Date: 2019-12-25 20:34:43 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 51941 rows and 64 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] 51941 64
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:skmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:pam | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:mclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:skmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:pam | 2 | 1.000 | 0.998 | 0.999 | ** | |
| CV:mclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:hclust | 2 | 1.000 | 0.998 | 0.999 | ** | |
| MAD:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:skmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:pam | 2 | 1.000 | 1.000 | 1.000 | ** | |
| MAD:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:hclust | 3 | 1.000 | 0.973 | 0.987 | ** | 2 |
| ATC:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:skmeans | 3 | 1.000 | 0.989 | 0.995 | ** | 2 |
| ATC:pam | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:mclust | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:NMF | 2 | 1.000 | 1.000 | 1.000 | ** | |
| CV:hclust | 3 | 0.918 | 0.903 | 0.943 | * | 2 |
| MAD:mclust | 3 | 0.912 | 0.862 | 0.936 | * | 2 |
| SD:hclust | 3 | 0.903 | 0.941 | 0.959 | * | 2 |
**: 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 1.000 1.000 0.508 0.492 0.492
#> CV:NMF 2 1 1.000 1.000 0.508 0.492 0.492
#> MAD:NMF 2 1 1.000 1.000 0.508 0.492 0.492
#> ATC:NMF 2 1 1.000 1.000 0.508 0.492 0.492
#> SD:skmeans 2 1 1.000 1.000 0.508 0.492 0.492
#> CV:skmeans 2 1 1.000 1.000 0.508 0.492 0.492
#> MAD:skmeans 2 1 1.000 1.000 0.508 0.492 0.492
#> ATC:skmeans 2 1 1.000 1.000 0.508 0.492 0.492
#> SD:mclust 2 1 1.000 1.000 0.508 0.492 0.492
#> CV:mclust 2 1 1.000 1.000 0.508 0.492 0.492
#> MAD:mclust 2 1 1.000 1.000 0.508 0.492 0.492
#> ATC:mclust 2 1 1.000 1.000 0.508 0.492 0.492
#> SD:kmeans 2 1 1.000 1.000 0.508 0.492 0.492
#> CV:kmeans 2 1 1.000 1.000 0.508 0.492 0.492
#> MAD:kmeans 2 1 1.000 1.000 0.508 0.492 0.492
#> ATC:kmeans 2 1 1.000 1.000 0.508 0.492 0.492
#> SD:pam 2 1 1.000 1.000 0.508 0.492 0.492
#> CV:pam 2 1 0.998 0.999 0.508 0.492 0.492
#> MAD:pam 2 1 1.000 1.000 0.508 0.492 0.492
#> ATC:pam 2 1 1.000 1.000 0.508 0.492 0.492
#> SD:hclust 2 1 1.000 1.000 0.508 0.492 0.492
#> CV:hclust 2 1 0.993 0.997 0.508 0.492 0.492
#> MAD:hclust 2 1 0.998 0.999 0.508 0.492 0.492
#> ATC:hclust 2 1 1.000 1.000 0.508 0.492 0.492
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.726 0.838 0.896 0.1856 0.944 0.887
#> CV:NMF 3 0.725 0.791 0.886 0.2041 0.927 0.852
#> MAD:NMF 3 0.764 0.809 0.897 0.1883 0.944 0.887
#> ATC:NMF 3 0.900 0.938 0.946 0.0899 1.000 1.000
#> SD:skmeans 3 0.664 0.707 0.839 0.2108 0.944 0.887
#> CV:skmeans 3 0.563 0.775 0.809 0.2381 0.897 0.791
#> MAD:skmeans 3 0.603 0.735 0.843 0.2167 0.933 0.864
#> ATC:skmeans 3 1.000 0.989 0.995 0.0614 0.970 0.940
#> SD:mclust 3 0.755 0.807 0.899 0.1709 0.933 0.864
#> CV:mclust 3 0.892 0.871 0.929 0.1747 0.905 0.806
#> MAD:mclust 3 0.912 0.862 0.936 0.1098 0.957 0.912
#> ATC:mclust 3 0.652 0.652 0.846 0.1860 0.985 0.969
#> SD:kmeans 3 0.702 0.777 0.867 0.1931 0.933 0.864
#> CV:kmeans 3 0.780 0.890 0.894 0.1978 0.905 0.806
#> MAD:kmeans 3 0.714 0.713 0.792 0.1991 0.875 0.746
#> ATC:kmeans 3 0.754 0.921 0.865 0.2090 0.891 0.778
#> SD:pam 3 0.799 0.762 0.875 0.2142 0.881 0.758
#> CV:pam 3 0.815 0.756 0.831 0.1859 0.885 0.767
#> MAD:pam 3 0.779 0.694 0.802 0.2193 0.885 0.767
#> ATC:pam 3 0.886 0.933 0.945 0.2021 0.881 0.758
#> SD:hclust 3 0.903 0.941 0.959 0.1321 0.933 0.864
#> CV:hclust 3 0.918 0.903 0.943 0.1213 0.933 0.864
#> MAD:hclust 3 0.899 0.928 0.949 0.1401 0.933 0.864
#> ATC:hclust 3 1.000 0.973 0.987 0.0779 0.970 0.940
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.604 0.711 0.822 0.1029 0.960 0.908
#> CV:NMF 4 0.562 0.633 0.791 0.1189 0.932 0.840
#> MAD:NMF 4 0.559 0.765 0.815 0.1152 0.957 0.902
#> ATC:NMF 4 0.714 0.784 0.896 0.0665 0.985 0.969
#> SD:skmeans 4 0.511 0.578 0.725 0.1630 0.854 0.670
#> CV:skmeans 4 0.506 0.453 0.697 0.1774 0.875 0.684
#> MAD:skmeans 4 0.509 0.484 0.704 0.1707 0.849 0.653
#> ATC:skmeans 4 0.791 0.883 0.924 0.0809 1.000 0.999
#> SD:mclust 4 0.657 0.706 0.816 0.1491 0.889 0.748
#> CV:mclust 4 0.688 0.719 0.828 0.1436 0.907 0.769
#> MAD:mclust 4 0.770 0.807 0.892 0.1516 0.915 0.812
#> ATC:mclust 4 0.611 0.553 0.757 0.1242 0.889 0.768
#> SD:kmeans 4 0.592 0.681 0.773 0.1124 1.000 1.000
#> CV:kmeans 4 0.645 0.625 0.750 0.1051 0.873 0.680
#> MAD:kmeans 4 0.594 0.604 0.803 0.1016 0.879 0.713
#> ATC:kmeans 4 0.620 0.660 0.786 0.1064 0.918 0.788
#> SD:pam 4 0.795 0.724 0.839 0.0356 0.970 0.924
#> CV:pam 4 0.555 0.769 0.770 0.0905 0.921 0.805
#> MAD:pam 4 0.571 0.497 0.705 0.1231 0.898 0.733
#> ATC:pam 4 0.861 0.796 0.870 0.0571 0.963 0.900
#> SD:hclust 4 0.877 0.903 0.940 0.0422 0.998 0.995
#> CV:hclust 4 0.879 0.880 0.938 0.0410 0.983 0.961
#> MAD:hclust 4 0.918 0.917 0.927 0.0314 1.000 1.000
#> ATC:hclust 4 0.841 0.826 0.896 0.1188 0.960 0.913
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.553 0.497 0.739 0.0911 0.959 0.898
#> CV:NMF 5 0.520 0.575 0.723 0.0853 0.954 0.876
#> MAD:NMF 5 0.538 0.551 0.720 0.0888 0.941 0.856
#> ATC:NMF 5 0.624 0.730 0.841 0.0686 0.985 0.968
#> SD:skmeans 5 0.512 0.516 0.666 0.0713 0.970 0.904
#> CV:skmeans 5 0.507 0.417 0.624 0.0633 0.923 0.752
#> MAD:skmeans 5 0.509 0.413 0.616 0.0684 0.955 0.856
#> ATC:skmeans 5 0.703 0.717 0.865 0.0776 0.941 0.874
#> SD:mclust 5 0.632 0.622 0.742 0.0791 0.944 0.844
#> CV:mclust 5 0.638 0.560 0.757 0.0979 0.871 0.624
#> MAD:mclust 5 0.682 0.679 0.841 0.0824 0.972 0.926
#> ATC:mclust 5 0.586 0.464 0.660 0.0824 0.835 0.611
#> SD:kmeans 5 0.546 0.408 0.694 0.0746 0.890 0.745
#> CV:kmeans 5 0.664 0.679 0.811 0.0741 0.901 0.704
#> MAD:kmeans 5 0.542 0.701 0.748 0.0708 0.923 0.787
#> ATC:kmeans 5 0.572 0.652 0.764 0.0785 0.955 0.861
#> SD:pam 5 0.705 0.639 0.775 0.0325 0.906 0.771
#> CV:pam 5 0.545 0.732 0.752 0.0299 1.000 1.000
#> MAD:pam 5 0.559 0.400 0.713 0.0327 0.862 0.607
#> ATC:pam 5 0.886 0.791 0.876 0.0211 0.969 0.910
#> SD:hclust 5 0.851 0.829 0.907 0.0295 0.985 0.965
#> CV:hclust 5 0.815 0.834 0.916 0.0334 0.997 0.993
#> MAD:hclust 5 0.867 0.836 0.918 0.0331 0.984 0.963
#> ATC:hclust 5 0.810 0.732 0.844 0.0521 0.972 0.935
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.563 0.386 0.660 0.0575 0.878 0.678
#> CV:NMF 6 0.552 0.426 0.670 0.0482 0.970 0.909
#> MAD:NMF 6 0.536 0.395 0.652 0.0603 0.969 0.912
#> ATC:NMF 6 0.564 0.586 0.799 0.0587 0.970 0.935
#> SD:skmeans 6 0.525 0.342 0.607 0.0478 0.959 0.869
#> CV:skmeans 6 0.513 0.241 0.548 0.0454 0.880 0.597
#> MAD:skmeans 6 0.516 0.298 0.594 0.0456 0.928 0.759
#> ATC:skmeans 6 0.632 0.597 0.821 0.0844 0.985 0.962
#> SD:mclust 6 0.642 0.702 0.768 0.0591 0.838 0.510
#> CV:mclust 6 0.714 0.758 0.848 0.0482 0.950 0.802
#> MAD:mclust 6 0.616 0.668 0.773 0.0630 0.960 0.885
#> ATC:mclust 6 0.593 0.352 0.629 0.0558 0.779 0.440
#> SD:kmeans 6 0.575 0.420 0.642 0.0550 0.878 0.641
#> CV:kmeans 6 0.635 0.625 0.757 0.0398 1.000 1.000
#> MAD:kmeans 6 0.577 0.493 0.707 0.0513 0.934 0.793
#> ATC:kmeans 6 0.621 0.618 0.717 0.0527 0.948 0.824
#> SD:pam 6 0.713 0.631 0.783 0.0219 0.935 0.831
#> CV:pam 6 0.547 0.644 0.735 0.0223 0.953 0.875
#> MAD:pam 6 0.550 0.540 0.682 0.0242 0.893 0.660
#> ATC:pam 6 0.854 0.698 0.847 0.0439 0.921 0.768
#> SD:hclust 6 0.842 0.811 0.891 0.0321 0.986 0.965
#> CV:hclust 6 0.824 0.794 0.900 0.0309 0.986 0.965
#> MAD:hclust 6 0.809 0.820 0.897 0.0298 1.000 0.999
#> ATC:hclust 6 0.686 0.630 0.743 0.0777 0.914 0.794
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n disease.state(p) individual(p) k
#> SD:NMF 64 9.19e-15 1 2
#> CV:NMF 64 9.19e-15 1 2
#> MAD:NMF 64 9.19e-15 1 2
#> ATC:NMF 64 9.19e-15 1 2
#> SD:skmeans 64 9.19e-15 1 2
#> CV:skmeans 64 9.19e-15 1 2
#> MAD:skmeans 64 9.19e-15 1 2
#> ATC:skmeans 64 9.19e-15 1 2
#> SD:mclust 64 9.19e-15 1 2
#> CV:mclust 64 9.19e-15 1 2
#> MAD:mclust 64 9.19e-15 1 2
#> ATC:mclust 64 9.19e-15 1 2
#> SD:kmeans 64 9.19e-15 1 2
#> CV:kmeans 64 9.19e-15 1 2
#> MAD:kmeans 64 9.19e-15 1 2
#> ATC:kmeans 64 9.19e-15 1 2
#> SD:pam 64 9.19e-15 1 2
#> CV:pam 64 9.19e-15 1 2
#> MAD:pam 64 9.19e-15 1 2
#> ATC:pam 64 9.19e-15 1 2
#> SD:hclust 64 9.19e-15 1 2
#> CV:hclust 64 9.19e-15 1 2
#> MAD:hclust 64 9.19e-15 1 2
#> ATC:hclust 64 9.19e-15 1 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) individual(p) k
#> SD:NMF 62 3.44e-14 0.999 3
#> CV:NMF 58 2.54e-13 0.979 3
#> MAD:NMF 61 5.68e-14 0.999 3
#> ATC:NMF 64 9.19e-15 1.000 3
#> SD:skmeans 57 4.19e-13 0.998 3
#> CV:skmeans 60 9.36e-14 0.999 3
#> MAD:skmeans 58 2.54e-13 0.998 3
#> ATC:skmeans 64 1.27e-14 0.999 3
#> SD:mclust 60 9.36e-14 0.999 3
#> CV:mclust 61 5.68e-14 0.999 3
#> MAD:mclust 60 9.36e-14 0.999 3
#> ATC:mclust 52 4.58e-12 1.000 3
#> SD:kmeans 60 9.36e-14 0.999 3
#> CV:kmeans 62 3.44e-14 0.999 3
#> MAD:kmeans 57 4.19e-13 0.998 3
#> ATC:kmeans 64 1.27e-14 0.999 3
#> SD:pam 55 1.14e-12 0.998 3
#> CV:pam 57 4.19e-13 0.998 3
#> MAD:pam 50 1.39e-11 0.997 3
#> ATC:pam 62 3.44e-14 0.999 3
#> SD:hclust 63 2.09e-14 0.999 3
#> CV:hclust 63 2.09e-14 0.999 3
#> MAD:hclust 63 2.09e-14 0.999 3
#> ATC:hclust 64 1.27e-14 0.999 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) individual(p) k
#> SD:NMF 54 1.88e-12 0.997 4
#> CV:NMF 49 2.29e-11 0.994 4
#> MAD:NMF 59 1.54e-13 0.998 4
#> ATC:NMF 57 3.27e-13 1.000 4
#> SD:skmeans 51 4.89e-11 0.879 4
#> CV:skmeans 29 5.04e-07 0.538 4
#> MAD:skmeans 34 1.98e-07 0.738 4
#> ATC:skmeans 62 2.54e-14 1.000 4
#> SD:mclust 57 2.57e-12 0.895 4
#> CV:mclust 58 1.57e-12 0.977 4
#> MAD:mclust 60 5.88e-13 0.926 4
#> ATC:mclust 51 4.89e-11 0.962 4
#> SD:kmeans 60 9.36e-14 0.999 4
#> CV:kmeans 50 7.99e-11 0.878 4
#> MAD:kmeans 55 6.87e-12 0.941 4
#> ATC:kmeans 55 6.87e-12 0.941 4
#> SD:pam 51 8.42e-12 0.997 4
#> CV:pam 58 2.54e-13 0.998 4
#> MAD:pam 42 4.01e-09 0.780 4
#> ATC:pam 59 9.61e-13 0.991 4
#> SD:hclust 62 3.44e-14 0.999 4
#> CV:hclust 58 1.98e-13 1.000 4
#> MAD:hclust 63 2.09e-14 0.999 4
#> ATC:hclust 60 5.88e-13 0.991 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) individual(p) k
#> SD:NMF 37 8.73e-09 0.966 5
#> CV:NMF 44 2.79e-10 0.435 5
#> MAD:NMF 47 3.48e-10 0.982 5
#> ATC:NMF 54 1.88e-12 0.997 5
#> SD:skmeans 47 3.48e-10 0.853 5
#> CV:skmeans 26 2.26e-06 0.835 5
#> MAD:skmeans 21 2.75e-05 0.788 5
#> ATC:skmeans 57 4.19e-13 0.997 5
#> SD:mclust 50 7.99e-11 0.844 5
#> CV:mclust 46 5.67e-10 0.564 5
#> MAD:mclust 55 3.25e-11 0.937 5
#> ATC:mclust 29 5.04e-07 0.585 5
#> SD:kmeans 43 2.46e-09 0.972 5
#> CV:kmeans 52 3.00e-11 0.934 5
#> MAD:kmeans 60 5.88e-13 0.963 5
#> ATC:kmeans 54 1.12e-11 0.952 5
#> SD:pam 41 2.73e-09 0.994 5
#> CV:pam 55 1.14e-12 0.998 5
#> MAD:pam 30 3.06e-07 0.793 5
#> ATC:pam 50 1.39e-11 0.997 5
#> SD:hclust 59 1.54e-13 0.998 5
#> CV:hclust 57 3.32e-13 1.000 5
#> MAD:hclust 59 1.54e-13 0.998 5
#> ATC:hclust 55 1.14e-12 0.998 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) individual(p) k
#> SD:NMF 24 2.50e-05 0.959 6
#> CV:NMF 34 4.09e-08 0.959 6
#> MAD:NMF 28 8.32e-07 0.428 6
#> ATC:NMF 50 1.39e-11 0.993 6
#> SD:skmeans 20 4.54e-05 0.467 6
#> CV:skmeans 3 NA NA 6
#> MAD:skmeans 4 NA NA 6
#> ATC:skmeans 46 5.67e-10 0.992 6
#> SD:mclust 58 3.15e-11 0.900 6
#> CV:mclust 58 3.15e-11 0.868 6
#> MAD:mclust 56 2.01e-11 0.893 6
#> ATC:mclust 18 4.40e-04 0.360 6
#> SD:kmeans 33 1.19e-06 0.735 6
#> CV:kmeans 52 3.00e-11 0.955 6
#> MAD:kmeans 44 1.51e-09 0.873 6
#> ATC:kmeans 49 5.84e-10 0.782 6
#> SD:pam 45 1.69e-10 0.997 6
#> CV:pam 54 1.88e-12 0.997 6
#> MAD:pam 45 9.25e-10 0.866 6
#> ATC:pam 48 3.78e-11 0.993 6
#> SD:hclust 58 2.54e-13 0.998 6
#> CV:hclust 58 2.54e-13 0.998 6
#> MAD:hclust 58 2.54e-13 0.998 6
#> ATC:hclust 42 4.01e-09 0.999 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 51941 rows and 64 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 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.903 0.941 0.959 0.1321 0.933 0.864
#> 4 4 0.877 0.903 0.940 0.0422 0.998 0.995
#> 5 5 0.851 0.829 0.907 0.0295 0.985 0.965
#> 6 6 0.842 0.811 0.891 0.0321 0.986 0.965
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.0000 1.000 0.000 1 0.000
#> GSM215052 2 0.0000 1.000 0.000 1 0.000
#> GSM215053 2 0.0000 1.000 0.000 1 0.000
#> GSM215054 2 0.0000 1.000 0.000 1 0.000
#> GSM215055 2 0.0000 1.000 0.000 1 0.000
#> GSM215056 2 0.0000 1.000 0.000 1 0.000
#> GSM215057 2 0.0000 1.000 0.000 1 0.000
#> GSM215058 2 0.0000 1.000 0.000 1 0.000
#> GSM215059 2 0.0000 1.000 0.000 1 0.000
#> GSM215060 2 0.0000 1.000 0.000 1 0.000
#> GSM215061 2 0.0000 1.000 0.000 1 0.000
#> GSM215062 2 0.0000 1.000 0.000 1 0.000
#> GSM215063 2 0.0000 1.000 0.000 1 0.000
#> GSM215064 2 0.0000 1.000 0.000 1 0.000
#> GSM215065 2 0.0000 1.000 0.000 1 0.000
#> GSM215066 2 0.0000 1.000 0.000 1 0.000
#> GSM215067 2 0.0000 1.000 0.000 1 0.000
#> GSM215068 2 0.0000 1.000 0.000 1 0.000
#> GSM215069 2 0.0000 1.000 0.000 1 0.000
#> GSM215070 2 0.0000 1.000 0.000 1 0.000
#> GSM215071 2 0.0000 1.000 0.000 1 0.000
#> GSM215072 2 0.0000 1.000 0.000 1 0.000
#> GSM215073 2 0.0000 1.000 0.000 1 0.000
#> GSM215074 2 0.0000 1.000 0.000 1 0.000
#> GSM215075 2 0.0000 1.000 0.000 1 0.000
#> GSM215076 2 0.0000 1.000 0.000 1 0.000
#> GSM215077 2 0.0000 1.000 0.000 1 0.000
#> GSM215078 2 0.0000 1.000 0.000 1 0.000
#> GSM215079 2 0.0000 1.000 0.000 1 0.000
#> GSM215080 2 0.0000 1.000 0.000 1 0.000
#> GSM215081 2 0.0000 1.000 0.000 1 0.000
#> GSM215082 2 0.0000 1.000 0.000 1 0.000
#> GSM215083 1 0.3267 0.882 0.884 0 0.116
#> GSM215084 1 0.0592 0.924 0.988 0 0.012
#> GSM215085 3 0.5216 0.750 0.260 0 0.740
#> GSM215086 3 0.3340 0.851 0.120 0 0.880
#> GSM215087 1 0.0747 0.928 0.984 0 0.016
#> GSM215088 3 0.4887 0.879 0.228 0 0.772
#> GSM215089 1 0.0237 0.926 0.996 0 0.004
#> GSM215090 1 0.0892 0.923 0.980 0 0.020
#> GSM215091 1 0.2878 0.896 0.904 0 0.096
#> GSM215092 1 0.1031 0.926 0.976 0 0.024
#> GSM215093 3 0.4887 0.881 0.228 0 0.772
#> GSM215094 1 0.0424 0.928 0.992 0 0.008
#> GSM215095 1 0.0237 0.926 0.996 0 0.004
#> GSM215096 1 0.2878 0.896 0.904 0 0.096
#> GSM215097 1 0.2261 0.913 0.932 0 0.068
#> GSM215098 1 0.0747 0.928 0.984 0 0.016
#> GSM215099 1 0.2066 0.916 0.940 0 0.060
#> GSM215100 1 0.0424 0.929 0.992 0 0.008
#> GSM215101 1 0.0892 0.929 0.980 0 0.020
#> GSM215102 1 0.3816 0.833 0.852 0 0.148
#> GSM215103 1 0.3816 0.843 0.852 0 0.148
#> GSM215104 1 0.3038 0.885 0.896 0 0.104
#> GSM215105 1 0.1643 0.922 0.956 0 0.044
#> GSM215106 1 0.2878 0.896 0.904 0 0.096
#> GSM215107 1 0.0592 0.926 0.988 0 0.012
#> GSM215108 1 0.5926 0.336 0.644 0 0.356
#> GSM215109 3 0.4291 0.884 0.180 0 0.820
#> GSM215110 1 0.2261 0.896 0.932 0 0.068
#> GSM215111 1 0.1753 0.921 0.952 0 0.048
#> GSM215112 1 0.0424 0.928 0.992 0 0.008
#> GSM215113 1 0.0000 0.927 1.000 0 0.000
#> GSM215114 1 0.1163 0.928 0.972 0 0.028
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215052 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215053 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215054 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215055 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215056 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215057 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215058 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215059 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215060 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215061 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215062 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215063 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215064 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215065 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215066 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215067 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215068 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215069 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215070 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215071 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215072 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215073 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215074 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215075 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215076 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215077 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215078 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215079 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215080 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215081 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215082 2 0.000 1.000 0.000 1 0.000 0.000
#> GSM215083 1 0.383 0.861 0.848 0 0.076 0.076
#> GSM215084 1 0.187 0.897 0.928 0 0.000 0.072
#> GSM215085 4 0.473 0.000 0.108 0 0.100 0.792
#> GSM215086 3 0.470 0.535 0.004 0 0.676 0.320
#> GSM215087 1 0.147 0.900 0.948 0 0.000 0.052
#> GSM215088 3 0.267 0.731 0.040 0 0.908 0.052
#> GSM215089 1 0.166 0.898 0.944 0 0.004 0.052
#> GSM215090 1 0.225 0.890 0.920 0 0.012 0.068
#> GSM215091 1 0.300 0.879 0.892 0 0.060 0.048
#> GSM215092 1 0.208 0.895 0.916 0 0.000 0.084
#> GSM215093 3 0.149 0.738 0.044 0 0.952 0.004
#> GSM215094 1 0.147 0.902 0.948 0 0.000 0.052
#> GSM215095 1 0.156 0.901 0.944 0 0.000 0.056
#> GSM215096 1 0.300 0.879 0.892 0 0.060 0.048
#> GSM215097 1 0.231 0.894 0.924 0 0.044 0.032
#> GSM215098 1 0.147 0.900 0.948 0 0.000 0.052
#> GSM215099 1 0.232 0.897 0.924 0 0.036 0.040
#> GSM215100 1 0.139 0.902 0.952 0 0.000 0.048
#> GSM215101 1 0.147 0.904 0.948 0 0.000 0.052
#> GSM215102 1 0.483 0.775 0.776 0 0.068 0.156
#> GSM215103 1 0.456 0.814 0.796 0 0.064 0.140
#> GSM215104 1 0.380 0.853 0.836 0 0.032 0.132
#> GSM215105 1 0.184 0.900 0.944 0 0.028 0.028
#> GSM215106 1 0.300 0.879 0.892 0 0.060 0.048
#> GSM215107 1 0.147 0.904 0.948 0 0.000 0.052
#> GSM215108 1 0.746 0.189 0.508 0 0.256 0.236
#> GSM215109 3 0.460 0.623 0.028 0 0.760 0.212
#> GSM215110 1 0.405 0.825 0.828 0 0.048 0.124
#> GSM215111 1 0.173 0.899 0.948 0 0.028 0.024
#> GSM215112 1 0.121 0.901 0.960 0 0.000 0.040
#> GSM215113 1 0.102 0.902 0.968 0 0.000 0.032
#> GSM215114 1 0.214 0.900 0.928 0 0.016 0.056
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215052 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215053 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215054 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215055 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215056 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215057 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215058 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215059 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215060 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215061 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215062 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215063 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215064 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215065 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215066 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215067 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215068 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215069 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215070 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215071 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215072 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215073 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215074 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215075 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215076 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215077 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215078 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215079 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215080 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215081 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215082 2 0.0000 1.0000 0.000 1 0.000 0.000 0.000
#> GSM215083 1 0.4135 0.7837 0.820 0 0.064 0.044 0.072
#> GSM215084 1 0.3184 0.8139 0.852 0 0.000 0.048 0.100
#> GSM215085 4 0.3051 0.0000 0.076 0 0.060 0.864 0.000
#> GSM215086 3 0.6740 0.2856 0.004 0 0.460 0.276 0.260
#> GSM215087 1 0.2597 0.8309 0.896 0 0.004 0.060 0.040
#> GSM215088 3 0.1357 0.6771 0.004 0 0.948 0.048 0.000
#> GSM215089 1 0.3595 0.7733 0.816 0 0.000 0.044 0.140
#> GSM215090 1 0.4369 0.6769 0.740 0 0.000 0.052 0.208
#> GSM215091 1 0.3146 0.8177 0.876 0 0.056 0.040 0.028
#> GSM215092 1 0.3269 0.8117 0.848 0 0.000 0.056 0.096
#> GSM215093 3 0.0854 0.6724 0.008 0 0.976 0.004 0.012
#> GSM215094 1 0.2304 0.8359 0.908 0 0.000 0.048 0.044
#> GSM215095 1 0.2632 0.8285 0.888 0 0.000 0.040 0.072
#> GSM215096 1 0.3146 0.8177 0.876 0 0.056 0.040 0.028
#> GSM215097 1 0.2617 0.8303 0.904 0 0.036 0.032 0.028
#> GSM215098 1 0.2419 0.8343 0.904 0 0.004 0.064 0.028
#> GSM215099 1 0.2696 0.8318 0.900 0 0.028 0.032 0.040
#> GSM215100 1 0.2569 0.8292 0.892 0 0.000 0.040 0.068
#> GSM215101 1 0.3090 0.8278 0.860 0 0.000 0.052 0.088
#> GSM215102 1 0.3968 0.6009 0.716 0 0.004 0.004 0.276
#> GSM215103 1 0.4462 0.7050 0.768 0 0.044 0.020 0.168
#> GSM215104 1 0.3902 0.7583 0.804 0 0.016 0.028 0.152
#> GSM215105 1 0.2523 0.8363 0.908 0 0.028 0.024 0.040
#> GSM215106 1 0.3146 0.8180 0.876 0 0.056 0.040 0.028
#> GSM215107 1 0.2304 0.8378 0.908 0 0.000 0.044 0.048
#> GSM215108 5 0.4648 -0.1121 0.464 0 0.012 0.000 0.524
#> GSM215109 5 0.5310 -0.5581 0.024 0 0.428 0.016 0.532
#> GSM215110 1 0.6211 0.0932 0.464 0 0.008 0.108 0.420
#> GSM215111 1 0.2366 0.8367 0.916 0 0.028 0.028 0.028
#> GSM215112 1 0.2390 0.8315 0.908 0 0.004 0.044 0.044
#> GSM215113 1 0.2260 0.8339 0.908 0 0.000 0.028 0.064
#> GSM215114 1 0.3040 0.8280 0.876 0 0.012 0.044 0.068
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 2 0.0146 0.9849 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215052 2 0.0291 0.9826 0.000 0.992 0.004 0.004 0.000 0.000
#> GSM215053 2 0.0146 0.9849 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215054 2 0.0146 0.9849 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215055 2 0.0146 0.9849 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215056 2 0.0146 0.9849 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215057 2 0.0146 0.9849 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215058 2 0.1577 0.9505 0.000 0.940 0.036 0.016 0.008 0.000
#> GSM215059 2 0.0146 0.9849 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215060 2 0.0146 0.9849 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215061 2 0.0146 0.9838 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM215062 2 0.1750 0.9445 0.000 0.932 0.040 0.016 0.012 0.000
#> GSM215063 2 0.0146 0.9849 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215064 2 0.1750 0.9445 0.000 0.932 0.040 0.016 0.012 0.000
#> GSM215065 2 0.0146 0.9849 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215066 2 0.0000 0.9846 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215067 2 0.0146 0.9849 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215068 2 0.0146 0.9838 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM215069 2 0.0146 0.9849 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215070 2 0.0405 0.9810 0.000 0.988 0.008 0.004 0.000 0.000
#> GSM215071 2 0.0291 0.9826 0.000 0.992 0.004 0.004 0.000 0.000
#> GSM215072 2 0.1511 0.9534 0.000 0.944 0.032 0.012 0.012 0.000
#> GSM215073 2 0.0146 0.9849 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215074 2 0.0146 0.9849 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215075 2 0.0146 0.9838 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM215076 2 0.1750 0.9445 0.000 0.932 0.040 0.016 0.012 0.000
#> GSM215077 2 0.0291 0.9826 0.000 0.992 0.004 0.004 0.000 0.000
#> GSM215078 2 0.0146 0.9849 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215079 2 0.0000 0.9846 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215080 2 0.0000 0.9846 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215081 2 0.1750 0.9445 0.000 0.932 0.040 0.016 0.012 0.000
#> GSM215082 2 0.0405 0.9810 0.000 0.988 0.008 0.004 0.000 0.000
#> GSM215083 1 0.4175 0.7873 0.804 0.000 0.080 0.036 0.024 0.056
#> GSM215084 1 0.2859 0.8140 0.828 0.000 0.016 0.000 0.156 0.000
#> GSM215085 4 0.1265 0.0000 0.044 0.000 0.000 0.948 0.000 0.008
#> GSM215086 3 0.6708 -0.2661 0.004 0.000 0.512 0.180 0.072 0.232
#> GSM215087 1 0.3268 0.8209 0.852 0.000 0.028 0.072 0.044 0.004
#> GSM215088 6 0.2144 0.8156 0.004 0.000 0.040 0.048 0.000 0.908
#> GSM215089 1 0.3721 0.6993 0.752 0.000 0.016 0.012 0.220 0.000
#> GSM215090 1 0.4609 0.4028 0.608 0.000 0.016 0.024 0.352 0.000
#> GSM215091 1 0.2886 0.8219 0.880 0.000 0.032 0.032 0.008 0.048
#> GSM215092 1 0.3593 0.8011 0.784 0.000 0.020 0.016 0.180 0.000
#> GSM215093 6 0.1575 0.8189 0.000 0.000 0.032 0.032 0.000 0.936
#> GSM215094 1 0.2843 0.8344 0.876 0.000 0.044 0.048 0.032 0.000
#> GSM215095 1 0.2445 0.8278 0.868 0.000 0.008 0.004 0.120 0.000
#> GSM215096 1 0.2886 0.8219 0.880 0.000 0.032 0.032 0.008 0.048
#> GSM215097 1 0.2662 0.8293 0.896 0.000 0.028 0.028 0.020 0.028
#> GSM215098 1 0.3039 0.8283 0.864 0.000 0.028 0.076 0.028 0.004
#> GSM215099 1 0.2814 0.8303 0.888 0.000 0.032 0.028 0.032 0.020
#> GSM215100 1 0.2701 0.8087 0.864 0.000 0.004 0.028 0.104 0.000
#> GSM215101 1 0.3813 0.8021 0.788 0.000 0.024 0.036 0.152 0.000
#> GSM215102 1 0.5185 0.5646 0.624 0.000 0.260 0.004 0.108 0.004
#> GSM215103 1 0.4844 0.7150 0.720 0.000 0.188 0.020 0.032 0.040
#> GSM215104 1 0.4241 0.7582 0.764 0.000 0.168 0.020 0.032 0.016
#> GSM215105 1 0.2674 0.8273 0.892 0.000 0.012 0.028 0.048 0.020
#> GSM215106 1 0.2886 0.8221 0.880 0.000 0.032 0.032 0.008 0.048
#> GSM215107 1 0.2831 0.8319 0.868 0.000 0.016 0.032 0.084 0.000
#> GSM215108 3 0.4855 -0.0981 0.408 0.000 0.544 0.004 0.040 0.004
#> GSM215109 3 0.4275 -0.1879 0.008 0.000 0.644 0.000 0.020 0.328
#> GSM215110 5 0.2402 0.0000 0.120 0.000 0.012 0.000 0.868 0.000
#> GSM215111 1 0.2701 0.8299 0.892 0.000 0.016 0.028 0.044 0.020
#> GSM215112 1 0.3236 0.8214 0.856 0.000 0.032 0.060 0.048 0.004
#> GSM215113 1 0.2203 0.8222 0.896 0.000 0.004 0.016 0.084 0.000
#> GSM215114 1 0.3893 0.8147 0.820 0.000 0.068 0.056 0.044 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> SD:hclust 64 9.19e-15 1.000 2
#> SD:hclust 63 2.09e-14 0.999 3
#> SD:hclust 62 3.44e-14 0.999 4
#> SD:hclust 59 1.54e-13 0.998 5
#> SD:hclust 58 2.54e-13 0.998 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 51941 rows and 64 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.702 0.777 0.867 0.1931 0.933 0.864
#> 4 4 0.592 0.681 0.773 0.1124 1.000 1.000
#> 5 5 0.546 0.408 0.694 0.0746 0.890 0.745
#> 6 6 0.575 0.420 0.642 0.0550 0.878 0.641
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.4121 0.8570 0.000 0.832 0.168
#> GSM215052 2 0.3116 0.8813 0.000 0.892 0.108
#> GSM215053 2 0.4452 0.8556 0.000 0.808 0.192
#> GSM215054 2 0.5098 0.8390 0.000 0.752 0.248
#> GSM215055 2 0.4796 0.8534 0.000 0.780 0.220
#> GSM215056 2 0.4842 0.8510 0.000 0.776 0.224
#> GSM215057 2 0.3340 0.8977 0.000 0.880 0.120
#> GSM215058 2 0.4291 0.8601 0.000 0.820 0.180
#> GSM215059 2 0.2537 0.9060 0.000 0.920 0.080
#> GSM215060 2 0.2537 0.9060 0.000 0.920 0.080
#> GSM215061 2 0.1643 0.9101 0.000 0.956 0.044
#> GSM215062 2 0.3686 0.8647 0.000 0.860 0.140
#> GSM215063 2 0.5098 0.8390 0.000 0.752 0.248
#> GSM215064 2 0.3686 0.8647 0.000 0.860 0.140
#> GSM215065 2 0.2537 0.9060 0.000 0.920 0.080
#> GSM215066 2 0.0237 0.9090 0.000 0.996 0.004
#> GSM215067 2 0.4974 0.8459 0.000 0.764 0.236
#> GSM215068 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM215069 2 0.2448 0.9068 0.000 0.924 0.076
#> GSM215070 2 0.3038 0.8810 0.000 0.896 0.104
#> GSM215071 2 0.1860 0.9109 0.000 0.948 0.052
#> GSM215072 2 0.3686 0.8647 0.000 0.860 0.140
#> GSM215073 2 0.2537 0.9060 0.000 0.920 0.080
#> GSM215074 2 0.2537 0.9060 0.000 0.920 0.080
#> GSM215075 2 0.0237 0.9084 0.000 0.996 0.004
#> GSM215076 2 0.4062 0.8604 0.000 0.836 0.164
#> GSM215077 2 0.0747 0.9092 0.000 0.984 0.016
#> GSM215078 2 0.2537 0.9074 0.000 0.920 0.080
#> GSM215079 2 0.0000 0.9083 0.000 1.000 0.000
#> GSM215080 2 0.0424 0.9094 0.000 0.992 0.008
#> GSM215081 2 0.3619 0.8656 0.000 0.864 0.136
#> GSM215082 2 0.2959 0.8816 0.000 0.900 0.100
#> GSM215083 1 0.5882 -0.0625 0.652 0.000 0.348
#> GSM215084 1 0.0892 0.8088 0.980 0.000 0.020
#> GSM215085 3 0.6291 0.8382 0.468 0.000 0.532
#> GSM215086 3 0.6140 0.9529 0.404 0.000 0.596
#> GSM215087 1 0.2448 0.7856 0.924 0.000 0.076
#> GSM215088 3 0.6140 0.9529 0.404 0.000 0.596
#> GSM215089 1 0.0424 0.8140 0.992 0.000 0.008
#> GSM215090 1 0.0424 0.8140 0.992 0.000 0.008
#> GSM215091 1 0.3116 0.7591 0.892 0.000 0.108
#> GSM215092 1 0.0747 0.8112 0.984 0.000 0.016
#> GSM215093 3 0.6095 0.9493 0.392 0.000 0.608
#> GSM215094 1 0.0424 0.8156 0.992 0.000 0.008
#> GSM215095 1 0.0000 0.8165 1.000 0.000 0.000
#> GSM215096 1 0.3116 0.7591 0.892 0.000 0.108
#> GSM215097 1 0.3551 0.7319 0.868 0.000 0.132
#> GSM215098 1 0.2448 0.7856 0.924 0.000 0.076
#> GSM215099 1 0.0592 0.8168 0.988 0.000 0.012
#> GSM215100 1 0.0592 0.8146 0.988 0.000 0.012
#> GSM215101 1 0.0424 0.8140 0.992 0.000 0.008
#> GSM215102 1 0.6079 -0.3850 0.612 0.000 0.388
#> GSM215103 1 0.4235 0.6709 0.824 0.000 0.176
#> GSM215104 1 0.3941 0.7061 0.844 0.000 0.156
#> GSM215105 1 0.0747 0.8165 0.984 0.000 0.016
#> GSM215106 1 0.3192 0.7563 0.888 0.000 0.112
#> GSM215107 1 0.0000 0.8165 1.000 0.000 0.000
#> GSM215108 1 0.6168 -0.4631 0.588 0.000 0.412
#> GSM215109 3 0.6095 0.9493 0.392 0.000 0.608
#> GSM215110 1 0.6045 -0.4271 0.620 0.000 0.380
#> GSM215111 1 0.0237 0.8170 0.996 0.000 0.004
#> GSM215112 1 0.0592 0.8167 0.988 0.000 0.012
#> GSM215113 1 0.0424 0.8140 0.992 0.000 0.008
#> GSM215114 1 0.2711 0.7837 0.912 0.000 0.088
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.6656 0.680 0.000 0.620 0.160 0.220
#> GSM215052 2 0.5130 0.717 0.000 0.668 0.020 0.312
#> GSM215053 2 0.6449 0.683 0.000 0.644 0.152 0.204
#> GSM215054 2 0.6672 0.666 0.000 0.620 0.168 0.212
#> GSM215055 2 0.6209 0.699 0.000 0.656 0.112 0.232
#> GSM215056 2 0.6289 0.693 0.000 0.648 0.116 0.236
#> GSM215057 2 0.4234 0.778 0.000 0.816 0.052 0.132
#> GSM215058 2 0.4992 0.658 0.000 0.524 0.000 0.476
#> GSM215059 2 0.2675 0.797 0.000 0.908 0.044 0.048
#> GSM215060 2 0.2830 0.795 0.000 0.900 0.040 0.060
#> GSM215061 2 0.0524 0.804 0.000 0.988 0.008 0.004
#> GSM215062 2 0.4855 0.683 0.000 0.600 0.000 0.400
#> GSM215063 2 0.6796 0.663 0.000 0.596 0.152 0.252
#> GSM215064 2 0.4830 0.685 0.000 0.608 0.000 0.392
#> GSM215065 2 0.2124 0.800 0.000 0.932 0.028 0.040
#> GSM215066 2 0.1356 0.804 0.000 0.960 0.008 0.032
#> GSM215067 2 0.6648 0.673 0.000 0.612 0.140 0.248
#> GSM215068 2 0.1584 0.804 0.000 0.952 0.012 0.036
#> GSM215069 2 0.1042 0.804 0.000 0.972 0.008 0.020
#> GSM215070 2 0.5108 0.718 0.000 0.672 0.020 0.308
#> GSM215071 2 0.2644 0.804 0.000 0.908 0.032 0.060
#> GSM215072 2 0.5150 0.681 0.000 0.596 0.008 0.396
#> GSM215073 2 0.2500 0.797 0.000 0.916 0.040 0.044
#> GSM215074 2 0.2759 0.796 0.000 0.904 0.044 0.052
#> GSM215075 2 0.1677 0.804 0.000 0.948 0.012 0.040
#> GSM215076 2 0.5982 0.652 0.000 0.524 0.040 0.436
#> GSM215077 2 0.2376 0.800 0.000 0.916 0.016 0.068
#> GSM215078 2 0.2300 0.799 0.000 0.924 0.028 0.048
#> GSM215079 2 0.1452 0.804 0.000 0.956 0.008 0.036
#> GSM215080 2 0.1356 0.804 0.000 0.960 0.008 0.032
#> GSM215081 2 0.4830 0.685 0.000 0.608 0.000 0.392
#> GSM215082 2 0.5173 0.714 0.000 0.660 0.020 0.320
#> GSM215083 1 0.6383 0.210 0.568 0.000 0.356 0.076
#> GSM215084 1 0.2737 0.690 0.888 0.000 0.008 0.104
#> GSM215085 3 0.6466 0.805 0.288 0.000 0.608 0.104
#> GSM215086 3 0.5267 0.905 0.240 0.000 0.712 0.048
#> GSM215087 1 0.3301 0.722 0.876 0.000 0.076 0.048
#> GSM215088 3 0.4808 0.918 0.236 0.000 0.736 0.028
#> GSM215089 1 0.2342 0.706 0.912 0.000 0.008 0.080
#> GSM215090 1 0.2976 0.676 0.872 0.000 0.008 0.120
#> GSM215091 1 0.5007 0.653 0.760 0.000 0.172 0.068
#> GSM215092 1 0.2859 0.691 0.880 0.000 0.008 0.112
#> GSM215093 3 0.4900 0.918 0.236 0.000 0.732 0.032
#> GSM215094 1 0.1661 0.741 0.944 0.000 0.004 0.052
#> GSM215095 1 0.0524 0.740 0.988 0.000 0.004 0.008
#> GSM215096 1 0.5077 0.658 0.760 0.000 0.160 0.080
#> GSM215097 1 0.4874 0.655 0.764 0.000 0.180 0.056
#> GSM215098 1 0.3761 0.718 0.852 0.000 0.080 0.068
#> GSM215099 1 0.3617 0.724 0.860 0.000 0.076 0.064
#> GSM215100 1 0.2654 0.732 0.888 0.000 0.004 0.108
#> GSM215101 1 0.2198 0.718 0.920 0.000 0.008 0.072
#> GSM215102 1 0.7740 -0.336 0.416 0.000 0.348 0.236
#> GSM215103 1 0.5710 0.589 0.708 0.000 0.192 0.100
#> GSM215104 1 0.5751 0.610 0.712 0.000 0.164 0.124
#> GSM215105 1 0.3009 0.735 0.892 0.000 0.056 0.052
#> GSM215106 1 0.5272 0.646 0.744 0.000 0.172 0.084
#> GSM215107 1 0.0895 0.739 0.976 0.000 0.004 0.020
#> GSM215108 1 0.7497 -0.411 0.424 0.000 0.396 0.180
#> GSM215109 3 0.5489 0.884 0.240 0.000 0.700 0.060
#> GSM215110 1 0.7235 -0.147 0.532 0.000 0.288 0.180
#> GSM215111 1 0.2282 0.741 0.924 0.000 0.024 0.052
#> GSM215112 1 0.1722 0.738 0.944 0.000 0.008 0.048
#> GSM215113 1 0.2125 0.731 0.920 0.000 0.004 0.076
#> GSM215114 1 0.3301 0.724 0.876 0.000 0.048 0.076
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.7315 -0.52449 0.000 0.480 0.096 0.104 0.320
#> GSM215052 2 0.4684 0.07988 0.000 0.728 0.024 0.220 0.028
#> GSM215053 2 0.6908 -0.55283 0.000 0.496 0.068 0.088 0.348
#> GSM215054 5 0.7228 0.65269 0.000 0.388 0.088 0.092 0.432
#> GSM215055 5 0.4201 0.83809 0.000 0.408 0.000 0.000 0.592
#> GSM215056 5 0.4126 0.86601 0.000 0.380 0.000 0.000 0.620
#> GSM215057 2 0.4876 -0.25368 0.000 0.576 0.000 0.028 0.396
#> GSM215058 2 0.5884 -0.77123 0.000 0.480 0.000 0.420 0.100
#> GSM215059 2 0.3109 0.44266 0.000 0.800 0.000 0.000 0.200
#> GSM215060 2 0.3143 0.42613 0.000 0.796 0.000 0.000 0.204
#> GSM215061 2 0.1121 0.54806 0.000 0.956 0.000 0.000 0.044
#> GSM215062 2 0.4256 -0.60731 0.000 0.564 0.000 0.436 0.000
#> GSM215063 5 0.4283 0.86415 0.000 0.348 0.008 0.000 0.644
#> GSM215064 2 0.4242 -0.60059 0.000 0.572 0.000 0.428 0.000
#> GSM215065 2 0.2561 0.50601 0.000 0.856 0.000 0.000 0.144
#> GSM215066 2 0.0451 0.53823 0.000 0.988 0.000 0.004 0.008
#> GSM215067 5 0.4211 0.87318 0.000 0.360 0.004 0.000 0.636
#> GSM215068 2 0.0324 0.53723 0.000 0.992 0.000 0.004 0.004
#> GSM215069 2 0.1544 0.55043 0.000 0.932 0.000 0.000 0.068
#> GSM215070 2 0.4733 0.09813 0.000 0.728 0.024 0.216 0.032
#> GSM215071 2 0.3090 0.51430 0.000 0.876 0.016 0.052 0.056
#> GSM215072 2 0.4675 -0.61833 0.000 0.544 0.004 0.444 0.008
#> GSM215073 2 0.2929 0.46721 0.000 0.820 0.000 0.000 0.180
#> GSM215074 2 0.3074 0.44638 0.000 0.804 0.000 0.000 0.196
#> GSM215075 2 0.0960 0.53402 0.000 0.972 0.008 0.004 0.016
#> GSM215076 4 0.4950 0.00000 0.000 0.424 0.008 0.552 0.016
#> GSM215077 2 0.2897 0.50125 0.000 0.888 0.020 0.052 0.040
#> GSM215078 2 0.2690 0.49141 0.000 0.844 0.000 0.000 0.156
#> GSM215079 2 0.0451 0.53531 0.000 0.988 0.000 0.004 0.008
#> GSM215080 2 0.0451 0.53531 0.000 0.988 0.000 0.004 0.008
#> GSM215081 2 0.4383 -0.59643 0.000 0.572 0.000 0.424 0.004
#> GSM215082 2 0.4979 0.00392 0.000 0.700 0.024 0.240 0.036
#> GSM215083 1 0.6009 0.25582 0.580 0.000 0.324 0.032 0.064
#> GSM215084 1 0.4587 0.61420 0.724 0.000 0.008 0.228 0.040
#> GSM215085 3 0.6758 0.55898 0.280 0.000 0.544 0.040 0.136
#> GSM215086 3 0.4531 0.72524 0.136 0.000 0.776 0.020 0.068
#> GSM215087 1 0.4182 0.65489 0.812 0.000 0.076 0.028 0.084
#> GSM215088 3 0.3190 0.73431 0.140 0.000 0.840 0.012 0.008
#> GSM215089 1 0.4677 0.62254 0.716 0.000 0.012 0.236 0.036
#> GSM215090 1 0.4914 0.57201 0.672 0.000 0.008 0.280 0.040
#> GSM215091 1 0.4504 0.60199 0.768 0.000 0.152 0.012 0.068
#> GSM215092 1 0.5161 0.58715 0.672 0.000 0.016 0.264 0.048
#> GSM215093 3 0.3216 0.73575 0.116 0.000 0.852 0.020 0.012
#> GSM215094 1 0.2899 0.68481 0.880 0.000 0.008 0.036 0.076
#> GSM215095 1 0.2519 0.68966 0.884 0.000 0.000 0.100 0.016
#> GSM215096 1 0.4340 0.61030 0.780 0.000 0.148 0.012 0.060
#> GSM215097 1 0.5666 0.59673 0.692 0.000 0.176 0.088 0.044
#> GSM215098 1 0.3870 0.65083 0.820 0.000 0.080 0.008 0.092
#> GSM215099 1 0.4334 0.67256 0.796 0.000 0.044 0.124 0.036
#> GSM215100 1 0.4715 0.63895 0.728 0.000 0.012 0.212 0.048
#> GSM215101 1 0.4513 0.63687 0.748 0.000 0.008 0.192 0.052
#> GSM215102 3 0.8310 0.37834 0.292 0.000 0.320 0.260 0.128
#> GSM215103 1 0.5960 0.53407 0.672 0.000 0.164 0.048 0.116
#> GSM215104 1 0.5979 0.55476 0.676 0.000 0.152 0.056 0.116
#> GSM215105 1 0.3825 0.68048 0.832 0.000 0.044 0.096 0.028
#> GSM215106 1 0.5084 0.59354 0.740 0.000 0.152 0.036 0.072
#> GSM215107 1 0.2623 0.68989 0.884 0.000 0.004 0.096 0.016
#> GSM215108 3 0.8227 0.41194 0.312 0.000 0.352 0.200 0.136
#> GSM215109 3 0.5258 0.71949 0.124 0.000 0.740 0.060 0.076
#> GSM215110 1 0.7903 -0.26564 0.344 0.000 0.260 0.324 0.072
#> GSM215111 1 0.3594 0.68300 0.844 0.000 0.032 0.096 0.028
#> GSM215112 1 0.2846 0.67895 0.884 0.000 0.012 0.028 0.076
#> GSM215113 1 0.4153 0.65375 0.756 0.000 0.008 0.212 0.024
#> GSM215114 1 0.4425 0.65162 0.796 0.000 0.056 0.040 0.108
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 2 0.7719 -0.4672 0.000 0.384 0.024 0.288 0.180 0.124
#> GSM215052 2 0.5706 -0.3249 0.000 0.552 0.068 0.016 0.020 0.344
#> GSM215053 2 0.7582 -0.4068 0.000 0.448 0.032 0.236 0.172 0.112
#> GSM215054 4 0.7720 0.4708 0.000 0.308 0.024 0.368 0.180 0.120
#> GSM215055 4 0.3905 0.7027 0.000 0.356 0.000 0.636 0.004 0.004
#> GSM215056 4 0.3606 0.7910 0.000 0.284 0.000 0.708 0.004 0.004
#> GSM215057 2 0.4598 -0.2583 0.000 0.504 0.004 0.464 0.000 0.028
#> GSM215058 6 0.5057 0.8018 0.000 0.288 0.004 0.096 0.000 0.612
#> GSM215059 2 0.2912 0.5442 0.000 0.784 0.000 0.216 0.000 0.000
#> GSM215060 2 0.2772 0.5806 0.000 0.816 0.000 0.180 0.004 0.000
#> GSM215061 2 0.1007 0.6570 0.000 0.968 0.004 0.016 0.008 0.004
#> GSM215062 6 0.3706 0.8823 0.000 0.380 0.000 0.000 0.000 0.620
#> GSM215063 4 0.3109 0.7905 0.000 0.224 0.000 0.772 0.004 0.000
#> GSM215064 6 0.3717 0.8824 0.000 0.384 0.000 0.000 0.000 0.616
#> GSM215065 2 0.1714 0.6386 0.000 0.908 0.000 0.092 0.000 0.000
#> GSM215066 2 0.0653 0.6522 0.000 0.980 0.004 0.000 0.004 0.012
#> GSM215067 4 0.3429 0.8024 0.000 0.252 0.000 0.740 0.004 0.004
#> GSM215068 2 0.0798 0.6503 0.000 0.976 0.004 0.004 0.004 0.012
#> GSM215069 2 0.0937 0.6572 0.000 0.960 0.000 0.040 0.000 0.000
#> GSM215070 2 0.5726 -0.3457 0.000 0.544 0.068 0.016 0.020 0.352
#> GSM215071 2 0.4016 0.5887 0.000 0.816 0.064 0.052 0.020 0.048
#> GSM215072 6 0.4436 0.8587 0.000 0.368 0.020 0.004 0.004 0.604
#> GSM215073 2 0.2668 0.5913 0.000 0.828 0.000 0.168 0.004 0.000
#> GSM215074 2 0.2979 0.5720 0.000 0.804 0.000 0.188 0.004 0.004
#> GSM215075 2 0.1317 0.6499 0.000 0.956 0.004 0.016 0.008 0.016
#> GSM215076 6 0.3817 0.7400 0.000 0.228 0.008 0.016 0.004 0.744
#> GSM215077 2 0.3594 0.5745 0.000 0.840 0.064 0.024 0.020 0.052
#> GSM215078 2 0.2734 0.6051 0.000 0.840 0.000 0.148 0.004 0.008
#> GSM215079 2 0.0260 0.6567 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM215080 2 0.0260 0.6567 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM215081 6 0.3717 0.8824 0.000 0.384 0.000 0.000 0.000 0.616
#> GSM215082 2 0.5922 -0.4308 0.000 0.512 0.068 0.024 0.020 0.376
#> GSM215083 1 0.4581 0.4296 0.744 0.000 0.172 0.036 0.028 0.020
#> GSM215084 5 0.4622 0.4236 0.404 0.000 0.004 0.020 0.564 0.008
#> GSM215085 1 0.7396 -0.4933 0.384 0.000 0.380 0.108 0.052 0.076
#> GSM215086 3 0.5461 0.7210 0.160 0.000 0.696 0.064 0.044 0.036
#> GSM215087 1 0.3078 0.4923 0.848 0.000 0.000 0.032 0.104 0.016
#> GSM215088 3 0.3625 0.7566 0.156 0.000 0.800 0.012 0.024 0.008
#> GSM215089 5 0.3986 0.3324 0.464 0.000 0.000 0.004 0.532 0.000
#> GSM215090 5 0.4161 0.4668 0.348 0.000 0.000 0.004 0.632 0.016
#> GSM215091 1 0.1781 0.5404 0.924 0.000 0.060 0.008 0.008 0.000
#> GSM215092 5 0.4433 0.4277 0.416 0.000 0.000 0.016 0.560 0.008
#> GSM215093 3 0.3690 0.7585 0.136 0.000 0.808 0.024 0.024 0.008
#> GSM215094 1 0.3963 0.4410 0.756 0.000 0.000 0.040 0.192 0.012
#> GSM215095 1 0.4382 0.2101 0.612 0.000 0.000 0.020 0.360 0.008
#> GSM215096 1 0.1655 0.5439 0.936 0.000 0.044 0.004 0.012 0.004
#> GSM215097 1 0.5168 0.4325 0.716 0.000 0.076 0.048 0.144 0.016
#> GSM215098 1 0.2851 0.5187 0.868 0.000 0.000 0.036 0.080 0.016
#> GSM215099 1 0.4750 0.3094 0.656 0.000 0.004 0.040 0.284 0.016
#> GSM215100 1 0.5006 -0.0628 0.528 0.000 0.000 0.040 0.416 0.016
#> GSM215101 1 0.4389 -0.2728 0.512 0.000 0.000 0.016 0.468 0.004
#> GSM215102 5 0.7615 -0.1496 0.180 0.000 0.276 0.024 0.408 0.112
#> GSM215103 1 0.4243 0.4724 0.780 0.000 0.136 0.028 0.016 0.040
#> GSM215104 1 0.4833 0.4812 0.760 0.000 0.100 0.036 0.052 0.052
#> GSM215105 1 0.4098 0.4112 0.732 0.000 0.000 0.036 0.220 0.012
#> GSM215106 1 0.3277 0.5267 0.860 0.000 0.056 0.036 0.032 0.016
#> GSM215107 1 0.4639 0.3072 0.644 0.000 0.000 0.036 0.304 0.016
#> GSM215108 3 0.8039 0.0443 0.288 0.000 0.300 0.032 0.252 0.128
#> GSM215109 3 0.4978 0.7092 0.104 0.000 0.740 0.016 0.052 0.088
#> GSM215110 5 0.5912 0.2407 0.108 0.000 0.196 0.008 0.628 0.060
#> GSM215111 1 0.4176 0.4001 0.720 0.000 0.000 0.036 0.232 0.012
#> GSM215112 1 0.3825 0.4450 0.776 0.000 0.000 0.036 0.172 0.016
#> GSM215113 1 0.4820 -0.0884 0.528 0.000 0.000 0.032 0.428 0.012
#> GSM215114 1 0.4258 0.4698 0.792 0.000 0.036 0.040 0.108 0.024
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> SD:kmeans 64 9.19e-15 1.000 2
#> SD:kmeans 60 9.36e-14 0.999 3
#> SD:kmeans 60 9.36e-14 0.999 4
#> SD:kmeans 43 2.46e-09 0.972 5
#> SD:kmeans 33 1.19e-06 0.735 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 51941 rows and 64 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.664 0.707 0.839 0.2108 0.944 0.887
#> 4 4 0.511 0.578 0.725 0.1630 0.854 0.670
#> 5 5 0.512 0.516 0.666 0.0713 0.970 0.904
#> 6 6 0.525 0.342 0.607 0.0478 0.959 0.869
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.2959 0.9067 0.000 0.900 0.100
#> GSM215052 2 0.4931 0.8486 0.000 0.768 0.232
#> GSM215053 2 0.1753 0.9120 0.000 0.952 0.048
#> GSM215054 2 0.1964 0.9066 0.000 0.944 0.056
#> GSM215055 2 0.1860 0.9085 0.000 0.948 0.052
#> GSM215056 2 0.1753 0.9061 0.000 0.952 0.048
#> GSM215057 2 0.2066 0.9089 0.000 0.940 0.060
#> GSM215058 2 0.5733 0.7974 0.000 0.676 0.324
#> GSM215059 2 0.1411 0.9105 0.000 0.964 0.036
#> GSM215060 2 0.1289 0.9088 0.000 0.968 0.032
#> GSM215061 2 0.0747 0.9126 0.000 0.984 0.016
#> GSM215062 2 0.5785 0.7882 0.000 0.668 0.332
#> GSM215063 2 0.2066 0.9070 0.000 0.940 0.060
#> GSM215064 2 0.5785 0.7876 0.000 0.668 0.332
#> GSM215065 2 0.0892 0.9114 0.000 0.980 0.020
#> GSM215066 2 0.1529 0.9124 0.000 0.960 0.040
#> GSM215067 2 0.1964 0.9063 0.000 0.944 0.056
#> GSM215068 2 0.1643 0.9118 0.000 0.956 0.044
#> GSM215069 2 0.1031 0.9117 0.000 0.976 0.024
#> GSM215070 2 0.4887 0.8456 0.000 0.772 0.228
#> GSM215071 2 0.1860 0.9114 0.000 0.948 0.052
#> GSM215072 2 0.5733 0.7901 0.000 0.676 0.324
#> GSM215073 2 0.1289 0.9106 0.000 0.968 0.032
#> GSM215074 2 0.1163 0.9105 0.000 0.972 0.028
#> GSM215075 2 0.1643 0.9135 0.000 0.956 0.044
#> GSM215076 2 0.5785 0.7887 0.000 0.668 0.332
#> GSM215077 2 0.2537 0.9054 0.000 0.920 0.080
#> GSM215078 2 0.1289 0.9116 0.000 0.968 0.032
#> GSM215079 2 0.2261 0.9097 0.000 0.932 0.068
#> GSM215080 2 0.1753 0.9123 0.000 0.952 0.048
#> GSM215081 2 0.5733 0.7911 0.000 0.676 0.324
#> GSM215082 2 0.5363 0.8248 0.000 0.724 0.276
#> GSM215083 1 0.6180 -0.4744 0.584 0.000 0.416
#> GSM215084 1 0.1964 0.7140 0.944 0.000 0.056
#> GSM215085 1 0.5882 -0.1118 0.652 0.000 0.348
#> GSM215086 3 0.6267 0.9172 0.452 0.000 0.548
#> GSM215087 1 0.2448 0.6955 0.924 0.000 0.076
#> GSM215088 3 0.6260 0.9144 0.448 0.000 0.552
#> GSM215089 1 0.2796 0.7082 0.908 0.000 0.092
#> GSM215090 1 0.3038 0.6865 0.896 0.000 0.104
#> GSM215091 1 0.4346 0.6134 0.816 0.000 0.184
#> GSM215092 1 0.3752 0.6836 0.856 0.000 0.144
#> GSM215093 3 0.6215 0.9299 0.428 0.000 0.572
#> GSM215094 1 0.1860 0.7029 0.948 0.000 0.052
#> GSM215095 1 0.1289 0.7030 0.968 0.000 0.032
#> GSM215096 1 0.3116 0.6870 0.892 0.000 0.108
#> GSM215097 1 0.5591 0.3085 0.696 0.000 0.304
#> GSM215098 1 0.3116 0.6941 0.892 0.000 0.108
#> GSM215099 1 0.4002 0.6498 0.840 0.000 0.160
#> GSM215100 1 0.3619 0.6668 0.864 0.000 0.136
#> GSM215101 1 0.3412 0.6967 0.876 0.000 0.124
#> GSM215102 1 0.5882 -0.1403 0.652 0.000 0.348
#> GSM215103 1 0.5988 -0.1526 0.632 0.000 0.368
#> GSM215104 1 0.4750 0.5307 0.784 0.000 0.216
#> GSM215105 1 0.2711 0.7102 0.912 0.000 0.088
#> GSM215106 1 0.4235 0.6227 0.824 0.000 0.176
#> GSM215107 1 0.2066 0.7172 0.940 0.000 0.060
#> GSM215108 1 0.6045 -0.3522 0.620 0.000 0.380
#> GSM215109 3 0.6267 0.9251 0.452 0.000 0.548
#> GSM215110 1 0.5785 -0.0245 0.668 0.000 0.332
#> GSM215111 1 0.2448 0.7093 0.924 0.000 0.076
#> GSM215112 1 0.1529 0.6986 0.960 0.000 0.040
#> GSM215113 1 0.2165 0.7111 0.936 0.000 0.064
#> GSM215114 1 0.2356 0.6964 0.928 0.000 0.072
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.513 0.5322 0.000 0.668 0.020 0.312
#> GSM215052 4 0.550 0.4330 0.000 0.464 0.016 0.520
#> GSM215053 2 0.429 0.6674 0.000 0.772 0.016 0.212
#> GSM215054 2 0.384 0.6718 0.000 0.816 0.016 0.168
#> GSM215055 2 0.327 0.7054 0.000 0.856 0.012 0.132
#> GSM215056 2 0.385 0.6618 0.000 0.808 0.012 0.180
#> GSM215057 2 0.425 0.6193 0.000 0.768 0.012 0.220
#> GSM215058 4 0.450 0.6883 0.000 0.316 0.000 0.684
#> GSM215059 2 0.247 0.7101 0.000 0.892 0.000 0.108
#> GSM215060 2 0.247 0.7233 0.000 0.900 0.004 0.096
#> GSM215061 2 0.338 0.7030 0.000 0.848 0.012 0.140
#> GSM215062 4 0.413 0.7496 0.000 0.260 0.000 0.740
#> GSM215063 2 0.401 0.6400 0.000 0.800 0.016 0.184
#> GSM215064 4 0.410 0.7481 0.000 0.256 0.000 0.744
#> GSM215065 2 0.348 0.6990 0.000 0.840 0.012 0.148
#> GSM215066 2 0.460 0.5983 0.000 0.736 0.016 0.248
#> GSM215067 2 0.425 0.6293 0.000 0.768 0.012 0.220
#> GSM215068 2 0.458 0.5628 0.000 0.728 0.012 0.260
#> GSM215069 2 0.372 0.6697 0.000 0.820 0.012 0.168
#> GSM215070 4 0.551 0.2904 0.000 0.484 0.016 0.500
#> GSM215071 2 0.432 0.5921 0.000 0.760 0.012 0.228
#> GSM215072 4 0.482 0.7463 0.000 0.296 0.012 0.692
#> GSM215073 2 0.194 0.7191 0.000 0.924 0.000 0.076
#> GSM215074 2 0.265 0.7175 0.000 0.880 0.000 0.120
#> GSM215075 2 0.472 0.6054 0.000 0.720 0.016 0.264
#> GSM215076 4 0.416 0.7247 0.000 0.240 0.004 0.756
#> GSM215077 2 0.509 0.4010 0.000 0.660 0.016 0.324
#> GSM215078 2 0.354 0.7093 0.000 0.828 0.008 0.164
#> GSM215079 2 0.465 0.4465 0.000 0.684 0.004 0.312
#> GSM215080 2 0.459 0.5481 0.000 0.712 0.008 0.280
#> GSM215081 4 0.461 0.7367 0.000 0.304 0.004 0.692
#> GSM215082 4 0.529 0.5505 0.000 0.404 0.012 0.584
#> GSM215083 3 0.573 0.3038 0.428 0.000 0.544 0.028
#> GSM215084 1 0.310 0.6651 0.868 0.000 0.120 0.012
#> GSM215085 3 0.541 0.4305 0.408 0.000 0.576 0.016
#> GSM215086 3 0.398 0.6793 0.192 0.000 0.796 0.012
#> GSM215087 1 0.373 0.6397 0.848 0.000 0.108 0.044
#> GSM215088 3 0.431 0.6796 0.192 0.000 0.784 0.024
#> GSM215089 1 0.432 0.6552 0.776 0.000 0.204 0.020
#> GSM215090 1 0.432 0.6341 0.776 0.000 0.204 0.020
#> GSM215091 1 0.562 0.4956 0.640 0.000 0.320 0.040
#> GSM215092 1 0.429 0.6286 0.772 0.000 0.212 0.016
