Date: 2019-12-25 21:31:38 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 72 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 72
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 | ||
|---|---|---|---|---|---|---|
| CV:pam | 6 | 1.000 | 0.972 | 0.984 | ** | 2,3,4,5 |
| MAD:kmeans | 2 | 1.000 | 0.996 | 0.998 | ** | |
| MAD:mclust | 6 | 1.000 | 0.976 | 0.989 | ** | 3,4,5 |
| ATC:kmeans | 2 | 1.000 | 1.000 | 1.000 | ** | |
| SD:mclust | 6 | 0.998 | 0.965 | 0.976 | ** | 2,4,5 |
| MAD:pam | 6 | 0.996 | 0.965 | 0.978 | ** | 2,3,5 |
| CV:NMF | 3 | 0.994 | 0.955 | 0.973 | ** | 2 |
| MAD:NMF | 4 | 0.993 | 0.960 | 0.973 | ** | 2 |
| CV:mclust | 6 | 0.992 | 0.958 | 0.976 | ** | 2,3,4,5 |
| CV:skmeans | 6 | 0.991 | 0.940 | 0.973 | ** | 2,4,5 |
| SD:skmeans | 6 | 0.989 | 0.926 | 0.969 | ** | 2,4,5 |
| ATC:mclust | 2 | 0.982 | 0.946 | 0.967 | ** | |
| MAD:skmeans | 6 | 0.979 | 0.941 | 0.961 | ** | 2,4,5 |
| ATC:hclust | 2 | 0.964 | 0.968 | 0.977 | ** | |
| SD:kmeans | 4 | 0.957 | 0.955 | 0.963 | ** | 2 |
| SD:NMF | 4 | 0.956 | 0.938 | 0.955 | ** | 2 |
| CV:hclust | 6 | 0.956 | 0.902 | 0.943 | ** | 5 |
| ATC:NMF | 3 | 0.931 | 0.913 | 0.964 | * | 2 |
| ATC:skmeans | 6 | 0.928 | 0.849 | 0.924 | * | 2,5 |
| CV:kmeans | 4 | 0.926 | 0.933 | 0.948 | * | 2 |
| SD:pam | 6 | 0.910 | 0.920 | 0.954 | * | 2,3,5 |
| ATC:pam | 5 | 0.910 | 0.865 | 0.946 | * | 2,3 |
| SD:hclust | 6 | 0.909 | 0.886 | 0.942 | * | 2,3 |
| MAD:hclust | 2 | 0.719 | 0.852 | 0.934 |
**: 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 0.981 0.991 0.484 0.512 0.512
#> CV:NMF 2 0.971 0.951 0.979 0.478 0.512 0.512
#> MAD:NMF 2 1.000 0.975 0.991 0.490 0.512 0.512
#> ATC:NMF 2 0.914 0.931 0.971 0.449 0.559 0.559
#> SD:skmeans 2 1.000 1.000 1.000 0.501 0.499 0.499
#> CV:skmeans 2 1.000 0.981 0.992 0.500 0.499 0.499
#> MAD:skmeans 2 1.000 0.993 0.997 0.502 0.499 0.499
#> ATC:skmeans 2 1.000 0.995 0.998 0.481 0.518 0.518
#> SD:mclust 2 1.000 0.948 0.965 0.418 0.593 0.593
#> CV:mclust 2 1.000 0.949 0.978 0.434 0.549 0.549
#> MAD:mclust 2 0.519 0.921 0.934 0.422 0.593 0.593
#> ATC:mclust 2 0.982 0.946 0.967 0.479 0.507 0.507
#> SD:kmeans 2 1.000 0.984 0.990 0.492 0.507 0.507
#> CV:kmeans 2 0.942 0.946 0.978 0.483 0.518 0.518
#> MAD:kmeans 2 1.000 0.996 0.998 0.498 0.503 0.503
#> ATC:kmeans 2 1.000 1.000 1.000 0.351 0.649 0.649
#> SD:pam 2 1.000 0.978 0.990 0.499 0.499 0.499
#> CV:pam 2 1.000 0.965 0.987 0.497 0.503 0.503
#> MAD:pam 2 1.000 0.974 0.990 0.505 0.495 0.495
#> ATC:pam 2 1.000 0.983 0.992 0.310 0.700 0.700
#> SD:hclust 2 1.000 0.964 0.983 0.490 0.512 0.512
#> CV:hclust 2 0.862 0.925 0.966 0.488 0.512 0.512
#> MAD:hclust 2 0.719 0.852 0.934 0.498 0.499 0.499
#> ATC:hclust 2 0.964 0.968 0.977 0.366 0.634 0.634
get_stats(res_list, k = 3)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 3 0.825 0.865 0.926 0.378 0.750 0.539
#> CV:NMF 3 0.994 0.955 0.973 0.409 0.753 0.544
#> MAD:NMF 3 0.744 0.791 0.903 0.331 0.806 0.633
#> ATC:NMF 3 0.931 0.913 0.964 0.474 0.766 0.587
#> SD:skmeans 3 0.781 0.873 0.922 0.315 0.814 0.636
#> CV:skmeans 3 0.766 0.855 0.927 0.329 0.797 0.608
#> MAD:skmeans 3 0.780 0.645 0.845 0.303 0.892 0.790
#> ATC:skmeans 3 0.758 0.910 0.946 0.315 0.803 0.632
#> SD:mclust 3 0.864 0.929 0.962 0.590 0.745 0.571
#> CV:mclust 3 0.927 0.960 0.981 0.554 0.775 0.590
#> MAD:mclust 3 0.906 0.875 0.948 0.585 0.745 0.571
#> ATC:mclust 3 0.485 0.758 0.844 0.283 0.583 0.377
#> SD:kmeans 3 0.676 0.552 0.779 0.317 0.836 0.700
#> CV:kmeans 3 0.699 0.840 0.876 0.343 0.737 0.527
#> MAD:kmeans 3 0.679 0.769 0.857 0.292 0.775 0.579
#> ATC:kmeans 3 0.886 0.877 0.953 0.782 0.649 0.490
#> SD:pam 3 1.000 0.968 0.987 0.344 0.706 0.476
#> CV:pam 3 1.000 0.973 0.989 0.347 0.712 0.487
#> MAD:pam 3 0.981 0.938 0.976 0.334 0.712 0.481
#> ATC:pam 3 1.000 0.975 0.990 0.949 0.695 0.564
#> SD:hclust 3 0.968 0.938 0.966 0.143 0.934 0.872
#> CV:hclust 3 0.883 0.906 0.955 0.156 0.934 0.872
#> MAD:hclust 3 0.788 0.854 0.919 0.249 0.844 0.687
#> ATC:hclust 3 0.694 0.932 0.949 0.158 0.972 0.956
get_stats(res_list, k = 4)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 4 0.956 0.938 0.955 0.0834 0.937 0.808
#> CV:NMF 4 0.843 0.518 0.874 0.0645 0.944 0.834
#> MAD:NMF 4 0.993 0.960 0.973 0.1161 0.815 0.542
#> ATC:NMF 4 0.628 0.679 0.823 0.1280 0.865 0.625
#> SD:skmeans 4 1.000 0.962 0.984 0.1087 0.921 0.770
#> CV:skmeans 4 0.932 0.941 0.943 0.1015 0.906 0.732
#> MAD:skmeans 4 1.000 0.945 0.977 0.1173 0.785 0.523
#> ATC:skmeans 4 0.816 0.756 0.885 0.1185 0.884 0.693
#> SD:mclust 4 0.998 0.961 0.981 0.1282 0.886 0.675
#> CV:mclust 4 0.968 0.930 0.966 0.1073 0.868 0.626
#> MAD:mclust 4 0.946 0.927 0.966 0.1206 0.881 0.661
#> ATC:mclust 4 0.625 0.726 0.810 0.1734 0.685 0.368
#> SD:kmeans 4 0.957 0.955 0.963 0.1278 0.813 0.572
#> CV:kmeans 4 0.926 0.933 0.948 0.1292 0.924 0.775
#> MAD:kmeans 4 0.814 0.860 0.909 0.1293 0.813 0.529
#> ATC:kmeans 4 0.719 0.679 0.864 0.1701 0.822 0.559
#> SD:pam 4 0.873 0.903 0.935 0.0989 0.924 0.775
#> CV:pam 4 0.900 0.908 0.947 0.1024 0.924 0.775
#> MAD:pam 4 0.884 0.832 0.914 0.0958 0.907 0.724
#> ATC:pam 4 0.816 0.881 0.924 0.1903 0.851 0.632
#> SD:hclust 4 0.787 0.773 0.885 0.2794 0.770 0.510
#> CV:hclust 4 0.823 0.895 0.924 0.2794 0.819 0.595
#> MAD:hclust 4 0.771 0.792 0.862 0.1349 0.949 0.854
#> ATC:hclust 4 0.663 0.803 0.898 0.5468 0.716 0.531
get_stats(res_list, k = 5)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 5 0.855 0.855 0.911 0.0755 0.914 0.699
#> CV:NMF 5 0.832 0.781 0.887 0.0786 0.887 0.646
#> MAD:NMF 5 0.861 0.833 0.892 0.0717 0.905 0.670
#> ATC:NMF 5 0.698 0.675 0.819 0.0642 0.869 0.547
#> SD:skmeans 5 1.000 0.951 0.980 0.0596 0.946 0.805
#> CV:skmeans 5 1.000 0.951 0.979 0.0573 0.946 0.805
#> MAD:skmeans 5 0.989 0.946 0.976 0.0601 0.924 0.730
#> ATC:skmeans 5 0.949 0.903 0.963 0.0795 0.905 0.689
#> SD:mclust 5 1.000 0.961 0.984 0.0323 0.976 0.905
#> CV:mclust 5 0.997 0.964 0.977 0.0360 0.976 0.905
#> MAD:mclust 5 1.000 0.963 0.985 0.0339 0.963 0.856
#> ATC:mclust 5 0.739 0.868 0.898 0.0894 0.910 0.679
#> SD:kmeans 5 0.853 0.784 0.876 0.0585 0.984 0.938
#> CV:kmeans 5 0.840 0.800 0.858 0.0597 1.000 1.000
#> MAD:kmeans 5 0.789 0.878 0.841 0.0623 0.948 0.806
#> ATC:kmeans 5 0.765 0.727 0.847 0.0661 0.875 0.581
#> SD:pam 5 1.000 0.972 0.988 0.0658 0.948 0.806
#> CV:pam 5 0.937 0.925 0.961 0.0617 0.937 0.766
#> MAD:pam 5 1.000 0.957 0.984 0.0636 0.933 0.751
#> ATC:pam 5 0.910 0.865 0.946 0.0655 0.931 0.754
#> SD:hclust 5 0.835 0.862 0.861 0.0384 0.951 0.830
#> CV:hclust 5 0.911 0.901 0.940 0.0409 0.978 0.918
#> MAD:hclust 5 0.798 0.755 0.871 0.0250 0.984 0.947
#> ATC:hclust 5 0.716 0.792 0.889 0.0381 0.994 0.982
get_stats(res_list, k = 6)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> SD:NMF 6 0.834 0.762 0.875 0.0191 0.963 0.845
#> CV:NMF 6 0.801 0.741 0.857 0.0261 0.982 0.923
#> MAD:NMF 6 0.799 0.725 0.837 0.0229 0.962 0.839
#> ATC:NMF 6 0.697 0.610 0.737 0.0361 0.978 0.899
#> SD:skmeans 6 0.989 0.926 0.969 0.0363 0.964 0.844
#> CV:skmeans 6 0.991 0.940 0.973 0.0378 0.967 0.854
#> MAD:skmeans 6 0.979 0.941 0.961 0.0341 0.965 0.845
#> ATC:skmeans 6 0.928 0.849 0.924 0.0300 0.959 0.833
#> SD:mclust 6 0.998 0.965 0.976 0.0432 0.965 0.846
#> CV:mclust 6 0.992 0.958 0.976 0.0481 0.957 0.812
#> MAD:mclust 6 1.000 0.976 0.989 0.0433 0.965 0.846
#> ATC:mclust 6 0.860 0.780 0.902 0.0434 0.932 0.696
#> SD:kmeans 6 0.857 0.817 0.830 0.0406 0.941 0.767
#> CV:kmeans 6 0.831 0.795 0.813 0.0392 0.917 0.694
#> MAD:kmeans 6 0.859 0.826 0.853 0.0434 0.961 0.825
#> ATC:kmeans 6 0.771 0.701 0.823 0.0469 0.937 0.724
#> SD:pam 6 0.910 0.920 0.954 0.0301 0.951 0.786
#> CV:pam 6 1.000 0.972 0.984 0.0293 0.950 0.781
#> MAD:pam 6 0.996 0.965 0.978 0.0270 0.940 0.744
#> ATC:pam 6 0.882 0.856 0.933 0.0229 0.985 0.934
#> SD:hclust 6 0.909 0.886 0.942 0.0604 0.952 0.819
#> CV:hclust 6 0.956 0.902 0.943 0.0505 0.958 0.829
#> MAD:hclust 6 0.842 0.845 0.902 0.0831 0.897 0.654
#> ATC:hclust 6 0.686 0.774 0.867 0.1318 0.836 0.523
Following heatmap plots the partition for each combination of methods and the lightness correspond to the silhouette scores for samples in each method. On top the consensus subgroup is inferred from all methods by taking the mean silhouette scores as weight.
collect_stats(res_list, k = 2)
collect_stats(res_list, k = 3)
collect_stats(res_list, k = 4)
collect_stats(res_list, k = 5)
collect_stats(res_list, k = 6)
Collect partitions from all methods:
collect_classes(res_list, k = 2)
collect_classes(res_list, k = 3)
collect_classes(res_list, k = 4)
collect_classes(res_list, k = 5)
collect_classes(res_list, k = 6)
Overlap of top rows from different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "euler")
top_rows_overlap(res_list, top_n = 2000, method = "euler")
top_rows_overlap(res_list, top_n = 3000, method = "euler")
top_rows_overlap(res_list, top_n = 4000, method = "euler")
top_rows_overlap(res_list, top_n = 5000, method = "euler")
Also visualize the correspondance of rankings between different top-row methods:
top_rows_overlap(res_list, top_n = 1000, method = "correspondance")
top_rows_overlap(res_list, top_n = 2000, method = "correspondance")
top_rows_overlap(res_list, top_n = 3000, method = "correspondance")
top_rows_overlap(res_list, top_n = 4000, method = "correspondance")
top_rows_overlap(res_list, top_n = 5000, method = "correspondance")
Heatmaps of the top rows:
top_rows_heatmap(res_list, top_n = 1000)
top_rows_heatmap(res_list, top_n = 2000)
top_rows_heatmap(res_list, top_n = 3000)
top_rows_heatmap(res_list, top_n = 4000)
top_rows_heatmap(res_list, top_n = 5000)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res_list, k = 2)
#> n disease.state(p) tissue(p) k
#> SD:NMF 72 0.8526 4.67e-11 2
#> CV:NMF 70 0.9468 8.53e-12 2
#> MAD:NMF 71 0.8090 6.63e-11 2
#> ATC:NMF 69 0.7600 6.14e-05 2
#> SD:skmeans 72 0.7433 5.51e-10 2
#> CV:skmeans 72 0.7433 5.51e-10 2
#> MAD:skmeans 72 0.7433 5.51e-10 2
#> ATC:skmeans 72 0.2536 1.95e-01 2
#> SD:mclust 70 0.8058 3.77e-12 2
#> CV:mclust 68 0.8755 1.70e-13 2
#> MAD:mclust 72 0.7222 4.87e-11 2
#> ATC:mclust 70 0.8192 3.13e-11 2
#> SD:kmeans 72 0.7308 1.25e-10 2
#> CV:kmeans 71 0.9068 2.13e-11 2
#> MAD:kmeans 72 0.7703 2.85e-10 2
#> ATC:kmeans 72 0.0545 2.17e-01 2
#> SD:pam 72 0.7433 5.51e-10 2
#> CV:pam 70 0.7686 2.34e-10 2
#> MAD:pam 71 0.5743 1.09e-09 2
#> ATC:pam 72 0.0319 1.68e-01 2
#> SD:hclust 72 0.4844 9.33e-11 2
#> CV:hclust 72 0.4844 9.33e-11 2
#> MAD:hclust 67 0.2518 6.18e-07 2
#> ATC:hclust 72 0.0430 2.32e-01 2
test_to_known_factors(res_list, k = 3)
#> n disease.state(p) tissue(p) k
#> SD:NMF 70 0.99523 1.25e-25 3
#> CV:NMF 71 0.99922 4.63e-26 3
#> MAD:NMF 66 0.87126 1.59e-13 3
#> ATC:NMF 69 0.57541 1.69e-11 3
#> SD:skmeans 71 0.93150 2.52e-21 3
#> CV:skmeans 70 0.91536 1.37e-22 3
#> MAD:skmeans 51 0.91735 2.24e-17 3
#> ATC:skmeans 69 0.60660 1.67e-08 3
#> SD:mclust 71 0.80874 8.57e-21 3
#> CV:mclust 71 0.99998 2.81e-27 3
#> MAD:mclust 64 0.99472 3.61e-24 3
#> ATC:mclust 66 0.12089 1.85e-09 3
#> SD:kmeans 59 0.31137 3.16e-11 3
#> CV:kmeans 69 0.97494 4.15e-22 3
#> MAD:kmeans 68 0.43507 8.84e-14 3
#> ATC:kmeans 67 0.09589 2.74e-04 3
#> SD:pam 71 0.96376 6.89e-23 3
#> CV:pam 71 0.87069 8.22e-23 3
#> MAD:pam 70 0.76458 3.88e-20 3
#> ATC:pam 71 0.12855 3.14e-06 3
#> SD:hclust 72 0.05286 3.04e-11 3
#> CV:hclust 70 0.06070 7.31e-11 3
#> MAD:hclust 68 0.18973 6.32e-14 3
#> ATC:hclust 72 0.00445 4.62e-01 3
test_to_known_factors(res_list, k = 4)
#> n disease.state(p) tissue(p) k
#> SD:NMF 71 0.14493 2.99e-22 4
#> CV:NMF 50 0.95086 5.03e-16 4
#> MAD:NMF 72 0.06882 4.07e-22 4
#> ATC:NMF 60 0.06287 1.91e-08 4
#> SD:skmeans 70 0.12178 4.52e-18 4
#> CV:skmeans 70 0.12178 4.52e-18 4
#> MAD:skmeans 70 0.12178 4.52e-18 4
#> ATC:skmeans 56 0.30532 7.65e-08 4
#> SD:mclust 71 0.69059 7.53e-21 4
#> CV:mclust 69 0.34512 8.64e-21 4
#> MAD:mclust 70 0.54776 1.29e-20 4
#> ATC:mclust 66 0.00108 5.09e-11 4
#> SD:kmeans 72 0.12061 1.48e-20 4
#> CV:kmeans 72 0.12061 1.48e-20 4
#> MAD:kmeans 71 0.04851 1.41e-20 4
#> ATC:kmeans 58 0.12565 2.37e-07 4
#> SD:pam 72 0.12061 1.48e-20 4
#> CV:pam 71 0.04851 1.41e-20 4
#> MAD:pam 58 0.46908 3.64e-19 4
#> ATC:pam 70 0.02010 1.32e-11 4
#> SD:hclust 64 0.73873 1.23e-22 4
#> CV:hclust 70 0.17966 5.57e-22 4
#> MAD:hclust 70 0.06494 1.96e-13 4
#> ATC:hclust 63 0.04100 1.36e-04 4
test_to_known_factors(res_list, k = 5)
#> n disease.state(p) tissue(p) k
#> SD:NMF 69 0.000564 3.70e-19 5
#> CV:NMF 64 0.026153 6.73e-20 5
#> MAD:NMF 67 0.000606 4.91e-19 5
#> ATC:NMF 61 0.260422 8.91e-16 5
#> SD:skmeans 69 0.013355 1.10e-20 5
#> CV:skmeans 69 0.013355 1.10e-20 5
#> MAD:skmeans 70 0.035126 1.07e-20 5
#> ATC:skmeans 67 0.122189 9.69e-11 5
#> SD:mclust 71 0.118440 3.49e-21 5
#> CV:mclust 71 0.118440 3.49e-21 5
#> MAD:mclust 70 0.134326 9.11e-21 5
#> ATC:mclust 71 0.003400 8.72e-13 5
#> SD:kmeans 64 0.030348 2.26e-18 5
#> CV:kmeans 70 0.179661 5.57e-22 5
#> MAD:kmeans 71 0.025696 1.63e-19 5
#> ATC:kmeans 63 0.137660 1.83e-10 5
#> SD:pam 71 0.020610 4.24e-19 5
#> CV:pam 70 0.007995 4.07e-19 5
#> MAD:pam 70 0.029267 1.05e-18 5
#> ATC:pam 66 0.047779 3.59e-10 5
#> SD:hclust 70 0.179661 5.57e-22 5
#> CV:hclust 70 0.213399 3.92e-22 5
#> MAD:hclust 65 0.467855 2.58e-14 5
#> ATC:hclust 63 0.094149 1.94e-05 5
test_to_known_factors(res_list, k = 6)
#> n disease.state(p) tissue(p) k
#> SD:NMF 64 3.79e-04 1.79e-18 6
#> CV:NMF 62 3.50e-03 2.39e-19 6
#> MAD:NMF 62 8.36e-05 1.24e-18 6
#> ATC:NMF 54 2.87e-01 1.57e-17 6
#> SD:skmeans 69 5.50e-02 1.47e-20 6
#> CV:skmeans 70 2.70e-02 3.72e-20 6
#> MAD:skmeans 70 5.07e-02 5.87e-21 6
#> ATC:skmeans 67 1.92e-01 2.38e-10 6
#> SD:mclust 71 7.39e-02 4.84e-20 6
#> CV:mclust 72 1.20e-01 2.01e-20 6
#> MAD:mclust 71 7.39e-02 4.84e-20 6
#> ATC:mclust 65 2.21e-03 7.83e-11 6
#> SD:kmeans 64 2.03e-01 5.30e-20 6
#> CV:kmeans 66 1.62e-01 2.33e-19 6
#> MAD:kmeans 66 3.12e-01 2.35e-19 6
#> ATC:kmeans 62 3.56e-01 3.48e-11 6
#> SD:pam 71 1.20e-01 2.31e-21 6
#> CV:pam 72 1.41e-01 9.23e-22 6
#> MAD:pam 72 1.41e-01 9.23e-22 6
#> ATC:pam 67 5.20e-02 4.40e-11 6
#> SD:hclust 70 1.89e-01 3.05e-21 6
#> CV:hclust 70 1.43e-01 5.96e-21 6
#> MAD:hclust 66 2.30e-01 8.09e-21 6
#> ATC:hclust 66 1.05e-01 2.79e-08 6
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["SD", "hclust"]
# you can also extract it by
# res = res_list["SD:hclust"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 72 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 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 0.964 0.983 0.4895 0.512 0.512
#> 3 3 0.968 0.938 0.966 0.1430 0.934 0.872
#> 4 4 0.787 0.773 0.885 0.2794 0.770 0.510
#> 5 5 0.835 0.862 0.861 0.0384 0.951 0.830
#> 6 6 0.909 0.886 0.942 0.0604 0.952 0.819
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM876886 1 0.000 0.977 1.000 0.000
#> GSM876887 1 0.000 0.977 1.000 0.000
#> GSM876888 1 0.000 0.977 1.000 0.000
#> GSM876889 1 0.163 0.965 0.976 0.024
#> GSM876890 1 0.000 0.977 1.000 0.000
#> GSM876891 1 0.184 0.963 0.972 0.028
#> GSM876862 1 0.000 0.977 1.000 0.000
#> GSM876863 1 0.000 0.977 1.000 0.000
#> GSM876864 1 0.000 0.977 1.000 0.000
#> GSM876865 1 0.000 0.977 1.000 0.000
#> GSM876866 1 0.000 0.977 1.000 0.000
#> GSM876867 1 0.000 0.977 1.000 0.000
#> GSM876838 2 0.000 0.989 0.000 1.000
#> GSM876839 2 0.000 0.989 0.000 1.000
#> GSM876840 2 0.000 0.989 0.000 1.000
#> GSM876841 2 0.000 0.989 0.000 1.000
#> GSM876842 2 0.000 0.989 0.000 1.000
#> GSM876843 2 0.000 0.989 0.000 1.000
#> GSM876892 1 0.000 0.977 1.000 0.000
#> GSM876893 1 0.000 0.977 1.000 0.000
#> GSM876894 1 0.184 0.963 0.972 0.028
#> GSM876895 1 0.260 0.951 0.956 0.044
#> GSM876896 2 0.000 0.989 0.000 1.000
#> GSM876897 2 0.000 0.989 0.000 1.000
#> GSM876868 1 0.000 0.977 1.000 0.000
#> GSM876869 1 0.000 0.977 1.000 0.000
#> GSM876870 1 0.000 0.977 1.000 0.000
#> GSM876871 1 0.000 0.977 1.000 0.000
#> GSM876872 2 0.563 0.849 0.132 0.868
#> GSM876873 2 0.563 0.849 0.132 0.868
#> GSM876844 2 0.000 0.989 0.000 1.000
#> GSM876845 2 0.000 0.989 0.000 1.000
#> GSM876846 2 0.000 0.989 0.000 1.000
#> GSM876847 2 0.000 0.989 0.000 1.000
#> GSM876848 2 0.000 0.989 0.000 1.000
#> GSM876849 2 0.000 0.989 0.000 1.000
#> GSM876898 1 0.000 0.977 1.000 0.000
#> GSM876899 1 0.260 0.951 0.956 0.044
#> GSM876900 1 0.000 0.977 1.000 0.000
#> GSM876901 1 0.000 0.977 1.000 0.000
#> GSM876902 2 0.242 0.952 0.040 0.960
#> GSM876903 1 0.260 0.951 0.956 0.044
#> GSM876904 1 0.000 0.977 1.000 0.000
#> GSM876874 1 0.000 0.977 1.000 0.000
#> GSM876875 1 0.000 0.977 1.000 0.000
#> GSM876876 1 0.000 0.977 1.000 0.000
#> GSM876877 1 0.000 0.977 1.000 0.000
#> GSM876878 1 0.000 0.977 1.000 0.000
#> GSM876879 1 0.000 0.977 1.000 0.000
#> GSM876880 1 0.000 0.977 1.000 0.000
#> GSM876850 2 0.000 0.989 0.000 1.000
#> GSM876851 2 0.000 0.989 0.000 1.000
#> GSM876852 2 0.000 0.989 0.000 1.000
#> GSM876853 2 0.000 0.989 0.000 1.000
#> GSM876854 2 0.000 0.989 0.000 1.000
#> GSM876855 2 0.000 0.989 0.000 1.000
#> GSM876856 2 0.000 0.989 0.000 1.000
#> GSM876905 1 0.000 0.977 1.000 0.000
#> GSM876906 1 0.184 0.963 0.972 0.028
#> GSM876907 1 0.260 0.951 0.956 0.044
#> GSM876908 1 0.184 0.963 0.972 0.028
#> GSM876909 1 0.260 0.951 0.956 0.044
#> GSM876881 2 0.000 0.989 0.000 1.000
#> GSM876882 1 0.000 0.977 1.000 0.000
#> GSM876883 1 0.876 0.596 0.704 0.296
#> GSM876884 1 0.000 0.977 1.000 0.000
#> GSM876885 1 0.876 0.596 0.704 0.296
#> GSM876857 1 0.000 0.977 1.000 0.000
#> GSM876858 2 0.000 0.989 0.000 1.000
#> GSM876859 2 0.000 0.989 0.000 1.000
#> GSM876860 2 0.000 0.989 0.000 1.000
#> GSM876861 2 0.000 0.989 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876887 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876888 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876889 1 0.1031 0.957 0.976 0.000 0.024
#> GSM876890 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876891 1 0.1964 0.940 0.944 0.000 0.056
#> GSM876862 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876863 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876864 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876865 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876866 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876867 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876838 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876839 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876840 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876841 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876842 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876843 3 0.5760 0.645 0.000 0.328 0.672
#> GSM876892 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876893 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876894 1 0.1964 0.940 0.944 0.000 0.056
#> GSM876895 1 0.2537 0.923 0.920 0.000 0.080
#> GSM876896 3 0.1411 0.817 0.000 0.036 0.964
#> GSM876897 3 0.1411 0.817 0.000 0.036 0.964
#> GSM876868 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876869 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876870 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876871 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876872 3 0.2878 0.779 0.096 0.000 0.904
#> GSM876873 3 0.2878 0.779 0.096 0.000 0.904
#> GSM876844 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876845 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876846 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876847 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876848 3 0.5650 0.671 0.000 0.312 0.688
#> GSM876849 3 0.5650 0.671 0.000 0.312 0.688
#> GSM876898 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876899 1 0.2537 0.923 0.920 0.000 0.080
#> GSM876900 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876901 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876902 3 0.0237 0.808 0.004 0.000 0.996
#> GSM876903 1 0.2537 0.923 0.920 0.000 0.080
#> GSM876904 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876874 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876875 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876876 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876877 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876878 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876879 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876880 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876850 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876851 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876852 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876853 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876854 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876855 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876856 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876905 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876906 1 0.1964 0.940 0.944 0.000 0.056
#> GSM876907 1 0.2537 0.923 0.920 0.000 0.080
#> GSM876908 1 0.1964 0.940 0.944 0.000 0.056
#> GSM876909 1 0.2537 0.923 0.920 0.000 0.080
#> GSM876881 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876882 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876883 1 0.5529 0.589 0.704 0.000 0.296
#> GSM876884 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876885 1 0.5529 0.589 0.704 0.000 0.296
#> GSM876857 1 0.0000 0.970 1.000 0.000 0.000
#> GSM876858 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876859 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876860 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876861 2 0.0000 1.000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.4008 0.849 0.000 0.000 0.756 0.244
#> GSM876887 3 0.4008 0.849 0.000 0.000 0.756 0.244
#> GSM876888 3 0.4008 0.849 0.000 0.000 0.756 0.244
#> GSM876889 3 0.3528 0.840 0.000 0.000 0.808 0.192
#> GSM876890 3 0.4008 0.849 0.000 0.000 0.756 0.244
#> GSM876891 3 0.0707 0.808 0.000 0.000 0.980 0.020
#> GSM876862 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876863 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876864 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876865 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876866 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876867 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876838 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876839 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876840 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876841 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876842 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876843 4 0.7412 0.416 0.200 0.296 0.000 0.504
#> GSM876892 3 0.4008 0.849 0.000 0.000 0.756 0.244
#> GSM876893 3 0.4008 0.849 0.000 0.000 0.756 0.244
#> GSM876894 3 0.0707 0.808 0.000 0.000 0.980 0.020
#> GSM876895 3 0.0188 0.793 0.004 0.000 0.996 0.000
#> GSM876896 4 0.5688 0.566 0.464 0.000 0.024 0.512
#> GSM876897 4 0.5688 0.566 0.464 0.000 0.024 0.512
#> GSM876868 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876869 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876870 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876871 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876872 1 0.6957 -0.586 0.472 0.000 0.112 0.416
#> GSM876873 1 0.6957 -0.586 0.472 0.000 0.112 0.416
#> GSM876844 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876845 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876846 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876847 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876848 4 0.7479 0.474 0.244 0.252 0.000 0.504
#> GSM876849 4 0.7479 0.474 0.244 0.252 0.000 0.504
#> GSM876898 3 0.4008 0.849 0.000 0.000 0.756 0.244
#> GSM876899 3 0.0188 0.793 0.004 0.000 0.996 0.000
#> GSM876900 3 0.4008 0.849 0.000 0.000 0.756 0.244
#> GSM876901 3 0.4008 0.849 0.000 0.000 0.756 0.244
#> GSM876902 4 0.6527 0.553 0.416 0.000 0.076 0.508
#> GSM876903 3 0.0188 0.793 0.004 0.000 0.996 0.000
#> GSM876904 3 0.4008 0.849 0.000 0.000 0.756 0.244
#> GSM876874 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876875 1 0.5295 0.866 0.504 0.000 0.008 0.488
#> GSM876876 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876877 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876878 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876879 1 0.5295 0.866 0.504 0.000 0.008 0.488
#> GSM876880 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876850 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876851 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876852 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876853 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876854 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876855 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876856 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876905 3 0.4008 0.849 0.000 0.000 0.756 0.244
#> GSM876906 3 0.0707 0.808 0.000 0.000 0.980 0.020
#> GSM876907 3 0.0188 0.793 0.004 0.000 0.996 0.000
#> GSM876908 3 0.0707 0.808 0.000 0.000 0.980 0.020
#> GSM876909 3 0.0188 0.793 0.004 0.000 0.996 0.000
#> GSM876881 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876882 4 0.5781 -0.859 0.484 0.000 0.028 0.488
#> GSM876883 4 0.5812 -0.193 0.136 0.000 0.156 0.708
#> GSM876884 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876885 4 0.5812 -0.193 0.136 0.000 0.156 0.708
#> GSM876857 1 0.4998 0.877 0.512 0.000 0.000 0.488
#> GSM876858 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876859 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876860 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876861 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
#> GSM876886 3 0.2719 0.823 0.144 0.000 0.852 0.000 NA
#> GSM876887 3 0.2719 0.823 0.144 0.000 0.852 0.000 NA
#> GSM876888 3 0.2605 0.823 0.148 0.000 0.852 0.000 NA
#> GSM876889 3 0.2068 0.810 0.092 0.000 0.904 0.000 NA
#> GSM876890 3 0.2719 0.823 0.144 0.000 0.852 0.000 NA
#> GSM876891 3 0.2813 0.756 0.000 0.000 0.832 0.000 NA
#> GSM876862 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876863 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876864 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876865 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876866 1 0.1282 0.908 0.952 0.000 0.044 0.000 NA
#> GSM876867 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876838 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876839 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876840 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876841 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876842 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876843 4 0.6495 0.628 0.000 0.188 0.000 0.424 NA
#> GSM876892 3 0.2719 0.823 0.144 0.000 0.852 0.000 NA
#> GSM876893 3 0.2605 0.823 0.148 0.000 0.852 0.000 NA
#> GSM876894 3 0.2813 0.756 0.000 0.000 0.832 0.000 NA
#> GSM876895 3 0.3424 0.721 0.000 0.000 0.760 0.000 NA
#> GSM876896 4 0.0000 0.744 0.000 0.000 0.000 1.000 NA
#> GSM876897 4 0.0000 0.744 0.000 0.000 0.000 1.000 NA
#> GSM876868 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876869 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876870 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876871 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876872 4 0.4227 0.641 0.000 0.000 0.000 0.580 NA
#> GSM876873 4 0.4227 0.641 0.000 0.000 0.000 0.580 NA
#> GSM876844 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876845 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876846 2 0.0162 0.996 0.000 0.996 0.000 0.000 NA
#> GSM876847 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876848 4 0.6224 0.668 0.000 0.144 0.000 0.468 NA
#> GSM876849 4 0.6224 0.668 0.000 0.144 0.000 0.468 NA
#> GSM876898 3 0.2605 0.823 0.148 0.000 0.852 0.000 NA
#> GSM876899 3 0.3395 0.724 0.000 0.000 0.764 0.000 NA
#> GSM876900 3 0.2605 0.823 0.148 0.000 0.852 0.000 NA
#> GSM876901 3 0.2605 0.823 0.148 0.000 0.852 0.000 NA
#> GSM876902 4 0.1851 0.732 0.000 0.000 0.000 0.912 NA
#> GSM876903 3 0.3424 0.721 0.000 0.000 0.760 0.000 NA
#> GSM876904 3 0.2605 0.823 0.148 0.000 0.852 0.000 NA
#> GSM876874 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876875 1 0.1430 0.902 0.944 0.000 0.052 0.000 NA
#> GSM876876 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876877 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876878 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876879 1 0.1430 0.902 0.944 0.000 0.052 0.000 NA
#> GSM876880 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876850 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876851 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876852 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876853 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876854 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876855 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876856 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876905 3 0.2605 0.823 0.148 0.000 0.852 0.000 NA
#> GSM876906 3 0.2813 0.756 0.000 0.000 0.832 0.000 NA
#> GSM876907 3 0.3424 0.721 0.000 0.000 0.760 0.000 NA
#> GSM876908 3 0.2813 0.756 0.000 0.000 0.832 0.000 NA
#> GSM876909 3 0.3424 0.721 0.000 0.000 0.760 0.000 NA
#> GSM876881 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876882 1 0.2221 0.881 0.912 0.000 0.052 0.000 NA
#> GSM876883 1 0.6272 0.267 0.468 0.000 0.152 0.000 NA
#> GSM876884 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876885 1 0.6272 0.267 0.468 0.000 0.152 0.000 NA
#> GSM876857 1 0.0000 0.938 1.000 0.000 0.000 0.000 NA
#> GSM876858 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876859 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876860 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
#> GSM876861 2 0.0000 1.000 0.000 1.000 0.000 0.000 NA
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM876886 3 0.0000 0.9790 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876887 3 0.0000 0.9790 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876888 3 0.0458 0.9848 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM876889 3 0.1141 0.9278 0.000 0.000 0.948 0.000 0.052 0.000
#> GSM876890 3 0.0000 0.9790 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876891 5 0.2793 0.8290 0.000 0.000 0.200 0.000 0.800 0.000
#> GSM876862 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.2260 0.8134 0.860 0.000 0.140 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876840 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876841 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876843 6 0.1007 0.8854 0.000 0.044 0.000 0.000 0.000 0.956
#> GSM876892 3 0.0000 0.9790 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876893 3 0.0458 0.9848 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM876894 5 0.2793 0.8290 0.000 0.000 0.200 0.000 0.800 0.000
#> GSM876895 5 0.0000 0.8610 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876896 4 0.3797 0.5903 0.000 0.000 0.000 0.580 0.000 0.420
#> GSM876897 4 0.3797 0.5903 0.000 0.000 0.000 0.580 0.000 0.420
#> GSM876868 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 0.6197 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876873 4 0.0000 0.6197 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876844 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876846 2 0.2300 0.8306 0.000 0.856 0.000 0.000 0.000 0.144
#> GSM876847 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876848 6 0.0000 0.9422 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM876849 6 0.0000 0.9422 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM876898 3 0.0458 0.9848 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM876899 5 0.0146 0.8615 0.000 0.000 0.004 0.000 0.996 0.000
#> GSM876900 3 0.0458 0.9848 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM876901 3 0.0458 0.9848 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM876902 4 0.3547 0.6362 0.000 0.000 0.000 0.668 0.000 0.332
#> GSM876903 5 0.0000 0.8610 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876904 3 0.0458 0.9848 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM876874 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.2340 0.8066 0.852 0.000 0.148 0.000 0.000 0.000
#> GSM876876 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876879 1 0.2340 0.8066 0.852 0.000 0.148 0.000 0.000 0.000
#> GSM876880 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876852 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876853 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876854 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876855 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876856 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876905 3 0.0458 0.9848 0.016 0.000 0.984 0.000 0.000 0.000
#> GSM876906 5 0.2793 0.8290 0.000 0.000 0.200 0.000 0.800 0.000
#> GSM876907 5 0.0000 0.8610 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876908 5 0.2793 0.8290 0.000 0.000 0.200 0.000 0.800 0.000
#> GSM876909 5 0.0000 0.8610 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876881 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876882 1 0.3101 0.7834 0.820 0.000 0.148 0.032 0.000 0.000
#> GSM876883 1 0.7025 0.0771 0.376 0.000 0.148 0.368 0.108 0.000
#> GSM876884 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876885 1 0.7025 0.0771 0.376 0.000 0.148 0.368 0.108 0.000
#> GSM876857 1 0.0000 0.9095 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876859 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876860 2 0.0000 0.9927 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876861 2 0.0000 0.9927 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 disease.state(p) tissue(p) k
#> SD:hclust 72 0.4844 9.33e-11 2
#> SD:hclust 72 0.0529 3.04e-11 3
#> SD:hclust 64 0.7387 1.23e-22 4
#> SD:hclust 70 0.1797 5.57e-22 5
#> SD:hclust 70 0.1886 3.05e-21 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 72 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 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 0.984 0.990 0.4923 0.507 0.507
#> 3 3 0.676 0.552 0.779 0.3172 0.836 0.700
#> 4 4 0.957 0.955 0.963 0.1278 0.813 0.572
#> 5 5 0.853 0.784 0.876 0.0585 0.984 0.938
#> 6 6 0.857 0.817 0.830 0.0406 0.941 0.767
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
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
#> GSM876886 1 0.0000 0.990 1.000 0.000
#> GSM876887 1 0.0000 0.990 1.000 0.000
#> GSM876888 1 0.0672 0.993 0.992 0.008
#> GSM876889 1 0.0000 0.990 1.000 0.000
#> GSM876890 1 0.0000 0.990 1.000 0.000
#> GSM876891 1 0.0672 0.993 0.992 0.008
#> GSM876862 1 0.0672 0.993 0.992 0.008
#> GSM876863 1 0.0672 0.993 0.992 0.008
#> GSM876864 1 0.0672 0.993 0.992 0.008
#> GSM876865 1 0.0672 0.993 0.992 0.008
#> GSM876866 1 0.0000 0.990 1.000 0.000
#> GSM876867 1 0.0672 0.993 0.992 0.008
#> GSM876838 2 0.0000 0.990 0.000 1.000
#> GSM876839 2 0.0000 0.990 0.000 1.000
#> GSM876840 2 0.0000 0.990 0.000 1.000
#> GSM876841 2 0.0000 0.990 0.000 1.000
#> GSM876842 2 0.0000 0.990 0.000 1.000
#> GSM876843 2 0.0672 0.986 0.008 0.992
#> GSM876892 1 0.0672 0.993 0.992 0.008
#> GSM876893 1 0.0672 0.993 0.992 0.008
#> GSM876894 1 0.0672 0.993 0.992 0.008
#> GSM876895 2 0.7219 0.750 0.200 0.800
#> GSM876896 2 0.0672 0.986 0.008 0.992
#> GSM876897 2 0.0672 0.986 0.008 0.992
#> GSM876868 1 0.0672 0.993 0.992 0.008
#> GSM876869 1 0.0672 0.993 0.992 0.008
#> GSM876870 1 0.0672 0.993 0.992 0.008
#> GSM876871 1 0.0672 0.993 0.992 0.008
#> GSM876872 1 0.0000 0.990 1.000 0.000
#> GSM876873 1 0.0000 0.990 1.000 0.000
#> GSM876844 2 0.0000 0.990 0.000 1.000
#> GSM876845 2 0.0000 0.990 0.000 1.000
#> GSM876846 2 0.0000 0.990 0.000 1.000
#> GSM876847 2 0.0000 0.990 0.000 1.000
#> GSM876848 2 0.0672 0.986 0.008 0.992
#> GSM876849 2 0.0672 0.986 0.008 0.992
#> GSM876898 1 0.0672 0.993 0.992 0.008
#> GSM876899 1 0.0672 0.993 0.992 0.008
#> GSM876900 1 0.0672 0.993 0.992 0.008
#> GSM876901 1 0.0672 0.993 0.992 0.008
#> GSM876902 1 0.6801 0.776 0.820 0.180
#> GSM876903 2 0.0938 0.982 0.012 0.988
#> GSM876904 1 0.0672 0.993 0.992 0.008
#> GSM876874 1 0.0672 0.993 0.992 0.008
#> GSM876875 1 0.0000 0.990 1.000 0.000
#> GSM876876 1 0.0672 0.993 0.992 0.008
#> GSM876877 1 0.0672 0.993 0.992 0.008
#> GSM876878 1 0.0672 0.993 0.992 0.008
#> GSM876879 1 0.0000 0.990 1.000 0.000
#> GSM876880 1 0.0672 0.993 0.992 0.008
#> GSM876850 2 0.0000 0.990 0.000 1.000
#> GSM876851 2 0.0000 0.990 0.000 1.000
#> GSM876852 2 0.0000 0.990 0.000 1.000
#> GSM876853 2 0.0000 0.990 0.000 1.000
#> GSM876854 2 0.0000 0.990 0.000 1.000
#> GSM876855 2 0.0000 0.990 0.000 1.000
#> GSM876856 2 0.0000 0.990 0.000 1.000
#> GSM876905 1 0.0672 0.993 0.992 0.008
#> GSM876906 1 0.0672 0.993 0.992 0.008
#> GSM876907 2 0.0938 0.982 0.012 0.988
#> GSM876908 1 0.0672 0.993 0.992 0.008
#> GSM876909 2 0.0938 0.982 0.012 0.988
#> GSM876881 2 0.0000 0.990 0.000 1.000
#> GSM876882 1 0.0000 0.990 1.000 0.000
#> GSM876883 1 0.0000 0.990 1.000 0.000
#> GSM876884 1 0.0672 0.993 0.992 0.008
#> GSM876885 1 0.0000 0.990 1.000 0.000
#> GSM876857 1 0.0672 0.993 0.992 0.008
#> GSM876858 2 0.0000 0.990 0.000 1.000
#> GSM876859 2 0.0000 0.990 0.000 1.000
#> GSM876860 2 0.0000 0.990 0.000 1.000
#> GSM876861 2 0.0000 0.990 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 1 0.0000 0.5244 1.000 0.000 0.000
#> GSM876887 1 0.0747 0.5102 0.984 0.000 0.016
#> GSM876888 1 0.0000 0.5244 1.000 0.000 0.000
#> GSM876889 1 0.6140 -0.2014 0.596 0.000 0.404
#> GSM876890 1 0.0747 0.5102 0.984 0.000 0.016
#> GSM876891 1 0.6140 -0.2014 0.596 0.000 0.404
#> GSM876862 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876863 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876864 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876865 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876866 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876867 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876838 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876839 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876840 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876841 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876842 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876843 3 0.6140 -0.7127 0.000 0.404 0.596
#> GSM876892 1 0.0237 0.5214 0.996 0.000 0.004
#> GSM876893 1 0.0000 0.5244 1.000 0.000 0.000
#> GSM876894 1 0.6140 -0.2014 0.596 0.000 0.404
#> GSM876895 1 0.9550 -0.5733 0.404 0.192 0.404
#> GSM876896 3 0.5397 0.5792 0.280 0.000 0.720
#> GSM876897 3 0.4861 0.5774 0.192 0.008 0.800
#> GSM876868 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876869 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876870 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876871 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876872 3 0.6111 0.5263 0.396 0.000 0.604
#> GSM876873 3 0.6111 0.5263 0.396 0.000 0.604
#> GSM876844 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876845 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876846 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876847 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876848 3 0.4931 -0.3463 0.000 0.232 0.768
#> GSM876849 3 0.2711 0.0949 0.000 0.088 0.912
#> GSM876898 1 0.0000 0.5244 1.000 0.000 0.000
#> GSM876899 1 0.6140 -0.2014 0.596 0.000 0.404
#> GSM876900 1 0.0237 0.5214 0.996 0.000 0.004
#> GSM876901 1 0.0237 0.5214 0.996 0.000 0.004
#> GSM876902 3 0.6111 0.5263 0.396 0.000 0.604
#> GSM876903 3 0.9577 0.5193 0.400 0.196 0.404
#> GSM876904 1 0.0000 0.5244 1.000 0.000 0.000
#> GSM876874 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876875 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876876 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876877 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876878 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876879 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876880 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876850 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876851 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876852 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876853 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876854 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876855 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876856 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876905 1 0.0000 0.5244 1.000 0.000 0.000
#> GSM876906 1 0.6140 -0.2014 0.596 0.000 0.404
#> GSM876907 1 0.9550 -0.5733 0.404 0.192 0.404
#> GSM876908 1 0.6140 -0.2014 0.596 0.000 0.404
#> GSM876909 3 0.9577 0.5193 0.400 0.196 0.404
#> GSM876881 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876882 1 0.5859 0.6352 0.656 0.344 0.000
#> GSM876883 1 0.6140 -0.2014 0.596 0.000 0.404
#> GSM876884 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876885 1 0.6140 -0.2014 0.596 0.000 0.404
#> GSM876857 1 0.6111 0.6478 0.604 0.396 0.000
#> GSM876858 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876859 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876860 2 0.6111 1.0000 0.000 0.604 0.396
#> GSM876861 2 0.6111 1.0000 0.000 0.604 0.396
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.1637 0.936 0.060 0.000 0.940 0.000
#> GSM876887 3 0.1637 0.936 0.060 0.000 0.940 0.000
#> GSM876888 3 0.1637 0.936 0.060 0.000 0.940 0.000
#> GSM876889 3 0.1624 0.929 0.028 0.000 0.952 0.020
#> GSM876890 3 0.1637 0.936 0.060 0.000 0.940 0.000
#> GSM876891 3 0.1624 0.929 0.028 0.000 0.952 0.020
#> GSM876862 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.983 0.000 1.000 0.000 0.000
#> GSM876839 2 0.0921 0.985 0.000 0.972 0.028 0.000
#> GSM876840 2 0.0336 0.980 0.000 0.992 0.000 0.008
#> GSM876841 2 0.0921 0.985 0.000 0.972 0.028 0.000
#> GSM876842 2 0.0000 0.983 0.000 1.000 0.000 0.000
#> GSM876843 4 0.4193 0.653 0.000 0.268 0.000 0.732
#> GSM876892 3 0.1637 0.936 0.060 0.000 0.940 0.000
#> GSM876893 3 0.1637 0.936 0.060 0.000 0.940 0.000
#> GSM876894 3 0.0921 0.930 0.028 0.000 0.972 0.000
#> GSM876895 3 0.2530 0.868 0.000 0.000 0.888 0.112
#> GSM876896 4 0.0336 0.940 0.000 0.000 0.008 0.992
#> GSM876897 4 0.0336 0.940 0.000 0.000 0.008 0.992
#> GSM876868 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876872 4 0.0336 0.940 0.000 0.000 0.008 0.992
#> GSM876873 4 0.0336 0.940 0.000 0.000 0.008 0.992
#> GSM876844 2 0.0000 0.983 0.000 1.000 0.000 0.000
#> GSM876845 2 0.0921 0.985 0.000 0.972 0.028 0.000
#> GSM876846 2 0.0336 0.980 0.000 0.992 0.000 0.008
#> GSM876847 2 0.0921 0.985 0.000 0.972 0.028 0.000
#> GSM876848 4 0.2011 0.885 0.000 0.080 0.000 0.920
#> GSM876849 4 0.0707 0.930 0.000 0.020 0.000 0.980
#> GSM876898 3 0.1637 0.936 0.060 0.000 0.940 0.000
#> GSM876899 3 0.3182 0.895 0.028 0.000 0.876 0.096
#> GSM876900 3 0.1637 0.936 0.060 0.000 0.940 0.000
#> GSM876901 3 0.1637 0.936 0.060 0.000 0.940 0.000
#> GSM876902 4 0.0336 0.940 0.000 0.000 0.008 0.992
#> GSM876903 3 0.2530 0.868 0.000 0.000 0.888 0.112
#> GSM876904 3 0.1637 0.936 0.060 0.000 0.940 0.000
#> GSM876874 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876875 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876876 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876879 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876880 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876850 2 0.0921 0.985 0.000 0.972 0.028 0.000
#> GSM876851 2 0.0921 0.985 0.000 0.972 0.028 0.000
#> GSM876852 2 0.0000 0.983 0.000 1.000 0.000 0.000
#> GSM876853 2 0.0000 0.983 0.000 1.000 0.000 0.000
#> GSM876854 2 0.0336 0.980 0.000 0.992 0.000 0.008
#> GSM876855 2 0.0336 0.980 0.000 0.992 0.000 0.008
#> GSM876856 2 0.0336 0.980 0.000 0.992 0.000 0.008
#> GSM876905 3 0.1637 0.936 0.060 0.000 0.940 0.000
#> GSM876906 3 0.1624 0.929 0.028 0.000 0.952 0.020
#> GSM876907 3 0.2530 0.868 0.000 0.000 0.888 0.112
#> GSM876908 3 0.1624 0.929 0.028 0.000 0.952 0.020
#> GSM876909 3 0.2530 0.868 0.000 0.000 0.888 0.112
#> GSM876881 2 0.0921 0.985 0.000 0.972 0.028 0.000
#> GSM876882 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876883 3 0.5119 0.806 0.124 0.000 0.764 0.112
#> GSM876884 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876885 3 0.5066 0.810 0.120 0.000 0.768 0.112
#> GSM876857 1 0.0000 1.000 1.000 0.000 0.000 0.000
#> GSM876858 2 0.0921 0.985 0.000 0.972 0.028 0.000
#> GSM876859 2 0.0921 0.985 0.000 0.972 0.028 0.000
#> GSM876860 2 0.0921 0.985 0.000 0.972 0.028 0.000
#> GSM876861 2 0.0921 0.985 0.000 0.972 0.028 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM876886 3 0.0912 0.686 0.016 0.000 0.972 0.000 0.012
#> GSM876887 3 0.0912 0.686 0.016 0.000 0.972 0.000 0.012
#> GSM876888 3 0.0671 0.693 0.016 0.000 0.980 0.000 0.004
#> GSM876889 3 0.3636 0.538 0.000 0.000 0.728 0.000 0.272
#> GSM876890 3 0.0671 0.693 0.016 0.000 0.980 0.000 0.004
#> GSM876891 3 0.4029 0.492 0.000 0.000 0.680 0.004 0.316
#> GSM876862 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.1792 0.892 0.000 0.916 0.000 0.000 0.084
#> GSM876839 2 0.0162 0.899 0.000 0.996 0.000 0.000 0.004
#> GSM876840 2 0.3689 0.826 0.000 0.740 0.000 0.004 0.256
#> GSM876841 2 0.0162 0.899 0.000 0.996 0.000 0.000 0.004
#> GSM876842 2 0.2471 0.880 0.000 0.864 0.000 0.000 0.136
#> GSM876843 4 0.5500 0.581 0.000 0.124 0.000 0.640 0.236
#> GSM876892 3 0.0510 0.695 0.016 0.000 0.984 0.000 0.000
#> GSM876893 3 0.0510 0.695 0.016 0.000 0.984 0.000 0.000
#> GSM876894 3 0.3684 0.531 0.000 0.000 0.720 0.000 0.280
#> GSM876895 3 0.5330 0.245 0.000 0.000 0.548 0.056 0.396
#> GSM876896 4 0.0162 0.829 0.000 0.000 0.000 0.996 0.004
#> GSM876897 4 0.0162 0.829 0.000 0.000 0.000 0.996 0.004
#> GSM876868 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.3774 0.685 0.000 0.000 0.000 0.704 0.296
#> GSM876873 4 0.3774 0.685 0.000 0.000 0.000 0.704 0.296
#> GSM876844 2 0.2471 0.880 0.000 0.864 0.000 0.000 0.136
#> GSM876845 2 0.0000 0.898 0.000 1.000 0.000 0.000 0.000
#> GSM876846 2 0.3662 0.826 0.000 0.744 0.000 0.004 0.252
#> GSM876847 2 0.0290 0.897 0.000 0.992 0.000 0.000 0.008
#> GSM876848 4 0.2632 0.798 0.000 0.040 0.000 0.888 0.072
#> GSM876849 4 0.1251 0.824 0.000 0.008 0.000 0.956 0.036
#> GSM876898 3 0.0510 0.695 0.016 0.000 0.984 0.000 0.000
#> GSM876899 3 0.5188 0.367 0.000 0.000 0.600 0.056 0.344
#> GSM876900 3 0.0510 0.695 0.016 0.000 0.984 0.000 0.000
#> GSM876901 3 0.0510 0.695 0.016 0.000 0.984 0.000 0.000
#> GSM876902 4 0.1341 0.809 0.000 0.000 0.000 0.944 0.056
#> GSM876903 3 0.5274 0.325 0.000 0.000 0.572 0.056 0.372
#> GSM876904 3 0.0510 0.695 0.016 0.000 0.984 0.000 0.000
#> GSM876874 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.2074 0.874 0.896 0.000 0.000 0.000 0.104
#> GSM876876 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876879 1 0.3895 0.609 0.680 0.000 0.000 0.000 0.320
#> GSM876880 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0290 0.897 0.000 0.992 0.000 0.000 0.008
#> GSM876851 2 0.0000 0.898 0.000 1.000 0.000 0.000 0.000
#> GSM876852 2 0.3424 0.838 0.000 0.760 0.000 0.000 0.240
#> GSM876853 2 0.1792 0.892 0.000 0.916 0.000 0.000 0.084
#> GSM876854 2 0.3508 0.831 0.000 0.748 0.000 0.000 0.252
#> GSM876855 2 0.3689 0.826 0.000 0.740 0.000 0.004 0.256
#> GSM876856 2 0.3689 0.826 0.000 0.740 0.000 0.004 0.256
#> GSM876905 3 0.0510 0.695 0.016 0.000 0.984 0.000 0.000
#> GSM876906 3 0.4251 0.484 0.000 0.000 0.672 0.012 0.316
#> GSM876907 3 0.5274 0.325 0.000 0.000 0.572 0.056 0.372
#> GSM876908 3 0.4251 0.484 0.000 0.000 0.672 0.012 0.316
#> GSM876909 3 0.5274 0.325 0.000 0.000 0.572 0.056 0.372
#> GSM876881 2 0.1043 0.886 0.000 0.960 0.000 0.000 0.040
#> GSM876882 1 0.3983 0.576 0.660 0.000 0.000 0.000 0.340
#> GSM876883 5 0.5001 0.989 0.040 0.000 0.260 0.016 0.684
#> GSM876884 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876885 5 0.4953 0.989 0.036 0.000 0.264 0.016 0.684
#> GSM876857 1 0.0000 0.960 1.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.1197 0.888 0.000 0.952 0.000 0.000 0.048
#> GSM876859 2 0.1197 0.888 0.000 0.952 0.000 0.000 0.048
#> GSM876860 2 0.1197 0.888 0.000 0.952 0.000 0.000 0.048
#> GSM876861 2 0.1197 0.888 0.000 0.952 0.000 0.000 0.048
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM876886 3 0.3898 0.969 0.000 0.000 0.684 0.000 0.296 0.020
#> GSM876887 3 0.4047 0.963 0.000 0.000 0.676 0.000 0.296 0.028
#> GSM876888 3 0.3428 0.986 0.000 0.000 0.696 0.000 0.304 0.000
#> GSM876889 5 0.4384 0.022 0.000 0.000 0.348 0.000 0.616 0.036
#> GSM876890 3 0.3853 0.977 0.000 0.000 0.680 0.000 0.304 0.016
#> GSM876891 5 0.1049 0.902 0.000 0.000 0.032 0.000 0.960 0.008
#> GSM876862 1 0.0000 0.954 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0146 0.953 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.954 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0972 0.944 0.964 0.000 0.028 0.008 0.000 0.000
#> GSM876866 1 0.0146 0.953 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM876867 1 0.0260 0.954 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM876838 2 0.2969 0.822 0.000 0.776 0.000 0.000 0.000 0.224
#> GSM876839 2 0.3728 0.831 0.000 0.652 0.000 0.000 0.004 0.344
#> GSM876840 2 0.1010 0.720 0.000 0.960 0.036 0.004 0.000 0.000
#> GSM876841 2 0.3728 0.831 0.000 0.652 0.000 0.000 0.004 0.344
#> GSM876842 2 0.2491 0.808 0.000 0.836 0.000 0.000 0.000 0.164
#> GSM876843 4 0.5487 0.443 0.000 0.364 0.096 0.528 0.000 0.012
#> GSM876892 3 0.3446 0.989 0.000 0.000 0.692 0.000 0.308 0.000
#> GSM876893 3 0.3446 0.989 0.000 0.000 0.692 0.000 0.308 0.000
#> GSM876894 5 0.1918 0.834 0.000 0.000 0.088 0.000 0.904 0.008
#> GSM876895 5 0.0405 0.893 0.000 0.000 0.004 0.000 0.988 0.008
#> GSM876896 4 0.0653 0.764 0.000 0.000 0.004 0.980 0.012 0.004
#> GSM876897 4 0.0508 0.765 0.000 0.000 0.000 0.984 0.012 0.004
#> GSM876868 1 0.0000 0.954 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0146 0.954 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM876870 1 0.1802 0.926 0.916 0.000 0.072 0.012 0.000 0.000
#> GSM876871 1 0.1643 0.931 0.924 0.000 0.068 0.008 0.000 0.000
#> GSM876872 4 0.5113 0.452 0.000 0.000 0.040 0.572 0.028 0.360
#> GSM876873 4 0.5113 0.452 0.000 0.000 0.040 0.572 0.028 0.360
#> GSM876844 2 0.2491 0.808 0.000 0.836 0.000 0.000 0.000 0.164
#> GSM876845 2 0.3742 0.831 0.000 0.648 0.000 0.000 0.004 0.348
#> GSM876846 2 0.2333 0.712 0.000 0.896 0.060 0.004 0.000 0.040
#> GSM876847 2 0.3942 0.826 0.000 0.624 0.004 0.000 0.004 0.368
#> GSM876848 4 0.2739 0.737 0.000 0.048 0.064 0.876 0.000 0.012
#> GSM876849 4 0.2026 0.753 0.000 0.004 0.060 0.916 0.008 0.012
#> GSM876898 3 0.3446 0.989 0.000 0.000 0.692 0.000 0.308 0.000
#> GSM876899 5 0.0632 0.908 0.000 0.000 0.024 0.000 0.976 0.000
#> GSM876900 3 0.3446 0.989 0.000 0.000 0.692 0.000 0.308 0.000
#> GSM876901 3 0.3446 0.989 0.000 0.000 0.692 0.000 0.308 0.000
#> GSM876902 4 0.1922 0.749 0.000 0.000 0.012 0.924 0.040 0.024
#> GSM876903 5 0.0000 0.905 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876904 3 0.3446 0.989 0.000 0.000 0.692 0.000 0.308 0.000
#> GSM876874 1 0.0972 0.944 0.964 0.000 0.028 0.008 0.000 0.000
#> GSM876875 1 0.3861 0.576 0.744 0.000 0.028 0.008 0.000 0.220
#> GSM876876 1 0.0632 0.951 0.976 0.000 0.024 0.000 0.000 0.000
#> GSM876877 1 0.0713 0.951 0.972 0.000 0.028 0.000 0.000 0.000
#> GSM876878 1 0.1285 0.938 0.944 0.000 0.052 0.004 0.000 0.000
#> GSM876879 6 0.4945 0.394 0.412 0.000 0.056 0.004 0.000 0.528
#> GSM876880 1 0.0713 0.951 0.972 0.000 0.028 0.000 0.000 0.000
#> GSM876850 2 0.3942 0.826 0.000 0.624 0.004 0.000 0.004 0.368
#> GSM876851 2 0.3728 0.831 0.000 0.652 0.000 0.000 0.004 0.344
#> GSM876852 2 0.0790 0.724 0.000 0.968 0.032 0.000 0.000 0.000
#> GSM876853 2 0.2969 0.822 0.000 0.776 0.000 0.000 0.000 0.224
#> GSM876854 2 0.0865 0.722 0.000 0.964 0.036 0.000 0.000 0.000
#> GSM876855 2 0.1010 0.720 0.000 0.960 0.036 0.004 0.000 0.000
#> GSM876856 2 0.1010 0.720 0.000 0.960 0.036 0.004 0.000 0.000
#> GSM876905 3 0.3446 0.989 0.000 0.000 0.692 0.000 0.308 0.000
#> GSM876906 5 0.0713 0.907 0.000 0.000 0.028 0.000 0.972 0.000
#> GSM876907 5 0.0000 0.905 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876908 5 0.0713 0.907 0.000 0.000 0.028 0.000 0.972 0.000
#> GSM876909 5 0.0000 0.905 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876881 2 0.4378 0.814 0.000 0.588 0.008 0.000 0.016 0.388
#> GSM876882 6 0.4736 0.428 0.396 0.000 0.052 0.000 0.000 0.552
#> GSM876883 6 0.4808 0.388 0.000 0.000 0.052 0.004 0.368 0.576
#> GSM876884 1 0.1802 0.926 0.916 0.000 0.072 0.012 0.000 0.000
#> GSM876885 6 0.4808 0.388 0.000 0.000 0.052 0.004 0.368 0.576
#> GSM876857 1 0.0000 0.954 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.5331 0.799 0.000 0.588 0.072 0.000 0.024 0.316
#> GSM876859 2 0.5331 0.799 0.000 0.588 0.072 0.000 0.024 0.316
#> GSM876860 2 0.5331 0.799 0.000 0.588 0.072 0.000 0.024 0.316
#> GSM876861 2 0.5331 0.799 0.000 0.588 0.072 0.000 0.024 0.316
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> SD:kmeans 72 0.7308 1.25e-10 2
#> SD:kmeans 59 0.3114 3.16e-11 3
#> SD:kmeans 72 0.1206 1.48e-20 4
#> SD:kmeans 64 0.0303 2.26e-18 5
#> SD:kmeans 64 0.2032 5.30e-20 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 72 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 0.5013 0.499 0.499
#> 3 3 0.781 0.873 0.922 0.3147 0.814 0.636
#> 4 4 1.000 0.962 0.984 0.1087 0.921 0.770
#> 5 5 1.000 0.951 0.980 0.0596 0.946 0.805
#> 6 6 0.989 0.926 0.969 0.0363 0.964 0.844
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
#> GSM876886 1 0 1 1 0
#> GSM876887 1 0 1 1 0
#> GSM876888 1 0 1 1 0
#> GSM876889 1 0 1 1 0
#> GSM876890 1 0 1 1 0
#> GSM876891 1 0 1 1 0
#> GSM876862 1 0 1 1 0
#> GSM876863 1 0 1 1 0
#> GSM876864 1 0 1 1 0
#> GSM876865 1 0 1 1 0
#> GSM876866 1 0 1 1 0
#> GSM876867 1 0 1 1 0
#> GSM876838 2 0 1 0 1
#> GSM876839 2 0 1 0 1
#> GSM876840 2 0 1 0 1
#> GSM876841 2 0 1 0 1
#> GSM876842 2 0 1 0 1
#> GSM876843 2 0 1 0 1
#> GSM876892 1 0 1 1 0
#> GSM876893 1 0 1 1 0
#> GSM876894 1 0 1 1 0
#> GSM876895 2 0 1 0 1
#> GSM876896 2 0 1 0 1
#> GSM876897 2 0 1 0 1
#> GSM876868 1 0 1 1 0
#> GSM876869 1 0 1 1 0
#> GSM876870 1 0 1 1 0
#> GSM876871 1 0 1 1 0
#> GSM876872 1 0 1 1 0
#> GSM876873 1 0 1 1 0
#> GSM876844 2 0 1 0 1
#> GSM876845 2 0 1 0 1
#> GSM876846 2 0 1 0 1
#> GSM876847 2 0 1 0 1
#> GSM876848 2 0 1 0 1
#> GSM876849 2 0 1 0 1
#> GSM876898 1 0 1 1 0
#> GSM876899 2 0 1 0 1
#> GSM876900 1 0 1 1 0
#> GSM876901 1 0 1 1 0
#> GSM876902 2 0 1 0 1
#> GSM876903 2 0 1 0 1
#> GSM876904 1 0 1 1 0
#> GSM876874 1 0 1 1 0
#> GSM876875 1 0 1 1 0
#> GSM876876 1 0 1 1 0
#> GSM876877 1 0 1 1 0
#> GSM876878 1 0 1 1 0
#> GSM876879 1 0 1 1 0
#> GSM876880 1 0 1 1 0
#> GSM876850 2 0 1 0 1
#> GSM876851 2 0 1 0 1
#> GSM876852 2 0 1 0 1
#> GSM876853 2 0 1 0 1
#> GSM876854 2 0 1 0 1
#> GSM876855 2 0 1 0 1
#> GSM876856 2 0 1 0 1
#> GSM876905 1 0 1 1 0
#> GSM876906 1 0 1 1 0
#> GSM876907 2 0 1 0 1
#> GSM876908 1 0 1 1 0
#> GSM876909 2 0 1 0 1
#> GSM876881 2 0 1 0 1
#> GSM876882 1 0 1 1 0
#> GSM876883 1 0 1 1 0
#> GSM876884 1 0 1 1 0
#> GSM876885 1 0 1 1 0
#> GSM876857 1 0 1 1 0
#> GSM876858 2 0 1 0 1
#> GSM876859 2 0 1 0 1
#> GSM876860 2 0 1 0 1
#> GSM876861 2 0 1 0 1
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 3 0.5178 0.831 0.256 0.000 0.744
#> GSM876887 3 0.5178 0.831 0.256 0.000 0.744
#> GSM876888 3 0.5178 0.831 0.256 0.000 0.744
#> GSM876889 3 0.0000 0.766 0.000 0.000 1.000
#> GSM876890 3 0.5178 0.831 0.256 0.000 0.744
#> GSM876891 3 0.0000 0.766 0.000 0.000 1.000
#> GSM876862 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876863 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876864 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876865 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876866 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876867 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876838 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876839 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876840 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876841 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876842 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876843 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876892 3 0.5178 0.831 0.256 0.000 0.744
#> GSM876893 3 0.5178 0.831 0.256 0.000 0.744
#> GSM876894 3 0.0000 0.766 0.000 0.000 1.000
#> GSM876895 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876896 2 0.5178 0.750 0.000 0.744 0.256
#> GSM876897 2 0.5178 0.750 0.000 0.744 0.256
#> GSM876868 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876869 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876870 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876871 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876872 1 0.5178 0.671 0.744 0.000 0.256
#> GSM876873 1 0.5178 0.671 0.744 0.000 0.256
#> GSM876844 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876845 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876846 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876847 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876848 2 0.0424 0.943 0.000 0.992 0.008
#> GSM876849 2 0.4842 0.780 0.000 0.776 0.224
#> GSM876898 3 0.5178 0.831 0.256 0.000 0.744
#> GSM876899 3 0.0000 0.766 0.000 0.000 1.000
#> GSM876900 3 0.5178 0.831 0.256 0.000 0.744
#> GSM876901 3 0.5178 0.831 0.256 0.000 0.744
#> GSM876902 3 0.5678 0.281 0.000 0.316 0.684
#> GSM876903 2 0.5178 0.750 0.000 0.744 0.256
#> GSM876904 3 0.5178 0.831 0.256 0.000 0.744
#> GSM876874 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876875 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876876 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876877 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876878 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876879 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876880 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876850 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876851 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876852 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876853 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876854 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876855 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876856 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876905 3 0.5178 0.831 0.256 0.000 0.744
#> GSM876906 3 0.0000 0.766 0.000 0.000 1.000
#> GSM876907 2 0.5138 0.754 0.000 0.748 0.252
#> GSM876908 3 0.0000 0.766 0.000 0.000 1.000
#> GSM876909 2 0.5016 0.765 0.000 0.760 0.240
#> GSM876881 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876882 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876883 1 0.4974 0.695 0.764 0.000 0.236
#> GSM876884 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876885 1 0.5016 0.691 0.760 0.000 0.240
