Date: 2019-12-25 22:22:04 CET, cola version: 1.3.2
Document is loading...
All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 12150 rows and 54 columns.
#> Top rows are extracted by 'SD, CV, MAD, ATC' methods.
#> Subgroups are detected by 'hclust, kmeans, skmeans, pam, mclust, NMF' method.
#> Number of partitions are tried for k = 2, 3, 4, 5, 6.
#> Performed in total 30000 partitions by row resampling.
#>
#> Following methods can be applied to this 'ConsensusPartitionList' object:
#> [1] "cola_report" "collect_classes" "collect_plots" "collect_stats"
#> [5] "colnames" "functional_enrichment" "get_anno_col" "get_anno"
#> [9] "get_classes" "get_matrix" "get_membership" "get_stats"
#> [13] "is_best_k" "is_stable_k" "ncol" "nrow"
#> [17] "rownames" "show" "suggest_best_k" "test_to_known_factors"
#> [21] "top_rows_heatmap" "top_rows_overlap"
#>
#> You can get result for a single method by, e.g. object["SD", "hclust"] or object["SD:hclust"]
#> or a subset of methods by object[c("SD", "CV")], c("hclust", "kmeans")]
The call of run_all_consensus_partition_methods() was:
#> run_all_consensus_partition_methods(data = mat, mc.cores = 4, anno = anno)
Dimension of the input matrix:
mat = get_matrix(res_list)
dim(mat)
#> [1] 12150 54
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:hclust | 3 | 1.000 | 0.934 | 0.968 | ** | |
| SD:skmeans | 3 | 1.000 | 0.993 | 0.997 | ** | |
| SD:mclust | 3 | 1.000 | 0.993 | 0.997 | ** | |
| SD:NMF | 3 | 1.000 | 0.996 | 0.998 | ** | 2 |
| MAD:kmeans | 3 | 1.000 | 0.971 | 0.965 | ** | |
| MAD:mclust | 3 | 1.000 | 0.974 | 0.990 | ** | |
| MAD:NMF | 3 | 1.000 | 0.998 | 0.999 | ** | 2 |
| ATC:hclust | 3 | 1.000 | 0.978 | 0.989 | ** | |
| ATC:kmeans | 3 | 1.000 | 0.953 | 0.965 | ** | |
| ATC:pam | 3 | 1.000 | 1.000 | 1.000 | ** | 2 |
| ATC:NMF | 3 | 1.000 | 0.973 | 0.990 | ** | 2 |
| SD:kmeans | 3 | 0.980 | 0.978 | 0.956 | ** | |
| MAD:skmeans | 3 | 0.970 | 0.960 | 0.984 | ** | 2 |
| SD:pam | 4 | 0.969 | 0.920 | 0.968 | ** | 2,3 |
| CV:NMF | 3 | 0.964 | 0.965 | 0.979 | ** | 2 |
| CV:pam | 3 | 0.942 | 0.950 | 0.976 | * | 2 |
| MAD:hclust | 3 | 0.940 | 0.941 | 0.974 | * | 2 |
| MAD:pam | 5 | 0.936 | 0.947 | 0.965 | * | 2,3 |
| ATC:skmeans | 3 | 0.916 | 0.920 | 0.969 | * | |
| ATC:mclust | 3 | 0.912 | 0.910 | 0.964 | * | |
| CV:mclust | 3 | 0.866 | 0.948 | 0.970 | ||
| CV:hclust | 5 | 0.805 | 0.827 | 0.896 | ||
| CV:skmeans | 3 | 0.776 | 0.903 | 0.950 | ||
| CV:kmeans | 3 | 0.680 | 0.955 | 0.933 |
**: 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 0.989 0.995 0.358 0.648 0.648
#> CV:NMF 2 1.000 0.980 0.992 0.362 0.648 0.648
#> MAD:NMF 2 1.000 0.982 0.992 0.361 0.648 0.648
#> ATC:NMF 2 1.000 0.970 0.988 0.382 0.628 0.628
#> SD:skmeans 2 0.708 0.928 0.956 0.465 0.516 0.516
#> CV:skmeans 2 0.708 0.883 0.935 0.456 0.516 0.516
#> MAD:skmeans 2 1.000 0.984 0.990 0.481 0.516 0.516
#> ATC:skmeans 2 0.704 0.824 0.914 0.450 0.516 0.516
#> SD:mclust 2 0.688 0.921 0.952 0.467 0.508 0.508
#> CV:mclust 2 0.688 0.925 0.950 0.466 0.508 0.508
#> MAD:mclust 2 0.688 0.883 0.931 0.447 0.508 0.508
#> ATC:mclust 2 0.816 0.924 0.967 0.406 0.591 0.591
#> SD:kmeans 2 0.508 0.846 0.856 0.337 0.648 0.648
#> CV:kmeans 2 0.508 0.887 0.883 0.344 0.648 0.648
#> MAD:kmeans 2 0.508 0.847 0.858 0.340 0.648 0.648
#> ATC:kmeans 2 0.405 0.808 0.844 0.347 0.648 0.648
#> SD:pam 2 1.000 1.000 1.000 0.353 0.648 0.648
#> CV:pam 2 1.000 0.999 0.999 0.353 0.648 0.648
#> MAD:pam 2 1.000 1.000 1.000 0.353 0.648 0.648
#> ATC:pam 2 1.000 1.000 1.000 0.353 0.648 0.648
#> SD:hclust 2 0.514 0.881 0.911 0.306 0.693 0.693
#> CV:hclust 2 0.517 0.817 0.884 0.308 0.743 0.743
#> MAD:hclust 2 1.000 0.926 0.953 0.291 0.743 0.743
#> ATC:hclust 2 0.481 0.843 0.885 0.293 0.743 0.743
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 1.000 0.996 0.998 0.651 0.762 0.632
#> CV:NMF 3 0.964 0.965 0.979 0.664 0.762 0.632
#> MAD:NMF 3 1.000 0.998 0.999 0.637 0.762 0.632
#> ATC:NMF 3 1.000 0.973 0.990 0.571 0.728 0.580
#> SD:skmeans 3 1.000 0.993 0.997 0.323 0.818 0.664
#> CV:skmeans 3 0.776 0.903 0.950 0.376 0.818 0.664
#> MAD:skmeans 3 0.970 0.960 0.984 0.277 0.818 0.664
#> ATC:skmeans 3 0.916 0.920 0.969 0.369 0.814 0.658
#> SD:mclust 3 1.000 0.993 0.997 0.239 0.916 0.835
#> CV:mclust 3 0.866 0.948 0.970 0.272 0.916 0.835
#> MAD:mclust 3 1.000 0.974 0.990 0.304 0.916 0.835
#> ATC:mclust 3 0.912 0.910 0.964 0.415 0.781 0.645
#> SD:kmeans 3 0.980 0.978 0.956 0.667 0.776 0.655
#> CV:kmeans 3 0.680 0.955 0.933 0.652 0.776 0.655
#> MAD:kmeans 3 1.000 0.971 0.965 0.685 0.776 0.655
#> ATC:kmeans 3 1.000 0.953 0.965 0.574 0.810 0.707
#> SD:pam 3 1.000 0.958 0.985 0.439 0.849 0.767
#> CV:pam 3 0.942 0.950 0.976 0.490 0.849 0.767
#> MAD:pam 3 1.000 0.985 0.992 0.449 0.849 0.767
#> ATC:pam 3 1.000 1.000 1.000 0.538 0.810 0.707
#> SD:hclust 3 1.000 0.934 0.968 0.835 0.732 0.613
#> CV:hclust 3 0.435 0.797 0.826 0.693 0.715 0.616
#> MAD:hclust 3 0.940 0.941 0.974 0.933 0.715 0.616
#> ATC:hclust 3 1.000 0.978 0.989 0.883 0.715 0.616
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.769 0.793 0.872 0.2337 0.839 0.614
#> CV:NMF 4 0.778 0.809 0.873 0.2136 0.871 0.688
#> MAD:NMF 4 0.752 0.653 0.820 0.2255 0.859 0.660
#> ATC:NMF 4 0.824 0.893 0.935 0.2377 0.829 0.578
#> SD:skmeans 4 0.804 0.760 0.878 0.2001 0.806 0.536
#> CV:skmeans 4 0.785 0.817 0.892 0.1852 0.806 0.536
#> MAD:skmeans 4 0.796 0.640 0.830 0.2073 0.818 0.555
#> ATC:skmeans 4 0.816 0.795 0.906 0.2207 0.829 0.574
#> SD:mclust 4 0.820 0.892 0.936 0.2022 0.906 0.778
#> CV:mclust 4 0.835 0.875 0.931 0.1725 0.891 0.743
#> MAD:mclust 4 0.840 0.877 0.932 0.1924 0.891 0.743
#> ATC:mclust 4 0.675 0.643 0.841 0.2128 0.884 0.733
#> SD:kmeans 4 0.763 0.861 0.886 0.2272 0.878 0.712
#> CV:kmeans 4 0.760 0.872 0.882 0.2033 0.878 0.712
#> MAD:kmeans 4 0.756 0.850 0.881 0.2189 0.866 0.684
#> ATC:kmeans 4 0.667 0.583 0.809 0.2305 0.955 0.902
#> SD:pam 4 0.969 0.920 0.968 0.2122 0.885 0.770
#> CV:pam 4 0.804 0.898 0.945 0.1917 0.892 0.782
#> MAD:pam 4 0.864 0.936 0.963 0.2079 0.892 0.782
#> ATC:pam 4 0.786 0.937 0.925 0.0862 0.990 0.977
#> SD:hclust 4 0.838 0.842 0.925 0.1928 0.906 0.778
#> CV:hclust 4 0.686 0.771 0.857 0.2889 0.850 0.680
#> MAD:hclust 4 0.823 0.855 0.938 0.2122 0.868 0.711
#> ATC:hclust 4 0.750 0.765 0.897 0.2042 0.883 0.744
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.822 0.816 0.897 0.0811 0.883 0.598
#> CV:NMF 5 0.848 0.850 0.915 0.0843 0.894 0.650
#> MAD:NMF 5 0.828 0.800 0.902 0.0897 0.909 0.688
#> ATC:NMF 5 0.724 0.709 0.835 0.0471 0.983 0.931
#> SD:skmeans 5 0.889 0.855 0.927 0.0948 0.901 0.638
#> CV:skmeans 5 0.885 0.842 0.920 0.0891 0.915 0.680
#> MAD:skmeans 5 0.869 0.818 0.911 0.0910 0.884 0.582
#> ATC:skmeans 5 0.784 0.760 0.868 0.0638 0.904 0.637
#> SD:mclust 5 0.800 0.817 0.897 0.1005 0.899 0.701
#> CV:mclust 5 0.826 0.799 0.909 0.0982 0.908 0.713
#> MAD:mclust 5 0.805 0.825 0.906 0.1020 0.908 0.713
#> ATC:mclust 5 0.646 0.578 0.736 0.0873 0.897 0.692
#> SD:kmeans 5 0.735 0.847 0.873 0.0818 0.941 0.806
#> CV:kmeans 5 0.751 0.864 0.895 0.0929 0.922 0.755
#> MAD:kmeans 5 0.718 0.772 0.851 0.0886 0.944 0.807
#> ATC:kmeans 5 0.612 0.593 0.755 0.1106 0.823 0.580
#> SD:pam 5 0.829 0.901 0.941 0.1042 0.950 0.872
#> CV:pam 5 0.825 0.887 0.918 0.0967 0.951 0.875
#> MAD:pam 5 0.936 0.947 0.965 0.0838 0.951 0.875
#> ATC:pam 5 0.695 0.844 0.875 0.1972 0.816 0.588
#> SD:hclust 5 0.775 0.756 0.866 0.0901 0.936 0.805
#> CV:hclust 5 0.805 0.827 0.896 0.0968 0.902 0.703
#> MAD:hclust 5 0.786 0.714 0.820 0.0723 0.870 0.607
#> ATC:hclust 5 0.780 0.634 0.849 0.0284 0.869 0.697
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.853 0.762 0.878 0.0454 0.921 0.648
#> CV:NMF 6 0.837 0.682 0.847 0.0418 0.988 0.943
#> MAD:NMF 6 0.836 0.707 0.851 0.0461 0.939 0.731
#> ATC:NMF 6 0.722 0.679 0.813 0.0417 0.880 0.552
#> SD:skmeans 6 0.858 0.723 0.862 0.0341 0.955 0.773
#> CV:skmeans 6 0.861 0.732 0.860 0.0342 0.945 0.728
#> MAD:skmeans 6 0.843 0.703 0.834 0.0329 0.965 0.819
#> ATC:skmeans 6 0.802 0.655 0.799 0.0310 0.987 0.930
#> SD:mclust 6 0.827 0.853 0.892 0.0442 0.951 0.803
#> CV:mclust 6 0.838 0.856 0.893 0.0506 0.951 0.795
#> MAD:mclust 6 0.855 0.886 0.919 0.0399 0.951 0.795
#> ATC:mclust 6 0.658 0.514 0.741 0.0520 0.850 0.495
#> SD:kmeans 6 0.765 0.789 0.841 0.0606 1.000 1.000
#> CV:kmeans 6 0.776 0.807 0.861 0.0544 1.000 1.000
#> MAD:kmeans 6 0.741 0.728 0.815 0.0469 1.000 1.000
#> ATC:kmeans 6 0.627 0.560 0.746 0.0487 0.955 0.822
#> SD:pam 6 0.846 0.797 0.923 0.0655 0.945 0.842
#> CV:pam 6 0.753 0.852 0.893 0.0603 0.962 0.891
#> MAD:pam 6 0.853 0.826 0.916 0.0702 0.962 0.891
#> ATC:pam 6 0.780 0.813 0.889 0.0918 0.977 0.912
#> SD:hclust 6 0.802 0.718 0.830 0.0572 0.989 0.958
#> CV:hclust 6 0.817 0.782 0.902 0.0355 0.980 0.916
#> MAD:hclust 6 0.839 0.840 0.908 0.0559 0.958 0.817
#> ATC:hclust 6 0.750 0.684 0.875 0.0660 0.890 0.732
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n tissue(p) k
#> SD:NMF 54 0.398 2
#> CV:NMF 53 0.397 2
#> MAD:NMF 54 0.398 2
#> ATC:NMF 53 0.397 2
#> SD:skmeans 54 0.398 2
#> CV:skmeans 52 0.396 2
#> MAD:skmeans 54 0.398 2
#> ATC:skmeans 51 0.395 2
#> SD:mclust 53 0.397 2
#> CV:mclust 54 0.398 2
#> MAD:mclust 53 0.397 2
#> ATC:mclust 53 0.397 2
#> SD:kmeans 54 0.398 2
#> CV:kmeans 54 0.398 2
#> MAD:kmeans 54 0.398 2
#> ATC:kmeans 46 0.389 2
#> SD:pam 54 0.398 2
#> CV:pam 54 0.398 2
#> MAD:pam 54 0.398 2
#> ATC:pam 54 0.398 2
#> SD:hclust 54 0.398 2
#> CV:hclust 52 0.396 2
#> MAD:hclust 52 0.396 2
#> ATC:hclust 54 0.398 2
test_to_known_factors(res_list, k = 3)
#> n tissue(p) k
#> SD:NMF 54 0.374 3
#> CV:NMF 54 0.374 3
#> MAD:NMF 54 0.374 3
#> ATC:NMF 53 0.373 3
#> SD:skmeans 54 0.374 3
#> CV:skmeans 53 0.373 3
#> MAD:skmeans 53 0.373 3
#> ATC:skmeans 52 0.372 3
#> SD:mclust 54 0.374 3
#> CV:mclust 54 0.374 3
#> MAD:mclust 53 0.373 3
#> ATC:mclust 52 0.372 3
#> SD:kmeans 54 0.374 3
#> CV:kmeans 54 0.374 3
#> MAD:kmeans 54 0.374 3
#> ATC:kmeans 52 0.372 3
#> SD:pam 53 0.373 3
#> CV:pam 54 0.374 3
#> MAD:pam 54 0.374 3
#> ATC:pam 54 0.374 3
#> SD:hclust 52 0.372 3
#> CV:hclust 47 0.366 3
#> MAD:hclust 52 0.372 3
#> ATC:hclust 54 0.374 3
test_to_known_factors(res_list, k = 4)
#> n tissue(p) k
#> SD:NMF 49 0.348 4
#> CV:NMF 49 0.348 4
#> MAD:NMF 43 0.409 4
#> ATC:NMF 53 0.431 4
#> SD:skmeans 50 0.349 4
#> CV:skmeans 50 0.349 4
#> MAD:skmeans 37 0.402 4
#> ATC:skmeans 47 0.436 4
#> SD:mclust 53 0.353 4
#> CV:mclust 52 0.352 4
#> MAD:mclust 52 0.352 4
#> ATC:mclust 36 0.411 4
#> SD:kmeans 53 0.353 4
#> CV:kmeans 53 0.353 4
#> MAD:kmeans 54 0.355 4
#> ATC:kmeans 25 0.394 4
#> SD:pam 51 0.483 4
#> CV:pam 52 0.487 4
#> MAD:pam 53 0.489 4
#> ATC:pam 54 0.355 4
#> SD:hclust 49 0.348 4
#> CV:hclust 43 0.409 4
#> MAD:hclust 51 0.350 4
#> ATC:hclust 43 0.409 4
test_to_known_factors(res_list, k = 5)
#> n tissue(p) k
#> SD:NMF 50 0.443 5
#> CV:NMF 51 0.443 5
#> MAD:NMF 48 0.427 5
#> ATC:NMF 47 0.422 5
#> SD:skmeans 49 0.429 5
#> CV:skmeans 49 0.429 5
#> MAD:skmeans 48 0.441 5
#> ATC:skmeans 46 0.463 5
#> SD:mclust 50 0.407 5
#> CV:mclust 48 0.405 5
#> MAD:mclust 51 0.482 5
#> ATC:mclust 35 0.400 5
#> SD:kmeans 52 0.484 5
#> CV:kmeans 51 0.481 5
#> MAD:kmeans 50 0.481 5
#> ATC:kmeans 40 0.426 5
#> SD:pam 53 0.452 5
#> CV:pam 54 0.455 5
#> MAD:pam 54 0.455 5
#> ATC:pam 53 0.402 5
#> SD:hclust 44 0.463 5
#> CV:hclust 48 0.421 5
#> MAD:hclust 45 0.402 5
#> ATC:hclust 27 0.386 5
test_to_known_factors(res_list, k = 6)
#> n tissue(p) k
#> SD:NMF 48 0.404 6
#> CV:NMF 43 0.444 6
#> MAD:NMF 45 0.413 6
#> ATC:NMF 45 0.451 6
#> SD:skmeans 42 0.482 6
#> CV:skmeans 43 0.463 6
#> MAD:skmeans 40 0.511 6
#> ATC:skmeans 38 0.520 6
#> SD:mclust 51 0.448 6
#> CV:mclust 53 0.407 6
#> MAD:mclust 53 0.417 6
#> ATC:mclust 21 0.384 6
#> SD:kmeans 53 0.485 6
#> CV:kmeans 51 0.481 6
#> MAD:kmeans 48 0.476 6
#> ATC:kmeans 35 0.397 6
#> SD:pam 48 0.398 6
#> CV:pam 53 0.638 6
#> MAD:pam 50 0.400 6
#> ATC:pam 52 0.588 6
#> SD:hclust 42 0.421 6
#> CV:hclust 43 0.456 6
#> MAD:hclust 50 0.399 6
#> ATC:hclust 44 0.410 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.514 0.881 0.911 0.3056 0.693 0.693
#> 3 3 1.000 0.934 0.968 0.8352 0.732 0.613
#> 4 4 0.838 0.842 0.925 0.1928 0.906 0.778
#> 5 5 0.775 0.756 0.866 0.0901 0.936 0.805
#> 6 6 0.802 0.718 0.830 0.0572 0.989 0.958
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
#> GSM28815 1 0.0000 0.926 1.000 0.000
#> GSM28816 1 0.0000 0.926 1.000 0.000
#> GSM28817 1 0.0000 0.926 1.000 0.000
#> GSM11327 2 0.9977 0.508 0.472 0.528
#> GSM28825 1 0.6887 0.813 0.816 0.184
#> GSM11322 1 0.6887 0.813 0.816 0.184
#> GSM28828 1 0.6887 0.813 0.816 0.184
#> GSM11346 1 0.6887 0.813 0.816 0.184
#> GSM28808 1 0.6887 0.813 0.816 0.184
#> GSM11332 1 0.6887 0.813 0.816 0.184
#> GSM28811 1 0.6887 0.813 0.816 0.184
#> GSM11334 1 0.6887 0.813 0.816 0.184
#> GSM11340 1 0.6887 0.813 0.816 0.184
#> GSM28812 1 0.6887 0.813 0.816 0.184
#> GSM11345 1 0.0000 0.926 1.000 0.000
#> GSM28819 1 0.0000 0.926 1.000 0.000
#> GSM11321 2 0.6887 0.919 0.184 0.816
#> GSM28820 1 0.0000 0.926 1.000 0.000
#> GSM11339 1 0.0000 0.926 1.000 0.000
#> GSM28804 1 0.0376 0.924 0.996 0.004
#> GSM28823 1 0.0000 0.926 1.000 0.000
#> GSM11336 1 0.0000 0.926 1.000 0.000
#> GSM11342 1 0.0000 0.926 1.000 0.000
#> GSM11333 1 0.0000 0.926 1.000 0.000
#> GSM28802 1 0.0000 0.926 1.000 0.000
#> GSM28803 2 0.6887 0.919 0.184 0.816
#> GSM11343 2 0.6887 0.919 0.184 0.816
#> GSM11347 2 0.6887 0.919 0.184 0.816
#> GSM28824 1 0.0000 0.926 1.000 0.000
#> GSM28813 1 0.0000 0.926 1.000 0.000
#> GSM28827 1 0.0000 0.926 1.000 0.000
#> GSM11337 1 0.0000 0.926 1.000 0.000
#> GSM28814 2 0.6887 0.919 0.184 0.816
#> GSM11331 1 0.0938 0.915 0.988 0.012
#> GSM11344 2 0.6887 0.919 0.184 0.816
#> GSM11330 2 0.6887 0.919 0.184 0.816
#> GSM11325 2 0.6887 0.919 0.184 0.816
#> GSM11338 1 0.0000 0.926 1.000 0.000
#> GSM28806 1 0.0000 0.926 1.000 0.000
#> GSM28826 1 0.0000 0.926 1.000 0.000
#> GSM28818 1 0.0000 0.926 1.000 0.000
#> GSM28821 1 0.6887 0.813 0.816 0.184
#> GSM28807 1 0.0376 0.924 0.996 0.004
#> GSM28822 1 0.0376 0.924 0.996 0.004
#> GSM11328 1 0.6887 0.813 0.816 0.184
#> GSM11323 1 0.0938 0.915 0.988 0.012
#> GSM11324 1 0.0000 0.926 1.000 0.000
#> GSM11341 1 0.5629 0.759 0.868 0.132
#> GSM11326 2 0.9977 0.508 0.472 0.528
#> GSM28810 1 0.0000 0.926 1.000 0.000
#> GSM11335 1 0.0376 0.924 0.996 0.004
#> GSM28809 1 0.0000 0.926 1.000 0.000
#> GSM11329 1 0.0000 0.926 1.000 0.000
#> GSM28805 1 0.0000 0.926 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.0000 0.986 1.000 0.000 0.000
#> GSM28816 1 0.0000 0.986 1.000 0.000 0.000
#> GSM28817 1 0.0000 0.986 1.000 0.000 0.000
#> GSM11327 3 0.6295 0.201 0.472 0.000 0.528
#> GSM28825 2 0.1163 1.000 0.028 0.972 0.000
#> GSM11322 2 0.1163 1.000 0.028 0.972 0.000
#> GSM28828 2 0.1163 1.000 0.028 0.972 0.000
#> GSM11346 2 0.1163 1.000 0.028 0.972 0.000
#> GSM28808 2 0.1163 1.000 0.028 0.972 0.000
#> GSM11332 2 0.1163 1.000 0.028 0.972 0.000
#> GSM28811 2 0.1163 1.000 0.028 0.972 0.000
#> GSM11334 2 0.1163 1.000 0.028 0.972 0.000
#> GSM11340 2 0.1163 1.000 0.028 0.972 0.000
#> GSM28812 2 0.1163 1.000 0.028 0.972 0.000
#> GSM11345 1 0.0000 0.986 1.000 0.000 0.000
#> GSM28819 1 0.0000 0.986 1.000 0.000 0.000
#> GSM11321 3 0.0237 0.853 0.004 0.000 0.996
#> GSM28820 1 0.0000 0.986 1.000 0.000 0.000
#> GSM11339 1 0.0000 0.986 1.000 0.000 0.000
#> GSM28804 1 0.1525 0.964 0.964 0.032 0.004
#> GSM28823 1 0.0000 0.986 1.000 0.000 0.000
#> GSM11336 1 0.0000 0.986 1.000 0.000 0.000
#> GSM11342 1 0.0000 0.986 1.000 0.000 0.000
#> GSM11333 1 0.0000 0.986 1.000 0.000 0.000
#> GSM28802 1 0.0000 0.986 1.000 0.000 0.000
#> GSM28803 3 0.0237 0.853 0.004 0.000 0.996
#> GSM11343 3 0.0237 0.853 0.004 0.000 0.996
#> GSM11347 3 0.0237 0.853 0.004 0.000 0.996
#> GSM28824 1 0.0000 0.986 1.000 0.000 0.000
#> GSM28813 1 0.0000 0.986 1.000 0.000 0.000
#> GSM28827 1 0.0000 0.986 1.000 0.000 0.000
#> GSM11337 1 0.0000 0.986 1.000 0.000 0.000
#> GSM28814 3 0.0237 0.853 0.004 0.000 0.996
#> GSM11331 1 0.0592 0.977 0.988 0.000 0.012
#> GSM11344 3 0.0237 0.853 0.004 0.000 0.996
#> GSM11330 3 0.0237 0.853 0.004 0.000 0.996
#> GSM11325 3 0.0237 0.853 0.004 0.000 0.996
#> GSM11338 1 0.0000 0.986 1.000 0.000 0.000
#> GSM28806 1 0.0237 0.984 0.996 0.004 0.000
#> GSM28826 1 0.0000 0.986 1.000 0.000 0.000
#> GSM28818 1 0.1163 0.968 0.972 0.028 0.000
#> GSM28821 2 0.1163 1.000 0.028 0.972 0.000
#> GSM28807 1 0.1399 0.966 0.968 0.028 0.004
#> GSM28822 1 0.1525 0.964 0.964 0.032 0.004
#> GSM11328 2 0.1163 1.000 0.028 0.972 0.000
#> GSM11323 1 0.0592 0.977 0.988 0.000 0.012
#> GSM11324 1 0.0000 0.986 1.000 0.000 0.000
#> GSM11341 1 0.4799 0.808 0.836 0.032 0.132
#> GSM11326 3 0.6295 0.201 0.472 0.000 0.528
#> GSM28810 1 0.1163 0.968 0.972 0.028 0.000
#> GSM11335 1 0.1399 0.966 0.968 0.028 0.004
#> GSM28809 1 0.1163 0.968 0.972 0.028 0.000
#> GSM11329 1 0.0000 0.986 1.000 0.000 0.000
#> GSM28805 1 0.0000 0.986 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.1389 0.900 0.952 0 0.000 0.048
#> GSM28816 1 0.1389 0.900 0.952 0 0.000 0.048
#> GSM28817 1 0.0000 0.920 1.000 0 0.000 0.000
#> GSM11327 3 0.5833 0.189 0.440 0 0.528 0.032
#> GSM28825 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11345 1 0.0000 0.920 1.000 0 0.000 0.000
#> GSM28819 1 0.0000 0.920 1.000 0 0.000 0.000
#> GSM11321 3 0.2760 0.778 0.000 0 0.872 0.128
#> GSM28820 1 0.0000 0.920 1.000 0 0.000 0.000
#> GSM11339 1 0.0000 0.920 1.000 0 0.000 0.000
#> GSM28804 4 0.3649 0.927 0.204 0 0.000 0.796
#> GSM28823 1 0.0000 0.920 1.000 0 0.000 0.000
#> GSM11336 1 0.1940 0.882 0.924 0 0.000 0.076
#> GSM11342 1 0.0000 0.920 1.000 0 0.000 0.000
#> GSM11333 1 0.1389 0.900 0.952 0 0.000 0.048
#> GSM28802 1 0.0000 0.920 1.000 0 0.000 0.000
#> GSM28803 3 0.2760 0.778 0.000 0 0.872 0.128
#> GSM11343 3 0.0188 0.786 0.000 0 0.996 0.004
#> GSM11347 3 0.0000 0.786 0.000 0 1.000 0.000
#> GSM28824 1 0.1940 0.882 0.924 0 0.000 0.076
#> GSM28813 1 0.1940 0.882 0.924 0 0.000 0.076
#> GSM28827 1 0.0000 0.920 1.000 0 0.000 0.000
#> GSM11337 1 0.0000 0.920 1.000 0 0.000 0.000
#> GSM28814 3 0.2760 0.778 0.000 0 0.872 0.128
#> GSM11331 1 0.1488 0.900 0.956 0 0.012 0.032
#> GSM11344 3 0.0000 0.786 0.000 0 1.000 0.000
#> GSM11330 3 0.0000 0.786 0.000 0 1.000 0.000
#> GSM11325 3 0.2760 0.778 0.000 0 0.872 0.128
#> GSM11338 1 0.1940 0.882 0.924 0 0.000 0.076
#> GSM28806 1 0.0188 0.918 0.996 0 0.000 0.004
#> GSM28826 1 0.0000 0.920 1.000 0 0.000 0.000
#> GSM28818 1 0.4855 0.107 0.600 0 0.000 0.400
#> GSM28821 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28807 4 0.3688 0.926 0.208 0 0.000 0.792
#> GSM28822 4 0.3649 0.927 0.204 0 0.000 0.796
#> GSM11328 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11323 1 0.1488 0.900 0.956 0 0.012 0.032
#> GSM11324 1 0.0000 0.920 1.000 0 0.000 0.000
#> GSM11341 4 0.1940 0.753 0.076 0 0.000 0.924
#> GSM11326 3 0.5833 0.189 0.440 0 0.528 0.032
#> GSM28810 1 0.4522 0.354 0.680 0 0.000 0.320
#> GSM11335 4 0.4072 0.880 0.252 0 0.000 0.748
#> GSM28809 1 0.4855 0.107 0.600 0 0.000 0.400
#> GSM11329 1 0.0000 0.920 1.000 0 0.000 0.000
#> GSM28805 1 0.0000 0.920 1.000 0 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 1 0.3242 0.360 0.784 0 0.000 0.000 0.216
#> GSM28816 1 0.3242 0.360 0.784 0 0.000 0.000 0.216
#> GSM28817 1 0.0000 0.791 1.000 0 0.000 0.000 0.000
#> GSM11327 3 0.6747 0.306 0.216 0 0.416 0.004 0.364
#> GSM28825 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11345 1 0.0000 0.791 1.000 0 0.000 0.000 0.000
#> GSM28819 1 0.0000 0.791 1.000 0 0.000 0.000 0.000
#> GSM11321 3 0.1671 0.775 0.000 0 0.924 0.076 0.000
#> GSM28820 1 0.0000 0.791 1.000 0 0.000 0.000 0.000
#> GSM11339 1 0.0000 0.791 1.000 0 0.000 0.000 0.000
#> GSM28804 4 0.1732 0.797 0.080 0 0.000 0.920 0.000
#> GSM28823 1 0.0000 0.791 1.000 0 0.000 0.000 0.000
#> GSM11336 5 0.4278 1.000 0.452 0 0.000 0.000 0.548
#> GSM11342 1 0.0000 0.791 1.000 0 0.000 0.000 0.000
#> GSM11333 1 0.3242 0.360 0.784 0 0.000 0.000 0.216
#> GSM28802 1 0.0000 0.791 1.000 0 0.000 0.000 0.000
#> GSM28803 3 0.1671 0.775 0.000 0 0.924 0.076 0.000
#> GSM11343 3 0.2127 0.791 0.000 0 0.892 0.000 0.108
#> GSM11347 3 0.2286 0.790 0.000 0 0.888 0.004 0.108
#> GSM28824 5 0.4278 1.000 0.452 0 0.000 0.000 0.548
#> GSM28813 5 0.4278 1.000 0.452 0 0.000 0.000 0.548
#> GSM28827 1 0.0000 0.791 1.000 0 0.000 0.000 0.000
#> GSM11337 1 0.0000 0.791 1.000 0 0.000 0.000 0.000
#> GSM28814 3 0.1671 0.775 0.000 0 0.924 0.076 0.000
#> GSM11331 1 0.3612 0.257 0.732 0 0.000 0.000 0.268
#> GSM11344 3 0.2286 0.790 0.000 0 0.888 0.004 0.108
#> GSM11330 3 0.2286 0.790 0.000 0 0.888 0.004 0.108
#> GSM11325 3 0.1671 0.775 0.000 0 0.924 0.076 0.000
#> GSM11338 5 0.4278 1.000 0.452 0 0.000 0.000 0.548
#> GSM28806 1 0.0162 0.787 0.996 0 0.000 0.004 0.000
#> GSM28826 1 0.0000 0.791 1.000 0 0.000 0.000 0.000
#> GSM28818 1 0.5872 0.242 0.600 0 0.000 0.168 0.232
#> GSM28821 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28807 4 0.5840 0.774 0.164 0 0.000 0.604 0.232
#> GSM28822 4 0.1732 0.797 0.080 0 0.000 0.920 0.000
#> GSM11328 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11323 1 0.3612 0.257 0.732 0 0.000 0.000 0.268
#> GSM11324 1 0.0000 0.791 1.000 0 0.000 0.000 0.000
#> GSM11341 4 0.4324 0.720 0.004 0 0.052 0.760 0.184
#> GSM11326 3 0.6747 0.306 0.216 0 0.416 0.004 0.364
#> GSM28810 1 0.4356 0.199 0.648 0 0.000 0.340 0.012
#> GSM11335 4 0.6133 0.720 0.220 0 0.000 0.564 0.216
#> GSM28809 1 0.5872 0.242 0.600 0 0.000 0.168 0.232
#> GSM11329 1 0.0000 0.791 1.000 0 0.000 0.000 0.000
#> GSM28805 1 0.0000 0.791 1.000 0 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
#> GSM28815 1 0.4056 0.0245 0.576 0 0.000 0.004 0.416 0.004
#> GSM28816 1 0.4056 0.0245 0.576 0 0.000 0.004 0.416 0.004
#> GSM28817 1 0.0000 0.7926 1.000 0 0.000 0.000 0.000 0.000
#> GSM11327 6 0.6302 1.0000 0.044 0 0.248 0.000 0.180 0.528
#> GSM28825 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11345 1 0.0000 0.7926 1.000 0 0.000 0.000 0.000 0.000
#> GSM28819 1 0.0000 0.7926 1.000 0 0.000 0.000 0.000 0.000
#> GSM11321 3 0.0000 0.6140 0.000 0 1.000 0.000 0.000 0.000
#> GSM28820 1 0.0000 0.7926 1.000 0 0.000 0.000 0.000 0.000
#> GSM11339 1 0.0146 0.7907 0.996 0 0.000 0.000 0.000 0.004
#> GSM28804 4 0.5314 0.6273 0.000 0 0.000 0.584 0.152 0.264
#> GSM28823 1 0.0000 0.7926 1.000 0 0.000 0.000 0.000 0.000
#> GSM11336 5 0.2823 1.0000 0.204 0 0.000 0.000 0.796 0.000
#> GSM11342 1 0.0000 0.7926 1.000 0 0.000 0.000 0.000 0.000
#> GSM11333 1 0.4056 0.0245 0.576 0 0.000 0.004 0.416 0.004
#> GSM28802 1 0.0000 0.7926 1.000 0 0.000 0.000 0.000 0.000
#> GSM28803 3 0.0000 0.6140 0.000 0 1.000 0.000 0.000 0.000
#> GSM11343 3 0.3847 0.4962 0.000 0 0.544 0.000 0.000 0.456
#> GSM11347 3 0.3851 0.4939 0.000 0 0.540 0.000 0.000 0.460
#> GSM28824 5 0.2823 1.0000 0.204 0 0.000 0.000 0.796 0.000
#> GSM28813 5 0.2823 1.0000 0.204 0 0.000 0.000 0.796 0.000
#> GSM28827 1 0.0260 0.7893 0.992 0 0.000 0.000 0.000 0.008
#> GSM11337 1 0.0260 0.7893 0.992 0 0.000 0.000 0.000 0.008
#> GSM28814 3 0.0000 0.6140 0.000 0 1.000 0.000 0.000 0.000
#> GSM11331 1 0.5490 0.2084 0.560 0 0.000 0.000 0.180 0.260
#> GSM11344 3 0.3851 0.4939 0.000 0 0.540 0.000 0.000 0.460
#> GSM11330 3 0.3851 0.4939 0.000 0 0.540 0.000 0.000 0.460
#> GSM11325 3 0.0000 0.6140 0.000 0 1.000 0.000 0.000 0.000
#> GSM11338 5 0.2823 1.0000 0.204 0 0.000 0.000 0.796 0.000
#> GSM28806 1 0.0291 0.7895 0.992 0 0.000 0.004 0.000 0.004
#> GSM28826 1 0.0260 0.7893 0.992 0 0.000 0.000 0.000 0.008
#> GSM28818 1 0.3971 0.2419 0.548 0 0.000 0.448 0.000 0.004
#> GSM28821 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28807 4 0.2003 0.6326 0.116 0 0.000 0.884 0.000 0.000
#> GSM28822 4 0.5314 0.6273 0.000 0 0.000 0.584 0.152 0.264
#> GSM11328 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11323 1 0.5490 0.2084 0.560 0 0.000 0.000 0.180 0.260
#> GSM11324 1 0.0000 0.7926 1.000 0 0.000 0.000 0.000 0.000
#> GSM11341 4 0.4854 0.6342 0.000 0 0.128 0.724 0.044 0.104
#> GSM11326 6 0.6302 1.0000 0.044 0 0.248 0.000 0.180 0.528
#> GSM28810 1 0.3620 0.3857 0.648 0 0.000 0.352 0.000 0.000
#> GSM11335 4 0.2823 0.5816 0.204 0 0.000 0.796 0.000 0.000
#> GSM28809 1 0.4072 0.2379 0.544 0 0.000 0.448 0.000 0.008
#> GSM11329 1 0.0000 0.7926 1.000 0 0.000 0.000 0.000 0.000
#> GSM28805 1 0.0000 0.7926 1.000 0 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> SD:hclust 54 0.398 2
#> SD:hclust 52 0.372 3
#> SD:hclust 49 0.348 4
#> SD:hclust 44 0.463 5
#> SD:hclust 42 0.421 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.508 0.846 0.856 0.3371 0.648 0.648
#> 3 3 0.980 0.978 0.956 0.6674 0.776 0.655
#> 4 4 0.763 0.861 0.886 0.2272 0.878 0.712
#> 5 5 0.735 0.847 0.873 0.0818 0.941 0.806
#> 6 6 0.765 0.789 0.841 0.0606 1.000 1.000
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
#> GSM28815 1 0.0000 0.867 1.000 0.000
#> GSM28816 1 0.0000 0.867 1.000 0.000
#> GSM28817 1 0.0000 0.867 1.000 0.000
#> GSM11327 1 0.9286 0.599 0.656 0.344
#> GSM28825 2 0.9358 1.000 0.352 0.648
#> GSM11322 2 0.9358 1.000 0.352 0.648
#> GSM28828 2 0.9358 1.000 0.352 0.648
#> GSM11346 2 0.9358 1.000 0.352 0.648
#> GSM28808 2 0.9358 1.000 0.352 0.648
#> GSM11332 2 0.9358 1.000 0.352 0.648
#> GSM28811 2 0.9358 1.000 0.352 0.648
#> GSM11334 2 0.9358 1.000 0.352 0.648
#> GSM11340 2 0.9358 1.000 0.352 0.648
#> GSM28812 2 0.9358 1.000 0.352 0.648
#> GSM11345 1 0.0000 0.867 1.000 0.000
#> GSM28819 1 0.0000 0.867 1.000 0.000
#> GSM11321 1 0.9358 0.594 0.648 0.352
#> GSM28820 1 0.0000 0.867 1.000 0.000
#> GSM11339 1 0.0000 0.867 1.000 0.000
#> GSM28804 1 0.0000 0.867 1.000 0.000
#> GSM28823 1 0.0000 0.867 1.000 0.000
#> GSM11336 1 0.0672 0.861 0.992 0.008
#> GSM11342 1 0.0000 0.867 1.000 0.000
#> GSM11333 1 0.0000 0.867 1.000 0.000
#> GSM28802 1 0.0000 0.867 1.000 0.000
#> GSM28803 1 0.9358 0.594 0.648 0.352
#> GSM11343 1 0.9358 0.594 0.648 0.352
#> GSM11347 1 0.9358 0.594 0.648 0.352
#> GSM28824 1 0.0672 0.861 0.992 0.008
#> GSM28813 1 0.0672 0.861 0.992 0.008
#> GSM28827 1 0.0000 0.867 1.000 0.000
#> GSM11337 1 0.0672 0.861 0.992 0.008
#> GSM28814 1 0.9358 0.594 0.648 0.352
#> GSM11331 1 0.0000 0.867 1.000 0.000
#> GSM11344 1 0.9358 0.594 0.648 0.352
#> GSM11330 1 0.9358 0.594 0.648 0.352
#> GSM11325 1 0.9358 0.594 0.648 0.352
#> GSM11338 1 0.0672 0.861 0.992 0.008
#> GSM28806 1 0.0000 0.867 1.000 0.000
#> GSM28826 1 0.0000 0.867 1.000 0.000
#> GSM28818 1 0.0000 0.867 1.000 0.000
#> GSM28821 2 0.9358 1.000 0.352 0.648
#> GSM28807 1 0.0000 0.867 1.000 0.000
#> GSM28822 1 0.0000 0.867 1.000 0.000
#> GSM11328 2 0.9358 1.000 0.352 0.648
#> GSM11323 1 0.0000 0.867 1.000 0.000
#> GSM11324 1 0.0000 0.867 1.000 0.000
#> GSM11341 1 0.0672 0.859 0.992 0.008
#> GSM11326 1 0.9286 0.599 0.656 0.344
#> GSM28810 1 0.0000 0.867 1.000 0.000
#> GSM11335 1 0.0000 0.867 1.000 0.000
#> GSM28809 1 0.0000 0.867 1.000 0.000
#> GSM11329 1 0.0000 0.867 1.000 0.000
#> GSM28805 1 0.0000 0.867 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.0000 0.975 1.000 0.000 0.000
#> GSM28816 1 0.0000 0.975 1.000 0.000 0.000
#> GSM28817 1 0.0000 0.975 1.000 0.000 0.000
#> GSM11327 3 0.2537 0.989 0.080 0.000 0.920
#> GSM28825 2 0.1964 1.000 0.056 0.944 0.000
#> GSM11322 2 0.1964 1.000 0.056 0.944 0.000
#> GSM28828 2 0.1964 1.000 0.056 0.944 0.000
#> GSM11346 2 0.1964 1.000 0.056 0.944 0.000
#> GSM28808 2 0.1964 1.000 0.056 0.944 0.000
#> GSM11332 2 0.1964 1.000 0.056 0.944 0.000
#> GSM28811 2 0.1964 1.000 0.056 0.944 0.000
#> GSM11334 2 0.1964 1.000 0.056 0.944 0.000
#> GSM11340 2 0.1964 1.000 0.056 0.944 0.000
#> GSM28812 2 0.1964 1.000 0.056 0.944 0.000
#> GSM11345 1 0.0747 0.973 0.984 0.000 0.016
#> GSM28819 1 0.0000 0.975 1.000 0.000 0.000
#> GSM11321 3 0.3802 0.985 0.080 0.032 0.888
#> GSM28820 1 0.0000 0.975 1.000 0.000 0.000
#> GSM11339 1 0.1411 0.966 0.964 0.000 0.036
#> GSM28804 1 0.1964 0.956 0.944 0.000 0.056
#> GSM28823 1 0.0000 0.975 1.000 0.000 0.000
#> GSM11336 1 0.1919 0.954 0.956 0.020 0.024
#> GSM11342 1 0.0000 0.975 1.000 0.000 0.000
#> GSM11333 1 0.1163 0.969 0.972 0.000 0.028
#> GSM28802 1 0.0000 0.975 1.000 0.000 0.000
#> GSM28803 3 0.3802 0.985 0.080 0.032 0.888
#> GSM11343 3 0.2772 0.989 0.080 0.004 0.916
#> GSM11347 3 0.2772 0.989 0.080 0.004 0.916
#> GSM28824 1 0.1919 0.954 0.956 0.020 0.024
#> GSM28813 1 0.2050 0.951 0.952 0.020 0.028
#> GSM28827 1 0.0000 0.975 1.000 0.000 0.000
#> GSM11337 1 0.1919 0.954 0.956 0.020 0.024
#> GSM28814 3 0.3802 0.985 0.080 0.032 0.888
#> GSM11331 1 0.0000 0.975 1.000 0.000 0.000
#> GSM11344 3 0.2772 0.989 0.080 0.004 0.916
#> GSM11330 3 0.2772 0.989 0.080 0.004 0.916
#> GSM11325 3 0.3802 0.985 0.080 0.032 0.888
#> GSM11338 1 0.1919 0.954 0.956 0.020 0.024
#> GSM28806 1 0.1411 0.966 0.964 0.000 0.036
#> GSM28826 1 0.0237 0.973 0.996 0.004 0.000
#> GSM28818 1 0.1964 0.956 0.944 0.000 0.056
#> GSM28821 2 0.1964 1.000 0.056 0.944 0.000
#> GSM28807 1 0.1964 0.956 0.944 0.000 0.056
#> GSM28822 1 0.1964 0.956 0.944 0.000 0.056
#> GSM11328 2 0.1964 1.000 0.056 0.944 0.000
#> GSM11323 1 0.0000 0.975 1.000 0.000 0.000
#> GSM11324 1 0.0000 0.975 1.000 0.000 0.000
#> GSM11341 1 0.1964 0.956 0.944 0.000 0.056
#> GSM11326 3 0.2537 0.989 0.080 0.000 0.920
#> GSM28810 1 0.1964 0.956 0.944 0.000 0.056
#> GSM11335 1 0.1964 0.956 0.944 0.000 0.056
#> GSM28809 1 0.0892 0.972 0.980 0.000 0.020
#> GSM11329 1 0.0000 0.975 1.000 0.000 0.000
#> GSM28805 1 0.0000 0.975 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.2530 0.804 0.888 0.000 0.000 0.112
#> GSM28816 1 0.3123 0.783 0.844 0.000 0.000 0.156
#> GSM28817 1 0.0188 0.825 0.996 0.000 0.000 0.004
#> GSM11327 3 0.1059 0.967 0.016 0.000 0.972 0.012
#> GSM28825 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM11322 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM28828 2 0.0188 0.993 0.000 0.996 0.004 0.000
#> GSM11346 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM28808 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM11332 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM28811 2 0.1042 0.983 0.000 0.972 0.008 0.020
#> GSM11334 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM11340 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM28812 2 0.0000 0.994 0.000 1.000 0.000 0.000
#> GSM11345 1 0.0336 0.824 0.992 0.000 0.000 0.008
#> GSM28819 1 0.0336 0.825 0.992 0.000 0.000 0.008
#> GSM11321 3 0.2450 0.960 0.016 0.000 0.912 0.072
#> GSM28820 1 0.0336 0.825 0.992 0.000 0.000 0.008
#> GSM11339 1 0.1211 0.807 0.960 0.000 0.000 0.040
#> GSM28804 4 0.4855 0.962 0.400 0.000 0.000 0.600
#> GSM28823 1 0.1022 0.815 0.968 0.000 0.000 0.032
#> GSM11336 1 0.4792 0.615 0.680 0.000 0.008 0.312
#> GSM11342 1 0.1022 0.815 0.968 0.000 0.000 0.032
#> GSM11333 1 0.3172 0.781 0.840 0.000 0.000 0.160
#> GSM28802 1 0.2149 0.804 0.912 0.000 0.000 0.088
#> GSM28803 3 0.2450 0.960 0.016 0.000 0.912 0.072
#> GSM11343 3 0.1182 0.969 0.016 0.000 0.968 0.016
#> GSM11347 3 0.1182 0.969 0.016 0.000 0.968 0.016
#> GSM28824 1 0.4792 0.615 0.680 0.000 0.008 0.312
#> GSM28813 1 0.4792 0.615 0.680 0.000 0.008 0.312
#> GSM28827 1 0.0469 0.821 0.988 0.000 0.000 0.012
#> GSM11337 1 0.4049 0.702 0.780 0.000 0.008 0.212
#> GSM28814 3 0.2450 0.960 0.016 0.000 0.912 0.072
#> GSM11331 1 0.1716 0.790 0.936 0.000 0.000 0.064
#> GSM11344 3 0.1182 0.969 0.016 0.000 0.968 0.016
#> GSM11330 3 0.1182 0.969 0.016 0.000 0.968 0.016
#> GSM11325 3 0.2450 0.960 0.016 0.000 0.912 0.072
#> GSM11338 1 0.4697 0.618 0.696 0.000 0.008 0.296
#> GSM28806 1 0.4585 -0.164 0.668 0.000 0.000 0.332
#> GSM28826 1 0.2469 0.792 0.892 0.000 0.000 0.108
#> GSM28818 4 0.4866 0.959 0.404 0.000 0.000 0.596
#> GSM28821 2 0.1042 0.983 0.000 0.972 0.008 0.020
#> GSM28807 4 0.4843 0.961 0.396 0.000 0.000 0.604
#> GSM28822 4 0.4855 0.962 0.400 0.000 0.000 0.600
#> GSM11328 2 0.1042 0.983 0.000 0.972 0.008 0.020
#> GSM11323 1 0.1716 0.790 0.936 0.000 0.000 0.064
#> GSM11324 1 0.0188 0.824 0.996 0.000 0.000 0.004
#> GSM11341 4 0.5167 0.882 0.340 0.000 0.016 0.644
#> GSM11326 3 0.1182 0.966 0.016 0.000 0.968 0.016
#> GSM28810 4 0.4967 0.887 0.452 0.000 0.000 0.548
#> GSM11335 4 0.4855 0.959 0.400 0.000 0.000 0.600
#> GSM28809 1 0.1118 0.807 0.964 0.000 0.000 0.036
#> GSM11329 1 0.0469 0.821 0.988 0.000 0.000 0.012
#> GSM28805 1 0.0469 0.821 0.988 0.000 0.000 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 1 0.3317 0.736 0.840 0.000 0.000 0.044 0.116
#> GSM28816 1 0.4233 0.549 0.748 0.000 0.000 0.044 0.208
#> GSM28817 1 0.0609 0.835 0.980 0.000 0.000 0.000 0.020
#> GSM11327 3 0.1644 0.884 0.004 0.000 0.940 0.008 0.048
#> GSM28825 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM28828 2 0.0162 0.963 0.000 0.996 0.000 0.000 0.004
#> GSM11346 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM28811 2 0.3446 0.887 0.000 0.840 0.004 0.048 0.108
#> GSM11334 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM11345 1 0.0794 0.832 0.972 0.000 0.000 0.000 0.028
#> GSM28819 1 0.0880 0.830 0.968 0.000 0.000 0.000 0.032
#> GSM11321 3 0.4109 0.871 0.004 0.000 0.788 0.060 0.148
#> GSM28820 1 0.0880 0.830 0.968 0.000 0.000 0.000 0.032
#> GSM11339 1 0.1597 0.818 0.940 0.000 0.000 0.048 0.012
#> GSM28804 4 0.3639 0.895 0.144 0.000 0.000 0.812 0.044
#> GSM28823 1 0.1818 0.812 0.932 0.000 0.000 0.024 0.044
#> GSM11336 5 0.4327 0.991 0.360 0.000 0.000 0.008 0.632
#> GSM11342 1 0.1818 0.812 0.932 0.000 0.000 0.024 0.044
#> GSM11333 1 0.4519 0.482 0.720 0.000 0.000 0.052 0.228
#> GSM28802 1 0.1851 0.784 0.912 0.000 0.000 0.000 0.088
#> GSM28803 3 0.4109 0.871 0.004 0.000 0.788 0.060 0.148
#> GSM11343 3 0.0833 0.897 0.004 0.000 0.976 0.004 0.016
#> GSM11347 3 0.1442 0.895 0.004 0.000 0.952 0.012 0.032
#> GSM28824 5 0.4327 0.991 0.360 0.000 0.000 0.008 0.632
#> GSM28813 5 0.4327 0.991 0.360 0.000 0.000 0.008 0.632
#> GSM28827 1 0.0451 0.836 0.988 0.000 0.000 0.004 0.008
#> GSM11337 1 0.3305 0.536 0.776 0.000 0.000 0.000 0.224
#> GSM28814 3 0.4109 0.871 0.004 0.000 0.788 0.060 0.148
#> GSM11331 1 0.2927 0.773 0.872 0.000 0.000 0.068 0.060
#> GSM11344 3 0.1442 0.895 0.004 0.000 0.952 0.012 0.032
#> GSM11330 3 0.1442 0.895 0.004 0.000 0.952 0.012 0.032
#> GSM11325 3 0.4109 0.871 0.004 0.000 0.788 0.060 0.148
#> GSM11338 5 0.4114 0.973 0.376 0.000 0.000 0.000 0.624
#> GSM28806 1 0.3707 0.472 0.716 0.000 0.000 0.284 0.000
#> GSM28826 1 0.2471 0.728 0.864 0.000 0.000 0.000 0.136
#> GSM28818 4 0.2891 0.881 0.176 0.000 0.000 0.824 0.000
#> GSM28821 2 0.3446 0.887 0.000 0.840 0.004 0.048 0.108
#> GSM28807 4 0.3106 0.892 0.132 0.000 0.000 0.844 0.024
#> GSM28822 4 0.3639 0.895 0.144 0.000 0.000 0.812 0.044
#> GSM11328 2 0.3446 0.887 0.000 0.840 0.004 0.048 0.108
#> GSM11323 1 0.2927 0.773 0.872 0.000 0.000 0.068 0.060
#> GSM11324 1 0.0000 0.837 1.000 0.000 0.000 0.000 0.000
#> GSM11341 4 0.3584 0.872 0.112 0.000 0.012 0.836 0.040
#> GSM11326 3 0.2381 0.866 0.004 0.000 0.908 0.036 0.052
#> GSM28810 4 0.4436 0.545 0.396 0.000 0.000 0.596 0.008
#> GSM11335 4 0.3197 0.891 0.140 0.000 0.000 0.836 0.024
#> GSM28809 1 0.2270 0.796 0.904 0.000 0.000 0.076 0.020
#> GSM11329 1 0.0000 0.837 1.000 0.000 0.000 0.000 0.000
#> GSM28805 1 0.0000 0.837 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
#> GSM28815 1 0.3951 0.716 0.804 0.000 0.000 0.052 0.072 NA
#> GSM28816 1 0.5052 0.600 0.700 0.000 0.000 0.052 0.168 NA
#> GSM28817 1 0.3435 0.725 0.804 0.000 0.000 0.000 0.060 NA
#> GSM11327 3 0.2745 0.795 0.000 0.000 0.876 0.012 0.056 NA
#> GSM28825 2 0.0000 0.933 0.000 1.000 0.000 0.000 0.000 NA
#> GSM11322 2 0.0000 0.933 0.000 1.000 0.000 0.000 0.000 NA
#> GSM28828 2 0.0603 0.927 0.000 0.980 0.000 0.000 0.004 NA
#> GSM11346 2 0.0000 0.933 0.000 1.000 0.000 0.000 0.000 NA
#> GSM28808 2 0.0363 0.931 0.000 0.988 0.000 0.000 0.012 NA
#> GSM11332 2 0.0260 0.932 0.000 0.992 0.000 0.000 0.008 NA
#> GSM28811 2 0.3986 0.791 0.000 0.732 0.000 0.008 0.032 NA
#> GSM11334 2 0.0000 0.933 0.000 1.000 0.000 0.000 0.000 NA
#> GSM11340 2 0.0260 0.932 0.000 0.992 0.000 0.000 0.008 NA
#> GSM28812 2 0.0000 0.933 0.000 1.000 0.000 0.000 0.000 NA
#> GSM11345 1 0.3548 0.718 0.796 0.000 0.000 0.000 0.068 NA
#> GSM28819 1 0.3602 0.717 0.792 0.000 0.000 0.000 0.072 NA
#> GSM11321 3 0.4180 0.771 0.000 0.000 0.632 0.012 0.008 NA
#> GSM28820 1 0.3602 0.717 0.792 0.000 0.000 0.000 0.072 NA
#> GSM11339 1 0.2563 0.754 0.880 0.000 0.000 0.076 0.004 NA
#> GSM28804 4 0.3907 0.802 0.032 0.000 0.000 0.800 0.064 NA
#> GSM28823 1 0.4702 0.668 0.716 0.000 0.000 0.024 0.084 NA
#> GSM11336 5 0.2695 0.992 0.144 0.000 0.000 0.004 0.844 NA
#> GSM11342 1 0.4702 0.668 0.716 0.000 0.000 0.024 0.084 NA
#> GSM11333 1 0.5418 0.572 0.672 0.000 0.000 0.076 0.168 NA
#> GSM28802 1 0.2081 0.761 0.916 0.000 0.000 0.012 0.036 NA
#> GSM28803 3 0.4180 0.771 0.000 0.000 0.632 0.012 0.008 NA
#> GSM11343 3 0.0146 0.817 0.000 0.000 0.996 0.000 0.004 NA
#> GSM11347 3 0.0777 0.814 0.000 0.000 0.972 0.000 0.004 NA
#> GSM28824 5 0.2695 0.992 0.144 0.000 0.000 0.004 0.844 NA
#> GSM28813 5 0.2442 0.991 0.144 0.000 0.000 0.004 0.852 NA
#> GSM28827 1 0.0458 0.772 0.984 0.000 0.000 0.000 0.000 NA
#> GSM11337 1 0.3252 0.711 0.828 0.000 0.000 0.012 0.128 NA
#> GSM28814 3 0.4180 0.771 0.000 0.000 0.632 0.012 0.008 NA
#> GSM11331 1 0.4334 0.676 0.752 0.000 0.000 0.156 0.024 NA
#> GSM11344 3 0.0777 0.814 0.000 0.000 0.972 0.000 0.004 NA
#> GSM11330 3 0.0777 0.814 0.000 0.000 0.972 0.000 0.004 NA
#> GSM11325 3 0.4180 0.771 0.000 0.000 0.632 0.012 0.008 NA
#> GSM11338 5 0.2593 0.983 0.148 0.000 0.000 0.000 0.844 NA
#> GSM28806 1 0.4111 0.554 0.676 0.000 0.000 0.296 0.004 NA
#> GSM28826 1 0.2593 0.747 0.884 0.000 0.000 0.012 0.068 NA
#> GSM28818 4 0.2748 0.783 0.120 0.000 0.000 0.856 0.008 NA
#> GSM28821 2 0.4012 0.788 0.000 0.728 0.000 0.008 0.032 NA
#> GSM28807 4 0.1477 0.821 0.048 0.000 0.000 0.940 0.004 NA
#> GSM28822 4 0.3988 0.808 0.040 0.000 0.000 0.796 0.060 NA
#> GSM11328 2 0.3986 0.791 0.000 0.732 0.000 0.008 0.032 NA
#> GSM11323 1 0.4334 0.676 0.752 0.000 0.000 0.156 0.024 NA
#> GSM11324 1 0.2346 0.755 0.868 0.000 0.000 0.000 0.008 NA
#> GSM11341 4 0.3320 0.798 0.012 0.000 0.004 0.840 0.052 NA
#> GSM11326 3 0.3913 0.749 0.000 0.000 0.804 0.092 0.044 NA
#> GSM28810 4 0.3898 0.440 0.336 0.000 0.000 0.652 0.000 NA
#> GSM11335 4 0.1542 0.821 0.052 0.000 0.000 0.936 0.004 NA
#> GSM28809 1 0.3492 0.699 0.788 0.000 0.000 0.176 0.004 NA
#> GSM11329 1 0.1444 0.769 0.928 0.000 0.000 0.000 0.000 NA
#> GSM28805 1 0.1116 0.770 0.960 0.000 0.000 0.008 0.004 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 tissue(p) k
#> SD:kmeans 54 0.398 2
#> SD:kmeans 54 0.374 3
#> SD:kmeans 53 0.353 4
#> SD:kmeans 52 0.484 5
#> SD:kmeans 53 0.485 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.708 0.928 0.956 0.4654 0.516 0.516
#> 3 3 1.000 0.993 0.997 0.3231 0.818 0.664
#> 4 4 0.804 0.760 0.878 0.2001 0.806 0.536
#> 5 5 0.889 0.855 0.927 0.0948 0.901 0.638
#> 6 6 0.858 0.723 0.862 0.0341 0.955 0.773
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
#> GSM28815 1 0.204 0.951 0.968 0.032
#> GSM28816 1 0.745 0.726 0.788 0.212
#> GSM28817 1 0.000 0.984 1.000 0.000
#> GSM11327 1 0.000 0.984 1.000 0.000
#> GSM28825 2 0.000 0.895 0.000 1.000
#> GSM11322 2 0.000 0.895 0.000 1.000
#> GSM28828 2 0.000 0.895 0.000 1.000
#> GSM11346 2 0.000 0.895 0.000 1.000
#> GSM28808 2 0.000 0.895 0.000 1.000
#> GSM11332 2 0.000 0.895 0.000 1.000
#> GSM28811 2 0.000 0.895 0.000 1.000
#> GSM11334 2 0.000 0.895 0.000 1.000
#> GSM11340 2 0.000 0.895 0.000 1.000
#> GSM28812 2 0.000 0.895 0.000 1.000
#> GSM11345 1 0.000 0.984 1.000 0.000
#> GSM28819 1 0.000 0.984 1.000 0.000
#> GSM11321 2 0.760 0.829 0.220 0.780
#> GSM28820 1 0.000 0.984 1.000 0.000
#> GSM11339 1 0.000 0.984 1.000 0.000
#> GSM28804 1 0.753 0.720 0.784 0.216
#> GSM28823 1 0.000 0.984 1.000 0.000
#> GSM11336 1 0.000 0.984 1.000 0.000
#> GSM11342 1 0.000 0.984 1.000 0.000
#> GSM11333 1 0.000 0.984 1.000 0.000
#> GSM28802 1 0.000 0.984 1.000 0.000
#> GSM28803 2 0.760 0.829 0.220 0.780
#> GSM11343 2 0.753 0.832 0.216 0.784
#> GSM11347 2 0.753 0.832 0.216 0.784
#> GSM28824 1 0.000 0.984 1.000 0.000
#> GSM28813 1 0.000 0.984 1.000 0.000
#> GSM28827 1 0.000 0.984 1.000 0.000
#> GSM11337 1 0.000 0.984 1.000 0.000
#> GSM28814 2 0.760 0.829 0.220 0.780
#> GSM11331 1 0.000 0.984 1.000 0.000
#> GSM11344 2 0.753 0.832 0.216 0.784
#> GSM11330 2 0.753 0.832 0.216 0.784
#> GSM11325 2 0.760 0.829 0.220 0.780
#> GSM11338 1 0.000 0.984 1.000 0.000
#> GSM28806 1 0.000 0.984 1.000 0.000
#> GSM28826 1 0.000 0.984 1.000 0.000
#> GSM28818 1 0.000 0.984 1.000 0.000
#> GSM28821 2 0.000 0.895 0.000 1.000
#> GSM28807 1 0.000 0.984 1.000 0.000
#> GSM28822 1 0.000 0.984 1.000 0.000
#> GSM11328 2 0.000 0.895 0.000 1.000
#> GSM11323 1 0.000 0.984 1.000 0.000
#> GSM11324 1 0.000 0.984 1.000 0.000
#> GSM11341 2 0.714 0.841 0.196 0.804
#> GSM11326 1 0.000 0.984 1.000 0.000
#> GSM28810 1 0.000 0.984 1.000 0.000
#> GSM11335 1 0.000 0.984 1.000 0.000
#> GSM28809 1 0.000 0.984 1.000 0.000
#> GSM11329 1 0.000 0.984 1.000 0.000
#> GSM28805 1 0.000 0.984 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.0000 0.997 1.000 0.000 0.000
#> GSM28816 1 0.1031 0.976 0.976 0.024 0.000
#> GSM28817 1 0.0000 0.997 1.000 0.000 0.000
#> GSM11327 3 0.0000 0.991 0.000 0.000 1.000
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11345 1 0.0000 0.997 1.000 0.000 0.000
#> GSM28819 1 0.0000 0.997 1.000 0.000 0.000
#> GSM11321 3 0.0000 0.991 0.000 0.000 1.000
#> GSM28820 1 0.0000 0.997 1.000 0.000 0.000
#> GSM11339 1 0.0000 0.997 1.000 0.000 0.000
