Date: 2019-12-25 20:45:01 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 21163 rows and 56 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] 21163 56
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:NMF | 3 | 1.000 | 0.969 | 0.986 | ** | 2 |
| CV:NMF | 3 | 1.000 | 0.980 | 0.990 | ** | 2 |
| MAD:hclust | 3 | 1.000 | 0.972 | 0.985 | ** | 2 |
| MAD:kmeans | 3 | 1.000 | 0.936 | 0.956 | ** | |
| ATC:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:mclust | 5 | 1.000 | 0.965 | 0.983 | ** | 2,4 |
| ATC:NMF | 3 | 1.000 | 0.965 | 0.986 | ** | |
| MAD:NMF | 3 | 0.975 | 0.927 | 0.974 | ** | 2 |
| MAD:pam | 6 | 0.964 | 0.924 | 0.960 | ** | 2,3,5 |
| SD:hclust | 4 | 0.952 | 0.924 | 0.961 | ** | 2,3 |
| ATC:hclust | 6 | 0.941 | 0.882 | 0.948 | * | 2,3 |
| ATC:skmeans | 6 | 0.938 | 0.788 | 0.902 | * | 2,3,4 |
| MAD:mclust | 6 | 0.935 | 0.858 | 0.928 | * | 2,5 |
| CV:skmeans | 5 | 0.928 | 0.871 | 0.930 | * | 2,3,4 |
| SD:skmeans | 5 | 0.923 | 0.777 | 0.907 | * | 2,3,4 |
| ATC:pam | 6 | 0.920 | 0.807 | 0.919 | * | 2,3 |
| SD:pam | 6 | 0.917 | 0.868 | 0.909 | * | 2,3,5 |
| CV:mclust | 6 | 0.917 | 0.869 | 0.930 | * | 2,5 |
| MAD:skmeans | 5 | 0.916 | 0.881 | 0.936 | * | 2,3,4 |
| SD:mclust | 5 | 0.912 | 0.865 | 0.936 | * | 2 |
| CV:pam | 6 | 0.904 | 0.869 | 0.889 | * | 2,3,5 |
| CV:hclust | 3 | 0.869 | 0.953 | 0.975 | ||
| SD:kmeans | 3 | 0.741 | 0.958 | 0.943 | ||
| CV:kmeans | 3 | 0.726 | 0.976 | 0.935 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 1.000 0.998 0.999 0.432 0.569 0.569
#> CV:NMF 2 1.000 1.000 1.000 0.431 0.569 0.569
#> MAD:NMF 2 0.963 0.982 0.991 0.456 0.544 0.544
#> ATC:NMF 2 0.889 0.913 0.965 0.489 0.514 0.514
#> SD:skmeans 2 1.000 1.000 1.000 0.431 0.569 0.569
#> CV:skmeans 2 1.000 1.000 1.000 0.431 0.569 0.569
#> MAD:skmeans 2 1.000 1.000 1.000 0.431 0.569 0.569
#> ATC:skmeans 2 1.000 0.978 0.992 0.437 0.569 0.569
#> SD:mclust 2 1.000 1.000 1.000 0.431 0.569 0.569
#> CV:mclust 2 1.000 1.000 1.000 0.431 0.569 0.569
#> MAD:mclust 2 1.000 1.000 1.000 0.431 0.569 0.569
#> ATC:mclust 2 1.000 1.000 1.000 0.431 0.569 0.569
#> SD:kmeans 2 0.584 0.915 0.939 0.443 0.569 0.569
#> CV:kmeans 2 0.584 0.946 0.960 0.440 0.569 0.569
#> MAD:kmeans 2 0.616 0.936 0.949 0.439 0.569 0.569
#> ATC:kmeans 2 1.000 1.000 1.000 0.431 0.569 0.569
#> SD:pam 2 1.000 1.000 1.000 0.431 0.569 0.569
#> CV:pam 2 1.000 1.000 1.000 0.431 0.569 0.569
#> MAD:pam 2 1.000 1.000 1.000 0.431 0.569 0.569
#> ATC:pam 2 1.000 1.000 1.000 0.431 0.569 0.569
#> SD:hclust 2 1.000 0.977 0.989 0.371 0.618 0.618
#> CV:hclust 2 0.795 0.950 0.973 0.381 0.618 0.618
#> MAD:hclust 2 1.000 0.970 0.985 0.392 0.618 0.618
#> ATC:hclust 2 1.000 0.988 0.987 0.431 0.569 0.569
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 1.000 0.969 0.986 0.557 0.761 0.580
#> CV:NMF 3 1.000 0.980 0.990 0.557 0.761 0.580
#> MAD:NMF 3 0.975 0.927 0.974 0.477 0.731 0.527
#> ATC:NMF 3 1.000 0.965 0.986 0.377 0.706 0.481
#> SD:skmeans 3 1.000 0.978 0.989 0.568 0.753 0.567
#> CV:skmeans 3 1.000 0.974 0.988 0.568 0.753 0.567
#> MAD:skmeans 3 1.000 0.971 0.987 0.570 0.753 0.567
#> ATC:skmeans 3 1.000 0.947 0.978 0.547 0.755 0.569
#> SD:mclust 3 0.790 0.830 0.923 0.536 0.773 0.601
#> CV:mclust 3 0.766 0.788 0.910 0.527 0.781 0.615
#> MAD:mclust 3 0.819 0.893 0.937 0.514 0.766 0.590
#> ATC:mclust 3 0.811 0.963 0.964 0.535 0.761 0.580
#> SD:kmeans 3 0.741 0.958 0.943 0.461 0.761 0.580
#> CV:kmeans 3 0.726 0.976 0.935 0.460 0.761 0.580
#> MAD:kmeans 3 1.000 0.936 0.956 0.499 0.766 0.590
#> ATC:kmeans 3 0.733 0.986 0.942 0.485 0.761 0.580
#> SD:pam 3 1.000 0.993 0.997 0.539 0.766 0.590
#> CV:pam 3 1.000 0.985 0.994 0.537 0.766 0.590
#> MAD:pam 3 1.000 0.996 0.998 0.540 0.766 0.590
#> ATC:pam 3 1.000 1.000 1.000 0.542 0.766 0.590
#> SD:hclust 3 1.000 0.976 0.989 0.760 0.724 0.554
#> CV:hclust 3 0.869 0.953 0.975 0.719 0.724 0.554
#> MAD:hclust 3 1.000 0.972 0.985 0.686 0.724 0.554
#> ATC:hclust 3 1.000 0.985 0.989 0.552 0.761 0.580
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.755 0.681 0.829 0.1145 0.871 0.639
#> CV:NMF 4 0.777 0.730 0.838 0.1145 0.927 0.783
#> MAD:NMF 4 0.778 0.752 0.873 0.1144 0.899 0.699
#> ATC:NMF 4 0.811 0.707 0.856 0.0934 0.911 0.737
#> SD:skmeans 4 0.964 0.930 0.972 0.1077 0.899 0.700
#> CV:skmeans 4 0.937 0.897 0.961 0.1103 0.899 0.700
#> MAD:skmeans 4 0.959 0.947 0.976 0.1093 0.910 0.730
#> ATC:skmeans 4 0.965 0.967 0.980 0.1059 0.921 0.759
#> SD:mclust 4 0.890 0.899 0.943 0.1186 0.862 0.633
#> CV:mclust 4 0.891 0.918 0.959 0.1182 0.875 0.666
#> MAD:mclust 4 0.829 0.771 0.908 0.1390 0.845 0.580
#> ATC:mclust 4 0.970 0.926 0.969 0.1247 0.894 0.692
#> SD:kmeans 4 0.779 0.787 0.857 0.1245 0.917 0.753
#> CV:kmeans 4 0.765 0.702 0.846 0.1276 0.966 0.898
#> MAD:kmeans 4 0.782 0.799 0.849 0.1123 0.903 0.714
#> ATC:kmeans 4 0.773 0.663 0.783 0.1211 0.951 0.851
#> SD:pam 4 0.848 0.762 0.906 0.1300 0.860 0.611
#> CV:pam 4 0.868 0.857 0.923 0.1279 0.876 0.655
#> MAD:pam 4 0.788 0.770 0.888 0.1322 0.850 0.588
#> ATC:pam 4 0.888 0.831 0.923 0.1381 0.909 0.729
#> SD:hclust 4 0.952 0.924 0.961 0.1440 0.906 0.727
#> CV:hclust 4 0.864 0.805 0.889 0.1368 0.918 0.761
#> MAD:hclust 4 0.860 0.791 0.887 0.1246 0.906 0.727
#> ATC:hclust 4 0.870 0.896 0.868 0.0961 0.914 0.741
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.725 0.625 0.770 0.0319 0.963 0.860
#> CV:NMF 5 0.708 0.595 0.789 0.0414 0.953 0.829
#> MAD:NMF 5 0.703 0.527 0.783 0.0247 0.951 0.819
#> ATC:NMF 5 0.762 0.709 0.815 0.0547 0.906 0.664
#> SD:skmeans 5 0.923 0.777 0.907 0.0466 0.924 0.719
#> CV:skmeans 5 0.928 0.871 0.930 0.0479 0.955 0.822
#> MAD:skmeans 5 0.916 0.881 0.936 0.0478 0.952 0.812
#> ATC:skmeans 5 0.894 0.766 0.873 0.0435 0.984 0.939
#> SD:mclust 5 0.912 0.865 0.936 0.0606 0.924 0.730
#> CV:mclust 5 0.910 0.851 0.932 0.0718 0.911 0.689
#> MAD:mclust 5 0.917 0.905 0.945 0.0601 0.912 0.676
#> ATC:mclust 5 1.000 0.965 0.983 0.0674 0.892 0.618
#> SD:kmeans 5 0.713 0.585 0.788 0.0673 0.951 0.820
#> CV:kmeans 5 0.732 0.743 0.800 0.0680 0.932 0.783
#> MAD:kmeans 5 0.734 0.651 0.804 0.0679 0.949 0.801
#> ATC:kmeans 5 0.753 0.659 0.782 0.0793 0.902 0.679
#> SD:pam 5 0.925 0.891 0.953 0.0605 0.936 0.751
#> CV:pam 5 0.926 0.904 0.955 0.0651 0.916 0.692
#> MAD:pam 5 0.919 0.852 0.943 0.0627 0.942 0.770
#> ATC:pam 5 0.829 0.798 0.885 0.0467 0.946 0.788
#> SD:hclust 5 0.892 0.820 0.913 0.0464 0.975 0.898
#> CV:hclust 5 0.860 0.684 0.857 0.0513 0.957 0.841
#> MAD:hclust 5 0.834 0.884 0.912 0.0564 0.961 0.843
#> ATC:hclust 5 0.841 0.893 0.930 0.0573 0.953 0.820
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.709 0.610 0.741 0.0371 0.946 0.787
#> CV:NMF 6 0.692 0.586 0.710 0.0401 0.945 0.786
#> MAD:NMF 6 0.692 0.501 0.687 0.0407 0.869 0.565
#> ATC:NMF 6 0.750 0.707 0.822 0.0320 0.967 0.848
#> SD:skmeans 6 0.866 0.759 0.877 0.0347 0.949 0.781
#> CV:skmeans 6 0.854 0.789 0.869 0.0348 0.986 0.932
#> MAD:skmeans 6 0.834 0.626 0.821 0.0391 0.972 0.872
#> ATC:skmeans 6 0.938 0.788 0.902 0.0359 0.933 0.733
#> SD:mclust 6 0.889 0.805 0.903 0.0384 0.946 0.759
#> CV:mclust 6 0.917 0.869 0.930 0.0340 0.955 0.797
#> MAD:mclust 6 0.935 0.858 0.928 0.0403 0.944 0.744
#> ATC:mclust 6 0.888 0.939 0.947 0.0270 0.971 0.860
#> SD:kmeans 6 0.709 0.696 0.771 0.0483 0.901 0.598
#> CV:kmeans 6 0.703 0.626 0.753 0.0519 0.902 0.629
#> MAD:kmeans 6 0.730 0.713 0.775 0.0438 0.915 0.633
#> ATC:kmeans 6 0.762 0.657 0.775 0.0478 0.926 0.714
#> SD:pam 6 0.917 0.868 0.909 0.0296 0.969 0.850
#> CV:pam 6 0.904 0.869 0.889 0.0307 0.968 0.846
#> MAD:pam 6 0.964 0.924 0.960 0.0271 0.968 0.846
#> ATC:pam 6 0.920 0.807 0.919 0.0482 0.961 0.815
#> SD:hclust 6 0.854 0.790 0.868 0.0438 0.982 0.920
#> CV:hclust 6 0.848 0.847 0.894 0.0418 0.937 0.737
#> MAD:hclust 6 0.834 0.832 0.864 0.0434 0.953 0.777
#> ATC:hclust 6 0.941 0.882 0.948 0.0422 0.969 0.862
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n disease.state(p) tissue(p) k
#> SD:NMF 56 5.06e-01 5.82e-11 2
#> CV:NMF 56 5.06e-01 5.82e-11 2
#> MAD:NMF 56 1.39e-01 2.28e-09 2
#> ATC:NMF 54 4.98e-02 4.31e-07 2
#> SD:skmeans 56 5.06e-01 5.82e-11 2
#> CV:skmeans 56 5.06e-01 5.82e-11 2
#> MAD:skmeans 56 5.06e-01 5.82e-11 2
#> ATC:skmeans 55 4.16e-01 9.18e-11 2
#> SD:mclust 56 5.06e-01 5.82e-11 2
#> CV:mclust 56 5.06e-01 5.82e-11 2
#> MAD:mclust 56 5.06e-01 5.82e-11 2
#> ATC:mclust 56 5.06e-01 5.82e-11 2
#> SD:kmeans 56 5.06e-01 5.82e-11 2
#> CV:kmeans 56 5.06e-01 5.82e-11 2
#> MAD:kmeans 56 5.06e-01 5.82e-11 2
#> ATC:kmeans 56 5.06e-01 5.82e-11 2
#> SD:pam 56 5.06e-01 5.82e-11 2
#> CV:pam 56 5.06e-01 5.82e-11 2
#> MAD:pam 56 5.06e-01 5.82e-11 2
#> ATC:pam 56 5.06e-01 5.82e-11 2
#> SD:hclust 55 1.64e-04 4.80e-03 2
#> CV:hclust 56 6.76e-05 2.37e-03 2
#> MAD:hclust 56 6.76e-05 2.37e-03 2
#> ATC:hclust 56 5.06e-01 5.82e-11 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) tissue(p) k
#> SD:NMF 56 0.001210 7.06e-11 3
#> CV:NMF 56 0.001210 7.06e-11 3
#> MAD:NMF 53 0.002548 2.23e-10 3
#> ATC:NMF 55 0.003610 9.94e-10 3
#> SD:skmeans 56 0.010546 4.13e-10 3
#> CV:skmeans 56 0.010546 4.13e-10 3
#> MAD:skmeans 56 0.010546 4.13e-10 3
#> ATC:skmeans 53 0.016952 1.59e-09 3
#> SD:mclust 54 0.001785 9.10e-10 3
#> CV:mclust 45 0.000879 3.07e-09 3
#> MAD:mclust 55 0.004148 8.30e-10 3
#> ATC:mclust 56 0.001443 3.53e-10 3
#> SD:kmeans 55 0.000726 1.84e-10 3
#> CV:kmeans 56 0.001210 7.06e-11 3
#> MAD:kmeans 54 0.000847 7.20e-10 3
#> ATC:kmeans 56 0.001443 3.53e-10 3
#> SD:pam 56 0.000528 2.02e-10 3
#> CV:pam 56 0.000528 2.02e-10 3
#> MAD:pam 56 0.000528 2.02e-10 3
#> ATC:pam 56 0.000515 2.02e-10 3
#> SD:hclust 55 0.000406 2.72e-10 3
#> CV:hclust 56 0.000185 1.01e-10 3
#> MAD:hclust 56 0.000185 1.01e-10 3
#> ATC:hclust 56 0.013479 9.47e-10 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) tissue(p) k
#> SD:NMF 43 2.38e-03 1.86e-08 4
#> CV:NMF 48 2.37e-04 3.83e-10 4
#> MAD:NMF 48 1.23e-03 2.40e-09 4
#> ATC:NMF 42 5.28e-01 5.06e-07 4
#> SD:skmeans 54 5.64e-04 1.63e-09 4
#> CV:skmeans 53 1.06e-04 3.97e-09 4
#> MAD:skmeans 55 3.01e-04 1.65e-09 4
#> ATC:skmeans 56 4.57e-04 1.41e-09 4
#> SD:mclust 55 7.84e-05 2.32e-11 4
#> CV:mclust 53 9.94e-05 1.11e-10 4
#> MAD:mclust 48 7.93e-04 2.70e-10 4
#> ATC:mclust 53 3.94e-03 6.91e-10 4
#> SD:kmeans 52 1.58e-04 7.49e-10 4
#> CV:kmeans 47 4.03e-03 1.20e-09 4
#> MAD:kmeans 52 1.31e-04 2.07e-09 4
#> ATC:kmeans 45 2.72e-03 1.01e-07 4
#> SD:pam 44 1.16e-03 2.46e-08 4
#> CV:pam 55 2.50e-05 6.20e-11 4
#> MAD:pam 48 2.88e-04 9.55e-09 4
#> ATC:pam 49 1.22e-03 1.01e-08 4
#> SD:hclust 55 1.69e-05 3.96e-10 4
#> CV:hclust 53 7.35e-05 3.44e-10 4
#> MAD:hclust 49 5.14e-05 4.77e-08 4
#> ATC:hclust 54 1.88e-02 9.34e-09 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) tissue(p) k
#> SD:NMF 40 2.93e-01 1.53e-07 5
#> CV:NMF 40 1.61e-02 4.65e-08 5
#> MAD:NMF 31 4.67e-01 4.77e-06 5
#> ATC:NMF 50 2.02e-02 8.77e-08 5
#> SD:skmeans 51 4.61e-04 2.90e-09 5
#> CV:skmeans 52 2.62e-04 1.42e-08 5
#> MAD:skmeans 53 1.27e-04 6.91e-09 5
#> ATC:skmeans 42 3.02e-03 2.24e-07 5
#> SD:mclust 53 1.78e-03 2.07e-10 5
#> CV:mclust 51 5.42e-04 2.99e-09 5
#> MAD:mclust 56 5.03e-05 4.55e-09 5
#> ATC:mclust 56 5.22e-06 2.70e-09 5
#> SD:kmeans 45 1.67e-04 1.34e-06 5
#> CV:kmeans 51 1.14e-04 4.53e-09 5
#> MAD:kmeans 46 9.45e-05 2.01e-07 5
#> ATC:kmeans 45 6.13e-06 6.01e-08 5
#> SD:pam 54 2.00e-03 8.34e-10 5
#> CV:pam 54 2.00e-03 8.34e-10 5
#> MAD:pam 51 8.28e-05 3.04e-09 5
#> ATC:pam 51 8.03e-03 1.46e-08 5
#> SD:hclust 50 4.03e-04 2.30e-08 5
#> CV:hclust 47 2.81e-04 6.63e-08 5
#> MAD:hclust 55 1.36e-04 1.95e-09 5
#> ATC:hclust 54 3.59e-02 7.70e-08 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) tissue(p) k
#> SD:NMF 42 3.55e-03 1.73e-07 6
#> CV:NMF 38 3.15e-01 1.34e-06 6
#> MAD:NMF 27 4.05e-01 1.55e-04 6
#> ATC:NMF 50 2.10e-02 1.72e-07 6
#> SD:skmeans 47 8.91e-04 3.29e-08 6
#> CV:skmeans 51 2.07e-03 1.77e-08 6
#> MAD:skmeans 42 3.87e-04 2.30e-07 6
#> ATC:skmeans 52 2.37e-04 1.45e-08 6
#> SD:mclust 52 1.96e-02 2.76e-09 6
#> CV:mclust 54 5.03e-05 5.16e-09 6
#> MAD:mclust 52 1.36e-02 9.86e-09 6
#> ATC:mclust 56 1.31e-04 1.27e-09 6
#> SD:kmeans 47 2.57e-04 4.79e-07 6
#> CV:kmeans 45 9.66e-05 3.82e-07 6
#> MAD:kmeans 51 6.20e-05 2.23e-07 6
#> ATC:kmeans 45 1.02e-04 7.85e-08 6
#> SD:pam 54 5.84e-03 9.31e-10 6
#> CV:pam 55 8.10e-04 6.32e-09 6
#> MAD:pam 55 8.10e-04 6.32e-09 6
#> ATC:pam 49 4.98e-04 2.14e-07 6
#> SD:hclust 54 1.33e-04 5.28e-09 6
#> CV:hclust 54 9.44e-04 3.56e-09 6
#> MAD:hclust 54 2.83e-05 3.10e-08 6
#> ATC:hclust 53 4.66e-03 7.90e-08 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 21163 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.977 0.989 0.3710 0.618 0.618
#> 3 3 1.000 0.976 0.989 0.7604 0.724 0.554
#> 4 4 0.952 0.924 0.961 0.1440 0.906 0.727
#> 5 5 0.892 0.820 0.913 0.0464 0.975 0.898
#> 6 6 0.854 0.790 0.868 0.0438 0.982 0.920
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM329660 1 0.0000 1.000 1.000 0.000
#> GSM329663 1 0.0000 1.000 1.000 0.000
#> GSM329664 1 0.0000 1.000 1.000 0.000
#> GSM329666 1 0.0000 1.000 1.000 0.000
#> GSM329667 1 0.0000 1.000 1.000 0.000
#> GSM329670 1 0.0000 1.000 1.000 0.000
#> GSM329672 1 0.0000 1.000 1.000 0.000
#> GSM329674 1 0.0000 1.000 1.000 0.000
#> GSM329661 2 0.0000 0.955 0.000 1.000
#> GSM329669 1 0.0000 1.000 1.000 0.000
#> GSM329662 1 0.0000 1.000 1.000 0.000
#> GSM329665 1 0.0000 1.000 1.000 0.000
#> GSM329668 1 0.0000 1.000 1.000 0.000
#> GSM329671 1 0.0000 1.000 1.000 0.000
#> GSM329673 1 0.0000 1.000 1.000 0.000
#> GSM329675 1 0.0000 1.000 1.000 0.000
#> GSM329676 1 0.0000 1.000 1.000 0.000
#> GSM329677 2 0.3274 0.922 0.060 0.940
#> GSM329679 1 0.0000 1.000 1.000 0.000
#> GSM329681 2 0.0000 0.955 0.000 1.000
#> GSM329683 2 0.0000 0.955 0.000 1.000
#> GSM329686 2 0.0000 0.955 0.000 1.000
#> GSM329689 2 0.0000 0.955 0.000 1.000
#> GSM329678 2 0.9358 0.492 0.352 0.648
#> GSM329680 2 0.0000 0.955 0.000 1.000
#> GSM329685 2 0.0000 0.955 0.000 1.000
#> GSM329688 2 0.0000 0.955 0.000 1.000
#> GSM329691 2 0.0000 0.955 0.000 1.000
#> GSM329682 1 0.0000 1.000 1.000 0.000
#> GSM329684 1 0.0000 1.000 1.000 0.000
#> GSM329687 1 0.0000 1.000 1.000 0.000
#> GSM329690 1 0.0000 1.000 1.000 0.000
#> GSM329692 1 0.0000 1.000 1.000 0.000
#> GSM329694 1 0.0376 0.996 0.996 0.004
#> GSM329697 1 0.0000 1.000 1.000 0.000
#> GSM329700 1 0.0000 1.000 1.000 0.000
#> GSM329703 1 0.0000 1.000 1.000 0.000
#> GSM329704 1 0.0376 0.996 0.996 0.004
#> GSM329707 2 0.3274 0.922 0.060 0.940
#> GSM329709 1 0.0000 1.000 1.000 0.000
#> GSM329711 1 0.0000 1.000 1.000 0.000
#> GSM329714 1 0.0000 1.000 1.000 0.000
#> GSM329693 1 0.0000 1.000 1.000 0.000
#> GSM329696 1 0.0000 1.000 1.000 0.000
#> GSM329699 1 0.0000 1.000 1.000 0.000
#> GSM329702 1 0.0000 1.000 1.000 0.000
#> GSM329706 2 0.5178 0.870 0.116 0.884
#> GSM329708 2 0.0000 0.955 0.000 1.000
#> GSM329710 1 0.0000 1.000 1.000 0.000
#> GSM329713 1 0.0000 1.000 1.000 0.000
#> GSM329695 1 0.0000 1.000 1.000 0.000
#> GSM329698 1 0.0000 1.000 1.000 0.000
#> GSM329701 1 0.0000 1.000 1.000 0.000
#> GSM329705 1 0.0000 1.000 1.000 0.000
#> GSM329712 1 0.0000 1.000 1.000 0.000
#> GSM329715 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.0000 1.000 0 1.000 0.000
#> GSM329663 2 0.0000 1.000 0 1.000 0.000
#> GSM329664 2 0.0000 1.000 0 1.000 0.000
#> GSM329666 2 0.0000 1.000 0 1.000 0.000
#> GSM329667 2 0.0000 1.000 0 1.000 0.000
#> GSM329670 2 0.0000 1.000 0 1.000 0.000
#> GSM329672 2 0.0000 1.000 0 1.000 0.000
#> GSM329674 2 0.0000 1.000 0 1.000 0.000
#> GSM329661 3 0.0000 0.949 0 0.000 1.000
#> GSM329669 2 0.0000 1.000 0 1.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000
#> GSM329677 3 0.2066 0.916 0 0.060 0.940
#> GSM329679 2 0.0000 1.000 0 1.000 0.000
#> GSM329681 3 0.0000 0.949 0 0.000 1.000
#> GSM329683 3 0.0000 0.949 0 0.000 1.000
#> GSM329686 3 0.0000 0.949 0 0.000 1.000
#> GSM329689 3 0.0000 0.949 0 0.000 1.000
#> GSM329678 3 0.5905 0.496 0 0.352 0.648
#> GSM329680 3 0.0000 0.949 0 0.000 1.000
#> GSM329685 3 0.0000 0.949 0 0.000 1.000
#> GSM329688 3 0.0000 0.949 0 0.000 1.000
#> GSM329691 3 0.0000 0.949 0 0.000 1.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000
#> GSM329692 2 0.0000 1.000 0 1.000 0.000
#> GSM329694 2 0.0237 0.996 0 0.996 0.004
#> GSM329697 2 0.0000 1.000 0 1.000 0.000
#> GSM329700 2 0.0000 1.000 0 1.000 0.000
#> GSM329703 2 0.0000 1.000 0 1.000 0.000
#> GSM329704 2 0.0237 0.996 0 0.996 0.004
#> GSM329707 3 0.2066 0.916 0 0.060 0.940
#> GSM329709 2 0.0000 1.000 0 1.000 0.000
#> GSM329711 2 0.0000 1.000 0 1.000 0.000
#> GSM329714 2 0.0000 1.000 0 1.000 0.000
#> GSM329693 2 0.0000 1.000 0 1.000 0.000
#> GSM329696 2 0.0000 1.000 0 1.000 0.000
#> GSM329699 2 0.0000 1.000 0 1.000 0.000
#> GSM329702 2 0.0000 1.000 0 1.000 0.000
#> GSM329706 3 0.3267 0.867 0 0.116 0.884
#> GSM329708 3 0.0000 0.949 0 0.000 1.000
#> GSM329710 2 0.0000 1.000 0 1.000 0.000
#> GSM329713 1 0.0000 1.000 1 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000
#> GSM329712 2 0.0000 1.000 0 1.000 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.0817 0.975 0 0.976 0.000 0.024
#> GSM329663 2 0.0707 0.977 0 0.980 0.000 0.020
#> GSM329664 2 0.0817 0.958 0 0.976 0.000 0.024
#> GSM329666 2 0.0707 0.977 0 0.980 0.000 0.020
#> GSM329667 2 0.0707 0.960 0 0.980 0.000 0.020
#> GSM329670 2 0.0707 0.977 0 0.980 0.000 0.020
#> GSM329672 2 0.0817 0.960 0 0.976 0.000 0.024
#> GSM329674 2 0.0707 0.977 0 0.980 0.000 0.020
#> GSM329661 3 0.0000 0.954 0 0.000 1.000 0.000
#> GSM329669 2 0.0707 0.977 0 0.980 0.000 0.020
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329677 3 0.1716 0.919 0 0.000 0.936 0.064
#> GSM329679 2 0.0817 0.960 0 0.976 0.000 0.024
#> GSM329681 3 0.0000 0.954 0 0.000 1.000 0.000
#> GSM329683 3 0.0000 0.954 0 0.000 1.000 0.000
#> GSM329686 3 0.0000 0.954 0 0.000 1.000 0.000
#> GSM329689 3 0.0000 0.954 0 0.000 1.000 0.000
#> GSM329678 3 0.4697 0.513 0 0.000 0.644 0.356
#> GSM329680 3 0.0000 0.954 0 0.000 1.000 0.000
#> GSM329685 3 0.0000 0.954 0 0.000 1.000 0.000
#> GSM329688 3 0.0000 0.954 0 0.000 1.000 0.000
#> GSM329691 3 0.0000 0.954 0 0.000 1.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329692 4 0.0336 0.850 0 0.008 0.000 0.992
#> GSM329694 4 0.4898 0.331 0 0.416 0.000 0.584
#> GSM329697 2 0.0707 0.977 0 0.980 0.000 0.020
#> GSM329700 4 0.4605 0.568 0 0.336 0.000 0.664
#> GSM329703 4 0.0336 0.850 0 0.008 0.000 0.992
#> GSM329704 2 0.2216 0.887 0 0.908 0.000 0.092
#> GSM329707 3 0.1716 0.919 0 0.000 0.936 0.064
#> GSM329709 2 0.0707 0.977 0 0.980 0.000 0.020
#> GSM329711 2 0.1211 0.966 0 0.960 0.000 0.040
#> GSM329714 4 0.4605 0.568 0 0.336 0.000 0.664
#> GSM329693 4 0.0336 0.850 0 0.008 0.000 0.992
#> GSM329696 4 0.0336 0.850 0 0.008 0.000 0.992
#> GSM329699 4 0.0336 0.850 0 0.008 0.000 0.992
#> GSM329702 2 0.0707 0.977 0 0.980 0.000 0.020
#> GSM329706 3 0.2647 0.869 0 0.000 0.880 0.120
#> GSM329708 3 0.0000 0.954 0 0.000 1.000 0.000
#> GSM329710 4 0.0336 0.850 0 0.008 0.000 0.992
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329712 2 0.1211 0.966 0 0.960 0.000 0.040
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.0451 0.862 0 0.988 0.000 0.004 0.008
#> GSM329663 2 0.0000 0.871 0 1.000 0.000 0.000 0.000
#> GSM329664 5 0.3752 0.948 0 0.292 0.000 0.000 0.708
#> GSM329666 2 0.0000 0.871 0 1.000 0.000 0.000 0.000
#> GSM329667 5 0.3774 0.946 0 0.296 0.000 0.000 0.704
#> GSM329670 2 0.0000 0.871 0 1.000 0.000 0.000 0.000
#> GSM329672 2 0.4552 -0.463 0 0.524 0.000 0.008 0.468
#> GSM329674 2 0.0000 0.871 0 1.000 0.000 0.000 0.000
#> GSM329661 3 0.2732 0.846 0 0.000 0.840 0.000 0.160
#> GSM329669 2 0.0000 0.871 0 1.000 0.000 0.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329677 3 0.2516 0.839 0 0.000 0.860 0.000 0.140
#> GSM329679 2 0.4552 -0.463 0 0.524 0.000 0.008 0.468
#> GSM329681 3 0.3074 0.850 0 0.000 0.804 0.000 0.196
#> GSM329683 3 0.3074 0.850 0 0.000 0.804 0.000 0.196
#> GSM329686 3 0.0000 0.879 0 0.000 1.000 0.000 0.000
#> GSM329689 3 0.3074 0.850 0 0.000 0.804 0.000 0.196
#> GSM329678 3 0.5990 0.455 0 0.000 0.568 0.280 0.152
#> GSM329680 3 0.0000 0.879 0 0.000 1.000 0.000 0.000
#> GSM329685 3 0.0000 0.879 0 0.000 1.000 0.000 0.000
#> GSM329688 3 0.0000 0.879 0 0.000 1.000 0.000 0.000
#> GSM329691 3 0.0000 0.879 0 0.000 1.000 0.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329692 4 0.0510 0.814 0 0.000 0.000 0.984 0.016
#> GSM329694 4 0.4268 0.195 0 0.000 0.000 0.556 0.444
#> GSM329697 2 0.0000 0.871 0 1.000 0.000 0.000 0.000
#> GSM329700 4 0.3966 0.435 0 0.336 0.000 0.664 0.000
#> GSM329703 4 0.0000 0.818 0 0.000 0.000 1.000 0.000
#> GSM329704 5 0.4552 0.905 0 0.264 0.000 0.040 0.696
#> GSM329707 3 0.2516 0.839 0 0.000 0.860 0.000 0.140
#> GSM329709 2 0.0000 0.871 0 1.000 0.000 0.000 0.000
#> GSM329711 2 0.0794 0.845 0 0.972 0.000 0.028 0.000
#> GSM329714 4 0.3966 0.435 0 0.336 0.000 0.664 0.000
#> GSM329693 4 0.0000 0.818 0 0.000 0.000 1.000 0.000
#> GSM329696 4 0.0000 0.818 0 0.000 0.000 1.000 0.000
#> GSM329699 4 0.0000 0.818 0 0.000 0.000 1.000 0.000
#> GSM329702 2 0.0000 0.871 0 1.000 0.000 0.000 0.000
#> GSM329706 3 0.3723 0.801 0 0.000 0.804 0.044 0.152
#> GSM329708 3 0.2732 0.846 0 0.000 0.840 0.000 0.160
#> GSM329710 4 0.0510 0.814 0 0.000 0.000 0.984 0.016
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329712 2 0.0794 0.845 0 0.972 0.000 0.028 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 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
#> GSM329660 2 0.0935 0.955 0.000 0.964 0.000 0.004 0.032 NA
#> GSM329663 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 NA
#> GSM329664 5 0.0146 0.756 0.000 0.000 0.000 0.000 0.996 NA
#> GSM329666 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 NA
#> GSM329667 5 0.0000 0.757 0.000 0.000 0.000 0.000 1.000 NA
#> GSM329670 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 NA
#> GSM329672 5 0.3833 0.611 0.000 0.344 0.000 0.008 0.648 NA
#> GSM329674 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 NA
#> GSM329661 3 0.3634 0.693 0.000 0.000 0.644 0.000 0.000 NA
#> GSM329669 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 NA
#> GSM329662 1 0.0146 0.856 0.996 0.000 0.000 0.000 0.000 NA
#> GSM329665 1 0.0000 0.857 1.000 0.000 0.000 0.000 0.000 NA
#> GSM329668 1 0.0000 0.857 1.000 0.000 0.000 0.000 0.000 NA
#> GSM329671 1 0.3823 0.679 0.564 0.000 0.000 0.000 0.000 NA
#> GSM329673 1 0.0146 0.856 0.996 0.000 0.000 0.000 0.000 NA
#> GSM329675 1 0.0547 0.849 0.980 0.000 0.000 0.000 0.000 NA
#> GSM329676 1 0.0000 0.857 1.000 0.000 0.000 0.000 0.000 NA
#> GSM329677 3 0.2562 0.755 0.000 0.000 0.828 0.000 0.000 NA
#> GSM329679 5 0.3833 0.611 0.000 0.344 0.000 0.008 0.648 NA
#> GSM329681 3 0.3756 0.705 0.000 0.000 0.600 0.000 0.000 NA
#> GSM329683 3 0.3756 0.705 0.000 0.000 0.600 0.000 0.000 NA
#> GSM329686 3 0.0000 0.796 0.000 0.000 1.000 0.000 0.000 NA
#> GSM329689 3 0.3756 0.705 0.000 0.000 0.600 0.000 0.000 NA
#> GSM329678 3 0.5381 0.432 0.000 0.000 0.568 0.280 0.000 NA
#> GSM329680 3 0.0000 0.796 0.000 0.000 1.000 0.000 0.000 NA
#> GSM329685 3 0.0000 0.796 0.000 0.000 1.000 0.000 0.000 NA
#> GSM329688 3 0.0000 0.796 0.000 0.000 1.000 0.000 0.000 NA
#> GSM329691 3 0.0000 0.796 0.000 0.000 1.000 0.000 0.000 NA
#> GSM329682 1 0.0000 0.857 1.000 0.000 0.000 0.000 0.000 NA
#> GSM329684 1 0.0547 0.849 0.980 0.000 0.000 0.000 0.000 NA
#> GSM329687 1 0.0547 0.857 0.980 0.000 0.000 0.000 0.000 NA
#> GSM329690 1 0.3823 0.679 0.564 0.000 0.000 0.000 0.000 NA
#> GSM329692 4 0.0458 0.816 0.000 0.000 0.000 0.984 0.000 NA
#> GSM329694 4 0.4475 0.132 0.000 0.000 0.000 0.556 0.412 NA
#> GSM329697 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 NA
#> GSM329700 4 0.3684 0.530 0.000 0.332 0.000 0.664 0.004 NA
#> GSM329703 4 0.0000 0.821 0.000 0.000 0.000 1.000 0.000 NA
#> GSM329704 5 0.1720 0.732 0.000 0.000 0.000 0.040 0.928 NA
#> GSM329707 3 0.2562 0.755 0.000 0.000 0.828 0.000 0.000 NA
#> GSM329709 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 NA
#> GSM329711 2 0.0713 0.966 0.000 0.972 0.000 0.028 0.000 NA
#> GSM329714 4 0.3684 0.530 0.000 0.332 0.000 0.664 0.004 NA
#> GSM329693 4 0.0000 0.821 0.000 0.000 0.000 1.000 0.000 NA
#> GSM329696 4 0.0000 0.821 0.000 0.000 0.000 1.000 0.000 NA
#> GSM329699 4 0.0000 0.821 0.000 0.000 0.000 1.000 0.000 NA
#> GSM329702 2 0.0000 0.989 0.000 1.000 0.000 0.000 0.000 NA
#> GSM329706 3 0.3344 0.731 0.000 0.000 0.804 0.044 0.000 NA
#> GSM329708 3 0.3634 0.693 0.000 0.000 0.644 0.000 0.000 NA
#> GSM329710 4 0.0458 0.816 0.000 0.000 0.000 0.984 0.000 NA
#> GSM329713 1 0.3823 0.679 0.564 0.000 0.000 0.000 0.000 NA
#> GSM329695 1 0.3823 0.679 0.564 0.000 0.000 0.000 0.000 NA
#> GSM329698 1 0.2941 0.805 0.780 0.000 0.000 0.000 0.000 NA
#> GSM329701 1 0.2941 0.805 0.780 0.000 0.000 0.000 0.000 NA
#> GSM329705 1 0.0547 0.857 0.980 0.000 0.000 0.000 0.000 NA
#> GSM329712 2 0.0713 0.966 0.000 0.972 0.000 0.028 0.000 NA
#> GSM329715 1 0.2941 0.805 0.780 0.000 0.000 0.000 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> SD:hclust 55 1.64e-04 4.80e-03 2
#> SD:hclust 55 4.06e-04 2.72e-10 3
#> SD:hclust 55 1.69e-05 3.96e-10 4
#> SD:hclust 50 4.03e-04 2.30e-08 5
#> SD:hclust 54 1.33e-04 5.28e-09 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21163 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.584 0.915 0.939 0.4431 0.569 0.569
#> 3 3 0.741 0.958 0.943 0.4607 0.761 0.580
#> 4 4 0.779 0.787 0.857 0.1245 0.917 0.753
#> 5 5 0.713 0.585 0.788 0.0673 0.951 0.820
#> 6 6 0.709 0.696 0.771 0.0483 0.901 0.598
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
#> GSM329660 2 0.738 0.847 0.208 0.792
#> GSM329663 2 0.738 0.847 0.208 0.792
#> GSM329664 2 0.000 0.901 0.000 1.000
#> GSM329666 2 0.738 0.847 0.208 0.792
#> GSM329667 2 0.730 0.848 0.204 0.796
#> GSM329670 2 0.738 0.847 0.208 0.792
#> GSM329672 2 0.738 0.847 0.208 0.792
#> GSM329674 2 0.738 0.847 0.208 0.792
#> GSM329661 2 0.000 0.901 0.000 1.000
#> GSM329669 2 0.738 0.847 0.208 0.792
#> GSM329662 1 0.000 1.000 1.000 0.000
#> GSM329665 1 0.000 1.000 1.000 0.000
#> GSM329668 1 0.000 1.000 1.000 0.000
#> GSM329671 1 0.000 1.000 1.000 0.000
#> GSM329673 1 0.000 1.000 1.000 0.000
#> GSM329675 1 0.000 1.000 1.000 0.000
#> GSM329676 1 0.000 1.000 1.000 0.000
#> GSM329677 2 0.000 0.901 0.000 1.000
#> GSM329679 2 0.738 0.847 0.208 0.792
#> GSM329681 2 0.000 0.901 0.000 1.000
#> GSM329683 2 0.000 0.901 0.000 1.000
#> GSM329686 2 0.000 0.901 0.000 1.000
#> GSM329689 2 0.000 0.901 0.000 1.000
#> GSM329678 2 0.000 0.901 0.000 1.000
#> GSM329680 2 0.000 0.901 0.000 1.000
#> GSM329685 2 0.000 0.901 0.000 1.000
#> GSM329688 2 0.000 0.901 0.000 1.000
#> GSM329691 2 0.000 0.901 0.000 1.000
#> GSM329682 1 0.000 1.000 1.000 0.000
#> GSM329684 1 0.000 1.000 1.000 0.000
#> GSM329687 1 0.000 1.000 1.000 0.000
#> GSM329690 1 0.000 1.000 1.000 0.000
#> GSM329692 2 0.000 0.901 0.000 1.000
#> GSM329694 2 0.000 0.901 0.000 1.000
#> GSM329697 2 0.738 0.847 0.208 0.792
#> GSM329700 2 0.738 0.847 0.208 0.792
#> GSM329703 2 0.224 0.896 0.036 0.964
#> GSM329704 2 0.000 0.901 0.000 1.000
#> GSM329707 2 0.000 0.901 0.000 1.000
#> GSM329709 2 0.738 0.847 0.208 0.792
#> GSM329711 2 0.738 0.847 0.208 0.792
#> GSM329714 2 0.738 0.847 0.208 0.792
#> GSM329693 2 0.224 0.896 0.036 0.964
#> GSM329696 2 0.224 0.896 0.036 0.964
#> GSM329699 2 0.000 0.901 0.000 1.000
#> GSM329702 2 0.738 0.847 0.208 0.792
#> GSM329706 2 0.000 0.901 0.000 1.000
#> GSM329708 2 0.000 0.901 0.000 1.000
#> GSM329710 2 0.000 0.901 0.000 1.000
#> GSM329713 1 0.000 1.000 1.000 0.000
#> GSM329695 1 0.000 1.000 1.000 0.000
#> GSM329698 1 0.000 1.000 1.000 0.000
#> GSM329701 1 0.000 1.000 1.000 0.000
#> GSM329705 1 0.000 1.000 1.000 0.000
#> GSM329712 2 0.738 0.847 0.208 0.792
#> GSM329715 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329663 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329664 2 0.3192 0.857 0.000 0.888 0.112
#> GSM329666 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329667 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329670 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329672 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329674 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329661 3 0.3192 0.971 0.000 0.112 0.888
#> GSM329669 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329662 1 0.2878 0.956 0.904 0.000 0.096
#> GSM329665 1 0.1163 0.965 0.972 0.000 0.028
#> GSM329668 1 0.0892 0.966 0.980 0.000 0.020
#> GSM329671 1 0.0747 0.964 0.984 0.000 0.016
#> GSM329673 1 0.2878 0.956 0.904 0.000 0.096
#> GSM329675 1 0.2878 0.956 0.904 0.000 0.096
#> GSM329676 1 0.2878 0.956 0.904 0.000 0.096
#> GSM329677 3 0.3192 0.971 0.000 0.112 0.888
#> GSM329679 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329681 3 0.3192 0.971 0.000 0.112 0.888
#> GSM329683 3 0.3192 0.971 0.000 0.112 0.888
#> GSM329686 3 0.3192 0.971 0.000 0.112 0.888
#> GSM329689 3 0.3192 0.971 0.000 0.112 0.888
#> GSM329678 3 0.3192 0.971 0.000 0.112 0.888
#> GSM329680 3 0.3192 0.971 0.000 0.112 0.888
#> GSM329685 3 0.3192 0.971 0.000 0.112 0.888
#> GSM329688 3 0.3192 0.971 0.000 0.112 0.888
#> GSM329691 3 0.3192 0.971 0.000 0.112 0.888
#> GSM329682 1 0.2261 0.960 0.932 0.000 0.068
#> GSM329684 1 0.2878 0.956 0.904 0.000 0.096
#> GSM329687 1 0.2878 0.956 0.904 0.000 0.096
#> GSM329690 1 0.0747 0.964 0.984 0.000 0.016
#> GSM329692 3 0.3192 0.971 0.000 0.112 0.888
#> GSM329694 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329697 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329700 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329703 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329704 2 0.3192 0.857 0.000 0.888 0.112
#> GSM329707 3 0.3192 0.971 0.000 0.112 0.888
#> GSM329709 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329711 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329714 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329693 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329696 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329699 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329702 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329706 3 0.3192 0.971 0.000 0.112 0.888
#> GSM329708 3 0.3192 0.971 0.000 0.112 0.888
#> GSM329710 3 0.6308 0.257 0.000 0.492 0.508
#> GSM329713 1 0.0592 0.965 0.988 0.000 0.012
#> GSM329695 1 0.0592 0.965 0.988 0.000 0.012
#> GSM329698 1 0.0592 0.965 0.988 0.000 0.012
#> GSM329701 1 0.0592 0.965 0.988 0.000 0.012
#> GSM329705 1 0.0000 0.966 1.000 0.000 0.000
#> GSM329712 2 0.0000 0.988 0.000 1.000 0.000
#> GSM329715 1 0.0592 0.965 0.988 0.000 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.0000 0.8832 0.000 1.000 0.000 0.000
#> GSM329663 2 0.0000 0.8832 0.000 1.000 0.000 0.000
#> GSM329664 2 0.4030 0.6708 0.000 0.836 0.092 0.072
#> GSM329666 2 0.0000 0.8832 0.000 1.000 0.000 0.000
#> GSM329667 2 0.1792 0.8150 0.000 0.932 0.000 0.068
#> GSM329670 2 0.0000 0.8832 0.000 1.000 0.000 0.000
#> GSM329672 2 0.0188 0.8810 0.000 0.996 0.000 0.004
#> GSM329674 2 0.0000 0.8832 0.000 1.000 0.000 0.000
#> GSM329661 3 0.3367 0.8608 0.000 0.028 0.864 0.108
#> GSM329669 2 0.0000 0.8832 0.000 1.000 0.000 0.000
#> GSM329662 1 0.3726 0.8707 0.788 0.000 0.000 0.212
#> GSM329665 1 0.1211 0.8968 0.960 0.000 0.000 0.040
#> GSM329668 1 0.1389 0.8972 0.952 0.000 0.000 0.048
#> GSM329671 1 0.2149 0.8869 0.912 0.000 0.000 0.088
#> GSM329673 1 0.3649 0.8714 0.796 0.000 0.000 0.204
#> GSM329675 1 0.3726 0.8700 0.788 0.000 0.000 0.212
#> GSM329676 1 0.3649 0.8723 0.796 0.000 0.000 0.204
#> GSM329677 3 0.2546 0.8793 0.000 0.028 0.912 0.060
#> GSM329679 2 0.0188 0.8810 0.000 0.996 0.000 0.004
#> GSM329681 3 0.2032 0.8998 0.000 0.028 0.936 0.036
#> GSM329683 3 0.1388 0.9062 0.000 0.028 0.960 0.012
#> GSM329686 3 0.0921 0.9070 0.000 0.028 0.972 0.000
#> GSM329689 3 0.1388 0.9062 0.000 0.028 0.960 0.012
#> GSM329678 3 0.5764 0.1957 0.000 0.028 0.520 0.452
#> GSM329680 3 0.1109 0.9069 0.000 0.028 0.968 0.004
#> GSM329685 3 0.0921 0.9070 0.000 0.028 0.972 0.000
#> GSM329688 3 0.0921 0.9070 0.000 0.028 0.972 0.000
#> GSM329691 3 0.0921 0.9070 0.000 0.028 0.972 0.000
#> GSM329682 1 0.3123 0.8812 0.844 0.000 0.000 0.156
#> GSM329684 1 0.3726 0.8700 0.788 0.000 0.000 0.212
#> GSM329687 1 0.3486 0.8747 0.812 0.000 0.000 0.188
#> GSM329690 1 0.2843 0.8839 0.892 0.000 0.020 0.088
#> GSM329692 4 0.5460 0.0432 0.000 0.028 0.340 0.632
#> GSM329694 4 0.4955 0.6763 0.000 0.444 0.000 0.556
#> GSM329697 2 0.0000 0.8832 0.000 1.000 0.000 0.000
#> GSM329700 2 0.2345 0.7744 0.000 0.900 0.000 0.100
#> GSM329703 4 0.4992 0.6861 0.000 0.476 0.000 0.524
#> GSM329704 2 0.5842 0.3723 0.000 0.688 0.092 0.220
#> GSM329707 3 0.2915 0.8790 0.000 0.028 0.892 0.080
#> GSM329709 2 0.0000 0.8832 0.000 1.000 0.000 0.000
#> GSM329711 2 0.2081 0.7987 0.000 0.916 0.000 0.084
#> GSM329714 2 0.4855 -0.3490 0.000 0.600 0.000 0.400
#> GSM329693 4 0.4992 0.6861 0.000 0.476 0.000 0.524
#> GSM329696 4 0.4992 0.6861 0.000 0.476 0.000 0.524
#> GSM329699 4 0.4989 0.6876 0.000 0.472 0.000 0.528
#> GSM329702 2 0.0000 0.8832 0.000 1.000 0.000 0.000
#> GSM329706 3 0.5300 0.6010 0.000 0.028 0.664 0.308
#> GSM329708 3 0.3367 0.8608 0.000 0.028 0.864 0.108
#> GSM329710 4 0.6586 0.5077 0.000 0.184 0.184 0.632
#> GSM329713 1 0.2773 0.8857 0.900 0.000 0.028 0.072
#> GSM329695 1 0.2773 0.8857 0.900 0.000 0.028 0.072
#> GSM329698 1 0.2773 0.8857 0.900 0.000 0.028 0.072
#> GSM329701 1 0.1940 0.8887 0.924 0.000 0.000 0.076
#> GSM329705 1 0.0000 0.8967 1.000 0.000 0.000 0.000
#> GSM329712 2 0.2081 0.7987 0.000 0.916 0.000 0.084
#> GSM329715 1 0.1940 0.8887 0.924 0.000 0.000 0.076
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.2011 0.838 0.000 0.908 0.000 0.004 0.088
#> GSM329663 2 0.1357 0.847 0.000 0.948 0.000 0.004 0.048
#> GSM329664 2 0.5733 0.528 0.000 0.552 0.044 0.024 0.380
#> GSM329666 2 0.1121 0.856 0.000 0.956 0.000 0.000 0.044
#> GSM329667 2 0.4339 0.692 0.000 0.684 0.000 0.020 0.296
#> GSM329670 2 0.0566 0.847 0.000 0.984 0.000 0.004 0.012
#> GSM329672 2 0.2471 0.834 0.000 0.864 0.000 0.000 0.136
#> GSM329674 2 0.1121 0.856 0.000 0.956 0.000 0.000 0.044
#> GSM329661 3 0.4129 0.836 0.000 0.016 0.808 0.076 0.100
#> GSM329669 2 0.0162 0.847 0.000 0.996 0.000 0.004 0.000
#> GSM329662 1 0.4307 -0.929 0.504 0.000 0.000 0.000 0.496
#> GSM329665 1 0.3612 0.322 0.800 0.000 0.000 0.028 0.172
#> GSM329668 1 0.4210 0.223 0.756 0.000 0.004 0.036 0.204
#> GSM329671 1 0.1492 0.516 0.948 0.000 0.008 0.040 0.004
#> GSM329673 1 0.4451 -0.938 0.504 0.000 0.000 0.004 0.492
#> GSM329675 5 0.4706 1.000 0.488 0.000 0.008 0.004 0.500
#> GSM329676 1 0.4287 -0.830 0.540 0.000 0.000 0.000 0.460
#> GSM329677 3 0.4391 0.749 0.000 0.016 0.744 0.024 0.216
#> GSM329679 2 0.2471 0.834 0.000 0.864 0.000 0.000 0.136
#> GSM329681 3 0.2937 0.869 0.000 0.016 0.884 0.060 0.040
#> GSM329683 3 0.1974 0.880 0.000 0.016 0.932 0.016 0.036
#> GSM329686 3 0.0510 0.884 0.000 0.016 0.984 0.000 0.000
#> GSM329689 3 0.1891 0.881 0.000 0.016 0.936 0.016 0.032
#> GSM329678 4 0.4169 0.574 0.000 0.016 0.256 0.724 0.004
#> GSM329680 3 0.1018 0.883 0.000 0.016 0.968 0.016 0.000
#> GSM329685 3 0.0510 0.884 0.000 0.016 0.984 0.000 0.000
#> GSM329688 3 0.0510 0.884 0.000 0.016 0.984 0.000 0.000
#> GSM329691 3 0.0510 0.884 0.000 0.016 0.984 0.000 0.000
#> GSM329682 1 0.4171 -0.653 0.604 0.000 0.000 0.000 0.396
#> GSM329684 5 0.4706 1.000 0.488 0.000 0.008 0.004 0.500
#> GSM329687 1 0.4256 -0.774 0.564 0.000 0.000 0.000 0.436
#> GSM329690 1 0.2517 0.509 0.884 0.000 0.008 0.104 0.004
#> GSM329692 4 0.3463 0.680 0.000 0.016 0.128 0.836 0.020
#> GSM329694 4 0.4627 0.787 0.000 0.188 0.000 0.732 0.080
#> GSM329697 2 0.1121 0.856 0.000 0.956 0.000 0.000 0.044
#> GSM329700 2 0.3389 0.758 0.000 0.836 0.000 0.116 0.048
#> GSM329703 4 0.3305 0.817 0.000 0.224 0.000 0.776 0.000
#> GSM329704 2 0.7227 0.242 0.000 0.416 0.044 0.160 0.380
#> GSM329707 3 0.5048 0.737 0.000 0.016 0.676 0.040 0.268
#> GSM329709 2 0.1121 0.856 0.000 0.956 0.000 0.000 0.044
#> GSM329711 2 0.1965 0.791 0.000 0.904 0.000 0.096 0.000
#> GSM329714 4 0.5440 0.472 0.000 0.396 0.000 0.540 0.064
#> GSM329693 4 0.3305 0.817 0.000 0.224 0.000 0.776 0.000
#> GSM329696 4 0.3305 0.817 0.000 0.224 0.000 0.776 0.000
#> GSM329699 4 0.3398 0.818 0.000 0.216 0.000 0.780 0.004
#> GSM329702 2 0.1121 0.856 0.000 0.956 0.000 0.000 0.044
#> GSM329706 3 0.6794 0.412 0.000 0.016 0.508 0.240 0.236
#> GSM329708 3 0.4129 0.836 0.000 0.016 0.808 0.076 0.100
#> GSM329710 4 0.3568 0.748 0.000 0.064 0.080 0.844 0.012
#> GSM329713 1 0.1732 0.519 0.920 0.000 0.000 0.080 0.000
#> GSM329695 1 0.1732 0.519 0.920 0.000 0.000 0.080 0.000
#> GSM329698 1 0.1732 0.519 0.920 0.000 0.000 0.080 0.000
#> GSM329701 1 0.0324 0.527 0.992 0.000 0.004 0.004 0.000
#> GSM329705 1 0.2377 0.404 0.872 0.000 0.000 0.000 0.128
#> GSM329712 2 0.1965 0.791 0.000 0.904 0.000 0.096 0.000
#> GSM329715 1 0.0162 0.526 0.996 0.000 0.004 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329660 2 0.4426 0.7783 0.000 0.748 0.000 0.020 0.100 0.132
#> GSM329663 2 0.3893 0.7760 0.000 0.764 0.000 0.000 0.080 0.156
#> GSM329664 5 0.4045 0.4667 0.000 0.268 0.036 0.000 0.696 0.000
#> GSM329666 2 0.0713 0.8370 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM329667 5 0.4933 -0.0689 0.000 0.432 0.000 0.000 0.504 0.064
#> GSM329670 2 0.3027 0.7984 0.000 0.824 0.000 0.000 0.028 0.148
#> GSM329672 2 0.2431 0.8002 0.000 0.860 0.000 0.000 0.132 0.008
#> GSM329674 2 0.0713 0.8370 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM329661 3 0.4471 0.8017 0.000 0.000 0.756 0.040 0.080 0.124
#> GSM329669 2 0.1556 0.8271 0.000 0.920 0.000 0.000 0.000 0.080
#> GSM329662 1 0.1049 0.7261 0.960 0.000 0.000 0.000 0.032 0.008
#> GSM329665 1 0.3984 -0.0929 0.648 0.000 0.000 0.000 0.016 0.336
#> GSM329668 1 0.4546 0.1083 0.660 0.000 0.000 0.012 0.040 0.288
#> GSM329671 6 0.5144 0.7900 0.404 0.000 0.000 0.028 0.036 0.532
#> GSM329673 1 0.1007 0.7250 0.956 0.000 0.000 0.000 0.044 0.000
#> GSM329675 1 0.1765 0.7018 0.904 0.000 0.000 0.000 0.096 0.000
#> GSM329676 1 0.0508 0.7247 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM329677 5 0.4439 0.2891 0.000 0.000 0.432 0.000 0.540 0.028
#> GSM329679 2 0.2431 0.8002 0.000 0.860 0.000 0.000 0.132 0.008
#> GSM329681 3 0.3256 0.8656 0.000 0.000 0.840 0.016 0.048 0.096
#> GSM329683 3 0.2750 0.8763 0.000 0.000 0.868 0.004 0.048 0.080
#> GSM329686 3 0.0146 0.8937 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM329689 3 0.2789 0.8739 0.000 0.000 0.864 0.004 0.044 0.088
#> GSM329678 4 0.3820 0.6327 0.000 0.000 0.204 0.756 0.008 0.032
#> GSM329680 3 0.0748 0.8852 0.000 0.000 0.976 0.004 0.004 0.016
#> GSM329685 3 0.0146 0.8937 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM329688 3 0.0146 0.8937 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM329691 3 0.0146 0.8937 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM329682 1 0.1672 0.6999 0.932 0.000 0.000 0.004 0.016 0.048
#> GSM329684 1 0.1765 0.7018 0.904 0.000 0.000 0.000 0.096 0.000
#> GSM329687 1 0.0993 0.7192 0.964 0.000 0.000 0.000 0.012 0.024
#> GSM329690 6 0.5785 0.8238 0.364 0.000 0.000 0.048 0.068 0.520
#> GSM329692 4 0.2696 0.7474 0.000 0.000 0.076 0.872 0.004 0.048
#> GSM329694 4 0.4126 0.7875 0.000 0.084 0.000 0.784 0.100 0.032
#> GSM329697 2 0.0713 0.8370 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM329700 2 0.6024 0.6355 0.000 0.604 0.000 0.152 0.068 0.176
#> GSM329703 4 0.2146 0.8379 0.000 0.116 0.000 0.880 0.000 0.004
#> GSM329704 5 0.4867 0.5237 0.000 0.204 0.036 0.064 0.696 0.000
#> GSM329707 5 0.4763 0.3097 0.000 0.000 0.372 0.004 0.576 0.048
#> GSM329709 2 0.0713 0.8370 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM329711 2 0.3955 0.7561 0.000 0.772 0.000 0.132 0.004 0.092
#> GSM329714 4 0.6752 0.3434 0.000 0.252 0.000 0.492 0.088 0.168
#> GSM329693 4 0.2146 0.8379 0.000 0.116 0.000 0.880 0.000 0.004
#> GSM329696 4 0.2003 0.8380 0.000 0.116 0.000 0.884 0.000 0.000
#> GSM329699 4 0.2243 0.8377 0.000 0.112 0.000 0.880 0.004 0.004
#> GSM329702 2 0.0713 0.8370 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM329706 5 0.6105 0.4370 0.000 0.000 0.268 0.164 0.536 0.032
#> GSM329708 3 0.4471 0.8017 0.000 0.000 0.756 0.040 0.080 0.124
#> GSM329710 4 0.2851 0.7959 0.000 0.044 0.032 0.880 0.004 0.040
#> GSM329713 6 0.5507 0.8477 0.376 0.000 0.000 0.048 0.044 0.532
#> GSM329695 6 0.5507 0.8477 0.376 0.000 0.000 0.048 0.044 0.532
#> GSM329698 6 0.5329 0.8479 0.376 0.000 0.000 0.032 0.048 0.544
#> GSM329701 6 0.3817 0.8072 0.432 0.000 0.000 0.000 0.000 0.568
#> GSM329705 1 0.3911 -0.2240 0.624 0.000 0.000 0.000 0.008 0.368
#> GSM329712 2 0.3955 0.7561 0.000 0.772 0.000 0.132 0.004 0.092
#> GSM329715 6 0.3961 0.7936 0.440 0.000 0.000 0.000 0.004 0.556
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> SD:kmeans 56 0.505684 5.82e-11 2
#> SD:kmeans 55 0.000726 1.84e-10 3
#> SD:kmeans 52 0.000158 7.49e-10 4
#> SD:kmeans 45 0.000167 1.34e-06 5
#> SD:kmeans 47 0.000257 4.79e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "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 21163 rows and 56 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4311 0.569 0.569
#> 3 3 1.000 0.978 0.989 0.5683 0.753 0.567
#> 4 4 0.964 0.930 0.972 0.1077 0.899 0.700
#> 5 5 0.923 0.777 0.907 0.0466 0.924 0.719
#> 6 6 0.866 0.759 0.877 0.0347 0.949 0.781
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM329660 2 0 1 0 1
#> GSM329663 2 0 1 0 1
#> GSM329664 2 0 1 0 1
#> GSM329666 2 0 1 0 1
#> GSM329667 2 0 1 0 1
#> GSM329670 2 0 1 0 1
#> GSM329672 2 0 1 0 1
#> GSM329674 2 0 1 0 1
#> GSM329661 2 0 1 0 1
#> GSM329669 2 0 1 0 1
#> GSM329662 1 0 1 1 0
#> GSM329665 1 0 1 1 0
#> GSM329668 1 0 1 1 0
#> GSM329671 1 0 1 1 0
#> GSM329673 1 0 1 1 0
#> GSM329675 1 0 1 1 0
#> GSM329676 1 0 1 1 0
#> GSM329677 2 0 1 0 1
#> GSM329679 2 0 1 0 1
#> GSM329681 2 0 1 0 1
#> GSM329683 2 0 1 0 1
#> GSM329686 2 0 1 0 1
#> GSM329689 2 0 1 0 1
#> GSM329678 2 0 1 0 1
#> GSM329680 2 0 1 0 1
#> GSM329685 2 0 1 0 1
#> GSM329688 2 0 1 0 1
#> GSM329691 2 0 1 0 1
#> GSM329682 1 0 1 1 0
#> GSM329684 1 0 1 1 0
#> GSM329687 1 0 1 1 0
#> GSM329690 1 0 1 1 0
#> GSM329692 2 0 1 0 1
#> GSM329694 2 0 1 0 1
#> GSM329697 2 0 1 0 1
#> GSM329700 2 0 1 0 1
#> GSM329703 2 0 1 0 1
#> GSM329704 2 0 1 0 1
#> GSM329707 2 0 1 0 1
#> GSM329709 2 0 1 0 1
#> GSM329711 2 0 1 0 1
#> GSM329714 2 0 1 0 1
#> GSM329693 2 0 1 0 1
#> GSM329696 2 0 1 0 1
#> GSM329699 2 0 1 0 1
#> GSM329702 2 0 1 0 1
#> GSM329706 2 0 1 0 1
#> GSM329708 2 0 1 0 1