#> GSM215093 3 0.322 0.6666 0.128 0.000 0.860 0.012
#> GSM215094 1 0.284 0.6649 0.896 0.000 0.076 0.028
#> GSM215095 1 0.151 0.6632 0.956 0.000 0.028 0.016
#> GSM215096 1 0.479 0.5837 0.756 0.000 0.204 0.040
#> GSM215097 1 0.530 0.3492 0.580 0.000 0.408 0.012
#> GSM215098 1 0.416 0.6472 0.792 0.000 0.188 0.020
#> GSM215099 1 0.430 0.5580 0.716 0.000 0.284 0.000
#> GSM215100 1 0.431 0.6040 0.736 0.000 0.260 0.004
#> GSM215101 1 0.452 0.6346 0.768 0.000 0.204 0.028
#> GSM215102 1 0.559 -0.0975 0.520 0.000 0.460 0.020
#> GSM215103 1 0.628 -0.1016 0.476 0.000 0.468 0.056
#> GSM215104 1 0.540 0.4252 0.644 0.000 0.328 0.028
#> GSM215105 1 0.461 0.6154 0.752 0.000 0.224 0.024
#> GSM215106 1 0.506 0.5448 0.692 0.000 0.284 0.024
#> GSM215107 1 0.334 0.6792 0.860 0.000 0.120 0.020
#> GSM215108 3 0.531 0.3684 0.412 0.000 0.576 0.012
#> GSM215109 3 0.389 0.6693 0.196 0.000 0.796 0.008
#> GSM215110 1 0.539 -0.0232 0.532 0.000 0.456 0.012
#> GSM215111 1 0.446 0.6472 0.768 0.000 0.208 0.024
#> GSM215112 1 0.270 0.6442 0.904 0.000 0.068 0.028
#> GSM215113 1 0.292 0.6731 0.860 0.000 0.140 0.000
#> GSM215114 1 0.488 0.5638 0.756 0.000 0.196 0.048
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.690 0.25517 0.000 0.400 0.004 0.304 NA
#> GSM215052 4 0.635 0.32637 0.000 0.348 0.000 0.480 NA
#> GSM215053 2 0.603 0.53655 0.000 0.568 0.000 0.164 NA
#> GSM215054 2 0.612 0.53317 0.000 0.572 0.004 0.156 NA
#> GSM215055 2 0.518 0.60314 0.000 0.696 0.004 0.112 NA
#> GSM215056 2 0.529 0.58565 0.000 0.684 0.004 0.116 NA
#> GSM215057 2 0.525 0.57435 0.000 0.692 0.004 0.176 NA
#> GSM215058 4 0.480 0.65631 0.000 0.196 0.000 0.716 NA
#> GSM215059 2 0.411 0.64871 0.000 0.796 0.004 0.084 NA
#> GSM215060 2 0.279 0.66845 0.000 0.880 0.000 0.056 NA
#> GSM215061 2 0.436 0.63112 0.000 0.768 0.000 0.104 NA
#> GSM215062 4 0.301 0.71057 0.000 0.172 0.000 0.824 NA
#> GSM215063 2 0.592 0.51926 0.000 0.600 0.004 0.140 NA
#> GSM215064 4 0.325 0.70776 0.000 0.184 0.000 0.808 NA
#> GSM215065 2 0.373 0.65040 0.000 0.816 0.000 0.112 NA
#> GSM215066 2 0.522 0.56218 0.000 0.684 0.000 0.176 NA
#> GSM215067 2 0.591 0.54139 0.000 0.616 0.004 0.192 NA
#> GSM215068 2 0.510 0.55649 0.000 0.696 0.000 0.176 NA
#> GSM215069 2 0.409 0.62856 0.000 0.788 0.000 0.128 NA
#> GSM215070 4 0.612 0.30584 0.000 0.412 0.000 0.460 NA
#> GSM215071 2 0.473 0.52747 0.000 0.724 0.000 0.188 NA
#> GSM215072 4 0.436 0.71188 0.000 0.184 0.000 0.752 NA
#> GSM215073 2 0.320 0.66248 0.000 0.860 0.004 0.056 NA
#> GSM215074 2 0.381 0.65807 0.000 0.812 0.000 0.096 NA
#> GSM215075 2 0.564 0.56361 0.000 0.636 0.000 0.176 NA
#> GSM215076 4 0.338 0.67198 0.000 0.104 0.000 0.840 NA
#> GSM215077 2 0.549 0.38795 0.000 0.628 0.000 0.264 NA
#> GSM215078 2 0.519 0.63196 0.000 0.688 0.000 0.144 NA
#> GSM215079 2 0.614 0.49515 0.000 0.576 0.004 0.248 NA
#> GSM215080 2 0.529 0.56307 0.000 0.672 0.000 0.200 NA
#> GSM215081 4 0.415 0.67865 0.000 0.216 0.000 0.748 NA
#> GSM215082 4 0.601 0.46625 0.000 0.332 0.000 0.536 NA
#> GSM215083 3 0.607 0.29069 0.368 0.000 0.516 0.004 NA
#> GSM215084 1 0.407 0.60777 0.800 0.000 0.100 0.004 NA
#> GSM215085 3 0.639 0.21107 0.380 0.000 0.468 0.004 NA
#> GSM215086 3 0.334 0.57923 0.100 0.000 0.848 0.004 NA
#> GSM215087 1 0.498 0.52716 0.676 0.000 0.072 0.000 NA
#> GSM215088 3 0.381 0.58072 0.116 0.000 0.816 0.004 NA
#> GSM215089 1 0.444 0.60484 0.756 0.000 0.156 0.000 NA
#> GSM215090 1 0.522 0.53456 0.692 0.000 0.208 0.008 NA
#> GSM215091 1 0.625 0.39208 0.564 0.000 0.228 0.004 NA
#> GSM215092 1 0.449 0.57103 0.740 0.000 0.192 0.000 NA
#> GSM215093 3 0.293 0.58022 0.068 0.000 0.872 0.000 NA
#> GSM215094 1 0.399 0.60990 0.792 0.000 0.068 0.000 NA
#> GSM215095 1 0.286 0.62396 0.864 0.000 0.024 0.000 NA
#> GSM215096 1 0.555 0.53272 0.656 0.000 0.132 0.004 NA
#> GSM215097 1 0.592 0.12814 0.508 0.000 0.396 0.004 NA
#> GSM215098 1 0.556 0.54319 0.660 0.000 0.164 0.004 NA
#> GSM215099 1 0.501 0.50797 0.684 0.000 0.232 0.000 NA
#> GSM215100 1 0.508 0.51156 0.692 0.000 0.220 0.004 NA
#> GSM215101 1 0.503 0.58481 0.724 0.000 0.148 0.008 NA
#> GSM215102 3 0.547 0.17417 0.428 0.000 0.516 0.004 NA
#> GSM215103 3 0.645 0.17097 0.360 0.000 0.456 0.000 NA
#> GSM215104 1 0.582 0.33259 0.572 0.000 0.324 0.004 NA
#> GSM215105 1 0.466 0.56519 0.740 0.000 0.148 0.000 NA
#> GSM215106 1 0.616 0.36729 0.572 0.000 0.252 0.004 NA
#> GSM215107 1 0.386 0.62701 0.808 0.000 0.100 0.000 NA
#> GSM215108 3 0.576 0.20420 0.416 0.000 0.496 0.000 NA
#> GSM215109 3 0.332 0.58105 0.116 0.000 0.840 0.000 NA
#> GSM215110 1 0.573 -0.00755 0.484 0.000 0.432 0.000 NA
#> GSM215111 1 0.400 0.60142 0.796 0.000 0.120 0.000 NA
#> GSM215112 1 0.420 0.57253 0.752 0.000 0.044 0.000 NA
#> GSM215113 1 0.347 0.62308 0.836 0.000 0.092 0.000 NA
#> GSM215114 1 0.576 0.44886 0.612 0.000 0.152 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 5 0.672 0.000000 0.000 0.300 0.004 0.192 0.456 NA
#> GSM215052 4 0.701 0.127961 0.000 0.296 0.008 0.384 0.268 NA
#> GSM215053 2 0.560 -0.145139 0.000 0.476 0.000 0.076 0.424 NA
#> GSM215054 2 0.590 -0.368504 0.000 0.464 0.008 0.048 0.428 NA
#> GSM215055 2 0.555 0.160510 0.000 0.596 0.000 0.084 0.284 NA
#> GSM215056 2 0.511 0.180654 0.000 0.612 0.004 0.036 0.316 NA
#> GSM215057 2 0.559 0.264811 0.000 0.636 0.004 0.100 0.220 NA
#> GSM215058 4 0.515 0.515063 0.000 0.144 0.000 0.696 0.112 NA
#> GSM215059 2 0.355 0.407416 0.000 0.828 0.004 0.052 0.096 NA
#> GSM215060 2 0.386 0.383743 0.000 0.792 0.000 0.056 0.132 NA
#> GSM215061 2 0.512 0.323870 0.000 0.668 0.000 0.092 0.212 NA
#> GSM215062 4 0.222 0.624930 0.000 0.104 0.000 0.884 0.012 NA
#> GSM215063 2 0.594 0.008635 0.000 0.524 0.008 0.068 0.356 NA
#> GSM215064 4 0.297 0.611536 0.000 0.128 0.000 0.836 0.036 NA
#> GSM215065 2 0.399 0.415689 0.000 0.780 0.004 0.072 0.136 NA
#> GSM215066 2 0.601 0.237001 0.000 0.564 0.000 0.176 0.228 NA
#> GSM215067 2 0.556 0.189548 0.000 0.600 0.004 0.072 0.288 NA
#> GSM215068 2 0.624 0.179100 0.000 0.504 0.000 0.192 0.276 NA
#> GSM215069 2 0.440 0.390875 0.000 0.748 0.000 0.116 0.120 NA
#> GSM215070 4 0.717 0.130489 0.000 0.304 0.008 0.376 0.252 NA
#> GSM215071 2 0.555 0.289505 0.000 0.644 0.004 0.124 0.196 NA
#> GSM215072 4 0.367 0.619853 0.000 0.092 0.000 0.812 0.080 NA
#> GSM215073 2 0.308 0.420054 0.000 0.848 0.000 0.032 0.104 NA
#> GSM215074 2 0.421 0.370530 0.000 0.776 0.000 0.080 0.112 NA
#> GSM215075 2 0.587 0.103743 0.000 0.556 0.004 0.108 0.304 NA
#> GSM215076 4 0.371 0.584973 0.000 0.076 0.000 0.808 0.100 NA
#> GSM215077 2 0.671 0.109382 0.000 0.476 0.008 0.220 0.256 NA
#> GSM215078 2 0.504 0.285450 0.000 0.656 0.000 0.124 0.212 NA
#> GSM215079 2 0.644 0.058194 0.000 0.480 0.000 0.292 0.188 NA
#> GSM215080 2 0.619 0.218366 0.000 0.548 0.000 0.220 0.192 NA
#> GSM215081 4 0.313 0.613414 0.000 0.152 0.000 0.820 0.024 NA
#> GSM215082 4 0.695 0.299955 0.000 0.264 0.008 0.456 0.212 NA
#> GSM215083 1 0.673 0.034222 0.420 0.000 0.344 0.008 0.036 NA
#> GSM215084 1 0.446 0.531475 0.760 0.000 0.092 0.008 0.020 NA
#> GSM215085 1 0.658 -0.025250 0.396 0.000 0.372 0.004 0.028 NA
#> GSM215086 3 0.500 0.532413 0.140 0.000 0.720 0.012 0.028 NA
#> GSM215087 1 0.514 0.439161 0.496 0.000 0.048 0.000 0.016 NA
#> GSM215088 3 0.462 0.543266 0.144 0.000 0.732 0.000 0.024 NA
#> GSM215089 1 0.459 0.514791 0.740 0.000 0.116 0.000 0.028 NA
#> GSM215090 1 0.439 0.505416 0.748 0.000 0.120 0.004 0.008 NA
#> GSM215091 1 0.647 0.317418 0.428 0.000 0.196 0.000 0.032 NA
#> GSM215092 1 0.543 0.448425 0.656 0.000 0.188 0.012 0.016 NA
#> GSM215093 3 0.370 0.574475 0.072 0.000 0.828 0.008 0.032 NA
#> GSM215094 1 0.520 0.532352 0.656 0.000 0.052 0.012 0.028 NA
#> GSM215095 1 0.403 0.561512 0.772 0.000 0.016 0.012 0.028 NA
#> GSM215096 1 0.586 0.484548 0.552 0.000 0.100 0.008 0.024 NA
#> GSM215097 1 0.639 0.249270 0.520 0.000 0.256 0.012 0.024 NA
#> GSM215098 1 0.528 0.481516 0.564 0.000 0.080 0.000 0.012 NA
#> GSM215099 1 0.540 0.479029 0.668 0.000 0.172 0.016 0.016 NA
#> GSM215100 1 0.487 0.495945 0.704 0.000 0.156 0.008 0.008 NA
#> GSM215101 1 0.533 0.488915 0.660 0.000 0.108 0.008 0.020 NA
#> GSM215102 3 0.650 0.198396 0.408 0.000 0.420 0.016 0.032 NA
#> GSM215103 3 0.722 0.215222 0.244 0.000 0.384 0.016 0.052 NA
#> GSM215104 1 0.555 0.403778 0.624 0.000 0.188 0.000 0.024 NA
#> GSM215105 1 0.498 0.536405 0.704 0.000 0.116 0.008 0.016 NA
#> GSM215106 1 0.623 0.433089 0.552 0.000 0.188 0.008 0.028 NA
#> GSM215107 1 0.469 0.561086 0.704 0.000 0.064 0.004 0.016 NA
#> GSM215108 3 0.668 0.226101 0.384 0.000 0.424 0.012 0.048 NA
#> GSM215109 3 0.426 0.578919 0.124 0.000 0.768 0.004 0.016 NA
#> GSM215110 1 0.585 0.000221 0.520 0.000 0.364 0.008 0.028 NA
#> GSM215111 1 0.455 0.540200 0.744 0.000 0.112 0.008 0.012 NA
#> GSM215112 1 0.433 0.500231 0.608 0.000 0.012 0.000 0.012 NA
#> GSM215113 1 0.316 0.548698 0.840 0.000 0.072 0.000 0.004 NA
#> GSM215114 1 0.575 0.367825 0.456 0.000 0.072 0.004 0.028 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> SD:skmeans 64 9.19e-15 1.000 2
#> SD:skmeans 57 4.19e-13 0.998 3
#> SD:skmeans 51 4.89e-11 0.879 4
#> SD:skmeans 47 3.48e-10 0.853 5
#> SD:skmeans 20 4.54e-05 0.467 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 51941 rows and 64 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.799 0.762 0.875 0.2142 0.881 0.758
#> 4 4 0.795 0.724 0.839 0.0356 0.970 0.924
#> 5 5 0.705 0.639 0.775 0.0325 0.906 0.771
#> 6 6 0.713 0.631 0.783 0.0219 0.935 0.831
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.0000 1.0000 0.000 1 0.000
#> GSM215052 2 0.0000 1.0000 0.000 1 0.000
#> GSM215053 2 0.0000 1.0000 0.000 1 0.000
#> GSM215054 2 0.0000 1.0000 0.000 1 0.000
#> GSM215055 2 0.0000 1.0000 0.000 1 0.000
#> GSM215056 2 0.0000 1.0000 0.000 1 0.000
#> GSM215057 2 0.0000 1.0000 0.000 1 0.000
#> GSM215058 2 0.0000 1.0000 0.000 1 0.000
#> GSM215059 2 0.0000 1.0000 0.000 1 0.000
#> GSM215060 2 0.0000 1.0000 0.000 1 0.000
#> GSM215061 2 0.0000 1.0000 0.000 1 0.000
#> GSM215062 2 0.0000 1.0000 0.000 1 0.000
#> GSM215063 2 0.0000 1.0000 0.000 1 0.000
#> GSM215064 2 0.0000 1.0000 0.000 1 0.000
#> GSM215065 2 0.0000 1.0000 0.000 1 0.000
#> GSM215066 2 0.0000 1.0000 0.000 1 0.000
#> GSM215067 2 0.0000 1.0000 0.000 1 0.000
#> GSM215068 2 0.0000 1.0000 0.000 1 0.000
#> GSM215069 2 0.0000 1.0000 0.000 1 0.000
#> GSM215070 2 0.0000 1.0000 0.000 1 0.000
#> GSM215071 2 0.0000 1.0000 0.000 1 0.000
#> GSM215072 2 0.0000 1.0000 0.000 1 0.000
#> GSM215073 2 0.0000 1.0000 0.000 1 0.000
#> GSM215074 2 0.0000 1.0000 0.000 1 0.000
#> GSM215075 2 0.0000 1.0000 0.000 1 0.000
#> GSM215076 2 0.0000 1.0000 0.000 1 0.000
#> GSM215077 2 0.0000 1.0000 0.000 1 0.000
#> GSM215078 2 0.0000 1.0000 0.000 1 0.000
#> GSM215079 2 0.0000 1.0000 0.000 1 0.000
#> GSM215080 2 0.0000 1.0000 0.000 1 0.000
#> GSM215081 2 0.0000 1.0000 0.000 1 0.000
#> GSM215082 2 0.0000 1.0000 0.000 1 0.000
#> GSM215083 1 0.1753 0.6914 0.952 0 0.048
#> GSM215084 3 0.3879 0.6782 0.152 0 0.848
#> GSM215085 1 0.4842 0.6206 0.776 0 0.224
#> GSM215086 1 0.1411 0.6970 0.964 0 0.036
#> GSM215087 3 0.6302 0.1156 0.480 0 0.520
#> GSM215088 1 0.4235 0.6660 0.824 0 0.176
#> GSM215089 1 0.6062 0.3892 0.616 0 0.384
#> GSM215090 3 0.5835 0.4480 0.340 0 0.660
#> GSM215091 1 0.0892 0.7003 0.980 0 0.020
#> GSM215092 3 0.4887 0.6775 0.228 0 0.772
#> GSM215093 1 0.4062 0.6652 0.836 0 0.164
#> GSM215094 3 0.5810 0.5919 0.336 0 0.664
#> GSM215095 3 0.4121 0.6638 0.168 0 0.832
#> GSM215096 1 0.2959 0.6971 0.900 0 0.100
#> GSM215097 1 0.1529 0.6893 0.960 0 0.040
#> GSM215098 1 0.4504 0.6404 0.804 0 0.196
#> GSM215099 1 0.6008 -0.0178 0.628 0 0.372
#> GSM215100 1 0.4654 0.6089 0.792 0 0.208
#> GSM215101 1 0.6260 0.2196 0.552 0 0.448
#> GSM215102 1 0.6095 0.0557 0.608 0 0.392
#> GSM215103 1 0.3816 0.6815 0.852 0 0.148
#> GSM215104 1 0.4452 0.5921 0.808 0 0.192
#> GSM215105 3 0.6008 0.6018 0.372 0 0.628
#> GSM215106 1 0.1643 0.7064 0.956 0 0.044
#> GSM215107 3 0.6302 0.1455 0.480 0 0.520
#> GSM215108 1 0.5926 0.0313 0.644 0 0.356
#> GSM215109 1 0.1964 0.6822 0.944 0 0.056
#> GSM215110 3 0.4504 0.5774 0.196 0 0.804
#> GSM215111 3 0.6295 0.4270 0.472 0 0.528
#> GSM215112 3 0.4887 0.6539 0.228 0 0.772
#> GSM215113 3 0.5327 0.6454 0.272 0 0.728
#> GSM215114 1 0.5591 0.5260 0.696 0 0.304
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.0000 0.98849 0.000 1.000 0.000 0.000
#> GSM215052 2 0.0000 0.98849 0.000 1.000 0.000 0.000
#> GSM215053 2 0.0000 0.98849 0.000 1.000 0.000 0.000
#> GSM215054 2 0.0188 0.98799 0.000 0.996 0.000 0.004
#> GSM215055 2 0.0188 0.98863 0.000 0.996 0.000 0.004
#> GSM215056 2 0.0188 0.98799 0.000 0.996 0.000 0.004
#> GSM215057 2 0.0336 0.98786 0.000 0.992 0.000 0.008
#> GSM215058 2 0.1474 0.95983 0.000 0.948 0.000 0.052
#> GSM215059 2 0.0336 0.98786 0.000 0.992 0.000 0.008
#> GSM215060 2 0.0188 0.98863 0.000 0.996 0.000 0.004
#> GSM215061 2 0.0188 0.98863 0.000 0.996 0.000 0.004
#> GSM215062 2 0.1474 0.95983 0.000 0.948 0.000 0.052
#> GSM215063 2 0.0336 0.98786 0.000 0.992 0.000 0.008
#> GSM215064 2 0.1557 0.95997 0.000 0.944 0.000 0.056
#> GSM215065 2 0.0188 0.98863 0.000 0.996 0.000 0.004
#> GSM215066 2 0.0188 0.98863 0.000 0.996 0.000 0.004
#> GSM215067 2 0.0336 0.98786 0.000 0.992 0.000 0.008
#> GSM215068 2 0.0188 0.98863 0.000 0.996 0.000 0.004
#> GSM215069 2 0.0188 0.98863 0.000 0.996 0.000 0.004
#> GSM215070 2 0.0188 0.98745 0.000 0.996 0.000 0.004
#> GSM215071 2 0.0336 0.98786 0.000 0.992 0.000 0.008
#> GSM215072 2 0.1474 0.95983 0.000 0.948 0.000 0.052
#> GSM215073 2 0.0188 0.98863 0.000 0.996 0.000 0.004
#> GSM215074 2 0.0188 0.98799 0.000 0.996 0.000 0.004
#> GSM215075 2 0.0000 0.98849 0.000 1.000 0.000 0.000
#> GSM215076 2 0.1474 0.95983 0.000 0.948 0.000 0.052
#> GSM215077 2 0.0188 0.98863 0.000 0.996 0.000 0.004
#> GSM215078 2 0.0000 0.98849 0.000 1.000 0.000 0.000
#> GSM215079 2 0.0000 0.98849 0.000 1.000 0.000 0.000
#> GSM215080 2 0.0000 0.98849 0.000 1.000 0.000 0.000
#> GSM215081 2 0.1474 0.95983 0.000 0.948 0.000 0.052
#> GSM215082 2 0.0336 0.98709 0.000 0.992 0.000 0.008
#> GSM215083 1 0.2973 0.61644 0.884 0.000 0.096 0.020
#> GSM215084 3 0.3962 0.69436 0.124 0.000 0.832 0.044
#> GSM215085 1 0.6532 0.36595 0.572 0.000 0.092 0.336
#> GSM215086 1 0.2662 0.61811 0.900 0.000 0.084 0.016
#> GSM215087 1 0.6458 0.00550 0.520 0.000 0.408 0.072
#> GSM215088 1 0.4292 0.59909 0.820 0.000 0.080 0.100
#> GSM215089 1 0.5331 0.39462 0.644 0.000 0.332 0.024
#> GSM215090 3 0.5403 0.40039 0.348 0.000 0.628 0.024
#> GSM215091 1 0.1610 0.62392 0.952 0.000 0.032 0.016
#> GSM215092 3 0.4669 0.68932 0.200 0.000 0.764 0.036
#> GSM215093 1 0.5810 0.46806 0.672 0.000 0.072 0.256
#> GSM215094 3 0.7023 0.50736 0.312 0.000 0.544 0.144
#> GSM215095 3 0.5180 0.65560 0.196 0.000 0.740 0.064
#> GSM215096 1 0.4424 0.59077 0.812 0.000 0.100 0.088
#> GSM215097 1 0.2401 0.61351 0.904 0.000 0.092 0.004
#> GSM215098 1 0.4274 0.57117 0.820 0.000 0.108 0.072
#> GSM215099 1 0.6347 0.01918 0.524 0.000 0.412 0.064
#> GSM215100 1 0.4983 0.50320 0.704 0.000 0.272 0.024
#> GSM215101 1 0.5269 0.32988 0.620 0.000 0.364 0.016
#> GSM215102 1 0.6961 0.13665 0.548 0.000 0.316 0.136
#> GSM215103 1 0.3617 0.62223 0.860 0.000 0.064 0.076
#> GSM215104 1 0.5630 0.51280 0.724 0.000 0.140 0.136
#> GSM215105 3 0.5966 0.59789 0.280 0.000 0.648 0.072
#> GSM215106 1 0.1209 0.62858 0.964 0.000 0.032 0.004
#> GSM215107 1 0.6268 -0.01391 0.496 0.000 0.448 0.056
#> GSM215108 1 0.7108 0.00189 0.512 0.000 0.348 0.140
#> GSM215109 1 0.6156 0.37989 0.592 0.000 0.064 0.344
#> GSM215110 3 0.4010 0.55375 0.100 0.000 0.836 0.064
#> GSM215111 3 0.5971 0.41303 0.368 0.000 0.584 0.048
#> GSM215112 3 0.6420 0.60537 0.228 0.000 0.640 0.132
#> GSM215113 3 0.4701 0.68516 0.164 0.000 0.780 0.056
#> GSM215114 1 0.5564 0.48564 0.708 0.000 0.216 0.076
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.0162 0.963 0.000 0.996 0.000 0.000 0.004
#> GSM215052 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM215053 2 0.0162 0.963 0.000 0.996 0.000 0.000 0.004
#> GSM215054 2 0.0290 0.963 0.000 0.992 0.000 0.000 0.008
#> GSM215055 2 0.0162 0.964 0.000 0.996 0.000 0.000 0.004
#> GSM215056 2 0.0290 0.963 0.000 0.992 0.000 0.000 0.008
#> GSM215057 2 0.0290 0.963 0.000 0.992 0.000 0.000 0.008
#> GSM215058 2 0.2773 0.856 0.000 0.836 0.000 0.000 0.164
#> GSM215059 2 0.0290 0.963 0.000 0.992 0.000 0.000 0.008
#> GSM215060 2 0.0162 0.964 0.000 0.996 0.000 0.000 0.004
#> GSM215061 2 0.0162 0.964 0.000 0.996 0.000 0.000 0.004
#> GSM215062 2 0.2852 0.846 0.000 0.828 0.000 0.000 0.172
#> GSM215063 2 0.0290 0.963 0.000 0.992 0.000 0.000 0.008
#> GSM215064 2 0.2891 0.847 0.000 0.824 0.000 0.000 0.176
#> GSM215065 2 0.0162 0.964 0.000 0.996 0.000 0.000 0.004
#> GSM215066 2 0.0162 0.964 0.000 0.996 0.000 0.000 0.004
#> GSM215067 2 0.0290 0.963 0.000 0.992 0.000 0.000 0.008
#> GSM215068 2 0.0162 0.964 0.000 0.996 0.000 0.000 0.004
#> GSM215069 2 0.0162 0.964 0.000 0.996 0.000 0.000 0.004
#> GSM215070 2 0.0404 0.961 0.000 0.988 0.000 0.000 0.012
#> GSM215071 2 0.0290 0.963 0.000 0.992 0.000 0.000 0.008
#> GSM215072 2 0.2813 0.852 0.000 0.832 0.000 0.000 0.168
#> GSM215073 2 0.0162 0.964 0.000 0.996 0.000 0.000 0.004
#> GSM215074 2 0.0290 0.963 0.000 0.992 0.000 0.000 0.008
#> GSM215075 2 0.0162 0.963 0.000 0.996 0.000 0.000 0.004
#> GSM215076 2 0.2891 0.845 0.000 0.824 0.000 0.000 0.176
#> GSM215077 2 0.0162 0.964 0.000 0.996 0.000 0.000 0.004
#> GSM215078 2 0.0162 0.963 0.000 0.996 0.000 0.000 0.004
#> GSM215079 2 0.0290 0.962 0.000 0.992 0.000 0.000 0.008
#> GSM215080 2 0.0000 0.964 0.000 1.000 0.000 0.000 0.000
#> GSM215081 2 0.2813 0.852 0.000 0.832 0.000 0.000 0.168
#> GSM215082 2 0.1043 0.947 0.000 0.960 0.000 0.000 0.040
#> GSM215083 3 0.2909 0.670 0.140 0.000 0.848 0.012 0.000
#> GSM215084 1 0.4335 0.341 0.740 0.000 0.036 0.220 0.004
#> GSM215085 5 0.7136 0.000 0.232 0.000 0.296 0.024 0.448
#> GSM215086 3 0.3730 0.665 0.112 0.000 0.828 0.048 0.012
#> GSM215087 1 0.4151 0.145 0.652 0.000 0.344 0.004 0.000
#> GSM215088 3 0.4327 0.613 0.360 0.000 0.632 0.008 0.000
#> GSM215089 3 0.6271 0.239 0.412 0.000 0.440 0.148 0.000
#> GSM215090 1 0.5791 0.329 0.616 0.000 0.196 0.188 0.000
#> GSM215091 3 0.2424 0.670 0.132 0.000 0.868 0.000 0.000
#> GSM215092 1 0.4771 0.315 0.712 0.000 0.060 0.224 0.004
#> GSM215093 3 0.6541 0.203 0.196 0.000 0.612 0.056 0.136
#> GSM215094 1 0.4979 0.347 0.700 0.000 0.228 0.064 0.008
#> GSM215095 1 0.2408 0.398 0.892 0.000 0.016 0.092 0.000
#> GSM215096 3 0.3741 0.516 0.264 0.000 0.732 0.004 0.000
#> GSM215097 3 0.3546 0.663 0.116 0.000 0.832 0.048 0.004
#> GSM215098 3 0.4196 0.584 0.356 0.000 0.640 0.004 0.000
#> GSM215099 1 0.5915 0.187 0.476 0.000 0.432 0.088 0.004
#> GSM215100 3 0.5912 0.467 0.184 0.000 0.616 0.196 0.004
#> GSM215101 1 0.5498 -0.235 0.496 0.000 0.440 0.064 0.000
#> GSM215102 1 0.6464 0.130 0.468 0.000 0.412 0.092 0.028
#> GSM215103 3 0.5176 0.666 0.172 0.000 0.716 0.096 0.016
#> GSM215104 3 0.5640 0.355 0.308 0.000 0.608 0.072 0.012
#> GSM215105 1 0.4254 0.399 0.740 0.000 0.220 0.040 0.000
#> GSM215106 3 0.2732 0.681 0.160 0.000 0.840 0.000 0.000
#> GSM215107 1 0.4655 0.158 0.644 0.000 0.328 0.028 0.000
#> GSM215108 1 0.6250 0.182 0.496 0.000 0.400 0.080 0.024
#> GSM215109 4 0.7837 -0.320 0.092 0.000 0.256 0.436 0.216
#> GSM215110 4 0.5665 -0.113 0.384 0.000 0.072 0.540 0.004
#> GSM215111 1 0.5644 0.403 0.584 0.000 0.316 0.100 0.000
#> GSM215112 1 0.1041 0.430 0.964 0.000 0.032 0.004 0.000
#> GSM215113 1 0.5147 0.290 0.664 0.000 0.068 0.264 0.004
#> GSM215114 3 0.4440 0.417 0.468 0.000 0.528 0.004 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 2 0.0748 0.94876 0.000 0.976 0.016 0.004 0.000 0.004
#> GSM215052 2 0.0603 0.94987 0.000 0.980 0.016 0.004 0.000 0.000
#> GSM215053 2 0.0748 0.94876 0.000 0.976 0.016 0.004 0.000 0.004
#> GSM215054 2 0.0862 0.94856 0.000 0.972 0.016 0.008 0.000 0.004
#> GSM215055 2 0.0000 0.95136 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215056 2 0.0665 0.95055 0.000 0.980 0.008 0.008 0.000 0.004
#> GSM215057 2 0.0260 0.95033 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM215058 2 0.3144 0.83350 0.000 0.808 0.016 0.004 0.000 0.172
#> GSM215059 2 0.0260 0.95033 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM215060 2 0.0000 0.95136 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215061 2 0.0000 0.95136 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215062 2 0.3023 0.78393 0.000 0.768 0.000 0.000 0.000 0.232
#> GSM215063 2 0.0260 0.95033 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM215064 2 0.3023 0.78393 0.000 0.768 0.000 0.000 0.000 0.232
#> GSM215065 2 0.0000 0.95136 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215066 2 0.0000 0.95136 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215067 2 0.0260 0.95033 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM215068 2 0.0000 0.95136 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215069 2 0.0000 0.95136 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215070 2 0.1003 0.94515 0.000 0.964 0.016 0.000 0.000 0.020
#> GSM215071 2 0.0146 0.95081 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM215072 2 0.2946 0.83512 0.000 0.812 0.012 0.000 0.000 0.176
#> GSM215073 2 0.0146 0.95115 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM215074 2 0.0964 0.94812 0.000 0.968 0.016 0.012 0.000 0.004
#> GSM215075 2 0.0748 0.94876 0.000 0.976 0.016 0.004 0.000 0.004
#> GSM215076 2 0.3136 0.78893 0.000 0.768 0.004 0.000 0.000 0.228
#> GSM215077 2 0.0000 0.95136 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215078 2 0.0653 0.94984 0.000 0.980 0.012 0.004 0.000 0.004
#> GSM215079 2 0.0862 0.94806 0.000 0.972 0.016 0.004 0.000 0.008
#> GSM215080 2 0.0146 0.95149 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM215081 2 0.3311 0.80629 0.000 0.780 0.012 0.004 0.000 0.204
#> GSM215082 2 0.1679 0.93351 0.000 0.936 0.016 0.012 0.000 0.036
#> GSM215083 1 0.2036 0.58511 0.916 0.000 0.008 0.028 0.048 0.000
#> GSM215084 5 0.4511 0.56592 0.116 0.000 0.036 0.084 0.760 0.004
#> GSM215085 4 0.4094 0.00000 0.224 0.000 0.008 0.728 0.040 0.000
#> GSM215086 1 0.3214 0.55152 0.860 0.000 0.068 0.012 0.028 0.032
#> GSM215087 1 0.5478 -0.05670 0.452 0.000 0.000 0.124 0.424 0.000
#> GSM215088 1 0.4294 0.55410 0.728 0.000 0.004 0.188 0.080 0.000
#> GSM215089 1 0.4788 0.30943 0.560 0.000 0.000 0.028 0.396 0.016
#> GSM215090 5 0.4641 0.32079 0.304 0.000 0.004 0.028 0.648 0.016
#> GSM215091 1 0.0858 0.57484 0.968 0.000 0.000 0.028 0.004 0.000
#> GSM215092 5 0.4602 0.57235 0.172 0.000 0.048 0.028 0.740 0.012
#> GSM215093 1 0.6724 -0.01952 0.420 0.000 0.016 0.096 0.068 0.400
#> GSM215094 5 0.6650 0.35048 0.308 0.000 0.060 0.172 0.460 0.000
#> GSM215095 5 0.4494 0.56269 0.140 0.000 0.004 0.136 0.720 0.000
#> GSM215096 1 0.3243 0.49764 0.812 0.000 0.004 0.156 0.028 0.000
#> GSM215097 1 0.2152 0.57883 0.912 0.000 0.040 0.012 0.036 0.000
#> GSM215098 1 0.3961 0.53779 0.764 0.000 0.000 0.124 0.112 0.000
#> GSM215099 1 0.6036 0.00253 0.516 0.000 0.040 0.112 0.332 0.000
#> GSM215100 1 0.4957 0.44369 0.668 0.000 0.044 0.016 0.256 0.016
#> GSM215101 1 0.4524 0.24989 0.560 0.000 0.000 0.036 0.404 0.000
#> GSM215102 1 0.7314 0.05936 0.480 0.000 0.092 0.148 0.248 0.032
#> GSM215103 1 0.3730 0.58012 0.812 0.000 0.100 0.028 0.060 0.000
#> GSM215104 1 0.5442 0.41479 0.672 0.000 0.068 0.156 0.104 0.000
#> GSM215105 5 0.5466 0.47851 0.300 0.000 0.000 0.136 0.560 0.004
#> GSM215106 1 0.1232 0.58997 0.956 0.000 0.004 0.016 0.024 0.000
#> GSM215107 5 0.5318 -0.01064 0.448 0.000 0.004 0.088 0.460 0.000
#> GSM215108 1 0.7055 -0.07056 0.464 0.000 0.076 0.152 0.292 0.016
#> GSM215109 3 0.2865 0.00000 0.140 0.000 0.840 0.012 0.008 0.000
#> GSM215110 5 0.7180 -0.26416 0.012 0.000 0.108 0.136 0.444 0.300
#> GSM215111 5 0.5507 0.35280 0.372 0.000 0.008 0.092 0.524 0.004
#> GSM215112 5 0.5146 0.51510 0.148 0.000 0.000 0.236 0.616 0.000
#> GSM215113 5 0.4229 0.56267 0.132 0.000 0.056 0.032 0.776 0.004
#> GSM215114 1 0.4834 0.44949 0.660 0.000 0.000 0.128 0.212 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> SD:pam 64 9.19e-15 1.000 2
#> SD:pam 55 1.14e-12 0.998 3
#> SD:pam 51 8.42e-12 0.997 4
#> SD:pam 41 2.73e-09 0.994 5
#> SD:pam 45 1.69e-10 0.997 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 51941 rows and 64 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.755 0.807 0.899 0.1709 0.933 0.864
#> 4 4 0.657 0.706 0.816 0.1491 0.889 0.748
#> 5 5 0.632 0.622 0.742 0.0791 0.944 0.844
#> 6 6 0.642 0.702 0.768 0.0591 0.838 0.510
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.0892 0.9314 0.000 0.980 0.020
#> GSM215052 2 0.4654 0.8616 0.000 0.792 0.208
#> GSM215053 2 0.0592 0.9330 0.000 0.988 0.012
#> GSM215054 2 0.0592 0.9330 0.000 0.988 0.012
#> GSM215055 2 0.0424 0.9340 0.000 0.992 0.008
#> GSM215056 2 0.0237 0.9335 0.000 0.996 0.004
#> GSM215057 2 0.0424 0.9340 0.000 0.992 0.008
#> GSM215058 2 0.4121 0.8807 0.000 0.832 0.168
#> GSM215059 2 0.0424 0.9340 0.000 0.992 0.008
#> GSM215060 2 0.0424 0.9340 0.000 0.992 0.008
#> GSM215061 2 0.0424 0.9340 0.000 0.992 0.008
#> GSM215062 2 0.4654 0.8616 0.000 0.792 0.208
#> GSM215063 2 0.1289 0.9262 0.000 0.968 0.032
#> GSM215064 2 0.4654 0.8616 0.000 0.792 0.208
#> GSM215065 2 0.0237 0.9342 0.000 0.996 0.004
#> GSM215066 2 0.0424 0.9340 0.000 0.992 0.008
#> GSM215067 2 0.1031 0.9258 0.000 0.976 0.024
#> GSM215068 2 0.0424 0.9340 0.000 0.992 0.008
#> GSM215069 2 0.0424 0.9340 0.000 0.992 0.008
#> GSM215070 2 0.4654 0.8616 0.000 0.792 0.208
#> GSM215071 2 0.3038 0.9047 0.000 0.896 0.104
#> GSM215072 2 0.4654 0.8616 0.000 0.792 0.208
#> GSM215073 2 0.0424 0.9340 0.000 0.992 0.008
#> GSM215074 2 0.0424 0.9340 0.000 0.992 0.008
#> GSM215075 2 0.0424 0.9340 0.000 0.992 0.008
#> GSM215076 2 0.4654 0.8616 0.000 0.792 0.208
#> GSM215077 2 0.4178 0.8789 0.000 0.828 0.172
#> GSM215078 2 0.0237 0.9342 0.000 0.996 0.004
#> GSM215079 2 0.0000 0.9339 0.000 1.000 0.000
#> GSM215080 2 0.0000 0.9339 0.000 1.000 0.000
#> GSM215081 2 0.4654 0.8616 0.000 0.792 0.208
#> GSM215082 2 0.4654 0.8616 0.000 0.792 0.208
#> GSM215083 1 0.1643 0.8057 0.956 0.000 0.044
#> GSM215084 1 0.4605 0.6164 0.796 0.000 0.204
#> GSM215085 1 0.5733 -0.1194 0.676 0.000 0.324
#> GSM215086 3 0.6235 0.7653 0.436 0.000 0.564
#> GSM215087 1 0.0237 0.8531 0.996 0.000 0.004
#> GSM215088 3 0.6252 0.7595 0.444 0.000 0.556
#> GSM215089 1 0.0000 0.8561 1.000 0.000 0.000
#> GSM215090 1 0.0000 0.8561 1.000 0.000 0.000
#> GSM215091 1 0.0237 0.8525 0.996 0.000 0.004
#> GSM215092 1 0.0000 0.8561 1.000 0.000 0.000
#> GSM215093 3 0.6192 0.7715 0.420 0.000 0.580
#> GSM215094 1 0.4605 0.6164 0.796 0.000 0.204
#> GSM215095 1 0.0000 0.8561 1.000 0.000 0.000
#> GSM215096 1 0.1163 0.8346 0.972 0.000 0.028
#> GSM215097 1 0.0000 0.8561 1.000 0.000 0.000
#> GSM215098 1 0.0000 0.8561 1.000 0.000 0.000
#> GSM215099 1 0.0000 0.8561 1.000 0.000 0.000
#> GSM215100 1 0.0000 0.8561 1.000 0.000 0.000
#> GSM215101 1 0.0000 0.8561 1.000 0.000 0.000
#> GSM215102 1 0.6154 -0.0568 0.592 0.000 0.408
#> GSM215103 1 0.4654 0.6109 0.792 0.000 0.208
#> GSM215104 1 0.4605 0.6164 0.796 0.000 0.204
#> GSM215105 1 0.0000 0.8561 1.000 0.000 0.000
#> GSM215106 1 0.0000 0.8561 1.000 0.000 0.000
#> GSM215107 1 0.0000 0.8561 1.000 0.000 0.000
#> GSM215108 3 0.6299 0.3758 0.476 0.000 0.524
#> GSM215109 3 0.5016 0.6539 0.240 0.000 0.760
#> GSM215110 1 0.5560 0.0743 0.700 0.000 0.300
#> GSM215111 1 0.0000 0.8561 1.000 0.000 0.000
#> GSM215112 1 0.0000 0.8561 1.000 0.000 0.000
#> GSM215113 1 0.0000 0.8561 1.000 0.000 0.000
#> GSM215114 1 0.4346 0.6477 0.816 0.000 0.184
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.5093 0.553 0.000 0.640 0.012 0.348
#> GSM215052 4 0.4564 0.886 0.000 0.328 0.000 0.672
#> GSM215053 2 0.5668 0.572 0.000 0.652 0.048 0.300
#> GSM215054 2 0.5668 0.572 0.000 0.652 0.048 0.300
#> GSM215055 2 0.2032 0.760 0.000 0.936 0.028 0.036
#> GSM215056 2 0.5198 0.615 0.000 0.708 0.040 0.252
#> GSM215057 2 0.0000 0.779 0.000 1.000 0.000 0.000
#> GSM215058 2 0.4907 -0.103 0.000 0.580 0.000 0.420
#> GSM215059 2 0.0000 0.779 0.000 1.000 0.000 0.000
#> GSM215060 2 0.0000 0.779 0.000 1.000 0.000 0.000
#> GSM215061 2 0.0000 0.779 0.000 1.000 0.000 0.000
#> GSM215062 4 0.4624 0.908 0.000 0.340 0.000 0.660
#> GSM215063 2 0.5836 0.558 0.000 0.640 0.056 0.304
#> GSM215064 4 0.4697 0.908 0.000 0.356 0.000 0.644
#> GSM215065 2 0.0592 0.774 0.000 0.984 0.000 0.016
#> GSM215066 2 0.1022 0.767 0.000 0.968 0.000 0.032
#> GSM215067 2 0.5472 0.587 0.000 0.676 0.044 0.280
#> GSM215068 2 0.0188 0.777 0.000 0.996 0.000 0.004
#> GSM215069 2 0.0000 0.779 0.000 1.000 0.000 0.000
#> GSM215070 4 0.4866 0.873 0.000 0.404 0.000 0.596
#> GSM215071 2 0.3907 0.365 0.000 0.768 0.000 0.232
#> GSM215072 4 0.4843 0.881 0.000 0.396 0.000 0.604
#> GSM215073 2 0.0000 0.779 0.000 1.000 0.000 0.000
#> GSM215074 2 0.0000 0.779 0.000 1.000 0.000 0.000
#> GSM215075 2 0.0592 0.774 0.000 0.984 0.000 0.016
#> GSM215076 4 0.3494 0.660 0.000 0.172 0.004 0.824
#> GSM215077 2 0.4916 -0.448 0.000 0.576 0.000 0.424
#> GSM215078 2 0.1211 0.761 0.000 0.960 0.000 0.040
#> GSM215079 2 0.2469 0.719 0.000 0.892 0.000 0.108
#> GSM215080 2 0.2149 0.734 0.000 0.912 0.000 0.088
#> GSM215081 4 0.4730 0.905 0.000 0.364 0.000 0.636
#> GSM215082 4 0.4643 0.909 0.000 0.344 0.000 0.656
#> GSM215083 1 0.3105 0.760 0.868 0.000 0.120 0.012
#> GSM215084 1 0.4764 0.691 0.748 0.000 0.220 0.032
#> GSM215085 1 0.5069 0.300 0.664 0.000 0.320 0.016
#> GSM215086 3 0.4188 0.903 0.244 0.000 0.752 0.004
#> GSM215087 1 0.1584 0.819 0.952 0.000 0.036 0.012
#> GSM215088 3 0.4594 0.868 0.280 0.000 0.712 0.008
#> GSM215089 1 0.0336 0.827 0.992 0.000 0.008 0.000
#> GSM215090 1 0.2222 0.816 0.924 0.000 0.060 0.016
#> GSM215091 1 0.1975 0.814 0.936 0.000 0.048 0.016
#> GSM215092 1 0.1488 0.824 0.956 0.000 0.032 0.012
#> GSM215093 3 0.4262 0.904 0.236 0.000 0.756 0.008
#> GSM215094 1 0.4387 0.695 0.776 0.000 0.200 0.024
#> GSM215095 1 0.0657 0.828 0.984 0.000 0.004 0.012
#> GSM215096 1 0.2473 0.805 0.908 0.000 0.080 0.012
#> GSM215097 1 0.1151 0.827 0.968 0.000 0.024 0.008
#> GSM215098 1 0.1042 0.825 0.972 0.000 0.020 0.008
#> GSM215099 1 0.2142 0.816 0.928 0.000 0.056 0.016
#> GSM215100 1 0.2300 0.816 0.920 0.000 0.064 0.016
#> GSM215101 1 0.1488 0.819 0.956 0.000 0.032 0.012
#> GSM215102 1 0.5984 0.354 0.580 0.000 0.372 0.048
#> GSM215103 1 0.4826 0.634 0.716 0.000 0.264 0.020
#> GSM215104 1 0.4446 0.694 0.776 0.000 0.196 0.028
#> GSM215105 1 0.1635 0.820 0.948 0.000 0.044 0.008
#> GSM215106 1 0.0804 0.826 0.980 0.000 0.012 0.008
#> GSM215107 1 0.1975 0.815 0.936 0.000 0.048 0.016
#> GSM215108 1 0.6134 0.102 0.508 0.000 0.444 0.048
#> GSM215109 3 0.3105 0.786 0.120 0.000 0.868 0.012
#> GSM215110 1 0.5698 0.356 0.636 0.000 0.320 0.044
#> GSM215111 1 0.1545 0.821 0.952 0.000 0.040 0.008
#> GSM215112 1 0.0804 0.827 0.980 0.000 0.012 0.008
#> GSM215113 1 0.2222 0.816 0.924 0.000 0.060 0.016
#> GSM215114 1 0.4635 0.687 0.756 0.000 0.216 0.028
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.6268 0.190 0.000 0.552 0.004 0.268 NA
#> GSM215052 4 0.0955 0.797 0.000 0.028 0.000 0.968 NA
#> GSM215053 2 0.5261 0.373 0.000 0.572 0.004 0.044 NA
#> GSM215054 2 0.5206 0.371 0.000 0.572 0.004 0.040 NA
#> GSM215055 2 0.5585 0.614 0.000 0.652 0.004 0.208 NA
#> GSM215056 2 0.4987 0.443 0.000 0.648 0.004 0.044 NA
#> GSM215057 2 0.3305 0.679 0.000 0.776 0.000 0.224 NA
#> GSM215058 4 0.4128 0.664 0.000 0.220 0.020 0.752 NA
#> GSM215059 2 0.3305 0.679 0.000 0.776 0.000 0.224 NA
#> GSM215060 2 0.3305 0.679 0.000 0.776 0.000 0.224 NA
#> GSM215061 2 0.3491 0.678 0.000 0.768 0.000 0.228 NA
#> GSM215062 4 0.1393 0.801 0.000 0.024 0.008 0.956 NA
#> GSM215063 2 0.4798 0.364 0.000 0.576 0.004 0.016 NA
#> GSM215064 4 0.1978 0.800 0.000 0.032 0.024 0.932 NA
#> GSM215065 2 0.3305 0.679 0.000 0.776 0.000 0.224 NA
#> GSM215066 2 0.3783 0.657 0.000 0.740 0.008 0.252 NA
#> GSM215067 2 0.4457 0.419 0.000 0.656 0.004 0.012 NA
#> GSM215068 2 0.3521 0.673 0.000 0.764 0.004 0.232 NA
#> GSM215069 2 0.3305 0.679 0.000 0.776 0.000 0.224 NA
#> GSM215070 4 0.1197 0.799 0.000 0.048 0.000 0.952 NA
#> GSM215071 4 0.4227 0.116 0.000 0.420 0.000 0.580 NA
#> GSM215072 4 0.1124 0.800 0.000 0.036 0.000 0.960 NA
#> GSM215073 2 0.3461 0.678 0.000 0.772 0.000 0.224 NA
#> GSM215074 2 0.3336 0.676 0.000 0.772 0.000 0.228 NA
#> GSM215075 2 0.3741 0.652 0.000 0.732 0.004 0.264 NA
#> GSM215076 4 0.3060 0.672 0.000 0.128 0.000 0.848 NA
#> GSM215077 4 0.2929 0.658 0.000 0.180 0.000 0.820 NA
#> GSM215078 2 0.4937 0.394 0.000 0.544 0.000 0.428 NA
#> GSM215079 4 0.4653 -0.257 0.000 0.472 0.012 0.516 NA
#> GSM215080 2 0.4648 0.286 0.000 0.524 0.012 0.464 NA
#> GSM215081 4 0.2379 0.796 0.000 0.048 0.028 0.912 NA
#> GSM215082 4 0.0771 0.801 0.000 0.020 0.004 0.976 NA
#> GSM215083 1 0.5538 0.684 0.644 0.000 0.144 0.000 NA
#> GSM215084 1 0.4449 0.610 0.752 0.000 0.080 0.000 NA
#> GSM215085 1 0.6097 0.441 0.556 0.000 0.276 0.000 NA
#> GSM215086 3 0.2540 0.909 0.088 0.000 0.888 0.000 NA
#> GSM215087 1 0.4503 0.718 0.704 0.000 0.040 0.000 NA
#> GSM215088 3 0.3510 0.872 0.128 0.000 0.832 0.008 NA
#> GSM215089 1 0.3319 0.743 0.820 0.000 0.020 0.000 NA
#> GSM215090 1 0.1493 0.711 0.948 0.000 0.028 0.000 NA
#> GSM215091 1 0.5112 0.702 0.664 0.000 0.080 0.000 NA
#> GSM215092 1 0.0451 0.728 0.988 0.000 0.004 0.000 NA
#> GSM215093 3 0.2420 0.908 0.088 0.000 0.896 0.008 NA
#> GSM215094 1 0.5672 0.612 0.544 0.000 0.088 0.000 NA
#> GSM215095 1 0.3690 0.737 0.780 0.000 0.020 0.000 NA
#> GSM215096 1 0.4878 0.713 0.676 0.000 0.060 0.000 NA
#> GSM215097 1 0.3459 0.741 0.832 0.000 0.052 0.000 NA
#> GSM215098 1 0.4404 0.721 0.712 0.000 0.036 0.000 NA
#> GSM215099 1 0.1399 0.713 0.952 0.000 0.028 0.000 NA
#> GSM215100 1 0.1661 0.710 0.940 0.000 0.036 0.000 NA
#> GSM215101 1 0.4430 0.718 0.708 0.000 0.036 0.000 NA
#> GSM215102 1 0.6163 0.322 0.536 0.000 0.164 0.000 NA
#> GSM215103 1 0.6477 0.504 0.456 0.000 0.192 0.000 NA
#> GSM215104 1 0.4986 0.589 0.688 0.000 0.084 0.000 NA
#> GSM215105 1 0.1012 0.720 0.968 0.000 0.020 0.000 NA
#> GSM215106 1 0.4313 0.727 0.732 0.000 0.040 0.000 NA
#> GSM215107 1 0.1399 0.711 0.952 0.000 0.028 0.000 NA
#> GSM215108 1 0.6704 0.168 0.448 0.000 0.216 0.004 NA
#> GSM215109 3 0.4077 0.810 0.044 0.000 0.780 0.004 NA
#> GSM215110 1 0.4783 0.497 0.724 0.000 0.176 0.000 NA
#> GSM215111 1 0.0566 0.724 0.984 0.000 0.012 0.000 NA
#> GSM215112 1 0.4167 0.725 0.724 0.000 0.024 0.000 NA
#> GSM215113 1 0.1399 0.713 0.952 0.000 0.028 0.000 NA
#> GSM215114 1 0.5735 0.620 0.532 0.000 0.092 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 4 0.6021 0.5113 0.000 0.272 0.000 0.492 0.008 0.228
#> GSM215052 6 0.3539 0.8790 0.000 0.220 0.000 0.024 0.000 0.756
#> GSM215053 4 0.4201 0.7745 0.000 0.300 0.000 0.664 0.000 0.036
#> GSM215054 4 0.4210 0.7750 0.000 0.288 0.000 0.672 0.000 0.040
#> GSM215055 2 0.2234 0.7158 0.000 0.872 0.000 0.124 0.000 0.004
#> GSM215056 4 0.3862 0.5621 0.000 0.476 0.000 0.524 0.000 0.000
#> GSM215057 2 0.0146 0.8533 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM215058 6 0.5207 0.6887 0.000 0.356 0.012 0.060 0.004 0.568
#> GSM215059 2 0.0000 0.8534 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215060 2 0.0000 0.8534 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215061 2 0.0972 0.8434 0.000 0.964 0.000 0.028 0.000 0.008
#> GSM215062 6 0.4586 0.8781 0.000 0.236 0.004 0.036 0.024 0.700
#> GSM215063 4 0.2994 0.6948 0.000 0.208 0.000 0.788 0.004 0.000
#> GSM215064 6 0.4915 0.8741 0.000 0.236 0.012 0.044 0.024 0.684
#> GSM215065 2 0.0146 0.8531 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM215066 2 0.1296 0.8419 0.000 0.948 0.000 0.004 0.004 0.044
#> GSM215067 4 0.3852 0.6814 0.000 0.384 0.000 0.612 0.004 0.000
#> GSM215068 2 0.0820 0.8501 0.000 0.972 0.000 0.012 0.000 0.016
#> GSM215069 2 0.0000 0.8534 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215070 6 0.3126 0.8809 0.000 0.248 0.000 0.000 0.000 0.752
#> GSM215071 2 0.3956 0.2075 0.000 0.656 0.004 0.004 0.004 0.332
#> GSM215072 6 0.3050 0.8841 0.000 0.236 0.000 0.000 0.000 0.764
#> GSM215073 2 0.0547 0.8470 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM215074 2 0.0806 0.8514 0.000 0.972 0.000 0.020 0.000 0.008
#> GSM215075 2 0.1625 0.8334 0.000 0.928 0.000 0.012 0.000 0.060
#> GSM215076 6 0.3548 0.7930 0.000 0.152 0.000 0.048 0.004 0.796
#> GSM215077 6 0.4147 0.5375 0.000 0.436 0.000 0.012 0.000 0.552
#> GSM215078 2 0.3490 0.6951 0.000 0.784 0.000 0.040 0.000 0.176
#> GSM215079 2 0.3905 0.5371 0.000 0.716 0.000 0.024 0.004 0.256
#> GSM215080 2 0.3361 0.6849 0.000 0.788 0.000 0.020 0.004 0.188
#> GSM215081 6 0.4811 0.8760 0.000 0.240 0.012 0.036 0.024 0.688
#> GSM215082 6 0.3050 0.8855 0.000 0.236 0.000 0.000 0.000 0.764
#> GSM215083 1 0.3765 0.6855 0.780 0.000 0.164 0.000 0.048 0.008
#> GSM215084 5 0.4081 0.6712 0.120 0.000 0.064 0.032 0.784 0.000
#> GSM215085 1 0.6320 -0.0131 0.420 0.000 0.340 0.000 0.224 0.016
#> GSM215086 3 0.1605 0.8765 0.032 0.000 0.940 0.000 0.012 0.016
#> GSM215087 1 0.0767 0.7750 0.976 0.000 0.012 0.004 0.008 0.000
#> GSM215088 3 0.2620 0.8499 0.076 0.000 0.884 0.004 0.024 0.012
#> GSM215089 1 0.3244 0.4051 0.732 0.000 0.000 0.000 0.268 0.000
#> GSM215090 5 0.3136 0.7513 0.228 0.000 0.004 0.000 0.768 0.000
#> GSM215091 1 0.1477 0.7678 0.940 0.000 0.048 0.004 0.008 0.000
#> GSM215092 5 0.3717 0.6336 0.384 0.000 0.000 0.000 0.616 0.000
#> GSM215093 3 0.1476 0.8737 0.028 0.000 0.948 0.004 0.008 0.012
#> GSM215094 1 0.4905 0.6329 0.728 0.000 0.080 0.076 0.116 0.000
#> GSM215095 1 0.1501 0.7343 0.924 0.000 0.000 0.000 0.076 0.000
#> GSM215096 1 0.0777 0.7758 0.972 0.000 0.024 0.004 0.000 0.000
#> GSM215097 1 0.4580 0.1726 0.612 0.000 0.052 0.000 0.336 0.000
#> GSM215098 1 0.0291 0.7742 0.992 0.000 0.000 0.004 0.004 0.000
#> GSM215099 5 0.2996 0.7487 0.228 0.000 0.000 0.000 0.772 0.000
#> GSM215100 5 0.3136 0.7513 0.228 0.000 0.004 0.000 0.768 0.000
#> GSM215101 1 0.0291 0.7743 0.992 0.000 0.004 0.004 0.000 0.000
#> GSM215102 5 0.6389 0.4283 0.088 0.000 0.172 0.092 0.616 0.032
#> GSM215103 1 0.5431 0.5561 0.652 0.000 0.208 0.052 0.088 0.000
#> GSM215104 5 0.6205 0.5207 0.232 0.000 0.112 0.084 0.572 0.000
#> GSM215105 5 0.3531 0.6967 0.328 0.000 0.000 0.000 0.672 0.000
#> GSM215106 1 0.1075 0.7592 0.952 0.000 0.000 0.000 0.048 0.000
#> GSM215107 5 0.3314 0.7461 0.256 0.000 0.004 0.000 0.740 0.000
#> GSM215108 5 0.8068 -0.0309 0.088 0.000 0.228 0.108 0.420 0.156
#> GSM215109 3 0.5529 0.7130 0.004 0.000 0.672 0.060 0.116 0.148
#> GSM215110 5 0.5759 0.6627 0.192 0.000 0.152 0.004 0.620 0.032
#> GSM215111 5 0.3607 0.6805 0.348 0.000 0.000 0.000 0.652 0.000
#> GSM215112 1 0.0458 0.7707 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM215113 5 0.3189 0.7512 0.236 0.000 0.004 0.000 0.760 0.000
#> GSM215114 1 0.3969 0.6833 0.800 0.000 0.084 0.040 0.076 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> SD:mclust 64 9.19e-15 1.000 2
#> SD:mclust 60 9.36e-14 0.999 3
#> SD:mclust 57 2.57e-12 0.895 4
#> SD:mclust 50 7.99e-11 0.844 5
#> SD:mclust 58 3.15e-11 0.900 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 51941 rows and 64 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.726 0.838 0.896 0.1856 0.944 0.887
#> 4 4 0.604 0.711 0.822 0.1029 0.960 0.908
#> 5 5 0.553 0.497 0.739 0.0911 0.959 0.898
#> 6 6 0.563 0.386 0.660 0.0575 0.878 0.678
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.5785 0.657 0.000 0.668 0.332
#> GSM215052 2 0.1964 0.925 0.000 0.944 0.056
#> GSM215053 2 0.4842 0.791 0.000 0.776 0.224
#> GSM215054 2 0.5363 0.736 0.000 0.724 0.276
#> GSM215055 2 0.1411 0.923 0.000 0.964 0.036
#> GSM215056 2 0.2711 0.902 0.000 0.912 0.088
#> GSM215057 2 0.0592 0.929 0.000 0.988 0.012
#> GSM215058 2 0.3038 0.905 0.000 0.896 0.104
#> GSM215059 2 0.0892 0.928 0.000 0.980 0.020
#> GSM215060 2 0.0747 0.929 0.000 0.984 0.016
#> GSM215061 2 0.0592 0.929 0.000 0.988 0.012
#> GSM215062 2 0.3192 0.890 0.000 0.888 0.112
#> GSM215063 2 0.5465 0.720 0.000 0.712 0.288
#> GSM215064 2 0.3038 0.895 0.000 0.896 0.104
#> GSM215065 2 0.1860 0.919 0.000 0.948 0.052
#> GSM215066 2 0.0592 0.928 0.000 0.988 0.012
#> GSM215067 2 0.3752 0.863 0.000 0.856 0.144
#> GSM215068 2 0.1289 0.927 0.000 0.968 0.032
#> GSM215069 2 0.1163 0.926 0.000 0.972 0.028
#> GSM215070 2 0.1860 0.925 0.000 0.948 0.052
#> GSM215071 2 0.1411 0.925 0.000 0.964 0.036
#> GSM215072 2 0.1753 0.926 0.000 0.952 0.048
#> GSM215073 2 0.0424 0.928 0.000 0.992 0.008
#> GSM215074 2 0.0424 0.928 0.000 0.992 0.008
#> GSM215075 2 0.0424 0.928 0.000 0.992 0.008
#> GSM215076 2 0.5138 0.785 0.000 0.748 0.252
#> GSM215077 2 0.1529 0.926 0.000 0.960 0.040
#> GSM215078 2 0.1643 0.921 0.000 0.956 0.044
#> GSM215079 2 0.0892 0.928 0.000 0.980 0.020
#> GSM215080 2 0.0892 0.928 0.000 0.980 0.020
#> GSM215081 2 0.2959 0.898 0.000 0.900 0.100
#> GSM215082 2 0.1643 0.923 0.000 0.956 0.044
#> GSM215083 1 0.4702 0.717 0.788 0.000 0.212
#> GSM215084 1 0.0237 0.850 0.996 0.000 0.004
#> GSM215085 1 0.5835 0.423 0.660 0.000 0.340
#> GSM215086 3 0.4974 0.892 0.236 0.000 0.764
#> GSM215087 1 0.2261 0.819 0.932 0.000 0.068
#> GSM215088 3 0.5882 0.752 0.348 0.000 0.652
#> GSM215089 1 0.0747 0.852 0.984 0.000 0.016
#> GSM215090 1 0.2625 0.836 0.916 0.000 0.084
#> GSM215091 1 0.2165 0.843 0.936 0.000 0.064
#> GSM215092 1 0.2878 0.832 0.904 0.000 0.096
#> GSM215093 3 0.4861 0.853 0.192 0.008 0.800
#> GSM215094 1 0.2711 0.796 0.912 0.000 0.088
#> GSM215095 1 0.2448 0.808 0.924 0.000 0.076
#> GSM215096 1 0.2165 0.818 0.936 0.000 0.064
#> GSM215097 1 0.4605 0.739 0.796 0.000 0.204
#> GSM215098 1 0.0592 0.850 0.988 0.000 0.012
#> GSM215099 1 0.3038 0.828 0.896 0.000 0.104
#> GSM215100 1 0.3192 0.821 0.888 0.000 0.112
#> GSM215101 1 0.1964 0.848 0.944 0.000 0.056
#> GSM215102 1 0.5397 0.591 0.720 0.000 0.280
#> GSM215103 1 0.4291 0.761 0.820 0.000 0.180
#> GSM215104 1 0.3192 0.821 0.888 0.000 0.112
#> GSM215105 1 0.0424 0.852 0.992 0.000 0.008
#> GSM215106 1 0.1411 0.851 0.964 0.000 0.036
#> GSM215107 1 0.0237 0.849 0.996 0.000 0.004
#> GSM215108 1 0.5431 0.583 0.716 0.000 0.284
#> GSM215109 3 0.5216 0.888 0.260 0.000 0.740
#> GSM215110 1 0.5835 0.416 0.660 0.000 0.340
#> GSM215111 1 0.0747 0.852 0.984 0.000 0.016
#> GSM215112 1 0.2625 0.800 0.916 0.000 0.084
#> GSM215113 1 0.0000 0.850 1.000 0.000 0.000
#> GSM215114 1 0.2066 0.822 0.940 0.000 0.060
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.6664 0.493 0.000 0.580 0.308 0.112
#> GSM215052 2 0.3463 0.854 0.000 0.864 0.096 0.040
#> GSM215053 2 0.4914 0.640 0.000 0.676 0.312 0.012
#> GSM215054 2 0.4990 0.591 0.000 0.640 0.352 0.008
#> GSM215055 2 0.2469 0.847 0.000 0.892 0.108 0.000
#> GSM215056 2 0.3123 0.822 0.000 0.844 0.156 0.000
#> GSM215057 2 0.1118 0.879 0.000 0.964 0.036 0.000
#> GSM215058 2 0.2976 0.865 0.000 0.872 0.120 0.008
#> GSM215059 2 0.1118 0.877 0.000 0.964 0.036 0.000
#> GSM215060 2 0.1302 0.870 0.000 0.956 0.044 0.000
#> GSM215061 2 0.0921 0.874 0.000 0.972 0.028 0.000
#> GSM215062 2 0.3806 0.830 0.000 0.824 0.156 0.020
#> GSM215063 2 0.5643 0.423 0.000 0.548 0.428 0.024
#> GSM215064 2 0.4093 0.824 0.004 0.816 0.156 0.024
#> GSM215065 2 0.1004 0.878 0.000 0.972 0.024 0.004
#> GSM215066 2 0.1256 0.879 0.000 0.964 0.028 0.008
#> GSM215067 2 0.4328 0.743 0.000 0.748 0.244 0.008
#> GSM215068 2 0.0707 0.878 0.000 0.980 0.020 0.000
#> GSM215069 2 0.0657 0.878 0.000 0.984 0.012 0.004
#> GSM215070 2 0.3587 0.854 0.000 0.860 0.088 0.052
#> GSM215071 2 0.1302 0.875 0.000 0.956 0.044 0.000
#> GSM215072 2 0.4590 0.811 0.000 0.792 0.148 0.060
#> GSM215073 2 0.0817 0.876 0.000 0.976 0.024 0.000
#> GSM215074 2 0.0817 0.877 0.000 0.976 0.024 0.000
#> GSM215075 2 0.0592 0.879 0.000 0.984 0.016 0.000
#> GSM215076 2 0.7317 0.441 0.000 0.528 0.204 0.268
#> GSM215077 2 0.2882 0.865 0.000 0.892 0.084 0.024
#> GSM215078 2 0.2021 0.876 0.000 0.932 0.056 0.012
#> GSM215079 2 0.0817 0.877 0.000 0.976 0.024 0.000
#> GSM215080 2 0.1022 0.877 0.000 0.968 0.032 0.000
#> GSM215081 2 0.3105 0.845 0.000 0.856 0.140 0.004
#> GSM215082 2 0.2589 0.859 0.000 0.884 0.116 0.000
#> GSM215083 1 0.6386 0.448 0.648 0.000 0.140 0.212
#> GSM215084 1 0.4238 0.707 0.796 0.000 0.028 0.176
#> GSM215085 1 0.7613 -0.190 0.472 0.000 0.288 0.240
#> GSM215086 3 0.6536 0.626 0.088 0.000 0.560 0.352
#> GSM215087 1 0.2131 0.793 0.932 0.000 0.036 0.032
#> GSM215088 3 0.7269 0.534 0.200 0.000 0.536 0.264
#> GSM215089 1 0.2466 0.794 0.916 0.000 0.028 0.056
#> GSM215090 1 0.3647 0.766 0.852 0.000 0.040 0.108
#> GSM215091 1 0.3367 0.767 0.864 0.000 0.108 0.028
#> GSM215092 1 0.3711 0.757 0.836 0.000 0.024 0.140
#> GSM215093 3 0.6604 0.603 0.072 0.004 0.528 0.396
#> GSM215094 1 0.3090 0.769 0.888 0.000 0.056 0.056
#> GSM215095 1 0.1833 0.792 0.944 0.000 0.032 0.024
#> GSM215096 1 0.3088 0.778 0.888 0.000 0.052 0.060
#> GSM215097 1 0.6159 0.530 0.676 0.000 0.172 0.152
#> GSM215098 1 0.2224 0.795 0.928 0.000 0.032 0.040
#> GSM215099 1 0.3581 0.774 0.852 0.000 0.032 0.116
#> GSM215100 1 0.3999 0.740 0.824 0.000 0.036 0.140
#> GSM215101 1 0.2670 0.790 0.904 0.000 0.024 0.072
#> GSM215102 4 0.5793 0.453 0.324 0.000 0.048 0.628
#> GSM215103 1 0.5440 0.173 0.596 0.000 0.020 0.384
#> GSM215104 1 0.4980 0.506 0.680 0.000 0.016 0.304
#> GSM215105 1 0.2385 0.798 0.920 0.000 0.028 0.052
#> GSM215106 1 0.3164 0.783 0.884 0.000 0.052 0.064
#> GSM215107 1 0.0927 0.801 0.976 0.000 0.008 0.016
#> GSM215108 4 0.5052 0.388 0.244 0.000 0.036 0.720
#> GSM215109 4 0.4508 -0.235 0.036 0.000 0.184 0.780
#> GSM215110 4 0.6693 0.350 0.424 0.000 0.088 0.488
#> GSM215111 1 0.1545 0.800 0.952 0.000 0.008 0.040
#> GSM215112 1 0.2224 0.789 0.928 0.000 0.040 0.032
#> GSM215113 1 0.2329 0.796 0.916 0.000 0.012 0.072
#> GSM215114 1 0.3243 0.774 0.876 0.000 0.036 0.088
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.748 -0.0440 0.000 0.532 0.156 0.144 0.168
#> GSM215052 2 0.445 0.4486 0.000 0.724 0.000 0.048 0.228
#> GSM215053 2 0.595 0.3741 0.000 0.660 0.132 0.032 0.176
#> GSM215054 2 0.635 0.3008 0.000 0.612 0.156 0.032 0.200
#> GSM215055 2 0.270 0.6553 0.000 0.880 0.012 0.008 0.100
#> GSM215056 2 0.379 0.6061 0.000 0.816 0.036 0.012 0.136
#> GSM215057 2 0.219 0.6810 0.000 0.904 0.000 0.012 0.084
#> GSM215058 2 0.397 0.3906 0.000 0.692 0.000 0.004 0.304
#> GSM215059 2 0.183 0.6786 0.000 0.924 0.000 0.008 0.068
#> GSM215060 2 0.189 0.6755 0.000 0.920 0.008 0.000 0.072
#> GSM215061 2 0.127 0.6832 0.000 0.948 0.000 0.000 0.052
#> GSM215062 2 0.455 -0.0275 0.000 0.556 0.004 0.004 0.436
#> GSM215063 2 0.690 0.1103 0.000 0.528 0.248 0.032 0.192
#> GSM215064 2 0.442 -0.0302 0.000 0.552 0.004 0.000 0.444
#> GSM215065 2 0.134 0.6868 0.000 0.944 0.000 0.000 0.056
#> GSM215066 2 0.185 0.6801 0.000 0.912 0.000 0.000 0.088
#> GSM215067 2 0.570 0.4157 0.000 0.668 0.116 0.020 0.196
#> GSM215068 2 0.179 0.6746 0.000 0.916 0.000 0.000 0.084
#> GSM215069 2 0.127 0.6829 0.000 0.948 0.000 0.000 0.052
#> GSM215070 2 0.496 0.3916 0.000 0.700 0.000 0.096 0.204
#> GSM215071 2 0.210 0.6736 0.000 0.916 0.004 0.012 0.068
#> GSM215072 2 0.474 0.0227 0.000 0.572 0.000 0.020 0.408
#> GSM215073 2 0.143 0.6799 0.000 0.944 0.000 0.004 0.052
#> GSM215074 2 0.163 0.6812 0.000 0.936 0.000 0.008 0.056
#> GSM215075 2 0.230 0.6798 0.000 0.900 0.004 0.008 0.088
#> GSM215076 5 0.709 0.0000 0.000 0.312 0.024 0.212 0.452
#> GSM215077 2 0.333 0.6182 0.000 0.824 0.000 0.024 0.152
#> GSM215078 2 0.308 0.6577 0.000 0.864 0.008 0.028 0.100
#> GSM215079 2 0.217 0.6754 0.000 0.904 0.004 0.004 0.088
#> GSM215080 2 0.234 0.6599 0.000 0.884 0.004 0.000 0.112
