Date: 2019-12-25 22:15:56 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 11993 rows and 57 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] 11993 57
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 | 2 | 1.000 | 0.975 | 0.982 | ** | |
| SD:skmeans | 3 | 1.000 | 0.989 | 0.995 | ** | 2 |
| SD:mclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:skmeans | 3 | 1.000 | 0.995 | 0.998 | ** | 2 |
| CV:mclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:skmeans | 3 | 1.000 | 0.997 | 0.999 | ** | 2 |
| ATC:mclust | 4 | 1.000 | 0.966 | 0.982 | ** | 3 |
| CV:NMF | 3 | 0.976 | 0.948 | 0.976 | ** | 2 |
| SD:NMF | 3 | 0.974 | 0.946 | 0.976 | ** | 2 |
| MAD:NMF | 3 | 0.954 | 0.947 | 0.972 | ** | |
| MAD:mclust | 3 | 0.935 | 0.963 | 0.979 | * | 2 |
| ATC:pam | 6 | 0.931 | 0.824 | 0.925 | * | 4,5 |
| MAD:pam | 3 | 0.927 | 0.918 | 0.967 | * | |
| ATC:skmeans | 6 | 0.923 | 0.872 | 0.936 | * | 2,3,4,5 |
| ATC:NMF | 3 | 0.906 | 0.912 | 0.961 | * | |
| CV:pam | 3 | 0.882 | 0.893 | 0.957 | ||
| CV:kmeans | 2 | 0.874 | 0.965 | 0.974 | ||
| SD:pam | 3 | 0.841 | 0.872 | 0.946 | ||
| MAD:hclust | 3 | 0.832 | 0.890 | 0.951 | ||
| ATC:hclust | 4 | 0.826 | 0.892 | 0.933 | ||
| ATC:kmeans | 2 | 0.781 | 0.872 | 0.944 | ||
| MAD:kmeans | 3 | 0.739 | 0.977 | 0.942 | ||
| SD:hclust | 2 | 0.674 | 0.934 | 0.949 | ||
| CV:hclust | 2 | 0.561 | 0.891 | 0.917 |
**: 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 0.927 0.969 0.985 0.471 0.536 0.536
#> CV:NMF 2 0.927 0.961 0.982 0.472 0.536 0.536
#> MAD:NMF 2 0.892 0.829 0.940 0.482 0.504 0.504
#> ATC:NMF 2 0.825 0.907 0.961 0.486 0.510 0.510
#> SD:skmeans 2 1.000 1.000 1.000 0.464 0.536 0.536
#> CV:skmeans 2 1.000 1.000 1.000 0.464 0.536 0.536
#> MAD:skmeans 2 1.000 0.997 0.998 0.465 0.536 0.536
#> ATC:skmeans 2 1.000 0.950 0.981 0.508 0.492 0.492
#> SD:mclust 2 1.000 1.000 1.000 0.464 0.536 0.536
#> CV:mclust 2 1.000 1.000 1.000 0.464 0.536 0.536
#> MAD:mclust 2 1.000 1.000 1.000 0.464 0.536 0.536
#> ATC:mclust 2 0.518 0.861 0.909 0.462 0.536 0.536
#> SD:kmeans 2 1.000 0.975 0.982 0.467 0.536 0.536
#> CV:kmeans 2 0.874 0.965 0.974 0.467 0.536 0.536
#> MAD:kmeans 2 0.669 0.893 0.934 0.474 0.536 0.536
#> ATC:kmeans 2 0.781 0.872 0.944 0.500 0.491 0.491
#> SD:pam 2 0.665 0.830 0.930 0.495 0.495 0.495
#> CV:pam 2 0.639 0.835 0.932 0.498 0.492 0.492
#> MAD:pam 2 0.622 0.755 0.904 0.495 0.491 0.491
#> ATC:pam 2 0.823 0.904 0.959 0.501 0.495 0.495
#> SD:hclust 2 0.674 0.934 0.949 0.469 0.536 0.536
#> CV:hclust 2 0.561 0.891 0.917 0.469 0.536 0.536
#> MAD:hclust 2 0.408 0.851 0.897 0.471 0.536 0.536
#> ATC:hclust 2 0.501 0.881 0.931 0.488 0.499 0.499
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.974 0.946 0.976 0.434 0.786 0.600
#> CV:NMF 3 0.976 0.948 0.976 0.431 0.786 0.600
#> MAD:NMF 3 0.954 0.947 0.972 0.399 0.713 0.484
#> ATC:NMF 3 0.906 0.912 0.961 0.392 0.736 0.518
#> SD:skmeans 3 1.000 0.989 0.995 0.461 0.786 0.600
#> CV:skmeans 3 1.000 0.995 0.998 0.461 0.786 0.600
#> MAD:skmeans 3 1.000 0.997 0.999 0.460 0.786 0.600
#> ATC:skmeans 3 0.906 0.891 0.955 0.316 0.706 0.469
#> SD:mclust 3 0.718 0.933 0.885 0.396 0.787 0.603
#> CV:mclust 3 0.725 0.947 0.892 0.414 0.787 0.603
#> MAD:mclust 3 0.935 0.963 0.979 0.454 0.787 0.603
#> ATC:mclust 3 0.911 0.910 0.957 0.457 0.723 0.513
#> SD:kmeans 3 0.713 0.941 0.908 0.399 0.786 0.600
#> CV:kmeans 3 0.713 0.950 0.909 0.395 0.786 0.600
#> MAD:kmeans 3 0.739 0.977 0.942 0.395 0.786 0.600
#> ATC:kmeans 3 0.768 0.800 0.902 0.345 0.685 0.448
#> SD:pam 3 0.841 0.872 0.946 0.350 0.731 0.506
#> CV:pam 3 0.882 0.893 0.957 0.354 0.719 0.487
#> MAD:pam 3 0.927 0.918 0.967 0.363 0.742 0.520
#> ATC:pam 3 0.861 0.901 0.959 0.345 0.696 0.459
#> SD:hclust 3 0.867 0.862 0.936 0.410 0.793 0.614
#> CV:hclust 3 0.856 0.865 0.938 0.411 0.793 0.614
#> MAD:hclust 3 0.832 0.890 0.951 0.423 0.787 0.603
#> ATC:hclust 3 0.651 0.863 0.888 0.344 0.842 0.683
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.849 0.843 0.933 0.1141 0.851 0.583
#> CV:NMF 4 0.860 0.833 0.931 0.1123 0.859 0.604
#> MAD:NMF 4 0.853 0.830 0.926 0.1131 0.868 0.628
#> ATC:NMF 4 0.841 0.858 0.908 0.1005 0.903 0.712
#> SD:skmeans 4 0.797 0.851 0.901 0.0898 0.932 0.792
#> CV:skmeans 4 0.826 0.862 0.907 0.0882 0.932 0.792
#> MAD:skmeans 4 0.843 0.893 0.930 0.0873 0.932 0.792
#> ATC:skmeans 4 0.920 0.876 0.947 0.0904 0.941 0.819
#> SD:mclust 4 0.811 0.833 0.921 0.1206 0.837 0.567
#> CV:mclust 4 0.797 0.798 0.894 0.1105 0.855 0.603
#> MAD:mclust 4 0.779 0.793 0.903 0.0876 0.943 0.824
#> ATC:mclust 4 1.000 0.966 0.982 0.0869 0.947 0.837
#> SD:kmeans 4 0.755 0.781 0.819 0.1217 0.943 0.823
#> CV:kmeans 4 0.819 0.841 0.828 0.1287 0.937 0.805
#> MAD:kmeans 4 0.816 0.845 0.785 0.1155 0.937 0.805
#> ATC:kmeans 4 0.774 0.795 0.878 0.1076 0.915 0.750
#> SD:pam 4 0.778 0.845 0.912 0.0970 0.932 0.796
#> CV:pam 4 0.874 0.870 0.935 0.0882 0.934 0.798
#> MAD:pam 4 0.890 0.910 0.944 0.0892 0.934 0.798
#> ATC:pam 4 0.976 0.902 0.962 0.1082 0.893 0.686
#> SD:hclust 4 0.825 0.761 0.880 0.0953 0.956 0.868
#> CV:hclust 4 0.836 0.784 0.885 0.1001 0.944 0.833
#> MAD:hclust 4 0.813 0.872 0.919 0.0809 0.968 0.902
#> ATC:hclust 4 0.826 0.892 0.933 0.1162 0.929 0.790
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.776 0.718 0.841 0.0501 0.976 0.901
#> CV:NMF 5 0.780 0.733 0.852 0.0474 0.967 0.869
#> MAD:NMF 5 0.785 0.700 0.856 0.0510 0.939 0.775
#> ATC:NMF 5 0.740 0.764 0.836 0.0480 0.942 0.788
#> SD:skmeans 5 0.726 0.734 0.841 0.0678 0.925 0.724
#> CV:skmeans 5 0.748 0.742 0.850 0.0686 0.932 0.750
#> MAD:skmeans 5 0.790 0.773 0.865 0.0649 0.938 0.769
#> ATC:skmeans 5 0.919 0.793 0.912 0.0658 0.959 0.849
#> SD:mclust 5 0.855 0.783 0.866 0.0912 0.954 0.828
#> CV:mclust 5 0.820 0.769 0.865 0.0859 0.945 0.800
#> MAD:mclust 5 0.774 0.720 0.858 0.0788 0.902 0.653
#> ATC:mclust 5 0.857 0.800 0.814 0.0805 0.913 0.695
#> SD:kmeans 5 0.746 0.798 0.835 0.0734 0.897 0.637
#> CV:kmeans 5 0.755 0.784 0.825 0.0656 0.920 0.705
#> MAD:kmeans 5 0.747 0.756 0.813 0.0653 0.910 0.671
#> ATC:kmeans 5 0.770 0.771 0.837 0.0568 0.922 0.719
#> SD:pam 5 0.805 0.797 0.895 0.0753 0.920 0.717
#> CV:pam 5 0.820 0.781 0.884 0.0712 0.955 0.834
#> MAD:pam 5 0.872 0.834 0.914 0.0550 0.961 0.853
#> ATC:pam 5 0.990 0.941 0.975 0.0620 0.930 0.736
#> SD:hclust 5 0.839 0.749 0.861 0.0426 0.976 0.917
#> CV:hclust 5 0.844 0.770 0.870 0.0390 0.974 0.910
#> MAD:hclust 5 0.805 0.781 0.872 0.0413 0.977 0.923
#> ATC:hclust 5 0.816 0.872 0.860 0.0656 0.959 0.849
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.758 0.641 0.794 0.0380 0.950 0.784
#> CV:NMF 6 0.744 0.635 0.793 0.0433 0.947 0.774
#> MAD:NMF 6 0.751 0.640 0.800 0.0398 0.956 0.816
#> ATC:NMF 6 0.725 0.706 0.813 0.0361 0.935 0.739
#> SD:skmeans 6 0.734 0.691 0.801 0.0366 0.967 0.848
#> CV:skmeans 6 0.719 0.678 0.793 0.0371 0.961 0.822
#> MAD:skmeans 6 0.744 0.714 0.820 0.0357 0.992 0.965
#> ATC:skmeans 6 0.923 0.872 0.936 0.0319 0.965 0.852
#> SD:mclust 6 0.869 0.775 0.874 0.0506 0.915 0.642
#> CV:mclust 6 0.871 0.801 0.884 0.0525 0.921 0.671
#> MAD:mclust 6 0.818 0.713 0.830 0.0517 0.919 0.630
#> ATC:mclust 6 0.860 0.872 0.907 0.0515 0.910 0.614
#> SD:kmeans 6 0.749 0.718 0.791 0.0365 0.950 0.763
#> CV:kmeans 6 0.758 0.742 0.819 0.0431 0.950 0.766
#> MAD:kmeans 6 0.767 0.722 0.807 0.0439 0.960 0.807
#> ATC:kmeans 6 0.796 0.588 0.824 0.0426 0.977 0.894
#> SD:pam 6 0.788 0.745 0.854 0.0282 0.981 0.910
#> CV:pam 6 0.806 0.748 0.857 0.0317 0.972 0.880
#> MAD:pam 6 0.843 0.776 0.871 0.0356 0.969 0.869
#> ATC:pam 6 0.931 0.824 0.925 0.0231 0.959 0.811
#> SD:hclust 6 0.853 0.733 0.851 0.0302 0.974 0.906
#> CV:hclust 6 0.857 0.744 0.823 0.0297 0.963 0.860
#> MAD:hclust 6 0.804 0.753 0.825 0.0376 0.984 0.941
#> ATC:hclust 6 0.839 0.869 0.875 0.0287 0.981 0.918
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 cell.type(p) disease.state(p) k
#> SD:NMF 57 3.90e-13 0.0525 2
#> CV:NMF 57 3.90e-13 0.0525 2
#> MAD:NMF 51 7.81e-12 0.2057 2
#> ATC:NMF 55 3.96e-05 0.3102 2
#> SD:skmeans 57 3.90e-13 0.0525 2
#> CV:skmeans 57 3.90e-13 0.0525 2
#> MAD:skmeans 57 3.90e-13 0.0525 2
#> ATC:skmeans 55 3.96e-04 0.4648 2
#> SD:mclust 57 3.90e-13 0.0525 2
#> CV:mclust 57 3.90e-13 0.0525 2
#> MAD:mclust 57 3.90e-13 0.0525 2
#> ATC:mclust 57 1.51e-04 0.3057 2
#> SD:kmeans 57 3.90e-13 0.0525 2
#> CV:kmeans 57 3.90e-13 0.0525 2
#> MAD:kmeans 57 3.90e-13 0.0525 2
#> ATC:kmeans 55 3.96e-04 0.4648 2
#> SD:pam 52 2.17e-08 0.7907 2
#> CV:pam 53 1.24e-08 0.7651 2
#> MAD:pam 50 5.48e-07 0.6466 2
#> ATC:pam 55 9.28e-05 0.4563 2
#> SD:hclust 57 3.90e-13 0.0525 2
#> CV:hclust 57 3.90e-13 0.0525 2
#> MAD:hclust 57 3.90e-13 0.0525 2
#> ATC:hclust 57 2.04e-01 0.0251 2
test_to_known_factors(res_list, k = 3)
#> n cell.type(p) disease.state(p) k
#> SD:NMF 56 6.91e-13 0.000873 3
#> CV:NMF 56 6.91e-13 0.000873 3
#> MAD:NMF 57 4.19e-13 0.000423 3
#> ATC:NMF 53 3.10e-12 0.000593 3
#> SD:skmeans 57 4.19e-13 0.000423 3
#> CV:skmeans 57 4.19e-13 0.000423 3
#> MAD:skmeans 57 4.19e-13 0.000423 3
#> ATC:skmeans 52 4.17e-11 0.000923 3
#> SD:mclust 57 4.19e-13 0.000276 3
#> CV:mclust 57 4.19e-13 0.000276 3
#> MAD:mclust 57 4.19e-13 0.000276 3
#> ATC:mclust 55 1.14e-12 0.000291 3
#> SD:kmeans 57 4.19e-13 0.000423 3
#> CV:kmeans 57 4.19e-13 0.000423 3
#> MAD:kmeans 57 4.19e-13 0.000423 3
#> ATC:kmeans 47 5.27e-10 0.050292 3
#> SD:pam 53 3.10e-12 0.005200 3
#> CV:pam 55 1.14e-12 0.005334 3
#> MAD:pam 54 1.88e-12 0.001248 3
#> ATC:pam 54 1.70e-11 0.000569 3
#> SD:hclust 53 3.10e-12 0.007090 3
#> CV:hclust 53 3.10e-12 0.007090 3
#> MAD:hclust 54 1.88e-12 0.001274 3
#> ATC:hclust 57 9.33e-09 0.000167 3
test_to_known_factors(res_list, k = 4)
#> n cell.type(p) disease.state(p) k
#> SD:NMF 52 2.05e-09 2.57e-03 4
#> CV:NMF 53 1.30e-09 1.88e-04 4
#> MAD:NMF 51 1.93e-09 5.28e-05 4
#> ATC:NMF 56 9.59e-11 8.60e-06 4
#> SD:skmeans 55 6.87e-12 3.23e-04 4
#> CV:skmeans 55 6.87e-12 3.23e-04 4
#> MAD:skmeans 55 6.87e-12 1.92e-04 4
#> ATC:skmeans 51 4.89e-11 9.50e-04 4
#> SD:mclust 51 4.89e-11 1.35e-03 4
#> CV:mclust 51 4.89e-11 3.85e-04 4
#> MAD:mclust 52 3.00e-11 3.76e-04 4
#> ATC:mclust 57 2.57e-12 2.60e-04 4
#> SD:kmeans 55 6.87e-12 8.63e-04 4
#> CV:kmeans 56 4.20e-12 1.13e-03 4
#> MAD:kmeans 56 4.20e-12 2.78e-03 4
#> ATC:kmeans 52 3.00e-11 3.05e-04 4
#> SD:pam 55 4.19e-11 7.64e-04 4
#> CV:pam 54 1.12e-11 8.76e-04 4
#> MAD:pam 55 4.19e-11 1.34e-04 4
#> ATC:pam 54 6.81e-11 2.20e-04 4
#> SD:hclust 48 2.13e-10 4.95e-04 4
#> CV:hclust 48 2.13e-10 1.75e-04 4
#> MAD:hclust 56 4.20e-12 4.06e-03 4
#> ATC:hclust 57 2.57e-12 3.86e-04 4
test_to_known_factors(res_list, k = 5)
#> n cell.type(p) disease.state(p) k
#> SD:NMF 48 4.95e-09 8.09e-03 5
#> CV:NMF 49 2.19e-08 2.57e-03 5
#> MAD:NMF 47 6.99e-09 2.87e-03 5
#> ATC:NMF 53 3.72e-10 4.55e-03 5
#> SD:skmeans 47 3.48e-10 3.31e-04 5
#> CV:skmeans 47 3.48e-10 3.31e-04 5
#> MAD:skmeans 48 2.13e-10 7.71e-04 5
#> ATC:skmeans 50 3.61e-10 1.49e-03 5
#> SD:mclust 51 2.23e-10 8.03e-03 5
#> CV:mclust 52 1.38e-10 2.55e-03 5
#> MAD:mclust 45 9.25e-10 8.97e-04 5
#> ATC:mclust 53 8.52e-11 4.08e-03 5
#> SD:kmeans 53 8.52e-11 1.10e-04 5
#> CV:kmeans 51 2.23e-10 1.06e-04 5
#> MAD:kmeans 50 3.61e-10 2.09e-04 5
#> ATC:kmeans 52 1.38e-10 6.34e-03 5
#> SD:pam 53 8.52e-11 6.78e-05 5
#> CV:pam 51 2.23e-10 8.84e-05 5
#> MAD:pam 54 3.06e-10 1.33e-04 5
#> ATC:pam 56 1.21e-10 1.00e-03 5
#> SD:hclust 49 5.84e-10 4.24e-04 5
#> CV:hclust 49 5.84e-10 8.21e-04 5
#> MAD:hclust 54 5.26e-11 3.36e-03 5
#> ATC:hclust 57 1.24e-11 9.27e-05 5
test_to_known_factors(res_list, k = 6)
#> n cell.type(p) disease.state(p) k
#> SD:NMF 46 5.31e-08 2.44e-03 6
#> CV:NMF 45 8.29e-08 5.40e-03 6
#> MAD:NMF 47 7.51e-08 3.52e-03 6
#> ATC:NMF 52 5.39e-10 1.85e-03 6
#> SD:skmeans 46 5.67e-10 1.69e-04 6
#> CV:skmeans 47 1.52e-09 2.08e-04 6
#> MAD:skmeans 47 1.52e-09 2.44e-04 6
#> ATC:skmeans 53 3.36e-10 7.81e-04 6
#> SD:mclust 52 5.39e-10 2.51e-03 6
#> CV:mclust 52 5.39e-10 2.51e-03 6
#> MAD:mclust 44 2.32e-08 1.31e-03 6
#> ATC:mclust 55 1.31e-10 5.16e-03 6
#> SD:kmeans 49 2.22e-09 1.73e-03 6
#> CV:kmeans 47 1.52e-09 2.41e-05 6
#> MAD:kmeans 44 1.51e-09 5.58e-04 6
#> ATC:kmeans 43 1.03e-08 1.78e-02 6
#> SD:pam 44 6.42e-09 4.36e-05 6
#> CV:pam 47 1.52e-09 7.90e-05 6
#> MAD:pam 51 1.24e-09 9.48e-05 6
#> ATC:pam 52 2.97e-09 1.15e-05 6
#> SD:hclust 49 5.84e-10 3.71e-04 6
#> CV:hclust 51 8.65e-10 2.70e-05 6
#> MAD:hclust 50 3.61e-10 2.82e-04 6
#> ATC:hclust 57 5.06e-11 2.13e-04 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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.674 0.934 0.949 0.4687 0.536 0.536
#> 3 3 0.867 0.862 0.936 0.4099 0.793 0.614
#> 4 4 0.825 0.761 0.880 0.0953 0.956 0.868
#> 5 5 0.839 0.749 0.861 0.0426 0.976 0.917
#> 6 6 0.853 0.733 0.851 0.0302 0.974 0.906
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
#> GSM23185 1 0.6343 0.897 0.840 0.160
#> GSM23186 1 0.0938 0.930 0.988 0.012
#> GSM23187 1 0.6343 0.897 0.840 0.160
#> GSM23188 1 0.6343 0.897 0.840 0.160
#> GSM23189 1 0.6343 0.897 0.840 0.160
#> GSM23190 1 0.6343 0.897 0.840 0.160
#> GSM23191 1 0.5629 0.907 0.868 0.132
#> GSM23192 1 0.3274 0.925 0.940 0.060
#> GSM23193 1 0.5519 0.909 0.872 0.128
#> GSM23194 1 0.6247 0.899 0.844 0.156
#> GSM23195 1 0.3431 0.925 0.936 0.064
#> GSM23159 1 0.0000 0.931 1.000 0.000
#> GSM23160 1 0.6343 0.897 0.840 0.160
#> GSM23161 1 0.0000 0.931 1.000 0.000
#> GSM23162 1 0.5842 0.905 0.860 0.140
#> GSM23163 1 0.0000 0.931 1.000 0.000
#> GSM23164 1 0.0000 0.931 1.000 0.000
#> GSM23165 1 0.0000 0.931 1.000 0.000
#> GSM23166 1 0.0000 0.931 1.000 0.000
#> GSM23167 1 0.0000 0.931 1.000 0.000
#> GSM23168 1 0.6343 0.897 0.840 0.160
#> GSM23169 1 0.6247 0.899 0.844 0.156
#> GSM23170 1 0.0000 0.931 1.000 0.000
#> GSM23171 1 0.0000 0.931 1.000 0.000
#> GSM23172 1 0.0000 0.931 1.000 0.000
#> GSM23173 1 0.6148 0.901 0.848 0.152
#> GSM23174 1 0.0000 0.931 1.000 0.000
#> GSM23175 1 0.0000 0.931 1.000 0.000
#> GSM23176 1 0.0000 0.931 1.000 0.000
#> GSM23177 1 0.0000 0.931 1.000 0.000
#> GSM23178 1 0.0000 0.931 1.000 0.000
#> GSM23179 1 0.6343 0.897 0.840 0.160
#> GSM23180 1 0.0000 0.931 1.000 0.000
#> GSM23181 1 0.0000 0.931 1.000 0.000
#> GSM23182 1 0.0000 0.931 1.000 0.000
#> GSM23183 1 0.2236 0.928 0.964 0.036
#> GSM23184 1 0.6343 0.897 0.840 0.160
#> GSM23196 2 0.0000 0.975 0.000 1.000
#> GSM23197 2 0.0000 0.975 0.000 1.000
#> GSM23198 2 0.0000 0.975 0.000 1.000
#> GSM23199 2 0.0000 0.975 0.000 1.000
#> GSM23200 2 0.0000 0.975 0.000 1.000
#> GSM23201 2 0.3733 0.940 0.072 0.928
#> GSM23202 2 0.3733 0.940 0.072 0.928
#> GSM23203 2 0.0000 0.975 0.000 1.000
#> GSM23204 2 0.0000 0.975 0.000 1.000
#> GSM23205 2 0.3733 0.940 0.072 0.928
#> GSM23206 2 0.0000 0.975 0.000 1.000
#> GSM23207 2 0.0000 0.975 0.000 1.000
#> GSM23208 2 0.0000 0.975 0.000 1.000
#> GSM23209 2 0.0000 0.975 0.000 1.000
#> GSM23210 2 0.0000 0.975 0.000 1.000
#> GSM23211 2 0.0000 0.975 0.000 1.000
#> GSM23212 2 0.3733 0.940 0.072 0.928
#> GSM23213 2 0.3733 0.940 0.072 0.928
#> GSM23214 2 0.3733 0.940 0.072 0.928
#> GSM23215 2 0.0000 0.975 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.852 0.000 0.000 1.000
#> GSM23186 1 0.2878 0.854 0.904 0.000 0.096
#> GSM23187 3 0.0000 0.852 0.000 0.000 1.000
#> GSM23188 3 0.0000 0.852 0.000 0.000 1.000
#> GSM23189 3 0.0000 0.852 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.852 0.000 0.000 1.000
#> GSM23191 3 0.6225 0.367 0.432 0.000 0.568
#> GSM23192 1 0.6252 0.122 0.556 0.000 0.444
#> GSM23193 3 0.6267 0.308 0.452 0.000 0.548
#> GSM23194 3 0.4555 0.747 0.200 0.000 0.800
#> GSM23195 1 0.6045 0.328 0.620 0.000 0.380
#> GSM23159 1 0.0000 0.927 1.000 0.000 0.000
#> GSM23160 3 0.1964 0.849 0.056 0.000 0.944
#> GSM23161 1 0.0000 0.927 1.000 0.000 0.000
#> GSM23162 3 0.5138 0.710 0.252 0.000 0.748
#> GSM23163 1 0.0892 0.918 0.980 0.000 0.020
#> GSM23164 1 0.0000 0.927 1.000 0.000 0.000
#> GSM23165 1 0.0237 0.926 0.996 0.000 0.004
#> GSM23166 1 0.0000 0.927 1.000 0.000 0.000
#> GSM23167 1 0.0237 0.926 0.996 0.000 0.004
#> GSM23168 3 0.1643 0.851 0.044 0.000 0.956
#> GSM23169 3 0.5138 0.714 0.252 0.000 0.748
#> GSM23170 1 0.0000 0.927 1.000 0.000 0.000
#> GSM23171 1 0.0000 0.927 1.000 0.000 0.000
#> GSM23172 1 0.0237 0.926 0.996 0.000 0.004
#> GSM23173 3 0.4178 0.786 0.172 0.000 0.828
#> GSM23174 1 0.0000 0.927 1.000 0.000 0.000
#> GSM23175 1 0.0000 0.927 1.000 0.000 0.000
#> GSM23176 1 0.0237 0.926 0.996 0.000 0.004
#> GSM23177 1 0.0000 0.927 1.000 0.000 0.000
#> GSM23178 1 0.0424 0.924 0.992 0.000 0.008
#> GSM23179 3 0.1643 0.852 0.044 0.000 0.956
#> GSM23180 1 0.1411 0.908 0.964 0.000 0.036
#> GSM23181 1 0.1411 0.908 0.964 0.000 0.036
#> GSM23182 1 0.1411 0.908 0.964 0.000 0.036
#> GSM23183 1 0.5138 0.631 0.748 0.000 0.252
#> GSM23184 3 0.0000 0.852 0.000 0.000 1.000
#> GSM23196 2 0.0000 0.974 0.000 1.000 0.000
#> GSM23197 2 0.0000 0.974 0.000 1.000 0.000
#> GSM23198 2 0.0000 0.974 0.000 1.000 0.000
#> GSM23199 2 0.0000 0.974 0.000 1.000 0.000
#> GSM23200 2 0.0000 0.974 0.000 1.000 0.000
#> GSM23201 2 0.2356 0.938 0.072 0.928 0.000
#> GSM23202 2 0.2356 0.938 0.072 0.928 0.000
#> GSM23203 2 0.0000 0.974 0.000 1.000 0.000
#> GSM23204 2 0.0000 0.974 0.000 1.000 0.000
#> GSM23205 2 0.2356 0.938 0.072 0.928 0.000
#> GSM23206 2 0.0000 0.974 0.000 1.000 0.000
#> GSM23207 2 0.0000 0.974 0.000 1.000 0.000
#> GSM23208 2 0.0000 0.974 0.000 1.000 0.000
#> GSM23209 2 0.0000 0.974 0.000 1.000 0.000
#> GSM23210 2 0.0000 0.974 0.000 1.000 0.000
#> GSM23211 2 0.0000 0.974 0.000 1.000 0.000
#> GSM23212 2 0.2356 0.938 0.072 0.928 0.000
#> GSM23213 2 0.2356 0.938 0.072 0.928 0.000
#> GSM23214 2 0.2356 0.938 0.072 0.928 0.000
#> GSM23215 2 0.0000 0.974 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0336 0.8064 0.000 0.000 0.992 0.008
#> GSM23186 1 0.4853 0.6189 0.744 0.000 0.036 0.220
#> GSM23187 3 0.0336 0.8064 0.000 0.000 0.992 0.008
#> GSM23188 3 0.0336 0.8064 0.000 0.000 0.992 0.008
#> GSM23189 3 0.0336 0.8064 0.000 0.000 0.992 0.008
#> GSM23190 3 0.0336 0.8064 0.000 0.000 0.992 0.008
#> GSM23191 4 0.6700 0.4910 0.112 0.000 0.316 0.572
#> GSM23192 4 0.5962 0.5694 0.180 0.000 0.128 0.692
#> GSM23193 4 0.6808 0.5324 0.128 0.000 0.300 0.572
#> GSM23194 3 0.5288 -0.0207 0.008 0.000 0.520 0.472
#> GSM23195 4 0.7516 0.3459 0.328 0.000 0.200 0.472
#> GSM23159 1 0.0921 0.8326 0.972 0.000 0.000 0.028
#> GSM23160 3 0.2443 0.7802 0.024 0.000 0.916 0.060
#> GSM23161 1 0.1716 0.8211 0.936 0.000 0.000 0.064
#> GSM23162 3 0.6005 -0.0791 0.040 0.000 0.500 0.460
#> GSM23163 1 0.3032 0.7755 0.868 0.000 0.008 0.124
#> GSM23164 1 0.2011 0.8130 0.920 0.000 0.000 0.080
#> GSM23165 1 0.1302 0.8210 0.956 0.000 0.000 0.044
#> GSM23166 1 0.1940 0.8157 0.924 0.000 0.000 0.076
#> GSM23167 1 0.1302 0.8210 0.956 0.000 0.000 0.044
#> GSM23168 3 0.2021 0.7880 0.012 0.000 0.932 0.056
#> GSM23169 3 0.6595 0.3642 0.124 0.000 0.608 0.268
#> GSM23170 1 0.1474 0.8264 0.948 0.000 0.000 0.052
#> GSM23171 1 0.0707 0.8321 0.980 0.000 0.000 0.020
#> GSM23172 1 0.1302 0.8210 0.956 0.000 0.000 0.044
#> GSM23173 3 0.5280 0.6037 0.096 0.000 0.748 0.156
#> GSM23174 1 0.0188 0.8312 0.996 0.000 0.000 0.004
#> GSM23175 1 0.0336 0.8297 0.992 0.000 0.000 0.008
#> GSM23176 1 0.1302 0.8210 0.956 0.000 0.000 0.044
#> GSM23177 1 0.1389 0.8288 0.952 0.000 0.000 0.048
#> GSM23178 1 0.1792 0.8298 0.932 0.000 0.000 0.068
#> GSM23179 3 0.1824 0.7925 0.004 0.000 0.936 0.060
#> GSM23180 1 0.4866 0.3887 0.596 0.000 0.000 0.404
#> GSM23181 1 0.4866 0.3887 0.596 0.000 0.000 0.404
#> GSM23182 1 0.4866 0.3887 0.596 0.000 0.000 0.404
#> GSM23183 1 0.6745 -0.1131 0.480 0.000 0.092 0.428
#> GSM23184 3 0.0336 0.8047 0.000 0.000 0.992 0.008
#> GSM23196 2 0.0000 0.9778 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.9778 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.9778 0.000 1.000 0.000 0.000
#> GSM23199 2 0.0000 0.9778 0.000 1.000 0.000 0.000
#> GSM23200 2 0.0000 0.9778 0.000 1.000 0.000 0.000
#> GSM23201 2 0.1867 0.9468 0.000 0.928 0.000 0.072
#> GSM23202 2 0.1867 0.9468 0.000 0.928 0.000 0.072
#> GSM23203 2 0.0000 0.9778 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.9778 0.000 1.000 0.000 0.000
#> GSM23205 2 0.1867 0.9468 0.000 0.928 0.000 0.072
#> GSM23206 2 0.0000 0.9778 0.000 1.000 0.000 0.000
#> GSM23207 2 0.0000 0.9778 0.000 1.000 0.000 0.000
#> GSM23208 2 0.0000 0.9778 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.9778 0.000 1.000 0.000 0.000
#> GSM23210 2 0.0000 0.9778 0.000 1.000 0.000 0.000
#> GSM23211 2 0.0000 0.9778 0.000 1.000 0.000 0.000
#> GSM23212 2 0.1867 0.9468 0.000 0.928 0.000 0.072
#> GSM23213 2 0.1867 0.9468 0.000 0.928 0.000 0.072
#> GSM23214 2 0.1867 0.9468 0.000 0.928 0.000 0.072
#> GSM23215 2 0.0000 0.9778 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.0000 0.798 0.000 0.000 1.000 0.000 0.000
#> GSM23186 1 0.6034 0.031 0.476 0.000 0.012 0.080 0.432
#> GSM23187 3 0.0000 0.798 0.000 0.000 1.000 0.000 0.000
#> GSM23188 3 0.0000 0.798 0.000 0.000 1.000 0.000 0.000
#> GSM23189 3 0.0000 0.798 0.000 0.000 1.000 0.000 0.000
#> GSM23190 3 0.0000 0.798 0.000 0.000 1.000 0.000 0.000
#> GSM23191 4 0.3825 0.763 0.060 0.000 0.136 0.804 0.000
#> GSM23192 5 0.6631 0.152 0.060 0.000 0.064 0.420 0.456
#> GSM23193 4 0.4737 0.739 0.076 0.000 0.136 0.764 0.024
#> GSM23194 3 0.6651 -0.191 0.000 0.000 0.444 0.300 0.256
#> GSM23195 5 0.4048 0.563 0.068 0.000 0.036 0.072 0.824
#> GSM23159 1 0.2228 0.788 0.912 0.000 0.000 0.040 0.048
#> GSM23160 3 0.3184 0.754 0.012 0.000 0.868 0.052 0.068
#> GSM23161 1 0.1942 0.783 0.920 0.000 0.000 0.068 0.012
#> GSM23162 4 0.5108 0.600 0.024 0.000 0.304 0.648 0.024
#> GSM23163 1 0.4550 0.640 0.744 0.000 0.004 0.064 0.188
#> GSM23164 1 0.2189 0.776 0.904 0.000 0.000 0.084 0.012
#> GSM23165 1 0.3051 0.750 0.864 0.000 0.000 0.060 0.076
#> GSM23166 1 0.2130 0.779 0.908 0.000 0.000 0.080 0.012
#> GSM23167 1 0.2989 0.752 0.868 0.000 0.000 0.060 0.072
#> GSM23168 3 0.2625 0.770 0.012 0.000 0.900 0.048 0.040
#> GSM23169 3 0.7054 0.148 0.028 0.000 0.416 0.172 0.384
#> GSM23170 1 0.1943 0.790 0.924 0.000 0.000 0.056 0.020
#> GSM23171 1 0.1310 0.795 0.956 0.000 0.000 0.024 0.020
#> GSM23172 1 0.2729 0.759 0.884 0.000 0.000 0.056 0.060
#> GSM23173 3 0.6277 0.410 0.016 0.000 0.548 0.116 0.320
#> GSM23174 1 0.0865 0.794 0.972 0.000 0.000 0.024 0.004
#> GSM23175 1 0.0798 0.793 0.976 0.000 0.000 0.008 0.016
#> GSM23176 1 0.3051 0.750 0.864 0.000 0.000 0.060 0.076
#> GSM23177 1 0.1670 0.792 0.936 0.000 0.000 0.052 0.012
#> GSM23178 1 0.2535 0.791 0.892 0.000 0.000 0.076 0.032
#> GSM23179 3 0.2536 0.772 0.004 0.000 0.900 0.044 0.052
#> GSM23180 1 0.5365 0.323 0.528 0.000 0.000 0.416 0.056
#> GSM23181 1 0.5365 0.323 0.528 0.000 0.000 0.416 0.056
#> GSM23182 1 0.5365 0.323 0.528 0.000 0.000 0.416 0.056
#> GSM23183 5 0.4519 0.578 0.188 0.000 0.012 0.048 0.752
#> GSM23184 3 0.0771 0.794 0.000 0.000 0.976 0.020 0.004
#> GSM23196 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM23199 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM23200 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM23201 2 0.1704 0.944 0.000 0.928 0.000 0.068 0.004
#> GSM23202 2 0.1704 0.944 0.000 0.928 0.000 0.068 0.004
#> GSM23203 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM23205 2 0.1704 0.944 0.000 0.928 0.000 0.068 0.004
#> GSM23206 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM23207 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM23208 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM23210 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM23211 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
#> GSM23212 2 0.1704 0.944 0.000 0.928 0.000 0.068 0.004
#> GSM23213 2 0.1704 0.944 0.000 0.928 0.000 0.068 0.004
#> GSM23214 2 0.1704 0.944 0.000 0.928 0.000 0.068 0.004
#> GSM23215 2 0.0000 0.977 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0000 0.7989 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23186 6 0.3357 0.3405 0.224 0.000 0.004 0.008 0.000 0.764
#> GSM23187 3 0.0000 0.7989 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23188 3 0.0000 0.7989 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23189 3 0.0000 0.7989 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23190 3 0.0000 0.7989 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23191 5 0.2045 0.8090 0.028 0.000 0.024 0.028 0.920 0.000
#> GSM23192 6 0.6484 0.0289 0.016 0.000 0.052 0.088 0.416 0.428
#> GSM23193 5 0.1994 0.7888 0.040 0.000 0.020 0.008 0.924 0.008
#> GSM23194 3 0.7119 -0.1631 0.000 0.000 0.412 0.108 0.300 0.180
#> GSM23195 6 0.4467 0.3532 0.000 0.000 0.004 0.376 0.028 0.592
#> GSM23159 1 0.3060 0.7324 0.836 0.000 0.000 0.020 0.012 0.132
#> GSM23160 3 0.3445 0.5607 0.000 0.000 0.744 0.244 0.012 0.000
#> GSM23161 1 0.2003 0.7471 0.912 0.000 0.000 0.044 0.044 0.000
#> GSM23162 5 0.4735 0.6071 0.016 0.000 0.128 0.128 0.724 0.004
#> GSM23163 1 0.4569 0.5240 0.636 0.000 0.000 0.016 0.028 0.320
#> GSM23164 1 0.2258 0.7407 0.896 0.000 0.000 0.044 0.060 0.000
#> GSM23165 1 0.3708 0.6739 0.752 0.000 0.000 0.020 0.008 0.220
#> GSM23166 1 0.2190 0.7427 0.900 0.000 0.000 0.040 0.060 0.000
#> GSM23167 1 0.3623 0.6804 0.764 0.000 0.000 0.020 0.008 0.208
#> GSM23168 3 0.3488 0.6133 0.000 0.000 0.780 0.184 0.036 0.000
#> GSM23169 4 0.5388 0.6890 0.004 0.000 0.156 0.684 0.096 0.060
#> GSM23170 1 0.2245 0.7558 0.908 0.000 0.000 0.040 0.036 0.016
#> GSM23171 1 0.1838 0.7606 0.928 0.000 0.000 0.012 0.020 0.040
#> GSM23172 1 0.3393 0.6912 0.784 0.000 0.000 0.020 0.004 0.192
#> GSM23173 4 0.4928 0.6944 0.000 0.000 0.288 0.640 0.040 0.032
#> GSM23174 1 0.1787 0.7562 0.920 0.000 0.000 0.008 0.004 0.068
#> GSM23175 1 0.1434 0.7573 0.940 0.000 0.000 0.012 0.000 0.048
#> GSM23176 1 0.3652 0.6782 0.760 0.000 0.000 0.020 0.008 0.212
#> GSM23177 1 0.2007 0.7552 0.920 0.000 0.000 0.032 0.036 0.012
#> GSM23178 1 0.2896 0.7543 0.864 0.000 0.000 0.012 0.044 0.080
#> GSM23179 3 0.3003 0.6658 0.000 0.000 0.812 0.172 0.016 0.000
#> GSM23180 1 0.6134 0.1953 0.476 0.000 0.000 0.108 0.372 0.044
#> GSM23181 1 0.6134 0.1953 0.476 0.000 0.000 0.108 0.372 0.044
#> GSM23182 1 0.6134 0.1953 0.476 0.000 0.000 0.108 0.372 0.044
#> GSM23183 6 0.3606 0.4875 0.016 0.000 0.004 0.156 0.024 0.800
#> GSM23184 3 0.0972 0.7848 0.000 0.000 0.964 0.028 0.008 0.000
#> GSM23196 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23199 2 0.0146 0.9712 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM23200 2 0.0146 0.9712 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM23201 2 0.1942 0.9346 0.000 0.916 0.000 0.064 0.012 0.008
#> GSM23202 2 0.2001 0.9339 0.000 0.912 0.000 0.068 0.012 0.008
#> GSM23203 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23205 2 0.1942 0.9346 0.000 0.916 0.000 0.064 0.012 0.008
#> GSM23206 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23207 2 0.0146 0.9712 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM23208 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23210 2 0.0146 0.9712 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM23211 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23212 2 0.2001 0.9339 0.000 0.912 0.000 0.068 0.012 0.008
#> GSM23213 2 0.2001 0.9339 0.000 0.912 0.000 0.068 0.012 0.008
#> GSM23214 2 0.2001 0.9339 0.000 0.912 0.000 0.068 0.012 0.008
#> GSM23215 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> SD:hclust 57 3.90e-13 0.052490 2
#> SD:hclust 53 3.10e-12 0.007090 3
#> SD:hclust 48 2.13e-10 0.000495 4
#> SD:hclust 49 5.84e-10 0.000424 5
#> SD:hclust 49 5.84e-10 0.000371 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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.975 0.982 0.4667 0.536 0.536
#> 3 3 0.713 0.941 0.908 0.3995 0.786 0.600
#> 4 4 0.755 0.781 0.819 0.1217 0.943 0.823
#> 5 5 0.746 0.798 0.835 0.0734 0.897 0.637
#> 6 6 0.749 0.718 0.791 0.0365 0.950 0.763
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
#> GSM23185 1 0.3274 0.951 0.940 0.060
#> GSM23186 1 0.0000 0.974 1.000 0.000
#> GSM23187 1 0.3274 0.951 0.940 0.060
#> GSM23188 1 0.3274 0.951 0.940 0.060
#> GSM23189 1 0.3274 0.951 0.940 0.060
#> GSM23190 1 0.3274 0.951 0.940 0.060
#> GSM23191 1 0.0000 0.974 1.000 0.000
#> GSM23192 1 0.0000 0.974 1.000 0.000
#> GSM23193 1 0.0000 0.974 1.000 0.000
#> GSM23194 1 0.3274 0.951 0.940 0.060
#> GSM23195 1 0.0000 0.974 1.000 0.000
#> GSM23159 1 0.1184 0.978 0.984 0.016
#> GSM23160 1 0.3274 0.951 0.940 0.060
#> GSM23161 1 0.1184 0.978 0.984 0.016
#> GSM23162 1 0.0672 0.974 0.992 0.008
#> GSM23163 1 0.1184 0.978 0.984 0.016
#> GSM23164 1 0.1184 0.978 0.984 0.016
#> GSM23165 1 0.1184 0.978 0.984 0.016
#> GSM23166 1 0.1184 0.978 0.984 0.016
#> GSM23167 1 0.1184 0.978 0.984 0.016
#> GSM23168 1 0.3274 0.951 0.940 0.060
#> GSM23169 1 0.0000 0.974 1.000 0.000
#> GSM23170 1 0.1184 0.978 0.984 0.016
#> GSM23171 1 0.1184 0.978 0.984 0.016
#> GSM23172 1 0.1184 0.978 0.984 0.016
#> GSM23173 1 0.0000 0.974 1.000 0.000
#> GSM23174 1 0.1184 0.978 0.984 0.016
#> GSM23175 1 0.1184 0.978 0.984 0.016
#> GSM23176 1 0.1184 0.978 0.984 0.016
#> GSM23177 1 0.1184 0.978 0.984 0.016
#> GSM23178 1 0.1184 0.978 0.984 0.016
#> GSM23179 1 0.3274 0.951 0.940 0.060
#> GSM23180 1 0.1184 0.978 0.984 0.016
#> GSM23181 1 0.1184 0.978 0.984 0.016
#> GSM23182 1 0.1184 0.978 0.984 0.016
#> GSM23183 1 0.0000 0.974 1.000 0.000
#> GSM23184 1 0.3274 0.951 0.940 0.060
#> GSM23196 2 0.0000 0.991 0.000 1.000
#> GSM23197 2 0.0000 0.991 0.000 1.000
#> GSM23198 2 0.0000 0.991 0.000 1.000
#> GSM23199 2 0.0000 0.991 0.000 1.000
#> GSM23200 2 0.0000 0.991 0.000 1.000
#> GSM23201 2 0.0000 0.991 0.000 1.000
#> GSM23202 2 0.2948 0.950 0.052 0.948
#> GSM23203 2 0.0000 0.991 0.000 1.000
#> GSM23204 2 0.0000 0.991 0.000 1.000
#> GSM23205 2 0.0000 0.991 0.000 1.000
#> GSM23206 2 0.0000 0.991 0.000 1.000
#> GSM23207 2 0.0000 0.991 0.000 1.000
#> GSM23208 2 0.0000 0.991 0.000 1.000
#> GSM23209 2 0.0000 0.991 0.000 1.000
#> GSM23210 2 0.0000 0.991 0.000 1.000
#> GSM23211 2 0.0000 0.991 0.000 1.000
#> GSM23212 2 0.0000 0.991 0.000 1.000
#> GSM23213 2 0.2948 0.950 0.052 0.948
#> GSM23214 2 0.2948 0.950 0.052 0.948
#> GSM23215 2 0.0000 0.991 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.929 0.000 0.000 1.000
#> GSM23186 1 0.4887 0.881 0.772 0.000 0.228
#> GSM23187 3 0.0000 0.929 0.000 0.000 1.000
#> GSM23188 3 0.0000 0.929 0.000 0.000 1.000
#> GSM23189 3 0.0000 0.929 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.929 0.000 0.000 1.000
#> GSM23191 3 0.4172 0.840 0.156 0.004 0.840
#> GSM23192 3 0.4399 0.800 0.188 0.000 0.812
#> GSM23193 3 0.3784 0.864 0.132 0.004 0.864
#> GSM23194 3 0.1031 0.939 0.024 0.000 0.976
#> GSM23195 3 0.4233 0.833 0.160 0.004 0.836
#> GSM23159 1 0.3752 0.989 0.856 0.000 0.144
#> GSM23160 3 0.1031 0.939 0.024 0.000 0.976
#> GSM23161 1 0.3752 0.989 0.856 0.000 0.144
#> GSM23162 3 0.1267 0.938 0.024 0.004 0.972
#> GSM23163 1 0.3752 0.989 0.856 0.000 0.144
#> GSM23164 1 0.3752 0.989 0.856 0.000 0.144
#> GSM23165 1 0.3752 0.989 0.856 0.000 0.144
#> GSM23166 1 0.3752 0.989 0.856 0.000 0.144
#> GSM23167 1 0.3752 0.989 0.856 0.000 0.144
#> GSM23168 3 0.1031 0.939 0.024 0.000 0.976
#> GSM23169 3 0.1267 0.938 0.024 0.004 0.972
#> GSM23170 1 0.3752 0.989 0.856 0.000 0.144
#> GSM23171 1 0.3752 0.989 0.856 0.000 0.144
#> GSM23172 1 0.3752 0.989 0.856 0.000 0.144
#> GSM23173 3 0.1031 0.939 0.024 0.000 0.976
#> GSM23174 1 0.3619 0.984 0.864 0.000 0.136
#> GSM23175 1 0.3619 0.984 0.864 0.000 0.136
#> GSM23176 1 0.3752 0.989 0.856 0.000 0.144
#> GSM23177 1 0.3752 0.989 0.856 0.000 0.144
#> GSM23178 1 0.3752 0.989 0.856 0.000 0.144
#> GSM23179 3 0.1031 0.939 0.024 0.000 0.976
#> GSM23180 1 0.3851 0.982 0.860 0.004 0.136
#> GSM23181 1 0.3619 0.984 0.864 0.000 0.136
#> GSM23182 1 0.3573 0.962 0.876 0.004 0.120
#> GSM23183 3 0.4399 0.798 0.188 0.000 0.812
#> GSM23184 3 0.1031 0.939 0.024 0.000 0.976
#> GSM23196 2 0.4270 0.940 0.116 0.860 0.024
#> GSM23197 2 0.4397 0.939 0.116 0.856 0.028
#> GSM23198 2 0.4397 0.939 0.116 0.856 0.028
#> GSM23199 2 0.0000 0.932 0.000 1.000 0.000
#> GSM23200 2 0.2959 0.940 0.100 0.900 0.000
#> GSM23201 2 0.1163 0.927 0.028 0.972 0.000
#> GSM23202 2 0.1163 0.927 0.028 0.972 0.000
#> GSM23203 2 0.4397 0.939 0.116 0.856 0.028
#> GSM23204 2 0.4397 0.939 0.116 0.856 0.028
#> GSM23205 2 0.1163 0.927 0.028 0.972 0.000
#> GSM23206 2 0.4270 0.940 0.116 0.860 0.024
#> GSM23207 2 0.0892 0.929 0.020 0.980 0.000
#> GSM23208 2 0.4397 0.939 0.116 0.856 0.028
#> GSM23209 2 0.4397 0.939 0.116 0.856 0.028
#> GSM23210 2 0.0237 0.932 0.004 0.996 0.000
#> GSM23211 2 0.4397 0.939 0.116 0.856 0.028
#> GSM23212 2 0.1163 0.927 0.028 0.972 0.000
#> GSM23213 2 0.1163 0.927 0.028 0.972 0.000
#> GSM23214 2 0.1163 0.927 0.028 0.972 0.000
#> GSM23215 2 0.3886 0.941 0.096 0.880 0.024
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.1209 0.861 0.032 0.000 0.964 0.004
#> GSM23186 1 0.4635 0.781 0.796 0.000 0.080 0.124
#> GSM23187 3 0.1356 0.861 0.032 0.000 0.960 0.008
#> GSM23188 3 0.1356 0.861 0.032 0.000 0.960 0.008
#> GSM23189 3 0.1356 0.861 0.032 0.000 0.960 0.008
#> GSM23190 3 0.1356 0.861 0.032 0.000 0.960 0.008
#> GSM23191 3 0.7201 0.625 0.148 0.000 0.496 0.356
#> GSM23192 3 0.7030 0.626 0.120 0.000 0.472 0.408
#> GSM23193 3 0.7013 0.651 0.128 0.000 0.516 0.356
#> GSM23194 3 0.2722 0.857 0.032 0.000 0.904 0.064
#> GSM23195 3 0.7164 0.660 0.156 0.000 0.524 0.320
#> GSM23159 1 0.0469 0.917 0.988 0.000 0.000 0.012
#> GSM23160 3 0.1022 0.861 0.032 0.000 0.968 0.000
#> GSM23161 1 0.0921 0.910 0.972 0.000 0.000 0.028
#> GSM23162 3 0.4375 0.828 0.032 0.000 0.788 0.180
#> GSM23163 1 0.1211 0.910 0.960 0.000 0.000 0.040
#> GSM23164 1 0.1867 0.889 0.928 0.000 0.000 0.072
#> GSM23165 1 0.1118 0.912 0.964 0.000 0.000 0.036
#> GSM23166 1 0.1867 0.889 0.928 0.000 0.000 0.072
#> GSM23167 1 0.1118 0.912 0.964 0.000 0.000 0.036
#> GSM23168 3 0.1022 0.861 0.032 0.000 0.968 0.000
#> GSM23169 3 0.4199 0.834 0.032 0.000 0.804 0.164
#> GSM23170 1 0.0000 0.917 1.000 0.000 0.000 0.000
#> GSM23171 1 0.0188 0.917 0.996 0.000 0.000 0.004
#> GSM23172 1 0.1118 0.912 0.964 0.000 0.000 0.036
#> GSM23173 3 0.3694 0.844 0.032 0.000 0.844 0.124
#> GSM23174 1 0.0188 0.916 0.996 0.000 0.000 0.004
#> GSM23175 1 0.0000 0.917 1.000 0.000 0.000 0.000
#> GSM23176 1 0.1118 0.912 0.964 0.000 0.000 0.036
#> GSM23177 1 0.0188 0.916 0.996 0.000 0.000 0.004
#> GSM23178 1 0.0592 0.917 0.984 0.000 0.000 0.016
#> GSM23179 3 0.1022 0.861 0.032 0.000 0.968 0.000
#> GSM23180 1 0.4898 0.572 0.584 0.000 0.000 0.416
#> GSM23181 1 0.3873 0.779 0.772 0.000 0.000 0.228
#> GSM23182 1 0.4941 0.550 0.564 0.000 0.000 0.436
#> GSM23183 3 0.7258 0.642 0.164 0.000 0.508 0.328
#> GSM23184 3 0.1022 0.861 0.032 0.000 0.968 0.000
#> GSM23196 2 0.0188 0.823 0.000 0.996 0.004 0.000
#> GSM23197 2 0.0000 0.824 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0188 0.823 0.000 0.996 0.004 0.000
#> GSM23199 2 0.5493 -0.767 0.000 0.528 0.016 0.456
#> GSM23200 2 0.2021 0.746 0.000 0.932 0.012 0.056
#> GSM23201 4 0.5558 0.955 0.000 0.432 0.020 0.548
#> GSM23202 4 0.4933 0.965 0.000 0.432 0.000 0.568
#> GSM23203 2 0.0188 0.823 0.000 0.996 0.004 0.000
#> GSM23204 2 0.0000 0.824 0.000 1.000 0.000 0.000
#> GSM23205 4 0.5558 0.955 0.000 0.432 0.020 0.548
#> GSM23206 2 0.0000 0.824 0.000 1.000 0.000 0.000
#> GSM23207 4 0.5296 0.833 0.000 0.492 0.008 0.500
#> GSM23208 2 0.0188 0.823 0.000 0.996 0.004 0.000
#> GSM23209 2 0.0000 0.824 0.000 1.000 0.000 0.000
#> GSM23210 2 0.5760 -0.771 0.000 0.524 0.028 0.448
#> GSM23211 2 0.0000 0.824 0.000 1.000 0.000 0.000
#> GSM23212 4 0.4933 0.965 0.000 0.432 0.000 0.568
#> GSM23213 4 0.4933 0.965 0.000 0.432 0.000 0.568
#> GSM23214 4 0.4933 0.965 0.000 0.432 0.000 0.568
#> GSM23215 2 0.3307 0.619 0.000 0.868 0.028 0.104
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.0579 0.857 0.008 0.000 0.984 0.008 0.000
#> GSM23186 1 0.7068 0.320 0.516 0.000 0.040 0.208 0.236
#> GSM23187 3 0.0579 0.857 0.008 0.000 0.984 0.008 0.000
#> GSM23188 3 0.0579 0.857 0.008 0.000 0.984 0.008 0.000
#> GSM23189 3 0.0579 0.857 0.008 0.000 0.984 0.008 0.000
#> GSM23190 3 0.0579 0.857 0.008 0.000 0.984 0.008 0.000
#> GSM23191 5 0.4865 0.645 0.088 0.000 0.160 0.012 0.740
#> GSM23192 5 0.5687 0.653 0.064 0.000 0.108 0.120 0.708
#> GSM23193 5 0.4812 0.630 0.076 0.000 0.172 0.012 0.740
#> GSM23194 3 0.4314 0.708 0.008 0.000 0.780 0.068 0.144
#> GSM23195 5 0.7015 0.518 0.064 0.000 0.192 0.184 0.560
#> GSM23159 1 0.1211 0.885 0.960 0.000 0.000 0.016 0.024
#> GSM23160 3 0.1405 0.850 0.008 0.000 0.956 0.016 0.020
#> GSM23161 1 0.1774 0.858 0.932 0.000 0.000 0.016 0.052
#> GSM23162 3 0.5218 0.216 0.008 0.000 0.516 0.028 0.448
#> GSM23163 1 0.3670 0.841 0.820 0.000 0.000 0.068 0.112
#> GSM23164 1 0.2077 0.832 0.908 0.000 0.000 0.008 0.084
#> GSM23165 1 0.3090 0.853 0.860 0.000 0.000 0.052 0.088
#> GSM23166 1 0.1894 0.842 0.920 0.000 0.000 0.008 0.072
#> GSM23167 1 0.3090 0.853 0.860 0.000 0.000 0.052 0.088
#> GSM23168 3 0.1405 0.850 0.008 0.000 0.956 0.016 0.020
#> GSM23169 3 0.6335 0.314 0.008 0.000 0.528 0.144 0.320
#> GSM23170 1 0.0162 0.883 0.996 0.000 0.000 0.004 0.000
#> GSM23171 1 0.0162 0.885 0.996 0.000 0.000 0.004 0.000
#> GSM23172 1 0.3019 0.854 0.864 0.000 0.000 0.048 0.088
#> GSM23173 3 0.5124 0.643 0.008 0.000 0.704 0.092 0.196
#> GSM23174 1 0.0290 0.883 0.992 0.000 0.000 0.008 0.000
#> GSM23175 1 0.0162 0.884 0.996 0.000 0.000 0.004 0.000
#> GSM23176 1 0.3090 0.853 0.860 0.000 0.000 0.052 0.088
#> GSM23177 1 0.0566 0.880 0.984 0.000 0.000 0.004 0.012
#> GSM23178 1 0.2300 0.873 0.904 0.000 0.000 0.024 0.072
#> GSM23179 3 0.1200 0.852 0.008 0.000 0.964 0.016 0.012
#> GSM23180 5 0.3916 0.642 0.256 0.000 0.000 0.012 0.732
#> GSM23181 5 0.4446 0.200 0.476 0.000 0.000 0.004 0.520
#> GSM23182 5 0.4817 0.614 0.264 0.000 0.000 0.056 0.680
#> GSM23183 5 0.6843 0.523 0.052 0.000 0.196 0.180 0.572
#> GSM23184 3 0.0290 0.857 0.008 0.000 0.992 0.000 0.000
#> GSM23196 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0451 0.947 0.000 0.988 0.004 0.000 0.008
#> GSM23198 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000
#> GSM23199 4 0.4538 0.858 0.000 0.348 0.004 0.636 0.012
#> GSM23200 2 0.2930 0.711 0.000 0.832 0.000 0.164 0.004
#> GSM23201 4 0.5158 0.920 0.000 0.264 0.000 0.656 0.080
#> GSM23202 4 0.4326 0.937 0.000 0.264 0.000 0.708 0.028
#> GSM23203 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0451 0.947 0.000 0.988 0.004 0.000 0.008
#> GSM23205 4 0.5105 0.920 0.000 0.264 0.000 0.660 0.076
#> GSM23206 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000
#> GSM23207 4 0.4109 0.927 0.000 0.288 0.000 0.700 0.012
#> GSM23208 2 0.0000 0.949 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0451 0.947 0.000 0.988 0.004 0.000 0.008
#> GSM23210 4 0.5213 0.882 0.000 0.320 0.000 0.616 0.064
#> GSM23211 2 0.0451 0.947 0.000 0.988 0.004 0.000 0.008
#> GSM23212 4 0.3967 0.938 0.000 0.264 0.000 0.724 0.012
#> GSM23213 4 0.3967 0.938 0.000 0.264 0.000 0.724 0.012
#> GSM23214 4 0.4326 0.937 0.000 0.264 0.000 0.708 0.028
#> GSM23215 2 0.3758 0.732 0.000 0.824 0.008 0.112 0.056
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0000 0.8538 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23186 6 0.5310 0.2331 0.316 0.032 0.012 0.000 0.036 0.604
#> GSM23187 3 0.0146 0.8547 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM23188 3 0.0146 0.8547 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM23189 3 0.0146 0.8547 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM23190 3 0.0000 0.8538 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23191 5 0.2267 0.5158 0.020 0.004 0.064 0.000 0.904 0.008
#> GSM23192 5 0.5319 -0.0768 0.020 0.008 0.044 0.000 0.544 0.384
#> GSM23193 5 0.2238 0.5115 0.016 0.004 0.068 0.000 0.904 0.008
#> GSM23194 3 0.5862 0.4624 0.000 0.056 0.616 0.000 0.184 0.144
#> GSM23195 6 0.5762 0.5137 0.052 0.000 0.104 0.000 0.236 0.608
#> GSM23159 1 0.1232 0.8834 0.956 0.016 0.000 0.000 0.004 0.024
#> GSM23160 3 0.2872 0.8299 0.000 0.080 0.868 0.000 0.024 0.028
#> GSM23161 1 0.2113 0.8599 0.912 0.048 0.000 0.000 0.032 0.008
#> GSM23162 5 0.5233 0.1495 0.000 0.072 0.260 0.000 0.636 0.032
#> GSM23163 1 0.3917 0.8216 0.784 0.052 0.000 0.000 0.020 0.144
#> GSM23164 1 0.2789 0.8145 0.864 0.044 0.000 0.000 0.088 0.004
#> GSM23165 1 0.3395 0.8182 0.812 0.048 0.000 0.000 0.004 0.136
#> GSM23166 1 0.2519 0.8349 0.884 0.044 0.000 0.000 0.068 0.004
#> GSM23167 1 0.3314 0.8241 0.820 0.048 0.000 0.000 0.004 0.128
#> GSM23168 3 0.2793 0.8299 0.000 0.080 0.872 0.000 0.024 0.024
#> GSM23169 6 0.7156 0.2336 0.000 0.080 0.292 0.000 0.268 0.360
#> GSM23170 1 0.1307 0.8813 0.952 0.032 0.000 0.000 0.008 0.008
#> GSM23171 1 0.0508 0.8844 0.984 0.012 0.000 0.000 0.004 0.000
#> GSM23172 1 0.3355 0.8218 0.816 0.048 0.000 0.000 0.004 0.132
#> GSM23173 3 0.6783 0.1655 0.004 0.092 0.484 0.000 0.128 0.292
#> GSM23174 1 0.0909 0.8812 0.968 0.020 0.000 0.000 0.012 0.000
#> GSM23175 1 0.0508 0.8836 0.984 0.004 0.000 0.000 0.012 0.000
#> GSM23176 1 0.3355 0.8218 0.816 0.048 0.000 0.000 0.004 0.132
#> GSM23177 1 0.1251 0.8784 0.956 0.024 0.000 0.000 0.012 0.008
#> GSM23178 1 0.3019 0.8657 0.864 0.048 0.000 0.000 0.028 0.060
#> GSM23179 3 0.3019 0.8261 0.000 0.080 0.860 0.000 0.024 0.036
#> GSM23180 5 0.4668 0.5434 0.208 0.048 0.000 0.004 0.712 0.028
#> GSM23181 5 0.5126 0.4135 0.348 0.048 0.000 0.000 0.580 0.024
#> GSM23182 5 0.5122 0.5339 0.220 0.048 0.000 0.024 0.684 0.024
#> GSM23183 6 0.5651 0.5044 0.040 0.000 0.104 0.000 0.248 0.608
#> GSM23184 3 0.1296 0.8512 0.000 0.032 0.952 0.000 0.004 0.012
#> GSM23196 2 0.3352 0.9450 0.000 0.776 0.000 0.208 0.008 0.008
#> GSM23197 2 0.3243 0.9502 0.000 0.780 0.000 0.208 0.004 0.008
#> GSM23198 2 0.3352 0.9450 0.000 0.776 0.000 0.208 0.008 0.008
#> GSM23199 4 0.3514 0.7692 0.000 0.040 0.000 0.832 0.048 0.080
#> GSM23200 4 0.5477 -0.3743 0.000 0.452 0.000 0.464 0.040 0.044
#> GSM23201 4 0.3617 0.7602 0.000 0.000 0.000 0.736 0.020 0.244
#> GSM23202 4 0.1686 0.8094 0.000 0.000 0.000 0.924 0.012 0.064
#> GSM23203 2 0.3352 0.9450 0.000 0.776 0.000 0.208 0.008 0.008
#> GSM23204 2 0.3341 0.9496 0.000 0.776 0.000 0.208 0.004 0.012
#> GSM23205 4 0.3617 0.7602 0.000 0.000 0.000 0.736 0.020 0.244
#> GSM23206 2 0.2994 0.9506 0.000 0.788 0.000 0.208 0.000 0.004
#> GSM23207 4 0.1552 0.8041 0.000 0.004 0.000 0.940 0.020 0.036
#> GSM23208 2 0.2854 0.9501 0.000 0.792 0.000 0.208 0.000 0.000
#> GSM23209 2 0.3341 0.9496 0.000 0.776 0.000 0.208 0.004 0.012
#> GSM23210 4 0.3867 0.7650 0.000 0.008 0.000 0.760 0.040 0.192
#> GSM23211 2 0.3341 0.9496 0.000 0.776 0.000 0.208 0.004 0.012
#> GSM23212 4 0.0146 0.8154 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM23213 4 0.0146 0.8154 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM23214 4 0.1625 0.8102 0.000 0.000 0.000 0.928 0.012 0.060
#> GSM23215 2 0.5992 0.5803 0.000 0.532 0.000 0.288 0.024 0.156
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 cell.type(p) disease.state(p) k
#> SD:kmeans 57 3.90e-13 0.052490 2
#> SD:kmeans 57 4.19e-13 0.000423 3
#> SD:kmeans 55 6.87e-12 0.000863 4
#> SD:kmeans 53 8.52e-11 0.000110 5
#> SD:kmeans 49 2.22e-09 0.001727 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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4642 0.536 0.536
#> 3 3 1.000 0.989 0.995 0.4609 0.786 0.600
#> 4 4 0.797 0.851 0.901 0.0898 0.932 0.792
#> 5 5 0.726 0.734 0.841 0.0678 0.925 0.724
#> 6 6 0.734 0.691 0.801 0.0366 0.967 0.848
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
#> GSM23185 1 0 1 1 0
#> GSM23186 1 0 1 1 0
#> GSM23187 1 0 1 1 0
#> GSM23188 1 0 1 1 0
#> GSM23189 1 0 1 1 0
#> GSM23190 1 0 1 1 0
#> GSM23191 1 0 1 1 0
#> GSM23192 1 0 1 1 0
#> GSM23193 1 0 1 1 0
#> GSM23194 1 0 1 1 0
#> GSM23195 1 0 1 1 0
#> GSM23159 1 0 1 1 0
#> GSM23160 1 0 1 1 0
#> GSM23161 1 0 1 1 0
#> GSM23162 1 0 1 1 0
#> GSM23163 1 0 1 1 0
#> GSM23164 1 0 1 1 0
#> GSM23165 1 0 1 1 0
#> GSM23166 1 0 1 1 0
#> GSM23167 1 0 1 1 0
#> GSM23168 1 0 1 1 0
#> GSM23169 1 0 1 1 0
#> GSM23170 1 0 1 1 0
#> GSM23171 1 0 1 1 0
#> GSM23172 1 0 1 1 0
#> GSM23173 1 0 1 1 0
#> GSM23174 1 0 1 1 0
#> GSM23175 1 0 1 1 0
#> GSM23176 1 0 1 1 0
#> GSM23177 1 0 1 1 0
#> GSM23178 1 0 1 1 0
#> GSM23179 1 0 1 1 0
#> GSM23180 1 0 1 1 0
#> GSM23181 1 0 1 1 0
#> GSM23182 1 0 1 1 0
#> GSM23183 1 0 1 1 0
#> GSM23184 1 0 1 1 0
#> GSM23196 2 0 1 0 1
#> GSM23197 2 0 1 0 1
#> GSM23198 2 0 1 0 1
#> GSM23199 2 0 1 0 1
#> GSM23200 2 0 1 0 1
#> GSM23201 2 0 1 0 1
#> GSM23202 2 0 1 0 1
#> GSM23203 2 0 1 0 1
#> GSM23204 2 0 1 0 1
#> GSM23205 2 0 1 0 1
#> GSM23206 2 0 1 0 1
#> GSM23207 2 0 1 0 1
#> GSM23208 2 0 1 0 1
#> GSM23209 2 0 1 0 1
#> GSM23210 2 0 1 0 1
#> GSM23211 2 0 1 0 1
#> GSM23212 2 0 1 0 1
#> GSM23213 2 0 1 0 1
#> GSM23214 2 0 1 0 1
#> GSM23215 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.992 0.000 0 1.000
#> GSM23186 1 0.4062 0.804 0.836 0 0.164
#> GSM23187 3 0.0000 0.992 0.000 0 1.000
#> GSM23188 3 0.0000 0.992 0.000 0 1.000
#> GSM23189 3 0.0000 0.992 0.000 0 1.000
#> GSM23190 3 0.0000 0.992 0.000 0 1.000
#> GSM23191 3 0.1643 0.956 0.044 0 0.956
#> GSM23192 3 0.1031 0.975 0.024 0 0.976
#> GSM23193 3 0.0424 0.987 0.008 0 0.992
#> GSM23194 3 0.0000 0.992 0.000 0 1.000
#> GSM23195 3 0.0237 0.989 0.004 0 0.996
#> GSM23159 1 0.0000 0.991 1.000 0 0.000
#> GSM23160 3 0.0000 0.992 0.000 0 1.000
#> GSM23161 1 0.0000 0.991 1.000 0 0.000
#> GSM23162 3 0.0000 0.992 0.000 0 1.000
#> GSM23163 1 0.0237 0.987 0.996 0 0.004
#> GSM23164 1 0.0000 0.991 1.000 0 0.000
#> GSM23165 1 0.0000 0.991 1.000 0 0.000
#> GSM23166 1 0.0000 0.991 1.000 0 0.000
#> GSM23167 1 0.0000 0.991 1.000 0 0.000
#> GSM23168 3 0.0000 0.992 0.000 0 1.000
#> GSM23169 3 0.0000 0.992 0.000 0 1.000
#> GSM23170 1 0.0000 0.991 1.000 0 0.000
#> GSM23171 1 0.0000 0.991 1.000 0 0.000
#> GSM23172 1 0.0000 0.991 1.000 0 0.000
#> GSM23173 3 0.0000 0.992 0.000 0 1.000
#> GSM23174 1 0.0000 0.991 1.000 0 0.000
#> GSM23175 1 0.0000 0.991 1.000 0 0.000
#> GSM23176 1 0.0000 0.991 1.000 0 0.000
#> GSM23177 1 0.0000 0.991 1.000 0 0.000
#> GSM23178 1 0.0000 0.991 1.000 0 0.000
#> GSM23179 3 0.0000 0.992 0.000 0 1.000
#> GSM23180 1 0.0000 0.991 1.000 0 0.000
#> GSM23181 1 0.0000 0.991 1.000 0 0.000
#> GSM23182 1 0.0000 0.991 1.000 0 0.000
#> GSM23183 3 0.2066 0.939 0.060 0 0.940
#> GSM23184 3 0.0000 0.992 0.000 0 1.000
#> GSM23196 2 0.0000 1.000 0.000 1 0.000
#> GSM23197 2 0.0000 1.000 0.000 1 0.000
#> GSM23198 2 0.0000 1.000 0.000 1 0.000
#> GSM23199 2 0.0000 1.000 0.000 1 0.000
#> GSM23200 2 0.0000 1.000 0.000 1 0.000
#> GSM23201 2 0.0000 1.000 0.000 1 0.000
#> GSM23202 2 0.0000 1.000 0.000 1 0.000
#> GSM23203 2 0.0000 1.000 0.000 1 0.000
#> GSM23204 2 0.0000 1.000 0.000 1 0.000
#> GSM23205 2 0.0000 1.000 0.000 1 0.000
#> GSM23206 2 0.0000 1.000 0.000 1 0.000
#> GSM23207 2 0.0000 1.000 0.000 1 0.000
#> GSM23208 2 0.0000 1.000 0.000 1 0.000
#> GSM23209 2 0.0000 1.000 0.000 1 0.000
#> GSM23210 2 0.0000 1.000 0.000 1 0.000
#> GSM23211 2 0.0000 1.000 0.000 1 0.000
#> GSM23212 2 0.0000 1.000 0.000 1 0.000
#> GSM23213 2 0.0000 1.000 0.000 1 0.000
#> GSM23214 2 0.0000 1.000 0.000 1 0.000
#> GSM23215 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM23186 1 0.4072 0.791 0.828 0.000 0.120 0.052
#> GSM23187 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM23188 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM23189 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM23190 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM23191 3 0.5693 0.713 0.072 0.000 0.688 0.240
#> GSM23192 3 0.5874 0.721 0.124 0.000 0.700 0.176