#> GSM329710 2 0 1 0 1
#> GSM329713 1 0 1 1 0
#> GSM329695 1 0 1 1 0
#> GSM329698 1 0 1 1 0
#> GSM329701 1 0 1 1 0
#> GSM329705 1 0 1 1 0
#> GSM329712 2 0 1 0 1
#> GSM329715 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.000 1.000 0 1.000 0.000
#> GSM329663 2 0.000 1.000 0 1.000 0.000
#> GSM329664 3 0.435 0.795 0 0.184 0.816
#> GSM329666 2 0.000 1.000 0 1.000 0.000
#> GSM329667 2 0.000 1.000 0 1.000 0.000
#> GSM329670 2 0.000 1.000 0 1.000 0.000
#> GSM329672 2 0.000 1.000 0 1.000 0.000
#> GSM329674 2 0.000 1.000 0 1.000 0.000
#> GSM329661 3 0.000 0.965 0 0.000 1.000
#> GSM329669 2 0.000 1.000 0 1.000 0.000
#> GSM329662 1 0.000 1.000 1 0.000 0.000
#> GSM329665 1 0.000 1.000 1 0.000 0.000
#> GSM329668 1 0.000 1.000 1 0.000 0.000
#> GSM329671 1 0.000 1.000 1 0.000 0.000
#> GSM329673 1 0.000 1.000 1 0.000 0.000
#> GSM329675 1 0.000 1.000 1 0.000 0.000
#> GSM329676 1 0.000 1.000 1 0.000 0.000
#> GSM329677 3 0.000 0.965 0 0.000 1.000
#> GSM329679 2 0.000 1.000 0 1.000 0.000
#> GSM329681 3 0.000 0.965 0 0.000 1.000
#> GSM329683 3 0.000 0.965 0 0.000 1.000
#> GSM329686 3 0.000 0.965 0 0.000 1.000
#> GSM329689 3 0.000 0.965 0 0.000 1.000
#> GSM329678 3 0.000 0.965 0 0.000 1.000
#> GSM329680 3 0.000 0.965 0 0.000 1.000
#> GSM329685 3 0.000 0.965 0 0.000 1.000
#> GSM329688 3 0.000 0.965 0 0.000 1.000
#> GSM329691 3 0.000 0.965 0 0.000 1.000
#> GSM329682 1 0.000 1.000 1 0.000 0.000
#> GSM329684 1 0.000 1.000 1 0.000 0.000
#> GSM329687 1 0.000 1.000 1 0.000 0.000
#> GSM329690 1 0.000 1.000 1 0.000 0.000
#> GSM329692 3 0.000 0.965 0 0.000 1.000
#> GSM329694 3 0.480 0.748 0 0.220 0.780
#> GSM329697 2 0.000 1.000 0 1.000 0.000
#> GSM329700 2 0.000 1.000 0 1.000 0.000
#> GSM329703 2 0.000 1.000 0 1.000 0.000
#> GSM329704 3 0.455 0.776 0 0.200 0.800
#> GSM329707 3 0.000 0.965 0 0.000 1.000
#> GSM329709 2 0.000 1.000 0 1.000 0.000
#> GSM329711 2 0.000 1.000 0 1.000 0.000
#> GSM329714 2 0.000 1.000 0 1.000 0.000
#> GSM329693 2 0.000 1.000 0 1.000 0.000
#> GSM329696 2 0.000 1.000 0 1.000 0.000
#> GSM329699 2 0.000 1.000 0 1.000 0.000
#> GSM329702 2 0.000 1.000 0 1.000 0.000
#> GSM329706 3 0.000 0.965 0 0.000 1.000
#> GSM329708 3 0.000 0.965 0 0.000 1.000
#> GSM329710 3 0.000 0.965 0 0.000 1.000
#> GSM329713 1 0.000 1.000 1 0.000 0.000
#> GSM329695 1 0.000 1.000 1 0.000 0.000
#> GSM329698 1 0.000 1.000 1 0.000 0.000
#> GSM329701 1 0.000 1.000 1 0.000 0.000
#> GSM329705 1 0.000 1.000 1 0.000 0.000
#> GSM329712 2 0.000 1.000 0 1.000 0.000
#> GSM329715 1 0.000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.0000 0.979 0 1.000 0.000 0.000
#> GSM329663 2 0.0000 0.979 0 1.000 0.000 0.000
#> GSM329664 3 0.3870 0.727 0 0.208 0.788 0.004
#> GSM329666 2 0.0000 0.979 0 1.000 0.000 0.000
#> GSM329667 2 0.0188 0.977 0 0.996 0.000 0.004
#> GSM329670 2 0.0000 0.979 0 1.000 0.000 0.000
#> GSM329672 2 0.0188 0.977 0 0.996 0.000 0.004
#> GSM329674 2 0.0000 0.979 0 1.000 0.000 0.000
#> GSM329661 3 0.0000 0.960 0 0.000 1.000 0.000
#> GSM329669 2 0.0000 0.979 0 1.000 0.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329677 3 0.0000 0.960 0 0.000 1.000 0.000
#> GSM329679 2 0.0188 0.977 0 0.996 0.000 0.004
#> GSM329681 3 0.0000 0.960 0 0.000 1.000 0.000
#> GSM329683 3 0.0000 0.960 0 0.000 1.000 0.000
#> GSM329686 3 0.0000 0.960 0 0.000 1.000 0.000
#> GSM329689 3 0.0000 0.960 0 0.000 1.000 0.000
#> GSM329678 4 0.4955 0.148 0 0.000 0.444 0.556
#> GSM329680 3 0.0000 0.960 0 0.000 1.000 0.000
#> GSM329685 3 0.0000 0.960 0 0.000 1.000 0.000
#> GSM329688 3 0.0000 0.960 0 0.000 1.000 0.000
#> GSM329691 3 0.0000 0.960 0 0.000 1.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329692 4 0.0707 0.882 0 0.000 0.020 0.980
#> GSM329694 4 0.0672 0.885 0 0.008 0.008 0.984
#> GSM329697 2 0.0000 0.979 0 1.000 0.000 0.000
#> GSM329700 2 0.3764 0.721 0 0.784 0.000 0.216
#> GSM329703 4 0.0188 0.891 0 0.004 0.000 0.996
#> GSM329704 3 0.3908 0.721 0 0.212 0.784 0.004
#> GSM329707 3 0.0188 0.957 0 0.000 0.996 0.004
#> GSM329709 2 0.0000 0.979 0 1.000 0.000 0.000
#> GSM329711 2 0.0921 0.959 0 0.972 0.000 0.028
#> GSM329714 4 0.4564 0.441 0 0.328 0.000 0.672
#> GSM329693 4 0.0188 0.891 0 0.004 0.000 0.996
#> GSM329696 4 0.0188 0.891 0 0.004 0.000 0.996
#> GSM329699 4 0.0188 0.891 0 0.004 0.000 0.996
#> GSM329702 2 0.0000 0.979 0 1.000 0.000 0.000
#> GSM329706 3 0.0707 0.944 0 0.000 0.980 0.020
#> GSM329708 3 0.0000 0.960 0 0.000 1.000 0.000
#> GSM329710 4 0.0188 0.890 0 0.000 0.004 0.996
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329712 2 0.0921 0.959 0 0.972 0.000 0.028
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.0703 0.9518 0.000 0.976 0.000 0.000 0.024
#> GSM329663 2 0.0404 0.9548 0.000 0.988 0.000 0.000 0.012
#> GSM329664 5 0.1498 0.6412 0.000 0.008 0.016 0.024 0.952
#> GSM329666 2 0.0290 0.9565 0.000 0.992 0.000 0.000 0.008
#> GSM329667 5 0.2230 0.5542 0.000 0.116 0.000 0.000 0.884
#> GSM329670 2 0.0510 0.9544 0.000 0.984 0.000 0.000 0.016
#> GSM329672 2 0.1341 0.9314 0.000 0.944 0.000 0.000 0.056
#> GSM329674 2 0.0290 0.9565 0.000 0.992 0.000 0.000 0.008
#> GSM329661 3 0.4450 0.7006 0.000 0.000 0.508 0.488 0.004
#> GSM329669 2 0.0609 0.9522 0.000 0.980 0.000 0.000 0.020
#> GSM329662 1 0.0162 0.9939 0.996 0.000 0.000 0.000 0.004
#> GSM329665 1 0.0000 0.9941 1.000 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 0.9941 1.000 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0404 0.9922 0.988 0.000 0.000 0.000 0.012
#> GSM329673 1 0.0162 0.9939 0.996 0.000 0.000 0.000 0.004
#> GSM329675 1 0.0162 0.9939 0.996 0.000 0.000 0.000 0.004
#> GSM329676 1 0.0162 0.9939 0.996 0.000 0.000 0.000 0.004
#> GSM329677 5 0.6417 0.2357 0.000 0.000 0.172 0.404 0.424
#> GSM329679 2 0.1341 0.9314 0.000 0.944 0.000 0.000 0.056
#> GSM329681 3 0.4450 0.7006 0.000 0.000 0.508 0.488 0.004
#> GSM329683 3 0.4561 0.7022 0.000 0.000 0.504 0.488 0.008
#> GSM329686 3 0.4561 0.7022 0.000 0.000 0.504 0.488 0.008
#> GSM329689 3 0.4561 0.7022 0.000 0.000 0.504 0.488 0.008
#> GSM329678 3 0.0162 0.0423 0.000 0.000 0.996 0.000 0.004
#> GSM329680 3 0.4561 0.7022 0.000 0.000 0.504 0.488 0.008
#> GSM329685 3 0.4561 0.7022 0.000 0.000 0.504 0.488 0.008
#> GSM329688 3 0.4561 0.7022 0.000 0.000 0.504 0.488 0.008
#> GSM329691 3 0.4561 0.7022 0.000 0.000 0.504 0.488 0.008
#> GSM329682 1 0.0162 0.9939 0.996 0.000 0.000 0.000 0.004
#> GSM329684 1 0.0162 0.9939 0.996 0.000 0.000 0.000 0.004
#> GSM329687 1 0.0162 0.9939 0.996 0.000 0.000 0.000 0.004
#> GSM329690 1 0.0404 0.9922 0.988 0.000 0.000 0.000 0.012
#> GSM329692 3 0.4781 -0.8294 0.000 0.000 0.552 0.428 0.020
#> GSM329694 3 0.6685 -0.6763 0.000 0.000 0.436 0.280 0.284
#> GSM329697 2 0.0290 0.9565 0.000 0.992 0.000 0.000 0.008
#> GSM329700 2 0.3445 0.8265 0.000 0.824 0.000 0.140 0.036
#> GSM329703 4 0.4305 0.8993 0.000 0.000 0.488 0.512 0.000
#> GSM329704 5 0.1498 0.6412 0.000 0.008 0.016 0.024 0.952
#> GSM329707 5 0.5474 0.5280 0.000 0.000 0.076 0.348 0.576
#> GSM329709 2 0.0290 0.9565 0.000 0.992 0.000 0.000 0.008
#> GSM329711 2 0.2331 0.9028 0.000 0.900 0.000 0.080 0.020
#> GSM329714 4 0.6799 0.3953 0.000 0.332 0.128 0.504 0.036
#> GSM329693 4 0.4305 0.8993 0.000 0.000 0.488 0.512 0.000
#> GSM329696 4 0.4305 0.8993 0.000 0.000 0.488 0.512 0.000
#> GSM329699 4 0.4305 0.8993 0.000 0.000 0.488 0.512 0.000
#> GSM329702 2 0.0290 0.9565 0.000 0.992 0.000 0.000 0.008
#> GSM329706 5 0.5916 0.5032 0.000 0.000 0.120 0.336 0.544
#> GSM329708 3 0.4305 0.6976 0.000 0.000 0.512 0.488 0.000
#> GSM329710 4 0.4307 0.8936 0.000 0.000 0.496 0.504 0.000
#> GSM329713 1 0.0404 0.9922 0.988 0.000 0.000 0.000 0.012
#> GSM329695 1 0.0404 0.9922 0.988 0.000 0.000 0.000 0.012
#> GSM329698 1 0.0404 0.9922 0.988 0.000 0.000 0.000 0.012
#> GSM329701 1 0.0404 0.9922 0.988 0.000 0.000 0.000 0.012
#> GSM329705 1 0.0000 0.9941 1.000 0.000 0.000 0.000 0.000
#> GSM329712 2 0.2331 0.9028 0.000 0.900 0.000 0.080 0.020
#> GSM329715 1 0.0290 0.9930 0.992 0.000 0.000 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329660 2 0.3175 0.605 0.000 0.744 0.000 0.000 0.000 0.256
#> GSM329663 2 0.3499 0.411 0.000 0.680 0.000 0.000 0.000 0.320
#> GSM329664 5 0.0146 0.670 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM329666 2 0.0000 0.784 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329667 5 0.3790 0.479 0.000 0.156 0.000 0.000 0.772 0.072
#> GSM329670 2 0.3531 0.405 0.000 0.672 0.000 0.000 0.000 0.328
#> GSM329672 2 0.0622 0.775 0.000 0.980 0.000 0.000 0.012 0.008
#> GSM329674 2 0.0000 0.784 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329661 3 0.0632 0.920 0.000 0.000 0.976 0.000 0.000 0.024
#> GSM329669 2 0.2969 0.635 0.000 0.776 0.000 0.000 0.000 0.224
#> GSM329662 1 0.1501 0.936 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM329665 1 0.0547 0.946 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM329668 1 0.0260 0.946 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM329671 1 0.1267 0.939 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM329673 1 0.1501 0.936 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM329675 1 0.1501 0.936 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM329676 1 0.1501 0.936 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM329677 3 0.3867 -0.260 0.000 0.000 0.512 0.000 0.488 0.000
#> GSM329679 2 0.0622 0.775 0.000 0.980 0.000 0.000 0.012 0.008
#> GSM329681 3 0.0713 0.918 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM329683 3 0.0363 0.925 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM329686 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329689 3 0.0363 0.925 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM329678 4 0.4482 0.401 0.000 0.000 0.384 0.580 0.000 0.036
#> GSM329680 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329685 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329688 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329691 3 0.0000 0.927 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329682 1 0.1007 0.943 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM329684 1 0.1501 0.936 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM329687 1 0.1444 0.937 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM329690 1 0.1327 0.938 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM329692 4 0.4540 0.625 0.000 0.000 0.036 0.632 0.008 0.324
#> GSM329694 4 0.5738 0.486 0.000 0.000 0.000 0.496 0.192 0.312
#> GSM329697 2 0.0000 0.784 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329700 6 0.5165 0.641 0.000 0.228 0.000 0.156 0.000 0.616
#> GSM329703 4 0.0000 0.739 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329704 5 0.0146 0.670 0.000 0.004 0.000 0.000 0.996 0.000
#> GSM329707 5 0.4045 0.537 0.000 0.000 0.312 0.000 0.664 0.024
#> GSM329709 2 0.0000 0.784 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329711 2 0.5005 0.375 0.000 0.628 0.000 0.124 0.000 0.248
#> GSM329714 6 0.4732 0.661 0.000 0.068 0.000 0.320 0.000 0.612
#> GSM329693 4 0.0000 0.739 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329696 4 0.0000 0.739 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329699 4 0.0000 0.739 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329702 2 0.0000 0.784 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329706 5 0.4507 0.438 0.000 0.000 0.372 0.020 0.596 0.012
#> GSM329708 3 0.0713 0.918 0.000 0.000 0.972 0.000 0.000 0.028
#> GSM329710 4 0.2994 0.698 0.000 0.000 0.000 0.788 0.004 0.208
#> GSM329713 1 0.1327 0.938 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM329695 1 0.1327 0.938 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM329698 1 0.1327 0.938 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM329701 1 0.1267 0.939 0.940 0.000 0.000 0.000 0.000 0.060
#> GSM329705 1 0.0547 0.946 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM329712 2 0.5005 0.375 0.000 0.628 0.000 0.124 0.000 0.248
#> GSM329715 1 0.0937 0.943 0.960 0.000 0.000 0.000 0.000 0.040
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> SD:skmeans 56 0.505684 5.82e-11 2
#> SD:skmeans 56 0.010546 4.13e-10 3
#> SD:skmeans 54 0.000564 1.63e-09 4
#> SD:skmeans 51 0.000461 2.90e-09 5
#> SD:skmeans 47 0.000891 3.29e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "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 21163 rows and 56 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 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 1.000 1.000 0.4311 0.569 0.569
#> 3 3 1.000 0.993 0.997 0.5391 0.766 0.590
#> 4 4 0.848 0.762 0.906 0.1300 0.860 0.611
#> 5 5 0.925 0.891 0.953 0.0605 0.936 0.751
#> 6 6 0.917 0.868 0.909 0.0296 0.969 0.850
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 5
There is also optional best \(k\) = 2 3 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
#> GSM329660 2 0 1 0 1
#> GSM329663 2 0 1 0 1
#> GSM329664 2 0 1 0 1
#> GSM329666 2 0 1 0 1
#> GSM329667 2 0 1 0 1
#> GSM329670 2 0 1 0 1
#> GSM329672 2 0 1 0 1
#> GSM329674 2 0 1 0 1
#> GSM329661 2 0 1 0 1
#> GSM329669 2 0 1 0 1
#> GSM329662 1 0 1 1 0
#> GSM329665 1 0 1 1 0
#> GSM329668 1 0 1 1 0
#> GSM329671 1 0 1 1 0
#> GSM329673 1 0 1 1 0
#> GSM329675 1 0 1 1 0
#> GSM329676 1 0 1 1 0
#> GSM329677 2 0 1 0 1
#> GSM329679 2 0 1 0 1
#> GSM329681 2 0 1 0 1
#> GSM329683 2 0 1 0 1
#> GSM329686 2 0 1 0 1
#> GSM329689 2 0 1 0 1
#> GSM329678 2 0 1 0 1
#> GSM329680 2 0 1 0 1
#> GSM329685 2 0 1 0 1
#> GSM329688 2 0 1 0 1
#> GSM329691 2 0 1 0 1
#> GSM329682 1 0 1 1 0
#> GSM329684 1 0 1 1 0
#> GSM329687 1 0 1 1 0
#> GSM329690 1 0 1 1 0
#> GSM329692 2 0 1 0 1
#> GSM329694 2 0 1 0 1
#> GSM329697 2 0 1 0 1
#> GSM329700 2 0 1 0 1
#> GSM329703 2 0 1 0 1
#> GSM329704 2 0 1 0 1
#> GSM329707 2 0 1 0 1
#> GSM329709 2 0 1 0 1
#> GSM329711 2 0 1 0 1
#> GSM329714 2 0 1 0 1
#> GSM329693 2 0 1 0 1
#> GSM329696 2 0 1 0 1
#> GSM329699 2 0 1 0 1
#> GSM329702 2 0 1 0 1
#> GSM329706 2 0 1 0 1
#> GSM329708 2 0 1 0 1
#> GSM329710 2 0 1 0 1
#> GSM329713 1 0 1 1 0
#> GSM329695 1 0 1 1 0
#> GSM329698 1 0 1 1 0
#> GSM329701 1 0 1 1 0
#> GSM329705 1 0 1 1 0
#> GSM329712 2 0 1 0 1
#> GSM329715 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.000 1.000 0 1.000 0.000
#> GSM329663 2 0.000 1.000 0 1.000 0.000
#> GSM329664 2 0.000 1.000 0 1.000 0.000
#> GSM329666 2 0.000 1.000 0 1.000 0.000
#> GSM329667 2 0.000 1.000 0 1.000 0.000
#> GSM329670 2 0.000 1.000 0 1.000 0.000
#> GSM329672 2 0.000 1.000 0 1.000 0.000
#> GSM329674 2 0.000 1.000 0 1.000 0.000
#> GSM329661 3 0.000 0.986 0 0.000 1.000
#> GSM329669 2 0.000 1.000 0 1.000 0.000
#> GSM329662 1 0.000 1.000 1 0.000 0.000
#> GSM329665 1 0.000 1.000 1 0.000 0.000
#> GSM329668 1 0.000 1.000 1 0.000 0.000
#> GSM329671 1 0.000 1.000 1 0.000 0.000
#> GSM329673 1 0.000 1.000 1 0.000 0.000
#> GSM329675 1 0.000 1.000 1 0.000 0.000
#> GSM329676 1 0.000 1.000 1 0.000 0.000
#> GSM329677 3 0.000 0.986 0 0.000 1.000
#> GSM329679 2 0.000 1.000 0 1.000 0.000
#> GSM329681 3 0.000 0.986 0 0.000 1.000
#> GSM329683 3 0.000 0.986 0 0.000 1.000
#> GSM329686 3 0.000 0.986 0 0.000 1.000
#> GSM329689 3 0.000 0.986 0 0.000 1.000
#> GSM329678 3 0.000 0.986 0 0.000 1.000
#> GSM329680 3 0.000 0.986 0 0.000 1.000
#> GSM329685 3 0.000 0.986 0 0.000 1.000
#> GSM329688 3 0.000 0.986 0 0.000 1.000
#> GSM329691 3 0.000 0.986 0 0.000 1.000
#> GSM329682 1 0.000 1.000 1 0.000 0.000
#> GSM329684 1 0.000 1.000 1 0.000 0.000
#> GSM329687 1 0.000 1.000 1 0.000 0.000
#> GSM329690 1 0.000 1.000 1 0.000 0.000
#> GSM329692 3 0.341 0.861 0 0.124 0.876
#> GSM329694 2 0.000 1.000 0 1.000 0.000
#> GSM329697 2 0.000 1.000 0 1.000 0.000
#> GSM329700 2 0.000 1.000 0 1.000 0.000
#> GSM329703 2 0.000 1.000 0 1.000 0.000
#> GSM329704 2 0.000 1.000 0 1.000 0.000
#> GSM329707 3 0.186 0.940 0 0.052 0.948
#> GSM329709 2 0.000 1.000 0 1.000 0.000
#> GSM329711 2 0.000 1.000 0 1.000 0.000
#> GSM329714 2 0.000 1.000 0 1.000 0.000
#> GSM329693 2 0.000 1.000 0 1.000 0.000
#> GSM329696 2 0.000 1.000 0 1.000 0.000
#> GSM329699 2 0.000 1.000 0 1.000 0.000
#> GSM329702 2 0.000 1.000 0 1.000 0.000
#> GSM329706 3 0.000 0.986 0 0.000 1.000
#> GSM329708 3 0.000 0.986 0 0.000 1.000
#> GSM329710 2 0.000 1.000 0 1.000 0.000
#> GSM329713 1 0.000 1.000 1 0.000 0.000
#> GSM329695 1 0.000 1.000 1 0.000 0.000
#> GSM329698 1 0.000 1.000 1 0.000 0.000
#> GSM329701 1 0.000 1.000 1 0.000 0.000
#> GSM329705 1 0.000 1.000 1 0.000 0.000
#> GSM329712 2 0.000 1.000 0 1.000 0.000
#> GSM329715 1 0.000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.0000 0.835 0 1.000 0.000 0.000
#> GSM329663 2 0.1022 0.801 0 0.968 0.000 0.032
#> GSM329664 4 0.4843 0.259 0 0.396 0.000 0.604
#> GSM329666 2 0.0000 0.835 0 1.000 0.000 0.000
#> GSM329667 2 0.4866 0.228 0 0.596 0.000 0.404
#> GSM329670 2 0.0000 0.835 0 1.000 0.000 0.000
#> GSM329672 2 0.4866 0.228 0 0.596 0.000 0.404
#> GSM329674 2 0.0000 0.835 0 1.000 0.000 0.000
#> GSM329661 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329669 2 0.0000 0.835 0 1.000 0.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329677 3 0.4661 0.462 0 0.000 0.652 0.348
#> GSM329679 2 0.4866 0.228 0 0.596 0.000 0.404
#> GSM329681 3 0.3764 0.679 0 0.000 0.784 0.216
#> GSM329683 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329686 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329689 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329678 4 0.0000 0.628 0 0.000 0.000 1.000
#> GSM329680 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329685 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329688 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329691 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329692 4 0.0000 0.628 0 0.000 0.000 1.000
#> GSM329694 4 0.4843 0.259 0 0.396 0.000 0.604
#> GSM329697 2 0.0000 0.835 0 1.000 0.000 0.000
#> GSM329700 2 0.3610 0.516 0 0.800 0.000 0.200
#> GSM329703 4 0.4866 0.370 0 0.404 0.000 0.596
#> GSM329704 4 0.4843 0.259 0 0.396 0.000 0.604
#> GSM329707 4 0.6391 0.352 0 0.304 0.092 0.604
#> GSM329709 2 0.0000 0.835 0 1.000 0.000 0.000
#> GSM329711 2 0.0000 0.835 0 1.000 0.000 0.000
#> GSM329714 4 0.4746 0.407 0 0.368 0.000 0.632
#> GSM329693 4 0.4866 0.370 0 0.404 0.000 0.596
#> GSM329696 4 0.4866 0.370 0 0.404 0.000 0.596
#> GSM329699 4 0.0336 0.629 0 0.008 0.000 0.992
#> GSM329702 2 0.0000 0.835 0 1.000 0.000 0.000
#> GSM329706 4 0.2081 0.595 0 0.000 0.084 0.916
#> GSM329708 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329710 4 0.0336 0.629 0 0.008 0.000 0.992
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329712 2 0.0000 0.835 0 1.000 0.000 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 5 0.3274 0.690 0 0.220 0.000 0.000 0.780
#> GSM329663 2 0.0000 0.924 0 1.000 0.000 0.000 0.000
#> GSM329664 5 0.0290 0.850 0 0.008 0.000 0.000 0.992
#> GSM329666 2 0.0000 0.924 0 1.000 0.000 0.000 0.000
#> GSM329667 5 0.3242 0.695 0 0.216 0.000 0.000 0.784
#> GSM329670 2 0.0000 0.924 0 1.000 0.000 0.000 0.000
#> GSM329672 2 0.0794 0.907 0 0.972 0.000 0.000 0.028
#> GSM329674 2 0.0000 0.924 0 1.000 0.000 0.000 0.000
#> GSM329661 3 0.0290 0.946 0 0.000 0.992 0.000 0.008
#> GSM329669 2 0.0000 0.924 0 1.000 0.000 0.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329677 5 0.1478 0.805 0 0.000 0.064 0.000 0.936
#> GSM329679 2 0.2690 0.767 0 0.844 0.000 0.000 0.156
#> GSM329681 3 0.3305 0.754 0 0.000 0.776 0.000 0.224
#> GSM329683 3 0.0290 0.946 0 0.000 0.992 0.000 0.008
#> GSM329686 3 0.0000 0.948 0 0.000 1.000 0.000 0.000
#> GSM329689 3 0.3242 0.764 0 0.000 0.784 0.000 0.216
#> GSM329678 4 0.2127 0.852 0 0.000 0.000 0.892 0.108
#> GSM329680 3 0.0000 0.948 0 0.000 1.000 0.000 0.000
#> GSM329685 3 0.0000 0.948 0 0.000 1.000 0.000 0.000
#> GSM329688 3 0.0000 0.948 0 0.000 1.000 0.000 0.000
#> GSM329691 3 0.0000 0.948 0 0.000 1.000 0.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329692 5 0.4256 0.121 0 0.000 0.000 0.436 0.564
#> GSM329694 5 0.0290 0.850 0 0.008 0.000 0.000 0.992
#> GSM329697 2 0.0000 0.924 0 1.000 0.000 0.000 0.000
#> GSM329700 2 0.4283 0.211 0 0.544 0.000 0.456 0.000
#> GSM329703 4 0.0000 0.937 0 0.000 0.000 1.000 0.000
#> GSM329704 5 0.0290 0.850 0 0.008 0.000 0.000 0.992
#> GSM329707 5 0.0000 0.846 0 0.000 0.000 0.000 1.000
#> GSM329709 2 0.0000 0.924 0 1.000 0.000 0.000 0.000
#> GSM329711 2 0.1965 0.868 0 0.904 0.000 0.096 0.000
#> GSM329714 4 0.3628 0.714 0 0.012 0.000 0.772 0.216
#> GSM329693 4 0.0000 0.937 0 0.000 0.000 1.000 0.000
#> GSM329696 4 0.0000 0.937 0 0.000 0.000 1.000 0.000
#> GSM329699 4 0.0000 0.937 0 0.000 0.000 1.000 0.000
#> GSM329702 2 0.0000 0.924 0 1.000 0.000 0.000 0.000
#> GSM329706 5 0.0609 0.842 0 0.000 0.000 0.020 0.980
#> GSM329708 3 0.0000 0.948 0 0.000 1.000 0.000 0.000
#> GSM329710 4 0.0000 0.937 0 0.000 0.000 1.000 0.000
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329712 2 0.2020 0.865 0 0.900 0.000 0.100 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 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
#> GSM329660 6 0.4923 0.7298 0.000 0.172 0.000 0.000 0.172 0.656
#> GSM329663 2 0.0632 0.8992 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM329664 5 0.0000 0.8231 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM329666 2 0.0000 0.9094 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329667 5 0.0000 0.8231 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM329670 2 0.0000 0.9094 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329672 2 0.2378 0.7559 0.000 0.848 0.000 0.000 0.152 0.000
#> GSM329674 2 0.0000 0.9094 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329661 3 0.3515 0.7747 0.000 0.000 0.676 0.000 0.000 0.324
#> GSM329669 6 0.3756 0.8293 0.000 0.400 0.000 0.000 0.000 0.600
#> GSM329662 1 0.0000 0.9969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 0.9969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 0.9969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0146 0.9957 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM329673 1 0.0000 0.9969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 0.9969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 0.9969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329677 5 0.4725 0.5275 0.000 0.000 0.064 0.000 0.604 0.332
#> GSM329679 2 0.3101 0.6132 0.000 0.756 0.000 0.000 0.244 0.000
#> GSM329681 3 0.3547 0.7714 0.000 0.000 0.668 0.000 0.000 0.332
#> GSM329683 3 0.3547 0.7714 0.000 0.000 0.668 0.000 0.000 0.332
#> GSM329686 3 0.0000 0.8613 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329689 3 0.3547 0.7714 0.000 0.000 0.668 0.000 0.000 0.332
#> GSM329678 4 0.0260 0.9308 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM329680 3 0.0000 0.8613 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329685 3 0.0000 0.8613 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329688 3 0.0000 0.8613 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329691 3 0.0000 0.8613 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329682 1 0.0000 0.9969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0000 0.9969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329687 1 0.0000 0.9969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0363 0.9925 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM329692 5 0.4739 0.0262 0.000 0.000 0.000 0.436 0.516 0.048
#> GSM329694 5 0.0000 0.8231 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM329697 2 0.0632 0.8992 0.000 0.976 0.000 0.000 0.024 0.000
#> GSM329700 6 0.4342 0.8810 0.000 0.308 0.000 0.008 0.028 0.656
#> GSM329703 4 0.0000 0.9368 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329704 5 0.0000 0.8231 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM329707 5 0.2996 0.7033 0.000 0.000 0.000 0.000 0.772 0.228
#> GSM329709 2 0.0000 0.9094 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329711 6 0.3592 0.8890 0.000 0.344 0.000 0.000 0.000 0.656
#> GSM329714 4 0.4443 0.4879 0.000 0.000 0.000 0.648 0.300 0.052
#> GSM329693 4 0.0000 0.9368 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329696 4 0.0000 0.9368 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329699 4 0.0000 0.9368 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329702 2 0.0000 0.9094 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329706 5 0.0632 0.8145 0.000 0.000 0.000 0.024 0.976 0.000
#> GSM329708 3 0.0000 0.8613 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329710 4 0.0000 0.9368 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329713 1 0.0363 0.9925 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM329695 1 0.0363 0.9925 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM329698 1 0.0363 0.9925 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM329701 1 0.0260 0.9942 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM329705 1 0.0000 0.9969 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329712 6 0.3714 0.8908 0.000 0.340 0.000 0.000 0.004 0.656
#> GSM329715 1 0.0000 0.9969 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> SD:pam 56 0.505684 5.82e-11 2
#> SD:pam 56 0.000528 2.02e-10 3
#> SD:pam 44 0.001155 2.46e-08 4
#> SD:pam 54 0.001995 8.34e-10 5
#> SD:pam 54 0.005841 9.31e-10 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 21163 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4311 0.569 0.569
#> 3 3 0.790 0.830 0.923 0.5364 0.773 0.601
#> 4 4 0.890 0.899 0.943 0.1186 0.862 0.633
#> 5 5 0.912 0.865 0.936 0.0606 0.924 0.730
#> 6 6 0.889 0.805 0.903 0.0384 0.946 0.759
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2
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
#> GSM329660 2 0 1 0 1
#> GSM329663 2 0 1 0 1
#> GSM329664 2 0 1 0 1
#> GSM329666 2 0 1 0 1
#> GSM329667 2 0 1 0 1
#> GSM329670 2 0 1 0 1
#> GSM329672 2 0 1 0 1
#> GSM329674 2 0 1 0 1
#> GSM329661 2 0 1 0 1
#> GSM329669 2 0 1 0 1
#> GSM329662 1 0 1 1 0
#> GSM329665 1 0 1 1 0
#> GSM329668 1 0 1 1 0
#> GSM329671 1 0 1 1 0
#> GSM329673 1 0 1 1 0
#> GSM329675 1 0 1 1 0
#> GSM329676 1 0 1 1 0
#> GSM329677 2 0 1 0 1
#> GSM329679 2 0 1 0 1
#> GSM329681 2 0 1 0 1
#> GSM329683 2 0 1 0 1
#> GSM329686 2 0 1 0 1
#> GSM329689 2 0 1 0 1
#> GSM329678 2 0 1 0 1
#> GSM329680 2 0 1 0 1
#> GSM329685 2 0 1 0 1
#> GSM329688 2 0 1 0 1
#> GSM329691 2 0 1 0 1
#> GSM329682 1 0 1 1 0
#> GSM329684 1 0 1 1 0
#> GSM329687 1 0 1 1 0
#> GSM329690 1 0 1 1 0
#> GSM329692 2 0 1 0 1
#> GSM329694 2 0 1 0 1
#> GSM329697 2 0 1 0 1
#> GSM329700 2 0 1 0 1
#> GSM329703 2 0 1 0 1
#> GSM329704 2 0 1 0 1
#> GSM329707 2 0 1 0 1
#> GSM329709 2 0 1 0 1
#> GSM329711 2 0 1 0 1
#> GSM329714 2 0 1 0 1
#> GSM329693 2 0 1 0 1
#> GSM329696 2 0 1 0 1
#> GSM329699 2 0 1 0 1
#> GSM329702 2 0 1 0 1
#> GSM329706 2 0 1 0 1
#> GSM329708 2 0 1 0 1
#> GSM329710 2 0 1 0 1
#> GSM329713 1 0 1 1 0
#> GSM329695 1 0 1 1 0
#> GSM329698 1 0 1 1 0
#> GSM329701 1 0 1 1 0
#> GSM329705 1 0 1 1 0
#> GSM329712 2 0 1 0 1
#> GSM329715 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.0000 0.8253 0 1.000 0.000
#> GSM329663 2 0.0000 0.8253 0 1.000 0.000
#> GSM329664 3 0.6299 0.0901 0 0.476 0.524
#> GSM329666 2 0.0000 0.8253 0 1.000 0.000
#> GSM329667 2 0.4654 0.6546 0 0.792 0.208
#> GSM329670 2 0.0000 0.8253 0 1.000 0.000
#> GSM329672 2 0.0000 0.8253 0 1.000 0.000
#> GSM329674 2 0.0000 0.8253 0 1.000 0.000
#> GSM329661 3 0.0237 0.9211 0 0.004 0.996
#> GSM329669 2 0.0000 0.8253 0 1.000 0.000
#> GSM329662 1 0.0000 1.0000 1 0.000 0.000
#> GSM329665 1 0.0000 1.0000 1 0.000 0.000
#> GSM329668 1 0.0000 1.0000 1 0.000 0.000
#> GSM329671 1 0.0000 1.0000 1 0.000 0.000
#> GSM329673 1 0.0000 1.0000 1 0.000 0.000
#> GSM329675 1 0.0000 1.0000 1 0.000 0.000
#> GSM329676 1 0.0000 1.0000 1 0.000 0.000
#> GSM329677 3 0.0424 0.9206 0 0.008 0.992
#> GSM329679 2 0.0000 0.8253 0 1.000 0.000
#> GSM329681 3 0.0424 0.9206 0 0.008 0.992
#> GSM329683 3 0.0000 0.9202 0 0.000 1.000
#> GSM329686 3 0.0000 0.9202 0 0.000 1.000
#> GSM329689 3 0.0424 0.9206 0 0.008 0.992
#> GSM329678 2 0.6062 0.5232 0 0.616 0.384
#> GSM329680 3 0.0424 0.9206 0 0.008 0.992
#> GSM329685 3 0.0000 0.9202 0 0.000 1.000
#> GSM329688 3 0.0000 0.9202 0 0.000 1.000
#> GSM329691 3 0.0000 0.9202 0 0.000 1.000
#> GSM329682 1 0.0000 1.0000 1 0.000 0.000
#> GSM329684 1 0.0000 1.0000 1 0.000 0.000
#> GSM329687 1 0.0000 1.0000 1 0.000 0.000
#> GSM329690 1 0.0000 1.0000 1 0.000 0.000
#> GSM329692 2 0.5968 0.5581 0 0.636 0.364
#> GSM329694 2 0.5216 0.6656 0 0.740 0.260
#> GSM329697 2 0.0000 0.8253 0 1.000 0.000
#> GSM329700 2 0.0000 0.8253 0 1.000 0.000
#> GSM329703 2 0.5968 0.5581 0 0.636 0.364
#> GSM329704 2 0.6192 0.1946 0 0.580 0.420
#> GSM329707 3 0.3941 0.7531 0 0.156 0.844
#> GSM329709 2 0.0000 0.8253 0 1.000 0.000
#> GSM329711 2 0.0000 0.8253 0 1.000 0.000
#> GSM329714 2 0.1529 0.8083 0 0.960 0.040
#> GSM329693 2 0.5968 0.5581 0 0.636 0.364
#> GSM329696 2 0.5968 0.5581 0 0.636 0.364
#> GSM329699 2 0.5968 0.5581 0 0.636 0.364
#> GSM329702 2 0.0000 0.8253 0 1.000 0.000
#> GSM329706 3 0.4121 0.7340 0 0.168 0.832
#> GSM329708 3 0.0237 0.9211 0 0.004 0.996
#> GSM329710 2 0.5968 0.5581 0 0.636 0.364
#> GSM329713 1 0.0000 1.0000 1 0.000 0.000
#> GSM329695 1 0.0000 1.0000 1 0.000 0.000
#> GSM329698 1 0.0000 1.0000 1 0.000 0.000
#> GSM329701 1 0.0000 1.0000 1 0.000 0.000
#> GSM329705 1 0.0000 1.0000 1 0.000 0.000
#> GSM329712 2 0.0000 0.8253 0 1.000 0.000
#> GSM329715 1 0.0000 1.0000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.3610 0.766 0 0.800 0.000 0.200
#> GSM329663 2 0.1022 0.840 0 0.968 0.000 0.032
#> GSM329664 2 0.1913 0.824 0 0.940 0.040 0.020
#> GSM329666 2 0.0000 0.839 0 1.000 0.000 0.000
#> GSM329667 2 0.1389 0.836 0 0.952 0.000 0.048
#> GSM329670 2 0.3610 0.766 0 0.800 0.000 0.200
#> GSM329672 2 0.1118 0.838 0 0.964 0.000 0.036
#> GSM329674 2 0.0000 0.839 0 1.000 0.000 0.000
#> GSM329661 3 0.0000 0.977 0 0.000 1.000 0.000
#> GSM329669 2 0.3610 0.766 0 0.800 0.000 0.200
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329677 3 0.3610 0.744 0 0.200 0.800 0.000
#> GSM329679 2 0.1022 0.839 0 0.968 0.000 0.032
#> GSM329681 3 0.0000 0.977 0 0.000 1.000 0.000
#> GSM329683 3 0.0000 0.977 0 0.000 1.000 0.000
#> GSM329686 3 0.0000 0.977 0 0.000 1.000 0.000
#> GSM329689 3 0.0000 0.977 0 0.000 1.000 0.000
#> GSM329678 4 0.0000 0.997 0 0.000 0.000 1.000
#> GSM329680 3 0.0000 0.977 0 0.000 1.000 0.000
#> GSM329685 3 0.0000 0.977 0 0.000 1.000 0.000
#> GSM329688 3 0.0000 0.977 0 0.000 1.000 0.000
#> GSM329691 3 0.0000 0.977 0 0.000 1.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329692 4 0.0000 0.997 0 0.000 0.000 1.000
#> GSM329694 2 0.4585 0.536 0 0.668 0.000 0.332
#> GSM329697 2 0.0000 0.839 0 1.000 0.000 0.000
#> GSM329700 2 0.4164 0.737 0 0.736 0.000 0.264
#> GSM329703 4 0.0188 0.997 0 0.004 0.000 0.996
#> GSM329704 2 0.1389 0.836 0 0.952 0.000 0.048
#> GSM329707 2 0.6397 0.536 0 0.652 0.164 0.184
#> GSM329709 2 0.0000 0.839 0 1.000 0.000 0.000
#> GSM329711 2 0.3726 0.758 0 0.788 0.000 0.212
#> GSM329714 2 0.3610 0.766 0 0.800 0.000 0.200
#> GSM329693 4 0.0188 0.997 0 0.004 0.000 0.996
#> GSM329696 4 0.0188 0.997 0 0.004 0.000 0.996
#> GSM329699 4 0.0188 0.997 0 0.004 0.000 0.996
#> GSM329702 2 0.0000 0.839 0 1.000 0.000 0.000
#> GSM329706 2 0.5582 0.345 0 0.576 0.024 0.400
#> GSM329708 3 0.0000 0.977 0 0.000 1.000 0.000
#> GSM329710 4 0.0000 0.997 0 0.000 0.000 1.000
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329712 2 0.4431 0.687 0 0.696 0.000 0.304
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.0000 0.855 0 1.000 0.000 0.000 0.000
#> GSM329663 2 0.0000 0.855 0 1.000 0.000 0.000 0.000
#> GSM329664 5 0.1908 0.825 0 0.092 0.000 0.000 0.908
#> GSM329666 2 0.0162 0.856 0 0.996 0.000 0.000 0.004
#> GSM329667 5 0.3177 0.744 0 0.208 0.000 0.000 0.792
#> GSM329670 2 0.0000 0.855 0 1.000 0.000 0.000 0.000
#> GSM329672 2 0.1270 0.821 0 0.948 0.000 0.000 0.052
#> GSM329674 2 0.0162 0.856 0 0.996 0.000 0.000 0.004
#> GSM329661 3 0.0703 0.950 0 0.000 0.976 0.000 0.024
#> GSM329669 2 0.0000 0.855 0 1.000 0.000 0.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329677 5 0.3534 0.534 0 0.000 0.256 0.000 0.744
#> GSM329679 2 0.1410 0.814 0 0.940 0.000 0.000 0.060
#> GSM329681 3 0.2966 0.825 0 0.000 0.816 0.000 0.184
#> GSM329683 3 0.0963 0.946 0 0.000 0.964 0.000 0.036
#> GSM329686 3 0.0703 0.950 0 0.000 0.976 0.000 0.024
#> GSM329689 3 0.2605 0.866 0 0.000 0.852 0.000 0.148
#> GSM329678 4 0.0324 0.894 0 0.000 0.004 0.992 0.004
#> GSM329680 3 0.1043 0.924 0 0.000 0.960 0.040 0.000
#> GSM329685 3 0.0000 0.951 0 0.000 1.000 0.000 0.000
#> GSM329688 3 0.0000 0.951 0 0.000 1.000 0.000 0.000
#> GSM329691 3 0.0000 0.951 0 0.000 1.000 0.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329692 4 0.3241 0.765 0 0.024 0.000 0.832 0.144
#> GSM329694 4 0.6463 0.301 0 0.228 0.000 0.496 0.276
#> GSM329697 2 0.0162 0.856 0 0.996 0.000 0.000 0.004
#> GSM329700 2 0.4045 0.508 0 0.644 0.000 0.356 0.000
#> GSM329703 4 0.0000 0.899 0 0.000 0.000 1.000 0.000
#> GSM329704 5 0.2280 0.816 0 0.120 0.000 0.000 0.880
#> GSM329707 5 0.0000 0.794 0 0.000 0.000 0.000 1.000
#> GSM329709 2 0.0162 0.856 0 0.996 0.000 0.000 0.004
#> GSM329711 2 0.4030 0.514 0 0.648 0.000 0.352 0.000
#> GSM329714 2 0.5181 0.426 0 0.588 0.000 0.360 0.052
#> GSM329693 4 0.0000 0.899 0 0.000 0.000 1.000 0.000
#> GSM329696 4 0.0000 0.899 0 0.000 0.000 1.000 0.000
#> GSM329699 4 0.0000 0.899 0 0.000 0.000 1.000 0.000
#> GSM329702 2 0.0162 0.856 0 0.996 0.000 0.000 0.004
#> GSM329706 5 0.2964 0.748 0 0.024 0.000 0.120 0.856
#> GSM329708 3 0.0000 0.951 0 0.000 1.000 0.000 0.000
#> GSM329710 4 0.0000 0.899 0 0.000 0.000 1.000 0.000
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329712 2 0.4114 0.469 0 0.624 0.000 0.376 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 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
#> GSM329660 6 0.4045 0.518 0.000 0.428 0.000 0.000 0.008 0.564
#> GSM329663 2 0.4543 -0.147 0.000 0.576 0.000 0.000 0.040 0.384
#> GSM329664 5 0.4757 0.664 0.000 0.180 0.000 0.000 0.676 0.144
#> GSM329666 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329667 2 0.3221 0.650 0.000 0.792 0.000 0.000 0.188 0.020
#> GSM329670 6 0.4032 0.530 0.000 0.420 0.000 0.000 0.008 0.572
#> GSM329672 2 0.0146 0.886 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM329674 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329661 3 0.0363 0.870 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM329669 6 0.3797 0.533 0.000 0.420 0.000 0.000 0.000 0.580
#> GSM329662 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329673 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0363 0.990 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM329676 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329677 5 0.2882 0.509 0.000 0.000 0.180 0.000 0.812 0.008
#> GSM329679 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329681 3 0.5045 0.404 0.000 0.000 0.552 0.000 0.364 0.084
#> GSM329683 3 0.0458 0.868 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM329686 3 0.0363 0.870 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM329689 3 0.5035 0.410 0.000 0.000 0.556 0.000 0.360 0.084
#> GSM329678 4 0.0363 0.957 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM329680 3 0.0363 0.866 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM329685 3 0.0000 0.870 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329688 3 0.0000 0.870 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329691 3 0.0000 0.870 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329682 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0363 0.990 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM329687 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329692 4 0.3014 0.767 0.000 0.000 0.000 0.804 0.012 0.184
#> GSM329694 6 0.4180 -0.212 0.000 0.008 0.000 0.012 0.348 0.632
#> GSM329697 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329700 6 0.2854 0.699 0.000 0.208 0.000 0.000 0.000 0.792
#> GSM329703 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329704 5 0.4762 0.665 0.000 0.148 0.000 0.000 0.676 0.176
#> GSM329707 5 0.1802 0.690 0.000 0.072 0.000 0.000 0.916 0.012
#> GSM329709 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329711 6 0.2664 0.704 0.000 0.184 0.000 0.000 0.000 0.816
#> GSM329714 6 0.0547 0.530 0.000 0.020 0.000 0.000 0.000 0.980
#> GSM329693 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329696 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329699 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329702 2 0.0000 0.890 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329706 5 0.3490 0.659 0.000 0.000 0.000 0.008 0.724 0.268
#> GSM329708 3 0.2219 0.744 0.000 0.000 0.864 0.136 0.000 0.000
#> GSM329710 4 0.0260 0.960 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM329713 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329695 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329698 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329701 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329705 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329712 6 0.2664 0.704 0.000 0.184 0.000 0.000 0.000 0.816
#> GSM329715 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> SD:mclust 56 5.06e-01 5.82e-11 2
#> SD:mclust 54 1.79e-03 9.10e-10 3
#> SD:mclust 55 7.84e-05 2.32e-11 4
#> SD:mclust 53 1.78e-03 2.07e-10 5
#> SD:mclust 52 1.96e-02 2.76e-09 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21163 rows and 56 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 1.000 0.998 0.999 0.4316 0.569 0.569
#> 3 3 1.000 0.969 0.986 0.5565 0.761 0.580
#> 4 4 0.755 0.681 0.829 0.1145 0.871 0.639
#> 5 5 0.725 0.625 0.770 0.0319 0.963 0.860
#> 6 6 0.709 0.610 0.741 0.0371 0.946 0.787
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
#> GSM329660 2 0.0000 0.999 0.000 1.000
#> GSM329663 2 0.0000 0.999 0.000 1.000
#> GSM329664 2 0.0000 0.999 0.000 1.000
#> GSM329666 2 0.0000 0.999 0.000 1.000
#> GSM329667 2 0.0000 0.999 0.000 1.000
#> GSM329670 2 0.0938 0.988 0.012 0.988
#> GSM329672 2 0.0000 0.999 0.000 1.000
#> GSM329674 2 0.0000 0.999 0.000 1.000
#> GSM329661 2 0.0000 0.999 0.000 1.000
#> GSM329669 2 0.2043 0.968 0.032 0.968
#> GSM329662 1 0.0000 1.000 1.000 0.000
#> GSM329665 1 0.0000 1.000 1.000 0.000
#> GSM329668 1 0.0000 1.000 1.000 0.000
#> GSM329671 1 0.0000 1.000 1.000 0.000
#> GSM329673 1 0.0000 1.000 1.000 0.000
#> GSM329675 1 0.0000 1.000 1.000 0.000
#> GSM329676 1 0.0000 1.000 1.000 0.000
#> GSM329677 2 0.0000 0.999 0.000 1.000
#> GSM329679 2 0.0000 0.999 0.000 1.000
#> GSM329681 2 0.0000 0.999 0.000 1.000
#> GSM329683 2 0.0000 0.999 0.000 1.000
#> GSM329686 2 0.0000 0.999 0.000 1.000
#> GSM329689 2 0.0000 0.999 0.000 1.000
#> GSM329678 2 0.0000 0.999 0.000 1.000
#> GSM329680 2 0.0000 0.999 0.000 1.000
#> GSM329685 2 0.0000 0.999 0.000 1.000
#> GSM329688 2 0.0000 0.999 0.000 1.000
#> GSM329691 2 0.0000 0.999 0.000 1.000
#> GSM329682 1 0.0000 1.000 1.000 0.000
#> GSM329684 1 0.0000 1.000 1.000 0.000
#> GSM329687 1 0.0000 1.000 1.000 0.000
#> GSM329690 1 0.0000 1.000 1.000 0.000
#> GSM329692 2 0.0000 0.999 0.000 1.000
#> GSM329694 2 0.0000 0.999 0.000 1.000
#> GSM329697 2 0.0000 0.999 0.000 1.000
#> GSM329700 2 0.0000 0.999 0.000 1.000
#> GSM329703 2 0.0000 0.999 0.000 1.000
#> GSM329704 2 0.0000 0.999 0.000 1.000
#> GSM329707 2 0.0000 0.999 0.000 1.000
#> GSM329709 2 0.0000 0.999 0.000 1.000
#> GSM329711 2 0.0000 0.999 0.000 1.000
#> GSM329714 2 0.0000 0.999 0.000 1.000
#> GSM329693 2 0.0000 0.999 0.000 1.000
#> GSM329696 2 0.0000 0.999 0.000 1.000
#> GSM329699 2 0.0000 0.999 0.000 1.000
#> GSM329702 2 0.0000 0.999 0.000 1.000
#> GSM329706 2 0.0000 0.999 0.000 1.000
#> GSM329708 2 0.0000 0.999 0.000 1.000
#> GSM329710 2 0.0000 0.999 0.000 1.000
#> GSM329713 1 0.0000 1.000 1.000 0.000
#> GSM329695 1 0.0000 1.000 1.000 0.000
#> GSM329698 1 0.0000 1.000 1.000 0.000
#> GSM329701 1 0.0000 1.000 1.000 0.000
#> GSM329705 1 0.0000 1.000 1.000 0.000
#> GSM329712 2 0.0000 0.999 0.000 1.000
#> GSM329715 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.0000 0.965 0 1.000 0.000
#> GSM329663 2 0.0000 0.965 0 1.000 0.000
#> GSM329664 2 0.5733 0.555 0 0.676 0.324
#> GSM329666 2 0.0000 0.965 0 1.000 0.000
#> GSM329667 2 0.0000 0.965 0 1.000 0.000
#> GSM329670 2 0.0000 0.965 0 1.000 0.000
#> GSM329672 2 0.0000 0.965 0 1.000 0.000
#> GSM329674 2 0.0000 0.965 0 1.000 0.000
#> GSM329661 3 0.0000 0.998 0 0.000 1.000
#> GSM329669 2 0.0000 0.965 0 1.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000
#> GSM329677 3 0.0000 0.998 0 0.000 1.000
#> GSM329679 2 0.0000 0.965 0 1.000 0.000
#> GSM329681 3 0.0000 0.998 0 0.000 1.000
#> GSM329683 3 0.0000 0.998 0 0.000 1.000
#> GSM329686 3 0.0000 0.998 0 0.000 1.000
#> GSM329689 3 0.0000 0.998 0 0.000 1.000
#> GSM329678 3 0.0000 0.998 0 0.000 1.000
#> GSM329680 3 0.0000 0.998 0 0.000 1.000
#> GSM329685 3 0.0000 0.998 0 0.000 1.000
#> GSM329688 3 0.0000 0.998 0 0.000 1.000
#> GSM329691 3 0.0000 0.998 0 0.000 1.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000
#> GSM329692 3 0.0000 0.998 0 0.000 1.000
#> GSM329694 2 0.0892 0.950 0 0.980 0.020
#> GSM329697 2 0.0000 0.965 0 1.000 0.000
#> GSM329700 2 0.0000 0.965 0 1.000 0.000
#> GSM329703 2 0.0000 0.965 0 1.000 0.000
#> GSM329704 2 0.5497 0.616 0 0.708 0.292
#> GSM329707 3 0.0000 0.998 0 0.000 1.000
#> GSM329709 2 0.0000 0.965 0 1.000 0.000
#> GSM329711 2 0.0000 0.965 0 1.000 0.000
#> GSM329714 2 0.0000 0.965 0 1.000 0.000
#> GSM329693 2 0.0000 0.965 0 1.000 0.000
#> GSM329696 2 0.0000 0.965 0 1.000 0.000
#> GSM329699 2 0.3267 0.861 0 0.884 0.116
#> GSM329702 2 0.0000 0.965 0 1.000 0.000
#> GSM329706 3 0.0000 0.998 0 0.000 1.000
#> GSM329708 3 0.0000 0.998 0 0.000 1.000
#> GSM329710 3 0.1163 0.969 0 0.028 0.972
#> GSM329713 1 0.0000 1.000 1 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000
#> GSM329712 2 0.0000 0.965 0 1.000 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.1489 0.8070 0 0.952 0.004 0.044
#> GSM329663 2 0.2081 0.8077 0 0.916 0.000 0.084
#> GSM329664 3 0.5150 0.1994 0 0.396 0.596 0.008
#> GSM329666 2 0.0336 0.7996 0 0.992 0.000 0.008
#> GSM329667 2 0.4482 0.5503 0 0.728 0.264 0.008
#> GSM329670 2 0.3266 0.7862 0 0.832 0.000 0.168
#> GSM329672 2 0.2611 0.7363 0 0.896 0.096 0.008
#> GSM329674 2 0.3688 0.7689 0 0.792 0.000 0.208
#> GSM329661 3 0.4877 0.4208 0 0.000 0.592 0.408
#> GSM329669 2 0.4164 0.7291 0 0.736 0.000 0.264
#> GSM329662 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329677 3 0.0469 0.5792 0 0.012 0.988 0.000
#> GSM329679 2 0.2675 0.7337 0 0.892 0.100 0.008
#> GSM329681 3 0.2216 0.6096 0 0.000 0.908 0.092
#> GSM329683 3 0.3569 0.5954 0 0.000 0.804 0.196