#> GSM215081 2 0.410 0.2251 0.000 0.628 0.000 0.000 0.372
#> GSM215082 2 0.391 0.4872 0.000 0.740 0.004 0.008 0.248
#> GSM215083 3 0.568 -0.0576 0.420 0.000 0.520 0.036 0.024
#> GSM215084 1 0.476 0.4681 0.644 0.000 0.008 0.328 0.020
#> GSM215085 3 0.563 0.3962 0.212 0.000 0.680 0.056 0.052
#> GSM215086 3 0.498 0.3826 0.016 0.000 0.740 0.112 0.132
#> GSM215087 1 0.442 0.6892 0.780 0.000 0.148 0.048 0.024
#> GSM215088 3 0.484 0.4455 0.072 0.000 0.772 0.104 0.052
#> GSM215089 1 0.431 0.6563 0.780 0.000 0.040 0.160 0.020
#> GSM215090 1 0.554 0.5846 0.680 0.000 0.088 0.208 0.024
#> GSM215091 1 0.457 0.6232 0.720 0.000 0.240 0.020 0.020
#> GSM215092 1 0.491 0.5304 0.684 0.000 0.020 0.268 0.028
#> GSM215093 3 0.579 0.2646 0.012 0.000 0.616 0.276 0.096
#> GSM215094 1 0.474 0.6932 0.780 0.000 0.056 0.068 0.096
#> GSM215095 1 0.246 0.7187 0.908 0.000 0.012 0.048 0.032
#> GSM215096 1 0.512 0.6379 0.732 0.000 0.152 0.024 0.092
#> GSM215097 1 0.604 0.2370 0.524 0.000 0.392 0.044 0.040
#> GSM215098 1 0.403 0.6847 0.792 0.000 0.164 0.020 0.024
#> GSM215099 1 0.394 0.7068 0.808 0.000 0.140 0.036 0.016
#> GSM215100 1 0.430 0.6867 0.788 0.000 0.104 0.100 0.008
#> GSM215101 1 0.461 0.6375 0.756 0.000 0.048 0.176 0.020
#> GSM215102 4 0.535 0.4707 0.212 0.000 0.092 0.684 0.012
#> GSM215103 1 0.680 0.1658 0.496 0.000 0.116 0.348 0.040
#> GSM215104 1 0.644 0.4042 0.572 0.000 0.128 0.272 0.028
#> GSM215105 1 0.429 0.7010 0.800 0.000 0.120 0.036 0.044
#> GSM215106 1 0.505 0.5903 0.700 0.000 0.232 0.020 0.048
#> GSM215107 1 0.279 0.7146 0.884 0.000 0.016 0.084 0.016
#> GSM215108 4 0.679 0.4197 0.140 0.000 0.128 0.612 0.120
#> GSM215109 4 0.594 0.2172 0.020 0.000 0.196 0.644 0.140
#> GSM215110 4 0.668 0.2646 0.340 0.000 0.100 0.516 0.044
#> GSM215111 1 0.274 0.7195 0.892 0.000 0.064 0.012 0.032
#> GSM215112 1 0.330 0.7096 0.868 0.000 0.060 0.032 0.040
#> GSM215113 1 0.364 0.6888 0.828 0.000 0.028 0.128 0.016
#> GSM215114 1 0.480 0.6715 0.752 0.000 0.056 0.164 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 2 0.742 0.1163 0.000 0.456 0.196 0.096 0.024 0.228
#> GSM215052 2 0.498 -0.3500 0.000 0.584 0.000 0.340 0.004 0.072
#> GSM215053 2 0.634 0.3482 0.000 0.592 0.180 0.164 0.028 0.036
#> GSM215054 2 0.610 0.3988 0.000 0.632 0.176 0.116 0.032 0.044
#> GSM215055 2 0.382 0.5845 0.000 0.812 0.084 0.080 0.016 0.008
#> GSM215056 2 0.381 0.5651 0.000 0.800 0.084 0.100 0.016 0.000
#> GSM215057 2 0.316 0.5705 0.000 0.820 0.020 0.152 0.008 0.000
#> GSM215058 4 0.462 0.6054 0.000 0.480 0.016 0.492 0.004 0.008
#> GSM215059 2 0.243 0.6150 0.000 0.884 0.012 0.092 0.012 0.000
#> GSM215060 2 0.137 0.6328 0.000 0.944 0.012 0.044 0.000 0.000
#> GSM215061 2 0.173 0.6168 0.000 0.920 0.000 0.072 0.004 0.004
#> GSM215062 4 0.461 0.7527 0.008 0.384 0.000 0.584 0.012 0.012
#> GSM215063 2 0.672 0.0996 0.000 0.412 0.388 0.136 0.056 0.008
#> GSM215064 4 0.434 0.7538 0.004 0.388 0.000 0.592 0.008 0.008
#> GSM215065 2 0.184 0.6298 0.000 0.920 0.008 0.064 0.008 0.000
#> GSM215066 2 0.313 0.5623 0.000 0.836 0.008 0.132 0.016 0.008
#> GSM215067 2 0.623 0.2822 0.000 0.560 0.244 0.144 0.048 0.004
#> GSM215068 2 0.299 0.5040 0.000 0.812 0.000 0.176 0.008 0.004
#> GSM215069 2 0.164 0.6111 0.000 0.924 0.000 0.068 0.008 0.000
#> GSM215070 2 0.553 -0.2438 0.000 0.580 0.000 0.276 0.012 0.132
#> GSM215071 2 0.264 0.5507 0.000 0.864 0.004 0.116 0.004 0.012
#> GSM215072 4 0.519 0.7232 0.000 0.392 0.000 0.524 0.004 0.080
#> GSM215073 2 0.166 0.6323 0.000 0.936 0.012 0.044 0.004 0.004
#> GSM215074 2 0.152 0.6317 0.000 0.940 0.008 0.044 0.008 0.000
#> GSM215075 2 0.289 0.5827 0.000 0.852 0.004 0.120 0.008 0.016
#> GSM215076 4 0.635 0.4243 0.000 0.180 0.016 0.492 0.012 0.300
#> GSM215077 2 0.463 0.3740 0.000 0.732 0.012 0.156 0.008 0.092
#> GSM215078 2 0.340 0.6027 0.000 0.848 0.012 0.060 0.020 0.060
#> GSM215079 2 0.270 0.5963 0.000 0.860 0.004 0.120 0.008 0.008
#> GSM215080 2 0.287 0.5686 0.000 0.840 0.000 0.140 0.008 0.012
#> GSM215081 4 0.417 0.6959 0.000 0.456 0.000 0.532 0.012 0.000
#> GSM215082 2 0.421 -0.2810 0.000 0.604 0.004 0.380 0.004 0.008
#> GSM215083 1 0.688 -0.0764 0.444 0.000 0.356 0.024 0.056 0.120
#> GSM215084 5 0.521 0.3810 0.444 0.000 0.000 0.008 0.480 0.068
#> GSM215085 3 0.803 0.3860 0.236 0.000 0.424 0.084 0.132 0.124
#> GSM215086 3 0.624 0.4407 0.068 0.000 0.620 0.056 0.052 0.204
#> GSM215087 1 0.414 0.4740 0.776 0.000 0.036 0.028 0.152 0.008
#> GSM215088 3 0.595 0.5159 0.072 0.000 0.660 0.024 0.128 0.116
#> GSM215089 1 0.443 -0.2256 0.528 0.000 0.012 0.004 0.452 0.004
#> GSM215090 5 0.549 0.2537 0.432 0.000 0.052 0.020 0.488 0.008
#> GSM215091 1 0.491 0.4716 0.716 0.000 0.148 0.008 0.108 0.020
#> GSM215092 5 0.503 0.4649 0.400 0.000 0.004 0.012 0.544 0.040
#> GSM215093 3 0.596 0.4301 0.012 0.000 0.604 0.040 0.108 0.236
#> GSM215094 1 0.477 0.3914 0.708 0.000 0.008 0.096 0.180 0.008
#> GSM215095 1 0.340 0.4380 0.800 0.000 0.012 0.020 0.168 0.000
#> GSM215096 1 0.401 0.5031 0.812 0.000 0.044 0.068 0.064 0.012
#> GSM215097 1 0.666 0.2929 0.508 0.000 0.304 0.020 0.108 0.060
#> GSM215098 1 0.411 0.4974 0.796 0.000 0.056 0.028 0.108 0.012
#> GSM215099 1 0.490 0.4668 0.732 0.000 0.080 0.008 0.136 0.044
#> GSM215100 1 0.522 0.3617 0.680 0.000 0.048 0.012 0.212 0.048
#> GSM215101 1 0.472 -0.3167 0.500 0.000 0.016 0.008 0.468 0.008
#> GSM215102 6 0.613 0.2004 0.084 0.000 0.020 0.024 0.420 0.452
#> GSM215103 6 0.682 -0.0746 0.400 0.000 0.056 0.020 0.116 0.408
#> GSM215104 1 0.635 0.1429 0.560 0.000 0.032 0.020 0.148 0.240
#> GSM215105 1 0.525 0.4634 0.716 0.000 0.092 0.048 0.124 0.020
#> GSM215106 1 0.491 0.4728 0.740 0.000 0.140 0.028 0.056 0.036
#> GSM215107 1 0.338 0.3823 0.776 0.000 0.004 0.008 0.208 0.004
#> GSM215108 6 0.395 0.4043 0.060 0.000 0.012 0.024 0.096 0.808
#> GSM215109 6 0.285 0.2933 0.004 0.000 0.064 0.008 0.052 0.872
#> GSM215110 5 0.590 0.0212 0.088 0.000 0.048 0.032 0.652 0.180
#> GSM215111 1 0.367 0.4864 0.800 0.000 0.028 0.028 0.144 0.000
#> GSM215112 1 0.314 0.4790 0.836 0.000 0.008 0.024 0.128 0.004
#> GSM215113 1 0.484 0.2505 0.644 0.000 0.020 0.016 0.300 0.020
#> GSM215114 1 0.481 0.2940 0.684 0.000 0.020 0.028 0.248 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 disease.state(p) individual(p) k
#> SD:NMF 64 9.19e-15 1.000 2
#> SD:NMF 62 3.44e-14 0.999 3
#> SD:NMF 54 1.88e-12 0.997 4
#> SD:NMF 37 8.73e-09 0.966 5
#> SD:NMF 24 2.50e-05 0.959 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 51941 rows and 64 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.993 0.997 0.5083 0.492 0.492
#> 3 3 0.918 0.903 0.943 0.1213 0.933 0.864
#> 4 4 0.879 0.880 0.938 0.0410 0.983 0.961
#> 5 5 0.815 0.834 0.916 0.0334 0.997 0.993
#> 6 6 0.824 0.794 0.900 0.0309 0.986 0.965
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> attr(,"optional")
#> [1] 2
There is also optional best \(k\) = 2 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0.0000 0.999 0.000 1.000
#> GSM215052 2 0.0000 0.999 0.000 1.000
#> GSM215053 2 0.0000 0.999 0.000 1.000
#> GSM215054 2 0.0000 0.999 0.000 1.000
#> GSM215055 2 0.0000 0.999 0.000 1.000
#> GSM215056 2 0.0000 0.999 0.000 1.000
#> GSM215057 2 0.0000 0.999 0.000 1.000
#> GSM215058 2 0.0000 0.999 0.000 1.000
#> GSM215059 2 0.0000 0.999 0.000 1.000
#> GSM215060 2 0.0000 0.999 0.000 1.000
#> GSM215061 2 0.0000 0.999 0.000 1.000
#> GSM215062 2 0.0000 0.999 0.000 1.000
#> GSM215063 2 0.1184 0.984 0.016 0.984
#> GSM215064 2 0.0000 0.999 0.000 1.000
#> GSM215065 2 0.0000 0.999 0.000 1.000
#> GSM215066 2 0.0000 0.999 0.000 1.000
#> GSM215067 2 0.1184 0.984 0.016 0.984
#> GSM215068 2 0.0000 0.999 0.000 1.000
#> GSM215069 2 0.0000 0.999 0.000 1.000
#> GSM215070 2 0.0000 0.999 0.000 1.000
#> GSM215071 2 0.0000 0.999 0.000 1.000
#> GSM215072 2 0.0000 0.999 0.000 1.000
#> GSM215073 2 0.0000 0.999 0.000 1.000
#> GSM215074 2 0.0000 0.999 0.000 1.000
#> GSM215075 2 0.0000 0.999 0.000 1.000
#> GSM215076 2 0.0000 0.999 0.000 1.000
#> GSM215077 2 0.0000 0.999 0.000 1.000
#> GSM215078 2 0.0000 0.999 0.000 1.000
#> GSM215079 2 0.0000 0.999 0.000 1.000
#> GSM215080 2 0.0000 0.999 0.000 1.000
#> GSM215081 2 0.0000 0.999 0.000 1.000
#> GSM215082 2 0.0000 0.999 0.000 1.000
#> GSM215083 1 0.0000 0.994 1.000 0.000
#> GSM215084 1 0.0000 0.994 1.000 0.000
#> GSM215085 1 0.0000 0.994 1.000 0.000
#> GSM215086 1 0.0938 0.984 0.988 0.012
#> GSM215087 1 0.0000 0.994 1.000 0.000
#> GSM215088 1 0.0376 0.991 0.996 0.004
#> GSM215089 1 0.0000 0.994 1.000 0.000
#> GSM215090 1 0.0000 0.994 1.000 0.000
#> GSM215091 1 0.0000 0.994 1.000 0.000
#> GSM215092 1 0.0000 0.994 1.000 0.000
#> GSM215093 1 0.6247 0.816 0.844 0.156
#> GSM215094 1 0.0000 0.994 1.000 0.000
#> GSM215095 1 0.0000 0.994 1.000 0.000
#> GSM215096 1 0.0000 0.994 1.000 0.000
#> GSM215097 1 0.0000 0.994 1.000 0.000
#> GSM215098 1 0.0000 0.994 1.000 0.000
#> GSM215099 1 0.0000 0.994 1.000 0.000
#> GSM215100 1 0.0000 0.994 1.000 0.000
#> GSM215101 1 0.0000 0.994 1.000 0.000
#> GSM215102 1 0.0000 0.994 1.000 0.000
#> GSM215103 1 0.0000 0.994 1.000 0.000
#> GSM215104 1 0.0000 0.994 1.000 0.000
#> GSM215105 1 0.0000 0.994 1.000 0.000
#> GSM215106 1 0.0000 0.994 1.000 0.000
#> GSM215107 1 0.0000 0.994 1.000 0.000
#> GSM215108 1 0.0000 0.994 1.000 0.000
#> GSM215109 1 0.0000 0.994 1.000 0.000
#> GSM215110 1 0.0000 0.994 1.000 0.000
#> GSM215111 1 0.0000 0.994 1.000 0.000
#> GSM215112 1 0.0000 0.994 1.000 0.000
#> GSM215113 1 0.0000 0.994 1.000 0.000
#> GSM215114 1 0.0000 0.994 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215052 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215053 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215054 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215055 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215056 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215057 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215058 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215059 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215060 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215061 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215062 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215063 2 0.1163 0.973 0.000 0.972 0.028
#> GSM215064 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215065 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215066 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215067 2 0.1163 0.973 0.000 0.972 0.028
#> GSM215068 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215069 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215070 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215071 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215072 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215073 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215074 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215075 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215076 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215077 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215078 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215079 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215080 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215081 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215082 2 0.0000 0.998 0.000 1.000 0.000
#> GSM215083 1 0.3686 0.794 0.860 0.000 0.140
#> GSM215084 1 0.1411 0.910 0.964 0.000 0.036
#> GSM215085 3 0.5291 0.625 0.268 0.000 0.732
#> GSM215086 3 0.3686 0.638 0.140 0.000 0.860
#> GSM215087 1 0.0747 0.914 0.984 0.000 0.016
#> GSM215088 3 0.6235 0.579 0.436 0.000 0.564
#> GSM215089 1 0.1289 0.917 0.968 0.000 0.032
#> GSM215090 1 0.1964 0.904 0.944 0.000 0.056
#> GSM215091 1 0.0747 0.916 0.984 0.000 0.016
#> GSM215092 1 0.1753 0.912 0.952 0.000 0.048
#> GSM215093 3 0.9136 0.547 0.400 0.144 0.456
#> GSM215094 1 0.1163 0.916 0.972 0.000 0.028
#> GSM215095 1 0.0592 0.916 0.988 0.000 0.012
#> GSM215096 1 0.0747 0.916 0.984 0.000 0.016
#> GSM215097 1 0.1411 0.915 0.964 0.000 0.036
#> GSM215098 1 0.0592 0.913 0.988 0.000 0.012
#> GSM215099 1 0.1529 0.914 0.960 0.000 0.040
#> GSM215100 1 0.1643 0.908 0.956 0.000 0.044
#> GSM215101 1 0.1860 0.903 0.948 0.000 0.052
#> GSM215102 1 0.2537 0.885 0.920 0.000 0.080
#> GSM215103 1 0.3551 0.821 0.868 0.000 0.132
#> GSM215104 1 0.2711 0.876 0.912 0.000 0.088
#> GSM215105 1 0.1860 0.911 0.948 0.000 0.052
#> GSM215106 1 0.1411 0.915 0.964 0.000 0.036
#> GSM215107 1 0.2711 0.872 0.912 0.000 0.088
#> GSM215108 1 0.6180 -0.257 0.584 0.000 0.416
#> GSM215109 3 0.6244 0.578 0.440 0.000 0.560
#> GSM215110 1 0.4702 0.651 0.788 0.000 0.212
#> GSM215111 1 0.1289 0.915 0.968 0.000 0.032
#> GSM215112 1 0.0592 0.913 0.988 0.000 0.012
#> GSM215113 1 0.1289 0.917 0.968 0.000 0.032
#> GSM215114 1 0.0892 0.915 0.980 0.000 0.020
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215052 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215053 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215054 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215055 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215056 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215057 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215058 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215059 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215060 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215061 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215062 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215063 2 0.1388 0.960 0.000 0.960 0.028 0.012
#> GSM215064 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215065 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215066 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215067 2 0.1388 0.960 0.000 0.960 0.028 0.012
#> GSM215068 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215069 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215070 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215071 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215072 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215073 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215074 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215075 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215076 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215077 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215078 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215079 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215080 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215081 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215082 2 0.0000 0.997 0.000 1.000 0.000 0.000
#> GSM215083 1 0.4008 0.792 0.820 0.000 0.148 0.032
#> GSM215084 1 0.1661 0.918 0.944 0.000 0.052 0.004
#> GSM215085 4 0.2111 0.000 0.044 0.000 0.024 0.932
#> GSM215086 3 0.5284 -0.160 0.016 0.000 0.616 0.368
#> GSM215087 1 0.0895 0.923 0.976 0.000 0.020 0.004
#> GSM215088 3 0.5179 0.475 0.220 0.000 0.728 0.052
#> GSM215089 1 0.1510 0.923 0.956 0.000 0.028 0.016
#> GSM215090 1 0.3354 0.861 0.872 0.000 0.084 0.044
#> GSM215091 1 0.0657 0.923 0.984 0.000 0.004 0.012
#> GSM215092 1 0.1975 0.917 0.936 0.000 0.048 0.016
#> GSM215093 3 0.7362 0.373 0.220 0.132 0.612 0.036
#> GSM215094 1 0.1488 0.922 0.956 0.000 0.032 0.012
#> GSM215095 1 0.0524 0.924 0.988 0.000 0.008 0.004
#> GSM215096 1 0.0657 0.923 0.984 0.000 0.004 0.012
#> GSM215097 1 0.1297 0.923 0.964 0.000 0.016 0.020
#> GSM215098 1 0.0657 0.921 0.984 0.000 0.012 0.004
#> GSM215099 1 0.1520 0.923 0.956 0.000 0.024 0.020
#> GSM215100 1 0.2111 0.908 0.932 0.000 0.044 0.024
#> GSM215101 1 0.2483 0.900 0.916 0.000 0.052 0.032
#> GSM215102 1 0.3907 0.814 0.828 0.000 0.140 0.032
#> GSM215103 1 0.4017 0.819 0.828 0.000 0.128 0.044
#> GSM215104 1 0.3486 0.863 0.864 0.000 0.092 0.044
#> GSM215105 1 0.1724 0.921 0.948 0.000 0.020 0.032
#> GSM215106 1 0.1510 0.923 0.956 0.000 0.028 0.016
#> GSM215107 1 0.3082 0.873 0.884 0.000 0.084 0.032
#> GSM215108 3 0.7184 0.351 0.416 0.000 0.448 0.136
#> GSM215109 3 0.5109 0.447 0.196 0.000 0.744 0.060
#> GSM215110 1 0.5472 0.510 0.676 0.000 0.280 0.044
#> GSM215111 1 0.1174 0.922 0.968 0.000 0.012 0.020
#> GSM215112 1 0.0657 0.921 0.984 0.000 0.012 0.004
#> GSM215113 1 0.1297 0.925 0.964 0.000 0.020 0.016
#> GSM215114 1 0.0895 0.923 0.976 0.000 0.020 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215052 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215053 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215054 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215055 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215056 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215057 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215058 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215059 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215060 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215061 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215062 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215063 2 0.2127 0.8825 0.000 0.892 0.108 0.000 0.000
#> GSM215064 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215065 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215066 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215067 2 0.2127 0.8825 0.000 0.892 0.108 0.000 0.000
#> GSM215068 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215069 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215070 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215071 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215072 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215073 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215074 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215075 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215076 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215077 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215078 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215079 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215080 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215081 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215082 2 0.0000 0.9929 0.000 1.000 0.000 0.000 0.000
#> GSM215083 1 0.4498 0.7326 0.772 0.000 0.140 0.012 0.076
#> GSM215084 1 0.2241 0.8698 0.908 0.000 0.008 0.008 0.076
#> GSM215085 4 0.0898 0.0000 0.020 0.000 0.008 0.972 0.000
#> GSM215086 3 0.6845 0.0456 0.004 0.000 0.384 0.244 0.368
#> GSM215087 1 0.1082 0.8812 0.964 0.000 0.008 0.000 0.028
#> GSM215088 3 0.4093 0.3482 0.092 0.000 0.808 0.012 0.088
#> GSM215089 1 0.2074 0.8788 0.920 0.000 0.016 0.004 0.060
#> GSM215090 1 0.5005 0.6876 0.744 0.000 0.064 0.036 0.156
#> GSM215091 1 0.0798 0.8824 0.976 0.000 0.008 0.000 0.016
#> GSM215092 1 0.2569 0.8675 0.896 0.000 0.016 0.012 0.076
#> GSM215093 3 0.6090 0.2745 0.136 0.064 0.692 0.012 0.096
#> GSM215094 1 0.1830 0.8801 0.932 0.000 0.012 0.004 0.052
#> GSM215095 1 0.0579 0.8831 0.984 0.000 0.008 0.000 0.008
#> GSM215096 1 0.0798 0.8824 0.976 0.000 0.008 0.000 0.016
#> GSM215097 1 0.1538 0.8820 0.948 0.000 0.008 0.008 0.036
#> GSM215098 1 0.1124 0.8807 0.960 0.000 0.004 0.000 0.036
#> GSM215099 1 0.1756 0.8827 0.940 0.000 0.016 0.008 0.036
#> GSM215100 1 0.2800 0.8620 0.888 0.000 0.016 0.024 0.072
#> GSM215101 1 0.3448 0.8459 0.856 0.000 0.028 0.036 0.080
#> GSM215102 1 0.4392 0.7084 0.748 0.000 0.048 0.004 0.200
#> GSM215103 1 0.4794 0.7179 0.744 0.000 0.080 0.012 0.164
#> GSM215104 1 0.3755 0.8038 0.816 0.000 0.032 0.012 0.140
#> GSM215105 1 0.1949 0.8804 0.932 0.000 0.016 0.012 0.040
#> GSM215106 1 0.1787 0.8823 0.936 0.000 0.016 0.004 0.044
#> GSM215107 1 0.3750 0.8092 0.836 0.000 0.040 0.028 0.096
#> GSM215108 5 0.6299 0.1838 0.328 0.000 0.080 0.036 0.556
#> GSM215109 5 0.5722 -0.2757 0.068 0.000 0.280 0.024 0.628
#> GSM215110 1 0.6504 0.1398 0.504 0.000 0.088 0.036 0.372
#> GSM215111 1 0.1412 0.8827 0.952 0.000 0.008 0.004 0.036
#> GSM215112 1 0.0955 0.8792 0.968 0.000 0.004 0.000 0.028
#> GSM215113 1 0.1605 0.8853 0.944 0.000 0.012 0.004 0.040
#> GSM215114 1 0.1195 0.8813 0.960 0.000 0.012 0.000 0.028
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 2 0.0146 0.98646 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215052 2 0.0146 0.98578 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215053 2 0.0146 0.98646 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215054 2 0.0146 0.98646 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215055 2 0.0146 0.98646 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215056 2 0.0146 0.98646 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215057 2 0.0000 0.98725 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215058 2 0.0000 0.98725 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215059 2 0.0000 0.98725 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215060 2 0.0146 0.98646 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215061 2 0.0146 0.98646 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215062 2 0.0146 0.98578 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215063 2 0.2932 0.81376 0.000 0.836 0.000 0.004 0.140 0.020
#> GSM215064 2 0.0146 0.98578 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215065 2 0.0000 0.98725 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215066 2 0.0000 0.98725 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215067 2 0.2932 0.81376 0.000 0.836 0.000 0.004 0.140 0.020
#> GSM215068 2 0.0000 0.98725 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215069 2 0.0000 0.98725 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215070 2 0.0000 0.98725 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215071 2 0.0000 0.98725 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215072 2 0.0146 0.98578 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215073 2 0.0146 0.98646 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215074 2 0.0000 0.98725 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215075 2 0.0146 0.98646 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215076 2 0.0146 0.98578 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215077 2 0.0000 0.98725 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215078 2 0.0146 0.98646 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215079 2 0.0000 0.98725 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215080 2 0.0000 0.98725 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215081 2 0.0000 0.98725 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215082 2 0.0146 0.98578 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215083 1 0.4883 0.63665 0.732 0.000 0.084 0.012 0.032 0.140
#> GSM215084 1 0.2879 0.80753 0.864 0.000 0.072 0.000 0.056 0.008
#> GSM215085 4 0.0260 0.00000 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM215086 3 0.7267 -0.12661 0.000 0.000 0.412 0.180 0.140 0.268
#> GSM215087 1 0.1693 0.83517 0.936 0.000 0.032 0.000 0.020 0.012
#> GSM215088 6 0.1514 0.50178 0.036 0.000 0.012 0.004 0.004 0.944
#> GSM215089 1 0.3440 0.76890 0.824 0.000 0.040 0.000 0.116 0.020
#> GSM215090 1 0.5754 -0.04602 0.560 0.000 0.028 0.020 0.336 0.056
#> GSM215091 1 0.1148 0.83815 0.960 0.000 0.020 0.000 0.016 0.004
#> GSM215092 1 0.3196 0.79226 0.840 0.000 0.036 0.000 0.108 0.016
#> GSM215093 6 0.6407 0.50001 0.080 0.008 0.072 0.020 0.220 0.600
#> GSM215094 1 0.2339 0.83488 0.904 0.000 0.056 0.004 0.020 0.016
#> GSM215095 1 0.1078 0.83907 0.964 0.000 0.012 0.000 0.016 0.008
#> GSM215096 1 0.1148 0.83815 0.960 0.000 0.020 0.000 0.016 0.004
#> GSM215097 1 0.2002 0.83540 0.920 0.000 0.040 0.000 0.028 0.012
#> GSM215098 1 0.1478 0.83598 0.944 0.000 0.032 0.000 0.020 0.004
#> GSM215099 1 0.2152 0.83587 0.912 0.000 0.036 0.000 0.040 0.012
#> GSM215100 1 0.3430 0.79691 0.840 0.000 0.044 0.008 0.088 0.020
#> GSM215101 1 0.3927 0.75383 0.800 0.000 0.052 0.020 0.120 0.008
#> GSM215102 1 0.5253 0.53095 0.672 0.000 0.204 0.004 0.084 0.036
#> GSM215103 1 0.5004 0.63530 0.712 0.000 0.172 0.008 0.044 0.064
#> GSM215104 1 0.4100 0.73223 0.780 0.000 0.152 0.016 0.032 0.020
#> GSM215105 1 0.2228 0.83481 0.912 0.000 0.044 0.004 0.024 0.016
#> GSM215106 1 0.2252 0.83307 0.908 0.000 0.044 0.000 0.028 0.020
#> GSM215107 1 0.4455 0.64247 0.740 0.000 0.072 0.000 0.164 0.024
#> GSM215108 3 0.4646 -0.00972 0.260 0.000 0.680 0.020 0.004 0.036
#> GSM215109 3 0.5864 -0.05105 0.020 0.000 0.588 0.008 0.144 0.240
#> GSM215110 5 0.4954 0.00000 0.248 0.000 0.072 0.000 0.660 0.020
#> GSM215111 1 0.1806 0.83632 0.928 0.000 0.044 0.000 0.020 0.008
#> GSM215112 1 0.1485 0.83035 0.944 0.000 0.028 0.000 0.024 0.004
#> GSM215113 1 0.1949 0.84031 0.924 0.000 0.036 0.000 0.020 0.020
#> GSM215114 1 0.1666 0.83319 0.936 0.000 0.036 0.000 0.020 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> CV:hclust 64 9.19e-15 1.000 2
#> CV:hclust 63 2.09e-14 0.999 3
#> CV:hclust 58 1.98e-13 1.000 4
#> CV:hclust 57 3.32e-13 1.000 5
#> CV:hclust 58 2.54e-13 0.998 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 51941 rows and 64 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.780 0.890 0.894 0.1978 0.905 0.806
#> 4 4 0.645 0.625 0.750 0.1051 0.873 0.680
#> 5 5 0.664 0.679 0.811 0.0741 0.901 0.704
#> 6 6 0.635 0.625 0.757 0.0398 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] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.5327 0.826 0.000 0.728 0.272
#> GSM215052 2 0.2066 0.921 0.000 0.940 0.060
#> GSM215053 2 0.5098 0.832 0.000 0.752 0.248
#> GSM215054 2 0.5327 0.826 0.000 0.728 0.272
#> GSM215055 2 0.4654 0.860 0.000 0.792 0.208
#> GSM215056 2 0.5254 0.830 0.000 0.736 0.264
#> GSM215057 2 0.2625 0.918 0.000 0.916 0.084
#> GSM215058 2 0.3038 0.918 0.000 0.896 0.104
#> GSM215059 2 0.1163 0.928 0.000 0.972 0.028
#> GSM215060 2 0.2356 0.922 0.000 0.928 0.072
#> GSM215061 2 0.0892 0.928 0.000 0.980 0.020
#> GSM215062 2 0.1860 0.921 0.000 0.948 0.052
#> GSM215063 2 0.5363 0.826 0.000 0.724 0.276
#> GSM215064 2 0.1860 0.921 0.000 0.948 0.052
#> GSM215065 2 0.0892 0.927 0.000 0.980 0.020
#> GSM215066 2 0.0000 0.927 0.000 1.000 0.000
#> GSM215067 2 0.5327 0.829 0.000 0.728 0.272
#> GSM215068 2 0.0000 0.927 0.000 1.000 0.000
#> GSM215069 2 0.0237 0.927 0.000 0.996 0.004
#> GSM215070 2 0.1860 0.922 0.000 0.948 0.052
#> GSM215071 2 0.1411 0.925 0.000 0.964 0.036
#> GSM215072 2 0.1964 0.921 0.000 0.944 0.056
#> GSM215073 2 0.1643 0.926 0.000 0.956 0.044
#> GSM215074 2 0.2261 0.925 0.000 0.932 0.068
#> GSM215075 2 0.3116 0.911 0.000 0.892 0.108
#> GSM215076 2 0.3941 0.899 0.000 0.844 0.156
#> GSM215077 2 0.1643 0.922 0.000 0.956 0.044
#> GSM215078 2 0.1289 0.928 0.000 0.968 0.032
#> GSM215079 2 0.0237 0.928 0.000 0.996 0.004
#> GSM215080 2 0.0000 0.927 0.000 1.000 0.000
#> GSM215081 2 0.1163 0.923 0.000 0.972 0.028
#> GSM215082 2 0.1643 0.922 0.000 0.956 0.044
#> GSM215083 1 0.5529 0.223 0.704 0.000 0.296
#> GSM215084 1 0.1643 0.912 0.956 0.000 0.044
#> GSM215085 3 0.5905 0.910 0.352 0.000 0.648
#> GSM215086 3 0.5859 0.912 0.344 0.000 0.656
#> GSM215087 1 0.0424 0.940 0.992 0.000 0.008
#> GSM215088 3 0.5760 0.915 0.328 0.000 0.672
#> GSM215089 1 0.0237 0.940 0.996 0.000 0.004
#> GSM215090 1 0.0592 0.936 0.988 0.000 0.012
#> GSM215091 1 0.0424 0.939 0.992 0.000 0.008
#> GSM215092 1 0.1964 0.896 0.944 0.000 0.056
#> GSM215093 3 0.5529 0.890 0.296 0.000 0.704
#> GSM215094 1 0.0237 0.941 0.996 0.000 0.004
#> GSM215095 1 0.0000 0.940 1.000 0.000 0.000
#> GSM215096 1 0.0592 0.939 0.988 0.000 0.012
#> GSM215097 1 0.0592 0.938 0.988 0.000 0.012
#> GSM215098 1 0.0424 0.940 0.992 0.000 0.008
#> GSM215099 1 0.0237 0.940 0.996 0.000 0.004
#> GSM215100 1 0.0747 0.937 0.984 0.000 0.016
#> GSM215101 1 0.0424 0.940 0.992 0.000 0.008
#> GSM215102 3 0.6309 0.633 0.496 0.000 0.504
#> GSM215103 1 0.5363 0.370 0.724 0.000 0.276
#> GSM215104 1 0.2066 0.899 0.940 0.000 0.060
#> GSM215105 1 0.0592 0.939 0.988 0.000 0.012
#> GSM215106 1 0.0747 0.937 0.984 0.000 0.016
#> GSM215107 1 0.0592 0.940 0.988 0.000 0.012
#> GSM215108 3 0.5882 0.903 0.348 0.000 0.652
#> GSM215109 3 0.5650 0.908 0.312 0.000 0.688
#> GSM215110 3 0.6062 0.876 0.384 0.000 0.616
#> GSM215111 1 0.0424 0.939 0.992 0.000 0.008
#> GSM215112 1 0.0424 0.940 0.992 0.000 0.008
#> GSM215113 1 0.0000 0.940 1.000 0.000 0.000
#> GSM215114 1 0.1643 0.914 0.956 0.000 0.044
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.1743 0.505 0.000 0.940 0.056 0.004
#> GSM215052 4 0.6163 0.746 0.000 0.416 0.052 0.532
#> GSM215053 2 0.1297 0.504 0.000 0.964 0.016 0.020
#> GSM215054 2 0.1824 0.505 0.000 0.936 0.060 0.004
#> GSM215055 2 0.2198 0.482 0.000 0.920 0.008 0.072
#> GSM215056 2 0.1284 0.506 0.000 0.964 0.024 0.012
#> GSM215057 2 0.5040 -0.218 0.000 0.628 0.008 0.364
#> GSM215058 2 0.6097 -0.254 0.000 0.580 0.056 0.364
#> GSM215059 4 0.5000 0.681 0.000 0.496 0.000 0.504
#> GSM215060 2 0.4790 -0.275 0.000 0.620 0.000 0.380
#> GSM215061 2 0.5000 -0.711 0.000 0.504 0.000 0.496
#> GSM215062 4 0.6087 0.760 0.000 0.412 0.048 0.540
#> GSM215063 2 0.2021 0.495 0.000 0.936 0.040 0.024
#> GSM215064 4 0.6016 0.783 0.000 0.412 0.044 0.544
#> GSM215065 4 0.4998 0.714 0.000 0.488 0.000 0.512
#> GSM215066 4 0.4967 0.801 0.000 0.452 0.000 0.548
#> GSM215067 2 0.2408 0.500 0.000 0.920 0.044 0.036
#> GSM215068 4 0.4972 0.796 0.000 0.456 0.000 0.544
#> GSM215069 4 0.4972 0.796 0.000 0.456 0.000 0.544
#> GSM215070 4 0.5847 0.786 0.000 0.404 0.036 0.560
#> GSM215071 4 0.5203 0.820 0.000 0.416 0.008 0.576
#> GSM215072 4 0.6163 0.751 0.000 0.416 0.052 0.532
#> GSM215073 2 0.4967 -0.574 0.000 0.548 0.000 0.452
#> GSM215074 2 0.5229 -0.462 0.000 0.564 0.008 0.428
#> GSM215075 2 0.5417 0.139 0.000 0.676 0.040 0.284
#> GSM215076 2 0.6483 -0.023 0.000 0.584 0.092 0.324
#> GSM215077 4 0.5172 0.821 0.000 0.404 0.008 0.588
#> GSM215078 2 0.4996 -0.674 0.000 0.516 0.000 0.484
#> GSM215079 4 0.4972 0.798 0.000 0.456 0.000 0.544
#> GSM215080 4 0.4961 0.805 0.000 0.448 0.000 0.552
#> GSM215081 4 0.5517 0.817 0.000 0.412 0.020 0.568
#> GSM215082 4 0.5756 0.795 0.000 0.400 0.032 0.568
#> GSM215083 1 0.5110 0.373 0.656 0.000 0.328 0.016
#> GSM215084 1 0.2892 0.866 0.896 0.000 0.036 0.068
#> GSM215085 3 0.6112 0.848 0.196 0.000 0.676 0.128
#> GSM215086 3 0.5355 0.860 0.180 0.000 0.736 0.084
#> GSM215087 1 0.0469 0.912 0.988 0.000 0.000 0.012
#> GSM215088 3 0.3498 0.879 0.160 0.000 0.832 0.008
#> GSM215089 1 0.1388 0.910 0.960 0.000 0.012 0.028
#> GSM215090 1 0.3808 0.760 0.812 0.000 0.012 0.176
#> GSM215091 1 0.0657 0.913 0.984 0.000 0.004 0.012
#> GSM215092 1 0.3996 0.817 0.836 0.000 0.060 0.104
#> GSM215093 3 0.3856 0.871 0.136 0.000 0.832 0.032
#> GSM215094 1 0.0779 0.911 0.980 0.000 0.004 0.016
#> GSM215095 1 0.0592 0.911 0.984 0.000 0.000 0.016
#> GSM215096 1 0.0592 0.912 0.984 0.000 0.000 0.016
#> GSM215097 1 0.0927 0.911 0.976 0.000 0.016 0.008
#> GSM215098 1 0.0657 0.912 0.984 0.000 0.004 0.012
#> GSM215099 1 0.0927 0.911 0.976 0.000 0.016 0.008
#> GSM215100 1 0.2224 0.898 0.928 0.000 0.032 0.040
#> GSM215101 1 0.1151 0.910 0.968 0.000 0.008 0.024
#> GSM215102 3 0.7450 0.710 0.264 0.000 0.508 0.228
#> GSM215103 1 0.6201 0.353 0.620 0.000 0.300 0.080
#> GSM215104 1 0.3966 0.821 0.840 0.000 0.072 0.088
#> GSM215105 1 0.1297 0.911 0.964 0.000 0.020 0.016
#> GSM215106 1 0.1510 0.907 0.956 0.000 0.028 0.016
#> GSM215107 1 0.1510 0.913 0.956 0.000 0.016 0.028
#> GSM215108 3 0.5842 0.863 0.168 0.000 0.704 0.128
#> GSM215109 3 0.4415 0.876 0.140 0.000 0.804 0.056
#> GSM215110 3 0.6977 0.801 0.212 0.000 0.584 0.204
#> GSM215111 1 0.1174 0.911 0.968 0.000 0.020 0.012
#> GSM215112 1 0.0895 0.911 0.976 0.000 0.004 0.020
#> GSM215113 1 0.0804 0.914 0.980 0.000 0.008 0.012
#> GSM215114 1 0.2385 0.881 0.920 0.000 0.028 0.052
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 5 0.5709 0.744 0.000 0.240 0.008 0.116 0.636
#> GSM215052 2 0.4445 0.309 0.000 0.676 0.000 0.300 0.024
#> GSM215053 5 0.5297 0.766 0.000 0.272 0.012 0.060 0.656
#> GSM215054 5 0.5527 0.761 0.000 0.232 0.008 0.104 0.656
#> GSM215055 5 0.4837 0.642 0.000 0.344 0.012 0.016 0.628
#> GSM215056 5 0.4649 0.785 0.000 0.244 0.004 0.044 0.708
#> GSM215057 2 0.4451 0.251 0.000 0.712 0.000 0.040 0.248
#> GSM215058 2 0.6409 -0.440 0.000 0.536 0.004 0.244 0.216
#> GSM215059 2 0.1768 0.681 0.000 0.924 0.004 0.000 0.072
#> GSM215060 2 0.3247 0.562 0.000 0.840 0.008 0.016 0.136
#> GSM215061 2 0.0963 0.694 0.000 0.964 0.000 0.000 0.036
#> GSM215062 2 0.4040 0.421 0.000 0.724 0.000 0.260 0.016
#> GSM215063 5 0.5771 0.747 0.000 0.208 0.028 0.100 0.664
#> GSM215064 2 0.3759 0.492 0.000 0.764 0.000 0.220 0.016
#> GSM215065 2 0.0703 0.698 0.000 0.976 0.000 0.000 0.024
#> GSM215066 2 0.0324 0.703 0.000 0.992 0.000 0.004 0.004
#> GSM215067 5 0.6074 0.742 0.000 0.228 0.032 0.108 0.632
#> GSM215068 2 0.0324 0.703 0.000 0.992 0.000 0.004 0.004
#> GSM215069 2 0.0324 0.703 0.000 0.992 0.000 0.004 0.004
#> GSM215070 2 0.4194 0.420 0.000 0.720 0.004 0.260 0.016
#> GSM215071 2 0.2522 0.649 0.000 0.880 0.000 0.108 0.012
#> GSM215072 2 0.4269 0.339 0.000 0.684 0.000 0.300 0.016
#> GSM215073 2 0.2464 0.640 0.000 0.892 0.012 0.004 0.092
#> GSM215074 2 0.3044 0.598 0.000 0.840 0.004 0.008 0.148
#> GSM215075 2 0.5770 -0.080 0.000 0.636 0.012 0.112 0.240
#> GSM215076 4 0.6655 0.000 0.000 0.368 0.000 0.404 0.228
#> GSM215077 2 0.2358 0.652 0.000 0.888 0.000 0.104 0.008
#> GSM215078 2 0.1843 0.687 0.000 0.932 0.008 0.008 0.052
#> GSM215079 2 0.0566 0.703 0.000 0.984 0.000 0.012 0.004
#> GSM215080 2 0.0324 0.703 0.000 0.992 0.000 0.004 0.004
#> GSM215081 2 0.2424 0.621 0.000 0.868 0.000 0.132 0.000
#> GSM215082 2 0.3671 0.489 0.000 0.756 0.000 0.236 0.008
#> GSM215083 1 0.4987 0.437 0.616 0.000 0.340 0.044 0.000
#> GSM215084 1 0.3986 0.829 0.828 0.000 0.044 0.080 0.048
#> GSM215085 3 0.6476 0.760 0.084 0.000 0.636 0.164 0.116
#> GSM215086 3 0.5037 0.781 0.076 0.000 0.760 0.100 0.064
#> GSM215087 1 0.1202 0.897 0.960 0.000 0.004 0.032 0.004
#> GSM215088 3 0.2625 0.802 0.056 0.000 0.900 0.028 0.016
#> GSM215089 1 0.1026 0.897 0.968 0.000 0.004 0.024 0.004
#> GSM215090 1 0.4504 0.710 0.748 0.000 0.016 0.200 0.036
#> GSM215091 1 0.1012 0.897 0.968 0.000 0.012 0.020 0.000
#> GSM215092 1 0.4762 0.748 0.760 0.000 0.056 0.152 0.032
#> GSM215093 3 0.3054 0.775 0.032 0.000 0.880 0.060 0.028
#> GSM215094 1 0.1202 0.895 0.960 0.000 0.004 0.032 0.004
#> GSM215095 1 0.0510 0.898 0.984 0.000 0.000 0.016 0.000
#> GSM215096 1 0.0880 0.897 0.968 0.000 0.000 0.032 0.000
#> GSM215097 1 0.1106 0.896 0.964 0.000 0.024 0.012 0.000
#> GSM215098 1 0.1300 0.897 0.956 0.000 0.016 0.028 0.000
#> GSM215099 1 0.0854 0.898 0.976 0.000 0.012 0.008 0.004
#> GSM215100 1 0.2193 0.888 0.920 0.000 0.044 0.028 0.008
#> GSM215101 1 0.2564 0.876 0.904 0.000 0.020 0.052 0.024
#> GSM215102 3 0.7465 0.624 0.196 0.000 0.428 0.324 0.052
#> GSM215103 1 0.6285 0.469 0.608 0.000 0.244 0.112 0.036
#> GSM215104 1 0.4431 0.795 0.796 0.000 0.052 0.108 0.044
#> GSM215105 1 0.1372 0.899 0.956 0.000 0.024 0.016 0.004
#> GSM215106 1 0.1605 0.894 0.944 0.000 0.040 0.012 0.004
#> GSM215107 1 0.2499 0.886 0.908 0.000 0.040 0.036 0.016
#> GSM215108 3 0.6157 0.783 0.068 0.000 0.644 0.212 0.076
#> GSM215109 3 0.4123 0.798 0.056 0.000 0.820 0.080 0.044
#> GSM215110 3 0.6806 0.721 0.144 0.000 0.560 0.248 0.048
#> GSM215111 1 0.1074 0.896 0.968 0.000 0.016 0.012 0.004
#> GSM215112 1 0.1281 0.896 0.956 0.000 0.012 0.032 0.000
#> GSM215113 1 0.0451 0.898 0.988 0.000 0.000 0.008 0.004
#> GSM215114 1 0.3308 0.849 0.864 0.000 0.028 0.076 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 5 0.6119 0.581 0.000 0.144 0.000 0.024 0.444 0.388
#> GSM215052 2 0.4821 0.134 0.000 0.556 0.008 0.400 0.032 0.004
#> GSM215053 5 0.6674 0.598 0.000 0.220 0.004 0.032 0.416 0.328
#> GSM215054 5 0.5934 0.597 0.000 0.148 0.000 0.012 0.444 0.396
#> GSM215055 5 0.6659 0.527 0.000 0.292 0.004 0.048 0.472 0.184
#> GSM215056 5 0.5465 0.665 0.000 0.160 0.008 0.044 0.676 0.112
#> GSM215057 2 0.4840 0.293 0.000 0.640 0.008 0.040 0.300 0.012
#> GSM215058 2 0.6691 -0.446 0.000 0.420 0.004 0.312 0.232 0.032
#> GSM215059 2 0.2113 0.658 0.000 0.896 0.004 0.008 0.092 0.000
#> GSM215060 2 0.3511 0.589 0.000 0.816 0.008 0.012 0.136 0.028
#> GSM215061 2 0.1647 0.669 0.000 0.940 0.008 0.004 0.032 0.016
#> GSM215062 2 0.4402 0.276 0.000 0.632 0.000 0.336 0.016 0.016
#> GSM215063 5 0.2967 0.629 0.000 0.136 0.004 0.008 0.840 0.012
#> GSM215064 2 0.4240 0.346 0.000 0.672 0.000 0.296 0.016 0.016
#> GSM215065 2 0.0972 0.672 0.000 0.964 0.000 0.008 0.028 0.000
#> GSM215066 2 0.0146 0.675 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM215067 5 0.2810 0.624 0.000 0.156 0.004 0.008 0.832 0.000
#> GSM215068 2 0.0291 0.675 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM215069 2 0.0146 0.675 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM215070 2 0.4528 0.335 0.000 0.624 0.008 0.340 0.024 0.004
#> GSM215071 2 0.3176 0.619 0.000 0.824 0.008 0.148 0.016 0.004
#> GSM215072 2 0.4310 0.186 0.000 0.576 0.004 0.404 0.016 0.000
#> GSM215073 2 0.2872 0.636 0.000 0.868 0.004 0.016 0.088 0.024
#> GSM215074 2 0.3470 0.585 0.000 0.792 0.000 0.020 0.176 0.012
#> GSM215075 2 0.5837 -0.144 0.000 0.544 0.000 0.024 0.128 0.304
#> GSM215076 4 0.7387 0.000 0.000 0.268 0.004 0.384 0.108 0.236
#> GSM215077 2 0.2978 0.622 0.000 0.840 0.008 0.136 0.008 0.008
#> GSM215078 2 0.2452 0.664 0.000 0.900 0.008 0.020 0.056 0.016
#> GSM215079 2 0.1059 0.673 0.000 0.964 0.000 0.016 0.016 0.004
#> GSM215080 2 0.0146 0.676 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM215081 2 0.2913 0.547 0.000 0.812 0.000 0.180 0.004 0.004
#> GSM215082 2 0.4302 0.348 0.000 0.632 0.008 0.344 0.012 0.004
#> GSM215083 1 0.5117 0.552 0.644 0.000 0.276 0.016 0.016 0.048
#> GSM215084 1 0.3671 0.806 0.820 0.000 0.032 0.068 0.000 0.080
#> GSM215085 3 0.7018 0.658 0.048 0.000 0.532 0.240 0.092 0.088
#> GSM215086 3 0.5203 0.705 0.052 0.000 0.728 0.112 0.028 0.080
#> GSM215087 1 0.0964 0.868 0.968 0.000 0.000 0.012 0.004 0.016
#> GSM215088 3 0.3107 0.733 0.036 0.000 0.872 0.020 0.036 0.036
#> GSM215089 1 0.3027 0.850 0.832 0.000 0.016 0.004 0.004 0.144
#> GSM215090 1 0.5700 0.478 0.540 0.000 0.008 0.112 0.008 0.332
#> GSM215091 1 0.1296 0.871 0.948 0.000 0.004 0.004 0.000 0.044
#> GSM215092 1 0.5644 0.698 0.668 0.000 0.052 0.112 0.012 0.156
#> GSM215093 3 0.4456 0.690 0.044 0.000 0.764 0.016 0.144 0.032
#> GSM215094 1 0.1262 0.868 0.956 0.000 0.000 0.016 0.008 0.020
#> GSM215095 1 0.0665 0.868 0.980 0.000 0.000 0.008 0.004 0.008
#> GSM215096 1 0.0603 0.871 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM215097 1 0.2290 0.868 0.892 0.000 0.020 0.004 0.000 0.084
#> GSM215098 1 0.1067 0.871 0.964 0.000 0.004 0.004 0.004 0.024
#> GSM215099 1 0.2449 0.867 0.884 0.000 0.016 0.004 0.004 0.092
#> GSM215100 1 0.3156 0.859 0.840 0.000 0.024 0.012 0.004 0.120
#> GSM215101 1 0.3216 0.855 0.848 0.000 0.008 0.036 0.012 0.096
#> GSM215102 3 0.7249 0.599 0.116 0.000 0.408 0.236 0.000 0.240
#> GSM215103 1 0.6018 0.494 0.592 0.000 0.260 0.060 0.012 0.076
#> GSM215104 1 0.4490 0.781 0.768 0.000 0.036 0.084 0.008 0.104
#> GSM215105 1 0.2253 0.870 0.896 0.000 0.012 0.004 0.004 0.084
#> GSM215106 1 0.2126 0.870 0.904 0.000 0.020 0.004 0.000 0.072
#> GSM215107 1 0.2753 0.859 0.872 0.000 0.008 0.048 0.000 0.072
#> GSM215108 3 0.5830 0.711 0.052 0.000 0.632 0.200 0.008 0.108
#> GSM215109 3 0.3141 0.736 0.028 0.000 0.856 0.064 0.000 0.052
#> GSM215110 3 0.7049 0.623 0.072 0.000 0.440 0.188 0.008 0.292
#> GSM215111 1 0.2056 0.868 0.904 0.000 0.012 0.004 0.000 0.080
#> GSM215112 1 0.1059 0.867 0.964 0.000 0.000 0.016 0.004 0.016
#> GSM215113 1 0.1531 0.873 0.928 0.000 0.000 0.000 0.004 0.068
#> GSM215114 1 0.2587 0.846 0.892 0.000 0.016 0.036 0.004 0.052
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> CV:kmeans 64 9.19e-15 1.000 2
#> CV:kmeans 62 3.44e-14 0.999 3
#> CV:kmeans 50 7.99e-11 0.878 4
#> CV:kmeans 52 3.00e-11 0.934 5
#> CV:kmeans 52 3.00e-11 0.955 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 51941 rows and 64 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.563 0.775 0.809 0.2381 0.897 0.791
#> 4 4 0.506 0.453 0.697 0.1774 0.875 0.684
#> 5 5 0.507 0.417 0.624 0.0633 0.923 0.752
#> 6 6 0.513 0.241 0.548 0.0454 0.880 0.597
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.5178 0.901 0.000 0.744 0.256
#> GSM215052 2 0.4605 0.909 0.000 0.796 0.204
#> GSM215053 2 0.4346 0.903 0.000 0.816 0.184
#> GSM215054 2 0.4887 0.894 0.000 0.772 0.228
#> GSM215055 2 0.4291 0.907 0.000 0.820 0.180
#> GSM215056 2 0.4654 0.898 0.000 0.792 0.208
#> GSM215057 2 0.4002 0.917 0.000 0.840 0.160
#> GSM215058 2 0.5058 0.906 0.000 0.756 0.244
#> GSM215059 2 0.2711 0.925 0.000 0.912 0.088
#> GSM215060 2 0.3192 0.920 0.000 0.888 0.112
#> GSM215061 2 0.2711 0.925 0.000 0.912 0.088
#> GSM215062 2 0.3941 0.901 0.000 0.844 0.156
#> GSM215063 2 0.4887 0.896 0.000 0.772 0.228
#> GSM215064 2 0.4002 0.903 0.000 0.840 0.160
#> GSM215065 2 0.1411 0.919 0.000 0.964 0.036
#> GSM215066 2 0.2448 0.923 0.000 0.924 0.076
#> GSM215067 2 0.4931 0.899 0.000 0.768 0.232
#> GSM215068 2 0.1753 0.921 0.000 0.952 0.048
#> GSM215069 2 0.1643 0.920 0.000 0.956 0.044
#> GSM215070 2 0.4291 0.911 0.000 0.820 0.180
#> GSM215071 2 0.3038 0.923 0.000 0.896 0.104
#> GSM215072 2 0.4555 0.906 0.000 0.800 0.200
#> GSM215073 2 0.1753 0.920 0.000 0.952 0.048
#> GSM215074 2 0.3482 0.921 0.000 0.872 0.128
#> GSM215075 2 0.3752 0.922 0.000 0.856 0.144
#> GSM215076 2 0.5465 0.895 0.000 0.712 0.288
#> GSM215077 2 0.2625 0.919 0.000 0.916 0.084
#> GSM215078 2 0.3192 0.925 0.000 0.888 0.112
#> GSM215079 2 0.2537 0.921 0.000 0.920 0.080
#> GSM215080 2 0.1860 0.922 0.000 0.948 0.052
#> GSM215081 2 0.3482 0.905 0.000 0.872 0.128
#> GSM215082 2 0.4235 0.908 0.000 0.824 0.176
#> GSM215083 1 0.6225 -0.458 0.568 0.000 0.432
#> GSM215084 1 0.3116 0.721 0.892 0.000 0.108
#> GSM215085 3 0.6295 0.757 0.472 0.000 0.528
#> GSM215086 3 0.6192 0.822 0.420 0.000 0.580
#> GSM215087 1 0.1753 0.730 0.952 0.000 0.048
#> GSM215088 3 0.6095 0.836 0.392 0.000 0.608
#> GSM215089 1 0.3816 0.695 0.852 0.000 0.148
#> GSM215090 1 0.5098 0.517 0.752 0.000 0.248
#> GSM215091 1 0.2066 0.734 0.940 0.000 0.060
#> GSM215092 1 0.5706 0.162 0.680 0.000 0.320
#> GSM215093 3 0.5835 0.802 0.340 0.000 0.660
#> GSM215094 1 0.1753 0.736 0.952 0.000 0.048
#> GSM215095 1 0.0237 0.714 0.996 0.000 0.004
#> GSM215096 1 0.1289 0.730 0.968 0.000 0.032
#> GSM215097 1 0.5138 0.514 0.748 0.000 0.252
#> GSM215098 1 0.3686 0.701 0.860 0.000 0.140
#> GSM215099 1 0.4002 0.683 0.840 0.000 0.160
#> GSM215100 1 0.5678 0.279 0.684 0.000 0.316
#> GSM215101 1 0.4931 0.526 0.768 0.000 0.232
#> GSM215102 3 0.6302 0.726 0.480 0.000 0.520
#> GSM215103 3 0.6307 0.692 0.488 0.000 0.512
#> GSM215104 1 0.5254 0.415 0.736 0.000 0.264
#> GSM215105 1 0.3038 0.725 0.896 0.000 0.104
#> GSM215106 1 0.3941 0.690 0.844 0.000 0.156
#> GSM215107 1 0.3879 0.695 0.848 0.000 0.152
#> GSM215108 3 0.6295 0.760 0.472 0.000 0.528
#> GSM215109 3 0.6008 0.830 0.372 0.000 0.628
#> GSM215110 3 0.6126 0.837 0.400 0.000 0.600
#> GSM215111 1 0.3816 0.706 0.852 0.000 0.148
#> GSM215112 1 0.1031 0.722 0.976 0.000 0.024
#> GSM215113 1 0.1753 0.735 0.952 0.000 0.048
#> GSM215114 1 0.4346 0.655 0.816 0.000 0.184
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 4 0.500 0.4478 0.000 0.328 0.012 0.660
#> GSM215052 4 0.548 0.1517 0.000 0.396 0.020 0.584
#> GSM215053 4 0.526 0.2533 0.000 0.448 0.008 0.544
#> GSM215054 4 0.472 0.4505 0.000 0.300 0.008 0.692
#> GSM215055 2 0.541 -0.2319 0.000 0.496 0.012 0.492
#> GSM215056 4 0.504 0.3227 0.000 0.404 0.004 0.592
#> GSM215057 2 0.484 0.2078 0.000 0.648 0.004 0.348
#> GSM215058 4 0.492 0.1859 0.000 0.428 0.000 0.572
#> GSM215059 2 0.413 0.4685 0.000 0.740 0.000 0.260
#> GSM215060 2 0.489 0.1957 0.000 0.636 0.004 0.360
#> GSM215061 2 0.432 0.4566 0.000 0.760 0.012 0.228
#> GSM215062 2 0.519 0.2156 0.000 0.580 0.008 0.412
#> GSM215063 4 0.472 0.4537 0.000 0.324 0.004 0.672
#> GSM215064 2 0.467 0.3793 0.000 0.700 0.008 0.292
#> GSM215065 2 0.307 0.5128 0.000 0.848 0.000 0.152
#> GSM215066 2 0.331 0.5122 0.000 0.840 0.004 0.156
#> GSM215067 4 0.443 0.4427 0.000 0.304 0.000 0.696
#> GSM215068 2 0.321 0.5220 0.000 0.848 0.004 0.148
#> GSM215069 2 0.267 0.5272 0.000 0.892 0.008 0.100
#> GSM215070 2 0.547 0.1829 0.000 0.544 0.016 0.440
#> GSM215071 2 0.515 0.3886 0.000 0.664 0.020 0.316
#> GSM215072 4 0.540 -0.0911 0.000 0.476 0.012 0.512
#> GSM215073 2 0.397 0.4696 0.000 0.788 0.008 0.204
#> GSM215074 2 0.461 0.3658 0.000 0.692 0.004 0.304
#> GSM215075 2 0.519 0.0582 0.000 0.580 0.008 0.412
#> GSM215076 4 0.487 0.3524 0.000 0.304 0.012 0.684
#> GSM215077 2 0.458 0.4439 0.000 0.728 0.012 0.260
#> GSM215078 2 0.508 0.2966 0.000 0.644 0.012 0.344
#> GSM215079 2 0.344 0.5022 0.000 0.816 0.000 0.184
#> GSM215080 2 0.419 0.4556 0.000 0.764 0.008 0.228
#> GSM215081 2 0.404 0.4350 0.000 0.752 0.000 0.248
#> GSM215082 2 0.513 0.3222 0.000 0.632 0.012 0.356
#> GSM215083 3 0.544 0.2478 0.420 0.000 0.564 0.016
#> GSM215084 1 0.433 0.6549 0.768 0.000 0.216 0.016
#> GSM215085 3 0.472 0.6214 0.280 0.000 0.708 0.012
#> GSM215086 3 0.440 0.6612 0.224 0.000 0.760 0.016
#> GSM215087 1 0.291 0.6730 0.888 0.000 0.092 0.020
#> GSM215088 3 0.363 0.6949 0.160 0.000 0.828 0.012
#> GSM215089 1 0.487 0.6085 0.720 0.000 0.256 0.024
#> GSM215090 1 0.524 0.4653 0.628 0.000 0.356 0.016
#> GSM215091 1 0.414 0.6555 0.788 0.000 0.196 0.016
#> GSM215092 1 0.538 0.2217 0.536 0.000 0.452 0.012
#> GSM215093 3 0.382 0.6814 0.120 0.000 0.840 0.040
#> GSM215094 1 0.359 0.6781 0.824 0.000 0.168 0.008
#> GSM215095 1 0.212 0.6717 0.924 0.000 0.068 0.008
#> GSM215096 1 0.334 0.6831 0.856 0.000 0.128 0.016
#> GSM215097 1 0.567 0.3523 0.572 0.000 0.400 0.028
#> GSM215098 1 0.439 0.6421 0.752 0.000 0.236 0.012
#> GSM215099 1 0.474 0.6304 0.728 0.000 0.252 0.020
#> GSM215100 1 0.522 0.3206 0.568 0.000 0.424 0.008
#> GSM215101 1 0.550 0.4146 0.604 0.000 0.372 0.024
#> GSM215102 3 0.442 0.6030 0.256 0.000 0.736 0.008
#> GSM215103 3 0.536 0.3963 0.360 0.000 0.620 0.020
#> GSM215104 1 0.521 0.3223 0.572 0.000 0.420 0.008
#> GSM215105 1 0.471 0.6260 0.732 0.000 0.248 0.020
#> GSM215106 1 0.458 0.6256 0.748 0.000 0.232 0.020
#> GSM215107 1 0.433 0.6305 0.748 0.000 0.244 0.008
#> GSM215108 3 0.435 0.6479 0.232 0.000 0.756 0.012
#> GSM215109 3 0.271 0.6941 0.112 0.000 0.884 0.004
#> GSM215110 3 0.459 0.6113 0.280 0.000 0.712 0.008
#> GSM215111 1 0.425 0.6629 0.768 0.000 0.220 0.012
#> GSM215112 1 0.261 0.6741 0.896 0.000 0.096 0.008
#> GSM215113 1 0.408 0.6739 0.800 0.000 0.180 0.020
#> GSM215114 1 0.487 0.5779 0.720 0.000 0.256 0.024
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 4 0.520 0.4393 0.000 0.188 0.000 0.684 NA
#> GSM215052 2 0.661 0.2496 0.000 0.456 0.000 0.300 NA
#> GSM215053 4 0.511 0.4687 0.000 0.240 0.004 0.680 NA
#> GSM215054 4 0.448 0.5110 0.000 0.124 0.016 0.780 NA
#> GSM215055 4 0.473 0.4206 0.000 0.284 0.000 0.672 NA
#> GSM215056 4 0.467 0.5113 0.000 0.176 0.012 0.748 NA
#> GSM215057 4 0.582 -0.0844 0.000 0.448 0.000 0.460 NA
#> GSM215058 2 0.646 0.0360 0.000 0.432 0.004 0.408 NA
#> GSM215059 2 0.527 0.3121 0.000 0.628 0.000 0.296 NA
#> GSM215060 4 0.563 0.0700 0.000 0.424 0.000 0.500 NA
#> GSM215061 2 0.543 0.1860 0.000 0.576 0.000 0.352 NA
#> GSM215062 2 0.570 0.4020 0.000 0.628 0.000 0.184 NA
#> GSM215063 4 0.480 0.5177 0.000 0.160 0.024 0.752 NA
#> GSM215064 2 0.512 0.4235 0.000 0.696 0.000 0.136 NA
