 0 0.000
#> GSM247883 4 0.492 0.381 0.428 0 0 0.572
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.000 0.9654 0.000 0 1.000 0.000 0.000
#> GSM246088 3 0.000 0.9654 0.000 0 1.000 0.000 0.000
#> GSM246089 3 0.393 0.6685 0.000 0 0.672 0.000 0.328
#> GSM246090 3 0.000 0.9654 0.000 0 1.000 0.000 0.000
#> GSM246119 3 0.000 0.9654 0.000 0 1.000 0.000 0.000
#> GSM246120 3 0.000 0.9654 0.000 0 1.000 0.000 0.000
#> GSM246121 3 0.000 0.9654 0.000 0 1.000 0.000 0.000
#> GSM246122 3 0.000 0.9654 0.000 0 1.000 0.000 0.000
#> GSM246123 3 0.000 0.9654 0.000 0 1.000 0.000 0.000
#> GSM246422 4 0.415 -0.0313 0.000 0 0.000 0.612 0.388
#> GSM246423 4 0.415 -0.0313 0.000 0 0.000 0.612 0.388
#> GSM246484 4 0.415 -0.0313 0.000 0 0.000 0.612 0.388
#> GSM246485 4 0.000 0.4843 0.000 0 0.000 1.000 0.000
#> GSM246486 4 0.000 0.4843 0.000 0 0.000 1.000 0.000
#> GSM246487 4 0.000 0.4843 0.000 0 0.000 1.000 0.000
#> GSM246488 4 0.000 0.4843 0.000 0 0.000 1.000 0.000
#> GSM246489 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM246490 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM246491 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM247162 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM247163 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM247164 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM247165 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM247166 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM247168 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM247169 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM247171 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM247173 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM247174 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM247175 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM247188 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM247189 4 0.277 0.3402 0.000 0 0.000 0.836 0.164
#> GSM247190 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM247650 1 0.088 0.9614 0.968 0 0.000 0.000 0.032
#> GSM247651 1 0.051 0.9706 0.984 0 0.000 0.000 0.016
#> GSM247652 1 0.000 0.9728 1.000 0 0.000 0.000 0.000
#> GSM247653 1 0.029 0.9727 0.992 0 0.000 0.000 0.008
#> GSM247654 1 0.000 0.9728 1.000 0 0.000 0.000 0.000
#> GSM247655 1 0.051 0.9706 0.984 0 0.000 0.000 0.016
#> GSM247656 1 0.000 0.9728 1.000 0 0.000 0.000 0.000
#> GSM247657 1 0.000 0.9728 1.000 0 0.000 0.000 0.000
#> GSM247658 1 0.029 0.9723 0.992 0 0.000 0.000 0.008
#> GSM247659 1 0.000 0.9728 1.000 0 0.000 0.000 0.000
#> GSM247660 1 0.051 0.9706 0.984 0 0.000 0.000 0.016
#> GSM247661 1 0.029 0.9727 0.992 0 0.000 0.000 0.008
#> GSM247662 1 0.000 0.9728 1.000 0 0.000 0.000 0.000
#> GSM247663 1 0.167 0.9234 0.924 0 0.000 0.000 0.076
#> GSM247856 1 0.000 0.9728 1.000 0 0.000 0.000 0.000
#> GSM247857 1 0.000 0.9728 1.000 0 0.000 0.000 0.000
#> GSM247859 1 0.202 0.8620 0.900 0 0.000 0.100 0.000
#> GSM247860 1 0.029 0.9727 0.992 0 0.000 0.000 0.008
#> GSM247862 1 0.051 0.9706 0.984 0 0.000 0.000 0.016
#> GSM247864 1 0.051 0.9706 0.984 0 0.000 0.000 0.016
#> GSM247865 4 0.424 0.0552 0.428 0 0.000 0.572 0.000
#> GSM247866 1 0.029 0.9727 0.992 0 0.000 0.000 0.008
#> GSM247876 1 0.173 0.9194 0.920 0 0.000 0.000 0.080
#> GSM247877 5 0.532 0.3638 0.188 0 0.000 0.140 0.672
#> GSM247878 5 0.426 0.0730 0.000 0 0.000 0.436 0.564
#> GSM247879 1 0.300 0.7900 0.812 0 0.000 0.000 0.188
#> GSM247881 1 0.000 0.9728 1.000 0 0.000 0.000 0.000
#> GSM247883 4 0.424 0.0552 0.428 0 0.000 0.572 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0000 1.000 0.000 0 1.00 0.000 0.000 0.000
#> GSM246088 3 0.0000 1.000 0.000 0 1.00 0.000 0.000 0.000
#> GSM246089 6 0.3309 0.000 0.000 0 0.28 0.000 0.000 0.720
#> GSM246090 3 0.0000 1.000 0.000 0 1.00 0.000 0.000 0.000
#> GSM246119 3 0.0000 1.000 0.000 0 1.00 0.000 0.000 0.000
#> GSM246120 3 0.0000 1.000 0.000 0 1.00 0.000 0.000 0.000
#> GSM246121 3 0.0000 1.000 0.000 0 1.00 0.000 0.000 0.000
#> GSM246122 3 0.0000 1.000 0.000 0 1.00 0.000 0.000 0.000
#> GSM246123 3 0.0000 1.000 0.000 0 1.00 0.000 0.000 0.000
#> GSM246422 4 0.3050 0.376 0.000 0 0.00 0.764 0.236 0.000
#> GSM246423 4 0.3050 0.376 0.000 0 0.00 0.764 0.236 0.000
#> GSM246484 4 0.3050 0.376 0.000 0 0.00 0.764 0.236 0.000
#> GSM246485 4 0.2730 0.674 0.000 0 0.00 0.808 0.000 0.192
#> GSM246486 4 0.2730 0.674 0.000 0 0.00 0.808 0.000 0.192
#> GSM246487 4 0.2730 0.674 0.000 0 0.00 0.808 0.000 0.192
#> GSM246488 4 0.2730 0.674 0.000 0 0.00 0.808 0.000 0.192
#> GSM246489 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM246490 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM246491 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM247162 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM247163 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM247164 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM247165 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM247166 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM247168 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM247169 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM247171 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM247173 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM247174 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM247175 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM247188 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM247189 4 0.0000 0.600 0.000 0 0.00 1.000 0.000 0.000
#> GSM247190 2 0.0000 1.000 0.000 1 0.00 0.000 0.000 0.000
#> GSM247650 1 0.1261 0.873 0.952 0 0.00 0.000 0.024 0.024
#> GSM247651 1 0.0909 0.878 0.968 0 0.00 0.000 0.012 0.020
#> GSM247652 1 0.0000 0.882 1.000 0 0.00 0.000 0.000 0.000
#> GSM247653 1 0.3276 0.779 0.816 0 0.00 0.000 0.132 0.052
#> GSM247654 1 0.0000 0.882 1.000 0 0.00 0.000 0.000 0.000
#> GSM247655 1 0.0909 0.878 0.968 0 0.00 0.000 0.012 0.020
#> GSM247656 1 0.0000 0.882 1.000 0 0.00 0.000 0.000 0.000
#> GSM247657 1 0.0000 0.882 1.000 0 0.00 0.000 0.000 0.000
#> GSM247658 1 0.0405 0.881 0.988 0 0.00 0.000 0.008 0.004
#> GSM247659 1 0.0000 0.882 1.000 0 0.00 0.000 0.000 0.000
#> GSM247660 1 0.0909 0.878 0.968 0 0.00 0.000 0.012 0.020
#> GSM247661 1 0.3276 0.779 0.816 0 0.00 0.000 0.132 0.052
#> GSM247662 1 0.0000 0.882 1.000 0 0.00 0.000 0.000 0.000
#> GSM247663 1 0.2376 0.835 0.888 0 0.00 0.000 0.068 0.044
#> GSM247856 1 0.0000 0.882 1.000 0 0.00 0.000 0.000 0.000
#> GSM247857 1 0.0000 0.882 1.000 0 0.00 0.000 0.000 0.000
#> GSM247859 1 0.1814 0.820 0.900 0 0.00 0.100 0.000 0.000
#> GSM247860 1 0.3276 0.779 0.816 0 0.00 0.000 0.132 0.052
#> GSM247862 1 0.0909 0.878 0.968 0 0.00 0.000 0.012 0.020
#> GSM247864 1 0.0909 0.878 0.968 0 0.00 0.000 0.012 0.020
#> GSM247865 1 0.5848 -0.137 0.428 0 0.00 0.380 0.000 0.192
#> GSM247866 1 0.3276 0.779 0.816 0 0.00 0.000 0.132 0.052
#> GSM247876 1 0.2433 0.832 0.884 0 0.00 0.000 0.072 0.044
#> GSM247877 5 0.2278 0.485 0.004 0 0.00 0.128 0.868 0.000
#> GSM247878 5 0.3804 0.221 0.000 0 0.00 0.424 0.576 0.000
#> GSM247879 1 0.4552 0.437 0.592 0 0.00 0.000 0.364 0.044
#> GSM247881 1 0.0000 0.882 1.000 0 0.00 0.000 0.000 0.000
#> GSM247883 1 0.5848 -0.137 0.428 0 0.00 0.380 0.000 0.192
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:hclust 61 5.49e-08 2
#> ATC:hclust 61 3.64e-19 3
#> ATC:hclust 58 8.60e-22 4
#> ATC:hclust 49 2.62e-20 5
#> ATC:hclust 52 3.67e-20 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 21168 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.847 0.943 0.973 0.4695 0.515 0.515
#> 3 3 0.659 0.782 0.841 0.3161 0.734 0.550
#> 4 4 0.679 0.899 0.896 0.1203 0.863 0.668
#> 5 5 0.791 0.854 0.878 0.0811 1.000 1.000
#> 6 6 0.785 0.772 0.830 0.0496 0.943 0.800
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
#> GSM246087 1 0.000 1.000 1.000 0.000
#> GSM246088 1 0.000 1.000 1.000 0.000
#> GSM246089 1 0.000 1.000 1.000 0.000
#> GSM246090 1 0.000 1.000 1.000 0.000
#> GSM246119 1 0.000 1.000 1.000 0.000
#> GSM246120 1 0.000 1.000 1.000 0.000
#> GSM246121 1 0.000 1.000 1.000 0.000
#> GSM246122 1 0.000 1.000 1.000 0.000
#> GSM246123 1 0.000 1.000 1.000 0.000
#> GSM246422 2 0.917 0.589 0.332 0.668
#> GSM246423 2 0.917 0.589 0.332 0.668
#> GSM246484 2 0.917 0.589 0.332 0.668
#> GSM246485 2 0.917 0.589 0.332 0.668
#> GSM246486 2 0.000 0.925 0.000 1.000
#> GSM246487 2 0.917 0.589 0.332 0.668
#> GSM246488 2 0.000 0.925 0.000 1.000
#> GSM246489 2 0.000 0.925 0.000 1.000
#> GSM246490 2 0.000 0.925 0.000 1.000
#> GSM246491 2 0.000 0.925 0.000 1.000
#> GSM247162 2 0.000 0.925 0.000 1.000
#> GSM247163 2 0.000 0.925 0.000 1.000
#> GSM247164 2 0.000 0.925 0.000 1.000
#> GSM247165 2 0.000 0.925 0.000 1.000
#> GSM247166 2 0.000 0.925 0.000 1.000
#> GSM247168 2 0.000 0.925 0.000 1.000
#> GSM247169 2 0.000 0.925 0.000 1.000
#> GSM247171 2 0.000 0.925 0.000 1.000
#> GSM247173 2 0.000 0.925 0.000 1.000
#> GSM247174 2 0.000 0.925 0.000 1.000
#> GSM247175 2 0.000 0.925 0.000 1.000
#> GSM247188 2 0.000 0.925 0.000 1.000
#> GSM247189 2 0.000 0.925 0.000 1.000
#> GSM247190 2 0.000 0.925 0.000 1.000
#> GSM247650 1 0.000 1.000 1.000 0.000
#> GSM247651 1 0.000 1.000 1.000 0.000
#> GSM247652 1 0.000 1.000 1.000 0.000
#> GSM247653 1 0.000 1.000 1.000 0.000
#> GSM247654 1 0.000 1.000 1.000 0.000
#> GSM247655 1 0.000 1.000 1.000 0.000
#> GSM247656 1 0.000 1.000 1.000 0.000
#> GSM247657 1 0.000 1.000 1.000 0.000
#> GSM247658 1 0.000 1.000 1.000 0.000
#> GSM247659 1 0.000 1.000 1.000 0.000
#> GSM247660 1 0.000 1.000 1.000 0.000
#> GSM247661 1 0.000 1.000 1.000 0.000
#> GSM247662 1 0.000 1.000 1.000 0.000
#> GSM247663 1 0.000 1.000 1.000 0.000
#> GSM247856 1 0.000 1.000 1.000 0.000
#> GSM247857 1 0.000 1.000 1.000 0.000
#> GSM247859 1 0.000 1.000 1.000 0.000
#> GSM247860 1 0.000 1.000 1.000 0.000
#> GSM247862 1 0.000 1.000 1.000 0.000
#> GSM247864 1 0.000 1.000 1.000 0.000
#> GSM247865 1 0.000 1.000 1.000 0.000
#> GSM247866 1 0.000 1.000 1.000 0.000
#> GSM247876 1 0.000 1.000 1.000 0.000
#> GSM247877 1 0.000 1.000 1.000 0.000
#> GSM247878 1 0.000 1.000 1.000 0.000
#> GSM247879 1 0.000 1.000 1.000 0.000
#> GSM247881 1 0.000 1.000 1.000 0.000
#> GSM247883 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.6225 1.000 0.432 0.000 0.568
#> GSM246088 3 0.6225 1.000 0.432 0.000 0.568
#> GSM246089 3 0.6225 1.000 0.432 0.000 0.568
#> GSM246090 3 0.6225 1.000 0.432 0.000 0.568
#> GSM246119 3 0.6225 1.000 0.432 0.000 0.568
#> GSM246120 3 0.6225 1.000 0.432 0.000 0.568
#> GSM246121 3 0.6225 1.000 0.432 0.000 0.568
#> GSM246122 3 0.6225 1.000 0.432 0.000 0.568
#> GSM246123 3 0.6225 1.000 0.432 0.000 0.568
#> GSM246422 1 0.6244 0.625 0.560 0.440 0.000
#> GSM246423 1 0.6244 0.625 0.560 0.440 0.000
#> GSM246484 1 0.6244 0.625 0.560 0.440 0.000
#> GSM246485 1 0.6244 0.625 0.560 0.440 0.000
#> GSM246486 2 0.2796 0.662 0.000 0.908 0.092
#> GSM246487 1 0.6244 0.625 0.560 0.440 0.000
#> GSM246488 2 0.0424 0.574 0.000 0.992 0.008
#> GSM246489 2 0.6180 0.933 0.000 0.584 0.416
#> GSM246490 2 0.6180 0.933 0.000 0.584 0.416
#> GSM246491 2 0.6180 0.933 0.000 0.584 0.416
#> GSM247162 2 0.6180 0.933 0.000 0.584 0.416
#> GSM247163 2 0.6180 0.933 0.000 0.584 0.416
#> GSM247164 2 0.6180 0.933 0.000 0.584 0.416
#> GSM247165 2 0.6180 0.933 0.000 0.584 0.416
#> GSM247166 2 0.6225 0.928 0.000 0.568 0.432
#> GSM247168 2 0.6225 0.928 0.000 0.568 0.432
#> GSM247169 2 0.6225 0.928 0.000 0.568 0.432
#> GSM247171 2 0.6180 0.933 0.000 0.584 0.416
#> GSM247173 2 0.6180 0.933 0.000 0.584 0.416