#> GSM28804 1 0.0237 0.995 0.996 0.004 0.000
#> GSM28823 1 0.0000 0.997 1.000 0.000 0.000
#> GSM11336 1 0.0892 0.980 0.980 0.000 0.020
#> GSM11342 1 0.0000 0.997 1.000 0.000 0.000
#> GSM11333 1 0.0000 0.997 1.000 0.000 0.000
#> GSM28802 1 0.0000 0.997 1.000 0.000 0.000
#> GSM28803 3 0.0000 0.991 0.000 0.000 1.000
#> GSM11343 3 0.0000 0.991 0.000 0.000 1.000
#> GSM11347 3 0.0000 0.991 0.000 0.000 1.000
#> GSM28824 3 0.2448 0.902 0.076 0.000 0.924
#> GSM28813 3 0.0592 0.980 0.012 0.000 0.988
#> GSM28827 1 0.0000 0.997 1.000 0.000 0.000
#> GSM11337 1 0.0000 0.997 1.000 0.000 0.000
#> GSM28814 3 0.0000 0.991 0.000 0.000 1.000
#> GSM11331 1 0.0237 0.995 0.996 0.000 0.004
#> GSM11344 3 0.0000 0.991 0.000 0.000 1.000
#> GSM11330 3 0.0000 0.991 0.000 0.000 1.000
#> GSM11325 3 0.0000 0.991 0.000 0.000 1.000
#> GSM11338 1 0.0747 0.984 0.984 0.000 0.016
#> GSM28806 1 0.0000 0.997 1.000 0.000 0.000
#> GSM28826 1 0.0000 0.997 1.000 0.000 0.000
#> GSM28818 1 0.0000 0.997 1.000 0.000 0.000
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28807 1 0.0237 0.995 0.996 0.000 0.004
#> GSM28822 1 0.0237 0.995 0.996 0.000 0.004
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11323 1 0.0237 0.995 0.996 0.000 0.004
#> GSM11324 1 0.0000 0.997 1.000 0.000 0.000
#> GSM11341 3 0.0000 0.991 0.000 0.000 1.000
#> GSM11326 3 0.0000 0.991 0.000 0.000 1.000
#> GSM28810 1 0.0237 0.995 0.996 0.000 0.004
#> GSM11335 1 0.0237 0.995 0.996 0.000 0.004
#> GSM28809 1 0.0000 0.997 1.000 0.000 0.000
#> GSM11329 1 0.0000 0.997 1.000 0.000 0.000
#> GSM28805 1 0.0000 0.997 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.2469 0.623 0.892 0.000 0.000 0.108
#> GSM28816 1 0.2654 0.617 0.888 0.004 0.000 0.108
#> GSM28817 1 0.4843 0.567 0.604 0.000 0.000 0.396
#> GSM11327 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11345 1 0.4985 0.432 0.532 0.000 0.000 0.468
#> GSM28819 1 0.4843 0.567 0.604 0.000 0.000 0.396
#> GSM11321 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM28820 1 0.4843 0.567 0.604 0.000 0.000 0.396
#> GSM11339 4 0.4605 0.138 0.336 0.000 0.000 0.664
#> GSM28804 4 0.0592 0.801 0.016 0.000 0.000 0.984
#> GSM28823 1 0.4877 0.556 0.592 0.000 0.000 0.408
#> GSM11336 1 0.0592 0.662 0.984 0.000 0.000 0.016
#> GSM11342 1 0.4877 0.556 0.592 0.000 0.000 0.408
#> GSM11333 1 0.3356 0.544 0.824 0.000 0.000 0.176
#> GSM28802 1 0.0921 0.666 0.972 0.000 0.000 0.028
#> GSM28803 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11343 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11347 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM28824 1 0.1059 0.658 0.972 0.000 0.012 0.016
#> GSM28813 1 0.1256 0.652 0.964 0.000 0.028 0.008
#> GSM28827 1 0.4941 0.524 0.564 0.000 0.000 0.436
#> GSM11337 1 0.0817 0.665 0.976 0.000 0.000 0.024
#> GSM28814 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11331 4 0.2611 0.736 0.096 0.000 0.008 0.896
#> GSM11344 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11330 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11325 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11338 1 0.0000 0.663 1.000 0.000 0.000 0.000
#> GSM28806 4 0.0707 0.797 0.020 0.000 0.000 0.980
#> GSM28826 1 0.0817 0.665 0.976 0.000 0.000 0.024
#> GSM28818 4 0.0469 0.804 0.012 0.000 0.000 0.988
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28807 4 0.0188 0.806 0.004 0.000 0.000 0.996
#> GSM28822 4 0.0469 0.803 0.012 0.000 0.000 0.988
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11323 4 0.2081 0.752 0.084 0.000 0.000 0.916
#> GSM11324 1 0.4888 0.555 0.588 0.000 0.000 0.412
#> GSM11341 4 0.4999 -0.173 0.000 0.000 0.492 0.508
#> GSM11326 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM28810 4 0.0000 0.805 0.000 0.000 0.000 1.000
#> GSM11335 4 0.0188 0.806 0.004 0.000 0.000 0.996
#> GSM28809 4 0.4643 0.118 0.344 0.000 0.000 0.656
#> GSM11329 1 0.4898 0.551 0.584 0.000 0.000 0.416
#> GSM28805 1 0.4888 0.556 0.588 0.000 0.000 0.412
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 5 0.2735 0.855 0.084 0.000 0.000 0.036 0.880
#> GSM28816 5 0.1728 0.871 0.036 0.004 0.000 0.020 0.940
#> GSM28817 1 0.0671 0.857 0.980 0.000 0.000 0.016 0.004
#> GSM11327 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11345 1 0.0798 0.856 0.976 0.000 0.000 0.016 0.008
#> GSM28819 1 0.0798 0.855 0.976 0.000 0.000 0.008 0.016
#> GSM11321 3 0.0162 0.997 0.000 0.000 0.996 0.000 0.004
#> GSM28820 1 0.0807 0.856 0.976 0.000 0.000 0.012 0.012
#> GSM11339 1 0.5068 0.388 0.592 0.000 0.000 0.364 0.044
#> GSM28804 4 0.0807 0.858 0.012 0.000 0.000 0.976 0.012
#> GSM28823 1 0.0693 0.856 0.980 0.000 0.000 0.012 0.008
#> GSM11336 5 0.0880 0.880 0.032 0.000 0.000 0.000 0.968
#> GSM11342 1 0.0693 0.856 0.980 0.000 0.000 0.012 0.008
#> GSM11333 5 0.5027 0.674 0.188 0.000 0.000 0.112 0.700
#> GSM28802 1 0.4350 0.184 0.588 0.000 0.000 0.004 0.408
#> GSM28803 3 0.0162 0.997 0.000 0.000 0.996 0.000 0.004
#> GSM11343 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM11347 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM28824 5 0.0880 0.880 0.032 0.000 0.000 0.000 0.968
#> GSM28813 5 0.0880 0.880 0.032 0.000 0.000 0.000 0.968
#> GSM28827 1 0.2409 0.809 0.900 0.000 0.000 0.032 0.068
#> GSM11337 5 0.2462 0.849 0.112 0.000 0.000 0.008 0.880
#> GSM28814 3 0.0162 0.997 0.000 0.000 0.996 0.000 0.004
#> GSM11331 4 0.6006 0.409 0.328 0.000 0.012 0.564 0.096
#> GSM11344 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM11330 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM11325 3 0.0162 0.997 0.000 0.000 0.996 0.000 0.004
#> GSM11338 5 0.1732 0.871 0.080 0.000 0.000 0.000 0.920
#> GSM28806 4 0.2448 0.813 0.088 0.000 0.000 0.892 0.020
#> GSM28826 5 0.4080 0.683 0.252 0.000 0.000 0.020 0.728
#> GSM28818 4 0.0510 0.861 0.016 0.000 0.000 0.984 0.000
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM28807 4 0.0290 0.860 0.008 0.000 0.000 0.992 0.000
#> GSM28822 4 0.0693 0.859 0.012 0.000 0.000 0.980 0.008
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11323 4 0.5778 0.426 0.324 0.000 0.004 0.576 0.096
#> GSM11324 1 0.0798 0.855 0.976 0.000 0.000 0.016 0.008
#> GSM11341 4 0.2806 0.751 0.000 0.000 0.152 0.844 0.004
#> GSM11326 3 0.0162 0.995 0.000 0.000 0.996 0.004 0.000
#> GSM28810 4 0.0794 0.856 0.028 0.000 0.000 0.972 0.000
#> GSM11335 4 0.0290 0.860 0.008 0.000 0.000 0.992 0.000
#> GSM28809 1 0.5393 0.132 0.504 0.000 0.000 0.440 0.056
#> GSM11329 1 0.1281 0.846 0.956 0.000 0.000 0.012 0.032
#> GSM28805 1 0.1281 0.843 0.956 0.000 0.000 0.012 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 6 0.4612 -0.2754 0.012 0 0.000 0.020 0.424 0.544
#> GSM28816 5 0.4089 0.2497 0.000 0 0.000 0.008 0.524 0.468
#> GSM28817 1 0.0692 0.7875 0.976 0 0.000 0.000 0.004 0.020
#> GSM11327 3 0.1152 0.9293 0.000 0 0.952 0.000 0.004 0.044
#> GSM28825 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11345 1 0.0291 0.7878 0.992 0 0.000 0.000 0.004 0.004
#> GSM28819 1 0.0146 0.7879 0.996 0 0.000 0.000 0.004 0.000
#> GSM11321 3 0.1700 0.9364 0.000 0 0.916 0.004 0.000 0.080
#> GSM28820 1 0.0146 0.7879 0.996 0 0.000 0.000 0.004 0.000
#> GSM11339 1 0.6358 -0.0495 0.396 0 0.000 0.316 0.012 0.276
#> GSM28804 4 0.1285 0.8396 0.004 0 0.000 0.944 0.000 0.052
#> GSM28823 1 0.1812 0.7492 0.912 0 0.000 0.008 0.000 0.080
#> GSM11336 5 0.0000 0.7331 0.000 0 0.000 0.000 1.000 0.000
#> GSM11342 1 0.1812 0.7492 0.912 0 0.000 0.008 0.000 0.080
#> GSM11333 5 0.6339 0.2826 0.056 0 0.000 0.136 0.512 0.296
#> GSM28802 1 0.5561 0.3137 0.564 0 0.000 0.004 0.168 0.264
#> GSM28803 3 0.1700 0.9364 0.000 0 0.916 0.004 0.000 0.080
#> GSM11343 3 0.0000 0.9485 0.000 0 1.000 0.000 0.000 0.000
#> GSM11347 3 0.0260 0.9482 0.000 0 0.992 0.000 0.000 0.008
#> GSM28824 5 0.0000 0.7331 0.000 0 0.000 0.000 1.000 0.000
#> GSM28813 5 0.0000 0.7331 0.000 0 0.000 0.000 1.000 0.000
#> GSM28827 6 0.4656 -0.0100 0.420 0 0.000 0.028 0.008 0.544
#> GSM11337 5 0.4348 0.4513 0.056 0 0.000 0.000 0.676 0.268
#> GSM28814 3 0.1700 0.9364 0.000 0 0.916 0.004 0.000 0.080
#> GSM11331 6 0.6217 0.3758 0.092 0 0.060 0.232 0.020 0.596
#> GSM11344 3 0.0260 0.9482 0.000 0 0.992 0.000 0.000 0.008
#> GSM11330 3 0.0260 0.9482 0.000 0 0.992 0.000 0.000 0.008
#> GSM11325 3 0.1700 0.9364 0.000 0 0.916 0.004 0.000 0.080
#> GSM11338 5 0.1007 0.7090 0.044 0 0.000 0.000 0.956 0.000
#> GSM28806 4 0.3735 0.7008 0.124 0 0.000 0.784 0.000 0.092
#> GSM28826 6 0.5191 -0.1718 0.092 0 0.000 0.000 0.400 0.508
#> GSM28818 4 0.2112 0.8445 0.016 0 0.000 0.896 0.000 0.088
#> GSM28821 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28807 4 0.1765 0.8406 0.000 0 0.000 0.904 0.000 0.096
#> GSM28822 4 0.1082 0.8450 0.004 0 0.000 0.956 0.000 0.040
#> GSM11328 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11323 6 0.6152 0.3730 0.084 0 0.060 0.236 0.020 0.600
#> GSM11324 1 0.0692 0.7853 0.976 0 0.000 0.004 0.000 0.020
#> GSM11341 4 0.2433 0.7910 0.000 0 0.072 0.884 0.000 0.044
#> GSM11326 3 0.1700 0.9006 0.000 0 0.916 0.004 0.000 0.080
#> GSM28810 4 0.2964 0.7585 0.004 0 0.000 0.792 0.000 0.204
#> GSM11335 4 0.2178 0.8255 0.000 0 0.000 0.868 0.000 0.132
#> GSM28809 6 0.6102 0.2315 0.200 0 0.000 0.316 0.012 0.472
#> GSM11329 1 0.1910 0.7393 0.892 0 0.000 0.000 0.000 0.108
#> GSM28805 1 0.3872 0.3526 0.604 0 0.000 0.000 0.004 0.392
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> SD:skmeans 54 0.398 2
#> SD:skmeans 54 0.374 3
#> SD:skmeans 50 0.349 4
#> SD:skmeans 49 0.429 5
#> SD:skmeans 42 0.482 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 1.000 1.000 0.3528 0.648 0.648
#> 3 3 1.000 0.958 0.985 0.4388 0.849 0.767
#> 4 4 0.969 0.920 0.968 0.2122 0.885 0.770
#> 5 5 0.829 0.901 0.941 0.1042 0.950 0.872
#> 6 6 0.846 0.797 0.923 0.0655 0.945 0.842
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
#> GSM28815 1 0 1 1 0
#> GSM28816 1 0 1 1 0
#> GSM28817 1 0 1 1 0
#> GSM11327 1 0 1 1 0
#> GSM28825 2 0 1 0 1
#> GSM11322 2 0 1 0 1
#> GSM28828 2 0 1 0 1
#> GSM11346 2 0 1 0 1
#> GSM28808 2 0 1 0 1
#> GSM11332 2 0 1 0 1
#> GSM28811 2 0 1 0 1
#> GSM11334 2 0 1 0 1
#> GSM11340 2 0 1 0 1
#> GSM28812 2 0 1 0 1
#> GSM11345 1 0 1 1 0
#> GSM28819 1 0 1 1 0
#> GSM11321 1 0 1 1 0
#> GSM28820 1 0 1 1 0
#> GSM11339 1 0 1 1 0
#> GSM28804 1 0 1 1 0
#> GSM28823 1 0 1 1 0
#> GSM11336 1 0 1 1 0
#> GSM11342 1 0 1 1 0
#> GSM11333 1 0 1 1 0
#> GSM28802 1 0 1 1 0
#> GSM28803 1 0 1 1 0
#> GSM11343 1 0 1 1 0
#> GSM11347 1 0 1 1 0
#> GSM28824 1 0 1 1 0
#> GSM28813 1 0 1 1 0
#> GSM28827 1 0 1 1 0
#> GSM11337 1 0 1 1 0
#> GSM28814 1 0 1 1 0
#> GSM11331 1 0 1 1 0
#> GSM11344 1 0 1 1 0
#> GSM11330 1 0 1 1 0
#> GSM11325 1 0 1 1 0
#> GSM11338 1 0 1 1 0
#> GSM28806 1 0 1 1 0
#> GSM28826 1 0 1 1 0
#> GSM28818 1 0 1 1 0
#> GSM28821 2 0 1 0 1
#> GSM28807 1 0 1 1 0
#> GSM28822 1 0 1 1 0
#> GSM11328 2 0 1 0 1
#> GSM11323 1 0 1 1 0
#> GSM11324 1 0 1 1 0
#> GSM11341 1 0 1 1 0
#> GSM11326 1 0 1 1 0
#> GSM28810 1 0 1 1 0
#> GSM11335 1 0 1 1 0
#> GSM28809 1 0 1 1 0
#> GSM11329 1 0 1 1 0
#> GSM28805 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.0000 0.984 1.000 0 0.000
#> GSM28816 1 0.0000 0.984 1.000 0 0.000
#> GSM28817 1 0.0000 0.984 1.000 0 0.000
#> GSM11327 1 0.6154 0.267 0.592 0 0.408
#> GSM28825 2 0.0000 1.000 0.000 1 0.000
#> GSM11322 2 0.0000 1.000 0.000 1 0.000
#> GSM28828 2 0.0000 1.000 0.000 1 0.000
#> GSM11346 2 0.0000 1.000 0.000 1 0.000
#> GSM28808 2 0.0000 1.000 0.000 1 0.000
#> GSM11332 2 0.0000 1.000 0.000 1 0.000
#> GSM28811 2 0.0000 1.000 0.000 1 0.000
#> GSM11334 2 0.0000 1.000 0.000 1 0.000
#> GSM11340 2 0.0000 1.000 0.000 1 0.000
#> GSM28812 2 0.0000 1.000 0.000 1 0.000
#> GSM11345 1 0.0000 0.984 1.000 0 0.000
#> GSM28819 1 0.0000 0.984 1.000 0 0.000
#> GSM11321 3 0.5465 0.577 0.288 0 0.712
#> GSM28820 1 0.0000 0.984 1.000 0 0.000
#> GSM11339 1 0.0000 0.984 1.000 0 0.000
#> GSM28804 1 0.0000 0.984 1.000 0 0.000
#> GSM28823 1 0.0000 0.984 1.000 0 0.000
#> GSM11336 1 0.0000 0.984 1.000 0 0.000
#> GSM11342 1 0.0000 0.984 1.000 0 0.000
#> GSM11333 1 0.0000 0.984 1.000 0 0.000
#> GSM28802 1 0.0000 0.984 1.000 0 0.000
#> GSM28803 3 0.0424 0.905 0.008 0 0.992
#> GSM11343 3 0.0000 0.910 0.000 0 1.000
#> GSM11347 3 0.0000 0.910 0.000 0 1.000
#> GSM28824 1 0.0000 0.984 1.000 0 0.000
#> GSM28813 1 0.0000 0.984 1.000 0 0.000
#> GSM28827 1 0.0000 0.984 1.000 0 0.000
#> GSM11337 1 0.0000 0.984 1.000 0 0.000
#> GSM28814 1 0.0237 0.981 0.996 0 0.004
#> GSM11331 1 0.0000 0.984 1.000 0 0.000
#> GSM11344 3 0.0000 0.910 0.000 0 1.000
#> GSM11330 3 0.0000 0.910 0.000 0 1.000
#> GSM11325 1 0.0424 0.977 0.992 0 0.008
#> GSM11338 1 0.0000 0.984 1.000 0 0.000
#> GSM28806 1 0.0000 0.984 1.000 0 0.000
#> GSM28826 1 0.0000 0.984 1.000 0 0.000
#> GSM28818 1 0.0000 0.984 1.000 0 0.000
#> GSM28821 2 0.0000 1.000 0.000 1 0.000
#> GSM28807 1 0.0000 0.984 1.000 0 0.000
#> GSM28822 1 0.0000 0.984 1.000 0 0.000
#> GSM11328 2 0.0000 1.000 0.000 1 0.000
#> GSM11323 1 0.0000 0.984 1.000 0 0.000
#> GSM11324 1 0.0000 0.984 1.000 0 0.000
#> GSM11341 1 0.0000 0.984 1.000 0 0.000
#> GSM11326 1 0.2878 0.879 0.904 0 0.096
#> GSM28810 1 0.0000 0.984 1.000 0 0.000
#> GSM11335 1 0.0000 0.984 1.000 0 0.000
#> GSM28809 1 0.0000 0.984 1.000 0 0.000
#> GSM11329 1 0.0000 0.984 1.000 0 0.000
#> GSM28805 1 0.0000 0.984 1.000 0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM28816 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM28817 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM11327 4 0.4685 0.741 0.060 0 0.156 0.784
#> GSM28825 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11345 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM28819 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM11321 3 0.5078 0.428 0.272 0 0.700 0.028
#> GSM28820 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM11339 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM28804 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM28823 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM11336 4 0.0921 0.871 0.028 0 0.000 0.972
#> GSM11342 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM11333 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM28802 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM28803 4 0.4817 0.387 0.000 0 0.388 0.612
#> GSM11343 3 0.0000 0.853 0.000 0 1.000 0.000
#> GSM11347 3 0.0000 0.853 0.000 0 1.000 0.000
#> GSM28824 4 0.0921 0.871 0.028 0 0.000 0.972
#> GSM28813 4 0.0921 0.871 0.028 0 0.000 0.972
#> GSM28827 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM11337 1 0.4961 0.190 0.552 0 0.000 0.448
#> GSM28814 1 0.2773 0.860 0.880 0 0.004 0.116
#> GSM11331 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM11344 3 0.0000 0.853 0.000 0 1.000 0.000
#> GSM11330 3 0.0000 0.853 0.000 0 1.000 0.000
#> GSM11325 1 0.0921 0.949 0.972 0 0.000 0.028
#> GSM11338 4 0.0921 0.871 0.028 0 0.000 0.972
#> GSM28806 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM28826 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM28818 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM28821 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28807 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM28822 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM11328 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11323 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM11324 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM11341 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM11326 1 0.2216 0.880 0.908 0 0.092 0.000
#> GSM28810 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM11335 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM28809 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM11329 1 0.0000 0.976 1.000 0 0.000 0.000
#> GSM28805 1 0.0000 0.976 1.000 0 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM28816 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM28817 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM11327 5 0.354 0.751 0.032 0 0.000 0.156 0.812
#> GSM28825 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11322 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28828 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11346 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28808 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11332 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28811 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11334 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11340 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28812 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11345 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM28819 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM11321 3 0.311 0.713 0.000 0 0.800 0.200 0.000
#> GSM28820 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM11339 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM28804 1 0.311 0.830 0.800 0 0.200 0.000 0.000
#> GSM28823 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM11336 5 0.000 0.946 0.000 0 0.000 0.000 1.000
#> GSM11342 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM11333 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM28802 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM28803 3 0.311 0.713 0.000 0 0.800 0.200 0.000
#> GSM11343 4 0.000 1.000 0.000 0 0.000 1.000 0.000
#> GSM11347 4 0.000 1.000 0.000 0 0.000 1.000 0.000
#> GSM28824 5 0.000 0.946 0.000 0 0.000 0.000 1.000
#> GSM28813 5 0.000 0.946 0.000 0 0.000 0.000 1.000
#> GSM28827 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM11337 1 0.427 0.301 0.552 0 0.000 0.000 0.448
#> GSM28814 3 0.368 0.753 0.172 0 0.800 0.004 0.024
#> GSM11331 1 0.273 0.853 0.840 0 0.160 0.000 0.000
#> GSM11344 4 0.000 1.000 0.000 0 0.000 1.000 0.000
#> GSM11330 4 0.000 1.000 0.000 0 0.000 1.000 0.000
#> GSM11325 3 0.311 0.732 0.200 0 0.800 0.000 0.000
#> GSM11338 5 0.000 0.946 0.000 0 0.000 0.000 1.000
#> GSM28806 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM28826 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM28818 1 0.252 0.863 0.860 0 0.140 0.000 0.000
#> GSM28821 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28807 1 0.311 0.830 0.800 0 0.200 0.000 0.000
#> GSM28822 1 0.311 0.830 0.800 0 0.200 0.000 0.000
#> GSM11328 2 0.000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11323 1 0.269 0.855 0.844 0 0.156 0.000 0.000
#> GSM11324 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM11341 1 0.311 0.830 0.800 0 0.200 0.000 0.000
#> GSM11326 1 0.191 0.866 0.908 0 0.000 0.092 0.000
#> GSM28810 1 0.311 0.830 0.800 0 0.200 0.000 0.000
#> GSM11335 1 0.311 0.830 0.800 0 0.200 0.000 0.000
#> GSM28809 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM11329 1 0.000 0.917 1.000 0 0.000 0.000 0.000
#> GSM28805 1 0.000 0.917 1.000 0 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
#> GSM28815 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
#> GSM28816 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
#> GSM28817 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
#> GSM11327 5 0.3210 0.7687 0.036 0 0.000 0.000 0.812 0.152
#> GSM28825 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11345 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
#> GSM28819 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
#> GSM11321 3 0.0000 0.9985 0.000 0 1.000 0.000 0.000 0.000
#> GSM28820 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
#> GSM11339 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
#> GSM28804 4 0.3823 0.9873 0.436 0 0.000 0.564 0.000 0.000
#> GSM28823 1 0.3828 0.0865 0.560 0 0.000 0.440 0.000 0.000
#> GSM11336 5 0.0000 0.9505 0.000 0 0.000 0.000 1.000 0.000
#> GSM11342 1 0.3828 0.0865 0.560 0 0.000 0.440 0.000 0.000
#> GSM11333 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
#> GSM28802 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
#> GSM28803 3 0.0146 0.9955 0.000 0 0.996 0.000 0.000 0.004
#> GSM11343 6 0.0000 1.0000 0.000 0 0.000 0.000 0.000 1.000
#> GSM11347 6 0.0000 1.0000 0.000 0 0.000 0.000 0.000 1.000
#> GSM28824 5 0.0000 0.9505 0.000 0 0.000 0.000 1.000 0.000
#> GSM28813 5 0.0000 0.9505 0.000 0 0.000 0.000 1.000 0.000
#> GSM28827 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
#> GSM11337 1 0.3838 -0.2516 0.552 0 0.000 0.000 0.448 0.000
#> GSM28814 3 0.0000 0.9985 0.000 0 1.000 0.000 0.000 0.000
#> GSM11331 1 0.2454 0.5652 0.840 0 0.000 0.160 0.000 0.000
#> GSM11344 6 0.0000 1.0000 0.000 0 0.000 0.000 0.000 1.000
#> GSM11330 6 0.0000 1.0000 0.000 0 0.000 0.000 0.000 1.000
#> GSM11325 3 0.0000 0.9985 0.000 0 1.000 0.000 0.000 0.000
#> GSM11338 5 0.0000 0.9505 0.000 0 0.000 0.000 1.000 0.000
#> GSM28806 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
#> GSM28826 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
#> GSM28818 1 0.2260 0.6050 0.860 0 0.000 0.140 0.000 0.000
#> GSM28821 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28807 1 0.3756 -0.5172 0.600 0 0.000 0.400 0.000 0.000
#> GSM28822 4 0.3828 0.9912 0.440 0 0.000 0.560 0.000 0.000
#> GSM11328 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11323 1 0.2416 0.5741 0.844 0 0.000 0.156 0.000 0.000
#> GSM11324 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
#> GSM11341 4 0.3833 0.9872 0.444 0 0.000 0.556 0.000 0.000
#> GSM11326 1 0.1556 0.7034 0.920 0 0.000 0.000 0.000 0.080
#> GSM28810 1 0.2793 0.4630 0.800 0 0.000 0.200 0.000 0.000
#> GSM11335 1 0.2793 0.4630 0.800 0 0.000 0.200 0.000 0.000
#> GSM28809 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
#> GSM11329 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
#> GSM28805 1 0.0000 0.7949 1.000 0 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> SD:pam 54 0.398 2
#> SD:pam 53 0.373 3
#> SD:pam 51 0.483 4
#> SD:pam 53 0.452 5
#> SD:pam 48 0.398 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.688 0.921 0.952 0.4671 0.508 0.508
#> 3 3 1.000 0.993 0.997 0.2386 0.916 0.835
#> 4 4 0.820 0.892 0.936 0.2022 0.906 0.778
#> 5 5 0.800 0.817 0.897 0.1005 0.899 0.701
#> 6 6 0.827 0.853 0.892 0.0442 0.951 0.803
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM28815 1 0.0376 0.979 0.996 0.004
#> GSM28816 1 0.2043 0.952 0.968 0.032
#> GSM28817 1 0.0000 0.981 1.000 0.000
#> GSM11327 2 0.7453 0.845 0.212 0.788
#> GSM28825 2 0.0000 0.891 0.000 1.000
#> GSM11322 2 0.0000 0.891 0.000 1.000
#> GSM28828 2 0.0000 0.891 0.000 1.000
#> GSM11346 2 0.0000 0.891 0.000 1.000
#> GSM28808 2 0.0000 0.891 0.000 1.000
#> GSM11332 2 0.0000 0.891 0.000 1.000
#> GSM28811 2 0.0000 0.891 0.000 1.000
#> GSM11334 2 0.0000 0.891 0.000 1.000
#> GSM11340 2 0.0000 0.891 0.000 1.000
#> GSM28812 2 0.0000 0.891 0.000 1.000
#> GSM11345 1 0.0000 0.981 1.000 0.000
#> GSM28819 1 0.0000 0.981 1.000 0.000
#> GSM11321 2 0.7453 0.845 0.212 0.788
#> GSM28820 1 0.0000 0.981 1.000 0.000
#> GSM11339 1 0.0000 0.981 1.000 0.000
#> GSM28804 1 0.1184 0.971 0.984 0.016
#> GSM28823 1 0.0000 0.981 1.000 0.000
#> GSM11336 1 0.0000 0.981 1.000 0.000
#> GSM11342 1 0.0000 0.981 1.000 0.000
#> GSM11333 1 0.0000 0.981 1.000 0.000
#> GSM28802 1 0.0000 0.981 1.000 0.000
#> GSM28803 2 0.7453 0.845 0.212 0.788
#> GSM11343 2 0.7453 0.845 0.212 0.788
#> GSM11347 2 0.7453 0.845 0.212 0.788
#> GSM28824 1 0.0000 0.981 1.000 0.000
#> GSM28813 1 0.0000 0.981 1.000 0.000
#> GSM28827 1 0.0000 0.981 1.000 0.000
#> GSM11337 1 0.0000 0.981 1.000 0.000
#> GSM28814 2 0.7453 0.845 0.212 0.788
#> GSM11331 1 0.0000 0.981 1.000 0.000
#> GSM11344 2 0.7453 0.845 0.212 0.788
#> GSM11330 2 0.7453 0.845 0.212 0.788
#> GSM11325 2 0.7453 0.845 0.212 0.788
#> GSM11338 1 0.0000 0.981 1.000 0.000
#> GSM28806 1 0.0000 0.981 1.000 0.000
#> GSM28826 1 0.0000 0.981 1.000 0.000
#> GSM28818 1 0.1184 0.971 0.984 0.016
#> GSM28821 2 0.0000 0.891 0.000 1.000
#> GSM28807 1 0.1184 0.971 0.984 0.016
#> GSM28822 1 0.1184 0.971 0.984 0.016
#> GSM11328 2 0.0000 0.891 0.000 1.000
#> GSM11323 1 0.0000 0.981 1.000 0.000
#> GSM11324 1 0.0000 0.981 1.000 0.000
#> GSM11341 1 0.9460 0.285 0.636 0.364
#> GSM11326 2 0.7453 0.845 0.212 0.788
#> GSM28810 1 0.1184 0.971 0.984 0.016
#> GSM11335 1 0.1184 0.971 0.984 0.016
#> GSM28809 1 0.0000 0.981 1.000 0.000
#> GSM11329 1 0.0000 0.981 1.000 0.000
#> GSM28805 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
#> GSM28815 1 0.000 0.995 1.000 0.000 0.000
#> GSM28816 1 0.000 0.995 1.000 0.000 0.000
#> GSM28817 1 0.000 0.995 1.000 0.000 0.000
#> GSM11327 3 0.000 1.000 0.000 0.000 1.000
#> GSM28825 2 0.000 1.000 0.000 1.000 0.000
#> GSM11322 2 0.000 1.000 0.000 1.000 0.000
#> GSM28828 2 0.000 1.000 0.000 1.000 0.000
#> GSM11346 2 0.000 1.000 0.000 1.000 0.000
#> GSM28808 2 0.000 1.000 0.000 1.000 0.000
#> GSM11332 2 0.000 1.000 0.000 1.000 0.000
#> GSM28811 2 0.000 1.000 0.000 1.000 0.000
#> GSM11334 2 0.000 1.000 0.000 1.000 0.000
#> GSM11340 2 0.000 1.000 0.000 1.000 0.000
#> GSM28812 2 0.000 1.000 0.000 1.000 0.000
#> GSM11345 1 0.000 0.995 1.000 0.000 0.000
#> GSM28819 1 0.000 0.995 1.000 0.000 0.000
#> GSM11321 3 0.000 1.000 0.000 0.000 1.000
#> GSM28820 1 0.000 0.995 1.000 0.000 0.000
#> GSM11339 1 0.000 0.995 1.000 0.000 0.000
#> GSM28804 1 0.000 0.995 1.000 0.000 0.000
#> GSM28823 1 0.000 0.995 1.000 0.000 0.000
#> GSM11336 1 0.000 0.995 1.000 0.000 0.000
#> GSM11342 1 0.000 0.995 1.000 0.000 0.000
#> GSM11333 1 0.000 0.995 1.000 0.000 0.000
#> GSM28802 1 0.000 0.995 1.000 0.000 0.000
#> GSM28803 3 0.000 1.000 0.000 0.000 1.000
#> GSM11343 3 0.000 1.000 0.000 0.000 1.000
#> GSM11347 3 0.000 1.000 0.000 0.000 1.000
#> GSM28824 1 0.000 0.995 1.000 0.000 0.000
#> GSM28813 1 0.000 0.995 1.000 0.000 0.000
#> GSM28827 1 0.000 0.995 1.000 0.000 0.000
#> GSM11337 1 0.000 0.995 1.000 0.000 0.000
#> GSM28814 3 0.000 1.000 0.000 0.000 1.000
#> GSM11331 1 0.000 0.995 1.000 0.000 0.000
#> GSM11344 3 0.000 1.000 0.000 0.000 1.000
#> GSM11330 3 0.000 1.000 0.000 0.000 1.000
#> GSM11325 3 0.000 1.000 0.000 0.000 1.000
#> GSM11338 1 0.000 0.995 1.000 0.000 0.000
#> GSM28806 1 0.000 0.995 1.000 0.000 0.000
#> GSM28826 1 0.000 0.995 1.000 0.000 0.000
#> GSM28818 1 0.000 0.995 1.000 0.000 0.000
#> GSM28821 2 0.000 1.000 0.000 1.000 0.000
#> GSM28807 1 0.000 0.995 1.000 0.000 0.000
#> GSM28822 1 0.000 0.995 1.000 0.000 0.000
#> GSM11328 2 0.000 1.000 0.000 1.000 0.000
#> GSM11323 1 0.000 0.995 1.000 0.000 0.000
#> GSM11324 1 0.000 0.995 1.000 0.000 0.000
#> GSM11341 1 0.487 0.802 0.828 0.144 0.028
#> GSM11326 3 0.000 1.000 0.000 0.000 1.000
#> GSM28810 1 0.000 0.995 1.000 0.000 0.000
#> GSM11335 1 0.000 0.995 1.000 0.000 0.000
#> GSM28809 1 0.000 0.995 1.000 0.000 0.000
#> GSM11329 1 0.000 0.995 1.000 0.000 0.000
#> GSM28805 1 0.000 0.995 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.0000 0.874 1.000 0.000 0.00 0.000
#> GSM28816 1 0.0000 0.874 1.000 0.000 0.00 0.000
#> GSM28817 1 0.0000 0.874 1.000 0.000 0.00 0.000
#> GSM11327 3 0.0000 0.997 0.000 0.000 1.00 0.000
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.00 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.00 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.00 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.00 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.00 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.00 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.00 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.00 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.00 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.00 0.000
#> GSM11345 1 0.3444 0.830 0.816 0.000 0.00 0.184
#> GSM28819 1 0.3311 0.839 0.828 0.000 0.00 0.172
#> GSM11321 3 0.0000 0.997 0.000 0.000 1.00 0.000
#> GSM28820 1 0.3024 0.848 0.852 0.000 0.00 0.148
#> GSM11339 1 0.0188 0.874 0.996 0.000 0.00 0.004
#> GSM28804 4 0.4331 0.639 0.288 0.000 0.00 0.712
#> GSM28823 1 0.3569 0.822 0.804 0.000 0.00 0.196
#> GSM11336 1 0.0188 0.874 0.996 0.000 0.00 0.004
#> GSM11342 1 0.3569 0.822 0.804 0.000 0.00 0.196
#> GSM11333 1 0.0188 0.874 0.996 0.000 0.00 0.004
#> GSM28802 1 0.1118 0.873 0.964 0.000 0.00 0.036
#> GSM28803 3 0.0000 0.997 0.000 0.000 1.00 0.000
#> GSM11343 3 0.0000 0.997 0.000 0.000 1.00 0.000
#> GSM11347 3 0.0000 0.997 0.000 0.000 1.00 0.000
#> GSM28824 1 0.0336 0.874 0.992 0.000 0.00 0.008
#> GSM28813 1 0.0336 0.874 0.992 0.000 0.00 0.008
#> GSM28827 1 0.3172 0.842 0.840 0.000 0.00 0.160
#> GSM11337 1 0.0188 0.874 0.996 0.000 0.00 0.004
#> GSM28814 3 0.0000 0.997 0.000 0.000 1.00 0.000
#> GSM11331 1 0.4454 0.720 0.692 0.000 0.00 0.308
#> GSM11344 3 0.0000 0.997 0.000 0.000 1.00 0.000
#> GSM11330 3 0.0000 0.997 0.000 0.000 1.00 0.000
#> GSM11325 3 0.0000 0.997 0.000 0.000 1.00 0.000
#> GSM11338 1 0.0188 0.874 0.996 0.000 0.00 0.004
#> GSM28806 1 0.4406 0.730 0.700 0.000 0.00 0.300
#> GSM28826 1 0.0188 0.874 0.996 0.000 0.00 0.004
#> GSM28818 1 0.3528 0.694 0.808 0.000 0.00 0.192
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.00 0.000
#> GSM28807 4 0.0469 0.856 0.012 0.000 0.00 0.988
#> GSM28822 4 0.0336 0.858 0.008 0.000 0.00 0.992
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.00 0.000
#> GSM11323 1 0.4454 0.720 0.692 0.000 0.00 0.308
#> GSM11324 1 0.3311 0.836 0.828 0.000 0.00 0.172
#> GSM11341 4 0.2973 0.739 0.000 0.144 0.00 0.856
#> GSM11326 3 0.0707 0.977 0.000 0.000 0.98 0.020
#> GSM28810 1 0.4972 0.459 0.544 0.000 0.00 0.456
#> GSM11335 4 0.0000 0.855 0.000 0.000 0.00 1.000
#> GSM28809 1 0.0336 0.875 0.992 0.000 0.00 0.008
#> GSM11329 1 0.2814 0.852 0.868 0.000 0.00 0.132
#> GSM28805 1 0.0000 0.874 1.000 0.000 0.00 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 1 0.1544 0.801 0.932 0.000 0.000 0.000 0.068
#> GSM28816 1 0.1608 0.801 0.928 0.000 0.000 0.000 0.072
#> GSM28817 1 0.0880 0.799 0.968 0.000 0.000 0.000 0.032
#> GSM11327 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM28825 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM28828 2 0.0162 0.997 0.000 0.996 0.000 0.004 0.000
#> GSM11346 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM11345 1 0.2139 0.793 0.916 0.000 0.000 0.052 0.032
#> GSM28819 1 0.4817 0.577 0.656 0.000 0.000 0.044 0.300
#> GSM11321 3 0.0162 0.987 0.000 0.000 0.996 0.000 0.004
#> GSM28820 1 0.4402 0.474 0.636 0.000 0.000 0.012 0.352
#> GSM11339 1 0.1732 0.801 0.920 0.000 0.000 0.000 0.080
#> GSM28804 4 0.1830 0.704 0.068 0.000 0.000 0.924 0.008
#> GSM28823 1 0.1877 0.802 0.924 0.000 0.000 0.064 0.012
#> GSM11336 5 0.3857 0.495 0.312 0.000 0.000 0.000 0.688
#> GSM11342 1 0.1845 0.802 0.928 0.000 0.000 0.056 0.016
#> GSM11333 1 0.1792 0.800 0.916 0.000 0.000 0.000 0.084
#> GSM28802 1 0.4746 0.139 0.504 0.000 0.000 0.016 0.480
#> GSM28803 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM11343 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM11347 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM28824 5 0.1478 0.846 0.064 0.000 0.000 0.000 0.936
#> GSM28813 5 0.1341 0.841 0.056 0.000 0.000 0.000 0.944
#> GSM28827 1 0.1484 0.805 0.944 0.000 0.000 0.008 0.048
#> GSM11337 1 0.4210 0.349 0.588 0.000 0.000 0.000 0.412
#> GSM28814 3 0.0162 0.987 0.000 0.000 0.996 0.000 0.004
#> GSM11331 1 0.5531 0.614 0.664 0.000 0.004 0.168 0.164
#> GSM11344 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM11330 3 0.0000 0.989 0.000 0.000 1.000 0.000 0.000
#> GSM11325 3 0.0162 0.987 0.000 0.000 0.996 0.000 0.004
#> GSM11338 5 0.1965 0.838 0.096 0.000 0.000 0.000 0.904
#> GSM28806 1 0.3810 0.734 0.792 0.000 0.000 0.168 0.040
#> GSM28826 1 0.3857 0.574 0.688 0.000 0.000 0.000 0.312
#> GSM28818 4 0.5091 0.555 0.372 0.000 0.000 0.584 0.044
#> GSM28821 2 0.0324 0.994 0.004 0.992 0.000 0.004 0.000
#> GSM28807 4 0.2930 0.770 0.164 0.000 0.000 0.832 0.004
#> GSM28822 4 0.3010 0.768 0.172 0.000 0.000 0.824 0.004
#> GSM11328 2 0.0162 0.997 0.000 0.996 0.000 0.004 0.000
#> GSM11323 1 0.4855 0.685 0.720 0.000 0.000 0.168 0.112
#> GSM11324 1 0.1750 0.803 0.936 0.000 0.000 0.036 0.028
#> GSM11341 4 0.1525 0.671 0.004 0.036 0.000 0.948 0.012
#> GSM11326 3 0.2144 0.904 0.000 0.000 0.912 0.068 0.020
#> GSM28810 4 0.4298 0.570 0.352 0.000 0.000 0.640 0.008
#> GSM11335 4 0.2069 0.743 0.076 0.000 0.000 0.912 0.012
#> GSM28809 1 0.0880 0.807 0.968 0.000 0.000 0.000 0.032
#> GSM11329 1 0.1121 0.802 0.956 0.000 0.000 0.000 0.044
#> GSM28805 1 0.1792 0.799 0.916 0.000 0.000 0.000 0.084
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 1 0.2043 0.801 0.912 0.000 0.000 0.012 0.012 0.064
#> GSM28816 1 0.2515 0.791 0.888 0.000 0.000 0.016 0.024 0.072
#> GSM28817 1 0.1405 0.829 0.948 0.000 0.000 0.024 0.024 0.004
#> GSM11327 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM28825 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28828 2 0.0146 0.989 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM11346 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28811 2 0.0146 0.989 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM11334 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11345 1 0.2257 0.811 0.876 0.000 0.000 0.116 0.000 0.008
#> GSM28819 1 0.4321 0.647 0.716 0.000 0.000 0.036 0.228 0.020
#> GSM11321 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM28820 1 0.4809 0.173 0.548 0.000 0.000 0.028 0.408 0.016
#> GSM11339 1 0.1528 0.830 0.944 0.000 0.000 0.028 0.012 0.016
#> GSM28804 4 0.0935 0.928 0.032 0.000 0.000 0.964 0.000 0.004
#> GSM28823 1 0.3593 0.785 0.788 0.000 0.000 0.164 0.044 0.004
#> GSM11336 5 0.1444 0.752 0.072 0.000 0.000 0.000 0.928 0.000
#> GSM11342 1 0.3752 0.783 0.772 0.000 0.000 0.164 0.064 0.000
#> GSM11333 1 0.2495 0.792 0.892 0.000 0.000 0.016 0.032 0.060
#> GSM28802 5 0.5021 0.474 0.328 0.000 0.000 0.016 0.600 0.056
#> GSM28803 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11343 6 0.3023 1.000 0.000 0.000 0.232 0.000 0.000 0.768
#> GSM11347 6 0.3023 1.000 0.000 0.000 0.232 0.000 0.000 0.768
#> GSM28824 5 0.0000 0.766 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28813 5 0.0000 0.766 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28827 1 0.1934 0.827 0.916 0.000 0.000 0.040 0.044 0.000
#> GSM11337 5 0.4994 0.495 0.320 0.000 0.000 0.016 0.608 0.056
#> GSM28814 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11331 1 0.4721 0.707 0.672 0.000 0.000 0.212 0.000 0.116
#> GSM11344 6 0.3023 1.000 0.000 0.000 0.232 0.000 0.000 0.768
#> GSM11330 6 0.3023 1.000 0.000 0.000 0.232 0.000 0.000 0.768
#> GSM11325 3 0.0000 0.977 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11338 5 0.0146 0.767 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM28806 1 0.4357 0.721 0.696 0.000 0.000 0.232 0.000 0.072
#> GSM28826 1 0.4492 0.658 0.724 0.000 0.000 0.020 0.192 0.064
#> GSM28818 4 0.2882 0.776 0.180 0.000 0.000 0.812 0.000 0.008
#> GSM28821 2 0.1861 0.933 0.036 0.928 0.000 0.020 0.000 0.016
#> GSM28807 4 0.0937 0.935 0.040 0.000 0.000 0.960 0.000 0.000
#> GSM28822 4 0.0790 0.935 0.032 0.000 0.000 0.968 0.000 0.000
#> GSM11328 2 0.0692 0.972 0.000 0.976 0.000 0.020 0.000 0.004
#> GSM11323 1 0.4582 0.715 0.684 0.000 0.000 0.216 0.000 0.100
#> GSM11324 1 0.1226 0.830 0.952 0.000 0.000 0.040 0.004 0.004
#> GSM11341 4 0.3043 0.839 0.020 0.000 0.008 0.832 0.000 0.140
#> GSM11326 3 0.1863 0.884 0.000 0.000 0.920 0.044 0.000 0.036
#> GSM28810 4 0.0865 0.935 0.036 0.000 0.000 0.964 0.000 0.000
#> GSM11335 4 0.1049 0.935 0.032 0.000 0.000 0.960 0.000 0.008
#> GSM28809 1 0.0260 0.825 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM11329 1 0.1720 0.827 0.928 0.000 0.000 0.032 0.040 0.000
#> GSM28805 1 0.1353 0.827 0.952 0.000 0.000 0.024 0.012 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 tissue(p) k
#> SD:mclust 53 0.397 2
#> SD:mclust 54 0.374 3
#> SD:mclust 53 0.353 4
#> SD:mclust 50 0.407 5
#> SD:mclust 51 0.448 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.989 0.995 0.3580 0.648 0.648
#> 3 3 1.000 0.996 0.998 0.6514 0.762 0.632
#> 4 4 0.769 0.793 0.872 0.2337 0.839 0.614
#> 5 5 0.822 0.816 0.897 0.0811 0.883 0.598
#> 6 6 0.853 0.762 0.878 0.0454 0.921 0.648
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
#> GSM28815 1 0.000 0.994 1.000 0.000
#> GSM28816 1 0.821 0.656 0.744 0.256
#> GSM28817 1 0.000 0.994 1.000 0.000
#> GSM11327 1 0.000 0.994 1.000 0.000
#> GSM28825 2 0.000 1.000 0.000 1.000
#> GSM11322 2 0.000 1.000 0.000 1.000
#> GSM28828 2 0.000 1.000 0.000 1.000
#> GSM11346 2 0.000 1.000 0.000 1.000
#> GSM28808 2 0.000 1.000 0.000 1.000
#> GSM11332 2 0.000 1.000 0.000 1.000
#> GSM28811 2 0.000 1.000 0.000 1.000
#> GSM11334 2 0.000 1.000 0.000 1.000
#> GSM11340 2 0.000 1.000 0.000 1.000
#> GSM28812 2 0.000 1.000 0.000 1.000
#> GSM11345 1 0.000 0.994 1.000 0.000
#> GSM28819 1 0.000 0.994 1.000 0.000
#> GSM11321 1 0.000 0.994 1.000 0.000
#> GSM28820 1 0.000 0.994 1.000 0.000
#> GSM11339 1 0.000 0.994 1.000 0.000
#> GSM28804 1 0.000 0.994 1.000 0.000
#> GSM28823 1 0.000 0.994 1.000 0.000
#> GSM11336 1 0.000 0.994 1.000 0.000
#> GSM11342 1 0.000 0.994 1.000 0.000
#> GSM11333 1 0.000 0.994 1.000 0.000
#> GSM28802 1 0.000 0.994 1.000 0.000
#> GSM28803 1 0.000 0.994 1.000 0.000
#> GSM11343 1 0.000 0.994 1.000 0.000
#> GSM11347 1 0.000 0.994 1.000 0.000
#> GSM28824 1 0.000 0.994 1.000 0.000
#> GSM28813 1 0.000 0.994 1.000 0.000
#> GSM28827 1 0.000 0.994 1.000 0.000
#> GSM11337 1 0.000 0.994 1.000 0.000
#> GSM28814 1 0.000 0.994 1.000 0.000
#> GSM11331 1 0.000 0.994 1.000 0.000
#> GSM11344 1 0.000 0.994 1.000 0.000
#> GSM11330 1 0.000 0.994 1.000 0.000
#> GSM11325 1 0.000 0.994 1.000 0.000
#> GSM11338 1 0.000 0.994 1.000 0.000
#> GSM28806 1 0.000 0.994 1.000 0.000
#> GSM28826 1 0.000 0.994 1.000 0.000
#> GSM28818 1 0.000 0.994 1.000 0.000
#> GSM28821 2 0.000 1.000 0.000 1.000
#> GSM28807 1 0.000 0.994 1.000 0.000
#> GSM28822 1 0.000 0.994 1.000 0.000
#> GSM11328 2 0.000 1.000 0.000 1.000
#> GSM11323 1 0.000 0.994 1.000 0.000
#> GSM11324 1 0.000 0.994 1.000 0.000
#> GSM11341 1 0.000 0.994 1.000 0.000
#> GSM11326 1 0.000 0.994 1.000 0.000
#> GSM28810 1 0.000 0.994 1.000 0.000
#> GSM11335 1 0.000 0.994 1.000 0.000
#> GSM28809 1 0.000 0.994 1.000 0.000
#> GSM11329 1 0.000 0.994 1.000 0.000
#> GSM28805 1 0.000 0.994 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.000 0.998 1.000 0 0.000
#> GSM28816 1 0.000 0.998 1.000 0 0.000
#> GSM28817 1 0.000 0.998 1.000 0 0.000
#> GSM11327 3 0.000 0.996 0.000 0 1.000
#> GSM28825 2 0.000 1.000 0.000 1 0.000
#> GSM11322 2 0.000 1.000 0.000 1 0.000
#> GSM28828 2 0.000 1.000 0.000 1 0.000
#> GSM11346 2 0.000 1.000 0.000 1 0.000
#> GSM28808 2 0.000 1.000 0.000 1 0.000
#> GSM11332 2 0.000 1.000 0.000 1 0.000
#> GSM28811 2 0.000 1.000 0.000 1 0.000
#> GSM11334 2 0.000 1.000 0.000 1 0.000
#> GSM11340 2 0.000 1.000 0.000 1 0.000
#> GSM28812 2 0.000 1.000 0.000 1 0.000
#> GSM11345 1 0.000 0.998 1.000 0 0.000
#> GSM28819 1 0.000 0.998 1.000 0 0.000
#> GSM11321 3 0.000 0.996 0.000 0 1.000
#> GSM28820 1 0.000 0.998 1.000 0 0.000
#> GSM11339 1 0.000 0.998 1.000 0 0.000
#> GSM28804 1 0.000 0.998 1.000 0 0.000
#> GSM28823 1 0.000 0.998 1.000 0 0.000
#> GSM11336 1 0.000 0.998 1.000 0 0.000
#> GSM11342 1 0.000 0.998 1.000 0 0.000
#> GSM11333 1 0.000 0.998 1.000 0 0.000
#> GSM28802 1 0.000 0.998 1.000 0 0.000
#> GSM28803 3 0.000 0.996 0.000 0 1.000
#> GSM11343 3 0.000 0.996 0.000 0 1.000
#> GSM11347 3 0.000 0.996 0.000 0 1.000
#> GSM28824 1 0.000 0.998 1.000 0 0.000
#> GSM28813 1 0.196 0.940 0.944 0 0.056
#> GSM28827 1 0.000 0.998 1.000 0 0.000
#> GSM11337 1 0.000 0.998 1.000 0 0.000
#> GSM28814 3 0.000 0.996 0.000 0 1.000
#> GSM11331 1 0.000 0.998 1.000 0 0.000
#> GSM11344 3 0.000 0.996 0.000 0 1.000
#> GSM11330 3 0.000 0.996 0.000 0 1.000
#> GSM11325 3 0.000 0.996 0.000 0 1.000
#> GSM11338 1 0.000 0.998 1.000 0 0.000
#> GSM28806 1 0.000 0.998 1.000 0 0.000
#> GSM28826 1 0.000 0.998 1.000 0 0.000
#> GSM28818 1 0.000 0.998 1.000 0 0.000
#> GSM28821 2 0.000 1.000 0.000 1 0.000
#> GSM28807 1 0.000 0.998 1.000 0 0.000
#> GSM28822 1 0.000 0.998 1.000 0 0.000
#> GSM11328 2 0.000 1.000 0.000 1 0.000
#> GSM11323 1 0.000 0.998 1.000 0 0.000
#> GSM11324 1 0.000 0.998 1.000 0 0.000
#> GSM11341 3 0.116 0.962 0.028 0 0.972
#> GSM11326 3 0.000 0.996 0.000 0 1.000
#> GSM28810 1 0.000 0.998 1.000 0 0.000
#> GSM11335 1 0.000 0.998 1.000 0 0.000
#> GSM28809 1 0.000 0.998 1.000 0 0.000
#> GSM11329 1 0.000 0.998 1.000 0 0.000
#> GSM28805 1 0.000 0.998 1.000 0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.3649 0.7525 0.796 0.000 0.000 0.204
#> GSM28816 1 0.2197 0.6843 0.916 0.004 0.000 0.080
#> GSM28817 1 0.4406 0.7356 0.700 0.000 0.000 0.300
#> GSM11327 3 0.1022 0.9484 0.032 0.000 0.968 0.000
#> GSM28825 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11345 1 0.4790 0.6148 0.620 0.000 0.000 0.380
#> GSM28819 1 0.4193 0.7497 0.732 0.000 0.000 0.268
#> GSM11321 3 0.1792 0.9350 0.068 0.000 0.932 0.000
#> GSM28820 1 0.4164 0.7508 0.736 0.000 0.000 0.264
#> GSM11339 4 0.4866 0.0487 0.404 0.000 0.000 0.596
#> GSM28804 4 0.1022 0.7872 0.032 0.000 0.000 0.968
#> GSM28823 1 0.4406 0.7368 0.700 0.000 0.000 0.300
#> GSM11336 1 0.0592 0.7183 0.984 0.000 0.000 0.016
#> GSM11342 1 0.4382 0.7390 0.704 0.000 0.000 0.296
#> GSM11333 1 0.2921 0.6513 0.860 0.000 0.000 0.140
#> GSM28802 1 0.1557 0.7383 0.944 0.000 0.000 0.056
#> GSM28803 3 0.1302 0.9457 0.044 0.000 0.956 0.000
#> GSM11343 3 0.0000 0.9510 0.000 0.000 1.000 0.000
#> GSM11347 3 0.0000 0.9510 0.000 0.000 1.000 0.000
#> GSM28824 1 0.0592 0.7183 0.984 0.000 0.000 0.016
#> GSM28813 1 0.1510 0.6974 0.956 0.000 0.028 0.016
#> GSM28827 1 0.4406 0.7353 0.700 0.000 0.000 0.300
#> GSM11337 1 0.0336 0.7299 0.992 0.000 0.000 0.008
#> GSM28814 3 0.2999 0.8904 0.132 0.000 0.864 0.004