#> GSM23193 3 0.4281 0.809 0.028 0.000 0.792 0.180
#> GSM23194 3 0.0336 0.921 0.000 0.000 0.992 0.008
#> GSM23195 3 0.4010 0.834 0.100 0.000 0.836 0.064
#> GSM23159 1 0.0817 0.926 0.976 0.000 0.000 0.024
#> GSM23160 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM23161 1 0.2281 0.909 0.904 0.000 0.000 0.096
#> GSM23162 3 0.1716 0.900 0.000 0.000 0.936 0.064
#> GSM23163 1 0.1824 0.918 0.936 0.000 0.004 0.060
#> GSM23164 1 0.2408 0.904 0.896 0.000 0.000 0.104
#> GSM23165 1 0.0817 0.918 0.976 0.000 0.000 0.024
#> GSM23166 1 0.2408 0.903 0.896 0.000 0.000 0.104
#> GSM23167 1 0.0817 0.918 0.976 0.000 0.000 0.024
#> GSM23168 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM23169 3 0.1109 0.915 0.004 0.000 0.968 0.028
#> GSM23170 1 0.0817 0.926 0.976 0.000 0.000 0.024
#> GSM23171 1 0.0469 0.925 0.988 0.000 0.000 0.012
#> GSM23172 1 0.0817 0.918 0.976 0.000 0.000 0.024
#> GSM23173 3 0.0927 0.915 0.008 0.000 0.976 0.016
#> GSM23174 1 0.1389 0.923 0.952 0.000 0.000 0.048
#> GSM23175 1 0.0921 0.926 0.972 0.000 0.000 0.028
#> GSM23176 1 0.0817 0.918 0.976 0.000 0.000 0.024
#> GSM23177 1 0.1302 0.924 0.956 0.000 0.000 0.044
#> GSM23178 1 0.1867 0.920 0.928 0.000 0.000 0.072
#> GSM23179 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM23180 1 0.4898 0.537 0.584 0.000 0.000 0.416
#> GSM23181 1 0.3688 0.829 0.792 0.000 0.000 0.208
#> GSM23182 4 0.4916 -0.215 0.424 0.000 0.000 0.576
#> GSM23183 3 0.5889 0.681 0.212 0.000 0.688 0.100
#> GSM23184 3 0.0000 0.923 0.000 0.000 1.000 0.000
#> GSM23196 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM23199 2 0.3074 0.773 0.000 0.848 0.000 0.152
#> GSM23200 2 0.0921 0.917 0.000 0.972 0.000 0.028
#> GSM23201 4 0.4103 0.830 0.000 0.256 0.000 0.744
#> GSM23202 4 0.4103 0.830 0.000 0.256 0.000 0.744
#> GSM23203 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM23205 4 0.4500 0.750 0.000 0.316 0.000 0.684
#> GSM23206 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM23207 2 0.4661 0.305 0.000 0.652 0.000 0.348
#> GSM23208 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM23210 2 0.2469 0.835 0.000 0.892 0.000 0.108
#> GSM23211 2 0.0000 0.936 0.000 1.000 0.000 0.000
#> GSM23212 4 0.4103 0.830 0.000 0.256 0.000 0.744
#> GSM23213 4 0.4103 0.830 0.000 0.256 0.000 0.744
#> GSM23214 4 0.4103 0.830 0.000 0.256 0.000 0.744
#> GSM23215 2 0.0188 0.934 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.0671 0.907273 0.000 0.000 0.980 0.004 0.016
#> GSM23186 1 0.6636 0.240602 0.544 0.000 0.132 0.032 0.292
#> GSM23187 3 0.0579 0.907035 0.000 0.000 0.984 0.008 0.008
#> GSM23188 3 0.1082 0.903437 0.000 0.000 0.964 0.008 0.028
#> GSM23189 3 0.0324 0.907265 0.000 0.000 0.992 0.004 0.004
#> GSM23190 3 0.0451 0.908177 0.000 0.000 0.988 0.004 0.008
#> GSM23191 5 0.5337 0.485622 0.060 0.000 0.192 0.040 0.708
#> GSM23192 5 0.5388 0.450453 0.068 0.000 0.224 0.024 0.684
#> GSM23193 5 0.5382 0.314772 0.040 0.000 0.340 0.016 0.604
#> GSM23194 3 0.2660 0.832657 0.000 0.000 0.864 0.008 0.128
#> GSM23195 5 0.7086 0.121136 0.156 0.000 0.380 0.036 0.428
#> GSM23159 1 0.2179 0.821079 0.896 0.000 0.000 0.004 0.100
#> GSM23160 3 0.0609 0.904793 0.000 0.000 0.980 0.000 0.020
#> GSM23161 1 0.3724 0.751335 0.788 0.000 0.000 0.028 0.184
#> GSM23162 3 0.3783 0.661752 0.000 0.000 0.740 0.008 0.252
#> GSM23163 1 0.3850 0.756733 0.792 0.000 0.004 0.032 0.172
#> GSM23164 1 0.3779 0.740278 0.776 0.000 0.000 0.024 0.200
#> GSM23165 1 0.2361 0.794575 0.892 0.000 0.000 0.012 0.096
#> GSM23166 1 0.3863 0.725719 0.772 0.000 0.000 0.028 0.200
#> GSM23167 1 0.1942 0.810955 0.920 0.000 0.000 0.012 0.068
#> GSM23168 3 0.1740 0.887128 0.000 0.000 0.932 0.012 0.056
#> GSM23169 3 0.4615 0.702309 0.020 0.000 0.736 0.032 0.212
#> GSM23170 1 0.2331 0.825362 0.900 0.000 0.000 0.020 0.080
#> GSM23171 1 0.1845 0.829795 0.928 0.000 0.000 0.016 0.056
#> GSM23172 1 0.1830 0.809591 0.924 0.000 0.000 0.008 0.068
#> GSM23173 3 0.3913 0.796277 0.036 0.000 0.824 0.032 0.108
#> GSM23174 1 0.2304 0.813016 0.892 0.000 0.000 0.008 0.100
#> GSM23175 1 0.2597 0.820342 0.884 0.000 0.000 0.024 0.092
#> GSM23176 1 0.2448 0.807232 0.892 0.000 0.000 0.020 0.088
#> GSM23177 1 0.2293 0.821006 0.900 0.000 0.000 0.016 0.084
#> GSM23178 1 0.3476 0.793023 0.804 0.000 0.000 0.020 0.176
#> GSM23179 3 0.1041 0.903659 0.000 0.000 0.964 0.004 0.032
#> GSM23180 5 0.5804 0.303491 0.304 0.000 0.000 0.120 0.576
#> GSM23181 5 0.5238 -0.159726 0.476 0.000 0.000 0.044 0.480
#> GSM23182 5 0.6578 0.295627 0.284 0.000 0.000 0.248 0.468
#> GSM23183 5 0.7167 0.249327 0.152 0.000 0.332 0.048 0.468
#> GSM23184 3 0.0771 0.905178 0.000 0.000 0.976 0.004 0.020
#> GSM23196 2 0.0000 0.914675 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.914675 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.914675 0.000 1.000 0.000 0.000 0.000
#> GSM23199 2 0.2852 0.766174 0.000 0.828 0.000 0.172 0.000
#> GSM23200 2 0.1851 0.856869 0.000 0.912 0.000 0.088 0.000
#> GSM23201 4 0.2648 0.875664 0.000 0.152 0.000 0.848 0.000
#> GSM23202 4 0.1908 0.908126 0.000 0.092 0.000 0.908 0.000
#> GSM23203 2 0.0000 0.914675 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.914675 0.000 1.000 0.000 0.000 0.000
#> GSM23205 4 0.4101 0.529285 0.000 0.372 0.000 0.628 0.000
#> GSM23206 2 0.0000 0.914675 0.000 1.000 0.000 0.000 0.000
#> GSM23207 2 0.4287 0.000279 0.000 0.540 0.000 0.460 0.000
#> GSM23208 2 0.0000 0.914675 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.914675 0.000 1.000 0.000 0.000 0.000
#> GSM23210 2 0.3039 0.729368 0.000 0.808 0.000 0.192 0.000
#> GSM23211 2 0.0000 0.914675 0.000 1.000 0.000 0.000 0.000
#> GSM23212 4 0.1965 0.907491 0.000 0.096 0.000 0.904 0.000
#> GSM23213 4 0.1908 0.908126 0.000 0.092 0.000 0.908 0.000
#> GSM23214 4 0.1908 0.908126 0.000 0.092 0.000 0.908 0.000
#> GSM23215 2 0.0963 0.894830 0.000 0.964 0.000 0.036 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.1341 0.8311 0.000 0.000 0.948 0.000 0.024 0.028
#> GSM23186 6 0.6012 -0.0606 0.436 0.000 0.056 0.016 0.040 0.452
#> GSM23187 3 0.0547 0.8327 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM23188 3 0.1477 0.8289 0.000 0.000 0.940 0.004 0.008 0.048
#> GSM23189 3 0.0858 0.8317 0.000 0.000 0.968 0.004 0.000 0.028
#> GSM23190 3 0.1059 0.8329 0.000 0.000 0.964 0.004 0.016 0.016
#> GSM23191 5 0.5015 0.3314 0.044 0.000 0.088 0.012 0.728 0.128
#> GSM23192 6 0.6653 0.1178 0.080 0.000 0.124 0.000 0.368 0.428
#> GSM23193 5 0.5642 0.1935 0.016 0.000 0.204 0.012 0.628 0.140
#> GSM23194 3 0.4207 0.6931 0.000 0.000 0.732 0.012 0.048 0.208
#> GSM23195 6 0.6149 0.4223 0.064 0.000 0.256 0.004 0.104 0.572
#> GSM23159 1 0.4222 0.7523 0.760 0.000 0.000 0.012 0.120 0.108
#> GSM23160 3 0.2019 0.8247 0.000 0.000 0.900 0.000 0.012 0.088
#> GSM23161 1 0.4616 0.6923 0.708 0.000 0.000 0.008 0.180 0.104
#> GSM23162 3 0.5567 0.4395 0.000 0.000 0.584 0.016 0.272 0.128
#> GSM23163 1 0.4590 0.6660 0.712 0.000 0.004 0.004 0.096 0.184
#> GSM23164 1 0.4488 0.6419 0.692 0.000 0.000 0.016 0.248 0.044
#> GSM23165 1 0.2971 0.7445 0.832 0.000 0.000 0.004 0.020 0.144
#> GSM23166 1 0.4607 0.6540 0.684 0.000 0.000 0.016 0.248 0.052
#> GSM23167 1 0.2455 0.7654 0.872 0.000 0.000 0.004 0.012 0.112
#> GSM23168 3 0.2734 0.8152 0.000 0.000 0.864 0.008 0.024 0.104
#> GSM23169 3 0.5157 0.5329 0.004 0.000 0.616 0.004 0.096 0.280
#> GSM23170 1 0.2591 0.7938 0.880 0.000 0.000 0.004 0.064 0.052
#> GSM23171 1 0.2998 0.7868 0.852 0.000 0.000 0.004 0.076 0.068
#> GSM23172 1 0.2624 0.7707 0.856 0.000 0.000 0.000 0.020 0.124
#> GSM23173 3 0.4694 0.6301 0.016 0.000 0.668 0.000 0.052 0.264
#> GSM23174 1 0.3505 0.7639 0.808 0.000 0.000 0.008 0.136 0.048
#> GSM23175 1 0.3932 0.7687 0.796 0.000 0.000 0.024 0.092 0.088
#> GSM23176 1 0.2766 0.7664 0.852 0.000 0.000 0.004 0.020 0.124
#> GSM23177 1 0.3752 0.7745 0.804 0.000 0.000 0.020 0.116 0.060
#> GSM23178 1 0.3592 0.7624 0.812 0.000 0.000 0.020 0.124 0.044
#> GSM23179 3 0.2976 0.8048 0.000 0.000 0.844 0.012 0.020 0.124
#> GSM23180 5 0.4426 0.4946 0.168 0.000 0.000 0.036 0.744 0.052
#> GSM23181 5 0.5393 0.2565 0.352 0.000 0.000 0.024 0.556 0.068
#> GSM23182 5 0.6164 0.4420 0.240 0.000 0.000 0.156 0.556 0.048
#> GSM23183 6 0.6148 0.4565 0.076 0.000 0.196 0.008 0.112 0.608
#> GSM23184 3 0.1332 0.8307 0.000 0.000 0.952 0.008 0.012 0.028
#> GSM23196 2 0.0291 0.9203 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM23197 2 0.0436 0.9204 0.000 0.988 0.000 0.004 0.004 0.004
#> GSM23198 2 0.0146 0.9213 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM23199 2 0.4158 0.6045 0.000 0.720 0.000 0.236 0.020 0.024
#> GSM23200 2 0.2946 0.7707 0.000 0.824 0.000 0.160 0.004 0.012
#> GSM23201 4 0.3740 0.7538 0.000 0.136 0.000 0.800 0.032 0.032
#> GSM23202 4 0.1820 0.7970 0.000 0.056 0.000 0.924 0.008 0.012
#> GSM23203 2 0.0146 0.9213 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM23204 2 0.0665 0.9180 0.000 0.980 0.000 0.008 0.008 0.004
#> GSM23205 4 0.4585 0.6099 0.000 0.304 0.000 0.648 0.020 0.028
#> GSM23206 2 0.0551 0.9199 0.000 0.984 0.000 0.004 0.008 0.004
#> GSM23207 4 0.4652 0.0961 0.000 0.472 0.000 0.496 0.012 0.020
#> GSM23208 2 0.0000 0.9217 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23209 2 0.0291 0.9212 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM23210 2 0.3658 0.7060 0.000 0.776 0.000 0.188 0.020 0.016
#> GSM23211 2 0.0291 0.9217 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM23212 4 0.1615 0.8033 0.000 0.064 0.000 0.928 0.004 0.004
#> GSM23213 4 0.1781 0.8014 0.000 0.060 0.000 0.924 0.008 0.008
#> GSM23214 4 0.1462 0.7996 0.000 0.056 0.000 0.936 0.000 0.008
#> GSM23215 2 0.2015 0.8824 0.000 0.916 0.000 0.056 0.012 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
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 cell.type(p) disease.state(p) k
#> SD:skmeans 57 3.90e-13 0.052490 2
#> SD:skmeans 57 4.19e-13 0.000423 3
#> SD:skmeans 55 6.87e-12 0.000323 4
#> SD:skmeans 47 3.48e-10 0.000331 5
#> SD:skmeans 46 5.67e-10 0.000169 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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.665 0.830 0.930 0.4948 0.495 0.495
#> 3 3 0.841 0.872 0.946 0.3496 0.731 0.506
#> 4 4 0.778 0.845 0.912 0.0970 0.932 0.796
#> 5 5 0.805 0.797 0.895 0.0753 0.920 0.717
#> 6 6 0.788 0.745 0.854 0.0282 0.981 0.910
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
#> GSM23185 2 0.9286 0.5183 0.344 0.656
#> GSM23186 1 0.0000 0.9455 1.000 0.000
#> GSM23187 2 0.9358 0.5018 0.352 0.648
#> GSM23188 2 0.5946 0.7889 0.144 0.856
#> GSM23189 2 0.6712 0.7595 0.176 0.824
#> GSM23190 2 0.8386 0.6495 0.268 0.732
#> GSM23191 1 0.0000 0.9455 1.000 0.000
#> GSM23192 1 0.0000 0.9455 1.000 0.000
#> GSM23193 1 0.0000 0.9455 1.000 0.000
#> GSM23194 1 0.9983 -0.0194 0.524 0.476
#> GSM23195 2 0.9833 0.3192 0.424 0.576
#> GSM23159 1 0.0000 0.9455 1.000 0.000
#> GSM23160 1 0.7299 0.7087 0.796 0.204
#> GSM23161 1 0.0000 0.9455 1.000 0.000
#> GSM23162 1 0.0000 0.9455 1.000 0.000
#> GSM23163 1 0.0000 0.9455 1.000 0.000
#> GSM23164 1 0.0000 0.9455 1.000 0.000
#> GSM23165 1 0.0000 0.9455 1.000 0.000
#> GSM23166 1 0.0000 0.9455 1.000 0.000
#> GSM23167 1 0.0000 0.9455 1.000 0.000
#> GSM23168 1 0.3584 0.8841 0.932 0.068
#> GSM23169 1 0.0000 0.9455 1.000 0.000
#> GSM23170 1 0.0000 0.9455 1.000 0.000
#> GSM23171 1 0.0000 0.9455 1.000 0.000
#> GSM23172 1 0.0000 0.9455 1.000 0.000
#> GSM23173 1 0.3274 0.8923 0.940 0.060
#> GSM23174 1 0.0000 0.9455 1.000 0.000
#> GSM23175 1 0.0000 0.9455 1.000 0.000
#> GSM23176 1 0.0000 0.9455 1.000 0.000
#> GSM23177 1 0.0000 0.9455 1.000 0.000
#> GSM23178 1 0.0000 0.9455 1.000 0.000
#> GSM23179 1 0.9460 0.3679 0.636 0.364
#> GSM23180 1 0.0000 0.9455 1.000 0.000
#> GSM23181 1 0.0000 0.9455 1.000 0.000
#> GSM23182 1 0.0000 0.9455 1.000 0.000
#> GSM23183 1 0.0000 0.9455 1.000 0.000
#> GSM23184 1 0.7528 0.6892 0.784 0.216
#> GSM23196 2 0.0000 0.8841 0.000 1.000
#> GSM23197 2 0.0000 0.8841 0.000 1.000
#> GSM23198 2 0.0000 0.8841 0.000 1.000
#> GSM23199 2 0.0000 0.8841 0.000 1.000
#> GSM23200 2 0.0000 0.8841 0.000 1.000
#> GSM23201 2 0.1184 0.8771 0.016 0.984
#> GSM23202 2 0.9795 0.3204 0.416 0.584
#> GSM23203 2 0.0000 0.8841 0.000 1.000
#> GSM23204 2 0.0000 0.8841 0.000 1.000
#> GSM23205 2 0.0000 0.8841 0.000 1.000
#> GSM23206 2 0.0000 0.8841 0.000 1.000
#> GSM23207 2 0.0000 0.8841 0.000 1.000
#> GSM23208 2 0.0000 0.8841 0.000 1.000
#> GSM23209 2 0.0000 0.8841 0.000 1.000
#> GSM23210 2 0.0000 0.8841 0.000 1.000
#> GSM23211 2 0.0000 0.8841 0.000 1.000
#> GSM23212 2 0.0376 0.8826 0.004 0.996
#> GSM23213 2 0.4939 0.8219 0.108 0.892
#> GSM23214 2 0.9460 0.4709 0.364 0.636
#> GSM23215 2 0.0000 0.8841 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.8915 0.000 0.000 1.000
#> GSM23186 1 0.4121 0.7614 0.832 0.000 0.168
#> GSM23187 3 0.0000 0.8915 0.000 0.000 1.000
#> GSM23188 3 0.0000 0.8915 0.000 0.000 1.000
#> GSM23189 3 0.0000 0.8915 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.8915 0.000 0.000 1.000
#> GSM23191 1 0.3038 0.8262 0.896 0.000 0.104
#> GSM23192 1 0.5926 0.4267 0.644 0.000 0.356
#> GSM23193 3 0.6026 0.5085 0.376 0.000 0.624
#> GSM23194 3 0.0000 0.8915 0.000 0.000 1.000
#> GSM23195 3 0.5733 0.6070 0.324 0.000 0.676
#> GSM23159 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23160 3 0.0000 0.8915 0.000 0.000 1.000
#> GSM23161 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23162 3 0.1753 0.8711 0.048 0.000 0.952
#> GSM23163 1 0.0237 0.9350 0.996 0.000 0.004
#> GSM23164 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23165 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23166 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23167 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23168 3 0.0000 0.8915 0.000 0.000 1.000
#> GSM23169 3 0.3816 0.8085 0.148 0.000 0.852
#> GSM23170 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23171 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23172 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23173 3 0.4654 0.7546 0.208 0.000 0.792
#> GSM23174 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23175 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23176 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23177 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23178 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23179 3 0.0000 0.8915 0.000 0.000 1.000
#> GSM23180 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23181 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23182 1 0.0000 0.9382 1.000 0.000 0.000
#> GSM23183 3 0.6280 0.3071 0.460 0.000 0.540
#> GSM23184 3 0.0000 0.8915 0.000 0.000 1.000
#> GSM23196 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23197 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23198 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23199 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23200 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23201 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23202 1 0.6295 0.0551 0.528 0.472 0.000
#> GSM23203 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23204 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23205 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23206 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23207 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23208 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23209 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23210 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23211 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23212 2 0.0000 0.9748 0.000 1.000 0.000
#> GSM23213 2 0.2165 0.9113 0.064 0.936 0.000
#> GSM23214 2 0.5835 0.4701 0.340 0.660 0.000
#> GSM23215 2 0.0000 0.9748 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0336 0.867 0.000 0.000 0.992 0.008
#> GSM23186 1 0.3732 0.822 0.852 0.000 0.092 0.056
#> GSM23187 3 0.0336 0.867 0.000 0.000 0.992 0.008
#> GSM23188 3 0.0336 0.867 0.000 0.000 0.992 0.008
#> GSM23189 3 0.0336 0.867 0.000 0.000 0.992 0.008
#> GSM23190 3 0.0336 0.867 0.000 0.000 0.992 0.008
#> GSM23191 1 0.5995 0.666 0.660 0.000 0.084 0.256
#> GSM23192 1 0.6745 0.576 0.604 0.000 0.244 0.152
#> GSM23193 3 0.6805 0.528 0.260 0.000 0.592 0.148
#> GSM23194 3 0.0336 0.866 0.000 0.000 0.992 0.008
#> GSM23195 3 0.5206 0.633 0.308 0.000 0.668 0.024
#> GSM23159 1 0.1474 0.914 0.948 0.000 0.000 0.052
#> GSM23160 3 0.0000 0.866 0.000 0.000 1.000 0.000
#> GSM23161 1 0.1637 0.905 0.940 0.000 0.000 0.060
#> GSM23162 3 0.3117 0.821 0.028 0.000 0.880 0.092
#> GSM23163 1 0.1743 0.902 0.940 0.000 0.004 0.056
#> GSM23164 1 0.2345 0.899 0.900 0.000 0.000 0.100
#> GSM23165 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> GSM23166 1 0.2469 0.903 0.892 0.000 0.000 0.108
#> GSM23167 1 0.0188 0.915 0.996 0.000 0.000 0.004
#> GSM23168 3 0.0707 0.864 0.000 0.000 0.980 0.020
#> GSM23169 3 0.4163 0.794 0.076 0.000 0.828 0.096
#> GSM23170 1 0.0469 0.916 0.988 0.000 0.000 0.012
#> GSM23171 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> GSM23172 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> GSM23173 3 0.4399 0.737 0.212 0.000 0.768 0.020
#> GSM23174 1 0.1940 0.907 0.924 0.000 0.000 0.076
#> GSM23175 1 0.0817 0.917 0.976 0.000 0.000 0.024
#> GSM23176 1 0.0707 0.912 0.980 0.000 0.000 0.020
#> GSM23177 1 0.0000 0.915 1.000 0.000 0.000 0.000
#> GSM23178 1 0.2345 0.899 0.900 0.000 0.000 0.100
#> GSM23179 3 0.0592 0.865 0.000 0.000 0.984 0.016
#> GSM23180 1 0.2345 0.899 0.900 0.000 0.000 0.100
#> GSM23181 1 0.2345 0.899 0.900 0.000 0.000 0.100
#> GSM23182 4 0.4134 0.507 0.260 0.000 0.000 0.740
#> GSM23183 3 0.6315 0.375 0.396 0.000 0.540 0.064
#> GSM23184 3 0.0000 0.866 0.000 0.000 1.000 0.000
#> GSM23196 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM23199 2 0.1211 0.914 0.000 0.960 0.000 0.040
#> GSM23200 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM23201 4 0.2973 0.863 0.000 0.144 0.000 0.856
#> GSM23202 4 0.3123 0.855 0.000 0.156 0.000 0.844
#> GSM23203 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM23205 2 0.4761 0.274 0.000 0.628 0.000 0.372
#> GSM23206 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM23207 2 0.3610 0.714 0.000 0.800 0.000 0.200
#> GSM23208 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM23210 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM23211 2 0.0000 0.949 0.000 1.000 0.000 0.000
#> GSM23212 4 0.3123 0.855 0.000 0.156 0.000 0.844
#> GSM23213 4 0.2281 0.864 0.000 0.096 0.000 0.904
#> GSM23214 4 0.1940 0.853 0.000 0.076 0.000 0.924
#> GSM23215 2 0.0000 0.949 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.0162 0.8790 0.000 0.000 0.996 0.000 0.004
#> GSM23186 1 0.3573 0.7652 0.812 0.000 0.036 0.000 0.152
#> GSM23187 3 0.0162 0.8790 0.000 0.000 0.996 0.000 0.004
#> GSM23188 3 0.0162 0.8790 0.000 0.000 0.996 0.000 0.004
#> GSM23189 3 0.0162 0.8790 0.000 0.000 0.996 0.000 0.004
#> GSM23190 3 0.0162 0.8790 0.000 0.000 0.996 0.000 0.004
#> GSM23191 5 0.2352 0.6971 0.092 0.000 0.008 0.004 0.896
#> GSM23192 5 0.0671 0.6566 0.004 0.000 0.016 0.000 0.980
#> GSM23193 5 0.1597 0.6711 0.012 0.000 0.048 0.000 0.940
#> GSM23194 3 0.0609 0.8749 0.000 0.000 0.980 0.000 0.020
#> GSM23195 3 0.6043 0.3048 0.320 0.000 0.540 0.000 0.140
#> GSM23159 1 0.1608 0.8612 0.928 0.000 0.000 0.000 0.072
#> GSM23160 3 0.0162 0.8780 0.000 0.000 0.996 0.000 0.004
#> GSM23161 1 0.3366 0.7559 0.768 0.000 0.000 0.000 0.232
#> GSM23162 5 0.4829 -0.0832 0.020 0.000 0.480 0.000 0.500
#> GSM23163 1 0.3143 0.7664 0.796 0.000 0.000 0.000 0.204
#> GSM23164 1 0.3177 0.7632 0.792 0.000 0.000 0.000 0.208
#> GSM23165 1 0.0000 0.8751 1.000 0.000 0.000 0.000 0.000
#> GSM23166 1 0.3816 0.6890 0.696 0.000 0.000 0.000 0.304
#> GSM23167 1 0.0162 0.8752 0.996 0.000 0.000 0.000 0.004
#> GSM23168 3 0.1270 0.8565 0.000 0.000 0.948 0.000 0.052
#> GSM23169 3 0.4990 0.4364 0.048 0.000 0.628 0.000 0.324
#> GSM23170 1 0.0880 0.8792 0.968 0.000 0.000 0.000 0.032
#> GSM23171 1 0.0404 0.8763 0.988 0.000 0.000 0.000 0.012
#> GSM23172 1 0.0404 0.8763 0.988 0.000 0.000 0.000 0.012
#> GSM23173 3 0.5105 0.5324 0.264 0.000 0.660 0.000 0.076
#> GSM23174 1 0.1965 0.8432 0.904 0.000 0.000 0.000 0.096
#> GSM23175 1 0.0880 0.8764 0.968 0.000 0.000 0.000 0.032
#> GSM23176 1 0.1792 0.8563 0.916 0.000 0.000 0.000 0.084
#> GSM23177 1 0.0794 0.8751 0.972 0.000 0.000 0.000 0.028
#> GSM23178 1 0.2179 0.8318 0.888 0.000 0.000 0.000 0.112
#> GSM23179 3 0.0880 0.8686 0.000 0.000 0.968 0.000 0.032
#> GSM23180 5 0.4060 0.5481 0.360 0.000 0.000 0.000 0.640
#> GSM23181 5 0.4074 0.5446 0.364 0.000 0.000 0.000 0.636
#> GSM23182 5 0.5731 0.6083 0.196 0.000 0.000 0.180 0.624
#> GSM23183 5 0.5557 0.5889 0.260 0.000 0.116 0.000 0.624
#> GSM23184 3 0.0290 0.8769 0.000 0.000 0.992 0.000 0.008
#> GSM23196 2 0.0000 0.9368 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.9368 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.9368 0.000 1.000 0.000 0.000 0.000
#> GSM23199 2 0.2020 0.8520 0.000 0.900 0.000 0.100 0.000
#> GSM23200 2 0.0000 0.9368 0.000 1.000 0.000 0.000 0.000
#> GSM23201 4 0.0162 0.9944 0.000 0.004 0.000 0.996 0.000
#> GSM23202 4 0.0000 0.9986 0.000 0.000 0.000 1.000 0.000
#> GSM23203 2 0.0000 0.9368 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.9368 0.000 1.000 0.000 0.000 0.000
#> GSM23205 2 0.3932 0.5084 0.000 0.672 0.000 0.328 0.000
#> GSM23206 2 0.0000 0.9368 0.000 1.000 0.000 0.000 0.000
#> GSM23207 2 0.4219 0.3185 0.000 0.584 0.000 0.416 0.000
#> GSM23208 2 0.0000 0.9368 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.9368 0.000 1.000 0.000 0.000 0.000
#> GSM23210 2 0.0000 0.9368 0.000 1.000 0.000 0.000 0.000
#> GSM23211 2 0.0000 0.9368 0.000 1.000 0.000 0.000 0.000
#> GSM23212 4 0.0000 0.9986 0.000 0.000 0.000 1.000 0.000
#> GSM23213 4 0.0000 0.9986 0.000 0.000 0.000 1.000 0.000
#> GSM23214 4 0.0000 0.9986 0.000 0.000 0.000 1.000 0.000
#> GSM23215 2 0.0000 0.9368 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0000 0.8754 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23186 1 0.5738 0.3570 0.536 0.000 0.016 0.000 0.128 0.320
#> GSM23187 3 0.0000 0.8754 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23188 3 0.0000 0.8754 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23189 3 0.0260 0.8759 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM23190 3 0.0000 0.8754 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23191 5 0.0865 0.4472 0.036 0.000 0.000 0.000 0.964 0.000
#> GSM23192 5 0.3163 0.2921 0.000 0.000 0.004 0.000 0.764 0.232
#> GSM23193 5 0.0405 0.4321 0.004 0.000 0.000 0.000 0.988 0.008
#> GSM23194 3 0.2340 0.8604 0.000 0.000 0.852 0.000 0.000 0.148
#> GSM23195 6 0.4659 0.5625 0.260 0.000 0.028 0.000 0.036 0.676
#> GSM23159 1 0.1480 0.8217 0.940 0.000 0.000 0.000 0.040 0.020
#> GSM23160 3 0.2178 0.8645 0.000 0.000 0.868 0.000 0.000 0.132
#> GSM23161 1 0.4563 0.6727 0.700 0.000 0.000 0.000 0.164 0.136
#> GSM23162 5 0.5615 0.0537 0.012 0.000 0.280 0.000 0.568 0.140
#> GSM23163 1 0.4910 0.6616 0.656 0.000 0.000 0.000 0.152 0.192
#> GSM23164 1 0.3017 0.7843 0.844 0.000 0.000 0.000 0.084 0.072
#> GSM23165 1 0.1957 0.8066 0.888 0.000 0.000 0.000 0.000 0.112
#> GSM23166 1 0.4336 0.7047 0.724 0.000 0.000 0.000 0.160 0.116
#> GSM23167 1 0.1411 0.8275 0.936 0.000 0.000 0.000 0.004 0.060
#> GSM23168 3 0.3200 0.8321 0.000 0.000 0.788 0.000 0.016 0.196
#> GSM23169 3 0.5522 0.4517 0.024 0.000 0.604 0.000 0.260 0.112
#> GSM23170 1 0.2039 0.8310 0.904 0.000 0.000 0.000 0.020 0.076
#> GSM23171 1 0.0458 0.8273 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM23172 1 0.1610 0.8123 0.916 0.000 0.000 0.000 0.000 0.084
#> GSM23173 6 0.4734 0.4106 0.120 0.000 0.208 0.000 0.000 0.672
#> GSM23174 1 0.1719 0.8073 0.924 0.000 0.000 0.000 0.060 0.016
#> GSM23175 1 0.0909 0.8278 0.968 0.000 0.000 0.000 0.020 0.012
#> GSM23176 1 0.3455 0.7884 0.800 0.000 0.000 0.000 0.056 0.144
#> GSM23177 1 0.2494 0.8225 0.864 0.000 0.000 0.000 0.016 0.120
#> GSM23178 1 0.2404 0.8067 0.884 0.000 0.000 0.000 0.080 0.036
#> GSM23179 3 0.3071 0.8422 0.000 0.000 0.804 0.000 0.016 0.180
#> GSM23180 5 0.3993 0.1930 0.476 0.000 0.000 0.000 0.520 0.004
#> GSM23181 5 0.3867 0.1704 0.488 0.000 0.000 0.000 0.512 0.000
#> GSM23182 5 0.5694 0.2835 0.188 0.000 0.000 0.304 0.508 0.000
#> GSM23183 6 0.5283 0.4524 0.180 0.000 0.004 0.000 0.196 0.620
#> GSM23184 3 0.2454 0.8569 0.000 0.000 0.840 0.000 0.000 0.160
#> GSM23196 2 0.0000 0.9351 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.9351 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.9351 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23199 2 0.1814 0.8513 0.000 0.900 0.000 0.100 0.000 0.000
#> GSM23200 2 0.0000 0.9351 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23201 4 0.0146 0.9937 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM23202 4 0.0000 0.9984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23203 2 0.0000 0.9351 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.9351 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23205 2 0.3563 0.4885 0.000 0.664 0.000 0.336 0.000 0.000
#> GSM23206 2 0.0000 0.9351 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23207 2 0.3747 0.3757 0.000 0.604 0.000 0.396 0.000 0.000
#> GSM23208 2 0.0000 0.9351 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.9351 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23210 2 0.0000 0.9351 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23211 2 0.0000 0.9351 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23212 4 0.0000 0.9984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23213 4 0.0000 0.9984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23214 4 0.0000 0.9984 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23215 2 0.0000 0.9351 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> SD:pam 52 2.17e-08 7.91e-01 2
#> SD:pam 53 3.10e-12 5.20e-03 3
#> SD:pam 55 4.19e-11 7.64e-04 4
#> SD:pam 53 8.52e-11 6.78e-05 5
#> SD:pam 44 6.42e-09 4.36e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4642 0.536 0.536
#> 3 3 0.718 0.933 0.885 0.3957 0.787 0.603
#> 4 4 0.811 0.833 0.921 0.1206 0.837 0.567
#> 5 5 0.855 0.783 0.866 0.0912 0.954 0.828
#> 6 6 0.869 0.775 0.874 0.0506 0.915 0.642
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
#> GSM23185 1 0 1 1 0
#> GSM23186 1 0 1 1 0
#> GSM23187 1 0 1 1 0
#> GSM23188 1 0 1 1 0
#> GSM23189 1 0 1 1 0
#> GSM23190 1 0 1 1 0
#> GSM23191 1 0 1 1 0
#> GSM23192 1 0 1 1 0
#> GSM23193 1 0 1 1 0
#> GSM23194 1 0 1 1 0
#> GSM23195 1 0 1 1 0
#> GSM23159 1 0 1 1 0
#> GSM23160 1 0 1 1 0
#> GSM23161 1 0 1 1 0
#> GSM23162 1 0 1 1 0
#> GSM23163 1 0 1 1 0
#> GSM23164 1 0 1 1 0
#> GSM23165 1 0 1 1 0
#> GSM23166 1 0 1 1 0
#> GSM23167 1 0 1 1 0
#> GSM23168 1 0 1 1 0
#> GSM23169 1 0 1 1 0
#> GSM23170 1 0 1 1 0
#> GSM23171 1 0 1 1 0
#> GSM23172 1 0 1 1 0
#> GSM23173 1 0 1 1 0
#> GSM23174 1 0 1 1 0
#> GSM23175 1 0 1 1 0
#> GSM23176 1 0 1 1 0
#> GSM23177 1 0 1 1 0
#> GSM23178 1 0 1 1 0
#> GSM23179 1 0 1 1 0
#> GSM23180 1 0 1 1 0
#> GSM23181 1 0 1 1 0
#> GSM23182 1 0 1 1 0
#> GSM23183 1 0 1 1 0
#> GSM23184 1 0 1 1 0
#> GSM23196 2 0 1 0 1
#> GSM23197 2 0 1 0 1
#> GSM23198 2 0 1 0 1
#> GSM23199 2 0 1 0 1
#> GSM23200 2 0 1 0 1
#> GSM23201 2 0 1 0 1
#> GSM23202 2 0 1 0 1
#> GSM23203 2 0 1 0 1
#> GSM23204 2 0 1 0 1
#> GSM23205 2 0 1 0 1
#> GSM23206 2 0 1 0 1
#> GSM23207 2 0 1 0 1
#> GSM23208 2 0 1 0 1
#> GSM23209 2 0 1 0 1
#> GSM23210 2 0 1 0 1
#> GSM23211 2 0 1 0 1
#> GSM23212 2 0 1 0 1
#> GSM23213 2 0 1 0 1
#> GSM23214 2 0 1 0 1
#> GSM23215 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.4399 0.959 0.188 0.000 0.812
#> GSM23186 1 0.1964 0.915 0.944 0.000 0.056
#> GSM23187 3 0.4399 0.959 0.188 0.000 0.812
#> GSM23188 3 0.4750 0.941 0.216 0.000 0.784
#> GSM23189 3 0.4605 0.950 0.204 0.000 0.796
#> GSM23190 3 0.4399 0.959 0.188 0.000 0.812
#> GSM23191 3 0.4399 0.959 0.188 0.000 0.812
#> GSM23192 3 0.4399 0.959 0.188 0.000 0.812
#> GSM23193 3 0.4399 0.959 0.188 0.000 0.812
#> GSM23194 3 0.4399 0.959 0.188 0.000 0.812
#> GSM23195 3 0.5968 0.771 0.364 0.000 0.636
#> GSM23159 1 0.0000 0.970 1.000 0.000 0.000
#> GSM23160 3 0.4399 0.959 0.188 0.000 0.812
#> GSM23161 1 0.1163 0.956 0.972 0.000 0.028
#> GSM23162 3 0.4399 0.959 0.188 0.000 0.812
#> GSM23163 1 0.0747 0.963 0.984 0.000 0.016
#> GSM23164 1 0.1163 0.956 0.972 0.000 0.028
#> GSM23165 1 0.0000 0.970 1.000 0.000 0.000
#> GSM23166 1 0.1163 0.956 0.972 0.000 0.028
#> GSM23167 1 0.0000 0.970 1.000 0.000 0.000
#> GSM23168 3 0.4399 0.959 0.188 0.000 0.812
#> GSM23169 3 0.4399 0.959 0.188 0.000 0.812
#> GSM23170 1 0.0000 0.970 1.000 0.000 0.000
#> GSM23171 1 0.0000 0.970 1.000 0.000 0.000
#> GSM23172 1 0.0000 0.970 1.000 0.000 0.000
#> GSM23173 3 0.5621 0.853 0.308 0.000 0.692
#> GSM23174 1 0.0000 0.970 1.000 0.000 0.000
#> GSM23175 1 0.0000 0.970 1.000 0.000 0.000
#> GSM23176 1 0.0000 0.970 1.000 0.000 0.000
#> GSM23177 1 0.0892 0.961 0.980 0.000 0.020
#> GSM23178 1 0.0000 0.970 1.000 0.000 0.000
#> GSM23179 3 0.4399 0.959 0.188 0.000 0.812
#> GSM23180 3 0.5016 0.922 0.240 0.000 0.760
#> GSM23181 1 0.4605 0.678 0.796 0.000 0.204
#> GSM23182 3 0.5098 0.915 0.248 0.000 0.752
#> GSM23183 3 0.5948 0.778 0.360 0.000 0.640
#> GSM23184 3 0.4399 0.959 0.188 0.000 0.812
#> GSM23196 2 0.4399 0.924 0.000 0.812 0.188
#> GSM23197 2 0.4399 0.924 0.000 0.812 0.188
#> GSM23198 2 0.4399 0.924 0.000 0.812 0.188
#> GSM23199 2 0.0000 0.924 0.000 1.000 0.000
#> GSM23200 2 0.4399 0.924 0.000 0.812 0.188
#> GSM23201 2 0.0000 0.924 0.000 1.000 0.000
#> GSM23202 2 0.0000 0.924 0.000 1.000 0.000
#> GSM23203 2 0.4399 0.924 0.000 0.812 0.188
#> GSM23204 2 0.4399 0.924 0.000 0.812 0.188
#> GSM23205 2 0.0000 0.924 0.000 1.000 0.000
#> GSM23206 2 0.4399 0.924 0.000 0.812 0.188
#> GSM23207 2 0.0000 0.924 0.000 1.000 0.000
#> GSM23208 2 0.4399 0.924 0.000 0.812 0.188
#> GSM23209 2 0.4399 0.924 0.000 0.812 0.188
#> GSM23210 2 0.0000 0.924 0.000 1.000 0.000
#> GSM23211 2 0.4399 0.924 0.000 0.812 0.188
#> GSM23212 2 0.0000 0.924 0.000 1.000 0.000
#> GSM23213 2 0.0000 0.924 0.000 1.000 0.000
#> GSM23214 2 0.0000 0.924 0.000 1.000 0.000
#> GSM23215 2 0.0000 0.924 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0000 0.868 0.000 0.000 1.000 0.000
#> GSM23186 1 0.1820 0.860 0.944 0.000 0.036 0.020
#> GSM23187 3 0.0000 0.868 0.000 0.000 1.000 0.000
#> GSM23188 3 0.0000 0.868 0.000 0.000 1.000 0.000
#> GSM23189 3 0.0000 0.868 0.000 0.000 1.000 0.000
#> GSM23190 3 0.0000 0.868 0.000 0.000 1.000 0.000
#> GSM23191 3 0.6155 0.238 0.412 0.000 0.536 0.052
#> GSM23192 3 0.5060 0.285 0.412 0.000 0.584 0.004
#> GSM23193 3 0.4459 0.727 0.188 0.000 0.780 0.032
#> GSM23194 3 0.0188 0.868 0.004 0.000 0.996 0.000
#> GSM23195 1 0.5339 0.420 0.624 0.000 0.356 0.020
#> GSM23159 1 0.0469 0.887 0.988 0.000 0.000 0.012
#> GSM23160 3 0.0000 0.868 0.000 0.000 1.000 0.000
#> GSM23161 1 0.0188 0.888 0.996 0.000 0.000 0.004
#> GSM23162 3 0.4008 0.768 0.148 0.000 0.820 0.032
#> GSM23163 1 0.0804 0.884 0.980 0.000 0.008 0.012
#> GSM23164 1 0.0000 0.888 1.000 0.000 0.000 0.000
#> GSM23165 1 0.0592 0.885 0.984 0.000 0.000 0.016
#> GSM23166 1 0.0000 0.888 1.000 0.000 0.000 0.000
#> GSM23167 1 0.0188 0.888 0.996 0.000 0.000 0.004
#> GSM23168 3 0.0469 0.866 0.012 0.000 0.988 0.000
#> GSM23169 3 0.4155 0.666 0.240 0.000 0.756 0.004
#> GSM23170 1 0.0000 0.888 1.000 0.000 0.000 0.000
#> GSM23171 1 0.0188 0.888 0.996 0.000 0.000 0.004
#> GSM23172 1 0.0188 0.888 0.996 0.000 0.000 0.004
#> GSM23173 1 0.5570 0.170 0.540 0.000 0.440 0.020
#> GSM23174 1 0.0188 0.888 0.996 0.000 0.000 0.004
#> GSM23175 1 0.0188 0.888 0.996 0.000 0.000 0.004
#> GSM23176 1 0.0707 0.884 0.980 0.000 0.000 0.020
#> GSM23177 1 0.0000 0.888 1.000 0.000 0.000 0.000
#> GSM23178 1 0.0000 0.888 1.000 0.000 0.000 0.000
#> GSM23179 3 0.0336 0.867 0.008 0.000 0.992 0.000
#> GSM23180 1 0.5866 0.418 0.624 0.000 0.324 0.052
#> GSM23181 1 0.0469 0.884 0.988 0.000 0.012 0.000
#> GSM23182 1 0.5866 0.418 0.624 0.000 0.324 0.052
#> GSM23183 1 0.4988 0.558 0.692 0.000 0.288 0.020
#> GSM23184 3 0.0000 0.868 0.000 0.000 1.000 0.000
#> GSM23196 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM23199 4 0.3356 0.885 0.000 0.176 0.000 0.824
#> GSM23200 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM23201 4 0.0707 0.918 0.000 0.020 0.000 0.980
#> GSM23202 4 0.0707 0.918 0.000 0.020 0.000 0.980
#> GSM23203 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM23205 4 0.1637 0.922 0.000 0.060 0.000 0.940
#> GSM23206 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM23207 4 0.3400 0.882 0.000 0.180 0.000 0.820
#> GSM23208 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM23210 4 0.3311 0.888 0.000 0.172 0.000 0.828
#> GSM23211 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM23212 4 0.1557 0.922 0.000 0.056 0.000 0.944
#> GSM23213 4 0.0707 0.918 0.000 0.020 0.000 0.980
#> GSM23214 4 0.0707 0.918 0.000 0.020 0.000 0.980
#> GSM23215 4 0.3311 0.888 0.000 0.172 0.000 0.828
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.0000 0.8806 0.000 0.000 1.000 0.000 0.000
#> GSM23186 1 0.4074 0.7006 0.636 0.000 0.000 0.000 0.364
#> GSM23187 3 0.0000 0.8806 0.000 0.000 1.000 0.000 0.000
#> GSM23188 3 0.0000 0.8806 0.000 0.000 1.000 0.000 0.000
#> GSM23189 3 0.0000 0.8806 0.000 0.000 1.000 0.000 0.000
#> GSM23190 3 0.0000 0.8806 0.000 0.000 1.000 0.000 0.000
#> GSM23191 5 0.4380 0.5124 0.000 0.000 0.376 0.008 0.616
#> GSM23192 3 0.4610 -0.0762 0.012 0.000 0.556 0.000 0.432
#> GSM23193 3 0.3796 0.4327 0.000 0.000 0.700 0.000 0.300
#> GSM23194 3 0.0000 0.8806 0.000 0.000 1.000 0.000 0.000
#> GSM23195 1 0.3304 0.6824 0.816 0.000 0.016 0.000 0.168
#> GSM23159 1 0.0609 0.7620 0.980 0.000 0.000 0.000 0.020
#> GSM23160 3 0.0290 0.8741 0.000 0.000 0.992 0.000 0.008
#> GSM23161 1 0.1121 0.7337 0.956 0.000 0.000 0.000 0.044
#> GSM23162 3 0.3424 0.5595 0.000 0.000 0.760 0.000 0.240
#> GSM23163 1 0.0510 0.7588 0.984 0.000 0.000 0.000 0.016
#> GSM23164 1 0.3707 0.3788 0.716 0.000 0.000 0.000 0.284
#> GSM23165 1 0.4074 0.6992 0.636 0.000 0.000 0.000 0.364
#> GSM23166 1 0.3684 0.3879 0.720 0.000 0.000 0.000 0.280
#> GSM23167 1 0.3816 0.7207 0.696 0.000 0.000 0.000 0.304
#> GSM23168 3 0.0000 0.8806 0.000 0.000 1.000 0.000 0.000
#> GSM23169 3 0.2513 0.7646 0.008 0.000 0.876 0.000 0.116
#> GSM23170 1 0.3452 0.7403 0.756 0.000 0.000 0.000 0.244
#> GSM23171 1 0.2605 0.7627 0.852 0.000 0.000 0.000 0.148
#> GSM23172 1 0.3796 0.7212 0.700 0.000 0.000 0.000 0.300
#> GSM23173 1 0.6342 0.0448 0.476 0.000 0.356 0.000 0.168
#> GSM23174 1 0.2929 0.7587 0.820 0.000 0.000 0.000 0.180
#> GSM23175 1 0.0510 0.7573 0.984 0.000 0.000 0.000 0.016
#> GSM23176 1 0.4015 0.7068 0.652 0.000 0.000 0.000 0.348
#> GSM23177 1 0.0000 0.7565 1.000 0.000 0.000 0.000 0.000
#> GSM23178 1 0.0162 0.7584 0.996 0.000 0.000 0.000 0.004
#> GSM23179 3 0.0000 0.8806 0.000 0.000 1.000 0.000 0.000
#> GSM23180 5 0.5514 0.6807 0.068 0.000 0.292 0.012 0.628
#> GSM23181 5 0.4297 0.1253 0.472 0.000 0.000 0.000 0.528
#> GSM23182 5 0.5514 0.6807 0.068 0.000 0.292 0.012 0.628
#> GSM23183 1 0.3304 0.6807 0.816 0.000 0.016 0.000 0.168
#> GSM23184 3 0.0000 0.8806 0.000 0.000 1.000 0.000 0.000
#> GSM23196 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM23199 4 0.1410 0.9538 0.000 0.060 0.000 0.940 0.000
#> GSM23200 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM23201 4 0.0000 0.9691 0.000 0.000 0.000 1.000 0.000
#> GSM23202 4 0.0000 0.9691 0.000 0.000 0.000 1.000 0.000
#> GSM23203 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM23205 4 0.0162 0.9697 0.000 0.004 0.000 0.996 0.000
#> GSM23206 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM23207 4 0.1341 0.9562 0.000 0.056 0.000 0.944 0.000
#> GSM23208 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM23210 4 0.1544 0.9468 0.000 0.068 0.000 0.932 0.000
#> GSM23211 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM23212 4 0.0162 0.9697 0.000 0.004 0.000 0.996 0.000
#> GSM23213 4 0.0000 0.9691 0.000 0.000 0.000 1.000 0.000
#> GSM23214 4 0.0000 0.9691 0.000 0.000 0.000 1.000 0.000
#> GSM23215 4 0.1341 0.9562 0.000 0.056 0.000 0.944 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0000 0.9426 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23186 6 0.3629 0.6516 0.276 0.000 0.000 0.000 0.012 0.712
#> GSM23187 3 0.0000 0.9426 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23188 3 0.0000 0.9426 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23189 3 0.0000 0.9426 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23190 3 0.0000 0.9426 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23191 5 0.0000 0.6812 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM23192 5 0.3671 0.6142 0.000 0.000 0.208 0.000 0.756 0.036
#> GSM23193 5 0.4117 0.5862 0.000 0.000 0.296 0.000 0.672 0.032
#> GSM23194 3 0.1921 0.8906 0.000 0.000 0.916 0.000 0.052 0.032
#> GSM23195 1 0.6188 -0.0982 0.404 0.000 0.004 0.000 0.288 0.304
#> GSM23159 1 0.1957 0.6744 0.888 0.000 0.000 0.000 0.000 0.112
#> GSM23160 3 0.0405 0.9407 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM23161 1 0.0146 0.6825 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM23162 5 0.4219 0.5531 0.000 0.000 0.320 0.000 0.648 0.032
#> GSM23163 1 0.1610 0.6859 0.916 0.000 0.000 0.000 0.000 0.084
#> GSM23164 1 0.2201 0.6372 0.896 0.000 0.000 0.000 0.076 0.028
#> GSM23165 6 0.2300 0.7872 0.144 0.000 0.000 0.000 0.000 0.856
#> GSM23166 1 0.2218 0.6239 0.884 0.000 0.000 0.000 0.104 0.012
#> GSM23167 6 0.2527 0.7956 0.168 0.000 0.000 0.000 0.000 0.832
#> GSM23168 3 0.1644 0.9045 0.000 0.000 0.932 0.000 0.040 0.028
#> GSM23169 3 0.4330 0.5374 0.004 0.000 0.680 0.000 0.272 0.044
#> GSM23170 1 0.3578 0.4085 0.660 0.000 0.000 0.000 0.000 0.340
#> GSM23171 1 0.3266 0.5275 0.728 0.000 0.000 0.000 0.000 0.272
#> GSM23172 6 0.2527 0.7956 0.168 0.000 0.000 0.000 0.000 0.832
#> GSM23173 6 0.7515 0.1172 0.276 0.000 0.136 0.000 0.292 0.296
#> GSM23174 1 0.3244 0.5417 0.732 0.000 0.000 0.000 0.000 0.268
#> GSM23175 1 0.1863 0.6867 0.896 0.000 0.000 0.000 0.000 0.104
#> GSM23176 6 0.2491 0.7963 0.164 0.000 0.000 0.000 0.000 0.836
#> GSM23177 1 0.0790 0.6869 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM23178 1 0.1501 0.6865 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM23179 3 0.0603 0.9371 0.000 0.000 0.980 0.000 0.016 0.004
#> GSM23180 5 0.3424 0.6741 0.092 0.000 0.000 0.000 0.812 0.096
#> GSM23181 1 0.5274 -0.1166 0.492 0.000 0.000 0.000 0.408 0.100
#> GSM23182 5 0.3611 0.6649 0.108 0.000 0.000 0.000 0.796 0.096
#> GSM23183 1 0.6680 0.1751 0.484 0.000 0.084 0.000 0.288 0.144
#> GSM23184 3 0.0260 0.9415 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM23196 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23199 4 0.0790 0.9742 0.000 0.032 0.000 0.968 0.000 0.000
#> GSM23200 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23201 4 0.0146 0.9808 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM23202 4 0.0000 0.9821 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23203 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23205 4 0.0000 0.9821 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23206 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23207 4 0.0790 0.9742 0.000 0.032 0.000 0.968 0.000 0.000
#> GSM23208 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23210 4 0.0790 0.9742 0.000 0.032 0.000 0.968 0.000 0.000
#> GSM23211 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23212 4 0.0000 0.9821 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23213 4 0.0000 0.9821 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23214 4 0.0146 0.9808 0.000 0.000 0.000 0.996 0.004 0.000
#> GSM23215 4 0.0790 0.9742 0.000 0.032 0.000 0.968 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 cell.type(p) disease.state(p) k
#> SD:mclust 57 3.90e-13 0.052490 2
#> SD:mclust 57 4.19e-13 0.000276 3
#> SD:mclust 51 4.89e-11 0.001353 4
#> SD:mclust 51 2.23e-10 0.008026 5
#> SD:mclust 52 5.39e-10 0.002514 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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.927 0.969 0.985 0.4711 0.536 0.536
#> 3 3 0.974 0.946 0.976 0.4344 0.786 0.600
#> 4 4 0.849 0.843 0.933 0.1141 0.851 0.583
#> 5 5 0.776 0.718 0.841 0.0501 0.976 0.901
#> 6 6 0.758 0.641 0.794 0.0380 0.950 0.784
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
#> GSM23185 1 0.6887 0.793 0.816 0.184
#> GSM23186 1 0.0000 0.976 1.000 0.000
#> GSM23187 1 0.5059 0.878 0.888 0.112
#> GSM23188 1 0.8909 0.591 0.692 0.308
#> GSM23189 1 0.5842 0.847 0.860 0.140
#> GSM23190 1 0.4939 0.882 0.892 0.108
#> GSM23191 1 0.0000 0.976 1.000 0.000
#> GSM23192 1 0.0000 0.976 1.000 0.000
#> GSM23193 1 0.0000 0.976 1.000 0.000
#> GSM23194 1 0.0000 0.976 1.000 0.000
#> GSM23195 1 0.0000 0.976 1.000 0.000
#> GSM23159 1 0.0000 0.976 1.000 0.000
#> GSM23160 1 0.0000 0.976 1.000 0.000
#> GSM23161 1 0.0000 0.976 1.000 0.000
#> GSM23162 1 0.0000 0.976 1.000 0.000
#> GSM23163 1 0.0000 0.976 1.000 0.000
#> GSM23164 1 0.0000 0.976 1.000 0.000
#> GSM23165 1 0.0000 0.976 1.000 0.000
#> GSM23166 1 0.0000 0.976 1.000 0.000
#> GSM23167 1 0.0000 0.976 1.000 0.000
#> GSM23168 1 0.0000 0.976 1.000 0.000
#> GSM23169 1 0.0000 0.976 1.000 0.000
#> GSM23170 1 0.0000 0.976 1.000 0.000
#> GSM23171 1 0.0000 0.976 1.000 0.000
#> GSM23172 1 0.0000 0.976 1.000 0.000
#> GSM23173 1 0.0000 0.976 1.000 0.000
#> GSM23174 1 0.0000 0.976 1.000 0.000
#> GSM23175 1 0.0000 0.976 1.000 0.000
#> GSM23176 1 0.0000 0.976 1.000 0.000
#> GSM23177 1 0.0000 0.976 1.000 0.000
#> GSM23178 1 0.0000 0.976 1.000 0.000
#> GSM23179 1 0.0000 0.976 1.000 0.000
#> GSM23180 1 0.0000 0.976 1.000 0.000
#> GSM23181 1 0.0000 0.976 1.000 0.000
#> GSM23182 1 0.0000 0.976 1.000 0.000
#> GSM23183 1 0.0000 0.976 1.000 0.000
#> GSM23184 1 0.0000 0.976 1.000 0.000
#> GSM23196 2 0.0000 0.999 0.000 1.000
#> GSM23197 2 0.0000 0.999 0.000 1.000
#> GSM23198 2 0.0000 0.999 0.000 1.000
#> GSM23199 2 0.0000 0.999 0.000 1.000
#> GSM23200 2 0.0000 0.999 0.000 1.000
#> GSM23201 2 0.0000 0.999 0.000 1.000
#> GSM23202 2 0.0938 0.988 0.012 0.988
#> GSM23203 2 0.0000 0.999 0.000 1.000
#> GSM23204 2 0.0000 0.999 0.000 1.000
#> GSM23205 2 0.0000 0.999 0.000 1.000
#> GSM23206 2 0.0000 0.999 0.000 1.000
#> GSM23207 2 0.0000 0.999 0.000 1.000
#> GSM23208 2 0.0000 0.999 0.000 1.000
#> GSM23209 2 0.0000 0.999 0.000 1.000
#> GSM23210 2 0.0000 0.999 0.000 1.000
#> GSM23211 2 0.0000 0.999 0.000 1.000
#> GSM23212 2 0.0000 0.999 0.000 1.000
#> GSM23213 2 0.0000 0.999 0.000 1.000
#> GSM23214 2 0.0000 0.999 0.000 1.000
#> GSM23215 2 0.0000 0.999 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.940 0.000 0.000 1.000
#> GSM23186 1 0.2878 0.883 0.904 0.000 0.096
#> GSM23187 3 0.0000 0.940 0.000 0.000 1.000
#> GSM23188 3 0.0000 0.940 0.000 0.000 1.000
#> GSM23189 3 0.0000 0.940 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.940 0.000 0.000 1.000
#> GSM23191 3 0.6260 0.257 0.448 0.000 0.552
#> GSM23192 3 0.5497 0.623 0.292 0.000 0.708
#> GSM23193 3 0.2878 0.879 0.096 0.000 0.904
#> GSM23194 3 0.0000 0.940 0.000 0.000 1.000
#> GSM23195 3 0.1643 0.918 0.044 0.000 0.956
#> GSM23159 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23160 3 0.0000 0.940 0.000 0.000 1.000
#> GSM23161 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23162 3 0.0237 0.939 0.004 0.000 0.996
#> GSM23163 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23164 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23165 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23166 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23167 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23168 3 0.0000 0.940 0.000 0.000 1.000
#> GSM23169 3 0.0592 0.936 0.012 0.000 0.988
#> GSM23170 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23171 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23172 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23173 3 0.0237 0.939 0.004 0.000 0.996
#> GSM23174 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23175 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23176 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23177 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23178 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23179 3 0.0000 0.940 0.000 0.000 1.000
#> GSM23180 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23181 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23182 1 0.0000 0.994 1.000 0.000 0.000
#> GSM23183 3 0.3192 0.865 0.112 0.000 0.888
#> GSM23184 3 0.0000 0.940 0.000 0.000 1.000
#> GSM23196 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23197 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23198 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23199 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23200 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23201 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23202 2 0.4887 0.711 0.228 0.772 0.000
#> GSM23203 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23204 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23205 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23206 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23207 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23208 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23209 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23210 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23211 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23212 2 0.0000 0.985 0.000 1.000 0.000
#> GSM23213 2 0.0747 0.972 0.016 0.984 0.000
#> GSM23214 2 0.1411 0.954 0.036 0.964 0.000
#> GSM23215 2 0.0000 0.985 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM23186 1 0.0188 0.959 0.996 0.000 0.000 0.004
#> GSM23187 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM23188 3 0.0336 0.923 0.000 0.000 0.992 0.008
#> GSM23189 3 0.0336 0.923 0.000 0.000 0.992 0.008
#> GSM23190 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM23191 4 0.2868 0.697 0.000 0.000 0.136 0.864
#> GSM23192 3 0.4872 0.484 0.004 0.000 0.640 0.356
#> GSM23193 3 0.4817 0.415 0.000 0.000 0.612 0.388
#> GSM23194 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM23195 1 0.2271 0.882 0.916 0.000 0.076 0.008
#> GSM23159 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM23160 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM23161 1 0.2469 0.856 0.892 0.000 0.000 0.108
#> GSM23162 3 0.0336 0.922 0.000 0.000 0.992 0.008
#> GSM23163 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM23164 4 0.4866 0.344 0.404 0.000 0.000 0.596
#> GSM23165 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM23166 4 0.4933 0.267 0.432 0.000 0.000 0.568
#> GSM23167 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM23168 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM23169 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM23170 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM23171 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM23172 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM23173 3 0.3668 0.727 0.188 0.000 0.808 0.004
#> GSM23174 1 0.0817 0.944 0.976 0.000 0.000 0.024
#> GSM23175 1 0.0188 0.960 0.996 0.000 0.000 0.004
#> GSM23176 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM23177 1 0.0188 0.960 0.996 0.000 0.000 0.004
#> GSM23178 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM23179 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM23180 4 0.0336 0.801 0.008 0.000 0.000 0.992
#> GSM23181 4 0.1211 0.797 0.040 0.000 0.000 0.960
