Date: 2019-12-25 20:43:24 CET, cola version: 1.3.2
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All available functions which can be applied to this res_list object:
res_list
#> A 'ConsensusPartitionList' object with 24 methods.
#> On a matrix with 51941 rows and 59 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 59
The density distribution for each sample is visualized as in one column in the following heatmap. The clustering is based on the distance which is the Kolmogorov-Smirnov statistic between two distributions.
library(ComplexHeatmap)
densityHeatmap(mat, top_annotation = HeatmapAnnotation(df = get_anno(res_list),
col = get_anno_col(res_list)), ylab = "value", cluster_columns = TRUE, show_column_names = FALSE,
mc.cores = 4)
Folowing table shows the best k (number of partitions) for each combination
of top-value methods and partition methods. Clicking on the method name in
the table goes to the section for a single combination of methods.
The cola vignette explains the definition of the metrics used for determining the best number of partitions.
suggest_best_k(res_list)
| The best k | 1-PAC | Mean silhouette | Concordance | Optional k | ||
|---|---|---|---|---|---|---|
| SD:hclust | 2 | 1.000 | 0.995 | 0.998 | ** | |
| SD:mclust | 6 | 1.000 | 0.976 | 0.982 | ** | 5 |
| SD:NMF | 2 | 1.000 | 0.983 | 0.993 | ** | |
| CV:hclust | 6 | 1.000 | 0.966 | 0.986 | ** | 2 |
| CV:mclust | 6 | 1.000 | 0.990 | 0.995 | ** | 5 |
| MAD:skmeans | 4 | 1.000 | 0.964 | 0.977 | ** | 2,3 |
| MAD:mclust | 6 | 1.000 | 0.988 | 0.993 | ** | 2,3,4,5 |
| ATC:hclust | 2 | 1.000 | 0.978 | 0.990 | ** | |
| ATC:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| ATC:NMF | 3 | 0.999 | 0.977 | 0.987 | ** | 2 |
| MAD:pam | 6 | 0.990 | 0.961 | 0.984 | ** | 2,3,4,5 |
| ATC:mclust | 6 | 0.976 | 0.920 | 0.965 | ** | 2,4,5 |
| MAD:hclust | 6 | 0.947 | 0.966 | 0.964 | * | 5 |
| ATC:pam | 6 | 0.946 | 0.946 | 0.971 | * | 2,4 |
| SD:pam | 6 | 0.946 | 0.962 | 0.985 | * | 2,4 |
| CV:pam | 6 | 0.946 | 0.977 | 0.991 | * | 2 |
| CV:NMF | 6 | 0.940 | 0.934 | 0.941 | * | 2,5 |
| CV:skmeans | 5 | 0.933 | 0.918 | 0.930 | * | 2,3,4 |
| ATC:skmeans | 6 | 0.910 | 0.925 | 0.939 | * | 2,3,4 |
| MAD:NMF | 4 | 0.905 | 0.893 | 0.947 | * | 3 |
| SD:skmeans | 6 | 0.901 | 0.940 | 0.928 | * | 2,3,4 |
| SD:kmeans | 5 | 0.672 | 0.812 | 0.739 | ||
| MAD:kmeans | 2 | 0.369 | 0.872 | 0.894 | ||
| CV:kmeans | 2 | 0.327 | 0.913 | 0.884 |
**: 1-PAC > 0.95, *: 1-PAC > 0.9
Cumulative distribution function curves of consensus matrix for all methods.
collect_plots(res_list, fun = plot_ecdf)
Consensus heatmaps for all methods. (What is a consensus heatmap?)
collect_plots(res_list, k = 2, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = consensus_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = consensus_heatmap, mc.cores = 4)
Membership heatmaps for all methods. (What is a membership heatmap?)
collect_plots(res_list, k = 2, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 3, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 4, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 5, fun = membership_heatmap, mc.cores = 4)
collect_plots(res_list, k = 6, fun = membership_heatmap, mc.cores = 4)
Signature heatmaps for all methods. (What is a signature heatmap?)
Note in following heatmaps, rows are scaled.
collect_plots(res_list, k = 2, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 3, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 4, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 5, fun = get_signatures, mc.cores = 4)
collect_plots(res_list, k = 6, fun = get_signatures, mc.cores = 4)
The statistics used for measuring the stability of consensus partitioning. (How are they defined?)
get_stats(res_list, k = 2)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 2 1.000 0.983 0.993 0.473 0.524 0.524
#> CV:NMF 2 0.930 0.957 0.979 0.495 0.499 0.499
#> MAD:NMF 2 0.829 0.893 0.957 0.504 0.493 0.493
#> ATC:NMF 2 1.000 0.986 0.994 0.441 0.556 0.556
#> SD:skmeans 2 1.000 1.000 1.000 0.484 0.516 0.516
#> CV:skmeans 2 1.000 0.955 0.981 0.502 0.499 0.499
#> MAD:skmeans 2 1.000 0.991 0.995 0.508 0.493 0.493
#> ATC:skmeans 2 1.000 0.958 0.983 0.476 0.516 0.516
#> SD:mclust 2 0.364 0.375 0.756 0.306 0.691 0.691
#> CV:mclust 2 0.483 0.955 0.921 0.427 0.524 0.524
#> MAD:mclust 2 1.000 0.997 0.998 0.477 0.524 0.524
#> ATC:mclust 2 1.000 0.998 0.999 0.497 0.503 0.503
#> SD:kmeans 2 0.380 0.938 0.901 0.389 0.544 0.544
#> CV:kmeans 2 0.327 0.913 0.884 0.378 0.544 0.544
#> MAD:kmeans 2 0.369 0.872 0.894 0.447 0.544 0.544
#> ATC:kmeans 2 1.000 1.000 1.000 0.445 0.556 0.556
#> SD:pam 2 1.000 0.997 0.999 0.432 0.569 0.569
#> CV:pam 2 0.964 0.973 0.987 0.408 0.598 0.598
#> MAD:pam 2 1.000 0.968 0.986 0.453 0.556 0.556
#> ATC:pam 2 1.000 1.000 1.000 0.432 0.569 0.569
#> SD:hclust 2 1.000 0.995 0.998 0.126 0.871 0.871
#> CV:hclust 2 1.000 1.000 1.000 0.129 0.871 0.871
#> MAD:hclust 2 0.484 0.946 0.887 0.417 0.509 0.509
#> ATC:hclust 2 1.000 0.978 0.990 0.461 0.534 0.534
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.695 0.776 0.857 0.214 0.958 0.920
#> CV:NMF 3 0.649 0.759 0.852 0.247 0.777 0.580
#> MAD:NMF 3 0.947 0.937 0.975 0.303 0.802 0.617
#> ATC:NMF 3 0.999 0.977 0.987 0.342 0.837 0.711
#> SD:skmeans 3 1.000 0.997 0.997 0.368 0.779 0.589
#> CV:skmeans 3 1.000 0.976 0.989 0.319 0.737 0.521
#> MAD:skmeans 3 1.000 0.980 0.991 0.302 0.787 0.593
#> ATC:skmeans 3 0.967 0.897 0.963 0.267 0.849 0.714
#> SD:mclust 3 0.658 0.786 0.880 0.922 0.633 0.512
#> CV:mclust 3 0.775 0.909 0.936 0.334 0.640 0.459
#> MAD:mclust 3 1.000 0.973 0.980 0.353 0.833 0.681
#> ATC:mclust 3 0.881 0.934 0.957 0.335 0.710 0.482
#> SD:kmeans 3 0.657 0.752 0.837 0.451 0.839 0.714
#> CV:kmeans 3 0.586 0.728 0.810 0.526 1.000 1.000
#> MAD:kmeans 3 0.599 0.871 0.876 0.394 0.784 0.608
#> ATC:kmeans 3 0.763 0.931 0.935 0.372 0.797 0.638
#> SD:pam 3 0.840 0.948 0.943 0.268 0.861 0.755
#> CV:pam 3 0.736 0.893 0.937 0.319 0.823 0.714
#> MAD:pam 3 1.000 0.957 0.984 0.384 0.825 0.685
#> ATC:pam 3 0.828 0.936 0.949 0.302 0.861 0.755
#> SD:hclust 3 0.482 0.884 0.923 2.753 0.649 0.598
#> CV:hclust 3 0.477 0.809 0.786 2.586 0.562 0.497
#> MAD:hclust 3 0.843 0.942 0.935 0.455 0.874 0.752
#> ATC:hclust 3 0.781 0.865 0.932 0.142 0.953 0.912
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.661 0.854 0.893 0.1966 0.771 0.551
#> CV:NMF 4 0.897 0.925 0.952 0.1261 0.964 0.894
#> MAD:NMF 4 0.905 0.893 0.947 0.0749 0.930 0.803
#> ATC:NMF 4 0.721 0.691 0.801 0.1519 0.891 0.743
#> SD:skmeans 4 0.906 0.942 0.949 0.1061 0.886 0.679
#> CV:skmeans 4 0.939 0.961 0.970 0.1146 0.886 0.679
#> MAD:skmeans 4 1.000 0.964 0.977 0.1068 0.908 0.739
#> ATC:skmeans 4 0.915 0.934 0.964 0.1297 0.878 0.698
#> SD:mclust 4 0.855 0.838 0.908 0.1925 0.795 0.574
#> CV:mclust 4 0.855 0.897 0.927 0.2457 0.742 0.482
#> MAD:mclust 4 1.000 0.961 0.981 0.1298 0.863 0.641
#> ATC:mclust 4 0.912 0.889 0.942 0.0970 0.947 0.837
#> SD:kmeans 4 0.664 0.664 0.809 0.1709 0.944 0.867
#> CV:kmeans 4 0.621 0.622 0.759 0.1738 0.683 0.452
#> MAD:kmeans 4 0.659 0.690 0.766 0.1295 0.932 0.809
#> ATC:kmeans 4 0.774 0.766 0.842 0.1428 0.959 0.889
#> SD:pam 4 1.000 0.985 0.995 0.1370 0.942 0.865
#> CV:pam 4 0.675 0.748 0.888 0.1824 0.891 0.771
#> MAD:pam 4 1.000 0.975 0.992 0.0811 0.915 0.783
#> ATC:pam 4 1.000 0.989 0.990 0.0997 0.947 0.879
#> SD:hclust 4 0.595 0.856 0.897 0.2667 0.881 0.771
#> CV:hclust 4 0.752 0.810 0.869 0.3843 0.765 0.546
#> MAD:hclust 4 0.807 0.932 0.924 0.1559 0.897 0.731
#> ATC:hclust 4 0.793 0.865 0.914 0.2029 0.841 0.683
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.825 0.832 0.905 0.0745 0.819 0.518
#> CV:NMF 5 0.912 0.908 0.944 0.0909 0.846 0.561
#> MAD:NMF 5 0.896 0.919 0.944 0.0603 0.868 0.609
#> ATC:NMF 5 0.836 0.902 0.906 0.0881 0.866 0.625
#> SD:skmeans 5 0.895 0.936 0.932 0.0424 0.967 0.872
#> CV:skmeans 5 0.933 0.918 0.930 0.0398 0.965 0.866
#> MAD:skmeans 5 0.886 0.842 0.887 0.0477 0.933 0.763
#> ATC:skmeans 5 1.000 0.970 0.983 0.0504 0.991 0.968
#> SD:mclust 5 0.996 0.971 0.985 0.0809 0.899 0.690
#> CV:mclust 5 1.000 0.999 0.999 0.0705 0.949 0.824
#> MAD:mclust 5 1.000 0.979 0.984 0.0571 0.915 0.708
#> ATC:mclust 5 0.961 0.889 0.959 0.0469 0.948 0.813
#> SD:kmeans 5 0.672 0.812 0.739 0.1024 0.777 0.465
#> CV:kmeans 5 0.670 0.771 0.837 0.0924 0.891 0.662
#> MAD:kmeans 5 0.737 0.739 0.783 0.0792 0.939 0.806
#> ATC:kmeans 5 0.721 0.624 0.764 0.0806 0.890 0.682
#> SD:pam 5 0.842 0.883 0.934 0.1254 0.881 0.697
#> CV:pam 5 0.744 0.802 0.855 0.1476 0.762 0.440
#> MAD:pam 5 0.990 0.957 0.983 0.0943 0.925 0.770
#> ATC:pam 5 0.837 0.861 0.909 0.2401 0.840 0.586
#> SD:hclust 5 0.757 0.852 0.922 0.1361 0.881 0.715
#> CV:hclust 5 0.887 0.897 0.942 0.1016 0.949 0.860
#> MAD:hclust 5 0.935 0.944 0.964 0.0648 0.974 0.908
#> ATC:hclust 5 0.799 0.855 0.912 0.0542 0.991 0.974
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.882 0.897 0.919 0.0573 0.942 0.781
#> CV:NMF 6 0.940 0.934 0.941 0.0396 0.972 0.883
#> MAD:NMF 6 0.836 0.806 0.872 0.0642 0.971 0.882
#> ATC:NMF 6 0.921 0.880 0.906 0.0309 1.000 1.000
#> SD:skmeans 6 0.901 0.940 0.928 0.0456 0.981 0.919
#> CV:skmeans 6 0.894 0.937 0.936 0.0405 0.981 0.919
#> MAD:skmeans 6 0.829 0.855 0.904 0.0468 0.984 0.931
#> ATC:skmeans 6 0.910 0.925 0.939 0.0351 0.974 0.910
#> SD:mclust 6 1.000 0.976 0.982 0.0431 0.971 0.881
#> CV:mclust 6 1.000 0.990 0.995 0.0374 0.971 0.881
#> MAD:mclust 6 1.000 0.988 0.993 0.0249 0.982 0.923
#> ATC:mclust 6 0.976 0.920 0.965 0.0263 0.970 0.873
#> SD:kmeans 6 0.756 0.912 0.879 0.0638 0.971 0.881
#> CV:kmeans 6 0.852 0.894 0.868 0.0614 0.964 0.854
#> MAD:kmeans 6 0.795 0.764 0.782 0.0456 0.936 0.766
#> ATC:kmeans 6 0.736 0.843 0.772 0.0462 0.869 0.520
#> SD:pam 6 0.946 0.962 0.985 0.1178 0.915 0.709
#> CV:pam 6 0.946 0.977 0.991 0.0755 0.981 0.919
#> MAD:pam 6 0.990 0.961 0.984 0.0444 0.967 0.873
#> ATC:pam 6 0.946 0.946 0.971 0.0875 0.937 0.720
#> SD:hclust 6 0.833 0.636 0.801 0.1121 0.791 0.483
#> CV:hclust 6 1.000 0.966 0.986 0.1131 0.897 0.673
#> MAD:hclust 6 0.947 0.966 0.964 0.0420 0.963 0.853
#> ATC:hclust 6 0.817 0.878 0.875 0.0771 0.888 0.677
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 time(p) k
#> SD:NMF 59 0.4110 2
#> CV:NMF 59 0.7866 2
#> MAD:NMF 55 0.9514 2
#> ATC:NMF 59 0.9587 2
#> SD:skmeans 59 0.5430 2
#> CV:skmeans 57 0.7910 2
#> MAD:skmeans 59 0.9973 2
#> ATC:skmeans 58 0.9791 2
#> SD:mclust 23 NA 2
#> CV:mclust 59 0.8004 2
#> MAD:mclust 59 0.8004 2
#> ATC:mclust 59 0.9802 2
#> SD:kmeans 59 0.4467 2
#> CV:kmeans 59 0.6547 2
#> MAD:kmeans 59 0.7950 2
#> ATC:kmeans 59 0.9587 2
#> SD:pam 59 0.9705 2
#> CV:pam 59 0.7530 2
#> MAD:pam 58 0.9821 2
#> ATC:pam 59 0.9705 2
#> SD:hclust 59 0.0997 2
#> CV:hclust 59 0.0997 2
#> MAD:hclust 59 0.9982 2
#> ATC:hclust 59 0.9786 2
test_to_known_factors(res_list, k = 3)
#> n time(p) k
#> SD:NMF 57 0.327 3
#> CV:NMF 49 0.999 3
#> MAD:NMF 58 0.982 3
#> ATC:NMF 59 0.997 3
#> SD:skmeans 59 0.669 3
#> CV:skmeans 59 0.669 3
#> MAD:skmeans 59 0.953 3
#> ATC:skmeans 55 0.994 3
#> SD:mclust 54 0.305 3
#> CV:mclust 59 0.377 3
#> MAD:mclust 59 0.976 3
#> ATC:mclust 57 0.993 3
#> SD:kmeans 48 0.857 3
#> CV:kmeans 59 0.655 3
#> MAD:kmeans 58 0.951 3
#> ATC:kmeans 59 0.988 3
#> SD:pam 57 0.976 3
#> CV:pam 57 0.965 3
#> MAD:pam 58 0.995 3
#> ATC:pam 58 0.995 3
#> SD:hclust 55 0.341 3
#> CV:hclust 53 0.396 3
#> MAD:hclust 59 1.000 3
#> ATC:hclust 59 0.996 3
test_to_known_factors(res_list, k = 4)
#> n time(p) k
#> SD:NMF 58 0.693 4
#> CV:NMF 59 0.678 4
#> MAD:NMF 56 0.650 4
#> ATC:NMF 45 0.989 4
#> SD:skmeans 59 0.983 4
#> CV:skmeans 59 0.983 4
#> MAD:skmeans 59 1.000 4
#> ATC:skmeans 59 0.999 4
#> SD:mclust 57 0.611 4
#> CV:mclust 55 0.643 4
#> MAD:mclust 58 1.000 4
#> ATC:mclust 59 0.979 4
#> SD:kmeans 48 0.661 4
#> CV:kmeans 46 0.999 4
#> MAD:kmeans 46 0.985 4
#> ATC:kmeans 52 1.000 4
#> SD:pam 59 0.629 4
#> CV:pam 50 0.821 4
#> MAD:pam 58 0.998 4
#> ATC:pam 59 0.999 4
#> SD:hclust 55 0.535 4
#> CV:hclust 53 0.585 4
#> MAD:hclust 59 1.000 4
#> ATC:hclust 52 0.990 4
test_to_known_factors(res_list, k = 5)
#> n time(p) k
#> SD:NMF 54 0.831 5
#> CV:NMF 58 0.870 5
#> MAD:NMF 58 0.631 5
#> ATC:NMF 58 1.000 5
#> SD:skmeans 59 0.992 5
#> CV:skmeans 58 0.987 5
#> MAD:skmeans 56 1.000 5
#> ATC:skmeans 59 0.987 5
#> SD:mclust 59 0.856 5
#> CV:mclust 59 0.856 5
#> MAD:mclust 59 0.999 5
#> ATC:mclust 54 0.999 5
#> SD:kmeans 58 0.872 5
#> CV:kmeans 44 0.656 5
#> MAD:kmeans 55 1.000 5
#> ATC:kmeans 51 1.000 5
#> SD:pam 56 0.741 5
#> CV:pam 53 1.000 5
#> MAD:pam 58 0.998 5
#> ATC:pam 58 0.974 5
#> SD:hclust 53 0.817 5
#> CV:hclust 59 0.780 5
#> MAD:hclust 59 0.877 5
#> ATC:hclust 56 0.989 5
test_to_known_factors(res_list, k = 6)
#> n time(p) k
#> SD:NMF 57 0.929 6
#> CV:NMF 59 0.945 6
#> MAD:NMF 56 0.863 6
#> ATC:NMF 56 0.999 6
#> SD:skmeans 59 0.945 6
#> CV:skmeans 58 0.935 6
#> MAD:skmeans 58 0.927 6
#> ATC:skmeans 57 0.834 6
#> SD:mclust 59 0.939 6
#> CV:mclust 59 0.939 6
#> MAD:mclust 59 0.986 6
#> ATC:mclust 57 0.908 6
#> SD:kmeans 59 0.939 6
#> CV:kmeans 59 0.939 6
#> MAD:kmeans 57 0.775 6
#> ATC:kmeans 56 0.947 6
#> SD:pam 59 0.939 6
#> CV:pam 59 0.939 6
#> MAD:pam 59 0.658 6
#> ATC:pam 59 0.966 6
#> SD:hclust 52 0.915 6
#> CV:hclust 57 0.931 6
#> MAD:hclust 59 0.965 6
#> ATC:hclust 55 0.998 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 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.995 0.998 0.126 0.871 0.871
#> 3 3 0.482 0.884 0.923 2.753 0.649 0.598
#> 4 4 0.595 0.856 0.897 0.267 0.881 0.771
#> 5 5 0.757 0.852 0.922 0.136 0.881 0.715
#> 6 6 0.833 0.636 0.801 0.112 0.791 0.483
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
#> GSM155448 1 0.000 1.000 1.000 0.000
#> GSM155452 1 0.000 1.000 1.000 0.000
#> GSM155455 1 0.000 1.000 1.000 0.000
#> GSM155459 1 0.000 1.000 1.000 0.000
#> GSM155463 1 0.000 1.000 1.000 0.000
#> GSM155467 1 0.000 1.000 1.000 0.000
#> GSM155471 1 0.000 1.000 1.000 0.000
#> GSM155475 1 0.000 1.000 1.000 0.000
#> GSM155479 1 0.000 1.000 1.000 0.000
#> GSM155483 1 0.000 1.000 1.000 0.000
#> GSM155487 2 0.552 0.853 0.128 0.872
#> GSM155491 1 0.000 1.000 1.000 0.000
#> GSM155495 1 0.000 1.000 1.000 0.000
#> GSM155499 1 0.000 1.000 1.000 0.000
#> GSM155503 1 0.000 1.000 1.000 0.000
#> GSM155449 1 0.000 1.000 1.000 0.000
#> GSM155456 1 0.000 1.000 1.000 0.000
#> GSM155460 1 0.000 1.000 1.000 0.000
#> GSM155464 1 0.000 1.000 1.000 0.000
#> GSM155468 1 0.000 1.000 1.000 0.000
#> GSM155472 1 0.000 1.000 1.000 0.000
#> GSM155476 1 0.000 1.000 1.000 0.000
#> GSM155480 1 0.000 1.000 1.000 0.000
#> GSM155484 1 0.000 1.000 1.000 0.000
#> GSM155488 1 0.000 1.000 1.000 0.000
#> GSM155492 1 0.000 1.000 1.000 0.000
#> GSM155496 1 0.000 1.000 1.000 0.000
#> GSM155500 1 0.000 1.000 1.000 0.000
#> GSM155504 1 0.000 1.000 1.000 0.000
#> GSM155450 1 0.000 1.000 1.000 0.000
#> GSM155453 1 0.000 1.000 1.000 0.000
#> GSM155457 1 0.000 1.000 1.000 0.000
#> GSM155461 1 0.000 1.000 1.000 0.000
#> GSM155465 1 0.000 1.000 1.000 0.000
#> GSM155469 1 0.000 1.000 1.000 0.000
#> GSM155473 1 0.000 1.000 1.000 0.000
#> GSM155477 1 0.000 1.000 1.000 0.000
#> GSM155481 1 0.000 1.000 1.000 0.000
#> GSM155485 1 0.000 1.000 1.000 0.000
#> GSM155489 1 0.000 1.000 1.000 0.000
#> GSM155493 1 0.000 1.000 1.000 0.000
#> GSM155497 1 0.000 1.000 1.000 0.000
#> GSM155501 1 0.000 1.000 1.000 0.000
#> GSM155505 1 0.000 1.000 1.000 0.000
#> GSM155451 1 0.000 1.000 1.000 0.000
#> GSM155454 1 0.000 1.000 1.000 0.000
#> GSM155458 1 0.000 1.000 1.000 0.000
#> GSM155462 1 0.000 1.000 1.000 0.000
#> GSM155466 1 0.000 1.000 1.000 0.000
#> GSM155470 1 0.000 1.000 1.000 0.000
#> GSM155474 1 0.000 1.000 1.000 0.000
#> GSM155478 2 0.000 0.957 0.000 1.000
#> GSM155482 2 0.000 0.957 0.000 1.000
#> GSM155486 1 0.000 1.000 1.000 0.000
#> GSM155490 2 0.000 0.957 0.000 1.000
#> GSM155494 1 0.000 1.000 1.000 0.000
#> GSM155498 1 0.000 1.000 1.000 0.000
#> GSM155502 1 0.000 1.000 1.000 0.000
#> GSM155506 1 0.000 1.000 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 2 0.362 1.000 0.136 0.864 0.000
#> GSM155452 2 0.362 1.000 0.136 0.864 0.000
#> GSM155455 1 0.608 0.244 0.612 0.388 0.000
#> GSM155459 1 0.000 0.926 1.000 0.000 0.000
#> GSM155463 1 0.000 0.926 1.000 0.000 0.000
#> GSM155467 1 0.000 0.926 1.000 0.000 0.000
#> GSM155471 1 0.000 0.926 1.000 0.000 0.000
#> GSM155475 1 0.000 0.926 1.000 0.000 0.000
#> GSM155479 1 0.000 0.926 1.000 0.000 0.000
#> GSM155483 1 0.000 0.926 1.000 0.000 0.000
#> GSM155487 3 0.375 0.768 0.120 0.008 0.872
#> GSM155491 1 0.362 0.806 0.864 0.136 0.000
#> GSM155495 1 0.000 0.926 1.000 0.000 0.000
#> GSM155499 2 0.362 1.000 0.136 0.864 0.000
#> GSM155503 2 0.362 1.000 0.136 0.864 0.000
#> GSM155449 2 0.362 1.000 0.136 0.864 0.000
#> GSM155456 1 0.608 0.244 0.612 0.388 0.000
#> GSM155460 1 0.000 0.926 1.000 0.000 0.000
#> GSM155464 1 0.000 0.926 1.000 0.000 0.000
#> GSM155468 1 0.000 0.926 1.000 0.000 0.000
#> GSM155472 1 0.000 0.926 1.000 0.000 0.000
#> GSM155476 1 0.000 0.926 1.000 0.000 0.000
#> GSM155480 1 0.000 0.926 1.000 0.000 0.000
#> GSM155484 1 0.000 0.926 1.000 0.000 0.000
#> GSM155488 1 0.000 0.926 1.000 0.000 0.000
#> GSM155492 1 0.362 0.806 0.864 0.136 0.000
#> GSM155496 1 0.000 0.926 1.000 0.000 0.000
#> GSM155500 2 0.362 1.000 0.136 0.864 0.000
#> GSM155504 2 0.362 1.000 0.136 0.864 0.000
#> GSM155450 2 0.362 1.000 0.136 0.864 0.000
#> GSM155453 2 0.362 1.000 0.136 0.864 0.000
#> GSM155457 1 0.608 0.244 0.612 0.388 0.000
#> GSM155461 1 0.000 0.926 1.000 0.000 0.000
#> GSM155465 1 0.000 0.926 1.000 0.000 0.000
#> GSM155469 1 0.000 0.926 1.000 0.000 0.000
#> GSM155473 1 0.000 0.926 1.000 0.000 0.000
#> GSM155477 1 0.000 0.926 1.000 0.000 0.000
#> GSM155481 1 0.000 0.926 1.000 0.000 0.000
#> GSM155485 1 0.000 0.926 1.000 0.000 0.000
#> GSM155489 1 0.000 0.926 1.000 0.000 0.000
#> GSM155493 1 0.362 0.806 0.864 0.136 0.000
#> GSM155497 1 0.362 0.806 0.864 0.136 0.000
#> GSM155501 2 0.362 1.000 0.136 0.864 0.000
#> GSM155505 2 0.362 1.000 0.136 0.864 0.000
#> GSM155451 2 0.362 1.000 0.136 0.864 0.000
#> GSM155454 2 0.362 1.000 0.136 0.864 0.000
#> GSM155458 1 0.608 0.244 0.612 0.388 0.000
#> GSM155462 1 0.000 0.926 1.000 0.000 0.000
#> GSM155466 1 0.000 0.926 1.000 0.000 0.000
#> GSM155470 1 0.000 0.926 1.000 0.000 0.000
#> GSM155474 1 0.000 0.926 1.000 0.000 0.000
#> GSM155478 3 0.000 0.933 0.000 0.000 1.000
#> GSM155482 3 0.000 0.933 0.000 0.000 1.000
#> GSM155486 1 0.000 0.926 1.000 0.000 0.000
#> GSM155490 3 0.000 0.933 0.000 0.000 1.000
#> GSM155494 1 0.362 0.806 0.864 0.136 0.000
#> GSM155498 1 0.362 0.806 0.864 0.136 0.000
#> GSM155502 2 0.362 1.000 0.136 0.864 0.000
#> GSM155506 2 0.362 1.000 0.136 0.864 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 2 0.265 0.801 0.120 0.88 0.000 0.000
#> GSM155452 2 0.265 0.801 0.120 0.88 0.000 0.000
#> GSM155455 1 0.485 0.376 0.600 0.40 0.000 0.000
#> GSM155459 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155463 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155467 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155471 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155475 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155479 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155483 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155487 4 0.298 0.863 0.000 0.12 0.008 0.872
#> GSM155491 3 0.317 1.000 0.160 0.00 0.840 0.000
#> GSM155495 1 0.369 0.662 0.792 0.00 0.208 0.000
#> GSM155499 2 0.317 0.819 0.000 0.84 0.160 0.000
#> GSM155503 2 0.317 0.819 0.000 0.84 0.160 0.000
#> GSM155449 2 0.265 0.801 0.120 0.88 0.000 0.000
#> GSM155456 1 0.485 0.376 0.600 0.40 0.000 0.000
#> GSM155460 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155464 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155468 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155472 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155476 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155480 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155484 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155488 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155492 3 0.317 1.000 0.160 0.00 0.840 0.000
#> GSM155496 1 0.369 0.662 0.792 0.00 0.208 0.000
#> GSM155500 2 0.317 0.819 0.000 0.84 0.160 0.000
#> GSM155504 2 0.317 0.819 0.000 0.84 0.160 0.000
#> GSM155450 2 0.265 0.801 0.120 0.88 0.000 0.000
#> GSM155453 2 0.265 0.801 0.120 0.88 0.000 0.000
#> GSM155457 1 0.485 0.376 0.600 0.40 0.000 0.000
#> GSM155461 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155465 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155469 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155473 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155477 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155481 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155485 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155489 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155493 3 0.317 1.000 0.160 0.00 0.840 0.000
#> GSM155497 3 0.317 1.000 0.160 0.00 0.840 0.000
#> GSM155501 2 0.317 0.819 0.000 0.84 0.160 0.000
#> GSM155505 2 0.317 0.819 0.000 0.84 0.160 0.000
#> GSM155451 2 0.265 0.801 0.120 0.88 0.000 0.000
#> GSM155454 2 0.265 0.801 0.120 0.88 0.000 0.000
#> GSM155458 1 0.485 0.376 0.600 0.40 0.000 0.000
#> GSM155462 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155466 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155470 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155474 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155478 4 0.000 0.955 0.000 0.00 0.000 1.000
#> GSM155482 4 0.000 0.955 0.000 0.00 0.000 1.000
#> GSM155486 1 0.000 0.922 1.000 0.00 0.000 0.000
#> GSM155490 4 0.000 0.955 0.000 0.00 0.000 1.000
#> GSM155494 3 0.317 1.000 0.160 0.00 0.840 0.000
#> GSM155498 3 0.317 1.000 0.160 0.00 0.840 0.000
#> GSM155502 2 0.317 0.819 0.000 0.84 0.160 0.000
#> GSM155506 2 0.317 0.819 0.000 0.84 0.160 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.242 0.655 0.000 0.132 0.000 0.868 0.000
#> GSM155452 4 0.242 0.655 0.000 0.132 0.000 0.868 0.000
#> GSM155455 4 0.430 0.345 0.484 0.000 0.000 0.516 0.000
#> GSM155459 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155463 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155467 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155479 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155483 1 0.242 0.849 0.868 0.000 0.000 0.132 0.000
#> GSM155487 5 0.238 0.854 0.000 0.128 0.000 0.000 0.872
#> GSM155491 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155495 1 0.569 0.443 0.580 0.000 0.316 0.104 0.000
#> GSM155499 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155503 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155449 4 0.242 0.655 0.000 0.132 0.000 0.868 0.000
#> GSM155456 4 0.430 0.345 0.484 0.000 0.000 0.516 0.000
#> GSM155460 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155464 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155468 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155472 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155476 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155480 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155484 1 0.242 0.849 0.868 0.000 0.000 0.132 0.000
#> GSM155488 1 0.242 0.849 0.868 0.000 0.000 0.132 0.000
#> GSM155492 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155496 1 0.569 0.443 0.580 0.000 0.316 0.104 0.000
#> GSM155500 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155504 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155450 4 0.242 0.655 0.000 0.132 0.000 0.868 0.000
#> GSM155453 4 0.242 0.655 0.000 0.132 0.000 0.868 0.000
#> GSM155457 4 0.430 0.345 0.484 0.000 0.000 0.516 0.000
#> GSM155461 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155465 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155469 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155473 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155481 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155485 1 0.242 0.849 0.868 0.000 0.000 0.132 0.000
#> GSM155489 1 0.242 0.849 0.868 0.000 0.000 0.132 0.000
#> GSM155493 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155497 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155501 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155505 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155451 4 0.242 0.655 0.000 0.132 0.000 0.868 0.000
#> GSM155454 4 0.242 0.655 0.000 0.132 0.000 0.868 0.000
#> GSM155458 4 0.430 0.345 0.484 0.000 0.000 0.516 0.000
#> GSM155462 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155466 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155470 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.000 0.936 1.000 0.000 0.000 0.000 0.000
#> GSM155478 5 0.000 0.953 0.000 0.000 0.000 0.000 1.000
#> GSM155482 5 0.000 0.953 0.000 0.000 0.000 0.000 1.000
#> GSM155486 1 0.242 0.849 0.868 0.000 0.000 0.132 0.000
#> GSM155490 5 0.000 0.953 0.000 0.000 0.000 0.000 1.000
#> GSM155494 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155498 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155502 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155506 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 1 0.459 -0.329 0.484 0.000 0.000 0.480 0.036 0.000
#> GSM155452 1 0.459 -0.329 0.484 0.000 0.000 0.480 0.036 0.000
#> GSM155455 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM155459 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155463 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155467 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155471 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155475 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155479 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155483 5 0.282 0.884 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM155487 6 0.452 0.807 0.000 0.128 0.000 0.000 0.168 0.704
#> GSM155491 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155495 5 0.472 0.554 0.068 0.000 0.316 0.000 0.616 0.000
#> GSM155499 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155503 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155449 1 0.459 -0.329 0.484 0.000 0.000 0.480 0.036 0.000
#> GSM155456 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM155460 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155464 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155468 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155472 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155476 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155480 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155484 5 0.282 0.884 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM155488 5 0.282 0.884 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM155492 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155496 5 0.472 0.554 0.068 0.000 0.316 0.000 0.616 0.000
#> GSM155500 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155504 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155450 1 0.459 -0.329 0.484 0.000 0.000 0.480 0.036 0.000
#> GSM155453 1 0.459 -0.329 0.484 0.000 0.000 0.480 0.036 0.000
#> GSM155457 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM155461 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155465 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155469 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155473 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155477 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155481 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155485 5 0.282 0.884 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM155489 5 0.282 0.884 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM155493 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155497 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155501 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155505 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155451 1 0.459 -0.329 0.484 0.000 0.000 0.480 0.036 0.000
#> GSM155454 1 0.459 -0.329 0.484 0.000 0.000 0.480 0.036 0.000
#> GSM155458 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM155462 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155466 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155470 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155474 1 0.387 0.544 0.516 0.000 0.000 0.484 0.000 0.000
#> GSM155478 6 0.000 0.895 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM155482 6 0.000 0.895 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM155486 5 0.282 0.884 0.204 0.000 0.000 0.000 0.796 0.000
#> GSM155490 6 0.253 0.878 0.000 0.000 0.000 0.000 0.168 0.832
#> GSM155494 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155498 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155502 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155506 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n time(p) k
#> SD:hclust 59 0.0997 2
#> SD:hclust 55 0.3414 3
#> SD:hclust 55 0.5353 4
#> SD:hclust 53 0.8168 5
#> SD:hclust 52 0.9150 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 59 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 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.380 0.938 0.901 0.3887 0.544 0.544
#> 3 3 0.657 0.752 0.837 0.4512 0.839 0.714
#> 4 4 0.664 0.664 0.809 0.1709 0.944 0.867
#> 5 5 0.672 0.812 0.739 0.1024 0.777 0.465
#> 6 6 0.756 0.912 0.879 0.0638 0.971 0.881
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 2 0.8267 0.963 0.260 0.740
#> GSM155452 2 0.8267 0.963 0.260 0.740
#> GSM155455 2 0.8608 0.933 0.284 0.716
#> GSM155459 1 0.0000 0.959 1.000 0.000
#> GSM155463 1 0.0000 0.959 1.000 0.000
#> GSM155467 1 0.0000 0.959 1.000 0.000
#> GSM155471 1 0.0000 0.959 1.000 0.000
#> GSM155475 1 0.0000 0.959 1.000 0.000
#> GSM155479 1 0.0000 0.959 1.000 0.000
#> GSM155483 1 0.0672 0.956 0.992 0.008
#> GSM155487 2 0.5629 0.867 0.132 0.868
#> GSM155491 1 0.5946 0.848 0.856 0.144
#> GSM155495 1 0.5737 0.854 0.864 0.136
#> GSM155499 2 0.8267 0.963 0.260 0.740
#> GSM155503 2 0.8267 0.963 0.260 0.740
#> GSM155449 2 0.8267 0.963 0.260 0.740
#> GSM155456 1 0.0000 0.959 1.000 0.000
#> GSM155460 1 0.0000 0.959 1.000 0.000
#> GSM155464 1 0.0000 0.959 1.000 0.000
#> GSM155468 1 0.0000 0.959 1.000 0.000
#> GSM155472 1 0.0000 0.959 1.000 0.000
#> GSM155476 1 0.0000 0.959 1.000 0.000
#> GSM155480 1 0.0000 0.959 1.000 0.000
#> GSM155484 1 0.0672 0.956 0.992 0.008
#> GSM155488 1 0.0000 0.959 1.000 0.000
#> GSM155492 1 0.5946 0.848 0.856 0.144
#> GSM155496 1 0.5842 0.851 0.860 0.140
#> GSM155500 2 0.8267 0.963 0.260 0.740
#> GSM155504 2 0.8267 0.963 0.260 0.740
#> GSM155450 2 0.8267 0.963 0.260 0.740
#> GSM155453 2 0.8267 0.963 0.260 0.740
#> GSM155457 1 0.0000 0.959 1.000 0.000
#> GSM155461 1 0.0000 0.959 1.000 0.000
#> GSM155465 1 0.0000 0.959 1.000 0.000
#> GSM155469 1 0.0000 0.959 1.000 0.000
#> GSM155473 1 0.0000 0.959 1.000 0.000
#> GSM155477 1 0.0000 0.959 1.000 0.000
#> GSM155481 1 0.0000 0.959 1.000 0.000
#> GSM155485 1 0.0672 0.956 0.992 0.008
#> GSM155489 1 0.0672 0.956 0.992 0.008
#> GSM155493 1 0.5946 0.848 0.856 0.144
#> GSM155497 1 0.5946 0.848 0.856 0.144
#> GSM155501 2 0.8267 0.963 0.260 0.740
#> GSM155505 2 0.8267 0.963 0.260 0.740
#> GSM155451 2 0.8267 0.963 0.260 0.740
#> GSM155454 2 0.8267 0.963 0.260 0.740
#> GSM155458 1 0.0000 0.959 1.000 0.000
#> GSM155462 1 0.0000 0.959 1.000 0.000
#> GSM155466 1 0.0000 0.959 1.000 0.000
#> GSM155470 1 0.0000 0.959 1.000 0.000
#> GSM155474 1 0.0000 0.959 1.000 0.000
#> GSM155478 2 0.5629 0.867 0.132 0.868
#> GSM155482 2 0.5629 0.867 0.132 0.868
#> GSM155486 1 0.0672 0.956 0.992 0.008
#> GSM155490 2 0.5629 0.867 0.132 0.868
#> GSM155494 1 0.5946 0.848 0.856 0.144
#> GSM155498 1 0.5946 0.848 0.856 0.144
#> GSM155502 2 0.8267 0.963 0.260 0.740
#> GSM155506 2 0.8267 0.963 0.260 0.740
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 2 0.601 0.8262 0.032 0.748 0.220
#> GSM155452 2 0.601 0.8262 0.032 0.748 0.220
#> GSM155455 1 0.951 0.0256 0.484 0.296 0.220
#> GSM155459 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155463 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155467 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155471 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155475 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155479 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155483 1 0.435 0.4758 0.816 0.000 0.184
#> GSM155487 2 0.546 0.7086 0.000 0.712 0.288
#> GSM155491 3 0.630 0.9938 0.480 0.000 0.520
#> GSM155495 1 0.543 -0.0734 0.716 0.000 0.284
#> GSM155499 2 0.129 0.8608 0.032 0.968 0.000
#> GSM155503 2 0.129 0.8608 0.032 0.968 0.000
#> GSM155449 2 0.601 0.8262 0.032 0.748 0.220
#> GSM155456 1 0.475 0.4785 0.784 0.000 0.216
#> GSM155460 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155464 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155468 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155472 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155476 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155480 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155484 1 0.435 0.4758 0.816 0.000 0.184
#> GSM155488 1 0.540 0.4433 0.792 0.028 0.180
#> GSM155492 3 0.630 0.9938 0.480 0.000 0.520
#> GSM155496 3 0.631 0.9616 0.496 0.000 0.504
#> GSM155500 2 0.129 0.8608 0.032 0.968 0.000
#> GSM155504 2 0.129 0.8608 0.032 0.968 0.000
#> GSM155450 2 0.601 0.8262 0.032 0.748 0.220
#> GSM155453 2 0.601 0.8262 0.032 0.748 0.220
#> GSM155457 1 0.475 0.4785 0.784 0.000 0.216
#> GSM155461 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155465 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155469 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155473 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155477 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155481 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155485 1 0.429 0.4867 0.820 0.000 0.180
#> GSM155489 1 0.435 0.4758 0.816 0.000 0.184
#> GSM155493 3 0.630 0.9938 0.480 0.000 0.520
#> GSM155497 3 0.630 0.9938 0.480 0.000 0.520
#> GSM155501 2 0.129 0.8608 0.032 0.968 0.000
#> GSM155505 2 0.129 0.8608 0.032 0.968 0.000
#> GSM155451 2 0.601 0.8262 0.032 0.748 0.220
#> GSM155454 2 0.601 0.8262 0.032 0.748 0.220
#> GSM155458 1 0.826 0.2419 0.632 0.152 0.216
#> GSM155462 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155466 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155470 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155474 1 0.000 0.8179 1.000 0.000 0.000
#> GSM155478 2 0.568 0.6949 0.000 0.684 0.316
#> GSM155482 2 0.568 0.6949 0.000 0.684 0.316
#> GSM155486 1 0.435 0.4758 0.816 0.000 0.184
#> GSM155490 2 0.562 0.6941 0.000 0.692 0.308
#> GSM155494 3 0.630 0.9938 0.480 0.000 0.520
#> GSM155498 3 0.630 0.9938 0.480 0.000 0.520
#> GSM155502 2 0.129 0.8608 0.032 0.968 0.000
#> GSM155506 2 0.129 0.8608 0.032 0.968 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 2 0.4888 0.623 0.000 0.588 0.000 0.412
#> GSM155452 2 0.4888 0.623 0.000 0.588 0.000 0.412
#> GSM155455 4 0.8328 -0.243 0.264 0.296 0.020 0.420
#> GSM155459 1 0.0707 0.801 0.980 0.000 0.000 0.020
#> GSM155463 1 0.0707 0.801 0.980 0.000 0.000 0.020
#> GSM155467 1 0.0000 0.805 1.000 0.000 0.000 0.000
#> GSM155471 1 0.0188 0.804 0.996 0.000 0.000 0.004
#> GSM155475 1 0.0188 0.804 0.996 0.000 0.000 0.004
#> GSM155479 1 0.0188 0.804 0.996 0.000 0.000 0.004
#> GSM155483 1 0.7524 0.268 0.552 0.012 0.240 0.196
#> GSM155487 4 0.7419 0.693 0.000 0.396 0.168 0.436
#> GSM155491 3 0.3764 0.995 0.216 0.000 0.784 0.000
#> GSM155495 1 0.6882 0.156 0.548 0.000 0.328 0.124
#> GSM155499 2 0.0000 0.635 0.000 1.000 0.000 0.000
#> GSM155503 2 0.0000 0.635 0.000 1.000 0.000 0.000
#> GSM155449 2 0.4888 0.623 0.000 0.588 0.000 0.412
#> GSM155456 1 0.5487 0.336 0.580 0.000 0.020 0.400
#> GSM155460 1 0.0707 0.801 0.980 0.000 0.000 0.020
#> GSM155464 1 0.0707 0.801 0.980 0.000 0.000 0.020
#> GSM155468 1 0.0000 0.805 1.000 0.000 0.000 0.000
#> GSM155472 1 0.0000 0.805 1.000 0.000 0.000 0.000
#> GSM155476 1 0.0000 0.805 1.000 0.000 0.000 0.000
#> GSM155480 1 0.0188 0.804 0.996 0.000 0.000 0.004
#> GSM155484 1 0.7524 0.268 0.552 0.012 0.240 0.196
#> GSM155488 1 0.8921 0.153 0.476 0.096 0.232 0.196
#> GSM155492 3 0.3764 0.995 0.216 0.000 0.784 0.000
#> GSM155496 3 0.3610 0.974 0.200 0.000 0.800 0.000
#> GSM155500 2 0.0000 0.635 0.000 1.000 0.000 0.000
#> GSM155504 2 0.0000 0.635 0.000 1.000 0.000 0.000
#> GSM155450 2 0.4888 0.623 0.000 0.588 0.000 0.412
#> GSM155453 2 0.4888 0.623 0.000 0.588 0.000 0.412
#> GSM155457 1 0.5508 0.324 0.572 0.000 0.020 0.408
#> GSM155461 1 0.0707 0.801 0.980 0.000 0.000 0.020
#> GSM155465 1 0.0707 0.801 0.980 0.000 0.000 0.020
#> GSM155469 1 0.0000 0.805 1.000 0.000 0.000 0.000
#> GSM155473 1 0.0188 0.804 0.996 0.000 0.000 0.004
#> GSM155477 1 0.0000 0.805 1.000 0.000 0.000 0.000
#> GSM155481 1 0.0188 0.804 0.996 0.000 0.000 0.004
#> GSM155485 1 0.7524 0.268 0.552 0.012 0.240 0.196
#> GSM155489 1 0.7524 0.268 0.552 0.012 0.240 0.196
#> GSM155493 3 0.3764 0.995 0.216 0.000 0.784 0.000
#> GSM155497 3 0.3945 0.994 0.216 0.000 0.780 0.004
#> GSM155501 2 0.0000 0.635 0.000 1.000 0.000 0.000
#> GSM155505 2 0.0000 0.635 0.000 1.000 0.000 0.000
#> GSM155451 2 0.4888 0.623 0.000 0.588 0.000 0.412
#> GSM155454 2 0.4888 0.623 0.000 0.588 0.000 0.412
#> GSM155458 1 0.5928 0.300 0.560 0.012 0.020 0.408
#> GSM155462 1 0.0707 0.801 0.980 0.000 0.000 0.020
#> GSM155466 1 0.0707 0.801 0.980 0.000 0.000 0.020
#> GSM155470 1 0.0000 0.805 1.000 0.000 0.000 0.000
#> GSM155474 1 0.0188 0.804 0.996 0.000 0.000 0.004
#> GSM155478 4 0.7770 0.699 0.012 0.376 0.164 0.448
#> GSM155482 4 0.7770 0.699 0.012 0.376 0.164 0.448
#> GSM155486 1 0.7524 0.268 0.552 0.012 0.240 0.196
#> GSM155490 4 0.7419 0.693 0.000 0.396 0.168 0.436
#> GSM155494 3 0.3764 0.995 0.216 0.000 0.784 0.000
#> GSM155498 3 0.3945 0.994 0.216 0.000 0.780 0.004
#> GSM155502 2 0.0000 0.635 0.000 1.000 0.000 0.000
#> GSM155506 2 0.0000 0.635 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.4165 0.736 0.000 0.320 0.008 0.672 0.000
#> GSM155452 4 0.4165 0.736 0.000 0.320 0.008 0.672 0.000
#> GSM155455 4 0.7015 0.641 0.152 0.112 0.052 0.632 0.052
#> GSM155459 1 0.2027 0.944 0.928 0.000 0.008 0.024 0.040
#> GSM155463 1 0.2027 0.944 0.928 0.000 0.008 0.024 0.040
#> GSM155467 1 0.0162 0.967 0.996 0.000 0.000 0.004 0.000
#> GSM155471 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.0162 0.967 0.996 0.000 0.000 0.004 0.000
#> GSM155479 1 0.0162 0.967 0.996 0.000 0.000 0.004 0.000
#> GSM155483 3 0.5350 0.533 0.292 0.024 0.644 0.000 0.040
#> GSM155487 5 0.3928 0.976 0.000 0.296 0.000 0.004 0.700
#> GSM155491 3 0.7908 0.544 0.120 0.000 0.452 0.224 0.204
#> GSM155495 3 0.3814 0.539 0.276 0.000 0.720 0.000 0.004
#> GSM155499 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155503 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155449 4 0.4165 0.736 0.000 0.320 0.008 0.672 0.000
#> GSM155456 4 0.5980 0.547 0.280 0.000 0.052 0.616 0.052
#> GSM155460 1 0.2027 0.944 0.928 0.000 0.008 0.024 0.040
#> GSM155464 1 0.2027 0.944 0.928 0.000 0.008 0.024 0.040
#> GSM155468 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM155472 1 0.0162 0.967 0.996 0.000 0.000 0.004 0.000
#> GSM155476 1 0.0162 0.967 0.996 0.000 0.000 0.004 0.000
#> GSM155480 1 0.0162 0.967 0.996 0.000 0.000 0.004 0.000
#> GSM155484 3 0.5350 0.533 0.292 0.024 0.644 0.000 0.040
#> GSM155488 3 0.6178 0.456 0.244 0.096 0.620 0.000 0.040
#> GSM155492 3 0.7908 0.544 0.120 0.000 0.452 0.224 0.204
#> GSM155496 3 0.7806 0.537 0.108 0.000 0.464 0.220 0.208
#> GSM155500 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155504 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155450 4 0.3895 0.739 0.000 0.320 0.000 0.680 0.000
#> GSM155453 4 0.3895 0.739 0.000 0.320 0.000 0.680 0.000
#> GSM155457 4 0.5918 0.561 0.268 0.000 0.052 0.628 0.052
#> GSM155461 1 0.1934 0.946 0.932 0.000 0.008 0.020 0.040
#> GSM155465 1 0.2027 0.944 0.928 0.000 0.008 0.024 0.040
#> GSM155469 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM155473 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.0162 0.967 0.996 0.000 0.000 0.004 0.000
#> GSM155481 1 0.0162 0.967 0.996 0.000 0.000 0.004 0.000
#> GSM155485 3 0.5350 0.533 0.292 0.024 0.644 0.000 0.040
#> GSM155489 3 0.5350 0.533 0.292 0.024 0.644 0.000 0.040
#> GSM155493 3 0.7908 0.544 0.120 0.000 0.452 0.224 0.204
#> GSM155497 3 0.7925 0.543 0.120 0.000 0.448 0.228 0.204
#> GSM155501 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155505 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155451 4 0.3895 0.739 0.000 0.320 0.000 0.680 0.000
#> GSM155454 4 0.3895 0.739 0.000 0.320 0.000 0.680 0.000
#> GSM155458 4 0.5918 0.561 0.268 0.000 0.052 0.628 0.052
#> GSM155462 1 0.2027 0.944 0.928 0.000 0.008 0.024 0.040
#> GSM155466 1 0.2027 0.944 0.928 0.000 0.008 0.024 0.040
#> GSM155470 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM155478 5 0.4865 0.976 0.004 0.284 0.008 0.028 0.676
#> GSM155482 5 0.4865 0.976 0.004 0.284 0.008 0.028 0.676
#> GSM155486 3 0.5350 0.533 0.292 0.024 0.644 0.000 0.040
#> GSM155490 5 0.3928 0.976 0.000 0.296 0.000 0.004 0.700
#> GSM155494 3 0.7908 0.544 0.120 0.000 0.452 0.224 0.204
#> GSM155498 3 0.7925 0.543 0.120 0.000 0.448 0.228 0.204
#> GSM155502 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155506 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.3946 0.786 0.000 0.228 0.004 0.736 0.028 0.004
#> GSM155452 4 0.3946 0.786 0.000 0.228 0.004 0.736 0.028 0.004
#> GSM155455 4 0.5205 0.660 0.060 0.020 0.016 0.732 0.136 0.036
#> GSM155459 1 0.2919 0.905 0.872 0.000 0.000 0.044 0.044 0.040
#> GSM155463 1 0.2985 0.905 0.868 0.000 0.000 0.044 0.048 0.040
#> GSM155467 1 0.0000 0.939 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.0405 0.939 0.988 0.000 0.000 0.008 0.004 0.000
#> GSM155475 1 0.0779 0.935 0.976 0.000 0.000 0.008 0.008 0.008
#> GSM155479 1 0.0881 0.933 0.972 0.000 0.000 0.008 0.012 0.008
#> GSM155483 5 0.4469 0.974 0.128 0.012 0.124 0.000 0.736 0.000
#> GSM155487 6 0.4100 0.954 0.000 0.092 0.020 0.028 0.056 0.804
#> GSM155491 3 0.1007 0.988 0.044 0.000 0.956 0.000 0.000 0.000
#> GSM155495 5 0.4822 0.933 0.120 0.000 0.156 0.012 0.708 0.004
#> GSM155499 2 0.0146 0.996 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM155503 2 0.0146 0.996 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM155449 4 0.3946 0.786 0.000 0.228 0.004 0.736 0.028 0.004
#> GSM155456 4 0.5159 0.633 0.088 0.000 0.016 0.712 0.148 0.036
#> GSM155460 1 0.2919 0.905 0.872 0.000 0.000 0.044 0.044 0.040
#> GSM155464 1 0.2985 0.905 0.868 0.000 0.000 0.044 0.048 0.040
#> GSM155468 1 0.0260 0.939 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM155472 1 0.0984 0.936 0.968 0.000 0.000 0.008 0.012 0.012
#> GSM155476 1 0.0881 0.934 0.972 0.000 0.000 0.008 0.012 0.008
#> GSM155480 1 0.0976 0.933 0.968 0.000 0.000 0.008 0.016 0.008
#> GSM155484 5 0.4469 0.974 0.128 0.012 0.124 0.000 0.736 0.000
#> GSM155488 5 0.4698 0.889 0.128 0.080 0.052 0.000 0.740 0.000
#> GSM155492 3 0.1007 0.988 0.044 0.000 0.956 0.000 0.000 0.000
#> GSM155496 3 0.1842 0.971 0.036 0.000 0.932 0.012 0.008 0.012
#> GSM155500 2 0.0146 0.996 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM155504 2 0.0146 0.996 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM155450 4 0.2996 0.795 0.000 0.228 0.000 0.772 0.000 0.000
#> GSM155453 4 0.2996 0.795 0.000 0.228 0.000 0.772 0.000 0.000
#> GSM155457 4 0.5063 0.641 0.080 0.000 0.016 0.720 0.148 0.036
#> GSM155461 1 0.2851 0.905 0.876 0.000 0.000 0.040 0.044 0.040
#> GSM155465 1 0.2985 0.905 0.868 0.000 0.000 0.044 0.048 0.040
#> GSM155469 1 0.0405 0.939 0.988 0.000 0.000 0.004 0.008 0.000
#> GSM155473 1 0.0405 0.939 0.988 0.000 0.000 0.008 0.004 0.000
#> GSM155477 1 0.0779 0.935 0.976 0.000 0.000 0.008 0.008 0.008
#> GSM155481 1 0.0881 0.933 0.972 0.000 0.000 0.008 0.012 0.008
#> GSM155485 5 0.4469 0.974 0.128 0.012 0.124 0.000 0.736 0.000
#> GSM155489 5 0.4469 0.974 0.128 0.012 0.124 0.000 0.736 0.000
#> GSM155493 3 0.1007 0.988 0.044 0.000 0.956 0.000 0.000 0.000
#> GSM155497 3 0.1862 0.980 0.044 0.000 0.928 0.008 0.004 0.016
#> GSM155501 2 0.0146 0.996 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM155505 2 0.0146 0.996 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM155451 4 0.2996 0.795 0.000 0.228 0.000 0.772 0.000 0.000
#> GSM155454 4 0.2996 0.795 0.000 0.228 0.000 0.772 0.000 0.000
#> GSM155458 4 0.5027 0.643 0.080 0.000 0.016 0.724 0.144 0.036
#> GSM155462 1 0.2919 0.905 0.872 0.000 0.000 0.044 0.044 0.040
#> GSM155466 1 0.2985 0.905 0.868 0.000 0.000 0.044 0.048 0.040
#> GSM155470 1 0.0405 0.939 0.988 0.000 0.000 0.004 0.008 0.000
#> GSM155474 1 0.0405 0.939 0.988 0.000 0.000 0.008 0.004 0.000
#> GSM155478 6 0.2269 0.955 0.012 0.080 0.000 0.000 0.012 0.896
#> GSM155482 6 0.2269 0.955 0.012 0.080 0.000 0.000 0.012 0.896
#> GSM155486 5 0.4469 0.974 0.128 0.012 0.124 0.000 0.736 0.000
#> GSM155490 6 0.4120 0.954 0.000 0.092 0.024 0.028 0.052 0.804
#> GSM155494 3 0.1007 0.988 0.044 0.000 0.956 0.000 0.000 0.000
#> GSM155498 3 0.1862 0.980 0.044 0.000 0.928 0.008 0.004 0.016
#> GSM155502 2 0.0146 0.996 0.000 0.996 0.000 0.000 0.004 0.000
#> GSM155506 2 0.0146 0.996 0.000 0.996 0.000 0.000 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n time(p) k
#> SD:kmeans 59 0.447 2
#> SD:kmeans 48 0.857 3
#> SD:kmeans 48 0.661 4
#> SD:kmeans 58 0.872 5
#> SD:kmeans 59 0.939 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 59 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4844 0.516 0.516
#> 3 3 1.000 0.997 0.997 0.3683 0.779 0.589
#> 4 4 0.906 0.942 0.949 0.1061 0.886 0.679
#> 5 5 0.895 0.936 0.932 0.0424 0.967 0.872
#> 6 6 0.901 0.940 0.928 0.0456 0.981 0.919
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 2 0 1 0 1
#> GSM155452 2 0 1 0 1
#> GSM155455 2 0 1 0 1
#> GSM155459 1 0 1 1 0
#> GSM155463 1 0 1 1 0
#> GSM155467 1 0 1 1 0
#> GSM155471 1 0 1 1 0
#> GSM155475 1 0 1 1 0
#> GSM155479 1 0 1 1 0
#> GSM155483 1 0 1 1 0
#> GSM155487 2 0 1 0 1
#> GSM155491 1 0 1 1 0
#> GSM155495 1 0 1 1 0
#> GSM155499 2 0 1 0 1
#> GSM155503 2 0 1 0 1
#> GSM155449 2 0 1 0 1
#> GSM155456 1 0 1 1 0
#> GSM155460 1 0 1 1 0
#> GSM155464 1 0 1 1 0
#> GSM155468 1 0 1 1 0
#> GSM155472 1 0 1 1 0
#> GSM155476 1 0 1 1 0
#> GSM155480 1 0 1 1 0
#> GSM155484 1 0 1 1 0
#> GSM155488 2 0 1 0 1
#> GSM155492 1 0 1 1 0
#> GSM155496 1 0 1 1 0
#> GSM155500 2 0 1 0 1
#> GSM155504 2 0 1 0 1
#> GSM155450 2 0 1 0 1
#> GSM155453 2 0 1 0 1
#> GSM155457 2 0 1 0 1
#> GSM155461 1 0 1 1 0
#> GSM155465 1 0 1 1 0
#> GSM155469 1 0 1 1 0
#> GSM155473 1 0 1 1 0
#> GSM155477 1 0 1 1 0
#> GSM155481 1 0 1 1 0
#> GSM155485 1 0 1 1 0
#> GSM155489 1 0 1 1 0
#> GSM155493 1 0 1 1 0
#> GSM155497 1 0 1 1 0
#> GSM155501 2 0 1 0 1
#> GSM155505 2 0 1 0 1
#> GSM155451 2 0 1 0 1
#> GSM155454 2 0 1 0 1
#> GSM155458 2 0 1 0 1
#> GSM155462 1 0 1 1 0
#> GSM155466 1 0 1 1 0
#> GSM155470 1 0 1 1 0
#> GSM155474 1 0 1 1 0
#> GSM155478 2 0 1 0 1
#> GSM155482 2 0 1 0 1
#> GSM155486 1 0 1 1 0
#> GSM155490 2 0 1 0 1
#> GSM155494 1 0 1 1 0
#> GSM155498 1 0 1 1 0
#> GSM155502 2 0 1 0 1
#> GSM155506 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 2 0.0000 0.996 0.000 1.000 0.000
#> GSM155452 2 0.0000 0.996 0.000 1.000 0.000
#> GSM155455 2 0.0000 0.996 0.000 1.000 0.000
#> GSM155459 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155463 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155467 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155471 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155475 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155479 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155483 3 0.0000 0.994 0.000 0.000 1.000
#> GSM155487 2 0.0424 0.997 0.000 0.992 0.008
#> GSM155491 3 0.0424 0.996 0.008 0.000 0.992
#> GSM155495 3 0.0424 0.996 0.008 0.000 0.992
#> GSM155499 2 0.0424 0.997 0.000 0.992 0.008
#> GSM155503 2 0.0424 0.997 0.000 0.992 0.008
#> GSM155449 2 0.0000 0.996 0.000 1.000 0.000
#> GSM155456 1 0.0424 0.992 0.992 0.008 0.000
#> GSM155460 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155464 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155468 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155472 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155476 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155480 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155484 3 0.0000 0.994 0.000 0.000 1.000
#> GSM155488 3 0.0000 0.994 0.000 0.000 1.000
#> GSM155492 3 0.0424 0.996 0.008 0.000 0.992
#> GSM155496 3 0.0424 0.996 0.008 0.000 0.992
#> GSM155500 2 0.0424 0.997 0.000 0.992 0.008
#> GSM155504 2 0.0424 0.997 0.000 0.992 0.008
#> GSM155450 2 0.0000 0.996 0.000 1.000 0.000
#> GSM155453 2 0.0000 0.996 0.000 1.000 0.000
#> GSM155457 1 0.0592 0.988 0.988 0.012 0.000
#> GSM155461 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155465 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155469 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155473 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155477 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155481 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155485 3 0.0000 0.994 0.000 0.000 1.000
#> GSM155489 3 0.0000 0.994 0.000 0.000 1.000
#> GSM155493 3 0.0424 0.996 0.008 0.000 0.992
#> GSM155497 3 0.0424 0.996 0.008 0.000 0.992
#> GSM155501 2 0.0424 0.997 0.000 0.992 0.008
#> GSM155505 2 0.0424 0.997 0.000 0.992 0.008
#> GSM155451 2 0.0000 0.996 0.000 1.000 0.000
#> GSM155454 2 0.0000 0.996 0.000 1.000 0.000
#> GSM155458 2 0.0000 0.996 0.000 1.000 0.000