#> GSM876857 1 0.0000 0.942 1.000 0.000 0.000
#> GSM876858 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876859 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876860 2 0.0000 0.948 0.000 1.000 0.000
#> GSM876861 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
#> GSM876886 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM876887 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM876888 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM876889 3 0.0188 0.995 0.000 0.000 0.996 0.004
#> GSM876890 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM876891 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM876862 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876839 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876840 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876841 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876842 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876843 4 0.3649 0.750 0.000 0.204 0.000 0.796
#> GSM876892 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM876893 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM876894 3 0.0000 0.996 0.000 0.000 1.000 0.000
#> GSM876895 2 0.0376 0.993 0.000 0.992 0.004 0.004
#> GSM876896 4 0.0188 0.965 0.000 0.004 0.000 0.996
#> GSM876897 4 0.0188 0.965 0.000 0.004 0.000 0.996
#> GSM876868 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876872 4 0.0188 0.963 0.004 0.000 0.000 0.996
#> GSM876873 4 0.0188 0.963 0.004 0.000 0.000 0.996
#> GSM876844 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876845 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876846 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876847 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876848 4 0.0188 0.965 0.000 0.004 0.000 0.996
#> GSM876849 4 0.0188 0.965 0.000 0.004 0.000 0.996
#> GSM876898 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM876899 3 0.0188 0.994 0.000 0.000 0.996 0.004
#> GSM876900 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM876901 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM876902 4 0.0000 0.963 0.000 0.000 0.000 1.000
#> GSM876903 2 0.0376 0.993 0.000 0.992 0.004 0.004
#> GSM876904 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM876874 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876875 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876876 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876879 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876880 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876851 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876852 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876853 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876854 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876855 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876856 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876905 3 0.0188 0.998 0.004 0.000 0.996 0.000
#> GSM876906 3 0.0188 0.994 0.000 0.000 0.996 0.004
#> GSM876907 2 0.0376 0.993 0.000 0.992 0.004 0.004
#> GSM876908 3 0.0188 0.994 0.000 0.000 0.996 0.004
#> GSM876909 2 0.0376 0.993 0.000 0.992 0.004 0.004
#> GSM876881 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876882 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876883 1 0.4866 0.346 0.596 0.000 0.000 0.404
#> GSM876884 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876885 1 0.4866 0.346 0.596 0.000 0.000 0.404
#> GSM876857 1 0.0000 0.960 1.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876859 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876860 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876861 2 0.0000 0.999 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
#> GSM876886 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM876887 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM876888 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM876889 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM876890 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM876891 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM876862 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876840 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876841 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876843 4 0.4138 0.385 0.000 0.384 0.000 0.616 0.000
#> GSM876892 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM876893 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM876894 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM876895 5 0.0703 0.979 0.000 0.024 0.000 0.000 0.976
#> GSM876896 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000
#> GSM876897 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000
#> GSM876868 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.0290 0.917 0.000 0.000 0.000 0.992 0.008
#> GSM876873 4 0.0290 0.917 0.000 0.000 0.000 0.992 0.008
#> GSM876844 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876846 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876847 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876848 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000
#> GSM876849 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000
#> GSM876898 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM876899 5 0.0703 0.973 0.000 0.000 0.024 0.000 0.976
#> GSM876900 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM876901 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM876902 4 0.0000 0.920 0.000 0.000 0.000 1.000 0.000
#> GSM876903 5 0.0703 0.979 0.000 0.024 0.000 0.000 0.976
#> GSM876904 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM876874 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.0510 0.948 0.984 0.000 0.000 0.000 0.016
#> GSM876876 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876879 1 0.0703 0.943 0.976 0.000 0.000 0.000 0.024
#> GSM876880 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876852 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876853 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876854 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876855 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876856 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876905 3 0.0000 1.000 0.000 0.000 1.000 0.000 0.000
#> GSM876906 5 0.0703 0.973 0.000 0.000 0.024 0.000 0.976
#> GSM876907 5 0.0703 0.979 0.000 0.024 0.000 0.000 0.976
#> GSM876908 5 0.0703 0.973 0.000 0.000 0.024 0.000 0.976
#> GSM876909 5 0.0703 0.979 0.000 0.024 0.000 0.000 0.976
#> GSM876881 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876882 1 0.0703 0.943 0.976 0.000 0.000 0.000 0.024
#> GSM876883 1 0.4779 0.356 0.588 0.000 0.000 0.388 0.024
#> GSM876884 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876885 1 0.4779 0.356 0.588 0.000 0.000 0.388 0.024
#> GSM876857 1 0.0000 0.957 1.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876859 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876860 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876861 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
#> GSM876886 3 0.0260 0.993 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM876887 3 0.0260 0.993 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM876888 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876889 3 0.0790 0.976 0.000 0.000 0.968 0.000 0.000 0.032
#> GSM876890 3 0.0260 0.993 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM876891 3 0.0458 0.989 0.000 0.000 0.984 0.000 0.000 0.016
#> GSM876862 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876840 2 0.0713 0.978 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM876841 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876843 4 0.2697 0.608 0.000 0.188 0.000 0.812 0.000 0.000
#> GSM876892 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876893 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876894 3 0.0260 0.991 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM876895 5 0.0405 0.987 0.000 0.004 0.000 0.000 0.988 0.008
#> GSM876896 4 0.0713 0.903 0.000 0.000 0.000 0.972 0.000 0.028
#> GSM876897 4 0.0632 0.905 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM876868 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876872 6 0.3866 0.131 0.000 0.000 0.000 0.484 0.000 0.516
#> GSM876873 6 0.3833 0.226 0.000 0.000 0.000 0.444 0.000 0.556
#> GSM876844 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876846 2 0.0713 0.978 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM876847 2 0.0146 0.991 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM876848 4 0.0000 0.900 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876849 4 0.0146 0.902 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM876898 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876899 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876900 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876901 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876902 4 0.0713 0.903 0.000 0.000 0.000 0.972 0.000 0.028
#> GSM876903 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876904 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876874 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.3765 0.312 0.596 0.000 0.000 0.000 0.000 0.404
#> GSM876876 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876879 6 0.2854 0.569 0.208 0.000 0.000 0.000 0.000 0.792
#> GSM876880 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0146 0.991 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM876851 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876852 2 0.0260 0.989 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM876853 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876854 2 0.0713 0.978 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM876855 2 0.0713 0.978 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM876856 2 0.0713 0.978 0.000 0.972 0.000 0.028 0.000 0.000
#> GSM876905 3 0.0000 0.995 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876906 5 0.0260 0.993 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM876907 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876908 5 0.0260 0.993 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM876909 5 0.0000 0.995 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876881 2 0.0146 0.991 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM876882 6 0.0937 0.707 0.040 0.000 0.000 0.000 0.000 0.960
#> GSM876883 6 0.0717 0.712 0.016 0.000 0.000 0.008 0.000 0.976
#> GSM876884 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876885 6 0.0717 0.712 0.016 0.000 0.000 0.008 0.000 0.976
#> GSM876857 1 0.0000 0.975 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0146 0.991 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM876859 2 0.0146 0.991 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM876860 2 0.0146 0.991 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM876861 2 0.0146 0.991 0.000 0.996 0.000 0.000 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 disease.state(p) tissue(p) k
#> SD:skmeans 72 0.7433 5.51e-10 2
#> SD:skmeans 71 0.9315 2.52e-21 3
#> SD:skmeans 70 0.1218 4.52e-18 4
#> SD:skmeans 69 0.0134 1.10e-20 5
#> SD:skmeans 69 0.0550 1.47e-20 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 72 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 0.978 0.990 0.4987 0.499 0.499
#> 3 3 1.000 0.968 0.987 0.3438 0.706 0.476
#> 4 4 0.873 0.903 0.935 0.0989 0.924 0.775
#> 5 5 1.000 0.972 0.988 0.0658 0.948 0.806
#> 6 6 0.910 0.920 0.954 0.0301 0.951 0.786
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 5
There is also optional best \(k\) = 2 3 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM876886 1 0.000 1.000 1.000 0.000
#> GSM876887 1 0.000 1.000 1.000 0.000
#> GSM876888 1 0.000 1.000 1.000 0.000
#> GSM876889 1 0.000 1.000 1.000 0.000
#> GSM876890 1 0.000 1.000 1.000 0.000
#> GSM876891 1 0.000 1.000 1.000 0.000
#> GSM876862 1 0.000 1.000 1.000 0.000
#> GSM876863 1 0.000 1.000 1.000 0.000
#> GSM876864 1 0.000 1.000 1.000 0.000
#> GSM876865 1 0.000 1.000 1.000 0.000
#> GSM876866 1 0.000 1.000 1.000 0.000
#> GSM876867 1 0.000 1.000 1.000 0.000
#> GSM876838 2 0.000 0.977 0.000 1.000
#> GSM876839 2 0.000 0.977 0.000 1.000
#> GSM876840 2 0.000 0.977 0.000 1.000
#> GSM876841 2 0.000 0.977 0.000 1.000
#> GSM876842 2 0.000 0.977 0.000 1.000
#> GSM876843 2 0.000 0.977 0.000 1.000
#> GSM876892 1 0.000 1.000 1.000 0.000
#> GSM876893 1 0.000 1.000 1.000 0.000
#> GSM876894 1 0.000 1.000 1.000 0.000
#> GSM876895 2 0.456 0.885 0.096 0.904
#> GSM876896 2 0.000 0.977 0.000 1.000
#> GSM876897 2 0.000 0.977 0.000 1.000
#> GSM876868 1 0.000 1.000 1.000 0.000
#> GSM876869 1 0.000 1.000 1.000 0.000
#> GSM876870 1 0.000 1.000 1.000 0.000
#> GSM876871 1 0.000 1.000 1.000 0.000
#> GSM876872 1 0.000 1.000 1.000 0.000
#> GSM876873 1 0.000 1.000 1.000 0.000
#> GSM876844 2 0.000 0.977 0.000 1.000
#> GSM876845 2 0.000 0.977 0.000 1.000
#> GSM876846 2 0.000 0.977 0.000 1.000
#> GSM876847 2 0.000 0.977 0.000 1.000
#> GSM876848 2 0.000 0.977 0.000 1.000
#> GSM876849 2 0.000 0.977 0.000 1.000
#> GSM876898 1 0.000 1.000 1.000 0.000
#> GSM876899 2 0.855 0.626 0.280 0.720
#> GSM876900 1 0.000 1.000 1.000 0.000
#> GSM876901 1 0.000 1.000 1.000 0.000
#> GSM876902 2 0.904 0.542 0.320 0.680
#> GSM876903 2 0.000 0.977 0.000 1.000
#> GSM876904 1 0.000 1.000 1.000 0.000
#> GSM876874 1 0.000 1.000 1.000 0.000
#> GSM876875 1 0.000 1.000 1.000 0.000
#> GSM876876 1 0.000 1.000 1.000 0.000
#> GSM876877 1 0.000 1.000 1.000 0.000
#> GSM876878 1 0.000 1.000 1.000 0.000
#> GSM876879 1 0.000 1.000 1.000 0.000
#> GSM876880 1 0.000 1.000 1.000 0.000
#> GSM876850 2 0.000 0.977 0.000 1.000
#> GSM876851 2 0.000 0.977 0.000 1.000
#> GSM876852 2 0.000 0.977 0.000 1.000
#> GSM876853 2 0.000 0.977 0.000 1.000
#> GSM876854 2 0.000 0.977 0.000 1.000
#> GSM876855 2 0.000 0.977 0.000 1.000
#> GSM876856 2 0.000 0.977 0.000 1.000
#> GSM876905 1 0.000 1.000 1.000 0.000
#> GSM876906 1 0.000 1.000 1.000 0.000
#> GSM876907 2 0.000 0.977 0.000 1.000
#> GSM876908 1 0.000 1.000 1.000 0.000
#> GSM876909 2 0.000 0.977 0.000 1.000
#> GSM876881 2 0.000 0.977 0.000 1.000
#> GSM876882 1 0.000 1.000 1.000 0.000
#> GSM876883 1 0.000 1.000 1.000 0.000
#> GSM876884 1 0.000 1.000 1.000 0.000
#> GSM876885 1 0.000 1.000 1.000 0.000
#> GSM876857 1 0.000 1.000 1.000 0.000
#> GSM876858 2 0.000 0.977 0.000 1.000
#> GSM876859 2 0.000 0.977 0.000 1.000
#> GSM876860 2 0.000 0.977 0.000 1.000
#> GSM876861 2 0.000 0.977 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876887 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876888 3 0.2448 0.897 0.076 0.000 0.924
#> GSM876889 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876890 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876891 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876862 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876863 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876864 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876865 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876866 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876867 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876838 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876839 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876840 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876841 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876842 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876843 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876892 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876893 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876894 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876895 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876896 3 0.4887 0.706 0.000 0.228 0.772
#> GSM876897 3 0.6154 0.334 0.000 0.408 0.592
#> GSM876868 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876869 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876870 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876871 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876872 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876873 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876844 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876845 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876846 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876847 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876848 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876849 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876898 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876899 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876900 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876901 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876902 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876903 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876904 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876874 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876875 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876876 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876877 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876878 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876879 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876880 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876850 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876851 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876852 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876853 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876854 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876855 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876856 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876905 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876906 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876907 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876908 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876909 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876881 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876882 1 0.4887 0.699 0.772 0.000 0.228
#> GSM876883 3 0.0747 0.958 0.016 0.000 0.984
#> GSM876884 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876885 3 0.0000 0.971 0.000 0.000 1.000
#> GSM876857 1 0.0000 0.988 1.000 0.000 0.000
#> GSM876858 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876859 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876860 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876861 2 0.0000 1.000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM876887 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM876888 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM876889 3 0.0817 0.856 0.000 0.000 0.976 0.024
#> GSM876890 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM876891 3 0.3400 0.821 0.000 0.000 0.820 0.180
#> GSM876862 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876839 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876840 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876841 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876842 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876843 4 0.4817 0.557 0.000 0.388 0.000 0.612
#> GSM876892 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM876893 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM876894 3 0.1867 0.849 0.000 0.000 0.928 0.072
#> GSM876895 3 0.6428 0.687 0.000 0.112 0.624 0.264
#> GSM876896 4 0.3219 0.814 0.000 0.164 0.000 0.836
#> GSM876897 4 0.3528 0.809 0.000 0.192 0.000 0.808
#> GSM876868 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 0.739 0.000 0.000 0.000 1.000
#> GSM876873 4 0.0000 0.739 0.000 0.000 0.000 1.000
#> GSM876844 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876845 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876846 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876847 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876848 4 0.4164 0.762 0.000 0.264 0.000 0.736
#> GSM876849 4 0.4164 0.762 0.000 0.264 0.000 0.736
#> GSM876898 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM876899 3 0.4164 0.788 0.000 0.000 0.736 0.264
#> GSM876900 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM876901 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM876902 4 0.0000 0.739 0.000 0.000 0.000 1.000
#> GSM876903 3 0.4817 0.677 0.000 0.000 0.612 0.388
#> GSM876904 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM876874 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876875 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876876 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876879 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876880 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876851 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876852 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876853 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876854 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876855 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876856 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876905 3 0.0000 0.858 0.000 0.000 1.000 0.000
#> GSM876906 3 0.4164 0.788 0.000 0.000 0.736 0.264
#> GSM876907 3 0.4164 0.788 0.000 0.000 0.736 0.264
#> GSM876908 3 0.4164 0.788 0.000 0.000 0.736 0.264
#> GSM876909 3 0.6273 0.702 0.000 0.100 0.636 0.264
#> GSM876881 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876882 1 0.3172 0.778 0.840 0.000 0.160 0.000
#> GSM876883 3 0.4936 0.692 0.004 0.000 0.624 0.372
#> GSM876884 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876885 3 0.4817 0.677 0.000 0.000 0.612 0.388
#> GSM876857 1 0.0000 0.990 1.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876859 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876860 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876861 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
#> GSM876886 3 0.0000 0.994 0.0 0.000 1.000 0.000 0.000
#> GSM876887 3 0.0000 0.994 0.0 0.000 1.000 0.000 0.000
#> GSM876888 3 0.0000 0.994 0.0 0.000 1.000 0.000 0.000
#> GSM876889 3 0.1341 0.937 0.0 0.000 0.944 0.000 0.056
#> GSM876890 3 0.0000 0.994 0.0 0.000 1.000 0.000 0.000
#> GSM876891 5 0.1043 0.960 0.0 0.000 0.040 0.000 0.960
#> GSM876862 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876840 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876841 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876843 4 0.2561 0.842 0.0 0.144 0.000 0.856 0.000
#> GSM876892 3 0.0000 0.994 0.0 0.000 1.000 0.000 0.000
#> GSM876893 3 0.0000 0.994 0.0 0.000 1.000 0.000 0.000
#> GSM876894 5 0.1043 0.960 0.0 0.000 0.040 0.000 0.960
#> GSM876895 5 0.0000 0.990 0.0 0.000 0.000 0.000 1.000
#> GSM876896 4 0.0000 0.949 0.0 0.000 0.000 1.000 0.000
#> GSM876897 4 0.0000 0.949 0.0 0.000 0.000 1.000 0.000
#> GSM876868 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 0.949 0.0 0.000 0.000 1.000 0.000
#> GSM876873 4 0.0000 0.949 0.0 0.000 0.000 1.000 0.000
#> GSM876844 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876846 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876847 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876848 4 0.2516 0.846 0.0 0.140 0.000 0.860 0.000
#> GSM876849 4 0.0000 0.949 0.0 0.000 0.000 1.000 0.000
#> GSM876898 3 0.0000 0.994 0.0 0.000 1.000 0.000 0.000
#> GSM876899 5 0.0000 0.990 0.0 0.000 0.000 0.000 1.000
#> GSM876900 3 0.0000 0.994 0.0 0.000 1.000 0.000 0.000
#> GSM876901 3 0.0000 0.994 0.0 0.000 1.000 0.000 0.000
#> GSM876902 4 0.0000 0.949 0.0 0.000 0.000 1.000 0.000
#> GSM876903 5 0.0000 0.990 0.0 0.000 0.000 0.000 1.000
#> GSM876904 3 0.0000 0.994 0.0 0.000 1.000 0.000 0.000
#> GSM876874 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876875 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876876 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876879 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876880 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876852 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876853 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876854 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876855 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876856 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876905 3 0.0000 0.994 0.0 0.000 1.000 0.000 0.000
#> GSM876906 5 0.0000 0.990 0.0 0.000 0.000 0.000 1.000
#> GSM876907 5 0.0000 0.990 0.0 0.000 0.000 0.000 1.000
#> GSM876908 5 0.0000 0.990 0.0 0.000 0.000 0.000 1.000
#> GSM876909 5 0.0000 0.990 0.0 0.000 0.000 0.000 1.000
#> GSM876881 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876882 1 0.4182 0.328 0.6 0.000 0.000 0.000 0.400
#> GSM876883 5 0.0000 0.990 0.0 0.000 0.000 0.000 1.000
#> GSM876884 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876885 5 0.0404 0.983 0.0 0.000 0.000 0.012 0.988
#> GSM876857 1 0.0000 0.977 1.0 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876859 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876860 2 0.0000 1.000 0.0 1.000 0.000 0.000 0.000
#> GSM876861 2 0.0000 1.000 0.0 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
#> GSM876886 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876887 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876888 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876889 3 0.0937 0.9433 0.000 0.000 0.960 0.000 0.040 0.000
#> GSM876890 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876891 3 0.2300 0.8439 0.000 0.000 0.856 0.000 0.144 0.000
#> GSM876862 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.9414 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.9414 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876840 2 0.0000 0.9414 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876841 2 0.0000 0.9414 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 0.9414 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876843 4 0.2491 0.7472 0.000 0.164 0.000 0.836 0.000 0.000
#> GSM876892 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876893 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876894 3 0.2300 0.8439 0.000 0.000 0.856 0.000 0.144 0.000
#> GSM876895 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876896 4 0.0000 0.8350 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876897 4 0.0000 0.8350 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876868 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.3843 0.0453 0.000 0.000 0.000 0.548 0.000 0.452
#> GSM876873 6 0.2527 0.7007 0.000 0.000 0.000 0.168 0.000 0.832
#> GSM876844 2 0.0000 0.9414 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 0.9414 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876846 2 0.1556 0.9190 0.000 0.920 0.000 0.000 0.000 0.080
#> GSM876847 2 0.2378 0.8929 0.000 0.848 0.000 0.000 0.000 0.152
#> GSM876848 4 0.2491 0.7472 0.000 0.164 0.000 0.836 0.000 0.000
#> GSM876849 4 0.0000 0.8350 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876898 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876899 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876900 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876901 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876902 4 0.0000 0.8350 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876903 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876904 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876874 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876875 6 0.2793 0.7788 0.200 0.000 0.000 0.000 0.000 0.800
#> GSM876876 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0146 0.9956 0.996 0.000 0.000 0.000 0.000 0.004
#> GSM876879 6 0.2491 0.8152 0.164 0.000 0.000 0.000 0.000 0.836
#> GSM876880 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.2300 0.8963 0.000 0.856 0.000 0.000 0.000 0.144
#> GSM876851 2 0.0000 0.9414 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876852 2 0.0000 0.9414 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876853 2 0.0000 0.9414 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876854 2 0.0000 0.9414 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876855 2 0.0000 0.9414 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876856 2 0.0000 0.9414 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876905 3 0.0000 0.9723 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876906 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876907 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876908 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876909 5 0.0000 1.0000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876881 2 0.2491 0.8871 0.000 0.836 0.000 0.000 0.000 0.164
#> GSM876882 6 0.2491 0.8152 0.164 0.000 0.000 0.000 0.000 0.836
#> GSM876883 6 0.2491 0.7625 0.000 0.000 0.000 0.000 0.164 0.836
#> GSM876884 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876885 6 0.2595 0.7638 0.000 0.000 0.000 0.004 0.160 0.836
#> GSM876857 1 0.0000 0.9997 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.2491 0.8871 0.000 0.836 0.000 0.000 0.000 0.164
#> GSM876859 2 0.2491 0.8871 0.000 0.836 0.000 0.000 0.000 0.164
#> GSM876860 2 0.2491 0.8871 0.000 0.836 0.000 0.000 0.000 0.164
#> GSM876861 2 0.2491 0.8871 0.000 0.836 0.000 0.000 0.000 0.164
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> SD:pam 72 0.7433 5.51e-10 2
#> SD:pam 71 0.9638 6.89e-23 3
#> SD:pam 72 0.1206 1.48e-20 4
#> SD:pam 71 0.0206 4.24e-19 5
#> SD:pam 71 0.1200 2.31e-21 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 72 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 1.000 0.948 0.965 0.4182 0.593 0.593
#> 3 3 0.864 0.929 0.962 0.5904 0.745 0.571
#> 4 4 0.998 0.961 0.981 0.1282 0.886 0.675
#> 5 5 1.000 0.961 0.984 0.0323 0.976 0.905
#> 6 6 0.998 0.965 0.976 0.0432 0.965 0.846
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 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
#> GSM876886 2 0.311 0.957 0.056 0.944
#> GSM876887 2 0.311 0.957 0.056 0.944
#> GSM876888 2 0.311 0.957 0.056 0.944
#> GSM876889 2 0.311 0.957 0.056 0.944
#> GSM876890 2 0.311 0.957 0.056 0.944
#> GSM876891 2 0.311 0.957 0.056 0.944
#> GSM876862 1 0.000 1.000 1.000 0.000
#> GSM876863 1 0.000 1.000 1.000 0.000
#> GSM876864 1 0.000 1.000 1.000 0.000
#> GSM876865 1 0.000 1.000 1.000 0.000
#> GSM876866 1 0.000 1.000 1.000 0.000
#> GSM876867 1 0.000 1.000 1.000 0.000
#> GSM876838 2 0.000 0.950 0.000 1.000
#> GSM876839 2 0.000 0.950 0.000 1.000
#> GSM876840 2 0.000 0.950 0.000 1.000
#> GSM876841 2 0.000 0.950 0.000 1.000
#> GSM876842 2 0.000 0.950 0.000 1.000
#> GSM876843 2 0.000 0.950 0.000 1.000
#> GSM876892 2 0.311 0.957 0.056 0.944
#> GSM876893 2 0.311 0.957 0.056 0.944
#> GSM876894 2 0.311 0.957 0.056 0.944
#> GSM876895 2 0.311 0.957 0.056 0.944
#> GSM876896 2 0.311 0.957 0.056 0.944
#> GSM876897 2 0.311 0.957 0.056 0.944
#> GSM876868 1 0.000 1.000 1.000 0.000
#> GSM876869 1 0.000 1.000 1.000 0.000
#> GSM876870 1 0.000 1.000 1.000 0.000
#> GSM876871 1 0.000 1.000 1.000 0.000
#> GSM876872 2 0.327 0.954 0.060 0.940
#> GSM876873 2 0.327 0.954 0.060 0.940
#> GSM876844 2 0.000 0.950 0.000 1.000
#> GSM876845 2 0.000 0.950 0.000 1.000
#> GSM876846 2 0.000 0.950 0.000 1.000
#> GSM876847 2 0.000 0.950 0.000 1.000
#> GSM876848 2 0.311 0.957 0.056 0.944
#> GSM876849 2 0.311 0.957 0.056 0.944
#> GSM876898 2 0.311 0.957 0.056 0.944
#> GSM876899 2 0.311 0.957 0.056 0.944
#> GSM876900 2 0.311 0.957 0.056 0.944
#> GSM876901 2 0.311 0.957 0.056 0.944
#> GSM876902 2 0.311 0.957 0.056 0.944
#> GSM876903 2 0.311 0.957 0.056 0.944
#> GSM876904 2 0.311 0.957 0.056 0.944
#> GSM876874 1 0.000 1.000 1.000 0.000
#> GSM876875 1 0.000 1.000 1.000 0.000
#> GSM876876 1 0.000 1.000 1.000 0.000
#> GSM876877 1 0.000 1.000 1.000 0.000
#> GSM876878 1 0.000 1.000 1.000 0.000
#> GSM876879 1 0.000 1.000 1.000 0.000
#> GSM876880 1 0.000 1.000 1.000 0.000
#> GSM876850 2 0.000 0.950 0.000 1.000
#> GSM876851 2 0.000 0.950 0.000 1.000
#> GSM876852 2 0.000 0.950 0.000 1.000
#> GSM876853 2 0.000 0.950 0.000 1.000
#> GSM876854 2 0.000 0.950 0.000 1.000
#> GSM876855 2 0.000 0.950 0.000 1.000
#> GSM876856 2 0.000 0.950 0.000 1.000
#> GSM876905 2 0.311 0.957 0.056 0.944
#> GSM876906 2 0.311 0.957 0.056 0.944
#> GSM876907 2 0.311 0.957 0.056 0.944
#> GSM876908 2 0.311 0.957 0.056 0.944
#> GSM876909 2 0.311 0.957 0.056 0.944
#> GSM876881 2 0.000 0.950 0.000 1.000
#> GSM876882 1 0.000 1.000 1.000 0.000
#> GSM876883 2 0.994 0.267 0.456 0.544
#> GSM876884 1 0.000 1.000 1.000 0.000
#> GSM876885 2 0.994 0.267 0.456 0.544
#> GSM876857 1 0.000 1.000 1.000 0.000
#> GSM876858 2 0.000 0.950 0.000 1.000
#> GSM876859 2 0.000 0.950 0.000 1.000
#> GSM876860 2 0.000 0.950 0.000 1.000
#> GSM876861 2 0.000 0.950 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876887 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876888 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876889 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876890 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876891 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876862 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876863 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876864 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876865 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876866 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876867 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876838 2 0.0237 0.996 0.000 0.996 0.004
#> GSM876839 2 0.0237 0.996 0.000 0.996 0.004
#> GSM876840 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876841 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876842 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876843 3 0.6244 0.319 0.000 0.440 0.560
#> GSM876892 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876893 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876894 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876895 3 0.6438 0.764 0.188 0.064 0.748
#> GSM876896 3 0.4178 0.811 0.172 0.000 0.828
#> GSM876897 3 0.4178 0.811 0.172 0.000 0.828
#> GSM876868 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876869 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876870 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876871 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876872 3 0.5178 0.729 0.256 0.000 0.744
#> GSM876873 3 0.5178 0.729 0.256 0.000 0.744
#> GSM876844 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876845 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876846 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876847 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876848 3 0.5178 0.694 0.000 0.256 0.744
#> GSM876849 3 0.5178 0.694 0.000 0.256 0.744
#> GSM876898 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876899 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876900 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876901 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876902 3 0.4178 0.811 0.172 0.000 0.828
#> GSM876903 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876904 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876874 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876875 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876876 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876877 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876878 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876879 1 0.0237 0.995 0.996 0.000 0.004
#> GSM876880 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876850 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876851 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876852 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876853 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876854 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876855 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876856 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876905 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876906 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876907 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876908 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876909 3 0.0000 0.908 0.000 0.000 1.000
#> GSM876881 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876882 1 0.0424 0.991 0.992 0.000 0.008
#> GSM876883 3 0.5216 0.724 0.260 0.000 0.740
#> GSM876884 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876885 3 0.5216 0.724 0.260 0.000 0.740
#> GSM876857 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876858 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876859 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876860 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876861 2 0.0000 1.000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876887 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876888 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876889 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876890 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876891 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876862 1 0.0000 0.996 1.000 0.00 0.000 0.000
#> GSM876863 1 0.0188 0.992 0.996 0.00 0.000 0.004
#> GSM876864 1 0.0000 0.996 1.000 0.00 0.000 0.000
#> GSM876865 1 0.0000 0.996 1.000 0.00 0.000 0.000
#> GSM876866 4 0.4222 0.685 0.272 0.00 0.000 0.728
#> GSM876867 1 0.0000 0.996 1.000 0.00 0.000 0.000
#> GSM876838 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876839 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876840 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876841 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876842 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876843 4 0.3801 0.713 0.000 0.22 0.000 0.780
#> GSM876892 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876893 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876894 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876895 3 0.5884 0.335 0.044 0.00 0.592 0.364
#> GSM876896 4 0.0000 0.922 0.000 0.00 0.000 1.000
#> GSM876897 4 0.0000 0.922 0.000 0.00 0.000 1.000
#> GSM876868 1 0.0000 0.996 1.000 0.00 0.000 0.000
#> GSM876869 1 0.0000 0.996 1.000 0.00 0.000 0.000
#> GSM876870 1 0.0000 0.996 1.000 0.00 0.000 0.000
#> GSM876871 1 0.0000 0.996 1.000 0.00 0.000 0.000
#> GSM876872 4 0.0000 0.922 0.000 0.00 0.000 1.000
#> GSM876873 4 0.0000 0.922 0.000 0.00 0.000 1.000
#> GSM876844 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876845 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876846 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876847 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876848 4 0.0000 0.922 0.000 0.00 0.000 1.000
#> GSM876849 4 0.0000 0.922 0.000 0.00 0.000 1.000
#> GSM876898 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876899 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876900 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876901 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876902 4 0.0000 0.922 0.000 0.00 0.000 1.000
#> GSM876903 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876904 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876874 1 0.0000 0.996 1.000 0.00 0.000 0.000
#> GSM876875 1 0.1474 0.940 0.948 0.00 0.000 0.052
#> GSM876876 1 0.0000 0.996 1.000 0.00 0.000 0.000
#> GSM876877 1 0.0000 0.996 1.000 0.00 0.000 0.000
#> GSM876878 1 0.0336 0.989 0.992 0.00 0.000 0.008
#> GSM876879 4 0.3024 0.850 0.148 0.00 0.000 0.852
#> GSM876880 1 0.0000 0.996 1.000 0.00 0.000 0.000
#> GSM876850 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876851 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876852 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876853 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876854 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876855 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876856 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876905 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876906 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876907 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876908 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876909 3 0.0000 0.980 0.000 0.00 1.000 0.000
#> GSM876881 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876882 4 0.2216 0.895 0.092 0.00 0.000 0.908
#> GSM876883 4 0.2149 0.897 0.088 0.00 0.000 0.912
#> GSM876884 1 0.0000 0.996 1.000 0.00 0.000 0.000
#> GSM876885 4 0.2149 0.897 0.088 0.00 0.000 0.912
#> GSM876857 1 0.0000 0.996 1.000 0.00 0.000 0.000
#> GSM876858 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876859 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876860 2 0.0000 1.000 0.000 1.00 0.000 0.000
#> GSM876861 2 0.0000 1.000 0.000 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
#> GSM876886 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876887 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876888 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876889 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876890 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876891 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876862 1 0.0000 0.972 1.000 0.000 0.0 0.000 0.000
#> GSM876863 1 0.3636 0.613 0.728 0.000 0.0 0.000 0.272
#> GSM876864 1 0.0000 0.972 1.000 0.000 0.0 0.000 0.000
#> GSM876865 1 0.0000 0.972 1.000 0.000 0.0 0.000 0.000
#> GSM876866 5 0.0000 0.927 0.000 0.000 0.0 0.000 1.000
#> GSM876867 1 0.0000 0.972 1.000 0.000 0.0 0.000 0.000
#> GSM876838 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876839 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876840 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876841 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876842 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876843 4 0.0162 0.994 0.000 0.004 0.0 0.996 0.000
#> GSM876892 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876893 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876894 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876895 3 0.4949 0.353 0.000 0.028 0.6 0.368 0.004
#> GSM876896 4 0.0000 0.999 0.000 0.000 0.0 1.000 0.000
#> GSM876897 4 0.0000 0.999 0.000 0.000 0.0 1.000 0.000
#> GSM876868 1 0.0000 0.972 1.000 0.000 0.0 0.000 0.000
#> GSM876869 1 0.0000 0.972 1.000 0.000 0.0 0.000 0.000
#> GSM876870 1 0.0000 0.972 1.000 0.000 0.0 0.000 0.000
#> GSM876871 1 0.0000 0.972 1.000 0.000 0.0 0.000 0.000
#> GSM876872 4 0.0000 0.999 0.000 0.000 0.0 1.000 0.000
#> GSM876873 4 0.0000 0.999 0.000 0.000 0.0 1.000 0.000
#> GSM876844 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876845 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876846 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876847 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876848 4 0.0000 0.999 0.000 0.000 0.0 1.000 0.000
#> GSM876849 4 0.0000 0.999 0.000 0.000 0.0 1.000 0.000
#> GSM876898 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876899 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876900 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876901 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876902 4 0.0000 0.999 0.000 0.000 0.0 1.000 0.000
#> GSM876903 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876904 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876874 1 0.0000 0.972 1.000 0.000 0.0 0.000 0.000
#> GSM876875 5 0.1732 0.862 0.080 0.000 0.0 0.000 0.920
#> GSM876876 1 0.0000 0.972 1.000 0.000 0.0 0.000 0.000
#> GSM876877 1 0.0000 0.972 1.000 0.000 0.0 0.000 0.000
#> GSM876878 1 0.2424 0.839 0.868 0.000 0.0 0.000 0.132
#> GSM876879 5 0.0000 0.927 0.000 0.000 0.0 0.000 1.000
#> GSM876880 1 0.0000 0.972 1.000 0.000 0.0 0.000 0.000
#> GSM876850 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876851 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876852 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876853 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876854 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876855 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876856 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876905 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876906 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876907 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876908 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876909 3 0.0000 0.979 0.000 0.000 1.0 0.000 0.000
#> GSM876881 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876882 5 0.0000 0.927 0.000 0.000 0.0 0.000 1.000
#> GSM876883 5 0.0162 0.926 0.000 0.000 0.0 0.004 0.996
#> GSM876884 1 0.0000 0.972 1.000 0.000 0.0 0.000 0.000
#> GSM876885 5 0.3424 0.668 0.000 0.000 0.0 0.240 0.760
#> GSM876857 1 0.0000 0.972 1.000 0.000 0.0 0.000 0.000
#> GSM876858 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876859 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876860 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
#> GSM876861 2 0.0000 1.000 0.000 1.000 0.0 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM876886 3 0.0000 0.964 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876887 3 0.0000 0.964 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876888 3 0.0000 0.964 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876889 3 0.0713 0.962 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM876890 3 0.0000 0.964 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876891 3 0.0713 0.962 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM876862 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876866 6 0.0458 0.952 0.016 0.000 0.000 0.000 0.000 0.984
#> GSM876867 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0363 0.982 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM876839 2 0.0363 0.982 0.000 0.988 0.000 0.000 0.012 0.000
#> GSM876840 5 0.1444 0.968 0.000 0.072 0.000 0.000 0.928 0.000
#> GSM876841 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876843 4 0.0363 0.983 0.000 0.012 0.000 0.988 0.000 0.000
#> GSM876892 3 0.0000 0.964 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876893 3 0.0000 0.964 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876894 3 0.0713 0.962 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM876895 3 0.5557 0.466 0.000 0.200 0.600 0.188 0.012 0.000
#> GSM876896 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876897 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876868 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876873 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876844 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876846 5 0.1444 0.968 0.000 0.072 0.000 0.000 0.928 0.000
#> GSM876847 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876848 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876849 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876898 3 0.0000 0.964 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876899 3 0.1267 0.949 0.000 0.000 0.940 0.000 0.060 0.000
#> GSM876900 3 0.0000 0.964 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876901 3 0.0000 0.964 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876902 4 0.0000 0.998 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876903 3 0.1267 0.949 0.000 0.000 0.940 0.000 0.060 0.000
#> GSM876904 3 0.0713 0.962 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM876874 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876875 6 0.0146 0.961 0.004 0.000 0.000 0.000 0.000 0.996
#> GSM876876 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.2003 0.871 0.884 0.000 0.000 0.000 0.000 0.116
#> GSM876879 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM876880 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876852 5 0.2730 0.838 0.000 0.192 0.000 0.000 0.808 0.000
#> GSM876853 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876854 5 0.1444 0.968 0.000 0.072 0.000 0.000 0.928 0.000
#> GSM876855 5 0.1444 0.968 0.000 0.072 0.000 0.000 0.928 0.000
#> GSM876856 5 0.1444 0.968 0.000 0.072 0.000 0.000 0.928 0.000
#> GSM876905 3 0.0000 0.964 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876906 3 0.0713 0.962 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM876907 3 0.1267 0.949 0.000 0.000 0.940 0.000 0.060 0.000
#> GSM876908 3 0.0713 0.962 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM876909 3 0.1267 0.949 0.000 0.000 0.940 0.000 0.060 0.000
#> GSM876881 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876882 6 0.0000 0.961 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM876883 6 0.0458 0.956 0.000 0.000 0.000 0.016 0.000 0.984
#> GSM876884 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876885 6 0.2135 0.849 0.000 0.000 0.000 0.128 0.000 0.872
#> GSM876857 1 0.0000 0.992 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876859 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876860 2 0.0000 0.992 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876861 2 0.1444 0.915 0.000 0.928 0.000 0.000 0.072 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> SD:mclust 70 0.8058 3.77e-12 2
#> SD:mclust 71 0.8087 8.57e-21 3
#> SD:mclust 71 0.6906 7.53e-21 4
#> SD:mclust 71 0.1184 3.49e-21 5
#> SD:mclust 71 0.0739 4.84e-20 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 72 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 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 0.981 0.991 0.4839 0.512 0.512
#> 3 3 0.825 0.865 0.926 0.3785 0.750 0.539
#> 4 4 0.956 0.938 0.955 0.0834 0.937 0.808
#> 5 5 0.855 0.855 0.911 0.0755 0.914 0.699
#> 6 6 0.834 0.762 0.875 0.0191 0.963 0.845
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
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
#> GSM876886 1 0.000 1.000 1.000 0.000
#> GSM876887 1 0.000 1.000 1.000 0.000
#> GSM876888 1 0.000 1.000 1.000 0.000
#> GSM876889 1 0.000 1.000 1.000 0.000
#> GSM876890 1 0.000 1.000 1.000 0.000
#> GSM876891 1 0.000 1.000 1.000 0.000
#> GSM876862 1 0.000 1.000 1.000 0.000
#> GSM876863 1 0.000 1.000 1.000 0.000
#> GSM876864 1 0.000 1.000 1.000 0.000
#> GSM876865 1 0.000 1.000 1.000 0.000
#> GSM876866 1 0.000 1.000 1.000 0.000
#> GSM876867 1 0.000 1.000 1.000 0.000
#> GSM876838 2 0.000 0.976 0.000 1.000
#> GSM876839 2 0.000 0.976 0.000 1.000
#> GSM876840 2 0.000 0.976 0.000 1.000
#> GSM876841 2 0.000 0.976 0.000 1.000
#> GSM876842 2 0.000 0.976 0.000 1.000
#> GSM876843 2 0.000 0.976 0.000 1.000
#> GSM876892 1 0.000 1.000 1.000 0.000
#> GSM876893 1 0.000 1.000 1.000 0.000
#> GSM876894 1 0.000 1.000 1.000 0.000
#> GSM876895 2 0.802 0.702 0.244 0.756
#> GSM876896 1 0.000 1.000 1.000 0.000
#> GSM876897 2 0.000 0.976 0.000 1.000
#> GSM876868 1 0.000 1.000 1.000 0.000
#> GSM876869 1 0.000 1.000 1.000 0.000
#> GSM876870 1 0.000 1.000 1.000 0.000
#> GSM876871 1 0.000 1.000 1.000 0.000
#> GSM876872 1 0.000 1.000 1.000 0.000
#> GSM876873 1 0.000 1.000 1.000 0.000
#> GSM876844 2 0.000 0.976 0.000 1.000
#> GSM876845 2 0.000 0.976 0.000 1.000
#> GSM876846 2 0.000 0.976 0.000 1.000
#> GSM876847 2 0.000 0.976 0.000 1.000
#> GSM876848 2 0.000 0.976 0.000 1.000
#> GSM876849 2 0.000 0.976 0.000 1.000
#> GSM876898 1 0.000 1.000 1.000 0.000
#> GSM876899 1 0.000 1.000 1.000 0.000
#> GSM876900 1 0.000 1.000 1.000 0.000
#> GSM876901 1 0.000 1.000 1.000 0.000
#> GSM876902 1 0.000 1.000 1.000 0.000
#> GSM876903 2 0.584 0.845 0.140 0.860
#> GSM876904 1 0.000 1.000 1.000 0.000
#> GSM876874 1 0.000 1.000 1.000 0.000
#> GSM876875 1 0.000 1.000 1.000 0.000
#> GSM876876 1 0.000 1.000 1.000 0.000
#> GSM876877 1 0.000 1.000 1.000 0.000
#> GSM876878 1 0.000 1.000 1.000 0.000
#> GSM876879 1 0.000 1.000 1.000 0.000
#> GSM876880 1 0.000 1.000 1.000 0.000
#> GSM876850 2 0.000 0.976 0.000 1.000
#> GSM876851 2 0.000 0.976 0.000 1.000
#> GSM876852 2 0.000 0.976 0.000 1.000
#> GSM876853 2 0.000 0.976 0.000 1.000
#> GSM876854 2 0.000 0.976 0.000 1.000
#> GSM876855 2 0.000 0.976 0.000 1.000
#> GSM876856 2 0.000 0.976 0.000 1.000
#> GSM876905 1 0.000 1.000 1.000 0.000
#> GSM876906 1 0.000 1.000 1.000 0.000
#> GSM876907 2 0.753 0.746 0.216 0.784
#> GSM876908 1 0.000 1.000 1.000 0.000
#> GSM876909 2 0.388 0.911 0.076 0.924
#> GSM876881 2 0.000 0.976 0.000 1.000
#> GSM876882 1 0.000 1.000 1.000 0.000
#> GSM876883 1 0.000 1.000 1.000 0.000
#> GSM876884 1 0.000 1.000 1.000 0.000
#> GSM876885 1 0.000 1.000 1.000 0.000
#> GSM876857 1 0.000 1.000 1.000 0.000
#> GSM876858 2 0.000 0.976 0.000 1.000
#> GSM876859 2 0.000 0.976 0.000 1.000
#> GSM876860 2 0.000 0.976 0.000 1.000
#> GSM876861 2 0.000 0.976 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 3 0.5882 0.654 0.348 0.000 0.652
#> GSM876887 3 0.4555 0.756 0.200 0.000 0.800
#> GSM876888 3 0.5968 0.639 0.364 0.000 0.636
#> GSM876889 3 0.0237 0.797 0.004 0.000 0.996
#> GSM876890 3 0.2537 0.791 0.080 0.000 0.920
#> GSM876891 3 0.0424 0.797 0.008 0.000 0.992
#> GSM876862 1 0.0000 0.964 1.000 0.000 0.000
#> GSM876863 1 0.0237 0.962 0.996 0.000 0.004
#> GSM876864 1 0.0000 0.964 1.000 0.000 0.000
#> GSM876865 1 0.0000 0.964 1.000 0.000 0.000
#> GSM876866 1 0.0747 0.955 0.984 0.000 0.016
#> GSM876867 1 0.0000 0.964 1.000 0.000 0.000
#> GSM876838 2 0.0000 0.982 0.000 1.000 0.000
#> GSM876839 2 0.0237 0.981 0.000 0.996 0.004
#> GSM876840 2 0.0000 0.982 0.000 1.000 0.000
#> GSM876841 2 0.0000 0.982 0.000 1.000 0.000
#> GSM876842 2 0.0000 0.982 0.000 1.000 0.000
#> GSM876843 2 0.0000 0.982 0.000 1.000 0.000
#> GSM876892 3 0.5465 0.711 0.288 0.000 0.712
#> GSM876893 3 0.5835 0.669 0.340 0.000 0.660
#> GSM876894 3 0.0892 0.798 0.020 0.000 0.980
#> GSM876895 2 0.2496 0.910 0.068 0.928 0.004
#> GSM876896 3 0.0237 0.795 0.000 0.004 0.996
#> GSM876897 3 0.0747 0.791 0.000 0.016 0.984
#> GSM876868 1 0.0000 0.964 1.000 0.000 0.000
#> GSM876869 1 0.0000 0.964 1.000 0.000 0.000
#> GSM876870 1 0.0000 0.964 1.000 0.000 0.000
#> GSM876871 1 0.0000 0.964 1.000 0.000 0.000
#> GSM876872 1 0.6252 0.231 0.556 0.000 0.444
#> GSM876873 3 0.6235 0.101 0.436 0.000 0.564
#> GSM876844 2 0.0000 0.982 0.000 1.000 0.000
#> GSM876845 2 0.0237 0.981 0.000 0.996 0.004
#> GSM876846 2 0.0000 0.982 0.000 1.000 0.000
#> GSM876847 2 0.0237 0.981 0.000 0.996 0.004
#> GSM876848 2 0.0000 0.982 0.000 1.000 0.000
#> GSM876849 2 0.5810 0.552 0.000 0.664 0.336
#> GSM876898 3 0.6008 0.631 0.372 0.000 0.628
#> GSM876899 3 0.0237 0.797 0.004 0.000 0.996
#> GSM876900 3 0.5497 0.708 0.292 0.000 0.708
#> GSM876901 3 0.5621 0.697 0.308 0.000 0.692
#> GSM876902 3 0.0237 0.797 0.004 0.000 0.996
#> GSM876903 3 0.1411 0.785 0.000 0.036 0.964
#> GSM876904 3 0.5988 0.635 0.368 0.000 0.632
#> GSM876874 1 0.0000 0.964 1.000 0.000 0.000
#> GSM876875 1 0.0892 0.953 0.980 0.000 0.020
#> GSM876876 1 0.0000 0.964 1.000 0.000 0.000
#> GSM876877 1 0.0000 0.964 1.000 0.000 0.000
#> GSM876878 1 0.0237 0.962 0.996 0.000 0.004
#> GSM876879 1 0.0892 0.953 0.980 0.000 0.020
#> GSM876880 1 0.0000 0.964 1.000 0.000 0.000
#> GSM876850 2 0.0237 0.981 0.000 0.996 0.004
#> GSM876851 2 0.0237 0.981 0.000 0.996 0.004
#> GSM876852 2 0.0000 0.982 0.000 1.000 0.000
#> GSM876853 2 0.0000 0.982 0.000 1.000 0.000
#> GSM876854 2 0.0000 0.982 0.000 1.000 0.000
#> GSM876855 2 0.0000 0.982 0.000 1.000 0.000
#> GSM876856 2 0.0000 0.982 0.000 1.000 0.000
#> GSM876905 3 0.5905 0.653 0.352 0.000 0.648
#> GSM876906 3 0.0237 0.797 0.004 0.000 0.996
#> GSM876907 3 0.3192 0.755 0.000 0.112 0.888
#> GSM876908 3 0.0237 0.797 0.004 0.000 0.996
#> GSM876909 3 0.4931 0.645 0.000 0.232 0.768
#> GSM876881 2 0.0237 0.981 0.000 0.996 0.004
#> GSM876882 1 0.1163 0.947 0.972 0.000 0.028
#> GSM876883 1 0.2165 0.912 0.936 0.000 0.064
#> GSM876884 1 0.0000 0.964 1.000 0.000 0.000
#> GSM876885 1 0.2537 0.895 0.920 0.000 0.080
#> GSM876857 1 0.0000 0.964 1.000 0.000 0.000
#> GSM876858 2 0.0237 0.981 0.000 0.996 0.004
#> GSM876859 2 0.0000 0.982 0.000 1.000 0.000
#> GSM876860 2 0.0000 0.982 0.000 1.000 0.000
#> GSM876861 2 0.0000 0.982 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.0921 0.9495 0.000 0.000 0.972 0.028
#> GSM876887 3 0.1474 0.9478 0.000 0.000 0.948 0.052
#> GSM876888 3 0.1302 0.9299 0.000 0.000 0.956 0.044
#> GSM876889 3 0.2149 0.9279 0.000 0.000 0.912 0.088
#> GSM876890 3 0.1389 0.9488 0.000 0.000 0.952 0.048
#> GSM876891 3 0.1389 0.9486 0.000 0.000 0.952 0.048
#> GSM876862 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876838 2 0.0469 0.9776 0.000 0.988 0.000 0.012
#> GSM876839 2 0.0000 0.9781 0.000 1.000 0.000 0.000
#> GSM876840 2 0.0592 0.9764 0.000 0.984 0.000 0.016
#> GSM876841 2 0.0336 0.9774 0.000 0.992 0.000 0.008
#> GSM876842 2 0.0469 0.9776 0.000 0.988 0.000 0.012
#> GSM876843 2 0.1302 0.9549 0.000 0.956 0.000 0.044
#> GSM876892 3 0.0469 0.9487 0.000 0.000 0.988 0.012
#> GSM876893 3 0.1118 0.9344 0.000 0.000 0.964 0.036
#> GSM876894 3 0.1302 0.9494 0.000 0.000 0.956 0.044
#> GSM876895 2 0.2466 0.9043 0.056 0.916 0.000 0.028
#> GSM876896 4 0.3528 0.7507 0.000 0.000 0.192 0.808
#> GSM876897 4 0.3591 0.7640 0.000 0.008 0.168 0.824
#> GSM876868 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876872 4 0.4894 0.7467 0.120 0.000 0.100 0.780
#> GSM876873 4 0.4827 0.7615 0.092 0.000 0.124 0.784
#> GSM876844 2 0.0469 0.9776 0.000 0.988 0.000 0.012
#> GSM876845 2 0.0592 0.9758 0.000 0.984 0.000 0.016
#> GSM876846 2 0.0469 0.9776 0.000 0.988 0.000 0.012
#> GSM876847 2 0.0817 0.9727 0.000 0.976 0.000 0.024
#> GSM876848 4 0.4998 0.0648 0.000 0.488 0.000 0.512
#> GSM876849 4 0.4294 0.6731 0.008 0.204 0.008 0.780
#> GSM876898 3 0.1940 0.9065 0.000 0.000 0.924 0.076
#> GSM876899 3 0.1557 0.9466 0.000 0.000 0.944 0.056
#> GSM876900 3 0.0188 0.9469 0.000 0.000 0.996 0.004
#> GSM876901 3 0.0000 0.9479 0.000 0.000 1.000 0.000
#> GSM876902 4 0.3569 0.7470 0.000 0.000 0.196 0.804
#> GSM876903 3 0.2973 0.8701 0.000 0.000 0.856 0.144
#> GSM876904 3 0.1716 0.9160 0.000 0.000 0.936 0.064
#> GSM876874 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876875 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876876 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876879 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876880 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876850 2 0.1211 0.9629 0.000 0.960 0.000 0.040
#> GSM876851 2 0.0336 0.9774 0.000 0.992 0.000 0.008
#> GSM876852 2 0.0592 0.9764 0.000 0.984 0.000 0.016
#> GSM876853 2 0.0188 0.9782 0.000 0.996 0.000 0.004
#> GSM876854 2 0.0469 0.9776 0.000 0.988 0.000 0.012
#> GSM876855 2 0.0592 0.9764 0.000 0.984 0.000 0.016
#> GSM876856 2 0.0592 0.9764 0.000 0.984 0.000 0.016
#> GSM876905 3 0.1118 0.9344 0.000 0.000 0.964 0.036
#> GSM876906 3 0.1867 0.9388 0.000 0.000 0.928 0.072
#> GSM876907 3 0.1557 0.9456 0.000 0.000 0.944 0.056