#> GSM11331 4 0.5407 0.4029 0.296 0.000 0.036 0.668
#> GSM11344 3 0.0000 0.9510 0.000 0.000 1.000 0.000
#> GSM11330 3 0.0000 0.9510 0.000 0.000 1.000 0.000
#> GSM11325 3 0.3498 0.8626 0.160 0.000 0.832 0.008
#> GSM11338 1 0.0000 0.7262 1.000 0.000 0.000 0.000
#> GSM28806 4 0.2345 0.7413 0.100 0.000 0.000 0.900
#> GSM28826 1 0.0000 0.7262 1.000 0.000 0.000 0.000
#> GSM28818 4 0.1302 0.7907 0.044 0.000 0.000 0.956
#> GSM28821 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28807 4 0.0817 0.7860 0.024 0.000 0.000 0.976
#> GSM28822 4 0.0592 0.7884 0.016 0.000 0.000 0.984
#> GSM11328 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11323 4 0.4193 0.4958 0.268 0.000 0.000 0.732
#> GSM11324 1 0.4431 0.7315 0.696 0.000 0.000 0.304
#> GSM11341 4 0.4560 0.3574 0.004 0.000 0.296 0.700
#> GSM11326 3 0.0469 0.9458 0.000 0.000 0.988 0.012
#> GSM28810 4 0.0921 0.7850 0.028 0.000 0.000 0.972
#> GSM11335 4 0.0707 0.7898 0.020 0.000 0.000 0.980
#> GSM28809 1 0.4989 0.2983 0.528 0.000 0.000 0.472
#> GSM11329 1 0.4431 0.7315 0.696 0.000 0.000 0.304
#> GSM28805 1 0.4331 0.7429 0.712 0.000 0.000 0.288
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 1 0.3519 0.618 0.776 0.000 0.000 0.008 0.216
#> GSM28816 5 0.3405 0.764 0.108 0.024 0.000 0.020 0.848
#> GSM28817 1 0.0324 0.898 0.992 0.000 0.000 0.004 0.004
#> GSM11327 3 0.1704 0.798 0.000 0.000 0.928 0.004 0.068
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11345 1 0.0162 0.899 0.996 0.000 0.000 0.004 0.000
#> GSM28819 1 0.0451 0.894 0.988 0.000 0.000 0.008 0.004
#> GSM11321 3 0.4775 0.671 0.004 0.000 0.660 0.032 0.304
#> GSM28820 1 0.0162 0.897 0.996 0.000 0.000 0.004 0.000
#> GSM11339 1 0.1704 0.862 0.928 0.000 0.000 0.068 0.004
#> GSM28804 4 0.1357 0.884 0.048 0.000 0.000 0.948 0.004
#> GSM28823 1 0.0324 0.897 0.992 0.000 0.000 0.004 0.004
#> GSM11336 5 0.1478 0.760 0.064 0.000 0.000 0.000 0.936
#> GSM11342 1 0.0162 0.898 0.996 0.000 0.000 0.000 0.004
#> GSM11333 5 0.4227 0.676 0.292 0.000 0.000 0.016 0.692
#> GSM28802 1 0.4557 0.481 0.700 0.000 0.004 0.032 0.264
#> GSM28803 3 0.4181 0.709 0.000 0.000 0.712 0.020 0.268
#> GSM11343 3 0.0404 0.813 0.000 0.000 0.988 0.000 0.012
#> GSM11347 3 0.0290 0.813 0.000 0.000 0.992 0.008 0.000
#> GSM28824 5 0.1270 0.751 0.052 0.000 0.000 0.000 0.948
#> GSM28813 5 0.1282 0.741 0.044 0.000 0.004 0.000 0.952
#> GSM28827 1 0.0324 0.898 0.992 0.000 0.000 0.004 0.004
#> GSM11337 5 0.4283 0.338 0.456 0.000 0.000 0.000 0.544
#> GSM28814 3 0.5052 0.541 0.000 0.000 0.552 0.036 0.412
#> GSM11331 1 0.4123 0.751 0.800 0.000 0.128 0.060 0.012
#> GSM11344 3 0.0000 0.813 0.000 0.000 1.000 0.000 0.000
#> GSM11330 3 0.0566 0.811 0.000 0.000 0.984 0.012 0.004
#> GSM11325 3 0.5341 0.501 0.008 0.000 0.524 0.036 0.432
#> GSM11338 5 0.2329 0.772 0.124 0.000 0.000 0.000 0.876
#> GSM28806 4 0.4497 0.365 0.424 0.000 0.000 0.568 0.008
#> GSM28826 5 0.4582 0.433 0.416 0.000 0.000 0.012 0.572
#> GSM28818 4 0.1571 0.883 0.060 0.000 0.000 0.936 0.004
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM28807 4 0.1197 0.885 0.048 0.000 0.000 0.952 0.000
#> GSM28822 4 0.1197 0.885 0.048 0.000 0.000 0.952 0.000
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11323 1 0.4704 0.691 0.748 0.000 0.084 0.160 0.008
#> GSM11324 1 0.0162 0.899 0.996 0.000 0.000 0.004 0.000
#> GSM11341 4 0.1197 0.838 0.000 0.000 0.048 0.952 0.000
#> GSM11326 3 0.1243 0.803 0.004 0.000 0.960 0.028 0.008
#> GSM28810 4 0.3353 0.780 0.196 0.000 0.008 0.796 0.000
#> GSM11335 4 0.2079 0.873 0.064 0.000 0.020 0.916 0.000
#> GSM28809 1 0.3134 0.797 0.848 0.000 0.000 0.120 0.032
#> GSM11329 1 0.0290 0.898 0.992 0.000 0.000 0.008 0.000
#> GSM28805 1 0.0162 0.898 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
#> GSM28815 1 0.5124 0.3269 0.588 0.000 0.000 0.008 0.324 0.080
#> GSM28816 5 0.3784 0.7914 0.060 0.008 0.000 0.016 0.812 0.104
#> GSM28817 1 0.0748 0.8614 0.976 0.000 0.004 0.000 0.016 0.004
#> GSM11327 3 0.3102 0.5934 0.000 0.000 0.816 0.000 0.156 0.028
#> GSM28825 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11345 1 0.1152 0.8537 0.952 0.000 0.000 0.000 0.004 0.044
#> GSM28819 1 0.2006 0.8064 0.892 0.000 0.000 0.000 0.004 0.104
#> GSM11321 6 0.1686 0.6775 0.000 0.000 0.064 0.000 0.012 0.924
#> GSM28820 1 0.0858 0.8593 0.968 0.000 0.000 0.000 0.004 0.028
#> GSM11339 1 0.2414 0.8330 0.896 0.000 0.000 0.036 0.012 0.056
#> GSM28804 4 0.0260 0.9284 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM28823 1 0.0692 0.8640 0.976 0.000 0.000 0.000 0.004 0.020
#> GSM11336 5 0.0146 0.8555 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM11342 1 0.0603 0.8644 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM11333 5 0.5209 0.6444 0.180 0.000 0.000 0.044 0.680 0.096
#> GSM28802 6 0.3911 0.3227 0.368 0.000 0.000 0.000 0.008 0.624
#> GSM28803 6 0.3387 0.5874 0.000 0.000 0.164 0.000 0.040 0.796
#> GSM11343 3 0.2996 0.6120 0.000 0.000 0.772 0.000 0.000 0.228
#> GSM11347 3 0.2454 0.6679 0.000 0.000 0.840 0.000 0.000 0.160
#> GSM28824 5 0.0291 0.8559 0.000 0.000 0.004 0.000 0.992 0.004
#> GSM28813 5 0.0632 0.8530 0.000 0.000 0.000 0.000 0.976 0.024
#> GSM28827 1 0.1116 0.8517 0.960 0.000 0.008 0.000 0.004 0.028
#> GSM11337 5 0.3637 0.7194 0.164 0.000 0.000 0.000 0.780 0.056
#> GSM28814 6 0.2308 0.6741 0.000 0.000 0.068 0.000 0.040 0.892
#> GSM11331 3 0.5557 0.2315 0.372 0.000 0.536 0.004 0.032 0.056
#> GSM11344 3 0.2562 0.6626 0.000 0.000 0.828 0.000 0.000 0.172
#> GSM11330 3 0.2219 0.6721 0.000 0.000 0.864 0.000 0.000 0.136
#> GSM11325 6 0.1768 0.6818 0.004 0.000 0.040 0.004 0.020 0.932
#> GSM11338 5 0.0717 0.8573 0.008 0.000 0.000 0.000 0.976 0.016
#> GSM28806 1 0.5517 0.0606 0.472 0.000 0.000 0.396 0.000 0.132
#> GSM28826 6 0.6049 -0.0850 0.256 0.000 0.000 0.000 0.356 0.388
#> GSM28818 4 0.0767 0.9254 0.012 0.000 0.004 0.976 0.000 0.008
#> GSM28821 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28807 4 0.0547 0.9264 0.000 0.000 0.020 0.980 0.000 0.000
#> GSM28822 4 0.0000 0.9287 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM11328 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11323 3 0.5515 0.0109 0.452 0.000 0.464 0.004 0.024 0.056
#> GSM11324 1 0.0260 0.8628 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM11341 4 0.0146 0.9285 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM11326 3 0.0291 0.6432 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM28810 4 0.3909 0.6359 0.236 0.000 0.020 0.732 0.000 0.012
#> GSM11335 4 0.1296 0.9126 0.004 0.000 0.044 0.948 0.000 0.004
#> GSM28809 1 0.4889 0.6831 0.752 0.000 0.032 0.044 0.112 0.060
#> GSM11329 1 0.0363 0.8648 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM28805 1 0.0692 0.8648 0.976 0.000 0.000 0.000 0.004 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> SD:NMF 54 0.398 2
#> SD:NMF 54 0.374 3
#> SD:NMF 49 0.348 4
#> SD:NMF 50 0.443 5
#> SD:NMF 48 0.404 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.517 0.817 0.884 0.3084 0.743 0.743
#> 3 3 0.435 0.797 0.826 0.6932 0.715 0.616
#> 4 4 0.686 0.771 0.857 0.2889 0.850 0.680
#> 5 5 0.805 0.827 0.896 0.0968 0.902 0.703
#> 6 6 0.817 0.782 0.902 0.0355 0.980 0.916
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
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
#> GSM28815 1 0.2423 0.865 0.960 0.040
#> GSM28816 1 0.2778 0.862 0.952 0.048
#> GSM28817 1 0.0000 0.876 1.000 0.000
#> GSM11327 1 0.9977 -0.417 0.528 0.472
#> GSM28825 1 0.7950 0.751 0.760 0.240
#> GSM11322 1 0.7950 0.751 0.760 0.240
#> GSM28828 1 0.7950 0.751 0.760 0.240
#> GSM11346 1 0.7950 0.751 0.760 0.240
#> GSM28808 1 0.7950 0.751 0.760 0.240
#> GSM11332 1 0.7950 0.751 0.760 0.240
#> GSM28811 1 0.7950 0.751 0.760 0.240
#> GSM11334 1 0.7950 0.751 0.760 0.240
#> GSM11340 1 0.7950 0.751 0.760 0.240
#> GSM28812 1 0.7950 0.751 0.760 0.240
#> GSM11345 1 0.0000 0.876 1.000 0.000
#> GSM28819 1 0.0000 0.876 1.000 0.000
#> GSM11321 2 0.8207 1.000 0.256 0.744
#> GSM28820 1 0.0000 0.876 1.000 0.000
#> GSM11339 1 0.0000 0.876 1.000 0.000
#> GSM28804 1 0.3733 0.854 0.928 0.072
#> GSM28823 1 0.0000 0.876 1.000 0.000
#> GSM11336 1 0.0000 0.876 1.000 0.000
#> GSM11342 1 0.0000 0.876 1.000 0.000
#> GSM11333 1 0.2778 0.862 0.952 0.048
#> GSM28802 1 0.0000 0.876 1.000 0.000
#> GSM28803 2 0.8207 1.000 0.256 0.744
#> GSM11343 2 0.8207 1.000 0.256 0.744
#> GSM11347 2 0.8207 1.000 0.256 0.744
#> GSM28824 1 0.0000 0.876 1.000 0.000
#> GSM28813 1 0.0000 0.876 1.000 0.000
#> GSM28827 1 0.0000 0.876 1.000 0.000
#> GSM11337 1 0.0000 0.876 1.000 0.000
#> GSM28814 2 0.8207 1.000 0.256 0.744
#> GSM11331 1 0.0000 0.876 1.000 0.000
#> GSM11344 2 0.8207 1.000 0.256 0.744
#> GSM11330 2 0.8207 1.000 0.256 0.744
#> GSM11325 2 0.8207 1.000 0.256 0.744
#> GSM11338 1 0.0000 0.876 1.000 0.000
#> GSM28806 1 0.0000 0.876 1.000 0.000
#> GSM28826 1 0.0000 0.876 1.000 0.000
#> GSM28818 1 0.0938 0.874 0.988 0.012
#> GSM28821 1 0.7950 0.751 0.760 0.240
#> GSM28807 1 0.1633 0.869 0.976 0.024
#> GSM28822 1 0.3114 0.862 0.944 0.056
#> GSM11328 1 0.7950 0.751 0.760 0.240
#> GSM11323 1 0.0000 0.876 1.000 0.000
#> GSM11324 1 0.0000 0.876 1.000 0.000
#> GSM11341 1 0.2043 0.865 0.968 0.032
#> GSM11326 1 0.9977 -0.417 0.528 0.472
#> GSM28810 1 0.0938 0.874 0.988 0.012
#> GSM11335 1 0.1633 0.869 0.976 0.024
#> GSM28809 1 0.0938 0.874 0.988 0.012
#> GSM11329 1 0.0000 0.876 1.000 0.000
#> GSM28805 1 0.0000 0.876 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.1878 0.787 0.952 0.044 0.004
#> GSM28816 1 0.2280 0.776 0.940 0.052 0.008
#> GSM28817 1 0.0000 0.829 1.000 0.000 0.000
#> GSM11327 1 0.6295 -0.293 0.528 0.000 0.472
#> GSM28825 2 0.5431 1.000 0.284 0.716 0.000
#> GSM11322 2 0.5431 1.000 0.284 0.716 0.000
#> GSM28828 2 0.5431 1.000 0.284 0.716 0.000
#> GSM11346 2 0.5431 1.000 0.284 0.716 0.000
#> GSM28808 2 0.5431 1.000 0.284 0.716 0.000
#> GSM11332 2 0.5431 1.000 0.284 0.716 0.000
#> GSM28811 2 0.5431 1.000 0.284 0.716 0.000
#> GSM11334 2 0.5431 1.000 0.284 0.716 0.000
#> GSM11340 2 0.5431 1.000 0.284 0.716 0.000
#> GSM28812 2 0.5431 1.000 0.284 0.716 0.000
#> GSM11345 1 0.0000 0.829 1.000 0.000 0.000
#> GSM28819 1 0.0000 0.829 1.000 0.000 0.000
#> GSM11321 3 0.4654 1.000 0.208 0.000 0.792
#> GSM28820 1 0.0000 0.829 1.000 0.000 0.000
#> GSM11339 1 0.0237 0.827 0.996 0.004 0.000
#> GSM28804 1 0.9445 0.355 0.472 0.336 0.192
#> GSM28823 1 0.0000 0.829 1.000 0.000 0.000
#> GSM11336 1 0.0000 0.829 1.000 0.000 0.000
#> GSM11342 1 0.0000 0.829 1.000 0.000 0.000
#> GSM11333 1 0.2280 0.776 0.940 0.052 0.008
#> GSM28802 1 0.0000 0.829 1.000 0.000 0.000
#> GSM28803 3 0.4654 1.000 0.208 0.000 0.792
#> GSM11343 3 0.4654 1.000 0.208 0.000 0.792
#> GSM11347 3 0.4654 1.000 0.208 0.000 0.792
#> GSM28824 1 0.0000 0.829 1.000 0.000 0.000
#> GSM28813 1 0.0000 0.829 1.000 0.000 0.000
#> GSM28827 1 0.0000 0.829 1.000 0.000 0.000
#> GSM11337 1 0.0000 0.829 1.000 0.000 0.000
#> GSM28814 3 0.4654 1.000 0.208 0.000 0.792
#> GSM11331 1 0.0000 0.829 1.000 0.000 0.000
#> GSM11344 3 0.4654 1.000 0.208 0.000 0.792
#> GSM11330 3 0.4654 1.000 0.208 0.000 0.792
#> GSM11325 3 0.4654 1.000 0.208 0.000 0.792
#> GSM11338 1 0.0000 0.829 1.000 0.000 0.000
#> GSM28806 1 0.0237 0.827 0.996 0.004 0.000
#> GSM28826 1 0.0000 0.829 1.000 0.000 0.000
#> GSM28818 1 0.4937 0.699 0.824 0.148 0.028
#> GSM28821 2 0.5431 1.000 0.284 0.716 0.000
#> GSM28807 1 0.9359 0.379 0.508 0.284 0.208
#> GSM28822 1 0.9517 0.352 0.472 0.320 0.208
#> GSM11328 2 0.5431 1.000 0.284 0.716 0.000
#> GSM11323 1 0.0000 0.829 1.000 0.000 0.000
#> GSM11324 1 0.0000 0.829 1.000 0.000 0.000
#> GSM11341 1 0.9422 0.368 0.500 0.284 0.216
#> GSM11326 1 0.6295 -0.293 0.528 0.000 0.472
#> GSM28810 1 0.6476 0.627 0.748 0.184 0.068
#> GSM11335 1 0.9359 0.379 0.508 0.284 0.208
#> GSM28809 1 0.3983 0.715 0.852 0.144 0.004
#> GSM11329 1 0.0000 0.829 1.000 0.000 0.000
#> GSM28805 1 0.0000 0.829 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.5386 0.504 0.632 0 0.024 0.344
#> GSM28816 1 0.5649 0.492 0.620 0 0.036 0.344
#> GSM28817 1 0.0000 0.771 1.000 0 0.000 0.000
#> GSM11327 3 0.4933 0.422 0.432 0 0.568 0.000
#> GSM28825 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11345 1 0.0000 0.771 1.000 0 0.000 0.000
#> GSM28819 1 0.0000 0.771 1.000 0 0.000 0.000
#> GSM11321 3 0.2345 0.890 0.100 0 0.900 0.000
#> GSM28820 1 0.0000 0.771 1.000 0 0.000 0.000
#> GSM11339 1 0.0469 0.768 0.988 0 0.000 0.012
#> GSM28804 4 0.5291 0.910 0.324 0 0.024 0.652
#> GSM28823 1 0.0188 0.770 0.996 0 0.000 0.004
#> GSM11336 1 0.6951 0.429 0.544 0 0.132 0.324
#> GSM11342 1 0.0188 0.770 0.996 0 0.000 0.004
#> GSM11333 1 0.5630 0.482 0.608 0 0.032 0.360
#> GSM28802 1 0.0188 0.771 0.996 0 0.000 0.004
#> GSM28803 3 0.2345 0.890 0.100 0 0.900 0.000
#> GSM11343 3 0.2345 0.890 0.100 0 0.900 0.000
#> GSM11347 3 0.2345 0.890 0.100 0 0.900 0.000
#> GSM28824 1 0.6951 0.429 0.544 0 0.132 0.324
#> GSM28813 1 0.6951 0.429 0.544 0 0.132 0.324
#> GSM28827 1 0.0188 0.771 0.996 0 0.000 0.004
#> GSM11337 1 0.1109 0.754 0.968 0 0.028 0.004
#> GSM28814 3 0.2345 0.890 0.100 0 0.900 0.000
#> GSM11331 1 0.0336 0.767 0.992 0 0.000 0.008
#> GSM11344 3 0.2345 0.890 0.100 0 0.900 0.000
#> GSM11330 3 0.2345 0.890 0.100 0 0.900 0.000
#> GSM11325 3 0.2345 0.890 0.100 0 0.900 0.000
#> GSM11338 1 0.6951 0.429 0.544 0 0.132 0.324
#> GSM28806 1 0.0336 0.767 0.992 0 0.000 0.008
#> GSM28826 1 0.0376 0.770 0.992 0 0.004 0.004
#> GSM28818 1 0.3907 0.319 0.768 0 0.000 0.232
#> GSM28821 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28807 4 0.4713 0.926 0.360 0 0.000 0.640
#> GSM28822 4 0.4543 0.917 0.324 0 0.000 0.676
#> GSM11328 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11323 1 0.0336 0.767 0.992 0 0.000 0.008
#> GSM11324 1 0.0000 0.771 1.000 0 0.000 0.000
#> GSM11341 4 0.5007 0.926 0.356 0 0.008 0.636
#> GSM11326 3 0.4933 0.422 0.432 0 0.568 0.000
#> GSM28810 1 0.4193 0.188 0.732 0 0.000 0.268
#> GSM11335 4 0.4955 0.807 0.444 0 0.000 0.556
#> GSM28809 1 0.3649 0.399 0.796 0 0.000 0.204
#> GSM11329 1 0.0000 0.771 1.000 0 0.000 0.000
#> GSM28805 1 0.0188 0.771 0.996 0 0.004 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 5 0.4331 0.684 0.400 0 0.004 0.000 0.596
#> GSM28816 5 0.4415 0.690 0.388 0 0.008 0.000 0.604
#> GSM28817 1 0.0000 0.898 1.000 0 0.000 0.000 0.000
#> GSM11327 3 0.5124 0.417 0.288 0 0.644 0.000 0.068
#> GSM28825 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11345 1 0.0000 0.898 1.000 0 0.000 0.000 0.000
#> GSM28819 1 0.0000 0.898 1.000 0 0.000 0.000 0.000
#> GSM11321 3 0.0613 0.888 0.008 0 0.984 0.004 0.004
#> GSM28820 1 0.0000 0.898 1.000 0 0.000 0.000 0.000
#> GSM11339 1 0.0579 0.892 0.984 0 0.000 0.008 0.008
#> GSM28804 4 0.3365 0.640 0.004 0 0.008 0.808 0.180
#> GSM28823 1 0.0162 0.897 0.996 0 0.000 0.000 0.004
#> GSM11336 5 0.3895 0.796 0.320 0 0.000 0.000 0.680
#> GSM11342 1 0.0162 0.897 0.996 0 0.000 0.000 0.004
#> GSM11333 5 0.4380 0.701 0.376 0 0.008 0.000 0.616
#> GSM28802 1 0.0162 0.896 0.996 0 0.000 0.000 0.004
#> GSM28803 3 0.0613 0.888 0.008 0 0.984 0.004 0.004
#> GSM11343 3 0.0290 0.889 0.008 0 0.992 0.000 0.000
#> GSM11347 3 0.0290 0.889 0.008 0 0.992 0.000 0.000
#> GSM28824 5 0.3895 0.796 0.320 0 0.000 0.000 0.680
#> GSM28813 5 0.3895 0.796 0.320 0 0.000 0.000 0.680
#> GSM28827 1 0.0451 0.893 0.988 0 0.004 0.000 0.008
#> GSM11337 1 0.1282 0.860 0.952 0 0.004 0.000 0.044
#> GSM28814 3 0.0613 0.888 0.008 0 0.984 0.004 0.004
#> GSM11331 1 0.1928 0.812 0.920 0 0.004 0.004 0.072
#> GSM11344 3 0.0290 0.889 0.008 0 0.992 0.000 0.000
#> GSM11330 3 0.0290 0.889 0.008 0 0.992 0.000 0.000
#> GSM11325 3 0.0613 0.888 0.008 0 0.984 0.004 0.004
#> GSM11338 5 0.3895 0.796 0.320 0 0.000 0.000 0.680
#> GSM28806 1 0.0324 0.895 0.992 0 0.000 0.004 0.004
#> GSM28826 1 0.0510 0.890 0.984 0 0.000 0.000 0.016
#> GSM28818 1 0.4101 0.422 0.664 0 0.000 0.332 0.004
#> GSM28821 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28807 4 0.3109 0.671 0.200 0 0.000 0.800 0.000
#> GSM28822 4 0.2930 0.650 0.004 0 0.000 0.832 0.164
#> GSM11328 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11323 1 0.1928 0.812 0.920 0 0.004 0.004 0.072
#> GSM11324 1 0.0000 0.898 1.000 0 0.000 0.000 0.000
#> GSM11341 4 0.2488 0.701 0.124 0 0.000 0.872 0.004
#> GSM11326 3 0.5124 0.417 0.288 0 0.644 0.000 0.068
#> GSM28810 1 0.3949 0.470 0.696 0 0.000 0.300 0.004
#> GSM11335 4 0.4331 0.392 0.400 0 0.000 0.596 0.004
#> GSM28809 1 0.4122 0.485 0.688 0 0.004 0.304 0.004
#> GSM11329 1 0.0000 0.898 1.000 0 0.000 0.000 0.000
#> GSM28805 1 0.0162 0.897 0.996 0 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
#> GSM28815 5 0.2912 0.499 0.216 0 0.000 0.000 0.784 0.000
#> GSM28816 5 0.2312 0.475 0.112 0 0.000 0.000 0.876 0.012
#> GSM28817 1 0.0000 0.917 1.000 0 0.000 0.000 0.000 0.000
#> GSM11327 3 0.4788 0.432 0.276 0 0.648 0.000 0.068 0.008
#> GSM28825 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11345 1 0.0000 0.917 1.000 0 0.000 0.000 0.000 0.000
#> GSM28819 1 0.0000 0.917 1.000 0 0.000 0.000 0.000 0.000
#> GSM11321 3 0.0260 0.879 0.000 0 0.992 0.008 0.000 0.000
#> GSM28820 1 0.0000 0.917 1.000 0 0.000 0.000 0.000 0.000
#> GSM11339 1 0.0520 0.911 0.984 0 0.000 0.008 0.008 0.000
#> GSM28804 6 0.2912 0.966 0.000 0 0.000 0.172 0.012 0.816
#> GSM28823 1 0.0146 0.916 0.996 0 0.000 0.000 0.004 0.000
#> GSM11336 5 0.5583 0.700 0.284 0 0.000 0.000 0.536 0.180
#> GSM11342 1 0.0146 0.916 0.996 0 0.000 0.000 0.004 0.000
#> GSM11333 5 0.2170 0.467 0.100 0 0.000 0.000 0.888 0.012
#> GSM28802 1 0.0146 0.916 0.996 0 0.000 0.000 0.004 0.000
#> GSM28803 3 0.0260 0.879 0.000 0 0.992 0.008 0.000 0.000
#> GSM11343 3 0.0000 0.879 0.000 0 1.000 0.000 0.000 0.000
#> GSM11347 3 0.0000 0.879 0.000 0 1.000 0.000 0.000 0.000
#> GSM28824 5 0.5583 0.700 0.284 0 0.000 0.000 0.536 0.180
#> GSM28813 5 0.5583 0.700 0.284 0 0.000 0.000 0.536 0.180
#> GSM28827 1 0.0405 0.914 0.988 0 0.000 0.000 0.008 0.004
#> GSM11337 1 0.1196 0.886 0.952 0 0.000 0.000 0.008 0.040
#> GSM28814 3 0.0260 0.879 0.000 0 0.992 0.008 0.000 0.000
#> GSM11331 1 0.1845 0.837 0.916 0 0.000 0.004 0.072 0.008
#> GSM11344 3 0.0000 0.879 0.000 0 1.000 0.000 0.000 0.000
#> GSM11330 3 0.0000 0.879 0.000 0 1.000 0.000 0.000 0.000
#> GSM11325 3 0.0260 0.879 0.000 0 0.992 0.008 0.000 0.000
#> GSM11338 5 0.5583 0.700 0.284 0 0.000 0.000 0.536 0.180
#> GSM28806 1 0.0291 0.914 0.992 0 0.000 0.004 0.004 0.000
#> GSM28826 1 0.0632 0.906 0.976 0 0.000 0.000 0.024 0.000
#> GSM28818 4 0.3991 0.160 0.472 0 0.000 0.524 0.004 0.000
#> GSM28821 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28807 4 0.1812 0.166 0.008 0 0.000 0.912 0.000 0.080
#> GSM28822 6 0.2762 0.966 0.000 0 0.000 0.196 0.000 0.804
#> GSM11328 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11323 1 0.1845 0.837 0.916 0 0.000 0.004 0.072 0.008
#> GSM11324 1 0.0000 0.917 1.000 0 0.000 0.000 0.000 0.000
#> GSM11341 4 0.1387 0.122 0.000 0 0.000 0.932 0.000 0.068
#> GSM11326 3 0.4788 0.432 0.276 0 0.648 0.000 0.068 0.008
#> GSM28810 1 0.3828 0.342 0.696 0 0.000 0.288 0.004 0.012
#> GSM11335 4 0.4477 0.320 0.380 0 0.000 0.588 0.004 0.028
#> GSM28809 1 0.4129 -0.328 0.496 0 0.000 0.496 0.004 0.004
#> GSM11329 1 0.0000 0.917 1.000 0 0.000 0.000 0.000 0.000
#> GSM28805 1 0.0363 0.913 0.988 0 0.000 0.000 0.012 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> CV:hclust 52 0.396 2
#> CV:hclust 47 0.366 3
#> CV:hclust 43 0.409 4
#> CV:hclust 48 0.421 5
#> CV:hclust 43 0.456 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.508 0.887 0.883 0.3439 0.648 0.648
#> 3 3 0.680 0.955 0.933 0.6520 0.776 0.655
#> 4 4 0.760 0.872 0.882 0.2033 0.878 0.712
#> 5 5 0.751 0.864 0.895 0.0929 0.922 0.755
#> 6 6 0.776 0.807 0.861 0.0544 1.000 1.000
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
#> GSM28815 1 0.0000 0.901 1.000 0.000
#> GSM28816 1 0.0000 0.901 1.000 0.000
#> GSM28817 1 0.0000 0.901 1.000 0.000
#> GSM11327 1 0.8267 0.722 0.740 0.260
#> GSM28825 2 0.8555 1.000 0.280 0.720
#> GSM11322 2 0.8555 1.000 0.280 0.720
#> GSM28828 2 0.8555 1.000 0.280 0.720
#> GSM11346 2 0.8555 1.000 0.280 0.720
#> GSM28808 2 0.8555 1.000 0.280 0.720
#> GSM11332 2 0.8555 1.000 0.280 0.720
#> GSM28811 2 0.8555 1.000 0.280 0.720
#> GSM11334 2 0.8555 1.000 0.280 0.720
#> GSM11340 2 0.8555 1.000 0.280 0.720
#> GSM28812 2 0.8555 1.000 0.280 0.720
#> GSM11345 1 0.0000 0.901 1.000 0.000
#> GSM28819 1 0.0000 0.901 1.000 0.000
#> GSM11321 1 0.8555 0.712 0.720 0.280
#> GSM28820 1 0.0000 0.901 1.000 0.000
#> GSM11339 1 0.0000 0.901 1.000 0.000
#> GSM28804 1 0.1184 0.895 0.984 0.016
#> GSM28823 1 0.0000 0.901 1.000 0.000
#> GSM11336 1 0.1414 0.899 0.980 0.020
#> GSM11342 1 0.0000 0.901 1.000 0.000
#> GSM11333 1 0.0000 0.901 1.000 0.000
#> GSM28802 1 0.0000 0.901 1.000 0.000
#> GSM28803 1 0.8555 0.712 0.720 0.280
#> GSM11343 1 0.8555 0.712 0.720 0.280
#> GSM11347 1 0.8555 0.712 0.720 0.280
#> GSM28824 1 0.1414 0.899 0.980 0.020
#> GSM28813 1 0.1414 0.899 0.980 0.020
#> GSM28827 1 0.0000 0.901 1.000 0.000
#> GSM11337 1 0.0672 0.900 0.992 0.008
#> GSM28814 1 0.8555 0.712 0.720 0.280
#> GSM11331 1 0.1184 0.899 0.984 0.016
#> GSM11344 1 0.8555 0.712 0.720 0.280
#> GSM11330 1 0.8555 0.712 0.720 0.280
#> GSM11325 1 0.8555 0.712 0.720 0.280
#> GSM11338 1 0.1414 0.899 0.980 0.020
#> GSM28806 1 0.0000 0.901 1.000 0.000
#> GSM28826 1 0.0000 0.901 1.000 0.000
#> GSM28818 1 0.1184 0.895 0.984 0.016
#> GSM28821 2 0.8555 1.000 0.280 0.720
#> GSM28807 1 0.2043 0.893 0.968 0.032
#> GSM28822 1 0.1414 0.895 0.980 0.020
#> GSM11328 2 0.8555 1.000 0.280 0.720
#> GSM11323 1 0.1184 0.899 0.984 0.016
#> GSM11324 1 0.0000 0.901 1.000 0.000
#> GSM11341 1 0.2948 0.884 0.948 0.052
#> GSM11326 1 0.8267 0.722 0.740 0.260
#> GSM28810 1 0.1414 0.895 0.980 0.020
#> GSM11335 1 0.2043 0.893 0.968 0.032
#> GSM28809 1 0.0000 0.901 1.000 0.000
#> GSM11329 1 0.0000 0.901 1.000 0.000
#> GSM28805 1 0.0000 0.901 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.0000 0.947 1.000 0.000 0.000
#> GSM28816 1 0.0747 0.945 0.984 0.000 0.016
#> GSM28817 1 0.0237 0.947 0.996 0.000 0.004
#> GSM11327 3 0.3686 0.995 0.140 0.000 0.860
#> GSM28825 2 0.1289 0.999 0.032 0.968 0.000
#> GSM11322 2 0.1289 0.999 0.032 0.968 0.000
#> GSM28828 2 0.1289 0.999 0.032 0.968 0.000
#> GSM11346 2 0.1289 0.999 0.032 0.968 0.000
#> GSM28808 2 0.1525 0.998 0.032 0.964 0.004
#> GSM11332 2 0.1525 0.998 0.032 0.964 0.004
#> GSM28811 2 0.1289 0.999 0.032 0.968 0.000
#> GSM11334 2 0.1525 0.998 0.032 0.964 0.004
#> GSM11340 2 0.1525 0.998 0.032 0.964 0.004
#> GSM28812 2 0.1289 0.999 0.032 0.968 0.000
#> GSM11345 1 0.0424 0.948 0.992 0.000 0.008
#> GSM28819 1 0.0592 0.946 0.988 0.000 0.012
#> GSM11321 3 0.4411 0.993 0.140 0.016 0.844
#> GSM28820 1 0.0592 0.946 0.988 0.000 0.012
#> GSM11339 1 0.1289 0.939 0.968 0.000 0.032
#> GSM28804 1 0.3267 0.892 0.884 0.000 0.116
#> GSM28823 1 0.0424 0.947 0.992 0.000 0.008
#> GSM11336 1 0.3528 0.892 0.892 0.016 0.092
#> GSM11342 1 0.0424 0.947 0.992 0.000 0.008
#> GSM11333 1 0.1031 0.944 0.976 0.000 0.024
#> GSM28802 1 0.0592 0.946 0.988 0.000 0.012
#> GSM28803 3 0.4411 0.993 0.140 0.016 0.844
#> GSM11343 3 0.3918 0.995 0.140 0.004 0.856
#> GSM11347 3 0.3686 0.995 0.140 0.000 0.860
#> GSM28824 1 0.3528 0.892 0.892 0.016 0.092
#> GSM28813 1 0.3528 0.892 0.892 0.016 0.092
#> GSM28827 1 0.0237 0.947 0.996 0.000 0.004
#> GSM11337 1 0.2492 0.924 0.936 0.016 0.048
#> GSM28814 3 0.4411 0.993 0.140 0.016 0.844
#> GSM11331 1 0.1163 0.939 0.972 0.000 0.028
#> GSM11344 3 0.3686 0.995 0.140 0.000 0.860
#> GSM11330 3 0.3686 0.995 0.140 0.000 0.860
#> GSM11325 3 0.4411 0.993 0.140 0.016 0.844
#> GSM11338 1 0.3528 0.892 0.892 0.016 0.092
#> GSM28806 1 0.1289 0.939 0.968 0.000 0.032
#> GSM28826 1 0.0592 0.946 0.988 0.000 0.012
#> GSM28818 1 0.3038 0.897 0.896 0.000 0.104
#> GSM28821 2 0.1289 0.999 0.032 0.968 0.000
#> GSM28807 1 0.3412 0.890 0.876 0.000 0.124
#> GSM28822 1 0.3340 0.892 0.880 0.000 0.120
#> GSM11328 2 0.1289 0.999 0.032 0.968 0.000
#> GSM11323 1 0.1163 0.939 0.972 0.000 0.028
#> GSM11324 1 0.0237 0.947 0.996 0.000 0.004
#> GSM11341 1 0.3340 0.892 0.880 0.000 0.120
#> GSM11326 3 0.3686 0.995 0.140 0.000 0.860
#> GSM28810 1 0.3340 0.892 0.880 0.000 0.120
#> GSM11335 1 0.3412 0.890 0.876 0.000 0.124
#> GSM28809 1 0.0424 0.946 0.992 0.000 0.008
#> GSM11329 1 0.0237 0.947 0.996 0.000 0.004
#> GSM28805 1 0.0237 0.947 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.1118 0.833 0.964 0.000 0.000 0.036
#> GSM28816 1 0.3757 0.753 0.828 0.000 0.020 0.152
#> GSM28817 1 0.0188 0.837 0.996 0.000 0.000 0.004
#> GSM11327 3 0.2111 0.957 0.044 0.000 0.932 0.024
#> GSM28825 2 0.0188 0.995 0.004 0.996 0.000 0.000
#> GSM11322 2 0.0188 0.995 0.004 0.996 0.000 0.000
#> GSM28828 2 0.0188 0.995 0.004 0.996 0.000 0.000
#> GSM11346 2 0.0188 0.995 0.004 0.996 0.000 0.000
#> GSM28808 2 0.0188 0.995 0.004 0.996 0.000 0.000
#> GSM11332 2 0.0188 0.995 0.004 0.996 0.000 0.000
#> GSM28811 2 0.1124 0.985 0.004 0.972 0.012 0.012
#> GSM11334 2 0.0188 0.995 0.004 0.996 0.000 0.000
#> GSM11340 2 0.0188 0.995 0.004 0.996 0.000 0.000
#> GSM28812 2 0.0188 0.995 0.004 0.996 0.000 0.000
#> GSM11345 1 0.0336 0.836 0.992 0.000 0.000 0.008
#> GSM28819 1 0.0336 0.837 0.992 0.000 0.000 0.008
#> GSM11321 3 0.3538 0.950 0.044 0.004 0.868 0.084
#> GSM28820 1 0.0336 0.837 0.992 0.000 0.000 0.008
#> GSM11339 1 0.0921 0.821 0.972 0.000 0.000 0.028
#> GSM28804 4 0.4855 0.963 0.400 0.000 0.000 0.600
#> GSM28823 1 0.1022 0.828 0.968 0.000 0.000 0.032
#> GSM11336 1 0.5453 0.585 0.660 0.000 0.036 0.304
#> GSM11342 1 0.1022 0.828 0.968 0.000 0.000 0.032
#> GSM11333 1 0.3808 0.743 0.812 0.000 0.012 0.176
#> GSM28802 1 0.1716 0.819 0.936 0.000 0.000 0.064
#> GSM28803 3 0.3538 0.950 0.044 0.004 0.868 0.084
#> GSM11343 3 0.1888 0.960 0.044 0.000 0.940 0.016
#> GSM11347 3 0.2111 0.959 0.044 0.000 0.932 0.024
#> GSM28824 1 0.5453 0.585 0.660 0.000 0.036 0.304
#> GSM28813 1 0.5453 0.585 0.660 0.000 0.036 0.304
#> GSM28827 1 0.0000 0.836 1.000 0.000 0.000 0.000
#> GSM11337 1 0.4540 0.688 0.772 0.000 0.032 0.196
#> GSM28814 3 0.3538 0.950 0.044 0.004 0.868 0.084
#> GSM11331 1 0.1489 0.812 0.952 0.000 0.004 0.044
#> GSM11344 3 0.2111 0.959 0.044 0.000 0.932 0.024
#> GSM11330 3 0.2111 0.959 0.044 0.000 0.932 0.024
#> GSM11325 3 0.3538 0.950 0.044 0.004 0.868 0.084
#> GSM11338 1 0.5282 0.602 0.688 0.000 0.036 0.276
#> GSM28806 1 0.3726 0.402 0.788 0.000 0.000 0.212
#> GSM28826 1 0.1940 0.811 0.924 0.000 0.000 0.076
#> GSM28818 4 0.4888 0.954 0.412 0.000 0.000 0.588
#> GSM28821 2 0.1124 0.985 0.004 0.972 0.012 0.012
#> GSM28807 4 0.4843 0.961 0.396 0.000 0.000 0.604
#> GSM28822 4 0.4855 0.963 0.400 0.000 0.000 0.600
#> GSM11328 2 0.1124 0.985 0.004 0.972 0.012 0.012
#> GSM11323 1 0.1489 0.812 0.952 0.000 0.004 0.044
#> GSM11324 1 0.0000 0.836 1.000 0.000 0.000 0.000
#> GSM11341 4 0.5386 0.923 0.368 0.000 0.020 0.612
#> GSM11326 3 0.2313 0.953 0.044 0.000 0.924 0.032
#> GSM28810 4 0.4985 0.864 0.468 0.000 0.000 0.532
#> GSM11335 4 0.4866 0.959 0.404 0.000 0.000 0.596
#> GSM28809 1 0.0921 0.822 0.972 0.000 0.000 0.028
#> GSM11329 1 0.0000 0.836 1.000 0.000 0.000 0.000
#> GSM28805 1 0.0000 0.836 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
#> GSM28815 1 0.1211 0.850 0.960 0.000 0.000 0.024 0.016
#> GSM28816 1 0.4508 0.440 0.708 0.000 0.004 0.032 0.256
#> GSM28817 1 0.1124 0.848 0.960 0.000 0.000 0.004 0.036
#> GSM11327 3 0.1525 0.919 0.012 0.000 0.948 0.004 0.036
#> GSM28825 2 0.0000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM28808 2 0.0451 0.970 0.000 0.988 0.004 0.000 0.008
#> GSM11332 2 0.0451 0.970 0.000 0.988 0.004 0.000 0.008
#> GSM28811 2 0.2361 0.923 0.000 0.892 0.000 0.012 0.096
#> GSM11334 2 0.0451 0.970 0.000 0.988 0.004 0.000 0.008
#> GSM11340 2 0.0451 0.970 0.000 0.988 0.004 0.000 0.008
#> GSM28812 2 0.0000 0.972 0.000 1.000 0.000 0.000 0.000
#> GSM11345 1 0.1124 0.849 0.960 0.000 0.000 0.004 0.036
#> GSM28819 1 0.1043 0.846 0.960 0.000 0.000 0.000 0.040
#> GSM11321 3 0.3325 0.918 0.008 0.000 0.856 0.056 0.080
#> GSM28820 1 0.1043 0.846 0.960 0.000 0.000 0.000 0.040
#> GSM11339 1 0.0955 0.849 0.968 0.000 0.000 0.028 0.004
#> GSM28804 4 0.3372 0.935 0.120 0.000 0.004 0.840 0.036
#> GSM28823 1 0.2659 0.807 0.888 0.000 0.000 0.052 0.060
#> GSM11336 5 0.4088 0.990 0.276 0.000 0.004 0.008 0.712
#> GSM11342 1 0.2659 0.807 0.888 0.000 0.000 0.052 0.060
#> GSM11333 1 0.4628 0.377 0.688 0.000 0.004 0.032 0.276
#> GSM28802 1 0.1106 0.846 0.964 0.000 0.000 0.012 0.024
#> GSM28803 3 0.3325 0.918 0.008 0.000 0.856 0.056 0.080
#> GSM11343 3 0.1280 0.931 0.008 0.000 0.960 0.008 0.024
#> GSM11347 3 0.1200 0.929 0.008 0.000 0.964 0.012 0.016
#> GSM28824 5 0.3992 0.993 0.280 0.000 0.004 0.004 0.712
#> GSM28813 5 0.3992 0.993 0.280 0.000 0.004 0.004 0.712
#> GSM28827 1 0.0898 0.853 0.972 0.000 0.000 0.008 0.020
#> GSM11337 1 0.3074 0.633 0.804 0.000 0.000 0.000 0.196
#> GSM28814 3 0.3325 0.918 0.008 0.000 0.856 0.056 0.080
#> GSM11331 1 0.2791 0.810 0.892 0.000 0.016 0.056 0.036
#> GSM11344 3 0.1200 0.929 0.008 0.000 0.964 0.012 0.016
#> GSM11330 3 0.1200 0.929 0.008 0.000 0.964 0.012 0.016
#> GSM11325 3 0.3325 0.918 0.008 0.000 0.856 0.056 0.080
#> GSM11338 5 0.3838 0.987 0.280 0.000 0.004 0.000 0.716
#> GSM28806 1 0.2707 0.760 0.860 0.000 0.000 0.132 0.008
#> GSM28826 1 0.1408 0.834 0.948 0.000 0.000 0.008 0.044
#> GSM28818 4 0.3086 0.925 0.180 0.000 0.000 0.816 0.004
#> GSM28821 2 0.2361 0.923 0.000 0.892 0.000 0.012 0.096
#> GSM28807 4 0.2753 0.959 0.136 0.000 0.000 0.856 0.008
#> GSM28822 4 0.3061 0.958 0.136 0.000 0.000 0.844 0.020
#> GSM11328 2 0.2361 0.923 0.000 0.892 0.000 0.012 0.096
#> GSM11323 1 0.2791 0.810 0.892 0.000 0.016 0.056 0.036
#> GSM11324 1 0.0451 0.853 0.988 0.000 0.000 0.008 0.004
#> GSM11341 4 0.3361 0.954 0.128 0.000 0.012 0.840 0.020
#> GSM11326 3 0.2305 0.901 0.012 0.000 0.916 0.028 0.044
#> GSM28810 1 0.4821 -0.150 0.516 0.000 0.000 0.464 0.020
#> GSM11335 4 0.2909 0.957 0.140 0.000 0.000 0.848 0.012
#> GSM28809 1 0.1725 0.836 0.936 0.000 0.000 0.044 0.020
#> GSM11329 1 0.0451 0.853 0.988 0.000 0.000 0.008 0.004
#> GSM28805 1 0.0671 0.854 0.980 0.000 0.000 0.016 0.004
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 1 0.2402 0.790 0.896 0.000 0.000 0.012 0.032 NA
#> GSM28816 1 0.5857 0.347 0.556 0.000 0.000 0.020 0.264 NA
#> GSM28817 1 0.2361 0.785 0.884 0.000 0.000 0.000 0.028 NA
#> GSM11327 3 0.5333 0.780 0.004 0.000 0.604 0.020 0.072 NA
#> GSM28825 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 NA
#> GSM11322 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 NA
#> GSM28828 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 NA
#> GSM11346 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 NA
#> GSM28808 2 0.0260 0.952 0.000 0.992 0.000 0.000 0.000 NA
#> GSM11332 2 0.0260 0.952 0.000 0.992 0.000 0.000 0.000 NA
#> GSM28811 2 0.3122 0.857 0.000 0.816 0.000 0.004 0.020 NA
#> GSM11334 2 0.0260 0.952 0.000 0.992 0.000 0.000 0.000 NA
#> GSM11340 2 0.0260 0.952 0.000 0.992 0.000 0.000 0.000 NA
#> GSM28812 2 0.0000 0.953 0.000 1.000 0.000 0.000 0.000 NA
#> GSM11345 1 0.2436 0.784 0.880 0.000 0.000 0.000 0.032 NA
#> GSM28819 1 0.2436 0.784 0.880 0.000 0.000 0.000 0.032 NA
#> GSM11321 3 0.0436 0.787 0.004 0.000 0.988 0.004 0.000 NA
#> GSM28820 1 0.2436 0.784 0.880 0.000 0.000 0.000 0.032 NA
#> GSM11339 1 0.1148 0.807 0.960 0.000 0.000 0.016 0.004 NA
#> GSM28804 4 0.3466 0.846 0.036 0.000 0.000 0.832 0.040 NA
#> GSM28823 1 0.4623 0.678 0.716 0.000 0.000 0.024 0.068 NA
#> GSM11336 5 0.2101 0.996 0.100 0.000 0.004 0.004 0.892 NA
#> GSM11342 1 0.4623 0.678 0.716 0.000 0.000 0.024 0.068 NA
#> GSM11333 1 0.5957 0.342 0.552 0.000 0.000 0.028 0.268 NA
#> GSM28802 1 0.1624 0.802 0.936 0.000 0.000 0.012 0.008 NA
#> GSM28803 3 0.0146 0.789 0.004 0.000 0.996 0.000 0.000 NA
#> GSM11343 3 0.3586 0.823 0.004 0.000 0.712 0.004 0.000 NA
#> GSM11347 3 0.3807 0.815 0.004 0.000 0.628 0.000 0.000 NA
#> GSM28824 5 0.2101 0.996 0.100 0.000 0.004 0.004 0.892 NA
#> GSM28813 5 0.1958 0.996 0.100 0.000 0.000 0.004 0.896 NA
#> GSM28827 1 0.0713 0.807 0.972 0.000 0.000 0.000 0.000 NA
#> GSM11337 1 0.3345 0.693 0.788 0.000 0.000 0.000 0.184 NA
#> GSM28814 3 0.0436 0.787 0.004 0.000 0.988 0.004 0.000 NA
#> GSM11331 1 0.4635 0.682 0.728 0.000 0.000 0.136 0.020 NA
#> GSM11344 3 0.3807 0.815 0.004 0.000 0.628 0.000 0.000 NA
#> GSM11330 3 0.3807 0.815 0.004 0.000 0.628 0.000 0.000 NA
#> GSM11325 3 0.0436 0.787 0.004 0.000 0.988 0.004 0.000 NA
#> GSM11338 5 0.1863 0.992 0.104 0.000 0.000 0.000 0.896 NA
#> GSM28806 1 0.2887 0.769 0.844 0.000 0.000 0.120 0.000 NA
#> GSM28826 1 0.2325 0.789 0.900 0.000 0.000 0.008 0.044 NA
#> GSM28818 4 0.2871 0.734 0.192 0.000 0.000 0.804 0.000 NA
#> GSM28821 2 0.3122 0.857 0.000 0.816 0.000 0.004 0.020 NA
#> GSM28807 4 0.1793 0.879 0.032 0.000 0.000 0.928 0.004 NA
#> GSM28822 4 0.2831 0.881 0.044 0.000 0.000 0.876 0.028 NA
#> GSM11328 2 0.3122 0.857 0.000 0.816 0.000 0.004 0.020 NA
#> GSM11323 1 0.4635 0.682 0.728 0.000 0.000 0.136 0.020 NA
#> GSM11324 1 0.1204 0.803 0.944 0.000 0.000 0.000 0.000 NA
#> GSM11341 4 0.2371 0.883 0.032 0.000 0.000 0.900 0.016 NA
#> GSM11326 3 0.6044 0.736 0.004 0.000 0.552 0.080 0.060 NA
#> GSM28810 1 0.4620 0.215 0.532 0.000 0.000 0.428 0.000 NA
#> GSM11335 4 0.1793 0.879 0.032 0.000 0.000 0.928 0.004 NA
#> GSM28809 1 0.2201 0.791 0.896 0.000 0.000 0.076 0.000 NA
#> GSM11329 1 0.0405 0.806 0.988 0.000 0.000 0.000 0.004 NA
#> GSM28805 1 0.1340 0.803 0.948 0.000 0.000 0.008 0.004 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 tissue(p) k
#> CV:kmeans 54 0.398 2
#> CV:kmeans 54 0.374 3
#> CV:kmeans 53 0.353 4
#> CV:kmeans 51 0.481 5
#> CV:kmeans 51 0.481 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.708 0.883 0.935 0.4558 0.516 0.516
#> 3 3 0.776 0.903 0.950 0.3763 0.818 0.664
#> 4 4 0.785 0.817 0.892 0.1852 0.806 0.536
#> 5 5 0.885 0.842 0.920 0.0891 0.915 0.680
#> 6 6 0.861 0.732 0.860 0.0342 0.945 0.728
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
#> GSM28815 1 0.0000 0.975 1.000 0.000
#> GSM28816 1 0.9129 0.491 0.672 0.328
#> GSM28817 1 0.0000 0.975 1.000 0.000
#> GSM11327 1 0.0000 0.975 1.000 0.000
#> GSM28825 2 0.0000 0.840 0.000 1.000
#> GSM11322 2 0.0000 0.840 0.000 1.000
#> GSM28828 2 0.0000 0.840 0.000 1.000
#> GSM11346 2 0.0000 0.840 0.000 1.000
#> GSM28808 2 0.0000 0.840 0.000 1.000
#> GSM11332 2 0.0000 0.840 0.000 1.000
#> GSM28811 2 0.0000 0.840 0.000 1.000
#> GSM11334 2 0.0000 0.840 0.000 1.000
#> GSM11340 2 0.0000 0.840 0.000 1.000
#> GSM28812 2 0.0000 0.840 0.000 1.000
#> GSM11345 1 0.0000 0.975 1.000 0.000
#> GSM28819 1 0.0000 0.975 1.000 0.000
#> GSM11321 2 0.9087 0.707 0.324 0.676
#> GSM28820 1 0.0000 0.975 1.000 0.000
#> GSM11339 1 0.0000 0.975 1.000 0.000
#> GSM28804 1 0.9087 0.498 0.676 0.324
#> GSM28823 1 0.0000 0.975 1.000 0.000
#> GSM11336 1 0.0000 0.975 1.000 0.000
#> GSM11342 1 0.0000 0.975 1.000 0.000
#> GSM11333 1 0.0376 0.971 0.996 0.004
#> GSM28802 1 0.0000 0.975 1.000 0.000
#> GSM28803 2 0.9087 0.707 0.324 0.676
#> GSM11343 2 0.9087 0.707 0.324 0.676
#> GSM11347 2 0.9087 0.707 0.324 0.676
#> GSM28824 1 0.0000 0.975 1.000 0.000
#> GSM28813 1 0.0000 0.975 1.000 0.000
#> GSM28827 1 0.0000 0.975 1.000 0.000
#> GSM11337 1 0.0000 0.975 1.000 0.000
#> GSM28814 2 0.9087 0.707 0.324 0.676
#> GSM11331 1 0.0000 0.975 1.000 0.000
#> GSM11344 2 0.9087 0.707 0.324 0.676
#> GSM11330 2 0.9087 0.707 0.324 0.676
#> GSM11325 2 0.9087 0.707 0.324 0.676
#> GSM11338 1 0.0000 0.975 1.000 0.000
#> GSM28806 1 0.0000 0.975 1.000 0.000
#> GSM28826 1 0.0000 0.975 1.000 0.000
#> GSM28818 1 0.0000 0.975 1.000 0.000
#> GSM28821 2 0.0000 0.840 0.000 1.000
#> GSM28807 1 0.0000 0.975 1.000 0.000
#> GSM28822 1 0.0000 0.975 1.000 0.000
#> GSM11328 2 0.0000 0.840 0.000 1.000
#> GSM11323 1 0.0000 0.975 1.000 0.000
#> GSM11324 1 0.0000 0.975 1.000 0.000
#> GSM11341 2 0.8499 0.736 0.276 0.724
#> GSM11326 1 0.0000 0.975 1.000 0.000
#> GSM28810 1 0.0000 0.975 1.000 0.000
#> GSM11335 1 0.0000 0.975 1.000 0.000
#> GSM28809 1 0.0000 0.975 1.000 0.000
#> GSM11329 1 0.0000 0.975 1.000 0.000
#> GSM28805 1 0.0672 0.966 0.992 0.008
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.0000 0.920 1.000 0.000 0.000
#> GSM28816 1 0.6168 0.386 0.588 0.412 0.000
#> GSM28817 1 0.0000 0.920 1.000 0.000 0.000
#> GSM11327 3 0.0000 0.939 0.000 0.000 1.000
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11345 1 0.0000 0.920 1.000 0.000 0.000
#> GSM28819 1 0.0237 0.919 0.996 0.000 0.004
#> GSM11321 3 0.0000 0.939 0.000 0.000 1.000
#> GSM28820 1 0.0237 0.919 0.996 0.000 0.004
#> GSM11339 1 0.0000 0.920 1.000 0.000 0.000
#> GSM28804 1 0.5938 0.688 0.732 0.248 0.020
#> GSM28823 1 0.0000 0.920 1.000 0.000 0.000
#> GSM11336 1 0.3816 0.818 0.852 0.000 0.148
#> GSM11342 1 0.0000 0.920 1.000 0.000 0.000
#> GSM11333 1 0.0000 0.920 1.000 0.000 0.000
#> GSM28802 1 0.2165 0.891 0.936 0.000 0.064
#> GSM28803 3 0.0000 0.939 0.000 0.000 1.000
#> GSM11343 3 0.0000 0.939 0.000 0.000 1.000
#> GSM11347 3 0.0000 0.939 0.000 0.000 1.000
#> GSM28824 3 0.5621 0.602 0.308 0.000 0.692
#> GSM28813 3 0.5327 0.664 0.272 0.000 0.728
#> GSM28827 1 0.0000 0.920 1.000 0.000 0.000
#> GSM11337 1 0.2537 0.881 0.920 0.000 0.080
#> GSM28814 3 0.0000 0.939 0.000 0.000 1.000
#> GSM11331 1 0.3816 0.843 0.852 0.000 0.148
#> GSM11344 3 0.0000 0.939 0.000 0.000 1.000
#> GSM11330 3 0.0000 0.939 0.000 0.000 1.000
#> GSM11325 3 0.0000 0.939 0.000 0.000 1.000
#> GSM11338 1 0.2959 0.866 0.900 0.000 0.100
#> GSM28806 1 0.1643 0.907 0.956 0.000 0.044
#> GSM28826 1 0.2448 0.884 0.924 0.000 0.076
#> GSM28818 1 0.1529 0.909 0.960 0.000 0.040
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28807 1 0.3816 0.842 0.852 0.000 0.148
#> GSM28822 1 0.3686 0.849 0.860 0.000 0.140
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11323 1 0.3752 0.846 0.856 0.000 0.144
#> GSM11324 1 0.0000 0.920 1.000 0.000 0.000
#> GSM11341 3 0.1753 0.894 0.048 0.000 0.952
#> GSM11326 3 0.0000 0.939 0.000 0.000 1.000
#> GSM28810 1 0.3267 0.867 0.884 0.000 0.116
#> GSM11335 1 0.3816 0.842 0.852 0.000 0.148
#> GSM28809 1 0.0000 0.920 1.000 0.000 0.000
#> GSM11329 1 0.0000 0.920 1.000 0.000 0.000
#> GSM28805 1 0.0000 0.920 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.2868 0.662 0.864 0.000 0.000 0.136
#> GSM28816 1 0.6074 0.427 0.668 0.228 0.000 0.104
#> GSM28817 1 0.4277 0.710 0.720 0.000 0.000 0.280
#> GSM11327 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11345 1 0.4855 0.553 0.600 0.000 0.000 0.400
#> GSM28819 1 0.4277 0.710 0.720 0.000 0.000 0.280
#> GSM11321 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM28820 1 0.4277 0.710 0.720 0.000 0.000 0.280
#> GSM11339 4 0.3907 0.595 0.232 0.000 0.000 0.768
#> GSM28804 4 0.1474 0.806 0.052 0.000 0.000 0.948
#> GSM28823 1 0.4406 0.700 0.700 0.000 0.000 0.300
#> GSM11336 1 0.1174 0.718 0.968 0.000 0.012 0.020
#> GSM11342 1 0.4406 0.700 0.700 0.000 0.000 0.300
#> GSM11333 1 0.4072 0.493 0.748 0.000 0.000 0.252
#> GSM28802 1 0.0817 0.731 0.976 0.000 0.000 0.024
#> GSM28803 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11343 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11347 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM28824 1 0.1724 0.709 0.948 0.000 0.032 0.020
#> GSM28813 1 0.1798 0.706 0.944 0.000 0.040 0.016
#> GSM28827 1 0.4661 0.643 0.652 0.000 0.000 0.348
#> GSM11337 1 0.0336 0.727 0.992 0.000 0.000 0.008
#> GSM28814 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11331 4 0.4931 0.700 0.132 0.000 0.092 0.776
#> GSM11344 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11330 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11325 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11338 1 0.0000 0.726 1.000 0.000 0.000 0.000
#> GSM28806 4 0.0707 0.833 0.020 0.000 0.000 0.980
#> GSM28826 1 0.0937 0.723 0.976 0.000 0.012 0.012
#> GSM28818 4 0.0336 0.837 0.008 0.000 0.000 0.992
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28807 4 0.0188 0.837 0.004 0.000 0.000 0.996
#> GSM28822 4 0.0336 0.836 0.008 0.000 0.000 0.992
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11323 4 0.4764 0.712 0.124 0.000 0.088 0.788
#> GSM11324 1 0.4454 0.690 0.692 0.000 0.000 0.308
#> GSM11341 4 0.4564 0.384 0.000 0.000 0.328 0.672
#> GSM11326 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM28810 4 0.0592 0.834 0.016 0.000 0.000 0.984
#> GSM11335 4 0.0000 0.837 0.000 0.000 0.000 1.000
#> GSM28809 4 0.4250 0.483 0.276 0.000 0.000 0.724
#> GSM11329 1 0.4431 0.695 0.696 0.000 0.000 0.304
#> GSM28805 1 0.4382 0.703 0.704 0.000 0.000 0.296
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 5 0.3531 0.80476 0.148 0.000 0.000 0.036 0.816
#> GSM28816 5 0.1701 0.86661 0.012 0.028 0.000 0.016 0.944
#> GSM28817 1 0.1205 0.86611 0.956 0.000 0.000 0.004 0.040
#> GSM11327 3 0.0290 0.99215 0.000 0.000 0.992 0.000 0.008
#> GSM28825 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM11345 1 0.1082 0.86436 0.964 0.000 0.000 0.028 0.008
#> GSM28819 1 0.1251 0.86575 0.956 0.000 0.000 0.008 0.036
#> GSM11321 3 0.0000 0.99821 0.000 0.000 1.000 0.000 0.000
#> GSM28820 1 0.1082 0.86728 0.964 0.000 0.000 0.008 0.028
#> GSM11339 1 0.5286 0.00901 0.504 0.000 0.000 0.448 0.048
#> GSM28804 4 0.0807 0.80552 0.012 0.000 0.000 0.976 0.012
#> GSM28823 1 0.1399 0.86453 0.952 0.000 0.000 0.020 0.028
#> GSM11336 5 0.1282 0.88909 0.044 0.000 0.000 0.004 0.952
#> GSM11342 1 0.1399 0.86453 0.952 0.000 0.000 0.020 0.028
#> GSM11333 5 0.3289 0.81838 0.048 0.000 0.000 0.108 0.844
#> GSM28802 1 0.4288 0.33257 0.612 0.000 0.000 0.004 0.384