#> GSM247174 2 0.6225 0.928 0.000 0.568 0.432
#> GSM247175 2 0.6180 0.933 0.000 0.584 0.416
#> GSM247188 2 0.6225 0.928 0.000 0.568 0.432
#> GSM247189 2 0.0237 0.569 0.000 0.996 0.004
#> GSM247190 2 0.6180 0.933 0.000 0.584 0.416
#> GSM247650 1 0.1031 0.663 0.976 0.000 0.024
#> GSM247651 1 0.5254 0.703 0.736 0.264 0.000
#> GSM247652 1 0.1031 0.663 0.976 0.000 0.024
#> GSM247653 1 0.1031 0.663 0.976 0.000 0.024
#> GSM247654 1 0.1031 0.663 0.976 0.000 0.024
#> GSM247655 1 0.5254 0.703 0.736 0.264 0.000
#> GSM247656 1 0.1163 0.657 0.972 0.000 0.028
#> GSM247657 1 0.0237 0.677 0.996 0.000 0.004
#> GSM247658 1 0.0475 0.679 0.992 0.004 0.004
#> GSM247659 1 0.1031 0.663 0.976 0.000 0.024
#> GSM247660 1 0.5254 0.703 0.736 0.264 0.000
#> GSM247661 1 0.1031 0.663 0.976 0.000 0.024
#> GSM247662 1 0.1031 0.663 0.976 0.000 0.024
#> GSM247663 1 0.0592 0.672 0.988 0.000 0.012
#> GSM247856 1 0.1031 0.663 0.976 0.000 0.024
#> GSM247857 1 0.0000 0.679 1.000 0.000 0.000
#> GSM247859 1 0.5058 0.704 0.756 0.244 0.000
#> GSM247860 1 0.0237 0.680 0.996 0.004 0.000
#> GSM247862 1 0.4796 0.703 0.780 0.220 0.000
#> GSM247864 1 0.5254 0.703 0.736 0.264 0.000
#> GSM247865 1 0.6180 0.640 0.584 0.416 0.000
#> GSM247866 1 0.5254 0.703 0.736 0.264 0.000
#> GSM247876 1 0.0000 0.679 1.000 0.000 0.000
#> GSM247877 1 0.6180 0.640 0.584 0.416 0.000
#> GSM247878 1 0.6180 0.640 0.584 0.416 0.000
#> GSM247879 1 0.0592 0.672 0.988 0.000 0.012
#> GSM247881 1 0.0000 0.679 1.000 0.000 0.000
#> GSM247883 1 0.6180 0.640 0.584 0.416 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.3108 0.990 0.112 0.000 0.872 0.016
#> GSM246088 3 0.3108 0.990 0.112 0.000 0.872 0.016
#> GSM246089 3 0.3793 0.966 0.112 0.000 0.844 0.044
#> GSM246090 3 0.3108 0.990 0.112 0.000 0.872 0.016
#> GSM246119 3 0.2530 0.990 0.112 0.000 0.888 0.000
#> GSM246120 3 0.2530 0.990 0.112 0.000 0.888 0.000
#> GSM246121 3 0.2530 0.990 0.112 0.000 0.888 0.000
#> GSM246122 3 0.3108 0.990 0.112 0.000 0.872 0.016
#> GSM246123 3 0.2530 0.990 0.112 0.000 0.888 0.000
#> GSM246422 4 0.4442 0.839 0.236 0.004 0.008 0.752
#> GSM246423 4 0.4442 0.839 0.236 0.004 0.008 0.752
#> GSM246484 4 0.4442 0.839 0.236 0.004 0.008 0.752
#> GSM246485 4 0.4682 0.836 0.236 0.004 0.016 0.744
#> GSM246486 4 0.5228 0.565 0.000 0.312 0.024 0.664
#> GSM246487 4 0.4822 0.834 0.240 0.004 0.020 0.736
#> GSM246488 4 0.4826 0.624 0.000 0.264 0.020 0.716
#> GSM246489 2 0.0336 0.924 0.000 0.992 0.008 0.000
#> GSM246490 2 0.0336 0.924 0.000 0.992 0.008 0.000
#> GSM246491 2 0.0336 0.924 0.000 0.992 0.008 0.000
#> GSM247162 2 0.0336 0.924 0.000 0.992 0.008 0.000
#> GSM247163 2 0.0336 0.924 0.000 0.992 0.008 0.000
#> GSM247164 2 0.0336 0.926 0.000 0.992 0.008 0.000
#> GSM247165 2 0.0336 0.924 0.000 0.992 0.008 0.000
#> GSM247166 2 0.4039 0.911 0.000 0.836 0.080 0.084
#> GSM247168 2 0.4039 0.911 0.000 0.836 0.080 0.084
#> GSM247169 2 0.4039 0.911 0.000 0.836 0.080 0.084
#> GSM247171 2 0.0188 0.925 0.000 0.996 0.004 0.000
#> GSM247173 2 0.3056 0.923 0.000 0.888 0.040 0.072
#> GSM247174 2 0.4039 0.911 0.000 0.836 0.080 0.084
#> GSM247175 2 0.3312 0.921 0.000 0.876 0.052 0.072
#> GSM247188 2 0.4039 0.911 0.000 0.836 0.080 0.084
#> GSM247189 4 0.4250 0.613 0.000 0.276 0.000 0.724
#> GSM247190 2 0.3056 0.923 0.000 0.888 0.040 0.072
#> GSM247650 1 0.0921 0.935 0.972 0.000 0.028 0.000
#> GSM247651 1 0.1716 0.910 0.936 0.000 0.000 0.064
#> GSM247652 1 0.0921 0.935 0.972 0.000 0.028 0.000
#> GSM247653 1 0.2466 0.872 0.900 0.000 0.004 0.096
#> GSM247654 1 0.0921 0.935 0.972 0.000 0.028 0.000
#> GSM247655 1 0.1716 0.910 0.936 0.000 0.000 0.064
#> GSM247656 1 0.1356 0.929 0.960 0.000 0.032 0.008
#> GSM247657 1 0.0817 0.936 0.976 0.000 0.024 0.000
#> GSM247658 1 0.0188 0.933 0.996 0.000 0.000 0.004
#> GSM247659 1 0.0921 0.935 0.972 0.000 0.028 0.000
#> GSM247660 1 0.1716 0.910 0.936 0.000 0.000 0.064
#> GSM247661 1 0.2466 0.872 0.900 0.000 0.004 0.096
#> GSM247662 1 0.0921 0.935 0.972 0.000 0.028 0.000
#> GSM247663 1 0.1406 0.933 0.960 0.000 0.024 0.016
#> GSM247856 1 0.0921 0.935 0.972 0.000 0.028 0.000
#> GSM247857 1 0.0817 0.936 0.976 0.000 0.024 0.000
#> GSM247859 1 0.1637 0.913 0.940 0.000 0.000 0.060
#> GSM247860 1 0.2345 0.874 0.900 0.000 0.000 0.100
#> GSM247862 1 0.2760 0.869 0.872 0.000 0.000 0.128
#> GSM247864 1 0.1716 0.910 0.936 0.000 0.000 0.064
#> GSM247865 1 0.3166 0.833 0.868 0.000 0.016 0.116
#> GSM247866 1 0.2868 0.864 0.864 0.000 0.000 0.136
#> GSM247876 1 0.0895 0.936 0.976 0.000 0.020 0.004
#> GSM247877 4 0.4482 0.790 0.264 0.000 0.008 0.728
#> GSM247878 4 0.4567 0.787 0.276 0.000 0.008 0.716
#> GSM247879 1 0.1724 0.929 0.948 0.000 0.020 0.032
#> GSM247881 1 0.0817 0.936 0.976 0.000 0.024 0.000
#> GSM247883 1 0.3166 0.833 0.868 0.000 0.016 0.116
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.1243 0.983 0.028 0.000 0.960 0.004 NA
#> GSM246088 3 0.1243 0.983 0.028 0.000 0.960 0.004 NA
#> GSM246089 3 0.3291 0.907 0.028 0.000 0.856 0.016 NA
#> GSM246090 3 0.1243 0.983 0.028 0.000 0.960 0.004 NA
#> GSM246119 3 0.0955 0.983 0.028 0.000 0.968 0.000 NA
#> GSM246120 3 0.0955 0.983 0.028 0.000 0.968 0.000 NA
#> GSM246121 3 0.0794 0.983 0.028 0.000 0.972 0.000 NA
#> GSM246122 3 0.1243 0.983 0.028 0.000 0.960 0.004 NA
#> GSM246123 3 0.0955 0.983 0.028 0.000 0.968 0.000 NA
#> GSM246422 4 0.1121 0.830 0.044 0.000 0.000 0.956 NA
#> GSM246423 4 0.1121 0.830 0.044 0.000 0.000 0.956 NA
#> GSM246484 4 0.1121 0.830 0.044 0.000 0.000 0.956 NA
#> GSM246485 4 0.4622 0.816 0.060 0.000 0.024 0.768 NA
#> GSM246486 4 0.6020 0.720 0.000 0.160 0.024 0.644 NA
#> GSM246487 4 0.6020 0.740 0.160 0.000 0.024 0.644 NA
#> GSM246488 4 0.4512 0.797 0.000 0.044 0.024 0.768 NA
#> GSM246489 2 0.1211 0.893 0.000 0.960 0.000 0.016 NA
#> GSM246490 2 0.1211 0.893 0.000 0.960 0.000 0.016 NA
#> GSM246491 2 0.1211 0.893 0.000 0.960 0.000 0.016 NA
#> GSM247162 2 0.1211 0.893 0.000 0.960 0.000 0.016 NA
#> GSM247163 2 0.1211 0.893 0.000 0.960 0.000 0.016 NA
#> GSM247164 2 0.0671 0.896 0.000 0.980 0.000 0.016 NA
#> GSM247165 2 0.1211 0.893 0.000 0.960 0.000 0.016 NA
#> GSM247166 2 0.3826 0.838 0.000 0.752 0.004 0.008 NA
#> GSM247168 2 0.3826 0.840 0.000 0.752 0.004 0.008 NA
#> GSM247169 2 0.3883 0.836 0.000 0.744 0.004 0.008 NA
#> GSM247171 2 0.0693 0.896 0.000 0.980 0.000 0.012 NA
#> GSM247173 2 0.1671 0.892 0.000 0.924 0.000 0.000 NA
#> GSM247174 2 0.3671 0.841 0.000 0.756 0.000 0.008 NA
#> GSM247175 2 0.2424 0.880 0.000 0.868 0.000 0.000 NA
#> GSM247188 2 0.3671 0.841 0.000 0.756 0.000 0.008 NA
#> GSM247189 4 0.3523 0.811 0.000 0.044 0.004 0.832 NA
#> GSM247190 2 0.1671 0.892 0.000 0.924 0.000 0.000 NA
#> GSM247650 1 0.0290 0.882 0.992 0.000 0.000 0.000 NA
#> GSM247651 1 0.3003 0.831 0.812 0.000 0.000 0.000 NA
#> GSM247652 1 0.0000 0.883 1.000 0.000 0.000 0.000 NA
#> GSM247653 1 0.4030 0.689 0.648 0.000 0.000 0.000 NA
#> GSM247654 1 0.0000 0.883 1.000 0.000 0.000 0.000 NA
#> GSM247655 1 0.1341 0.874 0.944 0.000 0.000 0.000 NA
#> GSM247656 1 0.0000 0.883 1.000 0.000 0.000 0.000 NA
#> GSM247657 1 0.0162 0.882 0.996 0.000 0.000 0.000 NA
#> GSM247658 1 0.0000 0.883 1.000 0.000 0.000 0.000 NA
#> GSM247659 1 0.0000 0.883 1.000 0.000 0.000 0.000 NA
#> GSM247660 1 0.2605 0.846 0.852 0.000 0.000 0.000 NA
#> GSM247661 1 0.4030 0.689 0.648 0.000 0.000 0.000 NA
#> GSM247662 1 0.0000 0.883 1.000 0.000 0.000 0.000 NA
#> GSM247663 1 0.2891 0.833 0.824 0.000 0.000 0.000 NA
#> GSM247856 1 0.0000 0.883 1.000 0.000 0.000 0.000 NA
#> GSM247857 1 0.0290 0.881 0.992 0.000 0.000 0.000 NA
#> GSM247859 1 0.0290 0.881 0.992 0.000 0.000 0.000 NA
#> GSM247860 1 0.4030 0.689 0.648 0.000 0.000 0.000 NA
#> GSM247862 1 0.3774 0.740 0.704 0.000 0.000 0.000 NA
#> GSM247864 1 0.2929 0.834 0.820 0.000 0.000 0.000 NA
#> GSM247865 1 0.2522 0.821 0.896 0.000 0.024 0.004 NA
#> GSM247866 1 0.4294 0.583 0.532 0.000 0.000 0.000 NA
#> GSM247876 1 0.2179 0.858 0.888 0.000 0.000 0.000 NA
#> GSM247877 4 0.4734 0.707 0.064 0.000 0.000 0.704 NA
#> GSM247878 4 0.4734 0.707 0.064 0.000 0.000 0.704 NA
#> GSM247879 1 0.3177 0.814 0.792 0.000 0.000 0.000 NA
#> GSM247881 1 0.0290 0.881 0.992 0.000 0.000 0.000 NA
#> GSM247883 1 0.2522 0.821 0.896 0.000 0.024 0.004 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0291 0.959 0.004 0.000 0.992 0.000 0.004 NA
#> GSM246088 3 0.0291 0.959 0.004 0.000 0.992 0.000 0.004 NA
#> GSM246089 3 0.4429 0.791 0.004 0.000 0.740 0.012 0.076 NA
#> GSM246090 3 0.0291 0.959 0.004 0.000 0.992 0.000 0.004 NA
#> GSM246119 3 0.1413 0.956 0.004 0.000 0.948 0.008 0.036 NA
#> GSM246120 3 0.1413 0.956 0.004 0.000 0.948 0.008 0.036 NA
#> GSM246121 3 0.0922 0.958 0.004 0.000 0.968 0.004 0.024 NA
#> GSM246122 3 0.0291 0.959 0.004 0.000 0.992 0.000 0.004 NA
#> GSM246123 3 0.1413 0.956 0.004 0.000 0.948 0.008 0.036 NA
#> GSM246422 4 0.3465 0.760 0.020 0.000 0.000 0.828 0.056 NA
#> GSM246423 4 0.3465 0.760 0.020 0.000 0.000 0.828 0.056 NA
#> GSM246484 4 0.3465 0.760 0.020 0.000 0.000 0.828 0.056 NA
#> GSM246485 4 0.2800 0.737 0.052 0.000 0.000 0.876 0.020 NA
#> GSM246486 4 0.4527 0.625 0.000 0.228 0.000 0.704 0.024 NA
#> GSM246487 4 0.4921 0.563 0.192 0.016 0.000 0.708 0.020 NA
#> GSM246488 4 0.2934 0.739 0.000 0.064 0.000 0.868 0.024 NA
#> GSM246489 2 0.0146 0.830 0.000 0.996 0.000 0.000 0.004 NA
#> GSM246490 2 0.0260 0.831 0.000 0.992 0.000 0.000 0.008 NA
#> GSM246491 2 0.0260 0.831 0.000 0.992 0.000 0.000 0.008 NA
#> GSM247162 2 0.0405 0.831 0.000 0.988 0.000 0.000 0.008 NA
#> GSM247163 2 0.0363 0.829 0.000 0.988 0.000 0.000 0.012 NA
#> GSM247164 2 0.0972 0.834 0.000 0.964 0.000 0.000 0.008 NA
#> GSM247165 2 0.0146 0.830 0.000 0.996 0.000 0.000 0.004 NA
#> GSM247166 2 0.4897 0.699 0.000 0.556 0.004 0.000 0.056 NA
#> GSM247168 2 0.4897 0.699 0.000 0.556 0.004 0.000 0.056 NA
#> GSM247169 2 0.4723 0.698 0.000 0.548 0.004 0.000 0.040 NA
#> GSM247171 2 0.1204 0.832 0.000 0.944 0.000 0.000 0.000 NA
#> GSM247173 2 0.2219 0.826 0.000 0.864 0.000 0.000 0.000 NA
#> GSM247174 2 0.3843 0.707 0.000 0.548 0.000 0.000 0.000 NA
#> GSM247175 2 0.2883 0.808 0.000 0.788 0.000 0.000 0.000 NA
#> GSM247188 2 0.3843 0.707 0.000 0.548 0.000 0.000 0.000 NA
#> GSM247189 4 0.1219 0.755 0.000 0.048 0.000 0.948 0.000 NA
#> GSM247190 2 0.2300 0.824 0.000 0.856 0.000 0.000 0.000 NA
#> GSM247650 1 0.0993 0.814 0.964 0.000 0.000 0.000 0.024 NA
#> GSM247651 1 0.4790 0.503 0.680 0.000 0.000 0.004 0.196 NA
#> GSM247652 1 0.0458 0.819 0.984 0.000 0.000 0.000 0.016 NA
#> GSM247653 5 0.3563 0.919 0.336 0.000 0.000 0.000 0.664 NA
#> GSM247654 1 0.0458 0.819 0.984 0.000 0.000 0.000 0.016 NA
#> GSM247655 1 0.2926 0.737 0.844 0.000 0.000 0.004 0.028 NA
#> GSM247656 1 0.0603 0.817 0.980 0.000 0.004 0.000 0.016 NA
#> GSM247657 1 0.0363 0.819 0.988 0.000 0.000 0.000 0.012 NA
#> GSM247658 1 0.0547 0.818 0.980 0.000 0.000 0.000 0.020 NA
#> GSM247659 1 0.0363 0.819 0.988 0.000 0.000 0.000 0.012 NA
#> GSM247660 1 0.4508 0.551 0.716 0.000 0.000 0.004 0.164 NA
#> GSM247661 5 0.3563 0.919 0.336 0.000 0.000 0.000 0.664 NA
#> GSM247662 1 0.0458 0.819 0.984 0.000 0.000 0.000 0.016 NA
#> GSM247663 1 0.4817 0.482 0.676 0.000 0.000 0.004 0.200 NA
#> GSM247856 1 0.0363 0.819 0.988 0.000 0.000 0.000 0.012 NA
#> GSM247857 1 0.0603 0.815 0.980 0.000 0.000 0.000 0.004 NA
#> GSM247859 1 0.0837 0.812 0.972 0.000 0.000 0.004 0.004 NA
#> GSM247860 5 0.3563 0.919 0.336 0.000 0.000 0.000 0.664 NA
#> GSM247862 5 0.4141 0.753 0.432 0.000 0.000 0.000 0.556 NA
#> GSM247864 1 0.4790 0.503 0.680 0.000 0.000 0.004 0.196 NA