#> GSM876908 3 0.1716 0.9431 0.000 0.000 0.936 0.064
#> GSM876909 3 0.2053 0.9380 0.000 0.004 0.924 0.072
#> GSM876881 2 0.1637 0.9473 0.000 0.940 0.000 0.060
#> GSM876882 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876883 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876884 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876885 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876857 1 0.0000 1.0000 1.000 0.000 0.000 0.000
#> GSM876858 2 0.0707 0.9745 0.000 0.980 0.000 0.020
#> GSM876859 2 0.0592 0.9758 0.000 0.984 0.000 0.016
#> GSM876860 2 0.0707 0.9745 0.000 0.980 0.000 0.020
#> GSM876861 2 0.0707 0.9745 0.000 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
#> GSM876886 3 0.0955 0.931 0.000 0.000 0.968 0.004 0.028
#> GSM876887 3 0.0703 0.934 0.000 0.000 0.976 0.024 0.000
#> GSM876888 3 0.2450 0.884 0.000 0.000 0.896 0.028 0.076
#> GSM876889 3 0.1341 0.924 0.000 0.000 0.944 0.056 0.000
#> GSM876890 3 0.0290 0.936 0.000 0.000 0.992 0.008 0.000
#> GSM876891 3 0.0880 0.933 0.000 0.000 0.968 0.032 0.000
#> GSM876862 1 0.0579 0.966 0.984 0.000 0.000 0.008 0.008
#> GSM876863 1 0.0000 0.970 1.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0898 0.959 0.972 0.000 0.000 0.008 0.020
#> GSM876865 1 0.0000 0.970 1.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.0324 0.967 0.992 0.000 0.000 0.004 0.004
#> GSM876867 1 0.0162 0.970 0.996 0.000 0.000 0.000 0.004
#> GSM876838 2 0.1197 0.897 0.000 0.952 0.000 0.000 0.048
#> GSM876839 2 0.1671 0.882 0.000 0.924 0.000 0.000 0.076
#> GSM876840 2 0.0451 0.888 0.000 0.988 0.000 0.004 0.008
#> GSM876841 2 0.3395 0.684 0.000 0.764 0.000 0.000 0.236
#> GSM876842 2 0.1043 0.899 0.000 0.960 0.000 0.000 0.040
#> GSM876843 2 0.2249 0.809 0.000 0.896 0.000 0.096 0.008
#> GSM876892 3 0.0865 0.932 0.000 0.000 0.972 0.004 0.024
#> GSM876893 3 0.1251 0.926 0.000 0.000 0.956 0.008 0.036
#> GSM876894 3 0.1043 0.930 0.000 0.000 0.960 0.040 0.000
#> GSM876895 5 0.4139 0.786 0.084 0.132 0.000 0.000 0.784
#> GSM876896 4 0.1638 0.745 0.000 0.000 0.064 0.932 0.004
#> GSM876897 4 0.1772 0.746 0.000 0.020 0.032 0.940 0.008
#> GSM876868 1 0.1267 0.949 0.960 0.000 0.004 0.012 0.024
#> GSM876869 1 0.0771 0.961 0.976 0.000 0.000 0.004 0.020
#> GSM876870 1 0.0000 0.970 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.970 1.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.3010 0.750 0.172 0.000 0.000 0.824 0.004
#> GSM876873 4 0.2930 0.755 0.164 0.000 0.000 0.832 0.004
#> GSM876844 2 0.1043 0.899 0.000 0.960 0.000 0.000 0.040
#> GSM876845 2 0.3684 0.596 0.000 0.720 0.000 0.000 0.280
#> GSM876846 2 0.1043 0.899 0.000 0.960 0.000 0.000 0.040
#> GSM876847 5 0.3932 0.652 0.000 0.328 0.000 0.000 0.672
#> GSM876848 2 0.2462 0.792 0.000 0.880 0.000 0.112 0.008
#> GSM876849 4 0.3768 0.613 0.004 0.228 0.000 0.760 0.008
#> GSM876898 3 0.1082 0.930 0.000 0.000 0.964 0.008 0.028
#> GSM876899 3 0.1410 0.922 0.000 0.000 0.940 0.060 0.000
#> GSM876900 3 0.0000 0.936 0.000 0.000 1.000 0.000 0.000
#> GSM876901 3 0.0162 0.936 0.000 0.000 0.996 0.000 0.004
#> GSM876902 4 0.2674 0.703 0.000 0.000 0.140 0.856 0.004
#> GSM876903 3 0.6006 0.442 0.000 0.000 0.584 0.220 0.196
#> GSM876904 3 0.1740 0.912 0.000 0.000 0.932 0.012 0.056
#> GSM876874 1 0.0451 0.968 0.988 0.000 0.000 0.004 0.008
#> GSM876875 1 0.0324 0.967 0.992 0.000 0.000 0.004 0.004
#> GSM876876 1 0.0324 0.969 0.992 0.000 0.000 0.004 0.004
#> GSM876877 1 0.0324 0.969 0.992 0.000 0.000 0.004 0.004
#> GSM876878 1 0.0324 0.967 0.992 0.000 0.000 0.004 0.004
#> GSM876879 1 0.0693 0.960 0.980 0.000 0.000 0.008 0.012
#> GSM876880 1 0.0162 0.970 0.996 0.000 0.000 0.000 0.004
#> GSM876850 5 0.3913 0.659 0.000 0.324 0.000 0.000 0.676
#> GSM876851 2 0.2773 0.794 0.000 0.836 0.000 0.000 0.164
#> GSM876852 2 0.0290 0.897 0.000 0.992 0.000 0.000 0.008
#> GSM876853 2 0.1851 0.874 0.000 0.912 0.000 0.000 0.088
#> GSM876854 2 0.0404 0.898 0.000 0.988 0.000 0.000 0.012
#> GSM876855 2 0.0510 0.886 0.000 0.984 0.000 0.016 0.000
#> GSM876856 2 0.0324 0.894 0.000 0.992 0.000 0.004 0.004
#> GSM876905 3 0.0566 0.935 0.000 0.000 0.984 0.004 0.012
#> GSM876906 3 0.1831 0.910 0.000 0.000 0.920 0.076 0.004
#> GSM876907 5 0.4726 0.543 0.000 0.004 0.256 0.044 0.696
#> GSM876908 3 0.1831 0.910 0.000 0.000 0.920 0.076 0.004
#> GSM876909 5 0.3795 0.641 0.000 0.004 0.184 0.024 0.788
#> GSM876881 5 0.2732 0.842 0.000 0.160 0.000 0.000 0.840
#> GSM876882 1 0.0693 0.960 0.980 0.000 0.000 0.008 0.012
#> GSM876883 1 0.4193 0.452 0.684 0.000 0.000 0.304 0.012
#> GSM876884 1 0.0000 0.970 1.000 0.000 0.000 0.000 0.000
#> GSM876885 4 0.4489 0.343 0.420 0.000 0.000 0.572 0.008
#> GSM876857 1 0.0898 0.959 0.972 0.000 0.000 0.008 0.020
#> GSM876858 5 0.2605 0.846 0.000 0.148 0.000 0.000 0.852
#> GSM876859 5 0.2648 0.846 0.000 0.152 0.000 0.000 0.848
#> GSM876860 5 0.2605 0.846 0.000 0.148 0.000 0.000 0.852
#> GSM876861 5 0.2605 0.846 0.000 0.148 0.000 0.000 0.852
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM876886 3 0.0146 0.9584 0.000 0.000 0.996 0.000 0.000 NA
#> GSM876887 3 0.0436 0.9571 0.000 0.000 0.988 0.004 0.004 NA
#> GSM876888 3 0.0458 0.9548 0.000 0.000 0.984 0.000 0.000 NA
#> GSM876889 3 0.0922 0.9499 0.000 0.000 0.968 0.024 0.004 NA
#> GSM876890 3 0.0000 0.9588 0.000 0.000 1.000 0.000 0.000 NA
#> GSM876891 3 0.0551 0.9560 0.000 0.000 0.984 0.008 0.004 NA
#> GSM876862 1 0.1267 0.8742 0.940 0.000 0.000 0.000 0.000 NA
#> GSM876863 1 0.0363 0.8889 0.988 0.000 0.000 0.000 0.000 NA
#> GSM876864 1 0.1700 0.8636 0.916 0.000 0.004 0.000 0.000 NA
#> GSM876865 1 0.0146 0.8899 0.996 0.000 0.000 0.000 0.000 NA
#> GSM876866 1 0.0508 0.8888 0.984 0.000 0.000 0.000 0.004 NA
#> GSM876867 1 0.0547 0.8869 0.980 0.000 0.000 0.000 0.000 NA
#> GSM876838 2 0.0508 0.8256 0.000 0.984 0.000 0.000 0.012 NA
#> GSM876839 2 0.1594 0.8113 0.000 0.932 0.000 0.000 0.016 NA
#> GSM876840 2 0.2263 0.7887 0.000 0.884 0.000 0.016 0.000 NA
#> GSM876841 2 0.3078 0.7464 0.000 0.836 0.000 0.000 0.108 NA
#> GSM876842 2 0.0520 0.8255 0.000 0.984 0.000 0.000 0.008 NA
#> GSM876843 2 0.3921 0.6699 0.000 0.768 0.000 0.116 0.000 NA
#> GSM876892 3 0.0000 0.9588 0.000 0.000 1.000 0.000 0.000 NA
#> GSM876893 3 0.0363 0.9568 0.000 0.000 0.988 0.000 0.000 NA
#> GSM876894 3 0.0748 0.9531 0.000 0.000 0.976 0.016 0.004 NA
#> GSM876895 5 0.6027 0.6414 0.064 0.168 0.000 0.020 0.640 NA
#> GSM876896 4 0.1262 0.6198 0.000 0.000 0.016 0.956 0.020 NA
#> GSM876897 4 0.0717 0.6225 0.000 0.000 0.016 0.976 0.000 NA
#> GSM876868 1 0.2948 0.7769 0.804 0.000 0.008 0.000 0.000 NA
#> GSM876869 1 0.2260 0.8251 0.860 0.000 0.000 0.000 0.000 NA
#> GSM876870 1 0.0146 0.8899 0.996 0.000 0.000 0.000 0.000 NA
#> GSM876871 1 0.0000 0.8898 1.000 0.000 0.000 0.000 0.000 NA
#> GSM876872 4 0.5093 0.5119 0.176 0.000 0.000 0.632 0.000 NA
#> GSM876873 4 0.6054 0.1646 0.348 0.000 0.000 0.392 0.000 NA
#> GSM876844 2 0.0291 0.8252 0.000 0.992 0.000 0.004 0.004 NA
#> GSM876845 2 0.3416 0.7115 0.000 0.804 0.000 0.000 0.140 NA
#> GSM876846 2 0.3095 0.7631 0.000 0.840 0.000 0.036 0.008 NA
#> GSM876847 2 0.5211 0.1053 0.000 0.516 0.000 0.000 0.388 NA
#> GSM876848 4 0.5396 0.0801 0.000 0.396 0.000 0.488 0.000 NA
#> GSM876849 4 0.4323 0.5381 0.004 0.120 0.000 0.748 0.004 NA
#> GSM876898 3 0.0363 0.9564 0.000 0.000 0.988 0.000 0.000 NA
#> GSM876899 3 0.1116 0.9457 0.000 0.000 0.960 0.028 0.008 NA
#> GSM876900 3 0.0146 0.9585 0.000 0.000 0.996 0.000 0.000 NA
#> GSM876901 3 0.0000 0.9588 0.000 0.000 1.000 0.000 0.000 NA
#> GSM876902 4 0.3047 0.5792 0.000 0.000 0.084 0.848 0.004 NA
#> GSM876903 3 0.6396 0.4490 0.000 0.012 0.596 0.180 0.108 NA
#> GSM876904 3 0.0363 0.9564 0.000 0.000 0.988 0.000 0.000 NA
#> GSM876874 1 0.1501 0.8675 0.924 0.000 0.000 0.000 0.000 NA
#> GSM876875 1 0.0935 0.8818 0.964 0.000 0.000 0.000 0.004 NA
#> GSM876876 1 0.0146 0.8901 0.996 0.000 0.004 0.000 0.000 NA
#> GSM876877 1 0.0458 0.8877 0.984 0.000 0.000 0.000 0.000 NA
#> GSM876878 1 0.0777 0.8850 0.972 0.000 0.000 0.000 0.004 NA
#> GSM876879 1 0.2664 0.7655 0.816 0.000 0.000 0.000 0.000 NA
#> GSM876880 1 0.0000 0.8898 1.000 0.000 0.000 0.000 0.000 NA
#> GSM876850 2 0.5414 -0.0573 0.000 0.468 0.000 0.000 0.416 NA
#> GSM876851 2 0.2685 0.7748 0.000 0.868 0.000 0.000 0.072 NA
#> GSM876852 2 0.1606 0.8178 0.000 0.932 0.000 0.004 0.008 NA
#> GSM876853 2 0.1633 0.8114 0.000 0.932 0.000 0.000 0.024 NA
#> GSM876854 2 0.1285 0.8167 0.000 0.944 0.000 0.004 0.000 NA
#> GSM876855 2 0.2019 0.7989 0.000 0.900 0.000 0.012 0.000 NA
#> GSM876856 2 0.2070 0.7942 0.000 0.892 0.000 0.008 0.000 NA
#> GSM876905 3 0.0260 0.9576 0.000 0.000 0.992 0.000 0.000 NA
#> GSM876906 3 0.1642 0.9300 0.000 0.000 0.936 0.032 0.004 NA
#> GSM876907 5 0.4672 0.4214 0.000 0.000 0.340 0.048 0.608 NA
#> GSM876908 3 0.1755 0.9286 0.000 0.000 0.932 0.028 0.008 NA
#> GSM876909 5 0.3542 0.6394 0.000 0.004 0.168 0.020 0.796 NA
#> GSM876881 5 0.4503 0.6594 0.000 0.204 0.000 0.000 0.696 NA
#> GSM876882 1 0.3373 0.6838 0.744 0.000 0.000 0.008 0.000 NA
#> GSM876883 1 0.5471 0.3499 0.560 0.000 0.000 0.172 0.000 NA
#> GSM876884 1 0.0632 0.8859 0.976 0.000 0.000 0.000 0.000 NA
#> GSM876885 1 0.5610 0.2894 0.536 0.000 0.000 0.192 0.000 NA
#> GSM876857 1 0.2260 0.8251 0.860 0.000 0.000 0.000 0.000 NA
#> GSM876858 5 0.1327 0.7843 0.000 0.064 0.000 0.000 0.936 NA
#> GSM876859 5 0.1910 0.7763 0.000 0.108 0.000 0.000 0.892 NA
#> GSM876860 5 0.1327 0.7848 0.000 0.064 0.000 0.000 0.936 NA
#> GSM876861 5 0.1141 0.7776 0.000 0.052 0.000 0.000 0.948 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> SD:NMF 72 0.852599 4.67e-11 2
#> SD:NMF 70 0.995235 1.25e-25 3
#> SD:NMF 71 0.144927 2.99e-22 4
#> SD:NMF 69 0.000564 3.70e-19 5
#> SD:NMF 64 0.000379 1.79e-18 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 72 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 0.862 0.925 0.966 0.4885 0.512 0.512
#> 3 3 0.883 0.906 0.955 0.1561 0.934 0.872
#> 4 4 0.823 0.895 0.924 0.2794 0.819 0.595
#> 5 5 0.911 0.901 0.940 0.0409 0.978 0.918
#> 6 6 0.956 0.902 0.943 0.0505 0.958 0.829
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
#> GSM876886 1 0.0000 0.960 1.000 0.000
#> GSM876887 1 0.0000 0.960 1.000 0.000
#> GSM876888 1 0.0000 0.960 1.000 0.000
#> GSM876889 1 0.0376 0.958 0.996 0.004
#> GSM876890 1 0.0000 0.960 1.000 0.000
#> GSM876891 1 0.0672 0.956 0.992 0.008
#> GSM876862 1 0.0000 0.960 1.000 0.000
#> GSM876863 1 0.0000 0.960 1.000 0.000
#> GSM876864 1 0.0000 0.960 1.000 0.000
#> GSM876865 1 0.0000 0.960 1.000 0.000
#> GSM876866 1 0.0000 0.960 1.000 0.000
#> GSM876867 1 0.0000 0.960 1.000 0.000
#> GSM876838 2 0.0376 0.968 0.004 0.996
#> GSM876839 2 0.0376 0.968 0.004 0.996
#> GSM876840 2 0.0000 0.966 0.000 1.000
#> GSM876841 2 0.0376 0.968 0.004 0.996
#> GSM876842 2 0.0376 0.968 0.004 0.996
#> GSM876843 2 0.0000 0.966 0.000 1.000
#> GSM876892 1 0.0000 0.960 1.000 0.000
#> GSM876893 1 0.0000 0.960 1.000 0.000
#> GSM876894 1 0.0672 0.956 0.992 0.008
#> GSM876895 1 0.6887 0.781 0.816 0.184
#> GSM876896 2 0.3431 0.917 0.064 0.936
#> GSM876897 2 0.3431 0.917 0.064 0.936
#> GSM876868 1 0.0000 0.960 1.000 0.000
#> GSM876869 1 0.0000 0.960 1.000 0.000
#> GSM876870 1 0.0000 0.960 1.000 0.000
#> GSM876871 1 0.0000 0.960 1.000 0.000
#> GSM876872 2 0.8909 0.546 0.308 0.692
#> GSM876873 2 0.8909 0.546 0.308 0.692
#> GSM876844 2 0.0376 0.968 0.004 0.996
#> GSM876845 2 0.0376 0.968 0.004 0.996
#> GSM876846 2 0.0000 0.966 0.000 1.000
#> GSM876847 2 0.0376 0.968 0.004 0.996
#> GSM876848 2 0.0000 0.966 0.000 1.000
#> GSM876849 2 0.0000 0.966 0.000 1.000
#> GSM876898 1 0.0000 0.960 1.000 0.000
#> GSM876899 1 0.5408 0.850 0.876 0.124
#> GSM876900 1 0.0000 0.960 1.000 0.000
#> GSM876901 1 0.0000 0.960 1.000 0.000
#> GSM876902 2 0.3431 0.917 0.064 0.936
#> GSM876903 1 0.6887 0.781 0.816 0.184
#> GSM876904 1 0.0000 0.960 1.000 0.000
#> GSM876874 1 0.0000 0.960 1.000 0.000
#> GSM876875 1 0.0000 0.960 1.000 0.000
#> GSM876876 1 0.0000 0.960 1.000 0.000
#> GSM876877 1 0.0000 0.960 1.000 0.000
#> GSM876878 1 0.0000 0.960 1.000 0.000
#> GSM876879 1 0.0000 0.960 1.000 0.000
#> GSM876880 1 0.0000 0.960 1.000 0.000
#> GSM876850 2 0.0376 0.968 0.004 0.996
#> GSM876851 2 0.0376 0.968 0.004 0.996
#> GSM876852 2 0.0376 0.968 0.004 0.996
#> GSM876853 2 0.0376 0.968 0.004 0.996
#> GSM876854 2 0.0000 0.966 0.000 1.000
#> GSM876855 2 0.0000 0.966 0.000 1.000
#> GSM876856 2 0.0000 0.966 0.000 1.000
#> GSM876905 1 0.0000 0.960 1.000 0.000
#> GSM876906 1 0.0672 0.956 0.992 0.008
#> GSM876907 1 0.6887 0.781 0.816 0.184
#> GSM876908 1 0.0672 0.956 0.992 0.008
#> GSM876909 1 0.6887 0.781 0.816 0.184
#> GSM876881 2 0.0376 0.968 0.004 0.996
#> GSM876882 1 0.0000 0.960 1.000 0.000
#> GSM876883 1 0.9087 0.507 0.676 0.324
#> GSM876884 1 0.0000 0.960 1.000 0.000
#> GSM876885 1 0.9087 0.507 0.676 0.324
#> GSM876857 1 0.0000 0.960 1.000 0.000
#> GSM876858 2 0.0376 0.968 0.004 0.996
#> GSM876859 2 0.0376 0.968 0.004 0.996
#> GSM876860 2 0.0376 0.968 0.004 0.996
#> GSM876861 2 0.0376 0.968 0.004 0.996
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876887 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876888 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876889 1 0.0424 0.951 0.992 0.000 0.008
#> GSM876890 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876891 1 0.0661 0.949 0.988 0.004 0.008
#> GSM876862 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876863 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876864 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876865 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876866 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876867 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876838 2 0.0000 0.992 0.000 1.000 0.000
#> GSM876839 2 0.0000 0.992 0.000 1.000 0.000
#> GSM876840 2 0.0747 0.981 0.000 0.984 0.016
#> GSM876841 2 0.0000 0.992 0.000 1.000 0.000
#> GSM876842 2 0.0000 0.992 0.000 1.000 0.000
#> GSM876843 3 0.5254 0.656 0.000 0.264 0.736
#> GSM876892 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876893 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876894 1 0.0661 0.949 0.988 0.004 0.008
#> GSM876895 1 0.4575 0.777 0.812 0.004 0.184
#> GSM876896 3 0.0237 0.777 0.000 0.004 0.996
#> GSM876897 3 0.0237 0.777 0.000 0.004 0.996
#> GSM876868 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876869 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876870 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876871 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876872 3 0.5058 0.623 0.244 0.000 0.756
#> GSM876873 3 0.5058 0.623 0.244 0.000 0.756
#> GSM876844 2 0.0000 0.992 0.000 1.000 0.000
#> GSM876845 2 0.0000 0.992 0.000 1.000 0.000
#> GSM876846 2 0.2448 0.911 0.000 0.924 0.076
#> GSM876847 2 0.0000 0.992 0.000 1.000 0.000
#> GSM876848 3 0.5254 0.656 0.000 0.264 0.736
#> GSM876849 3 0.5254 0.656 0.000 0.264 0.736
#> GSM876898 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876899 1 0.3644 0.845 0.872 0.004 0.124
#> GSM876900 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876901 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876902 3 0.0237 0.777 0.000 0.004 0.996
#> GSM876903 1 0.4575 0.777 0.812 0.004 0.184
#> GSM876904 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876874 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876875 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876876 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876877 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876878 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876879 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876880 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876850 2 0.0000 0.992 0.000 1.000 0.000
#> GSM876851 2 0.0000 0.992 0.000 1.000 0.000
#> GSM876852 2 0.0000 0.992 0.000 1.000 0.000
#> GSM876853 2 0.0000 0.992 0.000 1.000 0.000
#> GSM876854 2 0.0747 0.981 0.000 0.984 0.016
#> GSM876855 2 0.0747 0.981 0.000 0.984 0.016
#> GSM876856 2 0.0747 0.981 0.000 0.984 0.016
#> GSM876905 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876906 1 0.0661 0.949 0.988 0.004 0.008
#> GSM876907 1 0.4575 0.777 0.812 0.004 0.184
#> GSM876908 1 0.0661 0.949 0.988 0.004 0.008
#> GSM876909 1 0.4575 0.777 0.812 0.004 0.184
#> GSM876881 2 0.0000 0.992 0.000 1.000 0.000
#> GSM876882 1 0.0747 0.943 0.984 0.000 0.016
#> GSM876883 1 0.5988 0.358 0.632 0.000 0.368
#> GSM876884 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876885 1 0.5988 0.358 0.632 0.000 0.368
#> GSM876857 1 0.0237 0.953 0.996 0.000 0.004
#> GSM876858 2 0.0000 0.992 0.000 1.000 0.000
#> GSM876859 2 0.0000 0.992 0.000 1.000 0.000
#> GSM876860 2 0.0000 0.992 0.000 1.000 0.000
#> GSM876861 2 0.0000 0.992 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.234 0.9495 0.100 0.000 0.900 0.000
#> GSM876887 3 0.234 0.9495 0.100 0.000 0.900 0.000
#> GSM876888 3 0.234 0.9495 0.100 0.000 0.900 0.000
#> GSM876889 3 0.228 0.9484 0.096 0.000 0.904 0.000
#> GSM876890 3 0.234 0.9495 0.100 0.000 0.900 0.000
#> GSM876891 3 0.208 0.9434 0.084 0.000 0.916 0.000
#> GSM876862 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876863 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876864 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876865 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876866 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876867 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876838 2 0.000 0.9801 0.000 1.000 0.000 0.000
#> GSM876839 2 0.000 0.9801 0.000 1.000 0.000 0.000
#> GSM876840 2 0.172 0.9404 0.000 0.936 0.064 0.000
#> GSM876841 2 0.000 0.9801 0.000 1.000 0.000 0.000
#> GSM876842 2 0.000 0.9801 0.000 1.000 0.000 0.000
#> GSM876843 4 0.539 0.7209 0.000 0.204 0.072 0.724
#> GSM876892 3 0.234 0.9495 0.100 0.000 0.900 0.000
#> GSM876893 3 0.234 0.9495 0.100 0.000 0.900 0.000
#> GSM876894 3 0.208 0.9434 0.084 0.000 0.916 0.000
#> GSM876895 3 0.531 0.8213 0.084 0.000 0.740 0.176
#> GSM876896 4 0.000 0.8120 0.000 0.000 0.000 1.000
#> GSM876897 4 0.000 0.8120 0.000 0.000 0.000 1.000
#> GSM876868 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876869 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876870 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876871 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876872 4 0.512 0.6768 0.080 0.000 0.164 0.756
#> GSM876873 4 0.512 0.6768 0.080 0.000 0.164 0.756
#> GSM876844 2 0.000 0.9801 0.000 1.000 0.000 0.000
#> GSM876845 2 0.000 0.9801 0.000 1.000 0.000 0.000
#> GSM876846 2 0.347 0.8657 0.000 0.868 0.072 0.060
#> GSM876847 2 0.000 0.9801 0.000 1.000 0.000 0.000
#> GSM876848 4 0.539 0.7209 0.000 0.204 0.072 0.724
#> GSM876849 4 0.539 0.7209 0.000 0.204 0.072 0.724
#> GSM876898 3 0.234 0.9495 0.100 0.000 0.900 0.000
#> GSM876899 3 0.459 0.8713 0.084 0.000 0.800 0.116
#> GSM876900 3 0.234 0.9495 0.100 0.000 0.900 0.000
#> GSM876901 3 0.234 0.9495 0.100 0.000 0.900 0.000
#> GSM876902 4 0.000 0.8120 0.000 0.000 0.000 1.000
#> GSM876903 3 0.531 0.8213 0.084 0.000 0.740 0.176
#> GSM876904 3 0.234 0.9495 0.100 0.000 0.900 0.000
#> GSM876874 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876875 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876876 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876877 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876878 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876879 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876880 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876850 2 0.000 0.9801 0.000 1.000 0.000 0.000
#> GSM876851 2 0.000 0.9801 0.000 1.000 0.000 0.000
#> GSM876852 2 0.000 0.9801 0.000 1.000 0.000 0.000
#> GSM876853 2 0.000 0.9801 0.000 1.000 0.000 0.000
#> GSM876854 2 0.172 0.9404 0.000 0.936 0.064 0.000
#> GSM876855 2 0.172 0.9404 0.000 0.936 0.064 0.000
#> GSM876856 2 0.172 0.9404 0.000 0.936 0.064 0.000
#> GSM876905 3 0.234 0.9495 0.100 0.000 0.900 0.000
#> GSM876906 3 0.208 0.9434 0.084 0.000 0.916 0.000
#> GSM876907 3 0.531 0.8213 0.084 0.000 0.740 0.176
#> GSM876908 3 0.208 0.9434 0.084 0.000 0.916 0.000
#> GSM876909 3 0.531 0.8213 0.084 0.000 0.740 0.176
#> GSM876881 2 0.000 0.9801 0.000 1.000 0.000 0.000
#> GSM876882 1 0.198 0.8892 0.936 0.000 0.048 0.016
#> GSM876883 1 0.736 0.0226 0.468 0.000 0.164 0.368
#> GSM876884 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876885 1 0.736 0.0226 0.468 0.000 0.164 0.368
#> GSM876857 1 0.000 0.9440 1.000 0.000 0.000 0.000
#> GSM876858 2 0.000 0.9801 0.000 1.000 0.000 0.000
#> GSM876859 2 0.000 0.9801 0.000 1.000 0.000 0.000
#> GSM876860 2 0.000 0.9801 0.000 1.000 0.000 0.000
#> GSM876861 2 0.000 0.9801 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
#> GSM876886 3 0.0451 0.949 0.004 0.000 0.988 0.000 0.008
#> GSM876887 3 0.0451 0.949 0.004 0.000 0.988 0.000 0.008
#> GSM876888 3 0.0404 0.950 0.012 0.000 0.988 0.000 0.000
#> GSM876889 3 0.0290 0.949 0.000 0.000 0.992 0.000 0.008
#> GSM876890 3 0.0451 0.949 0.004 0.000 0.988 0.000 0.008
#> GSM876891 3 0.0404 0.947 0.000 0.000 0.988 0.000 0.012
#> GSM876862 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.0451 0.982 0.988 0.000 0.004 0.000 0.008
#> GSM876867 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM876840 2 0.1478 0.937 0.000 0.936 0.000 0.000 0.064
#> GSM876841 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM876843 4 0.6298 0.651 0.000 0.188 0.000 0.520 0.292
#> GSM876892 3 0.0451 0.949 0.004 0.000 0.988 0.000 0.008
#> GSM876893 3 0.0404 0.950 0.012 0.000 0.988 0.000 0.000
#> GSM876894 3 0.0404 0.947 0.000 0.000 0.988 0.000 0.012
#> GSM876895 3 0.3196 0.839 0.000 0.000 0.804 0.004 0.192
#> GSM876896 4 0.0000 0.544 0.000 0.000 0.000 1.000 0.000
#> GSM876897 4 0.0000 0.544 0.000 0.000 0.000 1.000 0.000
#> GSM876868 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876872 5 0.4306 0.367 0.000 0.000 0.000 0.492 0.508
#> GSM876873 5 0.4306 0.367 0.000 0.000 0.000 0.492 0.508
#> GSM876844 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM876846 2 0.2516 0.854 0.000 0.860 0.000 0.000 0.140
#> GSM876847 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM876848 4 0.6298 0.651 0.000 0.188 0.000 0.520 0.292
#> GSM876849 4 0.6298 0.651 0.000 0.188 0.000 0.520 0.292
#> GSM876898 3 0.0404 0.950 0.012 0.000 0.988 0.000 0.000
#> GSM876899 3 0.2536 0.883 0.000 0.000 0.868 0.004 0.128
#> GSM876900 3 0.0404 0.950 0.012 0.000 0.988 0.000 0.000
#> GSM876901 3 0.0404 0.950 0.012 0.000 0.988 0.000 0.000
#> GSM876902 4 0.0000 0.544 0.000 0.000 0.000 1.000 0.000
#> GSM876903 3 0.3196 0.839 0.000 0.000 0.804 0.004 0.192
#> GSM876904 3 0.0404 0.950 0.012 0.000 0.988 0.000 0.000
#> GSM876874 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.0451 0.982 0.988 0.000 0.004 0.000 0.008
#> GSM876876 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876879 1 0.0451 0.982 0.988 0.000 0.004 0.000 0.008
#> GSM876880 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM876852 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM876853 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM876854 2 0.1478 0.937 0.000 0.936 0.000 0.000 0.064
#> GSM876855 2 0.1478 0.937 0.000 0.936 0.000 0.000 0.064
#> GSM876856 2 0.1478 0.937 0.000 0.936 0.000 0.000 0.064
#> GSM876905 3 0.0404 0.950 0.012 0.000 0.988 0.000 0.000
#> GSM876906 3 0.0404 0.947 0.000 0.000 0.988 0.000 0.012
#> GSM876907 3 0.3196 0.839 0.000 0.000 0.804 0.004 0.192
#> GSM876908 3 0.0404 0.947 0.000 0.000 0.988 0.000 0.012
#> GSM876909 3 0.3196 0.839 0.000 0.000 0.804 0.004 0.192
#> GSM876881 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM876882 1 0.2005 0.902 0.924 0.000 0.004 0.016 0.056
#> GSM876883 5 0.6006 0.557 0.376 0.000 0.004 0.104 0.516
#> GSM876884 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876885 5 0.6006 0.557 0.376 0.000 0.004 0.104 0.516
#> GSM876857 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM876859 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM876860 2 0.0000 0.979 0.000 1.000 0.000 0.000 0.000
#> GSM876861 2 0.0000 0.979 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
#> GSM876886 3 0.0000 0.992 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876887 3 0.0000 0.992 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876888 3 0.0260 0.994 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM876889 3 0.0146 0.989 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM876890 3 0.0000 0.992 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876891 5 0.3151 0.819 0.000 0.000 0.252 0.000 0.748 0.000
#> GSM876862 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.0363 0.982 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876840 2 0.1444 0.935 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM876841 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876842 2 0.0260 0.972 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM876843 4 0.0000 0.691 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876892 3 0.0000 0.992 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876893 3 0.0260 0.994 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM876894 5 0.3151 0.819 0.000 0.000 0.252 0.000 0.748 0.000
#> GSM876895 5 0.0547 0.834 0.000 0.000 0.020 0.000 0.980 0.000
#> GSM876896 4 0.4335 0.622 0.000 0.000 0.000 0.508 0.020 0.472
#> GSM876897 4 0.4335 0.622 0.000 0.000 0.000 0.508 0.020 0.472
#> GSM876868 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876872 6 0.0000 0.351 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM876873 6 0.0000 0.351 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM876844 2 0.0260 0.972 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM876845 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876846 2 0.2854 0.787 0.000 0.792 0.000 0.208 0.000 0.000
#> GSM876847 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876848 4 0.0000 0.691 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876849 4 0.0000 0.691 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876898 3 0.0260 0.994 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM876899 5 0.1610 0.843 0.000 0.000 0.084 0.000 0.916 0.000
#> GSM876900 3 0.0260 0.994 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM876901 3 0.0260 0.994 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM876902 4 0.4335 0.622 0.000 0.000 0.000 0.508 0.020 0.472
#> GSM876903 5 0.0547 0.834 0.000 0.000 0.020 0.000 0.980 0.000
#> GSM876904 3 0.0260 0.994 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM876874 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.0363 0.982 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM876876 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876879 1 0.0363 0.982 0.988 0.000 0.012 0.000 0.000 0.000
#> GSM876880 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876852 2 0.0260 0.972 0.000 0.992 0.000 0.008 0.000 0.000
#> GSM876853 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876854 2 0.1444 0.935 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM876855 2 0.1444 0.935 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM876856 2 0.1444 0.935 0.000 0.928 0.000 0.072 0.000 0.000
#> GSM876905 3 0.0260 0.994 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM876906 5 0.3151 0.819 0.000 0.000 0.252 0.000 0.748 0.000
#> GSM876907 5 0.0547 0.834 0.000 0.000 0.020 0.000 0.980 0.000
#> GSM876908 5 0.3151 0.819 0.000 0.000 0.252 0.000 0.748 0.000
#> GSM876909 5 0.0547 0.834 0.000 0.000 0.020 0.000 0.980 0.000
#> GSM876881 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876882 1 0.1686 0.902 0.924 0.000 0.012 0.000 0.000 0.064
#> GSM876883 6 0.4026 0.550 0.376 0.000 0.012 0.000 0.000 0.612
#> GSM876884 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876885 6 0.4026 0.550 0.376 0.000 0.012 0.000 0.000 0.612
#> GSM876857 1 0.0000 0.993 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876859 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876860 2 0.0000 0.975 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876861 2 0.0000 0.975 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 disease.state(p) tissue(p) k
#> CV:hclust 72 0.4844 9.33e-11 2
#> CV:hclust 70 0.0607 7.31e-11 3
#> CV:hclust 70 0.1797 5.57e-22 4
#> CV:hclust 70 0.2134 3.92e-22 5
#> CV:hclust 70 0.1429 5.96e-21 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 72 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 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 0.942 0.946 0.978 0.4830 0.518 0.518
#> 3 3 0.699 0.840 0.876 0.3434 0.737 0.527
#> 4 4 0.926 0.933 0.948 0.1292 0.924 0.775
#> 5 5 0.840 0.800 0.858 0.0597 1.000 1.000
#> 6 6 0.831 0.795 0.813 0.0392 0.917 0.694
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
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
#> GSM876886 1 0.0000 0.9756 1.000 0.000
#> GSM876887 1 0.0000 0.9756 1.000 0.000
#> GSM876888 1 0.0376 0.9767 0.996 0.004
#> GSM876889 1 0.0000 0.9756 1.000 0.000
#> GSM876890 1 0.0000 0.9756 1.000 0.000
#> GSM876891 1 0.0000 0.9756 1.000 0.000
#> GSM876862 1 0.0376 0.9767 0.996 0.004
#> GSM876863 1 0.0000 0.9756 1.000 0.000
#> GSM876864 1 0.0376 0.9767 0.996 0.004
#> GSM876865 1 0.0376 0.9767 0.996 0.004
#> GSM876866 1 0.0000 0.9756 1.000 0.000
#> GSM876867 1 0.0376 0.9767 0.996 0.004
#> GSM876838 2 0.0000 0.9766 0.000 1.000
#> GSM876839 2 0.0000 0.9766 0.000 1.000
#> GSM876840 2 0.0000 0.9766 0.000 1.000
#> GSM876841 2 0.0000 0.9766 0.000 1.000
#> GSM876842 2 0.0000 0.9766 0.000 1.000
#> GSM876843 2 0.0376 0.9739 0.004 0.996
#> GSM876892 1 0.0000 0.9756 1.000 0.000
#> GSM876893 1 0.0376 0.9767 0.996 0.004
#> GSM876894 1 0.0376 0.9767 0.996 0.004
#> GSM876895 1 0.8207 0.6463 0.744 0.256
#> GSM876896 2 0.7745 0.7165 0.228 0.772
#> GSM876897 2 0.0376 0.9739 0.004 0.996
#> GSM876868 1 0.0376 0.9767 0.996 0.004
#> GSM876869 1 0.0376 0.9767 0.996 0.004
#> GSM876870 1 0.0376 0.9767 0.996 0.004
#> GSM876871 1 0.0376 0.9767 0.996 0.004
#> GSM876872 1 0.0000 0.9756 1.000 0.000
#> GSM876873 1 0.0000 0.9756 1.000 0.000
#> GSM876844 2 0.0000 0.9766 0.000 1.000
#> GSM876845 2 0.0000 0.9766 0.000 1.000
#> GSM876846 2 0.0000 0.9766 0.000 1.000
#> GSM876847 2 0.0000 0.9766 0.000 1.000
#> GSM876848 2 0.0376 0.9739 0.004 0.996
#> GSM876849 2 0.0376 0.9739 0.004 0.996
#> GSM876898 1 0.0376 0.9767 0.996 0.004
#> GSM876899 1 0.0376 0.9767 0.996 0.004
#> GSM876900 1 0.0376 0.9767 0.996 0.004
#> GSM876901 1 0.0376 0.9767 0.996 0.004
#> GSM876902 1 0.6048 0.8114 0.852 0.148
#> GSM876903 2 0.6887 0.7794 0.184 0.816
#> GSM876904 1 0.0376 0.9767 0.996 0.004
#> GSM876874 1 0.0376 0.9767 0.996 0.004
#> GSM876875 1 0.0000 0.9756 1.000 0.000
#> GSM876876 1 0.0376 0.9767 0.996 0.004
#> GSM876877 1 0.0376 0.9767 0.996 0.004
#> GSM876878 1 0.0376 0.9767 0.996 0.004
#> GSM876879 1 0.0000 0.9756 1.000 0.000
#> GSM876880 1 0.0376 0.9767 0.996 0.004
#> GSM876850 2 0.0000 0.9766 0.000 1.000
#> GSM876851 2 0.0000 0.9766 0.000 1.000
#> GSM876852 2 0.0000 0.9766 0.000 1.000
#> GSM876853 2 0.0000 0.9766 0.000 1.000
#> GSM876854 2 0.0000 0.9766 0.000 1.000
#> GSM876855 2 0.0000 0.9766 0.000 1.000
#> GSM876856 2 0.0000 0.9766 0.000 1.000
#> GSM876905 1 0.0376 0.9767 0.996 0.004
#> GSM876906 1 0.0376 0.9767 0.996 0.004
#> GSM876907 1 1.0000 -0.0227 0.500 0.500
#> GSM876908 1 0.0376 0.9767 0.996 0.004
#> GSM876909 2 0.6801 0.7849 0.180 0.820
#> GSM876881 2 0.0000 0.9766 0.000 1.000
#> GSM876882 1 0.0000 0.9756 1.000 0.000
#> GSM876883 1 0.0000 0.9756 1.000 0.000
#> GSM876884 1 0.0376 0.9767 0.996 0.004
#> GSM876885 1 0.0000 0.9756 1.000 0.000
#> GSM876857 1 0.0376 0.9767 0.996 0.004
#> GSM876858 2 0.0000 0.9766 0.000 1.000
#> GSM876859 2 0.0000 0.9766 0.000 1.000
#> GSM876860 2 0.0000 0.9766 0.000 1.000
#> GSM876861 2 0.0000 0.9766 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 3 0.630 0.536 0.480 0.000 0.520
#> GSM876887 3 0.497 0.767 0.236 0.000 0.764
#> GSM876888 3 0.631 0.519 0.488 0.000 0.512
#> GSM876889 3 0.440 0.787 0.188 0.000 0.812
#> GSM876890 3 0.497 0.767 0.236 0.000 0.764
#> GSM876891 3 0.440 0.787 0.188 0.000 0.812
#> GSM876862 1 0.000 0.994 1.000 0.000 0.000
#> GSM876863 1 0.000 0.994 1.000 0.000 0.000
#> GSM876864 1 0.000 0.994 1.000 0.000 0.000
#> GSM876865 1 0.000 0.994 1.000 0.000 0.000
#> GSM876866 1 0.000 0.994 1.000 0.000 0.000
#> GSM876867 1 0.000 0.994 1.000 0.000 0.000
#> GSM876838 2 0.000 0.961 0.000 1.000 0.000
#> GSM876839 2 0.000 0.961 0.000 1.000 0.000
#> GSM876840 2 0.000 0.961 0.000 1.000 0.000
#> GSM876841 2 0.000 0.961 0.000 1.000 0.000
#> GSM876842 2 0.000 0.961 0.000 1.000 0.000
#> GSM876843 2 0.440 0.816 0.000 0.812 0.188
#> GSM876892 3 0.630 0.543 0.476 0.000 0.524
#> GSM876893 3 0.630 0.536 0.480 0.000 0.520
#> GSM876894 3 0.440 0.787 0.188 0.000 0.812
#> GSM876895 3 0.458 0.786 0.184 0.004 0.812
#> GSM876896 3 0.445 0.466 0.000 0.192 0.808
#> GSM876897 3 0.445 0.466 0.000 0.192 0.808
#> GSM876868 1 0.000 0.994 1.000 0.000 0.000
#> GSM876869 1 0.000 0.994 1.000 0.000 0.000
#> GSM876870 1 0.000 0.994 1.000 0.000 0.000
#> GSM876871 1 0.000 0.994 1.000 0.000 0.000
#> GSM876872 3 0.000 0.680 0.000 0.000 1.000
#> GSM876873 3 0.000 0.680 0.000 0.000 1.000
#> GSM876844 2 0.000 0.961 0.000 1.000 0.000
#> GSM876845 2 0.000 0.961 0.000 1.000 0.000
#> GSM876846 2 0.000 0.961 0.000 1.000 0.000
#> GSM876847 2 0.000 0.961 0.000 1.000 0.000
#> GSM876848 2 0.590 0.623 0.000 0.648 0.352
#> GSM876849 2 0.630 0.389 0.000 0.516 0.484
#> GSM876898 3 0.630 0.536 0.480 0.000 0.520
#> GSM876899 3 0.440 0.787 0.188 0.000 0.812
#> GSM876900 3 0.630 0.543 0.476 0.000 0.524
#> GSM876901 3 0.630 0.543 0.476 0.000 0.524
#> GSM876902 3 0.000 0.680 0.000 0.000 1.000
#> GSM876903 3 0.557 0.744 0.108 0.080 0.812
#> GSM876904 3 0.630 0.536 0.480 0.000 0.520
#> GSM876874 1 0.000 0.994 1.000 0.000 0.000
#> GSM876875 1 0.000 0.994 1.000 0.000 0.000
#> GSM876876 1 0.000 0.994 1.000 0.000 0.000
#> GSM876877 1 0.000 0.994 1.000 0.000 0.000
#> GSM876878 1 0.000 0.994 1.000 0.000 0.000
#> GSM876879 1 0.000 0.994 1.000 0.000 0.000
#> GSM876880 1 0.000 0.994 1.000 0.000 0.000
#> GSM876850 2 0.000 0.961 0.000 1.000 0.000
#> GSM876851 2 0.000 0.961 0.000 1.000 0.000
#> GSM876852 2 0.000 0.961 0.000 1.000 0.000
#> GSM876853 2 0.000 0.961 0.000 1.000 0.000
#> GSM876854 2 0.000 0.961 0.000 1.000 0.000
#> GSM876855 2 0.000 0.961 0.000 1.000 0.000
#> GSM876856 2 0.000 0.961 0.000 1.000 0.000
#> GSM876905 3 0.630 0.536 0.480 0.000 0.520
#> GSM876906 3 0.440 0.787 0.188 0.000 0.812
#> GSM876907 3 0.458 0.786 0.184 0.004 0.812
#> GSM876908 3 0.440 0.787 0.188 0.000 0.812
#> GSM876909 3 0.557 0.744 0.108 0.080 0.812
#> GSM876881 2 0.000 0.961 0.000 1.000 0.000
#> GSM876882 1 0.236 0.881 0.928 0.000 0.072
#> GSM876883 3 0.440 0.787 0.188 0.000 0.812
#> GSM876884 1 0.000 0.994 1.000 0.000 0.000
#> GSM876885 3 0.440 0.787 0.188 0.000 0.812
#> GSM876857 1 0.000 0.994 1.000 0.000 0.000
#> GSM876858 2 0.000 0.961 0.000 1.000 0.000
#> GSM876859 2 0.000 0.961 0.000 1.000 0.000
#> GSM876860 2 0.000 0.961 0.000 1.000 0.000
#> GSM876861 2 0.000 0.961 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.2081 0.890 0.084 0.000 0.916 0.000
#> GSM876887 3 0.0707 0.896 0.020 0.000 0.980 0.000
#> GSM876888 3 0.2149 0.889 0.088 0.000 0.912 0.000
#> GSM876889 3 0.2198 0.887 0.008 0.000 0.920 0.072
#> GSM876890 3 0.0707 0.896 0.020 0.000 0.980 0.000
#> GSM876891 3 0.2256 0.893 0.020 0.000 0.924 0.056
#> GSM876862 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM876839 2 0.0469 0.978 0.000 0.988 0.012 0.000
#> GSM876840 2 0.1824 0.943 0.000 0.936 0.004 0.060
#> GSM876841 2 0.0469 0.978 0.000 0.988 0.012 0.000
#> GSM876842 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM876843 4 0.4360 0.649 0.000 0.248 0.008 0.744
#> GSM876892 3 0.2081 0.890 0.084 0.000 0.916 0.000
#> GSM876893 3 0.2149 0.889 0.088 0.000 0.912 0.000
#> GSM876894 3 0.0895 0.896 0.020 0.000 0.976 0.004
#> GSM876895 3 0.3585 0.835 0.004 0.004 0.828 0.164
#> GSM876896 4 0.1716 0.896 0.000 0.000 0.064 0.936
#> GSM876897 4 0.1716 0.896 0.000 0.000 0.064 0.936
#> GSM876868 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876872 4 0.1792 0.896 0.000 0.000 0.068 0.932
#> GSM876873 4 0.1792 0.896 0.000 0.000 0.068 0.932
#> GSM876844 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM876845 2 0.0469 0.978 0.000 0.988 0.012 0.000
#> GSM876846 2 0.1970 0.940 0.000 0.932 0.008 0.060
#> GSM876847 2 0.0469 0.978 0.000 0.988 0.012 0.000
#> GSM876848 4 0.3351 0.778 0.000 0.148 0.008 0.844
#> GSM876849 4 0.1722 0.862 0.000 0.048 0.008 0.944
#> GSM876898 3 0.2149 0.889 0.088 0.000 0.912 0.000
#> GSM876899 3 0.3606 0.858 0.020 0.000 0.840 0.140
#> GSM876900 3 0.2081 0.890 0.084 0.000 0.916 0.000
#> GSM876901 3 0.2149 0.889 0.088 0.000 0.912 0.000
#> GSM876902 4 0.1716 0.896 0.000 0.000 0.064 0.936
#> GSM876903 3 0.3300 0.844 0.000 0.008 0.848 0.144
#> GSM876904 3 0.2149 0.889 0.088 0.000 0.912 0.000
#> GSM876874 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876875 1 0.0188 0.994 0.996 0.000 0.004 0.000
#> GSM876876 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876879 1 0.0188 0.994 0.996 0.000 0.004 0.000
#> GSM876880 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876850 2 0.0469 0.978 0.000 0.988 0.012 0.000
#> GSM876851 2 0.0469 0.978 0.000 0.988 0.012 0.000
#> GSM876852 2 0.0188 0.975 0.000 0.996 0.004 0.000
#> GSM876853 2 0.0000 0.976 0.000 1.000 0.000 0.000
#> GSM876854 2 0.1824 0.943 0.000 0.936 0.004 0.060
#> GSM876855 2 0.1824 0.943 0.000 0.936 0.004 0.060
#> GSM876856 2 0.1824 0.943 0.000 0.936 0.004 0.060
#> GSM876905 3 0.2149 0.889 0.088 0.000 0.912 0.000
#> GSM876906 3 0.2413 0.892 0.020 0.000 0.916 0.064
#> GSM876907 3 0.3391 0.847 0.004 0.004 0.844 0.148
#> GSM876908 3 0.2413 0.892 0.020 0.000 0.916 0.064
#> GSM876909 3 0.3351 0.844 0.000 0.008 0.844 0.148
#> GSM876881 2 0.0657 0.977 0.000 0.984 0.012 0.004
#> GSM876882 1 0.0817 0.970 0.976 0.000 0.024 0.000
#> GSM876883 3 0.5077 0.793 0.080 0.000 0.760 0.160
#> GSM876884 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876885 3 0.4417 0.827 0.044 0.000 0.796 0.160
#> GSM876857 1 0.0000 0.998 1.000 0.000 0.000 0.000
#> GSM876858 2 0.0657 0.977 0.000 0.984 0.012 0.004
#> GSM876859 2 0.0657 0.977 0.000 0.984 0.012 0.004
#> GSM876860 2 0.0657 0.977 0.000 0.984 0.012 0.004
#> GSM876861 2 0.0657 0.977 0.000 0.984 0.012 0.004
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM876886 3 0.4482 0.7376 0.012 0.000 0.612 0.000 0.376
#> GSM876887 3 0.4114 0.7397 0.000 0.000 0.624 0.000 0.376
#> GSM876888 3 0.4444 0.7427 0.012 0.000 0.624 0.000 0.364
#> GSM876889 3 0.0609 0.7037 0.000 0.000 0.980 0.000 0.020
#> GSM876890 3 0.4088 0.7414 0.000 0.000 0.632 0.000 0.368
#> GSM876891 3 0.0000 0.7093 0.000 0.000 1.000 0.000 0.000
#> GSM876862 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.1410 0.9130 0.940 0.000 0.000 0.000 0.060
#> GSM876867 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.1478 0.8857 0.000 0.936 0.000 0.000 0.064
#> GSM876839 2 0.0404 0.8895 0.000 0.988 0.000 0.000 0.012
#> GSM876840 2 0.4761 0.7823 0.000 0.732 0.000 0.124 0.144
#> GSM876841 2 0.0404 0.8895 0.000 0.988 0.000 0.000 0.012
#> GSM876842 2 0.1544 0.8850 0.000 0.932 0.000 0.000 0.068
#> GSM876843 4 0.4317 0.6496 0.000 0.116 0.000 0.772 0.112
#> GSM876892 3 0.4444 0.7427 0.012 0.000 0.624 0.000 0.364
#> GSM876893 3 0.4444 0.7427 0.012 0.000 0.624 0.000 0.364
#> GSM876894 3 0.2179 0.7278 0.000 0.000 0.888 0.000 0.112
#> GSM876895 3 0.2653 0.6339 0.000 0.000 0.880 0.024 0.096
#> GSM876896 4 0.3416 0.8245 0.000 0.000 0.088 0.840 0.072
#> GSM876897 4 0.3416 0.8245 0.000 0.000 0.088 0.840 0.072
#> GSM876868 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.5672 0.7284 0.000 0.000 0.104 0.584 0.312
#> GSM876873 4 0.5672 0.7284 0.000 0.000 0.104 0.584 0.312
#> GSM876844 2 0.1544 0.8850 0.000 0.932 0.000 0.000 0.068
#> GSM876845 2 0.0609 0.8885 0.000 0.980 0.000 0.000 0.020
#> GSM876846 2 0.4889 0.7713 0.000 0.720 0.000 0.136 0.144
#> GSM876847 2 0.0609 0.8885 0.000 0.980 0.000 0.000 0.020
#> GSM876848 4 0.1981 0.7805 0.000 0.048 0.000 0.924 0.028
#> GSM876849 4 0.0771 0.8037 0.000 0.020 0.004 0.976 0.000
#> GSM876898 3 0.4444 0.7427 0.012 0.000 0.624 0.000 0.364
#> GSM876899 3 0.1310 0.6879 0.000 0.000 0.956 0.020 0.024
#> GSM876900 3 0.4444 0.7427 0.012 0.000 0.624 0.000 0.364
#> GSM876901 3 0.4444 0.7427 0.012 0.000 0.624 0.000 0.364
#> GSM876902 4 0.3980 0.8097 0.000 0.000 0.128 0.796 0.076
#> GSM876903 3 0.1872 0.6745 0.000 0.000 0.928 0.020 0.052
#> GSM876904 3 0.4444 0.7427 0.012 0.000 0.624 0.000 0.364
#> GSM876874 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.2929 0.8098 0.820 0.000 0.000 0.000 0.180
#> GSM876876 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876879 1 0.4484 0.6319 0.668 0.000 0.000 0.024 0.308
#> GSM876880 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0609 0.8885 0.000 0.980 0.000 0.000 0.020
#> GSM876851 2 0.0510 0.8891 0.000 0.984 0.000 0.000 0.016
#> GSM876852 2 0.2763 0.8540 0.000 0.848 0.000 0.004 0.148
#> GSM876853 2 0.1608 0.8857 0.000 0.928 0.000 0.000 0.072
#> GSM876854 2 0.4761 0.7823 0.000 0.732 0.000 0.124 0.144
#> GSM876855 2 0.4761 0.7823 0.000 0.732 0.000 0.124 0.144
#> GSM876856 2 0.4761 0.7823 0.000 0.732 0.000 0.124 0.144
#> GSM876905 3 0.4444 0.7427 0.012 0.000 0.624 0.000 0.364
#> GSM876906 3 0.0000 0.7093 0.000 0.000 1.000 0.000 0.000
#> GSM876907 3 0.1872 0.6745 0.000 0.000 0.928 0.020 0.052
#> GSM876908 3 0.0000 0.7093 0.000 0.000 1.000 0.000 0.000
#> GSM876909 3 0.1872 0.6745 0.000 0.000 0.928 0.020 0.052
#> GSM876881 2 0.2074 0.8589 0.000 0.896 0.000 0.000 0.104
#> GSM876882 1 0.4858 0.6137 0.656 0.000 0.012 0.024 0.308
#> GSM876883 3 0.6024 0.0908 0.040 0.000 0.532 0.044 0.384
#> GSM876884 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876885 3 0.5840 0.1013 0.020 0.000 0.540 0.056 0.384
#> GSM876857 1 0.0000 0.9537 1.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.2020 0.8626 0.000 0.900 0.000 0.000 0.100
#> GSM876859 2 0.2020 0.8626 0.000 0.900 0.000 0.000 0.100
#> GSM876860 2 0.2020 0.8626 0.000 0.900 0.000 0.000 0.100
#> GSM876861 2 0.2020 0.8626 0.000 0.900 0.000 0.000 0.100
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM876886 3 0.4482 0.951 0.000 0.000 0.600 0.000 0.360 0.040
#> GSM876887 3 0.4482 0.951 0.000 0.000 0.600 0.000 0.360 0.040
#> GSM876888 3 0.3684 0.984 0.000 0.000 0.628 0.000 0.372 0.000
#> GSM876889 5 0.4447 0.443 0.000 0.000 0.224 0.008 0.704 0.064
#> GSM876890 3 0.4322 0.963 0.000 0.000 0.600 0.000 0.372 0.028
#> GSM876891 5 0.1556 0.870 0.000 0.000 0.080 0.000 0.920 0.000
#> GSM876862 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0858 0.932 0.968 0.000 0.028 0.004 0.000 0.000
#> GSM876864 1 0.0260 0.935 0.992 0.000 0.008 0.000 0.000 0.000
#> GSM876865 1 0.0713 0.932 0.972 0.000 0.028 0.000 0.000 0.000
#> GSM876866 1 0.2554 0.850 0.876 0.000 0.028 0.004 0.000 0.092
#> GSM876867 1 0.0146 0.936 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM876838 2 0.2532 0.806 0.000 0.884 0.060 0.004 0.000 0.052
#> GSM876839 2 0.0291 0.813 0.000 0.992 0.000 0.004 0.000 0.004
#> GSM876840 2 0.6324 0.648 0.000 0.580 0.144 0.104 0.000 0.172
#> GSM876841 2 0.0146 0.813 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM876842 2 0.2591 0.805 0.000 0.880 0.064 0.004 0.000 0.052
#> GSM876843 4 0.5926 0.501 0.000 0.080 0.148 0.624 0.000 0.148
#> GSM876892 3 0.3684 0.984 0.000 0.000 0.628 0.000 0.372 0.000
#> GSM876893 3 0.3684 0.984 0.000 0.000 0.628 0.000 0.372 0.000
#> GSM876894 5 0.2003 0.817 0.000 0.000 0.116 0.000 0.884 0.000
#> GSM876895 5 0.0547 0.858 0.000 0.000 0.000 0.000 0.980 0.020
#> GSM876896 4 0.2826 0.752 0.000 0.000 0.000 0.856 0.092 0.052
#> GSM876897 4 0.2826 0.752 0.000 0.000 0.000 0.856 0.092 0.052
#> GSM876868 1 0.0547 0.933 0.980 0.000 0.020 0.000 0.000 0.000
#> GSM876869 1 0.0547 0.933 0.980 0.000 0.020 0.000 0.000 0.000
#> GSM876870 1 0.1367 0.930 0.944 0.000 0.044 0.012 0.000 0.000
#> GSM876871 1 0.1265 0.931 0.948 0.000 0.044 0.008 0.000 0.000
#> GSM876872 6 0.4721 0.167 0.000 0.000 0.004 0.464 0.036 0.496
#> GSM876873 6 0.4721 0.167 0.000 0.000 0.004 0.464 0.036 0.496
#> GSM876844 2 0.2591 0.805 0.000 0.880 0.064 0.004 0.000 0.052
#> GSM876845 2 0.0436 0.812 0.000 0.988 0.004 0.004 0.000 0.004
#> GSM876846 2 0.6694 0.579 0.000 0.528 0.188 0.112 0.000 0.172
#> GSM876847 2 0.0436 0.812 0.000 0.988 0.004 0.004 0.000 0.004
#> GSM876848 4 0.3212 0.720 0.000 0.028 0.068 0.856 0.004 0.044
#> GSM876849 4 0.2495 0.747 0.000 0.000 0.060 0.892 0.032 0.016
#> GSM876898 3 0.3684 0.984 0.000 0.000 0.628 0.000 0.372 0.000
#> GSM876899 5 0.0935 0.879 0.000 0.000 0.032 0.000 0.964 0.004
#> GSM876900 3 0.3684 0.984 0.000 0.000 0.628 0.000 0.372 0.000
#> GSM876901 3 0.3684 0.984 0.000 0.000 0.628 0.000 0.372 0.000
#> GSM876902 4 0.3065 0.742 0.000 0.000 0.004 0.844 0.100 0.052
#> GSM876903 5 0.0146 0.876 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM876904 3 0.3684 0.984 0.000 0.000 0.628 0.000 0.372 0.000
#> GSM876874 1 0.0000 0.936 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.4226 0.250 0.580 0.000 0.012 0.004 0.000 0.404
#> GSM876876 1 0.1367 0.930 0.944 0.000 0.044 0.012 0.000 0.000
#> GSM876877 1 0.1196 0.931 0.952 0.000 0.040 0.008 0.000 0.000
#> GSM876878 1 0.1820 0.923 0.928 0.000 0.044 0.012 0.000 0.016
#> GSM876879 6 0.3684 0.434 0.332 0.000 0.000 0.004 0.000 0.664
#> GSM876880 1 0.1196 0.931 0.952 0.000 0.040 0.008 0.000 0.000
#> GSM876850 2 0.0436 0.812 0.000 0.988 0.004 0.004 0.000 0.004
#> GSM876851 2 0.0146 0.813 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM876852 2 0.4741 0.723 0.000 0.692 0.148 0.004 0.000 0.156
#> GSM876853 2 0.2533 0.805 0.000 0.884 0.056 0.004 0.000 0.056
#> GSM876854 2 0.6269 0.656 0.000 0.588 0.144 0.104 0.000 0.164
#> GSM876855 2 0.6269 0.656 0.000 0.588 0.144 0.104 0.000 0.164
#> GSM876856 2 0.6351 0.646 0.000 0.576 0.144 0.104 0.000 0.176
#> GSM876905 3 0.3684 0.984 0.000 0.000 0.628 0.000 0.372 0.000
#> GSM876906 5 0.1556 0.870 0.000 0.000 0.080 0.000 0.920 0.000
#> GSM876907 5 0.0146 0.876 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM876908 5 0.1556 0.870 0.000 0.000 0.080 0.000 0.920 0.000
#> GSM876909 5 0.0146 0.876 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM876881 2 0.3275 0.765 0.000 0.848 0.068 0.004 0.016 0.064
#> GSM876882 6 0.3482 0.469 0.316 0.000 0.000 0.000 0.000 0.684
#> GSM876883 6 0.4065 0.516 0.004 0.000 0.004 0.024 0.260 0.708
#> GSM876884 1 0.1367 0.930 0.944 0.000 0.044 0.012 0.000 0.000
#> GSM876885 6 0.4065 0.516 0.004 0.000 0.004 0.024 0.260 0.708
#> GSM876857 1 0.0547 0.933 0.980 0.000 0.020 0.000 0.000 0.000
#> GSM876858 2 0.4010 0.752 0.000 0.800 0.096 0.004 0.032 0.068
#> GSM876859 2 0.4010 0.752 0.000 0.800 0.096 0.004 0.032 0.068
#> GSM876860 2 0.4010 0.752 0.000 0.800 0.096 0.004 0.032 0.068
#> GSM876861 2 0.4010 0.752 0.000 0.800 0.096 0.004 0.032 0.068
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> CV:kmeans 71 0.907 2.13e-11 2
#> CV:kmeans 69 0.975 4.15e-22 3
#> CV:kmeans 72 0.121 1.48e-20 4
#> CV:kmeans 70 0.180 5.57e-22 5
#> CV:kmeans 66 0.162 2.33e-19 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 72 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 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 0.981 0.992 0.5000 0.499 0.499
#> 3 3 0.766 0.855 0.927 0.3294 0.797 0.608
#> 4 4 0.932 0.941 0.943 0.1015 0.906 0.732
#> 5 5 1.000 0.951 0.979 0.0573 0.946 0.805
#> 6 6 0.991 0.940 0.973 0.0378 0.967 0.854
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
#> GSM876886 1 0.000 0.996 1.000 0.000
#> GSM876887 1 0.000 0.996 1.000 0.000
#> GSM876888 1 0.000 0.996 1.000 0.000
#> GSM876889 1 0.000 0.996 1.000 0.000
#> GSM876890 1 0.000 0.996 1.000 0.000
#> GSM876891 1 0.000 0.996 1.000 0.000
#> GSM876862 1 0.000 0.996 1.000 0.000
#> GSM876863 1 0.000 0.996 1.000 0.000
#> GSM876864 1 0.000 0.996 1.000 0.000
#> GSM876865 1 0.000 0.996 1.000 0.000
#> GSM876866 1 0.000 0.996 1.000 0.000
#> GSM876867 1 0.000 0.996 1.000 0.000
#> GSM876838 2 0.000 0.985 0.000 1.000
#> GSM876839 2 0.000 0.985 0.000 1.000
#> GSM876840 2 0.000 0.985 0.000 1.000
#> GSM876841 2 0.000 0.985 0.000 1.000
#> GSM876842 2 0.000 0.985 0.000 1.000
#> GSM876843 2 0.000 0.985 0.000 1.000
#> GSM876892 1 0.000 0.996 1.000 0.000
#> GSM876893 1 0.000 0.996 1.000 0.000
#> GSM876894 1 0.000 0.996 1.000 0.000
#> GSM876895 2 0.000 0.985 0.000 1.000
#> GSM876896 2 0.000 0.985 0.000 1.000
#> GSM876897 2 0.000 0.985 0.000 1.000
#> GSM876868 1 0.000 0.996 1.000 0.000
#> GSM876869 1 0.000 0.996 1.000 0.000
#> GSM876870 1 0.000 0.996 1.000 0.000
#> GSM876871 1 0.000 0.996 1.000 0.000
#> GSM876872 1 0.595 0.827 0.856 0.144
#> GSM876873 1 0.000 0.996 1.000 0.000
#> GSM876844 2 0.000 0.985 0.000 1.000
#> GSM876845 2 0.000 0.985 0.000 1.000
#> GSM876846 2 0.000 0.985 0.000 1.000
#> GSM876847 2 0.000 0.985 0.000 1.000
#> GSM876848 2 0.000 0.985 0.000 1.000
#> GSM876849 2 0.000 0.985 0.000 1.000
#> GSM876898 1 0.000 0.996 1.000 0.000
#> GSM876899 2 0.839 0.641 0.268 0.732
#> GSM876900 1 0.000 0.996 1.000 0.000
#> GSM876901 1 0.000 0.996 1.000 0.000
#> GSM876902 2 0.680 0.782 0.180 0.820
#> GSM876903 2 0.000 0.985 0.000 1.000
#> GSM876904 1 0.000 0.996 1.000 0.000
#> GSM876874 1 0.000 0.996 1.000 0.000
#> GSM876875 1 0.000 0.996 1.000 0.000
#> GSM876876 1 0.000 0.996 1.000 0.000
#> GSM876877 1 0.000 0.996 1.000 0.000
#> GSM876878 1 0.000 0.996 1.000 0.000
#> GSM876879 1 0.000 0.996 1.000 0.000
#> GSM876880 1 0.000 0.996 1.000 0.000
#> GSM876850 2 0.000 0.985 0.000 1.000
#> GSM876851 2 0.000 0.985 0.000 1.000
#> GSM876852 2 0.000 0.985 0.000 1.000
#> GSM876853 2 0.000 0.985 0.000 1.000
#> GSM876854 2 0.000 0.985 0.000 1.000
#> GSM876855 2 0.000 0.985 0.000 1.000
#> GSM876856 2 0.000 0.985 0.000 1.000
#> GSM876905 1 0.000 0.996 1.000 0.000
#> GSM876906 1 0.000 0.996 1.000 0.000
#> GSM876907 2 0.000 0.985 0.000 1.000
#> GSM876908 1 0.000 0.996 1.000 0.000
#> GSM876909 2 0.000 0.985 0.000 1.000
#> GSM876881 2 0.000 0.985 0.000 1.000
#> GSM876882 1 0.000 0.996 1.000 0.000
#> GSM876883 1 0.000 0.996 1.000 0.000
#> GSM876884 1 0.000 0.996 1.000 0.000
#> GSM876885 1 0.000 0.996 1.000 0.000
#> GSM876857 1 0.000 0.996 1.000 0.000
#> GSM876858 2 0.000 0.985 0.000 1.000
#> GSM876859 2 0.000 0.985 0.000 1.000
#> GSM876860 2 0.000 0.985 0.000 1.000
#> GSM876861 2 0.000 0.985 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 3 0.4842 0.800 0.224 0.000 0.776
#> GSM876887 3 0.1753 0.817 0.048 0.000 0.952
#> GSM876888 3 0.4842 0.800 0.224 0.000 0.776
#> GSM876889 3 0.0000 0.811 0.000 0.000 1.000
#> GSM876890 3 0.1529 0.816 0.040 0.000 0.960
#> GSM876891 3 0.0000 0.811 0.000 0.000 1.000
#> GSM876862 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876863 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876864 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876865 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876866 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876867 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876838 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876839 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876840 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876841 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876842 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876843 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876892 3 0.4842 0.800 0.224 0.000 0.776
#> GSM876893 3 0.4842 0.800 0.224 0.000 0.776
#> GSM876894 3 0.0000 0.811 0.000 0.000 1.000
#> GSM876895 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876896 2 0.5926 0.524 0.000 0.644 0.356
#> GSM876897 2 0.4842 0.737 0.000 0.776 0.224
#> GSM876868 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876869 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876870 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876871 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876872 1 0.5926 0.535 0.644 0.000 0.356
#> GSM876873 1 0.5926 0.535 0.644 0.000 0.356
#> GSM876844 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876845 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876846 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876847 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876848 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876849 2 0.4291 0.784 0.000 0.820 0.180
#> GSM876898 3 0.4842 0.800 0.224 0.000 0.776
#> GSM876899 3 0.0000 0.811 0.000 0.000 1.000
#> GSM876900 3 0.4842 0.800 0.224 0.000 0.776
#> GSM876901 3 0.4842 0.800 0.224 0.000 0.776
#> GSM876902 3 0.4452 0.636 0.000 0.192 0.808
#> GSM876903 2 0.6111 0.457 0.000 0.604 0.396
#> GSM876904 3 0.4842 0.800 0.224 0.000 0.776
#> GSM876874 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876875 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876876 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876877 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876878 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876879 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876880 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876850 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876851 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876852 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876853 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876854 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876855 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876856 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876905 3 0.4842 0.800 0.224 0.000 0.776
#> GSM876906 3 0.0000 0.811 0.000 0.000 1.000
#> GSM876907 3 0.6309 -0.218 0.000 0.496 0.504
#> GSM876908 3 0.0000 0.811 0.000 0.000 1.000
#> GSM876909 2 0.4796 0.715 0.000 0.780 0.220
#> GSM876881 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876882 1 0.0237 0.941 0.996 0.000 0.004
#> GSM876883 1 0.4555 0.736 0.800 0.000 0.200
#> GSM876884 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876885 1 0.4605 0.732 0.796 0.000 0.204
#> GSM876857 1 0.0000 0.944 1.000 0.000 0.000
#> GSM876858 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876859 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876860 2 0.0000 0.950 0.000 1.000 0.000
#> GSM876861 2 0.0000 0.950 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.0188 0.992 0.004 0.000 0.996 0.000
#> GSM876887 3 0.0188 0.992 0.004 0.000 0.996 0.000
#> GSM876888 3 0.0188 0.992 0.004 0.000 0.996 0.000
#> GSM876889 3 0.0188 0.989 0.000 0.000 0.996 0.004
#> GSM876890 3 0.0188 0.992 0.004 0.000 0.996 0.000
#> GSM876891 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM876862 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876839 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876840 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876841 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876842 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876843 4 0.3688 0.786 0.000 0.208 0.000 0.792
#> GSM876892 3 0.0188 0.992 0.004 0.000 0.996 0.000
#> GSM876893 3 0.0188 0.992 0.004 0.000 0.996 0.000
#> GSM876894 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM876895 2 0.0188 0.970 0.000 0.996 0.004 0.000
#> GSM876896 4 0.0000 0.933 0.000 0.000 0.000 1.000
#> GSM876897 4 0.0000 0.933 0.000 0.000 0.000 1.000
#> GSM876868 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 0.933 0.000 0.000 0.000 1.000
#> GSM876873 4 0.0000 0.933 0.000 0.000 0.000 1.000
#> GSM876844 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876845 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876846 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876847 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876848 4 0.2345 0.898 0.000 0.100 0.000 0.900
#> GSM876849 4 0.2345 0.898 0.000 0.100 0.000 0.900
#> GSM876898 3 0.0188 0.992 0.004 0.000 0.996 0.000
#> GSM876899 3 0.2345 0.888 0.000 0.000 0.900 0.100
#> GSM876900 3 0.0188 0.992 0.004 0.000 0.996 0.000
#> GSM876901 3 0.0188 0.992 0.004 0.000 0.996 0.000
#> GSM876902 4 0.0000 0.933 0.000 0.000 0.000 1.000
#> GSM876903 2 0.4549 0.780 0.000 0.804 0.096 0.100
#> GSM876904 3 0.0188 0.992 0.004 0.000 0.996 0.000
#> GSM876874 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876875 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876876 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876879 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876880 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876851 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876852 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876853 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876854 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876855 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876856 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876905 3 0.0188 0.992 0.004 0.000 0.996 0.000
#> GSM876906 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM876907 2 0.4669 0.770 0.000 0.796 0.104 0.100
#> GSM876908 3 0.0000 0.990 0.000 0.000 1.000 0.000
#> GSM876909 2 0.4549 0.780 0.000 0.804 0.096 0.100
#> GSM876881 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876882 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876883 1 0.4790 0.406 0.620 0.000 0.000 0.380
#> GSM876884 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876885 1 0.4790 0.406 0.620 0.000 0.000 0.380
#> GSM876857 1 0.0000 0.962 1.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876859 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876860 2 0.0000 0.973 0.000 1.000 0.000 0.000
#> GSM876861 2 0.0000 0.973 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
#> GSM876886 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM876887 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM876888 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM876889 3 0.0609 0.979 0.000 0.000 0.980 0.020 0.000
#> GSM876890 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM876891 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM876862 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM876840 2 0.0162 0.997 0.000 0.996 0.000 0.000 0.004
#> GSM876841 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM876843 4 0.4288 0.380 0.000 0.384 0.000 0.612 0.004
#> GSM876892 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM876893 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM876894 3 0.0162 0.995 0.000 0.000 0.996 0.000 0.004
#> GSM876895 5 0.0794 0.977 0.000 0.028 0.000 0.000 0.972
#> GSM876896 4 0.0000 0.919 0.000 0.000 0.000 1.000 0.000
#> GSM876897 4 0.0000 0.919 0.000 0.000 0.000 1.000 0.000
#> GSM876868 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.0290 0.916 0.000 0.000 0.000 0.992 0.008
#> GSM876873 4 0.0290 0.916 0.000 0.000 0.000 0.992 0.008
#> GSM876844 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM876846 2 0.0162 0.997 0.000 0.996 0.000 0.000 0.004
#> GSM876847 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM876848 4 0.0162 0.917 0.000 0.000 0.000 0.996 0.004