#> GSM28803 3 0.0000 0.99821 0.000 0.000 1.000 0.000 0.000
#> GSM11343 3 0.0000 0.99821 0.000 0.000 1.000 0.000 0.000
#> GSM11347 3 0.0000 0.99821 0.000 0.000 1.000 0.000 0.000
#> GSM28824 5 0.1282 0.88909 0.044 0.000 0.000 0.004 0.952
#> GSM28813 5 0.1282 0.88909 0.044 0.000 0.000 0.004 0.952
#> GSM28827 1 0.3051 0.80157 0.864 0.000 0.000 0.060 0.076
#> GSM11337 5 0.2462 0.85744 0.112 0.000 0.000 0.008 0.880
#> GSM28814 3 0.0000 0.99821 0.000 0.000 1.000 0.000 0.000
#> GSM11331 4 0.6631 0.31167 0.376 0.000 0.068 0.496 0.060
#> GSM11344 3 0.0000 0.99821 0.000 0.000 1.000 0.000 0.000
#> GSM11330 3 0.0000 0.99821 0.000 0.000 1.000 0.000 0.000
#> GSM11325 3 0.0000 0.99821 0.000 0.000 1.000 0.000 0.000
#> GSM11338 5 0.1792 0.87735 0.084 0.000 0.000 0.000 0.916
#> GSM28806 4 0.2561 0.76225 0.096 0.000 0.000 0.884 0.020
#> GSM28826 5 0.3809 0.68364 0.256 0.000 0.008 0.000 0.736
#> GSM28818 4 0.0880 0.80646 0.032 0.000 0.000 0.968 0.000
#> GSM28821 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM28807 4 0.0162 0.80751 0.004 0.000 0.000 0.996 0.000
#> GSM28822 4 0.0579 0.80675 0.008 0.000 0.000 0.984 0.008
#> GSM11328 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000
#> GSM11323 4 0.6657 0.33331 0.364 0.000 0.060 0.504 0.072
#> GSM11324 1 0.0798 0.86371 0.976 0.000 0.000 0.016 0.008
#> GSM11341 4 0.2011 0.76420 0.000 0.000 0.088 0.908 0.004
#> GSM11326 3 0.0324 0.99247 0.000 0.000 0.992 0.004 0.004
#> GSM28810 4 0.1282 0.80253 0.044 0.000 0.000 0.952 0.004
#> GSM11335 4 0.0290 0.80861 0.008 0.000 0.000 0.992 0.000
#> GSM28809 4 0.5604 0.03578 0.460 0.000 0.000 0.468 0.072
#> GSM11329 1 0.1364 0.85372 0.952 0.000 0.000 0.012 0.036
#> GSM28805 1 0.1942 0.84359 0.920 0.000 0.000 0.012 0.068
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 6 0.4693 0.0512 0.028 0.00 0.000 0.020 0.332 0.620
#> GSM28816 5 0.5284 0.4162 0.004 0.04 0.000 0.028 0.552 0.376
#> GSM28817 1 0.0820 0.7760 0.972 0.00 0.000 0.000 0.012 0.016
#> GSM11327 3 0.1552 0.9417 0.000 0.00 0.940 0.004 0.020 0.036
#> GSM28825 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM11345 1 0.0458 0.7766 0.984 0.00 0.000 0.000 0.016 0.000
#> GSM28819 1 0.0692 0.7765 0.976 0.00 0.000 0.000 0.020 0.004
#> GSM11321 3 0.1082 0.9617 0.000 0.00 0.956 0.000 0.004 0.040
#> GSM28820 1 0.0692 0.7765 0.976 0.00 0.000 0.000 0.020 0.004
#> GSM11339 4 0.6597 -0.0495 0.320 0.00 0.000 0.392 0.028 0.260
#> GSM28804 4 0.1606 0.7734 0.004 0.00 0.000 0.932 0.008 0.056
#> GSM28823 1 0.2766 0.6980 0.844 0.00 0.000 0.008 0.008 0.140
#> GSM11336 5 0.0603 0.7585 0.016 0.00 0.000 0.000 0.980 0.004
#> GSM11342 1 0.2766 0.6980 0.844 0.00 0.000 0.008 0.008 0.140
#> GSM11333 5 0.6124 0.4046 0.060 0.00 0.000 0.104 0.540 0.296
#> GSM28802 1 0.5760 0.2321 0.508 0.00 0.000 0.000 0.224 0.268
#> GSM28803 3 0.0858 0.9653 0.000 0.00 0.968 0.000 0.004 0.028
#> GSM11343 3 0.0000 0.9693 0.000 0.00 1.000 0.000 0.000 0.000
#> GSM11347 3 0.0260 0.9690 0.000 0.00 0.992 0.000 0.000 0.008
#> GSM28824 5 0.0508 0.7592 0.012 0.00 0.000 0.000 0.984 0.004
#> GSM28813 5 0.0363 0.7587 0.012 0.00 0.000 0.000 0.988 0.000
#> GSM28827 6 0.4625 0.1851 0.356 0.00 0.000 0.020 0.020 0.604
#> GSM11337 5 0.4418 0.5469 0.072 0.00 0.000 0.008 0.716 0.204
#> GSM28814 3 0.1010 0.9630 0.000 0.00 0.960 0.000 0.004 0.036
#> GSM11331 6 0.6306 0.4596 0.084 0.00 0.048 0.232 0.040 0.596
#> GSM11344 3 0.0260 0.9690 0.000 0.00 0.992 0.000 0.000 0.008
#> GSM11330 3 0.0260 0.9690 0.000 0.00 0.992 0.000 0.000 0.008
#> GSM11325 3 0.1082 0.9617 0.000 0.00 0.956 0.000 0.004 0.040
#> GSM11338 5 0.1501 0.7261 0.076 0.00 0.000 0.000 0.924 0.000
#> GSM28806 4 0.4513 0.6141 0.152 0.00 0.000 0.724 0.008 0.116
#> GSM28826 6 0.5451 -0.0669 0.092 0.00 0.004 0.004 0.400 0.500
#> GSM28818 4 0.2106 0.7759 0.032 0.00 0.000 0.904 0.000 0.064
#> GSM28821 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM28807 4 0.1141 0.7803 0.000 0.00 0.000 0.948 0.000 0.052
#> GSM28822 4 0.1307 0.7819 0.008 0.00 0.000 0.952 0.008 0.032
#> GSM11328 2 0.0000 1.0000 0.000 1.00 0.000 0.000 0.000 0.000
#> GSM11323 6 0.6243 0.4303 0.092 0.00 0.032 0.264 0.036 0.576
#> GSM11324 1 0.1949 0.7359 0.904 0.00 0.000 0.004 0.004 0.088
#> GSM11341 4 0.1528 0.7686 0.000 0.00 0.048 0.936 0.000 0.016
#> GSM11326 3 0.1367 0.9419 0.000 0.00 0.944 0.012 0.000 0.044
#> GSM28810 4 0.3424 0.6568 0.024 0.00 0.000 0.772 0.000 0.204
#> GSM11335 4 0.1753 0.7642 0.004 0.00 0.000 0.912 0.000 0.084
#> GSM28809 6 0.6402 0.3182 0.244 0.00 0.000 0.276 0.024 0.456
#> GSM11329 1 0.2964 0.6393 0.792 0.00 0.000 0.000 0.004 0.204
#> GSM28805 1 0.4250 0.1729 0.528 0.00 0.000 0.000 0.016 0.456
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> CV:skmeans 52 0.396 2
#> CV:skmeans 53 0.373 3
#> CV:skmeans 50 0.349 4
#> CV:skmeans 49 0.429 5
#> CV:skmeans 43 0.463 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.999 0.999 0.3534 0.648 0.648
#> 3 3 0.942 0.950 0.976 0.4903 0.849 0.767
#> 4 4 0.804 0.898 0.945 0.1917 0.892 0.782
#> 5 5 0.825 0.887 0.918 0.0967 0.951 0.875
#> 6 6 0.753 0.852 0.893 0.0603 0.962 0.891
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
#> GSM28815 1 0.000 0.999 1.000 0.000
#> GSM28816 1 0.184 0.971 0.972 0.028
#> GSM28817 1 0.000 0.999 1.000 0.000
#> GSM11327 1 0.000 0.999 1.000 0.000
#> GSM28825 2 0.000 1.000 0.000 1.000
#> GSM11322 2 0.000 1.000 0.000 1.000
#> GSM28828 2 0.000 1.000 0.000 1.000
#> GSM11346 2 0.000 1.000 0.000 1.000
#> GSM28808 2 0.000 1.000 0.000 1.000
#> GSM11332 2 0.000 1.000 0.000 1.000
#> GSM28811 2 0.000 1.000 0.000 1.000
#> GSM11334 2 0.000 1.000 0.000 1.000
#> GSM11340 2 0.000 1.000 0.000 1.000
#> GSM28812 2 0.000 1.000 0.000 1.000
#> GSM11345 1 0.000 0.999 1.000 0.000
#> GSM28819 1 0.000 0.999 1.000 0.000
#> GSM11321 1 0.000 0.999 1.000 0.000
#> GSM28820 1 0.000 0.999 1.000 0.000
#> GSM11339 1 0.000 0.999 1.000 0.000
#> GSM28804 1 0.000 0.999 1.000 0.000
#> GSM28823 1 0.000 0.999 1.000 0.000
#> GSM11336 1 0.000 0.999 1.000 0.000
#> GSM11342 1 0.000 0.999 1.000 0.000
#> GSM11333 1 0.000 0.999 1.000 0.000
#> GSM28802 1 0.000 0.999 1.000 0.000
#> GSM28803 1 0.000 0.999 1.000 0.000
#> GSM11343 1 0.000 0.999 1.000 0.000
#> GSM11347 1 0.000 0.999 1.000 0.000
#> GSM28824 1 0.000 0.999 1.000 0.000
#> GSM28813 1 0.000 0.999 1.000 0.000
#> GSM28827 1 0.000 0.999 1.000 0.000
#> GSM11337 1 0.000 0.999 1.000 0.000
#> GSM28814 1 0.000 0.999 1.000 0.000
#> GSM11331 1 0.000 0.999 1.000 0.000
#> GSM11344 1 0.000 0.999 1.000 0.000
#> GSM11330 1 0.000 0.999 1.000 0.000
#> GSM11325 1 0.000 0.999 1.000 0.000
#> GSM11338 1 0.000 0.999 1.000 0.000
#> GSM28806 1 0.000 0.999 1.000 0.000
#> GSM28826 1 0.000 0.999 1.000 0.000
#> GSM28818 1 0.000 0.999 1.000 0.000
#> GSM28821 2 0.000 1.000 0.000 1.000
#> GSM28807 1 0.000 0.999 1.000 0.000
#> GSM28822 1 0.000 0.999 1.000 0.000
#> GSM11328 2 0.000 1.000 0.000 1.000
#> GSM11323 1 0.000 0.999 1.000 0.000
#> GSM11324 1 0.000 0.999 1.000 0.000
#> GSM11341 1 0.000 0.999 1.000 0.000
#> GSM11326 1 0.000 0.999 1.000 0.000
#> GSM28810 1 0.000 0.999 1.000 0.000
#> GSM11335 1 0.000 0.999 1.000 0.000
#> GSM28809 1 0.000 0.999 1.000 0.000
#> GSM11329 1 0.000 0.999 1.000 0.000
#> GSM28805 1 0.000 0.999 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.000 0.963 1.000 0.000 0.000
#> GSM28816 1 0.141 0.934 0.964 0.036 0.000
#> GSM28817 1 0.000 0.963 1.000 0.000 0.000
#> GSM11327 1 0.510 0.709 0.752 0.000 0.248
#> GSM28825 2 0.000 1.000 0.000 1.000 0.000
#> GSM11322 2 0.000 1.000 0.000 1.000 0.000
#> GSM28828 2 0.000 1.000 0.000 1.000 0.000
#> GSM11346 2 0.000 1.000 0.000 1.000 0.000
#> GSM28808 2 0.000 1.000 0.000 1.000 0.000
#> GSM11332 2 0.000 1.000 0.000 1.000 0.000
#> GSM28811 2 0.000 1.000 0.000 1.000 0.000
#> GSM11334 2 0.000 1.000 0.000 1.000 0.000
#> GSM11340 2 0.000 1.000 0.000 1.000 0.000
#> GSM28812 2 0.000 1.000 0.000 1.000 0.000
#> GSM11345 1 0.000 0.963 1.000 0.000 0.000
#> GSM28819 1 0.000 0.963 1.000 0.000 0.000
#> GSM11321 3 0.000 1.000 0.000 0.000 1.000
#> GSM28820 1 0.000 0.963 1.000 0.000 0.000
#> GSM11339 1 0.000 0.963 1.000 0.000 0.000
#> GSM28804 1 0.000 0.963 1.000 0.000 0.000
#> GSM28823 1 0.000 0.963 1.000 0.000 0.000
#> GSM11336 1 0.000 0.963 1.000 0.000 0.000
#> GSM11342 1 0.000 0.963 1.000 0.000 0.000
#> GSM11333 1 0.000 0.963 1.000 0.000 0.000
#> GSM28802 1 0.000 0.963 1.000 0.000 0.000
#> GSM28803 3 0.000 1.000 0.000 0.000 1.000
#> GSM11343 3 0.000 1.000 0.000 0.000 1.000
#> GSM11347 3 0.000 1.000 0.000 0.000 1.000
#> GSM28824 1 0.000 0.963 1.000 0.000 0.000
#> GSM28813 1 0.000 0.963 1.000 0.000 0.000
#> GSM28827 1 0.000 0.963 1.000 0.000 0.000
#> GSM11337 1 0.000 0.963 1.000 0.000 0.000
#> GSM28814 1 0.565 0.603 0.688 0.000 0.312
#> GSM11331 1 0.000 0.963 1.000 0.000 0.000
#> GSM11344 3 0.000 1.000 0.000 0.000 1.000
#> GSM11330 3 0.000 1.000 0.000 0.000 1.000
#> GSM11325 1 0.465 0.761 0.792 0.000 0.208
#> GSM11338 1 0.000 0.963 1.000 0.000 0.000
#> GSM28806 1 0.000 0.963 1.000 0.000 0.000
#> GSM28826 1 0.000 0.963 1.000 0.000 0.000
#> GSM28818 1 0.000 0.963 1.000 0.000 0.000
#> GSM28821 2 0.000 1.000 0.000 1.000 0.000
#> GSM28807 1 0.000 0.963 1.000 0.000 0.000
#> GSM28822 1 0.000 0.963 1.000 0.000 0.000
#> GSM11328 2 0.000 1.000 0.000 1.000 0.000
#> GSM11323 1 0.141 0.936 0.964 0.000 0.036
#> GSM11324 1 0.000 0.963 1.000 0.000 0.000
#> GSM11341 1 0.382 0.831 0.852 0.000 0.148
#> GSM11326 1 0.562 0.611 0.692 0.000 0.308
#> GSM28810 1 0.000 0.963 1.000 0.000 0.000
#> GSM11335 1 0.000 0.963 1.000 0.000 0.000
#> GSM28809 1 0.000 0.963 1.000 0.000 0.000
#> GSM11329 1 0.000 0.963 1.000 0.000 0.000
#> GSM28805 1 0.000 0.963 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.0000 0.935 1.000 0.000 0.000 0.000
#> GSM28816 1 0.1474 0.893 0.948 0.052 0.000 0.000
#> GSM28817 1 0.0188 0.935 0.996 0.000 0.000 0.004
#> GSM11327 4 0.5803 0.684 0.104 0.000 0.196 0.700
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11345 1 0.0469 0.933 0.988 0.000 0.000 0.012
#> GSM28819 1 0.0469 0.933 0.988 0.000 0.000 0.012
#> GSM11321 3 0.2345 0.863 0.000 0.000 0.900 0.100
#> GSM28820 1 0.0469 0.933 0.988 0.000 0.000 0.012
#> GSM11339 1 0.0000 0.935 1.000 0.000 0.000 0.000
#> GSM28804 1 0.0188 0.935 0.996 0.000 0.000 0.004
#> GSM28823 1 0.0469 0.933 0.988 0.000 0.000 0.012
#> GSM11336 4 0.2469 0.936 0.108 0.000 0.000 0.892
#> GSM11342 1 0.0469 0.933 0.988 0.000 0.000 0.012
#> GSM11333 1 0.0000 0.935 1.000 0.000 0.000 0.000
#> GSM28802 1 0.0000 0.935 1.000 0.000 0.000 0.000
#> GSM28803 3 0.4776 0.540 0.000 0.000 0.624 0.376
#> GSM11343 3 0.0000 0.911 0.000 0.000 1.000 0.000
#> GSM11347 3 0.0000 0.911 0.000 0.000 1.000 0.000
#> GSM28824 4 0.2469 0.936 0.108 0.000 0.000 0.892
#> GSM28813 4 0.2469 0.936 0.108 0.000 0.000 0.892
#> GSM28827 1 0.0000 0.935 1.000 0.000 0.000 0.000
#> GSM11337 1 0.4746 0.361 0.632 0.000 0.000 0.368
#> GSM28814 1 0.6535 0.404 0.588 0.000 0.312 0.100
#> GSM11331 1 0.0336 0.934 0.992 0.000 0.000 0.008
#> GSM11344 3 0.0000 0.911 0.000 0.000 1.000 0.000
#> GSM11330 3 0.0000 0.911 0.000 0.000 1.000 0.000
#> GSM11325 1 0.5747 0.610 0.704 0.000 0.196 0.100
#> GSM11338 4 0.2469 0.936 0.108 0.000 0.000 0.892
#> GSM28806 1 0.0469 0.933 0.988 0.000 0.000 0.012
#> GSM28826 1 0.0000 0.935 1.000 0.000 0.000 0.000
#> GSM28818 1 0.0000 0.935 1.000 0.000 0.000 0.000
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28807 1 0.0707 0.932 0.980 0.000 0.000 0.020
#> GSM28822 1 0.0336 0.934 0.992 0.000 0.000 0.008
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11323 1 0.0707 0.932 0.980 0.000 0.000 0.020
#> GSM11324 1 0.0000 0.935 1.000 0.000 0.000 0.000
#> GSM11341 1 0.3196 0.809 0.856 0.000 0.136 0.008
#> GSM11326 1 0.4454 0.580 0.692 0.000 0.308 0.000
#> GSM28810 1 0.0336 0.934 0.992 0.000 0.000 0.008
#> GSM11335 1 0.0707 0.932 0.980 0.000 0.000 0.020
#> GSM28809 1 0.0188 0.935 0.996 0.000 0.000 0.004
#> GSM11329 1 0.0000 0.935 1.000 0.000 0.000 0.000
#> GSM28805 1 0.0000 0.935 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
#> GSM28815 1 0.0000 0.902 1.000 0.000 0.000 0.000 0.000
#> GSM28816 1 0.1341 0.876 0.944 0.056 0.000 0.000 0.000
#> GSM28817 1 0.0000 0.902 1.000 0.000 0.000 0.000 0.000
#> GSM11327 5 0.3231 0.680 0.004 0.000 0.196 0.000 0.800
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11345 1 0.0290 0.901 0.992 0.000 0.000 0.000 0.008
#> GSM28819 1 0.0290 0.901 0.992 0.000 0.000 0.000 0.008
#> GSM11321 3 0.0000 0.805 0.000 0.000 1.000 0.000 0.000
#> GSM28820 1 0.0290 0.901 0.992 0.000 0.000 0.000 0.008
#> GSM11339 1 0.0000 0.902 1.000 0.000 0.000 0.000 0.000
#> GSM28804 1 0.3999 0.692 0.656 0.000 0.000 0.344 0.000
#> GSM28823 1 0.0290 0.901 0.992 0.000 0.000 0.000 0.008
#> GSM11336 5 0.0000 0.935 0.000 0.000 0.000 0.000 1.000
#> GSM11342 1 0.0290 0.901 0.992 0.000 0.000 0.000 0.008
#> GSM11333 1 0.0162 0.902 0.996 0.000 0.000 0.004 0.000
#> GSM28802 1 0.0000 0.902 1.000 0.000 0.000 0.000 0.000
#> GSM28803 3 0.0000 0.805 0.000 0.000 1.000 0.000 0.000
#> GSM11343 4 0.3999 1.000 0.000 0.000 0.344 0.656 0.000
#> GSM11347 4 0.3999 1.000 0.000 0.000 0.344 0.656 0.000
#> GSM28824 5 0.0000 0.935 0.000 0.000 0.000 0.000 1.000
#> GSM28813 5 0.0000 0.935 0.000 0.000 0.000 0.000 1.000
#> GSM28827 1 0.0000 0.902 1.000 0.000 0.000 0.000 0.000
#> GSM11337 1 0.4126 0.510 0.620 0.000 0.000 0.000 0.380
#> GSM28814 3 0.1341 0.813 0.056 0.000 0.944 0.000 0.000
#> GSM11331 1 0.2280 0.862 0.880 0.000 0.000 0.120 0.000
#> GSM11344 4 0.3999 1.000 0.000 0.000 0.344 0.656 0.000
#> GSM11330 4 0.3999 1.000 0.000 0.000 0.344 0.656 0.000
#> GSM11325 3 0.2561 0.686 0.144 0.000 0.856 0.000 0.000
#> GSM11338 5 0.0000 0.935 0.000 0.000 0.000 0.000 1.000
#> GSM28806 1 0.0290 0.901 0.992 0.000 0.000 0.000 0.008
#> GSM28826 1 0.0000 0.902 1.000 0.000 0.000 0.000 0.000
#> GSM28818 1 0.2280 0.863 0.880 0.000 0.000 0.120 0.000
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM28807 1 0.3999 0.692 0.656 0.000 0.000 0.344 0.000
#> GSM28822 1 0.3999 0.692 0.656 0.000 0.000 0.344 0.000
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM11323 1 0.2280 0.862 0.880 0.000 0.000 0.120 0.000
#> GSM11324 1 0.0000 0.902 1.000 0.000 0.000 0.000 0.000
#> GSM11341 1 0.3999 0.692 0.656 0.000 0.000 0.344 0.000
#> GSM11326 1 0.3752 0.630 0.708 0.000 0.292 0.000 0.000
#> GSM28810 1 0.2424 0.856 0.868 0.000 0.000 0.132 0.000
#> GSM11335 1 0.3109 0.815 0.800 0.000 0.000 0.200 0.000
#> GSM28809 1 0.0290 0.901 0.992 0.000 0.000 0.008 0.000
#> GSM11329 1 0.0000 0.902 1.000 0.000 0.000 0.000 0.000
#> GSM28805 1 0.0000 0.902 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
#> GSM28815 1 0.2946 0.799 0.812 0 0.012 0.176 0.00 0.000
#> GSM28816 1 0.2980 0.798 0.808 0 0.012 0.180 0.00 0.000
#> GSM28817 1 0.2923 0.793 0.848 0 0.000 0.052 0.00 0.100
#> GSM11327 5 0.3046 0.691 0.000 0 0.188 0.000 0.80 0.012
#> GSM28825 2 0.0000 1.000 0.000 1 0.000 0.000 0.00 0.000
#> GSM11322 2 0.0000 1.000 0.000 1 0.000 0.000 0.00 0.000
#> GSM28828 2 0.0000 1.000 0.000 1 0.000 0.000 0.00 0.000
#> GSM11346 2 0.0000 1.000 0.000 1 0.000 0.000 0.00 0.000
#> GSM28808 2 0.0000 1.000 0.000 1 0.000 0.000 0.00 0.000
#> GSM11332 2 0.0000 1.000 0.000 1 0.000 0.000 0.00 0.000
#> GSM28811 2 0.0000 1.000 0.000 1 0.000 0.000 0.00 0.000
#> GSM11334 2 0.0000 1.000 0.000 1 0.000 0.000 0.00 0.000
#> GSM11340 2 0.0000 1.000 0.000 1 0.000 0.000 0.00 0.000
#> GSM28812 2 0.0000 1.000 0.000 1 0.000 0.000 0.00 0.000
#> GSM11345 1 0.2593 0.772 0.844 0 0.000 0.008 0.00 0.148
#> GSM28819 1 0.2593 0.772 0.844 0 0.000 0.008 0.00 0.148
#> GSM11321 3 0.0363 0.876 0.000 0 0.988 0.000 0.00 0.012
#> GSM28820 1 0.2593 0.772 0.844 0 0.000 0.008 0.00 0.148
#> GSM11339 1 0.2593 0.806 0.844 0 0.008 0.148 0.00 0.000
#> GSM28804 1 0.3766 0.599 0.748 0 0.000 0.212 0.00 0.040
#> GSM28823 4 0.5167 1.000 0.240 0 0.000 0.612 0.00 0.148
#> GSM11336 5 0.0000 0.935 0.000 0 0.000 0.000 1.00 0.000
#> GSM11342 4 0.5167 1.000 0.240 0 0.000 0.612 0.00 0.148
#> GSM11333 1 0.2980 0.798 0.808 0 0.012 0.180 0.00 0.000
#> GSM28802 1 0.2946 0.799 0.812 0 0.012 0.176 0.00 0.000
#> GSM28803 3 0.0363 0.876 0.000 0 0.988 0.000 0.00 0.012
#> GSM11343 6 0.2697 1.000 0.000 0 0.188 0.000 0.00 0.812
#> GSM11347 6 0.2697 1.000 0.000 0 0.188 0.000 0.00 0.812
#> GSM28824 5 0.0000 0.935 0.000 0 0.000 0.000 1.00 0.000
#> GSM28813 5 0.0000 0.935 0.000 0 0.000 0.000 1.00 0.000
#> GSM28827 1 0.2513 0.806 0.852 0 0.008 0.140 0.00 0.000
#> GSM11337 1 0.3945 0.444 0.612 0 0.000 0.008 0.38 0.000
#> GSM28814 3 0.0000 0.876 0.000 0 1.000 0.000 0.00 0.000
#> GSM11331 1 0.0291 0.803 0.992 0 0.000 0.004 0.00 0.004
#> GSM11344 6 0.2697 1.000 0.000 0 0.188 0.000 0.00 0.812
#> GSM11330 6 0.2697 1.000 0.000 0 0.188 0.000 0.00 0.812
#> GSM11325 3 0.2778 0.686 0.008 0 0.824 0.168 0.00 0.000
#> GSM11338 5 0.0000 0.935 0.000 0 0.000 0.000 1.00 0.000
#> GSM28806 1 0.2006 0.792 0.892 0 0.000 0.004 0.00 0.104
#> GSM28826 1 0.2946 0.799 0.812 0 0.012 0.176 0.00 0.000
#> GSM28818 1 0.0260 0.803 0.992 0 0.000 0.008 0.00 0.000
#> GSM28821 2 0.0000 1.000 0.000 1 0.000 0.000 0.00 0.000
#> GSM28807 1 0.3766 0.599 0.748 0 0.000 0.212 0.00 0.040
#> GSM28822 1 0.3766 0.599 0.748 0 0.000 0.212 0.00 0.040
#> GSM11328 2 0.0000 1.000 0.000 1 0.000 0.000 0.00 0.000
#> GSM11323 1 0.0405 0.802 0.988 0 0.000 0.004 0.00 0.008
#> GSM11324 1 0.2923 0.793 0.848 0 0.000 0.052 0.00 0.100
#> GSM11341 1 0.3766 0.599 0.748 0 0.000 0.212 0.00 0.040
#> GSM11326 1 0.3377 0.695 0.784 0 0.188 0.000 0.00 0.028
#> GSM28810 1 0.0291 0.803 0.992 0 0.000 0.004 0.00 0.004
#> GSM11335 1 0.1297 0.790 0.948 0 0.000 0.012 0.00 0.040
#> GSM28809 1 0.0000 0.805 1.000 0 0.000 0.000 0.00 0.000
#> GSM11329 1 0.2513 0.806 0.852 0 0.008 0.140 0.00 0.000
#> GSM28805 1 0.2946 0.799 0.812 0 0.012 0.176 0.00 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> CV:pam 54 0.398 2
#> CV:pam 54 0.374 3
#> CV:pam 52 0.487 4
#> CV:pam 54 0.455 5
#> CV:pam 53 0.638 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.688 0.925 0.950 0.4657 0.508 0.508
#> 3 3 0.866 0.948 0.970 0.2717 0.916 0.835
#> 4 4 0.835 0.875 0.931 0.1725 0.891 0.743
#> 5 5 0.826 0.799 0.909 0.0982 0.908 0.713
#> 6 6 0.838 0.856 0.893 0.0506 0.951 0.795
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
#> GSM28815 1 0.0000 0.984 1.000 0.000
#> GSM28816 1 0.4161 0.904 0.916 0.084
#> GSM28817 1 0.0000 0.984 1.000 0.000
#> GSM11327 2 0.7674 0.835 0.224 0.776
#> GSM28825 2 0.0000 0.885 0.000 1.000
#> GSM11322 2 0.0000 0.885 0.000 1.000
#> GSM28828 2 0.0000 0.885 0.000 1.000
#> GSM11346 2 0.0000 0.885 0.000 1.000
#> GSM28808 2 0.0000 0.885 0.000 1.000
#> GSM11332 2 0.0000 0.885 0.000 1.000
#> GSM28811 2 0.0000 0.885 0.000 1.000
#> GSM11334 2 0.0000 0.885 0.000 1.000
#> GSM11340 2 0.0000 0.885 0.000 1.000
#> GSM28812 2 0.0000 0.885 0.000 1.000
#> GSM11345 1 0.0000 0.984 1.000 0.000
#> GSM28819 1 0.0000 0.984 1.000 0.000
#> GSM11321 2 0.7674 0.835 0.224 0.776
#> GSM28820 1 0.0000 0.984 1.000 0.000
#> GSM11339 1 0.0000 0.984 1.000 0.000
#> GSM28804 1 0.1633 0.968 0.976 0.024
#> GSM28823 1 0.0000 0.984 1.000 0.000
#> GSM11336 1 0.0000 0.984 1.000 0.000
#> GSM11342 1 0.0000 0.984 1.000 0.000
#> GSM11333 1 0.0000 0.984 1.000 0.000
#> GSM28802 1 0.0000 0.984 1.000 0.000
#> GSM28803 2 0.7674 0.835 0.224 0.776
#> GSM11343 2 0.7674 0.835 0.224 0.776
#> GSM11347 2 0.7674 0.835 0.224 0.776
#> GSM28824 1 0.0000 0.984 1.000 0.000
#> GSM28813 1 0.0000 0.984 1.000 0.000
#> GSM28827 1 0.0000 0.984 1.000 0.000
#> GSM11337 1 0.0000 0.984 1.000 0.000
#> GSM28814 2 0.7674 0.835 0.224 0.776
#> GSM11331 1 0.0376 0.981 0.996 0.004
#> GSM11344 2 0.7674 0.835 0.224 0.776
#> GSM11330 2 0.7674 0.835 0.224 0.776
#> GSM11325 2 0.7674 0.835 0.224 0.776
#> GSM11338 1 0.0000 0.984 1.000 0.000
#> GSM28806 1 0.0000 0.984 1.000 0.000
#> GSM28826 1 0.0000 0.984 1.000 0.000
#> GSM28818 1 0.1633 0.968 0.976 0.024
#> GSM28821 2 0.0000 0.885 0.000 1.000
#> GSM28807 1 0.1633 0.968 0.976 0.024
#> GSM28822 1 0.1633 0.968 0.976 0.024
#> GSM11328 2 0.0000 0.885 0.000 1.000
#> GSM11323 1 0.0376 0.981 0.996 0.004
#> GSM11324 1 0.0000 0.984 1.000 0.000
#> GSM11341 1 0.7376 0.686 0.792 0.208
#> GSM11326 2 0.7674 0.835 0.224 0.776
#> GSM28810 1 0.1633 0.968 0.976 0.024
#> GSM11335 1 0.1633 0.968 0.976 0.024
#> GSM28809 1 0.0000 0.984 1.000 0.000
#> GSM11329 1 0.0000 0.984 1.000 0.000
#> GSM28805 1 0.0000 0.984 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.0000 0.947 1.000 0.000 0.000
#> GSM28816 1 0.2625 0.892 0.916 0.084 0.000
#> GSM28817 1 0.0000 0.947 1.000 0.000 0.000
#> GSM11327 3 0.0000 1.000 0.000 0.000 1.000
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11345 1 0.0424 0.944 0.992 0.000 0.008
#> GSM28819 1 0.0000 0.947 1.000 0.000 0.000
#> GSM11321 3 0.0000 1.000 0.000 0.000 1.000
#> GSM28820 1 0.0000 0.947 1.000 0.000 0.000
#> GSM11339 1 0.0000 0.947 1.000 0.000 0.000
#> GSM28804 1 0.1289 0.933 0.968 0.000 0.032
#> GSM28823 1 0.0000 0.947 1.000 0.000 0.000
#> GSM11336 1 0.0000 0.947 1.000 0.000 0.000
#> GSM11342 1 0.0000 0.947 1.000 0.000 0.000
#> GSM11333 1 0.0000 0.947 1.000 0.000 0.000
#> GSM28802 1 0.0000 0.947 1.000 0.000 0.000
#> GSM28803 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11343 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11347 3 0.0000 1.000 0.000 0.000 1.000
#> GSM28824 1 0.0000 0.947 1.000 0.000 0.000
#> GSM28813 1 0.0000 0.947 1.000 0.000 0.000
#> GSM28827 1 0.0000 0.947 1.000 0.000 0.000
#> GSM11337 1 0.0000 0.947 1.000 0.000 0.000
#> GSM28814 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11331 1 0.4605 0.802 0.796 0.000 0.204
#> GSM11344 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11330 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11325 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11338 1 0.0000 0.947 1.000 0.000 0.000
#> GSM28806 1 0.0892 0.939 0.980 0.000 0.020
#> GSM28826 1 0.0000 0.947 1.000 0.000 0.000
#> GSM28818 1 0.1031 0.937 0.976 0.000 0.024
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28807 1 0.4555 0.806 0.800 0.000 0.200
#> GSM28822 1 0.4555 0.806 0.800 0.000 0.200
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11323 1 0.4555 0.806 0.800 0.000 0.200
#> GSM11324 1 0.0000 0.947 1.000 0.000 0.000
#> GSM11341 1 0.5660 0.781 0.772 0.028 0.200
#> GSM11326 3 0.0000 1.000 0.000 0.000 1.000
#> GSM28810 1 0.4555 0.806 0.800 0.000 0.200
#> GSM11335 1 0.4555 0.806 0.800 0.000 0.200
#> GSM28809 1 0.0000 0.947 1.000 0.000 0.000
#> GSM11329 1 0.0000 0.947 1.000 0.000 0.000
#> GSM28805 1 0.0000 0.947 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.0188 0.881 0.996 0.000 0.000 0.004
#> GSM28816 1 0.1004 0.866 0.972 0.024 0.000 0.004
#> GSM28817 1 0.0188 0.881 0.996 0.000 0.000 0.004
#> GSM11327 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11345 1 0.3400 0.840 0.820 0.000 0.000 0.180
#> GSM28819 1 0.3266 0.850 0.832 0.000 0.000 0.168
#> GSM11321 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM28820 1 0.2921 0.862 0.860 0.000 0.000 0.140
#> GSM11339 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM28804 4 0.3873 0.635 0.228 0.000 0.000 0.772
#> GSM28823 1 0.3444 0.837 0.816 0.000 0.000 0.184
#> GSM11336 1 0.0188 0.881 0.996 0.000 0.000 0.004
#> GSM11342 1 0.3444 0.837 0.816 0.000 0.000 0.184
#> GSM11333 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM28802 1 0.2408 0.871 0.896 0.000 0.000 0.104
#> GSM28803 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11343 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11347 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM28824 1 0.0188 0.881 0.996 0.000 0.000 0.004
#> GSM28813 1 0.0188 0.881 0.996 0.000 0.000 0.004
#> GSM28827 1 0.3024 0.858 0.852 0.000 0.000 0.148
#> GSM11337 1 0.0188 0.881 0.996 0.000 0.000 0.004
#> GSM28814 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11331 1 0.4088 0.790 0.764 0.000 0.004 0.232
#> GSM11344 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11330 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11325 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM11338 1 0.0188 0.881 0.996 0.000 0.000 0.004
#> GSM28806 1 0.3486 0.837 0.812 0.000 0.000 0.188
#> GSM28826 1 0.0188 0.881 0.996 0.000 0.000 0.004
#> GSM28818 1 0.4277 0.438 0.720 0.000 0.000 0.280
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM28807 4 0.0707 0.764 0.020 0.000 0.000 0.980
#> GSM28822 4 0.0592 0.764 0.016 0.000 0.000 0.984
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM11323 1 0.3907 0.793 0.768 0.000 0.000 0.232
#> GSM11324 1 0.3311 0.845 0.828 0.000 0.000 0.172
#> GSM11341 4 0.2814 0.641 0.000 0.132 0.000 0.868
#> GSM11326 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM28810 4 0.4999 -0.291 0.492 0.000 0.000 0.508
#> GSM11335 4 0.0469 0.763 0.012 0.000 0.000 0.988
#> GSM28809 1 0.0000 0.880 1.000 0.000 0.000 0.000
#> GSM11329 1 0.2921 0.861 0.860 0.000 0.000 0.140
#> GSM28805 1 0.0188 0.881 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 1 0.1043 0.840 0.960 0.000 0.000 0.000 0.040
#> GSM28816 1 0.1121 0.840 0.956 0.000 0.000 0.000 0.044
#> GSM28817 1 0.0290 0.843 0.992 0.000 0.000 0.000 0.008
#> GSM11327 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM28825 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM11345 1 0.0609 0.843 0.980 0.000 0.000 0.020 0.000
#> GSM28819 1 0.4420 0.532 0.692 0.000 0.000 0.028 0.280
#> GSM11321 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM28820 1 0.4300 -0.129 0.524 0.000 0.000 0.000 0.476
#> GSM11339 1 0.0963 0.839 0.964 0.000 0.000 0.000 0.036
#> GSM28804 4 0.1043 0.663 0.040 0.000 0.000 0.960 0.000
#> GSM28823 1 0.1965 0.829 0.924 0.000 0.000 0.052 0.024
#> GSM11336 5 0.4138 0.397 0.384 0.000 0.000 0.000 0.616
#> GSM11342 1 0.1469 0.835 0.948 0.000 0.000 0.036 0.016
#> GSM11333 1 0.1608 0.833 0.928 0.000 0.000 0.000 0.072
#> GSM28802 5 0.4649 0.240 0.404 0.000 0.000 0.016 0.580
#> GSM28803 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM11343 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM11347 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM28824 5 0.0963 0.693 0.036 0.000 0.000 0.000 0.964
#> GSM28813 5 0.0703 0.683 0.024 0.000 0.000 0.000 0.976
#> GSM28827 1 0.0162 0.844 0.996 0.000 0.000 0.000 0.004
#> GSM11337 1 0.4297 -0.112 0.528 0.000 0.000 0.000 0.472
#> GSM28814 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM11331 1 0.4599 0.664 0.744 0.000 0.004 0.072 0.180
#> GSM11344 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM11330 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM11325 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM11338 5 0.1792 0.687 0.084 0.000 0.000 0.000 0.916
#> GSM28806 1 0.3780 0.747 0.812 0.000 0.000 0.072 0.116
#> GSM28826 1 0.2561 0.770 0.856 0.000 0.000 0.000 0.144
#> GSM28818 4 0.4440 0.421 0.468 0.000 0.000 0.528 0.004
#> GSM28821 2 0.0609 0.980 0.000 0.980 0.000 0.000 0.020
#> GSM28807 4 0.2773 0.740 0.164 0.000 0.000 0.836 0.000
#> GSM28822 4 0.2848 0.740 0.156 0.000 0.000 0.840 0.004
#> GSM11328 2 0.0000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM11323 1 0.4096 0.718 0.784 0.000 0.000 0.072 0.144
#> GSM11324 1 0.0566 0.844 0.984 0.000 0.000 0.004 0.012
#> GSM11341 4 0.0880 0.639 0.000 0.032 0.000 0.968 0.000
#> GSM11326 3 0.0609 0.978 0.000 0.000 0.980 0.020 0.000
#> GSM28810 4 0.4582 0.465 0.416 0.000 0.000 0.572 0.012
#> GSM11335 4 0.2233 0.732 0.104 0.000 0.000 0.892 0.004
#> GSM28809 1 0.0000 0.844 1.000 0.000 0.000 0.000 0.000
#> GSM11329 1 0.0000 0.844 1.000 0.000 0.000 0.000 0.000
#> GSM28805 1 0.0963 0.839 0.964 0.000 0.000 0.000 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 1 0.0458 0.839 0.984 0.000 0.000 0.000 0.000 0.016
#> GSM28816 1 0.1168 0.832 0.956 0.000 0.000 0.000 0.028 0.016
#> GSM28817 1 0.0146 0.842 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM11327 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM28825 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28828 2 0.1141 0.965 0.000 0.948 0.000 0.000 0.000 0.052
#> GSM11346 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28811 2 0.1141 0.965 0.000 0.948 0.000 0.000 0.000 0.052
#> GSM11334 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11345 1 0.2473 0.814 0.856 0.000 0.000 0.136 0.000 0.008
#> GSM28819 1 0.4678 0.345 0.640 0.000 0.000 0.044 0.304 0.012
#> GSM11321 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM28820 5 0.4192 0.508 0.412 0.000 0.000 0.016 0.572 0.000
#> GSM11339 1 0.0291 0.844 0.992 0.000 0.000 0.004 0.000 0.004
#> GSM28804 4 0.1700 0.899 0.048 0.000 0.000 0.928 0.000 0.024
#> GSM28823 1 0.2948 0.786 0.804 0.000 0.000 0.188 0.000 0.008
#> GSM11336 5 0.2631 0.655 0.180 0.000 0.000 0.000 0.820 0.000
#> GSM11342 1 0.2948 0.786 0.804 0.000 0.000 0.188 0.000 0.008
#> GSM11333 1 0.1588 0.812 0.924 0.000 0.000 0.000 0.072 0.004
#> GSM28802 5 0.4089 0.628 0.352 0.000 0.000 0.004 0.632 0.012
#> GSM28803 3 0.0363 0.979 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM11343 6 0.3464 1.000 0.000 0.000 0.312 0.000 0.000 0.688
#> GSM11347 6 0.3464 1.000 0.000 0.000 0.312 0.000 0.000 0.688
#> GSM28824 5 0.0260 0.700 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM28813 5 0.0000 0.695 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28827 1 0.1584 0.843 0.928 0.000 0.000 0.064 0.000 0.008
#> GSM11337 5 0.3699 0.643 0.336 0.000 0.000 0.000 0.660 0.004
#> GSM28814 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11331 1 0.5371 0.621 0.616 0.000 0.008 0.164 0.000 0.212
#> GSM11344 6 0.3464 1.000 0.000 0.000 0.312 0.000 0.000 0.688
#> GSM11330 6 0.3464 1.000 0.000 0.000 0.312 0.000 0.000 0.688
#> GSM11325 3 0.0000 0.991 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11338 5 0.0000 0.695 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28806 1 0.4206 0.736 0.724 0.000 0.004 0.212 0.000 0.060
#> GSM28826 1 0.1332 0.835 0.952 0.000 0.000 0.008 0.028 0.012
#> GSM28818 4 0.3276 0.699 0.228 0.000 0.004 0.764 0.000 0.004
#> GSM28821 2 0.1471 0.956 0.004 0.932 0.000 0.000 0.000 0.064
#> GSM28807 4 0.0937 0.917 0.040 0.000 0.000 0.960 0.000 0.000
#> GSM28822 4 0.0547 0.921 0.020 0.000 0.000 0.980 0.000 0.000
#> GSM11328 2 0.1141 0.965 0.000 0.948 0.000 0.000 0.000 0.052
#> GSM11323 1 0.5537 0.598 0.592 0.000 0.008 0.188 0.000 0.212
#> GSM11324 1 0.1701 0.841 0.920 0.000 0.000 0.072 0.000 0.008
#> GSM11341 4 0.1908 0.874 0.004 0.000 0.000 0.900 0.000 0.096
#> GSM11326 3 0.0458 0.971 0.000 0.000 0.984 0.016 0.000 0.000
#> GSM28810 4 0.0692 0.920 0.020 0.000 0.004 0.976 0.000 0.000
#> GSM11335 4 0.0458 0.920 0.016 0.000 0.000 0.984 0.000 0.000
#> GSM28809 1 0.0363 0.843 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM11329 1 0.1049 0.846 0.960 0.000 0.000 0.032 0.000 0.008
#> GSM28805 1 0.0291 0.844 0.992 0.000 0.000 0.004 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> CV:mclust 54 0.398 2
#> CV:mclust 54 0.374 3
#> CV:mclust 52 0.352 4
#> CV:mclust 48 0.405 5
#> CV:mclust 53 0.407 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.980 0.992 0.3615 0.648 0.648
#> 3 3 0.964 0.965 0.979 0.6637 0.762 0.632
#> 4 4 0.778 0.809 0.873 0.2136 0.871 0.688
#> 5 5 0.848 0.850 0.915 0.0843 0.894 0.650
#> 6 6 0.837 0.682 0.847 0.0418 0.988 0.943
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
#> GSM28815 1 0.000 0.989 1.000 0.000
#> GSM28816 1 0.958 0.391 0.620 0.380
#> GSM28817 1 0.000 0.989 1.000 0.000
#> GSM11327 1 0.000 0.989 1.000 0.000
#> GSM28825 2 0.000 1.000 0.000 1.000
#> GSM11322 2 0.000 1.000 0.000 1.000
#> GSM28828 2 0.000 1.000 0.000 1.000
#> GSM11346 2 0.000 1.000 0.000 1.000
#> GSM28808 2 0.000 1.000 0.000 1.000
#> GSM11332 2 0.000 1.000 0.000 1.000
#> GSM28811 2 0.000 1.000 0.000 1.000
#> GSM11334 2 0.000 1.000 0.000 1.000
#> GSM11340 2 0.000 1.000 0.000 1.000
#> GSM28812 2 0.000 1.000 0.000 1.000
#> GSM11345 1 0.000 0.989 1.000 0.000
#> GSM28819 1 0.000 0.989 1.000 0.000
#> GSM11321 1 0.000 0.989 1.000 0.000
#> GSM28820 1 0.000 0.989 1.000 0.000
#> GSM11339 1 0.000 0.989 1.000 0.000
#> GSM28804 1 0.295 0.938 0.948 0.052
#> GSM28823 1 0.000 0.989 1.000 0.000
#> GSM11336 1 0.000 0.989 1.000 0.000
#> GSM11342 1 0.000 0.989 1.000 0.000
#> GSM11333 1 0.000 0.989 1.000 0.000
#> GSM28802 1 0.000 0.989 1.000 0.000
#> GSM28803 1 0.000 0.989 1.000 0.000
#> GSM11343 1 0.000 0.989 1.000 0.000
#> GSM11347 1 0.000 0.989 1.000 0.000
#> GSM28824 1 0.000 0.989 1.000 0.000
#> GSM28813 1 0.000 0.989 1.000 0.000
#> GSM28827 1 0.000 0.989 1.000 0.000
#> GSM11337 1 0.000 0.989 1.000 0.000
#> GSM28814 1 0.000 0.989 1.000 0.000
#> GSM11331 1 0.000 0.989 1.000 0.000
#> GSM11344 1 0.000 0.989 1.000 0.000
#> GSM11330 1 0.000 0.989 1.000 0.000
#> GSM11325 1 0.000 0.989 1.000 0.000
#> GSM11338 1 0.000 0.989 1.000 0.000
#> GSM28806 1 0.000 0.989 1.000 0.000
#> GSM28826 1 0.000 0.989 1.000 0.000
#> GSM28818 1 0.000 0.989 1.000 0.000
#> GSM28821 2 0.000 1.000 0.000 1.000
#> GSM28807 1 0.000 0.989 1.000 0.000
#> GSM28822 1 0.000 0.989 1.000 0.000
#> GSM11328 2 0.000 1.000 0.000 1.000
#> GSM11323 1 0.000 0.989 1.000 0.000
#> GSM11324 1 0.000 0.989 1.000 0.000
#> GSM11341 1 0.000 0.989 1.000 0.000
#> GSM11326 1 0.000 0.989 1.000 0.000
#> GSM28810 1 0.000 0.989 1.000 0.000
#> GSM11335 1 0.000 0.989 1.000 0.000
#> GSM28809 1 0.000 0.989 1.000 0.000
#> GSM11329 1 0.000 0.989 1.000 0.000
#> GSM28805 1 0.000 0.989 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.0000 0.965 1.000 0.000 0.000
#> GSM28816 1 0.4235 0.811 0.824 0.176 0.000
#> GSM28817 1 0.0000 0.965 1.000 0.000 0.000
#> GSM11327 3 0.0000 0.995 0.000 0.000 1.000
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11345 1 0.0000 0.965 1.000 0.000 0.000
#> GSM28819 1 0.0237 0.965 0.996 0.000 0.004
#> GSM11321 3 0.0000 0.995 0.000 0.000 1.000
#> GSM28820 1 0.0000 0.965 1.000 0.000 0.000
#> GSM11339 1 0.0000 0.965 1.000 0.000 0.000
#> GSM28804 1 0.0747 0.962 0.984 0.000 0.016
#> GSM28823 1 0.0000 0.965 1.000 0.000 0.000
#> GSM11336 1 0.1964 0.939 0.944 0.000 0.056
#> GSM11342 1 0.0000 0.965 1.000 0.000 0.000
#> GSM11333 1 0.0000 0.965 1.000 0.000 0.000
#> GSM28802 1 0.1031 0.958 0.976 0.000 0.024
#> GSM28803 3 0.0000 0.995 0.000 0.000 1.000
#> GSM11343 3 0.0000 0.995 0.000 0.000 1.000
#> GSM11347 3 0.0000 0.995 0.000 0.000 1.000
#> GSM28824 1 0.1753 0.944 0.952 0.000 0.048
#> GSM28813 1 0.4702 0.779 0.788 0.000 0.212
#> GSM28827 1 0.0000 0.965 1.000 0.000 0.000
#> GSM11337 1 0.1031 0.958 0.976 0.000 0.024
#> GSM28814 3 0.0000 0.995 0.000 0.000 1.000
#> GSM11331 1 0.3267 0.893 0.884 0.000 0.116
#> GSM11344 3 0.0000 0.995 0.000 0.000 1.000
#> GSM11330 3 0.0000 0.995 0.000 0.000 1.000
#> GSM11325 3 0.0000 0.995 0.000 0.000 1.000
#> GSM11338 1 0.3752 0.863 0.856 0.000 0.144
#> GSM28806 1 0.0000 0.965 1.000 0.000 0.000
#> GSM28826 1 0.2796 0.914 0.908 0.000 0.092
#> GSM28818 1 0.0424 0.964 0.992 0.000 0.008
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28807 1 0.0747 0.962 0.984 0.000 0.016
#> GSM28822 1 0.0747 0.962 0.984 0.000 0.016
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11323 1 0.2878 0.912 0.904 0.000 0.096
#> GSM11324 1 0.0000 0.965 1.000 0.000 0.000
#> GSM11341 3 0.1643 0.945 0.044 0.000 0.956
#> GSM11326 3 0.0000 0.995 0.000 0.000 1.000
#> GSM28810 1 0.0747 0.962 0.984 0.000 0.016
#> GSM11335 1 0.0747 0.962 0.984 0.000 0.016
#> GSM28809 1 0.0000 0.965 1.000 0.000 0.000
#> GSM11329 1 0.0000 0.965 1.000 0.000 0.000
#> GSM28805 1 0.0000 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
#> GSM28815 1 0.2647 0.7624 0.880 0.000 0.000 0.120
#> GSM28816 1 0.7714 0.3135 0.400 0.224 0.000 0.376
#> GSM28817 1 0.0469 0.7730 0.988 0.000 0.000 0.012
#> GSM11327 3 0.1022 0.9716 0.000 0.000 0.968 0.032
#> GSM28825 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11345 1 0.1792 0.7249 0.932 0.000 0.000 0.068
#> GSM28819 1 0.0000 0.7730 1.000 0.000 0.000 0.000
#> GSM11321 3 0.1022 0.9727 0.000 0.000 0.968 0.032
#> GSM28820 1 0.0188 0.7736 0.996 0.000 0.000 0.004
#> GSM11339 1 0.4356 0.3756 0.708 0.000 0.000 0.292
#> GSM28804 4 0.3649 0.8894 0.204 0.000 0.000 0.796
#> GSM28823 1 0.0000 0.7730 1.000 0.000 0.000 0.000
#> GSM11336 1 0.4222 0.7068 0.728 0.000 0.000 0.272
#> GSM11342 1 0.0000 0.7730 1.000 0.000 0.000 0.000
#> GSM11333 1 0.4992 0.4981 0.524 0.000 0.000 0.476
#> GSM28802 1 0.2647 0.7563 0.880 0.000 0.000 0.120
#> GSM28803 3 0.1118 0.9714 0.000 0.000 0.964 0.036
#> GSM11343 3 0.0000 0.9746 0.000 0.000 1.000 0.000
#> GSM11347 3 0.0188 0.9744 0.000 0.000 0.996 0.004
#> GSM28824 1 0.4401 0.7049 0.724 0.000 0.004 0.272
#> GSM28813 1 0.5256 0.6855 0.692 0.000 0.036 0.272
#> GSM28827 1 0.0336 0.7697 0.992 0.000 0.000 0.008
#> GSM11337 1 0.3975 0.7231 0.760 0.000 0.000 0.240
#> GSM28814 3 0.1389 0.9646 0.000 0.000 0.952 0.048
#> GSM11331 1 0.7036 0.1707 0.576 0.000 0.212 0.212
#> GSM11344 3 0.0188 0.9744 0.000 0.000 0.996 0.004
#> GSM11330 3 0.0188 0.9744 0.000 0.000 0.996 0.004
#> GSM11325 3 0.1807 0.9565 0.008 0.000 0.940 0.052
#> GSM11338 1 0.4072 0.7172 0.748 0.000 0.000 0.252
#> GSM28806 4 0.4817 0.6996 0.388 0.000 0.000 0.612
#> GSM28826 1 0.4453 0.7157 0.744 0.000 0.012 0.244
#> GSM28818 4 0.3801 0.8906 0.220 0.000 0.000 0.780
#> GSM28821 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28807 4 0.3649 0.8894 0.204 0.000 0.000 0.796
#> GSM28822 4 0.3764 0.8925 0.216 0.000 0.000 0.784
#> GSM11328 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11323 1 0.6454 -0.0266 0.572 0.000 0.084 0.344
#> GSM11324 1 0.0000 0.7730 1.000 0.000 0.000 0.000
#> GSM11341 4 0.4511 0.5331 0.008 0.000 0.268 0.724
#> GSM11326 3 0.0592 0.9698 0.000 0.000 0.984 0.016
#> GSM28810 4 0.4277 0.8523 0.280 0.000 0.000 0.720
#> GSM11335 4 0.3837 0.8900 0.224 0.000 0.000 0.776
#> GSM28809 1 0.3311 0.6641 0.828 0.000 0.000 0.172
#> GSM11329 1 0.0188 0.7714 0.996 0.000 0.000 0.004
#> GSM28805 1 0.0188 0.7722 0.996 0.000 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 1 0.4058 0.611 0.740 0 0.000 0.024 0.236
#> GSM28816 5 0.1774 0.795 0.016 0 0.000 0.052 0.932
#> GSM28817 1 0.1106 0.867 0.964 0 0.000 0.012 0.024
#> GSM11327 3 0.1410 0.914 0.000 0 0.940 0.000 0.060
#> GSM28825 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11345 1 0.0510 0.869 0.984 0 0.000 0.016 0.000
#> GSM28819 1 0.0510 0.866 0.984 0 0.000 0.000 0.016
#> GSM11321 3 0.2922 0.901 0.016 0 0.880 0.024 0.080
#> GSM28820 1 0.0794 0.865 0.972 0 0.000 0.000 0.028
#> GSM11339 1 0.2351 0.835 0.896 0 0.000 0.088 0.016
#> GSM28804 4 0.1579 0.915 0.032 0 0.000 0.944 0.024
#> GSM28823 1 0.0404 0.868 0.988 0 0.000 0.000 0.012
#> GSM11336 5 0.1197 0.824 0.048 0 0.000 0.000 0.952
#> GSM11342 1 0.0771 0.865 0.976 0 0.000 0.004 0.020
#> GSM11333 5 0.1992 0.807 0.032 0 0.000 0.044 0.924
#> GSM28802 1 0.3897 0.646 0.768 0 0.000 0.028 0.204
#> GSM28803 3 0.2722 0.902 0.000 0 0.872 0.020 0.108
#> GSM11343 3 0.0794 0.922 0.000 0 0.972 0.000 0.028
#> GSM11347 3 0.0000 0.922 0.000 0 1.000 0.000 0.000
#> GSM28824 5 0.1124 0.821 0.036 0 0.004 0.000 0.960
#> GSM28813 5 0.1168 0.818 0.032 0 0.008 0.000 0.960
#> GSM28827 1 0.0693 0.870 0.980 0 0.000 0.012 0.008
#> GSM11337 5 0.4264 0.499 0.376 0 0.000 0.004 0.620
#> GSM28814 3 0.3606 0.862 0.008 0 0.816 0.024 0.152
#> GSM11331 1 0.4045 0.769 0.808 0 0.128 0.044 0.020
#> GSM11344 3 0.0000 0.922 0.000 0 1.000 0.000 0.000
#> GSM11330 3 0.0324 0.920 0.000 0 0.992 0.004 0.004
#> GSM11325 3 0.4536 0.786 0.020 0 0.740 0.028 0.212
#> GSM11338 5 0.3086 0.774 0.180 0 0.000 0.004 0.816
#> GSM28806 1 0.4538 0.018 0.540 0 0.000 0.452 0.008
#> GSM28826 5 0.5333 0.458 0.368 0 0.032 0.016 0.584
#> GSM28818 4 0.1774 0.918 0.052 0 0.000 0.932 0.016
#> GSM28821 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28807 4 0.1168 0.919 0.032 0 0.000 0.960 0.008
#> GSM28822 4 0.1251 0.920 0.036 0 0.000 0.956 0.008
#> GSM11328 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11323 1 0.4598 0.734 0.768 0 0.140 0.076 0.016
#> GSM11324 1 0.0671 0.870 0.980 0 0.000 0.016 0.004
#> GSM11341 4 0.1569 0.877 0.004 0 0.044 0.944 0.008
#> GSM11326 3 0.1041 0.909 0.000 0 0.964 0.032 0.004
#> GSM28810 4 0.3961 0.674 0.248 0 0.016 0.736 0.000
#> GSM11335 4 0.2069 0.900 0.076 0 0.012 0.912 0.000
#> GSM28809 1 0.4054 0.748 0.788 0 0.000 0.140 0.072
#> GSM11329 1 0.0566 0.870 0.984 0 0.000 0.012 0.004
#> GSM28805 1 0.0798 0.870 0.976 0 0.000 0.008 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 1 0.5517 0.3522 0.608 0 0.000 0.016 0.228 0.148
#> GSM28816 5 0.5087 0.3154 0.020 0 0.000 0.040 0.520 0.420
#> GSM28817 1 0.0909 0.7453 0.968 0 0.000 0.000 0.020 0.012
#> GSM11327 3 0.4176 0.5215 0.000 0 0.720 0.000 0.212 0.068
#> GSM28825 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11345 1 0.0260 0.7470 0.992 0 0.000 0.000 0.000 0.008
#> GSM28819 1 0.0603 0.7447 0.980 0 0.000 0.000 0.004 0.016
#> GSM11321 3 0.4378 0.1960 0.016 0 0.528 0.000 0.004 0.452
#> GSM28820 1 0.0692 0.7456 0.976 0 0.000 0.000 0.004 0.020
#> GSM11339 1 0.3314 0.6817 0.828 0 0.000 0.076 0.004 0.092
#> GSM28804 4 0.1910 0.8397 0.000 0 0.000 0.892 0.000 0.108
#> GSM28823 1 0.0951 0.7435 0.968 0 0.008 0.000 0.004 0.020
#> GSM11336 5 0.0291 0.7704 0.004 0 0.000 0.000 0.992 0.004
#> GSM11342 1 0.0951 0.7435 0.968 0 0.008 0.000 0.004 0.020
#> GSM11333 5 0.4991 0.3664 0.020 0 0.000 0.036 0.548 0.396
#> GSM28802 1 0.4384 -0.0230 0.520 0 0.004 0.000 0.016 0.460
#> GSM28803 3 0.3719 0.5654 0.000 0 0.728 0.000 0.024 0.248
#> GSM11343 3 0.1285 0.7222 0.000 0 0.944 0.000 0.004 0.052
#> GSM11347 3 0.0000 0.7313 0.000 0 1.000 0.000 0.000 0.000
#> GSM28824 5 0.0146 0.7705 0.004 0 0.000 0.000 0.996 0.000
#> GSM28813 5 0.0000 0.7698 0.000 0 0.000 0.000 1.000 0.000