#> GSM155462 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155466 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155470 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155474 1 0.0000 0.999 1.000 0.000 0.000
#> GSM155478 2 0.0424 0.997 0.000 0.992 0.008
#> GSM155482 2 0.0424 0.997 0.000 0.992 0.008
#> GSM155486 3 0.0000 0.994 0.000 0.000 1.000
#> GSM155490 2 0.0424 0.997 0.000 0.992 0.008
#> GSM155494 3 0.0424 0.996 0.008 0.000 0.992
#> GSM155498 3 0.0424 0.996 0.008 0.000 0.992
#> GSM155502 2 0.0424 0.997 0.000 0.992 0.008
#> GSM155506 2 0.0424 0.997 0.000 0.992 0.008
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 4 0.164 0.950 0.000 0.060 0.000 0.940
#> GSM155452 4 0.164 0.950 0.000 0.060 0.000 0.940
#> GSM155455 4 0.164 0.950 0.000 0.060 0.000 0.940
#> GSM155459 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155463 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155467 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155471 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155475 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155479 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155483 3 0.309 0.933 0.000 0.052 0.888 0.060
#> GSM155487 2 0.000 0.855 0.000 1.000 0.000 0.000
#> GSM155491 3 0.000 0.960 0.000 0.000 1.000 0.000
#> GSM155495 3 0.000 0.960 0.000 0.000 1.000 0.000
#> GSM155499 2 0.317 0.904 0.000 0.840 0.000 0.160
#> GSM155503 2 0.317 0.904 0.000 0.840 0.000 0.160
#> GSM155449 4 0.164 0.950 0.000 0.060 0.000 0.940
#> GSM155456 4 0.380 0.676 0.220 0.000 0.000 0.780
#> GSM155460 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155464 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155468 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155472 1 0.139 0.954 0.952 0.048 0.000 0.000
#> GSM155476 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155480 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155484 3 0.309 0.933 0.000 0.052 0.888 0.060
#> GSM155488 2 0.529 0.625 0.000 0.724 0.216 0.060
#> GSM155492 3 0.000 0.960 0.000 0.000 1.000 0.000
#> GSM155496 3 0.000 0.960 0.000 0.000 1.000 0.000
#> GSM155500 2 0.317 0.904 0.000 0.840 0.000 0.160
#> GSM155504 2 0.317 0.904 0.000 0.840 0.000 0.160
#> GSM155450 4 0.164 0.950 0.000 0.060 0.000 0.940
#> GSM155453 4 0.164 0.950 0.000 0.060 0.000 0.940
#> GSM155457 4 0.215 0.849 0.088 0.000 0.000 0.912
#> GSM155461 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155465 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155469 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155473 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155477 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155481 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155485 3 0.309 0.933 0.000 0.052 0.888 0.060
#> GSM155489 3 0.309 0.933 0.000 0.052 0.888 0.060
#> GSM155493 3 0.000 0.960 0.000 0.000 1.000 0.000
#> GSM155497 3 0.000 0.960 0.000 0.000 1.000 0.000
#> GSM155501 2 0.317 0.904 0.000 0.840 0.000 0.160
#> GSM155505 2 0.317 0.904 0.000 0.840 0.000 0.160
#> GSM155451 4 0.164 0.950 0.000 0.060 0.000 0.940
#> GSM155454 4 0.164 0.950 0.000 0.060 0.000 0.940
#> GSM155458 4 0.164 0.950 0.000 0.060 0.000 0.940
#> GSM155462 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155466 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155470 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155474 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155478 2 0.000 0.855 0.000 1.000 0.000 0.000
#> GSM155482 2 0.000 0.855 0.000 1.000 0.000 0.000
#> GSM155486 3 0.309 0.933 0.000 0.052 0.888 0.060
#> GSM155490 2 0.000 0.855 0.000 1.000 0.000 0.000
#> GSM155494 3 0.000 0.960 0.000 0.000 1.000 0.000
#> GSM155498 3 0.000 0.960 0.000 0.000 1.000 0.000
#> GSM155502 2 0.317 0.904 0.000 0.840 0.000 0.160
#> GSM155506 2 0.317 0.904 0.000 0.840 0.000 0.160
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.0324 0.963 0.000 0.004 0.000 0.992 0.004
#> GSM155452 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM155455 4 0.0609 0.961 0.000 0.000 0.000 0.980 0.020
#> GSM155459 1 0.0162 0.993 0.996 0.000 0.000 0.000 0.004
#> GSM155463 1 0.0162 0.993 0.996 0.000 0.000 0.000 0.004
#> GSM155467 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.0162 0.993 0.996 0.000 0.000 0.000 0.004
#> GSM155479 1 0.0162 0.993 0.996 0.000 0.000 0.000 0.004
#> GSM155483 5 0.3480 0.923 0.000 0.000 0.248 0.000 0.752
#> GSM155487 2 0.0000 0.710 0.000 1.000 0.000 0.000 0.000
#> GSM155491 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155495 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155499 2 0.5628 0.864 0.000 0.624 0.000 0.132 0.244
#> GSM155503 2 0.5628 0.864 0.000 0.624 0.000 0.132 0.244
#> GSM155449 4 0.0324 0.963 0.000 0.004 0.000 0.992 0.004
#> GSM155456 4 0.2824 0.807 0.116 0.000 0.000 0.864 0.020
#> GSM155460 1 0.0162 0.993 0.996 0.000 0.000 0.000 0.004
#> GSM155464 1 0.0162 0.993 0.996 0.000 0.000 0.000 0.004
#> GSM155468 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155472 1 0.1952 0.912 0.912 0.084 0.000 0.000 0.004
#> GSM155476 1 0.0162 0.993 0.996 0.000 0.000 0.000 0.004
#> GSM155480 1 0.0162 0.993 0.996 0.000 0.000 0.000 0.004
#> GSM155484 5 0.3480 0.923 0.000 0.000 0.248 0.000 0.752
#> GSM155488 5 0.1012 0.645 0.000 0.012 0.020 0.000 0.968
#> GSM155492 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155496 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155500 2 0.5628 0.864 0.000 0.624 0.000 0.132 0.244
#> GSM155504 2 0.5628 0.864 0.000 0.624 0.000 0.132 0.244
#> GSM155450 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM155453 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM155457 4 0.1568 0.925 0.036 0.000 0.000 0.944 0.020
#> GSM155461 1 0.0162 0.993 0.996 0.000 0.000 0.000 0.004
#> GSM155465 1 0.0162 0.993 0.996 0.000 0.000 0.000 0.004
#> GSM155469 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155473 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.0162 0.993 0.996 0.000 0.000 0.000 0.004
#> GSM155481 1 0.0162 0.993 0.996 0.000 0.000 0.000 0.004
#> GSM155485 5 0.3480 0.923 0.000 0.000 0.248 0.000 0.752
#> GSM155489 5 0.3480 0.923 0.000 0.000 0.248 0.000 0.752
#> GSM155493 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155497 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155501 2 0.5628 0.864 0.000 0.624 0.000 0.132 0.244
#> GSM155505 2 0.5628 0.864 0.000 0.624 0.000 0.132 0.244
#> GSM155451 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM155454 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM155458 4 0.0609 0.961 0.000 0.000 0.000 0.980 0.020
#> GSM155462 1 0.0162 0.993 0.996 0.000 0.000 0.000 0.004
#> GSM155466 1 0.0162 0.993 0.996 0.000 0.000 0.000 0.004
#> GSM155470 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155478 2 0.0162 0.708 0.000 0.996 0.000 0.000 0.004
#> GSM155482 2 0.0162 0.708 0.000 0.996 0.000 0.000 0.004
#> GSM155486 5 0.3480 0.923 0.000 0.000 0.248 0.000 0.752
#> GSM155490 2 0.0162 0.708 0.000 0.996 0.000 0.000 0.004
#> GSM155494 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155498 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155502 2 0.5628 0.864 0.000 0.624 0.000 0.132 0.244
#> GSM155506 2 0.5628 0.864 0.000 0.624 0.000 0.132 0.244
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.1501 0.932 0.000 0.076 0.000 0.924 0.000 0.000
#> GSM155452 4 0.1007 0.948 0.000 0.044 0.000 0.956 0.000 0.000
#> GSM155455 4 0.1826 0.919 0.000 0.004 0.000 0.924 0.020 0.052
#> GSM155459 1 0.3333 0.867 0.820 0.012 0.000 0.000 0.032 0.136
#> GSM155463 1 0.3333 0.867 0.820 0.012 0.000 0.000 0.032 0.136
#> GSM155467 1 0.0260 0.906 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM155471 1 0.0858 0.904 0.968 0.000 0.000 0.004 0.000 0.028
#> GSM155475 1 0.1364 0.896 0.944 0.000 0.000 0.004 0.004 0.048
#> GSM155479 1 0.1226 0.899 0.952 0.000 0.000 0.004 0.004 0.040
#> GSM155483 5 0.1285 0.985 0.000 0.004 0.052 0.000 0.944 0.000
#> GSM155487 6 0.3050 1.000 0.000 0.236 0.000 0.000 0.000 0.764
#> GSM155491 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155495 3 0.0547 0.979 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM155499 2 0.0363 1.000 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM155503 2 0.0363 1.000 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM155449 4 0.1501 0.932 0.000 0.076 0.000 0.924 0.000 0.000
#> GSM155456 4 0.2039 0.908 0.012 0.000 0.000 0.916 0.020 0.052
#> GSM155460 1 0.3333 0.867 0.820 0.012 0.000 0.000 0.032 0.136
#> GSM155464 1 0.3333 0.867 0.820 0.012 0.000 0.000 0.032 0.136
#> GSM155468 1 0.0777 0.905 0.972 0.000 0.000 0.000 0.004 0.024
#> GSM155472 1 0.3043 0.759 0.796 0.000 0.000 0.004 0.004 0.196
#> GSM155476 1 0.1226 0.899 0.952 0.000 0.000 0.004 0.004 0.040
#> GSM155480 1 0.1226 0.899 0.952 0.000 0.000 0.004 0.004 0.040
#> GSM155484 5 0.1285 0.985 0.000 0.004 0.052 0.000 0.944 0.000
#> GSM155488 5 0.1204 0.922 0.000 0.056 0.000 0.000 0.944 0.000
#> GSM155492 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155496 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155500 2 0.0363 1.000 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM155504 2 0.0363 1.000 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM155450 4 0.1007 0.948 0.000 0.044 0.000 0.956 0.000 0.000
#> GSM155453 4 0.1007 0.948 0.000 0.044 0.000 0.956 0.000 0.000
#> GSM155457 4 0.1938 0.911 0.008 0.000 0.000 0.920 0.020 0.052
#> GSM155461 1 0.3333 0.867 0.820 0.012 0.000 0.000 0.032 0.136
#> GSM155465 1 0.3333 0.867 0.820 0.012 0.000 0.000 0.032 0.136
#> GSM155469 1 0.0777 0.905 0.972 0.000 0.000 0.000 0.004 0.024
#> GSM155473 1 0.0858 0.904 0.968 0.000 0.000 0.004 0.000 0.028
#> GSM155477 1 0.1226 0.899 0.952 0.000 0.000 0.004 0.004 0.040
#> GSM155481 1 0.1226 0.899 0.952 0.000 0.000 0.004 0.004 0.040
#> GSM155485 5 0.1285 0.985 0.000 0.004 0.052 0.000 0.944 0.000
#> GSM155489 5 0.1285 0.985 0.000 0.004 0.052 0.000 0.944 0.000
#> GSM155493 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155497 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155501 2 0.0363 1.000 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM155505 2 0.0363 1.000 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM155451 4 0.1141 0.946 0.000 0.052 0.000 0.948 0.000 0.000
#> GSM155454 4 0.1007 0.948 0.000 0.044 0.000 0.956 0.000 0.000
#> GSM155458 4 0.1826 0.919 0.000 0.004 0.000 0.924 0.020 0.052
#> GSM155462 1 0.3333 0.867 0.820 0.012 0.000 0.000 0.032 0.136
#> GSM155466 1 0.3333 0.867 0.820 0.012 0.000 0.000 0.032 0.136
#> GSM155470 1 0.0777 0.905 0.972 0.000 0.000 0.000 0.004 0.024
#> GSM155474 1 0.0858 0.904 0.968 0.000 0.000 0.004 0.000 0.028
#> GSM155478 6 0.3050 1.000 0.000 0.236 0.000 0.000 0.000 0.764
#> GSM155482 6 0.3050 1.000 0.000 0.236 0.000 0.000 0.000 0.764
#> GSM155486 5 0.1285 0.985 0.000 0.004 0.052 0.000 0.944 0.000
#> GSM155490 6 0.3050 1.000 0.000 0.236 0.000 0.000 0.000 0.764
#> GSM155494 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155498 3 0.0000 0.997 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155502 2 0.0363 1.000 0.000 0.988 0.000 0.012 0.000 0.000
#> GSM155506 2 0.0363 1.000 0.000 0.988 0.000 0.012 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n time(p) k
#> SD:skmeans 59 0.543 2
#> SD:skmeans 59 0.669 3
#> SD:skmeans 59 0.983 4
#> SD:skmeans 59 0.992 5
#> SD:skmeans 59 0.945 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 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'SD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.997 0.999 0.432 0.569 0.569
#> 3 3 0.840 0.948 0.943 0.268 0.861 0.755
#> 4 4 1.000 0.985 0.995 0.137 0.942 0.865
#> 5 5 0.842 0.883 0.934 0.125 0.881 0.697
#> 6 6 0.946 0.962 0.985 0.118 0.915 0.709
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 4
There is also optional best \(k\) = 2 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 2 0.0000 0.998 0.000 1.000
#> GSM155452 2 0.1843 0.971 0.028 0.972
#> GSM155455 1 0.0000 0.999 1.000 0.000
#> GSM155459 1 0.0000 0.999 1.000 0.000
#> GSM155463 1 0.0000 0.999 1.000 0.000
#> GSM155467 1 0.0000 0.999 1.000 0.000
#> GSM155471 1 0.0000 0.999 1.000 0.000
#> GSM155475 1 0.0000 0.999 1.000 0.000
#> GSM155479 1 0.0000 0.999 1.000 0.000
#> GSM155483 1 0.0000 0.999 1.000 0.000
#> GSM155487 2 0.0000 0.998 0.000 1.000
#> GSM155491 1 0.0000 0.999 1.000 0.000
#> GSM155495 1 0.0000 0.999 1.000 0.000
#> GSM155499 2 0.0000 0.998 0.000 1.000
#> GSM155503 2 0.0000 0.998 0.000 1.000
#> GSM155449 2 0.0000 0.998 0.000 1.000
#> GSM155456 1 0.0000 0.999 1.000 0.000
#> GSM155460 1 0.0000 0.999 1.000 0.000
#> GSM155464 1 0.0000 0.999 1.000 0.000
#> GSM155468 1 0.0000 0.999 1.000 0.000
#> GSM155472 1 0.0000 0.999 1.000 0.000
#> GSM155476 1 0.0000 0.999 1.000 0.000
#> GSM155480 1 0.0000 0.999 1.000 0.000
#> GSM155484 1 0.0000 0.999 1.000 0.000
#> GSM155488 2 0.0000 0.998 0.000 1.000
#> GSM155492 1 0.0000 0.999 1.000 0.000
#> GSM155496 1 0.0000 0.999 1.000 0.000
#> GSM155500 2 0.0000 0.998 0.000 1.000
#> GSM155504 2 0.0000 0.998 0.000 1.000
#> GSM155450 2 0.0000 0.998 0.000 1.000
#> GSM155453 2 0.0000 0.998 0.000 1.000
#> GSM155457 1 0.0000 0.999 1.000 0.000
#> GSM155461 1 0.0000 0.999 1.000 0.000
#> GSM155465 1 0.0000 0.999 1.000 0.000
#> GSM155469 1 0.0000 0.999 1.000 0.000
#> GSM155473 1 0.0000 0.999 1.000 0.000
#> GSM155477 1 0.0000 0.999 1.000 0.000
#> GSM155481 1 0.0000 0.999 1.000 0.000
#> GSM155485 1 0.0000 0.999 1.000 0.000
#> GSM155489 1 0.0000 0.999 1.000 0.000
#> GSM155493 1 0.0000 0.999 1.000 0.000
#> GSM155497 1 0.0000 0.999 1.000 0.000
#> GSM155501 2 0.0000 0.998 0.000 1.000
#> GSM155505 2 0.0000 0.998 0.000 1.000
#> GSM155451 2 0.0000 0.998 0.000 1.000
#> GSM155454 2 0.0000 0.998 0.000 1.000
#> GSM155458 1 0.0000 0.999 1.000 0.000
#> GSM155462 1 0.0000 0.999 1.000 0.000
#> GSM155466 1 0.0000 0.999 1.000 0.000
#> GSM155470 1 0.0000 0.999 1.000 0.000
#> GSM155474 1 0.0000 0.999 1.000 0.000
#> GSM155478 1 0.0938 0.988 0.988 0.012
#> GSM155482 1 0.2236 0.963 0.964 0.036
#> GSM155486 1 0.0000 0.999 1.000 0.000
#> GSM155490 2 0.0000 0.998 0.000 1.000
#> GSM155494 1 0.0000 0.999 1.000 0.000
#> GSM155498 1 0.0000 0.999 1.000 0.000
#> GSM155502 2 0.0000 0.998 0.000 1.000
#> GSM155506 2 0.0000 0.998 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 2 0.000 0.967 0.000 1.000 0.000
#> GSM155452 2 0.000 0.967 0.000 1.000 0.000
#> GSM155455 1 0.000 0.972 1.000 0.000 0.000
#> GSM155459 1 0.000 0.972 1.000 0.000 0.000
#> GSM155463 1 0.000 0.972 1.000 0.000 0.000
#> GSM155467 1 0.000 0.972 1.000 0.000 0.000
#> GSM155471 1 0.000 0.972 1.000 0.000 0.000
#> GSM155475 1 0.000 0.972 1.000 0.000 0.000
#> GSM155479 1 0.000 0.972 1.000 0.000 0.000
#> GSM155483 1 0.000 0.972 1.000 0.000 0.000
#> GSM155487 2 0.556 0.718 0.000 0.700 0.300
#> GSM155491 3 0.556 1.000 0.300 0.000 0.700
#> GSM155495 1 0.103 0.940 0.976 0.000 0.024
#> GSM155499 2 0.000 0.967 0.000 1.000 0.000
#> GSM155503 2 0.000 0.967 0.000 1.000 0.000
#> GSM155449 2 0.116 0.935 0.028 0.972 0.000
#> GSM155456 1 0.000 0.972 1.000 0.000 0.000
#> GSM155460 1 0.000 0.972 1.000 0.000 0.000
#> GSM155464 1 0.000 0.972 1.000 0.000 0.000
#> GSM155468 1 0.000 0.972 1.000 0.000 0.000
#> GSM155472 1 0.000 0.972 1.000 0.000 0.000
#> GSM155476 1 0.000 0.972 1.000 0.000 0.000
#> GSM155480 1 0.000 0.972 1.000 0.000 0.000
#> GSM155484 1 0.000 0.972 1.000 0.000 0.000
#> GSM155488 2 0.000 0.967 0.000 1.000 0.000
#> GSM155492 3 0.556 1.000 0.300 0.000 0.700
#> GSM155496 3 0.556 1.000 0.300 0.000 0.700
#> GSM155500 2 0.000 0.967 0.000 1.000 0.000
#> GSM155504 2 0.000 0.967 0.000 1.000 0.000
#> GSM155450 2 0.000 0.967 0.000 1.000 0.000
#> GSM155453 2 0.000 0.967 0.000 1.000 0.000
#> GSM155457 1 0.000 0.972 1.000 0.000 0.000
#> GSM155461 1 0.000 0.972 1.000 0.000 0.000
#> GSM155465 1 0.000 0.972 1.000 0.000 0.000
#> GSM155469 1 0.000 0.972 1.000 0.000 0.000
#> GSM155473 1 0.000 0.972 1.000 0.000 0.000
#> GSM155477 1 0.000 0.972 1.000 0.000 0.000
#> GSM155481 1 0.000 0.972 1.000 0.000 0.000
#> GSM155485 1 0.000 0.972 1.000 0.000 0.000
#> GSM155489 1 0.000 0.972 1.000 0.000 0.000
#> GSM155493 3 0.556 1.000 0.300 0.000 0.700
#> GSM155497 3 0.556 1.000 0.300 0.000 0.700
#> GSM155501 2 0.000 0.967 0.000 1.000 0.000
#> GSM155505 2 0.000 0.967 0.000 1.000 0.000
#> GSM155451 2 0.000 0.967 0.000 1.000 0.000
#> GSM155454 2 0.000 0.967 0.000 1.000 0.000
#> GSM155458 1 0.000 0.972 1.000 0.000 0.000
#> GSM155462 1 0.000 0.972 1.000 0.000 0.000
#> GSM155466 1 0.000 0.972 1.000 0.000 0.000
#> GSM155470 1 0.000 0.972 1.000 0.000 0.000
#> GSM155474 1 0.000 0.972 1.000 0.000 0.000
#> GSM155478 1 0.556 0.495 0.700 0.000 0.300
#> GSM155482 1 0.556 0.495 0.700 0.000 0.300
#> GSM155486 1 0.000 0.972 1.000 0.000 0.000
#> GSM155490 2 0.556 0.718 0.000 0.700 0.300
#> GSM155494 3 0.556 1.000 0.300 0.000 0.700
#> GSM155498 3 0.556 1.000 0.300 0.000 0.700
#> GSM155502 2 0.000 0.967 0.000 1.000 0.000
#> GSM155506 2 0.000 0.967 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM155452 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM155455 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155459 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155463 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155467 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155471 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155475 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155479 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155483 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155487 4 0.4222 0.626 0.000 0.272 0.000 0.728
#> GSM155491 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM155495 1 0.1118 0.961 0.964 0.000 0.036 0.000
#> GSM155499 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM155503 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM155449 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM155456 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155460 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155464 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155468 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155472 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155476 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155480 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155484 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155488 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM155492 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM155496 3 0.0336 0.985 0.008 0.000 0.992 0.000
#> GSM155500 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM155504 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM155450 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM155453 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM155457 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155461 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155465 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155469 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155473 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155477 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155481 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155485 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155489 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155493 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM155497 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM155501 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM155505 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM155451 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM155454 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM155458 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155462 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155466 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155470 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155478 4 0.0000 0.875 0.000 0.000 0.000 1.000
#> GSM155482 4 0.0000 0.875 0.000 0.000 0.000 1.000
#> GSM155486 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM155490 4 0.0000 0.875 0.000 0.000 0.000 1.000
#> GSM155494 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM155498 3 0.0000 0.997 0.000 0.000 1.000 0.000
#> GSM155502 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM155506 2 0.0000 1.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.260 0.736 0.000 0.148 0.000 0.852 0.000
#> GSM155452 4 0.260 0.736 0.000 0.148 0.000 0.852 0.000
#> GSM155455 4 0.260 0.637 0.148 0.000 0.000 0.852 0.000
#> GSM155459 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155463 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155467 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155479 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155483 1 0.260 0.854 0.852 0.000 0.000 0.148 0.000
#> GSM155487 5 0.364 0.622 0.000 0.272 0.000 0.000 0.728
#> GSM155491 3 0.000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM155495 1 0.368 0.812 0.808 0.000 0.044 0.148 0.000
#> GSM155499 2 0.000 0.973 0.000 1.000 0.000 0.000 0.000
#> GSM155503 2 0.000 0.973 0.000 1.000 0.000 0.000 0.000
#> GSM155449 4 0.260 0.736 0.000 0.148 0.000 0.852 0.000
#> GSM155456 4 0.426 0.412 0.440 0.000 0.000 0.560 0.000
#> GSM155460 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155464 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155468 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155472 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155476 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155480 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155484 1 0.260 0.854 0.852 0.000 0.000 0.148 0.000
#> GSM155488 2 0.260 0.767 0.000 0.852 0.000 0.148 0.000
#> GSM155492 3 0.000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM155496 3 0.029 0.985 0.008 0.000 0.992 0.000 0.000
#> GSM155500 2 0.000 0.973 0.000 1.000 0.000 0.000 0.000
#> GSM155504 2 0.000 0.973 0.000 1.000 0.000 0.000 0.000
#> GSM155450 4 0.260 0.736 0.000 0.148 0.000 0.852 0.000
#> GSM155453 4 0.260 0.736 0.000 0.148 0.000 0.852 0.000
#> GSM155457 4 0.426 0.412 0.440 0.000 0.000 0.560 0.000
#> GSM155461 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155465 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155469 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155473 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155481 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155485 1 0.260 0.854 0.852 0.000 0.000 0.148 0.000
#> GSM155489 1 0.260 0.854 0.852 0.000 0.000 0.148 0.000
#> GSM155493 3 0.000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM155497 3 0.000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM155501 2 0.000 0.973 0.000 1.000 0.000 0.000 0.000
#> GSM155505 2 0.000 0.973 0.000 1.000 0.000 0.000 0.000
#> GSM155451 4 0.307 0.694 0.000 0.196 0.000 0.804 0.000
#> GSM155454 4 0.260 0.736 0.000 0.148 0.000 0.852 0.000
#> GSM155458 4 0.426 0.412 0.440 0.000 0.000 0.560 0.000
#> GSM155462 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155466 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155470 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.000 0.962 1.000 0.000 0.000 0.000 0.000
#> GSM155478 5 0.000 0.899 0.000 0.000 0.000 0.000 1.000
#> GSM155482 5 0.000 0.899 0.000 0.000 0.000 0.000 1.000
#> GSM155486 1 0.260 0.854 0.852 0.000 0.000 0.148 0.000
#> GSM155490 5 0.000 0.899 0.000 0.000 0.000 0.000 1.000
#> GSM155494 3 0.000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM155498 3 0.000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM155502 2 0.000 0.973 0.000 1.000 0.000 0.000 0.000
#> GSM155506 2 0.000 0.973 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.000 0.913 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM155452 4 0.000 0.913 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM155455 4 0.000 0.913 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM155459 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155463 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155467 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155479 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155483 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155487 6 0.327 0.626 0.000 0.272 0.000 0.000 0.000 0.728
#> GSM155491 3 0.000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155495 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155499 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155503 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155449 4 0.000 0.913 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM155456 4 0.256 0.777 0.172 0.000 0.000 0.828 0.000 0.000
#> GSM155460 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155464 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155468 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155472 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155476 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155480 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155484 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155488 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155492 3 0.000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155496 3 0.159 0.910 0.004 0.000 0.924 0.000 0.072 0.000
#> GSM155500 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155504 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155450 4 0.000 0.913 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM155453 4 0.000 0.913 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM155457 4 0.256 0.777 0.172 0.000 0.000 0.828 0.000 0.000
#> GSM155461 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155465 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155469 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155473 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155481 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155485 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155489 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155493 3 0.000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155497 3 0.000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155501 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155505 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155451 4 0.107 0.875 0.000 0.048 0.000 0.952 0.000 0.000
#> GSM155454 4 0.000 0.913 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM155458 4 0.256 0.777 0.172 0.000 0.000 0.828 0.000 0.000
#> GSM155462 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155466 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155470 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155478 6 0.000 0.902 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM155482 6 0.000 0.902 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM155486 5 0.000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155490 6 0.000 0.902 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM155494 3 0.000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155498 3 0.000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155502 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155506 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n time(p) k
#> SD:pam 59 0.971 2
#> SD:pam 57 0.976 3
#> SD:pam 59 0.629 4
#> SD:pam 56 0.741 5
#> SD:pam 59 0.939 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 59 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.364 0.375 0.756 0.3060 0.691 0.691
#> 3 3 0.658 0.786 0.880 0.9216 0.633 0.512
#> 4 4 0.855 0.838 0.908 0.1925 0.795 0.574
#> 5 5 0.996 0.971 0.985 0.0809 0.899 0.690
#> 6 6 1.000 0.976 0.982 0.0431 0.971 0.881
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 5
There is also optional best \(k\) = 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 1 0.978 0.218 0.588 0.412
#> GSM155452 1 0.978 0.218 0.588 0.412
#> GSM155455 1 0.966 0.251 0.608 0.392
#> GSM155459 1 0.000 0.595 1.000 0.000
#> GSM155463 1 0.000 0.595 1.000 0.000
#> GSM155467 1 0.000 0.595 1.000 0.000
#> GSM155471 1 0.000 0.595 1.000 0.000
#> GSM155475 1 0.000 0.595 1.000 0.000
#> GSM155479 1 0.000 0.595 1.000 0.000
#> GSM155483 1 0.975 0.229 0.592 0.408
#> GSM155487 2 0.000 0.447 0.000 1.000
#> GSM155491 1 0.980 0.200 0.584 0.416
#> GSM155495 1 0.975 0.229 0.592 0.408
#> GSM155499 2 1.000 0.250 0.488 0.512
#> GSM155503 2 1.000 0.239 0.492 0.508
#> GSM155449 1 0.978 0.218 0.588 0.412
#> GSM155456 1 0.644 0.504 0.836 0.164
#> GSM155460 1 0.000 0.595 1.000 0.000
#> GSM155464 1 0.000 0.595 1.000 0.000
#> GSM155468 1 0.000 0.595 1.000 0.000
#> GSM155472 1 0.653 0.401 0.832 0.168
#> GSM155476 1 0.000 0.595 1.000 0.000
#> GSM155480 1 0.000 0.595 1.000 0.000
#> GSM155484 1 0.975 0.229 0.592 0.408
#> GSM155488 1 0.975 0.229 0.592 0.408
#> GSM155492 1 0.980 0.200 0.584 0.416
#> GSM155496 1 0.990 0.141 0.560 0.440
#> GSM155500 2 1.000 0.250 0.488 0.512
#> GSM155504 2 1.000 0.239 0.492 0.508
#> GSM155450 1 0.978 0.218 0.588 0.412
#> GSM155453 1 0.978 0.218 0.588 0.412
#> GSM155457 1 0.653 0.501 0.832 0.168
#> GSM155461 1 0.000 0.595 1.000 0.000
#> GSM155465 1 0.000 0.595 1.000 0.000
#> GSM155469 1 0.000 0.595 1.000 0.000
#> GSM155473 1 0.000 0.595 1.000 0.000
#> GSM155477 1 0.000 0.595 1.000 0.000
#> GSM155481 1 0.000 0.595 1.000 0.000
#> GSM155485 1 0.975 0.229 0.592 0.408
#> GSM155489 1 0.975 0.229 0.592 0.408
#> GSM155493 1 0.980 0.200 0.584 0.416
#> GSM155497 1 0.980 0.200 0.584 0.416
#> GSM155501 1 1.000 -0.258 0.504 0.496
#> GSM155505 2 1.000 0.250 0.488 0.512
#> GSM155451 1 0.978 0.218 0.588 0.412
#> GSM155454 1 0.978 0.218 0.588 0.412
#> GSM155458 1 0.966 0.251 0.608 0.392
#> GSM155462 1 0.000 0.595 1.000 0.000
#> GSM155466 1 0.000 0.595 1.000 0.000
#> GSM155470 1 0.000 0.595 1.000 0.000
#> GSM155474 1 0.000 0.595 1.000 0.000
#> GSM155478 2 0.000 0.447 0.000 1.000
#> GSM155482 2 0.000 0.447 0.000 1.000
#> GSM155486 1 0.975 0.229 0.592 0.408
#> GSM155490 2 0.000 0.447 0.000 1.000
#> GSM155494 1 0.980 0.200 0.584 0.416
#> GSM155498 1 0.980 0.200 0.584 0.416
#> GSM155502 2 1.000 0.239 0.492 0.508
#> GSM155506 2 1.000 0.239 0.492 0.508
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 1 0.9527 0.304 0.464 0.204 0.332
#> GSM155452 1 0.9014 0.494 0.560 0.208 0.232
#> GSM155455 1 0.4233 0.778 0.836 0.160 0.004
#> GSM155459 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155463 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155467 1 0.0892 0.862 0.980 0.000 0.020
#> GSM155471 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155475 1 0.1031 0.860 0.976 0.000 0.024
#> GSM155479 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155483 3 0.1031 0.830 0.024 0.000 0.976
#> GSM155487 2 0.1289 1.000 0.000 0.968 0.032
#> GSM155491 3 0.2796 0.802 0.092 0.000 0.908
#> GSM155495 3 0.1031 0.830 0.024 0.000 0.976
#> GSM155499 3 0.5465 0.685 0.000 0.288 0.712
#> GSM155503 3 0.5465 0.685 0.000 0.288 0.712
#> GSM155449 1 0.9009 0.495 0.560 0.204 0.236
#> GSM155456 1 0.4233 0.778 0.836 0.160 0.004
#> GSM155460 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155464 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155468 1 0.0892 0.862 0.980 0.000 0.020
#> GSM155472 1 0.1525 0.855 0.964 0.032 0.004
#> GSM155476 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155480 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155484 3 0.1031 0.830 0.024 0.000 0.976
#> GSM155488 3 0.1129 0.828 0.020 0.004 0.976
#> GSM155492 3 0.1964 0.819 0.056 0.000 0.944
#> GSM155496 3 0.1031 0.830 0.024 0.000 0.976
#> GSM155500 3 0.5465 0.685 0.000 0.288 0.712
#> GSM155504 3 0.5465 0.685 0.000 0.288 0.712
#> GSM155450 1 0.8907 0.507 0.568 0.248 0.184
#> GSM155453 1 0.8937 0.502 0.564 0.252 0.184
#> GSM155457 1 0.4233 0.778 0.836 0.160 0.004
#> GSM155461 1 0.1031 0.860 0.976 0.000 0.024
#> GSM155465 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155469 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155473 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155477 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155481 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155485 3 0.1031 0.830 0.024 0.000 0.976
#> GSM155489 3 0.1031 0.830 0.024 0.000 0.976
#> GSM155493 3 0.2625 0.806 0.084 0.000 0.916
#> GSM155497 3 0.2878 0.798 0.096 0.000 0.904
#> GSM155501 3 0.5465 0.685 0.000 0.288 0.712
#> GSM155505 3 0.5465 0.685 0.000 0.288 0.712
#> GSM155451 1 0.8985 0.498 0.564 0.220 0.216
#> GSM155454 1 0.8889 0.494 0.560 0.276 0.164
#> GSM155458 1 0.4233 0.778 0.836 0.160 0.004
#> GSM155462 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155466 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155470 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155474 1 0.0000 0.868 1.000 0.000 0.000
#> GSM155478 2 0.1289 1.000 0.000 0.968 0.032
#> GSM155482 2 0.1289 1.000 0.000 0.968 0.032
#> GSM155486 3 0.1031 0.830 0.024 0.000 0.976
#> GSM155490 2 0.1289 1.000 0.000 0.968 0.032
#> GSM155494 3 0.2796 0.802 0.092 0.000 0.908
#> GSM155498 3 0.3192 0.786 0.112 0.000 0.888
#> GSM155502 3 0.5465 0.685 0.000 0.288 0.712
#> GSM155506 3 0.5465 0.685 0.000 0.288 0.712
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 2 0.4868 0.241 0.012 0.684 0.304 0.00
#> GSM155452 2 0.1284 0.615 0.012 0.964 0.024 0.00
#> GSM155455 1 0.4564 0.576 0.672 0.328 0.000 0.00
#> GSM155459 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155463 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155467 1 0.1022 0.912 0.968 0.000 0.032 0.00
#> GSM155471 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155475 1 0.1022 0.912 0.968 0.000 0.032 0.00
#> GSM155479 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155483 3 0.0000 0.947 0.000 0.000 1.000 0.00
#> GSM155487 4 0.4277 1.000 0.000 0.280 0.000 0.72
#> GSM155491 3 0.1940 0.923 0.076 0.000 0.924 0.00
#> GSM155495 3 0.0469 0.946 0.000 0.012 0.988 0.00
#> GSM155499 2 0.5308 0.758 0.000 0.684 0.036 0.28
#> GSM155503 2 0.5308 0.758 0.000 0.684 0.036 0.28
#> GSM155449 2 0.4844 0.247 0.012 0.688 0.300 0.00
#> GSM155456 1 0.4431 0.616 0.696 0.304 0.000 0.00
#> GSM155460 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155464 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155468 1 0.0921 0.915 0.972 0.000 0.028 0.00
#> GSM155472 1 0.3852 0.755 0.808 0.180 0.012 0.00
#> GSM155476 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155480 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155484 3 0.0469 0.946 0.000 0.012 0.988 0.00
#> GSM155488 3 0.0469 0.946 0.000 0.012 0.988 0.00
#> GSM155492 3 0.1211 0.938 0.040 0.000 0.960 0.00
#> GSM155496 3 0.0188 0.947 0.004 0.000 0.996 0.00
#> GSM155500 2 0.5308 0.758 0.000 0.684 0.036 0.28
#> GSM155504 2 0.5308 0.758 0.000 0.684 0.036 0.28
#> GSM155450 2 0.0469 0.633 0.012 0.988 0.000 0.00
#> GSM155453 2 0.0469 0.633 0.012 0.988 0.000 0.00
#> GSM155457 1 0.4431 0.616 0.696 0.304 0.000 0.00
#> GSM155461 1 0.1022 0.912 0.968 0.000 0.032 0.00
#> GSM155465 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155469 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155473 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155477 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155481 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155485 3 0.0000 0.947 0.000 0.000 1.000 0.00
#> GSM155489 3 0.0469 0.946 0.000 0.012 0.988 0.00
#> GSM155493 3 0.1867 0.926 0.072 0.000 0.928 0.00
#> GSM155497 3 0.1940 0.923 0.076 0.000 0.924 0.00
#> GSM155501 2 0.5308 0.758 0.000 0.684 0.036 0.28
#> GSM155505 2 0.5308 0.758 0.000 0.684 0.036 0.28
#> GSM155451 2 0.0469 0.633 0.012 0.988 0.000 0.00
#> GSM155454 2 0.0469 0.633 0.012 0.988 0.000 0.00
#> GSM155458 1 0.4431 0.616 0.696 0.304 0.000 0.00
#> GSM155462 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155466 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155470 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155474 1 0.0000 0.931 1.000 0.000 0.000 0.00
#> GSM155478 4 0.4277 1.000 0.000 0.280 0.000 0.72
#> GSM155482 4 0.4277 1.000 0.000 0.280 0.000 0.72
#> GSM155486 3 0.0469 0.946 0.000 0.012 0.988 0.00
#> GSM155490 4 0.4277 1.000 0.000 0.280 0.000 0.72
#> GSM155494 3 0.1940 0.923 0.076 0.000 0.924 0.00
#> GSM155498 3 0.2149 0.914 0.088 0.000 0.912 0.00
#> GSM155502 2 0.5308 0.758 0.000 0.684 0.036 0.28
#> GSM155506 2 0.5308 0.758 0.000 0.684 0.036 0.28
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.1956 0.902 0.000 0.008 0.076 0.916 0
#> GSM155452 4 0.0404 0.970 0.000 0.000 0.012 0.988 0
#> GSM155455 4 0.0609 0.968 0.020 0.000 0.000 0.980 0
#> GSM155459 1 0.0000 0.982 1.000 0.000 0.000 0.000 0
#> GSM155463 1 0.0000 0.982 1.000 0.000 0.000 0.000 0
#> GSM155467 1 0.0703 0.967 0.976 0.000 0.024 0.000 0
#> GSM155471 1 0.0000 0.982 1.000 0.000 0.000 0.000 0
#> GSM155475 1 0.0963 0.957 0.964 0.000 0.036 0.000 0
#> GSM155479 1 0.0000 0.982 1.000 0.000 0.000 0.000 0
#> GSM155483 3 0.0000 0.964 0.000 0.000 1.000 0.000 0
#> GSM155487 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM155491 3 0.1478 0.939 0.064 0.000 0.936 0.000 0
#> GSM155495 3 0.0000 0.964 0.000 0.000 1.000 0.000 0
#> GSM155499 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> GSM155503 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> GSM155449 4 0.1082 0.955 0.000 0.008 0.028 0.964 0
#> GSM155456 4 0.0609 0.968 0.020 0.000 0.000 0.980 0
#> GSM155460 1 0.0000 0.982 1.000 0.000 0.000 0.000 0
#> GSM155464 1 0.0000 0.982 1.000 0.000 0.000 0.000 0
#> GSM155468 1 0.0798 0.969 0.976 0.000 0.016 0.008 0
#> GSM155472 1 0.3011 0.829 0.844 0.000 0.016 0.140 0
#> GSM155476 1 0.0000 0.982 1.000 0.000 0.000 0.000 0
#> GSM155480 1 0.0000 0.982 1.000 0.000 0.000 0.000 0
#> GSM155484 3 0.0000 0.964 0.000 0.000 1.000 0.000 0
#> GSM155488 3 0.0000 0.964 0.000 0.000 1.000 0.000 0
#> GSM155492 3 0.0703 0.958 0.024 0.000 0.976 0.000 0
#> GSM155496 3 0.0000 0.964 0.000 0.000 1.000 0.000 0
#> GSM155500 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> GSM155504 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> GSM155450 4 0.0000 0.971 0.000 0.000 0.000 1.000 0
#> GSM155453 4 0.0000 0.971 0.000 0.000 0.000 1.000 0
#> GSM155457 4 0.0609 0.968 0.020 0.000 0.000 0.980 0
#> GSM155461 1 0.0963 0.957 0.964 0.000 0.036 0.000 0
#> GSM155465 1 0.0000 0.982 1.000 0.000 0.000 0.000 0
#> GSM155469 1 0.0000 0.982 1.000 0.000 0.000 0.000 0
#> GSM155473 1 0.0000 0.982 1.000 0.000 0.000 0.000 0
#> GSM155477 1 0.0000 0.982 1.000 0.000 0.000 0.000 0
#> GSM155481 1 0.1341 0.934 0.944 0.000 0.000 0.056 0
#> GSM155485 3 0.0000 0.964 0.000 0.000 1.000 0.000 0
#> GSM155489 3 0.0000 0.964 0.000 0.000 1.000 0.000 0
#> GSM155493 3 0.1341 0.944 0.056 0.000 0.944 0.000 0
#> GSM155497 3 0.1478 0.939 0.064 0.000 0.936 0.000 0
#> GSM155501 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> GSM155505 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> GSM155451 4 0.0404 0.970 0.000 0.000 0.012 0.988 0
#> GSM155454 4 0.0000 0.971 0.000 0.000 0.000 1.000 0
#> GSM155458 4 0.0609 0.968 0.020 0.000 0.000 0.980 0
#> GSM155462 1 0.0162 0.980 0.996 0.000 0.000 0.004 0
#> GSM155466 1 0.0000 0.982 1.000 0.000 0.000 0.000 0
#> GSM155470 1 0.0000 0.982 1.000 0.000 0.000 0.000 0
#> GSM155474 1 0.0290 0.978 0.992 0.000 0.000 0.008 0
#> GSM155478 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM155482 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM155486 3 0.0000 0.964 0.000 0.000 1.000 0.000 0
#> GSM155490 5 0.0000 1.000 0.000 0.000 0.000 0.000 1
#> GSM155494 3 0.1478 0.939 0.064 0.000 0.936 0.000 0
#> GSM155498 3 0.1544 0.935 0.068 0.000 0.932 0.000 0
#> GSM155502 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
#> GSM155506 2 0.0000 1.000 0.000 1.000 0.000 0.000 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.0146 0.985 0.000 0 0.000 0.996 0.004 0
#> GSM155452 4 0.0363 0.986 0.000 0 0.012 0.988 0.000 0
#> GSM155455 4 0.0632 0.981 0.000 0 0.024 0.976 0.000 0
#> GSM155459 1 0.0260 0.974 0.992 0 0.008 0.000 0.000 0
#> GSM155463 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155467 1 0.1556 0.929 0.920 0 0.080 0.000 0.000 0
#> GSM155471 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155475 1 0.1714 0.920 0.908 0 0.092 0.000 0.000 0
#> GSM155479 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155483 5 0.0000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM155487 6 0.0000 1.000 0.000 0 0.000 0.000 0.000 1
#> GSM155491 3 0.0972 0.955 0.008 0 0.964 0.000 0.028 0
#> GSM155495 5 0.0000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM155499 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM155503 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM155449 4 0.0146 0.985 0.000 0 0.000 0.996 0.004 0
#> GSM155456 4 0.0632 0.981 0.000 0 0.024 0.976 0.000 0
#> GSM155460 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155464 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155468 1 0.1556 0.929 0.920 0 0.080 0.000 0.000 0
#> GSM155472 1 0.1913 0.922 0.908 0 0.080 0.012 0.000 0
#> GSM155476 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155480 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155484 5 0.0000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM155488 5 0.0000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM155492 3 0.1757 0.928 0.008 0 0.916 0.000 0.076 0
#> GSM155496 3 0.2762 0.797 0.000 0 0.804 0.000 0.196 0
#> GSM155500 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM155504 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM155450 4 0.0363 0.986 0.000 0 0.012 0.988 0.000 0
#> GSM155453 4 0.0363 0.986 0.000 0 0.012 0.988 0.000 0
#> GSM155457 4 0.0632 0.981 0.000 0 0.024 0.976 0.000 0
#> GSM155461 1 0.1714 0.920 0.908 0 0.092 0.000 0.000 0
#> GSM155465 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155469 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155473 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155477 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155481 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155485 5 0.0000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM155489 5 0.0000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM155493 3 0.0972 0.955 0.008 0 0.964 0.000 0.028 0
#> GSM155497 3 0.0972 0.955 0.008 0 0.964 0.000 0.028 0
#> GSM155501 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM155505 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM155451 4 0.0363 0.986 0.000 0 0.012 0.988 0.000 0
#> GSM155454 4 0.0363 0.986 0.000 0 0.012 0.988 0.000 0
#> GSM155458 4 0.0632 0.981 0.000 0 0.024 0.976 0.000 0
#> GSM155462 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155466 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155470 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155474 1 0.0000 0.979 1.000 0 0.000 0.000 0.000 0
#> GSM155478 6 0.0000 1.000 0.000 0 0.000 0.000 0.000 1
#> GSM155482 6 0.0000 1.000 0.000 0 0.000 0.000 0.000 1
#> GSM155486 5 0.0000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM155490 6 0.0000 1.000 0.000 0 0.000 0.000 0.000 1
#> GSM155494 3 0.0972 0.955 0.008 0 0.964 0.000 0.028 0
#> GSM155498 3 0.1257 0.945 0.020 0 0.952 0.000 0.028 0
#> GSM155502 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM155506 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
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 time(p) k
#> SD:mclust 23 NA 2
#> SD:mclust 54 0.305 3
#> SD:mclust 57 0.611 4
#> SD:mclust 59 0.856 5
#> SD:mclust 59 0.939 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 59 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 0.983 0.993 0.4730 0.524 0.524
#> 3 3 0.695 0.776 0.857 0.2141 0.958 0.920
#> 4 4 0.661 0.854 0.893 0.1966 0.771 0.551
#> 5 5 0.825 0.832 0.905 0.0745 0.819 0.518
#> 6 6 0.882 0.897 0.919 0.0573 0.942 0.781
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
#> GSM155448 2 0.0000 0.982 0.000 1.000
#> GSM155452 2 0.0000 0.982 0.000 1.000
#> GSM155455 2 0.0672 0.975 0.008 0.992
#> GSM155459 1 0.0000 0.999 1.000 0.000
#> GSM155463 1 0.0000 0.999 1.000 0.000
#> GSM155467 1 0.0000 0.999 1.000 0.000
#> GSM155471 1 0.0000 0.999 1.000 0.000
#> GSM155475 1 0.0000 0.999 1.000 0.000
#> GSM155479 1 0.0000 0.999 1.000 0.000
#> GSM155483 1 0.0000 0.999 1.000 0.000
#> GSM155487 2 0.0000 0.982 0.000 1.000
#> GSM155491 1 0.0000 0.999 1.000 0.000
#> GSM155495 1 0.0000 0.999 1.000 0.000
#> GSM155499 2 0.0000 0.982 0.000 1.000
#> GSM155503 2 0.0000 0.982 0.000 1.000
#> GSM155449 2 0.0000 0.982 0.000 1.000
#> GSM155456 1 0.0000 0.999 1.000 0.000
#> GSM155460 1 0.0000 0.999 1.000 0.000
#> GSM155464 1 0.0000 0.999 1.000 0.000
#> GSM155468 1 0.0000 0.999 1.000 0.000
#> GSM155472 1 0.0000 0.999 1.000 0.000
#> GSM155476 1 0.0000 0.999 1.000 0.000
#> GSM155480 1 0.0000 0.999 1.000 0.000
#> GSM155484 1 0.0000 0.999 1.000 0.000
#> GSM155488 2 0.2603 0.942 0.044 0.956
#> GSM155492 1 0.0000 0.999 1.000 0.000
#> GSM155496 1 0.0000 0.999 1.000 0.000
#> GSM155500 2 0.0000 0.982 0.000 1.000
#> GSM155504 2 0.0000 0.982 0.000 1.000
#> GSM155450 2 0.0000 0.982 0.000 1.000
#> GSM155453 2 0.0000 0.982 0.000 1.000
#> GSM155457 1 0.0376 0.995 0.996 0.004
#> GSM155461 1 0.0000 0.999 1.000 0.000
#> GSM155465 1 0.0000 0.999 1.000 0.000
#> GSM155469 1 0.0000 0.999 1.000 0.000
#> GSM155473 1 0.0000 0.999 1.000 0.000
#> GSM155477 1 0.0000 0.999 1.000 0.000
#> GSM155481 1 0.0000 0.999 1.000 0.000
#> GSM155485 1 0.0000 0.999 1.000 0.000
#> GSM155489 1 0.2236 0.962 0.964 0.036
#> GSM155493 1 0.0000 0.999 1.000 0.000
#> GSM155497 1 0.0000 0.999 1.000 0.000
#> GSM155501 2 0.0000 0.982 0.000 1.000
#> GSM155505 2 0.0000 0.982 0.000 1.000
#> GSM155451 2 0.0000 0.982 0.000 1.000
#> GSM155454 2 0.0000 0.982 0.000 1.000
#> GSM155458 2 0.9170 0.507 0.332 0.668
#> GSM155462 1 0.0000 0.999 1.000 0.000
#> GSM155466 1 0.0000 0.999 1.000 0.000
#> GSM155470 1 0.0000 0.999 1.000 0.000
#> GSM155474 1 0.0000 0.999 1.000 0.000
#> GSM155478 2 0.0000 0.982 0.000 1.000
#> GSM155482 2 0.0000 0.982 0.000 1.000
#> GSM155486 1 0.0938 0.987 0.988 0.012
#> GSM155490 2 0.0000 0.982 0.000 1.000
#> GSM155494 1 0.0000 0.999 1.000 0.000
#> GSM155498 1 0.0000 0.999 1.000 0.000
#> GSM155502 2 0.0000 0.982 0.000 1.000
#> GSM155506 2 0.0000 0.982 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 2 0.0747 0.840 0.000 0.984 0.016
#> GSM155452 2 0.1753 0.810 0.000 0.952 0.048
#> GSM155455 2 0.5926 0.282 0.000 0.644 0.356
#> GSM155459 1 0.5591 0.840 0.696 0.000 0.304
#> GSM155463 1 0.5810 0.842 0.664 0.000 0.336
#> GSM155467 1 0.5810 0.842 0.664 0.000 0.336
#> GSM155471 1 0.5810 0.842 0.664 0.000 0.336
#> GSM155475 1 0.5706 0.843 0.680 0.000 0.320
#> GSM155479 1 0.5785 0.843 0.668 0.000 0.332
#> GSM155483 1 0.0747 0.714 0.984 0.016 0.000
#> GSM155487 3 0.5926 0.853 0.000 0.356 0.644
#> GSM155491 1 0.0000 0.719 1.000 0.000 0.000
#> GSM155495 1 0.0747 0.707 0.984 0.000 0.016
#> GSM155499 2 0.1289 0.842 0.000 0.968 0.032
#> GSM155503 2 0.1643 0.836 0.000 0.956 0.044
#> GSM155449 2 0.0747 0.840 0.000 0.984 0.016
#> GSM155456 1 0.9074 0.690 0.500 0.148 0.352
#> GSM155460 1 0.5706 0.843 0.680 0.000 0.320
#> GSM155464 1 0.5785 0.843 0.668 0.000 0.332
#> GSM155468 1 0.5882 0.839 0.652 0.000 0.348
#> GSM155472 1 0.5988 0.829 0.632 0.000 0.368
#> GSM155476 1 0.5948 0.833 0.640 0.000 0.360
#> GSM155480 1 0.5926 0.835 0.644 0.000 0.356
#> GSM155484 1 0.2982 0.668 0.920 0.056 0.024
#> GSM155488 2 0.4602 0.694 0.040 0.852 0.108
#> GSM155492 1 0.0000 0.719 1.000 0.000 0.000
#> GSM155496 1 0.0000 0.719 1.000 0.000 0.000
#> GSM155500 2 0.1411 0.842 0.000 0.964 0.036
#> GSM155504 2 0.1860 0.827 0.000 0.948 0.052
#> GSM155450 2 0.1643 0.815 0.000 0.956 0.044
#> GSM155453 2 0.0892 0.837 0.000 0.980 0.020
#> GSM155457 1 0.9736 0.558 0.416 0.228 0.356
#> GSM155461 1 0.5706 0.843 0.680 0.000 0.320
#> GSM155465 1 0.5733 0.843 0.676 0.000 0.324
#> GSM155469 1 0.5882 0.838 0.652 0.000 0.348
#> GSM155473 1 0.5733 0.843 0.676 0.000 0.324
#> GSM155477 1 0.5810 0.842 0.664 0.000 0.336
#> GSM155481 1 0.5785 0.843 0.668 0.000 0.332
#> GSM155485 1 0.2297 0.713 0.944 0.036 0.020
#> GSM155489 1 0.5426 0.535 0.820 0.088 0.092
#> GSM155493 1 0.0000 0.719 1.000 0.000 0.000
#> GSM155497 1 0.0000 0.719 1.000 0.000 0.000
#> GSM155501 2 0.1411 0.842 0.000 0.964 0.036
#> GSM155505 2 0.1411 0.842 0.000 0.964 0.036
#> GSM155451 2 0.0747 0.840 0.000 0.984 0.016
#> GSM155454 2 0.0747 0.840 0.000 0.984 0.016
#> GSM155458 2 0.8472 0.127 0.100 0.540 0.360
#> GSM155462 1 0.5591 0.840 0.696 0.000 0.304
#> GSM155466 1 0.5760 0.843 0.672 0.000 0.328
#> GSM155470 1 0.5835 0.841 0.660 0.000 0.340
#> GSM155474 1 0.5810 0.842 0.664 0.000 0.336
#> GSM155478 3 0.5461 0.838 0.008 0.244 0.748
#> GSM155482 3 0.5763 0.879 0.008 0.276 0.716
#> GSM155486 1 0.4095 0.623 0.880 0.056 0.064
#> GSM155490 3 0.6205 0.872 0.008 0.336 0.656
#> GSM155494 1 0.0000 0.719 1.000 0.000 0.000
#> GSM155498 1 0.0000 0.719 1.000 0.000 0.000
#> GSM155502 2 0.1643 0.836 0.000 0.956 0.044
#> GSM155506 2 0.1411 0.842 0.000 0.964 0.036
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 2 0.2549 0.860 0.004 0.916 0.056 0.024
#> GSM155452 2 0.6332 0.728 0.136 0.712 0.120 0.032
#> GSM155455 1 0.7046 0.495 0.640 0.208 0.120 0.032
#> GSM155459 1 0.2704 0.852 0.876 0.000 0.124 0.000
#> GSM155463 1 0.0817 0.897 0.976 0.000 0.024 0.000
#> GSM155467 1 0.2081 0.881 0.916 0.000 0.084 0.000
#> GSM155471 1 0.0188 0.895 0.996 0.000 0.004 0.000
#> GSM155475 1 0.2704 0.852 0.876 0.000 0.124 0.000
#> GSM155479 1 0.2149 0.879 0.912 0.000 0.088 0.000
#> GSM155483 3 0.4446 0.844 0.196 0.028 0.776 0.000
#> GSM155487 4 0.1022 1.000 0.000 0.032 0.000 0.968
#> GSM155491 3 0.2973 0.888 0.144 0.000 0.856 0.000
#> GSM155495 3 0.3198 0.866 0.080 0.040 0.880 0.000
#> GSM155499 2 0.0524 0.877 0.000 0.988 0.004 0.008
#> GSM155503 2 0.0804 0.876 0.000 0.980 0.012 0.008
#> GSM155449 2 0.4524 0.829 0.048 0.828 0.096 0.028
#> GSM155456 1 0.4226 0.765 0.832 0.020 0.120 0.028
#> GSM155460 1 0.2281 0.874 0.904 0.000 0.096 0.000