#> GSM876849 4 0.0162 0.917 0.000 0.000 0.000 0.996 0.004
#> GSM876898 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM876899 5 0.0794 0.969 0.000 0.000 0.028 0.000 0.972
#> GSM876900 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM876901 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM876902 4 0.0000 0.919 0.000 0.000 0.000 1.000 0.000
#> GSM876903 5 0.0794 0.977 0.000 0.028 0.000 0.000 0.972
#> GSM876904 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM876874 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.0510 0.949 0.984 0.000 0.000 0.000 0.016
#> GSM876876 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876879 1 0.0703 0.944 0.976 0.000 0.000 0.000 0.024
#> GSM876880 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM876852 2 0.0162 0.997 0.000 0.996 0.000 0.000 0.004
#> GSM876853 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM876854 2 0.0162 0.997 0.000 0.996 0.000 0.000 0.004
#> GSM876855 2 0.0162 0.997 0.000 0.996 0.000 0.000 0.004
#> GSM876856 2 0.0162 0.997 0.000 0.996 0.000 0.000 0.004
#> GSM876905 3 0.0000 0.998 0.000 0.000 1.000 0.000 0.000
#> GSM876906 5 0.0794 0.969 0.000 0.000 0.028 0.000 0.972
#> GSM876907 5 0.0794 0.977 0.000 0.028 0.000 0.000 0.972
#> GSM876908 5 0.0794 0.969 0.000 0.000 0.028 0.000 0.972
#> GSM876909 5 0.0794 0.977 0.000 0.028 0.000 0.000 0.972
#> GSM876881 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM876882 1 0.0865 0.942 0.972 0.000 0.000 0.004 0.024
#> GSM876883 1 0.4734 0.399 0.604 0.000 0.000 0.372 0.024
#> GSM876884 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876885 1 0.4734 0.399 0.604 0.000 0.000 0.372 0.024
#> GSM876857 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM876859 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM876860 2 0.0000 0.999 0.000 1.000 0.000 0.000 0.000
#> GSM876861 2 0.0000 0.999 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
#> GSM876886 3 0.0260 0.992 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM876887 3 0.0260 0.992 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM876888 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876889 3 0.0937 0.966 0.000 0.000 0.960 0.000 0.000 0.040
#> GSM876890 3 0.0260 0.992 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM876891 3 0.0363 0.990 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM876862 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876840 2 0.0777 0.979 0.000 0.972 0.000 0.024 0.000 0.004
#> GSM876841 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876842 2 0.0146 0.991 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM876843 4 0.2668 0.659 0.000 0.168 0.000 0.828 0.000 0.004
#> GSM876892 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876893 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876894 3 0.0405 0.987 0.000 0.000 0.988 0.000 0.008 0.004
#> GSM876895 5 0.0405 0.987 0.000 0.008 0.000 0.000 0.988 0.004
#> GSM876896 4 0.0632 0.844 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM876897 4 0.0632 0.844 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM876868 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.3515 0.613 0.000 0.000 0.000 0.676 0.000 0.324
#> GSM876873 4 0.3810 0.468 0.000 0.000 0.000 0.572 0.000 0.428
#> GSM876844 2 0.0146 0.991 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM876845 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876846 2 0.0858 0.976 0.000 0.968 0.000 0.028 0.000 0.004
#> GSM876847 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876848 4 0.0146 0.837 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM876849 4 0.0000 0.839 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876898 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876899 5 0.0000 0.997 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876900 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876901 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876902 4 0.0713 0.843 0.000 0.000 0.000 0.972 0.000 0.028
#> GSM876903 5 0.0000 0.997 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876904 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876874 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876875 6 0.3860 0.174 0.472 0.000 0.000 0.000 0.000 0.528
#> GSM876876 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876879 6 0.2135 0.714 0.128 0.000 0.000 0.000 0.000 0.872
#> GSM876880 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876852 2 0.0146 0.991 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM876853 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876854 2 0.0777 0.979 0.000 0.972 0.000 0.024 0.000 0.004
#> GSM876855 2 0.0777 0.979 0.000 0.972 0.000 0.024 0.000 0.004
#> GSM876856 2 0.0777 0.979 0.000 0.972 0.000 0.024 0.000 0.004
#> GSM876905 3 0.0000 0.994 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876906 5 0.0146 0.995 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM876907 5 0.0000 0.997 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876908 5 0.0146 0.995 0.000 0.000 0.000 0.000 0.996 0.004
#> GSM876909 5 0.0000 0.997 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876881 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876882 6 0.0632 0.755 0.024 0.000 0.000 0.000 0.000 0.976
#> GSM876883 6 0.0622 0.748 0.012 0.000 0.000 0.008 0.000 0.980
#> GSM876884 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876885 6 0.0622 0.743 0.008 0.000 0.000 0.012 0.000 0.980
#> GSM876857 1 0.0000 1.000 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876859 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876860 2 0.0000 0.993 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876861 2 0.0000 0.993 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 disease.state(p) tissue(p) k
#> CV:skmeans 72 0.7433 5.51e-10 2
#> CV:skmeans 70 0.9154 1.37e-22 3
#> CV:skmeans 70 0.1218 4.52e-18 4
#> CV:skmeans 69 0.0134 1.10e-20 5
#> CV:skmeans 70 0.0270 3.72e-20 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 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.965 0.987 0.4972 0.503 0.503
#> 3 3 1.000 0.973 0.989 0.3465 0.712 0.487
#> 4 4 0.900 0.908 0.947 0.1024 0.924 0.775
#> 5 5 0.937 0.925 0.961 0.0617 0.937 0.766
#> 6 6 1.000 0.972 0.984 0.0293 0.950 0.781
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
#> GSM876886 1 0.000 0.989 1.000 0.000
#> GSM876887 1 0.000 0.989 1.000 0.000
#> GSM876888 1 0.000 0.989 1.000 0.000
#> GSM876889 1 0.000 0.989 1.000 0.000
#> GSM876890 1 0.000 0.989 1.000 0.000
#> GSM876891 1 0.000 0.989 1.000 0.000
#> GSM876862 1 0.000 0.989 1.000 0.000
#> GSM876863 1 0.000 0.989 1.000 0.000
#> GSM876864 1 0.000 0.989 1.000 0.000
#> GSM876865 1 0.000 0.989 1.000 0.000
#> GSM876866 1 0.000 0.989 1.000 0.000
#> GSM876867 1 0.000 0.989 1.000 0.000
#> GSM876838 2 0.000 0.982 0.000 1.000
#> GSM876839 2 0.000 0.982 0.000 1.000
#> GSM876840 2 0.000 0.982 0.000 1.000
#> GSM876841 2 0.000 0.982 0.000 1.000
#> GSM876842 2 0.000 0.982 0.000 1.000
#> GSM876843 2 0.000 0.982 0.000 1.000
#> GSM876892 1 0.000 0.989 1.000 0.000
#> GSM876893 1 0.000 0.989 1.000 0.000
#> GSM876894 1 0.000 0.989 1.000 0.000
#> GSM876895 2 0.529 0.857 0.120 0.880
#> GSM876896 2 0.260 0.941 0.044 0.956
#> GSM876897 2 0.000 0.982 0.000 1.000
#> GSM876868 1 0.000 0.989 1.000 0.000
#> GSM876869 1 0.000 0.989 1.000 0.000
#> GSM876870 1 0.000 0.989 1.000 0.000
#> GSM876871 1 0.000 0.989 1.000 0.000
#> GSM876872 1 0.000 0.989 1.000 0.000
#> GSM876873 1 0.000 0.989 1.000 0.000
#> GSM876844 2 0.000 0.982 0.000 1.000
#> GSM876845 2 0.000 0.982 0.000 1.000
#> GSM876846 2 0.000 0.982 0.000 1.000
#> GSM876847 2 0.000 0.982 0.000 1.000
#> GSM876848 2 0.000 0.982 0.000 1.000
#> GSM876849 2 0.000 0.982 0.000 1.000
#> GSM876898 1 0.000 0.989 1.000 0.000
#> GSM876899 2 0.955 0.401 0.376 0.624
#> GSM876900 1 0.000 0.989 1.000 0.000
#> GSM876901 1 0.000 0.989 1.000 0.000
#> GSM876902 1 0.983 0.248 0.576 0.424
#> GSM876903 2 0.000 0.982 0.000 1.000
#> GSM876904 1 0.000 0.989 1.000 0.000
#> GSM876874 1 0.000 0.989 1.000 0.000
#> GSM876875 1 0.000 0.989 1.000 0.000
#> GSM876876 1 0.000 0.989 1.000 0.000
#> GSM876877 1 0.000 0.989 1.000 0.000
#> GSM876878 1 0.000 0.989 1.000 0.000
#> GSM876879 1 0.000 0.989 1.000 0.000
#> GSM876880 1 0.000 0.989 1.000 0.000
#> GSM876850 2 0.000 0.982 0.000 1.000
#> GSM876851 2 0.000 0.982 0.000 1.000
#> GSM876852 2 0.000 0.982 0.000 1.000
#> GSM876853 2 0.000 0.982 0.000 1.000
#> GSM876854 2 0.000 0.982 0.000 1.000
#> GSM876855 2 0.000 0.982 0.000 1.000
#> GSM876856 2 0.000 0.982 0.000 1.000
#> GSM876905 1 0.000 0.989 1.000 0.000
#> GSM876906 1 0.000 0.989 1.000 0.000
#> GSM876907 2 0.000 0.982 0.000 1.000
#> GSM876908 1 0.000 0.989 1.000 0.000
#> GSM876909 2 0.000 0.982 0.000 1.000
#> GSM876881 2 0.000 0.982 0.000 1.000
#> GSM876882 1 0.000 0.989 1.000 0.000
#> GSM876883 1 0.000 0.989 1.000 0.000
#> GSM876884 1 0.000 0.989 1.000 0.000
#> GSM876885 1 0.000 0.989 1.000 0.000
#> GSM876857 1 0.000 0.989 1.000 0.000
#> GSM876858 2 0.000 0.982 0.000 1.000
#> GSM876859 2 0.000 0.982 0.000 1.000
#> GSM876860 2 0.000 0.982 0.000 1.000
#> GSM876861 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
#> GSM876886 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876887 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876888 3 0.0237 0.977 0.004 0.0 0.996
#> GSM876889 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876890 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876891 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876862 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876863 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876864 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876865 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876866 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876867 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876838 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876839 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876840 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876841 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876842 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876843 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876892 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876893 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876894 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876895 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876896 3 0.4555 0.763 0.000 0.2 0.800
#> GSM876897 3 0.4555 0.763 0.000 0.2 0.800
#> GSM876868 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876869 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876870 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876871 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876872 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876873 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876844 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876845 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876846 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876847 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876848 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876849 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876898 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876899 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876900 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876901 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876902 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876903 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876904 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876874 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876875 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876876 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876877 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876878 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876879 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876880 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876850 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876851 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876852 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876853 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876854 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876855 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876856 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876905 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876906 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876907 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876908 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876909 3 0.0000 0.981 0.000 0.0 1.000
#> GSM876881 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876882 1 0.5760 0.498 0.672 0.0 0.328
#> GSM876883 3 0.2261 0.918 0.068 0.0 0.932
#> GSM876884 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876885 3 0.1031 0.961 0.024 0.0 0.976
#> GSM876857 1 0.0000 0.982 1.000 0.0 0.000
#> GSM876858 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876859 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876860 2 0.0000 1.000 0.000 1.0 0.000
#> GSM876861 2 0.0000 1.000 0.000 1.0 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.000 0.868 0.000 0.000 1.000 0.000
#> GSM876887 3 0.000 0.868 0.000 0.000 1.000 0.000
#> GSM876888 3 0.000 0.868 0.000 0.000 1.000 0.000
#> GSM876889 3 0.322 0.842 0.000 0.000 0.836 0.164
#> GSM876890 3 0.000 0.868 0.000 0.000 1.000 0.000
#> GSM876891 3 0.357 0.834 0.000 0.000 0.804 0.196
#> GSM876862 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876863 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876864 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876865 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876866 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876867 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876838 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876839 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876840 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876841 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876842 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876843 4 0.493 0.312 0.000 0.432 0.000 0.568
#> GSM876892 3 0.000 0.868 0.000 0.000 1.000 0.000
#> GSM876893 3 0.000 0.868 0.000 0.000 1.000 0.000
#> GSM876894 3 0.000 0.868 0.000 0.000 1.000 0.000
#> GSM876895 3 0.361 0.832 0.000 0.000 0.800 0.200
#> GSM876896 4 0.000 0.837 0.000 0.000 0.000 1.000
#> GSM876897 4 0.000 0.837 0.000 0.000 0.000 1.000
#> GSM876868 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876869 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876870 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876871 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876872 4 0.000 0.837 0.000 0.000 0.000 1.000
#> GSM876873 4 0.000 0.837 0.000 0.000 0.000 1.000
#> GSM876844 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876845 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876846 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876847 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876848 4 0.361 0.745 0.000 0.200 0.000 0.800
#> GSM876849 4 0.361 0.745 0.000 0.200 0.000 0.800
#> GSM876898 3 0.000 0.868 0.000 0.000 1.000 0.000
#> GSM876899 3 0.361 0.832 0.000 0.000 0.800 0.200
#> GSM876900 3 0.000 0.868 0.000 0.000 1.000 0.000
#> GSM876901 3 0.000 0.868 0.000 0.000 1.000 0.000
#> GSM876902 4 0.000 0.837 0.000 0.000 0.000 1.000
#> GSM876903 3 0.485 0.604 0.000 0.000 0.600 0.400
#> GSM876904 3 0.000 0.868 0.000 0.000 1.000 0.000
#> GSM876874 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876875 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876876 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876877 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876878 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876879 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876880 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876850 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876851 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876852 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876853 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876854 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876855 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876856 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876905 3 0.000 0.868 0.000 0.000 1.000 0.000
#> GSM876906 3 0.361 0.832 0.000 0.000 0.800 0.200
#> GSM876907 3 0.361 0.832 0.000 0.000 0.800 0.200
#> GSM876908 3 0.361 0.832 0.000 0.000 0.800 0.200
#> GSM876909 3 0.361 0.832 0.000 0.000 0.800 0.200
#> GSM876881 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876882 1 0.312 0.781 0.844 0.000 0.156 0.000
#> GSM876883 3 0.510 0.551 0.004 0.000 0.568 0.428
#> GSM876884 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876885 3 0.493 0.550 0.000 0.000 0.568 0.432
#> GSM876857 1 0.000 0.990 1.000 0.000 0.000 0.000
#> GSM876858 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876859 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876860 2 0.000 1.000 0.000 1.000 0.000 0.000
#> GSM876861 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
#> GSM876886 3 0.000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876887 3 0.000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876888 3 0.000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876889 3 0.300 0.738 0.000 0.000 0.812 0.000 0.188
#> GSM876890 3 0.000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876891 5 0.340 0.698 0.000 0.000 0.236 0.000 0.764
#> GSM876862 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876867 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876839 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876840 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876841 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876842 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876843 4 0.415 0.458 0.000 0.388 0.000 0.612 0.000
#> GSM876892 3 0.000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876893 3 0.000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876894 5 0.340 0.698 0.000 0.000 0.236 0.000 0.764
#> GSM876895 5 0.000 0.863 0.000 0.000 0.000 0.000 1.000
#> GSM876896 4 0.223 0.815 0.000 0.000 0.000 0.884 0.116
#> GSM876897 4 0.223 0.815 0.000 0.000 0.000 0.884 0.116
#> GSM876868 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.000 0.806 0.000 0.000 0.000 1.000 0.000
#> GSM876873 4 0.000 0.806 0.000 0.000 0.000 1.000 0.000
#> GSM876844 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876845 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876846 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876847 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876848 4 0.307 0.752 0.000 0.196 0.000 0.804 0.000
#> GSM876849 4 0.223 0.807 0.000 0.116 0.000 0.884 0.000
#> GSM876898 3 0.000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876899 5 0.000 0.863 0.000 0.000 0.000 0.000 1.000
#> GSM876900 3 0.000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876901 3 0.000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876902 4 0.218 0.816 0.000 0.000 0.000 0.888 0.112
#> GSM876903 5 0.000 0.863 0.000 0.000 0.000 0.000 1.000
#> GSM876904 3 0.000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876874 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.154 0.932 0.932 0.000 0.000 0.068 0.000
#> GSM876876 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876879 1 0.223 0.884 0.884 0.000 0.000 0.116 0.000
#> GSM876880 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876851 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876852 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876853 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876854 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876855 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876856 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876905 3 0.000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876906 5 0.000 0.863 0.000 0.000 0.000 0.000 1.000
#> GSM876907 5 0.000 0.863 0.000 0.000 0.000 0.000 1.000
#> GSM876908 5 0.000 0.863 0.000 0.000 0.000 0.000 1.000
#> GSM876909 5 0.000 0.863 0.000 0.000 0.000 0.000 1.000
#> GSM876881 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876882 5 0.612 0.354 0.360 0.000 0.000 0.136 0.504
#> GSM876883 5 0.340 0.787 0.036 0.000 0.000 0.136 0.828
#> GSM876884 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876885 5 0.331 0.750 0.000 0.000 0.000 0.224 0.776
#> GSM876857 1 0.000 0.990 1.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876859 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876860 2 0.000 1.000 0.000 1.000 0.000 0.000 0.000
#> GSM876861 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
#> GSM876886 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876887 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876888 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876889 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876890 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876891 3 0.0146 0.996 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM876862 1 0.0000 0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.2378 0.812 0.848 0.000 0.000 0.000 0.000 0.152
#> GSM876867 1 0.0000 0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876840 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876841 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876843 4 0.2823 0.718 0.000 0.204 0.000 0.796 0.000 0.000
#> GSM876892 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876893 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876894 3 0.0146 0.996 0.000 0.000 0.996 0.000 0.004 0.000
#> GSM876895 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876896 4 0.0260 0.923 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM876897 4 0.0260 0.923 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM876868 1 0.0000 0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876872 6 0.1957 0.889 0.000 0.000 0.000 0.112 0.000 0.888
#> GSM876873 6 0.1141 0.931 0.000 0.000 0.000 0.052 0.000 0.948
#> GSM876844 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876846 2 0.0632 0.978 0.000 0.976 0.000 0.000 0.000 0.024
#> GSM876847 2 0.0520 0.982 0.000 0.984 0.000 0.008 0.000 0.008
#> GSM876848 4 0.1204 0.894 0.000 0.056 0.000 0.944 0.000 0.000
#> GSM876849 4 0.0260 0.921 0.000 0.008 0.000 0.992 0.000 0.000
#> GSM876898 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876899 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876900 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876901 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876902 4 0.0260 0.923 0.000 0.000 0.000 0.992 0.008 0.000
#> GSM876903 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876904 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876874 1 0.0000 0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876875 6 0.1610 0.904 0.084 0.000 0.000 0.000 0.000 0.916
#> GSM876876 1 0.0000 0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0363 0.979 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM876879 6 0.0937 0.949 0.040 0.000 0.000 0.000 0.000 0.960
#> GSM876880 1 0.0000 0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0622 0.980 0.000 0.980 0.000 0.008 0.000 0.012
#> GSM876851 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876852 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876853 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876854 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876855 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876856 2 0.0000 0.986 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876905 3 0.0000 0.999 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876906 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876907 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876908 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876909 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876881 2 0.1196 0.967 0.000 0.952 0.000 0.008 0.000 0.040
#> GSM876882 6 0.0937 0.949 0.040 0.000 0.000 0.000 0.000 0.960
#> GSM876883 6 0.1010 0.949 0.036 0.000 0.000 0.000 0.004 0.960
#> GSM876884 1 0.0000 0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876885 6 0.1074 0.935 0.000 0.000 0.000 0.028 0.012 0.960
#> GSM876857 1 0.0000 0.989 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.1196 0.967 0.000 0.952 0.000 0.008 0.000 0.040
#> GSM876859 2 0.1196 0.967 0.000 0.952 0.000 0.008 0.000 0.040
#> GSM876860 2 0.1196 0.967 0.000 0.952 0.000 0.008 0.000 0.040
#> GSM876861 2 0.1196 0.967 0.000 0.952 0.000 0.008 0.000 0.040
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> CV:pam 70 0.76865 2.34e-10 2
#> CV:pam 71 0.87069 8.22e-23 3
#> CV:pam 71 0.04851 1.41e-20 4
#> CV:pam 70 0.00799 4.07e-19 5
#> CV:pam 72 0.14097 9.23e-22 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 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.949 0.978 0.4339 0.549 0.549
#> 3 3 0.927 0.960 0.981 0.5540 0.775 0.590
#> 4 4 0.968 0.930 0.966 0.1073 0.868 0.626
#> 5 5 0.997 0.964 0.977 0.0360 0.976 0.905
#> 6 6 0.992 0.958 0.976 0.0481 0.957 0.812
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
#> GSM876886 2 0.000 1.000 0.000 1.000
#> GSM876887 2 0.000 1.000 0.000 1.000
#> GSM876888 2 0.000 1.000 0.000 1.000
#> GSM876889 2 0.000 1.000 0.000 1.000
#> GSM876890 2 0.000 1.000 0.000 1.000
#> GSM876891 2 0.000 1.000 0.000 1.000
#> GSM876862 1 0.000 0.929 1.000 0.000
#> GSM876863 1 0.000 0.929 1.000 0.000
#> GSM876864 1 0.000 0.929 1.000 0.000
#> GSM876865 1 0.000 0.929 1.000 0.000
#> GSM876866 1 0.000 0.929 1.000 0.000
#> GSM876867 1 0.000 0.929 1.000 0.000
#> GSM876838 2 0.000 1.000 0.000 1.000
#> GSM876839 2 0.000 1.000 0.000 1.000
#> GSM876840 2 0.000 1.000 0.000 1.000
#> GSM876841 2 0.000 1.000 0.000 1.000
#> GSM876842 2 0.000 1.000 0.000 1.000
#> GSM876843 2 0.000 1.000 0.000 1.000
#> GSM876892 2 0.000 1.000 0.000 1.000
#> GSM876893 2 0.000 1.000 0.000 1.000
#> GSM876894 2 0.000 1.000 0.000 1.000
#> GSM876895 2 0.000 1.000 0.000 1.000
#> GSM876896 2 0.000 1.000 0.000 1.000
#> GSM876897 2 0.000 1.000 0.000 1.000
#> GSM876868 1 0.000 0.929 1.000 0.000
#> GSM876869 1 0.000 0.929 1.000 0.000
#> GSM876870 1 0.000 0.929 1.000 0.000
#> GSM876871 1 0.000 0.929 1.000 0.000
#> GSM876872 1 0.969 0.430 0.604 0.396
#> GSM876873 1 0.969 0.430 0.604 0.396
#> GSM876844 2 0.000 1.000 0.000 1.000
#> GSM876845 2 0.000 1.000 0.000 1.000
#> GSM876846 2 0.000 1.000 0.000 1.000
#> GSM876847 2 0.000 1.000 0.000 1.000
#> GSM876848 2 0.000 1.000 0.000 1.000
#> GSM876849 2 0.000 1.000 0.000 1.000
#> GSM876898 2 0.000 1.000 0.000 1.000
#> GSM876899 2 0.000 1.000 0.000 1.000
#> GSM876900 2 0.000 1.000 0.000 1.000
#> GSM876901 2 0.000 1.000 0.000 1.000
#> GSM876902 2 0.000 1.000 0.000 1.000
#> GSM876903 2 0.000 1.000 0.000 1.000
#> GSM876904 2 0.000 1.000 0.000 1.000
#> GSM876874 1 0.000 0.929 1.000 0.000
#> GSM876875 1 0.000 0.929 1.000 0.000
#> GSM876876 1 0.000 0.929 1.000 0.000
#> GSM876877 1 0.000 0.929 1.000 0.000
#> GSM876878 1 0.000 0.929 1.000 0.000
#> GSM876879 1 0.000 0.929 1.000 0.000
#> GSM876880 1 0.000 0.929 1.000 0.000
#> GSM876850 2 0.000 1.000 0.000 1.000
#> GSM876851 2 0.000 1.000 0.000 1.000
#> GSM876852 2 0.000 1.000 0.000 1.000
#> GSM876853 2 0.000 1.000 0.000 1.000
#> GSM876854 2 0.000 1.000 0.000 1.000
#> GSM876855 2 0.000 1.000 0.000 1.000
#> GSM876856 2 0.000 1.000 0.000 1.000
#> GSM876905 2 0.000 1.000 0.000 1.000
#> GSM876906 2 0.000 1.000 0.000 1.000
#> GSM876907 2 0.000 1.000 0.000 1.000
#> GSM876908 2 0.000 1.000 0.000 1.000
#> GSM876909 2 0.000 1.000 0.000 1.000
#> GSM876881 2 0.000 1.000 0.000 1.000
#> GSM876882 1 0.000 0.929 1.000 0.000
#> GSM876883 1 0.969 0.430 0.604 0.396
#> GSM876884 1 0.000 0.929 1.000 0.000
#> GSM876885 1 0.969 0.430 0.604 0.396
#> GSM876857 1 0.000 0.929 1.000 0.000
#> GSM876858 2 0.000 1.000 0.000 1.000
#> GSM876859 2 0.000 1.000 0.000 1.000
#> GSM876860 2 0.000 1.000 0.000 1.000
#> GSM876861 2 0.000 1.000 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 3 0.000 1.000 0.000 0.000 1.00
#> GSM876887 3 0.000 1.000 0.000 0.000 1.00
#> GSM876888 3 0.000 1.000 0.000 0.000 1.00
#> GSM876889 3 0.000 1.000 0.000 0.000 1.00
#> GSM876890 3 0.000 1.000 0.000 0.000 1.00
#> GSM876891 3 0.000 1.000 0.000 0.000 1.00
#> GSM876862 1 0.000 0.971 1.000 0.000 0.00
#> GSM876863 1 0.000 0.971 1.000 0.000 0.00
#> GSM876864 1 0.000 0.971 1.000 0.000 0.00
#> GSM876865 1 0.000 0.971 1.000 0.000 0.00
#> GSM876866 1 0.000 0.971 1.000 0.000 0.00
#> GSM876867 1 0.000 0.971 1.000 0.000 0.00
#> GSM876838 2 0.000 0.970 0.000 1.000 0.00
#> GSM876839 2 0.000 0.970 0.000 1.000 0.00
#> GSM876840 2 0.000 0.970 0.000 1.000 0.00
#> GSM876841 2 0.000 0.970 0.000 1.000 0.00
#> GSM876842 2 0.000 0.970 0.000 1.000 0.00
#> GSM876843 2 0.000 0.970 0.000 1.000 0.00
#> GSM876892 3 0.000 1.000 0.000 0.000 1.00
#> GSM876893 3 0.000 1.000 0.000 0.000 1.00
#> GSM876894 3 0.000 1.000 0.000 0.000 1.00
#> GSM876895 2 0.867 0.459 0.252 0.588 0.16
#> GSM876896 3 0.000 1.000 0.000 0.000 1.00
#> GSM876897 3 0.000 1.000 0.000 0.000 1.00
#> GSM876868 1 0.000 0.971 1.000 0.000 0.00
#> GSM876869 1 0.000 0.971 1.000 0.000 0.00
#> GSM876870 1 0.000 0.971 1.000 0.000 0.00
#> GSM876871 1 0.000 0.971 1.000 0.000 0.00
#> GSM876872 1 0.400 0.829 0.840 0.000 0.16
#> GSM876873 1 0.400 0.829 0.840 0.000 0.16
#> GSM876844 2 0.000 0.970 0.000 1.000 0.00
#> GSM876845 2 0.000 0.970 0.000 1.000 0.00
#> GSM876846 2 0.000 0.970 0.000 1.000 0.00
#> GSM876847 2 0.000 0.970 0.000 1.000 0.00
#> GSM876848 2 0.400 0.805 0.000 0.840 0.16
#> GSM876849 2 0.400 0.805 0.000 0.840 0.16
#> GSM876898 3 0.000 1.000 0.000 0.000 1.00
#> GSM876899 3 0.000 1.000 0.000 0.000 1.00
#> GSM876900 3 0.000 1.000 0.000 0.000 1.00
#> GSM876901 3 0.000 1.000 0.000 0.000 1.00
#> GSM876902 3 0.000 1.000 0.000 0.000 1.00
#> GSM876903 3 0.000 1.000 0.000 0.000 1.00
#> GSM876904 3 0.000 1.000 0.000 0.000 1.00
#> GSM876874 1 0.000 0.971 1.000 0.000 0.00
#> GSM876875 1 0.000 0.971 1.000 0.000 0.00
#> GSM876876 1 0.000 0.971 1.000 0.000 0.00
#> GSM876877 1 0.000 0.971 1.000 0.000 0.00
#> GSM876878 1 0.000 0.971 1.000 0.000 0.00
#> GSM876879 1 0.000 0.971 1.000 0.000 0.00
#> GSM876880 1 0.000 0.971 1.000 0.000 0.00
#> GSM876850 2 0.000 0.970 0.000 1.000 0.00
#> GSM876851 2 0.000 0.970 0.000 1.000 0.00
#> GSM876852 2 0.000 0.970 0.000 1.000 0.00
#> GSM876853 2 0.000 0.970 0.000 1.000 0.00
#> GSM876854 2 0.000 0.970 0.000 1.000 0.00
#> GSM876855 2 0.000 0.970 0.000 1.000 0.00
#> GSM876856 2 0.000 0.970 0.000 1.000 0.00
#> GSM876905 3 0.000 1.000 0.000 0.000 1.00
#> GSM876906 3 0.000 1.000 0.000 0.000 1.00
#> GSM876907 3 0.000 1.000 0.000 0.000 1.00
#> GSM876908 3 0.000 1.000 0.000 0.000 1.00
#> GSM876909 3 0.000 1.000 0.000 0.000 1.00
#> GSM876881 2 0.000 0.970 0.000 1.000 0.00
#> GSM876882 1 0.000 0.971 1.000 0.000 0.00
#> GSM876883 1 0.400 0.829 0.840 0.000 0.16
#> GSM876884 1 0.000 0.971 1.000 0.000 0.00
#> GSM876885 1 0.400 0.829 0.840 0.000 0.16
#> GSM876857 1 0.000 0.971 1.000 0.000 0.00
#> GSM876858 2 0.000 0.970 0.000 1.000 0.00
#> GSM876859 2 0.000 0.970 0.000 1.000 0.00
#> GSM876860 2 0.000 0.970 0.000 1.000 0.00
#> GSM876861 2 0.000 0.970 0.000 1.000 0.00
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876887 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876888 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876889 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876890 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876891 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876862 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM876863 1 0.0188 0.991 0.996 0.000 0.000 0.004
#> GSM876864 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM876866 4 0.4933 0.432 0.432 0.000 0.000 0.568
#> GSM876867 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876839 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876840 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876841 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876842 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876843 4 0.4477 0.467 0.000 0.312 0.000 0.688
#> GSM876892 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876893 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876894 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876895 3 0.6352 0.306 0.016 0.040 0.576 0.368
#> GSM876896 4 0.0000 0.821 0.000 0.000 0.000 1.000
#> GSM876897 4 0.0000 0.821 0.000 0.000 0.000 1.000
#> GSM876868 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 0.821 0.000 0.000 0.000 1.000
#> GSM876873 4 0.0000 0.821 0.000 0.000 0.000 1.000
#> GSM876844 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876845 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876846 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876847 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876848 4 0.0336 0.818 0.000 0.008 0.000 0.992
#> GSM876849 4 0.0000 0.821 0.000 0.000 0.000 1.000
#> GSM876898 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876899 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876900 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876901 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876902 4 0.0000 0.821 0.000 0.000 0.000 1.000
#> GSM876903 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876904 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876874 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM876875 1 0.1637 0.920 0.940 0.000 0.000 0.060
#> GSM876876 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM876879 4 0.4817 0.526 0.388 0.000 0.000 0.612
#> GSM876880 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876851 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876852 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876853 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876854 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876855 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876856 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876905 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876906 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876907 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876908 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876909 3 0.0000 0.979 0.000 0.000 1.000 0.000
#> GSM876881 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876882 4 0.4277 0.684 0.280 0.000 0.000 0.720
#> GSM876883 4 0.4277 0.684 0.280 0.000 0.000 0.720
#> GSM876884 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM876885 4 0.4277 0.684 0.280 0.000 0.000 0.720
#> GSM876857 1 0.0000 0.995 1.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876859 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876860 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876861 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
#> GSM876886 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876887 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876888 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876889 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876890 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876891 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876862 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0963 0.967 0.964 0.000 0.000 0.000 0.036
#> GSM876864 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0404 0.986 0.988 0.000 0.000 0.000 0.012
#> GSM876866 5 0.3291 0.886 0.088 0.000 0.000 0.064 0.848
#> GSM876867 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM876840 2 0.1478 0.956 0.000 0.936 0.000 0.000 0.064
#> GSM876841 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM876843 4 0.2471 0.769 0.000 0.136 0.000 0.864 0.000
#> GSM876892 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876893 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876894 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876895 3 0.5642 0.466 0.000 0.000 0.624 0.240 0.136
#> GSM876896 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM876897 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM876868 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM876873 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM876844 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM876846 2 0.1478 0.956 0.000 0.936 0.000 0.000 0.064
#> GSM876847 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM876848 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM876849 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM876898 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876899 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876900 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876901 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876902 4 0.0000 0.968 0.000 0.000 0.000 1.000 0.000
#> GSM876903 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876904 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876874 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM876875 5 0.3454 0.874 0.100 0.000 0.000 0.064 0.836
#> GSM876876 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.1043 0.963 0.960 0.000 0.000 0.000 0.040
#> GSM876879 5 0.1478 0.924 0.000 0.000 0.000 0.064 0.936
#> GSM876880 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM876852 2 0.1478 0.956 0.000 0.936 0.000 0.000 0.064
#> GSM876853 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM876854 2 0.1478 0.956 0.000 0.936 0.000 0.000 0.064
#> GSM876855 2 0.1478 0.956 0.000 0.936 0.000 0.000 0.064
#> GSM876856 2 0.1478 0.956 0.000 0.936 0.000 0.000 0.064
#> GSM876905 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876906 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876907 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876908 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876909 3 0.0000 0.981 0.000 0.000 1.000 0.000 0.000
#> GSM876881 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM876882 5 0.1608 0.926 0.000 0.000 0.000 0.072 0.928
#> GSM876883 5 0.1851 0.922 0.000 0.000 0.000 0.088 0.912
#> GSM876884 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM876885 5 0.2377 0.892 0.000 0.000 0.000 0.128 0.872
#> GSM876857 1 0.0000 0.994 1.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM876859 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM876860 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000
#> GSM876861 2 0.0000 0.983 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
#> GSM876886 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876887 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876888 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876889 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876890 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876891 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876862 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 6 0.2941 0.709 0.220 0.000 0.000 0.000 0.000 0.780
#> GSM876864 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0363 0.980 0.988 0.000 0.000 0.000 0.000 0.012
#> GSM876866 6 0.0632 0.903 0.024 0.000 0.000 0.000 0.000 0.976
#> GSM876867 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876840 5 0.0937 0.965 0.000 0.040 0.000 0.000 0.960 0.000
#> GSM876841 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876842 2 0.0713 0.979 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM876843 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876892 3 0.0363 0.972 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM876893 3 0.0363 0.972 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM876894 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876895 3 0.4101 0.522 0.000 0.000 0.664 0.308 0.000 0.028
#> GSM876896 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876897 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876868 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876873 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876844 2 0.0713 0.979 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM876845 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876846 5 0.0937 0.965 0.000 0.040 0.000 0.000 0.960 0.000
#> GSM876847 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876848 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876849 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876898 3 0.0363 0.972 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM876899 3 0.0713 0.963 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM876900 3 0.0363 0.972 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM876901 3 0.0363 0.972 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM876902 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876903 3 0.0713 0.963 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM876904 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876874 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876875 6 0.0713 0.902 0.028 0.000 0.000 0.000 0.000 0.972
#> GSM876876 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.2092 0.856 0.876 0.000 0.000 0.000 0.000 0.124
#> GSM876879 6 0.0547 0.903 0.020 0.000 0.000 0.000 0.000 0.980
#> GSM876880 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876852 5 0.2562 0.821 0.000 0.172 0.000 0.000 0.828 0.000
#> GSM876853 2 0.0000 0.985 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876854 5 0.0937 0.965 0.000 0.040 0.000 0.000 0.960 0.000
#> GSM876855 5 0.0937 0.965 0.000 0.040 0.000 0.000 0.960 0.000
#> GSM876856 5 0.0937 0.965 0.000 0.040 0.000 0.000 0.960 0.000
#> GSM876905 3 0.0363 0.972 0.000 0.000 0.988 0.000 0.012 0.000
#> GSM876906 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876907 3 0.0713 0.963 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM876908 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876909 3 0.0713 0.963 0.000 0.000 0.972 0.000 0.028 0.000
#> GSM876881 2 0.0713 0.979 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM876882 6 0.0291 0.897 0.004 0.000 0.000 0.004 0.000 0.992
#> GSM876883 6 0.1075 0.881 0.000 0.000 0.000 0.048 0.000 0.952
#> GSM876884 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876885 6 0.2562 0.766 0.000 0.000 0.000 0.172 0.000 0.828
#> GSM876857 1 0.0000 0.990 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0713 0.979 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM876859 2 0.0260 0.984 0.000 0.992 0.000 0.000 0.008 0.000
#> GSM876860 2 0.0713 0.979 0.000 0.972 0.000 0.000 0.028 0.000
#> GSM876861 2 0.1075 0.963 0.000 0.952 0.000 0.000 0.048 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> CV:mclust 68 0.876 1.70e-13 2
#> CV:mclust 71 1.000 2.81e-27 3
#> CV:mclust 69 0.345 8.64e-21 4
#> CV:mclust 71 0.118 3.49e-21 5
#> CV:mclust 72 0.120 2.01e-20 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 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'CV' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.971 0.951 0.979 0.4779 0.512 0.512
#> 3 3 0.994 0.955 0.973 0.4094 0.753 0.544
#> 4 4 0.843 0.518 0.874 0.0645 0.944 0.834
#> 5 5 0.832 0.781 0.887 0.0786 0.887 0.646
#> 6 6 0.801 0.741 0.857 0.0261 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] 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
#> GSM876886 1 0.000 1.000 1.000 0.000
#> GSM876887 1 0.000 1.000 1.000 0.000
#> GSM876888 1 0.000 1.000 1.000 0.000
#> GSM876889 1 0.000 1.000 1.000 0.000
#> GSM876890 1 0.000 1.000 1.000 0.000
#> GSM876891 1 0.000 1.000 1.000 0.000
#> GSM876862 1 0.000 1.000 1.000 0.000
#> GSM876863 1 0.000 1.000 1.000 0.000
#> GSM876864 1 0.000 1.000 1.000 0.000
#> GSM876865 1 0.000 1.000 1.000 0.000
#> GSM876866 1 0.000 1.000 1.000 0.000
#> GSM876867 1 0.000 1.000 1.000 0.000
#> GSM876838 2 0.000 0.945 0.000 1.000
#> GSM876839 2 0.000 0.945 0.000 1.000
#> GSM876840 2 0.000 0.945 0.000 1.000
#> GSM876841 2 0.000 0.945 0.000 1.000
#> GSM876842 2 0.000 0.945 0.000 1.000
#> GSM876843 2 0.000 0.945 0.000 1.000
#> GSM876892 1 0.000 1.000 1.000 0.000
#> GSM876893 1 0.000 1.000 1.000 0.000
#> GSM876894 1 0.000 1.000 1.000 0.000
#> GSM876895 2 0.998 0.194 0.472 0.528
#> GSM876896 1 0.000 1.000 1.000 0.000
#> GSM876897 2 0.760 0.732 0.220 0.780
#> GSM876868 1 0.000 1.000 1.000 0.000
#> GSM876869 1 0.000 1.000 1.000 0.000
#> GSM876870 1 0.000 1.000 1.000 0.000
#> GSM876871 1 0.000 1.000 1.000 0.000
#> GSM876872 1 0.000 1.000 1.000 0.000
#> GSM876873 1 0.000 1.000 1.000 0.000
#> GSM876844 2 0.000 0.945 0.000 1.000
#> GSM876845 2 0.000 0.945 0.000 1.000
#> GSM876846 2 0.000 0.945 0.000 1.000
#> GSM876847 2 0.000 0.945 0.000 1.000
#> GSM876848 2 0.000 0.945 0.000 1.000
#> GSM876849 2 0.000 0.945 0.000 1.000
#> GSM876898 1 0.000 1.000 1.000 0.000
#> GSM876899 1 0.000 1.000 1.000 0.000
#> GSM876900 1 0.000 1.000 1.000 0.000
#> GSM876901 1 0.000 1.000 1.000 0.000
#> GSM876902 1 0.000 1.000 1.000 0.000
#> GSM876903 2 0.781 0.716 0.232 0.768
#> GSM876904 1 0.000 1.000 1.000 0.000
#> GSM876874 1 0.000 1.000 1.000 0.000
#> GSM876875 1 0.000 1.000 1.000 0.000
#> GSM876876 1 0.000 1.000 1.000 0.000
#> GSM876877 1 0.000 1.000 1.000 0.000
#> GSM876878 1 0.000 1.000 1.000 0.000
#> GSM876879 1 0.000 1.000 1.000 0.000
#> GSM876880 1 0.000 1.000 1.000 0.000
#> GSM876850 2 0.000 0.945 0.000 1.000
#> GSM876851 2 0.000 0.945 0.000 1.000
#> GSM876852 2 0.000 0.945 0.000 1.000
#> GSM876853 2 0.000 0.945 0.000 1.000
#> GSM876854 2 0.000 0.945 0.000 1.000
#> GSM876855 2 0.000 0.945 0.000 1.000
#> GSM876856 2 0.000 0.945 0.000 1.000
#> GSM876905 1 0.000 1.000 1.000 0.000
#> GSM876906 1 0.000 1.000 1.000 0.000
#> GSM876907 2 0.985 0.326 0.428 0.572
#> GSM876908 1 0.000 1.000 1.000 0.000
#> GSM876909 2 0.625 0.808 0.156 0.844
#> GSM876881 2 0.000 0.945 0.000 1.000
#> GSM876882 1 0.000 1.000 1.000 0.000
#> GSM876883 1 0.000 1.000 1.000 0.000
#> GSM876884 1 0.000 1.000 1.000 0.000
#> GSM876885 1 0.000 1.000 1.000 0.000
#> GSM876857 1 0.000 1.000 1.000 0.000
#> GSM876858 2 0.000 0.945 0.000 1.000
#> GSM876859 2 0.000 0.945 0.000 1.000
#> GSM876860 2 0.000 0.945 0.000 1.000
#> GSM876861 2 0.000 0.945 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 3 0.2356 0.945 0.072 0.000 0.928
#> GSM876887 3 0.1289 0.966 0.032 0.000 0.968
#> GSM876888 3 0.3816 0.865 0.148 0.000 0.852
#> GSM876889 3 0.0592 0.968 0.012 0.000 0.988
#> GSM876890 3 0.0592 0.968 0.012 0.000 0.988
#> GSM876891 3 0.0592 0.968 0.012 0.000 0.988
#> GSM876862 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876863 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876864 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876865 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876866 1 0.0592 0.963 0.988 0.000 0.012
#> GSM876867 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876838 2 0.0000 0.988 0.000 1.000 0.000
#> GSM876839 2 0.0000 0.988 0.000 1.000 0.000
#> GSM876840 2 0.0592 0.985 0.000 0.988 0.012
#> GSM876841 2 0.0000 0.988 0.000 1.000 0.000
#> GSM876842 2 0.0000 0.988 0.000 1.000 0.000
#> GSM876843 2 0.0592 0.985 0.000 0.988 0.012
#> GSM876892 3 0.1411 0.965 0.036 0.000 0.964
#> GSM876893 3 0.1860 0.958 0.052 0.000 0.948
#> GSM876894 3 0.0592 0.968 0.012 0.000 0.988
#> GSM876895 2 0.4228 0.817 0.148 0.844 0.008
#> GSM876896 3 0.0000 0.962 0.000 0.000 1.000
#> GSM876897 3 0.0424 0.959 0.000 0.008 0.992
#> GSM876868 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876869 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876870 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876871 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876872 1 0.5254 0.671 0.736 0.000 0.264
#> GSM876873 1 0.6026 0.441 0.624 0.000 0.376
#> GSM876844 2 0.0000 0.988 0.000 1.000 0.000
#> GSM876845 2 0.0000 0.988 0.000 1.000 0.000
#> GSM876846 2 0.0592 0.985 0.000 0.988 0.012
#> GSM876847 2 0.0000 0.988 0.000 1.000 0.000
#> GSM876848 2 0.0592 0.985 0.000 0.988 0.012
#> GSM876849 2 0.2448 0.930 0.000 0.924 0.076
#> GSM876898 3 0.2878 0.927 0.096 0.000 0.904
#> GSM876899 3 0.0592 0.968 0.012 0.000 0.988
#> GSM876900 3 0.1411 0.965 0.036 0.000 0.964
#> GSM876901 3 0.1753 0.960 0.048 0.000 0.952
#> GSM876902 3 0.0592 0.968 0.012 0.000 0.988
#> GSM876903 3 0.1129 0.959 0.004 0.020 0.976
#> GSM876904 3 0.2711 0.932 0.088 0.000 0.912
#> GSM876874 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876875 1 0.0592 0.963 0.988 0.000 0.012
#> GSM876876 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876877 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876878 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876879 1 0.0592 0.963 0.988 0.000 0.012
#> GSM876880 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876850 2 0.0000 0.988 0.000 1.000 0.000
#> GSM876851 2 0.0000 0.988 0.000 1.000 0.000
#> GSM876852 2 0.0592 0.985 0.000 0.988 0.012
#> GSM876853 2 0.0000 0.988 0.000 1.000 0.000
#> GSM876854 2 0.0592 0.985 0.000 0.988 0.012
#> GSM876855 2 0.0592 0.985 0.000 0.988 0.012
#> GSM876856 2 0.0592 0.985 0.000 0.988 0.012
#> GSM876905 3 0.2165 0.951 0.064 0.000 0.936
#> GSM876906 3 0.0592 0.968 0.012 0.000 0.988
#> GSM876907 3 0.0983 0.961 0.004 0.016 0.980
#> GSM876908 3 0.0592 0.968 0.012 0.000 0.988
#> GSM876909 3 0.2066 0.932 0.000 0.060 0.940
#> GSM876881 2 0.0000 0.988 0.000 1.000 0.000
#> GSM876882 1 0.0747 0.960 0.984 0.000 0.016
#> GSM876883 1 0.1031 0.955 0.976 0.000 0.024
#> GSM876884 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876885 1 0.1031 0.955 0.976 0.000 0.024
#> GSM876857 1 0.0000 0.968 1.000 0.000 0.000
#> GSM876858 2 0.0000 0.988 0.000 1.000 0.000
#> GSM876859 2 0.0000 0.988 0.000 1.000 0.000
#> GSM876860 2 0.0000 0.988 0.000 1.000 0.000
#> GSM876861 2 0.0000 0.988 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.4941 -0.46024 0.000 0.000 0.564 0.436
#> GSM876887 3 0.4877 -0.37000 0.000 0.000 0.592 0.408
#> GSM876888 4 0.4977 0.69078 0.000 0.000 0.460 0.540
#> GSM876889 3 0.4830 -0.38216 0.000 0.000 0.608 0.392
#> GSM876890 3 0.4877 -0.37000 0.000 0.000 0.592 0.408
#> GSM876891 3 0.4866 -0.36680 0.000 0.000 0.596 0.404
#> GSM876862 1 0.0188 0.99433 0.996 0.000 0.000 0.004
#> GSM876863 1 0.0336 0.99329 0.992 0.000 0.000 0.008
#> GSM876864 1 0.0188 0.99433 0.996 0.000 0.000 0.004
#> GSM876865 1 0.0000 0.99437 1.000 0.000 0.000 0.000
#> GSM876866 1 0.0336 0.99329 0.992 0.000 0.000 0.008
#> GSM876867 1 0.0188 0.99433 0.996 0.000 0.000 0.004
#> GSM876838 2 0.0000 0.90778 0.000 1.000 0.000 0.000
#> GSM876839 2 0.1118 0.90735 0.000 0.964 0.000 0.036
#> GSM876840 2 0.1022 0.90208 0.000 0.968 0.000 0.032
#> GSM876841 2 0.1389 0.90610 0.000 0.952 0.000 0.048
#> GSM876842 2 0.0000 0.90778 0.000 1.000 0.000 0.000
#> GSM876843 2 0.2131 0.88769 0.000 0.932 0.032 0.036
#> GSM876892 3 0.4933 -0.44325 0.000 0.000 0.568 0.432
#> GSM876893 3 0.4981 -0.58318 0.000 0.000 0.536 0.464
#> GSM876894 3 0.4877 -0.37000 0.000 0.000 0.592 0.408
#> GSM876895 2 0.6511 0.69929 0.084 0.596 0.004 0.316
#> GSM876896 3 0.0469 -0.00707 0.000 0.000 0.988 0.012
#> GSM876897 3 0.1211 -0.00155 0.000 0.000 0.960 0.040
#> GSM876868 1 0.0188 0.99433 0.996 0.000 0.000 0.004
#> GSM876869 1 0.0188 0.99433 0.996 0.000 0.000 0.004
#> GSM876870 1 0.0188 0.99399 0.996 0.000 0.000 0.004
#> GSM876871 1 0.0188 0.99433 0.996 0.000 0.000 0.004
#> GSM876872 3 0.5406 -0.36012 0.480 0.000 0.508 0.012
#> GSM876873 3 0.5217 -0.10973 0.380 0.000 0.608 0.012
#> GSM876844 2 0.0000 0.90778 0.000 1.000 0.000 0.000
#> GSM876845 2 0.1474 0.90555 0.000 0.948 0.000 0.052
#> GSM876846 2 0.0469 0.90648 0.000 0.988 0.000 0.012
#> GSM876847 2 0.3356 0.87027 0.000 0.824 0.000 0.176
#> GSM876848 2 0.5200 0.70235 0.000 0.700 0.264 0.036
#> GSM876849 2 0.6387 0.50859 0.008 0.532 0.412 0.048
#> GSM876898 4 0.4998 0.68303 0.000 0.000 0.488 0.512
#> GSM876899 3 0.4877 -0.37000 0.000 0.000 0.592 0.408
#> GSM876900 3 0.4925 -0.42926 0.000 0.000 0.572 0.428
#> GSM876901 3 0.4948 -0.48238 0.000 0.000 0.560 0.440
#> GSM876902 3 0.0000 -0.01319 0.000 0.000 1.000 0.000
#> GSM876903 3 0.4804 -0.39615 0.000 0.000 0.616 0.384
#> GSM876904 3 0.5000 -0.72668 0.000 0.000 0.504 0.496
#> GSM876874 1 0.0188 0.99433 0.996 0.000 0.000 0.004
#> GSM876875 1 0.0336 0.99329 0.992 0.000 0.000 0.008
#> GSM876876 1 0.0000 0.99437 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0188 0.99433 0.996 0.000 0.000 0.004
#> GSM876878 1 0.0336 0.99329 0.992 0.000 0.000 0.008
#> GSM876879 1 0.0469 0.99165 0.988 0.000 0.000 0.012
#> GSM876880 1 0.0188 0.99433 0.996 0.000 0.000 0.004
#> GSM876850 2 0.4008 0.83171 0.000 0.756 0.000 0.244
#> GSM876851 2 0.1389 0.90610 0.000 0.952 0.000 0.048
#> GSM876852 2 0.0707 0.90523 0.000 0.980 0.000 0.020
#> GSM876853 2 0.0592 0.90828 0.000 0.984 0.000 0.016
#> GSM876854 2 0.0592 0.90584 0.000 0.984 0.000 0.016
#> GSM876855 2 0.1022 0.90208 0.000 0.968 0.000 0.032
#> GSM876856 2 0.0707 0.90524 0.000 0.980 0.000 0.020
#> GSM876905 3 0.4977 -0.56701 0.000 0.000 0.540 0.460
#> GSM876906 3 0.4855 -0.36972 0.000 0.000 0.600 0.400
#> GSM876907 3 0.4925 -0.50671 0.000 0.000 0.572 0.428
#> GSM876908 3 0.4866 -0.36680 0.000 0.000 0.596 0.404
#> GSM876909 4 0.4992 0.61596 0.000 0.000 0.476 0.524
#> GSM876881 2 0.4564 0.77762 0.000 0.672 0.000 0.328
#> GSM876882 1 0.0469 0.99165 0.988 0.000 0.000 0.012
#> GSM876883 1 0.0804 0.98689 0.980 0.000 0.008 0.012
#> GSM876884 1 0.0336 0.99329 0.992 0.000 0.000 0.008
#> GSM876885 1 0.0804 0.98689 0.980 0.000 0.008 0.012
#> GSM876857 1 0.0188 0.99433 0.996 0.000 0.000 0.004
#> GSM876858 2 0.3266 0.87459 0.000 0.832 0.000 0.168
#> GSM876859 2 0.2760 0.88876 0.000 0.872 0.000 0.128
#> GSM876860 2 0.3074 0.88079 0.000 0.848 0.000 0.152
#> GSM876861 2 0.3024 0.88221 0.000 0.852 0.000 0.148
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM876886 3 0.1731 0.8725 0.004 0.000 0.932 0.060 0.004
#> GSM876887 3 0.0963 0.8873 0.000 0.000 0.964 0.036 0.000
#> GSM876888 3 0.4017 0.6640 0.004 0.000 0.736 0.248 0.012
#> GSM876889 3 0.1608 0.8769 0.000 0.000 0.928 0.072 0.000
#> GSM876890 3 0.0880 0.8879 0.000 0.000 0.968 0.032 0.000
#> GSM876891 3 0.1410 0.8815 0.000 0.000 0.940 0.060 0.000
#> GSM876862 1 0.1195 0.9203 0.960 0.000 0.000 0.028 0.012
#> GSM876863 1 0.0162 0.9309 0.996 0.000 0.000 0.004 0.000
#> GSM876864 1 0.1597 0.9089 0.940 0.000 0.000 0.048 0.012
#> GSM876865 1 0.0324 0.9310 0.992 0.000 0.000 0.004 0.004
#> GSM876866 1 0.0162 0.9309 0.996 0.000 0.000 0.004 0.000
#> GSM876867 1 0.0510 0.9291 0.984 0.000 0.000 0.016 0.000
#> GSM876838 2 0.0880 0.8667 0.000 0.968 0.000 0.000 0.032
#> GSM876839 2 0.1792 0.8374 0.000 0.916 0.000 0.000 0.084
#> GSM876840 2 0.0162 0.8653 0.000 0.996 0.000 0.004 0.000
#> GSM876841 2 0.4210 0.3242 0.000 0.588 0.000 0.000 0.412
#> GSM876842 2 0.0880 0.8667 0.000 0.968 0.000 0.000 0.032
#> GSM876843 2 0.0510 0.8585 0.000 0.984 0.000 0.016 0.000
#> GSM876892 3 0.0963 0.8828 0.000 0.000 0.964 0.036 0.000
#> GSM876893 3 0.2068 0.8563 0.004 0.000 0.904 0.092 0.000
#> GSM876894 3 0.1608 0.8769 0.000 0.000 0.928 0.072 0.000
#> GSM876895 5 0.3801 0.7135 0.112 0.032 0.000 0.028 0.828
#> GSM876896 4 0.3999 0.5645 0.000 0.000 0.344 0.656 0.000
#> GSM876897 4 0.4118 0.5700 0.000 0.004 0.336 0.660 0.000
#> GSM876868 1 0.2727 0.8614 0.888 0.000 0.012 0.080 0.020
#> GSM876869 1 0.1648 0.9097 0.940 0.000 0.000 0.040 0.020
#> GSM876870 1 0.0162 0.9309 0.996 0.000 0.000 0.004 0.000
#> GSM876871 1 0.0324 0.9310 0.992 0.000 0.000 0.004 0.004
#> GSM876872 4 0.4192 0.3060 0.404 0.000 0.000 0.596 0.000
#> GSM876873 4 0.4639 0.4006 0.368 0.000 0.020 0.612 0.000
#> GSM876844 2 0.0794 0.8677 0.000 0.972 0.000 0.000 0.028
#> GSM876845 2 0.4201 0.3375 0.000 0.592 0.000 0.000 0.408
#> GSM876846 2 0.0404 0.8694 0.000 0.988 0.000 0.000 0.012
#> GSM876847 5 0.3561 0.6125 0.000 0.260 0.000 0.000 0.740
#> GSM876848 2 0.0703 0.8530 0.000 0.976 0.000 0.024 0.000
#> GSM876849 2 0.4415 0.3586 0.008 0.604 0.000 0.388 0.000
#> GSM876898 3 0.2179 0.8443 0.000 0.000 0.888 0.112 0.000
#> GSM876899 3 0.1608 0.8769 0.000 0.000 0.928 0.072 0.000
#> GSM876900 3 0.0162 0.8884 0.000 0.000 0.996 0.004 0.000
#> GSM876901 3 0.0404 0.8879 0.000 0.000 0.988 0.012 0.000
#> GSM876902 4 0.4045 0.5481 0.000 0.000 0.356 0.644 0.000
#> GSM876903 3 0.5290 0.5102 0.000 0.000 0.676 0.140 0.184
#> GSM876904 3 0.1965 0.8564 0.000 0.000 0.904 0.096 0.000
#> GSM876874 1 0.1701 0.9073 0.936 0.000 0.000 0.048 0.016
#> GSM876875 1 0.0290 0.9300 0.992 0.000 0.000 0.008 0.000
#> GSM876876 1 0.0404 0.9300 0.988 0.000 0.000 0.012 0.000
#> GSM876877 1 0.0771 0.9273 0.976 0.000 0.000 0.020 0.004
#> GSM876878 1 0.0290 0.9300 0.992 0.000 0.000 0.008 0.000
#> GSM876879 1 0.0290 0.9300 0.992 0.000 0.000 0.008 0.000
#> GSM876880 1 0.0290 0.9306 0.992 0.000 0.000 0.008 0.000
#> GSM876850 5 0.3586 0.6045 0.000 0.264 0.000 0.000 0.736
#> GSM876851 2 0.3586 0.6348 0.000 0.736 0.000 0.000 0.264
#> GSM876852 2 0.0510 0.8694 0.000 0.984 0.000 0.000 0.016
#> GSM876853 2 0.2329 0.8053 0.000 0.876 0.000 0.000 0.124
#> GSM876854 2 0.0290 0.8690 0.000 0.992 0.000 0.000 0.008
#> GSM876855 2 0.0000 0.8669 0.000 1.000 0.000 0.000 0.000
#> GSM876856 2 0.0162 0.8682 0.000 0.996 0.000 0.000 0.004
#> GSM876905 3 0.1704 0.8702 0.004 0.000 0.928 0.068 0.000
#> GSM876906 3 0.1792 0.8688 0.000 0.000 0.916 0.084 0.000
#> GSM876907 5 0.4630 0.3023 0.000 0.000 0.396 0.016 0.588
#> GSM876908 3 0.1732 0.8719 0.000 0.000 0.920 0.080 0.000
#> GSM876909 5 0.3612 0.5903 0.000 0.000 0.228 0.008 0.764
#> GSM876881 5 0.1270 0.8132 0.000 0.052 0.000 0.000 0.948
#> GSM876882 1 0.0290 0.9300 0.992 0.000 0.000 0.008 0.000
#> GSM876883 1 0.3876 0.4413 0.684 0.000 0.000 0.316 0.000
#> GSM876884 1 0.0162 0.9309 0.996 0.000 0.000 0.004 0.000
#> GSM876885 1 0.4262 0.0448 0.560 0.000 0.000 0.440 0.000
#> GSM876857 1 0.1364 0.9158 0.952 0.000 0.000 0.036 0.012
#> GSM876858 5 0.0963 0.8167 0.000 0.036 0.000 0.000 0.964
#> GSM876859 5 0.0963 0.8167 0.000 0.036 0.000 0.000 0.964
#> GSM876860 5 0.0963 0.8167 0.000 0.036 0.000 0.000 0.964
#> GSM876861 5 0.1041 0.8145 0.000 0.032 0.000 0.004 0.964
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM876886 3 0.1364 0.9225 0.020 0.000 0.952 0.012 0.000 NA
#> GSM876887 3 0.0603 0.9323 0.004 0.000 0.980 0.016 0.000 NA
#> GSM876888 3 0.2365 0.8802 0.024 0.000 0.896 0.012 0.000 NA
#> GSM876889 3 0.1075 0.9221 0.000 0.000 0.952 0.048 0.000 NA
#> GSM876890 3 0.0547 0.9309 0.000 0.000 0.980 0.020 0.000 NA
#> GSM876891 3 0.0632 0.9301 0.000 0.000 0.976 0.024 0.000 NA
#> GSM876862 1 0.1910 0.8124 0.892 0.000 0.000 0.000 0.000 NA