#> GSM247865 1 0.2326 0.754 0.900 0.000 0.000 0.012 0.028 NA
#> GSM247866 5 0.3468 0.836 0.264 0.000 0.000 0.000 0.728 NA
#> GSM247876 1 0.3985 0.651 0.768 0.000 0.000 0.004 0.088 NA
#> GSM247877 4 0.6480 0.458 0.024 0.000 0.000 0.428 0.256 NA
#> GSM247878 4 0.6480 0.458 0.024 0.000 0.000 0.428 0.256 NA
#> GSM247879 1 0.5388 0.305 0.600 0.000 0.000 0.004 0.228 NA
#> GSM247881 1 0.0458 0.816 0.984 0.000 0.000 0.000 0.000 NA
#> GSM247883 1 0.2326 0.754 0.900 0.000 0.000 0.012 0.028 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:kmeans 61 5.68e-14 2
#> ATC:kmeans 61 3.74e-21 3
#> ATC:kmeans 61 2.38e-22 4
#> ATC:kmeans 61 2.38e-22 5
#> ATC:kmeans 57 5.72e-21 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 21168 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.991 0.996 0.4964 0.503 0.503
#> 3 3 0.900 0.932 0.962 0.2802 0.803 0.624
#> 4 4 0.754 0.800 0.906 0.1530 0.839 0.581
#> 5 5 0.750 0.720 0.853 0.0636 0.925 0.718
#> 6 6 0.762 0.652 0.796 0.0348 0.943 0.743
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
#> GSM246087 1 0.000 1.000 1.000 0.000
#> GSM246088 1 0.000 1.000 1.000 0.000
#> GSM246089 1 0.000 1.000 1.000 0.000
#> GSM246090 1 0.000 1.000 1.000 0.000
#> GSM246119 1 0.000 1.000 1.000 0.000
#> GSM246120 1 0.000 1.000 1.000 0.000
#> GSM246121 1 0.000 1.000 1.000 0.000
#> GSM246122 1 0.000 1.000 1.000 0.000
#> GSM246123 1 0.000 1.000 1.000 0.000
#> GSM246422 2 0.000 0.990 0.000 1.000
#> GSM246423 2 0.000 0.990 0.000 1.000
#> GSM246484 2 0.000 0.990 0.000 1.000
#> GSM246485 2 0.000 0.990 0.000 1.000
#> GSM246486 2 0.000 0.990 0.000 1.000
#> GSM246487 2 0.000 0.990 0.000 1.000
#> GSM246488 2 0.000 0.990 0.000 1.000
#> GSM246489 2 0.000 0.990 0.000 1.000
#> GSM246490 2 0.000 0.990 0.000 1.000
#> GSM246491 2 0.000 0.990 0.000 1.000
#> GSM247162 2 0.000 0.990 0.000 1.000
#> GSM247163 2 0.000 0.990 0.000 1.000
#> GSM247164 2 0.000 0.990 0.000 1.000
#> GSM247165 2 0.000 0.990 0.000 1.000
#> GSM247166 2 0.000 0.990 0.000 1.000
#> GSM247168 2 0.000 0.990 0.000 1.000
#> GSM247169 2 0.000 0.990 0.000 1.000
#> GSM247171 2 0.000 0.990 0.000 1.000
#> GSM247173 2 0.000 0.990 0.000 1.000
#> GSM247174 2 0.000 0.990 0.000 1.000
#> GSM247175 2 0.000 0.990 0.000 1.000
#> GSM247188 2 0.000 0.990 0.000 1.000
#> GSM247189 2 0.000 0.990 0.000 1.000
#> GSM247190 2 0.000 0.990 0.000 1.000
#> GSM247650 1 0.000 1.000 1.000 0.000
#> GSM247651 1 0.000 1.000 1.000 0.000
#> GSM247652 1 0.000 1.000 1.000 0.000
#> GSM247653 1 0.000 1.000 1.000 0.000
#> GSM247654 1 0.000 1.000 1.000 0.000
#> GSM247655 1 0.000 1.000 1.000 0.000
#> GSM247656 1 0.000 1.000 1.000 0.000
#> GSM247657 1 0.000 1.000 1.000 0.000
#> GSM247658 1 0.000 1.000 1.000 0.000
#> GSM247659 1 0.000 1.000 1.000 0.000
#> GSM247660 1 0.000 1.000 1.000 0.000
#> GSM247661 1 0.000 1.000 1.000 0.000
#> GSM247662 1 0.000 1.000 1.000 0.000
#> GSM247663 1 0.000 1.000 1.000 0.000
#> GSM247856 1 0.000 1.000 1.000 0.000
#> GSM247857 1 0.000 1.000 1.000 0.000
#> GSM247859 1 0.000 1.000 1.000 0.000
#> GSM247860 1 0.000 1.000 1.000 0.000
#> GSM247862 1 0.000 1.000 1.000 0.000
#> GSM247864 1 0.000 1.000 1.000 0.000
#> GSM247865 2 0.802 0.677 0.244 0.756
#> GSM247866 1 0.000 1.000 1.000 0.000
#> GSM247876 1 0.000 1.000 1.000 0.000
#> GSM247877 1 0.000 1.000 1.000 0.000
#> GSM247878 1 0.000 1.000 1.000 0.000
#> GSM247879 1 0.000 1.000 1.000 0.000
#> GSM247881 1 0.000 1.000 1.000 0.000
#> GSM247883 2 0.000 0.990 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 0.994 0.000 0.000 1.000
#> GSM246088 3 0.0000 0.994 0.000 0.000 1.000
#> GSM246089 3 0.0000 0.994 0.000 0.000 1.000
#> GSM246090 3 0.0000 0.994 0.000 0.000 1.000
#> GSM246119 3 0.0000 0.994 0.000 0.000 1.000
#> GSM246120 3 0.0000 0.994 0.000 0.000 1.000
#> GSM246121 3 0.0000 0.994 0.000 0.000 1.000
#> GSM246122 3 0.0000 0.994 0.000 0.000 1.000
#> GSM246123 3 0.0000 0.994 0.000 0.000 1.000
#> GSM246422 1 0.0237 0.819 0.996 0.004 0.000
#> GSM246423 1 0.0237 0.819 0.996 0.004 0.000
#> GSM246484 1 0.0237 0.819 0.996 0.004 0.000
#> GSM246485 1 0.5905 0.345 0.648 0.352 0.000
#> GSM246486 2 0.0000 0.988 0.000 1.000 0.000
#> GSM246487 2 0.0424 0.981 0.008 0.992 0.000
#> GSM246488 2 0.0000 0.988 0.000 1.000 0.000
#> GSM246489 2 0.0000 0.988 0.000 1.000 0.000
#> GSM246490 2 0.0000 0.988 0.000 1.000 0.000
#> GSM246491 2 0.0000 0.988 0.000 1.000 0.000
#> GSM247162 2 0.0000 0.988 0.000 1.000 0.000
#> GSM247163 2 0.0000 0.988 0.000 1.000 0.000
#> GSM247164 2 0.0000 0.988 0.000 1.000 0.000
#> GSM247165 2 0.0000 0.988 0.000 1.000 0.000
#> GSM247166 2 0.0000 0.988 0.000 1.000 0.000
#> GSM247168 2 0.0000 0.988 0.000 1.000 0.000
#> GSM247169 2 0.0000 0.988 0.000 1.000 0.000
#> GSM247171 2 0.0000 0.988 0.000 1.000 0.000
#> GSM247173 2 0.0000 0.988 0.000 1.000 0.000
#> GSM247174 2 0.0000 0.988 0.000 1.000 0.000
#> GSM247175 2 0.0000 0.988 0.000 1.000 0.000
#> GSM247188 2 0.0000 0.988 0.000 1.000 0.000
#> GSM247189 2 0.4750 0.746 0.216 0.784 0.000
#> GSM247190 2 0.0000 0.988 0.000 1.000 0.000
#> GSM247650 3 0.0000 0.994 0.000 0.000 1.000
#> GSM247651 1 0.4750 0.793 0.784 0.000 0.216
#> GSM247652 3 0.0000 0.994 0.000 0.000 1.000
#> GSM247653 3 0.0237 0.991 0.004 0.000 0.996
#> GSM247654 3 0.0000 0.994 0.000 0.000 1.000
#> GSM247655 1 0.4796 0.790 0.780 0.000 0.220
#> GSM247656 3 0.0000 0.994 0.000 0.000 1.000
#> GSM247657 3 0.0000 0.994 0.000 0.000 1.000
#> GSM247658 3 0.0000 0.994 0.000 0.000 1.000
#> GSM247659 3 0.0000 0.994 0.000 0.000 1.000
#> GSM247660 1 0.4750 0.793 0.784 0.000 0.216
#> GSM247661 3 0.0237 0.991 0.004 0.000 0.996
#> GSM247662 3 0.0000 0.994 0.000 0.000 1.000
#> GSM247663 3 0.0747 0.982 0.016 0.000 0.984
#> GSM247856 3 0.0000 0.994 0.000 0.000 1.000
#> GSM247857 3 0.0000 0.994 0.000 0.000 1.000
#> GSM247859 3 0.1163 0.968 0.028 0.000 0.972
#> GSM247860 3 0.2165 0.921 0.064 0.000 0.936
#> GSM247862 1 0.6126 0.491 0.600 0.000 0.400
#> GSM247864 1 0.4750 0.793 0.784 0.000 0.216
#> GSM247865 1 0.2486 0.800 0.932 0.060 0.008
#> GSM247866 1 0.4796 0.790 0.780 0.000 0.220
#> GSM247876 3 0.0592 0.985 0.012 0.000 0.988
#> GSM247877 1 0.0000 0.819 1.000 0.000 0.000
#> GSM247878 1 0.0000 0.819 1.000 0.000 0.000
#> GSM247879 3 0.0592 0.985 0.012 0.000 0.988
#> GSM247881 3 0.0000 0.994 0.000 0.000 1.000
#> GSM247883 2 0.1015 0.970 0.012 0.980 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM246088 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM246089 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM246090 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM246119 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM246120 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM246121 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM246122 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM246123 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM246422 4 0.0000 0.756 0.000 0.000 0.000 1.000
#> GSM246423 4 0.0000 0.756 0.000 0.000 0.000 1.000
#> GSM246484 4 0.0000 0.756 0.000 0.000 0.000 1.000
#> GSM246485 4 0.1211 0.752 0.000 0.040 0.000 0.960
#> GSM246486 2 0.3266 0.772 0.000 0.832 0.000 0.168
#> GSM246487 2 0.4933 0.210 0.000 0.568 0.000 0.432
#> GSM246488 4 0.4933 0.134 0.000 0.432 0.000 0.568
#> GSM246489 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM246490 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM246491 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM247162 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM247163 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM247164 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM247165 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM247166 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM247168 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM247169 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM247171 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM247173 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM247174 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM247175 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM247188 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM247189 4 0.3311 0.683 0.000 0.172 0.000 0.828
#> GSM247190 2 0.0000 0.953 0.000 1.000 0.000 0.000
#> GSM247650 3 0.4008 0.723 0.244 0.000 0.756 0.000
#> GSM247651 1 0.0927 0.857 0.976 0.000 0.008 0.016
#> GSM247652 3 0.3764 0.754 0.216 0.000 0.784 0.000
#> GSM247653 1 0.1637 0.860 0.940 0.000 0.060 0.000
#> GSM247654 3 0.4382 0.653 0.296 0.000 0.704 0.000
#> GSM247655 1 0.0524 0.861 0.988 0.000 0.008 0.004
#> GSM247656 3 0.0188 0.881 0.004 0.000 0.996 0.000
#> GSM247657 3 0.4500 0.621 0.316 0.000 0.684 0.000
#> GSM247658 1 0.3610 0.767 0.800 0.000 0.200 0.000
#> GSM247659 3 0.0469 0.878 0.012 0.000 0.988 0.000
#> GSM247660 1 0.0672 0.860 0.984 0.000 0.008 0.008
#> GSM247661 1 0.1867 0.856 0.928 0.000 0.072 0.000
#> GSM247662 3 0.3074 0.803 0.152 0.000 0.848 0.000
#> GSM247663 1 0.2814 0.825 0.868 0.000 0.132 0.000
#> GSM247856 3 0.0000 0.882 0.000 0.000 1.000 0.000
#> GSM247857 3 0.4277 0.688 0.280 0.000 0.720 0.000
#> GSM247859 1 0.4843 0.281 0.604 0.000 0.396 0.000
#> GSM247860 1 0.0921 0.863 0.972 0.000 0.028 0.000
#> GSM247862 1 0.0336 0.861 0.992 0.000 0.008 0.000
#> GSM247864 1 0.0804 0.859 0.980 0.000 0.008 0.012
#> GSM247865 4 0.6456 0.271 0.408 0.040 0.016 0.536
#> GSM247866 1 0.0804 0.859 0.980 0.000 0.008 0.012
#> GSM247876 1 0.3764 0.748 0.784 0.000 0.216 0.000
#> GSM247877 4 0.4605 0.485 0.336 0.000 0.000 0.664
#> GSM247878 4 0.4431 0.529 0.304 0.000 0.000 0.696
#> GSM247879 1 0.3908 0.766 0.784 0.000 0.212 0.004
#> GSM247881 3 0.4193 0.701 0.268 0.000 0.732 0.000
#> GSM247883 2 0.3940 0.783 0.116 0.844 0.012 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 0.8687 0.000 0.000 1.000 0.000 0.000
#> GSM246088 3 0.0000 0.8687 0.000 0.000 1.000 0.000 0.000
#> GSM246089 3 0.0162 0.8647 0.004 0.000 0.996 0.000 0.000
#> GSM246090 3 0.0000 0.8687 0.000 0.000 1.000 0.000 0.000
#> GSM246119 3 0.0000 0.8687 0.000 0.000 1.000 0.000 0.000
#> GSM246120 3 0.0000 0.8687 0.000 0.000 1.000 0.000 0.000
#> GSM246121 3 0.0000 0.8687 0.000 0.000 1.000 0.000 0.000
#> GSM246122 3 0.0000 0.8687 0.000 0.000 1.000 0.000 0.000
#> GSM246123 3 0.0000 0.8687 0.000 0.000 1.000 0.000 0.000
#> GSM246422 4 0.0000 0.7374 0.000 0.000 0.000 1.000 0.000
#> GSM246423 4 0.0000 0.7374 0.000 0.000 0.000 1.000 0.000
#> GSM246484 4 0.0000 0.7374 0.000 0.000 0.000 1.000 0.000
#> GSM246485 4 0.2438 0.7162 0.000 0.060 0.000 0.900 0.040
#> GSM246486 2 0.3954 0.6812 0.000 0.772 0.000 0.192 0.036
#> GSM246487 2 0.5243 0.1521 0.000 0.540 0.000 0.412 0.048
#> GSM246488 4 0.5037 0.2781 0.000 0.376 0.000 0.584 0.040
#> GSM246489 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM246490 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM246491 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM247162 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM247163 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM247164 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM247165 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM247166 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM247168 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM247169 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM247171 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM247174 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM247175 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM247189 4 0.3123 0.6641 0.000 0.184 0.000 0.812 0.004