#> GSM215065 2 0.453 0.4081 0.000 0.732 0.000 0.204 NA
#> GSM215066 2 0.431 0.4325 0.000 0.760 0.000 0.172 NA
#> GSM215067 4 0.497 0.4547 0.000 0.192 0.000 0.704 NA
#> GSM215068 2 0.430 0.4509 0.000 0.752 0.000 0.192 NA
#> GSM215069 2 0.454 0.4460 0.000 0.740 0.000 0.184 NA
#> GSM215070 2 0.625 0.3442 0.000 0.536 0.000 0.268 NA
#> GSM215071 2 0.608 0.3535 0.000 0.560 0.000 0.272 NA
#> GSM215072 2 0.642 0.3037 0.000 0.508 0.000 0.260 NA
#> GSM215073 2 0.569 0.2250 0.000 0.552 0.000 0.356 NA
#> GSM215074 2 0.575 0.2059 0.000 0.540 0.000 0.364 NA
#> GSM215075 2 0.604 -0.1005 0.000 0.448 0.000 0.436 NA
#> GSM215076 4 0.651 0.0741 0.000 0.296 0.000 0.480 NA
#> GSM215077 2 0.551 0.4565 0.000 0.652 0.000 0.176 NA
#> GSM215078 2 0.624 0.0739 0.000 0.456 0.000 0.400 NA
#> GSM215079 2 0.486 0.4367 0.000 0.732 0.004 0.152 NA
#> GSM215080 2 0.488 0.4388 0.000 0.708 0.000 0.200 NA
#> GSM215081 2 0.422 0.4633 0.000 0.780 0.000 0.100 NA
#> GSM215082 2 0.576 0.4128 0.000 0.620 0.000 0.192 NA
#> GSM215083 3 0.671 0.2419 0.304 0.000 0.480 0.008 NA
#> GSM215084 1 0.519 0.5555 0.684 0.000 0.192 0.000 NA
#> GSM215085 3 0.594 0.5025 0.224 0.000 0.608 0.004 NA
#> GSM215086 3 0.499 0.5909 0.124 0.000 0.720 0.004 NA
#> GSM215087 1 0.476 0.6020 0.704 0.000 0.052 0.004 NA
#> GSM215088 3 0.402 0.6226 0.092 0.000 0.804 0.004 NA
#> GSM215089 1 0.585 0.5495 0.624 0.000 0.188 0.004 NA
#> GSM215090 1 0.661 0.3399 0.460 0.000 0.284 0.000 NA
#> GSM215091 1 0.504 0.6012 0.692 0.000 0.100 0.000 NA
#> GSM215092 1 0.677 0.2184 0.436 0.000 0.324 0.004 NA
#> GSM215093 3 0.370 0.6196 0.044 0.000 0.844 0.036 NA
#> GSM215094 1 0.463 0.6159 0.744 0.000 0.120 0.000 NA
#> GSM215095 1 0.309 0.6251 0.864 0.000 0.040 0.004 NA
#> GSM215096 1 0.416 0.6217 0.792 0.000 0.084 0.004 NA
#> GSM215097 1 0.639 0.3512 0.508 0.000 0.324 0.004 NA
#> GSM215098 1 0.560 0.5561 0.640 0.000 0.160 0.000 NA
#> GSM215099 1 0.558 0.5747 0.668 0.000 0.160 0.008 NA
#> GSM215100 1 0.642 0.3315 0.488 0.000 0.316 0.000 NA
#> GSM215101 1 0.651 0.3766 0.484 0.000 0.284 0.000 NA
#> GSM215102 3 0.551 0.5029 0.244 0.000 0.636 0.000 NA
#> GSM215103 3 0.624 0.3749 0.276 0.000 0.536 0.000 NA
#> GSM215104 1 0.640 0.3023 0.488 0.000 0.324 0.000 NA
#> GSM215105 1 0.457 0.6105 0.756 0.000 0.148 0.004 NA
#> GSM215106 1 0.541 0.5706 0.664 0.000 0.176 0.000 NA
#> GSM215107 1 0.601 0.5037 0.584 0.000 0.220 0.000 NA
#> GSM215108 3 0.552 0.5576 0.216 0.000 0.656 0.004 NA
#> GSM215109 3 0.334 0.6315 0.072 0.000 0.852 0.004 NA
#> GSM215110 3 0.534 0.5048 0.224 0.000 0.660 0.000 NA
#> GSM215111 1 0.527 0.5842 0.680 0.000 0.168 0.000 NA
#> GSM215112 1 0.476 0.5955 0.716 0.000 0.080 0.000 NA
#> GSM215113 1 0.440 0.6243 0.780 0.000 0.104 0.008 NA
#> GSM215114 1 0.582 0.4975 0.608 0.000 0.168 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 6 0.664 0.3635 0.000 0.184 0.004 0.048 0.284 0.480
#> GSM215052 5 0.552 0.4437 0.000 0.176 0.008 0.028 0.656 0.132
#> GSM215053 6 0.647 0.3657 0.000 0.340 0.008 0.060 0.104 0.488
#> GSM215054 6 0.608 0.5349 0.000 0.148 0.012 0.044 0.188 0.608
#> GSM215055 6 0.622 0.3398 0.000 0.372 0.000 0.028 0.152 0.448
#> GSM215056 6 0.606 0.5074 0.000 0.264 0.004 0.024 0.160 0.548
#> GSM215057 2 0.634 0.0108 0.000 0.480 0.000 0.032 0.184 0.304
#> GSM215058 5 0.664 0.1828 0.000 0.244 0.004 0.040 0.476 0.236
#> GSM215059 2 0.510 0.3735 0.000 0.648 0.000 0.008 0.128 0.216
#> GSM215060 2 0.582 0.1382 0.000 0.588 0.004 0.024 0.140 0.244
#> GSM215061 2 0.498 0.3824 0.000 0.688 0.004 0.016 0.100 0.192
#> GSM215062 5 0.497 0.2877 0.000 0.352 0.000 0.032 0.588 0.028
#> GSM215063 6 0.539 0.5489 0.000 0.168 0.004 0.012 0.176 0.640
#> GSM215064 2 0.543 -0.1619 0.000 0.460 0.000 0.024 0.456 0.060
#> GSM215065 2 0.308 0.4506 0.000 0.848 0.000 0.008 0.092 0.052
#> GSM215066 2 0.435 0.3812 0.000 0.728 0.000 0.020 0.204 0.048
#> GSM215067 6 0.628 0.4445 0.000 0.252 0.004 0.020 0.220 0.504
#> GSM215068 2 0.534 0.3521 0.000 0.660 0.000 0.036 0.192 0.112
#> GSM215069 2 0.352 0.4547 0.000 0.820 0.000 0.016 0.108 0.056
#> GSM215070 5 0.520 0.3605 0.000 0.336 0.000 0.016 0.580 0.068
#> GSM215071 2 0.593 0.0922 0.000 0.492 0.000 0.020 0.356 0.132
#> GSM215072 5 0.447 0.4885 0.000 0.184 0.000 0.012 0.724 0.080
#> GSM215073 2 0.516 0.3024 0.000 0.640 0.000 0.012 0.112 0.236
#> GSM215074 2 0.603 0.2028 0.000 0.508 0.000 0.012 0.216 0.264
#> GSM215075 2 0.662 -0.0454 0.000 0.476 0.000 0.052 0.208 0.264
#> GSM215076 5 0.567 0.3567 0.000 0.156 0.004 0.016 0.604 0.220
#> GSM215077 2 0.542 0.0370 0.000 0.508 0.000 0.020 0.404 0.068
#> GSM215078 2 0.625 0.2137 0.000 0.508 0.000 0.028 0.212 0.252
#> GSM215079 2 0.572 0.3083 0.000 0.624 0.000 0.048 0.200 0.128
#> GSM215080 2 0.523 0.3694 0.000 0.660 0.000 0.028 0.208 0.104
#> GSM215081 2 0.504 -0.0371 0.000 0.512 0.000 0.020 0.432 0.036
#> GSM215082 5 0.505 0.4361 0.000 0.264 0.000 0.016 0.640 0.080
#> GSM215083 3 0.715 0.0648 0.264 0.000 0.392 0.276 0.008 0.060
#> GSM215084 1 0.640 0.1749 0.576 0.000 0.188 0.176 0.024 0.036
#> GSM215085 3 0.665 0.3164 0.188 0.000 0.520 0.228 0.008 0.056
#> GSM215086 3 0.583 0.4006 0.096 0.000 0.644 0.188 0.012 0.060
#> GSM215087 1 0.513 0.2576 0.696 0.000 0.068 0.192 0.020 0.024
#> GSM215088 3 0.563 0.4304 0.092 0.000 0.688 0.132 0.024 0.064
#> GSM215089 4 0.641 0.2413 0.392 0.000 0.164 0.416 0.012 0.016
#> GSM215090 4 0.653 0.2824 0.292 0.000 0.224 0.456 0.008 0.020
#> GSM215091 1 0.596 0.1697 0.600 0.000 0.080 0.260 0.024 0.036
#> GSM215092 3 0.690 -0.3192 0.312 0.000 0.340 0.312 0.024 0.012
#> GSM215093 3 0.621 0.4188 0.060 0.000 0.636 0.148 0.036 0.120
#> GSM215094 1 0.514 0.2973 0.692 0.000 0.120 0.160 0.012 0.016
#> GSM215095 1 0.384 0.3288 0.792 0.000 0.024 0.152 0.008 0.024
#> GSM215096 1 0.422 0.3183 0.784 0.000 0.072 0.112 0.012 0.020
#> GSM215097 1 0.667 -0.1783 0.440 0.000 0.172 0.344 0.012 0.032
#> GSM215098 1 0.625 0.0120 0.512 0.000 0.148 0.304 0.004 0.032
#> GSM215099 1 0.587 0.0606 0.604 0.000 0.132 0.228 0.012 0.024
#> GSM215100 4 0.657 0.2729 0.352 0.000 0.216 0.404 0.004 0.024
#> GSM215101 1 0.669 -0.2077 0.392 0.000 0.204 0.368 0.008 0.028
#> GSM215102 3 0.647 0.2836 0.168 0.000 0.572 0.192 0.020 0.048
#> GSM215103 3 0.729 0.1554 0.208 0.000 0.448 0.252 0.024 0.068
#> GSM215104 1 0.693 -0.0329 0.404 0.000 0.292 0.256 0.008 0.040
#> GSM215105 1 0.541 0.1863 0.648 0.000 0.092 0.228 0.012 0.020
#> GSM215106 1 0.628 0.1333 0.532 0.000 0.164 0.264 0.004 0.036
#> GSM215107 1 0.598 0.1380 0.560 0.000 0.140 0.272 0.008 0.020
#> GSM215108 3 0.603 0.3934 0.152 0.000 0.636 0.144 0.024 0.044
#> GSM215109 3 0.417 0.4601 0.044 0.000 0.804 0.088 0.032 0.032
#> GSM215110 3 0.619 0.2779 0.116 0.000 0.556 0.280 0.016 0.032
#> GSM215111 1 0.569 0.0319 0.576 0.000 0.104 0.296 0.012 0.012
#> GSM215112 1 0.456 0.3190 0.720 0.000 0.044 0.208 0.008 0.020
#> GSM215113 1 0.541 0.0116 0.568 0.000 0.112 0.312 0.000 0.008
#> GSM215114 1 0.634 0.2397 0.604 0.000 0.148 0.172 0.028 0.048
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> CV:skmeans 64 9.19e-15 1.000 2
#> CV:skmeans 60 9.36e-14 0.999 3
#> CV:skmeans 29 5.04e-07 0.538 4
#> CV:skmeans 26 2.26e-06 0.835 5
#> CV:skmeans 3 NA NA 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 51941 rows and 64 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.998 0.999 0.5084 0.492 0.492
#> 3 3 0.815 0.756 0.831 0.1859 0.885 0.767
#> 4 4 0.555 0.769 0.770 0.0905 0.921 0.805
#> 5 5 0.545 0.732 0.752 0.0299 1.000 1.000
#> 6 6 0.547 0.644 0.735 0.0223 0.953 0.875
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0.0000 1.000 0.000 1.000
#> GSM215052 2 0.0000 1.000 0.000 1.000
#> GSM215053 2 0.0000 1.000 0.000 1.000
#> GSM215054 2 0.0000 1.000 0.000 1.000
#> GSM215055 2 0.0000 1.000 0.000 1.000
#> GSM215056 2 0.0000 1.000 0.000 1.000
#> GSM215057 2 0.0000 1.000 0.000 1.000
#> GSM215058 2 0.0000 1.000 0.000 1.000
#> GSM215059 2 0.0000 1.000 0.000 1.000
#> GSM215060 2 0.0000 1.000 0.000 1.000
#> GSM215061 2 0.0000 1.000 0.000 1.000
#> GSM215062 2 0.0000 1.000 0.000 1.000
#> GSM215063 2 0.0000 1.000 0.000 1.000
#> GSM215064 2 0.0000 1.000 0.000 1.000
#> GSM215065 2 0.0000 1.000 0.000 1.000
#> GSM215066 2 0.0000 1.000 0.000 1.000
#> GSM215067 2 0.0000 1.000 0.000 1.000
#> GSM215068 2 0.0000 1.000 0.000 1.000
#> GSM215069 2 0.0000 1.000 0.000 1.000
#> GSM215070 2 0.0000 1.000 0.000 1.000
#> GSM215071 2 0.0000 1.000 0.000 1.000
#> GSM215072 2 0.0000 1.000 0.000 1.000
#> GSM215073 2 0.0000 1.000 0.000 1.000
#> GSM215074 2 0.0000 1.000 0.000 1.000
#> GSM215075 2 0.0000 1.000 0.000 1.000
#> GSM215076 2 0.0000 1.000 0.000 1.000
#> GSM215077 2 0.0000 1.000 0.000 1.000
#> GSM215078 2 0.0000 1.000 0.000 1.000
#> GSM215079 2 0.0000 1.000 0.000 1.000
#> GSM215080 2 0.0000 1.000 0.000 1.000
#> GSM215081 2 0.0000 1.000 0.000 1.000
#> GSM215082 2 0.0000 1.000 0.000 1.000
#> GSM215083 1 0.0000 0.998 1.000 0.000
#> GSM215084 1 0.0000 0.998 1.000 0.000
#> GSM215085 1 0.0376 0.995 0.996 0.004
#> GSM215086 1 0.0000 0.998 1.000 0.000
#> GSM215087 1 0.0000 0.998 1.000 0.000
#> GSM215088 1 0.0000 0.998 1.000 0.000
#> GSM215089 1 0.0000 0.998 1.000 0.000
#> GSM215090 1 0.0000 0.998 1.000 0.000
#> GSM215091 1 0.0000 0.998 1.000 0.000
#> GSM215092 1 0.0000 0.998 1.000 0.000
#> GSM215093 1 0.0000 0.998 1.000 0.000
#> GSM215094 1 0.0000 0.998 1.000 0.000
#> GSM215095 1 0.0000 0.998 1.000 0.000
#> GSM215096 1 0.0000 0.998 1.000 0.000
#> GSM215097 1 0.0000 0.998 1.000 0.000
#> GSM215098 1 0.0000 0.998 1.000 0.000
#> GSM215099 1 0.0000 0.998 1.000 0.000
#> GSM215100 1 0.0000 0.998 1.000 0.000
#> GSM215101 1 0.1414 0.980 0.980 0.020
#> GSM215102 1 0.0000 0.998 1.000 0.000
#> GSM215103 1 0.0000 0.998 1.000 0.000
#> GSM215104 1 0.0000 0.998 1.000 0.000
#> GSM215105 1 0.0000 0.998 1.000 0.000
#> GSM215106 1 0.0000 0.998 1.000 0.000
#> GSM215107 1 0.0000 0.998 1.000 0.000
#> GSM215108 1 0.0000 0.998 1.000 0.000
#> GSM215109 1 0.2043 0.968 0.968 0.032
#> GSM215110 1 0.0000 0.998 1.000 0.000
#> GSM215111 1 0.0000 0.998 1.000 0.000
#> GSM215112 1 0.0000 0.998 1.000 0.000
#> GSM215113 1 0.0000 0.998 1.000 0.000
#> GSM215114 1 0.0000 0.998 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.1411 0.9779 0.000 0.964 0.036
#> GSM215052 2 0.0892 0.9803 0.000 0.980 0.020
#> GSM215053 2 0.0592 0.9803 0.000 0.988 0.012
#> GSM215054 2 0.0424 0.9801 0.000 0.992 0.008
#> GSM215055 2 0.1753 0.9799 0.000 0.952 0.048
#> GSM215056 2 0.0747 0.9808 0.000 0.984 0.016
#> GSM215057 2 0.1860 0.9785 0.000 0.948 0.052
#> GSM215058 2 0.1753 0.9778 0.000 0.952 0.048
#> GSM215059 2 0.0892 0.9819 0.000 0.980 0.020
#> GSM215060 2 0.1411 0.9779 0.000 0.964 0.036
#> GSM215061 2 0.1411 0.9795 0.000 0.964 0.036
#> GSM215062 2 0.1860 0.9771 0.000 0.948 0.052
#> GSM215063 2 0.0592 0.9811 0.000 0.988 0.012
#> GSM215064 2 0.1860 0.9755 0.000 0.948 0.052
#> GSM215065 2 0.1411 0.9779 0.000 0.964 0.036
#> GSM215066 2 0.1860 0.9803 0.000 0.948 0.052
#> GSM215067 2 0.1031 0.9815 0.000 0.976 0.024
#> GSM215068 2 0.1529 0.9808 0.000 0.960 0.040
#> GSM215069 2 0.1411 0.9779 0.000 0.964 0.036
#> GSM215070 2 0.1163 0.9817 0.000 0.972 0.028
#> GSM215071 2 0.1753 0.9791 0.000 0.952 0.048
#> GSM215072 2 0.1860 0.9741 0.000 0.948 0.052
#> GSM215073 2 0.1411 0.9793 0.000 0.964 0.036
#> GSM215074 2 0.0592 0.9803 0.000 0.988 0.012
#> GSM215075 2 0.1031 0.9815 0.000 0.976 0.024
#> GSM215076 2 0.2261 0.9764 0.000 0.932 0.068
#> GSM215077 2 0.1529 0.9789 0.000 0.960 0.040
#> GSM215078 2 0.1289 0.9820 0.000 0.968 0.032
#> GSM215079 2 0.1529 0.9746 0.000 0.960 0.040
#> GSM215080 2 0.1289 0.9790 0.000 0.968 0.032
#> GSM215081 2 0.1964 0.9745 0.000 0.944 0.056
#> GSM215082 2 0.1643 0.9733 0.000 0.956 0.044
#> GSM215083 1 0.4062 0.6137 0.836 0.000 0.164
#> GSM215084 1 0.6286 -0.4612 0.536 0.000 0.464
#> GSM215085 3 0.4178 0.3964 0.172 0.000 0.828
#> GSM215086 1 0.3412 0.6536 0.876 0.000 0.124
#> GSM215087 3 0.6295 0.6558 0.472 0.000 0.528
#> GSM215088 1 0.4399 0.5492 0.812 0.000 0.188
#> GSM215089 1 0.1411 0.7107 0.964 0.000 0.036
#> GSM215090 1 0.5926 0.0216 0.644 0.000 0.356
#> GSM215091 1 0.0237 0.6958 0.996 0.000 0.004
#> GSM215092 1 0.6154 -0.2162 0.592 0.000 0.408
#> GSM215093 1 0.1411 0.7077 0.964 0.000 0.036
#> GSM215094 3 0.6008 0.8067 0.372 0.000 0.628
#> GSM215095 1 0.6026 -0.0411 0.624 0.000 0.376
#> GSM215096 1 0.6244 -0.4685 0.560 0.000 0.440
#> GSM215097 1 0.3340 0.6694 0.880 0.000 0.120
#> GSM215098 1 0.2959 0.6883 0.900 0.000 0.100
#> GSM215099 3 0.6140 0.8054 0.404 0.000 0.596
#> GSM215100 1 0.1529 0.7032 0.960 0.000 0.040
#> GSM215101 1 0.1860 0.7028 0.948 0.000 0.052
#> GSM215102 3 0.6215 0.7771 0.428 0.000 0.572
#> GSM215103 1 0.1964 0.7065 0.944 0.000 0.056
#> GSM215104 3 0.6204 0.7801 0.424 0.000 0.576
#> GSM215105 3 0.6154 0.7898 0.408 0.000 0.592
#> GSM215106 1 0.1964 0.7115 0.944 0.000 0.056
#> GSM215107 1 0.3038 0.6689 0.896 0.000 0.104
#> GSM215108 3 0.6302 0.6879 0.480 0.000 0.520
#> GSM215109 1 0.2173 0.7054 0.944 0.008 0.048
#> GSM215110 1 0.2165 0.7061 0.936 0.000 0.064
#> GSM215111 3 0.6291 0.7295 0.468 0.000 0.532
#> GSM215112 3 0.5948 0.7991 0.360 0.000 0.640
#> GSM215113 3 0.6008 0.8037 0.372 0.000 0.628
#> GSM215114 1 0.5948 0.0346 0.640 0.000 0.360
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.3764 0.895 0.000 0.784 0.000 0.216
#> GSM215052 2 0.4040 0.887 0.000 0.752 0.000 0.248
#> GSM215053 2 0.3801 0.890 0.000 0.780 0.000 0.220
#> GSM215054 2 0.3837 0.888 0.000 0.776 0.000 0.224
#> GSM215055 2 0.1940 0.886 0.000 0.924 0.000 0.076
#> GSM215056 2 0.3356 0.903 0.000 0.824 0.000 0.176
#> GSM215057 2 0.3610 0.900 0.000 0.800 0.000 0.200
#> GSM215058 2 0.3219 0.898 0.000 0.836 0.000 0.164
#> GSM215059 2 0.2149 0.900 0.000 0.912 0.000 0.088
#> GSM215060 2 0.0921 0.877 0.000 0.972 0.000 0.028
#> GSM215061 2 0.1557 0.890 0.000 0.944 0.000 0.056
#> GSM215062 2 0.3764 0.892 0.000 0.784 0.000 0.216
#> GSM215063 2 0.3311 0.903 0.000 0.828 0.000 0.172
#> GSM215064 2 0.4193 0.881 0.000 0.732 0.000 0.268
#> GSM215065 2 0.0921 0.877 0.000 0.972 0.000 0.028
#> GSM215066 2 0.3311 0.899 0.000 0.828 0.000 0.172
#> GSM215067 2 0.3400 0.899 0.000 0.820 0.000 0.180
#> GSM215068 2 0.1302 0.887 0.000 0.956 0.000 0.044
#> GSM215069 2 0.0921 0.877 0.000 0.972 0.000 0.028
#> GSM215070 2 0.3356 0.901 0.000 0.824 0.000 0.176
#> GSM215071 2 0.1940 0.880 0.000 0.924 0.000 0.076
#> GSM215072 2 0.4277 0.876 0.000 0.720 0.000 0.280
#> GSM215073 2 0.1867 0.890 0.000 0.928 0.000 0.072
#> GSM215074 2 0.3975 0.886 0.000 0.760 0.000 0.240
#> GSM215075 2 0.3610 0.896 0.000 0.800 0.000 0.200
#> GSM215076 2 0.3172 0.889 0.000 0.840 0.000 0.160
#> GSM215077 2 0.1022 0.888 0.000 0.968 0.000 0.032
#> GSM215078 2 0.2469 0.906 0.000 0.892 0.000 0.108
#> GSM215079 2 0.4454 0.862 0.000 0.692 0.000 0.308
#> GSM215080 2 0.1557 0.892 0.000 0.944 0.000 0.056
#> GSM215081 2 0.4431 0.865 0.000 0.696 0.000 0.304
#> GSM215082 2 0.4431 0.864 0.000 0.696 0.000 0.304
#> GSM215083 3 0.4933 0.606 0.432 0.000 0.568 0.000
#> GSM215084 1 0.3726 0.610 0.788 0.000 0.212 0.000
#> GSM215085 4 0.6716 0.000 0.404 0.000 0.092 0.504
#> GSM215086 3 0.4883 0.660 0.288 0.000 0.696 0.016
#> GSM215087 1 0.2868 0.718 0.864 0.000 0.136 0.000
#> GSM215088 3 0.5119 0.525 0.440 0.000 0.556 0.004
#> GSM215089 3 0.4431 0.813 0.304 0.000 0.696 0.000
#> GSM215090 1 0.4746 0.176 0.632 0.000 0.368 0.000
#> GSM215091 3 0.4072 0.802 0.252 0.000 0.748 0.000
#> GSM215092 1 0.4277 0.467 0.720 0.000 0.280 0.000
#> GSM215093 3 0.4277 0.814 0.280 0.000 0.720 0.000
#> GSM215094 1 0.0817 0.705 0.976 0.000 0.024 0.000
#> GSM215095 1 0.4277 0.435 0.720 0.000 0.280 0.000
#> GSM215096 1 0.4222 0.497 0.728 0.000 0.272 0.000
#> GSM215097 3 0.4761 0.757 0.372 0.000 0.628 0.000
#> GSM215098 3 0.4624 0.780 0.340 0.000 0.660 0.000
#> GSM215099 1 0.1867 0.736 0.928 0.000 0.072 0.000
#> GSM215100 3 0.4406 0.808 0.300 0.000 0.700 0.000
#> GSM215101 3 0.4543 0.797 0.324 0.000 0.676 0.000
#> GSM215102 1 0.2760 0.725 0.872 0.000 0.128 0.000
#> GSM215103 3 0.4804 0.809 0.276 0.000 0.708 0.016
#> GSM215104 1 0.2469 0.724 0.892 0.000 0.108 0.000
#> GSM215105 1 0.1637 0.731 0.940 0.000 0.060 0.000
#> GSM215106 3 0.4585 0.799 0.332 0.000 0.668 0.000
#> GSM215107 3 0.4843 0.697 0.396 0.000 0.604 0.000
#> GSM215108 1 0.3448 0.697 0.828 0.000 0.168 0.004
#> GSM215109 3 0.6013 0.770 0.288 0.000 0.640 0.072
#> GSM215110 3 0.5021 0.696 0.240 0.000 0.724 0.036
#> GSM215111 1 0.2921 0.734 0.860 0.000 0.140 0.000
#> GSM215112 1 0.0921 0.697 0.972 0.000 0.028 0.000
#> GSM215113 1 0.0469 0.704 0.988 0.000 0.012 0.000
#> GSM215114 1 0.4643 0.328 0.656 0.000 0.344 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.3561 0.876 0.000 0.740 0.000 0.000 NA
#> GSM215052 2 0.4025 0.863 0.000 0.700 0.000 0.008 NA
#> GSM215053 2 0.3684 0.867 0.000 0.720 0.000 0.000 NA
#> GSM215054 2 0.3661 0.865 0.000 0.724 0.000 0.000 NA
#> GSM215055 2 0.1792 0.861 0.000 0.916 0.000 0.000 NA
#> GSM215056 2 0.3242 0.882 0.000 0.784 0.000 0.000 NA
#> GSM215057 2 0.3561 0.875 0.000 0.740 0.000 0.000 NA
#> GSM215058 2 0.3210 0.875 0.000 0.788 0.000 0.000 NA
#> GSM215059 2 0.1851 0.879 0.000 0.912 0.000 0.000 NA
#> GSM215060 2 0.0162 0.852 0.000 0.996 0.000 0.000 NA
#> GSM215061 2 0.1197 0.870 0.000 0.952 0.000 0.000 NA
#> GSM215062 2 0.3586 0.868 0.000 0.736 0.000 0.000 NA
#> GSM215063 2 0.3003 0.883 0.000 0.812 0.000 0.000 NA
#> GSM215064 2 0.3949 0.852 0.000 0.668 0.000 0.000 NA
#> GSM215065 2 0.0162 0.852 0.000 0.996 0.000 0.000 NA
#> GSM215066 2 0.3336 0.878 0.000 0.772 0.000 0.000 NA
#> GSM215067 2 0.2813 0.879 0.000 0.832 0.000 0.000 NA
#> GSM215068 2 0.1043 0.864 0.000 0.960 0.000 0.000 NA
#> GSM215069 2 0.0162 0.852 0.000 0.996 0.000 0.000 NA
#> GSM215070 2 0.3642 0.879 0.000 0.760 0.000 0.008 NA
#> GSM215071 2 0.1484 0.855 0.000 0.944 0.000 0.008 NA
#> GSM215072 2 0.4101 0.851 0.000 0.664 0.000 0.004 NA
#> GSM215073 2 0.1197 0.867 0.000 0.952 0.000 0.000 NA
#> GSM215074 2 0.3752 0.863 0.000 0.708 0.000 0.000 NA
#> GSM215075 2 0.3508 0.874 0.000 0.748 0.000 0.000 NA
#> GSM215076 2 0.3171 0.863 0.000 0.816 0.000 0.008 NA
#> GSM215077 2 0.1282 0.872 0.000 0.952 0.000 0.004 NA
#> GSM215078 2 0.2471 0.887 0.000 0.864 0.000 0.000 NA
#> GSM215079 2 0.4126 0.833 0.000 0.620 0.000 0.000 NA
#> GSM215080 2 0.1341 0.871 0.000 0.944 0.000 0.000 NA
#> GSM215081 2 0.4114 0.837 0.000 0.624 0.000 0.000 NA
#> GSM215082 2 0.4380 0.832 0.000 0.616 0.000 0.008 NA
#> GSM215083 3 0.4726 0.565 0.400 0.000 0.580 0.020 NA
#> GSM215084 1 0.3366 0.627 0.784 0.000 0.212 0.004 NA
#> GSM215085 4 0.3835 0.000 0.244 0.000 0.012 0.744 NA
#> GSM215086 3 0.6815 0.367 0.152 0.000 0.520 0.032 NA
#> GSM215087 1 0.2723 0.717 0.864 0.000 0.124 0.012 NA
#> GSM215088 3 0.6068 0.442 0.368 0.000 0.540 0.028 NA
#> GSM215089 3 0.3636 0.736 0.272 0.000 0.728 0.000 NA
#> GSM215090 1 0.5370 0.189 0.588 0.000 0.356 0.048 NA
#> GSM215091 3 0.3274 0.730 0.220 0.000 0.780 0.000 NA
#> GSM215092 1 0.4275 0.492 0.696 0.000 0.284 0.020 NA
#> GSM215093 3 0.3835 0.739 0.244 0.000 0.744 0.012 NA
#> GSM215094 1 0.0609 0.732 0.980 0.000 0.020 0.000 NA
#> GSM215095 1 0.3661 0.468 0.724 0.000 0.276 0.000 NA
#> GSM215096 1 0.3816 0.461 0.696 0.000 0.304 0.000 NA
#> GSM215097 3 0.4135 0.681 0.340 0.000 0.656 0.004 NA
#> GSM215098 3 0.4927 0.702 0.296 0.000 0.652 0.052 NA
#> GSM215099 1 0.1851 0.741 0.912 0.000 0.088 0.000 NA
#> GSM215100 3 0.4520 0.733 0.284 0.000 0.684 0.032 NA
#> GSM215101 3 0.3774 0.723 0.296 0.000 0.704 0.000 NA
#> GSM215102 1 0.3213 0.708 0.836 0.000 0.144 0.016 NA
#> GSM215103 3 0.5032 0.727 0.248 0.000 0.688 0.052 NA
#> GSM215104 1 0.2723 0.722 0.864 0.000 0.124 0.012 NA
#> GSM215105 1 0.1410 0.735 0.940 0.000 0.060 0.000 NA
#> GSM215106 3 0.3837 0.712 0.308 0.000 0.692 0.000 NA
#> GSM215107 3 0.4126 0.609 0.380 0.000 0.620 0.000 NA
#> GSM215108 1 0.4393 0.649 0.756 0.000 0.168 0.076 NA
#> GSM215109 3 0.7348 0.448 0.180 0.000 0.540 0.104 NA
#> GSM215110 3 0.4965 0.538 0.152 0.000 0.748 0.064 NA
#> GSM215111 1 0.2561 0.727 0.856 0.000 0.144 0.000 NA
#> GSM215112 1 0.1549 0.724 0.944 0.000 0.016 0.040 NA
#> GSM215113 1 0.0404 0.725 0.988 0.000 0.012 0.000 NA
#> GSM215114 1 0.5142 0.268 0.600 0.000 0.348 0.052 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 2 0.3489 0.8594 0.000 0.708 0.000 0.004 0.288 0.000
#> GSM215052 2 0.4106 0.8440 0.000 0.664 0.000 0.020 0.312 0.004
#> GSM215053 2 0.3565 0.8502 0.000 0.692 0.000 0.004 0.304 0.000
#> GSM215054 2 0.3428 0.8476 0.000 0.696 0.000 0.000 0.304 0.000
#> GSM215055 2 0.1663 0.8418 0.000 0.912 0.000 0.000 0.088 0.000
#> GSM215056 2 0.3050 0.8657 0.000 0.764 0.000 0.000 0.236 0.000
#> GSM215057 2 0.3528 0.8552 0.000 0.700 0.000 0.004 0.296 0.000
#> GSM215058 2 0.3290 0.8562 0.000 0.744 0.000 0.004 0.252 0.000
#> GSM215059 2 0.1863 0.8647 0.000 0.896 0.000 0.000 0.104 0.000
#> GSM215060 2 0.0000 0.8324 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215061 2 0.1141 0.8508 0.000 0.948 0.000 0.000 0.052 0.000
#> GSM215062 2 0.3309 0.8495 0.000 0.720 0.000 0.000 0.280 0.000
#> GSM215063 2 0.2838 0.8675 0.000 0.808 0.000 0.004 0.188 0.000
#> GSM215064 2 0.3695 0.8287 0.000 0.624 0.000 0.000 0.376 0.000
#> GSM215065 2 0.0000 0.8324 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215066 2 0.3198 0.8597 0.000 0.740 0.000 0.000 0.260 0.000
#> GSM215067 2 0.2703 0.8609 0.000 0.824 0.000 0.004 0.172 0.000
#> GSM215068 2 0.0865 0.8444 0.000 0.964 0.000 0.000 0.036 0.000
#> GSM215069 2 0.0000 0.8324 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215070 2 0.3721 0.8603 0.000 0.728 0.000 0.016 0.252 0.004
#> GSM215071 2 0.1672 0.8340 0.000 0.932 0.000 0.016 0.048 0.004
#> GSM215072 2 0.3996 0.8304 0.000 0.636 0.000 0.008 0.352 0.004
#> GSM215073 2 0.1082 0.8471 0.000 0.956 0.000 0.004 0.040 0.000
#> GSM215074 2 0.3619 0.8458 0.000 0.680 0.000 0.004 0.316 0.000
#> GSM215075 2 0.3309 0.8559 0.000 0.720 0.000 0.000 0.280 0.000
#> GSM215076 2 0.3277 0.8399 0.000 0.792 0.000 0.016 0.188 0.004
#> GSM215077 2 0.1285 0.8551 0.000 0.944 0.000 0.000 0.052 0.004
#> GSM215078 2 0.2491 0.8723 0.000 0.836 0.000 0.000 0.164 0.000
#> GSM215079 2 0.3915 0.8134 0.000 0.584 0.000 0.004 0.412 0.000
#> GSM215080 2 0.1444 0.8576 0.000 0.928 0.000 0.000 0.072 0.000
#> GSM215081 2 0.3797 0.8128 0.000 0.580 0.000 0.000 0.420 0.000
#> GSM215082 2 0.4242 0.8071 0.000 0.572 0.000 0.012 0.412 0.004
#> GSM215083 3 0.3189 0.5331 0.184 0.000 0.796 0.020 0.000 0.000
#> GSM215084 1 0.3915 0.6171 0.584 0.000 0.412 0.000 0.000 0.004
#> GSM215085 4 0.2513 0.0000 0.140 0.000 0.008 0.852 0.000 0.000
#> GSM215086 5 0.7035 0.0000 0.096 0.000 0.396 0.028 0.400 0.080
#> GSM215087 1 0.4019 0.7293 0.652 0.000 0.332 0.012 0.000 0.004
#> GSM215088 3 0.5803 0.2686 0.208 0.000 0.624 0.016 0.024 0.128
#> GSM215089 3 0.1267 0.6069 0.060 0.000 0.940 0.000 0.000 0.000
#> GSM215090 3 0.5527 -0.0941 0.380 0.000 0.536 0.048 0.024 0.012
#> GSM215091 3 0.0146 0.5822 0.004 0.000 0.996 0.000 0.000 0.000
#> GSM215092 1 0.4492 0.4402 0.496 0.000 0.480 0.008 0.000 0.016
#> GSM215093 3 0.1268 0.6042 0.036 0.000 0.952 0.008 0.000 0.004
#> GSM215094 1 0.2941 0.7647 0.780 0.000 0.220 0.000 0.000 0.000
#> GSM215095 1 0.3857 0.4617 0.532 0.000 0.468 0.000 0.000 0.000
#> GSM215096 3 0.3862 -0.3913 0.476 0.000 0.524 0.000 0.000 0.000
#> GSM215097 3 0.2278 0.6055 0.128 0.000 0.868 0.004 0.000 0.000
#> GSM215098 3 0.3050 0.5950 0.092 0.000 0.852 0.044 0.000 0.012
#> GSM215099 1 0.3464 0.7560 0.688 0.000 0.312 0.000 0.000 0.000
#> GSM215100 3 0.2331 0.5929 0.080 0.000 0.888 0.032 0.000 0.000
#> GSM215101 3 0.1765 0.5806 0.096 0.000 0.904 0.000 0.000 0.000
#> GSM215102 1 0.4139 0.6990 0.644 0.000 0.336 0.008 0.000 0.012
#> GSM215103 3 0.2832 0.5894 0.048 0.000 0.884 0.032 0.012 0.024
#> GSM215104 1 0.3861 0.7309 0.672 0.000 0.316 0.008 0.000 0.004
#> GSM215105 1 0.3198 0.7659 0.740 0.000 0.260 0.000 0.000 0.000
#> GSM215106 3 0.1663 0.6076 0.088 0.000 0.912 0.000 0.000 0.000
#> GSM215107 3 0.2527 0.5366 0.168 0.000 0.832 0.000 0.000 0.000
#> GSM215108 1 0.6239 0.5611 0.508 0.000 0.340 0.068 0.004 0.080
#> GSM215109 3 0.7335 -0.3729 0.104 0.000 0.424 0.040 0.092 0.340
#> GSM215110 3 0.4919 -0.2399 0.068 0.000 0.544 0.000 0.000 0.388
#> GSM215111 1 0.3647 0.7302 0.640 0.000 0.360 0.000 0.000 0.000
#> GSM215112 1 0.3877 0.7540 0.748 0.000 0.208 0.040 0.000 0.004
#> GSM215113 1 0.2883 0.7591 0.788 0.000 0.212 0.000 0.000 0.000
#> GSM215114 3 0.5045 -0.2137 0.404 0.000 0.536 0.044 0.000 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> CV:pam 64 9.19e-15 1.000 2
#> CV:pam 57 4.19e-13 0.998 3
#> CV:pam 58 2.54e-13 0.998 4
#> CV:pam 55 1.14e-12 0.998 5
#> CV:pam 54 1.88e-12 0.997 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 51941 rows and 64 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.892 0.871 0.929 0.1747 0.905 0.806
#> 4 4 0.688 0.719 0.828 0.1436 0.907 0.769
#> 5 5 0.638 0.560 0.757 0.0979 0.871 0.624
#> 6 6 0.714 0.758 0.848 0.0482 0.950 0.802
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.0237 0.9838 0.000 0.996 0.004
#> GSM215052 2 0.1964 0.9623 0.000 0.944 0.056
#> GSM215053 2 0.0237 0.9838 0.000 0.996 0.004
#> GSM215054 2 0.0237 0.9838 0.000 0.996 0.004
#> GSM215055 2 0.0000 0.9844 0.000 1.000 0.000
#> GSM215056 2 0.0237 0.9838 0.000 0.996 0.004
#> GSM215057 2 0.0237 0.9842 0.000 0.996 0.004
#> GSM215058 2 0.0424 0.9828 0.000 0.992 0.008
#> GSM215059 2 0.0237 0.9842 0.000 0.996 0.004
#> GSM215060 2 0.0000 0.9844 0.000 1.000 0.000
#> GSM215061 2 0.0000 0.9844 0.000 1.000 0.000
#> GSM215062 2 0.2066 0.9617 0.000 0.940 0.060
#> GSM215063 2 0.0237 0.9838 0.000 0.996 0.004
#> GSM215064 2 0.1860 0.9664 0.000 0.948 0.052
#> GSM215065 2 0.0237 0.9842 0.000 0.996 0.004
#> GSM215066 2 0.0237 0.9842 0.000 0.996 0.004
#> GSM215067 2 0.0237 0.9838 0.000 0.996 0.004
#> GSM215068 2 0.0237 0.9842 0.000 0.996 0.004
#> GSM215069 2 0.0237 0.9842 0.000 0.996 0.004
#> GSM215070 2 0.1964 0.9623 0.000 0.944 0.056
#> GSM215071 2 0.1753 0.9662 0.000 0.952 0.048
#> GSM215072 2 0.1964 0.9623 0.000 0.944 0.056
#> GSM215073 2 0.0000 0.9844 0.000 1.000 0.000
#> GSM215074 2 0.0237 0.9842 0.000 0.996 0.004
#> GSM215075 2 0.0000 0.9844 0.000 1.000 0.000
#> GSM215076 2 0.1964 0.9623 0.000 0.944 0.056
#> GSM215077 2 0.1753 0.9662 0.000 0.952 0.048
#> GSM215078 2 0.0000 0.9844 0.000 1.000 0.000
#> GSM215079 2 0.0237 0.9842 0.000 0.996 0.004
#> GSM215080 2 0.0000 0.9844 0.000 1.000 0.000
#> GSM215081 2 0.0424 0.9838 0.000 0.992 0.008
#> GSM215082 2 0.1860 0.9643 0.000 0.948 0.052
#> GSM215083 1 0.3816 0.7530 0.852 0.000 0.148
#> GSM215084 1 0.4291 0.7274 0.820 0.000 0.180
#> GSM215085 3 0.6235 0.5656 0.436 0.000 0.564
#> GSM215086 3 0.4346 0.7280 0.184 0.000 0.816
#> GSM215087 1 0.0000 0.9046 1.000 0.000 0.000
#> GSM215088 3 0.4887 0.7265 0.228 0.000 0.772
#> GSM215089 1 0.0237 0.9057 0.996 0.000 0.004
#> GSM215090 1 0.1753 0.8785 0.952 0.000 0.048
#> GSM215091 1 0.0000 0.9046 1.000 0.000 0.000
#> GSM215092 1 0.0592 0.9048 0.988 0.000 0.012
#> GSM215093 3 0.4291 0.7266 0.180 0.000 0.820
#> GSM215094 1 0.2066 0.8697 0.940 0.000 0.060
#> GSM215095 1 0.0424 0.9052 0.992 0.000 0.008
#> GSM215096 1 0.0592 0.9052 0.988 0.000 0.012
#> GSM215097 1 0.0237 0.9056 0.996 0.000 0.004
#> GSM215098 1 0.0000 0.9046 1.000 0.000 0.000
#> GSM215099 1 0.1411 0.8880 0.964 0.000 0.036
#> GSM215100 1 0.1529 0.8855 0.960 0.000 0.040
#> GSM215101 1 0.1860 0.8705 0.948 0.000 0.052
#> GSM215102 1 0.6225 -0.0615 0.568 0.000 0.432
#> GSM215103 3 0.6140 0.4178 0.404 0.000 0.596
#> GSM215104 1 0.4842 0.6573 0.776 0.000 0.224
#> GSM215105 1 0.0000 0.9046 1.000 0.000 0.000
#> GSM215106 1 0.0424 0.9051 0.992 0.000 0.008
#> GSM215107 1 0.0237 0.9053 0.996 0.000 0.004
#> GSM215108 3 0.6267 0.4022 0.452 0.000 0.548
#> GSM215109 3 0.2261 0.6690 0.068 0.000 0.932
#> GSM215110 3 0.6252 0.5457 0.444 0.000 0.556
#> GSM215111 1 0.0000 0.9046 1.000 0.000 0.000
#> GSM215112 1 0.0424 0.9052 0.992 0.000 0.008
#> GSM215113 1 0.0237 0.9055 0.996 0.000 0.004
#> GSM215114 1 0.5465 0.5250 0.712 0.000 0.288
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 4 0.4331 0.91669 0.000 0.288 0.000 0.712
#> GSM215052 2 0.1388 0.54096 0.000 0.960 0.012 0.028
#> GSM215053 4 0.4008 0.95395 0.000 0.244 0.000 0.756
#> GSM215054 4 0.3975 0.94828 0.000 0.240 0.000 0.760
#> GSM215055 2 0.4866 0.44766 0.000 0.596 0.000 0.404
#> GSM215056 4 0.4193 0.95242 0.000 0.268 0.000 0.732
#> GSM215057 2 0.4277 0.73112 0.000 0.720 0.000 0.280
#> GSM215058 2 0.4941 -0.00422 0.000 0.564 0.000 0.436
#> GSM215059 2 0.4356 0.73351 0.000 0.708 0.000 0.292
#> GSM215060 2 0.4277 0.73112 0.000 0.720 0.000 0.280
#> GSM215061 2 0.4277 0.73112 0.000 0.720 0.000 0.280
#> GSM215062 2 0.2412 0.60908 0.000 0.908 0.008 0.084
#> GSM215063 4 0.4040 0.95160 0.000 0.248 0.000 0.752
#> GSM215064 2 0.2530 0.63036 0.000 0.888 0.000 0.112
#> GSM215065 2 0.4356 0.73351 0.000 0.708 0.000 0.292
#> GSM215066 2 0.4356 0.73351 0.000 0.708 0.000 0.292
#> GSM215067 4 0.4222 0.94812 0.000 0.272 0.000 0.728
#> GSM215068 2 0.4356 0.73351 0.000 0.708 0.000 0.292
#> GSM215069 2 0.4356 0.73351 0.000 0.708 0.000 0.292
#> GSM215070 2 0.0937 0.55734 0.000 0.976 0.012 0.012
#> GSM215071 2 0.1722 0.59621 0.000 0.944 0.008 0.048
#> GSM215072 2 0.1059 0.55296 0.000 0.972 0.012 0.016
#> GSM215073 2 0.4331 0.73292 0.000 0.712 0.000 0.288
#> GSM215074 2 0.4277 0.73112 0.000 0.720 0.000 0.280
#> GSM215075 2 0.4277 0.72837 0.000 0.720 0.000 0.280
#> GSM215076 2 0.4635 -0.04650 0.000 0.720 0.012 0.268
#> GSM215077 2 0.1722 0.59675 0.000 0.944 0.008 0.048
#> GSM215078 2 0.4304 0.72910 0.000 0.716 0.000 0.284
#> GSM215079 2 0.4356 0.73351 0.000 0.708 0.000 0.292
#> GSM215080 2 0.4304 0.73445 0.000 0.716 0.000 0.284
#> GSM215081 2 0.4277 0.73256 0.000 0.720 0.000 0.280
#> GSM215082 2 0.0937 0.56081 0.000 0.976 0.012 0.012
#> GSM215083 1 0.4422 0.52919 0.736 0.000 0.256 0.008
#> GSM215084 1 0.5134 0.49405 0.680 0.016 0.300 0.004
#> GSM215085 3 0.7068 0.67863 0.296 0.000 0.548 0.156
#> GSM215086 3 0.6756 0.73804 0.188 0.000 0.612 0.200
#> GSM215087 1 0.0000 0.89475 1.000 0.000 0.000 0.000
#> GSM215088 3 0.6964 0.72781 0.228 0.000 0.584 0.188
#> GSM215089 1 0.0000 0.89475 1.000 0.000 0.000 0.000
#> GSM215090 1 0.2011 0.83111 0.920 0.000 0.080 0.000
#> GSM215091 1 0.0000 0.89475 1.000 0.000 0.000 0.000
#> GSM215092 1 0.0188 0.89401 0.996 0.000 0.004 0.000
#> GSM215093 3 0.6194 0.74348 0.132 0.000 0.668 0.200
#> GSM215094 1 0.2466 0.81688 0.900 0.000 0.096 0.004
#> GSM215095 1 0.0469 0.89185 0.988 0.000 0.012 0.000
#> GSM215096 1 0.0592 0.88989 0.984 0.000 0.016 0.000
#> GSM215097 1 0.0000 0.89475 1.000 0.000 0.000 0.000
#> GSM215098 1 0.0000 0.89475 1.000 0.000 0.000 0.000
#> GSM215099 1 0.0817 0.88290 0.976 0.000 0.024 0.000
#> GSM215100 1 0.1557 0.85741 0.944 0.000 0.056 0.000
#> GSM215101 1 0.1211 0.87413 0.960 0.000 0.040 0.000
#> GSM215102 3 0.4700 0.64773 0.196 0.016 0.772 0.016
#> GSM215103 3 0.4569 0.60372 0.220 0.012 0.760 0.008
#> GSM215104 1 0.5805 -0.01022 0.500 0.016 0.476 0.008
#> GSM215105 1 0.0188 0.89395 0.996 0.000 0.004 0.000
#> GSM215106 1 0.0000 0.89475 1.000 0.000 0.000 0.000
#> GSM215107 1 0.0000 0.89475 1.000 0.000 0.000 0.000
#> GSM215108 3 0.4008 0.69522 0.136 0.012 0.832 0.020
#> GSM215109 3 0.1674 0.68616 0.004 0.012 0.952 0.032
#> GSM215110 3 0.6627 0.68027 0.300 0.000 0.588 0.112
#> GSM215111 1 0.0000 0.89475 1.000 0.000 0.000 0.000
#> GSM215112 1 0.0188 0.89410 0.996 0.000 0.004 0.000
#> GSM215113 1 0.0000 0.89475 1.000 0.000 0.000 0.000
#> GSM215114 1 0.5500 0.33199 0.600 0.016 0.380 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.6816 -0.0509 0.000 0.360 0.000 0.316 0.324
#> GSM215052 4 0.3551 0.7832 0.000 0.220 0.000 0.772 0.008
#> GSM215053 5 0.6722 0.0145 0.000 0.316 0.000 0.268 0.416
#> GSM215054 5 0.6710 0.0382 0.000 0.304 0.000 0.272 0.424
#> GSM215055 2 0.5766 0.4639 0.000 0.616 0.000 0.164 0.220
#> GSM215056 2 0.6764 -0.1058 0.000 0.368 0.000 0.268 0.364
#> GSM215057 2 0.2570 0.6814 0.000 0.888 0.000 0.084 0.028
#> GSM215058 4 0.5815 -0.0331 0.000 0.396 0.000 0.508 0.096
#> GSM215059 2 0.0290 0.6821 0.000 0.992 0.000 0.000 0.008
#> GSM215060 2 0.2520 0.6785 0.000 0.896 0.000 0.048 0.056
#> GSM215061 2 0.1997 0.6881 0.000 0.924 0.000 0.036 0.040
#> GSM215062 4 0.4640 0.6225 0.000 0.400 0.000 0.584 0.016
#> GSM215063 5 0.6678 0.0299 0.000 0.312 0.000 0.256 0.432
#> GSM215064 2 0.4718 -0.3766 0.000 0.540 0.000 0.444 0.016
#> GSM215065 2 0.0912 0.6725 0.000 0.972 0.000 0.012 0.016
#> GSM215066 2 0.2006 0.6639 0.000 0.916 0.000 0.072 0.012
#> GSM215067 2 0.6738 -0.0914 0.000 0.376 0.000 0.256 0.368
#> GSM215068 2 0.1774 0.6694 0.000 0.932 0.000 0.052 0.016
#> GSM215069 2 0.0912 0.6839 0.000 0.972 0.000 0.012 0.016
#> GSM215070 4 0.3395 0.7869 0.000 0.236 0.000 0.764 0.000
#> GSM215071 4 0.3661 0.7674 0.000 0.276 0.000 0.724 0.000
#> GSM215072 4 0.3210 0.7832 0.000 0.212 0.000 0.788 0.000
#> GSM215073 2 0.1741 0.6890 0.000 0.936 0.000 0.024 0.040
#> GSM215074 2 0.2740 0.6787 0.000 0.876 0.000 0.096 0.028
#> GSM215075 2 0.3863 0.6395 0.000 0.796 0.000 0.152 0.052
#> GSM215076 4 0.3297 0.6225 0.000 0.084 0.000 0.848 0.068
#> GSM215077 4 0.3774 0.7476 0.000 0.296 0.000 0.704 0.000
#> GSM215078 2 0.4495 0.5320 0.000 0.712 0.000 0.244 0.044
#> GSM215079 2 0.2727 0.6253 0.000 0.868 0.000 0.116 0.016
#> GSM215080 2 0.2864 0.6422 0.000 0.864 0.000 0.112 0.024
#> GSM215081 2 0.3586 0.4934 0.000 0.792 0.000 0.188 0.020
#> GSM215082 4 0.3969 0.7506 0.000 0.304 0.000 0.692 0.004
#> GSM215083 1 0.4088 0.4960 0.688 0.000 0.304 0.000 0.008
#> GSM215084 1 0.6539 0.2594 0.544 0.000 0.228 0.012 0.216
#> GSM215085 3 0.3789 0.6883 0.212 0.000 0.768 0.000 0.020
#> GSM215086 3 0.2536 0.7244 0.128 0.000 0.868 0.000 0.004
#> GSM215087 1 0.0579 0.8910 0.984 0.000 0.008 0.000 0.008
#> GSM215088 3 0.2833 0.7255 0.140 0.000 0.852 0.004 0.004
#> GSM215089 1 0.0451 0.8913 0.988 0.000 0.004 0.000 0.008
#> GSM215090 1 0.2462 0.8105 0.880 0.000 0.112 0.000 0.008
#> GSM215091 1 0.0798 0.8902 0.976 0.000 0.016 0.000 0.008
#> GSM215092 1 0.0912 0.8896 0.972 0.000 0.016 0.000 0.012
#> GSM215093 3 0.2678 0.7092 0.100 0.000 0.880 0.004 0.016
#> GSM215094 1 0.3471 0.7623 0.836 0.000 0.072 0.000 0.092
#> GSM215095 1 0.0992 0.8899 0.968 0.000 0.008 0.000 0.024
#> GSM215096 1 0.1117 0.8881 0.964 0.000 0.016 0.000 0.020
#> GSM215097 1 0.0324 0.8909 0.992 0.000 0.004 0.000 0.004
#> GSM215098 1 0.0566 0.8913 0.984 0.000 0.004 0.000 0.012
#> GSM215099 1 0.1331 0.8745 0.952 0.000 0.040 0.000 0.008
#> GSM215100 1 0.2358 0.8216 0.888 0.000 0.104 0.000 0.008
#> GSM215101 1 0.1484 0.8753 0.944 0.000 0.048 0.000 0.008
#> GSM215102 5 0.5710 -0.4526 0.060 0.000 0.464 0.008 0.468
#> GSM215103 3 0.6164 0.2807 0.104 0.000 0.480 0.008 0.408
#> GSM215104 5 0.7128 -0.3284 0.344 0.000 0.292 0.012 0.352
#> GSM215105 1 0.0451 0.8921 0.988 0.000 0.004 0.000 0.008
#> GSM215106 1 0.0693 0.8916 0.980 0.000 0.012 0.000 0.008
#> GSM215107 1 0.0451 0.8910 0.988 0.000 0.008 0.000 0.004
#> GSM215108 5 0.5121 -0.4495 0.028 0.000 0.468 0.004 0.500
#> GSM215109 3 0.4415 0.3651 0.000 0.000 0.604 0.008 0.388
#> GSM215110 3 0.5024 0.6694 0.212 0.000 0.692 0.000 0.096
#> GSM215111 1 0.0162 0.8910 0.996 0.000 0.004 0.000 0.000
#> GSM215112 1 0.0703 0.8905 0.976 0.000 0.000 0.000 0.024
#> GSM215113 1 0.0404 0.8912 0.988 0.000 0.000 0.000 0.012
#> GSM215114 1 0.6792 0.0671 0.480 0.000 0.300 0.012 0.208
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 4 0.2685 0.868 0.000 0.072 0.000 0.868 0.060 0.000
#> GSM215052 5 0.2383 0.815 0.000 0.096 0.000 0.024 0.880 0.000
#> GSM215053 4 0.1398 0.878 0.000 0.052 0.000 0.940 0.008 0.000
#> GSM215054 4 0.1398 0.877 0.000 0.052 0.000 0.940 0.008 0.000
#> GSM215055 4 0.4361 0.558 0.000 0.308 0.000 0.648 0.044 0.000
#> GSM215056 4 0.2302 0.879 0.000 0.120 0.000 0.872 0.008 0.000
#> GSM215057 2 0.1575 0.852 0.000 0.936 0.000 0.032 0.032 0.000
#> GSM215058 5 0.5958 0.120 0.000 0.248 0.000 0.304 0.448 0.000
#> GSM215059 2 0.0653 0.846 0.000 0.980 0.004 0.004 0.012 0.000
#> GSM215060 2 0.2851 0.807 0.000 0.844 0.004 0.132 0.020 0.000
#> GSM215061 2 0.2622 0.827 0.000 0.868 0.004 0.104 0.024 0.000
#> GSM215062 5 0.4064 0.604 0.000 0.336 0.000 0.020 0.644 0.000
#> GSM215063 4 0.2307 0.874 0.000 0.064 0.000 0.900 0.024 0.012
#> GSM215064 2 0.4246 0.102 0.000 0.580 0.000 0.020 0.400 0.000
#> GSM215065 2 0.0767 0.846 0.000 0.976 0.004 0.008 0.012 0.000
#> GSM215066 2 0.1340 0.848 0.000 0.948 0.004 0.008 0.040 0.000
#> GSM215067 4 0.3375 0.849 0.000 0.156 0.000 0.808 0.024 0.012
#> GSM215068 2 0.0458 0.849 0.000 0.984 0.000 0.000 0.016 0.000
#> GSM215069 2 0.0767 0.848 0.000 0.976 0.004 0.012 0.008 0.000
#> GSM215070 5 0.2320 0.828 0.000 0.132 0.000 0.004 0.864 0.000
#> GSM215071 5 0.3104 0.795 0.000 0.204 0.000 0.004 0.788 0.004
#> GSM215072 5 0.2243 0.827 0.000 0.112 0.000 0.004 0.880 0.004
#> GSM215073 2 0.2488 0.822 0.000 0.864 0.004 0.124 0.008 0.000
#> GSM215074 2 0.2190 0.844 0.000 0.900 0.000 0.060 0.040 0.000
#> GSM215075 2 0.4199 0.730 0.000 0.748 0.000 0.100 0.148 0.004
#> GSM215076 5 0.1918 0.708 0.000 0.008 0.000 0.088 0.904 0.000
#> GSM215077 5 0.2913 0.809 0.000 0.180 0.000 0.004 0.812 0.004
#> GSM215078 2 0.5479 0.409 0.000 0.556 0.000 0.136 0.304 0.004
#> GSM215079 2 0.1349 0.840 0.000 0.940 0.000 0.004 0.056 0.000
#> GSM215080 2 0.2030 0.841 0.000 0.908 0.000 0.028 0.064 0.000
#> GSM215081 2 0.2404 0.785 0.000 0.872 0.000 0.016 0.112 0.000
#> GSM215082 5 0.2805 0.812 0.000 0.184 0.000 0.004 0.812 0.000
#> GSM215083 1 0.3933 0.680 0.740 0.000 0.220 0.000 0.008 0.032
#> GSM215084 1 0.5313 0.179 0.536 0.000 0.048 0.008 0.016 0.392
#> GSM215085 3 0.2680 0.804 0.108 0.000 0.860 0.000 0.000 0.032
#> GSM215086 3 0.0972 0.847 0.028 0.000 0.964 0.000 0.000 0.008
#> GSM215087 1 0.1138 0.883 0.960 0.000 0.012 0.000 0.004 0.024
#> GSM215088 3 0.1082 0.851 0.040 0.000 0.956 0.000 0.000 0.004
#> GSM215089 1 0.0622 0.884 0.980 0.000 0.012 0.000 0.000 0.008
#> GSM215090 1 0.3142 0.836 0.856 0.000 0.032 0.004 0.024 0.084
#> GSM215091 1 0.1381 0.880 0.952 0.000 0.020 0.004 0.004 0.020
#> GSM215092 1 0.2017 0.874 0.920 0.000 0.004 0.008 0.020 0.048
#> GSM215093 3 0.1749 0.824 0.024 0.000 0.932 0.008 0.000 0.036
#> GSM215094 1 0.3116 0.782 0.836 0.000 0.016 0.012 0.004 0.132
#> GSM215095 1 0.1729 0.875 0.936 0.000 0.012 0.012 0.004 0.036
#> GSM215096 1 0.1750 0.873 0.932 0.000 0.016 0.012 0.000 0.040
#> GSM215097 1 0.1262 0.885 0.956 0.000 0.020 0.000 0.008 0.016
#> GSM215098 1 0.1026 0.884 0.968 0.000 0.008 0.008 0.004 0.012
#> GSM215099 1 0.2538 0.861 0.892 0.000 0.012 0.008 0.020 0.068
#> GSM215100 1 0.3067 0.842 0.860 0.000 0.028 0.004 0.024 0.084
#> GSM215101 1 0.1760 0.877 0.936 0.000 0.028 0.012 0.004 0.020
#> GSM215102 6 0.2848 0.689 0.036 0.000 0.104 0.000 0.004 0.856
#> GSM215103 6 0.4582 0.636 0.160 0.000 0.116 0.000 0.008 0.716
#> GSM215104 6 0.4972 0.337 0.372 0.000 0.056 0.000 0.008 0.564
#> GSM215105 1 0.1321 0.882 0.952 0.000 0.024 0.000 0.004 0.020
#> GSM215106 1 0.1296 0.884 0.952 0.000 0.032 0.004 0.000 0.012
#> GSM215107 1 0.2050 0.874 0.920 0.000 0.032 0.004 0.008 0.036
#> GSM215108 6 0.2404 0.675 0.016 0.000 0.112 0.000 0.000 0.872
#> GSM215109 6 0.3221 0.569 0.000 0.000 0.220 0.004 0.004 0.772
#> GSM215110 3 0.5025 0.562 0.136 0.000 0.632 0.000 0.000 0.232
#> GSM215111 1 0.1401 0.881 0.948 0.000 0.028 0.000 0.004 0.020
#> GSM215112 1 0.1843 0.873 0.932 0.000 0.016 0.016 0.004 0.032
#> GSM215113 1 0.1590 0.881 0.944 0.000 0.008 0.008 0.012 0.028
#> GSM215114 1 0.4648 0.142 0.548 0.000 0.044 0.000 0.000 0.408
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> CV:mclust 64 9.19e-15 1.000 2
#> CV:mclust 61 5.68e-14 0.999 3
#> CV:mclust 58 1.57e-12 0.977 4
#> CV:mclust 46 5.67e-10 0.564 5
#> CV:mclust 58 3.15e-11 0.868 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 51941 rows and 64 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.725 0.791 0.886 0.2041 0.927 0.852
#> 4 4 0.562 0.633 0.791 0.1189 0.932 0.840
#> 5 5 0.520 0.575 0.723 0.0853 0.954 0.876
#> 6 6 0.552 0.426 0.670 0.0482 0.970 0.909
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.6095 0.461 0.000 0.608 0.392
#> GSM215052 2 0.3619 0.849 0.000 0.864 0.136
#> GSM215053 2 0.4750 0.760 0.000 0.784 0.216
#> GSM215054 2 0.6154 0.445 0.000 0.592 0.408
#> GSM215055 2 0.1860 0.899 0.000 0.948 0.052
#> GSM215056 2 0.4062 0.816 0.000 0.836 0.164
#> GSM215057 2 0.0747 0.911 0.000 0.984 0.016
#> GSM215058 2 0.2711 0.878 0.000 0.912 0.088
#> GSM215059 2 0.0424 0.911 0.000 0.992 0.008
#> GSM215060 2 0.0892 0.909 0.000 0.980 0.020
#> GSM215061 2 0.0424 0.911 0.000 0.992 0.008
#> GSM215062 2 0.1860 0.902 0.000 0.948 0.052
#> GSM215063 3 0.6309 -0.290 0.000 0.496 0.504
#> GSM215064 2 0.2356 0.891 0.000 0.928 0.072
#> GSM215065 2 0.1964 0.897 0.000 0.944 0.056
#> GSM215066 2 0.1411 0.905 0.000 0.964 0.036
#> GSM215067 2 0.5138 0.710 0.000 0.748 0.252
#> GSM215068 2 0.0747 0.910 0.000 0.984 0.016
#> GSM215069 2 0.1411 0.905 0.000 0.964 0.036
#> GSM215070 2 0.3038 0.872 0.000 0.896 0.104
#> GSM215071 2 0.0592 0.911 0.000 0.988 0.012
#> GSM215072 2 0.1964 0.897 0.000 0.944 0.056
#> GSM215073 2 0.0747 0.910 0.000 0.984 0.016
#> GSM215074 2 0.0747 0.909 0.000 0.984 0.016
#> GSM215075 2 0.0424 0.911 0.000 0.992 0.008
#> GSM215076 2 0.5560 0.669 0.000 0.700 0.300
#> GSM215077 2 0.0424 0.911 0.000 0.992 0.008
#> GSM215078 2 0.1031 0.910 0.000 0.976 0.024
#> GSM215079 2 0.1289 0.907 0.000 0.968 0.032
#> GSM215080 2 0.1031 0.908 0.000 0.976 0.024
#> GSM215081 2 0.1964 0.897 0.000 0.944 0.056
#> GSM215082 2 0.0592 0.911 0.000 0.988 0.012
#> GSM215083 1 0.4702 0.745 0.788 0.000 0.212
#> GSM215084 1 0.1289 0.876 0.968 0.000 0.032
#> GSM215085 1 0.5859 0.483 0.656 0.000 0.344
#> GSM215086 3 0.5810 0.530 0.336 0.000 0.664
#> GSM215087 1 0.2261 0.856 0.932 0.000 0.068
#> GSM215088 3 0.5706 0.572 0.320 0.000 0.680
#> GSM215089 1 0.0892 0.877 0.980 0.000 0.020
#> GSM215090 1 0.2066 0.869 0.940 0.000 0.060
#> GSM215091 1 0.1411 0.875 0.964 0.000 0.036
#> GSM215092 1 0.2537 0.856 0.920 0.000 0.080
#> GSM215093 3 0.4351 0.651 0.168 0.004 0.828
#> GSM215094 1 0.1964 0.862 0.944 0.000 0.056
#> GSM215095 1 0.2711 0.828 0.912 0.000 0.088
#> GSM215096 1 0.1643 0.867 0.956 0.000 0.044
#> GSM215097 1 0.2625 0.856 0.916 0.000 0.084
#> GSM215098 1 0.1031 0.874 0.976 0.000 0.024
#> GSM215099 1 0.1643 0.871 0.956 0.000 0.044
#> GSM215100 1 0.1753 0.870 0.952 0.000 0.048
#> GSM215101 1 0.1411 0.876 0.964 0.000 0.036
#> GSM215102 1 0.6008 0.439 0.628 0.000 0.372
#> GSM215103 1 0.5835 0.535 0.660 0.000 0.340
#> GSM215104 1 0.2796 0.855 0.908 0.000 0.092
#> GSM215105 1 0.1411 0.878 0.964 0.000 0.036
#> GSM215106 1 0.1411 0.877 0.964 0.000 0.036
#> GSM215107 1 0.0747 0.873 0.984 0.000 0.016
#> GSM215108 1 0.4750 0.737 0.784 0.000 0.216
#> GSM215109 3 0.4842 0.646 0.224 0.000 0.776
#> GSM215110 1 0.6225 0.180 0.568 0.000 0.432
#> GSM215111 1 0.1753 0.874 0.952 0.000 0.048
#> GSM215112 1 0.2796 0.824 0.908 0.000 0.092
#> GSM215113 1 0.0747 0.874 0.984 0.000 0.016
#> GSM215114 1 0.2448 0.858 0.924 0.000 0.076
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 3 0.585 -0.1162 0.000 0.452 0.516 0.032
#> GSM215052 2 0.644 0.5769 0.000 0.648 0.168 0.184
#> GSM215053 2 0.524 0.4336 0.000 0.628 0.356 0.016
#> GSM215054 2 0.601 0.0458 0.000 0.488 0.472 0.040
#> GSM215055 2 0.215 0.8169 0.000 0.912 0.088 0.000
#> GSM215056 2 0.419 0.6824 0.000 0.752 0.244 0.004
#> GSM215057 2 0.102 0.8332 0.000 0.968 0.032 0.000
#> GSM215058 2 0.450 0.7446 0.000 0.764 0.212 0.024
#> GSM215059 2 0.140 0.8350 0.000 0.956 0.040 0.004
#> GSM215060 2 0.234 0.8199 0.000 0.900 0.100 0.000
#> GSM215061 2 0.149 0.8325 0.000 0.952 0.044 0.004
#> GSM215062 2 0.384 0.7957 0.000 0.836 0.128 0.036
#> GSM215063 3 0.597 0.3353 0.000 0.316 0.624 0.060
#> GSM215064 2 0.388 0.7968 0.000 0.840 0.112 0.048
#> GSM215065 2 0.256 0.8267 0.000 0.908 0.072 0.020
#> GSM215066 2 0.155 0.8347 0.000 0.952 0.040 0.008
#> GSM215067 2 0.540 0.4624 0.000 0.628 0.348 0.024
#> GSM215068 2 0.136 0.8354 0.000 0.960 0.032 0.008
#> GSM215069 2 0.149 0.8345 0.000 0.956 0.032 0.012
#> GSM215070 2 0.612 0.6241 0.000 0.680 0.156 0.164
#> GSM215071 2 0.252 0.8246 0.000 0.912 0.064 0.024
#> GSM215072 2 0.566 0.6824 0.000 0.720 0.156 0.124
#> GSM215073 2 0.181 0.8324 0.000 0.940 0.052 0.008
#> GSM215074 2 0.130 0.8329 0.000 0.956 0.044 0.000
#> GSM215075 2 0.131 0.8364 0.000 0.960 0.036 0.004
#> GSM215076 2 0.750 0.2777 0.000 0.500 0.252 0.248
#> GSM215077 2 0.297 0.8222 0.000 0.892 0.072 0.036
#> GSM215078 2 0.198 0.8331 0.000 0.936 0.048 0.016
#> GSM215079 2 0.194 0.8350 0.000 0.936 0.052 0.012
#> GSM215080 2 0.185 0.8342 0.000 0.940 0.048 0.012
#> GSM215081 2 0.233 0.8242 0.000 0.916 0.072 0.012
#> GSM215082 2 0.281 0.8184 0.000 0.896 0.080 0.024
#> GSM215083 1 0.667 0.2940 0.620 0.000 0.212 0.168
#> GSM215084 1 0.385 0.6574 0.800 0.000 0.008 0.192
#> GSM215085 1 0.784 -0.3542 0.396 0.000 0.336 0.268
#> GSM215086 3 0.696 -0.0230 0.148 0.000 0.564 0.288
#> GSM215087 1 0.234 0.7743 0.912 0.000 0.008 0.080
#> GSM215088 3 0.712 -0.0787 0.140 0.000 0.508 0.352
#> GSM215089 1 0.304 0.7878 0.880 0.000 0.020 0.100
#> GSM215090 1 0.456 0.7272 0.792 0.000 0.056 0.152
#> GSM215091 1 0.306 0.7907 0.888 0.000 0.040 0.072
#> GSM215092 1 0.458 0.7018 0.788 0.000 0.052 0.160
#> GSM215093 3 0.601 0.1128 0.052 0.000 0.588 0.360
#> GSM215094 1 0.233 0.7641 0.908 0.000 0.004 0.088
#> GSM215095 1 0.247 0.7604 0.908 0.000 0.012 0.080
#> GSM215096 1 0.189 0.7769 0.936 0.000 0.008 0.056
#> GSM215097 1 0.461 0.7094 0.788 0.000 0.056 0.156
#> GSM215098 1 0.234 0.7880 0.912 0.000 0.008 0.080
#> GSM215099 1 0.340 0.7746 0.868 0.000 0.040 0.092
#> GSM215100 1 0.441 0.7395 0.808 0.000 0.064 0.128
#> GSM215101 1 0.415 0.7514 0.824 0.000 0.056 0.120
#> GSM215102 4 0.570 0.6168 0.292 0.000 0.052 0.656
#> GSM215103 4 0.681 0.6068 0.344 0.000 0.112 0.544
#> GSM215104 1 0.472 0.3441 0.672 0.000 0.004 0.324
#> GSM215105 1 0.284 0.7890 0.896 0.000 0.028 0.076
#> GSM215106 1 0.297 0.7877 0.892 0.000 0.036 0.072
#> GSM215107 1 0.168 0.7894 0.948 0.000 0.012 0.040
#> GSM215108 4 0.582 0.4259 0.432 0.000 0.032 0.536
#> GSM215109 4 0.582 0.2032 0.084 0.000 0.232 0.684
#> GSM215110 4 0.748 0.4677 0.332 0.000 0.192 0.476
#> GSM215111 1 0.301 0.7847 0.888 0.000 0.032 0.080
#> GSM215112 1 0.280 0.7494 0.892 0.000 0.016 0.092
#> GSM215113 1 0.198 0.7931 0.928 0.000 0.004 0.068
#> GSM215114 1 0.414 0.6219 0.780 0.000 0.012 0.208
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 4 0.621 0.4817 0.000 0.272 0.076 0.604 0.048
#> GSM215052 2 0.728 0.4741 0.000 0.548 0.156 0.192 0.104
#> GSM215053 2 0.673 -0.1452 0.000 0.484 0.032 0.364 0.120
#> GSM215054 4 0.658 0.4315 0.000 0.288 0.028 0.548 0.136
#> GSM215055 2 0.381 0.6833 0.000 0.792 0.000 0.168 0.040
#> GSM215056 2 0.478 0.2727 0.000 0.584 0.004 0.396 0.016
#> GSM215057 2 0.236 0.7497 0.000 0.900 0.000 0.076 0.024
#> GSM215058 2 0.591 0.5492 0.000 0.600 0.028 0.304 0.068
#> GSM215059 2 0.301 0.7411 0.000 0.864 0.004 0.104 0.028
#> GSM215060 2 0.392 0.6565 0.000 0.784 0.004 0.180 0.032
#> GSM215061 2 0.185 0.7504 0.000 0.936 0.008 0.036 0.020
#> GSM215062 2 0.567 0.6509 0.000 0.688 0.032 0.168 0.112
#> GSM215063 4 0.448 0.4413 0.000 0.176 0.032 0.764 0.028
#> GSM215064 2 0.515 0.6822 0.000 0.728 0.020 0.144 0.108
#> GSM215065 2 0.195 0.7508 0.004 0.932 0.004 0.044 0.016
#> GSM215066 2 0.260 0.7488 0.000 0.896 0.004 0.060 0.040
#> GSM215067 4 0.528 0.3225 0.000 0.372 0.020 0.584 0.024
#> GSM215068 2 0.152 0.7560 0.000 0.944 0.000 0.044 0.012