#> GSM23182 4 0.0336 0.801 0.008 0.000 0.000 0.992
#> GSM23183 1 0.4328 0.655 0.748 0.000 0.244 0.008
#> GSM23184 3 0.0000 0.927 0.000 0.000 1.000 0.000
#> GSM23196 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM23199 2 0.0336 0.938 0.000 0.992 0.000 0.008
#> GSM23200 2 0.0188 0.940 0.000 0.996 0.000 0.004
#> GSM23201 4 0.1211 0.800 0.000 0.040 0.000 0.960
#> GSM23202 4 0.2704 0.759 0.000 0.124 0.000 0.876
#> GSM23203 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM23205 2 0.4477 0.530 0.000 0.688 0.000 0.312
#> GSM23206 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM23207 2 0.0336 0.938 0.000 0.992 0.000 0.008
#> GSM23208 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM23210 2 0.0188 0.940 0.000 0.996 0.000 0.004
#> GSM23211 2 0.0000 0.941 0.000 1.000 0.000 0.000
#> GSM23212 2 0.4985 0.120 0.000 0.532 0.000 0.468
#> GSM23213 4 0.4008 0.607 0.000 0.244 0.000 0.756
#> GSM23214 4 0.2973 0.740 0.000 0.144 0.000 0.856
#> GSM23215 2 0.0188 0.940 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.3074 0.7335 0.000 0.000 0.804 0.000 0.196
#> GSM23186 1 0.2674 0.8196 0.856 0.000 0.000 0.004 0.140
#> GSM23187 3 0.0609 0.8036 0.000 0.000 0.980 0.000 0.020
#> GSM23188 3 0.1732 0.7942 0.000 0.000 0.920 0.000 0.080
#> GSM23189 3 0.0609 0.8033 0.000 0.000 0.980 0.000 0.020
#> GSM23190 3 0.2966 0.7403 0.000 0.000 0.816 0.000 0.184
#> GSM23191 4 0.1943 0.7256 0.000 0.000 0.020 0.924 0.056
#> GSM23192 3 0.6821 -0.0106 0.000 0.000 0.348 0.336 0.316
#> GSM23193 3 0.4663 0.3764 0.000 0.000 0.604 0.376 0.020
#> GSM23194 3 0.2561 0.7671 0.000 0.000 0.856 0.000 0.144
#> GSM23195 5 0.6108 0.3638 0.208 0.000 0.224 0.000 0.568
#> GSM23159 1 0.0992 0.9459 0.968 0.000 0.000 0.008 0.024
#> GSM23160 3 0.1792 0.7946 0.000 0.000 0.916 0.000 0.084
#> GSM23161 1 0.3527 0.7922 0.828 0.000 0.000 0.116 0.056
#> GSM23162 3 0.2300 0.7895 0.000 0.000 0.908 0.040 0.052
#> GSM23163 1 0.0000 0.9562 1.000 0.000 0.000 0.000 0.000
#> GSM23164 4 0.4451 0.5212 0.248 0.000 0.000 0.712 0.040
#> GSM23165 1 0.0000 0.9562 1.000 0.000 0.000 0.000 0.000
#> GSM23166 4 0.4668 0.4806 0.272 0.000 0.000 0.684 0.044
#> GSM23167 1 0.0000 0.9562 1.000 0.000 0.000 0.000 0.000
#> GSM23168 3 0.1831 0.7959 0.000 0.000 0.920 0.004 0.076
#> GSM23169 3 0.2179 0.7897 0.000 0.000 0.896 0.004 0.100
#> GSM23170 1 0.0703 0.9476 0.976 0.000 0.000 0.000 0.024
#> GSM23171 1 0.0000 0.9562 1.000 0.000 0.000 0.000 0.000
#> GSM23172 1 0.0290 0.9553 0.992 0.000 0.000 0.000 0.008
#> GSM23173 3 0.4762 0.5575 0.064 0.000 0.700 0.000 0.236
#> GSM23174 1 0.1124 0.9352 0.960 0.000 0.000 0.036 0.004
#> GSM23175 1 0.0671 0.9507 0.980 0.000 0.000 0.004 0.016
#> GSM23176 1 0.0000 0.9562 1.000 0.000 0.000 0.000 0.000
#> GSM23177 1 0.1628 0.9205 0.936 0.000 0.000 0.008 0.056
#> GSM23178 1 0.0162 0.9555 0.996 0.000 0.000 0.000 0.004
#> GSM23179 3 0.1851 0.7909 0.000 0.000 0.912 0.000 0.088
#> GSM23180 4 0.0609 0.7511 0.000 0.000 0.000 0.980 0.020
#> GSM23181 4 0.2491 0.7377 0.036 0.000 0.000 0.896 0.068
#> GSM23182 4 0.1270 0.7473 0.000 0.000 0.000 0.948 0.052
#> GSM23183 5 0.6909 0.2215 0.268 0.000 0.288 0.008 0.436
#> GSM23184 3 0.1851 0.7894 0.000 0.000 0.912 0.000 0.088
#> GSM23196 2 0.0794 0.8342 0.000 0.972 0.000 0.000 0.028
#> GSM23197 2 0.1410 0.8190 0.000 0.940 0.000 0.000 0.060
#> GSM23198 2 0.1792 0.8199 0.000 0.916 0.000 0.000 0.084
#> GSM23199 2 0.2773 0.7757 0.000 0.836 0.000 0.000 0.164
#> GSM23200 2 0.3774 0.6520 0.000 0.704 0.000 0.000 0.296
#> GSM23201 4 0.1522 0.7429 0.000 0.044 0.000 0.944 0.012
#> GSM23202 4 0.3579 0.6577 0.000 0.072 0.000 0.828 0.100
#> GSM23203 2 0.0609 0.8347 0.000 0.980 0.000 0.000 0.020
#> GSM23204 2 0.2127 0.7905 0.000 0.892 0.000 0.000 0.108
#> GSM23205 2 0.4527 0.3743 0.000 0.596 0.000 0.392 0.012
#> GSM23206 2 0.0162 0.8341 0.000 0.996 0.000 0.000 0.004
#> GSM23207 2 0.4323 0.5925 0.000 0.656 0.000 0.012 0.332
#> GSM23208 2 0.0000 0.8345 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0963 0.8275 0.000 0.964 0.000 0.000 0.036
#> GSM23210 2 0.2233 0.8105 0.000 0.892 0.000 0.004 0.104
#> GSM23211 2 0.0404 0.8330 0.000 0.988 0.000 0.000 0.012
#> GSM23212 2 0.6610 0.1386 0.000 0.428 0.000 0.220 0.352
#> GSM23213 5 0.6660 -0.2295 0.000 0.228 0.000 0.380 0.392
#> GSM23214 4 0.5443 0.3110 0.000 0.084 0.000 0.604 0.312
#> GSM23215 2 0.1341 0.8210 0.000 0.944 0.000 0.000 0.056
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.4767 0.61221 0.000 0.000 0.676 0.168 0.000 0.156
#> GSM23186 1 0.4461 0.17053 0.564 0.000 0.000 0.032 0.000 0.404
#> GSM23187 3 0.2361 0.73431 0.000 0.000 0.884 0.028 0.000 0.088
#> GSM23188 3 0.3819 0.67523 0.000 0.000 0.764 0.064 0.000 0.172
#> GSM23189 3 0.2122 0.73836 0.000 0.000 0.900 0.024 0.000 0.076
#> GSM23190 3 0.4354 0.66249 0.000 0.004 0.720 0.196 0.000 0.080
#> GSM23191 5 0.2852 0.64536 0.000 0.000 0.000 0.080 0.856 0.064
#> GSM23192 6 0.5763 0.58716 0.000 0.000 0.048 0.156 0.172 0.624
#> GSM23193 3 0.5535 0.29863 0.000 0.000 0.516 0.048 0.392 0.044
#> GSM23194 3 0.4757 0.03874 0.000 0.000 0.484 0.048 0.000 0.468
#> GSM23195 6 0.4766 0.74001 0.124 0.000 0.056 0.084 0.000 0.736
#> GSM23159 1 0.1564 0.88548 0.936 0.000 0.000 0.024 0.000 0.040
#> GSM23160 3 0.2680 0.73328 0.000 0.000 0.868 0.056 0.000 0.076
#> GSM23161 1 0.5883 0.56329 0.652 0.000 0.008 0.092 0.132 0.116
#> GSM23162 3 0.3126 0.73285 0.000 0.000 0.856 0.072 0.044 0.028
#> GSM23163 1 0.1341 0.88670 0.948 0.000 0.000 0.028 0.000 0.024
#> GSM23164 5 0.5327 0.46564 0.240 0.000 0.000 0.068 0.644 0.048
#> GSM23165 1 0.0806 0.89510 0.972 0.000 0.000 0.008 0.000 0.020
#> GSM23166 5 0.5913 0.40819 0.268 0.000 0.004 0.072 0.588 0.068
#> GSM23167 1 0.0405 0.89634 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM23168 3 0.3746 0.70826 0.004 0.000 0.800 0.084 0.004 0.108
#> GSM23169 3 0.3832 0.71230 0.000 0.000 0.776 0.104 0.000 0.120
#> GSM23170 1 0.1053 0.88720 0.964 0.000 0.004 0.012 0.000 0.020
#> GSM23171 1 0.0717 0.89622 0.976 0.000 0.000 0.008 0.000 0.016
#> GSM23172 1 0.0508 0.89740 0.984 0.000 0.000 0.004 0.000 0.012
#> GSM23173 3 0.4758 0.65761 0.044 0.000 0.732 0.092 0.000 0.132
#> GSM23174 1 0.1464 0.88531 0.944 0.000 0.000 0.004 0.036 0.016
#> GSM23175 1 0.1074 0.89414 0.960 0.000 0.000 0.012 0.000 0.028
#> GSM23176 1 0.0000 0.89747 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23177 1 0.3039 0.79869 0.852 0.000 0.008 0.056 0.000 0.084
#> GSM23178 1 0.0603 0.89740 0.980 0.000 0.000 0.004 0.000 0.016
#> GSM23179 3 0.2680 0.73549 0.000 0.000 0.868 0.056 0.000 0.076
#> GSM23180 5 0.1524 0.65423 0.000 0.000 0.000 0.008 0.932 0.060
#> GSM23181 5 0.3154 0.59102 0.004 0.000 0.000 0.012 0.800 0.184
#> GSM23182 5 0.1082 0.64304 0.000 0.000 0.000 0.040 0.956 0.004
#> GSM23183 6 0.3028 0.76954 0.104 0.000 0.040 0.008 0.000 0.848
#> GSM23184 3 0.2309 0.74120 0.000 0.000 0.888 0.084 0.000 0.028
#> GSM23196 2 0.1267 0.79339 0.000 0.940 0.000 0.060 0.000 0.000
#> GSM23197 2 0.1075 0.79576 0.000 0.952 0.000 0.048 0.000 0.000
#> GSM23198 2 0.2762 0.66287 0.000 0.804 0.000 0.196 0.000 0.000
#> GSM23199 2 0.3727 0.20413 0.000 0.612 0.000 0.388 0.000 0.000
#> GSM23200 2 0.3868 -0.21673 0.000 0.508 0.000 0.492 0.000 0.000
#> GSM23201 5 0.1732 0.63244 0.000 0.072 0.000 0.004 0.920 0.004
#> GSM23202 5 0.3897 0.39761 0.000 0.040 0.000 0.196 0.756 0.008
#> GSM23203 2 0.0865 0.80515 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM23204 2 0.1910 0.74812 0.000 0.892 0.000 0.108 0.000 0.000
#> GSM23205 5 0.4440 0.00958 0.000 0.420 0.000 0.016 0.556 0.008
#> GSM23206 2 0.0260 0.81159 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM23207 4 0.4335 0.06504 0.000 0.472 0.000 0.508 0.020 0.000
#> GSM23208 2 0.0260 0.81131 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM23209 2 0.0547 0.80718 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM23210 2 0.2994 0.63879 0.000 0.788 0.000 0.208 0.004 0.000
#> GSM23211 2 0.0363 0.80936 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM23212 4 0.5680 0.55754 0.000 0.292 0.000 0.516 0.192 0.000
#> GSM23213 4 0.5648 0.52513 0.000 0.116 0.000 0.516 0.356 0.012
#> GSM23214 4 0.4651 0.27935 0.000 0.040 0.000 0.480 0.480 0.000
#> GSM23215 2 0.1531 0.78166 0.000 0.928 0.000 0.068 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
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 cell.type(p) disease.state(p) k
#> SD:NMF 57 3.90e-13 0.052490 2
#> SD:NMF 56 6.91e-13 0.000873 3
#> SD:NMF 52 2.05e-09 0.002566 4
#> SD:NMF 48 4.95e-09 0.008091 5
#> SD:NMF 46 5.31e-08 0.002442 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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.561 0.891 0.917 0.4688 0.536 0.536
#> 3 3 0.856 0.865 0.938 0.4114 0.793 0.614
#> 4 4 0.836 0.784 0.885 0.1001 0.944 0.833
#> 5 5 0.844 0.770 0.870 0.0390 0.974 0.910
#> 6 6 0.857 0.744 0.823 0.0297 0.963 0.860
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
#> GSM23185 1 0.8327 0.810 0.736 0.264
#> GSM23186 1 0.2778 0.876 0.952 0.048
#> GSM23187 1 0.8327 0.810 0.736 0.264
#> GSM23188 1 0.8327 0.810 0.736 0.264
#> GSM23189 1 0.8327 0.810 0.736 0.264
#> GSM23190 1 0.8327 0.810 0.736 0.264
#> GSM23191 1 0.7674 0.835 0.776 0.224
#> GSM23192 1 0.5519 0.864 0.872 0.128
#> GSM23193 1 0.7219 0.845 0.800 0.200
#> GSM23194 1 0.8016 0.824 0.756 0.244
#> GSM23195 1 0.6712 0.852 0.824 0.176
#> GSM23159 1 0.0376 0.876 0.996 0.004
#> GSM23160 1 0.8327 0.810 0.736 0.264
#> GSM23161 1 0.0376 0.876 0.996 0.004
#> GSM23162 1 0.7745 0.833 0.772 0.228
#> GSM23163 1 0.2043 0.877 0.968 0.032
#> GSM23164 1 0.0376 0.876 0.996 0.004
#> GSM23165 1 0.0376 0.876 0.996 0.004
#> GSM23166 1 0.0376 0.876 0.996 0.004
#> GSM23167 1 0.0376 0.876 0.996 0.004
#> GSM23168 1 0.8327 0.810 0.736 0.264
#> GSM23169 1 0.7528 0.839 0.784 0.216
#> GSM23170 1 0.0376 0.876 0.996 0.004
#> GSM23171 1 0.0376 0.876 0.996 0.004
#> GSM23172 1 0.0376 0.876 0.996 0.004
#> GSM23173 1 0.7950 0.826 0.760 0.240
#> GSM23174 1 0.0376 0.876 0.996 0.004
#> GSM23175 1 0.0376 0.876 0.996 0.004
#> GSM23176 1 0.0376 0.876 0.996 0.004
#> GSM23177 1 0.0376 0.876 0.996 0.004
#> GSM23178 1 0.0376 0.876 0.996 0.004
#> GSM23179 1 0.8267 0.813 0.740 0.260
#> GSM23180 1 0.0938 0.877 0.988 0.012
#> GSM23181 1 0.0938 0.877 0.988 0.012
#> GSM23182 1 0.0938 0.877 0.988 0.012
#> GSM23183 1 0.4161 0.872 0.916 0.084
#> GSM23184 1 0.8327 0.810 0.736 0.264
#> GSM23196 2 0.0000 0.973 0.000 1.000
#> GSM23197 2 0.0000 0.973 0.000 1.000
#> GSM23198 2 0.0000 0.973 0.000 1.000
#> GSM23199 2 0.0000 0.973 0.000 1.000
#> GSM23200 2 0.0000 0.973 0.000 1.000
#> GSM23201 2 0.3733 0.935 0.072 0.928
#> GSM23202 2 0.3733 0.935 0.072 0.928
#> GSM23203 2 0.0000 0.973 0.000 1.000
#> GSM23204 2 0.0000 0.973 0.000 1.000
#> GSM23205 2 0.3733 0.935 0.072 0.928
#> GSM23206 2 0.0000 0.973 0.000 1.000
#> GSM23207 2 0.0000 0.973 0.000 1.000
#> GSM23208 2 0.0000 0.973 0.000 1.000
#> GSM23209 2 0.0000 0.973 0.000 1.000
#> GSM23210 2 0.0000 0.973 0.000 1.000
#> GSM23211 2 0.0000 0.973 0.000 1.000
#> GSM23212 2 0.3733 0.935 0.072 0.928
#> GSM23213 2 0.3733 0.935 0.072 0.928
#> GSM23214 2 0.3733 0.935 0.072 0.928
#> GSM23215 2 0.0000 0.973 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.864 0.000 0.000 1.000
#> GSM23186 1 0.3816 0.798 0.852 0.000 0.148
#> GSM23187 3 0.0000 0.864 0.000 0.000 1.000
#> GSM23188 3 0.0000 0.864 0.000 0.000 1.000
#> GSM23189 3 0.0000 0.864 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.864 0.000 0.000 1.000
#> GSM23191 3 0.6126 0.421 0.400 0.000 0.600
#> GSM23192 1 0.5882 0.456 0.652 0.000 0.348
#> GSM23193 3 0.6267 0.271 0.452 0.000 0.548
#> GSM23194 3 0.4750 0.727 0.216 0.000 0.784
#> GSM23195 1 0.6180 0.233 0.584 0.000 0.416
#> GSM23159 1 0.0000 0.924 1.000 0.000 0.000
#> GSM23160 3 0.1411 0.861 0.036 0.000 0.964
#> GSM23161 1 0.0592 0.920 0.988 0.000 0.012
#> GSM23162 3 0.5363 0.662 0.276 0.000 0.724
#> GSM23163 1 0.2356 0.872 0.928 0.000 0.072
#> GSM23164 1 0.0000 0.924 1.000 0.000 0.000
#> GSM23165 1 0.0237 0.924 0.996 0.000 0.004
#> GSM23166 1 0.0000 0.924 1.000 0.000 0.000
#> GSM23167 1 0.0237 0.924 0.996 0.000 0.004
#> GSM23168 3 0.0892 0.865 0.020 0.000 0.980
#> GSM23169 3 0.4605 0.755 0.204 0.000 0.796
#> GSM23170 1 0.0237 0.924 0.996 0.000 0.004
#> GSM23171 1 0.0000 0.924 1.000 0.000 0.000
#> GSM23172 1 0.0237 0.924 0.996 0.000 0.004
#> GSM23173 3 0.2959 0.832 0.100 0.000 0.900
#> GSM23174 1 0.0000 0.924 1.000 0.000 0.000
#> GSM23175 1 0.0000 0.924 1.000 0.000 0.000
#> GSM23176 1 0.0237 0.924 0.996 0.000 0.004
#> GSM23177 1 0.0000 0.924 1.000 0.000 0.000
#> GSM23178 1 0.0000 0.924 1.000 0.000 0.000
#> GSM23179 3 0.1031 0.864 0.024 0.000 0.976
#> GSM23180 1 0.0892 0.917 0.980 0.000 0.020
#> GSM23181 1 0.0892 0.917 0.980 0.000 0.020
#> GSM23182 1 0.0892 0.917 0.980 0.000 0.020
#> GSM23183 1 0.5529 0.564 0.704 0.000 0.296
#> GSM23184 3 0.0237 0.865 0.004 0.000 0.996
#> GSM23196 2 0.0000 0.975 0.000 1.000 0.000
#> GSM23197 2 0.0000 0.975 0.000 1.000 0.000
#> GSM23198 2 0.0000 0.975 0.000 1.000 0.000
#> GSM23199 2 0.0000 0.975 0.000 1.000 0.000
#> GSM23200 2 0.0000 0.975 0.000 1.000 0.000
#> GSM23201 2 0.2356 0.939 0.072 0.928 0.000
#> GSM23202 2 0.2356 0.939 0.072 0.928 0.000
#> GSM23203 2 0.0000 0.975 0.000 1.000 0.000
#> GSM23204 2 0.0000 0.975 0.000 1.000 0.000
#> GSM23205 2 0.2356 0.939 0.072 0.928 0.000
#> GSM23206 2 0.0000 0.975 0.000 1.000 0.000
#> GSM23207 2 0.0000 0.975 0.000 1.000 0.000
#> GSM23208 2 0.0000 0.975 0.000 1.000 0.000
#> GSM23209 2 0.0000 0.975 0.000 1.000 0.000
#> GSM23210 2 0.0000 0.975 0.000 1.000 0.000
#> GSM23211 2 0.0000 0.975 0.000 1.000 0.000
#> GSM23212 2 0.2356 0.939 0.072 0.928 0.000
#> GSM23213 2 0.2356 0.939 0.072 0.928 0.000
#> GSM23214 2 0.2356 0.939 0.072 0.928 0.000
#> GSM23215 2 0.0000 0.975 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0336 0.84314 0.000 0.000 0.992 0.008
#> GSM23186 1 0.6041 0.35437 0.608 0.000 0.060 0.332
#> GSM23187 3 0.0336 0.84314 0.000 0.000 0.992 0.008
#> GSM23188 3 0.0336 0.84314 0.000 0.000 0.992 0.008
#> GSM23189 3 0.0336 0.84314 0.000 0.000 0.992 0.008
#> GSM23190 3 0.0336 0.84314 0.000 0.000 0.992 0.008
#> GSM23191 4 0.6229 0.23887 0.056 0.000 0.416 0.528
#> GSM23192 4 0.6039 0.59251 0.188 0.000 0.128 0.684
#> GSM23193 4 0.6574 0.37009 0.088 0.000 0.364 0.548
#> GSM23194 3 0.5050 0.18250 0.004 0.000 0.588 0.408
#> GSM23195 4 0.6626 0.54749 0.160 0.000 0.216 0.624
#> GSM23159 1 0.1716 0.83744 0.936 0.000 0.000 0.064
#> GSM23160 3 0.1798 0.82780 0.016 0.000 0.944 0.040
#> GSM23161 1 0.1824 0.84010 0.936 0.000 0.004 0.060
#> GSM23162 3 0.5881 0.00609 0.036 0.000 0.544 0.420
#> GSM23163 1 0.4538 0.65233 0.760 0.000 0.024 0.216
#> GSM23164 1 0.1867 0.83306 0.928 0.000 0.000 0.072
#> GSM23165 1 0.1474 0.83092 0.948 0.000 0.000 0.052
#> GSM23166 1 0.1792 0.83480 0.932 0.000 0.000 0.068
#> GSM23167 1 0.1389 0.83236 0.952 0.000 0.000 0.048
#> GSM23168 3 0.1356 0.83321 0.008 0.000 0.960 0.032
#> GSM23169 3 0.5566 0.55845 0.072 0.000 0.704 0.224
#> GSM23170 1 0.1389 0.84229 0.952 0.000 0.000 0.048
#> GSM23171 1 0.0188 0.84177 0.996 0.000 0.000 0.004
#> GSM23172 1 0.1302 0.83320 0.956 0.000 0.000 0.044
#> GSM23173 3 0.3707 0.74025 0.028 0.000 0.840 0.132
#> GSM23174 1 0.1118 0.84517 0.964 0.000 0.000 0.036
#> GSM23175 1 0.0000 0.84273 1.000 0.000 0.000 0.000
#> GSM23176 1 0.1474 0.83092 0.948 0.000 0.000 0.052
#> GSM23177 1 0.1716 0.83864 0.936 0.000 0.000 0.064
#> GSM23178 1 0.1716 0.84137 0.936 0.000 0.000 0.064
#> GSM23179 3 0.1488 0.83476 0.012 0.000 0.956 0.032
#> GSM23180 1 0.4855 0.44418 0.600 0.000 0.000 0.400
#> GSM23181 1 0.4855 0.44418 0.600 0.000 0.000 0.400
#> GSM23182 1 0.4855 0.44418 0.600 0.000 0.000 0.400
#> GSM23183 4 0.6634 0.46754 0.292 0.000 0.116 0.592
#> GSM23184 3 0.0469 0.84031 0.000 0.000 0.988 0.012
#> GSM23196 2 0.0000 0.97784 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.97784 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.97784 0.000 1.000 0.000 0.000
#> GSM23199 2 0.0000 0.97784 0.000 1.000 0.000 0.000
#> GSM23200 2 0.0000 0.97784 0.000 1.000 0.000 0.000
#> GSM23201 2 0.1867 0.94692 0.000 0.928 0.000 0.072
#> GSM23202 2 0.1867 0.94692 0.000 0.928 0.000 0.072
#> GSM23203 2 0.0000 0.97784 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.97784 0.000 1.000 0.000 0.000
#> GSM23205 2 0.1867 0.94692 0.000 0.928 0.000 0.072
#> GSM23206 2 0.0000 0.97784 0.000 1.000 0.000 0.000
#> GSM23207 2 0.0000 0.97784 0.000 1.000 0.000 0.000
#> GSM23208 2 0.0000 0.97784 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.97784 0.000 1.000 0.000 0.000
#> GSM23210 2 0.0000 0.97784 0.000 1.000 0.000 0.000
#> GSM23211 2 0.0000 0.97784 0.000 1.000 0.000 0.000
#> GSM23212 2 0.1867 0.94692 0.000 0.928 0.000 0.072
#> GSM23213 2 0.1867 0.94692 0.000 0.928 0.000 0.072
#> GSM23214 2 0.1867 0.94692 0.000 0.928 0.000 0.072
#> GSM23215 2 0.0000 0.97784 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.0451 0.81621 0.000 0.000 0.988 0.004 0.008
#> GSM23186 5 0.5503 0.21334 0.404 0.000 0.020 0.032 0.544
#> GSM23187 3 0.0162 0.81849 0.000 0.000 0.996 0.000 0.004
#> GSM23188 3 0.0162 0.81849 0.000 0.000 0.996 0.000 0.004
#> GSM23189 3 0.0162 0.81849 0.000 0.000 0.996 0.000 0.004
#> GSM23190 3 0.0162 0.81849 0.000 0.000 0.996 0.000 0.004
#> GSM23191 4 0.3870 0.84134 0.016 0.000 0.176 0.792 0.016
#> GSM23192 5 0.6294 0.31135 0.076 0.000 0.044 0.304 0.576
#> GSM23193 4 0.4823 0.80745 0.036 0.000 0.164 0.752 0.048
#> GSM23194 3 0.6615 -0.00934 0.004 0.000 0.492 0.236 0.268
#> GSM23195 5 0.4245 0.51103 0.040 0.000 0.076 0.072 0.812
#> GSM23159 1 0.2676 0.77074 0.884 0.000 0.000 0.036 0.080
#> GSM23160 3 0.3008 0.78148 0.004 0.000 0.868 0.092 0.036
#> GSM23161 1 0.2605 0.79219 0.896 0.000 0.004 0.056 0.044
#> GSM23162 4 0.4645 0.73312 0.016 0.000 0.300 0.672 0.012
#> GSM23163 1 0.4797 0.41534 0.676 0.000 0.004 0.040 0.280
#> GSM23164 1 0.2653 0.78205 0.880 0.000 0.000 0.096 0.024
#> GSM23165 1 0.2209 0.76742 0.912 0.000 0.000 0.032 0.056
#> GSM23166 1 0.2482 0.78799 0.892 0.000 0.000 0.084 0.024
#> GSM23167 1 0.2139 0.76989 0.916 0.000 0.000 0.032 0.052
#> GSM23168 3 0.2570 0.78683 0.000 0.000 0.888 0.084 0.028
#> GSM23169 3 0.6824 0.34805 0.024 0.000 0.524 0.204 0.248
#> GSM23170 1 0.2079 0.79697 0.916 0.000 0.000 0.064 0.020
#> GSM23171 1 0.0693 0.79806 0.980 0.000 0.000 0.008 0.012
#> GSM23172 1 0.1992 0.77380 0.924 0.000 0.000 0.032 0.044
#> GSM23173 3 0.5750 0.56275 0.008 0.000 0.644 0.144 0.204
#> GSM23174 1 0.1670 0.80262 0.936 0.000 0.000 0.052 0.012
#> GSM23175 1 0.0579 0.79919 0.984 0.000 0.000 0.008 0.008
#> GSM23176 1 0.2209 0.76742 0.912 0.000 0.000 0.032 0.056
#> GSM23177 1 0.2248 0.79301 0.900 0.000 0.000 0.088 0.012
#> GSM23178 1 0.2325 0.79557 0.904 0.000 0.000 0.068 0.028
#> GSM23179 3 0.2504 0.79423 0.000 0.000 0.896 0.064 0.040
#> GSM23180 1 0.5928 0.32191 0.500 0.000 0.000 0.392 0.108
#> GSM23181 1 0.5928 0.32191 0.500 0.000 0.000 0.392 0.108
#> GSM23182 1 0.5928 0.32191 0.500 0.000 0.000 0.392 0.108
#> GSM23183 5 0.3717 0.59215 0.100 0.000 0.040 0.024 0.836
#> GSM23184 3 0.0794 0.81217 0.000 0.000 0.972 0.028 0.000
#> GSM23196 2 0.0000 0.97702 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.97702 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.97702 0.000 1.000 0.000 0.000 0.000
#> GSM23199 2 0.0000 0.97702 0.000 1.000 0.000 0.000 0.000
#> GSM23200 2 0.0000 0.97702 0.000 1.000 0.000 0.000 0.000
#> GSM23201 2 0.1608 0.94492 0.000 0.928 0.000 0.072 0.000
#> GSM23202 2 0.1608 0.94492 0.000 0.928 0.000 0.072 0.000
#> GSM23203 2 0.0000 0.97702 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.97702 0.000 1.000 0.000 0.000 0.000
#> GSM23205 2 0.1608 0.94492 0.000 0.928 0.000 0.072 0.000
#> GSM23206 2 0.0000 0.97702 0.000 1.000 0.000 0.000 0.000
#> GSM23207 2 0.0000 0.97702 0.000 1.000 0.000 0.000 0.000
#> GSM23208 2 0.0000 0.97702 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.97702 0.000 1.000 0.000 0.000 0.000
#> GSM23210 2 0.0000 0.97702 0.000 1.000 0.000 0.000 0.000
#> GSM23211 2 0.0000 0.97702 0.000 1.000 0.000 0.000 0.000
#> GSM23212 2 0.1608 0.94492 0.000 0.928 0.000 0.072 0.000
#> GSM23213 2 0.1608 0.94492 0.000 0.928 0.000 0.072 0.000
#> GSM23214 2 0.1608 0.94492 0.000 0.928 0.000 0.072 0.000
#> GSM23215 2 0.0000 0.97702 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0260 0.7824 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM23186 6 0.5599 0.3909 0.368 0.000 0.004 0.060 0.032 0.536
#> GSM23187 3 0.0000 0.7853 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23188 3 0.0000 0.7853 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23189 3 0.0000 0.7853 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23190 3 0.0000 0.7853 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23191 5 0.4176 0.5719 0.000 0.000 0.044 0.244 0.708 0.004
#> GSM23192 6 0.6228 0.3778 0.028 0.000 0.012 0.216 0.180 0.564
#> GSM23193 5 0.4603 0.5431 0.004 0.000 0.040 0.316 0.636 0.004
#> GSM23194 3 0.6838 0.0221 0.000 0.000 0.424 0.056 0.248 0.272
#> GSM23195 6 0.4356 0.5425 0.024 0.000 0.004 0.132 0.076 0.764
#> GSM23159 1 0.4040 0.6177 0.772 0.000 0.000 0.140 0.012 0.076
#> GSM23160 3 0.4767 0.6616 0.000 0.000 0.716 0.072 0.176 0.036
#> GSM23161 1 0.4235 0.6306 0.684 0.000 0.000 0.280 0.012 0.024
#> GSM23162 5 0.4057 0.5472 0.000 0.000 0.124 0.108 0.764 0.004
#> GSM23163 1 0.4948 0.3104 0.648 0.000 0.000 0.080 0.012 0.260
#> GSM23164 1 0.3515 0.5912 0.676 0.000 0.000 0.324 0.000 0.000
#> GSM23165 1 0.0603 0.6951 0.980 0.000 0.000 0.016 0.000 0.004
#> GSM23166 1 0.3446 0.6187 0.692 0.000 0.000 0.308 0.000 0.000
#> GSM23167 1 0.0458 0.6977 0.984 0.000 0.000 0.016 0.000 0.000
#> GSM23168 3 0.3972 0.7055 0.000 0.000 0.784 0.076 0.124 0.016
#> GSM23169 5 0.7665 -0.1565 0.004 0.000 0.260 0.196 0.352 0.188
#> GSM23170 1 0.3288 0.6548 0.724 0.000 0.000 0.276 0.000 0.000
#> GSM23171 1 0.2340 0.7353 0.852 0.000 0.000 0.148 0.000 0.000
#> GSM23172 1 0.0260 0.7056 0.992 0.000 0.000 0.008 0.000 0.000
#> GSM23173 3 0.7392 0.1261 0.000 0.000 0.372 0.224 0.272 0.132
#> GSM23174 1 0.2664 0.7243 0.816 0.000 0.000 0.184 0.000 0.000
#> GSM23175 1 0.2378 0.7340 0.848 0.000 0.000 0.152 0.000 0.000
#> GSM23176 1 0.0603 0.6951 0.980 0.000 0.000 0.016 0.000 0.004
#> GSM23177 1 0.3288 0.6555 0.724 0.000 0.000 0.276 0.000 0.000
#> GSM23178 1 0.2527 0.7135 0.832 0.000 0.000 0.168 0.000 0.000
#> GSM23179 3 0.4110 0.7040 0.000 0.000 0.776 0.068 0.132 0.024
#> GSM23180 4 0.3490 1.0000 0.268 0.000 0.000 0.724 0.000 0.008
#> GSM23181 4 0.3490 1.0000 0.268 0.000 0.000 0.724 0.000 0.008
#> GSM23182 4 0.3490 1.0000 0.268 0.000 0.000 0.724 0.000 0.008
#> GSM23183 6 0.2221 0.5999 0.040 0.000 0.004 0.044 0.004 0.908
#> GSM23184 3 0.1498 0.7729 0.000 0.000 0.940 0.028 0.032 0.000
#> GSM23196 2 0.0000 0.9757 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.9757 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.9757 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23199 2 0.0000 0.9757 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23200 2 0.0146 0.9743 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM23201 2 0.1444 0.9433 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM23202 2 0.1501 0.9419 0.000 0.924 0.000 0.076 0.000 0.000
#> GSM23203 2 0.0000 0.9757 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.9757 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23205 2 0.1444 0.9433 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM23206 2 0.0000 0.9757 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23207 2 0.0146 0.9743 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM23208 2 0.0000 0.9757 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.9757 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23210 2 0.0000 0.9757 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23211 2 0.0000 0.9757 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23212 2 0.1501 0.9419 0.000 0.924 0.000 0.076 0.000 0.000
#> GSM23213 2 0.1501 0.9419 0.000 0.924 0.000 0.076 0.000 0.000
#> GSM23214 2 0.1501 0.9419 0.000 0.924 0.000 0.076 0.000 0.000
#> GSM23215 2 0.0000 0.9757 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> CV:hclust 57 3.90e-13 0.052490 2
#> CV:hclust 53 3.10e-12 0.007090 3
#> CV:hclust 48 2.13e-10 0.000175 4
#> CV:hclust 49 5.84e-10 0.000821 5
#> CV:hclust 51 8.65e-10 0.000027 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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.874 0.965 0.974 0.4673 0.536 0.536
#> 3 3 0.713 0.950 0.909 0.3953 0.786 0.600
#> 4 4 0.819 0.841 0.828 0.1287 0.937 0.805
#> 5 5 0.755 0.784 0.825 0.0656 0.920 0.705
#> 6 6 0.758 0.742 0.819 0.0431 0.950 0.766
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
#> GSM23185 1 0.3879 0.935 0.924 0.076
#> GSM23186 1 0.0000 0.963 1.000 0.000
#> GSM23187 1 0.3879 0.935 0.924 0.076
#> GSM23188 1 0.3879 0.935 0.924 0.076
#> GSM23189 1 0.3879 0.935 0.924 0.076
#> GSM23190 1 0.3879 0.935 0.924 0.076
#> GSM23191 1 0.0376 0.963 0.996 0.004
#> GSM23192 1 0.0000 0.963 1.000 0.000
#> GSM23193 1 0.0000 0.963 1.000 0.000
#> GSM23194 1 0.3879 0.935 0.924 0.076
#> GSM23195 1 0.0376 0.963 0.996 0.004
#> GSM23159 1 0.1843 0.968 0.972 0.028
#> GSM23160 1 0.3879 0.935 0.924 0.076
#> GSM23161 1 0.1843 0.968 0.972 0.028
#> GSM23162 1 0.0938 0.962 0.988 0.012
#> GSM23163 1 0.1633 0.967 0.976 0.024
#> GSM23164 1 0.1843 0.968 0.972 0.028
#> GSM23165 1 0.1843 0.968 0.972 0.028
#> GSM23166 1 0.1843 0.968 0.972 0.028
#> GSM23167 1 0.1843 0.968 0.972 0.028
#> GSM23168 1 0.3879 0.935 0.924 0.076
#> GSM23169 1 0.0000 0.963 1.000 0.000
#> GSM23170 1 0.1843 0.968 0.972 0.028
#> GSM23171 1 0.1843 0.968 0.972 0.028
#> GSM23172 1 0.1843 0.968 0.972 0.028
#> GSM23173 1 0.0376 0.963 0.996 0.004
#> GSM23174 1 0.1843 0.968 0.972 0.028
#> GSM23175 1 0.1843 0.968 0.972 0.028
#> GSM23176 1 0.1843 0.968 0.972 0.028
#> GSM23177 1 0.1843 0.968 0.972 0.028
#> GSM23178 1 0.1843 0.968 0.972 0.028
#> GSM23179 1 0.3879 0.935 0.924 0.076
#> GSM23180 1 0.1843 0.968 0.972 0.028
#> GSM23181 1 0.1843 0.968 0.972 0.028
#> GSM23182 1 0.1843 0.968 0.972 0.028
#> GSM23183 1 0.0000 0.963 1.000 0.000
#> GSM23184 1 0.3879 0.935 0.924 0.076
#> GSM23196 2 0.0000 0.988 0.000 1.000
#> GSM23197 2 0.0000 0.988 0.000 1.000
#> GSM23198 2 0.0000 0.988 0.000 1.000
#> GSM23199 2 0.0000 0.988 0.000 1.000
#> GSM23200 2 0.0000 0.988 0.000 1.000
#> GSM23201 2 0.0000 0.988 0.000 1.000
#> GSM23202 2 0.3733 0.928 0.072 0.928
#> GSM23203 2 0.0000 0.988 0.000 1.000
#> GSM23204 2 0.0000 0.988 0.000 1.000
#> GSM23205 2 0.0000 0.988 0.000 1.000
#> GSM23206 2 0.0000 0.988 0.000 1.000
#> GSM23207 2 0.0000 0.988 0.000 1.000
#> GSM23208 2 0.0000 0.988 0.000 1.000
#> GSM23209 2 0.0000 0.988 0.000 1.000
#> GSM23210 2 0.0000 0.988 0.000 1.000
#> GSM23211 2 0.0000 0.988 0.000 1.000
#> GSM23212 2 0.0000 0.988 0.000 1.000
#> GSM23213 2 0.3584 0.932 0.068 0.932
#> GSM23214 2 0.3584 0.932 0.068 0.932
#> GSM23215 2 0.0000 0.988 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.943 0.000 0.000 1.000
#> GSM23186 1 0.4062 0.987 0.836 0.000 0.164
#> GSM23187 3 0.0000 0.943 0.000 0.000 1.000
#> GSM23188 3 0.0000 0.943 0.000 0.000 1.000
#> GSM23189 3 0.0000 0.943 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.943 0.000 0.000 1.000
#> GSM23191 3 0.3918 0.858 0.140 0.004 0.856
#> GSM23192 3 0.3816 0.850 0.148 0.000 0.852
#> GSM23193 3 0.3784 0.868 0.132 0.004 0.864
#> GSM23194 3 0.0747 0.950 0.016 0.000 0.984
#> GSM23195 3 0.3500 0.882 0.116 0.004 0.880
#> GSM23159 1 0.3941 0.995 0.844 0.000 0.156
#> GSM23160 3 0.0747 0.950 0.016 0.000 0.984
#> GSM23161 1 0.3941 0.995 0.844 0.000 0.156
#> GSM23162 3 0.0983 0.949 0.016 0.004 0.980
#> GSM23163 1 0.3941 0.995 0.844 0.000 0.156
#> GSM23164 1 0.3941 0.995 0.844 0.000 0.156
#> GSM23165 1 0.3941 0.995 0.844 0.000 0.156
#> GSM23166 1 0.3941 0.995 0.844 0.000 0.156
#> GSM23167 1 0.3941 0.995 0.844 0.000 0.156
#> GSM23168 3 0.0747 0.950 0.016 0.000 0.984
#> GSM23169 3 0.0983 0.949 0.016 0.004 0.980
#> GSM23170 1 0.3941 0.995 0.844 0.000 0.156
#> GSM23171 1 0.3941 0.995 0.844 0.000 0.156
#> GSM23172 1 0.3941 0.995 0.844 0.000 0.156
#> GSM23173 3 0.0983 0.949 0.016 0.004 0.980
#> GSM23174 1 0.3752 0.986 0.856 0.000 0.144
#> GSM23175 1 0.3816 0.989 0.852 0.000 0.148
#> GSM23176 1 0.3941 0.995 0.844 0.000 0.156
#> GSM23177 1 0.3941 0.995 0.844 0.000 0.156
#> GSM23178 1 0.3941 0.995 0.844 0.000 0.156
#> GSM23179 3 0.0747 0.950 0.016 0.000 0.984
#> GSM23180 1 0.3983 0.984 0.852 0.004 0.144
#> GSM23181 1 0.3752 0.986 0.856 0.000 0.144
#> GSM23182 1 0.3983 0.984 0.852 0.004 0.144
#> GSM23183 3 0.3619 0.865 0.136 0.000 0.864
#> GSM23184 3 0.0747 0.950 0.016 0.000 0.984
#> GSM23196 2 0.4418 0.938 0.132 0.848 0.020
#> GSM23197 2 0.4418 0.938 0.132 0.848 0.020
#> GSM23198 2 0.4418 0.938 0.132 0.848 0.020
#> GSM23199 2 0.0000 0.930 0.000 1.000 0.000
#> GSM23200 2 0.3551 0.938 0.132 0.868 0.000
#> GSM23201 2 0.1031 0.925 0.024 0.976 0.000
#> GSM23202 2 0.1031 0.925 0.024 0.976 0.000
#> GSM23203 2 0.4418 0.938 0.132 0.848 0.020
#> GSM23204 2 0.4418 0.938 0.132 0.848 0.020
#> GSM23205 2 0.0892 0.926 0.020 0.980 0.000
#> GSM23206 2 0.4418 0.938 0.132 0.848 0.020
#> GSM23207 2 0.0592 0.927 0.012 0.988 0.000
#> GSM23208 2 0.4418 0.938 0.132 0.848 0.020
#> GSM23209 2 0.4418 0.938 0.132 0.848 0.020
#> GSM23210 2 0.0424 0.928 0.008 0.992 0.000
#> GSM23211 2 0.4418 0.938 0.132 0.848 0.020
#> GSM23212 2 0.1031 0.925 0.024 0.976 0.000
#> GSM23213 2 0.1031 0.925 0.024 0.976 0.000
#> GSM23214 2 0.1031 0.925 0.024 0.976 0.000
#> GSM23215 2 0.3752 0.939 0.096 0.884 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0804 0.871 0.012 0.008 0.980 0.000
#> GSM23186 1 0.2589 0.888 0.884 0.116 0.000 0.000
#> GSM23187 3 0.0469 0.871 0.012 0.000 0.988 0.000
#> GSM23188 3 0.0469 0.871 0.012 0.000 0.988 0.000
#> GSM23189 3 0.0469 0.871 0.012 0.000 0.988 0.000
#> GSM23190 3 0.0804 0.871 0.012 0.008 0.980 0.000
#> GSM23191 3 0.6575 0.702 0.092 0.348 0.560 0.000
#> GSM23192 3 0.6659 0.670 0.088 0.400 0.512 0.000
#> GSM23193 3 0.6412 0.715 0.080 0.348 0.572 0.000
#> GSM23194 3 0.1798 0.870 0.016 0.040 0.944 0.000
#> GSM23195 3 0.6519 0.722 0.096 0.320 0.584 0.000
#> GSM23159 1 0.0188 0.930 0.996 0.004 0.000 0.000
#> GSM23160 3 0.0592 0.872 0.016 0.000 0.984 0.000
#> GSM23161 1 0.0921 0.927 0.972 0.028 0.000 0.000
#> GSM23162 3 0.3836 0.841 0.016 0.168 0.816 0.000
#> GSM23163 1 0.1474 0.925 0.948 0.052 0.000 0.000
#> GSM23164 1 0.1211 0.921 0.960 0.040 0.000 0.000
#> GSM23165 1 0.0921 0.928 0.972 0.028 0.000 0.000
#> GSM23166 1 0.1302 0.920 0.956 0.044 0.000 0.000
#> GSM23167 1 0.0921 0.928 0.972 0.028 0.000 0.000
#> GSM23168 3 0.0592 0.872 0.016 0.000 0.984 0.000
#> GSM23169 3 0.4214 0.827 0.016 0.204 0.780 0.000
#> GSM23170 1 0.0188 0.931 0.996 0.004 0.000 0.000
#> GSM23171 1 0.0000 0.930 1.000 0.000 0.000 0.000
#> GSM23172 1 0.0921 0.928 0.972 0.028 0.000 0.000
#> GSM23173 3 0.2593 0.862 0.016 0.080 0.904 0.000
#> GSM23174 1 0.0000 0.930 1.000 0.000 0.000 0.000
#> GSM23175 1 0.0000 0.930 1.000 0.000 0.000 0.000
#> GSM23176 1 0.0921 0.928 0.972 0.028 0.000 0.000
#> GSM23177 1 0.0188 0.930 0.996 0.004 0.000 0.000
#> GSM23178 1 0.1557 0.924 0.944 0.056 0.000 0.000
#> GSM23179 3 0.0592 0.872 0.016 0.000 0.984 0.000
#> GSM23180 1 0.6106 0.613 0.604 0.332 0.000 0.064
#> GSM23181 1 0.3975 0.777 0.760 0.240 0.000 0.000
#> GSM23182 1 0.6374 0.598 0.592 0.324 0.000 0.084
#> GSM23183 3 0.6532 0.714 0.092 0.336 0.572 0.000
#> GSM23184 3 0.0927 0.872 0.016 0.008 0.976 0.000
#> GSM23196 2 0.5070 0.990 0.000 0.580 0.004 0.416
#> GSM23197 2 0.5070 0.990 0.000 0.580 0.004 0.416
#> GSM23198 2 0.5070 0.990 0.000 0.580 0.004 0.416
#> GSM23199 4 0.2814 0.687 0.000 0.132 0.000 0.868
#> GSM23200 2 0.4977 0.905 0.000 0.540 0.000 0.460
#> GSM23201 4 0.0657 0.841 0.000 0.004 0.012 0.984
#> GSM23202 4 0.0188 0.844 0.000 0.000 0.004 0.996
#> GSM23203 2 0.5070 0.990 0.000 0.580 0.004 0.416
#> GSM23204 2 0.5070 0.990 0.000 0.580 0.004 0.416
#> GSM23205 4 0.0804 0.841 0.000 0.008 0.012 0.980
#> GSM23206 2 0.5070 0.990 0.000 0.580 0.004 0.416
#> GSM23207 4 0.1637 0.802 0.000 0.060 0.000 0.940
#> GSM23208 2 0.5070 0.990 0.000 0.580 0.004 0.416
#> GSM23209 2 0.5070 0.990 0.000 0.580 0.004 0.416
#> GSM23210 4 0.2546 0.765 0.000 0.092 0.008 0.900
#> GSM23211 2 0.5070 0.990 0.000 0.580 0.004 0.416
#> GSM23212 4 0.0000 0.844 0.000 0.000 0.000 1.000
#> GSM23213 4 0.0000 0.844 0.000 0.000 0.000 1.000
#> GSM23214 4 0.0188 0.844 0.000 0.000 0.004 0.996
#> GSM23215 4 0.5292 -0.762 0.000 0.480 0.008 0.512
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.0451 0.85626 0.004 0.008 0.988 0.000 0.000
#> GSM23186 1 0.6362 0.45158 0.552 0.264 0.008 0.000 0.176
#> GSM23187 3 0.0451 0.85626 0.004 0.008 0.988 0.000 0.000
#> GSM23188 3 0.0451 0.85626 0.004 0.008 0.988 0.000 0.000
#> GSM23189 3 0.0451 0.85626 0.004 0.008 0.988 0.000 0.000
#> GSM23190 3 0.0451 0.85626 0.004 0.008 0.988 0.000 0.000
#> GSM23191 5 0.4210 0.61744 0.036 0.000 0.224 0.000 0.740
#> GSM23192 5 0.5760 0.64900 0.036 0.120 0.160 0.000 0.684
#> GSM23193 5 0.4210 0.61744 0.036 0.000 0.224 0.000 0.740
#> GSM23194 3 0.3909 0.72431 0.004 0.064 0.808 0.000 0.124
#> GSM23195 5 0.6875 0.51072 0.024 0.220 0.240 0.000 0.516
#> GSM23159 1 0.1281 0.86747 0.956 0.032 0.000 0.000 0.012
#> GSM23160 3 0.1471 0.84896 0.004 0.020 0.952 0.000 0.024
#> GSM23161 1 0.2054 0.84242 0.920 0.028 0.000 0.000 0.052
#> GSM23162 3 0.4604 0.32146 0.004 0.008 0.584 0.000 0.404
#> GSM23163 1 0.3955 0.82211 0.800 0.116 0.000 0.000 0.084
#> GSM23164 1 0.1638 0.84229 0.932 0.004 0.000 0.000 0.064
#> GSM23165 1 0.2983 0.84283 0.864 0.096 0.000 0.000 0.040
#> GSM23166 1 0.1638 0.84180 0.932 0.004 0.000 0.000 0.064
#> GSM23167 1 0.2927 0.84432 0.868 0.092 0.000 0.000 0.040
#> GSM23168 3 0.1560 0.84762 0.004 0.020 0.948 0.000 0.028
#> GSM23169 3 0.6279 0.21614 0.004 0.148 0.520 0.000 0.328
#> GSM23170 1 0.0693 0.86853 0.980 0.012 0.000 0.000 0.008
#> GSM23171 1 0.0671 0.86969 0.980 0.016 0.000 0.000 0.004
#> GSM23172 1 0.2983 0.84283 0.864 0.096 0.000 0.000 0.040
#> GSM23173 3 0.4781 0.65548 0.004 0.080 0.728 0.000 0.188
#> GSM23174 1 0.0162 0.86666 0.996 0.000 0.000 0.000 0.004
#> GSM23175 1 0.0162 0.86666 0.996 0.000 0.000 0.000 0.004
#> GSM23176 1 0.2927 0.84432 0.868 0.092 0.000 0.000 0.040
#> GSM23177 1 0.0324 0.86574 0.992 0.004 0.000 0.000 0.004
#> GSM23178 1 0.2645 0.85726 0.888 0.044 0.000 0.000 0.068
#> GSM23179 3 0.1356 0.85033 0.004 0.028 0.956 0.000 0.012
#> GSM23180 5 0.4329 0.47414 0.312 0.000 0.000 0.016 0.672
#> GSM23181 1 0.4300 0.00155 0.524 0.000 0.000 0.000 0.476
#> GSM23182 5 0.5107 0.47271 0.296 0.000 0.000 0.064 0.640
#> GSM23183 5 0.6750 0.54647 0.024 0.220 0.216 0.000 0.540
#> GSM23184 3 0.0451 0.85496 0.004 0.000 0.988 0.000 0.008
#> GSM23196 2 0.4142 0.94835 0.000 0.684 0.004 0.308 0.004
#> GSM23197 2 0.3837 0.94997 0.000 0.692 0.000 0.308 0.000
#> GSM23198 2 0.4142 0.94835 0.000 0.684 0.004 0.308 0.004
#> GSM23199 4 0.2835 0.82919 0.000 0.080 0.004 0.880 0.036
#> GSM23200 2 0.4843 0.77042 0.000 0.552 0.004 0.428 0.016
#> GSM23201 4 0.2074 0.89577 0.000 0.000 0.000 0.896 0.104
#> GSM23202 4 0.1270 0.90998 0.000 0.000 0.000 0.948 0.052
#> GSM23203 2 0.4142 0.94835 0.000 0.684 0.004 0.308 0.004
#> GSM23204 2 0.3837 0.94997 0.000 0.692 0.000 0.308 0.000
#> GSM23205 4 0.2074 0.89577 0.000 0.000 0.000 0.896 0.104
#> GSM23206 2 0.3837 0.94997 0.000 0.692 0.000 0.308 0.000
#> GSM23207 4 0.1012 0.90297 0.000 0.020 0.000 0.968 0.012
#> GSM23208 2 0.3990 0.94938 0.000 0.688 0.000 0.308 0.004
#> GSM23209 2 0.3837 0.94997 0.000 0.692 0.000 0.308 0.000
#> GSM23210 4 0.3102 0.84968 0.000 0.056 0.000 0.860 0.084
#> GSM23211 2 0.3837 0.94997 0.000 0.692 0.000 0.308 0.000
#> GSM23212 4 0.0703 0.91252 0.000 0.000 0.000 0.976 0.024
#> GSM23213 4 0.0609 0.91303 0.000 0.000 0.000 0.980 0.020
#> GSM23214 4 0.1270 0.90998 0.000 0.000 0.000 0.948 0.052
#> GSM23215 2 0.5492 0.65364 0.000 0.504 0.000 0.432 0.064
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0146 0.8670 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM23186 6 0.4230 0.1548 0.292 0.004 0.004 0.000 0.024 0.676
#> GSM23187 3 0.0000 0.8682 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23188 3 0.0000 0.8682 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23189 3 0.0000 0.8682 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23190 3 0.0260 0.8666 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM23191 5 0.1699 0.4877 0.016 0.000 0.032 0.000 0.936 0.016
#> GSM23192 5 0.5282 -0.1784 0.016 0.016 0.032 0.000 0.524 0.412
#> GSM23193 5 0.1679 0.4849 0.012 0.000 0.036 0.000 0.936 0.016
#> GSM23194 3 0.5336 0.5593 0.000 0.056 0.676 0.000 0.168 0.100
#> GSM23195 6 0.6096 0.4756 0.012 0.044 0.108 0.000 0.252 0.584
#> GSM23159 1 0.1657 0.8587 0.928 0.016 0.000 0.000 0.000 0.056
#> GSM23160 3 0.2852 0.8452 0.000 0.064 0.872 0.000 0.044 0.020
#> GSM23161 1 0.2851 0.8134 0.876 0.040 0.000 0.000 0.040 0.044
#> GSM23162 5 0.5181 0.0126 0.000 0.052 0.348 0.000 0.576 0.024
#> GSM23163 1 0.4175 0.7770 0.716 0.028 0.000 0.000 0.016 0.240
#> GSM23164 1 0.2384 0.8202 0.896 0.040 0.000 0.000 0.056 0.008
#> GSM23165 1 0.3610 0.7976 0.768 0.028 0.000 0.000 0.004 0.200
#> GSM23166 1 0.2384 0.8202 0.896 0.040 0.000 0.000 0.056 0.008
#> GSM23167 1 0.3549 0.8024 0.776 0.028 0.000 0.000 0.004 0.192
#> GSM23168 3 0.2852 0.8452 0.000 0.064 0.872 0.000 0.044 0.020
#> GSM23169 6 0.7115 0.2355 0.000 0.076 0.292 0.000 0.264 0.368
#> GSM23170 1 0.1364 0.8612 0.952 0.020 0.000 0.000 0.012 0.016
#> GSM23171 1 0.1232 0.8616 0.956 0.016 0.000 0.000 0.004 0.024
#> GSM23172 1 0.3610 0.7976 0.768 0.028 0.000 0.000 0.004 0.200
#> GSM23173 3 0.6564 0.3376 0.000 0.104 0.540 0.000 0.144 0.212
#> GSM23174 1 0.0820 0.8555 0.972 0.016 0.000 0.000 0.012 0.000
#> GSM23175 1 0.0993 0.8579 0.964 0.024 0.000 0.000 0.012 0.000
#> GSM23176 1 0.3610 0.7976 0.768 0.028 0.000 0.000 0.004 0.200
#> GSM23177 1 0.1296 0.8487 0.952 0.032 0.000 0.000 0.012 0.004
#> GSM23178 1 0.4219 0.8168 0.776 0.040 0.000 0.000 0.064 0.120
#> GSM23179 3 0.2911 0.8431 0.000 0.072 0.868 0.000 0.036 0.024
#> GSM23180 5 0.4420 0.5318 0.200 0.032 0.000 0.000 0.728 0.040
#> GSM23181 5 0.4987 0.4043 0.340 0.040 0.000 0.000 0.596 0.024
#> GSM23182 5 0.5017 0.5225 0.208 0.032 0.000 0.008 0.692 0.060
#> GSM23183 6 0.5866 0.4565 0.012 0.036 0.088 0.000 0.272 0.592
#> GSM23184 3 0.1599 0.8643 0.000 0.028 0.940 0.000 0.024 0.008
#> GSM23196 2 0.3250 0.9369 0.000 0.788 0.000 0.196 0.004 0.012
#> GSM23197 2 0.2762 0.9405 0.000 0.804 0.000 0.196 0.000 0.000
#> GSM23198 2 0.3250 0.9369 0.000 0.788 0.000 0.196 0.004 0.012
#> GSM23199 4 0.2875 0.8570 0.000 0.036 0.000 0.872 0.028 0.064
#> GSM23200 2 0.4688 0.6641 0.000 0.572 0.000 0.388 0.012 0.028
#> GSM23201 4 0.3141 0.8630 0.000 0.000 0.000 0.788 0.012 0.200
#> GSM23202 4 0.1967 0.8942 0.000 0.000 0.000 0.904 0.012 0.084
#> GSM23203 2 0.3250 0.9369 0.000 0.788 0.000 0.196 0.004 0.012
#> GSM23204 2 0.2762 0.9405 0.000 0.804 0.000 0.196 0.000 0.000
#> GSM23205 4 0.3141 0.8630 0.000 0.000 0.000 0.788 0.012 0.200
#> GSM23206 2 0.2762 0.9405 0.000 0.804 0.000 0.196 0.000 0.000
#> GSM23207 4 0.0777 0.8934 0.000 0.004 0.000 0.972 0.000 0.024
#> GSM23208 2 0.2902 0.9399 0.000 0.800 0.000 0.196 0.004 0.000
#> GSM23209 2 0.2762 0.9405 0.000 0.804 0.000 0.196 0.000 0.000
#> GSM23210 4 0.2794 0.8685 0.000 0.004 0.000 0.840 0.012 0.144
#> GSM23211 2 0.2762 0.9405 0.000 0.804 0.000 0.196 0.000 0.000
#> GSM23212 4 0.0405 0.8997 0.000 0.000 0.000 0.988 0.004 0.008
#> GSM23213 4 0.0405 0.8997 0.000 0.000 0.000 0.988 0.004 0.008
#> GSM23214 4 0.1644 0.8963 0.000 0.000 0.000 0.920 0.004 0.076
#> GSM23215 2 0.5540 0.6571 0.000 0.576 0.000 0.300 0.020 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 cell.type(p) disease.state(p) k
#> CV:kmeans 57 3.90e-13 5.25e-02 2
#> CV:kmeans 57 4.19e-13 4.23e-04 3
#> CV:kmeans 56 4.20e-12 1.13e-03 4
#> CV:kmeans 51 2.23e-10 1.06e-04 5
#> CV:kmeans 47 1.52e-09 2.41e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "skmeans"]
# you can also extract it by
# res = res_list["CV:skmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 11993 rows and 57 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 1.000 1.000 0.4642 0.536 0.536
#> 3 3 1.000 0.995 0.998 0.4609 0.786 0.600
#> 4 4 0.826 0.862 0.907 0.0882 0.932 0.792
#> 5 5 0.748 0.742 0.850 0.0686 0.932 0.750
#> 6 6 0.719 0.678 0.793 0.0371 0.961 0.822
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
#> GSM23185 1 0 1 1 0
#> GSM23186 1 0 1 1 0
#> GSM23187 1 0 1 1 0
#> GSM23188 1 0 1 1 0
#> GSM23189 1 0 1 1 0
#> GSM23190 1 0 1 1 0
#> GSM23191 1 0 1 1 0
#> GSM23192 1 0 1 1 0
#> GSM23193 1 0 1 1 0
#> GSM23194 1 0 1 1 0
#> GSM23195 1 0 1 1 0
#> GSM23159 1 0 1 1 0
#> GSM23160 1 0 1 1 0
#> GSM23161 1 0 1 1 0
#> GSM23162 1 0 1 1 0
#> GSM23163 1 0 1 1 0
#> GSM23164 1 0 1 1 0
#> GSM23165 1 0 1 1 0
#> GSM23166 1 0 1 1 0
#> GSM23167 1 0 1 1 0
#> GSM23168 1 0 1 1 0
#> GSM23169 1 0 1 1 0
#> GSM23170 1 0 1 1 0
#> GSM23171 1 0 1 1 0
#> GSM23172 1 0 1 1 0
#> GSM23173 1 0 1 1 0
#> GSM23174 1 0 1 1 0
#> GSM23175 1 0 1 1 0
#> GSM23176 1 0 1 1 0
#> GSM23177 1 0 1 1 0
#> GSM23178 1 0 1 1 0
#> GSM23179 1 0 1 1 0
#> GSM23180 1 0 1 1 0
#> GSM23181 1 0 1 1 0
#> GSM23182 1 0 1 1 0
#> GSM23183 1 0 1 1 0
#> GSM23184 1 0 1 1 0
#> GSM23196 2 0 1 0 1
#> GSM23197 2 0 1 0 1
#> GSM23198 2 0 1 0 1
#> GSM23199 2 0 1 0 1
#> GSM23200 2 0 1 0 1
#> GSM23201 2 0 1 0 1
#> GSM23202 2 0 1 0 1
#> GSM23203 2 0 1 0 1
#> GSM23204 2 0 1 0 1
#> GSM23205 2 0 1 0 1
#> GSM23206 2 0 1 0 1
#> GSM23207 2 0 1 0 1
#> GSM23208 2 0 1 0 1
#> GSM23209 2 0 1 0 1
#> GSM23210 2 0 1 0 1
#> GSM23211 2 0 1 0 1
#> GSM23212 2 0 1 0 1
#> GSM23213 2 0 1 0 1
#> GSM23214 2 0 1 0 1
#> GSM23215 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.995 0.000 0 1.000
#> GSM23186 1 0.1643 0.955 0.956 0 0.044
#> GSM23187 3 0.0000 0.995 0.000 0 1.000
#> GSM23188 3 0.0000 0.995 0.000 0 1.000
#> GSM23189 3 0.0000 0.995 0.000 0 1.000
#> GSM23190 3 0.0000 0.995 0.000 0 1.000
#> GSM23191 3 0.1289 0.970 0.032 0 0.968
#> GSM23192 3 0.1289 0.969 0.032 0 0.968
#> GSM23193 3 0.0747 0.984 0.016 0 0.984
#> GSM23194 3 0.0000 0.995 0.000 0 1.000
#> GSM23195 3 0.0000 0.995 0.000 0 1.000
#> GSM23159 1 0.0000 0.997 1.000 0 0.000
#> GSM23160 3 0.0000 0.995 0.000 0 1.000
#> GSM23161 1 0.0000 0.997 1.000 0 0.000
#> GSM23162 3 0.0000 0.995 0.000 0 1.000
#> GSM23163 1 0.0237 0.994 0.996 0 0.004
#> GSM23164 1 0.0000 0.997 1.000 0 0.000
#> GSM23165 1 0.0000 0.997 1.000 0 0.000
#> GSM23166 1 0.0000 0.997 1.000 0 0.000
#> GSM23167 1 0.0000 0.997 1.000 0 0.000
#> GSM23168 3 0.0000 0.995 0.000 0 1.000
#> GSM23169 3 0.0000 0.995 0.000 0 1.000
#> GSM23170 1 0.0000 0.997 1.000 0 0.000
#> GSM23171 1 0.0000 0.997 1.000 0 0.000
#> GSM23172 1 0.0000 0.997 1.000 0 0.000
#> GSM23173 3 0.0000 0.995 0.000 0 1.000
#> GSM23174 1 0.0000 0.997 1.000 0 0.000
#> GSM23175 1 0.0000 0.997 1.000 0 0.000
#> GSM23176 1 0.0000 0.997 1.000 0 0.000
#> GSM23177 1 0.0000 0.997 1.000 0 0.000
#> GSM23178 1 0.0000 0.997 1.000 0 0.000
#> GSM23179 3 0.0000 0.995 0.000 0 1.000
#> GSM23180 1 0.0000 0.997 1.000 0 0.000
#> GSM23181 1 0.0000 0.997 1.000 0 0.000
#> GSM23182 1 0.0000 0.997 1.000 0 0.000
#> GSM23183 3 0.0592 0.987 0.012 0 0.988
#> GSM23184 3 0.0000 0.995 0.000 0 1.000
#> GSM23196 2 0.0000 1.000 0.000 1 0.000
#> GSM23197 2 0.0000 1.000 0.000 1 0.000
#> GSM23198 2 0.0000 1.000 0.000 1 0.000
#> GSM23199 2 0.0000 1.000 0.000 1 0.000
#> GSM23200 2 0.0000 1.000 0.000 1 0.000
#> GSM23201 2 0.0000 1.000 0.000 1 0.000
#> GSM23202 2 0.0000 1.000 0.000 1 0.000
#> GSM23203 2 0.0000 1.000 0.000 1 0.000
#> GSM23204 2 0.0000 1.000 0.000 1 0.000
#> GSM23205 2 0.0000 1.000 0.000 1 0.000
#> GSM23206 2 0.0000 1.000 0.000 1 0.000
#> GSM23207 2 0.0000 1.000 0.000 1 0.000
#> GSM23208 2 0.0000 1.000 0.000 1 0.000
#> GSM23209 2 0.0000 1.000 0.000 1 0.000
#> GSM23210 2 0.0000 1.000 0.000 1 0.000
#> GSM23211 2 0.0000 1.000 0.000 1 0.000
#> GSM23212 2 0.0000 1.000 0.000 1 0.000
#> GSM23213 2 0.0000 1.000 0.000 1 0.000
#> GSM23214 2 0.0000 1.000 0.000 1 0.000
#> GSM23215 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0188 0.929 0.000 0.000 0.996 0.004
#> GSM23186 1 0.3168 0.867 0.884 0.000 0.060 0.056
#> GSM23187 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM23188 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM23189 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM23190 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM23191 3 0.5877 0.672 0.068 0.000 0.656 0.276
#> GSM23192 3 0.6075 0.696 0.128 0.000 0.680 0.192
#> GSM23193 3 0.4524 0.794 0.028 0.000 0.768 0.204
#> GSM23194 3 0.0592 0.927 0.000 0.000 0.984 0.016
#> GSM23195 3 0.3245 0.876 0.056 0.000 0.880 0.064
#> GSM23159 1 0.1118 0.937 0.964 0.000 0.000 0.036
#> GSM23160 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM23161 1 0.1716 0.928 0.936 0.000 0.000 0.064
#> GSM23162 3 0.1389 0.914 0.000 0.000 0.952 0.048
#> GSM23163 1 0.1389 0.933 0.952 0.000 0.000 0.048
#> GSM23164 1 0.2281 0.910 0.904 0.000 0.000 0.096
#> GSM23165 1 0.0817 0.931 0.976 0.000 0.000 0.024
#> GSM23166 1 0.2216 0.913 0.908 0.000 0.000 0.092
#> GSM23167 1 0.0817 0.933 0.976 0.000 0.000 0.024
#> GSM23168 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM23169 3 0.1004 0.924 0.004 0.000 0.972 0.024
#> GSM23170 1 0.0469 0.937 0.988 0.000 0.000 0.012
#> GSM23171 1 0.0188 0.936 0.996 0.000 0.000 0.004
#> GSM23172 1 0.0592 0.933 0.984 0.000 0.000 0.016
#> GSM23173 3 0.0592 0.927 0.000 0.000 0.984 0.016
#> GSM23174 1 0.1302 0.934 0.956 0.000 0.000 0.044
#> GSM23175 1 0.0592 0.938 0.984 0.000 0.000 0.016
#> GSM23176 1 0.0592 0.933 0.984 0.000 0.000 0.016
#> GSM23177 1 0.0469 0.937 0.988 0.000 0.000 0.012
#> GSM23178 1 0.1389 0.931 0.952 0.000 0.000 0.048
#> GSM23179 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM23180 1 0.4898 0.514 0.584 0.000 0.000 0.416
#> GSM23181 1 0.3444 0.842 0.816 0.000 0.000 0.184
#> GSM23182 4 0.4843 -0.147 0.396 0.000 0.000 0.604
#> GSM23183 3 0.4727 0.804 0.108 0.000 0.792 0.100
#> GSM23184 3 0.0000 0.930 0.000 0.000 1.000 0.000
#> GSM23196 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM23199 2 0.2760 0.805 0.000 0.872 0.000 0.128
#> GSM23200 2 0.0469 0.939 0.000 0.988 0.000 0.012
#> GSM23201 4 0.4277 0.804 0.000 0.280 0.000 0.720
#> GSM23202 4 0.4222 0.812 0.000 0.272 0.000 0.728
#> GSM23203 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM23205 4 0.4830 0.632 0.000 0.392 0.000 0.608
#> GSM23206 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM23207 2 0.4382 0.435 0.000 0.704 0.000 0.296
#> GSM23208 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM23210 2 0.1867 0.881 0.000 0.928 0.000 0.072
#> GSM23211 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM23212 4 0.4222 0.812 0.000 0.272 0.000 0.728
#> GSM23213 4 0.4222 0.812 0.000 0.272 0.000 0.728
#> GSM23214 4 0.4193 0.810 0.000 0.268 0.000 0.732
#> GSM23215 2 0.0336 0.942 0.000 0.992 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.1331 0.8650 0.000 0.000 0.952 0.008 0.040
#> GSM23186 1 0.6096 0.4414 0.624 0.000 0.080 0.044 0.252
#> GSM23187 3 0.0290 0.8695 0.000 0.000 0.992 0.000 0.008
#> GSM23188 3 0.0609 0.8687 0.000 0.000 0.980 0.000 0.020
#> GSM23189 3 0.0771 0.8683 0.000 0.000 0.976 0.004 0.020
#> GSM23190 3 0.1043 0.8681 0.000 0.000 0.960 0.000 0.040
#> GSM23191 5 0.5085 0.4458 0.036 0.000 0.232 0.032 0.700
#> GSM23192 5 0.5465 0.3800 0.056 0.000 0.280 0.020 0.644
#> GSM23193 5 0.5037 0.2499 0.024 0.000 0.352 0.012 0.612