#> GSM329686 3 0.4164 0.5711 0 0.000 0.736 0.264
#> GSM329689 3 0.2281 0.6100 0 0.000 0.904 0.096
#> GSM329678 4 0.4713 0.0887 0 0.000 0.360 0.640
#> GSM329680 3 0.4730 0.4969 0 0.000 0.636 0.364
#> GSM329685 3 0.4925 0.3926 0 0.000 0.572 0.428
#> GSM329688 3 0.4972 0.3331 0 0.000 0.544 0.456
#> GSM329691 3 0.4697 0.5054 0 0.000 0.644 0.356
#> GSM329682 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329692 4 0.4933 -0.0502 0 0.000 0.432 0.568
#> GSM329694 2 0.2859 0.7521 0 0.880 0.112 0.008
#> GSM329697 2 0.1211 0.8073 0 0.960 0.000 0.040
#> GSM329700 2 0.3975 0.7473 0 0.760 0.000 0.240
#> GSM329703 4 0.3444 0.4828 0 0.184 0.000 0.816
#> GSM329704 3 0.5193 0.1680 0 0.412 0.580 0.008
#> GSM329707 3 0.3933 0.4490 0 0.200 0.792 0.008
#> GSM329709 2 0.2408 0.8053 0 0.896 0.000 0.104
#> GSM329711 2 0.4746 0.6110 0 0.632 0.000 0.368
#> GSM329714 2 0.4761 0.5790 0 0.628 0.000 0.372
#> GSM329693 4 0.4500 0.1408 0 0.316 0.000 0.684
#> GSM329696 4 0.3219 0.5123 0 0.164 0.000 0.836
#> GSM329699 4 0.2345 0.5621 0 0.100 0.000 0.900
#> GSM329702 2 0.0469 0.7916 0 0.988 0.012 0.000
#> GSM329706 3 0.2256 0.5862 0 0.020 0.924 0.056
#> GSM329708 4 0.4855 -0.0122 0 0.000 0.400 0.600
#> GSM329710 4 0.2281 0.4610 0 0.000 0.096 0.904
#> GSM329713 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329712 2 0.4776 0.5992 0 0.624 0.000 0.376
#> GSM329715 1 0.0000 1.0000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.2660 0.7169 0.000 0.864 0.000 0.128 0.008
#> GSM329663 2 0.3051 0.6992 0.000 0.864 0.000 0.076 0.060
#> GSM329664 3 0.7853 0.2303 0.000 0.288 0.340 0.308 0.064
#> GSM329666 2 0.1792 0.7097 0.000 0.916 0.000 0.084 0.000
#> GSM329667 2 0.5963 0.4338 0.000 0.596 0.060 0.308 0.036
#> GSM329670 2 0.4258 0.6191 0.000 0.768 0.000 0.160 0.072
#> GSM329672 2 0.3612 0.6129 0.000 0.764 0.000 0.228 0.008
#> GSM329674 2 0.2305 0.7063 0.000 0.896 0.000 0.092 0.012
#> GSM329661 5 0.4752 0.7059 0.000 0.000 0.412 0.020 0.568
#> GSM329669 2 0.2561 0.6808 0.000 0.856 0.000 0.144 0.000
#> GSM329662 1 0.1043 0.9646 0.960 0.000 0.000 0.000 0.040
#> GSM329665 1 0.0510 0.9723 0.984 0.000 0.000 0.000 0.016
#> GSM329668 1 0.0404 0.9730 0.988 0.000 0.000 0.000 0.012
#> GSM329671 1 0.0290 0.9716 0.992 0.000 0.000 0.000 0.008
#> GSM329673 1 0.0510 0.9720 0.984 0.000 0.000 0.000 0.016
#> GSM329675 1 0.0794 0.9693 0.972 0.000 0.000 0.000 0.028
#> GSM329676 1 0.0794 0.9693 0.972 0.000 0.000 0.000 0.028
#> GSM329677 3 0.4649 0.3430 0.000 0.004 0.732 0.200 0.064
#> GSM329679 2 0.4216 0.5747 0.000 0.720 0.008 0.260 0.012
#> GSM329681 5 0.5092 0.5696 0.000 0.000 0.440 0.036 0.524
#> GSM329683 3 0.3398 -0.0690 0.000 0.000 0.780 0.004 0.216
#> GSM329686 3 0.0963 0.2834 0.000 0.000 0.964 0.036 0.000
#> GSM329689 3 0.4334 0.1818 0.000 0.000 0.768 0.092 0.140
#> GSM329678 3 0.4747 -0.0749 0.000 0.000 0.500 0.484 0.016
#> GSM329680 3 0.3112 0.2203 0.000 0.000 0.856 0.100 0.044
#> GSM329685 3 0.3696 0.1515 0.000 0.000 0.772 0.212 0.016
#> GSM329688 3 0.3659 0.1483 0.000 0.000 0.768 0.220 0.012
#> GSM329691 3 0.2522 0.2563 0.000 0.000 0.880 0.108 0.012
#> GSM329682 1 0.0162 0.9730 0.996 0.000 0.000 0.000 0.004
#> GSM329684 1 0.1341 0.9561 0.944 0.000 0.000 0.000 0.056
#> GSM329687 1 0.0609 0.9714 0.980 0.000 0.000 0.000 0.020
#> GSM329690 1 0.1478 0.9489 0.936 0.000 0.000 0.000 0.064
#> GSM329692 5 0.6711 0.5763 0.000 0.004 0.396 0.204 0.396
#> GSM329694 2 0.4728 0.5944 0.000 0.764 0.128 0.088 0.020
#> GSM329697 2 0.0609 0.7263 0.000 0.980 0.000 0.000 0.020
#> GSM329700 2 0.3675 0.6369 0.000 0.788 0.000 0.188 0.024
#> GSM329703 4 0.4251 0.7109 0.000 0.316 0.012 0.672 0.000
#> GSM329704 3 0.7815 0.2292 0.000 0.292 0.340 0.308 0.060
#> GSM329707 3 0.7185 0.2610 0.000 0.128 0.496 0.308 0.068
#> GSM329709 2 0.1485 0.7232 0.000 0.948 0.000 0.032 0.020
#> GSM329711 2 0.3689 0.5481 0.000 0.740 0.000 0.256 0.004
#> GSM329714 2 0.4003 0.4574 0.000 0.704 0.000 0.288 0.008
#> GSM329693 4 0.4586 0.6816 0.000 0.336 0.016 0.644 0.004
#> GSM329696 4 0.5360 0.7543 0.000 0.244 0.076 0.668 0.012
#> GSM329699 4 0.5413 0.6829 0.000 0.172 0.164 0.664 0.000
#> GSM329702 2 0.2179 0.7017 0.000 0.896 0.000 0.100 0.004
#> GSM329706 3 0.4792 0.3458 0.000 0.012 0.712 0.232 0.044
#> GSM329708 5 0.5865 0.7117 0.000 0.000 0.360 0.108 0.532
#> GSM329710 4 0.8136 0.0694 0.000 0.124 0.192 0.348 0.336
#> GSM329713 1 0.1965 0.9281 0.904 0.000 0.000 0.000 0.096
#> GSM329695 1 0.1908 0.9309 0.908 0.000 0.000 0.000 0.092
#> GSM329698 1 0.1121 0.9590 0.956 0.000 0.000 0.000 0.044
#> GSM329701 1 0.0609 0.9686 0.980 0.000 0.000 0.000 0.020
#> GSM329705 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM329712 2 0.3766 0.5244 0.000 0.728 0.000 0.268 0.004
#> GSM329715 1 0.0290 0.9716 0.992 0.000 0.000 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329660 2 0.3025 0.6668 0.000 0.820 0.000 0.024 0.156 0.000
#> GSM329663 2 0.4896 0.5608 0.000 0.708 0.000 0.116 0.148 0.028
#> GSM329664 5 0.4261 0.6433 0.000 0.112 0.156 0.000 0.732 0.000
#> GSM329666 2 0.2854 0.6385 0.000 0.792 0.000 0.000 0.208 0.000
#> GSM329667 5 0.4118 0.0194 0.000 0.396 0.004 0.000 0.592 0.008
#> GSM329670 2 0.4806 0.5047 0.000 0.708 0.000 0.160 0.112 0.020
#> GSM329672 2 0.3872 0.3725 0.000 0.604 0.000 0.000 0.392 0.004
#> GSM329674 2 0.2000 0.6448 0.000 0.916 0.000 0.048 0.032 0.004
#> GSM329661 6 0.1888 0.7615 0.000 0.000 0.068 0.004 0.012 0.916
#> GSM329669 2 0.1434 0.6281 0.000 0.940 0.000 0.048 0.012 0.000
#> GSM329662 1 0.1219 0.8990 0.948 0.000 0.000 0.048 0.004 0.000
#> GSM329665 1 0.0790 0.9073 0.968 0.000 0.000 0.032 0.000 0.000
#> GSM329668 1 0.0603 0.9116 0.980 0.000 0.000 0.016 0.004 0.000
#> GSM329671 1 0.2285 0.9064 0.900 0.000 0.000 0.064 0.028 0.008
#> GSM329673 1 0.0865 0.9046 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM329675 1 0.1007 0.9021 0.956 0.000 0.000 0.044 0.000 0.000
#> GSM329676 1 0.0937 0.9035 0.960 0.000 0.000 0.040 0.000 0.000
#> GSM329677 3 0.4964 -0.1138 0.000 0.000 0.484 0.040 0.464 0.012
#> GSM329679 2 0.3717 0.3820 0.000 0.616 0.000 0.000 0.384 0.000
#> GSM329681 6 0.2653 0.7319 0.000 0.000 0.100 0.004 0.028 0.868
#> GSM329683 3 0.6680 0.1194 0.000 0.000 0.420 0.072 0.140 0.368
#> GSM329686 3 0.3792 0.5747 0.000 0.000 0.792 0.044 0.144 0.020
#> GSM329689 3 0.6731 0.2768 0.000 0.000 0.468 0.072 0.288 0.172
#> GSM329678 3 0.3799 0.1793 0.000 0.000 0.704 0.276 0.000 0.020
#> GSM329680 3 0.3825 0.6185 0.000 0.000 0.812 0.044 0.072 0.072
#> GSM329685 3 0.0935 0.6294 0.000 0.000 0.964 0.032 0.000 0.004
#> GSM329688 3 0.0806 0.6282 0.000 0.000 0.972 0.020 0.000 0.008
#> GSM329691 3 0.2428 0.6423 0.000 0.000 0.896 0.024 0.060 0.020
#> GSM329682 1 0.1592 0.9113 0.940 0.000 0.000 0.032 0.020 0.008
#> GSM329684 1 0.1349 0.8953 0.940 0.000 0.000 0.056 0.004 0.000
#> GSM329687 1 0.0865 0.9046 0.964 0.000 0.000 0.036 0.000 0.000
#> GSM329690 1 0.3917 0.8556 0.780 0.000 0.000 0.144 0.064 0.012
#> GSM329692 6 0.4263 0.7183 0.000 0.016 0.232 0.028 0.004 0.720
#> GSM329694 2 0.6202 0.4310 0.000 0.556 0.004 0.040 0.244 0.156
#> GSM329697 2 0.2804 0.6661 0.000 0.852 0.000 0.024 0.120 0.004
#> GSM329700 2 0.3725 0.5767 0.000 0.792 0.000 0.140 0.060 0.008
#> GSM329703 4 0.6035 0.6135 0.000 0.396 0.152 0.436 0.016 0.000
#> GSM329704 5 0.4314 0.6450 0.000 0.096 0.184 0.000 0.720 0.000
#> GSM329707 5 0.4273 0.5597 0.000 0.028 0.248 0.004 0.708 0.012
#> GSM329709 2 0.3207 0.6533 0.000 0.828 0.000 0.044 0.124 0.004
#> GSM329711 2 0.2778 0.4929 0.000 0.824 0.000 0.168 0.008 0.000
#> GSM329714 2 0.4593 0.4912 0.000 0.708 0.012 0.220 0.052 0.008
#> GSM329693 2 0.6048 -0.7094 0.000 0.416 0.212 0.368 0.004 0.000
#> GSM329696 4 0.6680 0.7752 0.000 0.244 0.288 0.436 0.016 0.016
#> GSM329699 4 0.6001 0.7503 0.000 0.208 0.340 0.448 0.004 0.000
#> GSM329702 2 0.3151 0.5990 0.000 0.748 0.000 0.000 0.252 0.000
#> GSM329706 5 0.4744 0.0480 0.000 0.004 0.440 0.024 0.524 0.008
#> GSM329708 6 0.2805 0.7702 0.000 0.000 0.160 0.012 0.000 0.828
#> GSM329710 6 0.6992 0.3614 0.000 0.080 0.192 0.220 0.012 0.496
#> GSM329713 1 0.4324 0.8219 0.736 0.000 0.000 0.188 0.060 0.016
#> GSM329695 1 0.4317 0.8252 0.740 0.000 0.000 0.180 0.064 0.016
#> GSM329698 1 0.3224 0.8798 0.828 0.000 0.000 0.128 0.036 0.008
#> GSM329701 1 0.2859 0.8921 0.856 0.000 0.000 0.108 0.028 0.008
#> GSM329705 1 0.2101 0.9084 0.912 0.000 0.000 0.052 0.028 0.008
#> GSM329712 2 0.2871 0.4509 0.000 0.804 0.000 0.192 0.004 0.000
#> GSM329715 1 0.2285 0.9060 0.900 0.000 0.000 0.064 0.028 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> SD:NMF 56 0.50568 5.82e-11 2
#> SD:NMF 56 0.00121 7.06e-11 3
#> SD:NMF 43 0.00238 1.86e-08 4
#> SD:NMF 40 0.29301 1.53e-07 5
#> SD:NMF 42 0.00355 1.73e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 21163 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.795 0.950 0.973 0.3809 0.618 0.618
#> 3 3 0.869 0.953 0.975 0.7192 0.724 0.554
#> 4 4 0.864 0.805 0.889 0.1368 0.918 0.761
#> 5 5 0.860 0.684 0.857 0.0513 0.957 0.841
#> 6 6 0.848 0.847 0.894 0.0418 0.937 0.737
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
#> GSM329660 1 0.0376 0.978 0.996 0.004
#> GSM329663 1 0.0376 0.978 0.996 0.004
#> GSM329664 1 0.5519 0.870 0.872 0.128
#> GSM329666 1 0.0376 0.978 0.996 0.004
#> GSM329667 1 0.5178 0.880 0.884 0.116
#> GSM329670 1 0.0376 0.978 0.996 0.004
#> GSM329672 1 0.5178 0.880 0.884 0.116
#> GSM329674 1 0.0376 0.978 0.996 0.004
#> GSM329661 2 0.0000 0.949 0.000 1.000
#> GSM329669 1 0.0376 0.978 0.996 0.004
#> GSM329662 1 0.0000 0.978 1.000 0.000
#> GSM329665 1 0.0000 0.978 1.000 0.000
#> GSM329668 1 0.0000 0.978 1.000 0.000
#> GSM329671 1 0.0000 0.978 1.000 0.000
#> GSM329673 1 0.0000 0.978 1.000 0.000
#> GSM329675 1 0.0000 0.978 1.000 0.000
#> GSM329676 1 0.0000 0.978 1.000 0.000
#> GSM329677 2 0.7376 0.765 0.208 0.792
#> GSM329679 1 0.5178 0.880 0.884 0.116
#> GSM329681 2 0.0000 0.949 0.000 1.000
#> GSM329683 2 0.0000 0.949 0.000 1.000
#> GSM329686 2 0.0000 0.949 0.000 1.000
#> GSM329689 2 0.0000 0.949 0.000 1.000
#> GSM329678 2 0.3431 0.909 0.064 0.936
#> GSM329680 2 0.0000 0.949 0.000 1.000
#> GSM329685 2 0.0000 0.949 0.000 1.000
#> GSM329688 2 0.0000 0.949 0.000 1.000
#> GSM329691 2 0.0000 0.949 0.000 1.000
#> GSM329682 1 0.0000 0.978 1.000 0.000
#> GSM329684 1 0.0000 0.978 1.000 0.000
#> GSM329687 1 0.0000 0.978 1.000 0.000
#> GSM329690 1 0.0000 0.978 1.000 0.000
#> GSM329692 1 0.1184 0.972 0.984 0.016
#> GSM329694 1 0.5519 0.870 0.872 0.128
#> GSM329697 1 0.0376 0.978 0.996 0.004
#> GSM329700 1 0.0376 0.978 0.996 0.004
#> GSM329703 1 0.1184 0.972 0.984 0.016
#> GSM329704 1 0.5178 0.880 0.884 0.116
#> GSM329707 2 0.7376 0.765 0.208 0.792
#> GSM329709 1 0.0376 0.978 0.996 0.004
#> GSM329711 1 0.0376 0.978 0.996 0.004
#> GSM329714 1 0.0376 0.978 0.996 0.004
#> GSM329693 1 0.1184 0.972 0.984 0.016
#> GSM329696 1 0.1184 0.972 0.984 0.016
#> GSM329699 1 0.1184 0.972 0.984 0.016
#> GSM329702 1 0.0376 0.978 0.996 0.004
#> GSM329706 2 0.5946 0.842 0.144 0.856
#> GSM329708 2 0.0000 0.949 0.000 1.000
#> GSM329710 1 0.1184 0.972 0.984 0.016
#> GSM329713 1 0.0000 0.978 1.000 0.000
#> GSM329695 1 0.0000 0.978 1.000 0.000
#> GSM329698 1 0.0000 0.978 1.000 0.000
#> GSM329701 1 0.0000 0.978 1.000 0.000
#> GSM329705 1 0.0000 0.978 1.000 0.000
#> GSM329712 1 0.0376 0.978 0.996 0.004
#> GSM329715 1 0.0000 0.978 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.0000 0.965 0 1.000 0.000
#> GSM329663 2 0.0000 0.965 0 1.000 0.000
#> GSM329664 2 0.3412 0.884 0 0.876 0.124
#> GSM329666 2 0.0000 0.965 0 1.000 0.000
#> GSM329667 2 0.3192 0.892 0 0.888 0.112
#> GSM329670 2 0.0000 0.965 0 1.000 0.000
#> GSM329672 2 0.3192 0.892 0 0.888 0.112
#> GSM329674 2 0.0000 0.965 0 1.000 0.000
#> GSM329661 3 0.0000 0.945 0 0.000 1.000
#> GSM329669 2 0.0000 0.965 0 1.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000
#> GSM329677 3 0.4702 0.755 0 0.212 0.788
#> GSM329679 2 0.3192 0.892 0 0.888 0.112
#> GSM329681 3 0.0000 0.945 0 0.000 1.000
#> GSM329683 3 0.0000 0.945 0 0.000 1.000
#> GSM329686 3 0.0000 0.945 0 0.000 1.000
#> GSM329689 3 0.0000 0.945 0 0.000 1.000
#> GSM329678 3 0.2165 0.905 0 0.064 0.936
#> GSM329680 3 0.0000 0.945 0 0.000 1.000
#> GSM329685 3 0.0000 0.945 0 0.000 1.000
#> GSM329688 3 0.0000 0.945 0 0.000 1.000
#> GSM329691 3 0.0000 0.945 0 0.000 1.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000
#> GSM329692 2 0.0592 0.962 0 0.988 0.012
#> GSM329694 2 0.3412 0.884 0 0.876 0.124
#> GSM329697 2 0.0000 0.965 0 1.000 0.000
#> GSM329700 2 0.0000 0.965 0 1.000 0.000
#> GSM329703 2 0.0592 0.962 0 0.988 0.012
#> GSM329704 2 0.3192 0.892 0 0.888 0.112
#> GSM329707 3 0.4702 0.755 0 0.212 0.788
#> GSM329709 2 0.0000 0.965 0 1.000 0.000
#> GSM329711 2 0.0000 0.965 0 1.000 0.000
#> GSM329714 2 0.0000 0.965 0 1.000 0.000
#> GSM329693 2 0.0592 0.962 0 0.988 0.012
#> GSM329696 2 0.0592 0.962 0 0.988 0.012
#> GSM329699 2 0.0592 0.962 0 0.988 0.012
#> GSM329702 2 0.0000 0.965 0 1.000 0.000
#> GSM329706 3 0.3816 0.833 0 0.148 0.852
#> GSM329708 3 0.0000 0.945 0 0.000 1.000
#> GSM329710 2 0.0592 0.962 0 0.988 0.012
#> GSM329713 1 0.0000 1.000 1 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000
#> GSM329712 2 0.0000 0.965 0 1.000 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.0188 0.770 0 0.996 0.000 0.004
#> GSM329663 2 0.0000 0.773 0 1.000 0.000 0.000
#> GSM329664 2 0.4605 0.549 0 0.664 0.000 0.336
#> GSM329666 2 0.0000 0.773 0 1.000 0.000 0.000
#> GSM329667 2 0.4103 0.629 0 0.744 0.000 0.256
#> GSM329670 2 0.0000 0.773 0 1.000 0.000 0.000
#> GSM329672 2 0.4040 0.636 0 0.752 0.000 0.248
#> GSM329674 2 0.0000 0.773 0 1.000 0.000 0.000
#> GSM329661 3 0.0000 0.921 0 0.000 1.000 0.000
#> GSM329669 2 0.0000 0.773 0 1.000 0.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329677 3 0.4605 0.682 0 0.000 0.664 0.336
#> GSM329679 2 0.4040 0.636 0 0.752 0.000 0.248
#> GSM329681 3 0.0000 0.921 0 0.000 1.000 0.000
#> GSM329683 3 0.0000 0.921 0 0.000 1.000 0.000
#> GSM329686 3 0.0469 0.922 0 0.000 0.988 0.012
#> GSM329689 3 0.0000 0.921 0 0.000 1.000 0.000
#> GSM329678 3 0.2053 0.876 0 0.004 0.924 0.072
#> GSM329680 3 0.0469 0.922 0 0.000 0.988 0.012
#> GSM329685 3 0.0469 0.922 0 0.000 0.988 0.012
#> GSM329688 3 0.0469 0.922 0 0.000 0.988 0.012
#> GSM329691 3 0.0469 0.922 0 0.000 0.988 0.012
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329692 4 0.4134 0.859 0 0.260 0.000 0.740
#> GSM329694 4 0.4996 -0.353 0 0.484 0.000 0.516
#> GSM329697 2 0.0000 0.773 0 1.000 0.000 0.000
#> GSM329700 2 0.4776 -0.038 0 0.624 0.000 0.376
#> GSM329703 4 0.4134 0.859 0 0.260 0.000 0.740
#> GSM329704 2 0.4134 0.626 0 0.740 0.000 0.260
#> GSM329707 3 0.4605 0.682 0 0.000 0.664 0.336
#> GSM329709 2 0.0000 0.773 0 1.000 0.000 0.000
#> GSM329711 2 0.3266 0.581 0 0.832 0.000 0.168
#> GSM329714 2 0.4776 -0.038 0 0.624 0.000 0.376
#> GSM329693 4 0.4134 0.859 0 0.260 0.000 0.740
#> GSM329696 4 0.4134 0.859 0 0.260 0.000 0.740
#> GSM329699 4 0.4134 0.859 0 0.260 0.000 0.740
#> GSM329702 2 0.0000 0.773 0 1.000 0.000 0.000
#> GSM329706 3 0.4222 0.740 0 0.000 0.728 0.272
#> GSM329708 3 0.0000 0.921 0 0.000 1.000 0.000
#> GSM329710 4 0.4134 0.859 0 0.260 0.000 0.740
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329712 2 0.3266 0.581 0 0.832 0.000 0.168
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.0324 0.720 0 0.992 0.000 0.004 0.004
#> GSM329663 2 0.0000 0.725 0 1.000 0.000 0.000 0.000
#> GSM329664 5 0.4656 0.319 0 0.480 0.012 0.000 0.508
#> GSM329666 2 0.0000 0.725 0 1.000 0.000 0.000 0.000
#> GSM329667 2 0.4262 -0.437 0 0.560 0.000 0.000 0.440
#> GSM329670 2 0.0000 0.725 0 1.000 0.000 0.000 0.000
#> GSM329672 2 0.4235 -0.392 0 0.576 0.000 0.000 0.424
#> GSM329674 2 0.0000 0.725 0 1.000 0.000 0.000 0.000
#> GSM329661 3 0.4306 0.610 0 0.000 0.508 0.000 0.492
#> GSM329669 2 0.0000 0.725 0 1.000 0.000 0.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329677 3 0.3913 0.456 0 0.000 0.676 0.000 0.324
#> GSM329679 2 0.4235 -0.392 0 0.576 0.000 0.000 0.424
#> GSM329681 3 0.4304 0.614 0 0.000 0.516 0.000 0.484
#> GSM329683 3 0.4304 0.614 0 0.000 0.516 0.000 0.484
#> GSM329686 3 0.0000 0.727 0 0.000 1.000 0.000 0.000
#> GSM329689 3 0.4304 0.614 0 0.000 0.516 0.000 0.484
#> GSM329678 3 0.1478 0.704 0 0.000 0.936 0.064 0.000
#> GSM329680 3 0.0000 0.727 0 0.000 1.000 0.000 0.000
#> GSM329685 3 0.0000 0.727 0 0.000 1.000 0.000 0.000
#> GSM329688 3 0.0000 0.727 0 0.000 1.000 0.000 0.000
#> GSM329691 3 0.0000 0.727 0 0.000 1.000 0.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329692 4 0.0000 0.848 0 0.000 0.000 1.000 0.000
#> GSM329694 5 0.6733 0.505 0 0.296 0.000 0.288 0.416
#> GSM329697 2 0.0000 0.725 0 1.000 0.000 0.000 0.000
#> GSM329700 4 0.4074 0.336 0 0.364 0.000 0.636 0.000
#> GSM329703 4 0.0000 0.848 0 0.000 0.000 1.000 0.000
#> GSM329704 2 0.4268 -0.449 0 0.556 0.000 0.000 0.444
#> GSM329707 3 0.3913 0.456 0 0.000 0.676 0.000 0.324
#> GSM329709 2 0.0000 0.725 0 1.000 0.000 0.000 0.000
#> GSM329711 2 0.2813 0.518 0 0.832 0.000 0.168 0.000
#> GSM329714 4 0.4074 0.336 0 0.364 0.000 0.636 0.000
#> GSM329693 4 0.0000 0.848 0 0.000 0.000 1.000 0.000
#> GSM329696 4 0.0000 0.848 0 0.000 0.000 1.000 0.000
#> GSM329699 4 0.0000 0.848 0 0.000 0.000 1.000 0.000
#> GSM329702 2 0.0000 0.725 0 1.000 0.000 0.000 0.000
#> GSM329706 3 0.3561 0.515 0 0.000 0.740 0.000 0.260
#> GSM329708 3 0.4306 0.610 0 0.000 0.508 0.000 0.492
#> GSM329710 4 0.0000 0.848 0 0.000 0.000 1.000 0.000
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329712 2 0.2813 0.518 0 0.832 0.000 0.168 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 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
#> GSM329660 2 0.0603 0.945 0.000 0.980 0.000 0.004 0.016 0.000
#> GSM329663 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329664 5 0.0000 0.784 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM329666 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329667 5 0.1556 0.845 0.000 0.080 0.000 0.000 0.920 0.000
#> GSM329670 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329672 5 0.2912 0.805 0.000 0.216 0.000 0.000 0.784 0.000
#> GSM329674 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329661 3 0.2762 0.817 0.000 0.000 0.804 0.000 0.000 0.196
#> GSM329669 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329662 1 0.2491 0.907 0.836 0.000 0.164 0.000 0.000 0.000
#> GSM329665 1 0.2491 0.907 0.836 0.000 0.164 0.000 0.000 0.000
#> GSM329668 1 0.2491 0.907 0.836 0.000 0.164 0.000 0.000 0.000
#> GSM329671 1 0.0260 0.918 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM329673 1 0.2491 0.907 0.836 0.000 0.164 0.000 0.000 0.000
#> GSM329675 1 0.2697 0.896 0.812 0.000 0.188 0.000 0.000 0.000
#> GSM329676 1 0.2491 0.907 0.836 0.000 0.164 0.000 0.000 0.000
#> GSM329677 6 0.3563 0.620 0.000 0.000 0.000 0.000 0.336 0.664
#> GSM329679 5 0.2912 0.805 0.000 0.216 0.000 0.000 0.784 0.000
#> GSM329681 3 0.3717 0.860 0.000 0.000 0.616 0.000 0.000 0.384
#> GSM329683 3 0.3717 0.860 0.000 0.000 0.616 0.000 0.000 0.384
#> GSM329686 6 0.0000 0.797 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM329689 3 0.3717 0.860 0.000 0.000 0.616 0.000 0.000 0.384
#> GSM329678 6 0.1327 0.734 0.000 0.000 0.000 0.064 0.000 0.936
#> GSM329680 6 0.0000 0.797 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM329685 6 0.0000 0.797 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM329688 6 0.0000 0.797 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM329691 6 0.0000 0.797 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM329682 1 0.2491 0.907 0.836 0.000 0.164 0.000 0.000 0.000
#> GSM329684 1 0.2697 0.896 0.812 0.000 0.188 0.000 0.000 0.000
#> GSM329687 1 0.0000 0.919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0260 0.918 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM329692 4 0.0000 0.863 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329694 5 0.3595 0.615 0.000 0.008 0.000 0.288 0.704 0.000
#> GSM329697 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329700 4 0.3659 0.495 0.000 0.364 0.000 0.636 0.000 0.000
#> GSM329703 4 0.0000 0.863 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329704 5 0.1610 0.846 0.000 0.084 0.000 0.000 0.916 0.000
#> GSM329707 6 0.3563 0.620 0.000 0.000 0.000 0.000 0.336 0.664
#> GSM329709 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329711 2 0.2527 0.805 0.000 0.832 0.000 0.168 0.000 0.000
#> GSM329714 4 0.3659 0.495 0.000 0.364 0.000 0.636 0.000 0.000
#> GSM329693 4 0.0000 0.863 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329696 4 0.0000 0.863 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329699 4 0.0000 0.863 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329702 2 0.0000 0.958 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329706 6 0.3198 0.665 0.000 0.000 0.000 0.000 0.260 0.740
#> GSM329708 3 0.2762 0.817 0.000 0.000 0.804 0.000 0.000 0.196
#> GSM329710 4 0.0000 0.863 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329713 1 0.0260 0.918 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM329695 1 0.0260 0.918 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM329698 1 0.0260 0.918 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM329701 1 0.0260 0.918 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM329705 1 0.0000 0.919 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329712 2 0.2527 0.805 0.000 0.832 0.000 0.168 0.000 0.000
#> GSM329715 1 0.0260 0.918 0.992 0.000 0.008 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> CV:hclust 56 6.76e-05 2.37e-03 2
#> CV:hclust 56 1.85e-04 1.01e-10 3
#> CV:hclust 53 7.35e-05 3.44e-10 4
#> CV:hclust 47 2.81e-04 6.63e-08 5
#> CV:hclust 54 9.44e-04 3.56e-09 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 21163 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.584 0.946 0.960 0.4397 0.569 0.569
#> 3 3 0.726 0.976 0.935 0.4599 0.761 0.580
#> 4 4 0.765 0.702 0.846 0.1276 0.966 0.898
#> 5 5 0.732 0.743 0.800 0.0680 0.932 0.783
#> 6 6 0.703 0.626 0.753 0.0519 0.902 0.629
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
#> GSM329660 2 0.5842 0.902 0.140 0.860
#> GSM329663 2 0.5842 0.902 0.140 0.860
#> GSM329664 2 0.0000 0.937 0.000 1.000
#> GSM329666 2 0.5842 0.902 0.140 0.860
#> GSM329667 2 0.5737 0.903 0.136 0.864
#> GSM329670 2 0.5842 0.902 0.140 0.860
#> GSM329672 2 0.5842 0.902 0.140 0.860
#> GSM329674 2 0.5842 0.902 0.140 0.860
#> GSM329661 2 0.0000 0.937 0.000 1.000
#> GSM329669 2 0.5842 0.902 0.140 0.860
#> GSM329662 1 0.0000 1.000 1.000 0.000
#> GSM329665 1 0.0000 1.000 1.000 0.000
#> GSM329668 1 0.0000 1.000 1.000 0.000
#> GSM329671 1 0.0000 1.000 1.000 0.000
#> GSM329673 1 0.0000 1.000 1.000 0.000
#> GSM329675 1 0.0000 1.000 1.000 0.000
#> GSM329676 1 0.0000 1.000 1.000 0.000
#> GSM329677 2 0.0000 0.937 0.000 1.000
#> GSM329679 2 0.5842 0.902 0.140 0.860
#> GSM329681 2 0.0000 0.937 0.000 1.000
#> GSM329683 2 0.0000 0.937 0.000 1.000
#> GSM329686 2 0.0000 0.937 0.000 1.000
#> GSM329689 2 0.0000 0.937 0.000 1.000
#> GSM329678 2 0.0000 0.937 0.000 1.000
#> GSM329680 2 0.0000 0.937 0.000 1.000
#> GSM329685 2 0.0000 0.937 0.000 1.000
#> GSM329688 2 0.0000 0.937 0.000 1.000
#> GSM329691 2 0.0000 0.937 0.000 1.000
#> GSM329682 1 0.0000 1.000 1.000 0.000
#> GSM329684 1 0.0000 1.000 1.000 0.000
#> GSM329687 1 0.0000 1.000 1.000 0.000
#> GSM329690 1 0.0000 1.000 1.000 0.000
#> GSM329692 2 0.0000 0.937 0.000 1.000
#> GSM329694 2 0.0000 0.937 0.000 1.000
#> GSM329697 2 0.5842 0.902 0.140 0.860
#> GSM329700 2 0.5842 0.902 0.140 0.860
#> GSM329703 2 0.0376 0.936 0.004 0.996
#> GSM329704 2 0.0000 0.937 0.000 1.000
#> GSM329707 2 0.0000 0.937 0.000 1.000
#> GSM329709 2 0.5842 0.902 0.140 0.860
#> GSM329711 2 0.5842 0.902 0.140 0.860
#> GSM329714 2 0.5842 0.902 0.140 0.860
#> GSM329693 2 0.0376 0.936 0.004 0.996
#> GSM329696 2 0.0376 0.936 0.004 0.996
#> GSM329699 2 0.0000 0.937 0.000 1.000
#> GSM329702 2 0.5842 0.902 0.140 0.860
#> GSM329706 2 0.0000 0.937 0.000 1.000
#> GSM329708 2 0.0000 0.937 0.000 1.000
#> GSM329710 2 0.0000 0.937 0.000 1.000
#> GSM329713 1 0.0000 1.000 1.000 0.000
#> GSM329695 1 0.0000 1.000 1.000 0.000
#> GSM329698 1 0.0000 1.000 1.000 0.000
#> GSM329701 1 0.0000 1.000 1.000 0.000
#> GSM329705 1 0.0000 1.000 1.000 0.000
#> GSM329712 2 0.5842 0.902 0.140 0.860
#> GSM329715 1 0.0000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329663 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329664 2 0.4974 0.890 0.000 0.764 0.236
#> GSM329666 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329667 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329670 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329672 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329674 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329661 3 0.0000 0.999 0.000 0.000 1.000
#> GSM329669 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329662 1 0.2261 0.949 0.932 0.068 0.000
#> GSM329665 1 0.0237 0.952 0.996 0.004 0.000
#> GSM329668 1 0.1411 0.952 0.964 0.036 0.000
#> GSM329671 1 0.2537 0.944 0.920 0.080 0.000
#> GSM329673 1 0.2261 0.949 0.932 0.068 0.000
#> GSM329675 1 0.2261 0.949 0.932 0.068 0.000
#> GSM329676 1 0.2261 0.949 0.932 0.068 0.000
#> GSM329677 3 0.0000 0.999 0.000 0.000 1.000
#> GSM329679 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329681 3 0.0000 0.999 0.000 0.000 1.000
#> GSM329683 3 0.0000 0.999 0.000 0.000 1.000
#> GSM329686 3 0.0000 0.999 0.000 0.000 1.000
#> GSM329689 3 0.0000 0.999 0.000 0.000 1.000
#> GSM329678 3 0.0000 0.999 0.000 0.000 1.000
#> GSM329680 3 0.0000 0.999 0.000 0.000 1.000
#> GSM329685 3 0.0000 0.999 0.000 0.000 1.000
#> GSM329688 3 0.0000 0.999 0.000 0.000 1.000
#> GSM329691 3 0.0000 0.999 0.000 0.000 1.000
#> GSM329682 1 0.2165 0.949 0.936 0.064 0.000
#> GSM329684 1 0.2261 0.949 0.932 0.068 0.000
#> GSM329687 1 0.2261 0.949 0.932 0.068 0.000
#> GSM329690 1 0.2537 0.944 0.920 0.080 0.000
#> GSM329692 3 0.0000 0.999 0.000 0.000 1.000
#> GSM329694 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329697 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329700 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329703 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329704 2 0.4974 0.890 0.000 0.764 0.236
#> GSM329707 3 0.0000 0.999 0.000 0.000 1.000
#> GSM329709 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329711 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329714 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329693 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329696 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329699 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329702 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329706 3 0.0000 0.999 0.000 0.000 1.000
#> GSM329708 3 0.0000 0.999 0.000 0.000 1.000
#> GSM329710 3 0.0424 0.990 0.000 0.008 0.992
#> GSM329713 1 0.2537 0.944 0.920 0.080 0.000
#> GSM329695 1 0.2537 0.944 0.920 0.080 0.000
#> GSM329698 1 0.2537 0.944 0.920 0.080 0.000
#> GSM329701 1 0.2537 0.944 0.920 0.080 0.000
#> GSM329705 1 0.0000 0.952 1.000 0.000 0.000
#> GSM329712 2 0.3816 0.991 0.000 0.852 0.148
#> GSM329715 1 0.2537 0.944 0.920 0.080 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.0188 0.7918 0.000 0.996 0.000 0.004
#> GSM329663 2 0.0000 0.7928 0.000 1.000 0.000 0.000
#> GSM329664 2 0.4282 0.6342 0.000 0.816 0.060 0.124
#> GSM329666 2 0.0000 0.7928 0.000 1.000 0.000 0.000
#> GSM329667 2 0.2704 0.7011 0.000 0.876 0.000 0.124
#> GSM329670 2 0.0000 0.7928 0.000 1.000 0.000 0.000
#> GSM329672 2 0.0188 0.7918 0.000 0.996 0.000 0.004
#> GSM329674 2 0.0000 0.7928 0.000 1.000 0.000 0.000
#> GSM329661 3 0.4046 0.8141 0.000 0.048 0.828 0.124
#> GSM329669 2 0.0000 0.7928 0.000 1.000 0.000 0.000
#> GSM329662 1 0.2714 0.8917 0.884 0.000 0.004 0.112
#> GSM329665 1 0.1256 0.9024 0.964 0.000 0.028 0.008
#> GSM329668 1 0.2399 0.9018 0.920 0.000 0.032 0.048
#> GSM329671 1 0.3523 0.8873 0.856 0.000 0.032 0.112
#> GSM329673 1 0.2714 0.8917 0.884 0.000 0.004 0.112
#> GSM329675 1 0.2859 0.8910 0.880 0.000 0.008 0.112
#> GSM329676 1 0.2714 0.8917 0.884 0.000 0.004 0.112
#> GSM329677 3 0.3991 0.7798 0.000 0.048 0.832 0.120
#> GSM329679 2 0.0188 0.7918 0.000 0.996 0.000 0.004
#> GSM329681 3 0.3156 0.8506 0.000 0.048 0.884 0.068
#> GSM329683 3 0.3156 0.8506 0.000 0.048 0.884 0.068
#> GSM329686 3 0.1389 0.8599 0.000 0.048 0.952 0.000
#> GSM329689 3 0.3081 0.8517 0.000 0.048 0.888 0.064
#> GSM329678 3 0.6145 -0.3807 0.000 0.048 0.492 0.460
#> GSM329680 3 0.1389 0.8599 0.000 0.048 0.952 0.000
#> GSM329685 3 0.1389 0.8599 0.000 0.048 0.952 0.000
#> GSM329688 3 0.1389 0.8599 0.000 0.048 0.952 0.000
#> GSM329691 3 0.1389 0.8599 0.000 0.048 0.952 0.000
#> GSM329682 1 0.2469 0.8953 0.892 0.000 0.000 0.108
#> GSM329684 1 0.2859 0.8910 0.880 0.000 0.008 0.112
#> GSM329687 1 0.2469 0.8927 0.892 0.000 0.000 0.108
#> GSM329690 1 0.3377 0.8841 0.848 0.000 0.012 0.140
#> GSM329692 4 0.5773 0.4703 0.000 0.048 0.320 0.632
#> GSM329694 4 0.4972 -0.2212 0.000 0.456 0.000 0.544
#> GSM329697 2 0.0000 0.7928 0.000 1.000 0.000 0.000
#> GSM329700 2 0.4277 0.5205 0.000 0.720 0.000 0.280
#> GSM329703 2 0.4998 -0.0156 0.000 0.512 0.000 0.488
#> GSM329704 2 0.4282 0.6342 0.000 0.816 0.060 0.124
#> GSM329707 3 0.4761 0.7827 0.000 0.048 0.768 0.184
#> GSM329709 2 0.0000 0.7928 0.000 1.000 0.000 0.000
#> GSM329711 2 0.2216 0.7429 0.000 0.908 0.000 0.092
#> GSM329714 2 0.4406 0.4914 0.000 0.700 0.000 0.300
#> GSM329693 2 0.4998 -0.0156 0.000 0.512 0.000 0.488
#> GSM329696 2 0.4998 -0.0156 0.000 0.512 0.000 0.488
#> GSM329699 2 0.5000 -0.0356 0.000 0.504 0.000 0.496
#> GSM329702 2 0.0000 0.7928 0.000 1.000 0.000 0.000
#> GSM329706 3 0.4994 0.6917 0.000 0.048 0.744 0.208
#> GSM329708 3 0.4046 0.8141 0.000 0.048 0.828 0.124
#> GSM329710 4 0.5773 0.4703 0.000 0.048 0.320 0.632
#> GSM329713 1 0.3300 0.8834 0.848 0.000 0.008 0.144
#> GSM329695 1 0.3300 0.8834 0.848 0.000 0.008 0.144
#> GSM329698 1 0.3208 0.8835 0.848 0.000 0.004 0.148
#> GSM329701 1 0.3278 0.8877 0.864 0.000 0.020 0.116
#> GSM329705 1 0.1297 0.9018 0.964 0.000 0.020 0.016
#> GSM329712 2 0.2216 0.7429 0.000 0.908 0.000 0.092
#> GSM329715 1 0.3278 0.8877 0.864 0.000 0.020 0.116
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.1952 0.814 0.000 0.912 0.000 0.004 NA
#> GSM329663 2 0.2074 0.806 0.000 0.896 0.000 0.000 NA
#> GSM329664 2 0.6164 0.497 0.000 0.584 0.052 0.056 NA
#> GSM329666 2 0.0000 0.821 0.000 1.000 0.000 0.000 NA
#> GSM329667 2 0.4693 0.632 0.000 0.700 0.000 0.056 NA
#> GSM329670 2 0.1608 0.809 0.000 0.928 0.000 0.000 NA
#> GSM329672 2 0.1341 0.814 0.000 0.944 0.000 0.000 NA
#> GSM329674 2 0.0000 0.821 0.000 1.000 0.000 0.000 NA
#> GSM329661 3 0.4555 0.800 0.000 0.016 0.776 0.096 NA
#> GSM329669 2 0.0865 0.816 0.000 0.972 0.000 0.004 NA
#> GSM329662 1 0.0510 0.787 0.984 0.000 0.000 0.016 NA
#> GSM329665 1 0.4096 0.808 0.784 0.000 0.000 0.072 NA
#> GSM329668 1 0.4183 0.807 0.780 0.000 0.000 0.084 NA
#> GSM329671 1 0.5627 0.772 0.548 0.000 0.000 0.084 NA
#> GSM329673 1 0.0404 0.788 0.988 0.000 0.000 0.012 NA
#> GSM329675 1 0.0865 0.785 0.972 0.000 0.004 0.024 NA
#> GSM329676 1 0.0162 0.789 0.996 0.000 0.000 0.004 NA
#> GSM329677 3 0.5141 0.693 0.000 0.016 0.688 0.056 NA
#> GSM329679 2 0.1341 0.814 0.000 0.944 0.000 0.000 NA
#> GSM329681 3 0.3538 0.843 0.000 0.016 0.848 0.056 NA
#> GSM329683 3 0.3174 0.848 0.000 0.016 0.868 0.036 NA
#> GSM329686 3 0.0510 0.861 0.000 0.016 0.984 0.000 NA
#> GSM329689 3 0.2861 0.852 0.000 0.016 0.884 0.024 NA
#> GSM329678 4 0.4618 0.450 0.000 0.016 0.344 0.636 NA
#> GSM329680 3 0.0671 0.860 0.000 0.016 0.980 0.004 NA
#> GSM329685 3 0.0510 0.861 0.000 0.016 0.984 0.000 NA
#> GSM329688 3 0.0510 0.861 0.000 0.016 0.984 0.000 NA
#> GSM329691 3 0.0510 0.861 0.000 0.016 0.984 0.000 NA
#> GSM329682 1 0.1444 0.796 0.948 0.000 0.000 0.012 NA
#> GSM329684 1 0.0865 0.785 0.972 0.000 0.004 0.024 NA
#> GSM329687 1 0.0693 0.791 0.980 0.000 0.000 0.008 NA
#> GSM329690 1 0.5036 0.760 0.516 0.000 0.000 0.032 NA
#> GSM329692 4 0.4370 0.597 0.000 0.016 0.176 0.768 NA
#> GSM329694 4 0.4769 0.716 0.000 0.256 0.000 0.688 NA
#> GSM329697 2 0.0000 0.821 0.000 1.000 0.000 0.000 NA
#> GSM329700 2 0.5331 0.446 0.000 0.640 0.000 0.268 NA
#> GSM329703 4 0.3730 0.745 0.000 0.288 0.000 0.712 NA
#> GSM329704 2 0.6221 0.492 0.000 0.580 0.052 0.060 NA
#> GSM329707 3 0.5663 0.685 0.000 0.016 0.612 0.068 NA
#> GSM329709 2 0.0000 0.821 0.000 1.000 0.000 0.000 NA
#> GSM329711 2 0.3152 0.718 0.000 0.840 0.000 0.136 NA
#> GSM329714 2 0.5794 0.088 0.000 0.520 0.000 0.384 NA
#> GSM329693 4 0.3730 0.745 0.000 0.288 0.000 0.712 NA
#> GSM329696 4 0.3730 0.745 0.000 0.288 0.000 0.712 NA
#> GSM329699 4 0.3730 0.745 0.000 0.288 0.000 0.712 NA
#> GSM329702 2 0.0000 0.821 0.000 1.000 0.000 0.000 NA
#> GSM329706 3 0.6435 0.563 0.000 0.016 0.568 0.176 NA
#> GSM329708 3 0.4555 0.800 0.000 0.016 0.776 0.096 NA
#> GSM329710 4 0.3964 0.606 0.000 0.016 0.176 0.788 NA
#> GSM329713 1 0.5170 0.756 0.512 0.000 0.012 0.020 NA
#> GSM329695 1 0.5170 0.756 0.512 0.000 0.012 0.020 NA
#> GSM329698 1 0.4821 0.759 0.516 0.000 0.000 0.020 NA
#> GSM329701 1 0.5281 0.773 0.548 0.000 0.000 0.052 NA
#> GSM329705 1 0.4303 0.808 0.752 0.000 0.000 0.056 NA
#> GSM329712 2 0.3152 0.718 0.000 0.840 0.000 0.136 NA
#> GSM329715 1 0.5330 0.774 0.548 0.000 0.000 0.056 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329660 2 0.4819 0.7315 0.000 0.708 0.000 0.020 0.152 0.120
#> GSM329663 2 0.4484 0.7328 0.000 0.728 0.000 0.012 0.168 0.092
#> GSM329664 5 0.4721 0.3522 0.000 0.364 0.024 0.020 0.592 0.000
#> GSM329666 2 0.0260 0.7783 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM329667 2 0.4644 -0.0793 0.000 0.512 0.000 0.020 0.456 0.012
#> GSM329670 2 0.3514 0.7558 0.000 0.804 0.000 0.000 0.108 0.088
#> GSM329672 2 0.2070 0.7478 0.000 0.896 0.000 0.012 0.092 0.000
#> GSM329674 2 0.0260 0.7783 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM329661 3 0.5261 0.6989 0.000 0.000 0.688 0.064 0.092 0.156
#> GSM329669 2 0.3150 0.7616 0.000 0.832 0.000 0.000 0.064 0.104
#> GSM329662 6 0.3737 0.9241 0.392 0.000 0.000 0.000 0.000 0.608
#> GSM329665 1 0.4074 -0.1450 0.656 0.000 0.000 0.004 0.016 0.324
#> GSM329668 1 0.4918 -0.2994 0.604 0.000 0.000 0.028 0.032 0.336
#> GSM329671 1 0.1401 0.6796 0.948 0.000 0.000 0.020 0.028 0.004
#> GSM329673 6 0.3747 0.9238 0.396 0.000 0.000 0.000 0.000 0.604
#> GSM329675 6 0.4290 0.8947 0.364 0.000 0.000 0.020 0.004 0.612
#> GSM329676 6 0.4010 0.9173 0.408 0.000 0.000 0.008 0.000 0.584
#> GSM329677 3 0.4326 -0.3153 0.000 0.000 0.496 0.008 0.488 0.008
#> GSM329679 2 0.2019 0.7494 0.000 0.900 0.000 0.012 0.088 0.000
#> GSM329681 3 0.4102 0.7679 0.000 0.000 0.788 0.036 0.092 0.084
#> GSM329683 3 0.3699 0.7768 0.000 0.000 0.812 0.020 0.092 0.076
#> GSM329686 3 0.0000 0.8006 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329689 3 0.3596 0.7787 0.000 0.000 0.820 0.020 0.088 0.072
#> GSM329678 4 0.3571 0.6106 0.000 0.000 0.216 0.760 0.004 0.020
#> GSM329680 3 0.0748 0.7953 0.000 0.000 0.976 0.016 0.004 0.004
#> GSM329685 3 0.0000 0.8006 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329688 3 0.0000 0.8006 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329691 3 0.0000 0.8006 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329682 6 0.4484 0.8395 0.460 0.000 0.000 0.016 0.008 0.516
#> GSM329684 6 0.4290 0.8947 0.364 0.000 0.000 0.020 0.004 0.612
#> GSM329687 6 0.4268 0.9004 0.428 0.000 0.000 0.012 0.004 0.556
#> GSM329690 1 0.2972 0.6841 0.836 0.000 0.000 0.036 0.128 0.000
#> GSM329692 4 0.4019 0.6723 0.000 0.000 0.076 0.796 0.040 0.088
#> GSM329694 4 0.4576 0.7425 0.000 0.120 0.000 0.748 0.092 0.040
#> GSM329697 2 0.0260 0.7783 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM329700 2 0.6965 0.4396 0.000 0.484 0.000 0.224 0.152 0.140
#> GSM329703 4 0.2624 0.7924 0.000 0.148 0.000 0.844 0.004 0.004
#> GSM329704 5 0.4721 0.3522 0.000 0.364 0.024 0.020 0.592 0.000
#> GSM329707 5 0.4771 0.0825 0.000 0.000 0.388 0.016 0.568 0.028
#> GSM329709 2 0.0260 0.7783 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM329711 2 0.5299 0.6631 0.000 0.688 0.000 0.144 0.068 0.100
#> GSM329714 4 0.7204 0.0251 0.000 0.308 0.000 0.400 0.152 0.140
#> GSM329693 4 0.2624 0.7924 0.000 0.148 0.000 0.844 0.004 0.004
#> GSM329696 4 0.2340 0.7926 0.000 0.148 0.000 0.852 0.000 0.000
#> GSM329699 4 0.2584 0.7929 0.000 0.144 0.000 0.848 0.004 0.004
#> GSM329702 2 0.0260 0.7783 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM329706 5 0.5467 0.1921 0.000 0.000 0.408 0.096 0.488 0.008
#> GSM329708 3 0.5261 0.6989 0.000 0.000 0.688 0.064 0.092 0.156
#> GSM329710 4 0.3125 0.6858 0.000 0.000 0.076 0.852 0.016 0.056
#> GSM329713 1 0.2911 0.6812 0.832 0.000 0.000 0.024 0.144 0.000
#> GSM329695 1 0.2911 0.6812 0.832 0.000 0.000 0.024 0.144 0.000
#> GSM329698 1 0.2662 0.6866 0.856 0.000 0.000 0.024 0.120 0.000
#> GSM329701 1 0.0146 0.6861 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM329705 1 0.3383 0.1044 0.728 0.000 0.000 0.004 0.000 0.268
#> GSM329712 2 0.5299 0.6631 0.000 0.688 0.000 0.144 0.068 0.100
#> GSM329715 1 0.0405 0.6833 0.988 0.000 0.000 0.000 0.004 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> CV:kmeans 56 5.06e-01 5.82e-11 2
#> CV:kmeans 56 1.21e-03 7.06e-11 3
#> CV:kmeans 47 4.03e-03 1.20e-09 4
#> CV:kmeans 51 1.14e-04 4.53e-09 5
#> CV:kmeans 45 9.66e-05 3.82e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 21163 rows and 56 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4311 0.569 0.569
#> 3 3 1.000 0.974 0.988 0.5679 0.753 0.567
#> 4 4 0.937 0.897 0.961 0.1103 0.899 0.700
#> 5 5 0.928 0.871 0.930 0.0479 0.955 0.822
#> 6 6 0.854 0.789 0.869 0.0348 0.986 0.932
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM329660 2 0 1 0 1
#> GSM329663 2 0 1 0 1
#> GSM329664 2 0 1 0 1
#> GSM329666 2 0 1 0 1
#> GSM329667 2 0 1 0 1
#> GSM329670 2 0 1 0 1
#> GSM329672 2 0 1 0 1
#> GSM329674 2 0 1 0 1
#> GSM329661 2 0 1 0 1
#> GSM329669 2 0 1 0 1
#> GSM329662 1 0 1 1 0
#> GSM329665 1 0 1 1 0
#> GSM329668 1 0 1 1 0
#> GSM329671 1 0 1 1 0
#> GSM329673 1 0 1 1 0
#> GSM329675 1 0 1 1 0
#> GSM329676 1 0 1 1 0
#> GSM329677 2 0 1 0 1
#> GSM329679 2 0 1 0 1
#> GSM329681 2 0 1 0 1
#> GSM329683 2 0 1 0 1
#> GSM329686 2 0 1 0 1
#> GSM329689 2 0 1 0 1
#> GSM329678 2 0 1 0 1
#> GSM329680 2 0 1 0 1
#> GSM329685 2 0 1 0 1
#> GSM329688 2 0 1 0 1
#> GSM329691 2 0 1 0 1
#> GSM329682 1 0 1 1 0
#> GSM329684 1 0 1 1 0
#> GSM329687 1 0 1 1 0
#> GSM329690 1 0 1 1 0
#> GSM329692 2 0 1 0 1
#> GSM329694 2 0 1 0 1
#> GSM329697 2 0 1 0 1
#> GSM329700 2 0 1 0 1
#> GSM329703 2 0 1 0 1
#> GSM329704 2 0 1 0 1
#> GSM329707 2 0 1 0 1
#> GSM329709 2 0 1 0 1
#> GSM329711 2 0 1 0 1
#> GSM329714 2 0 1 0 1
#> GSM329693 2 0 1 0 1
#> GSM329696 2 0 1 0 1
#> GSM329699 2 0 1 0 1
#> GSM329702 2 0 1 0 1
#> GSM329706 2 0 1 0 1
#> GSM329708 2 0 1 0 1
#> GSM329710 2 0 1 0 1
#> GSM329713 1 0 1 1 0
#> GSM329695 1 0 1 1 0
#> GSM329698 1 0 1 1 0
#> GSM329701 1 0 1 1 0
#> GSM329705 1 0 1 1 0
#> GSM329712 2 0 1 0 1
#> GSM329715 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.0000 0.999 0 1.000 0.000
#> GSM329663 2 0.0000 0.999 0 1.000 0.000
#> GSM329664 3 0.4702 0.758 0 0.212 0.788
#> GSM329666 2 0.0000 0.999 0 1.000 0.000
#> GSM329667 2 0.0000 0.999 0 1.000 0.000
#> GSM329670 2 0.0000 0.999 0 1.000 0.000
#> GSM329672 2 0.0000 0.999 0 1.000 0.000
#> GSM329674 2 0.0000 0.999 0 1.000 0.000
#> GSM329661 3 0.0000 0.961 0 0.000 1.000
#> GSM329669 2 0.0000 0.999 0 1.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000
#> GSM329677 3 0.0000 0.961 0 0.000 1.000
#> GSM329679 2 0.0000 0.999 0 1.000 0.000
#> GSM329681 3 0.0000 0.961 0 0.000 1.000
#> GSM329683 3 0.0000 0.961 0 0.000 1.000
#> GSM329686 3 0.0000 0.961 0 0.000 1.000
#> GSM329689 3 0.0000 0.961 0 0.000 1.000
#> GSM329678 3 0.0000 0.961 0 0.000 1.000
#> GSM329680 3 0.0000 0.961 0 0.000 1.000
#> GSM329685 3 0.0000 0.961 0 0.000 1.000
#> GSM329688 3 0.0000 0.961 0 0.000 1.000
#> GSM329691 3 0.0000 0.961 0 0.000 1.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000
#> GSM329692 3 0.0000 0.961 0 0.000 1.000
#> GSM329694 3 0.5098 0.705 0 0.248 0.752
#> GSM329697 2 0.0000 0.999 0 1.000 0.000
#> GSM329700 2 0.0000 0.999 0 1.000 0.000
#> GSM329703 2 0.0237 0.996 0 0.996 0.004
#> GSM329704 3 0.4702 0.758 0 0.212 0.788
#> GSM329707 3 0.0000 0.961 0 0.000 1.000
#> GSM329709 2 0.0000 0.999 0 1.000 0.000
#> GSM329711 2 0.0000 0.999 0 1.000 0.000
#> GSM329714 2 0.0000 0.999 0 1.000 0.000
#> GSM329693 2 0.0000 0.999 0 1.000 0.000
#> GSM329696 2 0.0237 0.996 0 0.996 0.004
#> GSM329699 2 0.0237 0.996 0 0.996 0.004
#> GSM329702 2 0.0000 0.999 0 1.000 0.000
#> GSM329706 3 0.0000 0.961 0 0.000 1.000
#> GSM329708 3 0.0000 0.961 0 0.000 1.000
#> GSM329710 3 0.0000 0.961 0 0.000 1.000
#> GSM329713 1 0.0000 1.000 1 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000
#> GSM329712 2 0.0000 0.999 0 1.000 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.0188 0.9400 0 0.996 0.000 0.004
#> GSM329663 2 0.0188 0.9400 0 0.996 0.000 0.004
#> GSM329664 3 0.4697 0.4720 0 0.356 0.644 0.000
#> GSM329666 2 0.0000 0.9409 0 1.000 0.000 0.000
#> GSM329667 2 0.0000 0.9409 0 1.000 0.000 0.000
#> GSM329670 2 0.0188 0.9400 0 0.996 0.000 0.004
#> GSM329672 2 0.0000 0.9409 0 1.000 0.000 0.000
#> GSM329674 2 0.0000 0.9409 0 1.000 0.000 0.000
#> GSM329661 3 0.0000 0.9394 0 0.000 1.000 0.000
#> GSM329669 2 0.0188 0.9400 0 0.996 0.000 0.004
#> GSM329662 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329677 3 0.0000 0.9394 0 0.000 1.000 0.000
#> GSM329679 2 0.0000 0.9409 0 1.000 0.000 0.000
#> GSM329681 3 0.0000 0.9394 0 0.000 1.000 0.000
#> GSM329683 3 0.0000 0.9394 0 0.000 1.000 0.000
#> GSM329686 3 0.0000 0.9394 0 0.000 1.000 0.000
#> GSM329689 3 0.0000 0.9394 0 0.000 1.000 0.000
#> GSM329678 4 0.4981 0.0831 0 0.000 0.464 0.536
#> GSM329680 3 0.0000 0.9394 0 0.000 1.000 0.000
#> GSM329685 3 0.0000 0.9394 0 0.000 1.000 0.000
#> GSM329688 3 0.0000 0.9394 0 0.000 1.000 0.000
#> GSM329691 3 0.0000 0.9394 0 0.000 1.000 0.000
#> GSM329682 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329692 4 0.0469 0.8902 0 0.000 0.012 0.988
#> GSM329694 4 0.0524 0.8910 0 0.004 0.008 0.988
#> GSM329697 2 0.0000 0.9409 0 1.000 0.000 0.000
#> GSM329700 2 0.4981 0.1882 0 0.536 0.000 0.464
#> GSM329703 4 0.0000 0.8938 0 0.000 0.000 1.000
#> GSM329704 3 0.4564 0.5275 0 0.328 0.672 0.000
#> GSM329707 3 0.0000 0.9394 0 0.000 1.000 0.000
#> GSM329709 2 0.0000 0.9409 0 1.000 0.000 0.000