#> GSM247190 2 0.0000 0.9557 0.000 1.000 0.000 0.000 0.000
#> GSM247650 3 0.6301 -0.2223 0.180 0.000 0.512 0.000 0.308
#> GSM247651 1 0.3476 0.7771 0.804 0.000 0.000 0.020 0.176
#> GSM247652 5 0.5077 0.5846 0.040 0.000 0.392 0.000 0.568
#> GSM247653 1 0.1469 0.7733 0.948 0.000 0.036 0.000 0.016
#> GSM247654 5 0.5498 0.6300 0.076 0.000 0.356 0.000 0.568
#> GSM247655 1 0.4130 0.7057 0.696 0.000 0.000 0.012 0.292
#> GSM247656 3 0.3636 0.4614 0.000 0.000 0.728 0.000 0.272
#> GSM247657 5 0.5306 0.6701 0.072 0.000 0.316 0.000 0.612
#> GSM247658 1 0.5834 0.3572 0.584 0.000 0.132 0.000 0.284
#> GSM247659 3 0.3586 0.4840 0.000 0.000 0.736 0.000 0.264
#> GSM247660 1 0.3280 0.7807 0.812 0.000 0.000 0.012 0.176
#> GSM247661 1 0.1981 0.7592 0.920 0.000 0.064 0.000 0.016
#> GSM247662 5 0.4890 0.4566 0.024 0.000 0.452 0.000 0.524
#> GSM247663 1 0.5040 0.7081 0.680 0.000 0.084 0.000 0.236
#> GSM247856 3 0.1410 0.8161 0.000 0.000 0.940 0.000 0.060
#> GSM247857 5 0.5067 0.6835 0.064 0.000 0.288 0.000 0.648
#> GSM247859 5 0.3866 0.5852 0.096 0.000 0.096 0.000 0.808
#> GSM247860 1 0.0912 0.7781 0.972 0.000 0.012 0.000 0.016
#> GSM247862 1 0.0794 0.7815 0.972 0.000 0.000 0.000 0.028
#> GSM247864 1 0.2536 0.7872 0.868 0.000 0.000 0.004 0.128
#> GSM247865 5 0.6057 0.0948 0.164 0.008 0.000 0.224 0.604
#> GSM247866 1 0.0162 0.7743 0.996 0.000 0.000 0.000 0.004
#> GSM247876 1 0.6110 0.3787 0.476 0.000 0.128 0.000 0.396
#> GSM247877 4 0.5297 0.3080 0.360 0.000 0.000 0.580 0.060
#> GSM247878 4 0.5203 0.3632 0.332 0.000 0.000 0.608 0.060
#> GSM247879 1 0.5466 0.6655 0.656 0.000 0.152 0.000 0.192
#> GSM247881 5 0.4666 0.6850 0.056 0.000 0.240 0.000 0.704
#> GSM247883 5 0.3101 0.4602 0.024 0.100 0.000 0.012 0.864
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0000 0.8461 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246088 3 0.0000 0.8461 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246089 3 0.0000 0.8461 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246090 3 0.0000 0.8461 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246119 3 0.0000 0.8461 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246120 3 0.0000 0.8461 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246121 3 0.0000 0.8461 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246122 3 0.0000 0.8461 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246123 3 0.0000 0.8461 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246422 4 0.0458 0.6705 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM246423 4 0.0458 0.6705 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM246484 4 0.0458 0.6705 0.000 0.000 0.000 0.984 0.016 0.000
#> GSM246485 4 0.4488 0.6480 0.020 0.048 0.000 0.724 0.004 0.204
#> GSM246486 2 0.5793 0.1807 0.020 0.580 0.000 0.204 0.000 0.196
#> GSM246487 4 0.6778 0.3986 0.032 0.344 0.000 0.368 0.004 0.252
#> GSM246488 4 0.5989 0.5824 0.016 0.260 0.000 0.528 0.000 0.196
#> GSM246489 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246490 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246491 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247162 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247163 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247164 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247165 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247166 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247168 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247169 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247171 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247174 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247175 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247189 4 0.3460 0.6115 0.000 0.220 0.000 0.760 0.000 0.020
#> GSM247190 2 0.0000 0.9697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247650 3 0.6047 -0.0129 0.220 0.000 0.480 0.000 0.292 0.008
#> GSM247651 5 0.1781 0.4892 0.060 0.000 0.000 0.008 0.924 0.008
#> GSM247652 1 0.4651 0.6120 0.676 0.000 0.256 0.000 0.052 0.016
#> GSM247653 6 0.4987 0.9251 0.044 0.000 0.012 0.000 0.420 0.524
#> GSM247654 1 0.5244 0.6301 0.652 0.000 0.232 0.000 0.080 0.036
#> GSM247655 5 0.3183 0.4848 0.164 0.000 0.000 0.008 0.812 0.016
#> GSM247656 3 0.3747 0.2222 0.396 0.000 0.604 0.000 0.000 0.000
#> GSM247657 1 0.4562 0.6653 0.720 0.000 0.196 0.000 0.056 0.028
#> GSM247658 1 0.7391 -0.0792 0.324 0.000 0.112 0.000 0.284 0.280
#> GSM247659 3 0.4151 0.1555 0.412 0.000 0.576 0.000 0.004 0.008
#> GSM247660 5 0.2052 0.4643 0.056 0.000 0.000 0.004 0.912 0.028
#> GSM247661 6 0.4913 0.9364 0.028 0.000 0.020 0.000 0.428 0.524
#> GSM247662 1 0.4868 0.4532 0.588 0.000 0.352 0.000 0.052 0.008
#> GSM247663 5 0.3936 0.4961 0.124 0.000 0.088 0.000 0.780 0.008
#> GSM247856 3 0.2527 0.7532 0.084 0.000 0.880 0.000 0.004 0.032
#> GSM247857 1 0.4197 0.6745 0.752 0.000 0.172 0.000 0.060 0.016
#> GSM247859 1 0.3755 0.6024 0.816 0.000 0.056 0.000 0.084 0.044
#> GSM247860 6 0.4453 0.9374 0.020 0.000 0.004 0.000 0.452 0.524
#> GSM247862 5 0.4531 -0.8783 0.032 0.000 0.000 0.000 0.504 0.464
#> GSM247864 5 0.2069 0.3553 0.020 0.000 0.000 0.004 0.908 0.068
#> GSM247865 1 0.6861 0.0957 0.424 0.000 0.000 0.128 0.104 0.344
#> GSM247866 6 0.4097 0.8987 0.008 0.000 0.000 0.000 0.492 0.500
#> GSM247876 5 0.5522 0.4139 0.240 0.000 0.108 0.000 0.620 0.032
#> GSM247877 5 0.4399 0.2135 0.000 0.000 0.000 0.460 0.516 0.024
#> GSM247878 5 0.4407 0.1737 0.000 0.000 0.000 0.480 0.496 0.024
#> GSM247879 5 0.4670 0.4693 0.072 0.000 0.148 0.004 0.740 0.036
#> GSM247881 1 0.3457 0.6680 0.820 0.000 0.116 0.000 0.052 0.012
#> GSM247883 1 0.4204 0.4119 0.716 0.012 0.000 0.008 0.020 0.244
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:skmeans 61 2.53e-12 2
#> ATC:skmeans 59 2.62e-10 3
#> ATC:skmeans 56 9.11e-12 4
#> ATC:skmeans 49 3.43e-16 5
#> ATC:skmeans 42 2.63e-13 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 21168 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.932 0.953 0.978 0.4497 0.564 0.564
#> 3 3 1.000 0.971 0.987 0.3419 0.838 0.712
#> 4 4 1.000 0.972 0.989 0.1370 0.911 0.780
#> 5 5 0.850 0.839 0.918 0.1094 0.920 0.747
#> 6 6 0.819 0.691 0.882 0.0365 0.975 0.896
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> 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
#> GSM246087 1 0.000 0.967 1.000 0.000
#> GSM246088 1 0.000 0.967 1.000 0.000
#> GSM246089 1 0.000 0.967 1.000 0.000
#> GSM246090 1 0.000 0.967 1.000 0.000
#> GSM246119 1 0.000 0.967 1.000 0.000
#> GSM246120 1 0.000 0.967 1.000 0.000
#> GSM246121 1 0.000 0.967 1.000 0.000
#> GSM246122 1 0.000 0.967 1.000 0.000
#> GSM246123 1 0.000 0.967 1.000 0.000
#> GSM246422 1 0.844 0.663 0.728 0.272
#> GSM246423 1 0.814 0.693 0.748 0.252
#> GSM246484 1 0.844 0.663 0.728 0.272
#> GSM246485 1 0.850 0.656 0.724 0.276
#> GSM246486 2 0.000 1.000 0.000 1.000
#> GSM246487 1 0.814 0.693 0.748 0.252
#> GSM246488 2 0.000 1.000 0.000 1.000
#> GSM246489 2 0.000 1.000 0.000 1.000
#> GSM246490 2 0.000 1.000 0.000 1.000
#> GSM246491 2 0.000 1.000 0.000 1.000
#> GSM247162 2 0.000 1.000 0.000 1.000
#> GSM247163 2 0.000 1.000 0.000 1.000
#> GSM247164 2 0.000 1.000 0.000 1.000
#> GSM247165 2 0.000 1.000 0.000 1.000
#> GSM247166 2 0.000 1.000 0.000 1.000
#> GSM247168 2 0.000 1.000 0.000 1.000
#> GSM247169 2 0.000 1.000 0.000 1.000
#> GSM247171 2 0.000 1.000 0.000 1.000
#> GSM247173 2 0.000 1.000 0.000 1.000
#> GSM247174 2 0.000 1.000 0.000 1.000
#> GSM247175 2 0.000 1.000 0.000 1.000
#> GSM247188 2 0.000 1.000 0.000 1.000
#> GSM247189 2 0.000 1.000 0.000 1.000
#> GSM247190 2 0.000 1.000 0.000 1.000
#> GSM247650 1 0.000 0.967 1.000 0.000
#> GSM247651 1 0.000 0.967 1.000 0.000
#> GSM247652 1 0.000 0.967 1.000 0.000
#> GSM247653 1 0.000 0.967 1.000 0.000
#> GSM247654 1 0.000 0.967 1.000 0.000
#> GSM247655 1 0.000 0.967 1.000 0.000
#> GSM247656 1 0.000 0.967 1.000 0.000
#> GSM247657 1 0.000 0.967 1.000 0.000
#> GSM247658 1 0.000 0.967 1.000 0.000
#> GSM247659 1 0.000 0.967 1.000 0.000
#> GSM247660 1 0.000 0.967 1.000 0.000
#> GSM247661 1 0.000 0.967 1.000 0.000
#> GSM247662 1 0.000 0.967 1.000 0.000
#> GSM247663 1 0.000 0.967 1.000 0.000
#> GSM247856 1 0.000 0.967 1.000 0.000
#> GSM247857 1 0.000 0.967 1.000 0.000
#> GSM247859 1 0.000 0.967 1.000 0.000
#> GSM247860 1 0.000 0.967 1.000 0.000
#> GSM247862 1 0.000 0.967 1.000 0.000
#> GSM247864 1 0.000 0.967 1.000 0.000
#> GSM247865 1 0.000 0.967 1.000 0.000
#> GSM247866 1 0.000 0.967 1.000 0.000
#> GSM247876 1 0.000 0.967 1.000 0.000
#> GSM247877 1 0.000 0.967 1.000 0.000
#> GSM247878 1 0.000 0.967 1.000 0.000
#> GSM247879 1 0.000 0.967 1.000 0.000
#> GSM247881 1 0.000 0.967 1.000 0.000
#> GSM247883 1 0.000 0.967 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1.000
#> GSM246422 1 0.5058 0.698 0.756 0.244 0.000
#> GSM246423 1 0.0592 0.963 0.988 0.012 0.000
#> GSM246484 1 0.5058 0.698 0.756 0.244 0.000
#> GSM246485 1 0.5138 0.686 0.748 0.252 0.000
#> GSM246486 2 0.0000 1.000 0.000 1.000 0.000
#> GSM246487 1 0.0000 0.973 1.000 0.000 0.000
#> GSM246488 2 0.0000 1.000 0.000 1.000 0.000
#> GSM246489 2 0.0000 1.000 0.000 1.000 0.000
#> GSM246490 2 0.0000 1.000 0.000 1.000 0.000
#> GSM246491 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247162 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247163 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247164 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247165 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247166 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247168 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247169 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247171 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247173 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247174 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247175 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247188 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247189 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247190 2 0.0000 1.000 0.000 1.000 0.000
#> GSM247650 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247651 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247652 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247653 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247654 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247655 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247656 1 0.0747 0.960 0.984 0.000 0.016
#> GSM247657 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247658 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247659 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247660 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247661 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247662 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247663 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247856 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247857 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247859 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247860 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247862 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247864 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247865 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247866 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247876 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247877 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247878 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247879 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247881 1 0.0000 0.973 1.000 0.000 0.000