#> GSM23194 3 0.2660 0.8204 0.000 0.000 0.864 0.008 0.128
#> GSM23195 3 0.6690 0.1435 0.116 0.000 0.492 0.032 0.360
#> GSM23159 1 0.2984 0.8412 0.860 0.000 0.000 0.032 0.108
#> GSM23160 3 0.1281 0.8681 0.000 0.000 0.956 0.012 0.032
#> GSM23161 1 0.3280 0.7932 0.812 0.000 0.000 0.012 0.176
#> GSM23162 3 0.3861 0.6427 0.000 0.000 0.728 0.008 0.264
#> GSM23163 1 0.3441 0.8206 0.824 0.000 0.004 0.024 0.148
#> GSM23164 1 0.2852 0.7873 0.828 0.000 0.000 0.000 0.172
#> GSM23165 1 0.2511 0.8216 0.892 0.000 0.000 0.028 0.080
#> GSM23166 1 0.3366 0.7412 0.784 0.000 0.000 0.004 0.212
#> GSM23167 1 0.1800 0.8393 0.932 0.000 0.000 0.020 0.048
#> GSM23168 3 0.2079 0.8572 0.000 0.000 0.916 0.020 0.064
#> GSM23169 3 0.4065 0.7200 0.008 0.000 0.760 0.020 0.212
#> GSM23170 1 0.1740 0.8549 0.932 0.000 0.000 0.012 0.056
#> GSM23171 1 0.1485 0.8569 0.948 0.000 0.000 0.020 0.032
#> GSM23172 1 0.1800 0.8414 0.932 0.000 0.000 0.020 0.048
#> GSM23173 3 0.3414 0.8022 0.020 0.000 0.844 0.020 0.116
#> GSM23174 1 0.2077 0.8481 0.908 0.000 0.000 0.008 0.084
#> GSM23175 1 0.2331 0.8492 0.900 0.000 0.000 0.020 0.080
#> GSM23176 1 0.1914 0.8357 0.924 0.000 0.000 0.016 0.060
#> GSM23177 1 0.2068 0.8485 0.904 0.000 0.000 0.004 0.092
#> GSM23178 1 0.2970 0.8128 0.828 0.000 0.000 0.004 0.168
#> GSM23179 3 0.0865 0.8695 0.000 0.000 0.972 0.004 0.024
#> GSM23180 5 0.5461 0.3623 0.284 0.000 0.000 0.096 0.620
#> GSM23181 5 0.4980 -0.1578 0.484 0.000 0.000 0.028 0.488
#> GSM23182 5 0.6504 0.3339 0.288 0.000 0.000 0.228 0.484
#> GSM23183 5 0.6751 -0.0556 0.116 0.000 0.412 0.032 0.440
#> GSM23184 3 0.1205 0.8673 0.000 0.000 0.956 0.004 0.040
#> GSM23196 2 0.0000 0.9178 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.9178 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.9178 0.000 1.000 0.000 0.000 0.000
#> GSM23199 2 0.3074 0.7368 0.000 0.804 0.000 0.196 0.000
#> GSM23200 2 0.1478 0.8793 0.000 0.936 0.000 0.064 0.000
#> GSM23201 4 0.2536 0.9038 0.000 0.128 0.000 0.868 0.004
#> GSM23202 4 0.1732 0.9290 0.000 0.080 0.000 0.920 0.000
#> GSM23203 2 0.0000 0.9178 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.9178 0.000 1.000 0.000 0.000 0.000
#> GSM23205 4 0.3814 0.7176 0.000 0.276 0.000 0.720 0.004
#> GSM23206 2 0.0000 0.9178 0.000 1.000 0.000 0.000 0.000
#> GSM23207 2 0.4420 0.0758 0.000 0.548 0.000 0.448 0.004
#> GSM23208 2 0.0000 0.9178 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.9178 0.000 1.000 0.000 0.000 0.000
#> GSM23210 2 0.2891 0.7583 0.000 0.824 0.000 0.176 0.000
#> GSM23211 2 0.0000 0.9178 0.000 1.000 0.000 0.000 0.000
#> GSM23212 4 0.1952 0.9325 0.000 0.084 0.000 0.912 0.004
#> GSM23213 4 0.1952 0.9325 0.000 0.084 0.000 0.912 0.004
#> GSM23214 4 0.1952 0.9325 0.000 0.084 0.000 0.912 0.004
#> GSM23215 2 0.1197 0.8912 0.000 0.952 0.000 0.048 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.1686 0.8169 0.000 0.000 0.924 0.000 0.012 0.064
#> GSM23186 6 0.6876 0.0939 0.400 0.000 0.092 0.020 0.080 0.408
#> GSM23187 3 0.1226 0.8206 0.000 0.000 0.952 0.004 0.004 0.040
#> GSM23188 3 0.1556 0.8122 0.000 0.000 0.920 0.000 0.000 0.080
#> GSM23189 3 0.1327 0.8174 0.000 0.000 0.936 0.000 0.000 0.064
#> GSM23190 3 0.2039 0.8142 0.000 0.000 0.908 0.004 0.016 0.072
#> GSM23191 5 0.5718 0.1643 0.024 0.000 0.128 0.012 0.628 0.208
#> GSM23192 6 0.6427 0.1516 0.040 0.000 0.116 0.012 0.352 0.480
#> GSM23193 5 0.5988 0.0835 0.012 0.000 0.256 0.012 0.560 0.160
#> GSM23194 3 0.4145 0.6609 0.000 0.000 0.724 0.004 0.052 0.220
#> GSM23195 6 0.5478 0.4908 0.100 0.000 0.204 0.000 0.048 0.648
#> GSM23159 1 0.4330 0.7235 0.748 0.000 0.000 0.012 0.140 0.100
#> GSM23160 3 0.2203 0.8064 0.000 0.000 0.896 0.004 0.016 0.084
#> GSM23161 1 0.4588 0.6897 0.700 0.000 0.000 0.024 0.228 0.048
#> GSM23162 3 0.5594 0.4674 0.000 0.000 0.592 0.012 0.220 0.176
#> GSM23163 1 0.5441 0.6168 0.652 0.000 0.004 0.028 0.120 0.196
#> GSM23164 1 0.4416 0.6348 0.668 0.000 0.000 0.012 0.288 0.032
#> GSM23165 1 0.3260 0.6893 0.824 0.000 0.000 0.012 0.028 0.136
#> GSM23166 1 0.4753 0.6137 0.648 0.000 0.000 0.016 0.288 0.048
#> GSM23167 1 0.2545 0.7468 0.888 0.000 0.000 0.020 0.024 0.068
#> GSM23168 3 0.2979 0.7952 0.000 0.000 0.852 0.004 0.056 0.088
#> GSM23169 3 0.5118 0.5765 0.008 0.000 0.644 0.016 0.064 0.268
#> GSM23170 1 0.2826 0.7686 0.856 0.000 0.000 0.008 0.112 0.024
#> GSM23171 1 0.3558 0.7664 0.812 0.000 0.000 0.008 0.108 0.072
#> GSM23172 1 0.2925 0.7366 0.860 0.000 0.000 0.008 0.052 0.080
#> GSM23173 3 0.4813 0.6211 0.028 0.000 0.684 0.008 0.036 0.244
#> GSM23174 1 0.3590 0.7330 0.776 0.000 0.000 0.004 0.188 0.032
#> GSM23175 1 0.3555 0.7348 0.780 0.000 0.000 0.000 0.176 0.044
#> GSM23176 1 0.3500 0.7175 0.820 0.000 0.000 0.012 0.064 0.104
#> GSM23177 1 0.3503 0.7548 0.808 0.000 0.000 0.016 0.144 0.032
#> GSM23178 1 0.4274 0.7149 0.748 0.000 0.000 0.016 0.168 0.068
#> GSM23179 3 0.2760 0.7984 0.000 0.000 0.856 0.004 0.024 0.116
#> GSM23180 5 0.4620 0.4637 0.220 0.000 0.000 0.032 0.704 0.044
#> GSM23181 5 0.4735 0.0871 0.384 0.000 0.000 0.004 0.568 0.044
#> GSM23182 5 0.5268 0.4355 0.240 0.000 0.000 0.104 0.636 0.020
#> GSM23183 6 0.5517 0.5019 0.068 0.000 0.204 0.004 0.068 0.656
#> GSM23184 3 0.1950 0.8162 0.000 0.000 0.912 0.000 0.024 0.064
#> GSM23196 2 0.0000 0.9235 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23197 2 0.0146 0.9234 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM23198 2 0.0000 0.9235 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23199 2 0.3716 0.5947 0.000 0.732 0.000 0.248 0.012 0.008
#> GSM23200 2 0.2695 0.7866 0.000 0.844 0.000 0.144 0.004 0.008
#> GSM23201 4 0.3465 0.7669 0.000 0.156 0.000 0.804 0.024 0.016
#> GSM23202 4 0.1728 0.8009 0.000 0.064 0.000 0.924 0.004 0.008
#> GSM23203 2 0.0000 0.9235 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23204 2 0.0405 0.9215 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM23205 4 0.4710 0.5574 0.000 0.336 0.000 0.616 0.024 0.024
#> GSM23206 2 0.0405 0.9221 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM23207 4 0.4227 0.1285 0.000 0.488 0.000 0.500 0.008 0.004
#> GSM23208 2 0.0146 0.9234 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM23209 2 0.0405 0.9215 0.000 0.988 0.000 0.000 0.008 0.004
#> GSM23210 2 0.3450 0.6722 0.000 0.772 0.000 0.208 0.008 0.012
#> GSM23211 2 0.0000 0.9235 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23212 4 0.1942 0.8010 0.000 0.064 0.000 0.916 0.012 0.008
#> GSM23213 4 0.1728 0.8026 0.000 0.064 0.000 0.924 0.008 0.004
#> GSM23214 4 0.1615 0.8024 0.000 0.064 0.000 0.928 0.004 0.004
#> GSM23215 2 0.2068 0.8763 0.000 0.916 0.000 0.048 0.020 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
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 cell.type(p) disease.state(p) k
#> CV:skmeans 57 3.90e-13 0.052490 2
#> CV:skmeans 57 4.19e-13 0.000423 3
#> CV:skmeans 55 6.87e-12 0.000323 4
#> CV:skmeans 47 3.48e-10 0.000331 5
#> CV:skmeans 47 1.52e-09 0.000208 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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.639 0.835 0.932 0.4977 0.492 0.492
#> 3 3 0.882 0.893 0.957 0.3535 0.719 0.487
#> 4 4 0.874 0.870 0.935 0.0882 0.934 0.798
#> 5 5 0.820 0.781 0.884 0.0712 0.955 0.834
#> 6 6 0.806 0.748 0.857 0.0317 0.972 0.880
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
#> GSM23185 2 0.7674 0.711 0.224 0.776
#> GSM23186 1 0.0000 0.948 1.000 0.000
#> GSM23187 2 0.8207 0.665 0.256 0.744
#> GSM23188 2 0.5842 0.797 0.140 0.860
#> GSM23189 2 0.6623 0.769 0.172 0.828
#> GSM23190 2 0.7219 0.740 0.200 0.800
#> GSM23191 1 0.0000 0.948 1.000 0.000
#> GSM23192 1 0.0000 0.948 1.000 0.000
#> GSM23193 1 0.0000 0.948 1.000 0.000
#> GSM23194 2 0.9983 0.142 0.476 0.524
#> GSM23195 2 0.9988 0.128 0.480 0.520
#> GSM23159 1 0.0000 0.948 1.000 0.000
#> GSM23160 1 0.8443 0.597 0.728 0.272
#> GSM23161 1 0.0000 0.948 1.000 0.000
#> GSM23162 1 0.0000 0.948 1.000 0.000
#> GSM23163 1 0.0000 0.948 1.000 0.000
#> GSM23164 1 0.0000 0.948 1.000 0.000
#> GSM23165 1 0.0000 0.948 1.000 0.000
#> GSM23166 1 0.0000 0.948 1.000 0.000
#> GSM23167 1 0.0000 0.948 1.000 0.000
#> GSM23168 1 0.6801 0.751 0.820 0.180
#> GSM23169 1 0.0000 0.948 1.000 0.000
#> GSM23170 1 0.0000 0.948 1.000 0.000
#> GSM23171 1 0.0000 0.948 1.000 0.000
#> GSM23172 1 0.0000 0.948 1.000 0.000
#> GSM23173 1 0.5737 0.809 0.864 0.136
#> GSM23174 1 0.0000 0.948 1.000 0.000
#> GSM23175 1 0.0000 0.948 1.000 0.000
#> GSM23176 1 0.0000 0.948 1.000 0.000
#> GSM23177 1 0.0000 0.948 1.000 0.000
#> GSM23178 1 0.0000 0.948 1.000 0.000
#> GSM23179 1 0.9522 0.360 0.628 0.372
#> GSM23180 1 0.0000 0.948 1.000 0.000
#> GSM23181 1 0.0000 0.948 1.000 0.000
#> GSM23182 1 0.0000 0.948 1.000 0.000
#> GSM23183 1 0.0000 0.948 1.000 0.000
#> GSM23184 1 0.8955 0.512 0.688 0.312
#> GSM23196 2 0.0000 0.888 0.000 1.000
#> GSM23197 2 0.0000 0.888 0.000 1.000
#> GSM23198 2 0.0000 0.888 0.000 1.000
#> GSM23199 2 0.0000 0.888 0.000 1.000
#> GSM23200 2 0.0000 0.888 0.000 1.000
#> GSM23201 2 0.0000 0.888 0.000 1.000
#> GSM23202 2 0.9850 0.281 0.428 0.572
#> GSM23203 2 0.0000 0.888 0.000 1.000
#> GSM23204 2 0.0000 0.888 0.000 1.000
#> GSM23205 2 0.0000 0.888 0.000 1.000
#> GSM23206 2 0.0000 0.888 0.000 1.000
#> GSM23207 2 0.0000 0.888 0.000 1.000
#> GSM23208 2 0.0000 0.888 0.000 1.000
#> GSM23209 2 0.0000 0.888 0.000 1.000
#> GSM23210 2 0.0000 0.888 0.000 1.000
#> GSM23211 2 0.0000 0.888 0.000 1.000
#> GSM23212 2 0.0000 0.888 0.000 1.000
#> GSM23213 2 0.0672 0.884 0.008 0.992
#> GSM23214 2 0.7950 0.662 0.240 0.760
#> GSM23215 2 0.0000 0.888 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.9204 0.000 0.000 1.000
#> GSM23186 1 0.4974 0.6615 0.764 0.000 0.236
#> GSM23187 3 0.0000 0.9204 0.000 0.000 1.000
#> GSM23188 3 0.0000 0.9204 0.000 0.000 1.000
#> GSM23189 3 0.0000 0.9204 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.9204 0.000 0.000 1.000
#> GSM23191 1 0.5016 0.6181 0.760 0.000 0.240
#> GSM23192 3 0.6225 0.2252 0.432 0.000 0.568
#> GSM23193 3 0.3752 0.8185 0.144 0.000 0.856
#> GSM23194 3 0.0000 0.9204 0.000 0.000 1.000
#> GSM23195 3 0.4654 0.7485 0.208 0.000 0.792
#> GSM23159 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23160 3 0.0000 0.9204 0.000 0.000 1.000
#> GSM23161 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23162 3 0.0000 0.9204 0.000 0.000 1.000
#> GSM23163 1 0.1411 0.9114 0.964 0.000 0.036
#> GSM23164 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23165 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23166 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23167 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23168 3 0.0000 0.9204 0.000 0.000 1.000
#> GSM23169 3 0.0747 0.9132 0.016 0.000 0.984
#> GSM23170 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23171 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23172 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23173 3 0.2711 0.8673 0.088 0.000 0.912
#> GSM23174 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23175 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23176 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23177 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23178 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23179 3 0.0000 0.9204 0.000 0.000 1.000
#> GSM23180 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23181 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23182 1 0.0000 0.9426 1.000 0.000 0.000
#> GSM23183 3 0.5678 0.5870 0.316 0.000 0.684
#> GSM23184 3 0.0000 0.9204 0.000 0.000 1.000
#> GSM23196 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23197 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23198 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23199 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23200 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23201 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23202 1 0.6305 0.0336 0.516 0.484 0.000
#> GSM23203 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23204 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23205 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23206 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23207 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23208 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23209 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23210 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23211 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23212 2 0.0000 0.9847 0.000 1.000 0.000
#> GSM23213 2 0.0237 0.9809 0.004 0.996 0.000
#> GSM23214 2 0.5098 0.6534 0.248 0.752 0.000
#> GSM23215 2 0.0000 0.9847 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0000 0.900 0.000 0.000 1.000 0.000
#> GSM23186 1 0.5077 0.724 0.760 0.000 0.160 0.080
#> GSM23187 3 0.0000 0.900 0.000 0.000 1.000 0.000
#> GSM23188 3 0.0000 0.900 0.000 0.000 1.000 0.000
#> GSM23189 3 0.0000 0.900 0.000 0.000 1.000 0.000
#> GSM23190 3 0.0000 0.900 0.000 0.000 1.000 0.000
#> GSM23191 1 0.7088 0.403 0.568 0.000 0.204 0.228
#> GSM23192 3 0.6646 0.078 0.428 0.000 0.488 0.084
#> GSM23193 3 0.4224 0.791 0.100 0.000 0.824 0.076
#> GSM23194 3 0.0000 0.900 0.000 0.000 1.000 0.000
#> GSM23195 3 0.4798 0.726 0.180 0.000 0.768 0.052
#> GSM23159 1 0.0469 0.942 0.988 0.000 0.000 0.012
#> GSM23160 3 0.0000 0.900 0.000 0.000 1.000 0.000
#> GSM23161 1 0.2011 0.905 0.920 0.000 0.000 0.080
#> GSM23162 3 0.0188 0.898 0.000 0.000 0.996 0.004
#> GSM23163 1 0.2813 0.887 0.896 0.000 0.024 0.080
#> GSM23164 1 0.0592 0.943 0.984 0.000 0.000 0.016
#> GSM23165 1 0.0188 0.944 0.996 0.000 0.000 0.004
#> GSM23166 1 0.1637 0.920 0.940 0.000 0.000 0.060
#> GSM23167 1 0.0188 0.944 0.996 0.000 0.000 0.004
#> GSM23168 3 0.0188 0.898 0.000 0.000 0.996 0.004
#> GSM23169 3 0.1767 0.876 0.012 0.000 0.944 0.044
#> GSM23170 1 0.0469 0.943 0.988 0.000 0.000 0.012
#> GSM23171 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM23172 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM23173 3 0.2480 0.841 0.088 0.000 0.904 0.008
#> GSM23174 1 0.0000 0.944 1.000 0.000 0.000 0.000
#> GSM23175 1 0.0188 0.944 0.996 0.000 0.000 0.004
#> GSM23176 1 0.0707 0.940 0.980 0.000 0.000 0.020
#> GSM23177 1 0.0336 0.944 0.992 0.000 0.000 0.008
#> GSM23178 1 0.0188 0.944 0.996 0.000 0.000 0.004
#> GSM23179 3 0.0000 0.900 0.000 0.000 1.000 0.000
#> GSM23180 1 0.0188 0.944 0.996 0.000 0.000 0.004
#> GSM23181 1 0.0188 0.944 0.996 0.000 0.000 0.004
#> GSM23182 4 0.4643 0.455 0.344 0.000 0.000 0.656
#> GSM23183 3 0.5417 0.602 0.284 0.000 0.676 0.040
#> GSM23184 3 0.0000 0.900 0.000 0.000 1.000 0.000
#> GSM23196 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM23199 2 0.1389 0.919 0.000 0.952 0.000 0.048
#> GSM23200 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM23201 4 0.2081 0.909 0.000 0.084 0.000 0.916
#> GSM23202 4 0.2081 0.909 0.000 0.084 0.000 0.916
#> GSM23203 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM23205 2 0.4164 0.602 0.000 0.736 0.000 0.264
#> GSM23206 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM23207 2 0.3688 0.726 0.000 0.792 0.000 0.208
#> GSM23208 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM23210 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM23211 2 0.0000 0.959 0.000 1.000 0.000 0.000
#> GSM23212 4 0.2081 0.909 0.000 0.084 0.000 0.916
#> GSM23213 4 0.2011 0.908 0.000 0.080 0.000 0.920
#> GSM23214 4 0.2011 0.908 0.000 0.080 0.000 0.920
#> GSM23215 2 0.0000 0.959 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.0162 0.882 0.000 0.000 0.996 0.000 0.004
#> GSM23186 1 0.4780 0.631 0.692 0.000 0.060 0.000 0.248
#> GSM23187 3 0.0162 0.882 0.000 0.000 0.996 0.000 0.004
#> GSM23188 3 0.0162 0.882 0.000 0.000 0.996 0.000 0.004
#> GSM23189 3 0.0162 0.882 0.000 0.000 0.996 0.000 0.004
#> GSM23190 3 0.0162 0.882 0.000 0.000 0.996 0.000 0.004
#> GSM23191 5 0.4261 0.694 0.096 0.000 0.076 0.024 0.804
#> GSM23192 5 0.1117 0.672 0.020 0.000 0.016 0.000 0.964
#> GSM23193 5 0.3132 0.663 0.008 0.000 0.172 0.000 0.820
#> GSM23194 3 0.0162 0.882 0.000 0.000 0.996 0.000 0.004
#> GSM23195 3 0.6438 0.177 0.220 0.000 0.500 0.000 0.280
#> GSM23159 1 0.0880 0.825 0.968 0.000 0.000 0.000 0.032
#> GSM23160 3 0.0000 0.881 0.000 0.000 1.000 0.000 0.000
#> GSM23161 1 0.3796 0.638 0.700 0.000 0.000 0.000 0.300
#> GSM23162 3 0.3534 0.588 0.000 0.000 0.744 0.000 0.256
#> GSM23163 1 0.3661 0.678 0.724 0.000 0.000 0.000 0.276
#> GSM23164 1 0.2605 0.783 0.852 0.000 0.000 0.000 0.148
#> GSM23165 1 0.0880 0.821 0.968 0.000 0.000 0.000 0.032
#> GSM23166 1 0.3534 0.695 0.744 0.000 0.000 0.000 0.256
#> GSM23167 1 0.0609 0.827 0.980 0.000 0.000 0.000 0.020
#> GSM23168 3 0.0290 0.879 0.000 0.000 0.992 0.000 0.008
#> GSM23169 3 0.3282 0.693 0.008 0.000 0.804 0.000 0.188
#> GSM23170 1 0.0794 0.827 0.972 0.000 0.000 0.000 0.028
#> GSM23171 1 0.0162 0.826 0.996 0.000 0.000 0.000 0.004
#> GSM23172 1 0.0510 0.823 0.984 0.000 0.000 0.000 0.016
#> GSM23173 3 0.5446 0.503 0.164 0.000 0.660 0.000 0.176
#> GSM23174 1 0.0404 0.826 0.988 0.000 0.000 0.000 0.012
#> GSM23175 1 0.0290 0.825 0.992 0.000 0.000 0.000 0.008
#> GSM23176 1 0.2471 0.792 0.864 0.000 0.000 0.000 0.136
#> GSM23177 1 0.1544 0.819 0.932 0.000 0.000 0.000 0.068
#> GSM23178 1 0.0609 0.823 0.980 0.000 0.000 0.000 0.020
#> GSM23179 3 0.0290 0.879 0.000 0.000 0.992 0.000 0.008
#> GSM23180 1 0.4297 -0.019 0.528 0.000 0.000 0.000 0.472
#> GSM23181 1 0.4287 0.038 0.540 0.000 0.000 0.000 0.460
#> GSM23182 5 0.6651 0.376 0.248 0.000 0.000 0.312 0.440
#> GSM23183 5 0.6060 0.491 0.208 0.000 0.216 0.000 0.576
#> GSM23184 3 0.0162 0.880 0.000 0.000 0.996 0.000 0.004
#> GSM23196 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000
#> GSM23199 2 0.1908 0.872 0.000 0.908 0.000 0.092 0.000
#> GSM23200 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000
#> GSM23201 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM23202 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM23203 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000
#> GSM23205 2 0.3508 0.656 0.000 0.748 0.000 0.252 0.000
#> GSM23206 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000
#> GSM23207 2 0.4045 0.472 0.000 0.644 0.000 0.356 0.000
#> GSM23208 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000
#> GSM23210 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000
#> GSM23211 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000
#> GSM23212 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM23213 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM23214 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM23215 2 0.0000 0.947 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0146 0.924 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM23186 1 0.5799 0.402 0.460 0.000 0.016 0.000 0.116 0.408
#> GSM23187 3 0.0146 0.924 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM23188 3 0.0146 0.924 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM23189 3 0.0146 0.924 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM23190 3 0.0146 0.924 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM23191 5 0.0291 0.459 0.004 0.000 0.000 0.004 0.992 0.000
#> GSM23192 5 0.3634 0.110 0.000 0.000 0.000 0.000 0.644 0.356
#> GSM23193 5 0.0508 0.456 0.000 0.000 0.004 0.000 0.984 0.012
#> GSM23194 3 0.1267 0.918 0.000 0.000 0.940 0.000 0.000 0.060
#> GSM23195 6 0.5781 0.530 0.180 0.000 0.120 0.000 0.068 0.632
#> GSM23159 1 0.1434 0.775 0.940 0.000 0.000 0.000 0.012 0.048
#> GSM23160 3 0.1814 0.906 0.000 0.000 0.900 0.000 0.000 0.100
#> GSM23161 1 0.4638 0.664 0.692 0.000 0.000 0.000 0.152 0.156
#> GSM23162 5 0.4988 -0.135 0.000 0.000 0.448 0.000 0.484 0.068
#> GSM23163 1 0.5156 0.641 0.600 0.000 0.000 0.000 0.128 0.272
#> GSM23164 1 0.3156 0.752 0.800 0.000 0.000 0.000 0.020 0.180
#> GSM23165 1 0.2996 0.732 0.772 0.000 0.000 0.000 0.000 0.228
#> GSM23166 1 0.4030 0.706 0.756 0.000 0.000 0.000 0.104 0.140
#> GSM23167 1 0.2300 0.765 0.856 0.000 0.000 0.000 0.000 0.144
#> GSM23168 3 0.2431 0.888 0.000 0.000 0.860 0.000 0.008 0.132
#> GSM23169 3 0.4064 0.732 0.008 0.000 0.768 0.000 0.132 0.092
#> GSM23170 1 0.1814 0.776 0.900 0.000 0.000 0.000 0.000 0.100
#> GSM23171 1 0.0363 0.770 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM23172 1 0.1910 0.755 0.892 0.000 0.000 0.000 0.000 0.108
#> GSM23173 6 0.4749 0.400 0.092 0.000 0.260 0.000 0.000 0.648
#> GSM23174 1 0.0405 0.769 0.988 0.000 0.000 0.000 0.004 0.008
#> GSM23175 1 0.0858 0.771 0.968 0.000 0.000 0.000 0.004 0.028
#> GSM23176 1 0.3876 0.720 0.700 0.000 0.000 0.000 0.024 0.276
#> GSM23177 1 0.3217 0.751 0.768 0.000 0.000 0.000 0.008 0.224
#> GSM23178 1 0.1625 0.772 0.928 0.000 0.000 0.000 0.012 0.060
#> GSM23179 3 0.2178 0.894 0.000 0.000 0.868 0.000 0.000 0.132
#> GSM23180 1 0.3979 0.273 0.540 0.000 0.000 0.000 0.456 0.004
#> GSM23181 1 0.3833 0.313 0.556 0.000 0.000 0.000 0.444 0.000
#> GSM23182 5 0.5774 0.148 0.176 0.000 0.000 0.384 0.440 0.000
#> GSM23183 6 0.5717 0.289 0.156 0.000 0.016 0.000 0.256 0.572
#> GSM23184 3 0.1714 0.910 0.000 0.000 0.908 0.000 0.000 0.092
#> GSM23196 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23199 2 0.1501 0.886 0.000 0.924 0.000 0.076 0.000 0.000
#> GSM23200 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23201 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23202 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23203 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23205 2 0.3198 0.642 0.000 0.740 0.000 0.260 0.000 0.000
#> GSM23206 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23207 2 0.3547 0.525 0.000 0.668 0.000 0.332 0.000 0.000
#> GSM23208 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23210 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23211 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23212 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23213 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23214 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23215 2 0.0000 0.948 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
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 cell.type(p) disease.state(p) k
#> CV:pam 53 1.24e-08 7.65e-01 2
#> CV:pam 55 1.14e-12 5.33e-03 3
#> CV:pam 54 1.12e-11 8.76e-04 4
#> CV:pam 51 2.23e-10 8.84e-05 5
#> CV:pam 47 1.52e-09 7.90e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4642 0.536 0.536
#> 3 3 0.725 0.947 0.892 0.4139 0.787 0.603
#> 4 4 0.797 0.798 0.894 0.1105 0.855 0.603
#> 5 5 0.820 0.769 0.865 0.0859 0.945 0.800
#> 6 6 0.871 0.801 0.884 0.0525 0.921 0.671
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
#> GSM23185 1 0 1 1 0
#> GSM23186 1 0 1 1 0
#> GSM23187 1 0 1 1 0
#> GSM23188 1 0 1 1 0
#> GSM23189 1 0 1 1 0
#> GSM23190 1 0 1 1 0
#> GSM23191 1 0 1 1 0
#> GSM23192 1 0 1 1 0
#> GSM23193 1 0 1 1 0
#> GSM23194 1 0 1 1 0
#> GSM23195 1 0 1 1 0
#> GSM23159 1 0 1 1 0
#> GSM23160 1 0 1 1 0
#> GSM23161 1 0 1 1 0
#> GSM23162 1 0 1 1 0
#> GSM23163 1 0 1 1 0
#> GSM23164 1 0 1 1 0
#> GSM23165 1 0 1 1 0
#> GSM23166 1 0 1 1 0
#> GSM23167 1 0 1 1 0
#> GSM23168 1 0 1 1 0
#> GSM23169 1 0 1 1 0
#> GSM23170 1 0 1 1 0
#> GSM23171 1 0 1 1 0
#> GSM23172 1 0 1 1 0
#> GSM23173 1 0 1 1 0
#> GSM23174 1 0 1 1 0
#> GSM23175 1 0 1 1 0
#> GSM23176 1 0 1 1 0
#> GSM23177 1 0 1 1 0
#> GSM23178 1 0 1 1 0
#> GSM23179 1 0 1 1 0
#> GSM23180 1 0 1 1 0
#> GSM23181 1 0 1 1 0
#> GSM23182 1 0 1 1 0
#> GSM23183 1 0 1 1 0
#> GSM23184 1 0 1 1 0
#> GSM23196 2 0 1 0 1
#> GSM23197 2 0 1 0 1
#> GSM23198 2 0 1 0 1
#> GSM23199 2 0 1 0 1
#> GSM23200 2 0 1 0 1
#> GSM23201 2 0 1 0 1
#> GSM23202 2 0 1 0 1
#> GSM23203 2 0 1 0 1
#> GSM23204 2 0 1 0 1
#> GSM23205 2 0 1 0 1
#> GSM23206 2 0 1 0 1
#> GSM23207 2 0 1 0 1
#> GSM23208 2 0 1 0 1
#> GSM23209 2 0 1 0 1
#> GSM23210 2 0 1 0 1
#> GSM23211 2 0 1 0 1
#> GSM23212 2 0 1 0 1
#> GSM23213 2 0 1 0 1
#> GSM23214 2 0 1 0 1
#> GSM23215 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.958 0.000 0.000 1.000
#> GSM23186 1 0.4796 0.869 0.780 0.000 0.220
#> GSM23187 3 0.0000 0.958 0.000 0.000 1.000
#> GSM23188 3 0.0237 0.956 0.004 0.000 0.996
#> GSM23189 3 0.0000 0.958 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.958 0.000 0.000 1.000
#> GSM23191 3 0.1529 0.946 0.040 0.000 0.960
#> GSM23192 3 0.1529 0.946 0.040 0.000 0.960
#> GSM23193 3 0.0424 0.956 0.008 0.000 0.992
#> GSM23194 3 0.0000 0.958 0.000 0.000 1.000
#> GSM23195 3 0.3816 0.844 0.148 0.000 0.852
#> GSM23159 1 0.3412 0.977 0.876 0.000 0.124
#> GSM23160 3 0.0000 0.958 0.000 0.000 1.000
#> GSM23161 1 0.3482 0.976 0.872 0.000 0.128
#> GSM23162 3 0.0000 0.958 0.000 0.000 1.000
#> GSM23163 1 0.3482 0.976 0.872 0.000 0.128
#> GSM23164 1 0.3482 0.976 0.872 0.000 0.128
#> GSM23165 1 0.3412 0.977 0.876 0.000 0.124
#> GSM23166 1 0.3482 0.976 0.872 0.000 0.128
#> GSM23167 1 0.3412 0.977 0.876 0.000 0.124
#> GSM23168 3 0.0000 0.958 0.000 0.000 1.000
#> GSM23169 3 0.1529 0.946 0.040 0.000 0.960
#> GSM23170 1 0.3412 0.977 0.876 0.000 0.124
#> GSM23171 1 0.3412 0.977 0.876 0.000 0.124
#> GSM23172 1 0.3412 0.977 0.876 0.000 0.124
#> GSM23173 3 0.2878 0.906 0.096 0.000 0.904
#> GSM23174 1 0.3412 0.977 0.876 0.000 0.124
#> GSM23175 1 0.3412 0.977 0.876 0.000 0.124
#> GSM23176 1 0.3412 0.977 0.876 0.000 0.124
#> GSM23177 1 0.3482 0.976 0.872 0.000 0.128
#> GSM23178 1 0.3412 0.977 0.876 0.000 0.124
#> GSM23179 3 0.0000 0.958 0.000 0.000 1.000
#> GSM23180 3 0.2711 0.912 0.088 0.000 0.912
#> GSM23181 1 0.5621 0.729 0.692 0.000 0.308
#> GSM23182 3 0.2711 0.912 0.088 0.000 0.912
#> GSM23183 3 0.3752 0.849 0.144 0.000 0.856
#> GSM23184 3 0.0000 0.958 0.000 0.000 1.000
#> GSM23196 2 0.3412 0.950 0.124 0.876 0.000
#> GSM23197 2 0.3412 0.950 0.124 0.876 0.000
#> GSM23198 2 0.3412 0.950 0.124 0.876 0.000
#> GSM23199 2 0.0000 0.950 0.000 1.000 0.000
#> GSM23200 2 0.3412 0.950 0.124 0.876 0.000
#> GSM23201 2 0.0000 0.950 0.000 1.000 0.000
#> GSM23202 2 0.0000 0.950 0.000 1.000 0.000
#> GSM23203 2 0.3412 0.950 0.124 0.876 0.000
#> GSM23204 2 0.3412 0.950 0.124 0.876 0.000
#> GSM23205 2 0.0000 0.950 0.000 1.000 0.000
#> GSM23206 2 0.3412 0.950 0.124 0.876 0.000
#> GSM23207 2 0.0000 0.950 0.000 1.000 0.000
#> GSM23208 2 0.3412 0.950 0.124 0.876 0.000
#> GSM23209 2 0.3412 0.950 0.124 0.876 0.000
#> GSM23210 2 0.0000 0.950 0.000 1.000 0.000
#> GSM23211 2 0.3412 0.950 0.124 0.876 0.000
#> GSM23212 2 0.0000 0.950 0.000 1.000 0.000
#> GSM23213 2 0.0000 0.950 0.000 1.000 0.000
#> GSM23214 2 0.0000 0.950 0.000 1.000 0.000
#> GSM23215 2 0.0000 0.950 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0000 0.8668 0.000 0.000 1.000 0.000
#> GSM23186 1 0.3081 0.8234 0.888 0.000 0.048 0.064
#> GSM23187 3 0.0000 0.8668 0.000 0.000 1.000 0.000
#> GSM23188 3 0.0188 0.8654 0.000 0.000 0.996 0.004
#> GSM23189 3 0.0000 0.8668 0.000 0.000 1.000 0.000
#> GSM23190 3 0.0000 0.8668 0.000 0.000 1.000 0.000
#> GSM23191 3 0.6232 0.4546 0.332 0.000 0.596 0.072
#> GSM23192 3 0.4564 0.5175 0.328 0.000 0.672 0.000
#> GSM23193 3 0.4452 0.7499 0.156 0.000 0.796 0.048
#> GSM23194 3 0.0336 0.8650 0.008 0.000 0.992 0.000
#> GSM23195 1 0.6387 0.0421 0.492 0.000 0.444 0.064
#> GSM23159 1 0.0921 0.8678 0.972 0.000 0.000 0.028
#> GSM23160 3 0.0000 0.8668 0.000 0.000 1.000 0.000
#> GSM23161 1 0.0188 0.8702 0.996 0.000 0.000 0.004
#> GSM23162 3 0.3004 0.8243 0.060 0.000 0.892 0.048
#> GSM23163 1 0.1545 0.8625 0.952 0.000 0.008 0.040
#> GSM23164 1 0.0336 0.8686 0.992 0.000 0.000 0.008
#> GSM23165 1 0.1716 0.8547 0.936 0.000 0.000 0.064
#> GSM23166 1 0.0336 0.8698 0.992 0.000 0.000 0.008
#> GSM23167 1 0.1022 0.8668 0.968 0.000 0.000 0.032
#> GSM23168 3 0.0000 0.8668 0.000 0.000 1.000 0.000
#> GSM23169 3 0.4914 0.6779 0.208 0.000 0.748 0.044
#> GSM23170 1 0.0188 0.8693 0.996 0.000 0.000 0.004
#> GSM23171 1 0.0469 0.8699 0.988 0.000 0.000 0.012
#> GSM23172 1 0.0817 0.8685 0.976 0.000 0.000 0.024
#> GSM23173 3 0.6286 0.2781 0.384 0.000 0.552 0.064
#> GSM23174 1 0.0804 0.8665 0.980 0.000 0.008 0.012
#> GSM23175 1 0.0469 0.8673 0.988 0.000 0.000 0.012
#> GSM23176 1 0.1302 0.8635 0.956 0.000 0.000 0.044
#> GSM23177 1 0.0592 0.8683 0.984 0.000 0.000 0.016
#> GSM23178 1 0.0188 0.8693 0.996 0.000 0.000 0.004
#> GSM23179 3 0.0000 0.8668 0.000 0.000 1.000 0.000
#> GSM23180 1 0.6600 0.0976 0.520 0.000 0.396 0.084
#> GSM23181 1 0.1767 0.8459 0.944 0.000 0.044 0.012
#> GSM23182 1 0.6600 0.0976 0.520 0.000 0.396 0.084
#> GSM23183 1 0.6286 0.2497 0.552 0.000 0.384 0.064
#> GSM23184 3 0.0000 0.8668 0.000 0.000 1.000 0.000
#> GSM23196 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM23199 4 0.4585 0.7632 0.000 0.332 0.000 0.668
#> GSM23200 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM23201 4 0.1940 0.8526 0.000 0.076 0.000 0.924
#> GSM23202 4 0.1940 0.8526 0.000 0.076 0.000 0.924
#> GSM23203 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM23205 4 0.2814 0.8553 0.000 0.132 0.000 0.868
#> GSM23206 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM23207 4 0.4643 0.7468 0.000 0.344 0.000 0.656
#> GSM23208 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM23210 4 0.4564 0.7674 0.000 0.328 0.000 0.672
#> GSM23211 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM23212 4 0.2704 0.8559 0.000 0.124 0.000 0.876
#> GSM23213 4 0.1940 0.8526 0.000 0.076 0.000 0.924
#> GSM23214 4 0.1940 0.8526 0.000 0.076 0.000 0.924
#> GSM23215 4 0.4564 0.7674 0.000 0.328 0.000 0.672
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.0162 0.837 0.000 0.000 0.996 0.000 0.004
#> GSM23186 1 0.4264 0.691 0.620 0.000 0.004 0.000 0.376
#> GSM23187 3 0.0162 0.837 0.000 0.000 0.996 0.000 0.004
#> GSM23188 3 0.0162 0.837 0.000 0.000 0.996 0.000 0.004
#> GSM23189 3 0.0162 0.837 0.000 0.000 0.996 0.000 0.004
#> GSM23190 3 0.0162 0.837 0.000 0.000 0.996 0.000 0.004
#> GSM23191 5 0.5039 0.885 0.008 0.000 0.360 0.028 0.604
#> GSM23192 3 0.4746 -0.554 0.016 0.000 0.504 0.000 0.480
#> GSM23193 3 0.4225 -0.092 0.004 0.000 0.632 0.000 0.364
#> GSM23194 3 0.0000 0.835 0.000 0.000 1.000 0.000 0.000
#> GSM23195 1 0.4370 0.638 0.744 0.000 0.056 0.000 0.200
#> GSM23159 1 0.0404 0.773 0.988 0.000 0.000 0.000 0.012
#> GSM23160 3 0.0963 0.808 0.000 0.000 0.964 0.000 0.036
#> GSM23161 1 0.0609 0.765 0.980 0.000 0.000 0.000 0.020
#> GSM23162 3 0.3551 0.483 0.008 0.000 0.772 0.000 0.220
#> GSM23163 1 0.0162 0.772 0.996 0.000 0.000 0.000 0.004
#> GSM23164 1 0.3305 0.600 0.776 0.000 0.000 0.000 0.224
#> GSM23165 1 0.4060 0.702 0.640 0.000 0.000 0.000 0.360
#> GSM23166 1 0.3480 0.568 0.752 0.000 0.000 0.000 0.248
#> GSM23167 1 0.3752 0.728 0.708 0.000 0.000 0.000 0.292
#> GSM23168 3 0.0000 0.835 0.000 0.000 1.000 0.000 0.000
#> GSM23169 3 0.3438 0.605 0.020 0.000 0.808 0.000 0.172
#> GSM23170 1 0.3366 0.748 0.768 0.000 0.000 0.000 0.232
#> GSM23171 1 0.2280 0.772 0.880 0.000 0.000 0.000 0.120
#> GSM23172 1 0.3730 0.729 0.712 0.000 0.000 0.000 0.288
#> GSM23173 1 0.6537 -0.103 0.404 0.000 0.400 0.000 0.196
#> GSM23174 1 0.2929 0.765 0.820 0.000 0.000 0.000 0.180
#> GSM23175 1 0.0290 0.772 0.992 0.000 0.000 0.000 0.008
#> GSM23176 1 0.3857 0.722 0.688 0.000 0.000 0.000 0.312
#> GSM23177 1 0.0000 0.771 1.000 0.000 0.000 0.000 0.000
#> GSM23178 1 0.0000 0.771 1.000 0.000 0.000 0.000 0.000
#> GSM23179 3 0.0290 0.833 0.000 0.000 0.992 0.000 0.008
#> GSM23180 5 0.5653 0.947 0.028 0.000 0.312 0.048 0.612
#> GSM23181 1 0.4448 0.071 0.516 0.000 0.004 0.000 0.480
#> GSM23182 5 0.5653 0.947 0.028 0.000 0.312 0.048 0.612
#> GSM23183 1 0.4303 0.643 0.752 0.000 0.056 0.000 0.192
#> GSM23184 3 0.0404 0.831 0.000 0.000 0.988 0.000 0.012
#> GSM23196 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23199 4 0.2020 0.933 0.000 0.100 0.000 0.900 0.000
#> GSM23200 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23201 4 0.0000 0.939 0.000 0.000 0.000 1.000 0.000
#> GSM23202 4 0.0000 0.939 0.000 0.000 0.000 1.000 0.000
#> GSM23203 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23205 4 0.0794 0.945 0.000 0.028 0.000 0.972 0.000
#> GSM23206 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23207 4 0.2074 0.931 0.000 0.104 0.000 0.896 0.000
#> GSM23208 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23210 4 0.2074 0.931 0.000 0.104 0.000 0.896 0.000
#> GSM23211 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23212 4 0.1270 0.945 0.000 0.052 0.000 0.948 0.000
#> GSM23213 4 0.0000 0.939 0.000 0.000 0.000 1.000 0.000
#> GSM23214 4 0.0000 0.939 0.000 0.000 0.000 1.000 0.000
#> GSM23215 4 0.1908 0.937 0.000 0.092 0.000 0.908 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0146 0.96460 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM23186 6 0.3368 0.60858 0.232 0.000 0.000 0.000 0.012 0.756
#> GSM23187 3 0.0000 0.96538 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23188 3 0.0000 0.96538 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23189 3 0.0000 0.96538 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23190 3 0.0000 0.96538 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23191 5 0.0146 0.71193 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM23192 5 0.3905 0.60540 0.004 0.000 0.256 0.000 0.716 0.024
#> GSM23193 5 0.3841 0.66754 0.000 0.000 0.256 0.000 0.716 0.028
#> GSM23194 3 0.0891 0.94469 0.000 0.000 0.968 0.000 0.008 0.024
#> GSM23195 1 0.6550 0.08711 0.432 0.000 0.032 0.000 0.232 0.304
#> GSM23159 1 0.1910 0.73688 0.892 0.000 0.000 0.000 0.000 0.108
#> GSM23160 3 0.0260 0.96001 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM23161 1 0.1007 0.74388 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM23162 5 0.4210 0.55804 0.000 0.000 0.336 0.000 0.636 0.028
#> GSM23163 1 0.1714 0.74172 0.908 0.000 0.000 0.000 0.000 0.092
#> GSM23164 1 0.0713 0.72091 0.972 0.000 0.000 0.000 0.028 0.000
#> GSM23165 6 0.1075 0.75584 0.048 0.000 0.000 0.000 0.000 0.952
#> GSM23166 1 0.1528 0.71885 0.936 0.000 0.000 0.000 0.048 0.016
#> GSM23167 6 0.1814 0.77452 0.100 0.000 0.000 0.000 0.000 0.900
#> GSM23168 3 0.0508 0.95769 0.000 0.000 0.984 0.000 0.004 0.012
#> GSM23169 3 0.3854 0.66387 0.004 0.000 0.760 0.000 0.188 0.048
#> GSM23170 1 0.3684 0.44914 0.628 0.000 0.000 0.000 0.000 0.372
#> GSM23171 1 0.3175 0.62550 0.744 0.000 0.000 0.000 0.000 0.256
#> GSM23172 6 0.1814 0.77452 0.100 0.000 0.000 0.000 0.000 0.900
#> GSM23173 6 0.7727 0.09075 0.240 0.000 0.240 0.000 0.244 0.276
#> GSM23174 1 0.2854 0.63323 0.792 0.000 0.000 0.000 0.000 0.208
#> GSM23175 1 0.1267 0.74198 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM23176 6 0.1765 0.77528 0.096 0.000 0.000 0.000 0.000 0.904
#> GSM23177 1 0.1387 0.74402 0.932 0.000 0.000 0.000 0.000 0.068
#> GSM23178 1 0.1556 0.74399 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM23179 3 0.0146 0.96460 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM23180 5 0.2147 0.71616 0.084 0.000 0.000 0.000 0.896 0.020
#> GSM23181 1 0.4238 -0.00715 0.540 0.000 0.000 0.000 0.444 0.016
#> GSM23182 5 0.2147 0.71616 0.084 0.000 0.000 0.000 0.896 0.020
#> GSM23183 1 0.6965 0.24533 0.480 0.000 0.124 0.000 0.228 0.168
#> GSM23184 3 0.0000 0.96538 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23196 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23199 4 0.1075 0.96122 0.000 0.048 0.000 0.952 0.000 0.000
#> GSM23200 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23201 4 0.0000 0.97515 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23202 4 0.0000 0.97515 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23203 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23205 4 0.0000 0.97515 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23206 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23207 4 0.1007 0.96310 0.000 0.044 0.000 0.956 0.000 0.000
#> GSM23208 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23210 4 0.1075 0.96122 0.000 0.048 0.000 0.952 0.000 0.000
#> GSM23211 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23212 4 0.0000 0.97515 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23213 4 0.0000 0.97515 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23214 4 0.0000 0.97515 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23215 4 0.1075 0.96122 0.000 0.048 0.000 0.952 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 cell.type(p) disease.state(p) k
#> CV:mclust 57 3.90e-13 0.052490 2
#> CV:mclust 57 4.19e-13 0.000276 3
#> CV:mclust 51 4.89e-11 0.000385 4
#> CV:mclust 52 1.38e-10 0.002549 5
#> CV:mclust 52 5.39e-10 0.002514 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 11993 rows and 57 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 0.927 0.961 0.982 0.4721 0.536 0.536
#> 3 3 0.976 0.948 0.976 0.4310 0.786 0.600
#> 4 4 0.860 0.833 0.931 0.1123 0.859 0.604
#> 5 5 0.780 0.733 0.852 0.0474 0.967 0.869
#> 6 6 0.744 0.635 0.793 0.0433 0.947 0.774
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
#> GSM23185 1 0.767 0.737 0.776 0.224
#> GSM23186 1 0.000 0.972 1.000 0.000
#> GSM23187 1 0.574 0.848 0.864 0.136
#> GSM23188 1 0.913 0.556 0.672 0.328
#> GSM23189 1 0.697 0.786 0.812 0.188
#> GSM23190 1 0.584 0.843 0.860 0.140
#> GSM23191 1 0.000 0.972 1.000 0.000
#> GSM23192 1 0.000 0.972 1.000 0.000
#> GSM23193 1 0.000 0.972 1.000 0.000
#> GSM23194 1 0.000 0.972 1.000 0.000
#> GSM23195 1 0.000 0.972 1.000 0.000
#> GSM23159 1 0.000 0.972 1.000 0.000
#> GSM23160 1 0.000 0.972 1.000 0.000
#> GSM23161 1 0.000 0.972 1.000 0.000
#> GSM23162 1 0.000 0.972 1.000 0.000
#> GSM23163 1 0.000 0.972 1.000 0.000
#> GSM23164 1 0.000 0.972 1.000 0.000
#> GSM23165 1 0.000 0.972 1.000 0.000
#> GSM23166 1 0.000 0.972 1.000 0.000
#> GSM23167 1 0.000 0.972 1.000 0.000
#> GSM23168 1 0.000 0.972 1.000 0.000
#> GSM23169 1 0.000 0.972 1.000 0.000
#> GSM23170 1 0.000 0.972 1.000 0.000
#> GSM23171 1 0.000 0.972 1.000 0.000
#> GSM23172 1 0.000 0.972 1.000 0.000
#> GSM23173 1 0.000 0.972 1.000 0.000
#> GSM23174 1 0.000 0.972 1.000 0.000
#> GSM23175 1 0.000 0.972 1.000 0.000
#> GSM23176 1 0.000 0.972 1.000 0.000
#> GSM23177 1 0.000 0.972 1.000 0.000
#> GSM23178 1 0.000 0.972 1.000 0.000
#> GSM23179 1 0.000 0.972 1.000 0.000
#> GSM23180 1 0.000 0.972 1.000 0.000
#> GSM23181 1 0.000 0.972 1.000 0.000
#> GSM23182 1 0.000 0.972 1.000 0.000
#> GSM23183 1 0.000 0.972 1.000 0.000
#> GSM23184 1 0.000 0.972 1.000 0.000
#> GSM23196 2 0.000 0.998 0.000 1.000
#> GSM23197 2 0.000 0.998 0.000 1.000
#> GSM23198 2 0.000 0.998 0.000 1.000
#> GSM23199 2 0.000 0.998 0.000 1.000
#> GSM23200 2 0.000 0.998 0.000 1.000
#> GSM23201 2 0.000 0.998 0.000 1.000
#> GSM23202 2 0.224 0.961 0.036 0.964
#> GSM23203 2 0.000 0.998 0.000 1.000
#> GSM23204 2 0.000 0.998 0.000 1.000
#> GSM23205 2 0.000 0.998 0.000 1.000
#> GSM23206 2 0.000 0.998 0.000 1.000
#> GSM23207 2 0.000 0.998 0.000 1.000
#> GSM23208 2 0.000 0.998 0.000 1.000
#> GSM23209 2 0.000 0.998 0.000 1.000
#> GSM23210 2 0.000 0.998 0.000 1.000
#> GSM23211 2 0.000 0.998 0.000 1.000
#> GSM23212 2 0.000 0.998 0.000 1.000
#> GSM23213 2 0.000 0.998 0.000 1.000
#> GSM23214 2 0.000 0.998 0.000 1.000
#> GSM23215 2 0.000 0.998 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.939 0.000 0.000 1.000
#> GSM23186 1 0.2066 0.929 0.940 0.000 0.060
#> GSM23187 3 0.0000 0.939 0.000 0.000 1.000
#> GSM23188 3 0.0000 0.939 0.000 0.000 1.000
#> GSM23189 3 0.0000 0.939 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.939 0.000 0.000 1.000
#> GSM23191 3 0.6260 0.267 0.448 0.000 0.552
#> GSM23192 3 0.5497 0.628 0.292 0.000 0.708
#> GSM23193 3 0.3551 0.845 0.132 0.000 0.868
#> GSM23194 3 0.0000 0.939 0.000 0.000 1.000
#> GSM23195 3 0.1163 0.928 0.028 0.000 0.972
#> GSM23159 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23160 3 0.0000 0.939 0.000 0.000 1.000
#> GSM23161 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23162 3 0.0424 0.937 0.008 0.000 0.992
#> GSM23163 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23164 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23165 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23166 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23167 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23168 3 0.0000 0.939 0.000 0.000 1.000
#> GSM23169 3 0.0892 0.932 0.020 0.000 0.980
#> GSM23170 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23171 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23172 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23173 3 0.0424 0.937 0.008 0.000 0.992
#> GSM23174 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23175 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23176 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23177 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23178 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23179 3 0.0000 0.939 0.000 0.000 1.000
#> GSM23180 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23181 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23182 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23183 3 0.2878 0.879 0.096 0.000 0.904
#> GSM23184 3 0.0000 0.939 0.000 0.000 1.000
#> GSM23196 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23197 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23198 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23199 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23200 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23201 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23202 2 0.4654 0.744 0.208 0.792 0.000
#> GSM23203 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23204 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23205 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23206 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23207 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23208 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23209 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23210 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23211 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23212 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23213 2 0.0747 0.974 0.016 0.984 0.000
#> GSM23214 2 0.1031 0.967 0.024 0.976 0.000
#> GSM23215 2 0.0000 0.986 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0188 0.9482 0.000 0.000 0.996 0.004
#> GSM23186 1 0.0000 0.9160 1.000 0.000 0.000 0.000
#> GSM23187 3 0.0000 0.9495 0.000 0.000 1.000 0.000
#> GSM23188 3 0.0000 0.9495 0.000 0.000 1.000 0.000
#> GSM23189 3 0.0000 0.9495 0.000 0.000 1.000 0.000
#> GSM23190 3 0.0188 0.9482 0.000 0.000 0.996 0.004
#> GSM23191 4 0.3539 0.6613 0.004 0.000 0.176 0.820
#> GSM23192 3 0.4741 0.5467 0.004 0.000 0.668 0.328
#> GSM23193 3 0.4103 0.6782 0.000 0.000 0.744 0.256
#> GSM23194 3 0.0000 0.9495 0.000 0.000 1.000 0.000
#> GSM23195 1 0.3528 0.7182 0.808 0.000 0.192 0.000
#> GSM23159 1 0.0000 0.9160 1.000 0.000 0.000 0.000
#> GSM23160 3 0.0000 0.9495 0.000 0.000 1.000 0.000
#> GSM23161 1 0.1867 0.8623 0.928 0.000 0.000 0.072
#> GSM23162 3 0.0188 0.9475 0.000 0.000 0.996 0.004
#> GSM23163 1 0.0000 0.9160 1.000 0.000 0.000 0.000
#> GSM23164 1 0.4999 -0.0241 0.508 0.000 0.000 0.492
#> GSM23165 1 0.0000 0.9160 1.000 0.000 0.000 0.000
#> GSM23166 4 0.4999 -0.0862 0.492 0.000 0.000 0.508
#> GSM23167 1 0.0000 0.9160 1.000 0.000 0.000 0.000
#> GSM23168 3 0.0000 0.9495 0.000 0.000 1.000 0.000
#> GSM23169 3 0.0000 0.9495 0.000 0.000 1.000 0.000
#> GSM23170 1 0.0000 0.9160 1.000 0.000 0.000 0.000
#> GSM23171 1 0.0188 0.9141 0.996 0.000 0.000 0.004
#> GSM23172 1 0.0000 0.9160 1.000 0.000 0.000 0.000
#> GSM23173 3 0.1940 0.8787 0.076 0.000 0.924 0.000
#> GSM23174 1 0.1022 0.8955 0.968 0.000 0.000 0.032
#> GSM23175 1 0.0336 0.9121 0.992 0.000 0.000 0.008
#> GSM23176 1 0.0000 0.9160 1.000 0.000 0.000 0.000
#> GSM23177 1 0.0000 0.9160 1.000 0.000 0.000 0.000
#> GSM23178 1 0.0000 0.9160 1.000 0.000 0.000 0.000
#> GSM23179 3 0.0000 0.9495 0.000 0.000 1.000 0.000
#> GSM23180 4 0.0188 0.8174 0.004 0.000 0.000 0.996
#> GSM23181 4 0.1474 0.8001 0.052 0.000 0.000 0.948
#> GSM23182 4 0.0188 0.8174 0.004 0.000 0.000 0.996
#> GSM23183 1 0.4697 0.4646 0.644 0.000 0.356 0.000
#> GSM23184 3 0.0188 0.9482 0.000 0.000 0.996 0.004
#> GSM23196 2 0.0000 0.9440 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0188 0.9420 0.000 0.996 0.000 0.004
#> GSM23198 2 0.0000 0.9440 0.000 1.000 0.000 0.000
#> GSM23199 2 0.0592 0.9380 0.000 0.984 0.000 0.016
#> GSM23200 2 0.0336 0.9417 0.000 0.992 0.000 0.008
#> GSM23201 4 0.2011 0.8106 0.000 0.080 0.000 0.920
#> GSM23202 4 0.2469 0.7975 0.000 0.108 0.000 0.892
#> GSM23203 2 0.0000 0.9440 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0188 0.9420 0.000 0.996 0.000 0.004
#> GSM23205 2 0.4222 0.6128 0.000 0.728 0.000 0.272
#> GSM23206 2 0.0000 0.9440 0.000 1.000 0.000 0.000
#> GSM23207 2 0.0707 0.9354 0.000 0.980 0.000 0.020
#> GSM23208 2 0.0000 0.9440 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.9440 0.000 1.000 0.000 0.000
#> GSM23210 2 0.0592 0.9380 0.000 0.984 0.000 0.016
#> GSM23211 2 0.0000 0.9440 0.000 1.000 0.000 0.000
#> GSM23212 2 0.4916 0.2500 0.000 0.576 0.000 0.424
#> GSM23213 4 0.4008 0.6348 0.000 0.244 0.000 0.756
#> GSM23214 4 0.2921 0.7723 0.000 0.140 0.000 0.860
#> GSM23215 2 0.0188 0.9432 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.3109 0.6912 0.000 0.000 0.800 0.000 0.200
#> GSM23186 1 0.2179 0.8593 0.888 0.000 0.000 0.000 0.112
#> GSM23187 3 0.0703 0.7743 0.000 0.000 0.976 0.000 0.024
#> GSM23188 3 0.1410 0.7685 0.000 0.000 0.940 0.000 0.060
#> GSM23189 3 0.0404 0.7726 0.000 0.000 0.988 0.000 0.012
#> GSM23190 3 0.3177 0.6803 0.000 0.000 0.792 0.000 0.208
#> GSM23191 4 0.2992 0.6022 0.000 0.000 0.064 0.868 0.068
#> GSM23192 3 0.6804 -0.0588 0.000 0.000 0.372 0.304 0.324
#> GSM23193 3 0.4555 0.3495 0.000 0.000 0.636 0.344 0.020
#> GSM23194 3 0.1851 0.7540 0.000 0.000 0.912 0.000 0.088
#> GSM23195 5 0.6294 0.6694 0.192 0.000 0.284 0.000 0.524
#> GSM23159 1 0.0880 0.9493 0.968 0.000 0.000 0.000 0.032
#> GSM23160 3 0.1478 0.7622 0.000 0.000 0.936 0.000 0.064
#> GSM23161 1 0.2989 0.8386 0.868 0.000 0.000 0.072 0.060
#> GSM23162 3 0.2569 0.7533 0.000 0.000 0.892 0.040 0.068
#> GSM23163 1 0.0510 0.9604 0.984 0.000 0.000 0.000 0.016
#> GSM23164 4 0.5220 0.1834 0.440 0.000 0.000 0.516 0.044
#> GSM23165 1 0.0290 0.9599 0.992 0.000 0.000 0.000 0.008
#> GSM23166 4 0.5313 0.2566 0.388 0.000 0.000 0.556 0.056
#> GSM23167 1 0.0000 0.9600 1.000 0.000 0.000 0.000 0.000
#> GSM23168 3 0.1671 0.7577 0.000 0.000 0.924 0.000 0.076
#> GSM23169 3 0.1831 0.7563 0.000 0.000 0.920 0.004 0.076
#> GSM23170 1 0.0510 0.9570 0.984 0.000 0.000 0.000 0.016
#> GSM23171 1 0.0162 0.9600 0.996 0.000 0.000 0.000 0.004
#> GSM23172 1 0.0404 0.9596 0.988 0.000 0.000 0.000 0.012
#> GSM23173 3 0.4083 0.4936 0.028 0.000 0.744 0.000 0.228
#> GSM23174 1 0.1041 0.9415 0.964 0.000 0.000 0.032 0.004
#> GSM23175 1 0.0404 0.9600 0.988 0.000 0.000 0.000 0.012
#> GSM23176 1 0.0290 0.9594 0.992 0.000 0.000 0.000 0.008
#> GSM23177 1 0.1043 0.9389 0.960 0.000 0.000 0.000 0.040
#> GSM23178 1 0.0451 0.9602 0.988 0.000 0.000 0.004 0.008
#> GSM23179 3 0.1608 0.7585 0.000 0.000 0.928 0.000 0.072
#> GSM23180 4 0.0794 0.6658 0.000 0.000 0.000 0.972 0.028
#> GSM23181 4 0.3459 0.6179 0.116 0.000 0.000 0.832 0.052
#> GSM23182 4 0.1608 0.6682 0.000 0.000 0.000 0.928 0.072
#> GSM23183 5 0.6742 0.6618 0.276 0.000 0.316 0.000 0.408
#> GSM23184 3 0.2690 0.7238 0.000 0.000 0.844 0.000 0.156
#> GSM23196 2 0.0290 0.8689 0.000 0.992 0.000 0.000 0.008
#> GSM23197 2 0.1121 0.8608 0.000 0.956 0.000 0.000 0.044
#> GSM23198 2 0.1608 0.8531 0.000 0.928 0.000 0.000 0.072
#> GSM23199 2 0.2424 0.8232 0.000 0.868 0.000 0.000 0.132