#> GSM28827 1 0.1606 0.7359 0.932 0 0.000 0.008 0.004 0.056
#> GSM11337 5 0.2956 0.6475 0.088 0 0.000 0.000 0.848 0.064
#> GSM28814 3 0.4223 0.4090 0.000 0 0.612 0.004 0.016 0.368
#> GSM11331 1 0.6630 0.0990 0.380 0 0.320 0.020 0.004 0.276
#> GSM11344 3 0.0260 0.7316 0.000 0 0.992 0.000 0.000 0.008
#> GSM11330 3 0.0865 0.7214 0.000 0 0.964 0.000 0.000 0.036
#> GSM11325 6 0.4357 -0.1005 0.016 0 0.304 0.000 0.020 0.660
#> GSM11338 5 0.0865 0.7580 0.036 0 0.000 0.000 0.964 0.000
#> GSM28806 1 0.5509 0.2236 0.524 0 0.000 0.328 0.000 0.148
#> GSM28826 6 0.6190 -0.0250 0.280 0 0.004 0.000 0.316 0.400
#> GSM28818 4 0.0914 0.9027 0.016 0 0.000 0.968 0.000 0.016
#> GSM28821 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28807 4 0.0260 0.9050 0.000 0 0.000 0.992 0.000 0.008
#> GSM28822 4 0.0146 0.9038 0.000 0 0.000 0.996 0.000 0.004
#> GSM11328 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11323 1 0.7157 0.0894 0.368 0 0.296 0.056 0.008 0.272
#> GSM11324 1 0.1010 0.7441 0.960 0 0.000 0.004 0.000 0.036
#> GSM11341 4 0.0520 0.9045 0.000 0 0.008 0.984 0.000 0.008
#> GSM11326 3 0.2994 0.6057 0.000 0 0.788 0.000 0.004 0.208
#> GSM28810 4 0.3982 0.6421 0.200 0 0.000 0.740 0.000 0.060
#> GSM11335 4 0.2001 0.8774 0.008 0 0.012 0.912 0.000 0.068
#> GSM28809 1 0.5525 0.5242 0.660 0 0.000 0.144 0.056 0.140
#> GSM11329 1 0.0692 0.7472 0.976 0 0.000 0.004 0.000 0.020
#> GSM28805 1 0.1714 0.7256 0.908 0 0.000 0.000 0.000 0.092
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> CV:NMF 53 0.397 2
#> CV:NMF 54 0.374 3
#> CV:NMF 49 0.348 4
#> CV:NMF 51 0.443 5
#> CV:NMF 43 0.444 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.926 0.953 0.2914 0.743 0.743
#> 3 3 0.940 0.941 0.974 0.9326 0.715 0.616
#> 4 4 0.823 0.855 0.938 0.2122 0.868 0.711
#> 5 5 0.786 0.714 0.820 0.0723 0.870 0.607
#> 6 6 0.839 0.840 0.908 0.0559 0.958 0.817
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
#> GSM28815 1 0.358 0.935 0.932 0.068
#> GSM28816 1 0.358 0.935 0.932 0.068
#> GSM28817 1 0.000 0.951 1.000 0.000
#> GSM11327 1 0.980 0.207 0.584 0.416
#> GSM28825 1 0.358 0.935 0.932 0.068
#> GSM11322 1 0.358 0.935 0.932 0.068
#> GSM28828 1 0.358 0.935 0.932 0.068
#> GSM11346 1 0.358 0.935 0.932 0.068
#> GSM28808 1 0.358 0.935 0.932 0.068
#> GSM11332 1 0.358 0.935 0.932 0.068
#> GSM28811 1 0.358 0.935 0.932 0.068
#> GSM11334 1 0.358 0.935 0.932 0.068
#> GSM11340 1 0.358 0.935 0.932 0.068
#> GSM28812 1 0.358 0.935 0.932 0.068
#> GSM11345 1 0.000 0.951 1.000 0.000
#> GSM28819 1 0.000 0.951 1.000 0.000
#> GSM11321 2 0.358 1.000 0.068 0.932
#> GSM28820 1 0.000 0.951 1.000 0.000
#> GSM11339 1 0.000 0.951 1.000 0.000
#> GSM28804 1 0.358 0.935 0.932 0.068
#> GSM28823 1 0.000 0.951 1.000 0.000
#> GSM11336 1 0.000 0.951 1.000 0.000
#> GSM11342 1 0.000 0.951 1.000 0.000
#> GSM11333 1 0.358 0.935 0.932 0.068
#> GSM28802 1 0.000 0.951 1.000 0.000
#> GSM28803 2 0.358 1.000 0.068 0.932
#> GSM11343 2 0.358 1.000 0.068 0.932
#> GSM11347 2 0.358 1.000 0.068 0.932
#> GSM28824 1 0.000 0.951 1.000 0.000
#> GSM28813 1 0.000 0.951 1.000 0.000
#> GSM28827 1 0.000 0.951 1.000 0.000
#> GSM11337 1 0.000 0.951 1.000 0.000
#> GSM28814 2 0.358 1.000 0.068 0.932
#> GSM11331 1 0.000 0.951 1.000 0.000
#> GSM11344 2 0.358 1.000 0.068 0.932
#> GSM11330 2 0.358 1.000 0.068 0.932
#> GSM11325 2 0.358 1.000 0.068 0.932
#> GSM11338 1 0.000 0.951 1.000 0.000
#> GSM28806 1 0.000 0.951 1.000 0.000
#> GSM28826 1 0.000 0.951 1.000 0.000
#> GSM28818 1 0.000 0.951 1.000 0.000
#> GSM28821 1 0.358 0.935 0.932 0.068
#> GSM28807 1 0.000 0.951 1.000 0.000
#> GSM28822 1 0.358 0.935 0.932 0.068
#> GSM11328 1 0.358 0.935 0.932 0.068
#> GSM11323 1 0.000 0.951 1.000 0.000
#> GSM11324 1 0.000 0.951 1.000 0.000
#> GSM11341 1 0.118 0.941 0.984 0.016
#> GSM11326 1 0.980 0.207 0.584 0.416
#> GSM28810 1 0.000 0.951 1.000 0.000
#> GSM11335 1 0.000 0.951 1.000 0.000
#> GSM28809 1 0.000 0.951 1.000 0.000
#> GSM11329 1 0.000 0.951 1.000 0.000
#> GSM28805 1 0.000 0.951 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.2261 0.909 0.932 0.068 0.000
#> GSM28816 1 0.2261 0.909 0.932 0.068 0.000
#> GSM28817 1 0.0000 0.957 1.000 0.000 0.000
#> GSM11327 1 0.6180 0.319 0.584 0.000 0.416
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11345 1 0.0000 0.957 1.000 0.000 0.000
#> GSM28819 1 0.0000 0.957 1.000 0.000 0.000
#> GSM11321 3 0.0000 1.000 0.000 0.000 1.000
#> GSM28820 1 0.0000 0.957 1.000 0.000 0.000
#> GSM11339 1 0.0000 0.957 1.000 0.000 0.000
#> GSM28804 1 0.3551 0.852 0.868 0.132 0.000
#> GSM28823 1 0.0000 0.957 1.000 0.000 0.000
#> GSM11336 1 0.0000 0.957 1.000 0.000 0.000
#> GSM11342 1 0.0000 0.957 1.000 0.000 0.000
#> GSM11333 1 0.2261 0.909 0.932 0.068 0.000
#> GSM28802 1 0.0000 0.957 1.000 0.000 0.000
#> GSM28803 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11343 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11347 3 0.0000 1.000 0.000 0.000 1.000
#> GSM28824 1 0.0000 0.957 1.000 0.000 0.000
#> GSM28813 1 0.0000 0.957 1.000 0.000 0.000
#> GSM28827 1 0.0000 0.957 1.000 0.000 0.000
#> GSM11337 1 0.0000 0.957 1.000 0.000 0.000
#> GSM28814 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11331 1 0.0000 0.957 1.000 0.000 0.000
#> GSM11344 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11330 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11325 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11338 1 0.0000 0.957 1.000 0.000 0.000
#> GSM28806 1 0.0000 0.957 1.000 0.000 0.000
#> GSM28826 1 0.0000 0.957 1.000 0.000 0.000
#> GSM28818 1 0.0000 0.957 1.000 0.000 0.000
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28807 1 0.0237 0.954 0.996 0.004 0.000
#> GSM28822 1 0.3551 0.852 0.868 0.132 0.000
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11323 1 0.0000 0.957 1.000 0.000 0.000
#> GSM11324 1 0.0000 0.957 1.000 0.000 0.000
#> GSM11341 1 0.2902 0.900 0.920 0.064 0.016
#> GSM11326 1 0.6180 0.319 0.584 0.000 0.416
#> GSM28810 1 0.0000 0.957 1.000 0.000 0.000
#> GSM11335 1 0.0000 0.957 1.000 0.000 0.000
#> GSM28809 1 0.0000 0.957 1.000 0.000 0.000
#> GSM11329 1 0.0000 0.957 1.000 0.000 0.000
#> GSM28805 1 0.0000 0.957 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.2814 0.795 0.868 0 0.000 0.132
#> GSM28816 1 0.2814 0.795 0.868 0 0.000 0.132
#> GSM28817 1 0.0469 0.894 0.988 0 0.000 0.012
#> GSM11327 1 0.4898 0.300 0.584 0 0.416 0.000
#> GSM28825 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11345 1 0.0336 0.895 0.992 0 0.000 0.008
#> GSM28819 1 0.0336 0.895 0.992 0 0.000 0.008
#> GSM11321 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM28820 1 0.0336 0.895 0.992 0 0.000 0.008
#> GSM11339 1 0.2921 0.756 0.860 0 0.000 0.140
#> GSM28804 4 0.0336 0.733 0.008 0 0.000 0.992
#> GSM28823 1 0.0336 0.895 0.992 0 0.000 0.008
#> GSM11336 1 0.0336 0.892 0.992 0 0.000 0.008
#> GSM11342 1 0.0336 0.895 0.992 0 0.000 0.008
#> GSM11333 1 0.2814 0.795 0.868 0 0.000 0.132
#> GSM28802 1 0.0188 0.895 0.996 0 0.000 0.004
#> GSM28803 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM11343 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM11347 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM28824 1 0.0336 0.892 0.992 0 0.000 0.008
#> GSM28813 1 0.0336 0.892 0.992 0 0.000 0.008
#> GSM28827 1 0.0000 0.895 1.000 0 0.000 0.000
#> GSM11337 1 0.0000 0.895 1.000 0 0.000 0.000
#> GSM28814 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM11331 1 0.0188 0.895 0.996 0 0.000 0.004
#> GSM11344 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM11330 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM11325 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM11338 1 0.0336 0.892 0.992 0 0.000 0.008
#> GSM28806 1 0.3024 0.748 0.852 0 0.000 0.148
#> GSM28826 1 0.0000 0.895 1.000 0 0.000 0.000
#> GSM28818 4 0.4008 0.759 0.244 0 0.000 0.756
#> GSM28821 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28807 4 0.2868 0.791 0.136 0 0.000 0.864
#> GSM28822 4 0.0336 0.733 0.008 0 0.000 0.992
#> GSM11328 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11323 1 0.0188 0.895 0.996 0 0.000 0.004
#> GSM11324 1 0.0336 0.895 0.992 0 0.000 0.008
#> GSM11341 4 0.2522 0.768 0.076 0 0.016 0.908
#> GSM11326 1 0.4898 0.300 0.584 0 0.416 0.000
#> GSM28810 1 0.5000 -0.295 0.500 0 0.000 0.500
#> GSM11335 4 0.4643 0.623 0.344 0 0.000 0.656
#> GSM28809 4 0.4804 0.560 0.384 0 0.000 0.616
#> GSM11329 1 0.0336 0.895 0.992 0 0.000 0.008
#> GSM28805 1 0.0469 0.894 0.988 0 0.000 0.012
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 5 0.000 0.5179 0.000 0 0.000 0.000 1.000
#> GSM28816 5 0.000 0.5179 0.000 0 0.000 0.000 1.000
#> GSM28817 1 0.443 0.7479 0.540 0 0.000 0.004 0.456
#> GSM11327 1 0.557 0.0368 0.512 0 0.416 0.000 0.072
#> GSM28825 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM11322 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM28828 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM11346 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM28808 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM11332 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM28811 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM11334 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM11340 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM28812 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM11345 1 0.426 0.7756 0.560 0 0.000 0.000 0.440
#> GSM28819 1 0.426 0.7756 0.560 0 0.000 0.000 0.440
#> GSM11321 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM28820 1 0.426 0.7756 0.560 0 0.000 0.000 0.440
#> GSM11339 5 0.618 -0.3418 0.408 0 0.000 0.136 0.456
#> GSM28804 4 0.601 0.5483 0.356 0 0.000 0.520 0.124
#> GSM28823 1 0.426 0.7756 0.560 0 0.000 0.000 0.440
#> GSM11336 5 0.377 0.4465 0.296 0 0.000 0.000 0.704
#> GSM11342 1 0.426 0.7756 0.560 0 0.000 0.000 0.440
#> GSM11333 5 0.000 0.5179 0.000 0 0.000 0.000 1.000
#> GSM28802 1 0.430 0.7076 0.520 0 0.000 0.000 0.480
#> GSM28803 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM11343 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM11347 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM28824 5 0.377 0.4465 0.296 0 0.000 0.000 0.704
#> GSM28813 5 0.377 0.4465 0.296 0 0.000 0.000 0.704
#> GSM28827 1 0.426 0.7605 0.564 0 0.000 0.000 0.436
#> GSM11337 1 0.426 0.7605 0.564 0 0.000 0.000 0.436
#> GSM28814 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM11331 1 0.418 0.7246 0.600 0 0.000 0.000 0.400
#> GSM11344 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM11330 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM11325 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM11338 5 0.377 0.4465 0.296 0 0.000 0.000 0.704
#> GSM28806 5 0.621 -0.3326 0.404 0 0.000 0.140 0.456
#> GSM28826 1 0.426 0.7605 0.564 0 0.000 0.000 0.436
#> GSM28818 4 0.370 0.6811 0.100 0 0.000 0.820 0.080
#> GSM28821 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM28807 4 0.170 0.6932 0.068 0 0.000 0.928 0.004
#> GSM28822 4 0.601 0.5483 0.356 0 0.000 0.520 0.124
#> GSM11328 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM11323 1 0.418 0.7246 0.600 0 0.000 0.000 0.400
#> GSM11324 1 0.426 0.7756 0.560 0 0.000 0.000 0.440
#> GSM11341 4 0.184 0.6510 0.056 0 0.016 0.928 0.000
#> GSM11326 1 0.557 0.0368 0.512 0 0.416 0.000 0.072
#> GSM28810 4 0.577 0.2276 0.108 0 0.000 0.564 0.328
#> GSM11335 4 0.483 0.5851 0.104 0 0.000 0.720 0.176
#> GSM28809 4 0.489 0.5437 0.256 0 0.000 0.680 0.064
#> GSM11329 1 0.426 0.7756 0.560 0 0.000 0.000 0.440
#> GSM28805 1 0.443 0.7479 0.540 0 0.000 0.004 0.456
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 5 0.2941 0.669 0.064 0 0.000 0.004 0.856 0.076
#> GSM28816 5 0.2941 0.669 0.064 0 0.000 0.004 0.856 0.076
#> GSM28817 1 0.0665 0.881 0.980 0 0.000 0.008 0.008 0.004
#> GSM11327 1 0.4804 0.255 0.540 0 0.416 0.000 0.032 0.012
#> GSM28825 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11345 1 0.0000 0.888 1.000 0 0.000 0.000 0.000 0.000
#> GSM28819 1 0.0000 0.888 1.000 0 0.000 0.000 0.000 0.000
#> GSM11321 3 0.0363 0.993 0.000 0 0.988 0.000 0.012 0.000
#> GSM28820 1 0.0000 0.888 1.000 0 0.000 0.000 0.000 0.000
#> GSM11339 1 0.3367 0.713 0.836 0 0.000 0.088 0.020 0.056
#> GSM28804 6 0.1663 1.000 0.000 0 0.000 0.088 0.000 0.912
#> GSM28823 1 0.0000 0.888 1.000 0 0.000 0.000 0.000 0.000
#> GSM11336 5 0.3330 0.779 0.284 0 0.000 0.000 0.716 0.000
#> GSM11342 1 0.0000 0.888 1.000 0 0.000 0.000 0.000 0.000
#> GSM11333 5 0.2941 0.669 0.064 0 0.000 0.004 0.856 0.076
#> GSM28802 1 0.1138 0.870 0.960 0 0.000 0.004 0.024 0.012
#> GSM28803 3 0.0363 0.993 0.000 0 0.988 0.000 0.012 0.000
#> GSM11343 3 0.0000 0.993 0.000 0 1.000 0.000 0.000 0.000
#> GSM11347 3 0.0000 0.993 0.000 0 1.000 0.000 0.000 0.000
#> GSM28824 5 0.3330 0.779 0.284 0 0.000 0.000 0.716 0.000
#> GSM28813 5 0.3330 0.779 0.284 0 0.000 0.000 0.716 0.000
#> GSM28827 1 0.0717 0.883 0.976 0 0.000 0.000 0.016 0.008
#> GSM11337 1 0.0717 0.883 0.976 0 0.000 0.000 0.016 0.008
#> GSM28814 3 0.0363 0.993 0.000 0 0.988 0.000 0.012 0.000
#> GSM11331 1 0.1151 0.864 0.956 0 0.000 0.000 0.032 0.012
#> GSM11344 3 0.0000 0.993 0.000 0 1.000 0.000 0.000 0.000
#> GSM11330 3 0.0000 0.993 0.000 0 1.000 0.000 0.000 0.000
#> GSM11325 3 0.0363 0.993 0.000 0 0.988 0.000 0.012 0.000
#> GSM11338 5 0.3330 0.779 0.284 0 0.000 0.000 0.716 0.000
#> GSM28806 1 0.3262 0.706 0.840 0 0.000 0.080 0.012 0.068
#> GSM28826 1 0.0717 0.883 0.976 0 0.000 0.000 0.016 0.008
#> GSM28818 4 0.4099 0.626 0.152 0 0.000 0.764 0.012 0.072
#> GSM28821 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28807 4 0.3717 0.507 0.064 0 0.000 0.776 0.000 0.160
#> GSM28822 6 0.1663 1.000 0.000 0 0.000 0.088 0.000 0.912
#> GSM11328 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11323 1 0.1151 0.864 0.956 0 0.000 0.000 0.032 0.012
#> GSM11324 1 0.0000 0.888 1.000 0 0.000 0.000 0.000 0.000
#> GSM11341 4 0.1555 0.330 0.000 0 0.012 0.940 0.008 0.040
#> GSM11326 1 0.4804 0.255 0.540 0 0.416 0.000 0.032 0.012
#> GSM28810 4 0.5147 0.462 0.436 0 0.000 0.480 0.000 0.084
#> GSM11335 4 0.4757 0.610 0.280 0 0.000 0.636 0.000 0.084
#> GSM28809 4 0.3684 0.587 0.300 0 0.000 0.692 0.004 0.004
#> GSM11329 1 0.0000 0.888 1.000 0 0.000 0.000 0.000 0.000
#> GSM28805 1 0.0665 0.881 0.980 0 0.000 0.008 0.008 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:hclust 52 0.396 2
#> MAD:hclust 52 0.372 3
#> MAD:hclust 51 0.350 4
#> MAD:hclust 45 0.402 5
#> MAD:hclust 50 0.399 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.508 0.847 0.858 0.3404 0.648 0.648
#> 3 3 1.000 0.971 0.965 0.6848 0.776 0.655
#> 4 4 0.756 0.850 0.881 0.2189 0.866 0.684
#> 5 5 0.718 0.772 0.851 0.0886 0.944 0.807
#> 6 6 0.741 0.728 0.815 0.0469 1.000 1.000
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
#> GSM28815 1 0.925 0.870 0.66 0.34
#> GSM28816 1 0.925 0.870 0.66 0.34
#> GSM28817 1 0.925 0.870 0.66 0.34
#> GSM11327 1 0.000 0.602 1.00 0.00
#> GSM28825 2 0.000 1.000 0.00 1.00
#> GSM11322 2 0.000 1.000 0.00 1.00
#> GSM28828 2 0.000 1.000 0.00 1.00
#> GSM11346 2 0.000 1.000 0.00 1.00
#> GSM28808 2 0.000 1.000 0.00 1.00
#> GSM11332 2 0.000 1.000 0.00 1.00
#> GSM28811 2 0.000 1.000 0.00 1.00
#> GSM11334 2 0.000 1.000 0.00 1.00
#> GSM11340 2 0.000 1.000 0.00 1.00
#> GSM28812 2 0.000 1.000 0.00 1.00
#> GSM11345 1 0.925 0.870 0.66 0.34
#> GSM28819 1 0.925 0.870 0.66 0.34
#> GSM11321 1 0.141 0.590 0.98 0.02
#> GSM28820 1 0.925 0.870 0.66 0.34
#> GSM11339 1 0.925 0.870 0.66 0.34
#> GSM28804 1 0.925 0.870 0.66 0.34
#> GSM28823 1 0.925 0.870 0.66 0.34
#> GSM11336 1 0.925 0.870 0.66 0.34
#> GSM11342 1 0.925 0.870 0.66 0.34
#> GSM11333 1 0.925 0.870 0.66 0.34
#> GSM28802 1 0.925 0.870 0.66 0.34
#> GSM28803 1 0.141 0.590 0.98 0.02
#> GSM11343 1 0.141 0.590 0.98 0.02
#> GSM11347 1 0.141 0.590 0.98 0.02
#> GSM28824 1 0.925 0.870 0.66 0.34
#> GSM28813 1 0.925 0.870 0.66 0.34
#> GSM28827 1 0.925 0.870 0.66 0.34
#> GSM11337 1 0.925 0.870 0.66 0.34
#> GSM28814 1 0.141 0.590 0.98 0.02
#> GSM11331 1 0.925 0.870 0.66 0.34
#> GSM11344 1 0.141 0.590 0.98 0.02
#> GSM11330 1 0.141 0.590 0.98 0.02
#> GSM11325 1 0.141 0.590 0.98 0.02
#> GSM11338 1 0.925 0.870 0.66 0.34
#> GSM28806 1 0.925 0.870 0.66 0.34
#> GSM28826 1 0.925 0.870 0.66 0.34
#> GSM28818 1 0.925 0.870 0.66 0.34
#> GSM28821 2 0.000 1.000 0.00 1.00
#> GSM28807 1 0.925 0.870 0.66 0.34
#> GSM28822 1 0.925 0.870 0.66 0.34
#> GSM11328 2 0.000 1.000 0.00 1.00
#> GSM11323 1 0.925 0.870 0.66 0.34
#> GSM11324 1 0.925 0.870 0.66 0.34
#> GSM11341 1 0.943 0.847 0.64 0.36
#> GSM11326 1 0.000 0.602 1.00 0.00
#> GSM28810 1 0.925 0.870 0.66 0.34
#> GSM11335 1 0.925 0.870 0.66 0.34
#> GSM28809 1 0.925 0.870 0.66 0.34
#> GSM11329 1 0.925 0.870 0.66 0.34
#> GSM28805 1 0.925 0.870 0.66 0.34
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.1643 0.972 0.956 0.000 0.044
#> GSM28816 1 0.1643 0.972 0.956 0.000 0.044
#> GSM28817 1 0.1529 0.972 0.960 0.000 0.040
#> GSM11327 3 0.0424 0.992 0.008 0.000 0.992
#> GSM28825 2 0.1411 1.000 0.036 0.964 0.000
#> GSM11322 2 0.1411 1.000 0.036 0.964 0.000
#> GSM28828 2 0.1411 1.000 0.036 0.964 0.000
#> GSM11346 2 0.1411 1.000 0.036 0.964 0.000
#> GSM28808 2 0.1411 1.000 0.036 0.964 0.000
#> GSM11332 2 0.1411 1.000 0.036 0.964 0.000
#> GSM28811 2 0.1411 1.000 0.036 0.964 0.000
#> GSM11334 2 0.1411 1.000 0.036 0.964 0.000
#> GSM11340 2 0.1411 1.000 0.036 0.964 0.000
#> GSM28812 2 0.1411 1.000 0.036 0.964 0.000
#> GSM11345 1 0.1529 0.972 0.960 0.000 0.040
#> GSM28819 1 0.1529 0.972 0.960 0.000 0.040
#> GSM11321 3 0.1315 0.990 0.008 0.020 0.972
#> GSM28820 1 0.1529 0.972 0.960 0.000 0.040
#> GSM11339 1 0.0000 0.960 1.000 0.000 0.000
#> GSM28804 1 0.0237 0.959 0.996 0.000 0.004
#> GSM28823 1 0.1529 0.972 0.960 0.000 0.040
#> GSM11336 1 0.2280 0.966 0.940 0.008 0.052
#> GSM11342 1 0.1529 0.972 0.960 0.000 0.040
#> GSM11333 1 0.0237 0.959 0.996 0.000 0.004
#> GSM28802 1 0.1529 0.972 0.960 0.000 0.040
#> GSM28803 3 0.1315 0.990 0.008 0.020 0.972
#> GSM11343 3 0.0661 0.991 0.008 0.004 0.988
#> GSM11347 3 0.0848 0.991 0.008 0.008 0.984
#> GSM28824 1 0.2280 0.966 0.940 0.008 0.052
#> GSM28813 1 0.2280 0.966 0.940 0.008 0.052
#> GSM28827 1 0.1529 0.972 0.960 0.000 0.040
#> GSM11337 1 0.2173 0.968 0.944 0.008 0.048
#> GSM28814 3 0.1315 0.990 0.008 0.020 0.972
#> GSM11331 1 0.1529 0.972 0.960 0.000 0.040
#> GSM11344 3 0.0848 0.991 0.008 0.008 0.984
#> GSM11330 3 0.0848 0.991 0.008 0.008 0.984
#> GSM11325 3 0.1315 0.990 0.008 0.020 0.972
#> GSM11338 1 0.2280 0.966 0.940 0.008 0.052
#> GSM28806 1 0.0000 0.960 1.000 0.000 0.000
#> GSM28826 1 0.1989 0.969 0.948 0.004 0.048
#> GSM28818 1 0.0000 0.960 1.000 0.000 0.000
#> GSM28821 2 0.1411 1.000 0.036 0.964 0.000
#> GSM28807 1 0.0000 0.960 1.000 0.000 0.000
#> GSM28822 1 0.0000 0.960 1.000 0.000 0.000
#> GSM11328 2 0.1411 1.000 0.036 0.964 0.000
#> GSM11323 1 0.1529 0.972 0.960 0.000 0.040
#> GSM11324 1 0.1529 0.972 0.960 0.000 0.040
#> GSM11341 1 0.5690 0.553 0.708 0.004 0.288
#> GSM11326 3 0.0424 0.992 0.008 0.000 0.992
#> GSM28810 1 0.0000 0.960 1.000 0.000 0.000
#> GSM11335 1 0.0000 0.960 1.000 0.000 0.000
#> GSM28809 1 0.0000 0.960 1.000 0.000 0.000
#> GSM11329 1 0.1529 0.972 0.960 0.000 0.040
#> GSM28805 1 0.1529 0.972 0.960 0.000 0.040
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.1474 0.746 0.948 0.000 0.000 0.052
#> GSM28816 1 0.2011 0.728 0.920 0.000 0.000 0.080
#> GSM28817 1 0.3219 0.794 0.836 0.000 0.000 0.164
#> GSM11327 3 0.0937 0.959 0.012 0.000 0.976 0.012
#> GSM28825 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM11322 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM28828 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM11346 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM28808 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM11332 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM28811 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> GSM11334 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM11340 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM28812 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM11345 1 0.3219 0.794 0.836 0.000 0.000 0.164
#> GSM28819 1 0.3219 0.794 0.836 0.000 0.000 0.164
#> GSM11321 3 0.1940 0.958 0.000 0.000 0.924 0.076
#> GSM28820 1 0.3219 0.794 0.836 0.000 0.000 0.164
#> GSM11339 1 0.4500 0.524 0.684 0.000 0.000 0.316
#> GSM28804 4 0.4072 0.888 0.252 0.000 0.000 0.748
#> GSM28823 1 0.3311 0.792 0.828 0.000 0.000 0.172
#> GSM11336 1 0.3528 0.624 0.808 0.000 0.000 0.192
#> GSM11342 1 0.3311 0.792 0.828 0.000 0.000 0.172
#> GSM11333 1 0.3219 0.652 0.836 0.000 0.000 0.164
#> GSM28802 1 0.1211 0.775 0.960 0.000 0.000 0.040
#> GSM28803 3 0.1940 0.958 0.000 0.000 0.924 0.076
#> GSM11343 3 0.0188 0.965 0.000 0.000 0.996 0.004
#> GSM11347 3 0.0707 0.963 0.000 0.000 0.980 0.020
#> GSM28824 1 0.3528 0.624 0.808 0.000 0.000 0.192
#> GSM28813 1 0.3444 0.626 0.816 0.000 0.000 0.184
#> GSM28827 1 0.3024 0.797 0.852 0.000 0.000 0.148
#> GSM11337 1 0.1792 0.719 0.932 0.000 0.000 0.068
#> GSM28814 3 0.1940 0.958 0.000 0.000 0.924 0.076
#> GSM11331 1 0.3266 0.784 0.832 0.000 0.000 0.168
#> GSM11344 3 0.0707 0.963 0.000 0.000 0.980 0.020
#> GSM11330 3 0.0707 0.963 0.000 0.000 0.980 0.020
#> GSM11325 3 0.1940 0.958 0.000 0.000 0.924 0.076
#> GSM11338 1 0.3024 0.645 0.852 0.000 0.000 0.148
#> GSM28806 4 0.4790 0.715 0.380 0.000 0.000 0.620
#> GSM28826 1 0.0188 0.760 0.996 0.000 0.000 0.004
#> GSM28818 4 0.4454 0.858 0.308 0.000 0.000 0.692
#> GSM28821 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> GSM28807 4 0.4072 0.888 0.252 0.000 0.000 0.748
#> GSM28822 4 0.4072 0.888 0.252 0.000 0.000 0.748
#> GSM11328 2 0.0188 0.998 0.000 0.996 0.000 0.004
#> GSM11323 1 0.3266 0.784 0.832 0.000 0.000 0.168
#> GSM11324 1 0.3266 0.793 0.832 0.000 0.000 0.168
#> GSM11341 4 0.4599 0.697 0.112 0.000 0.088 0.800
#> GSM11326 3 0.1059 0.958 0.012 0.000 0.972 0.016
#> GSM28810 4 0.4564 0.844 0.328 0.000 0.000 0.672
#> GSM11335 4 0.4250 0.880 0.276 0.000 0.000 0.724
#> GSM28809 1 0.3907 0.716 0.768 0.000 0.000 0.232
#> GSM11329 1 0.3219 0.793 0.836 0.000 0.000 0.164
#> GSM28805 1 0.3074 0.796 0.848 0.000 0.000 0.152
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 1 0.4693 0.4757 0.700 0.000 0.000 0.056 0.244
#> GSM28816 1 0.5273 0.0656 0.588 0.000 0.000 0.060 0.352
#> GSM28817 1 0.1211 0.7400 0.960 0.000 0.000 0.016 0.024
#> GSM11327 3 0.2625 0.8634 0.000 0.000 0.876 0.016 0.108
#> GSM28825 2 0.0000 0.9756 0.000 1.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 0.9756 0.000 1.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 0.9756 0.000 1.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 0.9756 0.000 1.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 0.9756 0.000 1.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 0.9756 0.000 1.000 0.000 0.000 0.000
#> GSM28811 2 0.2482 0.9247 0.000 0.892 0.000 0.024 0.084
#> GSM11334 2 0.0000 0.9756 0.000 1.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 0.9756 0.000 1.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 0.9756 0.000 1.000 0.000 0.000 0.000
#> GSM11345 1 0.1469 0.7352 0.948 0.000 0.000 0.016 0.036
#> GSM28819 1 0.1549 0.7335 0.944 0.000 0.000 0.016 0.040
#> GSM11321 3 0.3670 0.8877 0.000 0.000 0.820 0.068 0.112
#> GSM28820 1 0.1549 0.7335 0.944 0.000 0.000 0.016 0.040
#> GSM11339 1 0.4114 0.5367 0.732 0.000 0.000 0.244 0.024
#> GSM28804 4 0.3558 0.7998 0.108 0.000 0.000 0.828 0.064
#> GSM28823 1 0.2409 0.7103 0.900 0.000 0.000 0.032 0.068
#> GSM11336 5 0.4602 0.9389 0.316 0.000 0.000 0.028 0.656
#> GSM11342 1 0.2409 0.7103 0.900 0.000 0.000 0.032 0.068
#> GSM11333 1 0.6046 -0.0208 0.524 0.000 0.000 0.132 0.344
#> GSM28802 1 0.2929 0.6262 0.820 0.000 0.000 0.000 0.180
#> GSM28803 3 0.3670 0.8877 0.000 0.000 0.820 0.068 0.112
#> GSM11343 3 0.0451 0.8992 0.000 0.000 0.988 0.008 0.004
#> GSM11347 3 0.1444 0.8927 0.000 0.000 0.948 0.012 0.040
#> GSM28824 5 0.4602 0.9389 0.316 0.000 0.000 0.028 0.656
#> GSM28813 5 0.4540 0.9371 0.320 0.000 0.000 0.024 0.656
#> GSM28827 1 0.1845 0.7334 0.928 0.000 0.000 0.016 0.056
#> GSM11337 1 0.3642 0.5194 0.760 0.000 0.000 0.008 0.232
#> GSM28814 3 0.3670 0.8877 0.000 0.000 0.820 0.068 0.112
#> GSM11331 1 0.3955 0.6570 0.800 0.000 0.000 0.084 0.116
#> GSM11344 3 0.1444 0.8927 0.000 0.000 0.948 0.012 0.040
#> GSM11330 3 0.1444 0.8927 0.000 0.000 0.948 0.012 0.040
#> GSM11325 3 0.3670 0.8877 0.000 0.000 0.820 0.068 0.112
#> GSM11338 5 0.4219 0.8198 0.416 0.000 0.000 0.000 0.584
#> GSM28806 4 0.4961 0.3570 0.448 0.000 0.000 0.524 0.028
#> GSM28826 1 0.3551 0.5449 0.772 0.000 0.000 0.008 0.220
#> GSM28818 4 0.3942 0.7541 0.232 0.000 0.000 0.748 0.020
#> GSM28821 2 0.2597 0.9194 0.000 0.884 0.000 0.024 0.092
#> GSM28807 4 0.2900 0.8072 0.108 0.000 0.000 0.864 0.028
#> GSM28822 4 0.3493 0.8013 0.108 0.000 0.000 0.832 0.060
#> GSM11328 2 0.2482 0.9247 0.000 0.892 0.000 0.024 0.084
#> GSM11323 1 0.3955 0.6570 0.800 0.000 0.000 0.084 0.116
#> GSM11324 1 0.0671 0.7440 0.980 0.000 0.000 0.016 0.004
#> GSM11341 4 0.2804 0.7422 0.044 0.000 0.016 0.892 0.048
#> GSM11326 3 0.3063 0.8550 0.004 0.000 0.864 0.036 0.096
#> GSM28810 4 0.4682 0.5981 0.356 0.000 0.000 0.620 0.024
#> GSM11335 4 0.3002 0.8063 0.116 0.000 0.000 0.856 0.028
#> GSM28809 1 0.3921 0.6258 0.784 0.000 0.000 0.172 0.044
#> GSM11329 1 0.0671 0.7441 0.980 0.000 0.000 0.016 0.004
#> GSM28805 1 0.1124 0.7409 0.960 0.000 0.000 0.004 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 1 0.519 0.571 0.684 0.000 0.000 0.044 0.172 0.100
#> GSM28816 1 0.601 0.348 0.552 0.000 0.000 0.044 0.284 0.120
#> GSM28817 1 0.317 0.701 0.848 0.000 0.000 0.024 0.036 0.092
#> GSM11327 3 0.514 0.674 0.004 0.000 0.708 0.052 0.140 0.096
#> GSM28825 2 0.000 0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11322 2 0.000 0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28828 2 0.000 0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11346 2 0.000 0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28808 2 0.026 0.941 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM11332 2 0.000 0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28811 2 0.332 0.821 0.000 0.772 0.000 0.000 0.016 0.212
#> GSM11334 2 0.000 0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11340 2 0.000 0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28812 2 0.000 0.944 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11345 1 0.333 0.700 0.840 0.000 0.000 0.032 0.036 0.092
#> GSM28819 1 0.332 0.699 0.840 0.000 0.000 0.028 0.040 0.092
#> GSM11321 3 0.385 0.794 0.000 0.000 0.692 0.004 0.012 0.292
#> GSM28820 1 0.327 0.701 0.844 0.000 0.000 0.028 0.040 0.088
#> GSM11339 1 0.465 0.548 0.700 0.000 0.000 0.224 0.036 0.040
#> GSM28804 4 0.452 0.649 0.044 0.000 0.000 0.740 0.052 0.164
#> GSM28823 1 0.390 0.674 0.792 0.000 0.000 0.024 0.056 0.128
#> GSM11336 5 0.222 0.962 0.136 0.000 0.000 0.000 0.864 0.000
#> GSM11342 1 0.390 0.674 0.792 0.000 0.000 0.024 0.056 0.128
#> GSM11333 1 0.651 0.291 0.508 0.000 0.000 0.092 0.288 0.112
#> GSM28802 1 0.312 0.675 0.840 0.000 0.000 0.008 0.112 0.040
#> GSM28803 3 0.385 0.794 0.000 0.000 0.692 0.004 0.012 0.292
#> GSM11343 3 0.101 0.810 0.000 0.000 0.956 0.000 0.000 0.044
#> GSM11347 3 0.105 0.799 0.000 0.000 0.960 0.000 0.008 0.032
#> GSM28824 5 0.222 0.962 0.136 0.000 0.000 0.000 0.864 0.000
#> GSM28813 5 0.247 0.960 0.136 0.000 0.000 0.000 0.856 0.008
#> GSM28827 1 0.197 0.709 0.920 0.000 0.000 0.012 0.048 0.020
#> GSM11337 1 0.369 0.617 0.768 0.000 0.000 0.008 0.196 0.028
#> GSM28814 3 0.385 0.794 0.000 0.000 0.692 0.004 0.012 0.292
#> GSM11331 1 0.623 0.471 0.588 0.000 0.000 0.188 0.104 0.120
#> GSM11344 3 0.105 0.799 0.000 0.000 0.960 0.000 0.008 0.032
#> GSM11330 3 0.105 0.799 0.000 0.000 0.960 0.000 0.008 0.032
#> GSM11325 3 0.385 0.794 0.000 0.000 0.692 0.004 0.012 0.292
#> GSM11338 5 0.334 0.891 0.204 0.000 0.000 0.000 0.776 0.020
#> GSM28806 4 0.484 0.128 0.456 0.000 0.000 0.500 0.032 0.012
#> GSM28826 1 0.376 0.641 0.788 0.000 0.000 0.012 0.152 0.048
#> GSM28818 4 0.331 0.665 0.200 0.000 0.000 0.780 0.020 0.000
#> GSM28821 2 0.349 0.814 0.004 0.764 0.000 0.000 0.016 0.216
#> GSM28807 4 0.262 0.702 0.044 0.000 0.000 0.888 0.024 0.044
#> GSM28822 4 0.395 0.671 0.036 0.000 0.000 0.788 0.040 0.136
#> GSM11328 2 0.332 0.821 0.000 0.772 0.000 0.000 0.016 0.212
#> GSM11323 1 0.623 0.471 0.588 0.000 0.000 0.188 0.104 0.120
#> GSM11324 1 0.292 0.709 0.864 0.000 0.000 0.032 0.020 0.084
#> GSM11341 4 0.297 0.659 0.000 0.000 0.004 0.840 0.028 0.128
#> GSM11326 3 0.561 0.648 0.008 0.000 0.680 0.088 0.116 0.108
#> GSM28810 4 0.393 0.487 0.332 0.000 0.000 0.656 0.008 0.004
#> GSM11335 4 0.277 0.699 0.044 0.000 0.000 0.880 0.028 0.048
#> GSM28809 1 0.424 0.579 0.716 0.000 0.000 0.232 0.040 0.012
#> GSM11329 1 0.231 0.713 0.888 0.000 0.000 0.028 0.000 0.084
#> GSM28805 1 0.186 0.707 0.920 0.000 0.000 0.000 0.044 0.036
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:kmeans 54 0.398 2
#> MAD:kmeans 54 0.374 3
#> MAD:kmeans 54 0.355 4
#> MAD:kmeans 50 0.481 5
#> MAD:kmeans 48 0.476 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.984 0.990 0.4812 0.516 0.516
#> 3 3 0.970 0.960 0.984 0.2771 0.818 0.664
#> 4 4 0.796 0.640 0.830 0.2073 0.818 0.555
#> 5 5 0.869 0.818 0.911 0.0910 0.884 0.582
#> 6 6 0.843 0.703 0.834 0.0329 0.965 0.819
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
#> GSM28815 1 0.0000 0.996 1.000 0.000
#> GSM28816 1 0.2948 0.946 0.948 0.052
#> GSM28817 1 0.0000 0.996 1.000 0.000
#> GSM11327 1 0.0000 0.996 1.000 0.000
#> GSM28825 2 0.0000 0.978 0.000 1.000
#> GSM11322 2 0.0000 0.978 0.000 1.000
#> GSM28828 2 0.0000 0.978 0.000 1.000
#> GSM11346 2 0.0000 0.978 0.000 1.000
#> GSM28808 2 0.0000 0.978 0.000 1.000
#> GSM11332 2 0.0000 0.978 0.000 1.000
#> GSM28811 2 0.0000 0.978 0.000 1.000
#> GSM11334 2 0.0000 0.978 0.000 1.000
#> GSM11340 2 0.0000 0.978 0.000 1.000
#> GSM28812 2 0.0000 0.978 0.000 1.000
#> GSM11345 1 0.0000 0.996 1.000 0.000
#> GSM28819 1 0.0000 0.996 1.000 0.000
#> GSM11321 2 0.3114 0.957 0.056 0.944
#> GSM28820 1 0.0000 0.996 1.000 0.000
#> GSM11339 1 0.0000 0.996 1.000 0.000
#> GSM28804 1 0.3114 0.943 0.944 0.056
#> GSM28823 1 0.0000 0.996 1.000 0.000
#> GSM11336 1 0.0000 0.996 1.000 0.000
#> GSM11342 1 0.0000 0.996 1.000 0.000
#> GSM11333 1 0.0000 0.996 1.000 0.000
#> GSM28802 1 0.0000 0.996 1.000 0.000
#> GSM28803 2 0.4431 0.923 0.092 0.908
#> GSM11343 2 0.0376 0.977 0.004 0.996
#> GSM11347 2 0.3114 0.957 0.056 0.944
#> GSM28824 1 0.0000 0.996 1.000 0.000
#> GSM28813 1 0.0000 0.996 1.000 0.000
#> GSM28827 1 0.0000 0.996 1.000 0.000
#> GSM11337 1 0.0000 0.996 1.000 0.000
#> GSM28814 2 0.3114 0.957 0.056 0.944
#> GSM11331 1 0.0000 0.996 1.000 0.000
#> GSM11344 2 0.3114 0.957 0.056 0.944
#> GSM11330 2 0.3114 0.957 0.056 0.944
#> GSM11325 2 0.3114 0.957 0.056 0.944
#> GSM11338 1 0.0000 0.996 1.000 0.000
#> GSM28806 1 0.0000 0.996 1.000 0.000
#> GSM28826 1 0.0000 0.996 1.000 0.000
#> GSM28818 1 0.0000 0.996 1.000 0.000
#> GSM28821 2 0.0000 0.978 0.000 1.000
#> GSM28807 1 0.0000 0.996 1.000 0.000
#> GSM28822 1 0.0938 0.986 0.988 0.012
#> GSM11328 2 0.0000 0.978 0.000 1.000
#> GSM11323 1 0.0000 0.996 1.000 0.000
#> GSM11324 1 0.0000 0.996 1.000 0.000
#> GSM11341 2 0.0000 0.978 0.000 1.000
#> GSM11326 1 0.0000 0.996 1.000 0.000
#> GSM28810 1 0.0000 0.996 1.000 0.000
#> GSM11335 1 0.0000 0.996 1.000 0.000
#> GSM28809 1 0.0000 0.996 1.000 0.000
#> GSM11329 1 0.0000 0.996 1.000 0.000
#> GSM28805 1 0.0000 0.996 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.000 0.985 1.000 0.000 0.000
#> GSM28816 1 0.450 0.762 0.804 0.196 0.000
#> GSM28817 1 0.000 0.985 1.000 0.000 0.000
#> GSM11327 3 0.000 0.948 0.000 0.000 1.000
#> GSM28825 2 0.000 1.000 0.000 1.000 0.000
#> GSM11322 2 0.000 1.000 0.000 1.000 0.000
#> GSM28828 2 0.000 1.000 0.000 1.000 0.000
#> GSM11346 2 0.000 1.000 0.000 1.000 0.000
#> GSM28808 2 0.000 1.000 0.000 1.000 0.000
#> GSM11332 2 0.000 1.000 0.000 1.000 0.000
#> GSM28811 2 0.000 1.000 0.000 1.000 0.000
#> GSM11334 2 0.000 1.000 0.000 1.000 0.000
#> GSM11340 2 0.000 1.000 0.000 1.000 0.000
#> GSM28812 2 0.000 1.000 0.000 1.000 0.000
#> GSM11345 1 0.000 0.985 1.000 0.000 0.000
#> GSM28819 1 0.000 0.985 1.000 0.000 0.000
#> GSM11321 3 0.000 0.948 0.000 0.000 1.000
#> GSM28820 1 0.000 0.985 1.000 0.000 0.000
#> GSM11339 1 0.000 0.985 1.000 0.000 0.000
#> GSM28804 1 0.445 0.767 0.808 0.192 0.000
#> GSM28823 1 0.000 0.985 1.000 0.000 0.000
#> GSM11336 1 0.000 0.985 1.000 0.000 0.000
#> GSM11342 1 0.000 0.985 1.000 0.000 0.000
#> GSM11333 1 0.000 0.985 1.000 0.000 0.000
#> GSM28802 1 0.000 0.985 1.000 0.000 0.000
#> GSM28803 3 0.000 0.948 0.000 0.000 1.000
#> GSM11343 3 0.000 0.948 0.000 0.000 1.000
#> GSM11347 3 0.000 0.948 0.000 0.000 1.000
#> GSM28824 3 0.588 0.492 0.348 0.000 0.652
#> GSM28813 3 0.362 0.809 0.136 0.000 0.864
#> GSM28827 1 0.000 0.985 1.000 0.000 0.000
#> GSM11337 1 0.000 0.985 1.000 0.000 0.000
#> GSM28814 3 0.000 0.948 0.000 0.000 1.000
#> GSM11331 1 0.000 0.985 1.000 0.000 0.000
#> GSM11344 3 0.000 0.948 0.000 0.000 1.000
#> GSM11330 3 0.000 0.948 0.000 0.000 1.000
#> GSM11325 3 0.000 0.948 0.000 0.000 1.000
#> GSM11338 1 0.000 0.985 1.000 0.000 0.000
#> GSM28806 1 0.000 0.985 1.000 0.000 0.000
#> GSM28826 1 0.000 0.985 1.000 0.000 0.000
#> GSM28818 1 0.000 0.985 1.000 0.000 0.000
#> GSM28821 2 0.000 1.000 0.000 1.000 0.000
#> GSM28807 1 0.000 0.985 1.000 0.000 0.000
#> GSM28822 1 0.000 0.985 1.000 0.000 0.000
#> GSM11328 2 0.000 1.000 0.000 1.000 0.000
#> GSM11323 1 0.000 0.985 1.000 0.000 0.000
#> GSM11324 1 0.000 0.985 1.000 0.000 0.000
#> GSM11341 3 0.000 0.948 0.000 0.000 1.000
#> GSM11326 3 0.000 0.948 0.000 0.000 1.000
#> GSM28810 1 0.000 0.985 1.000 0.000 0.000
#> GSM11335 1 0.000 0.985 1.000 0.000 0.000
#> GSM28809 1 0.000 0.985 1.000 0.000 0.000
#> GSM11329 1 0.000 0.985 1.000 0.000 0.000
#> GSM28805 1 0.000 0.985 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.3726 0.37157 0.788 0.000 0.000 0.212
#> GSM28816 1 0.5235 0.30647 0.716 0.048 0.000 0.236
#> GSM28817 1 0.5000 0.19706 0.504 0.000 0.000 0.496
#> GSM11327 3 0.0000 0.97653 0.000 0.000 1.000 0.000
#> GSM28825 2 0.0000 1.00000 0.000 1.000 0.000 0.000
#> GSM11322 2 0.0000 1.00000 0.000 1.000 0.000 0.000
#> GSM28828 2 0.0000 1.00000 0.000 1.000 0.000 0.000
#> GSM11346 2 0.0000 1.00000 0.000 1.000 0.000 0.000
#> GSM28808 2 0.0000 1.00000 0.000 1.000 0.000 0.000
#> GSM11332 2 0.0000 1.00000 0.000 1.000 0.000 0.000
#> GSM28811 2 0.0000 1.00000 0.000 1.000 0.000 0.000
#> GSM11334 2 0.0000 1.00000 0.000 1.000 0.000 0.000
#> GSM11340 2 0.0000 1.00000 0.000 1.000 0.000 0.000
#> GSM28812 2 0.0000 1.00000 0.000 1.000 0.000 0.000
#> GSM11345 1 0.5000 0.19706 0.504 0.000 0.000 0.496
#> GSM28819 1 0.5000 0.19706 0.504 0.000 0.000 0.496
#> GSM11321 3 0.0000 0.97653 0.000 0.000 1.000 0.000
#> GSM28820 1 0.5000 0.19706 0.504 0.000 0.000 0.496
#> GSM11339 4 0.1474 0.72782 0.052 0.000 0.000 0.948
#> GSM28804 4 0.2706 0.65419 0.080 0.020 0.000 0.900
#> GSM28823 1 0.5000 0.19706 0.504 0.000 0.000 0.496
#> GSM11336 1 0.1302 0.50292 0.956 0.000 0.000 0.044
#> GSM11342 1 0.5000 0.19706 0.504 0.000 0.000 0.496
#> GSM11333 1 0.4985 0.00623 0.532 0.000 0.000 0.468
#> GSM28802 1 0.1557 0.51012 0.944 0.000 0.000 0.056
#> GSM28803 3 0.0000 0.97653 0.000 0.000 1.000 0.000
#> GSM11343 3 0.0000 0.97653 0.000 0.000 1.000 0.000
#> GSM11347 3 0.0000 0.97653 0.000 0.000 1.000 0.000
#> GSM28824 1 0.2111 0.49501 0.932 0.000 0.024 0.044
#> GSM28813 1 0.2174 0.49062 0.928 0.000 0.052 0.020
#> GSM28827 4 0.4999 -0.23321 0.492 0.000 0.000 0.508
#> GSM11337 1 0.1389 0.51498 0.952 0.000 0.000 0.048
#> GSM28814 3 0.0000 0.97653 0.000 0.000 1.000 0.000
#> GSM11331 4 0.5088 -0.02953 0.424 0.000 0.004 0.572
#> GSM11344 3 0.0000 0.97653 0.000 0.000 1.000 0.000
#> GSM11330 3 0.0000 0.97653 0.000 0.000 1.000 0.000
#> GSM11325 3 0.0000 0.97653 0.000 0.000 1.000 0.000
#> GSM11338 1 0.0000 0.51328 1.000 0.000 0.000 0.000
#> GSM28806 4 0.0921 0.73631 0.028 0.000 0.000 0.972
#> GSM28826 1 0.1118 0.51569 0.964 0.000 0.000 0.036
#> GSM28818 4 0.0469 0.73591 0.012 0.000 0.000 0.988
#> GSM28821 2 0.0000 1.00000 0.000 1.000 0.000 0.000
#> GSM28807 4 0.0707 0.73235 0.020 0.000 0.000 0.980
#> GSM28822 4 0.1389 0.70910 0.048 0.000 0.000 0.952
#> GSM11328 2 0.0000 1.00000 0.000 1.000 0.000 0.000
#> GSM11323 4 0.5097 -0.03658 0.428 0.000 0.004 0.568
#> GSM11324 1 0.5000 0.19706 0.504 0.000 0.000 0.496
#> GSM11341 3 0.4188 0.71443 0.000 0.004 0.752 0.244
#> GSM11326 3 0.0000 0.97653 0.000 0.000 1.000 0.000
#> GSM28810 4 0.0592 0.73667 0.016 0.000 0.000 0.984
#> GSM11335 4 0.0469 0.73778 0.012 0.000 0.000 0.988
#> GSM28809 4 0.3123 0.61092 0.156 0.000 0.000 0.844
#> GSM11329 1 0.5000 0.19706 0.504 0.000 0.000 0.496
#> GSM28805 1 0.4994 0.19869 0.520 0.000 0.000 0.480
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 5 0.2514 0.792 0.044 0 0.000 0.060 0.896
#> GSM28816 5 0.1697 0.796 0.008 0 0.000 0.060 0.932
#> GSM28817 1 0.0162 0.814 0.996 0 0.000 0.004 0.000
#> GSM11327 3 0.0404 0.989 0.000 0 0.988 0.000 0.012
#> GSM28825 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11345 1 0.0510 0.813 0.984 0 0.000 0.016 0.000
#> GSM28819 1 0.0671 0.812 0.980 0 0.000 0.016 0.004
#> GSM11321 3 0.0000 0.998 0.000 0 1.000 0.000 0.000
#> GSM28820 1 0.0671 0.812 0.980 0 0.000 0.016 0.004
#> GSM11339 4 0.4042 0.701 0.212 0 0.000 0.756 0.032
#> GSM28804 4 0.1907 0.828 0.028 0 0.000 0.928 0.044
#> GSM28823 1 0.0000 0.813 1.000 0 0.000 0.000 0.000
#> GSM11336 5 0.1205 0.810 0.040 0 0.000 0.004 0.956
#> GSM11342 1 0.0000 0.813 1.000 0 0.000 0.000 0.000
#> GSM11333 5 0.4183 0.445 0.008 0 0.000 0.324 0.668
#> GSM28802 1 0.4622 -0.031 0.548 0 0.000 0.012 0.440
#> GSM28803 3 0.0000 0.998 0.000 0 1.000 0.000 0.000
#> GSM11343 3 0.0000 0.998 0.000 0 1.000 0.000 0.000
#> GSM11347 3 0.0000 0.998 0.000 0 1.000 0.000 0.000
#> GSM28824 5 0.1205 0.810 0.040 0 0.000 0.004 0.956
#> GSM28813 5 0.1205 0.810 0.040 0 0.000 0.004 0.956
#> GSM28827 1 0.4707 0.586 0.716 0 0.000 0.072 0.212
#> GSM11337 5 0.3852 0.672 0.220 0 0.000 0.020 0.760
#> GSM28814 3 0.0000 0.998 0.000 0 1.000 0.000 0.000
#> GSM11331 1 0.6569 0.287 0.468 0 0.000 0.240 0.292
#> GSM11344 3 0.0000 0.998 0.000 0 1.000 0.000 0.000
#> GSM11330 3 0.0000 0.998 0.000 0 1.000 0.000 0.000
#> GSM11325 3 0.0000 0.998 0.000 0 1.000 0.000 0.000
#> GSM11338 5 0.4045 0.467 0.356 0 0.000 0.000 0.644
#> GSM28806 4 0.2879 0.817 0.100 0 0.000 0.868 0.032
#> GSM28826 5 0.3696 0.687 0.212 0 0.000 0.016 0.772
#> GSM28818 4 0.0609 0.847 0.020 0 0.000 0.980 0.000
#> GSM28821 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28807 4 0.0510 0.846 0.016 0 0.000 0.984 0.000
#> GSM28822 4 0.1399 0.836 0.020 0 0.000 0.952 0.028
#> GSM11328 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11323 1 0.6569 0.287 0.468 0 0.000 0.240 0.292
#> GSM11324 1 0.0703 0.813 0.976 0 0.000 0.024 0.000
#> GSM11341 4 0.4430 0.423 0.000 0 0.360 0.628 0.012
#> GSM11326 3 0.0162 0.996 0.000 0 0.996 0.000 0.004
#> GSM28810 4 0.1430 0.843 0.052 0 0.000 0.944 0.004
#> GSM11335 4 0.0703 0.846 0.024 0 0.000 0.976 0.000
#> GSM28809 4 0.5260 0.524 0.264 0 0.000 0.648 0.088
#> GSM11329 1 0.1012 0.810 0.968 0 0.000 0.012 0.020
#> GSM28805 1 0.1942 0.777 0.920 0 0.000 0.012 0.068
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 6 0.5116 -0.24688 0.020 0.000 0.000 0.040 0.464 0.476
#> GSM28816 5 0.4434 0.17362 0.000 0.000 0.000 0.028 0.544 0.428
#> GSM28817 1 0.0632 0.84141 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM11327 3 0.2039 0.91303 0.000 0.000 0.904 0.000 0.020 0.076
#> GSM28825 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11345 1 0.0146 0.84282 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM28819 1 0.0260 0.84283 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM11321 3 0.1204 0.94533 0.000 0.000 0.944 0.000 0.000 0.056
#> GSM28820 1 0.0260 0.84283 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM11339 4 0.6079 0.41672 0.208 0.000 0.000 0.524 0.020 0.248
#> GSM28804 4 0.2615 0.69503 0.004 0.000 0.000 0.852 0.008 0.136
#> GSM28823 1 0.1364 0.83082 0.944 0.000 0.000 0.004 0.004 0.048
#> GSM11336 5 0.0146 0.63133 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM11342 1 0.1364 0.83082 0.944 0.000 0.000 0.004 0.004 0.048
#> GSM11333 5 0.5667 0.28966 0.000 0.000 0.000 0.192 0.520 0.288
#> GSM28802 1 0.6096 -0.14903 0.380 0.000 0.000 0.000 0.332 0.288
#> GSM28803 3 0.0865 0.95012 0.000 0.000 0.964 0.000 0.000 0.036
#> GSM11343 3 0.0000 0.95411 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11347 3 0.0547 0.95367 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM28824 5 0.0146 0.63133 0.004 0.000 0.000 0.000 0.996 0.000
#> GSM28813 5 0.0291 0.62965 0.004 0.000 0.000 0.000 0.992 0.004
#> GSM28827 6 0.5687 0.19798 0.412 0.000 0.000 0.036 0.068 0.484
#> GSM11337 5 0.5508 0.00282 0.112 0.000 0.000 0.008 0.532 0.348
#> GSM28814 3 0.1141 0.94659 0.000 0.000 0.948 0.000 0.000 0.052
#> GSM11331 6 0.6700 0.48757 0.132 0.000 0.016 0.216 0.084 0.552
#> GSM11344 3 0.0547 0.95367 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM11330 3 0.0547 0.95367 0.000 0.000 0.980 0.000 0.000 0.020
#> GSM11325 3 0.1267 0.94356 0.000 0.000 0.940 0.000 0.000 0.060
#> GSM11338 5 0.3050 0.44310 0.236 0.000 0.000 0.000 0.764 0.000
#> GSM28806 4 0.4954 0.63671 0.096 0.000 0.000 0.700 0.032 0.172
#> GSM28826 6 0.5493 0.04403 0.112 0.000 0.000 0.004 0.396 0.488
#> GSM28818 4 0.2866 0.71591 0.024 0.000 0.000 0.864 0.020 0.092