#> GSM329711 2 0.3074 0.8131 0 0.848 0.000 0.152
#> GSM329714 4 0.4072 0.5580 0 0.252 0.000 0.748
#> GSM329693 4 0.0000 0.8938 0 0.000 0.000 1.000
#> GSM329696 4 0.0000 0.8938 0 0.000 0.000 1.000
#> GSM329699 4 0.0000 0.8938 0 0.000 0.000 1.000
#> GSM329702 2 0.0000 0.9409 0 1.000 0.000 0.000
#> GSM329706 3 0.0000 0.9394 0 0.000 1.000 0.000
#> GSM329708 3 0.0000 0.9394 0 0.000 1.000 0.000
#> GSM329710 4 0.0188 0.8933 0 0.000 0.004 0.996
#> GSM329713 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329712 2 0.3074 0.8131 0 0.848 0.000 0.152
#> GSM329715 1 0.0000 1.0000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.0510 0.892 0.000 0.984 0.000 0.000 0.016
#> GSM329663 2 0.0404 0.896 0.000 0.988 0.000 0.000 0.012
#> GSM329664 5 0.1568 0.669 0.000 0.020 0.036 0.000 0.944
#> GSM329666 2 0.1544 0.899 0.000 0.932 0.000 0.000 0.068
#> GSM329667 5 0.3177 0.477 0.000 0.208 0.000 0.000 0.792
#> GSM329670 2 0.0290 0.895 0.000 0.992 0.000 0.000 0.008
#> GSM329672 2 0.2852 0.828 0.000 0.828 0.000 0.000 0.172
#> GSM329674 2 0.1544 0.899 0.000 0.932 0.000 0.000 0.068
#> GSM329661 3 0.0290 0.989 0.000 0.000 0.992 0.000 0.008
#> GSM329669 2 0.0510 0.892 0.000 0.984 0.000 0.000 0.016
#> GSM329662 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0162 0.998 0.996 0.000 0.000 0.000 0.004
#> GSM329673 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM329677 5 0.4227 0.543 0.000 0.000 0.420 0.000 0.580
#> GSM329679 2 0.2852 0.828 0.000 0.828 0.000 0.000 0.172
#> GSM329681 3 0.0290 0.989 0.000 0.000 0.992 0.000 0.008
#> GSM329683 3 0.0162 0.991 0.000 0.000 0.996 0.000 0.004
#> GSM329686 3 0.0162 0.992 0.000 0.000 0.996 0.000 0.004
#> GSM329689 3 0.0162 0.991 0.000 0.000 0.996 0.000 0.004
#> GSM329678 4 0.4341 0.415 0.000 0.000 0.364 0.628 0.008
#> GSM329680 3 0.0162 0.992 0.000 0.000 0.996 0.000 0.004
#> GSM329685 3 0.0162 0.992 0.000 0.000 0.996 0.000 0.004
#> GSM329688 3 0.0162 0.992 0.000 0.000 0.996 0.000 0.004
#> GSM329691 3 0.0162 0.992 0.000 0.000 0.996 0.000 0.004
#> GSM329682 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM329687 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0162 0.998 0.996 0.000 0.000 0.000 0.004
#> GSM329692 4 0.2124 0.817 0.000 0.000 0.056 0.916 0.028
#> GSM329694 4 0.2127 0.798 0.000 0.000 0.000 0.892 0.108
#> GSM329697 2 0.1544 0.899 0.000 0.932 0.000 0.000 0.068
#> GSM329700 2 0.4820 0.424 0.000 0.632 0.000 0.332 0.036
#> GSM329703 4 0.0000 0.852 0.000 0.000 0.000 1.000 0.000
#> GSM329704 5 0.1568 0.669 0.000 0.020 0.036 0.000 0.944
#> GSM329707 5 0.4161 0.577 0.000 0.000 0.392 0.000 0.608
#> GSM329709 2 0.1544 0.899 0.000 0.932 0.000 0.000 0.068
#> GSM329711 2 0.2172 0.852 0.000 0.908 0.000 0.076 0.016
#> GSM329714 4 0.4990 0.254 0.000 0.384 0.000 0.580 0.036
#> GSM329693 4 0.0000 0.852 0.000 0.000 0.000 1.000 0.000
#> GSM329696 4 0.0000 0.852 0.000 0.000 0.000 1.000 0.000
#> GSM329699 4 0.0000 0.852 0.000 0.000 0.000 1.000 0.000
#> GSM329702 2 0.1544 0.899 0.000 0.932 0.000 0.000 0.068
#> GSM329706 5 0.4201 0.564 0.000 0.000 0.408 0.000 0.592
#> GSM329708 3 0.0510 0.981 0.000 0.000 0.984 0.000 0.016
#> GSM329710 4 0.0671 0.848 0.000 0.000 0.004 0.980 0.016
#> GSM329713 1 0.0162 0.998 0.996 0.000 0.000 0.000 0.004
#> GSM329695 1 0.0162 0.998 0.996 0.000 0.000 0.000 0.004
#> GSM329698 1 0.0162 0.998 0.996 0.000 0.000 0.000 0.004
#> GSM329701 1 0.0162 0.998 0.996 0.000 0.000 0.000 0.004
#> GSM329705 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000
#> GSM329712 2 0.2172 0.852 0.000 0.908 0.000 0.076 0.016
#> GSM329715 1 0.0162 0.998 0.996 0.000 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329660 2 0.3383 0.565 0.000 0.728 0.000 0.000 0.004 0.268
#> GSM329663 2 0.3330 0.488 0.000 0.716 0.000 0.000 0.000 0.284
#> GSM329664 5 0.0603 0.634 0.000 0.016 0.004 0.000 0.980 0.000
#> GSM329666 2 0.0000 0.762 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329667 5 0.3770 0.379 0.000 0.244 0.000 0.000 0.728 0.028
#> GSM329670 2 0.3390 0.478 0.000 0.704 0.000 0.000 0.000 0.296
#> GSM329672 2 0.1556 0.722 0.000 0.920 0.000 0.000 0.080 0.000
#> GSM329674 2 0.0000 0.762 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329661 3 0.1204 0.946 0.000 0.000 0.944 0.000 0.000 0.056
#> GSM329669 2 0.3175 0.578 0.000 0.744 0.000 0.000 0.000 0.256
#> GSM329662 1 0.1779 0.923 0.920 0.000 0.000 0.000 0.016 0.064
#> GSM329665 1 0.0000 0.932 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0508 0.932 0.984 0.000 0.000 0.000 0.004 0.012
#> GSM329671 1 0.1644 0.922 0.920 0.000 0.000 0.000 0.004 0.076
#> GSM329673 1 0.1779 0.923 0.920 0.000 0.000 0.000 0.016 0.064
#> GSM329675 1 0.1779 0.923 0.920 0.000 0.000 0.000 0.016 0.064
#> GSM329676 1 0.1779 0.923 0.920 0.000 0.000 0.000 0.016 0.064
#> GSM329677 5 0.3765 0.533 0.000 0.000 0.404 0.000 0.596 0.000
#> GSM329679 2 0.1610 0.720 0.000 0.916 0.000 0.000 0.084 0.000
#> GSM329681 3 0.1814 0.918 0.000 0.000 0.900 0.000 0.000 0.100
#> GSM329683 3 0.1387 0.940 0.000 0.000 0.932 0.000 0.000 0.068
#> GSM329686 3 0.0000 0.955 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329689 3 0.1387 0.940 0.000 0.000 0.932 0.000 0.000 0.068
#> GSM329678 4 0.4127 0.568 0.000 0.000 0.284 0.680 0.000 0.036
#> GSM329680 3 0.0146 0.953 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM329685 3 0.0000 0.955 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329688 3 0.0000 0.955 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329691 3 0.0000 0.955 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329682 1 0.1500 0.927 0.936 0.000 0.000 0.000 0.012 0.052
#> GSM329684 1 0.1779 0.923 0.920 0.000 0.000 0.000 0.016 0.064
#> GSM329687 1 0.1657 0.925 0.928 0.000 0.000 0.000 0.016 0.056
#> GSM329690 1 0.1858 0.917 0.904 0.000 0.000 0.000 0.004 0.092
#> GSM329692 4 0.4252 0.678 0.000 0.000 0.036 0.652 0.000 0.312
#> GSM329694 4 0.4517 0.669 0.000 0.000 0.000 0.648 0.060 0.292
#> GSM329697 2 0.0000 0.762 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329700 6 0.5195 0.910 0.000 0.176 0.000 0.208 0.000 0.616
#> GSM329703 4 0.0146 0.801 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM329704 5 0.0603 0.634 0.000 0.016 0.004 0.000 0.980 0.000
#> GSM329707 5 0.4537 0.630 0.000 0.000 0.264 0.000 0.664 0.072
#> GSM329709 2 0.0000 0.762 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329711 2 0.5206 0.251 0.000 0.588 0.000 0.128 0.000 0.284
#> GSM329714 6 0.5096 0.915 0.000 0.132 0.000 0.252 0.000 0.616
#> GSM329693 4 0.0146 0.801 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM329696 4 0.0000 0.803 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329699 4 0.0000 0.803 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329702 2 0.0000 0.762 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329706 5 0.3782 0.595 0.000 0.000 0.360 0.000 0.636 0.004
#> GSM329708 3 0.1327 0.943 0.000 0.000 0.936 0.000 0.000 0.064
#> GSM329710 4 0.2513 0.775 0.000 0.000 0.008 0.852 0.000 0.140
#> GSM329713 1 0.1858 0.917 0.904 0.000 0.000 0.000 0.004 0.092
#> GSM329695 1 0.1858 0.917 0.904 0.000 0.000 0.000 0.004 0.092
#> GSM329698 1 0.1858 0.917 0.904 0.000 0.000 0.000 0.004 0.092
#> GSM329701 1 0.1753 0.919 0.912 0.000 0.000 0.000 0.004 0.084
#> GSM329705 1 0.0260 0.932 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM329712 2 0.5190 0.259 0.000 0.592 0.000 0.128 0.000 0.280
#> GSM329715 1 0.1471 0.924 0.932 0.000 0.000 0.000 0.004 0.064
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> CV:skmeans 56 0.505684 5.82e-11 2
#> CV:skmeans 56 0.010546 4.13e-10 3
#> CV:skmeans 53 0.000106 3.97e-09 4
#> CV:skmeans 52 0.000262 1.42e-08 5
#> CV:skmeans 51 0.002075 1.77e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 21163 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4311 0.569 0.569
#> 3 3 1.000 0.985 0.994 0.5365 0.766 0.590
#> 4 4 0.868 0.857 0.923 0.1279 0.876 0.655
#> 5 5 0.926 0.904 0.955 0.0651 0.916 0.692
#> 6 6 0.904 0.869 0.889 0.0307 0.968 0.846
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 5
There is also optional best \(k\) = 2 3 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
#> GSM329660 2 0 1 0 1
#> GSM329663 2 0 1 0 1
#> GSM329664 2 0 1 0 1
#> GSM329666 2 0 1 0 1
#> GSM329667 2 0 1 0 1
#> GSM329670 2 0 1 0 1
#> GSM329672 2 0 1 0 1
#> GSM329674 2 0 1 0 1
#> GSM329661 2 0 1 0 1
#> GSM329669 2 0 1 0 1
#> GSM329662 1 0 1 1 0
#> GSM329665 1 0 1 1 0
#> GSM329668 1 0 1 1 0
#> GSM329671 1 0 1 1 0
#> GSM329673 1 0 1 1 0
#> GSM329675 1 0 1 1 0
#> GSM329676 1 0 1 1 0
#> GSM329677 2 0 1 0 1
#> GSM329679 2 0 1 0 1
#> GSM329681 2 0 1 0 1
#> GSM329683 2 0 1 0 1
#> GSM329686 2 0 1 0 1
#> GSM329689 2 0 1 0 1
#> GSM329678 2 0 1 0 1
#> GSM329680 2 0 1 0 1
#> GSM329685 2 0 1 0 1
#> GSM329688 2 0 1 0 1
#> GSM329691 2 0 1 0 1
#> GSM329682 1 0 1 1 0
#> GSM329684 1 0 1 1 0
#> GSM329687 1 0 1 1 0
#> GSM329690 1 0 1 1 0
#> GSM329692 2 0 1 0 1
#> GSM329694 2 0 1 0 1
#> GSM329697 2 0 1 0 1
#> GSM329700 2 0 1 0 1
#> GSM329703 2 0 1 0 1
#> GSM329704 2 0 1 0 1
#> GSM329707 2 0 1 0 1
#> GSM329709 2 0 1 0 1
#> GSM329711 2 0 1 0 1
#> GSM329714 2 0 1 0 1
#> GSM329693 2 0 1 0 1
#> GSM329696 2 0 1 0 1
#> GSM329699 2 0 1 0 1
#> GSM329702 2 0 1 0 1
#> GSM329706 2 0 1 0 1
#> GSM329708 2 0 1 0 1
#> GSM329710 2 0 1 0 1
#> GSM329713 1 0 1 1 0
#> GSM329695 1 0 1 1 0
#> GSM329698 1 0 1 1 0
#> GSM329701 1 0 1 1 0
#> GSM329705 1 0 1 1 0
#> GSM329712 2 0 1 0 1
#> GSM329715 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.0000 1.000 0 1.000 0.000
#> GSM329663 2 0.0000 1.000 0 1.000 0.000
#> GSM329664 2 0.0000 1.000 0 1.000 0.000
#> GSM329666 2 0.0000 1.000 0 1.000 0.000
#> GSM329667 2 0.0000 1.000 0 1.000 0.000
#> GSM329670 2 0.0000 1.000 0 1.000 0.000
#> GSM329672 2 0.0000 1.000 0 1.000 0.000
#> GSM329674 2 0.0000 1.000 0 1.000 0.000
#> GSM329661 3 0.0000 0.972 0 0.000 1.000
#> GSM329669 2 0.0000 1.000 0 1.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000
#> GSM329677 3 0.0000 0.972 0 0.000 1.000
#> GSM329679 2 0.0000 1.000 0 1.000 0.000
#> GSM329681 3 0.0000 0.972 0 0.000 1.000
#> GSM329683 3 0.0000 0.972 0 0.000 1.000
#> GSM329686 3 0.0000 0.972 0 0.000 1.000
#> GSM329689 3 0.0000 0.972 0 0.000 1.000
#> GSM329678 3 0.0000 0.972 0 0.000 1.000
#> GSM329680 3 0.0000 0.972 0 0.000 1.000
#> GSM329685 3 0.0000 0.972 0 0.000 1.000
#> GSM329688 3 0.0000 0.972 0 0.000 1.000
#> GSM329691 3 0.0000 0.972 0 0.000 1.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000
#> GSM329692 3 0.2796 0.887 0 0.092 0.908
#> GSM329694 2 0.0000 1.000 0 1.000 0.000
#> GSM329697 2 0.0000 1.000 0 1.000 0.000
#> GSM329700 2 0.0000 1.000 0 1.000 0.000
#> GSM329703 2 0.0000 1.000 0 1.000 0.000
#> GSM329704 2 0.0000 1.000 0 1.000 0.000
#> GSM329707 3 0.5178 0.661 0 0.256 0.744
#> GSM329709 2 0.0000 1.000 0 1.000 0.000
#> GSM329711 2 0.0000 1.000 0 1.000 0.000
#> GSM329714 2 0.0000 1.000 0 1.000 0.000
#> GSM329693 2 0.0000 1.000 0 1.000 0.000
#> GSM329696 2 0.0000 1.000 0 1.000 0.000
#> GSM329699 2 0.0000 1.000 0 1.000 0.000
#> GSM329702 2 0.0000 1.000 0 1.000 0.000
#> GSM329706 3 0.0000 0.972 0 0.000 1.000
#> GSM329708 3 0.0000 0.972 0 0.000 1.000
#> GSM329710 2 0.0237 0.996 0 0.996 0.004
#> GSM329713 1 0.0000 1.000 1 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000
#> GSM329712 2 0.0000 1.000 0 1.000 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.000 0.832 0 1.000 0.000 0.000
#> GSM329663 2 0.139 0.820 0 0.952 0.000 0.048
#> GSM329664 2 0.462 0.662 0 0.660 0.000 0.340
#> GSM329666 2 0.000 0.832 0 1.000 0.000 0.000
#> GSM329667 2 0.430 0.702 0 0.716 0.000 0.284
#> GSM329670 2 0.000 0.832 0 1.000 0.000 0.000
#> GSM329672 2 0.430 0.702 0 0.716 0.000 0.284
#> GSM329674 2 0.000 0.832 0 1.000 0.000 0.000
#> GSM329661 3 0.000 0.944 0 0.000 1.000 0.000
#> GSM329669 2 0.000 0.832 0 1.000 0.000 0.000
#> GSM329662 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329665 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329668 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329671 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329673 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329675 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329676 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329677 3 0.416 0.658 0 0.000 0.736 0.264
#> GSM329679 2 0.430 0.702 0 0.716 0.000 0.284
#> GSM329681 3 0.384 0.717 0 0.000 0.776 0.224
#> GSM329683 3 0.000 0.944 0 0.000 1.000 0.000
#> GSM329686 3 0.000 0.944 0 0.000 1.000 0.000
#> GSM329689 3 0.000 0.944 0 0.000 1.000 0.000
#> GSM329678 4 0.380 0.645 0 0.000 0.220 0.780
#> GSM329680 3 0.000 0.944 0 0.000 1.000 0.000
#> GSM329685 3 0.000 0.944 0 0.000 1.000 0.000
#> GSM329688 3 0.000 0.944 0 0.000 1.000 0.000
#> GSM329691 3 0.000 0.944 0 0.000 1.000 0.000
#> GSM329682 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329684 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329687 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329690 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329692 4 0.000 0.786 0 0.000 0.000 1.000
#> GSM329694 2 0.462 0.662 0 0.660 0.000 0.340
#> GSM329697 2 0.000 0.832 0 1.000 0.000 0.000
#> GSM329700 2 0.156 0.798 0 0.944 0.000 0.056
#> GSM329703 4 0.430 0.729 0 0.284 0.000 0.716
#> GSM329704 2 0.462 0.662 0 0.660 0.000 0.340
#> GSM329707 2 0.752 0.381 0 0.464 0.196 0.340
#> GSM329709 2 0.000 0.832 0 1.000 0.000 0.000
#> GSM329711 2 0.000 0.832 0 1.000 0.000 0.000
#> GSM329714 4 0.369 0.768 0 0.208 0.000 0.792
#> GSM329693 4 0.430 0.729 0 0.284 0.000 0.716
#> GSM329696 4 0.430 0.729 0 0.284 0.000 0.716
#> GSM329699 4 0.000 0.786 0 0.000 0.000 1.000
#> GSM329702 2 0.000 0.832 0 1.000 0.000 0.000
#> GSM329706 4 0.102 0.767 0 0.000 0.032 0.968
#> GSM329708 3 0.000 0.944 0 0.000 1.000 0.000
#> GSM329710 4 0.000 0.786 0 0.000 0.000 1.000
#> GSM329713 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329695 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329698 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329701 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329705 1 0.000 1.000 1 0.000 0.000 0.000
#> GSM329712 2 0.000 0.832 0 1.000 0.000 0.000
#> GSM329715 1 0.000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 5 0.3534 0.663 0 0.256 0.000 0.000 0.744
#> GSM329663 2 0.0162 0.950 0 0.996 0.000 0.000 0.004
#> GSM329664 5 0.0162 0.906 0 0.004 0.000 0.000 0.996
#> GSM329666 2 0.0000 0.952 0 1.000 0.000 0.000 0.000
#> GSM329667 5 0.3177 0.722 0 0.208 0.000 0.000 0.792
#> GSM329670 2 0.0000 0.952 0 1.000 0.000 0.000 0.000
#> GSM329672 2 0.2690 0.806 0 0.844 0.000 0.000 0.156
#> GSM329674 2 0.0000 0.952 0 1.000 0.000 0.000 0.000
#> GSM329661 3 0.1197 0.910 0 0.000 0.952 0.000 0.048
#> GSM329669 2 0.0000 0.952 0 1.000 0.000 0.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329677 5 0.0703 0.887 0 0.000 0.024 0.000 0.976
#> GSM329679 2 0.3452 0.668 0 0.756 0.000 0.000 0.244
#> GSM329681 3 0.3534 0.743 0 0.000 0.744 0.000 0.256
#> GSM329683 3 0.2561 0.852 0 0.000 0.856 0.000 0.144
#> GSM329686 3 0.0000 0.927 0 0.000 1.000 0.000 0.000
#> GSM329689 3 0.3177 0.803 0 0.000 0.792 0.000 0.208
#> GSM329678 4 0.0880 0.866 0 0.000 0.000 0.968 0.032
#> GSM329680 3 0.0000 0.927 0 0.000 1.000 0.000 0.000
#> GSM329685 3 0.0000 0.927 0 0.000 1.000 0.000 0.000
#> GSM329688 3 0.0000 0.927 0 0.000 1.000 0.000 0.000
#> GSM329691 3 0.0000 0.927 0 0.000 1.000 0.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329692 4 0.4088 0.468 0 0.000 0.000 0.632 0.368
#> GSM329694 5 0.0162 0.906 0 0.004 0.000 0.000 0.996
#> GSM329697 2 0.0000 0.952 0 1.000 0.000 0.000 0.000
#> GSM329700 4 0.5172 0.455 0 0.324 0.000 0.616 0.060
#> GSM329703 4 0.0000 0.882 0 0.000 0.000 1.000 0.000
#> GSM329704 5 0.0162 0.906 0 0.004 0.000 0.000 0.996
#> GSM329707 5 0.0000 0.903 0 0.000 0.000 0.000 1.000
#> GSM329709 2 0.0000 0.952 0 1.000 0.000 0.000 0.000
#> GSM329711 2 0.0880 0.934 0 0.968 0.000 0.032 0.000
#> GSM329714 4 0.2074 0.825 0 0.000 0.000 0.896 0.104
#> GSM329693 4 0.0000 0.882 0 0.000 0.000 1.000 0.000
#> GSM329696 4 0.0000 0.882 0 0.000 0.000 1.000 0.000
#> GSM329699 4 0.0000 0.882 0 0.000 0.000 1.000 0.000
#> GSM329702 2 0.0000 0.952 0 1.000 0.000 0.000 0.000
#> GSM329706 5 0.0290 0.901 0 0.000 0.000 0.008 0.992
#> GSM329708 3 0.0000 0.927 0 0.000 1.000 0.000 0.000
#> GSM329710 4 0.0000 0.882 0 0.000 0.000 1.000 0.000
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329712 2 0.1043 0.928 0 0.960 0.000 0.040 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 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
#> GSM329660 6 0.4494 0.710 0.000 0.092 0.000 0.000 0.216 0.692
#> GSM329663 2 0.1910 0.803 0.000 0.892 0.000 0.000 0.108 0.000
#> GSM329664 5 0.0632 0.886 0.000 0.024 0.000 0.000 0.976 0.000
#> GSM329666 2 0.0000 0.839 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329667 5 0.0632 0.886 0.000 0.024 0.000 0.000 0.976 0.000
#> GSM329670 2 0.0000 0.839 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329672 2 0.3221 0.667 0.000 0.736 0.000 0.000 0.264 0.000
#> GSM329674 2 0.0146 0.835 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM329661 3 0.3789 0.809 0.000 0.000 0.716 0.000 0.024 0.260
#> GSM329669 6 0.3563 0.790 0.000 0.336 0.000 0.000 0.000 0.664
#> GSM329662 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329673 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329677 5 0.3122 0.763 0.000 0.000 0.020 0.000 0.804 0.176
#> GSM329679 2 0.3737 0.470 0.000 0.608 0.000 0.000 0.392 0.000
#> GSM329681 3 0.3789 0.809 0.000 0.000 0.716 0.000 0.024 0.260
#> GSM329683 3 0.3789 0.809 0.000 0.000 0.716 0.000 0.024 0.260
#> GSM329686 3 0.0000 0.877 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329689 3 0.3789 0.809 0.000 0.000 0.716 0.000 0.024 0.260
#> GSM329678 4 0.0000 0.898 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329680 3 0.0000 0.877 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329685 3 0.0000 0.877 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329688 3 0.0000 0.877 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329691 3 0.0000 0.877 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329682 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329687 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0632 0.984 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM329692 4 0.5202 0.533 0.000 0.000 0.000 0.600 0.140 0.260
#> GSM329694 5 0.0632 0.886 0.000 0.024 0.000 0.000 0.976 0.000
#> GSM329697 2 0.1910 0.803 0.000 0.892 0.000 0.000 0.108 0.000
#> GSM329700 6 0.4690 0.775 0.000 0.112 0.000 0.016 0.156 0.716
#> GSM329703 4 0.0000 0.898 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329704 5 0.0632 0.886 0.000 0.024 0.000 0.000 0.976 0.000
#> GSM329707 5 0.2300 0.807 0.000 0.000 0.000 0.000 0.856 0.144
#> GSM329709 2 0.0000 0.839 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329711 6 0.3330 0.835 0.000 0.284 0.000 0.000 0.000 0.716
#> GSM329714 4 0.4599 0.604 0.000 0.000 0.000 0.684 0.212 0.104
#> GSM329693 4 0.0000 0.898 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329696 4 0.0000 0.898 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329699 4 0.0000 0.898 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329702 2 0.0000 0.839 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329706 5 0.2178 0.804 0.000 0.000 0.000 0.132 0.868 0.000
#> GSM329708 3 0.0000 0.877 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329710 4 0.0000 0.898 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329713 1 0.0632 0.984 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM329695 1 0.0632 0.984 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM329698 1 0.0632 0.984 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM329701 1 0.0458 0.987 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM329705 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329712 6 0.3330 0.835 0.000 0.284 0.000 0.000 0.000 0.716
#> GSM329715 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> CV:pam 56 0.505684 5.82e-11 2
#> CV:pam 56 0.000528 2.02e-10 3
#> CV:pam 55 0.000025 6.20e-11 4
#> CV:pam 54 0.001995 8.34e-10 5
#> CV:pam 55 0.000810 6.32e-09 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "mclust"]
# you can also extract it by
# res = res_list["CV:mclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 21163 rows and 56 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 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 1.000 1.000 0.4311 0.569 0.569
#> 3 3 0.766 0.788 0.910 0.5265 0.781 0.615
#> 4 4 0.891 0.918 0.959 0.1182 0.875 0.666
#> 5 5 0.910 0.851 0.932 0.0718 0.911 0.689
#> 6 6 0.917 0.869 0.930 0.0340 0.955 0.797
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 5
There is also optional best \(k\) = 2 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
#> GSM329660 2 0 1 0 1
#> GSM329663 2 0 1 0 1
#> GSM329664 2 0 1 0 1
#> GSM329666 2 0 1 0 1
#> GSM329667 2 0 1 0 1
#> GSM329670 2 0 1 0 1
#> GSM329672 2 0 1 0 1
#> GSM329674 2 0 1 0 1
#> GSM329661 2 0 1 0 1
#> GSM329669 2 0 1 0 1
#> GSM329662 1 0 1 1 0
#> GSM329665 1 0 1 1 0
#> GSM329668 1 0 1 1 0
#> GSM329671 1 0 1 1 0
#> GSM329673 1 0 1 1 0
#> GSM329675 1 0 1 1 0
#> GSM329676 1 0 1 1 0
#> GSM329677 2 0 1 0 1
#> GSM329679 2 0 1 0 1
#> GSM329681 2 0 1 0 1
#> GSM329683 2 0 1 0 1
#> GSM329686 2 0 1 0 1
#> GSM329689 2 0 1 0 1
#> GSM329678 2 0 1 0 1
#> GSM329680 2 0 1 0 1
#> GSM329685 2 0 1 0 1
#> GSM329688 2 0 1 0 1
#> GSM329691 2 0 1 0 1
#> GSM329682 1 0 1 1 0
#> GSM329684 1 0 1 1 0
#> GSM329687 1 0 1 1 0
#> GSM329690 1 0 1 1 0
#> GSM329692 2 0 1 0 1
#> GSM329694 2 0 1 0 1
#> GSM329697 2 0 1 0 1
#> GSM329700 2 0 1 0 1
#> GSM329703 2 0 1 0 1
#> GSM329704 2 0 1 0 1
#> GSM329707 2 0 1 0 1
#> GSM329709 2 0 1 0 1
#> GSM329711 2 0 1 0 1
#> GSM329714 2 0 1 0 1
#> GSM329693 2 0 1 0 1
#> GSM329696 2 0 1 0 1
#> GSM329699 2 0 1 0 1
#> GSM329702 2 0 1 0 1
#> GSM329706 2 0 1 0 1
#> GSM329708 2 0 1 0 1
#> GSM329710 2 0 1 0 1
#> GSM329713 1 0 1 1 0
#> GSM329695 1 0 1 1 0
#> GSM329698 1 0 1 1 0
#> GSM329701 1 0 1 1 0
#> GSM329705 1 0 1 1 0
#> GSM329712 2 0 1 0 1
#> GSM329715 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.0000 0.789 0 1.000 0.000
#> GSM329663 2 0.0000 0.789 0 1.000 0.000
#> GSM329664 2 0.5760 0.461 0 0.672 0.328
#> GSM329666 2 0.0000 0.789 0 1.000 0.000
#> GSM329667 2 0.1860 0.760 0 0.948 0.052
#> GSM329670 2 0.0000 0.789 0 1.000 0.000
#> GSM329672 2 0.0000 0.789 0 1.000 0.000
#> GSM329674 2 0.0000 0.789 0 1.000 0.000
#> GSM329661 3 0.0000 0.922 0 0.000 1.000
#> GSM329669 2 0.0000 0.789 0 1.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000
#> GSM329677 3 0.1031 0.909 0 0.024 0.976
#> GSM329679 2 0.0000 0.789 0 1.000 0.000
#> GSM329681 3 0.0592 0.918 0 0.012 0.988
#> GSM329683 3 0.0000 0.922 0 0.000 1.000
#> GSM329686 3 0.0000 0.922 0 0.000 1.000
#> GSM329689 3 0.0237 0.921 0 0.004 0.996
#> GSM329678 2 0.6274 0.330 0 0.544 0.456
#> GSM329680 3 0.0237 0.921 0 0.004 0.996
#> GSM329685 3 0.0000 0.922 0 0.000 1.000
#> GSM329688 3 0.0000 0.922 0 0.000 1.000
#> GSM329691 3 0.0000 0.922 0 0.000 1.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000
#> GSM329692 2 0.6274 0.330 0 0.544 0.456
#> GSM329694 2 0.6274 0.330 0 0.544 0.456
#> GSM329697 2 0.0000 0.789 0 1.000 0.000
#> GSM329700 2 0.0000 0.789 0 1.000 0.000
#> GSM329703 2 0.6274 0.330 0 0.544 0.456
#> GSM329704 2 0.5591 0.504 0 0.696 0.304
#> GSM329707 3 0.5621 0.414 0 0.308 0.692
#> GSM329709 2 0.0000 0.789 0 1.000 0.000
#> GSM329711 2 0.0000 0.789 0 1.000 0.000
#> GSM329714 2 0.0000 0.789 0 1.000 0.000
#> GSM329693 2 0.6274 0.330 0 0.544 0.456
#> GSM329696 2 0.6274 0.330 0 0.544 0.456
#> GSM329699 2 0.6274 0.330 0 0.544 0.456
#> GSM329702 2 0.0000 0.789 0 1.000 0.000
#> GSM329706 3 0.5621 0.414 0 0.308 0.692
#> GSM329708 3 0.0892 0.912 0 0.020 0.980
#> GSM329710 2 0.6274 0.330 0 0.544 0.456
#> GSM329713 1 0.0000 1.000 1 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000
#> GSM329712 2 0.0000 0.789 0 1.000 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.2530 0.862 0 0.888 0.000 0.112
#> GSM329663 2 0.0469 0.888 0 0.988 0.000 0.012
#> GSM329664 2 0.1510 0.875 0 0.956 0.028 0.016
#> GSM329666 2 0.0000 0.889 0 1.000 0.000 0.000
#> GSM329667 2 0.0000 0.889 0 1.000 0.000 0.000
#> GSM329670 2 0.2530 0.862 0 0.888 0.000 0.112
#> GSM329672 2 0.0000 0.889 0 1.000 0.000 0.000
#> GSM329674 2 0.0000 0.889 0 1.000 0.000 0.000
#> GSM329661 3 0.0000 0.982 0 0.000 1.000 0.000
#> GSM329669 2 0.2530 0.862 0 0.888 0.000 0.112
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329677 3 0.3217 0.827 0 0.128 0.860 0.012
#> GSM329679 2 0.0000 0.889 0 1.000 0.000 0.000
#> GSM329681 3 0.0336 0.976 0 0.000 0.992 0.008
#> GSM329683 3 0.0000 0.982 0 0.000 1.000 0.000
#> GSM329686 3 0.0000 0.982 0 0.000 1.000 0.000
#> GSM329689 3 0.0188 0.980 0 0.000 0.996 0.004
#> GSM329678 4 0.0000 0.980 0 0.000 0.000 1.000
#> GSM329680 3 0.0188 0.980 0 0.000 0.996 0.004
#> GSM329685 3 0.0000 0.982 0 0.000 1.000 0.000
#> GSM329688 3 0.0000 0.982 0 0.000 1.000 0.000
#> GSM329691 3 0.0000 0.982 0 0.000 1.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329692 4 0.0000 0.980 0 0.000 0.000 1.000
#> GSM329694 2 0.4817 0.390 0 0.612 0.000 0.388
#> GSM329697 2 0.0000 0.889 0 1.000 0.000 0.000
#> GSM329700 2 0.2704 0.856 0 0.876 0.000 0.124
#> GSM329703 4 0.0000 0.980 0 0.000 0.000 1.000
#> GSM329704 2 0.0592 0.887 0 0.984 0.000 0.016
#> GSM329707 2 0.6371 0.465 0 0.608 0.300 0.092
#> GSM329709 2 0.0000 0.889 0 1.000 0.000 0.000
#> GSM329711 2 0.2589 0.860 0 0.884 0.000 0.116
#> GSM329714 2 0.2647 0.859 0 0.880 0.000 0.120
#> GSM329693 4 0.0000 0.980 0 0.000 0.000 1.000
#> GSM329696 4 0.0000 0.980 0 0.000 0.000 1.000
#> GSM329699 4 0.2281 0.870 0 0.096 0.000 0.904
#> GSM329702 2 0.0000 0.889 0 1.000 0.000 0.000
#> GSM329706 2 0.5217 0.389 0 0.608 0.012 0.380
#> GSM329708 3 0.0000 0.982 0 0.000 1.000 0.000
#> GSM329710 4 0.0000 0.980 0 0.000 0.000 1.000
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329712 2 0.2589 0.860 0 0.884 0.000 0.116
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.0000 0.7894 0 1.000 0.000 0.000 0.000
#> GSM329663 2 0.0510 0.7939 0 0.984 0.000 0.000 0.016
#> GSM329664 5 0.1121 0.8270 0 0.044 0.000 0.000 0.956
#> GSM329666 2 0.2127 0.8058 0 0.892 0.000 0.000 0.108
#> GSM329667 5 0.3837 0.4713 0 0.308 0.000 0.000 0.692
#> GSM329670 2 0.0000 0.7894 0 1.000 0.000 0.000 0.000
#> GSM329672 2 0.2127 0.8058 0 0.892 0.000 0.000 0.108
#> GSM329674 2 0.2127 0.8058 0 0.892 0.000 0.000 0.108
#> GSM329661 3 0.0000 0.9814 0 0.000 1.000 0.000 0.000
#> GSM329669 2 0.0000 0.7894 0 1.000 0.000 0.000 0.000
#> GSM329662 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329677 5 0.3003 0.7178 0 0.000 0.188 0.000 0.812
#> GSM329679 2 0.2127 0.8058 0 0.892 0.000 0.000 0.108
#> GSM329681 3 0.1965 0.9077 0 0.000 0.904 0.000 0.096
#> GSM329683 3 0.0162 0.9800 0 0.000 0.996 0.000 0.004
#> GSM329686 3 0.0000 0.9814 0 0.000 1.000 0.000 0.000
#> GSM329689 3 0.1478 0.9366 0 0.000 0.936 0.000 0.064
#> GSM329678 4 0.0162 0.8946 0 0.000 0.000 0.996 0.004
#> GSM329680 3 0.0162 0.9800 0 0.000 0.996 0.000 0.004
#> GSM329685 3 0.0000 0.9814 0 0.000 1.000 0.000 0.000
#> GSM329688 3 0.0000 0.9814 0 0.000 1.000 0.000 0.000
#> GSM329691 3 0.0000 0.9814 0 0.000 1.000 0.000 0.000
#> GSM329682 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329692 4 0.1478 0.8611 0 0.000 0.000 0.936 0.064
#> GSM329694 4 0.4849 0.6703 0 0.140 0.000 0.724 0.136
#> GSM329697 2 0.2127 0.8058 0 0.892 0.000 0.000 0.108
#> GSM329700 2 0.4449 -0.0511 0 0.512 0.000 0.484 0.004
#> GSM329703 4 0.0000 0.8953 0 0.000 0.000 1.000 0.000
#> GSM329704 5 0.1270 0.8244 0 0.052 0.000 0.000 0.948
#> GSM329707 5 0.1043 0.8151 0 0.000 0.040 0.000 0.960
#> GSM329709 2 0.2127 0.8058 0 0.892 0.000 0.000 0.108
#> GSM329711 2 0.4171 0.2529 0 0.604 0.000 0.396 0.000
#> GSM329714 4 0.6206 0.3981 0 0.304 0.000 0.528 0.168
#> GSM329693 4 0.0000 0.8953 0 0.000 0.000 1.000 0.000
#> GSM329696 4 0.0000 0.8953 0 0.000 0.000 1.000 0.000
#> GSM329699 4 0.0000 0.8953 0 0.000 0.000 1.000 0.000
#> GSM329702 2 0.2127 0.8058 0 0.892 0.000 0.000 0.108
#> GSM329706 5 0.3141 0.7678 0 0.000 0.040 0.108 0.852
#> GSM329708 3 0.0000 0.9814 0 0.000 1.000 0.000 0.000
#> GSM329710 4 0.0162 0.8946 0 0.000 0.000 0.996 0.004
#> GSM329713 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329712 2 0.4321 0.2463 0 0.600 0.000 0.396 0.004
#> GSM329715 1 0.0000 1.0000 1 0.000 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
#> GSM329660 2 0.3323 0.714 0 0.752 0.000 0.000 0.008 0.240
#> GSM329663 2 0.3259 0.732 0 0.772 0.000 0.000 0.012 0.216
#> GSM329664 5 0.2679 0.833 0 0.096 0.000 0.000 0.864 0.040
#> GSM329666 2 0.0000 0.857 0 1.000 0.000 0.000 0.000 0.000
#> GSM329667 2 0.3620 0.304 0 0.648 0.000 0.000 0.352 0.000
#> GSM329670 2 0.3271 0.722 0 0.760 0.000 0.000 0.008 0.232
#> GSM329672 2 0.0000 0.857 0 1.000 0.000 0.000 0.000 0.000
#> GSM329674 2 0.0000 0.857 0 1.000 0.000 0.000 0.000 0.000
#> GSM329661 3 0.0146 0.873 0 0.000 0.996 0.000 0.004 0.000
#> GSM329669 2 0.3175 0.702 0 0.744 0.000 0.000 0.000 0.256
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329677 5 0.1462 0.802 0 0.000 0.056 0.000 0.936 0.008
#> GSM329679 2 0.0000 0.857 0 1.000 0.000 0.000 0.000 0.000
#> GSM329681 3 0.4910 0.610 0 0.000 0.656 0.000 0.192 0.152
#> GSM329683 3 0.0508 0.870 0 0.000 0.984 0.000 0.012 0.004
#> GSM329686 3 0.0146 0.873 0 0.000 0.996 0.000 0.004 0.000
#> GSM329689 3 0.4849 0.619 0 0.000 0.664 0.000 0.188 0.148
#> GSM329678 4 0.0547 0.963 0 0.000 0.000 0.980 0.000 0.020
#> GSM329680 3 0.0891 0.865 0 0.000 0.968 0.000 0.024 0.008
#> GSM329685 3 0.0146 0.873 0 0.000 0.996 0.000 0.004 0.000
#> GSM329688 3 0.0146 0.872 0 0.000 0.996 0.000 0.000 0.004
#> GSM329691 3 0.0146 0.872 0 0.000 0.996 0.000 0.000 0.004
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329692 4 0.2402 0.870 0 0.000 0.000 0.868 0.012 0.120
#> GSM329694 6 0.3333 0.538 0 0.024 0.000 0.000 0.192 0.784
#> GSM329697 2 0.0000 0.857 0 1.000 0.000 0.000 0.000 0.000
#> GSM329700 6 0.1863 0.876 0 0.104 0.000 0.000 0.000 0.896
#> GSM329703 4 0.0260 0.973 0 0.000 0.000 0.992 0.000 0.008
#> GSM329704 5 0.3274 0.812 0 0.096 0.000 0.000 0.824 0.080
#> GSM329707 5 0.1738 0.844 0 0.052 0.004 0.000 0.928 0.016
#> GSM329709 2 0.0000 0.857 0 1.000 0.000 0.000 0.000 0.000
#> GSM329711 6 0.2003 0.866 0 0.116 0.000 0.000 0.000 0.884
#> GSM329714 6 0.1692 0.837 0 0.048 0.000 0.008 0.012 0.932
#> GSM329693 4 0.0363 0.972 0 0.000 0.000 0.988 0.000 0.012
#> GSM329696 4 0.0260 0.973 0 0.000 0.000 0.992 0.000 0.008
#> GSM329699 4 0.0260 0.973 0 0.000 0.000 0.992 0.000 0.008
#> GSM329702 2 0.0000 0.857 0 1.000 0.000 0.000 0.000 0.000
#> GSM329706 5 0.3570 0.724 0 0.016 0.004 0.000 0.752 0.228
#> GSM329708 3 0.3819 0.435 0 0.000 0.652 0.340 0.000 0.008
#> GSM329710 4 0.0000 0.970 0 0.000 0.000 1.000 0.000 0.000
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329712 6 0.1863 0.876 0 0.104 0.000 0.000 0.000 0.896
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> CV:mclust 56 5.06e-01 5.82e-11 2
#> CV:mclust 45 8.79e-04 3.07e-09 3
#> CV:mclust 53 9.94e-05 1.11e-10 4
#> CV:mclust 51 5.42e-04 2.99e-09 5
#> CV:mclust 54 5.03e-05 5.16e-09 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["CV", "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 21163 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4311 0.569 0.569
#> 3 3 1.000 0.980 0.990 0.5574 0.761 0.580
#> 4 4 0.777 0.730 0.838 0.1145 0.927 0.783
#> 5 5 0.708 0.595 0.789 0.0414 0.953 0.829
#> 6 6 0.692 0.586 0.710 0.0401 0.945 0.786
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
#> GSM329660 2 0 1 0 1
#> GSM329663 2 0 1 0 1
#> GSM329664 2 0 1 0 1
#> GSM329666 2 0 1 0 1
#> GSM329667 2 0 1 0 1
#> GSM329670 2 0 1 0 1
#> GSM329672 2 0 1 0 1
#> GSM329674 2 0 1 0 1
#> GSM329661 2 0 1 0 1
#> GSM329669 2 0 1 0 1
#> GSM329662 1 0 1 1 0
#> GSM329665 1 0 1 1 0
#> GSM329668 1 0 1 1 0
#> GSM329671 1 0 1 1 0
#> GSM329673 1 0 1 1 0
#> GSM329675 1 0 1 1 0
#> GSM329676 1 0 1 1 0
#> GSM329677 2 0 1 0 1
#> GSM329679 2 0 1 0 1
#> GSM329681 2 0 1 0 1
#> GSM329683 2 0 1 0 1
#> GSM329686 2 0 1 0 1
#> GSM329689 2 0 1 0 1
#> GSM329678 2 0 1 0 1
#> GSM329680 2 0 1 0 1
#> GSM329685 2 0 1 0 1
#> GSM329688 2 0 1 0 1
#> GSM329691 2 0 1 0 1
#> GSM329682 1 0 1 1 0
#> GSM329684 1 0 1 1 0
#> GSM329687 1 0 1 1 0
#> GSM329690 1 0 1 1 0
#> GSM329692 2 0 1 0 1
#> GSM329694 2 0 1 0 1
#> GSM329697 2 0 1 0 1
#> GSM329700 2 0 1 0 1
#> GSM329703 2 0 1 0 1
#> GSM329704 2 0 1 0 1
#> GSM329707 2 0 1 0 1
#> GSM329709 2 0 1 0 1
#> GSM329711 2 0 1 0 1
#> GSM329714 2 0 1 0 1
#> GSM329693 2 0 1 0 1
#> GSM329696 2 0 1 0 1
#> GSM329699 2 0 1 0 1
#> GSM329702 2 0 1 0 1
#> GSM329706 2 0 1 0 1
#> GSM329708 2 0 1 0 1
#> GSM329710 2 0 1 0 1
#> GSM329713 1 0 1 1 0
#> GSM329695 1 0 1 1 0
#> GSM329698 1 0 1 1 0
#> GSM329701 1 0 1 1 0
#> GSM329705 1 0 1 1 0
#> GSM329712 2 0 1 0 1
#> GSM329715 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.0000 0.974 0 1.000 0.000
#> GSM329663 2 0.0000 0.974 0 1.000 0.000
#> GSM329664 2 0.3879 0.836 0 0.848 0.152
#> GSM329666 2 0.0000 0.974 0 1.000 0.000
#> GSM329667 2 0.0000 0.974 0 1.000 0.000
#> GSM329670 2 0.0000 0.974 0 1.000 0.000
#> GSM329672 2 0.0000 0.974 0 1.000 0.000
#> GSM329674 2 0.0000 0.974 0 1.000 0.000
#> GSM329661 3 0.0000 0.999 0 0.000 1.000
#> GSM329669 2 0.0000 0.974 0 1.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000
#> GSM329677 3 0.0000 0.999 0 0.000 1.000
#> GSM329679 2 0.0000 0.974 0 1.000 0.000
#> GSM329681 3 0.0000 0.999 0 0.000 1.000
#> GSM329683 3 0.0000 0.999 0 0.000 1.000
#> GSM329686 3 0.0000 0.999 0 0.000 1.000
#> GSM329689 3 0.0000 0.999 0 0.000 1.000
#> GSM329678 3 0.0000 0.999 0 0.000 1.000
#> GSM329680 3 0.0000 0.999 0 0.000 1.000
#> GSM329685 3 0.0000 0.999 0 0.000 1.000
#> GSM329688 3 0.0000 0.999 0 0.000 1.000
#> GSM329691 3 0.0000 0.999 0 0.000 1.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000
#> GSM329692 3 0.0000 0.999 0 0.000 1.000
#> GSM329694 2 0.1529 0.945 0 0.960 0.040
#> GSM329697 2 0.0000 0.974 0 1.000 0.000
#> GSM329700 2 0.0000 0.974 0 1.000 0.000
#> GSM329703 2 0.0000 0.974 0 1.000 0.000
#> GSM329704 2 0.4555 0.775 0 0.800 0.200
#> GSM329707 3 0.0000 0.999 0 0.000 1.000
#> GSM329709 2 0.0000 0.974 0 1.000 0.000
#> GSM329711 2 0.0000 0.974 0 1.000 0.000
#> GSM329714 2 0.0000 0.974 0 1.000 0.000
#> GSM329693 2 0.0000 0.974 0 1.000 0.000
#> GSM329696 2 0.0237 0.972 0 0.996 0.004
#> GSM329699 2 0.4178 0.813 0 0.828 0.172
#> GSM329702 2 0.0000 0.974 0 1.000 0.000
#> GSM329706 3 0.0000 0.999 0 0.000 1.000
#> GSM329708 3 0.0000 0.999 0 0.000 1.000
#> GSM329710 3 0.0424 0.991 0 0.008 0.992
#> GSM329713 1 0.0000 1.000 1 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000
#> GSM329712 2 0.0000 0.974 0 1.000 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.1022 0.772 0.000 0.968 0.000 0.032
#> GSM329663 2 0.0817 0.773 0.000 0.976 0.000 0.024
#> GSM329664 2 0.6120 0.225 0.000 0.520 0.432 0.048
#> GSM329666 2 0.0336 0.772 0.000 0.992 0.000 0.008
#> GSM329667 2 0.3570 0.698 0.000 0.860 0.092 0.048
#> GSM329670 2 0.2469 0.750 0.000 0.892 0.000 0.108
#> GSM329672 2 0.1854 0.748 0.000 0.940 0.012 0.048
#> GSM329674 2 0.3074 0.727 0.000 0.848 0.000 0.152
#> GSM329661 3 0.2921 0.741 0.000 0.000 0.860 0.140
#> GSM329669 2 0.4331 0.618 0.000 0.712 0.000 0.288
#> GSM329662 1 0.0336 0.996 0.992 0.000 0.000 0.008
#> GSM329665 1 0.0188 0.997 0.996 0.000 0.000 0.004
#> GSM329668 1 0.0188 0.997 0.996 0.000 0.000 0.004
#> GSM329671 1 0.0188 0.995 0.996 0.000 0.000 0.004
#> GSM329673 1 0.0336 0.996 0.992 0.000 0.000 0.008
#> GSM329675 1 0.0336 0.996 0.992 0.000 0.000 0.008
#> GSM329676 1 0.0336 0.996 0.992 0.000 0.000 0.008
#> GSM329677 3 0.1635 0.695 0.000 0.008 0.948 0.044
#> GSM329679 2 0.2586 0.734 0.000 0.912 0.040 0.048
#> GSM329681 3 0.0000 0.726 0.000 0.000 1.000 0.000
#> GSM329683 3 0.2216 0.745 0.000 0.000 0.908 0.092
#> GSM329686 3 0.2281 0.746 0.000 0.000 0.904 0.096
#> GSM329689 3 0.0000 0.726 0.000 0.000 1.000 0.000
#> GSM329678 4 0.4888 -0.196 0.000 0.000 0.412 0.588
#> GSM329680 3 0.4250 0.689 0.000 0.000 0.724 0.276
#> GSM329685 3 0.4697 0.603 0.000 0.000 0.644 0.356
#> GSM329688 3 0.4761 0.583 0.000 0.000 0.628 0.372
#> GSM329691 3 0.4222 0.692 0.000 0.000 0.728 0.272
#> GSM329682 1 0.0188 0.996 0.996 0.000 0.000 0.004
#> GSM329684 1 0.0336 0.996 0.992 0.000 0.000 0.008
#> GSM329687 1 0.0336 0.996 0.992 0.000 0.000 0.008
#> GSM329690 1 0.0188 0.995 0.996 0.000 0.000 0.004
#> GSM329692 3 0.4941 0.351 0.000 0.000 0.564 0.436
#> GSM329694 2 0.2976 0.710 0.000 0.872 0.120 0.008
#> GSM329697 2 0.0707 0.773 0.000 0.980 0.000 0.020
#> GSM329700 2 0.4331 0.617 0.000 0.712 0.000 0.288
#> GSM329703 4 0.2654 0.736 0.000 0.108 0.004 0.888
#> GSM329704 2 0.6125 0.210 0.000 0.516 0.436 0.048
#> GSM329707 3 0.4100 0.574 0.000 0.128 0.824 0.048
#> GSM329709 2 0.1022 0.772 0.000 0.968 0.000 0.032
#> GSM329711 2 0.4830 0.476 0.000 0.608 0.000 0.392
#> GSM329714 2 0.4925 0.378 0.000 0.572 0.000 0.428
#> GSM329693 4 0.3764 0.563 0.000 0.216 0.000 0.784
#> GSM329696 4 0.2654 0.736 0.000 0.108 0.004 0.888
#> GSM329699 4 0.1929 0.710 0.000 0.036 0.024 0.940
#> GSM329702 2 0.0592 0.770 0.000 0.984 0.000 0.016
#> GSM329706 3 0.3606 0.690 0.000 0.024 0.844 0.132
#> GSM329708 3 0.5000 0.291 0.000 0.000 0.500 0.500
#> GSM329710 4 0.3444 0.526 0.000 0.000 0.184 0.816
#> GSM329713 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM329695 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM329698 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM329701 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM329705 1 0.0000 0.997 1.000 0.000 0.000 0.000
#> GSM329712 2 0.4843 0.469 0.000 0.604 0.000 0.396
#> GSM329715 1 0.0000 0.997 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.2672 0.6589 0.000 0.872 0.008 0.116 0.004
#> GSM329663 2 0.4258 0.6060 0.000 0.744 0.004 0.220 0.032
#> GSM329664 2 0.4410 0.0824 0.000 0.556 0.440 0.000 0.004
#> GSM329666 2 0.1671 0.6637 0.000 0.924 0.000 0.076 0.000
#> GSM329667 2 0.2848 0.5563 0.000 0.840 0.156 0.000 0.004
#> GSM329670 2 0.5246 0.4257 0.000 0.564 0.000 0.384 0.052
#> GSM329672 2 0.1270 0.6246 0.000 0.948 0.052 0.000 0.000
#> GSM329674 2 0.3807 0.5984 0.000 0.748 0.000 0.240 0.012
#> GSM329661 5 0.4637 0.5916 0.000 0.000 0.292 0.036 0.672
#> GSM329669 2 0.4341 0.4342 0.000 0.592 0.000 0.404 0.004
#> GSM329662 1 0.1544 0.9416 0.932 0.000 0.000 0.000 0.068
#> GSM329665 1 0.1121 0.9488 0.956 0.000 0.000 0.000 0.044
#> GSM329668 1 0.0290 0.9514 0.992 0.000 0.000 0.000 0.008
#> GSM329671 1 0.0510 0.9493 0.984 0.000 0.000 0.000 0.016
#> GSM329673 1 0.1121 0.9488 0.956 0.000 0.000 0.000 0.044
#> GSM329675 1 0.1410 0.9446 0.940 0.000 0.000 0.000 0.060
#> GSM329676 1 0.1341 0.9458 0.944 0.000 0.000 0.000 0.056
#> GSM329677 3 0.1638 0.5406 0.000 0.064 0.932 0.000 0.004
#> GSM329679 2 0.1732 0.6106 0.000 0.920 0.080 0.000 0.000
#> GSM329681 5 0.4171 0.4436 0.000 0.000 0.396 0.000 0.604
#> GSM329683 3 0.5188 -0.1236 0.000 0.000 0.540 0.044 0.416
#> GSM329686 3 0.3242 0.5799 0.000 0.000 0.844 0.116 0.040
#> GSM329689 3 0.3928 0.2053 0.000 0.000 0.700 0.004 0.296
#> GSM329678 4 0.5431 -0.2016 0.000 0.000 0.424 0.516 0.060
#> GSM329680 3 0.4428 0.5493 0.000 0.000 0.756 0.160 0.084
#> GSM329685 3 0.4777 0.4801 0.000 0.000 0.680 0.268 0.052
#> GSM329688 3 0.4907 0.4652 0.000 0.000 0.664 0.280 0.056
#> GSM329691 3 0.3944 0.5717 0.000 0.000 0.788 0.160 0.052
#> GSM329682 1 0.0000 0.9512 1.000 0.000 0.000 0.000 0.000
#> GSM329684 1 0.1608 0.9398 0.928 0.000 0.000 0.000 0.072
#> GSM329687 1 0.1270 0.9469 0.948 0.000 0.000 0.000 0.052
#> GSM329690 1 0.2124 0.9145 0.900 0.000 0.000 0.004 0.096
#> GSM329692 5 0.5877 0.6418 0.000 0.000 0.200 0.196 0.604
#> GSM329694 2 0.4830 0.5677 0.000 0.768 0.120 0.068 0.044
#> GSM329697 2 0.2669 0.6620 0.000 0.876 0.000 0.104 0.020
#> GSM329700 2 0.4740 0.3242 0.000 0.516 0.000 0.468 0.016
#> GSM329703 4 0.2077 0.6252 0.000 0.084 0.000 0.908 0.008
#> GSM329704 2 0.4383 0.1111 0.000 0.572 0.424 0.000 0.004
#> GSM329707 3 0.4941 0.2452 0.000 0.328 0.628 0.000 0.044
#> GSM329709 2 0.2674 0.6594 0.000 0.868 0.000 0.120 0.012
#> GSM329711 2 0.4297 0.3257 0.000 0.528 0.000 0.472 0.000
#> GSM329714 4 0.4658 -0.2958 0.000 0.484 0.000 0.504 0.012
#> GSM329693 4 0.2919 0.6242 0.000 0.104 0.024 0.868 0.004
#> GSM329696 4 0.2640 0.6068 0.000 0.052 0.016 0.900 0.032
#> GSM329699 4 0.3059 0.5138 0.000 0.016 0.120 0.856 0.008
#> GSM329702 2 0.1628 0.6599 0.000 0.936 0.008 0.056 0.000
#> GSM329706 3 0.2332 0.5410 0.000 0.076 0.904 0.016 0.004
#> GSM329708 5 0.5466 0.6616 0.000 0.000 0.192 0.152 0.656
#> GSM329710 5 0.6040 0.2407 0.000 0.012 0.080 0.452 0.456
#> GSM329713 1 0.2629 0.8876 0.860 0.000 0.000 0.004 0.136
#> GSM329695 1 0.2583 0.8905 0.864 0.000 0.000 0.004 0.132
#> GSM329698 1 0.1831 0.9248 0.920 0.000 0.000 0.004 0.076
#> GSM329701 1 0.0880 0.9451 0.968 0.000 0.000 0.000 0.032
#> GSM329705 1 0.0290 0.9505 0.992 0.000 0.000 0.000 0.008
#> GSM329712 2 0.4448 0.3026 0.000 0.516 0.000 0.480 0.004
#> GSM329715 1 0.0404 0.9500 0.988 0.000 0.000 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329660 2 0.1666 0.67322 0.000 0.936 0.000 0.020 0.008 NA
#> GSM329663 2 0.5649 0.54725 0.000 0.644 0.032 0.136 0.008 NA
#> GSM329664 5 0.4981 0.20101 0.000 0.340 0.004 0.000 0.584 NA
#> GSM329666 2 0.1434 0.66858 0.000 0.940 0.000 0.012 0.048 NA
#> GSM329667 2 0.4979 0.38186 0.000 0.604 0.004 0.000 0.312 NA
#> GSM329670 2 0.5831 0.44207 0.000 0.560 0.024 0.276 0.000 NA
#> GSM329672 2 0.3201 0.56937 0.000 0.780 0.000 0.000 0.208 NA
#> GSM329674 2 0.3231 0.62347 0.000 0.800 0.008 0.180 0.000 NA
#> GSM329661 3 0.1672 0.76363 0.000 0.000 0.932 0.004 0.048 NA
#> GSM329669 2 0.3421 0.57071 0.000 0.736 0.000 0.256 0.000 NA
#> GSM329662 1 0.1267 0.84011 0.940 0.000 0.000 0.000 0.000 NA
#> GSM329665 1 0.0363 0.85380 0.988 0.000 0.000 0.000 0.000 NA
#> GSM329668 1 0.0937 0.85852 0.960 0.000 0.000 0.000 0.000 NA
#> GSM329671 1 0.2527 0.84293 0.832 0.000 0.000 0.000 0.000 NA
#> GSM329673 1 0.0713 0.85054 0.972 0.000 0.000 0.000 0.000 NA
#> GSM329675 1 0.1267 0.84011 0.940 0.000 0.000 0.000 0.000 NA
#> GSM329676 1 0.1267 0.84011 0.940 0.000 0.000 0.000 0.000 NA
#> GSM329677 5 0.0748 0.50489 0.000 0.004 0.004 0.000 0.976 NA
#> GSM329679 2 0.3050 0.54478 0.000 0.764 0.000 0.000 0.236 NA
#> GSM329681 3 0.2088 0.74154 0.000 0.000 0.904 0.000 0.068 NA
#> GSM329683 3 0.5212 0.36109 0.000 0.000 0.592 0.024 0.324 NA