#> GSM23200 2 0.3636 0.7165 0.000 0.728 0.000 0.000 0.272
#> GSM23201 4 0.1704 0.6663 0.000 0.068 0.000 0.928 0.004
#> GSM23202 4 0.3401 0.6501 0.000 0.064 0.000 0.840 0.096
#> GSM23203 2 0.0162 0.8687 0.000 0.996 0.000 0.000 0.004
#> GSM23204 2 0.1792 0.8418 0.000 0.916 0.000 0.000 0.084
#> GSM23205 2 0.4101 0.4279 0.000 0.628 0.000 0.372 0.000
#> GSM23206 2 0.0162 0.8684 0.000 0.996 0.000 0.000 0.004
#> GSM23207 2 0.4290 0.6663 0.000 0.680 0.000 0.016 0.304
#> GSM23208 2 0.0000 0.8686 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0880 0.8639 0.000 0.968 0.000 0.000 0.032
#> GSM23210 2 0.1270 0.8608 0.000 0.948 0.000 0.000 0.052
#> GSM23211 2 0.0609 0.8664 0.000 0.980 0.000 0.000 0.020
#> GSM23212 2 0.6526 0.2645 0.000 0.452 0.000 0.204 0.344
#> GSM23213 4 0.6434 0.3289 0.000 0.176 0.000 0.432 0.392
#> GSM23214 4 0.5163 0.5203 0.000 0.068 0.000 0.636 0.296
#> GSM23215 2 0.1197 0.8597 0.000 0.952 0.000 0.000 0.048
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.4774 0.6067 0.000 0.000 0.672 0.192 0.000 0.136
#> GSM23186 1 0.4424 0.3781 0.632 0.000 0.000 0.044 0.000 0.324
#> GSM23187 3 0.2680 0.7178 0.000 0.000 0.860 0.032 0.000 0.108
#> GSM23188 3 0.3435 0.6962 0.000 0.000 0.804 0.060 0.000 0.136
#> GSM23189 3 0.2266 0.7217 0.000 0.000 0.880 0.012 0.000 0.108
#> GSM23190 3 0.4556 0.6373 0.000 0.000 0.688 0.212 0.000 0.100
#> GSM23191 5 0.3264 0.5689 0.000 0.000 0.012 0.076 0.840 0.072
#> GSM23192 6 0.6639 0.4882 0.004 0.000 0.080 0.164 0.220 0.532
#> GSM23193 3 0.4851 0.2237 0.000 0.000 0.524 0.008 0.428 0.040
#> GSM23194 3 0.4504 0.3846 0.000 0.000 0.592 0.040 0.000 0.368
#> GSM23195 6 0.5620 0.6926 0.120 0.000 0.104 0.112 0.000 0.664
#> GSM23159 1 0.1779 0.8541 0.920 0.000 0.000 0.016 0.000 0.064
#> GSM23160 3 0.2706 0.7075 0.000 0.000 0.860 0.036 0.000 0.104
#> GSM23161 1 0.6203 0.5532 0.612 0.000 0.020 0.056 0.120 0.192
#> GSM23162 3 0.2891 0.7221 0.000 0.000 0.872 0.032 0.036 0.060
#> GSM23163 1 0.2722 0.8464 0.872 0.000 0.004 0.032 0.004 0.088
#> GSM23164 5 0.5789 0.3343 0.280 0.000 0.004 0.036 0.584 0.096
#> GSM23165 1 0.0146 0.8804 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM23166 5 0.6119 0.3528 0.248 0.000 0.020 0.036 0.588 0.108
#> GSM23167 1 0.0363 0.8811 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM23168 3 0.3493 0.6774 0.000 0.000 0.796 0.056 0.000 0.148
#> GSM23169 3 0.3506 0.7053 0.000 0.000 0.792 0.052 0.000 0.156
#> GSM23170 1 0.1700 0.8658 0.928 0.000 0.000 0.024 0.000 0.048
#> GSM23171 1 0.0146 0.8806 0.996 0.000 0.000 0.004 0.000 0.000
#> GSM23172 1 0.0405 0.8804 0.988 0.000 0.000 0.004 0.000 0.008
#> GSM23173 3 0.5315 0.5556 0.072 0.000 0.676 0.072 0.000 0.180
#> GSM23174 1 0.1967 0.8432 0.904 0.000 0.000 0.000 0.084 0.012
#> GSM23175 1 0.1124 0.8777 0.956 0.000 0.000 0.008 0.000 0.036
#> GSM23176 1 0.0547 0.8815 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM23177 1 0.4203 0.7457 0.772 0.000 0.020 0.052 0.008 0.148
#> GSM23178 1 0.1080 0.8770 0.960 0.000 0.000 0.004 0.004 0.032
#> GSM23179 3 0.2747 0.7176 0.000 0.000 0.860 0.044 0.000 0.096
#> GSM23180 5 0.2197 0.5960 0.000 0.000 0.000 0.056 0.900 0.044
#> GSM23181 5 0.3900 0.5282 0.008 0.000 0.000 0.048 0.764 0.180
#> GSM23182 5 0.2404 0.5635 0.000 0.000 0.000 0.112 0.872 0.016
#> GSM23183 6 0.4381 0.7164 0.136 0.000 0.080 0.028 0.000 0.756
#> GSM23184 3 0.2867 0.7195 0.000 0.000 0.848 0.112 0.000 0.040
#> GSM23196 2 0.0713 0.8250 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM23197 2 0.1007 0.8143 0.000 0.956 0.000 0.044 0.000 0.000
#> GSM23198 2 0.2793 0.6621 0.000 0.800 0.000 0.200 0.000 0.000
#> GSM23199 2 0.3830 0.2470 0.000 0.620 0.000 0.376 0.000 0.004
#> GSM23200 2 0.3868 -0.2116 0.000 0.504 0.000 0.496 0.000 0.000
#> GSM23201 5 0.2274 0.5647 0.000 0.088 0.000 0.012 0.892 0.008
#> GSM23202 5 0.4336 0.3651 0.004 0.040 0.000 0.212 0.728 0.016
#> GSM23203 2 0.0458 0.8289 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM23204 2 0.1970 0.7755 0.000 0.900 0.000 0.092 0.000 0.008
#> GSM23205 5 0.4636 -0.0742 0.000 0.484 0.000 0.024 0.484 0.008
#> GSM23206 2 0.0146 0.8302 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM23207 4 0.3843 0.1323 0.000 0.452 0.000 0.548 0.000 0.000
#> GSM23208 2 0.0260 0.8301 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM23209 2 0.0547 0.8245 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM23210 2 0.2668 0.7041 0.000 0.828 0.000 0.168 0.000 0.004
#> GSM23211 2 0.0000 0.8299 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23212 4 0.5417 0.6232 0.000 0.244 0.000 0.576 0.180 0.000
#> GSM23213 4 0.5315 0.5472 0.000 0.084 0.000 0.584 0.316 0.016
#> GSM23214 4 0.4847 0.3843 0.000 0.048 0.000 0.532 0.416 0.004
#> GSM23215 2 0.1556 0.7928 0.000 0.920 0.000 0.080 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)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
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 cell.type(p) disease.state(p) k
#> CV:NMF 57 3.90e-13 0.052490 2
#> CV:NMF 56 6.91e-13 0.000873 3
#> CV:NMF 53 1.30e-09 0.000188 4
#> CV:NMF 49 2.19e-08 0.002572 5
#> CV:NMF 45 8.29e-08 0.005398 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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.408 0.851 0.897 0.4706 0.536 0.536
#> 3 3 0.832 0.890 0.951 0.4227 0.787 0.603
#> 4 4 0.813 0.872 0.919 0.0809 0.968 0.902
#> 5 5 0.805 0.781 0.872 0.0413 0.977 0.923
#> 6 6 0.804 0.753 0.825 0.0376 0.984 0.941
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
#> GSM23185 1 0.8909 0.766 0.692 0.308
#> GSM23186 1 0.1414 0.843 0.980 0.020
#> GSM23187 1 0.8909 0.766 0.692 0.308
#> GSM23188 1 0.8909 0.766 0.692 0.308
#> GSM23189 1 0.8909 0.766 0.692 0.308
#> GSM23190 1 0.8909 0.766 0.692 0.308
#> GSM23191 1 0.8763 0.773 0.704 0.296
#> GSM23192 1 0.5946 0.824 0.856 0.144
#> GSM23193 1 0.8555 0.780 0.720 0.280
#> GSM23194 1 0.8861 0.769 0.696 0.304
#> GSM23195 1 0.6148 0.822 0.848 0.152
#> GSM23159 1 0.0000 0.844 1.000 0.000
#> GSM23160 1 0.8909 0.766 0.692 0.308
#> GSM23161 1 0.0000 0.844 1.000 0.000
#> GSM23162 1 0.8861 0.769 0.696 0.304
#> GSM23163 1 0.0376 0.844 0.996 0.004
#> GSM23164 1 0.0000 0.844 1.000 0.000
#> GSM23165 1 0.0000 0.844 1.000 0.000
#> GSM23166 1 0.0000 0.844 1.000 0.000
#> GSM23167 1 0.0000 0.844 1.000 0.000
#> GSM23168 1 0.8909 0.766 0.692 0.308
#> GSM23169 1 0.8909 0.766 0.692 0.308
#> GSM23170 1 0.0000 0.844 1.000 0.000
#> GSM23171 1 0.0000 0.844 1.000 0.000
#> GSM23172 1 0.0000 0.844 1.000 0.000
#> GSM23173 1 0.8909 0.766 0.692 0.308
#> GSM23174 1 0.0000 0.844 1.000 0.000
#> GSM23175 1 0.0000 0.844 1.000 0.000
#> GSM23176 1 0.0000 0.844 1.000 0.000
#> GSM23177 1 0.0000 0.844 1.000 0.000
#> GSM23178 1 0.0000 0.844 1.000 0.000
#> GSM23179 1 0.8909 0.766 0.692 0.308
#> GSM23180 1 0.0376 0.844 0.996 0.004
#> GSM23181 1 0.0376 0.844 0.996 0.004
#> GSM23182 1 0.0376 0.844 0.996 0.004
#> GSM23183 1 0.6048 0.823 0.852 0.148
#> GSM23184 1 0.8909 0.766 0.692 0.308
#> GSM23196 2 0.0000 0.948 0.000 1.000
#> GSM23197 2 0.0000 0.948 0.000 1.000
#> GSM23198 2 0.0000 0.948 0.000 1.000
#> GSM23199 2 0.0000 0.948 0.000 1.000
#> GSM23200 2 0.0000 0.948 0.000 1.000
#> GSM23201 2 0.5629 0.872 0.132 0.868
#> GSM23202 2 0.5629 0.872 0.132 0.868
#> GSM23203 2 0.0000 0.948 0.000 1.000
#> GSM23204 2 0.0000 0.948 0.000 1.000
#> GSM23205 2 0.5629 0.872 0.132 0.868
#> GSM23206 2 0.0000 0.948 0.000 1.000
#> GSM23207 2 0.0000 0.948 0.000 1.000
#> GSM23208 2 0.0000 0.948 0.000 1.000
#> GSM23209 2 0.0000 0.948 0.000 1.000
#> GSM23210 2 0.0000 0.948 0.000 1.000
#> GSM23211 2 0.0000 0.948 0.000 1.000
#> GSM23212 2 0.5629 0.872 0.132 0.868
#> GSM23213 2 0.5629 0.872 0.132 0.868
#> GSM23214 2 0.5629 0.872 0.132 0.868
#> GSM23215 2 0.0000 0.948 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.914 0.000 0.000 1.000
#> GSM23186 1 0.2878 0.863 0.904 0.000 0.096
#> GSM23187 3 0.0000 0.914 0.000 0.000 1.000
#> GSM23188 3 0.0000 0.914 0.000 0.000 1.000
#> GSM23189 3 0.0000 0.914 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.914 0.000 0.000 1.000
#> GSM23191 3 0.2261 0.885 0.068 0.000 0.932
#> GSM23192 1 0.6307 -0.110 0.512 0.000 0.488
#> GSM23193 3 0.4399 0.766 0.188 0.000 0.812
#> GSM23194 3 0.1964 0.894 0.056 0.000 0.944
#> GSM23195 3 0.6154 0.343 0.408 0.000 0.592
#> GSM23159 1 0.0000 0.962 1.000 0.000 0.000
#> GSM23160 3 0.0237 0.914 0.004 0.000 0.996
#> GSM23161 1 0.0000 0.962 1.000 0.000 0.000
#> GSM23162 3 0.1163 0.908 0.028 0.000 0.972
#> GSM23163 1 0.0592 0.953 0.988 0.000 0.012
#> GSM23164 1 0.0000 0.962 1.000 0.000 0.000
#> GSM23165 1 0.0000 0.962 1.000 0.000 0.000
#> GSM23166 1 0.0000 0.962 1.000 0.000 0.000
#> GSM23167 1 0.0000 0.962 1.000 0.000 0.000
#> GSM23168 3 0.0000 0.914 0.000 0.000 1.000
#> GSM23169 3 0.1643 0.902 0.044 0.000 0.956
#> GSM23170 1 0.0000 0.962 1.000 0.000 0.000
#> GSM23171 1 0.0000 0.962 1.000 0.000 0.000
#> GSM23172 1 0.0000 0.962 1.000 0.000 0.000
#> GSM23173 3 0.1031 0.910 0.024 0.000 0.976
#> GSM23174 1 0.0000 0.962 1.000 0.000 0.000
#> GSM23175 1 0.0000 0.962 1.000 0.000 0.000
#> GSM23176 1 0.0000 0.962 1.000 0.000 0.000
#> GSM23177 1 0.0000 0.962 1.000 0.000 0.000
#> GSM23178 1 0.0000 0.962 1.000 0.000 0.000
#> GSM23179 3 0.0424 0.914 0.008 0.000 0.992
#> GSM23180 1 0.0829 0.954 0.984 0.012 0.004
#> GSM23181 1 0.0829 0.954 0.984 0.012 0.004
#> GSM23182 1 0.0829 0.954 0.984 0.012 0.004
#> GSM23183 3 0.6295 0.150 0.472 0.000 0.528
#> GSM23184 3 0.0000 0.914 0.000 0.000 1.000
#> GSM23196 2 0.0424 0.955 0.000 0.992 0.008
#> GSM23197 2 0.0424 0.955 0.000 0.992 0.008
#> GSM23198 2 0.0424 0.955 0.000 0.992 0.008
#> GSM23199 2 0.0424 0.955 0.000 0.992 0.008
#> GSM23200 2 0.0424 0.955 0.000 0.992 0.008
#> GSM23201 2 0.3412 0.890 0.124 0.876 0.000
#> GSM23202 2 0.3412 0.890 0.124 0.876 0.000
#> GSM23203 2 0.0424 0.955 0.000 0.992 0.008
#> GSM23204 2 0.0424 0.955 0.000 0.992 0.008
#> GSM23205 2 0.3412 0.890 0.124 0.876 0.000
#> GSM23206 2 0.0424 0.955 0.000 0.992 0.008
#> GSM23207 2 0.0424 0.955 0.000 0.992 0.008
#> GSM23208 2 0.0424 0.955 0.000 0.992 0.008
#> GSM23209 2 0.0424 0.955 0.000 0.992 0.008
#> GSM23210 2 0.0424 0.955 0.000 0.992 0.008
#> GSM23211 2 0.0424 0.955 0.000 0.992 0.008
#> GSM23212 2 0.3412 0.890 0.124 0.876 0.000
#> GSM23213 2 0.3412 0.890 0.124 0.876 0.000
#> GSM23214 2 0.3412 0.890 0.124 0.876 0.000
#> GSM23215 2 0.0424 0.955 0.000 0.992 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0469 0.894 0.000 0.000 0.988 0.012
#> GSM23186 1 0.4502 0.681 0.748 0.000 0.016 0.236
#> GSM23187 3 0.0469 0.894 0.000 0.000 0.988 0.012
#> GSM23188 3 0.0469 0.894 0.000 0.000 0.988 0.012
#> GSM23189 3 0.0469 0.894 0.000 0.000 0.988 0.012
#> GSM23190 3 0.0469 0.894 0.000 0.000 0.988 0.012
#> GSM23191 3 0.3392 0.815 0.020 0.000 0.856 0.124
#> GSM23192 4 0.5533 0.871 0.132 0.000 0.136 0.732
#> GSM23193 3 0.5142 0.643 0.064 0.000 0.744 0.192
#> GSM23194 3 0.4790 0.377 0.000 0.000 0.620 0.380
#> GSM23195 4 0.5240 0.848 0.072 0.000 0.188 0.740
#> GSM23159 1 0.0921 0.903 0.972 0.000 0.000 0.028
#> GSM23160 3 0.0592 0.885 0.000 0.000 0.984 0.016
#> GSM23161 1 0.0336 0.906 0.992 0.000 0.000 0.008
#> GSM23162 3 0.2408 0.849 0.000 0.000 0.896 0.104
#> GSM23163 1 0.2466 0.855 0.900 0.000 0.004 0.096
#> GSM23164 1 0.0336 0.906 0.992 0.000 0.000 0.008
#> GSM23165 1 0.0921 0.904 0.972 0.000 0.000 0.028
#> GSM23166 1 0.0336 0.906 0.992 0.000 0.000 0.008
#> GSM23167 1 0.0921 0.904 0.972 0.000 0.000 0.028
#> GSM23168 3 0.0188 0.889 0.000 0.000 0.996 0.004
#> GSM23169 3 0.3695 0.806 0.016 0.000 0.828 0.156
#> GSM23170 1 0.0336 0.906 0.992 0.000 0.000 0.008
#> GSM23171 1 0.0336 0.907 0.992 0.000 0.000 0.008
#> GSM23172 1 0.0921 0.904 0.972 0.000 0.000 0.028
#> GSM23173 3 0.2704 0.833 0.000 0.000 0.876 0.124
#> GSM23174 1 0.0000 0.907 1.000 0.000 0.000 0.000
#> GSM23175 1 0.0336 0.907 0.992 0.000 0.000 0.008
#> GSM23176 1 0.0921 0.904 0.972 0.000 0.000 0.028
#> GSM23177 1 0.0336 0.906 0.992 0.000 0.000 0.008
#> GSM23178 1 0.0921 0.904 0.972 0.000 0.000 0.028
#> GSM23179 3 0.2408 0.858 0.000 0.000 0.896 0.104
#> GSM23180 1 0.4522 0.602 0.680 0.000 0.000 0.320
#> GSM23181 1 0.4500 0.607 0.684 0.000 0.000 0.316
#> GSM23182 1 0.4522 0.602 0.680 0.000 0.000 0.320
#> GSM23183 4 0.4662 0.896 0.092 0.000 0.112 0.796
#> GSM23184 3 0.0469 0.894 0.000 0.000 0.988 0.012
#> GSM23196 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23199 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23200 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23201 2 0.2868 0.893 0.000 0.864 0.000 0.136
#> GSM23202 2 0.2868 0.893 0.000 0.864 0.000 0.136
#> GSM23203 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23205 2 0.2868 0.893 0.000 0.864 0.000 0.136
#> GSM23206 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23207 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23208 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23210 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23211 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23212 2 0.2868 0.893 0.000 0.864 0.000 0.136
#> GSM23213 2 0.2868 0.893 0.000 0.864 0.000 0.136
#> GSM23214 2 0.2868 0.893 0.000 0.864 0.000 0.136
#> GSM23215 2 0.0000 0.956 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.0000 0.7344 0.000 0.000 1.000 0.000 0.000
#> GSM23186 1 0.5268 0.5262 0.612 0.000 0.000 0.068 0.320
#> GSM23187 3 0.0000 0.7344 0.000 0.000 1.000 0.000 0.000
#> GSM23188 3 0.0000 0.7344 0.000 0.000 1.000 0.000 0.000
#> GSM23189 3 0.0000 0.7344 0.000 0.000 1.000 0.000 0.000
#> GSM23190 3 0.0000 0.7344 0.000 0.000 1.000 0.000 0.000
#> GSM23191 4 0.4604 0.8323 0.000 0.000 0.428 0.560 0.012
#> GSM23192 5 0.3018 0.8499 0.024 0.000 0.020 0.080 0.876
#> GSM23193 4 0.6511 0.7427 0.032 0.000 0.392 0.484 0.092
#> GSM23194 3 0.5125 0.0255 0.000 0.000 0.544 0.040 0.416
#> GSM23195 5 0.2863 0.8453 0.000 0.000 0.064 0.060 0.876
#> GSM23159 1 0.1907 0.8500 0.928 0.000 0.000 0.044 0.028
#> GSM23160 3 0.2012 0.6777 0.000 0.000 0.920 0.060 0.020
#> GSM23161 1 0.2020 0.8462 0.900 0.000 0.000 0.100 0.000
#> GSM23162 4 0.4650 0.7832 0.000 0.000 0.468 0.520 0.012
#> GSM23163 1 0.4309 0.7616 0.768 0.000 0.000 0.084 0.148
#> GSM23164 1 0.2020 0.8462 0.900 0.000 0.000 0.100 0.000
#> GSM23165 1 0.1568 0.8466 0.944 0.000 0.000 0.036 0.020
#> GSM23166 1 0.1965 0.8474 0.904 0.000 0.000 0.096 0.000
#> GSM23167 1 0.1568 0.8466 0.944 0.000 0.000 0.036 0.020
#> GSM23168 3 0.1300 0.6985 0.000 0.000 0.956 0.028 0.016
#> GSM23169 3 0.6180 -0.2502 0.000 0.000 0.460 0.404 0.136
#> GSM23170 1 0.1410 0.8546 0.940 0.000 0.000 0.060 0.000
#> GSM23171 1 0.0703 0.8562 0.976 0.000 0.000 0.024 0.000
#> GSM23172 1 0.1399 0.8492 0.952 0.000 0.000 0.028 0.020
#> GSM23173 3 0.5811 -0.0088 0.000 0.000 0.552 0.340 0.108
#> GSM23174 1 0.1544 0.8583 0.932 0.000 0.000 0.068 0.000
#> GSM23175 1 0.0510 0.8560 0.984 0.000 0.000 0.016 0.000
#> GSM23176 1 0.1485 0.8482 0.948 0.000 0.000 0.032 0.020
#> GSM23177 1 0.1478 0.8538 0.936 0.000 0.000 0.064 0.000
#> GSM23178 1 0.1485 0.8480 0.948 0.000 0.000 0.032 0.020
#> GSM23179 3 0.3346 0.5799 0.000 0.000 0.844 0.064 0.092
#> GSM23180 1 0.6008 0.5317 0.560 0.000 0.000 0.292 0.148
#> GSM23181 1 0.5991 0.5367 0.564 0.000 0.000 0.288 0.148
#> GSM23182 1 0.6008 0.5317 0.560 0.000 0.000 0.292 0.148
#> GSM23183 5 0.0898 0.8897 0.000 0.000 0.020 0.008 0.972
#> GSM23184 3 0.0000 0.7344 0.000 0.000 1.000 0.000 0.000
#> GSM23196 2 0.0000 0.9531 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.9531 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.9531 0.000 1.000 0.000 0.000 0.000
#> GSM23199 2 0.0000 0.9531 0.000 1.000 0.000 0.000 0.000
#> GSM23200 2 0.0000 0.9531 0.000 1.000 0.000 0.000 0.000
#> GSM23201 2 0.2561 0.8845 0.000 0.856 0.000 0.144 0.000
#> GSM23202 2 0.2561 0.8845 0.000 0.856 0.000 0.144 0.000
#> GSM23203 2 0.0000 0.9531 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.9531 0.000 1.000 0.000 0.000 0.000
#> GSM23205 2 0.2561 0.8845 0.000 0.856 0.000 0.144 0.000
#> GSM23206 2 0.0000 0.9531 0.000 1.000 0.000 0.000 0.000
#> GSM23207 2 0.0000 0.9531 0.000 1.000 0.000 0.000 0.000
#> GSM23208 2 0.0000 0.9531 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.9531 0.000 1.000 0.000 0.000 0.000
#> GSM23210 2 0.0000 0.9531 0.000 1.000 0.000 0.000 0.000
#> GSM23211 2 0.0000 0.9531 0.000 1.000 0.000 0.000 0.000
#> GSM23212 2 0.2561 0.8845 0.000 0.856 0.000 0.144 0.000
#> GSM23213 2 0.2561 0.8845 0.000 0.856 0.000 0.144 0.000
#> GSM23214 2 0.2561 0.8845 0.000 0.856 0.000 0.144 0.000
#> GSM23215 2 0.0000 0.9531 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0000 0.879 0.000 0.000 1.000 NA 0.000 0.000
#> GSM23186 1 0.6123 0.367 0.352 0.000 0.000 NA 0.000 0.308
#> GSM23187 3 0.0000 0.879 0.000 0.000 1.000 NA 0.000 0.000
#> GSM23188 3 0.0000 0.879 0.000 0.000 1.000 NA 0.000 0.000
#> GSM23189 3 0.0000 0.879 0.000 0.000 1.000 NA 0.000 0.000
#> GSM23190 3 0.0000 0.879 0.000 0.000 1.000 NA 0.000 0.000
#> GSM23191 5 0.3515 0.612 0.016 0.000 0.192 NA 0.780 0.000
#> GSM23192 6 0.3251 0.829 0.012 0.000 0.016 NA 0.060 0.856
#> GSM23193 5 0.5995 0.548 0.036 0.000 0.184 NA 0.644 0.048
#> GSM23194 3 0.4881 0.215 0.000 0.000 0.540 NA 0.044 0.408
#> GSM23195 6 0.2647 0.837 0.000 0.000 0.016 NA 0.020 0.876
#> GSM23159 1 0.3688 0.722 0.724 0.000 0.000 NA 0.000 0.020
#> GSM23160 3 0.3018 0.753 0.000 0.000 0.848 NA 0.112 0.016
#> GSM23161 1 0.0547 0.678 0.980 0.000 0.000 NA 0.000 0.000
#> GSM23162 5 0.2883 0.612 0.000 0.000 0.212 NA 0.788 0.000
#> GSM23163 1 0.5255 0.624 0.588 0.000 0.000 NA 0.000 0.140
#> GSM23164 1 0.0458 0.679 0.984 0.000 0.000 NA 0.000 0.000
#> GSM23165 1 0.4099 0.711 0.612 0.000 0.000 NA 0.000 0.016
#> GSM23166 1 0.0363 0.681 0.988 0.000 0.000 NA 0.000 0.000
#> GSM23167 1 0.4088 0.713 0.616 0.000 0.000 NA 0.000 0.016
#> GSM23168 3 0.2171 0.814 0.000 0.000 0.912 NA 0.040 0.016
#> GSM23169 5 0.6848 0.414 0.000 0.000 0.148 NA 0.456 0.096
#> GSM23170 1 0.1501 0.706 0.924 0.000 0.000 NA 0.000 0.000
#> GSM23171 1 0.3409 0.732 0.700 0.000 0.000 NA 0.000 0.000
#> GSM23172 1 0.4076 0.715 0.620 0.000 0.000 NA 0.000 0.016
#> GSM23173 5 0.7073 0.401 0.000 0.000 0.216 NA 0.432 0.096
#> GSM23174 1 0.3023 0.734 0.768 0.000 0.000 NA 0.000 0.000
#> GSM23175 1 0.3446 0.730 0.692 0.000 0.000 NA 0.000 0.000
#> GSM23176 1 0.4064 0.715 0.624 0.000 0.000 NA 0.000 0.016
#> GSM23177 1 0.0937 0.696 0.960 0.000 0.000 NA 0.000 0.000
#> GSM23178 1 0.4076 0.715 0.620 0.000 0.000 NA 0.000 0.016
#> GSM23179 3 0.3411 0.748 0.000 0.000 0.836 NA 0.032 0.088
#> GSM23180 1 0.5426 0.274 0.604 0.000 0.000 NA 0.016 0.116
#> GSM23181 1 0.5342 0.279 0.608 0.000 0.000 NA 0.012 0.116
#> GSM23182 1 0.5426 0.274 0.604 0.000 0.000 NA 0.016 0.116
#> GSM23183 6 0.0964 0.875 0.000 0.000 0.016 NA 0.004 0.968
#> GSM23184 3 0.0000 0.879 0.000 0.000 1.000 NA 0.000 0.000
#> GSM23196 2 0.0000 0.939 0.000 1.000 0.000 NA 0.000 0.000
#> GSM23197 2 0.0000 0.939 0.000 1.000 0.000 NA 0.000 0.000
#> GSM23198 2 0.0000 0.939 0.000 1.000 0.000 NA 0.000 0.000
#> GSM23199 2 0.0000 0.939 0.000 1.000 0.000 NA 0.000 0.000
#> GSM23200 2 0.0000 0.939 0.000 1.000 0.000 NA 0.000 0.000
#> GSM23201 2 0.3053 0.848 0.000 0.812 0.000 NA 0.020 0.000
#> GSM23202 2 0.3053 0.848 0.000 0.812 0.000 NA 0.020 0.000
#> GSM23203 2 0.0000 0.939 0.000 1.000 0.000 NA 0.000 0.000
#> GSM23204 2 0.0000 0.939 0.000 1.000 0.000 NA 0.000 0.000
#> GSM23205 2 0.3053 0.848 0.000 0.812 0.000 NA 0.020 0.000
#> GSM23206 2 0.0000 0.939 0.000 1.000 0.000 NA 0.000 0.000
#> GSM23207 2 0.0000 0.939 0.000 1.000 0.000 NA 0.000 0.000
#> GSM23208 2 0.0000 0.939 0.000 1.000 0.000 NA 0.000 0.000
#> GSM23209 2 0.0000 0.939 0.000 1.000 0.000 NA 0.000 0.000
#> GSM23210 2 0.0000 0.939 0.000 1.000 0.000 NA 0.000 0.000
#> GSM23211 2 0.0000 0.939 0.000 1.000 0.000 NA 0.000 0.000
#> GSM23212 2 0.3053 0.848 0.000 0.812 0.000 NA 0.020 0.000
#> GSM23213 2 0.3053 0.848 0.000 0.812 0.000 NA 0.020 0.000
#> GSM23214 2 0.3053 0.848 0.000 0.812 0.000 NA 0.020 0.000
#> GSM23215 2 0.0000 0.939 0.000 1.000 0.000 NA 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 cell.type(p) disease.state(p) k
#> MAD:hclust 57 3.90e-13 0.052490 2
#> MAD:hclust 54 1.88e-12 0.001274 3
#> MAD:hclust 56 4.20e-12 0.004059 4
#> MAD:hclust 54 5.26e-11 0.003358 5
#> MAD:hclust 50 3.61e-10 0.000282 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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.669 0.893 0.934 0.4742 0.536 0.536
#> 3 3 0.739 0.977 0.942 0.3954 0.786 0.600
#> 4 4 0.816 0.845 0.785 0.1155 0.937 0.805
#> 5 5 0.747 0.756 0.813 0.0653 0.910 0.671
#> 6 6 0.767 0.722 0.807 0.0439 0.960 0.807
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
#> GSM23185 1 0.7883 0.768 0.764 0.236
#> GSM23186 1 0.0376 0.913 0.996 0.004
#> GSM23187 1 0.7883 0.768 0.764 0.236
#> GSM23188 1 0.7883 0.768 0.764 0.236
#> GSM23189 1 0.7883 0.768 0.764 0.236
#> GSM23190 1 0.7883 0.768 0.764 0.236
#> GSM23191 1 0.0938 0.911 0.988 0.012
#> GSM23192 1 0.0000 0.912 1.000 0.000
#> GSM23193 1 0.0000 0.912 1.000 0.000
#> GSM23194 1 0.7674 0.780 0.776 0.224
#> GSM23195 1 0.0000 0.912 1.000 0.000
#> GSM23159 1 0.1414 0.917 0.980 0.020
#> GSM23160 1 0.7674 0.780 0.776 0.224
#> GSM23161 1 0.1414 0.917 0.980 0.020
#> GSM23162 1 0.5842 0.841 0.860 0.140
#> GSM23163 1 0.1414 0.917 0.980 0.020
#> GSM23164 1 0.1414 0.917 0.980 0.020
#> GSM23165 1 0.1414 0.917 0.980 0.020
#> GSM23166 1 0.1414 0.917 0.980 0.020
#> GSM23167 1 0.1414 0.917 0.980 0.020
#> GSM23168 1 0.7674 0.780 0.776 0.224
#> GSM23169 1 0.0000 0.912 1.000 0.000
#> GSM23170 1 0.1414 0.917 0.980 0.020
#> GSM23171 1 0.1414 0.917 0.980 0.020
#> GSM23172 1 0.1414 0.917 0.980 0.020
#> GSM23173 1 0.0672 0.912 0.992 0.008
#> GSM23174 1 0.1414 0.917 0.980 0.020
#> GSM23175 1 0.1414 0.917 0.980 0.020
#> GSM23176 1 0.1414 0.917 0.980 0.020
#> GSM23177 1 0.1414 0.917 0.980 0.020
#> GSM23178 1 0.1414 0.917 0.980 0.020
#> GSM23179 1 0.7674 0.780 0.776 0.224
#> GSM23180 1 0.1414 0.917 0.980 0.020
#> GSM23181 1 0.1414 0.917 0.980 0.020
#> GSM23182 1 0.1414 0.917 0.980 0.020
#> GSM23183 1 0.0000 0.912 1.000 0.000
#> GSM23184 1 0.7674 0.780 0.776 0.224
#> GSM23196 2 0.0000 0.960 0.000 1.000
#> GSM23197 2 0.0000 0.960 0.000 1.000
#> GSM23198 2 0.0000 0.960 0.000 1.000
#> GSM23199 2 0.0000 0.960 0.000 1.000
#> GSM23200 2 0.0000 0.960 0.000 1.000
#> GSM23201 2 0.0000 0.960 0.000 1.000
#> GSM23202 2 0.7883 0.712 0.236 0.764
#> GSM23203 2 0.0000 0.960 0.000 1.000
#> GSM23204 2 0.0000 0.960 0.000 1.000
#> GSM23205 2 0.0000 0.960 0.000 1.000
#> GSM23206 2 0.0000 0.960 0.000 1.000
#> GSM23207 2 0.0000 0.960 0.000 1.000
#> GSM23208 2 0.0000 0.960 0.000 1.000
#> GSM23209 2 0.0000 0.960 0.000 1.000
#> GSM23210 2 0.0000 0.960 0.000 1.000
#> GSM23211 2 0.0000 0.960 0.000 1.000
#> GSM23212 2 0.0000 0.960 0.000 1.000
#> GSM23213 2 0.7528 0.739 0.216 0.784
#> GSM23214 2 0.7528 0.739 0.216 0.784
#> GSM23215 2 0.0000 0.960 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.3193 0.978 0.100 0.004 0.896
#> GSM23186 1 0.1289 0.962 0.968 0.000 0.032
#> GSM23187 3 0.3193 0.978 0.100 0.004 0.896
#> GSM23188 3 0.3193 0.978 0.100 0.004 0.896
#> GSM23189 3 0.3193 0.978 0.100 0.004 0.896
#> GSM23190 3 0.3193 0.978 0.100 0.004 0.896
#> GSM23191 3 0.3412 0.987 0.124 0.000 0.876
#> GSM23192 3 0.3482 0.986 0.128 0.000 0.872
#> GSM23193 3 0.3340 0.988 0.120 0.000 0.880
#> GSM23194 3 0.3573 0.989 0.120 0.004 0.876
#> GSM23195 3 0.3482 0.986 0.128 0.000 0.872
#> GSM23159 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23160 3 0.3573 0.989 0.120 0.004 0.876
#> GSM23161 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23162 3 0.3340 0.988 0.120 0.000 0.880
#> GSM23163 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23164 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23165 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23166 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23167 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23168 3 0.3573 0.989 0.120 0.004 0.876
#> GSM23169 3 0.3412 0.988 0.124 0.000 0.876
#> GSM23170 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23171 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23172 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23173 3 0.3412 0.988 0.124 0.000 0.876
#> GSM23174 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23175 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23176 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23177 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23178 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23179 3 0.3573 0.989 0.120 0.004 0.876
#> GSM23180 1 0.0237 0.993 0.996 0.000 0.004
#> GSM23181 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23182 1 0.1031 0.971 0.976 0.000 0.024
#> GSM23183 3 0.3482 0.986 0.128 0.000 0.872
#> GSM23184 3 0.3573 0.989 0.120 0.004 0.876
#> GSM23196 2 0.0892 0.957 0.000 0.980 0.020
#> GSM23197 2 0.0892 0.957 0.000 0.980 0.020
#> GSM23198 2 0.0892 0.957 0.000 0.980 0.020
#> GSM23199 2 0.2537 0.955 0.000 0.920 0.080
#> GSM23200 2 0.1860 0.957 0.000 0.948 0.052
#> GSM23201 2 0.3038 0.951 0.000 0.896 0.104
#> GSM23202 2 0.3038 0.951 0.000 0.896 0.104
#> GSM23203 2 0.0892 0.957 0.000 0.980 0.020
#> GSM23204 2 0.0892 0.957 0.000 0.980 0.020
#> GSM23205 2 0.3038 0.951 0.000 0.896 0.104
#> GSM23206 2 0.0892 0.957 0.000 0.980 0.020
#> GSM23207 2 0.2959 0.952 0.000 0.900 0.100
#> GSM23208 2 0.0892 0.957 0.000 0.980 0.020
#> GSM23209 2 0.0892 0.957 0.000 0.980 0.020
#> GSM23210 2 0.2448 0.955 0.000 0.924 0.076
#> GSM23211 2 0.0892 0.957 0.000 0.980 0.020
#> GSM23212 2 0.3038 0.951 0.000 0.896 0.104
#> GSM23213 2 0.3038 0.951 0.000 0.896 0.104
#> GSM23214 2 0.3038 0.951 0.000 0.896 0.104
#> GSM23215 2 0.1529 0.957 0.000 0.960 0.040
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0524 0.878 0.008 0.004 0.988 0.000
#> GSM23186 1 0.4939 0.772 0.740 0.220 0.040 0.000
#> GSM23187 3 0.0524 0.878 0.008 0.004 0.988 0.000
#> GSM23188 3 0.0524 0.878 0.008 0.004 0.988 0.000
#> GSM23189 3 0.0524 0.878 0.008 0.004 0.988 0.000
#> GSM23190 3 0.0336 0.878 0.008 0.000 0.992 0.000
#> GSM23191 3 0.5055 0.791 0.008 0.368 0.624 0.000
#> GSM23192 3 0.5161 0.765 0.008 0.400 0.592 0.000
#> GSM23193 3 0.5040 0.793 0.008 0.364 0.628 0.000
#> GSM23194 3 0.1890 0.878 0.008 0.056 0.936 0.000
#> GSM23195 3 0.4990 0.796 0.008 0.352 0.640 0.000
#> GSM23159 1 0.0524 0.921 0.988 0.008 0.004 0.000
#> GSM23160 3 0.1042 0.877 0.008 0.020 0.972 0.000
#> GSM23161 1 0.1576 0.914 0.948 0.048 0.004 0.000
#> GSM23162 3 0.3933 0.855 0.008 0.200 0.792 0.000
#> GSM23163 1 0.1661 0.916 0.944 0.052 0.004 0.000
#> GSM23164 1 0.1576 0.914 0.948 0.048 0.004 0.000
#> GSM23165 1 0.1004 0.920 0.972 0.024 0.004 0.000
#> GSM23166 1 0.1576 0.914 0.948 0.048 0.004 0.000
#> GSM23167 1 0.1004 0.920 0.972 0.024 0.004 0.000
#> GSM23168 3 0.1042 0.877 0.008 0.020 0.972 0.000
#> GSM23169 3 0.4511 0.836 0.008 0.268 0.724 0.000
#> GSM23170 1 0.0376 0.921 0.992 0.004 0.004 0.000
#> GSM23171 1 0.0376 0.921 0.992 0.004 0.004 0.000
#> GSM23172 1 0.1004 0.920 0.972 0.024 0.004 0.000
#> GSM23173 3 0.3893 0.856 0.008 0.196 0.796 0.000
#> GSM23174 1 0.0592 0.920 0.984 0.016 0.000 0.000
#> GSM23175 1 0.0376 0.921 0.992 0.004 0.004 0.000
#> GSM23176 1 0.0895 0.919 0.976 0.020 0.004 0.000
#> GSM23177 1 0.0524 0.921 0.988 0.008 0.004 0.000
#> GSM23178 1 0.1004 0.920 0.972 0.024 0.004 0.000
#> GSM23179 3 0.0672 0.878 0.008 0.008 0.984 0.000
#> GSM23180 1 0.7020 0.547 0.532 0.332 0.000 0.136
#> GSM23181 1 0.3311 0.841 0.828 0.172 0.000 0.000
#> GSM23182 1 0.7327 0.516 0.504 0.320 0.000 0.176
#> GSM23183 3 0.5007 0.794 0.008 0.356 0.636 0.000
#> GSM23184 3 0.0672 0.878 0.008 0.008 0.984 0.000
#> GSM23196 2 0.4948 0.989 0.000 0.560 0.000 0.440
#> GSM23197 2 0.4948 0.989 0.000 0.560 0.000 0.440
#> GSM23198 2 0.4948 0.989 0.000 0.560 0.000 0.440
#> GSM23199 4 0.4049 0.519 0.000 0.212 0.008 0.780
#> GSM23200 4 0.4356 0.187 0.000 0.292 0.000 0.708
#> GSM23201 4 0.0336 0.797 0.000 0.000 0.008 0.992
#> GSM23202 4 0.0469 0.792 0.012 0.000 0.000 0.988
#> GSM23203 2 0.4948 0.989 0.000 0.560 0.000 0.440
#> GSM23204 2 0.4948 0.989 0.000 0.560 0.000 0.440
#> GSM23205 4 0.0336 0.797 0.000 0.000 0.008 0.992
#> GSM23206 2 0.4948 0.989 0.000 0.560 0.000 0.440
#> GSM23207 4 0.3172 0.632 0.000 0.160 0.000 0.840
#> GSM23208 2 0.4948 0.989 0.000 0.560 0.000 0.440
#> GSM23209 2 0.4948 0.989 0.000 0.560 0.000 0.440
#> GSM23210 4 0.4086 0.509 0.000 0.216 0.008 0.776
#> GSM23211 2 0.4948 0.989 0.000 0.560 0.000 0.440
#> GSM23212 4 0.0188 0.798 0.004 0.000 0.000 0.996
#> GSM23213 4 0.0336 0.797 0.008 0.000 0.000 0.992
#> GSM23214 4 0.0336 0.797 0.008 0.000 0.000 0.992
#> GSM23215 2 0.5292 0.890 0.000 0.512 0.008 0.480
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.0162 0.889 0.000 0.000 0.996 0.000 0.004
#> GSM23186 1 0.6756 0.462 0.516 0.000 0.016 0.232 0.236
#> GSM23187 3 0.0000 0.889 0.000 0.000 1.000 0.000 0.000
#> GSM23188 3 0.0000 0.889 0.000 0.000 1.000 0.000 0.000
#> GSM23189 3 0.0000 0.889 0.000 0.000 1.000 0.000 0.000
#> GSM23190 3 0.0162 0.889 0.000 0.000 0.996 0.000 0.004
#> GSM23191 5 0.3521 0.654 0.004 0.000 0.232 0.000 0.764
#> GSM23192 5 0.5305 0.664 0.000 0.000 0.196 0.132 0.672
#> GSM23193 5 0.3395 0.653 0.000 0.000 0.236 0.000 0.764
#> GSM23194 3 0.3975 0.637 0.000 0.000 0.792 0.064 0.144
#> GSM23195 5 0.6135 0.638 0.004 0.000 0.236 0.180 0.580
#> GSM23159 1 0.0798 0.879 0.976 0.000 0.000 0.016 0.008
#> GSM23160 3 0.1399 0.877 0.000 0.000 0.952 0.020 0.028
#> GSM23161 1 0.2409 0.855 0.900 0.000 0.000 0.032 0.068
#> GSM23162 5 0.4658 0.196 0.000 0.000 0.484 0.012 0.504
#> GSM23163 1 0.3828 0.855 0.808 0.000 0.000 0.072 0.120
#> GSM23164 1 0.2344 0.857 0.904 0.000 0.000 0.032 0.064
#> GSM23165 1 0.3119 0.860 0.860 0.000 0.000 0.072 0.068
#> GSM23166 1 0.2409 0.855 0.900 0.000 0.000 0.032 0.068
#> GSM23167 1 0.3119 0.860 0.860 0.000 0.000 0.072 0.068
#> GSM23168 3 0.1485 0.877 0.000 0.000 0.948 0.020 0.032
#> GSM23169 5 0.5990 0.430 0.000 0.000 0.384 0.116 0.500
#> GSM23170 1 0.1211 0.880 0.960 0.000 0.000 0.024 0.016
#> GSM23171 1 0.0992 0.880 0.968 0.000 0.000 0.024 0.008
#> GSM23172 1 0.3119 0.860 0.860 0.000 0.000 0.072 0.068
#> GSM23173 3 0.5715 -0.181 0.000 0.000 0.524 0.088 0.388
#> GSM23174 1 0.0807 0.876 0.976 0.000 0.000 0.012 0.012
#> GSM23175 1 0.0771 0.880 0.976 0.000 0.000 0.020 0.004
#> GSM23176 1 0.3119 0.860 0.860 0.000 0.000 0.072 0.068
#> GSM23177 1 0.1211 0.874 0.960 0.000 0.000 0.024 0.016
#> GSM23178 1 0.2992 0.862 0.868 0.000 0.000 0.064 0.068
#> GSM23179 3 0.1216 0.882 0.000 0.000 0.960 0.020 0.020
#> GSM23180 5 0.4141 0.476 0.248 0.000 0.000 0.024 0.728
#> GSM23181 1 0.4109 0.614 0.700 0.000 0.000 0.012 0.288
#> GSM23182 5 0.5263 0.434 0.240 0.000 0.000 0.100 0.660
#> GSM23183 5 0.6135 0.638 0.004 0.000 0.236 0.180 0.580
#> GSM23184 3 0.0671 0.887 0.000 0.000 0.980 0.004 0.016
#> GSM23196 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0290 0.905 0.000 0.992 0.000 0.000 0.008
#> GSM23198 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM23199 4 0.4774 0.749 0.000 0.424 0.000 0.556 0.020
#> GSM23200 2 0.4291 -0.569 0.000 0.536 0.000 0.464 0.000
#> GSM23201 4 0.5732 0.857 0.000 0.296 0.000 0.588 0.116
#> GSM23202 4 0.5384 0.859 0.004 0.288 0.000 0.632 0.076
#> GSM23203 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0290 0.905 0.000 0.992 0.000 0.000 0.008
#> GSM23205 4 0.5691 0.857 0.000 0.296 0.000 0.592 0.112
#> GSM23206 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM23207 4 0.4299 0.802 0.000 0.388 0.000 0.608 0.004
#> GSM23208 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0290 0.905 0.000 0.992 0.000 0.000 0.008
#> GSM23210 4 0.5334 0.720 0.000 0.436 0.000 0.512 0.052
#> GSM23211 2 0.0000 0.908 0.000 1.000 0.000 0.000 0.000
#> GSM23212 4 0.4249 0.869 0.000 0.296 0.000 0.688 0.016
#> GSM23213 4 0.4249 0.869 0.000 0.296 0.000 0.688 0.016
#> GSM23214 4 0.5218 0.865 0.000 0.296 0.000 0.632 0.072
#> GSM23215 2 0.2592 0.781 0.000 0.892 0.000 0.056 0.052
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0000 0.92068 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23186 6 0.6209 0.11931 0.252 0.040 0.004 0.000 0.152 0.552
#> GSM23187 3 0.0000 0.92068 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23188 3 0.0000 0.92068 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23189 3 0.0000 0.92068 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23190 3 0.0000 0.92068 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23191 5 0.1398 0.47367 0.000 0.000 0.052 0.000 0.940 0.008
#> GSM23192 5 0.4435 -0.08217 0.000 0.004 0.028 0.000 0.604 0.364
#> GSM23193 5 0.1942 0.46653 0.000 0.008 0.064 0.000 0.916 0.012
#> GSM23194 3 0.5093 0.40167 0.000 0.004 0.644 0.000 0.204 0.148
#> GSM23195 6 0.4831 0.31580 0.000 0.000 0.060 0.000 0.392 0.548
#> GSM23159 1 0.1364 0.84145 0.952 0.012 0.000 0.000 0.020 0.016
#> GSM23160 3 0.2222 0.89008 0.000 0.040 0.908 0.000 0.012 0.040
#> GSM23161 1 0.2969 0.80254 0.860 0.020 0.000 0.000 0.088 0.032
#> GSM23162 5 0.4521 0.20536 0.000 0.016 0.292 0.000 0.660 0.032
#> GSM23163 1 0.4249 0.81217 0.776 0.048 0.000 0.000 0.060 0.116
#> GSM23164 1 0.2990 0.80365 0.860 0.020 0.000 0.000 0.084 0.036
#> GSM23165 1 0.3544 0.79992 0.800 0.080 0.000 0.000 0.000 0.120
#> GSM23166 1 0.2990 0.80365 0.860 0.020 0.000 0.000 0.084 0.036
#> GSM23167 1 0.3544 0.79992 0.800 0.080 0.000 0.000 0.000 0.120
#> GSM23168 3 0.2222 0.89008 0.000 0.040 0.908 0.000 0.012 0.040
#> GSM23169 5 0.6357 -0.28744 0.000 0.032 0.164 0.000 0.412 0.392
#> GSM23170 1 0.1458 0.84515 0.948 0.016 0.000 0.000 0.016 0.020
#> GSM23171 1 0.1572 0.84017 0.936 0.036 0.000 0.000 0.000 0.028
#> GSM23172 1 0.3544 0.79992 0.800 0.080 0.000 0.000 0.000 0.120
#> GSM23173 6 0.6864 -0.00692 0.000 0.044 0.328 0.000 0.300 0.328
#> GSM23174 1 0.1275 0.84022 0.956 0.012 0.000 0.000 0.016 0.016
#> GSM23175 1 0.1340 0.84221 0.948 0.040 0.000 0.000 0.004 0.008
#> GSM23176 1 0.3685 0.79983 0.796 0.080 0.000 0.000 0.004 0.120
#> GSM23177 1 0.1452 0.83890 0.948 0.012 0.000 0.000 0.020 0.020
#> GSM23178 1 0.3534 0.80170 0.800 0.076 0.000 0.000 0.000 0.124
#> GSM23179 3 0.2257 0.88782 0.000 0.040 0.904 0.000 0.008 0.048
#> GSM23180 5 0.4115 0.41161 0.132 0.020 0.000 0.004 0.780 0.064
#> GSM23181 1 0.5005 0.24698 0.540 0.020 0.000 0.000 0.404 0.036
#> GSM23182 5 0.5198 0.38291 0.124 0.020 0.000 0.036 0.716 0.104
#> GSM23183 6 0.4831 0.31580 0.000 0.000 0.060 0.000 0.392 0.548
#> GSM23184 3 0.0405 0.91868 0.000 0.004 0.988 0.000 0.000 0.008
#> GSM23196 2 0.2491 0.97477 0.000 0.836 0.000 0.164 0.000 0.000
#> GSM23197 2 0.2558 0.97011 0.000 0.840 0.000 0.156 0.000 0.004
#> GSM23198 2 0.2491 0.97477 0.000 0.836 0.000 0.164 0.000 0.000
#> GSM23199 4 0.3095 0.83035 0.000 0.052 0.000 0.856 0.020 0.072
#> GSM23200 4 0.3790 0.68329 0.000 0.184 0.000 0.772 0.020 0.024
#> GSM23201 4 0.3740 0.81124 0.000 0.008 0.000 0.728 0.012 0.252
#> GSM23202 4 0.2613 0.83611 0.000 0.000 0.000 0.848 0.012 0.140
#> GSM23203 2 0.2491 0.97477 0.000 0.836 0.000 0.164 0.000 0.000
#> GSM23204 2 0.2558 0.97011 0.000 0.840 0.000 0.156 0.000 0.004
#> GSM23205 4 0.3716 0.81312 0.000 0.008 0.000 0.732 0.012 0.248
#> GSM23206 2 0.2491 0.97477 0.000 0.836 0.000 0.164 0.000 0.000
#> GSM23207 4 0.2103 0.83823 0.000 0.040 0.000 0.916 0.020 0.024
#> GSM23208 2 0.2491 0.97477 0.000 0.836 0.000 0.164 0.000 0.000
#> GSM23209 2 0.2558 0.97011 0.000 0.840 0.000 0.156 0.000 0.004
#> GSM23210 4 0.3624 0.81880 0.000 0.060 0.000 0.812 0.016 0.112
#> GSM23211 2 0.2491 0.97477 0.000 0.836 0.000 0.164 0.000 0.000
#> GSM23212 4 0.0000 0.85471 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23213 4 0.0458 0.85524 0.000 0.000 0.000 0.984 0.000 0.016
#> GSM23214 4 0.2613 0.83633 0.000 0.000 0.000 0.848 0.012 0.140
#> GSM23215 2 0.4653 0.79216 0.000 0.684 0.000 0.196 0.000 0.120
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 cell.type(p) disease.state(p) k
#> MAD:kmeans 57 3.90e-13 0.052490 2
#> MAD:kmeans 57 4.19e-13 0.000423 3
#> MAD:kmeans 56 4.20e-12 0.002783 4
#> MAD:kmeans 50 3.61e-10 0.000209 5
#> MAD:kmeans 44 1.51e-09 0.000558 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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.997 0.998 0.4645 0.536 0.536
#> 3 3 1.000 0.997 0.999 0.4601 0.786 0.600
#> 4 4 0.843 0.893 0.930 0.0873 0.932 0.792
#> 5 5 0.790 0.773 0.865 0.0649 0.938 0.769
#> 6 6 0.744 0.714 0.820 0.0357 0.992 0.965
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
#> GSM23185 1 0.0672 0.994 0.992 0.008
#> GSM23186 1 0.0000 0.997 1.000 0.000
#> GSM23187 1 0.0672 0.994 0.992 0.008
#> GSM23188 1 0.0672 0.994 0.992 0.008
#> GSM23189 1 0.0672 0.994 0.992 0.008
#> GSM23190 1 0.0672 0.994 0.992 0.008
#> GSM23191 1 0.0000 0.997 1.000 0.000
#> GSM23192 1 0.0000 0.997 1.000 0.000
#> GSM23193 1 0.0000 0.997 1.000 0.000
#> GSM23194 1 0.0672 0.994 0.992 0.008
#> GSM23195 1 0.0000 0.997 1.000 0.000
#> GSM23159 1 0.0000 0.997 1.000 0.000
#> GSM23160 1 0.0672 0.994 0.992 0.008
#> GSM23161 1 0.0000 0.997 1.000 0.000
#> GSM23162 1 0.0672 0.994 0.992 0.008
#> GSM23163 1 0.0000 0.997 1.000 0.000
#> GSM23164 1 0.0000 0.997 1.000 0.000
#> GSM23165 1 0.0000 0.997 1.000 0.000
#> GSM23166 1 0.0000 0.997 1.000 0.000
#> GSM23167 1 0.0000 0.997 1.000 0.000
#> GSM23168 1 0.0672 0.994 0.992 0.008
#> GSM23169 1 0.0000 0.997 1.000 0.000
#> GSM23170 1 0.0000 0.997 1.000 0.000
#> GSM23171 1 0.0000 0.997 1.000 0.000
#> GSM23172 1 0.0000 0.997 1.000 0.000
#> GSM23173 1 0.0376 0.996 0.996 0.004
#> GSM23174 1 0.0000 0.997 1.000 0.000
#> GSM23175 1 0.0000 0.997 1.000 0.000
#> GSM23176 1 0.0000 0.997 1.000 0.000
#> GSM23177 1 0.0000 0.997 1.000 0.000
#> GSM23178 1 0.0000 0.997 1.000 0.000
#> GSM23179 1 0.0672 0.994 0.992 0.008
#> GSM23180 1 0.0000 0.997 1.000 0.000
#> GSM23181 1 0.0000 0.997 1.000 0.000
#> GSM23182 1 0.0000 0.997 1.000 0.000
#> GSM23183 1 0.0000 0.997 1.000 0.000
#> GSM23184 1 0.0672 0.994 0.992 0.008
#> GSM23196 2 0.0000 0.999 0.000 1.000
#> GSM23197 2 0.0000 0.999 0.000 1.000
#> GSM23198 2 0.0000 0.999 0.000 1.000
#> GSM23199 2 0.0000 0.999 0.000 1.000
#> GSM23200 2 0.0000 0.999 0.000 1.000
#> GSM23201 2 0.0000 0.999 0.000 1.000
#> GSM23202 2 0.0672 0.993 0.008 0.992
#> GSM23203 2 0.0000 0.999 0.000 1.000
#> GSM23204 2 0.0000 0.999 0.000 1.000
#> GSM23205 2 0.0000 0.999 0.000 1.000
#> GSM23206 2 0.0000 0.999 0.000 1.000
#> GSM23207 2 0.0000 0.999 0.000 1.000
#> GSM23208 2 0.0000 0.999 0.000 1.000
#> GSM23209 2 0.0000 0.999 0.000 1.000
#> GSM23210 2 0.0000 0.999 0.000 1.000
#> GSM23211 2 0.0000 0.999 0.000 1.000
#> GSM23212 2 0.0000 0.999 0.000 1.000
#> GSM23213 2 0.0672 0.993 0.008 0.992
#> GSM23214 2 0.0672 0.993 0.008 0.992
#> GSM23215 2 0.0000 0.999 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.998 0.000 0 1.000
#> GSM23186 1 0.1643 0.954 0.956 0 0.044
#> GSM23187 3 0.0000 0.998 0.000 0 1.000
#> GSM23188 3 0.0000 0.998 0.000 0 1.000
#> GSM23189 3 0.0000 0.998 0.000 0 1.000
#> GSM23190 3 0.0000 0.998 0.000 0 1.000
#> GSM23191 3 0.0000 0.998 0.000 0 1.000
#> GSM23192 3 0.0892 0.981 0.020 0 0.980
#> GSM23193 3 0.0237 0.995 0.004 0 0.996
#> GSM23194 3 0.0000 0.998 0.000 0 1.000
#> GSM23195 3 0.0237 0.995 0.004 0 0.996
#> GSM23159 1 0.0000 0.998 1.000 0 0.000
#> GSM23160 3 0.0000 0.998 0.000 0 1.000
#> GSM23161 1 0.0000 0.998 1.000 0 0.000
#> GSM23162 3 0.0000 0.998 0.000 0 1.000
#> GSM23163 1 0.0000 0.998 1.000 0 0.000
#> GSM23164 1 0.0000 0.998 1.000 0 0.000
#> GSM23165 1 0.0000 0.998 1.000 0 0.000
#> GSM23166 1 0.0000 0.998 1.000 0 0.000
#> GSM23167 1 0.0000 0.998 1.000 0 0.000
#> GSM23168 3 0.0000 0.998 0.000 0 1.000
#> GSM23169 3 0.0000 0.998 0.000 0 1.000
#> GSM23170 1 0.0000 0.998 1.000 0 0.000
#> GSM23171 1 0.0000 0.998 1.000 0 0.000
#> GSM23172 1 0.0000 0.998 1.000 0 0.000
#> GSM23173 3 0.0000 0.998 0.000 0 1.000
#> GSM23174 1 0.0000 0.998 1.000 0 0.000
#> GSM23175 1 0.0000 0.998 1.000 0 0.000
#> GSM23176 1 0.0000 0.998 1.000 0 0.000
#> GSM23177 1 0.0000 0.998 1.000 0 0.000
#> GSM23178 1 0.0000 0.998 1.000 0 0.000
#> GSM23179 3 0.0000 0.998 0.000 0 1.000
#> GSM23180 1 0.0000 0.998 1.000 0 0.000
#> GSM23181 1 0.0000 0.998 1.000 0 0.000
#> GSM23182 1 0.0000 0.998 1.000 0 0.000
#> GSM23183 3 0.0592 0.989 0.012 0 0.988
#> GSM23184 3 0.0000 0.998 0.000 0 1.000
#> GSM23196 2 0.0000 1.000 0.000 1 0.000
#> GSM23197 2 0.0000 1.000 0.000 1 0.000
#> GSM23198 2 0.0000 1.000 0.000 1 0.000
#> GSM23199 2 0.0000 1.000 0.000 1 0.000
#> GSM23200 2 0.0000 1.000 0.000 1 0.000
#> GSM23201 2 0.0000 1.000 0.000 1 0.000
#> GSM23202 2 0.0000 1.000 0.000 1 0.000
#> GSM23203 2 0.0000 1.000 0.000 1 0.000
#> GSM23204 2 0.0000 1.000 0.000 1 0.000
#> GSM23205 2 0.0000 1.000 0.000 1 0.000
#> GSM23206 2 0.0000 1.000 0.000 1 0.000
#> GSM23207 2 0.0000 1.000 0.000 1 0.000
#> GSM23208 2 0.0000 1.000 0.000 1 0.000
#> GSM23209 2 0.0000 1.000 0.000 1 0.000
#> GSM23210 2 0.0000 1.000 0.000 1 0.000
#> GSM23211 2 0.0000 1.000 0.000 1 0.000
#> GSM23212 2 0.0000 1.000 0.000 1 0.000
#> GSM23213 2 0.0000 1.000 0.000 1 0.000
#> GSM23214 2 0.0000 1.000 0.000 1 0.000
#> GSM23215 2 0.0000 1.000 0.000 1 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0336 0.940 0.000 0.000 0.992 0.008
#> GSM23186 1 0.3533 0.851 0.864 0.000 0.056 0.080
#> GSM23187 3 0.0188 0.940 0.000 0.000 0.996 0.004
#> GSM23188 3 0.0188 0.940 0.000 0.000 0.996 0.004
#> GSM23189 3 0.0188 0.940 0.000 0.000 0.996 0.004
#> GSM23190 3 0.0188 0.940 0.000 0.000 0.996 0.004
#> GSM23191 3 0.4307 0.808 0.024 0.000 0.784 0.192
#> GSM23192 3 0.5951 0.712 0.152 0.000 0.696 0.152
#> GSM23193 3 0.2796 0.891 0.016 0.000 0.892 0.092
#> GSM23194 3 0.0707 0.938 0.000 0.000 0.980 0.020
#> GSM23195 3 0.3687 0.868 0.064 0.000 0.856 0.080
#> GSM23159 1 0.0469 0.956 0.988 0.000 0.000 0.012
#> GSM23160 3 0.0000 0.940 0.000 0.000 1.000 0.000
#> GSM23161 1 0.1211 0.943 0.960 0.000 0.000 0.040
#> GSM23162 3 0.0707 0.936 0.000 0.000 0.980 0.020
#> GSM23163 1 0.0817 0.952 0.976 0.000 0.000 0.024
#> GSM23164 1 0.0469 0.956 0.988 0.000 0.000 0.012
#> GSM23165 1 0.0336 0.956 0.992 0.000 0.000 0.008
#> GSM23166 1 0.0817 0.951 0.976 0.000 0.000 0.024
#> GSM23167 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM23168 3 0.0000 0.940 0.000 0.000 1.000 0.000
#> GSM23169 3 0.1211 0.931 0.000 0.000 0.960 0.040
#> GSM23170 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM23171 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM23172 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM23173 3 0.0817 0.935 0.000 0.000 0.976 0.024
#> GSM23174 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM23175 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM23176 1 0.0336 0.956 0.992 0.000 0.000 0.008
#> GSM23177 1 0.0000 0.958 1.000 0.000 0.000 0.000
#> GSM23178 1 0.0188 0.958 0.996 0.000 0.000 0.004
#> GSM23179 3 0.0000 0.940 0.000 0.000 1.000 0.000
#> GSM23180 1 0.4776 0.483 0.624 0.000 0.000 0.376
#> GSM23181 1 0.2345 0.895 0.900 0.000 0.000 0.100
#> GSM23182 4 0.4817 0.139 0.388 0.000 0.000 0.612
#> GSM23183 3 0.5204 0.755 0.160 0.000 0.752 0.088
#> GSM23184 3 0.0188 0.940 0.000 0.000 0.996 0.004
#> GSM23196 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23199 2 0.2408 0.870 0.000 0.896 0.000 0.104
#> GSM23200 2 0.1474 0.922 0.000 0.948 0.000 0.052
#> GSM23201 4 0.3569 0.856 0.000 0.196 0.000 0.804
#> GSM23202 4 0.3444 0.863 0.000 0.184 0.000 0.816
#> GSM23203 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23205 4 0.4250 0.758 0.000 0.276 0.000 0.724
#> GSM23206 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23207 2 0.4134 0.605 0.000 0.740 0.000 0.260
#> GSM23208 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23210 2 0.1637 0.915 0.000 0.940 0.000 0.060
#> GSM23211 2 0.0000 0.956 0.000 1.000 0.000 0.000
#> GSM23212 4 0.3444 0.863 0.000 0.184 0.000 0.816
#> GSM23213 4 0.3400 0.861 0.000 0.180 0.000 0.820
#> GSM23214 4 0.3444 0.863 0.000 0.184 0.000 0.816
#> GSM23215 2 0.0188 0.954 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.1124 0.8907 0.000 0.000 0.960 0.004 0.036
#> GSM23186 1 0.5355 0.3605 0.588 0.000 0.040 0.012 0.360
#> GSM23187 3 0.0865 0.8910 0.000 0.000 0.972 0.004 0.024
#> GSM23188 3 0.1205 0.8840 0.000 0.000 0.956 0.004 0.040
#> GSM23189 3 0.0771 0.8899 0.000 0.000 0.976 0.004 0.020
#> GSM23190 3 0.0955 0.8903 0.000 0.000 0.968 0.004 0.028
#> GSM23191 5 0.5637 0.3802 0.024 0.000 0.312 0.052 0.612
#> GSM23192 5 0.4333 0.4615 0.048 0.000 0.212 0.000 0.740
#> GSM23193 5 0.5173 0.0928 0.012 0.000 0.460 0.020 0.508
#> GSM23194 3 0.3003 0.7541 0.000 0.000 0.812 0.000 0.188
#> GSM23195 5 0.5718 0.2244 0.068 0.000 0.380 0.008 0.544
#> GSM23159 1 0.1809 0.8933 0.928 0.000 0.000 0.012 0.060
#> GSM23160 3 0.0290 0.8884 0.000 0.000 0.992 0.000 0.008
#> GSM23161 1 0.2338 0.8705 0.884 0.000 0.000 0.004 0.112
#> GSM23162 3 0.3274 0.6791 0.000 0.000 0.780 0.000 0.220
#> GSM23163 1 0.2464 0.8773 0.888 0.000 0.000 0.016 0.096
#> GSM23164 1 0.2513 0.8632 0.876 0.000 0.000 0.008 0.116
#> GSM23165 1 0.1568 0.8838 0.944 0.000 0.000 0.020 0.036
#> GSM23166 1 0.2439 0.8650 0.876 0.000 0.000 0.004 0.120
#> GSM23167 1 0.1386 0.8877 0.952 0.000 0.000 0.016 0.032
#> GSM23168 3 0.1697 0.8666 0.000 0.000 0.932 0.008 0.060
#> GSM23169 3 0.3635 0.6380 0.000 0.000 0.748 0.004 0.248
#> GSM23170 1 0.0794 0.8963 0.972 0.000 0.000 0.000 0.028
#> GSM23171 1 0.1364 0.8958 0.952 0.000 0.000 0.012 0.036
#> GSM23172 1 0.1399 0.8856 0.952 0.000 0.000 0.020 0.028
#> GSM23173 3 0.3080 0.7904 0.008 0.000 0.844 0.008 0.140
#> GSM23174 1 0.1741 0.8931 0.936 0.000 0.000 0.024 0.040
#> GSM23175 1 0.1648 0.8923 0.940 0.000 0.000 0.020 0.040
#> GSM23176 1 0.1195 0.8889 0.960 0.000 0.000 0.012 0.028
#> GSM23177 1 0.1341 0.8921 0.944 0.000 0.000 0.000 0.056
#> GSM23178 1 0.1981 0.8926 0.920 0.000 0.000 0.016 0.064
#> GSM23179 3 0.0963 0.8837 0.000 0.000 0.964 0.000 0.036
#> GSM23180 5 0.6175 0.1625 0.332 0.000 0.000 0.152 0.516
#> GSM23181 1 0.4822 0.5833 0.664 0.000 0.000 0.048 0.288
#> GSM23182 5 0.6818 0.1146 0.328 0.000 0.000 0.316 0.356
#> GSM23183 5 0.5735 0.2965 0.076 0.000 0.348 0.008 0.568
#> GSM23184 3 0.1041 0.8837 0.000 0.000 0.964 0.004 0.032
#> GSM23196 2 0.0000 0.9201 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.9201 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.9201 0.000 1.000 0.000 0.000 0.000
#> GSM23199 2 0.3395 0.6998 0.000 0.764 0.000 0.236 0.000
#> GSM23200 2 0.2471 0.8243 0.000 0.864 0.000 0.136 0.000
#> GSM23201 4 0.2612 0.8941 0.000 0.124 0.000 0.868 0.008
#> GSM23202 4 0.1571 0.9245 0.004 0.060 0.000 0.936 0.000
#> GSM23203 2 0.0000 0.9201 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.9201 0.000 1.000 0.000 0.000 0.000
#> GSM23205 4 0.3508 0.7400 0.000 0.252 0.000 0.748 0.000
#> GSM23206 2 0.0000 0.9201 0.000 1.000 0.000 0.000 0.000
#> GSM23207 2 0.4101 0.4113 0.000 0.628 0.000 0.372 0.000
#> GSM23208 2 0.0000 0.9201 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.9201 0.000 1.000 0.000 0.000 0.000
#> GSM23210 2 0.2732 0.7936 0.000 0.840 0.000 0.160 0.000
#> GSM23211 2 0.0000 0.9201 0.000 1.000 0.000 0.000 0.000
#> GSM23212 4 0.1608 0.9264 0.000 0.072 0.000 0.928 0.000
#> GSM23213 4 0.1410 0.9249 0.000 0.060 0.000 0.940 0.000
#> GSM23214 4 0.1478 0.9271 0.000 0.064 0.000 0.936 0.000
#> GSM23215 2 0.0703 0.9069 0.000 0.976 0.000 0.024 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.1542 0.800340 0.000 0.000 0.936 0.004 0.008 0.052
#> GSM23186 1 0.6116 0.161604 0.476 0.000 0.040 0.008 0.084 0.392
#> GSM23187 3 0.0713 0.802738 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM23188 3 0.1387 0.793677 0.000 0.000 0.932 0.000 0.000 0.068