#> GSM876863 1 0.0603 0.8420 0.980 0.000 0.000 0.004 0.000 NA
#> GSM876864 1 0.2300 0.7947 0.856 0.000 0.000 0.000 0.000 NA
#> GSM876865 1 0.0790 0.8424 0.968 0.000 0.000 0.000 0.000 NA
#> GSM876866 1 0.0508 0.8432 0.984 0.000 0.000 0.004 0.000 NA
#> GSM876867 1 0.1141 0.8332 0.948 0.000 0.000 0.000 0.000 NA
#> GSM876838 2 0.1549 0.8581 0.000 0.936 0.000 0.000 0.020 NA
#> GSM876839 2 0.2384 0.8372 0.000 0.884 0.000 0.000 0.032 NA
#> GSM876840 2 0.1644 0.8382 0.000 0.932 0.000 0.028 0.000 NA
#> GSM876841 2 0.3893 0.7234 0.000 0.768 0.000 0.000 0.140 NA
#> GSM876842 2 0.1594 0.8571 0.000 0.932 0.000 0.000 0.016 NA
#> GSM876843 2 0.3409 0.7273 0.000 0.808 0.000 0.144 0.004 NA
#> GSM876892 3 0.0767 0.9306 0.004 0.000 0.976 0.012 0.000 NA
#> GSM876893 3 0.0964 0.9290 0.004 0.000 0.968 0.012 0.000 NA
#> GSM876894 3 0.1124 0.9242 0.000 0.000 0.956 0.036 0.000 NA
#> GSM876895 5 0.6098 0.5538 0.100 0.068 0.000 0.084 0.668 NA
#> GSM876896 4 0.2135 0.6283 0.000 0.000 0.128 0.872 0.000 NA
#> GSM876897 4 0.2275 0.6250 0.000 0.000 0.096 0.888 0.008 NA
#> GSM876868 1 0.3646 0.6584 0.700 0.000 0.004 0.004 0.000 NA
#> GSM876869 1 0.3101 0.7183 0.756 0.000 0.000 0.000 0.000 NA
#> GSM876870 1 0.0777 0.8407 0.972 0.000 0.000 0.004 0.000 NA
#> GSM876871 1 0.0363 0.8426 0.988 0.000 0.000 0.000 0.000 NA
#> GSM876872 4 0.5501 0.1235 0.336 0.000 0.000 0.520 0.000 NA
#> GSM876873 1 0.5763 0.0957 0.464 0.000 0.000 0.356 0.000 NA
#> GSM876844 2 0.1168 0.8608 0.000 0.956 0.000 0.000 0.016 NA
#> GSM876845 2 0.3977 0.7139 0.000 0.760 0.000 0.000 0.144 NA
#> GSM876846 2 0.2401 0.8171 0.000 0.892 0.000 0.060 0.004 NA
#> GSM876847 5 0.5592 0.2929 0.000 0.368 0.000 0.000 0.484 NA
#> GSM876848 2 0.4628 0.3865 0.000 0.608 0.000 0.344 0.004 NA
#> GSM876849 4 0.4480 0.3034 0.000 0.304 0.000 0.648 0.004 NA
#> GSM876898 3 0.1167 0.9272 0.008 0.000 0.960 0.012 0.000 NA
#> GSM876899 3 0.1471 0.9103 0.000 0.000 0.932 0.064 0.000 NA
#> GSM876900 3 0.0260 0.9333 0.008 0.000 0.992 0.000 0.000 NA
#> GSM876901 3 0.0405 0.9334 0.008 0.000 0.988 0.004 0.000 NA
#> GSM876902 4 0.4136 0.5348 0.000 0.000 0.248 0.708 0.004 NA
#> GSM876903 3 0.6164 0.4220 0.000 0.004 0.600 0.192 0.128 NA
#> GSM876904 3 0.1452 0.9205 0.020 0.000 0.948 0.012 0.000 NA
#> GSM876874 1 0.2178 0.8011 0.868 0.000 0.000 0.000 0.000 NA
#> GSM876875 1 0.1461 0.8305 0.940 0.000 0.000 0.016 0.000 NA
#> GSM876876 1 0.0405 0.8426 0.988 0.000 0.004 0.000 0.000 NA
#> GSM876877 1 0.1075 0.8343 0.952 0.000 0.000 0.000 0.000 NA
#> GSM876878 1 0.0972 0.8388 0.964 0.000 0.000 0.008 0.000 NA
#> GSM876879 1 0.3608 0.7180 0.788 0.000 0.000 0.064 0.000 NA
#> GSM876880 1 0.0363 0.8411 0.988 0.000 0.000 0.000 0.000 NA
#> GSM876850 5 0.5683 0.3380 0.000 0.348 0.000 0.000 0.484 NA
#> GSM876851 2 0.3167 0.7982 0.000 0.832 0.000 0.000 0.072 NA
#> GSM876852 2 0.0405 0.8613 0.000 0.988 0.000 0.004 0.008 NA
#> GSM876853 2 0.2331 0.8392 0.000 0.888 0.000 0.000 0.032 NA
#> GSM876854 2 0.0146 0.8606 0.000 0.996 0.000 0.004 0.000 NA
#> GSM876855 2 0.1401 0.8494 0.000 0.948 0.000 0.020 0.004 NA
#> GSM876856 2 0.1572 0.8404 0.000 0.936 0.000 0.028 0.000 NA
#> GSM876905 3 0.0984 0.9289 0.008 0.000 0.968 0.012 0.000 NA
#> GSM876906 3 0.2106 0.8949 0.000 0.000 0.904 0.064 0.000 NA
#> GSM876907 5 0.4868 0.2196 0.000 0.000 0.396 0.052 0.548 NA
#> GSM876908 3 0.1845 0.9056 0.000 0.000 0.920 0.052 0.000 NA
#> GSM876909 5 0.3232 0.5846 0.000 0.000 0.160 0.008 0.812 NA
#> GSM876881 5 0.3727 0.6594 0.000 0.088 0.000 0.000 0.784 NA
#> GSM876882 1 0.3860 0.6950 0.764 0.000 0.000 0.072 0.000 NA
#> GSM876883 1 0.5437 0.4134 0.576 0.000 0.000 0.228 0.000 NA
#> GSM876884 1 0.1049 0.8378 0.960 0.000 0.000 0.008 0.000 NA
#> GSM876885 1 0.5539 0.3716 0.556 0.000 0.000 0.244 0.000 NA
#> GSM876857 1 0.2730 0.7609 0.808 0.000 0.000 0.000 0.000 NA
#> GSM876858 5 0.0748 0.7030 0.000 0.016 0.000 0.004 0.976 NA
#> GSM876859 5 0.0632 0.7055 0.000 0.024 0.000 0.000 0.976 NA
#> GSM876860 5 0.0603 0.7040 0.000 0.016 0.000 0.000 0.980 NA
#> GSM876861 5 0.0881 0.6967 0.000 0.012 0.000 0.008 0.972 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> CV:NMF 70 0.9468 8.53e-12 2
#> CV:NMF 71 0.9992 4.63e-26 3
#> CV:NMF 50 0.9509 5.03e-16 4
#> CV:NMF 64 0.0262 6.73e-20 5
#> CV:NMF 62 0.0035 2.39e-19 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 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'hclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.719 0.852 0.934 0.4985 0.499 0.499
#> 3 3 0.788 0.854 0.919 0.2489 0.844 0.687
#> 4 4 0.771 0.792 0.862 0.1349 0.949 0.854
#> 5 5 0.798 0.755 0.871 0.0250 0.984 0.947
#> 6 6 0.842 0.845 0.902 0.0831 0.897 0.654
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
#> GSM876886 1 0.000 0.985 1.000 0.000
#> GSM876887 1 0.000 0.985 1.000 0.000
#> GSM876888 1 0.000 0.985 1.000 0.000
#> GSM876889 1 0.971 0.139 0.600 0.400
#> GSM876890 1 0.000 0.985 1.000 0.000
#> GSM876891 2 0.994 0.341 0.456 0.544
#> GSM876862 1 0.000 0.985 1.000 0.000
#> GSM876863 1 0.000 0.985 1.000 0.000
#> GSM876864 1 0.000 0.985 1.000 0.000
#> GSM876865 1 0.000 0.985 1.000 0.000
#> GSM876866 1 0.000 0.985 1.000 0.000
#> GSM876867 1 0.000 0.985 1.000 0.000
#> GSM876838 2 0.000 0.881 0.000 1.000
#> GSM876839 2 0.000 0.881 0.000 1.000
#> GSM876840 2 0.000 0.881 0.000 1.000
#> GSM876841 2 0.000 0.881 0.000 1.000
#> GSM876842 2 0.000 0.881 0.000 1.000
#> GSM876843 2 0.000 0.881 0.000 1.000
#> GSM876892 1 0.000 0.985 1.000 0.000
#> GSM876893 1 0.000 0.985 1.000 0.000
#> GSM876894 2 0.994 0.341 0.456 0.544
#> GSM876895 2 0.929 0.566 0.344 0.656
#> GSM876896 2 0.000 0.881 0.000 1.000
#> GSM876897 2 0.000 0.881 0.000 1.000
#> GSM876868 1 0.000 0.985 1.000 0.000
#> GSM876869 1 0.000 0.985 1.000 0.000
#> GSM876870 1 0.000 0.985 1.000 0.000
#> GSM876871 1 0.000 0.985 1.000 0.000
#> GSM876872 2 0.260 0.858 0.044 0.956
#> GSM876873 2 0.260 0.858 0.044 0.956
#> GSM876844 2 0.000 0.881 0.000 1.000
#> GSM876845 2 0.000 0.881 0.000 1.000
#> GSM876846 2 0.000 0.881 0.000 1.000
#> GSM876847 2 0.000 0.881 0.000 1.000
#> GSM876848 2 0.000 0.881 0.000 1.000
#> GSM876849 2 0.000 0.881 0.000 1.000
#> GSM876898 1 0.000 0.985 1.000 0.000
#> GSM876899 2 0.929 0.566 0.344 0.656
#> GSM876900 1 0.000 0.985 1.000 0.000
#> GSM876901 1 0.000 0.985 1.000 0.000
#> GSM876902 2 0.118 0.873 0.016 0.984
#> GSM876903 2 0.929 0.566 0.344 0.656
#> GSM876904 1 0.000 0.985 1.000 0.000
#> GSM876874 1 0.000 0.985 1.000 0.000
#> GSM876875 1 0.000 0.985 1.000 0.000
#> GSM876876 1 0.000 0.985 1.000 0.000
#> GSM876877 1 0.000 0.985 1.000 0.000
#> GSM876878 1 0.000 0.985 1.000 0.000
#> GSM876879 1 0.000 0.985 1.000 0.000
#> GSM876880 1 0.000 0.985 1.000 0.000
#> GSM876850 2 0.000 0.881 0.000 1.000
#> GSM876851 2 0.000 0.881 0.000 1.000
#> GSM876852 2 0.000 0.881 0.000 1.000
#> GSM876853 2 0.000 0.881 0.000 1.000
#> GSM876854 2 0.000 0.881 0.000 1.000
#> GSM876855 2 0.000 0.881 0.000 1.000
#> GSM876856 2 0.000 0.881 0.000 1.000
#> GSM876905 1 0.000 0.985 1.000 0.000
#> GSM876906 2 0.994 0.341 0.456 0.544
#> GSM876907 2 0.929 0.566 0.344 0.656
#> GSM876908 2 0.994 0.341 0.456 0.544
#> GSM876909 2 0.929 0.566 0.344 0.656
#> GSM876881 2 0.000 0.881 0.000 1.000
#> GSM876882 1 0.000 0.985 1.000 0.000
#> GSM876883 2 0.943 0.509 0.360 0.640
#> GSM876884 1 0.000 0.985 1.000 0.000
#> GSM876885 2 0.943 0.509 0.360 0.640
#> GSM876857 1 0.000 0.985 1.000 0.000
#> GSM876858 2 0.000 0.881 0.000 1.000
#> GSM876859 2 0.000 0.881 0.000 1.000
#> GSM876860 2 0.000 0.881 0.000 1.000
#> GSM876861 2 0.000 0.881 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876887 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876888 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876889 1 0.6180 -0.0831 0.584 0.000 0.416
#> GSM876890 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876891 3 0.6215 0.5153 0.428 0.000 0.572
#> GSM876862 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876863 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876864 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876865 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876866 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876867 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876838 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876839 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876840 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876841 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876842 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876843 3 0.6111 0.2088 0.000 0.396 0.604
#> GSM876892 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876893 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876894 3 0.6215 0.5153 0.428 0.000 0.572
#> GSM876895 3 0.5621 0.6488 0.308 0.000 0.692
#> GSM876896 3 0.3412 0.5935 0.000 0.124 0.876
#> GSM876897 3 0.3412 0.5935 0.000 0.124 0.876
#> GSM876868 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876869 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876870 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876871 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876872 3 0.0424 0.6514 0.008 0.000 0.992
#> GSM876873 3 0.0424 0.6514 0.008 0.000 0.992
#> GSM876844 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876845 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876846 2 0.0892 0.9793 0.000 0.980 0.020
#> GSM876847 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876848 3 0.6095 0.2175 0.000 0.392 0.608
#> GSM876849 3 0.6095 0.2175 0.000 0.392 0.608
#> GSM876898 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876899 3 0.5621 0.6488 0.308 0.000 0.692
#> GSM876900 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876901 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876902 3 0.0892 0.6410 0.000 0.020 0.980
#> GSM876903 3 0.5621 0.6488 0.308 0.000 0.692
#> GSM876904 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876874 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876875 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876876 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876877 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876878 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876879 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876880 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876850 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876851 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876852 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876853 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876854 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876855 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876856 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876905 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876906 3 0.6215 0.5153 0.428 0.000 0.572
#> GSM876907 3 0.5621 0.6488 0.308 0.000 0.692
#> GSM876908 3 0.6215 0.5153 0.428 0.000 0.572
#> GSM876909 3 0.5621 0.6488 0.308 0.000 0.692
#> GSM876881 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876882 1 0.0747 0.9626 0.984 0.000 0.016
#> GSM876883 3 0.5760 0.5615 0.328 0.000 0.672
#> GSM876884 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876885 3 0.5760 0.5615 0.328 0.000 0.672
#> GSM876857 1 0.0000 0.9814 1.000 0.000 0.000
#> GSM876858 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876859 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876860 2 0.0000 0.9990 0.000 1.000 0.000
#> GSM876861 2 0.0000 0.9990 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 1 0.4888 0.578 0.588 0.000 0.412 0.000
#> GSM876887 1 0.4888 0.578 0.588 0.000 0.412 0.000
#> GSM876888 1 0.4888 0.578 0.588 0.000 0.412 0.000
#> GSM876889 3 0.3219 0.637 0.164 0.000 0.836 0.000
#> GSM876890 1 0.4888 0.578 0.588 0.000 0.412 0.000
#> GSM876891 3 0.0336 0.817 0.008 0.000 0.992 0.000
#> GSM876862 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876839 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876840 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876841 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876842 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876843 4 0.4697 0.582 0.000 0.356 0.000 0.644
#> GSM876892 1 0.4888 0.578 0.588 0.000 0.412 0.000
#> GSM876893 1 0.4888 0.578 0.588 0.000 0.412 0.000
#> GSM876894 3 0.0336 0.817 0.008 0.000 0.992 0.000
#> GSM876895 3 0.2530 0.806 0.000 0.000 0.888 0.112
#> GSM876896 4 0.1474 0.715 0.000 0.052 0.000 0.948
#> GSM876897 4 0.1474 0.715 0.000 0.052 0.000 0.948
#> GSM876868 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876872 4 0.3837 0.542 0.000 0.000 0.224 0.776
#> GSM876873 4 0.3837 0.542 0.000 0.000 0.224 0.776
#> GSM876844 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876845 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876846 2 0.0707 0.975 0.000 0.980 0.000 0.020
#> GSM876847 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876848 4 0.4522 0.636 0.000 0.320 0.000 0.680
#> GSM876849 4 0.4522 0.636 0.000 0.320 0.000 0.680
#> GSM876898 1 0.4888 0.578 0.588 0.000 0.412 0.000
#> GSM876899 3 0.2530 0.806 0.000 0.000 0.888 0.112
#> GSM876900 1 0.4888 0.578 0.588 0.000 0.412 0.000
#> GSM876901 1 0.4888 0.578 0.588 0.000 0.412 0.000
#> GSM876902 4 0.2053 0.664 0.000 0.004 0.072 0.924
#> GSM876903 3 0.2530 0.806 0.000 0.000 0.888 0.112
#> GSM876904 1 0.4888 0.578 0.588 0.000 0.412 0.000
#> GSM876874 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876875 1 0.3074 0.751 0.848 0.000 0.152 0.000
#> GSM876876 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876878 1 0.0817 0.795 0.976 0.000 0.024 0.000
#> GSM876879 1 0.3074 0.751 0.848 0.000 0.152 0.000
#> GSM876880 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876851 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876852 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876853 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876854 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876855 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876856 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876905 1 0.4888 0.578 0.588 0.000 0.412 0.000
#> GSM876906 3 0.0336 0.817 0.008 0.000 0.992 0.000
#> GSM876907 3 0.2530 0.806 0.000 0.000 0.888 0.112
#> GSM876908 3 0.0336 0.817 0.008 0.000 0.992 0.000
#> GSM876909 3 0.2530 0.806 0.000 0.000 0.888 0.112
#> GSM876881 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876882 1 0.3494 0.740 0.824 0.000 0.172 0.004
#> GSM876883 3 0.6810 0.438 0.156 0.000 0.596 0.248
#> GSM876884 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876885 3 0.6810 0.438 0.156 0.000 0.596 0.248
#> GSM876857 1 0.0000 0.800 1.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876859 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876860 2 0.0000 0.999 0.000 1.000 0.000 0.000
#> GSM876861 2 0.0000 0.999 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
#> GSM876886 1 0.465 0.583 0.580 0.000 0.016 0.000 0.404
#> GSM876887 1 0.465 0.583 0.580 0.000 0.016 0.000 0.404
#> GSM876888 1 0.465 0.583 0.580 0.000 0.016 0.000 0.404
#> GSM876889 5 0.328 0.557 0.156 0.000 0.020 0.000 0.824
#> GSM876890 1 0.465 0.583 0.580 0.000 0.016 0.000 0.404
#> GSM876891 5 0.000 0.847 0.000 0.000 0.000 0.000 1.000
#> GSM876862 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876867 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876839 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876840 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876841 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876842 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876843 4 0.242 0.618 0.000 0.132 0.000 0.868 0.000
#> GSM876892 1 0.465 0.583 0.580 0.000 0.016 0.000 0.404
#> GSM876893 1 0.465 0.583 0.580 0.000 0.016 0.000 0.404
#> GSM876894 5 0.000 0.847 0.000 0.000 0.000 0.000 1.000
#> GSM876895 5 0.279 0.850 0.000 0.000 0.064 0.056 0.880
#> GSM876896 4 0.430 0.419 0.000 0.000 0.472 0.528 0.000
#> GSM876897 4 0.430 0.419 0.000 0.000 0.472 0.528 0.000
#> GSM876868 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876872 3 0.121 0.298 0.000 0.000 0.960 0.016 0.024
#> GSM876873 3 0.121 0.298 0.000 0.000 0.960 0.016 0.024
#> GSM876844 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876845 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876846 2 0.112 0.952 0.000 0.956 0.000 0.044 0.000
#> GSM876847 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876848 4 0.141 0.679 0.000 0.060 0.000 0.940 0.000
#> GSM876849 4 0.141 0.679 0.000 0.060 0.000 0.940 0.000
#> GSM876898 1 0.465 0.583 0.580 0.000 0.016 0.000 0.404
#> GSM876899 5 0.279 0.850 0.000 0.000 0.064 0.056 0.880
#> GSM876900 1 0.465 0.583 0.580 0.000 0.016 0.000 0.404
#> GSM876901 1 0.465 0.583 0.580 0.000 0.016 0.000 0.404
#> GSM876902 3 0.481 -0.434 0.000 0.000 0.576 0.400 0.024
#> GSM876903 5 0.279 0.850 0.000 0.000 0.064 0.056 0.880
#> GSM876904 1 0.465 0.583 0.580 0.000 0.016 0.000 0.404
#> GSM876874 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.365 0.729 0.816 0.000 0.036 0.004 0.144
#> GSM876876 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.120 0.773 0.960 0.000 0.012 0.000 0.028
#> GSM876879 1 0.365 0.729 0.816 0.000 0.036 0.004 0.144
#> GSM876880 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876851 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876852 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876853 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876854 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876855 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876856 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876905 1 0.465 0.583 0.580 0.000 0.016 0.000 0.404
#> GSM876906 5 0.000 0.847 0.000 0.000 0.000 0.000 1.000
#> GSM876907 5 0.279 0.850 0.000 0.000 0.064 0.056 0.880
#> GSM876908 5 0.000 0.847 0.000 0.000 0.000 0.000 1.000
#> GSM876909 5 0.279 0.850 0.000 0.000 0.064 0.056 0.880
#> GSM876881 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876882 1 0.407 0.715 0.792 0.000 0.060 0.004 0.144
#> GSM876883 3 0.624 0.183 0.124 0.000 0.452 0.004 0.420
#> GSM876884 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876885 3 0.624 0.183 0.124 0.000 0.452 0.004 0.420
#> GSM876857 1 0.000 0.784 1.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876859 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876860 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
#> GSM876861 2 0.000 0.998 0.000 1.000 0.000 0.000 0.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM876886 3 0.2340 0.9488 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM876887 3 0.2340 0.9488 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM876888 3 0.2340 0.9488 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM876889 3 0.3930 0.1130 0.000 0.000 0.576 0.000 0.420 0.004
#> GSM876890 3 0.2340 0.9488 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM876891 5 0.2048 0.8717 0.000 0.000 0.120 0.000 0.880 0.000
#> GSM876862 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876840 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876841 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876843 6 0.4996 0.1527 0.000 0.072 0.000 0.408 0.000 0.520
#> GSM876892 3 0.2340 0.9488 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM876893 3 0.2340 0.9488 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM876894 5 0.2048 0.8717 0.000 0.000 0.120 0.000 0.880 0.000
#> GSM876895 5 0.0000 0.8996 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876896 4 0.1863 0.5697 0.000 0.000 0.000 0.896 0.000 0.104
#> GSM876897 4 0.1863 0.5697 0.000 0.000 0.000 0.896 0.000 0.104
#> GSM876868 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.3774 0.5203 0.000 0.000 0.000 0.592 0.000 0.408
#> GSM876873 4 0.3774 0.5203 0.000 0.000 0.000 0.592 0.000 0.408
#> GSM876844 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876846 2 0.1501 0.9184 0.000 0.924 0.000 0.000 0.000 0.076
#> GSM876847 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876848 6 0.3774 0.1781 0.000 0.000 0.000 0.408 0.000 0.592
#> GSM876849 6 0.3774 0.1781 0.000 0.000 0.000 0.408 0.000 0.592
#> GSM876898 3 0.2340 0.9488 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM876899 5 0.0000 0.8996 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876900 3 0.2340 0.9488 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM876901 3 0.2340 0.9488 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM876902 4 0.0632 0.6052 0.000 0.000 0.000 0.976 0.000 0.024
#> GSM876903 5 0.0000 0.8996 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876904 3 0.2340 0.9488 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM876874 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.3390 0.6685 0.704 0.000 0.296 0.000 0.000 0.000
#> GSM876876 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.1387 0.8970 0.932 0.000 0.068 0.000 0.000 0.000
#> GSM876879 1 0.3390 0.6685 0.704 0.000 0.296 0.000 0.000 0.000
#> GSM876880 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876852 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876853 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876854 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876855 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876856 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876905 3 0.2340 0.9488 0.148 0.000 0.852 0.000 0.000 0.000
#> GSM876906 5 0.2048 0.8717 0.000 0.000 0.120 0.000 0.880 0.000
#> GSM876907 5 0.0000 0.8996 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876908 5 0.2048 0.8717 0.000 0.000 0.120 0.000 0.880 0.000
#> GSM876909 5 0.0000 0.8996 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876881 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876882 1 0.4028 0.6199 0.668 0.000 0.308 0.000 0.000 0.024
#> GSM876883 6 0.6347 0.0901 0.000 0.000 0.308 0.012 0.276 0.404
#> GSM876884 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876885 6 0.6347 0.0901 0.000 0.000 0.308 0.012 0.276 0.404
#> GSM876857 1 0.0000 0.9472 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876859 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876860 2 0.0000 0.9962 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876861 2 0.0000 0.9962 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 disease.state(p) tissue(p) k
#> MAD:hclust 67 0.2518 6.18e-07 2
#> MAD:hclust 68 0.1897 6.32e-14 3
#> MAD:hclust 70 0.0649 1.96e-13 4
#> MAD:hclust 65 0.4679 2.58e-14 5
#> MAD:hclust 66 0.2298 8.09e-21 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 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'kmeans' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.996 0.998 0.4981 0.503 0.503
#> 3 3 0.679 0.769 0.857 0.2918 0.775 0.579
#> 4 4 0.814 0.860 0.909 0.1293 0.813 0.529
#> 5 5 0.789 0.878 0.841 0.0623 0.948 0.806
#> 6 6 0.859 0.826 0.853 0.0434 0.961 0.825
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
#> GSM876886 1 0.0000 0.997 1.000 0.000
#> GSM876887 1 0.0000 0.997 1.000 0.000
#> GSM876888 1 0.0000 0.997 1.000 0.000
#> GSM876889 1 0.0000 0.997 1.000 0.000
#> GSM876890 1 0.0000 0.997 1.000 0.000
#> GSM876891 1 0.0000 0.997 1.000 0.000
#> GSM876862 1 0.0000 0.997 1.000 0.000
#> GSM876863 1 0.0000 0.997 1.000 0.000
#> GSM876864 1 0.0000 0.997 1.000 0.000
#> GSM876865 1 0.0000 0.997 1.000 0.000
#> GSM876866 1 0.0000 0.997 1.000 0.000
#> GSM876867 1 0.0000 0.997 1.000 0.000
#> GSM876838 2 0.0000 1.000 0.000 1.000
#> GSM876839 2 0.0000 1.000 0.000 1.000
#> GSM876840 2 0.0000 1.000 0.000 1.000
#> GSM876841 2 0.0000 1.000 0.000 1.000
#> GSM876842 2 0.0000 1.000 0.000 1.000
#> GSM876843 2 0.0000 1.000 0.000 1.000
#> GSM876892 1 0.0000 0.997 1.000 0.000
#> GSM876893 1 0.0000 0.997 1.000 0.000
#> GSM876894 1 0.0000 0.997 1.000 0.000
#> GSM876895 2 0.0000 1.000 0.000 1.000
#> GSM876896 2 0.0000 1.000 0.000 1.000
#> GSM876897 2 0.0000 1.000 0.000 1.000
#> GSM876868 1 0.0000 0.997 1.000 0.000
#> GSM876869 1 0.0000 0.997 1.000 0.000
#> GSM876870 1 0.0000 0.997 1.000 0.000
#> GSM876871 1 0.0000 0.997 1.000 0.000
#> GSM876872 1 0.0672 0.989 0.992 0.008
#> GSM876873 1 0.0000 0.997 1.000 0.000
#> GSM876844 2 0.0000 1.000 0.000 1.000
#> GSM876845 2 0.0000 1.000 0.000 1.000
#> GSM876846 2 0.0000 1.000 0.000 1.000
#> GSM876847 2 0.0000 1.000 0.000 1.000
#> GSM876848 2 0.0000 1.000 0.000 1.000
#> GSM876849 2 0.0000 1.000 0.000 1.000
#> GSM876898 1 0.0000 0.997 1.000 0.000
#> GSM876899 1 0.5059 0.874 0.888 0.112
#> GSM876900 1 0.0000 0.997 1.000 0.000
#> GSM876901 1 0.0000 0.997 1.000 0.000
#> GSM876902 2 0.0938 0.988 0.012 0.988
#> GSM876903 2 0.0000 1.000 0.000 1.000
#> GSM876904 1 0.0000 0.997 1.000 0.000
#> GSM876874 1 0.0000 0.997 1.000 0.000
#> GSM876875 1 0.0000 0.997 1.000 0.000
#> GSM876876 1 0.0000 0.997 1.000 0.000
#> GSM876877 1 0.0000 0.997 1.000 0.000
#> GSM876878 1 0.0000 0.997 1.000 0.000
#> GSM876879 1 0.0000 0.997 1.000 0.000
#> GSM876880 1 0.0000 0.997 1.000 0.000
#> GSM876850 2 0.0000 1.000 0.000 1.000
#> GSM876851 2 0.0000 1.000 0.000 1.000
#> GSM876852 2 0.0000 1.000 0.000 1.000
#> GSM876853 2 0.0000 1.000 0.000 1.000
#> GSM876854 2 0.0000 1.000 0.000 1.000
#> GSM876855 2 0.0000 1.000 0.000 1.000
#> GSM876856 2 0.0000 1.000 0.000 1.000
#> GSM876905 1 0.0000 0.997 1.000 0.000
#> GSM876906 1 0.0000 0.997 1.000 0.000
#> GSM876907 2 0.0000 1.000 0.000 1.000
#> GSM876908 1 0.0000 0.997 1.000 0.000
#> GSM876909 2 0.0000 1.000 0.000 1.000
#> GSM876881 2 0.0000 1.000 0.000 1.000
#> GSM876882 1 0.0000 0.997 1.000 0.000
#> GSM876883 1 0.0000 0.997 1.000 0.000
#> GSM876884 1 0.0000 0.997 1.000 0.000
#> GSM876885 1 0.0000 0.997 1.000 0.000
#> GSM876857 1 0.0000 0.997 1.000 0.000
#> GSM876858 2 0.0000 1.000 0.000 1.000
#> GSM876859 2 0.0000 1.000 0.000 1.000
#> GSM876860 2 0.0000 1.000 0.000 1.000
#> GSM876861 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
#> GSM876886 1 0.579 0.597 0.668 0.000 0.332
#> GSM876887 1 0.588 0.567 0.652 0.000 0.348
#> GSM876888 1 0.418 0.739 0.828 0.000 0.172
#> GSM876889 3 0.518 0.644 0.256 0.000 0.744
#> GSM876890 1 0.583 0.582 0.660 0.000 0.340
#> GSM876891 3 0.518 0.644 0.256 0.000 0.744
#> GSM876862 1 0.000 0.842 1.000 0.000 0.000
#> GSM876863 1 0.000 0.842 1.000 0.000 0.000
#> GSM876864 1 0.000 0.842 1.000 0.000 0.000
#> GSM876865 1 0.000 0.842 1.000 0.000 0.000
#> GSM876866 1 0.000 0.842 1.000 0.000 0.000
#> GSM876867 1 0.000 0.842 1.000 0.000 0.000
#> GSM876838 2 0.000 0.968 0.000 1.000 0.000
#> GSM876839 2 0.000 0.968 0.000 1.000 0.000
#> GSM876840 2 0.000 0.968 0.000 1.000 0.000
#> GSM876841 2 0.000 0.968 0.000 1.000 0.000
#> GSM876842 2 0.000 0.968 0.000 1.000 0.000
#> GSM876843 2 0.518 0.680 0.000 0.744 0.256
#> GSM876892 1 0.579 0.597 0.668 0.000 0.332
#> GSM876893 1 0.579 0.597 0.668 0.000 0.332
#> GSM876894 3 0.518 0.644 0.256 0.000 0.744
#> GSM876895 3 0.518 0.651 0.000 0.256 0.744
#> GSM876896 3 0.480 0.497 0.000 0.220 0.780
#> GSM876897 3 0.586 0.251 0.000 0.344 0.656
#> GSM876868 1 0.000 0.842 1.000 0.000 0.000
#> GSM876869 1 0.000 0.842 1.000 0.000 0.000
#> GSM876870 1 0.000 0.842 1.000 0.000 0.000
#> GSM876871 1 0.000 0.842 1.000 0.000 0.000
#> GSM876872 3 0.000 0.686 0.000 0.000 1.000
#> GSM876873 3 0.000 0.686 0.000 0.000 1.000
#> GSM876844 2 0.000 0.968 0.000 1.000 0.000
#> GSM876845 2 0.000 0.968 0.000 1.000 0.000
#> GSM876846 2 0.000 0.968 0.000 1.000 0.000
#> GSM876847 2 0.000 0.968 0.000 1.000 0.000
#> GSM876848 2 0.618 0.404 0.000 0.584 0.416
#> GSM876849 3 0.624 -0.074 0.000 0.440 0.560
#> GSM876898 1 0.579 0.597 0.668 0.000 0.332
#> GSM876899 3 0.537 0.646 0.252 0.004 0.744
#> GSM876900 1 0.579 0.597 0.668 0.000 0.332
#> GSM876901 1 0.579 0.597 0.668 0.000 0.332
#> GSM876902 3 0.000 0.686 0.000 0.000 1.000
#> GSM876903 3 0.518 0.651 0.000 0.256 0.744
#> GSM876904 1 0.579 0.597 0.668 0.000 0.332
#> GSM876874 1 0.000 0.842 1.000 0.000 0.000
#> GSM876875 1 0.000 0.842 1.000 0.000 0.000
#> GSM876876 1 0.000 0.842 1.000 0.000 0.000
#> GSM876877 1 0.000 0.842 1.000 0.000 0.000
#> GSM876878 1 0.000 0.842 1.000 0.000 0.000
#> GSM876879 1 0.000 0.842 1.000 0.000 0.000
#> GSM876880 1 0.000 0.842 1.000 0.000 0.000
#> GSM876850 2 0.000 0.968 0.000 1.000 0.000
#> GSM876851 2 0.000 0.968 0.000 1.000 0.000
#> GSM876852 2 0.000 0.968 0.000 1.000 0.000
#> GSM876853 2 0.000 0.968 0.000 1.000 0.000
#> GSM876854 2 0.000 0.968 0.000 1.000 0.000
#> GSM876855 2 0.000 0.968 0.000 1.000 0.000
#> GSM876856 2 0.000 0.968 0.000 1.000 0.000
#> GSM876905 1 0.579 0.597 0.668 0.000 0.332
#> GSM876906 3 0.518 0.644 0.256 0.000 0.744
#> GSM876907 3 0.518 0.651 0.000 0.256 0.744
#> GSM876908 3 0.518 0.644 0.256 0.000 0.744
#> GSM876909 3 0.518 0.651 0.000 0.256 0.744
#> GSM876881 2 0.000 0.968 0.000 1.000 0.000
#> GSM876882 1 0.280 0.791 0.908 0.000 0.092
#> GSM876883 3 0.518 0.644 0.256 0.000 0.744
#> GSM876884 1 0.000 0.842 1.000 0.000 0.000
#> GSM876885 3 0.518 0.644 0.256 0.000 0.744
#> GSM876857 1 0.000 0.842 1.000 0.000 0.000
#> GSM876858 2 0.000 0.968 0.000 1.000 0.000
#> GSM876859 2 0.000 0.968 0.000 1.000 0.000
#> GSM876860 2 0.000 0.968 0.000 1.000 0.000
#> GSM876861 2 0.000 0.968 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.4356 0.660 0.292 0.000 0.708 0.000
#> GSM876887 3 0.4456 0.665 0.280 0.000 0.716 0.004
#> GSM876888 3 0.4356 0.660 0.292 0.000 0.708 0.000
#> GSM876889 3 0.3893 0.627 0.008 0.000 0.796 0.196
#> GSM876890 3 0.4483 0.663 0.284 0.000 0.712 0.004
#> GSM876891 3 0.3725 0.629 0.008 0.000 0.812 0.180
#> GSM876862 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM876839 2 0.0336 0.996 0.000 0.992 0.008 0.000
#> GSM876840 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM876841 2 0.0336 0.996 0.000 0.992 0.008 0.000
#> GSM876842 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM876843 4 0.4790 0.426 0.000 0.380 0.000 0.620
#> GSM876892 3 0.4356 0.660 0.292 0.000 0.708 0.000
#> GSM876893 3 0.4356 0.660 0.292 0.000 0.708 0.000
#> GSM876894 3 0.0524 0.634 0.008 0.000 0.988 0.004
#> GSM876895 3 0.4103 0.589 0.000 0.000 0.744 0.256
#> GSM876896 4 0.0376 0.875 0.000 0.004 0.004 0.992
#> GSM876897 4 0.1576 0.875 0.000 0.048 0.004 0.948
#> GSM876868 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM876873 4 0.0000 0.873 0.000 0.000 0.000 1.000
#> GSM876844 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM876845 2 0.0336 0.996 0.000 0.992 0.008 0.000
#> GSM876846 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM876847 2 0.0336 0.996 0.000 0.992 0.008 0.000
#> GSM876848 4 0.3024 0.799 0.000 0.148 0.000 0.852
#> GSM876849 4 0.1576 0.875 0.000 0.048 0.004 0.948
#> GSM876898 3 0.4356 0.660 0.292 0.000 0.708 0.000
#> GSM876899 3 0.4283 0.593 0.004 0.000 0.740 0.256
#> GSM876900 3 0.4356 0.660 0.292 0.000 0.708 0.000
#> GSM876901 3 0.4331 0.662 0.288 0.000 0.712 0.000
#> GSM876902 4 0.0188 0.872 0.000 0.000 0.004 0.996
#> GSM876903 3 0.4103 0.589 0.000 0.000 0.744 0.256
#> GSM876904 3 0.4356 0.660 0.292 0.000 0.708 0.000
#> GSM876874 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876875 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876876 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876879 1 0.0188 0.995 0.996 0.000 0.000 0.004
#> GSM876880 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876850 2 0.0336 0.996 0.000 0.992 0.008 0.000
#> GSM876851 2 0.0336 0.996 0.000 0.992 0.008 0.000
#> GSM876852 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM876853 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM876854 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM876855 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM876856 2 0.0000 0.995 0.000 1.000 0.000 0.000
#> GSM876905 3 0.4356 0.660 0.292 0.000 0.708 0.000
#> GSM876906 3 0.3972 0.623 0.008 0.000 0.788 0.204
#> GSM876907 3 0.4103 0.589 0.000 0.000 0.744 0.256
#> GSM876908 3 0.3972 0.623 0.008 0.000 0.788 0.204
#> GSM876909 3 0.4103 0.589 0.000 0.000 0.744 0.256
#> GSM876881 2 0.0336 0.996 0.000 0.992 0.008 0.000
#> GSM876882 1 0.0188 0.995 0.996 0.000 0.000 0.004
#> GSM876883 3 0.4452 0.596 0.008 0.000 0.732 0.260
#> GSM876884 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876885 3 0.4452 0.596 0.008 0.000 0.732 0.260
#> GSM876857 1 0.0000 0.999 1.000 0.000 0.000 0.000
#> GSM876858 2 0.0336 0.996 0.000 0.992 0.008 0.000
#> GSM876859 2 0.0336 0.996 0.000 0.992 0.008 0.000
#> GSM876860 2 0.0336 0.996 0.000 0.992 0.008 0.000
#> GSM876861 2 0.0336 0.996 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
#> GSM876886 3 0.2690 0.993 0.156 0.000 0.844 0.000 0.000
#> GSM876887 3 0.2471 0.965 0.136 0.000 0.864 0.000 0.000
#> GSM876888 3 0.2690 0.993 0.156 0.000 0.844 0.000 0.000
#> GSM876889 5 0.4937 0.788 0.000 0.000 0.428 0.028 0.544
#> GSM876890 3 0.2516 0.972 0.140 0.000 0.860 0.000 0.000
#> GSM876891 5 0.5086 0.808 0.000 0.000 0.396 0.040 0.564
#> GSM876862 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0771 0.915 0.000 0.976 0.020 0.000 0.004
#> GSM876839 2 0.0609 0.917 0.000 0.980 0.000 0.000 0.020
#> GSM876840 2 0.3758 0.867 0.000 0.824 0.112 0.008 0.056
#> GSM876841 2 0.0609 0.917 0.000 0.980 0.000 0.000 0.020
#> GSM876842 2 0.2331 0.898 0.000 0.900 0.080 0.000 0.020
#> GSM876843 4 0.6648 0.440 0.000 0.252 0.112 0.580 0.056
#> GSM876892 3 0.2690 0.993 0.156 0.000 0.844 0.000 0.000
#> GSM876893 3 0.2690 0.993 0.156 0.000 0.844 0.000 0.000
#> GSM876894 5 0.4256 0.758 0.000 0.000 0.436 0.000 0.564
#> GSM876895 5 0.5726 0.826 0.000 0.008 0.284 0.096 0.612
#> GSM876896 4 0.0404 0.826 0.000 0.000 0.000 0.988 0.012
#> GSM876897 4 0.0404 0.826 0.000 0.000 0.000 0.988 0.012
#> GSM876868 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.4437 0.693 0.000 0.000 0.020 0.664 0.316
#> GSM876873 4 0.4437 0.693 0.000 0.000 0.020 0.664 0.316
#> GSM876844 2 0.2331 0.898 0.000 0.900 0.080 0.000 0.020
#> GSM876845 2 0.0609 0.917 0.000 0.980 0.000 0.000 0.020
#> GSM876846 2 0.3807 0.866 0.000 0.820 0.116 0.008 0.056
#> GSM876847 2 0.0703 0.917 0.000 0.976 0.000 0.000 0.024
#> GSM876848 4 0.2653 0.792 0.000 0.052 0.020 0.900 0.028
#> GSM876849 4 0.0324 0.824 0.000 0.004 0.000 0.992 0.004
#> GSM876898 3 0.2690 0.993 0.156 0.000 0.844 0.000 0.000
#> GSM876899 5 0.5652 0.827 0.000 0.000 0.344 0.092 0.564
#> GSM876900 3 0.2690 0.993 0.156 0.000 0.844 0.000 0.000
#> GSM876901 3 0.2690 0.993 0.156 0.000 0.844 0.000 0.000
#> GSM876902 4 0.0404 0.826 0.000 0.000 0.000 0.988 0.012
#> GSM876903 5 0.5726 0.826 0.000 0.008 0.284 0.096 0.612
#> GSM876904 3 0.2690 0.993 0.156 0.000 0.844 0.000 0.000
#> GSM876874 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.1942 0.894 0.920 0.000 0.012 0.000 0.068
#> GSM876876 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876879 1 0.4571 0.605 0.664 0.000 0.020 0.004 0.312
#> GSM876880 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0703 0.917 0.000 0.976 0.000 0.000 0.024
#> GSM876851 2 0.0609 0.917 0.000 0.980 0.000 0.000 0.020
#> GSM876852 2 0.3477 0.871 0.000 0.832 0.112 0.000 0.056
#> GSM876853 2 0.0898 0.915 0.000 0.972 0.020 0.000 0.008
#> GSM876854 2 0.3758 0.867 0.000 0.824 0.112 0.008 0.056
#> GSM876855 2 0.3758 0.867 0.000 0.824 0.112 0.008 0.056
#> GSM876856 2 0.3758 0.867 0.000 0.824 0.112 0.008 0.056
#> GSM876905 3 0.2690 0.993 0.156 0.000 0.844 0.000 0.000
#> GSM876906 5 0.5294 0.820 0.000 0.000 0.380 0.056 0.564
#> GSM876907 5 0.5726 0.826 0.000 0.008 0.284 0.096 0.612
#> GSM876908 5 0.5294 0.820 0.000 0.000 0.380 0.056 0.564
#> GSM876909 5 0.5726 0.826 0.000 0.008 0.284 0.096 0.612
#> GSM876881 2 0.1670 0.903 0.000 0.936 0.012 0.000 0.052
#> GSM876882 1 0.4589 0.599 0.660 0.000 0.020 0.004 0.316
#> GSM876883 5 0.2932 0.519 0.000 0.000 0.104 0.032 0.864
#> GSM876884 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876885 5 0.2932 0.519 0.000 0.000 0.104 0.032 0.864
#> GSM876857 1 0.0000 0.959 1.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.1774 0.903 0.000 0.932 0.016 0.000 0.052
#> GSM876859 2 0.1774 0.903 0.000 0.932 0.016 0.000 0.052
#> GSM876860 2 0.1774 0.903 0.000 0.932 0.016 0.000 0.052
#> GSM876861 2 0.1774 0.903 0.000 0.932 0.016 0.000 0.052
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM876886 3 0.2200 0.924 0.080 0.000 0.900 0.004 0.004 0.012
#> GSM876887 3 0.2352 0.897 0.052 0.000 0.900 0.004 0.004 0.040
#> GSM876888 3 0.1556 0.933 0.080 0.000 0.920 0.000 0.000 0.000
#> GSM876889 3 0.5088 -0.209 0.000 0.000 0.516 0.004 0.412 0.068
#> GSM876890 3 0.2173 0.914 0.064 0.000 0.904 0.004 0.000 0.028
#> GSM876891 5 0.3190 0.927 0.000 0.000 0.220 0.000 0.772 0.008
#> GSM876862 1 0.0000 0.972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0146 0.972 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM876864 1 0.0000 0.972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0146 0.972 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM876866 1 0.0146 0.972 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM876867 1 0.0405 0.971 0.988 0.000 0.000 0.004 0.008 0.000
#> GSM876838 2 0.2115 0.835 0.000 0.916 0.032 0.032 0.020 0.000
#> GSM876839 2 0.0000 0.840 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876840 2 0.4900 0.720 0.000 0.624 0.032 0.312 0.032 0.000
#> GSM876841 2 0.0000 0.840 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876842 2 0.3117 0.821 0.000 0.848 0.032 0.100 0.020 0.000
#> GSM876843 4 0.1692 0.510 0.000 0.048 0.000 0.932 0.012 0.008
#> GSM876892 3 0.1700 0.935 0.080 0.000 0.916 0.000 0.004 0.000
#> GSM876893 3 0.1700 0.935 0.080 0.000 0.916 0.000 0.004 0.000
#> GSM876894 5 0.3217 0.924 0.000 0.000 0.224 0.000 0.768 0.008
#> GSM876895 5 0.2765 0.915 0.000 0.016 0.132 0.004 0.848 0.000
#> GSM876896 4 0.4015 0.856 0.000 0.000 0.000 0.616 0.012 0.372
#> GSM876897 4 0.4015 0.856 0.000 0.000 0.000 0.616 0.012 0.372
#> GSM876868 1 0.0146 0.972 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM876869 1 0.0146 0.972 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM876870 1 0.0993 0.965 0.964 0.000 0.000 0.012 0.024 0.000
#> GSM876871 1 0.0820 0.968 0.972 0.000 0.000 0.012 0.016 0.000
#> GSM876872 6 0.1075 0.316 0.000 0.000 0.000 0.048 0.000 0.952
#> GSM876873 6 0.1075 0.316 0.000 0.000 0.000 0.048 0.000 0.952
#> GSM876844 2 0.3117 0.821 0.000 0.848 0.032 0.100 0.020 0.000
#> GSM876845 2 0.0146 0.840 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM876846 2 0.4601 0.704 0.000 0.612 0.020 0.348 0.020 0.000
#> GSM876847 2 0.0146 0.840 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM876848 4 0.3586 0.829 0.000 0.000 0.000 0.720 0.012 0.268
#> GSM876849 4 0.3819 0.851 0.000 0.000 0.000 0.672 0.012 0.316
#> GSM876898 3 0.1700 0.935 0.080 0.000 0.916 0.000 0.004 0.000
#> GSM876899 5 0.3023 0.930 0.000 0.000 0.212 0.000 0.784 0.004
#> GSM876900 3 0.1700 0.935 0.080 0.000 0.916 0.000 0.004 0.000
#> GSM876901 3 0.1700 0.935 0.080 0.000 0.916 0.000 0.004 0.000
#> GSM876902 4 0.4057 0.847 0.000 0.000 0.000 0.600 0.012 0.388
#> GSM876903 5 0.2765 0.915 0.000 0.016 0.132 0.004 0.848 0.000
#> GSM876904 3 0.1700 0.935 0.080 0.000 0.916 0.000 0.004 0.000
#> GSM876874 1 0.0000 0.972 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.3649 0.721 0.800 0.000 0.004 0.000 0.084 0.112
#> GSM876876 1 0.0820 0.968 0.972 0.000 0.000 0.012 0.016 0.000
#> GSM876877 1 0.0820 0.968 0.972 0.000 0.000 0.012 0.016 0.000
#> GSM876878 1 0.0993 0.965 0.964 0.000 0.000 0.012 0.024 0.000
#> GSM876879 6 0.5125 0.444 0.360 0.000 0.004 0.000 0.080 0.556
#> GSM876880 1 0.0820 0.968 0.972 0.000 0.000 0.012 0.016 0.000
#> GSM876850 2 0.0146 0.840 0.000 0.996 0.004 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.840 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876852 2 0.4852 0.728 0.000 0.636 0.032 0.300 0.032 0.000
#> GSM876853 2 0.2188 0.835 0.000 0.912 0.032 0.036 0.020 0.000
#> GSM876854 2 0.4900 0.720 0.000 0.624 0.032 0.312 0.032 0.000
#> GSM876855 2 0.4900 0.720 0.000 0.624 0.032 0.312 0.032 0.000
#> GSM876856 2 0.4900 0.720 0.000 0.624 0.032 0.312 0.032 0.000
#> GSM876905 3 0.1700 0.935 0.080 0.000 0.916 0.000 0.004 0.000
#> GSM876906 5 0.3161 0.930 0.000 0.000 0.216 0.000 0.776 0.008
#> GSM876907 5 0.2765 0.915 0.000 0.016 0.132 0.004 0.848 0.000
#> GSM876908 5 0.3161 0.930 0.000 0.000 0.216 0.000 0.776 0.008
#> GSM876909 5 0.2765 0.915 0.000 0.016 0.132 0.004 0.848 0.000
#> GSM876881 2 0.1842 0.817 0.000 0.932 0.012 0.008 0.036 0.012
#> GSM876882 6 0.5032 0.513 0.324 0.000 0.008 0.000 0.072 0.596
#> GSM876883 6 0.4551 0.463 0.000 0.000 0.048 0.000 0.344 0.608
#> GSM876884 1 0.0993 0.965 0.964 0.000 0.000 0.012 0.024 0.000
#> GSM876885 6 0.4551 0.463 0.000 0.000 0.048 0.000 0.344 0.608
#> GSM876857 1 0.0146 0.972 0.996 0.000 0.000 0.000 0.004 0.000
#> GSM876858 2 0.3366 0.796 0.000 0.844 0.048 0.012 0.084 0.012
#> GSM876859 2 0.3366 0.796 0.000 0.844 0.048 0.012 0.084 0.012
#> GSM876860 2 0.3366 0.796 0.000 0.844 0.048 0.012 0.084 0.012
#> GSM876861 2 0.3366 0.796 0.000 0.844 0.048 0.012 0.084 0.012
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> MAD:kmeans 72 0.7703 2.85e-10 2
#> MAD:kmeans 68 0.4351 8.84e-14 3
#> MAD:kmeans 71 0.0485 1.41e-20 4
#> MAD:kmeans 71 0.0257 1.63e-19 5
#> MAD:kmeans 66 0.3125 2.35e-19 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 72 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 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 0.993 0.997 0.5018 0.499 0.499
#> 3 3 0.780 0.645 0.845 0.3032 0.892 0.790
#> 4 4 1.000 0.945 0.977 0.1173 0.785 0.523
#> 5 5 0.989 0.946 0.976 0.0601 0.924 0.730
#> 6 6 0.979 0.941 0.961 0.0341 0.965 0.845
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
#> GSM876886 1 0.0000 0.995 1.000 0.000
#> GSM876887 1 0.0000 0.995 1.000 0.000
#> GSM876888 1 0.0000 0.995 1.000 0.000
#> GSM876889 1 0.0000 0.995 1.000 0.000
#> GSM876890 1 0.0000 0.995 1.000 0.000
#> GSM876891 1 0.0000 0.995 1.000 0.000
#> GSM876862 1 0.0000 0.995 1.000 0.000
#> GSM876863 1 0.0000 0.995 1.000 0.000
#> GSM876864 1 0.0000 0.995 1.000 0.000
#> GSM876865 1 0.0000 0.995 1.000 0.000
#> GSM876866 1 0.0000 0.995 1.000 0.000
#> GSM876867 1 0.0000 0.995 1.000 0.000
#> GSM876838 2 0.0000 1.000 0.000 1.000
#> GSM876839 2 0.0000 1.000 0.000 1.000
#> GSM876840 2 0.0000 1.000 0.000 1.000
#> GSM876841 2 0.0000 1.000 0.000 1.000
#> GSM876842 2 0.0000 1.000 0.000 1.000
#> GSM876843 2 0.0000 1.000 0.000 1.000
#> GSM876892 1 0.0000 0.995 1.000 0.000
#> GSM876893 1 0.0000 0.995 1.000 0.000
#> GSM876894 1 0.0000 0.995 1.000 0.000
#> GSM876895 2 0.0000 1.000 0.000 1.000
#> GSM876896 2 0.0000 1.000 0.000 1.000
#> GSM876897 2 0.0000 1.000 0.000 1.000
#> GSM876868 1 0.0000 0.995 1.000 0.000
#> GSM876869 1 0.0000 0.995 1.000 0.000
#> GSM876870 1 0.0000 0.995 1.000 0.000
#> GSM876871 1 0.0000 0.995 1.000 0.000
#> GSM876872 1 0.7219 0.751 0.800 0.200
#> GSM876873 1 0.0938 0.983 0.988 0.012
#> GSM876844 2 0.0000 1.000 0.000 1.000
#> GSM876845 2 0.0000 1.000 0.000 1.000
#> GSM876846 2 0.0000 1.000 0.000 1.000
#> GSM876847 2 0.0000 1.000 0.000 1.000
#> GSM876848 2 0.0000 1.000 0.000 1.000
#> GSM876849 2 0.0000 1.000 0.000 1.000
#> GSM876898 1 0.0000 0.995 1.000 0.000
#> GSM876899 2 0.0000 1.000 0.000 1.000
#> GSM876900 1 0.0000 0.995 1.000 0.000
#> GSM876901 1 0.0000 0.995 1.000 0.000
#> GSM876902 2 0.0000 1.000 0.000 1.000
#> GSM876903 2 0.0000 1.000 0.000 1.000
#> GSM876904 1 0.0000 0.995 1.000 0.000
#> GSM876874 1 0.0000 0.995 1.000 0.000
#> GSM876875 1 0.0000 0.995 1.000 0.000
#> GSM876876 1 0.0000 0.995 1.000 0.000
#> GSM876877 1 0.0000 0.995 1.000 0.000
#> GSM876878 1 0.0000 0.995 1.000 0.000
#> GSM876879 1 0.0000 0.995 1.000 0.000
#> GSM876880 1 0.0000 0.995 1.000 0.000
#> GSM876850 2 0.0000 1.000 0.000 1.000
#> GSM876851 2 0.0000 1.000 0.000 1.000
#> GSM876852 2 0.0000 1.000 0.000 1.000
#> GSM876853 2 0.0000 1.000 0.000 1.000
#> GSM876854 2 0.0000 1.000 0.000 1.000
#> GSM876855 2 0.0000 1.000 0.000 1.000
#> GSM876856 2 0.0000 1.000 0.000 1.000
#> GSM876905 1 0.0000 0.995 1.000 0.000
#> GSM876906 1 0.0000 0.995 1.000 0.000
#> GSM876907 2 0.0000 1.000 0.000 1.000
#> GSM876908 1 0.0000 0.995 1.000 0.000
#> GSM876909 2 0.0000 1.000 0.000 1.000
#> GSM876881 2 0.0000 1.000 0.000 1.000
#> GSM876882 1 0.0000 0.995 1.000 0.000
#> GSM876883 1 0.0000 0.995 1.000 0.000
#> GSM876884 1 0.0000 0.995 1.000 0.000
#> GSM876885 1 0.0000 0.995 1.000 0.000
#> GSM876857 1 0.0000 0.995 1.000 0.000
#> GSM876858 2 0.0000 1.000 0.000 1.000
#> GSM876859 2 0.0000 1.000 0.000 1.000
#> GSM876860 2 0.0000 1.000 0.000 1.000
#> GSM876861 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
#> GSM876886 1 0.6309 0.3075 0.504 0.000 0.496
#> GSM876887 1 0.6309 0.3075 0.504 0.000 0.496
#> GSM876888 1 0.6309 0.3075 0.504 0.000 0.496
#> GSM876889 3 0.6682 0.9617 0.008 0.488 0.504
#> GSM876890 1 0.6309 0.3075 0.504 0.000 0.496
#> GSM876891 3 0.7289 0.9769 0.028 0.468 0.504
#> GSM876862 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876863 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876864 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876865 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876866 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876867 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876838 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876839 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876840 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876841 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876842 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876843 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876892 1 0.6309 0.3075 0.504 0.000 0.496
#> GSM876893 1 0.6309 0.3075 0.504 0.000 0.496
#> GSM876894 3 0.7289 0.9769 0.028 0.468 0.504
#> GSM876895 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876896 2 0.0424 0.2807 0.000 0.992 0.008
#> GSM876897 2 0.0424 0.2807 0.000 0.992 0.008
#> GSM876868 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876869 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876870 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876871 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876872 2 0.6291 -0.4081 0.468 0.532 0.000
#> GSM876873 1 0.6309 -0.0545 0.504 0.496 0.000
#> GSM876844 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876845 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876846 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876847 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876848 2 0.6291 0.8425 0.000 0.532 0.468
#> GSM876849 2 0.5678 0.7197 0.000 0.684 0.316
#> GSM876898 1 0.6309 0.3075 0.504 0.000 0.496
#> GSM876899 3 0.6308 0.9205 0.000 0.492 0.508
#> GSM876900 1 0.6309 0.3075 0.504 0.000 0.496
#> GSM876901 1 0.6309 0.3075 0.504 0.000 0.496
#> GSM876902 2 0.0000 0.2633 0.000 1.000 0.000
#> GSM876903 2 0.1411 0.2906 0.000 0.964 0.036
#> GSM876904 1 0.6309 0.3075 0.504 0.000 0.496
#> GSM876874 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876875 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876876 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876877 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876878 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876879 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876880 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876850 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876851 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876852 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876853 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876854 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876855 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876856 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876905 1 0.6309 0.3075 0.504 0.000 0.496
#> GSM876906 3 0.7289 0.9769 0.028 0.468 0.504
#> GSM876907 2 0.1411 0.2906 0.000 0.964 0.036
#> GSM876908 3 0.7289 0.9769 0.028 0.468 0.504
#> GSM876909 2 0.1860 0.3204 0.000 0.948 0.052
#> GSM876881 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876882 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876883 1 0.6302 -0.0282 0.520 0.480 0.000
#> GSM876884 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876885 1 0.6307 -0.0379 0.512 0.488 0.000
#> GSM876857 1 0.0000 0.7348 1.000 0.000 0.000
#> GSM876858 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876859 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876860 2 0.6309 0.8611 0.000 0.504 0.496
#> GSM876861 2 0.6309 0.8611 0.000 0.504 0.496
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.0707 0.9873 0.020 0.000 0.980 0.000
#> GSM876887 3 0.0707 0.9873 0.020 0.000 0.980 0.000
#> GSM876888 3 0.0707 0.9873 0.020 0.000 0.980 0.000
#> GSM876889 3 0.0707 0.9734 0.000 0.000 0.980 0.020
#> GSM876890 3 0.0707 0.9873 0.020 0.000 0.980 0.000
#> GSM876891 3 0.0000 0.9771 0.000 0.000 1.000 0.000
#> GSM876862 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876839 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876840 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876841 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876842 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876843 4 0.3649 0.7105 0.000 0.204 0.000 0.796
#> GSM876892 3 0.0707 0.9873 0.020 0.000 0.980 0.000
#> GSM876893 3 0.0707 0.9873 0.020 0.000 0.980 0.000
#> GSM876894 3 0.0000 0.9771 0.000 0.000 1.000 0.000
#> GSM876895 2 0.1042 0.9757 0.000 0.972 0.020 0.008
#> GSM876896 4 0.0336 0.9020 0.000 0.008 0.000 0.992
#> GSM876897 4 0.0336 0.9020 0.000 0.008 0.000 0.992
#> GSM876868 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876872 4 0.0376 0.8999 0.004 0.004 0.000 0.992
#> GSM876873 4 0.0336 0.8965 0.008 0.000 0.000 0.992
#> GSM876844 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876845 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876846 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876847 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876848 4 0.0336 0.9020 0.000 0.008 0.000 0.992
#> GSM876849 4 0.0336 0.9020 0.000 0.008 0.000 0.992
#> GSM876898 3 0.0707 0.9873 0.020 0.000 0.980 0.000
#> GSM876899 3 0.1452 0.9375 0.000 0.036 0.956 0.008
#> GSM876900 3 0.0707 0.9873 0.020 0.000 0.980 0.000
#> GSM876901 3 0.0707 0.9873 0.020 0.000 0.980 0.000
#> GSM876902 4 0.0336 0.9020 0.000 0.008 0.000 0.992
#> GSM876903 2 0.1042 0.9757 0.000 0.972 0.020 0.008
#> GSM876904 3 0.0707 0.9873 0.020 0.000 0.980 0.000
#> GSM876874 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876875 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876876 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876879 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876880 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876851 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876852 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876853 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876854 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876855 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876856 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876905 3 0.0707 0.9873 0.020 0.000 0.980 0.000
#> GSM876906 3 0.0336 0.9738 0.000 0.000 0.992 0.008
#> GSM876907 2 0.1042 0.9757 0.000 0.972 0.020 0.008
#> GSM876908 3 0.0336 0.9738 0.000 0.000 0.992 0.008
#> GSM876909 2 0.1042 0.9757 0.000 0.972 0.020 0.008
#> GSM876881 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876882 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876883 1 0.4977 0.0413 0.540 0.000 0.000 0.460
#> GSM876884 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876885 4 0.4999 -0.0125 0.492 0.000 0.000 0.508
#> GSM876857 1 0.0000 0.9747 1.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876859 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876860 2 0.0000 0.9954 0.000 1.000 0.000 0.000
#> GSM876861 2 0.0000 0.9954 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
#> GSM876886 3 0.0162 0.989 0.004 0.000 0.996 0.000 0.000
#> GSM876887 3 0.0162 0.989 0.004 0.000 0.996 0.000 0.000
#> GSM876888 3 0.0162 0.989 0.004 0.000 0.996 0.000 0.000
#> GSM876889 3 0.0162 0.985 0.000 0.000 0.996 0.004 0.000
#> GSM876890 3 0.0162 0.989 0.004 0.000 0.996 0.000 0.000
#> GSM876891 3 0.0162 0.985 0.000 0.000 0.996 0.000 0.004
#> GSM876862 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876840 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876841 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876843 2 0.3999 0.475 0.000 0.656 0.000 0.344 0.000
#> GSM876892 3 0.0162 0.989 0.004 0.000 0.996 0.000 0.000
#> GSM876893 3 0.0162 0.989 0.004 0.000 0.996 0.000 0.000
#> GSM876894 3 0.2424 0.845 0.000 0.000 0.868 0.000 0.132
#> GSM876895 5 0.2329 0.846 0.000 0.124 0.000 0.000 0.876
#> GSM876896 4 0.0000 0.866 0.000 0.000 0.000 1.000 0.000
#> GSM876897 4 0.0000 0.866 0.000 0.000 0.000 1.000 0.000
#> GSM876868 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.0703 0.860 0.000 0.000 0.000 0.976 0.024
#> GSM876873 4 0.0703 0.860 0.000 0.000 0.000 0.976 0.024
#> GSM876844 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876846 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876847 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876848 4 0.0290 0.861 0.000 0.008 0.000 0.992 0.000
#> GSM876849 4 0.0000 0.866 0.000 0.000 0.000 1.000 0.000
#> GSM876898 3 0.0162 0.989 0.004 0.000 0.996 0.000 0.000
#> GSM876899 5 0.0880 0.944 0.000 0.000 0.032 0.000 0.968
#> GSM876900 3 0.0162 0.989 0.004 0.000 0.996 0.000 0.000
#> GSM876901 3 0.0162 0.989 0.004 0.000 0.996 0.000 0.000
#> GSM876902 4 0.0000 0.866 0.000 0.000 0.000 1.000 0.000
#> GSM876903 5 0.0880 0.951 0.000 0.032 0.000 0.000 0.968
#> GSM876904 3 0.0162 0.989 0.004 0.000 0.996 0.000 0.000
#> GSM876874 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.0451 0.987 0.988 0.000 0.004 0.000 0.008
#> GSM876876 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876879 1 0.1041 0.966 0.964 0.000 0.004 0.000 0.032
#> GSM876880 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876852 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876853 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876854 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876855 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876856 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876905 3 0.0162 0.989 0.004 0.000 0.996 0.000 0.000
#> GSM876906 5 0.0880 0.944 0.000 0.000 0.032 0.000 0.968
#> GSM876907 5 0.0880 0.951 0.000 0.032 0.000 0.000 0.968
#> GSM876908 5 0.0880 0.944 0.000 0.000 0.032 0.000 0.968
#> GSM876909 5 0.0880 0.951 0.000 0.032 0.000 0.000 0.968
#> GSM876881 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876882 1 0.1041 0.966 0.964 0.000 0.004 0.000 0.032
#> GSM876883 4 0.5137 0.330 0.416 0.000 0.004 0.548 0.032
#> GSM876884 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876885 4 0.4672 0.597 0.284 0.000 0.004 0.680 0.032
#> GSM876857 1 0.0000 0.996 1.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876859 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876860 2 0.0000 0.982 0.000 1.000 0.000 0.000 0.000
#> GSM876861 2 0.0000 0.982 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
#> GSM876886 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876887 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876888 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876889 3 0.0260 0.981 0.000 0.000 0.992 0.000 0.000 0.008
#> GSM876890 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876891 3 0.0363 0.978 0.000 0.000 0.988 0.000 0.000 0.012
#> GSM876862 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876840 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876841 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876843 4 0.0547 0.964 0.000 0.020 0.000 0.980 0.000 0.000
#> GSM876892 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876893 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876894 3 0.2653 0.820 0.000 0.000 0.844 0.000 0.144 0.012
#> GSM876895 5 0.2340 0.755 0.000 0.148 0.000 0.000 0.852 0.000
#> GSM876896 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876897 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876868 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876872 6 0.3578 0.471 0.000 0.000 0.000 0.340 0.000 0.660
#> GSM876873 6 0.3499 0.501 0.000 0.000 0.000 0.320 0.000 0.680
#> GSM876844 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876846 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876847 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876848 4 0.0146 0.988 0.000 0.004 0.000 0.996 0.000 0.000
#> GSM876849 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876898 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876899 5 0.0000 0.958 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876900 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876901 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876902 4 0.0000 0.991 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876903 5 0.0000 0.958 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876904 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876874 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.3409 0.545 0.700 0.000 0.000 0.000 0.000 0.300
#> GSM876876 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876879 6 0.3684 0.315 0.372 0.000 0.000 0.000 0.000 0.628
#> GSM876880 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876852 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876853 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876854 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876855 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876856 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876905 3 0.0000 0.986 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876906 5 0.0260 0.956 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM876907 5 0.0000 0.958 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876908 5 0.0260 0.956 0.000 0.000 0.000 0.000 0.992 0.008
#> GSM876909 5 0.0000 0.958 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876881 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876882 6 0.0458 0.730 0.016 0.000 0.000 0.000 0.000 0.984
#> GSM876883 6 0.0405 0.732 0.008 0.000 0.000 0.004 0.000 0.988
#> GSM876884 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876885 6 0.0405 0.730 0.004 0.000 0.000 0.008 0.000 0.988
#> GSM876857 1 0.0000 0.981 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876859 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876860 2 0.0000 1.000 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876861 2 0.0000 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 disease.state(p) tissue(p) k
#> MAD:skmeans 72 0.7433 5.51e-10 2
#> MAD:skmeans 51 0.9173 2.24e-17 3
#> MAD:skmeans 70 0.1218 4.52e-18 4
#> MAD:skmeans 70 0.0351 1.07e-20 5
#> MAD:skmeans 70 0.0507 5.87e-21 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 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'MAD' method.