#> GSM155464 1 0.0817 0.897 0.976 0.000 0.024 0.000
#> GSM155468 1 0.0000 0.894 1.000 0.000 0.000 0.000
#> GSM155472 1 0.2741 0.820 0.892 0.000 0.012 0.096
#> GSM155476 1 0.0524 0.889 0.988 0.004 0.008 0.000
#> GSM155480 1 0.1302 0.870 0.956 0.000 0.044 0.000
#> GSM155484 3 0.5690 0.787 0.116 0.168 0.716 0.000
#> GSM155488 2 0.2658 0.813 0.004 0.904 0.080 0.012
#> GSM155492 3 0.2814 0.893 0.132 0.000 0.868 0.000
#> GSM155496 3 0.2831 0.890 0.120 0.004 0.876 0.000
#> GSM155500 2 0.0672 0.877 0.000 0.984 0.008 0.008
#> GSM155504 2 0.1151 0.870 0.000 0.968 0.024 0.008
#> GSM155450 2 0.6283 0.734 0.132 0.716 0.120 0.032
#> GSM155453 2 0.5915 0.765 0.104 0.744 0.120 0.032
#> GSM155457 1 0.4801 0.743 0.808 0.040 0.120 0.032
#> GSM155461 1 0.2704 0.852 0.876 0.000 0.124 0.000
#> GSM155465 1 0.2081 0.881 0.916 0.000 0.084 0.000
#> GSM155469 1 0.0000 0.894 1.000 0.000 0.000 0.000
#> GSM155473 1 0.1637 0.891 0.940 0.000 0.060 0.000
#> GSM155477 1 0.1474 0.893 0.948 0.000 0.052 0.000
#> GSM155481 1 0.0921 0.897 0.972 0.000 0.028 0.000
#> GSM155485 3 0.5719 0.811 0.176 0.112 0.712 0.000
#> GSM155489 3 0.5517 0.632 0.040 0.272 0.684 0.004
#> GSM155493 3 0.2814 0.893 0.132 0.000 0.868 0.000
#> GSM155497 3 0.2814 0.893 0.132 0.000 0.868 0.000
#> GSM155501 2 0.0927 0.874 0.000 0.976 0.016 0.008
#> GSM155505 2 0.0672 0.877 0.000 0.984 0.008 0.008
#> GSM155451 2 0.4331 0.835 0.048 0.840 0.084 0.028
#> GSM155454 2 0.4115 0.833 0.016 0.836 0.120 0.028
#> GSM155458 1 0.5857 0.672 0.748 0.100 0.120 0.032
#> GSM155462 1 0.2704 0.852 0.876 0.000 0.124 0.000
#> GSM155466 1 0.1637 0.891 0.940 0.000 0.060 0.000
#> GSM155470 1 0.0188 0.892 0.996 0.000 0.004 0.000
#> GSM155474 1 0.0000 0.894 1.000 0.000 0.000 0.000
#> GSM155478 4 0.1022 1.000 0.000 0.032 0.000 0.968
#> GSM155482 4 0.1022 1.000 0.000 0.032 0.000 0.968
#> GSM155486 3 0.5412 0.787 0.096 0.168 0.736 0.000
#> GSM155490 4 0.1022 1.000 0.000 0.032 0.000 0.968
#> GSM155494 3 0.2868 0.892 0.136 0.000 0.864 0.000
#> GSM155498 3 0.3024 0.885 0.148 0.000 0.852 0.000
#> GSM155502 2 0.0927 0.874 0.000 0.976 0.016 0.008
#> GSM155506 2 0.0672 0.877 0.000 0.984 0.008 0.008
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.4451 0.458 0.000 0.492 0.004 0.504 0.000
#> GSM155452 4 0.2574 0.792 0.000 0.112 0.012 0.876 0.000
#> GSM155455 4 0.2127 0.793 0.000 0.108 0.000 0.892 0.000
#> GSM155459 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155463 1 0.0404 0.915 0.988 0.012 0.000 0.000 0.000
#> GSM155467 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155479 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155483 1 0.5008 0.611 0.708 0.140 0.152 0.000 0.000
#> GSM155487 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM155491 3 0.1197 0.987 0.048 0.000 0.952 0.000 0.000
#> GSM155495 3 0.1012 0.954 0.020 0.012 0.968 0.000 0.000
#> GSM155499 2 0.0510 0.868 0.000 0.984 0.016 0.000 0.000
#> GSM155503 2 0.0162 0.872 0.000 0.996 0.004 0.000 0.000
#> GSM155449 4 0.4249 0.581 0.000 0.432 0.000 0.568 0.000
#> GSM155456 4 0.2674 0.680 0.140 0.004 0.000 0.856 0.000
#> GSM155460 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155464 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155468 1 0.0609 0.910 0.980 0.020 0.000 0.000 0.000
#> GSM155472 1 0.5773 0.438 0.616 0.000 0.000 0.216 0.168
#> GSM155476 1 0.1124 0.897 0.960 0.036 0.004 0.000 0.000
#> GSM155480 1 0.1124 0.897 0.960 0.036 0.004 0.000 0.000
#> GSM155484 1 0.6282 0.158 0.496 0.340 0.164 0.000 0.000
#> GSM155488 2 0.2377 0.773 0.000 0.872 0.128 0.000 0.000
#> GSM155492 3 0.1121 0.988 0.044 0.000 0.956 0.000 0.000
#> GSM155496 3 0.1430 0.980 0.052 0.004 0.944 0.000 0.000
#> GSM155500 2 0.0000 0.873 0.000 1.000 0.000 0.000 0.000
#> GSM155504 2 0.0000 0.873 0.000 1.000 0.000 0.000 0.000
#> GSM155450 4 0.2516 0.802 0.000 0.140 0.000 0.860 0.000
#> GSM155453 4 0.2516 0.802 0.000 0.140 0.000 0.860 0.000
#> GSM155457 4 0.2629 0.684 0.136 0.004 0.000 0.860 0.000
#> GSM155461 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155465 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155469 1 0.1205 0.893 0.956 0.040 0.004 0.000 0.000
#> GSM155473 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155481 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155485 1 0.5967 0.315 0.556 0.308 0.136 0.000 0.000
#> GSM155489 2 0.3922 0.719 0.040 0.780 0.180 0.000 0.000
#> GSM155493 3 0.1121 0.988 0.044 0.000 0.956 0.000 0.000
#> GSM155497 3 0.1282 0.988 0.044 0.000 0.952 0.004 0.000
#> GSM155501 2 0.0162 0.873 0.000 0.996 0.004 0.000 0.000
#> GSM155505 2 0.0162 0.873 0.000 0.996 0.004 0.000 0.000
#> GSM155451 4 0.3949 0.706 0.000 0.332 0.000 0.668 0.000
#> GSM155454 4 0.4150 0.644 0.000 0.388 0.000 0.612 0.000
#> GSM155458 4 0.2984 0.792 0.032 0.108 0.000 0.860 0.000
#> GSM155462 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155466 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155470 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.921 1.000 0.000 0.000 0.000 0.000
#> GSM155478 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM155482 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM155486 2 0.6610 0.236 0.280 0.460 0.260 0.000 0.000
#> GSM155490 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM155494 3 0.1282 0.988 0.044 0.000 0.952 0.004 0.000
#> GSM155498 3 0.1357 0.986 0.048 0.000 0.948 0.004 0.000
#> GSM155502 2 0.0162 0.873 0.000 0.996 0.004 0.000 0.000
#> GSM155506 2 0.0703 0.864 0.000 0.976 0.024 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.4867 0.570 0.004 0.304 0.028 0.636 0.028 0.00
#> GSM155452 4 0.1536 0.860 0.000 0.016 0.004 0.940 0.040 0.00
#> GSM155455 4 0.0862 0.863 0.008 0.016 0.000 0.972 0.004 0.00
#> GSM155459 1 0.0632 0.963 0.976 0.000 0.000 0.000 0.024 0.00
#> GSM155463 1 0.0692 0.963 0.976 0.000 0.004 0.000 0.020 0.00
#> GSM155467 1 0.0146 0.966 0.996 0.000 0.004 0.000 0.000 0.00
#> GSM155471 1 0.0520 0.965 0.984 0.000 0.000 0.008 0.008 0.00
#> GSM155475 1 0.0551 0.966 0.984 0.000 0.004 0.004 0.008 0.00
#> GSM155479 1 0.1196 0.952 0.952 0.000 0.000 0.008 0.040 0.00
#> GSM155483 5 0.5356 0.789 0.184 0.008 0.168 0.004 0.636 0.00
#> GSM155487 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.00
#> GSM155491 3 0.0458 0.931 0.000 0.000 0.984 0.000 0.016 0.00
#> GSM155495 3 0.2871 0.731 0.000 0.004 0.804 0.000 0.192 0.00
#> GSM155499 2 0.0717 0.979 0.000 0.976 0.000 0.016 0.008 0.00
#> GSM155503 2 0.0363 0.986 0.000 0.988 0.000 0.000 0.012 0.00
#> GSM155449 4 0.4415 0.370 0.004 0.420 0.000 0.556 0.020 0.00
#> GSM155456 4 0.1812 0.812 0.080 0.000 0.000 0.912 0.008 0.00
#> GSM155460 1 0.0713 0.962 0.972 0.000 0.000 0.000 0.028 0.00
#> GSM155464 1 0.0858 0.959 0.968 0.000 0.004 0.000 0.028 0.00
#> GSM155468 1 0.0603 0.965 0.980 0.000 0.004 0.000 0.016 0.00
#> GSM155472 1 0.3606 0.768 0.800 0.000 0.000 0.052 0.008 0.14
#> GSM155476 1 0.1785 0.933 0.928 0.016 0.000 0.008 0.048 0.00
#> GSM155480 1 0.0891 0.962 0.968 0.000 0.000 0.008 0.024 0.00
#> GSM155484 5 0.5554 0.821 0.144 0.032 0.172 0.004 0.648 0.00
#> GSM155488 5 0.4708 0.351 0.008 0.356 0.040 0.000 0.596 0.00
#> GSM155492 3 0.0865 0.929 0.000 0.000 0.964 0.000 0.036 0.00
#> GSM155496 3 0.1267 0.915 0.000 0.000 0.940 0.000 0.060 0.00
#> GSM155500 2 0.0291 0.987 0.000 0.992 0.000 0.004 0.004 0.00
#> GSM155504 2 0.0547 0.983 0.000 0.980 0.000 0.000 0.020 0.00
#> GSM155450 4 0.1434 0.867 0.000 0.048 0.000 0.940 0.012 0.00
#> GSM155453 4 0.1265 0.867 0.000 0.044 0.000 0.948 0.008 0.00
#> GSM155457 4 0.1265 0.846 0.044 0.000 0.000 0.948 0.008 0.00
#> GSM155461 1 0.0692 0.963 0.976 0.000 0.004 0.000 0.020 0.00
#> GSM155465 1 0.0692 0.964 0.976 0.000 0.004 0.000 0.020 0.00
#> GSM155469 1 0.0405 0.966 0.988 0.000 0.004 0.000 0.008 0.00
#> GSM155473 1 0.0653 0.965 0.980 0.000 0.004 0.012 0.004 0.00
#> GSM155477 1 0.0547 0.964 0.980 0.000 0.000 0.000 0.020 0.00
#> GSM155481 1 0.0820 0.962 0.972 0.000 0.000 0.012 0.016 0.00
#> GSM155485 5 0.5439 0.812 0.164 0.020 0.164 0.004 0.648 0.00
#> GSM155489 5 0.5017 0.738 0.048 0.072 0.184 0.000 0.696 0.00
#> GSM155493 3 0.0790 0.930 0.000 0.000 0.968 0.000 0.032 0.00
#> GSM155497 3 0.1075 0.904 0.000 0.000 0.952 0.000 0.048 0.00
#> GSM155501 2 0.0146 0.987 0.000 0.996 0.000 0.000 0.004 0.00
#> GSM155505 2 0.0520 0.983 0.000 0.984 0.000 0.008 0.008 0.00
#> GSM155451 4 0.1967 0.856 0.000 0.084 0.000 0.904 0.012 0.00
#> GSM155454 4 0.2812 0.838 0.000 0.048 0.000 0.856 0.096 0.00
#> GSM155458 4 0.1036 0.858 0.024 0.008 0.000 0.964 0.004 0.00
#> GSM155462 1 0.1387 0.928 0.932 0.000 0.000 0.000 0.068 0.00
#> GSM155466 1 0.0603 0.964 0.980 0.000 0.004 0.000 0.016 0.00
#> GSM155470 1 0.0603 0.964 0.980 0.000 0.000 0.004 0.016 0.00
#> GSM155474 1 0.0622 0.964 0.980 0.000 0.000 0.012 0.008 0.00
#> GSM155478 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.00
#> GSM155482 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.00
#> GSM155486 5 0.5574 0.809 0.116 0.040 0.192 0.004 0.648 0.00
#> GSM155490 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.00
#> GSM155494 3 0.0260 0.928 0.000 0.000 0.992 0.000 0.008 0.00
#> GSM155498 3 0.0865 0.912 0.000 0.000 0.964 0.000 0.036 0.00
#> GSM155502 2 0.0000 0.988 0.000 1.000 0.000 0.000 0.000 0.00
#> GSM155506 2 0.0260 0.988 0.000 0.992 0.000 0.000 0.008 0.00
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 time(p) k
#> SD:NMF 59 0.411 2
#> SD:NMF 57 0.327 3
#> SD:NMF 58 0.693 4
#> SD:NMF 54 0.831 5
#> SD:NMF 57 0.929 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 59 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.129 0.871 0.871
#> 3 3 0.477 0.809 0.786 2.586 0.562 0.497
#> 4 4 0.752 0.810 0.869 0.384 0.765 0.546
#> 5 5 0.887 0.897 0.942 0.102 0.949 0.860
#> 6 6 1.000 0.966 0.986 0.113 0.897 0.673
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2
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
#> GSM155448 1 0 1 1 0
#> GSM155452 1 0 1 1 0
#> GSM155455 1 0 1 1 0
#> GSM155459 1 0 1 1 0
#> GSM155463 1 0 1 1 0
#> GSM155467 1 0 1 1 0
#> GSM155471 1 0 1 1 0
#> GSM155475 1 0 1 1 0
#> GSM155479 1 0 1 1 0
#> GSM155483 1 0 1 1 0
#> GSM155487 2 0 1 0 1
#> GSM155491 1 0 1 1 0
#> GSM155495 1 0 1 1 0
#> GSM155499 1 0 1 1 0
#> GSM155503 1 0 1 1 0
#> GSM155449 1 0 1 1 0
#> GSM155456 1 0 1 1 0
#> GSM155460 1 0 1 1 0
#> GSM155464 1 0 1 1 0
#> GSM155468 1 0 1 1 0
#> GSM155472 1 0 1 1 0
#> GSM155476 1 0 1 1 0
#> GSM155480 1 0 1 1 0
#> GSM155484 1 0 1 1 0
#> GSM155488 1 0 1 1 0
#> GSM155492 1 0 1 1 0
#> GSM155496 1 0 1 1 0
#> GSM155500 1 0 1 1 0
#> GSM155504 1 0 1 1 0
#> GSM155450 1 0 1 1 0
#> GSM155453 1 0 1 1 0
#> GSM155457 1 0 1 1 0
#> GSM155461 1 0 1 1 0
#> GSM155465 1 0 1 1 0
#> GSM155469 1 0 1 1 0
#> GSM155473 1 0 1 1 0
#> GSM155477 1 0 1 1 0
#> GSM155481 1 0 1 1 0
#> GSM155485 1 0 1 1 0
#> GSM155489 1 0 1 1 0
#> GSM155493 1 0 1 1 0
#> GSM155497 1 0 1 1 0
#> GSM155501 1 0 1 1 0
#> GSM155505 1 0 1 1 0
#> GSM155451 1 0 1 1 0
#> GSM155454 1 0 1 1 0
#> GSM155458 1 0 1 1 0
#> GSM155462 1 0 1 1 0
#> GSM155466 1 0 1 1 0
#> GSM155470 1 0 1 1 0
#> GSM155474 1 0 1 1 0
#> GSM155478 2 0 1 0 1
#> GSM155482 2 0 1 0 1
#> GSM155486 1 0 1 1 0
#> GSM155490 2 0 1 0 1
#> GSM155494 1 0 1 1 0
#> GSM155498 1 0 1 1 0
#> GSM155502 1 0 1 1 0
#> GSM155506 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 2 0.0237 0.888 0.004 0.996 0
#> GSM155452 2 0.0237 0.888 0.004 0.996 0
#> GSM155455 2 0.0237 0.888 0.004 0.996 0
#> GSM155459 1 0.5859 0.872 0.656 0.344 0
#> GSM155463 1 0.5859 0.872 0.656 0.344 0
#> GSM155467 1 0.5859 0.872 0.656 0.344 0
#> GSM155471 1 0.5859 0.872 0.656 0.344 0
#> GSM155475 1 0.5859 0.872 0.656 0.344 0
#> GSM155479 1 0.5859 0.872 0.656 0.344 0
#> GSM155483 2 0.5431 0.451 0.284 0.716 0
#> GSM155487 3 0.0000 1.000 0.000 0.000 1
#> GSM155491 1 0.0000 0.538 1.000 0.000 0
#> GSM155495 1 0.5835 0.869 0.660 0.340 0
#> GSM155499 2 0.0000 0.886 0.000 1.000 0
#> GSM155503 2 0.0000 0.886 0.000 1.000 0
#> GSM155449 2 0.0237 0.888 0.004 0.996 0
#> GSM155456 2 0.0237 0.888 0.004 0.996 0
#> GSM155460 1 0.5859 0.872 0.656 0.344 0
#> GSM155464 1 0.5859 0.872 0.656 0.344 0
#> GSM155468 1 0.5859 0.872 0.656 0.344 0
#> GSM155472 1 0.5859 0.872 0.656 0.344 0
#> GSM155476 1 0.5859 0.872 0.656 0.344 0
#> GSM155480 1 0.5859 0.872 0.656 0.344 0
#> GSM155484 2 0.5431 0.451 0.284 0.716 0
#> GSM155488 2 0.5431 0.451 0.284 0.716 0
#> GSM155492 1 0.0000 0.538 1.000 0.000 0
#> GSM155496 1 0.5835 0.869 0.660 0.340 0
#> GSM155500 2 0.0000 0.886 0.000 1.000 0
#> GSM155504 2 0.0000 0.886 0.000 1.000 0
#> GSM155450 2 0.0237 0.888 0.004 0.996 0
#> GSM155453 2 0.0237 0.888 0.004 0.996 0
#> GSM155457 2 0.0237 0.888 0.004 0.996 0
#> GSM155461 1 0.5859 0.872 0.656 0.344 0
#> GSM155465 1 0.5859 0.872 0.656 0.344 0
#> GSM155469 1 0.5859 0.872 0.656 0.344 0
#> GSM155473 1 0.5859 0.872 0.656 0.344 0
#> GSM155477 1 0.5859 0.872 0.656 0.344 0
#> GSM155481 1 0.5859 0.872 0.656 0.344 0
#> GSM155485 2 0.5431 0.451 0.284 0.716 0
#> GSM155489 2 0.5431 0.451 0.284 0.716 0
#> GSM155493 1 0.0000 0.538 1.000 0.000 0
#> GSM155497 1 0.0000 0.538 1.000 0.000 0
#> GSM155501 2 0.0000 0.886 0.000 1.000 0
#> GSM155505 2 0.0000 0.886 0.000 1.000 0
#> GSM155451 2 0.0237 0.888 0.004 0.996 0
#> GSM155454 2 0.0237 0.888 0.004 0.996 0
#> GSM155458 2 0.0237 0.888 0.004 0.996 0
#> GSM155462 1 0.5859 0.872 0.656 0.344 0
#> GSM155466 1 0.5859 0.872 0.656 0.344 0
#> GSM155470 1 0.5859 0.872 0.656 0.344 0
#> GSM155474 1 0.5859 0.872 0.656 0.344 0
#> GSM155478 3 0.0000 1.000 0.000 0.000 1
#> GSM155482 3 0.0000 1.000 0.000 0.000 1
#> GSM155486 2 0.5431 0.451 0.284 0.716 0
#> GSM155490 3 0.0000 1.000 0.000 0.000 1
#> GSM155494 1 0.0000 0.538 1.000 0.000 0
#> GSM155498 1 0.0000 0.538 1.000 0.000 0
#> GSM155502 2 0.0000 0.886 0.000 1.000 0
#> GSM155506 2 0.0000 0.886 0.000 1.000 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 2 0.480 0.801 0.384 0.616 0.000 0
#> GSM155452 2 0.480 0.801 0.384 0.616 0.000 0
#> GSM155455 2 0.480 0.801 0.384 0.616 0.000 0
#> GSM155459 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155463 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155467 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155471 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155475 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155479 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155483 1 0.495 0.459 0.620 0.376 0.004 0
#> GSM155487 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM155491 3 0.000 1.000 0.000 0.000 1.000 0
#> GSM155495 1 0.488 0.816 0.592 0.000 0.408 0
#> GSM155499 2 0.000 0.718 0.000 1.000 0.000 0
#> GSM155503 2 0.000 0.718 0.000 1.000 0.000 0
#> GSM155449 2 0.480 0.801 0.384 0.616 0.000 0
#> GSM155456 2 0.480 0.801 0.384 0.616 0.000 0
#> GSM155460 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155464 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155468 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155472 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155476 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155480 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155484 1 0.495 0.459 0.620 0.376 0.004 0
#> GSM155488 1 0.495 0.459 0.620 0.376 0.004 0
#> GSM155492 3 0.000 1.000 0.000 0.000 1.000 0
#> GSM155496 1 0.488 0.816 0.592 0.000 0.408 0
#> GSM155500 2 0.000 0.718 0.000 1.000 0.000 0
#> GSM155504 2 0.000 0.718 0.000 1.000 0.000 0
#> GSM155450 2 0.480 0.801 0.384 0.616 0.000 0
#> GSM155453 2 0.480 0.801 0.384 0.616 0.000 0
#> GSM155457 2 0.480 0.801 0.384 0.616 0.000 0
#> GSM155461 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155465 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155469 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155473 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155477 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155481 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155485 1 0.495 0.459 0.620 0.376 0.004 0
#> GSM155489 1 0.495 0.459 0.620 0.376 0.004 0
#> GSM155493 3 0.000 1.000 0.000 0.000 1.000 0
#> GSM155497 3 0.000 1.000 0.000 0.000 1.000 0
#> GSM155501 2 0.000 0.718 0.000 1.000 0.000 0
#> GSM155505 2 0.000 0.718 0.000 1.000 0.000 0
#> GSM155451 2 0.480 0.801 0.384 0.616 0.000 0
#> GSM155454 2 0.480 0.801 0.384 0.616 0.000 0
#> GSM155458 2 0.480 0.801 0.384 0.616 0.000 0
#> GSM155462 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155466 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155470 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155474 1 0.478 0.858 0.624 0.000 0.376 0
#> GSM155478 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM155482 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM155486 1 0.495 0.459 0.620 0.376 0.004 0
#> GSM155490 4 0.000 1.000 0.000 0.000 0.000 1
#> GSM155494 3 0.000 1.000 0.000 0.000 1.000 0
#> GSM155498 3 0.000 1.000 0.000 0.000 1.000 0
#> GSM155502 2 0.000 0.718 0.000 1.000 0.000 0
#> GSM155506 2 0.000 0.718 0.000 1.000 0.000 0
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.000 1.000 0.000 0.000 0.000 1 0
#> GSM155452 4 0.000 1.000 0.000 0.000 0.000 1 0
#> GSM155455 4 0.000 1.000 0.000 0.000 0.000 1 0
#> GSM155459 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155463 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155467 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155471 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155475 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155479 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155483 1 0.535 0.563 0.624 0.292 0.084 0 0
#> GSM155487 5 0.000 1.000 0.000 0.000 0.000 0 1
#> GSM155491 3 0.179 1.000 0.084 0.000 0.916 0 0
#> GSM155495 1 0.391 0.519 0.676 0.000 0.324 0 0
#> GSM155499 2 0.000 1.000 0.000 1.000 0.000 0 0
#> GSM155503 2 0.000 1.000 0.000 1.000 0.000 0 0
#> GSM155449 4 0.000 1.000 0.000 0.000 0.000 1 0
#> GSM155456 4 0.000 1.000 0.000 0.000 0.000 1 0
#> GSM155460 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155464 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155468 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155472 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155476 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155480 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155484 1 0.535 0.563 0.624 0.292 0.084 0 0
#> GSM155488 1 0.535 0.563 0.624 0.292 0.084 0 0
#> GSM155492 3 0.179 1.000 0.084 0.000 0.916 0 0
#> GSM155496 1 0.391 0.519 0.676 0.000 0.324 0 0
#> GSM155500 2 0.000 1.000 0.000 1.000 0.000 0 0
#> GSM155504 2 0.000 1.000 0.000 1.000 0.000 0 0
#> GSM155450 4 0.000 1.000 0.000 0.000 0.000 1 0
#> GSM155453 4 0.000 1.000 0.000 0.000 0.000 1 0
#> GSM155457 4 0.000 1.000 0.000 0.000 0.000 1 0
#> GSM155461 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155465 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155469 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155473 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155477 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155481 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155485 1 0.535 0.563 0.624 0.292 0.084 0 0
#> GSM155489 1 0.535 0.563 0.624 0.292 0.084 0 0
#> GSM155493 3 0.179 1.000 0.084 0.000 0.916 0 0
#> GSM155497 3 0.179 1.000 0.084 0.000 0.916 0 0
#> GSM155501 2 0.000 1.000 0.000 1.000 0.000 0 0
#> GSM155505 2 0.000 1.000 0.000 1.000 0.000 0 0
#> GSM155451 4 0.000 1.000 0.000 0.000 0.000 1 0
#> GSM155454 4 0.000 1.000 0.000 0.000 0.000 1 0
#> GSM155458 4 0.000 1.000 0.000 0.000 0.000 1 0
#> GSM155462 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155466 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155470 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155474 1 0.000 0.888 1.000 0.000 0.000 0 0
#> GSM155478 5 0.000 1.000 0.000 0.000 0.000 0 1
#> GSM155482 5 0.000 1.000 0.000 0.000 0.000 0 1
#> GSM155486 1 0.535 0.563 0.624 0.292 0.084 0 0
#> GSM155490 5 0.000 1.000 0.000 0.000 0.000 0 1
#> GSM155494 3 0.179 1.000 0.084 0.000 0.916 0 0
#> GSM155498 3 0.179 1.000 0.084 0.000 0.916 0 0
#> GSM155502 2 0.000 1.000 0.000 1.000 0.000 0 0
#> GSM155506 2 0.000 1.000 0.000 1.000 0.000 0 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.000 1.000 0 0 0.000 1 0.000 0
#> GSM155452 4 0.000 1.000 0 0 0.000 1 0.000 0
#> GSM155455 4 0.000 1.000 0 0 0.000 1 0.000 0
#> GSM155459 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155463 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155467 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155471 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155475 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155479 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155483 5 0.000 0.867 0 0 0.000 0 1.000 0
#> GSM155487 6 0.000 1.000 0 0 0.000 0 0.000 1
#> GSM155491 3 0.000 1.000 0 0 1.000 0 0.000 0
#> GSM155495 5 0.377 0.409 0 0 0.408 0 0.592 0
#> GSM155499 2 0.000 1.000 0 1 0.000 0 0.000 0
#> GSM155503 2 0.000 1.000 0 1 0.000 0 0.000 0
#> GSM155449 4 0.000 1.000 0 0 0.000 1 0.000 0
#> GSM155456 4 0.000 1.000 0 0 0.000 1 0.000 0
#> GSM155460 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155464 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155468 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155472 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155476 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155480 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155484 5 0.000 0.867 0 0 0.000 0 1.000 0
#> GSM155488 5 0.000 0.867 0 0 0.000 0 1.000 0
#> GSM155492 3 0.000 1.000 0 0 1.000 0 0.000 0
#> GSM155496 5 0.377 0.409 0 0 0.408 0 0.592 0
#> GSM155500 2 0.000 1.000 0 1 0.000 0 0.000 0
#> GSM155504 2 0.000 1.000 0 1 0.000 0 0.000 0
#> GSM155450 4 0.000 1.000 0 0 0.000 1 0.000 0
#> GSM155453 4 0.000 1.000 0 0 0.000 1 0.000 0
#> GSM155457 4 0.000 1.000 0 0 0.000 1 0.000 0
#> GSM155461 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155465 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155469 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155473 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155477 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155481 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155485 5 0.000 0.867 0 0 0.000 0 1.000 0
#> GSM155489 5 0.000 0.867 0 0 0.000 0 1.000 0
#> GSM155493 3 0.000 1.000 0 0 1.000 0 0.000 0
#> GSM155497 3 0.000 1.000 0 0 1.000 0 0.000 0
#> GSM155501 2 0.000 1.000 0 1 0.000 0 0.000 0
#> GSM155505 2 0.000 1.000 0 1 0.000 0 0.000 0
#> GSM155451 4 0.000 1.000 0 0 0.000 1 0.000 0
#> GSM155454 4 0.000 1.000 0 0 0.000 1 0.000 0
#> GSM155458 4 0.000 1.000 0 0 0.000 1 0.000 0
#> GSM155462 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155466 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155470 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155474 1 0.000 1.000 1 0 0.000 0 0.000 0
#> GSM155478 6 0.000 1.000 0 0 0.000 0 0.000 1
#> GSM155482 6 0.000 1.000 0 0 0.000 0 0.000 1
#> GSM155486 5 0.000 0.867 0 0 0.000 0 1.000 0
#> GSM155490 6 0.000 1.000 0 0 0.000 0 0.000 1
#> GSM155494 3 0.000 1.000 0 0 1.000 0 0.000 0
#> GSM155498 3 0.000 1.000 0 0 1.000 0 0.000 0
#> GSM155502 2 0.000 1.000 0 1 0.000 0 0.000 0
#> GSM155506 2 0.000 1.000 0 1 0.000 0 0.000 0
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 time(p) k
#> CV:hclust 59 0.0997 2
#> CV:hclust 53 0.3959 3
#> CV:hclust 53 0.5847 4
#> CV:hclust 59 0.7798 5
#> CV:hclust 57 0.9314 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 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.327 0.913 0.884 0.3778 0.544 0.544
#> 3 3 0.586 0.728 0.810 0.5262 1.000 1.000
#> 4 4 0.621 0.622 0.759 0.1738 0.683 0.452
#> 5 5 0.670 0.771 0.837 0.0924 0.891 0.662
#> 6 6 0.852 0.894 0.868 0.0614 0.964 0.854
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
#> GSM155448 2 0.9087 0.913 0.324 0.676
#> GSM155452 2 0.9286 0.888 0.344 0.656
#> GSM155455 1 0.0376 0.945 0.996 0.004
#> GSM155459 1 0.0000 0.947 1.000 0.000
#> GSM155463 1 0.0000 0.947 1.000 0.000
#> GSM155467 1 0.0000 0.947 1.000 0.000
#> GSM155471 1 0.0000 0.947 1.000 0.000
#> GSM155475 1 0.0000 0.947 1.000 0.000
#> GSM155479 1 0.0000 0.947 1.000 0.000
#> GSM155483 1 0.5059 0.866 0.888 0.112
#> GSM155487 2 0.5294 0.793 0.120 0.880
#> GSM155491 1 0.5519 0.857 0.872 0.128
#> GSM155495 1 0.4562 0.883 0.904 0.096
#> GSM155499 2 0.8813 0.935 0.300 0.700
#> GSM155503 2 0.8813 0.935 0.300 0.700
#> GSM155449 2 0.9087 0.913 0.324 0.676
#> GSM155456 1 0.0376 0.945 0.996 0.004
#> GSM155460 1 0.0000 0.947 1.000 0.000
#> GSM155464 1 0.0000 0.947 1.000 0.000
#> GSM155468 1 0.0000 0.947 1.000 0.000
#> GSM155472 1 0.0000 0.947 1.000 0.000
#> GSM155476 1 0.0000 0.947 1.000 0.000
#> GSM155480 1 0.0000 0.947 1.000 0.000
#> GSM155484 1 0.5059 0.866 0.888 0.112
#> GSM155488 2 0.8909 0.925 0.308 0.692
#> GSM155492 1 0.5519 0.857 0.872 0.128
#> GSM155496 1 0.5519 0.857 0.872 0.128
#> GSM155500 2 0.8813 0.935 0.300 0.700
#> GSM155504 2 0.8813 0.935 0.300 0.700
#> GSM155450 2 0.8813 0.933 0.300 0.700
#> GSM155453 2 0.8813 0.933 0.300 0.700
#> GSM155457 1 0.0376 0.945 0.996 0.004
#> GSM155461 1 0.0000 0.947 1.000 0.000
#> GSM155465 1 0.0000 0.947 1.000 0.000
#> GSM155469 1 0.0000 0.947 1.000 0.000
#> GSM155473 1 0.0000 0.947 1.000 0.000
#> GSM155477 1 0.0000 0.947 1.000 0.000
#> GSM155481 1 0.0000 0.947 1.000 0.000
#> GSM155485 1 0.5059 0.866 0.888 0.112
#> GSM155489 1 0.5059 0.866 0.888 0.112
#> GSM155493 1 0.5519 0.857 0.872 0.128
#> GSM155497 1 0.5519 0.857 0.872 0.128
#> GSM155501 2 0.8813 0.935 0.300 0.700
#> GSM155505 2 0.8813 0.935 0.300 0.700
#> GSM155451 2 0.8763 0.934 0.296 0.704
#> GSM155454 2 0.8813 0.933 0.300 0.700
#> GSM155458 1 0.0376 0.945 0.996 0.004
#> GSM155462 1 0.0000 0.947 1.000 0.000
#> GSM155466 1 0.0000 0.947 1.000 0.000
#> GSM155470 1 0.0000 0.947 1.000 0.000
#> GSM155474 1 0.0000 0.947 1.000 0.000
#> GSM155478 2 0.6801 0.789 0.180 0.820
#> GSM155482 2 0.6801 0.789 0.180 0.820
#> GSM155486 1 0.5059 0.866 0.888 0.112
#> GSM155490 2 0.5294 0.793 0.120 0.880
#> GSM155494 1 0.5519 0.857 0.872 0.128
#> GSM155498 1 0.5519 0.857 0.872 0.128
#> GSM155502 2 0.8813 0.935 0.300 0.700
#> GSM155506 2 0.8813 0.935 0.300 0.700
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 2 0.677 0.782 0.032 0.664 NA
#> GSM155452 2 0.677 0.782 0.032 0.664 NA
#> GSM155455 1 0.677 0.506 0.664 0.032 NA
#> GSM155459 1 0.000 0.815 1.000 0.000 NA
#> GSM155463 1 0.000 0.815 1.000 0.000 NA
#> GSM155467 1 0.000 0.815 1.000 0.000 NA
#> GSM155471 1 0.000 0.815 1.000 0.000 NA
#> GSM155475 1 0.000 0.815 1.000 0.000 NA
#> GSM155479 1 0.000 0.815 1.000 0.000 NA
#> GSM155483 1 0.856 0.572 0.608 0.208 NA
#> GSM155487 2 0.525 0.721 0.000 0.736 NA
#> GSM155491 1 0.666 0.575 0.528 0.008 NA
#> GSM155495 1 0.706 0.563 0.516 0.020 NA
#> GSM155499 2 0.103 0.834 0.024 0.976 NA
#> GSM155503 2 0.103 0.834 0.024 0.976 NA
#> GSM155449 2 0.677 0.782 0.032 0.664 NA
#> GSM155456 1 0.556 0.562 0.700 0.000 NA
#> GSM155460 1 0.000 0.815 1.000 0.000 NA
#> GSM155464 1 0.000 0.815 1.000 0.000 NA
#> GSM155468 1 0.000 0.815 1.000 0.000 NA
#> GSM155472 1 0.000 0.815 1.000 0.000 NA
#> GSM155476 1 0.000 0.815 1.000 0.000 NA
#> GSM155480 1 0.000 0.815 1.000 0.000 NA
#> GSM155484 1 0.856 0.572 0.608 0.208 NA
#> GSM155488 2 0.379 0.800 0.060 0.892 NA
#> GSM155492 1 0.666 0.575 0.528 0.008 NA
#> GSM155496 1 0.667 0.572 0.524 0.008 NA
#> GSM155500 2 0.103 0.834 0.024 0.976 NA
#> GSM155504 2 0.103 0.834 0.024 0.976 NA
#> GSM155450 2 0.666 0.784 0.028 0.668 NA
#> GSM155453 2 0.666 0.784 0.028 0.668 NA
#> GSM155457 1 0.556 0.562 0.700 0.000 NA
#> GSM155461 1 0.000 0.815 1.000 0.000 NA
#> GSM155465 1 0.000 0.815 1.000 0.000 NA
#> GSM155469 1 0.000 0.815 1.000 0.000 NA
#> GSM155473 1 0.000 0.815 1.000 0.000 NA
#> GSM155477 1 0.000 0.815 1.000 0.000 NA
#> GSM155481 1 0.000 0.815 1.000 0.000 NA
#> GSM155485 1 0.856 0.572 0.608 0.208 NA
#> GSM155489 1 0.881 0.531 0.580 0.236 NA
#> GSM155493 1 0.666 0.575 0.528 0.008 NA
#> GSM155497 1 0.666 0.575 0.528 0.008 NA
#> GSM155501 2 0.103 0.834 0.024 0.976 NA
#> GSM155505 2 0.103 0.834 0.024 0.976 NA
#> GSM155451 2 0.666 0.784 0.028 0.668 NA
#> GSM155454 2 0.654 0.784 0.024 0.672 NA
#> GSM155458 1 0.556 0.562 0.700 0.000 NA
#> GSM155462 1 0.000 0.815 1.000 0.000 NA
#> GSM155466 1 0.000 0.815 1.000 0.000 NA
#> GSM155470 1 0.000 0.815 1.000 0.000 NA
#> GSM155474 1 0.000 0.815 1.000 0.000 NA
#> GSM155478 2 0.947 0.502 0.208 0.484 NA
#> GSM155482 2 0.947 0.502 0.208 0.484 NA
#> GSM155486 1 0.856 0.572 0.608 0.208 NA
#> GSM155490 2 0.525 0.721 0.000 0.736 NA
#> GSM155494 1 0.666 0.575 0.528 0.008 NA
#> GSM155498 1 0.666 0.575 0.528 0.008 NA
#> GSM155502 2 0.103 0.834 0.024 0.976 NA
#> GSM155506 2 0.103 0.834 0.024 0.976 NA
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 4 0.540 0.631 0.012 0.384 0.004 0.600
#> GSM155452 4 0.540 0.631 0.012 0.384 0.004 0.600
#> GSM155455 4 0.584 0.477 0.400 0.000 0.036 0.564
#> GSM155459 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155463 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155467 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155471 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155475 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155479 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155483 1 0.973 -0.138 0.352 0.260 0.224 0.164
#> GSM155487 3 0.528 -0.298 0.000 0.464 0.528 0.008
#> GSM155491 3 0.803 0.639 0.252 0.008 0.428 0.312
#> GSM155495 3 0.813 0.601 0.232 0.012 0.392 0.364
#> GSM155499 2 0.000 0.955 0.000 1.000 0.000 0.000
#> GSM155503 2 0.000 0.955 0.000 1.000 0.000 0.000
#> GSM155449 4 0.540 0.631 0.012 0.384 0.004 0.600
#> GSM155456 4 0.585 0.472 0.404 0.000 0.036 0.560
#> GSM155460 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155464 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155468 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155472 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155476 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155480 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155484 1 0.973 -0.138 0.352 0.260 0.224 0.164
#> GSM155488 2 0.614 0.613 0.028 0.724 0.132 0.116
#> GSM155492 3 0.803 0.639 0.252 0.008 0.428 0.312
#> GSM155496 3 0.800 0.637 0.244 0.008 0.432 0.316
#> GSM155500 2 0.000 0.955 0.000 1.000 0.000 0.000
#> GSM155504 2 0.000 0.955 0.000 1.000 0.000 0.000
#> GSM155450 4 0.523 0.632 0.012 0.384 0.000 0.604
#> GSM155453 4 0.523 0.632 0.012 0.384 0.000 0.604
#> GSM155457 4 0.585 0.472 0.404 0.000 0.036 0.560
#> GSM155461 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155465 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155469 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155473 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155477 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155481 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155485 1 0.973 -0.138 0.352 0.260 0.224 0.164
#> GSM155489 1 0.975 -0.152 0.344 0.268 0.224 0.164
#> GSM155493 3 0.803 0.639 0.252 0.008 0.428 0.312
#> GSM155497 3 0.803 0.639 0.252 0.008 0.428 0.312
#> GSM155501 2 0.000 0.955 0.000 1.000 0.000 0.000
#> GSM155505 2 0.000 0.955 0.000 1.000 0.000 0.000
#> GSM155451 4 0.523 0.632 0.012 0.384 0.000 0.604
#> GSM155454 4 0.523 0.632 0.012 0.384 0.000 0.604
#> GSM155458 4 0.585 0.472 0.404 0.000 0.036 0.560
#> GSM155462 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155466 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155470 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155474 1 0.000 0.846 1.000 0.000 0.000 0.000
#> GSM155478 3 0.829 -0.120 0.096 0.316 0.500 0.088
#> GSM155482 3 0.829 -0.120 0.096 0.316 0.500 0.088
#> GSM155486 1 0.973 -0.138 0.352 0.260 0.224 0.164
#> GSM155490 3 0.528 -0.298 0.000 0.464 0.528 0.008
#> GSM155494 3 0.803 0.639 0.252 0.008 0.428 0.312
#> GSM155498 3 0.792 0.634 0.256 0.004 0.428 0.312
#> GSM155502 2 0.000 0.955 0.000 1.000 0.000 0.000
#> GSM155506 2 0.000 0.955 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.0613 0.818 0.000 0.004 0.008 0.984 0.004
#> GSM155452 4 0.0613 0.818 0.000 0.004 0.008 0.984 0.004
#> GSM155455 4 0.5806 0.682 0.192 0.008 0.048 0.688 0.064
#> GSM155459 1 0.1124 0.974 0.960 0.004 0.000 0.000 0.036
#> GSM155463 1 0.1124 0.974 0.960 0.004 0.000 0.000 0.036
#> GSM155467 1 0.0000 0.983 1.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.0162 0.983 0.996 0.000 0.000 0.004 0.000
#> GSM155475 1 0.0162 0.983 0.996 0.000 0.000 0.004 0.000
#> GSM155479 1 0.0162 0.983 0.996 0.000 0.000 0.004 0.000
#> GSM155483 2 0.8418 0.173 0.172 0.348 0.232 0.000 0.248
#> GSM155487 5 0.4025 0.851 0.000 0.292 0.000 0.008 0.700
#> GSM155491 3 0.2020 0.931 0.100 0.000 0.900 0.000 0.000
#> GSM155495 3 0.6884 0.494 0.068 0.156 0.580 0.000 0.196
#> GSM155499 2 0.3177 0.495 0.000 0.792 0.000 0.208 0.000
#> GSM155503 2 0.3455 0.495 0.000 0.784 0.008 0.208 0.000
#> GSM155449 4 0.0613 0.818 0.000 0.004 0.008 0.984 0.004
#> GSM155456 4 0.5806 0.682 0.192 0.008 0.048 0.688 0.064
#> GSM155460 1 0.1124 0.974 0.960 0.004 0.000 0.000 0.036
#> GSM155464 1 0.1124 0.974 0.960 0.004 0.000 0.000 0.036
#> GSM155468 1 0.0162 0.983 0.996 0.000 0.000 0.000 0.004
#> GSM155472 1 0.0162 0.983 0.996 0.000 0.000 0.004 0.000
#> GSM155476 1 0.0162 0.983 0.996 0.000 0.000 0.004 0.000
#> GSM155480 1 0.0162 0.983 0.996 0.000 0.000 0.004 0.000
#> GSM155484 2 0.8418 0.173 0.172 0.348 0.232 0.000 0.248
#> GSM155488 2 0.5629 0.265 0.004 0.664 0.044 0.040 0.248
#> GSM155492 3 0.2020 0.931 0.100 0.000 0.900 0.000 0.000
#> GSM155496 3 0.1768 0.898 0.072 0.000 0.924 0.000 0.004
#> GSM155500 2 0.3177 0.495 0.000 0.792 0.000 0.208 0.000
#> GSM155504 2 0.3455 0.495 0.000 0.784 0.008 0.208 0.000
#> GSM155450 4 0.0162 0.821 0.000 0.004 0.000 0.996 0.000
#> GSM155453 4 0.0162 0.821 0.000 0.004 0.000 0.996 0.000
#> GSM155457 4 0.5806 0.682 0.192 0.008 0.048 0.688 0.064
#> GSM155461 1 0.1124 0.974 0.960 0.004 0.000 0.000 0.036
#> GSM155465 1 0.1124 0.974 0.960 0.004 0.000 0.000 0.036
#> GSM155469 1 0.0162 0.983 0.996 0.000 0.000 0.000 0.004
#> GSM155473 1 0.0162 0.983 0.996 0.000 0.000 0.004 0.000
#> GSM155477 1 0.0162 0.983 0.996 0.000 0.000 0.004 0.000
#> GSM155481 1 0.0162 0.983 0.996 0.000 0.000 0.004 0.000
#> GSM155485 2 0.8418 0.173 0.172 0.348 0.232 0.000 0.248
#> GSM155489 2 0.8400 0.174 0.168 0.352 0.232 0.000 0.248
#> GSM155493 3 0.2020 0.931 0.100 0.000 0.900 0.000 0.000
#> GSM155497 3 0.2179 0.930 0.100 0.004 0.896 0.000 0.000
#> GSM155501 2 0.3177 0.495 0.000 0.792 0.000 0.208 0.000
#> GSM155505 2 0.3455 0.495 0.000 0.784 0.008 0.208 0.000
#> GSM155451 4 0.0162 0.821 0.000 0.004 0.000 0.996 0.000
#> GSM155454 4 0.0162 0.821 0.000 0.004 0.000 0.996 0.000
#> GSM155458 4 0.5806 0.682 0.192 0.008 0.048 0.688 0.064
#> GSM155462 1 0.1124 0.974 0.960 0.004 0.000 0.000 0.036
#> GSM155466 1 0.1124 0.974 0.960 0.004 0.000 0.000 0.036
#> GSM155470 1 0.0162 0.983 0.996 0.000 0.000 0.000 0.004
#> GSM155474 1 0.0162 0.983 0.996 0.000 0.000 0.004 0.000
#> GSM155478 5 0.5102 0.862 0.076 0.148 0.000 0.036 0.740
#> GSM155482 5 0.5102 0.862 0.076 0.148 0.000 0.036 0.740
#> GSM155486 2 0.8418 0.173 0.172 0.348 0.232 0.000 0.248
#> GSM155490 5 0.4253 0.851 0.000 0.284 0.008 0.008 0.700
#> GSM155494 3 0.2020 0.931 0.100 0.000 0.900 0.000 0.000
#> GSM155498 3 0.2179 0.930 0.100 0.004 0.896 0.000 0.000
#> GSM155502 2 0.3177 0.495 0.000 0.792 0.000 0.208 0.000
#> GSM155506 2 0.3455 0.495 0.000 0.784 0.008 0.208 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.1057 0.861 0.004 0.012 0.004 0.968 0.008 0.004
#> GSM155452 4 0.1387 0.860 0.004 0.012 0.008 0.956 0.008 0.012
#> GSM155455 4 0.5327 0.758 0.080 0.000 0.016 0.696 0.164 0.044
#> GSM155459 1 0.3624 0.867 0.824 0.028 0.000 0.004 0.100 0.044
#> GSM155463 1 0.3624 0.867 0.824 0.028 0.000 0.004 0.100 0.044
#> GSM155467 1 0.0291 0.911 0.992 0.004 0.000 0.000 0.004 0.000
#> GSM155471 1 0.0951 0.910 0.968 0.000 0.000 0.008 0.020 0.004
#> GSM155475 1 0.1261 0.907 0.956 0.004 0.000 0.008 0.028 0.004
#> GSM155479 1 0.1413 0.904 0.948 0.004 0.000 0.008 0.036 0.004
#> GSM155483 5 0.5762 0.891 0.068 0.104 0.180 0.004 0.644 0.000
#> GSM155487 6 0.3579 0.935 0.000 0.120 0.008 0.000 0.064 0.808
#> GSM155491 3 0.1007 0.983 0.044 0.000 0.956 0.000 0.000 0.000
#> GSM155495 5 0.4622 0.603 0.016 0.012 0.356 0.000 0.608 0.008
#> GSM155499 2 0.2308 0.985 0.000 0.896 0.012 0.076 0.016 0.000
#> GSM155503 2 0.1501 0.985 0.000 0.924 0.000 0.076 0.000 0.000
#> GSM155449 4 0.1057 0.861 0.004 0.012 0.004 0.968 0.008 0.004
#> GSM155456 4 0.5468 0.749 0.084 0.000 0.016 0.680 0.176 0.044
#> GSM155460 1 0.3624 0.867 0.824 0.028 0.000 0.004 0.100 0.044
#> GSM155464 1 0.3624 0.867 0.824 0.028 0.000 0.004 0.100 0.044
#> GSM155468 1 0.0717 0.910 0.976 0.000 0.000 0.000 0.016 0.008
#> GSM155472 1 0.1413 0.905 0.948 0.004 0.000 0.008 0.036 0.004
#> GSM155476 1 0.1338 0.906 0.952 0.004 0.000 0.008 0.032 0.004
#> GSM155480 1 0.1413 0.904 0.948 0.004 0.000 0.008 0.036 0.004
#> GSM155484 5 0.5762 0.891 0.068 0.104 0.180 0.004 0.644 0.000
#> GSM155488 5 0.3940 0.546 0.008 0.336 0.000 0.004 0.652 0.000
#> GSM155492 3 0.1007 0.983 0.044 0.000 0.956 0.000 0.000 0.000
#> GSM155496 3 0.1870 0.918 0.012 0.012 0.932 0.000 0.032 0.012
#> GSM155500 2 0.2308 0.985 0.000 0.896 0.012 0.076 0.016 0.000
#> GSM155504 2 0.1501 0.985 0.000 0.924 0.000 0.076 0.000 0.000
#> GSM155450 4 0.0458 0.862 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM155453 4 0.0862 0.862 0.000 0.016 0.004 0.972 0.000 0.008
#> GSM155457 4 0.5468 0.749 0.084 0.000 0.016 0.680 0.176 0.044
#> GSM155461 1 0.3624 0.867 0.824 0.028 0.000 0.004 0.100 0.044
#> GSM155465 1 0.3624 0.867 0.824 0.028 0.000 0.004 0.100 0.044
#> GSM155469 1 0.0717 0.910 0.976 0.000 0.000 0.000 0.016 0.008
#> GSM155473 1 0.0951 0.910 0.968 0.000 0.000 0.008 0.020 0.004
#> GSM155477 1 0.1338 0.906 0.952 0.004 0.000 0.008 0.032 0.004
#> GSM155481 1 0.1413 0.904 0.948 0.004 0.000 0.008 0.036 0.004
#> GSM155485 5 0.5762 0.891 0.068 0.104 0.180 0.004 0.644 0.000
#> GSM155489 5 0.5841 0.888 0.068 0.112 0.180 0.004 0.636 0.000
#> GSM155493 3 0.1007 0.983 0.044 0.000 0.956 0.000 0.000 0.000
#> GSM155497 3 0.1367 0.980 0.044 0.000 0.944 0.000 0.000 0.012
#> GSM155501 2 0.2308 0.985 0.000 0.896 0.012 0.076 0.016 0.000
#> GSM155505 2 0.1501 0.985 0.000 0.924 0.000 0.076 0.000 0.000
#> GSM155451 4 0.0458 0.862 0.000 0.016 0.000 0.984 0.000 0.000
#> GSM155454 4 0.0862 0.862 0.000 0.016 0.004 0.972 0.000 0.008
#> GSM155458 4 0.5358 0.757 0.080 0.000 0.016 0.692 0.168 0.044
#> GSM155462 1 0.3624 0.867 0.824 0.028 0.000 0.004 0.100 0.044
#> GSM155466 1 0.3624 0.867 0.824 0.028 0.000 0.004 0.100 0.044
#> GSM155470 1 0.0717 0.910 0.976 0.000 0.000 0.000 0.016 0.008
#> GSM155474 1 0.0951 0.910 0.968 0.000 0.000 0.008 0.020 0.004
#> GSM155478 6 0.2589 0.935 0.028 0.056 0.000 0.004 0.020 0.892
#> GSM155482 6 0.2589 0.935 0.028 0.056 0.000 0.004 0.020 0.892
#> GSM155486 5 0.5762 0.891 0.068 0.104 0.180 0.004 0.644 0.000
#> GSM155490 6 0.3579 0.935 0.000 0.120 0.008 0.000 0.064 0.808
#> GSM155494 3 0.1007 0.983 0.044 0.000 0.956 0.000 0.000 0.000
#> GSM155498 3 0.1367 0.980 0.044 0.000 0.944 0.000 0.000 0.012
#> GSM155502 2 0.2308 0.985 0.000 0.896 0.012 0.076 0.016 0.000
#> GSM155506 2 0.1501 0.985 0.000 0.924 0.000 0.076 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 time(p) k
#> CV:kmeans 59 0.655 2
#> CV:kmeans 59 0.655 3
#> CV:kmeans 46 0.999 4
#> CV:kmeans 44 0.656 5
#> CV:kmeans 59 0.939 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 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 5.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.955 0.981 0.5016 0.499 0.499
#> 3 3 1.000 0.976 0.989 0.3189 0.737 0.521
#> 4 4 0.939 0.961 0.970 0.1146 0.886 0.679
#> 5 5 0.933 0.918 0.930 0.0398 0.965 0.866
#> 6 6 0.894 0.937 0.936 0.0405 0.981 0.919
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 2 0.0000 0.977 0.000 1.000
#> GSM155452 2 0.0000 0.977 0.000 1.000
#> GSM155455 1 0.9323 0.476 0.652 0.348
#> GSM155459 1 0.0000 0.982 1.000 0.000
#> GSM155463 1 0.0000 0.982 1.000 0.000
#> GSM155467 1 0.0000 0.982 1.000 0.000
#> GSM155471 1 0.0000 0.982 1.000 0.000
#> GSM155475 1 0.0000 0.982 1.000 0.000
#> GSM155479 1 0.0000 0.982 1.000 0.000
#> GSM155483 2 0.2778 0.943 0.048 0.952
#> GSM155487 2 0.0000 0.977 0.000 1.000
#> GSM155491 1 0.0000 0.982 1.000 0.000
#> GSM155495 2 0.9427 0.451 0.360 0.640
#> GSM155499 2 0.0000 0.977 0.000 1.000
#> GSM155503 2 0.0000 0.977 0.000 1.000
#> GSM155449 2 0.0000 0.977 0.000 1.000
#> GSM155456 1 0.0000 0.982 1.000 0.000
#> GSM155460 1 0.0000 0.982 1.000 0.000
#> GSM155464 1 0.0000 0.982 1.000 0.000
#> GSM155468 1 0.0000 0.982 1.000 0.000
#> GSM155472 1 0.0000 0.982 1.000 0.000
#> GSM155476 1 0.0000 0.982 1.000 0.000
#> GSM155480 1 0.0000 0.982 1.000 0.000
#> GSM155484 2 0.2778 0.943 0.048 0.952
#> GSM155488 2 0.0000 0.977 0.000 1.000
#> GSM155492 1 0.0000 0.982 1.000 0.000
#> GSM155496 1 0.0000 0.982 1.000 0.000
#> GSM155500 2 0.0000 0.977 0.000 1.000
#> GSM155504 2 0.0000 0.977 0.000 1.000
#> GSM155450 2 0.0000 0.977 0.000 1.000
#> GSM155453 2 0.0000 0.977 0.000 1.000
#> GSM155457 1 0.0000 0.982 1.000 0.000
#> GSM155461 1 0.0000 0.982 1.000 0.000
#> GSM155465 1 0.0000 0.982 1.000 0.000
#> GSM155469 1 0.0000 0.982 1.000 0.000
#> GSM155473 1 0.0000 0.982 1.000 0.000
#> GSM155477 1 0.0000 0.982 1.000 0.000
#> GSM155481 1 0.0000 0.982 1.000 0.000
#> GSM155485 2 0.2778 0.943 0.048 0.952
#> GSM155489 2 0.0938 0.969 0.012 0.988
#> GSM155493 1 0.0000 0.982 1.000 0.000
#> GSM155497 1 0.0000 0.982 1.000 0.000
#> GSM155501 2 0.0000 0.977 0.000 1.000
#> GSM155505 2 0.0000 0.977 0.000 1.000
#> GSM155451 2 0.0000 0.977 0.000 1.000
#> GSM155454 2 0.0000 0.977 0.000 1.000
#> GSM155458 1 0.7528 0.726 0.784 0.216
#> GSM155462 1 0.0000 0.982 1.000 0.000
#> GSM155466 1 0.0000 0.982 1.000 0.000
#> GSM155470 1 0.0000 0.982 1.000 0.000
#> GSM155474 1 0.0000 0.982 1.000 0.000
#> GSM155478 2 0.0000 0.977 0.000 1.000
#> GSM155482 2 0.0000 0.977 0.000 1.000
#> GSM155486 2 0.2778 0.943 0.048 0.952
#> GSM155490 2 0.0000 0.977 0.000 1.000
#> GSM155494 1 0.0000 0.982 1.000 0.000
#> GSM155498 1 0.0000 0.982 1.000 0.000
#> GSM155502 2 0.0000 0.977 0.000 1.000
#> GSM155506 2 0.0000 0.977 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 2 0.0237 0.973 0.000 0.996 0.004
#> GSM155452 2 0.0237 0.973 0.000 0.996 0.004
#> GSM155455 2 0.3644 0.842 0.124 0.872 0.004
#> GSM155459 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155463 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155467 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155471 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155475 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155479 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155483 3 0.0237 0.987 0.000 0.004 0.996
#> GSM155487 2 0.0000 0.974 0.000 1.000 0.000
#> GSM155491 3 0.0000 0.987 0.000 0.000 1.000
#> GSM155495 3 0.0237 0.987 0.000 0.004 0.996
#> GSM155499 2 0.0000 0.974 0.000 1.000 0.000
#> GSM155503 2 0.0000 0.974 0.000 1.000 0.000
#> GSM155449 2 0.0237 0.973 0.000 0.996 0.004
#> GSM155456 1 0.0237 0.996 0.996 0.000 0.004
#> GSM155460 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155464 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155468 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155472 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155476 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155480 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155484 3 0.0237 0.987 0.000 0.004 0.996
#> GSM155488 3 0.3816 0.833 0.000 0.148 0.852
#> GSM155492 3 0.0000 0.987 0.000 0.000 1.000
#> GSM155496 3 0.0000 0.987 0.000 0.000 1.000
#> GSM155500 2 0.0000 0.974 0.000 1.000 0.000
#> GSM155504 2 0.0000 0.974 0.000 1.000 0.000
#> GSM155450 2 0.0237 0.973 0.000 0.996 0.004
#> GSM155453 2 0.0237 0.973 0.000 0.996 0.004
#> GSM155457 1 0.0237 0.996 0.996 0.000 0.004
#> GSM155461 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155465 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155469 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155473 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155477 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155481 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155485 3 0.0237 0.987 0.000 0.004 0.996
#> GSM155489 3 0.0237 0.987 0.000 0.004 0.996
#> GSM155493 3 0.0000 0.987 0.000 0.000 1.000
#> GSM155497 3 0.0000 0.987 0.000 0.000 1.000
#> GSM155501 2 0.0000 0.974 0.000 1.000 0.000
#> GSM155505 2 0.0000 0.974 0.000 1.000 0.000
#> GSM155451 2 0.0237 0.973 0.000 0.996 0.004
#> GSM155454 2 0.0237 0.973 0.000 0.996 0.004
#> GSM155458 2 0.5690 0.606 0.288 0.708 0.004
#> GSM155462 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155466 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155470 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155474 1 0.0000 1.000 1.000 0.000 0.000
#> GSM155478 2 0.0000 0.974 0.000 1.000 0.000
#> GSM155482 2 0.0000 0.974 0.000 1.000 0.000
#> GSM155486 3 0.0237 0.987 0.000 0.004 0.996
#> GSM155490 2 0.0000 0.974 0.000 1.000 0.000
#> GSM155494 3 0.0000 0.987 0.000 0.000 1.000
#> GSM155498 3 0.0000 0.987 0.000 0.000 1.000
#> GSM155502 2 0.0000 0.974 0.000 1.000 0.000
#> GSM155506 2 0.0000 0.974 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 4 0.0000 0.985 0.000 0.000 0.000 1.000
#> GSM155452 4 0.0000 0.985 0.000 0.000 0.000 1.000
#> GSM155455 4 0.0000 0.985 0.000 0.000 0.000 1.000
#> GSM155459 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155463 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155467 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155471 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155475 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155479 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155483 3 0.3837 0.824 0.000 0.224 0.776 0.000
#> GSM155487 2 0.0592 0.967 0.000 0.984 0.000 0.016
#> GSM155491 3 0.0000 0.904 0.000 0.000 1.000 0.000
#> GSM155495 3 0.0592 0.901 0.000 0.016 0.984 0.000
#> GSM155499 2 0.1557 0.980 0.000 0.944 0.000 0.056
#> GSM155503 2 0.1557 0.980 0.000 0.944 0.000 0.056
#> GSM155449 4 0.0000 0.985 0.000 0.000 0.000 1.000
#> GSM155456 4 0.1557 0.929 0.056 0.000 0.000 0.944
#> GSM155460 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155464 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155468 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155472 1 0.0336 0.992 0.992 0.008 0.000 0.000
#> GSM155476 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155480 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155484 3 0.3837 0.824 0.000 0.224 0.776 0.000
#> GSM155488 2 0.0657 0.951 0.000 0.984 0.012 0.004
#> GSM155492 3 0.0000 0.904 0.000 0.000 1.000 0.000
#> GSM155496 3 0.0000 0.904 0.000 0.000 1.000 0.000
#> GSM155500 2 0.1557 0.980 0.000 0.944 0.000 0.056
#> GSM155504 2 0.1557 0.980 0.000 0.944 0.000 0.056
#> GSM155450 4 0.0000 0.985 0.000 0.000 0.000 1.000
#> GSM155453 4 0.0000 0.985 0.000 0.000 0.000 1.000
#> GSM155457 4 0.1557 0.929 0.056 0.000 0.000 0.944
#> GSM155461 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155465 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155469 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155473 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155477 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155481 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155485 3 0.3837 0.824 0.000 0.224 0.776 0.000
#> GSM155489 3 0.3837 0.824 0.000 0.224 0.776 0.000
#> GSM155493 3 0.0000 0.904 0.000 0.000 1.000 0.000
#> GSM155497 3 0.0000 0.904 0.000 0.000 1.000 0.000
#> GSM155501 2 0.1557 0.980 0.000 0.944 0.000 0.056
#> GSM155505 2 0.1557 0.980 0.000 0.944 0.000 0.056
#> GSM155451 4 0.0000 0.985 0.000 0.000 0.000 1.000
#> GSM155454 4 0.0000 0.985 0.000 0.000 0.000 1.000
#> GSM155458 4 0.0000 0.985 0.000 0.000 0.000 1.000
#> GSM155462 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155466 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155470 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM155478 2 0.0927 0.964 0.008 0.976 0.000 0.016
#> GSM155482 2 0.0927 0.964 0.008 0.976 0.000 0.016
#> GSM155486 3 0.3837 0.824 0.000 0.224 0.776 0.000
#> GSM155490 2 0.0592 0.967 0.000 0.984 0.000 0.016
#> GSM155494 3 0.0000 0.904 0.000 0.000 1.000 0.000
#> GSM155498 3 0.0000 0.904 0.000 0.000 1.000 0.000
#> GSM155502 2 0.1557 0.980 0.000 0.944 0.000 0.056
#> GSM155506 2 0.1557 0.980 0.000 0.944 0.000 0.056
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000
#> GSM155452 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000
#> GSM155455 4 0.0290 0.986 0.000 0.000 0.008 0.992 0.000
#> GSM155459 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM155463 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM155467 1 0.0162 0.995 0.996 0.000 0.004 0.000 0.000
#> GSM155471 1 0.0162 0.995 0.996 0.000 0.004 0.000 0.000
#> GSM155475 1 0.0162 0.995 0.996 0.000 0.004 0.000 0.000
#> GSM155479 1 0.0162 0.995 0.996 0.000 0.004 0.000 0.000
#> GSM155483 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000
#> GSM155487 2 0.3171 0.719 0.000 0.816 0.176 0.000 0.008
#> GSM155491 3 0.3003 1.000 0.000 0.000 0.812 0.000 0.188
#> GSM155495 5 0.4210 -0.109 0.000 0.000 0.412 0.000 0.588
#> GSM155499 2 0.3452 0.859 0.000 0.820 0.000 0.032 0.148
#> GSM155503 2 0.3452 0.859 0.000 0.820 0.000 0.032 0.148
#> GSM155449 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000
#> GSM155456 4 0.1168 0.953 0.032 0.000 0.008 0.960 0.000
#> GSM155460 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM155464 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM155468 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM155472 1 0.1992 0.927 0.924 0.032 0.044 0.000 0.000
#> GSM155476 1 0.0324 0.992 0.992 0.004 0.004 0.000 0.000
#> GSM155480 1 0.0162 0.995 0.996 0.000 0.004 0.000 0.000