#> GSM215069 2 0.171 0.7512 0.000 0.940 0.004 0.040 0.016
#> GSM215070 2 0.701 0.4944 0.000 0.576 0.188 0.148 0.088
#> GSM215071 2 0.424 0.7324 0.000 0.812 0.052 0.088 0.048
#> GSM215072 2 0.715 0.5047 0.000 0.572 0.160 0.144 0.124
#> GSM215073 2 0.220 0.7422 0.000 0.916 0.004 0.056 0.024
#> GSM215074 2 0.271 0.7296 0.000 0.860 0.000 0.132 0.008
#> GSM215075 2 0.301 0.7492 0.000 0.868 0.004 0.092 0.036
#> GSM215076 2 0.831 -0.0296 0.000 0.328 0.296 0.244 0.132
#> GSM215077 2 0.439 0.7255 0.000 0.804 0.048 0.080 0.068
#> GSM215078 2 0.323 0.7512 0.000 0.868 0.020 0.072 0.040
#> GSM215079 2 0.204 0.7589 0.000 0.920 0.000 0.056 0.024
#> GSM215080 2 0.296 0.7546 0.000 0.876 0.008 0.080 0.036
#> GSM215081 2 0.357 0.7299 0.000 0.836 0.004 0.092 0.068
#> GSM215082 2 0.500 0.6877 0.000 0.748 0.032 0.140 0.080
#> GSM215083 1 0.694 0.2763 0.560 0.000 0.064 0.140 0.236
#> GSM215084 1 0.525 0.4749 0.632 0.000 0.292 0.000 0.076
#> GSM215085 5 0.835 0.3511 0.268 0.000 0.136 0.272 0.324
#> GSM215086 5 0.700 0.3829 0.044 0.004 0.120 0.332 0.500
#> GSM215087 1 0.288 0.7594 0.868 0.000 0.032 0.000 0.100
#> GSM215088 4 0.757 -0.3486 0.056 0.000 0.240 0.436 0.268
#> GSM215089 1 0.501 0.7108 0.724 0.000 0.088 0.012 0.176
#> GSM215090 1 0.588 0.6024 0.644 0.000 0.140 0.016 0.200
#> GSM215091 1 0.311 0.7569 0.856 0.004 0.012 0.008 0.120
#> GSM215092 1 0.571 0.6368 0.676 0.000 0.176 0.024 0.124
#> GSM215093 4 0.598 -0.1137 0.012 0.000 0.180 0.628 0.180
#> GSM215094 1 0.371 0.7299 0.824 0.000 0.108 0.004 0.064
#> GSM215095 1 0.231 0.7581 0.912 0.000 0.016 0.012 0.060
#> GSM215096 1 0.268 0.7521 0.884 0.000 0.036 0.000 0.080
#> GSM215097 1 0.555 0.6408 0.648 0.000 0.076 0.016 0.260
#> GSM215098 1 0.226 0.7601 0.908 0.000 0.028 0.000 0.064
#> GSM215099 1 0.411 0.7514 0.776 0.000 0.060 0.000 0.164
#> GSM215100 1 0.490 0.7018 0.696 0.000 0.052 0.008 0.244
#> GSM215101 1 0.547 0.6968 0.696 0.004 0.096 0.016 0.188
#> GSM215102 3 0.492 0.5570 0.164 0.000 0.744 0.028 0.064
#> GSM215103 3 0.657 0.4716 0.220 0.000 0.608 0.092 0.080
#> GSM215104 1 0.586 0.1773 0.500 0.000 0.400 0.000 0.100
#> GSM215105 1 0.454 0.7165 0.740 0.000 0.048 0.008 0.204
#> GSM215106 1 0.407 0.7380 0.792 0.000 0.048 0.008 0.152
#> GSM215107 1 0.277 0.7653 0.876 0.000 0.032 0.000 0.092
#> GSM215108 3 0.599 0.4511 0.172 0.000 0.656 0.032 0.140
#> GSM215109 3 0.407 0.3931 0.004 0.000 0.800 0.100 0.096
#> GSM215110 3 0.742 0.3050 0.192 0.000 0.500 0.072 0.236
#> GSM215111 1 0.385 0.7453 0.796 0.000 0.036 0.004 0.164
#> GSM215112 1 0.248 0.7499 0.904 0.000 0.028 0.008 0.060
#> GSM215113 1 0.291 0.7651 0.860 0.000 0.024 0.000 0.116
#> GSM215114 1 0.501 0.5938 0.684 0.000 0.232 0.000 0.084
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 3 0.649 0.2631 0.000 0.168 0.552 0.028 0.028 0.224
#> GSM215052 2 0.632 -0.2320 0.000 0.468 0.044 0.004 0.116 0.368
#> GSM215053 2 0.710 -0.1482 0.000 0.392 0.320 0.072 0.004 0.212
#> GSM215054 3 0.682 0.2271 0.000 0.176 0.520 0.044 0.028 0.232
#> GSM215055 2 0.517 0.4981 0.000 0.680 0.160 0.020 0.004 0.136
#> GSM215056 2 0.572 0.1962 0.000 0.516 0.352 0.004 0.008 0.120
#> GSM215057 2 0.346 0.6458 0.000 0.808 0.084 0.000 0.000 0.108
#> GSM215058 2 0.564 0.2285 0.000 0.560 0.160 0.000 0.008 0.272
#> GSM215059 2 0.292 0.6558 0.000 0.848 0.052 0.000 0.000 0.100
#> GSM215060 2 0.437 0.5717 0.000 0.740 0.136 0.008 0.000 0.116
#> GSM215061 2 0.114 0.6702 0.000 0.948 0.000 0.000 0.000 0.052
#> GSM215062 2 0.514 0.2558 0.004 0.584 0.016 0.004 0.040 0.352
#> GSM215063 3 0.372 0.3112 0.000 0.080 0.812 0.004 0.012 0.092
#> GSM215064 2 0.433 0.4563 0.008 0.676 0.012 0.004 0.008 0.292
#> GSM215065 2 0.167 0.6715 0.000 0.928 0.008 0.004 0.000 0.060
#> GSM215066 2 0.195 0.6679 0.000 0.908 0.000 0.016 0.000 0.076
#> GSM215067 3 0.568 0.1369 0.000 0.268 0.560 0.004 0.004 0.164
#> GSM215068 2 0.184 0.6716 0.000 0.912 0.004 0.004 0.000 0.080
#> GSM215069 2 0.105 0.6731 0.000 0.964 0.012 0.004 0.000 0.020
#> GSM215070 2 0.612 0.0874 0.000 0.552 0.036 0.000 0.184 0.228
#> GSM215071 2 0.368 0.6004 0.000 0.800 0.008 0.000 0.068 0.124
#> GSM215072 2 0.578 -0.0616 0.000 0.512 0.012 0.004 0.116 0.356
#> GSM215073 2 0.239 0.6595 0.000 0.892 0.020 0.012 0.000 0.076
#> GSM215074 2 0.388 0.6105 0.000 0.780 0.120 0.000 0.004 0.096
#> GSM215075 2 0.405 0.6075 0.000 0.776 0.036 0.020 0.008 0.160
#> GSM215076 6 0.737 0.0000 0.000 0.256 0.072 0.020 0.232 0.420
#> GSM215077 2 0.333 0.6216 0.000 0.820 0.008 0.000 0.040 0.132
#> GSM215078 2 0.280 0.6577 0.000 0.868 0.012 0.004 0.020 0.096
#> GSM215079 2 0.283 0.6688 0.000 0.856 0.024 0.008 0.000 0.112
#> GSM215080 2 0.226 0.6576 0.000 0.884 0.004 0.008 0.000 0.104
#> GSM215081 2 0.307 0.6031 0.000 0.788 0.008 0.000 0.000 0.204
#> GSM215082 2 0.394 0.5325 0.000 0.724 0.008 0.000 0.024 0.244
#> GSM215083 1 0.703 0.1310 0.444 0.000 0.276 0.220 0.028 0.032
#> GSM215084 1 0.613 0.3220 0.516 0.000 0.004 0.124 0.324 0.032
#> GSM215085 3 0.810 -0.4443 0.236 0.000 0.316 0.296 0.056 0.096
#> GSM215086 4 0.757 0.0000 0.040 0.000 0.336 0.388 0.084 0.152
#> GSM215087 1 0.333 0.6787 0.832 0.004 0.000 0.120 0.016 0.028
#> GSM215088 3 0.670 -0.2710 0.032 0.000 0.552 0.200 0.172 0.044
#> GSM215089 1 0.573 0.5541 0.540 0.000 0.008 0.336 0.104 0.012
#> GSM215090 1 0.671 0.4200 0.516 0.000 0.032 0.264 0.156 0.032
#> GSM215091 1 0.408 0.6816 0.772 0.000 0.028 0.168 0.020 0.012
#> GSM215092 1 0.704 0.3948 0.492 0.000 0.032 0.240 0.188 0.048
#> GSM215093 3 0.442 0.0659 0.008 0.000 0.780 0.076 0.080 0.056
#> GSM215094 1 0.449 0.6103 0.752 0.000 0.004 0.116 0.108 0.020
#> GSM215095 1 0.230 0.6704 0.904 0.000 0.000 0.052 0.020 0.024
#> GSM215096 1 0.271 0.6672 0.880 0.000 0.004 0.068 0.040 0.008
#> GSM215097 1 0.568 0.5557 0.528 0.000 0.036 0.376 0.052 0.008
#> GSM215098 1 0.309 0.6788 0.844 0.000 0.004 0.116 0.008 0.028
#> GSM215099 1 0.512 0.6461 0.656 0.000 0.008 0.248 0.072 0.016
#> GSM215100 1 0.565 0.6009 0.568 0.000 0.012 0.328 0.068 0.024
#> GSM215101 1 0.673 0.4988 0.512 0.000 0.020 0.292 0.104 0.072
#> GSM215102 5 0.425 0.4503 0.088 0.000 0.020 0.096 0.784 0.012
#> GSM215103 5 0.727 0.3421 0.200 0.000 0.100 0.092 0.532 0.076
#> GSM215104 5 0.651 0.1075 0.376 0.000 0.008 0.120 0.448 0.048
#> GSM215105 1 0.509 0.6318 0.660 0.000 0.008 0.252 0.056 0.024
#> GSM215106 1 0.440 0.6747 0.756 0.000 0.024 0.168 0.032 0.020
#> GSM215107 1 0.489 0.6502 0.720 0.000 0.012 0.176 0.056 0.036
#> GSM215108 5 0.645 0.3398 0.116 0.000 0.020 0.136 0.608 0.120
#> GSM215109 5 0.536 0.2588 0.000 0.000 0.080 0.092 0.684 0.144
#> GSM215110 5 0.744 0.1732 0.064 0.000 0.104 0.316 0.440 0.076
#> GSM215111 1 0.430 0.6754 0.732 0.000 0.020 0.216 0.016 0.016
#> GSM215112 1 0.295 0.6621 0.868 0.000 0.004 0.076 0.032 0.020
#> GSM215113 1 0.424 0.6778 0.748 0.000 0.004 0.188 0.040 0.020
#> GSM215114 1 0.536 0.4817 0.640 0.000 0.008 0.072 0.252 0.028
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> CV:NMF 64 9.19e-15 1.000 2
#> CV:NMF 58 2.54e-13 0.979 3
#> CV:NMF 49 2.29e-11 0.994 4
#> CV:NMF 44 2.79e-10 0.435 5
#> CV:NMF 34 4.09e-08 0.959 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 51941 rows and 64 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.998 0.999 0.5084 0.492 0.492
#> 3 3 0.899 0.928 0.949 0.1401 0.933 0.864
#> 4 4 0.918 0.917 0.927 0.0314 1.000 1.000
#> 5 5 0.867 0.836 0.918 0.0331 0.984 0.963
#> 6 6 0.809 0.820 0.897 0.0298 1.000 0.999
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0.000 1.000 0.000 1.000
#> GSM215052 2 0.000 1.000 0.000 1.000
#> GSM215053 2 0.000 1.000 0.000 1.000
#> GSM215054 2 0.000 1.000 0.000 1.000
#> GSM215055 2 0.000 1.000 0.000 1.000
#> GSM215056 2 0.000 1.000 0.000 1.000
#> GSM215057 2 0.000 1.000 0.000 1.000
#> GSM215058 2 0.000 1.000 0.000 1.000
#> GSM215059 2 0.000 1.000 0.000 1.000
#> GSM215060 2 0.000 1.000 0.000 1.000
#> GSM215061 2 0.000 1.000 0.000 1.000
#> GSM215062 2 0.000 1.000 0.000 1.000
#> GSM215063 2 0.000 1.000 0.000 1.000
#> GSM215064 2 0.000 1.000 0.000 1.000
#> GSM215065 2 0.000 1.000 0.000 1.000
#> GSM215066 2 0.000 1.000 0.000 1.000
#> GSM215067 2 0.000 1.000 0.000 1.000
#> GSM215068 2 0.000 1.000 0.000 1.000
#> GSM215069 2 0.000 1.000 0.000 1.000
#> GSM215070 2 0.000 1.000 0.000 1.000
#> GSM215071 2 0.000 1.000 0.000 1.000
#> GSM215072 2 0.000 1.000 0.000 1.000
#> GSM215073 2 0.000 1.000 0.000 1.000
#> GSM215074 2 0.000 1.000 0.000 1.000
#> GSM215075 2 0.000 1.000 0.000 1.000
#> GSM215076 2 0.000 1.000 0.000 1.000
#> GSM215077 2 0.000 1.000 0.000 1.000
#> GSM215078 2 0.000 1.000 0.000 1.000
#> GSM215079 2 0.000 1.000 0.000 1.000
#> GSM215080 2 0.000 1.000 0.000 1.000
#> GSM215081 2 0.000 1.000 0.000 1.000
#> GSM215082 2 0.000 1.000 0.000 1.000
#> GSM215083 1 0.000 0.998 1.000 0.000
#> GSM215084 1 0.000 0.998 1.000 0.000
#> GSM215085 1 0.000 0.998 1.000 0.000
#> GSM215086 1 0.000 0.998 1.000 0.000
#> GSM215087 1 0.000 0.998 1.000 0.000
#> GSM215088 1 0.000 0.998 1.000 0.000
#> GSM215089 1 0.000 0.998 1.000 0.000
#> GSM215090 1 0.000 0.998 1.000 0.000
#> GSM215091 1 0.000 0.998 1.000 0.000
#> GSM215092 1 0.000 0.998 1.000 0.000
#> GSM215093 1 0.295 0.945 0.948 0.052
#> GSM215094 1 0.000 0.998 1.000 0.000
#> GSM215095 1 0.000 0.998 1.000 0.000
#> GSM215096 1 0.000 0.998 1.000 0.000
#> GSM215097 1 0.000 0.998 1.000 0.000
#> GSM215098 1 0.000 0.998 1.000 0.000
#> GSM215099 1 0.000 0.998 1.000 0.000
#> GSM215100 1 0.000 0.998 1.000 0.000
#> GSM215101 1 0.000 0.998 1.000 0.000
#> GSM215102 1 0.000 0.998 1.000 0.000
#> GSM215103 1 0.000 0.998 1.000 0.000
#> GSM215104 1 0.000 0.998 1.000 0.000
#> GSM215105 1 0.000 0.998 1.000 0.000
#> GSM215106 1 0.000 0.998 1.000 0.000
#> GSM215107 1 0.000 0.998 1.000 0.000
#> GSM215108 1 0.000 0.998 1.000 0.000
#> GSM215109 1 0.000 0.998 1.000 0.000
#> GSM215110 1 0.000 0.998 1.000 0.000
#> GSM215111 1 0.000 0.998 1.000 0.000
#> GSM215112 1 0.000 0.998 1.000 0.000
#> GSM215113 1 0.000 0.998 1.000 0.000
#> GSM215114 1 0.000 0.998 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215052 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215053 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215054 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215055 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215056 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215057 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215058 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215059 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215060 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215061 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215062 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215063 2 0.1860 0.951 0.000 0.948 0.052
#> GSM215064 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215065 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215066 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215067 2 0.1860 0.951 0.000 0.948 0.052
#> GSM215068 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215069 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215070 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215071 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215072 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215073 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215074 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215075 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215076 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215077 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215078 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215079 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215080 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215081 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215082 2 0.0000 0.997 0.000 1.000 0.000
#> GSM215083 1 0.3816 0.832 0.852 0.000 0.148
#> GSM215084 1 0.1289 0.906 0.968 0.000 0.032
#> GSM215085 3 0.5465 0.810 0.288 0.000 0.712
#> GSM215086 3 0.3619 0.829 0.136 0.000 0.864
#> GSM215087 1 0.0747 0.915 0.984 0.000 0.016
#> GSM215088 3 0.4931 0.872 0.232 0.000 0.768
#> GSM215089 1 0.1860 0.915 0.948 0.000 0.052
#> GSM215090 1 0.2448 0.879 0.924 0.000 0.076
#> GSM215091 1 0.2165 0.907 0.936 0.000 0.064
#> GSM215092 1 0.2066 0.908 0.940 0.000 0.060
#> GSM215093 3 0.4654 0.864 0.208 0.000 0.792
#> GSM215094 1 0.1031 0.914 0.976 0.000 0.024
#> GSM215095 1 0.0592 0.914 0.988 0.000 0.012
#> GSM215096 1 0.1529 0.914 0.960 0.000 0.040
#> GSM215097 1 0.1964 0.911 0.944 0.000 0.056
#> GSM215098 1 0.0592 0.914 0.988 0.000 0.012
#> GSM215099 1 0.1163 0.916 0.972 0.000 0.028
#> GSM215100 1 0.1753 0.903 0.952 0.000 0.048
#> GSM215101 1 0.1529 0.901 0.960 0.000 0.040
#> GSM215102 1 0.4291 0.777 0.820 0.000 0.180
#> GSM215103 1 0.4178 0.808 0.828 0.000 0.172
#> GSM215104 1 0.3340 0.868 0.880 0.000 0.120
#> GSM215105 1 0.2066 0.910 0.940 0.000 0.060
#> GSM215106 1 0.2165 0.906 0.936 0.000 0.064
#> GSM215107 1 0.1411 0.914 0.964 0.000 0.036
#> GSM215108 1 0.6008 0.236 0.628 0.000 0.372
#> GSM215109 3 0.5327 0.849 0.272 0.000 0.728
#> GSM215110 1 0.4121 0.772 0.832 0.000 0.168
#> GSM215111 1 0.2066 0.910 0.940 0.000 0.060
#> GSM215112 1 0.0892 0.915 0.980 0.000 0.020
#> GSM215113 1 0.1753 0.915 0.952 0.000 0.048
#> GSM215114 1 0.1163 0.915 0.972 0.000 0.028
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215052 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215053 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215054 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215055 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215056 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215057 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215058 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215059 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215060 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215061 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215062 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215063 2 0.1706 0.949 0.000 0.948 0.016 NA
#> GSM215064 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215065 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215066 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215067 2 0.1706 0.949 0.000 0.948 0.016 NA
#> GSM215068 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215069 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215070 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215071 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215072 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215073 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215074 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215075 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215076 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215077 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215078 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215079 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215080 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215081 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215082 2 0.0000 0.997 0.000 1.000 0.000 NA
#> GSM215083 1 0.4015 0.840 0.832 0.000 0.116 NA
#> GSM215084 1 0.1118 0.904 0.964 0.000 0.000 NA
#> GSM215085 3 0.7242 0.673 0.148 0.000 0.476 NA
#> GSM215086 3 0.5713 0.795 0.040 0.000 0.620 NA
#> GSM215087 1 0.0927 0.910 0.976 0.000 0.016 NA
#> GSM215088 3 0.5926 0.805 0.060 0.000 0.632 NA
#> GSM215089 1 0.1837 0.911 0.944 0.000 0.028 NA
#> GSM215090 1 0.2611 0.870 0.896 0.000 0.008 NA
#> GSM215091 1 0.2060 0.905 0.932 0.000 0.052 NA
#> GSM215092 1 0.2048 0.902 0.928 0.000 0.008 NA
#> GSM215093 3 0.5864 0.806 0.072 0.000 0.664 NA
#> GSM215094 1 0.1004 0.909 0.972 0.000 0.004 NA
#> GSM215095 1 0.0672 0.910 0.984 0.000 0.008 NA
#> GSM215096 1 0.1388 0.910 0.960 0.000 0.028 NA
#> GSM215097 1 0.1975 0.908 0.936 0.000 0.048 NA
#> GSM215098 1 0.0672 0.909 0.984 0.000 0.008 NA
#> GSM215099 1 0.1182 0.912 0.968 0.000 0.016 NA
#> GSM215100 1 0.1824 0.897 0.936 0.000 0.004 NA
#> GSM215101 1 0.2345 0.873 0.900 0.000 0.000 NA
#> GSM215102 1 0.4638 0.775 0.788 0.000 0.152 NA
#> GSM215103 1 0.4364 0.823 0.808 0.000 0.136 NA
#> GSM215104 1 0.3453 0.872 0.868 0.000 0.080 NA
#> GSM215105 1 0.1913 0.908 0.940 0.000 0.040 NA
#> GSM215106 1 0.2021 0.904 0.932 0.000 0.056 NA
#> GSM215107 1 0.1398 0.910 0.956 0.000 0.004 NA
#> GSM215108 1 0.6120 0.153 0.520 0.000 0.432 NA
#> GSM215109 3 0.2466 0.802 0.096 0.000 0.900 NA
#> GSM215110 1 0.5851 0.555 0.660 0.000 0.068 NA
#> GSM215111 1 0.1888 0.908 0.940 0.000 0.044 NA
#> GSM215112 1 0.0927 0.911 0.976 0.000 0.016 NA
#> GSM215113 1 0.1520 0.911 0.956 0.000 0.020 NA
#> GSM215114 1 0.1256 0.911 0.964 0.000 0.028 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215052 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215053 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215054 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215055 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215056 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215057 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215058 2 0.0290 0.989 0.000 0.992 0.000 0.000 0.008
#> GSM215059 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215060 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215061 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215062 2 0.0693 0.982 0.000 0.980 0.000 0.008 0.012
#> GSM215063 2 0.1525 0.949 0.000 0.948 0.004 0.036 0.012
#> GSM215064 2 0.0693 0.982 0.000 0.980 0.000 0.008 0.012
#> GSM215065 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215066 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215067 2 0.1525 0.949 0.000 0.948 0.004 0.036 0.012
#> GSM215068 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215069 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215070 2 0.0290 0.989 0.000 0.992 0.000 0.000 0.008
#> GSM215071 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215072 2 0.0162 0.992 0.000 0.996 0.000 0.000 0.004
#> GSM215073 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215074 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215075 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215076 2 0.0693 0.982 0.000 0.980 0.000 0.008 0.012
#> GSM215077 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215078 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215079 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215080 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215081 2 0.0579 0.984 0.000 0.984 0.000 0.008 0.008
#> GSM215082 2 0.0000 0.994 0.000 1.000 0.000 0.000 0.000
#> GSM215083 1 0.4900 0.728 0.764 0.000 0.068 0.048 0.120
#> GSM215084 1 0.1608 0.843 0.928 0.000 0.000 0.072 0.000
#> GSM215085 5 0.2719 0.247 0.048 0.000 0.068 0.000 0.884
#> GSM215086 5 0.6745 0.045 0.004 0.000 0.336 0.224 0.436
#> GSM215087 1 0.1471 0.859 0.952 0.000 0.004 0.024 0.020
#> GSM215088 3 0.1012 0.555 0.012 0.000 0.968 0.020 0.000
#> GSM215089 1 0.2072 0.859 0.928 0.000 0.020 0.036 0.016
#> GSM215090 1 0.3728 0.703 0.804 0.000 0.008 0.164 0.024
#> GSM215091 1 0.2363 0.855 0.912 0.000 0.024 0.012 0.052
#> GSM215092 1 0.2947 0.824 0.876 0.000 0.016 0.088 0.020
#> GSM215093 3 0.3511 0.587 0.012 0.000 0.848 0.068 0.072
#> GSM215094 1 0.1547 0.858 0.948 0.000 0.004 0.032 0.016
#> GSM215095 1 0.1012 0.860 0.968 0.000 0.000 0.020 0.012
#> GSM215096 1 0.1538 0.862 0.948 0.000 0.008 0.008 0.036
#> GSM215097 1 0.2060 0.861 0.928 0.000 0.024 0.012 0.036
#> GSM215098 1 0.1106 0.859 0.964 0.000 0.000 0.024 0.012
#> GSM215099 1 0.1483 0.862 0.952 0.000 0.008 0.028 0.012
#> GSM215100 1 0.2505 0.821 0.888 0.000 0.000 0.092 0.020
#> GSM215101 1 0.2929 0.773 0.840 0.000 0.000 0.152 0.008
#> GSM215102 1 0.5639 0.606 0.712 0.000 0.120 0.104 0.064
#> GSM215103 1 0.5245 0.709 0.740 0.000 0.072 0.060 0.128
#> GSM215104 1 0.4113 0.795 0.820 0.000 0.044 0.052 0.084
#> GSM215105 1 0.2228 0.858 0.920 0.000 0.016 0.020 0.044
#> GSM215106 1 0.2537 0.850 0.904 0.000 0.024 0.016 0.056
#> GSM215107 1 0.2012 0.857 0.920 0.000 0.000 0.060 0.020
#> GSM215108 1 0.7977 -0.247 0.420 0.000 0.180 0.120 0.280
#> GSM215109 3 0.6673 0.149 0.028 0.000 0.516 0.132 0.324
#> GSM215110 4 0.4169 0.000 0.256 0.000 0.004 0.724 0.016
#> GSM215111 1 0.2395 0.857 0.912 0.000 0.016 0.024 0.048
#> GSM215112 1 0.1403 0.859 0.952 0.000 0.000 0.024 0.024
#> GSM215113 1 0.1948 0.860 0.932 0.000 0.008 0.036 0.024
#> GSM215114 1 0.2417 0.857 0.912 0.000 0.016 0.040 0.032
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 2 0.1542 0.9548 0.000 0.936 0.000 0.004 0.008 0.052
#> GSM215052 2 0.0551 0.9693 0.000 0.984 0.000 0.004 0.004 0.008
#> GSM215053 2 0.1340 0.9602 0.000 0.948 0.000 0.004 0.008 0.040
#> GSM215054 2 0.1578 0.9480 0.000 0.936 0.000 0.004 0.012 0.048
#> GSM215055 2 0.1225 0.9567 0.000 0.952 0.000 0.000 0.012 0.036
#> GSM215056 2 0.1578 0.9480 0.000 0.936 0.000 0.004 0.012 0.048
#> GSM215057 2 0.1194 0.9630 0.000 0.956 0.000 0.004 0.008 0.032
#> GSM215058 2 0.1590 0.9573 0.000 0.936 0.000 0.008 0.008 0.048
#> GSM215059 2 0.0146 0.9702 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM215060 2 0.0436 0.9695 0.000 0.988 0.000 0.004 0.004 0.004
#> GSM215061 2 0.0000 0.9703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215062 2 0.1719 0.9365 0.000 0.928 0.000 0.008 0.008 0.056
#> GSM215063 2 0.2699 0.9057 0.000 0.884 0.052 0.004 0.012 0.048
#> GSM215064 2 0.1719 0.9365 0.000 0.928 0.000 0.008 0.008 0.056
#> GSM215065 2 0.0000 0.9703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215066 2 0.0000 0.9703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215067 2 0.2699 0.9057 0.000 0.884 0.052 0.004 0.012 0.048
#> GSM215068 2 0.0000 0.9703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215069 2 0.0000 0.9703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215070 2 0.0777 0.9669 0.000 0.972 0.000 0.004 0.000 0.024
#> GSM215071 2 0.0146 0.9702 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM215072 2 0.0790 0.9619 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM215073 2 0.0146 0.9702 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM215074 2 0.0436 0.9695 0.000 0.988 0.000 0.004 0.004 0.004
#> GSM215075 2 0.0603 0.9673 0.000 0.980 0.000 0.000 0.004 0.016
#> GSM215076 2 0.2169 0.9162 0.000 0.900 0.000 0.008 0.012 0.080
#> GSM215077 2 0.0000 0.9703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215078 2 0.0291 0.9698 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM215079 2 0.0000 0.9703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215080 2 0.0000 0.9703 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215081 2 0.1268 0.9511 0.000 0.952 0.000 0.008 0.004 0.036
#> GSM215082 2 0.0405 0.9700 0.000 0.988 0.000 0.000 0.004 0.008
#> GSM215083 1 0.4869 0.7572 0.744 0.000 0.064 0.024 0.036 0.132
#> GSM215084 1 0.2239 0.8579 0.900 0.000 0.000 0.008 0.072 0.020
#> GSM215085 6 0.3802 0.0000 0.012 0.000 0.036 0.180 0.000 0.772
#> GSM215086 4 0.2032 0.0000 0.004 0.000 0.068 0.912 0.012 0.004
#> GSM215087 1 0.1706 0.8675 0.936 0.000 0.004 0.004 0.032 0.024
#> GSM215088 3 0.2925 0.4556 0.000 0.000 0.856 0.104 0.016 0.024
#> GSM215089 1 0.2280 0.8702 0.912 0.000 0.008 0.016 0.036 0.028
#> GSM215090 1 0.3993 0.7258 0.764 0.000 0.004 0.016 0.184 0.032
#> GSM215091 1 0.2208 0.8660 0.912 0.000 0.016 0.012 0.008 0.052
#> GSM215092 1 0.3327 0.8398 0.844 0.000 0.016 0.008 0.092 0.040
#> GSM215093 3 0.2255 0.5223 0.004 0.000 0.912 0.036 0.020 0.028
#> GSM215094 1 0.1644 0.8686 0.932 0.000 0.000 0.000 0.040 0.028
#> GSM215095 1 0.0972 0.8702 0.964 0.000 0.000 0.000 0.028 0.008
#> GSM215096 1 0.1413 0.8719 0.948 0.000 0.004 0.004 0.008 0.036
#> GSM215097 1 0.2037 0.8709 0.924 0.000 0.012 0.016 0.012 0.036
#> GSM215098 1 0.1478 0.8676 0.944 0.000 0.000 0.004 0.032 0.020
#> GSM215099 1 0.1693 0.8708 0.936 0.000 0.000 0.012 0.032 0.020
#> GSM215100 1 0.2878 0.8345 0.860 0.000 0.000 0.016 0.100 0.024
#> GSM215101 1 0.3627 0.7916 0.796 0.000 0.000 0.020 0.156 0.028
#> GSM215102 1 0.5630 0.6656 0.680 0.000 0.076 0.012 0.100 0.132
#> GSM215103 1 0.5250 0.7429 0.724 0.000 0.060 0.044 0.044 0.128
#> GSM215104 1 0.4127 0.8097 0.804 0.000 0.032 0.028 0.040 0.096
#> GSM215105 1 0.2158 0.8678 0.912 0.000 0.004 0.012 0.016 0.056
#> GSM215106 1 0.2572 0.8615 0.896 0.000 0.012 0.024 0.016 0.052
#> GSM215107 1 0.2434 0.8681 0.892 0.000 0.000 0.008 0.064 0.036
#> GSM215108 1 0.8208 -0.1220 0.388 0.000 0.128 0.152 0.084 0.248
#> GSM215109 3 0.7017 0.0309 0.028 0.000 0.396 0.368 0.036 0.172
#> GSM215110 5 0.2808 0.0000 0.092 0.000 0.004 0.028 0.868 0.008
#> GSM215111 1 0.2276 0.8682 0.908 0.000 0.004 0.016 0.020 0.052
#> GSM215112 1 0.1642 0.8679 0.936 0.000 0.000 0.004 0.032 0.028
#> GSM215113 1 0.2051 0.8705 0.916 0.000 0.000 0.008 0.036 0.040
#> GSM215114 1 0.2594 0.8658 0.892 0.000 0.016 0.004 0.048 0.040
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> MAD:hclust 64 9.19e-15 1.000 2
#> MAD:hclust 63 2.09e-14 0.999 3
#> MAD:hclust 63 2.09e-14 0.999 4
#> MAD:hclust 59 1.54e-13 0.998 5
#> MAD:hclust 58 2.54e-13 0.998 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 51941 rows and 64 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.714 0.713 0.792 0.1991 0.875 0.746
#> 4 4 0.594 0.604 0.803 0.1016 0.879 0.713
#> 5 5 0.542 0.701 0.748 0.0708 0.923 0.787
#> 6 6 0.577 0.493 0.707 0.0513 0.934 0.793
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.5650 0.809 0.312 0.688 0.000
#> GSM215052 2 0.1964 0.909 0.056 0.944 0.000
#> GSM215053 2 0.5591 0.818 0.304 0.696 0.000
#> GSM215054 2 0.5882 0.800 0.348 0.652 0.000
#> GSM215055 2 0.5591 0.821 0.304 0.696 0.000
#> GSM215056 2 0.5650 0.816 0.312 0.688 0.000
#> GSM215057 2 0.5178 0.850 0.256 0.744 0.000
#> GSM215058 2 0.5431 0.834 0.284 0.716 0.000
#> GSM215059 2 0.1753 0.910 0.048 0.952 0.000
#> GSM215060 2 0.4235 0.878 0.176 0.824 0.000
#> GSM215061 2 0.1411 0.910 0.036 0.964 0.000
#> GSM215062 2 0.2165 0.897 0.064 0.936 0.000
#> GSM215063 2 0.5785 0.806 0.332 0.668 0.000
#> GSM215064 2 0.2165 0.897 0.064 0.936 0.000
#> GSM215065 2 0.1529 0.909 0.040 0.960 0.000
#> GSM215066 2 0.0237 0.909 0.004 0.996 0.000
#> GSM215067 2 0.5733 0.810 0.324 0.676 0.000
#> GSM215068 2 0.0000 0.909 0.000 1.000 0.000
#> GSM215069 2 0.1529 0.910 0.040 0.960 0.000
#> GSM215070 2 0.1411 0.910 0.036 0.964 0.000
#> GSM215071 2 0.1643 0.910 0.044 0.956 0.000
#> GSM215072 2 0.2356 0.897 0.072 0.928 0.000
#> GSM215073 2 0.1860 0.908 0.052 0.948 0.000
#> GSM215074 2 0.2959 0.903 0.100 0.900 0.000
#> GSM215075 2 0.1643 0.906 0.044 0.956 0.000
#> GSM215076 2 0.2959 0.892 0.100 0.900 0.000
#> GSM215077 2 0.0892 0.910 0.020 0.980 0.000
#> GSM215078 2 0.1753 0.912 0.048 0.952 0.000
#> GSM215079 2 0.0000 0.909 0.000 1.000 0.000
#> GSM215080 2 0.0424 0.909 0.008 0.992 0.000
#> GSM215081 2 0.2066 0.897 0.060 0.940 0.000
#> GSM215082 2 0.2165 0.904 0.064 0.936 0.000
#> GSM215083 3 0.5291 0.134 0.268 0.000 0.732
#> GSM215084 1 0.6215 0.923 0.572 0.000 0.428
#> GSM215085 3 0.1031 0.573 0.024 0.000 0.976
#> GSM215086 3 0.0237 0.576 0.004 0.000 0.996
#> GSM215087 1 0.6291 0.891 0.532 0.000 0.468
#> GSM215088 3 0.0000 0.575 0.000 0.000 1.000
#> GSM215089 1 0.6244 0.919 0.560 0.000 0.440
#> GSM215090 1 0.6225 0.929 0.568 0.000 0.432
#> GSM215091 3 0.6309 -0.833 0.500 0.000 0.500
#> GSM215092 1 0.6235 0.912 0.564 0.000 0.436
#> GSM215093 3 0.0592 0.567 0.012 0.000 0.988
#> GSM215094 1 0.6215 0.937 0.572 0.000 0.428
#> GSM215095 1 0.6215 0.937 0.572 0.000 0.428
#> GSM215096 1 0.6305 0.858 0.516 0.000 0.484
#> GSM215097 3 0.6295 -0.775 0.472 0.000 0.528
#> GSM215098 1 0.6308 0.835 0.508 0.000 0.492
#> GSM215099 1 0.6235 0.935 0.564 0.000 0.436
#> GSM215100 1 0.6225 0.938 0.568 0.000 0.432
#> GSM215101 1 0.6225 0.938 0.568 0.000 0.432
#> GSM215102 3 0.4002 0.478 0.160 0.000 0.840
#> GSM215103 3 0.5926 -0.303 0.356 0.000 0.644
#> GSM215104 3 0.6305 -0.781 0.484 0.000 0.516
#> GSM215105 1 0.6280 0.907 0.540 0.000 0.460
#> GSM215106 3 0.6308 -0.810 0.492 0.000 0.508
#> GSM215107 1 0.6235 0.935 0.564 0.000 0.436
#> GSM215108 3 0.1964 0.562 0.056 0.000 0.944
#> GSM215109 3 0.0000 0.575 0.000 0.000 1.000
#> GSM215110 3 0.2878 0.524 0.096 0.000 0.904
#> GSM215111 1 0.6260 0.922 0.552 0.000 0.448
#> GSM215112 1 0.6225 0.937 0.568 0.000 0.432
#> GSM215113 1 0.6225 0.938 0.568 0.000 0.432
#> GSM215114 1 0.6308 0.835 0.508 0.000 0.492
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.6688 -0.710 0.000 0.492 0.088 0.420
#> GSM215052 2 0.3182 0.623 0.000 0.876 0.028 0.096
#> GSM215053 2 0.6188 -0.712 0.000 0.548 0.056 0.396
#> GSM215054 4 0.6451 0.811 0.000 0.456 0.068 0.476
#> GSM215055 2 0.5203 -0.680 0.000 0.576 0.008 0.416
#> GSM215056 2 0.5158 -0.820 0.000 0.524 0.004 0.472
#> GSM215057 2 0.5823 -0.339 0.000 0.608 0.044 0.348
#> GSM215058 2 0.7001 -0.199 0.000 0.544 0.140 0.316
#> GSM215059 2 0.1637 0.644 0.000 0.940 0.000 0.060
#> GSM215060 2 0.3710 0.399 0.000 0.804 0.004 0.192
#> GSM215061 2 0.1661 0.656 0.000 0.944 0.004 0.052
#> GSM215062 2 0.4344 0.563 0.000 0.816 0.108 0.076
#> GSM215063 4 0.5600 0.900 0.000 0.468 0.020 0.512
#> GSM215064 2 0.4344 0.563 0.000 0.816 0.108 0.076
#> GSM215065 2 0.1557 0.645 0.000 0.944 0.000 0.056
#> GSM215066 2 0.0779 0.666 0.000 0.980 0.004 0.016
#> GSM215067 4 0.5506 0.898 0.000 0.472 0.016 0.512
#> GSM215068 2 0.0376 0.668 0.000 0.992 0.004 0.004
#> GSM215069 2 0.1302 0.654 0.000 0.956 0.000 0.044
#> GSM215070 2 0.2002 0.660 0.000 0.936 0.020 0.044
#> GSM215071 2 0.1389 0.651 0.000 0.952 0.000 0.048
#> GSM215072 2 0.4535 0.558 0.000 0.804 0.112 0.084
#> GSM215073 2 0.1978 0.634 0.000 0.928 0.004 0.068
#> GSM215074 2 0.3377 0.546 0.000 0.848 0.012 0.140
#> GSM215075 2 0.3239 0.603 0.000 0.880 0.068 0.052
#> GSM215076 2 0.5902 0.401 0.000 0.696 0.184 0.120
#> GSM215077 2 0.1174 0.667 0.000 0.968 0.012 0.020
#> GSM215078 2 0.2563 0.639 0.000 0.908 0.020 0.072
#> GSM215079 2 0.1284 0.669 0.000 0.964 0.012 0.024
#> GSM215080 2 0.0524 0.667 0.000 0.988 0.008 0.004
#> GSM215081 2 0.3948 0.585 0.000 0.840 0.096 0.064
#> GSM215082 2 0.3383 0.625 0.000 0.872 0.076 0.052
#> GSM215083 1 0.6027 0.296 0.664 0.000 0.244 0.092
#> GSM215084 1 0.3836 0.800 0.816 0.000 0.016 0.168
#> GSM215085 3 0.6652 0.792 0.316 0.000 0.576 0.108
#> GSM215086 3 0.5156 0.844 0.236 0.000 0.720 0.044
#> GSM215087 1 0.1975 0.849 0.936 0.000 0.016 0.048
#> GSM215088 3 0.4900 0.847 0.236 0.000 0.732 0.032
#> GSM215089 1 0.3907 0.809 0.828 0.000 0.032 0.140
#> GSM215090 1 0.3969 0.796 0.804 0.000 0.016 0.180
#> GSM215091 1 0.2408 0.837 0.920 0.000 0.036 0.044
#> GSM215092 1 0.4501 0.756 0.764 0.000 0.024 0.212
#> GSM215093 3 0.5022 0.835 0.220 0.000 0.736 0.044
#> GSM215094 1 0.2048 0.854 0.928 0.000 0.008 0.064
#> GSM215095 1 0.1970 0.854 0.932 0.000 0.008 0.060
#> GSM215096 1 0.1042 0.854 0.972 0.000 0.008 0.020
#> GSM215097 1 0.3716 0.828 0.852 0.000 0.052 0.096
#> GSM215098 1 0.1820 0.850 0.944 0.000 0.020 0.036
#> GSM215099 1 0.3479 0.824 0.840 0.000 0.012 0.148
#> GSM215100 1 0.3428 0.829 0.844 0.000 0.012 0.144
#> GSM215101 1 0.3271 0.837 0.856 0.000 0.012 0.132
#> GSM215102 3 0.7469 0.601 0.368 0.000 0.452 0.180
#> GSM215103 1 0.4920 0.617 0.768 0.000 0.164 0.068
#> GSM215104 1 0.3286 0.818 0.876 0.000 0.044 0.080
#> GSM215105 1 0.1890 0.855 0.936 0.000 0.008 0.056
#> GSM215106 1 0.2036 0.840 0.936 0.000 0.032 0.032
#> GSM215107 1 0.1807 0.859 0.940 0.000 0.008 0.052
#> GSM215108 3 0.6156 0.785 0.344 0.000 0.592 0.064
#> GSM215109 3 0.4262 0.847 0.236 0.000 0.756 0.008
#> GSM215110 3 0.7503 0.692 0.300 0.000 0.488 0.212
#> GSM215111 1 0.1256 0.852 0.964 0.000 0.008 0.028
#> GSM215112 1 0.1302 0.856 0.956 0.000 0.000 0.044
#> GSM215113 1 0.3161 0.835 0.864 0.000 0.012 0.124
#> GSM215114 1 0.2174 0.844 0.928 0.000 0.020 0.052
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 4 0.7777 0.613 0.000 0.296 0.088 0.428 NA
#> GSM215052 2 0.4927 0.640 0.000 0.752 0.032 0.072 NA
#> GSM215053 4 0.7014 0.646 0.000 0.356 0.072 0.480 NA
#> GSM215054 4 0.7368 0.672 0.000 0.248 0.092 0.516 NA
#> GSM215055 4 0.4852 0.666 0.000 0.380 0.008 0.596 NA
#> GSM215056 4 0.4686 0.703 0.000 0.332 0.016 0.644 NA
#> GSM215057 4 0.5972 0.514 0.000 0.420 0.008 0.488 NA
#> GSM215058 4 0.7144 0.400 0.000 0.328 0.012 0.344 NA
#> GSM215059 2 0.2588 0.718 0.000 0.884 0.008 0.100 NA
#> GSM215060 2 0.4065 0.494 0.000 0.752 0.008 0.224 NA
#> GSM215061 2 0.2708 0.726 0.000 0.892 0.016 0.072 NA
#> GSM215062 2 0.4268 0.571 0.000 0.708 0.000 0.024 NA
#> GSM215063 4 0.5765 0.711 0.000 0.276 0.040 0.632 NA
#> GSM215064 2 0.4268 0.571 0.000 0.708 0.000 0.024 NA
#> GSM215065 2 0.2177 0.725 0.000 0.908 0.004 0.080 NA
#> GSM215066 2 0.1617 0.742 0.000 0.948 0.012 0.020 NA
#> GSM215067 4 0.5702 0.710 0.000 0.276 0.040 0.636 NA
#> GSM215068 2 0.0451 0.750 0.000 0.988 0.000 0.004 NA
#> GSM215069 2 0.1830 0.730 0.000 0.924 0.000 0.068 NA
#> GSM215070 2 0.3831 0.700 0.000 0.824 0.016 0.048 NA
#> GSM215071 2 0.2179 0.730 0.000 0.912 0.008 0.072 NA
#> GSM215072 2 0.4465 0.544 0.000 0.672 0.000 0.024 NA
#> GSM215073 2 0.2856 0.700 0.000 0.872 0.008 0.104 NA
#> GSM215074 2 0.4234 0.625 0.000 0.776 0.012 0.172 NA
#> GSM215075 2 0.4367 0.614 0.000 0.796 0.028 0.064 NA
#> GSM215076 2 0.5827 0.274 0.000 0.532 0.016 0.060 NA
#> GSM215077 2 0.2387 0.741 0.000 0.908 0.004 0.048 NA
#> GSM215078 2 0.3412 0.713 0.000 0.852 0.012 0.088 NA
#> GSM215079 2 0.1498 0.747 0.000 0.952 0.008 0.024 NA
#> GSM215080 2 0.0740 0.748 0.000 0.980 0.004 0.008 NA
#> GSM215081 2 0.3878 0.612 0.000 0.748 0.000 0.016 NA
#> GSM215082 2 0.4256 0.657 0.000 0.764 0.004 0.048 NA
#> GSM215083 1 0.6479 0.326 0.612 0.000 0.220 0.060 NA
#> GSM215084 1 0.4037 0.758 0.752 0.000 0.004 0.020 NA
#> GSM215085 3 0.6732 0.721 0.280 0.000 0.560 0.092 NA
#> GSM215086 3 0.4037 0.803 0.176 0.000 0.784 0.028 NA
#> GSM215087 1 0.2095 0.816 0.928 0.000 0.020 0.024 NA
#> GSM215088 3 0.5356 0.800 0.180 0.000 0.712 0.040 NA
#> GSM215089 1 0.3972 0.772 0.764 0.000 0.016 0.008 NA
#> GSM215090 1 0.4065 0.753 0.752 0.000 0.008 0.016 NA
#> GSM215091 1 0.2878 0.793 0.888 0.000 0.048 0.016 NA
#> GSM215092 1 0.5086 0.661 0.660 0.000 0.016 0.036 NA
#> GSM215093 3 0.5446 0.778 0.148 0.000 0.720 0.056 NA
#> GSM215094 1 0.2017 0.820 0.912 0.000 0.000 0.008 NA
#> GSM215095 1 0.2068 0.819 0.904 0.000 0.000 0.004 NA
#> GSM215096 1 0.1278 0.822 0.960 0.000 0.020 0.004 NA
#> GSM215097 1 0.4564 0.778 0.764 0.000 0.072 0.012 NA
#> GSM215098 1 0.2640 0.810 0.900 0.000 0.032 0.016 NA
#> GSM215099 1 0.3774 0.780 0.780 0.000 0.012 0.008 NA
#> GSM215100 1 0.4012 0.779 0.760 0.000 0.012 0.012 NA
#> GSM215101 1 0.3693 0.796 0.808 0.000 0.004 0.032 NA
#> GSM215102 3 0.7494 0.501 0.328 0.000 0.368 0.036 NA
#> GSM215103 1 0.5150 0.656 0.740 0.000 0.140 0.040 NA
#> GSM215104 1 0.4298 0.775 0.804 0.000 0.064 0.032 NA
#> GSM215105 1 0.3135 0.818 0.868 0.000 0.020 0.024 NA
#> GSM215106 1 0.3223 0.787 0.868 0.000 0.052 0.016 NA
#> GSM215107 1 0.2597 0.821 0.896 0.000 0.004 0.040 NA
#> GSM215108 3 0.6143 0.733 0.288 0.000 0.596 0.036 NA
#> GSM215109 3 0.3660 0.804 0.176 0.000 0.800 0.016 NA
#> GSM215110 3 0.7366 0.660 0.224 0.000 0.440 0.040 NA
#> GSM215111 1 0.2204 0.819 0.920 0.000 0.016 0.016 NA
#> GSM215112 1 0.1310 0.820 0.956 0.000 0.000 0.024 NA
#> GSM215113 1 0.3731 0.796 0.800 0.000 0.016 0.012 NA
#> GSM215114 1 0.2687 0.806 0.900 0.000 0.028 0.028 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 4 0.561 0.63374 0.000 0.220 0.000 0.580 0.008 0.192
#> GSM215052 2 0.510 0.50609 0.000 0.696 0.008 0.100 0.024 0.172
#> GSM215053 4 0.713 0.52838 0.000 0.308 0.008 0.428 0.088 0.168
#> GSM215054 4 0.520 0.67981 0.000 0.204 0.000 0.640 0.008 0.148
#> GSM215055 2 0.740 -0.49654 0.000 0.396 0.004 0.240 0.116 0.244
#> GSM215056 2 0.774 -0.55252 0.000 0.300 0.004 0.232 0.176 0.288
#> GSM215057 6 0.668 0.08998 0.000 0.392 0.000 0.088 0.116 0.404
#> GSM215058 6 0.566 0.06256 0.000 0.200 0.000 0.128 0.044 0.628
#> GSM215059 2 0.196 0.64079 0.000 0.920 0.000 0.024 0.008 0.048
#> GSM215060 2 0.351 0.54656 0.000 0.824 0.004 0.036 0.020 0.116
#> GSM215061 2 0.259 0.64111 0.000 0.892 0.004 0.056 0.020 0.028
#> GSM215062 2 0.433 0.25495 0.000 0.564 0.004 0.000 0.016 0.416
#> GSM215063 6 0.811 -0.01868 0.000 0.232 0.028 0.196 0.212 0.332
#> GSM215064 2 0.433 0.25495 0.000 0.564 0.004 0.000 0.016 0.416
#> GSM215065 2 0.143 0.64523 0.000 0.940 0.000 0.004 0.004 0.052
#> GSM215066 2 0.189 0.65020 0.000 0.924 0.000 0.048 0.012 0.016
#> GSM215067 6 0.805 -0.00906 0.000 0.236 0.024 0.192 0.212 0.336
#> GSM215068 2 0.117 0.65880 0.000 0.960 0.000 0.020 0.008 0.012
#> GSM215069 2 0.122 0.64893 0.000 0.948 0.000 0.000 0.004 0.048
#> GSM215070 2 0.429 0.55081 0.000 0.744 0.004 0.048 0.016 0.188
#> GSM215071 2 0.184 0.64542 0.000 0.928 0.004 0.012 0.008 0.048
#> GSM215072 2 0.418 0.25034 0.000 0.556 0.004 0.000 0.008 0.432
#> GSM215073 2 0.251 0.63149 0.000 0.896 0.004 0.024 0.020 0.056
#> GSM215074 2 0.410 0.56144 0.000 0.788 0.000 0.068 0.040 0.104
#> GSM215075 2 0.434 0.48690 0.000 0.728 0.004 0.212 0.016 0.040
#> GSM215076 6 0.663 -0.02015 0.000 0.376 0.028 0.080 0.056 0.460
#> GSM215077 2 0.180 0.65370 0.000 0.928 0.008 0.008 0.004 0.052
#> GSM215078 2 0.272 0.64484 0.000 0.884 0.008 0.032 0.012 0.064
#> GSM215079 2 0.228 0.65230 0.000 0.900 0.000 0.052 0.004 0.044
#> GSM215080 2 0.170 0.65863 0.000 0.936 0.004 0.012 0.008 0.040
#> GSM215081 2 0.389 0.31031 0.000 0.596 0.000 0.000 0.004 0.400
#> GSM215082 2 0.467 0.40445 0.000 0.656 0.004 0.028 0.020 0.292
#> GSM215083 1 0.646 0.25376 0.592 0.000 0.204 0.096 0.084 0.024
#> GSM215084 1 0.373 0.45261 0.652 0.000 0.000 0.004 0.344 0.000
#> GSM215085 3 0.695 0.56134 0.144 0.000 0.584 0.100 0.092 0.080
#> GSM215086 3 0.387 0.73578 0.064 0.000 0.824 0.048 0.016 0.048
#> GSM215087 1 0.271 0.72254 0.872 0.000 0.004 0.068 0.056 0.000
#> GSM215088 3 0.396 0.73295 0.064 0.000 0.816 0.072 0.024 0.024
#> GSM215089 1 0.400 0.60057 0.708 0.000 0.004 0.028 0.260 0.000
#> GSM215090 1 0.469 0.45222 0.628 0.000 0.000 0.048 0.316 0.008
#> GSM215091 1 0.332 0.71589 0.840 0.000 0.028 0.092 0.040 0.000
#> GSM215092 5 0.425 -0.23388 0.476 0.000 0.004 0.004 0.512 0.004
#> GSM215093 3 0.414 0.70575 0.044 0.000 0.812 0.056 0.052 0.036
#> GSM215094 1 0.246 0.72559 0.876 0.000 0.000 0.028 0.096 0.000
#> GSM215095 1 0.257 0.72228 0.864 0.000 0.000 0.024 0.112 0.000
#> GSM215096 1 0.130 0.73998 0.952 0.000 0.004 0.032 0.012 0.000
#> GSM215097 1 0.469 0.65519 0.732 0.000 0.036 0.088 0.144 0.000
#> GSM215098 1 0.399 0.71917 0.800 0.000 0.020 0.100 0.072 0.008
#> GSM215099 1 0.435 0.61233 0.716 0.000 0.004 0.040 0.228 0.012
#> GSM215100 1 0.452 0.60515 0.696 0.000 0.004 0.044 0.244 0.012
#> GSM215101 1 0.464 0.63232 0.684 0.000 0.000 0.088 0.224 0.004
#> GSM215102 5 0.643 0.23978 0.200 0.000 0.324 0.012 0.452 0.012
#> GSM215103 1 0.542 0.55499 0.704 0.000 0.120 0.080 0.080 0.016
#> GSM215104 1 0.444 0.67201 0.784 0.000 0.060 0.044 0.092 0.020
#> GSM215105 1 0.273 0.72570 0.876 0.000 0.004 0.032 0.080 0.008
#> GSM215106 1 0.308 0.71113 0.864 0.000 0.028 0.068 0.036 0.004
#> GSM215107 1 0.325 0.72431 0.820 0.000 0.000 0.056 0.124 0.000
#> GSM215108 3 0.675 0.41029 0.180 0.000 0.568 0.076 0.148 0.028
#> GSM215109 3 0.239 0.74477 0.064 0.000 0.900 0.012 0.008 0.016
#> GSM215110 5 0.658 -0.00506 0.120 0.000 0.360 0.024 0.464 0.032
#> GSM215111 1 0.215 0.73176 0.912 0.000 0.004 0.044 0.036 0.004
#> GSM215112 1 0.274 0.72195 0.864 0.000 0.000 0.060 0.076 0.000
#> GSM215113 1 0.377 0.66465 0.772 0.000 0.004 0.028 0.188 0.008
#> GSM215114 1 0.321 0.71693 0.844 0.000 0.012 0.076 0.068 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> MAD:kmeans 64 9.19e-15 1.000 2
#> MAD:kmeans 57 4.19e-13 0.998 3
#> MAD:kmeans 55 6.87e-12 0.941 4
#> MAD:kmeans 60 5.88e-13 0.963 5
#> MAD:kmeans 44 1.51e-09 0.873 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 51941 rows and 64 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.603 0.735 0.843 0.2167 0.933 0.864
#> 4 4 0.509 0.484 0.704 0.1707 0.849 0.653
#> 5 5 0.509 0.413 0.616 0.0684 0.955 0.856
#> 6 6 0.516 0.298 0.594 0.0456 0.928 0.759
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.3941 0.9251 0.000 0.844 0.156
#> GSM215052 2 0.3482 0.9252 0.000 0.872 0.128
#> GSM215053 2 0.3551 0.9224 0.000 0.868 0.132
#> GSM215054 2 0.3879 0.9146 0.000 0.848 0.152
#> GSM215055 2 0.3619 0.9220 0.000 0.864 0.136
#> GSM215056 2 0.3879 0.9175 0.000 0.848 0.152
#> GSM215057 2 0.3879 0.9241 0.000 0.848 0.152
#> GSM215058 2 0.5178 0.8729 0.000 0.744 0.256
#> GSM215059 2 0.1860 0.9320 0.000 0.948 0.052
#> GSM215060 2 0.2796 0.9253 0.000 0.908 0.092
#> GSM215061 2 0.1753 0.9360 0.000 0.952 0.048
#> GSM215062 2 0.4452 0.8740 0.000 0.808 0.192
#> GSM215063 2 0.4121 0.9114 0.000 0.832 0.168
#> GSM215064 2 0.4452 0.8740 0.000 0.808 0.192
#> GSM215065 2 0.1753 0.9327 0.000 0.952 0.048
#> GSM215066 2 0.1411 0.9304 0.000 0.964 0.036
#> GSM215067 2 0.3816 0.9156 0.000 0.852 0.148
#> GSM215068 2 0.1529 0.9296 0.000 0.960 0.040
#> GSM215069 2 0.1289 0.9317 0.000 0.968 0.032
#> GSM215070 2 0.3412 0.9283 0.000 0.876 0.124
#> GSM215071 2 0.1289 0.9341 0.000 0.968 0.032
#> GSM215072 2 0.4235 0.8937 0.000 0.824 0.176
#> GSM215073 2 0.1411 0.9311 0.000 0.964 0.036
#> GSM215074 2 0.2711 0.9290 0.000 0.912 0.088
#> GSM215075 2 0.1964 0.9361 0.000 0.944 0.056
#> GSM215076 2 0.4931 0.8769 0.000 0.768 0.232
#> GSM215077 2 0.1411 0.9333 0.000 0.964 0.036
#> GSM215078 2 0.1753 0.9361 0.000 0.952 0.048
#> GSM215079 2 0.2066 0.9351 0.000 0.940 0.060
#> GSM215080 2 0.2165 0.9308 0.000 0.936 0.064
#> GSM215081 2 0.4346 0.8776 0.000 0.816 0.184
#> GSM215082 2 0.3192 0.9261 0.000 0.888 0.112
#> GSM215083 1 0.6095 -0.1515 0.608 0.000 0.392
#> GSM215084 1 0.2448 0.7397 0.924 0.000 0.076
#> GSM215085 1 0.6309 -0.6261 0.504 0.000 0.496
#> GSM215086 3 0.5905 0.8901 0.352 0.000 0.648
#> GSM215087 1 0.1289 0.7320 0.968 0.000 0.032
#> GSM215088 3 0.6140 0.8514 0.404 0.000 0.596
#> GSM215089 1 0.3038 0.7328 0.896 0.000 0.104
#> GSM215090 1 0.2959 0.7326 0.900 0.000 0.100
#> GSM215091 1 0.3116 0.7110 0.892 0.000 0.108
#> GSM215092 1 0.4702 0.6033 0.788 0.000 0.212
#> GSM215093 3 0.5905 0.8912 0.352 0.000 0.648
#> GSM215094 1 0.1163 0.7326 0.972 0.000 0.028
#> GSM215095 1 0.0237 0.7222 0.996 0.000 0.004
#> GSM215096 1 0.1411 0.7346 0.964 0.000 0.036
#> GSM215097 1 0.5650 0.3271 0.688 0.000 0.312
#> GSM215098 1 0.3412 0.7204 0.876 0.000 0.124
#> GSM215099 1 0.3116 0.7325 0.892 0.000 0.108
#> GSM215100 1 0.3816 0.7047 0.852 0.000 0.148
#> GSM215101 1 0.3941 0.6980 0.844 0.000 0.156
#> GSM215102 1 0.6274 -0.4727 0.544 0.000 0.456
#> GSM215103 1 0.6008 -0.0514 0.628 0.000 0.372
#> GSM215104 1 0.5016 0.5187 0.760 0.000 0.240
#> GSM215105 1 0.2448 0.7394 0.924 0.000 0.076
#> GSM215106 1 0.3192 0.7239 0.888 0.000 0.112
#> GSM215107 1 0.2796 0.7371 0.908 0.000 0.092
#> GSM215108 1 0.6291 -0.5131 0.532 0.000 0.468
#> GSM215109 3 0.5948 0.8907 0.360 0.000 0.640
#> GSM215110 3 0.6286 0.6985 0.464 0.000 0.536
#> GSM215111 1 0.2878 0.7325 0.904 0.000 0.096
#> GSM215112 1 0.0592 0.7255 0.988 0.000 0.012
#> GSM215113 1 0.2959 0.7357 0.900 0.000 0.100
#> GSM215114 1 0.1753 0.7365 0.952 0.000 0.048
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.544 0.2230 0.000 0.596 0.020 0.384
#> GSM215052 2 0.549 0.0423 0.000 0.532 0.016 0.452
#> GSM215053 2 0.416 0.4748 0.000 0.768 0.008 0.224
#> GSM215054 2 0.419 0.4469 0.000 0.764 0.008 0.228
#> GSM215055 2 0.335 0.5014 0.000 0.836 0.004 0.160
#> GSM215056 2 0.402 0.4459 0.000 0.792 0.012 0.196
#> GSM215057 2 0.479 0.3452 0.000 0.680 0.008 0.312
#> GSM215058 4 0.514 0.3548 0.000 0.360 0.012 0.628
#> GSM215059 2 0.401 0.4885 0.000 0.756 0.000 0.244
#> GSM215060 2 0.276 0.5375 0.000 0.872 0.000 0.128
#> GSM215061 2 0.477 0.4640 0.000 0.684 0.008 0.308
#> GSM215062 4 0.485 0.5896 0.000 0.268 0.020 0.712
#> GSM215063 2 0.417 0.4065 0.000 0.776 0.012 0.212
#> GSM215064 4 0.471 0.6059 0.000 0.248 0.020 0.732
#> GSM215065 2 0.422 0.4866 0.000 0.748 0.004 0.248
#> GSM215066 2 0.511 0.2812 0.000 0.608 0.008 0.384
#> GSM215067 2 0.405 0.4110 0.000 0.768 0.004 0.228
#> GSM215068 2 0.527 0.0806 0.000 0.536 0.008 0.456
#> GSM215069 2 0.474 0.4151 0.000 0.668 0.004 0.328
#> GSM215070 2 0.525 -0.0174 0.000 0.552 0.008 0.440
#> GSM215071 2 0.488 0.4321 0.000 0.664 0.008 0.328
#> GSM215072 4 0.525 0.5725 0.000 0.336 0.020 0.644
#> GSM215073 2 0.412 0.5099 0.000 0.772 0.008 0.220
#> GSM215074 2 0.371 0.5166 0.000 0.804 0.004 0.192
#> GSM215075 2 0.543 0.3196 0.000 0.568 0.016 0.416
#> GSM215076 4 0.511 0.5131 0.000 0.308 0.020 0.672
#> GSM215077 2 0.504 0.3484 0.000 0.628 0.008 0.364
#> GSM215078 2 0.465 0.4477 0.000 0.704 0.008 0.288
#> GSM215079 2 0.534 0.1171 0.000 0.564 0.012 0.424
#> GSM215080 4 0.530 -0.0356 0.000 0.496 0.008 0.496
#> GSM215081 4 0.503 0.5700 0.000 0.312 0.016 0.672
#> GSM215082 4 0.525 0.2786 0.000 0.440 0.008 0.552
#> GSM215083 3 0.607 0.2571 0.456 0.000 0.500 0.044
#> GSM215084 1 0.366 0.7035 0.836 0.000 0.144 0.020
#> GSM215085 3 0.551 0.5748 0.332 0.000 0.636 0.032
#> GSM215086 3 0.344 0.6671 0.136 0.000 0.848 0.016
#> GSM215087 1 0.382 0.7005 0.840 0.000 0.120 0.040
#> GSM215088 3 0.410 0.6574 0.192 0.000 0.792 0.016
#> GSM215089 1 0.442 0.6856 0.784 0.000 0.184 0.032
#> GSM215090 1 0.422 0.6868 0.792 0.000 0.184 0.024
#> GSM215091 1 0.484 0.6597 0.756 0.000 0.200 0.044
#> GSM215092 1 0.496 0.4964 0.696 0.000 0.284 0.020
#> GSM215093 3 0.350 0.6653 0.132 0.000 0.848 0.020
#> GSM215094 1 0.205 0.7208 0.928 0.000 0.064 0.008
#> GSM215095 1 0.136 0.7156 0.960 0.000 0.032 0.008
#> GSM215096 1 0.361 0.7121 0.840 0.000 0.140 0.020
#> GSM215097 1 0.577 -0.0149 0.512 0.000 0.460 0.028
#> GSM215098 1 0.531 0.5834 0.692 0.000 0.268 0.040
#> GSM215099 1 0.410 0.6843 0.792 0.000 0.192 0.016
#> GSM215100 1 0.490 0.6388 0.724 0.000 0.248 0.028
#> GSM215101 1 0.397 0.6906 0.804 0.000 0.180 0.016
#> GSM215102 3 0.576 0.3445 0.452 0.000 0.520 0.028
#> GSM215103 1 0.627 -0.0117 0.484 0.000 0.460 0.056
#> GSM215104 1 0.534 0.5058 0.668 0.000 0.300 0.032
#> GSM215105 1 0.415 0.7073 0.804 0.000 0.168 0.028
#> GSM215106 1 0.493 0.6341 0.728 0.000 0.240 0.032
#> GSM215107 1 0.320 0.7228 0.856 0.000 0.136 0.008
#> GSM215108 3 0.533 0.4770 0.420 0.000 0.568 0.012
#> GSM215109 3 0.361 0.6679 0.140 0.000 0.840 0.020
#> GSM215110 3 0.530 0.4813 0.408 0.000 0.580 0.012
#> GSM215111 1 0.365 0.7072 0.832 0.000 0.152 0.016
#> GSM215112 1 0.252 0.7153 0.908 0.000 0.076 0.016
#> GSM215113 1 0.366 0.7236 0.840 0.000 0.136 0.024
#> GSM215114 1 0.455 0.6714 0.784 0.000 0.172 0.044
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 4 0.653 -0.1055 0.000 0.304 0.004 0.496 NA
#> GSM215052 2 0.649 0.0549 0.000 0.436 0.008 0.412 NA
#> GSM215053 2 0.626 0.3566 0.000 0.516 0.000 0.312 NA
#> GSM215054 2 0.662 0.2838 0.000 0.420 0.000 0.360 NA
#> GSM215055 2 0.592 0.4161 0.000 0.596 0.000 0.220 NA
#> GSM215056 2 0.668 0.3468 0.000 0.476 0.004 0.244 NA
#> GSM215057 2 0.661 0.2136 0.000 0.460 0.004 0.344 NA
#> GSM215058 4 0.509 0.3578 0.000 0.196 0.000 0.692 NA
#> GSM215059 2 0.459 0.4510 0.000 0.748 0.000 0.132 NA
#> GSM215060 2 0.520 0.4734 0.000 0.688 0.000 0.152 NA
#> GSM215061 2 0.465 0.4389 0.000 0.736 0.000 0.172 NA
#> GSM215062 4 0.557 0.4766 0.000 0.364 0.004 0.564 NA
#> GSM215063 2 0.689 0.2580 0.000 0.392 0.004 0.332 NA
#> GSM215064 4 0.551 0.5002 0.000 0.344 0.004 0.584 NA
#> GSM215065 2 0.306 0.4566 0.000 0.860 0.000 0.096 NA