#> Subgroups are detected by 'pam' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 6.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 1.000 0.974 0.990 0.5050 0.495 0.495
#> 3 3 0.981 0.938 0.976 0.3343 0.712 0.481
#> 4 4 0.884 0.832 0.914 0.0958 0.907 0.724
#> 5 5 1.000 0.957 0.984 0.0636 0.933 0.751
#> 6 6 0.996 0.965 0.978 0.0270 0.940 0.744
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 2 3 5
There is also optional best \(k\) = 2 3 5 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM876886 1 0.000 0.996 1.000 0.000
#> GSM876887 1 0.000 0.996 1.000 0.000
#> GSM876888 1 0.000 0.996 1.000 0.000
#> GSM876889 1 0.000 0.996 1.000 0.000
#> GSM876890 1 0.000 0.996 1.000 0.000
#> GSM876891 1 0.163 0.972 0.976 0.024
#> GSM876862 1 0.000 0.996 1.000 0.000
#> GSM876863 1 0.000 0.996 1.000 0.000
#> GSM876864 1 0.000 0.996 1.000 0.000
#> GSM876865 1 0.000 0.996 1.000 0.000
#> GSM876866 1 0.000 0.996 1.000 0.000
#> GSM876867 1 0.000 0.996 1.000 0.000
#> GSM876838 2 0.000 0.981 0.000 1.000
#> GSM876839 2 0.000 0.981 0.000 1.000
#> GSM876840 2 0.000 0.981 0.000 1.000
#> GSM876841 2 0.000 0.981 0.000 1.000
#> GSM876842 2 0.000 0.981 0.000 1.000
#> GSM876843 2 0.000 0.981 0.000 1.000
#> GSM876892 1 0.000 0.996 1.000 0.000
#> GSM876893 1 0.000 0.996 1.000 0.000
#> GSM876894 1 0.000 0.996 1.000 0.000
#> GSM876895 2 0.000 0.981 0.000 1.000
#> GSM876896 2 0.000 0.981 0.000 1.000
#> GSM876897 2 0.000 0.981 0.000 1.000
#> GSM876868 1 0.000 0.996 1.000 0.000
#> GSM876869 1 0.000 0.996 1.000 0.000
#> GSM876870 1 0.000 0.996 1.000 0.000
#> GSM876871 1 0.000 0.996 1.000 0.000
#> GSM876872 1 0.529 0.860 0.880 0.120
#> GSM876873 1 0.000 0.996 1.000 0.000
#> GSM876844 2 0.000 0.981 0.000 1.000
#> GSM876845 2 0.000 0.981 0.000 1.000
#> GSM876846 2 0.000 0.981 0.000 1.000
#> GSM876847 2 0.000 0.981 0.000 1.000
#> GSM876848 2 0.000 0.981 0.000 1.000
#> GSM876849 2 0.000 0.981 0.000 1.000
#> GSM876898 1 0.000 0.996 1.000 0.000
#> GSM876899 2 0.000 0.981 0.000 1.000
#> GSM876900 1 0.000 0.996 1.000 0.000
#> GSM876901 1 0.000 0.996 1.000 0.000
#> GSM876902 2 0.000 0.981 0.000 1.000
#> GSM876903 2 0.000 0.981 0.000 1.000
#> GSM876904 1 0.000 0.996 1.000 0.000
#> GSM876874 1 0.000 0.996 1.000 0.000
#> GSM876875 1 0.000 0.996 1.000 0.000
#> GSM876876 1 0.000 0.996 1.000 0.000
#> GSM876877 1 0.000 0.996 1.000 0.000
#> GSM876878 1 0.000 0.996 1.000 0.000
#> GSM876879 1 0.000 0.996 1.000 0.000
#> GSM876880 1 0.000 0.996 1.000 0.000
#> GSM876850 2 0.000 0.981 0.000 1.000
#> GSM876851 2 0.000 0.981 0.000 1.000
#> GSM876852 2 0.000 0.981 0.000 1.000
#> GSM876853 2 0.000 0.981 0.000 1.000
#> GSM876854 2 0.000 0.981 0.000 1.000
#> GSM876855 2 0.000 0.981 0.000 1.000
#> GSM876856 2 0.000 0.981 0.000 1.000
#> GSM876905 1 0.000 0.996 1.000 0.000
#> GSM876906 2 0.975 0.325 0.408 0.592
#> GSM876907 2 0.000 0.981 0.000 1.000
#> GSM876908 2 0.730 0.743 0.204 0.796
#> GSM876909 2 0.000 0.981 0.000 1.000
#> GSM876881 2 0.000 0.981 0.000 1.000
#> GSM876882 1 0.000 0.996 1.000 0.000
#> GSM876883 1 0.000 0.996 1.000 0.000
#> GSM876884 1 0.000 0.996 1.000 0.000
#> GSM876885 1 0.000 0.996 1.000 0.000
#> GSM876857 1 0.000 0.996 1.000 0.000
#> GSM876858 2 0.000 0.981 0.000 1.000
#> GSM876859 2 0.000 0.981 0.000 1.000
#> GSM876860 2 0.000 0.981 0.000 1.000
#> GSM876861 2 0.000 0.981 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 3 0.559 0.564 0.304 0.000 0.696
#> GSM876887 3 0.000 0.955 0.000 0.000 1.000
#> GSM876888 1 0.000 0.980 1.000 0.000 0.000
#> GSM876889 3 0.000 0.955 0.000 0.000 1.000
#> GSM876890 3 0.000 0.955 0.000 0.000 1.000
#> GSM876891 3 0.000 0.955 0.000 0.000 1.000
#> GSM876862 1 0.000 0.980 1.000 0.000 0.000
#> GSM876863 1 0.000 0.980 1.000 0.000 0.000
#> GSM876864 1 0.000 0.980 1.000 0.000 0.000
#> GSM876865 1 0.000 0.980 1.000 0.000 0.000
#> GSM876866 1 0.000 0.980 1.000 0.000 0.000
#> GSM876867 1 0.000 0.980 1.000 0.000 0.000
#> GSM876838 2 0.000 0.986 0.000 1.000 0.000
#> GSM876839 2 0.000 0.986 0.000 1.000 0.000
#> GSM876840 2 0.000 0.986 0.000 1.000 0.000
#> GSM876841 2 0.000 0.986 0.000 1.000 0.000
#> GSM876842 2 0.000 0.986 0.000 1.000 0.000
#> GSM876843 2 0.000 0.986 0.000 1.000 0.000
#> GSM876892 3 0.000 0.955 0.000 0.000 1.000
#> GSM876893 3 0.245 0.886 0.076 0.000 0.924
#> GSM876894 3 0.000 0.955 0.000 0.000 1.000
#> GSM876895 3 0.000 0.955 0.000 0.000 1.000
#> GSM876896 3 0.613 0.307 0.000 0.400 0.600
#> GSM876897 2 0.562 0.543 0.000 0.692 0.308
#> GSM876868 1 0.000 0.980 1.000 0.000 0.000
#> GSM876869 1 0.000 0.980 1.000 0.000 0.000
#> GSM876870 1 0.000 0.980 1.000 0.000 0.000
#> GSM876871 1 0.000 0.980 1.000 0.000 0.000
#> GSM876872 3 0.000 0.955 0.000 0.000 1.000
#> GSM876873 3 0.000 0.955 0.000 0.000 1.000
#> GSM876844 2 0.000 0.986 0.000 1.000 0.000
#> GSM876845 2 0.000 0.986 0.000 1.000 0.000
#> GSM876846 2 0.000 0.986 0.000 1.000 0.000
#> GSM876847 2 0.000 0.986 0.000 1.000 0.000
#> GSM876848 2 0.000 0.986 0.000 1.000 0.000
#> GSM876849 2 0.000 0.986 0.000 1.000 0.000
#> GSM876898 3 0.000 0.955 0.000 0.000 1.000
#> GSM876899 3 0.000 0.955 0.000 0.000 1.000
#> GSM876900 3 0.000 0.955 0.000 0.000 1.000
#> GSM876901 3 0.000 0.955 0.000 0.000 1.000
#> GSM876902 3 0.000 0.955 0.000 0.000 1.000
#> GSM876903 3 0.000 0.955 0.000 0.000 1.000
#> GSM876904 3 0.000 0.955 0.000 0.000 1.000
#> GSM876874 1 0.000 0.980 1.000 0.000 0.000
#> GSM876875 1 0.000 0.980 1.000 0.000 0.000
#> GSM876876 1 0.000 0.980 1.000 0.000 0.000
#> GSM876877 1 0.000 0.980 1.000 0.000 0.000
#> GSM876878 1 0.000 0.980 1.000 0.000 0.000
#> GSM876879 1 0.000 0.980 1.000 0.000 0.000
#> GSM876880 1 0.000 0.980 1.000 0.000 0.000
#> GSM876850 2 0.000 0.986 0.000 1.000 0.000
#> GSM876851 2 0.000 0.986 0.000 1.000 0.000
#> GSM876852 2 0.000 0.986 0.000 1.000 0.000
#> GSM876853 2 0.000 0.986 0.000 1.000 0.000
#> GSM876854 2 0.000 0.986 0.000 1.000 0.000
#> GSM876855 2 0.000 0.986 0.000 1.000 0.000
#> GSM876856 2 0.000 0.986 0.000 1.000 0.000
#> GSM876905 3 0.529 0.629 0.268 0.000 0.732
#> GSM876906 3 0.000 0.955 0.000 0.000 1.000
#> GSM876907 3 0.000 0.955 0.000 0.000 1.000
#> GSM876908 3 0.000 0.955 0.000 0.000 1.000
#> GSM876909 3 0.000 0.955 0.000 0.000 1.000
#> GSM876881 2 0.000 0.986 0.000 1.000 0.000
#> GSM876882 1 0.608 0.347 0.612 0.000 0.388
#> GSM876883 3 0.000 0.955 0.000 0.000 1.000
#> GSM876884 1 0.000 0.980 1.000 0.000 0.000
#> GSM876885 3 0.000 0.955 0.000 0.000 1.000
#> GSM876857 1 0.000 0.980 1.000 0.000 0.000
#> GSM876858 2 0.000 0.986 0.000 1.000 0.000
#> GSM876859 2 0.000 0.986 0.000 1.000 0.000
#> GSM876860 2 0.000 0.986 0.000 1.000 0.000
#> GSM876861 2 0.000 0.986 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM876887 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM876888 3 0.0188 0.987 0.004 0.000 0.996 0.000
#> GSM876889 3 0.0592 0.976 0.000 0.000 0.984 0.016
#> GSM876890 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM876891 4 0.4933 0.426 0.000 0.000 0.432 0.568
#> GSM876862 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876839 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876840 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876841 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876842 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876843 2 0.4933 0.379 0.000 0.568 0.000 0.432
#> GSM876892 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM876893 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM876894 3 0.1474 0.930 0.000 0.000 0.948 0.052
#> GSM876895 4 0.5097 0.398 0.000 0.428 0.004 0.568
#> GSM876896 4 0.1940 0.570 0.000 0.076 0.000 0.924
#> GSM876897 4 0.3942 0.393 0.000 0.236 0.000 0.764
#> GSM876868 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 0.586 0.000 0.000 0.000 1.000
#> GSM876873 4 0.0000 0.586 0.000 0.000 0.000 1.000
#> GSM876844 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876845 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876846 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876847 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876848 2 0.4933 0.379 0.000 0.568 0.000 0.432
#> GSM876849 2 0.4933 0.379 0.000 0.568 0.000 0.432
#> GSM876898 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM876899 4 0.4933 0.426 0.000 0.000 0.432 0.568
#> GSM876900 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM876901 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM876902 4 0.0000 0.586 0.000 0.000 0.000 1.000
#> GSM876903 4 0.5097 0.398 0.000 0.428 0.004 0.568
#> GSM876904 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM876874 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876875 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876876 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876879 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876880 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876851 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876852 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876853 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876854 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876855 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876856 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876905 3 0.0000 0.992 0.000 0.000 1.000 0.000
#> GSM876906 4 0.4933 0.426 0.000 0.000 0.432 0.568
#> GSM876907 4 0.5602 0.428 0.000 0.408 0.024 0.568
#> GSM876908 4 0.4933 0.426 0.000 0.000 0.432 0.568
#> GSM876909 4 0.5097 0.398 0.000 0.428 0.004 0.568
#> GSM876881 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876882 1 0.3764 0.701 0.784 0.000 0.216 0.000
#> GSM876883 4 0.4933 0.426 0.000 0.000 0.432 0.568
#> GSM876884 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876885 4 0.4933 0.426 0.000 0.000 0.432 0.568
#> GSM876857 1 0.0000 0.987 1.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876859 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876860 2 0.0000 0.933 0.000 1.000 0.000 0.000
#> GSM876861 2 0.0000 0.933 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
#> GSM876886 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM876887 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM876888 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM876889 5 0.416 0.3592 0.000 0.000 0.392 0.000 0.608
#> GSM876890 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM876891 5 0.000 0.9607 0.000 0.000 0.000 0.000 1.000
#> GSM876862 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876867 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876839 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876840 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876841 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876842 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876843 4 0.238 0.8610 0.000 0.128 0.000 0.872 0.000
#> GSM876892 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM876893 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM876894 5 0.000 0.9607 0.000 0.000 0.000 0.000 1.000
#> GSM876895 5 0.000 0.9607 0.000 0.000 0.000 0.000 1.000
#> GSM876896 4 0.000 0.9544 0.000 0.000 0.000 1.000 0.000
#> GSM876897 4 0.000 0.9544 0.000 0.000 0.000 1.000 0.000
#> GSM876868 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.000 0.9544 0.000 0.000 0.000 1.000 0.000
#> GSM876873 4 0.000 0.9544 0.000 0.000 0.000 1.000 0.000
#> GSM876844 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876845 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876846 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876847 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876848 4 0.238 0.8610 0.000 0.128 0.000 0.872 0.000
#> GSM876849 4 0.000 0.9544 0.000 0.000 0.000 1.000 0.000
#> GSM876898 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM876899 5 0.000 0.9607 0.000 0.000 0.000 0.000 1.000
#> GSM876900 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM876901 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM876902 4 0.000 0.9544 0.000 0.000 0.000 1.000 0.000
#> GSM876903 5 0.000 0.9607 0.000 0.000 0.000 0.000 1.000
#> GSM876904 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM876874 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876875 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876876 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876879 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876880 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876851 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876852 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876853 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876854 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876855 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876856 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876905 3 0.000 1.0000 0.000 0.000 1.000 0.000 0.000
#> GSM876906 5 0.000 0.9607 0.000 0.000 0.000 0.000 1.000
#> GSM876907 5 0.000 0.9607 0.000 0.000 0.000 0.000 1.000
#> GSM876908 5 0.000 0.9607 0.000 0.000 0.000 0.000 1.000
#> GSM876909 5 0.000 0.9607 0.000 0.000 0.000 0.000 1.000
#> GSM876881 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876882 1 0.430 0.0385 0.512 0.000 0.000 0.000 0.488
#> GSM876883 5 0.000 0.9607 0.000 0.000 0.000 0.000 1.000
#> GSM876884 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876885 5 0.000 0.9607 0.000 0.000 0.000 0.000 1.000
#> GSM876857 1 0.000 0.9720 1.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876859 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876860 2 0.000 1.0000 0.000 1.000 0.000 0.000 0.000
#> GSM876861 2 0.000 1.0000 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
#> GSM876886 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876887 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876888 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876889 3 0.1075 0.950 0.000 0.000 0.952 0.000 0.048 0.000
#> GSM876890 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876891 3 0.1663 0.915 0.000 0.000 0.912 0.000 0.088 0.000
#> GSM876862 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876866 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876867 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0458 0.983 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM876839 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876840 2 0.0458 0.983 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM876841 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876842 2 0.0458 0.983 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM876843 4 0.2358 0.849 0.000 0.108 0.000 0.876 0.000 0.016
#> GSM876892 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876893 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876894 3 0.1501 0.927 0.000 0.000 0.924 0.000 0.076 0.000
#> GSM876895 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876896 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876897 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876868 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876872 6 0.2491 0.829 0.000 0.000 0.000 0.164 0.000 0.836
#> GSM876873 6 0.2219 0.851 0.000 0.000 0.000 0.136 0.000 0.864
#> GSM876844 2 0.0458 0.983 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM876845 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876846 2 0.0713 0.982 0.000 0.972 0.000 0.000 0.000 0.028
#> GSM876847 2 0.0363 0.980 0.000 0.988 0.000 0.000 0.000 0.012
#> GSM876848 4 0.2358 0.849 0.000 0.108 0.000 0.876 0.000 0.016
#> GSM876849 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876898 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876899 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876900 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876901 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876902 4 0.0000 0.924 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876903 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876904 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876874 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876875 6 0.2300 0.804 0.144 0.000 0.000 0.000 0.000 0.856
#> GSM876876 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.1556 0.912 0.920 0.000 0.000 0.000 0.000 0.080
#> GSM876879 6 0.1141 0.896 0.052 0.000 0.000 0.000 0.000 0.948
#> GSM876880 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0458 0.979 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM876851 2 0.0000 0.983 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876852 2 0.0458 0.983 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM876853 2 0.0458 0.983 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM876854 2 0.0458 0.983 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM876855 2 0.0458 0.983 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM876856 2 0.0458 0.983 0.000 0.984 0.000 0.000 0.000 0.016
#> GSM876905 3 0.0000 0.983 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876906 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876907 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876908 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876909 5 0.0000 1.000 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876881 2 0.0865 0.970 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM876882 6 0.1141 0.896 0.052 0.000 0.000 0.000 0.000 0.948
#> GSM876883 6 0.1141 0.889 0.000 0.000 0.000 0.000 0.052 0.948
#> GSM876884 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876885 6 0.1141 0.889 0.000 0.000 0.000 0.000 0.052 0.948
#> GSM876857 1 0.0000 0.995 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0865 0.970 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM876859 2 0.0865 0.970 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM876860 2 0.0865 0.970 0.000 0.964 0.000 0.000 0.000 0.036
#> GSM876861 2 0.0865 0.970 0.000 0.964 0.000 0.000 0.000 0.036
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> MAD:pam 71 0.5743 1.09e-09 2
#> MAD:pam 70 0.7646 3.88e-20 3
#> MAD:pam 58 0.4691 3.64e-19 4
#> MAD:pam 70 0.0293 1.05e-18 5
#> MAD:pam 72 0.1410 9.23e-22 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 72 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 0.519 0.921 0.934 0.4219 0.593 0.593
#> 3 3 0.906 0.875 0.948 0.5846 0.745 0.571
#> 4 4 0.946 0.927 0.966 0.1206 0.881 0.661
#> 5 5 1.000 0.963 0.985 0.0339 0.963 0.856
#> 6 6 1.000 0.976 0.989 0.0433 0.965 0.846
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 6
#> attr(,"optional")
#> [1] 3 4 5
There is also optional best \(k\) = 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
#> GSM876886 2 0.541 0.914 0.124 0.876
#> GSM876887 2 0.541 0.914 0.124 0.876
#> GSM876888 2 0.541 0.914 0.124 0.876
#> GSM876889 2 0.518 0.916 0.116 0.884
#> GSM876890 2 0.541 0.914 0.124 0.876
#> GSM876891 2 0.518 0.916 0.116 0.884
#> GSM876862 1 0.000 1.000 1.000 0.000
#> GSM876863 1 0.000 1.000 1.000 0.000
#> GSM876864 1 0.000 1.000 1.000 0.000
#> GSM876865 1 0.000 1.000 1.000 0.000
#> GSM876866 1 0.000 1.000 1.000 0.000
#> GSM876867 1 0.000 1.000 1.000 0.000
#> GSM876838 2 0.000 0.905 0.000 1.000
#> GSM876839 2 0.000 0.905 0.000 1.000
#> GSM876840 2 0.000 0.905 0.000 1.000
#> GSM876841 2 0.000 0.905 0.000 1.000
#> GSM876842 2 0.000 0.905 0.000 1.000
#> GSM876843 2 0.242 0.910 0.040 0.960
#> GSM876892 2 0.541 0.914 0.124 0.876
#> GSM876893 2 0.541 0.914 0.124 0.876
#> GSM876894 2 0.518 0.916 0.116 0.884
#> GSM876895 2 0.671 0.875 0.176 0.824
#> GSM876896 2 0.574 0.907 0.136 0.864
#> GSM876897 2 0.574 0.907 0.136 0.864
#> GSM876868 1 0.000 1.000 1.000 0.000
#> GSM876869 1 0.000 1.000 1.000 0.000
#> GSM876870 1 0.000 1.000 1.000 0.000
#> GSM876871 1 0.000 1.000 1.000 0.000
#> GSM876872 2 0.895 0.713 0.312 0.688
#> GSM876873 2 0.895 0.713 0.312 0.688
#> GSM876844 2 0.000 0.905 0.000 1.000
#> GSM876845 2 0.000 0.905 0.000 1.000
#> GSM876846 2 0.000 0.905 0.000 1.000
#> GSM876847 2 0.000 0.905 0.000 1.000
#> GSM876848 2 0.634 0.884 0.160 0.840
#> GSM876849 2 0.871 0.739 0.292 0.708
#> GSM876898 2 0.541 0.914 0.124 0.876
#> GSM876899 2 0.518 0.916 0.116 0.884
#> GSM876900 2 0.541 0.914 0.124 0.876
#> GSM876901 2 0.541 0.914 0.124 0.876
#> GSM876902 2 0.574 0.907 0.136 0.864
#> GSM876903 2 0.518 0.916 0.116 0.884
#> GSM876904 2 0.541 0.914 0.124 0.876
#> GSM876874 1 0.000 1.000 1.000 0.000
#> GSM876875 1 0.000 1.000 1.000 0.000
#> GSM876876 1 0.000 1.000 1.000 0.000
#> GSM876877 1 0.000 1.000 1.000 0.000
#> GSM876878 1 0.000 1.000 1.000 0.000
#> GSM876879 1 0.000 1.000 1.000 0.000
#> GSM876880 1 0.000 1.000 1.000 0.000
#> GSM876850 2 0.000 0.905 0.000 1.000
#> GSM876851 2 0.000 0.905 0.000 1.000
#> GSM876852 2 0.000 0.905 0.000 1.000
#> GSM876853 2 0.000 0.905 0.000 1.000
#> GSM876854 2 0.000 0.905 0.000 1.000
#> GSM876855 2 0.000 0.905 0.000 1.000
#> GSM876856 2 0.000 0.905 0.000 1.000
#> GSM876905 2 0.541 0.914 0.124 0.876
#> GSM876906 2 0.518 0.916 0.116 0.884
#> GSM876907 2 0.518 0.916 0.116 0.884
#> GSM876908 2 0.518 0.916 0.116 0.884
#> GSM876909 2 0.518 0.916 0.116 0.884
#> GSM876881 2 0.000 0.905 0.000 1.000
#> GSM876882 1 0.000 1.000 1.000 0.000
#> GSM876883 2 0.895 0.713 0.312 0.688
#> GSM876884 1 0.000 1.000 1.000 0.000
#> GSM876885 2 0.895 0.713 0.312 0.688
#> GSM876857 1 0.000 1.000 1.000 0.000
#> GSM876858 2 0.000 0.905 0.000 1.000
#> GSM876859 2 0.000 0.905 0.000 1.000
#> GSM876860 2 0.000 0.905 0.000 1.000
#> GSM876861 2 0.000 0.905 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876887 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876888 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876889 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876890 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876891 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876862 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876863 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876864 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876865 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876866 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876867 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876838 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876839 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876840 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876841 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876842 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876843 3 0.6307 0.177 0.000 0.488 0.512
#> GSM876892 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876893 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876894 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876895 3 0.7346 0.291 0.032 0.432 0.536
#> GSM876896 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876897 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876868 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876869 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876870 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876871 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876872 3 0.6286 0.249 0.464 0.000 0.536
#> GSM876873 3 0.6286 0.249 0.464 0.000 0.536
#> GSM876844 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876845 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876846 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876847 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876848 3 0.6286 0.247 0.000 0.464 0.536
#> GSM876849 3 0.6286 0.247 0.000 0.464 0.536
#> GSM876898 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876899 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876900 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876901 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876902 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876903 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876904 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876874 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876875 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876876 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876877 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876878 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876879 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876880 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876850 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876851 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876852 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876853 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876854 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876855 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876856 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876905 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876906 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876907 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876908 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876909 3 0.0000 0.871 0.000 0.000 1.000
#> GSM876881 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876882 1 0.0592 0.986 0.988 0.000 0.012
#> GSM876883 3 0.6286 0.249 0.464 0.000 0.536
#> GSM876884 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876885 3 0.6286 0.249 0.464 0.000 0.536
#> GSM876857 1 0.0000 0.999 1.000 0.000 0.000
#> GSM876858 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876859 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876860 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876861 2 0.0000 1.000 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876887 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876888 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876889 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876890 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876891 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876862 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM876863 1 0.2868 0.817 0.864 0.000 0.000 0.136
#> GSM876864 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0592 0.955 0.984 0.000 0.000 0.016
#> GSM876866 4 0.4746 0.495 0.368 0.000 0.000 0.632
#> GSM876867 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876839 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876840 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876841 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876842 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876843 4 0.3726 0.679 0.000 0.212 0.000 0.788
#> GSM876892 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876893 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876894 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876895 4 0.4948 0.201 0.000 0.000 0.440 0.560
#> GSM876896 4 0.0000 0.830 0.000 0.000 0.000 1.000
#> GSM876897 4 0.0000 0.830 0.000 0.000 0.000 1.000
#> GSM876868 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 0.830 0.000 0.000 0.000 1.000
#> GSM876873 4 0.0000 0.830 0.000 0.000 0.000 1.000
#> GSM876844 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876845 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876846 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876847 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876848 4 0.2149 0.789 0.000 0.088 0.000 0.912
#> GSM876849 4 0.0000 0.830 0.000 0.000 0.000 1.000
#> GSM876898 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876899 3 0.0336 0.993 0.000 0.000 0.992 0.008
#> GSM876900 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876901 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876902 4 0.0000 0.830 0.000 0.000 0.000 1.000
#> GSM876903 3 0.0336 0.993 0.000 0.000 0.992 0.008
#> GSM876904 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876874 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM876875 1 0.4331 0.536 0.712 0.000 0.000 0.288
#> GSM876876 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM876878 1 0.0707 0.951 0.980 0.000 0.000 0.020
#> GSM876879 4 0.4661 0.536 0.348 0.000 0.000 0.652
#> GSM876880 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876851 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876852 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876853 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876854 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876855 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876856 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876905 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876906 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876907 3 0.0336 0.993 0.000 0.000 0.992 0.008
#> GSM876908 3 0.0000 0.998 0.000 0.000 1.000 0.000
#> GSM876909 3 0.0336 0.993 0.000 0.000 0.992 0.008
#> GSM876881 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876882 4 0.3569 0.742 0.196 0.000 0.000 0.804
#> GSM876883 4 0.3266 0.766 0.168 0.000 0.000 0.832
#> GSM876884 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM876885 4 0.3266 0.766 0.168 0.000 0.000 0.832
#> GSM876857 1 0.0000 0.966 1.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876859 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876860 2 0.0000 1.000 0.000 1.000 0.000 0.000
#> GSM876861 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
#> GSM876886 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876887 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876888 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876889 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876890 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876891 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876862 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.4294 0.118 0.532 0.000 0.000 0.000 0.468
#> GSM876864 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM876866 5 0.0404 0.996 0.000 0.000 0.000 0.012 0.988
#> GSM876867 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM876840 2 0.0404 0.992 0.000 0.988 0.000 0.000 0.012
#> GSM876841 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM876843 4 0.0162 0.994 0.000 0.004 0.000 0.996 0.000
#> GSM876892 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876893 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876894 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876895 3 0.6183 0.329 0.000 0.308 0.544 0.144 0.004
#> GSM876896 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM876897 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM876868 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM876873 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM876844 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM876846 2 0.0404 0.992 0.000 0.988 0.000 0.000 0.012
#> GSM876847 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM876848 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM876849 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM876898 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876899 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876900 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876901 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876902 4 0.0000 0.999 0.000 0.000 0.000 1.000 0.000
#> GSM876903 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876904 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876874 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM876875 5 0.0566 0.993 0.004 0.000 0.000 0.012 0.984
#> GSM876876 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0162 0.964 0.996 0.000 0.000 0.000 0.004
#> GSM876879 5 0.0404 0.996 0.000 0.000 0.000 0.012 0.988
#> GSM876880 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM876852 2 0.0404 0.992 0.000 0.988 0.000 0.000 0.012
#> GSM876853 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM876854 2 0.0404 0.992 0.000 0.988 0.000 0.000 0.012
#> GSM876855 2 0.0404 0.992 0.000 0.988 0.000 0.000 0.012
#> GSM876856 2 0.0404 0.992 0.000 0.988 0.000 0.000 0.012
#> GSM876905 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876906 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876907 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876908 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876909 3 0.0000 0.975 0.000 0.000 1.000 0.000 0.000
#> GSM876881 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM876882 5 0.0404 0.996 0.000 0.000 0.000 0.012 0.988
#> GSM876883 5 0.0404 0.996 0.000 0.000 0.000 0.012 0.988
#> GSM876884 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM876885 5 0.0703 0.987 0.000 0.000 0.000 0.024 0.976
#> GSM876857 1 0.0000 0.968 1.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM876859 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM876860 2 0.0000 0.997 0.000 1.000 0.000 0.000 0.000
#> GSM876861 2 0.0000 0.997 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
#> GSM876886 3 0.0000 0.975 0.000 0.000 1.000 0.00 0.000 0.000
#> GSM876887 3 0.0000 0.975 0.000 0.000 1.000 0.00 0.000 0.000
#> GSM876888 3 0.0000 0.975 0.000 0.000 1.000 0.00 0.000 0.000
#> GSM876889 3 0.0260 0.974 0.000 0.000 0.992 0.00 0.008 0.000
#> GSM876890 3 0.0000 0.975 0.000 0.000 1.000 0.00 0.000 0.000
#> GSM876891 3 0.0260 0.974 0.000 0.000 0.992 0.00 0.008 0.000
#> GSM876862 1 0.0000 0.997 1.000 0.000 0.000 0.00 0.000 0.000
#> GSM876863 1 0.1007 0.954 0.956 0.000 0.000 0.00 0.000 0.044
#> GSM876864 1 0.0000 0.997 1.000 0.000 0.000 0.00 0.000 0.000
#> GSM876865 1 0.0000 0.997 1.000 0.000 0.000 0.00 0.000 0.000
#> GSM876866 6 0.0000 1.000 0.000 0.000 0.000 0.00 0.000 1.000
#> GSM876867 1 0.0000 0.997 1.000 0.000 0.000 0.00 0.000 0.000
#> GSM876838 2 0.0000 0.993 0.000 1.000 0.000 0.00 0.000 0.000
#> GSM876839 2 0.0000 0.993 0.000 1.000 0.000 0.00 0.000 0.000
#> GSM876840 5 0.0260 0.964 0.000 0.008 0.000 0.00 0.992 0.000
#> GSM876841 2 0.0146 0.993 0.000 0.996 0.000 0.00 0.004 0.000
#> GSM876842 2 0.0260 0.992 0.000 0.992 0.000 0.00 0.008 0.000
#> GSM876843 4 0.0000 1.000 0.000 0.000 0.000 1.00 0.000 0.000
#> GSM876892 3 0.0000 0.975 0.000 0.000 1.000 0.00 0.000 0.000
#> GSM876893 3 0.0000 0.975 0.000 0.000 1.000 0.00 0.000 0.000
#> GSM876894 3 0.0146 0.975 0.000 0.000 0.996 0.00 0.004 0.000
#> GSM876895 3 0.4834 0.395 0.000 0.340 0.596 0.06 0.000 0.004
#> GSM876896 4 0.0000 1.000 0.000 0.000 0.000 1.00 0.000 0.000
#> GSM876897 4 0.0000 1.000 0.000 0.000 0.000 1.00 0.000 0.000
#> GSM876868 1 0.0000 0.997 1.000 0.000 0.000 0.00 0.000 0.000
#> GSM876869 1 0.0000 0.997 1.000 0.000 0.000 0.00 0.000 0.000
#> GSM876870 1 0.0000 0.997 1.000 0.000 0.000 0.00 0.000 0.000
#> GSM876871 1 0.0000 0.997 1.000 0.000 0.000 0.00 0.000 0.000
#> GSM876872 4 0.0000 1.000 0.000 0.000 0.000 1.00 0.000 0.000
#> GSM876873 4 0.0000 1.000 0.000 0.000 0.000 1.00 0.000 0.000
#> GSM876844 2 0.0260 0.992 0.000 0.992 0.000 0.00 0.008 0.000
#> GSM876845 2 0.0000 0.993 0.000 1.000 0.000 0.00 0.000 0.000
#> GSM876846 5 0.0260 0.964 0.000 0.008 0.000 0.00 0.992 0.000
#> GSM876847 2 0.0000 0.993 0.000 1.000 0.000 0.00 0.000 0.000
#> GSM876848 4 0.0000 1.000 0.000 0.000 0.000 1.00 0.000 0.000
#> GSM876849 4 0.0000 1.000 0.000 0.000 0.000 1.00 0.000 0.000
#> GSM876898 3 0.0000 0.975 0.000 0.000 1.000 0.00 0.000 0.000
#> GSM876899 3 0.0260 0.974 0.000 0.000 0.992 0.00 0.008 0.000
#> GSM876900 3 0.0000 0.975 0.000 0.000 1.000 0.00 0.000 0.000
#> GSM876901 3 0.0000 0.975 0.000 0.000 1.000 0.00 0.000 0.000
#> GSM876902 4 0.0000 1.000 0.000 0.000 0.000 1.00 0.000 0.000
#> GSM876903 3 0.0260 0.974 0.000 0.000 0.992 0.00 0.008 0.000
#> GSM876904 3 0.0146 0.975 0.000 0.000 0.996 0.00 0.004 0.000
#> GSM876874 1 0.0000 0.997 1.000 0.000 0.000 0.00 0.000 0.000
#> GSM876875 6 0.0000 1.000 0.000 0.000 0.000 0.00 0.000 1.000
#> GSM876876 1 0.0000 0.997 1.000 0.000 0.000 0.00 0.000 0.000
#> GSM876877 1 0.0000 0.997 1.000 0.000 0.000 0.00 0.000 0.000
#> GSM876878 1 0.0000 0.997 1.000 0.000 0.000 0.00 0.000 0.000
#> GSM876879 6 0.0000 1.000 0.000 0.000 0.000 0.00 0.000 1.000
#> GSM876880 1 0.0000 0.997 1.000 0.000 0.000 0.00 0.000 0.000
#> GSM876850 2 0.0000 0.993 0.000 1.000 0.000 0.00 0.000 0.000
#> GSM876851 2 0.0000 0.993 0.000 1.000 0.000 0.00 0.000 0.000
#> GSM876852 5 0.2260 0.817 0.000 0.140 0.000 0.00 0.860 0.000
#> GSM876853 2 0.0146 0.993 0.000 0.996 0.000 0.00 0.004 0.000
#> GSM876854 5 0.0260 0.964 0.000 0.008 0.000 0.00 0.992 0.000
#> GSM876855 5 0.0260 0.964 0.000 0.008 0.000 0.00 0.992 0.000
#> GSM876856 5 0.0260 0.964 0.000 0.008 0.000 0.00 0.992 0.000
#> GSM876905 3 0.0000 0.975 0.000 0.000 1.000 0.00 0.000 0.000
#> GSM876906 3 0.0260 0.974 0.000 0.000 0.992 0.00 0.008 0.000
#> GSM876907 3 0.0260 0.974 0.000 0.000 0.992 0.00 0.008 0.000
#> GSM876908 3 0.0260 0.974 0.000 0.000 0.992 0.00 0.008 0.000
#> GSM876909 3 0.0260 0.974 0.000 0.000 0.992 0.00 0.008 0.000
#> GSM876881 2 0.0000 0.993 0.000 1.000 0.000 0.00 0.000 0.000
#> GSM876882 6 0.0000 1.000 0.000 0.000 0.000 0.00 0.000 1.000
#> GSM876883 6 0.0000 1.000 0.000 0.000 0.000 0.00 0.000 1.000
#> GSM876884 1 0.0000 0.997 1.000 0.000 0.000 0.00 0.000 0.000
#> GSM876885 6 0.0000 1.000 0.000 0.000 0.000 0.00 0.000 1.000
#> GSM876857 1 0.0000 0.997 1.000 0.000 0.000 0.00 0.000 0.000
#> GSM876858 2 0.0260 0.992 0.000 0.992 0.000 0.00 0.008 0.000
#> GSM876859 2 0.0260 0.992 0.000 0.992 0.000 0.00 0.008 0.000
#> GSM876860 2 0.0260 0.992 0.000 0.992 0.000 0.00 0.008 0.000
#> GSM876861 2 0.1141 0.950 0.000 0.948 0.000 0.00 0.052 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> MAD:mclust 72 0.7222 4.87e-11 2
#> MAD:mclust 64 0.9947 3.61e-24 3
#> MAD:mclust 70 0.5478 1.29e-20 4
#> MAD:mclust 70 0.1343 9.11e-21 5
#> MAD:mclust 71 0.0739 4.84e-20 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 72 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 1.000 0.975 0.991 0.4901 0.512 0.512
#> 3 3 0.744 0.791 0.903 0.3308 0.806 0.633
#> 4 4 0.993 0.960 0.973 0.1161 0.815 0.542
#> 5 5 0.861 0.833 0.892 0.0717 0.905 0.670
#> 6 6 0.799 0.725 0.837 0.0229 0.962 0.839
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
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
#> GSM876886 1 0.000 0.988 1.000 0.000
#> GSM876887 1 0.000 0.988 1.000 0.000
#> GSM876888 1 0.000 0.988 1.000 0.000
#> GSM876889 1 0.000 0.988 1.000 0.000
#> GSM876890 1 0.000 0.988 1.000 0.000
#> GSM876891 1 0.000 0.988 1.000 0.000
#> GSM876862 1 0.000 0.988 1.000 0.000
#> GSM876863 1 0.000 0.988 1.000 0.000
#> GSM876864 1 0.000 0.988 1.000 0.000
#> GSM876865 1 0.000 0.988 1.000 0.000
#> GSM876866 1 0.000 0.988 1.000 0.000
#> GSM876867 1 0.000 0.988 1.000 0.000
#> GSM876838 2 0.000 0.995 0.000 1.000
#> GSM876839 2 0.000 0.995 0.000 1.000
#> GSM876840 2 0.000 0.995 0.000 1.000
#> GSM876841 2 0.000 0.995 0.000 1.000
#> GSM876842 2 0.000 0.995 0.000 1.000
#> GSM876843 2 0.000 0.995 0.000 1.000
#> GSM876892 1 0.000 0.988 1.000 0.000
#> GSM876893 1 0.000 0.988 1.000 0.000
#> GSM876894 1 0.000 0.988 1.000 0.000
#> GSM876895 2 0.482 0.885 0.104 0.896
#> GSM876896 1 0.999 0.066 0.520 0.480
#> GSM876897 2 0.000 0.995 0.000 1.000
#> GSM876868 1 0.000 0.988 1.000 0.000
#> GSM876869 1 0.000 0.988 1.000 0.000
#> GSM876870 1 0.000 0.988 1.000 0.000
#> GSM876871 1 0.000 0.988 1.000 0.000
#> GSM876872 1 0.000 0.988 1.000 0.000
#> GSM876873 1 0.000 0.988 1.000 0.000
#> GSM876844 2 0.000 0.995 0.000 1.000
#> GSM876845 2 0.000 0.995 0.000 1.000
#> GSM876846 2 0.000 0.995 0.000 1.000
#> GSM876847 2 0.000 0.995 0.000 1.000
#> GSM876848 2 0.000 0.995 0.000 1.000
#> GSM876849 2 0.000 0.995 0.000 1.000
#> GSM876898 1 0.000 0.988 1.000 0.000
#> GSM876899 1 0.163 0.964 0.976 0.024
#> GSM876900 1 0.000 0.988 1.000 0.000
#> GSM876901 1 0.000 0.988 1.000 0.000
#> GSM876902 1 0.000 0.988 1.000 0.000
#> GSM876903 2 0.118 0.981 0.016 0.984
#> GSM876904 1 0.000 0.988 1.000 0.000
#> GSM876874 1 0.000 0.988 1.000 0.000
#> GSM876875 1 0.000 0.988 1.000 0.000
#> GSM876876 1 0.000 0.988 1.000 0.000
#> GSM876877 1 0.000 0.988 1.000 0.000
#> GSM876878 1 0.000 0.988 1.000 0.000
#> GSM876879 1 0.000 0.988 1.000 0.000
#> GSM876880 1 0.000 0.988 1.000 0.000
#> GSM876850 2 0.000 0.995 0.000 1.000
#> GSM876851 2 0.000 0.995 0.000 1.000
#> GSM876852 2 0.000 0.995 0.000 1.000
#> GSM876853 2 0.000 0.995 0.000 1.000
#> GSM876854 2 0.000 0.995 0.000 1.000
#> GSM876855 2 0.000 0.995 0.000 1.000
#> GSM876856 2 0.000 0.995 0.000 1.000
#> GSM876905 1 0.000 0.988 1.000 0.000
#> GSM876906 1 0.000 0.988 1.000 0.000
#> GSM876907 2 0.163 0.974 0.024 0.976
#> GSM876908 1 0.000 0.988 1.000 0.000
#> GSM876909 2 0.000 0.995 0.000 1.000
#> GSM876881 2 0.000 0.995 0.000 1.000
#> GSM876882 1 0.000 0.988 1.000 0.000
#> GSM876883 1 0.000 0.988 1.000 0.000
#> GSM876884 1 0.000 0.988 1.000 0.000
#> GSM876885 1 0.000 0.988 1.000 0.000
#> GSM876857 1 0.000 0.988 1.000 0.000
#> GSM876858 2 0.000 0.995 0.000 1.000
#> GSM876859 2 0.000 0.995 0.000 1.000
#> GSM876860 2 0.000 0.995 0.000 1.000
#> GSM876861 2 0.000 0.995 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 1 0.5560 0.663 0.700 0.000 0.300
#> GSM876887 1 0.5785 0.617 0.668 0.000 0.332
#> GSM876888 1 0.5397 0.679 0.720 0.000 0.280
#> GSM876889 3 0.1163 0.806 0.028 0.000 0.972
#> GSM876890 1 0.6286 0.326 0.536 0.000 0.464
#> GSM876891 3 0.4121 0.685 0.168 0.000 0.832
#> GSM876862 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876863 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876864 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876865 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876866 1 0.0424 0.837 0.992 0.000 0.008
#> GSM876867 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876838 2 0.0000 0.968 0.000 1.000 0.000
#> GSM876839 2 0.0237 0.967 0.000 0.996 0.004
#> GSM876840 2 0.0000 0.968 0.000 1.000 0.000
#> GSM876841 2 0.0237 0.967 0.000 0.996 0.004
#> GSM876842 2 0.0000 0.968 0.000 1.000 0.000
#> GSM876843 2 0.0424 0.964 0.000 0.992 0.008
#> GSM876892 1 0.5560 0.663 0.700 0.000 0.300
#> GSM876893 1 0.5560 0.663 0.700 0.000 0.300
#> GSM876894 3 0.5465 0.464 0.288 0.000 0.712
#> GSM876895 2 0.2261 0.894 0.068 0.932 0.000
#> GSM876896 3 0.0829 0.802 0.004 0.012 0.984
#> GSM876897 3 0.3686 0.744 0.000 0.140 0.860
#> GSM876868 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876869 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876870 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876871 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876872 3 0.4842 0.675 0.224 0.000 0.776
#> GSM876873 3 0.4887 0.672 0.228 0.000 0.772
#> GSM876844 2 0.0000 0.968 0.000 1.000 0.000
#> GSM876845 2 0.0237 0.967 0.000 0.996 0.004
#> GSM876846 2 0.0000 0.968 0.000 1.000 0.000
#> GSM876847 2 0.0424 0.966 0.000 0.992 0.008
#> GSM876848 2 0.3482 0.834 0.000 0.872 0.128
#> GSM876849 3 0.5591 0.495 0.000 0.304 0.696
#> GSM876898 1 0.5465 0.670 0.712 0.000 0.288
#> GSM876899 3 0.1163 0.806 0.028 0.000 0.972
#> GSM876900 1 0.5560 0.663 0.700 0.000 0.300
#> GSM876901 1 0.5560 0.663 0.700 0.000 0.300
#> GSM876902 3 0.0747 0.804 0.016 0.000 0.984
#> GSM876903 3 0.2356 0.789 0.000 0.072 0.928
#> GSM876904 1 0.5465 0.672 0.712 0.000 0.288
#> GSM876874 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876875 1 0.0592 0.836 0.988 0.000 0.012
#> GSM876876 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876877 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876878 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876879 1 0.0747 0.834 0.984 0.000 0.016
#> GSM876880 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876850 2 0.0592 0.963 0.000 0.988 0.012
#> GSM876851 2 0.0237 0.967 0.000 0.996 0.004
#> GSM876852 2 0.0000 0.968 0.000 1.000 0.000
#> GSM876853 2 0.0237 0.967 0.000 0.996 0.004
#> GSM876854 2 0.0000 0.968 0.000 1.000 0.000
#> GSM876855 2 0.0000 0.968 0.000 1.000 0.000
#> GSM876856 2 0.0000 0.968 0.000 1.000 0.000
#> GSM876905 1 0.5560 0.663 0.700 0.000 0.300
#> GSM876906 3 0.1289 0.805 0.032 0.000 0.968
#> GSM876907 3 0.5529 0.551 0.000 0.296 0.704
#> GSM876908 3 0.1289 0.805 0.032 0.000 0.968
#> GSM876909 2 0.6215 0.168 0.000 0.572 0.428
#> GSM876881 2 0.0592 0.963 0.000 0.988 0.012
#> GSM876882 1 0.0747 0.834 0.984 0.000 0.016
#> GSM876883 1 0.6274 -0.111 0.544 0.000 0.456
#> GSM876884 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876885 3 0.6299 0.245 0.476 0.000 0.524
#> GSM876857 1 0.0000 0.839 1.000 0.000 0.000
#> GSM876858 2 0.0237 0.967 0.000 0.996 0.004
#> GSM876859 2 0.0000 0.968 0.000 1.000 0.000
#> GSM876860 2 0.0000 0.968 0.000 1.000 0.000
#> GSM876861 2 0.0000 0.968 0.000 1.000 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.0804 0.967 0.008 0.000 0.980 0.012
#> GSM876887 3 0.1211 0.967 0.000 0.000 0.960 0.040
#> GSM876888 3 0.0524 0.962 0.004 0.000 0.988 0.008
#> GSM876889 3 0.1940 0.946 0.000 0.000 0.924 0.076
#> GSM876890 3 0.1211 0.967 0.000 0.000 0.960 0.040
#> GSM876891 3 0.1211 0.967 0.000 0.000 0.960 0.040
#> GSM876862 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM876863 1 0.0188 0.986 0.996 0.000 0.000 0.004
#> GSM876864 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM876866 1 0.0188 0.986 0.996 0.000 0.000 0.004
#> GSM876867 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM876839 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM876840 2 0.0592 0.985 0.000 0.984 0.000 0.016
#> GSM876841 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM876842 2 0.0188 0.990 0.000 0.996 0.000 0.004
#> GSM876843 2 0.1867 0.931 0.000 0.928 0.000 0.072
#> GSM876892 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM876893 3 0.0336 0.964 0.000 0.000 0.992 0.008
#> GSM876894 3 0.1022 0.968 0.000 0.000 0.968 0.032
#> GSM876895 2 0.0524 0.984 0.008 0.988 0.000 0.004
#> GSM876896 4 0.1557 0.887 0.000 0.000 0.056 0.944
#> GSM876897 4 0.1452 0.892 0.000 0.008 0.036 0.956
#> GSM876868 1 0.0188 0.985 0.996 0.000 0.004 0.000
#> GSM876869 1 0.0188 0.985 0.996 0.000 0.004 0.000
#> GSM876870 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM876872 4 0.2521 0.881 0.064 0.000 0.024 0.912
#> GSM876873 4 0.2596 0.878 0.068 0.000 0.024 0.908
#> GSM876844 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM876845 2 0.0188 0.989 0.000 0.996 0.000 0.004
#> GSM876846 2 0.0469 0.987 0.000 0.988 0.000 0.012
#> GSM876847 2 0.0469 0.985 0.000 0.988 0.000 0.012
#> GSM876848 4 0.4431 0.556 0.000 0.304 0.000 0.696
#> GSM876849 4 0.1743 0.876 0.000 0.056 0.004 0.940
#> GSM876898 3 0.0469 0.962 0.000 0.000 0.988 0.012
#> GSM876899 3 0.1302 0.966 0.000 0.000 0.956 0.044
#> GSM876900 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM876901 3 0.0000 0.967 0.000 0.000 1.000 0.000
#> GSM876902 4 0.1867 0.877 0.000 0.000 0.072 0.928
#> GSM876903 3 0.3306 0.857 0.000 0.004 0.840 0.156
#> GSM876904 3 0.0336 0.964 0.000 0.000 0.992 0.008
#> GSM876874 1 0.0188 0.985 0.996 0.000 0.004 0.000
#> GSM876875 1 0.0188 0.986 0.996 0.000 0.000 0.004
#> GSM876876 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0188 0.985 0.996 0.000 0.004 0.000
#> GSM876878 1 0.0188 0.986 0.996 0.000 0.000 0.004
#> GSM876879 1 0.0188 0.986 0.996 0.000 0.000 0.004
#> GSM876880 1 0.0000 0.986 1.000 0.000 0.000 0.000
#> GSM876850 2 0.0469 0.985 0.000 0.988 0.000 0.012
#> GSM876851 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM876852 2 0.0592 0.985 0.000 0.984 0.000 0.016
#> GSM876853 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM876854 2 0.0469 0.987 0.000 0.988 0.000 0.012
#> GSM876855 2 0.0707 0.982 0.000 0.980 0.000 0.020
#> GSM876856 2 0.0592 0.985 0.000 0.984 0.000 0.016
#> GSM876905 3 0.0336 0.964 0.000 0.000 0.992 0.008
#> GSM876906 3 0.1716 0.955 0.000 0.000 0.936 0.064
#> GSM876907 3 0.1211 0.967 0.000 0.000 0.960 0.040
#> GSM876908 3 0.1474 0.962 0.000 0.000 0.948 0.052
#> GSM876909 3 0.1356 0.964 0.000 0.008 0.960 0.032
#> GSM876881 2 0.0469 0.985 0.000 0.988 0.000 0.012
#> GSM876882 1 0.0188 0.986 0.996 0.000 0.000 0.004
#> GSM876883 1 0.2216 0.900 0.908 0.000 0.000 0.092
#> GSM876884 1 0.0188 0.986 0.996 0.000 0.000 0.004
#> GSM876885 1 0.2921 0.843 0.860 0.000 0.000 0.140
#> GSM876857 1 0.0188 0.985 0.996 0.000 0.004 0.000
#> GSM876858 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM876859 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM876860 2 0.0000 0.990 0.000 1.000 0.000 0.000
#> GSM876861 2 0.0000 0.990 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
#> GSM876886 3 0.0794 0.9445 0.000 0.000 0.972 0.000 0.028
#> GSM876887 3 0.1168 0.9483 0.000 0.000 0.960 0.008 0.032
#> GSM876888 3 0.1282 0.9307 0.000 0.000 0.952 0.004 0.044
#> GSM876889 3 0.2077 0.9324 0.000 0.000 0.920 0.040 0.040
#> GSM876890 3 0.0324 0.9541 0.000 0.000 0.992 0.004 0.004
#> GSM876891 3 0.1469 0.9446 0.000 0.000 0.948 0.016 0.036
#> GSM876862 1 0.0898 0.9481 0.972 0.000 0.008 0.000 0.020
#> GSM876863 1 0.0290 0.9500 0.992 0.000 0.000 0.000 0.008
#> GSM876864 1 0.1251 0.9408 0.956 0.000 0.008 0.000 0.036
#> GSM876865 1 0.0290 0.9509 0.992 0.000 0.000 0.000 0.008
#> GSM876866 1 0.0566 0.9500 0.984 0.000 0.004 0.000 0.012
#> GSM876867 1 0.0693 0.9500 0.980 0.000 0.008 0.000 0.012
#> GSM876838 2 0.0794 0.8759 0.000 0.972 0.000 0.000 0.028
#> GSM876839 2 0.1544 0.8511 0.000 0.932 0.000 0.000 0.068
#> GSM876840 2 0.0693 0.8688 0.000 0.980 0.000 0.008 0.012
#> GSM876841 2 0.2690 0.7477 0.000 0.844 0.000 0.000 0.156
#> GSM876842 2 0.0609 0.8782 0.000 0.980 0.000 0.000 0.020
#> GSM876843 2 0.3563 0.6440 0.000 0.780 0.000 0.208 0.012
#> GSM876892 3 0.0404 0.9520 0.000 0.000 0.988 0.000 0.012
#> GSM876893 3 0.0566 0.9506 0.000 0.000 0.984 0.004 0.012
#> GSM876894 3 0.1915 0.9365 0.000 0.000 0.928 0.032 0.040
#> GSM876895 5 0.5435 0.6739 0.072 0.352 0.000 0.000 0.576
#> GSM876896 4 0.0451 0.7696 0.000 0.000 0.004 0.988 0.008
#> GSM876897 4 0.0613 0.7664 0.000 0.004 0.004 0.984 0.008
#> GSM876868 1 0.1626 0.9292 0.940 0.000 0.016 0.000 0.044
#> GSM876869 1 0.1331 0.9386 0.952 0.000 0.008 0.000 0.040
#> GSM876870 1 0.0162 0.9504 0.996 0.000 0.000 0.000 0.004
#> GSM876871 1 0.0290 0.9509 0.992 0.000 0.000 0.000 0.008
#> GSM876872 4 0.3688 0.7515 0.124 0.000 0.000 0.816 0.060
#> GSM876873 4 0.4221 0.7471 0.112 0.000 0.000 0.780 0.108
#> GSM876844 2 0.0703 0.8774 0.000 0.976 0.000 0.000 0.024
#> GSM876845 2 0.2852 0.7192 0.000 0.828 0.000 0.000 0.172
#> GSM876846 2 0.0510 0.8788 0.000 0.984 0.000 0.000 0.016
#> GSM876847 5 0.4304 0.4839 0.000 0.484 0.000 0.000 0.516
#> GSM876848 2 0.3628 0.6341 0.000 0.772 0.000 0.216 0.012
#> GSM876849 4 0.3174 0.6870 0.004 0.132 0.000 0.844 0.020
#> GSM876898 3 0.0324 0.9530 0.000 0.000 0.992 0.004 0.004
#> GSM876899 3 0.2300 0.9258 0.000 0.000 0.908 0.040 0.052
#> GSM876900 3 0.0404 0.9538 0.000 0.000 0.988 0.000 0.012
#> GSM876901 3 0.0000 0.9537 0.000 0.000 1.000 0.000 0.000
#> GSM876902 4 0.1195 0.7679 0.000 0.000 0.028 0.960 0.012
#> GSM876903 4 0.6748 0.3470 0.000 0.004 0.288 0.456 0.252
#> GSM876904 3 0.0771 0.9476 0.000 0.000 0.976 0.004 0.020
#> GSM876874 1 0.0992 0.9476 0.968 0.000 0.008 0.000 0.024
#> GSM876875 1 0.0510 0.9471 0.984 0.000 0.000 0.000 0.016
#> GSM876876 1 0.0451 0.9511 0.988 0.000 0.008 0.000 0.004
#> GSM876877 1 0.0898 0.9481 0.972 0.000 0.008 0.000 0.020
#> GSM876878 1 0.0510 0.9471 0.984 0.000 0.000 0.000 0.016
#> GSM876879 1 0.0880 0.9384 0.968 0.000 0.000 0.000 0.032
#> GSM876880 1 0.0451 0.9511 0.988 0.000 0.008 0.000 0.004
#> GSM876850 5 0.4262 0.5881 0.000 0.440 0.000 0.000 0.560
#> GSM876851 2 0.2471 0.7781 0.000 0.864 0.000 0.000 0.136
#> GSM876852 2 0.0162 0.8761 0.000 0.996 0.000 0.004 0.000
#> GSM876853 2 0.1965 0.8260 0.000 0.904 0.000 0.000 0.096
#> GSM876854 2 0.0000 0.8770 0.000 1.000 0.000 0.000 0.000
#> GSM876855 2 0.0693 0.8688 0.000 0.980 0.000 0.008 0.012
#> GSM876856 2 0.0566 0.8710 0.000 0.984 0.000 0.004 0.012
#> GSM876905 3 0.0324 0.9530 0.000 0.000 0.992 0.004 0.004
#> GSM876906 3 0.3116 0.8878 0.000 0.000 0.860 0.064 0.076
#> GSM876907 5 0.3850 0.4472 0.000 0.004 0.172 0.032 0.792
#> GSM876908 3 0.3201 0.8822 0.000 0.000 0.852 0.052 0.096
#> GSM876909 5 0.3309 0.5371 0.000 0.024 0.108 0.016 0.852
#> GSM876881 5 0.3707 0.7871 0.000 0.284 0.000 0.000 0.716
#> GSM876882 1 0.1430 0.9194 0.944 0.000 0.000 0.004 0.052
#> GSM876883 1 0.5484 0.0538 0.540 0.000 0.000 0.392 0.068
#> GSM876884 1 0.0290 0.9497 0.992 0.000 0.000 0.000 0.008
#> GSM876885 4 0.5593 0.4615 0.340 0.000 0.000 0.572 0.088
#> GSM876857 1 0.1331 0.9386 0.952 0.000 0.008 0.000 0.040
#> GSM876858 5 0.3612 0.7948 0.000 0.268 0.000 0.000 0.732
#> GSM876859 5 0.3636 0.7940 0.000 0.272 0.000 0.000 0.728
#> GSM876860 5 0.3561 0.7943 0.000 0.260 0.000 0.000 0.740
#> GSM876861 5 0.3534 0.7931 0.000 0.256 0.000 0.000 0.744
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM876886 3 0.0806 0.9282 0.008 0.000 0.972 0.000 0.000 NA
#> GSM876887 3 0.0291 0.9347 0.000 0.000 0.992 0.004 0.000 NA
#> GSM876888 3 0.1563 0.9015 0.012 0.000 0.932 0.000 0.000 NA
#> GSM876889 3 0.1237 0.9246 0.000 0.000 0.956 0.020 0.004 NA
#> GSM876890 3 0.0000 0.9357 0.000 0.000 1.000 0.000 0.000 NA
#> GSM876891 3 0.0551 0.9332 0.000 0.000 0.984 0.004 0.004 NA
#> GSM876862 1 0.2964 0.7611 0.792 0.000 0.004 0.000 0.000 NA
#> GSM876863 1 0.0000 0.8281 1.000 0.000 0.000 0.000 0.000 NA
#> GSM876864 1 0.3405 0.7199 0.724 0.000 0.004 0.000 0.000 NA
#> GSM876865 1 0.0291 0.8275 0.992 0.000 0.000 0.000 0.004 NA
#> GSM876866 1 0.0000 0.8281 1.000 0.000 0.000 0.000 0.000 NA
#> GSM876867 1 0.1644 0.8168 0.920 0.000 0.004 0.000 0.000 NA
#> GSM876838 2 0.0777 0.8288 0.000 0.972 0.000 0.000 0.024 NA
#> GSM876839 2 0.2066 0.8031 0.000 0.908 0.000 0.000 0.040 NA
#> GSM876840 2 0.1341 0.8137 0.000 0.948 0.000 0.024 0.000 NA
#> GSM876841 2 0.3522 0.7017 0.000 0.800 0.000 0.000 0.128 NA
#> GSM876842 2 0.0547 0.8305 0.000 0.980 0.000 0.000 0.020 NA
#> GSM876843 2 0.4201 0.4083 0.000 0.664 0.000 0.300 0.000 NA
#> GSM876892 3 0.0405 0.9346 0.004 0.000 0.988 0.000 0.000 NA
#> GSM876893 3 0.0603 0.9323 0.004 0.000 0.980 0.000 0.000 NA
#> GSM876894 3 0.1194 0.9248 0.000 0.000 0.956 0.008 0.004 NA
#> GSM876895 5 0.5711 0.4056 0.052 0.416 0.000 0.016 0.492 NA
#> GSM876896 4 0.0858 0.7209 0.000 0.000 0.004 0.968 0.000 NA
#> GSM876897 4 0.0436 0.7194 0.000 0.004 0.004 0.988 0.000 NA
#> GSM876868 1 0.3819 0.6329 0.624 0.000 0.004 0.000 0.000 NA
#> GSM876869 1 0.3742 0.6575 0.648 0.000 0.004 0.000 0.000 NA
#> GSM876870 1 0.0508 0.8261 0.984 0.000 0.000 0.000 0.004 NA
#> GSM876871 1 0.0146 0.8278 0.996 0.000 0.000 0.000 0.000 NA
#> GSM876872 4 0.4521 0.6224 0.108 0.000 0.000 0.712 0.004 NA
#> GSM876873 4 0.6327 0.2197 0.324 0.000 0.000 0.364 0.008 NA
#> GSM876844 2 0.0547 0.8305 0.000 0.980 0.000 0.000 0.020 NA
#> GSM876845 2 0.3770 0.6664 0.000 0.776 0.000 0.000 0.148 NA
#> GSM876846 2 0.2138 0.7810 0.000 0.908 0.000 0.052 0.004 NA
#> GSM876847 2 0.5164 0.1874 0.000 0.584 0.000 0.000 0.300 NA
#> GSM876848 4 0.4146 0.5091 0.000 0.288 0.000 0.676 0.000 NA
#> GSM876849 4 0.3172 0.6472 0.000 0.148 0.000 0.816 0.000 NA
#> GSM876898 3 0.0405 0.9346 0.004 0.000 0.988 0.000 0.000 NA
#> GSM876899 3 0.1957 0.9049 0.000 0.000 0.920 0.024 0.008 NA
#> GSM876900 3 0.0146 0.9355 0.000 0.000 0.996 0.000 0.000 NA
#> GSM876901 3 0.0000 0.9357 0.000 0.000 1.000 0.000 0.000 NA
#> GSM876902 4 0.1829 0.7103 0.000 0.000 0.024 0.920 0.000 NA
#> GSM876903 3 0.6444 0.3492 0.000 0.000 0.516 0.132 0.072 NA
#> GSM876904 3 0.0508 0.9339 0.004 0.000 0.984 0.000 0.000 NA
#> GSM876874 1 0.3290 0.7336 0.744 0.000 0.004 0.000 0.000 NA
#> GSM876875 1 0.0692 0.8232 0.976 0.000 0.000 0.000 0.004 NA
#> GSM876876 1 0.0777 0.8269 0.972 0.000 0.004 0.000 0.000 NA
#> GSM876877 1 0.1806 0.8130 0.908 0.000 0.004 0.000 0.000 NA
#> GSM876878 1 0.0508 0.8260 0.984 0.000 0.000 0.000 0.004 NA
#> GSM876879 1 0.2482 0.7377 0.848 0.000 0.000 0.000 0.004 NA
#> GSM876880 1 0.0858 0.8266 0.968 0.000 0.004 0.000 0.000 NA
#> GSM876850 5 0.5634 0.2483 0.000 0.416 0.000 0.000 0.436 NA
#> GSM876851 2 0.3277 0.7371 0.000 0.824 0.000 0.000 0.092 NA
#> GSM876852 2 0.0603 0.8287 0.000 0.980 0.000 0.000 0.004 NA
#> GSM876853 2 0.2511 0.7846 0.000 0.880 0.000 0.000 0.056 NA
#> GSM876854 2 0.0632 0.8264 0.000 0.976 0.000 0.000 0.000 NA
#> GSM876855 2 0.0858 0.8236 0.000 0.968 0.000 0.004 0.000 NA
#> GSM876856 2 0.1334 0.8135 0.000 0.948 0.000 0.020 0.000 NA
#> GSM876905 3 0.0291 0.9353 0.004 0.000 0.992 0.000 0.000 NA
#> GSM876906 3 0.3036 0.8418 0.000 0.000 0.840 0.028 0.008 NA
#> GSM876907 5 0.6645 0.0446 0.000 0.008 0.396 0.056 0.416 NA
#> GSM876908 3 0.2887 0.8558 0.000 0.000 0.856 0.032 0.008 NA
#> GSM876909 5 0.4123 0.4658 0.000 0.008 0.136 0.016 0.780 NA
#> GSM876881 5 0.5156 0.5747 0.000 0.272 0.000 0.000 0.600 NA
#> GSM876882 1 0.3380 0.6330 0.748 0.000 0.000 0.004 0.004 NA
#> GSM876883 1 0.5369 0.3514 0.584 0.000 0.000 0.116 0.008 NA
#> GSM876884 1 0.0508 0.8261 0.984 0.000 0.000 0.000 0.004 NA
#> GSM876885 1 0.6028 0.1938 0.516 0.000 0.000 0.152 0.024 NA
#> GSM876857 1 0.3714 0.6650 0.656 0.000 0.004 0.000 0.000 NA
#> GSM876858 5 0.2793 0.6819 0.000 0.200 0.000 0.000 0.800 NA
#> GSM876859 5 0.3330 0.6367 0.000 0.284 0.000 0.000 0.716 NA
#> GSM876860 5 0.2730 0.6828 0.000 0.192 0.000 0.000 0.808 NA
#> GSM876861 5 0.2378 0.6761 0.000 0.152 0.000 0.000 0.848 NA
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> MAD:NMF 71 8.09e-01 6.63e-11 2
#> MAD:NMF 66 8.71e-01 1.59e-13 3
#> MAD:NMF 72 6.88e-02 4.07e-22 4
#> MAD:NMF 67 6.06e-04 4.91e-19 5
#> MAD:NMF 62 8.36e-05 1.24e-18 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 72 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 0.964 0.968 0.977 0.3657 0.634 0.634
#> 3 3 0.694 0.932 0.949 0.1576 0.972 0.956
#> 4 4 0.663 0.803 0.898 0.5468 0.716 0.531
#> 5 5 0.716 0.792 0.889 0.0381 0.994 0.982
#> 6 6 0.686 0.774 0.867 0.1318 0.836 0.523
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
#> GSM876886 1 0.311 0.961 0.944 0.056
#> GSM876887 1 0.311 0.961 0.944 0.056
#> GSM876888 1 0.000 0.978 1.000 0.000