#> GSM155484 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000
#> GSM155488 5 0.3003 0.622 0.000 0.188 0.000 0.000 0.812
#> GSM155492 3 0.3003 1.000 0.000 0.000 0.812 0.000 0.188
#> GSM155496 3 0.3003 1.000 0.000 0.000 0.812 0.000 0.188
#> GSM155500 2 0.3452 0.859 0.000 0.820 0.000 0.032 0.148
#> GSM155504 2 0.3452 0.859 0.000 0.820 0.000 0.032 0.148
#> GSM155450 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000
#> GSM155453 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000
#> GSM155457 4 0.1168 0.953 0.032 0.000 0.008 0.960 0.000
#> GSM155461 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM155465 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM155469 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM155473 1 0.0162 0.995 0.996 0.000 0.004 0.000 0.000
#> GSM155477 1 0.0162 0.995 0.996 0.000 0.004 0.000 0.000
#> GSM155481 1 0.0162 0.995 0.996 0.000 0.004 0.000 0.000
#> GSM155485 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000
#> GSM155489 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000
#> GSM155493 3 0.3003 1.000 0.000 0.000 0.812 0.000 0.188
#> GSM155497 3 0.3003 1.000 0.000 0.000 0.812 0.000 0.188
#> GSM155501 2 0.3452 0.859 0.000 0.820 0.000 0.032 0.148
#> GSM155505 2 0.3452 0.859 0.000 0.820 0.000 0.032 0.148
#> GSM155451 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000
#> GSM155454 4 0.0000 0.988 0.000 0.000 0.000 1.000 0.000
#> GSM155458 4 0.0290 0.986 0.000 0.000 0.008 0.992 0.000
#> GSM155462 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM155466 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM155470 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.0162 0.995 0.996 0.000 0.004 0.000 0.000
#> GSM155478 2 0.3048 0.716 0.000 0.820 0.176 0.000 0.004
#> GSM155482 2 0.3048 0.716 0.000 0.820 0.176 0.000 0.004
#> GSM155486 5 0.0000 0.860 0.000 0.000 0.000 0.000 1.000
#> GSM155490 2 0.3171 0.719 0.000 0.816 0.176 0.000 0.008
#> GSM155494 3 0.3003 1.000 0.000 0.000 0.812 0.000 0.188
#> GSM155498 3 0.3003 1.000 0.000 0.000 0.812 0.000 0.188
#> GSM155502 2 0.3452 0.859 0.000 0.820 0.000 0.032 0.148
#> GSM155506 2 0.3452 0.859 0.000 0.820 0.000 0.032 0.148
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.0146 0.965 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM155452 4 0.0146 0.965 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM155455 4 0.2039 0.937 0.000 0.000 0.000 0.904 0.020 0.076
#> GSM155459 1 0.2697 0.904 0.872 0.004 0.000 0.004 0.028 0.092
#> GSM155463 1 0.2697 0.904 0.872 0.004 0.000 0.004 0.028 0.092
#> GSM155467 1 0.0146 0.927 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM155471 1 0.0603 0.926 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM155475 1 0.1152 0.919 0.952 0.000 0.000 0.000 0.004 0.044
#> GSM155479 1 0.1429 0.917 0.940 0.000 0.000 0.004 0.004 0.052
#> GSM155483 5 0.1341 0.918 0.000 0.024 0.028 0.000 0.948 0.000
#> GSM155487 6 0.2969 0.992 0.000 0.224 0.000 0.000 0.000 0.776
#> GSM155491 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155495 5 0.3797 0.320 0.000 0.000 0.420 0.000 0.580 0.000
#> GSM155499 2 0.0146 1.000 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM155503 2 0.0146 1.000 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM155449 4 0.0146 0.965 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM155456 4 0.2182 0.935 0.004 0.000 0.000 0.900 0.020 0.076
#> GSM155460 1 0.2697 0.904 0.872 0.004 0.000 0.004 0.028 0.092
#> GSM155464 1 0.2697 0.904 0.872 0.004 0.000 0.004 0.028 0.092
#> GSM155468 1 0.0603 0.927 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM155472 1 0.2902 0.782 0.800 0.000 0.000 0.000 0.004 0.196
#> GSM155476 1 0.1493 0.916 0.936 0.000 0.000 0.004 0.004 0.056
#> GSM155480 1 0.1429 0.917 0.940 0.000 0.000 0.004 0.004 0.052
#> GSM155484 5 0.1341 0.918 0.000 0.024 0.028 0.000 0.948 0.000
#> GSM155488 5 0.1141 0.887 0.000 0.052 0.000 0.000 0.948 0.000
#> GSM155492 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155496 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155500 2 0.0146 1.000 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM155504 2 0.0146 1.000 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM155450 4 0.0146 0.965 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM155453 4 0.0146 0.965 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM155457 4 0.2182 0.935 0.004 0.000 0.000 0.900 0.020 0.076
#> GSM155461 1 0.2554 0.903 0.876 0.004 0.000 0.000 0.028 0.092
#> GSM155465 1 0.2697 0.904 0.872 0.004 0.000 0.004 0.028 0.092
#> GSM155469 1 0.0603 0.927 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM155473 1 0.0603 0.926 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM155477 1 0.1493 0.916 0.936 0.000 0.000 0.004 0.004 0.056
#> GSM155481 1 0.1364 0.918 0.944 0.000 0.000 0.004 0.004 0.048
#> GSM155485 5 0.1341 0.918 0.000 0.024 0.028 0.000 0.948 0.000
#> GSM155489 5 0.1341 0.918 0.000 0.024 0.028 0.000 0.948 0.000
#> GSM155493 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155497 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155501 2 0.0146 1.000 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM155505 2 0.0146 1.000 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM155451 4 0.0146 0.965 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM155454 4 0.0146 0.965 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM155458 4 0.2039 0.937 0.000 0.000 0.000 0.904 0.020 0.076
#> GSM155462 1 0.2697 0.904 0.872 0.004 0.000 0.004 0.028 0.092
#> GSM155466 1 0.2697 0.904 0.872 0.004 0.000 0.004 0.028 0.092
#> GSM155470 1 0.0603 0.927 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM155474 1 0.0603 0.926 0.980 0.000 0.000 0.000 0.004 0.016
#> GSM155478 6 0.2912 0.992 0.000 0.216 0.000 0.000 0.000 0.784
#> GSM155482 6 0.2912 0.992 0.000 0.216 0.000 0.000 0.000 0.784
#> GSM155486 5 0.1341 0.918 0.000 0.024 0.028 0.000 0.948 0.000
#> GSM155490 6 0.2969 0.992 0.000 0.224 0.000 0.000 0.000 0.776
#> GSM155494 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155498 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155502 2 0.0146 1.000 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM155506 2 0.0146 1.000 0.000 0.996 0.000 0.004 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 time(p) k
#> CV:skmeans 57 0.791 2
#> CV:skmeans 59 0.669 3
#> CV:skmeans 59 0.983 4
#> CV:skmeans 58 0.987 5
#> CV:skmeans 58 0.935 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 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.964 0.973 0.987 0.4077 0.598 0.598
#> 3 3 0.736 0.893 0.937 0.3195 0.823 0.714
#> 4 4 0.675 0.748 0.888 0.1824 0.891 0.771
#> 5 5 0.744 0.802 0.855 0.1476 0.762 0.440
#> 6 6 0.946 0.977 0.991 0.0755 0.981 0.919
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2
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
#> GSM155448 1 0.7056 0.769 0.808 0.192
#> GSM155452 1 0.5059 0.874 0.888 0.112
#> GSM155455 1 0.0000 0.987 1.000 0.000
#> GSM155459 1 0.0000 0.987 1.000 0.000
#> GSM155463 1 0.0000 0.987 1.000 0.000
#> GSM155467 1 0.0000 0.987 1.000 0.000
#> GSM155471 1 0.0000 0.987 1.000 0.000
#> GSM155475 1 0.0000 0.987 1.000 0.000
#> GSM155479 1 0.0000 0.987 1.000 0.000
#> GSM155483 1 0.0000 0.987 1.000 0.000
#> GSM155487 2 0.0000 0.986 0.000 1.000
#> GSM155491 1 0.0000 0.987 1.000 0.000
#> GSM155495 1 0.0000 0.987 1.000 0.000
#> GSM155499 2 0.0000 0.986 0.000 1.000
#> GSM155503 2 0.0000 0.986 0.000 1.000
#> GSM155449 1 0.0672 0.980 0.992 0.008
#> GSM155456 1 0.0000 0.987 1.000 0.000
#> GSM155460 1 0.0000 0.987 1.000 0.000
#> GSM155464 1 0.0000 0.987 1.000 0.000
#> GSM155468 1 0.0000 0.987 1.000 0.000
#> GSM155472 1 0.0000 0.987 1.000 0.000
#> GSM155476 1 0.0000 0.987 1.000 0.000
#> GSM155480 1 0.0000 0.987 1.000 0.000
#> GSM155484 1 0.3879 0.914 0.924 0.076
#> GSM155488 2 0.0000 0.986 0.000 1.000
#> GSM155492 1 0.0000 0.987 1.000 0.000
#> GSM155496 1 0.0000 0.987 1.000 0.000
#> GSM155500 2 0.0000 0.986 0.000 1.000
#> GSM155504 2 0.0000 0.986 0.000 1.000
#> GSM155450 2 0.0000 0.986 0.000 1.000
#> GSM155453 2 0.0000 0.986 0.000 1.000
#> GSM155457 1 0.0000 0.987 1.000 0.000
#> GSM155461 1 0.0000 0.987 1.000 0.000
#> GSM155465 1 0.0000 0.987 1.000 0.000
#> GSM155469 1 0.0000 0.987 1.000 0.000
#> GSM155473 1 0.0000 0.987 1.000 0.000
#> GSM155477 1 0.0000 0.987 1.000 0.000
#> GSM155481 1 0.0000 0.987 1.000 0.000
#> GSM155485 1 0.0000 0.987 1.000 0.000
#> GSM155489 2 0.7219 0.748 0.200 0.800
#> GSM155493 1 0.0000 0.987 1.000 0.000
#> GSM155497 1 0.0000 0.987 1.000 0.000
#> GSM155501 2 0.0000 0.986 0.000 1.000
#> GSM155505 2 0.0000 0.986 0.000 1.000
#> GSM155451 2 0.0000 0.986 0.000 1.000
#> GSM155454 2 0.0000 0.986 0.000 1.000
#> GSM155458 1 0.0000 0.987 1.000 0.000
#> GSM155462 1 0.0000 0.987 1.000 0.000
#> GSM155466 1 0.0000 0.987 1.000 0.000
#> GSM155470 1 0.0000 0.987 1.000 0.000
#> GSM155474 1 0.0000 0.987 1.000 0.000
#> GSM155478 1 0.0000 0.987 1.000 0.000
#> GSM155482 1 0.0000 0.987 1.000 0.000
#> GSM155486 1 0.6247 0.817 0.844 0.156
#> GSM155490 2 0.0000 0.986 0.000 1.000
#> GSM155494 1 0.0000 0.987 1.000 0.000
#> GSM155498 1 0.0000 0.987 1.000 0.000
#> GSM155502 2 0.0000 0.986 0.000 1.000
#> GSM155506 2 0.0000 0.986 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 1 0.4504 0.697 0.804 0.196 0.000
#> GSM155452 1 0.6037 0.700 0.788 0.112 0.100
#> GSM155455 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155459 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155463 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155467 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155471 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155475 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155479 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155483 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155487 2 0.4555 0.812 0.000 0.800 0.200
#> GSM155491 3 0.4555 1.000 0.200 0.000 0.800
#> GSM155495 1 0.6260 -0.168 0.552 0.000 0.448
#> GSM155499 2 0.0000 0.956 0.000 1.000 0.000
#> GSM155503 2 0.0000 0.956 0.000 1.000 0.000
#> GSM155449 1 0.0424 0.931 0.992 0.008 0.000
#> GSM155456 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155460 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155464 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155468 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155472 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155476 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155480 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155484 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155488 2 0.0000 0.956 0.000 1.000 0.000
#> GSM155492 3 0.4555 1.000 0.200 0.000 0.800
#> GSM155496 3 0.4555 1.000 0.200 0.000 0.800
#> GSM155500 2 0.0000 0.956 0.000 1.000 0.000
#> GSM155504 2 0.0000 0.956 0.000 1.000 0.000
#> GSM155450 2 0.4178 0.708 0.172 0.828 0.000
#> GSM155453 2 0.0000 0.956 0.000 1.000 0.000
#> GSM155457 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155461 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155465 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155469 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155473 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155477 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155481 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155485 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155489 1 0.8626 0.196 0.580 0.280 0.140
#> GSM155493 3 0.4555 1.000 0.200 0.000 0.800
#> GSM155497 3 0.4555 1.000 0.200 0.000 0.800
#> GSM155501 2 0.0000 0.956 0.000 1.000 0.000
#> GSM155505 2 0.0000 0.956 0.000 1.000 0.000
#> GSM155451 2 0.0000 0.956 0.000 1.000 0.000
#> GSM155454 2 0.0000 0.956 0.000 1.000 0.000
#> GSM155458 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155462 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155466 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155470 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155474 1 0.0000 0.939 1.000 0.000 0.000
#> GSM155478 1 0.4555 0.714 0.800 0.000 0.200
#> GSM155482 1 0.4555 0.714 0.800 0.000 0.200
#> GSM155486 1 0.1753 0.889 0.952 0.000 0.048
#> GSM155490 2 0.4555 0.812 0.000 0.800 0.200
#> GSM155494 3 0.4555 1.000 0.200 0.000 0.800
#> GSM155498 3 0.4555 1.000 0.200 0.000 0.800
#> GSM155502 2 0.0000 0.956 0.000 1.000 0.000
#> GSM155506 2 0.0000 0.956 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 1 0.612 0.462 0.676 0.192 0.000 0.132
#> GSM155452 1 0.522 0.625 0.756 0.112 0.000 0.132
#> GSM155455 1 0.281 0.787 0.868 0.000 0.000 0.132
#> GSM155459 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155463 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155467 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155471 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155475 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155479 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155483 1 0.450 0.511 0.684 0.316 0.000 0.000
#> GSM155487 4 0.281 0.194 0.000 0.132 0.000 0.868
#> GSM155491 3 0.000 0.927 0.000 0.000 1.000 0.000
#> GSM155495 3 0.711 0.369 0.152 0.316 0.532 0.000
#> GSM155499 2 0.450 0.809 0.000 0.684 0.000 0.316
#> GSM155503 2 0.450 0.809 0.000 0.684 0.000 0.316
#> GSM155449 1 0.314 0.778 0.860 0.008 0.000 0.132
#> GSM155456 1 0.281 0.787 0.868 0.000 0.000 0.132
#> GSM155460 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155464 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155468 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155472 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155476 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155480 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155484 1 0.450 0.511 0.684 0.316 0.000 0.000
#> GSM155488 2 0.000 0.480 0.000 1.000 0.000 0.000
#> GSM155492 3 0.000 0.927 0.000 0.000 1.000 0.000
#> GSM155496 3 0.000 0.927 0.000 0.000 1.000 0.000
#> GSM155500 2 0.450 0.809 0.000 0.684 0.000 0.316
#> GSM155504 2 0.450 0.809 0.000 0.684 0.000 0.316
#> GSM155450 2 0.697 0.514 0.140 0.552 0.000 0.308
#> GSM155453 2 0.496 0.744 0.000 0.552 0.000 0.448
#> GSM155457 1 0.281 0.787 0.868 0.000 0.000 0.132
#> GSM155461 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155465 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155469 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155473 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155477 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155481 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155485 1 0.450 0.511 0.684 0.316 0.000 0.000
#> GSM155489 2 0.713 -0.202 0.320 0.528 0.152 0.000
#> GSM155493 3 0.000 0.927 0.000 0.000 1.000 0.000
#> GSM155497 3 0.000 0.927 0.000 0.000 1.000 0.000
#> GSM155501 2 0.450 0.809 0.000 0.684 0.000 0.316
#> GSM155505 2 0.450 0.809 0.000 0.684 0.000 0.316
#> GSM155451 2 0.496 0.744 0.000 0.552 0.000 0.448
#> GSM155454 2 0.496 0.744 0.000 0.552 0.000 0.448
#> GSM155458 1 0.281 0.787 0.868 0.000 0.000 0.132
#> GSM155462 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155466 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155470 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155474 1 0.000 0.891 1.000 0.000 0.000 0.000
#> GSM155478 4 0.496 0.401 0.448 0.000 0.000 0.552
#> GSM155482 4 0.496 0.401 0.448 0.000 0.000 0.552
#> GSM155486 1 0.583 0.419 0.632 0.316 0.052 0.000
#> GSM155490 4 0.281 0.194 0.000 0.132 0.000 0.868
#> GSM155494 3 0.000 0.927 0.000 0.000 1.000 0.000
#> GSM155498 3 0.000 0.927 0.000 0.000 1.000 0.000
#> GSM155502 2 0.450 0.809 0.000 0.684 0.000 0.316
#> GSM155506 2 0.450 0.809 0.000 0.684 0.000 0.316
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.293 0.815 0.180 0.000 0.000 0.820 0.000
#> GSM155452 4 0.293 0.815 0.180 0.000 0.000 0.820 0.000
#> GSM155455 4 0.293 0.815 0.180 0.000 0.000 0.820 0.000
#> GSM155459 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155463 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155467 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155479 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155483 5 0.420 0.681 0.408 0.000 0.000 0.000 0.592
#> GSM155487 2 0.000 0.389 0.000 1.000 0.000 0.000 0.000
#> GSM155491 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155495 5 0.483 0.189 0.028 0.000 0.380 0.000 0.592
#> GSM155499 2 0.646 0.709 0.000 0.412 0.000 0.180 0.408
#> GSM155503 2 0.646 0.709 0.000 0.412 0.000 0.180 0.408
#> GSM155449 4 0.293 0.815 0.180 0.000 0.000 0.820 0.000
#> GSM155456 4 0.384 0.708 0.308 0.000 0.000 0.692 0.000
#> GSM155460 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155464 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155468 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155472 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155476 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155480 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155484 5 0.420 0.681 0.408 0.000 0.000 0.000 0.592
#> GSM155488 5 0.000 0.186 0.000 0.000 0.000 0.000 1.000
#> GSM155492 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155496 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155500 2 0.646 0.709 0.000 0.412 0.000 0.180 0.408
#> GSM155504 2 0.646 0.709 0.000 0.412 0.000 0.180 0.408
#> GSM155450 4 0.000 0.724 0.000 0.000 0.000 1.000 0.000
#> GSM155453 4 0.000 0.724 0.000 0.000 0.000 1.000 0.000
#> GSM155457 4 0.384 0.708 0.308 0.000 0.000 0.692 0.000
#> GSM155461 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155465 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155469 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155473 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155481 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155485 5 0.420 0.681 0.408 0.000 0.000 0.000 0.592
#> GSM155489 5 0.512 0.598 0.168 0.000 0.136 0.000 0.696
#> GSM155493 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155497 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155501 2 0.646 0.709 0.000 0.412 0.000 0.180 0.408
#> GSM155505 2 0.646 0.709 0.000 0.412 0.000 0.180 0.408
#> GSM155451 4 0.000 0.724 0.000 0.000 0.000 1.000 0.000
#> GSM155454 4 0.000 0.724 0.000 0.000 0.000 1.000 0.000
#> GSM155458 4 0.384 0.708 0.308 0.000 0.000 0.692 0.000
#> GSM155462 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155466 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155470 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155478 2 0.421 -0.063 0.412 0.588 0.000 0.000 0.000
#> GSM155482 2 0.421 -0.063 0.412 0.588 0.000 0.000 0.000
#> GSM155486 5 0.517 0.708 0.356 0.000 0.052 0.000 0.592
#> GSM155490 2 0.000 0.389 0.000 1.000 0.000 0.000 0.000
#> GSM155494 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155498 3 0.000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155502 2 0.646 0.709 0.000 0.412 0.000 0.180 0.408
#> GSM155506 2 0.646 0.709 0.000 0.412 0.000 0.180 0.408
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.000 0.941 0.000 0.000 0 1.000 0 0.000
#> GSM155452 4 0.000 0.941 0.000 0.000 0 1.000 0 0.000
#> GSM155455 4 0.000 0.941 0.000 0.000 0 1.000 0 0.000
#> GSM155459 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155463 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155467 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155471 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155475 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155479 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155483 5 0.000 1.000 0.000 0.000 0 0.000 1 0.000
#> GSM155487 6 0.249 0.804 0.000 0.164 0 0.000 0 0.836
#> GSM155491 3 0.000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM155495 5 0.000 1.000 0.000 0.000 0 0.000 1 0.000
#> GSM155499 2 0.000 1.000 0.000 1.000 0 0.000 0 0.000
#> GSM155503 2 0.000 1.000 0.000 1.000 0 0.000 0 0.000
#> GSM155449 4 0.000 0.941 0.000 0.000 0 1.000 0 0.000
#> GSM155456 4 0.214 0.837 0.128 0.000 0 0.872 0 0.000
#> GSM155460 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155464 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155468 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155472 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155476 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155480 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155484 5 0.000 1.000 0.000 0.000 0 0.000 1 0.000
#> GSM155488 5 0.000 1.000 0.000 0.000 0 0.000 1 0.000
#> GSM155492 3 0.000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM155496 3 0.000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM155500 2 0.000 1.000 0.000 1.000 0 0.000 0 0.000
#> GSM155504 2 0.000 1.000 0.000 1.000 0 0.000 0 0.000
#> GSM155450 4 0.000 0.941 0.000 0.000 0 1.000 0 0.000
#> GSM155453 4 0.000 0.941 0.000 0.000 0 1.000 0 0.000
#> GSM155457 4 0.214 0.837 0.128 0.000 0 0.872 0 0.000
#> GSM155461 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155465 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155469 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155473 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155477 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155481 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155485 5 0.000 1.000 0.000 0.000 0 0.000 1 0.000
#> GSM155489 5 0.000 1.000 0.000 0.000 0 0.000 1 0.000
#> GSM155493 3 0.000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM155497 3 0.000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM155501 2 0.000 1.000 0.000 1.000 0 0.000 0 0.000
#> GSM155505 2 0.000 1.000 0.000 1.000 0 0.000 0 0.000
#> GSM155451 4 0.000 0.941 0.000 0.000 0 1.000 0 0.000
#> GSM155454 4 0.000 0.941 0.000 0.000 0 1.000 0 0.000
#> GSM155458 4 0.214 0.837 0.128 0.000 0 0.872 0 0.000
#> GSM155462 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155466 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155470 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155474 1 0.000 1.000 1.000 0.000 0 0.000 0 0.000
#> GSM155478 6 0.000 0.942 0.000 0.000 0 0.000 0 1.000
#> GSM155482 6 0.000 0.942 0.000 0.000 0 0.000 0 1.000
#> GSM155486 5 0.000 1.000 0.000 0.000 0 0.000 1 0.000
#> GSM155490 6 0.000 0.942 0.000 0.000 0 0.000 0 1.000
#> GSM155494 3 0.000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM155498 3 0.000 1.000 0.000 0.000 1 0.000 0 0.000
#> GSM155502 2 0.000 1.000 0.000 1.000 0 0.000 0 0.000
#> GSM155506 2 0.000 1.000 0.000 1.000 0 0.000 0 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 time(p) k
#> CV:pam 59 0.753 2
#> CV:pam 57 0.965 3
#> CV:pam 50 0.821 4
#> CV:pam 53 1.000 5
#> CV:pam 59 0.939 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 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.483 0.955 0.921 0.4271 0.524 0.524
#> 3 3 0.775 0.909 0.936 0.3344 0.640 0.459
#> 4 4 0.855 0.897 0.927 0.2457 0.742 0.482
#> 5 5 1.000 0.999 0.999 0.0705 0.949 0.824
#> 6 6 1.000 0.990 0.995 0.0374 0.971 0.881
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 5
There is also optional best \(k\) = 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 2 0.118 0.966 0.016 0.984
#> GSM155452 2 0.118 0.966 0.016 0.984
#> GSM155455 2 0.242 0.947 0.040 0.960
#> GSM155459 1 0.605 0.988 0.852 0.148
#> GSM155463 1 0.605 0.988 0.852 0.148
#> GSM155467 1 0.605 0.988 0.852 0.148
#> GSM155471 1 0.605 0.988 0.852 0.148
#> GSM155475 1 0.605 0.988 0.852 0.148
#> GSM155479 1 0.605 0.988 0.852 0.148
#> GSM155483 2 0.118 0.966 0.016 0.984
#> GSM155487 2 0.605 0.822 0.148 0.852
#> GSM155491 2 0.118 0.966 0.016 0.984
#> GSM155495 2 0.118 0.966 0.016 0.984
#> GSM155499 2 0.000 0.960 0.000 1.000
#> GSM155503 2 0.000 0.960 0.000 1.000
#> GSM155449 2 0.118 0.966 0.016 0.984
#> GSM155456 2 0.563 0.831 0.132 0.868
#> GSM155460 1 0.605 0.988 0.852 0.148
#> GSM155464 1 0.605 0.988 0.852 0.148
#> GSM155468 1 0.605 0.988 0.852 0.148
#> GSM155472 1 0.634 0.715 0.840 0.160
#> GSM155476 1 0.605 0.988 0.852 0.148
#> GSM155480 1 0.605 0.988 0.852 0.148
#> GSM155484 2 0.118 0.966 0.016 0.984
#> GSM155488 2 0.118 0.966 0.016 0.984
#> GSM155492 2 0.118 0.966 0.016 0.984
#> GSM155496 2 0.118 0.966 0.016 0.984
#> GSM155500 2 0.000 0.960 0.000 1.000
#> GSM155504 2 0.000 0.960 0.000 1.000
#> GSM155450 2 0.118 0.966 0.016 0.984
#> GSM155453 2 0.118 0.966 0.016 0.984
#> GSM155457 2 0.402 0.902 0.080 0.920
#> GSM155461 1 0.605 0.988 0.852 0.148
#> GSM155465 1 0.605 0.988 0.852 0.148
#> GSM155469 1 0.605 0.988 0.852 0.148
#> GSM155473 1 0.605 0.988 0.852 0.148
#> GSM155477 1 0.605 0.988 0.852 0.148
#> GSM155481 1 0.605 0.988 0.852 0.148
#> GSM155485 2 0.118 0.966 0.016 0.984
#> GSM155489 2 0.118 0.966 0.016 0.984
#> GSM155493 2 0.118 0.966 0.016 0.984
#> GSM155497 2 0.118 0.966 0.016 0.984
#> GSM155501 2 0.000 0.960 0.000 1.000
#> GSM155505 2 0.000 0.960 0.000 1.000
#> GSM155451 2 0.118 0.966 0.016 0.984
#> GSM155454 2 0.118 0.966 0.016 0.984
#> GSM155458 2 0.242 0.947 0.040 0.960
#> GSM155462 1 0.605 0.988 0.852 0.148
#> GSM155466 1 0.605 0.988 0.852 0.148
#> GSM155470 1 0.605 0.988 0.852 0.148
#> GSM155474 1 0.605 0.988 0.852 0.148
#> GSM155478 2 0.605 0.822 0.148 0.852
#> GSM155482 2 0.605 0.822 0.148 0.852
#> GSM155486 2 0.118 0.966 0.016 0.984
#> GSM155490 2 0.605 0.822 0.148 0.852
#> GSM155494 2 0.118 0.966 0.016 0.984
#> GSM155498 2 0.118 0.966 0.016 0.984
#> GSM155502 2 0.000 0.960 0.000 1.000
#> GSM155506 2 0.000 0.960 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 1 0.5426 0.838 0.820 0.092 0.088
#> GSM155452 1 0.5426 0.838 0.820 0.092 0.088
#> GSM155455 1 0.5346 0.841 0.824 0.088 0.088
#> GSM155459 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155463 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155467 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155471 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155475 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155479 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155483 3 0.0000 0.932 0.000 0.000 1.000
#> GSM155487 2 0.2796 1.000 0.000 0.908 0.092
#> GSM155491 3 0.0000 0.932 0.000 0.000 1.000
#> GSM155495 3 0.0000 0.932 0.000 0.000 1.000
#> GSM155499 3 0.4121 0.877 0.000 0.168 0.832
#> GSM155503 3 0.4121 0.877 0.000 0.168 0.832
#> GSM155449 1 0.5426 0.838 0.820 0.092 0.088
#> GSM155456 1 0.5346 0.841 0.824 0.088 0.088
#> GSM155460 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155464 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155468 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155472 1 0.0747 0.920 0.984 0.016 0.000
#> GSM155476 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155480 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155484 3 0.0000 0.932 0.000 0.000 1.000
#> GSM155488 3 0.0237 0.930 0.000 0.004 0.996
#> GSM155492 3 0.0000 0.932 0.000 0.000 1.000
#> GSM155496 3 0.0000 0.932 0.000 0.000 1.000
#> GSM155500 3 0.4121 0.877 0.000 0.168 0.832
#> GSM155504 3 0.4121 0.877 0.000 0.168 0.832
#> GSM155450 1 0.5426 0.838 0.820 0.092 0.088
#> GSM155453 1 0.5426 0.838 0.820 0.092 0.088
#> GSM155457 1 0.5346 0.841 0.824 0.088 0.088
#> GSM155461 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155465 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155469 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155473 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155477 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155481 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155485 3 0.0000 0.932 0.000 0.000 1.000
#> GSM155489 3 0.0000 0.932 0.000 0.000 1.000
#> GSM155493 3 0.0000 0.932 0.000 0.000 1.000
#> GSM155497 3 0.0000 0.932 0.000 0.000 1.000
#> GSM155501 3 0.4121 0.877 0.000 0.168 0.832
#> GSM155505 3 0.4121 0.877 0.000 0.168 0.832
#> GSM155451 1 0.5426 0.838 0.820 0.092 0.088
#> GSM155454 1 0.6510 0.770 0.756 0.156 0.088
#> GSM155458 1 0.5346 0.841 0.824 0.088 0.088
#> GSM155462 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155466 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155470 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155474 1 0.0000 0.927 1.000 0.000 0.000
#> GSM155478 2 0.2796 1.000 0.000 0.908 0.092
#> GSM155482 2 0.2796 1.000 0.000 0.908 0.092
#> GSM155486 3 0.0000 0.932 0.000 0.000 1.000
#> GSM155490 2 0.2796 1.000 0.000 0.908 0.092
#> GSM155494 3 0.0000 0.932 0.000 0.000 1.000
#> GSM155498 3 0.0000 0.932 0.000 0.000 1.000
#> GSM155502 3 0.4121 0.877 0.000 0.168 0.832
#> GSM155506 3 0.4121 0.877 0.000 0.168 0.832
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 2 0.4164 0.735 0.000 0.736 0.000 0.264
#> GSM155452 2 0.4164 0.735 0.000 0.736 0.000 0.264
#> GSM155455 2 0.7627 0.496 0.272 0.472 0.000 0.256
#> GSM155459 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155463 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155467 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155471 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155475 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155479 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155483 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM155487 4 0.2149 1.000 0.000 0.000 0.088 0.912
#> GSM155491 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM155495 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM155499 2 0.0817 0.735 0.000 0.976 0.024 0.000
#> GSM155503 2 0.0817 0.735 0.000 0.976 0.024 0.000
#> GSM155449 2 0.4164 0.735 0.000 0.736 0.000 0.264
#> GSM155456 2 0.7627 0.496 0.272 0.472 0.000 0.256
#> GSM155460 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155464 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155468 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155472 1 0.1302 0.947 0.956 0.000 0.000 0.044
#> GSM155476 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155480 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155484 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM155488 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM155492 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM155496 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM155500 2 0.0817 0.735 0.000 0.976 0.024 0.000
#> GSM155504 2 0.0817 0.735 0.000 0.976 0.024 0.000
#> GSM155450 2 0.4164 0.735 0.000 0.736 0.000 0.264
#> GSM155453 2 0.4164 0.735 0.000 0.736 0.000 0.264
#> GSM155457 2 0.7627 0.496 0.272 0.472 0.000 0.256
#> GSM155461 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155465 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155469 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155473 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155477 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155481 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155485 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM155489 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM155493 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM155497 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM155501 2 0.0817 0.735 0.000 0.976 0.024 0.000
#> GSM155505 2 0.0817 0.735 0.000 0.976 0.024 0.000
#> GSM155451 2 0.4164 0.735 0.000 0.736 0.000 0.264
#> GSM155454 2 0.4164 0.735 0.000 0.736 0.000 0.264
#> GSM155458 2 0.7627 0.496 0.272 0.472 0.000 0.256
#> GSM155462 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155466 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155470 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM155478 4 0.2149 1.000 0.000 0.000 0.088 0.912
#> GSM155482 4 0.2149 1.000 0.000 0.000 0.088 0.912
#> GSM155486 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM155490 4 0.2149 1.000 0.000 0.000 0.088 0.912
#> GSM155494 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM155498 3 0.0000 1.000 0.000 0.000 1.000 0.000
#> GSM155502 2 0.0817 0.735 0.000 0.976 0.024 0.000
#> GSM155506 2 0.0817 0.735 0.000 0.976 0.024 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.0000 0.998 0.000 0 0 1.000 0
#> GSM155452 4 0.0000 0.998 0.000 0 0 1.000 0
#> GSM155455 4 0.0162 0.996 0.004 0 0 0.996 0
#> GSM155459 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155463 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155467 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155471 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155475 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155479 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155483 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM155487 5 0.0000 1.000 0.000 0 0 0.000 1
#> GSM155491 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM155495 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM155499 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM155503 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM155449 4 0.0000 0.998 0.000 0 0 1.000 0
#> GSM155456 4 0.0162 0.996 0.004 0 0 0.996 0
#> GSM155460 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155464 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155468 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155472 1 0.0404 0.988 0.988 0 0 0.012 0
#> GSM155476 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155480 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155484 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM155488 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM155492 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM155496 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM155500 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM155504 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM155450 4 0.0000 0.998 0.000 0 0 1.000 0
#> GSM155453 4 0.0000 0.998 0.000 0 0 1.000 0
#> GSM155457 4 0.0162 0.996 0.004 0 0 0.996 0
#> GSM155461 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155465 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155469 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155473 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155477 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155481 1 0.0162 0.995 0.996 0 0 0.004 0
#> GSM155485 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM155489 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM155493 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM155497 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM155501 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM155505 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM155451 4 0.0000 0.998 0.000 0 0 1.000 0
#> GSM155454 4 0.0000 0.998 0.000 0 0 1.000 0
#> GSM155458 4 0.0162 0.996 0.004 0 0 0.996 0
#> GSM155462 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155466 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155470 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155474 1 0.0000 0.999 1.000 0 0 0.000 0
#> GSM155478 5 0.0000 1.000 0.000 0 0 0.000 1
#> GSM155482 5 0.0000 1.000 0.000 0 0 0.000 1
#> GSM155486 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM155490 5 0.0000 1.000 0.000 0 0 0.000 1
#> GSM155494 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM155498 3 0.0000 1.000 0.000 0 1 0.000 0
#> GSM155502 2 0.0000 1.000 0.000 1 0 0.000 0
#> GSM155506 2 0.0000 1.000 0.000 1 0 0.000 0
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0
#> GSM155452 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0
#> GSM155455 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0
#> GSM155459 1 0.0146 0.996 0.996 0 0.000 0.004 0.000 0
#> GSM155463 1 0.0000 0.998 1.000 0 0.000 0.000 0.000 0
#> GSM155467 1 0.0000 0.998 1.000 0 0.000 0.000 0.000 0
#> GSM155471 1 0.0000 0.998 1.000 0 0.000 0.000 0.000 0
#> GSM155475 1 0.0000 0.998 1.000 0 0.000 0.000 0.000 0
#> GSM155479 1 0.0000 0.998 1.000 0 0.000 0.000 0.000 0
#> GSM155483 5 0.0000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM155487 6 0.0000 1.000 0.000 0 0.000 0.000 0.000 1
#> GSM155491 3 0.0000 0.949 0.000 0 1.000 0.000 0.000 0
#> GSM155495 5 0.0000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM155499 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM155503 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM155449 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0
#> GSM155456 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0
#> GSM155460 1 0.0000 0.998 1.000 0 0.000 0.000 0.000 0
#> GSM155464 1 0.0000 0.998 1.000 0 0.000 0.000 0.000 0
#> GSM155468 1 0.0000 0.998 1.000 0 0.000 0.000 0.000 0
#> GSM155472 1 0.0260 0.991 0.992 0 0.000 0.008 0.000 0
#> GSM155476 1 0.0146 0.996 0.996 0 0.000 0.004 0.000 0
#> GSM155480 1 0.0146 0.996 0.996 0 0.000 0.004 0.000 0
#> GSM155484 5 0.0000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM155488 5 0.0000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM155492 3 0.2003 0.878 0.000 0 0.884 0.000 0.116 0
#> GSM155496 3 0.2378 0.844 0.000 0 0.848 0.000 0.152 0
#> GSM155500 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM155504 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM155450 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0
#> GSM155453 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0
#> GSM155457 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0
#> GSM155461 1 0.0000 0.998 1.000 0 0.000 0.000 0.000 0
#> GSM155465 1 0.0000 0.998 1.000 0 0.000 0.000 0.000 0
#> GSM155469 1 0.0146 0.996 0.996 0 0.000 0.004 0.000 0
#> GSM155473 1 0.0000 0.998 1.000 0 0.000 0.000 0.000 0
#> GSM155477 1 0.0000 0.998 1.000 0 0.000 0.000 0.000 0
#> GSM155481 1 0.0146 0.996 0.996 0 0.000 0.004 0.000 0
#> GSM155485 5 0.0000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM155489 5 0.0000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM155493 3 0.0000 0.949 0.000 0 1.000 0.000 0.000 0
#> GSM155497 3 0.0000 0.949 0.000 0 1.000 0.000 0.000 0
#> GSM155501 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM155505 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM155451 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0
#> GSM155454 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0
#> GSM155458 4 0.0000 1.000 0.000 0 0.000 1.000 0.000 0
#> GSM155462 1 0.0000 0.998 1.000 0 0.000 0.000 0.000 0
#> GSM155466 1 0.0000 0.998 1.000 0 0.000 0.000 0.000 0
#> GSM155470 1 0.0146 0.996 0.996 0 0.000 0.004 0.000 0
#> GSM155474 1 0.0000 0.998 1.000 0 0.000 0.000 0.000 0
#> GSM155478 6 0.0000 1.000 0.000 0 0.000 0.000 0.000 1
#> GSM155482 6 0.0000 1.000 0.000 0 0.000 0.000 0.000 1
#> GSM155486 5 0.0000 1.000 0.000 0 0.000 0.000 1.000 0
#> GSM155490 6 0.0000 1.000 0.000 0 0.000 0.000 0.000 1
#> GSM155494 3 0.0000 0.949 0.000 0 1.000 0.000 0.000 0
#> GSM155498 3 0.0000 0.949 0.000 0 1.000 0.000 0.000 0
#> GSM155502 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
#> GSM155506 2 0.0000 1.000 0.000 1 0.000 0.000 0.000 0
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 time(p) k
#> CV:mclust 59 0.800 2
#> CV:mclust 59 0.377 3
#> CV:mclust 55 0.643 4
#> CV:mclust 59 0.856 5
#> CV:mclust 59 0.939 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 59 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.930 0.957 0.979 0.4947 0.499 0.499
#> 3 3 0.649 0.759 0.852 0.2466 0.777 0.580
#> 4 4 0.897 0.925 0.952 0.1261 0.964 0.894
#> 5 5 0.912 0.908 0.944 0.0909 0.846 0.561
#> 6 6 0.940 0.934 0.941 0.0396 0.972 0.883
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 5
There is also optional best \(k\) = 2 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 2 0.0000 0.953 0.000 1.000
#> GSM155452 2 0.0000 0.953 0.000 1.000
#> GSM155455 1 0.2423 0.957 0.960 0.040
#> GSM155459 1 0.0000 0.998 1.000 0.000
#> GSM155463 1 0.0000 0.998 1.000 0.000
#> GSM155467 1 0.0000 0.998 1.000 0.000
#> GSM155471 1 0.0000 0.998 1.000 0.000
#> GSM155475 1 0.0000 0.998 1.000 0.000
#> GSM155479 1 0.0000 0.998 1.000 0.000
#> GSM155483 2 0.9427 0.502 0.360 0.640
#> GSM155487 2 0.0000 0.953 0.000 1.000
#> GSM155491 1 0.0000 0.998 1.000 0.000
#> GSM155495 2 0.7602 0.751 0.220 0.780
#> GSM155499 2 0.0000 0.953 0.000 1.000
#> GSM155503 2 0.0000 0.953 0.000 1.000
#> GSM155449 2 0.0000 0.953 0.000 1.000
#> GSM155456 1 0.0000 0.998 1.000 0.000
#> GSM155460 1 0.0000 0.998 1.000 0.000
#> GSM155464 1 0.0000 0.998 1.000 0.000
#> GSM155468 1 0.0000 0.998 1.000 0.000
#> GSM155472 1 0.0000 0.998 1.000 0.000
#> GSM155476 1 0.0000 0.998 1.000 0.000
#> GSM155480 1 0.0000 0.998 1.000 0.000
#> GSM155484 2 0.6887 0.795 0.184 0.816
#> GSM155488 2 0.0000 0.953 0.000 1.000
#> GSM155492 1 0.0000 0.998 1.000 0.000
#> GSM155496 1 0.2043 0.965 0.968 0.032
#> GSM155500 2 0.0000 0.953 0.000 1.000
#> GSM155504 2 0.0000 0.953 0.000 1.000
#> GSM155450 2 0.0000 0.953 0.000 1.000
#> GSM155453 2 0.0000 0.953 0.000 1.000
#> GSM155457 1 0.0000 0.998 1.000 0.000
#> GSM155461 1 0.0000 0.998 1.000 0.000
#> GSM155465 1 0.0000 0.998 1.000 0.000
#> GSM155469 1 0.0000 0.998 1.000 0.000
#> GSM155473 1 0.0000 0.998 1.000 0.000
#> GSM155477 1 0.0000 0.998 1.000 0.000
#> GSM155481 1 0.0000 0.998 1.000 0.000
#> GSM155485 2 0.7883 0.728 0.236 0.764
#> GSM155489 2 0.0000 0.953 0.000 1.000
#> GSM155493 1 0.0000 0.998 1.000 0.000
#> GSM155497 1 0.0000 0.998 1.000 0.000
#> GSM155501 2 0.0000 0.953 0.000 1.000
#> GSM155505 2 0.0000 0.953 0.000 1.000
#> GSM155451 2 0.0000 0.953 0.000 1.000
#> GSM155454 2 0.0000 0.953 0.000 1.000
#> GSM155458 1 0.0000 0.998 1.000 0.000
#> GSM155462 1 0.0000 0.998 1.000 0.000
#> GSM155466 1 0.0000 0.998 1.000 0.000
#> GSM155470 1 0.0000 0.998 1.000 0.000
#> GSM155474 1 0.0000 0.998 1.000 0.000
#> GSM155478 2 0.0672 0.948 0.008 0.992
#> GSM155482 2 0.0672 0.948 0.008 0.992
#> GSM155486 2 0.6048 0.833 0.148 0.852
#> GSM155490 2 0.0376 0.951 0.004 0.996
#> GSM155494 1 0.0000 0.998 1.000 0.000
#> GSM155498 1 0.0000 0.998 1.000 0.000
#> GSM155502 2 0.0000 0.953 0.000 1.000
#> GSM155506 2 0.0000 0.953 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 2 0.0000 0.903 0.000 1.000 0.000
#> GSM155452 2 0.1182 0.889 0.012 0.976 0.012
#> GSM155455 1 0.5858 0.597 0.740 0.240 0.020
#> GSM155459 1 0.0237 0.947 0.996 0.000 0.004
#> GSM155463 1 0.0000 0.950 1.000 0.000 0.000
#> GSM155467 1 0.0000 0.950 1.000 0.000 0.000
#> GSM155471 1 0.0000 0.950 1.000 0.000 0.000
#> GSM155475 1 0.0000 0.950 1.000 0.000 0.000
#> GSM155479 1 0.0000 0.950 1.000 0.000 0.000
#> GSM155483 3 0.8614 0.607 0.228 0.172 0.600
#> GSM155487 2 0.6274 0.440 0.000 0.544 0.456
#> GSM155491 3 0.6286 0.443 0.464 0.000 0.536
#> GSM155495 3 0.8009 0.504 0.100 0.276 0.624
#> GSM155499 2 0.1411 0.905 0.000 0.964 0.036
#> GSM155503 2 0.1529 0.904 0.000 0.960 0.040
#> GSM155449 2 0.0592 0.899 0.000 0.988 0.012
#> GSM155456 1 0.2486 0.889 0.932 0.060 0.008
#> GSM155460 1 0.0000 0.950 1.000 0.000 0.000
#> GSM155464 1 0.0000 0.950 1.000 0.000 0.000
#> GSM155468 1 0.0829 0.940 0.984 0.004 0.012
#> GSM155472 1 0.4485 0.777 0.844 0.020 0.136
#> GSM155476 1 0.1182 0.934 0.976 0.012 0.012
#> GSM155480 1 0.0829 0.940 0.984 0.004 0.012
#> GSM155484 3 0.7104 0.382 0.032 0.360 0.608
#> GSM155488 2 0.4235 0.735 0.000 0.824 0.176
#> GSM155492 3 0.6416 0.571 0.376 0.008 0.616
#> GSM155496 3 0.6398 0.573 0.372 0.008 0.620
#> GSM155500 2 0.1289 0.906 0.000 0.968 0.032
#> GSM155504 2 0.1529 0.904 0.000 0.960 0.040
#> GSM155450 2 0.0592 0.899 0.000 0.988 0.012
#> GSM155453 2 0.0424 0.900 0.000 0.992 0.008
#> GSM155457 1 0.3989 0.806 0.864 0.124 0.012
#> GSM155461 1 0.0000 0.950 1.000 0.000 0.000
#> GSM155465 1 0.0000 0.950 1.000 0.000 0.000
#> GSM155469 1 0.0424 0.945 0.992 0.000 0.008
#> GSM155473 1 0.0000 0.950 1.000 0.000 0.000
#> GSM155477 1 0.0000 0.950 1.000 0.000 0.000
#> GSM155481 1 0.0000 0.950 1.000 0.000 0.000
#> GSM155485 3 0.8230 0.426 0.088 0.348 0.564
#> GSM155489 3 0.6079 0.311 0.000 0.388 0.612
#> GSM155493 3 0.6282 0.563 0.384 0.004 0.612
#> GSM155497 3 0.6079 0.558 0.388 0.000 0.612
#> GSM155501 2 0.1529 0.904 0.000 0.960 0.040
#> GSM155505 2 0.0892 0.906 0.000 0.980 0.020
#> GSM155451 2 0.0747 0.897 0.000 0.984 0.016
#> GSM155454 2 0.0747 0.905 0.000 0.984 0.016
#> GSM155458 1 0.5551 0.652 0.768 0.212 0.020
#> GSM155462 1 0.0237 0.947 0.996 0.000 0.004
#> GSM155466 1 0.0000 0.950 1.000 0.000 0.000
#> GSM155470 1 0.0000 0.950 1.000 0.000 0.000
#> GSM155474 1 0.0000 0.950 1.000 0.000 0.000
#> GSM155478 3 0.9539 -0.116 0.204 0.336 0.460
#> GSM155482 3 0.9479 -0.139 0.192 0.348 0.460
#> GSM155486 3 0.6975 0.384 0.028 0.356 0.616
#> GSM155490 2 0.6280 0.438 0.000 0.540 0.460
#> GSM155494 3 0.6140 0.538 0.404 0.000 0.596
#> GSM155498 3 0.6302 0.409 0.480 0.000 0.520
#> GSM155502 2 0.1529 0.904 0.000 0.960 0.040
#> GSM155506 2 0.1529 0.904 0.000 0.960 0.040
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 2 0.1124 0.918 0.012 0.972 0.004 0.012
#> GSM155452 2 0.2161 0.891 0.048 0.932 0.004 0.016
#> GSM155455 1 0.3829 0.804 0.828 0.152 0.004 0.016
#> GSM155459 1 0.1302 0.950 0.956 0.000 0.044 0.000
#> GSM155463 1 0.0707 0.953 0.980 0.000 0.020 0.000
#> GSM155467 1 0.1302 0.950 0.956 0.000 0.044 0.000
#> GSM155471 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM155475 1 0.1302 0.950 0.956 0.000 0.044 0.000
#> GSM155479 1 0.1302 0.950 0.956 0.000 0.044 0.000
#> GSM155483 3 0.1888 0.911 0.000 0.044 0.940 0.016
#> GSM155487 4 0.0592 0.988 0.000 0.016 0.000 0.984
#> GSM155491 3 0.1474 0.895 0.052 0.000 0.948 0.000
#> GSM155495 3 0.0336 0.925 0.000 0.008 0.992 0.000
#> GSM155499 2 0.1888 0.933 0.000 0.940 0.044 0.016
#> GSM155503 2 0.2142 0.929 0.000 0.928 0.056 0.016
#> GSM155449 2 0.1471 0.912 0.024 0.960 0.004 0.012
#> GSM155456 1 0.2457 0.892 0.912 0.076 0.004 0.008
#> GSM155460 1 0.1302 0.950 0.956 0.000 0.044 0.000
#> GSM155464 1 0.0336 0.952 0.992 0.000 0.008 0.000
#> GSM155468 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM155472 1 0.1716 0.922 0.936 0.000 0.000 0.064
#> GSM155476 1 0.0469 0.946 0.988 0.012 0.000 0.000
#> GSM155480 1 0.0336 0.948 0.992 0.008 0.000 0.000
#> GSM155484 3 0.2450 0.896 0.000 0.072 0.912 0.016
#> GSM155488 2 0.3390 0.849 0.000 0.852 0.132 0.016
#> GSM155492 3 0.0592 0.925 0.016 0.000 0.984 0.000
#> GSM155496 3 0.0188 0.926 0.004 0.000 0.996 0.000
#> GSM155500 2 0.1975 0.932 0.000 0.936 0.048 0.016
#> GSM155504 2 0.2142 0.929 0.000 0.928 0.056 0.016
#> GSM155450 2 0.2075 0.895 0.044 0.936 0.004 0.016
#> GSM155453 2 0.1985 0.899 0.040 0.940 0.004 0.016
#> GSM155457 1 0.3350 0.846 0.864 0.116 0.004 0.016
#> GSM155461 1 0.1302 0.950 0.956 0.000 0.044 0.000
#> GSM155465 1 0.1211 0.951 0.960 0.000 0.040 0.000
#> GSM155469 1 0.0000 0.951 1.000 0.000 0.000 0.000
#> GSM155473 1 0.1211 0.951 0.960 0.000 0.040 0.000
#> GSM155477 1 0.1022 0.952 0.968 0.000 0.032 0.000
#> GSM155481 1 0.0469 0.953 0.988 0.000 0.012 0.000
#> GSM155485 3 0.3335 0.837 0.000 0.128 0.856 0.016
#> GSM155489 3 0.2593 0.889 0.000 0.080 0.904 0.016
#> GSM155493 3 0.0592 0.925 0.016 0.000 0.984 0.000
#> GSM155497 3 0.0895 0.923 0.020 0.000 0.976 0.004
#> GSM155501 2 0.2060 0.931 0.000 0.932 0.052 0.016
#> GSM155505 2 0.1610 0.932 0.000 0.952 0.032 0.016
#> GSM155451 2 0.1114 0.918 0.016 0.972 0.004 0.008
#> GSM155454 2 0.0376 0.923 0.000 0.992 0.004 0.004
#> GSM155458 1 0.3730 0.814 0.836 0.144 0.004 0.016
#> GSM155462 1 0.1302 0.950 0.956 0.000 0.044 0.000
#> GSM155466 1 0.1118 0.952 0.964 0.000 0.036 0.000
#> GSM155470 1 0.0188 0.950 0.996 0.000 0.000 0.004
#> GSM155474 1 0.0188 0.950 0.996 0.000 0.000 0.004
#> GSM155478 4 0.0376 0.990 0.004 0.004 0.000 0.992
#> GSM155482 4 0.0376 0.990 0.004 0.004 0.000 0.992
#> GSM155486 3 0.2450 0.896 0.000 0.072 0.912 0.016
#> GSM155490 4 0.0592 0.988 0.000 0.016 0.000 0.984
#> GSM155494 3 0.1022 0.915 0.032 0.000 0.968 0.000
#> GSM155498 3 0.1743 0.889 0.056 0.000 0.940 0.004
#> GSM155502 2 0.2060 0.931 0.000 0.932 0.052 0.016
#> GSM155506 2 0.2060 0.931 0.000 0.932 0.052 0.016
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.3424 0.814 0.000 0.240 0.000 0.760 0.000
#> GSM155452 4 0.0609 0.844 0.000 0.020 0.000 0.980 0.000
#> GSM155455 4 0.1502 0.864 0.004 0.056 0.000 0.940 0.000
#> GSM155459 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155463 1 0.0290 0.971 0.992 0.008 0.000 0.000 0.000
#> GSM155467 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155479 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155483 2 0.5588 0.543 0.104 0.604 0.292 0.000 0.000
#> GSM155487 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM155491 3 0.0510 0.977 0.016 0.000 0.984 0.000 0.000
#> GSM155495 3 0.0963 0.947 0.000 0.036 0.964 0.000 0.000
#> GSM155499 2 0.0162 0.901 0.000 0.996 0.000 0.004 0.000
#> GSM155503 2 0.0162 0.901 0.000 0.996 0.000 0.004 0.000
#> GSM155449 4 0.2813 0.858 0.000 0.168 0.000 0.832 0.000
#> GSM155456 4 0.1608 0.810 0.072 0.000 0.000 0.928 0.000
#> GSM155460 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155464 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155468 1 0.0290 0.971 0.992 0.008 0.000 0.000 0.000
#> GSM155472 1 0.6092 0.313 0.564 0.000 0.000 0.180 0.256
#> GSM155476 1 0.0703 0.957 0.976 0.024 0.000 0.000 0.000
#> GSM155480 1 0.0510 0.965 0.984 0.016 0.000 0.000 0.000
#> GSM155484 2 0.3772 0.798 0.036 0.792 0.172 0.000 0.000
#> GSM155488 2 0.0963 0.890 0.000 0.964 0.036 0.000 0.000
#> GSM155492 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
#> GSM155496 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000
#> GSM155500 2 0.0162 0.901 0.000 0.996 0.000 0.004 0.000
#> GSM155504 2 0.0162 0.901 0.000 0.996 0.000 0.004 0.000
#> GSM155450 4 0.1908 0.874 0.000 0.092 0.000 0.908 0.000
#> GSM155453 4 0.2280 0.873 0.000 0.120 0.000 0.880 0.000
#> GSM155457 4 0.1956 0.814 0.076 0.008 0.000 0.916 0.000
#> GSM155461 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155465 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155469 1 0.0510 0.965 0.984 0.016 0.000 0.000 0.000
#> GSM155473 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155481 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155485 2 0.3115 0.839 0.036 0.852 0.112 0.000 0.000
#> GSM155489 2 0.2561 0.840 0.000 0.856 0.144 0.000 0.000
#> GSM155493 3 0.0162 0.985 0.004 0.000 0.996 0.000 0.000