#> GSM28821 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28807 4 0.1429 0.71698 0.004 0.000 0.000 0.940 0.004 0.052
#> GSM28822 4 0.2333 0.69992 0.004 0.000 0.000 0.872 0.004 0.120
#> GSM11328 2 0.0000 1.00000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11323 6 0.6721 0.48279 0.132 0.000 0.016 0.220 0.084 0.548
#> GSM11324 1 0.0405 0.83934 0.988 0.000 0.000 0.008 0.000 0.004
#> GSM11341 4 0.4854 0.49014 0.000 0.008 0.260 0.652 0.000 0.080
#> GSM11326 3 0.2377 0.90255 0.000 0.000 0.892 0.024 0.008 0.076
#> GSM28810 4 0.3242 0.67340 0.032 0.000 0.000 0.816 0.004 0.148
#> GSM11335 4 0.2070 0.70275 0.008 0.000 0.000 0.892 0.000 0.100
#> GSM28809 4 0.6779 0.16792 0.180 0.000 0.000 0.444 0.068 0.308
#> GSM11329 1 0.0790 0.83105 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM28805 1 0.4076 0.28873 0.620 0.000 0.000 0.000 0.016 0.364
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:skmeans 54 0.398 2
#> MAD:skmeans 53 0.373 3
#> MAD:skmeans 37 0.402 4
#> MAD:skmeans 48 0.441 5
#> MAD:skmeans 40 0.511 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.3530 0.648 0.648
#> 3 3 1.000 0.985 0.992 0.4490 0.849 0.767
#> 4 4 0.864 0.936 0.963 0.2079 0.892 0.782
#> 5 5 0.936 0.947 0.965 0.0838 0.951 0.875
#> 6 6 0.853 0.826 0.916 0.0702 0.962 0.891
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM28815 1 0.0000 1.000 1.000 0.000
#> GSM28816 1 0.0000 1.000 1.000 0.000
#> GSM28817 1 0.0000 1.000 1.000 0.000
#> GSM11327 1 0.0000 1.000 1.000 0.000
#> GSM28825 2 0.0000 1.000 0.000 1.000
#> GSM11322 2 0.0000 1.000 0.000 1.000
#> GSM28828 2 0.0000 1.000 0.000 1.000
#> GSM11346 2 0.0000 1.000 0.000 1.000
#> GSM28808 2 0.0000 1.000 0.000 1.000
#> GSM11332 2 0.0000 1.000 0.000 1.000
#> GSM28811 2 0.0000 1.000 0.000 1.000
#> GSM11334 2 0.0000 1.000 0.000 1.000
#> GSM11340 2 0.0000 1.000 0.000 1.000
#> GSM28812 2 0.0000 1.000 0.000 1.000
#> GSM11345 1 0.0000 1.000 1.000 0.000
#> GSM28819 1 0.0000 1.000 1.000 0.000
#> GSM11321 1 0.0000 1.000 1.000 0.000
#> GSM28820 1 0.0000 1.000 1.000 0.000
#> GSM11339 1 0.0000 1.000 1.000 0.000
#> GSM28804 1 0.0000 1.000 1.000 0.000
#> GSM28823 1 0.0000 1.000 1.000 0.000
#> GSM11336 1 0.0000 1.000 1.000 0.000
#> GSM11342 1 0.0000 1.000 1.000 0.000
#> GSM11333 1 0.0000 1.000 1.000 0.000
#> GSM28802 1 0.0000 1.000 1.000 0.000
#> GSM28803 1 0.0000 1.000 1.000 0.000
#> GSM11343 1 0.0672 0.992 0.992 0.008
#> GSM11347 1 0.0000 1.000 1.000 0.000
#> GSM28824 1 0.0000 1.000 1.000 0.000
#> GSM28813 1 0.0000 1.000 1.000 0.000
#> GSM28827 1 0.0000 1.000 1.000 0.000
#> GSM11337 1 0.0000 1.000 1.000 0.000
#> GSM28814 1 0.0000 1.000 1.000 0.000
#> GSM11331 1 0.0000 1.000 1.000 0.000
#> GSM11344 1 0.0000 1.000 1.000 0.000
#> GSM11330 1 0.0000 1.000 1.000 0.000
#> GSM11325 1 0.0000 1.000 1.000 0.000
#> GSM11338 1 0.0000 1.000 1.000 0.000
#> GSM28806 1 0.0000 1.000 1.000 0.000
#> GSM28826 1 0.0000 1.000 1.000 0.000
#> GSM28818 1 0.0000 1.000 1.000 0.000
#> GSM28821 2 0.0000 1.000 0.000 1.000
#> GSM28807 1 0.0000 1.000 1.000 0.000
#> GSM28822 1 0.0000 1.000 1.000 0.000
#> GSM11328 2 0.0000 1.000 0.000 1.000
#> GSM11323 1 0.0000 1.000 1.000 0.000
#> GSM11324 1 0.0000 1.000 1.000 0.000
#> GSM11341 1 0.0000 1.000 1.000 0.000
#> GSM11326 1 0.0000 1.000 1.000 0.000
#> GSM28810 1 0.0000 1.000 1.000 0.000
#> GSM11335 1 0.0000 1.000 1.000 0.000
#> GSM28809 1 0.0000 1.000 1.000 0.000
#> GSM11329 1 0.0000 1.000 1.000 0.000
#> GSM28805 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
#> GSM28815 1 0.000 0.988 1.000 0 0.000
#> GSM28816 1 0.000 0.988 1.000 0 0.000
#> GSM28817 1 0.000 0.988 1.000 0 0.000
#> GSM11327 1 0.334 0.875 0.880 0 0.120
#> GSM28825 2 0.000 1.000 0.000 1 0.000
#> GSM11322 2 0.000 1.000 0.000 1 0.000
#> GSM28828 2 0.000 1.000 0.000 1 0.000
#> GSM11346 2 0.000 1.000 0.000 1 0.000
#> GSM28808 2 0.000 1.000 0.000 1 0.000
#> GSM11332 2 0.000 1.000 0.000 1 0.000
#> GSM28811 2 0.000 1.000 0.000 1 0.000
#> GSM11334 2 0.000 1.000 0.000 1 0.000
#> GSM11340 2 0.000 1.000 0.000 1 0.000
#> GSM28812 2 0.000 1.000 0.000 1 0.000
#> GSM11345 1 0.000 0.988 1.000 0 0.000
#> GSM28819 1 0.000 0.988 1.000 0 0.000
#> GSM11321 3 0.000 1.000 0.000 0 1.000
#> GSM28820 1 0.000 0.988 1.000 0 0.000
#> GSM11339 1 0.000 0.988 1.000 0 0.000
#> GSM28804 1 0.000 0.988 1.000 0 0.000
#> GSM28823 1 0.000 0.988 1.000 0 0.000
#> GSM11336 1 0.000 0.988 1.000 0 0.000
#> GSM11342 1 0.000 0.988 1.000 0 0.000
#> GSM11333 1 0.000 0.988 1.000 0 0.000
#> GSM28802 1 0.000 0.988 1.000 0 0.000
#> GSM28803 3 0.000 1.000 0.000 0 1.000
#> GSM11343 3 0.000 1.000 0.000 0 1.000
#> GSM11347 3 0.000 1.000 0.000 0 1.000
#> GSM28824 1 0.000 0.988 1.000 0 0.000
#> GSM28813 1 0.000 0.988 1.000 0 0.000
#> GSM28827 1 0.000 0.988 1.000 0 0.000
#> GSM11337 1 0.000 0.988 1.000 0 0.000
#> GSM28814 1 0.362 0.856 0.864 0 0.136
#> GSM11331 1 0.000 0.988 1.000 0 0.000
#> GSM11344 3 0.000 1.000 0.000 0 1.000
#> GSM11330 3 0.000 1.000 0.000 0 1.000
#> GSM11325 1 0.236 0.926 0.928 0 0.072
#> GSM11338 1 0.000 0.988 1.000 0 0.000
#> GSM28806 1 0.000 0.988 1.000 0 0.000
#> GSM28826 1 0.000 0.988 1.000 0 0.000
#> GSM28818 1 0.000 0.988 1.000 0 0.000
#> GSM28821 2 0.000 1.000 0.000 1 0.000
#> GSM28807 1 0.000 0.988 1.000 0 0.000
#> GSM28822 1 0.000 0.988 1.000 0 0.000
#> GSM11328 2 0.000 1.000 0.000 1 0.000
#> GSM11323 1 0.000 0.988 1.000 0 0.000
#> GSM11324 1 0.000 0.988 1.000 0 0.000
#> GSM11341 1 0.000 0.988 1.000 0 0.000
#> GSM11326 1 0.271 0.910 0.912 0 0.088
#> GSM28810 1 0.000 0.988 1.000 0 0.000
#> GSM11335 1 0.000 0.988 1.000 0 0.000
#> GSM28809 1 0.000 0.988 1.000 0 0.000
#> GSM11329 1 0.000 0.988 1.000 0 0.000
#> GSM28805 1 0.000 0.988 1.000 0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM28816 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM28817 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM11327 4 0.286 0.9909 0.112 0 0.008 0.880
#> GSM28825 2 0.000 1.0000 0.000 1 0.000 0.000
#> GSM11322 2 0.000 1.0000 0.000 1 0.000 0.000
#> GSM28828 2 0.000 1.0000 0.000 1 0.000 0.000
#> GSM11346 2 0.000 1.0000 0.000 1 0.000 0.000
#> GSM28808 2 0.000 1.0000 0.000 1 0.000 0.000
#> GSM11332 2 0.000 1.0000 0.000 1 0.000 0.000
#> GSM28811 2 0.000 1.0000 0.000 1 0.000 0.000
#> GSM11334 2 0.000 1.0000 0.000 1 0.000 0.000
#> GSM11340 2 0.000 1.0000 0.000 1 0.000 0.000
#> GSM28812 2 0.000 1.0000 0.000 1 0.000 0.000
#> GSM11345 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM28819 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM11321 3 0.253 0.8737 0.000 0 0.888 0.112
#> GSM28820 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM11339 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM28804 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM28823 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM11336 4 0.253 0.9977 0.112 0 0.000 0.888
#> GSM11342 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM11333 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM28802 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM28803 3 0.458 0.6592 0.000 0 0.668 0.332
#> GSM11343 3 0.000 0.9245 0.000 0 1.000 0.000
#> GSM11347 3 0.000 0.9245 0.000 0 1.000 0.000
#> GSM28824 4 0.253 0.9977 0.112 0 0.000 0.888
#> GSM28813 4 0.253 0.9977 0.112 0 0.000 0.888
#> GSM28827 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM11337 1 0.433 0.5340 0.712 0 0.000 0.288
#> GSM28814 1 0.516 0.0542 0.516 0 0.004 0.480
#> GSM11331 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM11344 3 0.000 0.9245 0.000 0 1.000 0.000
#> GSM11330 3 0.000 0.9245 0.000 0 1.000 0.000
#> GSM11325 1 0.371 0.7967 0.848 0 0.040 0.112
#> GSM11338 4 0.253 0.9977 0.112 0 0.000 0.888
#> GSM28806 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM28826 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM28818 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM28821 2 0.000 1.0000 0.000 1 0.000 0.000
#> GSM28807 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM28822 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM11328 2 0.000 1.0000 0.000 1 0.000 0.000
#> GSM11323 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM11324 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM11341 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM11326 1 0.139 0.9181 0.952 0 0.048 0.000
#> GSM28810 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM11335 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM28809 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM11329 1 0.000 0.9642 1.000 0 0.000 0.000
#> GSM28805 1 0.000 0.9642 1.000 0 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 1 0.1341 0.942 0.944 0 0.056 0.000 0.000
#> GSM28816 1 0.1732 0.928 0.920 0 0.080 0.000 0.000
#> GSM28817 1 0.0000 0.961 1.000 0 0.000 0.000 0.000
#> GSM11327 5 0.0290 0.990 0.000 0 0.000 0.008 0.992
#> GSM28825 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11345 1 0.0000 0.961 1.000 0 0.000 0.000 0.000
#> GSM28819 1 0.0000 0.961 1.000 0 0.000 0.000 0.000
#> GSM11321 3 0.2929 0.805 0.000 0 0.820 0.180 0.000
#> GSM28820 1 0.0000 0.961 1.000 0 0.000 0.000 0.000
#> GSM11339 1 0.0162 0.960 0.996 0 0.004 0.000 0.000
#> GSM28804 1 0.2929 0.846 0.820 0 0.180 0.000 0.000
#> GSM28823 1 0.0000 0.961 1.000 0 0.000 0.000 0.000
#> GSM11336 5 0.0000 0.997 0.000 0 0.000 0.000 1.000
#> GSM11342 1 0.0000 0.961 1.000 0 0.000 0.000 0.000
#> GSM11333 1 0.1121 0.947 0.956 0 0.044 0.000 0.000
#> GSM28802 1 0.0703 0.955 0.976 0 0.024 0.000 0.000
#> GSM28803 3 0.2929 0.805 0.000 0 0.820 0.180 0.000
#> GSM11343 4 0.0000 1.000 0.000 0 0.000 1.000 0.000
#> GSM11347 4 0.0000 1.000 0.000 0 0.000 1.000 0.000
#> GSM28824 5 0.0000 0.997 0.000 0 0.000 0.000 1.000
#> GSM28813 5 0.0000 0.997 0.000 0 0.000 0.000 1.000
#> GSM28827 1 0.0000 0.961 1.000 0 0.000 0.000 0.000
#> GSM11337 1 0.3730 0.644 0.712 0 0.000 0.000 0.288
#> GSM28814 3 0.3010 0.724 0.000 0 0.824 0.004 0.172
#> GSM11331 1 0.0703 0.956 0.976 0 0.024 0.000 0.000
#> GSM11344 4 0.0000 1.000 0.000 0 0.000 1.000 0.000
#> GSM11330 4 0.0000 1.000 0.000 0 0.000 1.000 0.000
#> GSM11325 3 0.3309 0.709 0.128 0 0.836 0.036 0.000
#> GSM11338 5 0.0000 0.997 0.000 0 0.000 0.000 1.000
#> GSM28806 1 0.0000 0.961 1.000 0 0.000 0.000 0.000
#> GSM28826 1 0.1341 0.942 0.944 0 0.056 0.000 0.000
#> GSM28818 1 0.0000 0.961 1.000 0 0.000 0.000 0.000
#> GSM28821 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM28807 1 0.0290 0.959 0.992 0 0.008 0.000 0.000
#> GSM28822 1 0.2929 0.846 0.820 0 0.180 0.000 0.000
#> GSM11328 2 0.0000 1.000 0.000 1 0.000 0.000 0.000
#> GSM11323 1 0.0703 0.955 0.976 0 0.024 0.000 0.000
#> GSM11324 1 0.0000 0.961 1.000 0 0.000 0.000 0.000
#> GSM11341 1 0.2020 0.897 0.900 0 0.100 0.000 0.000
#> GSM11326 1 0.1197 0.937 0.952 0 0.000 0.048 0.000
#> GSM28810 1 0.0162 0.960 0.996 0 0.004 0.000 0.000
#> GSM11335 1 0.0162 0.960 0.996 0 0.004 0.000 0.000
#> GSM28809 1 0.0000 0.961 1.000 0 0.000 0.000 0.000
#> GSM11329 1 0.0000 0.961 1.000 0 0.000 0.000 0.000
#> GSM28805 1 0.1341 0.942 0.944 0 0.056 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 1 0.2416 0.6829 0.844 0 0.000 0.156 0.000 0.000
#> GSM28816 1 0.2948 0.6079 0.804 0 0.008 0.188 0.000 0.000
#> GSM28817 1 0.1814 0.7427 0.900 0 0.000 0.100 0.000 0.000
#> GSM11327 5 0.0146 0.9956 0.000 0 0.000 0.000 0.996 0.004
#> GSM28825 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11345 1 0.0000 0.8006 1.000 0 0.000 0.000 0.000 0.000
#> GSM28819 1 0.0000 0.8006 1.000 0 0.000 0.000 0.000 0.000
#> GSM11321 3 0.0000 0.9934 0.000 0 1.000 0.000 0.000 0.000
#> GSM28820 1 0.0000 0.8006 1.000 0 0.000 0.000 0.000 0.000
#> GSM11339 1 0.1863 0.7391 0.896 0 0.000 0.104 0.000 0.000
#> GSM28804 4 0.3765 0.9911 0.404 0 0.000 0.596 0.000 0.000
#> GSM28823 1 0.3774 0.0408 0.592 0 0.000 0.408 0.000 0.000
#> GSM11336 5 0.0000 0.9989 0.000 0 0.000 0.000 1.000 0.000
#> GSM11342 1 0.3774 0.0408 0.592 0 0.000 0.408 0.000 0.000
#> GSM11333 1 0.2553 0.6877 0.848 0 0.008 0.144 0.000 0.000
#> GSM28802 1 0.2346 0.7112 0.868 0 0.008 0.124 0.000 0.000
#> GSM28803 3 0.0260 0.9904 0.000 0 0.992 0.000 0.000 0.008
#> GSM11343 6 0.0146 0.9960 0.000 0 0.004 0.000 0.000 0.996
#> GSM11347 6 0.0000 0.9987 0.000 0 0.000 0.000 0.000 1.000
#> GSM28824 5 0.0000 0.9989 0.000 0 0.000 0.000 1.000 0.000
#> GSM28813 5 0.0000 0.9989 0.000 0 0.000 0.000 1.000 0.000
#> GSM28827 1 0.1610 0.7559 0.916 0 0.000 0.084 0.000 0.000
#> GSM11337 1 0.4771 0.0646 0.652 0 0.000 0.100 0.248 0.000
#> GSM28814 3 0.0260 0.9899 0.000 0 0.992 0.000 0.008 0.000
#> GSM11331 1 0.0632 0.7918 0.976 0 0.000 0.024 0.000 0.000
#> GSM11344 6 0.0000 0.9987 0.000 0 0.000 0.000 0.000 1.000
#> GSM11330 6 0.0000 0.9987 0.000 0 0.000 0.000 0.000 1.000
#> GSM11325 3 0.0000 0.9934 0.000 0 1.000 0.000 0.000 0.000
#> GSM11338 5 0.0000 0.9989 0.000 0 0.000 0.000 1.000 0.000
#> GSM28806 1 0.0000 0.8006 1.000 0 0.000 0.000 0.000 0.000
#> GSM28826 1 0.2669 0.6714 0.836 0 0.008 0.156 0.000 0.000
#> GSM28818 1 0.0000 0.8006 1.000 0 0.000 0.000 0.000 0.000
#> GSM28821 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28807 1 0.0260 0.7971 0.992 0 0.000 0.008 0.000 0.000
#> GSM28822 4 0.3774 0.9911 0.408 0 0.000 0.592 0.000 0.000
#> GSM11328 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11323 1 0.0632 0.7914 0.976 0 0.000 0.024 0.000 0.000
#> GSM11324 1 0.0000 0.8006 1.000 0 0.000 0.000 0.000 0.000
#> GSM11341 1 0.3198 0.0830 0.740 0 0.000 0.260 0.000 0.000
#> GSM11326 1 0.0458 0.7921 0.984 0 0.000 0.000 0.000 0.016
#> GSM28810 1 0.0146 0.7991 0.996 0 0.000 0.004 0.000 0.000
#> GSM11335 1 0.0146 0.7991 0.996 0 0.000 0.004 0.000 0.000
#> GSM28809 1 0.0000 0.8006 1.000 0 0.000 0.000 0.000 0.000
#> GSM11329 1 0.0000 0.8006 1.000 0 0.000 0.000 0.000 0.000
#> GSM28805 1 0.2416 0.6829 0.844 0 0.000 0.156 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:pam 54 0.398 2
#> MAD:pam 54 0.374 3
#> MAD:pam 53 0.489 4
#> MAD:pam 54 0.455 5
#> MAD:pam 50 0.400 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["MAD", "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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.688 0.883 0.931 0.4474 0.508 0.508
#> 3 3 1.000 0.974 0.990 0.3044 0.916 0.835
#> 4 4 0.840 0.877 0.932 0.1924 0.891 0.743
#> 5 5 0.805 0.825 0.906 0.1020 0.908 0.713
#> 6 6 0.855 0.886 0.919 0.0399 0.951 0.795
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
#> GSM28815 1 0.0000 0.985 1.000 0.000
#> GSM28816 1 0.0376 0.980 0.996 0.004
#> GSM28817 1 0.0000 0.985 1.000 0.000
#> GSM11327 2 0.9170 0.713 0.332 0.668
#> GSM28825 2 0.0000 0.821 0.000 1.000
#> GSM11322 2 0.0000 0.821 0.000 1.000
#> GSM28828 2 0.0938 0.822 0.012 0.988
#> GSM11346 2 0.0000 0.821 0.000 1.000
#> GSM28808 2 0.0000 0.821 0.000 1.000
#> GSM11332 2 0.0000 0.821 0.000 1.000
#> GSM28811 2 0.0938 0.822 0.012 0.988
#> GSM11334 2 0.0000 0.821 0.000 1.000
#> GSM11340 2 0.0000 0.821 0.000 1.000
#> GSM28812 2 0.0000 0.821 0.000 1.000
#> GSM11345 1 0.0000 0.985 1.000 0.000
#> GSM28819 1 0.0000 0.985 1.000 0.000
#> GSM11321 2 0.9170 0.713 0.332 0.668
#> GSM28820 1 0.0000 0.985 1.000 0.000
#> GSM11339 1 0.0000 0.985 1.000 0.000
#> GSM28804 1 0.0000 0.985 1.000 0.000
#> GSM28823 1 0.0000 0.985 1.000 0.000
#> GSM11336 1 0.0000 0.985 1.000 0.000
#> GSM11342 1 0.0000 0.985 1.000 0.000
#> GSM11333 1 0.0000 0.985 1.000 0.000
#> GSM28802 1 0.0000 0.985 1.000 0.000
#> GSM28803 2 0.9170 0.713 0.332 0.668
#> GSM11343 2 0.9170 0.713 0.332 0.668
#> GSM11347 2 0.9170 0.713 0.332 0.668
#> GSM28824 1 0.0000 0.985 1.000 0.000
#> GSM28813 1 0.0000 0.985 1.000 0.000
#> GSM28827 1 0.0000 0.985 1.000 0.000
#> GSM11337 1 0.0000 0.985 1.000 0.000
#> GSM28814 2 0.9170 0.713 0.332 0.668
#> GSM11331 1 0.0000 0.985 1.000 0.000
#> GSM11344 2 0.9170 0.713 0.332 0.668
#> GSM11330 2 0.9170 0.713 0.332 0.668
#> GSM11325 2 0.9170 0.713 0.332 0.668
#> GSM11338 1 0.0000 0.985 1.000 0.000
#> GSM28806 1 0.0000 0.985 1.000 0.000
#> GSM28826 1 0.0000 0.985 1.000 0.000
#> GSM28818 1 0.0000 0.985 1.000 0.000
#> GSM28821 2 0.0938 0.822 0.012 0.988
#> GSM28807 1 0.0000 0.985 1.000 0.000
#> GSM28822 1 0.0000 0.985 1.000 0.000
#> GSM11328 2 0.0938 0.822 0.012 0.988
#> GSM11323 1 0.0000 0.985 1.000 0.000
#> GSM11324 1 0.0000 0.985 1.000 0.000
#> GSM11341 1 0.9522 0.157 0.628 0.372
#> GSM11326 2 0.9170 0.713 0.332 0.668
#> GSM28810 1 0.0000 0.985 1.000 0.000
#> GSM11335 1 0.0000 0.985 1.000 0.000
#> GSM28809 1 0.0000 0.985 1.000 0.000
#> GSM11329 1 0.0000 0.985 1.000 0.000
#> GSM28805 1 0.0000 0.985 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28816 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28817 1 0.000 0.9840 1.000 0.000 0.000
#> GSM11327 3 0.000 1.0000 0.000 0.000 1.000
#> GSM28825 2 0.000 1.0000 0.000 1.000 0.000
#> GSM11322 2 0.000 1.0000 0.000 1.000 0.000
#> GSM28828 2 0.000 1.0000 0.000 1.000 0.000
#> GSM11346 2 0.000 1.0000 0.000 1.000 0.000
#> GSM28808 2 0.000 1.0000 0.000 1.000 0.000
#> GSM11332 2 0.000 1.0000 0.000 1.000 0.000
#> GSM28811 2 0.000 1.0000 0.000 1.000 0.000
#> GSM11334 2 0.000 1.0000 0.000 1.000 0.000
#> GSM11340 2 0.000 1.0000 0.000 1.000 0.000
#> GSM28812 2 0.000 1.0000 0.000 1.000 0.000
#> GSM11345 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28819 1 0.000 0.9840 1.000 0.000 0.000
#> GSM11321 3 0.000 1.0000 0.000 0.000 1.000
#> GSM28820 1 0.000 0.9840 1.000 0.000 0.000
#> GSM11339 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28804 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28823 1 0.000 0.9840 1.000 0.000 0.000
#> GSM11336 1 0.000 0.9840 1.000 0.000 0.000
#> GSM11342 1 0.000 0.9840 1.000 0.000 0.000
#> GSM11333 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28802 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28803 3 0.000 1.0000 0.000 0.000 1.000
#> GSM11343 3 0.000 1.0000 0.000 0.000 1.000
#> GSM11347 3 0.000 1.0000 0.000 0.000 1.000
#> GSM28824 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28813 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28827 1 0.000 0.9840 1.000 0.000 0.000
#> GSM11337 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28814 3 0.000 1.0000 0.000 0.000 1.000
#> GSM11331 1 0.000 0.9840 1.000 0.000 0.000
#> GSM11344 3 0.000 1.0000 0.000 0.000 1.000
#> GSM11330 3 0.000 1.0000 0.000 0.000 1.000
#> GSM11325 3 0.000 1.0000 0.000 0.000 1.000
#> GSM11338 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28806 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28826 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28818 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28821 2 0.000 1.0000 0.000 1.000 0.000
#> GSM28807 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28822 1 0.000 0.9840 1.000 0.000 0.000
#> GSM11328 2 0.000 1.0000 0.000 1.000 0.000
#> GSM11323 1 0.000 0.9840 1.000 0.000 0.000
#> GSM11324 1 0.000 0.9840 1.000 0.000 0.000
#> GSM11341 1 0.909 0.0743 0.484 0.144 0.372
#> GSM11326 3 0.000 1.0000 0.000 0.000 1.000
#> GSM28810 1 0.000 0.9840 1.000 0.000 0.000
#> GSM11335 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28809 1 0.000 0.9840 1.000 0.000 0.000
#> GSM11329 1 0.000 0.9840 1.000 0.000 0.000
#> GSM28805 1 0.000 0.9840 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.0469 0.8835 0.988 0.000 0.000 0.012
#> GSM28816 1 0.0469 0.8835 0.988 0.000 0.000 0.012
#> GSM28817 1 0.0336 0.8876 0.992 0.000 0.000 0.008
#> GSM11327 3 0.0000 0.9925 0.000 0.000 1.000 0.000
#> GSM28825 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11345 1 0.3074 0.8569 0.848 0.000 0.000 0.152
#> GSM28819 1 0.3024 0.8591 0.852 0.000 0.000 0.148
#> GSM11321 3 0.0000 0.9925 0.000 0.000 1.000 0.000
#> GSM28820 1 0.2814 0.8655 0.868 0.000 0.000 0.132
#> GSM11339 1 0.0469 0.8835 0.988 0.000 0.000 0.012
#> GSM28804 4 0.3569 0.6838 0.196 0.000 0.000 0.804
#> GSM28823 1 0.3074 0.8569 0.848 0.000 0.000 0.152
#> GSM11336 1 0.0000 0.8872 1.000 0.000 0.000 0.000
#> GSM11342 1 0.3074 0.8569 0.848 0.000 0.000 0.152
#> GSM11333 1 0.0469 0.8835 0.988 0.000 0.000 0.012
#> GSM28802 1 0.1302 0.8858 0.956 0.000 0.000 0.044
#> GSM28803 3 0.0000 0.9925 0.000 0.000 1.000 0.000
#> GSM11343 3 0.0000 0.9925 0.000 0.000 1.000 0.000
#> GSM11347 3 0.0000 0.9925 0.000 0.000 1.000 0.000
#> GSM28824 1 0.0592 0.8805 0.984 0.000 0.000 0.016
#> GSM28813 1 0.0592 0.8805 0.984 0.000 0.000 0.016
#> GSM28827 1 0.2973 0.8624 0.856 0.000 0.000 0.144
#> GSM11337 1 0.0000 0.8872 1.000 0.000 0.000 0.000
#> GSM28814 3 0.0000 0.9925 0.000 0.000 1.000 0.000
#> GSM11331 1 0.3486 0.8289 0.812 0.000 0.000 0.188
#> GSM11344 3 0.0000 0.9925 0.000 0.000 1.000 0.000
#> GSM11330 3 0.0000 0.9925 0.000 0.000 1.000 0.000
#> GSM11325 3 0.0469 0.9839 0.000 0.000 0.988 0.012
#> GSM11338 1 0.0000 0.8872 1.000 0.000 0.000 0.000
#> GSM28806 1 0.3486 0.8306 0.812 0.000 0.000 0.188
#> GSM28826 1 0.0000 0.8872 1.000 0.000 0.000 0.000
#> GSM28818 1 0.4916 -0.0497 0.576 0.000 0.000 0.424
#> GSM28821 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28807 4 0.1211 0.7881 0.040 0.000 0.000 0.960
#> GSM28822 4 0.1022 0.7880 0.032 0.000 0.000 0.968
#> GSM11328 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11323 1 0.3444 0.8305 0.816 0.000 0.000 0.184
#> GSM11324 1 0.3024 0.8591 0.852 0.000 0.000 0.148
#> GSM11341 4 0.3208 0.6442 0.000 0.148 0.004 0.848
#> GSM11326 3 0.1474 0.9419 0.000 0.000 0.948 0.052
#> GSM28810 4 0.4907 0.0762 0.420 0.000 0.000 0.580
#> GSM11335 4 0.1118 0.7875 0.036 0.000 0.000 0.964
#> GSM28809 1 0.0000 0.8872 1.000 0.000 0.000 0.000
#> GSM11329 1 0.2921 0.8640 0.860 0.000 0.000 0.140
#> GSM28805 1 0.0592 0.8823 0.984 0.000 0.000 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 1 0.2130 0.8256 0.908 0.000 0.000 0.012 0.080
#> GSM28816 1 0.2351 0.8215 0.896 0.000 0.000 0.016 0.088
#> GSM28817 1 0.1908 0.8154 0.908 0.000 0.000 0.000 0.092
#> GSM11327 3 0.0404 0.9836 0.000 0.000 0.988 0.000 0.012
#> GSM28825 2 0.0000 0.9964 0.000 1.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 0.9964 0.000 1.000 0.000 0.000 0.000
#> GSM28828 2 0.0162 0.9949 0.000 0.996 0.000 0.004 0.000
#> GSM11346 2 0.0000 0.9964 0.000 1.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 0.9964 0.000 1.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 0.9964 0.000 1.000 0.000 0.000 0.000
#> GSM28811 2 0.0290 0.9927 0.000 0.992 0.000 0.008 0.000
#> GSM11334 2 0.0000 0.9964 0.000 1.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 0.9964 0.000 1.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 0.9964 0.000 1.000 0.000 0.000 0.000
#> GSM11345 1 0.0566 0.8319 0.984 0.000 0.000 0.004 0.012
#> GSM28819 1 0.3662 0.6348 0.744 0.000 0.000 0.004 0.252
#> GSM11321 3 0.0000 0.9922 0.000 0.000 1.000 0.000 0.000
#> GSM28820 1 0.3366 0.6578 0.768 0.000 0.000 0.000 0.232
#> GSM11339 1 0.2280 0.8180 0.880 0.000 0.000 0.000 0.120
#> GSM28804 4 0.1579 0.7755 0.032 0.000 0.000 0.944 0.024
#> GSM28823 1 0.1750 0.8314 0.936 0.000 0.000 0.028 0.036
#> GSM11336 5 0.3143 0.7122 0.204 0.000 0.000 0.000 0.796
#> GSM11342 1 0.1943 0.8250 0.924 0.000 0.000 0.020 0.056
#> GSM11333 1 0.2351 0.8215 0.896 0.000 0.000 0.016 0.088
#> GSM28802 5 0.4306 -0.0488 0.492 0.000 0.000 0.000 0.508
#> GSM28803 3 0.0000 0.9922 0.000 0.000 1.000 0.000 0.000
#> GSM11343 3 0.0000 0.9922 0.000 0.000 1.000 0.000 0.000
#> GSM11347 3 0.0000 0.9922 0.000 0.000 1.000 0.000 0.000
#> GSM28824 5 0.1608 0.7757 0.072 0.000 0.000 0.000 0.928
#> GSM28813 5 0.1608 0.7757 0.072 0.000 0.000 0.000 0.928
#> GSM28827 1 0.1608 0.8161 0.928 0.000 0.000 0.000 0.072
#> GSM11337 1 0.4740 -0.0484 0.516 0.000 0.000 0.016 0.468
#> GSM28814 3 0.0000 0.9922 0.000 0.000 1.000 0.000 0.000
#> GSM11331 1 0.3413 0.7500 0.832 0.000 0.000 0.044 0.124
#> GSM11344 3 0.0000 0.9922 0.000 0.000 1.000 0.000 0.000
#> GSM11330 3 0.0000 0.9922 0.000 0.000 1.000 0.000 0.000
#> GSM11325 3 0.0000 0.9922 0.000 0.000 1.000 0.000 0.000
#> GSM11338 5 0.2233 0.7754 0.080 0.000 0.000 0.016 0.904
#> GSM28806 1 0.2067 0.8192 0.920 0.000 0.000 0.048 0.032
#> GSM28826 1 0.4738 0.0640 0.520 0.000 0.000 0.016 0.464
#> GSM28818 4 0.5091 0.6967 0.244 0.000 0.000 0.672 0.084
#> GSM28821 2 0.0960 0.9734 0.016 0.972 0.000 0.004 0.008
#> GSM28807 4 0.3171 0.8239 0.176 0.000 0.000 0.816 0.008
#> GSM28822 4 0.2970 0.8268 0.168 0.000 0.000 0.828 0.004
#> GSM11328 2 0.0162 0.9949 0.000 0.996 0.000 0.004 0.000
#> GSM11323 1 0.2514 0.8077 0.896 0.000 0.000 0.044 0.060
#> GSM11324 1 0.0955 0.8331 0.968 0.000 0.000 0.004 0.028
#> GSM11341 4 0.1117 0.7395 0.000 0.016 0.020 0.964 0.000
#> GSM11326 3 0.1731 0.9384 0.012 0.000 0.940 0.040 0.008
#> GSM28810 4 0.4464 0.7004 0.288 0.000 0.000 0.684 0.028
#> GSM11335 4 0.2338 0.8174 0.112 0.000 0.000 0.884 0.004
#> GSM28809 1 0.0865 0.8371 0.972 0.000 0.000 0.004 0.024
#> GSM11329 1 0.1544 0.8145 0.932 0.000 0.000 0.000 0.068
#> GSM28805 1 0.2329 0.8156 0.876 0.000 0.000 0.000 0.124
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 1 0.1966 0.871 0.924 0.000 0.000 0.028 0.024 0.024
#> GSM28816 1 0.3129 0.815 0.852 0.000 0.000 0.032 0.088 0.028
#> GSM28817 1 0.0551 0.897 0.984 0.000 0.000 0.004 0.004 0.008
#> GSM11327 3 0.0291 0.981 0.000 0.000 0.992 0.000 0.004 0.004
#> GSM28825 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28828 2 0.1074 0.970 0.000 0.960 0.000 0.012 0.000 0.028
#> GSM11346 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28811 2 0.1074 0.970 0.000 0.960 0.000 0.012 0.000 0.028
#> GSM11334 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11345 1 0.1151 0.892 0.956 0.000 0.000 0.032 0.000 0.012
#> GSM28819 1 0.3250 0.710 0.788 0.000 0.000 0.004 0.196 0.012
#> GSM11321 3 0.0458 0.978 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM28820 1 0.3481 0.651 0.756 0.000 0.000 0.004 0.228 0.012
#> GSM11339 1 0.1620 0.895 0.940 0.000 0.000 0.024 0.012 0.024
#> GSM28804 4 0.1606 0.934 0.056 0.000 0.000 0.932 0.004 0.008
#> GSM28823 1 0.2922 0.847 0.864 0.000 0.000 0.056 0.068 0.012
#> GSM11336 5 0.0935 0.728 0.032 0.000 0.004 0.000 0.964 0.000
#> GSM11342 1 0.2978 0.844 0.860 0.000 0.000 0.056 0.072 0.012
#> GSM11333 1 0.3069 0.812 0.852 0.000 0.000 0.032 0.096 0.020
#> GSM28802 5 0.4368 0.591 0.328 0.000 0.000 0.012 0.640 0.020
#> GSM28803 3 0.0260 0.982 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM11343 6 0.2219 1.000 0.000 0.000 0.136 0.000 0.000 0.864
#> GSM11347 6 0.2219 1.000 0.000 0.000 0.136 0.000 0.000 0.864
#> GSM28824 5 0.0291 0.721 0.004 0.000 0.004 0.000 0.992 0.000
#> GSM28813 5 0.0291 0.721 0.004 0.000 0.004 0.000 0.992 0.000
#> GSM28827 1 0.0551 0.897 0.984 0.000 0.000 0.004 0.004 0.008
#> GSM11337 5 0.4732 0.575 0.324 0.000 0.000 0.032 0.624 0.020
#> GSM28814 3 0.0146 0.982 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM11331 1 0.1984 0.880 0.912 0.000 0.000 0.056 0.000 0.032
#> GSM11344 6 0.2219 1.000 0.000 0.000 0.136 0.000 0.000 0.864
#> GSM11330 6 0.2219 1.000 0.000 0.000 0.136 0.000 0.000 0.864
#> GSM11325 3 0.0146 0.981 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM11338 5 0.1138 0.725 0.012 0.000 0.004 0.024 0.960 0.000
#> GSM28806 1 0.2122 0.871 0.900 0.000 0.000 0.076 0.000 0.024
#> GSM28826 5 0.4960 0.455 0.376 0.000 0.000 0.032 0.568 0.024
#> GSM28818 4 0.3198 0.809 0.188 0.000 0.000 0.796 0.008 0.008
#> GSM28821 2 0.1720 0.945 0.000 0.928 0.000 0.040 0.000 0.032
#> GSM28807 4 0.1501 0.943 0.076 0.000 0.000 0.924 0.000 0.000
#> GSM28822 4 0.1267 0.943 0.060 0.000 0.000 0.940 0.000 0.000
#> GSM11328 2 0.1245 0.966 0.000 0.952 0.000 0.016 0.000 0.032
#> GSM11323 1 0.2066 0.875 0.904 0.000 0.000 0.072 0.000 0.024
#> GSM11324 1 0.0622 0.897 0.980 0.000 0.000 0.008 0.000 0.012
#> GSM11341 4 0.2128 0.900 0.032 0.000 0.004 0.908 0.000 0.056
#> GSM11326 3 0.1168 0.943 0.000 0.000 0.956 0.028 0.000 0.016
#> GSM28810 4 0.1501 0.941 0.076 0.000 0.000 0.924 0.000 0.000
#> GSM11335 4 0.1531 0.943 0.068 0.000 0.000 0.928 0.000 0.004
#> GSM28809 1 0.0964 0.897 0.968 0.000 0.000 0.012 0.004 0.016
#> GSM11329 1 0.0653 0.897 0.980 0.000 0.000 0.004 0.004 0.012
#> GSM28805 1 0.1350 0.895 0.952 0.000 0.000 0.008 0.020 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:mclust 53 0.397 2
#> MAD:mclust 53 0.373 3
#> MAD:mclust 52 0.352 4
#> MAD:mclust 51 0.482 5
#> MAD:mclust 53 0.417 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.982 0.992 0.3614 0.648 0.648
#> 3 3 1.000 0.998 0.999 0.6367 0.762 0.632
#> 4 4 0.752 0.653 0.820 0.2255 0.859 0.660
#> 5 5 0.828 0.800 0.902 0.0897 0.909 0.688
#> 6 6 0.836 0.707 0.851 0.0461 0.939 0.731
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
#> GSM28815 1 0.0000 0.989 1.000 0.000
#> GSM28816 1 0.7376 0.743 0.792 0.208
#> GSM28817 1 0.0000 0.989 1.000 0.000
#> GSM11327 1 0.0000 0.989 1.000 0.000
#> GSM28825 2 0.0000 1.000 0.000 1.000
#> GSM11322 2 0.0000 1.000 0.000 1.000
#> GSM28828 2 0.0000 1.000 0.000 1.000
#> GSM11346 2 0.0000 1.000 0.000 1.000
#> GSM28808 2 0.0000 1.000 0.000 1.000
#> GSM11332 2 0.0000 1.000 0.000 1.000
#> GSM28811 2 0.0000 1.000 0.000 1.000
#> GSM11334 2 0.0000 1.000 0.000 1.000
#> GSM11340 2 0.0000 1.000 0.000 1.000
#> GSM28812 2 0.0000 1.000 0.000 1.000
#> GSM11345 1 0.0000 0.989 1.000 0.000
#> GSM28819 1 0.0000 0.989 1.000 0.000
#> GSM11321 1 0.0000 0.989 1.000 0.000
#> GSM28820 1 0.0000 0.989 1.000 0.000
#> GSM11339 1 0.0000 0.989 1.000 0.000
#> GSM28804 1 0.7674 0.719 0.776 0.224
#> GSM28823 1 0.0000 0.989 1.000 0.000
#> GSM11336 1 0.0000 0.989 1.000 0.000
#> GSM11342 1 0.0000 0.989 1.000 0.000
#> GSM11333 1 0.0000 0.989 1.000 0.000
#> GSM28802 1 0.0000 0.989 1.000 0.000
#> GSM28803 1 0.0000 0.989 1.000 0.000
#> GSM11343 1 0.0000 0.989 1.000 0.000
#> GSM11347 1 0.0000 0.989 1.000 0.000
#> GSM28824 1 0.0000 0.989 1.000 0.000
#> GSM28813 1 0.0000 0.989 1.000 0.000
#> GSM28827 1 0.0000 0.989 1.000 0.000
#> GSM11337 1 0.0000 0.989 1.000 0.000
#> GSM28814 1 0.0000 0.989 1.000 0.000
#> GSM11331 1 0.0000 0.989 1.000 0.000
#> GSM11344 1 0.0000 0.989 1.000 0.000
#> GSM11330 1 0.0000 0.989 1.000 0.000
#> GSM11325 1 0.0000 0.989 1.000 0.000
#> GSM11338 1 0.0000 0.989 1.000 0.000
#> GSM28806 1 0.0000 0.989 1.000 0.000
#> GSM28826 1 0.0000 0.989 1.000 0.000
#> GSM28818 1 0.0000 0.989 1.000 0.000
#> GSM28821 2 0.0000 1.000 0.000 1.000
#> GSM28807 1 0.0000 0.989 1.000 0.000
#> GSM28822 1 0.0000 0.989 1.000 0.000
#> GSM11328 2 0.0000 1.000 0.000 1.000
#> GSM11323 1 0.0000 0.989 1.000 0.000
#> GSM11324 1 0.0000 0.989 1.000 0.000
#> GSM11341 1 0.0672 0.982 0.992 0.008
#> GSM11326 1 0.0000 0.989 1.000 0.000
#> GSM28810 1 0.0000 0.989 1.000 0.000
#> GSM11335 1 0.0000 0.989 1.000 0.000
#> GSM28809 1 0.0000 0.989 1.000 0.000
#> GSM11329 1 0.0000 0.989 1.000 0.000
#> GSM28805 1 0.0000 0.989 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.0000 0.998 1.000 0.000 0.000
#> GSM28816 1 0.0592 0.987 0.988 0.012 0.000
#> GSM28817 1 0.0000 0.998 1.000 0.000 0.000
#> GSM11327 3 0.0000 0.999 0.000 0.000 1.000
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11345 1 0.0000 0.998 1.000 0.000 0.000
#> GSM28819 1 0.0000 0.998 1.000 0.000 0.000
#> GSM11321 3 0.0000 0.999 0.000 0.000 1.000
#> GSM28820 1 0.0000 0.998 1.000 0.000 0.000
#> GSM11339 1 0.0000 0.998 1.000 0.000 0.000
#> GSM28804 1 0.0000 0.998 1.000 0.000 0.000
#> GSM28823 1 0.0000 0.998 1.000 0.000 0.000
#> GSM11336 1 0.0000 0.998 1.000 0.000 0.000
#> GSM11342 1 0.0000 0.998 1.000 0.000 0.000
#> GSM11333 1 0.0000 0.998 1.000 0.000 0.000
#> GSM28802 1 0.0000 0.998 1.000 0.000 0.000
#> GSM28803 3 0.0000 0.999 0.000 0.000 1.000
#> GSM11343 3 0.0000 0.999 0.000 0.000 1.000
#> GSM11347 3 0.0000 0.999 0.000 0.000 1.000
#> GSM28824 1 0.0000 0.998 1.000 0.000 0.000
#> GSM28813 1 0.1411 0.963 0.964 0.000 0.036
#> GSM28827 1 0.0000 0.998 1.000 0.000 0.000
#> GSM11337 1 0.0000 0.998 1.000 0.000 0.000
#> GSM28814 3 0.0000 0.999 0.000 0.000 1.000
#> GSM11331 1 0.0237 0.995 0.996 0.000 0.004
#> GSM11344 3 0.0000 0.999 0.000 0.000 1.000
#> GSM11330 3 0.0000 0.999 0.000 0.000 1.000
#> GSM11325 3 0.0000 0.999 0.000 0.000 1.000
#> GSM11338 1 0.0000 0.998 1.000 0.000 0.000
#> GSM28806 1 0.0000 0.998 1.000 0.000 0.000
#> GSM28826 1 0.0000 0.998 1.000 0.000 0.000
#> GSM28818 1 0.0000 0.998 1.000 0.000 0.000
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28807 1 0.0000 0.998 1.000 0.000 0.000
#> GSM28822 1 0.0000 0.998 1.000 0.000 0.000
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11323 1 0.0000 0.998 1.000 0.000 0.000
#> GSM11324 1 0.0000 0.998 1.000 0.000 0.000
#> GSM11341 3 0.0592 0.988 0.000 0.012 0.988
#> GSM11326 3 0.0000 0.999 0.000 0.000 1.000
#> GSM28810 1 0.0000 0.998 1.000 0.000 0.000
#> GSM11335 1 0.0000 0.998 1.000 0.000 0.000
#> GSM28809 1 0.0000 0.998 1.000 0.000 0.000
#> GSM11329 1 0.0000 0.998 1.000 0.000 0.000
#> GSM28805 1 0.0000 0.998 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.3219 0.6083 0.836 0.000 0.000 0.164
#> GSM28816 4 0.6081 -0.4058 0.472 0.044 0.000 0.484
#> GSM28817 1 0.0817 0.6519 0.976 0.000 0.000 0.024
#> GSM11327 3 0.1389 0.9216 0.000 0.000 0.952 0.048
#> GSM28825 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11345 1 0.1118 0.6299 0.964 0.000 0.000 0.036
#> GSM28819 1 0.0921 0.6570 0.972 0.000 0.000 0.028
#> GSM11321 3 0.1716 0.9176 0.000 0.000 0.936 0.064
#> GSM28820 1 0.1557 0.6523 0.944 0.000 0.000 0.056
#> GSM11339 1 0.4222 0.1522 0.728 0.000 0.000 0.272
#> GSM28804 4 0.4855 0.5968 0.400 0.000 0.000 0.600
#> GSM28823 1 0.0921 0.6547 0.972 0.000 0.000 0.028
#> GSM11336 1 0.4977 0.4058 0.540 0.000 0.000 0.460
#> GSM11342 1 0.0921 0.6572 0.972 0.000 0.000 0.028
#> GSM11333 4 0.4955 -0.3697 0.444 0.000 0.000 0.556
#> GSM28802 1 0.4454 0.5028 0.692 0.000 0.000 0.308
#> GSM28803 3 0.1557 0.9211 0.000 0.000 0.944 0.056
#> GSM11343 3 0.0000 0.9287 0.000 0.000 1.000 0.000
#> GSM11347 3 0.0000 0.9287 0.000 0.000 1.000 0.000
#> GSM28824 1 0.4977 0.4058 0.540 0.000 0.000 0.460
#> GSM28813 1 0.5850 0.3745 0.512 0.000 0.032 0.456
#> GSM28827 1 0.0707 0.6475 0.980 0.000 0.000 0.020
#> GSM11337 1 0.4817 0.4639 0.612 0.000 0.000 0.388
#> GSM28814 3 0.3764 0.8052 0.000 0.000 0.784 0.216
#> GSM11331 1 0.3047 0.5644 0.872 0.000 0.012 0.116
#> GSM11344 3 0.0000 0.9287 0.000 0.000 1.000 0.000
#> GSM11330 3 0.0188 0.9279 0.000 0.000 0.996 0.004
#> GSM11325 3 0.4391 0.7612 0.008 0.000 0.740 0.252
#> GSM11338 1 0.4907 0.4417 0.580 0.000 0.000 0.420
#> GSM28806 1 0.4843 -0.3213 0.604 0.000 0.000 0.396
#> GSM28826 1 0.4916 0.4388 0.576 0.000 0.000 0.424
#> GSM28818 4 0.4925 0.5883 0.428 0.000 0.000 0.572
#> GSM28821 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28807 4 0.4866 0.5989 0.404 0.000 0.000 0.596
#> GSM28822 4 0.4866 0.5998 0.404 0.000 0.000 0.596
#> GSM11328 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11323 1 0.3300 0.5159 0.848 0.000 0.008 0.144
#> GSM11324 1 0.0921 0.6426 0.972 0.000 0.000 0.028
#> GSM11341 4 0.5799 -0.0467 0.024 0.004 0.420 0.552
#> GSM11326 3 0.0336 0.9274 0.000 0.000 0.992 0.008
#> GSM28810 4 0.4985 0.5392 0.468 0.000 0.000 0.532
#> GSM11335 4 0.5310 0.5897 0.412 0.000 0.012 0.576
#> GSM28809 1 0.2814 0.5366 0.868 0.000 0.000 0.132
#> GSM11329 1 0.0592 0.6446 0.984 0.000 0.000 0.016
#> GSM28805 1 0.0592 0.6565 0.984 0.000 0.000 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 1 0.4470 0.3921 0.616 0.000 0.000 0.012 0.372
#> GSM28816 5 0.1960 0.8357 0.048 0.004 0.000 0.020 0.928
#> GSM28817 1 0.0510 0.8493 0.984 0.000 0.000 0.000 0.016
#> GSM11327 3 0.2136 0.8384 0.000 0.000 0.904 0.008 0.088
#> GSM28825 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM11345 1 0.0000 0.8491 1.000 0.000 0.000 0.000 0.000
#> GSM28819 1 0.1124 0.8414 0.960 0.000 0.000 0.036 0.004
#> GSM11321 3 0.3989 0.7857 0.008 0.000 0.800 0.048 0.144
#> GSM28820 1 0.0898 0.8488 0.972 0.000 0.000 0.020 0.008
#> GSM11339 1 0.2358 0.7884 0.888 0.000 0.000 0.104 0.008
#> GSM28804 4 0.1768 0.9163 0.072 0.000 0.000 0.924 0.004
#> GSM28823 1 0.0609 0.8472 0.980 0.000 0.000 0.020 0.000
#> GSM11336 5 0.1121 0.8363 0.044 0.000 0.000 0.000 0.956
#> GSM11342 1 0.0771 0.8473 0.976 0.000 0.000 0.020 0.004
#> GSM11333 5 0.1965 0.8336 0.052 0.000 0.000 0.024 0.924
#> GSM28802 1 0.5229 0.1877 0.548 0.000 0.000 0.048 0.404
#> GSM28803 3 0.2997 0.8089 0.000 0.000 0.840 0.012 0.148
#> GSM11343 3 0.0880 0.8684 0.000 0.000 0.968 0.000 0.032
#> GSM11347 3 0.0000 0.8726 0.000 0.000 1.000 0.000 0.000
#> GSM28824 5 0.0703 0.8287 0.024 0.000 0.000 0.000 0.976
#> GSM28813 5 0.0566 0.8185 0.012 0.000 0.004 0.000 0.984
#> GSM28827 1 0.0671 0.8486 0.980 0.000 0.000 0.004 0.016
#> GSM11337 1 0.4449 0.0653 0.512 0.000 0.000 0.004 0.484
#> GSM28814 3 0.5375 0.2040 0.004 0.000 0.500 0.044 0.452
#> GSM11331 1 0.3354 0.7947 0.864 0.000 0.064 0.044 0.028
#> GSM11344 3 0.0000 0.8726 0.000 0.000 1.000 0.000 0.000
#> GSM11330 3 0.0000 0.8726 0.000 0.000 1.000 0.000 0.000
#> GSM11325 5 0.5901 -0.1194 0.016 0.000 0.404 0.064 0.516
#> GSM11338 5 0.2966 0.7464 0.184 0.000 0.000 0.000 0.816
#> GSM28806 1 0.4430 0.3534 0.628 0.000 0.000 0.360 0.012
#> GSM28826 5 0.3242 0.7035 0.216 0.000 0.000 0.000 0.784
#> GSM28818 4 0.2329 0.8999 0.124 0.000 0.000 0.876 0.000
#> GSM28821 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM28807 4 0.1608 0.9170 0.072 0.000 0.000 0.928 0.000
#> GSM28822 4 0.1608 0.9170 0.072 0.000 0.000 0.928 0.000
#> GSM11328 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM11323 1 0.3274 0.7999 0.868 0.000 0.048 0.060 0.024
#> GSM11324 1 0.0404 0.8492 0.988 0.000 0.000 0.000 0.012
#> GSM11341 4 0.1671 0.8358 0.000 0.000 0.076 0.924 0.000
#> GSM11326 3 0.1116 0.8585 0.004 0.000 0.964 0.028 0.004
#> GSM28810 4 0.3861 0.6894 0.284 0.000 0.004 0.712 0.000
#> GSM11335 4 0.2416 0.9079 0.100 0.000 0.012 0.888 0.000
#> GSM28809 1 0.2928 0.8005 0.872 0.000 0.000 0.064 0.064
#> GSM11329 1 0.0162 0.8497 0.996 0.000 0.000 0.000 0.004
#> GSM28805 1 0.0162 0.8497 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
#> GSM28815 5 0.5715 0.28783 0.364 0 0.000 0.004 0.484 0.148
#> GSM28816 5 0.3430 0.68018 0.004 0 0.000 0.016 0.772 0.208
#> GSM28817 1 0.0972 0.81146 0.964 0 0.000 0.000 0.008 0.028
#> GSM11327 3 0.5135 0.41560 0.000 0 0.616 0.000 0.240 0.144
#> GSM28825 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11345 1 0.0363 0.81381 0.988 0 0.000 0.000 0.000 0.012
#> GSM28819 1 0.1141 0.80036 0.948 0 0.000 0.000 0.000 0.052
#> GSM11321 6 0.4718 0.32611 0.036 0 0.384 0.000 0.008 0.572
#> GSM28820 1 0.0777 0.81269 0.972 0 0.000 0.000 0.004 0.024
#> GSM11339 1 0.2765 0.77827 0.876 0 0.000 0.064 0.016 0.044
#> GSM28804 4 0.0790 0.85682 0.000 0 0.000 0.968 0.000 0.032
#> GSM28823 1 0.0713 0.81019 0.972 0 0.000 0.000 0.000 0.028
#> GSM11336 5 0.0146 0.76526 0.004 0 0.000 0.000 0.996 0.000
#> GSM11342 1 0.0790 0.81112 0.968 0 0.000 0.000 0.000 0.032
#> GSM11333 5 0.4675 0.63672 0.008 0 0.000 0.096 0.696 0.200
#> GSM28802 1 0.4536 0.05544 0.496 0 0.004 0.000 0.024 0.476
#> GSM28803 3 0.4384 0.07497 0.000 0 0.616 0.000 0.036 0.348
#> GSM11343 3 0.1858 0.63892 0.000 0 0.904 0.000 0.004 0.092
#> GSM11347 3 0.0000 0.71553 0.000 0 1.000 0.000 0.000 0.000
#> GSM28824 5 0.0146 0.76349 0.000 0 0.000 0.000 0.996 0.004
#> GSM28813 5 0.0547 0.76045 0.000 0 0.000 0.000 0.980 0.020
#> GSM28827 1 0.2858 0.74569 0.844 0 0.000 0.000 0.032 0.124
#> GSM11337 5 0.3876 0.65989 0.108 0 0.000 0.000 0.772 0.120
#> GSM28814 6 0.5193 0.34401 0.000 0 0.344 0.000 0.104 0.552
#> GSM11331 6 0.7358 -0.20554 0.340 0 0.224 0.016 0.068 0.352
#> GSM11344 3 0.0000 0.71553 0.000 0 1.000 0.000 0.000 0.000
#> GSM11330 3 0.0713 0.71071 0.000 0 0.972 0.000 0.000 0.028
#> GSM11325 6 0.5514 0.42032 0.060 0 0.244 0.000 0.068 0.628
#> GSM11338 5 0.1594 0.76062 0.052 0 0.000 0.000 0.932 0.016
#> GSM28806 1 0.4500 0.57983 0.708 0 0.000 0.144 0.000 0.148
#> GSM28826 5 0.4897 0.58450 0.092 0 0.000 0.000 0.616 0.292
#> GSM28818 4 0.1594 0.85409 0.052 0 0.000 0.932 0.000 0.016
#> GSM28821 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000 0.000
#> GSM28807 4 0.0458 0.87152 0.000 0 0.000 0.984 0.000 0.016
#> GSM28822 4 0.0000 0.87251 0.000 0 0.000 1.000 0.000 0.000
#> GSM11328 2 0.0000 1.00000 0.000 1 0.000 0.000 0.000 0.000
#> GSM11323 1 0.7330 -0.00162 0.380 0 0.176 0.024 0.068 0.352
#> GSM11324 1 0.1124 0.81033 0.956 0 0.000 0.000 0.008 0.036
#> GSM11341 4 0.0000 0.87251 0.000 0 0.000 1.000 0.000 0.000
#> GSM11326 3 0.3240 0.55377 0.000 0 0.752 0.000 0.004 0.244
#> GSM28810 4 0.4135 0.52000 0.300 0 0.000 0.668 0.000 0.032
#> GSM11335 4 0.4065 0.76343 0.044 0 0.064 0.792 0.000 0.100
#> GSM28809 1 0.5880 0.50119 0.604 0 0.000 0.048 0.144 0.204
#> GSM11329 1 0.0291 0.81437 0.992 0 0.000 0.000 0.004 0.004
#> GSM28805 1 0.1333 0.80519 0.944 0 0.000 0.000 0.008 0.048
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> MAD:NMF 54 0.398 2
#> MAD:NMF 54 0.374 3
#> MAD:NMF 43 0.409 4
#> MAD:NMF 48 0.427 5
#> MAD:NMF 45 0.413 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 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 0.481 0.843 0.885 0.2931 0.743 0.743
#> 3 3 1.000 0.978 0.989 0.8826 0.715 0.616
#> 4 4 0.750 0.765 0.897 0.2042 0.883 0.744
#> 5 5 0.780 0.634 0.849 0.0284 0.869 0.697
#> 6 6 0.750 0.684 0.875 0.0660 0.890 0.732
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM28815 1 0.000 0.877 1.000 0.000
#> GSM28816 1 0.000 0.877 1.000 0.000
#> GSM28817 1 0.000 0.877 1.000 0.000
#> GSM11327 1 0.482 0.748 0.896 0.104
#> GSM28825 1 0.876 0.673 0.704 0.296
#> GSM11322 1 0.876 0.673 0.704 0.296
#> GSM28828 1 0.876 0.673 0.704 0.296
#> GSM11346 1 0.876 0.673 0.704 0.296
#> GSM28808 1 0.876 0.673 0.704 0.296
#> GSM11332 1 0.876 0.673 0.704 0.296
#> GSM28811 1 0.876 0.673 0.704 0.296
#> GSM11334 1 0.876 0.673 0.704 0.296