#> GSM876889 2 0.000 0.968 0.000 1.000
#> GSM876890 2 0.443 0.924 0.092 0.908
#> GSM876891 2 0.469 0.915 0.100 0.900
#> GSM876862 1 0.000 0.978 1.000 0.000
#> GSM876863 1 0.000 0.978 1.000 0.000
#> GSM876864 1 0.000 0.978 1.000 0.000
#> GSM876865 1 0.000 0.978 1.000 0.000
#> GSM876866 2 0.443 0.924 0.092 0.908
#> GSM876867 1 0.000 0.978 1.000 0.000
#> GSM876838 1 0.000 0.978 1.000 0.000
#> GSM876839 1 0.000 0.978 1.000 0.000
#> GSM876840 2 0.295 0.955 0.052 0.948
#> GSM876841 1 0.000 0.978 1.000 0.000
#> GSM876842 1 0.311 0.961 0.944 0.056
#> GSM876843 2 0.000 0.968 0.000 1.000
#> GSM876892 1 0.311 0.961 0.944 0.056
#> GSM876893 1 0.311 0.961 0.944 0.056
#> GSM876894 1 0.311 0.961 0.944 0.056
#> GSM876895 1 0.278 0.964 0.952 0.048
#> GSM876896 2 0.000 0.968 0.000 1.000
#> GSM876897 2 0.000 0.968 0.000 1.000
#> GSM876868 1 0.000 0.978 1.000 0.000
#> GSM876869 1 0.000 0.978 1.000 0.000
#> GSM876870 1 0.000 0.978 1.000 0.000
#> GSM876871 1 0.000 0.978 1.000 0.000
#> GSM876872 2 0.000 0.968 0.000 1.000
#> GSM876873 2 0.000 0.968 0.000 1.000
#> GSM876844 1 0.311 0.961 0.944 0.056
#> GSM876845 1 0.000 0.978 1.000 0.000
#> GSM876846 2 0.000 0.968 0.000 1.000
#> GSM876847 1 0.000 0.978 1.000 0.000
#> GSM876848 2 0.000 0.968 0.000 1.000
#> GSM876849 2 0.000 0.968 0.000 1.000
#> GSM876898 1 0.000 0.978 1.000 0.000
#> GSM876899 1 0.278 0.964 0.952 0.048
#> GSM876900 1 0.311 0.961 0.944 0.056
#> GSM876901 1 0.000 0.978 1.000 0.000
#> GSM876902 2 0.000 0.968 0.000 1.000
#> GSM876903 1 0.278 0.964 0.952 0.048
#> GSM876904 1 0.000 0.978 1.000 0.000
#> GSM876874 1 0.000 0.978 1.000 0.000
#> GSM876875 1 0.311 0.961 0.944 0.056
#> GSM876876 1 0.000 0.978 1.000 0.000
#> GSM876877 1 0.000 0.978 1.000 0.000
#> GSM876878 1 0.000 0.978 1.000 0.000
#> GSM876879 1 0.311 0.961 0.944 0.056
#> GSM876880 1 0.000 0.978 1.000 0.000
#> GSM876850 1 0.000 0.978 1.000 0.000
#> GSM876851 1 0.000 0.978 1.000 0.000
#> GSM876852 1 0.311 0.961 0.944 0.056
#> GSM876853 1 0.000 0.978 1.000 0.000
#> GSM876854 2 0.295 0.955 0.052 0.948
#> GSM876855 2 0.295 0.955 0.052 0.948
#> GSM876856 2 0.295 0.955 0.052 0.948
#> GSM876905 1 0.000 0.978 1.000 0.000
#> GSM876906 1 0.311 0.961 0.944 0.056
#> GSM876907 1 0.278 0.964 0.952 0.048
#> GSM876908 1 0.278 0.964 0.952 0.048
#> GSM876909 1 0.000 0.978 1.000 0.000
#> GSM876881 1 0.000 0.978 1.000 0.000
#> GSM876882 1 0.311 0.961 0.944 0.056
#> GSM876883 1 0.311 0.961 0.944 0.056
#> GSM876884 1 0.000 0.978 1.000 0.000
#> GSM876885 1 0.311 0.961 0.944 0.056
#> GSM876857 1 0.000 0.978 1.000 0.000
#> GSM876858 1 0.000 0.978 1.000 0.000
#> GSM876859 1 0.000 0.978 1.000 0.000
#> GSM876860 1 0.000 0.978 1.000 0.000
#> GSM876861 1 0.311 0.961 0.944 0.056
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 1 0.3816 0.889 0.852 0.148 0.000
#> GSM876887 1 0.3816 0.889 0.852 0.148 0.000
#> GSM876888 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876889 2 0.2796 0.900 0.000 0.908 0.092
#> GSM876890 2 0.0000 0.932 0.000 1.000 0.000
#> GSM876891 2 0.0424 0.922 0.008 0.992 0.000
#> GSM876862 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876863 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876864 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876865 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876866 2 0.0000 0.932 0.000 1.000 0.000
#> GSM876867 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876838 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876839 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876840 2 0.1529 0.953 0.000 0.960 0.040
#> GSM876841 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876842 1 0.3816 0.889 0.852 0.148 0.000
#> GSM876843 3 0.0000 0.914 0.000 0.000 1.000
#> GSM876892 1 0.3816 0.889 0.852 0.148 0.000
#> GSM876893 1 0.3816 0.889 0.852 0.148 0.000
#> GSM876894 1 0.3816 0.889 0.852 0.148 0.000
#> GSM876895 1 0.1964 0.932 0.944 0.056 0.000
#> GSM876896 3 0.3116 0.945 0.000 0.108 0.892
#> GSM876897 3 0.3116 0.945 0.000 0.108 0.892
#> GSM876868 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876869 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876870 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876871 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876872 3 0.3116 0.945 0.000 0.108 0.892
#> GSM876873 3 0.3116 0.945 0.000 0.108 0.892
#> GSM876844 1 0.3816 0.889 0.852 0.148 0.000
#> GSM876845 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876846 2 0.2796 0.900 0.000 0.908 0.092
#> GSM876847 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876848 3 0.0000 0.914 0.000 0.000 1.000
#> GSM876849 3 0.0000 0.914 0.000 0.000 1.000
#> GSM876898 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876899 1 0.1753 0.935 0.952 0.048 0.000
#> GSM876900 1 0.3816 0.889 0.852 0.148 0.000
#> GSM876901 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876902 3 0.3116 0.945 0.000 0.108 0.892
#> GSM876903 1 0.1753 0.935 0.952 0.048 0.000
#> GSM876904 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876874 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876875 1 0.3816 0.889 0.852 0.148 0.000
#> GSM876876 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876877 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876878 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876879 1 0.3816 0.889 0.852 0.148 0.000
#> GSM876880 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876850 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876851 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876852 1 0.3816 0.889 0.852 0.148 0.000
#> GSM876853 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876854 2 0.1529 0.953 0.000 0.960 0.040
#> GSM876855 2 0.1529 0.953 0.000 0.960 0.040
#> GSM876856 2 0.1529 0.953 0.000 0.960 0.040
#> GSM876905 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876906 1 0.3816 0.889 0.852 0.148 0.000
#> GSM876907 1 0.1753 0.935 0.952 0.048 0.000
#> GSM876908 1 0.1753 0.935 0.952 0.048 0.000
#> GSM876909 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876881 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876882 1 0.3816 0.889 0.852 0.148 0.000
#> GSM876883 1 0.3816 0.889 0.852 0.148 0.000
#> GSM876884 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876885 1 0.3816 0.889 0.852 0.148 0.000
#> GSM876857 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876858 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876859 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876860 1 0.0000 0.951 1.000 0.000 0.000
#> GSM876861 1 0.3816 0.889 0.852 0.148 0.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 2 0.000 0.872 0.000 1.000 0.000 0.0
#> GSM876887 2 0.000 0.872 0.000 1.000 0.000 0.0
#> GSM876888 1 0.476 0.454 0.628 0.372 0.000 0.0
#> GSM876889 3 0.000 0.905 0.000 0.000 1.000 0.0
#> GSM876890 3 0.222 0.934 0.000 0.092 0.908 0.0
#> GSM876891 3 0.234 0.924 0.000 0.100 0.900 0.0
#> GSM876862 1 0.000 0.824 1.000 0.000 0.000 0.0
#> GSM876863 1 0.476 0.454 0.628 0.372 0.000 0.0
#> GSM876864 1 0.000 0.824 1.000 0.000 0.000 0.0
#> GSM876865 1 0.476 0.454 0.628 0.372 0.000 0.0
#> GSM876866 3 0.222 0.934 0.000 0.092 0.908 0.0
#> GSM876867 1 0.000 0.824 1.000 0.000 0.000 0.0
#> GSM876838 2 0.302 0.835 0.148 0.852 0.000 0.0
#> GSM876839 2 0.302 0.835 0.148 0.852 0.000 0.0
#> GSM876840 3 0.147 0.955 0.000 0.052 0.948 0.0
#> GSM876841 2 0.302 0.835 0.148 0.852 0.000 0.0
#> GSM876842 2 0.000 0.872 0.000 1.000 0.000 0.0
#> GSM876843 4 0.000 0.860 0.000 0.000 0.000 1.0
#> GSM876892 2 0.000 0.872 0.000 1.000 0.000 0.0
#> GSM876893 2 0.000 0.872 0.000 1.000 0.000 0.0
#> GSM876894 2 0.000 0.872 0.000 1.000 0.000 0.0
#> GSM876895 2 0.222 0.860 0.092 0.908 0.000 0.0
#> GSM876896 4 0.361 0.909 0.000 0.000 0.200 0.8
#> GSM876897 4 0.361 0.909 0.000 0.000 0.200 0.8
#> GSM876868 1 0.000 0.824 1.000 0.000 0.000 0.0
#> GSM876869 1 0.000 0.824 1.000 0.000 0.000 0.0
#> GSM876870 1 0.000 0.824 1.000 0.000 0.000 0.0
#> GSM876871 1 0.000 0.824 1.000 0.000 0.000 0.0
#> GSM876872 4 0.361 0.909 0.000 0.000 0.200 0.8
#> GSM876873 4 0.361 0.909 0.000 0.000 0.200 0.8
#> GSM876844 2 0.000 0.872 0.000 1.000 0.000 0.0
#> GSM876845 2 0.302 0.835 0.148 0.852 0.000 0.0
#> GSM876846 3 0.000 0.905 0.000 0.000 1.000 0.0
#> GSM876847 2 0.302 0.835 0.148 0.852 0.000 0.0
#> GSM876848 4 0.000 0.860 0.000 0.000 0.000 1.0
#> GSM876849 4 0.000 0.860 0.000 0.000 0.000 1.0
#> GSM876898 1 0.102 0.831 0.968 0.032 0.000 0.0
#> GSM876899 2 0.234 0.858 0.100 0.900 0.000 0.0
#> GSM876900 2 0.000 0.872 0.000 1.000 0.000 0.0
#> GSM876901 1 0.476 0.454 0.628 0.372 0.000 0.0
#> GSM876902 4 0.361 0.909 0.000 0.000 0.200 0.8
#> GSM876903 2 0.234 0.858 0.100 0.900 0.000 0.0
#> GSM876904 1 0.476 0.454 0.628 0.372 0.000 0.0
#> GSM876874 1 0.000 0.824 1.000 0.000 0.000 0.0
#> GSM876875 2 0.000 0.872 0.000 1.000 0.000 0.0
#> GSM876876 1 0.112 0.830 0.964 0.036 0.000 0.0
#> GSM876877 1 0.000 0.824 1.000 0.000 0.000 0.0
#> GSM876878 1 0.112 0.830 0.964 0.036 0.000 0.0
#> GSM876879 2 0.000 0.872 0.000 1.000 0.000 0.0
#> GSM876880 1 0.102 0.831 0.968 0.032 0.000 0.0
#> GSM876850 2 0.302 0.835 0.148 0.852 0.000 0.0
#> GSM876851 2 0.302 0.835 0.148 0.852 0.000 0.0
#> GSM876852 2 0.000 0.872 0.000 1.000 0.000 0.0
#> GSM876853 2 0.302 0.835 0.148 0.852 0.000 0.0
#> GSM876854 3 0.147 0.955 0.000 0.052 0.948 0.0
#> GSM876855 3 0.147 0.955 0.000 0.052 0.948 0.0
#> GSM876856 3 0.147 0.955 0.000 0.052 0.948 0.0
#> GSM876905 1 0.476 0.454 0.628 0.372 0.000 0.0
#> GSM876906 2 0.000 0.872 0.000 1.000 0.000 0.0
#> GSM876907 2 0.234 0.858 0.100 0.900 0.000 0.0
#> GSM876908 2 0.234 0.858 0.100 0.900 0.000 0.0
#> GSM876909 2 0.443 0.597 0.304 0.696 0.000 0.0
#> GSM876881 1 0.208 0.802 0.916 0.084 0.000 0.0
#> GSM876882 2 0.000 0.872 0.000 1.000 0.000 0.0
#> GSM876883 2 0.000 0.872 0.000 1.000 0.000 0.0
#> GSM876884 1 0.102 0.831 0.968 0.032 0.000 0.0
#> GSM876885 2 0.000 0.872 0.000 1.000 0.000 0.0
#> GSM876857 1 0.215 0.806 0.912 0.088 0.000 0.0
#> GSM876858 2 0.492 0.270 0.428 0.572 0.000 0.0
#> GSM876859 2 0.492 0.270 0.428 0.572 0.000 0.0
#> GSM876860 2 0.492 0.270 0.428 0.572 0.000 0.0
#> GSM876861 2 0.000 0.872 0.000 1.000 0.000 0.0
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM876886 2 0.0703 0.870 0.000 0.976 0.024 0.000 0.000
#> GSM876887 2 0.0703 0.870 0.000 0.976 0.024 0.000 0.000
#> GSM876888 1 0.4074 0.411 0.636 0.364 0.000 0.000 0.000
#> GSM876889 3 0.3039 0.822 0.000 0.000 0.808 0.192 0.000
#> GSM876890 3 0.0510 0.914 0.000 0.016 0.984 0.000 0.000
#> GSM876891 3 0.0703 0.906 0.000 0.024 0.976 0.000 0.000
#> GSM876862 1 0.2293 0.758 0.900 0.000 0.016 0.000 0.084
#> GSM876863 1 0.4074 0.411 0.636 0.364 0.000 0.000 0.000
#> GSM876864 1 0.2293 0.758 0.900 0.000 0.016 0.000 0.084
#> GSM876865 1 0.4074 0.411 0.636 0.364 0.000 0.000 0.000
#> GSM876866 3 0.0510 0.914 0.000 0.016 0.984 0.000 0.000
#> GSM876867 1 0.2293 0.758 0.900 0.000 0.016 0.000 0.084
#> GSM876838 2 0.2690 0.825 0.156 0.844 0.000 0.000 0.000
#> GSM876839 2 0.2690 0.825 0.156 0.844 0.000 0.000 0.000
#> GSM876840 3 0.1043 0.931 0.000 0.000 0.960 0.040 0.000
#> GSM876841 2 0.2690 0.825 0.156 0.844 0.000 0.000 0.000
#> GSM876842 2 0.0703 0.870 0.000 0.976 0.024 0.000 0.000
#> GSM876843 5 0.1792 1.000 0.000 0.000 0.000 0.084 0.916
#> GSM876892 2 0.0703 0.870 0.000 0.976 0.024 0.000 0.000
#> GSM876893 2 0.0703 0.870 0.000 0.976 0.024 0.000 0.000
#> GSM876894 2 0.0703 0.870 0.000 0.976 0.024 0.000 0.000
#> GSM876895 2 0.1544 0.861 0.068 0.932 0.000 0.000 0.000
#> GSM876896 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM876897 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM876868 1 0.2293 0.758 0.900 0.000 0.016 0.000 0.084
#> GSM876869 1 0.2293 0.758 0.900 0.000 0.016 0.000 0.084
#> GSM876870 1 0.2293 0.758 0.900 0.000 0.016 0.000 0.084
#> GSM876871 1 0.2293 0.758 0.900 0.000 0.016 0.000 0.084
#> GSM876872 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM876873 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM876844 2 0.0703 0.870 0.000 0.976 0.024 0.000 0.000
#> GSM876845 2 0.2690 0.825 0.156 0.844 0.000 0.000 0.000
#> GSM876846 3 0.3109 0.814 0.000 0.000 0.800 0.200 0.000
#> GSM876847 2 0.2690 0.825 0.156 0.844 0.000 0.000 0.000
#> GSM876848 5 0.1792 1.000 0.000 0.000 0.000 0.084 0.916
#> GSM876849 5 0.1792 1.000 0.000 0.000 0.000 0.084 0.916
#> GSM876898 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000
#> GSM876899 2 0.1671 0.859 0.076 0.924 0.000 0.000 0.000
#> GSM876900 2 0.0703 0.870 0.000 0.976 0.024 0.000 0.000
#> GSM876901 1 0.4074 0.411 0.636 0.364 0.000 0.000 0.000
#> GSM876902 4 0.0000 1.000 0.000 0.000 0.000 1.000 0.000
#> GSM876903 2 0.1671 0.859 0.076 0.924 0.000 0.000 0.000
#> GSM876904 1 0.4074 0.411 0.636 0.364 0.000 0.000 0.000
#> GSM876874 1 0.2293 0.758 0.900 0.000 0.016 0.000 0.084
#> GSM876875 2 0.0703 0.870 0.000 0.976 0.024 0.000 0.000
#> GSM876876 1 0.0162 0.769 0.996 0.004 0.000 0.000 0.000
#> GSM876877 1 0.2293 0.758 0.900 0.000 0.016 0.000 0.084
#> GSM876878 1 0.0162 0.769 0.996 0.004 0.000 0.000 0.000
#> GSM876879 2 0.0703 0.870 0.000 0.976 0.024 0.000 0.000
#> GSM876880 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.2690 0.825 0.156 0.844 0.000 0.000 0.000
#> GSM876851 2 0.2690 0.825 0.156 0.844 0.000 0.000 0.000
#> GSM876852 2 0.0703 0.870 0.000 0.976 0.024 0.000 0.000
#> GSM876853 2 0.2690 0.825 0.156 0.844 0.000 0.000 0.000
#> GSM876854 3 0.1043 0.931 0.000 0.000 0.960 0.040 0.000
#> GSM876855 3 0.1043 0.931 0.000 0.000 0.960 0.040 0.000
#> GSM876856 3 0.1043 0.931 0.000 0.000 0.960 0.040 0.000
#> GSM876905 1 0.4074 0.411 0.636 0.364 0.000 0.000 0.000
#> GSM876906 2 0.0703 0.870 0.000 0.976 0.024 0.000 0.000
#> GSM876907 2 0.1671 0.859 0.076 0.924 0.000 0.000 0.000
#> GSM876908 2 0.1671 0.859 0.076 0.924 0.000 0.000 0.000
#> GSM876909 2 0.3857 0.599 0.312 0.688 0.000 0.000 0.000
#> GSM876881 1 0.1270 0.745 0.948 0.052 0.000 0.000 0.000
#> GSM876882 2 0.0703 0.870 0.000 0.976 0.024 0.000 0.000
#> GSM876883 2 0.0703 0.870 0.000 0.976 0.024 0.000 0.000
#> GSM876884 1 0.0000 0.769 1.000 0.000 0.000 0.000 0.000
#> GSM876885 2 0.0703 0.870 0.000 0.976 0.024 0.000 0.000
#> GSM876857 1 0.1410 0.746 0.940 0.060 0.000 0.000 0.000
#> GSM876858 2 0.4256 0.290 0.436 0.564 0.000 0.000 0.000
#> GSM876859 2 0.4256 0.290 0.436 0.564 0.000 0.000 0.000
#> GSM876860 2 0.4256 0.290 0.436 0.564 0.000 0.000 0.000
#> GSM876861 2 0.0703 0.870 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
#> GSM876886 5 0.000 0.867 0.000 0.000 0.000 0.000 1.000 0
#> GSM876887 5 0.000 0.867 0.000 0.000 0.000 0.000 1.000 0
#> GSM876888 2 0.386 0.332 0.480 0.520 0.000 0.000 0.000 0
#> GSM876889 3 0.460 0.773 0.000 0.152 0.696 0.152 0.000 0
#> GSM876890 3 0.328 0.849 0.000 0.152 0.808 0.000 0.040 0
#> GSM876891 3 0.341 0.843 0.000 0.152 0.800 0.000 0.048 0
#> GSM876862 1 0.000 0.881 1.000 0.000 0.000 0.000 0.000 0
#> GSM876863 2 0.386 0.332 0.480 0.520 0.000 0.000 0.000 0
#> GSM876864 1 0.000 0.881 1.000 0.000 0.000 0.000 0.000 0
#> GSM876865 2 0.386 0.332 0.480 0.520 0.000 0.000 0.000 0
#> GSM876866 3 0.328 0.849 0.000 0.152 0.808 0.000 0.040 0
#> GSM876867 1 0.000 0.881 1.000 0.000 0.000 0.000 0.000 0
#> GSM876838 2 0.238 0.658 0.000 0.848 0.000 0.000 0.152 0
#> GSM876839 2 0.238 0.658 0.000 0.848 0.000 0.000 0.152 0
#> GSM876840 3 0.000 0.878 0.000 0.000 1.000 0.000 0.000 0
#> GSM876841 2 0.238 0.658 0.000 0.848 0.000 0.000 0.152 0
#> GSM876842 5 0.313 0.715 0.000 0.248 0.000 0.000 0.752 0
#> GSM876843 6 0.000 1.000 0.000 0.000 0.000 0.000 0.000 1
#> GSM876892 5 0.000 0.867 0.000 0.000 0.000 0.000 1.000 0
#> GSM876893 5 0.000 0.867 0.000 0.000 0.000 0.000 1.000 0
#> GSM876894 5 0.026 0.866 0.000 0.008 0.000 0.000 0.992 0
#> GSM876895 5 0.279 0.741 0.000 0.200 0.000 0.000 0.800 0
#> GSM876896 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0
#> GSM876897 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0
#> GSM876868 1 0.000 0.881 1.000 0.000 0.000 0.000 0.000 0
#> GSM876869 1 0.000 0.881 1.000 0.000 0.000 0.000 0.000 0
#> GSM876870 1 0.000 0.881 1.000 0.000 0.000 0.000 0.000 0
#> GSM876871 1 0.000 0.881 1.000 0.000 0.000 0.000 0.000 0
#> GSM876872 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0
#> GSM876873 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0
#> GSM876844 5 0.313 0.715 0.000 0.248 0.000 0.000 0.752 0
#> GSM876845 2 0.238 0.658 0.000 0.848 0.000 0.000 0.152 0
#> GSM876846 3 0.245 0.779 0.000 0.000 0.840 0.160 0.000 0
#> GSM876847 2 0.238 0.658 0.000 0.848 0.000 0.000 0.152 0
#> GSM876848 6 0.000 1.000 0.000 0.000 0.000 0.000 0.000 1
#> GSM876849 6 0.000 1.000 0.000 0.000 0.000 0.000 0.000 1
#> GSM876898 1 0.242 0.819 0.844 0.156 0.000 0.000 0.000 0
#> GSM876899 5 0.291 0.723 0.000 0.216 0.000 0.000 0.784 0
#> GSM876900 5 0.000 0.867 0.000 0.000 0.000 0.000 1.000 0
#> GSM876901 2 0.386 0.332 0.480 0.520 0.000 0.000 0.000 0
#> GSM876902 4 0.000 1.000 0.000 0.000 0.000 1.000 0.000 0
#> GSM876903 5 0.291 0.723 0.000 0.216 0.000 0.000 0.784 0
#> GSM876904 2 0.386 0.332 0.480 0.520 0.000 0.000 0.000 0
#> GSM876874 1 0.000 0.881 1.000 0.000 0.000 0.000 0.000 0
#> GSM876875 5 0.000 0.867 0.000 0.000 0.000 0.000 1.000 0
#> GSM876876 1 0.245 0.815 0.840 0.160 0.000 0.000 0.000 0
#> GSM876877 1 0.000 0.881 1.000 0.000 0.000 0.000 0.000 0
#> GSM876878 1 0.245 0.815 0.840 0.160 0.000 0.000 0.000 0
#> GSM876879 5 0.000 0.867 0.000 0.000 0.000 0.000 1.000 0
#> GSM876880 1 0.242 0.819 0.844 0.156 0.000 0.000 0.000 0
#> GSM876850 2 0.238 0.658 0.000 0.848 0.000 0.000 0.152 0
#> GSM876851 2 0.238 0.658 0.000 0.848 0.000 0.000 0.152 0
#> GSM876852 5 0.313 0.715 0.000 0.248 0.000 0.000 0.752 0
#> GSM876853 2 0.238 0.658 0.000 0.848 0.000 0.000 0.152 0
#> GSM876854 3 0.000 0.878 0.000 0.000 1.000 0.000 0.000 0
#> GSM876855 3 0.000 0.878 0.000 0.000 1.000 0.000 0.000 0
#> GSM876856 3 0.000 0.878 0.000 0.000 1.000 0.000 0.000 0
#> GSM876905 2 0.386 0.332 0.480 0.520 0.000 0.000 0.000 0
#> GSM876906 5 0.026 0.866 0.000 0.008 0.000 0.000 0.992 0
#> GSM876907 5 0.291 0.723 0.000 0.216 0.000 0.000 0.784 0
#> GSM876908 5 0.291 0.723 0.000 0.216 0.000 0.000 0.784 0
#> GSM876909 2 0.430 0.662 0.156 0.728 0.000 0.000 0.116 0
#> GSM876881 1 0.282 0.763 0.796 0.204 0.000 0.000 0.000 0
#> GSM876882 5 0.000 0.867 0.000 0.000 0.000 0.000 1.000 0
#> GSM876883 5 0.000 0.867 0.000 0.000 0.000 0.000 1.000 0
#> GSM876884 1 0.242 0.819 0.844 0.156 0.000 0.000 0.000 0
#> GSM876885 5 0.000 0.867 0.000 0.000 0.000 0.000 1.000 0
#> GSM876857 1 0.291 0.715 0.784 0.216 0.000 0.000 0.000 0
#> GSM876858 2 0.331 0.596 0.280 0.720 0.000 0.000 0.000 0
#> GSM876859 2 0.331 0.596 0.280 0.720 0.000 0.000 0.000 0
#> GSM876860 2 0.331 0.596 0.280 0.720 0.000 0.000 0.000 0
#> GSM876861 5 0.313 0.715 0.000 0.248 0.000 0.000 0.752 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 disease.state(p) tissue(p) k
#> ATC:hclust 72 0.04298 2.32e-01 2
#> ATC:hclust 72 0.00445 4.62e-01 3
#> ATC:hclust 63 0.04100 1.36e-04 4
#> ATC:hclust 63 0.09415 1.94e-05 5
#> ATC:hclust 66 0.10482 2.79e-08 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["ATC", "kmeans"]
# you can also extract it by
# res = res_list["ATC:kmeans"]
A summary of res and all the functions that can be applied to it:
res
#> A 'ConsensusPartition' object with k = 2, 3, 4, 5, 6.
#> On a matrix with 51941 rows and 72 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 0.3512 0.649 0.649
#> 3 3 0.886 0.877 0.953 0.7817 0.649 0.490
#> 4 4 0.719 0.679 0.864 0.1701 0.822 0.559
#> 5 5 0.765 0.727 0.847 0.0661 0.875 0.581
#> 6 6 0.771 0.701 0.823 0.0469 0.937 0.724
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
#> GSM876886 1 0 1 1 0
#> GSM876887 1 0 1 1 0
#> GSM876888 1 0 1 1 0
#> GSM876889 2 0 1 0 1
#> GSM876890 2 0 1 0 1
#> GSM876891 1 0 1 1 0
#> GSM876862 1 0 1 1 0
#> GSM876863 1 0 1 1 0
#> GSM876864 1 0 1 1 0
#> GSM876865 1 0 1 1 0
#> GSM876866 2 0 1 0 1
#> GSM876867 1 0 1 1 0
#> GSM876838 1 0 1 1 0
#> GSM876839 1 0 1 1 0
#> GSM876840 2 0 1 0 1
#> GSM876841 1 0 1 1 0
#> GSM876842 1 0 1 1 0
#> GSM876843 2 0 1 0 1
#> GSM876892 1 0 1 1 0
#> GSM876893 1 0 1 1 0
#> GSM876894 1 0 1 1 0
#> GSM876895 1 0 1 1 0
#> GSM876896 2 0 1 0 1
#> GSM876897 2 0 1 0 1
#> GSM876868 1 0 1 1 0
#> GSM876869 1 0 1 1 0
#> GSM876870 1 0 1 1 0
#> GSM876871 1 0 1 1 0
#> GSM876872 2 0 1 0 1
#> GSM876873 2 0 1 0 1
#> GSM876844 1 0 1 1 0
#> GSM876845 1 0 1 1 0
#> GSM876846 2 0 1 0 1
#> GSM876847 1 0 1 1 0
#> GSM876848 2 0 1 0 1
#> GSM876849 2 0 1 0 1
#> GSM876898 1 0 1 1 0
#> GSM876899 1 0 1 1 0
#> GSM876900 1 0 1 1 0
#> GSM876901 1 0 1 1 0
#> GSM876902 2 0 1 0 1
#> GSM876903 1 0 1 1 0
#> GSM876904 1 0 1 1 0
#> GSM876874 1 0 1 1 0
#> GSM876875 1 0 1 1 0
#> GSM876876 1 0 1 1 0
#> GSM876877 1 0 1 1 0
#> GSM876878 1 0 1 1 0
#> GSM876879 1 0 1 1 0
#> GSM876880 1 0 1 1 0
#> GSM876850 1 0 1 1 0
#> GSM876851 1 0 1 1 0
#> GSM876852 1 0 1 1 0
#> GSM876853 1 0 1 1 0
#> GSM876854 2 0 1 0 1
#> GSM876855 2 0 1 0 1
#> GSM876856 2 0 1 0 1
#> GSM876905 1 0 1 1 0
#> GSM876906 1 0 1 1 0
#> GSM876907 1 0 1 1 0
#> GSM876908 1 0 1 1 0
#> GSM876909 1 0 1 1 0
#> GSM876881 1 0 1 1 0
#> GSM876882 1 0 1 1 0
#> GSM876883 1 0 1 1 0
#> GSM876884 1 0 1 1 0
#> GSM876885 1 0 1 1 0
#> GSM876857 1 0 1 1 0
#> GSM876858 1 0 1 1 0
#> GSM876859 1 0 1 1 0
#> GSM876860 1 0 1 1 0
#> GSM876861 1 0 1 1 0
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876887 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876888 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876889 2 0.0000 0.956 0.000 1.00 0.000
#> GSM876890 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876891 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876862 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876863 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876864 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876865 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876866 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876867 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876838 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876839 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876840 2 0.0000 0.956 0.000 1.00 0.000
#> GSM876841 3 0.5216 0.669 0.260 0.00 0.740
#> GSM876842 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876843 2 0.0000 0.956 0.000 1.00 0.000
#> GSM876892 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876893 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876894 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876895 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876896 2 0.0000 0.956 0.000 1.00 0.000
#> GSM876897 2 0.0000 0.956 0.000 1.00 0.000
#> GSM876868 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876869 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876870 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876871 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876872 2 0.0000 0.956 0.000 1.00 0.000
#> GSM876873 2 0.0000 0.956 0.000 1.00 0.000
#> GSM876844 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876845 3 0.5291 0.657 0.268 0.00 0.732
#> GSM876846 2 0.0000 0.956 0.000 1.00 0.000
#> GSM876847 3 0.6302 0.184 0.480 0.00 0.520
#> GSM876848 2 0.0000 0.956 0.000 1.00 0.000
#> GSM876849 2 0.0000 0.956 0.000 1.00 0.000
#> GSM876898 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876899 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876900 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876901 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876902 2 0.0000 0.956 0.000 1.00 0.000
#> GSM876903 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876904 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876874 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876875 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876876 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876877 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876878 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876879 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876880 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876850 3 0.6302 0.184 0.480 0.00 0.520
#> GSM876851 3 0.5216 0.669 0.260 0.00 0.740
#> GSM876852 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876853 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876854 2 0.0000 0.956 0.000 1.00 0.000
#> GSM876855 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876856 2 0.6302 0.140 0.000 0.52 0.480
#> GSM876905 1 0.0592 0.966 0.988 0.00 0.012
#> GSM876906 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876907 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876908 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876909 3 0.6302 0.184 0.480 0.00 0.520
#> GSM876881 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876882 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876883 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876884 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876885 3 0.0000 0.913 0.000 0.00 1.000
#> GSM876857 1 0.0000 0.979 1.000 0.00 0.000
#> GSM876858 3 0.5216 0.669 0.260 0.00 0.740
#> GSM876859 1 0.5859 0.382 0.656 0.00 0.344
#> GSM876860 3 0.2537 0.852 0.080 0.00 0.920
#> GSM876861 3 0.0000 0.913 0.000 0.00 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.3837 0.6961 0.000 0.224 0.776 0.000
#> GSM876887 3 0.1118 0.6696 0.000 0.036 0.964 0.000
#> GSM876888 1 0.3123 0.7814 0.844 0.156 0.000 0.000
#> GSM876889 4 0.4134 0.7718 0.000 0.000 0.260 0.740
#> GSM876890 3 0.0000 0.6535 0.000 0.000 1.000 0.000
#> GSM876891 3 0.1118 0.6696 0.000 0.036 0.964 0.000
#> GSM876862 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876863 1 0.3123 0.7814 0.844 0.156 0.000 0.000
#> GSM876864 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876866 3 0.0000 0.6535 0.000 0.000 1.000 0.000
#> GSM876867 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.7316 0.000 1.000 0.000 0.000
#> GSM876839 2 0.0000 0.7316 0.000 1.000 0.000 0.000
#> GSM876840 4 0.3837 0.8092 0.000 0.000 0.224 0.776
#> GSM876841 2 0.0000 0.7316 0.000 1.000 0.000 0.000
#> GSM876842 2 0.3266 0.5545 0.000 0.832 0.168 0.000
#> GSM876843 4 0.0000 0.9493 0.000 0.000 0.000 1.000
#> GSM876892 3 0.3837 0.6961 0.000 0.224 0.776 0.000
#> GSM876893 2 0.4916 0.2039 0.000 0.576 0.424 0.000
#> GSM876894 3 0.4356 0.6243 0.000 0.292 0.708 0.000
#> GSM876895 2 0.4877 0.2498 0.000 0.592 0.408 0.000
#> GSM876896 4 0.0000 0.9493 0.000 0.000 0.000 1.000
#> GSM876897 4 0.0000 0.9493 0.000 0.000 0.000 1.000
#> GSM876868 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876872 4 0.0921 0.9473 0.000 0.000 0.028 0.972
#> GSM876873 4 0.0921 0.9473 0.000 0.000 0.028 0.972
#> GSM876844 2 0.4164 0.3744 0.000 0.736 0.264 0.000
#> GSM876845 2 0.0000 0.7316 0.000 1.000 0.000 0.000
#> GSM876846 4 0.1118 0.9444 0.000 0.000 0.036 0.964
#> GSM876847 2 0.1637 0.7042 0.060 0.940 0.000 0.000
#> GSM876848 4 0.0000 0.9493 0.000 0.000 0.000 1.000
#> GSM876849 4 0.0000 0.9493 0.000 0.000 0.000 1.000
#> GSM876898 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876899 2 0.4877 0.2498 0.000 0.592 0.408 0.000
#> GSM876900 3 0.4804 0.4217 0.000 0.384 0.616 0.000
#> GSM876901 1 0.4992 0.0848 0.524 0.476 0.000 0.000
#> GSM876902 4 0.0592 0.9490 0.000 0.000 0.016 0.984
#> GSM876903 2 0.4866 0.2591 0.000 0.596 0.404 0.000
#> GSM876904 1 0.4981 0.1295 0.536 0.464 0.000 0.000
#> GSM876874 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876875 3 0.4222 0.6529 0.000 0.272 0.728 0.000
#> GSM876876 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876879 3 0.4222 0.6529 0.000 0.272 0.728 0.000
#> GSM876880 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876850 2 0.1637 0.7042 0.060 0.940 0.000 0.000
#> GSM876851 2 0.0000 0.7316 0.000 1.000 0.000 0.000
#> GSM876852 3 0.4977 0.1975 0.000 0.460 0.540 0.000
#> GSM876853 2 0.0000 0.7316 0.000 1.000 0.000 0.000
#> GSM876854 3 0.4967 -0.2471 0.000 0.000 0.548 0.452
#> GSM876855 3 0.3311 0.5326 0.000 0.172 0.828 0.000
#> GSM876856 3 0.4543 0.1573 0.000 0.000 0.676 0.324
#> GSM876905 2 0.4985 0.0382 0.468 0.532 0.000 0.000
#> GSM876906 3 0.4356 0.6243 0.000 0.292 0.708 0.000
#> GSM876907 2 0.3311 0.6071 0.000 0.828 0.172 0.000
#> GSM876908 2 0.4866 0.2591 0.000 0.596 0.404 0.000
#> GSM876909 2 0.1637 0.7042 0.060 0.940 0.000 0.000
#> GSM876881 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876882 3 0.3837 0.6961 0.000 0.224 0.776 0.000
#> GSM876883 3 0.3837 0.6961 0.000 0.224 0.776 0.000
#> GSM876884 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876885 3 0.3873 0.6934 0.000 0.228 0.772 0.000
#> GSM876857 1 0.0000 0.9265 1.000 0.000 0.000 0.000
#> GSM876858 2 0.0000 0.7316 0.000 1.000 0.000 0.000
#> GSM876859 2 0.2216 0.6749 0.092 0.908 0.000 0.000
#> GSM876860 2 0.0000 0.7316 0.000 1.000 0.000 0.000
#> GSM876861 2 0.4776 0.0949 0.000 0.624 0.376 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM876886 5 0.1341 0.825080 0.000 0.000 0.056 0.000 0.944
#> GSM876887 5 0.3305 0.627660 0.000 0.000 0.224 0.000 0.776
#> GSM876888 1 0.6507 0.637060 0.620 0.168 0.156 0.000 0.056
#> GSM876889 3 0.3336 0.595450 0.000 0.000 0.772 0.228 0.000
#> GSM876890 3 0.4060 0.477851 0.000 0.000 0.640 0.000 0.360
#> GSM876891 5 0.3305 0.627660 0.000 0.000 0.224 0.000 0.776
#> GSM876862 1 0.0510 0.863984 0.984 0.000 0.016 0.000 0.000
#> GSM876863 1 0.6539 0.632959 0.616 0.172 0.156 0.000 0.056
#> GSM876864 1 0.0404 0.864573 0.988 0.000 0.012 0.000 0.000
#> GSM876865 1 0.2439 0.841871 0.876 0.000 0.120 0.000 0.004
#> GSM876866 3 0.4088 0.461077 0.000 0.000 0.632 0.000 0.368
#> GSM876867 1 0.0000 0.865925 1.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0880 0.854993 0.000 0.968 0.000 0.000 0.032
#> GSM876839 2 0.0880 0.854993 0.000 0.968 0.000 0.000 0.032
#> GSM876840 3 0.3366 0.589880 0.000 0.000 0.768 0.232 0.000
#> GSM876841 2 0.0880 0.854993 0.000 0.968 0.000 0.000 0.032
#> GSM876842 2 0.3837 0.579460 0.000 0.692 0.000 0.000 0.308
#> GSM876843 4 0.0880 0.828859 0.000 0.032 0.000 0.968 0.000
#> GSM876892 5 0.1341 0.825080 0.000 0.000 0.056 0.000 0.944
#> GSM876893 5 0.1701 0.815056 0.000 0.048 0.016 0.000 0.936
#> GSM876894 5 0.0510 0.830318 0.000 0.016 0.000 0.000 0.984
#> GSM876895 5 0.1965 0.801986 0.000 0.096 0.000 0.000 0.904
#> GSM876896 4 0.1410 0.841995 0.000 0.000 0.060 0.940 0.000
#> GSM876897 4 0.1410 0.841995 0.000 0.000 0.060 0.940 0.000
#> GSM876868 1 0.0000 0.865925 1.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0404 0.864573 0.988 0.000 0.012 0.000 0.000
#> GSM876870 1 0.0000 0.865925 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0510 0.863984 0.984 0.000 0.016 0.000 0.000
#> GSM876872 4 0.3508 0.725872 0.000 0.000 0.252 0.748 0.000
#> GSM876873 4 0.3508 0.725872 0.000 0.000 0.252 0.748 0.000
#> GSM876844 2 0.4101 0.546654 0.000 0.664 0.004 0.000 0.332
#> GSM876845 2 0.0880 0.854993 0.000 0.968 0.000 0.000 0.032
#> GSM876846 3 0.4114 0.274128 0.000 0.000 0.624 0.376 0.000
#> GSM876847 2 0.0992 0.850614 0.008 0.968 0.000 0.000 0.024
#> GSM876848 4 0.0880 0.828859 0.000 0.032 0.000 0.968 0.000
#> GSM876849 4 0.0880 0.828859 0.000 0.032 0.000 0.968 0.000
#> GSM876898 1 0.2020 0.849606 0.900 0.000 0.100 0.000 0.000
#> GSM876899 5 0.1965 0.801986 0.000 0.096 0.000 0.000 0.904
#> GSM876900 5 0.0794 0.828469 0.000 0.028 0.000 0.000 0.972
#> GSM876901 1 0.8352 0.175723 0.344 0.288 0.156 0.000 0.212
#> GSM876902 4 0.3366 0.747447 0.000 0.000 0.232 0.768 0.000
#> GSM876903 5 0.1965 0.801986 0.000 0.096 0.000 0.000 0.904
#> GSM876904 1 0.8277 0.227146 0.368 0.284 0.156 0.000 0.192
#> GSM876874 1 0.0510 0.863984 0.984 0.000 0.016 0.000 0.000
#> GSM876875 5 0.1484 0.829253 0.000 0.008 0.048 0.000 0.944
#> GSM876876 1 0.2280 0.843317 0.880 0.000 0.120 0.000 0.000
#> GSM876877 1 0.0510 0.863984 0.984 0.000 0.016 0.000 0.000
#> GSM876878 1 0.2439 0.841871 0.876 0.000 0.120 0.000 0.004
#> GSM876879 5 0.1484 0.829253 0.000 0.008 0.048 0.000 0.944
#> GSM876880 1 0.0000 0.865925 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0992 0.850614 0.008 0.968 0.000 0.000 0.024
#> GSM876851 2 0.0880 0.854993 0.000 0.968 0.000 0.000 0.032
#> GSM876852 2 0.5252 0.422614 0.000 0.580 0.056 0.000 0.364
#> GSM876853 2 0.0880 0.854993 0.000 0.968 0.000 0.000 0.032
#> GSM876854 3 0.3841 0.631797 0.000 0.000 0.780 0.188 0.032
#> GSM876855 3 0.4444 0.625769 0.000 0.088 0.756 0.000 0.156
#> GSM876856 3 0.4691 0.659229 0.000 0.024 0.772 0.100 0.104
#> GSM876905 5 0.8173 0.000622 0.168 0.288 0.156 0.000 0.388
#> GSM876906 5 0.0510 0.830318 0.000 0.016 0.000 0.000 0.984
#> GSM876907 5 0.5111 -0.020885 0.000 0.464 0.036 0.000 0.500
#> GSM876908 5 0.2519 0.788219 0.000 0.100 0.016 0.000 0.884
#> GSM876909 2 0.3482 0.791388 0.008 0.844 0.052 0.000 0.096
#> GSM876881 1 0.2074 0.847513 0.896 0.000 0.104 0.000 0.000
#> GSM876882 5 0.1341 0.825080 0.000 0.000 0.056 0.000 0.944
#> GSM876883 5 0.1341 0.825080 0.000 0.000 0.056 0.000 0.944
#> GSM876884 1 0.0000 0.865925 1.000 0.000 0.000 0.000 0.000
#> GSM876885 5 0.1341 0.825080 0.000 0.000 0.056 0.000 0.944
#> GSM876857 1 0.2179 0.846220 0.888 0.000 0.112 0.000 0.000
#> GSM876858 2 0.2278 0.834920 0.000 0.908 0.032 0.000 0.060
#> GSM876859 2 0.3138 0.814462 0.024 0.876 0.048 0.000 0.052
#> GSM876860 2 0.2278 0.834920 0.000 0.908 0.032 0.000 0.060
#> GSM876861 2 0.4449 0.237686 0.000 0.512 0.004 0.000 0.484
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM876886 6 0.0508 0.7771 0.000 0.004 0.000 0.000 0.012 0.984
#> GSM876887 6 0.2888 0.6591 0.000 0.004 0.068 0.000 0.068 0.860
#> GSM876888 5 0.4617 0.3290 0.328 0.040 0.008 0.000 0.624 0.000
#> GSM876889 3 0.3557 0.7009 0.000 0.000 0.800 0.140 0.056 0.004
#> GSM876890 3 0.5116 0.4680 0.000 0.004 0.524 0.000 0.072 0.400
#> GSM876891 6 0.3155 0.6328 0.000 0.004 0.088 0.000 0.068 0.840
#> GSM876862 1 0.0725 0.8344 0.976 0.000 0.012 0.000 0.012 0.000
#> GSM876863 5 0.4541 0.3273 0.336 0.040 0.004 0.000 0.620 0.000
#> GSM876864 1 0.0000 0.8419 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.3881 0.4634 0.600 0.000 0.004 0.000 0.396 0.000
#> GSM876866 3 0.5132 0.4467 0.000 0.004 0.512 0.000 0.072 0.412
#> GSM876867 1 0.0000 0.8419 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0146 0.8446 0.000 0.996 0.000 0.000 0.000 0.004
#> GSM876839 2 0.0291 0.8438 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM876840 3 0.1714 0.7356 0.000 0.000 0.908 0.092 0.000 0.000
#> GSM876841 2 0.1152 0.8496 0.000 0.952 0.000 0.000 0.044 0.004
#> GSM876842 2 0.2912 0.7198 0.000 0.816 0.000 0.000 0.012 0.172
#> GSM876843 4 0.2234 0.8012 0.000 0.000 0.004 0.872 0.124 0.000
#> GSM876892 6 0.0922 0.7830 0.000 0.004 0.004 0.000 0.024 0.968
#> GSM876893 6 0.3679 0.7356 0.000 0.004 0.012 0.000 0.260 0.724
#> GSM876894 6 0.3593 0.7635 0.000 0.004 0.024 0.000 0.208 0.764
#> GSM876895 6 0.4430 0.7316 0.000 0.032 0.028 0.000 0.232 0.708
#> GSM876896 4 0.1204 0.8290 0.000 0.000 0.056 0.944 0.000 0.000
#> GSM876897 4 0.1204 0.8290 0.000 0.000 0.056 0.944 0.000 0.000
#> GSM876868 1 0.0000 0.8419 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.8419 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.8419 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0725 0.8344 0.976 0.000 0.012 0.000 0.012 0.000
#> GSM876872 4 0.3081 0.7527 0.000 0.000 0.220 0.776 0.004 0.000
#> GSM876873 4 0.3081 0.7527 0.000 0.000 0.220 0.776 0.004 0.000
#> GSM876844 2 0.2980 0.7135 0.000 0.808 0.000 0.000 0.012 0.180
#> GSM876845 2 0.1152 0.8496 0.000 0.952 0.000 0.000 0.044 0.004
#> GSM876846 3 0.2340 0.6827 0.000 0.000 0.852 0.148 0.000 0.000
#> GSM876847 2 0.1285 0.8457 0.004 0.944 0.000 0.000 0.052 0.000
#> GSM876848 4 0.2234 0.8012 0.000 0.000 0.004 0.872 0.124 0.000
#> GSM876849 4 0.2234 0.8012 0.000 0.000 0.004 0.872 0.124 0.000
#> GSM876898 1 0.3748 0.6203 0.688 0.000 0.012 0.000 0.300 0.000
#> GSM876899 6 0.4479 0.7249 0.000 0.032 0.028 0.000 0.240 0.700
#> GSM876900 6 0.3341 0.7668 0.000 0.004 0.012 0.000 0.208 0.776
#> GSM876901 5 0.4534 0.6732 0.096 0.072 0.000 0.000 0.760 0.072
#> GSM876902 4 0.2994 0.7631 0.000 0.000 0.208 0.788 0.004 0.000
#> GSM876903 6 0.4454 0.7287 0.000 0.032 0.028 0.000 0.236 0.704
#> GSM876904 5 0.4647 0.6661 0.108 0.068 0.004 0.000 0.756 0.064
#> GSM876874 1 0.1003 0.8347 0.964 0.000 0.020 0.000 0.016 0.000
#> GSM876875 6 0.1349 0.7887 0.000 0.004 0.000 0.000 0.056 0.940
#> GSM876876 1 0.3784 0.6118 0.680 0.000 0.012 0.000 0.308 0.000
#> GSM876877 1 0.0914 0.8346 0.968 0.000 0.016 0.000 0.016 0.000
#> GSM876878 1 0.4084 0.4566 0.588 0.000 0.012 0.000 0.400 0.000
#> GSM876879 6 0.1349 0.7887 0.000 0.004 0.000 0.000 0.056 0.940
#> GSM876880 1 0.0405 0.8405 0.988 0.000 0.008 0.000 0.004 0.000
#> GSM876850 2 0.1285 0.8457 0.004 0.944 0.000 0.000 0.052 0.000
#> GSM876851 2 0.1152 0.8496 0.000 0.952 0.000 0.000 0.044 0.004
#> GSM876852 2 0.4051 0.6789 0.000 0.760 0.056 0.000 0.012 0.172
#> GSM876853 2 0.0291 0.8438 0.000 0.992 0.000 0.000 0.004 0.004
#> GSM876854 3 0.1434 0.7540 0.000 0.000 0.940 0.048 0.000 0.012
#> GSM876855 3 0.1856 0.7316 0.000 0.048 0.920 0.000 0.000 0.032
#> GSM876856 3 0.1633 0.7552 0.000 0.000 0.932 0.044 0.000 0.024
#> GSM876905 5 0.4444 0.6458 0.044 0.076 0.000 0.000 0.760 0.120
#> GSM876906 6 0.3613 0.7663 0.000 0.008 0.024 0.000 0.196 0.772
#> GSM876907 5 0.6416 -0.1511 0.000 0.176 0.032 0.000 0.400 0.392
#> GSM876908 6 0.4525 0.7167 0.000 0.032 0.028 0.000 0.248 0.692
#> GSM876909 5 0.5167 0.2338 0.004 0.352 0.032 0.000 0.580 0.032
#> GSM876881 1 0.3905 0.5928 0.668 0.000 0.016 0.000 0.316 0.000
#> GSM876882 6 0.0146 0.7831 0.000 0.004 0.000 0.000 0.000 0.996
#> GSM876883 6 0.0146 0.7831 0.000 0.004 0.000 0.000 0.000 0.996
#> GSM876884 1 0.0405 0.8405 0.988 0.000 0.008 0.000 0.004 0.000
#> GSM876885 6 0.0146 0.7831 0.000 0.004 0.000 0.000 0.000 0.996
#> GSM876857 1 0.3050 0.6900 0.764 0.000 0.000 0.000 0.236 0.000
#> GSM876858 2 0.3580 0.7218 0.000 0.772 0.028 0.000 0.196 0.004
#> GSM876859 2 0.4560 0.3984 0.008 0.592 0.028 0.000 0.372 0.000
#> GSM876860 2 0.3580 0.7218 0.000 0.772 0.028 0.000 0.196 0.004
#> GSM876861 6 0.5449 0.0103 0.000 0.444 0.028 0.000 0.056 0.472
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> ATC:kmeans 72 0.0545 2.17e-01 2
#> ATC:kmeans 67 0.0959 2.74e-04 3
#> ATC:kmeans 58 0.1257 2.37e-07 4
#> ATC:kmeans 63 0.1377 1.83e-10 5
#> ATC:kmeans 62 0.3559 3.48e-11 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 72 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 0.995 0.998 0.4815 0.518 0.518
#> 3 3 0.758 0.910 0.946 0.3150 0.803 0.632
#> 4 4 0.816 0.756 0.885 0.1185 0.884 0.693
#> 5 5 0.949 0.903 0.963 0.0795 0.905 0.689
#> 6 6 0.928 0.849 0.924 0.0300 0.959 0.833
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
#> GSM876886 2 0.000 0.994 0.00 1.00
#> GSM876887 2 0.000 0.994 0.00 1.00
#> GSM876888 1 0.000 1.000 1.00 0.00
#> GSM876889 2 0.000 0.994 0.00 1.00
#> GSM876890 2 0.000 0.994 0.00 1.00
#> GSM876891 2 0.000 0.994 0.00 1.00
#> GSM876862 1 0.000 1.000 1.00 0.00
#> GSM876863 1 0.000 1.000 1.00 0.00
#> GSM876864 1 0.000 1.000 1.00 0.00
#> GSM876865 1 0.000 1.000 1.00 0.00
#> GSM876866 2 0.000 0.994 0.00 1.00
#> GSM876867 1 0.000 1.000 1.00 0.00
#> GSM876838 1 0.000 1.000 1.00 0.00
#> GSM876839 1 0.000 1.000 1.00 0.00
#> GSM876840 2 0.000 0.994 0.00 1.00
#> GSM876841 1 0.000 1.000 1.00 0.00
#> GSM876842 2 0.000 0.994 0.00 1.00
#> GSM876843 2 0.000 0.994 0.00 1.00
#> GSM876892 2 0.000 0.994 0.00 1.00
#> GSM876893 1 0.000 1.000 1.00 0.00
#> GSM876894 1 0.000 1.000 1.00 0.00
#> GSM876895 1 0.000 1.000 1.00 0.00
#> GSM876896 2 0.000 0.994 0.00 1.00
#> GSM876897 2 0.000 0.994 0.00 1.00
#> GSM876868 1 0.000 1.000 1.00 0.00
#> GSM876869 1 0.000 1.000 1.00 0.00
#> GSM876870 1 0.000 1.000 1.00 0.00
#> GSM876871 1 0.000 1.000 1.00 0.00
#> GSM876872 2 0.000 0.994 0.00 1.00
#> GSM876873 2 0.000 0.994 0.00 1.00
#> GSM876844 2 0.000 0.994 0.00 1.00
#> GSM876845 1 0.000 1.000 1.00 0.00
#> GSM876846 2 0.000 0.994 0.00 1.00
#> GSM876847 1 0.000 1.000 1.00 0.00
#> GSM876848 2 0.000 0.994 0.00 1.00
#> GSM876849 2 0.000 0.994 0.00 1.00
#> GSM876898 1 0.000 1.000 1.00 0.00
#> GSM876899 1 0.000 1.000 1.00 0.00
#> GSM876900 1 0.000 1.000 1.00 0.00
#> GSM876901 1 0.000 1.000 1.00 0.00
#> GSM876902 2 0.000 0.994 0.00 1.00
#> GSM876903 1 0.000 1.000 1.00 0.00
#> GSM876904 1 0.000 1.000 1.00 0.00
#> GSM876874 1 0.000 1.000 1.00 0.00
#> GSM876875 1 0.000 1.000 1.00 0.00
#> GSM876876 1 0.000 1.000 1.00 0.00
#> GSM876877 1 0.000 1.000 1.00 0.00
#> GSM876878 1 0.000 1.000 1.00 0.00
#> GSM876879 1 0.000 1.000 1.00 0.00
#> GSM876880 1 0.000 1.000 1.00 0.00
#> GSM876850 1 0.000 1.000 1.00 0.00
#> GSM876851 1 0.000 1.000 1.00 0.00
#> GSM876852 2 0.000 0.994 0.00 1.00
#> GSM876853 1 0.000 1.000 1.00 0.00
#> GSM876854 2 0.000 0.994 0.00 1.00
#> GSM876855 2 0.000 0.994 0.00 1.00
#> GSM876856 2 0.000 0.994 0.00 1.00
#> GSM876905 1 0.000 1.000 1.00 0.00
#> GSM876906 2 0.634 0.810 0.16 0.84
#> GSM876907 1 0.000 1.000 1.00 0.00
#> GSM876908 1 0.000 1.000 1.00 0.00
#> GSM876909 1 0.000 1.000 1.00 0.00
#> GSM876881 1 0.000 1.000 1.00 0.00
#> GSM876882 2 0.000 0.994 0.00 1.00
#> GSM876883 2 0.000 0.994 0.00 1.00
#> GSM876884 1 0.000 1.000 1.00 0.00
#> GSM876885 2 0.000 0.994 0.00 1.00
#> GSM876857 1 0.000 1.000 1.00 0.00
#> GSM876858 1 0.000 1.000 1.00 0.00
#> GSM876859 1 0.000 1.000 1.00 0.00
#> GSM876860 1 0.000 1.000 1.00 0.00
#> GSM876861 2 0.000 0.994 0.00 1.00
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 3 0.3267 0.8962 0.000 0.116 0.884
#> GSM876887 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876888 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876889 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876890 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876891 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876862 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876863 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876864 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876865 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876866 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876867 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876838 2 0.3267 0.9007 0.116 0.884 0.000
#> GSM876839 2 0.3267 0.9007 0.116 0.884 0.000
#> GSM876840 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876841 2 0.3267 0.9007 0.116 0.884 0.000
#> GSM876842 2 0.3267 0.8084 0.000 0.884 0.116
#> GSM876843 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876892 3 0.0237 0.9691 0.000 0.004 0.996
#> GSM876893 1 0.0237 0.9682 0.996 0.004 0.000
#> GSM876894 1 0.3267 0.8563 0.884 0.116 0.000
#> GSM876895 1 0.0237 0.9682 0.996 0.004 0.000
#> GSM876896 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876897 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876868 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876869 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876870 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876871 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876872 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876873 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876844 2 0.3267 0.8084 0.000 0.884 0.116
#> GSM876845 2 0.3267 0.9007 0.116 0.884 0.000
#> GSM876846 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876847 2 0.3267 0.9007 0.116 0.884 0.000
#> GSM876848 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876849 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876898 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876899 1 0.0237 0.9682 0.996 0.004 0.000
#> GSM876900 1 0.0237 0.9682 0.996 0.004 0.000
#> GSM876901 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876902 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876903 2 0.6309 0.1731 0.496 0.504 0.000
#> GSM876904 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876874 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876875 1 0.3267 0.8563 0.884 0.116 0.000
#> GSM876876 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876877 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876878 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876879 1 0.3267 0.8563 0.884 0.116 0.000
#> GSM876880 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876850 2 0.3267 0.9007 0.116 0.884 0.000
#> GSM876851 2 0.3267 0.9007 0.116 0.884 0.000
#> GSM876852 2 0.6126 0.3781 0.000 0.600 0.400
#> GSM876853 2 0.3267 0.9007 0.116 0.884 0.000
#> GSM876854 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876855 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876856 3 0.0000 0.9716 0.000 0.000 1.000
#> GSM876905 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876906 3 0.4110 0.7770 0.152 0.004 0.844
#> GSM876907 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876908 1 0.0237 0.9682 0.996 0.004 0.000
#> GSM876909 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876881 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876882 3 0.3267 0.8962 0.000 0.116 0.884
#> GSM876883 3 0.3267 0.8962 0.000 0.116 0.884
#> GSM876884 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876885 3 0.3267 0.8962 0.000 0.116 0.884
#> GSM876857 1 0.0000 0.9707 1.000 0.000 0.000
#> GSM876858 2 0.3686 0.8841 0.140 0.860 0.000
#> GSM876859 1 0.6215 0.0337 0.572 0.428 0.000
#> GSM876860 2 0.3686 0.8841 0.140 0.860 0.000
#> GSM876861 2 0.3412 0.8032 0.000 0.876 0.124
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.494 0.33048 0.000 0.000 0.564 0.436
#> GSM876887 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876888 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876889 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876890 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876891 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876862 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876863 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876864 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876865 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876866 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876867 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876838 2 0.112 0.87549 0.036 0.964 0.000 0.000
#> GSM876839 2 0.112 0.87549 0.036 0.964 0.000 0.000
#> GSM876840 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876841 2 0.112 0.87549 0.036 0.964 0.000 0.000
#> GSM876842 2 0.112 0.84089 0.000 0.964 0.000 0.036
#> GSM876843 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876892 4 0.112 0.91215 0.000 0.000 0.036 0.964
#> GSM876893 1 0.367 0.75286 0.848 0.036 0.116 0.000
#> GSM876894 3 0.158 0.41015 0.012 0.036 0.952 0.000
#> GSM876895 1 0.591 0.37482 0.528 0.036 0.436 0.000
#> GSM876896 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876897 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876868 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876869 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876870 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876871 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876872 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876873 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876844 2 0.112 0.84089 0.000 0.964 0.000 0.036
#> GSM876845 2 0.112 0.87549 0.036 0.964 0.000 0.000
#> GSM876846 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876847 2 0.112 0.87549 0.036 0.964 0.000 0.000
#> GSM876848 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876849 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876898 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876899 1 0.591 0.37482 0.528 0.036 0.436 0.000
#> GSM876900 1 0.581 0.44451 0.576 0.036 0.388 0.000
#> GSM876901 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876902 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876903 3 0.759 -0.15453 0.364 0.200 0.436 0.000
#> GSM876904 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876874 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876875 3 0.482 0.31243 0.388 0.000 0.612 0.000
#> GSM876876 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876877 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876878 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876879 3 0.482 0.31243 0.388 0.000 0.612 0.000
#> GSM876880 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876850 2 0.112 0.87549 0.036 0.964 0.000 0.000
#> GSM876851 2 0.112 0.87549 0.036 0.964 0.000 0.000
#> GSM876852 4 0.499 -0.00714 0.000 0.480 0.000 0.520
#> GSM876853 2 0.112 0.87549 0.036 0.964 0.000 0.000
#> GSM876854 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876855 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876856 4 0.000 0.95914 0.000 0.000 0.000 1.000
#> GSM876905 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876906 3 0.791 0.10918 0.116 0.036 0.436 0.412
#> GSM876907 1 0.591 0.37482 0.528 0.036 0.436 0.000
#> GSM876908 1 0.591 0.37482 0.528 0.036 0.436 0.000
#> GSM876909 1 0.422 0.62642 0.728 0.000 0.272 0.000
#> GSM876881 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876882 3 0.482 0.42098 0.000 0.000 0.612 0.388
#> GSM876883 3 0.482 0.42098 0.000 0.000 0.612 0.388
#> GSM876884 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876885 3 0.482 0.42098 0.000 0.000 0.612 0.388
#> GSM876857 1 0.000 0.88490 1.000 0.000 0.000 0.000
#> GSM876858 2 0.398 0.67446 0.240 0.760 0.000 0.000
#> GSM876859 2 0.499 0.16105 0.480 0.520 0.000 0.000
#> GSM876860 2 0.394 0.67912 0.236 0.764 0.000 0.000
#> GSM876861 2 0.353 0.67914 0.000 0.808 0.000 0.192
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM876886 3 0.0162 0.9972 0.000 0.000 0.996 0.004 0.000
#> GSM876887 4 0.0000 0.9925 0.000 0.000 0.000 1.000 0.000
#> GSM876888 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876889 4 0.0000 0.9925 0.000 0.000 0.000 1.000 0.000
#> GSM876890 4 0.0000 0.9925 0.000 0.000 0.000 1.000 0.000
#> GSM876891 4 0.0000 0.9925 0.000 0.000 0.000 1.000 0.000
#> GSM876862 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876866 4 0.0000 0.9925 0.000 0.000 0.000 1.000 0.000
#> GSM876867 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.8374 0.000 1.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.8374 0.000 1.000 0.000 0.000 0.000
#> GSM876840 4 0.0162 0.9907 0.000 0.000 0.004 0.996 0.000
#> GSM876841 2 0.0000 0.8374 0.000 1.000 0.000 0.000 0.000
#> GSM876842 2 0.0451 0.8326 0.000 0.988 0.004 0.000 0.008
#> GSM876843 4 0.0000 0.9925 0.000 0.000 0.000 1.000 0.000
#> GSM876892 4 0.2127 0.8772 0.000 0.000 0.000 0.892 0.108
#> GSM876893 5 0.3949 0.4964 0.332 0.000 0.000 0.000 0.668
#> GSM876894 5 0.0290 0.9282 0.000 0.000 0.008 0.000 0.992
#> GSM876895 5 0.0290 0.9379 0.008 0.000 0.000 0.000 0.992
#> GSM876896 4 0.0000 0.9925 0.000 0.000 0.000 1.000 0.000
#> GSM876897 4 0.0000 0.9925 0.000 0.000 0.000 1.000 0.000
#> GSM876868 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 0.9925 0.000 0.000 0.000 1.000 0.000
#> GSM876873 4 0.0000 0.9925 0.000 0.000 0.000 1.000 0.000
#> GSM876844 2 0.0451 0.8326 0.000 0.988 0.004 0.000 0.008
#> GSM876845 2 0.0000 0.8374 0.000 1.000 0.000 0.000 0.000
#> GSM876846 4 0.0162 0.9907 0.000 0.000 0.004 0.996 0.000
#> GSM876847 2 0.0000 0.8374 0.000 1.000 0.000 0.000 0.000
#> GSM876848 4 0.0000 0.9925 0.000 0.000 0.000 1.000 0.000
#> GSM876849 4 0.0000 0.9925 0.000 0.000 0.000 1.000 0.000
#> GSM876898 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876899 5 0.0290 0.9379 0.008 0.000 0.000 0.000 0.992
#> GSM876900 5 0.0290 0.9379 0.008 0.000 0.000 0.000 0.992
#> GSM876901 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876902 4 0.0000 0.9925 0.000 0.000 0.000 1.000 0.000
#> GSM876903 5 0.0290 0.9379 0.008 0.000 0.000 0.000 0.992
#> GSM876904 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876874 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876875 3 0.0162 0.9944 0.004 0.000 0.996 0.000 0.000
#> GSM876876 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876879 3 0.0162 0.9944 0.004 0.000 0.996 0.000 0.000
#> GSM876880 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.8374 0.000 1.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.8374 0.000 1.000 0.000 0.000 0.000
#> GSM876852 2 0.4706 0.0767 0.000 0.500 0.004 0.488 0.008
#> GSM876853 2 0.0000 0.8374 0.000 1.000 0.000 0.000 0.000
#> GSM876854 4 0.0162 0.9907 0.000 0.000 0.004 0.996 0.000
#> GSM876855 4 0.0162 0.9907 0.000 0.000 0.004 0.996 0.000
#> GSM876856 4 0.0162 0.9907 0.000 0.000 0.004 0.996 0.000
#> GSM876905 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876906 5 0.0324 0.9331 0.004 0.000 0.000 0.004 0.992
#> GSM876907 5 0.0290 0.9379 0.008 0.000 0.000 0.000 0.992
#> GSM876908 5 0.0290 0.9379 0.008 0.000 0.000 0.000 0.992
#> GSM876909 1 0.3607 0.6601 0.752 0.004 0.000 0.000 0.244
#> GSM876881 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876882 3 0.0162 0.9972 0.000 0.000 0.996 0.004 0.000
#> GSM876883 3 0.0162 0.9972 0.000 0.000 0.996 0.004 0.000
#> GSM876884 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876885 3 0.0162 0.9972 0.000 0.000 0.996 0.004 0.000
#> GSM876857 1 0.0000 0.9727 1.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.4201 0.3278 0.408 0.592 0.000 0.000 0.000
#> GSM876859 1 0.3895 0.4700 0.680 0.320 0.000 0.000 0.000
#> GSM876860 2 0.4150 0.3775 0.388 0.612 0.000 0.000 0.000
#> GSM876861 2 0.3768 0.6225 0.000 0.760 0.004 0.228 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM876886 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM876887 4 0.0260 0.957 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM876888 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876889 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876890 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876891 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876862 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876866 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876867 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0547 0.680 0.000 0.980 0.020 0.000 0.000 0.000
#> GSM876839 2 0.0547 0.680 0.000 0.980 0.020 0.000 0.000 0.000
#> GSM876840 4 0.0547 0.950 0.000 0.000 0.020 0.980 0.000 0.000
#> GSM876841 2 0.0000 0.697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876842 3 0.3866 0.709 0.000 0.484 0.516 0.000 0.000 0.000
#> GSM876843 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876892 4 0.3925 0.657 0.000 0.000 0.236 0.724 0.040 0.000
#> GSM876893 1 0.5998 -0.183 0.404 0.000 0.236 0.000 0.360 0.000
#> GSM876894 5 0.0260 0.952 0.000 0.000 0.008 0.000 0.992 0.000
#> GSM876895 5 0.0000 0.955 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876896 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876897 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876868 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876873 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876844 3 0.3866 0.709 0.000 0.484 0.516 0.000 0.000 0.000
#> GSM876845 2 0.0000 0.697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876846 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876847 2 0.0000 0.697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876848 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876849 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876898 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876899 5 0.0000 0.955 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876900 5 0.3050 0.791 0.000 0.000 0.236 0.000 0.764 0.000
#> GSM876901 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876902 4 0.0000 0.962 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876903 5 0.0000 0.955 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876904 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876874 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876875 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM876876 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876879 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM876880 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.697 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876852 3 0.5403 0.666 0.000 0.360 0.516 0.124 0.000 0.000
#> GSM876853 2 0.0547 0.680 0.000 0.980 0.020 0.000 0.000 0.000
#> GSM876854 4 0.0547 0.950 0.000 0.000 0.020 0.980 0.000 0.000
#> GSM876855 4 0.2562 0.800 0.000 0.000 0.172 0.828 0.000 0.000
#> GSM876856 4 0.2491 0.810 0.000 0.000 0.164 0.836 0.000 0.000
#> GSM876905 1 0.0146 0.950 0.996 0.000 0.004 0.000 0.000 0.000
#> GSM876906 5 0.1957 0.894 0.000 0.000 0.112 0.000 0.888 0.000
#> GSM876907 5 0.0000 0.955 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876908 5 0.0000 0.955 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876909 1 0.5733 0.361 0.568 0.124 0.024 0.000 0.284 0.000
#> GSM876881 1 0.0547 0.935 0.980 0.020 0.000 0.000 0.000 0.000
#> GSM876882 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM876883 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM876884 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876885 6 0.0000 1.000 0.000 0.000 0.000 0.000 0.000 1.000
#> GSM876857 1 0.0000 0.953 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.5579 0.286 0.204 0.548 0.248 0.000 0.000 0.000
#> GSM876859 2 0.5949 0.175 0.320 0.444 0.236 0.000 0.000 0.000
#> GSM876860 2 0.5579 0.286 0.204 0.548 0.248 0.000 0.000 0.000
#> GSM876861 3 0.3572 0.567 0.000 0.204 0.764 0.032 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> ATC:skmeans 72 0.254 1.95e-01 2
#> ATC:skmeans 69 0.607 1.67e-08 3
#> ATC:skmeans 56 0.305 7.65e-08 4
#> ATC:skmeans 67 0.122 9.69e-11 5
#> ATC:skmeans 67 0.192 2.38e-10 6
If matrix rows can be associated to genes, consider to use functional_enrichment(res,
...) to perform function enrichment for the signature genes. See this vignette for more detailed explanations.