#> GSM215066 2 0.517 0.3132 0.000 0.668 0.000 0.240 NA
#> GSM215067 2 0.668 0.2686 0.000 0.408 0.000 0.352 NA
#> GSM215068 2 0.462 0.2872 0.000 0.720 0.000 0.216 NA
#> GSM215069 2 0.214 0.4464 0.000 0.912 0.000 0.068 NA
#> GSM215070 2 0.637 0.0153 0.000 0.464 0.004 0.388 NA
#> GSM215071 2 0.370 0.4579 0.000 0.820 0.000 0.084 NA
#> GSM215072 4 0.559 0.4124 0.000 0.372 0.000 0.548 NA
#> GSM215073 2 0.365 0.4782 0.000 0.824 0.000 0.088 NA
#> GSM215074 2 0.606 0.4031 0.000 0.588 0.004 0.244 NA
#> GSM215075 2 0.582 0.3018 0.000 0.592 0.004 0.292 NA
#> GSM215076 4 0.544 0.4593 0.000 0.244 0.004 0.652 NA
#> GSM215077 2 0.564 0.2632 0.000 0.632 0.004 0.248 NA
#> GSM215078 2 0.586 0.3321 0.000 0.600 0.008 0.284 NA
#> GSM215079 2 0.552 0.2691 0.000 0.652 0.004 0.228 NA
#> GSM215080 2 0.497 0.2280 0.000 0.676 0.004 0.264 NA
#> GSM215081 4 0.555 0.4714 0.000 0.380 0.004 0.552 NA
#> GSM215082 4 0.607 0.2037 0.000 0.424 0.000 0.456 NA
#> GSM215083 3 0.655 0.2973 0.352 0.000 0.464 0.004 NA
#> GSM215084 1 0.433 0.6108 0.768 0.000 0.164 0.004 NA
#> GSM215085 3 0.571 0.4817 0.292 0.000 0.592 0.000 NA
#> GSM215086 3 0.370 0.5772 0.100 0.000 0.820 0.000 NA
#> GSM215087 1 0.443 0.5958 0.756 0.000 0.084 0.000 NA
#> GSM215088 3 0.483 0.5494 0.176 0.000 0.720 0.000 NA
#> GSM215089 1 0.498 0.5637 0.700 0.000 0.200 0.000 NA
#> GSM215090 1 0.475 0.6178 0.736 0.000 0.172 0.004 NA
#> GSM215091 1 0.576 0.4936 0.620 0.000 0.188 0.000 NA
#> GSM215092 1 0.549 0.4913 0.636 0.000 0.248 0.000 NA
#> GSM215093 3 0.356 0.5754 0.108 0.000 0.828 0.000 NA
#> GSM215094 1 0.330 0.6455 0.848 0.000 0.068 0.000 NA
#> GSM215095 1 0.217 0.6378 0.912 0.000 0.024 0.000 NA
#> GSM215096 1 0.459 0.6090 0.748 0.000 0.120 0.000 NA
#> GSM215097 1 0.649 -0.0667 0.420 0.000 0.416 0.004 NA
#> GSM215098 1 0.583 0.4593 0.616 0.000 0.240 0.004 NA
#> GSM215099 1 0.515 0.5631 0.684 0.000 0.204 0.000 NA
#> GSM215100 1 0.549 0.5516 0.648 0.000 0.216 0.000 NA
#> GSM215101 1 0.548 0.5359 0.656 0.000 0.176 0.000 NA
#> GSM215102 3 0.600 0.2499 0.368 0.000 0.512 0.000 NA
#> GSM215103 3 0.663 0.0115 0.388 0.000 0.392 0.000 NA
#> GSM215104 1 0.578 0.3746 0.584 0.000 0.312 0.004 NA
#> GSM215105 1 0.501 0.5957 0.708 0.000 0.156 0.000 NA
#> GSM215106 1 0.595 0.4912 0.592 0.000 0.192 0.000 NA
#> GSM215107 1 0.494 0.5885 0.712 0.000 0.172 0.000 NA
#> GSM215108 3 0.596 0.3852 0.340 0.000 0.536 0.000 NA
#> GSM215109 3 0.336 0.5796 0.080 0.000 0.844 0.000 NA
#> GSM215110 3 0.580 0.3944 0.312 0.000 0.572 0.000 NA
#> GSM215111 1 0.493 0.6005 0.716 0.000 0.144 0.000 NA
#> GSM215112 1 0.367 0.6256 0.820 0.000 0.068 0.000 NA
#> GSM215113 1 0.480 0.6037 0.720 0.000 0.184 0.000 NA
#> GSM215114 1 0.534 0.5459 0.660 0.000 0.116 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 4 0.704 0.1537 0.000 0.256 0.000 0.444 0.200 0.100
#> GSM215052 2 0.708 0.0442 0.000 0.384 0.000 0.288 0.252 0.076
#> GSM215053 2 0.649 -0.0796 0.000 0.472 0.008 0.356 0.108 0.056
#> GSM215054 4 0.621 0.3204 0.000 0.332 0.004 0.516 0.088 0.060
#> GSM215055 2 0.591 -0.1612 0.000 0.508 0.004 0.372 0.076 0.040
#> GSM215056 4 0.531 0.3617 0.000 0.368 0.000 0.552 0.048 0.032
#> GSM215057 4 0.623 0.2276 0.000 0.412 0.000 0.428 0.116 0.044
#> GSM215058 5 0.676 0.2621 0.000 0.172 0.004 0.352 0.420 0.052
#> GSM215059 2 0.505 0.2072 0.000 0.652 0.000 0.252 0.072 0.024
#> GSM215060 2 0.438 0.1142 0.000 0.664 0.000 0.296 0.028 0.012
#> GSM215061 2 0.528 0.3858 0.000 0.684 0.004 0.168 0.104 0.040
#> GSM215062 5 0.415 0.5930 0.000 0.176 0.000 0.076 0.744 0.004
#> GSM215063 4 0.502 0.4758 0.000 0.272 0.000 0.644 0.056 0.028
#> GSM215064 5 0.363 0.5961 0.000 0.176 0.000 0.040 0.780 0.004
#> GSM215065 2 0.395 0.3832 0.000 0.772 0.000 0.136 0.088 0.004
#> GSM215066 2 0.518 0.3898 0.000 0.664 0.000 0.068 0.224 0.044
#> GSM215067 4 0.564 0.4542 0.000 0.336 0.000 0.548 0.088 0.028
#> GSM215068 2 0.548 0.3981 0.000 0.624 0.000 0.128 0.224 0.024
#> GSM215069 2 0.468 0.4264 0.000 0.724 0.000 0.128 0.128 0.020
#> GSM215070 2 0.683 -0.0282 0.000 0.436 0.004 0.228 0.284 0.048
#> GSM215071 2 0.468 0.3695 0.000 0.724 0.000 0.136 0.120 0.020
#> GSM215072 5 0.561 0.5056 0.000 0.272 0.000 0.124 0.584 0.020
#> GSM215073 2 0.392 0.3522 0.000 0.772 0.000 0.164 0.052 0.012
#> GSM215074 2 0.520 0.1714 0.000 0.636 0.000 0.268 0.056 0.040
#> GSM215075 2 0.634 0.2974 0.000 0.552 0.000 0.208 0.176 0.064
#> GSM215076 5 0.631 0.4483 0.000 0.248 0.004 0.160 0.544 0.044
#> GSM215077 2 0.501 0.4074 0.000 0.708 0.000 0.148 0.096 0.048
#> GSM215078 2 0.535 0.3637 0.000 0.664 0.000 0.164 0.136 0.036
#> GSM215079 2 0.616 0.3058 0.000 0.556 0.000 0.156 0.240 0.048
#> GSM215080 2 0.510 0.3920 0.000 0.664 0.000 0.068 0.232 0.036
#> GSM215081 5 0.440 0.5514 0.000 0.272 0.000 0.036 0.680 0.012
#> GSM215082 5 0.674 0.1189 0.000 0.364 0.000 0.224 0.368 0.044
#> GSM215083 1 0.710 -0.2932 0.364 0.000 0.328 0.028 0.024 0.256
#> GSM215084 1 0.457 0.4770 0.748 0.000 0.120 0.004 0.024 0.104
#> GSM215085 3 0.675 0.0387 0.280 0.000 0.496 0.024 0.036 0.164
#> GSM215086 3 0.474 0.3439 0.072 0.000 0.756 0.036 0.020 0.116
#> GSM215087 1 0.557 0.3337 0.608 0.000 0.068 0.024 0.016 0.284
#> GSM215088 3 0.585 0.2593 0.116 0.000 0.592 0.028 0.008 0.256
#> GSM215089 1 0.610 0.3561 0.576 0.000 0.160 0.020 0.016 0.228
#> GSM215090 1 0.479 0.4643 0.692 0.000 0.112 0.004 0.004 0.188
#> GSM215091 1 0.638 0.1108 0.444 0.000 0.116 0.028 0.016 0.396
#> GSM215092 1 0.617 0.3075 0.564 0.000 0.228 0.024 0.012 0.172
#> GSM215093 3 0.491 0.3362 0.072 0.000 0.740 0.032 0.024 0.132
#> GSM215094 1 0.427 0.4960 0.776 0.000 0.044 0.016 0.024 0.140
#> GSM215095 1 0.357 0.4950 0.828 0.000 0.028 0.012 0.024 0.108
#> GSM215096 1 0.536 0.3631 0.624 0.000 0.068 0.024 0.008 0.276
#> GSM215097 1 0.712 -0.0444 0.388 0.000 0.292 0.036 0.020 0.264
#> GSM215098 1 0.642 0.2871 0.560 0.000 0.152 0.028 0.028 0.232
#> GSM215099 1 0.505 0.4764 0.688 0.000 0.116 0.008 0.012 0.176
#> GSM215100 1 0.581 0.4008 0.592 0.000 0.152 0.012 0.012 0.232
#> GSM215101 1 0.620 0.3735 0.572 0.000 0.132 0.020 0.028 0.248
#> GSM215102 3 0.628 0.0684 0.372 0.000 0.448 0.004 0.024 0.152
#> GSM215103 6 0.717 0.0000 0.272 0.000 0.308 0.032 0.024 0.364
#> GSM215104 1 0.627 0.2537 0.584 0.000 0.176 0.028 0.024 0.188
#> GSM215105 1 0.491 0.4179 0.696 0.000 0.096 0.004 0.016 0.188
#> GSM215106 1 0.575 0.2154 0.540 0.000 0.100 0.004 0.020 0.336
#> GSM215107 1 0.507 0.4510 0.700 0.000 0.100 0.008 0.024 0.168
#> GSM215108 3 0.642 0.1148 0.324 0.000 0.496 0.016 0.028 0.136
#> GSM215109 3 0.288 0.3639 0.076 0.000 0.872 0.004 0.020 0.028
#> GSM215110 3 0.592 0.2419 0.308 0.000 0.536 0.000 0.028 0.128
#> GSM215111 1 0.541 0.3704 0.660 0.000 0.084 0.016 0.024 0.216
#> GSM215112 1 0.426 0.4548 0.736 0.000 0.020 0.012 0.020 0.212
#> GSM215113 1 0.499 0.4655 0.732 0.000 0.096 0.016 0.036 0.120
#> GSM215114 1 0.572 0.2637 0.556 0.000 0.060 0.012 0.032 0.340
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> MAD:skmeans 64 9.19e-15 1.000 2
#> MAD:skmeans 58 2.54e-13 0.998 3
#> MAD:skmeans 34 1.98e-07 0.738 4
#> MAD:skmeans 21 2.75e-05 0.788 5
#> MAD:skmeans 4 NA NA 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 51941 rows and 64 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.779 0.694 0.802 0.2193 0.885 0.767
#> 4 4 0.571 0.497 0.705 0.1231 0.898 0.733
#> 5 5 0.559 0.400 0.713 0.0327 0.862 0.607
#> 6 6 0.550 0.540 0.682 0.0242 0.893 0.660
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.1411 0.9631 0.000 0.964 0.036
#> GSM215052 2 0.0892 0.9693 0.000 0.980 0.020
#> GSM215053 2 0.1163 0.9643 0.000 0.972 0.028
#> GSM215054 2 0.1163 0.9643 0.000 0.972 0.028
#> GSM215055 2 0.2066 0.9627 0.000 0.940 0.060
#> GSM215056 2 0.1289 0.9690 0.000 0.968 0.032
#> GSM215057 2 0.1643 0.9655 0.000 0.956 0.044
#> GSM215058 2 0.1753 0.9592 0.000 0.952 0.048
#> GSM215059 2 0.2066 0.9627 0.000 0.940 0.060
#> GSM215060 2 0.2066 0.9627 0.000 0.940 0.060
#> GSM215061 2 0.2066 0.9627 0.000 0.940 0.060
#> GSM215062 2 0.2537 0.9607 0.000 0.920 0.080
#> GSM215063 2 0.2066 0.9627 0.000 0.940 0.060
#> GSM215064 2 0.2261 0.9663 0.000 0.932 0.068
#> GSM215065 2 0.2066 0.9627 0.000 0.940 0.060
#> GSM215066 2 0.1643 0.9666 0.000 0.956 0.044
#> GSM215067 2 0.1529 0.9664 0.000 0.960 0.040
#> GSM215068 2 0.1753 0.9650 0.000 0.952 0.048
#> GSM215069 2 0.2066 0.9627 0.000 0.940 0.060
#> GSM215070 2 0.1411 0.9667 0.000 0.964 0.036
#> GSM215071 2 0.2066 0.9627 0.000 0.940 0.060
#> GSM215072 2 0.1753 0.9643 0.000 0.952 0.048
#> GSM215073 2 0.2066 0.9627 0.000 0.940 0.060
#> GSM215074 2 0.1031 0.9673 0.000 0.976 0.024
#> GSM215075 2 0.1964 0.9634 0.000 0.944 0.056
#> GSM215076 2 0.1643 0.9610 0.000 0.956 0.044
#> GSM215077 2 0.1163 0.9680 0.000 0.972 0.028
#> GSM215078 2 0.1031 0.9672 0.000 0.976 0.024
#> GSM215079 2 0.1643 0.9608 0.000 0.956 0.044
#> GSM215080 2 0.0747 0.9692 0.000 0.984 0.016
#> GSM215081 2 0.1643 0.9610 0.000 0.956 0.044
#> GSM215082 2 0.1753 0.9592 0.000 0.952 0.048
#> GSM215083 3 0.5988 0.5471 0.368 0.000 0.632
#> GSM215084 1 0.0424 0.5872 0.992 0.000 0.008
#> GSM215085 3 0.6309 0.3686 0.500 0.000 0.500
#> GSM215086 3 0.4974 0.7812 0.236 0.000 0.764
#> GSM215087 1 0.2448 0.5883 0.924 0.000 0.076
#> GSM215088 3 0.4974 0.7806 0.236 0.000 0.764
#> GSM215089 1 0.6180 0.1973 0.584 0.000 0.416
#> GSM215090 1 0.3116 0.5779 0.892 0.000 0.108
#> GSM215091 3 0.4842 0.7690 0.224 0.000 0.776
#> GSM215092 1 0.3619 0.5528 0.864 0.000 0.136
#> GSM215093 3 0.5216 0.7773 0.260 0.000 0.740
#> GSM215094 1 0.4002 0.4716 0.840 0.000 0.160
#> GSM215095 1 0.1529 0.5924 0.960 0.000 0.040
#> GSM215096 3 0.6308 0.3899 0.492 0.000 0.508
#> GSM215097 3 0.4796 0.7694 0.220 0.000 0.780
#> GSM215098 1 0.6295 -0.3373 0.528 0.000 0.472
#> GSM215099 1 0.2066 0.5759 0.940 0.000 0.060
#> GSM215100 1 0.5216 0.4397 0.740 0.000 0.260
#> GSM215101 1 0.6140 0.2177 0.596 0.000 0.404
#> GSM215102 1 0.6204 -0.2248 0.576 0.000 0.424
#> GSM215103 3 0.5678 0.6677 0.316 0.000 0.684
#> GSM215104 1 0.5905 0.0114 0.648 0.000 0.352
#> GSM215105 1 0.1643 0.5867 0.956 0.000 0.044
#> GSM215106 3 0.5497 0.7562 0.292 0.000 0.708
#> GSM215107 1 0.6140 0.2155 0.596 0.000 0.404
#> GSM215108 1 0.6215 -0.2229 0.572 0.000 0.428
#> GSM215109 3 0.5905 0.6786 0.352 0.000 0.648
#> GSM215110 1 0.6008 0.3697 0.628 0.000 0.372
#> GSM215111 1 0.6215 -0.2306 0.572 0.000 0.428
#> GSM215112 1 0.1031 0.5912 0.976 0.000 0.024
#> GSM215113 1 0.1031 0.5891 0.976 0.000 0.024
#> GSM215114 1 0.6244 0.1238 0.560 0.000 0.440
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.4661 0.339 0.000 0.652 0.000 0.348
#> GSM215052 2 0.3688 0.617 0.000 0.792 0.000 0.208
#> GSM215053 2 0.4431 0.460 0.000 0.696 0.000 0.304
#> GSM215054 2 0.4522 0.423 0.000 0.680 0.000 0.320
#> GSM215055 2 0.0817 0.718 0.000 0.976 0.000 0.024
#> GSM215056 2 0.3074 0.670 0.000 0.848 0.000 0.152
#> GSM215057 2 0.4331 0.472 0.000 0.712 0.000 0.288
#> GSM215058 4 0.4661 0.764 0.000 0.348 0.000 0.652
#> GSM215059 2 0.0000 0.714 0.000 1.000 0.000 0.000
#> GSM215060 2 0.0000 0.714 0.000 1.000 0.000 0.000
#> GSM215061 2 0.0336 0.717 0.000 0.992 0.000 0.008
#> GSM215062 2 0.4855 -0.332 0.000 0.600 0.000 0.400
#> GSM215063 2 0.0000 0.714 0.000 1.000 0.000 0.000
#> GSM215064 4 0.4925 0.638 0.000 0.428 0.000 0.572
#> GSM215065 2 0.0000 0.714 0.000 1.000 0.000 0.000
#> GSM215066 2 0.4994 -0.513 0.000 0.520 0.000 0.480
#> GSM215067 2 0.1940 0.709 0.000 0.924 0.000 0.076
#> GSM215068 2 0.0921 0.718 0.000 0.972 0.000 0.028
#> GSM215069 2 0.0000 0.714 0.000 1.000 0.000 0.000
#> GSM215070 2 0.4697 0.267 0.000 0.644 0.000 0.356
#> GSM215071 2 0.0336 0.711 0.000 0.992 0.000 0.008
#> GSM215072 4 0.4585 0.773 0.000 0.332 0.000 0.668
#> GSM215073 2 0.0000 0.714 0.000 1.000 0.000 0.000
#> GSM215074 2 0.3907 0.586 0.000 0.768 0.000 0.232
#> GSM215075 2 0.1940 0.708 0.000 0.924 0.000 0.076
#> GSM215076 4 0.4898 0.653 0.000 0.416 0.000 0.584
#> GSM215077 2 0.3726 0.612 0.000 0.788 0.000 0.212
#> GSM215078 2 0.4008 0.568 0.000 0.756 0.000 0.244
#> GSM215079 4 0.5000 0.363 0.000 0.496 0.000 0.504
#> GSM215080 2 0.3172 0.664 0.000 0.840 0.000 0.160
#> GSM215081 4 0.4356 0.785 0.000 0.292 0.000 0.708
#> GSM215082 4 0.4277 0.779 0.000 0.280 0.000 0.720
#> GSM215083 3 0.4543 0.569 0.324 0.000 0.676 0.000
#> GSM215084 1 0.0657 0.585 0.984 0.000 0.012 0.004
#> GSM215085 3 0.6529 0.344 0.388 0.000 0.532 0.080
#> GSM215086 3 0.4507 0.739 0.168 0.000 0.788 0.044
#> GSM215087 1 0.2402 0.583 0.912 0.000 0.076 0.012
#> GSM215088 3 0.3539 0.754 0.176 0.000 0.820 0.004
#> GSM215089 1 0.5088 0.227 0.572 0.000 0.424 0.004
#> GSM215090 1 0.3047 0.573 0.872 0.000 0.116 0.012
#> GSM215091 3 0.3219 0.745 0.164 0.000 0.836 0.000
#> GSM215092 1 0.3196 0.555 0.856 0.000 0.136 0.008
#> GSM215093 3 0.3649 0.755 0.204 0.000 0.796 0.000
#> GSM215094 1 0.3852 0.421 0.800 0.000 0.192 0.008
#> GSM215095 1 0.1545 0.590 0.952 0.000 0.040 0.008
#> GSM215096 3 0.5360 0.423 0.436 0.000 0.552 0.012
#> GSM215097 3 0.3172 0.745 0.160 0.000 0.840 0.000
#> GSM215098 3 0.5292 0.339 0.480 0.000 0.512 0.008
#> GSM215099 1 0.2542 0.561 0.904 0.000 0.084 0.012
#> GSM215100 1 0.4283 0.452 0.740 0.000 0.256 0.004
#> GSM215101 1 0.4907 0.227 0.580 0.000 0.420 0.000
#> GSM215102 1 0.5285 -0.296 0.524 0.000 0.468 0.008
#> GSM215103 3 0.4222 0.663 0.272 0.000 0.728 0.000
#> GSM215104 1 0.5290 -0.126 0.584 0.000 0.404 0.012
#> GSM215105 1 0.1938 0.579 0.936 0.000 0.052 0.012
#> GSM215106 3 0.4122 0.738 0.236 0.000 0.760 0.004
#> GSM215107 1 0.4888 0.240 0.588 0.000 0.412 0.000
#> GSM215108 1 0.5292 -0.318 0.512 0.000 0.480 0.008
#> GSM215109 3 0.4697 0.669 0.296 0.000 0.696 0.008
#> GSM215110 1 0.7149 0.315 0.528 0.000 0.316 0.156
#> GSM215111 1 0.5404 -0.314 0.512 0.000 0.476 0.012
#> GSM215112 1 0.1305 0.588 0.960 0.000 0.036 0.004
#> GSM215113 1 0.1356 0.587 0.960 0.000 0.032 0.008
#> GSM215114 1 0.4977 0.130 0.540 0.000 0.460 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.4101 0.3766 0.000 0.628 0.000 0.000 0.372
#> GSM215052 2 0.3210 0.6544 0.000 0.788 0.000 0.000 0.212
#> GSM215053 2 0.3876 0.5064 0.000 0.684 0.000 0.000 0.316
#> GSM215054 2 0.3983 0.4606 0.000 0.660 0.000 0.000 0.340
#> GSM215055 2 0.0703 0.7444 0.000 0.976 0.000 0.000 0.024
#> GSM215056 2 0.2732 0.6975 0.000 0.840 0.000 0.000 0.160
#> GSM215057 2 0.3876 0.4762 0.000 0.684 0.000 0.000 0.316
#> GSM215058 5 0.3612 0.7468 0.000 0.268 0.000 0.000 0.732
#> GSM215059 2 0.0000 0.7407 0.000 1.000 0.000 0.000 0.000
#> GSM215060 2 0.0000 0.7407 0.000 1.000 0.000 0.000 0.000
#> GSM215061 2 0.0290 0.7432 0.000 0.992 0.000 0.000 0.008
#> GSM215062 2 0.4297 -0.4200 0.000 0.528 0.000 0.000 0.472
#> GSM215063 2 0.0000 0.7407 0.000 1.000 0.000 0.000 0.000
#> GSM215064 5 0.4030 0.6534 0.000 0.352 0.000 0.000 0.648
#> GSM215065 2 0.0000 0.7407 0.000 1.000 0.000 0.000 0.000
#> GSM215066 5 0.4304 0.4568 0.000 0.484 0.000 0.000 0.516
#> GSM215067 2 0.1732 0.7350 0.000 0.920 0.000 0.000 0.080
#> GSM215068 2 0.0794 0.7443 0.000 0.972 0.000 0.000 0.028
#> GSM215069 2 0.0000 0.7407 0.000 1.000 0.000 0.000 0.000
#> GSM215070 2 0.4101 0.3261 0.000 0.628 0.000 0.000 0.372
#> GSM215071 2 0.0290 0.7376 0.000 0.992 0.000 0.000 0.008
#> GSM215072 5 0.3534 0.7512 0.000 0.256 0.000 0.000 0.744
#> GSM215073 2 0.0162 0.7412 0.000 0.996 0.000 0.000 0.004
#> GSM215074 2 0.3508 0.6084 0.000 0.748 0.000 0.000 0.252
#> GSM215075 2 0.1671 0.7361 0.000 0.924 0.000 0.000 0.076
#> GSM215076 5 0.4030 0.6455 0.000 0.352 0.000 0.000 0.648
#> GSM215077 2 0.3274 0.6454 0.000 0.780 0.000 0.000 0.220
#> GSM215078 2 0.3561 0.5967 0.000 0.740 0.000 0.000 0.260
#> GSM215079 5 0.4273 0.3734 0.000 0.448 0.000 0.000 0.552
#> GSM215080 2 0.2773 0.6947 0.000 0.836 0.000 0.000 0.164
#> GSM215081 5 0.3177 0.7583 0.000 0.208 0.000 0.000 0.792
#> GSM215082 5 0.3039 0.7507 0.000 0.192 0.000 0.000 0.808
#> GSM215083 1 0.3983 -0.1568 0.660 0.000 0.340 0.000 0.000
#> GSM215084 1 0.5795 0.1771 0.596 0.000 0.268 0.136 0.000
#> GSM215085 3 0.6658 0.1811 0.112 0.000 0.596 0.224 0.068
#> GSM215086 1 0.7795 -0.1711 0.424 0.000 0.316 0.152 0.108
#> GSM215087 1 0.4709 0.3064 0.612 0.000 0.364 0.024 0.000
#> GSM215088 1 0.4443 -0.3325 0.524 0.000 0.472 0.000 0.004
#> GSM215089 1 0.3239 0.3408 0.852 0.000 0.080 0.068 0.000
#> GSM215090 1 0.5144 0.2981 0.632 0.000 0.304 0.064 0.000
#> GSM215091 1 0.4278 -0.3058 0.548 0.000 0.452 0.000 0.000
#> GSM215092 1 0.5413 0.1579 0.664 0.000 0.164 0.172 0.000
#> GSM215093 3 0.4307 0.2821 0.500 0.000 0.500 0.000 0.000
#> GSM215094 3 0.4658 -0.0662 0.408 0.000 0.576 0.016 0.000
#> GSM215095 1 0.5899 0.1870 0.592 0.000 0.248 0.160 0.000
#> GSM215096 3 0.3242 0.5818 0.216 0.000 0.784 0.000 0.000
#> GSM215097 1 0.4425 -0.3087 0.544 0.000 0.452 0.004 0.000
#> GSM215098 1 0.4451 -0.3030 0.504 0.000 0.492 0.004 0.000
#> GSM215099 1 0.6080 0.2604 0.520 0.000 0.344 0.136 0.000
#> GSM215100 1 0.5006 0.2682 0.708 0.000 0.156 0.136 0.000
#> GSM215101 1 0.1124 0.3449 0.960 0.000 0.036 0.004 0.000
#> GSM215102 3 0.4558 0.5515 0.208 0.000 0.728 0.064 0.000
#> GSM215103 1 0.4171 -0.2318 0.604 0.000 0.396 0.000 0.000
#> GSM215104 3 0.3596 0.5311 0.200 0.000 0.784 0.016 0.000
#> GSM215105 1 0.4610 0.2801 0.556 0.000 0.432 0.012 0.000
#> GSM215106 3 0.4278 0.3644 0.452 0.000 0.548 0.000 0.000
#> GSM215107 1 0.0404 0.3390 0.988 0.000 0.012 0.000 0.000
#> GSM215108 3 0.3988 0.5759 0.196 0.000 0.768 0.036 0.000
#> GSM215109 3 0.4879 0.4684 0.360 0.000 0.612 0.020 0.008
#> GSM215110 4 0.5188 0.0000 0.328 0.000 0.060 0.612 0.000
#> GSM215111 3 0.3210 0.5731 0.212 0.000 0.788 0.000 0.000
#> GSM215112 1 0.4969 0.2691 0.588 0.000 0.376 0.036 0.000
#> GSM215113 1 0.6024 0.2160 0.560 0.000 0.288 0.152 0.000
#> GSM215114 1 0.2074 0.2986 0.896 0.000 0.104 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 2 0.4284 0.4045 0.000 0.596 0.000 0.008 0.012 0.384
#> GSM215052 2 0.3507 0.6772 0.000 0.764 0.000 0.008 0.012 0.216
#> GSM215053 2 0.4179 0.5353 0.000 0.652 0.000 0.016 0.008 0.324
#> GSM215054 2 0.4088 0.4960 0.000 0.636 0.000 0.008 0.008 0.348
#> GSM215055 2 0.1138 0.7652 0.000 0.960 0.000 0.012 0.004 0.024
#> GSM215056 2 0.3523 0.7203 0.000 0.796 0.000 0.028 0.012 0.164
#> GSM215057 2 0.4275 0.5025 0.000 0.644 0.000 0.020 0.008 0.328
#> GSM215058 6 0.2969 0.7135 0.000 0.224 0.000 0.000 0.000 0.776
#> GSM215059 2 0.0713 0.7517 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM215060 2 0.0146 0.7589 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM215061 2 0.0260 0.7627 0.000 0.992 0.000 0.000 0.000 0.008
#> GSM215062 6 0.3866 0.4333 0.000 0.484 0.000 0.000 0.000 0.516
#> GSM215063 2 0.0632 0.7535 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM215064 6 0.3428 0.6715 0.000 0.304 0.000 0.000 0.000 0.696
#> GSM215065 2 0.0260 0.7583 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM215066 6 0.3979 0.4220 0.000 0.456 0.000 0.004 0.000 0.540
#> GSM215067 2 0.2527 0.7534 0.000 0.880 0.000 0.032 0.004 0.084
#> GSM215068 2 0.0790 0.7642 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM215069 2 0.0260 0.7583 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM215070 2 0.3993 0.3229 0.000 0.592 0.000 0.000 0.008 0.400
#> GSM215071 2 0.1230 0.7500 0.000 0.956 0.000 0.028 0.008 0.008
#> GSM215072 6 0.2854 0.7327 0.000 0.208 0.000 0.000 0.000 0.792
#> GSM215073 2 0.0146 0.7600 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM215074 2 0.4178 0.6314 0.000 0.700 0.000 0.032 0.008 0.260
#> GSM215075 2 0.1556 0.7591 0.000 0.920 0.000 0.000 0.000 0.080
#> GSM215076 6 0.3390 0.6375 0.000 0.296 0.000 0.000 0.000 0.704
#> GSM215077 2 0.3357 0.6817 0.000 0.764 0.000 0.008 0.004 0.224
#> GSM215078 2 0.3360 0.6372 0.000 0.732 0.000 0.000 0.004 0.264
#> GSM215079 6 0.4344 0.3010 0.000 0.412 0.000 0.012 0.008 0.568
#> GSM215080 2 0.2773 0.7229 0.000 0.828 0.000 0.004 0.004 0.164
#> GSM215081 6 0.2416 0.7315 0.000 0.156 0.000 0.000 0.000 0.844
#> GSM215082 6 0.2402 0.7236 0.000 0.140 0.000 0.000 0.004 0.856
#> GSM215083 3 0.3528 0.5016 0.296 0.000 0.700 0.004 0.000 0.000
#> GSM215084 1 0.2262 0.5845 0.896 0.000 0.008 0.016 0.080 0.000
#> GSM215085 5 0.8702 -0.0788 0.192 0.000 0.188 0.188 0.316 0.116
#> GSM215086 4 0.4039 0.0000 0.016 0.000 0.352 0.632 0.000 0.000
#> GSM215087 1 0.2317 0.6151 0.900 0.000 0.064 0.016 0.020 0.000
#> GSM215088 3 0.2876 0.6448 0.148 0.000 0.836 0.008 0.004 0.004
#> GSM215089 1 0.4768 0.3507 0.532 0.000 0.416 0.000 0.052 0.000
#> GSM215090 1 0.2656 0.6148 0.860 0.000 0.120 0.012 0.008 0.000
#> GSM215091 3 0.2219 0.6436 0.136 0.000 0.864 0.000 0.000 0.000
#> GSM215092 1 0.3994 0.5721 0.776 0.000 0.100 0.008 0.116 0.000
#> GSM215093 3 0.3608 0.6378 0.148 0.000 0.788 0.064 0.000 0.000
#> GSM215094 1 0.3819 0.3573 0.756 0.000 0.200 0.040 0.004 0.000
#> GSM215095 1 0.2982 0.5960 0.856 0.000 0.032 0.016 0.096 0.000
#> GSM215096 3 0.4936 0.5335 0.408 0.000 0.536 0.048 0.008 0.000
#> GSM215097 3 0.2362 0.6436 0.136 0.000 0.860 0.000 0.004 0.000
#> GSM215098 1 0.4874 -0.3055 0.484 0.000 0.472 0.020 0.024 0.000
#> GSM215099 1 0.3831 0.5978 0.804 0.000 0.092 0.024 0.080 0.000
#> GSM215100 1 0.4870 0.5777 0.696 0.000 0.168 0.016 0.120 0.000
#> GSM215101 1 0.4018 0.3549 0.580 0.000 0.412 0.000 0.008 0.000
#> GSM215102 3 0.5869 0.4304 0.428 0.000 0.456 0.056 0.060 0.000
#> GSM215103 3 0.3126 0.5848 0.248 0.000 0.752 0.000 0.000 0.000
#> GSM215104 1 0.5318 -0.4035 0.504 0.000 0.420 0.052 0.024 0.000
#> GSM215105 1 0.2619 0.5874 0.884 0.000 0.056 0.048 0.012 0.000
#> GSM215106 3 0.3398 0.6813 0.216 0.000 0.768 0.012 0.004 0.000
#> GSM215107 1 0.3915 0.3578 0.584 0.000 0.412 0.000 0.004 0.000
#> GSM215108 3 0.5459 0.4616 0.436 0.000 0.480 0.052 0.032 0.000
#> GSM215109 3 0.5072 0.6222 0.228 0.000 0.680 0.052 0.024 0.016
#> GSM215110 5 0.3804 0.1188 0.336 0.000 0.008 0.000 0.656 0.000
#> GSM215111 3 0.5018 0.4413 0.464 0.000 0.480 0.044 0.012 0.000
#> GSM215112 1 0.1515 0.6043 0.944 0.000 0.028 0.008 0.020 0.000
#> GSM215113 1 0.3243 0.6035 0.844 0.000 0.048 0.020 0.088 0.000
#> GSM215114 1 0.3851 0.2598 0.540 0.000 0.460 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> MAD:pam 64 9.19e-15 1.000 2
#> MAD:pam 50 1.39e-11 0.997 3
#> MAD:pam 42 4.01e-09 0.780 4
#> MAD:pam 30 3.06e-07 0.793 5
#> MAD:pam 45 9.25e-10 0.866 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 51941 rows and 64 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.912 0.862 0.936 0.1098 0.957 0.912
#> 4 4 0.770 0.807 0.892 0.1516 0.915 0.812
#> 5 5 0.682 0.679 0.841 0.0824 0.972 0.926
#> 6 6 0.616 0.668 0.773 0.0630 0.960 0.885
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
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.0424 0.964 0.000 0.992 0.008
#> GSM215052 2 0.0892 0.961 0.000 0.980 0.020
#> GSM215053 2 0.0237 0.964 0.000 0.996 0.004
#> GSM215054 2 0.0592 0.963 0.000 0.988 0.012
#> GSM215055 2 0.0747 0.962 0.000 0.984 0.016
#> GSM215056 2 0.0592 0.963 0.000 0.988 0.012
#> GSM215057 2 0.0747 0.963 0.000 0.984 0.016
#> GSM215058 2 0.1529 0.952 0.000 0.960 0.040
#> GSM215059 2 0.0592 0.963 0.000 0.988 0.012
#> GSM215060 2 0.0592 0.963 0.000 0.988 0.012
#> GSM215061 2 0.0000 0.964 0.000 1.000 0.000
#> GSM215062 2 0.2165 0.937 0.000 0.936 0.064
#> GSM215063 2 0.6126 0.567 0.000 0.600 0.400
#> GSM215064 2 0.2165 0.937 0.000 0.936 0.064
#> GSM215065 2 0.0592 0.963 0.000 0.988 0.012
#> GSM215066 2 0.0237 0.964 0.000 0.996 0.004
#> GSM215067 2 0.6111 0.573 0.000 0.604 0.396
#> GSM215068 2 0.0237 0.964 0.000 0.996 0.004
#> GSM215069 2 0.0000 0.964 0.000 1.000 0.000
#> GSM215070 2 0.0892 0.961 0.000 0.980 0.020
#> GSM215071 2 0.0424 0.964 0.000 0.992 0.008
#> GSM215072 2 0.1163 0.958 0.000 0.972 0.028
#> GSM215073 2 0.0747 0.962 0.000 0.984 0.016
#> GSM215074 2 0.0892 0.962 0.000 0.980 0.020
#> GSM215075 2 0.0237 0.964 0.000 0.996 0.004
#> GSM215076 2 0.2066 0.939 0.000 0.940 0.060
#> GSM215077 2 0.0237 0.964 0.000 0.996 0.004
#> GSM215078 2 0.0000 0.964 0.000 1.000 0.000
#> GSM215079 2 0.0237 0.964 0.000 0.996 0.004
#> GSM215080 2 0.0237 0.964 0.000 0.996 0.004
#> GSM215081 2 0.2066 0.939 0.000 0.940 0.060
#> GSM215082 2 0.0592 0.963 0.000 0.988 0.012
#> GSM215083 1 0.1031 0.879 0.976 0.000 0.024
#> GSM215084 1 0.0000 0.907 1.000 0.000 0.000
#> GSM215085 1 0.5650 -0.210 0.688 0.000 0.312
#> GSM215086 3 0.6291 0.996 0.468 0.000 0.532
#> GSM215087 1 0.0237 0.905 0.996 0.000 0.004
#> GSM215088 1 0.6252 -0.772 0.556 0.000 0.444
#> GSM215089 1 0.0000 0.907 1.000 0.000 0.000
#> GSM215090 1 0.0000 0.907 1.000 0.000 0.000
#> GSM215091 1 0.0592 0.898 0.988 0.000 0.012
#> GSM215092 1 0.0000 0.907 1.000 0.000 0.000
#> GSM215093 3 0.6286 0.991 0.464 0.000 0.536
#> GSM215094 1 0.0237 0.905 0.996 0.000 0.004
#> GSM215095 1 0.0000 0.907 1.000 0.000 0.000
#> GSM215096 1 0.0237 0.905 0.996 0.000 0.004
#> GSM215097 1 0.0000 0.907 1.000 0.000 0.000
#> GSM215098 1 0.0237 0.905 0.996 0.000 0.004
#> GSM215099 1 0.0000 0.907 1.000 0.000 0.000
#> GSM215100 1 0.0000 0.907 1.000 0.000 0.000
#> GSM215101 1 0.0892 0.888 0.980 0.000 0.020
#> GSM215102 1 0.0237 0.904 0.996 0.000 0.004
#> GSM215103 1 0.3116 0.727 0.892 0.000 0.108
#> GSM215104 1 0.0000 0.907 1.000 0.000 0.000
#> GSM215105 1 0.0000 0.907 1.000 0.000 0.000
#> GSM215106 1 0.0000 0.907 1.000 0.000 0.000
#> GSM215107 1 0.0000 0.907 1.000 0.000 0.000
#> GSM215108 1 0.4452 0.455 0.808 0.000 0.192
#> GSM215109 3 0.6291 0.996 0.468 0.000 0.532
#> GSM215110 1 0.4605 0.397 0.796 0.000 0.204
#> GSM215111 1 0.0000 0.907 1.000 0.000 0.000
#> GSM215112 1 0.0237 0.905 0.996 0.000 0.004
#> GSM215113 1 0.0000 0.907 1.000 0.000 0.000
#> GSM215114 1 0.0592 0.898 0.988 0.000 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.5673 0.156 0.000 0.596 0.032 0.372
#> GSM215052 2 0.1151 0.826 0.000 0.968 0.008 0.024
#> GSM215053 2 0.5659 0.242 0.000 0.600 0.032 0.368
#> GSM215054 2 0.5861 -0.124 0.000 0.492 0.032 0.476
#> GSM215055 2 0.3447 0.789 0.000 0.852 0.020 0.128
#> GSM215056 2 0.4910 0.599 0.000 0.704 0.020 0.276
#> GSM215057 2 0.3219 0.804 0.000 0.868 0.020 0.112
#> GSM215058 2 0.3597 0.724 0.000 0.836 0.016 0.148
#> GSM215059 2 0.3219 0.799 0.000 0.868 0.020 0.112
#> GSM215060 2 0.3392 0.792 0.000 0.856 0.020 0.124
#> GSM215061 2 0.1389 0.828 0.000 0.952 0.000 0.048
#> GSM215062 2 0.4194 0.673 0.000 0.800 0.028 0.172
#> GSM215063 4 0.3444 1.000 0.000 0.184 0.000 0.816
#> GSM215064 2 0.4194 0.673 0.000 0.800 0.028 0.172
#> GSM215065 2 0.2714 0.807 0.000 0.884 0.004 0.112
#> GSM215066 2 0.0188 0.827 0.000 0.996 0.000 0.004
#> GSM215067 4 0.3444 1.000 0.000 0.184 0.000 0.816
#> GSM215068 2 0.0000 0.827 0.000 1.000 0.000 0.000
#> GSM215069 2 0.2053 0.822 0.000 0.924 0.004 0.072
#> GSM215070 2 0.1767 0.830 0.000 0.944 0.012 0.044
#> GSM215071 2 0.1970 0.825 0.000 0.932 0.008 0.060
#> GSM215072 2 0.1356 0.816 0.000 0.960 0.008 0.032
#> GSM215073 2 0.2918 0.805 0.000 0.876 0.008 0.116
#> GSM215074 2 0.3280 0.800 0.000 0.860 0.016 0.124
#> GSM215075 2 0.0376 0.827 0.000 0.992 0.004 0.004
#> GSM215076 2 0.5955 0.377 0.000 0.616 0.056 0.328
#> GSM215077 2 0.0524 0.828 0.000 0.988 0.004 0.008
#> GSM215078 2 0.1576 0.830 0.000 0.948 0.004 0.048
#> GSM215079 2 0.0188 0.827 0.000 0.996 0.000 0.004
#> GSM215080 2 0.0000 0.827 0.000 1.000 0.000 0.000
#> GSM215081 2 0.4149 0.678 0.000 0.804 0.028 0.168
#> GSM215082 2 0.0657 0.829 0.000 0.984 0.004 0.012
#> GSM215083 1 0.3257 0.769 0.844 0.000 0.152 0.004
#> GSM215084 1 0.0524 0.970 0.988 0.000 0.004 0.008
#> GSM215085 3 0.4401 0.731 0.272 0.000 0.724 0.004
#> GSM215086 3 0.2216 0.734 0.092 0.000 0.908 0.000
#> GSM215087 1 0.0376 0.970 0.992 0.000 0.004 0.004
#> GSM215088 3 0.3074 0.754 0.152 0.000 0.848 0.000
#> GSM215089 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM215090 1 0.0672 0.969 0.984 0.000 0.008 0.008
#> GSM215091 1 0.0376 0.970 0.992 0.000 0.004 0.004
#> GSM215092 1 0.0376 0.971 0.992 0.000 0.004 0.004
#> GSM215093 3 0.2480 0.728 0.088 0.000 0.904 0.008
#> GSM215094 1 0.0188 0.971 0.996 0.000 0.004 0.000
#> GSM215095 1 0.0188 0.971 0.996 0.000 0.000 0.004
#> GSM215096 1 0.0188 0.971 0.996 0.000 0.000 0.004
#> GSM215097 1 0.0376 0.971 0.992 0.000 0.004 0.004
#> GSM215098 1 0.0376 0.970 0.992 0.000 0.004 0.004
#> GSM215099 1 0.0524 0.970 0.988 0.000 0.004 0.008
#> GSM215100 1 0.0524 0.970 0.988 0.000 0.004 0.008
#> GSM215101 1 0.0657 0.966 0.984 0.000 0.012 0.004
#> GSM215102 1 0.1389 0.930 0.952 0.000 0.048 0.000
#> GSM215103 1 0.3710 0.693 0.804 0.000 0.192 0.004
#> GSM215104 1 0.0376 0.971 0.992 0.000 0.004 0.004
#> GSM215105 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM215106 1 0.0376 0.971 0.992 0.000 0.004 0.004
#> GSM215107 1 0.0376 0.971 0.992 0.000 0.004 0.004
#> GSM215108 3 0.5132 0.506 0.448 0.000 0.548 0.004
#> GSM215109 3 0.2216 0.734 0.092 0.000 0.908 0.000
#> GSM215110 3 0.4933 0.558 0.432 0.000 0.568 0.000
#> GSM215111 1 0.0000 0.972 1.000 0.000 0.000 0.000
#> GSM215112 1 0.0376 0.971 0.992 0.000 0.004 0.004
#> GSM215113 1 0.0376 0.971 0.992 0.000 0.004 0.004
#> GSM215114 1 0.0657 0.966 0.984 0.000 0.012 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.6300 -0.6335 0.000 0.428 0.000 0.152 0.420
#> GSM215052 2 0.3841 0.4707 0.000 0.780 0.000 0.032 0.188
#> GSM215053 2 0.6439 -0.6390 0.000 0.416 0.000 0.176 0.408
#> GSM215054 5 0.6742 0.4266 0.000 0.276 0.000 0.316 0.408
#> GSM215055 2 0.4593 0.6278 0.000 0.736 0.000 0.184 0.080
#> GSM215056 2 0.6572 -0.0946 0.000 0.460 0.000 0.312 0.228
#> GSM215057 2 0.4133 0.6478 0.000 0.768 0.000 0.180 0.052
#> GSM215058 2 0.5546 -0.2782 0.000 0.576 0.000 0.084 0.340
#> GSM215059 2 0.3883 0.6451 0.000 0.780 0.000 0.184 0.036
#> GSM215060 2 0.3810 0.6661 0.000 0.792 0.000 0.168 0.040
#> GSM215061 2 0.1741 0.7111 0.000 0.936 0.000 0.040 0.024
#> GSM215062 2 0.3838 0.4658 0.000 0.716 0.000 0.004 0.280
#> GSM215063 4 0.1341 0.9898 0.000 0.056 0.000 0.944 0.000
#> GSM215064 2 0.3838 0.4658 0.000 0.716 0.000 0.004 0.280
#> GSM215065 2 0.3513 0.6605 0.000 0.800 0.000 0.180 0.020
#> GSM215066 2 0.0451 0.7120 0.000 0.988 0.000 0.008 0.004
#> GSM215067 4 0.1410 0.9897 0.000 0.060 0.000 0.940 0.000
#> GSM215068 2 0.0162 0.7113 0.000 0.996 0.000 0.004 0.000
#> GSM215069 2 0.2079 0.7091 0.000 0.916 0.000 0.064 0.020
#> GSM215070 2 0.2221 0.7019 0.000 0.912 0.000 0.036 0.052
#> GSM215071 2 0.1965 0.7120 0.000 0.924 0.000 0.052 0.024
#> GSM215072 2 0.2573 0.6564 0.000 0.880 0.000 0.016 0.104
#> GSM215073 2 0.3577 0.6693 0.000 0.808 0.000 0.160 0.032
#> GSM215074 2 0.3958 0.6622 0.000 0.780 0.000 0.176 0.044
#> GSM215075 2 0.1300 0.7077 0.000 0.956 0.000 0.016 0.028
#> GSM215076 5 0.5200 0.5242 0.000 0.304 0.000 0.068 0.628
#> GSM215077 2 0.1195 0.7076 0.000 0.960 0.000 0.012 0.028
#> GSM215078 2 0.3555 0.6189 0.000 0.824 0.000 0.052 0.124
#> GSM215079 2 0.0566 0.7103 0.000 0.984 0.000 0.004 0.012
#> GSM215080 2 0.0290 0.7089 0.000 0.992 0.000 0.000 0.008
#> GSM215081 2 0.3741 0.4933 0.000 0.732 0.000 0.004 0.264
#> GSM215082 2 0.0693 0.7093 0.000 0.980 0.000 0.008 0.012
#> GSM215083 1 0.5153 0.6470 0.704 0.000 0.208 0.016 0.072
#> GSM215084 1 0.1942 0.8892 0.920 0.000 0.000 0.012 0.068
#> GSM215085 3 0.4350 0.7129 0.152 0.000 0.780 0.016 0.052
#> GSM215086 3 0.0324 0.7075 0.004 0.000 0.992 0.004 0.000
#> GSM215087 1 0.2674 0.8829 0.888 0.000 0.008 0.020 0.084
#> GSM215088 3 0.2972 0.7368 0.084 0.000 0.872 0.004 0.040
#> GSM215089 1 0.0727 0.9112 0.980 0.000 0.004 0.004 0.012
#> GSM215090 1 0.2403 0.8843 0.904 0.000 0.012 0.012 0.072
#> GSM215091 1 0.2900 0.8756 0.876 0.000 0.012 0.020 0.092
#> GSM215092 1 0.0955 0.9092 0.968 0.000 0.000 0.004 0.028
#> GSM215093 3 0.1644 0.7012 0.008 0.000 0.940 0.004 0.048
#> GSM215094 1 0.0968 0.9115 0.972 0.000 0.004 0.012 0.012
#> GSM215095 1 0.1195 0.9117 0.960 0.000 0.000 0.012 0.028
#> GSM215096 1 0.2331 0.8920 0.908 0.000 0.008 0.016 0.068
#> GSM215097 1 0.2604 0.8928 0.896 0.000 0.012 0.020 0.072
#> GSM215098 1 0.1913 0.9033 0.932 0.000 0.008 0.016 0.044
#> GSM215099 1 0.2006 0.8869 0.916 0.000 0.000 0.012 0.072
#> GSM215100 1 0.2166 0.8855 0.912 0.000 0.004 0.012 0.072
#> GSM215101 1 0.3047 0.8714 0.868 0.000 0.012 0.024 0.096
#> GSM215102 1 0.2916 0.8682 0.880 0.000 0.072 0.008 0.040
#> GSM215103 1 0.5324 0.6198 0.684 0.000 0.224 0.016 0.076
#> GSM215104 1 0.1041 0.9089 0.964 0.000 0.004 0.000 0.032
#> GSM215105 1 0.1444 0.9076 0.948 0.000 0.000 0.012 0.040
#> GSM215106 1 0.1408 0.9083 0.948 0.000 0.000 0.008 0.044
#> GSM215107 1 0.0912 0.9086 0.972 0.000 0.000 0.012 0.016
#> GSM215108 3 0.5132 0.6241 0.276 0.000 0.664 0.012 0.048
#> GSM215109 3 0.0324 0.7075 0.004 0.000 0.992 0.004 0.000
#> GSM215110 3 0.5388 0.5332 0.360 0.000 0.580 0.004 0.056
#> GSM215111 1 0.1444 0.9076 0.948 0.000 0.000 0.012 0.040
#> GSM215112 1 0.0960 0.9124 0.972 0.000 0.004 0.008 0.016
#> GSM215113 1 0.1195 0.9058 0.960 0.000 0.000 0.012 0.028
#> GSM215114 1 0.3150 0.8698 0.864 0.000 0.016 0.024 0.096
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 4 0.5461 0.7140 0.000 0.336 0.000 0.556 0.092 0.016
#> GSM215052 2 0.4985 0.2289 0.000 0.660 0.000 0.252 0.032 0.056
#> GSM215053 4 0.5472 0.7088 0.000 0.328 0.000 0.556 0.104 0.012
#> GSM215054 4 0.5852 0.5048 0.000 0.192 0.000 0.544 0.252 0.012
#> GSM215055 2 0.5843 0.5747 0.000 0.636 0.000 0.088 0.152 0.124
#> GSM215056 2 0.7298 -0.0745 0.000 0.396 0.000 0.232 0.252 0.120
#> GSM215057 2 0.5470 0.6060 0.000 0.672 0.000 0.068 0.136 0.124
#> GSM215058 4 0.5313 0.4543 0.000 0.464 0.000 0.464 0.036 0.036
#> GSM215059 2 0.4488 0.6581 0.000 0.752 0.000 0.060 0.140 0.048
#> GSM215060 2 0.5005 0.6397 0.000 0.712 0.000 0.068 0.148 0.072
#> GSM215061 2 0.2365 0.6911 0.000 0.896 0.000 0.068 0.024 0.012
#> GSM215062 2 0.4659 0.3977 0.000 0.612 0.004 0.336 0.000 0.048
#> GSM215063 5 0.0891 1.0000 0.000 0.024 0.000 0.008 0.968 0.000
#> GSM215064 2 0.4672 0.3940 0.000 0.608 0.004 0.340 0.000 0.048
#> GSM215065 2 0.4029 0.6738 0.000 0.784 0.000 0.052 0.132 0.032
#> GSM215066 2 0.1498 0.6943 0.000 0.940 0.000 0.032 0.000 0.028
#> GSM215067 5 0.0891 1.0000 0.000 0.024 0.000 0.008 0.968 0.000
#> GSM215068 2 0.1565 0.6981 0.000 0.940 0.000 0.028 0.004 0.028
#> GSM215069 2 0.2972 0.7023 0.000 0.868 0.000 0.052 0.048 0.032
#> GSM215070 2 0.3332 0.6610 0.000 0.840 0.000 0.072 0.020 0.068
#> GSM215071 2 0.2171 0.7086 0.000 0.912 0.000 0.040 0.032 0.016
#> GSM215072 2 0.3958 0.5907 0.000 0.784 0.000 0.136 0.020 0.060
#> GSM215073 2 0.3760 0.6780 0.000 0.800 0.000 0.052 0.128 0.020
#> GSM215074 2 0.5241 0.6364 0.000 0.692 0.000 0.076 0.152 0.080
#> GSM215075 2 0.2349 0.6732 0.000 0.892 0.000 0.080 0.008 0.020
#> GSM215076 4 0.3407 0.5042 0.000 0.168 0.000 0.800 0.016 0.016
#> GSM215077 2 0.2527 0.6685 0.000 0.880 0.000 0.084 0.004 0.032
#> GSM215078 2 0.4738 0.4817 0.000 0.712 0.000 0.192 0.056 0.040
#> GSM215079 2 0.1480 0.6909 0.000 0.940 0.000 0.040 0.000 0.020
#> GSM215080 2 0.1408 0.6917 0.000 0.944 0.000 0.036 0.000 0.020
#> GSM215081 2 0.4522 0.4531 0.000 0.648 0.004 0.300 0.000 0.048
#> GSM215082 2 0.1832 0.7042 0.000 0.928 0.000 0.032 0.008 0.032
#> GSM215083 1 0.5664 0.4206 0.548 0.000 0.264 0.000 0.004 0.184
#> GSM215084 1 0.2664 0.7267 0.816 0.000 0.000 0.000 0.000 0.184
#> GSM215085 3 0.3973 0.7154 0.084 0.000 0.768 0.000 0.004 0.144
#> GSM215086 3 0.0291 0.7096 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM215087 1 0.3330 0.7402 0.716 0.000 0.000 0.000 0.000 0.284
#> GSM215088 3 0.3510 0.7339 0.032 0.000 0.812 0.020 0.000 0.136
#> GSM215089 1 0.1753 0.8202 0.912 0.000 0.004 0.000 0.000 0.084
#> GSM215090 1 0.2902 0.7170 0.800 0.000 0.004 0.000 0.000 0.196
#> GSM215091 1 0.3830 0.6788 0.620 0.000 0.004 0.000 0.000 0.376
#> GSM215092 1 0.1910 0.8150 0.892 0.000 0.000 0.000 0.000 0.108
#> GSM215093 3 0.4315 0.6279 0.012 0.000 0.776 0.032 0.048 0.132
#> GSM215094 1 0.1444 0.8166 0.928 0.000 0.000 0.000 0.000 0.072
#> GSM215095 1 0.1501 0.8136 0.924 0.000 0.000 0.000 0.000 0.076
#> GSM215096 1 0.3383 0.7568 0.728 0.000 0.004 0.000 0.000 0.268
#> GSM215097 1 0.3424 0.7800 0.780 0.000 0.020 0.000 0.004 0.196
#> GSM215098 1 0.2462 0.8072 0.860 0.000 0.004 0.000 0.004 0.132
#> GSM215099 1 0.2762 0.7191 0.804 0.000 0.000 0.000 0.000 0.196
#> GSM215100 1 0.2871 0.7138 0.804 0.000 0.004 0.000 0.000 0.192
#> GSM215101 1 0.3684 0.6746 0.628 0.000 0.000 0.000 0.000 0.372
#> GSM215102 1 0.4151 0.7406 0.744 0.000 0.076 0.000 0.004 0.176
#> GSM215103 1 0.5536 0.5244 0.536 0.000 0.164 0.000 0.000 0.300
#> GSM215104 1 0.1949 0.8127 0.904 0.000 0.004 0.000 0.004 0.088
#> GSM215105 1 0.1204 0.8118 0.944 0.000 0.000 0.000 0.000 0.056
#> GSM215106 1 0.2053 0.8098 0.888 0.000 0.004 0.000 0.000 0.108
#> GSM215107 1 0.0790 0.8142 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM215108 3 0.5207 0.6158 0.212 0.000 0.628 0.000 0.004 0.156
#> GSM215109 3 0.0436 0.7091 0.004 0.000 0.988 0.000 0.004 0.004
#> GSM215110 3 0.5572 0.5766 0.260 0.000 0.588 0.008 0.004 0.140
#> GSM215111 1 0.0632 0.8126 0.976 0.000 0.000 0.000 0.000 0.024
#> GSM215112 1 0.1327 0.8156 0.936 0.000 0.000 0.000 0.000 0.064
#> GSM215113 1 0.0790 0.8081 0.968 0.000 0.000 0.000 0.000 0.032
#> GSM215114 1 0.3659 0.6777 0.636 0.000 0.000 0.000 0.000 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 disease.state(p) individual(p) k
#> MAD:mclust 64 9.19e-15 1.000 2
#> MAD:mclust 60 9.36e-14 0.999 3
#> MAD:mclust 60 5.88e-13 0.926 4
#> MAD:mclust 55 3.25e-11 0.937 5
#> MAD:mclust 56 2.01e-11 0.893 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 51941 rows and 64 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.764 0.809 0.897 0.1883 0.944 0.887
#> 4 4 0.559 0.765 0.815 0.1152 0.957 0.902
#> 5 5 0.538 0.551 0.720 0.0888 0.941 0.856
#> 6 6 0.536 0.395 0.652 0.0603 0.969 0.912
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.6168 0.509 0.000 0.588 0.412
#> GSM215052 2 0.1031 0.924 0.000 0.976 0.024
#> GSM215053 2 0.4654 0.805 0.000 0.792 0.208
#> GSM215054 2 0.5138 0.757 0.000 0.748 0.252
#> GSM215055 2 0.0592 0.926 0.000 0.988 0.012
#> GSM215056 2 0.3038 0.891 0.000 0.896 0.104
#> GSM215057 2 0.0424 0.926 0.000 0.992 0.008
#> GSM215058 2 0.3340 0.876 0.000 0.880 0.120
#> GSM215059 2 0.1289 0.924 0.000 0.968 0.032
#> GSM215060 2 0.0592 0.927 0.000 0.988 0.012
#> GSM215061 2 0.0592 0.927 0.000 0.988 0.012
#> GSM215062 2 0.2796 0.897 0.000 0.908 0.092
#> GSM215063 2 0.6126 0.523 0.000 0.600 0.400
#> GSM215064 2 0.2625 0.902 0.000 0.916 0.084
#> GSM215065 2 0.1860 0.918 0.000 0.948 0.052
#> GSM215066 2 0.1289 0.924 0.000 0.968 0.032
#> GSM215067 2 0.4452 0.819 0.000 0.808 0.192
#> GSM215068 2 0.1289 0.924 0.000 0.968 0.032
#> GSM215069 2 0.1753 0.919 0.000 0.952 0.048
#> GSM215070 2 0.0892 0.925 0.000 0.980 0.020
#> GSM215071 2 0.1031 0.925 0.000 0.976 0.024
#> GSM215072 2 0.0892 0.927 0.000 0.980 0.020
#> GSM215073 2 0.1289 0.924 0.000 0.968 0.032
#> GSM215074 2 0.0892 0.925 0.000 0.980 0.020
#> GSM215075 2 0.1031 0.927 0.000 0.976 0.024
#> GSM215076 2 0.2796 0.897 0.000 0.908 0.092
#> GSM215077 2 0.0592 0.926 0.000 0.988 0.012
#> GSM215078 2 0.2066 0.912 0.000 0.940 0.060
#> GSM215079 2 0.0892 0.927 0.000 0.980 0.020
#> GSM215080 2 0.1411 0.924 0.000 0.964 0.036
#> GSM215081 2 0.2625 0.902 0.000 0.916 0.084
#> GSM215082 2 0.0424 0.927 0.000 0.992 0.008
#> GSM215083 1 0.4504 0.688 0.804 0.000 0.196
#> GSM215084 1 0.1031 0.857 0.976 0.000 0.024
#> GSM215085 1 0.6302 -0.306 0.520 0.000 0.480
#> GSM215086 3 0.5363 0.853 0.276 0.000 0.724
#> GSM215087 1 0.2537 0.815 0.920 0.000 0.080
#> GSM215088 3 0.5968 0.712 0.364 0.000 0.636
#> GSM215089 1 0.0747 0.857 0.984 0.000 0.016
#> GSM215090 1 0.1753 0.851 0.952 0.000 0.048
#> GSM215091 1 0.1031 0.857 0.976 0.000 0.024
#> GSM215092 1 0.2066 0.841 0.940 0.000 0.060
#> GSM215093 3 0.4915 0.833 0.184 0.012 0.804
#> GSM215094 1 0.2066 0.832 0.940 0.000 0.060
#> GSM215095 1 0.2711 0.808 0.912 0.000 0.088
#> GSM215096 1 0.2165 0.829 0.936 0.000 0.064
#> GSM215097 1 0.4452 0.698 0.808 0.000 0.192
#> GSM215098 1 0.1411 0.852 0.964 0.000 0.036
#> GSM215099 1 0.1643 0.849 0.956 0.000 0.044
#> GSM215100 1 0.1753 0.847 0.952 0.000 0.048
#> GSM215101 1 0.1411 0.853 0.964 0.000 0.036
#> GSM215102 1 0.5178 0.573 0.744 0.000 0.256
#> GSM215103 1 0.2261 0.836 0.932 0.000 0.068
#> GSM215104 1 0.2796 0.816 0.908 0.000 0.092
#> GSM215105 1 0.1411 0.849 0.964 0.000 0.036
#> GSM215106 1 0.0747 0.857 0.984 0.000 0.016
#> GSM215107 1 0.0592 0.857 0.988 0.000 0.012
#> GSM215108 1 0.5706 0.406 0.680 0.000 0.320
#> GSM215109 3 0.4796 0.866 0.220 0.000 0.780
#> GSM215110 1 0.6280 -0.216 0.540 0.000 0.460
#> GSM215111 1 0.0592 0.857 0.988 0.000 0.012
#> GSM215112 1 0.2796 0.804 0.908 0.000 0.092
#> GSM215113 1 0.1289 0.858 0.968 0.000 0.032
#> GSM215114 1 0.2066 0.831 0.940 0.000 0.060
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.772 0.3507 0.000 0.448 0.280 NA
#> GSM215052 2 0.240 0.8616 0.000 0.904 0.004 NA
#> GSM215053 2 0.677 0.6258 0.000 0.600 0.152 NA
#> GSM215054 2 0.670 0.6442 0.000 0.608 0.148 NA
#> GSM215055 2 0.281 0.8413 0.000 0.868 0.000 NA
#> GSM215056 2 0.433 0.8035 0.000 0.792 0.032 NA
#> GSM215057 2 0.265 0.8499 0.000 0.888 0.004 NA
#> GSM215058 2 0.529 0.7921 0.000 0.728 0.064 NA
#> GSM215059 2 0.227 0.8540 0.000 0.912 0.004 NA
#> GSM215060 2 0.241 0.8494 0.000 0.896 0.000 NA
#> GSM215061 2 0.174 0.8601 0.000 0.940 0.004 NA
#> GSM215062 2 0.363 0.8132 0.000 0.812 0.004 NA
#> GSM215063 2 0.753 0.3860 0.000 0.476 0.208 NA
#> GSM215064 2 0.371 0.8101 0.000 0.804 0.004 NA
#> GSM215065 2 0.198 0.8598 0.000 0.928 0.004 NA
#> GSM215066 2 0.215 0.8579 0.000 0.912 0.000 NA
#> GSM215067 2 0.644 0.6249 0.000 0.608 0.100 NA
#> GSM215068 2 0.164 0.8560 0.000 0.940 0.000 NA
#> GSM215069 2 0.158 0.8595 0.000 0.948 0.004 NA
#> GSM215070 2 0.261 0.8606 0.000 0.896 0.008 NA
#> GSM215071 2 0.156 0.8602 0.000 0.944 0.000 NA
#> GSM215072 2 0.294 0.8475 0.000 0.868 0.004 NA
#> GSM215073 2 0.147 0.8585 0.000 0.948 0.000 NA
#> GSM215074 2 0.247 0.8474 0.000 0.892 0.000 NA
#> GSM215075 2 0.322 0.8486 0.000 0.860 0.012 NA
#> GSM215076 2 0.678 0.6481 0.000 0.596 0.148 NA
#> GSM215077 2 0.314 0.8420 0.000 0.860 0.008 NA
#> GSM215078 2 0.386 0.8249 0.000 0.824 0.024 NA
#> GSM215079 2 0.187 0.8577 0.000 0.928 0.000 NA
#> GSM215080 2 0.276 0.8467 0.000 0.872 0.000 NA
#> GSM215081 2 0.297 0.8337 0.000 0.856 0.000 NA
#> GSM215082 2 0.247 0.8569 0.000 0.900 0.004 NA
#> GSM215083 1 0.557 0.4657 0.624 0.000 0.344 NA
#> GSM215084 1 0.318 0.8171 0.876 0.000 0.028 NA
#> GSM215085 3 0.523 0.6772 0.236 0.000 0.716 NA
#> GSM215086 3 0.397 0.7377 0.072 0.000 0.840 NA
#> GSM215087 1 0.244 0.8131 0.916 0.000 0.024 NA
#> GSM215088 3 0.582 0.7276 0.192 0.000 0.700 NA
#> GSM215089 1 0.309 0.8348 0.888 0.000 0.060 NA
#> GSM215090 1 0.346 0.8281 0.864 0.000 0.096 NA
#> GSM215091 1 0.217 0.8441 0.928 0.000 0.052 NA
#> GSM215092 1 0.491 0.7679 0.776 0.000 0.140 NA
#> GSM215093 3 0.617 0.6997 0.100 0.000 0.652 NA
#> GSM215094 1 0.252 0.8278 0.912 0.000 0.024 NA
#> GSM215095 1 0.230 0.8166 0.920 0.000 0.016 NA
#> GSM215096 1 0.264 0.8116 0.904 0.000 0.020 NA
#> GSM215097 1 0.541 0.5796 0.668 0.000 0.296 NA
#> GSM215098 1 0.316 0.8321 0.872 0.000 0.108 NA
#> GSM215099 1 0.396 0.8198 0.836 0.000 0.112 NA
#> GSM215100 1 0.364 0.8192 0.848 0.000 0.120 NA
#> GSM215101 1 0.236 0.8416 0.920 0.000 0.056 NA
#> GSM215102 1 0.724 0.0713 0.500 0.000 0.344 NA
#> GSM215103 1 0.496 0.7449 0.756 0.000 0.188 NA
#> GSM215104 1 0.450 0.7367 0.764 0.000 0.212 NA
#> GSM215105 1 0.360 0.8035 0.860 0.000 0.056 NA
#> GSM215106 1 0.323 0.8303 0.880 0.000 0.072 NA
#> GSM215107 1 0.139 0.8412 0.960 0.000 0.028 NA
#> GSM215108 3 0.702 0.4609 0.344 0.000 0.524 NA
#> GSM215109 3 0.396 0.7271 0.044 0.000 0.832 NA
#> GSM215110 3 0.712 0.6150 0.248 0.000 0.560 NA
#> GSM215111 1 0.259 0.8388 0.912 0.000 0.048 NA
#> GSM215112 1 0.211 0.8197 0.932 0.000 0.024 NA
#> GSM215113 1 0.347 0.8296 0.868 0.000 0.064 NA
#> GSM215114 1 0.200 0.8271 0.936 0.000 0.020 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 5 0.810 0.4612 0.000 0.304 0.288 0.092 0.316
#> GSM215052 2 0.387 0.6587 0.000 0.776 0.008 0.016 0.200
#> GSM215053 2 0.694 -0.1206 0.000 0.528 0.188 0.036 0.248
#> GSM215054 2 0.710 -0.1658 0.000 0.500 0.136 0.056 0.308
#> GSM215055 2 0.372 0.5069 0.000 0.736 0.000 0.004 0.260
#> GSM215056 2 0.527 0.1463 0.000 0.588 0.024 0.020 0.368
#> GSM215057 2 0.352 0.6232 0.000 0.776 0.000 0.008 0.216
#> GSM215058 2 0.606 0.3613 0.000 0.552 0.016 0.088 0.344
#> GSM215059 2 0.324 0.5833 0.000 0.784 0.000 0.000 0.216
#> GSM215060 2 0.356 0.5668 0.000 0.780 0.000 0.012 0.208
#> GSM215061 2 0.248 0.6839 0.000 0.904 0.016 0.016 0.064
#> GSM215062 2 0.491 0.5619 0.000 0.692 0.004 0.060 0.244
#> GSM215063 5 0.729 0.6463 0.000 0.276 0.080 0.136 0.508
#> GSM215064 2 0.522 0.5358 0.000 0.668 0.004 0.080 0.248
#> GSM215065 2 0.246 0.6549 0.000 0.880 0.000 0.008 0.112
#> GSM215066 2 0.270 0.6819 0.000 0.880 0.008 0.012 0.100
#> GSM215067 5 0.660 0.5788 0.000 0.380 0.036 0.096 0.488
#> GSM215068 2 0.192 0.6892 0.000 0.924 0.004 0.008 0.064
#> GSM215069 2 0.183 0.6782 0.000 0.920 0.000 0.004 0.076
#> GSM215070 2 0.421 0.6450 0.000 0.760 0.016 0.020 0.204
#> GSM215071 2 0.224 0.6881 0.000 0.904 0.004 0.008 0.084
#> GSM215072 2 0.430 0.6070 0.000 0.740 0.000 0.044 0.216
#> GSM215073 2 0.207 0.6650 0.000 0.904 0.000 0.004 0.092
#> GSM215074 2 0.363 0.5885 0.000 0.772 0.000 0.012 0.216
#> GSM215075 2 0.416 0.6391 0.000 0.784 0.028 0.020 0.168
#> GSM215076 2 0.771 0.0963 0.000 0.460 0.124 0.132 0.284
#> GSM215077 2 0.359 0.6632 0.000 0.824 0.024 0.012 0.140
#> GSM215078 2 0.384 0.6322 0.000 0.808 0.032 0.012 0.148
#> GSM215079 2 0.270 0.6881 0.000 0.880 0.012 0.008 0.100
#> GSM215080 2 0.278 0.6807 0.000 0.868 0.004 0.012 0.116
#> GSM215081 2 0.464 0.5943 0.000 0.720 0.004 0.052 0.224
#> GSM215082 2 0.482 0.5861 0.000 0.696 0.000 0.068 0.236
#> GSM215083 1 0.583 0.1819 0.528 0.000 0.396 0.060 0.016
#> GSM215084 1 0.385 0.6443 0.752 0.000 0.016 0.232 0.000
#> GSM215085 3 0.591 0.2753 0.156 0.000 0.680 0.112 0.052
#> GSM215086 3 0.263 0.4264 0.012 0.000 0.896 0.068 0.024
#> GSM215087 1 0.291 0.7365 0.876 0.000 0.028 0.088 0.008
#> GSM215088 3 0.732 0.2839 0.084 0.000 0.528 0.220 0.168
#> GSM215089 1 0.379 0.6891 0.776 0.000 0.016 0.204 0.004
#> GSM215090 1 0.358 0.7193 0.828 0.000 0.028 0.132 0.012
#> GSM215091 1 0.321 0.7444 0.860 0.000 0.064 0.072 0.004
#> GSM215092 1 0.520 0.5672 0.672 0.000 0.052 0.260 0.016
#> GSM215093 3 0.748 0.2332 0.028 0.004 0.396 0.264 0.308
#> GSM215094 1 0.317 0.7340 0.856 0.000 0.020 0.112 0.012
#> GSM215095 1 0.199 0.7438 0.916 0.000 0.004 0.076 0.004
#> GSM215096 1 0.332 0.7371 0.844 0.000 0.056 0.100 0.000
#> GSM215097 1 0.638 0.2433 0.528 0.000 0.324 0.136 0.012
#> GSM215098 1 0.357 0.7214 0.824 0.000 0.120 0.056 0.000
#> GSM215099 1 0.487 0.6641 0.720 0.000 0.120 0.160 0.000
#> GSM215100 1 0.436 0.7068 0.768 0.000 0.112 0.120 0.000
#> GSM215101 1 0.277 0.7386 0.876 0.000 0.020 0.100 0.004
#> GSM215102 4 0.727 0.5292 0.304 0.000 0.212 0.448 0.036
#> GSM215103 1 0.598 0.4855 0.636 0.000 0.184 0.164 0.016
#> GSM215104 1 0.593 0.4769 0.632 0.000 0.204 0.152 0.012
#> GSM215105 1 0.545 0.6466 0.696 0.000 0.108 0.176 0.020
#> GSM215106 1 0.397 0.7276 0.808 0.000 0.096 0.092 0.004
#> GSM215107 1 0.246 0.7446 0.880 0.000 0.008 0.112 0.000
#> GSM215108 3 0.632 0.0509 0.208 0.000 0.624 0.124 0.044
#> GSM215109 3 0.488 0.3808 0.000 0.000 0.692 0.236 0.072
#> GSM215110 4 0.690 0.4214 0.160 0.000 0.328 0.484 0.028
#> GSM215111 1 0.396 0.7299 0.808 0.000 0.084 0.104 0.004
#> GSM215112 1 0.182 0.7441 0.932 0.000 0.024 0.044 0.000
#> GSM215113 1 0.456 0.6713 0.740 0.000 0.060 0.196 0.004