#> GSM11340 1 0.876 0.673 0.704 0.296
#> GSM28812 1 0.876 0.673 0.704 0.296
#> GSM11345 1 0.000 0.877 1.000 0.000
#> GSM28819 1 0.000 0.877 1.000 0.000
#> GSM11321 2 0.876 1.000 0.296 0.704
#> GSM28820 1 0.000 0.877 1.000 0.000
#> GSM11339 1 0.000 0.877 1.000 0.000
#> GSM28804 1 0.000 0.877 1.000 0.000
#> GSM28823 1 0.000 0.877 1.000 0.000
#> GSM11336 1 0.000 0.877 1.000 0.000
#> GSM11342 1 0.000 0.877 1.000 0.000
#> GSM11333 1 0.000 0.877 1.000 0.000
#> GSM28802 1 0.000 0.877 1.000 0.000
#> GSM28803 2 0.876 1.000 0.296 0.704
#> GSM11343 2 0.876 1.000 0.296 0.704
#> GSM11347 2 0.876 1.000 0.296 0.704
#> GSM28824 1 0.000 0.877 1.000 0.000
#> GSM28813 1 0.000 0.877 1.000 0.000
#> GSM28827 1 0.000 0.877 1.000 0.000
#> GSM11337 1 0.000 0.877 1.000 0.000
#> GSM28814 2 0.876 1.000 0.296 0.704
#> GSM11331 1 0.000 0.877 1.000 0.000
#> GSM11344 2 0.876 1.000 0.296 0.704
#> GSM11330 2 0.876 1.000 0.296 0.704
#> GSM11325 2 0.876 1.000 0.296 0.704
#> GSM11338 1 0.000 0.877 1.000 0.000
#> GSM28806 1 0.000 0.877 1.000 0.000
#> GSM28826 1 0.000 0.877 1.000 0.000
#> GSM28818 1 0.000 0.877 1.000 0.000
#> GSM28821 1 0.876 0.673 0.704 0.296
#> GSM28807 1 0.000 0.877 1.000 0.000
#> GSM28822 1 0.000 0.877 1.000 0.000
#> GSM11328 1 0.876 0.673 0.704 0.296
#> GSM11323 1 0.000 0.877 1.000 0.000
#> GSM11324 1 0.000 0.877 1.000 0.000
#> GSM11341 1 0.416 0.778 0.916 0.084
#> GSM11326 1 0.482 0.748 0.896 0.104
#> GSM28810 1 0.000 0.877 1.000 0.000
#> GSM11335 1 0.000 0.877 1.000 0.000
#> GSM28809 1 0.000 0.877 1.000 0.000
#> GSM11329 1 0.000 0.877 1.000 0.000
#> GSM28805 1 0.000 0.877 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.0000 0.981 1.000 0.000 0.000
#> GSM28816 1 0.0000 0.981 1.000 0.000 0.000
#> GSM28817 1 0.0000 0.981 1.000 0.000 0.000
#> GSM11327 1 0.3340 0.871 0.880 0.000 0.120
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11345 1 0.0000 0.981 1.000 0.000 0.000
#> GSM28819 1 0.0000 0.981 1.000 0.000 0.000
#> GSM11321 3 0.0000 1.000 0.000 0.000 1.000
#> GSM28820 1 0.0000 0.981 1.000 0.000 0.000
#> GSM11339 1 0.0000 0.981 1.000 0.000 0.000
#> GSM28804 1 0.2711 0.903 0.912 0.088 0.000
#> GSM28823 1 0.0000 0.981 1.000 0.000 0.000
#> GSM11336 1 0.0000 0.981 1.000 0.000 0.000
#> GSM11342 1 0.0000 0.981 1.000 0.000 0.000
#> GSM11333 1 0.0000 0.981 1.000 0.000 0.000
#> GSM28802 1 0.0000 0.981 1.000 0.000 0.000
#> GSM28803 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11343 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11347 3 0.0000 1.000 0.000 0.000 1.000
#> GSM28824 1 0.0000 0.981 1.000 0.000 0.000
#> GSM28813 1 0.0237 0.979 0.996 0.000 0.004
#> GSM28827 1 0.0000 0.981 1.000 0.000 0.000
#> GSM11337 1 0.0000 0.981 1.000 0.000 0.000
#> GSM28814 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11331 1 0.0000 0.981 1.000 0.000 0.000
#> GSM11344 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11330 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11325 3 0.0000 1.000 0.000 0.000 1.000
#> GSM11338 1 0.0237 0.979 0.996 0.000 0.004
#> GSM28806 1 0.0000 0.981 1.000 0.000 0.000
#> GSM28826 1 0.0000 0.981 1.000 0.000 0.000
#> GSM28818 1 0.0000 0.981 1.000 0.000 0.000
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28807 1 0.0000 0.981 1.000 0.000 0.000
#> GSM28822 1 0.2711 0.903 0.912 0.088 0.000
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11323 1 0.0000 0.981 1.000 0.000 0.000
#> GSM11324 1 0.0000 0.981 1.000 0.000 0.000
#> GSM11341 1 0.5582 0.807 0.812 0.088 0.100
#> GSM11326 1 0.3340 0.871 0.880 0.000 0.120
#> GSM28810 1 0.0000 0.981 1.000 0.000 0.000
#> GSM11335 1 0.0000 0.981 1.000 0.000 0.000
#> GSM28809 1 0.0000 0.981 1.000 0.000 0.000
#> GSM11329 1 0.0000 0.981 1.000 0.000 0.000
#> GSM28805 1 0.0000 0.981 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.4193 0.429 0.732 0 0.000 0.268
#> GSM28816 1 0.4193 0.429 0.732 0 0.000 0.268
#> GSM28817 1 0.0707 0.791 0.980 0 0.000 0.020
#> GSM11327 4 0.6400 0.675 0.252 0 0.116 0.632
#> GSM28825 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11345 1 0.1389 0.774 0.952 0 0.000 0.048
#> GSM28819 1 0.1389 0.774 0.952 0 0.000 0.048
#> GSM11321 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM28820 1 0.0707 0.791 0.980 0 0.000 0.020
#> GSM11339 1 0.0707 0.791 0.980 0 0.000 0.020
#> GSM28804 1 0.4222 0.401 0.728 0 0.000 0.272
#> GSM28823 1 0.0817 0.786 0.976 0 0.000 0.024
#> GSM11336 1 0.4564 0.271 0.672 0 0.000 0.328
#> GSM11342 1 0.0817 0.786 0.976 0 0.000 0.024
#> GSM11333 1 0.4193 0.429 0.732 0 0.000 0.268
#> GSM28802 1 0.0592 0.790 0.984 0 0.000 0.016
#> GSM28803 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM11343 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM11347 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM28824 4 0.4996 0.420 0.484 0 0.000 0.516
#> GSM28813 4 0.4790 0.645 0.380 0 0.000 0.620
#> GSM28827 1 0.0000 0.793 1.000 0 0.000 0.000
#> GSM11337 1 0.0000 0.793 1.000 0 0.000 0.000
#> GSM28814 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM11331 1 0.1022 0.785 0.968 0 0.000 0.032
#> GSM11344 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM11330 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM11325 3 0.0000 1.000 0.000 0 1.000 0.000
#> GSM11338 4 0.4790 0.645 0.380 0 0.000 0.620
#> GSM28806 1 0.0817 0.786 0.976 0 0.000 0.024
#> GSM28826 1 0.1637 0.763 0.940 0 0.000 0.060
#> GSM28818 1 0.4564 0.271 0.672 0 0.000 0.328
#> GSM28821 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM28807 1 0.4564 0.271 0.672 0 0.000 0.328
#> GSM28822 1 0.4477 0.335 0.688 0 0.000 0.312
#> GSM11328 2 0.0000 1.000 0.000 1 0.000 0.000
#> GSM11323 1 0.1022 0.785 0.968 0 0.000 0.032
#> GSM11324 1 0.1302 0.784 0.956 0 0.000 0.044
#> GSM11341 4 0.4564 0.242 0.328 0 0.000 0.672
#> GSM11326 4 0.6400 0.675 0.252 0 0.116 0.632
#> GSM28810 1 0.0592 0.790 0.984 0 0.000 0.016
#> GSM11335 1 0.1118 0.783 0.964 0 0.000 0.036
#> GSM28809 1 0.4564 0.271 0.672 0 0.000 0.328
#> GSM11329 1 0.0707 0.791 0.980 0 0.000 0.020
#> GSM28805 1 0.0707 0.791 0.980 0 0.000 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 1 0.029 0.4290 0.992 0 0.000 0.008 0.000
#> GSM28816 1 0.029 0.4290 0.992 0 0.000 0.008 0.000
#> GSM28817 1 0.351 0.5030 0.748 0 0.000 0.252 0.000
#> GSM11327 1 0.724 -0.0292 0.496 0 0.104 0.308 0.092
#> GSM28825 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM11322 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM28828 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM11346 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM28808 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM11332 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM28811 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM11334 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM11340 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM28812 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM11345 1 0.415 0.4688 0.652 0 0.000 0.344 0.004
#> GSM28819 1 0.415 0.4688 0.652 0 0.000 0.344 0.004
#> GSM11321 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM28820 1 0.351 0.5030 0.748 0 0.000 0.252 0.000
#> GSM11339 1 0.351 0.5030 0.748 0 0.000 0.252 0.000
#> GSM28804 4 0.417 0.8568 0.348 0 0.000 0.648 0.004
#> GSM28823 1 0.393 0.4588 0.672 0 0.000 0.328 0.000
#> GSM11336 1 0.185 0.3907 0.912 0 0.000 0.088 0.000
#> GSM11342 1 0.393 0.4588 0.672 0 0.000 0.328 0.000
#> GSM11333 1 0.029 0.4290 0.992 0 0.000 0.008 0.000
#> GSM28802 1 0.389 0.4726 0.680 0 0.000 0.320 0.000
#> GSM28803 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM11343 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM11347 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM28824 1 0.447 0.2417 0.732 0 0.000 0.212 0.056
#> GSM28813 1 0.532 0.1733 0.624 0 0.000 0.296 0.080
#> GSM28827 1 0.382 0.4879 0.696 0 0.000 0.304 0.000
#> GSM11337 1 0.382 0.4879 0.696 0 0.000 0.304 0.000
#> GSM28814 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM11331 1 0.408 0.4823 0.668 0 0.000 0.328 0.004
#> GSM11344 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM11330 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM11325 3 0.000 1.0000 0.000 0 1.000 0.000 0.000
#> GSM11338 1 0.532 0.1733 0.624 0 0.000 0.296 0.080
#> GSM28806 1 0.393 0.4588 0.672 0 0.000 0.328 0.000
#> GSM28826 1 0.420 0.4553 0.640 0 0.000 0.356 0.004
#> GSM28818 1 0.185 0.3907 0.912 0 0.000 0.088 0.000
#> GSM28821 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM28807 1 0.185 0.3907 0.912 0 0.000 0.088 0.000
#> GSM28822 4 0.487 0.8688 0.284 0 0.000 0.664 0.052
#> GSM11328 2 0.000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM11323 1 0.408 0.4823 0.668 0 0.000 0.328 0.004
#> GSM11324 1 0.395 0.4978 0.696 0 0.000 0.300 0.004
#> GSM11341 5 0.029 0.0000 0.000 0 0.000 0.008 0.992
#> GSM11326 1 0.724 -0.0292 0.496 0 0.104 0.308 0.092
#> GSM28810 1 0.389 0.4726 0.680 0 0.000 0.320 0.000
#> GSM11335 1 0.410 0.4796 0.664 0 0.000 0.332 0.004
#> GSM28809 1 0.185 0.3907 0.912 0 0.000 0.088 0.000
#> GSM11329 1 0.351 0.5030 0.748 0 0.000 0.252 0.000
#> GSM28805 1 0.351 0.5030 0.748 0 0.000 0.252 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 1 0.5745 0.2821 0.508 0 0 0 0.212 0.280
#> GSM28816 1 0.5745 0.2821 0.508 0 0 0 0.212 0.280
#> GSM28817 1 0.1806 0.6771 0.908 0 0 0 0.004 0.088
#> GSM11327 5 0.1501 0.6605 0.076 0 0 0 0.924 0.000
#> GSM28825 2 0.0000 1.0000 0.000 1 0 0 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1 0 0 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1 0 0 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1 0 0 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1 0 0 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1 0 0 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1 0 0 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1 0 0 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1 0 0 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1 0 0 0.000 0.000
#> GSM11345 1 0.1075 0.6673 0.952 0 0 0 0.048 0.000
#> GSM28819 1 0.1075 0.6673 0.952 0 0 0 0.048 0.000
#> GSM11321 3 0.0000 1.0000 0.000 0 1 0 0.000 0.000
#> GSM28820 1 0.1806 0.6771 0.908 0 0 0 0.004 0.088
#> GSM11339 1 0.1806 0.6771 0.908 0 0 0 0.004 0.088
#> GSM28804 1 0.3869 -0.6166 0.500 0 0 0 0.000 0.500
#> GSM28823 1 0.0692 0.6760 0.976 0 0 0 0.004 0.020
#> GSM11336 1 0.6063 0.0651 0.388 0 0 0 0.264 0.348
#> GSM11342 1 0.0692 0.6760 0.976 0 0 0 0.004 0.020
#> GSM11333 1 0.5745 0.2821 0.508 0 0 0 0.212 0.280
#> GSM28802 1 0.0508 0.6804 0.984 0 0 0 0.004 0.012
#> GSM28803 3 0.0000 1.0000 0.000 0 1 0 0.000 0.000
#> GSM11343 3 0.0000 1.0000 0.000 0 1 0 0.000 0.000
#> GSM11347 3 0.0000 1.0000 0.000 0 1 0 0.000 0.000
#> GSM28824 5 0.4420 0.6432 0.308 0 0 0 0.644 0.048
#> GSM28813 5 0.3641 0.7785 0.224 0 0 0 0.748 0.028
#> GSM28827 1 0.0000 0.6854 1.000 0 0 0 0.000 0.000
#> GSM11337 1 0.0000 0.6854 1.000 0 0 0 0.000 0.000
#> GSM28814 3 0.0000 1.0000 0.000 0 1 0 0.000 0.000
#> GSM11331 1 0.0790 0.6781 0.968 0 0 0 0.032 0.000
#> GSM11344 3 0.0000 1.0000 0.000 0 1 0 0.000 0.000
#> GSM11330 3 0.0000 1.0000 0.000 0 1 0 0.000 0.000
#> GSM11325 3 0.0000 1.0000 0.000 0 1 0 0.000 0.000
#> GSM11338 5 0.3641 0.7785 0.224 0 0 0 0.748 0.028
#> GSM28806 1 0.0692 0.6760 0.976 0 0 0 0.004 0.020
#> GSM28826 1 0.1267 0.6557 0.940 0 0 0 0.060 0.000
#> GSM28818 1 0.6034 0.0872 0.400 0 0 0 0.252 0.348
#> GSM28821 2 0.0000 1.0000 0.000 1 0 0 0.000 0.000
#> GSM28807 1 0.6034 0.0872 0.400 0 0 0 0.252 0.348
#> GSM28822 6 0.3607 0.0000 0.348 0 0 0 0.000 0.652
#> GSM11328 2 0.0000 1.0000 0.000 1 0 0 0.000 0.000
#> GSM11323 1 0.0790 0.6781 0.968 0 0 0 0.032 0.000
#> GSM11324 1 0.2119 0.6808 0.904 0 0 0 0.036 0.060
#> GSM11341 4 0.0000 0.0000 0.000 0 0 1 0.000 0.000
#> GSM11326 5 0.1501 0.6605 0.076 0 0 0 0.924 0.000
#> GSM28810 1 0.0508 0.6804 0.984 0 0 0 0.004 0.012
#> GSM11335 1 0.0865 0.6758 0.964 0 0 0 0.036 0.000
#> GSM28809 1 0.6034 0.0872 0.400 0 0 0 0.252 0.348
#> GSM11329 1 0.1806 0.6771 0.908 0 0 0 0.004 0.088
#> GSM28805 1 0.1806 0.6771 0.908 0 0 0 0.004 0.088
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> ATC:hclust 54 0.398 2
#> ATC:hclust 54 0.374 3
#> ATC:hclust 43 0.409 4
#> ATC:hclust 27 0.386 5
#> ATC:hclust 44 0.410 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.405 0.808 0.844 0.3472 0.648 0.648
#> 3 3 1.000 0.953 0.965 0.5736 0.810 0.707
#> 4 4 0.667 0.583 0.809 0.2305 0.955 0.902
#> 5 5 0.612 0.593 0.755 0.1106 0.823 0.580
#> 6 6 0.627 0.560 0.746 0.0487 0.955 0.822
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
#> GSM28815 1 0.925 0.849 0.660 0.340
#> GSM28816 1 0.925 0.849 0.660 0.340
#> GSM28817 1 0.925 0.849 0.660 0.340
#> GSM11327 1 0.343 0.608 0.936 0.064
#> GSM28825 2 0.000 0.985 0.000 1.000
#> GSM11322 2 0.000 0.985 0.000 1.000
#> GSM28828 2 0.000 0.985 0.000 1.000
#> GSM11346 2 0.000 0.985 0.000 1.000
#> GSM28808 2 0.000 0.985 0.000 1.000
#> GSM11332 2 0.000 0.985 0.000 1.000
#> GSM28811 2 0.000 0.985 0.000 1.000
#> GSM11334 2 0.000 0.985 0.000 1.000
#> GSM11340 2 0.000 0.985 0.000 1.000
#> GSM28812 2 0.000 0.985 0.000 1.000
#> GSM11345 1 0.921 0.849 0.664 0.336
#> GSM28819 1 0.921 0.849 0.664 0.336
#> GSM11321 1 0.482 0.463 0.896 0.104
#> GSM28820 1 0.925 0.849 0.660 0.340
#> GSM11339 1 0.925 0.849 0.660 0.340
#> GSM28804 1 0.925 0.849 0.660 0.340
#> GSM28823 1 0.921 0.849 0.664 0.336
#> GSM11336 1 0.925 0.849 0.660 0.340
#> GSM11342 1 0.921 0.849 0.664 0.336
#> GSM11333 1 0.925 0.849 0.660 0.340
#> GSM28802 1 0.921 0.849 0.664 0.336
#> GSM28803 1 0.482 0.463 0.896 0.104
#> GSM11343 1 0.482 0.463 0.896 0.104
#> GSM11347 1 0.482 0.463 0.896 0.104
#> GSM28824 1 0.925 0.849 0.660 0.340
#> GSM28813 1 0.921 0.849 0.664 0.336
#> GSM28827 1 0.925 0.849 0.660 0.340
#> GSM11337 1 0.925 0.849 0.660 0.340
#> GSM28814 1 0.482 0.463 0.896 0.104
#> GSM11331 1 0.921 0.849 0.664 0.336
#> GSM11344 1 0.482 0.463 0.896 0.104
#> GSM11330 1 0.482 0.463 0.896 0.104
#> GSM11325 1 0.482 0.463 0.896 0.104
#> GSM11338 1 0.921 0.849 0.664 0.336
#> GSM28806 1 0.921 0.849 0.664 0.336
#> GSM28826 1 0.925 0.849 0.660 0.340
#> GSM28818 1 0.925 0.849 0.660 0.340
#> GSM28821 2 0.482 0.813 0.104 0.896
#> GSM28807 1 0.925 0.849 0.660 0.340
#> GSM28822 1 0.921 0.849 0.664 0.336
#> GSM11328 2 0.000 0.985 0.000 1.000
#> GSM11323 1 0.921 0.849 0.664 0.336
#> GSM11324 1 0.925 0.849 0.660 0.340
#> GSM11341 1 0.990 0.720 0.560 0.440
#> GSM11326 1 0.443 0.633 0.908 0.092
#> GSM28810 1 0.921 0.849 0.664 0.336
#> GSM11335 1 0.921 0.849 0.664 0.336
#> GSM28809 1 0.925 0.849 0.660 0.340
#> GSM11329 1 0.925 0.849 0.660 0.340
#> GSM28805 1 0.925 0.849 0.660 0.340
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.0237 0.969 0.996 0.000 0.004
#> GSM28816 1 0.0237 0.969 0.996 0.000 0.004
#> GSM28817 1 0.0424 0.968 0.992 0.000 0.008
#> GSM11327 1 0.5835 0.481 0.660 0.000 0.340
#> GSM28825 2 0.0892 0.988 0.020 0.980 0.000
#> GSM11322 2 0.0892 0.988 0.020 0.980 0.000
#> GSM28828 2 0.2176 0.978 0.020 0.948 0.032
#> GSM11346 2 0.0892 0.988 0.020 0.980 0.000
#> GSM28808 2 0.0892 0.988 0.020 0.980 0.000
#> GSM11332 2 0.0892 0.988 0.020 0.980 0.000
#> GSM28811 2 0.2527 0.973 0.020 0.936 0.044
#> GSM11334 2 0.0892 0.988 0.020 0.980 0.000
#> GSM11340 2 0.0892 0.988 0.020 0.980 0.000
#> GSM28812 2 0.0892 0.988 0.020 0.980 0.000
#> GSM11345 1 0.0237 0.969 0.996 0.000 0.004
#> GSM28819 1 0.0237 0.969 0.996 0.000 0.004
#> GSM11321 3 0.2063 0.991 0.044 0.008 0.948
#> GSM28820 1 0.0000 0.969 1.000 0.000 0.000
#> GSM11339 1 0.0424 0.968 0.992 0.000 0.008
#> GSM28804 1 0.0892 0.959 0.980 0.000 0.020
#> GSM28823 1 0.0237 0.969 0.996 0.000 0.004
#> GSM11336 1 0.0237 0.969 0.996 0.000 0.004
#> GSM11342 1 0.0237 0.969 0.996 0.000 0.004
#> GSM11333 1 0.0237 0.969 0.996 0.000 0.004
#> GSM28802 1 0.0237 0.969 0.996 0.000 0.004
#> GSM28803 3 0.2063 0.991 0.044 0.008 0.948
#> GSM11343 3 0.2793 0.991 0.044 0.028 0.928
#> GSM11347 3 0.2793 0.991 0.044 0.028 0.928
#> GSM28824 1 0.0237 0.969 0.996 0.000 0.004
#> GSM28813 1 0.0000 0.969 1.000 0.000 0.000
#> GSM28827 1 0.0237 0.969 0.996 0.000 0.004
#> GSM11337 1 0.0237 0.969 0.996 0.000 0.004
#> GSM28814 3 0.2063 0.991 0.044 0.008 0.948
#> GSM11331 1 0.0000 0.969 1.000 0.000 0.000
#> GSM11344 3 0.2793 0.991 0.044 0.028 0.928
#> GSM11330 3 0.2793 0.991 0.044 0.028 0.928
#> GSM11325 3 0.2063 0.991 0.044 0.008 0.948
#> GSM11338 1 0.0000 0.969 1.000 0.000 0.000
#> GSM28806 1 0.0237 0.969 0.996 0.000 0.004
#> GSM28826 1 0.0000 0.969 1.000 0.000 0.000
#> GSM28818 1 0.0237 0.969 0.996 0.000 0.004
#> GSM28821 2 0.2743 0.969 0.020 0.928 0.052
#> GSM28807 1 0.0237 0.969 0.996 0.000 0.004
#> GSM28822 1 0.0747 0.960 0.984 0.000 0.016
#> GSM11328 2 0.2636 0.971 0.020 0.932 0.048
#> GSM11323 1 0.0000 0.969 1.000 0.000 0.000
#> GSM11324 1 0.0000 0.969 1.000 0.000 0.000
#> GSM11341 1 0.4589 0.781 0.820 0.008 0.172
#> GSM11326 1 0.5835 0.481 0.660 0.000 0.340
#> GSM28810 1 0.0237 0.969 0.996 0.000 0.004
#> GSM11335 1 0.0000 0.969 1.000 0.000 0.000
#> GSM28809 1 0.0237 0.969 0.996 0.000 0.004
#> GSM11329 1 0.0237 0.969 0.996 0.000 0.004
#> GSM28805 1 0.0237 0.969 0.996 0.000 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.466 0.4755 0.652 0.000 0.000 0.348
#> GSM28816 1 0.466 0.4755 0.652 0.000 0.000 0.348
#> GSM28817 1 0.478 0.4569 0.624 0.000 0.000 0.376
#> GSM11327 1 0.607 -0.0524 0.668 0.000 0.104 0.228
#> GSM28825 2 0.000 0.9342 0.000 1.000 0.000 0.000
#> GSM11322 2 0.000 0.9342 0.000 1.000 0.000 0.000
#> GSM28828 2 0.265 0.8897 0.000 0.880 0.000 0.120
#> GSM11346 2 0.000 0.9342 0.000 1.000 0.000 0.000
#> GSM28808 2 0.000 0.9342 0.000 1.000 0.000 0.000
#> GSM11332 2 0.000 0.9342 0.000 1.000 0.000 0.000
#> GSM28811 2 0.336 0.8623 0.000 0.824 0.000 0.176
#> GSM11334 2 0.000 0.9342 0.000 1.000 0.000 0.000
#> GSM11340 2 0.000 0.9342 0.000 1.000 0.000 0.000
#> GSM28812 2 0.000 0.9342 0.000 1.000 0.000 0.000
#> GSM11345 1 0.247 0.4606 0.892 0.000 0.000 0.108
#> GSM28819 1 0.253 0.4579 0.888 0.000 0.000 0.112
#> GSM11321 3 0.222 0.9574 0.000 0.000 0.908 0.092
#> GSM28820 1 0.317 0.5417 0.840 0.000 0.000 0.160
#> GSM11339 1 0.478 0.4569 0.624 0.000 0.000 0.376
#> GSM28804 4 0.488 -0.3813 0.408 0.000 0.000 0.592
#> GSM28823 1 0.307 0.4056 0.848 0.000 0.000 0.152
#> GSM11336 1 0.464 0.4775 0.656 0.000 0.000 0.344
#> GSM11342 1 0.302 0.4095 0.852 0.000 0.000 0.148
#> GSM11333 1 0.466 0.4755 0.652 0.000 0.000 0.348
#> GSM28802 1 0.307 0.4056 0.848 0.000 0.000 0.152
#> GSM28803 3 0.222 0.9574 0.000 0.000 0.908 0.092
#> GSM11343 3 0.000 0.9580 0.000 0.000 1.000 0.000
#> GSM11347 3 0.000 0.9580 0.000 0.000 1.000 0.000
#> GSM28824 1 0.353 0.5334 0.808 0.000 0.000 0.192
#> GSM28813 1 0.361 0.3383 0.800 0.000 0.000 0.200
#> GSM28827 1 0.458 0.4359 0.668 0.000 0.000 0.332
#> GSM11337 1 0.452 0.4908 0.680 0.000 0.000 0.320
#> GSM28814 3 0.228 0.9561 0.000 0.000 0.904 0.096
#> GSM11331 1 0.130 0.4940 0.956 0.000 0.000 0.044
#> GSM11344 3 0.000 0.9580 0.000 0.000 1.000 0.000
#> GSM11330 3 0.000 0.9580 0.000 0.000 1.000 0.000
#> GSM11325 3 0.228 0.9561 0.000 0.000 0.904 0.096
#> GSM11338 1 0.201 0.5072 0.920 0.000 0.000 0.080
#> GSM28806 1 0.327 0.4319 0.832 0.000 0.000 0.168
#> GSM28826 1 0.265 0.5384 0.880 0.000 0.000 0.120
#> GSM28818 1 0.462 0.4784 0.660 0.000 0.000 0.340
#> GSM28821 2 0.554 0.6005 0.028 0.612 0.000 0.360
#> GSM28807 1 0.460 0.4797 0.664 0.000 0.000 0.336
#> GSM28822 1 0.460 0.0191 0.664 0.000 0.000 0.336
#> GSM11328 2 0.336 0.8623 0.000 0.824 0.000 0.176
#> GSM11323 1 0.130 0.4940 0.956 0.000 0.000 0.044
#> GSM11324 1 0.187 0.5425 0.928 0.000 0.000 0.072
#> GSM11341 4 0.503 0.0523 0.400 0.000 0.004 0.596
#> GSM11326 1 0.607 -0.0524 0.668 0.000 0.104 0.228
#> GSM28810 1 0.327 0.4349 0.832 0.000 0.000 0.168
#> GSM11335 1 0.179 0.4719 0.932 0.000 0.000 0.068
#> GSM28809 1 0.460 0.4797 0.664 0.000 0.000 0.336
#> GSM11329 1 0.473 0.4669 0.636 0.000 0.000 0.364
#> GSM28805 1 0.484 0.4243 0.604 0.000 0.000 0.396
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 4 0.370 0.7766 0.240 0.000 0.000 0.752 0.008
#> GSM28816 4 0.367 0.7774 0.236 0.000 0.000 0.756 0.008
#> GSM28817 4 0.409 0.6906 0.368 0.000 0.000 0.632 0.000
#> GSM11327 1 0.710 -0.0266 0.472 0.000 0.032 0.192 0.304
#> GSM28825 2 0.000 0.8723 0.000 1.000 0.000 0.000 0.000
#> GSM11322 2 0.000 0.8723 0.000 1.000 0.000 0.000 0.000
#> GSM28828 2 0.340 0.7623 0.000 0.780 0.000 0.004 0.216
#> GSM11346 2 0.000 0.8723 0.000 1.000 0.000 0.000 0.000
#> GSM28808 2 0.000 0.8723 0.000 1.000 0.000 0.000 0.000
#> GSM11332 2 0.000 0.8723 0.000 1.000 0.000 0.000 0.000
#> GSM28811 2 0.425 0.6822 0.000 0.672 0.000 0.012 0.316
#> GSM11334 2 0.000 0.8723 0.000 1.000 0.000 0.000 0.000
#> GSM11340 2 0.000 0.8723 0.000 1.000 0.000 0.000 0.000
#> GSM28812 2 0.000 0.8723 0.000 1.000 0.000 0.000 0.000
#> GSM11345 1 0.164 0.5947 0.932 0.000 0.000 0.064 0.004
#> GSM28819 1 0.164 0.5947 0.932 0.000 0.000 0.064 0.004
#> GSM11321 3 0.321 0.9121 0.000 0.000 0.844 0.036 0.120
#> GSM28820 1 0.391 0.2554 0.676 0.000 0.000 0.324 0.000
#> GSM11339 4 0.410 0.7225 0.332 0.000 0.000 0.664 0.004
#> GSM28804 4 0.606 0.4090 0.244 0.000 0.000 0.572 0.184
#> GSM28823 1 0.195 0.5521 0.912 0.000 0.000 0.004 0.084
#> GSM11336 4 0.405 0.7253 0.204 0.000 0.000 0.760 0.036
#> GSM11342 1 0.195 0.5521 0.912 0.000 0.000 0.004 0.084
#> GSM11333 4 0.397 0.7785 0.236 0.000 0.000 0.744 0.020
#> GSM28802 1 0.185 0.5547 0.912 0.000 0.000 0.000 0.088
#> GSM28803 3 0.300 0.9139 0.000 0.000 0.856 0.028 0.116
#> GSM11343 3 0.000 0.9168 0.000 0.000 1.000 0.000 0.000
#> GSM11347 3 0.000 0.9168 0.000 0.000 1.000 0.000 0.000
#> GSM28824 4 0.549 0.2105 0.372 0.000 0.000 0.556 0.072
#> GSM28813 1 0.654 0.1514 0.480 0.000 0.000 0.248 0.272
#> GSM28827 1 0.402 0.0210 0.652 0.000 0.000 0.348 0.000
#> GSM11337 4 0.417 0.5750 0.396 0.000 0.000 0.604 0.000
#> GSM28814 3 0.321 0.9121 0.000 0.000 0.844 0.036 0.120
#> GSM11331 1 0.475 0.5614 0.724 0.000 0.000 0.184 0.092
#> GSM11344 3 0.000 0.9168 0.000 0.000 1.000 0.000 0.000
#> GSM11330 3 0.000 0.9168 0.000 0.000 1.000 0.000 0.000
#> GSM11325 3 0.321 0.9121 0.000 0.000 0.844 0.036 0.120
#> GSM11338 1 0.454 0.5108 0.712 0.000 0.000 0.240 0.048
#> GSM28806 1 0.324 0.5468 0.848 0.000 0.000 0.048 0.104
#> GSM28826 1 0.451 0.4252 0.676 0.000 0.000 0.296 0.028
#> GSM28818 4 0.385 0.7769 0.232 0.000 0.000 0.752 0.016
#> GSM28821 2 0.701 0.2939 0.012 0.420 0.000 0.248 0.320
#> GSM28807 4 0.402 0.7681 0.220 0.000 0.000 0.752 0.028
#> GSM28822 1 0.650 -0.2687 0.464 0.000 0.000 0.204 0.332
#> GSM11328 2 0.423 0.6856 0.000 0.676 0.000 0.012 0.312
#> GSM11323 1 0.475 0.5614 0.724 0.000 0.000 0.184 0.092
#> GSM11324 1 0.340 0.4501 0.764 0.000 0.000 0.236 0.000
#> GSM11341 5 0.517 0.0000 0.240 0.000 0.000 0.092 0.668
#> GSM11326 1 0.710 -0.0266 0.472 0.000 0.032 0.192 0.304
#> GSM28810 1 0.359 0.5400 0.828 0.000 0.000 0.088 0.084
#> GSM11335 1 0.460 0.5657 0.744 0.000 0.000 0.156 0.100
#> GSM28809 4 0.385 0.7704 0.220 0.000 0.000 0.760 0.020
#> GSM11329 4 0.430 0.4369 0.488 0.000 0.000 0.512 0.000
#> GSM28805 1 0.448 -0.2471 0.576 0.000 0.000 0.416 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 4 0.205 0.6780 0.028 0.000 0.000 0.912 0.004 0.056
#> GSM28816 4 0.205 0.6780 0.028 0.000 0.000 0.912 0.004 0.056
#> GSM28817 4 0.370 0.4124 0.272 0.000 0.000 0.712 0.000 0.016
#> GSM11327 5 0.454 0.6942 0.200 0.000 0.008 0.084 0.708 0.000
#> GSM28825 2 0.000 0.8324 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11322 2 0.000 0.8324 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28828 2 0.362 0.4669 0.016 0.756 0.000 0.000 0.008 0.220
#> GSM11346 2 0.000 0.8324 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28808 2 0.000 0.8324 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11332 2 0.000 0.8324 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28811 2 0.397 -0.0243 0.008 0.604 0.000 0.000 0.000 0.388
#> GSM11334 2 0.000 0.8324 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11340 2 0.000 0.8324 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28812 2 0.000 0.8324 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11345 1 0.423 0.6506 0.728 0.000 0.000 0.200 0.068 0.004
#> GSM28819 1 0.423 0.6506 0.728 0.000 0.000 0.200 0.068 0.004
#> GSM11321 3 0.441 0.8503 0.012 0.000 0.712 0.000 0.056 0.220
#> GSM28820 1 0.463 0.4673 0.556 0.000 0.000 0.400 0.044 0.000
#> GSM11339 4 0.337 0.5203 0.208 0.000 0.000 0.772 0.000 0.020
#> GSM28804 4 0.653 0.2333 0.192 0.000 0.000 0.532 0.076 0.200
#> GSM28823 1 0.334 0.6058 0.812 0.000 0.000 0.132 0.000 0.056
#> GSM11336 4 0.338 0.6132 0.004 0.000 0.000 0.820 0.112 0.064
#> GSM11342 1 0.334 0.6058 0.812 0.000 0.000 0.132 0.000 0.056
#> GSM11333 4 0.180 0.6903 0.024 0.000 0.000 0.932 0.020 0.024
#> GSM28802 1 0.285 0.6258 0.840 0.000 0.000 0.140 0.004 0.016
#> GSM28803 3 0.436 0.8529 0.016 0.000 0.728 0.000 0.056 0.200
#> GSM11343 3 0.000 0.8556 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11347 3 0.000 0.8556 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM28824 4 0.557 0.3213 0.060 0.000 0.000 0.632 0.228 0.080
#> GSM28813 5 0.526 0.6472 0.184 0.000 0.000 0.132 0.660 0.024
#> GSM28827 1 0.418 0.4548 0.600 0.000 0.000 0.384 0.012 0.004
#> GSM11337 4 0.423 0.0637 0.344 0.000 0.000 0.632 0.020 0.004
#> GSM28814 3 0.447 0.8501 0.016 0.000 0.712 0.000 0.056 0.216
#> GSM11331 1 0.576 0.4399 0.500 0.000 0.000 0.208 0.292 0.000
#> GSM11344 3 0.000 0.8556 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11330 3 0.000 0.8556 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11325 3 0.441 0.8503 0.012 0.000 0.712 0.000 0.056 0.220
#> GSM11338 1 0.628 0.4445 0.492 0.000 0.000 0.252 0.232 0.024
#> GSM28806 1 0.423 0.5740 0.748 0.000 0.000 0.160 0.008 0.084
#> GSM28826 1 0.610 0.4998 0.480 0.000 0.000 0.336 0.164 0.020
#> GSM28818 4 0.171 0.6902 0.020 0.000 0.000 0.936 0.028 0.016
#> GSM28821 6 0.584 0.0000 0.000 0.356 0.000 0.196 0.000 0.448
#> GSM28807 4 0.186 0.6819 0.004 0.000 0.000 0.924 0.040 0.032
#> GSM28822 1 0.705 -0.2600 0.368 0.000 0.000 0.096 0.172 0.364
#> GSM11328 2 0.375 -0.0312 0.000 0.604 0.000 0.000 0.000 0.396
#> GSM11323 1 0.576 0.4399 0.500 0.000 0.000 0.208 0.292 0.000
#> GSM11324 1 0.450 0.5765 0.624 0.000 0.000 0.328 0.048 0.000
#> GSM11341 5 0.543 0.1069 0.140 0.000 0.000 0.000 0.540 0.320
#> GSM11326 5 0.454 0.6942 0.200 0.000 0.008 0.084 0.708 0.000
#> GSM28810 1 0.365 0.6101 0.748 0.000 0.000 0.228 0.004 0.020
#> GSM11335 1 0.586 0.4190 0.500 0.000 0.000 0.196 0.300 0.004
#> GSM28809 4 0.179 0.6827 0.004 0.000 0.000 0.928 0.040 0.028
#> GSM11329 4 0.431 -0.1376 0.436 0.000 0.000 0.544 0.000 0.020
#> GSM28805 1 0.433 0.2904 0.520 0.000 0.000 0.460 0.000 0.020
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> ATC:kmeans 46 0.389 2
#> ATC:kmeans 52 0.372 3
#> ATC:kmeans 25 0.394 4
#> ATC:kmeans 40 0.426 5
#> ATC:kmeans 35 0.397 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.704 0.824 0.914 0.4503 0.516 0.516
#> 3 3 0.916 0.920 0.969 0.3694 0.814 0.658
#> 4 4 0.816 0.795 0.906 0.2207 0.829 0.574
#> 5 5 0.784 0.760 0.868 0.0638 0.904 0.637
#> 6 6 0.802 0.655 0.799 0.0310 0.987 0.930
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
#> GSM28815 1 0.000 0.956 1.000 0.000
#> GSM28816 1 0.929 0.412 0.656 0.344
#> GSM28817 1 0.000 0.956 1.000 0.000
#> GSM11327 1 0.000 0.956 1.000 0.000
#> GSM28825 2 0.000 0.797 0.000 1.000
#> GSM11322 2 0.000 0.797 0.000 1.000
#> GSM28828 2 0.000 0.797 0.000 1.000
#> GSM11346 2 0.000 0.797 0.000 1.000
#> GSM28808 2 0.000 0.797 0.000 1.000
#> GSM11332 2 0.000 0.797 0.000 1.000
#> GSM28811 2 0.000 0.797 0.000 1.000
#> GSM11334 2 0.000 0.797 0.000 1.000
#> GSM11340 2 0.000 0.797 0.000 1.000
#> GSM28812 2 0.000 0.797 0.000 1.000
#> GSM11345 1 0.000 0.956 1.000 0.000
#> GSM28819 1 0.000 0.956 1.000 0.000
#> GSM11321 2 0.973 0.575 0.404 0.596
#> GSM28820 1 0.000 0.956 1.000 0.000
#> GSM11339 1 0.000 0.956 1.000 0.000
#> GSM28804 1 0.973 0.285 0.596 0.404
#> GSM28823 1 0.000 0.956 1.000 0.000
#> GSM11336 1 0.000 0.956 1.000 0.000
#> GSM11342 1 0.000 0.956 1.000 0.000
#> GSM11333 1 0.000 0.956 1.000 0.000
#> GSM28802 1 0.000 0.956 1.000 0.000
#> GSM28803 2 0.973 0.575 0.404 0.596
#> GSM11343 2 0.973 0.575 0.404 0.596
#> GSM11347 2 0.973 0.575 0.404 0.596
#> GSM28824 1 0.000 0.956 1.000 0.000
#> GSM28813 1 0.000 0.956 1.000 0.000
#> GSM28827 1 0.000 0.956 1.000 0.000
#> GSM11337 1 0.000 0.956 1.000 0.000
#> GSM28814 2 0.973 0.575 0.404 0.596
#> GSM11331 1 0.000 0.956 1.000 0.000
#> GSM11344 2 0.973 0.575 0.404 0.596
#> GSM11330 2 0.973 0.575 0.404 0.596
#> GSM11325 2 0.973 0.575 0.404 0.596
#> GSM11338 1 0.000 0.956 1.000 0.000
#> GSM28806 1 0.000 0.956 1.000 0.000
#> GSM28826 1 0.000 0.956 1.000 0.000
#> GSM28818 1 0.000 0.956 1.000 0.000
#> GSM28821 2 0.000 0.797 0.000 1.000
#> GSM28807 1 0.000 0.956 1.000 0.000
#> GSM28822 1 0.913 0.290 0.672 0.328
#> GSM11328 2 0.000 0.797 0.000 1.000
#> GSM11323 1 0.000 0.956 1.000 0.000
#> GSM11324 1 0.000 0.956 1.000 0.000
#> GSM11341 2 0.900 0.644 0.316 0.684
#> GSM11326 1 0.000 0.956 1.000 0.000
#> GSM28810 1 0.000 0.956 1.000 0.000
#> GSM11335 1 0.000 0.956 1.000 0.000
#> GSM28809 1 0.000 0.956 1.000 0.000
#> GSM11329 1 0.000 0.956 1.000 0.000
#> GSM28805 1 0.000 0.956 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.000 0.9663 1.000 0.000 0.000
#> GSM28816 1 0.000 0.9663 1.000 0.000 0.000
#> GSM28817 1 0.000 0.9663 1.000 0.000 0.000
#> GSM11327 3 0.000 0.9653 0.000 0.000 1.000
#> GSM28825 2 0.000 0.9487 0.000 1.000 0.000
#> GSM11322 2 0.000 0.9487 0.000 1.000 0.000
#> GSM28828 2 0.000 0.9487 0.000 1.000 0.000
#> GSM11346 2 0.000 0.9487 0.000 1.000 0.000
#> GSM28808 2 0.000 0.9487 0.000 1.000 0.000
#> GSM11332 2 0.000 0.9487 0.000 1.000 0.000
#> GSM28811 2 0.000 0.9487 0.000 1.000 0.000
#> GSM11334 2 0.000 0.9487 0.000 1.000 0.000
#> GSM11340 2 0.000 0.9487 0.000 1.000 0.000
#> GSM28812 2 0.000 0.9487 0.000 1.000 0.000
#> GSM11345 1 0.175 0.9278 0.952 0.000 0.048
#> GSM28819 1 0.375 0.8334 0.856 0.000 0.144
#> GSM11321 3 0.000 0.9653 0.000 0.000 1.000
#> GSM28820 1 0.000 0.9663 1.000 0.000 0.000
#> GSM11339 1 0.000 0.9663 1.000 0.000 0.000
#> GSM28804 2 0.630 0.0999 0.476 0.524 0.000
#> GSM28823 1 0.400 0.8152 0.840 0.000 0.160
#> GSM11336 1 0.000 0.9663 1.000 0.000 0.000
#> GSM11342 1 0.000 0.9663 1.000 0.000 0.000
#> GSM11333 1 0.000 0.9663 1.000 0.000 0.000
#> GSM28802 1 0.400 0.8152 0.840 0.000 0.160
#> GSM28803 3 0.000 0.9653 0.000 0.000 1.000
#> GSM11343 3 0.000 0.9653 0.000 0.000 1.000
#> GSM11347 3 0.000 0.9653 0.000 0.000 1.000
#> GSM28824 1 0.000 0.9663 1.000 0.000 0.000
#> GSM28813 1 0.608 0.3992 0.612 0.000 0.388
#> GSM28827 1 0.000 0.9663 1.000 0.000 0.000
#> GSM11337 1 0.000 0.9663 1.000 0.000 0.000
#> GSM28814 3 0.000 0.9653 0.000 0.000 1.000
#> GSM11331 1 0.000 0.9663 1.000 0.000 0.000
#> GSM11344 3 0.000 0.9653 0.000 0.000 1.000
#> GSM11330 3 0.000 0.9653 0.000 0.000 1.000
#> GSM11325 3 0.000 0.9653 0.000 0.000 1.000
#> GSM11338 1 0.000 0.9663 1.000 0.000 0.000
#> GSM28806 1 0.000 0.9663 1.000 0.000 0.000
#> GSM28826 1 0.000 0.9663 1.000 0.000 0.000
#> GSM28818 1 0.000 0.9663 1.000 0.000 0.000
#> GSM28821 2 0.000 0.9487 0.000 1.000 0.000
#> GSM28807 1 0.000 0.9663 1.000 0.000 0.000
#> GSM28822 3 0.556 0.5687 0.300 0.000 0.700
#> GSM11328 2 0.000 0.9487 0.000 1.000 0.000
#> GSM11323 1 0.000 0.9663 1.000 0.000 0.000
#> GSM11324 1 0.000 0.9663 1.000 0.000 0.000
#> GSM11341 3 0.000 0.9653 0.000 0.000 1.000
#> GSM11326 3 0.000 0.9653 0.000 0.000 1.000
#> GSM28810 1 0.000 0.9663 1.000 0.000 0.000
#> GSM11335 1 0.000 0.9663 1.000 0.000 0.000
#> GSM28809 1 0.000 0.9663 1.000 0.000 0.000
#> GSM11329 1 0.000 0.9663 1.000 0.000 0.000
#> GSM28805 1 0.000 0.9663 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 4 0.0188 0.8150 0.004 0.000 0.000 0.996
#> GSM28816 4 0.0188 0.8150 0.004 0.000 0.000 0.996
#> GSM28817 4 0.4877 0.0499 0.408 0.000 0.000 0.592
#> GSM11327 3 0.0376 0.9926 0.004 0.000 0.992 0.004
#> GSM28825 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11345 1 0.0000 0.7664 1.000 0.000 0.000 0.000
#> GSM28819 1 0.0000 0.7664 1.000 0.000 0.000 0.000
#> GSM11321 3 0.0000 0.9984 0.000 0.000 1.000 0.000
#> GSM28820 1 0.4679 0.5753 0.648 0.000 0.000 0.352
#> GSM11339 4 0.1637 0.7768 0.060 0.000 0.000 0.940
#> GSM28804 4 0.4966 0.6215 0.156 0.076 0.000 0.768
#> GSM28823 1 0.0188 0.7674 0.996 0.000 0.000 0.004
#> GSM11336 4 0.0000 0.8142 0.000 0.000 0.000 1.000
#> GSM11342 1 0.0188 0.7674 0.996 0.000 0.000 0.004
#> GSM11333 4 0.0188 0.8150 0.004 0.000 0.000 0.996
#> GSM28802 1 0.0188 0.7674 0.996 0.000 0.000 0.004
#> GSM28803 3 0.0000 0.9984 0.000 0.000 1.000 0.000
#> GSM11343 3 0.0000 0.9984 0.000 0.000 1.000 0.000
#> GSM11347 3 0.0000 0.9984 0.000 0.000 1.000 0.000
#> GSM28824 4 0.1118 0.7909 0.036 0.000 0.000 0.964
#> GSM28813 4 0.7514 -0.1800 0.384 0.000 0.184 0.432
#> GSM28827 1 0.1716 0.7633 0.936 0.000 0.000 0.064
#> GSM11337 1 0.4994 0.3641 0.520 0.000 0.000 0.480
#> GSM28814 3 0.0000 0.9984 0.000 0.000 1.000 0.000
#> GSM11331 1 0.3266 0.7521 0.832 0.000 0.000 0.168
#> GSM11344 3 0.0000 0.9984 0.000 0.000 1.000 0.000
#> GSM11330 3 0.0000 0.9984 0.000 0.000 1.000 0.000
#> GSM11325 3 0.0000 0.9984 0.000 0.000 1.000 0.000
#> GSM11338 1 0.4877 0.4930 0.592 0.000 0.000 0.408
#> GSM28806 1 0.4605 0.2781 0.664 0.000 0.000 0.336
#> GSM28826 1 0.4888 0.4860 0.588 0.000 0.000 0.412
#> GSM28818 4 0.0188 0.8150 0.004 0.000 0.000 0.996
#> GSM28821 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM28807 4 0.0000 0.8142 0.000 0.000 0.000 1.000
#> GSM28822 4 0.7629 0.3136 0.264 0.000 0.264 0.472
#> GSM11328 2 0.0000 1.0000 0.000 1.000 0.000 0.000
#> GSM11323 1 0.3266 0.7521 0.832 0.000 0.000 0.168
#> GSM11324 1 0.3219 0.7538 0.836 0.000 0.000 0.164
#> GSM11341 3 0.0000 0.9984 0.000 0.000 1.000 0.000
#> GSM11326 3 0.0376 0.9926 0.004 0.000 0.992 0.004
#> GSM28810 1 0.0188 0.7674 0.996 0.000 0.000 0.004
#> GSM11335 1 0.3266 0.7521 0.832 0.000 0.000 0.168
#> GSM28809 4 0.0000 0.8142 0.000 0.000 0.000 1.000
#> GSM11329 1 0.4761 0.5354 0.628 0.000 0.000 0.372
#> GSM28805 1 0.2011 0.7577 0.920 0.000 0.000 0.080
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 5 0.0865 0.8110 0.004 0.000 0.000 0.024 0.972
#> GSM28816 5 0.0865 0.8110 0.004 0.000 0.000 0.024 0.972
#> GSM28817 5 0.4437 0.6231 0.140 0.000 0.000 0.100 0.760
#> GSM11327 3 0.3430 0.7787 0.220 0.000 0.776 0.004 0.000
#> GSM28825 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM11345 1 0.3928 0.4770 0.700 0.000 0.000 0.296 0.004
#> GSM28819 1 0.3884 0.4867 0.708 0.000 0.000 0.288 0.004
#> GSM11321 3 0.0000 0.9539 0.000 0.000 1.000 0.000 0.000
#> GSM28820 1 0.5814 0.5726 0.584 0.000 0.000 0.128 0.288
#> GSM11339 5 0.2661 0.7671 0.056 0.000 0.000 0.056 0.888
#> GSM28804 5 0.4568 0.5284 0.020 0.008 0.000 0.288 0.684
#> GSM28823 4 0.2732 0.7124 0.160 0.000 0.000 0.840 0.000
#> GSM11336 5 0.1792 0.7869 0.084 0.000 0.000 0.000 0.916
#> GSM11342 4 0.2732 0.7124 0.160 0.000 0.000 0.840 0.000
#> GSM11333 5 0.0324 0.8135 0.004 0.000 0.000 0.004 0.992
#> GSM28802 4 0.2605 0.7134 0.148 0.000 0.000 0.852 0.000
#> GSM28803 3 0.0000 0.9539 0.000 0.000 1.000 0.000 0.000
#> GSM11343 3 0.0000 0.9539 0.000 0.000 1.000 0.000 0.000
#> GSM11347 3 0.0000 0.9539 0.000 0.000 1.000 0.000 0.000
#> GSM28824 5 0.4503 0.4696 0.312 0.000 0.000 0.024 0.664
#> GSM28813 1 0.3822 0.6301 0.808 0.000 0.020 0.020 0.152
#> GSM28827 4 0.5807 0.1627 0.424 0.000 0.000 0.484 0.092
#> GSM11337 1 0.4599 0.4941 0.600 0.000 0.000 0.016 0.384
#> GSM28814 3 0.0000 0.9539 0.000 0.000 1.000 0.000 0.000
#> GSM11331 1 0.2124 0.6992 0.916 0.000 0.000 0.056 0.028
#> GSM11344 3 0.0000 0.9539 0.000 0.000 1.000 0.000 0.000
#> GSM11330 3 0.0000 0.9539 0.000 0.000 1.000 0.000 0.000
#> GSM11325 3 0.0000 0.9539 0.000 0.000 1.000 0.000 0.000
#> GSM11338 1 0.3163 0.6961 0.824 0.000 0.000 0.012 0.164
#> GSM28806 4 0.2659 0.6818 0.060 0.000 0.000 0.888 0.052
#> GSM28826 1 0.3821 0.6898 0.764 0.000 0.000 0.020 0.216
#> GSM28818 5 0.0703 0.8135 0.024 0.000 0.000 0.000 0.976
#> GSM28821 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM28807 5 0.1205 0.8097 0.040 0.000 0.000 0.004 0.956
#> GSM28822 4 0.5979 0.3869 0.044 0.000 0.124 0.668 0.164
#> GSM11328 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM11323 1 0.2079 0.6930 0.916 0.000 0.000 0.064 0.020
#> GSM11324 1 0.5032 0.6409 0.704 0.000 0.000 0.128 0.168
#> GSM11341 3 0.0566 0.9440 0.004 0.000 0.984 0.012 0.000
#> GSM11326 3 0.3430 0.7787 0.220 0.000 0.776 0.004 0.000
#> GSM28810 4 0.2966 0.7000 0.136 0.000 0.000 0.848 0.016
#> GSM11335 1 0.1648 0.6946 0.940 0.000 0.000 0.040 0.020
#> GSM28809 5 0.0880 0.8120 0.032 0.000 0.000 0.000 0.968
#> GSM11329 5 0.6606 -0.0896 0.228 0.000 0.000 0.328 0.444
#> GSM28805 4 0.6759 0.1247 0.348 0.000 0.000 0.384 0.268
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 5 0.3775 0.4972 0.016 0.000 0.000 0.228 0.744 0.012
#> GSM28816 5 0.3568 0.5089 0.016 0.000 0.000 0.212 0.764 0.008
#> GSM28817 5 0.6534 0.3572 0.124 0.000 0.000 0.148 0.556 0.172
#> GSM11327 3 0.5044 0.5951 0.220 0.000 0.656 0.116 0.004 0.004
#> GSM28825 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28828 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11346 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28811 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11334 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11345 1 0.4443 0.4330 0.656 0.000 0.000 0.036 0.008 0.300
#> GSM28819 1 0.4506 0.4313 0.652 0.000 0.000 0.040 0.008 0.300
#> GSM11321 3 0.0000 0.9200 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM28820 1 0.6953 0.3212 0.428 0.000 0.000 0.092 0.312 0.168
#> GSM11339 5 0.5626 0.4482 0.064 0.000 0.000 0.176 0.648 0.112
#> GSM28804 4 0.4780 0.2889 0.000 0.016 0.000 0.588 0.364 0.032
#> GSM28823 6 0.0865 0.5968 0.036 0.000 0.000 0.000 0.000 0.964
#> GSM11336 5 0.3159 0.5409 0.072 0.000 0.000 0.084 0.840 0.004
#> GSM11342 6 0.0865 0.5968 0.036 0.000 0.000 0.000 0.000 0.964
#> GSM11333 5 0.1806 0.5917 0.000 0.000 0.000 0.088 0.908 0.004
#> GSM28802 6 0.1708 0.5917 0.024 0.000 0.000 0.040 0.004 0.932
#> GSM28803 3 0.0000 0.9200 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11343 3 0.0000 0.9200 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11347 3 0.0000 0.9200 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM28824 5 0.5043 0.3393 0.196 0.000 0.000 0.136 0.660 0.008
#> GSM28813 1 0.4937 0.5253 0.696 0.000 0.004 0.132 0.156 0.012
#> GSM28827 6 0.7240 0.0393 0.328 0.000 0.000 0.164 0.132 0.376
#> GSM11337 1 0.5770 0.3737 0.512 0.000 0.000 0.112 0.356 0.020
#> GSM28814 3 0.0000 0.9200 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11331 1 0.4152 0.5441 0.764 0.000 0.000 0.136 0.012 0.088
#> GSM11344 3 0.0000 0.9200 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11330 3 0.0000 0.9200 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11325 3 0.0000 0.9200 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11338 1 0.4573 0.5917 0.720 0.000 0.000 0.084 0.180 0.016
#> GSM28806 6 0.3157 0.4587 0.016 0.000 0.000 0.088 0.048 0.848
#> GSM28826 1 0.4385 0.5967 0.724 0.000 0.000 0.056 0.204 0.016
#> GSM28818 5 0.0508 0.6269 0.012 0.000 0.000 0.004 0.984 0.000
#> GSM28821 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28807 5 0.1485 0.6176 0.028 0.000 0.000 0.024 0.944 0.004
#> GSM28822 4 0.5468 0.3779 0.008 0.000 0.088 0.660 0.040 0.204
#> GSM11328 2 0.0000 1.0000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11323 1 0.4064 0.5512 0.772 0.000 0.000 0.132 0.012 0.084
#> GSM11324 1 0.6432 0.4592 0.564 0.000 0.000 0.100 0.164 0.172
#> GSM11341 3 0.1075 0.8829 0.000 0.000 0.952 0.048 0.000 0.000
#> GSM11326 3 0.4994 0.6047 0.212 0.000 0.664 0.116 0.004 0.004
#> GSM28810 6 0.5836 0.3743 0.100 0.000 0.000 0.320 0.036 0.544
#> GSM11335 1 0.2704 0.5716 0.876 0.000 0.000 0.076 0.012 0.036
#> GSM28809 5 0.1088 0.6246 0.024 0.000 0.000 0.016 0.960 0.000
#> GSM11329 5 0.7484 -0.1145 0.156 0.000 0.000 0.204 0.348 0.292
#> GSM28805 6 0.7641 0.1487 0.216 0.000 0.000 0.248 0.208 0.328
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> ATC:skmeans 51 0.395 2
#> ATC:skmeans 52 0.372 3
#> ATC:skmeans 47 0.436 4
#> ATC:skmeans 46 0.463 5
#> ATC:skmeans 38 0.520 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.3528 0.648 0.648
#> 3 3 1.000 1.000 1.000 0.5382 0.810 0.707
#> 4 4 0.786 0.937 0.925 0.0862 0.990 0.977
#> 5 5 0.695 0.844 0.875 0.1972 0.816 0.588
#> 6 6 0.780 0.813 0.889 0.0918 0.977 0.912
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
#> GSM28815 1 0 1 1 0
#> GSM28816 1 0 1 1 0
#> GSM28817 1 0 1 1 0
#> GSM11327 1 0 1 1 0
#> GSM28825 2 0 1 0 1
#> GSM11322 2 0 1 0 1
#> GSM28828 2 0 1 0 1
#> GSM11346 2 0 1 0 1
#> GSM28808 2 0 1 0 1
#> GSM11332 2 0 1 0 1
#> GSM28811 2 0 1 0 1
#> GSM11334 2 0 1 0 1
#> GSM11340 2 0 1 0 1
#> GSM28812 2 0 1 0 1
#> GSM11345 1 0 1 1 0
#> GSM28819 1 0 1 1 0
#> GSM11321 1 0 1 1 0
#> GSM28820 1 0 1 1 0
#> GSM11339 1 0 1 1 0
#> GSM28804 1 0 1 1 0
#> GSM28823 1 0 1 1 0
#> GSM11336 1 0 1 1 0
#> GSM11342 1 0 1 1 0
#> GSM11333 1 0 1 1 0
#> GSM28802 1 0 1 1 0
#> GSM28803 1 0 1 1 0
#> GSM11343 1 0 1 1 0
#> GSM11347 1 0 1 1 0
#> GSM28824 1 0 1 1 0
#> GSM28813 1 0 1 1 0
#> GSM28827 1 0 1 1 0
#> GSM11337 1 0 1 1 0
#> GSM28814 1 0 1 1 0
#> GSM11331 1 0 1 1 0
#> GSM11344 1 0 1 1 0
#> GSM11330 1 0 1 1 0
#> GSM11325 1 0 1 1 0
#> GSM11338 1 0 1 1 0
#> GSM28806 1 0 1 1 0
#> GSM28826 1 0 1 1 0
#> GSM28818 1 0 1 1 0
#> GSM28821 2 0 1 0 1
#> GSM28807 1 0 1 1 0
#> GSM28822 1 0 1 1 0