#> GSM329686 5 0.5234 0.47612 0.000 0.000 0.048 0.208 0.668 NA
#> GSM329689 5 0.5358 0.00273 0.000 0.000 0.368 0.020 0.544 NA
#> GSM329678 4 0.5691 -0.13407 0.000 0.000 0.036 0.544 0.340 NA
#> GSM329680 5 0.6259 0.35252 0.000 0.000 0.096 0.304 0.524 NA
#> GSM329685 5 0.5412 0.36602 0.000 0.000 0.024 0.360 0.548 NA
#> GSM329688 5 0.5551 0.34706 0.000 0.000 0.028 0.372 0.528 NA
#> GSM329691 5 0.5608 0.41783 0.000 0.000 0.036 0.300 0.580 NA
#> GSM329682 1 0.1444 0.85862 0.928 0.000 0.000 0.000 0.000 NA
#> GSM329684 1 0.1387 0.83631 0.932 0.000 0.000 0.000 0.000 NA
#> GSM329687 1 0.0632 0.85183 0.976 0.000 0.000 0.000 0.000 NA
#> GSM329690 1 0.3684 0.73663 0.628 0.000 0.000 0.000 0.000 NA
#> GSM329692 3 0.2664 0.75525 0.000 0.000 0.848 0.136 0.016 NA
#> GSM329694 2 0.6099 0.51675 0.000 0.640 0.164 0.048 0.112 NA
#> GSM329697 2 0.1710 0.67320 0.000 0.940 0.008 0.020 0.012 NA
#> GSM329700 2 0.5291 0.39772 0.000 0.556 0.028 0.364 0.000 NA
#> GSM329703 4 0.3515 0.52327 0.000 0.192 0.012 0.780 0.000 NA
#> GSM329704 5 0.4724 0.20490 0.000 0.348 0.000 0.000 0.592 NA
#> GSM329707 5 0.4873 0.38228 0.000 0.172 0.048 0.000 0.712 NA
#> GSM329709 2 0.3342 0.66506 0.000 0.848 0.012 0.084 0.036 NA
#> GSM329711 2 0.4026 0.47508 0.000 0.636 0.000 0.348 0.000 NA
#> GSM329714 2 0.6113 0.26954 0.000 0.468 0.016 0.376 0.008 NA
#> GSM329693 4 0.3946 0.57145 0.000 0.208 0.000 0.748 0.012 NA
#> GSM329696 4 0.2742 0.66537 0.000 0.076 0.020 0.880 0.008 NA
#> GSM329699 4 0.2434 0.61794 0.000 0.032 0.000 0.896 0.056 NA
#> GSM329702 2 0.1897 0.65542 0.000 0.908 0.000 0.004 0.084 NA
#> GSM329706 5 0.1296 0.51360 0.000 0.012 0.000 0.032 0.952 NA
#> GSM329708 3 0.2860 0.76752 0.000 0.000 0.872 0.068 0.032 NA
#> GSM329710 3 0.5402 0.42733 0.000 0.020 0.584 0.336 0.024 NA
#> GSM329713 1 0.4076 0.65588 0.540 0.000 0.008 0.000 0.000 NA
#> GSM329695 1 0.3823 0.68047 0.564 0.000 0.000 0.000 0.000 NA
#> GSM329698 1 0.3446 0.77885 0.692 0.000 0.000 0.000 0.000 NA
#> GSM329701 1 0.3023 0.81889 0.768 0.000 0.000 0.000 0.000 NA
#> GSM329705 1 0.2048 0.85286 0.880 0.000 0.000 0.000 0.000 NA
#> GSM329712 2 0.3911 0.45228 0.000 0.624 0.000 0.368 0.000 NA
#> GSM329715 1 0.2491 0.84382 0.836 0.000 0.000 0.000 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> CV:NMF 56 0.505684 5.82e-11 2
#> CV:NMF 56 0.001210 7.06e-11 3
#> CV:NMF 48 0.000237 3.83e-10 4
#> CV:NMF 40 0.016126 4.65e-08 5
#> CV:NMF 38 0.314557 1.34e-06 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21163 rows and 56 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 1.000 0.970 0.985 0.3915 0.618 0.618
#> 3 3 1.000 0.972 0.985 0.6857 0.724 0.554
#> 4 4 0.860 0.791 0.887 0.1246 0.906 0.727
#> 5 5 0.834 0.884 0.912 0.0564 0.961 0.843
#> 6 6 0.834 0.832 0.864 0.0434 0.953 0.777
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
#> GSM329660 1 0.0376 0.980 0.996 0.004
#> GSM329663 1 0.0000 0.981 1.000 0.000
#> GSM329664 1 0.1184 0.973 0.984 0.016
#> GSM329666 1 0.0000 0.981 1.000 0.000
#> GSM329667 1 0.1184 0.973 0.984 0.016
#> GSM329670 1 0.0000 0.981 1.000 0.000
#> GSM329672 1 0.0000 0.981 1.000 0.000
#> GSM329674 1 0.0000 0.981 1.000 0.000
#> GSM329661 2 0.0000 0.992 0.000 1.000
#> GSM329669 1 0.0000 0.981 1.000 0.000
#> GSM329662 1 0.0000 0.981 1.000 0.000
#> GSM329665 1 0.0000 0.981 1.000 0.000
#> GSM329668 1 0.0000 0.981 1.000 0.000
#> GSM329671 1 0.0000 0.981 1.000 0.000
#> GSM329673 1 0.0000 0.981 1.000 0.000
#> GSM329675 1 0.0000 0.981 1.000 0.000
#> GSM329676 1 0.0000 0.981 1.000 0.000
#> GSM329677 2 0.0000 0.992 0.000 1.000
#> GSM329679 1 0.0000 0.981 1.000 0.000
#> GSM329681 2 0.0000 0.992 0.000 1.000
#> GSM329683 2 0.0000 0.992 0.000 1.000
#> GSM329686 2 0.0000 0.992 0.000 1.000
#> GSM329689 2 0.0000 0.992 0.000 1.000
#> GSM329678 2 0.4562 0.890 0.096 0.904
#> GSM329680 2 0.0000 0.992 0.000 1.000
#> GSM329685 2 0.0000 0.992 0.000 1.000
#> GSM329688 2 0.0000 0.992 0.000 1.000
#> GSM329691 2 0.0000 0.992 0.000 1.000
#> GSM329682 1 0.0000 0.981 1.000 0.000
#> GSM329684 1 0.0000 0.981 1.000 0.000
#> GSM329687 1 0.0000 0.981 1.000 0.000
#> GSM329690 1 0.0000 0.981 1.000 0.000
#> GSM329692 1 0.7674 0.735 0.776 0.224
#> GSM329694 1 0.1414 0.971 0.980 0.020
#> GSM329697 1 0.0000 0.981 1.000 0.000
#> GSM329700 1 0.0672 0.978 0.992 0.008
#> GSM329703 1 0.3114 0.942 0.944 0.056
#> GSM329704 1 0.1414 0.971 0.980 0.020
#> GSM329707 2 0.0000 0.992 0.000 1.000
#> GSM329709 1 0.0000 0.981 1.000 0.000
#> GSM329711 1 0.0000 0.981 1.000 0.000
#> GSM329714 1 0.0672 0.978 0.992 0.008
#> GSM329693 1 0.3114 0.942 0.944 0.056
#> GSM329696 1 0.3114 0.942 0.944 0.056
#> GSM329699 1 0.3114 0.942 0.944 0.056
#> GSM329702 1 0.0000 0.981 1.000 0.000
#> GSM329706 2 0.0376 0.989 0.004 0.996
#> GSM329708 2 0.0000 0.992 0.000 1.000
#> GSM329710 1 0.7674 0.735 0.776 0.224
#> GSM329713 1 0.0000 0.981 1.000 0.000
#> GSM329695 1 0.0000 0.981 1.000 0.000
#> GSM329698 1 0.0000 0.981 1.000 0.000
#> GSM329701 1 0.0000 0.981 1.000 0.000
#> GSM329705 1 0.0000 0.981 1.000 0.000
#> GSM329712 1 0.0000 0.981 1.000 0.000
#> GSM329715 1 0.0000 0.981 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.0237 0.968 0 0.996 0.004
#> GSM329663 2 0.0000 0.969 0 1.000 0.000
#> GSM329664 2 0.0747 0.966 0 0.984 0.016
#> GSM329666 2 0.0000 0.969 0 1.000 0.000
#> GSM329667 2 0.0747 0.966 0 0.984 0.016
#> GSM329670 2 0.0000 0.969 0 1.000 0.000
#> GSM329672 2 0.0000 0.969 0 1.000 0.000
#> GSM329674 2 0.0000 0.969 0 1.000 0.000
#> GSM329661 3 0.0000 0.991 0 0.000 1.000
#> GSM329669 2 0.0000 0.969 0 1.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000
#> GSM329677 3 0.0000 0.991 0 0.000 1.000
#> GSM329679 2 0.0000 0.969 0 1.000 0.000
#> GSM329681 3 0.0000 0.991 0 0.000 1.000
#> GSM329683 3 0.0000 0.991 0 0.000 1.000
#> GSM329686 3 0.0000 0.991 0 0.000 1.000
#> GSM329689 3 0.0000 0.991 0 0.000 1.000
#> GSM329678 3 0.2878 0.887 0 0.096 0.904
#> GSM329680 3 0.0000 0.991 0 0.000 1.000
#> GSM329685 3 0.0000 0.991 0 0.000 1.000
#> GSM329688 3 0.0000 0.991 0 0.000 1.000
#> GSM329691 3 0.0000 0.991 0 0.000 1.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000
#> GSM329692 2 0.4842 0.748 0 0.776 0.224
#> GSM329694 2 0.0892 0.964 0 0.980 0.020
#> GSM329697 2 0.0000 0.969 0 1.000 0.000
#> GSM329700 2 0.0424 0.968 0 0.992 0.008
#> GSM329703 2 0.1964 0.943 0 0.944 0.056
#> GSM329704 2 0.0892 0.964 0 0.980 0.020
#> GSM329707 3 0.0000 0.991 0 0.000 1.000
#> GSM329709 2 0.0000 0.969 0 1.000 0.000
#> GSM329711 2 0.0000 0.969 0 1.000 0.000
#> GSM329714 2 0.0424 0.968 0 0.992 0.008
#> GSM329693 2 0.1964 0.943 0 0.944 0.056
#> GSM329696 2 0.1964 0.943 0 0.944 0.056
#> GSM329699 2 0.1964 0.943 0 0.944 0.056
#> GSM329702 2 0.0000 0.969 0 1.000 0.000
#> GSM329706 3 0.0237 0.988 0 0.004 0.996
#> GSM329708 3 0.0000 0.991 0 0.000 1.000
#> GSM329710 2 0.4842 0.748 0 0.776 0.224
#> GSM329713 1 0.0000 1.000 1 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000
#> GSM329712 2 0.0000 0.969 0 1.000 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 4 0.4406 0.186 0 0.300 0.000 0.700
#> GSM329663 2 0.4977 0.571 0 0.540 0.000 0.460
#> GSM329664 2 0.0707 0.466 0 0.980 0.000 0.020
#> GSM329666 2 0.4977 0.571 0 0.540 0.000 0.460
#> GSM329667 2 0.0707 0.466 0 0.980 0.000 0.020
#> GSM329670 2 0.4977 0.571 0 0.540 0.000 0.460
#> GSM329672 2 0.0336 0.474 0 0.992 0.000 0.008
#> GSM329674 2 0.4977 0.571 0 0.540 0.000 0.460
#> GSM329661 3 0.0000 0.984 0 0.000 1.000 0.000
#> GSM329669 2 0.4977 0.571 0 0.540 0.000 0.460
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329677 3 0.0592 0.976 0 0.000 0.984 0.016
#> GSM329679 2 0.0336 0.474 0 0.992 0.000 0.008
#> GSM329681 3 0.0000 0.984 0 0.000 1.000 0.000
#> GSM329683 3 0.0000 0.984 0 0.000 1.000 0.000
#> GSM329686 3 0.0000 0.984 0 0.000 1.000 0.000
#> GSM329689 3 0.0000 0.984 0 0.000 1.000 0.000
#> GSM329678 3 0.3074 0.841 0 0.000 0.848 0.152
#> GSM329680 3 0.0000 0.984 0 0.000 1.000 0.000
#> GSM329685 3 0.0000 0.984 0 0.000 1.000 0.000
#> GSM329688 3 0.0000 0.984 0 0.000 1.000 0.000
#> GSM329691 3 0.0000 0.984 0 0.000 1.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329692 4 0.3266 0.623 0 0.000 0.168 0.832
#> GSM329694 2 0.4500 0.115 0 0.684 0.000 0.316
#> GSM329697 2 0.4977 0.571 0 0.540 0.000 0.460
#> GSM329700 4 0.3172 0.606 0 0.160 0.000 0.840
#> GSM329703 4 0.0000 0.771 0 0.000 0.000 1.000
#> GSM329704 2 0.3219 0.333 0 0.836 0.000 0.164
#> GSM329707 3 0.0592 0.976 0 0.000 0.984 0.016
#> GSM329709 2 0.4977 0.571 0 0.540 0.000 0.460
#> GSM329711 2 0.4994 0.537 0 0.520 0.000 0.480
#> GSM329714 4 0.3172 0.606 0 0.160 0.000 0.840
#> GSM329693 4 0.0000 0.771 0 0.000 0.000 1.000
#> GSM329696 4 0.0000 0.771 0 0.000 0.000 1.000
#> GSM329699 4 0.0000 0.771 0 0.000 0.000 1.000
#> GSM329702 2 0.4977 0.571 0 0.540 0.000 0.460
#> GSM329706 3 0.0817 0.970 0 0.000 0.976 0.024
#> GSM329708 3 0.0000 0.984 0 0.000 1.000 0.000
#> GSM329710 4 0.3266 0.623 0 0.000 0.168 0.832
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329712 2 0.4994 0.537 0 0.520 0.000 0.480
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 4 0.5314 0.498 0.000 0.420 0.000 0.528 0.052
#> GSM329663 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM329664 5 0.0000 0.739 0.000 0.000 0.000 0.000 1.000
#> GSM329666 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM329667 5 0.0000 0.739 0.000 0.000 0.000 0.000 1.000
#> GSM329670 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM329672 5 0.4283 0.584 0.000 0.348 0.000 0.008 0.644
#> GSM329674 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM329661 3 0.0000 0.984 0.000 0.000 1.000 0.000 0.000
#> GSM329669 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM329662 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000
#> GSM329671 1 0.2813 0.920 0.832 0.000 0.000 0.168 0.000
#> GSM329673 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000
#> GSM329677 3 0.0510 0.976 0.000 0.000 0.984 0.000 0.016
#> GSM329679 5 0.4283 0.584 0.000 0.348 0.000 0.008 0.644
#> GSM329681 3 0.0000 0.984 0.000 0.000 1.000 0.000 0.000
#> GSM329683 3 0.0000 0.984 0.000 0.000 1.000 0.000 0.000
#> GSM329686 3 0.0000 0.984 0.000 0.000 1.000 0.000 0.000
#> GSM329689 3 0.0000 0.984 0.000 0.000 1.000 0.000 0.000
#> GSM329678 3 0.2763 0.827 0.000 0.000 0.848 0.148 0.004
#> GSM329680 3 0.0000 0.984 0.000 0.000 1.000 0.000 0.000
#> GSM329685 3 0.0000 0.984 0.000 0.000 1.000 0.000 0.000
#> GSM329688 3 0.0000 0.984 0.000 0.000 1.000 0.000 0.000
#> GSM329691 3 0.0000 0.984 0.000 0.000 1.000 0.000 0.000
#> GSM329682 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0000 0.911 1.000 0.000 0.000 0.000 0.000
#> GSM329687 1 0.2773 0.921 0.836 0.000 0.000 0.164 0.000
#> GSM329690 1 0.2813 0.920 0.832 0.000 0.000 0.168 0.000
#> GSM329692 4 0.2813 0.647 0.000 0.000 0.168 0.832 0.000
#> GSM329694 5 0.3857 0.557 0.000 0.000 0.000 0.312 0.688
#> GSM329697 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM329700 4 0.4637 0.745 0.000 0.292 0.000 0.672 0.036
#> GSM329703 4 0.2813 0.819 0.000 0.168 0.000 0.832 0.000
#> GSM329704 5 0.2605 0.703 0.000 0.000 0.000 0.148 0.852
#> GSM329707 3 0.0510 0.976 0.000 0.000 0.984 0.000 0.016
#> GSM329709 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM329711 2 0.0771 0.970 0.000 0.976 0.000 0.020 0.004
#> GSM329714 4 0.4637 0.745 0.000 0.292 0.000 0.672 0.036
#> GSM329693 4 0.2813 0.819 0.000 0.168 0.000 0.832 0.000
#> GSM329696 4 0.2813 0.819 0.000 0.168 0.000 0.832 0.000
#> GSM329699 4 0.2813 0.819 0.000 0.168 0.000 0.832 0.000
#> GSM329702 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000
#> GSM329706 3 0.0771 0.971 0.000 0.000 0.976 0.004 0.020
#> GSM329708 3 0.0000 0.984 0.000 0.000 1.000 0.000 0.000
#> GSM329710 4 0.2813 0.647 0.000 0.000 0.168 0.832 0.000
#> GSM329713 1 0.2813 0.920 0.832 0.000 0.000 0.168 0.000
#> GSM329695 1 0.2813 0.920 0.832 0.000 0.000 0.168 0.000
#> GSM329698 1 0.2813 0.920 0.832 0.000 0.000 0.168 0.000
#> GSM329701 1 0.2813 0.920 0.832 0.000 0.000 0.168 0.000
#> GSM329705 1 0.2773 0.921 0.836 0.000 0.000 0.164 0.000
#> GSM329712 2 0.0771 0.970 0.000 0.976 0.000 0.020 0.004
#> GSM329715 1 0.2813 0.920 0.832 0.000 0.000 0.168 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329660 4 0.5100 0.51293 0.000 0.416 0.000 0.524 0.028 0.032
#> GSM329663 2 0.0000 0.99270 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329664 5 0.0000 0.73151 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM329666 2 0.0000 0.99270 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329667 5 0.0000 0.73151 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM329670 2 0.0000 0.99270 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329672 5 0.3847 0.58467 0.000 0.348 0.000 0.008 0.644 0.000
#> GSM329674 2 0.0000 0.99270 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329661 3 0.3050 0.81089 0.000 0.000 0.764 0.000 0.000 0.236
#> GSM329669 2 0.0000 0.99270 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329662 6 0.3371 0.99595 0.292 0.000 0.000 0.000 0.000 0.708
#> GSM329665 6 0.3371 0.99595 0.292 0.000 0.000 0.000 0.000 0.708
#> GSM329668 6 0.3371 0.99595 0.292 0.000 0.000 0.000 0.000 0.708
#> GSM329671 1 0.0000 0.82750 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329673 6 0.3371 0.99595 0.292 0.000 0.000 0.000 0.000 0.708
#> GSM329675 6 0.3330 0.98789 0.284 0.000 0.000 0.000 0.000 0.716
#> GSM329676 6 0.3371 0.99595 0.292 0.000 0.000 0.000 0.000 0.708
#> GSM329677 3 0.0458 0.91925 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM329679 5 0.3847 0.58467 0.000 0.348 0.000 0.008 0.644 0.000
#> GSM329681 3 0.0790 0.92021 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM329683 3 0.0790 0.92021 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM329686 3 0.1204 0.91875 0.000 0.000 0.944 0.000 0.000 0.056
#> GSM329689 3 0.0790 0.92021 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM329678 3 0.2520 0.79869 0.000 0.000 0.844 0.152 0.000 0.004
#> GSM329680 3 0.0146 0.92151 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM329685 3 0.1204 0.91875 0.000 0.000 0.944 0.000 0.000 0.056
#> GSM329688 3 0.1204 0.91875 0.000 0.000 0.944 0.000 0.000 0.056
#> GSM329691 3 0.1204 0.91875 0.000 0.000 0.944 0.000 0.000 0.056
#> GSM329682 6 0.3371 0.99595 0.292 0.000 0.000 0.000 0.000 0.708
#> GSM329684 6 0.3330 0.98789 0.284 0.000 0.000 0.000 0.000 0.716
#> GSM329687 1 0.3737 -0.00152 0.608 0.000 0.000 0.000 0.000 0.392
#> GSM329690 1 0.0000 0.82750 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329692 4 0.0000 0.69454 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329694 5 0.4361 0.54381 0.000 0.000 0.000 0.308 0.648 0.044
#> GSM329697 2 0.0000 0.99270 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329700 4 0.4272 0.75995 0.000 0.288 0.000 0.668 0.000 0.044
#> GSM329703 4 0.2527 0.83708 0.000 0.168 0.000 0.832 0.000 0.000
#> GSM329704 5 0.3268 0.69188 0.000 0.000 0.000 0.144 0.812 0.044
#> GSM329707 3 0.0458 0.91925 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM329709 2 0.0000 0.99270 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329711 2 0.0692 0.97012 0.000 0.976 0.000 0.020 0.000 0.004
#> GSM329714 4 0.4272 0.75995 0.000 0.288 0.000 0.668 0.000 0.044
#> GSM329693 4 0.2527 0.83708 0.000 0.168 0.000 0.832 0.000 0.000
#> GSM329696 4 0.2527 0.83708 0.000 0.168 0.000 0.832 0.000 0.000
#> GSM329699 4 0.2527 0.83708 0.000 0.168 0.000 0.832 0.000 0.000
#> GSM329702 2 0.0000 0.99270 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329706 3 0.0748 0.91702 0.000 0.000 0.976 0.004 0.016 0.004
#> GSM329708 3 0.5296 0.62739 0.000 0.000 0.596 0.168 0.000 0.236
#> GSM329710 4 0.0000 0.69454 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329713 1 0.0000 0.82750 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329695 1 0.0000 0.82750 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329698 1 0.1204 0.81420 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM329701 1 0.1007 0.82310 0.956 0.000 0.000 0.000 0.000 0.044
#> GSM329705 1 0.3737 -0.00152 0.608 0.000 0.000 0.000 0.000 0.392
#> GSM329712 2 0.0692 0.97012 0.000 0.976 0.000 0.020 0.000 0.004
#> GSM329715 1 0.1007 0.82310 0.956 0.000 0.000 0.000 0.000 0.044
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> MAD:hclust 56 6.76e-05 2.37e-03 2
#> MAD:hclust 56 1.85e-04 1.01e-10 3
#> MAD:hclust 49 5.14e-05 4.77e-08 4
#> MAD:hclust 55 1.36e-04 1.95e-09 5
#> MAD:hclust 54 2.83e-05 3.10e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 21163 rows and 56 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 0.616 0.936 0.949 0.4392 0.569 0.569
#> 3 3 1.000 0.936 0.956 0.4994 0.766 0.590
#> 4 4 0.782 0.799 0.849 0.1123 0.903 0.714
#> 5 5 0.734 0.651 0.804 0.0679 0.949 0.801
#> 6 6 0.730 0.713 0.775 0.0438 0.915 0.633
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
#> GSM329660 2 0.644 0.892 0.164 0.836
#> GSM329663 2 0.644 0.892 0.164 0.836
#> GSM329664 2 0.000 0.920 0.000 1.000
#> GSM329666 2 0.644 0.892 0.164 0.836
#> GSM329667 2 0.529 0.905 0.120 0.880
#> GSM329670 2 0.644 0.892 0.164 0.836
#> GSM329672 2 0.634 0.894 0.160 0.840
#> GSM329674 2 0.644 0.892 0.164 0.836
#> GSM329661 2 0.000 0.920 0.000 1.000
#> GSM329669 2 0.644 0.892 0.164 0.836
#> GSM329662 1 0.000 1.000 1.000 0.000
#> GSM329665 1 0.000 1.000 1.000 0.000
#> GSM329668 1 0.000 1.000 1.000 0.000
#> GSM329671 1 0.000 1.000 1.000 0.000
#> GSM329673 1 0.000 1.000 1.000 0.000
#> GSM329675 1 0.000 1.000 1.000 0.000
#> GSM329676 1 0.000 1.000 1.000 0.000
#> GSM329677 2 0.000 0.920 0.000 1.000
#> GSM329679 2 0.634 0.894 0.160 0.840
#> GSM329681 2 0.000 0.920 0.000 1.000
#> GSM329683 2 0.000 0.920 0.000 1.000
#> GSM329686 2 0.000 0.920 0.000 1.000
#> GSM329689 2 0.000 0.920 0.000 1.000
#> GSM329678 2 0.000 0.920 0.000 1.000
#> GSM329680 2 0.000 0.920 0.000 1.000
#> GSM329685 2 0.000 0.920 0.000 1.000
#> GSM329688 2 0.000 0.920 0.000 1.000
#> GSM329691 2 0.000 0.920 0.000 1.000
#> GSM329682 1 0.000 1.000 1.000 0.000
#> GSM329684 1 0.000 1.000 1.000 0.000
#> GSM329687 1 0.000 1.000 1.000 0.000
#> GSM329690 1 0.000 1.000 1.000 0.000
#> GSM329692 2 0.000 0.920 0.000 1.000
#> GSM329694 2 0.000 0.920 0.000 1.000
#> GSM329697 2 0.644 0.892 0.164 0.836
#> GSM329700 2 0.644 0.892 0.164 0.836
#> GSM329703 2 0.456 0.911 0.096 0.904
#> GSM329704 2 0.000 0.920 0.000 1.000
#> GSM329707 2 0.000 0.920 0.000 1.000
#> GSM329709 2 0.644 0.892 0.164 0.836
#> GSM329711 2 0.644 0.892 0.164 0.836
#> GSM329714 2 0.634 0.894 0.160 0.840
#> GSM329693 2 0.456 0.911 0.096 0.904
#> GSM329696 2 0.456 0.911 0.096 0.904
#> GSM329699 2 0.000 0.920 0.000 1.000
#> GSM329702 2 0.644 0.892 0.164 0.836
#> GSM329706 2 0.000 0.920 0.000 1.000
#> GSM329708 2 0.000 0.920 0.000 1.000
#> GSM329710 2 0.000 0.920 0.000 1.000
#> GSM329713 1 0.000 1.000 1.000 0.000
#> GSM329695 1 0.000 1.000 1.000 0.000
#> GSM329698 1 0.000 1.000 1.000 0.000
#> GSM329701 1 0.000 1.000 1.000 0.000
#> GSM329705 1 0.000 1.000 1.000 0.000
#> GSM329712 2 0.644 0.892 0.164 0.836
#> GSM329715 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329663 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329664 2 0.6280 0.0847 0.000 0.54 0.460
#> GSM329666 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329667 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329670 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329672 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329674 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329661 3 0.2066 1.0000 0.000 0.06 0.940
#> GSM329669 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329662 1 0.1753 0.9764 0.952 0.00 0.048
#> GSM329665 1 0.0000 0.9800 1.000 0.00 0.000
#> GSM329668 1 0.1289 0.9785 0.968 0.00 0.032
#> GSM329671 1 0.0592 0.9797 0.988 0.00 0.012
#> GSM329673 1 0.1753 0.9764 0.952 0.00 0.048
#> GSM329675 1 0.1753 0.9764 0.952 0.00 0.048
#> GSM329676 1 0.1753 0.9764 0.952 0.00 0.048
#> GSM329677 3 0.2066 1.0000 0.000 0.06 0.940
#> GSM329679 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329681 3 0.2066 1.0000 0.000 0.06 0.940
#> GSM329683 3 0.2066 1.0000 0.000 0.06 0.940
#> GSM329686 3 0.2066 1.0000 0.000 0.06 0.940
#> GSM329689 3 0.2066 1.0000 0.000 0.06 0.940
#> GSM329678 3 0.2066 1.0000 0.000 0.06 0.940
#> GSM329680 3 0.2066 1.0000 0.000 0.06 0.940
#> GSM329685 3 0.2066 1.0000 0.000 0.06 0.940
#> GSM329688 3 0.2066 1.0000 0.000 0.06 0.940
#> GSM329691 3 0.2066 1.0000 0.000 0.06 0.940
#> GSM329682 1 0.1643 0.9772 0.956 0.00 0.044
#> GSM329684 1 0.1753 0.9764 0.952 0.00 0.048
#> GSM329687 1 0.1643 0.9772 0.956 0.00 0.044
#> GSM329690 1 0.0592 0.9797 0.988 0.00 0.012
#> GSM329692 3 0.2066 1.0000 0.000 0.06 0.940
#> GSM329694 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329697 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329700 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329703 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329704 2 0.6280 0.0847 0.000 0.54 0.460
#> GSM329707 3 0.2066 1.0000 0.000 0.06 0.940
#> GSM329709 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329711 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329714 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329693 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329696 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329699 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329702 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329706 3 0.2066 1.0000 0.000 0.06 0.940
#> GSM329708 3 0.2066 1.0000 0.000 0.06 0.940
#> GSM329710 2 0.4291 0.7404 0.000 0.82 0.180
#> GSM329713 1 0.0592 0.9797 0.988 0.00 0.012
#> GSM329695 1 0.0592 0.9797 0.988 0.00 0.012
#> GSM329698 1 0.0592 0.9797 0.988 0.00 0.012
#> GSM329701 1 0.0592 0.9797 0.988 0.00 0.012
#> GSM329705 1 0.0424 0.9799 0.992 0.00 0.008
#> GSM329712 2 0.0000 0.9473 0.000 1.00 0.000
#> GSM329715 1 0.0592 0.9797 0.988 0.00 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.0592 0.853 0.000 0.984 0.000 0.016
#> GSM329663 2 0.0592 0.857 0.000 0.984 0.000 0.016
#> GSM329664 2 0.6968 0.131 0.000 0.552 0.308 0.140
#> GSM329666 2 0.0000 0.860 0.000 1.000 0.000 0.000
#> GSM329667 2 0.2921 0.713 0.000 0.860 0.000 0.140
#> GSM329670 2 0.0188 0.858 0.000 0.996 0.000 0.004
#> GSM329672 2 0.1022 0.848 0.000 0.968 0.000 0.032
#> GSM329674 2 0.0000 0.860 0.000 1.000 0.000 0.000
#> GSM329661 3 0.1833 0.918 0.000 0.032 0.944 0.024
#> GSM329669 2 0.0000 0.860 0.000 1.000 0.000 0.000
#> GSM329662 1 0.2805 0.881 0.888 0.000 0.012 0.100
#> GSM329665 1 0.2773 0.907 0.880 0.000 0.004 0.116
#> GSM329668 1 0.0657 0.905 0.984 0.000 0.004 0.012
#> GSM329671 1 0.3306 0.898 0.840 0.000 0.004 0.156
#> GSM329673 1 0.2805 0.881 0.888 0.000 0.012 0.100
#> GSM329675 1 0.2924 0.880 0.884 0.000 0.016 0.100
#> GSM329676 1 0.2401 0.886 0.904 0.000 0.004 0.092
#> GSM329677 3 0.2871 0.888 0.000 0.032 0.896 0.072
#> GSM329679 2 0.1022 0.848 0.000 0.968 0.000 0.032
#> GSM329681 3 0.1022 0.930 0.000 0.032 0.968 0.000
#> GSM329683 3 0.1022 0.930 0.000 0.032 0.968 0.000
#> GSM329686 3 0.1022 0.930 0.000 0.032 0.968 0.000
#> GSM329689 3 0.1022 0.930 0.000 0.032 0.968 0.000
#> GSM329678 3 0.5766 0.328 0.000 0.032 0.564 0.404
#> GSM329680 3 0.1022 0.930 0.000 0.032 0.968 0.000
#> GSM329685 3 0.1022 0.930 0.000 0.032 0.968 0.000
#> GSM329688 3 0.1022 0.930 0.000 0.032 0.968 0.000
#> GSM329691 3 0.1022 0.930 0.000 0.032 0.968 0.000
#> GSM329682 1 0.1151 0.901 0.968 0.000 0.008 0.024
#> GSM329684 1 0.2924 0.880 0.884 0.000 0.016 0.100
#> GSM329687 1 0.1824 0.894 0.936 0.000 0.004 0.060
#> GSM329690 1 0.3591 0.895 0.824 0.000 0.008 0.168
#> GSM329692 4 0.5530 0.226 0.000 0.032 0.336 0.632
#> GSM329694 4 0.4679 0.712 0.000 0.352 0.000 0.648
#> GSM329697 2 0.0000 0.860 0.000 1.000 0.000 0.000
#> GSM329700 2 0.3649 0.579 0.000 0.796 0.000 0.204
#> GSM329703 4 0.4925 0.716 0.000 0.428 0.000 0.572
#> GSM329704 4 0.7836 0.232 0.000 0.288 0.304 0.408
#> GSM329707 3 0.3638 0.857 0.000 0.032 0.848 0.120
#> GSM329709 2 0.0000 0.860 0.000 1.000 0.000 0.000
#> GSM329711 2 0.3528 0.597 0.000 0.808 0.000 0.192
#> GSM329714 4 0.4972 0.667 0.000 0.456 0.000 0.544
#> GSM329693 4 0.4925 0.716 0.000 0.428 0.000 0.572
#> GSM329696 4 0.4925 0.716 0.000 0.428 0.000 0.572
#> GSM329699 4 0.4830 0.724 0.000 0.392 0.000 0.608
#> GSM329702 2 0.0000 0.860 0.000 1.000 0.000 0.000
#> GSM329706 3 0.4833 0.745 0.000 0.032 0.740 0.228
#> GSM329708 3 0.1833 0.918 0.000 0.032 0.944 0.024
#> GSM329710 4 0.5717 0.701 0.000 0.324 0.044 0.632
#> GSM329713 1 0.3672 0.895 0.824 0.000 0.012 0.164
#> GSM329695 1 0.3672 0.895 0.824 0.000 0.012 0.164
#> GSM329698 1 0.3672 0.895 0.824 0.000 0.012 0.164
#> GSM329701 1 0.3172 0.897 0.840 0.000 0.000 0.160
#> GSM329705 1 0.2342 0.906 0.912 0.000 0.008 0.080
#> GSM329712 2 0.3528 0.597 0.000 0.808 0.000 0.192
#> GSM329715 1 0.3172 0.897 0.840 0.000 0.000 0.160
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.3180 0.7978 0.000 0.856 0.000 0.076 0.068
#> GSM329663 2 0.0865 0.8542 0.000 0.972 0.000 0.004 0.024
#> GSM329664 5 0.7602 -0.0804 0.000 0.304 0.192 0.068 0.436
#> GSM329666 2 0.0794 0.8602 0.000 0.972 0.000 0.000 0.028
#> GSM329667 2 0.5538 0.2987 0.000 0.504 0.000 0.068 0.428
#> GSM329670 2 0.0162 0.8549 0.000 0.996 0.000 0.000 0.004
#> GSM329672 2 0.2361 0.8314 0.000 0.892 0.000 0.012 0.096
#> GSM329674 2 0.0794 0.8602 0.000 0.972 0.000 0.000 0.028
#> GSM329661 3 0.2459 0.8373 0.000 0.004 0.904 0.052 0.040
#> GSM329669 2 0.0162 0.8549 0.000 0.996 0.000 0.000 0.004
#> GSM329662 1 0.4304 0.4163 0.516 0.000 0.000 0.000 0.484
#> GSM329665 1 0.3171 0.7018 0.816 0.000 0.000 0.008 0.176
#> GSM329668 1 0.3845 0.6716 0.760 0.000 0.004 0.012 0.224
#> GSM329671 1 0.0290 0.7291 0.992 0.000 0.000 0.008 0.000
#> GSM329673 1 0.4448 0.4132 0.516 0.000 0.000 0.004 0.480
#> GSM329675 5 0.4747 -0.5438 0.484 0.000 0.000 0.016 0.500
#> GSM329676 1 0.4268 0.4688 0.556 0.000 0.000 0.000 0.444
#> GSM329677 3 0.5324 0.5481 0.000 0.004 0.600 0.056 0.340
#> GSM329679 2 0.2361 0.8314 0.000 0.892 0.000 0.012 0.096
#> GSM329681 3 0.0613 0.8694 0.000 0.004 0.984 0.008 0.004
#> GSM329683 3 0.0324 0.8704 0.000 0.004 0.992 0.000 0.004
#> GSM329686 3 0.0162 0.8706 0.000 0.004 0.996 0.000 0.000
#> GSM329689 3 0.0324 0.8704 0.000 0.004 0.992 0.000 0.004
#> GSM329678 4 0.4499 0.1615 0.000 0.004 0.408 0.584 0.004
#> GSM329680 3 0.1205 0.8594 0.000 0.004 0.956 0.040 0.000
#> GSM329685 3 0.0162 0.8706 0.000 0.004 0.996 0.000 0.000
#> GSM329688 3 0.0162 0.8706 0.000 0.004 0.996 0.000 0.000
#> GSM329691 3 0.0162 0.8706 0.000 0.004 0.996 0.000 0.000
#> GSM329682 1 0.4335 0.5985 0.664 0.000 0.004 0.008 0.324
#> GSM329684 5 0.4747 -0.5438 0.484 0.000 0.000 0.016 0.500
#> GSM329687 1 0.4426 0.5453 0.612 0.000 0.004 0.004 0.380
#> GSM329690 1 0.1851 0.7118 0.912 0.000 0.000 0.088 0.000
#> GSM329692 4 0.3205 0.6315 0.000 0.004 0.176 0.816 0.004
#> GSM329694 4 0.4537 0.7895 0.000 0.184 0.000 0.740 0.076
#> GSM329697 2 0.0794 0.8602 0.000 0.972 0.000 0.000 0.028
#> GSM329700 2 0.4054 0.6325 0.000 0.748 0.000 0.224 0.028
#> GSM329703 4 0.3366 0.8232 0.000 0.232 0.000 0.768 0.000
#> GSM329704 5 0.8029 -0.0797 0.000 0.144 0.180 0.240 0.436
#> GSM329707 3 0.5409 0.5383 0.000 0.004 0.588 0.060 0.348
#> GSM329709 2 0.0794 0.8602 0.000 0.972 0.000 0.000 0.028
#> GSM329711 2 0.3551 0.6443 0.000 0.772 0.000 0.220 0.008
#> GSM329714 4 0.4712 0.7554 0.000 0.268 0.000 0.684 0.048
#> GSM329693 4 0.3366 0.8232 0.000 0.232 0.000 0.768 0.000
#> GSM329696 4 0.3366 0.8232 0.000 0.232 0.000 0.768 0.000
#> GSM329699 4 0.3366 0.8232 0.000 0.232 0.000 0.768 0.000
#> GSM329702 2 0.0794 0.8602 0.000 0.972 0.000 0.000 0.028
#> GSM329706 3 0.6370 0.4213 0.000 0.004 0.500 0.156 0.340
#> GSM329708 3 0.2536 0.8346 0.000 0.004 0.900 0.052 0.044
#> GSM329710 4 0.3360 0.8042 0.000 0.168 0.012 0.816 0.004
#> GSM329713 1 0.1851 0.7126 0.912 0.000 0.000 0.088 0.000
#> GSM329695 1 0.1851 0.7126 0.912 0.000 0.000 0.088 0.000
#> GSM329698 1 0.1792 0.7126 0.916 0.000 0.000 0.084 0.000
#> GSM329701 1 0.0000 0.7295 1.000 0.000 0.000 0.000 0.000
#> GSM329705 1 0.2233 0.7230 0.892 0.000 0.000 0.004 0.104
#> GSM329712 2 0.3551 0.6443 0.000 0.772 0.000 0.220 0.008
#> GSM329715 1 0.0162 0.7301 0.996 0.000 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329660 2 0.5113 0.6867 0.000 0.704 0.000 0.096 0.140 0.060
#> GSM329663 2 0.2772 0.7835 0.000 0.864 0.000 0.004 0.040 0.092
#> GSM329664 5 0.4141 0.6366 0.000 0.140 0.084 0.012 0.764 0.000
#> GSM329666 2 0.2250 0.8129 0.000 0.896 0.000 0.000 0.040 0.064
#> GSM329667 5 0.4391 0.4063 0.000 0.236 0.000 0.012 0.704 0.048
#> GSM329670 2 0.1588 0.7941 0.000 0.924 0.000 0.000 0.004 0.072
#> GSM329672 2 0.4391 0.7465 0.000 0.720 0.000 0.004 0.188 0.088
#> GSM329674 2 0.2250 0.8129 0.000 0.896 0.000 0.000 0.040 0.064
#> GSM329661 3 0.3940 0.8175 0.000 0.000 0.796 0.040 0.048 0.116
#> GSM329669 2 0.0405 0.8052 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM329662 1 0.0993 0.6933 0.964 0.000 0.000 0.012 0.024 0.000
#> GSM329665 1 0.4577 0.0804 0.684 0.000 0.000 0.012 0.056 0.248
#> GSM329668 1 0.4276 0.4195 0.748 0.000 0.000 0.024 0.052 0.176
#> GSM329671 6 0.5318 0.7493 0.452 0.000 0.000 0.020 0.056 0.472
#> GSM329673 1 0.1074 0.6927 0.960 0.000 0.000 0.012 0.028 0.000
#> GSM329675 1 0.2633 0.6455 0.864 0.000 0.000 0.032 0.104 0.000
#> GSM329676 1 0.0436 0.6916 0.988 0.000 0.000 0.004 0.004 0.004
#> GSM329677 5 0.4939 0.5424 0.000 0.000 0.380 0.004 0.556 0.060
#> GSM329679 2 0.4391 0.7465 0.000 0.720 0.000 0.004 0.188 0.088
#> GSM329681 3 0.2009 0.9000 0.000 0.000 0.904 0.008 0.004 0.084
#> GSM329683 3 0.0692 0.9218 0.000 0.000 0.976 0.000 0.004 0.020
#> GSM329686 3 0.0000 0.9259 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329689 3 0.1588 0.9034 0.000 0.000 0.924 0.004 0.000 0.072
#> GSM329678 4 0.4365 0.4438 0.000 0.000 0.292 0.664 0.004 0.040
#> GSM329680 3 0.1890 0.8988 0.000 0.000 0.916 0.024 0.000 0.060
#> GSM329685 3 0.0000 0.9259 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329688 3 0.0000 0.9259 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329691 3 0.0000 0.9259 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329682 1 0.2982 0.5725 0.820 0.000 0.000 0.012 0.004 0.164
#> GSM329684 1 0.2633 0.6455 0.864 0.000 0.000 0.032 0.104 0.000
#> GSM329687 1 0.2213 0.6502 0.888 0.000 0.000 0.008 0.004 0.100
#> GSM329690 6 0.4625 0.8228 0.356 0.000 0.000 0.020 0.020 0.604
#> GSM329692 4 0.2554 0.7282 0.000 0.000 0.092 0.876 0.004 0.028
#> GSM329694 4 0.4635 0.7535 0.000 0.092 0.000 0.736 0.140 0.032
#> GSM329697 2 0.2308 0.8128 0.000 0.892 0.000 0.000 0.040 0.068
#> GSM329700 2 0.5427 0.5623 0.000 0.644 0.000 0.224 0.048 0.084
#> GSM329703 4 0.2362 0.8379 0.000 0.136 0.000 0.860 0.000 0.004
#> GSM329704 5 0.4461 0.6294 0.000 0.056 0.080 0.100 0.764 0.000
#> GSM329707 5 0.5207 0.5699 0.000 0.000 0.352 0.012 0.564 0.072
#> GSM329709 2 0.2250 0.8129 0.000 0.896 0.000 0.000 0.040 0.064
#> GSM329711 2 0.3893 0.6253 0.000 0.744 0.000 0.220 0.020 0.016
#> GSM329714 4 0.5610 0.6100 0.000 0.244 0.000 0.620 0.060 0.076
#> GSM329693 4 0.2362 0.8379 0.000 0.136 0.000 0.860 0.000 0.004
#> GSM329696 4 0.2219 0.8384 0.000 0.136 0.000 0.864 0.000 0.000
#> GSM329699 4 0.2278 0.8394 0.000 0.128 0.000 0.868 0.000 0.004
#> GSM329702 2 0.2250 0.8129 0.000 0.896 0.000 0.000 0.040 0.064
#> GSM329706 5 0.5653 0.5930 0.000 0.000 0.328 0.052 0.560 0.060
#> GSM329708 3 0.3755 0.8168 0.000 0.000 0.812 0.036 0.052 0.100
#> GSM329710 4 0.2675 0.8141 0.000 0.080 0.012 0.880 0.004 0.024
#> GSM329713 6 0.4411 0.8365 0.356 0.000 0.000 0.028 0.004 0.612
#> GSM329695 6 0.4411 0.8365 0.356 0.000 0.000 0.028 0.004 0.612
#> GSM329698 6 0.3874 0.8376 0.356 0.000 0.000 0.000 0.008 0.636
#> GSM329701 6 0.4832 0.7785 0.440 0.000 0.000 0.012 0.032 0.516
#> GSM329705 1 0.4888 -0.3095 0.592 0.000 0.000 0.020 0.036 0.352
#> GSM329712 2 0.3893 0.6253 0.000 0.744 0.000 0.220 0.020 0.016
#> GSM329715 6 0.4832 0.7785 0.440 0.000 0.000 0.012 0.032 0.516
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> MAD:kmeans 56 5.06e-01 5.82e-11 2
#> MAD:kmeans 54 8.47e-04 7.20e-10 3
#> MAD:kmeans 52 1.31e-04 2.07e-09 4
#> MAD:kmeans 46 9.45e-05 2.01e-07 5
#> MAD:kmeans 51 6.20e-05 2.23e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 21163 rows and 56 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4311 0.569 0.569
#> 3 3 1.000 0.971 0.987 0.5696 0.753 0.567
#> 4 4 0.959 0.947 0.976 0.1093 0.910 0.730
#> 5 5 0.916 0.881 0.936 0.0478 0.952 0.812
#> 6 6 0.834 0.626 0.821 0.0391 0.972 0.872
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM329660 2 0 1 0 1
#> GSM329663 2 0 1 0 1
#> GSM329664 2 0 1 0 1
#> GSM329666 2 0 1 0 1
#> GSM329667 2 0 1 0 1
#> GSM329670 2 0 1 0 1
#> GSM329672 2 0 1 0 1
#> GSM329674 2 0 1 0 1
#> GSM329661 2 0 1 0 1
#> GSM329669 2 0 1 0 1
#> GSM329662 1 0 1 1 0
#> GSM329665 1 0 1 1 0
#> GSM329668 1 0 1 1 0
#> GSM329671 1 0 1 1 0
#> GSM329673 1 0 1 1 0
#> GSM329675 1 0 1 1 0
#> GSM329676 1 0 1 1 0
#> GSM329677 2 0 1 0 1
#> GSM329679 2 0 1 0 1
#> GSM329681 2 0 1 0 1
#> GSM329683 2 0 1 0 1
#> GSM329686 2 0 1 0 1
#> GSM329689 2 0 1 0 1
#> GSM329678 2 0 1 0 1
#> GSM329680 2 0 1 0 1
#> GSM329685 2 0 1 0 1
#> GSM329688 2 0 1 0 1
#> GSM329691 2 0 1 0 1
#> GSM329682 1 0 1 1 0
#> GSM329684 1 0 1 1 0
#> GSM329687 1 0 1 1 0
#> GSM329690 1 0 1 1 0
#> GSM329692 2 0 1 0 1
#> GSM329694 2 0 1 0 1
#> GSM329697 2 0 1 0 1
#> GSM329700 2 0 1 0 1
#> GSM329703 2 0 1 0 1
#> GSM329704 2 0 1 0 1
#> GSM329707 2 0 1 0 1
#> GSM329709 2 0 1 0 1
#> GSM329711 2 0 1 0 1
#> GSM329714 2 0 1 0 1
#> GSM329693 2 0 1 0 1
#> GSM329696 2 0 1 0 1
#> GSM329699 2 0 1 0 1
#> GSM329702 2 0 1 0 1
#> GSM329706 2 0 1 0 1
#> GSM329708 2 0 1 0 1
#> GSM329710 2 0 1 0 1
#> GSM329713 1 0 1 1 0
#> GSM329695 1 0 1 1 0
#> GSM329698 1 0 1 1 0
#> GSM329701 1 0 1 1 0
#> GSM329705 1 0 1 1 0
#> GSM329712 2 0 1 0 1
#> GSM329715 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.0000 0.988 0 1.000 0.000
#> GSM329663 2 0.0000 0.988 0 1.000 0.000
#> GSM329664 3 0.1289 0.944 0 0.032 0.968
#> GSM329666 2 0.0000 0.988 0 1.000 0.000
#> GSM329667 2 0.0000 0.988 0 1.000 0.000
#> GSM329670 2 0.0000 0.988 0 1.000 0.000
#> GSM329672 2 0.0000 0.988 0 1.000 0.000
#> GSM329674 2 0.0000 0.988 0 1.000 0.000
#> GSM329661 3 0.0000 0.970 0 0.000 1.000
#> GSM329669 2 0.0000 0.988 0 1.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000
#> GSM329677 3 0.0000 0.970 0 0.000 1.000
#> GSM329679 2 0.0000 0.988 0 1.000 0.000
#> GSM329681 3 0.0000 0.970 0 0.000 1.000
#> GSM329683 3 0.0000 0.970 0 0.000 1.000
#> GSM329686 3 0.0000 0.970 0 0.000 1.000
#> GSM329689 3 0.0000 0.970 0 0.000 1.000
#> GSM329678 3 0.0000 0.970 0 0.000 1.000
#> GSM329680 3 0.0000 0.970 0 0.000 1.000
#> GSM329685 3 0.0000 0.970 0 0.000 1.000
#> GSM329688 3 0.0000 0.970 0 0.000 1.000
#> GSM329691 3 0.0000 0.970 0 0.000 1.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000
#> GSM329692 3 0.0000 0.970 0 0.000 1.000
#> GSM329694 3 0.5431 0.613 0 0.284 0.716
#> GSM329697 2 0.0000 0.988 0 1.000 0.000
#> GSM329700 2 0.0000 0.988 0 1.000 0.000
#> GSM329703 2 0.0424 0.982 0 0.992 0.008
#> GSM329704 3 0.0000 0.970 0 0.000 1.000
#> GSM329707 3 0.0000 0.970 0 0.000 1.000
#> GSM329709 2 0.0000 0.988 0 1.000 0.000
#> GSM329711 2 0.0000 0.988 0 1.000 0.000
#> GSM329714 2 0.0000 0.988 0 1.000 0.000
#> GSM329693 2 0.0000 0.988 0 1.000 0.000
#> GSM329696 2 0.2165 0.929 0 0.936 0.064
#> GSM329699 2 0.3752 0.832 0 0.856 0.144
#> GSM329702 2 0.0000 0.988 0 1.000 0.000
#> GSM329706 3 0.0000 0.970 0 0.000 1.000
#> GSM329708 3 0.0000 0.970 0 0.000 1.000
#> GSM329710 3 0.4555 0.752 0 0.200 0.800
#> GSM329713 1 0.0000 1.000 1 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000
#> GSM329712 2 0.0000 0.988 0 1.000 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.0000 0.944 0 1.000 0.000 0.000
#> GSM329663 2 0.0000 0.944 0 1.000 0.000 0.000
#> GSM329664 3 0.1305 0.935 0 0.036 0.960 0.004
#> GSM329666 2 0.0000 0.944 0 1.000 0.000 0.000
#> GSM329667 2 0.0188 0.942 0 0.996 0.000 0.004
#> GSM329670 2 0.0000 0.944 0 1.000 0.000 0.000
#> GSM329672 2 0.0188 0.942 0 0.996 0.000 0.004
#> GSM329674 2 0.0000 0.944 0 1.000 0.000 0.000
#> GSM329661 3 0.0000 0.969 0 0.000 1.000 0.000
#> GSM329669 2 0.0000 0.944 0 1.000 0.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329677 3 0.0000 0.969 0 0.000 1.000 0.000
#> GSM329679 2 0.0188 0.942 0 0.996 0.000 0.004
#> GSM329681 3 0.0000 0.969 0 0.000 1.000 0.000
#> GSM329683 3 0.0000 0.969 0 0.000 1.000 0.000
#> GSM329686 3 0.0000 0.969 0 0.000 1.000 0.000
#> GSM329689 3 0.0000 0.969 0 0.000 1.000 0.000
#> GSM329678 3 0.4790 0.409 0 0.000 0.620 0.380
#> GSM329680 3 0.0000 0.969 0 0.000 1.000 0.000
#> GSM329685 3 0.0000 0.969 0 0.000 1.000 0.000
#> GSM329688 3 0.0000 0.969 0 0.000 1.000 0.000
#> GSM329691 3 0.0000 0.969 0 0.000 1.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329692 4 0.0188 0.974 0 0.000 0.004 0.996
#> GSM329694 4 0.0000 0.974 0 0.000 0.000 1.000
#> GSM329697 2 0.0000 0.944 0 1.000 0.000 0.000
#> GSM329700 2 0.3975 0.720 0 0.760 0.000 0.240
#> GSM329703 4 0.0188 0.976 0 0.004 0.000 0.996
#> GSM329704 3 0.1356 0.941 0 0.008 0.960 0.032
#> GSM329707 3 0.0188 0.966 0 0.000 0.996 0.004
#> GSM329709 2 0.0000 0.944 0 1.000 0.000 0.000
#> GSM329711 2 0.3942 0.726 0 0.764 0.000 0.236
#> GSM329714 4 0.2921 0.820 0 0.140 0.000 0.860
#> GSM329693 4 0.0188 0.976 0 0.004 0.000 0.996
#> GSM329696 4 0.0188 0.976 0 0.004 0.000 0.996
#> GSM329699 4 0.0188 0.976 0 0.004 0.000 0.996
#> GSM329702 2 0.0000 0.944 0 1.000 0.000 0.000
#> GSM329706 3 0.0000 0.969 0 0.000 1.000 0.000
#> GSM329708 3 0.0000 0.969 0 0.000 1.000 0.000
#> GSM329710 4 0.0188 0.974 0 0.000 0.004 0.996
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329712 2 0.3942 0.726 0 0.764 0.000 0.236
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.1121 0.926 0.000 0.956 0.000 0.000 0.044
#> GSM329663 2 0.0000 0.938 0.000 1.000 0.000 0.000 0.000
#> GSM329664 5 0.1671 0.710 0.000 0.000 0.076 0.000 0.924
#> GSM329666 2 0.0162 0.938 0.000 0.996 0.000 0.000 0.004
#> GSM329667 5 0.1671 0.627 0.000 0.076 0.000 0.000 0.924
#> GSM329670 2 0.0162 0.937 0.000 0.996 0.000 0.000 0.004
#> GSM329672 2 0.1671 0.898 0.000 0.924 0.000 0.000 0.076
#> GSM329674 2 0.0162 0.938 0.000 0.996 0.000 0.000 0.004
#> GSM329661 3 0.0162 0.942 0.000 0.000 0.996 0.000 0.004
#> GSM329669 2 0.1121 0.926 0.000 0.956 0.000 0.000 0.044
#> GSM329662 1 0.0404 0.989 0.988 0.000 0.000 0.000 0.012
#> GSM329665 1 0.0000 0.991 1.000 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0162 0.991 0.996 0.000 0.000 0.000 0.004
#> GSM329671 1 0.0404 0.991 0.988 0.000 0.000 0.000 0.012
#> GSM329673 1 0.0404 0.989 0.988 0.000 0.000 0.000 0.012
#> GSM329675 1 0.0404 0.989 0.988 0.000 0.000 0.000 0.012
#> GSM329676 1 0.0404 0.989 0.988 0.000 0.000 0.000 0.012
#> GSM329677 5 0.4297 0.493 0.000 0.000 0.472 0.000 0.528
#> GSM329679 2 0.1671 0.898 0.000 0.924 0.000 0.000 0.076
#> GSM329681 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM329683 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM329686 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM329689 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM329678 3 0.4135 0.417 0.000 0.000 0.656 0.340 0.004
#> GSM329680 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM329685 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM329688 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM329691 3 0.0000 0.946 0.000 0.000 1.000 0.000 0.000
#> GSM329682 1 0.0162 0.991 0.996 0.000 0.000 0.000 0.004
#> GSM329684 1 0.0404 0.989 0.988 0.000 0.000 0.000 0.012
#> GSM329687 1 0.0162 0.991 0.996 0.000 0.000 0.000 0.004
#> GSM329690 1 0.0404 0.991 0.988 0.000 0.000 0.000 0.012
#> GSM329692 4 0.2612 0.764 0.000 0.000 0.124 0.868 0.008
#> GSM329694 4 0.4235 0.335 0.000 0.000 0.000 0.576 0.424
#> GSM329697 2 0.0162 0.938 0.000 0.996 0.000 0.000 0.004
#> GSM329700 2 0.3681 0.825 0.000 0.808 0.000 0.148 0.044
#> GSM329703 4 0.0000 0.882 0.000 0.000 0.000 1.000 0.000
#> GSM329704 5 0.1671 0.710 0.000 0.000 0.076 0.000 0.924
#> GSM329707 5 0.3932 0.663 0.000 0.000 0.328 0.000 0.672
#> GSM329709 2 0.0162 0.938 0.000 0.996 0.000 0.000 0.004
#> GSM329711 2 0.3595 0.833 0.000 0.816 0.000 0.140 0.044
#> GSM329714 4 0.3365 0.733 0.000 0.120 0.000 0.836 0.044
#> GSM329693 4 0.0000 0.882 0.000 0.000 0.000 1.000 0.000
#> GSM329696 4 0.0000 0.882 0.000 0.000 0.000 1.000 0.000
#> GSM329699 4 0.0000 0.882 0.000 0.000 0.000 1.000 0.000
#> GSM329702 2 0.0162 0.938 0.000 0.996 0.000 0.000 0.004
#> GSM329706 5 0.4291 0.508 0.000 0.000 0.464 0.000 0.536
#> GSM329708 3 0.0290 0.938 0.000 0.000 0.992 0.000 0.008
#> GSM329710 4 0.0290 0.879 0.000 0.000 0.000 0.992 0.008
#> GSM329713 1 0.0404 0.991 0.988 0.000 0.000 0.000 0.012
#> GSM329695 1 0.0404 0.991 0.988 0.000 0.000 0.000 0.012
#> GSM329698 1 0.0404 0.991 0.988 0.000 0.000 0.000 0.012
#> GSM329701 1 0.0404 0.991 0.988 0.000 0.000 0.000 0.012
#> GSM329705 1 0.0404 0.991 0.988 0.000 0.000 0.000 0.012
#> GSM329712 2 0.3595 0.833 0.000 0.816 0.000 0.140 0.044
#> GSM329715 1 0.0404 0.991 0.988 0.000 0.000 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329660 2 0.0937 0.0497 0.000 0.960 0.000 0.000 0.000 0.040
#> GSM329663 6 0.3810 0.9131 0.000 0.428 0.000 0.000 0.000 0.572
#> GSM329664 5 0.0547 0.7355 0.000 0.000 0.020 0.000 0.980 0.000
#> GSM329666 2 0.3823 -0.1924 0.000 0.564 0.000 0.000 0.000 0.436
#> GSM329667 5 0.1918 0.6787 0.000 0.008 0.000 0.000 0.904 0.088
#> GSM329670 6 0.3857 0.9121 0.000 0.468 0.000 0.000 0.000 0.532
#> GSM329672 2 0.4570 -0.2348 0.000 0.528 0.000 0.000 0.036 0.436
#> GSM329674 2 0.3823 -0.1924 0.000 0.564 0.000 0.000 0.000 0.436
#> GSM329661 3 0.0146 0.9351 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM329669 2 0.1327 -0.0128 0.000 0.936 0.000 0.000 0.000 0.064
#> GSM329662 1 0.2212 0.8894 0.880 0.000 0.000 0.000 0.008 0.112
#> GSM329665 1 0.0547 0.9068 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM329668 1 0.1285 0.9047 0.944 0.000 0.000 0.000 0.004 0.052
#> GSM329671 1 0.2165 0.8915 0.884 0.000 0.000 0.000 0.008 0.108
#> GSM329673 1 0.2212 0.8894 0.880 0.000 0.000 0.000 0.008 0.112
#> GSM329675 1 0.2212 0.8894 0.880 0.000 0.000 0.000 0.008 0.112
#> GSM329676 1 0.2212 0.8894 0.880 0.000 0.000 0.000 0.008 0.112
#> GSM329677 5 0.3915 0.5248 0.000 0.000 0.412 0.000 0.584 0.004
#> GSM329679 2 0.4739 -0.2493 0.000 0.516 0.000 0.000 0.048 0.436