#> GSM23189 3 0.0858 0.803754 0.000 0.000 0.968 0.004 0.000 0.028
#> GSM23190 3 0.1219 0.802993 0.000 0.000 0.948 0.000 0.004 0.048
#> GSM23191 5 0.5701 0.159475 0.016 0.000 0.164 0.012 0.624 0.184
#> GSM23192 6 0.6231 0.419520 0.036 0.000 0.144 0.004 0.288 0.528
#> GSM23193 5 0.6101 -0.000514 0.016 0.000 0.304 0.008 0.520 0.152
#> GSM23194 3 0.3695 0.669449 0.000 0.000 0.776 0.000 0.060 0.164
#> GSM23195 6 0.5246 0.661871 0.044 0.000 0.240 0.004 0.056 0.656
#> GSM23159 1 0.3608 0.785665 0.800 0.000 0.000 0.004 0.128 0.068
#> GSM23160 3 0.2291 0.801140 0.000 0.000 0.904 0.012 0.040 0.044
#> GSM23161 1 0.4015 0.752440 0.744 0.000 0.000 0.012 0.208 0.036
#> GSM23162 3 0.5170 0.409049 0.000 0.000 0.596 0.004 0.296 0.104
#> GSM23163 1 0.3427 0.792353 0.824 0.000 0.000 0.008 0.088 0.080
#> GSM23164 1 0.3702 0.770003 0.760 0.000 0.000 0.008 0.208 0.024
#> GSM23165 1 0.2145 0.778019 0.900 0.000 0.000 0.000 0.028 0.072
#> GSM23166 1 0.3936 0.750910 0.736 0.000 0.000 0.012 0.228 0.024
#> GSM23167 1 0.2325 0.796886 0.892 0.000 0.000 0.000 0.060 0.048
#> GSM23168 3 0.3210 0.780857 0.000 0.000 0.844 0.012 0.072 0.072
#> GSM23169 3 0.5707 0.327297 0.004 0.000 0.544 0.008 0.132 0.312
#> GSM23170 1 0.2255 0.811972 0.892 0.000 0.000 0.004 0.088 0.016
#> GSM23171 1 0.2146 0.812309 0.908 0.000 0.000 0.008 0.060 0.024
#> GSM23172 1 0.1649 0.795269 0.932 0.000 0.000 0.000 0.032 0.036
#> GSM23173 3 0.5000 0.535318 0.004 0.000 0.652 0.004 0.100 0.240
#> GSM23174 1 0.2961 0.799494 0.840 0.000 0.000 0.008 0.132 0.020
#> GSM23175 1 0.3150 0.802494 0.840 0.000 0.000 0.012 0.112 0.036
#> GSM23176 1 0.2307 0.783962 0.896 0.000 0.000 0.004 0.032 0.068
#> GSM23177 1 0.3125 0.796833 0.828 0.000 0.000 0.004 0.136 0.032
#> GSM23178 1 0.2837 0.789468 0.856 0.000 0.000 0.000 0.088 0.056
#> GSM23179 3 0.2821 0.784237 0.000 0.000 0.860 0.004 0.040 0.096
#> GSM23180 5 0.5241 0.337984 0.224 0.000 0.000 0.052 0.660 0.064
#> GSM23181 1 0.5344 0.335709 0.520 0.000 0.000 0.024 0.400 0.056
#> GSM23182 5 0.6133 0.323620 0.204 0.000 0.000 0.188 0.564 0.044
#> GSM23183 6 0.5327 0.678300 0.060 0.000 0.220 0.000 0.064 0.656
#> GSM23184 3 0.1845 0.801313 0.000 0.000 0.920 0.000 0.028 0.052
#> GSM23196 2 0.0291 0.904928 0.000 0.992 0.000 0.004 0.004 0.000
#> GSM23197 2 0.0146 0.904988 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM23198 2 0.0405 0.905604 0.000 0.988 0.000 0.004 0.000 0.008
#> GSM23199 2 0.4561 0.578754 0.000 0.676 0.000 0.268 0.024 0.032
#> GSM23200 2 0.3159 0.786211 0.000 0.820 0.000 0.152 0.008 0.020
#> GSM23201 4 0.4007 0.821678 0.000 0.108 0.000 0.792 0.068 0.032
#> GSM23202 4 0.1693 0.887355 0.000 0.032 0.000 0.936 0.020 0.012
#> GSM23203 2 0.0291 0.905368 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM23204 2 0.0260 0.904450 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM23205 4 0.4570 0.709463 0.000 0.216 0.000 0.708 0.052 0.024
#> GSM23206 2 0.0436 0.905366 0.000 0.988 0.000 0.004 0.004 0.004
#> GSM23207 2 0.4510 0.379372 0.000 0.588 0.000 0.380 0.008 0.024
#> GSM23208 2 0.0146 0.905450 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM23209 2 0.0260 0.904450 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM23210 2 0.3154 0.805002 0.000 0.836 0.000 0.124 0.020 0.020
#> GSM23211 2 0.0260 0.904464 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM23212 4 0.1464 0.890031 0.000 0.036 0.000 0.944 0.004 0.016
#> GSM23213 4 0.1245 0.890901 0.000 0.032 0.000 0.952 0.000 0.016
#> GSM23214 4 0.1080 0.891855 0.000 0.032 0.000 0.960 0.004 0.004
#> GSM23215 2 0.1605 0.881287 0.000 0.940 0.000 0.032 0.016 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 cell.type(p) disease.state(p) k
#> MAD:skmeans 57 3.90e-13 0.052490 2
#> MAD:skmeans 57 4.19e-13 0.000423 3
#> MAD:skmeans 55 6.87e-12 0.000192 4
#> MAD:skmeans 48 2.13e-10 0.000771 5
#> MAD:skmeans 47 1.52e-09 0.000244 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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.622 0.755 0.904 0.4954 0.491 0.491
#> 3 3 0.927 0.918 0.967 0.3631 0.742 0.520
#> 4 4 0.890 0.910 0.944 0.0892 0.934 0.798
#> 5 5 0.872 0.834 0.914 0.0550 0.961 0.853
#> 6 6 0.843 0.776 0.871 0.0356 0.969 0.869
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
#> GSM23185 2 0.8386 0.65274 0.268 0.732
#> GSM23186 1 0.0000 0.91945 1.000 0.000
#> GSM23187 2 0.9170 0.57469 0.332 0.668
#> GSM23188 2 0.7219 0.71615 0.200 0.800
#> GSM23189 2 0.9044 0.59136 0.320 0.680
#> GSM23190 2 0.9129 0.58076 0.328 0.672
#> GSM23191 1 0.0000 0.91945 1.000 0.000
#> GSM23192 1 0.0000 0.91945 1.000 0.000
#> GSM23193 1 0.0000 0.91945 1.000 0.000
#> GSM23194 2 0.9522 0.50670 0.372 0.628
#> GSM23195 2 0.9522 0.50670 0.372 0.628
#> GSM23159 1 0.0000 0.91945 1.000 0.000
#> GSM23160 2 0.9954 0.29285 0.460 0.540
#> GSM23161 1 0.0000 0.91945 1.000 0.000
#> GSM23162 1 0.0672 0.91148 0.992 0.008
#> GSM23163 1 0.0000 0.91945 1.000 0.000
#> GSM23164 1 0.0000 0.91945 1.000 0.000
#> GSM23165 1 0.0000 0.91945 1.000 0.000
#> GSM23166 1 0.0000 0.91945 1.000 0.000
#> GSM23167 1 0.0000 0.91945 1.000 0.000
#> GSM23168 1 1.0000 -0.21761 0.500 0.500
#> GSM23169 1 0.0000 0.91945 1.000 0.000
#> GSM23170 1 0.0000 0.91945 1.000 0.000
#> GSM23171 1 0.0000 0.91945 1.000 0.000
#> GSM23172 1 0.0000 0.91945 1.000 0.000
#> GSM23173 1 0.9944 -0.06656 0.544 0.456
#> GSM23174 1 0.0000 0.91945 1.000 0.000
#> GSM23175 1 0.0000 0.91945 1.000 0.000
#> GSM23176 1 0.0000 0.91945 1.000 0.000
#> GSM23177 1 0.0000 0.91945 1.000 0.000
#> GSM23178 1 0.0000 0.91945 1.000 0.000
#> GSM23179 2 0.9710 0.44751 0.400 0.600
#> GSM23180 1 0.0000 0.91945 1.000 0.000
#> GSM23181 1 0.0000 0.91945 1.000 0.000
#> GSM23182 1 0.0000 0.91945 1.000 0.000
#> GSM23183 1 0.0000 0.91945 1.000 0.000
#> GSM23184 1 0.9896 0.00266 0.560 0.440
#> GSM23196 2 0.0000 0.83897 0.000 1.000
#> GSM23197 2 0.0000 0.83897 0.000 1.000
#> GSM23198 2 0.0000 0.83897 0.000 1.000
#> GSM23199 2 0.0000 0.83897 0.000 1.000
#> GSM23200 2 0.0000 0.83897 0.000 1.000
#> GSM23201 2 0.0000 0.83897 0.000 1.000
#> GSM23202 1 0.9661 0.27825 0.608 0.392
#> GSM23203 2 0.0000 0.83897 0.000 1.000
#> GSM23204 2 0.0000 0.83897 0.000 1.000
#> GSM23205 2 0.0000 0.83897 0.000 1.000
#> GSM23206 2 0.0000 0.83897 0.000 1.000
#> GSM23207 2 0.0000 0.83897 0.000 1.000
#> GSM23208 2 0.0000 0.83897 0.000 1.000
#> GSM23209 2 0.0000 0.83897 0.000 1.000
#> GSM23210 2 0.0000 0.83897 0.000 1.000
#> GSM23211 2 0.0000 0.83897 0.000 1.000
#> GSM23212 2 0.0000 0.83897 0.000 1.000
#> GSM23213 2 0.8144 0.58001 0.252 0.748
#> GSM23214 2 0.9491 0.35885 0.368 0.632
#> GSM23215 2 0.0000 0.83897 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.983 0.000 0.000 1.000
#> GSM23186 1 0.6204 0.262 0.576 0.000 0.424
#> GSM23187 3 0.0000 0.983 0.000 0.000 1.000
#> GSM23188 3 0.0000 0.983 0.000 0.000 1.000
#> GSM23189 3 0.0000 0.983 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.983 0.000 0.000 1.000
#> GSM23191 1 0.4346 0.752 0.816 0.000 0.184
#> GSM23192 3 0.4062 0.795 0.164 0.000 0.836
#> GSM23193 3 0.2165 0.926 0.064 0.000 0.936
#> GSM23194 3 0.0000 0.983 0.000 0.000 1.000
#> GSM23195 3 0.0661 0.977 0.008 0.004 0.988
#> GSM23159 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23160 3 0.0000 0.983 0.000 0.000 1.000
#> GSM23161 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23162 3 0.0000 0.983 0.000 0.000 1.000
#> GSM23163 1 0.0237 0.946 0.996 0.000 0.004
#> GSM23164 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23165 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23166 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23167 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23168 3 0.0000 0.983 0.000 0.000 1.000
#> GSM23169 3 0.0000 0.983 0.000 0.000 1.000
#> GSM23170 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23171 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23172 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23173 3 0.0424 0.979 0.008 0.000 0.992
#> GSM23174 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23175 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23176 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23177 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23178 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23179 3 0.0000 0.983 0.000 0.000 1.000
#> GSM23180 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23181 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23182 1 0.0000 0.949 1.000 0.000 0.000
#> GSM23183 3 0.0237 0.981 0.004 0.000 0.996
#> GSM23184 3 0.0000 0.983 0.000 0.000 1.000
#> GSM23196 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23197 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23198 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23199 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23200 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23201 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23202 1 0.5905 0.416 0.648 0.352 0.000
#> GSM23203 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23204 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23205 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23206 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23207 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23208 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23209 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23210 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23211 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23212 2 0.0000 0.962 0.000 1.000 0.000
#> GSM23213 2 0.5397 0.603 0.280 0.720 0.000
#> GSM23214 2 0.5988 0.415 0.368 0.632 0.000
#> GSM23215 2 0.0000 0.962 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM23186 1 0.5268 0.343 0.592 0.000 0.396 0.012
#> GSM23187 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM23188 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM23189 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM23190 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM23191 1 0.6204 0.628 0.672 0.000 0.164 0.164
#> GSM23192 3 0.4849 0.735 0.164 0.000 0.772 0.064
#> GSM23193 3 0.4297 0.820 0.084 0.000 0.820 0.096
#> GSM23194 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM23195 3 0.0712 0.956 0.008 0.004 0.984 0.004
#> GSM23159 1 0.1792 0.917 0.932 0.000 0.000 0.068
#> GSM23160 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM23161 1 0.1557 0.917 0.944 0.000 0.000 0.056
#> GSM23162 3 0.1854 0.932 0.012 0.000 0.940 0.048
#> GSM23163 1 0.1022 0.923 0.968 0.000 0.000 0.032
#> GSM23164 1 0.0817 0.924 0.976 0.000 0.000 0.024
#> GSM23165 1 0.1118 0.924 0.964 0.000 0.000 0.036
#> GSM23166 1 0.1302 0.922 0.956 0.000 0.000 0.044
#> GSM23167 1 0.0921 0.924 0.972 0.000 0.000 0.028
#> GSM23168 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM23169 3 0.1022 0.950 0.000 0.000 0.968 0.032
#> GSM23170 1 0.0336 0.927 0.992 0.000 0.000 0.008
#> GSM23171 1 0.1022 0.926 0.968 0.000 0.000 0.032
#> GSM23172 1 0.1118 0.924 0.964 0.000 0.000 0.036
#> GSM23173 3 0.1767 0.929 0.044 0.000 0.944 0.012
#> GSM23174 1 0.1637 0.920 0.940 0.000 0.000 0.060
#> GSM23175 1 0.1118 0.923 0.964 0.000 0.000 0.036
#> GSM23176 1 0.0921 0.923 0.972 0.000 0.000 0.028
#> GSM23177 1 0.1022 0.923 0.968 0.000 0.000 0.032
#> GSM23178 1 0.1118 0.924 0.964 0.000 0.000 0.036
#> GSM23179 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM23180 1 0.2011 0.900 0.920 0.000 0.000 0.080
#> GSM23181 1 0.2011 0.904 0.920 0.000 0.000 0.080
#> GSM23182 4 0.2345 0.771 0.100 0.000 0.000 0.900
#> GSM23183 3 0.0779 0.956 0.004 0.000 0.980 0.016
#> GSM23184 3 0.0000 0.963 0.000 0.000 1.000 0.000
#> GSM23196 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM23199 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM23200 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM23201 4 0.3074 0.929 0.000 0.152 0.000 0.848
#> GSM23202 4 0.2814 0.946 0.000 0.132 0.000 0.868
#> GSM23203 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM23205 2 0.4697 0.317 0.000 0.644 0.000 0.356
#> GSM23206 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM23207 2 0.0469 0.958 0.000 0.988 0.000 0.012
#> GSM23208 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM23210 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM23211 2 0.0000 0.969 0.000 1.000 0.000 0.000
#> GSM23212 4 0.2814 0.946 0.000 0.132 0.000 0.868
#> GSM23213 4 0.2814 0.946 0.000 0.132 0.000 0.868
#> GSM23214 4 0.2760 0.944 0.000 0.128 0.000 0.872
#> GSM23215 2 0.0000 0.969 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM23186 1 0.5142 0.232 0.564 0.000 0.392 0.000 0.044
#> GSM23187 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM23188 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM23189 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM23190 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM23191 5 0.3880 0.656 0.044 0.000 0.152 0.004 0.800
#> GSM23192 5 0.3932 0.399 0.000 0.000 0.328 0.000 0.672
#> GSM23193 5 0.3398 0.706 0.004 0.000 0.216 0.000 0.780
#> GSM23194 3 0.0290 0.894 0.000 0.000 0.992 0.000 0.008
#> GSM23195 3 0.3300 0.698 0.004 0.000 0.792 0.000 0.204
#> GSM23159 1 0.1341 0.875 0.944 0.000 0.000 0.000 0.056
#> GSM23160 3 0.0162 0.897 0.000 0.000 0.996 0.000 0.004
#> GSM23161 1 0.2561 0.867 0.856 0.000 0.000 0.000 0.144
#> GSM23162 5 0.4219 0.537 0.000 0.000 0.416 0.000 0.584
#> GSM23163 1 0.2179 0.879 0.896 0.000 0.000 0.004 0.100
#> GSM23164 1 0.1965 0.881 0.904 0.000 0.000 0.000 0.096
#> GSM23165 1 0.0324 0.890 0.992 0.000 0.000 0.004 0.004
#> GSM23166 1 0.2389 0.876 0.880 0.000 0.000 0.004 0.116
#> GSM23167 1 0.0000 0.890 1.000 0.000 0.000 0.000 0.000
#> GSM23168 3 0.0703 0.880 0.000 0.000 0.976 0.000 0.024
#> GSM23169 3 0.2612 0.756 0.008 0.000 0.868 0.000 0.124
#> GSM23170 1 0.0880 0.893 0.968 0.000 0.000 0.000 0.032
#> GSM23171 1 0.0609 0.893 0.980 0.000 0.000 0.000 0.020
#> GSM23172 1 0.0324 0.890 0.992 0.000 0.000 0.004 0.004
#> GSM23173 3 0.4583 0.626 0.064 0.000 0.740 0.004 0.192
#> GSM23174 1 0.1341 0.879 0.944 0.000 0.000 0.000 0.056
#> GSM23175 1 0.0404 0.889 0.988 0.000 0.000 0.000 0.012
#> GSM23176 1 0.2124 0.880 0.900 0.000 0.000 0.004 0.096
#> GSM23177 1 0.2124 0.882 0.900 0.000 0.000 0.004 0.096
#> GSM23178 1 0.0451 0.891 0.988 0.000 0.000 0.004 0.008
#> GSM23179 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM23180 1 0.4101 0.524 0.628 0.000 0.000 0.000 0.372
#> GSM23181 1 0.3074 0.769 0.804 0.000 0.000 0.000 0.196
#> GSM23182 4 0.5404 0.506 0.100 0.000 0.000 0.636 0.264
#> GSM23183 3 0.4009 0.522 0.004 0.000 0.684 0.000 0.312
#> GSM23184 3 0.0000 0.899 0.000 0.000 1.000 0.000 0.000
#> GSM23196 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> GSM23199 2 0.0162 0.965 0.000 0.996 0.000 0.004 0.000
#> GSM23200 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> GSM23201 4 0.1270 0.868 0.000 0.052 0.000 0.948 0.000
#> GSM23202 4 0.0162 0.910 0.000 0.004 0.000 0.996 0.000
#> GSM23203 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> GSM23205 2 0.4088 0.395 0.000 0.632 0.000 0.368 0.000
#> GSM23206 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> GSM23207 2 0.1197 0.927 0.000 0.952 0.000 0.048 0.000
#> GSM23208 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> GSM23210 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> GSM23211 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
#> GSM23212 4 0.0162 0.910 0.000 0.004 0.000 0.996 0.000
#> GSM23213 4 0.0162 0.910 0.000 0.004 0.000 0.996 0.000
#> GSM23214 4 0.0162 0.910 0.000 0.004 0.000 0.996 0.000
#> GSM23215 2 0.0000 0.968 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0000 0.8569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23186 6 0.6215 -0.0732 0.356 0.000 0.236 0.000 0.008 0.400
#> GSM23187 3 0.0000 0.8569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23188 3 0.0000 0.8569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23189 3 0.0000 0.8569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23190 3 0.0146 0.8558 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM23191 5 0.0881 0.8381 0.008 0.000 0.008 0.000 0.972 0.012
#> GSM23192 6 0.5844 0.1820 0.000 0.000 0.216 0.000 0.308 0.476
#> GSM23193 5 0.0837 0.8532 0.004 0.000 0.020 0.000 0.972 0.004
#> GSM23194 3 0.0000 0.8569 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23195 3 0.4189 -0.2418 0.004 0.000 0.552 0.000 0.008 0.436
#> GSM23159 1 0.1176 0.8376 0.956 0.000 0.000 0.000 0.020 0.024
#> GSM23160 3 0.2531 0.7543 0.000 0.000 0.856 0.000 0.012 0.132
#> GSM23161 1 0.2384 0.8322 0.884 0.000 0.000 0.000 0.032 0.084
#> GSM23162 5 0.3655 0.7120 0.004 0.000 0.108 0.000 0.800 0.088
#> GSM23163 1 0.3791 0.8189 0.732 0.000 0.000 0.000 0.032 0.236
#> GSM23164 1 0.2487 0.8382 0.876 0.000 0.000 0.000 0.032 0.092
#> GSM23165 1 0.3221 0.7964 0.736 0.000 0.000 0.000 0.000 0.264
#> GSM23166 1 0.2752 0.8388 0.856 0.000 0.000 0.000 0.036 0.108
#> GSM23167 1 0.2664 0.8283 0.816 0.000 0.000 0.000 0.000 0.184
#> GSM23168 3 0.2831 0.7379 0.000 0.000 0.840 0.000 0.024 0.136
#> GSM23169 3 0.4159 0.6038 0.000 0.000 0.744 0.000 0.116 0.140
#> GSM23170 1 0.3014 0.8342 0.804 0.000 0.000 0.000 0.012 0.184
#> GSM23171 1 0.1219 0.8492 0.948 0.000 0.000 0.000 0.004 0.048
#> GSM23172 1 0.2697 0.8363 0.812 0.000 0.000 0.000 0.000 0.188
#> GSM23173 6 0.4925 0.0261 0.024 0.000 0.436 0.000 0.024 0.516
#> GSM23174 1 0.0692 0.8391 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM23175 1 0.1219 0.8475 0.948 0.000 0.000 0.000 0.004 0.048
#> GSM23176 1 0.4170 0.7822 0.660 0.000 0.000 0.000 0.032 0.308
#> GSM23177 1 0.2740 0.8408 0.852 0.000 0.000 0.000 0.028 0.120
#> GSM23178 1 0.3266 0.7978 0.728 0.000 0.000 0.000 0.000 0.272
#> GSM23179 3 0.0914 0.8454 0.000 0.000 0.968 0.000 0.016 0.016
#> GSM23180 1 0.3898 0.5739 0.684 0.000 0.000 0.000 0.296 0.020
#> GSM23181 1 0.2572 0.7691 0.852 0.000 0.000 0.000 0.136 0.012
#> GSM23182 4 0.5031 0.5563 0.088 0.000 0.000 0.672 0.216 0.024
#> GSM23183 6 0.4837 0.2647 0.000 0.000 0.432 0.000 0.056 0.512
#> GSM23184 3 0.0777 0.8480 0.000 0.000 0.972 0.000 0.004 0.024
#> GSM23196 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23199 2 0.0146 0.9641 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM23200 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23201 4 0.1075 0.8707 0.000 0.048 0.000 0.952 0.000 0.000
#> GSM23202 4 0.0000 0.9154 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23203 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23205 2 0.3672 0.3969 0.000 0.632 0.000 0.368 0.000 0.000
#> GSM23206 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23207 2 0.1075 0.9246 0.000 0.952 0.000 0.048 0.000 0.000
#> GSM23208 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23210 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23211 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23212 4 0.0000 0.9154 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23213 4 0.0000 0.9154 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23214 4 0.0000 0.9154 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23215 2 0.0000 0.9671 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> MAD:pam 50 5.48e-07 6.47e-01 2
#> MAD:pam 54 1.88e-12 1.25e-03 3
#> MAD:pam 55 4.19e-11 1.34e-04 4
#> MAD:pam 54 3.06e-10 1.33e-04 5
#> MAD:pam 51 1.24e-09 9.48e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4642 0.536 0.536
#> 3 3 0.935 0.963 0.979 0.4536 0.787 0.603
#> 4 4 0.779 0.793 0.903 0.0876 0.943 0.824
#> 5 5 0.774 0.720 0.858 0.0788 0.902 0.653
#> 6 6 0.818 0.713 0.830 0.0517 0.919 0.630
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
#> GSM23185 1 0 1 1 0
#> GSM23186 1 0 1 1 0
#> GSM23187 1 0 1 1 0
#> GSM23188 1 0 1 1 0
#> GSM23189 1 0 1 1 0
#> GSM23190 1 0 1 1 0
#> GSM23191 1 0 1 1 0
#> GSM23192 1 0 1 1 0
#> GSM23193 1 0 1 1 0
#> GSM23194 1 0 1 1 0
#> GSM23195 1 0 1 1 0
#> GSM23159 1 0 1 1 0
#> GSM23160 1 0 1 1 0
#> GSM23161 1 0 1 1 0
#> GSM23162 1 0 1 1 0
#> GSM23163 1 0 1 1 0
#> GSM23164 1 0 1 1 0
#> GSM23165 1 0 1 1 0
#> GSM23166 1 0 1 1 0
#> GSM23167 1 0 1 1 0
#> GSM23168 1 0 1 1 0
#> GSM23169 1 0 1 1 0
#> GSM23170 1 0 1 1 0
#> GSM23171 1 0 1 1 0
#> GSM23172 1 0 1 1 0
#> GSM23173 1 0 1 1 0
#> GSM23174 1 0 1 1 0
#> GSM23175 1 0 1 1 0
#> GSM23176 1 0 1 1 0
#> GSM23177 1 0 1 1 0
#> GSM23178 1 0 1 1 0
#> GSM23179 1 0 1 1 0
#> GSM23180 1 0 1 1 0
#> GSM23181 1 0 1 1 0
#> GSM23182 1 0 1 1 0
#> GSM23183 1 0 1 1 0
#> GSM23184 1 0 1 1 0
#> GSM23196 2 0 1 0 1
#> GSM23197 2 0 1 0 1
#> GSM23198 2 0 1 0 1
#> GSM23199 2 0 1 0 1
#> GSM23200 2 0 1 0 1
#> GSM23201 2 0 1 0 1
#> GSM23202 2 0 1 0 1
#> GSM23203 2 0 1 0 1
#> GSM23204 2 0 1 0 1
#> GSM23205 2 0 1 0 1
#> GSM23206 2 0 1 0 1
#> GSM23207 2 0 1 0 1
#> GSM23208 2 0 1 0 1
#> GSM23209 2 0 1 0 1
#> GSM23210 2 0 1 0 1
#> GSM23211 2 0 1 0 1
#> GSM23212 2 0 1 0 1
#> GSM23213 2 0 1 0 1
#> GSM23214 2 0 1 0 1
#> GSM23215 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.978 0.000 0.000 1.000
#> GSM23186 1 0.5465 0.651 0.712 0.000 0.288
#> GSM23187 3 0.0000 0.978 0.000 0.000 1.000
#> GSM23188 3 0.0237 0.976 0.004 0.000 0.996
#> GSM23189 3 0.0000 0.978 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.978 0.000 0.000 1.000
#> GSM23191 3 0.0000 0.978 0.000 0.000 1.000
#> GSM23192 3 0.0000 0.978 0.000 0.000 1.000
#> GSM23193 3 0.0000 0.978 0.000 0.000 1.000
#> GSM23194 3 0.0000 0.978 0.000 0.000 1.000
#> GSM23195 3 0.1860 0.939 0.052 0.000 0.948
#> GSM23159 1 0.0424 0.958 0.992 0.000 0.008
#> GSM23160 3 0.0000 0.978 0.000 0.000 1.000
#> GSM23161 1 0.0237 0.956 0.996 0.000 0.004
#> GSM23162 3 0.0000 0.978 0.000 0.000 1.000
#> GSM23163 1 0.3619 0.858 0.864 0.000 0.136
#> GSM23164 1 0.0237 0.956 0.996 0.000 0.004
#> GSM23165 1 0.0424 0.958 0.992 0.000 0.008
#> GSM23166 1 0.0237 0.956 0.996 0.000 0.004
#> GSM23167 1 0.0424 0.958 0.992 0.000 0.008
#> GSM23168 3 0.0000 0.978 0.000 0.000 1.000
#> GSM23169 3 0.0000 0.978 0.000 0.000 1.000
#> GSM23170 1 0.0424 0.958 0.992 0.000 0.008
#> GSM23171 1 0.0747 0.955 0.984 0.000 0.016
#> GSM23172 1 0.0424 0.958 0.992 0.000 0.008
#> GSM23173 3 0.0747 0.968 0.016 0.000 0.984
#> GSM23174 1 0.1860 0.934 0.948 0.000 0.052
#> GSM23175 1 0.1289 0.946 0.968 0.000 0.032
#> GSM23176 1 0.0592 0.957 0.988 0.000 0.012
#> GSM23177 1 0.0424 0.958 0.992 0.000 0.008
#> GSM23178 1 0.0424 0.958 0.992 0.000 0.008
#> GSM23179 3 0.0000 0.978 0.000 0.000 1.000
#> GSM23180 3 0.3551 0.857 0.132 0.000 0.868
#> GSM23181 1 0.4121 0.808 0.832 0.000 0.168
#> GSM23182 3 0.3551 0.857 0.132 0.000 0.868
#> GSM23183 3 0.1860 0.939 0.052 0.000 0.948
#> GSM23184 3 0.0000 0.978 0.000 0.000 1.000
#> GSM23196 2 0.0000 0.999 0.000 1.000 0.000
#> GSM23197 2 0.0000 0.999 0.000 1.000 0.000
#> GSM23198 2 0.0000 0.999 0.000 1.000 0.000
#> GSM23199 2 0.0000 0.999 0.000 1.000 0.000
#> GSM23200 2 0.0000 0.999 0.000 1.000 0.000
#> GSM23201 2 0.0237 0.997 0.004 0.996 0.000
#> GSM23202 2 0.0237 0.997 0.004 0.996 0.000
#> GSM23203 2 0.0000 0.999 0.000 1.000 0.000
#> GSM23204 2 0.0000 0.999 0.000 1.000 0.000
#> GSM23205 2 0.0237 0.997 0.004 0.996 0.000
#> GSM23206 2 0.0000 0.999 0.000 1.000 0.000
#> GSM23207 2 0.0000 0.999 0.000 1.000 0.000
#> GSM23208 2 0.0000 0.999 0.000 1.000 0.000
#> GSM23209 2 0.0000 0.999 0.000 1.000 0.000
#> GSM23210 2 0.0000 0.999 0.000 1.000 0.000
#> GSM23211 2 0.0000 0.999 0.000 1.000 0.000
#> GSM23212 2 0.0237 0.997 0.004 0.996 0.000
#> GSM23213 2 0.0424 0.995 0.008 0.992 0.000
#> GSM23214 2 0.0424 0.995 0.008 0.992 0.000
#> GSM23215 2 0.0000 0.999 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0000 0.8782 0.000 0.000 1.000 0.000
#> GSM23186 1 0.5058 0.7561 0.768 0.000 0.128 0.104
#> GSM23187 3 0.0000 0.8782 0.000 0.000 1.000 0.000
#> GSM23188 3 0.0188 0.8780 0.000 0.000 0.996 0.004
#> GSM23189 3 0.0188 0.8780 0.000 0.000 0.996 0.004
#> GSM23190 3 0.0000 0.8782 0.000 0.000 1.000 0.000
#> GSM23191 3 0.2546 0.8440 0.092 0.000 0.900 0.008
#> GSM23192 3 0.2796 0.8412 0.092 0.000 0.892 0.016
#> GSM23193 3 0.1042 0.8751 0.020 0.000 0.972 0.008
#> GSM23194 3 0.0000 0.8782 0.000 0.000 1.000 0.000
#> GSM23195 3 0.6373 0.6113 0.248 0.000 0.636 0.116
#> GSM23159 1 0.0000 0.9644 1.000 0.000 0.000 0.000
#> GSM23160 3 0.0469 0.8766 0.000 0.000 0.988 0.012
#> GSM23161 1 0.0188 0.9634 0.996 0.000 0.000 0.004
#> GSM23162 3 0.0672 0.8770 0.008 0.000 0.984 0.008
#> GSM23163 1 0.2943 0.9071 0.892 0.000 0.032 0.076
#> GSM23164 1 0.0188 0.9634 0.996 0.000 0.000 0.004
#> GSM23165 1 0.2281 0.9181 0.904 0.000 0.000 0.096
#> GSM23166 1 0.0188 0.9634 0.996 0.000 0.000 0.004
#> GSM23167 1 0.0469 0.9609 0.988 0.000 0.000 0.012
#> GSM23168 3 0.0000 0.8782 0.000 0.000 1.000 0.000
#> GSM23169 3 0.1629 0.8697 0.024 0.000 0.952 0.024
#> GSM23170 1 0.0000 0.9644 1.000 0.000 0.000 0.000
#> GSM23171 1 0.0000 0.9644 1.000 0.000 0.000 0.000
#> GSM23172 1 0.1716 0.9371 0.936 0.000 0.000 0.064
#> GSM23173 3 0.5361 0.7458 0.148 0.000 0.744 0.108
#> GSM23174 1 0.0000 0.9644 1.000 0.000 0.000 0.000
#> GSM23175 1 0.0000 0.9644 1.000 0.000 0.000 0.000
#> GSM23176 1 0.1867 0.9327 0.928 0.000 0.000 0.072
#> GSM23177 1 0.0188 0.9634 0.996 0.000 0.000 0.004
#> GSM23178 1 0.0000 0.9644 1.000 0.000 0.000 0.000
#> GSM23179 3 0.0000 0.8782 0.000 0.000 1.000 0.000
#> GSM23180 3 0.5587 0.5166 0.372 0.000 0.600 0.028
#> GSM23181 1 0.0336 0.9622 0.992 0.000 0.000 0.008
#> GSM23182 3 0.5587 0.5166 0.372 0.000 0.600 0.028
#> GSM23183 3 0.6928 0.3412 0.372 0.000 0.512 0.116
#> GSM23184 3 0.0336 0.8778 0.000 0.000 0.992 0.008
#> GSM23196 2 0.0000 0.8393 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.8393 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.8393 0.000 1.000 0.000 0.000
#> GSM23199 2 0.5000 -0.2055 0.000 0.504 0.000 0.496
#> GSM23200 2 0.0000 0.8393 0.000 1.000 0.000 0.000
#> GSM23201 4 0.2589 0.9042 0.000 0.116 0.000 0.884
#> GSM23202 4 0.2589 0.9042 0.000 0.116 0.000 0.884
#> GSM23203 2 0.0000 0.8393 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.8393 0.000 1.000 0.000 0.000
#> GSM23205 4 0.2760 0.8994 0.000 0.128 0.000 0.872
#> GSM23206 2 0.0000 0.8393 0.000 1.000 0.000 0.000
#> GSM23207 2 0.4977 -0.0857 0.000 0.540 0.000 0.460
#> GSM23208 2 0.0000 0.8393 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.8393 0.000 1.000 0.000 0.000
#> GSM23210 2 0.4999 -0.1923 0.000 0.508 0.000 0.492
#> GSM23211 2 0.0000 0.8393 0.000 1.000 0.000 0.000
#> GSM23212 4 0.2760 0.8994 0.000 0.128 0.000 0.872
#> GSM23213 4 0.2589 0.9042 0.000 0.116 0.000 0.884
#> GSM23214 4 0.2589 0.9042 0.000 0.116 0.000 0.884
#> GSM23215 4 0.5000 0.0369 0.000 0.496 0.000 0.504
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.0000 0.863 0.000 0.000 1.000 0.000 0.000
#> GSM23186 1 0.3821 0.605 0.800 0.000 0.148 0.000 0.052
#> GSM23187 3 0.0000 0.863 0.000 0.000 1.000 0.000 0.000
#> GSM23188 3 0.0000 0.863 0.000 0.000 1.000 0.000 0.000
#> GSM23189 3 0.0000 0.863 0.000 0.000 1.000 0.000 0.000
#> GSM23190 3 0.0000 0.863 0.000 0.000 1.000 0.000 0.000
#> GSM23191 5 0.4156 0.428 0.004 0.000 0.288 0.008 0.700
#> GSM23192 5 0.4420 0.101 0.004 0.000 0.448 0.000 0.548
#> GSM23193 3 0.4030 0.367 0.000 0.000 0.648 0.000 0.352
#> GSM23194 3 0.0000 0.863 0.000 0.000 1.000 0.000 0.000
#> GSM23195 5 0.6361 0.327 0.296 0.000 0.196 0.000 0.508
#> GSM23159 1 0.2280 0.815 0.880 0.000 0.000 0.000 0.120
#> GSM23160 3 0.0510 0.853 0.000 0.000 0.984 0.000 0.016
#> GSM23161 1 0.3876 0.687 0.684 0.000 0.000 0.000 0.316
#> GSM23162 3 0.2648 0.708 0.000 0.000 0.848 0.000 0.152
#> GSM23163 1 0.2719 0.808 0.852 0.000 0.004 0.000 0.144
#> GSM23164 1 0.4291 0.465 0.536 0.000 0.000 0.000 0.464
#> GSM23165 1 0.1270 0.790 0.948 0.000 0.000 0.000 0.052
#> GSM23166 1 0.4287 0.469 0.540 0.000 0.000 0.000 0.460
#> GSM23167 1 0.1197 0.792 0.952 0.000 0.000 0.000 0.048
#> GSM23168 3 0.0000 0.863 0.000 0.000 1.000 0.000 0.000
#> GSM23169 3 0.3707 0.489 0.000 0.000 0.716 0.000 0.284
#> GSM23170 1 0.0000 0.807 1.000 0.000 0.000 0.000 0.000
#> GSM23171 1 0.1121 0.815 0.956 0.000 0.000 0.000 0.044
#> GSM23172 1 0.1197 0.792 0.952 0.000 0.000 0.000 0.048
#> GSM23173 3 0.6281 -0.125 0.160 0.000 0.488 0.000 0.352
#> GSM23174 1 0.3109 0.765 0.800 0.000 0.000 0.000 0.200
#> GSM23175 1 0.2852 0.797 0.828 0.000 0.000 0.000 0.172
#> GSM23176 1 0.1197 0.792 0.952 0.000 0.000 0.000 0.048
#> GSM23177 1 0.2648 0.806 0.848 0.000 0.000 0.000 0.152
#> GSM23178 1 0.2230 0.816 0.884 0.000 0.000 0.000 0.116
#> GSM23179 3 0.0000 0.863 0.000 0.000 1.000 0.000 0.000
#> GSM23180 5 0.3935 0.491 0.008 0.000 0.220 0.012 0.760
#> GSM23181 5 0.4283 -0.431 0.456 0.000 0.000 0.000 0.544
#> GSM23182 5 0.3935 0.491 0.008 0.000 0.220 0.012 0.760
#> GSM23183 5 0.6323 0.320 0.292 0.000 0.192 0.000 0.516
#> GSM23184 3 0.0404 0.856 0.000 0.000 0.988 0.000 0.012
#> GSM23196 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23199 4 0.4030 0.622 0.000 0.352 0.000 0.648 0.000
#> GSM23200 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23201 4 0.0000 0.821 0.000 0.000 0.000 1.000 0.000
#> GSM23202 4 0.0000 0.821 0.000 0.000 0.000 1.000 0.000
#> GSM23203 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23205 4 0.0290 0.823 0.000 0.008 0.000 0.992 0.000
#> GSM23206 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23207 4 0.4101 0.589 0.000 0.372 0.000 0.628 0.000
#> GSM23208 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23210 4 0.4126 0.578 0.000 0.380 0.000 0.620 0.000
#> GSM23211 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM23212 4 0.0404 0.822 0.000 0.012 0.000 0.988 0.000
#> GSM23213 4 0.0000 0.821 0.000 0.000 0.000 1.000 0.000
#> GSM23214 4 0.0000 0.821 0.000 0.000 0.000 1.000 0.000
#> GSM23215 4 0.3612 0.706 0.000 0.268 0.000 0.732 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0000 0.9375 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23186 6 0.5209 0.4717 0.172 0.000 0.048 0.000 0.096 0.684
#> GSM23187 3 0.0000 0.9375 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23188 3 0.0717 0.9216 0.016 0.000 0.976 0.000 0.008 0.000
#> GSM23189 3 0.0000 0.9375 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23190 3 0.0146 0.9379 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM23191 5 0.1074 0.5207 0.028 0.000 0.012 0.000 0.960 0.000
#> GSM23192 5 0.3670 0.4331 0.012 0.000 0.284 0.000 0.704 0.000
#> GSM23193 5 0.4066 0.2260 0.012 0.000 0.392 0.000 0.596 0.000
#> GSM23194 3 0.0547 0.9380 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM23195 5 0.6905 0.1513 0.316 0.000 0.096 0.000 0.436 0.152
#> GSM23159 1 0.3672 0.5253 0.632 0.000 0.000 0.000 0.000 0.368
#> GSM23160 3 0.0363 0.9391 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM23161 1 0.3506 0.6533 0.792 0.000 0.000 0.000 0.052 0.156
#> GSM23162 5 0.3851 0.0775 0.000 0.000 0.460 0.000 0.540 0.000
#> GSM23163 1 0.3629 0.6103 0.724 0.000 0.000 0.000 0.016 0.260
#> GSM23164 1 0.3307 0.6211 0.820 0.000 0.000 0.000 0.108 0.072
#> GSM23165 6 0.0146 0.7355 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM23166 1 0.3607 0.6265 0.796 0.000 0.000 0.000 0.112 0.092
#> GSM23167 6 0.0260 0.7382 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM23168 3 0.1007 0.9273 0.000 0.000 0.956 0.000 0.044 0.000
#> GSM23169 3 0.3844 0.4673 0.004 0.000 0.676 0.000 0.312 0.008
#> GSM23170 6 0.3578 0.2507 0.340 0.000 0.000 0.000 0.000 0.660
#> GSM23171 6 0.3804 -0.0315 0.424 0.000 0.000 0.000 0.000 0.576
#> GSM23172 6 0.0260 0.7382 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM23173 5 0.6081 0.1911 0.064 0.000 0.412 0.000 0.452 0.072
#> GSM23174 1 0.4066 0.2418 0.596 0.000 0.000 0.000 0.012 0.392
#> GSM23175 1 0.3468 0.5413 0.712 0.000 0.000 0.000 0.004 0.284
#> GSM23176 6 0.0260 0.7382 0.008 0.000 0.000 0.000 0.000 0.992
#> GSM23177 1 0.3309 0.6185 0.720 0.000 0.000 0.000 0.000 0.280
#> GSM23178 1 0.3659 0.5265 0.636 0.000 0.000 0.000 0.000 0.364
#> GSM23179 3 0.0865 0.9313 0.000 0.000 0.964 0.000 0.036 0.000
#> GSM23180 5 0.3101 0.4492 0.244 0.000 0.000 0.000 0.756 0.000
#> GSM23181 1 0.3247 0.5527 0.808 0.000 0.000 0.000 0.156 0.036
#> GSM23182 5 0.3101 0.4492 0.244 0.000 0.000 0.000 0.756 0.000
#> GSM23183 5 0.6948 0.1288 0.332 0.000 0.104 0.000 0.420 0.144
#> GSM23184 3 0.0937 0.9293 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM23196 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23199 4 0.2219 0.8731 0.000 0.136 0.000 0.864 0.000 0.000
#> GSM23200 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23201 4 0.0000 0.9276 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23202 4 0.0000 0.9276 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23203 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23205 4 0.0000 0.9276 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23206 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23207 4 0.2416 0.8569 0.000 0.156 0.000 0.844 0.000 0.000
#> GSM23208 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23210 4 0.2664 0.8289 0.000 0.184 0.000 0.816 0.000 0.000
#> GSM23211 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23212 4 0.0000 0.9276 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23213 4 0.0000 0.9276 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23214 4 0.0000 0.9276 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23215 4 0.1663 0.8999 0.000 0.088 0.000 0.912 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 cell.type(p) disease.state(p) k
#> MAD:mclust 57 3.90e-13 0.052490 2
#> MAD:mclust 57 4.19e-13 0.000276 3
#> MAD:mclust 52 3.00e-11 0.000376 4
#> MAD:mclust 45 9.25e-10 0.000897 5
#> MAD:mclust 44 2.32e-08 0.001311 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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.892 0.829 0.940 0.4816 0.504 0.504
#> 3 3 0.954 0.947 0.972 0.3988 0.713 0.484
#> 4 4 0.853 0.830 0.926 0.1131 0.868 0.628
#> 5 5 0.785 0.700 0.856 0.0510 0.939 0.775
#> 6 6 0.751 0.640 0.800 0.0398 0.956 0.816
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
#> GSM23185 2 0.000 0.1915 0.000 1.000
#> GSM23186 1 0.998 0.9719 0.524 0.476
#> GSM23187 2 0.541 -0.2144 0.124 0.876
#> GSM23188 2 0.373 0.3650 0.072 0.928
#> GSM23189 2 0.358 -0.0269 0.068 0.932
#> GSM23190 2 0.482 -0.1495 0.104 0.896
#> GSM23191 1 0.998 0.9719 0.524 0.476
#> GSM23192 1 0.998 0.9719 0.524 0.476
#> GSM23193 1 0.998 0.9719 0.524 0.476
#> GSM23194 1 1.000 0.9499 0.504 0.496
#> GSM23195 1 0.998 0.9719 0.524 0.476
#> GSM23159 1 0.998 0.9719 0.524 0.476
#> GSM23160 1 0.998 0.9719 0.524 0.476
#> GSM23161 1 0.998 0.9719 0.524 0.476
#> GSM23162 1 0.998 0.9719 0.524 0.476
#> GSM23163 1 0.998 0.9719 0.524 0.476
#> GSM23164 1 0.998 0.9719 0.524 0.476
#> GSM23165 1 0.998 0.9719 0.524 0.476
#> GSM23166 1 0.998 0.9719 0.524 0.476
#> GSM23167 1 0.998 0.9719 0.524 0.476
#> GSM23168 1 0.998 0.9719 0.524 0.476
#> GSM23169 1 0.998 0.9719 0.524 0.476
#> GSM23170 1 0.998 0.9719 0.524 0.476
#> GSM23171 1 0.998 0.9719 0.524 0.476
#> GSM23172 1 0.998 0.9719 0.524 0.476
#> GSM23173 1 0.998 0.9719 0.524 0.476
#> GSM23174 1 0.998 0.9719 0.524 0.476
#> GSM23175 1 0.998 0.9719 0.524 0.476
#> GSM23176 1 0.998 0.9719 0.524 0.476
#> GSM23177 1 0.998 0.9719 0.524 0.476
#> GSM23178 1 0.998 0.9719 0.524 0.476
#> GSM23179 1 0.999 0.9677 0.520 0.480
#> GSM23180 1 0.998 0.9719 0.524 0.476
#> GSM23181 1 0.998 0.9719 0.524 0.476
#> GSM23182 1 0.998 0.9719 0.524 0.476
#> GSM23183 1 0.998 0.9719 0.524 0.476
#> GSM23184 1 0.998 0.9719 0.524 0.476
#> GSM23196 2 0.998 0.8780 0.476 0.524
#> GSM23197 2 0.998 0.8780 0.476 0.524
#> GSM23198 2 0.998 0.8780 0.476 0.524
#> GSM23199 2 0.998 0.8780 0.476 0.524
#> GSM23200 2 0.998 0.8780 0.476 0.524
#> GSM23201 2 0.998 0.8780 0.476 0.524
#> GSM23202 1 0.871 -0.6535 0.708 0.292
#> GSM23203 2 0.998 0.8780 0.476 0.524
#> GSM23204 2 0.998 0.8780 0.476 0.524
#> GSM23205 2 0.998 0.8780 0.476 0.524
#> GSM23206 2 0.998 0.8780 0.476 0.524
#> GSM23207 2 0.998 0.8780 0.476 0.524
#> GSM23208 2 0.998 0.8780 0.476 0.524
#> GSM23209 2 0.998 0.8780 0.476 0.524
#> GSM23210 2 0.998 0.8780 0.476 0.524
#> GSM23211 2 0.998 0.8780 0.476 0.524
#> GSM23212 2 0.998 0.8780 0.476 0.524
#> GSM23213 2 0.999 0.8728 0.484 0.516
#> GSM23214 2 1.000 0.8699 0.488 0.512
#> GSM23215 2 0.998 0.8780 0.476 0.524
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.933 0.000 0.000 1.000
#> GSM23186 1 0.2066 0.929 0.940 0.000 0.060
#> GSM23187 3 0.0000 0.933 0.000 0.000 1.000
#> GSM23188 3 0.0000 0.933 0.000 0.000 1.000
#> GSM23189 3 0.0000 0.933 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.933 0.000 0.000 1.000
#> GSM23191 3 0.5733 0.614 0.324 0.000 0.676
#> GSM23192 3 0.5138 0.736 0.252 0.000 0.748
#> GSM23193 3 0.3879 0.856 0.152 0.000 0.848
#> GSM23194 3 0.0000 0.933 0.000 0.000 1.000
#> GSM23195 3 0.2878 0.901 0.096 0.000 0.904
#> GSM23159 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23160 3 0.0237 0.933 0.004 0.000 0.996
#> GSM23161 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23162 3 0.1643 0.926 0.044 0.000 0.956
#> GSM23163 1 0.0237 0.992 0.996 0.000 0.004
#> GSM23164 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23165 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23166 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23167 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23168 3 0.0747 0.932 0.016 0.000 0.984
#> GSM23169 3 0.2448 0.912 0.076 0.000 0.924
#> GSM23170 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23171 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23172 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23173 3 0.1643 0.926 0.044 0.000 0.956
#> GSM23174 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23175 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23176 1 0.0237 0.992 0.996 0.000 0.004
#> GSM23177 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23178 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23179 3 0.0000 0.933 0.000 0.000 1.000
#> GSM23180 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23181 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23182 1 0.0000 0.996 1.000 0.000 0.000
#> GSM23183 3 0.3551 0.874 0.132 0.000 0.868
#> GSM23184 3 0.0000 0.933 0.000 0.000 1.000
#> GSM23196 2 0.0000 0.977 0.000 1.000 0.000
#> GSM23197 2 0.0000 0.977 0.000 1.000 0.000
#> GSM23198 2 0.0000 0.977 0.000 1.000 0.000
#> GSM23199 2 0.0000 0.977 0.000 1.000 0.000
#> GSM23200 2 0.0000 0.977 0.000 1.000 0.000
#> GSM23201 2 0.0592 0.970 0.012 0.988 0.000
#> GSM23202 2 0.5733 0.536 0.324 0.676 0.000
#> GSM23203 2 0.0000 0.977 0.000 1.000 0.000
#> GSM23204 2 0.0000 0.977 0.000 1.000 0.000
#> GSM23205 2 0.0237 0.975 0.004 0.996 0.000
#> GSM23206 2 0.0000 0.977 0.000 1.000 0.000
#> GSM23207 2 0.0000 0.977 0.000 1.000 0.000
#> GSM23208 2 0.0000 0.977 0.000 1.000 0.000
#> GSM23209 2 0.0000 0.977 0.000 1.000 0.000
#> GSM23210 2 0.0000 0.977 0.000 1.000 0.000
#> GSM23211 2 0.0000 0.977 0.000 1.000 0.000
#> GSM23212 2 0.0000 0.977 0.000 1.000 0.000
#> GSM23213 2 0.1289 0.954 0.032 0.968 0.000
#> GSM23214 2 0.1643 0.943 0.044 0.956 0.000
#> GSM23215 2 0.0000 0.977 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0336 0.9650 0.000 0.000 0.992 0.008
#> GSM23186 1 0.0779 0.8758 0.980 0.000 0.016 0.004
#> GSM23187 3 0.0188 0.9655 0.000 0.000 0.996 0.004
#> GSM23188 3 0.0188 0.9655 0.000 0.000 0.996 0.004
#> GSM23189 3 0.0188 0.9655 0.000 0.000 0.996 0.004
#> GSM23190 3 0.0188 0.9652 0.000 0.000 0.996 0.004
#> GSM23191 4 0.4746 0.3270 0.000 0.000 0.368 0.632
#> GSM23192 3 0.3356 0.7946 0.000 0.000 0.824 0.176
#> GSM23193 3 0.3024 0.8320 0.000 0.000 0.852 0.148
#> GSM23194 3 0.0188 0.9655 0.000 0.000 0.996 0.004
#> GSM23195 1 0.4250 0.6169 0.724 0.000 0.276 0.000
#> GSM23159 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM23160 3 0.0000 0.9657 0.000 0.000 1.000 0.000
#> GSM23161 1 0.3219 0.7686 0.836 0.000 0.000 0.164
#> GSM23162 3 0.0707 0.9583 0.000 0.000 0.980 0.020
#> GSM23163 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM23164 1 0.4907 0.3530 0.580 0.000 0.000 0.420
#> GSM23165 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM23166 1 0.5070 0.3761 0.580 0.000 0.004 0.416
#> GSM23167 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM23168 3 0.0000 0.9657 0.000 0.000 1.000 0.000
#> GSM23169 3 0.0469 0.9612 0.000 0.000 0.988 0.012
#> GSM23170 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM23171 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM23172 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM23173 3 0.1867 0.9004 0.072 0.000 0.928 0.000
#> GSM23174 1 0.1302 0.8617 0.956 0.000 0.000 0.044
#> GSM23175 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM23176 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM23177 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM23178 1 0.0000 0.8853 1.000 0.000 0.000 0.000
#> GSM23179 3 0.0000 0.9657 0.000 0.000 1.000 0.000
#> GSM23180 4 0.0657 0.8319 0.012 0.000 0.004 0.984
#> GSM23181 4 0.2973 0.7205 0.144 0.000 0.000 0.856
#> GSM23182 4 0.0336 0.8344 0.008 0.000 0.000 0.992
#> GSM23183 1 0.4933 0.2953 0.568 0.000 0.432 0.000
#> GSM23184 3 0.0188 0.9652 0.000 0.000 0.996 0.004
#> GSM23196 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM23199 2 0.0592 0.9267 0.000 0.984 0.000 0.016
#> GSM23200 2 0.0469 0.9286 0.000 0.988 0.000 0.012
#> GSM23201 4 0.1792 0.8378 0.000 0.068 0.000 0.932
#> GSM23202 4 0.2011 0.8340 0.000 0.080 0.000 0.920
#> GSM23203 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM23205 2 0.4746 0.4017 0.000 0.632 0.000 0.368
#> GSM23206 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM23207 2 0.0921 0.9180 0.000 0.972 0.000 0.028
#> GSM23208 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM23210 2 0.0592 0.9267 0.000 0.984 0.000 0.016
#> GSM23211 2 0.0000 0.9322 0.000 1.000 0.000 0.000
#> GSM23212 2 0.4992 0.0815 0.000 0.524 0.000 0.476
#> GSM23213 4 0.4040 0.6269 0.000 0.248 0.000 0.752
#> GSM23214 4 0.2345 0.8218 0.000 0.100 0.000 0.900
#> GSM23215 2 0.0336 0.9301 0.000 0.992 0.000 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.2813 0.7613 0.000 0.000 0.832 0.000 0.168
#> GSM23186 1 0.2819 0.8841 0.884 0.000 0.024 0.012 0.080
#> GSM23187 3 0.0609 0.8269 0.000 0.000 0.980 0.000 0.020
#> GSM23188 3 0.0963 0.8252 0.000 0.000 0.964 0.000 0.036
#> GSM23189 3 0.0510 0.8265 0.000 0.000 0.984 0.000 0.016
#> GSM23190 3 0.3143 0.7286 0.000 0.000 0.796 0.000 0.204
#> GSM23191 4 0.2946 0.6133 0.000 0.000 0.088 0.868 0.044
#> GSM23192 3 0.6314 0.3218 0.004 0.000 0.548 0.260 0.188
#> GSM23193 3 0.3037 0.7690 0.004 0.000 0.864 0.100 0.032
#> GSM23194 3 0.1121 0.8236 0.000 0.000 0.956 0.000 0.044
#> GSM23195 5 0.5639 -0.1053 0.080 0.000 0.396 0.000 0.524
#> GSM23159 1 0.0510 0.9643 0.984 0.000 0.000 0.000 0.016
#> GSM23160 3 0.1197 0.8245 0.000 0.000 0.952 0.000 0.048
#> GSM23161 1 0.3551 0.7861 0.820 0.000 0.000 0.136 0.044
#> GSM23162 3 0.2308 0.8141 0.004 0.000 0.912 0.036 0.048
#> GSM23163 1 0.0510 0.9670 0.984 0.000 0.000 0.000 0.016
#> GSM23164 4 0.4620 0.4828 0.320 0.000 0.000 0.652 0.028
#> GSM23165 1 0.0510 0.9664 0.984 0.000 0.000 0.000 0.016
#> GSM23166 4 0.4949 0.3396 0.396 0.000 0.000 0.572 0.032
#> GSM23167 1 0.0510 0.9674 0.984 0.000 0.000 0.000 0.016
#> GSM23168 3 0.1571 0.8226 0.004 0.000 0.936 0.000 0.060
#> GSM23169 3 0.1638 0.8191 0.004 0.000 0.932 0.000 0.064
#> GSM23170 1 0.0162 0.9669 0.996 0.000 0.000 0.000 0.004
#> GSM23171 1 0.0162 0.9673 0.996 0.000 0.000 0.000 0.004
#> GSM23172 1 0.0404 0.9666 0.988 0.000 0.000 0.000 0.012
#> GSM23173 3 0.3897 0.6527 0.028 0.000 0.768 0.000 0.204
#> GSM23174 1 0.0671 0.9606 0.980 0.000 0.000 0.016 0.004
#> GSM23175 1 0.0671 0.9632 0.980 0.000 0.000 0.004 0.016
#> GSM23176 1 0.0510 0.9670 0.984 0.000 0.000 0.000 0.016
#> GSM23177 1 0.0703 0.9595 0.976 0.000 0.000 0.000 0.024
#> GSM23178 1 0.0162 0.9667 0.996 0.000 0.000 0.000 0.004
#> GSM23179 3 0.1341 0.8211 0.000 0.000 0.944 0.000 0.056
#> GSM23180 4 0.0794 0.6838 0.000 0.000 0.000 0.972 0.028
#> GSM23181 4 0.4297 0.6098 0.164 0.000 0.000 0.764 0.072
#> GSM23182 4 0.1792 0.6714 0.000 0.000 0.000 0.916 0.084
#> GSM23183 3 0.6704 -0.1396 0.204 0.000 0.416 0.004 0.376
#> GSM23184 3 0.2377 0.7929 0.000 0.000 0.872 0.000 0.128
#> GSM23196 2 0.0404 0.8048 0.000 0.988 0.000 0.000 0.012
#> GSM23197 2 0.2280 0.7597 0.000 0.880 0.000 0.000 0.120
#> GSM23198 2 0.1270 0.7952 0.000 0.948 0.000 0.000 0.052
#> GSM23199 2 0.2536 0.7561 0.000 0.868 0.000 0.004 0.128
#> GSM23200 2 0.3932 0.5379 0.000 0.672 0.000 0.000 0.328
#> GSM23201 4 0.0880 0.6790 0.000 0.032 0.000 0.968 0.000
#> GSM23202 4 0.2769 0.6438 0.000 0.032 0.000 0.876 0.092
#> GSM23203 2 0.0290 0.8051 0.000 0.992 0.000 0.000 0.008
#> GSM23204 2 0.2773 0.7278 0.000 0.836 0.000 0.000 0.164
#> GSM23205 2 0.4297 0.2142 0.000 0.528 0.000 0.472 0.000
#> GSM23206 2 0.0000 0.8051 0.000 1.000 0.000 0.000 0.000
#> GSM23207 2 0.4551 0.4461 0.000 0.616 0.000 0.016 0.368
#> GSM23208 2 0.0000 0.8051 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.1270 0.7917 0.000 0.948 0.000 0.000 0.052
#> GSM23210 2 0.2286 0.7690 0.000 0.888 0.000 0.004 0.108
#> GSM23211 2 0.0404 0.8034 0.000 0.988 0.000 0.000 0.012
#> GSM23212 2 0.6102 -0.0211 0.000 0.440 0.000 0.124 0.436
#> GSM23213 5 0.6498 -0.0702 0.000 0.224 0.000 0.292 0.484
#> GSM23214 4 0.5129 0.2498 0.000 0.056 0.000 0.616 0.328
#> GSM23215 2 0.2377 0.7572 0.000 0.872 0.000 0.000 0.128
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.4520 0.6472 0.000 0.000 0.704 0.168 0.000 0.128
#> GSM23186 1 0.4987 0.0963 0.516 0.000 0.004 0.040 0.008 0.432
#> GSM23187 3 0.1196 0.7960 0.000 0.000 0.952 0.008 0.000 0.040
#> GSM23188 3 0.2624 0.7614 0.000 0.000 0.856 0.020 0.000 0.124
#> GSM23189 3 0.1152 0.7966 0.000 0.000 0.952 0.004 0.000 0.044
#> GSM23190 3 0.3717 0.7290 0.000 0.000 0.780 0.148 0.000 0.072
#> GSM23191 5 0.3699 0.5503 0.000 0.000 0.040 0.036 0.812 0.112
#> GSM23192 6 0.5576 0.6013 0.004 0.000 0.112 0.064 0.152 0.668
#> GSM23193 3 0.3891 0.6691 0.000 0.000 0.768 0.004 0.164 0.064
#> GSM23194 3 0.3515 0.4835 0.000 0.000 0.676 0.000 0.000 0.324
#> GSM23195 6 0.6005 0.6749 0.036 0.000 0.148 0.256 0.000 0.560
#> GSM23159 1 0.1408 0.8778 0.944 0.000 0.000 0.020 0.000 0.036
#> GSM23160 3 0.2586 0.7825 0.000 0.000 0.868 0.032 0.000 0.100
#> GSM23161 1 0.5583 0.6256 0.652 0.000 0.000 0.060 0.116 0.172
#> GSM23162 3 0.1932 0.8019 0.000 0.000 0.924 0.020 0.016 0.040
#> GSM23163 1 0.2201 0.8683 0.896 0.000 0.000 0.028 0.000 0.076
#> GSM23164 5 0.5650 0.3610 0.284 0.000 0.000 0.040 0.588 0.088
#> GSM23165 1 0.0260 0.8884 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM23166 5 0.6190 0.2778 0.316 0.000 0.000 0.052 0.516 0.116
#> GSM23167 1 0.0692 0.8890 0.976 0.000 0.000 0.004 0.000 0.020
#> GSM23168 3 0.3585 0.7391 0.000 0.000 0.792 0.048 0.004 0.156
#> GSM23169 3 0.3703 0.7454 0.000 0.000 0.792 0.072 0.004 0.132
#> GSM23170 1 0.1421 0.8848 0.944 0.000 0.000 0.028 0.000 0.028
#> GSM23171 1 0.0000 0.8891 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23172 1 0.0146 0.8890 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM23173 3 0.4890 0.6657 0.032 0.000 0.708 0.096 0.000 0.164
#> GSM23174 1 0.1194 0.8845 0.956 0.000 0.000 0.004 0.032 0.008
#> GSM23175 1 0.1644 0.8772 0.932 0.000 0.000 0.028 0.000 0.040
#> GSM23176 1 0.1196 0.8858 0.952 0.000 0.000 0.008 0.000 0.040
#> GSM23177 1 0.3445 0.7764 0.796 0.000 0.000 0.048 0.000 0.156
#> GSM23178 1 0.0790 0.8847 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM23179 3 0.1908 0.7955 0.000 0.000 0.916 0.028 0.000 0.056
#> GSM23180 5 0.2311 0.5824 0.000 0.000 0.000 0.016 0.880 0.104