#> GSM155497 3 0.0324 0.984 0.004 0.000 0.992 0.004 0.000
#> GSM155501 2 0.0162 0.901 0.000 0.996 0.000 0.004 0.000
#> GSM155505 2 0.0162 0.901 0.000 0.996 0.000 0.004 0.000
#> GSM155451 4 0.3480 0.809 0.000 0.248 0.000 0.752 0.000
#> GSM155454 4 0.3999 0.668 0.000 0.344 0.000 0.656 0.000
#> GSM155458 4 0.2077 0.873 0.008 0.084 0.000 0.908 0.000
#> GSM155462 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155466 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155470 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.976 1.000 0.000 0.000 0.000 0.000
#> GSM155478 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM155482 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM155486 2 0.3724 0.778 0.020 0.776 0.204 0.000 0.000
#> GSM155490 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM155494 3 0.0162 0.985 0.004 0.000 0.996 0.000 0.000
#> GSM155498 3 0.0671 0.976 0.016 0.000 0.980 0.004 0.000
#> GSM155502 2 0.0162 0.901 0.000 0.996 0.000 0.004 0.000
#> GSM155506 2 0.0162 0.901 0.000 0.996 0.000 0.004 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.2617 0.895 0.004 0.080 0.000 0.876 0.040 0.000
#> GSM155452 4 0.0806 0.940 0.000 0.000 0.008 0.972 0.020 0.000
#> GSM155455 4 0.0405 0.946 0.004 0.008 0.000 0.988 0.000 0.000
#> GSM155459 1 0.1155 0.959 0.956 0.000 0.004 0.004 0.036 0.000
#> GSM155463 1 0.0777 0.964 0.972 0.000 0.004 0.000 0.024 0.000
#> GSM155467 1 0.0291 0.969 0.992 0.000 0.004 0.000 0.004 0.000
#> GSM155471 1 0.0146 0.969 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM155475 1 0.0603 0.967 0.980 0.000 0.004 0.000 0.016 0.000
#> GSM155479 1 0.0692 0.967 0.976 0.000 0.000 0.004 0.020 0.000
#> GSM155483 5 0.4063 0.862 0.020 0.052 0.160 0.000 0.768 0.000
#> GSM155487 6 0.0146 0.998 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM155491 3 0.0000 0.931 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155495 3 0.3629 0.554 0.000 0.012 0.712 0.000 0.276 0.000
#> GSM155499 2 0.0777 0.972 0.000 0.972 0.000 0.024 0.004 0.000
#> GSM155503 2 0.0520 0.989 0.000 0.984 0.000 0.008 0.008 0.000
#> GSM155449 4 0.3204 0.837 0.004 0.144 0.000 0.820 0.032 0.000
#> GSM155456 4 0.0777 0.935 0.024 0.000 0.000 0.972 0.004 0.000
#> GSM155460 1 0.1082 0.960 0.956 0.000 0.004 0.000 0.040 0.000
#> GSM155464 1 0.0777 0.964 0.972 0.000 0.004 0.000 0.024 0.000
#> GSM155468 1 0.0291 0.969 0.992 0.000 0.004 0.000 0.004 0.000
#> GSM155472 1 0.3991 0.731 0.764 0.000 0.000 0.044 0.016 0.176
#> GSM155476 1 0.1350 0.956 0.952 0.020 0.000 0.008 0.020 0.000
#> GSM155480 1 0.0692 0.967 0.976 0.000 0.000 0.004 0.020 0.000
#> GSM155484 5 0.4093 0.902 0.008 0.088 0.140 0.000 0.764 0.000
#> GSM155488 5 0.3912 0.600 0.000 0.340 0.012 0.000 0.648 0.000
#> GSM155492 3 0.0547 0.929 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM155496 3 0.1349 0.907 0.004 0.000 0.940 0.000 0.056 0.000
#> GSM155500 2 0.0260 0.992 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM155504 2 0.0405 0.987 0.000 0.988 0.000 0.004 0.008 0.000
#> GSM155450 4 0.0767 0.946 0.004 0.012 0.000 0.976 0.008 0.000
#> GSM155453 4 0.1138 0.943 0.000 0.012 0.004 0.960 0.024 0.000
#> GSM155457 4 0.0603 0.941 0.016 0.000 0.000 0.980 0.004 0.000
#> GSM155461 1 0.0603 0.968 0.980 0.000 0.004 0.000 0.016 0.000
#> GSM155465 1 0.0692 0.966 0.976 0.000 0.004 0.000 0.020 0.000
#> GSM155469 1 0.0146 0.969 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM155473 1 0.0291 0.969 0.992 0.000 0.004 0.000 0.004 0.000
#> GSM155477 1 0.0692 0.967 0.976 0.000 0.000 0.004 0.020 0.000
#> GSM155481 1 0.0622 0.967 0.980 0.000 0.000 0.008 0.012 0.000
#> GSM155485 5 0.4002 0.902 0.004 0.096 0.132 0.000 0.768 0.000
#> GSM155489 5 0.4279 0.881 0.000 0.128 0.140 0.000 0.732 0.000
#> GSM155493 3 0.0632 0.927 0.000 0.000 0.976 0.000 0.024 0.000
#> GSM155497 3 0.0547 0.924 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM155501 2 0.0146 0.990 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM155505 2 0.0260 0.992 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM155451 4 0.1268 0.940 0.004 0.036 0.000 0.952 0.008 0.000
#> GSM155454 4 0.2306 0.893 0.000 0.016 0.004 0.888 0.092 0.000
#> GSM155458 4 0.0520 0.946 0.008 0.008 0.000 0.984 0.000 0.000
#> GSM155462 1 0.1956 0.921 0.908 0.000 0.008 0.004 0.080 0.000
#> GSM155466 1 0.0692 0.966 0.976 0.000 0.004 0.000 0.020 0.000
#> GSM155470 1 0.0436 0.969 0.988 0.000 0.004 0.004 0.004 0.000
#> GSM155474 1 0.0405 0.969 0.988 0.000 0.004 0.000 0.008 0.000
#> GSM155478 6 0.0000 0.998 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM155482 6 0.0000 0.998 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM155486 5 0.4141 0.902 0.008 0.092 0.140 0.000 0.760 0.000
#> GSM155490 6 0.0146 0.998 0.000 0.000 0.000 0.000 0.004 0.996
#> GSM155494 3 0.0000 0.931 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155498 3 0.0547 0.921 0.000 0.000 0.980 0.000 0.020 0.000
#> GSM155502 2 0.0260 0.992 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM155506 2 0.0405 0.991 0.000 0.988 0.000 0.008 0.004 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n time(p) k
#> CV:NMF 59 0.787 2
#> CV:NMF 49 0.999 3
#> CV:NMF 59 0.678 4
#> CV:NMF 58 0.870 5
#> CV:NMF 59 0.945 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 59 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.484 0.946 0.887 0.4167 0.509 0.509
#> 3 3 0.843 0.942 0.935 0.4546 0.874 0.752
#> 4 4 0.807 0.932 0.924 0.1559 0.897 0.731
#> 5 5 0.935 0.944 0.964 0.0648 0.974 0.908
#> 6 6 0.947 0.966 0.964 0.0420 0.963 0.853
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 5
There is also optional best \(k\) = 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 2 0.0376 0.962 0.004 0.996
#> GSM155452 2 0.0376 0.962 0.004 0.996
#> GSM155455 2 0.3733 0.904 0.072 0.928
#> GSM155459 1 0.7376 0.975 0.792 0.208
#> GSM155463 1 0.7376 0.975 0.792 0.208
#> GSM155467 1 0.7376 0.975 0.792 0.208
#> GSM155471 1 0.7376 0.975 0.792 0.208
#> GSM155475 1 0.7376 0.975 0.792 0.208
#> GSM155479 1 0.7376 0.975 0.792 0.208
#> GSM155483 2 0.0000 0.962 0.000 1.000
#> GSM155487 2 0.7056 0.749 0.192 0.808
#> GSM155491 2 0.2423 0.944 0.040 0.960
#> GSM155495 2 0.2423 0.944 0.040 0.960
#> GSM155499 2 0.0000 0.962 0.000 1.000
#> GSM155503 2 0.0000 0.962 0.000 1.000
#> GSM155449 2 0.0376 0.962 0.004 0.996
#> GSM155456 2 0.3733 0.904 0.072 0.928
#> GSM155460 1 0.7376 0.975 0.792 0.208
#> GSM155464 1 0.7376 0.975 0.792 0.208
#> GSM155468 1 0.7376 0.975 0.792 0.208
#> GSM155472 1 0.7376 0.975 0.792 0.208
#> GSM155476 1 0.7376 0.975 0.792 0.208
#> GSM155480 1 0.7376 0.975 0.792 0.208
#> GSM155484 2 0.0000 0.962 0.000 1.000
#> GSM155488 2 0.0000 0.962 0.000 1.000
#> GSM155492 2 0.2423 0.944 0.040 0.960
#> GSM155496 2 0.2423 0.944 0.040 0.960
#> GSM155500 2 0.0000 0.962 0.000 1.000
#> GSM155504 2 0.0000 0.962 0.000 1.000
#> GSM155450 2 0.0376 0.962 0.004 0.996
#> GSM155453 2 0.0376 0.962 0.004 0.996
#> GSM155457 2 0.3733 0.904 0.072 0.928
#> GSM155461 1 0.7376 0.975 0.792 0.208
#> GSM155465 1 0.7376 0.975 0.792 0.208
#> GSM155469 1 0.7376 0.975 0.792 0.208
#> GSM155473 1 0.7376 0.975 0.792 0.208
#> GSM155477 1 0.7376 0.975 0.792 0.208
#> GSM155481 1 0.7376 0.975 0.792 0.208
#> GSM155485 2 0.0000 0.962 0.000 1.000
#> GSM155489 2 0.0000 0.962 0.000 1.000
#> GSM155493 2 0.2423 0.944 0.040 0.960
#> GSM155497 2 0.2423 0.944 0.040 0.960
#> GSM155501 2 0.0000 0.962 0.000 1.000
#> GSM155505 2 0.0000 0.962 0.000 1.000
#> GSM155451 2 0.0376 0.962 0.004 0.996
#> GSM155454 2 0.0376 0.962 0.004 0.996
#> GSM155458 2 0.3733 0.904 0.072 0.928
#> GSM155462 1 0.7376 0.975 0.792 0.208
#> GSM155466 1 0.7376 0.975 0.792 0.208
#> GSM155470 1 0.7376 0.975 0.792 0.208
#> GSM155474 1 0.7376 0.975 0.792 0.208
#> GSM155478 1 0.2423 0.737 0.960 0.040
#> GSM155482 1 0.2423 0.737 0.960 0.040
#> GSM155486 2 0.0000 0.962 0.000 1.000
#> GSM155490 2 0.7056 0.749 0.192 0.808
#> GSM155494 2 0.2423 0.944 0.040 0.960
#> GSM155498 2 0.2423 0.944 0.040 0.960
#> GSM155502 2 0.0000 0.962 0.000 1.000
#> GSM155506 2 0.0000 0.962 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 2 0.118 0.947 0.012 0.976 0.012
#> GSM155452 2 0.118 0.947 0.012 0.976 0.012
#> GSM155455 2 0.312 0.901 0.080 0.908 0.012
#> GSM155459 1 0.000 0.971 1.000 0.000 0.000
#> GSM155463 1 0.000 0.971 1.000 0.000 0.000
#> GSM155467 1 0.000 0.971 1.000 0.000 0.000
#> GSM155471 1 0.000 0.971 1.000 0.000 0.000
#> GSM155475 1 0.000 0.971 1.000 0.000 0.000
#> GSM155479 1 0.000 0.971 1.000 0.000 0.000
#> GSM155483 2 0.186 0.934 0.000 0.948 0.052
#> GSM155487 2 0.529 0.743 0.000 0.732 0.268
#> GSM155491 3 0.510 1.000 0.248 0.000 0.752
#> GSM155495 3 0.510 1.000 0.248 0.000 0.752
#> GSM155499 2 0.000 0.948 0.000 1.000 0.000
#> GSM155503 2 0.000 0.948 0.000 1.000 0.000
#> GSM155449 2 0.118 0.947 0.012 0.976 0.012
#> GSM155456 2 0.312 0.901 0.080 0.908 0.012
#> GSM155460 1 0.000 0.971 1.000 0.000 0.000
#> GSM155464 1 0.000 0.971 1.000 0.000 0.000
#> GSM155468 1 0.000 0.971 1.000 0.000 0.000
#> GSM155472 1 0.000 0.971 1.000 0.000 0.000
#> GSM155476 1 0.000 0.971 1.000 0.000 0.000
#> GSM155480 1 0.000 0.971 1.000 0.000 0.000
#> GSM155484 2 0.186 0.934 0.000 0.948 0.052
#> GSM155488 2 0.186 0.934 0.000 0.948 0.052
#> GSM155492 3 0.510 1.000 0.248 0.000 0.752
#> GSM155496 3 0.510 1.000 0.248 0.000 0.752
#> GSM155500 2 0.000 0.948 0.000 1.000 0.000
#> GSM155504 2 0.000 0.948 0.000 1.000 0.000
#> GSM155450 2 0.118 0.947 0.012 0.976 0.012
#> GSM155453 2 0.118 0.947 0.012 0.976 0.012
#> GSM155457 2 0.312 0.901 0.080 0.908 0.012
#> GSM155461 1 0.000 0.971 1.000 0.000 0.000
#> GSM155465 1 0.000 0.971 1.000 0.000 0.000
#> GSM155469 1 0.000 0.971 1.000 0.000 0.000
#> GSM155473 1 0.000 0.971 1.000 0.000 0.000
#> GSM155477 1 0.000 0.971 1.000 0.000 0.000
#> GSM155481 1 0.000 0.971 1.000 0.000 0.000
#> GSM155485 2 0.186 0.934 0.000 0.948 0.052
#> GSM155489 2 0.186 0.934 0.000 0.948 0.052
#> GSM155493 3 0.510 1.000 0.248 0.000 0.752
#> GSM155497 3 0.510 1.000 0.248 0.000 0.752
#> GSM155501 2 0.000 0.948 0.000 1.000 0.000
#> GSM155505 2 0.000 0.948 0.000 1.000 0.000
#> GSM155451 2 0.118 0.947 0.012 0.976 0.012
#> GSM155454 2 0.118 0.947 0.012 0.976 0.012
#> GSM155458 2 0.312 0.901 0.080 0.908 0.012
#> GSM155462 1 0.000 0.971 1.000 0.000 0.000
#> GSM155466 1 0.000 0.971 1.000 0.000 0.000
#> GSM155470 1 0.000 0.971 1.000 0.000 0.000
#> GSM155474 1 0.000 0.971 1.000 0.000 0.000
#> GSM155478 1 0.510 0.653 0.752 0.000 0.248
#> GSM155482 1 0.510 0.653 0.752 0.000 0.248
#> GSM155486 2 0.186 0.934 0.000 0.948 0.052
#> GSM155490 2 0.529 0.743 0.000 0.732 0.268
#> GSM155494 3 0.510 1.000 0.248 0.000 0.752
#> GSM155498 3 0.510 1.000 0.248 0.000 0.752
#> GSM155502 2 0.000 0.948 0.000 1.000 0.000
#> GSM155506 2 0.000 0.948 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 4 0.000 0.960 0.000 0.000 0.000 1.000
#> GSM155452 4 0.000 0.960 0.000 0.000 0.000 1.000
#> GSM155455 4 0.179 0.928 0.068 0.000 0.000 0.932
#> GSM155459 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155463 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155467 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155471 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155475 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155479 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155483 2 0.000 0.883 0.000 1.000 0.000 0.000
#> GSM155487 2 0.376 0.748 0.000 0.784 0.216 0.000
#> GSM155491 3 0.404 1.000 0.248 0.000 0.752 0.000
#> GSM155495 3 0.404 1.000 0.248 0.000 0.752 0.000
#> GSM155499 2 0.317 0.886 0.000 0.840 0.000 0.160
#> GSM155503 2 0.317 0.886 0.000 0.840 0.000 0.160
#> GSM155449 4 0.000 0.960 0.000 0.000 0.000 1.000
#> GSM155456 4 0.179 0.928 0.068 0.000 0.000 0.932
#> GSM155460 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155464 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155468 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155472 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155476 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155480 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155484 2 0.000 0.883 0.000 1.000 0.000 0.000
#> GSM155488 2 0.000 0.883 0.000 1.000 0.000 0.000
#> GSM155492 3 0.404 1.000 0.248 0.000 0.752 0.000
#> GSM155496 3 0.404 1.000 0.248 0.000 0.752 0.000
#> GSM155500 2 0.317 0.886 0.000 0.840 0.000 0.160
#> GSM155504 2 0.317 0.886 0.000 0.840 0.000 0.160
#> GSM155450 4 0.000 0.960 0.000 0.000 0.000 1.000
#> GSM155453 4 0.000 0.960 0.000 0.000 0.000 1.000
#> GSM155457 4 0.179 0.928 0.068 0.000 0.000 0.932
#> GSM155461 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155465 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155469 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155473 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155477 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155481 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155485 2 0.000 0.883 0.000 1.000 0.000 0.000
#> GSM155489 2 0.000 0.883 0.000 1.000 0.000 0.000
#> GSM155493 3 0.404 1.000 0.248 0.000 0.752 0.000
#> GSM155497 3 0.404 1.000 0.248 0.000 0.752 0.000
#> GSM155501 2 0.317 0.886 0.000 0.840 0.000 0.160
#> GSM155505 2 0.317 0.886 0.000 0.840 0.000 0.160
#> GSM155451 4 0.000 0.960 0.000 0.000 0.000 1.000
#> GSM155454 4 0.000 0.960 0.000 0.000 0.000 1.000
#> GSM155458 4 0.179 0.928 0.068 0.000 0.000 0.932
#> GSM155462 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155466 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155470 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155474 1 0.000 0.971 1.000 0.000 0.000 0.000
#> GSM155478 1 0.404 0.653 0.752 0.000 0.248 0.000
#> GSM155482 1 0.404 0.653 0.752 0.000 0.248 0.000
#> GSM155486 2 0.000 0.883 0.000 1.000 0.000 0.000
#> GSM155490 2 0.376 0.748 0.000 0.784 0.216 0.000
#> GSM155494 3 0.404 1.000 0.248 0.000 0.752 0.000
#> GSM155498 3 0.404 1.000 0.248 0.000 0.752 0.000
#> GSM155502 2 0.317 0.886 0.000 0.840 0.000 0.160
#> GSM155506 2 0.317 0.886 0.000 0.840 0.000 0.160
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.0404 0.942 0.000 0.000 0 0.988 0.012
#> GSM155452 4 0.0404 0.942 0.000 0.000 0 0.988 0.012
#> GSM155455 4 0.1544 0.911 0.068 0.000 0 0.932 0.000
#> GSM155459 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155463 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155467 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155471 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155475 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155479 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155483 2 0.0000 0.858 0.000 1.000 0 0.000 0.000
#> GSM155487 2 0.3242 0.650 0.000 0.784 0 0.000 0.216
#> GSM155491 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155495 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155499 2 0.2997 0.874 0.000 0.840 0 0.148 0.012
#> GSM155503 2 0.2997 0.874 0.000 0.840 0 0.148 0.012
#> GSM155449 4 0.0404 0.942 0.000 0.000 0 0.988 0.012
#> GSM155456 4 0.1544 0.911 0.068 0.000 0 0.932 0.000
#> GSM155460 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155464 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155468 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155472 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155476 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155480 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155484 2 0.0000 0.858 0.000 1.000 0 0.000 0.000
#> GSM155488 2 0.0000 0.858 0.000 1.000 0 0.000 0.000
#> GSM155492 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155496 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155500 2 0.2997 0.874 0.000 0.840 0 0.148 0.012
#> GSM155504 2 0.2997 0.874 0.000 0.840 0 0.148 0.012
#> GSM155450 4 0.0000 0.947 0.000 0.000 0 1.000 0.000
#> GSM155453 4 0.0000 0.947 0.000 0.000 0 1.000 0.000
#> GSM155457 4 0.1544 0.911 0.068 0.000 0 0.932 0.000
#> GSM155461 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155465 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155469 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155473 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155477 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155481 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155485 2 0.0000 0.858 0.000 1.000 0 0.000 0.000
#> GSM155489 2 0.0000 0.858 0.000 1.000 0 0.000 0.000
#> GSM155493 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155497 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155501 2 0.2997 0.874 0.000 0.840 0 0.148 0.012
#> GSM155505 2 0.2997 0.874 0.000 0.840 0 0.148 0.012
#> GSM155451 4 0.0000 0.947 0.000 0.000 0 1.000 0.000
#> GSM155454 4 0.0000 0.947 0.000 0.000 0 1.000 0.000
#> GSM155458 4 0.1544 0.911 0.068 0.000 0 0.932 0.000
#> GSM155462 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155466 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155470 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155474 1 0.0000 1.000 1.000 0.000 0 0.000 0.000
#> GSM155478 5 0.0404 1.000 0.012 0.000 0 0.000 0.988
#> GSM155482 5 0.0404 1.000 0.012 0.000 0 0.000 0.988
#> GSM155486 2 0.0000 0.858 0.000 1.000 0 0.000 0.000
#> GSM155490 2 0.3242 0.650 0.000 0.784 0 0.000 0.216
#> GSM155494 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155498 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155502 2 0.2997 0.874 0.000 0.840 0 0.148 0.012
#> GSM155506 2 0.2997 0.874 0.000 0.840 0 0.148 0.012
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.2378 0.887 0.000 0.152 0 0.848 0.000 0.000
#> GSM155452 4 0.2378 0.887 0.000 0.152 0 0.848 0.000 0.000
#> GSM155455 4 0.0458 0.909 0.016 0.000 0 0.984 0.000 0.000
#> GSM155459 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155463 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155467 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155471 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155475 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155479 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155483 5 0.2823 0.918 0.000 0.204 0 0.000 0.796 0.000
#> GSM155487 5 0.1180 0.722 0.000 0.012 0 0.016 0.960 0.012
#> GSM155491 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM155495 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM155499 2 0.0000 1.000 0.000 1.000 0 0.000 0.000 0.000
#> GSM155503 2 0.0000 1.000 0.000 1.000 0 0.000 0.000 0.000
#> GSM155449 4 0.2378 0.887 0.000 0.152 0 0.848 0.000 0.000
#> GSM155456 4 0.0458 0.909 0.016 0.000 0 0.984 0.000 0.000
#> GSM155460 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155464 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155468 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155472 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155476 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155480 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155484 5 0.2823 0.918 0.000 0.204 0 0.000 0.796 0.000
#> GSM155488 5 0.2823 0.918 0.000 0.204 0 0.000 0.796 0.000
#> GSM155492 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM155496 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM155500 2 0.0000 1.000 0.000 1.000 0 0.000 0.000 0.000
#> GSM155504 2 0.0000 1.000 0.000 1.000 0 0.000 0.000 0.000
#> GSM155450 4 0.1501 0.931 0.000 0.076 0 0.924 0.000 0.000
#> GSM155453 4 0.1501 0.931 0.000 0.076 0 0.924 0.000 0.000
#> GSM155457 4 0.0458 0.909 0.016 0.000 0 0.984 0.000 0.000
#> GSM155461 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155465 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155469 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155473 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155477 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155481 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155485 5 0.2823 0.918 0.000 0.204 0 0.000 0.796 0.000
#> GSM155489 5 0.2823 0.918 0.000 0.204 0 0.000 0.796 0.000
#> GSM155493 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM155497 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM155501 2 0.0000 1.000 0.000 1.000 0 0.000 0.000 0.000
#> GSM155505 2 0.0000 1.000 0.000 1.000 0 0.000 0.000 0.000
#> GSM155451 4 0.1501 0.931 0.000 0.076 0 0.924 0.000 0.000
#> GSM155454 4 0.1501 0.931 0.000 0.076 0 0.924 0.000 0.000
#> GSM155458 4 0.0458 0.909 0.016 0.000 0 0.984 0.000 0.000
#> GSM155462 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155466 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155470 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155474 1 0.0000 1.000 1.000 0.000 0 0.000 0.000 0.000
#> GSM155478 6 0.0000 1.000 0.000 0.000 0 0.000 0.000 1.000
#> GSM155482 6 0.0000 1.000 0.000 0.000 0 0.000 0.000 1.000
#> GSM155486 5 0.2823 0.918 0.000 0.204 0 0.000 0.796 0.000
#> GSM155490 5 0.1180 0.722 0.000 0.012 0 0.016 0.960 0.012
#> GSM155494 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM155498 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM155502 2 0.0000 1.000 0.000 1.000 0 0.000 0.000 0.000
#> GSM155506 2 0.0000 1.000 0.000 1.000 0 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 time(p) k
#> MAD:hclust 59 0.998 2
#> MAD:hclust 59 1.000 3
#> MAD:hclust 59 1.000 4
#> MAD:hclust 59 0.877 5
#> MAD:hclust 59 0.965 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 59 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 0.369 0.872 0.894 0.4468 0.544 0.544
#> 3 3 0.599 0.871 0.876 0.3941 0.784 0.608
#> 4 4 0.659 0.690 0.766 0.1295 0.932 0.809
#> 5 5 0.737 0.739 0.783 0.0792 0.939 0.806
#> 6 6 0.795 0.764 0.782 0.0456 0.936 0.766
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 2
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 2 0.5408 0.967 0.124 0.876
#> GSM155452 2 0.5408 0.967 0.124 0.876
#> GSM155455 2 0.8713 0.762 0.292 0.708
#> GSM155459 1 0.0000 0.891 1.000 0.000
#> GSM155463 1 0.0000 0.891 1.000 0.000
#> GSM155467 1 0.0000 0.891 1.000 0.000
#> GSM155471 1 0.0000 0.891 1.000 0.000
#> GSM155475 1 0.0000 0.891 1.000 0.000
#> GSM155479 1 0.0000 0.891 1.000 0.000
#> GSM155483 1 0.7883 0.777 0.764 0.236
#> GSM155487 2 0.3879 0.928 0.076 0.924
#> GSM155491 1 0.8327 0.771 0.736 0.264
#> GSM155495 1 0.8327 0.771 0.736 0.264
#> GSM155499 2 0.5408 0.967 0.124 0.876
#> GSM155503 2 0.5408 0.967 0.124 0.876
#> GSM155449 2 0.5408 0.967 0.124 0.876
#> GSM155456 1 0.0000 0.891 1.000 0.000
#> GSM155460 1 0.0000 0.891 1.000 0.000
#> GSM155464 1 0.0000 0.891 1.000 0.000
#> GSM155468 1 0.0000 0.891 1.000 0.000
#> GSM155472 1 0.0000 0.891 1.000 0.000
#> GSM155476 1 0.0000 0.891 1.000 0.000
#> GSM155480 1 0.0000 0.891 1.000 0.000
#> GSM155484 1 0.8443 0.743 0.728 0.272
#> GSM155488 2 0.3431 0.903 0.064 0.936
#> GSM155492 1 0.8327 0.771 0.736 0.264
#> GSM155496 1 0.8327 0.771 0.736 0.264
#> GSM155500 2 0.5408 0.967 0.124 0.876
#> GSM155504 2 0.5408 0.967 0.124 0.876
#> GSM155450 2 0.5408 0.967 0.124 0.876
#> GSM155453 2 0.5408 0.967 0.124 0.876
#> GSM155457 1 0.0376 0.889 0.996 0.004
#> GSM155461 1 0.0000 0.891 1.000 0.000
#> GSM155465 1 0.0000 0.891 1.000 0.000
#> GSM155469 1 0.0000 0.891 1.000 0.000
#> GSM155473 1 0.0000 0.891 1.000 0.000
#> GSM155477 1 0.0000 0.891 1.000 0.000
#> GSM155481 1 0.0000 0.891 1.000 0.000
#> GSM155485 1 0.8443 0.743 0.728 0.272
#> GSM155489 1 0.9087 0.667 0.676 0.324
#> GSM155493 1 0.8327 0.771 0.736 0.264
#> GSM155497 1 0.8327 0.771 0.736 0.264
#> GSM155501 2 0.5408 0.967 0.124 0.876
#> GSM155505 2 0.5408 0.967 0.124 0.876
#> GSM155451 2 0.5408 0.967 0.124 0.876
#> GSM155454 2 0.5408 0.967 0.124 0.876
#> GSM155458 2 0.8713 0.762 0.292 0.708
#> GSM155462 1 0.0000 0.891 1.000 0.000
#> GSM155466 1 0.0000 0.891 1.000 0.000
#> GSM155470 1 0.0000 0.891 1.000 0.000
#> GSM155474 1 0.0000 0.891 1.000 0.000
#> GSM155478 1 0.6712 0.725 0.824 0.176
#> GSM155482 1 0.6712 0.725 0.824 0.176
#> GSM155486 1 0.8443 0.743 0.728 0.272
#> GSM155490 2 0.3879 0.928 0.076 0.924
#> GSM155494 1 0.8327 0.771 0.736 0.264
#> GSM155498 1 0.8327 0.771 0.736 0.264
#> GSM155502 2 0.5408 0.967 0.124 0.876
#> GSM155506 2 0.5408 0.967 0.124 0.876
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 2 0.369 0.849 0.016 0.884 0.100
#> GSM155452 2 0.369 0.849 0.016 0.884 0.100
#> GSM155455 2 0.721 0.666 0.192 0.708 0.100
#> GSM155459 1 0.000 0.961 1.000 0.000 0.000
#> GSM155463 1 0.000 0.961 1.000 0.000 0.000
#> GSM155467 1 0.000 0.961 1.000 0.000 0.000
#> GSM155471 1 0.000 0.961 1.000 0.000 0.000
#> GSM155475 1 0.000 0.961 1.000 0.000 0.000
#> GSM155479 1 0.000 0.961 1.000 0.000 0.000
#> GSM155483 3 0.723 0.854 0.188 0.104 0.708
#> GSM155487 2 0.304 0.849 0.000 0.896 0.104
#> GSM155491 3 0.568 0.884 0.236 0.016 0.748
#> GSM155495 3 0.512 0.876 0.188 0.016 0.796
#> GSM155499 2 0.377 0.860 0.016 0.880 0.104
#> GSM155503 2 0.377 0.860 0.016 0.880 0.104
#> GSM155449 2 0.369 0.849 0.016 0.884 0.100
#> GSM155456 1 0.589 0.739 0.796 0.104 0.100
#> GSM155460 1 0.000 0.961 1.000 0.000 0.000
#> GSM155464 1 0.000 0.961 1.000 0.000 0.000
#> GSM155468 1 0.000 0.961 1.000 0.000 0.000
#> GSM155472 1 0.000 0.961 1.000 0.000 0.000
#> GSM155476 1 0.000 0.961 1.000 0.000 0.000
#> GSM155480 1 0.000 0.961 1.000 0.000 0.000
#> GSM155484 3 0.723 0.854 0.188 0.104 0.708
#> GSM155488 3 0.649 0.106 0.004 0.456 0.540
#> GSM155492 3 0.568 0.884 0.236 0.016 0.748
#> GSM155496 3 0.568 0.884 0.236 0.016 0.748
#> GSM155500 2 0.377 0.860 0.016 0.880 0.104
#> GSM155504 2 0.377 0.860 0.016 0.880 0.104
#> GSM155450 2 0.369 0.849 0.016 0.884 0.100
#> GSM155453 2 0.369 0.849 0.016 0.884 0.100
#> GSM155457 1 0.596 0.735 0.792 0.108 0.100
#> GSM155461 1 0.000 0.961 1.000 0.000 0.000
#> GSM155465 1 0.000 0.961 1.000 0.000 0.000
#> GSM155469 1 0.000 0.961 1.000 0.000 0.000
#> GSM155473 1 0.000 0.961 1.000 0.000 0.000
#> GSM155477 1 0.000 0.961 1.000 0.000 0.000
#> GSM155481 1 0.000 0.961 1.000 0.000 0.000
#> GSM155485 3 0.723 0.854 0.188 0.104 0.708
#> GSM155489 3 0.734 0.804 0.144 0.148 0.708
#> GSM155493 3 0.568 0.884 0.236 0.016 0.748
#> GSM155497 3 0.568 0.884 0.236 0.016 0.748
#> GSM155501 2 0.377 0.860 0.016 0.880 0.104
#> GSM155505 2 0.377 0.860 0.016 0.880 0.104
#> GSM155451 2 0.369 0.849 0.016 0.884 0.100
#> GSM155454 2 0.369 0.849 0.016 0.884 0.100
#> GSM155458 2 0.721 0.666 0.192 0.708 0.100
#> GSM155462 1 0.000 0.961 1.000 0.000 0.000
#> GSM155466 1 0.000 0.961 1.000 0.000 0.000
#> GSM155470 1 0.000 0.961 1.000 0.000 0.000
#> GSM155474 1 0.000 0.961 1.000 0.000 0.000
#> GSM155478 1 0.559 0.778 0.808 0.068 0.124
#> GSM155482 1 0.559 0.778 0.808 0.068 0.124
#> GSM155486 3 0.723 0.854 0.188 0.104 0.708
#> GSM155490 2 0.460 0.787 0.000 0.796 0.204
#> GSM155494 3 0.568 0.884 0.236 0.016 0.748
#> GSM155498 3 0.568 0.884 0.236 0.016 0.748
#> GSM155502 2 0.377 0.860 0.016 0.880 0.104
#> GSM155506 2 0.377 0.860 0.016 0.880 0.104
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 2 0.4985 0.306 0.000 0.532 0.000 0.468
#> GSM155452 2 0.4985 0.306 0.000 0.532 0.000 0.468
#> GSM155455 4 0.7866 0.462 0.144 0.284 0.036 0.536
#> GSM155459 1 0.2473 0.873 0.908 0.000 0.012 0.080
#> GSM155463 1 0.2473 0.873 0.908 0.000 0.012 0.080
#> GSM155467 1 0.0188 0.899 0.996 0.000 0.000 0.004
#> GSM155471 1 0.0336 0.899 0.992 0.000 0.000 0.008
#> GSM155475 1 0.0817 0.896 0.976 0.000 0.000 0.024
#> GSM155479 1 0.0921 0.895 0.972 0.000 0.000 0.028
#> GSM155483 3 0.8054 0.774 0.076 0.160 0.580 0.184
#> GSM155487 2 0.1510 0.634 0.000 0.956 0.016 0.028
#> GSM155491 3 0.3266 0.860 0.108 0.024 0.868 0.000
#> GSM155495 3 0.4452 0.849 0.080 0.048 0.836 0.036
#> GSM155499 2 0.0336 0.657 0.000 0.992 0.008 0.000
#> GSM155503 2 0.0336 0.657 0.000 0.992 0.008 0.000
#> GSM155449 2 0.4985 0.306 0.000 0.532 0.000 0.468
#> GSM155456 4 0.5894 0.589 0.428 0.000 0.036 0.536
#> GSM155460 1 0.2473 0.873 0.908 0.000 0.012 0.080
#> GSM155464 1 0.2473 0.873 0.908 0.000 0.012 0.080
#> GSM155468 1 0.0000 0.899 1.000 0.000 0.000 0.000
#> GSM155472 1 0.0779 0.896 0.980 0.000 0.004 0.016
#> GSM155476 1 0.0817 0.896 0.976 0.000 0.000 0.024
#> GSM155480 1 0.0921 0.895 0.972 0.000 0.000 0.028
#> GSM155484 3 0.8054 0.774 0.076 0.160 0.580 0.184
#> GSM155488 2 0.7268 -0.187 0.000 0.516 0.312 0.172
#> GSM155492 3 0.3266 0.860 0.108 0.024 0.868 0.000
#> GSM155496 3 0.3266 0.860 0.108 0.024 0.868 0.000
#> GSM155500 2 0.0336 0.657 0.000 0.992 0.008 0.000
#> GSM155504 2 0.0336 0.657 0.000 0.992 0.008 0.000
#> GSM155450 2 0.4985 0.306 0.000 0.532 0.000 0.468
#> GSM155453 2 0.4985 0.306 0.000 0.532 0.000 0.468
#> GSM155457 4 0.6058 0.596 0.424 0.004 0.036 0.536
#> GSM155461 1 0.2473 0.873 0.908 0.000 0.012 0.080
#> GSM155465 1 0.2473 0.873 0.908 0.000 0.012 0.080
#> GSM155469 1 0.0000 0.899 1.000 0.000 0.000 0.000
#> GSM155473 1 0.0336 0.899 0.992 0.000 0.000 0.008
#> GSM155477 1 0.0817 0.896 0.976 0.000 0.000 0.024
#> GSM155481 1 0.0921 0.895 0.972 0.000 0.000 0.028
#> GSM155485 3 0.8054 0.774 0.076 0.160 0.580 0.184
#> GSM155489 3 0.7711 0.721 0.036 0.200 0.580 0.184
#> GSM155493 3 0.3266 0.860 0.108 0.024 0.868 0.000
#> GSM155497 3 0.3266 0.860 0.108 0.024 0.868 0.000
#> GSM155501 2 0.0336 0.657 0.000 0.992 0.008 0.000
#> GSM155505 2 0.0336 0.657 0.000 0.992 0.008 0.000
#> GSM155451 2 0.4985 0.306 0.000 0.532 0.000 0.468
#> GSM155454 2 0.4985 0.306 0.000 0.532 0.000 0.468
#> GSM155458 4 0.7885 0.472 0.148 0.280 0.036 0.536
#> GSM155462 1 0.2473 0.873 0.908 0.000 0.012 0.080
#> GSM155466 1 0.2473 0.873 0.908 0.000 0.012 0.080
#> GSM155470 1 0.0000 0.899 1.000 0.000 0.000 0.000
#> GSM155474 1 0.0336 0.899 0.992 0.000 0.000 0.008
#> GSM155478 1 0.7060 0.153 0.544 0.016 0.088 0.352
#> GSM155482 1 0.7060 0.153 0.544 0.016 0.088 0.352
#> GSM155486 3 0.8054 0.774 0.076 0.160 0.580 0.184
#> GSM155490 2 0.6607 0.234 0.000 0.516 0.084 0.400
#> GSM155494 3 0.3266 0.860 0.108 0.024 0.868 0.000
#> GSM155498 3 0.3266 0.860 0.108 0.024 0.868 0.000
#> GSM155502 2 0.0336 0.657 0.000 0.992 0.008 0.000
#> GSM155506 2 0.0336 0.657 0.000 0.992 0.008 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.0162 0.7699 0.000 0.000 0.004 0.996 0.000
#> GSM155452 4 0.0162 0.7699 0.000 0.000 0.004 0.996 0.000
#> GSM155455 4 0.5945 0.6632 0.092 0.028 0.008 0.664 0.208
#> GSM155459 1 0.3700 0.7966 0.752 0.008 0.000 0.000 0.240
#> GSM155463 1 0.3480 0.7969 0.752 0.000 0.000 0.000 0.248
#> GSM155467 1 0.0566 0.8530 0.984 0.012 0.000 0.000 0.004
#> GSM155471 1 0.0000 0.8544 1.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.0963 0.8509 0.964 0.036 0.000 0.000 0.000
#> GSM155479 1 0.1357 0.8473 0.948 0.048 0.000 0.000 0.004
#> GSM155483 3 0.6856 0.5959 0.004 0.220 0.444 0.004 0.328
#> GSM155487 2 0.4538 0.8326 0.000 0.636 0.012 0.348 0.004
#> GSM155491 3 0.0404 0.7717 0.012 0.000 0.988 0.000 0.000
#> GSM155495 3 0.3266 0.7491 0.008 0.032 0.852 0.000 0.108
#> GSM155499 2 0.4430 0.8447 0.000 0.628 0.012 0.360 0.000
#> GSM155503 2 0.4430 0.8447 0.000 0.628 0.012 0.360 0.000
#> GSM155449 4 0.0162 0.7699 0.000 0.000 0.004 0.996 0.000
#> GSM155456 4 0.6969 0.5745 0.208 0.028 0.008 0.548 0.208
#> GSM155460 1 0.3508 0.7958 0.748 0.000 0.000 0.000 0.252
#> GSM155464 1 0.3480 0.7969 0.752 0.000 0.000 0.000 0.248
#> GSM155468 1 0.0609 0.8540 0.980 0.000 0.000 0.000 0.020
#> GSM155472 1 0.1549 0.8490 0.944 0.040 0.000 0.000 0.016
#> GSM155476 1 0.1484 0.8462 0.944 0.048 0.000 0.000 0.008
#> GSM155480 1 0.1484 0.8462 0.944 0.048 0.000 0.000 0.008
#> GSM155484 3 0.6856 0.5959 0.004 0.220 0.444 0.004 0.328
#> GSM155488 2 0.6234 0.0669 0.000 0.540 0.132 0.008 0.320
#> GSM155492 3 0.0404 0.7717 0.012 0.000 0.988 0.000 0.000
#> GSM155496 3 0.0693 0.7714 0.012 0.008 0.980 0.000 0.000
#> GSM155500 2 0.4430 0.8447 0.000 0.628 0.012 0.360 0.000
#> GSM155504 2 0.4430 0.8447 0.000 0.628 0.012 0.360 0.000
#> GSM155450 4 0.0000 0.7702 0.000 0.000 0.000 1.000 0.000
#> GSM155453 4 0.0000 0.7702 0.000 0.000 0.000 1.000 0.000
#> GSM155457 4 0.6969 0.5745 0.208 0.028 0.008 0.548 0.208
#> GSM155461 1 0.3700 0.7966 0.752 0.008 0.000 0.000 0.240
#> GSM155465 1 0.3480 0.7969 0.752 0.000 0.000 0.000 0.248
#> GSM155469 1 0.0609 0.8540 0.980 0.000 0.000 0.000 0.020
#> GSM155473 1 0.0000 0.8544 1.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.1484 0.8462 0.944 0.048 0.000 0.000 0.008
#> GSM155481 1 0.1357 0.8473 0.948 0.048 0.000 0.000 0.004
#> GSM155485 3 0.6856 0.5959 0.004 0.220 0.444 0.004 0.328
#> GSM155489 3 0.6865 0.5929 0.004 0.224 0.444 0.004 0.324
#> GSM155493 3 0.0404 0.7717 0.012 0.000 0.988 0.000 0.000
#> GSM155497 3 0.1413 0.7704 0.012 0.020 0.956 0.000 0.012
#> GSM155501 2 0.4430 0.8447 0.000 0.628 0.012 0.360 0.000
#> GSM155505 2 0.4430 0.8447 0.000 0.628 0.012 0.360 0.000
#> GSM155451 4 0.0000 0.7702 0.000 0.000 0.000 1.000 0.000
#> GSM155454 4 0.0000 0.7702 0.000 0.000 0.000 1.000 0.000
#> GSM155458 4 0.5945 0.6632 0.092 0.028 0.008 0.664 0.208
#> GSM155462 1 0.3700 0.7966 0.752 0.008 0.000 0.000 0.240
#> GSM155466 1 0.3480 0.7969 0.752 0.000 0.000 0.000 0.248
#> GSM155470 1 0.0609 0.8540 0.980 0.000 0.000 0.000 0.020
#> GSM155474 1 0.0000 0.8544 1.000 0.000 0.000 0.000 0.000
#> GSM155478 1 0.7475 0.2559 0.376 0.232 0.000 0.040 0.352
#> GSM155482 1 0.7475 0.2559 0.376 0.232 0.000 0.040 0.352
#> GSM155486 3 0.6856 0.5959 0.004 0.220 0.444 0.004 0.328
#> GSM155490 2 0.5064 0.1706 0.000 0.552 0.004 0.028 0.416
#> GSM155494 3 0.1095 0.7709 0.012 0.008 0.968 0.000 0.012
#> GSM155498 3 0.1413 0.7704 0.012 0.020 0.956 0.000 0.012
#> GSM155502 2 0.4430 0.8447 0.000 0.628 0.012 0.360 0.000
#> GSM155506 2 0.4430 0.8447 0.000 0.628 0.012 0.360 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.6696 0.750 0.000 0.272 0.000 0.492 0.148 0.088
#> GSM155452 4 0.6696 0.750 0.000 0.272 0.000 0.492 0.148 0.088
#> GSM155455 4 0.1152 0.579 0.004 0.044 0.000 0.952 0.000 0.000
#> GSM155459 1 0.1850 0.576 0.924 0.000 0.000 0.008 0.016 0.052
#> GSM155463 1 0.1757 0.578 0.928 0.000 0.000 0.008 0.012 0.052
#> GSM155467 1 0.5685 0.753 0.628 0.000 0.004 0.072 0.232 0.064
#> GSM155471 1 0.5500 0.754 0.636 0.000 0.000 0.068 0.232 0.064
#> GSM155475 1 0.6102 0.738 0.576 0.000 0.004 0.072 0.260 0.088
#> GSM155479 1 0.6184 0.735 0.568 0.000 0.004 0.072 0.260 0.096
#> GSM155483 5 0.5510 0.849 0.012 0.080 0.344 0.008 0.556 0.000
#> GSM155487 2 0.1176 0.948 0.000 0.956 0.000 0.024 0.020 0.000
#> GSM155491 3 0.0520 0.928 0.008 0.008 0.984 0.000 0.000 0.000
#> GSM155495 3 0.4057 0.494 0.008 0.008 0.740 0.008 0.224 0.012
#> GSM155499 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155503 2 0.0260 0.990 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM155449 4 0.6696 0.750 0.000 0.272 0.000 0.492 0.148 0.088
#> GSM155456 4 0.0937 0.526 0.040 0.000 0.000 0.960 0.000 0.000
#> GSM155460 1 0.1850 0.576 0.924 0.000 0.000 0.008 0.016 0.052
#> GSM155464 1 0.1757 0.578 0.928 0.000 0.000 0.008 0.012 0.052
#> GSM155468 1 0.5610 0.754 0.636 0.000 0.004 0.072 0.228 0.060
#> GSM155472 1 0.6184 0.736 0.568 0.000 0.004 0.072 0.260 0.096
#> GSM155476 1 0.6184 0.735 0.568 0.000 0.004 0.072 0.260 0.096
#> GSM155480 1 0.6184 0.735 0.568 0.000 0.004 0.072 0.260 0.096
#> GSM155484 5 0.5510 0.849 0.012 0.080 0.344 0.008 0.556 0.000
#> GSM155488 5 0.4847 0.363 0.000 0.404 0.036 0.012 0.548 0.000
#> GSM155492 3 0.0520 0.928 0.008 0.008 0.984 0.000 0.000 0.000
#> GSM155496 3 0.1140 0.924 0.008 0.008 0.964 0.008 0.000 0.012
#> GSM155500 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155504 2 0.0260 0.990 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM155450 4 0.6577 0.763 0.000 0.272 0.008 0.528 0.084 0.108
#> GSM155453 4 0.6577 0.763 0.000 0.272 0.008 0.528 0.084 0.108
#> GSM155457 4 0.0937 0.526 0.040 0.000 0.000 0.960 0.000 0.000
#> GSM155461 1 0.1850 0.576 0.924 0.000 0.000 0.008 0.016 0.052
#> GSM155465 1 0.1757 0.578 0.928 0.000 0.000 0.008 0.012 0.052
#> GSM155469 1 0.5610 0.754 0.636 0.000 0.004 0.072 0.228 0.060
#> GSM155473 1 0.5500 0.754 0.636 0.000 0.000 0.068 0.232 0.064
#> GSM155477 1 0.6184 0.735 0.568 0.000 0.004 0.072 0.260 0.096
#> GSM155481 1 0.6184 0.735 0.568 0.000 0.004 0.072 0.260 0.096
#> GSM155485 5 0.5510 0.849 0.012 0.080 0.344 0.008 0.556 0.000
#> GSM155489 5 0.5379 0.830 0.000 0.092 0.336 0.012 0.560 0.000
#> GSM155493 3 0.0520 0.928 0.008 0.008 0.984 0.000 0.000 0.000
#> GSM155497 3 0.1780 0.917 0.008 0.008 0.932 0.008 0.000 0.044
#> GSM155501 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155505 2 0.0260 0.990 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM155451 4 0.6577 0.763 0.000 0.272 0.008 0.528 0.084 0.108
#> GSM155454 4 0.6577 0.763 0.000 0.272 0.008 0.528 0.084 0.108
#> GSM155458 4 0.1010 0.572 0.004 0.036 0.000 0.960 0.000 0.000
#> GSM155462 1 0.1850 0.576 0.924 0.000 0.000 0.008 0.016 0.052
#> GSM155466 1 0.1757 0.578 0.928 0.000 0.000 0.008 0.012 0.052
#> GSM155470 1 0.5610 0.754 0.636 0.000 0.004 0.072 0.228 0.060
#> GSM155474 1 0.5500 0.754 0.636 0.000 0.000 0.068 0.232 0.064
#> GSM155478 6 0.4211 0.808 0.128 0.000 0.000 0.092 0.016 0.764
#> GSM155482 6 0.4211 0.808 0.128 0.000 0.000 0.092 0.016 0.764
#> GSM155486 5 0.5510 0.849 0.012 0.080 0.344 0.008 0.556 0.000
#> GSM155490 6 0.5608 0.527 0.000 0.132 0.000 0.060 0.156 0.652
#> GSM155494 3 0.1210 0.924 0.008 0.008 0.960 0.004 0.000 0.020
#> GSM155498 3 0.1780 0.917 0.008 0.008 0.932 0.008 0.000 0.044
#> GSM155502 2 0.0000 0.990 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155506 2 0.0260 0.990 0.000 0.992 0.000 0.000 0.008 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 time(p) k
#> MAD:kmeans 59 0.795 2
#> MAD:kmeans 58 0.951 3
#> MAD:kmeans 46 0.985 4
#> MAD:kmeans 55 1.000 5
#> MAD:kmeans 57 0.775 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 59 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.991 0.995 0.5076 0.493 0.493
#> 3 3 1.000 0.980 0.991 0.3019 0.787 0.593
#> 4 4 1.000 0.964 0.977 0.1068 0.908 0.739
#> 5 5 0.886 0.842 0.887 0.0477 0.933 0.763
#> 6 6 0.829 0.855 0.904 0.0468 0.984 0.931
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 2 0.0000 0.992 0.000 1.000
#> GSM155452 2 0.0000 0.992 0.000 1.000
#> GSM155455 1 0.2043 0.969 0.968 0.032
#> GSM155459 1 0.0000 0.997 1.000 0.000
#> GSM155463 1 0.0000 0.997 1.000 0.000
#> GSM155467 1 0.0000 0.997 1.000 0.000
#> GSM155471 1 0.0000 0.997 1.000 0.000
#> GSM155475 1 0.0000 0.997 1.000 0.000
#> GSM155479 1 0.0000 0.997 1.000 0.000
#> GSM155483 2 0.0000 0.992 0.000 1.000
#> GSM155487 2 0.0000 0.992 0.000 1.000
#> GSM155491 2 0.2043 0.974 0.032 0.968
#> GSM155495 2 0.0000 0.992 0.000 1.000
#> GSM155499 2 0.0000 0.992 0.000 1.000
#> GSM155503 2 0.0000 0.992 0.000 1.000
#> GSM155449 2 0.0000 0.992 0.000 1.000
#> GSM155456 1 0.0000 0.997 1.000 0.000
#> GSM155460 1 0.0000 0.997 1.000 0.000
#> GSM155464 1 0.0000 0.997 1.000 0.000
#> GSM155468 1 0.0000 0.997 1.000 0.000
#> GSM155472 1 0.0000 0.997 1.000 0.000
#> GSM155476 1 0.0000 0.997 1.000 0.000
#> GSM155480 1 0.0000 0.997 1.000 0.000
#> GSM155484 2 0.0000 0.992 0.000 1.000
#> GSM155488 2 0.0000 0.992 0.000 1.000
#> GSM155492 2 0.2043 0.974 0.032 0.968
#> GSM155496 2 0.2043 0.974 0.032 0.968
#> GSM155500 2 0.0000 0.992 0.000 1.000
#> GSM155504 2 0.0000 0.992 0.000 1.000
#> GSM155450 2 0.0000 0.992 0.000 1.000
#> GSM155453 2 0.0000 0.992 0.000 1.000
#> GSM155457 1 0.0672 0.991 0.992 0.008
#> GSM155461 1 0.0000 0.997 1.000 0.000
#> GSM155465 1 0.0000 0.997 1.000 0.000
#> GSM155469 1 0.0000 0.997 1.000 0.000
#> GSM155473 1 0.0000 0.997 1.000 0.000
#> GSM155477 1 0.0000 0.997 1.000 0.000
#> GSM155481 1 0.0000 0.997 1.000 0.000
#> GSM155485 2 0.0000 0.992 0.000 1.000
#> GSM155489 2 0.0000 0.992 0.000 1.000
#> GSM155493 2 0.2043 0.974 0.032 0.968
#> GSM155497 2 0.2043 0.974 0.032 0.968
#> GSM155501 2 0.0000 0.992 0.000 1.000
#> GSM155505 2 0.0000 0.992 0.000 1.000
#> GSM155451 2 0.0000 0.992 0.000 1.000
#> GSM155454 2 0.0000 0.992 0.000 1.000
#> GSM155458 1 0.2043 0.969 0.968 0.032
#> GSM155462 1 0.0000 0.997 1.000 0.000
#> GSM155466 1 0.0000 0.997 1.000 0.000
#> GSM155470 1 0.0000 0.997 1.000 0.000
#> GSM155474 1 0.0000 0.997 1.000 0.000
#> GSM155478 1 0.0000 0.997 1.000 0.000
#> GSM155482 1 0.0000 0.997 1.000 0.000
#> GSM155486 2 0.0000 0.992 0.000 1.000
#> GSM155490 2 0.0000 0.992 0.000 1.000
#> GSM155494 2 0.2043 0.974 0.032 0.968
#> GSM155498 2 0.2043 0.974 0.032 0.968
#> GSM155502 2 0.0000 0.992 0.000 1.000
#> GSM155506 2 0.0000 0.992 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 2 0.000 0.987 0.000 1.000 0
#> GSM155452 2 0.000 0.987 0.000 1.000 0
#> GSM155455 2 0.000 0.987 0.000 1.000 0
#> GSM155459 1 0.000 0.987 1.000 0.000 0
#> GSM155463 1 0.000 0.987 1.000 0.000 0
#> GSM155467 1 0.000 0.987 1.000 0.000 0
#> GSM155471 1 0.000 0.987 1.000 0.000 0
#> GSM155475 1 0.000 0.987 1.000 0.000 0
#> GSM155479 1 0.000 0.987 1.000 0.000 0
#> GSM155483 3 0.000 1.000 0.000 0.000 1
#> GSM155487 2 0.000 0.987 0.000 1.000 0
#> GSM155491 3 0.000 1.000 0.000 0.000 1
#> GSM155495 3 0.000 1.000 0.000 0.000 1
#> GSM155499 2 0.000 0.987 0.000 1.000 0
#> GSM155503 2 0.000 0.987 0.000 1.000 0
#> GSM155449 2 0.000 0.987 0.000 1.000 0
#> GSM155456 1 0.000 0.987 1.000 0.000 0
#> GSM155460 1 0.000 0.987 1.000 0.000 0
#> GSM155464 1 0.000 0.987 1.000 0.000 0
#> GSM155468 1 0.000 0.987 1.000 0.000 0
#> GSM155472 1 0.000 0.987 1.000 0.000 0
#> GSM155476 1 0.000 0.987 1.000 0.000 0
#> GSM155480 1 0.000 0.987 1.000 0.000 0
#> GSM155484 3 0.000 1.000 0.000 0.000 1
#> GSM155488 3 0.000 1.000 0.000 0.000 1
#> GSM155492 3 0.000 1.000 0.000 0.000 1
#> GSM155496 3 0.000 1.000 0.000 0.000 1
#> GSM155500 2 0.000 0.987 0.000 1.000 0
#> GSM155504 2 0.000 0.987 0.000 1.000 0
#> GSM155450 2 0.000 0.987 0.000 1.000 0
#> GSM155453 2 0.000 0.987 0.000 1.000 0
#> GSM155457 2 0.475 0.726 0.216 0.784 0
#> GSM155461 1 0.000 0.987 1.000 0.000 0
#> GSM155465 1 0.000 0.987 1.000 0.000 0
#> GSM155469 1 0.000 0.987 1.000 0.000 0
#> GSM155473 1 0.000 0.987 1.000 0.000 0
#> GSM155477 1 0.000 0.987 1.000 0.000 0
#> GSM155481 1 0.000 0.987 1.000 0.000 0
#> GSM155485 3 0.000 1.000 0.000 0.000 1
#> GSM155489 3 0.000 1.000 0.000 0.000 1
#> GSM155493 3 0.000 1.000 0.000 0.000 1
#> GSM155497 3 0.000 1.000 0.000 0.000 1
#> GSM155501 2 0.000 0.987 0.000 1.000 0
#> GSM155505 2 0.000 0.987 0.000 1.000 0
#> GSM155451 2 0.000 0.987 0.000 1.000 0
#> GSM155454 2 0.000 0.987 0.000 1.000 0
#> GSM155458 2 0.000 0.987 0.000 1.000 0
#> GSM155462 1 0.000 0.987 1.000 0.000 0
#> GSM155466 1 0.000 0.987 1.000 0.000 0
#> GSM155470 1 0.000 0.987 1.000 0.000 0
#> GSM155474 1 0.000 0.987 1.000 0.000 0
#> GSM155478 1 0.382 0.831 0.852 0.148 0
#> GSM155482 1 0.382 0.831 0.852 0.148 0
#> GSM155486 3 0.000 1.000 0.000 0.000 1
#> GSM155490 2 0.000 0.987 0.000 1.000 0
#> GSM155494 3 0.000 1.000 0.000 0.000 1
#> GSM155498 3 0.000 1.000 0.000 0.000 1
#> GSM155502 2 0.000 0.987 0.000 1.000 0
#> GSM155506 2 0.000 0.987 0.000 1.000 0
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 4 0.1302 0.973 0.00 0.044 0.000 0.956
#> GSM155452 4 0.0921 0.983 0.00 0.028 0.000 0.972
#> GSM155455 4 0.0000 0.974 0.00 0.000 0.000 1.000
#> GSM155459 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155463 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155467 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155471 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155475 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155479 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155483 3 0.1637 0.962 0.00 0.060 0.940 0.000
#> GSM155487 2 0.0707 0.992 0.00 0.980 0.000 0.020
#> GSM155491 3 0.0000 0.977 0.00 0.000 1.000 0.000
#> GSM155495 3 0.0000 0.977 0.00 0.000 1.000 0.000
#> GSM155499 2 0.0707 0.992 0.00 0.980 0.000 0.020
#> GSM155503 2 0.0707 0.992 0.00 0.980 0.000 0.020
#> GSM155449 4 0.1302 0.973 0.00 0.044 0.000 0.956
#> GSM155456 4 0.0707 0.954 0.02 0.000 0.000 0.980
#> GSM155460 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155464 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155468 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155472 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155476 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155480 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155484 3 0.1637 0.962 0.00 0.060 0.940 0.000
#> GSM155488 2 0.0921 0.948 0.00 0.972 0.028 0.000
#> GSM155492 3 0.0000 0.977 0.00 0.000 1.000 0.000
#> GSM155496 3 0.0000 0.977 0.00 0.000 1.000 0.000
#> GSM155500 2 0.0707 0.992 0.00 0.980 0.000 0.020
#> GSM155504 2 0.0707 0.992 0.00 0.980 0.000 0.020
#> GSM155450 4 0.0921 0.983 0.00 0.028 0.000 0.972
#> GSM155453 4 0.0921 0.983 0.00 0.028 0.000 0.972
#> GSM155457 4 0.0000 0.974 0.00 0.000 0.000 1.000
#> GSM155461 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155465 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155469 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155473 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155477 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155481 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155485 3 0.1637 0.962 0.00 0.060 0.940 0.000
#> GSM155489 3 0.1637 0.962 0.00 0.060 0.940 0.000
#> GSM155493 3 0.0000 0.977 0.00 0.000 1.000 0.000
#> GSM155497 3 0.0000 0.977 0.00 0.000 1.000 0.000
#> GSM155501 2 0.0707 0.992 0.00 0.980 0.000 0.020
#> GSM155505 2 0.0707 0.992 0.00 0.980 0.000 0.020
#> GSM155451 4 0.0921 0.983 0.00 0.028 0.000 0.972
#> GSM155454 4 0.0921 0.983 0.00 0.028 0.000 0.972
#> GSM155458 4 0.0000 0.974 0.00 0.000 0.000 1.000
#> GSM155462 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155466 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155470 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.974 1.00 0.000 0.000 0.000
#> GSM155478 1 0.5256 0.613 0.70 0.260 0.000 0.040
#> GSM155482 1 0.5256 0.613 0.70 0.260 0.000 0.040
#> GSM155486 3 0.1637 0.962 0.00 0.060 0.940 0.000
#> GSM155490 2 0.0000 0.976 0.00 1.000 0.000 0.000
#> GSM155494 3 0.0000 0.977 0.00 0.000 1.000 0.000
#> GSM155498 3 0.0000 0.977 0.00 0.000 1.000 0.000
#> GSM155502 2 0.0707 0.992 0.00 0.980 0.000 0.020
#> GSM155506 2 0.0707 0.992 0.00 0.980 0.000 0.020
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.1671 0.953 0.000 0.076 0.000 0.924 0.000
#> GSM155452 4 0.1478 0.958 0.000 0.064 0.000 0.936 0.000
#> GSM155455 4 0.0609 0.931 0.000 0.000 0.020 0.980 0.000
#> GSM155459 1 0.1121 0.945 0.956 0.000 0.044 0.000 0.000
#> GSM155463 1 0.1121 0.945 0.956 0.000 0.044 0.000 0.000
#> GSM155467 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.0162 0.952 0.996 0.000 0.004 0.000 0.000
#> GSM155475 1 0.1952 0.925 0.912 0.004 0.084 0.000 0.000
#> GSM155479 1 0.2068 0.921 0.904 0.004 0.092 0.000 0.000
#> GSM155483 5 0.0000 0.853 0.000 0.000 0.000 0.000 1.000
#> GSM155487 2 0.1952 0.869 0.000 0.912 0.084 0.004 0.000
#> GSM155491 3 0.4161 0.656 0.000 0.000 0.608 0.000 0.392
#> GSM155495 3 0.4161 0.656 0.000 0.000 0.608 0.000 0.392
#> GSM155499 2 0.0963 0.953 0.000 0.964 0.000 0.036 0.000
#> GSM155503 2 0.0963 0.953 0.000 0.964 0.000 0.036 0.000
#> GSM155449 4 0.1671 0.953 0.000 0.076 0.000 0.924 0.000
#> GSM155456 4 0.1568 0.893 0.036 0.000 0.020 0.944 0.000
#> GSM155460 1 0.1121 0.945 0.956 0.000 0.044 0.000 0.000
#> GSM155464 1 0.1121 0.945 0.956 0.000 0.044 0.000 0.000
#> GSM155468 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM155472 1 0.2068 0.921 0.904 0.004 0.092 0.000 0.000
#> GSM155476 1 0.2068 0.921 0.904 0.004 0.092 0.000 0.000
#> GSM155480 1 0.2068 0.921 0.904 0.004 0.092 0.000 0.000
#> GSM155484 5 0.0000 0.853 0.000 0.000 0.000 0.000 1.000
#> GSM155488 5 0.4150 0.223 0.000 0.388 0.000 0.000 0.612
#> GSM155492 3 0.4161 0.656 0.000 0.000 0.608 0.000 0.392
#> GSM155496 3 0.4161 0.656 0.000 0.000 0.608 0.000 0.392
#> GSM155500 2 0.0963 0.953 0.000 0.964 0.000 0.036 0.000
#> GSM155504 2 0.0963 0.953 0.000 0.964 0.000 0.036 0.000
#> GSM155450 4 0.1478 0.958 0.000 0.064 0.000 0.936 0.000
#> GSM155453 4 0.1478 0.958 0.000 0.064 0.000 0.936 0.000
#> GSM155457 4 0.0609 0.931 0.000 0.000 0.020 0.980 0.000
#> GSM155461 1 0.1121 0.945 0.956 0.000 0.044 0.000 0.000
#> GSM155465 1 0.1121 0.945 0.956 0.000 0.044 0.000 0.000
#> GSM155469 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM155473 1 0.0162 0.952 0.996 0.000 0.004 0.000 0.000
#> GSM155477 1 0.2068 0.921 0.904 0.004 0.092 0.000 0.000
#> GSM155481 1 0.2068 0.921 0.904 0.004 0.092 0.000 0.000
#> GSM155485 5 0.0000 0.853 0.000 0.000 0.000 0.000 1.000
#> GSM155489 5 0.0000 0.853 0.000 0.000 0.000 0.000 1.000
#> GSM155493 3 0.4161 0.656 0.000 0.000 0.608 0.000 0.392
#> GSM155497 3 0.4161 0.656 0.000 0.000 0.608 0.000 0.392
#> GSM155501 2 0.0963 0.953 0.000 0.964 0.000 0.036 0.000
#> GSM155505 2 0.0963 0.953 0.000 0.964 0.000 0.036 0.000
#> GSM155451 4 0.1544 0.957 0.000 0.068 0.000 0.932 0.000
#> GSM155454 4 0.1608 0.955 0.000 0.072 0.000 0.928 0.000
#> GSM155458 4 0.0609 0.931 0.000 0.000 0.020 0.980 0.000
#> GSM155462 1 0.1121 0.945 0.956 0.000 0.044 0.000 0.000
#> GSM155466 1 0.1121 0.945 0.956 0.000 0.044 0.000 0.000
#> GSM155470 1 0.0000 0.952 1.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.0162 0.952 0.996 0.000 0.004 0.000 0.000
#> GSM155478 3 0.7800 -0.135 0.328 0.272 0.340 0.060 0.000
#> GSM155482 3 0.7800 -0.135 0.328 0.272 0.340 0.060 0.000
#> GSM155486 5 0.0000 0.853 0.000 0.000 0.000 0.000 1.000
#> GSM155490 2 0.4877 0.643 0.000 0.692 0.236 0.000 0.072
#> GSM155494 3 0.4161 0.656 0.000 0.000 0.608 0.000 0.392
#> GSM155498 3 0.4161 0.656 0.000 0.000 0.608 0.000 0.392
#> GSM155502 2 0.0963 0.953 0.000 0.964 0.000 0.036 0.000
#> GSM155506 2 0.0963 0.953 0.000 0.964 0.000 0.036 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.2320 0.890 0.000 0.132 0.000 0.864 0.000 0.004
#> GSM155452 4 0.2003 0.901 0.000 0.116 0.000 0.884 0.000 0.000
#> GSM155455 4 0.2474 0.827 0.000 0.004 0.000 0.884 0.032 0.080
#> GSM155459 1 0.2889 0.808 0.856 0.000 0.000 0.004 0.044 0.096
#> GSM155463 1 0.2889 0.808 0.856 0.000 0.000 0.004 0.044 0.096
#> GSM155467 1 0.0363 0.834 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM155471 1 0.0260 0.835 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM155475 1 0.3201 0.731 0.780 0.000 0.000 0.000 0.012 0.208