#> GSM329681 3 0.0260 0.9338 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM329683 3 0.0146 0.9351 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM329686 3 0.0000 0.9358 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329689 3 0.0260 0.9338 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM329678 3 0.4750 0.1298 0.000 0.000 0.544 0.404 0.000 0.052
#> GSM329680 3 0.0000 0.9358 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329685 3 0.0000 0.9358 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329688 3 0.0000 0.9358 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329691 3 0.0000 0.9358 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329682 1 0.1462 0.9035 0.936 0.000 0.000 0.000 0.008 0.056
#> GSM329684 1 0.2212 0.8894 0.880 0.000 0.000 0.000 0.008 0.112
#> GSM329687 1 0.1643 0.9012 0.924 0.000 0.000 0.000 0.008 0.068
#> GSM329690 1 0.2257 0.8889 0.876 0.000 0.000 0.000 0.008 0.116
#> GSM329692 4 0.3121 0.8278 0.000 0.000 0.044 0.836 0.004 0.116
#> GSM329694 4 0.5238 0.5196 0.000 0.000 0.000 0.580 0.292 0.128
#> GSM329697 2 0.3823 -0.1924 0.000 0.564 0.000 0.000 0.000 0.436
#> GSM329700 2 0.4655 0.0194 0.000 0.680 0.000 0.112 0.000 0.208
#> GSM329703 4 0.0260 0.8908 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM329704 5 0.0547 0.7355 0.000 0.000 0.020 0.000 0.980 0.000
#> GSM329707 5 0.3081 0.7363 0.000 0.000 0.220 0.000 0.776 0.004
#> GSM329709 2 0.3823 -0.1924 0.000 0.564 0.000 0.000 0.000 0.436
#> GSM329711 2 0.2100 0.1388 0.000 0.884 0.000 0.112 0.000 0.004
#> GSM329714 2 0.5895 -0.1369 0.000 0.436 0.000 0.356 0.000 0.208
#> GSM329693 4 0.0260 0.8908 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM329696 4 0.0000 0.8904 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329699 4 0.0260 0.8908 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM329702 2 0.3823 -0.1924 0.000 0.564 0.000 0.000 0.000 0.436
#> GSM329706 5 0.3887 0.6122 0.000 0.000 0.360 0.000 0.632 0.008
#> GSM329708 3 0.0260 0.9331 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM329710 4 0.2100 0.8578 0.000 0.000 0.000 0.884 0.004 0.112
#> GSM329713 1 0.2257 0.8889 0.876 0.000 0.000 0.000 0.008 0.116
#> GSM329695 1 0.2257 0.8889 0.876 0.000 0.000 0.000 0.008 0.116
#> GSM329698 1 0.2257 0.8889 0.876 0.000 0.000 0.000 0.008 0.116
#> GSM329701 1 0.2165 0.8915 0.884 0.000 0.000 0.000 0.008 0.108
#> GSM329705 1 0.0632 0.9049 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM329712 2 0.2100 0.1388 0.000 0.884 0.000 0.112 0.000 0.004
#> GSM329715 1 0.2020 0.8943 0.896 0.000 0.000 0.000 0.008 0.096
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> MAD:skmeans 56 0.505684 5.82e-11 2
#> MAD:skmeans 56 0.010546 4.13e-10 3
#> MAD:skmeans 55 0.000301 1.65e-09 4
#> MAD:skmeans 53 0.000127 6.91e-09 5
#> MAD:skmeans 42 0.000387 2.30e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 21163 rows and 56 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 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 1.000 1.000 0.4311 0.569 0.569
#> 3 3 1.000 0.996 0.998 0.5402 0.766 0.590
#> 4 4 0.788 0.770 0.888 0.1322 0.850 0.588
#> 5 5 0.919 0.852 0.943 0.0627 0.942 0.770
#> 6 6 0.964 0.924 0.960 0.0271 0.968 0.846
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 5
There is also optional best \(k\) = 2 3 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
#> GSM329660 2 0 1 0 1
#> GSM329663 2 0 1 0 1
#> GSM329664 2 0 1 0 1
#> GSM329666 2 0 1 0 1
#> GSM329667 2 0 1 0 1
#> GSM329670 2 0 1 0 1
#> GSM329672 2 0 1 0 1
#> GSM329674 2 0 1 0 1
#> GSM329661 2 0 1 0 1
#> GSM329669 2 0 1 0 1
#> GSM329662 1 0 1 1 0
#> GSM329665 1 0 1 1 0
#> GSM329668 1 0 1 1 0
#> GSM329671 1 0 1 1 0
#> GSM329673 1 0 1 1 0
#> GSM329675 1 0 1 1 0
#> GSM329676 1 0 1 1 0
#> GSM329677 2 0 1 0 1
#> GSM329679 2 0 1 0 1
#> GSM329681 2 0 1 0 1
#> GSM329683 2 0 1 0 1
#> GSM329686 2 0 1 0 1
#> GSM329689 2 0 1 0 1
#> GSM329678 2 0 1 0 1
#> GSM329680 2 0 1 0 1
#> GSM329685 2 0 1 0 1
#> GSM329688 2 0 1 0 1
#> GSM329691 2 0 1 0 1
#> GSM329682 1 0 1 1 0
#> GSM329684 1 0 1 1 0
#> GSM329687 1 0 1 1 0
#> GSM329690 1 0 1 1 0
#> GSM329692 2 0 1 0 1
#> GSM329694 2 0 1 0 1
#> GSM329697 2 0 1 0 1
#> GSM329700 2 0 1 0 1
#> GSM329703 2 0 1 0 1
#> GSM329704 2 0 1 0 1
#> GSM329707 2 0 1 0 1
#> GSM329709 2 0 1 0 1
#> GSM329711 2 0 1 0 1
#> GSM329714 2 0 1 0 1
#> GSM329693 2 0 1 0 1
#> GSM329696 2 0 1 0 1
#> GSM329699 2 0 1 0 1
#> GSM329702 2 0 1 0 1
#> GSM329706 2 0 1 0 1
#> GSM329708 2 0 1 0 1
#> GSM329710 2 0 1 0 1
#> GSM329713 1 0 1 1 0
#> GSM329695 1 0 1 1 0
#> GSM329698 1 0 1 1 0
#> GSM329701 1 0 1 1 0
#> GSM329705 1 0 1 1 0
#> GSM329712 2 0 1 0 1
#> GSM329715 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.000 1.000 0 1.000 0.000
#> GSM329663 2 0.000 1.000 0 1.000 0.000
#> GSM329664 2 0.000 1.000 0 1.000 0.000
#> GSM329666 2 0.000 1.000 0 1.000 0.000
#> GSM329667 2 0.000 1.000 0 1.000 0.000
#> GSM329670 2 0.000 1.000 0 1.000 0.000
#> GSM329672 2 0.000 1.000 0 1.000 0.000
#> GSM329674 2 0.000 1.000 0 1.000 0.000
#> GSM329661 3 0.000 0.992 0 0.000 1.000
#> GSM329669 2 0.000 1.000 0 1.000 0.000
#> GSM329662 1 0.000 1.000 1 0.000 0.000
#> GSM329665 1 0.000 1.000 1 0.000 0.000
#> GSM329668 1 0.000 1.000 1 0.000 0.000
#> GSM329671 1 0.000 1.000 1 0.000 0.000
#> GSM329673 1 0.000 1.000 1 0.000 0.000
#> GSM329675 1 0.000 1.000 1 0.000 0.000
#> GSM329676 1 0.000 1.000 1 0.000 0.000
#> GSM329677 3 0.000 0.992 0 0.000 1.000
#> GSM329679 2 0.000 1.000 0 1.000 0.000
#> GSM329681 3 0.000 0.992 0 0.000 1.000
#> GSM329683 3 0.000 0.992 0 0.000 1.000
#> GSM329686 3 0.000 0.992 0 0.000 1.000
#> GSM329689 3 0.000 0.992 0 0.000 1.000
#> GSM329678 3 0.000 0.992 0 0.000 1.000
#> GSM329680 3 0.000 0.992 0 0.000 1.000
#> GSM329685 3 0.000 0.992 0 0.000 1.000
#> GSM329688 3 0.000 0.992 0 0.000 1.000
#> GSM329691 3 0.000 0.992 0 0.000 1.000
#> GSM329682 1 0.000 1.000 1 0.000 0.000
#> GSM329684 1 0.000 1.000 1 0.000 0.000
#> GSM329687 1 0.000 1.000 1 0.000 0.000
#> GSM329690 1 0.000 1.000 1 0.000 0.000
#> GSM329692 3 0.141 0.961 0 0.036 0.964
#> GSM329694 2 0.000 1.000 0 1.000 0.000
#> GSM329697 2 0.000 1.000 0 1.000 0.000
#> GSM329700 2 0.000 1.000 0 1.000 0.000
#> GSM329703 2 0.000 1.000 0 1.000 0.000
#> GSM329704 2 0.000 1.000 0 1.000 0.000
#> GSM329707 3 0.207 0.936 0 0.060 0.940
#> GSM329709 2 0.000 1.000 0 1.000 0.000
#> GSM329711 2 0.000 1.000 0 1.000 0.000
#> GSM329714 2 0.000 1.000 0 1.000 0.000
#> GSM329693 2 0.000 1.000 0 1.000 0.000
#> GSM329696 2 0.000 1.000 0 1.000 0.000
#> GSM329699 2 0.000 1.000 0 1.000 0.000
#> GSM329702 2 0.000 1.000 0 1.000 0.000
#> GSM329706 3 0.000 0.992 0 0.000 1.000
#> GSM329708 3 0.000 0.992 0 0.000 1.000
#> GSM329710 2 0.000 1.000 0 1.000 0.000
#> GSM329713 1 0.000 1.000 1 0.000 0.000
#> GSM329695 1 0.000 1.000 1 0.000 0.000
#> GSM329698 1 0.000 1.000 1 0.000 0.000
#> GSM329701 1 0.000 1.000 1 0.000 0.000
#> GSM329705 1 0.000 1.000 1 0.000 0.000
#> GSM329712 2 0.000 1.000 0 1.000 0.000
#> GSM329715 1 0.000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.3942 0.729 0 0.764 0.000 0.236
#> GSM329663 2 0.0921 0.816 0 0.972 0.000 0.028
#> GSM329664 4 0.4999 0.326 0 0.492 0.000 0.508
#> GSM329666 2 0.0000 0.834 0 1.000 0.000 0.000
#> GSM329667 4 0.4999 0.326 0 0.492 0.000 0.508
#> GSM329670 2 0.3610 0.762 0 0.800 0.000 0.200
#> GSM329672 2 0.2814 0.689 0 0.868 0.000 0.132
#> GSM329674 2 0.0188 0.834 0 0.996 0.000 0.004
#> GSM329661 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329669 2 0.3610 0.762 0 0.800 0.000 0.200
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329677 3 0.2647 0.813 0 0.000 0.880 0.120
#> GSM329679 2 0.2704 0.697 0 0.876 0.000 0.124
#> GSM329681 3 0.4907 0.156 0 0.000 0.580 0.420
#> GSM329683 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329686 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329689 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329678 4 0.3764 0.517 0 0.000 0.216 0.784
#> GSM329680 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329685 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329688 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329691 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329692 4 0.3668 0.540 0 0.004 0.188 0.808
#> GSM329694 4 0.4999 0.326 0 0.492 0.000 0.508
#> GSM329697 2 0.0000 0.834 0 1.000 0.000 0.000
#> GSM329700 4 0.4888 0.216 0 0.412 0.000 0.588
#> GSM329703 4 0.2704 0.582 0 0.124 0.000 0.876
#> GSM329704 4 0.4999 0.326 0 0.492 0.000 0.508
#> GSM329707 4 0.7216 0.378 0 0.156 0.336 0.508
#> GSM329709 2 0.0000 0.834 0 1.000 0.000 0.000
#> GSM329711 2 0.3649 0.759 0 0.796 0.000 0.204
#> GSM329714 4 0.2704 0.582 0 0.124 0.000 0.876
#> GSM329693 4 0.2704 0.582 0 0.124 0.000 0.876
#> GSM329696 4 0.2704 0.582 0 0.124 0.000 0.876
#> GSM329699 4 0.0336 0.613 0 0.008 0.000 0.992
#> GSM329702 2 0.0000 0.834 0 1.000 0.000 0.000
#> GSM329706 4 0.4948 0.110 0 0.000 0.440 0.560
#> GSM329708 3 0.0000 0.935 0 0.000 1.000 0.000
#> GSM329710 4 0.3610 0.582 0 0.200 0.000 0.800
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329712 2 0.3649 0.759 0 0.796 0.000 0.204
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 5 0.000 0.9770 0 0.000 0.000 0.000 1.000
#> GSM329663 2 0.000 0.8327 0 1.000 0.000 0.000 0.000
#> GSM329664 5 0.000 0.9770 0 0.000 0.000 0.000 1.000
#> GSM329666 2 0.000 0.8327 0 1.000 0.000 0.000 0.000
#> GSM329667 5 0.000 0.9770 0 0.000 0.000 0.000 1.000
#> GSM329670 2 0.000 0.8327 0 1.000 0.000 0.000 0.000
#> GSM329672 2 0.314 0.6576 0 0.796 0.000 0.000 0.204
#> GSM329674 2 0.000 0.8327 0 1.000 0.000 0.000 0.000
#> GSM329661 3 0.000 0.9720 0 0.000 1.000 0.000 0.000
#> GSM329669 2 0.000 0.8327 0 1.000 0.000 0.000 0.000
#> GSM329662 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329665 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329668 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329671 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329673 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329675 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329676 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329677 5 0.228 0.8337 0 0.000 0.120 0.000 0.880
#> GSM329679 2 0.420 0.2700 0 0.592 0.000 0.000 0.408
#> GSM329681 3 0.337 0.6836 0 0.000 0.768 0.000 0.232
#> GSM329683 3 0.000 0.9720 0 0.000 1.000 0.000 0.000
#> GSM329686 3 0.000 0.9720 0 0.000 1.000 0.000 0.000
#> GSM329689 3 0.000 0.9720 0 0.000 1.000 0.000 0.000
#> GSM329678 4 0.455 0.0484 0 0.000 0.008 0.532 0.460
#> GSM329680 3 0.000 0.9720 0 0.000 1.000 0.000 0.000
#> GSM329685 3 0.000 0.9720 0 0.000 1.000 0.000 0.000
#> GSM329688 3 0.000 0.9720 0 0.000 1.000 0.000 0.000
#> GSM329691 3 0.000 0.9720 0 0.000 1.000 0.000 0.000
#> GSM329682 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329684 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329687 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329690 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329692 4 0.314 0.7066 0 0.000 0.000 0.796 0.204
#> GSM329694 5 0.000 0.9770 0 0.000 0.000 0.000 1.000
#> GSM329697 2 0.000 0.8327 0 1.000 0.000 0.000 0.000
#> GSM329700 4 0.402 0.3468 0 0.348 0.000 0.652 0.000
#> GSM329703 4 0.000 0.8151 0 0.000 0.000 1.000 0.000
#> GSM329704 5 0.000 0.9770 0 0.000 0.000 0.000 1.000
#> GSM329707 5 0.000 0.9770 0 0.000 0.000 0.000 1.000
#> GSM329709 2 0.000 0.8327 0 1.000 0.000 0.000 0.000
#> GSM329711 2 0.429 0.0933 0 0.532 0.000 0.468 0.000
#> GSM329714 4 0.359 0.6479 0 0.000 0.000 0.736 0.264
#> GSM329693 4 0.000 0.8151 0 0.000 0.000 1.000 0.000
#> GSM329696 4 0.000 0.8151 0 0.000 0.000 1.000 0.000
#> GSM329699 4 0.000 0.8151 0 0.000 0.000 1.000 0.000
#> GSM329702 2 0.000 0.8327 0 1.000 0.000 0.000 0.000
#> GSM329706 5 0.000 0.9770 0 0.000 0.000 0.000 1.000
#> GSM329708 3 0.000 0.9720 0 0.000 1.000 0.000 0.000
#> GSM329710 4 0.000 0.8151 0 0.000 0.000 1.000 0.000
#> GSM329713 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329695 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329698 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329701 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329705 1 0.000 1.0000 1 0.000 0.000 0.000 0.000
#> GSM329712 2 0.429 0.0933 0 0.532 0.000 0.468 0.000
#> GSM329715 1 0.000 1.0000 1 0.000 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
#> GSM329660 6 0.1501 0.869 0 0.000 0.000 0.000 0.076 0.924
#> GSM329663 2 0.0146 0.901 0 0.996 0.000 0.000 0.000 0.004
#> GSM329664 5 0.0146 0.960 0 0.000 0.000 0.000 0.996 0.004
#> GSM329666 2 0.0000 0.902 0 1.000 0.000 0.000 0.000 0.000
#> GSM329667 5 0.0146 0.960 0 0.000 0.000 0.000 0.996 0.004
#> GSM329670 2 0.0000 0.902 0 1.000 0.000 0.000 0.000 0.000
#> GSM329672 2 0.2902 0.728 0 0.800 0.000 0.000 0.196 0.004
#> GSM329674 2 0.0000 0.902 0 1.000 0.000 0.000 0.000 0.000
#> GSM329661 3 0.1588 0.931 0 0.000 0.924 0.000 0.004 0.072
#> GSM329669 6 0.2597 0.859 0 0.176 0.000 0.000 0.000 0.824
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329677 5 0.3405 0.757 0 0.000 0.112 0.000 0.812 0.076
#> GSM329679 2 0.3955 0.262 0 0.560 0.000 0.000 0.436 0.004
#> GSM329681 3 0.3979 0.747 0 0.000 0.752 0.000 0.172 0.076
#> GSM329683 3 0.1644 0.930 0 0.000 0.920 0.000 0.004 0.076
#> GSM329686 3 0.0000 0.951 0 0.000 1.000 0.000 0.000 0.000
#> GSM329689 3 0.1644 0.930 0 0.000 0.920 0.000 0.004 0.076
#> GSM329678 4 0.0146 0.934 0 0.000 0.000 0.996 0.004 0.000
#> GSM329680 3 0.0000 0.951 0 0.000 1.000 0.000 0.000 0.000
#> GSM329685 3 0.0000 0.951 0 0.000 1.000 0.000 0.000 0.000
#> GSM329688 3 0.0000 0.951 0 0.000 1.000 0.000 0.000 0.000
#> GSM329691 3 0.0000 0.951 0 0.000 1.000 0.000 0.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329692 4 0.2823 0.761 0 0.000 0.000 0.796 0.204 0.000
#> GSM329694 5 0.0146 0.960 0 0.000 0.000 0.000 0.996 0.004
#> GSM329697 2 0.0146 0.901 0 0.996 0.000 0.000 0.000 0.004
#> GSM329700 6 0.1501 0.945 0 0.076 0.000 0.000 0.000 0.924
#> GSM329703 4 0.0000 0.936 0 0.000 0.000 1.000 0.000 0.000
#> GSM329704 5 0.0146 0.960 0 0.000 0.000 0.000 0.996 0.004
#> GSM329707 5 0.0000 0.958 0 0.000 0.000 0.000 1.000 0.000
#> GSM329709 2 0.0000 0.902 0 1.000 0.000 0.000 0.000 0.000
#> GSM329711 6 0.1501 0.945 0 0.076 0.000 0.000 0.000 0.924
#> GSM329714 4 0.3806 0.758 0 0.000 0.000 0.772 0.076 0.152
#> GSM329693 4 0.0000 0.936 0 0.000 0.000 1.000 0.000 0.000
#> GSM329696 4 0.0000 0.936 0 0.000 0.000 1.000 0.000 0.000
#> GSM329699 4 0.0000 0.936 0 0.000 0.000 1.000 0.000 0.000
#> GSM329702 2 0.0000 0.902 0 1.000 0.000 0.000 0.000 0.000
#> GSM329706 5 0.0146 0.958 0 0.000 0.000 0.004 0.996 0.000
#> GSM329708 3 0.0000 0.951 0 0.000 1.000 0.000 0.000 0.000
#> GSM329710 4 0.0000 0.936 0 0.000 0.000 1.000 0.000 0.000
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
#> GSM329712 6 0.1501 0.945 0 0.076 0.000 0.000 0.000 0.924
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> MAD:pam 56 5.06e-01 5.82e-11 2
#> MAD:pam 56 5.28e-04 2.02e-10 3
#> MAD:pam 48 2.88e-04 9.55e-09 4
#> MAD:pam 51 8.28e-05 3.04e-09 5
#> MAD:pam 55 8.10e-04 6.32e-09 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21163 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4311 0.569 0.569
#> 3 3 0.819 0.893 0.937 0.5143 0.766 0.590
#> 4 4 0.829 0.771 0.908 0.1390 0.845 0.580
#> 5 5 0.917 0.905 0.945 0.0601 0.912 0.676
#> 6 6 0.935 0.858 0.928 0.0403 0.944 0.744
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 5
There is also optional best \(k\) = 2 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
#> GSM329660 2 0 1 0 1
#> GSM329663 2 0 1 0 1
#> GSM329664 2 0 1 0 1
#> GSM329666 2 0 1 0 1
#> GSM329667 2 0 1 0 1
#> GSM329670 2 0 1 0 1
#> GSM329672 2 0 1 0 1
#> GSM329674 2 0 1 0 1
#> GSM329661 2 0 1 0 1
#> GSM329669 2 0 1 0 1
#> GSM329662 1 0 1 1 0
#> GSM329665 1 0 1 1 0
#> GSM329668 1 0 1 1 0
#> GSM329671 1 0 1 1 0
#> GSM329673 1 0 1 1 0
#> GSM329675 1 0 1 1 0
#> GSM329676 1 0 1 1 0
#> GSM329677 2 0 1 0 1
#> GSM329679 2 0 1 0 1
#> GSM329681 2 0 1 0 1
#> GSM329683 2 0 1 0 1
#> GSM329686 2 0 1 0 1
#> GSM329689 2 0 1 0 1
#> GSM329678 2 0 1 0 1
#> GSM329680 2 0 1 0 1
#> GSM329685 2 0 1 0 1
#> GSM329688 2 0 1 0 1
#> GSM329691 2 0 1 0 1
#> GSM329682 1 0 1 1 0
#> GSM329684 1 0 1 1 0
#> GSM329687 1 0 1 1 0
#> GSM329690 1 0 1 1 0
#> GSM329692 2 0 1 0 1
#> GSM329694 2 0 1 0 1
#> GSM329697 2 0 1 0 1
#> GSM329700 2 0 1 0 1
#> GSM329703 2 0 1 0 1
#> GSM329704 2 0 1 0 1
#> GSM329707 2 0 1 0 1
#> GSM329709 2 0 1 0 1
#> GSM329711 2 0 1 0 1
#> GSM329714 2 0 1 0 1
#> GSM329693 2 0 1 0 1
#> GSM329696 2 0 1 0 1
#> GSM329699 2 0 1 0 1
#> GSM329702 2 0 1 0 1
#> GSM329706 2 0 1 0 1
#> GSM329708 2 0 1 0 1
#> GSM329710 2 0 1 0 1
#> GSM329713 1 0 1 1 0
#> GSM329695 1 0 1 1 0
#> GSM329698 1 0 1 1 0
#> GSM329701 1 0 1 1 0
#> GSM329705 1 0 1 1 0
#> GSM329712 2 0 1 0 1
#> GSM329715 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.2165 0.916 0 0.936 0.064
#> GSM329663 2 0.2165 0.916 0 0.936 0.064
#> GSM329664 3 0.5882 0.522 0 0.348 0.652
#> GSM329666 2 0.0424 0.899 0 0.992 0.008
#> GSM329667 2 0.3752 0.863 0 0.856 0.144
#> GSM329670 2 0.0424 0.899 0 0.992 0.008
#> GSM329672 2 0.2165 0.916 0 0.936 0.064
#> GSM329674 2 0.0424 0.899 0 0.992 0.008
#> GSM329661 3 0.0000 0.890 0 0.000 1.000
#> GSM329669 2 0.0424 0.899 0 0.992 0.008
#> GSM329662 1 0.0000 1.000 1 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000
#> GSM329677 3 0.0000 0.890 0 0.000 1.000
#> GSM329679 2 0.2165 0.916 0 0.936 0.064
#> GSM329681 3 0.0000 0.890 0 0.000 1.000
#> GSM329683 3 0.0000 0.890 0 0.000 1.000
#> GSM329686 3 0.0000 0.890 0 0.000 1.000
#> GSM329689 3 0.0000 0.890 0 0.000 1.000
#> GSM329678 2 0.4504 0.845 0 0.804 0.196
#> GSM329680 3 0.0000 0.890 0 0.000 1.000
#> GSM329685 3 0.0000 0.890 0 0.000 1.000
#> GSM329688 3 0.0000 0.890 0 0.000 1.000
#> GSM329691 3 0.0000 0.890 0 0.000 1.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000
#> GSM329692 2 0.4504 0.845 0 0.804 0.196
#> GSM329694 2 0.2796 0.909 0 0.908 0.092
#> GSM329697 2 0.0747 0.903 0 0.984 0.016
#> GSM329700 2 0.1964 0.917 0 0.944 0.056
#> GSM329703 2 0.4504 0.845 0 0.804 0.196
#> GSM329704 3 0.6302 0.135 0 0.480 0.520
#> GSM329707 3 0.5678 0.572 0 0.316 0.684
#> GSM329709 2 0.0592 0.901 0 0.988 0.012
#> GSM329711 2 0.1964 0.917 0 0.944 0.056
#> GSM329714 2 0.2537 0.913 0 0.920 0.080
#> GSM329693 2 0.4504 0.845 0 0.804 0.196
#> GSM329696 2 0.4504 0.845 0 0.804 0.196
#> GSM329699 2 0.4504 0.845 0 0.804 0.196
#> GSM329702 2 0.0424 0.899 0 0.992 0.008
#> GSM329706 3 0.4796 0.672 0 0.220 0.780
#> GSM329708 3 0.0424 0.884 0 0.008 0.992
#> GSM329710 2 0.4504 0.845 0 0.804 0.196
#> GSM329713 1 0.0000 1.000 1 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000
#> GSM329712 2 0.1964 0.917 0 0.944 0.056
#> GSM329715 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 4 0.4877 0.328 0 0.408 0.000 0.592
#> GSM329663 2 0.2760 0.746 0 0.872 0.000 0.128
#> GSM329664 2 0.3539 0.671 0 0.820 0.176 0.004
#> GSM329666 2 0.0000 0.732 0 1.000 0.000 0.000
#> GSM329667 2 0.3486 0.732 0 0.812 0.000 0.188
#> GSM329670 2 0.4967 -0.195 0 0.548 0.000 0.452
#> GSM329672 2 0.3356 0.737 0 0.824 0.000 0.176
#> GSM329674 2 0.0000 0.732 0 1.000 0.000 0.000
#> GSM329661 3 0.0000 0.950 0 0.000 1.000 0.000
#> GSM329669 2 0.4967 -0.195 0 0.548 0.000 0.452
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329677 3 0.4907 0.281 0 0.420 0.580 0.000
#> GSM329679 2 0.3356 0.737 0 0.824 0.000 0.176
#> GSM329681 3 0.1022 0.924 0 0.032 0.968 0.000
#> GSM329683 3 0.0000 0.950 0 0.000 1.000 0.000
#> GSM329686 3 0.0000 0.950 0 0.000 1.000 0.000
#> GSM329689 3 0.0000 0.950 0 0.000 1.000 0.000
#> GSM329678 4 0.0000 0.782 0 0.000 0.000 1.000
#> GSM329680 3 0.0000 0.950 0 0.000 1.000 0.000
#> GSM329685 3 0.0000 0.950 0 0.000 1.000 0.000
#> GSM329688 3 0.0000 0.950 0 0.000 1.000 0.000
#> GSM329691 3 0.0000 0.950 0 0.000 1.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329692 4 0.0000 0.782 0 0.000 0.000 1.000
#> GSM329694 2 0.3649 0.721 0 0.796 0.000 0.204
#> GSM329697 2 0.1211 0.744 0 0.960 0.000 0.040
#> GSM329700 4 0.4804 0.373 0 0.384 0.000 0.616
#> GSM329703 4 0.0000 0.782 0 0.000 0.000 1.000
#> GSM329704 2 0.3610 0.724 0 0.800 0.000 0.200
#> GSM329707 2 0.4348 0.650 0 0.780 0.196 0.024
#> GSM329709 2 0.0817 0.741 0 0.976 0.000 0.024
#> GSM329711 4 0.4925 0.315 0 0.428 0.000 0.572
#> GSM329714 2 0.4967 -0.195 0 0.548 0.000 0.452
#> GSM329693 4 0.0000 0.782 0 0.000 0.000 1.000
#> GSM329696 4 0.0000 0.782 0 0.000 0.000 1.000
#> GSM329699 4 0.0000 0.782 0 0.000 0.000 1.000
#> GSM329702 2 0.0000 0.732 0 1.000 0.000 0.000
#> GSM329706 2 0.4323 0.714 0 0.776 0.020 0.204
#> GSM329708 3 0.0000 0.950 0 0.000 1.000 0.000
#> GSM329710 4 0.0000 0.782 0 0.000 0.000 1.000
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329712 4 0.4679 0.398 0 0.352 0.000 0.648
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.1851 0.920 0 0.912 0.000 0.088 0.000
#> GSM329663 2 0.1851 0.921 0 0.912 0.000 0.088 0.000
#> GSM329664 5 0.0404 0.888 0 0.012 0.000 0.000 0.988
#> GSM329666 2 0.0162 0.944 0 0.996 0.000 0.000 0.004
#> GSM329667 5 0.3182 0.873 0 0.032 0.000 0.124 0.844
#> GSM329670 2 0.0162 0.944 0 0.996 0.000 0.000 0.004
#> GSM329672 2 0.2011 0.920 0 0.908 0.000 0.088 0.004
#> GSM329674 2 0.0162 0.944 0 0.996 0.000 0.000 0.004
#> GSM329661 3 0.0880 0.950 0 0.000 0.968 0.000 0.032
#> GSM329669 2 0.0162 0.944 0 0.996 0.000 0.000 0.004
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329677 5 0.0963 0.867 0 0.000 0.036 0.000 0.964
#> GSM329679 2 0.1768 0.932 0 0.924 0.000 0.072 0.004
#> GSM329681 3 0.3242 0.792 0 0.000 0.784 0.000 0.216
#> GSM329683 3 0.0963 0.948 0 0.000 0.964 0.000 0.036
#> GSM329686 3 0.0000 0.959 0 0.000 1.000 0.000 0.000
#> GSM329689 3 0.2280 0.892 0 0.000 0.880 0.000 0.120
#> GSM329678 4 0.3039 0.621 0 0.000 0.192 0.808 0.000
#> GSM329680 3 0.0000 0.959 0 0.000 1.000 0.000 0.000
#> GSM329685 3 0.0000 0.959 0 0.000 1.000 0.000 0.000
#> GSM329688 3 0.0000 0.959 0 0.000 1.000 0.000 0.000
#> GSM329691 3 0.0000 0.959 0 0.000 1.000 0.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329692 4 0.0000 0.802 0 0.000 0.000 1.000 0.000
#> GSM329694 4 0.4101 0.583 0 0.332 0.000 0.664 0.004
#> GSM329697 2 0.1197 0.943 0 0.952 0.000 0.048 0.000
#> GSM329700 4 0.3636 0.700 0 0.272 0.000 0.728 0.000
#> GSM329703 4 0.0000 0.802 0 0.000 0.000 1.000 0.000
#> GSM329704 5 0.2818 0.884 0 0.012 0.000 0.132 0.856
#> GSM329707 5 0.0898 0.895 0 0.000 0.008 0.020 0.972
#> GSM329709 2 0.0880 0.946 0 0.968 0.000 0.032 0.000
#> GSM329711 4 0.3684 0.692 0 0.280 0.000 0.720 0.000
#> GSM329714 4 0.4972 0.605 0 0.336 0.000 0.620 0.044
#> GSM329693 4 0.0000 0.802 0 0.000 0.000 1.000 0.000
#> GSM329696 4 0.0000 0.802 0 0.000 0.000 1.000 0.000
#> GSM329699 4 0.0000 0.802 0 0.000 0.000 1.000 0.000
#> GSM329702 2 0.0162 0.944 0 0.996 0.000 0.000 0.004
#> GSM329706 5 0.2629 0.884 0 0.004 0.000 0.136 0.860
#> GSM329708 3 0.0000 0.959 0 0.000 1.000 0.000 0.000
#> GSM329710 4 0.0000 0.802 0 0.000 0.000 1.000 0.000
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329712 4 0.3561 0.711 0 0.260 0.000 0.740 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 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
#> GSM329660 6 0.3376 0.75262 0.000 0.220 0.000 0.016 0.000 0.764
#> GSM329663 2 0.3695 0.49635 0.000 0.712 0.000 0.016 0.000 0.272
#> GSM329664 5 0.2821 0.76611 0.000 0.152 0.000 0.000 0.832 0.016
#> GSM329666 2 0.0000 0.87288 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329667 2 0.4866 -0.13498 0.000 0.484 0.000 0.028 0.472 0.016
#> GSM329670 6 0.3126 0.73529 0.000 0.248 0.000 0.000 0.000 0.752
#> GSM329672 2 0.0713 0.85744 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM329674 2 0.0000 0.87288 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329661 3 0.0000 0.92335 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329669 6 0.3126 0.73529 0.000 0.248 0.000 0.000 0.000 0.752
#> GSM329662 1 0.0146 0.98656 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM329665 1 0.0000 0.98671 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0146 0.98656 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM329671 1 0.0146 0.98639 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM329673 1 0.0146 0.98656 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM329675 1 0.1556 0.93782 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM329676 1 0.0146 0.98656 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM329677 5 0.2048 0.77071 0.000 0.000 0.120 0.000 0.880 0.000
#> GSM329679 2 0.0632 0.86042 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM329681 3 0.3756 0.42918 0.000 0.000 0.600 0.000 0.400 0.000
#> GSM329683 3 0.0363 0.91761 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM329686 3 0.0000 0.92335 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329689 3 0.3126 0.69917 0.000 0.000 0.752 0.000 0.248 0.000
#> GSM329678 4 0.0260 0.99008 0.000 0.000 0.008 0.992 0.000 0.000
#> GSM329680 3 0.0000 0.92335 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329685 3 0.0000 0.92335 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329688 3 0.0000 0.92335 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329691 3 0.0000 0.92335 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329682 1 0.0146 0.98656 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM329684 1 0.1444 0.93892 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM329687 1 0.0146 0.98656 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM329690 1 0.0363 0.98561 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM329692 4 0.0000 0.99835 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329694 6 0.6441 -0.00466 0.000 0.120 0.000 0.060 0.400 0.420
#> GSM329697 2 0.0000 0.87288 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329700 6 0.2179 0.80924 0.000 0.036 0.000 0.064 0.000 0.900
#> GSM329703 4 0.0000 0.99835 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329704 5 0.3740 0.78130 0.000 0.064 0.000 0.028 0.812 0.096
#> GSM329707 5 0.0146 0.84627 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM329709 2 0.0000 0.87288 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329711 6 0.2179 0.80905 0.000 0.036 0.000 0.064 0.000 0.900
#> GSM329714 6 0.2265 0.80291 0.000 0.052 0.000 0.052 0.000 0.896
#> GSM329693 4 0.0000 0.99835 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329696 4 0.0000 0.99835 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329699 4 0.0000 0.99835 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329702 2 0.0000 0.87288 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329706 5 0.0713 0.84887 0.000 0.000 0.000 0.028 0.972 0.000
#> GSM329708 3 0.0363 0.91516 0.000 0.000 0.988 0.012 0.000 0.000
#> GSM329710 4 0.0000 0.99835 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329713 1 0.0363 0.98561 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM329695 1 0.0363 0.98561 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM329698 1 0.0363 0.98561 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM329701 1 0.0363 0.98561 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM329705 1 0.0000 0.98671 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329712 6 0.2164 0.80680 0.000 0.032 0.000 0.068 0.000 0.900
#> GSM329715 1 0.0363 0.98561 0.988 0.000 0.000 0.000 0.000 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> MAD:mclust 56 5.06e-01 5.82e-11 2
#> MAD:mclust 55 4.15e-03 8.30e-10 3
#> MAD:mclust 48 7.93e-04 2.70e-10 4
#> MAD:mclust 56 5.03e-05 4.55e-09 5
#> MAD:mclust 52 1.36e-02 9.86e-09 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21163 rows and 56 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 0.963 0.982 0.991 0.4563 0.544 0.544
#> 3 3 0.975 0.927 0.974 0.4772 0.731 0.527
#> 4 4 0.778 0.752 0.873 0.1144 0.899 0.699
#> 5 5 0.703 0.527 0.783 0.0247 0.951 0.819
#> 6 6 0.692 0.501 0.687 0.0407 0.869 0.565
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
#> GSM329660 2 0.000 0.993 0.000 1.000
#> GSM329663 2 0.000 0.993 0.000 1.000
#> GSM329664 2 0.000 0.993 0.000 1.000
#> GSM329666 2 0.506 0.876 0.112 0.888
#> GSM329667 2 0.000 0.993 0.000 1.000
#> GSM329670 1 0.595 0.837 0.856 0.144
#> GSM329672 2 0.000 0.993 0.000 1.000
#> GSM329674 2 0.469 0.891 0.100 0.900
#> GSM329661 2 0.000 0.993 0.000 1.000
#> GSM329669 1 0.494 0.881 0.892 0.108
#> GSM329662 1 0.000 0.986 1.000 0.000
#> GSM329665 1 0.000 0.986 1.000 0.000
#> GSM329668 1 0.000 0.986 1.000 0.000
#> GSM329671 1 0.000 0.986 1.000 0.000
#> GSM329673 1 0.000 0.986 1.000 0.000
#> GSM329675 1 0.000 0.986 1.000 0.000
#> GSM329676 1 0.000 0.986 1.000 0.000
#> GSM329677 2 0.000 0.993 0.000 1.000
#> GSM329679 2 0.000 0.993 0.000 1.000
#> GSM329681 2 0.000 0.993 0.000 1.000
#> GSM329683 2 0.000 0.993 0.000 1.000
#> GSM329686 2 0.000 0.993 0.000 1.000
#> GSM329689 2 0.000 0.993 0.000 1.000
#> GSM329678 2 0.000 0.993 0.000 1.000
#> GSM329680 2 0.000 0.993 0.000 1.000
#> GSM329685 2 0.000 0.993 0.000 1.000
#> GSM329688 2 0.000 0.993 0.000 1.000
#> GSM329691 2 0.000 0.993 0.000 1.000
#> GSM329682 1 0.000 0.986 1.000 0.000
#> GSM329684 1 0.000 0.986 1.000 0.000
#> GSM329687 1 0.000 0.986 1.000 0.000
#> GSM329690 1 0.000 0.986 1.000 0.000
#> GSM329692 2 0.000 0.993 0.000 1.000
#> GSM329694 2 0.000 0.993 0.000 1.000
#> GSM329697 2 0.000 0.993 0.000 1.000
#> GSM329700 2 0.000 0.993 0.000 1.000
#> GSM329703 2 0.000 0.993 0.000 1.000
#> GSM329704 2 0.000 0.993 0.000 1.000
#> GSM329707 2 0.000 0.993 0.000 1.000
#> GSM329709 2 0.000 0.993 0.000 1.000
#> GSM329711 2 0.000 0.993 0.000 1.000
#> GSM329714 2 0.000 0.993 0.000 1.000
#> GSM329693 2 0.000 0.993 0.000 1.000
#> GSM329696 2 0.000 0.993 0.000 1.000
#> GSM329699 2 0.000 0.993 0.000 1.000
#> GSM329702 2 0.204 0.964 0.032 0.968
#> GSM329706 2 0.000 0.993 0.000 1.000
#> GSM329708 2 0.000 0.993 0.000 1.000
#> GSM329710 2 0.000 0.993 0.000 1.000
#> GSM329713 1 0.000 0.986 1.000 0.000
#> GSM329695 1 0.000 0.986 1.000 0.000
#> GSM329698 1 0.000 0.986 1.000 0.000
#> GSM329701 1 0.000 0.986 1.000 0.000
#> GSM329705 1 0.000 0.986 1.000 0.000
#> GSM329712 2 0.000 0.993 0.000 1.000
#> GSM329715 1 0.000 0.986 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.0000 0.9730 0 1.000 0.000
#> GSM329663 2 0.0000 0.9730 0 1.000 0.000
#> GSM329664 3 0.6252 0.2264 0 0.444 0.556
#> GSM329666 2 0.0000 0.9730 0 1.000 0.000
#> GSM329667 2 0.0000 0.9730 0 1.000 0.000
#> GSM329670 2 0.0000 0.9730 0 1.000 0.000
#> GSM329672 2 0.0000 0.9730 0 1.000 0.000
#> GSM329674 2 0.0000 0.9730 0 1.000 0.000
#> GSM329661 3 0.0000 0.9386 0 0.000 1.000
#> GSM329669 2 0.0000 0.9730 0 1.000 0.000
#> GSM329662 1 0.0000 1.0000 1 0.000 0.000
#> GSM329665 1 0.0000 1.0000 1 0.000 0.000
#> GSM329668 1 0.0000 1.0000 1 0.000 0.000
#> GSM329671 1 0.0000 1.0000 1 0.000 0.000
#> GSM329673 1 0.0000 1.0000 1 0.000 0.000
#> GSM329675 1 0.0000 1.0000 1 0.000 0.000
#> GSM329676 1 0.0000 1.0000 1 0.000 0.000
#> GSM329677 3 0.0000 0.9386 0 0.000 1.000
#> GSM329679 2 0.0000 0.9730 0 1.000 0.000
#> GSM329681 3 0.0000 0.9386 0 0.000 1.000
#> GSM329683 3 0.0000 0.9386 0 0.000 1.000
#> GSM329686 3 0.0000 0.9386 0 0.000 1.000
#> GSM329689 3 0.0000 0.9386 0 0.000 1.000
#> GSM329678 3 0.0000 0.9386 0 0.000 1.000
#> GSM329680 3 0.0000 0.9386 0 0.000 1.000
#> GSM329685 3 0.0000 0.9386 0 0.000 1.000
#> GSM329688 3 0.0000 0.9386 0 0.000 1.000
#> GSM329691 3 0.0000 0.9386 0 0.000 1.000
#> GSM329682 1 0.0000 1.0000 1 0.000 0.000
#> GSM329684 1 0.0000 1.0000 1 0.000 0.000
#> GSM329687 1 0.0000 1.0000 1 0.000 0.000
#> GSM329690 1 0.0000 1.0000 1 0.000 0.000
#> GSM329692 3 0.0000 0.9386 0 0.000 1.000
#> GSM329694 2 0.0892 0.9535 0 0.980 0.020
#> GSM329697 2 0.0000 0.9730 0 1.000 0.000
#> GSM329700 2 0.0000 0.9730 0 1.000 0.000
#> GSM329703 2 0.0000 0.9730 0 1.000 0.000
#> GSM329704 3 0.6026 0.4111 0 0.376 0.624
#> GSM329707 3 0.0000 0.9386 0 0.000 1.000
#> GSM329709 2 0.0000 0.9730 0 1.000 0.000
#> GSM329711 2 0.0000 0.9730 0 1.000 0.000
#> GSM329714 2 0.0000 0.9730 0 1.000 0.000
#> GSM329693 2 0.0000 0.9730 0 1.000 0.000
#> GSM329696 2 0.0000 0.9730 0 1.000 0.000
#> GSM329699 2 0.6299 -0.0233 0 0.524 0.476
#> GSM329702 2 0.0000 0.9730 0 1.000 0.000
#> GSM329706 3 0.0000 0.9386 0 0.000 1.000
#> GSM329708 3 0.0000 0.9386 0 0.000 1.000
#> GSM329710 3 0.4121 0.7734 0 0.168 0.832
#> GSM329713 1 0.0000 1.0000 1 0.000 0.000
#> GSM329695 1 0.0000 1.0000 1 0.000 0.000
#> GSM329698 1 0.0000 1.0000 1 0.000 0.000
#> GSM329701 1 0.0000 1.0000 1 0.000 0.000
#> GSM329705 1 0.0000 1.0000 1 0.000 0.000
#> GSM329712 2 0.0000 0.9730 0 1.000 0.000
#> GSM329715 1 0.0000 1.0000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.0188 0.847 0 0.996 0.004 0.000
#> GSM329663 2 0.0895 0.849 0 0.976 0.004 0.020
#> GSM329664 3 0.4910 0.456 0 0.276 0.704 0.020
#> GSM329666 2 0.0000 0.847 0 1.000 0.000 0.000
#> GSM329667 2 0.4826 0.595 0 0.716 0.264 0.020
#> GSM329670 2 0.2530 0.821 0 0.888 0.000 0.112
#> GSM329672 2 0.2089 0.814 0 0.932 0.048 0.020
#> GSM329674 2 0.2921 0.809 0 0.860 0.000 0.140
#> GSM329661 3 0.4406 0.620 0 0.000 0.700 0.300
#> GSM329669 2 0.3837 0.750 0 0.776 0.000 0.224
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329677 3 0.0336 0.702 0 0.000 0.992 0.008
#> GSM329679 2 0.2706 0.793 0 0.900 0.080 0.020
#> GSM329681 3 0.1557 0.714 0 0.000 0.944 0.056
#> GSM329683 3 0.3528 0.700 0 0.000 0.808 0.192
#> GSM329686 3 0.3907 0.685 0 0.000 0.768 0.232
#> GSM329689 3 0.1637 0.715 0 0.000 0.940 0.060
#> GSM329678 4 0.4382 0.348 0 0.000 0.296 0.704
#> GSM329680 3 0.4040 0.677 0 0.000 0.752 0.248
#> GSM329685 3 0.4992 0.279 0 0.000 0.524 0.476
#> GSM329688 3 0.4998 0.249 0 0.000 0.512 0.488
#> GSM329691 3 0.4072 0.672 0 0.000 0.748 0.252
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329692 4 0.4406 0.342 0 0.000 0.300 0.700
#> GSM329694 2 0.3577 0.744 0 0.832 0.156 0.012
#> GSM329697 2 0.0657 0.848 0 0.984 0.004 0.012
#> GSM329700 2 0.4040 0.726 0 0.752 0.000 0.248
#> GSM329703 4 0.2814 0.671 0 0.132 0.000 0.868
#> GSM329704 3 0.4855 0.466 0 0.268 0.712 0.020
#> GSM329707 3 0.2973 0.626 0 0.096 0.884 0.020
#> GSM329709 2 0.1211 0.845 0 0.960 0.000 0.040
#> GSM329711 2 0.4250 0.696 0 0.724 0.000 0.276
#> GSM329714 4 0.4907 0.127 0 0.420 0.000 0.580
#> GSM329693 4 0.3837 0.545 0 0.224 0.000 0.776
#> GSM329696 4 0.2760 0.672 0 0.128 0.000 0.872
#> GSM329699 4 0.1474 0.664 0 0.052 0.000 0.948
#> GSM329702 2 0.0188 0.847 0 0.996 0.000 0.004
#> GSM329706 3 0.0469 0.704 0 0.000 0.988 0.012
#> GSM329708 4 0.4522 0.294 0 0.000 0.320 0.680
#> GSM329710 4 0.1722 0.629 0 0.008 0.048 0.944
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329712 2 0.4222 0.701 0 0.728 0.000 0.272
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.3452 0.7565 0.000 0.852 0.092 0.032 0.024
#> GSM329663 2 0.2095 0.7647 0.000 0.920 0.012 0.008 0.060
#> GSM329664 3 0.4029 0.2718 0.000 0.232 0.744 0.000 0.024
#> GSM329666 2 0.2208 0.7536 0.000 0.908 0.072 0.000 0.020
#> GSM329667 2 0.4974 0.2979 0.000 0.508 0.464 0.000 0.028
#> GSM329670 2 0.3192 0.7326 0.000 0.848 0.000 0.040 0.112
#> GSM329672 2 0.3929 0.6780 0.000 0.764 0.208 0.000 0.028
#> GSM329674 2 0.1830 0.7584 0.000 0.924 0.000 0.068 0.008
#> GSM329661 5 0.6628 0.0000 0.000 0.000 0.372 0.220 0.408
#> GSM329669 2 0.2616 0.7448 0.000 0.880 0.000 0.100 0.020
#> GSM329662 1 0.0609 0.9714 0.980 0.000 0.000 0.000 0.020
#> GSM329665 1 0.0162 0.9770 0.996 0.000 0.000 0.000 0.004
#> GSM329668 1 0.0000 0.9772 1.000 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0000 0.9772 1.000 0.000 0.000 0.000 0.000
#> GSM329673 1 0.0162 0.9770 0.996 0.000 0.000 0.000 0.004
#> GSM329675 1 0.0290 0.9762 0.992 0.000 0.000 0.000 0.008
#> GSM329676 1 0.0290 0.9762 0.992 0.000 0.000 0.000 0.008
#> GSM329677 3 0.2270 0.3758 0.000 0.000 0.904 0.076 0.020
#> GSM329679 2 0.4350 0.6232 0.000 0.704 0.268 0.000 0.028
#> GSM329681 3 0.5215 -0.3933 0.000 0.000 0.592 0.056 0.352
#> GSM329683 3 0.5467 0.0256 0.000 0.000 0.624 0.276 0.100
#> GSM329686 3 0.5274 0.0697 0.000 0.000 0.600 0.336 0.064
#> GSM329689 3 0.4376 0.2316 0.000 0.000 0.764 0.144 0.092
#> GSM329678 4 0.3016 0.2391 0.000 0.000 0.132 0.848 0.020
#> GSM329680 3 0.5648 -0.2406 0.000 0.000 0.476 0.448 0.076
#> GSM329685 4 0.5168 -0.1683 0.000 0.000 0.356 0.592 0.052
#> GSM329688 4 0.5077 -0.2513 0.000 0.000 0.392 0.568 0.040
#> GSM329691 3 0.5256 -0.0652 0.000 0.000 0.532 0.420 0.048
#> GSM329682 1 0.0162 0.9766 0.996 0.000 0.000 0.000 0.004
#> GSM329684 1 0.0880 0.9647 0.968 0.000 0.000 0.000 0.032
#> GSM329687 1 0.0162 0.9770 0.996 0.000 0.000 0.000 0.004
#> GSM329690 1 0.0880 0.9649 0.968 0.000 0.000 0.000 0.032
#> GSM329692 4 0.4680 0.0908 0.000 0.000 0.132 0.740 0.128
#> GSM329694 2 0.6242 0.3377 0.000 0.528 0.372 0.052 0.048
#> GSM329697 2 0.2436 0.7675 0.000 0.912 0.020 0.032 0.036
#> GSM329700 2 0.3432 0.7188 0.000 0.828 0.000 0.132 0.040
#> GSM329703 4 0.5202 0.2132 0.000 0.348 0.000 0.596 0.056
#> GSM329704 3 0.3970 0.2721 0.000 0.236 0.744 0.000 0.020
#> GSM329707 3 0.1012 0.3480 0.000 0.020 0.968 0.000 0.012
#> GSM329709 2 0.2244 0.7678 0.000 0.920 0.024 0.040 0.016
#> GSM329711 2 0.3687 0.6891 0.000 0.792 0.000 0.180 0.028
#> GSM329714 2 0.5535 0.2347 0.000 0.536 0.000 0.392 0.072
#> GSM329693 4 0.4774 0.1849 0.000 0.360 0.000 0.612 0.028
#> GSM329696 4 0.4355 0.4170 0.000 0.224 0.000 0.732 0.044
#> GSM329699 4 0.4045 0.4143 0.000 0.136 0.004 0.796 0.064
#> GSM329702 2 0.2669 0.7422 0.000 0.876 0.104 0.000 0.020
#> GSM329706 3 0.2193 0.3792 0.000 0.000 0.900 0.092 0.008
#> GSM329708 4 0.6540 -0.4792 0.000 0.000 0.236 0.476 0.288
#> GSM329710 4 0.5575 0.1787 0.000 0.068 0.020 0.644 0.268
#> GSM329713 1 0.2648 0.8724 0.848 0.000 0.000 0.000 0.152
#> GSM329695 1 0.2471 0.8868 0.864 0.000 0.000 0.000 0.136
#> GSM329698 1 0.0609 0.9710 0.980 0.000 0.000 0.000 0.020
#> GSM329701 1 0.0404 0.9742 0.988 0.000 0.000 0.000 0.012
#> GSM329705 1 0.0000 0.9772 1.000 0.000 0.000 0.000 0.000
#> GSM329712 2 0.3745 0.6816 0.000 0.780 0.000 0.196 0.024
#> GSM329715 1 0.0000 0.9772 1.000 0.000 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
#> GSM329660 2 0.3619 0.49169 0.000 0.680 0.000 NA 0.316 0.000
#> GSM329663 2 0.5873 0.54341 0.000 0.632 0.000 NA 0.144 0.084
#> GSM329664 5 0.1533 0.49981 0.000 0.012 0.016 NA 0.948 0.008
#> GSM329666 2 0.4176 0.28162 0.000 0.580 0.000 NA 0.404 0.000
#> GSM329667 5 0.3056 0.43033 0.000 0.184 0.000 NA 0.804 0.004
#> GSM329670 2 0.4609 0.59542 0.000 0.720 0.000 NA 0.116 0.012
#> GSM329672 5 0.4181 0.17173 0.000 0.384 0.000 NA 0.600 0.004
#> GSM329674 2 0.3849 0.53506 0.000 0.752 0.000 NA 0.208 0.008
#> GSM329661 6 0.3454 0.62753 0.000 0.000 0.224 NA 0.012 0.760
#> GSM329669 2 0.2135 0.62163 0.000 0.872 0.000 NA 0.128 0.000
#> GSM329662 1 0.1349 0.89743 0.940 0.000 0.000 NA 0.000 0.004
#> GSM329665 1 0.0603 0.91231 0.980 0.000 0.000 NA 0.000 0.004
#> GSM329668 1 0.0146 0.91522 0.996 0.000 0.000 NA 0.000 0.000
#> GSM329671 1 0.0865 0.91419 0.964 0.000 0.000 NA 0.000 0.000
#> GSM329673 1 0.0260 0.91426 0.992 0.000 0.000 NA 0.000 0.000
#> GSM329675 1 0.1082 0.90456 0.956 0.000 0.000 NA 0.000 0.004
#> GSM329676 1 0.0935 0.90744 0.964 0.000 0.000 NA 0.000 0.004
#> GSM329677 5 0.5755 0.00557 0.000 0.000 0.292 NA 0.568 0.108
#> GSM329679 5 0.3953 0.27326 0.000 0.328 0.000 NA 0.656 0.000
#> GSM329681 6 0.5007 0.64549 0.000 0.000 0.136 NA 0.100 0.712
#> GSM329683 3 0.6979 -0.07174 0.000 0.000 0.428 NA 0.212 0.280
#> GSM329686 3 0.5021 0.31672 0.000 0.000 0.684 NA 0.204 0.076
#> GSM329689 3 0.7201 -0.12198 0.000 0.000 0.344 NA 0.324 0.244
#> GSM329678 3 0.3756 0.38646 0.000 0.052 0.824 NA 0.004 0.060
#> GSM329680 3 0.4672 0.34674 0.000 0.000 0.700 NA 0.152 0.144
#> GSM329685 3 0.2255 0.43327 0.000 0.000 0.892 NA 0.088 0.016
#> GSM329688 3 0.1918 0.43548 0.000 0.000 0.904 NA 0.088 0.008
#> GSM329691 3 0.4255 0.37519 0.000 0.000 0.756 NA 0.156 0.068
#> GSM329682 1 0.1141 0.91080 0.948 0.000 0.000 NA 0.000 0.000
#> GSM329684 1 0.2207 0.87185 0.900 0.000 0.016 NA 0.000 0.008
#> GSM329687 1 0.0363 0.91369 0.988 0.000 0.000 NA 0.000 0.000
#> GSM329690 1 0.2883 0.82498 0.788 0.000 0.000 NA 0.000 0.000
#> GSM329692 3 0.4526 0.24509 0.000 0.044 0.664 NA 0.004 0.284
#> GSM329694 5 0.7616 0.14906 0.000 0.308 0.084 NA 0.416 0.140
#> GSM329697 2 0.5049 0.42272 0.000 0.624 0.000 NA 0.268 0.004
#> GSM329700 2 0.3488 0.63213 0.000 0.832 0.000 NA 0.084 0.032
#> GSM329703 2 0.5896 0.37356 0.000 0.624 0.200 NA 0.004 0.068
#> GSM329704 5 0.2177 0.49351 0.000 0.024 0.060 NA 0.908 0.004
#> GSM329707 5 0.3913 0.32903 0.000 0.000 0.156 NA 0.776 0.056
#> GSM329709 2 0.4411 0.42137 0.000 0.672 0.000 NA 0.276 0.004
#> GSM329711 2 0.2563 0.62074 0.000 0.888 0.008 NA 0.016 0.012
#> GSM329714 2 0.5497 0.54974 0.000 0.692 0.068 NA 0.016 0.080
#> GSM329693 2 0.5846 0.11251 0.000 0.512 0.364 NA 0.000 0.040
#> GSM329696 3 0.6116 0.20940 0.000 0.340 0.512 NA 0.004 0.040
#> GSM329699 3 0.6461 0.15228 0.000 0.344 0.472 NA 0.000 0.076
#> GSM329702 5 0.4097 -0.15451 0.000 0.492 0.000 NA 0.500 0.000
#> GSM329706 5 0.4693 0.17718 0.000 0.000 0.280 NA 0.660 0.032
#> GSM329708 3 0.4312 -0.08649 0.000 0.000 0.528 NA 0.008 0.456
#> GSM329710 3 0.6351 0.14089 0.000 0.152 0.488 NA 0.000 0.316
#> GSM329713 1 0.3819 0.64940 0.624 0.000 0.000 NA 0.000 0.004
#> GSM329695 1 0.3499 0.71760 0.680 0.000 0.000 NA 0.000 0.000
#> GSM329698 1 0.2300 0.86917 0.856 0.000 0.000 NA 0.000 0.000
#> GSM329701 1 0.1501 0.90295 0.924 0.000 0.000 NA 0.000 0.000
#> GSM329705 1 0.0790 0.91476 0.968 0.000 0.000 NA 0.000 0.000
#> GSM329712 2 0.2760 0.61647 0.000 0.884 0.012 NA 0.020 0.020
#> GSM329715 1 0.0937 0.91333 0.960 0.000 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 disease.state(p) tissue(p) k
#> MAD:NMF 56 0.13893 2.28e-09 2
#> MAD:NMF 53 0.00255 2.23e-10 3
#> MAD:NMF 48 0.00123 2.40e-09 4
#> MAD:NMF 31 0.46674 4.77e-06 5
#> MAD:NMF 27 0.40461 1.55e-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", "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 21163 rows and 56 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 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 0.988 0.987 0.4311 0.569 0.569
#> 3 3 1.000 0.985 0.989 0.5523 0.761 0.580
#> 4 4 0.870 0.896 0.868 0.0961 0.914 0.741
#> 5 5 0.841 0.893 0.930 0.0573 0.953 0.820
#> 6 6 0.941 0.882 0.948 0.0422 0.969 0.862
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
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM329660 2 0.204 0.985 0.032 0.968
#> GSM329663 2 0.204 0.985 0.032 0.968
#> GSM329664 2 0.000 0.981 0.000 1.000
#> GSM329666 2 0.204 0.985 0.032 0.968
#> GSM329667 2 0.000 0.981 0.000 1.000