#> GSM23181 5 0.4934 0.4517 0.052 0.000 0.000 0.044 0.684 0.220
#> GSM23182 5 0.2538 0.5437 0.000 0.000 0.000 0.124 0.860 0.016
#> GSM23183 6 0.5662 0.7277 0.112 0.000 0.116 0.112 0.000 0.660
#> GSM23184 3 0.2445 0.7810 0.000 0.000 0.872 0.108 0.000 0.020
#> GSM23196 2 0.0632 0.7863 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM23197 2 0.1814 0.7515 0.000 0.900 0.000 0.100 0.000 0.000
#> GSM23198 2 0.1501 0.7582 0.000 0.924 0.000 0.076 0.000 0.000
#> GSM23199 2 0.3288 0.4878 0.000 0.724 0.000 0.276 0.000 0.000
#> GSM23200 2 0.3857 -0.1397 0.000 0.532 0.000 0.468 0.000 0.000
#> GSM23201 5 0.0748 0.5848 0.000 0.004 0.000 0.016 0.976 0.004
#> GSM23202 5 0.2734 0.5071 0.000 0.004 0.000 0.148 0.840 0.008
#> GSM23203 2 0.0458 0.7887 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM23204 2 0.2454 0.6991 0.000 0.840 0.000 0.160 0.000 0.000
#> GSM23205 5 0.4037 0.0111 0.000 0.380 0.000 0.012 0.608 0.000
#> GSM23206 2 0.0000 0.7898 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23207 2 0.3999 -0.2633 0.000 0.500 0.000 0.496 0.004 0.000
#> GSM23208 2 0.0146 0.7897 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM23209 2 0.1075 0.7783 0.000 0.952 0.000 0.048 0.000 0.000
#> GSM23210 2 0.2793 0.6253 0.000 0.800 0.000 0.200 0.000 0.000
#> GSM23211 2 0.0458 0.7875 0.000 0.984 0.000 0.016 0.000 0.000
#> GSM23212 4 0.5515 0.6056 0.000 0.320 0.000 0.528 0.152 0.000
#> GSM23213 4 0.5483 0.5703 0.000 0.124 0.000 0.584 0.280 0.012
#> GSM23214 5 0.4472 -0.3418 0.000 0.028 0.000 0.476 0.496 0.000
#> GSM23215 2 0.2146 0.7380 0.000 0.880 0.000 0.116 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 cell.type(p) disease.state(p) k
#> MAD:NMF 51 7.81e-12 2.06e-01 2
#> MAD:NMF 57 4.19e-13 4.23e-04 3
#> MAD:NMF 51 1.93e-09 5.28e-05 4
#> MAD:NMF 47 6.99e-09 2.87e-03 5
#> MAD:NMF 47 7.51e-08 3.52e-03 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 11993 rows and 57 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 0.501 0.881 0.931 0.4880 0.499 0.499
#> 3 3 0.651 0.863 0.888 0.3444 0.842 0.683
#> 4 4 0.826 0.892 0.933 0.1162 0.929 0.790
#> 5 5 0.816 0.872 0.860 0.0656 0.959 0.849
#> 6 6 0.839 0.869 0.875 0.0287 0.981 0.918
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
#> GSM23185 2 0.141 0.904 0.020 0.980
#> GSM23186 1 0.605 0.806 0.852 0.148
#> GSM23187 2 0.141 0.904 0.020 0.980
#> GSM23188 2 0.141 0.904 0.020 0.980
#> GSM23189 2 0.141 0.904 0.020 0.980
#> GSM23190 2 0.141 0.904 0.020 0.980
#> GSM23191 2 0.814 0.769 0.252 0.748
#> GSM23192 2 0.781 0.793 0.232 0.768
#> GSM23193 2 0.955 0.548 0.376 0.624
#> GSM23194 2 0.295 0.898 0.052 0.948
#> GSM23195 2 0.781 0.793 0.232 0.768
#> GSM23159 1 0.000 0.948 1.000 0.000
#> GSM23160 2 0.595 0.862 0.144 0.856
#> GSM23161 1 0.000 0.948 1.000 0.000
#> GSM23162 2 0.753 0.808 0.216 0.784
#> GSM23163 1 0.000 0.948 1.000 0.000
#> GSM23164 1 0.000 0.948 1.000 0.000
#> GSM23165 1 0.000 0.948 1.000 0.000
#> GSM23166 1 0.000 0.948 1.000 0.000
#> GSM23167 1 0.000 0.948 1.000 0.000
#> GSM23168 2 0.595 0.862 0.144 0.856
#> GSM23169 2 0.767 0.800 0.224 0.776
#> GSM23170 1 0.000 0.948 1.000 0.000
#> GSM23171 1 0.000 0.948 1.000 0.000
#> GSM23172 1 0.000 0.948 1.000 0.000
#> GSM23173 2 0.753 0.808 0.216 0.784
#> GSM23174 1 0.000 0.948 1.000 0.000
#> GSM23175 1 0.000 0.948 1.000 0.000
#> GSM23176 1 0.000 0.948 1.000 0.000
#> GSM23177 1 0.000 0.948 1.000 0.000
#> GSM23178 1 0.000 0.948 1.000 0.000
#> GSM23179 2 0.295 0.898 0.052 0.948
#> GSM23180 1 0.000 0.948 1.000 0.000
#> GSM23181 1 0.000 0.948 1.000 0.000
#> GSM23182 1 0.000 0.948 1.000 0.000
#> GSM23183 2 0.781 0.793 0.232 0.768
#> GSM23184 2 0.529 0.875 0.120 0.880
#> GSM23196 2 0.000 0.902 0.000 1.000
#> GSM23197 2 0.000 0.902 0.000 1.000
#> GSM23198 2 0.000 0.902 0.000 1.000
#> GSM23199 2 0.563 0.863 0.132 0.868
#> GSM23200 2 0.000 0.902 0.000 1.000
#> GSM23201 1 0.839 0.641 0.732 0.268
#> GSM23202 1 0.482 0.875 0.896 0.104
#> GSM23203 2 0.000 0.902 0.000 1.000
#> GSM23204 2 0.000 0.902 0.000 1.000
#> GSM23205 1 0.839 0.641 0.732 0.268
#> GSM23206 2 0.000 0.902 0.000 1.000
#> GSM23207 2 0.000 0.902 0.000 1.000
#> GSM23208 2 0.000 0.902 0.000 1.000
#> GSM23209 2 0.000 0.902 0.000 1.000
#> GSM23210 2 0.563 0.863 0.132 0.868
#> GSM23211 2 0.000 0.902 0.000 1.000
#> GSM23212 1 0.482 0.875 0.896 0.104
#> GSM23213 1 0.482 0.875 0.896 0.104
#> GSM23214 1 0.482 0.875 0.896 0.104
#> GSM23215 2 0.000 0.902 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.4605 0.837 0.000 0.204 0.796
#> GSM23186 1 0.4351 0.737 0.828 0.004 0.168
#> GSM23187 3 0.4605 0.837 0.000 0.204 0.796
#> GSM23188 3 0.4605 0.837 0.000 0.204 0.796
#> GSM23189 3 0.4605 0.837 0.000 0.204 0.796
#> GSM23190 3 0.4605 0.837 0.000 0.204 0.796
#> GSM23191 3 0.4551 0.840 0.140 0.020 0.840
#> GSM23192 3 0.4446 0.866 0.112 0.032 0.856
#> GSM23193 3 0.5058 0.675 0.244 0.000 0.756
#> GSM23194 3 0.4178 0.853 0.000 0.172 0.828
#> GSM23195 3 0.4446 0.866 0.112 0.032 0.856
#> GSM23159 1 0.0000 0.896 1.000 0.000 0.000
#> GSM23160 3 0.5179 0.881 0.080 0.088 0.832
#> GSM23161 1 0.0000 0.896 1.000 0.000 0.000
#> GSM23162 3 0.4335 0.873 0.100 0.036 0.864
#> GSM23163 1 0.0892 0.889 0.980 0.000 0.020
#> GSM23164 1 0.0000 0.896 1.000 0.000 0.000
#> GSM23165 1 0.0892 0.889 0.980 0.000 0.020
#> GSM23166 1 0.0000 0.896 1.000 0.000 0.000
#> GSM23167 1 0.0892 0.889 0.980 0.000 0.020
#> GSM23168 3 0.5179 0.881 0.080 0.088 0.832
#> GSM23169 3 0.4489 0.870 0.108 0.036 0.856
#> GSM23170 1 0.0000 0.896 1.000 0.000 0.000
#> GSM23171 1 0.0000 0.896 1.000 0.000 0.000
#> GSM23172 1 0.0000 0.896 1.000 0.000 0.000
#> GSM23173 3 0.4335 0.873 0.100 0.036 0.864
#> GSM23174 1 0.0000 0.896 1.000 0.000 0.000
#> GSM23175 1 0.2261 0.874 0.932 0.000 0.068
#> GSM23176 1 0.0892 0.889 0.980 0.000 0.020
#> GSM23177 1 0.0000 0.896 1.000 0.000 0.000
#> GSM23178 1 0.0892 0.889 0.980 0.000 0.020
#> GSM23179 3 0.4178 0.853 0.000 0.172 0.828
#> GSM23180 1 0.2878 0.861 0.904 0.000 0.096
#> GSM23181 1 0.0000 0.896 1.000 0.000 0.000
#> GSM23182 1 0.2261 0.874 0.932 0.000 0.068
#> GSM23183 3 0.4446 0.866 0.112 0.032 0.856
#> GSM23184 3 0.5229 0.877 0.068 0.104 0.828
#> GSM23196 2 0.0000 0.968 0.000 1.000 0.000
#> GSM23197 2 0.0000 0.968 0.000 1.000 0.000
#> GSM23198 2 0.0000 0.968 0.000 1.000 0.000
#> GSM23199 2 0.3551 0.842 0.000 0.868 0.132
#> GSM23200 2 0.0000 0.968 0.000 1.000 0.000
#> GSM23201 1 0.8648 0.543 0.548 0.120 0.332
#> GSM23202 1 0.7360 0.738 0.692 0.096 0.212
#> GSM23203 2 0.0000 0.968 0.000 1.000 0.000
#> GSM23204 2 0.0000 0.968 0.000 1.000 0.000
#> GSM23205 1 0.8648 0.543 0.548 0.120 0.332
#> GSM23206 2 0.0000 0.968 0.000 1.000 0.000
#> GSM23207 2 0.0000 0.968 0.000 1.000 0.000
#> GSM23208 2 0.0000 0.968 0.000 1.000 0.000
#> GSM23209 2 0.0000 0.968 0.000 1.000 0.000
#> GSM23210 2 0.5363 0.687 0.000 0.724 0.276
#> GSM23211 2 0.0000 0.968 0.000 1.000 0.000
#> GSM23212 1 0.7360 0.738 0.692 0.096 0.212
#> GSM23213 1 0.7360 0.738 0.692 0.096 0.212
#> GSM23214 1 0.7360 0.738 0.692 0.096 0.212
#> GSM23215 2 0.0000 0.968 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.2413 0.865 0.000 0.064 0.916 0.020
#> GSM23186 1 0.3306 0.781 0.840 0.000 0.156 0.004
#> GSM23187 3 0.2413 0.865 0.000 0.064 0.916 0.020
#> GSM23188 3 0.2413 0.865 0.000 0.064 0.916 0.020
#> GSM23189 3 0.2413 0.865 0.000 0.064 0.916 0.020
#> GSM23190 3 0.2413 0.865 0.000 0.064 0.916 0.020
#> GSM23191 3 0.3984 0.829 0.040 0.000 0.828 0.132
#> GSM23192 3 0.3612 0.856 0.044 0.000 0.856 0.100
#> GSM23193 3 0.5598 0.663 0.076 0.000 0.704 0.220
#> GSM23194 3 0.1474 0.874 0.000 0.052 0.948 0.000
#> GSM23195 3 0.3612 0.856 0.044 0.000 0.856 0.100
#> GSM23159 1 0.0707 0.944 0.980 0.000 0.000 0.020
#> GSM23160 3 0.1520 0.884 0.024 0.000 0.956 0.020
#> GSM23161 1 0.0707 0.944 0.980 0.000 0.000 0.020
#> GSM23162 3 0.3051 0.870 0.028 0.000 0.884 0.088
#> GSM23163 1 0.0188 0.936 0.996 0.000 0.004 0.000
#> GSM23164 1 0.0707 0.944 0.980 0.000 0.000 0.020
#> GSM23165 1 0.0188 0.936 0.996 0.000 0.004 0.000
#> GSM23166 1 0.0707 0.944 0.980 0.000 0.000 0.020
#> GSM23167 1 0.0188 0.936 0.996 0.000 0.004 0.000
#> GSM23168 3 0.1520 0.884 0.024 0.000 0.956 0.020
#> GSM23169 3 0.3182 0.867 0.028 0.000 0.876 0.096
#> GSM23170 1 0.0707 0.944 0.980 0.000 0.000 0.020
#> GSM23171 1 0.0707 0.944 0.980 0.000 0.000 0.020
#> GSM23172 1 0.0707 0.944 0.980 0.000 0.000 0.020
#> GSM23173 3 0.3051 0.870 0.028 0.000 0.884 0.088
#> GSM23174 1 0.0707 0.944 0.980 0.000 0.000 0.020
#> GSM23175 1 0.3486 0.798 0.812 0.000 0.000 0.188
#> GSM23176 1 0.0188 0.936 0.996 0.000 0.004 0.000
#> GSM23177 1 0.0707 0.944 0.980 0.000 0.000 0.020
#> GSM23178 1 0.0188 0.936 0.996 0.000 0.004 0.000
#> GSM23179 3 0.1474 0.874 0.000 0.052 0.948 0.000
#> GSM23180 1 0.5328 0.651 0.704 0.000 0.048 0.248
#> GSM23181 1 0.0707 0.944 0.980 0.000 0.000 0.020
#> GSM23182 1 0.3649 0.779 0.796 0.000 0.000 0.204
#> GSM23183 3 0.3612 0.856 0.044 0.000 0.856 0.100
#> GSM23184 3 0.0707 0.882 0.020 0.000 0.980 0.000
#> GSM23196 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM23199 2 0.3024 0.807 0.000 0.852 0.000 0.148
#> GSM23200 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM23201 4 0.3157 0.836 0.000 0.004 0.144 0.852
#> GSM23202 4 0.0707 0.929 0.000 0.000 0.020 0.980
#> GSM23203 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM23205 4 0.3157 0.836 0.000 0.004 0.144 0.852
#> GSM23206 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM23207 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM23208 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM23210 2 0.6031 0.571 0.000 0.688 0.144 0.168
#> GSM23211 2 0.0000 0.962 0.000 1.000 0.000 0.000
#> GSM23212 4 0.0707 0.929 0.000 0.000 0.020 0.980
#> GSM23213 4 0.0707 0.929 0.000 0.000 0.020 0.980
#> GSM23214 4 0.0707 0.929 0.000 0.000 0.020 0.980
#> GSM23215 2 0.0000 0.962 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.3661 1.000 0.000 0.000 0.724 0.000 0.276
#> GSM23186 1 0.4993 0.742 0.684 0.000 0.248 0.004 0.064
#> GSM23187 3 0.3661 1.000 0.000 0.000 0.724 0.000 0.276
#> GSM23188 3 0.3661 1.000 0.000 0.000 0.724 0.000 0.276
#> GSM23189 3 0.3661 1.000 0.000 0.000 0.724 0.000 0.276
#> GSM23190 3 0.3661 1.000 0.000 0.000 0.724 0.000 0.276
#> GSM23191 5 0.1981 0.806 0.016 0.000 0.000 0.064 0.920
#> GSM23192 5 0.3183 0.763 0.000 0.000 0.156 0.016 0.828
#> GSM23193 5 0.4231 0.697 0.052 0.000 0.020 0.132 0.796
#> GSM23194 5 0.3143 0.664 0.000 0.000 0.204 0.000 0.796
#> GSM23195 5 0.3183 0.763 0.000 0.000 0.156 0.016 0.828
#> GSM23159 1 0.0000 0.907 1.000 0.000 0.000 0.000 0.000
#> GSM23160 5 0.1638 0.806 0.004 0.000 0.064 0.000 0.932
#> GSM23161 1 0.0000 0.907 1.000 0.000 0.000 0.000 0.000
#> GSM23162 5 0.0771 0.828 0.004 0.000 0.000 0.020 0.976
#> GSM23163 1 0.2921 0.862 0.844 0.000 0.148 0.004 0.004
#> GSM23164 1 0.0000 0.907 1.000 0.000 0.000 0.000 0.000
#> GSM23165 1 0.2921 0.862 0.844 0.000 0.148 0.004 0.004
#> GSM23166 1 0.0000 0.907 1.000 0.000 0.000 0.000 0.000
#> GSM23167 1 0.2921 0.862 0.844 0.000 0.148 0.004 0.004
#> GSM23168 5 0.1638 0.806 0.004 0.000 0.064 0.000 0.932
#> GSM23169 5 0.0955 0.827 0.004 0.000 0.000 0.028 0.968
#> GSM23170 1 0.0162 0.907 0.996 0.000 0.004 0.000 0.000
#> GSM23171 1 0.0000 0.907 1.000 0.000 0.000 0.000 0.000
#> GSM23172 1 0.0162 0.907 0.996 0.000 0.004 0.000 0.000
#> GSM23173 5 0.0771 0.828 0.004 0.000 0.000 0.020 0.976
#> GSM23174 1 0.0000 0.907 1.000 0.000 0.000 0.000 0.000
#> GSM23175 1 0.3805 0.793 0.828 0.000 0.020 0.108 0.044
#> GSM23176 1 0.2921 0.862 0.844 0.000 0.148 0.004 0.004
#> GSM23177 1 0.0000 0.907 1.000 0.000 0.000 0.000 0.000
#> GSM23178 1 0.2921 0.862 0.844 0.000 0.148 0.004 0.004
#> GSM23179 5 0.3039 0.658 0.000 0.000 0.192 0.000 0.808
#> GSM23180 1 0.5638 0.631 0.680 0.000 0.020 0.168 0.132
#> GSM23181 1 0.0000 0.907 1.000 0.000 0.000 0.000 0.000
#> GSM23182 1 0.4045 0.778 0.812 0.000 0.020 0.116 0.052
#> GSM23183 5 0.3183 0.763 0.000 0.000 0.156 0.016 0.828
#> GSM23184 5 0.2488 0.755 0.004 0.000 0.124 0.000 0.872
#> GSM23196 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM23199 2 0.2877 0.815 0.000 0.848 0.004 0.144 0.004
#> GSM23200 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM23201 4 0.2930 0.847 0.000 0.000 0.164 0.832 0.004
#> GSM23202 4 0.0290 0.931 0.000 0.000 0.000 0.992 0.008
#> GSM23203 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM23205 4 0.2930 0.847 0.000 0.000 0.164 0.832 0.004
#> GSM23206 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM23207 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM23208 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM23210 2 0.5350 0.602 0.000 0.684 0.164 0.148 0.004
#> GSM23211 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM23212 4 0.0290 0.931 0.000 0.000 0.000 0.992 0.008
#> GSM23213 4 0.0290 0.931 0.000 0.000 0.000 0.992 0.008
#> GSM23214 4 0.0290 0.931 0.000 0.000 0.000 0.992 0.008
#> GSM23215 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23186 1 0.5331 0.622 0.580 0.000 0.000 0.000 0.152 0.268
#> GSM23187 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23188 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23189 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23190 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23191 5 0.3358 0.777 0.008 0.000 0.116 0.052 0.824 0.000
#> GSM23192 6 0.3405 1.000 0.000 0.000 0.000 0.004 0.272 0.724
#> GSM23193 5 0.4228 0.602 0.044 0.000 0.060 0.120 0.776 0.000
#> GSM23194 5 0.4798 0.674 0.000 0.000 0.376 0.000 0.564 0.060
#> GSM23195 6 0.3405 1.000 0.000 0.000 0.000 0.004 0.272 0.724
#> GSM23159 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23160 5 0.3076 0.831 0.000 0.000 0.240 0.000 0.760 0.000
#> GSM23161 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23162 5 0.2778 0.829 0.000 0.000 0.168 0.008 0.824 0.000
#> GSM23163 1 0.4190 0.777 0.740 0.000 0.000 0.000 0.148 0.112
#> GSM23164 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23165 1 0.4190 0.777 0.740 0.000 0.000 0.000 0.148 0.112
#> GSM23166 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23167 1 0.4190 0.777 0.740 0.000 0.000 0.000 0.148 0.112
#> GSM23168 5 0.3076 0.831 0.000 0.000 0.240 0.000 0.760 0.000
#> GSM23169 5 0.2968 0.827 0.000 0.000 0.168 0.016 0.816 0.000
#> GSM23170 1 0.0146 0.868 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM23171 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23172 1 0.0291 0.867 0.992 0.000 0.000 0.000 0.004 0.004
#> GSM23173 5 0.2778 0.829 0.000 0.000 0.168 0.008 0.824 0.000
#> GSM23174 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23175 1 0.3274 0.758 0.824 0.000 0.000 0.096 0.080 0.000
#> GSM23176 1 0.4190 0.777 0.740 0.000 0.000 0.000 0.148 0.112
#> GSM23177 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23178 1 0.4190 0.777 0.740 0.000 0.000 0.000 0.148 0.112
#> GSM23179 5 0.3717 0.714 0.000 0.000 0.384 0.000 0.616 0.000
#> GSM23180 1 0.4798 0.624 0.672 0.000 0.000 0.156 0.172 0.000
#> GSM23181 1 0.0000 0.869 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23182 1 0.3469 0.743 0.808 0.000 0.000 0.104 0.088 0.000
#> GSM23183 6 0.3405 1.000 0.000 0.000 0.000 0.004 0.272 0.724
#> GSM23184 5 0.3446 0.796 0.000 0.000 0.308 0.000 0.692 0.000
#> GSM23196 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23199 2 0.2624 0.814 0.000 0.844 0.000 0.148 0.004 0.004
#> GSM23200 2 0.0146 0.961 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM23201 4 0.2632 0.878 0.000 0.000 0.000 0.832 0.004 0.164
#> GSM23202 4 0.0000 0.941 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23203 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23205 4 0.2632 0.878 0.000 0.000 0.000 0.832 0.004 0.164
#> GSM23206 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23207 2 0.0146 0.961 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM23208 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23210 2 0.4838 0.613 0.000 0.680 0.000 0.148 0.004 0.168
#> GSM23211 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23212 4 0.0000 0.941 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23213 4 0.0000 0.941 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23214 4 0.0000 0.941 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23215 2 0.0000 0.963 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> ATC:hclust 57 2.04e-01 2.51e-02 2
#> ATC:hclust 57 9.33e-09 1.67e-04 3
#> ATC:hclust 57 2.57e-12 3.86e-04 4
#> ATC:hclust 57 1.24e-11 9.27e-05 5
#> ATC:hclust 57 5.06e-11 2.13e-04 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 11993 rows and 57 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 0.781 0.872 0.944 0.5000 0.491 0.491
#> 3 3 0.768 0.800 0.902 0.3446 0.685 0.448
#> 4 4 0.774 0.795 0.878 0.1076 0.915 0.750
#> 5 5 0.770 0.771 0.837 0.0568 0.922 0.719
#> 6 6 0.796 0.588 0.824 0.0426 0.977 0.894
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
#> GSM23185 2 0.2043 0.9219 0.032 0.968
#> GSM23186 1 0.0000 0.9451 1.000 0.000
#> GSM23187 2 0.2043 0.9219 0.032 0.968
#> GSM23188 2 0.2043 0.9219 0.032 0.968
#> GSM23189 2 0.2043 0.9219 0.032 0.968
#> GSM23190 2 0.2043 0.9219 0.032 0.968
#> GSM23191 1 0.8713 0.5342 0.708 0.292
#> GSM23192 1 0.0672 0.9409 0.992 0.008
#> GSM23193 1 0.0672 0.9409 0.992 0.008
#> GSM23194 2 0.6438 0.8261 0.164 0.836
#> GSM23195 2 0.8608 0.6642 0.284 0.716
#> GSM23159 1 0.0000 0.9451 1.000 0.000
#> GSM23160 2 0.9209 0.5640 0.336 0.664
#> GSM23161 1 0.0000 0.9451 1.000 0.000
#> GSM23162 1 0.9944 0.0582 0.544 0.456
#> GSM23163 1 0.0000 0.9451 1.000 0.000
#> GSM23164 1 0.0000 0.9451 1.000 0.000
#> GSM23165 1 0.0000 0.9451 1.000 0.000
#> GSM23166 1 0.0000 0.9451 1.000 0.000
#> GSM23167 1 0.0000 0.9451 1.000 0.000
#> GSM23168 2 0.7139 0.7913 0.196 0.804
#> GSM23169 1 0.0672 0.9409 0.992 0.008
#> GSM23170 1 0.0000 0.9451 1.000 0.000
#> GSM23171 1 0.0000 0.9451 1.000 0.000
#> GSM23172 1 0.0000 0.9451 1.000 0.000
#> GSM23173 1 0.9954 0.0421 0.540 0.460
#> GSM23174 1 0.0000 0.9451 1.000 0.000
#> GSM23175 1 0.0000 0.9451 1.000 0.000
#> GSM23176 1 0.0000 0.9451 1.000 0.000
#> GSM23177 1 0.0000 0.9451 1.000 0.000
#> GSM23178 1 0.0000 0.9451 1.000 0.000
#> GSM23179 2 0.3114 0.9119 0.056 0.944
#> GSM23180 1 0.0000 0.9451 1.000 0.000
#> GSM23181 1 0.0000 0.9451 1.000 0.000
#> GSM23182 1 0.0000 0.9451 1.000 0.000
#> GSM23183 1 0.0672 0.9409 0.992 0.008
#> GSM23184 2 0.6531 0.8219 0.168 0.832
#> GSM23196 2 0.0000 0.9281 0.000 1.000
#> GSM23197 2 0.0000 0.9281 0.000 1.000
#> GSM23198 2 0.0000 0.9281 0.000 1.000
#> GSM23199 2 0.0000 0.9281 0.000 1.000
#> GSM23200 2 0.0000 0.9281 0.000 1.000
#> GSM23201 2 0.8861 0.6038 0.304 0.696
#> GSM23202 1 0.2043 0.9199 0.968 0.032
#> GSM23203 2 0.0000 0.9281 0.000 1.000
#> GSM23204 2 0.0000 0.9281 0.000 1.000
#> GSM23205 2 0.3733 0.8969 0.072 0.928
#> GSM23206 2 0.0000 0.9281 0.000 1.000
#> GSM23207 2 0.0000 0.9281 0.000 1.000
#> GSM23208 2 0.0000 0.9281 0.000 1.000
#> GSM23209 2 0.0000 0.9281 0.000 1.000
#> GSM23210 2 0.0000 0.9281 0.000 1.000
#> GSM23211 2 0.0000 0.9281 0.000 1.000
#> GSM23212 2 0.3733 0.8969 0.072 0.928
#> GSM23213 1 0.2603 0.9152 0.956 0.044
#> GSM23214 1 0.2603 0.9152 0.956 0.044
#> GSM23215 2 0.0000 0.9281 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.6286 0.266 0.000 0.464 0.536
#> GSM23186 1 0.0237 0.952 0.996 0.000 0.004
#> GSM23187 3 0.6286 0.266 0.000 0.464 0.536
#> GSM23188 3 0.6305 0.212 0.000 0.484 0.516
#> GSM23189 3 0.6286 0.266 0.000 0.464 0.536
#> GSM23190 3 0.6286 0.266 0.000 0.464 0.536
#> GSM23191 3 0.1525 0.793 0.032 0.004 0.964
#> GSM23192 3 0.1529 0.790 0.040 0.000 0.960
#> GSM23193 3 0.1411 0.792 0.036 0.000 0.964
#> GSM23194 3 0.1919 0.792 0.024 0.020 0.956
#> GSM23195 3 0.1163 0.792 0.028 0.000 0.972
#> GSM23159 1 0.0000 0.953 1.000 0.000 0.000
#> GSM23160 3 0.1919 0.792 0.024 0.020 0.956
#> GSM23161 1 0.0000 0.953 1.000 0.000 0.000
#> GSM23162 3 0.1525 0.793 0.032 0.004 0.964
#> GSM23163 1 0.0237 0.952 0.996 0.000 0.004
#> GSM23164 1 0.0000 0.953 1.000 0.000 0.000
#> GSM23165 1 0.0237 0.952 0.996 0.000 0.004
#> GSM23166 1 0.0000 0.953 1.000 0.000 0.000
#> GSM23167 1 0.0237 0.952 0.996 0.000 0.004
#> GSM23168 3 0.1919 0.792 0.024 0.020 0.956
#> GSM23169 3 0.1289 0.792 0.032 0.000 0.968
#> GSM23170 1 0.0000 0.953 1.000 0.000 0.000
#> GSM23171 1 0.0000 0.953 1.000 0.000 0.000
#> GSM23172 1 0.0000 0.953 1.000 0.000 0.000
#> GSM23173 3 0.1289 0.792 0.032 0.000 0.968
#> GSM23174 1 0.0000 0.953 1.000 0.000 0.000
#> GSM23175 1 0.0000 0.953 1.000 0.000 0.000
#> GSM23176 1 0.0237 0.952 0.996 0.000 0.004
#> GSM23177 1 0.0000 0.953 1.000 0.000 0.000
#> GSM23178 1 0.0237 0.952 0.996 0.000 0.004
#> GSM23179 3 0.1919 0.790 0.020 0.024 0.956
#> GSM23180 1 0.3412 0.830 0.876 0.000 0.124
#> GSM23181 1 0.0000 0.953 1.000 0.000 0.000
#> GSM23182 1 0.4654 0.721 0.792 0.000 0.208
#> GSM23183 3 0.1529 0.790 0.040 0.000 0.960
#> GSM23184 3 0.1919 0.792 0.024 0.020 0.956
#> GSM23196 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23197 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23198 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23199 2 0.1529 0.965 0.000 0.960 0.040
#> GSM23200 2 0.1529 0.965 0.000 0.960 0.040
#> GSM23201 3 0.2796 0.731 0.000 0.092 0.908
#> GSM23202 1 0.6944 0.164 0.516 0.016 0.468
#> GSM23203 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23204 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23205 3 0.5905 0.430 0.000 0.352 0.648
#> GSM23206 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23207 2 0.1529 0.965 0.000 0.960 0.040
#> GSM23208 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23209 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23210 2 0.1529 0.965 0.000 0.960 0.040
#> GSM23211 2 0.0000 0.986 0.000 1.000 0.000
#> GSM23212 3 0.5905 0.430 0.000 0.352 0.648
#> GSM23213 3 0.7931 0.412 0.284 0.092 0.624
#> GSM23214 3 0.7931 0.412 0.284 0.092 0.624
#> GSM23215 2 0.0000 0.986 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.2921 0.664 0.000 0.140 0.860 0.000
#> GSM23186 1 0.2124 0.928 0.924 0.000 0.008 0.068
#> GSM23187 3 0.2921 0.664 0.000 0.140 0.860 0.000
#> GSM23188 3 0.2921 0.664 0.000 0.140 0.860 0.000
#> GSM23189 3 0.2921 0.664 0.000 0.140 0.860 0.000
#> GSM23190 3 0.2921 0.664 0.000 0.140 0.860 0.000
#> GSM23191 3 0.4916 0.455 0.000 0.000 0.576 0.424
#> GSM23192 3 0.4477 0.599 0.000 0.000 0.688 0.312
#> GSM23193 3 0.4916 0.455 0.000 0.000 0.576 0.424
#> GSM23194 3 0.2011 0.699 0.000 0.000 0.920 0.080
#> GSM23195 3 0.4454 0.599 0.000 0.000 0.692 0.308
#> GSM23159 1 0.0817 0.947 0.976 0.000 0.000 0.024
#> GSM23160 3 0.0336 0.709 0.000 0.000 0.992 0.008
#> GSM23161 1 0.0817 0.947 0.976 0.000 0.000 0.024
#> GSM23162 3 0.4907 0.462 0.000 0.000 0.580 0.420
#> GSM23163 1 0.2124 0.928 0.924 0.000 0.008 0.068
#> GSM23164 1 0.0817 0.947 0.976 0.000 0.000 0.024
#> GSM23165 1 0.2124 0.928 0.924 0.000 0.008 0.068
#> GSM23166 1 0.0817 0.947 0.976 0.000 0.000 0.024
#> GSM23167 1 0.1557 0.935 0.944 0.000 0.000 0.056
#> GSM23168 3 0.0336 0.709 0.000 0.000 0.992 0.008
#> GSM23169 3 0.4907 0.462 0.000 0.000 0.580 0.420
#> GSM23170 1 0.0707 0.944 0.980 0.000 0.000 0.020
#> GSM23171 1 0.0817 0.947 0.976 0.000 0.000 0.024
#> GSM23172 1 0.0592 0.944 0.984 0.000 0.000 0.016
#> GSM23173 3 0.4697 0.553 0.000 0.000 0.644 0.356
#> GSM23174 1 0.0000 0.946 1.000 0.000 0.000 0.000
#> GSM23175 1 0.0817 0.947 0.976 0.000 0.000 0.024
#> GSM23176 1 0.2124 0.928 0.924 0.000 0.008 0.068
#> GSM23177 1 0.0817 0.947 0.976 0.000 0.000 0.024
#> GSM23178 1 0.2124 0.928 0.924 0.000 0.008 0.068
#> GSM23179 3 0.0336 0.709 0.000 0.000 0.992 0.008
#> GSM23180 1 0.4103 0.612 0.744 0.000 0.000 0.256
#> GSM23181 1 0.0817 0.947 0.976 0.000 0.000 0.024
#> GSM23182 4 0.4972 0.134 0.456 0.000 0.000 0.544
#> GSM23183 3 0.4477 0.599 0.000 0.000 0.688 0.312
#> GSM23184 3 0.0336 0.709 0.000 0.000 0.992 0.008
#> GSM23196 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM23199 2 0.4500 0.648 0.000 0.684 0.000 0.316
#> GSM23200 2 0.1637 0.910 0.000 0.940 0.000 0.060
#> GSM23201 4 0.2530 0.824 0.000 0.000 0.112 0.888
#> GSM23202 4 0.2563 0.842 0.020 0.000 0.072 0.908
#> GSM23203 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM23205 4 0.2699 0.834 0.000 0.028 0.068 0.904
#> GSM23206 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM23207 2 0.2647 0.868 0.000 0.880 0.000 0.120
#> GSM23208 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM23210 2 0.4304 0.694 0.000 0.716 0.000 0.284
#> GSM23211 2 0.0000 0.942 0.000 1.000 0.000 0.000
#> GSM23212 4 0.2623 0.832 0.000 0.028 0.064 0.908
#> GSM23213 4 0.2334 0.848 0.004 0.000 0.088 0.908
#> GSM23214 4 0.2334 0.848 0.004 0.000 0.088 0.908
#> GSM23215 2 0.0000 0.942 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.4029 0.8779 0.000 0.024 0.744 0.000 0.232
#> GSM23186 1 0.6343 0.7344 0.644 0.000 0.140 0.064 0.152
#> GSM23187 3 0.4029 0.8779 0.000 0.024 0.744 0.000 0.232
#> GSM23188 3 0.4029 0.8779 0.000 0.024 0.744 0.000 0.232
#> GSM23189 3 0.4029 0.8779 0.000 0.024 0.744 0.000 0.232
#> GSM23190 3 0.4029 0.8779 0.000 0.024 0.744 0.000 0.232
#> GSM23191 5 0.3401 0.8160 0.000 0.000 0.064 0.096 0.840
#> GSM23192 5 0.1430 0.7471 0.000 0.000 0.052 0.004 0.944
#> GSM23193 5 0.3454 0.8142 0.000 0.000 0.064 0.100 0.836
#> GSM23194 5 0.4210 -0.2176 0.000 0.000 0.412 0.000 0.588
#> GSM23195 5 0.1670 0.7466 0.000 0.000 0.052 0.012 0.936
#> GSM23159 1 0.0162 0.8652 0.996 0.000 0.000 0.000 0.004
#> GSM23160 3 0.4150 0.8051 0.000 0.000 0.612 0.000 0.388
#> GSM23161 1 0.0162 0.8652 0.996 0.000 0.000 0.000 0.004
#> GSM23162 5 0.3464 0.8159 0.000 0.000 0.068 0.096 0.836
#> GSM23163 1 0.5087 0.8055 0.748 0.000 0.136 0.060 0.056
#> GSM23164 1 0.0000 0.8657 1.000 0.000 0.000 0.000 0.000
#> GSM23165 1 0.5149 0.8036 0.744 0.000 0.136 0.064 0.056
#> GSM23166 1 0.0000 0.8657 1.000 0.000 0.000 0.000 0.000
#> GSM23167 1 0.3971 0.8269 0.804 0.000 0.136 0.052 0.008
#> GSM23168 3 0.4150 0.8051 0.000 0.000 0.612 0.000 0.388
#> GSM23169 5 0.3390 0.8143 0.000 0.000 0.060 0.100 0.840
#> GSM23170 1 0.2753 0.8481 0.876 0.000 0.104 0.012 0.008
#> GSM23171 1 0.0000 0.8657 1.000 0.000 0.000 0.000 0.000
#> GSM23172 1 0.2352 0.8523 0.896 0.000 0.092 0.004 0.008
#> GSM23173 5 0.3410 0.8147 0.000 0.000 0.068 0.092 0.840
#> GSM23174 1 0.0000 0.8657 1.000 0.000 0.000 0.000 0.000
#> GSM23175 1 0.0162 0.8652 0.996 0.000 0.000 0.000 0.004
#> GSM23176 1 0.5149 0.8036 0.744 0.000 0.136 0.064 0.056
#> GSM23177 1 0.0162 0.8652 0.996 0.000 0.000 0.000 0.004
#> GSM23178 1 0.5149 0.8036 0.744 0.000 0.136 0.064 0.056
#> GSM23179 3 0.4088 0.8210 0.000 0.000 0.632 0.000 0.368
#> GSM23180 1 0.4905 0.5604 0.696 0.000 0.000 0.080 0.224
#> GSM23181 1 0.0162 0.8652 0.996 0.000 0.000 0.000 0.004
#> GSM23182 1 0.6365 0.2489 0.520 0.000 0.000 0.252 0.228
#> GSM23183 5 0.1430 0.7471 0.000 0.000 0.052 0.004 0.944
#> GSM23184 3 0.4088 0.8210 0.000 0.000 0.632 0.000 0.368
#> GSM23196 2 0.0000 0.8948 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.8948 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.8948 0.000 1.000 0.000 0.000 0.000
#> GSM23199 4 0.6032 -0.1551 0.000 0.424 0.116 0.460 0.000
#> GSM23200 2 0.4844 0.6497 0.000 0.720 0.108 0.172 0.000
#> GSM23201 4 0.2358 0.8643 0.000 0.000 0.008 0.888 0.104
#> GSM23202 4 0.2179 0.8672 0.004 0.000 0.000 0.896 0.100
#> GSM23203 2 0.0000 0.8948 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.8948 0.000 1.000 0.000 0.000 0.000
#> GSM23205 4 0.2349 0.8621 0.000 0.004 0.012 0.900 0.084
#> GSM23206 2 0.0000 0.8948 0.000 1.000 0.000 0.000 0.000
#> GSM23207 2 0.5535 0.4913 0.000 0.620 0.108 0.272 0.000
#> GSM23208 2 0.0000 0.8948 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.8948 0.000 1.000 0.000 0.000 0.000
#> GSM23210 2 0.6037 0.0153 0.000 0.444 0.116 0.440 0.000
#> GSM23211 2 0.0000 0.8948 0.000 1.000 0.000 0.000 0.000
#> GSM23212 4 0.1731 0.8492 0.000 0.004 0.004 0.932 0.060
#> GSM23213 4 0.2179 0.8672 0.004 0.000 0.000 0.896 0.100
#> GSM23214 4 0.2179 0.8672 0.004 0.000 0.000 0.896 0.100
#> GSM23215 2 0.0000 0.8948 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.1625 0.8402 0.000 0.012 0.928 0.000 0.060 0.000
#> GSM23186 6 0.4315 0.0000 0.328 0.000 0.000 0.000 0.036 0.636
#> GSM23187 3 0.1625 0.8402 0.000 0.012 0.928 0.000 0.060 0.000
#> GSM23188 3 0.1625 0.8402 0.000 0.012 0.928 0.000 0.060 0.000
#> GSM23189 3 0.1625 0.8402 0.000 0.012 0.928 0.000 0.060 0.000
#> GSM23190 3 0.1625 0.8402 0.000 0.012 0.928 0.000 0.060 0.000
#> GSM23191 5 0.1528 0.8173 0.000 0.000 0.048 0.016 0.936 0.000
#> GSM23192 5 0.4282 0.7411 0.000 0.000 0.088 0.000 0.720 0.192
#> GSM23193 5 0.1666 0.8103 0.000 0.000 0.036 0.020 0.936 0.008
#> GSM23194 5 0.4463 0.5057 0.000 0.000 0.292 0.000 0.652 0.056
#> GSM23195 5 0.4282 0.7411 0.000 0.000 0.088 0.000 0.720 0.192
#> GSM23159 1 0.0000 0.6265 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23160 3 0.4034 0.6966 0.000 0.000 0.652 0.000 0.328 0.020
#> GSM23161 1 0.0000 0.6265 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23162 5 0.2068 0.8102 0.000 0.000 0.048 0.016 0.916 0.020
#> GSM23163 1 0.4175 -0.3596 0.524 0.000 0.000 0.000 0.012 0.464
#> GSM23164 1 0.0000 0.6265 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23165 1 0.3989 -0.3552 0.528 0.000 0.000 0.000 0.004 0.468
#> GSM23166 1 0.0000 0.6265 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23167 1 0.3937 -0.2220 0.572 0.000 0.004 0.000 0.000 0.424
#> GSM23168 3 0.4034 0.6966 0.000 0.000 0.652 0.000 0.328 0.020
#> GSM23169 5 0.1693 0.8145 0.000 0.000 0.032 0.020 0.936 0.012
#> GSM23170 1 0.3488 0.3174 0.744 0.000 0.004 0.000 0.008 0.244
#> GSM23171 1 0.0146 0.6257 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM23172 1 0.3357 0.3577 0.764 0.000 0.004 0.000 0.008 0.224
#> GSM23173 5 0.1644 0.8167 0.000 0.000 0.052 0.012 0.932 0.004
#> GSM23174 1 0.0405 0.6237 0.988 0.000 0.004 0.000 0.008 0.000
#> GSM23175 1 0.0291 0.6245 0.992 0.000 0.004 0.004 0.000 0.000
#> GSM23176 1 0.3989 -0.3552 0.528 0.000 0.000 0.000 0.004 0.468
#> GSM23177 1 0.0000 0.6265 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23178 1 0.3989 -0.3552 0.528 0.000 0.000 0.000 0.004 0.468
#> GSM23179 3 0.3711 0.7563 0.000 0.000 0.720 0.000 0.260 0.020
#> GSM23180 1 0.4183 0.2562 0.696 0.000 0.000 0.016 0.268 0.020
#> GSM23181 1 0.0551 0.6223 0.984 0.000 0.004 0.000 0.008 0.004
#> GSM23182 1 0.6141 0.0486 0.512 0.000 0.000 0.244 0.224 0.020
#> GSM23183 5 0.4282 0.7411 0.000 0.000 0.088 0.000 0.720 0.192
#> GSM23184 3 0.3711 0.7563 0.000 0.000 0.720 0.000 0.260 0.020
#> GSM23196 2 0.0000 0.8968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.8968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.8968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23199 4 0.7085 0.2750 0.000 0.256 0.060 0.376 0.004 0.304
#> GSM23200 2 0.6577 0.2900 0.000 0.512 0.060 0.160 0.004 0.264
#> GSM23201 4 0.1930 0.7972 0.000 0.000 0.000 0.916 0.036 0.048
#> GSM23202 4 0.0790 0.8004 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM23203 2 0.0000 0.8968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23204 2 0.0291 0.8944 0.000 0.992 0.004 0.000 0.000 0.004
#> GSM23205 4 0.1590 0.7964 0.000 0.000 0.008 0.936 0.008 0.048
#> GSM23206 2 0.0520 0.8913 0.000 0.984 0.008 0.000 0.000 0.008
#> GSM23207 2 0.6986 0.0463 0.000 0.420 0.060 0.232 0.004 0.284
#> GSM23208 2 0.0000 0.8968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.8968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23210 4 0.7090 0.2745 0.000 0.256 0.060 0.372 0.004 0.308
#> GSM23211 2 0.0000 0.8968 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23212 4 0.0862 0.7974 0.000 0.000 0.008 0.972 0.004 0.016
#> GSM23213 4 0.0790 0.8004 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM23214 4 0.0790 0.8004 0.000 0.000 0.000 0.968 0.032 0.000
#> GSM23215 2 0.0520 0.8913 0.000 0.984 0.008 0.000 0.000 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
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 cell.type(p) disease.state(p) k
#> ATC:kmeans 55 3.96e-04 0.464825 2
#> ATC:kmeans 47 5.27e-10 0.050292 3
#> ATC:kmeans 52 3.00e-11 0.000305 4
#> ATC:kmeans 52 1.38e-10 0.006335 5
#> ATC:kmeans 43 1.03e-08 0.017845 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 11993 rows and 57 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.950 0.981 0.5084 0.492 0.492
#> 3 3 0.906 0.891 0.955 0.3160 0.706 0.469
#> 4 4 0.920 0.876 0.947 0.0904 0.941 0.819
#> 5 5 0.919 0.793 0.912 0.0658 0.959 0.849
#> 6 6 0.923 0.872 0.936 0.0319 0.965 0.852
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4 5
There is also optional best \(k\) = 2 3 4 5 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
#> GSM23185 2 0.000 0.967 0.000 1.000
#> GSM23186 1 0.000 0.994 1.000 0.000
#> GSM23187 2 0.000 0.967 0.000 1.000
#> GSM23188 2 0.000 0.967 0.000 1.000
#> GSM23189 2 0.000 0.967 0.000 1.000
#> GSM23190 2 0.000 0.967 0.000 1.000
#> GSM23191 1 0.584 0.831 0.860 0.140
#> GSM23192 1 0.000 0.994 1.000 0.000
#> GSM23193 1 0.000 0.994 1.000 0.000
#> GSM23194 2 0.000 0.967 0.000 1.000
#> GSM23195 2 0.260 0.927 0.044 0.956
#> GSM23159 1 0.000 0.994 1.000 0.000
#> GSM23160 2 0.000 0.967 0.000 1.000
#> GSM23161 1 0.000 0.994 1.000 0.000
#> GSM23162 2 0.971 0.341 0.400 0.600
#> GSM23163 1 0.000 0.994 1.000 0.000
#> GSM23164 1 0.000 0.994 1.000 0.000
#> GSM23165 1 0.000 0.994 1.000 0.000
#> GSM23166 1 0.000 0.994 1.000 0.000
#> GSM23167 1 0.000 0.994 1.000 0.000
#> GSM23168 2 0.000 0.967 0.000 1.000
#> GSM23169 1 0.000 0.994 1.000 0.000
#> GSM23170 1 0.000 0.994 1.000 0.000
#> GSM23171 1 0.000 0.994 1.000 0.000
#> GSM23172 1 0.000 0.994 1.000 0.000
#> GSM23173 2 0.999 0.101 0.480 0.520
#> GSM23174 1 0.000 0.994 1.000 0.000
#> GSM23175 1 0.000 0.994 1.000 0.000
#> GSM23176 1 0.000 0.994 1.000 0.000
#> GSM23177 1 0.000 0.994 1.000 0.000
#> GSM23178 1 0.000 0.994 1.000 0.000
#> GSM23179 2 0.000 0.967 0.000 1.000
#> GSM23180 1 0.000 0.994 1.000 0.000
#> GSM23181 1 0.000 0.994 1.000 0.000
#> GSM23182 1 0.000 0.994 1.000 0.000
#> GSM23183 1 0.000 0.994 1.000 0.000
#> GSM23184 2 0.000 0.967 0.000 1.000
#> GSM23196 2 0.000 0.967 0.000 1.000
#> GSM23197 2 0.000 0.967 0.000 1.000
#> GSM23198 2 0.000 0.967 0.000 1.000
#> GSM23199 2 0.000 0.967 0.000 1.000
#> GSM23200 2 0.000 0.967 0.000 1.000
#> GSM23201 2 0.000 0.967 0.000 1.000
#> GSM23202 1 0.000 0.994 1.000 0.000
#> GSM23203 2 0.000 0.967 0.000 1.000
#> GSM23204 2 0.000 0.967 0.000 1.000
#> GSM23205 2 0.000 0.967 0.000 1.000
#> GSM23206 2 0.000 0.967 0.000 1.000
#> GSM23207 2 0.000 0.967 0.000 1.000
#> GSM23208 2 0.000 0.967 0.000 1.000
#> GSM23209 2 0.000 0.967 0.000 1.000
#> GSM23210 2 0.000 0.967 0.000 1.000
#> GSM23211 2 0.000 0.967 0.000 1.000
#> GSM23212 2 0.000 0.967 0.000 1.000
#> GSM23213 1 0.000 0.994 1.000 0.000
#> GSM23214 1 0.000 0.994 1.000 0.000
#> GSM23215 2 0.000 0.967 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.000 0.890 0.000 0.000 1.000
#> GSM23186 1 0.000 0.997 1.000 0.000 0.000
#> GSM23187 3 0.000 0.890 0.000 0.000 1.000
#> GSM23188 3 0.000 0.890 0.000 0.000 1.000
#> GSM23189 3 0.000 0.890 0.000 0.000 1.000
#> GSM23190 3 0.000 0.890 0.000 0.000 1.000
#> GSM23191 3 0.000 0.890 0.000 0.000 1.000
#> GSM23192 3 0.613 0.427 0.400 0.000 0.600
#> GSM23193 3 0.628 0.276 0.460 0.000 0.540
#> GSM23194 3 0.000 0.890 0.000 0.000 1.000
#> GSM23195 3 0.445 0.714 0.000 0.192 0.808
#> GSM23159 1 0.000 0.997 1.000 0.000 0.000
#> GSM23160 3 0.000 0.890 0.000 0.000 1.000
#> GSM23161 1 0.000 0.997 1.000 0.000 0.000
#> GSM23162 3 0.000 0.890 0.000 0.000 1.000
#> GSM23163 1 0.000 0.997 1.000 0.000 0.000
#> GSM23164 1 0.000 0.997 1.000 0.000 0.000
#> GSM23165 1 0.000 0.997 1.000 0.000 0.000
#> GSM23166 1 0.000 0.997 1.000 0.000 0.000
#> GSM23167 1 0.000 0.997 1.000 0.000 0.000
#> GSM23168 3 0.000 0.890 0.000 0.000 1.000
#> GSM23169 3 0.614 0.418 0.404 0.000 0.596
#> GSM23170 1 0.000 0.997 1.000 0.000 0.000
#> GSM23171 1 0.000 0.997 1.000 0.000 0.000
#> GSM23172 1 0.000 0.997 1.000 0.000 0.000
#> GSM23173 3 0.000 0.890 0.000 0.000 1.000
#> GSM23174 1 0.000 0.997 1.000 0.000 0.000
#> GSM23175 1 0.000 0.997 1.000 0.000 0.000
#> GSM23176 1 0.000 0.997 1.000 0.000 0.000
#> GSM23177 1 0.000 0.997 1.000 0.000 0.000
#> GSM23178 1 0.000 0.997 1.000 0.000 0.000
#> GSM23179 3 0.000 0.890 0.000 0.000 1.000
#> GSM23180 1 0.000 0.997 1.000 0.000 0.000
#> GSM23181 1 0.000 0.997 1.000 0.000 0.000
#> GSM23182 1 0.000 0.997 1.000 0.000 0.000
#> GSM23183 3 0.533 0.643 0.272 0.000 0.728
#> GSM23184 3 0.000 0.890 0.000 0.000 1.000
#> GSM23196 2 0.000 0.949 0.000 1.000 0.000
#> GSM23197 2 0.000 0.949 0.000 1.000 0.000
#> GSM23198 2 0.000 0.949 0.000 1.000 0.000
#> GSM23199 2 0.000 0.949 0.000 1.000 0.000
#> GSM23200 2 0.000 0.949 0.000 1.000 0.000
#> GSM23201 2 0.000 0.949 0.000 1.000 0.000
#> GSM23202 1 0.164 0.948 0.956 0.044 0.000
#> GSM23203 2 0.000 0.949 0.000 1.000 0.000
#> GSM23204 2 0.000 0.949 0.000 1.000 0.000
#> GSM23205 2 0.000 0.949 0.000 1.000 0.000
#> GSM23206 2 0.000 0.949 0.000 1.000 0.000
#> GSM23207 2 0.000 0.949 0.000 1.000 0.000
#> GSM23208 2 0.000 0.949 0.000 1.000 0.000
#> GSM23209 2 0.000 0.949 0.000 1.000 0.000
#> GSM23210 2 0.000 0.949 0.000 1.000 0.000
#> GSM23211 2 0.000 0.949 0.000 1.000 0.000
#> GSM23212 2 0.000 0.949 0.000 1.000 0.000
#> GSM23213 2 0.611 0.348 0.396 0.604 0.000
#> GSM23214 2 0.611 0.348 0.396 0.604 0.000
#> GSM23215 2 0.000 0.949 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0188 0.8389 0.000 0.004 0.996 0.000
#> GSM23186 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23187 3 0.0188 0.8389 0.000 0.004 0.996 0.000
#> GSM23188 3 0.0188 0.8389 0.000 0.004 0.996 0.000
#> GSM23189 3 0.0188 0.8389 0.000 0.004 0.996 0.000
#> GSM23190 3 0.0188 0.8389 0.000 0.004 0.996 0.000
#> GSM23191 3 0.0707 0.8296 0.000 0.000 0.980 0.020
#> GSM23192 3 0.5444 0.3711 0.424 0.000 0.560 0.016
#> GSM23193 3 0.5768 0.2680 0.456 0.000 0.516 0.028
#> GSM23194 3 0.0469 0.8360 0.000 0.000 0.988 0.012
#> GSM23195 3 0.6479 0.4990 0.000 0.140 0.636 0.224
#> GSM23159 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23160 3 0.0000 0.8392 0.000 0.000 1.000 0.000
#> GSM23161 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23162 3 0.0188 0.8382 0.000 0.000 0.996 0.004
#> GSM23163 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23164 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23165 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23166 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23167 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23168 3 0.0000 0.8392 0.000 0.000 1.000 0.000
#> GSM23169 3 0.5487 0.4156 0.400 0.000 0.580 0.020
#> GSM23170 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23171 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23172 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23173 3 0.0592 0.8346 0.000 0.000 0.984 0.016
#> GSM23174 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23175 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23176 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23177 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23178 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23179 3 0.0000 0.8392 0.000 0.000 1.000 0.000
#> GSM23180 1 0.0469 0.9604 0.988 0.000 0.000 0.012
#> GSM23181 1 0.0000 0.9716 1.000 0.000 0.000 0.000
#> GSM23182 1 0.4998 0.0711 0.512 0.000 0.000 0.488
#> GSM23183 3 0.5472 0.3337 0.440 0.000 0.544 0.016
#> GSM23184 3 0.0000 0.8392 0.000 0.000 1.000 0.000
#> GSM23196 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM23199 2 0.0188 0.9964 0.000 0.996 0.000 0.004
#> GSM23200 2 0.0188 0.9964 0.000 0.996 0.000 0.004
#> GSM23201 4 0.1792 0.9323 0.000 0.068 0.000 0.932
#> GSM23202 4 0.0592 0.9561 0.016 0.000 0.000 0.984
#> GSM23203 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM23205 4 0.2647 0.8837 0.000 0.120 0.000 0.880
#> GSM23206 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM23207 2 0.0188 0.9964 0.000 0.996 0.000 0.004
#> GSM23208 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM23210 2 0.0188 0.9964 0.000 0.996 0.000 0.004
#> GSM23211 2 0.0000 0.9986 0.000 1.000 0.000 0.000
#> GSM23212 4 0.0592 0.9534 0.000 0.016 0.000 0.984
#> GSM23213 4 0.0592 0.9561 0.016 0.000 0.000 0.984
#> GSM23214 4 0.0592 0.9561 0.016 0.000 0.000 0.984
#> GSM23215 2 0.0000 0.9986 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.3662 0.645 0.000 0.004 0.744 0.000 0.252
#> GSM23186 1 0.2280 0.853 0.880 0.000 0.000 0.000 0.120
#> GSM23187 3 0.3662 0.645 0.000 0.004 0.744 0.000 0.252
#> GSM23188 3 0.3662 0.645 0.000 0.004 0.744 0.000 0.252
#> GSM23189 3 0.3662 0.645 0.000 0.004 0.744 0.000 0.252
#> GSM23190 3 0.3662 0.645 0.000 0.004 0.744 0.000 0.252
#> GSM23191 3 0.3551 0.301 0.000 0.000 0.772 0.008 0.220
#> GSM23192 5 0.1117 0.702 0.020 0.000 0.016 0.000 0.964
#> GSM23193 3 0.7049 -0.231 0.256 0.000 0.400 0.012 0.332
#> GSM23194 5 0.4249 -0.114 0.000 0.000 0.432 0.000 0.568
#> GSM23195 5 0.0771 0.704 0.000 0.000 0.020 0.004 0.976
#> GSM23159 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23160 3 0.0000 0.557 0.000 0.000 1.000 0.000 0.000
#> GSM23161 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23162 3 0.2127 0.470 0.000 0.000 0.892 0.000 0.108
#> GSM23163 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23164 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23165 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23166 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23167 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23168 3 0.0162 0.559 0.000 0.000 0.996 0.000 0.004
#> GSM23169 5 0.4060 0.387 0.000 0.000 0.360 0.000 0.640
#> GSM23170 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23171 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23172 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23173 3 0.4302 -0.315 0.000 0.000 0.520 0.000 0.480
#> GSM23174 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23175 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23176 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23177 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23178 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23179 3 0.3508 0.644 0.000 0.000 0.748 0.000 0.252
#> GSM23180 1 0.0798 0.945 0.976 0.000 0.000 0.008 0.016
#> GSM23181 1 0.0000 0.965 1.000 0.000 0.000 0.000 0.000
#> GSM23182 1 0.4738 0.107 0.520 0.000 0.000 0.464 0.016
#> GSM23183 5 0.0798 0.708 0.008 0.000 0.016 0.000 0.976
#> GSM23184 3 0.3508 0.644 0.000 0.000 0.748 0.000 0.252
#> GSM23196 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM23199 2 0.0703 0.975 0.000 0.976 0.000 0.024 0.000
#> GSM23200 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM23201 4 0.0880 0.947 0.000 0.032 0.000 0.968 0.000
#> GSM23202 4 0.0000 0.966 0.000 0.000 0.000 1.000 0.000
#> GSM23203 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM23205 4 0.1965 0.878 0.000 0.096 0.000 0.904 0.000
#> GSM23206 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM23207 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM23208 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM23210 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM23211 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM23212 4 0.0000 0.966 0.000 0.000 0.000 1.000 0.000
#> GSM23213 4 0.0000 0.966 0.000 0.000 0.000 1.000 0.000
#> GSM23214 4 0.0000 0.966 0.000 0.000 0.000 1.000 0.000
#> GSM23215 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0000 0.864 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23186 1 0.4252 0.416 0.604 0.000 0.000 0.000 0.024 0.372
#> GSM23187 3 0.0000 0.864 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23188 3 0.0000 0.864 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23189 3 0.0000 0.864 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23190 3 0.0000 0.864 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23191 5 0.1584 0.889 0.000 0.000 0.064 0.000 0.928 0.008
#> GSM23192 6 0.1059 0.990 0.004 0.000 0.016 0.000 0.016 0.964
#> GSM23193 5 0.1649 0.858 0.040 0.000 0.008 0.000 0.936 0.016
#> GSM23194 3 0.4010 0.278 0.000 0.000 0.584 0.000 0.008 0.408
#> GSM23195 6 0.0717 0.990 0.000 0.000 0.016 0.000 0.008 0.976
#> GSM23159 1 0.0458 0.919 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM23160 3 0.3923 0.269 0.000 0.000 0.580 0.000 0.416 0.004
#> GSM23161 1 0.0458 0.919 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM23162 5 0.2003 0.863 0.000 0.000 0.116 0.000 0.884 0.000
#> GSM23163 1 0.0692 0.915 0.976 0.000 0.000 0.000 0.020 0.004
#> GSM23164 1 0.0458 0.919 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM23165 1 0.0891 0.912 0.968 0.000 0.000 0.000 0.024 0.008
#> GSM23166 1 0.0458 0.919 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM23167 1 0.0777 0.914 0.972 0.000 0.000 0.000 0.024 0.004
#> GSM23168 3 0.3314 0.603 0.000 0.000 0.740 0.000 0.256 0.004
#> GSM23169 5 0.2553 0.842 0.000 0.000 0.008 0.000 0.848 0.144
#> GSM23170 1 0.0692 0.915 0.976 0.000 0.000 0.000 0.020 0.004
#> GSM23171 1 0.0458 0.919 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM23172 1 0.0458 0.916 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM23173 5 0.3315 0.863 0.000 0.000 0.076 0.000 0.820 0.104
#> GSM23174 1 0.0000 0.918 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23175 1 0.0458 0.919 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM23176 1 0.0891 0.912 0.968 0.000 0.000 0.000 0.024 0.008
#> GSM23177 1 0.0458 0.919 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM23178 1 0.1088 0.908 0.960 0.000 0.000 0.000 0.024 0.016
#> GSM23179 3 0.0146 0.863 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM23180 1 0.3360 0.647 0.732 0.000 0.000 0.000 0.264 0.004
#> GSM23181 1 0.0458 0.919 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM23182 1 0.5888 0.246 0.500 0.000 0.000 0.212 0.284 0.004
#> GSM23183 6 0.0862 0.992 0.004 0.000 0.016 0.000 0.008 0.972
#> GSM23184 3 0.0260 0.861 0.000 0.000 0.992 0.000 0.008 0.000
#> GSM23196 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23199 2 0.2333 0.856 0.000 0.872 0.000 0.120 0.004 0.004
#> GSM23200 2 0.0146 0.985 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM23201 4 0.1851 0.923 0.000 0.024 0.000 0.928 0.036 0.012
#> GSM23202 4 0.0000 0.953 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23203 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23205 4 0.2833 0.837 0.000 0.104 0.000 0.860 0.024 0.012
#> GSM23206 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23207 2 0.0146 0.985 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM23208 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23210 2 0.0837 0.966 0.000 0.972 0.000 0.020 0.004 0.004
#> GSM23211 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23212 4 0.0000 0.953 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23213 4 0.0000 0.953 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23214 4 0.0000 0.953 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23215 2 0.0000 0.987 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> ATC:skmeans 55 3.96e-04 0.464825 2
#> ATC:skmeans 52 4.17e-11 0.000923 3
#> ATC:skmeans 51 4.89e-11 0.000950 4
#> ATC:skmeans 50 3.61e-10 0.001492 5
#> ATC:skmeans 53 3.36e-10 0.000781 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 11993 rows and 57 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 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 0.823 0.904 0.959 0.5013 0.495 0.495
#> 3 3 0.861 0.901 0.959 0.3448 0.696 0.459
#> 4 4 0.976 0.902 0.962 0.1082 0.893 0.686