#> GSM247883 1 0.0000 0.973 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM246088 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM246089 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM246090 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM246119 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM246120 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM246121 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM246122 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM246123 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM246422 4 0.000 0.956 0.000 0.000 0 1.000
#> GSM246423 4 0.000 0.956 0.000 0.000 0 1.000
#> GSM246484 4 0.000 0.956 0.000 0.000 0 1.000
#> GSM246485 1 0.482 0.360 0.612 0.000 0 0.388
#> GSM246486 2 0.156 0.941 0.000 0.944 0 0.056
#> GSM246487 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM246488 2 0.164 0.937 0.000 0.940 0 0.060
#> GSM246489 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM246490 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM246491 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM247162 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM247163 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM247164 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM247165 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM247166 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM247168 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM247169 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM247171 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM247173 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM247174 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM247175 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM247188 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM247189 4 0.331 0.776 0.000 0.172 0 0.828
#> GSM247190 2 0.000 0.993 0.000 1.000 0 0.000
#> GSM247650 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247651 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247652 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247653 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247654 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247655 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247656 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247657 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247658 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247659 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247660 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247661 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247662 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247663 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247856 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247857 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247859 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247860 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247862 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247864 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247865 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247866 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247876 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247877 4 0.000 0.956 0.000 0.000 0 1.000
#> GSM247878 4 0.000 0.956 0.000 0.000 0 1.000
#> GSM247879 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247881 1 0.000 0.985 1.000 0.000 0 0.000
#> GSM247883 1 0.000 0.985 1.000 0.000 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246088 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246089 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246090 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246119 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246120 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246121 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246122 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246123 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM246422 4 0.0000 0.821 0.000 0.000 0 1.000 0.000
#> GSM246423 4 0.0000 0.821 0.000 0.000 0 1.000 0.000
#> GSM246484 4 0.0000 0.821 0.000 0.000 0 1.000 0.000
#> GSM246485 1 0.5767 0.419 0.612 0.016 0 0.292 0.080
#> GSM246486 2 0.2233 0.902 0.000 0.904 0 0.016 0.080
#> GSM246487 1 0.1732 0.781 0.920 0.000 0 0.000 0.080
#> GSM246488 2 0.2331 0.898 0.000 0.900 0 0.020 0.080
#> GSM246489 2 0.0000 0.970 0.000 1.000 0 0.000 0.000
#> GSM246490 2 0.0000 0.970 0.000 1.000 0 0.000 0.000
#> GSM246491 2 0.0000 0.970 0.000 1.000 0 0.000 0.000
#> GSM247162 2 0.0000 0.970 0.000 1.000 0 0.000 0.000
#> GSM247163 2 0.0000 0.970 0.000 1.000 0 0.000 0.000
#> GSM247164 2 0.0000 0.970 0.000 1.000 0 0.000 0.000
#> GSM247165 2 0.0162 0.968 0.000 0.996 0 0.000 0.004
#> GSM247166 2 0.1043 0.961 0.000 0.960 0 0.000 0.040
#> GSM247168 2 0.0000 0.970 0.000 1.000 0 0.000 0.000
#> GSM247169 2 0.1410 0.954 0.000 0.940 0 0.000 0.060
#> GSM247171 2 0.0000 0.970 0.000 1.000 0 0.000 0.000
#> GSM247173 2 0.0290 0.969 0.000 0.992 0 0.000 0.008
#> GSM247174 2 0.1410 0.954 0.000 0.940 0 0.000 0.060
#> GSM247175 2 0.1410 0.954 0.000 0.940 0 0.000 0.060
#> GSM247188 2 0.1410 0.954 0.000 0.940 0 0.000 0.060
#> GSM247189 4 0.3438 0.673 0.000 0.172 0 0.808 0.020
#> GSM247190 2 0.1410 0.954 0.000 0.940 0 0.000 0.060
#> GSM247650 1 0.3452 0.610 0.756 0.000 0 0.000 0.244
#> GSM247651 1 0.3612 0.569 0.732 0.000 0 0.000 0.268
#> GSM247652 1 0.0000 0.861 1.000 0.000 0 0.000 0.000
#> GSM247653 5 0.3707 0.755 0.284 0.000 0 0.000 0.716
#> GSM247654 1 0.0290 0.857 0.992 0.000 0 0.000 0.008
#> GSM247655 1 0.3508 0.596 0.748 0.000 0 0.000 0.252
#> GSM247656 1 0.0000 0.861 1.000 0.000 0 0.000 0.000
#> GSM247657 1 0.0000 0.861 1.000 0.000 0 0.000 0.000
#> GSM247658 1 0.0162 0.859 0.996 0.000 0 0.000 0.004
#> GSM247659 1 0.0000 0.861 1.000 0.000 0 0.000 0.000
#> GSM247660 5 0.2561 0.808 0.144 0.000 0 0.000 0.856
#> GSM247661 5 0.4114 0.628 0.376 0.000 0 0.000 0.624
#> GSM247662 1 0.0000 0.861 1.000 0.000 0 0.000 0.000
#> GSM247663 1 0.4307 -0.180 0.504 0.000 0 0.000 0.496
#> GSM247856 1 0.0000 0.861 1.000 0.000 0 0.000 0.000
#> GSM247857 1 0.0000 0.861 1.000 0.000 0 0.000 0.000
#> GSM247859 1 0.0000 0.861 1.000 0.000 0 0.000 0.000
#> GSM247860 5 0.2561 0.809 0.144 0.000 0 0.000 0.856
#> GSM247862 5 0.2891 0.811 0.176 0.000 0 0.000 0.824
#> GSM247864 5 0.4210 0.429 0.412 0.000 0 0.000 0.588
#> GSM247865 1 0.0000 0.861 1.000 0.000 0 0.000 0.000
#> GSM247866 5 0.2516 0.806 0.140 0.000 0 0.000 0.860
#> GSM247876 1 0.0794 0.843 0.972 0.000 0 0.000 0.028
#> GSM247877 4 0.3612 0.657 0.000 0.000 0 0.732 0.268
#> GSM247878 4 0.3586 0.663 0.000 0.000 0 0.736 0.264
#> GSM247879 1 0.3452 0.609 0.756 0.000 0 0.000 0.244
#> GSM247881 1 0.0000 0.861 1.000 0.000 0 0.000 0.000
#> GSM247883 1 0.0000 0.861 1.000 0.000 0 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246088 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246089 3 0.3737 0.583 0.000 0.000 0.608 0.000 0.000 0.392
#> GSM246090 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246119 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246120 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246121 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246122 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246123 3 0.0000 0.958 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246422 4 0.0000 0.677 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM246423 4 0.0000 0.677 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM246484 4 0.0000 0.677 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM246485 6 0.6024 0.000 0.404 0.036 0.000 0.104 0.000 0.456
#> GSM246486 2 0.3847 0.311 0.000 0.544 0.000 0.000 0.000 0.456
#> GSM246487 1 0.3847 -0.690 0.544 0.000 0.000 0.000 0.000 0.456
#> GSM246488 2 0.3979 0.304 0.000 0.540 0.000 0.004 0.000 0.456
#> GSM246489 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246490 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246491 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247162 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247163 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247164 2 0.0146 0.902 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM247165 2 0.1204 0.870 0.000 0.944 0.000 0.000 0.000 0.056
#> GSM247166 2 0.1204 0.891 0.000 0.944 0.000 0.000 0.000 0.056
#> GSM247168 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247169 2 0.2003 0.870 0.000 0.884 0.000 0.000 0.000 0.116
#> GSM247171 2 0.0000 0.902 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247173 2 0.0458 0.900 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM247174 2 0.2003 0.870 0.000 0.884 0.000 0.000 0.000 0.116
#> GSM247175 2 0.2003 0.870 0.000 0.884 0.000 0.000 0.000 0.116
#> GSM247188 2 0.2003 0.870 0.000 0.884 0.000 0.000 0.000 0.116
#> GSM247189 4 0.5699 0.168 0.000 0.172 0.000 0.484 0.000 0.344
#> GSM247190 2 0.2003 0.870 0.000 0.884 0.000 0.000 0.000 0.116
#> GSM247650 1 0.3634 0.307 0.644 0.000 0.000 0.000 0.356 0.000
#> GSM247651 1 0.3717 0.261 0.616 0.000 0.000 0.000 0.384 0.000
#> GSM247652 1 0.0000 0.796 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247653 5 0.3134 0.637 0.144 0.000 0.000 0.000 0.820 0.036
#> GSM247654 1 0.0260 0.790 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM247655 1 0.3607 0.320 0.652 0.000 0.000 0.000 0.348 0.000
#> GSM247656 1 0.0000 0.796 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247657 1 0.0000 0.796 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247658 1 0.0146 0.793 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM247659 1 0.0000 0.796 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247660 5 0.0260 0.666 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM247661 5 0.4165 0.458 0.292 0.000 0.000 0.000 0.672 0.036
#> GSM247662 1 0.0000 0.796 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247663 5 0.3672 0.217 0.368 0.000 0.000 0.000 0.632 0.000
#> GSM247856 1 0.0000 0.796 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247857 1 0.0000 0.796 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247859 1 0.0000 0.796 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247860 5 0.1010 0.663 0.004 0.000 0.000 0.000 0.960 0.036
#> GSM247862 5 0.2092 0.673 0.124 0.000 0.000 0.000 0.876 0.000
#> GSM247864 5 0.3309 0.468 0.280 0.000 0.000 0.000 0.720 0.000
#> GSM247865 1 0.0146 0.793 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM247866 5 0.0146 0.663 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM247876 1 0.0937 0.755 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM247877 4 0.3756 0.378 0.000 0.000 0.000 0.600 0.400 0.000
#> GSM247878 4 0.3747 0.385 0.000 0.000 0.000 0.604 0.396 0.000
#> GSM247879 1 0.3578 0.331 0.660 0.000 0.000 0.000 0.340 0.000
#> GSM247881 1 0.0000 0.796 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247883 1 0.0000 0.796 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:pam 61 5.78e-10 2
#> ATC:pam 61 3.74e-21 3
#> ATC:pam 60 3.16e-21 4
#> ATC:pam 58 3.75e-19 5
#> ATC:pam 47 7.15e-17 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 21168 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.642 0.778 0.913 0.4559 0.552 0.552