#> GSM215114 1 0.306 0.7362 0.868 0.000 0.020 0.096 0.016
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 4 0.801 0.0579 0.000 0.240 0.208 0.332 0.020 0.200
#> GSM215052 2 0.546 0.2686 0.000 0.596 0.008 0.152 0.000 0.244
#> GSM215053 2 0.710 0.0471 0.000 0.496 0.228 0.128 0.012 0.136
#> GSM215054 2 0.724 -0.1181 0.000 0.440 0.184 0.252 0.004 0.120
#> GSM215055 2 0.423 0.4704 0.000 0.728 0.004 0.212 0.004 0.052
#> GSM215056 2 0.438 0.2541 0.000 0.600 0.000 0.368 0.000 0.032
#> GSM215057 2 0.490 0.4052 0.000 0.648 0.000 0.228 0.000 0.124
#> GSM215058 6 0.646 0.4409 0.000 0.324 0.008 0.208 0.016 0.444
#> GSM215059 2 0.355 0.5049 0.000 0.784 0.000 0.168 0.000 0.048
#> GSM215060 2 0.299 0.5277 0.000 0.824 0.000 0.152 0.000 0.024
#> GSM215061 2 0.305 0.5564 0.000 0.856 0.016 0.020 0.008 0.100
#> GSM215062 2 0.473 -0.1981 0.000 0.500 0.012 0.012 0.008 0.468
#> GSM215063 4 0.395 0.4691 0.000 0.236 0.004 0.732 0.008 0.020
#> GSM215064 2 0.444 -0.2360 0.000 0.492 0.012 0.004 0.004 0.488
#> GSM215065 2 0.157 0.5712 0.004 0.940 0.000 0.028 0.000 0.028
#> GSM215066 2 0.315 0.5419 0.000 0.828 0.012 0.012 0.004 0.144
#> GSM215067 4 0.457 0.3778 0.000 0.328 0.000 0.624 0.004 0.044
#> GSM215068 2 0.250 0.5491 0.000 0.872 0.008 0.004 0.004 0.112
#> GSM215069 2 0.167 0.5725 0.000 0.932 0.000 0.016 0.004 0.048
#> GSM215070 2 0.553 0.2554 0.000 0.580 0.004 0.196 0.000 0.220
#> GSM215071 2 0.166 0.5724 0.000 0.928 0.000 0.016 0.000 0.056
#> GSM215072 2 0.451 -0.0854 0.000 0.532 0.000 0.032 0.000 0.436
#> GSM215073 2 0.179 0.5716 0.000 0.924 0.000 0.040 0.000 0.036
#> GSM215074 2 0.368 0.5097 0.000 0.772 0.000 0.176 0.000 0.052
#> GSM215075 2 0.487 0.4052 0.000 0.692 0.024 0.044 0.012 0.228
#> GSM215076 6 0.706 0.5344 0.000 0.252 0.156 0.056 0.036 0.500
#> GSM215077 2 0.433 0.4514 0.000 0.732 0.024 0.032 0.004 0.208
#> GSM215078 2 0.504 0.4623 0.000 0.712 0.040 0.064 0.012 0.172
#> GSM215079 2 0.326 0.5464 0.000 0.820 0.004 0.020 0.008 0.148
#> GSM215080 2 0.384 0.4210 0.000 0.716 0.004 0.012 0.004 0.264
#> GSM215081 2 0.438 -0.0637 0.000 0.540 0.000 0.012 0.008 0.440
#> GSM215082 2 0.539 0.0775 0.000 0.556 0.000 0.092 0.012 0.340
#> GSM215083 1 0.686 0.0540 0.456 0.000 0.340 0.044 0.132 0.028
#> GSM215084 1 0.470 0.3139 0.524 0.000 0.000 0.012 0.440 0.024
#> GSM215085 3 0.719 0.4035 0.184 0.000 0.544 0.120 0.084 0.068
#> GSM215086 3 0.251 0.4682 0.004 0.000 0.896 0.032 0.052 0.016
#> GSM215087 1 0.326 0.6351 0.840 0.000 0.028 0.008 0.112 0.012
#> GSM215088 3 0.796 0.2167 0.128 0.000 0.388 0.260 0.180 0.044
#> GSM215089 1 0.467 0.4733 0.540 0.000 0.016 0.012 0.428 0.004
#> GSM215090 1 0.451 0.5809 0.688 0.000 0.028 0.020 0.260 0.004
#> GSM215091 1 0.404 0.6239 0.764 0.000 0.060 0.012 0.164 0.000
#> GSM215092 1 0.529 0.3048 0.496 0.000 0.032 0.008 0.440 0.024
#> GSM215093 4 0.640 -0.1966 0.048 0.004 0.176 0.612 0.128 0.032
#> GSM215094 1 0.434 0.6094 0.748 0.000 0.004 0.012 0.164 0.072
#> GSM215095 1 0.330 0.6340 0.804 0.000 0.004 0.008 0.172 0.012
#> GSM215096 1 0.351 0.6454 0.836 0.000 0.044 0.008 0.088 0.024
#> GSM215097 1 0.642 0.2089 0.424 0.000 0.296 0.012 0.264 0.004
#> GSM215098 1 0.481 0.5957 0.724 0.000 0.120 0.012 0.132 0.012
#> GSM215099 1 0.484 0.5378 0.632 0.000 0.076 0.000 0.288 0.004
#> GSM215100 1 0.457 0.5875 0.668 0.000 0.064 0.004 0.264 0.000
#> GSM215101 1 0.430 0.5936 0.700 0.000 0.020 0.012 0.260 0.008
#> GSM215102 5 0.753 0.4588 0.188 0.000 0.104 0.124 0.508 0.076
#> GSM215103 1 0.715 0.1867 0.452 0.000 0.176 0.040 0.292 0.040
#> GSM215104 1 0.648 0.2897 0.504 0.000 0.152 0.024 0.300 0.020
#> GSM215105 1 0.554 0.5557 0.676 0.000 0.072 0.024 0.184 0.044
#> GSM215106 1 0.491 0.6008 0.724 0.000 0.092 0.016 0.148 0.020
#> GSM215107 1 0.339 0.6404 0.812 0.000 0.016 0.000 0.148 0.024
#> GSM215108 3 0.665 0.3809 0.148 0.000 0.600 0.044 0.128 0.080
#> GSM215109 3 0.641 0.3206 0.000 0.000 0.552 0.128 0.228 0.092
#> GSM215110 5 0.666 0.4196 0.052 0.000 0.196 0.112 0.584 0.056
#> GSM215111 1 0.357 0.6414 0.828 0.000 0.024 0.008 0.104 0.036
#> GSM215112 1 0.209 0.6481 0.912 0.000 0.004 0.004 0.060 0.020
#> GSM215113 1 0.497 0.4642 0.560 0.000 0.032 0.004 0.388 0.016
#> GSM215114 1 0.336 0.6362 0.832 0.000 0.020 0.020 0.120 0.008
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> MAD:NMF 64 9.19e-15 1.000 2
#> MAD:NMF 61 5.68e-14 0.999 3
#> MAD:NMF 59 1.54e-13 0.998 4
#> MAD:NMF 47 3.48e-10 0.982 5
#> MAD:NMF 28 8.32e-07 0.428 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 51941 rows and 64 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 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 1.000 0.973 0.987 0.0779 0.970 0.940
#> 4 4 0.841 0.826 0.896 0.1188 0.960 0.913
#> 5 5 0.810 0.732 0.844 0.0521 0.972 0.935
#> 6 6 0.686 0.630 0.743 0.0777 0.914 0.794
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
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.0000 1.000 0.000 1 0.000
#> GSM215052 2 0.0000 1.000 0.000 1 0.000
#> GSM215053 2 0.0000 1.000 0.000 1 0.000
#> GSM215054 2 0.0000 1.000 0.000 1 0.000
#> GSM215055 2 0.0000 1.000 0.000 1 0.000
#> GSM215056 2 0.0000 1.000 0.000 1 0.000
#> GSM215057 2 0.0000 1.000 0.000 1 0.000
#> GSM215058 2 0.0000 1.000 0.000 1 0.000
#> GSM215059 2 0.0000 1.000 0.000 1 0.000
#> GSM215060 2 0.0000 1.000 0.000 1 0.000
#> GSM215061 2 0.0000 1.000 0.000 1 0.000
#> GSM215062 2 0.0000 1.000 0.000 1 0.000
#> GSM215063 2 0.0000 1.000 0.000 1 0.000
#> GSM215064 2 0.0000 1.000 0.000 1 0.000
#> GSM215065 2 0.0000 1.000 0.000 1 0.000
#> GSM215066 2 0.0000 1.000 0.000 1 0.000
#> GSM215067 2 0.0000 1.000 0.000 1 0.000
#> GSM215068 2 0.0000 1.000 0.000 1 0.000
#> GSM215069 2 0.0000 1.000 0.000 1 0.000
#> GSM215070 2 0.0000 1.000 0.000 1 0.000
#> GSM215071 2 0.0000 1.000 0.000 1 0.000
#> GSM215072 2 0.0000 1.000 0.000 1 0.000
#> GSM215073 2 0.0000 1.000 0.000 1 0.000
#> GSM215074 2 0.0000 1.000 0.000 1 0.000
#> GSM215075 2 0.0000 1.000 0.000 1 0.000
#> GSM215076 2 0.0000 1.000 0.000 1 0.000
#> GSM215077 2 0.0000 1.000 0.000 1 0.000
#> GSM215078 2 0.0000 1.000 0.000 1 0.000
#> GSM215079 2 0.0000 1.000 0.000 1 0.000
#> GSM215080 2 0.0000 1.000 0.000 1 0.000
#> GSM215081 2 0.0000 1.000 0.000 1 0.000
#> GSM215082 2 0.0000 1.000 0.000 1 0.000
#> GSM215083 1 0.0000 0.972 1.000 0 0.000
#> GSM215084 1 0.0000 0.972 1.000 0 0.000
#> GSM215085 1 0.0000 0.972 1.000 0 0.000
#> GSM215086 1 0.0000 0.972 1.000 0 0.000
#> GSM215087 1 0.0237 0.970 0.996 0 0.004
#> GSM215088 1 0.2165 0.924 0.936 0 0.064
#> GSM215089 1 0.0424 0.968 0.992 0 0.008
#> GSM215090 1 0.0000 0.972 1.000 0 0.000
#> GSM215091 1 0.0237 0.970 0.996 0 0.004
#> GSM215092 1 0.0000 0.972 1.000 0 0.000
#> GSM215093 3 0.0000 1.000 0.000 0 1.000
#> GSM215094 1 0.0000 0.972 1.000 0 0.000
#> GSM215095 1 0.0000 0.972 1.000 0 0.000
#> GSM215096 1 0.0237 0.970 0.996 0 0.004
#> GSM215097 1 0.0000 0.972 1.000 0 0.000
#> GSM215098 1 0.0000 0.972 1.000 0 0.000
#> GSM215099 1 0.0000 0.972 1.000 0 0.000
#> GSM215100 1 0.0000 0.972 1.000 0 0.000
#> GSM215101 1 0.0424 0.968 0.992 0 0.008
#> GSM215102 1 0.5621 0.586 0.692 0 0.308
#> GSM215103 1 0.1529 0.944 0.960 0 0.040
#> GSM215104 1 0.0000 0.972 1.000 0 0.000
#> GSM215105 1 0.0000 0.972 1.000 0 0.000
#> GSM215106 1 0.0000 0.972 1.000 0 0.000
#> GSM215107 1 0.0000 0.972 1.000 0 0.000
#> GSM215108 1 0.5733 0.556 0.676 0 0.324
#> GSM215109 3 0.0000 1.000 0.000 0 1.000
#> GSM215110 1 0.0000 0.972 1.000 0 0.000
#> GSM215111 1 0.0000 0.972 1.000 0 0.000
#> GSM215112 1 0.0000 0.972 1.000 0 0.000
#> GSM215113 1 0.0000 0.972 1.000 0 0.000
#> GSM215114 1 0.1529 0.944 0.960 0 0.040
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215052 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215053 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215054 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215055 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215056 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215057 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215058 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215059 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215060 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215061 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215062 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215063 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215064 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215065 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215066 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215067 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215068 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215069 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215070 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215071 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215072 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215073 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215074 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215075 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215076 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215077 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215078 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215079 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215080 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215081 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215082 2 0.0000 1.0000 0.000 1 0.000 0.000
#> GSM215083 1 0.1211 0.7528 0.960 0 0.000 0.040
#> GSM215084 1 0.4304 0.6592 0.716 0 0.000 0.284
#> GSM215085 1 0.0592 0.7539 0.984 0 0.000 0.016
#> GSM215086 1 0.3649 0.7401 0.796 0 0.000 0.204
#> GSM215087 1 0.2760 0.7303 0.872 0 0.000 0.128
#> GSM215088 1 0.4387 0.6007 0.776 0 0.024 0.200
#> GSM215089 1 0.5119 0.0452 0.556 0 0.004 0.440
#> GSM215090 1 0.4304 0.6592 0.716 0 0.000 0.284
#> GSM215091 1 0.2589 0.7289 0.884 0 0.000 0.116
#> GSM215092 1 0.4304 0.6592 0.716 0 0.000 0.284
#> GSM215093 3 0.0707 0.9589 0.000 0 0.980 0.020
#> GSM215094 1 0.2868 0.7373 0.864 0 0.000 0.136
#> GSM215095 1 0.1302 0.7470 0.956 0 0.000 0.044
#> GSM215096 1 0.2589 0.7289 0.884 0 0.000 0.116
#> GSM215097 1 0.3649 0.7401 0.796 0 0.000 0.204
#> GSM215098 1 0.2868 0.7373 0.864 0 0.000 0.136
#> GSM215099 1 0.4304 0.6592 0.716 0 0.000 0.284
#> GSM215100 1 0.4304 0.6592 0.716 0 0.000 0.284
#> GSM215101 1 0.5105 0.0644 0.564 0 0.004 0.432
#> GSM215102 4 0.7271 0.5239 0.216 0 0.244 0.540
#> GSM215103 1 0.3649 0.6240 0.796 0 0.000 0.204
#> GSM215104 1 0.1389 0.7552 0.952 0 0.000 0.048
#> GSM215105 1 0.3400 0.6293 0.820 0 0.000 0.180
#> GSM215106 1 0.1389 0.7552 0.952 0 0.000 0.048
#> GSM215107 1 0.4304 0.6592 0.716 0 0.000 0.284
#> GSM215108 4 0.6848 0.4592 0.160 0 0.248 0.592
#> GSM215109 3 0.1118 0.9590 0.000 0 0.964 0.036
#> GSM215110 4 0.3975 0.3315 0.240 0 0.000 0.760
#> GSM215111 1 0.2868 0.7384 0.864 0 0.000 0.136
#> GSM215112 1 0.1557 0.7541 0.944 0 0.000 0.056
#> GSM215113 1 0.4304 0.6585 0.716 0 0.000 0.284
#> GSM215114 1 0.3764 0.6368 0.784 0 0.000 0.216
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.0898 0.971 0.000 0.972 0.008 0.020 0.000
#> GSM215052 2 0.0865 0.967 0.000 0.972 0.000 0.024 0.004
#> GSM215053 2 0.0898 0.971 0.000 0.972 0.008 0.020 0.000
#> GSM215054 2 0.0898 0.971 0.000 0.972 0.008 0.020 0.000
#> GSM215055 2 0.0510 0.971 0.000 0.984 0.000 0.016 0.000
#> GSM215056 2 0.0510 0.971 0.000 0.984 0.000 0.016 0.000
#> GSM215057 2 0.0510 0.971 0.000 0.984 0.000 0.016 0.000
#> GSM215058 2 0.0000 0.973 0.000 1.000 0.000 0.000 0.000
#> GSM215059 2 0.0510 0.971 0.000 0.984 0.000 0.016 0.000
#> GSM215060 2 0.0404 0.974 0.000 0.988 0.000 0.012 0.000
#> GSM215061 2 0.0865 0.967 0.000 0.972 0.000 0.024 0.004
#> GSM215062 2 0.1970 0.938 0.000 0.924 0.012 0.060 0.004
#> GSM215063 2 0.0865 0.967 0.000 0.972 0.000 0.024 0.004
#> GSM215064 2 0.1970 0.938 0.000 0.924 0.012 0.060 0.004
#> GSM215065 2 0.1970 0.938 0.000 0.924 0.012 0.060 0.004
#> GSM215066 2 0.0693 0.972 0.000 0.980 0.008 0.012 0.000
#> GSM215067 2 0.1970 0.938 0.000 0.924 0.012 0.060 0.004
#> GSM215068 2 0.0693 0.972 0.000 0.980 0.008 0.012 0.000
#> GSM215069 2 0.0693 0.972 0.000 0.980 0.008 0.012 0.000
#> GSM215070 2 0.0898 0.971 0.000 0.972 0.008 0.020 0.000
#> GSM215071 2 0.0693 0.972 0.000 0.980 0.008 0.012 0.000
#> GSM215072 2 0.0290 0.973 0.000 0.992 0.008 0.000 0.000
#> GSM215073 2 0.0510 0.971 0.000 0.984 0.000 0.016 0.000
#> GSM215074 2 0.0451 0.973 0.000 0.988 0.008 0.004 0.000
#> GSM215075 2 0.0798 0.973 0.000 0.976 0.008 0.016 0.000
#> GSM215076 2 0.0898 0.971 0.000 0.972 0.008 0.020 0.000
#> GSM215077 2 0.0898 0.971 0.000 0.972 0.008 0.020 0.000
#> GSM215078 2 0.0898 0.971 0.000 0.972 0.008 0.020 0.000
#> GSM215079 2 0.0898 0.971 0.000 0.972 0.008 0.020 0.000
#> GSM215080 2 0.0898 0.971 0.000 0.972 0.008 0.020 0.000
#> GSM215081 2 0.0290 0.973 0.000 0.992 0.008 0.000 0.000
#> GSM215082 2 0.1970 0.938 0.000 0.924 0.012 0.060 0.004
#> GSM215083 1 0.1124 0.647 0.960 0.000 0.000 0.004 0.036
#> GSM215084 1 0.4161 0.512 0.608 0.000 0.000 0.392 0.000
#> GSM215085 1 0.0451 0.654 0.988 0.000 0.000 0.004 0.008
#> GSM215086 1 0.4765 0.641 0.704 0.000 0.000 0.228 0.068
#> GSM215087 1 0.3269 0.603 0.848 0.000 0.000 0.056 0.096
#> GSM215088 1 0.5551 0.338 0.664 0.000 0.012 0.104 0.220
#> GSM215089 5 0.5495 0.306 0.436 0.000 0.000 0.064 0.500
#> GSM215090 1 0.4161 0.512 0.608 0.000 0.000 0.392 0.000
#> GSM215091 1 0.4216 0.613 0.780 0.000 0.000 0.100 0.120
#> GSM215092 1 0.4161 0.512 0.608 0.000 0.000 0.392 0.000
#> GSM215093 3 0.4840 0.634 0.000 0.000 0.688 0.248 0.064
#> GSM215094 1 0.2329 0.662 0.876 0.000 0.000 0.124 0.000
#> GSM215095 1 0.3267 0.553 0.844 0.000 0.000 0.112 0.044
#> GSM215096 1 0.4117 0.618 0.788 0.000 0.000 0.096 0.116
#> GSM215097 1 0.4765 0.641 0.704 0.000 0.000 0.228 0.068
#> GSM215098 1 0.2329 0.662 0.876 0.000 0.000 0.124 0.000
#> GSM215099 1 0.4161 0.512 0.608 0.000 0.000 0.392 0.000
#> GSM215100 1 0.4161 0.512 0.608 0.000 0.000 0.392 0.000
#> GSM215101 5 0.5548 0.293 0.440 0.000 0.000 0.068 0.492
#> GSM215102 5 0.1808 0.173 0.044 0.000 0.012 0.008 0.936
#> GSM215103 1 0.5164 0.357 0.672 0.000 0.000 0.096 0.232
#> GSM215104 1 0.3130 0.655 0.856 0.000 0.000 0.096 0.048
#> GSM215105 1 0.5348 0.305 0.656 0.000 0.000 0.112 0.232
#> GSM215106 1 0.3130 0.655 0.856 0.000 0.000 0.096 0.048
#> GSM215107 1 0.4161 0.512 0.608 0.000 0.000 0.392 0.000
#> GSM215108 5 0.1507 0.118 0.012 0.000 0.012 0.024 0.952
#> GSM215109 3 0.3612 0.628 0.000 0.000 0.732 0.000 0.268
#> GSM215110 4 0.6569 0.000 0.124 0.000 0.020 0.480 0.376
#> GSM215111 1 0.4588 0.572 0.748 0.000 0.000 0.136 0.116
#> GSM215112 1 0.1872 0.643 0.928 0.000 0.000 0.052 0.020
#> GSM215113 1 0.4299 0.507 0.608 0.000 0.000 0.388 0.004
#> GSM215114 1 0.5195 0.393 0.676 0.000 0.000 0.108 0.216
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 2 0.2520 0.8760 0.000 0.872 0.108 0.012 0.008 0.000
#> GSM215052 2 0.2212 0.8592 0.000 0.880 0.000 0.000 0.008 0.112
#> GSM215053 2 0.2520 0.8760 0.000 0.872 0.108 0.012 0.008 0.000
#> GSM215054 2 0.2520 0.8760 0.000 0.872 0.108 0.012 0.008 0.000
#> GSM215055 2 0.1285 0.8891 0.000 0.944 0.000 0.000 0.004 0.052
#> GSM215056 2 0.1285 0.8891 0.000 0.944 0.000 0.000 0.004 0.052
#> GSM215057 2 0.1007 0.8919 0.000 0.956 0.000 0.000 0.000 0.044
#> GSM215058 2 0.0000 0.8978 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215059 2 0.0790 0.8943 0.000 0.968 0.000 0.000 0.000 0.032
#> GSM215060 2 0.0622 0.8984 0.000 0.980 0.008 0.000 0.000 0.012
#> GSM215061 2 0.2212 0.8592 0.000 0.880 0.000 0.000 0.008 0.112
#> GSM215062 2 0.3290 0.7845 0.000 0.776 0.000 0.000 0.016 0.208
#> GSM215063 2 0.2212 0.8592 0.000 0.880 0.000 0.000 0.008 0.112
#> GSM215064 2 0.3290 0.7845 0.000 0.776 0.000 0.000 0.016 0.208
#> GSM215065 2 0.3290 0.7845 0.000 0.776 0.000 0.000 0.016 0.208
#> GSM215066 2 0.1501 0.8939 0.000 0.924 0.076 0.000 0.000 0.000
#> GSM215067 2 0.3290 0.7845 0.000 0.776 0.000 0.000 0.016 0.208
#> GSM215068 2 0.1444 0.8946 0.000 0.928 0.072 0.000 0.000 0.000
#> GSM215069 2 0.1387 0.8954 0.000 0.932 0.068 0.000 0.000 0.000
#> GSM215070 2 0.2006 0.8844 0.000 0.892 0.104 0.000 0.004 0.000
#> GSM215071 2 0.1327 0.8960 0.000 0.936 0.064 0.000 0.000 0.000
#> GSM215072 2 0.0972 0.8948 0.000 0.964 0.000 0.000 0.008 0.028
#> GSM215073 2 0.0713 0.8950 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM215074 2 0.1501 0.8950 0.000 0.924 0.076 0.000 0.000 0.000
#> GSM215075 2 0.2070 0.8996 0.000 0.908 0.048 0.000 0.000 0.044
#> GSM215076 2 0.2520 0.8760 0.000 0.872 0.108 0.012 0.008 0.000
#> GSM215077 2 0.2520 0.8760 0.000 0.872 0.108 0.012 0.008 0.000
#> GSM215078 2 0.2520 0.8760 0.000 0.872 0.108 0.012 0.008 0.000
#> GSM215079 2 0.1863 0.8858 0.000 0.896 0.104 0.000 0.000 0.000
#> GSM215080 2 0.1863 0.8858 0.000 0.896 0.104 0.000 0.000 0.000
#> GSM215081 2 0.0972 0.8948 0.000 0.964 0.000 0.000 0.008 0.028
#> GSM215082 2 0.3290 0.7845 0.000 0.776 0.000 0.000 0.016 0.208
#> GSM215083 1 0.1010 0.4660 0.960 0.000 0.000 0.004 0.036 0.000
#> GSM215084 5 0.3737 0.8457 0.392 0.000 0.000 0.000 0.608 0.000
#> GSM215085 1 0.1204 0.4472 0.944 0.000 0.000 0.000 0.056 0.000
#> GSM215086 1 0.4181 -0.1308 0.644 0.000 0.000 0.028 0.328 0.000
#> GSM215087 1 0.3907 0.5037 0.764 0.000 0.000 0.152 0.084 0.000
#> GSM215088 1 0.4381 0.2809 0.536 0.000 0.024 0.440 0.000 0.000
#> GSM215089 1 0.6948 -0.1208 0.368 0.000 0.000 0.208 0.068 0.356
#> GSM215090 5 0.3727 0.8469 0.388 0.000 0.000 0.000 0.612 0.000
#> GSM215091 1 0.4680 0.3756 0.684 0.000 0.000 0.132 0.184 0.000
#> GSM215092 5 0.3737 0.8457 0.392 0.000 0.000 0.000 0.608 0.000
#> GSM215093 3 0.2542 0.0000 0.000 0.000 0.884 0.080 0.016 0.020
#> GSM215094 1 0.2664 0.2582 0.816 0.000 0.000 0.000 0.184 0.000
#> GSM215095 1 0.4166 0.4418 0.648 0.000 0.000 0.324 0.028 0.000
#> GSM215096 1 0.4024 0.3147 0.744 0.000 0.000 0.072 0.184 0.000
#> GSM215097 1 0.4181 -0.1308 0.644 0.000 0.000 0.028 0.328 0.000
#> GSM215098 1 0.2664 0.2582 0.816 0.000 0.000 0.000 0.184 0.000
#> GSM215099 5 0.3737 0.8457 0.392 0.000 0.000 0.000 0.608 0.000
#> GSM215100 5 0.3727 0.8469 0.388 0.000 0.000 0.000 0.612 0.000
#> GSM215101 1 0.6806 -0.0577 0.408 0.000 0.000 0.164 0.072 0.356
#> GSM215102 6 0.5055 0.8805 0.064 0.000 0.004 0.296 0.012 0.624
#> GSM215103 1 0.3851 0.2926 0.540 0.000 0.000 0.460 0.000 0.000
#> GSM215104 1 0.3315 0.2641 0.780 0.000 0.000 0.020 0.200 0.000
#> GSM215105 1 0.5656 0.2398 0.508 0.000 0.000 0.372 0.016 0.104
#> GSM215106 1 0.3315 0.2641 0.780 0.000 0.000 0.020 0.200 0.000
#> GSM215107 5 0.3727 0.8469 0.388 0.000 0.000 0.000 0.612 0.000
#> GSM215108 6 0.4349 0.8757 0.048 0.000 0.004 0.264 0.000 0.684
#> GSM215109 4 0.7430 0.0000 0.000 0.000 0.128 0.320 0.232 0.320
#> GSM215110 5 0.6257 -0.3482 0.060 0.000 0.000 0.096 0.440 0.404
#> GSM215111 1 0.5504 0.4512 0.604 0.000 0.000 0.244 0.136 0.016
#> GSM215112 1 0.3352 0.4574 0.816 0.000 0.000 0.072 0.112 0.000
#> GSM215113 5 0.3872 0.8398 0.392 0.000 0.000 0.000 0.604 0.004
#> GSM215114 1 0.4685 0.3159 0.520 0.000 0.000 0.436 0.044 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> ATC:hclust 64 9.19e-15 1.000 2
#> ATC:hclust 64 1.27e-14 0.999 3
#> ATC:hclust 60 5.88e-13 0.991 4
#> ATC:hclust 55 1.14e-12 0.998 5
#> ATC:hclust 42 4.01e-09 0.999 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 51941 rows and 64 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.754 0.921 0.865 0.2090 0.891 0.778
#> 4 4 0.620 0.660 0.786 0.1064 0.918 0.788
#> 5 5 0.572 0.652 0.764 0.0785 0.955 0.861
#> 6 6 0.621 0.618 0.717 0.0527 0.948 0.824
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.1411 0.895 0.000 0.964 0.036
#> GSM215052 2 0.4750 0.848 0.000 0.784 0.216
#> GSM215053 2 0.1163 0.897 0.000 0.972 0.028
#> GSM215054 2 0.1163 0.897 0.000 0.972 0.028
#> GSM215055 2 0.2356 0.896 0.000 0.928 0.072
#> GSM215056 2 0.5650 0.801 0.000 0.688 0.312
#> GSM215057 2 0.5760 0.797 0.000 0.672 0.328
#> GSM215058 2 0.1643 0.899 0.000 0.956 0.044
#> GSM215059 2 0.1163 0.901 0.000 0.972 0.028
#> GSM215060 2 0.0592 0.900 0.000 0.988 0.012
#> GSM215061 2 0.3551 0.876 0.000 0.868 0.132
#> GSM215062 2 0.6079 0.758 0.000 0.612 0.388
#> GSM215063 2 0.5178 0.825 0.000 0.744 0.256
#> GSM215064 2 0.6079 0.758 0.000 0.612 0.388
#> GSM215065 2 0.5859 0.780 0.000 0.656 0.344
#> GSM215066 2 0.0424 0.900 0.000 0.992 0.008
#> GSM215067 2 0.5882 0.779 0.000 0.652 0.348
#> GSM215068 2 0.1411 0.900 0.000 0.964 0.036
#> GSM215069 2 0.0592 0.900 0.000 0.988 0.012
#> GSM215070 2 0.1289 0.896 0.000 0.968 0.032
#> GSM215071 2 0.1031 0.898 0.000 0.976 0.024
#> GSM215072 2 0.4291 0.865 0.000 0.820 0.180
#> GSM215073 2 0.1289 0.899 0.000 0.968 0.032
#> GSM215074 2 0.1163 0.897 0.000 0.972 0.028
#> GSM215075 2 0.0892 0.901 0.000 0.980 0.020
#> GSM215076 2 0.2959 0.882 0.000 0.900 0.100
#> GSM215077 2 0.2356 0.891 0.000 0.928 0.072
#> GSM215078 2 0.2356 0.891 0.000 0.928 0.072
#> GSM215079 2 0.1289 0.896 0.000 0.968 0.032
#> GSM215080 2 0.0000 0.900 0.000 1.000 0.000
#> GSM215081 2 0.3879 0.874 0.000 0.848 0.152
#> GSM215082 2 0.5760 0.797 0.000 0.672 0.328
#> GSM215083 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215084 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215085 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215086 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215087 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215088 3 0.6244 0.999 0.440 0.000 0.560
#> GSM215089 3 0.6244 0.999 0.440 0.000 0.560
#> GSM215090 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215091 3 0.6244 0.999 0.440 0.000 0.560
#> GSM215092 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215093 3 0.6244 0.999 0.440 0.000 0.560
#> GSM215094 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215095 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215096 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215097 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215098 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215099 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215100 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215101 3 0.6252 0.993 0.444 0.000 0.556
#> GSM215102 3 0.6244 0.999 0.440 0.000 0.560
#> GSM215103 3 0.6244 0.999 0.440 0.000 0.560
#> GSM215104 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215105 1 0.4121 0.572 0.832 0.000 0.168
#> GSM215106 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215107 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215108 3 0.6244 0.999 0.440 0.000 0.560
#> GSM215109 3 0.6244 0.999 0.440 0.000 0.560
#> GSM215110 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215111 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215112 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215113 1 0.0000 0.986 1.000 0.000 0.000
#> GSM215114 3 0.6244 0.999 0.440 0.000 0.560
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.3107 0.6871 0.080 0.884 0.000 0.036
#> GSM215052 2 0.6934 -0.0232 0.152 0.572 0.000 0.276
#> GSM215053 2 0.1938 0.7068 0.052 0.936 0.000 0.012
#> GSM215054 2 0.1938 0.7068 0.052 0.936 0.000 0.012
#> GSM215055 2 0.4123 0.6347 0.044 0.820 0.000 0.136
#> GSM215056 2 0.5935 -0.5636 0.036 0.496 0.000 0.468
#> GSM215057 2 0.6275 -0.5573 0.056 0.484 0.000 0.460
#> GSM215058 2 0.4163 0.6526 0.096 0.828 0.000 0.076
#> GSM215059 2 0.3372 0.6797 0.036 0.868 0.000 0.096
#> GSM215060 2 0.2335 0.7070 0.020 0.920 0.000 0.060
#> GSM215061 2 0.5318 0.4782 0.072 0.732 0.000 0.196
#> GSM215062 4 0.6634 0.7900 0.108 0.312 0.000 0.580
#> GSM215063 2 0.6407 -0.3076 0.072 0.544 0.000 0.384
#> GSM215064 4 0.6634 0.7900 0.108 0.312 0.000 0.580
#> GSM215065 4 0.5220 0.8068 0.016 0.352 0.000 0.632
#> GSM215066 2 0.2586 0.7057 0.040 0.912 0.000 0.048
#> GSM215067 4 0.5220 0.8068 0.016 0.352 0.000 0.632
#> GSM215068 2 0.3542 0.6823 0.060 0.864 0.000 0.076
#> GSM215069 2 0.2179 0.7064 0.012 0.924 0.000 0.064
#> GSM215070 2 0.1256 0.7118 0.028 0.964 0.000 0.008
#> GSM215071 2 0.0779 0.7165 0.016 0.980 0.000 0.004
#> GSM215072 2 0.6623 0.2186 0.148 0.620 0.000 0.232
#> GSM215073 2 0.2032 0.7080 0.028 0.936 0.000 0.036
#> GSM215074 2 0.0927 0.7176 0.016 0.976 0.000 0.008
#> GSM215075 2 0.3164 0.6955 0.064 0.884 0.000 0.052
#> GSM215076 2 0.6084 0.4064 0.244 0.660 0.000 0.096
#> GSM215077 2 0.4499 0.6135 0.124 0.804 0.000 0.072
#> GSM215078 2 0.4499 0.6135 0.124 0.804 0.000 0.072
#> GSM215079 2 0.1722 0.7098 0.048 0.944 0.000 0.008
#> GSM215080 2 0.1929 0.7131 0.036 0.940 0.000 0.024
#> GSM215081 2 0.6320 0.3160 0.140 0.656 0.000 0.204
#> GSM215082 4 0.5917 0.6329 0.036 0.444 0.000 0.520
#> GSM215083 1 0.4730 0.8616 0.636 0.000 0.364 0.000
#> GSM215084 1 0.7475 0.7773 0.476 0.000 0.332 0.192
#> GSM215085 1 0.4730 0.8616 0.636 0.000 0.364 0.000
#> GSM215086 1 0.4730 0.8616 0.636 0.000 0.364 0.000
#> GSM215087 1 0.5587 0.8581 0.600 0.000 0.372 0.028
#> GSM215088 3 0.0188 0.8675 0.000 0.000 0.996 0.004
#> GSM215089 3 0.1488 0.8517 0.012 0.000 0.956 0.032
#> GSM215090 1 0.7438 0.7827 0.484 0.000 0.328 0.188
#> GSM215091 3 0.2973 0.6969 0.144 0.000 0.856 0.000
#> GSM215092 1 0.7321 0.7893 0.500 0.000 0.328 0.172
#> GSM215093 3 0.1792 0.8501 0.000 0.000 0.932 0.068
#> GSM215094 1 0.4897 0.8655 0.660 0.000 0.332 0.008
#> GSM215095 1 0.5835 0.8506 0.588 0.000 0.372 0.040
#> GSM215096 1 0.4817 0.8419 0.612 0.000 0.388 0.000
#> GSM215097 1 0.5110 0.8641 0.656 0.000 0.328 0.016
#> GSM215098 1 0.4661 0.8659 0.652 0.000 0.348 0.000
#> GSM215099 1 0.5311 0.8635 0.648 0.000 0.328 0.024
#> GSM215100 1 0.7410 0.7847 0.488 0.000 0.328 0.184
#> GSM215101 3 0.1936 0.8394 0.032 0.000 0.940 0.028
#> GSM215102 3 0.0921 0.8673 0.000 0.000 0.972 0.028
#> GSM215103 3 0.0707 0.8684 0.000 0.000 0.980 0.020
#> GSM215104 1 0.4713 0.8634 0.640 0.000 0.360 0.000
#> GSM215105 3 0.5833 -0.5445 0.440 0.000 0.528 0.032
#> GSM215106 1 0.4713 0.8634 0.640 0.000 0.360 0.000
#> GSM215107 1 0.7321 0.7893 0.500 0.000 0.328 0.172
#> GSM215108 3 0.0921 0.8673 0.000 0.000 0.972 0.028
#> GSM215109 3 0.1792 0.8501 0.000 0.000 0.932 0.068
#> GSM215110 1 0.7501 0.7737 0.472 0.000 0.332 0.196
#> GSM215111 1 0.5699 0.8454 0.588 0.000 0.380 0.032
#> GSM215112 1 0.5558 0.8628 0.608 0.000 0.364 0.028
#> GSM215113 1 0.7449 0.7800 0.480 0.000 0.332 0.188
#> GSM215114 3 0.0672 0.8641 0.008 0.000 0.984 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.3068 0.67033 0.000 0.876 0.032 0.020 NA
#> GSM215052 2 0.6786 0.00282 0.000 0.564 0.056 0.256 NA
#> GSM215053 2 0.1095 0.69737 0.000 0.968 0.012 0.008 NA
#> GSM215054 2 0.1095 0.69737 0.000 0.968 0.012 0.008 NA
#> GSM215055 2 0.5608 0.47061 0.000 0.672 0.012 0.148 NA
#> GSM215056 4 0.6736 0.59289 0.000 0.372 0.012 0.444 NA
#> GSM215057 4 0.6668 0.61357 0.000 0.344 0.004 0.448 NA
#> GSM215058 2 0.5362 0.52118 0.000 0.672 0.012 0.080 NA
#> GSM215059 2 0.4761 0.55616 0.000 0.728 0.000 0.104 NA
#> GSM215060 2 0.3073 0.67922 0.000 0.868 0.004 0.052 NA
#> GSM215061 2 0.4849 0.38587 0.000 0.712 0.032 0.232 NA
#> GSM215062 4 0.6012 0.73155 0.000 0.248 0.032 0.628 NA
#> GSM215063 2 0.5631 -0.23905 0.000 0.540 0.040 0.400 NA
#> GSM215064 4 0.6012 0.73155 0.000 0.248 0.032 0.628 NA
#> GSM215065 4 0.4598 0.74657 0.000 0.264 0.028 0.700 NA
#> GSM215066 2 0.1267 0.69598 0.000 0.960 0.012 0.024 NA
#> GSM215067 4 0.4598 0.74657 0.000 0.264 0.028 0.700 NA
#> GSM215068 2 0.2644 0.66143 0.000 0.896 0.008 0.060 NA
#> GSM215069 2 0.2654 0.68645 0.000 0.888 0.000 0.048 NA
#> GSM215070 2 0.2037 0.69896 0.000 0.920 0.004 0.012 NA
#> GSM215071 2 0.1569 0.70170 0.000 0.944 0.004 0.008 NA
#> GSM215072 2 0.7178 -0.02219 0.000 0.484 0.036 0.228 NA
#> GSM215073 2 0.2654 0.68375 0.000 0.884 0.000 0.032 NA
#> GSM215074 2 0.1412 0.70564 0.000 0.952 0.004 0.008 NA
#> GSM215075 2 0.2673 0.67392 0.000 0.900 0.020 0.044 NA
#> GSM215076 2 0.6447 0.30885 0.000 0.520 0.064 0.052 NA
#> GSM215077 2 0.5663 0.47497 0.000 0.620 0.028 0.052 NA
#> GSM215078 2 0.5663 0.47497 0.000 0.620 0.028 0.052 NA
#> GSM215079 2 0.1314 0.69804 0.000 0.960 0.012 0.012 NA
#> GSM215080 2 0.0727 0.69973 0.000 0.980 0.004 0.012 NA
#> GSM215081 2 0.7171 0.06429 0.000 0.512 0.048 0.208 NA
#> GSM215082 4 0.6785 0.68199 0.000 0.304 0.024 0.508 NA
#> GSM215083 1 0.0609 0.78027 0.980 0.000 0.020 0.000 NA
#> GSM215084 1 0.4201 0.66693 0.592 0.000 0.000 0.000 NA
#> GSM215085 1 0.0566 0.78105 0.984 0.000 0.012 0.000 NA
#> GSM215086 1 0.0609 0.78027 0.980 0.000 0.020 0.000 NA
#> GSM215087 1 0.4031 0.70648 0.796 0.000 0.148 0.008 NA
#> GSM215088 3 0.2891 0.88032 0.176 0.000 0.824 0.000 NA
#> GSM215089 3 0.4031 0.86929 0.160 0.000 0.788 0.004 NA
#> GSM215090 1 0.4171 0.67306 0.604 0.000 0.000 0.000 NA
#> GSM215091 3 0.4356 0.69008 0.340 0.000 0.648 0.000 NA
#> GSM215092 1 0.4150 0.67592 0.612 0.000 0.000 0.000 NA
#> GSM215093 3 0.6562 0.81226 0.144 0.000 0.628 0.148 NA
#> GSM215094 1 0.1041 0.78703 0.964 0.000 0.000 0.004 NA
#> GSM215095 1 0.4195 0.75478 0.816 0.000 0.064 0.044 NA
#> GSM215096 1 0.1638 0.75353 0.932 0.000 0.064 0.000 NA
#> GSM215097 1 0.1638 0.78809 0.932 0.000 0.004 0.000 NA
#> GSM215098 1 0.0955 0.78627 0.968 0.000 0.000 0.004 NA
#> GSM215099 1 0.2020 0.78425 0.900 0.000 0.000 0.000 NA
#> GSM215100 1 0.4171 0.67306 0.604 0.000 0.000 0.000 NA
#> GSM215101 3 0.4281 0.86184 0.172 0.000 0.768 0.004 NA
#> GSM215102 3 0.5176 0.86906 0.148 0.000 0.736 0.076 NA
#> GSM215103 3 0.3592 0.88322 0.168 0.000 0.808 0.012 NA
#> GSM215104 1 0.0510 0.78151 0.984 0.000 0.016 0.000 NA
#> GSM215105 1 0.5784 0.35091 0.636 0.000 0.268 0.040 NA
#> GSM215106 1 0.0510 0.78151 0.984 0.000 0.016 0.000 NA
#> GSM215107 1 0.4138 0.67800 0.616 0.000 0.000 0.000 NA
#> GSM215108 3 0.5176 0.86906 0.148 0.000 0.736 0.076 NA
#> GSM215109 3 0.6709 0.80919 0.144 0.000 0.616 0.148 NA
#> GSM215110 1 0.4666 0.64759 0.572 0.000 0.000 0.016 NA
#> GSM215111 1 0.3241 0.76278 0.872 0.000 0.052 0.040 NA
#> GSM215112 1 0.3593 0.74964 0.840 0.000 0.096 0.012 NA
#> GSM215113 1 0.4171 0.66821 0.604 0.000 0.000 0.000 NA
#> GSM215114 3 0.3167 0.87871 0.172 0.000 0.820 0.004 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 2 0.3862 0.6162 0.000 0.808 0.016 NA 0.044 0.016
#> GSM215052 2 0.6931 -0.0412 0.000 0.444 0.012 NA 0.056 0.316
#> GSM215053 2 0.1845 0.6559 0.000 0.916 0.008 NA 0.004 0.000
#> GSM215054 2 0.1845 0.6560 0.000 0.916 0.008 NA 0.004 0.000
#> GSM215055 2 0.6344 0.3963 0.000 0.612 0.016 NA 0.140 0.140
#> GSM215056 6 0.7522 0.4555 0.000 0.344 0.016 NA 0.140 0.364
#> GSM215057 6 0.7522 0.4984 0.000 0.304 0.004 NA 0.160 0.360
#> GSM215058 2 0.5619 0.4842 0.000 0.660 0.000 NA 0.128 0.132
#> GSM215059 2 0.5482 0.4976 0.000 0.676 0.004 NA 0.152 0.060
#> GSM215060 2 0.3836 0.6130 0.000 0.804 0.000 NA 0.108 0.032
#> GSM215061 2 0.5439 0.3302 0.000 0.608 0.008 NA 0.000 0.200
#> GSM215062 6 0.2454 0.6555 0.000 0.160 0.000 NA 0.000 0.840
#> GSM215063 2 0.6205 -0.3231 0.000 0.392 0.000 NA 0.004 0.288
#> GSM215064 6 0.2454 0.6555 0.000 0.160 0.000 NA 0.000 0.840
#> GSM215065 6 0.6146 0.6712 0.000 0.176 0.008 NA 0.020 0.544
#> GSM215066 2 0.2265 0.6558 0.000 0.896 0.004 NA 0.000 0.024
#> GSM215067 6 0.6146 0.6712 0.000 0.176 0.008 NA 0.020 0.544
#> GSM215068 2 0.3645 0.6276 0.000 0.828 0.004 NA 0.032 0.060
#> GSM215069 2 0.2985 0.6438 0.000 0.872 0.004 NA 0.044 0.032
#> GSM215070 2 0.1401 0.6667 0.000 0.948 0.004 NA 0.028 0.000
#> GSM215071 2 0.1881 0.6610 0.000 0.928 0.004 NA 0.040 0.008
#> GSM215072 2 0.6218 0.0410 0.000 0.492 0.004 NA 0.056 0.360
#> GSM215073 2 0.3584 0.6205 0.000 0.820 0.004 NA 0.104 0.012
#> GSM215074 2 0.1401 0.6670 0.000 0.948 0.004 NA 0.028 0.000
#> GSM215075 2 0.3622 0.6332 0.000 0.820 0.000 NA 0.032 0.048
#> GSM215076 2 0.7845 0.1289 0.000 0.420 0.032 NA 0.188 0.172
#> GSM215077 2 0.6295 0.4041 0.000 0.576 0.036 NA 0.228 0.020
#> GSM215078 2 0.6295 0.4041 0.000 0.576 0.036 NA 0.228 0.020
#> GSM215079 2 0.1152 0.6630 0.000 0.952 0.004 NA 0.000 0.000
#> GSM215080 2 0.1490 0.6647 0.000 0.948 0.004 NA 0.008 0.016
#> GSM215081 2 0.6050 0.1474 0.000 0.532 0.008 NA 0.052 0.336
#> GSM215082 6 0.7594 0.6057 0.000 0.276 0.024 NA 0.096 0.400
#> GSM215083 1 0.0603 0.7662 0.980 0.000 0.016 NA 0.000 0.004
#> GSM215084 5 0.4315 0.9184 0.384 0.000 0.004 NA 0.596 0.012
#> GSM215085 1 0.0146 0.7682 0.996 0.000 0.004 NA 0.000 0.000
#> GSM215086 1 0.0260 0.7678 0.992 0.000 0.008 NA 0.000 0.000
#> GSM215087 1 0.5550 0.4375 0.620 0.000 0.264 NA 0.080 0.020
#> GSM215088 3 0.2313 0.8191 0.100 0.000 0.884 NA 0.000 0.004
#> GSM215089 3 0.3658 0.7964 0.096 0.000 0.816 NA 0.072 0.004
#> GSM215090 5 0.3756 0.9313 0.400 0.000 0.000 NA 0.600 0.000
#> GSM215091 3 0.3482 0.5673 0.316 0.000 0.684 NA 0.000 0.000
#> GSM215092 5 0.3975 0.8875 0.452 0.000 0.000 NA 0.544 0.004
#> GSM215093 3 0.5335 0.7040 0.076 0.000 0.556 NA 0.016 0.000
#> GSM215094 1 0.1410 0.7428 0.944 0.000 0.000 NA 0.044 0.008
#> GSM215095 1 0.5869 0.5381 0.680 0.000 0.076 NA 0.112 0.092
#> GSM215096 1 0.1714 0.7238 0.908 0.000 0.092 NA 0.000 0.000
#> GSM215097 1 0.1663 0.6963 0.912 0.000 0.000 NA 0.088 0.000
#> GSM215098 1 0.1268 0.7497 0.952 0.000 0.000 NA 0.036 0.008
#> GSM215099 1 0.2092 0.6404 0.876 0.000 0.000 NA 0.124 0.000
#> GSM215100 5 0.3765 0.9313 0.404 0.000 0.000 NA 0.596 0.000
#> GSM215101 3 0.4356 0.7800 0.116 0.000 0.776 NA 0.072 0.020
#> GSM215102 3 0.4931 0.7911 0.080 0.000 0.716 NA 0.012 0.024
#> GSM215103 3 0.3058 0.8191 0.096 0.000 0.856 NA 0.004 0.020
#> GSM215104 1 0.0405 0.7668 0.988 0.000 0.008 NA 0.004 0.000
#> GSM215105 1 0.6666 0.3727 0.572 0.000 0.224 NA 0.068 0.092
#> GSM215106 1 0.0405 0.7668 0.988 0.000 0.008 NA 0.004 0.000
#> GSM215107 5 0.3843 0.8873 0.452 0.000 0.000 NA 0.548 0.000
#> GSM215108 3 0.4931 0.7911 0.080 0.000 0.716 NA 0.012 0.024
#> GSM215109 3 0.5496 0.6978 0.076 0.000 0.540 NA 0.016 0.004
#> GSM215110 5 0.4725 0.8942 0.372 0.000 0.004 NA 0.588 0.020
#> GSM215111 1 0.4682 0.6208 0.772 0.000 0.052 NA 0.072 0.076
#> GSM215112 1 0.5470 0.5181 0.688 0.000 0.160 NA 0.088 0.044
#> GSM215113 5 0.4174 0.9169 0.408 0.000 0.004 NA 0.580 0.004
#> GSM215114 3 0.3501 0.8054 0.104 0.000 0.832 NA 0.036 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> ATC:kmeans 64 9.19e-15 1.000 2
#> ATC:kmeans 64 1.27e-14 0.999 3
#> ATC:kmeans 55 6.87e-12 0.941 4
#> ATC:kmeans 54 1.12e-11 0.952 5
#> ATC:kmeans 49 5.84e-10 0.782 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 51941 rows and 64 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 1.000 0.989 0.995 0.0614 0.970 0.940
#> 4 4 0.791 0.883 0.924 0.0809 1.000 0.999
#> 5 5 0.703 0.717 0.865 0.0776 0.941 0.874
#> 6 6 0.632 0.597 0.821 0.0844 0.985 0.962
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
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.0000 1.000 0.000 1 0.000
#> GSM215052 2 0.0000 1.000 0.000 1 0.000
#> GSM215053 2 0.0000 1.000 0.000 1 0.000
#> GSM215054 2 0.0000 1.000 0.000 1 0.000
#> GSM215055 2 0.0000 1.000 0.000 1 0.000
#> GSM215056 2 0.0000 1.000 0.000 1 0.000
#> GSM215057 2 0.0000 1.000 0.000 1 0.000
#> GSM215058 2 0.0000 1.000 0.000 1 0.000
#> GSM215059 2 0.0000 1.000 0.000 1 0.000
#> GSM215060 2 0.0000 1.000 0.000 1 0.000
#> GSM215061 2 0.0000 1.000 0.000 1 0.000
#> GSM215062 2 0.0000 1.000 0.000 1 0.000
#> GSM215063 2 0.0000 1.000 0.000 1 0.000
#> GSM215064 2 0.0000 1.000 0.000 1 0.000
#> GSM215065 2 0.0000 1.000 0.000 1 0.000
#> GSM215066 2 0.0000 1.000 0.000 1 0.000
#> GSM215067 2 0.0000 1.000 0.000 1 0.000
#> GSM215068 2 0.0000 1.000 0.000 1 0.000
#> GSM215069 2 0.0000 1.000 0.000 1 0.000
#> GSM215070 2 0.0000 1.000 0.000 1 0.000
#> GSM215071 2 0.0000 1.000 0.000 1 0.000
#> GSM215072 2 0.0000 1.000 0.000 1 0.000
#> GSM215073 2 0.0000 1.000 0.000 1 0.000
#> GSM215074 2 0.0000 1.000 0.000 1 0.000
#> GSM215075 2 0.0000 1.000 0.000 1 0.000
#> GSM215076 2 0.0000 1.000 0.000 1 0.000
#> GSM215077 2 0.0000 1.000 0.000 1 0.000
#> GSM215078 2 0.0000 1.000 0.000 1 0.000
#> GSM215079 2 0.0000 1.000 0.000 1 0.000
#> GSM215080 2 0.0000 1.000 0.000 1 0.000
#> GSM215081 2 0.0000 1.000 0.000 1 0.000
#> GSM215082 2 0.0000 1.000 0.000 1 0.000
#> GSM215083 1 0.0000 0.992 1.000 0 0.000
#> GSM215084 1 0.0000 0.992 1.000 0 0.000
#> GSM215085 1 0.0000 0.992 1.000 0 0.000
#> GSM215086 1 0.0000 0.992 1.000 0 0.000
#> GSM215087 1 0.0000 0.992 1.000 0 0.000
#> GSM215088 1 0.0000 0.992 1.000 0 0.000
#> GSM215089 1 0.0000 0.992 1.000 0 0.000
#> GSM215090 1 0.0000 0.992 1.000 0 0.000
#> GSM215091 1 0.0000 0.992 1.000 0 0.000
#> GSM215092 1 0.0000 0.992 1.000 0 0.000
#> GSM215093 3 0.2959 0.890 0.100 0 0.900
#> GSM215094 1 0.0000 0.992 1.000 0 0.000
#> GSM215095 1 0.0000 0.992 1.000 0 0.000
#> GSM215096 1 0.0000 0.992 1.000 0 0.000
#> GSM215097 1 0.0000 0.992 1.000 0 0.000
#> GSM215098 1 0.0000 0.992 1.000 0 0.000
#> GSM215099 1 0.0000 0.992 1.000 0 0.000
#> GSM215100 1 0.0000 0.992 1.000 0 0.000
#> GSM215101 1 0.0000 0.992 1.000 0 0.000
#> GSM215102 1 0.2959 0.888 0.900 0 0.100
#> GSM215103 1 0.0424 0.985 0.992 0 0.008
#> GSM215104 1 0.0000 0.992 1.000 0 0.000
#> GSM215105 1 0.0424 0.985 0.992 0 0.008
#> GSM215106 1 0.0000 0.992 1.000 0 0.000
#> GSM215107 1 0.0000 0.992 1.000 0 0.000
#> GSM215108 1 0.3192 0.874 0.888 0 0.112
#> GSM215109 3 0.0000 0.900 0.000 0 1.000
#> GSM215110 1 0.0000 0.992 1.000 0 0.000
#> GSM215111 1 0.0000 0.992 1.000 0 0.000
#> GSM215112 1 0.0000 0.992 1.000 0 0.000
#> GSM215113 1 0.0000 0.992 1.000 0 0.000
#> GSM215114 1 0.0000 0.992 1.000 0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.0336 0.957 0.000 0.992 0.000 0.008
#> GSM215052 2 0.1118 0.947 0.000 0.964 0.000 0.036
#> GSM215053 2 0.0188 0.957 0.000 0.996 0.000 0.004
#> GSM215054 2 0.0188 0.957 0.000 0.996 0.000 0.004
#> GSM215055 2 0.0817 0.955 0.000 0.976 0.000 0.024
#> GSM215056 2 0.1211 0.951 0.000 0.960 0.000 0.040
#> GSM215057 2 0.1389 0.947 0.000 0.952 0.000 0.048
#> GSM215058 2 0.1022 0.953 0.000 0.968 0.000 0.032
#> GSM215059 2 0.0921 0.953 0.000 0.972 0.000 0.028
#> GSM215060 2 0.0336 0.957 0.000 0.992 0.000 0.008
#> GSM215061 2 0.0707 0.953 0.000 0.980 0.000 0.020
#> GSM215062 2 0.4431 0.699 0.000 0.696 0.000 0.304
#> GSM215063 2 0.0817 0.953 0.000 0.976 0.000 0.024
#> GSM215064 2 0.4431 0.699 0.000 0.696 0.000 0.304
#> GSM215065 2 0.2589 0.891 0.000 0.884 0.000 0.116
#> GSM215066 2 0.0188 0.957 0.000 0.996 0.000 0.004
#> GSM215067 2 0.2760 0.886 0.000 0.872 0.000 0.128
#> GSM215068 2 0.0469 0.957 0.000 0.988 0.000 0.012
#> GSM215069 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM215070 2 0.0188 0.957 0.000 0.996 0.000 0.004
#> GSM215071 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM215072 2 0.2345 0.915 0.000 0.900 0.000 0.100
#> GSM215073 2 0.0188 0.957 0.000 0.996 0.000 0.004
#> GSM215074 2 0.0000 0.957 0.000 1.000 0.000 0.000
#> GSM215075 2 0.0336 0.957 0.000 0.992 0.000 0.008
#> GSM215076 2 0.2216 0.915 0.000 0.908 0.000 0.092
#> GSM215077 2 0.0336 0.957 0.000 0.992 0.000 0.008
#> GSM215078 2 0.0336 0.957 0.000 0.992 0.000 0.008
#> GSM215079 2 0.0188 0.957 0.000 0.996 0.000 0.004
#> GSM215080 2 0.0188 0.957 0.000 0.996 0.000 0.004
#> GSM215081 2 0.2469 0.907 0.000 0.892 0.000 0.108
#> GSM215082 2 0.1302 0.949 0.000 0.956 0.000 0.044
#> GSM215083 1 0.0592 0.921 0.984 0.000 0.016 0.000
#> GSM215084 1 0.2814 0.895 0.868 0.000 0.132 0.000
#> GSM215085 1 0.0469 0.918 0.988 0.000 0.012 0.000
#> GSM215086 1 0.0817 0.920 0.976 0.000 0.024 0.000
#> GSM215087 1 0.1118 0.920 0.964 0.000 0.036 0.000
#> GSM215088 1 0.2868 0.890 0.864 0.000 0.136 0.000
#> GSM215089 1 0.4040 0.816 0.752 0.000 0.248 0.000
#> GSM215090 1 0.2408 0.907 0.896 0.000 0.104 0.000
#> GSM215091 1 0.0817 0.920 0.976 0.000 0.024 0.000
#> GSM215092 1 0.0188 0.920 0.996 0.000 0.004 0.000
#> GSM215093 3 0.4348 0.000 0.024 0.000 0.780 0.196
#> GSM215094 1 0.0336 0.918 0.992 0.000 0.008 0.000
#> GSM215095 1 0.1867 0.914 0.928 0.000 0.072 0.000
#> GSM215096 1 0.0469 0.918 0.988 0.000 0.012 0.000
#> GSM215097 1 0.0817 0.920 0.976 0.000 0.024 0.000
#> GSM215098 1 0.0336 0.918 0.992 0.000 0.008 0.000
#> GSM215099 1 0.0336 0.920 0.992 0.000 0.008 0.000
#> GSM215100 1 0.2011 0.914 0.920 0.000 0.080 0.000
#> GSM215101 1 0.3400 0.867 0.820 0.000 0.180 0.000
#> GSM215102 1 0.5038 0.739 0.684 0.000 0.296 0.020
#> GSM215103 1 0.3108 0.883 0.872 0.000 0.112 0.016
#> GSM215104 1 0.0469 0.918 0.988 0.000 0.012 0.000
#> GSM215105 1 0.3681 0.869 0.816 0.000 0.176 0.008
#> GSM215106 1 0.0469 0.918 0.988 0.000 0.012 0.000
#> GSM215107 1 0.0188 0.919 0.996 0.000 0.004 0.000
#> GSM215108 1 0.6028 0.674 0.644 0.000 0.280 0.076
#> GSM215109 4 0.4454 0.000 0.000 0.000 0.308 0.692
#> GSM215110 1 0.3444 0.865 0.816 0.000 0.184 0.000
#> GSM215111 1 0.2281 0.910 0.904 0.000 0.096 0.000
#> GSM215112 1 0.1211 0.919 0.960 0.000 0.040 0.000
#> GSM215113 1 0.2973 0.890 0.856 0.000 0.144 0.000
#> GSM215114 1 0.2589 0.904 0.884 0.000 0.116 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.0794 0.9041 0.000 0.972 0.000 0.028 0.000
#> GSM215052 2 0.2020 0.8488 0.000 0.900 0.000 0.100 0.000
#> GSM215053 2 0.0404 0.9045 0.000 0.988 0.000 0.012 0.000
#> GSM215054 2 0.0290 0.9044 0.000 0.992 0.000 0.008 0.000
#> GSM215055 2 0.1043 0.8969 0.000 0.960 0.000 0.040 0.000
#> GSM215056 2 0.1892 0.8678 0.000 0.916 0.004 0.080 0.000
#> GSM215057 2 0.2054 0.8666 0.000 0.916 0.008 0.072 0.004
#> GSM215058 2 0.1831 0.8682 0.000 0.920 0.004 0.076 0.000
#> GSM215059 2 0.1041 0.8971 0.000 0.964 0.004 0.032 0.000
#> GSM215060 2 0.0566 0.9054 0.000 0.984 0.004 0.012 0.000
#> GSM215061 2 0.1043 0.8914 0.000 0.960 0.000 0.040 0.000
#> GSM215062 4 0.3895 0.9916 0.000 0.320 0.000 0.680 0.000
#> GSM215063 2 0.1195 0.8907 0.000 0.960 0.012 0.028 0.000
#> GSM215064 4 0.3876 0.9916 0.000 0.316 0.000 0.684 0.000
#> GSM215065 2 0.3990 0.4722 0.000 0.740 0.012 0.244 0.004
#> GSM215066 2 0.0510 0.9046 0.000 0.984 0.000 0.016 0.000
#> GSM215067 2 0.4146 0.4079 0.000 0.716 0.012 0.268 0.004
#> GSM215068 2 0.0703 0.9054 0.000 0.976 0.000 0.024 0.000
#> GSM215069 2 0.0290 0.9057 0.000 0.992 0.000 0.008 0.000
#> GSM215070 2 0.0162 0.9050 0.000 0.996 0.000 0.004 0.000
#> GSM215071 2 0.0162 0.9050 0.000 0.996 0.000 0.004 0.000
#> GSM215072 2 0.3160 0.7172 0.000 0.808 0.004 0.188 0.000
#> GSM215073 2 0.0324 0.9051 0.000 0.992 0.004 0.004 0.000
#> GSM215074 2 0.0000 0.9053 0.000 1.000 0.000 0.000 0.000
#> GSM215075 2 0.0609 0.9044 0.000 0.980 0.000 0.020 0.000
#> GSM215076 2 0.3048 0.7264 0.000 0.820 0.004 0.176 0.000
#> GSM215077 2 0.0771 0.9044 0.000 0.976 0.004 0.020 0.000
#> GSM215078 2 0.0865 0.9037 0.000 0.972 0.004 0.024 0.000
#> GSM215079 2 0.0290 0.9044 0.000 0.992 0.000 0.008 0.000
#> GSM215080 2 0.0290 0.9044 0.000 0.992 0.000 0.008 0.000
#> GSM215081 2 0.3430 0.6419 0.000 0.776 0.004 0.220 0.000
#> GSM215082 2 0.2674 0.8017 0.000 0.856 0.004 0.140 0.000
#> GSM215083 1 0.1205 0.7842 0.956 0.000 0.040 0.000 0.004
#> GSM215084 1 0.3837 0.6013 0.692 0.000 0.308 0.000 0.000
#> GSM215085 1 0.0566 0.7731 0.984 0.000 0.012 0.004 0.000
#> GSM215086 1 0.0798 0.7763 0.976 0.000 0.016 0.008 0.000
#> GSM215087 1 0.2068 0.7767 0.904 0.000 0.092 0.004 0.000
#> GSM215088 1 0.4643 0.6370 0.732 0.000 0.208 0.008 0.052
#> GSM215089 1 0.4375 0.3255 0.576 0.000 0.420 0.000 0.004
#> GSM215090 1 0.3586 0.6649 0.736 0.000 0.264 0.000 0.000
#> GSM215091 1 0.1331 0.7707 0.952 0.000 0.040 0.008 0.000
#> GSM215092 1 0.1341 0.7835 0.944 0.000 0.056 0.000 0.000
#> GSM215093 5 0.1831 0.0000 0.004 0.000 0.076 0.000 0.920
#> GSM215094 1 0.0451 0.7752 0.988 0.000 0.008 0.004 0.000
#> GSM215095 1 0.3177 0.7205 0.792 0.000 0.208 0.000 0.000
#> GSM215096 1 0.0693 0.7719 0.980 0.000 0.012 0.008 0.000
#> GSM215097 1 0.0955 0.7794 0.968 0.000 0.028 0.004 0.000
#> GSM215098 1 0.0566 0.7731 0.984 0.000 0.012 0.004 0.000
#> GSM215099 1 0.0609 0.7823 0.980 0.000 0.020 0.000 0.000
#> GSM215100 1 0.3210 0.7169 0.788 0.000 0.212 0.000 0.000
#> GSM215101 1 0.3661 0.6451 0.724 0.000 0.276 0.000 0.000
#> GSM215102 3 0.4972 -0.1895 0.476 0.000 0.500 0.004 0.020
#> GSM215103 1 0.4030 0.6135 0.736 0.000 0.248 0.008 0.008
#> GSM215104 1 0.0566 0.7765 0.984 0.000 0.012 0.004 0.000
#> GSM215105 1 0.4066 0.5373 0.672 0.000 0.324 0.000 0.004
#> GSM215106 1 0.0693 0.7719 0.980 0.000 0.012 0.008 0.000
#> GSM215107 1 0.0510 0.7830 0.984 0.000 0.016 0.000 0.000
#> GSM215108 3 0.5029 -0.0598 0.444 0.000 0.528 0.004 0.024
#> GSM215109 3 0.6504 -0.6567 0.000 0.000 0.484 0.288 0.228
#> GSM215110 1 0.4015 0.5241 0.652 0.000 0.348 0.000 0.000
#> GSM215111 1 0.3242 0.7132 0.784 0.000 0.216 0.000 0.000
#> GSM215112 1 0.2179 0.7702 0.888 0.000 0.112 0.000 0.000
#> GSM215113 1 0.3774 0.6144 0.704 0.000 0.296 0.000 0.000
#> GSM215114 1 0.4173 0.6089 0.688 0.000 0.300 0.000 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 2 0.1844 0.8416 0.000 0.928 0.016 0.016 0.000 0.040
#> GSM215052 2 0.3689 0.7205 0.000 0.772 0.016 0.020 0.000 0.192
#> GSM215053 2 0.1350 0.8414 0.000 0.952 0.020 0.008 0.000 0.020
#> GSM215054 2 0.1251 0.8423 0.000 0.956 0.024 0.008 0.000 0.012
#> GSM215055 2 0.1555 0.8467 0.000 0.932 0.004 0.004 0.000 0.060
#> GSM215056 2 0.2798 0.8257 0.000 0.856 0.012 0.004 0.008 0.120
#> GSM215057 2 0.3726 0.7938 0.000 0.800 0.020 0.024 0.008 0.148
#> GSM215058 2 0.2883 0.8024 0.000 0.832 0.008 0.008 0.000 0.152
#> GSM215059 2 0.2901 0.8287 0.000 0.868 0.016 0.020 0.008 0.088
#> GSM215060 2 0.1870 0.8441 0.000 0.928 0.012 0.012 0.004 0.044
#> GSM215061 2 0.3724 0.7825 0.000 0.820 0.036 0.020 0.016 0.108
#> GSM215062 6 0.2420 0.9868 0.000 0.108 0.008 0.008 0.000 0.876
#> GSM215063 2 0.3992 0.7645 0.000 0.800 0.032 0.024 0.020 0.124
#> GSM215064 6 0.2420 0.9867 0.000 0.108 0.008 0.008 0.000 0.876
#> GSM215065 2 0.6493 0.0841 0.000 0.488 0.100 0.044 0.020 0.348
#> GSM215066 2 0.1843 0.8375 0.000 0.932 0.016 0.016 0.004 0.032
#> GSM215067 2 0.6110 0.3906 0.000 0.568 0.076 0.040 0.024 0.292
#> GSM215068 2 0.1606 0.8476 0.000 0.932 0.004 0.008 0.000 0.056
#> GSM215069 2 0.1552 0.8461 0.000 0.940 0.020 0.004 0.000 0.036
#> GSM215070 2 0.1053 0.8469 0.000 0.964 0.012 0.004 0.000 0.020
#> GSM215071 2 0.0622 0.8471 0.000 0.980 0.008 0.000 0.000 0.012
#> GSM215072 2 0.4115 0.5103 0.000 0.624 0.012 0.004 0.000 0.360
#> GSM215073 2 0.1862 0.8436 0.000 0.928 0.016 0.008 0.004 0.044
#> GSM215074 2 0.0767 0.8483 0.000 0.976 0.008 0.004 0.000 0.012
#> GSM215075 2 0.1692 0.8389 0.000 0.932 0.008 0.012 0.000 0.048
#> GSM215076 2 0.4437 0.5618 0.000 0.656 0.020 0.020 0.000 0.304
#> GSM215077 2 0.2713 0.8364 0.000 0.884 0.024 0.024 0.004 0.064
#> GSM215078 2 0.2653 0.8370 0.000 0.888 0.024 0.024 0.004 0.060
#> GSM215079 2 0.1086 0.8439 0.000 0.964 0.012 0.012 0.000 0.012
#> GSM215080 2 0.0692 0.8478 0.000 0.976 0.004 0.000 0.000 0.020
#> GSM215081 2 0.4102 0.4978 0.000 0.628 0.012 0.004 0.000 0.356
#> GSM215082 2 0.3733 0.7692 0.000 0.784 0.028 0.012 0.004 0.172
#> GSM215083 1 0.1531 0.6644 0.928 0.000 0.068 0.000 0.000 0.004
#> GSM215084 1 0.3782 0.2512 0.636 0.000 0.360 0.000 0.004 0.000
#> GSM215085 1 0.0858 0.6674 0.968 0.000 0.028 0.000 0.000 0.004
#> GSM215086 1 0.1082 0.6674 0.956 0.000 0.040 0.000 0.000 0.004
#> GSM215087 1 0.3309 0.5736 0.788 0.000 0.192 0.004 0.000 0.016
#> GSM215088 1 0.5352 0.1611 0.588 0.000 0.312 0.004 0.084 0.012
#> GSM215089 3 0.4189 0.3080 0.436 0.000 0.552 0.000 0.008 0.004
#> GSM215090 1 0.3684 0.3405 0.664 0.000 0.332 0.000 0.000 0.004
#> GSM215091 1 0.1956 0.6525 0.908 0.000 0.080 0.004 0.000 0.008
#> GSM215092 1 0.1007 0.6728 0.956 0.000 0.044 0.000 0.000 0.000
#> GSM215093 5 0.0632 0.0000 0.000 0.000 0.024 0.000 0.976 0.000