#> GSM11328 2 0 1 0 1
#> GSM11323 1 0 1 1 0
#> GSM11324 1 0 1 1 0
#> GSM11341 1 0 1 1 0
#> GSM11326 1 0 1 1 0
#> GSM28810 1 0 1 1 0
#> GSM11335 1 0 1 1 0
#> GSM28809 1 0 1 1 0
#> GSM11329 1 0 1 1 0
#> GSM28805 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0 1 1 0 0
#> GSM28816 1 0 1 1 0 0
#> GSM28817 1 0 1 1 0 0
#> GSM11327 1 0 1 1 0 0
#> GSM28825 2 0 1 0 1 0
#> GSM11322 2 0 1 0 1 0
#> GSM28828 2 0 1 0 1 0
#> GSM11346 2 0 1 0 1 0
#> GSM28808 2 0 1 0 1 0
#> GSM11332 2 0 1 0 1 0
#> GSM28811 2 0 1 0 1 0
#> GSM11334 2 0 1 0 1 0
#> GSM11340 2 0 1 0 1 0
#> GSM28812 2 0 1 0 1 0
#> GSM11345 1 0 1 1 0 0
#> GSM28819 1 0 1 1 0 0
#> GSM11321 3 0 1 0 0 1
#> GSM28820 1 0 1 1 0 0
#> GSM11339 1 0 1 1 0 0
#> GSM28804 1 0 1 1 0 0
#> GSM28823 1 0 1 1 0 0
#> GSM11336 1 0 1 1 0 0
#> GSM11342 1 0 1 1 0 0
#> GSM11333 1 0 1 1 0 0
#> GSM28802 1 0 1 1 0 0
#> GSM28803 3 0 1 0 0 1
#> GSM11343 3 0 1 0 0 1
#> GSM11347 3 0 1 0 0 1
#> GSM28824 1 0 1 1 0 0
#> GSM28813 1 0 1 1 0 0
#> GSM28827 1 0 1 1 0 0
#> GSM11337 1 0 1 1 0 0
#> GSM28814 3 0 1 0 0 1
#> GSM11331 1 0 1 1 0 0
#> GSM11344 3 0 1 0 0 1
#> GSM11330 3 0 1 0 0 1
#> GSM11325 3 0 1 0 0 1
#> GSM11338 1 0 1 1 0 0
#> GSM28806 1 0 1 1 0 0
#> GSM28826 1 0 1 1 0 0
#> GSM28818 1 0 1 1 0 0
#> GSM28821 2 0 1 0 1 0
#> GSM28807 1 0 1 1 0 0
#> GSM28822 1 0 1 1 0 0
#> GSM11328 2 0 1 0 1 0
#> GSM11323 1 0 1 1 0 0
#> GSM11324 1 0 1 1 0 0
#> GSM11341 1 0 1 1 0 0
#> GSM11326 1 0 1 1 0 0
#> GSM28810 1 0 1 1 0 0
#> GSM11335 1 0 1 1 0 0
#> GSM28809 1 0 1 1 0 0
#> GSM11329 1 0 1 1 0 0
#> GSM28805 1 0 1 1 0 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.2589 0.912 0.884 0.000 0.116 0.000
#> GSM28816 1 0.2589 0.912 0.884 0.000 0.116 0.000
#> GSM28817 1 0.2216 0.920 0.908 0.000 0.092 0.000
#> GSM11327 1 0.2149 0.908 0.912 0.000 0.088 0.000
#> GSM28825 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM11322 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM28828 2 0.0188 0.972 0.000 0.996 0.004 0.000
#> GSM11346 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM28808 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM11332 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM28811 2 0.1637 0.941 0.000 0.940 0.060 0.000
#> GSM11334 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM11340 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM28812 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM11345 1 0.1474 0.920 0.948 0.000 0.052 0.000
#> GSM28819 1 0.2149 0.908 0.912 0.000 0.088 0.000
#> GSM11321 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM28820 1 0.1211 0.922 0.960 0.000 0.040 0.000
#> GSM11339 1 0.2589 0.912 0.884 0.000 0.116 0.000
#> GSM28804 1 0.2589 0.912 0.884 0.000 0.116 0.000
#> GSM28823 1 0.1118 0.923 0.964 0.000 0.036 0.000
#> GSM11336 1 0.2921 0.913 0.860 0.000 0.140 0.000
#> GSM11342 1 0.0188 0.927 0.996 0.000 0.004 0.000
#> GSM11333 1 0.2589 0.912 0.884 0.000 0.116 0.000
#> GSM28802 1 0.0817 0.926 0.976 0.000 0.024 0.000
#> GSM28803 3 0.4164 1.000 0.000 0.000 0.736 0.264
#> GSM11343 3 0.4164 1.000 0.000 0.000 0.736 0.264
#> GSM11347 3 0.4164 1.000 0.000 0.000 0.736 0.264
#> GSM28824 1 0.2281 0.924 0.904 0.000 0.096 0.000
#> GSM28813 1 0.2149 0.908 0.912 0.000 0.088 0.000
#> GSM28827 1 0.1716 0.925 0.936 0.000 0.064 0.000
#> GSM11337 1 0.2149 0.908 0.912 0.000 0.088 0.000
#> GSM28814 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM11331 1 0.1716 0.925 0.936 0.000 0.064 0.000
#> GSM11344 3 0.4164 1.000 0.000 0.000 0.736 0.264
#> GSM11330 3 0.4164 1.000 0.000 0.000 0.736 0.264
#> GSM11325 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM11338 1 0.2149 0.908 0.912 0.000 0.088 0.000
#> GSM28806 1 0.2281 0.919 0.904 0.000 0.096 0.000
#> GSM28826 1 0.2149 0.908 0.912 0.000 0.088 0.000
#> GSM28818 1 0.2589 0.912 0.884 0.000 0.116 0.000
#> GSM28821 2 0.3539 0.802 0.004 0.820 0.176 0.000
#> GSM28807 1 0.2973 0.921 0.856 0.000 0.144 0.000
#> GSM28822 1 0.2589 0.912 0.884 0.000 0.116 0.000
#> GSM11328 2 0.1637 0.941 0.000 0.940 0.060 0.000
#> GSM11323 1 0.1118 0.928 0.964 0.000 0.036 0.000
#> GSM11324 1 0.0336 0.927 0.992 0.000 0.008 0.000
#> GSM11341 1 0.1940 0.913 0.924 0.000 0.076 0.000
#> GSM11326 1 0.2149 0.908 0.912 0.000 0.088 0.000
#> GSM28810 1 0.1716 0.925 0.936 0.000 0.064 0.000
#> GSM11335 1 0.1474 0.920 0.948 0.000 0.052 0.000
#> GSM28809 1 0.2281 0.919 0.904 0.000 0.096 0.000
#> GSM11329 1 0.2345 0.918 0.900 0.000 0.100 0.000
#> GSM28805 1 0.1792 0.924 0.932 0.000 0.068 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 1 0.0963 0.8625 0.964 0.000 0.0 0.00 0.036
#> GSM28816 1 0.0963 0.8625 0.964 0.000 0.0 0.00 0.036
#> GSM28817 1 0.0290 0.8721 0.992 0.000 0.0 0.00 0.008
#> GSM11327 5 0.3508 0.8594 0.252 0.000 0.0 0.00 0.748
#> GSM28825 2 0.0000 0.9485 0.000 1.000 0.0 0.00 0.000
#> GSM11322 2 0.0000 0.9485 0.000 1.000 0.0 0.00 0.000
#> GSM28828 2 0.0609 0.9406 0.000 0.980 0.0 0.02 0.000
#> GSM11346 2 0.0000 0.9485 0.000 1.000 0.0 0.00 0.000
#> GSM28808 2 0.0000 0.9485 0.000 1.000 0.0 0.00 0.000
#> GSM11332 2 0.0000 0.9485 0.000 1.000 0.0 0.00 0.000
#> GSM28811 2 0.3109 0.8397 0.000 0.800 0.0 0.20 0.000
#> GSM11334 2 0.0000 0.9485 0.000 1.000 0.0 0.00 0.000
#> GSM11340 2 0.0000 0.9485 0.000 1.000 0.0 0.00 0.000
#> GSM28812 2 0.0000 0.9485 0.000 1.000 0.0 0.00 0.000
#> GSM11345 1 0.3452 0.6068 0.756 0.000 0.0 0.00 0.244
#> GSM28819 5 0.3508 0.8594 0.252 0.000 0.0 0.00 0.748
#> GSM11321 4 0.3109 1.0000 0.000 0.000 0.2 0.80 0.000
#> GSM28820 5 0.4150 0.7187 0.388 0.000 0.0 0.00 0.612
#> GSM11339 1 0.0963 0.8625 0.964 0.000 0.0 0.00 0.036
#> GSM28804 1 0.0963 0.8625 0.964 0.000 0.0 0.00 0.036
#> GSM28823 5 0.4294 -0.0572 0.468 0.000 0.0 0.00 0.532
#> GSM11336 5 0.3837 0.7644 0.308 0.000 0.0 0.00 0.692
#> GSM11342 1 0.3895 0.5394 0.680 0.000 0.0 0.00 0.320
#> GSM11333 1 0.0963 0.8625 0.964 0.000 0.0 0.00 0.036
#> GSM28802 1 0.2561 0.7748 0.856 0.000 0.0 0.00 0.144
#> GSM28803 3 0.0000 1.0000 0.000 0.000 1.0 0.00 0.000
#> GSM11343 3 0.0000 1.0000 0.000 0.000 1.0 0.00 0.000
#> GSM11347 3 0.0000 1.0000 0.000 0.000 1.0 0.00 0.000
#> GSM28824 5 0.4278 0.6206 0.452 0.000 0.0 0.00 0.548
#> GSM28813 5 0.3508 0.8594 0.252 0.000 0.0 0.00 0.748
#> GSM28827 1 0.1121 0.8621 0.956 0.000 0.0 0.00 0.044
#> GSM11337 5 0.3534 0.8575 0.256 0.000 0.0 0.00 0.744
#> GSM28814 4 0.3109 1.0000 0.000 0.000 0.2 0.80 0.000
#> GSM11331 1 0.1121 0.8621 0.956 0.000 0.0 0.00 0.044
#> GSM11344 3 0.0000 1.0000 0.000 0.000 1.0 0.00 0.000
#> GSM11330 3 0.0000 1.0000 0.000 0.000 1.0 0.00 0.000
#> GSM11325 4 0.3109 1.0000 0.000 0.000 0.2 0.80 0.000
#> GSM11338 5 0.3508 0.8594 0.252 0.000 0.0 0.00 0.748
#> GSM28806 1 0.0290 0.8720 0.992 0.000 0.0 0.00 0.008
#> GSM28826 5 0.3508 0.8594 0.252 0.000 0.0 0.00 0.748
#> GSM28818 1 0.0880 0.8643 0.968 0.000 0.0 0.00 0.032
#> GSM28821 2 0.3266 0.8365 0.004 0.796 0.0 0.20 0.000
#> GSM28807 1 0.2516 0.7405 0.860 0.000 0.0 0.00 0.140
#> GSM28822 1 0.1043 0.8622 0.960 0.000 0.0 0.00 0.040
#> GSM11328 2 0.3109 0.8397 0.000 0.800 0.0 0.20 0.000
#> GSM11323 1 0.2891 0.7328 0.824 0.000 0.0 0.00 0.176
#> GSM11324 1 0.2377 0.7915 0.872 0.000 0.0 0.00 0.128
#> GSM11341 5 0.4114 0.7252 0.376 0.000 0.0 0.00 0.624
#> GSM11326 5 0.3508 0.8594 0.252 0.000 0.0 0.00 0.748
#> GSM28810 1 0.1121 0.8621 0.956 0.000 0.0 0.00 0.044
#> GSM11335 1 0.3452 0.6068 0.756 0.000 0.0 0.00 0.244
#> GSM28809 1 0.0404 0.8719 0.988 0.000 0.0 0.00 0.012
#> GSM11329 1 0.0000 0.8716 1.000 0.000 0.0 0.00 0.000
#> GSM28805 1 0.0963 0.8655 0.964 0.000 0.0 0.00 0.036
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 1 0.2597 0.765 0.824 0.000 0.000 0.176 0.000 0.000
#> GSM28816 1 0.2597 0.765 0.824 0.000 0.000 0.176 0.000 0.000
#> GSM28817 1 0.0291 0.833 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM11327 5 0.0000 0.855 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28825 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11322 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28828 2 0.0547 0.890 0.000 0.980 0.000 0.000 0.000 0.020
#> GSM11346 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28808 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11332 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28811 2 0.4887 0.676 0.000 0.660 0.000 0.156 0.000 0.184
#> GSM11334 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 0.899 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11345 1 0.3683 0.680 0.768 0.000 0.000 0.048 0.184 0.000
#> GSM28819 5 0.1434 0.841 0.012 0.000 0.000 0.048 0.940 0.000
#> GSM11321 6 0.2664 1.000 0.000 0.000 0.184 0.000 0.000 0.816
#> GSM28820 5 0.1387 0.819 0.068 0.000 0.000 0.000 0.932 0.000
#> GSM11339 1 0.2491 0.768 0.836 0.000 0.000 0.164 0.000 0.000
#> GSM28804 1 0.2597 0.765 0.824 0.000 0.000 0.176 0.000 0.000
#> GSM28823 4 0.4746 0.549 0.116 0.000 0.000 0.668 0.216 0.000
#> GSM11336 5 0.1434 0.832 0.048 0.000 0.000 0.012 0.940 0.000
#> GSM11342 4 0.3758 0.586 0.324 0.000 0.000 0.668 0.008 0.000
#> GSM11333 1 0.2848 0.763 0.816 0.000 0.000 0.176 0.008 0.000
#> GSM28802 1 0.3241 0.748 0.824 0.000 0.000 0.064 0.112 0.000
#> GSM28803 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11343 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11347 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM28824 5 0.3215 0.548 0.240 0.000 0.000 0.004 0.756 0.000
#> GSM28813 5 0.0000 0.855 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28827 1 0.1219 0.827 0.948 0.000 0.000 0.048 0.004 0.000
#> GSM11337 5 0.0865 0.852 0.036 0.000 0.000 0.000 0.964 0.000
#> GSM28814 6 0.2664 1.000 0.000 0.000 0.184 0.000 0.000 0.816
#> GSM11331 1 0.1219 0.827 0.948 0.000 0.000 0.048 0.004 0.000
#> GSM11344 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11330 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11325 6 0.2664 1.000 0.000 0.000 0.184 0.000 0.000 0.816
#> GSM11338 5 0.0363 0.857 0.012 0.000 0.000 0.000 0.988 0.000
#> GSM28806 1 0.1588 0.810 0.924 0.000 0.000 0.072 0.004 0.000
#> GSM28826 5 0.1434 0.841 0.012 0.000 0.000 0.048 0.940 0.000
#> GSM28818 1 0.1007 0.825 0.956 0.000 0.000 0.044 0.000 0.000
#> GSM28821 2 0.6166 0.478 0.024 0.504 0.000 0.288 0.000 0.184
#> GSM28807 1 0.1802 0.813 0.916 0.000 0.000 0.012 0.072 0.000
#> GSM28822 1 0.2597 0.765 0.824 0.000 0.000 0.176 0.000 0.000
#> GSM11328 2 0.4887 0.676 0.000 0.660 0.000 0.156 0.000 0.184
#> GSM11323 1 0.3044 0.756 0.836 0.000 0.000 0.048 0.116 0.000
#> GSM11324 1 0.3130 0.744 0.828 0.000 0.000 0.048 0.124 0.000
#> GSM11341 5 0.4497 0.247 0.328 0.000 0.000 0.048 0.624 0.000
#> GSM11326 5 0.0000 0.855 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM28810 1 0.1219 0.827 0.948 0.000 0.000 0.048 0.004 0.000
#> GSM11335 1 0.2996 0.662 0.772 0.000 0.000 0.000 0.228 0.000
#> GSM28809 1 0.1074 0.832 0.960 0.000 0.000 0.012 0.028 0.000
#> GSM11329 1 0.0291 0.832 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM28805 1 0.1219 0.830 0.948 0.000 0.000 0.048 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> ATC:pam 54 0.398 2
#> ATC:pam 54 0.374 3
#> ATC:pam 54 0.355 4
#> ATC:pam 53 0.402 5
#> ATC:pam 52 0.588 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.816 0.924 0.967 0.4065 0.591 0.591
#> 3 3 0.912 0.910 0.964 0.4151 0.781 0.645
#> 4 4 0.675 0.643 0.841 0.2128 0.884 0.733
#> 5 5 0.646 0.578 0.736 0.0873 0.897 0.692
#> 6 6 0.658 0.514 0.741 0.0520 0.850 0.495
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
#> GSM28815 1 0.7139 0.7581 0.804 0.196
#> GSM28816 1 0.7815 0.7024 0.768 0.232
#> GSM28817 1 0.0000 0.9737 1.000 0.000
#> GSM11327 1 0.0672 0.9708 0.992 0.008
#> GSM28825 2 0.0000 0.9364 0.000 1.000
#> GSM11322 2 0.0000 0.9364 0.000 1.000
#> GSM28828 2 0.0000 0.9364 0.000 1.000
#> GSM11346 2 0.0000 0.9364 0.000 1.000
#> GSM28808 2 0.0000 0.9364 0.000 1.000
#> GSM11332 2 0.0000 0.9364 0.000 1.000
#> GSM28811 2 0.0000 0.9364 0.000 1.000
#> GSM11334 2 0.0000 0.9364 0.000 1.000
#> GSM11340 2 0.0000 0.9364 0.000 1.000
#> GSM28812 2 0.0000 0.9364 0.000 1.000
#> GSM11345 1 0.0000 0.9737 1.000 0.000
#> GSM28819 1 0.0000 0.9737 1.000 0.000
#> GSM11321 1 0.0672 0.9708 0.992 0.008
#> GSM28820 1 0.0000 0.9737 1.000 0.000
#> GSM11339 1 0.7056 0.7637 0.808 0.192
#> GSM28804 2 0.6623 0.7825 0.172 0.828
#> GSM28823 1 0.0376 0.9718 0.996 0.004
#> GSM11336 1 0.0000 0.9737 1.000 0.000
#> GSM11342 1 0.0000 0.9737 1.000 0.000
#> GSM11333 1 0.5059 0.8671 0.888 0.112
#> GSM28802 1 0.0000 0.9737 1.000 0.000
#> GSM28803 1 0.0672 0.9708 0.992 0.008
#> GSM11343 1 0.0672 0.9708 0.992 0.008
#> GSM11347 1 0.0672 0.9708 0.992 0.008
#> GSM28824 1 0.0000 0.9737 1.000 0.000
#> GSM28813 1 0.0000 0.9737 1.000 0.000
#> GSM28827 1 0.0000 0.9737 1.000 0.000
#> GSM11337 1 0.0000 0.9737 1.000 0.000
#> GSM28814 1 0.0672 0.9708 0.992 0.008
#> GSM11331 1 0.0000 0.9737 1.000 0.000
#> GSM11344 1 0.0672 0.9708 0.992 0.008
#> GSM11330 1 0.0672 0.9708 0.992 0.008
#> GSM11325 1 0.0672 0.9708 0.992 0.008
#> GSM11338 1 0.0000 0.9737 1.000 0.000
#> GSM28806 1 0.0000 0.9737 1.000 0.000
#> GSM28826 1 0.0000 0.9737 1.000 0.000
#> GSM28818 1 0.4690 0.8804 0.900 0.100
#> GSM28821 2 0.0000 0.9364 0.000 1.000
#> GSM28807 1 0.0000 0.9737 1.000 0.000
#> GSM28822 2 0.9993 0.0643 0.484 0.516
#> GSM11328 2 0.0000 0.9364 0.000 1.000
#> GSM11323 1 0.0000 0.9737 1.000 0.000
#> GSM11324 1 0.0000 0.9737 1.000 0.000
#> GSM11341 2 0.7056 0.7541 0.192 0.808
#> GSM11326 1 0.0672 0.9708 0.992 0.008
#> GSM28810 1 0.0000 0.9737 1.000 0.000
#> GSM11335 1 0.0000 0.9737 1.000 0.000
#> GSM28809 1 0.0000 0.9737 1.000 0.000
#> GSM11329 1 0.0000 0.9737 1.000 0.000
#> GSM28805 1 0.0000 0.9737 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.0747 0.9620 0.984 0.000 0.016
#> GSM28816 1 0.1163 0.9530 0.972 0.000 0.028
#> GSM28817 1 0.0000 0.9709 1.000 0.000 0.000
#> GSM11327 1 0.5254 0.6657 0.736 0.000 0.264
#> GSM28825 2 0.0000 0.9273 0.000 1.000 0.000
#> GSM11322 2 0.0000 0.9273 0.000 1.000 0.000
#> GSM28828 2 0.0000 0.9273 0.000 1.000 0.000
#> GSM11346 2 0.0000 0.9273 0.000 1.000 0.000
#> GSM28808 2 0.0000 0.9273 0.000 1.000 0.000
#> GSM11332 2 0.0000 0.9273 0.000 1.000 0.000
#> GSM28811 2 0.0000 0.9273 0.000 1.000 0.000
#> GSM11334 2 0.0000 0.9273 0.000 1.000 0.000
#> GSM11340 2 0.0000 0.9273 0.000 1.000 0.000
#> GSM28812 2 0.0000 0.9273 0.000 1.000 0.000
#> GSM11345 1 0.0237 0.9715 0.996 0.000 0.004
#> GSM28819 1 0.0237 0.9715 0.996 0.000 0.004
#> GSM11321 3 0.0000 0.9443 0.000 0.000 1.000
#> GSM28820 1 0.0237 0.9715 0.996 0.000 0.004
#> GSM11339 1 0.0000 0.9709 1.000 0.000 0.000
#> GSM28804 2 0.7996 0.0534 0.464 0.476 0.060
#> GSM28823 1 0.0000 0.9709 1.000 0.000 0.000
#> GSM11336 1 0.0237 0.9715 0.996 0.000 0.004
#> GSM11342 1 0.0000 0.9709 1.000 0.000 0.000
#> GSM11333 1 0.0000 0.9709 1.000 0.000 0.000
#> GSM28802 1 0.0237 0.9715 0.996 0.000 0.004
#> GSM28803 3 0.0000 0.9443 0.000 0.000 1.000
#> GSM11343 3 0.0000 0.9443 0.000 0.000 1.000
#> GSM11347 3 0.0000 0.9443 0.000 0.000 1.000
#> GSM28824 1 0.1163 0.9557 0.972 0.000 0.028
#> GSM28813 1 0.1529 0.9462 0.960 0.000 0.040
#> GSM28827 1 0.0237 0.9715 0.996 0.000 0.004
#> GSM11337 1 0.0000 0.9709 1.000 0.000 0.000
#> GSM28814 3 0.0000 0.9443 0.000 0.000 1.000
#> GSM11331 1 0.0237 0.9715 0.996 0.000 0.004
#> GSM11344 3 0.0000 0.9443 0.000 0.000 1.000
#> GSM11330 3 0.0000 0.9443 0.000 0.000 1.000
#> GSM11325 3 0.0000 0.9443 0.000 0.000 1.000
#> GSM11338 1 0.0237 0.9715 0.996 0.000 0.004
#> GSM28806 1 0.0237 0.9715 0.996 0.000 0.004
#> GSM28826 1 0.0237 0.9715 0.996 0.000 0.004
#> GSM28818 1 0.0000 0.9709 1.000 0.000 0.000
#> GSM28821 2 0.2625 0.8235 0.084 0.916 0.000
#> GSM28807 1 0.0000 0.9709 1.000 0.000 0.000
#> GSM28822 1 0.5695 0.7738 0.804 0.120 0.076
#> GSM11328 2 0.0237 0.9240 0.004 0.996 0.000
#> GSM11323 1 0.0237 0.9715 0.996 0.000 0.004
#> GSM11324 1 0.0237 0.9715 0.996 0.000 0.004
#> GSM11341 3 0.8683 0.2999 0.120 0.340 0.540
#> GSM11326 1 0.5254 0.6657 0.736 0.000 0.264
#> GSM28810 1 0.0237 0.9715 0.996 0.000 0.004
#> GSM11335 1 0.0237 0.9715 0.996 0.000 0.004
#> GSM28809 1 0.0000 0.9709 1.000 0.000 0.000
#> GSM11329 1 0.0000 0.9709 1.000 0.000 0.000
#> GSM28805 1 0.0000 0.9709 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 4 0.4977 0.2954 0.460 0.000 0.000 0.540
#> GSM28816 4 0.4661 0.4125 0.348 0.000 0.000 0.652
#> GSM28817 1 0.4564 0.2329 0.672 0.000 0.000 0.328
#> GSM11327 1 0.4456 0.4765 0.716 0.000 0.004 0.280
#> GSM28825 2 0.0000 0.9615 0.000 1.000 0.000 0.000
#> GSM11322 2 0.0000 0.9615 0.000 1.000 0.000 0.000
#> GSM28828 2 0.3400 0.8323 0.000 0.820 0.000 0.180
#> GSM11346 2 0.0000 0.9615 0.000 1.000 0.000 0.000
#> GSM28808 2 0.0000 0.9615 0.000 1.000 0.000 0.000
#> GSM11332 2 0.0000 0.9615 0.000 1.000 0.000 0.000
#> GSM28811 2 0.3444 0.8290 0.000 0.816 0.000 0.184
#> GSM11334 2 0.0000 0.9615 0.000 1.000 0.000 0.000
#> GSM11340 2 0.0000 0.9615 0.000 1.000 0.000 0.000
#> GSM28812 2 0.0000 0.9615 0.000 1.000 0.000 0.000
#> GSM11345 1 0.0707 0.7003 0.980 0.000 0.000 0.020
#> GSM28819 1 0.0336 0.7001 0.992 0.000 0.000 0.008
#> GSM11321 3 0.0000 0.9873 0.000 0.000 1.000 0.000
#> GSM28820 1 0.0188 0.7005 0.996 0.000 0.000 0.004
#> GSM11339 1 0.4992 -0.2531 0.524 0.000 0.000 0.476
#> GSM28804 4 0.6635 0.0992 0.088 0.388 0.000 0.524
#> GSM28823 1 0.4855 0.1889 0.600 0.000 0.000 0.400
#> GSM11336 1 0.4134 0.5491 0.740 0.000 0.000 0.260
#> GSM11342 1 0.4855 0.1889 0.600 0.000 0.000 0.400
#> GSM11333 4 0.4981 0.2615 0.464 0.000 0.000 0.536
#> GSM28802 1 0.4500 0.3619 0.684 0.000 0.000 0.316
#> GSM28803 3 0.0817 0.9811 0.000 0.000 0.976 0.024
#> GSM11343 3 0.0000 0.9873 0.000 0.000 1.000 0.000
#> GSM11347 3 0.0592 0.9853 0.000 0.000 0.984 0.016
#> GSM28824 1 0.3649 0.5591 0.796 0.000 0.000 0.204
#> GSM28813 1 0.4250 0.4849 0.724 0.000 0.000 0.276
#> GSM28827 1 0.2149 0.6599 0.912 0.000 0.000 0.088
#> GSM11337 1 0.1867 0.6771 0.928 0.000 0.000 0.072
#> GSM28814 3 0.0000 0.9873 0.000 0.000 1.000 0.000
#> GSM11331 1 0.1637 0.6764 0.940 0.000 0.000 0.060
#> GSM11344 3 0.0592 0.9853 0.000 0.000 0.984 0.016
#> GSM11330 3 0.0188 0.9869 0.000 0.000 0.996 0.004
#> GSM11325 3 0.1302 0.9613 0.000 0.000 0.956 0.044
#> GSM11338 1 0.0707 0.7003 0.980 0.000 0.000 0.020
#> GSM28806 1 0.4713 0.2353 0.640 0.000 0.000 0.360
#> GSM28826 1 0.1022 0.6976 0.968 0.000 0.000 0.032
#> GSM28818 4 0.4941 0.3190 0.436 0.000 0.000 0.564
#> GSM28821 2 0.1302 0.9410 0.000 0.956 0.000 0.044
#> GSM28807 1 0.3311 0.6153 0.828 0.000 0.000 0.172
#> GSM28822 4 0.3942 0.4275 0.236 0.000 0.000 0.764
#> GSM11328 2 0.1211 0.9431 0.000 0.960 0.000 0.040
#> GSM11323 1 0.0188 0.6984 0.996 0.000 0.000 0.004
#> GSM11324 1 0.0188 0.7005 0.996 0.000 0.000 0.004
#> GSM11341 4 0.5410 0.1924 0.000 0.080 0.192 0.728
#> GSM11326 1 0.4456 0.4765 0.716 0.000 0.004 0.280
#> GSM28810 1 0.4222 0.4454 0.728 0.000 0.000 0.272
#> GSM11335 1 0.0336 0.6980 0.992 0.000 0.000 0.008
#> GSM28809 1 0.3569 0.6040 0.804 0.000 0.000 0.196
#> GSM11329 1 0.1716 0.6781 0.936 0.000 0.000 0.064
#> GSM28805 1 0.4661 0.1847 0.652 0.000 0.000 0.348
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 4 0.4893 0.1408 0.404 0.000 0.000 0.568 0.028
#> GSM28816 4 0.5552 0.2375 0.328 0.000 0.000 0.584 0.088
#> GSM28817 1 0.4434 0.4404 0.736 0.000 0.000 0.208 0.056
#> GSM11327 5 0.3783 0.8545 0.252 0.000 0.008 0.000 0.740
#> GSM28825 2 0.0162 0.9082 0.000 0.996 0.000 0.000 0.004
#> GSM11322 2 0.0000 0.9092 0.000 1.000 0.000 0.000 0.000
#> GSM28828 2 0.2006 0.8653 0.000 0.916 0.000 0.072 0.012
#> GSM11346 2 0.0000 0.9092 0.000 1.000 0.000 0.000 0.000
#> GSM28808 2 0.0324 0.9072 0.000 0.992 0.000 0.004 0.004
#> GSM11332 2 0.0000 0.9092 0.000 1.000 0.000 0.000 0.000
#> GSM28811 2 0.2006 0.8653 0.000 0.916 0.000 0.072 0.012
#> GSM11334 2 0.0000 0.9092 0.000 1.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 0.9092 0.000 1.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 0.9092 0.000 1.000 0.000 0.000 0.000
#> GSM11345 1 0.3565 0.5397 0.800 0.000 0.000 0.176 0.024
#> GSM28819 1 0.4104 0.5151 0.748 0.000 0.000 0.220 0.032
#> GSM11321 3 0.0162 0.9879 0.000 0.000 0.996 0.000 0.004
#> GSM28820 1 0.1082 0.5932 0.964 0.000 0.000 0.028 0.008
#> GSM11339 1 0.4867 0.1497 0.544 0.000 0.000 0.432 0.024
#> GSM28804 4 0.7512 0.3092 0.236 0.144 0.000 0.508 0.112
#> GSM28823 4 0.6366 0.1063 0.396 0.000 0.000 0.440 0.164
#> GSM11336 1 0.6621 -0.0262 0.428 0.000 0.000 0.224 0.348
#> GSM11342 4 0.6363 0.1109 0.392 0.000 0.000 0.444 0.164
#> GSM11333 4 0.5962 0.0476 0.424 0.000 0.000 0.468 0.108
#> GSM28802 1 0.4989 0.2567 0.552 0.000 0.000 0.416 0.032
#> GSM28803 3 0.0703 0.9841 0.000 0.000 0.976 0.000 0.024
#> GSM11343 3 0.0000 0.9888 0.000 0.000 1.000 0.000 0.000
#> GSM11347 3 0.0703 0.9841 0.000 0.000 0.976 0.000 0.024
#> GSM28824 5 0.4383 0.6979 0.424 0.000 0.000 0.004 0.572
#> GSM28813 5 0.4047 0.8445 0.320 0.000 0.000 0.004 0.676
#> GSM28827 1 0.3246 0.5081 0.808 0.000 0.000 0.184 0.008
#> GSM11337 1 0.2966 0.5263 0.816 0.000 0.000 0.184 0.000
#> GSM28814 3 0.0162 0.9889 0.000 0.000 0.996 0.000 0.004
#> GSM11331 1 0.1628 0.5712 0.936 0.000 0.000 0.056 0.008
#> GSM11344 3 0.0703 0.9841 0.000 0.000 0.976 0.000 0.024
#> GSM11330 3 0.0000 0.9888 0.000 0.000 1.000 0.000 0.000
#> GSM11325 3 0.0162 0.9879 0.000 0.000 0.996 0.000 0.004
#> GSM11338 1 0.1774 0.5826 0.932 0.000 0.000 0.052 0.016
#> GSM28806 1 0.5071 0.2267 0.540 0.000 0.000 0.424 0.036
#> GSM28826 1 0.0898 0.6009 0.972 0.000 0.000 0.020 0.008
#> GSM28818 4 0.6229 0.1875 0.320 0.000 0.000 0.516 0.164
#> GSM28821 2 0.7582 0.3520 0.144 0.504 0.000 0.228 0.124
#> GSM28807 1 0.6495 0.1103 0.480 0.000 0.000 0.216 0.304
#> GSM28822 4 0.7261 0.3116 0.204 0.068 0.008 0.556 0.164
#> GSM11328 2 0.6313 0.5734 0.036 0.612 0.000 0.228 0.124
#> GSM11323 1 0.0290 0.5968 0.992 0.000 0.000 0.008 0.000
#> GSM11324 1 0.0290 0.5984 0.992 0.000 0.000 0.008 0.000
#> GSM11341 4 0.7121 0.0485 0.000 0.156 0.068 0.540 0.236
#> GSM11326 5 0.3783 0.8545 0.252 0.000 0.008 0.000 0.740
#> GSM28810 1 0.4980 0.3064 0.584 0.000 0.000 0.380 0.036
#> GSM11335 1 0.0898 0.5913 0.972 0.000 0.000 0.020 0.008
#> GSM28809 1 0.6615 0.0556 0.444 0.000 0.000 0.232 0.324
#> GSM11329 1 0.3053 0.5248 0.828 0.000 0.000 0.164 0.008
#> GSM28805 1 0.5335 0.3540 0.644 0.000 0.000 0.260 0.096
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 1 0.3861 0.3982 0.672 0.000 0.000 0.316 0.004 0.008
#> GSM28816 1 0.5090 0.3743 0.592 0.000 0.000 0.336 0.048 0.024
#> GSM28817 4 0.3695 0.1421 0.376 0.000 0.000 0.624 0.000 0.000
#> GSM11327 5 0.0551 0.6861 0.004 0.000 0.008 0.000 0.984 0.004
#> GSM28825 2 0.0146 0.9188 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM11322 2 0.0000 0.9194 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28828 2 0.3266 0.6879 0.000 0.728 0.000 0.000 0.000 0.272
#> GSM11346 2 0.1866 0.8662 0.000 0.908 0.000 0.008 0.000 0.084
#> GSM28808 2 0.0260 0.9178 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM11332 2 0.0146 0.9180 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM28811 2 0.3490 0.6814 0.000 0.724 0.000 0.008 0.000 0.268
#> GSM11334 2 0.0000 0.9194 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11340 2 0.0000 0.9194 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 0.9194 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11345 1 0.3583 0.0566 0.728 0.000 0.000 0.260 0.004 0.008
#> GSM28819 1 0.3583 0.0562 0.728 0.000 0.000 0.260 0.004 0.008
#> GSM11321 3 0.1814 0.9103 0.000 0.000 0.900 0.000 0.000 0.100
#> GSM28820 1 0.3920 0.4505 0.768 0.000 0.000 0.120 0.112 0.000
#> GSM11339 1 0.4116 0.2432 0.572 0.000 0.000 0.416 0.000 0.012
#> GSM28804 4 0.6430 0.0303 0.364 0.036 0.000 0.448 0.004 0.148
#> GSM28823 6 0.5618 0.2028 0.160 0.000 0.000 0.340 0.000 0.500
#> GSM11336 1 0.5167 0.2376 0.564 0.000 0.000 0.060 0.360 0.016
#> GSM11342 6 0.5618 0.2028 0.160 0.000 0.000 0.340 0.000 0.500
#> GSM11333 1 0.4781 0.4159 0.644 0.000 0.000 0.276 0.076 0.004
#> GSM28802 4 0.5325 0.2457 0.392 0.000 0.000 0.500 0.000 0.108
#> GSM28803 3 0.0363 0.9500 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM11343 3 0.0000 0.9502 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11347 3 0.0363 0.9500 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM28824 5 0.4441 0.1844 0.344 0.000 0.004 0.032 0.620 0.000
#> GSM28813 5 0.2402 0.6816 0.140 0.000 0.004 0.000 0.856 0.000
#> GSM28827 4 0.4713 0.3552 0.320 0.000 0.000 0.620 0.056 0.004
#> GSM11337 1 0.2946 0.4583 0.808 0.000 0.000 0.184 0.004 0.004
#> GSM28814 3 0.1584 0.9273 0.000 0.000 0.928 0.008 0.000 0.064
#> GSM11331 1 0.3134 0.4171 0.820 0.000 0.000 0.036 0.144 0.000
#> GSM11344 3 0.0363 0.9500 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM11330 3 0.0000 0.9502 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM11325 3 0.2219 0.8788 0.000 0.000 0.864 0.000 0.000 0.136
#> GSM11338 1 0.2794 0.4278 0.840 0.000 0.000 0.012 0.144 0.004
#> GSM28806 1 0.4226 -0.3638 0.504 0.000 0.000 0.484 0.004 0.008
#> GSM28826 1 0.4059 0.4447 0.752 0.000 0.000 0.100 0.148 0.000
#> GSM28818 1 0.5375 0.4023 0.596 0.000 0.000 0.268 0.128 0.008
#> GSM28821 6 0.5369 0.4071 0.080 0.204 0.000 0.056 0.000 0.660
#> GSM28807 1 0.5727 0.3801 0.576 0.000 0.000 0.168 0.240 0.016
#> GSM28822 4 0.6769 0.1613 0.256 0.000 0.004 0.504 0.088 0.148
#> GSM11328 6 0.5003 0.3342 0.044 0.252 0.000 0.044 0.000 0.660
#> GSM11323 1 0.2869 0.4125 0.832 0.000 0.000 0.020 0.148 0.000
#> GSM11324 1 0.3062 0.4568 0.836 0.000 0.000 0.112 0.052 0.000
#> GSM11341 6 0.7382 0.3253 0.000 0.056 0.180 0.112 0.132 0.520
#> GSM11326 5 0.0696 0.6871 0.004 0.000 0.008 0.004 0.980 0.004
#> GSM28810 4 0.4165 0.3409 0.452 0.000 0.000 0.536 0.000 0.012
#> GSM11335 1 0.2886 0.4248 0.836 0.000 0.000 0.016 0.144 0.004
#> GSM28809 1 0.5104 0.2245 0.560 0.000 0.000 0.060 0.368 0.012
#> GSM11329 4 0.4732 0.3034 0.360 0.000 0.000 0.588 0.048 0.004
#> GSM28805 4 0.3956 0.4197 0.292 0.000 0.000 0.684 0.000 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> ATC:mclust 53 0.397 2
#> ATC:mclust 52 0.372 3
#> ATC:mclust 36 0.411 4
#> ATC:mclust 35 0.400 5
#> ATC:mclust 21 0.384 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 12150 rows and 54 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.970 0.988 0.3822 0.628 0.628
#> 3 3 1.000 0.973 0.990 0.5715 0.728 0.580
#> 4 4 0.824 0.893 0.935 0.2377 0.829 0.578
#> 5 5 0.724 0.709 0.835 0.0471 0.983 0.931
#> 6 6 0.722 0.679 0.813 0.0417 0.880 0.552
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
#> GSM28815 1 0.0376 0.982 0.996 0.004
#> GSM28816 1 0.9686 0.350 0.604 0.396
#> GSM28817 1 0.0376 0.982 0.996 0.004
#> GSM11327 1 0.0000 0.985 1.000 0.000
#> GSM28825 2 0.0000 0.993 0.000 1.000
#> GSM11322 2 0.0000 0.993 0.000 1.000
#> GSM28828 2 0.0000 0.993 0.000 1.000
#> GSM11346 2 0.0000 0.993 0.000 1.000
#> GSM28808 2 0.0000 0.993 0.000 1.000
#> GSM11332 2 0.0000 0.993 0.000 1.000
#> GSM28811 2 0.0000 0.993 0.000 1.000
#> GSM11334 2 0.0000 0.993 0.000 1.000
#> GSM11340 2 0.0000 0.993 0.000 1.000
#> GSM28812 2 0.0000 0.993 0.000 1.000
#> GSM11345 1 0.0000 0.985 1.000 0.000
#> GSM28819 1 0.0000 0.985 1.000 0.000
#> GSM11321 1 0.0000 0.985 1.000 0.000
#> GSM28820 1 0.0000 0.985 1.000 0.000
#> GSM11339 1 0.0376 0.982 0.996 0.004
#> GSM28804 2 0.4022 0.910 0.080 0.920
#> GSM28823 1 0.0000 0.985 1.000 0.000
#> GSM11336 1 0.0000 0.985 1.000 0.000
#> GSM11342 1 0.0000 0.985 1.000 0.000
#> GSM11333 1 0.0376 0.982 0.996 0.004
#> GSM28802 1 0.0000 0.985 1.000 0.000
#> GSM28803 1 0.0000 0.985 1.000 0.000
#> GSM11343 1 0.0000 0.985 1.000 0.000
#> GSM11347 1 0.0000 0.985 1.000 0.000
#> GSM28824 1 0.0000 0.985 1.000 0.000
#> GSM28813 1 0.0000 0.985 1.000 0.000
#> GSM28827 1 0.0000 0.985 1.000 0.000
#> GSM11337 1 0.0000 0.985 1.000 0.000
#> GSM28814 1 0.0000 0.985 1.000 0.000
#> GSM11331 1 0.0000 0.985 1.000 0.000
#> GSM11344 1 0.0000 0.985 1.000 0.000
#> GSM11330 1 0.0000 0.985 1.000 0.000
#> GSM11325 1 0.0000 0.985 1.000 0.000
#> GSM11338 1 0.0000 0.985 1.000 0.000
#> GSM28806 1 0.0000 0.985 1.000 0.000
#> GSM28826 1 0.0000 0.985 1.000 0.000
#> GSM28818 1 0.6801 0.777 0.820 0.180
#> GSM28821 2 0.0000 0.993 0.000 1.000
#> GSM28807 1 0.0000 0.985 1.000 0.000
#> GSM28822 1 0.0000 0.985 1.000 0.000
#> GSM11328 2 0.0000 0.993 0.000 1.000
#> GSM11323 1 0.0000 0.985 1.000 0.000
#> GSM11324 1 0.0000 0.985 1.000 0.000
#> GSM11341 1 0.0000 0.985 1.000 0.000
#> GSM11326 1 0.0000 0.985 1.000 0.000
#> GSM28810 1 0.0000 0.985 1.000 0.000
#> GSM11335 1 0.0000 0.985 1.000 0.000
#> GSM28809 1 0.0000 0.985 1.000 0.000
#> GSM11329 1 0.0000 0.985 1.000 0.000
#> GSM28805 1 0.0000 0.985 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM28815 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28816 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28817 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11327 3 0.0000 0.953 0.000 0.000 1.000
#> GSM28825 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11322 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28828 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11346 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28808 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11332 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28811 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11334 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11340 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28812 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11345 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28819 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11321 3 0.0000 0.953 0.000 0.000 1.000
#> GSM28820 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11339 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28804 1 0.0747 0.980 0.984 0.016 0.000
#> GSM28823 1 0.1163 0.970 0.972 0.000 0.028
#> GSM11336 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11342 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11333 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28802 1 0.1163 0.970 0.972 0.000 0.028
#> GSM28803 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11343 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11347 3 0.0000 0.953 0.000 0.000 1.000
#> GSM28824 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28813 1 0.2537 0.913 0.920 0.000 0.080
#> GSM28827 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11337 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28814 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11331 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11344 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11330 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11325 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11338 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28806 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28826 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28818 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28821 2 0.0000 1.000 0.000 1.000 0.000
#> GSM28807 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28822 3 0.6079 0.355 0.388 0.000 0.612
#> GSM11328 2 0.0000 1.000 0.000 1.000 0.000
#> GSM11323 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11324 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11341 3 0.0000 0.953 0.000 0.000 1.000
#> GSM11326 3 0.0000 0.953 0.000 0.000 1.000
#> GSM28810 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11335 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28809 1 0.0000 0.995 1.000 0.000 0.000
#> GSM11329 1 0.0000 0.995 1.000 0.000 0.000
#> GSM28805 1 0.0000 0.995 1.000 0.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM28815 1 0.3569 0.768 0.804 0.000 0.000 0.196
#> GSM28816 1 0.1940 0.901 0.924 0.000 0.000 0.076
#> GSM28817 4 0.4977 0.244 0.460 0.000 0.000 0.540
#> GSM11327 3 0.3123 0.845 0.156 0.000 0.844 0.000
#> GSM28825 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM11322 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM28828 2 0.0592 0.992 0.000 0.984 0.000 0.016
#> GSM11346 2 0.0188 0.996 0.000 0.996 0.000 0.004
#> GSM28808 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM11332 2 0.0188 0.995 0.000 0.996 0.000 0.004
#> GSM28811 2 0.0592 0.992 0.000 0.984 0.000 0.016
#> GSM11334 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM11340 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM28812 2 0.0000 0.996 0.000 1.000 0.000 0.000
#> GSM11345 4 0.3219 0.840 0.164 0.000 0.000 0.836
#> GSM28819 4 0.3881 0.832 0.172 0.000 0.016 0.812
#> GSM11321 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM28820 1 0.2973 0.839 0.856 0.000 0.000 0.144
#> GSM11339 4 0.4454 0.640 0.308 0.000 0.000 0.692
#> GSM28804 4 0.2831 0.847 0.120 0.004 0.000 0.876
#> GSM28823 4 0.1398 0.869 0.040 0.000 0.004 0.956
#> GSM11336 1 0.0188 0.917 0.996 0.000 0.000 0.004
#> GSM11342 4 0.1302 0.870 0.044 0.000 0.000 0.956
#> GSM11333 1 0.2281 0.889 0.904 0.000 0.000 0.096
#> GSM28802 4 0.1209 0.864 0.032 0.000 0.004 0.964
#> GSM28803 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM11343 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM11347 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM28824 1 0.0188 0.917 0.996 0.000 0.000 0.004
#> GSM28813 1 0.1489 0.876 0.952 0.000 0.044 0.004
#> GSM28827 4 0.2647 0.866 0.120 0.000 0.000 0.880
#> GSM11337 1 0.0707 0.921 0.980 0.000 0.000 0.020
#> GSM28814 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM11331 1 0.1302 0.916 0.956 0.000 0.000 0.044
#> GSM11344 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM11330 3 0.0000 0.964 0.000 0.000 1.000 0.000
#> GSM11325 3 0.0921 0.949 0.000 0.000 0.972 0.028
#> GSM11338 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> GSM28806 4 0.1302 0.870 0.044 0.000 0.000 0.956
#> GSM28826 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> GSM28818 1 0.1022 0.920 0.968 0.000 0.000 0.032
#> GSM28821 2 0.0592 0.992 0.000 0.984 0.000 0.016
#> GSM28807 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> GSM28822 4 0.3933 0.674 0.008 0.000 0.200 0.792
#> GSM11328 2 0.0336 0.995 0.000 0.992 0.000 0.008
#> GSM11323 1 0.2081 0.897 0.916 0.000 0.000 0.084
#> GSM11324 1 0.4431 0.550 0.696 0.000 0.000 0.304
#> GSM11341 3 0.0469 0.959 0.000 0.000 0.988 0.012
#> GSM11326 3 0.3074 0.846 0.152 0.000 0.848 0.000
#> GSM28810 4 0.1211 0.868 0.040 0.000 0.000 0.960
#> GSM11335 1 0.1118 0.919 0.964 0.000 0.000 0.036
#> GSM28809 1 0.0000 0.919 1.000 0.000 0.000 0.000
#> GSM11329 4 0.2704 0.864 0.124 0.000 0.000 0.876
#> GSM28805 4 0.2281 0.871 0.096 0.000 0.000 0.904
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM28815 5 0.6358 0.312 0.276 0.000 0.000 0.208 0.516
#> GSM28816 5 0.3861 0.755 0.128 0.000 0.000 0.068 0.804
#> GSM28817 1 0.4118 0.355 0.660 0.000 0.000 0.004 0.336
#> GSM11327 3 0.3513 0.712 0.000 0.000 0.800 0.020 0.180
#> GSM28825 2 0.0290 0.991 0.000 0.992 0.000 0.008 0.000
#> GSM11322 2 0.0162 0.991 0.004 0.996 0.000 0.000 0.000
#> GSM28828 2 0.1117 0.979 0.020 0.964 0.000 0.016 0.000
#> GSM11346 2 0.0451 0.991 0.004 0.988 0.000 0.008 0.000
#> GSM28808 2 0.0162 0.992 0.000 0.996 0.000 0.004 0.000
#> GSM11332 2 0.0162 0.991 0.004 0.996 0.000 0.000 0.000
#> GSM28811 2 0.0912 0.983 0.012 0.972 0.000 0.016 0.000
#> GSM11334 2 0.0000 0.991 0.000 1.000 0.000 0.000 0.000
#> GSM11340 2 0.0162 0.991 0.004 0.996 0.000 0.000 0.000
#> GSM28812 2 0.0162 0.992 0.000 0.996 0.000 0.004 0.000
#> GSM11345 1 0.3670 0.585 0.820 0.000 0.000 0.068 0.112
#> GSM28819 1 0.4695 0.566 0.780 0.000 0.040 0.084 0.096
#> GSM11321 3 0.1851 0.827 0.000 0.000 0.912 0.088 0.000
#> GSM28820 5 0.3863 0.663 0.248 0.000 0.000 0.012 0.740
#> GSM11339 1 0.5692 0.324 0.628 0.000 0.000 0.168 0.204
#> GSM28804 4 0.5611 0.656 0.344 0.012 0.000 0.584 0.060
#> GSM28823 1 0.4622 0.516 0.712 0.000 0.004 0.240 0.044
#> GSM11336 5 0.0693 0.790 0.008 0.000 0.000 0.012 0.980
#> GSM11342 1 0.4536 0.522 0.712 0.000 0.000 0.240 0.048
#> GSM11333 5 0.4803 0.645 0.096 0.000 0.000 0.184 0.720
#> GSM28802 1 0.3695 0.548 0.800 0.000 0.000 0.164 0.036
#> GSM28803 3 0.1197 0.847 0.000 0.000 0.952 0.048 0.000
#> GSM11343 3 0.0162 0.851 0.000 0.000 0.996 0.004 0.000
#> GSM11347 3 0.0290 0.851 0.000 0.000 0.992 0.008 0.000
#> GSM28824 5 0.0451 0.790 0.004 0.000 0.000 0.008 0.988
#> GSM28813 5 0.2104 0.726 0.000 0.000 0.060 0.024 0.916
#> GSM28827 1 0.2362 0.603 0.900 0.000 0.000 0.024 0.076
#> GSM11337 5 0.3409 0.769 0.160 0.000 0.000 0.024 0.816
#> GSM28814 3 0.1197 0.846 0.000 0.000 0.952 0.048 0.000
#> GSM11331 5 0.3851 0.708 0.212 0.000 0.004 0.016 0.768
#> GSM11344 3 0.0404 0.851 0.000 0.000 0.988 0.012 0.000
#> GSM11330 3 0.1410 0.842 0.000 0.000 0.940 0.060 0.000
#> GSM11325 3 0.4065 0.664 0.016 0.000 0.720 0.264 0.000
#> GSM11338 5 0.0960 0.795 0.016 0.000 0.004 0.008 0.972
#> GSM28806 1 0.5185 0.363 0.596 0.000 0.008 0.360 0.036
#> GSM28826 5 0.0693 0.797 0.012 0.000 0.000 0.008 0.980
#> GSM28818 5 0.2233 0.796 0.080 0.000 0.000 0.016 0.904
#> GSM28821 2 0.0510 0.987 0.016 0.984 0.000 0.000 0.000
#> GSM28807 5 0.0693 0.795 0.008 0.000 0.000 0.012 0.980
#> GSM28822 4 0.4985 0.707 0.244 0.000 0.076 0.680 0.000
#> GSM11328 2 0.0451 0.991 0.004 0.988 0.000 0.008 0.000
#> GSM11323 5 0.4445 0.623 0.300 0.000 0.000 0.024 0.676
#> GSM11324 5 0.4561 0.148 0.488 0.000 0.000 0.008 0.504
#> GSM11341 3 0.4151 0.522 0.000 0.000 0.652 0.344 0.004
#> GSM11326 3 0.4167 0.607 0.000 0.000 0.724 0.024 0.252
#> GSM28810 1 0.4824 -0.462 0.512 0.000 0.000 0.468 0.020
#> GSM11335 5 0.4618 0.733 0.192 0.000 0.024 0.036 0.748
#> GSM28809 5 0.0671 0.797 0.016 0.000 0.000 0.004 0.980
#> GSM11329 1 0.2795 0.613 0.872 0.000 0.000 0.028 0.100
#> GSM28805 1 0.4252 0.469 0.764 0.000 0.000 0.172 0.064
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM28815 1 0.6074 0.1182 0.452 0.000 0.000 0.336 0.204 0.008
#> GSM28816 5 0.4524 0.4741 0.336 0.000 0.000 0.048 0.616 0.000
#> GSM28817 1 0.3054 0.6258 0.848 0.000 0.000 0.004 0.076 0.072
#> GSM11327 3 0.4486 0.6792 0.004 0.000 0.756 0.052 0.144 0.044
#> GSM28825 2 0.0520 0.9870 0.000 0.984 0.000 0.000 0.008 0.008
#> GSM11322 2 0.0000 0.9885 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28828 2 0.1232 0.9731 0.004 0.956 0.000 0.000 0.016 0.024
#> GSM11346 2 0.0520 0.9863 0.000 0.984 0.000 0.000 0.008 0.008
#> GSM28808 2 0.0146 0.9884 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM11332 2 0.0146 0.9878 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM28811 2 0.1049 0.9720 0.000 0.960 0.000 0.000 0.008 0.032
#> GSM11334 2 0.0146 0.9878 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM11340 2 0.0000 0.9885 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM28812 2 0.0000 0.9885 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM11345 1 0.3039 0.5950 0.868 0.000 0.008 0.040 0.020 0.064
#> GSM28819 1 0.4571 0.5168 0.760 0.000 0.052 0.072 0.004 0.112
#> GSM11321 3 0.4683 0.5037 0.000 0.000 0.616 0.064 0.000 0.320
#> GSM28820 1 0.4934 0.1602 0.488 0.000 0.000 0.004 0.456 0.052
#> GSM11339 1 0.3715 0.5987 0.800 0.000 0.000 0.132 0.052 0.016
#> GSM28804 4 0.3798 0.7357 0.216 0.000 0.000 0.748 0.032 0.004
#> GSM28823 6 0.4599 0.6463 0.328 0.000 0.000 0.028 0.016 0.628
#> GSM11336 5 0.1176 0.7992 0.024 0.000 0.000 0.000 0.956 0.020
#> GSM11342 6 0.4495 0.6384 0.340 0.000 0.000 0.020 0.016 0.624
#> GSM11333 5 0.5032 0.5871 0.216 0.000 0.000 0.132 0.648 0.004
#> GSM28802 6 0.4284 0.5003 0.392 0.000 0.000 0.016 0.004 0.588
#> GSM28803 3 0.2527 0.7937 0.000 0.000 0.884 0.064 0.004 0.048
#> GSM11343 3 0.0291 0.8023 0.000 0.000 0.992 0.004 0.000 0.004
#> GSM11347 3 0.1794 0.7987 0.000 0.000 0.924 0.036 0.000 0.040
#> GSM28824 5 0.1088 0.8005 0.024 0.000 0.000 0.000 0.960 0.016
#> GSM28813 5 0.3347 0.6998 0.004 0.000 0.072 0.040 0.848 0.036
#> GSM28827 1 0.2556 0.5476 0.864 0.000 0.000 0.008 0.008 0.120
#> GSM11337 1 0.4170 0.4396 0.648 0.000 0.000 0.020 0.328 0.004
#> GSM28814 3 0.1863 0.7970 0.000 0.000 0.920 0.044 0.000 0.036
#> GSM11331 1 0.5119 0.3897 0.580 0.000 0.008 0.040 0.356 0.016
#> GSM11344 3 0.1720 0.8003 0.000 0.000 0.928 0.032 0.000 0.040
#> GSM11330 3 0.3424 0.7566 0.000 0.000 0.812 0.092 0.000 0.096
#> GSM11325 6 0.5405 0.0567 0.004 0.000 0.292 0.132 0.000 0.572
#> GSM11338 5 0.2643 0.7979 0.108 0.000 0.004 0.016 0.868 0.004
#> GSM28806 6 0.3785 0.5790 0.136 0.000 0.012 0.020 0.028 0.804
#> GSM28826 5 0.2851 0.7881 0.132 0.000 0.000 0.020 0.844 0.004
#> GSM28818 5 0.3409 0.6000 0.300 0.000 0.000 0.000 0.700 0.000
#> GSM28821 2 0.0696 0.9846 0.004 0.980 0.000 0.004 0.008 0.004
#> GSM28807 5 0.1267 0.8109 0.060 0.000 0.000 0.000 0.940 0.000
#> GSM28822 4 0.3072 0.7319 0.084 0.000 0.036 0.856 0.000 0.024
#> GSM11328 2 0.0622 0.9860 0.000 0.980 0.000 0.000 0.012 0.008
#> GSM11323 1 0.3940 0.6369 0.772 0.000 0.004 0.048 0.168 0.008
#> GSM11324 1 0.2113 0.6585 0.896 0.000 0.000 0.008 0.092 0.004
#> GSM11341 3 0.5125 0.4057 0.000 0.000 0.556 0.360 0.004 0.080
#> GSM11326 3 0.4265 0.6962 0.012 0.000 0.776 0.060 0.132 0.020
#> GSM28810 1 0.4091 -0.1890 0.520 0.000 0.000 0.472 0.000 0.008
#> GSM11335 1 0.5677 0.5459 0.652 0.000 0.048 0.056 0.216 0.028
#> GSM28809 5 0.1814 0.8093 0.100 0.000 0.000 0.000 0.900 0.000
#> GSM11329 1 0.3229 0.4936 0.804 0.000 0.000 0.004 0.020 0.172
#> GSM28805 1 0.2264 0.6210 0.888 0.000 0.000 0.096 0.012 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n tissue(p) k
#> ATC:NMF 53 0.397 2
#> ATC:NMF 53 0.373 3
#> ATC:NMF 53 0.431 4
#> ATC:NMF 47 0.422 5
#> ATC:NMF 45 0.451 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