#> 3 3 0.668 0.814 0.898 0.3735 0.727 0.537
#> 4 4 0.707 0.758 0.881 0.1159 0.946 0.851
#> 5 5 0.778 0.701 0.850 0.0991 0.938 0.808
#> 6 6 0.838 0.774 0.861 0.0271 0.936 0.759
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
#> GSM246087 1 0.0000 0.8845 1.000 0.000
#> GSM246088 1 0.0000 0.8845 1.000 0.000
#> GSM246089 1 0.0000 0.8845 1.000 0.000
#> GSM246090 1 0.0000 0.8845 1.000 0.000
#> GSM246119 1 0.0000 0.8845 1.000 0.000
#> GSM246120 1 0.0000 0.8845 1.000 0.000
#> GSM246121 1 0.0000 0.8845 1.000 0.000
#> GSM246122 1 0.0000 0.8845 1.000 0.000
#> GSM246123 1 0.0000 0.8845 1.000 0.000
#> GSM246422 1 0.9881 0.2957 0.564 0.436
#> GSM246423 1 0.9881 0.2957 0.564 0.436
#> GSM246484 1 0.9881 0.2957 0.564 0.436
#> GSM246485 1 0.9954 0.2339 0.540 0.460
#> GSM246486 2 0.5946 0.7660 0.144 0.856
#> GSM246487 2 0.9993 -0.0963 0.484 0.516
#> GSM246488 2 0.8144 0.5988 0.252 0.748
#> GSM246489 2 0.0000 0.9156 0.000 1.000
#> GSM246490 2 0.0000 0.9156 0.000 1.000
#> GSM246491 2 0.0000 0.9156 0.000 1.000
#> GSM247162 2 0.0000 0.9156 0.000 1.000
#> GSM247163 2 0.0000 0.9156 0.000 1.000
#> GSM247164 2 0.0000 0.9156 0.000 1.000
#> GSM247165 2 0.0000 0.9156 0.000 1.000
#> GSM247166 2 0.0000 0.9156 0.000 1.000
#> GSM247168 2 0.0000 0.9156 0.000 1.000
#> GSM247169 2 0.0000 0.9156 0.000 1.000
#> GSM247171 2 0.0000 0.9156 0.000 1.000
#> GSM247173 2 0.0000 0.9156 0.000 1.000
#> GSM247174 2 0.0000 0.9156 0.000 1.000
#> GSM247175 2 0.0000 0.9156 0.000 1.000
#> GSM247188 2 0.0000 0.9156 0.000 1.000
#> GSM247189 2 0.9909 0.0627 0.444 0.556
#> GSM247190 2 0.0000 0.9156 0.000 1.000
#> GSM247650 1 0.0376 0.8859 0.996 0.004
#> GSM247651 1 0.5842 0.7846 0.860 0.140
#> GSM247652 1 0.0376 0.8859 0.996 0.004
#> GSM247653 1 0.0376 0.8859 0.996 0.004
#> GSM247654 1 0.0376 0.8859 0.996 0.004
#> GSM247655 1 0.5842 0.7846 0.860 0.140
#> GSM247656 1 0.0376 0.8859 0.996 0.004
#> GSM247657 1 0.0376 0.8859 0.996 0.004
#> GSM247658 1 0.0376 0.8859 0.996 0.004
#> GSM247659 1 0.0376 0.8859 0.996 0.004
#> GSM247660 1 0.5842 0.7846 0.860 0.140
#> GSM247661 1 0.0376 0.8859 0.996 0.004
#> GSM247662 1 0.0376 0.8859 0.996 0.004
#> GSM247663 1 0.0376 0.8859 0.996 0.004
#> GSM247856 1 0.0376 0.8859 0.996 0.004
#> GSM247857 1 0.0376 0.8859 0.996 0.004
#> GSM247859 1 0.0376 0.8859 0.996 0.004
#> GSM247860 1 0.0376 0.8859 0.996 0.004
#> GSM247862 1 0.0376 0.8859 0.996 0.004
#> GSM247864 1 0.4298 0.8284 0.912 0.088
#> GSM247865 1 0.9896 0.2945 0.560 0.440
#> GSM247866 1 0.0376 0.8859 0.996 0.004
#> GSM247876 1 0.0376 0.8859 0.996 0.004
#> GSM247877 1 0.9522 0.4428 0.628 0.372
#> GSM247878 1 0.9522 0.4428 0.628 0.372
#> GSM247879 1 0.0376 0.8859 0.996 0.004
#> GSM247881 1 0.0376 0.8859 0.996 0.004
#> GSM247883 1 0.9896 0.2945 0.560 0.440
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.1529 0.776 0.040 0.000 0.960
#> GSM246088 3 0.1529 0.776 0.040 0.000 0.960
#> GSM246089 3 0.5016 0.723 0.240 0.000 0.760
#> GSM246090 3 0.1529 0.776 0.040 0.000 0.960
#> GSM246119 3 0.1529 0.776 0.040 0.000 0.960
#> GSM246120 3 0.1529 0.776 0.040 0.000 0.960
#> GSM246121 3 0.5621 0.682 0.308 0.000 0.692
#> GSM246122 3 0.1529 0.776 0.040 0.000 0.960
#> GSM246123 3 0.1529 0.776 0.040 0.000 0.960
#> GSM246422 3 0.6473 0.637 0.332 0.016 0.652
#> GSM246423 3 0.6473 0.637 0.332 0.016 0.652
#> GSM246484 3 0.6473 0.637 0.332 0.016 0.652
#> GSM246485 1 0.3686 0.766 0.860 0.140 0.000
#> GSM246486 2 0.6244 0.171 0.440 0.560 0.000
#> GSM246487 1 0.3267 0.794 0.884 0.116 0.000
#> GSM246488 1 0.6192 0.286 0.580 0.420 0.000
#> GSM246489 2 0.0000 0.965 0.000 1.000 0.000
#> GSM246490 2 0.0000 0.965 0.000 1.000 0.000
#> GSM246491 2 0.0000 0.965 0.000 1.000 0.000
#> GSM247162 2 0.0000 0.965 0.000 1.000 0.000
#> GSM247163 2 0.0000 0.965 0.000 1.000 0.000
#> GSM247164 2 0.0000 0.965 0.000 1.000 0.000
#> GSM247165 2 0.0000 0.965 0.000 1.000 0.000
#> GSM247166 2 0.0000 0.965 0.000 1.000 0.000
#> GSM247168 2 0.0000 0.965 0.000 1.000 0.000
#> GSM247169 2 0.0000 0.965 0.000 1.000 0.000
#> GSM247171 2 0.0000 0.965 0.000 1.000 0.000
#> GSM247173 2 0.0000 0.965 0.000 1.000 0.000
#> GSM247174 2 0.0000 0.965 0.000 1.000 0.000
#> GSM247175 2 0.0000 0.965 0.000 1.000 0.000
#> GSM247188 2 0.0000 0.965 0.000 1.000 0.000
#> GSM247189 3 0.9865 0.369 0.292 0.292 0.416
#> GSM247190 2 0.0000 0.965 0.000 1.000 0.000
#> GSM247650 1 0.2356 0.865 0.928 0.000 0.072
#> GSM247651 1 0.3752 0.833 0.856 0.000 0.144
#> GSM247652 1 0.0424 0.884 0.992 0.000 0.008
#> GSM247653 1 0.2261 0.874 0.932 0.000 0.068
#> GSM247654 1 0.0237 0.884 0.996 0.000 0.004
#> GSM247655 1 0.3686 0.836 0.860 0.000 0.140
#> GSM247656 1 0.0592 0.884 0.988 0.000 0.012
#> GSM247657 1 0.0237 0.884 0.996 0.000 0.004
#> GSM247658 1 0.0237 0.884 0.996 0.000 0.004
#> GSM247659 1 0.0000 0.884 1.000 0.000 0.000
#> GSM247660 1 0.3752 0.833 0.856 0.000 0.144
#> GSM247661 1 0.2959 0.862 0.900 0.000 0.100
#> GSM247662 1 0.0424 0.884 0.992 0.000 0.008
#> GSM247663 1 0.3752 0.832 0.856 0.000 0.144
#> GSM247856 1 0.0237 0.884 0.996 0.000 0.004
#> GSM247857 1 0.0000 0.884 1.000 0.000 0.000
#> GSM247859 1 0.0000 0.884 1.000 0.000 0.000
#> GSM247860 1 0.2066 0.875 0.940 0.000 0.060
#> GSM247862 1 0.3619 0.842 0.864 0.000 0.136
#> GSM247864 1 0.3752 0.833 0.856 0.000 0.144
#> GSM247865 1 0.2356 0.830 0.928 0.072 0.000
#> GSM247866 1 0.4062 0.816 0.836 0.000 0.164
#> GSM247876 1 0.1031 0.882 0.976 0.000 0.024
#> GSM247877 3 0.6180 0.635 0.332 0.008 0.660
#> GSM247878 3 0.6307 0.637 0.328 0.012 0.660
#> GSM247879 1 0.6026 0.226 0.624 0.000 0.376
#> GSM247881 1 0.0000 0.884 1.000 0.000 0.000
#> GSM247883 1 0.2356 0.830 0.928 0.072 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM246088 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM246089 3 0.3245 0.834 0.064 0.000 0.880 0.056
#> GSM246090 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM246119 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM246120 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM246121 3 0.2530 0.837 0.112 0.000 0.888 0.000
#> GSM246122 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM246123 3 0.0000 0.960 0.000 0.000 1.000 0.000
#> GSM246422 4 0.4462 0.832 0.064 0.132 0.000 0.804
#> GSM246423 4 0.4462 0.832 0.064 0.132 0.000 0.804
#> GSM246484 4 0.4462 0.832 0.064 0.132 0.000 0.804
#> GSM246485 1 0.6779 0.188 0.560 0.324 0.000 0.116
#> GSM246486 2 0.6704 0.253 0.264 0.600 0.000 0.136
#> GSM246487 1 0.6779 0.188 0.560 0.324 0.000 0.116
#> GSM246488 2 0.6794 0.212 0.280 0.584 0.000 0.136
#> GSM246489 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM246490 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM246491 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM247162 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM247163 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM247164 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM247165 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM247166 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM247168 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM247169 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM247171 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM247173 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM247174 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM247175 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM247188 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM247189 4 0.6784 0.441 0.368 0.104 0.000 0.528
#> GSM247190 2 0.0000 0.934 0.000 1.000 0.000 0.000
#> GSM247650 1 0.0000 0.761 1.000 0.000 0.000 0.000
#> GSM247651 1 0.4431 0.644 0.696 0.000 0.000 0.304
#> GSM247652 1 0.0000 0.761 1.000 0.000 0.000 0.000
#> GSM247653 1 0.4585 0.633 0.668 0.000 0.000 0.332
#> GSM247654 1 0.1211 0.759 0.960 0.000 0.000 0.040
#> GSM247655 1 0.4222 0.665 0.728 0.000 0.000 0.272
#> GSM247656 1 0.0188 0.760 0.996 0.000 0.000 0.004
#> GSM247657 1 0.1022 0.759 0.968 0.000 0.000 0.032
#> GSM247658 1 0.4250 0.665 0.724 0.000 0.000 0.276
#> GSM247659 1 0.0000 0.761 1.000 0.000 0.000 0.000
#> GSM247660 1 0.4431 0.644 0.696 0.000 0.000 0.304
#> GSM247661 1 0.4585 0.633 0.668 0.000 0.000 0.332
#> GSM247662 1 0.0188 0.760 0.996 0.000 0.000 0.004
#> GSM247663 1 0.1211 0.757 0.960 0.000 0.000 0.040
#> GSM247856 1 0.0000 0.761 1.000 0.000 0.000 0.000
#> GSM247857 1 0.0000 0.761 1.000 0.000 0.000 0.000
#> GSM247859 1 0.0000 0.761 1.000 0.000 0.000 0.000
#> GSM247860 1 0.4585 0.633 0.668 0.000 0.000 0.332
#> GSM247862 1 0.4585 0.633 0.668 0.000 0.000 0.332
#> GSM247864 1 0.4277 0.661 0.720 0.000 0.000 0.280
#> GSM247865 1 0.6299 0.252 0.600 0.320 0.000 0.080
#> GSM247866 1 0.4790 0.593 0.620 0.000 0.000 0.380
#> GSM247876 1 0.0000 0.761 1.000 0.000 0.000 0.000
#> GSM247877 4 0.1716 0.787 0.064 0.000 0.000 0.936
#> GSM247878 4 0.1716 0.787 0.064 0.000 0.000 0.936
#> GSM247879 1 0.2281 0.743 0.904 0.000 0.000 0.096
#> GSM247881 1 0.0000 0.761 1.000 0.000 0.000 0.000
#> GSM247883 1 0.5936 0.286 0.620 0.324 0.000 0.056
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0000 0.9859 0.000 0.000 1.000 0.000 0.000
#> GSM246088 3 0.0000 0.9859 0.000 0.000 1.000 0.000 0.000
#> GSM246089 3 0.1270 0.9514 0.000 0.000 0.948 0.000 0.052
#> GSM246090 3 0.0000 0.9859 0.000 0.000 1.000 0.000 0.000
#> GSM246119 3 0.0000 0.9859 0.000 0.000 1.000 0.000 0.000
#> GSM246120 3 0.0000 0.9859 0.000 0.000 1.000 0.000 0.000
#> GSM246121 3 0.1818 0.9397 0.024 0.000 0.932 0.000 0.044
#> GSM246122 3 0.0000 0.9859 0.000 0.000 1.000 0.000 0.000
#> GSM246123 3 0.0000 0.9859 0.000 0.000 1.000 0.000 0.000
#> GSM246422 4 0.0000 0.8388 0.000 0.000 0.000 1.000 0.000
#> GSM246423 4 0.0000 0.8388 0.000 0.000 0.000 1.000 0.000
#> GSM246484 4 0.0000 0.8388 0.000 0.000 0.000 1.000 0.000
#> GSM246485 5 0.5960 0.3953 0.264 0.004 0.000 0.140 0.592
#> GSM246486 5 0.6186 0.3247 0.016 0.224 0.000 0.156 0.604
#> GSM246487 5 0.6177 0.3232 0.400 0.000 0.000 0.136 0.464
#> GSM246488 5 0.6214 0.3120 0.016 0.172 0.000 0.208 0.604
#> GSM246489 2 0.0000 0.9976 0.000 1.000 0.000 0.000 0.000
#> GSM246490 2 0.0000 0.9976 0.000 1.000 0.000 0.000 0.000
#> GSM246491 2 0.0000 0.9976 0.000 1.000 0.000 0.000 0.000
#> GSM247162 2 0.0000 0.9976 0.000 1.000 0.000 0.000 0.000
#> GSM247163 2 0.0000 0.9976 0.000 1.000 0.000 0.000 0.000
#> GSM247164 2 0.0404 0.9864 0.000 0.988 0.000 0.012 0.000
#> GSM247165 2 0.0609 0.9776 0.000 0.980 0.000 0.020 0.000
#> GSM247166 2 0.0000 0.9976 0.000 1.000 0.000 0.000 0.000
#> GSM247168 2 0.0000 0.9976 0.000 1.000 0.000 0.000 0.000
#> GSM247169 2 0.0000 0.9976 0.000 1.000 0.000 0.000 0.000
#> GSM247171 2 0.0000 0.9976 0.000 1.000 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.9976 0.000 1.000 0.000 0.000 0.000
#> GSM247174 2 0.0000 0.9976 0.000 1.000 0.000 0.000 0.000
#> GSM247175 2 0.0000 0.9976 0.000 1.000 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.9976 0.000 1.000 0.000 0.000 0.000
#> GSM247189 4 0.6821 -0.0806 0.168 0.020 0.000 0.476 0.336
#> GSM247190 2 0.0000 0.9976 0.000 1.000 0.000 0.000 0.000
#> GSM247650 1 0.1608 0.6555 0.928 0.000 0.000 0.000 0.072
#> GSM247651 1 0.6495 0.2683 0.424 0.000 0.000 0.188 0.388
#> GSM247652 1 0.0000 0.6670 1.000 0.000 0.000 0.000 0.000
#> GSM247653 1 0.4161 0.5241 0.608 0.000 0.000 0.000 0.392
#> GSM247654 1 0.3109 0.6253 0.800 0.000 0.000 0.000 0.200
#> GSM247655 1 0.6475 0.2727 0.428 0.000 0.000 0.184 0.388
#> GSM247656 1 0.0404 0.6694 0.988 0.000 0.000 0.000 0.012