#> GSM215094 1 0.0713 0.6724 0.972 0.000 0.028 0.000 0.000 0.000
#> GSM215095 1 0.3606 0.4474 0.708 0.000 0.284 0.004 0.000 0.004
#> GSM215096 1 0.1155 0.6630 0.956 0.000 0.036 0.000 0.004 0.004
#> GSM215097 1 0.1364 0.6748 0.944 0.000 0.048 0.004 0.000 0.004
#> GSM215098 1 0.0713 0.6707 0.972 0.000 0.028 0.000 0.000 0.000
#> GSM215099 1 0.0692 0.6759 0.976 0.000 0.020 0.000 0.000 0.004
#> GSM215100 1 0.3288 0.4597 0.724 0.000 0.276 0.000 0.000 0.000
#> GSM215101 1 0.4218 0.1044 0.584 0.000 0.400 0.000 0.004 0.012
#> GSM215102 3 0.4344 0.6754 0.308 0.000 0.660 0.016 0.012 0.004
#> GSM215103 1 0.5443 -0.0708 0.548 0.000 0.376 0.032 0.020 0.024
#> GSM215104 1 0.0692 0.6690 0.976 0.000 0.020 0.000 0.000 0.004
#> GSM215105 1 0.4536 -0.3922 0.496 0.000 0.476 0.024 0.000 0.004
#> GSM215106 1 0.0777 0.6677 0.972 0.000 0.024 0.000 0.000 0.004
#> GSM215107 1 0.0713 0.6759 0.972 0.000 0.028 0.000 0.000 0.000
#> GSM215108 3 0.4628 0.6300 0.240 0.000 0.688 0.060 0.008 0.004
#> GSM215109 4 0.2365 0.0000 0.000 0.000 0.040 0.888 0.072 0.000
#> GSM215110 1 0.3944 -0.0473 0.568 0.000 0.428 0.000 0.004 0.000
#> GSM215111 1 0.3608 0.4247 0.716 0.000 0.272 0.012 0.000 0.000
#> GSM215112 1 0.3003 0.6019 0.812 0.000 0.172 0.000 0.000 0.016
#> GSM215113 1 0.3804 0.2681 0.656 0.000 0.336 0.008 0.000 0.000
#> GSM215114 1 0.4938 0.1120 0.572 0.000 0.380 0.016 0.012 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 disease.state(p) individual(p) k
#> ATC:skmeans 64 9.19e-15 1.000 2
#> ATC:skmeans 64 1.27e-14 0.999 3
#> ATC:skmeans 62 2.54e-14 1.000 4
#> ATC:skmeans 57 4.19e-13 0.997 5
#> ATC:skmeans 46 5.67e-10 0.992 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 51941 rows and 64 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 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.886 0.933 0.945 0.2021 0.881 0.758
#> 4 4 0.861 0.796 0.870 0.0571 0.963 0.900
#> 5 5 0.886 0.791 0.876 0.0211 0.969 0.910
#> 6 6 0.854 0.698 0.847 0.0439 0.921 0.768
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.000 1.000 0.000 1 0.000
#> GSM215052 2 0.000 1.000 0.000 1 0.000
#> GSM215053 2 0.000 1.000 0.000 1 0.000
#> GSM215054 2 0.000 1.000 0.000 1 0.000
#> GSM215055 2 0.000 1.000 0.000 1 0.000
#> GSM215056 2 0.000 1.000 0.000 1 0.000
#> GSM215057 2 0.000 1.000 0.000 1 0.000
#> GSM215058 2 0.000 1.000 0.000 1 0.000
#> GSM215059 2 0.000 1.000 0.000 1 0.000
#> GSM215060 2 0.000 1.000 0.000 1 0.000
#> GSM215061 2 0.000 1.000 0.000 1 0.000
#> GSM215062 2 0.000 1.000 0.000 1 0.000
#> GSM215063 2 0.000 1.000 0.000 1 0.000
#> GSM215064 2 0.000 1.000 0.000 1 0.000
#> GSM215065 2 0.000 1.000 0.000 1 0.000
#> GSM215066 2 0.000 1.000 0.000 1 0.000
#> GSM215067 2 0.000 1.000 0.000 1 0.000
#> GSM215068 2 0.000 1.000 0.000 1 0.000
#> GSM215069 2 0.000 1.000 0.000 1 0.000
#> GSM215070 2 0.000 1.000 0.000 1 0.000
#> GSM215071 2 0.000 1.000 0.000 1 0.000
#> GSM215072 2 0.000 1.000 0.000 1 0.000
#> GSM215073 2 0.000 1.000 0.000 1 0.000
#> GSM215074 2 0.000 1.000 0.000 1 0.000
#> GSM215075 2 0.000 1.000 0.000 1 0.000
#> GSM215076 2 0.000 1.000 0.000 1 0.000
#> GSM215077 2 0.000 1.000 0.000 1 0.000
#> GSM215078 2 0.000 1.000 0.000 1 0.000
#> GSM215079 2 0.000 1.000 0.000 1 0.000
#> GSM215080 2 0.000 1.000 0.000 1 0.000
#> GSM215081 2 0.000 1.000 0.000 1 0.000
#> GSM215082 2 0.000 1.000 0.000 1 0.000
#> GSM215083 1 0.254 0.919 0.920 0 0.080
#> GSM215084 1 0.000 0.913 1.000 0 0.000
#> GSM215085 1 0.254 0.919 0.920 0 0.080
#> GSM215086 1 0.254 0.919 0.920 0 0.080
#> GSM215087 3 0.429 0.880 0.180 0 0.820
#> GSM215088 3 0.319 0.890 0.112 0 0.888
#> GSM215089 3 0.382 0.896 0.148 0 0.852
#> GSM215090 1 0.000 0.913 1.000 0 0.000
#> GSM215091 3 0.470 0.886 0.212 0 0.788
#> GSM215092 1 0.000 0.913 1.000 0 0.000
#> GSM215093 3 0.406 0.898 0.164 0 0.836
#> GSM215094 1 0.103 0.918 0.976 0 0.024
#> GSM215095 1 0.608 0.268 0.612 0 0.388
#> GSM215096 3 0.475 0.883 0.216 0 0.784
#> GSM215097 1 0.254 0.919 0.920 0 0.080
#> GSM215098 1 0.263 0.917 0.916 0 0.084
#> GSM215099 1 0.103 0.918 0.976 0 0.024
#> GSM215100 1 0.000 0.913 1.000 0 0.000
#> GSM215101 3 0.375 0.897 0.144 0 0.856
#> GSM215102 3 0.627 0.401 0.452 0 0.548
#> GSM215103 3 0.424 0.900 0.176 0 0.824
#> GSM215104 1 0.254 0.919 0.920 0 0.080
#> GSM215105 1 0.362 0.870 0.864 0 0.136
#> GSM215106 1 0.254 0.919 0.920 0 0.080
#> GSM215107 1 0.000 0.913 1.000 0 0.000
#> GSM215108 3 0.429 0.899 0.180 0 0.820
#> GSM215109 3 0.216 0.819 0.064 0 0.936
#> GSM215110 1 0.000 0.913 1.000 0 0.000
#> GSM215111 1 0.254 0.919 0.920 0 0.080
#> GSM215112 1 0.375 0.867 0.856 0 0.144
#> GSM215113 1 0.000 0.913 1.000 0 0.000
#> GSM215114 3 0.319 0.890 0.112 0 0.888
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215052 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215053 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215054 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215055 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215056 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215057 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215058 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215059 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215060 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215061 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215062 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215063 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215064 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215065 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215066 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215067 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215068 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215069 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215070 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215071 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215072 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215073 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215074 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215075 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215076 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215077 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215078 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215079 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215080 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215081 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215082 2 0.0000 1.00000 0.000 1 0.000 0.000
#> GSM215083 1 0.0000 0.72951 1.000 0 0.000 0.000
#> GSM215084 4 0.4992 1.00000 0.476 0 0.000 0.524
#> GSM215085 1 0.0000 0.72951 1.000 0 0.000 0.000
#> GSM215086 1 0.0000 0.72951 1.000 0 0.000 0.000
#> GSM215087 3 0.3356 0.67384 0.176 0 0.824 0.000
#> GSM215088 3 0.0188 0.70084 0.004 0 0.996 0.000
#> GSM215089 3 0.2814 0.66664 0.000 0 0.868 0.132
#> GSM215090 4 0.4992 1.00000 0.476 0 0.000 0.524
#> GSM215091 3 0.4776 0.61950 0.376 0 0.624 0.000
#> GSM215092 4 0.4992 1.00000 0.476 0 0.000 0.524
#> GSM215093 3 0.4319 0.68906 0.228 0 0.760 0.012
#> GSM215094 1 0.0000 0.72951 1.000 0 0.000 0.000
#> GSM215095 1 0.7546 -0.00857 0.408 0 0.404 0.188
#> GSM215096 3 0.4804 0.61114 0.384 0 0.616 0.000
#> GSM215097 1 0.0000 0.72951 1.000 0 0.000 0.000
#> GSM215098 1 0.0469 0.71635 0.988 0 0.012 0.000
#> GSM215099 1 0.0000 0.72951 1.000 0 0.000 0.000
#> GSM215100 4 0.4992 1.00000 0.476 0 0.000 0.524
#> GSM215101 3 0.2814 0.69615 0.132 0 0.868 0.000
#> GSM215102 3 0.5000 0.36829 0.496 0 0.504 0.000
#> GSM215103 3 0.4008 0.68493 0.244 0 0.756 0.000
#> GSM215104 1 0.0000 0.72951 1.000 0 0.000 0.000
#> GSM215105 1 0.2921 0.53337 0.860 0 0.140 0.000
#> GSM215106 1 0.0000 0.72951 1.000 0 0.000 0.000
#> GSM215107 1 0.5000 -0.94155 0.500 0 0.000 0.500
#> GSM215108 3 0.4103 0.68361 0.256 0 0.744 0.000
#> GSM215109 3 0.4992 0.50292 0.000 0 0.524 0.476
#> GSM215110 4 0.4992 1.00000 0.476 0 0.000 0.524
#> GSM215111 1 0.0000 0.72951 1.000 0 0.000 0.000
#> GSM215112 1 0.4072 0.39210 0.748 0 0.252 0.000
#> GSM215113 1 0.4994 -0.89046 0.520 0 0.000 0.480
#> GSM215114 3 0.0188 0.70084 0.004 0 0.996 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.0510 0.98585 0.000 0.984 0.000 0.016 0.000
#> GSM215052 2 0.0963 0.97263 0.000 0.964 0.000 0.036 0.000
#> GSM215053 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215054 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215055 2 0.0404 0.98682 0.000 0.988 0.000 0.012 0.000
#> GSM215056 2 0.0404 0.98670 0.000 0.988 0.000 0.012 0.000
#> GSM215057 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215058 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215059 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215060 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215061 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215062 2 0.2130 0.92076 0.000 0.908 0.000 0.080 0.012
#> GSM215063 2 0.0510 0.98585 0.000 0.984 0.000 0.016 0.000
#> GSM215064 2 0.2130 0.92076 0.000 0.908 0.000 0.080 0.012
#> GSM215065 2 0.0290 0.98699 0.000 0.992 0.000 0.008 0.000
#> GSM215066 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215067 2 0.0404 0.98671 0.000 0.988 0.000 0.012 0.000
#> GSM215068 2 0.0510 0.98585 0.000 0.984 0.000 0.016 0.000
#> GSM215069 2 0.0510 0.98585 0.000 0.984 0.000 0.016 0.000
#> GSM215070 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215071 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215072 2 0.0510 0.98585 0.000 0.984 0.000 0.016 0.000
#> GSM215073 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215074 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215075 2 0.0510 0.98585 0.000 0.984 0.000 0.016 0.000
#> GSM215076 2 0.0510 0.98585 0.000 0.984 0.000 0.016 0.000
#> GSM215077 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215078 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215079 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215080 2 0.0000 0.98830 0.000 1.000 0.000 0.000 0.000
#> GSM215081 2 0.0510 0.98585 0.000 0.984 0.000 0.016 0.000
#> GSM215082 2 0.0510 0.98585 0.000 0.984 0.000 0.016 0.000
#> GSM215083 1 0.4088 0.90684 0.632 0.000 0.368 0.000 0.000
#> GSM215084 5 0.4538 0.82872 0.016 0.000 0.364 0.000 0.620
#> GSM215085 1 0.4088 0.90684 0.632 0.000 0.368 0.000 0.000
#> GSM215086 1 0.4088 0.90684 0.632 0.000 0.368 0.000 0.000
#> GSM215087 3 0.5569 0.46266 0.080 0.000 0.556 0.000 0.364
#> GSM215088 3 0.4074 0.45853 0.000 0.000 0.636 0.000 0.364
#> GSM215089 3 0.4210 0.45069 0.000 0.000 0.588 0.000 0.412
#> GSM215090 5 0.4538 0.82872 0.016 0.000 0.364 0.000 0.620
#> GSM215091 3 0.2471 0.32653 0.136 0.000 0.864 0.000 0.000
#> GSM215092 5 0.4538 0.82872 0.016 0.000 0.364 0.000 0.620
#> GSM215093 3 0.4688 0.06660 0.008 0.000 0.532 0.456 0.004
#> GSM215094 1 0.4088 0.90684 0.632 0.000 0.368 0.000 0.000
#> GSM215095 5 0.6265 -0.34470 0.220 0.000 0.240 0.000 0.540
#> GSM215096 3 0.2732 0.27742 0.160 0.000 0.840 0.000 0.000
#> GSM215097 1 0.4088 0.90684 0.632 0.000 0.368 0.000 0.000
#> GSM215098 1 0.4570 0.87997 0.632 0.000 0.348 0.000 0.020
#> GSM215099 1 0.4088 0.90684 0.632 0.000 0.368 0.000 0.000
#> GSM215100 5 0.4538 0.82872 0.016 0.000 0.364 0.000 0.620
#> GSM215101 3 0.5068 0.47708 0.044 0.000 0.592 0.000 0.364
#> GSM215102 3 0.4179 0.22543 0.152 0.000 0.776 0.072 0.000
#> GSM215103 3 0.1830 0.40096 0.040 0.000 0.932 0.028 0.000
#> GSM215104 1 0.4088 0.90684 0.632 0.000 0.368 0.000 0.000
#> GSM215105 1 0.4489 0.83162 0.572 0.000 0.420 0.008 0.000
#> GSM215106 1 0.4088 0.90684 0.632 0.000 0.368 0.000 0.000
#> GSM215107 5 0.4787 0.81713 0.028 0.000 0.364 0.000 0.608
#> GSM215108 3 0.2535 0.39206 0.032 0.000 0.892 0.076 0.000
#> GSM215109 4 0.5579 0.00000 0.368 0.000 0.080 0.552 0.000
#> GSM215110 5 0.4538 0.82872 0.016 0.000 0.364 0.000 0.620
#> GSM215111 1 0.4088 0.90684 0.632 0.000 0.368 0.000 0.000
#> GSM215112 1 0.5874 0.00175 0.528 0.000 0.108 0.000 0.364
#> GSM215113 5 0.5672 0.71792 0.088 0.000 0.368 0.000 0.544
#> GSM215114 3 0.4074 0.45853 0.000 0.000 0.636 0.000 0.364
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 2 0.0865 0.9767 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM215052 2 0.2053 0.8982 0.000 0.888 0.000 0.108 0.000 0.004
#> GSM215053 2 0.0146 0.9831 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM215054 2 0.0146 0.9831 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM215055 2 0.0547 0.9809 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM215056 2 0.0713 0.9784 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM215057 2 0.0000 0.9835 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215058 2 0.0146 0.9831 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM215059 2 0.0000 0.9835 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215060 2 0.0000 0.9835 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215061 2 0.0000 0.9835 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215062 4 0.6373 -0.1213 0.000 0.220 0.000 0.476 0.276 0.028
#> GSM215063 2 0.0790 0.9765 0.000 0.968 0.000 0.032 0.000 0.000
#> GSM215064 4 0.6373 -0.1213 0.000 0.220 0.000 0.476 0.276 0.028
#> GSM215065 2 0.0260 0.9826 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM215066 2 0.0000 0.9835 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215067 2 0.0547 0.9812 0.000 0.980 0.000 0.020 0.000 0.000
#> GSM215068 2 0.0790 0.9765 0.000 0.968 0.000 0.032 0.000 0.000
#> GSM215069 2 0.0632 0.9798 0.000 0.976 0.000 0.024 0.000 0.000
#> GSM215070 2 0.0146 0.9831 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM215071 2 0.0000 0.9835 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215072 2 0.0865 0.9767 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM215073 2 0.0000 0.9835 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215074 2 0.0146 0.9831 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM215075 2 0.0790 0.9765 0.000 0.968 0.000 0.032 0.000 0.000
#> GSM215076 2 0.0865 0.9767 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM215077 2 0.0000 0.9835 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM215078 2 0.0146 0.9831 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM215079 2 0.0146 0.9831 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM215080 2 0.0260 0.9835 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM215081 2 0.0865 0.9767 0.000 0.964 0.000 0.036 0.000 0.000
#> GSM215082 2 0.0713 0.9784 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM215083 1 0.0000 0.8285 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM215084 5 0.3288 0.9632 0.276 0.000 0.000 0.000 0.724 0.000
#> GSM215085 1 0.0000 0.8285 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM215086 1 0.0000 0.8285 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM215087 4 0.4646 -0.4351 0.040 0.000 0.460 0.500 0.000 0.000
#> GSM215088 3 0.3869 0.2680 0.000 0.000 0.500 0.500 0.000 0.000
#> GSM215089 3 0.4264 0.2705 0.000 0.000 0.500 0.484 0.016 0.000
#> GSM215090 5 0.3288 0.9632 0.276 0.000 0.000 0.000 0.724 0.000
#> GSM215091 1 0.3862 -0.0821 0.524 0.000 0.476 0.000 0.000 0.000
#> GSM215092 5 0.3288 0.9632 0.276 0.000 0.000 0.000 0.724 0.000
#> GSM215093 3 0.0806 0.1328 0.000 0.000 0.972 0.020 0.000 0.008
#> GSM215094 1 0.0000 0.8285 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM215095 4 0.6903 -0.0410 0.200 0.000 0.140 0.500 0.160 0.000
#> GSM215096 1 0.3854 -0.0395 0.536 0.000 0.464 0.000 0.000 0.000
#> GSM215097 1 0.0000 0.8285 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM215098 1 0.0547 0.8081 0.980 0.000 0.000 0.020 0.000 0.000
#> GSM215099 1 0.0000 0.8285 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM215100 5 0.3288 0.9632 0.276 0.000 0.000 0.000 0.724 0.000
#> GSM215101 4 0.3999 -0.4857 0.004 0.000 0.496 0.500 0.000 0.000
#> GSM215102 1 0.3838 0.0336 0.552 0.000 0.448 0.000 0.000 0.000
#> GSM215103 3 0.4399 0.0549 0.460 0.000 0.516 0.024 0.000 0.000
#> GSM215104 1 0.0000 0.8285 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM215105 1 0.0790 0.8025 0.968 0.000 0.032 0.000 0.000 0.000
#> GSM215106 1 0.0000 0.8285 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM215107 5 0.3446 0.9348 0.308 0.000 0.000 0.000 0.692 0.000
#> GSM215108 3 0.3864 -0.0167 0.480 0.000 0.520 0.000 0.000 0.000
#> GSM215109 6 0.0713 0.0000 0.000 0.000 0.028 0.000 0.000 0.972
#> GSM215110 5 0.3288 0.9632 0.276 0.000 0.000 0.000 0.724 0.000
#> GSM215111 1 0.0000 0.8285 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM215112 4 0.4337 0.0249 0.480 0.000 0.020 0.500 0.000 0.000
#> GSM215113 5 0.3737 0.8066 0.392 0.000 0.000 0.000 0.608 0.000
#> GSM215114 3 0.3869 0.2680 0.000 0.000 0.500 0.500 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> ATC:pam 64 9.19e-15 1.000 2
#> ATC:pam 62 3.44e-14 0.999 3
#> ATC:pam 59 9.61e-13 0.991 4
#> ATC:pam 50 1.39e-11 0.997 5
#> ATC:pam 48 3.78e-11 0.993 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 51941 rows and 64 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.652 0.652 0.846 0.1860 0.985 0.969
#> 4 4 0.611 0.553 0.757 0.1242 0.889 0.768
#> 5 5 0.586 0.464 0.660 0.0824 0.835 0.611
#> 6 6 0.593 0.352 0.629 0.0558 0.779 0.440
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.2959 0.889 0.000 0.900 0.100
#> GSM215052 2 0.1289 0.906 0.000 0.968 0.032
#> GSM215053 2 0.2537 0.895 0.000 0.920 0.080
#> GSM215054 2 0.2537 0.895 0.000 0.920 0.080
#> GSM215055 2 0.2959 0.900 0.000 0.900 0.100
#> GSM215056 2 0.4842 0.840 0.000 0.776 0.224
#> GSM215057 2 0.4931 0.835 0.000 0.768 0.232
#> GSM215058 2 0.2448 0.898 0.000 0.924 0.076
#> GSM215059 2 0.2711 0.900 0.000 0.912 0.088
#> GSM215060 2 0.3116 0.893 0.000 0.892 0.108
#> GSM215061 2 0.2959 0.890 0.000 0.900 0.100
#> GSM215062 2 0.4974 0.825 0.000 0.764 0.236
#> GSM215063 2 0.3686 0.875 0.000 0.860 0.140
#> GSM215064 2 0.4974 0.825 0.000 0.764 0.236
#> GSM215065 2 0.5254 0.813 0.000 0.736 0.264
#> GSM215066 2 0.0424 0.904 0.000 0.992 0.008
#> GSM215067 2 0.5138 0.821 0.000 0.748 0.252
#> GSM215068 2 0.2796 0.893 0.000 0.908 0.092
#> GSM215069 2 0.2796 0.895 0.000 0.908 0.092
#> GSM215070 2 0.2537 0.895 0.000 0.920 0.080
#> GSM215071 2 0.2878 0.899 0.000 0.904 0.096
#> GSM215072 2 0.2796 0.894 0.000 0.908 0.092
#> GSM215073 2 0.3116 0.893 0.000 0.892 0.108
#> GSM215074 2 0.1860 0.904 0.000 0.948 0.052
#> GSM215075 2 0.0424 0.905 0.000 0.992 0.008
#> GSM215076 2 0.2959 0.891 0.000 0.900 0.100
#> GSM215077 2 0.3482 0.886 0.000 0.872 0.128
#> GSM215078 2 0.3482 0.886 0.000 0.872 0.128
#> GSM215079 2 0.2711 0.893 0.000 0.912 0.088
#> GSM215080 2 0.2711 0.893 0.000 0.912 0.088
#> GSM215081 2 0.1163 0.905 0.000 0.972 0.028
#> GSM215082 2 0.5216 0.817 0.000 0.740 0.260
#> GSM215083 1 0.0747 0.667 0.984 0.000 0.016
#> GSM215084 1 0.2878 0.580 0.904 0.000 0.096
#> GSM215085 1 0.2165 0.650 0.936 0.000 0.064
#> GSM215086 1 0.0747 0.667 0.984 0.000 0.016
#> GSM215087 1 0.4452 0.484 0.808 0.000 0.192
#> GSM215088 1 0.4796 0.396 0.780 0.000 0.220
#> GSM215089 1 0.5397 0.279 0.720 0.000 0.280
#> GSM215090 1 0.2878 0.580 0.904 0.000 0.096
#> GSM215091 1 0.4452 0.485 0.808 0.000 0.192
#> GSM215092 1 0.0747 0.664 0.984 0.000 0.016
#> GSM215093 3 0.6307 0.000 0.488 0.000 0.512
#> GSM215094 1 0.3482 0.600 0.872 0.000 0.128
#> GSM215095 1 0.4399 0.507 0.812 0.000 0.188
#> GSM215096 1 0.3551 0.596 0.868 0.000 0.132
#> GSM215097 1 0.1163 0.666 0.972 0.000 0.028
#> GSM215098 1 0.3686 0.586 0.860 0.000 0.140
#> GSM215099 1 0.1163 0.664 0.972 0.000 0.028
#> GSM215100 1 0.2878 0.580 0.904 0.000 0.096
#> GSM215101 1 0.4399 0.483 0.812 0.000 0.188
#> GSM215102 1 0.5859 -0.356 0.656 0.000 0.344
#> GSM215103 1 0.5678 -0.138 0.684 0.000 0.316
#> GSM215104 1 0.0747 0.667 0.984 0.000 0.016
#> GSM215105 1 0.1031 0.659 0.976 0.000 0.024
#> GSM215106 1 0.0747 0.667 0.984 0.000 0.016
#> GSM215107 1 0.0747 0.664 0.984 0.000 0.016
#> GSM215108 1 0.5785 -0.312 0.668 0.000 0.332
#> GSM215109 1 0.6295 -0.865 0.528 0.000 0.472
#> GSM215110 1 0.2796 0.586 0.908 0.000 0.092
#> GSM215111 1 0.0747 0.664 0.984 0.000 0.016
#> GSM215112 1 0.4504 0.491 0.804 0.000 0.196
#> GSM215113 1 0.2878 0.580 0.904 0.000 0.096
#> GSM215114 1 0.5591 0.130 0.696 0.000 0.304
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.4955 0.5489 0.000 0.556 0.000 0.444
#> GSM215052 2 0.7080 0.1970 0.000 0.568 0.236 0.196
#> GSM215053 2 0.4898 0.5622 0.000 0.584 0.000 0.416
#> GSM215054 2 0.4916 0.5592 0.000 0.576 0.000 0.424
#> GSM215055 2 0.5630 0.2931 0.000 0.724 0.140 0.136
#> GSM215056 2 0.7628 -0.4816 0.000 0.472 0.260 0.268
#> GSM215057 2 0.7651 -0.5138 0.000 0.464 0.248 0.288
#> GSM215058 2 0.1256 0.5770 0.000 0.964 0.008 0.028
#> GSM215059 2 0.0657 0.5695 0.000 0.984 0.004 0.012
#> GSM215060 2 0.0524 0.5667 0.000 0.988 0.008 0.004
#> GSM215061 2 0.7613 -0.3151 0.000 0.472 0.240 0.288
#> GSM215062 4 0.7645 0.9484 0.000 0.264 0.268 0.468
#> GSM215063 2 0.7627 -0.4902 0.000 0.472 0.256 0.272
#> GSM215064 4 0.7645 0.9484 0.000 0.264 0.268 0.468
#> GSM215065 4 0.7767 0.9451 0.000 0.300 0.268 0.432
#> GSM215066 2 0.5257 0.4416 0.000 0.728 0.212 0.060
#> GSM215067 4 0.7777 0.9423 0.000 0.304 0.268 0.428
#> GSM215068 2 0.1411 0.5585 0.000 0.960 0.020 0.020
#> GSM215069 2 0.0376 0.5688 0.000 0.992 0.004 0.004
#> GSM215070 2 0.4830 0.5676 0.000 0.608 0.000 0.392
#> GSM215071 2 0.3907 0.5917 0.000 0.768 0.000 0.232
#> GSM215072 2 0.1059 0.5620 0.000 0.972 0.016 0.012
#> GSM215073 2 0.0672 0.5684 0.000 0.984 0.008 0.008
#> GSM215074 2 0.4795 0.5865 0.000 0.696 0.012 0.292
#> GSM215075 2 0.5314 0.4942 0.000 0.748 0.144 0.108
#> GSM215076 2 0.5366 0.5422 0.000 0.548 0.012 0.440
#> GSM215077 2 0.4941 0.5521 0.000 0.564 0.000 0.436
#> GSM215078 2 0.5112 0.5496 0.000 0.560 0.004 0.436
#> GSM215079 2 0.5088 0.5581 0.000 0.572 0.004 0.424
#> GSM215080 2 0.0336 0.5688 0.000 0.992 0.008 0.000
#> GSM215081 2 0.5291 0.4200 0.000 0.740 0.180 0.080
#> GSM215082 2 0.7836 -0.6400 0.000 0.400 0.272 0.328
#> GSM215083 1 0.1174 0.8025 0.968 0.000 0.012 0.020
#> GSM215084 1 0.1936 0.7884 0.940 0.000 0.028 0.032
#> GSM215085 1 0.2565 0.7856 0.912 0.000 0.056 0.032
#> GSM215086 1 0.1488 0.7953 0.956 0.000 0.012 0.032
#> GSM215087 1 0.3266 0.7082 0.832 0.000 0.168 0.000
#> GSM215088 1 0.5016 -0.0217 0.600 0.000 0.396 0.004
#> GSM215089 1 0.4819 0.2229 0.652 0.000 0.344 0.004
#> GSM215090 1 0.1936 0.7884 0.940 0.000 0.028 0.032
#> GSM215091 1 0.3726 0.6373 0.788 0.000 0.212 0.000
#> GSM215092 1 0.1610 0.7935 0.952 0.000 0.016 0.032
#> GSM215093 3 0.4857 0.7730 0.324 0.000 0.668 0.008
#> GSM215094 1 0.2706 0.7774 0.900 0.000 0.080 0.020
#> GSM215095 1 0.3355 0.7168 0.836 0.000 0.160 0.004
#> GSM215096 1 0.2662 0.7765 0.900 0.000 0.084 0.016
#> GSM215097 1 0.1724 0.7977 0.948 0.000 0.020 0.032
#> GSM215098 1 0.2775 0.7729 0.896 0.000 0.084 0.020
#> GSM215099 1 0.1297 0.7980 0.964 0.000 0.020 0.016
#> GSM215100 1 0.1936 0.7884 0.940 0.000 0.028 0.032
#> GSM215101 1 0.4018 0.6121 0.772 0.000 0.224 0.004
#> GSM215102 3 0.5894 0.7517 0.428 0.000 0.536 0.036
#> GSM215103 3 0.4961 0.5753 0.448 0.000 0.552 0.000
#> GSM215104 1 0.1488 0.7953 0.956 0.000 0.012 0.032
#> GSM215105 1 0.2032 0.7879 0.936 0.000 0.036 0.028
#> GSM215106 1 0.1488 0.7953 0.956 0.000 0.012 0.032
#> GSM215107 1 0.1610 0.7935 0.952 0.000 0.016 0.032
#> GSM215108 3 0.5971 0.7476 0.428 0.000 0.532 0.040
#> GSM215109 3 0.5517 0.7883 0.316 0.000 0.648 0.036
#> GSM215110 1 0.1936 0.7884 0.940 0.000 0.028 0.032
#> GSM215111 1 0.1406 0.7984 0.960 0.000 0.016 0.024
#> GSM215112 1 0.3402 0.7107 0.832 0.000 0.164 0.004
#> GSM215113 1 0.1936 0.7884 0.940 0.000 0.028 0.032
#> GSM215114 1 0.5105 -0.1919 0.564 0.000 0.432 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.5598 0.36408 0.000 0.524 0.000 NA 0.076
#> GSM215052 2 0.3641 0.44805 0.000 0.820 0.000 NA 0.120
#> GSM215053 2 0.5131 0.36469 0.000 0.588 0.000 NA 0.048
#> GSM215054 2 0.5351 0.37630 0.000 0.560 0.000 NA 0.060
#> GSM215055 2 0.3730 -0.27485 0.000 0.712 0.000 NA 0.288
#> GSM215056 2 0.1443 0.39250 0.000 0.948 0.004 NA 0.044
#> GSM215057 2 0.1124 0.39398 0.000 0.960 0.000 NA 0.036
#> GSM215058 2 0.5176 -0.81926 0.000 0.492 0.000 NA 0.468
#> GSM215059 2 0.4452 -0.95747 0.000 0.500 0.000 NA 0.496
#> GSM215060 5 0.4304 0.97669 0.000 0.484 0.000 NA 0.516
#> GSM215061 2 0.2962 0.44290 0.000 0.868 0.000 NA 0.084
#> GSM215062 2 0.4735 0.35279 0.000 0.680 0.000 NA 0.272
#> GSM215063 2 0.1041 0.40213 0.000 0.964 0.000 NA 0.032
#> GSM215064 2 0.4668 0.35275 0.000 0.684 0.000 NA 0.272
#> GSM215065 2 0.4488 0.34953 0.000 0.736 0.004 NA 0.212
#> GSM215066 2 0.2409 0.38214 0.000 0.900 0.000 NA 0.068
#> GSM215067 2 0.4316 0.34608 0.000 0.748 0.004 NA 0.208
#> GSM215068 5 0.4306 0.96398 0.000 0.492 0.000 NA 0.508
#> GSM215069 5 0.4306 0.97356 0.000 0.492 0.000 NA 0.508
#> GSM215070 2 0.4524 0.32783 0.000 0.644 0.000 NA 0.020
#> GSM215071 2 0.5687 -0.01782 0.000 0.628 0.000 NA 0.208
#> GSM215072 5 0.4306 0.96586 0.000 0.492 0.000 NA 0.508
#> GSM215073 5 0.4304 0.97669 0.000 0.484 0.000 NA 0.516
#> GSM215074 2 0.6166 0.06285 0.000 0.552 0.000 NA 0.188
#> GSM215075 2 0.4563 0.30370 0.000 0.708 0.000 NA 0.244
#> GSM215076 2 0.6074 0.37208 0.000 0.500 0.000 NA 0.128
#> GSM215077 2 0.5467 0.34878 0.000 0.548 0.000 NA 0.068
#> GSM215078 2 0.5423 0.35070 0.000 0.548 0.000 NA 0.064
#> GSM215079 2 0.5535 0.36864 0.000 0.536 0.000 NA 0.072
#> GSM215080 5 0.4305 0.97418 0.000 0.488 0.000 NA 0.512
#> GSM215081 2 0.2873 0.32096 0.000 0.860 0.000 NA 0.120
#> GSM215082 2 0.3213 0.37327 0.000 0.836 0.004 NA 0.144
#> GSM215083 1 0.1082 0.71272 0.964 0.000 0.008 NA 0.000
#> GSM215084 1 0.3752 0.64736 0.708 0.000 0.000 NA 0.000
#> GSM215085 1 0.3815 0.63196 0.824 0.000 0.080 NA 0.008
#> GSM215086 1 0.0960 0.70534 0.972 0.000 0.016 NA 0.004
#> GSM215087 1 0.5554 0.40916 0.616 0.000 0.292 NA 0.004
#> GSM215088 3 0.4305 0.49182 0.296 0.000 0.688 NA 0.012
#> GSM215089 3 0.4538 0.38680 0.364 0.000 0.620 NA 0.000
#> GSM215090 1 0.3774 0.64406 0.704 0.000 0.000 NA 0.000
#> GSM215091 1 0.5753 0.21949 0.552 0.000 0.360 NA 0.004
#> GSM215092 1 0.3636 0.65761 0.728 0.000 0.000 NA 0.000
#> GSM215093 3 0.2291 0.59257 0.024 0.000 0.916 NA 0.012
#> GSM215094 1 0.4089 0.62951 0.804 0.000 0.088 NA 0.008
#> GSM215095 1 0.5389 0.45996 0.648 0.000 0.260 NA 0.004
#> GSM215096 1 0.4037 0.62381 0.808 0.000 0.096 NA 0.008
#> GSM215097 1 0.1059 0.70459 0.968 0.000 0.020 NA 0.004
#> GSM215098 1 0.4075 0.61899 0.800 0.000 0.100 NA 0.004
#> GSM215099 1 0.1764 0.71310 0.928 0.000 0.008 NA 0.000
#> GSM215100 1 0.3752 0.64772 0.708 0.000 0.000 NA 0.000
#> GSM215101 3 0.5192 0.00393 0.472 0.000 0.492 NA 0.004
#> GSM215102 3 0.6630 0.39154 0.208 0.000 0.472 NA 0.004
#> GSM215103 3 0.2890 0.59693 0.160 0.000 0.836 NA 0.004
#> GSM215104 1 0.0833 0.70440 0.976 0.000 0.016 NA 0.004
#> GSM215105 1 0.4803 0.61616 0.720 0.000 0.096 NA 0.000
#> GSM215106 1 0.0833 0.70440 0.976 0.000 0.016 NA 0.004
#> GSM215107 1 0.3661 0.65565 0.724 0.000 0.000 NA 0.000
#> GSM215108 3 0.6640 0.38811 0.212 0.000 0.472 NA 0.004
#> GSM215109 3 0.4389 0.57245 0.036 0.000 0.768 NA 0.020
#> GSM215110 1 0.3752 0.64736 0.708 0.000 0.000 NA 0.000
#> GSM215111 1 0.2411 0.70555 0.884 0.000 0.008 NA 0.000
#> GSM215112 1 0.5482 0.44883 0.636 0.000 0.268 NA 0.004
#> GSM215113 1 0.3774 0.64545 0.704 0.000 0.000 NA 0.000
#> GSM215114 3 0.4025 0.56370 0.232 0.000 0.748 NA 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 6 0.3756 0.8358 0.000 0.400 0.000 NA 0.000 0.600
#> GSM215052 2 0.4882 -0.2367 0.000 0.576 0.000 NA 0.000 0.352
#> GSM215053 2 0.3874 -0.3161 0.000 0.636 0.000 NA 0.000 0.356
#> GSM215054 2 0.3782 -0.4558 0.000 0.588 0.000 NA 0.000 0.412
#> GSM215055 2 0.3924 0.4354 0.000 0.740 0.000 NA 0.000 0.052
#> GSM215056 2 0.2822 0.4150 0.000 0.852 0.000 NA 0.000 0.040
#> GSM215057 2 0.2618 0.4152 0.000 0.860 0.000 NA 0.000 0.024
#> GSM215058 2 0.4892 0.3246 0.000 0.628 0.000 NA 0.000 0.100
#> GSM215059 2 0.3652 0.4157 0.000 0.672 0.000 NA 0.000 0.004
#> GSM215060 2 0.3699 0.3975 0.000 0.660 0.000 NA 0.000 0.004
#> GSM215061 2 0.4494 0.0800 0.000 0.692 0.004 NA 0.000 0.232
#> GSM215062 2 0.5753 0.2373 0.004 0.516 0.004 NA 0.000 0.144
#> GSM215063 2 0.2506 0.3946 0.000 0.880 0.000 NA 0.000 0.052
#> GSM215064 2 0.5694 0.2428 0.004 0.524 0.004 NA 0.000 0.136
#> GSM215065 2 0.5381 0.2570 0.000 0.568 0.004 NA 0.000 0.124
#> GSM215066 2 0.3013 0.2291 0.000 0.832 0.004 NA 0.000 0.140
#> GSM215067 2 0.4735 0.3214 0.004 0.644 0.004 NA 0.000 0.056
#> GSM215068 2 0.3938 0.4184 0.000 0.660 0.000 NA 0.000 0.016
#> GSM215069 2 0.3636 0.4002 0.000 0.676 0.000 NA 0.000 0.004
#> GSM215070 2 0.3081 0.0645 0.000 0.776 0.000 NA 0.000 0.220
#> GSM215071 2 0.3602 0.2832 0.000 0.796 0.000 NA 0.000 0.116
#> GSM215072 2 0.4002 0.4087 0.000 0.660 0.000 NA 0.000 0.020
#> GSM215073 2 0.3774 0.3947 0.000 0.664 0.000 NA 0.000 0.008
#> GSM215074 2 0.4691 0.1029 0.000 0.672 0.000 NA 0.000 0.220
#> GSM215075 2 0.4704 0.0709 0.000 0.664 0.000 NA 0.000 0.236
#> GSM215076 6 0.4619 0.7484 0.000 0.392 0.000 NA 0.000 0.564
#> GSM215077 6 0.4141 0.8059 0.000 0.432 0.000 NA 0.000 0.556
#> GSM215078 6 0.4083 0.8001 0.000 0.460 0.000 NA 0.000 0.532
#> GSM215079 6 0.4018 0.8402 0.000 0.412 0.000 NA 0.000 0.580
#> GSM215080 2 0.3952 0.3889 0.000 0.672 0.000 NA 0.000 0.020
#> GSM215081 2 0.3183 0.3813 0.000 0.828 0.000 NA 0.000 0.112
#> GSM215082 2 0.5365 0.1751 0.008 0.616 0.000 NA 0.000 0.160
#> GSM215083 1 0.3961 0.3742 0.556 0.000 0.004 NA 0.440 0.000
#> GSM215084 5 0.0790 0.6409 0.032 0.000 0.000 NA 0.968 0.000
#> GSM215085 1 0.5886 0.5285 0.612 0.000 0.112 NA 0.220 0.004
#> GSM215086 1 0.3717 0.4620 0.616 0.000 0.000 NA 0.384 0.000
#> GSM215087 3 0.6932 0.0186 0.332 0.000 0.392 NA 0.220 0.004
#> GSM215088 3 0.3603 0.5905 0.036 0.000 0.840 NA 0.064 0.016
#> GSM215089 3 0.3961 0.5742 0.096 0.000 0.792 NA 0.096 0.012
#> GSM215090 5 0.0000 0.6391 0.000 0.000 0.000 NA 1.000 0.000
#> GSM215091 3 0.6626 0.1029 0.384 0.000 0.416 NA 0.144 0.004
#> GSM215092 5 0.0790 0.6363 0.032 0.000 0.000 NA 0.968 0.000
#> GSM215093 3 0.3857 0.5323 0.068 0.000 0.816 NA 0.004 0.044
#> GSM215094 1 0.6117 0.4635 0.588 0.000 0.144 NA 0.212 0.004
#> GSM215095 1 0.6848 -0.0210 0.412 0.000 0.336 NA 0.196 0.004
#> GSM215096 1 0.5943 0.4834 0.616 0.000 0.144 NA 0.184 0.004
#> GSM215097 1 0.3890 0.4566 0.596 0.000 0.004 NA 0.400 0.000
#> GSM215098 1 0.6138 0.4446 0.588 0.000 0.156 NA 0.200 0.004
#> GSM215099 5 0.3867 -0.3077 0.488 0.000 0.000 NA 0.512 0.000
#> GSM215100 5 0.0000 0.6391 0.000 0.000 0.000 NA 1.000 0.000
#> GSM215101 3 0.6123 0.3789 0.252 0.000 0.572 NA 0.120 0.004
#> GSM215102 5 0.8186 0.2370 0.232 0.000 0.216 NA 0.360 0.140
#> GSM215103 3 0.4415 0.5637 0.132 0.000 0.768 NA 0.052 0.008
#> GSM215104 1 0.3737 0.4621 0.608 0.000 0.000 NA 0.392 0.000
#> GSM215105 5 0.5863 0.0297 0.360 0.000 0.124 NA 0.500 0.008
#> GSM215106 1 0.3684 0.4605 0.628 0.000 0.000 NA 0.372 0.000
#> GSM215107 5 0.0937 0.6307 0.040 0.000 0.000 NA 0.960 0.000
#> GSM215108 5 0.8228 0.2308 0.232 0.000 0.216 NA 0.356 0.140
#> GSM215109 3 0.6961 0.3734 0.176 0.000 0.540 NA 0.024 0.168
#> GSM215110 5 0.0692 0.6422 0.020 0.000 0.004 NA 0.976 0.000
#> GSM215111 5 0.4086 -0.2146 0.464 0.000 0.008 NA 0.528 0.000
#> GSM215112 3 0.6971 -0.0403 0.336 0.000 0.376 NA 0.232 0.004
#> GSM215113 5 0.0632 0.6415 0.024 0.000 0.000 NA 0.976 0.000
#> GSM215114 3 0.3780 0.5864 0.032 0.000 0.828 NA 0.064 0.016
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> ATC:mclust 64 9.19e-15 1.000 2
#> ATC:mclust 52 4.58e-12 1.000 3
#> ATC:mclust 51 4.89e-11 0.962 4
#> ATC:mclust 29 5.04e-07 0.585 5
#> ATC:mclust 18 4.40e-04 0.360 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 51941 rows and 64 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.5084 0.492 0.492
#> 3 3 0.900 0.938 0.946 0.0899 1.000 1.000
#> 4 4 0.714 0.784 0.896 0.0665 0.985 0.969
#> 5 5 0.624 0.730 0.841 0.0686 0.985 0.968
#> 6 6 0.564 0.586 0.799 0.0587 0.970 0.935
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM215051 2 0 1 0 1
#> GSM215052 2 0 1 0 1
#> GSM215053 2 0 1 0 1
#> GSM215054 2 0 1 0 1
#> GSM215055 2 0 1 0 1
#> GSM215056 2 0 1 0 1
#> GSM215057 2 0 1 0 1
#> GSM215058 2 0 1 0 1
#> GSM215059 2 0 1 0 1
#> GSM215060 2 0 1 0 1
#> GSM215061 2 0 1 0 1
#> GSM215062 2 0 1 0 1
#> GSM215063 2 0 1 0 1
#> GSM215064 2 0 1 0 1
#> GSM215065 2 0 1 0 1
#> GSM215066 2 0 1 0 1
#> GSM215067 2 0 1 0 1
#> GSM215068 2 0 1 0 1
#> GSM215069 2 0 1 0 1
#> GSM215070 2 0 1 0 1
#> GSM215071 2 0 1 0 1
#> GSM215072 2 0 1 0 1
#> GSM215073 2 0 1 0 1
#> GSM215074 2 0 1 0 1
#> GSM215075 2 0 1 0 1
#> GSM215076 2 0 1 0 1
#> GSM215077 2 0 1 0 1
#> GSM215078 2 0 1 0 1
#> GSM215079 2 0 1 0 1
#> GSM215080 2 0 1 0 1
#> GSM215081 2 0 1 0 1
#> GSM215082 2 0 1 0 1
#> GSM215083 1 0 1 1 0
#> GSM215084 1 0 1 1 0
#> GSM215085 1 0 1 1 0
#> GSM215086 1 0 1 1 0
#> GSM215087 1 0 1 1 0
#> GSM215088 1 0 1 1 0
#> GSM215089 1 0 1 1 0
#> GSM215090 1 0 1 1 0
#> GSM215091 1 0 1 1 0
#> GSM215092 1 0 1 1 0
#> GSM215093 1 0 1 1 0
#> GSM215094 1 0 1 1 0
#> GSM215095 1 0 1 1 0
#> GSM215096 1 0 1 1 0
#> GSM215097 1 0 1 1 0
#> GSM215098 1 0 1 1 0
#> GSM215099 1 0 1 1 0
#> GSM215100 1 0 1 1 0
#> GSM215101 1 0 1 1 0
#> GSM215102 1 0 1 1 0
#> GSM215103 1 0 1 1 0
#> GSM215104 1 0 1 1 0
#> GSM215105 1 0 1 1 0
#> GSM215106 1 0 1 1 0
#> GSM215107 1 0 1 1 0
#> GSM215108 1 0 1 1 0
#> GSM215109 1 0 1 1 0
#> GSM215110 1 0 1 1 0
#> GSM215111 1 0 1 1 0
#> GSM215112 1 0 1 1 0
#> GSM215113 1 0 1 1 0
#> GSM215114 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM215051 2 0.1163 0.972 0.000 0.972 0.028
#> GSM215052 2 0.1163 0.971 0.000 0.972 0.028
#> GSM215053 2 0.0592 0.976 0.000 0.988 0.012
#> GSM215054 2 0.0747 0.976 0.000 0.984 0.016
#> GSM215055 2 0.0237 0.976 0.000 0.996 0.004
#> GSM215056 2 0.0237 0.976 0.000 0.996 0.004
#> GSM215057 2 0.0237 0.977 0.000 0.996 0.004
#> GSM215058 2 0.0424 0.976 0.000 0.992 0.008
#> GSM215059 2 0.0000 0.976 0.000 1.000 0.000
#> GSM215060 2 0.0237 0.977 0.000 0.996 0.004
#> GSM215061 2 0.0424 0.976 0.000 0.992 0.008
#> GSM215062 2 0.5926 0.701 0.000 0.644 0.356
#> GSM215063 2 0.0424 0.976 0.000 0.992 0.008
#> GSM215064 2 0.4291 0.862 0.000 0.820 0.180
#> GSM215065 2 0.1964 0.953 0.000 0.944 0.056
#> GSM215066 2 0.0592 0.976 0.000 0.988 0.012
#> GSM215067 2 0.2959 0.924 0.000 0.900 0.100
#> GSM215068 2 0.0000 0.976 0.000 1.000 0.000
#> GSM215069 2 0.0000 0.976 0.000 1.000 0.000
#> GSM215070 2 0.0592 0.976 0.000 0.988 0.012
#> GSM215071 2 0.0592 0.976 0.000 0.988 0.012
#> GSM215072 2 0.0000 0.976 0.000 1.000 0.000
#> GSM215073 2 0.0000 0.976 0.000 1.000 0.000
#> GSM215074 2 0.0237 0.976 0.000 0.996 0.004
#> GSM215075 2 0.0892 0.973 0.000 0.980 0.020
#> GSM215076 2 0.0892 0.974 0.000 0.980 0.020
#> GSM215077 2 0.2066 0.955 0.000 0.940 0.060
#> GSM215078 2 0.1529 0.966 0.000 0.960 0.040
#> GSM215079 2 0.0747 0.975 0.000 0.984 0.016
#> GSM215080 2 0.0237 0.976 0.000 0.996 0.004
#> GSM215081 2 0.0237 0.977 0.000 0.996 0.004
#> GSM215082 2 0.1031 0.973 0.000 0.976 0.024
#> GSM215083 1 0.0747 0.945 0.984 0.000 0.016
#> GSM215084 1 0.0424 0.946 0.992 0.000 0.008
#> GSM215085 1 0.2625 0.926 0.916 0.000 0.084
#> GSM215086 1 0.0747 0.945 0.984 0.000 0.016
#> GSM215087 1 0.2356 0.930 0.928 0.000 0.072
#> GSM215088 1 0.0592 0.946 0.988 0.000 0.012
#> GSM215089 1 0.1163 0.943 0.972 0.000 0.028
#> GSM215090 1 0.0000 0.946 1.000 0.000 0.000
#> GSM215091 1 0.0892 0.945 0.980 0.000 0.020
#> GSM215092 1 0.0000 0.946 1.000 0.000 0.000
#> GSM215093 1 0.3192 0.908 0.888 0.000 0.112
#> GSM215094 1 0.5431 0.806 0.716 0.000 0.284
#> GSM215095 1 0.2537 0.927 0.920 0.000 0.080
#> GSM215096 1 0.2711 0.925 0.912 0.000 0.088
#> GSM215097 1 0.0237 0.946 0.996 0.000 0.004
#> GSM215098 1 0.5431 0.805 0.716 0.000 0.284
#> GSM215099 1 0.0747 0.945 0.984 0.000 0.016
#> GSM215100 1 0.0000 0.946 1.000 0.000 0.000
#> GSM215101 1 0.0000 0.946 1.000 0.000 0.000
#> GSM215102 1 0.5497 0.792 0.708 0.000 0.292
#> GSM215103 1 0.0892 0.945 0.980 0.000 0.020
#> GSM215104 1 0.0237 0.946 0.996 0.000 0.004
#> GSM215105 1 0.0892 0.945 0.980 0.000 0.020
#> GSM215106 1 0.1031 0.944 0.976 0.000 0.024
#> GSM215107 1 0.1163 0.943 0.972 0.000 0.028
#> GSM215108 1 0.5465 0.794 0.712 0.000 0.288
#> GSM215109 1 0.5678 0.773 0.684 0.000 0.316
#> GSM215110 1 0.1529 0.940 0.960 0.000 0.040
#> GSM215111 1 0.0237 0.946 0.996 0.000 0.004
#> GSM215112 1 0.4605 0.861 0.796 0.000 0.204
#> GSM215113 1 0.1411 0.941 0.964 0.000 0.036
#> GSM215114 1 0.0592 0.947 0.988 0.000 0.012
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM215051 2 0.1520 0.9292 0.000 0.956 0.024 NA
#> GSM215052 2 0.2882 0.9107 0.000 0.892 0.024 NA
#> GSM215053 2 0.0779 0.9291 0.000 0.980 0.004 NA
#> GSM215054 2 0.1042 0.9295 0.000 0.972 0.008 NA
#> GSM215055 2 0.0927 0.9304 0.000 0.976 0.008 NA
#> GSM215056 2 0.3463 0.8919 0.000 0.864 0.040 NA
#> GSM215057 2 0.2644 0.9159 0.000 0.908 0.060 NA
#> GSM215058 2 0.2174 0.9223 0.000 0.928 0.052 NA
#> GSM215059 2 0.1510 0.9270 0.000 0.956 0.028 NA
#> GSM215060 2 0.0779 0.9293 0.000 0.980 0.016 NA
#> GSM215061 2 0.1284 0.9288 0.000 0.964 0.024 NA
#> GSM215062 2 0.5404 0.4749 0.000 0.512 0.012 NA
#> GSM215063 2 0.1059 0.9305 0.000 0.972 0.016 NA
#> GSM215064 2 0.5781 0.5911 0.000 0.584 0.036 NA
#> GSM215065 2 0.3245 0.8867 0.000 0.872 0.100 NA
#> GSM215066 2 0.0937 0.9297 0.000 0.976 0.012 NA
#> GSM215067 2 0.3754 0.8804 0.000 0.852 0.084 NA
#> GSM215068 2 0.0779 0.9297 0.000 0.980 0.004 NA
#> GSM215069 2 0.0336 0.9286 0.000 0.992 0.008 NA
#> GSM215070 2 0.0524 0.9295 0.000 0.988 0.004 NA
#> GSM215071 2 0.0376 0.9291 0.000 0.992 0.004 NA
#> GSM215072 2 0.2385 0.9208 0.000 0.920 0.052 NA
#> GSM215073 2 0.0469 0.9287 0.000 0.988 0.012 NA
#> GSM215074 2 0.0469 0.9301 0.000 0.988 0.000 NA
#> GSM215075 2 0.1209 0.9294 0.000 0.964 0.004 NA
#> GSM215076 2 0.3570 0.8940 0.000 0.860 0.092 NA
#> GSM215077 2 0.4728 0.7856 0.000 0.752 0.216 NA
#> GSM215078 2 0.3554 0.8756 0.000 0.844 0.136 NA
#> GSM215079 2 0.0592 0.9289 0.000 0.984 0.000 NA
#> GSM215080 2 0.0188 0.9287 0.000 0.996 0.000 NA
#> GSM215081 2 0.2363 0.9209 0.000 0.920 0.024 NA
#> GSM215082 2 0.4356 0.8432 0.000 0.804 0.148 NA
#> GSM215083 1 0.1297 0.8155 0.964 0.000 0.020 NA
#> GSM215084 1 0.1635 0.7966 0.948 0.000 0.044 NA
#> GSM215085 1 0.4163 0.5845 0.792 0.000 0.020 NA
#> GSM215086 1 0.3144 0.7621 0.884 0.000 0.072 NA
#> GSM215087 1 0.1488 0.8160 0.956 0.000 0.012 NA
#> GSM215088 1 0.1624 0.8111 0.952 0.000 0.028 NA
#> GSM215089 1 0.2593 0.7542 0.904 0.000 0.080 NA
#> GSM215090 1 0.1059 0.8110 0.972 0.000 0.016 NA
#> GSM215091 1 0.1767 0.8058 0.944 0.000 0.012 NA
#> GSM215092 1 0.0937 0.8162 0.976 0.000 0.012 NA
#> GSM215093 1 0.5144 0.2009 0.732 0.000 0.216 NA
#> GSM215094 1 0.4936 0.2171 0.672 0.000 0.012 NA
#> GSM215095 1 0.1724 0.8137 0.948 0.000 0.020 NA
#> GSM215096 1 0.4567 0.4494 0.740 0.000 0.016 NA
#> GSM215097 1 0.1624 0.8127 0.952 0.000 0.020 NA
#> GSM215098 1 0.4994 0.4558 0.744 0.000 0.048 NA
#> GSM215099 1 0.1305 0.8116 0.960 0.000 0.004 NA
#> GSM215100 1 0.0937 0.8128 0.976 0.000 0.012 NA
#> GSM215101 1 0.1510 0.8081 0.956 0.000 0.028 NA
#> GSM215102 1 0.3441 0.6719 0.856 0.000 0.120 NA
#> GSM215103 1 0.2542 0.7788 0.904 0.000 0.084 NA
#> GSM215104 1 0.1545 0.8134 0.952 0.000 0.008 NA
#> GSM215105 1 0.2522 0.7909 0.908 0.000 0.076 NA
#> GSM215106 1 0.3099 0.7448 0.876 0.000 0.020 NA
#> GSM215107 1 0.0921 0.8133 0.972 0.000 0.000 NA
#> GSM215108 1 0.4663 0.0898 0.716 0.000 0.272 NA
#> GSM215109 3 0.4989 0.0000 0.472 0.000 0.528 NA
#> GSM215110 1 0.2623 0.7671 0.908 0.000 0.064 NA
#> GSM215111 1 0.1151 0.8150 0.968 0.000 0.008 NA
#> GSM215112 1 0.2845 0.7691 0.896 0.000 0.028 NA
#> GSM215113 1 0.2021 0.7987 0.936 0.000 0.040 NA
#> GSM215114 1 0.2915 0.7552 0.892 0.000 0.080 NA
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM215051 2 0.2670 0.892 0.000 0.888 0.028 NA NA
#> GSM215052 2 0.4061 0.850 0.000 0.808 0.040 NA NA
#> GSM215053 2 0.1788 0.898 0.000 0.932 0.004 NA NA
#> GSM215054 2 0.2352 0.888 0.000 0.896 0.004 NA NA
#> GSM215055 2 0.0833 0.902 0.000 0.976 0.004 NA NA
#> GSM215056 2 0.3388 0.866 0.000 0.860 0.028 NA NA
#> GSM215057 2 0.2429 0.887 0.000 0.900 0.004 NA NA
#> GSM215058 2 0.1197 0.898 0.000 0.952 0.000 NA NA
#> GSM215059 2 0.1153 0.901 0.000 0.964 0.004 NA NA
#> GSM215060 2 0.0613 0.901 0.000 0.984 0.004 NA NA
#> GSM215061 2 0.2228 0.895 0.000 0.912 0.008 NA NA
#> GSM215062 2 0.6509 0.423 0.000 0.492 0.008 NA NA
#> GSM215063 2 0.0992 0.903 0.000 0.968 0.008 NA NA
#> GSM215064 2 0.6127 0.536 0.000 0.552 0.000 NA NA
#> GSM215065 2 0.2610 0.885 0.000 0.904 0.024 NA NA
#> GSM215066 2 0.2289 0.892 0.000 0.904 0.004 NA NA
#> GSM215067 2 0.1799 0.899 0.000 0.940 0.020 NA NA
#> GSM215068 2 0.1041 0.902 0.000 0.964 0.004 NA NA
#> GSM215069 2 0.0000 0.899 0.000 1.000 0.000 NA NA
#> GSM215070 2 0.0880 0.900 0.000 0.968 0.000 NA NA
#> GSM215071 2 0.0510 0.901 0.000 0.984 0.000 NA NA
#> GSM215072 2 0.2011 0.887 0.000 0.908 0.000 NA NA
#> GSM215073 2 0.0324 0.900 0.000 0.992 0.004 NA NA
#> GSM215074 2 0.0794 0.902 0.000 0.972 0.000 NA NA
#> GSM215075 2 0.1502 0.901 0.000 0.940 0.004 NA NA
#> GSM215076 2 0.4937 0.799 0.000 0.740 0.060 NA NA
#> GSM215077 2 0.5791 0.570 0.000 0.600 0.140 NA NA
#> GSM215078 2 0.4177 0.797 0.000 0.772 0.064 NA NA
#> GSM215079 2 0.1502 0.899 0.000 0.940 0.000 NA NA
#> GSM215080 2 0.0671 0.901 0.000 0.980 0.004 NA NA
#> GSM215081 2 0.3016 0.872 0.000 0.868 0.016 NA NA
#> GSM215082 2 0.5179 0.713 0.000 0.712 0.196 NA NA
#> GSM215083 1 0.2551 0.754 0.904 0.000 0.044 NA NA
#> GSM215084 1 0.1571 0.737 0.936 0.000 0.060 NA NA
#> GSM215085 1 0.4455 0.524 0.692 0.000 0.016 NA NA
#> GSM215086 1 0.5411 0.563 0.724 0.000 0.044 NA NA
#> GSM215087 1 0.1399 0.757 0.952 0.000 0.020 NA NA
#> GSM215088 1 0.5028 0.470 0.728 0.000 0.188 NA NA
#> GSM215089 1 0.3305 0.523 0.776 0.000 0.224 NA NA
#> GSM215090 1 0.0865 0.748 0.972 0.000 0.024 NA NA
#> GSM215091 1 0.2414 0.754 0.900 0.000 0.012 NA NA
#> GSM215092 1 0.1547 0.760 0.948 0.000 0.032 NA NA
#> GSM215093 3 0.6246 0.490 0.432 0.000 0.464 NA NA
#> GSM215094 1 0.4462 0.471 0.672 0.000 0.004 NA NA
#> GSM215095 1 0.2378 0.754 0.908 0.000 0.012 NA NA
#> GSM215096 1 0.4608 0.424 0.644 0.000 0.012 NA NA
#> GSM215097 1 0.2189 0.754 0.904 0.000 0.012 NA NA
#> GSM215098 1 0.4500 0.458 0.664 0.000 0.016 NA NA
#> GSM215099 1 0.2170 0.744 0.904 0.000 0.004 NA NA
#> GSM215100 1 0.1282 0.746 0.952 0.000 0.044 NA NA
#> GSM215101 1 0.1651 0.748 0.944 0.000 0.036 NA NA
#> GSM215102 1 0.4025 0.360 0.700 0.000 0.292 NA NA
#> GSM215103 1 0.5824 0.292 0.660 0.000 0.176 NA NA
#> GSM215104 1 0.2032 0.756 0.924 0.000 0.020 NA NA
#> GSM215105 1 0.3363 0.720 0.860 0.000 0.076 NA NA
#> GSM215106 1 0.3360 0.686 0.816 0.000 0.012 NA NA
#> GSM215107 1 0.1202 0.757 0.960 0.000 0.004 NA NA
#> GSM215108 1 0.5639 0.023 0.612 0.000 0.296 NA NA
#> GSM215109 3 0.6068 0.571 0.308 0.000 0.544 NA NA
#> GSM215110 1 0.3079 0.703 0.868 0.000 0.092 NA NA
#> GSM215111 1 0.1668 0.761 0.940 0.000 0.028 NA NA
#> GSM215112 1 0.3063 0.725 0.864 0.000 0.020 NA NA
#> GSM215113 1 0.1740 0.750 0.932 0.000 0.056 NA NA
#> GSM215114 1 0.4918 0.364 0.704 0.000 0.236 NA NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM215051 2 0.3298 0.6996 0.000 0.856 0.052 0.024 0.056 NA
#> GSM215052 2 0.4670 0.4377 0.000 0.732 0.072 0.012 0.168 NA
#> GSM215053 2 0.2401 0.7425 0.000 0.900 0.036 0.000 0.020 NA
#> GSM215054 2 0.3123 0.7016 0.000 0.868 0.024 0.020 0.028 NA
#> GSM215055 2 0.1180 0.7709 0.000 0.960 0.008 0.004 0.024 NA
#> GSM215056 2 0.3889 0.6149 0.000 0.808 0.096 0.008 0.068 NA
#> GSM215057 2 0.3973 0.6168 0.000 0.808 0.016 0.052 0.100 NA
#> GSM215058 2 0.2400 0.7006 0.000 0.872 0.004 0.008 0.116 NA
#> GSM215059 2 0.2334 0.7413 0.000 0.904 0.004 0.040 0.044 NA
#> GSM215060 2 0.0964 0.7711 0.000 0.968 0.004 0.016 0.000 NA
#> GSM215061 2 0.2742 0.7324 0.000 0.880 0.016 0.008 0.020 NA
#> GSM215062 5 0.4402 0.8354 0.000 0.412 0.004 0.000 0.564 NA
#> GSM215063 2 0.1774 0.7652 0.000 0.936 0.020 0.004 0.016 NA
#> GSM215064 5 0.4694 0.8114 0.000 0.472 0.004 0.020 0.496 NA
#> GSM215065 2 0.3120 0.6962 0.000 0.856 0.008 0.024 0.020 NA
#> GSM215066 2 0.2878 0.7077 0.000 0.872 0.020 0.004 0.028 NA
#> GSM215067 2 0.2818 0.7333 0.000 0.880 0.012 0.020 0.068 NA
#> GSM215068 2 0.1405 0.7660 0.000 0.948 0.024 0.000 0.024 NA
#> GSM215069 2 0.0405 0.7689 0.000 0.988 0.004 0.000 0.008 NA
#> GSM215070 2 0.0260 0.7699 0.000 0.992 0.000 0.000 0.008 NA
#> GSM215071 2 0.0291 0.7686 0.000 0.992 0.004 0.000 0.000 NA
#> GSM215072 2 0.3352 0.5982 0.000 0.800 0.012 0.016 0.172 NA
#> GSM215073 2 0.0696 0.7698 0.000 0.980 0.004 0.008 0.004 NA
#> GSM215074 2 0.0291 0.7687 0.000 0.992 0.004 0.000 0.004 NA
#> GSM215075 2 0.1749 0.7604 0.000 0.932 0.024 0.000 0.036 NA
#> GSM215076 2 0.5582 0.0578 0.000 0.644 0.032 0.072 0.232 NA
#> GSM215077 2 0.5115 -0.2128 0.000 0.560 0.000 0.356 0.080 NA
#> GSM215078 2 0.4173 0.4928 0.000 0.752 0.004 0.168 0.072 NA
#> GSM215079 2 0.1317 0.7691 0.000 0.956 0.004 0.008 0.016 NA
#> GSM215080 2 0.0551 0.7708 0.000 0.984 0.008 0.000 0.004 NA
#> GSM215081 2 0.3425 0.6005 0.000 0.800 0.028 0.008 0.164 NA
#> GSM215082 2 0.6167 -0.2194 0.000 0.572 0.280 0.072 0.056 NA
#> GSM215083 1 0.2206 0.7361 0.904 0.000 0.008 0.024 0.000 NA
#> GSM215084 1 0.3278 0.6965 0.840 0.000 0.108 0.028 0.004 NA
#> GSM215085 1 0.4353 0.5625 0.672 0.000 0.004 0.004 0.032 NA
#> GSM215086 1 0.6210 0.3599 0.564 0.000 0.040 0.088 0.024 NA
#> GSM215087 1 0.2452 0.7303 0.892 0.000 0.056 0.008 0.000 NA
#> GSM215088 1 0.5658 0.0272 0.516 0.000 0.396 0.016 0.036 NA
#> GSM215089 1 0.4757 0.4826 0.660 0.000 0.280 0.032 0.004 NA
#> GSM215090 1 0.2560 0.7134 0.872 0.000 0.092 0.000 0.000 NA
#> GSM215091 1 0.2849 0.7288 0.872 0.000 0.008 0.020 0.016 NA
#> GSM215092 1 0.2144 0.7401 0.912 0.000 0.032 0.004 0.004 NA
#> GSM215093 3 0.4122 0.0000 0.196 0.000 0.752 0.016 0.028 NA
#> GSM215094 1 0.4172 0.6536 0.764 0.000 0.008 0.016 0.044 NA
#> GSM215095 1 0.3191 0.7270 0.856 0.000 0.036 0.020 0.008 NA
#> GSM215096 1 0.4755 0.5615 0.680 0.000 0.000 0.016 0.068 NA
#> GSM215097 1 0.2847 0.7302 0.852 0.000 0.012 0.016 0.000 NA
#> GSM215098 1 0.3728 0.6349 0.748 0.000 0.012 0.004 0.008 NA
#> GSM215099 1 0.1555 0.7346 0.932 0.000 0.004 0.004 0.000 NA
#> GSM215100 1 0.2011 0.7266 0.912 0.000 0.064 0.004 0.000 NA
#> GSM215101 1 0.3306 0.7000 0.828 0.000 0.120 0.004 0.004 NA
#> GSM215102 1 0.5483 0.3260 0.584 0.000 0.308 0.088 0.008 NA
#> GSM215103 1 0.5382 -0.0567 0.496 0.000 0.032 0.436 0.016 NA
#> GSM215104 1 0.1845 0.7316 0.916 0.000 0.000 0.008 0.004 NA
#> GSM215105 1 0.3943 0.6480 0.760 0.000 0.020 0.196 0.004 NA
#> GSM215106 1 0.3144 0.6884 0.808 0.000 0.000 0.016 0.004 NA
#> GSM215107 1 0.1333 0.7348 0.944 0.000 0.000 0.008 0.000 NA
#> GSM215108 1 0.6812 -0.0350 0.472 0.000 0.160 0.308 0.028 NA
#> GSM215109 4 0.5732 0.0000 0.180 0.000 0.216 0.588 0.004 NA
#> GSM215110 1 0.5323 0.6073 0.704 0.000 0.160 0.044 0.028 NA
#> GSM215111 1 0.1628 0.7390 0.940 0.000 0.008 0.012 0.004 NA
#> GSM215112 1 0.2817 0.7312 0.872 0.000 0.040 0.004 0.008 NA
#> GSM215113 1 0.3277 0.7216 0.848 0.000 0.088 0.016 0.008 NA
#> GSM215114 1 0.5796 0.1041 0.544 0.000 0.352 0.020 0.028 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) individual(p) k
#> ATC:NMF 64 9.19e-15 1.000 2
#> ATC:NMF 64 9.19e-15 1.000 3
#> ATC:NMF 57 3.27e-13 1.000 4
#> ATC:NMF 54 1.88e-12 0.997 5
#> ATC:NMF 50 1.39e-11 0.993 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