#> 5 5 0.990 0.941 0.975 0.0620 0.930 0.736
#> 6 6 0.931 0.824 0.925 0.0231 0.959 0.811
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 5
There is also optional best \(k\) = 4 5 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
#> GSM23185 2 0.000 0.9581 0.000 1.000
#> GSM23186 1 0.000 0.9496 1.000 0.000
#> GSM23187 2 0.000 0.9581 0.000 1.000
#> GSM23188 2 0.000 0.9581 0.000 1.000
#> GSM23189 2 0.000 0.9581 0.000 1.000
#> GSM23190 2 0.000 0.9581 0.000 1.000
#> GSM23191 1 0.760 0.7328 0.780 0.220
#> GSM23192 1 0.000 0.9496 1.000 0.000
#> GSM23193 1 0.000 0.9496 1.000 0.000
#> GSM23194 2 0.311 0.9230 0.056 0.944
#> GSM23195 2 0.327 0.9196 0.060 0.940
#> GSM23159 1 0.000 0.9496 1.000 0.000
#> GSM23160 1 0.760 0.7328 0.780 0.220
#> GSM23161 1 0.000 0.9496 1.000 0.000
#> GSM23162 1 0.760 0.7328 0.780 0.220
#> GSM23163 1 0.000 0.9496 1.000 0.000
#> GSM23164 1 0.000 0.9496 1.000 0.000
#> GSM23165 1 0.000 0.9496 1.000 0.000
#> GSM23166 1 0.000 0.9496 1.000 0.000
#> GSM23167 1 0.000 0.9496 1.000 0.000
#> GSM23168 1 0.932 0.4886 0.652 0.348
#> GSM23169 1 0.000 0.9496 1.000 0.000
#> GSM23170 1 0.000 0.9496 1.000 0.000
#> GSM23171 1 0.000 0.9496 1.000 0.000
#> GSM23172 1 0.000 0.9496 1.000 0.000
#> GSM23173 1 0.722 0.7588 0.800 0.200
#> GSM23174 1 0.000 0.9496 1.000 0.000
#> GSM23175 1 0.000 0.9496 1.000 0.000
#> GSM23176 1 0.000 0.9496 1.000 0.000
#> GSM23177 1 0.000 0.9496 1.000 0.000
#> GSM23178 1 0.000 0.9496 1.000 0.000
#> GSM23179 2 0.295 0.9261 0.052 0.948
#> GSM23180 1 0.000 0.9496 1.000 0.000
#> GSM23181 1 0.000 0.9496 1.000 0.000
#> GSM23182 1 0.000 0.9496 1.000 0.000
#> GSM23183 1 0.000 0.9496 1.000 0.000
#> GSM23184 2 0.753 0.7217 0.216 0.784
#> GSM23196 2 0.000 0.9581 0.000 1.000
#> GSM23197 2 0.000 0.9581 0.000 1.000
#> GSM23198 2 0.000 0.9581 0.000 1.000
#> GSM23199 2 0.000 0.9581 0.000 1.000
#> GSM23200 2 0.000 0.9581 0.000 1.000
#> GSM23201 2 0.998 0.0116 0.476 0.524
#> GSM23202 1 0.000 0.9496 1.000 0.000
#> GSM23203 2 0.000 0.9581 0.000 1.000
#> GSM23204 2 0.000 0.9581 0.000 1.000
#> GSM23205 2 0.295 0.9261 0.052 0.948
#> GSM23206 2 0.000 0.9581 0.000 1.000
#> GSM23207 2 0.000 0.9581 0.000 1.000
#> GSM23208 2 0.000 0.9581 0.000 1.000
#> GSM23209 2 0.000 0.9581 0.000 1.000
#> GSM23210 2 0.000 0.9581 0.000 1.000
#> GSM23211 2 0.000 0.9581 0.000 1.000
#> GSM23212 2 0.311 0.9230 0.056 0.944
#> GSM23213 1 0.506 0.8528 0.888 0.112
#> GSM23214 1 0.343 0.9003 0.936 0.064
#> GSM23215 2 0.000 0.9581 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.9465 0.000 0.000 1.000
#> GSM23186 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23187 3 0.0747 0.9351 0.000 0.016 0.984
#> GSM23188 3 0.3879 0.7908 0.000 0.152 0.848
#> GSM23189 3 0.0000 0.9465 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.9465 0.000 0.000 1.000
#> GSM23191 3 0.0000 0.9465 0.000 0.000 1.000
#> GSM23192 3 0.0237 0.9444 0.004 0.000 0.996
#> GSM23193 3 0.3816 0.8143 0.148 0.000 0.852
#> GSM23194 3 0.0000 0.9465 0.000 0.000 1.000
#> GSM23195 3 0.0000 0.9465 0.000 0.000 1.000
#> GSM23159 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23160 3 0.0000 0.9465 0.000 0.000 1.000
#> GSM23161 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23162 3 0.0000 0.9465 0.000 0.000 1.000
#> GSM23163 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23164 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23165 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23166 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23167 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23168 3 0.0000 0.9465 0.000 0.000 1.000
#> GSM23169 3 0.3752 0.8187 0.144 0.000 0.856
#> GSM23170 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23171 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23172 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23173 3 0.0000 0.9465 0.000 0.000 1.000
#> GSM23174 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23175 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23176 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23177 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23178 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23179 3 0.0000 0.9465 0.000 0.000 1.000
#> GSM23180 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23181 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23182 1 0.0000 0.9658 1.000 0.000 0.000
#> GSM23183 3 0.0237 0.9443 0.004 0.000 0.996
#> GSM23184 3 0.0000 0.9465 0.000 0.000 1.000
#> GSM23196 2 0.0000 0.9489 0.000 1.000 0.000
#> GSM23197 2 0.0000 0.9489 0.000 1.000 0.000
#> GSM23198 2 0.0000 0.9489 0.000 1.000 0.000
#> GSM23199 2 0.0000 0.9489 0.000 1.000 0.000
#> GSM23200 2 0.0000 0.9489 0.000 1.000 0.000
#> GSM23201 3 0.6140 0.2808 0.000 0.404 0.596
#> GSM23202 1 0.3879 0.7928 0.848 0.000 0.152
#> GSM23203 2 0.0000 0.9489 0.000 1.000 0.000
#> GSM23204 2 0.0000 0.9489 0.000 1.000 0.000
#> GSM23205 2 0.4002 0.7935 0.000 0.840 0.160
#> GSM23206 2 0.0000 0.9489 0.000 1.000 0.000
#> GSM23207 2 0.0000 0.9489 0.000 1.000 0.000
#> GSM23208 2 0.0000 0.9489 0.000 1.000 0.000
#> GSM23209 2 0.0000 0.9489 0.000 1.000 0.000
#> GSM23210 2 0.0424 0.9431 0.000 0.992 0.008
#> GSM23211 2 0.0000 0.9489 0.000 1.000 0.000
#> GSM23212 2 0.4002 0.7935 0.000 0.840 0.160
#> GSM23213 2 0.9046 0.3585 0.312 0.528 0.160
#> GSM23214 1 0.9389 0.0872 0.468 0.352 0.180
#> GSM23215 2 0.0000 0.9489 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0000 0.9251 0.000 0.000 1.000 0.000
#> GSM23186 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23187 3 0.0000 0.9251 0.000 0.000 1.000 0.000
#> GSM23188 3 0.0000 0.9251 0.000 0.000 1.000 0.000
#> GSM23189 3 0.0000 0.9251 0.000 0.000 1.000 0.000
#> GSM23190 3 0.0000 0.9251 0.000 0.000 1.000 0.000
#> GSM23191 3 0.2408 0.8698 0.000 0.000 0.896 0.104
#> GSM23192 3 0.2522 0.8853 0.016 0.000 0.908 0.076
#> GSM23193 4 0.4998 0.0111 0.000 0.000 0.488 0.512
#> GSM23194 3 0.0707 0.9210 0.000 0.000 0.980 0.020
#> GSM23195 3 0.4898 0.2774 0.000 0.000 0.584 0.416
#> GSM23159 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23160 3 0.0592 0.9221 0.000 0.000 0.984 0.016
#> GSM23161 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23162 3 0.1557 0.9041 0.000 0.000 0.944 0.056
#> GSM23163 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23164 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23165 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23166 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23167 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23168 3 0.0000 0.9251 0.000 0.000 1.000 0.000
#> GSM23169 4 0.4996 0.0264 0.000 0.000 0.484 0.516
#> GSM23170 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23171 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23172 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23173 3 0.3764 0.7232 0.000 0.000 0.784 0.216
#> GSM23174 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23175 1 0.0921 0.9693 0.972 0.000 0.000 0.028
#> GSM23176 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23177 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23178 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23179 3 0.0000 0.9251 0.000 0.000 1.000 0.000
#> GSM23180 1 0.1389 0.9478 0.952 0.000 0.000 0.048
#> GSM23181 1 0.0000 0.9952 1.000 0.000 0.000 0.000
#> GSM23182 4 0.0000 0.8588 0.000 0.000 0.000 1.000
#> GSM23183 3 0.2271 0.8893 0.008 0.000 0.916 0.076
#> GSM23184 3 0.0000 0.9251 0.000 0.000 1.000 0.000
#> GSM23196 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> GSM23199 2 0.2149 0.9075 0.000 0.912 0.000 0.088
#> GSM23200 2 0.0469 0.9845 0.000 0.988 0.000 0.012
#> GSM23201 4 0.0000 0.8588 0.000 0.000 0.000 1.000
#> GSM23202 4 0.0000 0.8588 0.000 0.000 0.000 1.000
#> GSM23203 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> GSM23205 4 0.0336 0.8518 0.000 0.008 0.000 0.992
#> GSM23206 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> GSM23207 2 0.0469 0.9845 0.000 0.988 0.000 0.012
#> GSM23208 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> GSM23210 2 0.0469 0.9845 0.000 0.988 0.000 0.012
#> GSM23211 2 0.0000 0.9905 0.000 1.000 0.000 0.000
#> GSM23212 4 0.0000 0.8588 0.000 0.000 0.000 1.000
#> GSM23213 4 0.0000 0.8588 0.000 0.000 0.000 1.000
#> GSM23214 4 0.0000 0.8588 0.000 0.000 0.000 1.000
#> GSM23215 2 0.0000 0.9905 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000
#> GSM23186 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23187 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000
#> GSM23188 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000
#> GSM23189 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000
#> GSM23190 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000
#> GSM23191 5 0.0000 0.957 0.000 0.000 0.000 0.000 1.000
#> GSM23192 5 0.0000 0.957 0.000 0.000 0.000 0.000 1.000
#> GSM23193 5 0.0000 0.957 0.000 0.000 0.000 0.000 1.000
#> GSM23194 3 0.4294 0.150 0.000 0.000 0.532 0.000 0.468
#> GSM23195 5 0.0609 0.945 0.000 0.000 0.020 0.000 0.980
#> GSM23159 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23160 3 0.3003 0.753 0.000 0.000 0.812 0.000 0.188
#> GSM23161 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23162 5 0.0000 0.957 0.000 0.000 0.000 0.000 1.000
#> GSM23163 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23164 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23165 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23166 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23167 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23168 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000
#> GSM23169 5 0.0000 0.957 0.000 0.000 0.000 0.000 1.000
#> GSM23170 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23171 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23172 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23173 5 0.0000 0.957 0.000 0.000 0.000 0.000 1.000
#> GSM23174 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23175 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23176 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23177 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23178 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23179 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000
#> GSM23180 5 0.3305 0.676 0.224 0.000 0.000 0.000 0.776
#> GSM23181 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM23182 4 0.2648 0.811 0.000 0.000 0.000 0.848 0.152
#> GSM23183 5 0.0609 0.945 0.000 0.000 0.020 0.000 0.980
#> GSM23184 3 0.0000 0.923 0.000 0.000 1.000 0.000 0.000
#> GSM23196 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
#> GSM23199 2 0.1908 0.924 0.000 0.908 0.000 0.092 0.000
#> GSM23200 2 0.1908 0.924 0.000 0.908 0.000 0.092 0.000
#> GSM23201 4 0.0000 0.973 0.000 0.000 0.000 1.000 0.000
#> GSM23202 4 0.0000 0.973 0.000 0.000 0.000 1.000 0.000
#> GSM23203 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
#> GSM23205 4 0.0000 0.973 0.000 0.000 0.000 1.000 0.000
#> GSM23206 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
#> GSM23207 2 0.1908 0.924 0.000 0.908 0.000 0.092 0.000
#> GSM23208 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
#> GSM23210 2 0.1908 0.924 0.000 0.908 0.000 0.092 0.000
#> GSM23211 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
#> GSM23212 4 0.0000 0.973 0.000 0.000 0.000 1.000 0.000
#> GSM23213 4 0.0000 0.973 0.000 0.000 0.000 1.000 0.000
#> GSM23214 4 0.0000 0.973 0.000 0.000 0.000 1.000 0.000
#> GSM23215 2 0.0000 0.971 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0000 0.8357 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23186 6 0.3634 0.4239 0.356 0.000 0.000 0.000 0.000 0.644
#> GSM23187 3 0.0000 0.8357 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23188 3 0.0000 0.8357 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23189 3 0.0000 0.8357 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23190 3 0.0000 0.8357 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23191 5 0.1910 0.6229 0.000 0.000 0.000 0.000 0.892 0.108
#> GSM23192 6 0.0363 0.7922 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM23193 5 0.2048 0.6197 0.000 0.000 0.000 0.000 0.880 0.120
#> GSM23194 3 0.5051 0.5169 0.000 0.000 0.596 0.000 0.104 0.300
#> GSM23195 6 0.0363 0.7922 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM23159 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23160 5 0.3843 -0.1811 0.000 0.000 0.452 0.000 0.548 0.000
#> GSM23161 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23162 5 0.0000 0.6005 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM23163 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23164 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23165 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23166 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23167 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23168 5 0.3860 -0.2307 0.000 0.000 0.472 0.000 0.528 0.000
#> GSM23169 5 0.3126 0.5071 0.000 0.000 0.000 0.000 0.752 0.248
#> GSM23170 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23171 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23172 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23173 5 0.2135 0.6185 0.000 0.000 0.000 0.000 0.872 0.128
#> GSM23174 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23175 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23176 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23177 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23178 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23179 3 0.2950 0.7416 0.000 0.000 0.828 0.000 0.148 0.024
#> GSM23180 5 0.5355 0.0743 0.424 0.000 0.000 0.000 0.468 0.108
#> GSM23181 1 0.0000 1.0000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23182 4 0.2651 0.8319 0.000 0.000 0.000 0.860 0.112 0.028
#> GSM23183 6 0.0363 0.7922 0.000 0.000 0.000 0.000 0.012 0.988
#> GSM23184 3 0.4264 0.1098 0.000 0.000 0.496 0.000 0.488 0.016
#> GSM23196 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23199 2 0.2070 0.9108 0.000 0.896 0.000 0.092 0.000 0.012
#> GSM23200 2 0.1745 0.9302 0.000 0.920 0.000 0.068 0.000 0.012
#> GSM23201 4 0.1075 0.9307 0.000 0.000 0.000 0.952 0.048 0.000
#> GSM23202 4 0.0000 0.9626 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23203 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23205 4 0.0363 0.9569 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM23206 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23207 2 0.1745 0.9302 0.000 0.920 0.000 0.068 0.000 0.012
#> GSM23208 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23210 2 0.2164 0.9186 0.000 0.900 0.000 0.068 0.000 0.032
#> GSM23211 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23212 4 0.0000 0.9626 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23213 4 0.0000 0.9626 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23214 4 0.0000 0.9626 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23215 2 0.0000 0.9719 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n cell.type(p) disease.state(p) k
#> ATC:pam 55 9.28e-05 4.56e-01 2
#> ATC:pam 54 1.70e-11 5.69e-04 3
#> ATC:pam 54 6.81e-11 2.20e-04 4
#> ATC:pam 56 1.21e-10 1.00e-03 5
#> ATC:pam 52 2.97e-09 1.15e-05 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.518 0.861 0.909 0.4621 0.536 0.536
#> 3 3 0.911 0.910 0.957 0.4573 0.723 0.513
#> 4 4 1.000 0.966 0.982 0.0869 0.947 0.837
#> 5 5 0.857 0.800 0.814 0.0805 0.913 0.695
#> 6 6 0.860 0.872 0.907 0.0515 0.910 0.614
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
#> GSM23185 2 0.8713 0.758 0.292 0.708
#> GSM23186 1 0.0000 0.981 1.000 0.000
#> GSM23187 2 0.8713 0.758 0.292 0.708
#> GSM23188 2 0.8713 0.758 0.292 0.708
#> GSM23189 2 0.8713 0.758 0.292 0.708
#> GSM23190 2 0.8713 0.758 0.292 0.708
#> GSM23191 2 0.8713 0.758 0.292 0.708
#> GSM23192 1 0.5059 0.852 0.888 0.112
#> GSM23193 2 0.8713 0.758 0.292 0.708
#> GSM23194 2 0.8713 0.758 0.292 0.708
#> GSM23195 2 0.6247 0.806 0.156 0.844
#> GSM23159 1 0.0000 0.981 1.000 0.000
#> GSM23160 2 0.8713 0.758 0.292 0.708
#> GSM23161 1 0.0000 0.981 1.000 0.000
#> GSM23162 2 0.8713 0.758 0.292 0.708
#> GSM23163 1 0.0000 0.981 1.000 0.000
#> GSM23164 1 0.0000 0.981 1.000 0.000
#> GSM23165 1 0.0000 0.981 1.000 0.000
#> GSM23166 1 0.0000 0.981 1.000 0.000
#> GSM23167 1 0.0000 0.981 1.000 0.000
#> GSM23168 2 0.8713 0.758 0.292 0.708
#> GSM23169 2 0.8713 0.758 0.292 0.708
#> GSM23170 1 0.0000 0.981 1.000 0.000
#> GSM23171 1 0.0000 0.981 1.000 0.000
#> GSM23172 1 0.0000 0.981 1.000 0.000
#> GSM23173 2 0.8713 0.758 0.292 0.708
#> GSM23174 1 0.0000 0.981 1.000 0.000
#> GSM23175 1 0.0000 0.981 1.000 0.000
#> GSM23176 1 0.0000 0.981 1.000 0.000
#> GSM23177 1 0.0000 0.981 1.000 0.000
#> GSM23178 1 0.0000 0.981 1.000 0.000
#> GSM23179 2 0.8713 0.758 0.292 0.708
#> GSM23180 1 0.3584 0.910 0.932 0.068
#> GSM23181 1 0.0000 0.981 1.000 0.000
#> GSM23182 2 0.8555 0.764 0.280 0.720
#> GSM23183 1 0.5059 0.852 0.888 0.112
#> GSM23184 2 0.8713 0.758 0.292 0.708
#> GSM23196 2 0.0376 0.843 0.004 0.996
#> GSM23197 2 0.0376 0.843 0.004 0.996
#> GSM23198 2 0.0376 0.843 0.004 0.996
#> GSM23199 2 0.0376 0.843 0.004 0.996
#> GSM23200 2 0.0376 0.843 0.004 0.996
#> GSM23201 2 0.0376 0.843 0.004 0.996
#> GSM23202 2 0.0376 0.843 0.004 0.996
#> GSM23203 2 0.0376 0.843 0.004 0.996
#> GSM23204 2 0.0376 0.843 0.004 0.996
#> GSM23205 2 0.0376 0.843 0.004 0.996
#> GSM23206 2 0.0376 0.843 0.004 0.996
#> GSM23207 2 0.0376 0.843 0.004 0.996
#> GSM23208 2 0.0376 0.843 0.004 0.996
#> GSM23209 2 0.0376 0.843 0.004 0.996
#> GSM23210 2 0.0376 0.843 0.004 0.996
#> GSM23211 2 0.0376 0.843 0.004 0.996
#> GSM23212 2 0.0376 0.843 0.004 0.996
#> GSM23213 2 0.0376 0.843 0.004 0.996
#> GSM23214 2 0.0376 0.843 0.004 0.996
#> GSM23215 2 0.0376 0.843 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.924 0.000 0.000 1.000
#> GSM23186 1 0.1163 0.949 0.972 0.000 0.028
#> GSM23187 3 0.0000 0.924 0.000 0.000 1.000
#> GSM23188 3 0.0000 0.924 0.000 0.000 1.000
#> GSM23189 3 0.0000 0.924 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.924 0.000 0.000 1.000
#> GSM23191 3 0.0424 0.920 0.008 0.000 0.992
#> GSM23192 3 0.4702 0.745 0.212 0.000 0.788
#> GSM23193 3 0.0000 0.924 0.000 0.000 1.000
#> GSM23194 3 0.0000 0.924 0.000 0.000 1.000
#> GSM23195 3 0.3551 0.828 0.132 0.000 0.868
#> GSM23159 1 0.0000 0.980 1.000 0.000 0.000
#> GSM23160 3 0.0000 0.924 0.000 0.000 1.000
#> GSM23161 1 0.0000 0.980 1.000 0.000 0.000
#> GSM23162 3 0.0000 0.924 0.000 0.000 1.000
#> GSM23163 1 0.0000 0.980 1.000 0.000 0.000
#> GSM23164 1 0.0000 0.980 1.000 0.000 0.000
#> GSM23165 1 0.0000 0.980 1.000 0.000 0.000
#> GSM23166 1 0.0000 0.980 1.000 0.000 0.000
#> GSM23167 1 0.0000 0.980 1.000 0.000 0.000
#> GSM23168 3 0.0000 0.924 0.000 0.000 1.000
#> GSM23169 3 0.0000 0.924 0.000 0.000 1.000
#> GSM23170 1 0.0000 0.980 1.000 0.000 0.000
#> GSM23171 1 0.0000 0.980 1.000 0.000 0.000
#> GSM23172 1 0.0000 0.980 1.000 0.000 0.000
#> GSM23173 3 0.0000 0.924 0.000 0.000 1.000
#> GSM23174 1 0.0000 0.980 1.000 0.000 0.000
#> GSM23175 1 0.5058 0.628 0.756 0.000 0.244
#> GSM23176 1 0.0000 0.980 1.000 0.000 0.000
#> GSM23177 1 0.0000 0.980 1.000 0.000 0.000
#> GSM23178 1 0.0000 0.980 1.000 0.000 0.000
#> GSM23179 3 0.0000 0.924 0.000 0.000 1.000
#> GSM23180 3 0.6204 0.344 0.424 0.000 0.576
#> GSM23181 1 0.0000 0.980 1.000 0.000 0.000
#> GSM23182 3 0.5621 0.593 0.308 0.000 0.692
#> GSM23183 3 0.5529 0.627 0.296 0.000 0.704
#> GSM23184 3 0.0000 0.924 0.000 0.000 1.000
#> GSM23196 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23197 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23198 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23199 2 0.1411 0.955 0.000 0.964 0.036
#> GSM23200 2 0.1411 0.955 0.000 0.964 0.036
#> GSM23201 2 0.6026 0.462 0.000 0.624 0.376
#> GSM23202 2 0.1860 0.949 0.000 0.948 0.052
#> GSM23203 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23204 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23205 2 0.1860 0.949 0.000 0.948 0.052
#> GSM23206 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23207 2 0.1411 0.955 0.000 0.964 0.036
#> GSM23208 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23209 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23210 2 0.1860 0.949 0.000 0.948 0.052
#> GSM23211 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23212 2 0.1860 0.949 0.000 0.948 0.052
#> GSM23213 2 0.1860 0.949 0.000 0.948 0.052
#> GSM23214 2 0.1860 0.949 0.000 0.948 0.052
#> GSM23215 2 0.0000 0.957 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.0336 0.977 0.000 0.000 0.992 0.008
#> GSM23186 1 0.0336 0.989 0.992 0.000 0.008 0.000
#> GSM23187 3 0.0336 0.977 0.000 0.000 0.992 0.008
#> GSM23188 3 0.0336 0.977 0.000 0.000 0.992 0.008
#> GSM23189 3 0.0336 0.977 0.000 0.000 0.992 0.008
#> GSM23190 3 0.0336 0.977 0.000 0.000 0.992 0.008
#> GSM23191 3 0.0336 0.980 0.000 0.000 0.992 0.008
#> GSM23192 3 0.0921 0.968 0.000 0.000 0.972 0.028
#> GSM23193 3 0.0336 0.980 0.000 0.000 0.992 0.008
#> GSM23194 3 0.0188 0.980 0.000 0.000 0.996 0.004
#> GSM23195 3 0.0921 0.968 0.000 0.000 0.972 0.028
#> GSM23159 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23160 3 0.0000 0.980 0.000 0.000 1.000 0.000
#> GSM23161 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23162 3 0.0336 0.980 0.000 0.000 0.992 0.008
#> GSM23163 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23164 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23165 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23166 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23167 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23168 3 0.0188 0.980 0.000 0.000 0.996 0.004
#> GSM23169 3 0.0336 0.980 0.000 0.000 0.992 0.008
#> GSM23170 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23171 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23172 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23173 3 0.0336 0.980 0.000 0.000 0.992 0.008
#> GSM23174 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23175 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23176 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23177 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23178 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23179 3 0.0188 0.980 0.000 0.000 0.996 0.004
#> GSM23180 3 0.3300 0.810 0.144 0.000 0.848 0.008
#> GSM23181 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM23182 3 0.0336 0.980 0.000 0.000 0.992 0.008
#> GSM23183 3 0.1936 0.941 0.032 0.000 0.940 0.028
#> GSM23184 3 0.0000 0.980 0.000 0.000 1.000 0.000
#> GSM23196 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM23197 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM23198 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM23199 2 0.2342 0.901 0.000 0.912 0.008 0.080
#> GSM23200 2 0.2197 0.904 0.000 0.916 0.004 0.080
#> GSM23201 4 0.0469 0.995 0.000 0.000 0.012 0.988
#> GSM23202 4 0.0336 0.999 0.000 0.000 0.008 0.992
#> GSM23203 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM23204 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM23205 4 0.0336 0.999 0.000 0.000 0.008 0.992
#> GSM23206 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM23207 2 0.2342 0.901 0.000 0.912 0.008 0.080
#> GSM23208 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM23209 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM23210 2 0.4973 0.503 0.000 0.644 0.008 0.348
#> GSM23211 2 0.0000 0.952 0.000 1.000 0.000 0.000
#> GSM23212 4 0.0336 0.999 0.000 0.000 0.008 0.992
#> GSM23213 4 0.0336 0.999 0.000 0.000 0.008 0.992
#> GSM23214 4 0.0336 0.999 0.000 0.000 0.008 0.992
#> GSM23215 2 0.0000 0.952 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.0290 0.7648 0.008 0.000 0.992 0.000 0.000
#> GSM23186 1 0.4542 0.9801 0.536 0.000 0.000 0.008 0.456
#> GSM23187 3 0.0290 0.7648 0.008 0.000 0.992 0.000 0.000
#> GSM23188 3 0.0290 0.7648 0.008 0.000 0.992 0.000 0.000
#> GSM23189 3 0.0290 0.7648 0.008 0.000 0.992 0.000 0.000
#> GSM23190 3 0.0290 0.7648 0.008 0.000 0.992 0.000 0.000
#> GSM23191 3 0.4283 0.7255 0.000 0.456 0.544 0.000 0.000
#> GSM23192 3 0.5856 0.6687 0.000 0.456 0.468 0.012 0.064
#> GSM23193 3 0.4283 0.7255 0.000 0.456 0.544 0.000 0.000
#> GSM23194 3 0.0162 0.7672 0.000 0.004 0.996 0.000 0.000
#> GSM23195 3 0.4953 0.7160 0.000 0.440 0.532 0.028 0.000
#> GSM23159 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM23160 3 0.0000 0.7672 0.000 0.000 1.000 0.000 0.000
#> GSM23161 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM23162 3 0.4219 0.7332 0.000 0.416 0.584 0.000 0.000
#> GSM23163 1 0.4291 0.9975 0.536 0.000 0.000 0.000 0.464
#> GSM23164 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM23165 1 0.4291 0.9975 0.536 0.000 0.000 0.000 0.464
#> GSM23166 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM23167 1 0.4291 0.9975 0.536 0.000 0.000 0.000 0.464
#> GSM23168 3 0.0000 0.7672 0.000 0.000 1.000 0.000 0.000
#> GSM23169 3 0.4283 0.7255 0.000 0.456 0.544 0.000 0.000
#> GSM23170 1 0.4291 0.9975 0.536 0.000 0.000 0.000 0.464
#> GSM23171 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM23172 1 0.4291 0.9975 0.536 0.000 0.000 0.000 0.464
#> GSM23173 3 0.4283 0.7255 0.000 0.456 0.544 0.000 0.000
#> GSM23174 1 0.4291 0.9975 0.536 0.000 0.000 0.000 0.464
#> GSM23175 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM23176 1 0.4291 0.9975 0.536 0.000 0.000 0.000 0.464
#> GSM23177 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM23178 1 0.4291 0.9975 0.536 0.000 0.000 0.000 0.464
#> GSM23179 3 0.0000 0.7672 0.000 0.000 1.000 0.000 0.000
#> GSM23180 3 0.5241 0.7150 0.000 0.436 0.528 0.016 0.020
#> GSM23181 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000
#> GSM23182 3 0.5071 0.7170 0.000 0.440 0.532 0.016 0.012
#> GSM23183 2 0.6788 -0.4248 0.000 0.456 0.188 0.012 0.344
#> GSM23184 3 0.0000 0.7672 0.000 0.000 1.000 0.000 0.000
#> GSM23196 2 0.4283 0.8451 0.456 0.544 0.000 0.000 0.000
#> GSM23197 2 0.4283 0.8451 0.456 0.544 0.000 0.000 0.000
#> GSM23198 2 0.4283 0.8451 0.456 0.544 0.000 0.000 0.000
#> GSM23199 4 0.6392 -0.0423 0.332 0.184 0.000 0.484 0.000
#> GSM23200 2 0.6787 0.4690 0.332 0.380 0.000 0.288 0.000
#> GSM23201 4 0.1121 0.8289 0.000 0.044 0.000 0.956 0.000
#> GSM23202 4 0.0404 0.8542 0.000 0.000 0.000 0.988 0.012
#> GSM23203 2 0.4283 0.8451 0.456 0.544 0.000 0.000 0.000
#> GSM23204 2 0.4283 0.8451 0.456 0.544 0.000 0.000 0.000
#> GSM23205 4 0.0000 0.8532 0.000 0.000 0.000 1.000 0.000
#> GSM23206 2 0.4533 0.8385 0.448 0.544 0.000 0.008 0.000
#> GSM23207 2 0.6787 0.4690 0.332 0.380 0.000 0.288 0.000
#> GSM23208 2 0.4283 0.8451 0.456 0.544 0.000 0.000 0.000
#> GSM23209 2 0.4283 0.8451 0.456 0.544 0.000 0.000 0.000
#> GSM23210 4 0.4597 0.5257 0.260 0.044 0.000 0.696 0.000
#> GSM23211 2 0.4283 0.8451 0.456 0.544 0.000 0.000 0.000
#> GSM23212 4 0.0000 0.8532 0.000 0.000 0.000 1.000 0.000
#> GSM23213 4 0.0404 0.8542 0.000 0.000 0.000 0.988 0.012
#> GSM23214 4 0.0404 0.8542 0.000 0.000 0.000 0.988 0.012
#> GSM23215 2 0.4283 0.8451 0.456 0.544 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.0000 0.784 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23186 6 0.2302 0.963 0.120 0.000 0.000 0.000 0.008 0.872
#> GSM23187 3 0.0000 0.784 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23188 3 0.0000 0.784 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23189 3 0.0000 0.784 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23190 3 0.0000 0.784 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM23191 5 0.0146 0.957 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM23192 5 0.0146 0.957 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM23193 5 0.0000 0.956 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM23194 3 0.3584 0.749 0.000 0.000 0.688 0.000 0.308 0.004
#> GSM23195 5 0.0891 0.944 0.000 0.000 0.000 0.024 0.968 0.008
#> GSM23159 1 0.0260 0.993 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM23160 3 0.3489 0.767 0.000 0.000 0.708 0.000 0.288 0.004
#> GSM23161 1 0.0260 0.993 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM23162 3 0.3847 0.506 0.000 0.000 0.544 0.000 0.456 0.000
#> GSM23163 6 0.2178 0.974 0.132 0.000 0.000 0.000 0.000 0.868
#> GSM23164 1 0.0363 0.991 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM23165 6 0.2092 0.971 0.124 0.000 0.000 0.000 0.000 0.876
#> GSM23166 1 0.0865 0.966 0.964 0.000 0.000 0.000 0.000 0.036
#> GSM23167 6 0.2491 0.970 0.164 0.000 0.000 0.000 0.000 0.836
#> GSM23168 3 0.3489 0.767 0.000 0.000 0.708 0.000 0.288 0.004
#> GSM23169 5 0.0000 0.956 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM23170 6 0.2491 0.970 0.164 0.000 0.000 0.000 0.000 0.836
#> GSM23171 1 0.0260 0.993 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM23172 6 0.2527 0.968 0.168 0.000 0.000 0.000 0.000 0.832
#> GSM23173 5 0.0000 0.956 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM23174 6 0.2562 0.964 0.172 0.000 0.000 0.000 0.000 0.828
#> GSM23175 1 0.0000 0.986 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM23176 6 0.2135 0.973 0.128 0.000 0.000 0.000 0.000 0.872
#> GSM23177 1 0.0260 0.993 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM23178 6 0.2178 0.974 0.132 0.000 0.000 0.000 0.000 0.868
#> GSM23179 3 0.3489 0.767 0.000 0.000 0.708 0.000 0.288 0.004
#> GSM23180 5 0.2731 0.884 0.012 0.000 0.000 0.044 0.876 0.068
#> GSM23181 1 0.0260 0.993 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM23182 5 0.3213 0.839 0.004 0.000 0.000 0.084 0.836 0.076
#> GSM23183 5 0.0146 0.957 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM23184 3 0.3489 0.767 0.000 0.000 0.708 0.000 0.288 0.004
#> GSM23196 2 0.0000 0.863 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23197 2 0.0000 0.863 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23198 2 0.0000 0.863 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23199 2 0.3872 0.496 0.000 0.604 0.000 0.392 0.000 0.004
#> GSM23200 2 0.3862 0.503 0.000 0.608 0.000 0.388 0.000 0.004
#> GSM23201 4 0.1480 0.942 0.000 0.000 0.000 0.940 0.020 0.040
#> GSM23202 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23203 2 0.0000 0.863 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23204 2 0.0000 0.863 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23205 4 0.0146 0.986 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM23206 2 0.0260 0.859 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM23207 2 0.3862 0.503 0.000 0.608 0.000 0.388 0.000 0.004
#> GSM23208 2 0.0000 0.863 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23209 2 0.0000 0.863 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23210 2 0.3937 0.431 0.000 0.572 0.000 0.424 0.000 0.004
#> GSM23211 2 0.0000 0.863 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM23212 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23213 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23214 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM23215 2 0.0000 0.863 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
#> Error in mat[ceiling(1:nr/h_ratio), ceiling(1:nc/w_ratio), drop = FALSE]: subscript out of bounds
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 cell.type(p) disease.state(p) k
#> ATC:mclust 57 1.51e-04 0.305652 2
#> ATC:mclust 55 1.14e-12 0.000291 3
#> ATC:mclust 57 2.57e-12 0.000260 4
#> ATC:mclust 53 8.52e-11 0.004079 5
#> ATC:mclust 55 1.31e-10 0.005162 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 11993 rows and 57 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.825 0.907 0.961 0.4857 0.510 0.510
#> 3 3 0.906 0.912 0.961 0.3921 0.736 0.518
#> 4 4 0.841 0.858 0.908 0.1005 0.903 0.712
#> 5 5 0.740 0.764 0.836 0.0480 0.942 0.788
#> 6 6 0.725 0.706 0.813 0.0361 0.935 0.739
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
#> GSM23185 2 0.0000 0.964 0.000 1.000
#> GSM23186 1 0.0000 0.946 1.000 0.000
#> GSM23187 2 0.0000 0.964 0.000 1.000
#> GSM23188 2 0.0000 0.964 0.000 1.000
#> GSM23189 2 0.0000 0.964 0.000 1.000
#> GSM23190 2 0.0000 0.964 0.000 1.000
#> GSM23191 2 0.1633 0.947 0.024 0.976
#> GSM23192 1 0.8267 0.653 0.740 0.260
#> GSM23193 1 0.7453 0.729 0.788 0.212
#> GSM23194 2 0.0000 0.964 0.000 1.000
#> GSM23195 2 0.1633 0.947 0.024 0.976
#> GSM23159 1 0.0000 0.946 1.000 0.000
#> GSM23160 2 0.7219 0.744 0.200 0.800
#> GSM23161 1 0.0000 0.946 1.000 0.000
#> GSM23162 2 0.6438 0.794 0.164 0.836
#> GSM23163 1 0.0000 0.946 1.000 0.000
#> GSM23164 1 0.0000 0.946 1.000 0.000
#> GSM23165 1 0.0000 0.946 1.000 0.000
#> GSM23166 1 0.0000 0.946 1.000 0.000
#> GSM23167 1 0.0000 0.946 1.000 0.000
#> GSM23168 2 0.1414 0.950 0.020 0.980
#> GSM23169 1 0.6887 0.766 0.816 0.184
#> GSM23170 1 0.0000 0.946 1.000 0.000
#> GSM23171 1 0.0000 0.946 1.000 0.000
#> GSM23172 1 0.0000 0.946 1.000 0.000
#> GSM23173 2 0.8813 0.568 0.300 0.700
#> GSM23174 1 0.0000 0.946 1.000 0.000
#> GSM23175 1 0.0000 0.946 1.000 0.000
#> GSM23176 1 0.0000 0.946 1.000 0.000
#> GSM23177 1 0.0000 0.946 1.000 0.000
#> GSM23178 1 0.0000 0.946 1.000 0.000
#> GSM23179 2 0.0000 0.964 0.000 1.000
#> GSM23180 1 0.0000 0.946 1.000 0.000
#> GSM23181 1 0.0000 0.946 1.000 0.000
#> GSM23182 1 0.0000 0.946 1.000 0.000
#> GSM23183 1 0.9909 0.201 0.556 0.444
#> GSM23184 2 0.0000 0.964 0.000 1.000
#> GSM23196 2 0.0000 0.964 0.000 1.000
#> GSM23197 2 0.0000 0.964 0.000 1.000
#> GSM23198 2 0.0000 0.964 0.000 1.000
#> GSM23199 2 0.0000 0.964 0.000 1.000
#> GSM23200 2 0.0000 0.964 0.000 1.000
#> GSM23201 2 0.0000 0.964 0.000 1.000
#> GSM23202 2 0.9491 0.409 0.368 0.632
#> GSM23203 2 0.0000 0.964 0.000 1.000
#> GSM23204 2 0.0000 0.964 0.000 1.000
#> GSM23205 2 0.0000 0.964 0.000 1.000
#> GSM23206 2 0.0000 0.964 0.000 1.000
#> GSM23207 2 0.0000 0.964 0.000 1.000
#> GSM23208 2 0.0000 0.964 0.000 1.000
#> GSM23209 2 0.0000 0.964 0.000 1.000
#> GSM23210 2 0.0000 0.964 0.000 1.000
#> GSM23211 2 0.0000 0.964 0.000 1.000
#> GSM23212 2 0.0000 0.964 0.000 1.000
#> GSM23213 2 0.0000 0.964 0.000 1.000
#> GSM23214 2 0.0672 0.958 0.008 0.992
#> GSM23215 2 0.0000 0.964 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM23185 3 0.0000 0.916 0.000 0.000 1.000
#> GSM23186 1 0.1860 0.941 0.948 0.000 0.052
#> GSM23187 3 0.0000 0.916 0.000 0.000 1.000
#> GSM23188 3 0.0000 0.916 0.000 0.000 1.000
#> GSM23189 3 0.0000 0.916 0.000 0.000 1.000
#> GSM23190 3 0.0000 0.916 0.000 0.000 1.000
#> GSM23191 3 0.0000 0.916 0.000 0.000 1.000
#> GSM23192 3 0.1753 0.894 0.048 0.000 0.952
#> GSM23193 3 0.5968 0.476 0.364 0.000 0.636
#> GSM23194 3 0.0000 0.916 0.000 0.000 1.000
#> GSM23195 3 0.5180 0.765 0.032 0.156 0.812
#> GSM23159 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23160 3 0.0000 0.916 0.000 0.000 1.000
#> GSM23161 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23162 3 0.0000 0.916 0.000 0.000 1.000
#> GSM23163 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23164 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23165 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23166 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23167 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23168 3 0.0000 0.916 0.000 0.000 1.000
#> GSM23169 3 0.5968 0.476 0.364 0.000 0.636
#> GSM23170 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23171 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23172 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23173 3 0.2066 0.887 0.060 0.000 0.940
#> GSM23174 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23175 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23176 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23177 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23178 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23179 3 0.0000 0.916 0.000 0.000 1.000
#> GSM23180 1 0.0237 0.993 0.996 0.000 0.004
#> GSM23181 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23182 1 0.0000 0.997 1.000 0.000 0.000
#> GSM23183 3 0.1860 0.892 0.052 0.000 0.948
#> GSM23184 3 0.0000 0.916 0.000 0.000 1.000
#> GSM23196 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23197 2 0.5968 0.438 0.000 0.636 0.364
#> GSM23198 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23199 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23200 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23201 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23202 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23203 2 0.0237 0.955 0.000 0.996 0.004
#> GSM23204 3 0.5859 0.418 0.000 0.344 0.656
#> GSM23205 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23206 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23207 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23208 2 0.3116 0.859 0.000 0.892 0.108
#> GSM23209 2 0.5016 0.683 0.000 0.760 0.240
#> GSM23210 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23211 2 0.0237 0.955 0.000 0.996 0.004
#> GSM23212 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23213 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23214 2 0.0000 0.957 0.000 1.000 0.000
#> GSM23215 2 0.0000 0.957 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM23185 3 0.1661 0.917 0.000 0.052 0.944 0.004
#> GSM23186 1 0.0672 0.956 0.984 0.008 0.000 0.008
#> GSM23187 3 0.0592 0.938 0.000 0.016 0.984 0.000
#> GSM23188 3 0.0707 0.937 0.000 0.020 0.980 0.000
#> GSM23189 3 0.0592 0.938 0.000 0.016 0.984 0.000
#> GSM23190 3 0.1305 0.928 0.000 0.036 0.960 0.004
#> GSM23191 3 0.0000 0.941 0.000 0.000 1.000 0.000
#> GSM23192 3 0.0657 0.940 0.000 0.004 0.984 0.012
#> GSM23193 3 0.3219 0.836 0.000 0.000 0.836 0.164
#> GSM23194 3 0.0336 0.940 0.000 0.000 0.992 0.008
#> GSM23195 3 0.5409 0.768 0.044 0.044 0.772 0.140
#> GSM23159 1 0.1557 0.950 0.944 0.000 0.000 0.056
#> GSM23160 3 0.0000 0.941 0.000 0.000 1.000 0.000
#> GSM23161 1 0.1557 0.950 0.944 0.000 0.000 0.056
#> GSM23162 3 0.0817 0.935 0.000 0.000 0.976 0.024
#> GSM23163 1 0.0336 0.960 0.992 0.000 0.000 0.008
#> GSM23164 1 0.1474 0.952 0.948 0.000 0.000 0.052
#> GSM23165 1 0.0524 0.958 0.988 0.004 0.000 0.008
#> GSM23166 1 0.1211 0.956 0.960 0.000 0.000 0.040
#> GSM23167 1 0.0336 0.960 0.992 0.000 0.000 0.008
#> GSM23168 3 0.0000 0.941 0.000 0.000 1.000 0.000
#> GSM23169 3 0.2973 0.857 0.000 0.000 0.856 0.144
#> GSM23170 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM23171 1 0.1211 0.956 0.960 0.000 0.000 0.040
#> GSM23172 1 0.0000 0.961 1.000 0.000 0.000 0.000
#> GSM23173 3 0.1940 0.907 0.000 0.000 0.924 0.076
#> GSM23174 1 0.0188 0.961 0.996 0.000 0.000 0.004
#> GSM23175 1 0.4382 0.646 0.704 0.000 0.000 0.296
#> GSM23176 1 0.0336 0.960 0.992 0.000 0.000 0.008
#> GSM23177 1 0.1474 0.952 0.948 0.000 0.000 0.052
#> GSM23178 1 0.0336 0.960 0.992 0.000 0.000 0.008
#> GSM23179 3 0.0188 0.940 0.000 0.000 0.996 0.004
#> GSM23180 4 0.5428 0.578 0.120 0.000 0.140 0.740
#> GSM23181 1 0.0921 0.959 0.972 0.000 0.000 0.028
#> GSM23182 4 0.3400 0.680 0.064 0.000 0.064 0.872
#> GSM23183 3 0.4034 0.739 0.192 0.008 0.796 0.004
#> GSM23184 3 0.0376 0.940 0.000 0.004 0.992 0.004
#> GSM23196 2 0.2408 0.860 0.000 0.896 0.000 0.104
#> GSM23197 2 0.0927 0.855 0.000 0.976 0.016 0.008
#> GSM23198 2 0.2408 0.860 0.000 0.896 0.000 0.104
#> GSM23199 2 0.4164 0.719 0.000 0.736 0.000 0.264
#> GSM23200 2 0.3975 0.751 0.000 0.760 0.000 0.240
#> GSM23201 4 0.2530 0.778 0.000 0.100 0.004 0.896
#> GSM23202 4 0.2760 0.776 0.000 0.128 0.000 0.872
#> GSM23203 2 0.1716 0.872 0.000 0.936 0.000 0.064
#> GSM23204 2 0.0804 0.851 0.000 0.980 0.012 0.008
#> GSM23205 4 0.4961 0.107 0.000 0.448 0.000 0.552
#> GSM23206 2 0.0469 0.868 0.000 0.988 0.000 0.012
#> GSM23207 2 0.3975 0.751 0.000 0.760 0.000 0.240
#> GSM23208 2 0.0188 0.862 0.000 0.996 0.004 0.000
#> GSM23209 2 0.0376 0.860 0.000 0.992 0.004 0.004
#> GSM23210 2 0.4356 0.678 0.000 0.708 0.000 0.292
#> GSM23211 2 0.1211 0.874 0.000 0.960 0.000 0.040
#> GSM23212 4 0.4008 0.646 0.000 0.244 0.000 0.756
#> GSM23213 4 0.2647 0.781 0.000 0.120 0.000 0.880
#> GSM23214 4 0.2530 0.782 0.000 0.112 0.000 0.888
#> GSM23215 2 0.1118 0.874 0.000 0.964 0.000 0.036
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM23185 3 0.3163 0.811 0.000 0.164 0.824 0.000 0.012
#> GSM23186 1 0.2722 0.798 0.868 0.008 0.004 0.000 0.120
#> GSM23187 3 0.1117 0.859 0.000 0.016 0.964 0.000 0.020
#> GSM23188 3 0.2722 0.836 0.000 0.020 0.872 0.000 0.108
#> GSM23189 3 0.1697 0.856 0.000 0.060 0.932 0.000 0.008
#> GSM23190 3 0.3884 0.674 0.000 0.288 0.708 0.000 0.004
#> GSM23191 3 0.5006 0.685 0.000 0.180 0.704 0.000 0.116
#> GSM23192 3 0.3471 0.794 0.000 0.012 0.820 0.012 0.156
#> GSM23193 3 0.2669 0.826 0.000 0.000 0.876 0.020 0.104
#> GSM23194 3 0.2645 0.831 0.000 0.008 0.884 0.012 0.096
#> GSM23195 3 0.6172 0.524 0.000 0.012 0.600 0.216 0.172
#> GSM23159 1 0.4074 0.589 0.636 0.000 0.000 0.000 0.364
#> GSM23160 3 0.1877 0.853 0.000 0.064 0.924 0.000 0.012
#> GSM23161 1 0.2690 0.835 0.844 0.000 0.000 0.000 0.156
#> GSM23162 3 0.2729 0.839 0.000 0.028 0.884 0.004 0.084
#> GSM23163 1 0.0703 0.881 0.976 0.000 0.000 0.000 0.024
#> GSM23164 1 0.3274 0.784 0.780 0.000 0.000 0.000 0.220
#> GSM23165 1 0.0798 0.880 0.976 0.008 0.000 0.000 0.016
#> GSM23166 1 0.2605 0.840 0.852 0.000 0.000 0.000 0.148
#> GSM23167 1 0.0000 0.886 1.000 0.000 0.000 0.000 0.000
#> GSM23168 3 0.1877 0.853 0.000 0.064 0.924 0.000 0.012
#> GSM23169 3 0.1836 0.849 0.000 0.000 0.932 0.032 0.036
#> GSM23170 1 0.0000 0.886 1.000 0.000 0.000 0.000 0.000
#> GSM23171 1 0.1043 0.883 0.960 0.000 0.000 0.000 0.040
#> GSM23172 1 0.0162 0.886 0.996 0.000 0.000 0.000 0.004
#> GSM23173 3 0.1996 0.851 0.000 0.004 0.928 0.036 0.032
#> GSM23174 1 0.0794 0.886 0.972 0.000 0.000 0.000 0.028
#> GSM23175 1 0.3224 0.825 0.824 0.000 0.000 0.016 0.160
#> GSM23176 1 0.0510 0.882 0.984 0.000 0.000 0.000 0.016
#> GSM23177 1 0.4262 0.441 0.560 0.000 0.000 0.000 0.440
#> GSM23178 1 0.0955 0.878 0.968 0.004 0.000 0.000 0.028
#> GSM23179 3 0.0693 0.856 0.000 0.008 0.980 0.000 0.012
#> GSM23180 5 0.4386 0.760 0.036 0.000 0.096 0.068 0.800
#> GSM23181 1 0.0794 0.886 0.972 0.000 0.000 0.000 0.028
#> GSM23182 5 0.4305 0.786 0.008 0.000 0.048 0.176 0.768
#> GSM23183 3 0.5078 0.717 0.068 0.012 0.736 0.012 0.172
#> GSM23184 3 0.2136 0.845 0.000 0.088 0.904 0.000 0.008
#> GSM23196 4 0.4171 0.438 0.000 0.396 0.000 0.604 0.000
#> GSM23197 2 0.1569 0.761 0.000 0.944 0.008 0.044 0.004
#> GSM23198 4 0.4126 0.474 0.000 0.380 0.000 0.620 0.000
#> GSM23199 4 0.2929 0.771 0.000 0.180 0.000 0.820 0.000
#> GSM23200 4 0.2929 0.769 0.000 0.180 0.000 0.820 0.000
#> GSM23201 5 0.5524 0.567 0.000 0.092 0.004 0.276 0.628
#> GSM23202 4 0.2830 0.740 0.000 0.044 0.000 0.876 0.080
#> GSM23203 2 0.4171 0.349 0.000 0.604 0.000 0.396 0.000
#> GSM23204 2 0.0898 0.723 0.000 0.972 0.020 0.008 0.000
#> GSM23205 4 0.4360 0.616 0.000 0.284 0.000 0.692 0.024
#> GSM23206 2 0.3336 0.731 0.000 0.772 0.000 0.228 0.000
#> GSM23207 4 0.2966 0.768 0.000 0.184 0.000 0.816 0.000
#> GSM23208 2 0.2561 0.789 0.000 0.856 0.000 0.144 0.000
#> GSM23209 2 0.1430 0.771 0.000 0.944 0.004 0.052 0.000
#> GSM23210 4 0.2471 0.775 0.000 0.136 0.000 0.864 0.000
#> GSM23211 2 0.3684 0.654 0.000 0.720 0.000 0.280 0.000
#> GSM23212 4 0.0162 0.737 0.000 0.000 0.000 0.996 0.004
#> GSM23213 4 0.0162 0.737 0.000 0.000 0.000 0.996 0.004
#> GSM23214 4 0.1251 0.732 0.000 0.008 0.000 0.956 0.036
#> GSM23215 2 0.2732 0.784 0.000 0.840 0.000 0.160 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM23185 3 0.3432 0.7302 0.000 0.040 0.828 0.000 0.024 0.108
#> GSM23186 1 0.2998 0.8090 0.852 0.000 0.000 0.004 0.068 0.076
#> GSM23187 3 0.1738 0.7748 0.000 0.004 0.928 0.000 0.016 0.052
#> GSM23188 3 0.2810 0.7028 0.000 0.004 0.832 0.000 0.008 0.156
#> GSM23189 3 0.1036 0.7840 0.000 0.008 0.964 0.000 0.024 0.004
#> GSM23190 3 0.3790 0.7104 0.000 0.088 0.812 0.004 0.020 0.076
#> GSM23191 3 0.4714 0.6600 0.000 0.048 0.720 0.000 0.180 0.052
#> GSM23192 6 0.3946 0.8392 0.008 0.000 0.304 0.004 0.004 0.680
#> GSM23193 3 0.4093 0.6281 0.000 0.000 0.680 0.024 0.292 0.004
#> GSM23194 6 0.3620 0.7896 0.000 0.000 0.352 0.000 0.000 0.648
#> GSM23195 6 0.5051 0.7751 0.020 0.000 0.192 0.112 0.000 0.676
#> GSM23159 1 0.4333 0.5480 0.596 0.000 0.004 0.000 0.380 0.020
#> GSM23160 3 0.1007 0.7898 0.000 0.000 0.956 0.000 0.044 0.000
#> GSM23161 1 0.3161 0.7901 0.776 0.000 0.000 0.000 0.216 0.008
#> GSM23162 3 0.3187 0.7586 0.000 0.000 0.836 0.008 0.112 0.044
#> GSM23163 1 0.1059 0.8700 0.964 0.000 0.000 0.004 0.016 0.016
#> GSM23164 1 0.2593 0.8345 0.844 0.000 0.000 0.000 0.148 0.008
#> GSM23165 1 0.1897 0.8470 0.908 0.000 0.000 0.004 0.084 0.004
#> GSM23166 1 0.2442 0.8355 0.852 0.000 0.000 0.000 0.144 0.004
#> GSM23167 1 0.1003 0.8700 0.964 0.000 0.000 0.004 0.028 0.004
#> GSM23168 3 0.0972 0.7890 0.000 0.000 0.964 0.000 0.028 0.008
#> GSM23169 3 0.4840 0.5452 0.000 0.000 0.700 0.024 0.088 0.188
#> GSM23170 1 0.0551 0.8710 0.984 0.000 0.000 0.004 0.008 0.004
#> GSM23171 1 0.1196 0.8708 0.952 0.000 0.000 0.000 0.040 0.008
#> GSM23172 1 0.0260 0.8726 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM23173 3 0.5187 0.6318 0.000 0.000 0.696 0.152 0.068 0.084
#> GSM23174 1 0.0937 0.8712 0.960 0.000 0.000 0.000 0.040 0.000
#> GSM23175 1 0.3737 0.7872 0.772 0.000 0.000 0.036 0.184 0.008
#> GSM23176 1 0.1296 0.8637 0.948 0.000 0.000 0.004 0.044 0.004
#> GSM23177 1 0.4404 0.5116 0.576 0.000 0.008 0.000 0.400 0.016
#> GSM23178 1 0.1642 0.8604 0.936 0.000 0.000 0.004 0.028 0.032
#> GSM23179 3 0.2408 0.7480 0.000 0.000 0.876 0.004 0.012 0.108
#> GSM23180 5 0.4018 0.5107 0.016 0.000 0.120 0.072 0.788 0.004
#> GSM23181 1 0.1787 0.8671 0.920 0.000 0.000 0.004 0.068 0.008
#> GSM23182 5 0.3918 0.5377 0.000 0.000 0.036 0.208 0.748 0.008
#> GSM23183 6 0.4625 0.8253 0.072 0.000 0.236 0.008 0.000 0.684
#> GSM23184 3 0.2897 0.7444 0.000 0.012 0.852 0.004 0.012 0.120
#> GSM23196 2 0.3531 0.5178 0.000 0.672 0.000 0.328 0.000 0.000
#> GSM23197 2 0.1413 0.7902 0.000 0.948 0.004 0.036 0.008 0.004
#> GSM23198 2 0.3993 0.3305 0.000 0.592 0.000 0.400 0.000 0.008
#> GSM23199 4 0.3940 0.4209 0.000 0.348 0.000 0.640 0.000 0.012
#> GSM23200 4 0.2738 0.7242 0.000 0.176 0.000 0.820 0.000 0.004
#> GSM23201 5 0.7329 -0.0164 0.000 0.372 0.020 0.124 0.376 0.108
#> GSM23202 4 0.4794 0.6606 0.000 0.140 0.000 0.724 0.100 0.036
#> GSM23203 2 0.2773 0.7460 0.000 0.828 0.004 0.164 0.000 0.004
#> GSM23204 2 0.2058 0.7165 0.000 0.916 0.024 0.000 0.012 0.048
#> GSM23205 2 0.6593 0.2931 0.000 0.524 0.000 0.232 0.156 0.088
#> GSM23206 2 0.1926 0.7962 0.000 0.912 0.000 0.068 0.000 0.020
#> GSM23207 4 0.2814 0.7268 0.000 0.172 0.000 0.820 0.000 0.008
#> GSM23208 2 0.1429 0.7983 0.000 0.940 0.004 0.052 0.000 0.004
#> GSM23209 2 0.0696 0.7735 0.000 0.980 0.004 0.004 0.004 0.008
#> GSM23210 4 0.6003 0.2692 0.000 0.308 0.000 0.432 0.000 0.260
#> GSM23211 2 0.2146 0.7804 0.000 0.880 0.004 0.116 0.000 0.000
#> GSM23212 4 0.1124 0.7042 0.000 0.036 0.000 0.956 0.008 0.000
#> GSM23213 4 0.1448 0.6799 0.000 0.024 0.000 0.948 0.012 0.016
#> GSM23214 4 0.2803 0.6611 0.000 0.028 0.000 0.876 0.064 0.032
#> GSM23215 2 0.1010 0.7959 0.000 0.960 0.000 0.036 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
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 cell.type(p) disease.state(p) k
#> ATC:NMF 55 3.96e-05 3.10e-01 2
#> ATC:NMF 53 3.10e-12 5.93e-04 3
#> ATC:NMF 56 9.59e-11 8.60e-06 4
#> ATC:NMF 53 3.72e-10 4.55e-03 5
#> ATC:NMF 52 5.39e-10 1.85e-03 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
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