#> GSM247657 1 0.3074 0.6266 0.804 0.000 0.000 0.000 0.196
#> GSM247658 1 0.5421 0.5396 0.628 0.000 0.000 0.096 0.276
#> GSM247659 1 0.0290 0.6673 0.992 0.000 0.000 0.000 0.008
#> GSM247660 1 0.6436 0.2740 0.428 0.000 0.000 0.176 0.396
#> GSM247661 1 0.4182 0.5243 0.600 0.000 0.000 0.000 0.400
#> GSM247662 1 0.0290 0.6691 0.992 0.000 0.000 0.000 0.008
#> GSM247663 1 0.3561 0.4941 0.740 0.000 0.000 0.000 0.260
#> GSM247856 1 0.0703 0.6693 0.976 0.000 0.000 0.000 0.024
#> GSM247857 1 0.0162 0.6676 0.996 0.000 0.000 0.000 0.004
#> GSM247859 1 0.0000 0.6670 1.000 0.000 0.000 0.000 0.000
#> GSM247860 1 0.4182 0.5243 0.600 0.000 0.000 0.000 0.400
#> GSM247862 1 0.4905 0.4566 0.500 0.000 0.000 0.024 0.476
#> GSM247864 1 0.6475 0.2777 0.428 0.000 0.000 0.184 0.388
#> GSM247865 1 0.4907 0.2260 0.656 0.000 0.000 0.052 0.292
#> GSM247866 5 0.4613 -0.3862 0.360 0.000 0.000 0.020 0.620
#> GSM247876 1 0.2127 0.6335 0.892 0.000 0.000 0.000 0.108
#> GSM247877 4 0.1670 0.8104 0.012 0.000 0.000 0.936 0.052
#> GSM247878 4 0.1430 0.8158 0.004 0.000 0.000 0.944 0.052
#> GSM247879 1 0.4333 0.6130 0.740 0.000 0.000 0.048 0.212
#> GSM247881 1 0.0162 0.6676 0.996 0.000 0.000 0.000 0.004
#> GSM247883 1 0.4030 0.1359 0.648 0.000 0.000 0.000 0.352
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246088 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246089 3 0.5336 0.584 0.000 0.000 0.592 0.180 0.000 0.228
#> GSM246090 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246119 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246120 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246121 3 0.1152 0.917 0.004 0.000 0.952 0.000 0.000 0.044
#> GSM246122 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246123 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246422 5 0.2454 0.835 0.000 0.000 0.000 0.160 0.840 0.000
#> GSM246423 5 0.2454 0.835 0.000 0.000 0.000 0.160 0.840 0.000
#> GSM246484 5 0.2454 0.835 0.000 0.000 0.000 0.160 0.840 0.000
#> GSM246485 4 0.3592 0.751 0.020 0.000 0.000 0.740 0.000 0.240
#> GSM246486 4 0.3420 0.759 0.000 0.012 0.000 0.748 0.000 0.240
#> GSM246487 4 0.3151 0.493 0.252 0.000 0.000 0.748 0.000 0.000
#> GSM246488 4 0.3420 0.759 0.000 0.012 0.000 0.748 0.000 0.240
#> GSM246489 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246490 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246491 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247162 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247163 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247164 2 0.0146 0.991 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM247165 2 0.1610 0.907 0.000 0.916 0.000 0.084 0.000 0.000
#> GSM247166 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247168 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247169 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247171 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247173 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247174 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247175 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247189 4 0.3330 0.393 0.000 0.000 0.000 0.716 0.284 0.000
#> GSM247190 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247650 1 0.1720 0.763 0.928 0.000 0.000 0.040 0.000 0.032
#> GSM247651 6 0.6528 0.766 0.316 0.000 0.000 0.052 0.164 0.468
#> GSM247652 1 0.0000 0.779 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247653 1 0.3706 0.335 0.620 0.000 0.000 0.000 0.000 0.380
#> GSM247654 1 0.1700 0.743 0.916 0.000 0.000 0.000 0.004 0.080
#> GSM247655 6 0.6732 0.761 0.328 0.000 0.000 0.068 0.164 0.440
#> GSM247656 1 0.1168 0.776 0.956 0.000 0.000 0.016 0.000 0.028
#> GSM247657 1 0.1806 0.741 0.908 0.000 0.000 0.000 0.004 0.088
#> GSM247658 1 0.1858 0.735 0.904 0.000 0.000 0.000 0.004 0.092
#> GSM247659 1 0.1296 0.776 0.952 0.000 0.000 0.012 0.004 0.032
#> GSM247660 6 0.6584 0.765 0.320 0.000 0.000 0.056 0.164 0.460
#> GSM247661 1 0.4310 0.300 0.580 0.000 0.000 0.024 0.000 0.396
#> GSM247662 1 0.0000 0.779 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247663 1 0.4602 -0.290 0.572 0.000 0.000 0.044 0.000 0.384
#> GSM247856 1 0.1390 0.775 0.948 0.000 0.000 0.016 0.004 0.032
#> GSM247857 1 0.0000 0.779 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM247859 1 0.0777 0.770 0.972 0.000 0.000 0.024 0.000 0.004
#> GSM247860 1 0.3727 0.326 0.612 0.000 0.000 0.000 0.000 0.388
#> GSM247862 6 0.4617 0.124 0.444 0.000 0.000 0.024 0.008 0.524
#> GSM247864 6 0.6362 0.761 0.312 0.000 0.000 0.040 0.164 0.484
#> GSM247865 1 0.2994 0.572 0.788 0.000 0.000 0.208 0.000 0.004
#> GSM247866 6 0.3352 0.529 0.172 0.000 0.000 0.012 0.016 0.800
#> GSM247876 1 0.0935 0.778 0.964 0.000 0.000 0.004 0.000 0.032
#> GSM247877 5 0.2240 0.733 0.032 0.000 0.000 0.016 0.908 0.044
#> GSM247878 5 0.1549 0.765 0.000 0.000 0.000 0.020 0.936 0.044
#> GSM247879 1 0.2776 0.705 0.860 0.000 0.000 0.032 0.004 0.104
#> GSM247881 1 0.0405 0.776 0.988 0.000 0.000 0.008 0.000 0.004
#> GSM247883 1 0.3383 0.468 0.728 0.000 0.000 0.268 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:mclust 51 8.42e-12 2
#> ATC:mclust 57 2.32e-15 3
#> ATC:mclust 54 9.16e-20 4
#> ATC:mclust 47 7.65e-17 5
#> ATC:mclust 53 4.93e-17 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 21168 rows and 61 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.961 0.986 0.4914 0.508 0.508
#> 3 3 0.869 0.865 0.947 0.3342 0.751 0.549
#> 4 4 0.675 0.653 0.825 0.1239 0.797 0.489
#> 5 5 0.763 0.701 0.858 0.0554 0.954 0.820
#> 6 6 0.745 0.583 0.799 0.0306 0.975 0.889
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
#> GSM246087 1 0.0000 0.989 1.000 0.000
#> GSM246088 1 0.0000 0.989 1.000 0.000
#> GSM246089 1 0.0000 0.989 1.000 0.000
#> GSM246090 1 0.0000 0.989 1.000 0.000
#> GSM246119 1 0.0000 0.989 1.000 0.000
#> GSM246120 1 0.0000 0.989 1.000 0.000
#> GSM246121 1 0.0000 0.989 1.000 0.000
#> GSM246122 1 0.0000 0.989 1.000 0.000
#> GSM246123 1 0.0000 0.989 1.000 0.000
#> GSM246422 2 0.0000 0.980 0.000 1.000
#> GSM246423 2 0.0672 0.973 0.008 0.992
#> GSM246484 2 0.0000 0.980 0.000 1.000
#> GSM246485 2 0.0000 0.980 0.000 1.000
#> GSM246486 2 0.0000 0.980 0.000 1.000
#> GSM246487 2 0.0000 0.980 0.000 1.000
#> GSM246488 2 0.0000 0.980 0.000 1.000
#> GSM246489 2 0.0000 0.980 0.000 1.000
#> GSM246490 2 0.0000 0.980 0.000 1.000
#> GSM246491 2 0.0000 0.980 0.000 1.000
#> GSM247162 2 0.0000 0.980 0.000 1.000
#> GSM247163 2 0.0000 0.980 0.000 1.000
#> GSM247164 2 0.0000 0.980 0.000 1.000
#> GSM247165 2 0.0000 0.980 0.000 1.000
#> GSM247166 2 0.0000 0.980 0.000 1.000
#> GSM247168 2 0.0000 0.980 0.000 1.000
#> GSM247169 2 0.0000 0.980 0.000 1.000
#> GSM247171 2 0.0000 0.980 0.000 1.000
#> GSM247173 2 0.0000 0.980 0.000 1.000
#> GSM247174 2 0.0000 0.980 0.000 1.000
#> GSM247175 2 0.0000 0.980 0.000 1.000
#> GSM247188 2 0.0000 0.980 0.000 1.000
#> GSM247189 2 0.0000 0.980 0.000 1.000
#> GSM247190 2 0.0000 0.980 0.000 1.000
#> GSM247650 1 0.0000 0.989 1.000 0.000
#> GSM247651 1 0.0000 0.989 1.000 0.000
#> GSM247652 1 0.0000 0.989 1.000 0.000
#> GSM247653 1 0.0000 0.989 1.000 0.000
#> GSM247654 1 0.0000 0.989 1.000 0.000
#> GSM247655 1 0.0000 0.989 1.000 0.000
#> GSM247656 1 0.0000 0.989 1.000 0.000
#> GSM247657 1 0.0000 0.989 1.000 0.000
#> GSM247658 1 0.0000 0.989 1.000 0.000
#> GSM247659 1 0.0000 0.989 1.000 0.000
#> GSM247660 1 0.0000 0.989 1.000 0.000
#> GSM247661 1 0.0000 0.989 1.000 0.000
#> GSM247662 1 0.0000 0.989 1.000 0.000
#> GSM247663 1 0.0000 0.989 1.000 0.000
#> GSM247856 1 0.0000 0.989 1.000 0.000
#> GSM247857 1 0.0000 0.989 1.000 0.000
#> GSM247859 1 0.0000 0.989 1.000 0.000
#> GSM247860 1 0.0000 0.989 1.000 0.000
#> GSM247862 1 0.0000 0.989 1.000 0.000
#> GSM247864 1 0.0000 0.989 1.000 0.000
#> GSM247865 1 0.9635 0.342 0.612 0.388
#> GSM247866 1 0.0000 0.989 1.000 0.000
#> GSM247876 1 0.0000 0.989 1.000 0.000
#> GSM247877 1 0.0000 0.989 1.000 0.000
#> GSM247878 1 0.0000 0.989 1.000 0.000
#> GSM247879 1 0.0000 0.989 1.000 0.000
#> GSM247881 1 0.0000 0.989 1.000 0.000
#> GSM247883 2 0.9922 0.168 0.448 0.552
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM246087 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM246088 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM246089 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM246090 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM246119 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM246120 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM246121 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM246122 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM246123 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM246422 1 0.0000 0.9238 1.000 0.000 0.000
#> GSM246423 1 0.0000 0.9238 1.000 0.000 0.000
#> GSM246484 1 0.0000 0.9238 1.000 0.000 0.000
#> GSM246485 1 0.0000 0.9238 1.000 0.000 0.000
#> GSM246486 2 0.0747 0.9587 0.016 0.984 0.000
#> GSM246487 2 0.6095 0.2811 0.392 0.608 0.000
#> GSM246488 1 0.5968 0.4158 0.636 0.364 0.000
#> GSM246489 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM246490 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM246491 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM247162 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM247163 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM247164 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM247165 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM247166 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM247168 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM247169 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM247171 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM247173 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM247174 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM247175 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM247188 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM247189 1 0.0424 0.9182 0.992 0.008 0.000
#> GSM247190 2 0.0000 0.9736 0.000 1.000 0.000
#> GSM247650 3 0.0237 0.9222 0.004 0.000 0.996
#> GSM247651 1 0.0000 0.9238 1.000 0.000 0.000
#> GSM247652 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM247653 3 0.0424 0.9198 0.008 0.000 0.992
#> GSM247654 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM247655 1 0.0000 0.9238 1.000 0.000 0.000
#> GSM247656 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM247657 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM247658 3 0.4702 0.7136 0.212 0.000 0.788
#> GSM247659 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM247660 1 0.0000 0.9238 1.000 0.000 0.000
#> GSM247661 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM247662 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM247663 3 0.6274 0.1795 0.456 0.000 0.544
#> GSM247856 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM247857 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM247859 3 0.5431 0.6039 0.284 0.000 0.716
#> GSM247860 3 0.5591 0.5676 0.304 0.000 0.696
#> GSM247862 1 0.4887 0.6680 0.772 0.000 0.228
#> GSM247864 1 0.0237 0.9219 0.996 0.000 0.004
#> GSM247865 1 0.7529 0.4529 0.624 0.060 0.316
#> GSM247866 1 0.0237 0.9219 0.996 0.000 0.004
#> GSM247876 3 0.1031 0.9086 0.024 0.000 0.976
#> GSM247877 1 0.0000 0.9238 1.000 0.000 0.000
#> GSM247878 1 0.0000 0.9238 1.000 0.000 0.000
#> GSM247879 3 0.2537 0.8620 0.080 0.000 0.920
#> GSM247881 3 0.0000 0.9244 0.000 0.000 1.000
#> GSM247883 3 0.6952 0.0931 0.016 0.480 0.504