#> GSM329670 2 0.204 0.985 0.032 0.968
#> GSM329672 2 0.204 0.985 0.032 0.968
#> GSM329674 2 0.204 0.985 0.032 0.968
#> GSM329661 2 0.000 0.981 0.000 1.000
#> GSM329669 2 0.204 0.985 0.032 0.968
#> GSM329662 1 0.000 1.000 1.000 0.000
#> GSM329665 1 0.000 1.000 1.000 0.000
#> GSM329668 1 0.000 1.000 1.000 0.000
#> GSM329671 1 0.000 1.000 1.000 0.000
#> GSM329673 1 0.000 1.000 1.000 0.000
#> GSM329675 1 0.000 1.000 1.000 0.000
#> GSM329676 1 0.000 1.000 1.000 0.000
#> GSM329677 2 0.000 0.981 0.000 1.000
#> GSM329679 2 0.204 0.985 0.032 0.968
#> GSM329681 2 0.000 0.981 0.000 1.000
#> GSM329683 2 0.000 0.981 0.000 1.000
#> GSM329686 2 0.000 0.981 0.000 1.000
#> GSM329689 2 0.000 0.981 0.000 1.000
#> GSM329678 2 0.000 0.981 0.000 1.000
#> GSM329680 2 0.000 0.981 0.000 1.000
#> GSM329685 2 0.000 0.981 0.000 1.000
#> GSM329688 2 0.000 0.981 0.000 1.000
#> GSM329691 2 0.000 0.981 0.000 1.000
#> GSM329682 1 0.000 1.000 1.000 0.000
#> GSM329684 1 0.000 1.000 1.000 0.000
#> GSM329687 1 0.000 1.000 1.000 0.000
#> GSM329690 1 0.000 1.000 1.000 0.000
#> GSM329692 2 0.204 0.985 0.032 0.968
#> GSM329694 2 0.204 0.985 0.032 0.968
#> GSM329697 2 0.204 0.985 0.032 0.968
#> GSM329700 2 0.204 0.985 0.032 0.968
#> GSM329703 2 0.204 0.985 0.032 0.968
#> GSM329704 2 0.000 0.981 0.000 1.000
#> GSM329707 2 0.000 0.981 0.000 1.000
#> GSM329709 2 0.204 0.985 0.032 0.968
#> GSM329711 2 0.204 0.985 0.032 0.968
#> GSM329714 2 0.204 0.985 0.032 0.968
#> GSM329693 2 0.204 0.985 0.032 0.968
#> GSM329696 2 0.204 0.985 0.032 0.968
#> GSM329699 2 0.204 0.985 0.032 0.968
#> GSM329702 2 0.204 0.985 0.032 0.968
#> GSM329706 2 0.000 0.981 0.000 1.000
#> GSM329708 2 0.000 0.981 0.000 1.000
#> GSM329710 2 0.204 0.985 0.032 0.968
#> GSM329713 1 0.000 1.000 1.000 0.000
#> GSM329695 1 0.000 1.000 1.000 0.000
#> GSM329698 1 0.000 1.000 1.000 0.000
#> GSM329701 1 0.000 1.000 1.000 0.000
#> GSM329705 1 0.000 1.000 1.000 0.000
#> GSM329712 2 0.204 0.985 0.032 0.968
#> GSM329715 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.103 0.972 0 0.976 0.024
#> GSM329663 2 0.000 0.972 0 1.000 0.000
#> GSM329664 3 0.000 1.000 0 0.000 1.000
#> GSM329666 2 0.000 0.972 0 1.000 0.000
#> GSM329667 3 0.000 1.000 0 0.000 1.000
#> GSM329670 2 0.000 0.972 0 1.000 0.000
#> GSM329672 2 0.153 0.969 0 0.960 0.040
#> GSM329674 2 0.000 0.972 0 1.000 0.000
#> GSM329661 3 0.000 1.000 0 0.000 1.000
#> GSM329669 2 0.000 0.972 0 1.000 0.000
#> GSM329662 1 0.000 1.000 1 0.000 0.000
#> GSM329665 1 0.000 1.000 1 0.000 0.000
#> GSM329668 1 0.000 1.000 1 0.000 0.000
#> GSM329671 1 0.000 1.000 1 0.000 0.000
#> GSM329673 1 0.000 1.000 1 0.000 0.000
#> GSM329675 1 0.000 1.000 1 0.000 0.000
#> GSM329676 1 0.000 1.000 1 0.000 0.000
#> GSM329677 3 0.000 1.000 0 0.000 1.000
#> GSM329679 2 0.153 0.969 0 0.960 0.040
#> GSM329681 3 0.000 1.000 0 0.000 1.000
#> GSM329683 3 0.000 1.000 0 0.000 1.000
#> GSM329686 3 0.000 1.000 0 0.000 1.000
#> GSM329689 3 0.000 1.000 0 0.000 1.000
#> GSM329678 2 0.412 0.836 0 0.832 0.168
#> GSM329680 3 0.000 1.000 0 0.000 1.000
#> GSM329685 3 0.000 1.000 0 0.000 1.000
#> GSM329688 3 0.000 1.000 0 0.000 1.000
#> GSM329691 3 0.000 1.000 0 0.000 1.000
#> GSM329682 1 0.000 1.000 1 0.000 0.000
#> GSM329684 1 0.000 1.000 1 0.000 0.000
#> GSM329687 1 0.000 1.000 1 0.000 0.000
#> GSM329690 1 0.000 1.000 1 0.000 0.000
#> GSM329692 2 0.226 0.949 0 0.932 0.068
#> GSM329694 2 0.153 0.969 0 0.960 0.040
#> GSM329697 2 0.000 0.972 0 1.000 0.000
#> GSM329700 2 0.000 0.972 0 1.000 0.000
#> GSM329703 2 0.153 0.969 0 0.960 0.040
#> GSM329704 3 0.000 1.000 0 0.000 1.000
#> GSM329707 3 0.000 1.000 0 0.000 1.000
#> GSM329709 2 0.000 0.972 0 1.000 0.000
#> GSM329711 2 0.000 0.972 0 1.000 0.000
#> GSM329714 2 0.103 0.972 0 0.976 0.024
#> GSM329693 2 0.153 0.969 0 0.960 0.040
#> GSM329696 2 0.153 0.969 0 0.960 0.040
#> GSM329699 2 0.153 0.969 0 0.960 0.040
#> GSM329702 2 0.000 0.972 0 1.000 0.000
#> GSM329706 3 0.000 1.000 0 0.000 1.000
#> GSM329708 3 0.000 1.000 0 0.000 1.000
#> GSM329710 2 0.226 0.949 0 0.932 0.068
#> GSM329713 1 0.000 1.000 1 0.000 0.000
#> GSM329695 1 0.000 1.000 1 0.000 0.000
#> GSM329698 1 0.000 1.000 1 0.000 0.000
#> GSM329701 1 0.000 1.000 1 0.000 0.000
#> GSM329705 1 0.000 1.000 1 0.000 0.000
#> GSM329712 2 0.000 0.972 0 1.000 0.000
#> GSM329715 1 0.000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 4 0.4477 -0.0729 0.000 0.312 0.000 0.688
#> GSM329663 2 0.4898 0.9984 0.000 0.584 0.000 0.416
#> GSM329664 3 0.0336 0.9949 0.000 0.008 0.992 0.000
#> GSM329666 2 0.4898 0.9984 0.000 0.584 0.000 0.416
#> GSM329667 3 0.0336 0.9949 0.000 0.008 0.992 0.000
#> GSM329670 2 0.4898 0.9984 0.000 0.584 0.000 0.416
#> GSM329672 4 0.0000 0.8610 0.000 0.000 0.000 1.000
#> GSM329674 2 0.4898 0.9984 0.000 0.584 0.000 0.416
#> GSM329661 3 0.0000 0.9983 0.000 0.000 1.000 0.000
#> GSM329669 2 0.4898 0.9984 0.000 0.584 0.000 0.416
#> GSM329662 1 0.0000 0.8759 1.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 0.8759 1.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 0.8759 1.000 0.000 0.000 0.000
#> GSM329671 1 0.3610 0.9148 0.800 0.200 0.000 0.000
#> GSM329673 1 0.0000 0.8759 1.000 0.000 0.000 0.000
#> GSM329675 1 0.3688 0.7485 0.792 0.208 0.000 0.000
#> GSM329676 1 0.0000 0.8759 1.000 0.000 0.000 0.000
#> GSM329677 3 0.0000 0.9983 0.000 0.000 1.000 0.000
#> GSM329679 4 0.0000 0.8610 0.000 0.000 0.000 1.000
#> GSM329681 3 0.0188 0.9969 0.000 0.004 0.996 0.000
#> GSM329683 3 0.0000 0.9983 0.000 0.000 1.000 0.000
#> GSM329686 3 0.0000 0.9983 0.000 0.000 1.000 0.000
#> GSM329689 3 0.0000 0.9983 0.000 0.000 1.000 0.000
#> GSM329678 4 0.2976 0.6763 0.000 0.008 0.120 0.872
#> GSM329680 3 0.0000 0.9983 0.000 0.000 1.000 0.000
#> GSM329685 3 0.0000 0.9983 0.000 0.000 1.000 0.000
#> GSM329688 3 0.0000 0.9983 0.000 0.000 1.000 0.000
#> GSM329691 3 0.0000 0.9983 0.000 0.000 1.000 0.000
#> GSM329682 1 0.3528 0.9139 0.808 0.192 0.000 0.000
#> GSM329684 1 0.3688 0.7485 0.792 0.208 0.000 0.000
#> GSM329687 1 0.3610 0.9148 0.800 0.200 0.000 0.000
#> GSM329690 1 0.3610 0.9148 0.800 0.200 0.000 0.000
#> GSM329692 4 0.1042 0.8373 0.000 0.008 0.020 0.972
#> GSM329694 4 0.0000 0.8610 0.000 0.000 0.000 1.000
#> GSM329697 2 0.4898 0.9984 0.000 0.584 0.000 0.416
#> GSM329700 2 0.4898 0.9984 0.000 0.584 0.000 0.416
#> GSM329703 4 0.0000 0.8610 0.000 0.000 0.000 1.000
#> GSM329704 3 0.0336 0.9949 0.000 0.008 0.992 0.000
#> GSM329707 3 0.0188 0.9969 0.000 0.004 0.996 0.000
#> GSM329709 2 0.4898 0.9984 0.000 0.584 0.000 0.416
#> GSM329711 2 0.4907 0.9930 0.000 0.580 0.000 0.420
#> GSM329714 4 0.4477 -0.0729 0.000 0.312 0.000 0.688
#> GSM329693 4 0.0000 0.8610 0.000 0.000 0.000 1.000
#> GSM329696 4 0.0000 0.8610 0.000 0.000 0.000 1.000
#> GSM329699 4 0.0000 0.8610 0.000 0.000 0.000 1.000
#> GSM329702 2 0.4898 0.9984 0.000 0.584 0.000 0.416
#> GSM329706 3 0.0000 0.9983 0.000 0.000 1.000 0.000
#> GSM329708 3 0.0000 0.9983 0.000 0.000 1.000 0.000
#> GSM329710 4 0.1042 0.8373 0.000 0.008 0.020 0.972
#> GSM329713 1 0.3610 0.9148 0.800 0.200 0.000 0.000
#> GSM329695 1 0.3610 0.9148 0.800 0.200 0.000 0.000
#> GSM329698 1 0.3610 0.9148 0.800 0.200 0.000 0.000
#> GSM329701 1 0.3610 0.9148 0.800 0.200 0.000 0.000
#> GSM329705 1 0.3610 0.9148 0.800 0.200 0.000 0.000
#> GSM329712 2 0.4907 0.9930 0.000 0.580 0.000 0.420
#> GSM329715 1 0.3610 0.9148 0.800 0.200 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.4114 0.318 0.000 0.624 0.000 0.376 0.000
#> GSM329663 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> GSM329664 3 0.3060 0.877 0.000 0.000 0.848 0.128 0.024
#> GSM329666 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> GSM329667 3 0.3060 0.877 0.000 0.000 0.848 0.128 0.024
#> GSM329670 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> GSM329672 4 0.2377 0.969 0.000 0.128 0.000 0.872 0.000
#> GSM329674 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> GSM329661 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM329669 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> GSM329662 1 0.3508 0.759 0.748 0.000 0.000 0.000 0.252
#> GSM329665 1 0.3508 0.759 0.748 0.000 0.000 0.000 0.252
#> GSM329668 1 0.3508 0.759 0.748 0.000 0.000 0.000 0.252
#> GSM329671 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM329673 1 0.3508 0.759 0.748 0.000 0.000 0.000 0.252
#> GSM329675 5 0.0703 1.000 0.024 0.000 0.000 0.000 0.976
#> GSM329676 1 0.3508 0.759 0.748 0.000 0.000 0.000 0.252
#> GSM329677 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM329679 4 0.2377 0.969 0.000 0.128 0.000 0.872 0.000
#> GSM329681 3 0.0703 0.951 0.000 0.000 0.976 0.024 0.000
#> GSM329683 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM329686 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM329689 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM329678 4 0.2020 0.795 0.000 0.000 0.100 0.900 0.000
#> GSM329680 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM329685 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM329688 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM329691 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM329682 1 0.1043 0.878 0.960 0.000 0.000 0.000 0.040
#> GSM329684 5 0.0703 1.000 0.024 0.000 0.000 0.000 0.976
#> GSM329687 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM329692 4 0.2020 0.949 0.000 0.100 0.000 0.900 0.000
#> GSM329694 4 0.2377 0.969 0.000 0.128 0.000 0.872 0.000
#> GSM329697 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> GSM329700 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> GSM329703 4 0.2377 0.969 0.000 0.128 0.000 0.872 0.000
#> GSM329704 3 0.3060 0.877 0.000 0.000 0.848 0.128 0.024
#> GSM329707 3 0.2230 0.900 0.000 0.000 0.884 0.116 0.000
#> GSM329709 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> GSM329711 2 0.0162 0.917 0.000 0.996 0.000 0.004 0.000
#> GSM329714 2 0.4114 0.318 0.000 0.624 0.000 0.376 0.000
#> GSM329693 4 0.2377 0.969 0.000 0.128 0.000 0.872 0.000
#> GSM329696 4 0.2377 0.969 0.000 0.128 0.000 0.872 0.000
#> GSM329699 4 0.2377 0.969 0.000 0.128 0.000 0.872 0.000
#> GSM329702 2 0.0000 0.920 0.000 1.000 0.000 0.000 0.000
#> GSM329706 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM329708 3 0.0000 0.963 0.000 0.000 1.000 0.000 0.000
#> GSM329710 4 0.2020 0.949 0.000 0.100 0.000 0.900 0.000
#> GSM329713 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM329695 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM329698 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM329701 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM329705 1 0.0000 0.893 1.000 0.000 0.000 0.000 0.000
#> GSM329712 2 0.0162 0.917 0.000 0.996 0.000 0.004 0.000
#> GSM329715 1 0.0000 0.893 1.000 0.000 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
#> GSM329660 2 0.3823 0.261 0.000 0.564 0.000 0.436 0.000 0.000
#> GSM329663 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329664 5 0.0000 0.767 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM329666 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329667 5 0.0000 0.767 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM329670 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329672 4 0.0713 0.974 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM329674 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329661 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329669 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329662 1 0.3151 0.767 0.748 0.000 0.000 0.000 0.000 0.252
#> GSM329665 1 0.3151 0.767 0.748 0.000 0.000 0.000 0.000 0.252
#> GSM329668 1 0.3151 0.767 0.748 0.000 0.000 0.000 0.000 0.252
#> GSM329671 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329673 1 0.3151 0.767 0.748 0.000 0.000 0.000 0.000 0.252
#> GSM329675 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM329676 1 0.3151 0.767 0.748 0.000 0.000 0.000 0.000 0.252
#> GSM329677 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329679 4 0.0713 0.974 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM329681 3 0.0632 0.973 0.000 0.000 0.976 0.024 0.000 0.000
#> GSM329683 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329686 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329689 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329678 4 0.1814 0.839 0.000 0.000 0.100 0.900 0.000 0.000
#> GSM329680 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329685 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329688 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329691 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329682 1 0.0937 0.882 0.960 0.000 0.000 0.000 0.000 0.040
#> GSM329684 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM329687 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329692 4 0.0000 0.954 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329694 4 0.0713 0.974 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM329697 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329700 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329703 4 0.0713 0.974 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM329704 5 0.0146 0.766 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM329707 5 0.4184 0.298 0.000 0.000 0.408 0.016 0.576 0.000
#> GSM329709 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329711 2 0.0146 0.904 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM329714 2 0.3823 0.261 0.000 0.564 0.000 0.436 0.000 0.000
#> GSM329693 4 0.0713 0.974 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM329696 4 0.0713 0.974 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM329699 4 0.0713 0.974 0.000 0.028 0.000 0.972 0.000 0.000
#> GSM329702 2 0.0000 0.906 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329706 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329708 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329710 4 0.0000 0.954 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329713 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329695 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329698 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329701 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329705 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329712 2 0.0146 0.904 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM329715 1 0.0000 0.896 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> ATC:hclust 56 0.50568 5.82e-11 2
#> ATC:hclust 56 0.01348 9.47e-10 3
#> ATC:hclust 54 0.01879 9.34e-09 4
#> ATC:hclust 54 0.03588 7.70e-08 5
#> ATC:hclust 53 0.00466 7.90e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21163 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4311 0.569 0.569
#> 3 3 0.733 0.986 0.942 0.4850 0.761 0.580
#> 4 4 0.773 0.663 0.783 0.1211 0.951 0.851
#> 5 5 0.753 0.659 0.782 0.0793 0.902 0.679
#> 6 6 0.762 0.657 0.775 0.0478 0.926 0.714
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
#> GSM329660 2 0 1 0 1
#> GSM329663 2 0 1 0 1
#> GSM329664 2 0 1 0 1
#> GSM329666 2 0 1 0 1
#> GSM329667 2 0 1 0 1
#> GSM329670 2 0 1 0 1
#> GSM329672 2 0 1 0 1
#> GSM329674 2 0 1 0 1
#> GSM329661 2 0 1 0 1
#> GSM329669 2 0 1 0 1
#> GSM329662 1 0 1 1 0
#> GSM329665 1 0 1 1 0
#> GSM329668 1 0 1 1 0
#> GSM329671 1 0 1 1 0
#> GSM329673 1 0 1 1 0
#> GSM329675 1 0 1 1 0
#> GSM329676 1 0 1 1 0
#> GSM329677 2 0 1 0 1
#> GSM329679 2 0 1 0 1
#> GSM329681 2 0 1 0 1
#> GSM329683 2 0 1 0 1
#> GSM329686 2 0 1 0 1
#> GSM329689 2 0 1 0 1
#> GSM329678 2 0 1 0 1
#> GSM329680 2 0 1 0 1
#> GSM329685 2 0 1 0 1
#> GSM329688 2 0 1 0 1
#> GSM329691 2 0 1 0 1
#> GSM329682 1 0 1 1 0
#> GSM329684 1 0 1 1 0
#> GSM329687 1 0 1 1 0
#> GSM329690 1 0 1 1 0
#> GSM329692 2 0 1 0 1
#> GSM329694 2 0 1 0 1
#> GSM329697 2 0 1 0 1
#> GSM329700 2 0 1 0 1
#> GSM329703 2 0 1 0 1
#> GSM329704 2 0 1 0 1
#> GSM329707 2 0 1 0 1
#> GSM329709 2 0 1 0 1
#> GSM329711 2 0 1 0 1
#> GSM329714 2 0 1 0 1
#> GSM329693 2 0 1 0 1
#> GSM329696 2 0 1 0 1
#> GSM329699 2 0 1 0 1
#> GSM329702 2 0 1 0 1
#> GSM329706 2 0 1 0 1
#> GSM329708 2 0 1 0 1
#> GSM329710 2 0 1 0 1
#> GSM329713 1 0 1 1 0
#> GSM329695 1 0 1 1 0
#> GSM329698 1 0 1 1 0
#> GSM329701 1 0 1 1 0
#> GSM329705 1 0 1 1 0
#> GSM329712 2 0 1 0 1
#> GSM329715 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.000 0.997 0.000 1.000 0.000
#> GSM329663 2 0.000 0.997 0.000 1.000 0.000
#> GSM329664 3 0.382 1.000 0.000 0.148 0.852
#> GSM329666 2 0.000 0.997 0.000 1.000 0.000
#> GSM329667 2 0.000 0.997 0.000 1.000 0.000
#> GSM329670 2 0.000 0.997 0.000 1.000 0.000
#> GSM329672 2 0.000 0.997 0.000 1.000 0.000
#> GSM329674 2 0.000 0.997 0.000 1.000 0.000
#> GSM329661 3 0.382 1.000 0.000 0.148 0.852
#> GSM329669 2 0.000 0.997 0.000 1.000 0.000
#> GSM329662 1 0.312 0.954 0.892 0.000 0.108
#> GSM329665 1 0.263 0.961 0.916 0.000 0.084
#> GSM329668 1 0.263 0.961 0.916 0.000 0.084
#> GSM329671 1 0.000 0.965 1.000 0.000 0.000
#> GSM329673 1 0.296 0.957 0.900 0.000 0.100
#> GSM329675 1 0.382 0.937 0.852 0.000 0.148
#> GSM329676 1 0.263 0.961 0.916 0.000 0.084
#> GSM329677 3 0.382 1.000 0.000 0.148 0.852
#> GSM329679 2 0.000 0.997 0.000 1.000 0.000
#> GSM329681 3 0.382 1.000 0.000 0.148 0.852
#> GSM329683 3 0.382 1.000 0.000 0.148 0.852
#> GSM329686 3 0.382 1.000 0.000 0.148 0.852
#> GSM329689 3 0.382 1.000 0.000 0.148 0.852
#> GSM329678 3 0.382 1.000 0.000 0.148 0.852
#> GSM329680 3 0.382 1.000 0.000 0.148 0.852
#> GSM329685 3 0.382 1.000 0.000 0.148 0.852
#> GSM329688 3 0.382 1.000 0.000 0.148 0.852
#> GSM329691 3 0.382 1.000 0.000 0.148 0.852
#> GSM329682 1 0.196 0.965 0.944 0.000 0.056
#> GSM329684 1 0.382 0.937 0.852 0.000 0.148
#> GSM329687 1 0.196 0.965 0.944 0.000 0.056
#> GSM329690 1 0.000 0.965 1.000 0.000 0.000
#> GSM329692 2 0.175 0.940 0.000 0.952 0.048
#> GSM329694 2 0.000 0.997 0.000 1.000 0.000
#> GSM329697 2 0.000 0.997 0.000 1.000 0.000
#> GSM329700 2 0.000 0.997 0.000 1.000 0.000
#> GSM329703 2 0.000 0.997 0.000 1.000 0.000
#> GSM329704 3 0.382 1.000 0.000 0.148 0.852
#> GSM329707 3 0.382 1.000 0.000 0.148 0.852
#> GSM329709 2 0.000 0.997 0.000 1.000 0.000
#> GSM329711 2 0.000 0.997 0.000 1.000 0.000
#> GSM329714 2 0.000 0.997 0.000 1.000 0.000
#> GSM329693 2 0.000 0.997 0.000 1.000 0.000
#> GSM329696 2 0.000 0.997 0.000 1.000 0.000
#> GSM329699 2 0.000 0.997 0.000 1.000 0.000
#> GSM329702 2 0.000 0.997 0.000 1.000 0.000
#> GSM329706 3 0.382 1.000 0.000 0.148 0.852
#> GSM329708 3 0.382 1.000 0.000 0.148 0.852
#> GSM329710 2 0.000 0.997 0.000 1.000 0.000
#> GSM329713 1 0.000 0.965 1.000 0.000 0.000
#> GSM329695 1 0.000 0.965 1.000 0.000 0.000
#> GSM329698 1 0.000 0.965 1.000 0.000 0.000
#> GSM329701 1 0.000 0.965 1.000 0.000 0.000
#> GSM329705 1 0.000 0.965 1.000 0.000 0.000
#> GSM329712 2 0.000 0.997 0.000 1.000 0.000
#> GSM329715 1 0.000 0.965 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.4193 0.133317 0.000 0.732 0.000 0.268
#> GSM329663 2 0.0000 0.603568 0.000 1.000 0.000 0.000
#> GSM329664 3 0.4893 0.873725 0.000 0.064 0.768 0.168
#> GSM329666 2 0.0000 0.603568 0.000 1.000 0.000 0.000
#> GSM329667 2 0.4877 0.000401 0.000 0.592 0.000 0.408
#> GSM329670 2 0.0000 0.603568 0.000 1.000 0.000 0.000
#> GSM329672 2 0.3569 0.319778 0.000 0.804 0.000 0.196
#> GSM329674 2 0.0000 0.603568 0.000 1.000 0.000 0.000
#> GSM329661 3 0.1902 0.935651 0.000 0.064 0.932 0.004
#> GSM329669 2 0.0000 0.603568 0.000 1.000 0.000 0.000
#> GSM329662 1 0.3801 0.888015 0.780 0.000 0.000 0.220
#> GSM329665 1 0.3123 0.909558 0.844 0.000 0.000 0.156
#> GSM329668 1 0.3123 0.909558 0.844 0.000 0.000 0.156
#> GSM329671 1 0.0927 0.909602 0.976 0.000 0.008 0.016
#> GSM329673 1 0.3311 0.905486 0.828 0.000 0.000 0.172
#> GSM329675 1 0.4608 0.854428 0.692 0.000 0.004 0.304
#> GSM329676 1 0.3123 0.909558 0.844 0.000 0.000 0.156
#> GSM329677 3 0.4614 0.885597 0.000 0.064 0.792 0.144
#> GSM329679 2 0.4008 0.150415 0.000 0.756 0.000 0.244
#> GSM329681 3 0.2300 0.933455 0.000 0.064 0.920 0.016
#> GSM329683 3 0.2048 0.935756 0.000 0.064 0.928 0.008
#> GSM329686 3 0.2048 0.935756 0.000 0.064 0.928 0.008
#> GSM329689 3 0.1716 0.935845 0.000 0.064 0.936 0.000
#> GSM329678 3 0.3885 0.886197 0.000 0.064 0.844 0.092
#> GSM329680 3 0.1716 0.935845 0.000 0.064 0.936 0.000
#> GSM329685 3 0.2048 0.935756 0.000 0.064 0.928 0.008
#> GSM329688 3 0.2048 0.935756 0.000 0.064 0.928 0.008
#> GSM329691 3 0.1716 0.935845 0.000 0.064 0.936 0.000
#> GSM329682 1 0.2773 0.914426 0.880 0.000 0.004 0.116
#> GSM329684 1 0.4608 0.854428 0.692 0.000 0.004 0.304
#> GSM329687 1 0.2773 0.914426 0.880 0.000 0.004 0.116
#> GSM329690 1 0.2021 0.899798 0.932 0.000 0.056 0.012
#> GSM329692 4 0.5292 0.935615 0.000 0.480 0.008 0.512
#> GSM329694 4 0.5000 0.978065 0.000 0.496 0.000 0.504
#> GSM329697 2 0.0000 0.603568 0.000 1.000 0.000 0.000
#> GSM329700 2 0.3356 0.417949 0.000 0.824 0.000 0.176
#> GSM329703 2 0.4999 -0.944417 0.000 0.508 0.000 0.492
#> GSM329704 3 0.6171 0.676077 0.000 0.064 0.588 0.348
#> GSM329707 3 0.4758 0.880031 0.000 0.064 0.780 0.156
#> GSM329709 2 0.0000 0.603568 0.000 1.000 0.000 0.000
#> GSM329711 2 0.3311 0.426217 0.000 0.828 0.000 0.172
#> GSM329714 2 0.4661 -0.324240 0.000 0.652 0.000 0.348
#> GSM329693 2 0.4999 -0.944417 0.000 0.508 0.000 0.492
#> GSM329696 2 0.4999 -0.944417 0.000 0.508 0.000 0.492
#> GSM329699 4 0.5000 0.978065 0.000 0.496 0.000 0.504
#> GSM329702 2 0.0000 0.603568 0.000 1.000 0.000 0.000
#> GSM329706 3 0.4758 0.880031 0.000 0.064 0.780 0.156
#> GSM329708 3 0.2413 0.932570 0.000 0.064 0.916 0.020
#> GSM329710 4 0.5000 0.978065 0.000 0.496 0.000 0.504
#> GSM329713 1 0.2021 0.899798 0.932 0.000 0.056 0.012
#> GSM329695 1 0.2021 0.899798 0.932 0.000 0.056 0.012
#> GSM329698 1 0.2021 0.899798 0.932 0.000 0.056 0.012
#> GSM329701 1 0.1174 0.907119 0.968 0.000 0.020 0.012
#> GSM329705 1 0.0188 0.911984 0.996 0.000 0.004 0.000
#> GSM329712 2 0.3311 0.426217 0.000 0.828 0.000 0.172
#> GSM329715 1 0.0188 0.911984 0.996 0.000 0.004 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 4 0.4822 0.3386 0.000 0.288 0.000 0.664 0.048
#> GSM329663 2 0.4589 0.8969 0.000 0.704 0.000 0.248 0.048
#> GSM329664 3 0.5407 0.1661 0.000 0.048 0.524 0.004 0.424
#> GSM329666 2 0.3480 0.9211 0.000 0.752 0.000 0.248 0.000
#> GSM329667 5 0.6535 0.1109 0.000 0.232 0.000 0.292 0.476
#> GSM329670 2 0.4378 0.9041 0.000 0.716 0.000 0.248 0.036
#> GSM329672 2 0.5692 0.3010 0.000 0.472 0.000 0.448 0.080
#> GSM329674 2 0.3480 0.9211 0.000 0.752 0.000 0.248 0.000
#> GSM329661 3 0.1704 0.8096 0.000 0.068 0.928 0.004 0.000
#> GSM329669 2 0.4167 0.9019 0.000 0.724 0.000 0.252 0.024
#> GSM329662 1 0.4384 0.7893 0.660 0.016 0.000 0.000 0.324
#> GSM329665 1 0.3508 0.8280 0.748 0.000 0.000 0.000 0.252
#> GSM329668 1 0.3508 0.8280 0.748 0.000 0.000 0.000 0.252
#> GSM329671 1 0.0854 0.8258 0.976 0.008 0.004 0.000 0.012
#> GSM329673 1 0.3928 0.8098 0.700 0.004 0.000 0.000 0.296
#> GSM329675 1 0.4965 0.7113 0.520 0.028 0.000 0.000 0.452
#> GSM329676 1 0.3508 0.8280 0.748 0.000 0.000 0.000 0.252
#> GSM329677 3 0.5191 0.5442 0.000 0.080 0.672 0.004 0.244
#> GSM329679 4 0.5816 -0.3421 0.000 0.440 0.000 0.468 0.092
#> GSM329681 3 0.0912 0.8093 0.000 0.000 0.972 0.012 0.016
#> GSM329683 3 0.0162 0.8188 0.000 0.000 0.996 0.004 0.000
#> GSM329686 3 0.0324 0.8196 0.000 0.000 0.992 0.004 0.004
#> GSM329689 3 0.1443 0.8160 0.000 0.044 0.948 0.004 0.004
#> GSM329678 3 0.4004 0.5913 0.000 0.004 0.784 0.172 0.040
#> GSM329680 3 0.1282 0.8161 0.000 0.044 0.952 0.004 0.000
#> GSM329685 3 0.0324 0.8196 0.000 0.000 0.992 0.004 0.004
#> GSM329688 3 0.0324 0.8196 0.000 0.000 0.992 0.004 0.004
#> GSM329691 3 0.1443 0.8160 0.000 0.044 0.948 0.004 0.004
#> GSM329682 1 0.3074 0.8366 0.804 0.000 0.000 0.000 0.196
#> GSM329684 1 0.4965 0.7113 0.520 0.028 0.000 0.000 0.452
#> GSM329687 1 0.3074 0.8366 0.804 0.000 0.000 0.000 0.196
#> GSM329690 1 0.2233 0.7966 0.892 0.104 0.004 0.000 0.000
#> GSM329692 4 0.2536 0.5975 0.000 0.004 0.044 0.900 0.052
#> GSM329694 4 0.1197 0.6698 0.000 0.000 0.000 0.952 0.048
#> GSM329697 2 0.3480 0.9211 0.000 0.752 0.000 0.248 0.000
#> GSM329700 4 0.5065 -0.0135 0.000 0.420 0.000 0.544 0.036
#> GSM329703 4 0.0510 0.6835 0.000 0.016 0.000 0.984 0.000
#> GSM329704 5 0.7013 -0.0357 0.000 0.048 0.364 0.124 0.464
#> GSM329707 3 0.5289 0.4348 0.000 0.060 0.620 0.004 0.316
#> GSM329709 2 0.3480 0.9211 0.000 0.752 0.000 0.248 0.000
#> GSM329711 4 0.5071 -0.0291 0.000 0.424 0.000 0.540 0.036
#> GSM329714 4 0.3622 0.5854 0.000 0.136 0.000 0.816 0.048
#> GSM329693 4 0.0510 0.6835 0.000 0.016 0.000 0.984 0.000
#> GSM329696 4 0.0510 0.6835 0.000 0.016 0.000 0.984 0.000
#> GSM329699 4 0.0510 0.6794 0.000 0.000 0.000 0.984 0.016
#> GSM329702 2 0.3480 0.9211 0.000 0.752 0.000 0.248 0.000
#> GSM329706 3 0.5523 0.4571 0.000 0.084 0.616 0.004 0.296
#> GSM329708 3 0.1074 0.8088 0.000 0.004 0.968 0.012 0.016
#> GSM329710 4 0.0963 0.6721 0.000 0.000 0.000 0.964 0.036
#> GSM329713 1 0.2127 0.7967 0.892 0.108 0.000 0.000 0.000
#> GSM329695 1 0.2127 0.7967 0.892 0.108 0.000 0.000 0.000
#> GSM329698 1 0.2074 0.7967 0.896 0.104 0.000 0.000 0.000
#> GSM329701 1 0.0880 0.8194 0.968 0.032 0.000 0.000 0.000
#> GSM329705 1 0.0609 0.8300 0.980 0.000 0.000 0.000 0.020
#> GSM329712 4 0.5071 -0.0291 0.000 0.424 0.000 0.540 0.036
#> GSM329715 1 0.0771 0.8299 0.976 0.004 0.000 0.000 0.020
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329660 4 0.6646 -0.148 0.000 0.376 0.000 0.400 0.052 NA
#> GSM329663 2 0.2697 0.745 0.000 0.864 0.000 0.000 0.044 NA
#> GSM329664 5 0.3668 0.580 0.000 0.000 0.328 0.004 0.668 NA
#> GSM329666 2 0.0000 0.764 0.000 1.000 0.000 0.000 0.000 NA
#> GSM329667 5 0.5685 0.310 0.000 0.192 0.000 0.112 0.636 NA
#> GSM329670 2 0.2129 0.750 0.000 0.904 0.000 0.000 0.040 NA
#> GSM329672 2 0.5461 0.532 0.000 0.672 0.000 0.156 0.080 NA
#> GSM329674 2 0.0000 0.764 0.000 1.000 0.000 0.000 0.000 NA
#> GSM329661 3 0.2921 0.756 0.000 0.000 0.828 0.008 0.008 NA
#> GSM329669 2 0.3394 0.713 0.000 0.832 0.000 0.028 0.036 NA
#> GSM329662 1 0.1913 0.745 0.908 0.000 0.000 0.000 0.012 NA
#> GSM329665 1 0.0000 0.785 1.000 0.000 0.000 0.000 0.000 NA
#> GSM329668 1 0.0000 0.785 1.000 0.000 0.000 0.000 0.000 NA
#> GSM329671 1 0.3265 0.785 0.748 0.000 0.000 0.004 0.000 NA
#> GSM329673 1 0.1297 0.765 0.948 0.000 0.000 0.000 0.012 NA
#> GSM329675 1 0.5298 0.598 0.644 0.000 0.000 0.020 0.212 NA
#> GSM329676 1 0.0000 0.785 1.000 0.000 0.000 0.000 0.000 NA
#> GSM329677 3 0.5128 -0.293 0.000 0.000 0.548 0.008 0.376 NA
#> GSM329679 2 0.6037 0.458 0.000 0.612 0.000 0.172 0.124 NA
#> GSM329681 3 0.2398 0.760 0.000 0.000 0.888 0.004 0.028 NA
#> GSM329683 3 0.0458 0.801 0.000 0.000 0.984 0.000 0.000 NA
#> GSM329686 3 0.0405 0.802 0.000 0.000 0.988 0.000 0.004 NA
#> GSM329689 3 0.1900 0.777 0.000 0.000 0.916 0.008 0.008 NA
#> GSM329678 3 0.5705 0.298 0.000 0.000 0.592 0.268 0.040 NA
#> GSM329680 3 0.2355 0.777 0.000 0.000 0.876 0.008 0.004 NA
#> GSM329685 3 0.0405 0.802 0.000 0.000 0.988 0.000 0.004 NA
#> GSM329688 3 0.0405 0.802 0.000 0.000 0.988 0.000 0.004 NA
#> GSM329691 3 0.1957 0.778 0.000 0.000 0.912 0.008 0.008 NA
#> GSM329682 1 0.2213 0.794 0.908 0.000 0.000 0.032 0.012 NA
#> GSM329684 1 0.5298 0.598 0.644 0.000 0.000 0.020 0.212 NA
#> GSM329687 1 0.2213 0.794 0.908 0.000 0.000 0.032 0.012 NA
#> GSM329690 1 0.3843 0.724 0.548 0.000 0.000 0.000 0.000 NA
#> GSM329692 4 0.3402 0.800 0.000 0.052 0.012 0.852 0.040 NA
#> GSM329694 4 0.3714 0.801 0.000 0.064 0.000 0.820 0.044 NA
#> GSM329697 2 0.0000 0.764 0.000 1.000 0.000 0.000 0.000 NA
#> GSM329700 2 0.6145 0.327 0.000 0.508 0.000 0.324 0.040 NA
#> GSM329703 4 0.1588 0.828 0.000 0.072 0.000 0.924 0.000 NA
#> GSM329704 5 0.5081 0.583 0.000 0.000 0.224 0.088 0.664 NA
#> GSM329707 5 0.5075 0.407 0.000 0.000 0.452 0.004 0.480 NA
#> GSM329709 2 0.0000 0.764 0.000 1.000 0.000 0.000 0.000 NA
#> GSM329711 2 0.6145 0.327 0.000 0.508 0.000 0.324 0.040 NA
#> GSM329714 4 0.5835 0.488 0.000 0.188 0.000 0.616 0.052 NA
#> GSM329693 4 0.1588 0.828 0.000 0.072 0.000 0.924 0.000 NA
#> GSM329696 4 0.1588 0.828 0.000 0.072 0.000 0.924 0.000 NA
#> GSM329699 4 0.2206 0.826 0.000 0.064 0.000 0.904 0.008 NA
#> GSM329702 2 0.0000 0.764 0.000 1.000 0.000 0.000 0.000 NA
#> GSM329706 5 0.5218 0.386 0.000 0.000 0.456 0.008 0.468 NA
#> GSM329708 3 0.2604 0.754 0.000 0.000 0.872 0.004 0.028 NA
#> GSM329710 4 0.2950 0.815 0.000 0.064 0.000 0.868 0.036 NA
#> GSM329713 1 0.3971 0.724 0.548 0.000 0.000 0.000 0.004 NA
#> GSM329695 1 0.3971 0.724 0.548 0.000 0.000 0.000 0.004 NA
#> GSM329698 1 0.3971 0.725 0.548 0.000 0.000 0.004 0.000 NA
#> GSM329701 1 0.3934 0.773 0.676 0.000 0.000 0.020 0.000 NA
#> GSM329705 1 0.4056 0.786 0.732 0.000 0.000 0.032 0.012 NA
#> GSM329712 2 0.6145 0.327 0.000 0.508 0.000 0.324 0.040 NA
#> GSM329715 1 0.4124 0.785 0.728 0.000 0.000 0.036 0.012 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> ATC:kmeans 56 5.06e-01 5.82e-11 2
#> ATC:kmeans 56 1.44e-03 3.53e-10 3
#> ATC:kmeans 45 2.72e-03 1.01e-07 4
#> ATC:kmeans 45 6.13e-06 6.01e-08 5
#> ATC:kmeans 45 1.02e-04 7.85e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21163 rows and 56 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 0.978 0.992 0.4373 0.569 0.569
#> 3 3 1.000 0.947 0.978 0.5466 0.755 0.569
#> 4 4 0.965 0.967 0.980 0.1059 0.921 0.759
#> 5 5 0.894 0.766 0.873 0.0435 0.984 0.939
#> 6 6 0.938 0.788 0.902 0.0359 0.933 0.733
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM329660 2 0.000 0.988 0.000 1.000
#> GSM329663 2 0.000 0.988 0.000 1.000
#> GSM329664 2 0.000 0.988 0.000 1.000
#> GSM329666 2 0.000 0.988 0.000 1.000
#> GSM329667 2 0.000 0.988 0.000 1.000
#> GSM329670 2 0.985 0.255 0.428 0.572
#> GSM329672 2 0.000 0.988 0.000 1.000
#> GSM329674 2 0.000 0.988 0.000 1.000
#> GSM329661 2 0.000 0.988 0.000 1.000
#> GSM329669 2 0.184 0.961 0.028 0.972
#> GSM329662 1 0.000 1.000 1.000 0.000
#> GSM329665 1 0.000 1.000 1.000 0.000
#> GSM329668 1 0.000 1.000 1.000 0.000
#> GSM329671 1 0.000 1.000 1.000 0.000
#> GSM329673 1 0.000 1.000 1.000 0.000
#> GSM329675 1 0.000 1.000 1.000 0.000
#> GSM329676 1 0.000 1.000 1.000 0.000
#> GSM329677 2 0.000 0.988 0.000 1.000
#> GSM329679 2 0.000 0.988 0.000 1.000
#> GSM329681 2 0.000 0.988 0.000 1.000
#> GSM329683 2 0.000 0.988 0.000 1.000
#> GSM329686 2 0.000 0.988 0.000 1.000
#> GSM329689 2 0.000 0.988 0.000 1.000
#> GSM329678 2 0.000 0.988 0.000 1.000
#> GSM329680 2 0.000 0.988 0.000 1.000
#> GSM329685 2 0.000 0.988 0.000 1.000
#> GSM329688 2 0.000 0.988 0.000 1.000
#> GSM329691 2 0.000 0.988 0.000 1.000
#> GSM329682 1 0.000 1.000 1.000 0.000
#> GSM329684 1 0.000 1.000 1.000 0.000
#> GSM329687 1 0.000 1.000 1.000 0.000
#> GSM329690 1 0.000 1.000 1.000 0.000
#> GSM329692 2 0.000 0.988 0.000 1.000
#> GSM329694 2 0.000 0.988 0.000 1.000
#> GSM329697 2 0.000 0.988 0.000 1.000
#> GSM329700 2 0.000 0.988 0.000 1.000
#> GSM329703 2 0.000 0.988 0.000 1.000
#> GSM329704 2 0.000 0.988 0.000 1.000
#> GSM329707 2 0.000 0.988 0.000 1.000
#> GSM329709 2 0.000 0.988 0.000 1.000
#> GSM329711 2 0.000 0.988 0.000 1.000
#> GSM329714 2 0.000 0.988 0.000 1.000
#> GSM329693 2 0.000 0.988 0.000 1.000
#> GSM329696 2 0.000 0.988 0.000 1.000
#> GSM329699 2 0.000 0.988 0.000 1.000
#> GSM329702 2 0.000 0.988 0.000 1.000
#> GSM329706 2 0.000 0.988 0.000 1.000
#> GSM329708 2 0.000 0.988 0.000 1.000
#> GSM329710 2 0.000 0.988 0.000 1.000
#> GSM329713 1 0.000 1.000 1.000 0.000
#> GSM329695 1 0.000 1.000 1.000 0.000
#> GSM329698 1 0.000 1.000 1.000 0.000
#> GSM329701 1 0.000 1.000 1.000 0.000
#> GSM329705 1 0.000 1.000 1.000 0.000
#> GSM329712 2 0.000 0.988 0.000 1.000
#> GSM329715 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.000 0.936 0 1.000 0.000
#> GSM329663 2 0.000 0.936 0 1.000 0.000
#> GSM329664 3 0.000 1.000 0 0.000 1.000
#> GSM329666 2 0.000 0.936 0 1.000 0.000
#> GSM329667 3 0.000 1.000 0 0.000 1.000
#> GSM329670 2 0.000 0.936 0 1.000 0.000
#> GSM329672 2 0.000 0.936 0 1.000 0.000
#> GSM329674 2 0.000 0.936 0 1.000 0.000
#> GSM329661 3 0.000 1.000 0 0.000 1.000
#> GSM329669 2 0.000 0.936 0 1.000 0.000
#> GSM329662 1 0.000 1.000 1 0.000 0.000
#> GSM329665 1 0.000 1.000 1 0.000 0.000
#> GSM329668 1 0.000 1.000 1 0.000 0.000
#> GSM329671 1 0.000 1.000 1 0.000 0.000
#> GSM329673 1 0.000 1.000 1 0.000 0.000
#> GSM329675 1 0.000 1.000 1 0.000 0.000
#> GSM329676 1 0.000 1.000 1 0.000 0.000
#> GSM329677 3 0.000 1.000 0 0.000 1.000
#> GSM329679 2 0.103 0.918 0 0.976 0.024
#> GSM329681 3 0.000 1.000 0 0.000 1.000
#> GSM329683 3 0.000 1.000 0 0.000 1.000
#> GSM329686 3 0.000 1.000 0 0.000 1.000
#> GSM329689 3 0.000 1.000 0 0.000 1.000
#> GSM329678 3 0.000 1.000 0 0.000 1.000
#> GSM329680 3 0.000 1.000 0 0.000 1.000
#> GSM329685 3 0.000 1.000 0 0.000 1.000
#> GSM329688 3 0.000 1.000 0 0.000 1.000
#> GSM329691 3 0.000 1.000 0 0.000 1.000
#> GSM329682 1 0.000 1.000 1 0.000 0.000
#> GSM329684 1 0.000 1.000 1 0.000 0.000
#> GSM329687 1 0.000 1.000 1 0.000 0.000
#> GSM329690 1 0.000 1.000 1 0.000 0.000
#> GSM329692 3 0.000 1.000 0 0.000 1.000
#> GSM329694 2 0.613 0.403 0 0.600 0.400
#> GSM329697 2 0.000 0.936 0 1.000 0.000
#> GSM329700 2 0.000 0.936 0 1.000 0.000
#> GSM329703 2 0.000 0.936 0 1.000 0.000
#> GSM329704 3 0.000 1.000 0 0.000 1.000
#> GSM329707 3 0.000 1.000 0 0.000 1.000
#> GSM329709 2 0.000 0.936 0 1.000 0.000
#> GSM329711 2 0.000 0.936 0 1.000 0.000
#> GSM329714 2 0.000 0.936 0 1.000 0.000
#> GSM329693 2 0.000 0.936 0 1.000 0.000
#> GSM329696 2 0.000 0.936 0 1.000 0.000
#> GSM329699 2 0.614 0.394 0 0.596 0.404
#> GSM329702 2 0.000 0.936 0 1.000 0.000
#> GSM329706 3 0.000 1.000 0 0.000 1.000
#> GSM329708 3 0.000 1.000 0 0.000 1.000
#> GSM329710 2 0.613 0.403 0 0.600 0.400
#> GSM329713 1 0.000 1.000 1 0.000 0.000
#> GSM329695 1 0.000 1.000 1 0.000 0.000
#> GSM329698 1 0.000 1.000 1 0.000 0.000
#> GSM329701 1 0.000 1.000 1 0.000 0.000
#> GSM329705 1 0.000 1.000 1 0.000 0.000
#> GSM329712 2 0.000 0.936 0 1.000 0.000
#> GSM329715 1 0.000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.4222 0.720 0 0.728 0.000 0.272
#> GSM329663 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM329664 3 0.0336 0.995 0 0.000 0.992 0.008
#> GSM329666 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM329667 3 0.0336 0.995 0 0.000 0.992 0.008
#> GSM329670 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM329672 2 0.3528 0.789 0 0.808 0.000 0.192
#> GSM329674 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM329661 3 0.0000 0.997 0 0.000 1.000 0.000
#> GSM329669 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329677 3 0.0336 0.995 0 0.000 0.992 0.008
#> GSM329679 2 0.3569 0.785 0 0.804 0.000 0.196
#> GSM329681 3 0.0000 0.997 0 0.000 1.000 0.000
#> GSM329683 3 0.0000 0.997 0 0.000 1.000 0.000
#> GSM329686 3 0.0000 0.997 0 0.000 1.000 0.000
#> GSM329689 3 0.0000 0.997 0 0.000 1.000 0.000
#> GSM329678 3 0.0000 0.997 0 0.000 1.000 0.000
#> GSM329680 3 0.0000 0.997 0 0.000 1.000 0.000
#> GSM329685 3 0.0000 0.997 0 0.000 1.000 0.000
#> GSM329688 3 0.0000 0.997 0 0.000 1.000 0.000
#> GSM329691 3 0.0000 0.997 0 0.000 1.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329692 4 0.0707 0.975 0 0.000 0.020 0.980
#> GSM329694 4 0.0336 0.996 0 0.008 0.000 0.992
#> GSM329697 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM329700 2 0.2647 0.867 0 0.880 0.000 0.120
#> GSM329703 4 0.0336 0.996 0 0.008 0.000 0.992
#> GSM329704 3 0.0336 0.995 0 0.000 0.992 0.008
#> GSM329707 3 0.0336 0.995 0 0.000 0.992 0.008
#> GSM329709 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM329711 2 0.2589 0.870 0 0.884 0.000 0.116
#> GSM329714 4 0.0336 0.996 0 0.008 0.000 0.992
#> GSM329693 4 0.0336 0.996 0 0.008 0.000 0.992
#> GSM329696 4 0.0336 0.996 0 0.008 0.000 0.992
#> GSM329699 4 0.0336 0.996 0 0.008 0.000 0.992
#> GSM329702 2 0.0000 0.918 0 1.000 0.000 0.000
#> GSM329706 3 0.0336 0.995 0 0.000 0.992 0.008
#> GSM329708 3 0.0000 0.997 0 0.000 1.000 0.000
#> GSM329710 4 0.0336 0.996 0 0.008 0.000 0.992
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329712 2 0.2647 0.868 0 0.880 0.000 0.120
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.5195 0.0344 0.000 0.676 0.000 0.108 0.216
#> GSM329663 2 0.4088 0.3135 0.000 0.632 0.000 0.000 0.368
#> GSM329664 3 0.0404 0.7673 0.000 0.000 0.988 0.000 0.012
#> GSM329666 2 0.4161 0.3031 0.000 0.608 0.000 0.000 0.392
#> GSM329667 3 0.3949 0.3151 0.000 0.000 0.668 0.000 0.332
#> GSM329670 2 0.4088 0.3135 0.000 0.632 0.000 0.000 0.368
#> GSM329672 5 0.4623 0.9500 0.000 0.304 0.000 0.032 0.664
#> GSM329674 2 0.4161 0.3031 0.000 0.608 0.000 0.000 0.392
#> GSM329661 3 0.3707 0.8827 0.000 0.000 0.716 0.000 0.284
#> GSM329669 2 0.0162 0.3306 0.000 0.996 0.000 0.000 0.004
#> GSM329662 1 0.0000 0.9983 1.000 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 0.9983 1.000 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 0.9983 1.000 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0162 0.9980 0.996 0.000 0.000 0.000 0.004
#> GSM329673 1 0.0000 0.9983 1.000 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 0.9983 1.000 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 0.9983 1.000 0.000 0.000 0.000 0.000
#> GSM329677 3 0.0000 0.7748 0.000 0.000 1.000 0.000 0.000
#> GSM329679 5 0.4883 0.9509 0.000 0.300 0.000 0.048 0.652
#> GSM329681 3 0.3707 0.8827 0.000 0.000 0.716 0.000 0.284
#> GSM329683 3 0.3707 0.8827 0.000 0.000 0.716 0.000 0.284
#> GSM329686 3 0.3707 0.8827 0.000 0.000 0.716 0.000 0.284
#> GSM329689 3 0.3707 0.8827 0.000 0.000 0.716 0.000 0.284
#> GSM329678 3 0.3730 0.8808 0.000 0.000 0.712 0.000 0.288
#> GSM329680 3 0.3707 0.8827 0.000 0.000 0.716 0.000 0.284
#> GSM329685 3 0.3707 0.8827 0.000 0.000 0.716 0.000 0.284
#> GSM329688 3 0.3707 0.8827 0.000 0.000 0.716 0.000 0.284
#> GSM329691 3 0.3707 0.8827 0.000 0.000 0.716 0.000 0.284
#> GSM329682 1 0.0000 0.9983 1.000 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0000 0.9983 1.000 0.000 0.000 0.000 0.000
#> GSM329687 1 0.0000 0.9983 1.000 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0162 0.9980 0.996 0.000 0.000 0.000 0.004
#> GSM329692 4 0.2171 0.8416 0.000 0.000 0.064 0.912 0.024
#> GSM329694 4 0.2690 0.8001 0.000 0.000 0.000 0.844 0.156
#> GSM329697 2 0.4161 0.3031 0.000 0.608 0.000 0.000 0.392
#> GSM329700 2 0.2389 0.3346 0.000 0.880 0.000 0.116 0.004
#> GSM329703 4 0.0000 0.8989 0.000 0.000 0.000 1.000 0.000
#> GSM329704 3 0.0404 0.7673 0.000 0.000 0.988 0.000 0.012
#> GSM329707 3 0.0000 0.7748 0.000 0.000 1.000 0.000 0.000
#> GSM329709 2 0.4161 0.3031 0.000 0.608 0.000 0.000 0.392
#> GSM329711 2 0.2389 0.3346 0.000 0.880 0.000 0.116 0.004
#> GSM329714 4 0.4425 0.4866 0.000 0.392 0.000 0.600 0.008
#> GSM329693 4 0.0000 0.8989 0.000 0.000 0.000 1.000 0.000
#> GSM329696 4 0.0000 0.8989 0.000 0.000 0.000 1.000 0.000
#> GSM329699 4 0.0000 0.8989 0.000 0.000 0.000 1.000 0.000
#> GSM329702 2 0.4161 0.3031 0.000 0.608 0.000 0.000 0.392
#> GSM329706 3 0.0000 0.7748 0.000 0.000 1.000 0.000 0.000
#> GSM329708 3 0.3730 0.8808 0.000 0.000 0.712 0.000 0.288
#> GSM329710 4 0.0703 0.8900 0.000 0.000 0.000 0.976 0.024
#> GSM329713 1 0.0162 0.9980 0.996 0.000 0.000 0.000 0.004
#> GSM329695 1 0.0162 0.9980 0.996 0.000 0.000 0.000 0.004
#> GSM329698 1 0.0162 0.9980 0.996 0.000 0.000 0.000 0.004
#> GSM329701 1 0.0162 0.9980 0.996 0.000 0.000 0.000 0.004
#> GSM329705 1 0.0162 0.9980 0.996 0.000 0.000 0.000 0.004
#> GSM329712 2 0.2280 0.3331 0.000 0.880 0.000 0.120 0.000
#> GSM329715 1 0.0162 0.9980 0.996 0.000 0.000 0.000 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329660 6 0.2318 0.887 0.000 0.048 0.000 0.020 0.028 0.904
#> GSM329663 2 0.1549 0.845 0.000 0.936 0.000 0.000 0.020 0.044
#> GSM329664 5 0.3817 0.536 0.000 0.000 0.432 0.000 0.568 0.000
#> GSM329666 2 0.0000 0.871 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329667 5 0.1738 0.409 0.000 0.016 0.052 0.004 0.928 0.000
#> GSM329670 2 0.1528 0.842 0.000 0.936 0.000 0.000 0.016 0.048
#> GSM329672 2 0.4659 0.554 0.000 0.556 0.000 0.012 0.408 0.024
#> GSM329674 2 0.0000 0.871 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329661 3 0.0146 0.824 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM329669 6 0.3266 0.712 0.000 0.272 0.000 0.000 0.000 0.728
#> GSM329662 1 0.0405 0.961 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM329665 1 0.0146 0.963 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM329668 1 0.0146 0.963 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM329671 1 0.1713 0.960 0.928 0.000 0.000 0.000 0.028 0.044
#> GSM329673 1 0.0146 0.963 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM329675 1 0.0405 0.961 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM329676 1 0.0146 0.963 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM329677 3 0.3851 -0.399 0.000 0.000 0.540 0.000 0.460 0.000
#> GSM329679 2 0.4683 0.540 0.000 0.540 0.000 0.012 0.424 0.024
#> GSM329681 3 0.0000 0.826 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329683 3 0.0000 0.826 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329686 3 0.0000 0.826 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329689 3 0.0146 0.824 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM329678 3 0.0146 0.822 0.000 0.000 0.996 0.004 0.000 0.000
#> GSM329680 3 0.0000 0.826 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329685 3 0.0000 0.826 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329688 3 0.0000 0.826 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329691 3 0.0000 0.826 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329682 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0405 0.961 0.988 0.000 0.000 0.000 0.008 0.004
#> GSM329687 1 0.0000 0.964 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329690 1 0.1856 0.957 0.920 0.000 0.000 0.000 0.032 0.048
#> GSM329692 4 0.0547 0.898 0.000 0.000 0.020 0.980 0.000 0.000
#> GSM329694 4 0.3320 0.727 0.000 0.000 0.000 0.772 0.212 0.016
#> GSM329697 2 0.0000 0.871 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329700 6 0.2412 0.914 0.000 0.092 0.000 0.028 0.000 0.880
#> GSM329703 4 0.1610 0.919 0.000 0.000 0.000 0.916 0.000 0.084
#> GSM329704 5 0.3810 0.543 0.000 0.000 0.428 0.000 0.572 0.000
#> GSM329707 3 0.3857 -0.422 0.000 0.000 0.532 0.000 0.468 0.000
#> GSM329709 2 0.0000 0.871 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329711 6 0.2383 0.915 0.000 0.096 0.000 0.024 0.000 0.880
#> GSM329714 6 0.2019 0.831 0.000 0.000 0.000 0.088 0.012 0.900
#> GSM329693 4 0.1556 0.921 0.000 0.000 0.000 0.920 0.000 0.080
#> GSM329696 4 0.1444 0.923 0.000 0.000 0.000 0.928 0.000 0.072