#> GSM155479 1 0.3287 0.723 0.768 0.000 0.000 0.000 0.012 0.220
#> GSM155483 5 0.1753 0.973 0.000 0.004 0.084 0.000 0.912 0.000
#> GSM155487 2 0.3198 0.575 0.000 0.740 0.000 0.000 0.000 0.260
#> GSM155491 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155495 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155499 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155503 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155449 4 0.2320 0.890 0.000 0.132 0.000 0.864 0.000 0.004
#> GSM155456 4 0.2474 0.824 0.004 0.000 0.000 0.884 0.032 0.080
#> GSM155460 1 0.2889 0.808 0.856 0.000 0.000 0.004 0.044 0.096
#> GSM155464 1 0.2889 0.808 0.856 0.000 0.000 0.004 0.044 0.096
#> GSM155468 1 0.0260 0.835 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM155472 1 0.3470 0.697 0.740 0.000 0.000 0.000 0.012 0.248
#> GSM155476 1 0.3470 0.697 0.740 0.000 0.000 0.000 0.012 0.248
#> GSM155480 1 0.3445 0.701 0.744 0.000 0.000 0.000 0.012 0.244
#> GSM155484 5 0.1753 0.973 0.000 0.004 0.084 0.000 0.912 0.000
#> GSM155488 5 0.1663 0.859 0.000 0.088 0.000 0.000 0.912 0.000
#> GSM155492 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155496 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155500 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155504 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155450 4 0.1957 0.901 0.000 0.112 0.000 0.888 0.000 0.000
#> GSM155453 4 0.1957 0.901 0.000 0.112 0.000 0.888 0.000 0.000
#> GSM155457 4 0.2474 0.824 0.004 0.000 0.000 0.884 0.032 0.080
#> GSM155461 1 0.2889 0.808 0.856 0.000 0.000 0.004 0.044 0.096
#> GSM155465 1 0.2889 0.808 0.856 0.000 0.000 0.004 0.044 0.096
#> GSM155469 1 0.0260 0.835 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM155473 1 0.0260 0.835 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM155477 1 0.3470 0.697 0.740 0.000 0.000 0.000 0.012 0.248
#> GSM155481 1 0.3287 0.723 0.768 0.000 0.000 0.000 0.012 0.220
#> GSM155485 5 0.1753 0.973 0.000 0.004 0.084 0.000 0.912 0.000
#> GSM155489 5 0.1753 0.973 0.000 0.004 0.084 0.000 0.912 0.000
#> GSM155493 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155497 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155501 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155505 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155451 4 0.2003 0.901 0.000 0.116 0.000 0.884 0.000 0.000
#> GSM155454 4 0.2003 0.901 0.000 0.116 0.000 0.884 0.000 0.000
#> GSM155458 4 0.2474 0.827 0.000 0.004 0.000 0.884 0.032 0.080
#> GSM155462 1 0.2889 0.808 0.856 0.000 0.000 0.004 0.044 0.096
#> GSM155466 1 0.2889 0.808 0.856 0.000 0.000 0.004 0.044 0.096
#> GSM155470 1 0.0260 0.835 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM155474 1 0.0260 0.835 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM155478 6 0.2100 0.720 0.112 0.004 0.000 0.000 0.000 0.884
#> GSM155482 6 0.2100 0.720 0.112 0.004 0.000 0.000 0.000 0.884
#> GSM155486 5 0.1753 0.973 0.000 0.004 0.084 0.000 0.912 0.000
#> GSM155490 6 0.4437 0.127 0.000 0.392 0.000 0.000 0.032 0.576
#> GSM155494 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155498 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155502 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155506 2 0.0000 0.961 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n time(p) k
#> MAD:skmeans 59 0.997 2
#> MAD:skmeans 59 0.953 3
#> MAD:skmeans 59 1.000 4
#> MAD:skmeans 56 1.000 5
#> MAD:skmeans 58 0.927 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 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.00 0.968 0.986 0.4534 0.556 0.556
#> 3 3 1.00 0.957 0.984 0.3835 0.825 0.685
#> 4 4 1.00 0.975 0.992 0.0811 0.915 0.783
#> 5 5 0.99 0.957 0.983 0.0943 0.925 0.770
#> 6 6 0.99 0.961 0.984 0.0444 0.967 0.873
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4 5
There is also optional best \(k\) = 2 3 4 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 2 0.0000 1.000 0.000 1.000
#> GSM155452 2 0.0000 1.000 0.000 1.000
#> GSM155455 1 0.0376 0.976 0.996 0.004
#> GSM155459 1 0.0000 0.979 1.000 0.000
#> GSM155463 1 0.0000 0.979 1.000 0.000
#> GSM155467 1 0.0000 0.979 1.000 0.000
#> GSM155471 1 0.0000 0.979 1.000 0.000
#> GSM155475 1 0.0000 0.979 1.000 0.000
#> GSM155479 1 0.0000 0.979 1.000 0.000
#> GSM155483 1 0.0000 0.979 1.000 0.000
#> GSM155487 2 0.0000 1.000 0.000 1.000
#> GSM155491 1 0.0000 0.979 1.000 0.000
#> GSM155495 1 0.7056 0.767 0.808 0.192
#> GSM155499 2 0.0000 1.000 0.000 1.000
#> GSM155503 2 0.0000 1.000 0.000 1.000
#> GSM155449 2 0.0000 1.000 0.000 1.000
#> GSM155456 1 0.0000 0.979 1.000 0.000
#> GSM155460 1 0.0000 0.979 1.000 0.000
#> GSM155464 1 0.0000 0.979 1.000 0.000
#> GSM155468 1 0.0000 0.979 1.000 0.000
#> GSM155472 1 0.0000 0.979 1.000 0.000
#> GSM155476 1 0.0000 0.979 1.000 0.000
#> GSM155480 1 0.0000 0.979 1.000 0.000
#> GSM155484 1 0.7528 0.732 0.784 0.216
#> GSM155488 2 0.0000 1.000 0.000 1.000
#> GSM155492 1 0.0000 0.979 1.000 0.000
#> GSM155496 1 0.0000 0.979 1.000 0.000
#> GSM155500 2 0.0000 1.000 0.000 1.000
#> GSM155504 2 0.0000 1.000 0.000 1.000
#> GSM155450 2 0.0000 1.000 0.000 1.000
#> GSM155453 2 0.0000 1.000 0.000 1.000
#> GSM155457 1 0.0000 0.979 1.000 0.000
#> GSM155461 1 0.0000 0.979 1.000 0.000
#> GSM155465 1 0.0000 0.979 1.000 0.000
#> GSM155469 1 0.0000 0.979 1.000 0.000
#> GSM155473 1 0.0000 0.979 1.000 0.000
#> GSM155477 1 0.0000 0.979 1.000 0.000
#> GSM155481 1 0.0000 0.979 1.000 0.000
#> GSM155485 1 0.0000 0.979 1.000 0.000
#> GSM155489 2 0.0000 1.000 0.000 1.000
#> GSM155493 1 0.0000 0.979 1.000 0.000
#> GSM155497 1 0.0000 0.979 1.000 0.000
#> GSM155501 2 0.0000 1.000 0.000 1.000
#> GSM155505 2 0.0000 1.000 0.000 1.000
#> GSM155451 2 0.0000 1.000 0.000 1.000
#> GSM155454 2 0.0000 1.000 0.000 1.000
#> GSM155458 1 0.0000 0.979 1.000 0.000
#> GSM155462 1 0.0000 0.979 1.000 0.000
#> GSM155466 1 0.0000 0.979 1.000 0.000
#> GSM155470 1 0.0000 0.979 1.000 0.000
#> GSM155474 1 0.0000 0.979 1.000 0.000
#> GSM155478 1 0.0000 0.979 1.000 0.000
#> GSM155482 1 0.0000 0.979 1.000 0.000
#> GSM155486 1 0.9635 0.393 0.612 0.388
#> GSM155490 2 0.0000 1.000 0.000 1.000
#> GSM155494 1 0.0000 0.979 1.000 0.000
#> GSM155498 1 0.0000 0.979 1.000 0.000
#> GSM155502 2 0.0000 1.000 0.000 1.000
#> GSM155506 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155452 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155455 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155459 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155463 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155467 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155471 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155475 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155479 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155483 1 0.5591 0.5796 0.696 0.000 0.304
#> GSM155487 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155491 3 0.0000 0.9994 0.000 0.000 1.000
#> GSM155495 3 0.0000 0.9994 0.000 0.000 1.000
#> GSM155499 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155503 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155449 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155456 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155460 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155464 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155468 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155472 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155476 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155480 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155484 3 0.0237 0.9950 0.004 0.000 0.996
#> GSM155488 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155492 3 0.0000 0.9994 0.000 0.000 1.000
#> GSM155496 3 0.0000 0.9994 0.000 0.000 1.000
#> GSM155500 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155504 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155450 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155453 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155457 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155461 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155465 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155469 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155473 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155477 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155481 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155485 1 0.4399 0.7709 0.812 0.000 0.188
#> GSM155489 2 0.6299 0.0989 0.000 0.524 0.476
#> GSM155493 3 0.0000 0.9994 0.000 0.000 1.000
#> GSM155497 3 0.0000 0.9994 0.000 0.000 1.000
#> GSM155501 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155505 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155451 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155454 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155458 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155462 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155466 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155470 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155474 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155478 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155482 1 0.0000 0.9829 1.000 0.000 0.000
#> GSM155486 3 0.0000 0.9994 0.000 0.000 1.000
#> GSM155490 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155494 3 0.0000 0.9994 0.000 0.000 1.000
#> GSM155498 3 0.0000 0.9994 0.000 0.000 1.000
#> GSM155502 2 0.0000 0.9732 0.000 1.000 0.000
#> GSM155506 2 0.0000 0.9732 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 2 0.0000 1.000 0 1.00 0.000 0.000
#> GSM155452 2 0.0000 1.000 0 1.00 0.000 0.000
#> GSM155455 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155459 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155463 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155467 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155471 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155475 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155479 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155483 4 0.0000 0.914 0 0.00 0.000 1.000
#> GSM155487 2 0.0000 1.000 0 1.00 0.000 0.000
#> GSM155491 3 0.0000 1.000 0 0.00 1.000 0.000
#> GSM155495 4 0.0188 0.911 0 0.00 0.004 0.996
#> GSM155499 2 0.0000 1.000 0 1.00 0.000 0.000
#> GSM155503 2 0.0000 1.000 0 1.00 0.000 0.000
#> GSM155449 2 0.0000 1.000 0 1.00 0.000 0.000
#> GSM155456 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155460 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155464 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155468 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155472 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155476 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155480 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155484 4 0.0000 0.914 0 0.00 0.000 1.000
#> GSM155488 4 0.0000 0.914 0 0.00 0.000 1.000
#> GSM155492 3 0.0000 1.000 0 0.00 1.000 0.000
#> GSM155496 3 0.0000 1.000 0 0.00 1.000 0.000
#> GSM155500 2 0.0000 1.000 0 1.00 0.000 0.000
#> GSM155504 2 0.0000 1.000 0 1.00 0.000 0.000
#> GSM155450 2 0.0000 1.000 0 1.00 0.000 0.000
#> GSM155453 2 0.0000 1.000 0 1.00 0.000 0.000
#> GSM155457 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155461 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155465 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155469 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155473 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155477 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155481 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155485 4 0.0000 0.914 0 0.00 0.000 1.000
#> GSM155489 4 0.0000 0.914 0 0.00 0.000 1.000
#> GSM155493 3 0.0000 1.000 0 0.00 1.000 0.000
#> GSM155497 3 0.0000 1.000 0 0.00 1.000 0.000
#> GSM155501 2 0.0000 1.000 0 1.00 0.000 0.000
#> GSM155505 2 0.0000 1.000 0 1.00 0.000 0.000
#> GSM155451 2 0.0000 1.000 0 1.00 0.000 0.000
#> GSM155454 2 0.0000 1.000 0 1.00 0.000 0.000
#> GSM155458 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155462 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155466 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155470 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155474 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155478 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155482 1 0.0000 1.000 1 0.00 0.000 0.000
#> GSM155486 4 0.0000 0.914 0 0.00 0.000 1.000
#> GSM155490 4 0.4977 0.149 0 0.46 0.000 0.540
#> GSM155494 3 0.0000 1.000 0 0.00 1.000 0.000
#> GSM155498 3 0.0000 1.000 0 0.00 1.000 0.000
#> GSM155502 2 0.0000 1.000 0 1.00 0.000 0.000
#> GSM155506 2 0.0000 1.000 0 1.00 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.2179 0.881 0.00 0.112 0.000 0.888 0.000
#> GSM155452 4 0.0000 0.971 0.00 0.000 0.000 1.000 0.000
#> GSM155455 4 0.0000 0.971 0.00 0.000 0.000 1.000 0.000
#> GSM155459 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155463 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155467 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155471 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155475 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155479 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155483 5 0.0000 0.928 0.00 0.000 0.000 0.000 1.000
#> GSM155487 2 0.0000 1.000 0.00 1.000 0.000 0.000 0.000
#> GSM155491 3 0.0000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM155495 5 0.0162 0.925 0.00 0.000 0.004 0.000 0.996
#> GSM155499 2 0.0000 1.000 0.00 1.000 0.000 0.000 0.000
#> GSM155503 2 0.0000 1.000 0.00 1.000 0.000 0.000 0.000
#> GSM155449 4 0.0000 0.971 0.00 0.000 0.000 1.000 0.000
#> GSM155456 1 0.2929 0.794 0.82 0.000 0.000 0.180 0.000
#> GSM155460 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155464 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155468 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155472 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155476 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155480 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155484 5 0.0000 0.928 0.00 0.000 0.000 0.000 1.000
#> GSM155488 5 0.0000 0.928 0.00 0.000 0.000 0.000 1.000
#> GSM155492 3 0.0000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM155496 3 0.0000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM155500 2 0.0000 1.000 0.00 1.000 0.000 0.000 0.000
#> GSM155504 2 0.0000 1.000 0.00 1.000 0.000 0.000 0.000
#> GSM155450 4 0.0000 0.971 0.00 0.000 0.000 1.000 0.000
#> GSM155453 4 0.0000 0.971 0.00 0.000 0.000 1.000 0.000
#> GSM155457 1 0.2929 0.794 0.82 0.000 0.000 0.180 0.000
#> GSM155461 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155465 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155469 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155473 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155477 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155481 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155485 5 0.0000 0.928 0.00 0.000 0.000 0.000 1.000
#> GSM155489 5 0.0000 0.928 0.00 0.000 0.000 0.000 1.000
#> GSM155493 3 0.0000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM155497 3 0.0000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM155501 2 0.0000 1.000 0.00 1.000 0.000 0.000 0.000
#> GSM155505 2 0.0000 1.000 0.00 1.000 0.000 0.000 0.000
#> GSM155451 4 0.0000 0.971 0.00 0.000 0.000 1.000 0.000
#> GSM155454 4 0.1965 0.898 0.00 0.096 0.000 0.904 0.000
#> GSM155458 4 0.0000 0.971 0.00 0.000 0.000 1.000 0.000
#> GSM155462 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155466 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155470 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155478 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155482 1 0.0000 0.985 1.00 0.000 0.000 0.000 0.000
#> GSM155486 5 0.0000 0.928 0.00 0.000 0.000 0.000 1.000
#> GSM155490 5 0.4287 0.148 0.00 0.460 0.000 0.000 0.540
#> GSM155494 3 0.0000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM155498 3 0.0000 1.000 0.00 0.000 1.000 0.000 0.000
#> GSM155502 2 0.0000 1.000 0.00 1.000 0.000 0.000 0.000
#> GSM155506 2 0.0000 1.000 0.00 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.2730 0.756 0.0 0.192 0.000 0.808 0.000 0
#> GSM155452 4 0.0000 0.941 0.0 0.000 0.000 1.000 0.000 0
#> GSM155455 4 0.0000 0.941 0.0 0.000 0.000 1.000 0.000 0
#> GSM155459 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155463 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155467 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155471 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155475 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155479 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155483 5 0.0000 0.999 0.0 0.000 0.000 0.000 1.000 0
#> GSM155487 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000 0
#> GSM155491 3 0.0000 1.000 0.0 0.000 1.000 0.000 0.000 0
#> GSM155495 5 0.0146 0.995 0.0 0.000 0.004 0.000 0.996 0
#> GSM155499 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000 0
#> GSM155503 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000 0
#> GSM155449 4 0.0000 0.941 0.0 0.000 0.000 1.000 0.000 0
#> GSM155456 1 0.3409 0.600 0.7 0.000 0.000 0.300 0.000 0
#> GSM155460 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155464 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155468 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155472 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155476 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155480 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155484 5 0.0000 0.999 0.0 0.000 0.000 0.000 1.000 0
#> GSM155488 5 0.0000 0.999 0.0 0.000 0.000 0.000 1.000 0
#> GSM155492 3 0.0000 1.000 0.0 0.000 1.000 0.000 0.000 0
#> GSM155496 3 0.0000 1.000 0.0 0.000 1.000 0.000 0.000 0
#> GSM155500 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000 0
#> GSM155504 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000 0
#> GSM155450 4 0.0000 0.941 0.0 0.000 0.000 1.000 0.000 0
#> GSM155453 4 0.0000 0.941 0.0 0.000 0.000 1.000 0.000 0
#> GSM155457 1 0.3409 0.600 0.7 0.000 0.000 0.300 0.000 0
#> GSM155461 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155465 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155469 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155473 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155477 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155481 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155485 5 0.0000 0.999 0.0 0.000 0.000 0.000 1.000 0
#> GSM155489 5 0.0000 0.999 0.0 0.000 0.000 0.000 1.000 0
#> GSM155493 3 0.0000 1.000 0.0 0.000 1.000 0.000 0.000 0
#> GSM155497 3 0.0000 1.000 0.0 0.000 1.000 0.000 0.000 0
#> GSM155501 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000 0
#> GSM155505 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000 0
#> GSM155451 4 0.0000 0.941 0.0 0.000 0.000 1.000 0.000 0
#> GSM155454 4 0.2597 0.777 0.0 0.176 0.000 0.824 0.000 0
#> GSM155458 4 0.0000 0.941 0.0 0.000 0.000 1.000 0.000 0
#> GSM155462 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155466 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155470 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155474 1 0.0000 0.971 1.0 0.000 0.000 0.000 0.000 0
#> GSM155478 6 0.0000 1.000 0.0 0.000 0.000 0.000 0.000 1
#> GSM155482 6 0.0000 1.000 0.0 0.000 0.000 0.000 0.000 1
#> GSM155486 5 0.0000 0.999 0.0 0.000 0.000 0.000 1.000 0
#> GSM155490 6 0.0000 1.000 0.0 0.000 0.000 0.000 0.000 1
#> GSM155494 3 0.0000 1.000 0.0 0.000 1.000 0.000 0.000 0
#> GSM155498 3 0.0000 1.000 0.0 0.000 1.000 0.000 0.000 0
#> GSM155502 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000 0
#> GSM155506 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000 0
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 time(p) k
#> MAD:pam 58 0.982 2
#> MAD:pam 58 0.995 3
#> MAD:pam 58 0.998 4
#> MAD:pam 58 0.998 5
#> MAD:pam 59 0.658 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 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1 0.997 0.998 0.4770 0.524 0.524
#> 3 3 1 0.973 0.980 0.3529 0.833 0.681
#> 4 4 1 0.961 0.981 0.1298 0.863 0.641
#> 5 5 1 0.979 0.984 0.0571 0.915 0.708
#> 6 6 1 0.988 0.993 0.0249 0.982 0.923
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4 5
There is also optional best \(k\) = 2 3 4 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 2 0.000 0.997 0.000 1.000
#> GSM155452 2 0.000 0.997 0.000 1.000
#> GSM155455 2 0.000 0.997 0.000 1.000
#> GSM155459 1 0.000 1.000 1.000 0.000
#> GSM155463 1 0.000 1.000 1.000 0.000
#> GSM155467 1 0.000 1.000 1.000 0.000
#> GSM155471 1 0.000 1.000 1.000 0.000
#> GSM155475 1 0.000 1.000 1.000 0.000
#> GSM155479 1 0.000 1.000 1.000 0.000
#> GSM155483 2 0.000 0.997 0.000 1.000
#> GSM155487 2 0.000 0.997 0.000 1.000
#> GSM155491 2 0.000 0.997 0.000 1.000
#> GSM155495 2 0.000 0.997 0.000 1.000
#> GSM155499 2 0.000 0.997 0.000 1.000
#> GSM155503 2 0.000 0.997 0.000 1.000
#> GSM155449 2 0.000 0.997 0.000 1.000
#> GSM155456 2 0.000 0.997 0.000 1.000
#> GSM155460 1 0.000 1.000 1.000 0.000
#> GSM155464 1 0.000 1.000 1.000 0.000
#> GSM155468 1 0.000 1.000 1.000 0.000
#> GSM155472 1 0.000 1.000 1.000 0.000
#> GSM155476 1 0.000 1.000 1.000 0.000
#> GSM155480 1 0.000 1.000 1.000 0.000
#> GSM155484 2 0.000 0.997 0.000 1.000
#> GSM155488 2 0.000 0.997 0.000 1.000
#> GSM155492 2 0.000 0.997 0.000 1.000
#> GSM155496 2 0.000 0.997 0.000 1.000
#> GSM155500 2 0.000 0.997 0.000 1.000
#> GSM155504 2 0.000 0.997 0.000 1.000
#> GSM155450 2 0.000 0.997 0.000 1.000
#> GSM155453 2 0.000 0.997 0.000 1.000
#> GSM155457 2 0.000 0.997 0.000 1.000
#> GSM155461 1 0.000 1.000 1.000 0.000
#> GSM155465 1 0.000 1.000 1.000 0.000
#> GSM155469 1 0.000 1.000 1.000 0.000
#> GSM155473 1 0.000 1.000 1.000 0.000
#> GSM155477 1 0.000 1.000 1.000 0.000
#> GSM155481 1 0.000 1.000 1.000 0.000
#> GSM155485 2 0.000 0.997 0.000 1.000
#> GSM155489 2 0.000 0.997 0.000 1.000
#> GSM155493 2 0.000 0.997 0.000 1.000
#> GSM155497 2 0.000 0.997 0.000 1.000
#> GSM155501 2 0.000 0.997 0.000 1.000
#> GSM155505 2 0.000 0.997 0.000 1.000
#> GSM155451 2 0.000 0.997 0.000 1.000
#> GSM155454 2 0.000 0.997 0.000 1.000
#> GSM155458 2 0.000 0.997 0.000 1.000
#> GSM155462 1 0.000 1.000 1.000 0.000
#> GSM155466 1 0.000 1.000 1.000 0.000
#> GSM155470 1 0.000 1.000 1.000 0.000
#> GSM155474 1 0.000 1.000 1.000 0.000
#> GSM155478 2 0.278 0.951 0.048 0.952
#> GSM155482 2 0.278 0.951 0.048 0.952
#> GSM155486 2 0.000 0.997 0.000 1.000
#> GSM155490 2 0.000 0.997 0.000 1.000
#> GSM155494 2 0.000 0.997 0.000 1.000
#> GSM155498 2 0.000 0.997 0.000 1.000
#> GSM155502 2 0.000 0.997 0.000 1.000
#> GSM155506 2 0.000 0.997 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 2 0.000 1.000 0.000 1.000 0.000
#> GSM155452 2 0.000 1.000 0.000 1.000 0.000
#> GSM155455 2 0.000 1.000 0.000 1.000 0.000
#> GSM155459 1 0.000 1.000 1.000 0.000 0.000
#> GSM155463 1 0.000 1.000 1.000 0.000 0.000
#> GSM155467 1 0.000 1.000 1.000 0.000 0.000
#> GSM155471 1 0.000 1.000 1.000 0.000 0.000
#> GSM155475 1 0.000 1.000 1.000 0.000 0.000
#> GSM155479 1 0.000 1.000 1.000 0.000 0.000
#> GSM155483 3 0.000 0.952 0.000 0.000 1.000
#> GSM155487 3 0.263 0.939 0.000 0.084 0.916
#> GSM155491 3 0.000 0.952 0.000 0.000 1.000
#> GSM155495 3 0.000 0.952 0.000 0.000 1.000
#> GSM155499 3 0.263 0.939 0.000 0.084 0.916
#> GSM155503 3 0.263 0.939 0.000 0.084 0.916
#> GSM155449 2 0.000 1.000 0.000 1.000 0.000
#> GSM155456 2 0.000 1.000 0.000 1.000 0.000
#> GSM155460 1 0.000 1.000 1.000 0.000 0.000
#> GSM155464 1 0.000 1.000 1.000 0.000 0.000
#> GSM155468 1 0.000 1.000 1.000 0.000 0.000
#> GSM155472 1 0.000 1.000 1.000 0.000 0.000
#> GSM155476 1 0.000 1.000 1.000 0.000 0.000
#> GSM155480 1 0.000 1.000 1.000 0.000 0.000
#> GSM155484 3 0.000 0.952 0.000 0.000 1.000
#> GSM155488 3 0.000 0.952 0.000 0.000 1.000
#> GSM155492 3 0.000 0.952 0.000 0.000 1.000
#> GSM155496 3 0.000 0.952 0.000 0.000 1.000
#> GSM155500 3 0.263 0.939 0.000 0.084 0.916
#> GSM155504 3 0.263 0.939 0.000 0.084 0.916
#> GSM155450 2 0.000 1.000 0.000 1.000 0.000
#> GSM155453 2 0.000 1.000 0.000 1.000 0.000
#> GSM155457 2 0.000 1.000 0.000 1.000 0.000
#> GSM155461 1 0.000 1.000 1.000 0.000 0.000
#> GSM155465 1 0.000 1.000 1.000 0.000 0.000
#> GSM155469 1 0.000 1.000 1.000 0.000 0.000
#> GSM155473 1 0.000 1.000 1.000 0.000 0.000
#> GSM155477 1 0.000 1.000 1.000 0.000 0.000
#> GSM155481 1 0.000 1.000 1.000 0.000 0.000
#> GSM155485 3 0.000 0.952 0.000 0.000 1.000
#> GSM155489 3 0.000 0.952 0.000 0.000 1.000
#> GSM155493 3 0.000 0.952 0.000 0.000 1.000
#> GSM155497 3 0.000 0.952 0.000 0.000 1.000
#> GSM155501 3 0.263 0.939 0.000 0.084 0.916
#> GSM155505 3 0.263 0.939 0.000 0.084 0.916
#> GSM155451 2 0.000 1.000 0.000 1.000 0.000
#> GSM155454 2 0.000 1.000 0.000 1.000 0.000
#> GSM155458 2 0.000 1.000 0.000 1.000 0.000
#> GSM155462 1 0.000 1.000 1.000 0.000 0.000
#> GSM155466 1 0.000 1.000 1.000 0.000 0.000
#> GSM155470 1 0.000 1.000 1.000 0.000 0.000
#> GSM155474 1 0.000 1.000 1.000 0.000 0.000
#> GSM155478 3 0.550 0.849 0.096 0.088 0.816
#> GSM155482 3 0.550 0.849 0.096 0.088 0.816
#> GSM155486 3 0.000 0.952 0.000 0.000 1.000
#> GSM155490 3 0.263 0.939 0.000 0.084 0.916
#> GSM155494 3 0.000 0.952 0.000 0.000 1.000
#> GSM155498 3 0.000 0.952 0.000 0.000 1.000
#> GSM155502 3 0.263 0.939 0.000 0.084 0.916
#> GSM155506 3 0.263 0.939 0.000 0.084 0.916
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155452 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155455 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155459 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155463 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155467 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155471 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155475 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155479 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155483 3 0.1302 0.955 0.000 0.044 0.956 0.000
#> GSM155487 2 0.0000 0.947 0.000 1.000 0.000 0.000
#> GSM155491 3 0.0000 0.961 0.000 0.000 1.000 0.000
#> GSM155495 3 0.1302 0.955 0.000 0.044 0.956 0.000
#> GSM155499 2 0.0188 0.949 0.000 0.996 0.000 0.004
#> GSM155503 2 0.0188 0.949 0.000 0.996 0.000 0.004
#> GSM155449 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155456 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155460 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155464 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155468 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155472 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155476 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155480 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155484 3 0.1302 0.955 0.000 0.044 0.956 0.000
#> GSM155488 2 0.2149 0.866 0.000 0.912 0.088 0.000
#> GSM155492 3 0.0000 0.961 0.000 0.000 1.000 0.000
#> GSM155496 3 0.0000 0.961 0.000 0.000 1.000 0.000
#> GSM155500 2 0.0188 0.949 0.000 0.996 0.000 0.004
#> GSM155504 2 0.0188 0.949 0.000 0.996 0.000 0.004
#> GSM155450 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155453 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155457 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155461 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155465 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155469 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155473 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155477 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155481 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155485 3 0.1302 0.955 0.000 0.044 0.956 0.000
#> GSM155489 3 0.3764 0.744 0.000 0.216 0.784 0.000
#> GSM155493 3 0.0000 0.961 0.000 0.000 1.000 0.000
#> GSM155497 3 0.0000 0.961 0.000 0.000 1.000 0.000
#> GSM155501 2 0.0188 0.949 0.000 0.996 0.000 0.004
#> GSM155505 2 0.0188 0.949 0.000 0.996 0.000 0.004
#> GSM155451 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155454 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155458 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155462 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155466 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155470 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155478 1 0.2149 0.909 0.912 0.088 0.000 0.000
#> GSM155482 1 0.2149 0.909 0.912 0.088 0.000 0.000
#> GSM155486 3 0.1302 0.955 0.000 0.044 0.956 0.000
#> GSM155490 2 0.4776 0.368 0.000 0.624 0.376 0.000
#> GSM155494 3 0.0000 0.961 0.000 0.000 1.000 0.000
#> GSM155498 3 0.0000 0.961 0.000 0.000 1.000 0.000
#> GSM155502 2 0.0188 0.949 0.000 0.996 0.000 0.004
#> GSM155506 2 0.0188 0.949 0.000 0.996 0.000 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.0162 0.996 0.000 0.004 0.000 0.996 0.000
#> GSM155452 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM155455 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM155459 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155463 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155467 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155479 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155483 5 0.1851 0.931 0.000 0.000 0.088 0.000 0.912
#> GSM155487 5 0.3336 0.663 0.000 0.228 0.000 0.000 0.772
#> GSM155491 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155495 5 0.1908 0.928 0.000 0.000 0.092 0.000 0.908
#> GSM155499 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155503 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155449 4 0.0162 0.996 0.000 0.004 0.000 0.996 0.000
#> GSM155456 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM155460 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155464 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155468 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155472 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155476 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155480 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155484 5 0.1851 0.931 0.000 0.000 0.088 0.000 0.912
#> GSM155488 5 0.1851 0.931 0.000 0.000 0.088 0.000 0.912
#> GSM155492 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155496 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155500 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155504 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155450 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM155453 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM155457 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM155461 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155465 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155469 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155473 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155481 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155485 5 0.1851 0.931 0.000 0.000 0.088 0.000 0.912
#> GSM155489 5 0.1851 0.931 0.000 0.000 0.088 0.000 0.912
#> GSM155493 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155497 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155501 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155505 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155451 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM155454 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM155458 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM155462 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155466 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155470 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000
#> GSM155478 5 0.1270 0.868 0.052 0.000 0.000 0.000 0.948
#> GSM155482 5 0.1270 0.868 0.052 0.000 0.000 0.000 0.948
#> GSM155486 5 0.1851 0.931 0.000 0.000 0.088 0.000 0.912
#> GSM155490 5 0.0290 0.890 0.000 0.008 0.000 0.000 0.992
#> GSM155494 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155498 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155502 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM155506 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM155452 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM155455 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM155459 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155463 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155467 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155471 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155475 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155479 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155483 5 0.0000 0.997 0.000 0.000 0.000 0 1.000 0.000
#> GSM155487 6 0.1802 0.891 0.000 0.072 0.000 0 0.012 0.916
#> GSM155491 3 0.0000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM155495 5 0.0363 0.986 0.000 0.000 0.012 0 0.988 0.000
#> GSM155499 2 0.0000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM155503 2 0.0000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM155449 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM155456 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM155460 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155464 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155468 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155472 1 0.1007 0.958 0.956 0.000 0.000 0 0.000 0.044
#> GSM155476 1 0.0458 0.984 0.984 0.000 0.000 0 0.000 0.016
#> GSM155480 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155484 5 0.0000 0.997 0.000 0.000 0.000 0 1.000 0.000
#> GSM155488 6 0.2697 0.793 0.000 0.000 0.000 0 0.188 0.812
#> GSM155492 3 0.0000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM155496 3 0.0000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM155500 2 0.0000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM155504 2 0.0000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM155450 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM155453 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM155457 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM155461 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155465 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155469 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155473 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155477 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155481 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155485 5 0.0000 0.997 0.000 0.000 0.000 0 1.000 0.000
#> GSM155489 5 0.0000 0.997 0.000 0.000 0.000 0 1.000 0.000
#> GSM155493 3 0.0000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM155497 3 0.0000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM155501 2 0.0000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM155505 2 0.0000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM155451 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM155454 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM155458 4 0.0000 1.000 0.000 0.000 0.000 1 0.000 0.000
#> GSM155462 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155466 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155470 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155474 1 0.0000 0.997 1.000 0.000 0.000 0 0.000 0.000
#> GSM155478 6 0.0000 0.921 0.000 0.000 0.000 0 0.000 1.000
#> GSM155482 6 0.0000 0.921 0.000 0.000 0.000 0 0.000 1.000
#> GSM155486 5 0.0000 0.997 0.000 0.000 0.000 0 1.000 0.000
#> GSM155490 6 0.1075 0.915 0.000 0.000 0.000 0 0.048 0.952
#> GSM155494 3 0.0000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM155498 3 0.0000 1.000 0.000 0.000 1.000 0 0.000 0.000
#> GSM155502 2 0.0000 1.000 0.000 1.000 0.000 0 0.000 0.000
#> GSM155506 2 0.0000 1.000 0.000 1.000 0.000 0 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 time(p) k
#> MAD:mclust 59 0.800 2
#> MAD:mclust 59 0.976 3
#> MAD:mclust 58 1.000 4
#> MAD:mclust 59 0.999 5
#> MAD:mclust 59 0.986 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 59 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 4.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.829 0.893 0.957 0.5043 0.493 0.493
#> 3 3 0.947 0.937 0.975 0.3029 0.802 0.617
#> 4 4 0.905 0.893 0.947 0.0749 0.930 0.803
#> 5 5 0.896 0.919 0.944 0.0603 0.868 0.609
#> 6 6 0.836 0.806 0.872 0.0642 0.971 0.882
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 4
#> attr(,"optional")
#> [1] 3
There is also optional best \(k\) = 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 2 0.0000 0.9373 0.000 1.000
#> GSM155452 2 0.0000 0.9373 0.000 1.000
#> GSM155455 2 0.0000 0.9373 0.000 1.000
#> GSM155459 1 0.0000 0.9687 1.000 0.000
#> GSM155463 1 0.0000 0.9687 1.000 0.000
#> GSM155467 1 0.0000 0.9687 1.000 0.000
#> GSM155471 1 0.0000 0.9687 1.000 0.000
#> GSM155475 1 0.0000 0.9687 1.000 0.000
#> GSM155479 1 0.0000 0.9687 1.000 0.000
#> GSM155483 2 0.9896 0.2525 0.440 0.560
#> GSM155487 2 0.0000 0.9373 0.000 1.000
#> GSM155491 1 0.6531 0.7772 0.832 0.168
#> GSM155495 2 0.0000 0.9373 0.000 1.000
#> GSM155499 2 0.0000 0.9373 0.000 1.000
#> GSM155503 2 0.0000 0.9373 0.000 1.000
#> GSM155449 2 0.0000 0.9373 0.000 1.000
#> GSM155456 1 0.0376 0.9652 0.996 0.004
#> GSM155460 1 0.0000 0.9687 1.000 0.000
#> GSM155464 1 0.0000 0.9687 1.000 0.000
#> GSM155468 1 0.0000 0.9687 1.000 0.000
#> GSM155472 1 0.0000 0.9687 1.000 0.000
#> GSM155476 1 0.0000 0.9687 1.000 0.000
#> GSM155480 1 0.0000 0.9687 1.000 0.000
#> GSM155484 2 0.1414 0.9251 0.020 0.980
#> GSM155488 2 0.0000 0.9373 0.000 1.000
#> GSM155492 2 0.9460 0.4530 0.364 0.636
#> GSM155496 2 0.6148 0.7988 0.152 0.848
#> GSM155500 2 0.0000 0.9373 0.000 1.000
#> GSM155504 2 0.0000 0.9373 0.000 1.000
#> GSM155450 2 0.0000 0.9373 0.000 1.000
#> GSM155453 2 0.0000 0.9373 0.000 1.000
#> GSM155457 1 0.8207 0.6354 0.744 0.256
#> GSM155461 1 0.0000 0.9687 1.000 0.000
#> GSM155465 1 0.0000 0.9687 1.000 0.000
#> GSM155469 1 0.0000 0.9687 1.000 0.000
#> GSM155473 1 0.0000 0.9687 1.000 0.000
#> GSM155477 1 0.0000 0.9687 1.000 0.000
#> GSM155481 1 0.0000 0.9687 1.000 0.000
#> GSM155485 2 0.1184 0.9278 0.016 0.984
#> GSM155489 2 0.0000 0.9373 0.000 1.000
#> GSM155493 2 0.9996 0.0866 0.488 0.512
#> GSM155497 2 0.0000 0.9373 0.000 1.000
#> GSM155501 2 0.0000 0.9373 0.000 1.000
#> GSM155505 2 0.0000 0.9373 0.000 1.000
#> GSM155451 2 0.0000 0.9373 0.000 1.000
#> GSM155454 2 0.0000 0.9373 0.000 1.000
#> GSM155458 2 0.2603 0.9058 0.044 0.956
#> GSM155462 1 0.0000 0.9687 1.000 0.000
#> GSM155466 1 0.0000 0.9687 1.000 0.000
#> GSM155470 1 0.0000 0.9687 1.000 0.000
#> GSM155474 1 0.0000 0.9687 1.000 0.000
#> GSM155478 1 0.0000 0.9687 1.000 0.000
#> GSM155482 1 0.0000 0.9687 1.000 0.000
#> GSM155486 2 0.0672 0.9328 0.008 0.992
#> GSM155490 2 0.0000 0.9373 0.000 1.000
#> GSM155494 2 0.8081 0.6719 0.248 0.752
#> GSM155498 1 0.9209 0.4610 0.664 0.336
#> GSM155502 2 0.0000 0.9373 0.000 1.000
#> GSM155506 2 0.0000 0.9373 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 2 0.0000 0.948 0.000 1.000 0.000
#> GSM155452 2 0.0000 0.948 0.000 1.000 0.000
#> GSM155455 2 0.0000 0.948 0.000 1.000 0.000
#> GSM155459 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155463 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155467 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155471 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155475 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155479 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155483 3 0.0424 0.991 0.008 0.000 0.992
#> GSM155487 2 0.2261 0.889 0.000 0.932 0.068
#> GSM155491 3 0.0000 0.999 0.000 0.000 1.000
#> GSM155495 3 0.0000 0.999 0.000 0.000 1.000
#> GSM155499 2 0.0000 0.948 0.000 1.000 0.000
#> GSM155503 2 0.0237 0.946 0.000 0.996 0.004
#> GSM155449 2 0.0000 0.948 0.000 1.000 0.000
#> GSM155456 1 0.3816 0.831 0.852 0.148 0.000
#> GSM155460 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155464 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155468 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155472 1 0.0237 0.972 0.996 0.004 0.000
#> GSM155476 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155480 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155484 3 0.0000 0.999 0.000 0.000 1.000
#> GSM155488 2 0.5363 0.604 0.000 0.724 0.276
#> GSM155492 3 0.0000 0.999 0.000 0.000 1.000
#> GSM155496 3 0.0000 0.999 0.000 0.000 1.000
#> GSM155500 2 0.0000 0.948 0.000 1.000 0.000
#> GSM155504 2 0.0237 0.946 0.000 0.996 0.004
#> GSM155450 2 0.0000 0.948 0.000 1.000 0.000
#> GSM155453 2 0.0000 0.948 0.000 1.000 0.000
#> GSM155457 2 0.6307 -0.013 0.488 0.512 0.000
#> GSM155461 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155465 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155469 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155473 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155477 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155481 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155485 3 0.0000 0.999 0.000 0.000 1.000
#> GSM155489 3 0.0000 0.999 0.000 0.000 1.000
#> GSM155493 3 0.0000 0.999 0.000 0.000 1.000
#> GSM155497 3 0.0000 0.999 0.000 0.000 1.000
#> GSM155501 2 0.0000 0.948 0.000 1.000 0.000
#> GSM155505 2 0.0000 0.948 0.000 1.000 0.000
#> GSM155451 2 0.0000 0.948 0.000 1.000 0.000
#> GSM155454 2 0.0000 0.948 0.000 1.000 0.000
#> GSM155458 2 0.2448 0.875 0.076 0.924 0.000
#> GSM155462 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155466 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155470 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155474 1 0.0000 0.976 1.000 0.000 0.000
#> GSM155478 1 0.4346 0.784 0.816 0.184 0.000
#> GSM155482 1 0.4654 0.750 0.792 0.208 0.000
#> GSM155486 3 0.0000 0.999 0.000 0.000 1.000
#> GSM155490 2 0.0424 0.943 0.000 0.992 0.008
#> GSM155494 3 0.0000 0.999 0.000 0.000 1.000
#> GSM155498 3 0.0000 0.999 0.000 0.000 1.000
#> GSM155502 2 0.0000 0.948 0.000 1.000 0.000
#> GSM155506 2 0.0000 0.948 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 2 0.0336 0.869 0.000 0.992 0.000 0.008
#> GSM155452 2 0.0592 0.862 0.000 0.984 0.000 0.016
#> GSM155455 2 0.0779 0.860 0.004 0.980 0.000 0.016
#> GSM155459 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155463 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155467 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155471 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155475 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155479 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155483 3 0.0779 0.945 0.016 0.000 0.980 0.004
#> GSM155487 4 0.4422 0.519 0.000 0.256 0.008 0.736
#> GSM155491 3 0.0336 0.950 0.008 0.000 0.992 0.000
#> GSM155495 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM155499 2 0.4070 0.843 0.000 0.824 0.044 0.132
#> GSM155503 2 0.4234 0.837 0.000 0.816 0.052 0.132
#> GSM155449 2 0.0188 0.869 0.000 0.996 0.000 0.004
#> GSM155456 1 0.5237 0.387 0.628 0.356 0.000 0.016
#> GSM155460 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155464 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155468 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155472 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155476 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155480 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155484 3 0.0804 0.949 0.000 0.008 0.980 0.012
#> GSM155488 3 0.6229 0.466 0.000 0.204 0.664 0.132
#> GSM155492 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM155496 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM155500 2 0.3999 0.842 0.000 0.824 0.036 0.140
#> GSM155504 2 0.4234 0.837 0.000 0.816 0.052 0.132
#> GSM155450 2 0.0592 0.862 0.000 0.984 0.000 0.016
#> GSM155453 2 0.0336 0.866 0.000 0.992 0.000 0.008
#> GSM155457 2 0.4630 0.461 0.252 0.732 0.000 0.016
#> GSM155461 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155465 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155469 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155473 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155477 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155481 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155485 3 0.1059 0.943 0.000 0.012 0.972 0.016
#> GSM155489 3 0.1182 0.939 0.000 0.016 0.968 0.016
#> GSM155493 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM155497 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM155501 2 0.4123 0.841 0.000 0.820 0.044 0.136
#> GSM155505 2 0.3479 0.843 0.000 0.840 0.012 0.148
#> GSM155451 2 0.0000 0.868 0.000 1.000 0.000 0.000
#> GSM155454 2 0.0336 0.868 0.000 0.992 0.008 0.000
#> GSM155458 2 0.0779 0.860 0.004 0.980 0.000 0.016
#> GSM155462 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155466 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155470 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.979 1.000 0.000 0.000 0.000
#> GSM155478 4 0.2593 0.823 0.104 0.004 0.000 0.892
#> GSM155482 4 0.2593 0.823 0.104 0.004 0.000 0.892
#> GSM155486 3 0.0804 0.949 0.000 0.008 0.980 0.012
#> GSM155490 4 0.0707 0.795 0.000 0.020 0.000 0.980
#> GSM155494 3 0.0000 0.956 0.000 0.000 1.000 0.000
#> GSM155498 3 0.0188 0.953 0.004 0.000 0.996 0.000
#> GSM155502 2 0.4070 0.843 0.000 0.824 0.044 0.132
#> GSM155506 2 0.4070 0.843 0.000 0.824 0.044 0.132
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.2966 0.840 0.000 0.184 0.000 0.816 0.000
#> GSM155452 4 0.0963 0.905 0.000 0.036 0.000 0.964 0.000
#> GSM155455 4 0.0000 0.892 0.000 0.000 0.000 1.000 0.000
#> GSM155459 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155463 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155467 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155479 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155483 2 0.5747 0.323 0.088 0.504 0.408 0.000 0.000
#> GSM155487 2 0.2865 0.785 0.000 0.856 0.008 0.004 0.132
#> GSM155491 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155495 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155499 2 0.1908 0.861 0.000 0.908 0.000 0.092 0.000
#> GSM155503 2 0.1851 0.864 0.000 0.912 0.000 0.088 0.000
#> GSM155449 4 0.2852 0.853 0.000 0.172 0.000 0.828 0.000
#> GSM155456 4 0.0510 0.879 0.016 0.000 0.000 0.984 0.000
#> GSM155460 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155464 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155468 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155472 1 0.2595 0.878 0.888 0.000 0.000 0.080 0.032
#> GSM155476 1 0.0865 0.969 0.972 0.004 0.000 0.000 0.024
#> GSM155480 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155484 2 0.3949 0.662 0.004 0.696 0.300 0.000 0.000
#> GSM155488 2 0.1965 0.834 0.000 0.904 0.096 0.000 0.000
#> GSM155492 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155496 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155500 2 0.1851 0.864 0.000 0.912 0.000 0.088 0.000
#> GSM155504 2 0.1851 0.864 0.000 0.912 0.000 0.088 0.000
#> GSM155450 4 0.1197 0.906 0.000 0.048 0.000 0.952 0.000
#> GSM155453 4 0.1908 0.901 0.000 0.092 0.000 0.908 0.000
#> GSM155457 4 0.0162 0.892 0.004 0.000 0.000 0.996 0.000
#> GSM155461 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155465 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155469 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155473 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155481 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155485 2 0.2798 0.814 0.008 0.852 0.140 0.000 0.000
#> GSM155489 2 0.2516 0.817 0.000 0.860 0.140 0.000 0.000
#> GSM155493 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155497 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155501 2 0.1851 0.864 0.000 0.912 0.000 0.088 0.000
#> GSM155505 2 0.1851 0.864 0.000 0.912 0.000 0.088 0.000
#> GSM155451 4 0.2179 0.894 0.000 0.112 0.000 0.888 0.000
#> GSM155454 4 0.2773 0.860 0.000 0.164 0.000 0.836 0.000
#> GSM155458 4 0.0162 0.892 0.004 0.000 0.000 0.996 0.000
#> GSM155462 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155466 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155470 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM155478 5 0.0000 0.996 0.000 0.000 0.000 0.000 1.000
#> GSM155482 5 0.0000 0.996 0.000 0.000 0.000 0.000 1.000
#> GSM155486 2 0.3857 0.648 0.000 0.688 0.312 0.000 0.000
#> GSM155490 5 0.0290 0.991 0.000 0.008 0.000 0.000 0.992
#> GSM155494 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155498 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM155502 2 0.1851 0.864 0.000 0.912 0.000 0.088 0.000
#> GSM155506 2 0.1851 0.864 0.000 0.912 0.000 0.088 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.5086 0.6078 0.000 0.276 0.004 0.616 0.104 0.000
#> GSM155452 4 0.1789 0.8804 0.000 0.032 0.000 0.924 0.044 0.000
#> GSM155455 4 0.0260 0.8870 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM155459 1 0.3647 0.7117 0.640 0.000 0.000 0.000 0.360 0.000
#> GSM155463 1 0.3634 0.7134 0.644 0.000 0.000 0.000 0.356 0.000
#> GSM155467 1 0.0000 0.8399 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.0363 0.8407 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM155475 1 0.0363 0.8375 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM155479 1 0.0632 0.8338 0.976 0.000 0.000 0.000 0.024 0.000
#> GSM155483 5 0.4806 0.7522 0.036 0.108 0.132 0.000 0.724 0.000
#> GSM155487 2 0.5612 0.0113 0.000 0.520 0.000 0.000 0.308 0.172
#> GSM155491 3 0.0146 0.9784 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM155495 3 0.1267 0.9414 0.000 0.000 0.940 0.000 0.060 0.000
#> GSM155499 2 0.0862 0.8527 0.000 0.972 0.004 0.016 0.008 0.000
#> GSM155503 2 0.0603 0.8527 0.000 0.980 0.000 0.016 0.004 0.000
#> GSM155449 4 0.5054 0.5175 0.000 0.336 0.000 0.572 0.092 0.000
#> GSM155456 4 0.0520 0.8810 0.008 0.000 0.000 0.984 0.008 0.000
#> GSM155460 1 0.3659 0.7069 0.636 0.000 0.000 0.000 0.364 0.000