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM246087 3 0.0188 0.7711 0.004 0.000 0.996 0.000
#> GSM246088 3 0.0188 0.7711 0.004 0.000 0.996 0.000
#> GSM246089 3 0.3831 0.6097 0.204 0.000 0.792 0.004
#> GSM246090 3 0.0188 0.7711 0.004 0.000 0.996 0.000
#> GSM246119 3 0.0707 0.7653 0.020 0.000 0.980 0.000
#> GSM246120 3 0.0336 0.7695 0.008 0.000 0.992 0.000
#> GSM246121 3 0.1637 0.7456 0.060 0.000 0.940 0.000
#> GSM246122 3 0.0336 0.7704 0.008 0.000 0.992 0.000
#> GSM246123 3 0.0188 0.7702 0.004 0.000 0.996 0.000
#> GSM246422 4 0.0000 0.7754 0.000 0.000 0.000 1.000
#> GSM246423 4 0.0188 0.7752 0.004 0.000 0.000 0.996
#> GSM246484 4 0.0000 0.7754 0.000 0.000 0.000 1.000
#> GSM246485 4 0.1637 0.7599 0.060 0.000 0.000 0.940
#> GSM246486 2 0.1406 0.9231 0.016 0.960 0.000 0.024
#> GSM246487 1 0.7641 0.2383 0.500 0.264 0.004 0.232
#> GSM246488 4 0.5592 0.2777 0.024 0.404 0.000 0.572
#> GSM246489 2 0.0188 0.9552 0.004 0.996 0.000 0.000
#> GSM246490 2 0.0000 0.9577 0.000 1.000 0.000 0.000
#> GSM246491 2 0.0000 0.9577 0.000 1.000 0.000 0.000
#> GSM247162 2 0.0000 0.9577 0.000 1.000 0.000 0.000
#> GSM247163 2 0.0000 0.9577 0.000 1.000 0.000 0.000
#> GSM247164 2 0.0000 0.9577 0.000 1.000 0.000 0.000
#> GSM247165 2 0.0000 0.9577 0.000 1.000 0.000 0.000
#> GSM247166 2 0.0000 0.9577 0.000 1.000 0.000 0.000
#> GSM247168 2 0.0000 0.9577 0.000 1.000 0.000 0.000
#> GSM247169 2 0.0000 0.9577 0.000 1.000 0.000 0.000
#> GSM247171 2 0.0000 0.9577 0.000 1.000 0.000 0.000
#> GSM247173 2 0.0188 0.9553 0.004 0.996 0.000 0.000
#> GSM247174 2 0.0000 0.9577 0.000 1.000 0.000 0.000
#> GSM247175 2 0.0000 0.9577 0.000 1.000 0.000 0.000
#> GSM247188 2 0.0000 0.9577 0.000 1.000 0.000 0.000
#> GSM247189 4 0.1576 0.7552 0.004 0.048 0.000 0.948
#> GSM247190 2 0.0188 0.9553 0.004 0.996 0.000 0.000
#> GSM247650 3 0.3908 0.6089 0.212 0.000 0.784 0.004
#> GSM247651 4 0.4049 0.5753 0.212 0.000 0.008 0.780
#> GSM247652 1 0.4967 0.2916 0.548 0.000 0.452 0.000
#> GSM247653 1 0.2868 0.6321 0.864 0.000 0.136 0.000
#> GSM247654 1 0.4222 0.6063 0.728 0.000 0.272 0.000
#> GSM247655 1 0.5203 0.3021 0.576 0.000 0.008 0.416
#> GSM247656 3 0.3907 0.5793 0.232 0.000 0.768 0.000
#> GSM247657 1 0.4250 0.6029 0.724 0.000 0.276 0.000
#> GSM247658 1 0.5174 0.6742 0.756 0.000 0.152 0.092
#> GSM247659 3 0.4877 0.1369 0.408 0.000 0.592 0.000
#> GSM247660 1 0.4925 0.2144 0.572 0.000 0.000 0.428
#> GSM247661 1 0.3219 0.6077 0.836 0.000 0.164 0.000
#> GSM247662 3 0.4972 -0.0611 0.456 0.000 0.544 0.000
#> GSM247663 4 0.7646 0.0581 0.244 0.000 0.292 0.464
#> GSM247856 3 0.2704 0.7075 0.124 0.000 0.876 0.000
#> GSM247857 1 0.4866 0.3977 0.596 0.000 0.404 0.000
#> GSM247859 1 0.5747 0.6582 0.704 0.000 0.196 0.100
#> GSM247860 1 0.2859 0.6185 0.880 0.000 0.112 0.008
#> GSM247862 1 0.4776 0.6434 0.776 0.000 0.060 0.164
#> GSM247864 4 0.5403 0.3028 0.348 0.000 0.024 0.628
#> GSM247865 1 0.5934 0.6120 0.704 0.012 0.076 0.208
#> GSM247866 1 0.4482 0.3502 0.728 0.000 0.008 0.264
#> GSM247876 3 0.6147 0.4875 0.224 0.000 0.664 0.112
#> GSM247877 4 0.3257 0.6926 0.152 0.000 0.004 0.844
#> GSM247878 4 0.0592 0.7736 0.016 0.000 0.000 0.984
#> GSM247879 3 0.6795 0.1749 0.432 0.000 0.472 0.096
#> GSM247881 1 0.4761 0.4721 0.628 0.000 0.372 0.000
#> GSM247883 2 0.7517 -0.2559 0.388 0.428 0.184 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM246087 3 0.0671 0.8279 0.016 0.000 0.980 0.000 0.004
#> GSM246088 3 0.0566 0.8270 0.012 0.000 0.984 0.000 0.004
#> GSM246089 5 0.4015 0.3990 0.000 0.000 0.348 0.000 0.652
#> GSM246090 3 0.0671 0.8275 0.016 0.000 0.980 0.000 0.004
#> GSM246119 3 0.1670 0.7945 0.012 0.000 0.936 0.000 0.052
#> GSM246120 3 0.0865 0.8139 0.004 0.000 0.972 0.000 0.024
#> GSM246121 3 0.2723 0.7211 0.012 0.000 0.864 0.000 0.124
#> GSM246122 3 0.0898 0.8280 0.020 0.000 0.972 0.000 0.008
#> GSM246123 3 0.0671 0.8186 0.004 0.000 0.980 0.000 0.016
#> GSM246422 4 0.0000 0.7549 0.000 0.000 0.000 1.000 0.000
#> GSM246423 4 0.0609 0.7531 0.000 0.000 0.000 0.980 0.020
#> GSM246484 4 0.0290 0.7541 0.000 0.000 0.000 0.992 0.008
#> GSM246485 4 0.1670 0.7423 0.012 0.000 0.000 0.936 0.052
#> GSM246486 2 0.1082 0.9297 0.000 0.964 0.000 0.028 0.008
#> GSM246487 1 0.6646 0.4096 0.608 0.216 0.004 0.112 0.060
#> GSM246488 4 0.3978 0.6210 0.004 0.148 0.000 0.796 0.052
#> GSM246489 2 0.0000 0.9620 0.000 1.000 0.000 0.000 0.000
#> GSM246490 2 0.0000 0.9620 0.000 1.000 0.000 0.000 0.000
#> GSM246491 2 0.0000 0.9620 0.000 1.000 0.000 0.000 0.000
#> GSM247162 2 0.0000 0.9620 0.000 1.000 0.000 0.000 0.000
#> GSM247163 2 0.0000 0.9620 0.000 1.000 0.000 0.000 0.000
#> GSM247164 2 0.0000 0.9620 0.000 1.000 0.000 0.000 0.000
#> GSM247165 2 0.0000 0.9620 0.000 1.000 0.000 0.000 0.000
#> GSM247166 2 0.0000 0.9620 0.000 1.000 0.000 0.000 0.000
#> GSM247168 2 0.0000 0.9620 0.000 1.000 0.000 0.000 0.000
#> GSM247169 2 0.0000 0.9620 0.000 1.000 0.000 0.000 0.000
#> GSM247171 2 0.0000 0.9620 0.000 1.000 0.000 0.000 0.000
#> GSM247173 2 0.0162 0.9593 0.000 0.996 0.000 0.000 0.004
#> GSM247174 2 0.0000 0.9620 0.000 1.000 0.000 0.000 0.000
#> GSM247175 2 0.0000 0.9620 0.000 1.000 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.9620 0.000 1.000 0.000 0.000 0.000
#> GSM247189 4 0.2142 0.7365 0.004 0.028 0.000 0.920 0.048
#> GSM247190 2 0.0290 0.9563 0.000 0.992 0.000 0.000 0.008
#> GSM247650 3 0.2930 0.7650 0.164 0.000 0.832 0.000 0.004
#> GSM247651 4 0.5002 0.2885 0.364 0.000 0.000 0.596 0.040
#> GSM247652 1 0.3861 0.5627 0.728 0.000 0.264 0.000 0.008
#> GSM247653 1 0.3741 0.4869 0.732 0.000 0.004 0.000 0.264
#> GSM247654 1 0.1740 0.7224 0.932 0.000 0.056 0.000 0.012
#> GSM247655 1 0.2522 0.6965 0.880 0.000 0.000 0.108 0.012
#> GSM247656 3 0.2583 0.7880 0.132 0.000 0.864 0.000 0.004
#> GSM247657 1 0.1638 0.7218 0.932 0.000 0.064 0.000 0.004
#> GSM247658 1 0.2144 0.7001 0.912 0.000 0.020 0.000 0.068
#> GSM247659 3 0.4238 0.4850 0.368 0.000 0.628 0.000 0.004
#> GSM247660 1 0.3412 0.6457 0.820 0.000 0.000 0.152 0.028
#> GSM247661 1 0.4663 0.2203 0.604 0.000 0.020 0.000 0.376
#> GSM247662 3 0.5013 0.4714 0.352 0.000 0.612 0.008 0.028
#> GSM247663 4 0.7951 0.0331 0.292 0.000 0.260 0.368 0.080
#> GSM247856 3 0.2249 0.8098 0.096 0.000 0.896 0.000 0.008
#> GSM247857 1 0.4043 0.6088 0.756 0.000 0.220 0.012 0.012
#> GSM247859 1 0.1990 0.7204 0.920 0.000 0.068 0.008 0.004
#> GSM247860 5 0.4356 0.4909 0.340 0.000 0.012 0.000 0.648
#> GSM247862 1 0.2629 0.6729 0.880 0.000 0.004 0.012 0.104
#> GSM247864 1 0.5377 0.0370 0.496 0.000 0.004 0.456 0.044
#> GSM247865 1 0.4432 0.6769 0.820 0.040 0.028 0.064 0.048
#> GSM247866 5 0.4244 0.5837 0.268 0.000 0.004 0.016 0.712
#> GSM247876 3 0.6451 0.4551 0.212 0.000 0.612 0.048 0.128
#> GSM247877 4 0.4291 0.2029 0.000 0.000 0.000 0.536 0.464
#> GSM247878 4 0.1571 0.7414 0.004 0.000 0.000 0.936 0.060
#> GSM247879 5 0.3361 0.5935 0.020 0.000 0.092 0.032 0.856
#> GSM247881 1 0.2674 0.6877 0.856 0.000 0.140 0.000 0.004
#> GSM247883 2 0.6447 -0.0629 0.420 0.472 0.080 0.008 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM246087 3 0.1152 0.7233 0.004 0.000 0.952 0.000 0.044 0.000
#> GSM246088 3 0.0000 0.7323 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM246089 6 0.4084 0.0928 0.000 0.000 0.400 0.000 0.012 0.588
#> GSM246090 3 0.0260 0.7330 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM246119 3 0.0972 0.7145 0.000 0.000 0.964 0.000 0.008 0.028
#> GSM246120 3 0.0260 0.7295 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM246121 3 0.3351 0.5886 0.004 0.000 0.808 0.000 0.036 0.152
#> GSM246122 3 0.0692 0.7325 0.004 0.000 0.976 0.000 0.020 0.000
#> GSM246123 3 0.0858 0.7306 0.000 0.000 0.968 0.000 0.028 0.004
#> GSM246422 4 0.0000 0.7693 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM246423 4 0.0146 0.7687 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM246484 4 0.0146 0.7695 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM246485 4 0.6525 0.4493 0.104 0.036 0.000 0.556 0.260 0.044
#> GSM246486 2 0.1196 0.9195 0.000 0.952 0.000 0.040 0.008 0.000
#> GSM246487 1 0.7322 0.1080 0.464 0.196 0.000 0.124 0.204 0.012
#> GSM246488 4 0.2804 0.6752 0.000 0.120 0.000 0.852 0.024 0.004
#> GSM246489 2 0.0260 0.9536 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM246490 2 0.0000 0.9547 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM246491 2 0.0260 0.9530 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM247162 2 0.0260 0.9530 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM247163 2 0.0146 0.9539 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM247164 2 0.0000 0.9547 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247165 2 0.0458 0.9512 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM247166 2 0.0547 0.9493 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM247168 2 0.0547 0.9493 0.000 0.980 0.000 0.000 0.020 0.000
#> GSM247169 2 0.0458 0.9512 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM247171 2 0.0405 0.9509 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM247173 2 0.0000 0.9547 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247174 2 0.0146 0.9544 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM247175 2 0.0000 0.9547 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247188 2 0.0000 0.9547 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM247189 4 0.2119 0.7529 0.000 0.008 0.000 0.912 0.044 0.036
#> GSM247190 2 0.0146 0.9541 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM247650 3 0.5117 0.3223 0.116 0.000 0.596 0.000 0.288 0.000
#> GSM247651 4 0.5646 0.1993 0.348 0.000 0.000 0.532 0.100 0.020
#> GSM247652 1 0.4369 0.3783 0.720 0.000 0.116 0.000 0.164 0.000
#> GSM247653 1 0.4312 -0.0327 0.604 0.000 0.000 0.000 0.028 0.368
#> GSM247654 1 0.1341 0.6003 0.948 0.000 0.024 0.000 0.028 0.000
#> GSM247655 1 0.3907 0.5211 0.764 0.000 0.000 0.152 0.084 0.000
#> GSM247656 3 0.4327 0.4694 0.056 0.000 0.680 0.000 0.264 0.000
#> GSM247657 1 0.2011 0.6057 0.912 0.000 0.020 0.000 0.064 0.004
#> GSM247658 1 0.1485 0.6033 0.944 0.000 0.004 0.000 0.024 0.028
#> GSM247659 3 0.5817 0.0320 0.208 0.000 0.480 0.000 0.312 0.000
#> GSM247660 1 0.3233 0.5714 0.828 0.000 0.000 0.132 0.024 0.016
#> GSM247661 1 0.4700 -0.3002 0.500 0.000 0.000 0.000 0.044 0.456
#> GSM247662 3 0.6103 -0.0883 0.320 0.000 0.432 0.004 0.244 0.000
#> GSM247663 5 0.8177 0.4749 0.172 0.000 0.272 0.144 0.356 0.056
#> GSM247856 3 0.4176 0.5328 0.200 0.000 0.740 0.000 0.044 0.016
#> GSM247857 1 0.5044 0.2674 0.644 0.000 0.128 0.004 0.224 0.000
#> GSM247859 1 0.3702 0.4852 0.784 0.000 0.044 0.008 0.164 0.000
#> GSM247860 6 0.3937 0.2553 0.424 0.000 0.000 0.000 0.004 0.572
#> GSM247862 1 0.2112 0.5491 0.896 0.000 0.000 0.000 0.016 0.088
#> GSM247864 1 0.4661 0.0561 0.500 0.000 0.000 0.464 0.004 0.032
#> GSM247865 1 0.5531 0.4518 0.660 0.016 0.000 0.064 0.212 0.048
#> GSM247866 6 0.4157 0.4367 0.276 0.000 0.000 0.004 0.032 0.688
#> GSM247876 5 0.6174 0.5306 0.160 0.000 0.224 0.008 0.572 0.036
#> GSM247877 4 0.5303 0.4249 0.000 0.000 0.000 0.548 0.120 0.332
#> GSM247878 4 0.1934 0.7518 0.000 0.000 0.000 0.916 0.044 0.040
#> GSM247879 5 0.7599 0.1864 0.092 0.000 0.112 0.056 0.380 0.360
#> GSM247881 5 0.5428 0.2468 0.396 0.000 0.120 0.000 0.484 0.000
#> GSM247883 2 0.6913 -0.2032 0.272 0.420 0.064 0.000 0.244 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) k
#> ATC:NMF 59 1.54e-13 2
#> ATC:NMF 56 1.21e-09 3
#> ATC:NMF 46 7.13e-12 4
#> ATC:NMF 48 1.53e-12 5
#> ATC:NMF 39 5.47e-11 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