#> GSM329699 4 0.1444 0.923 0.000 0.000 0.000 0.928 0.000 0.072
#> GSM329702 2 0.0000 0.871 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329706 3 0.3868 -0.505 0.000 0.000 0.504 0.000 0.496 0.000
#> GSM329708 3 0.0000 0.826 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329710 4 0.0146 0.906 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM329713 1 0.1856 0.957 0.920 0.000 0.000 0.000 0.032 0.048
#> GSM329695 1 0.1856 0.957 0.920 0.000 0.000 0.000 0.032 0.048
#> GSM329698 1 0.1856 0.957 0.920 0.000 0.000 0.000 0.032 0.048
#> GSM329701 1 0.1789 0.959 0.924 0.000 0.000 0.000 0.032 0.044
#> GSM329705 1 0.1644 0.960 0.932 0.000 0.000 0.000 0.028 0.040
#> GSM329712 6 0.2383 0.915 0.000 0.096 0.000 0.024 0.000 0.880
#> GSM329715 1 0.1713 0.960 0.928 0.000 0.000 0.000 0.028 0.044
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> ATC:skmeans 55 0.415982 9.18e-11 2
#> ATC:skmeans 53 0.016952 1.59e-09 3
#> ATC:skmeans 56 0.000457 1.41e-09 4
#> ATC:skmeans 42 0.003021 2.24e-07 5
#> ATC:skmeans 52 0.000237 1.45e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21163 rows and 56 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 1.000 1.000 1.000 0.4311 0.569 0.569
#> 3 3 1.000 1.000 1.000 0.5417 0.766 0.590
#> 4 4 0.888 0.831 0.923 0.1381 0.909 0.729
#> 5 5 0.829 0.798 0.885 0.0467 0.946 0.788
#> 6 6 0.920 0.807 0.919 0.0482 0.961 0.815
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
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM329660 2 0 1 0 1
#> GSM329663 2 0 1 0 1
#> GSM329664 2 0 1 0 1
#> GSM329666 2 0 1 0 1
#> GSM329667 2 0 1 0 1
#> GSM329670 2 0 1 0 1
#> GSM329672 2 0 1 0 1
#> GSM329674 2 0 1 0 1
#> GSM329661 2 0 1 0 1
#> GSM329669 2 0 1 0 1
#> GSM329662 1 0 1 1 0
#> GSM329665 1 0 1 1 0
#> GSM329668 1 0 1 1 0
#> GSM329671 1 0 1 1 0
#> GSM329673 1 0 1 1 0
#> GSM329675 1 0 1 1 0
#> GSM329676 1 0 1 1 0
#> GSM329677 2 0 1 0 1
#> GSM329679 2 0 1 0 1
#> GSM329681 2 0 1 0 1
#> GSM329683 2 0 1 0 1
#> GSM329686 2 0 1 0 1
#> GSM329689 2 0 1 0 1
#> GSM329678 2 0 1 0 1
#> GSM329680 2 0 1 0 1
#> GSM329685 2 0 1 0 1
#> GSM329688 2 0 1 0 1
#> GSM329691 2 0 1 0 1
#> GSM329682 1 0 1 1 0
#> GSM329684 1 0 1 1 0
#> GSM329687 1 0 1 1 0
#> GSM329690 1 0 1 1 0
#> GSM329692 2 0 1 0 1
#> GSM329694 2 0 1 0 1
#> GSM329697 2 0 1 0 1
#> GSM329700 2 0 1 0 1
#> GSM329703 2 0 1 0 1
#> GSM329704 2 0 1 0 1
#> GSM329707 2 0 1 0 1
#> GSM329709 2 0 1 0 1
#> GSM329711 2 0 1 0 1
#> GSM329714 2 0 1 0 1
#> GSM329693 2 0 1 0 1
#> GSM329696 2 0 1 0 1
#> GSM329699 2 0 1 0 1
#> GSM329702 2 0 1 0 1
#> GSM329706 2 0 1 0 1
#> GSM329708 2 0 1 0 1
#> GSM329710 2 0 1 0 1
#> GSM329713 1 0 1 1 0
#> GSM329695 1 0 1 1 0
#> GSM329698 1 0 1 1 0
#> GSM329701 1 0 1 1 0
#> GSM329705 1 0 1 1 0
#> GSM329712 2 0 1 0 1
#> GSM329715 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0 1 0 1 0
#> GSM329663 2 0 1 0 1 0
#> GSM329664 3 0 1 0 0 1
#> GSM329666 2 0 1 0 1 0
#> GSM329667 2 0 1 0 1 0
#> GSM329670 2 0 1 0 1 0
#> GSM329672 2 0 1 0 1 0
#> GSM329674 2 0 1 0 1 0
#> GSM329661 3 0 1 0 0 1
#> GSM329669 2 0 1 0 1 0
#> GSM329662 1 0 1 1 0 0
#> GSM329665 1 0 1 1 0 0
#> GSM329668 1 0 1 1 0 0
#> GSM329671 1 0 1 1 0 0
#> GSM329673 1 0 1 1 0 0
#> GSM329675 1 0 1 1 0 0
#> GSM329676 1 0 1 1 0 0
#> GSM329677 3 0 1 0 0 1
#> GSM329679 2 0 1 0 1 0
#> GSM329681 3 0 1 0 0 1
#> GSM329683 3 0 1 0 0 1
#> GSM329686 3 0 1 0 0 1
#> GSM329689 3 0 1 0 0 1
#> GSM329678 3 0 1 0 0 1
#> GSM329680 3 0 1 0 0 1
#> GSM329685 3 0 1 0 0 1
#> GSM329688 3 0 1 0 0 1
#> GSM329691 3 0 1 0 0 1
#> GSM329682 1 0 1 1 0 0
#> GSM329684 1 0 1 1 0 0
#> GSM329687 1 0 1 1 0 0
#> GSM329690 1 0 1 1 0 0
#> GSM329692 2 0 1 0 1 0
#> GSM329694 2 0 1 0 1 0
#> GSM329697 2 0 1 0 1 0
#> GSM329700 2 0 1 0 1 0
#> GSM329703 2 0 1 0 1 0
#> GSM329704 2 0 1 0 1 0
#> GSM329707 3 0 1 0 0 1
#> GSM329709 2 0 1 0 1 0
#> GSM329711 2 0 1 0 1 0
#> GSM329714 2 0 1 0 1 0
#> GSM329693 2 0 1 0 1 0
#> GSM329696 2 0 1 0 1 0
#> GSM329699 2 0 1 0 1 0
#> GSM329702 2 0 1 0 1 0
#> GSM329706 3 0 1 0 0 1
#> GSM329708 3 0 1 0 0 1
#> GSM329710 2 0 1 0 1 0
#> GSM329713 1 0 1 1 0 0
#> GSM329695 1 0 1 1 0 0
#> GSM329698 1 0 1 1 0 0
#> GSM329701 1 0 1 1 0 0
#> GSM329705 1 0 1 1 0 0
#> GSM329712 2 0 1 0 1 0
#> GSM329715 1 0 1 1 0 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.3907 0.678 0 0.768 0.000 0.232
#> GSM329663 2 0.0336 0.779 0 0.992 0.000 0.008
#> GSM329664 3 0.0000 0.964 0 0.000 1.000 0.000
#> GSM329666 2 0.0336 0.779 0 0.992 0.000 0.008
#> GSM329667 2 0.0817 0.776 0 0.976 0.000 0.024
#> GSM329670 4 0.4989 0.411 0 0.472 0.000 0.528
#> GSM329672 2 0.0188 0.780 0 0.996 0.000 0.004
#> GSM329674 4 0.4989 0.411 0 0.472 0.000 0.528
#> GSM329661 3 0.0000 0.964 0 0.000 1.000 0.000
#> GSM329669 4 0.4989 0.411 0 0.472 0.000 0.528
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329677 3 0.0000 0.964 0 0.000 1.000 0.000
#> GSM329679 2 0.0188 0.780 0 0.996 0.000 0.004
#> GSM329681 3 0.0000 0.964 0 0.000 1.000 0.000
#> GSM329683 3 0.0000 0.964 0 0.000 1.000 0.000
#> GSM329686 3 0.0000 0.964 0 0.000 1.000 0.000
#> GSM329689 3 0.0000 0.964 0 0.000 1.000 0.000
#> GSM329678 3 0.5288 0.161 0 0.008 0.520 0.472
#> GSM329680 3 0.0000 0.964 0 0.000 1.000 0.000
#> GSM329685 3 0.0000 0.964 0 0.000 1.000 0.000
#> GSM329688 3 0.0000 0.964 0 0.000 1.000 0.000
#> GSM329691 3 0.0000 0.964 0 0.000 1.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329692 2 0.4989 0.381 0 0.528 0.000 0.472
#> GSM329694 2 0.3942 0.668 0 0.764 0.000 0.236
#> GSM329697 2 0.0336 0.779 0 0.992 0.000 0.008
#> GSM329700 4 0.1792 0.770 0 0.068 0.000 0.932
#> GSM329703 4 0.0000 0.752 0 0.000 0.000 1.000
#> GSM329704 2 0.4964 0.641 0 0.764 0.168 0.068
#> GSM329707 3 0.0000 0.964 0 0.000 1.000 0.000
#> GSM329709 2 0.0336 0.779 0 0.992 0.000 0.008
#> GSM329711 4 0.1792 0.770 0 0.068 0.000 0.932
#> GSM329714 4 0.2081 0.733 0 0.084 0.000 0.916
#> GSM329693 4 0.0000 0.752 0 0.000 0.000 1.000
#> GSM329696 4 0.0336 0.747 0 0.008 0.000 0.992
#> GSM329699 2 0.4989 0.381 0 0.528 0.000 0.472
#> GSM329702 2 0.0336 0.779 0 0.992 0.000 0.008
#> GSM329706 3 0.0000 0.964 0 0.000 1.000 0.000
#> GSM329708 3 0.0000 0.964 0 0.000 1.000 0.000
#> GSM329710 2 0.4989 0.381 0 0.528 0.000 0.472
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329712 4 0.1792 0.770 0 0.068 0.000 0.932
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.4866 0.248 0.000 0.580 0.000 0.028 0.392
#> GSM329663 2 0.0162 0.796 0.000 0.996 0.000 0.000 0.004
#> GSM329664 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> GSM329666 2 0.1121 0.792 0.000 0.956 0.000 0.000 0.044
#> GSM329667 2 0.0703 0.786 0.000 0.976 0.000 0.024 0.000
#> GSM329670 5 0.4306 0.300 0.000 0.492 0.000 0.000 0.508
#> GSM329672 2 0.0162 0.796 0.000 0.996 0.000 0.004 0.000
#> GSM329674 5 0.4306 0.300 0.000 0.492 0.000 0.000 0.508
#> GSM329661 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> GSM329669 5 0.2179 0.716 0.000 0.112 0.000 0.000 0.888
#> GSM329662 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000
#> GSM329673 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000
#> GSM329677 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> GSM329679 2 0.0162 0.796 0.000 0.996 0.000 0.004 0.000
#> GSM329681 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> GSM329683 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> GSM329686 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> GSM329689 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> GSM329678 4 0.5001 0.639 0.000 0.004 0.216 0.700 0.080
#> GSM329680 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> GSM329685 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> GSM329688 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> GSM329691 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> GSM329682 1 0.2230 0.881 0.884 0.000 0.000 0.116 0.000
#> GSM329684 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000
#> GSM329687 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000
#> GSM329690 1 0.4428 0.799 0.700 0.000 0.000 0.268 0.032
#> GSM329692 4 0.4660 0.780 0.000 0.192 0.000 0.728 0.080
#> GSM329694 2 0.4464 0.122 0.000 0.584 0.000 0.408 0.008
#> GSM329697 2 0.1121 0.792 0.000 0.956 0.000 0.000 0.044
#> GSM329700 5 0.1750 0.718 0.000 0.028 0.000 0.036 0.936
#> GSM329703 4 0.3636 0.756 0.000 0.000 0.000 0.728 0.272
#> GSM329704 2 0.4920 0.359 0.000 0.584 0.384 0.032 0.000
#> GSM329707 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> GSM329709 2 0.1121 0.792 0.000 0.956 0.000 0.000 0.044
#> GSM329711 5 0.0955 0.729 0.000 0.028 0.000 0.004 0.968
#> GSM329714 5 0.2221 0.693 0.000 0.052 0.000 0.036 0.912
#> GSM329693 4 0.3636 0.756 0.000 0.000 0.000 0.728 0.272
#> GSM329696 4 0.3741 0.760 0.000 0.004 0.000 0.732 0.264
#> GSM329699 4 0.4627 0.783 0.000 0.188 0.000 0.732 0.080
#> GSM329702 2 0.1121 0.792 0.000 0.956 0.000 0.000 0.044
#> GSM329706 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000
#> GSM329708 3 0.3586 0.597 0.000 0.000 0.736 0.264 0.000
#> GSM329710 4 0.4627 0.783 0.000 0.188 0.000 0.732 0.080
#> GSM329713 1 0.4428 0.799 0.700 0.000 0.000 0.268 0.032
#> GSM329695 1 0.4428 0.799 0.700 0.000 0.000 0.268 0.032
#> GSM329698 1 0.4428 0.799 0.700 0.000 0.000 0.268 0.032
#> GSM329701 1 0.3852 0.830 0.760 0.000 0.000 0.220 0.020
#> GSM329705 1 0.0000 0.909 1.000 0.000 0.000 0.000 0.000
#> GSM329712 5 0.1918 0.717 0.000 0.036 0.000 0.036 0.928
#> GSM329715 1 0.2230 0.881 0.884 0.000 0.000 0.116 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM329660 2 0.3930 0.193 0.000 0.576 0.000 0.004 0.000 0.420
#> GSM329663 2 0.0000 0.779 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329664 3 0.0146 0.973 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM329666 2 0.1444 0.769 0.000 0.928 0.000 0.000 0.000 0.072
#> GSM329667 2 0.0508 0.778 0.000 0.984 0.000 0.012 0.000 0.004
#> GSM329670 6 0.3804 0.337 0.000 0.424 0.000 0.000 0.000 0.576
#> GSM329672 2 0.0363 0.780 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM329674 6 0.3810 0.330 0.000 0.428 0.000 0.000 0.000 0.572
#> GSM329661 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329669 6 0.0146 0.755 0.000 0.004 0.000 0.000 0.000 0.996
#> GSM329662 1 0.0000 0.901 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 0.901 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 0.901 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0000 0.901 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329673 1 0.0000 0.901 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0865 0.877 0.964 0.000 0.000 0.000 0.036 0.000
#> GSM329676 1 0.0000 0.901 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329677 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329679 2 0.0363 0.780 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM329681 3 0.0146 0.973 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM329683 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329686 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329689 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329678 4 0.1010 0.943 0.000 0.000 0.036 0.960 0.000 0.004
#> GSM329680 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329685 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329688 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329691 3 0.0000 0.974 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329682 1 0.3823 0.185 0.564 0.000 0.000 0.000 0.436 0.000
#> GSM329684 1 0.0865 0.877 0.964 0.000 0.000 0.000 0.036 0.000
#> GSM329687 1 0.0000 0.901 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329690 5 0.0865 0.951 0.036 0.000 0.000 0.000 0.964 0.000
#> GSM329692 4 0.0146 0.983 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM329694 2 0.3804 0.235 0.000 0.576 0.000 0.424 0.000 0.000
#> GSM329697 2 0.1444 0.769 0.000 0.928 0.000 0.000 0.000 0.072
#> GSM329700 6 0.1141 0.754 0.000 0.000 0.000 0.052 0.000 0.948
#> GSM329703 4 0.0363 0.979 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM329704 2 0.4234 0.290 0.000 0.576 0.408 0.012 0.000 0.004
#> GSM329707 3 0.0146 0.973 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM329709 2 0.1444 0.769 0.000 0.928 0.000 0.000 0.000 0.072
#> GSM329711 6 0.0458 0.759 0.000 0.000 0.000 0.016 0.000 0.984
#> GSM329714 6 0.3925 0.590 0.000 0.056 0.000 0.200 0.000 0.744
#> GSM329693 4 0.0363 0.979 0.000 0.000 0.000 0.988 0.000 0.012
#> GSM329696 4 0.0000 0.985 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329699 4 0.0000 0.985 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329702 2 0.1444 0.769 0.000 0.928 0.000 0.000 0.000 0.072
#> GSM329706 3 0.0146 0.973 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM329708 3 0.3351 0.572 0.000 0.000 0.712 0.288 0.000 0.000
#> GSM329710 4 0.0000 0.985 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329713 5 0.0865 0.951 0.036 0.000 0.000 0.000 0.964 0.000
#> GSM329695 5 0.0865 0.951 0.036 0.000 0.000 0.000 0.964 0.000
#> GSM329698 5 0.0865 0.951 0.036 0.000 0.000 0.000 0.964 0.000
#> GSM329701 5 0.2697 0.782 0.188 0.000 0.000 0.000 0.812 0.000
#> GSM329705 1 0.0000 0.901 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329712 6 0.1765 0.746 0.000 0.024 0.000 0.052 0.000 0.924
#> GSM329715 1 0.3823 0.185 0.564 0.000 0.000 0.000 0.436 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> ATC:pam 56 0.505684 5.82e-11 2
#> ATC:pam 56 0.000515 2.02e-10 3
#> ATC:pam 49 0.001220 1.01e-08 4
#> ATC:pam 51 0.008034 1.46e-08 5
#> ATC:pam 49 0.000498 2.14e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "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 21163 rows and 56 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4311 0.569 0.569
#> 3 3 0.811 0.963 0.964 0.5352 0.761 0.580
#> 4 4 0.970 0.926 0.969 0.1247 0.894 0.692
#> 5 5 1.000 0.965 0.983 0.0674 0.892 0.618
#> 6 6 0.888 0.939 0.947 0.0270 0.971 0.860
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 4
There is also optional best \(k\) = 2 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM329660 2 0 1 0 1
#> GSM329663 2 0 1 0 1
#> GSM329664 2 0 1 0 1
#> GSM329666 2 0 1 0 1
#> GSM329667 2 0 1 0 1
#> GSM329670 2 0 1 0 1
#> GSM329672 2 0 1 0 1
#> GSM329674 2 0 1 0 1
#> GSM329661 2 0 1 0 1
#> GSM329669 2 0 1 0 1
#> GSM329662 1 0 1 1 0
#> GSM329665 1 0 1 1 0
#> GSM329668 1 0 1 1 0
#> GSM329671 1 0 1 1 0
#> GSM329673 1 0 1 1 0
#> GSM329675 1 0 1 1 0
#> GSM329676 1 0 1 1 0
#> GSM329677 2 0 1 0 1
#> GSM329679 2 0 1 0 1
#> GSM329681 2 0 1 0 1
#> GSM329683 2 0 1 0 1
#> GSM329686 2 0 1 0 1
#> GSM329689 2 0 1 0 1
#> GSM329678 2 0 1 0 1
#> GSM329680 2 0 1 0 1
#> GSM329685 2 0 1 0 1
#> GSM329688 2 0 1 0 1
#> GSM329691 2 0 1 0 1
#> GSM329682 1 0 1 1 0
#> GSM329684 1 0 1 1 0
#> GSM329687 1 0 1 1 0
#> GSM329690 1 0 1 1 0
#> GSM329692 2 0 1 0 1
#> GSM329694 2 0 1 0 1
#> GSM329697 2 0 1 0 1
#> GSM329700 2 0 1 0 1
#> GSM329703 2 0 1 0 1
#> GSM329704 2 0 1 0 1
#> GSM329707 2 0 1 0 1
#> GSM329709 2 0 1 0 1
#> GSM329711 2 0 1 0 1
#> GSM329714 2 0 1 0 1
#> GSM329693 2 0 1 0 1
#> GSM329696 2 0 1 0 1
#> GSM329699 2 0 1 0 1
#> GSM329702 2 0 1 0 1
#> GSM329706 2 0 1 0 1
#> GSM329708 2 0 1 0 1
#> GSM329710 2 0 1 0 1
#> GSM329713 1 0 1 1 0
#> GSM329695 1 0 1 1 0
#> GSM329698 1 0 1 1 0
#> GSM329701 1 0 1 1 0
#> GSM329705 1 0 1 1 0
#> GSM329712 2 0 1 0 1
#> GSM329715 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.3116 0.940 0 0.892 0.108
#> GSM329663 2 0.2066 0.937 0 0.940 0.060
#> GSM329664 3 0.1289 0.961 0 0.032 0.968
#> GSM329666 2 0.0000 0.917 0 1.000 0.000
#> GSM329667 2 0.3879 0.910 0 0.848 0.152
#> GSM329670 2 0.0000 0.917 0 1.000 0.000
#> GSM329672 2 0.3116 0.940 0 0.892 0.108
#> GSM329674 2 0.0000 0.917 0 1.000 0.000
#> GSM329661 3 0.0237 0.984 0 0.004 0.996
#> GSM329669 2 0.1031 0.927 0 0.976 0.024
#> GSM329662 1 0.0000 1.000 1 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000
#> GSM329677 3 0.0424 0.983 0 0.008 0.992
#> GSM329679 2 0.3116 0.940 0 0.892 0.108
#> GSM329681 3 0.0000 0.985 0 0.000 1.000
#> GSM329683 3 0.0000 0.985 0 0.000 1.000
#> GSM329686 3 0.0000 0.985 0 0.000 1.000
#> GSM329689 3 0.0424 0.983 0 0.008 0.992
#> GSM329678 3 0.0000 0.985 0 0.000 1.000
#> GSM329680 3 0.0000 0.985 0 0.000 1.000
#> GSM329685 3 0.0000 0.985 0 0.000 1.000
#> GSM329688 3 0.0000 0.985 0 0.000 1.000
#> GSM329691 3 0.0000 0.985 0 0.000 1.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000
#> GSM329692 2 0.3686 0.932 0 0.860 0.140
#> GSM329694 2 0.3551 0.934 0 0.868 0.132
#> GSM329697 2 0.0000 0.917 0 1.000 0.000
#> GSM329700 2 0.1529 0.933 0 0.960 0.040
#> GSM329703 2 0.3686 0.932 0 0.860 0.140
#> GSM329704 3 0.3686 0.835 0 0.140 0.860
#> GSM329707 3 0.0424 0.983 0 0.008 0.992
#> GSM329709 2 0.0000 0.917 0 1.000 0.000
#> GSM329711 2 0.1529 0.933 0 0.960 0.040
#> GSM329714 2 0.3267 0.939 0 0.884 0.116
#> GSM329693 2 0.3686 0.932 0 0.860 0.140
#> GSM329696 2 0.3686 0.932 0 0.860 0.140
#> GSM329699 2 0.3686 0.932 0 0.860 0.140
#> GSM329702 2 0.0000 0.917 0 1.000 0.000
#> GSM329706 3 0.0424 0.983 0 0.008 0.992
#> GSM329708 3 0.0000 0.985 0 0.000 1.000
#> GSM329710 2 0.3686 0.932 0 0.860 0.140
#> GSM329713 1 0.0000 1.000 1 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000
#> GSM329712 2 0.3038 0.940 0 0.896 0.104
#> GSM329715 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.0592 0.932 0 0.984 0.000 0.016
#> GSM329663 2 0.0592 0.932 0 0.984 0.000 0.016
#> GSM329664 3 0.0707 0.983 0 0.020 0.980 0.000
#> GSM329666 2 0.0000 0.935 0 1.000 0.000 0.000
#> GSM329667 2 0.0000 0.935 0 1.000 0.000 0.000
#> GSM329670 2 0.0592 0.932 0 0.984 0.000 0.016
#> GSM329672 2 0.0000 0.935 0 1.000 0.000 0.000
#> GSM329674 2 0.0000 0.935 0 1.000 0.000 0.000
#> GSM329661 3 0.0000 0.994 0 0.000 1.000 0.000
#> GSM329669 2 0.0592 0.932 0 0.984 0.000 0.016
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329677 3 0.0592 0.986 0 0.016 0.984 0.000
#> GSM329679 2 0.0000 0.935 0 1.000 0.000 0.000
#> GSM329681 3 0.0000 0.994 0 0.000 1.000 0.000
#> GSM329683 3 0.0000 0.994 0 0.000 1.000 0.000
#> GSM329686 3 0.0000 0.994 0 0.000 1.000 0.000
#> GSM329689 3 0.0000 0.994 0 0.000 1.000 0.000
#> GSM329678 4 0.0592 0.864 0 0.000 0.016 0.984
#> GSM329680 3 0.0000 0.994 0 0.000 1.000 0.000
#> GSM329685 3 0.0000 0.994 0 0.000 1.000 0.000
#> GSM329688 3 0.0000 0.994 0 0.000 1.000 0.000
#> GSM329691 3 0.0000 0.994 0 0.000 1.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329692 4 0.0000 0.875 0 0.000 0.000 1.000
#> GSM329694 2 0.4431 0.552 0 0.696 0.000 0.304
#> GSM329697 2 0.0000 0.935 0 1.000 0.000 0.000
#> GSM329700 2 0.4564 0.499 0 0.672 0.000 0.328
#> GSM329703 4 0.0000 0.875 0 0.000 0.000 1.000
#> GSM329704 2 0.0707 0.921 0 0.980 0.020 0.000
#> GSM329707 3 0.0592 0.986 0 0.016 0.984 0.000
#> GSM329709 2 0.0000 0.935 0 1.000 0.000 0.000
#> GSM329711 2 0.2921 0.815 0 0.860 0.000 0.140
#> GSM329714 4 0.4776 0.397 0 0.376 0.000 0.624
#> GSM329693 4 0.0000 0.875 0 0.000 0.000 1.000
#> GSM329696 4 0.0000 0.875 0 0.000 0.000 1.000
#> GSM329699 4 0.4730 0.426 0 0.364 0.000 0.636
#> GSM329702 2 0.0000 0.935 0 1.000 0.000 0.000
#> GSM329706 3 0.0592 0.986 0 0.016 0.984 0.000
#> GSM329708 3 0.0000 0.994 0 0.000 1.000 0.000
#> GSM329710 4 0.0000 0.875 0 0.000 0.000 1.000
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000
#> GSM329712 2 0.1118 0.920 0 0.964 0.000 0.036
#> GSM329715 1 0.0000 1.000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 2 0.0000 0.999 0 1.000 0.000 0.000 0.000
#> GSM329663 2 0.0000 0.999 0 1.000 0.000 0.000 0.000
#> GSM329664 5 0.0000 0.970 0 0.000 0.000 0.000 1.000
#> GSM329666 2 0.0000 0.999 0 1.000 0.000 0.000 0.000
#> GSM329667 5 0.0000 0.970 0 0.000 0.000 0.000 1.000
#> GSM329670 2 0.0000 0.999 0 1.000 0.000 0.000 0.000
#> GSM329672 2 0.0000 0.999 0 1.000 0.000 0.000 0.000
#> GSM329674 2 0.0000 0.999 0 1.000 0.000 0.000 0.000
#> GSM329661 3 0.3774 0.559 0 0.000 0.704 0.000 0.296
#> GSM329669 2 0.0000 0.999 0 1.000 0.000 0.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329677 5 0.1197 0.969 0 0.000 0.048 0.000 0.952
#> GSM329679 2 0.0404 0.987 0 0.988 0.000 0.000 0.012
#> GSM329681 3 0.0000 0.966 0 0.000 1.000 0.000 0.000
#> GSM329683 3 0.0000 0.966 0 0.000 1.000 0.000 0.000
#> GSM329686 3 0.0404 0.959 0 0.000 0.988 0.012 0.000
#> GSM329689 3 0.0000 0.966 0 0.000 1.000 0.000 0.000
#> GSM329678 3 0.0404 0.959 0 0.000 0.988 0.012 0.000
#> GSM329680 3 0.0000 0.966 0 0.000 1.000 0.000 0.000
#> GSM329685 3 0.0162 0.964 0 0.000 0.996 0.004 0.000
#> GSM329688 3 0.0000 0.966 0 0.000 1.000 0.000 0.000
#> GSM329691 3 0.0000 0.966 0 0.000 1.000 0.000 0.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329692 4 0.0000 0.945 0 0.000 0.000 1.000 0.000
#> GSM329694 4 0.0404 0.944 0 0.000 0.000 0.988 0.012
#> GSM329697 2 0.0000 0.999 0 1.000 0.000 0.000 0.000
#> GSM329700 4 0.1732 0.906 0 0.080 0.000 0.920 0.000
#> GSM329703 4 0.0000 0.945 0 0.000 0.000 1.000 0.000
#> GSM329704 5 0.0000 0.970 0 0.000 0.000 0.000 1.000
#> GSM329707 5 0.1197 0.969 0 0.000 0.048 0.000 0.952
#> GSM329709 2 0.0000 0.999 0 1.000 0.000 0.000 0.000
#> GSM329711 4 0.2179 0.880 0 0.112 0.000 0.888 0.000
#> GSM329714 4 0.0794 0.937 0 0.028 0.000 0.972 0.000
#> GSM329693 4 0.0162 0.945 0 0.000 0.000 0.996 0.004
#> GSM329696 4 0.0000 0.945 0 0.000 0.000 1.000 0.000
#> GSM329699 4 0.0404 0.944 0 0.000 0.000 0.988 0.012
#> GSM329702 2 0.0000 0.999 0 1.000 0.000 0.000 0.000
#> GSM329706 5 0.1197 0.969 0 0.000 0.048 0.000 0.952
#> GSM329708 3 0.0000 0.966 0 0.000 1.000 0.000 0.000
#> GSM329710 4 0.0000 0.945 0 0.000 0.000 1.000 0.000
#> GSM329713 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000 0.000 0.000
#> GSM329712 4 0.3480 0.715 0 0.248 0.000 0.752 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 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
#> GSM329660 6 0.404 0.865 0.000 0.180 0.000 0.076 0.000 0.744
#> GSM329663 2 0.000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329664 5 0.000 0.903 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM329666 2 0.000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329667 5 0.144 0.860 0.000 0.072 0.000 0.000 0.928 0.000
#> GSM329670 2 0.000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329672 2 0.000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329674 2 0.000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329661 3 0.297 0.680 0.000 0.000 0.776 0.000 0.224 0.000
#> GSM329669 2 0.150 0.904 0.000 0.924 0.000 0.000 0.000 0.076
#> GSM329662 1 0.000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329665 1 0.000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329668 1 0.000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329671 1 0.000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329673 1 0.000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329675 1 0.196 0.894 0.888 0.000 0.000 0.000 0.000 0.112
#> GSM329676 1 0.000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329677 5 0.196 0.907 0.000 0.000 0.112 0.000 0.888 0.000
#> GSM329679 2 0.000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329681 3 0.000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329683 3 0.000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329686 3 0.000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329689 3 0.000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329678 3 0.101 0.936 0.000 0.000 0.956 0.044 0.000 0.000
#> GSM329680 3 0.000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329685 3 0.000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329688 3 0.000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329691 3 0.000 0.965 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM329682 1 0.000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329684 1 0.196 0.894 0.888 0.000 0.000 0.000 0.000 0.112
#> GSM329687 1 0.000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329690 1 0.230 0.879 0.856 0.000 0.000 0.000 0.000 0.144
#> GSM329692 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329694 6 0.317 0.762 0.000 0.000 0.000 0.256 0.000 0.744
#> GSM329697 2 0.000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329700 6 0.415 0.898 0.000 0.108 0.000 0.148 0.000 0.744
#> GSM329703 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329704 5 0.000 0.903 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM329707 5 0.186 0.913 0.000 0.000 0.104 0.000 0.896 0.000
#> GSM329709 2 0.000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329711 6 0.415 0.899 0.000 0.112 0.000 0.144 0.000 0.744
#> GSM329714 6 0.404 0.876 0.000 0.076 0.000 0.180 0.000 0.744
#> GSM329693 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329696 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329699 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329702 2 0.000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM329706 5 0.186 0.913 0.000 0.000 0.104 0.000 0.896 0.000
#> GSM329708 3 0.101 0.936 0.000 0.000 0.956 0.044 0.000 0.000
#> GSM329710 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM329713 1 0.230 0.879 0.856 0.000 0.000 0.000 0.000 0.144
#> GSM329695 1 0.230 0.879 0.856 0.000 0.000 0.000 0.000 0.144
#> GSM329698 1 0.000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329701 1 0.000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329705 1 0.000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM329712 6 0.383 0.831 0.000 0.212 0.000 0.044 0.000 0.744
#> GSM329715 1 0.000 0.963 1.000 0.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> ATC:mclust 56 5.06e-01 5.82e-11 2
#> ATC:mclust 56 1.44e-03 3.53e-10 3
#> ATC:mclust 53 3.94e-03 6.91e-10 4
#> ATC:mclust 56 5.22e-06 2.70e-09 5
#> ATC:mclust 56 1.31e-04 1.27e-09 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 21163 rows and 56 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 0.889 0.913 0.965 0.4895 0.514 0.514
#> 3 3 1.000 0.965 0.986 0.3774 0.706 0.481
#> 4 4 0.811 0.707 0.856 0.0934 0.911 0.737
#> 5 5 0.762 0.709 0.815 0.0547 0.906 0.664
#> 6 6 0.750 0.707 0.822 0.0320 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
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
#> GSM329660 2 0.000 0.953 0.000 1.000
#> GSM329663 2 0.000 0.953 0.000 1.000
#> GSM329664 2 0.000 0.953 0.000 1.000
#> GSM329666 1 0.671 0.777 0.824 0.176
#> GSM329667 2 0.000 0.953 0.000 1.000
#> GSM329670 1 0.000 0.974 1.000 0.000
#> GSM329672 2 0.000 0.953 0.000 1.000
#> GSM329674 1 0.327 0.919 0.940 0.060
#> GSM329661 2 0.000 0.953 0.000 1.000
#> GSM329669 1 0.000 0.974 1.000 0.000
#> GSM329662 1 0.000 0.974 1.000 0.000
#> GSM329665 1 0.000 0.974 1.000 0.000
#> GSM329668 1 0.000 0.974 1.000 0.000
#> GSM329671 1 0.000 0.974 1.000 0.000
#> GSM329673 1 0.000 0.974 1.000 0.000
#> GSM329675 1 0.000 0.974 1.000 0.000
#> GSM329676 1 0.000 0.974 1.000 0.000
#> GSM329677 2 0.000 0.953 0.000 1.000
#> GSM329679 2 0.000 0.953 0.000 1.000
#> GSM329681 2 0.000 0.953 0.000 1.000
#> GSM329683 2 0.000 0.953 0.000 1.000
#> GSM329686 2 0.000 0.953 0.000 1.000
#> GSM329689 2 0.000 0.953 0.000 1.000
#> GSM329678 2 0.000 0.953 0.000 1.000
#> GSM329680 2 0.000 0.953 0.000 1.000
#> GSM329685 2 0.000 0.953 0.000 1.000
#> GSM329688 2 0.000 0.953 0.000 1.000
#> GSM329691 2 0.000 0.953 0.000 1.000
#> GSM329682 1 0.000 0.974 1.000 0.000
#> GSM329684 1 0.000 0.974 1.000 0.000
#> GSM329687 1 0.000 0.974 1.000 0.000
#> GSM329690 1 0.000 0.974 1.000 0.000
#> GSM329692 2 0.000 0.953 0.000 1.000
#> GSM329694 2 0.000 0.953 0.000 1.000
#> GSM329697 1 0.839 0.619 0.732 0.268
#> GSM329700 2 0.781 0.693 0.232 0.768
#> GSM329703 2 0.000 0.953 0.000 1.000
#> GSM329704 2 0.000 0.953 0.000 1.000
#> GSM329707 2 0.000 0.953 0.000 1.000
#> GSM329709 2 0.994 0.187 0.456 0.544
#> GSM329711 2 0.855 0.615 0.280 0.720
#> GSM329714 2 0.373 0.889 0.072 0.928
#> GSM329693 2 0.000 0.953 0.000 1.000
#> GSM329696 2 0.000 0.953 0.000 1.000
#> GSM329699 2 0.000 0.953 0.000 1.000
#> GSM329702 2 0.981 0.299 0.420 0.580
#> GSM329706 2 0.000 0.953 0.000 1.000
#> GSM329708 2 0.000 0.953 0.000 1.000
#> GSM329710 2 0.000 0.953 0.000 1.000
#> GSM329713 1 0.000 0.974 1.000 0.000
#> GSM329695 1 0.000 0.974 1.000 0.000
#> GSM329698 1 0.000 0.974 1.000 0.000
#> GSM329701 1 0.000 0.974 1.000 0.000
#> GSM329705 1 0.000 0.974 1.000 0.000
#> GSM329712 2 0.000 0.953 0.000 1.000
#> GSM329715 1 0.000 0.974 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM329660 2 0.0000 0.998 0 1.000 0.000
#> GSM329663 2 0.0000 0.998 0 1.000 0.000
#> GSM329664 3 0.0000 0.955 0 0.000 1.000
#> GSM329666 2 0.0000 0.998 0 1.000 0.000
#> GSM329667 3 0.6252 0.230 0 0.444 0.556
#> GSM329670 2 0.0000 0.998 0 1.000 0.000
#> GSM329672 2 0.0000 0.998 0 1.000 0.000
#> GSM329674 2 0.0000 0.998 0 1.000 0.000
#> GSM329661 3 0.0000 0.955 0 0.000 1.000
#> GSM329669 2 0.0000 0.998 0 1.000 0.000
#> GSM329662 1 0.0000 1.000 1 0.000 0.000
#> GSM329665 1 0.0000 1.000 1 0.000 0.000
#> GSM329668 1 0.0000 1.000 1 0.000 0.000
#> GSM329671 1 0.0000 1.000 1 0.000 0.000
#> GSM329673 1 0.0000 1.000 1 0.000 0.000
#> GSM329675 1 0.0000 1.000 1 0.000 0.000
#> GSM329676 1 0.0000 1.000 1 0.000 0.000
#> GSM329677 3 0.0000 0.955 0 0.000 1.000
#> GSM329679 2 0.0000 0.998 0 1.000 0.000
#> GSM329681 3 0.0000 0.955 0 0.000 1.000
#> GSM329683 3 0.0000 0.955 0 0.000 1.000
#> GSM329686 3 0.0000 0.955 0 0.000 1.000
#> GSM329689 3 0.0000 0.955 0 0.000 1.000
#> GSM329678 3 0.0000 0.955 0 0.000 1.000
#> GSM329680 3 0.0000 0.955 0 0.000 1.000
#> GSM329685 3 0.0000 0.955 0 0.000 1.000
#> GSM329688 3 0.0000 0.955 0 0.000 1.000
#> GSM329691 3 0.0000 0.955 0 0.000 1.000
#> GSM329682 1 0.0000 1.000 1 0.000 0.000
#> GSM329684 1 0.0000 1.000 1 0.000 0.000
#> GSM329687 1 0.0000 1.000 1 0.000 0.000
#> GSM329690 1 0.0000 1.000 1 0.000 0.000
#> GSM329692 3 0.5397 0.617 0 0.280 0.720
#> GSM329694 2 0.0000 0.998 0 1.000 0.000
#> GSM329697 2 0.0000 0.998 0 1.000 0.000
#> GSM329700 2 0.0000 0.998 0 1.000 0.000
#> GSM329703 2 0.0000 0.998 0 1.000 0.000
#> GSM329704 3 0.0000 0.955 0 0.000 1.000
#> GSM329707 3 0.0000 0.955 0 0.000 1.000
#> GSM329709 2 0.0000 0.998 0 1.000 0.000
#> GSM329711 2 0.0000 0.998 0 1.000 0.000
#> GSM329714 2 0.0000 0.998 0 1.000 0.000
#> GSM329693 2 0.0000 0.998 0 1.000 0.000
#> GSM329696 2 0.0000 0.998 0 1.000 0.000
#> GSM329699 2 0.0592 0.987 0 0.988 0.012
#> GSM329702 2 0.0000 0.998 0 1.000 0.000
#> GSM329706 3 0.0000 0.955 0 0.000 1.000
#> GSM329708 3 0.0000 0.955 0 0.000 1.000
#> GSM329710 2 0.0892 0.979 0 0.980 0.020
#> GSM329713 1 0.0000 1.000 1 0.000 0.000
#> GSM329695 1 0.0000 1.000 1 0.000 0.000
#> GSM329698 1 0.0000 1.000 1 0.000 0.000
#> GSM329701 1 0.0000 1.000 1 0.000 0.000
#> GSM329705 1 0.0000 1.000 1 0.000 0.000
#> GSM329712 2 0.0000 0.998 0 1.000 0.000
#> GSM329715 1 0.0000 1.000 1 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM329660 2 0.0188 0.8755 0 0.996 0.004 0.000
#> GSM329663 2 0.0921 0.8750 0 0.972 0.000 0.028
#> GSM329664 4 0.1940 0.7168 0 0.000 0.076 0.924
#> GSM329666 2 0.2345 0.8443 0 0.900 0.000 0.100
#> GSM329667 4 0.2385 0.6613 0 0.028 0.052 0.920
#> GSM329670 2 0.1302 0.8705 0 0.956 0.000 0.044
#> GSM329672 2 0.3172 0.8044 0 0.840 0.000 0.160
#> GSM329674 2 0.0592 0.8758 0 0.984 0.000 0.016
#> GSM329661 3 0.5000 -0.2933 0 0.000 0.500 0.500
#> GSM329669 2 0.0000 0.8758 0 1.000 0.000 0.000
#> GSM329662 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329665 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329668 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329671 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329673 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329675 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329676 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329677 4 0.4643 0.5890 0 0.000 0.344 0.656
#> GSM329679 2 0.3907 0.7370 0 0.768 0.000 0.232
#> GSM329681 3 0.4250 0.3602 0 0.000 0.724 0.276
#> GSM329683 3 0.4605 0.2685 0 0.000 0.664 0.336
#> GSM329686 3 0.4543 0.2912 0 0.000 0.676 0.324
#> GSM329689 4 0.4977 0.2835 0 0.000 0.460 0.540
#> GSM329678 3 0.0188 0.4800 0 0.000 0.996 0.004
#> GSM329680 3 0.4843 0.1059 0 0.000 0.604 0.396
#> GSM329685 3 0.2704 0.4749 0 0.000 0.876 0.124
#> GSM329688 3 0.3172 0.4604 0 0.000 0.840 0.160
#> GSM329691 3 0.4907 0.0186 0 0.000 0.580 0.420
#> GSM329682 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329684 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329687 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329690 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329692 3 0.2814 0.4200 0 0.132 0.868 0.000
#> GSM329694 2 0.0817 0.8698 0 0.976 0.024 0.000
#> GSM329697 2 0.1022 0.8742 0 0.968 0.000 0.032
#> GSM329700 2 0.0592 0.8727 0 0.984 0.016 0.000
#> GSM329703 2 0.4746 0.5422 0 0.632 0.368 0.000
#> GSM329704 4 0.2345 0.7293 0 0.000 0.100 0.900
#> GSM329707 4 0.4008 0.7217 0 0.000 0.244 0.756
#> GSM329709 2 0.1022 0.8742 0 0.968 0.000 0.032
#> GSM329711 2 0.0336 0.8747 0 0.992 0.008 0.000
#> GSM329714 2 0.3942 0.7071 0 0.764 0.236 0.000
#> GSM329693 2 0.4697 0.5621 0 0.644 0.356 0.000
#> GSM329696 2 0.4624 0.5852 0 0.660 0.340 0.000
#> GSM329699 3 0.4898 -0.0760 0 0.416 0.584 0.000
#> GSM329702 2 0.2973 0.8163 0 0.856 0.000 0.144
#> GSM329706 4 0.3873 0.7295 0 0.000 0.228 0.772
#> GSM329708 3 0.0336 0.4810 0 0.000 0.992 0.008
#> GSM329710 3 0.4843 -0.0175 0 0.396 0.604 0.000
#> GSM329713 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329695 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329698 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329701 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329705 1 0.0000 1.0000 1 0.000 0.000 0.000
#> GSM329712 2 0.0188 0.8755 0 0.996 0.004 0.000
#> GSM329715 1 0.0000 1.0000 1 0.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM329660 4 0.1012 0.684 0.000 0.012 0.000 0.968 0.020
#> GSM329663 4 0.3884 -0.104 0.000 0.288 0.000 0.708 0.004
#> GSM329664 5 0.0566 0.643 0.000 0.004 0.012 0.000 0.984
#> GSM329666 2 0.4872 0.784 0.000 0.540 0.000 0.436 0.024
#> GSM329667 5 0.2729 0.574 0.000 0.084 0.004 0.028 0.884
#> GSM329670 4 0.3912 0.217 0.000 0.228 0.000 0.752 0.020
#> GSM329672 2 0.5773 0.766 0.000 0.476 0.000 0.436 0.088
#> GSM329674 2 0.4306 0.657 0.000 0.508 0.000 0.492 0.000
#> GSM329661 5 0.4273 0.464 0.000 0.000 0.448 0.000 0.552
#> GSM329669 4 0.1544 0.617 0.000 0.068 0.000 0.932 0.000
#> GSM329662 1 0.1892 0.937 0.916 0.080 0.000 0.000 0.004
#> GSM329665 1 0.0404 0.977 0.988 0.012 0.000 0.000 0.000
#> GSM329668 1 0.0566 0.976 0.984 0.012 0.004 0.000 0.000
#> GSM329671 1 0.0290 0.977 0.992 0.008 0.000 0.000 0.000
#> GSM329673 1 0.0290 0.977 0.992 0.008 0.000 0.000 0.000
#> GSM329675 1 0.0771 0.973 0.976 0.020 0.004 0.000 0.000
#> GSM329676 1 0.0510 0.976 0.984 0.016 0.000 0.000 0.000
#> GSM329677 5 0.3561 0.682 0.000 0.000 0.260 0.000 0.740
#> GSM329679 2 0.5948 0.768 0.000 0.484 0.000 0.408 0.108
#> GSM329681 3 0.2970 0.628 0.000 0.004 0.828 0.000 0.168
#> GSM329683 3 0.3452 0.528 0.000 0.000 0.756 0.000 0.244
#> GSM329686 3 0.3366 0.553 0.000 0.000 0.768 0.000 0.232
#> GSM329689 5 0.4126 0.587 0.000 0.000 0.380 0.000 0.620
#> GSM329678 3 0.2387 0.630 0.000 0.048 0.908 0.040 0.004
#> GSM329680 3 0.4060 0.171 0.000 0.000 0.640 0.000 0.360
#> GSM329685 3 0.2351 0.669 0.000 0.016 0.896 0.000 0.088
#> GSM329688 3 0.2806 0.645 0.000 0.004 0.844 0.000 0.152
#> GSM329691 5 0.4283 0.440 0.000 0.000 0.456 0.000 0.544
#> GSM329682 1 0.0290 0.976 0.992 0.008 0.000 0.000 0.000
#> GSM329684 1 0.2548 0.907 0.876 0.116 0.004 0.000 0.004
#> GSM329687 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM329690 1 0.0510 0.974 0.984 0.016 0.000 0.000 0.000
#> GSM329692 3 0.3667 0.551 0.000 0.048 0.812 0.140 0.000
#> GSM329694 2 0.6538 0.541 0.000 0.480 0.248 0.272 0.000
#> GSM329697 2 0.3816 0.756 0.000 0.696 0.000 0.304 0.000
#> GSM329700 4 0.0671 0.688 0.000 0.016 0.004 0.980 0.000
#> GSM329703 4 0.4028 0.660 0.000 0.048 0.176 0.776 0.000
#> GSM329704 5 0.1082 0.653 0.000 0.008 0.028 0.000 0.964
#> GSM329707 5 0.5019 0.643 0.000 0.052 0.316 0.000 0.632
#> GSM329709 2 0.4066 0.770 0.000 0.672 0.000 0.324 0.004
#> GSM329711 4 0.0404 0.689 0.000 0.012 0.000 0.988 0.000
#> GSM329714 4 0.3479 0.677 0.000 0.084 0.080 0.836 0.000
#> GSM329693 4 0.4237 0.645 0.000 0.048 0.200 0.752 0.000
#> GSM329696 4 0.3779 0.629 0.000 0.012 0.236 0.752 0.000
#> GSM329699 4 0.4587 0.617 0.000 0.068 0.204 0.728 0.000
#> GSM329702 2 0.5337 0.782 0.000 0.508 0.000 0.440 0.052
#> GSM329706 5 0.2813 0.691 0.000 0.000 0.168 0.000 0.832
#> GSM329708 3 0.0854 0.661 0.000 0.004 0.976 0.008 0.012
#> GSM329710 3 0.4297 0.354 0.000 0.020 0.692 0.288 0.000
#> GSM329713 1 0.1792 0.932 0.916 0.084 0.000 0.000 0.000
#> GSM329695 1 0.1043 0.963 0.960 0.040 0.000 0.000 0.000
#> GSM329698 1 0.0510 0.974 0.984 0.016 0.000 0.000 0.000
#> GSM329701 1 0.0000 0.978 1.000 0.000 0.000 0.000 0.000
#> GSM329705 1 0.0162 0.977 0.996 0.004 0.000 0.000 0.000
#> GSM329712 4 0.0703 0.686 0.000 0.024 0.000 0.976 0.000
#> GSM329715 1 0.0000 0.978 1.000 0.000 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
#> GSM329660 4 0.4497 0.490 0.000 0.368 0.000 0.600 0.012 NA
#> GSM329663 2 0.4658 0.103 0.000 0.568 0.000 0.384 0.000 NA
#> GSM329664 5 0.2309 0.643 0.000 0.084 0.000 0.000 0.888 NA
#> GSM329666 2 0.2384 0.762 0.000 0.888 0.000 0.064 0.000 NA
#> GSM329667 2 0.4585 0.434 0.000 0.644 0.000 0.008 0.304 NA
#> GSM329670 4 0.5820 0.295 0.000 0.328 0.000 0.504 0.008 NA
#> GSM329672 2 0.1922 0.761 0.000 0.924 0.000 0.040 0.012 NA
#> GSM329674 2 0.4734 0.590 0.000 0.672 0.000 0.208 0.000 NA
#> GSM329661 5 0.3878 0.648 0.000 0.000 0.320 0.004 0.668 NA
#> GSM329669 4 0.3835 0.576 0.000 0.336 0.000 0.656 0.004 NA
#> GSM329662 1 0.2219 0.872 0.864 0.000 0.000 0.000 0.000 NA
#> GSM329665 1 0.0146 0.942 0.996 0.000 0.000 0.000 0.000 NA
#> GSM329668 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000 NA
#> GSM329671 1 0.0260 0.941 0.992 0.000 0.000 0.000 0.000 NA
#> GSM329673 1 0.0146 0.942 0.996 0.000 0.000 0.000 0.000 NA
#> GSM329675 1 0.1957 0.888 0.888 0.000 0.000 0.000 0.000 NA
#> GSM329676 1 0.0146 0.942 0.996 0.000 0.000 0.000 0.000 NA
#> GSM329677 5 0.2146 0.723 0.000 0.000 0.116 0.000 0.880 NA
#> GSM329679 2 0.2345 0.756 0.000 0.904 0.000 0.036 0.036 NA
#> GSM329681 3 0.1194 0.711 0.000 0.004 0.956 0.000 0.032 NA
#> GSM329683 3 0.2667 0.679 0.000 0.000 0.852 0.000 0.128 NA
#> GSM329686 3 0.3221 0.613 0.000 0.000 0.792 0.000 0.188 NA
#> GSM329689 5 0.3592 0.625 0.000 0.000 0.344 0.000 0.656 NA
#> GSM329678 3 0.3263 0.658 0.000 0.000 0.800 0.176 0.020 NA
#> GSM329680 3 0.3966 -0.170 0.000 0.000 0.552 0.004 0.444 NA
#> GSM329685 3 0.2716 0.698 0.000 0.000 0.868 0.008 0.096 NA
#> GSM329688 3 0.3210 0.644 0.000 0.000 0.804 0.000 0.168 NA
#> GSM329691 5 0.3881 0.533 0.000 0.000 0.396 0.000 0.600 NA
#> GSM329682 1 0.0260 0.941 0.992 0.000 0.000 0.000 0.000 NA
#> GSM329684 1 0.3265 0.772 0.748 0.000 0.000 0.000 0.004 NA
#> GSM329687 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000 NA
#> GSM329690 1 0.1267 0.922 0.940 0.000 0.000 0.000 0.000 NA
#> GSM329692 3 0.2199 0.681 0.000 0.000 0.892 0.088 0.000 NA
#> GSM329694 3 0.4469 0.263 0.000 0.388 0.584 0.012 0.000 NA
#> GSM329697 2 0.3697 0.670 0.000 0.732 0.004 0.016 0.000 NA
#> GSM329700 4 0.2632 0.757 0.000 0.164 0.000 0.832 0.000 NA
#> GSM329703 4 0.1655 0.771 0.000 0.008 0.052 0.932 0.000 NA
#> GSM329704 5 0.4511 0.579 0.000 0.224 0.036 0.004 0.712 NA
#> GSM329707 5 0.5634 0.631 0.000 0.156 0.256 0.000 0.576 NA
#> GSM329709 2 0.2709 0.740 0.000 0.848 0.000 0.020 0.000 NA
#> GSM329711 4 0.2378 0.763 0.000 0.152 0.000 0.848 0.000 NA
#> GSM329714 4 0.2089 0.766 0.000 0.020 0.020 0.916 0.000 NA
#> GSM329693 4 0.2013 0.763 0.000 0.008 0.076 0.908 0.000 NA
#> GSM329696 4 0.2068 0.763 0.000 0.008 0.080 0.904 0.000 NA
#> GSM329699 4 0.1769 0.769 0.000 0.012 0.060 0.924 0.000 NA
#> GSM329702 2 0.1738 0.766 0.000 0.928 0.000 0.052 0.004 NA
#> GSM329706 5 0.2100 0.722 0.000 0.000 0.112 0.000 0.884 NA
#> GSM329708 3 0.0951 0.709 0.000 0.000 0.968 0.020 0.004 NA
#> GSM329710 3 0.3281 0.593 0.000 0.004 0.784 0.200 0.000 NA
#> GSM329713 1 0.3879 0.692 0.688 0.020 0.000 0.000 0.000 NA
#> GSM329695 1 0.2302 0.878 0.872 0.008 0.000 0.000 0.000 NA
#> GSM329698 1 0.1007 0.929 0.956 0.000 0.000 0.000 0.000 NA
#> GSM329701 1 0.0260 0.941 0.992 0.000 0.000 0.000 0.000 NA
#> GSM329705 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000 NA
#> GSM329712 4 0.2697 0.745 0.000 0.188 0.000 0.812 0.000 NA
#> GSM329715 1 0.0000 0.942 1.000 0.000 0.000 0.000 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> ATC:NMF 54 0.04978 4.31e-07 2
#> ATC:NMF 55 0.00361 9.94e-10 3
#> ATC:NMF 42 0.52817 5.06e-07 4
#> ATC:NMF 50 0.02024 8.77e-08 5
#> ATC:NMF 50 0.02098 1.72e-07 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
sessionInfo()
#> R version 3.6.0 (2019-04-26)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: CentOS Linux 7 (Core)
#>
#> Matrix products: default
#> BLAS: /usr/lib64/libblas.so.3.4.2
#> LAPACK: /usr/lib64/liblapack.so.3.4.2
#>
#> locale:
#> [1] LC_CTYPE=en_GB.UTF-8 LC_NUMERIC=C LC_TIME=en_GB.UTF-8
#> [4] LC_COLLATE=en_GB.UTF-8 LC_MONETARY=en_GB.UTF-8 LC_MESSAGES=en_GB.UTF-8
#> [7] LC_PAPER=en_GB.UTF-8 LC_NAME=C LC_ADDRESS=C
#> [10] LC_TELEPHONE=C LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C
#>
#> attached base packages:
#> [1] grid stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] genefilter_1.66.0 ComplexHeatmap_2.3.1 markdown_1.1 knitr_1.26
#> [5] GetoptLong_0.1.7 cola_1.3.2
#>
#> loaded via a namespace (and not attached):
#> [1] circlize_0.4.8 shape_1.4.4 xfun_0.11 slam_0.1-46
#> [5] lattice_0.20-38 splines_3.6.0 colorspace_1.4-1 vctrs_0.2.0
#> [9] stats4_3.6.0 blob_1.2.0 XML_3.98-1.20 survival_2.44-1.1
#> [13] rlang_0.4.2 pillar_1.4.2 DBI_1.0.0 BiocGenerics_0.30.0
#> [17] bit64_0.9-7 RColorBrewer_1.1-2 matrixStats_0.55.0 stringr_1.4.0
#> [21] GlobalOptions_0.1.1 evaluate_0.14 memoise_1.1.0 Biobase_2.44.0
#> [25] IRanges_2.18.3 parallel_3.6.0 AnnotationDbi_1.46.1 highr_0.8
#> [29] Rcpp_1.0.3 xtable_1.8-4 backports_1.1.5 S4Vectors_0.22.1
#> [33] annotate_1.62.0 skmeans_0.2-11 bit_1.1-14 microbenchmark_1.4-7
#> [37] brew_1.0-6 impute_1.58.0 rjson_0.2.20 png_0.1-7
#> [41] digest_0.6.23 stringi_1.4.3 polyclip_1.10-0 clue_0.3-57
#> [45] tools_3.6.0 bitops_1.0-6 magrittr_1.5 eulerr_6.0.0
#> [49] RCurl_1.95-4.12 RSQLite_2.1.4 tibble_2.1.3 cluster_2.1.0
#> [53] crayon_1.3.4 pkgconfig_2.0.3 zeallot_0.1.0 Matrix_1.2-17
#> [57] xml2_1.2.2 httr_1.4.1 R6_2.4.1 mclust_5.4.5
#> [61] compiler_3.6.0