#> GSM155464 1 0.3659 0.7068 0.636 0.000 0.000 0.000 0.364 0.000
#> GSM155468 1 0.1219 0.8387 0.948 0.004 0.000 0.000 0.048 0.000
#> GSM155472 1 0.2136 0.7968 0.908 0.000 0.000 0.016 0.012 0.064
#> GSM155476 1 0.1401 0.8218 0.948 0.020 0.000 0.000 0.028 0.004
#> GSM155480 1 0.0972 0.8302 0.964 0.008 0.000 0.000 0.028 0.000
#> GSM155484 5 0.4933 0.8226 0.012 0.188 0.120 0.000 0.680 0.000
#> GSM155488 2 0.4388 -0.0436 0.000 0.572 0.028 0.000 0.400 0.000
#> GSM155492 3 0.0146 0.9784 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM155496 3 0.0937 0.9598 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM155500 2 0.0603 0.8527 0.000 0.980 0.000 0.016 0.004 0.000
#> GSM155504 2 0.1245 0.8467 0.000 0.952 0.000 0.016 0.032 0.000
#> GSM155450 4 0.0790 0.8906 0.000 0.032 0.000 0.968 0.000 0.000
#> GSM155453 4 0.1049 0.8906 0.000 0.032 0.000 0.960 0.008 0.000
#> GSM155457 4 0.0520 0.8810 0.008 0.000 0.000 0.984 0.008 0.000
#> GSM155461 1 0.3547 0.7289 0.668 0.000 0.000 0.000 0.332 0.000
#> GSM155465 1 0.3647 0.7103 0.640 0.000 0.000 0.000 0.360 0.000
#> GSM155469 1 0.1075 0.8385 0.952 0.000 0.000 0.000 0.048 0.000
#> GSM155473 1 0.0260 0.8403 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM155477 1 0.0363 0.8375 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM155481 1 0.0458 0.8363 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM155485 5 0.4945 0.8236 0.012 0.220 0.100 0.000 0.668 0.000
#> GSM155489 5 0.5527 0.4266 0.000 0.408 0.132 0.000 0.460 0.000
#> GSM155493 3 0.0405 0.9790 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM155497 3 0.0458 0.9771 0.000 0.000 0.984 0.000 0.016 0.000
#> GSM155501 2 0.1088 0.8503 0.000 0.960 0.000 0.016 0.024 0.000
#> GSM155505 2 0.0717 0.8455 0.000 0.976 0.000 0.016 0.008 0.000
#> GSM155451 4 0.1411 0.8831 0.000 0.060 0.000 0.936 0.004 0.000
#> GSM155454 4 0.2263 0.8642 0.000 0.056 0.000 0.896 0.048 0.000
#> GSM155458 4 0.0260 0.8870 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM155462 1 0.3830 0.6902 0.620 0.000 0.004 0.000 0.376 0.000
#> GSM155466 1 0.3607 0.7188 0.652 0.000 0.000 0.000 0.348 0.000
#> GSM155470 1 0.1204 0.8372 0.944 0.000 0.000 0.000 0.056 0.000
#> GSM155474 1 0.0260 0.8403 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM155478 6 0.0000 0.9951 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM155482 6 0.0000 0.9951 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM155486 5 0.5076 0.8128 0.004 0.236 0.124 0.000 0.636 0.000
#> GSM155490 6 0.0405 0.9902 0.000 0.004 0.000 0.000 0.008 0.988
#> GSM155494 3 0.0405 0.9789 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM155498 3 0.0551 0.9732 0.004 0.000 0.984 0.000 0.008 0.004
#> GSM155502 2 0.1168 0.8491 0.000 0.956 0.000 0.016 0.028 0.000
#> GSM155506 2 0.0603 0.8511 0.000 0.980 0.004 0.016 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 time(p) k
#> MAD:NMF 55 0.951 2
#> MAD:NMF 58 0.982 3
#> MAD:NMF 56 0.650 4
#> MAD:NMF 58 0.631 5
#> MAD:NMF 56 0.863 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 59 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 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 0.978 0.990 0.4605 0.534 0.534
#> 3 3 0.781 0.865 0.932 0.1423 0.953 0.912
#> 4 4 0.793 0.865 0.914 0.2029 0.841 0.683
#> 5 5 0.799 0.855 0.912 0.0542 0.991 0.974
#> 6 6 0.817 0.878 0.875 0.0771 0.888 0.677
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
#> GSM155448 1 0.000 1.000 1.000 0.000
#> GSM155452 1 0.000 1.000 1.000 0.000
#> GSM155455 1 0.000 1.000 1.000 0.000
#> GSM155459 1 0.000 1.000 1.000 0.000
#> GSM155463 1 0.000 1.000 1.000 0.000
#> GSM155467 1 0.000 1.000 1.000 0.000
#> GSM155471 1 0.000 1.000 1.000 0.000
#> GSM155475 1 0.000 1.000 1.000 0.000
#> GSM155479 1 0.000 1.000 1.000 0.000
#> GSM155483 2 0.000 0.971 0.000 1.000
#> GSM155487 2 0.000 0.971 0.000 1.000
#> GSM155491 1 0.000 1.000 1.000 0.000
#> GSM155495 2 0.000 0.971 0.000 1.000
#> GSM155499 2 0.000 0.971 0.000 1.000
#> GSM155503 2 0.000 0.971 0.000 1.000
#> GSM155449 1 0.000 1.000 1.000 0.000
#> GSM155456 1 0.000 1.000 1.000 0.000
#> GSM155460 1 0.000 1.000 1.000 0.000
#> GSM155464 1 0.000 1.000 1.000 0.000
#> GSM155468 1 0.000 1.000 1.000 0.000
#> GSM155472 1 0.000 1.000 1.000 0.000
#> GSM155476 1 0.000 1.000 1.000 0.000
#> GSM155480 1 0.000 1.000 1.000 0.000
#> GSM155484 2 0.000 0.971 0.000 1.000
#> GSM155488 2 0.000 0.971 0.000 1.000
#> GSM155492 1 0.000 1.000 1.000 0.000
#> GSM155496 2 0.000 0.971 0.000 1.000
#> GSM155500 2 0.000 0.971 0.000 1.000
#> GSM155504 2 0.000 0.971 0.000 1.000
#> GSM155450 1 0.000 1.000 1.000 0.000
#> GSM155453 2 0.866 0.616 0.288 0.712
#> GSM155457 1 0.000 1.000 1.000 0.000
#> GSM155461 1 0.000 1.000 1.000 0.000
#> GSM155465 1 0.000 1.000 1.000 0.000
#> GSM155469 1 0.000 1.000 1.000 0.000
#> GSM155473 1 0.000 1.000 1.000 0.000
#> GSM155477 1 0.000 1.000 1.000 0.000
#> GSM155481 1 0.000 1.000 1.000 0.000
#> GSM155485 2 0.000 0.971 0.000 1.000
#> GSM155489 2 0.000 0.971 0.000 1.000
#> GSM155493 1 0.000 1.000 1.000 0.000
#> GSM155497 1 0.000 1.000 1.000 0.000
#> GSM155501 2 0.000 0.971 0.000 1.000
#> GSM155505 2 0.000 0.971 0.000 1.000
#> GSM155451 2 0.866 0.616 0.288 0.712
#> GSM155454 2 0.000 0.971 0.000 1.000
#> GSM155458 1 0.000 1.000 1.000 0.000
#> GSM155462 1 0.000 1.000 1.000 0.000
#> GSM155466 1 0.000 1.000 1.000 0.000
#> GSM155470 1 0.000 1.000 1.000 0.000
#> GSM155474 1 0.000 1.000 1.000 0.000
#> GSM155478 1 0.000 1.000 1.000 0.000
#> GSM155482 1 0.000 1.000 1.000 0.000
#> GSM155486 2 0.000 0.971 0.000 1.000
#> GSM155490 2 0.000 0.971 0.000 1.000
#> GSM155494 1 0.000 1.000 1.000 0.000
#> GSM155498 1 0.000 1.000 1.000 0.000
#> GSM155502 2 0.000 0.971 0.000 1.000
#> GSM155506 2 0.000 0.971 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 1 0.0237 0.961 0.996 0.000 0.004
#> GSM155452 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155455 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155459 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155463 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155467 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155471 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155475 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155479 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155483 2 0.5785 0.568 0.000 0.668 0.332
#> GSM155487 2 0.0000 0.857 0.000 1.000 0.000
#> GSM155491 1 0.4555 0.785 0.800 0.000 0.200
#> GSM155495 3 0.4555 0.661 0.000 0.200 0.800
#> GSM155499 2 0.0000 0.857 0.000 1.000 0.000
#> GSM155503 2 0.0000 0.857 0.000 1.000 0.000
#> GSM155449 1 0.0237 0.961 0.996 0.000 0.004
#> GSM155456 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155460 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155464 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155468 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155472 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155476 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155480 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155484 2 0.5785 0.568 0.000 0.668 0.332
#> GSM155488 2 0.0000 0.857 0.000 1.000 0.000
#> GSM155492 1 0.4555 0.785 0.800 0.000 0.200
#> GSM155496 3 0.4555 0.661 0.000 0.200 0.800
#> GSM155500 2 0.0000 0.857 0.000 1.000 0.000
#> GSM155504 2 0.0000 0.857 0.000 1.000 0.000
#> GSM155450 1 0.0237 0.961 0.996 0.000 0.004
#> GSM155453 3 0.5431 0.626 0.284 0.000 0.716
#> GSM155457 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155461 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155465 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155469 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155473 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155477 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155481 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155485 2 0.5785 0.568 0.000 0.668 0.332
#> GSM155489 2 0.5785 0.568 0.000 0.668 0.332
#> GSM155493 1 0.4555 0.785 0.800 0.000 0.200
#> GSM155497 1 0.4555 0.785 0.800 0.000 0.200
#> GSM155501 2 0.0000 0.857 0.000 1.000 0.000
#> GSM155505 2 0.0000 0.857 0.000 1.000 0.000
#> GSM155451 3 0.5431 0.626 0.284 0.000 0.716
#> GSM155454 3 0.4555 0.661 0.000 0.200 0.800
#> GSM155458 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155462 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155466 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155470 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155474 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155478 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155482 1 0.0000 0.964 1.000 0.000 0.000
#> GSM155486 2 0.5785 0.568 0.000 0.668 0.332
#> GSM155490 2 0.0000 0.857 0.000 1.000 0.000
#> GSM155494 1 0.4555 0.785 0.800 0.000 0.200
#> GSM155498 1 0.4555 0.785 0.800 0.000 0.200
#> GSM155502 2 0.0000 0.857 0.000 1.000 0.000
#> GSM155506 2 0.0000 0.857 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 1 0.281 0.867 0.868 0.000 0.132 0.000
#> GSM155452 1 0.139 0.925 0.952 0.000 0.048 0.000
#> GSM155455 1 0.253 0.886 0.888 0.000 0.112 0.000
#> GSM155459 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155463 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155467 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155471 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155475 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155479 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155483 4 0.499 0.450 0.000 0.468 0.000 0.532
#> GSM155487 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM155491 3 0.139 0.905 0.048 0.000 0.952 0.000
#> GSM155495 4 0.000 0.541 0.000 0.000 0.000 1.000
#> GSM155499 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM155503 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM155449 1 0.281 0.867 0.868 0.000 0.132 0.000
#> GSM155456 1 0.253 0.886 0.888 0.000 0.112 0.000
#> GSM155460 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155464 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155468 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155472 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155476 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155480 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155484 4 0.499 0.450 0.000 0.468 0.000 0.532
#> GSM155488 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM155492 3 0.139 0.905 0.048 0.000 0.952 0.000
#> GSM155496 4 0.000 0.541 0.000 0.000 0.000 1.000
#> GSM155500 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM155504 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM155450 1 0.281 0.867 0.868 0.000 0.132 0.000
#> GSM155453 4 0.563 0.331 0.196 0.000 0.092 0.712
#> GSM155457 1 0.253 0.886 0.888 0.000 0.112 0.000
#> GSM155461 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155465 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155469 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155473 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155477 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155481 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155485 4 0.499 0.450 0.000 0.468 0.000 0.532
#> GSM155489 4 0.499 0.450 0.000 0.468 0.000 0.532
#> GSM155493 3 0.139 0.905 0.048 0.000 0.952 0.000
#> GSM155497 3 0.307 0.807 0.152 0.000 0.848 0.000
#> GSM155501 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM155505 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM155451 4 0.563 0.331 0.196 0.000 0.092 0.712
#> GSM155454 4 0.000 0.541 0.000 0.000 0.000 1.000
#> GSM155458 1 0.253 0.886 0.888 0.000 0.112 0.000
#> GSM155462 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155466 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155470 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155474 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155478 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155482 1 0.000 0.967 1.000 0.000 0.000 0.000
#> GSM155486 4 0.499 0.450 0.000 0.468 0.000 0.532
#> GSM155490 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM155494 3 0.139 0.905 0.048 0.000 0.952 0.000
#> GSM155498 3 0.307 0.807 0.152 0.000 0.848 0.000
#> GSM155502 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM155506 2 0.000 1.000 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 1 0.566 0.542 0.632 0.000 0.164 0.204 0.000
#> GSM155452 1 0.311 0.775 0.800 0.200 0.000 0.000 0.000
#> GSM155455 1 0.265 0.827 0.848 0.000 0.152 0.000 0.000
#> GSM155459 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155463 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155467 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155479 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155483 5 0.000 0.621 0.000 0.000 0.000 0.000 1.000
#> GSM155487 2 0.429 1.000 0.000 0.532 0.000 0.000 0.468
#> GSM155491 3 0.000 0.882 0.000 0.000 1.000 0.000 0.000
#> GSM155495 5 0.429 0.366 0.000 0.000 0.000 0.468 0.532
#> GSM155499 2 0.429 1.000 0.000 0.532 0.000 0.000 0.468
#> GSM155503 2 0.429 1.000 0.000 0.532 0.000 0.000 0.468
#> GSM155449 1 0.566 0.542 0.632 0.000 0.164 0.204 0.000
#> GSM155456 1 0.265 0.827 0.848 0.000 0.152 0.000 0.000
#> GSM155460 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155464 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155468 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155472 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155476 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155480 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155484 5 0.000 0.621 0.000 0.000 0.000 0.000 1.000
#> GSM155488 2 0.429 1.000 0.000 0.532 0.000 0.000 0.468
#> GSM155492 3 0.000 0.882 0.000 0.000 1.000 0.000 0.000
#> GSM155496 5 0.429 0.366 0.000 0.000 0.000 0.468 0.532
#> GSM155500 2 0.429 1.000 0.000 0.532 0.000 0.000 0.468
#> GSM155504 2 0.429 1.000 0.000 0.532 0.000 0.000 0.468
#> GSM155450 1 0.566 0.542 0.632 0.000 0.164 0.204 0.000
#> GSM155453 4 0.504 1.000 0.000 0.236 0.084 0.680 0.000
#> GSM155457 1 0.265 0.827 0.848 0.000 0.152 0.000 0.000
#> GSM155461 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155465 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155469 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155473 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155481 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155485 5 0.000 0.621 0.000 0.000 0.000 0.000 1.000
#> GSM155489 5 0.000 0.621 0.000 0.000 0.000 0.000 1.000
#> GSM155493 3 0.000 0.882 0.000 0.000 1.000 0.000 0.000
#> GSM155497 3 0.337 0.763 0.000 0.232 0.768 0.000 0.000
#> GSM155501 2 0.429 1.000 0.000 0.532 0.000 0.000 0.468
#> GSM155505 2 0.429 1.000 0.000 0.532 0.000 0.000 0.468
#> GSM155451 4 0.504 1.000 0.000 0.236 0.084 0.680 0.000
#> GSM155454 5 0.429 0.366 0.000 0.000 0.000 0.468 0.532
#> GSM155458 1 0.265 0.827 0.848 0.000 0.152 0.000 0.000
#> GSM155462 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155466 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155470 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155478 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155482 1 0.000 0.937 1.000 0.000 0.000 0.000 0.000
#> GSM155486 5 0.000 0.621 0.000 0.000 0.000 0.000 1.000
#> GSM155490 2 0.429 1.000 0.000 0.532 0.000 0.000 0.468
#> GSM155494 3 0.000 0.882 0.000 0.000 1.000 0.000 0.000
#> GSM155498 3 0.337 0.763 0.000 0.232 0.768 0.000 0.000
#> GSM155502 2 0.429 1.000 0.000 0.532 0.000 0.000 0.468
#> GSM155506 2 0.429 1.000 0.000 0.532 0.000 0.000 0.468
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.393 0.695 0.248 0.000 0.000 0.716 0.000 0.036
#> GSM155452 4 0.809 0.476 0.212 0.120 0.080 0.420 0.000 0.168
#> GSM155455 4 0.381 0.790 0.428 0.000 0.000 0.572 0.000 0.000
#> GSM155459 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155463 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155467 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155479 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155483 5 0.000 0.623 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155487 2 0.386 1.000 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM155491 3 0.156 0.839 0.000 0.000 0.920 0.080 0.000 0.000
#> GSM155495 5 0.656 0.436 0.000 0.176 0.000 0.208 0.532 0.084
#> GSM155499 2 0.386 1.000 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM155503 2 0.386 1.000 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM155449 4 0.393 0.695 0.248 0.000 0.000 0.716 0.000 0.036
#> GSM155456 4 0.381 0.790 0.428 0.000 0.000 0.572 0.000 0.000
#> GSM155460 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155464 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155468 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155472 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155476 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155480 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155484 5 0.000 0.623 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155488 2 0.386 1.000 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM155492 3 0.156 0.839 0.000 0.000 0.920 0.080 0.000 0.000
#> GSM155496 5 0.656 0.436 0.000 0.176 0.000 0.208 0.532 0.084
#> GSM155500 2 0.386 1.000 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM155504 2 0.386 1.000 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM155450 4 0.393 0.695 0.248 0.000 0.000 0.716 0.000 0.036
#> GSM155453 6 0.315 1.000 0.000 0.000 0.000 0.252 0.000 0.748
#> GSM155457 4 0.381 0.790 0.428 0.000 0.000 0.572 0.000 0.000
#> GSM155461 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155465 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155469 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155473 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155481 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155485 5 0.000 0.623 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155489 5 0.000 0.623 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155493 3 0.156 0.839 0.000 0.000 0.920 0.080 0.000 0.000
#> GSM155497 3 0.423 0.648 0.000 0.292 0.668 0.040 0.000 0.000
#> GSM155501 2 0.386 1.000 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM155505 2 0.386 1.000 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM155451 6 0.315 1.000 0.000 0.000 0.000 0.252 0.000 0.748
#> GSM155454 5 0.656 0.436 0.000 0.176 0.000 0.208 0.532 0.084
#> GSM155458 4 0.381 0.790 0.428 0.000 0.000 0.572 0.000 0.000
#> GSM155462 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155466 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155470 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155478 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155482 1 0.000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155486 5 0.000 0.623 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155490 2 0.386 1.000 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM155494 3 0.156 0.839 0.000 0.000 0.920 0.080 0.000 0.000
#> GSM155498 3 0.423 0.648 0.000 0.292 0.668 0.040 0.000 0.000
#> GSM155502 2 0.386 1.000 0.000 0.532 0.000 0.000 0.468 0.000
#> GSM155506 2 0.386 1.000 0.000 0.532 0.000 0.000 0.468 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 time(p) k
#> ATC:hclust 59 0.979 2
#> ATC:hclust 59 0.996 3
#> ATC:hclust 52 0.990 4
#> ATC:hclust 56 0.989 5
#> ATC:hclust 55 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["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 59 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 0.4447 0.556 0.556
#> 3 3 0.763 0.931 0.935 0.3719 0.797 0.638
#> 4 4 0.774 0.766 0.842 0.1428 0.959 0.889
#> 5 5 0.721 0.624 0.764 0.0806 0.890 0.682
#> 6 6 0.736 0.843 0.772 0.0462 0.869 0.520
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
#> GSM155448 1 0 1 1 0
#> GSM155452 1 0 1 1 0
#> GSM155455 1 0 1 1 0
#> GSM155459 1 0 1 1 0
#> GSM155463 1 0 1 1 0
#> GSM155467 1 0 1 1 0
#> GSM155471 1 0 1 1 0
#> GSM155475 1 0 1 1 0
#> GSM155479 1 0 1 1 0
#> GSM155483 2 0 1 0 1
#> GSM155487 2 0 1 0 1
#> GSM155491 1 0 1 1 0
#> GSM155495 2 0 1 0 1
#> GSM155499 2 0 1 0 1
#> GSM155503 2 0 1 0 1
#> GSM155449 1 0 1 1 0
#> GSM155456 1 0 1 1 0
#> GSM155460 1 0 1 1 0
#> GSM155464 1 0 1 1 0
#> GSM155468 1 0 1 1 0
#> GSM155472 1 0 1 1 0
#> GSM155476 1 0 1 1 0
#> GSM155480 1 0 1 1 0
#> GSM155484 2 0 1 0 1
#> GSM155488 2 0 1 0 1
#> GSM155492 1 0 1 1 0
#> GSM155496 2 0 1 0 1
#> GSM155500 2 0 1 0 1
#> GSM155504 2 0 1 0 1
#> GSM155450 1 0 1 1 0
#> GSM155453 1 0 1 1 0
#> GSM155457 1 0 1 1 0
#> GSM155461 1 0 1 1 0
#> GSM155465 1 0 1 1 0
#> GSM155469 1 0 1 1 0
#> GSM155473 1 0 1 1 0
#> GSM155477 1 0 1 1 0
#> GSM155481 1 0 1 1 0
#> GSM155485 2 0 1 0 1
#> GSM155489 2 0 1 0 1
#> GSM155493 1 0 1 1 0
#> GSM155497 1 0 1 1 0
#> GSM155501 2 0 1 0 1
#> GSM155505 2 0 1 0 1
#> GSM155451 1 0 1 1 0
#> GSM155454 2 0 1 0 1
#> GSM155458 1 0 1 1 0
#> GSM155462 1 0 1 1 0
#> GSM155466 1 0 1 1 0
#> GSM155470 1 0 1 1 0
#> GSM155474 1 0 1 1 0
#> GSM155478 1 0 1 1 0
#> GSM155482 1 0 1 1 0
#> GSM155486 2 0 1 0 1
#> GSM155490 2 0 1 0 1
#> GSM155494 1 0 1 1 0
#> GSM155498 1 0 1 1 0
#> GSM155502 2 0 1 0 1
#> GSM155506 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 3 0.5497 0.837 0.292 0.000 0.708
#> GSM155452 1 0.0237 0.989 0.996 0.000 0.004
#> GSM155455 1 0.0237 0.989 0.996 0.000 0.004
#> GSM155459 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155463 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155467 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155471 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155475 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155479 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155483 2 0.4605 0.877 0.000 0.796 0.204
#> GSM155487 2 0.0000 0.926 0.000 1.000 0.000
#> GSM155491 3 0.4605 0.887 0.204 0.000 0.796
#> GSM155495 2 0.4605 0.877 0.000 0.796 0.204
#> GSM155499 2 0.0000 0.926 0.000 1.000 0.000
#> GSM155503 2 0.0000 0.926 0.000 1.000 0.000
#> GSM155449 3 0.5497 0.837 0.292 0.000 0.708
#> GSM155456 1 0.0237 0.989 0.996 0.000 0.004
#> GSM155460 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155464 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155468 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155472 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155476 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155480 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155484 2 0.4605 0.877 0.000 0.796 0.204
#> GSM155488 2 0.0000 0.926 0.000 1.000 0.000
#> GSM155492 3 0.3412 0.849 0.124 0.000 0.876
#> GSM155496 3 0.0000 0.706 0.000 0.000 1.000
#> GSM155500 2 0.0000 0.926 0.000 1.000 0.000
#> GSM155504 2 0.0000 0.926 0.000 1.000 0.000
#> GSM155450 3 0.5497 0.837 0.292 0.000 0.708
#> GSM155453 3 0.0000 0.706 0.000 0.000 1.000
#> GSM155457 1 0.0237 0.989 0.996 0.000 0.004
#> GSM155461 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155465 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155469 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155473 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155477 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155481 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155485 2 0.4605 0.877 0.000 0.796 0.204
#> GSM155489 2 0.4605 0.877 0.000 0.796 0.204
#> GSM155493 3 0.3412 0.849 0.124 0.000 0.876
#> GSM155497 3 0.4605 0.887 0.204 0.000 0.796
#> GSM155501 2 0.0000 0.926 0.000 1.000 0.000
#> GSM155505 2 0.0000 0.926 0.000 1.000 0.000
#> GSM155451 3 0.5497 0.837 0.292 0.000 0.708
#> GSM155454 2 0.4605 0.877 0.000 0.796 0.204
#> GSM155458 1 0.3686 0.786 0.860 0.000 0.140
#> GSM155462 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155466 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155470 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155474 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155478 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155482 1 0.0000 0.993 1.000 0.000 0.000
#> GSM155486 2 0.4605 0.877 0.000 0.796 0.204
#> GSM155490 2 0.0000 0.926 0.000 1.000 0.000
#> GSM155494 3 0.4605 0.887 0.204 0.000 0.796
#> GSM155498 3 0.4605 0.887 0.204 0.000 0.796
#> GSM155502 2 0.0000 0.926 0.000 1.000 0.000
#> GSM155506 2 0.0000 0.926 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 4 0.6077 0.5565 0.044 0.000 0.460 0.496
#> GSM155452 1 0.6164 0.4110 0.644 0.000 0.092 0.264
#> GSM155455 1 0.6162 0.4248 0.620 0.000 0.076 0.304
#> GSM155459 1 0.0336 0.8705 0.992 0.000 0.000 0.008
#> GSM155463 1 0.2973 0.8538 0.856 0.000 0.000 0.144
#> GSM155467 1 0.2973 0.8538 0.856 0.000 0.000 0.144
#> GSM155471 1 0.2921 0.8547 0.860 0.000 0.000 0.140
#> GSM155475 1 0.0336 0.8705 0.992 0.000 0.000 0.008
#> GSM155479 1 0.0188 0.8712 0.996 0.000 0.000 0.004
#> GSM155483 2 0.4500 0.7745 0.000 0.684 0.000 0.316
#> GSM155487 2 0.0000 0.8681 0.000 1.000 0.000 0.000
#> GSM155491 3 0.0000 0.9377 0.000 0.000 1.000 0.000
#> GSM155495 2 0.4564 0.7660 0.000 0.672 0.000 0.328
#> GSM155499 2 0.0000 0.8681 0.000 1.000 0.000 0.000
#> GSM155503 2 0.0000 0.8681 0.000 1.000 0.000 0.000
#> GSM155449 4 0.6050 0.5494 0.044 0.000 0.432 0.524
#> GSM155456 1 0.6162 0.4248 0.620 0.000 0.076 0.304
#> GSM155460 1 0.0336 0.8705 0.992 0.000 0.000 0.008
#> GSM155464 1 0.2973 0.8538 0.856 0.000 0.000 0.144
#> GSM155468 1 0.2973 0.8538 0.856 0.000 0.000 0.144
#> GSM155472 1 0.2973 0.8538 0.856 0.000 0.000 0.144
#> GSM155476 1 0.2868 0.8553 0.864 0.000 0.000 0.136
#> GSM155480 1 0.2868 0.8553 0.864 0.000 0.000 0.136
#> GSM155484 2 0.4500 0.7745 0.000 0.684 0.000 0.316
#> GSM155488 2 0.0000 0.8681 0.000 1.000 0.000 0.000
#> GSM155492 3 0.1867 0.8937 0.000 0.000 0.928 0.072
#> GSM155496 4 0.4916 -0.1820 0.000 0.000 0.424 0.576
#> GSM155500 2 0.0000 0.8681 0.000 1.000 0.000 0.000
#> GSM155504 2 0.0000 0.8681 0.000 1.000 0.000 0.000
#> GSM155450 4 0.6077 0.5565 0.044 0.000 0.460 0.496
#> GSM155453 4 0.4948 0.4712 0.000 0.000 0.440 0.560
#> GSM155457 1 0.6162 0.4248 0.620 0.000 0.076 0.304
#> GSM155461 1 0.0000 0.8716 1.000 0.000 0.000 0.000
#> GSM155465 1 0.0336 0.8705 0.992 0.000 0.000 0.008
#> GSM155469 1 0.2973 0.8538 0.856 0.000 0.000 0.144
#> GSM155473 1 0.0000 0.8716 1.000 0.000 0.000 0.000
#> GSM155477 1 0.0188 0.8712 0.996 0.000 0.000 0.004
#> GSM155481 1 0.0188 0.8712 0.996 0.000 0.000 0.004
#> GSM155485 2 0.4500 0.7745 0.000 0.684 0.000 0.316
#> GSM155489 2 0.4500 0.7745 0.000 0.684 0.000 0.316
#> GSM155493 3 0.1867 0.8937 0.000 0.000 0.928 0.072
#> GSM155497 3 0.0657 0.9284 0.012 0.000 0.984 0.004
#> GSM155501 2 0.0000 0.8681 0.000 1.000 0.000 0.000
#> GSM155505 2 0.0000 0.8681 0.000 1.000 0.000 0.000
#> GSM155451 4 0.5912 0.5461 0.036 0.000 0.440 0.524
#> GSM155454 2 0.4992 0.5983 0.000 0.524 0.000 0.476
#> GSM155458 4 0.7207 -0.0072 0.376 0.000 0.144 0.480
#> GSM155462 1 0.0336 0.8705 0.992 0.000 0.000 0.008
#> GSM155466 1 0.0336 0.8705 0.992 0.000 0.000 0.008
#> GSM155470 1 0.0188 0.8712 0.996 0.000 0.000 0.004
#> GSM155474 1 0.0000 0.8716 1.000 0.000 0.000 0.000
#> GSM155478 1 0.3172 0.8456 0.840 0.000 0.000 0.160
#> GSM155482 1 0.3172 0.8456 0.840 0.000 0.000 0.160
#> GSM155486 2 0.4500 0.7745 0.000 0.684 0.000 0.316
#> GSM155490 2 0.0000 0.8681 0.000 1.000 0.000 0.000
#> GSM155494 3 0.0000 0.9377 0.000 0.000 1.000 0.000
#> GSM155498 3 0.0657 0.9284 0.012 0.000 0.984 0.004
#> GSM155502 2 0.0000 0.8681 0.000 1.000 0.000 0.000
#> GSM155506 2 0.0000 0.8681 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.4404 0.640 0.008 0.080 0.136 0.776 0.000
#> GSM155452 1 0.4967 -0.223 0.540 0.008 0.016 0.436 0.000
#> GSM155455 4 0.4046 0.555 0.296 0.000 0.008 0.696 0.000
#> GSM155459 1 0.0162 0.763 0.996 0.000 0.004 0.000 0.000
#> GSM155463 1 0.5941 0.675 0.608 0.164 0.004 0.224 0.000
#> GSM155467 1 0.5792 0.675 0.612 0.164 0.000 0.224 0.000
#> GSM155471 1 0.5714 0.682 0.624 0.164 0.000 0.212 0.000
#> GSM155475 1 0.0000 0.764 1.000 0.000 0.000 0.000 0.000
#> GSM155479 1 0.0000 0.764 1.000 0.000 0.000 0.000 0.000
#> GSM155483 5 0.0000 0.521 0.000 0.000 0.000 0.000 1.000
#> GSM155487 5 0.5576 -0.914 0.000 0.472 0.024 0.028 0.476
#> GSM155491 3 0.1544 0.951 0.000 0.000 0.932 0.068 0.000
#> GSM155495 5 0.2674 0.491 0.000 0.140 0.000 0.004 0.856
#> GSM155499 2 0.4300 0.998 0.000 0.524 0.000 0.000 0.476
#> GSM155503 2 0.4300 0.998 0.000 0.524 0.000 0.000 0.476
#> GSM155449 4 0.3831 0.645 0.008 0.044 0.136 0.812 0.000
#> GSM155456 4 0.4046 0.555 0.296 0.000 0.008 0.696 0.000
#> GSM155460 1 0.0162 0.763 0.996 0.000 0.004 0.000 0.000
#> GSM155464 1 0.5941 0.675 0.608 0.164 0.004 0.224 0.000
#> GSM155468 1 0.5816 0.672 0.608 0.164 0.000 0.228 0.000
#> GSM155472 1 0.5792 0.675 0.612 0.164 0.000 0.224 0.000
#> GSM155476 1 0.5379 0.699 0.668 0.164 0.000 0.168 0.000
#> GSM155480 1 0.5379 0.699 0.668 0.164 0.000 0.168 0.000
#> GSM155484 5 0.0000 0.521 0.000 0.000 0.000 0.000 1.000
#> GSM155488 5 0.5576 -0.914 0.000 0.472 0.024 0.028 0.476
#> GSM155492 3 0.2795 0.908 0.000 0.056 0.880 0.064 0.000
#> GSM155496 5 0.7467 0.104 0.000 0.260 0.156 0.088 0.496
#> GSM155500 2 0.4446 0.994 0.000 0.520 0.000 0.004 0.476
#> GSM155504 2 0.4300 0.998 0.000 0.524 0.000 0.000 0.476
#> GSM155450 4 0.4404 0.640 0.008 0.080 0.136 0.776 0.000
#> GSM155453 4 0.5895 0.447 0.000 0.260 0.152 0.588 0.000
#> GSM155457 4 0.4046 0.555 0.296 0.000 0.008 0.696 0.000
#> GSM155461 1 0.0162 0.763 0.996 0.000 0.004 0.000 0.000
#> GSM155465 1 0.0162 0.763 0.996 0.000 0.004 0.000 0.000
#> GSM155469 1 0.5816 0.672 0.608 0.164 0.000 0.228 0.000
#> GSM155473 1 0.0000 0.764 1.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.0000 0.764 1.000 0.000 0.000 0.000 0.000
#> GSM155481 1 0.0000 0.764 1.000 0.000 0.000 0.000 0.000
#> GSM155485 5 0.0000 0.521 0.000 0.000 0.000 0.000 1.000
#> GSM155489 5 0.0000 0.521 0.000 0.000 0.000 0.000 1.000
#> GSM155493 3 0.2795 0.908 0.000 0.056 0.880 0.064 0.000
#> GSM155497 3 0.2006 0.948 0.000 0.012 0.916 0.072 0.000
#> GSM155501 2 0.4300 0.998 0.000 0.524 0.000 0.000 0.476
#> GSM155505 2 0.4446 0.994 0.000 0.520 0.000 0.004 0.476
#> GSM155451 4 0.4926 0.571 0.000 0.132 0.152 0.716 0.000
#> GSM155454 5 0.5312 0.422 0.000 0.248 0.016 0.064 0.672
#> GSM155458 4 0.2986 0.642 0.084 0.020 0.020 0.876 0.000
#> GSM155462 1 0.0162 0.763 0.996 0.000 0.004 0.000 0.000
#> GSM155466 1 0.0162 0.763 0.996 0.000 0.004 0.000 0.000
#> GSM155470 1 0.0000 0.764 1.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.764 1.000 0.000 0.000 0.000 0.000
#> GSM155478 1 0.6592 0.619 0.544 0.196 0.016 0.244 0.000
#> GSM155482 1 0.6592 0.619 0.544 0.196 0.016 0.244 0.000
#> GSM155486 5 0.0000 0.521 0.000 0.000 0.000 0.000 1.000
#> GSM155490 5 0.5644 -0.912 0.000 0.468 0.024 0.032 0.476
#> GSM155494 3 0.1544 0.951 0.000 0.000 0.932 0.068 0.000
#> GSM155498 3 0.2006 0.948 0.000 0.012 0.916 0.072 0.000
#> GSM155502 2 0.4300 0.998 0.000 0.524 0.000 0.000 0.476
#> GSM155506 2 0.4300 0.998 0.000 0.524 0.000 0.000 0.476
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.3049 0.676 0.004 0.000 0.104 0.844 0.000 0.048
#> GSM155452 4 0.6267 0.319 0.424 0.000 0.016 0.432 0.028 0.100
#> GSM155455 4 0.5353 0.680 0.152 0.000 0.012 0.644 0.004 0.188
#> GSM155459 1 0.0547 0.981 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM155463 6 0.3851 0.947 0.460 0.000 0.000 0.000 0.000 0.540
#> GSM155467 6 0.3851 0.947 0.460 0.000 0.000 0.000 0.000 0.540
#> GSM155471 6 0.3851 0.947 0.460 0.000 0.000 0.000 0.000 0.540
#> GSM155475 1 0.0260 0.984 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM155479 1 0.0146 0.987 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM155483 5 0.3464 0.795 0.000 0.312 0.000 0.000 0.688 0.000
#> GSM155487 2 0.3385 0.799 0.000 0.788 0.000 0.032 0.000 0.180
#> GSM155491 3 0.1082 0.907 0.000 0.000 0.956 0.040 0.000 0.004
#> GSM155495 5 0.2869 0.735 0.000 0.148 0.000 0.000 0.832 0.020
#> GSM155499 2 0.0922 0.915 0.000 0.968 0.004 0.024 0.000 0.004
#> GSM155503 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155449 4 0.3112 0.677 0.004 0.000 0.104 0.840 0.000 0.052
#> GSM155456 4 0.5353 0.680 0.152 0.000 0.012 0.644 0.004 0.188
#> GSM155460 1 0.0547 0.981 0.980 0.000 0.000 0.000 0.020 0.000
#> GSM155464 6 0.3851 0.947 0.460 0.000 0.000 0.000 0.000 0.540
#> GSM155468 6 0.3851 0.947 0.460 0.000 0.000 0.000 0.000 0.540
#> GSM155472 6 0.3851 0.947 0.460 0.000 0.000 0.000 0.000 0.540
#> GSM155476 6 0.3868 0.898 0.496 0.000 0.000 0.000 0.000 0.504
#> GSM155480 6 0.3868 0.898 0.496 0.000 0.000 0.000 0.000 0.504
#> GSM155484 5 0.3464 0.795 0.000 0.312 0.000 0.000 0.688 0.000
#> GSM155488 2 0.4202 0.759 0.000 0.752 0.000 0.032 0.036 0.180
#> GSM155492 3 0.3133 0.853 0.000 0.000 0.856 0.072 0.040 0.032
#> GSM155496 5 0.5778 0.381 0.000 0.000 0.112 0.120 0.648 0.120
#> GSM155500 2 0.0146 0.922 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM155504 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155450 4 0.3049 0.676 0.004 0.000 0.104 0.844 0.000 0.048
#> GSM155453 4 0.5874 0.396 0.000 0.000 0.116 0.620 0.192 0.072
#> GSM155457 4 0.5353 0.680 0.152 0.000 0.012 0.644 0.004 0.188
#> GSM155461 1 0.0260 0.987 0.992 0.000 0.000 0.000 0.008 0.000
#> GSM155465 1 0.0363 0.986 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM155469 6 0.3851 0.947 0.460 0.000 0.000 0.000 0.000 0.540
#> GSM155473 1 0.0146 0.987 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM155477 1 0.0146 0.987 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM155481 1 0.0000 0.987 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155485 5 0.3464 0.795 0.000 0.312 0.000 0.000 0.688 0.000
#> GSM155489 5 0.3464 0.795 0.000 0.312 0.000 0.000 0.688 0.000
#> GSM155493 3 0.3133 0.853 0.000 0.000 0.856 0.072 0.040 0.032
#> GSM155497 3 0.2731 0.889 0.000 0.000 0.876 0.068 0.012 0.044
#> GSM155501 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155505 2 0.0146 0.922 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM155451 4 0.3684 0.595 0.004 0.000 0.112 0.816 0.024 0.044
#> GSM155454 5 0.5168 0.642 0.000 0.104 0.008 0.076 0.720 0.092
#> GSM155458 4 0.4147 0.693 0.044 0.000 0.016 0.744 0.000 0.196
#> GSM155462 1 0.0363 0.986 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM155466 1 0.0363 0.986 0.988 0.000 0.000 0.000 0.012 0.000
#> GSM155470 1 0.0146 0.987 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM155474 1 0.0146 0.987 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM155478 6 0.5450 0.829 0.412 0.000 0.004 0.012 0.072 0.500
#> GSM155482 6 0.5450 0.829 0.412 0.000 0.004 0.012 0.072 0.500
#> GSM155486 5 0.3464 0.795 0.000 0.312 0.000 0.000 0.688 0.000
#> GSM155490 2 0.3248 0.808 0.000 0.804 0.000 0.032 0.000 0.164
#> GSM155494 3 0.0937 0.907 0.000 0.000 0.960 0.040 0.000 0.000
#> GSM155498 3 0.2731 0.889 0.000 0.000 0.876 0.068 0.012 0.044
#> GSM155502 2 0.0000 0.923 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155506 2 0.0922 0.915 0.000 0.968 0.004 0.024 0.000 0.004
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n time(p) k
#> ATC:kmeans 59 0.959 2
#> ATC:kmeans 59 0.988 3
#> ATC:kmeans 52 1.000 4
#> ATC:kmeans 51 1.000 5
#> ATC:kmeans 56 0.947 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 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'skmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.958 0.983 0.4757 0.516 0.516
#> 3 3 0.967 0.897 0.963 0.2673 0.849 0.714
#> 4 4 0.915 0.934 0.964 0.1297 0.878 0.698
#> 5 5 1.000 0.970 0.983 0.0504 0.991 0.968
#> 6 6 0.910 0.925 0.939 0.0351 0.974 0.910
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 4
There is also optional best \(k\) = 2 3 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 1 0.000 1.000 1.000 0.000
#> GSM155452 1 0.000 1.000 1.000 0.000
#> GSM155455 1 0.000 1.000 1.000 0.000
#> GSM155459 1 0.000 1.000 1.000 0.000
#> GSM155463 1 0.000 1.000 1.000 0.000
#> GSM155467 1 0.000 1.000 1.000 0.000
#> GSM155471 1 0.000 1.000 1.000 0.000
#> GSM155475 1 0.000 1.000 1.000 0.000
#> GSM155479 1 0.000 1.000 1.000 0.000
#> GSM155483 2 0.000 0.955 0.000 1.000
#> GSM155487 2 0.000 0.955 0.000 1.000
#> GSM155491 1 0.000 1.000 1.000 0.000
#> GSM155495 2 0.000 0.955 0.000 1.000
#> GSM155499 2 0.000 0.955 0.000 1.000
#> GSM155503 2 0.000 0.955 0.000 1.000
#> GSM155449 1 0.000 1.000 1.000 0.000
#> GSM155456 1 0.000 1.000 1.000 0.000
#> GSM155460 1 0.000 1.000 1.000 0.000
#> GSM155464 1 0.000 1.000 1.000 0.000
#> GSM155468 1 0.000 1.000 1.000 0.000
#> GSM155472 1 0.000 1.000 1.000 0.000
#> GSM155476 1 0.000 1.000 1.000 0.000
#> GSM155480 1 0.000 1.000 1.000 0.000
#> GSM155484 2 0.000 0.955 0.000 1.000
#> GSM155488 2 0.000 0.955 0.000 1.000
#> GSM155492 2 1.000 0.100 0.488 0.512
#> GSM155496 2 0.000 0.955 0.000 1.000
#> GSM155500 2 0.000 0.955 0.000 1.000
#> GSM155504 2 0.000 0.955 0.000 1.000
#> GSM155450 1 0.000 1.000 1.000 0.000
#> GSM155453 2 0.000 0.955 0.000 1.000
#> GSM155457 1 0.000 1.000 1.000 0.000
#> GSM155461 1 0.000 1.000 1.000 0.000
#> GSM155465 1 0.000 1.000 1.000 0.000
#> GSM155469 1 0.000 1.000 1.000 0.000
#> GSM155473 1 0.000 1.000 1.000 0.000
#> GSM155477 1 0.000 1.000 1.000 0.000
#> GSM155481 1 0.000 1.000 1.000 0.000
#> GSM155485 2 0.000 0.955 0.000 1.000
#> GSM155489 2 0.000 0.955 0.000 1.000
#> GSM155493 2 0.697 0.764 0.188 0.812
#> GSM155497 1 0.000 1.000 1.000 0.000
#> GSM155501 2 0.000 0.955 0.000 1.000
#> GSM155505 2 0.000 0.955 0.000 1.000
#> GSM155451 2 0.891 0.577 0.308 0.692
#> GSM155454 2 0.000 0.955 0.000 1.000
#> GSM155458 1 0.000 1.000 1.000 0.000
#> GSM155462 1 0.000 1.000 1.000 0.000
#> GSM155466 1 0.000 1.000 1.000 0.000
#> GSM155470 1 0.000 1.000 1.000 0.000
#> GSM155474 1 0.000 1.000 1.000 0.000
#> GSM155478 1 0.000 1.000 1.000 0.000
#> GSM155482 1 0.000 1.000 1.000 0.000
#> GSM155486 2 0.000 0.955 0.000 1.000
#> GSM155490 2 0.000 0.955 0.000 1.000
#> GSM155494 1 0.000 1.000 1.000 0.000
#> GSM155498 1 0.000 1.000 1.000 0.000
#> GSM155502 2 0.000 0.955 0.000 1.000
#> GSM155506 2 0.000 0.955 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 3 0.6309 0.123 0.496 0.000 0.504
#> GSM155452 1 0.0424 0.971 0.992 0.000 0.008
#> GSM155455 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155459 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155463 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155467 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155471 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155475 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155479 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155483 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155487 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155491 3 0.0000 0.792 0.000 0.000 1.000
#> GSM155495 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155499 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155503 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155449 1 0.6308 -0.207 0.508 0.000 0.492
#> GSM155456 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155460 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155464 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155468 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155472 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155476 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155480 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155484 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155488 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155492 3 0.0000 0.792 0.000 0.000 1.000
#> GSM155496 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155500 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155504 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155450 3 0.6309 0.123 0.496 0.000 0.504
#> GSM155453 2 0.4346 0.755 0.000 0.816 0.184
#> GSM155457 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155461 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155465 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155469 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155473 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155477 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155481 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155485 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155489 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155493 3 0.0000 0.792 0.000 0.000 1.000
#> GSM155497 3 0.0000 0.792 0.000 0.000 1.000
#> GSM155501 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155505 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155451 3 0.8363 0.191 0.084 0.412 0.504
#> GSM155454 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155458 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155462 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155466 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155470 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155474 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155478 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155482 1 0.0000 0.980 1.000 0.000 0.000
#> GSM155486 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155490 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155494 3 0.0000 0.792 0.000 0.000 1.000
#> GSM155498 3 0.0000 0.792 0.000 0.000 1.000
#> GSM155502 2 0.0000 0.989 0.000 1.000 0.000
#> GSM155506 2 0.0000 0.989 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 4 0.000 0.617 0.000 0.000 0 1.000
#> GSM155452 4 0.487 0.620 0.404 0.000 0 0.596
#> GSM155455 4 0.487 0.620 0.404 0.000 0 0.596
#> GSM155459 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155463 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155467 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155471 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155475 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155479 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155483 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155487 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155491 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM155495 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155499 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155503 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155449 4 0.000 0.617 0.000 0.000 0 1.000
#> GSM155456 4 0.487 0.620 0.404 0.000 0 0.596
#> GSM155460 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155464 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155468 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155472 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155476 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155480 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155484 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155488 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155492 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM155496 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155500 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155504 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155450 4 0.000 0.617 0.000 0.000 0 1.000
#> GSM155453 4 0.208 0.549 0.000 0.084 0 0.916
#> GSM155457 4 0.487 0.620 0.404 0.000 0 0.596
#> GSM155461 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155465 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155469 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155473 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155477 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155481 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155485 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155489 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155493 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM155497 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM155501 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155505 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155451 4 0.000 0.617 0.000 0.000 0 1.000
#> GSM155454 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155458 4 0.487 0.620 0.404 0.000 0 0.596
#> GSM155462 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155466 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155470 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155474 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155478 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155482 1 0.000 1.000 1.000 0.000 0 0.000
#> GSM155486 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155490 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155494 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM155498 3 0.000 1.000 0.000 0.000 1 0.000
#> GSM155502 2 0.000 1.000 0.000 1.000 0 0.000
#> GSM155506 2 0.000 1.000 0.000 1.000 0 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.3561 0.716 0.000 0.000 0 0.740 0.260
#> GSM155452 4 0.0162 0.869 0.004 0.000 0 0.996 0.000
#> GSM155455 4 0.0162 0.869 0.004 0.000 0 0.996 0.000
#> GSM155459 1 0.0162 0.995 0.996 0.000 0 0.004 0.000
#> GSM155463 1 0.0000 0.995 1.000 0.000 0 0.000 0.000
#> GSM155467 1 0.0000 0.995 1.000 0.000 0 0.000 0.000
#> GSM155471 1 0.0000 0.995 1.000 0.000 0 0.000 0.000
#> GSM155475 1 0.0162 0.995 0.996 0.000 0 0.004 0.000
#> GSM155479 1 0.0162 0.995 0.996 0.000 0 0.004 0.000
#> GSM155483 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155487 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155491 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155495 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155499 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155503 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155449 4 0.3242 0.755 0.000 0.000 0 0.784 0.216
#> GSM155456 4 0.0162 0.869 0.004 0.000 0 0.996 0.000
#> GSM155460 1 0.0162 0.995 0.996 0.000 0 0.004 0.000
#> GSM155464 1 0.0000 0.995 1.000 0.000 0 0.000 0.000
#> GSM155468 1 0.0000 0.995 1.000 0.000 0 0.000 0.000
#> GSM155472 1 0.0000 0.995 1.000 0.000 0 0.000 0.000
#> GSM155476 1 0.0000 0.995 1.000 0.000 0 0.000 0.000
#> GSM155480 1 0.0000 0.995 1.000 0.000 0 0.000 0.000
#> GSM155484 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155488 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155492 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155496 2 0.0162 0.996 0.000 0.996 0 0.000 0.004
#> GSM155500 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155504 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155450 4 0.3895 0.635 0.000 0.000 0 0.680 0.320
#> GSM155453 5 0.0703 0.987 0.000 0.000 0 0.024 0.976
#> GSM155457 4 0.0162 0.869 0.004 0.000 0 0.996 0.000
#> GSM155461 1 0.0162 0.995 0.996 0.000 0 0.004 0.000
#> GSM155465 1 0.0162 0.995 0.996 0.000 0 0.004 0.000
#> GSM155469 1 0.0000 0.995 1.000 0.000 0 0.000 0.000
#> GSM155473 1 0.0162 0.995 0.996 0.000 0 0.004 0.000
#> GSM155477 1 0.0000 0.995 1.000 0.000 0 0.000 0.000
#> GSM155481 1 0.0162 0.995 0.996 0.000 0 0.004 0.000
#> GSM155485 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155489 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155493 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155497 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155501 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155505 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155451 5 0.0963 0.987 0.000 0.000 0 0.036 0.964
#> GSM155454 2 0.0162 0.996 0.000 0.996 0 0.000 0.004
#> GSM155458 4 0.0162 0.869 0.004 0.000 0 0.996 0.000
#> GSM155462 1 0.0162 0.995 0.996 0.000 0 0.004 0.000
#> GSM155466 1 0.0162 0.995 0.996 0.000 0 0.004 0.000
#> GSM155470 1 0.0162 0.995 0.996 0.000 0 0.004 0.000
#> GSM155474 1 0.0162 0.995 0.996 0.000 0 0.004 0.000
#> GSM155478 1 0.1106 0.965 0.964 0.000 0 0.012 0.024
#> GSM155482 1 0.1106 0.965 0.964 0.000 0 0.012 0.024
#> GSM155486 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155490 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155494 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155498 3 0.0000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155502 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
#> GSM155506 2 0.0000 1.000 0.000 1.000 0 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.5087 0.484 0.000 0.000 0.000 0.560 0.348 0.092
#> GSM155452 4 0.0260 0.796 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM155455 4 0.0260 0.796 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM155459 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155463 1 0.0146 0.994 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM155467 1 0.0146 0.994 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM155471 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155479 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155483 2 0.2260 0.901 0.000 0.860 0.000 0.000 0.000 0.140
#> GSM155487 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155491 3 0.0146 0.994 0.000 0.000 0.996 0.000 0.000 0.004
#> GSM155495 2 0.2562 0.883 0.000 0.828 0.000 0.000 0.000 0.172
#> GSM155499 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155503 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155449 4 0.4845 0.564 0.000 0.000 0.000 0.628 0.280 0.092
#> GSM155456 4 0.0260 0.796 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM155460 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155464 1 0.0146 0.994 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM155468 1 0.0146 0.994 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM155472 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155476 1 0.0260 0.989 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM155480 1 0.0146 0.994 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM155484 2 0.2260 0.901 0.000 0.860 0.000 0.000 0.000 0.140
#> GSM155488 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155492 3 0.0458 0.990 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM155496 2 0.3266 0.795 0.000 0.728 0.000 0.000 0.000 0.272
#> GSM155500 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155504 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155450 4 0.5104 0.448 0.000 0.000 0.000 0.540 0.372 0.088
#> GSM155453 5 0.1152 0.963 0.000 0.000 0.000 0.004 0.952 0.044
#> GSM155457 4 0.0260 0.796 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM155461 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155465 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155469 1 0.0146 0.994 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM155473 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155481 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155485 2 0.2260 0.901 0.000 0.860 0.000 0.000 0.000 0.140
#> GSM155489 2 0.2260 0.901 0.000 0.860 0.000 0.000 0.000 0.140
#> GSM155493 3 0.0458 0.990 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM155497 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155501 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155505 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155451 5 0.0146 0.963 0.000 0.000 0.000 0.004 0.996 0.000
#> GSM155454 2 0.2631 0.875 0.000 0.820 0.000 0.000 0.000 0.180
#> GSM155458 4 0.0260 0.796 0.008 0.000 0.000 0.992 0.000 0.000
#> GSM155462 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155466 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155470 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155478 6 0.3907 1.000 0.408 0.000 0.000 0.000 0.004 0.588
#> GSM155482 6 0.3907 1.000 0.408 0.000 0.000 0.000 0.004 0.588
#> GSM155486 2 0.2260 0.901 0.000 0.860 0.000 0.000 0.000 0.140
#> GSM155490 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155494 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155498 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155502 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155506 2 0.0000 0.932 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n time(p) k
#> ATC:skmeans 58 0.979 2
#> ATC:skmeans 55 0.994 3
#> ATC:skmeans 59 0.999 4
#> ATC:skmeans 59 0.987 5
#> ATC:skmeans 57 0.834 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 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 1.000 1.000 0.4319 0.569 0.569
#> 3 3 0.828 0.936 0.949 0.3016 0.861 0.755
#> 4 4 1.000 0.989 0.990 0.0997 0.947 0.879
#> 5 5 0.837 0.861 0.909 0.2401 0.840 0.586
#> 6 6 0.946 0.946 0.971 0.0875 0.937 0.720
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 4
There is also optional best \(k\) = 2 4 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 1 0 1 1 0
#> GSM155452 1 0 1 1 0
#> GSM155455 1 0 1 1 0
#> GSM155459 1 0 1 1 0
#> GSM155463 1 0 1 1 0
#> GSM155467 1 0 1 1 0
#> GSM155471 1 0 1 1 0
#> GSM155475 1 0 1 1 0
#> GSM155479 1 0 1 1 0
#> GSM155483 2 0 1 0 1
#> GSM155487 2 0 1 0 1
#> GSM155491 1 0 1 1 0
#> GSM155495 2 0 1 0 1
#> GSM155499 2 0 1 0 1
#> GSM155503 2 0 1 0 1
#> GSM155449 1 0 1 1 0
#> GSM155456 1 0 1 1 0
#> GSM155460 1 0 1 1 0
#> GSM155464 1 0 1 1 0
#> GSM155468 1 0 1 1 0
#> GSM155472 1 0 1 1 0
#> GSM155476 1 0 1 1 0
#> GSM155480 1 0 1 1 0
#> GSM155484 2 0 1 0 1
#> GSM155488 2 0 1 0 1
#> GSM155492 1 0 1 1 0
#> GSM155496 1 0 1 1 0
#> GSM155500 2 0 1 0 1
#> GSM155504 2 0 1 0 1
#> GSM155450 1 0 1 1 0
#> GSM155453 1 0 1 1 0
#> GSM155457 1 0 1 1 0
#> GSM155461 1 0 1 1 0
#> GSM155465 1 0 1 1 0
#> GSM155469 1 0 1 1 0
#> GSM155473 1 0 1 1 0
#> GSM155477 1 0 1 1 0
#> GSM155481 1 0 1 1 0
#> GSM155485 2 0 1 0 1
#> GSM155489 2 0 1 0 1
#> GSM155493 1 0 1 1 0
#> GSM155497 1 0 1 1 0
#> GSM155501 2 0 1 0 1
#> GSM155505 2 0 1 0 1
#> GSM155451 1 0 1 1 0
#> GSM155454 2 0 1 0 1
#> GSM155458 1 0 1 1 0
#> GSM155462 1 0 1 1 0
#> GSM155466 1 0 1 1 0
#> GSM155470 1 0 1 1 0
#> GSM155474 1 0 1 1 0
#> GSM155478 1 0 1 1 0
#> GSM155482 1 0 1 1 0
#> GSM155486 2 0 1 0 1
#> GSM155490 2 0 1 0 1
#> GSM155494 1 0 1 1 0
#> GSM155498 1 0 1 1 0
#> GSM155502 2 0 1 0 1
#> GSM155506 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155452 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155455 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155459 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155463 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155467 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155471 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155475 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155479 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155483 2 0.455 0.8774 0.000 0.8 0.200
#> GSM155487 2 0.000 0.9252 0.000 1.0 0.000
#> GSM155491 3 0.455 0.9520 0.200 0.0 0.800
#> GSM155495 2 0.455 0.8774 0.000 0.8 0.200
#> GSM155499 2 0.000 0.9252 0.000 1.0 0.000
#> GSM155503 2 0.000 0.9252 0.000 1.0 0.000
#> GSM155449 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155456 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155460 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155464 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155468 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155472 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155476 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155480 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155484 2 0.455 0.8774 0.000 0.8 0.200
#> GSM155488 2 0.000 0.9252 0.000 1.0 0.000
#> GSM155492 3 0.455 0.9520 0.200 0.0 0.800
#> GSM155496 3 0.000 0.6696 0.000 0.0 1.000
#> GSM155500 2 0.000 0.9252 0.000 1.0 0.000
#> GSM155504 2 0.000 0.9252 0.000 1.0 0.000
#> GSM155450 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155453 1 0.615 0.0186 0.592 0.0 0.408
#> GSM155457 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155461 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155465 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155469 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155473 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155477 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155481 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155485 2 0.455 0.8774 0.000 0.8 0.200
#> GSM155489 2 0.455 0.8774 0.000 0.8 0.200
#> GSM155493 3 0.455 0.9520 0.200 0.0 0.800
#> GSM155497 3 0.455 0.9520 0.200 0.0 0.800
#> GSM155501 2 0.000 0.9252 0.000 1.0 0.000
#> GSM155505 2 0.000 0.9252 0.000 1.0 0.000
#> GSM155451 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155454 2 0.455 0.8774 0.000 0.8 0.200
#> GSM155458 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155462 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155466 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155470 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155474 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155478 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155482 1 0.000 0.9848 1.000 0.0 0.000
#> GSM155486 2 0.455 0.8774 0.000 0.8 0.200
#> GSM155490 2 0.000 0.9252 0.000 1.0 0.000
#> GSM155494 3 0.455 0.9520 0.200 0.0 0.800
#> GSM155498 3 0.455 0.9520 0.200 0.0 0.800
#> GSM155502 2 0.000 0.9252 0.000 1.0 0.000
#> GSM155506 2 0.000 0.9252 0.000 1.0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 1 0.0817 0.982 0.976 0.000 0.024 0.000
#> GSM155452 1 0.0817 0.982 0.976 0.000 0.024 0.000
#> GSM155455 1 0.0817 0.982 0.976 0.000 0.024 0.000
#> GSM155459 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155463 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155467 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155471 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155475 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155479 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155483 3 0.0817 0.995 0.000 0.024 0.976 0.000
#> GSM155487 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM155491 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155495 3 0.0817 0.995 0.000 0.024 0.976 0.000
#> GSM155499 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM155503 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM155449 1 0.0817 0.982 0.976 0.000 0.024 0.000
#> GSM155456 1 0.0817 0.982 0.976 0.000 0.024 0.000
#> GSM155460 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155464 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155468 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155472 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155476 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155480 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155484 3 0.0817 0.995 0.000 0.024 0.976 0.000
#> GSM155488 2 0.2149 0.901 0.000 0.912 0.088 0.000
#> GSM155492 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155496 3 0.0817 0.967 0.000 0.000 0.976 0.024
#> GSM155500 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM155504 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM155450 1 0.0817 0.982 0.976 0.000 0.024 0.000
#> GSM155453 1 0.1792 0.943 0.932 0.000 0.068 0.000
#> GSM155457 1 0.0817 0.982 0.976 0.000 0.024 0.000
#> GSM155461 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155465 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155469 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155473 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155477 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155481 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155485 3 0.0817 0.995 0.000 0.024 0.976 0.000
#> GSM155489 3 0.0817 0.995 0.000 0.024 0.976 0.000
#> GSM155493 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155497 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155501 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM155505 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM155451 1 0.0817 0.982 0.976 0.000 0.024 0.000
#> GSM155454 3 0.0817 0.995 0.000 0.024 0.976 0.000
#> GSM155458 1 0.0817 0.982 0.976 0.000 0.024 0.000
#> GSM155462 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155466 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155470 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155478 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155482 1 0.0000 0.992 1.000 0.000 0.000 0.000
#> GSM155486 3 0.0817 0.995 0.000 0.024 0.976 0.000
#> GSM155490 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM155494 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155498 4 0.0000 1.000 0.000 0.000 0.000 1.000
#> GSM155502 2 0.0000 0.991 0.000 1.000 0.000 0.000
#> GSM155506 2 0.0000 0.991 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.418 0.683 0.400 0.000 0 0.600 0.000
#> GSM155452 1 0.000 0.345 1.000 0.000 0 0.000 0.000
#> GSM155455 4 0.418 0.683 0.400 0.000 0 0.600 0.000
#> GSM155459 1 0.418 0.940 0.600 0.000 0 0.400 0.000
#> GSM155463 4 0.000 0.696 0.000 0.000 0 1.000 0.000
#> GSM155467 4 0.000 0.696 0.000 0.000 0 1.000 0.000
#> GSM155471 4 0.000 0.696 0.000 0.000 0 1.000 0.000
#> GSM155475 1 0.418 0.940 0.600 0.000 0 0.400 0.000
#> GSM155479 1 0.418 0.940 0.600 0.000 0 0.400 0.000
#> GSM155483 5 0.000 1.000 0.000 0.000 0 0.000 1.000
#> GSM155487 2 0.000 0.989 0.000 1.000 0 0.000 0.000
#> GSM155491 3 0.000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155495 5 0.000 1.000 0.000 0.000 0 0.000 1.000
#> GSM155499 2 0.000 0.989 0.000 1.000 0 0.000 0.000
#> GSM155503 2 0.000 0.989 0.000 1.000 0 0.000 0.000
#> GSM155449 4 0.418 0.683 0.400 0.000 0 0.600 0.000
#> GSM155456 4 0.418 0.683 0.400 0.000 0 0.600 0.000
#> GSM155460 1 0.418 0.940 0.600 0.000 0 0.400 0.000
#> GSM155464 4 0.000 0.696 0.000 0.000 0 1.000 0.000
#> GSM155468 4 0.000 0.696 0.000 0.000 0 1.000 0.000
#> GSM155472 4 0.000 0.696 0.000 0.000 0 1.000 0.000
#> GSM155476 4 0.000 0.696 0.000 0.000 0 1.000 0.000
#> GSM155480 4 0.000 0.696 0.000 0.000 0 1.000 0.000
#> GSM155484 5 0.000 1.000 0.000 0.000 0 0.000 1.000
#> GSM155488 2 0.207 0.883 0.000 0.896 0 0.000 0.104
#> GSM155492 3 0.000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155496 5 0.000 1.000 0.000 0.000 0 0.000 1.000
#> GSM155500 2 0.000 0.989 0.000 1.000 0 0.000 0.000
#> GSM155504 2 0.000 0.989 0.000 1.000 0 0.000 0.000
#> GSM155450 4 0.418 0.683 0.400 0.000 0 0.600 0.000
#> GSM155453 4 0.418 0.683 0.400 0.000 0 0.600 0.000
#> GSM155457 4 0.418 0.683 0.400 0.000 0 0.600 0.000
#> GSM155461 1 0.418 0.940 0.600 0.000 0 0.400 0.000
#> GSM155465 1 0.418 0.940 0.600 0.000 0 0.400 0.000
#> GSM155469 4 0.000 0.696 0.000 0.000 0 1.000 0.000
#> GSM155473 1 0.430 0.811 0.512 0.000 0 0.488 0.000
#> GSM155477 1 0.418 0.940 0.600 0.000 0 0.400 0.000
#> GSM155481 1 0.418 0.940 0.600 0.000 0 0.400 0.000
#> GSM155485 5 0.000 1.000 0.000 0.000 0 0.000 1.000
#> GSM155489 5 0.000 1.000 0.000 0.000 0 0.000 1.000
#> GSM155493 3 0.000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155497 3 0.000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155501 2 0.000 0.989 0.000 1.000 0 0.000 0.000
#> GSM155505 2 0.000 0.989 0.000 1.000 0 0.000 0.000
#> GSM155451 4 0.418 0.683 0.400 0.000 0 0.600 0.000
#> GSM155454 5 0.000 1.000 0.000 0.000 0 0.000 1.000
#> GSM155458 4 0.418 0.683 0.400 0.000 0 0.600 0.000
#> GSM155462 1 0.418 0.940 0.600 0.000 0 0.400 0.000
#> GSM155466 1 0.418 0.940 0.600 0.000 0 0.400 0.000
#> GSM155470 1 0.418 0.940 0.600 0.000 0 0.400 0.000
#> GSM155474 4 0.000 0.696 0.000 0.000 0 1.000 0.000
#> GSM155478 4 0.000 0.696 0.000 0.000 0 1.000 0.000
#> GSM155482 4 0.000 0.696 0.000 0.000 0 1.000 0.000
#> GSM155486 5 0.000 1.000 0.000 0.000 0 0.000 1.000
#> GSM155490 2 0.000 0.989 0.000 1.000 0 0.000 0.000
#> GSM155494 3 0.000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155498 3 0.000 1.000 0.000 0.000 1 0.000 0.000
#> GSM155502 2 0.000 0.989 0.000 1.000 0 0.000 0.000
#> GSM155506 2 0.000 0.989 0.000 1.000 0 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.0000 0.847 0.000 0.000 0 1.000 0.000 0.000
#> GSM155452 1 0.0146 0.943 0.996 0.000 0 0.004 0.000 0.000
#> GSM155455 4 0.3266 0.756 0.000 0.000 0 0.728 0.000 0.272
#> GSM155459 1 0.0000 0.945 1.000 0.000 0 0.000 0.000 0.000
#> GSM155463 6 0.0000 0.998 0.000 0.000 0 0.000 0.000 1.000
#> GSM155467 6 0.0000 0.998 0.000 0.000 0 0.000 0.000 1.000
#> GSM155471 6 0.0000 0.998 0.000 0.000 0 0.000 0.000 1.000
#> GSM155475 1 0.0000 0.945 1.000 0.000 0 0.000 0.000 0.000
#> GSM155479 1 0.3076 0.719 0.760 0.000 0 0.000 0.000 0.240
#> GSM155483 5 0.0000 0.999 0.000 0.000 0 0.000 1.000 0.000
#> GSM155487 2 0.0000 0.989 0.000 1.000 0 0.000 0.000 0.000
#> GSM155491 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM155495 5 0.0000 0.999 0.000 0.000 0 0.000 1.000 0.000
#> GSM155499 2 0.0000 0.989 0.000 1.000 0 0.000 0.000 0.000
#> GSM155503 2 0.0000 0.989 0.000 1.000 0 0.000 0.000 0.000
#> GSM155449 4 0.0000 0.847 0.000 0.000 0 1.000 0.000 0.000
#> GSM155456 4 0.3266 0.756 0.000 0.000 0 0.728 0.000 0.272
#> GSM155460 1 0.0000 0.945 1.000 0.000 0 0.000 0.000 0.000
#> GSM155464 6 0.0000 0.998 0.000 0.000 0 0.000 0.000 1.000
#> GSM155468 6 0.0000 0.998 0.000 0.000 0 0.000 0.000 1.000
#> GSM155472 6 0.0000 0.998 0.000 0.000 0 0.000 0.000 1.000
#> GSM155476 6 0.0000 0.998 0.000 0.000 0 0.000 0.000 1.000
#> GSM155480 6 0.0000 0.998 0.000 0.000 0 0.000 0.000 1.000
#> GSM155484 5 0.0000 0.999 0.000 0.000 0 0.000 1.000 0.000
#> GSM155488 2 0.1863 0.883 0.000 0.896 0 0.000 0.104 0.000
#> GSM155492 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM155496 5 0.0260 0.992 0.000 0.000 0 0.008 0.992 0.000
#> GSM155500 2 0.0000 0.989 0.000 1.000 0 0.000 0.000 0.000
#> GSM155504 2 0.0000 0.989 0.000 1.000 0 0.000 0.000 0.000
#> GSM155450 4 0.0000 0.847 0.000 0.000 0 1.000 0.000 0.000
#> GSM155453 4 0.0000 0.847 0.000 0.000 0 1.000 0.000 0.000
#> GSM155457 4 0.3266 0.756 0.000 0.000 0 0.728 0.000 0.272
#> GSM155461 1 0.0146 0.943 0.996 0.000 0 0.000 0.000 0.004
#> GSM155465 1 0.0000 0.945 1.000 0.000 0 0.000 0.000 0.000
#> GSM155469 6 0.0000 0.998 0.000 0.000 0 0.000 0.000 1.000
#> GSM155473 1 0.0458 0.936 0.984 0.000 0 0.000 0.000 0.016
#> GSM155477 1 0.3076 0.719 0.760 0.000 0 0.000 0.000 0.240
#> GSM155481 1 0.0000 0.945 1.000 0.000 0 0.000 0.000 0.000
#> GSM155485 5 0.0000 0.999 0.000 0.000 0 0.000 1.000 0.000
#> GSM155489 5 0.0000 0.999 0.000 0.000 0 0.000 1.000 0.000
#> GSM155493 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM155497 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM155501 2 0.0000 0.989 0.000 1.000 0 0.000 0.000 0.000
#> GSM155505 2 0.0000 0.989 0.000 1.000 0 0.000 0.000 0.000
#> GSM155451 4 0.0000 0.847 0.000 0.000 0 1.000 0.000 0.000
#> GSM155454 5 0.0000 0.999 0.000 0.000 0 0.000 1.000 0.000
#> GSM155458 4 0.2597 0.816 0.000 0.000 0 0.824 0.000 0.176
#> GSM155462 1 0.0000 0.945 1.000 0.000 0 0.000 0.000 0.000
#> GSM155466 1 0.0000 0.945 1.000 0.000 0 0.000 0.000 0.000
#> GSM155470 1 0.1267 0.901 0.940 0.000 0 0.000 0.000 0.060
#> GSM155474 6 0.0547 0.974 0.020 0.000 0 0.000 0.000 0.980
#> GSM155478 6 0.0000 0.998 0.000 0.000 0 0.000 0.000 1.000
#> GSM155482 6 0.0000 0.998 0.000 0.000 0 0.000 0.000 1.000
#> GSM155486 5 0.0000 0.999 0.000 0.000 0 0.000 1.000 0.000
#> GSM155490 2 0.0000 0.989 0.000 1.000 0 0.000 0.000 0.000
#> GSM155494 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM155498 3 0.0000 1.000 0.000 0.000 1 0.000 0.000 0.000
#> GSM155502 2 0.0000 0.989 0.000 1.000 0 0.000 0.000 0.000
#> GSM155506 2 0.0000 0.989 0.000 1.000 0 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 time(p) k
#> ATC:pam 59 0.971 2
#> ATC:pam 58 0.995 3
#> ATC:pam 59 0.999 4
#> ATC:pam 58 0.974 5
#> ATC:pam 59 0.966 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 59 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 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.998 0.999 0.4972 0.503 0.503
#> 3 3 0.881 0.934 0.957 0.3351 0.710 0.482
#> 4 4 0.912 0.889 0.942 0.0970 0.947 0.837
#> 5 5 0.961 0.889 0.959 0.0469 0.948 0.813
#> 6 6 0.976 0.920 0.965 0.0263 0.970 0.873
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 4 5
There is also optional best \(k\) = 2 4 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM155448 1 0.0672 0.994 0.992 0.008
#> GSM155452 1 0.0672 0.994 0.992 0.008
#> GSM155455 1 0.0672 0.994 0.992 0.008
#> GSM155459 1 0.0000 0.997 1.000 0.000
#> GSM155463 1 0.0000 0.997 1.000 0.000
#> GSM155467 1 0.0000 0.997 1.000 0.000
#> GSM155471 1 0.0000 0.997 1.000 0.000
#> GSM155475 1 0.0000 0.997 1.000 0.000
#> GSM155479 1 0.0000 0.997 1.000 0.000
#> GSM155483 2 0.0000 1.000 0.000 1.000
#> GSM155487 2 0.0000 1.000 0.000 1.000
#> GSM155491 2 0.0000 1.000 0.000 1.000
#> GSM155495 2 0.0000 1.000 0.000 1.000
#> GSM155499 2 0.0000 1.000 0.000 1.000
#> GSM155503 2 0.0000 1.000 0.000 1.000
#> GSM155449 1 0.0672 0.994 0.992 0.008
#> GSM155456 1 0.0672 0.994 0.992 0.008
#> GSM155460 1 0.0000 0.997 1.000 0.000
#> GSM155464 1 0.0000 0.997 1.000 0.000
#> GSM155468 1 0.0000 0.997 1.000 0.000
#> GSM155472 1 0.0000 0.997 1.000 0.000
#> GSM155476 1 0.0000 0.997 1.000 0.000
#> GSM155480 1 0.0000 0.997 1.000 0.000
#> GSM155484 2 0.0000 1.000 0.000 1.000
#> GSM155488 2 0.0000 1.000 0.000 1.000
#> GSM155492 2 0.0000 1.000 0.000 1.000
#> GSM155496 2 0.0000 1.000 0.000 1.000
#> GSM155500 2 0.0000 1.000 0.000 1.000
#> GSM155504 2 0.0000 1.000 0.000 1.000
#> GSM155450 1 0.0672 0.994 0.992 0.008
#> GSM155453 1 0.0672 0.994 0.992 0.008
#> GSM155457 1 0.0672 0.994 0.992 0.008
#> GSM155461 1 0.0000 0.997 1.000 0.000
#> GSM155465 1 0.0000 0.997 1.000 0.000
#> GSM155469 1 0.0000 0.997 1.000 0.000
#> GSM155473 1 0.0000 0.997 1.000 0.000
#> GSM155477 1 0.0000 0.997 1.000 0.000
#> GSM155481 1 0.0000 0.997 1.000 0.000
#> GSM155485 2 0.0000 1.000 0.000 1.000
#> GSM155489 2 0.0000 1.000 0.000 1.000
#> GSM155493 2 0.0000 1.000 0.000 1.000
#> GSM155497 2 0.0000 1.000 0.000 1.000
#> GSM155501 2 0.0000 1.000 0.000 1.000
#> GSM155505 2 0.0000 1.000 0.000 1.000
#> GSM155451 1 0.0672 0.994 0.992 0.008
#> GSM155454 2 0.0000 1.000 0.000 1.000
#> GSM155458 1 0.0672 0.994 0.992 0.008
#> GSM155462 1 0.0000 0.997 1.000 0.000
#> GSM155466 1 0.0000 0.997 1.000 0.000
#> GSM155470 1 0.0000 0.997 1.000 0.000
#> GSM155474 1 0.0000 0.997 1.000 0.000
#> GSM155478 1 0.0376 0.996 0.996 0.004
#> GSM155482 1 0.0376 0.996 0.996 0.004
#> GSM155486 2 0.0000 1.000 0.000 1.000
#> GSM155490 2 0.0000 1.000 0.000 1.000
#> GSM155494 2 0.0000 1.000 0.000 1.000
#> GSM155498 2 0.0000 1.000 0.000 1.000
#> GSM155502 2 0.0000 1.000 0.000 1.000
#> GSM155506 2 0.0000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 3 0.196 0.929 0.056 0.000 0.944
#> GSM155452 3 0.196 0.929 0.056 0.000 0.944
#> GSM155455 3 0.196 0.929 0.056 0.000 0.944
#> GSM155459 1 0.000 1.000 1.000 0.000 0.000
#> GSM155463 1 0.000 1.000 1.000 0.000 0.000
#> GSM155467 1 0.000 1.000 1.000 0.000 0.000
#> GSM155471 1 0.000 1.000 1.000 0.000 0.000
#> GSM155475 1 0.000 1.000 1.000 0.000 0.000
#> GSM155479 1 0.000 1.000 1.000 0.000 0.000
#> GSM155483 2 0.406 0.896 0.000 0.836 0.164
#> GSM155487 2 0.000 0.931 0.000 1.000 0.000
#> GSM155491 3 0.000 0.913 0.000 0.000 1.000
#> GSM155495 2 0.406 0.896 0.000 0.836 0.164
#> GSM155499 2 0.000 0.931 0.000 1.000 0.000
#> GSM155503 2 0.000 0.931 0.000 1.000 0.000
#> GSM155449 3 0.196 0.929 0.056 0.000 0.944
#> GSM155456 3 0.196 0.929 0.056 0.000 0.944
#> GSM155460 1 0.000 1.000 1.000 0.000 0.000
#> GSM155464 1 0.000 1.000 1.000 0.000 0.000
#> GSM155468 1 0.000 1.000 1.000 0.000 0.000
#> GSM155472 1 0.000 1.000 1.000 0.000 0.000
#> GSM155476 1 0.000 1.000 1.000 0.000 0.000
#> GSM155480 1 0.000 1.000 1.000 0.000 0.000
#> GSM155484 2 0.406 0.896 0.000 0.836 0.164
#> GSM155488 2 0.312 0.907 0.000 0.892 0.108
#> GSM155492 3 0.000 0.913 0.000 0.000 1.000
#> GSM155496 3 0.000 0.913 0.000 0.000 1.000
#> GSM155500 2 0.000 0.931 0.000 1.000 0.000
#> GSM155504 2 0.000 0.931 0.000 1.000 0.000
#> GSM155450 3 0.196 0.929 0.056 0.000 0.944
#> GSM155453 3 0.196 0.929 0.056 0.000 0.944
#> GSM155457 3 0.196 0.929 0.056 0.000 0.944
#> GSM155461 1 0.000 1.000 1.000 0.000 0.000
#> GSM155465 1 0.000 1.000 1.000 0.000 0.000
#> GSM155469 1 0.000 1.000 1.000 0.000 0.000
#> GSM155473 1 0.000 1.000 1.000 0.000 0.000
#> GSM155477 1 0.000 1.000 1.000 0.000 0.000
#> GSM155481 1 0.000 1.000 1.000 0.000 0.000
#> GSM155485 2 0.406 0.896 0.000 0.836 0.164
#> GSM155489 2 0.406 0.896 0.000 0.836 0.164
#> GSM155493 3 0.000 0.913 0.000 0.000 1.000
#> GSM155497 3 0.000 0.913 0.000 0.000 1.000
#> GSM155501 2 0.000 0.931 0.000 1.000 0.000
#> GSM155505 2 0.000 0.931 0.000 1.000 0.000
#> GSM155451 3 0.196 0.929 0.056 0.000 0.944
#> GSM155454 3 0.196 0.896 0.000 0.056 0.944
#> GSM155458 3 0.196 0.929 0.056 0.000 0.944
#> GSM155462 1 0.000 1.000 1.000 0.000 0.000
#> GSM155466 1 0.000 1.000 1.000 0.000 0.000
#> GSM155470 1 0.000 1.000 1.000 0.000 0.000
#> GSM155474 1 0.000 1.000 1.000 0.000 0.000
#> GSM155478 3 0.604 0.483 0.380 0.000 0.620
#> GSM155482 3 0.604 0.483 0.380 0.000 0.620
#> GSM155486 2 0.406 0.896 0.000 0.836 0.164
#> GSM155490 2 0.226 0.920 0.000 0.932 0.068
#> GSM155494 3 0.000 0.913 0.000 0.000 1.000
#> GSM155498 3 0.000 0.913 0.000 0.000 1.000
#> GSM155502 2 0.000 0.931 0.000 1.000 0.000
#> GSM155506 2 0.000 0.931 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 4 0.000 0.911 0.000 0.000 0.000 1.000
#> GSM155452 4 0.000 0.911 0.000 0.000 0.000 1.000
#> GSM155455 4 0.000 0.911 0.000 0.000 0.000 1.000
#> GSM155459 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155463 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155467 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155471 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155475 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155479 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155483 2 0.470 0.646 0.000 0.644 0.356 0.000
#> GSM155487 2 0.000 0.819 0.000 1.000 0.000 0.000
#> GSM155491 3 0.000 0.981 0.000 0.000 1.000 0.000
#> GSM155495 2 0.470 0.646 0.000 0.644 0.356 0.000
#> GSM155499 2 0.000 0.819 0.000 1.000 0.000 0.000
#> GSM155503 2 0.000 0.819 0.000 1.000 0.000 0.000
#> GSM155449 4 0.000 0.911 0.000 0.000 0.000 1.000
#> GSM155456 4 0.000 0.911 0.000 0.000 0.000 1.000
#> GSM155460 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155464 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155468 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155472 1 0.102 0.964 0.968 0.000 0.000 0.032
#> GSM155476 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155480 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155484 2 0.470 0.646 0.000 0.644 0.356 0.000
#> GSM155488 2 0.425 0.701 0.000 0.724 0.276 0.000
#> GSM155492 3 0.000 0.981 0.000 0.000 1.000 0.000
#> GSM155496 3 0.215 0.872 0.000 0.088 0.912 0.000
#> GSM155500 2 0.000 0.819 0.000 1.000 0.000 0.000
#> GSM155504 2 0.000 0.819 0.000 1.000 0.000 0.000
#> GSM155450 4 0.000 0.911 0.000 0.000 0.000 1.000
#> GSM155453 4 0.000 0.911 0.000 0.000 0.000 1.000
#> GSM155457 4 0.000 0.911 0.000 0.000 0.000 1.000
#> GSM155461 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155465 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155469 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155473 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155477 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155481 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155485 2 0.470 0.646 0.000 0.644 0.356 0.000
#> GSM155489 2 0.470 0.646 0.000 0.644 0.356 0.000
#> GSM155493 3 0.000 0.981 0.000 0.000 1.000 0.000
#> GSM155497 3 0.000 0.981 0.000 0.000 1.000 0.000
#> GSM155501 2 0.000 0.819 0.000 1.000 0.000 0.000
#> GSM155505 2 0.000 0.819 0.000 1.000 0.000 0.000
#> GSM155451 4 0.000 0.911 0.000 0.000 0.000 1.000
#> GSM155454 4 0.387 0.694 0.000 0.228 0.000 0.772
#> GSM155458 4 0.000 0.911 0.000 0.000 0.000 1.000
#> GSM155462 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155466 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155470 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155474 1 0.000 0.998 1.000 0.000 0.000 0.000
#> GSM155478 4 0.443 0.596 0.304 0.000 0.000 0.696
#> GSM155482 4 0.443 0.596 0.304 0.000 0.000 0.696
#> GSM155486 2 0.470 0.646 0.000 0.644 0.356 0.000
#> GSM155490 2 0.130 0.808 0.000 0.956 0.044 0.000
#> GSM155494 3 0.000 0.981 0.000 0.000 1.000 0.000
#> GSM155498 3 0.000 0.981 0.000 0.000 1.000 0.000
#> GSM155502 2 0.000 0.819 0.000 1.000 0.000 0.000
#> GSM155506 2 0.000 0.819 0.000 1.000 0.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000
#> GSM155452 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000
#> GSM155455 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000
#> GSM155459 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155463 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155467 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155479 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155483 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM155487 2 0.0000 0.882 0.000 1.000 0.000 0.000 0.000
#> GSM155491 3 0.0000 0.931 0.000 0.000 1.000 0.000 0.000
#> GSM155495 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM155499 2 0.0000 0.882 0.000 1.000 0.000 0.000 0.000
#> GSM155503 2 0.0000 0.882 0.000 1.000 0.000 0.000 0.000
#> GSM155449 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000
#> GSM155456 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000
#> GSM155460 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155464 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155468 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155472 1 0.0404 0.986 0.988 0.000 0.000 0.012 0.000
#> GSM155476 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155480 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155484 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM155488 2 0.4273 0.247 0.000 0.552 0.000 0.000 0.448
#> GSM155492 3 0.0000 0.931 0.000 0.000 1.000 0.000 0.000
#> GSM155496 3 0.4171 0.334 0.000 0.000 0.604 0.000 0.396
#> GSM155500 2 0.0000 0.882 0.000 1.000 0.000 0.000 0.000
#> GSM155504 2 0.0000 0.882 0.000 1.000 0.000 0.000 0.000
#> GSM155450 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000
#> GSM155453 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000
#> GSM155457 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000
#> GSM155461 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155465 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155469 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155473 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155481 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155485 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM155489 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM155493 3 0.0000 0.931 0.000 0.000 1.000 0.000 0.000
#> GSM155497 3 0.0000 0.931 0.000 0.000 1.000 0.000 0.000
#> GSM155501 2 0.0000 0.882 0.000 1.000 0.000 0.000 0.000
#> GSM155505 2 0.0000 0.882 0.000 1.000 0.000 0.000 0.000
#> GSM155451 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000
#> GSM155454 2 0.4210 0.300 0.000 0.588 0.000 0.412 0.000
#> GSM155458 4 0.0000 0.890 0.000 0.000 0.000 1.000 0.000
#> GSM155462 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155466 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155470 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.999 1.000 0.000 0.000 0.000 0.000
#> GSM155478 4 0.4262 0.286 0.440 0.000 0.000 0.560 0.000
#> GSM155482 4 0.4219 0.349 0.416 0.000 0.000 0.584 0.000
#> GSM155486 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000
#> GSM155490 2 0.3913 0.525 0.000 0.676 0.000 0.000 0.324
#> GSM155494 3 0.0000 0.931 0.000 0.000 1.000 0.000 0.000
#> GSM155498 3 0.0000 0.931 0.000 0.000 1.000 0.000 0.000
#> GSM155502 2 0.0000 0.882 0.000 1.000 0.000 0.000 0.000
#> GSM155506 2 0.0000 0.882 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.0260 0.935 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM155452 4 0.0713 0.938 0.000 0.000 0.000 0.972 0.000 0.028
#> GSM155455 4 0.2135 0.913 0.000 0.000 0.000 0.872 0.000 0.128
#> GSM155459 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155463 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155467 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155471 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155475 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155479 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155483 5 0.0000 0.851 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155487 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155491 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155495 5 0.0000 0.851 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155499 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155503 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155449 4 0.0790 0.938 0.000 0.000 0.000 0.968 0.000 0.032
#> GSM155456 4 0.2135 0.913 0.000 0.000 0.000 0.872 0.000 0.128
#> GSM155460 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155464 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155468 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155472 1 0.0547 0.980 0.980 0.000 0.000 0.000 0.000 0.020
#> GSM155476 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155480 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155484 5 0.0000 0.851 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155488 5 0.3390 0.578 0.000 0.296 0.000 0.000 0.704 0.000
#> GSM155492 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155496 3 0.2996 0.680 0.000 0.000 0.772 0.000 0.228 0.000
#> GSM155500 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155504 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155450 4 0.0260 0.935 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM155453 4 0.0260 0.935 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM155457 4 0.2135 0.913 0.000 0.000 0.000 0.872 0.000 0.128
#> GSM155461 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155465 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155469 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155473 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155477 1 0.0146 0.995 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM155481 1 0.0260 0.992 0.992 0.000 0.000 0.000 0.000 0.008
#> GSM155485 5 0.0000 0.851 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155489 5 0.0000 0.851 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155493 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155497 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155501 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155505 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155451 4 0.0260 0.935 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM155454 2 0.3782 0.314 0.000 0.588 0.000 0.412 0.000 0.000
#> GSM155458 4 0.1957 0.920 0.000 0.000 0.000 0.888 0.000 0.112
#> GSM155462 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155466 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155470 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.998 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM155478 6 0.0937 0.980 0.040 0.000 0.000 0.000 0.000 0.960
#> GSM155482 6 0.0713 0.980 0.028 0.000 0.000 0.000 0.000 0.972
#> GSM155486 5 0.0000 0.851 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM155490 5 0.3851 0.234 0.000 0.460 0.000 0.000 0.540 0.000
#> GSM155494 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155498 3 0.0000 0.952 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM155502 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM155506 2 0.0000 0.942 0.000 1.000 0.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n time(p) k
#> ATC:mclust 59 0.980 2
#> ATC:mclust 57 0.993 3
#> ATC:mclust 59 0.979 4
#> ATC:mclust 54 0.999 5
#> ATC:mclust 57 0.908 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 59 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.986 0.994 0.4410 0.556 0.556
#> 3 3 0.999 0.977 0.987 0.3419 0.837 0.711
#> 4 4 0.721 0.691 0.801 0.1519 0.891 0.743
#> 5 5 0.836 0.902 0.906 0.0881 0.866 0.625
#> 6 6 0.921 0.880 0.906 0.0309 1.000 1.000
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 3
#> 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
#> GSM155448 1 0.000 0.999 1.000 0.000
#> GSM155452 1 0.000 0.999 1.000 0.000
#> GSM155455 1 0.000 0.999 1.000 0.000
#> GSM155459 1 0.000 0.999 1.000 0.000
#> GSM155463 1 0.000 0.999 1.000 0.000
#> GSM155467 1 0.000 0.999 1.000 0.000
#> GSM155471 1 0.000 0.999 1.000 0.000
#> GSM155475 1 0.000 0.999 1.000 0.000
#> GSM155479 1 0.000 0.999 1.000 0.000
#> GSM155483 2 0.000 0.982 0.000 1.000
#> GSM155487 2 0.000 0.982 0.000 1.000
#> GSM155491 1 0.000 0.999 1.000 0.000
#> GSM155495 2 0.000 0.982 0.000 1.000
#> GSM155499 2 0.000 0.982 0.000 1.000
#> GSM155503 2 0.000 0.982 0.000 1.000
#> GSM155449 1 0.000 0.999 1.000 0.000
#> GSM155456 1 0.000 0.999 1.000 0.000
#> GSM155460 1 0.000 0.999 1.000 0.000
#> GSM155464 1 0.000 0.999 1.000 0.000
#> GSM155468 1 0.000 0.999 1.000 0.000
#> GSM155472 1 0.000 0.999 1.000 0.000
#> GSM155476 1 0.000 0.999 1.000 0.000
#> GSM155480 1 0.000 0.999 1.000 0.000
#> GSM155484 2 0.000 0.982 0.000 1.000
#> GSM155488 2 0.000 0.982 0.000 1.000
#> GSM155492 1 0.000 0.999 1.000 0.000
#> GSM155496 2 0.900 0.537 0.316 0.684
#> GSM155500 2 0.000 0.982 0.000 1.000
#> GSM155504 2 0.000 0.982 0.000 1.000
#> GSM155450 1 0.000 0.999 1.000 0.000
#> GSM155453 1 0.204 0.966 0.968 0.032
#> GSM155457 1 0.000 0.999 1.000 0.000
#> GSM155461 1 0.000 0.999 1.000 0.000
#> GSM155465 1 0.000 0.999 1.000 0.000
#> GSM155469 1 0.000 0.999 1.000 0.000
#> GSM155473 1 0.000 0.999 1.000 0.000
#> GSM155477 1 0.000 0.999 1.000 0.000
#> GSM155481 1 0.000 0.999 1.000 0.000
#> GSM155485 2 0.000 0.982 0.000 1.000
#> GSM155489 2 0.000 0.982 0.000 1.000
#> GSM155493 1 0.000 0.999 1.000 0.000
#> GSM155497 1 0.000 0.999 1.000 0.000
#> GSM155501 2 0.000 0.982 0.000 1.000
#> GSM155505 2 0.000 0.982 0.000 1.000
#> GSM155451 1 0.000 0.999 1.000 0.000
#> GSM155454 2 0.000 0.982 0.000 1.000
#> GSM155458 1 0.000 0.999 1.000 0.000
#> GSM155462 1 0.000 0.999 1.000 0.000
#> GSM155466 1 0.000 0.999 1.000 0.000
#> GSM155470 1 0.000 0.999 1.000 0.000
#> GSM155474 1 0.000 0.999 1.000 0.000
#> GSM155478 1 0.000 0.999 1.000 0.000
#> GSM155482 1 0.000 0.999 1.000 0.000
#> GSM155486 2 0.000 0.982 0.000 1.000
#> GSM155490 2 0.000 0.982 0.000 1.000
#> GSM155494 1 0.000 0.999 1.000 0.000
#> GSM155498 1 0.000 0.999 1.000 0.000
#> GSM155502 2 0.000 0.982 0.000 1.000
#> GSM155506 2 0.000 0.982 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM155448 1 0.0892 0.984 0.980 0.000 0.020
#> GSM155452 1 0.0424 0.995 0.992 0.000 0.008
#> GSM155455 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155459 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155463 1 0.0000 0.997 1.000 0.000 0.000
#> GSM155467 1 0.0000 0.997 1.000 0.000 0.000
#> GSM155471 1 0.0000 0.997 1.000 0.000 0.000
#> GSM155475 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155479 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155483 2 0.1289 0.954 0.000 0.968 0.032
#> GSM155487 2 0.0237 0.970 0.000 0.996 0.004
#> GSM155491 3 0.0237 0.978 0.004 0.000 0.996
#> GSM155495 3 0.1163 0.958 0.000 0.028 0.972
#> GSM155499 2 0.0237 0.970 0.000 0.996 0.004
#> GSM155503 2 0.0000 0.970 0.000 1.000 0.000
#> GSM155449 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155456 1 0.0424 0.995 0.992 0.000 0.008
#> GSM155460 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155464 1 0.0000 0.997 1.000 0.000 0.000
#> GSM155468 1 0.0000 0.997 1.000 0.000 0.000
#> GSM155472 1 0.0000 0.997 1.000 0.000 0.000
#> GSM155476 1 0.0000 0.997 1.000 0.000 0.000
#> GSM155480 1 0.0000 0.997 1.000 0.000 0.000
#> GSM155484 2 0.0237 0.970 0.000 0.996 0.004
#> GSM155488 2 0.0237 0.970 0.000 0.996 0.004
#> GSM155492 3 0.0000 0.978 0.000 0.000 1.000
#> GSM155496 3 0.0000 0.978 0.000 0.000 1.000
#> GSM155500 2 0.0000 0.970 0.000 1.000 0.000
#> GSM155504 2 0.0000 0.970 0.000 1.000 0.000
#> GSM155450 1 0.0424 0.995 0.992 0.000 0.008
#> GSM155453 3 0.4399 0.864 0.044 0.092 0.864
#> GSM155457 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155461 1 0.0000 0.997 1.000 0.000 0.000
#> GSM155465 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155469 1 0.0000 0.997 1.000 0.000 0.000
#> GSM155473 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155477 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155481 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155485 2 0.2448 0.919 0.000 0.924 0.076
#> GSM155489 2 0.3340 0.876 0.000 0.880 0.120
#> GSM155493 3 0.0000 0.978 0.000 0.000 1.000
#> GSM155497 3 0.0237 0.978 0.004 0.000 0.996
#> GSM155501 2 0.0000 0.970 0.000 1.000 0.000
#> GSM155505 2 0.0000 0.970 0.000 1.000 0.000
#> GSM155451 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155454 2 0.4931 0.721 0.000 0.768 0.232
#> GSM155458 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155462 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155466 1 0.0000 0.997 1.000 0.000 0.000
#> GSM155470 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155474 1 0.0237 0.997 0.996 0.000 0.004
#> GSM155478 1 0.0000 0.997 1.000 0.000 0.000
#> GSM155482 1 0.0000 0.997 1.000 0.000 0.000
#> GSM155486 2 0.0424 0.968 0.000 0.992 0.008
#> GSM155490 2 0.0000 0.970 0.000 1.000 0.000
#> GSM155494 3 0.0237 0.978 0.004 0.000 0.996
#> GSM155498 3 0.0237 0.978 0.004 0.000 0.996
#> GSM155502 2 0.0000 0.970 0.000 1.000 0.000
#> GSM155506 2 0.0237 0.970 0.000 0.996 0.004
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM155448 4 0.7875 0.2658 0.316 0.000 0.296 0.388
#> GSM155452 4 0.7846 0.3042 0.300 0.000 0.296 0.404
#> GSM155455 1 0.7899 -0.2253 0.364 0.000 0.296 0.340
#> GSM155459 1 0.0336 0.8470 0.992 0.000 0.008 0.000
#> GSM155463 1 0.1211 0.8390 0.960 0.000 0.040 0.000
#> GSM155467 1 0.1716 0.8218 0.936 0.000 0.064 0.000
#> GSM155471 1 0.1211 0.8390 0.960 0.000 0.040 0.000
#> GSM155475 1 0.0336 0.8470 0.992 0.000 0.008 0.000
#> GSM155479 1 0.0592 0.8474 0.984 0.000 0.016 0.000
#> GSM155483 3 0.7566 0.8834 0.000 0.320 0.468 0.212
#> GSM155487 2 0.0000 0.9727 0.000 1.000 0.000 0.000
#> GSM155491 4 0.0817 0.5072 0.000 0.000 0.024 0.976
#> GSM155495 3 0.7575 0.7100 0.000 0.200 0.444 0.356
#> GSM155499 2 0.0000 0.9727 0.000 1.000 0.000 0.000
#> GSM155503 2 0.0000 0.9727 0.000 1.000 0.000 0.000
#> GSM155449 1 0.7769 -0.0148 0.432 0.000 0.296 0.272
#> GSM155456 1 0.7547 0.1448 0.488 0.000 0.276 0.236
#> GSM155460 1 0.0336 0.8470 0.992 0.000 0.008 0.000
#> GSM155464 1 0.1118 0.8409 0.964 0.000 0.036 0.000
#> GSM155468 1 0.1302 0.8366 0.956 0.000 0.044 0.000
#> GSM155472 1 0.0000 0.8485 1.000 0.000 0.000 0.000
#> GSM155476 1 0.0817 0.8454 0.976 0.000 0.024 0.000
#> GSM155480 1 0.1022 0.8425 0.968 0.000 0.032 0.000
#> GSM155484 3 0.6887 0.7394 0.000 0.444 0.452 0.104
#> GSM155488 2 0.0188 0.9681 0.000 0.996 0.004 0.000
#> GSM155492 4 0.2589 0.4117 0.000 0.000 0.116 0.884
#> GSM155496 4 0.4855 -0.2461 0.000 0.000 0.400 0.600
#> GSM155500 2 0.0000 0.9727 0.000 1.000 0.000 0.000
#> GSM155504 2 0.0000 0.9727 0.000 1.000 0.000 0.000
#> GSM155450 4 0.7828 0.3200 0.292 0.000 0.296 0.412
#> GSM155453 4 0.7407 0.4725 0.176 0.004 0.296 0.524
#> GSM155457 1 0.6876 0.3432 0.572 0.000 0.288 0.140
#> GSM155461 1 0.0707 0.8466 0.980 0.000 0.020 0.000
#> GSM155465 1 0.0188 0.8480 0.996 0.000 0.004 0.000
#> GSM155469 1 0.1211 0.8390 0.960 0.000 0.040 0.000
#> GSM155473 1 0.0188 0.8480 0.996 0.000 0.004 0.000
#> GSM155477 1 0.0592 0.8474 0.984 0.000 0.016 0.000
#> GSM155481 1 0.0336 0.8484 0.992 0.000 0.008 0.000
#> GSM155485 3 0.7620 0.8822 0.000 0.316 0.460 0.224
#> GSM155489 3 0.7638 0.8833 0.000 0.332 0.448 0.220
#> GSM155493 4 0.2973 0.3662 0.000 0.000 0.144 0.856
#> GSM155497 4 0.0188 0.5173 0.000 0.000 0.004 0.996
#> GSM155501 2 0.0000 0.9727 0.000 1.000 0.000 0.000
#> GSM155505 2 0.0000 0.9727 0.000 1.000 0.000 0.000
#> GSM155451 1 0.7782 -0.0278 0.428 0.000 0.296 0.276
#> GSM155454 2 0.4292 0.6780 0.000 0.820 0.080 0.100
#> GSM155458 1 0.7439 0.1840 0.500 0.000 0.296 0.204
#> GSM155462 1 0.0336 0.8470 0.992 0.000 0.008 0.000
#> GSM155466 1 0.0188 0.8487 0.996 0.000 0.004 0.000
#> GSM155470 1 0.0000 0.8485 1.000 0.000 0.000 0.000
#> GSM155474 1 0.0000 0.8485 1.000 0.000 0.000 0.000
#> GSM155478 1 0.1867 0.8080 0.928 0.000 0.072 0.000
#> GSM155482 1 0.2921 0.7531 0.860 0.000 0.140 0.000
#> GSM155486 3 0.7365 0.8292 0.000 0.400 0.440 0.160
#> GSM155490 2 0.0000 0.9727 0.000 1.000 0.000 0.000
#> GSM155494 4 0.1302 0.4927 0.000 0.000 0.044 0.956
#> GSM155498 4 0.0000 0.5170 0.000 0.000 0.000 1.000
#> GSM155502 2 0.0000 0.9727 0.000 1.000 0.000 0.000
#> GSM155506 2 0.0188 0.9683 0.000 0.996 0.004 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM155448 4 0.1701 0.895 0.048 0.000 0.016 0.936 0.000
#> GSM155452 4 0.3543 0.841 0.060 0.000 0.112 0.828 0.000
#> GSM155455 4 0.2889 0.896 0.084 0.000 0.044 0.872 0.000
#> GSM155459 1 0.1372 0.960 0.956 0.000 0.016 0.004 0.024
#> GSM155463 1 0.0798 0.965 0.976 0.000 0.008 0.000 0.016
#> GSM155467 1 0.1087 0.962 0.968 0.000 0.008 0.008 0.016
#> GSM155471 1 0.0960 0.965 0.972 0.000 0.008 0.004 0.016
#> GSM155475 1 0.1267 0.961 0.960 0.000 0.012 0.004 0.024
#> GSM155479 1 0.0740 0.967 0.980 0.000 0.008 0.008 0.004
#> GSM155483 5 0.4487 0.871 0.000 0.104 0.140 0.000 0.756
#> GSM155487 2 0.0324 0.981 0.000 0.992 0.004 0.004 0.000
#> GSM155491 3 0.2960 0.841 0.008 0.000 0.876 0.080 0.036
#> GSM155495 5 0.4958 0.801 0.000 0.084 0.224 0.000 0.692
#> GSM155499 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM155503 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM155449 4 0.1956 0.903 0.076 0.000 0.008 0.916 0.000
#> GSM155456 4 0.3354 0.860 0.140 0.000 0.024 0.832 0.004
#> GSM155460 1 0.1074 0.964 0.968 0.000 0.012 0.004 0.016
#> GSM155464 1 0.0693 0.966 0.980 0.000 0.008 0.000 0.012
#> GSM155468 1 0.0798 0.965 0.976 0.000 0.008 0.000 0.016
#> GSM155472 1 0.0162 0.968 0.996 0.000 0.000 0.004 0.000
#> GSM155476 1 0.1074 0.964 0.968 0.000 0.012 0.004 0.016
#> GSM155480 1 0.0290 0.968 0.992 0.000 0.000 0.000 0.008
#> GSM155484 5 0.4844 0.827 0.000 0.172 0.108 0.000 0.720
#> GSM155488 2 0.1341 0.933 0.000 0.944 0.000 0.000 0.056
#> GSM155492 3 0.4352 0.697 0.000 0.000 0.720 0.036 0.244
#> GSM155496 5 0.4321 0.421 0.000 0.000 0.396 0.004 0.600
#> GSM155500 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM155504 2 0.0162 0.983 0.000 0.996 0.004 0.000 0.000
#> GSM155450 4 0.1626 0.892 0.044 0.000 0.016 0.940 0.000
#> GSM155453 4 0.2235 0.876 0.032 0.004 0.040 0.920 0.004
#> GSM155457 4 0.2873 0.876 0.120 0.000 0.020 0.860 0.000
#> GSM155461 1 0.0727 0.967 0.980 0.000 0.004 0.004 0.012
#> GSM155465 1 0.0671 0.967 0.980 0.000 0.016 0.004 0.000
#> GSM155469 1 0.0798 0.965 0.976 0.000 0.008 0.000 0.016
#> GSM155473 1 0.0324 0.968 0.992 0.000 0.004 0.004 0.000
#> GSM155477 1 0.1306 0.961 0.960 0.000 0.016 0.008 0.016
#> GSM155481 1 0.0324 0.969 0.992 0.000 0.004 0.004 0.000
#> GSM155485 5 0.4636 0.874 0.000 0.124 0.132 0.000 0.744
#> GSM155489 5 0.4819 0.873 0.000 0.112 0.148 0.004 0.736
#> GSM155493 3 0.4326 0.660 0.000 0.000 0.708 0.028 0.264
#> GSM155497 3 0.2748 0.834 0.008 0.000 0.880 0.096 0.016
#> GSM155501 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM155505 2 0.0162 0.983 0.000 0.996 0.004 0.000 0.000
#> GSM155451 4 0.2407 0.898 0.088 0.000 0.012 0.896 0.004
#> GSM155454 4 0.5412 0.596 0.000 0.216 0.020 0.684 0.080
#> GSM155458 4 0.2358 0.895 0.104 0.000 0.008 0.888 0.000
#> GSM155462 1 0.1471 0.959 0.952 0.000 0.020 0.004 0.024
#> GSM155466 1 0.0566 0.968 0.984 0.000 0.004 0.000 0.012
#> GSM155470 1 0.0451 0.968 0.988 0.000 0.008 0.000 0.004
#> GSM155474 1 0.0162 0.968 0.996 0.000 0.000 0.004 0.000
#> GSM155478 1 0.4220 0.843 0.816 0.000 0.056 0.064 0.064
#> GSM155482 1 0.4091 0.811 0.804 0.000 0.020 0.132 0.044
#> GSM155486 5 0.4801 0.861 0.000 0.148 0.124 0.000 0.728
#> GSM155490 2 0.2418 0.919 0.000 0.912 0.044 0.020 0.024
#> GSM155494 3 0.3911 0.830 0.004 0.000 0.812 0.084 0.100
#> GSM155498 3 0.2408 0.823 0.008 0.000 0.892 0.096 0.004
#> GSM155502 2 0.0000 0.984 0.000 1.000 0.000 0.000 0.000
#> GSM155506 2 0.0290 0.979 0.000 0.992 0.000 0.000 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM155448 4 0.1078 0.951 0.008 0.000 0.016 0.964 0.000 NA
#> GSM155452 4 0.2384 0.907 0.032 0.000 0.084 0.884 0.000 NA
#> GSM155455 4 0.1787 0.944 0.032 0.000 0.020 0.932 0.000 NA
#> GSM155459 1 0.0862 0.946 0.972 0.000 0.016 0.008 0.000 NA
#> GSM155463 1 0.0692 0.946 0.976 0.000 0.020 0.000 0.000 NA
#> GSM155467 1 0.0891 0.944 0.968 0.000 0.024 0.000 0.000 NA
#> GSM155471 1 0.1036 0.943 0.964 0.000 0.024 0.008 0.000 NA
#> GSM155475 1 0.0862 0.946 0.972 0.000 0.016 0.004 0.000 NA
#> GSM155479 1 0.0806 0.945 0.972 0.000 0.020 0.000 0.000 NA
#> GSM155483 5 0.1075 0.843 0.000 0.048 0.000 0.000 0.952 NA
#> GSM155487 2 0.2611 0.857 0.000 0.864 0.000 0.008 0.012 NA
#> GSM155491 3 0.3762 0.884 0.004 0.000 0.760 0.020 0.208 NA
#> GSM155495 5 0.4472 0.734 0.000 0.132 0.052 0.000 0.756 NA
#> GSM155499 2 0.1686 0.896 0.000 0.924 0.000 0.012 0.000 NA
#> GSM155503 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000 NA
#> GSM155449 4 0.0951 0.950 0.008 0.000 0.004 0.968 0.000 NA
#> GSM155456 4 0.2068 0.928 0.048 0.000 0.016 0.916 0.000 NA
#> GSM155460 1 0.0870 0.946 0.972 0.000 0.012 0.012 0.000 NA
#> GSM155464 1 0.0622 0.948 0.980 0.000 0.012 0.000 0.000 NA
#> GSM155468 1 0.0692 0.946 0.976 0.000 0.020 0.000 0.000 NA
#> GSM155472 1 0.0717 0.946 0.976 0.000 0.000 0.008 0.000 NA
#> GSM155476 1 0.1148 0.943 0.960 0.000 0.020 0.004 0.000 NA
#> GSM155480 1 0.0260 0.949 0.992 0.000 0.008 0.000 0.000 NA
#> GSM155484 5 0.2333 0.813 0.000 0.120 0.004 0.000 0.872 NA
#> GSM155488 2 0.2412 0.852 0.000 0.880 0.000 0.000 0.092 NA
#> GSM155492 3 0.3515 0.816 0.000 0.000 0.676 0.000 0.324 NA
#> GSM155496 5 0.4823 0.214 0.000 0.004 0.300 0.004 0.632 NA
#> GSM155500 2 0.0260 0.925 0.000 0.992 0.000 0.000 0.000 NA
#> GSM155504 2 0.0146 0.926 0.000 0.996 0.000 0.000 0.000 NA
#> GSM155450 4 0.1015 0.952 0.012 0.000 0.004 0.968 0.004 NA
#> GSM155453 4 0.1515 0.940 0.000 0.000 0.020 0.944 0.008 NA
#> GSM155457 4 0.1794 0.945 0.028 0.000 0.024 0.932 0.000 NA
#> GSM155461 1 0.0405 0.948 0.988 0.000 0.008 0.004 0.000 NA
#> GSM155465 1 0.1173 0.943 0.960 0.000 0.016 0.016 0.000 NA
#> GSM155469 1 0.0603 0.947 0.980 0.000 0.016 0.000 0.000 NA
#> GSM155473 1 0.0665 0.949 0.980 0.000 0.008 0.004 0.000 NA
#> GSM155477 1 0.1003 0.944 0.964 0.000 0.020 0.000 0.000 NA
#> GSM155481 1 0.0622 0.949 0.980 0.000 0.012 0.000 0.000 NA
#> GSM155485 5 0.1267 0.851 0.000 0.060 0.000 0.000 0.940 NA
#> GSM155489 5 0.1387 0.852 0.000 0.068 0.000 0.000 0.932 NA
#> GSM155493 3 0.3758 0.817 0.000 0.000 0.668 0.008 0.324 NA
#> GSM155497 3 0.3604 0.864 0.004 0.000 0.796 0.032 0.160 NA
#> GSM155501 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000 NA
#> GSM155505 2 0.0260 0.926 0.000 0.992 0.000 0.000 0.000 NA
#> GSM155451 4 0.0984 0.950 0.008 0.000 0.012 0.968 0.000 NA
#> GSM155454 4 0.3170 0.880 0.000 0.072 0.008 0.860 0.028 NA
#> GSM155458 4 0.0909 0.951 0.020 0.000 0.000 0.968 0.000 NA
#> GSM155462 1 0.0964 0.947 0.968 0.000 0.016 0.004 0.000 NA
#> GSM155466 1 0.0767 0.948 0.976 0.000 0.012 0.004 0.000 NA
#> GSM155470 1 0.0520 0.949 0.984 0.000 0.008 0.000 0.000 NA
#> GSM155474 1 0.0405 0.949 0.988 0.000 0.000 0.004 0.000 NA
#> GSM155478 1 0.4693 0.486 0.564 0.000 0.004 0.040 0.000 NA
#> GSM155482 1 0.5031 0.430 0.528 0.000 0.004 0.064 0.000 NA
#> GSM155486 5 0.1908 0.845 0.000 0.096 0.000 0.000 0.900 NA
#> GSM155490 2 0.4205 0.526 0.000 0.564 0.000 0.000 0.016 NA
#> GSM155494 3 0.3705 0.882 0.004 0.000 0.740 0.020 0.236 NA
#> GSM155498 3 0.3416 0.847 0.004 0.000 0.816 0.032 0.140 NA
#> GSM155502 2 0.0000 0.927 0.000 1.000 0.000 0.000 0.000 NA
#> GSM155506 2 0.0692 0.921 0.000 0.976 0.000 0.004 0.000 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n time(p) k
#> ATC:NMF 59 0.959 2
#> ATC:NMF 59 0.997 3
#> ATC:NMF 45 0.989 4
#> ATC:NMF 58 1.000 5
#> ATC:NMF 56 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.
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