The object with results only for a single top-value method and a single partition method can be extracted as:
res = res_list["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 72 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 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 0.983 0.992 0.3103 0.700 0.700
#> 3 3 1.000 0.975 0.990 0.9485 0.695 0.564
#> 4 4 0.816 0.881 0.924 0.1903 0.851 0.632
#> 5 5 0.910 0.865 0.946 0.0655 0.931 0.754
#> 6 6 0.882 0.856 0.933 0.0229 0.985 0.934
suggest_best_k() suggests the best \(k\) based on these statistics. The rules are as follows:
suggest_best_k(res)
#> [1] 5
#> attr(,"optional")
#> [1] 2 3
There is also optional best \(k\) = 2 3 that is worth to check.
Following shows the table of the partitions (You need to click the show/hide
code output link to see it). The membership matrix (columns with name p*)
is inferred by
clue::cl_consensus()
function with the SE method. Basically the value in the membership matrix
represents the probability to belong to a certain group. The finall class
label for an item is determined with the group with highest probability it
belongs to.
In get_classes() function, the entropy is calculated from the membership
matrix and the silhouette score is calculated from the consensus matrix.
cbind(get_classes(res, k = 2), get_membership(res, k = 2))
#> class entropy silhouette p1 p2
#> GSM876886 1 0.000 0.990 1.000 0.000
#> GSM876887 1 0.000 0.990 1.000 0.000
#> GSM876888 1 0.000 0.990 1.000 0.000
#> GSM876889 2 0.000 1.000 0.000 1.000
#> GSM876890 1 0.781 0.709 0.768 0.232
#> GSM876891 1 0.000 0.990 1.000 0.000
#> GSM876862 1 0.000 0.990 1.000 0.000
#> GSM876863 1 0.000 0.990 1.000 0.000
#> GSM876864 1 0.000 0.990 1.000 0.000
#> GSM876865 1 0.000 0.990 1.000 0.000
#> GSM876866 1 0.662 0.798 0.828 0.172
#> GSM876867 1 0.000 0.990 1.000 0.000
#> GSM876838 1 0.000 0.990 1.000 0.000
#> GSM876839 1 0.000 0.990 1.000 0.000
#> GSM876840 2 0.000 1.000 0.000 1.000
#> GSM876841 1 0.000 0.990 1.000 0.000
#> GSM876842 1 0.000 0.990 1.000 0.000
#> GSM876843 2 0.000 1.000 0.000 1.000
#> GSM876892 1 0.000 0.990 1.000 0.000
#> GSM876893 1 0.000 0.990 1.000 0.000
#> GSM876894 1 0.000 0.990 1.000 0.000
#> GSM876895 1 0.000 0.990 1.000 0.000
#> GSM876896 2 0.000 1.000 0.000 1.000
#> GSM876897 2 0.000 1.000 0.000 1.000
#> GSM876868 1 0.000 0.990 1.000 0.000
#> GSM876869 1 0.000 0.990 1.000 0.000
#> GSM876870 1 0.000 0.990 1.000 0.000
#> GSM876871 1 0.000 0.990 1.000 0.000
#> GSM876872 2 0.000 1.000 0.000 1.000
#> GSM876873 2 0.000 1.000 0.000 1.000
#> GSM876844 1 0.000 0.990 1.000 0.000
#> GSM876845 1 0.000 0.990 1.000 0.000
#> GSM876846 2 0.000 1.000 0.000 1.000
#> GSM876847 1 0.000 0.990 1.000 0.000
#> GSM876848 2 0.000 1.000 0.000 1.000
#> GSM876849 2 0.000 1.000 0.000 1.000
#> GSM876898 1 0.000 0.990 1.000 0.000
#> GSM876899 1 0.000 0.990 1.000 0.000
#> GSM876900 1 0.000 0.990 1.000 0.000
#> GSM876901 1 0.000 0.990 1.000 0.000
#> GSM876902 2 0.000 1.000 0.000 1.000
#> GSM876903 1 0.000 0.990 1.000 0.000
#> GSM876904 1 0.000 0.990 1.000 0.000
#> GSM876874 1 0.000 0.990 1.000 0.000
#> GSM876875 1 0.000 0.990 1.000 0.000
#> GSM876876 1 0.000 0.990 1.000 0.000
#> GSM876877 1 0.000 0.990 1.000 0.000
#> GSM876878 1 0.000 0.990 1.000 0.000
#> GSM876879 1 0.000 0.990 1.000 0.000
#> GSM876880 1 0.000 0.990 1.000 0.000
#> GSM876850 1 0.000 0.990 1.000 0.000
#> GSM876851 1 0.000 0.990 1.000 0.000
#> GSM876852 1 0.000 0.990 1.000 0.000
#> GSM876853 1 0.000 0.990 1.000 0.000
#> GSM876854 2 0.000 1.000 0.000 1.000
#> GSM876855 1 0.644 0.809 0.836 0.164
#> GSM876856 2 0.000 1.000 0.000 1.000
#> GSM876905 1 0.000 0.990 1.000 0.000
#> GSM876906 1 0.000 0.990 1.000 0.000
#> GSM876907 1 0.000 0.990 1.000 0.000
#> GSM876908 1 0.000 0.990 1.000 0.000
#> GSM876909 1 0.000 0.990 1.000 0.000
#> GSM876881 1 0.000 0.990 1.000 0.000
#> GSM876882 1 0.000 0.990 1.000 0.000
#> GSM876883 1 0.000 0.990 1.000 0.000
#> GSM876884 1 0.000 0.990 1.000 0.000
#> GSM876885 1 0.000 0.990 1.000 0.000
#> GSM876857 1 0.000 0.990 1.000 0.000
#> GSM876858 1 0.000 0.990 1.000 0.000
#> GSM876859 1 0.000 0.990 1.000 0.000
#> GSM876860 1 0.000 0.990 1.000 0.000
#> GSM876861 1 0.000 0.990 1.000 0.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 3 0.0000 0.991 0.000 0 1.000
#> GSM876887 3 0.0000 0.991 0.000 0 1.000
#> GSM876888 1 0.1753 0.916 0.952 0 0.048
#> GSM876889 2 0.0000 1.000 0.000 1 0.000
#> GSM876890 3 0.0000 0.991 0.000 0 1.000
#> GSM876891 3 0.0000 0.991 0.000 0 1.000
#> GSM876862 1 0.0000 0.972 1.000 0 0.000
#> GSM876863 1 0.0000 0.972 1.000 0 0.000
#> GSM876864 1 0.0000 0.972 1.000 0 0.000
#> GSM876865 1 0.0000 0.972 1.000 0 0.000
#> GSM876866 3 0.0000 0.991 0.000 0 1.000
#> GSM876867 1 0.0000 0.972 1.000 0 0.000
#> GSM876838 3 0.0000 0.991 0.000 0 1.000
#> GSM876839 3 0.0000 0.991 0.000 0 1.000
#> GSM876840 2 0.0000 1.000 0.000 1 0.000
#> GSM876841 3 0.0000 0.991 0.000 0 1.000
#> GSM876842 3 0.0000 0.991 0.000 0 1.000
#> GSM876843 2 0.0000 1.000 0.000 1 0.000
#> GSM876892 3 0.0000 0.991 0.000 0 1.000
#> GSM876893 3 0.0000 0.991 0.000 0 1.000
#> GSM876894 3 0.0000 0.991 0.000 0 1.000
#> GSM876895 3 0.0000 0.991 0.000 0 1.000
#> GSM876896 2 0.0000 1.000 0.000 1 0.000
#> GSM876897 2 0.0000 1.000 0.000 1 0.000
#> GSM876868 1 0.0000 0.972 1.000 0 0.000
#> GSM876869 1 0.0000 0.972 1.000 0 0.000
#> GSM876870 1 0.0000 0.972 1.000 0 0.000
#> GSM876871 1 0.0000 0.972 1.000 0 0.000
#> GSM876872 2 0.0000 1.000 0.000 1 0.000
#> GSM876873 2 0.0000 1.000 0.000 1 0.000
#> GSM876844 3 0.0000 0.991 0.000 0 1.000
#> GSM876845 3 0.0000 0.991 0.000 0 1.000
#> GSM876846 2 0.0000 1.000 0.000 1 0.000
#> GSM876847 3 0.3619 0.843 0.136 0 0.864
#> GSM876848 2 0.0000 1.000 0.000 1 0.000
#> GSM876849 2 0.0000 1.000 0.000 1 0.000
#> GSM876898 1 0.0000 0.972 1.000 0 0.000
#> GSM876899 3 0.0000 0.991 0.000 0 1.000
#> GSM876900 3 0.0000 0.991 0.000 0 1.000
#> GSM876901 3 0.0000 0.991 0.000 0 1.000
#> GSM876902 2 0.0000 1.000 0.000 1 0.000
#> GSM876903 3 0.0000 0.991 0.000 0 1.000
#> GSM876904 3 0.0592 0.980 0.012 0 0.988
#> GSM876874 1 0.0000 0.972 1.000 0 0.000
#> GSM876875 3 0.0000 0.991 0.000 0 1.000
#> GSM876876 1 0.0000 0.972 1.000 0 0.000
#> GSM876877 1 0.0000 0.972 1.000 0 0.000
#> GSM876878 1 0.0000 0.972 1.000 0 0.000
#> GSM876879 3 0.0000 0.991 0.000 0 1.000
#> GSM876880 1 0.0000 0.972 1.000 0 0.000
#> GSM876850 3 0.4062 0.805 0.164 0 0.836
#> GSM876851 3 0.0000 0.991 0.000 0 1.000
#> GSM876852 3 0.0000 0.991 0.000 0 1.000
#> GSM876853 3 0.0000 0.991 0.000 0 1.000
#> GSM876854 2 0.0000 1.000 0.000 1 0.000
#> GSM876855 3 0.0000 0.991 0.000 0 1.000
#> GSM876856 2 0.0000 1.000 0.000 1 0.000
#> GSM876905 3 0.0000 0.991 0.000 0 1.000
#> GSM876906 3 0.0000 0.991 0.000 0 1.000
#> GSM876907 3 0.0000 0.991 0.000 0 1.000
#> GSM876908 3 0.0000 0.991 0.000 0 1.000
#> GSM876909 3 0.0000 0.991 0.000 0 1.000
#> GSM876881 1 0.0000 0.972 1.000 0 0.000
#> GSM876882 3 0.0000 0.991 0.000 0 1.000
#> GSM876883 3 0.0000 0.991 0.000 0 1.000
#> GSM876884 1 0.0000 0.972 1.000 0 0.000
#> GSM876885 3 0.0000 0.991 0.000 0 1.000
#> GSM876857 1 0.0000 0.972 1.000 0 0.000
#> GSM876858 3 0.0000 0.991 0.000 0 1.000
#> GSM876859 1 0.5835 0.474 0.660 0 0.340
#> GSM876860 3 0.0000 0.991 0.000 0 1.000
#> GSM876861 3 0.0000 0.991 0.000 0 1.000
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876887 3 0.0469 0.9368 0.000 0.012 0.988 0.000
#> GSM876888 1 0.1389 0.9280 0.952 0.000 0.048 0.000
#> GSM876889 4 0.3024 0.8909 0.000 0.148 0.000 0.852
#> GSM876890 3 0.3569 0.7208 0.000 0.196 0.804 0.000
#> GSM876891 3 0.1302 0.9075 0.000 0.044 0.956 0.000
#> GSM876862 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876866 3 0.3569 0.7208 0.000 0.196 0.804 0.000
#> GSM876867 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876838 2 0.3569 0.8050 0.000 0.804 0.196 0.000
#> GSM876839 2 0.3569 0.8050 0.000 0.804 0.196 0.000
#> GSM876840 4 0.3569 0.8613 0.000 0.196 0.000 0.804
#> GSM876841 2 0.3569 0.8050 0.000 0.804 0.196 0.000
#> GSM876842 2 0.4522 0.7088 0.000 0.680 0.320 0.000
#> GSM876843 4 0.0000 0.9451 0.000 0.000 0.000 1.000
#> GSM876892 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876893 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876894 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876895 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876896 4 0.0000 0.9451 0.000 0.000 0.000 1.000
#> GSM876897 4 0.0000 0.9451 0.000 0.000 0.000 1.000
#> GSM876868 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 0.9451 0.000 0.000 0.000 1.000
#> GSM876873 4 0.0000 0.9451 0.000 0.000 0.000 1.000
#> GSM876844 2 0.4830 0.6244 0.000 0.608 0.392 0.000
#> GSM876845 2 0.3569 0.8050 0.000 0.804 0.196 0.000
#> GSM876846 4 0.3024 0.8909 0.000 0.148 0.000 0.852
#> GSM876847 2 0.4462 0.7120 0.132 0.804 0.064 0.000
#> GSM876848 4 0.0000 0.9451 0.000 0.000 0.000 1.000
#> GSM876849 4 0.0000 0.9451 0.000 0.000 0.000 1.000
#> GSM876898 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876899 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876900 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876901 3 0.1792 0.8856 0.000 0.068 0.932 0.000
#> GSM876902 4 0.0000 0.9451 0.000 0.000 0.000 1.000
#> GSM876903 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876904 3 0.2053 0.8704 0.072 0.004 0.924 0.000
#> GSM876874 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876875 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876876 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876879 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876880 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876850 2 0.4244 0.6811 0.160 0.804 0.036 0.000
#> GSM876851 2 0.3569 0.8050 0.000 0.804 0.196 0.000
#> GSM876852 2 0.4697 0.6362 0.000 0.644 0.356 0.000
#> GSM876853 2 0.3569 0.8050 0.000 0.804 0.196 0.000
#> GSM876854 4 0.3569 0.8613 0.000 0.196 0.000 0.804
#> GSM876855 2 0.3688 0.6251 0.000 0.792 0.208 0.000
#> GSM876856 2 0.5649 0.0527 0.000 0.620 0.036 0.344
#> GSM876905 3 0.0188 0.9431 0.000 0.004 0.996 0.000
#> GSM876906 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876907 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876908 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876909 3 0.3569 0.7073 0.000 0.196 0.804 0.000
#> GSM876881 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876882 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876883 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876884 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876885 3 0.0000 0.9458 0.000 0.000 1.000 0.000
#> GSM876857 1 0.0000 0.9962 1.000 0.000 0.000 0.000
#> GSM876858 3 0.3610 0.7007 0.000 0.200 0.800 0.000
#> GSM876859 2 0.6483 0.2904 0.392 0.532 0.076 0.000
#> GSM876860 3 0.1792 0.8856 0.000 0.068 0.932 0.000
#> GSM876861 3 0.0000 0.9458 0.000 0.000 1.000 0.000
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM876886 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876887 5 0.0404 0.9461 0.000 0.000 0.012 0.000 0.988
#> GSM876888 1 0.1197 0.9299 0.952 0.000 0.000 0.000 0.048
#> GSM876889 3 0.3774 0.5169 0.000 0.000 0.704 0.296 0.000
#> GSM876890 3 0.2074 0.7244 0.000 0.000 0.896 0.000 0.104
#> GSM876891 5 0.1121 0.9188 0.000 0.000 0.044 0.000 0.956
#> GSM876862 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876866 3 0.3932 0.4995 0.000 0.000 0.672 0.000 0.328
#> GSM876867 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.8306 0.000 1.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.8306 0.000 1.000 0.000 0.000 0.000
#> GSM876840 3 0.0000 0.7611 0.000 0.000 1.000 0.000 0.000
#> GSM876841 2 0.0000 0.8306 0.000 1.000 0.000 0.000 0.000
#> GSM876842 2 0.4114 0.4476 0.000 0.624 0.000 0.000 0.376
#> GSM876843 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM876892 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876893 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876894 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876895 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876896 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM876897 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM876868 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM876873 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM876844 2 0.4182 0.4073 0.000 0.600 0.000 0.000 0.400
#> GSM876845 2 0.0000 0.8306 0.000 1.000 0.000 0.000 0.000
#> GSM876846 3 0.3774 0.5169 0.000 0.000 0.704 0.296 0.000
#> GSM876847 2 0.0000 0.8306 0.000 1.000 0.000 0.000 0.000
#> GSM876848 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM876849 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM876898 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876899 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876900 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876901 5 0.3109 0.7288 0.000 0.200 0.000 0.000 0.800
#> GSM876902 4 0.0000 1.0000 0.000 0.000 0.000 1.000 0.000
#> GSM876903 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876904 5 0.1892 0.8813 0.004 0.080 0.000 0.000 0.916
#> GSM876874 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876875 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876876 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876879 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876880 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.8306 0.000 1.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.8306 0.000 1.000 0.000 0.000 0.000
#> GSM876852 3 0.5988 0.3308 0.000 0.120 0.516 0.000 0.364
#> GSM876853 2 0.0000 0.8306 0.000 1.000 0.000 0.000 0.000
#> GSM876854 3 0.0000 0.7611 0.000 0.000 1.000 0.000 0.000
#> GSM876855 3 0.0000 0.7611 0.000 0.000 1.000 0.000 0.000
#> GSM876856 3 0.0000 0.7611 0.000 0.000 1.000 0.000 0.000
#> GSM876905 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876906 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876907 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876908 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876909 5 0.4171 0.3130 0.000 0.396 0.000 0.000 0.604
#> GSM876881 1 0.2773 0.7994 0.836 0.164 0.000 0.000 0.000
#> GSM876882 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876883 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876884 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876885 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
#> GSM876857 1 0.0000 0.9865 1.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.4291 0.0753 0.000 0.536 0.000 0.000 0.464
#> GSM876859 2 0.0703 0.8115 0.000 0.976 0.000 0.000 0.024
#> GSM876860 5 0.2516 0.8140 0.000 0.140 0.000 0.000 0.860
#> GSM876861 5 0.0000 0.9547 0.000 0.000 0.000 0.000 1.000
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM876886 3 0.2300 0.8464 0.000 0.000 0.856 0.000 0.000 0.144
#> GSM876887 3 0.3570 0.8002 0.000 0.000 0.792 0.000 0.064 0.144
#> GSM876888 1 0.1075 0.9264 0.952 0.000 0.048 0.000 0.000 0.000
#> GSM876889 4 0.1714 0.8901 0.000 0.000 0.000 0.908 0.092 0.000
#> GSM876890 5 0.3680 0.6939 0.000 0.000 0.072 0.000 0.784 0.144
#> GSM876891 3 0.2664 0.7433 0.000 0.000 0.816 0.000 0.184 0.000
#> GSM876862 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876863 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876864 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876865 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876866 5 0.5196 0.4531 0.000 0.000 0.252 0.000 0.604 0.144
#> GSM876867 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876838 2 0.0000 0.8214 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.8214 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876840 5 0.0000 0.8410 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876841 2 0.0000 0.8214 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876842 2 0.3695 0.4270 0.000 0.624 0.376 0.000 0.000 0.000
#> GSM876843 6 0.2300 1.0000 0.000 0.000 0.000 0.144 0.000 0.856
#> GSM876892 3 0.0000 0.8996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876893 3 0.0000 0.8996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876894 3 0.0000 0.8996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876895 3 0.0000 0.8996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876896 4 0.0000 0.9546 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876897 4 0.0000 0.9546 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876868 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876871 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876872 4 0.0000 0.9546 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876873 4 0.0000 0.9546 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876844 2 0.3756 0.3734 0.000 0.600 0.400 0.000 0.000 0.000
#> GSM876845 2 0.0000 0.8214 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876846 4 0.1910 0.8770 0.000 0.000 0.000 0.892 0.108 0.000
#> GSM876847 2 0.0000 0.8214 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876848 6 0.2300 1.0000 0.000 0.000 0.000 0.144 0.000 0.856
#> GSM876849 6 0.2300 1.0000 0.000 0.000 0.000 0.144 0.000 0.856
#> GSM876898 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876899 3 0.0000 0.8996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876900 3 0.0000 0.8996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876901 3 0.2793 0.7138 0.000 0.200 0.800 0.000 0.000 0.000
#> GSM876902 4 0.0000 0.9546 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876903 3 0.0000 0.8996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876904 3 0.1700 0.8480 0.004 0.080 0.916 0.000 0.000 0.000
#> GSM876874 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876875 3 0.2300 0.8464 0.000 0.000 0.856 0.000 0.000 0.144
#> GSM876876 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876877 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876878 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876879 3 0.2300 0.8464 0.000 0.000 0.856 0.000 0.000 0.144
#> GSM876880 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876850 2 0.0000 0.8214 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.8214 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876852 5 0.1204 0.8019 0.000 0.056 0.000 0.000 0.944 0.000
#> GSM876853 2 0.0000 0.8214 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876854 5 0.0000 0.8410 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876855 5 0.0000 0.8410 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876856 5 0.0000 0.8410 0.000 0.000 0.000 0.000 1.000 0.000
#> GSM876905 3 0.0000 0.8996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876906 3 0.0000 0.8996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876907 3 0.0000 0.8996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876908 3 0.0000 0.8996 0.000 0.000 1.000 0.000 0.000 0.000
#> GSM876909 3 0.3747 0.2992 0.000 0.396 0.604 0.000 0.000 0.000
#> GSM876881 1 0.2491 0.7827 0.836 0.164 0.000 0.000 0.000 0.000
#> GSM876882 3 0.2300 0.8464 0.000 0.000 0.856 0.000 0.000 0.144
#> GSM876883 3 0.2300 0.8464 0.000 0.000 0.856 0.000 0.000 0.144
#> GSM876884 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876885 3 0.2300 0.8464 0.000 0.000 0.856 0.000 0.000 0.144
#> GSM876857 1 0.0000 0.9857 1.000 0.000 0.000 0.000 0.000 0.000
#> GSM876858 2 0.3854 0.0828 0.000 0.536 0.464 0.000 0.000 0.000
#> GSM876859 2 0.0632 0.8026 0.000 0.976 0.024 0.000 0.000 0.000
#> GSM876860 3 0.2260 0.7912 0.000 0.140 0.860 0.000 0.000 0.000
#> GSM876861 3 0.0000 0.8996 0.000 0.000 1.000 0.000 0.000 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> ATC:pam 72 0.0319 1.68e-01 2
#> ATC:pam 71 0.1286 3.14e-06 3
#> ATC:pam 70 0.0201 1.32e-11 4
#> ATC:pam 66 0.0478 3.59e-10 5
#> ATC:pam 67 0.0520 4.40e-11 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 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'mclust' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 2.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.982 0.946 0.967 0.4791 0.507 0.507
#> 3 3 0.485 0.758 0.844 0.2827 0.583 0.377
#> 4 4 0.625 0.726 0.810 0.1734 0.685 0.368
#> 5 5 0.739 0.868 0.898 0.0894 0.910 0.679
#> 6 6 0.860 0.780 0.902 0.0434 0.932 0.696
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
#> GSM876886 1 0.1414 0.987 0.980 0.020
#> GSM876887 1 0.1843 0.984 0.972 0.028
#> GSM876888 1 0.1414 0.987 0.980 0.020
#> GSM876889 1 0.1414 0.987 0.980 0.020
#> GSM876890 1 0.1414 0.987 0.980 0.020
#> GSM876891 1 0.1414 0.987 0.980 0.020
#> GSM876862 1 0.0000 0.978 1.000 0.000
#> GSM876863 1 0.1414 0.987 0.980 0.020
#> GSM876864 1 0.0000 0.978 1.000 0.000
#> GSM876865 1 0.1414 0.987 0.980 0.020
#> GSM876866 1 0.1414 0.987 0.980 0.020
#> GSM876867 1 0.0000 0.978 1.000 0.000
#> GSM876838 2 0.0000 0.947 0.000 1.000
#> GSM876839 2 0.0000 0.947 0.000 1.000
#> GSM876840 2 0.0000 0.947 0.000 1.000
#> GSM876841 2 0.0000 0.947 0.000 1.000
#> GSM876842 2 0.0000 0.947 0.000 1.000
#> GSM876843 2 0.0000 0.947 0.000 1.000
#> GSM876892 1 0.1414 0.987 0.980 0.020
#> GSM876893 1 0.0000 0.978 1.000 0.000
#> GSM876894 1 0.1633 0.986 0.976 0.024
#> GSM876895 2 0.5946 0.846 0.144 0.856
#> GSM876896 1 0.1843 0.984 0.972 0.028
#> GSM876897 1 0.1843 0.984 0.972 0.028
#> GSM876868 1 0.0000 0.978 1.000 0.000
#> GSM876869 1 0.0000 0.978 1.000 0.000
#> GSM876870 1 0.0000 0.978 1.000 0.000
#> GSM876871 1 0.1414 0.987 0.980 0.020
#> GSM876872 1 0.1843 0.984 0.972 0.028
#> GSM876873 1 0.1843 0.984 0.972 0.028
#> GSM876844 2 0.0000 0.947 0.000 1.000
#> GSM876845 2 0.0000 0.947 0.000 1.000
#> GSM876846 2 0.0000 0.947 0.000 1.000
#> GSM876847 2 0.0000 0.947 0.000 1.000
#> GSM876848 2 0.0000 0.947 0.000 1.000
#> GSM876849 2 0.0000 0.947 0.000 1.000
#> GSM876898 1 0.1414 0.987 0.980 0.020
#> GSM876899 2 0.9732 0.375 0.404 0.596
#> GSM876900 1 0.1414 0.987 0.980 0.020
#> GSM876901 1 0.0000 0.978 1.000 0.000
#> GSM876902 1 0.1843 0.984 0.972 0.028
#> GSM876903 2 0.3879 0.915 0.076 0.924
#> GSM876904 1 0.0000 0.978 1.000 0.000
#> GSM876874 1 0.1414 0.987 0.980 0.020
#> GSM876875 1 0.1843 0.984 0.972 0.028
#> GSM876876 1 0.1414 0.987 0.980 0.020
#> GSM876877 1 0.1414 0.987 0.980 0.020
#> GSM876878 1 0.1414 0.987 0.980 0.020
#> GSM876879 1 0.1843 0.984 0.972 0.028
#> GSM876880 1 0.0672 0.982 0.992 0.008
#> GSM876850 2 0.0000 0.947 0.000 1.000
#> GSM876851 2 0.0000 0.947 0.000 1.000
#> GSM876852 2 0.0000 0.947 0.000 1.000
#> GSM876853 2 0.0000 0.947 0.000 1.000
#> GSM876854 2 0.0000 0.947 0.000 1.000
#> GSM876855 2 0.0000 0.947 0.000 1.000
#> GSM876856 2 0.0000 0.947 0.000 1.000
#> GSM876905 1 0.0000 0.978 1.000 0.000
#> GSM876906 1 0.6973 0.774 0.812 0.188
#> GSM876907 2 0.4298 0.905 0.088 0.912
#> GSM876908 2 0.9552 0.454 0.376 0.624
#> GSM876909 2 0.3584 0.921 0.068 0.932
#> GSM876881 2 0.3584 0.921 0.068 0.932
#> GSM876882 1 0.1843 0.984 0.972 0.028
#> GSM876883 1 0.1843 0.984 0.972 0.028
#> GSM876884 1 0.1414 0.987 0.980 0.020
#> GSM876885 1 0.1843 0.984 0.972 0.028
#> GSM876857 1 0.0000 0.978 1.000 0.000
#> GSM876858 2 0.3584 0.921 0.068 0.932
#> GSM876859 2 0.3584 0.921 0.068 0.932
#> GSM876860 2 0.3584 0.921 0.068 0.932
#> GSM876861 2 0.3584 0.921 0.068 0.932
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 3 0.5016 0.734 0.240 0.000 0.760
#> GSM876887 3 0.5016 0.734 0.240 0.000 0.760
#> GSM876888 1 0.0000 0.888 1.000 0.000 0.000
#> GSM876889 3 0.4121 0.760 0.168 0.000 0.832
#> GSM876890 3 0.2711 0.768 0.088 0.000 0.912
#> GSM876891 3 0.2165 0.762 0.064 0.000 0.936
#> GSM876862 1 0.1031 0.887 0.976 0.000 0.024
#> GSM876863 1 0.0000 0.888 1.000 0.000 0.000
#> GSM876864 1 0.0747 0.888 0.984 0.000 0.016
#> GSM876865 1 0.0000 0.888 1.000 0.000 0.000
#> GSM876866 3 0.2066 0.763 0.060 0.000 0.940
#> GSM876867 1 0.2959 0.859 0.900 0.000 0.100
#> GSM876838 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876839 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876840 3 0.6307 0.394 0.000 0.488 0.512
#> GSM876841 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876842 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876843 3 0.4346 0.711 0.000 0.184 0.816
#> GSM876892 3 0.2448 0.762 0.076 0.000 0.924
#> GSM876893 3 0.5591 0.528 0.304 0.000 0.696
#> GSM876894 3 0.3030 0.762 0.092 0.004 0.904
#> GSM876895 3 0.2599 0.771 0.016 0.052 0.932
#> GSM876896 3 0.4235 0.742 0.176 0.000 0.824
#> GSM876897 3 0.4235 0.742 0.176 0.000 0.824
#> GSM876868 1 0.1860 0.880 0.948 0.000 0.052
#> GSM876869 1 0.3038 0.857 0.896 0.000 0.104
#> GSM876870 1 0.2878 0.862 0.904 0.000 0.096
#> GSM876871 1 0.3752 0.831 0.856 0.000 0.144
#> GSM876872 3 0.4235 0.742 0.176 0.000 0.824
#> GSM876873 3 0.4235 0.742 0.176 0.000 0.824
#> GSM876844 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876845 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876846 3 0.4887 0.704 0.000 0.228 0.772
#> GSM876847 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876848 3 0.4346 0.711 0.000 0.184 0.816
#> GSM876849 3 0.4346 0.711 0.000 0.184 0.816
#> GSM876898 1 0.4062 0.807 0.836 0.000 0.164
#> GSM876899 3 0.2743 0.771 0.020 0.052 0.928
#> GSM876900 3 0.5216 0.586 0.260 0.000 0.740
#> GSM876901 1 0.6291 0.246 0.532 0.000 0.468
#> GSM876902 3 0.4235 0.742 0.176 0.000 0.824
#> GSM876903 3 0.2599 0.771 0.016 0.052 0.932
#> GSM876904 1 0.5968 0.540 0.636 0.000 0.364
#> GSM876874 1 0.0000 0.888 1.000 0.000 0.000
#> GSM876875 3 0.4931 0.735 0.232 0.000 0.768
#> GSM876876 1 0.0000 0.888 1.000 0.000 0.000
#> GSM876877 1 0.0000 0.888 1.000 0.000 0.000
#> GSM876878 1 0.0000 0.888 1.000 0.000 0.000
#> GSM876879 3 0.4931 0.735 0.232 0.000 0.768
#> GSM876880 1 0.0000 0.888 1.000 0.000 0.000
#> GSM876850 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876851 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876852 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876853 2 0.0000 1.000 0.000 1.000 0.000
#> GSM876854 3 0.6307 0.394 0.000 0.488 0.512
#> GSM876855 3 0.6307 0.394 0.000 0.488 0.512
#> GSM876856 3 0.6307 0.394 0.000 0.488 0.512
#> GSM876905 3 0.6204 0.241 0.424 0.000 0.576
#> GSM876906 3 0.2681 0.768 0.040 0.028 0.932
#> GSM876907 3 0.2599 0.771 0.016 0.052 0.932
#> GSM876908 3 0.2599 0.771 0.016 0.052 0.932
#> GSM876909 3 0.6113 0.594 0.012 0.300 0.688
#> GSM876881 3 0.5988 0.590 0.008 0.304 0.688
#> GSM876882 3 0.4931 0.735 0.232 0.000 0.768
#> GSM876883 3 0.4931 0.735 0.232 0.000 0.768
#> GSM876884 1 0.0000 0.888 1.000 0.000 0.000
#> GSM876885 3 0.4931 0.735 0.232 0.000 0.768
#> GSM876857 1 0.5760 0.572 0.672 0.000 0.328
#> GSM876858 3 0.5988 0.590 0.008 0.304 0.688
#> GSM876859 3 0.5988 0.590 0.008 0.304 0.688
#> GSM876860 3 0.5988 0.590 0.008 0.304 0.688
#> GSM876861 3 0.5988 0.590 0.008 0.304 0.688
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 1 0.1584 0.8423 0.952 0.000 0.012 0.036
#> GSM876887 1 0.6404 0.2119 0.608 0.000 0.296 0.096
#> GSM876888 1 0.0469 0.8542 0.988 0.000 0.000 0.012
#> GSM876889 3 0.7191 0.2014 0.148 0.000 0.500 0.352
#> GSM876890 3 0.6808 0.2897 0.120 0.000 0.560 0.320
#> GSM876891 3 0.3074 0.5910 0.152 0.000 0.848 0.000
#> GSM876862 1 0.0336 0.8591 0.992 0.000 0.008 0.000
#> GSM876863 1 0.0469 0.8542 0.988 0.000 0.000 0.012
#> GSM876864 1 0.0336 0.8591 0.992 0.000 0.008 0.000
#> GSM876865 1 0.0336 0.8555 0.992 0.000 0.000 0.008
#> GSM876866 3 0.5716 -0.0293 0.420 0.000 0.552 0.028
#> GSM876867 1 0.0336 0.8591 0.992 0.000 0.008 0.000
#> GSM876838 2 0.1211 0.8788 0.000 0.960 0.040 0.000
#> GSM876839 2 0.1211 0.8788 0.000 0.960 0.040 0.000
#> GSM876840 2 0.3400 0.7901 0.000 0.820 0.180 0.000
#> GSM876841 2 0.1211 0.8788 0.000 0.960 0.040 0.000
#> GSM876842 2 0.0000 0.8808 0.000 1.000 0.000 0.000
#> GSM876843 2 0.6148 0.6762 0.000 0.636 0.280 0.084
#> GSM876892 1 0.4331 0.6962 0.712 0.000 0.288 0.000
#> GSM876893 1 0.4331 0.6962 0.712 0.000 0.288 0.000
#> GSM876894 3 0.5339 0.7489 0.100 0.000 0.744 0.156
#> GSM876895 3 0.5427 0.7507 0.100 0.000 0.736 0.164
#> GSM876896 4 0.0336 0.6541 0.000 0.000 0.008 0.992
#> GSM876897 4 0.0336 0.6541 0.000 0.000 0.008 0.992
#> GSM876868 1 0.0336 0.8591 0.992 0.000 0.008 0.000
#> GSM876869 1 0.0336 0.8591 0.992 0.000 0.008 0.000
#> GSM876870 1 0.0336 0.8591 0.992 0.000 0.008 0.000
#> GSM876871 1 0.2589 0.8179 0.884 0.000 0.116 0.000
#> GSM876872 4 0.0817 0.6600 0.024 0.000 0.000 0.976
#> GSM876873 4 0.0817 0.6600 0.024 0.000 0.000 0.976
#> GSM876844 2 0.0000 0.8808 0.000 1.000 0.000 0.000
#> GSM876845 2 0.1211 0.8788 0.000 0.960 0.040 0.000
#> GSM876846 2 0.4594 0.7341 0.000 0.712 0.280 0.008
#> GSM876847 2 0.1211 0.8788 0.000 0.960 0.040 0.000
#> GSM876848 2 0.6422 0.6568 0.000 0.616 0.280 0.104
#> GSM876849 2 0.6422 0.6568 0.000 0.616 0.280 0.104
#> GSM876898 1 0.4277 0.7039 0.720 0.000 0.280 0.000
#> GSM876899 3 0.5470 0.7486 0.100 0.000 0.732 0.168
#> GSM876900 1 0.4331 0.6962 0.712 0.000 0.288 0.000
#> GSM876901 1 0.4331 0.6962 0.712 0.000 0.288 0.000
#> GSM876902 4 0.0336 0.6541 0.000 0.000 0.008 0.992
#> GSM876903 3 0.5427 0.7507 0.100 0.000 0.736 0.164
#> GSM876904 1 0.4331 0.6962 0.712 0.000 0.288 0.000
#> GSM876874 1 0.0524 0.8568 0.988 0.000 0.004 0.008
#> GSM876875 4 0.7847 0.5081 0.276 0.000 0.328 0.396
#> GSM876876 1 0.0469 0.8542 0.988 0.000 0.000 0.012
#> GSM876877 1 0.0927 0.8567 0.976 0.000 0.016 0.008
#> GSM876878 1 0.0469 0.8542 0.988 0.000 0.000 0.012
#> GSM876879 4 0.7841 0.5090 0.272 0.000 0.332 0.396
#> GSM876880 1 0.0524 0.8571 0.988 0.000 0.004 0.008
#> GSM876850 2 0.1211 0.8788 0.000 0.960 0.040 0.000
#> GSM876851 2 0.1211 0.8788 0.000 0.960 0.040 0.000
#> GSM876852 2 0.0000 0.8808 0.000 1.000 0.000 0.000
#> GSM876853 2 0.0336 0.8812 0.000 0.992 0.008 0.000
#> GSM876854 2 0.3400 0.7901 0.000 0.820 0.180 0.000
#> GSM876855 2 0.0000 0.8808 0.000 1.000 0.000 0.000
#> GSM876856 2 0.0000 0.8808 0.000 1.000 0.000 0.000
#> GSM876905 1 0.4331 0.6962 0.712 0.000 0.288 0.000
#> GSM876906 3 0.2345 0.6367 0.100 0.000 0.900 0.000
#> GSM876907 3 0.5427 0.7507 0.100 0.000 0.736 0.164
#> GSM876908 3 0.5427 0.7507 0.100 0.000 0.736 0.164
#> GSM876909 3 0.5913 0.7375 0.060 0.040 0.736 0.164
#> GSM876881 3 0.5913 0.7375 0.060 0.040 0.736 0.164
#> GSM876882 4 0.7830 0.5113 0.268 0.000 0.332 0.400
#> GSM876883 4 0.6717 0.4716 0.108 0.000 0.332 0.560
#> GSM876884 1 0.0336 0.8555 0.992 0.000 0.000 0.008
#> GSM876885 4 0.6717 0.4716 0.108 0.000 0.332 0.560
#> GSM876857 1 0.3400 0.7788 0.820 0.000 0.180 0.000
#> GSM876858 3 0.5788 0.6929 0.020 0.080 0.736 0.164
#> GSM876859 3 0.5548 0.6668 0.004 0.096 0.736 0.164
#> GSM876860 3 0.5628 0.6742 0.008 0.092 0.736 0.164
#> GSM876861 3 0.5922 0.7226 0.044 0.056 0.736 0.164
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM876886 1 0.3533 0.8389 0.840 0.000 0.108 0.012 0.040
#> GSM876887 1 0.3338 0.8053 0.852 0.000 0.076 0.068 0.004
#> GSM876888 1 0.4720 0.8708 0.736 0.000 0.124 0.000 0.140
#> GSM876889 5 0.4634 0.7638 0.120 0.000 0.136 0.000 0.744
#> GSM876890 5 0.4519 0.7688 0.100 0.000 0.148 0.000 0.752
#> GSM876891 5 0.3336 0.7340 0.000 0.000 0.228 0.000 0.772
#> GSM876862 1 0.3612 0.7825 0.732 0.000 0.268 0.000 0.000
#> GSM876863 1 0.4720 0.8708 0.736 0.000 0.124 0.000 0.140
#> GSM876864 1 0.3612 0.7825 0.732 0.000 0.268 0.000 0.000
#> GSM876865 1 0.4720 0.8708 0.736 0.000 0.124 0.000 0.140
#> GSM876866 5 0.4637 0.7586 0.100 0.000 0.160 0.000 0.740
#> GSM876867 3 0.0290 0.9438 0.008 0.000 0.992 0.000 0.000
#> GSM876838 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000
#> GSM876840 2 0.0290 0.9464 0.000 0.992 0.008 0.000 0.000
#> GSM876841 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000
#> GSM876843 2 0.5031 0.7489 0.148 0.724 0.008 0.120 0.000
#> GSM876892 3 0.0162 0.9469 0.000 0.000 0.996 0.000 0.004
#> GSM876893 3 0.0162 0.9469 0.000 0.000 0.996 0.000 0.004
#> GSM876894 5 0.1282 0.8779 0.000 0.000 0.044 0.004 0.952
#> GSM876895 5 0.0000 0.8987 0.000 0.000 0.000 0.000 1.000
#> GSM876896 4 0.0162 0.9615 0.004 0.000 0.000 0.996 0.000
#> GSM876897 4 0.0162 0.9615 0.004 0.000 0.000 0.996 0.000
#> GSM876868 1 0.3612 0.7825 0.732 0.000 0.268 0.000 0.000
#> GSM876869 3 0.0404 0.9404 0.012 0.000 0.988 0.000 0.000
#> GSM876870 3 0.4235 -0.0572 0.424 0.000 0.576 0.000 0.000
#> GSM876871 3 0.0290 0.9438 0.008 0.000 0.992 0.000 0.000
#> GSM876872 4 0.0162 0.9615 0.004 0.000 0.000 0.996 0.000
#> GSM876873 4 0.0162 0.9615 0.004 0.000 0.000 0.996 0.000
#> GSM876844 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000
#> GSM876846 2 0.3001 0.8538 0.144 0.844 0.008 0.004 0.000
#> GSM876847 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000
#> GSM876848 2 0.5137 0.7454 0.148 0.720 0.012 0.120 0.000
#> GSM876849 2 0.5137 0.7454 0.148 0.720 0.012 0.120 0.000
#> GSM876898 3 0.0290 0.9437 0.000 0.000 0.992 0.000 0.008
#> GSM876899 5 0.3636 0.5885 0.000 0.000 0.000 0.272 0.728
#> GSM876900 3 0.0162 0.9469 0.000 0.000 0.996 0.000 0.004
#> GSM876901 3 0.0162 0.9469 0.000 0.000 0.996 0.000 0.004
#> GSM876902 4 0.0162 0.9615 0.004 0.000 0.000 0.996 0.000
#> GSM876903 5 0.0000 0.8987 0.000 0.000 0.000 0.000 1.000
#> GSM876904 3 0.0162 0.9469 0.000 0.000 0.996 0.000 0.004
#> GSM876874 1 0.4720 0.8708 0.736 0.000 0.124 0.000 0.140
#> GSM876875 1 0.2648 0.7194 0.848 0.000 0.000 0.152 0.000
#> GSM876876 1 0.4720 0.8708 0.736 0.000 0.124 0.000 0.140
#> GSM876877 1 0.4720 0.8708 0.736 0.000 0.124 0.000 0.140
#> GSM876878 1 0.4720 0.8708 0.736 0.000 0.124 0.000 0.140
#> GSM876879 1 0.2648 0.7194 0.848 0.000 0.000 0.152 0.000
#> GSM876880 1 0.3988 0.7983 0.732 0.000 0.252 0.000 0.016
#> GSM876850 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000
#> GSM876852 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000
#> GSM876853 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000
#> GSM876854 2 0.0290 0.9464 0.000 0.992 0.008 0.000 0.000
#> GSM876855 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000
#> GSM876856 2 0.0000 0.9501 0.000 1.000 0.000 0.000 0.000
#> GSM876905 3 0.0162 0.9469 0.000 0.000 0.996 0.000 0.004
#> GSM876906 5 0.2280 0.8237 0.000 0.000 0.120 0.000 0.880
#> GSM876907 5 0.0000 0.8987 0.000 0.000 0.000 0.000 1.000
#> GSM876908 5 0.0162 0.8982 0.000 0.000 0.004 0.000 0.996
#> GSM876909 5 0.0703 0.8908 0.000 0.000 0.024 0.000 0.976
#> GSM876881 5 0.0000 0.8987 0.000 0.000 0.000 0.000 1.000
#> GSM876882 1 0.2648 0.7194 0.848 0.000 0.000 0.152 0.000
#> GSM876883 4 0.2329 0.9011 0.124 0.000 0.000 0.876 0.000
#> GSM876884 1 0.4720 0.8708 0.736 0.000 0.124 0.000 0.140
#> GSM876885 4 0.2329 0.9011 0.124 0.000 0.000 0.876 0.000
#> GSM876857 3 0.0162 0.9453 0.004 0.000 0.996 0.000 0.000
#> GSM876858 5 0.0162 0.8975 0.000 0.004 0.000 0.000 0.996
#> GSM876859 5 0.0000 0.8987 0.000 0.000 0.000 0.000 1.000
#> GSM876860 5 0.0162 0.8975 0.000 0.004 0.000 0.000 0.996
#> GSM876861 5 0.0162 0.8975 0.000 0.004 0.000 0.000 0.996
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM876886 1 0.0551 0.870 0.984 0.000 0.008 0.004 0.000 0.004
#> GSM876887 1 0.1606 0.840 0.932 0.000 0.008 0.004 0.000 0.056
#> GSM876888 1 0.0458 0.886 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM876889 5 0.5000 0.571 0.012 0.000 0.296 0.008 0.632 0.052
#> GSM876890 5 0.3967 0.599 0.008 0.000 0.316 0.008 0.668 0.000
#> GSM876891 5 0.3615 0.634 0.000 0.000 0.292 0.008 0.700 0.000
#> GSM876862 1 0.3109 0.724 0.772 0.000 0.224 0.000 0.000 0.004
#> GSM876863 1 0.0458 0.886 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM876864 1 0.3109 0.725 0.772 0.000 0.224 0.000 0.000 0.004
#> GSM876865 1 0.0458 0.886 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM876866 3 0.0984 0.807 0.012 0.000 0.968 0.008 0.012 0.000
#> GSM876867 3 0.3565 0.562 0.304 0.000 0.692 0.000 0.000 0.004
#> GSM876838 2 0.0000 0.930 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876839 2 0.0000 0.930 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876840 2 0.3847 0.203 0.000 0.544 0.000 0.456 0.000 0.000
#> GSM876841 2 0.0000 0.930 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876842 2 0.0000 0.930 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876843 4 0.0000 0.972 0.000 0.000 0.000 1.000 0.000 0.000
#> GSM876892 3 0.0436 0.830 0.004 0.000 0.988 0.004 0.004 0.000
#> GSM876893 3 0.0291 0.832 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM876894 5 0.0806 0.914 0.020 0.000 0.008 0.000 0.972 0.000
#> GSM876895 5 0.0520 0.918 0.008 0.000 0.008 0.000 0.984 0.000
#> GSM876896 6 0.1364 0.681 0.000 0.000 0.004 0.048 0.004 0.944
#> GSM876897 6 0.1364 0.681 0.000 0.000 0.004 0.048 0.004 0.944
#> GSM876868 1 0.3189 0.709 0.760 0.000 0.236 0.000 0.000 0.004
#> GSM876869 3 0.3872 0.382 0.392 0.000 0.604 0.000 0.000 0.004
#> GSM876870 1 0.3668 0.543 0.668 0.000 0.328 0.000 0.000 0.004
#> GSM876871 3 0.3354 0.650 0.240 0.000 0.752 0.000 0.004 0.004
#> GSM876872 6 0.1219 0.683 0.004 0.000 0.000 0.048 0.000 0.948
#> GSM876873 6 0.1219 0.683 0.004 0.000 0.000 0.048 0.000 0.948
#> GSM876844 2 0.0000 0.930 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876845 2 0.0000 0.930 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876846 4 0.1075 0.927 0.000 0.048 0.000 0.952 0.000 0.000
#> GSM876847 2 0.0000 0.930 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876848 4 0.0146 0.972 0.000 0.000 0.000 0.996 0.000 0.004
#> GSM876849 4 0.0260 0.971 0.000 0.000 0.000 0.992 0.000 0.008
#> GSM876898 3 0.2581 0.773 0.128 0.000 0.856 0.000 0.016 0.000
#> GSM876899 5 0.0806 0.914 0.020 0.000 0.008 0.000 0.972 0.000
#> GSM876900 3 0.0291 0.832 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM876901 3 0.0260 0.831 0.008 0.000 0.992 0.000 0.000 0.000
#> GSM876902 6 0.4226 0.458 0.000 0.000 0.008 0.052 0.216 0.724
#> GSM876903 5 0.0260 0.917 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM876904 3 0.0291 0.832 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM876874 1 0.0458 0.886 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM876875 6 0.4326 0.153 0.492 0.000 0.008 0.000 0.008 0.492
#> GSM876876 1 0.0458 0.886 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM876877 1 0.0458 0.886 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM876878 1 0.0458 0.886 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM876879 6 0.4326 0.153 0.492 0.000 0.008 0.000 0.008 0.492
#> GSM876880 1 0.2100 0.830 0.884 0.000 0.112 0.000 0.000 0.004
#> GSM876850 2 0.0000 0.930 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876851 2 0.0000 0.930 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876852 2 0.0000 0.930 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876853 2 0.0000 0.930 0.000 1.000 0.000 0.000 0.000 0.000
#> GSM876854 2 0.3843 0.215 0.000 0.548 0.000 0.452 0.000 0.000
#> GSM876855 2 0.0146 0.927 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM876856 2 0.0146 0.927 0.000 0.996 0.000 0.004 0.000 0.000
#> GSM876905 3 0.0291 0.832 0.004 0.000 0.992 0.000 0.004 0.000
#> GSM876906 5 0.0622 0.917 0.008 0.000 0.012 0.000 0.980 0.000
#> GSM876907 5 0.0520 0.918 0.008 0.000 0.008 0.000 0.984 0.000
#> GSM876908 5 0.0622 0.917 0.012 0.000 0.008 0.000 0.980 0.000
#> GSM876909 5 0.0520 0.916 0.008 0.000 0.008 0.000 0.984 0.000
#> GSM876881 5 0.0260 0.917 0.008 0.000 0.000 0.000 0.992 0.000
#> GSM876882 6 0.4326 0.153 0.492 0.000 0.008 0.000 0.008 0.492
#> GSM876883 6 0.1065 0.678 0.020 0.000 0.008 0.000 0.008 0.964
#> GSM876884 1 0.0458 0.886 0.984 0.000 0.000 0.000 0.016 0.000
#> GSM876885 6 0.1065 0.678 0.020 0.000 0.008 0.000 0.008 0.964
#> GSM876857 3 0.3521 0.612 0.268 0.000 0.724 0.000 0.004 0.004
#> GSM876858 5 0.0260 0.915 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM876859 5 0.0260 0.915 0.000 0.008 0.000 0.000 0.992 0.000
#> GSM876860 5 0.0363 0.913 0.000 0.012 0.000 0.000 0.988 0.000
#> GSM876861 5 0.0291 0.917 0.004 0.004 0.000 0.000 0.992 0.000
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> ATC:mclust 70 0.81917 3.13e-11 2
#> ATC:mclust 66 0.12089 1.85e-09 3
#> ATC:mclust 66 0.00108 5.09e-11 4
#> ATC:mclust 71 0.00340 8.72e-13 5
#> ATC:mclust 65 0.00221 7.83e-11 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 72 columns.
#> Top rows (1000, 2000, 3000, 4000, 5000) are extracted by 'ATC' method.
#> Subgroups are detected by 'NMF' method.
#> Performed in total 1250 partitions by row resampling.
#> Best k for subgroups seems to be 3.
#>
#> Following methods can be applied to this 'ConsensusPartition' object:
#> [1] "cola_report" "collect_classes" "collect_plots"
#> [4] "collect_stats" "colnames" "compare_signatures"
#> [7] "consensus_heatmap" "dimension_reduction" "functional_enrichment"
#> [10] "get_anno_col" "get_anno" "get_classes"
#> [13] "get_consensus" "get_matrix" "get_membership"
#> [16] "get_param" "get_signatures" "get_stats"
#> [19] "is_best_k" "is_stable_k" "membership_heatmap"
#> [22] "ncol" "nrow" "plot_ecdf"
#> [25] "rownames" "select_partition_number" "show"
#> [28] "suggest_best_k" "test_to_known_factors"
collect_plots() function collects all the plots made from res for all k (number of partitions)
into one single page to provide an easy and fast comparison between different k.
collect_plots(res)
The plots are:
k and the heatmap of
predicted classes for each k.k.k.k.All the plots in panels can be made by individual functions and they are plotted later in this section.
select_partition_number() produces several plots showing different
statistics for choosing “optimized” k. There are following statistics:
k;k, the area increased is defined as \(A_k - A_{k-1}\).The detailed explanations of these statistics can be found in the cola vignette.
Generally speaking, lower PAC score, higher mean silhouette score or higher
concordance corresponds to better partition. Rand index and Jaccard index
measure how similar the current partition is compared to partition with k-1.
If they are too similar, we won't accept k is better than k-1.
select_partition_number(res)
The numeric values for all these statistics can be obtained by get_stats().
get_stats(res)
#> k 1-PAC mean_silhouette concordance area_increased Rand Jaccard
#> 2 2 0.914 0.931 0.971 0.4489 0.559 0.559
#> 3 3 0.931 0.913 0.964 0.4736 0.766 0.587
#> 4 4 0.628 0.679 0.823 0.1280 0.865 0.625
#> 5 5 0.698 0.675 0.819 0.0642 0.869 0.547
#> 6 6 0.697 0.610 0.737 0.0361 0.978 0.899
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
#> GSM876886 2 0.0000 0.966 0.000 1.000
#> GSM876887 2 0.0000 0.966 0.000 1.000
#> GSM876888 1 0.1414 0.963 0.980 0.020
#> GSM876889 2 0.0000 0.966 0.000 1.000
#> GSM876890 2 0.0000 0.966 0.000 1.000
#> GSM876891 2 0.0000 0.966 0.000 1.000
#> GSM876862 1 0.0000 0.975 1.000 0.000
#> GSM876863 1 0.2236 0.951 0.964 0.036
#> GSM876864 1 0.0000 0.975 1.000 0.000
#> GSM876865 1 0.0000 0.975 1.000 0.000
#> GSM876866 2 0.0000 0.966 0.000 1.000
#> GSM876867 1 0.0000 0.975 1.000 0.000
#> GSM876838 2 0.0000 0.966 0.000 1.000
#> GSM876839 2 0.0000 0.966 0.000 1.000
#> GSM876840 2 0.0000 0.966 0.000 1.000
#> GSM876841 2 0.0000 0.966 0.000 1.000
#> GSM876842 2 0.0000 0.966 0.000 1.000
#> GSM876843 2 0.0000 0.966 0.000 1.000
#> GSM876892 2 0.0000 0.966 0.000 1.000
#> GSM876893 2 0.9393 0.464 0.356 0.644
#> GSM876894 2 0.0000 0.966 0.000 1.000
#> GSM876895 2 0.0000 0.966 0.000 1.000
#> GSM876896 2 0.0000 0.966 0.000 1.000
#> GSM876897 2 0.0000 0.966 0.000 1.000
#> GSM876868 1 0.0000 0.975 1.000 0.000
#> GSM876869 1 0.0000 0.975 1.000 0.000
#> GSM876870 1 0.0000 0.975 1.000 0.000
#> GSM876871 1 0.0000 0.975 1.000 0.000
#> GSM876872 2 0.0000 0.966 0.000 1.000
#> GSM876873 2 0.0000 0.966 0.000 1.000
#> GSM876844 2 0.0000 0.966 0.000 1.000
#> GSM876845 2 0.0000 0.966 0.000 1.000
#> GSM876846 2 0.0000 0.966 0.000 1.000
#> GSM876847 2 0.5737 0.831 0.136 0.864
#> GSM876848 2 0.0000 0.966 0.000 1.000
#> GSM876849 2 0.0000 0.966 0.000 1.000
#> GSM876898 1 0.0000 0.975 1.000 0.000
#> GSM876899 2 0.0000 0.966 0.000 1.000
#> GSM876900 2 0.1184 0.953 0.016 0.984
#> GSM876901 1 0.3431 0.925 0.936 0.064
#> GSM876902 2 0.0000 0.966 0.000 1.000
#> GSM876903 2 0.0000 0.966 0.000 1.000
#> GSM876904 1 0.1414 0.963 0.980 0.020
#> GSM876874 1 0.0000 0.975 1.000 0.000
#> GSM876875 2 0.7376 0.735 0.208 0.792
#> GSM876876 1 0.0000 0.975 1.000 0.000
#> GSM876877 1 0.0000 0.975 1.000 0.000
#> GSM876878 1 0.0000 0.975 1.000 0.000
#> GSM876879 2 0.3584 0.905 0.068 0.932
#> GSM876880 1 0.0000 0.975 1.000 0.000
#> GSM876850 2 0.9427 0.455 0.360 0.640
#> GSM876851 2 0.0000 0.966 0.000 1.000
#> GSM876852 2 0.0000 0.966 0.000 1.000
#> GSM876853 2 0.0000 0.966 0.000 1.000
#> GSM876854 2 0.0000 0.966 0.000 1.000
#> GSM876855 2 0.0000 0.966 0.000 1.000
#> GSM876856 2 0.0000 0.966 0.000 1.000
#> GSM876905 1 0.5059 0.872 0.888 0.112
#> GSM876906 2 0.0000 0.966 0.000 1.000
#> GSM876907 2 0.0376 0.963 0.004 0.996
#> GSM876908 2 0.0000 0.966 0.000 1.000
#> GSM876909 2 0.9850 0.272 0.428 0.572
#> GSM876881 1 0.0000 0.975 1.000 0.000
#> GSM876882 2 0.0000 0.966 0.000 1.000
#> GSM876883 2 0.0000 0.966 0.000 1.000
#> GSM876884 1 0.0000 0.975 1.000 0.000
#> GSM876885 2 0.0000 0.966 0.000 1.000
#> GSM876857 1 0.0000 0.975 1.000 0.000
#> GSM876858 2 0.0376 0.963 0.004 0.996
#> GSM876859 1 0.8386 0.627 0.732 0.268
#> GSM876860 2 0.0000 0.966 0.000 1.000
#> GSM876861 2 0.0000 0.966 0.000 1.000
cbind(get_classes(res, k = 3), get_membership(res, k = 3))
#> class entropy silhouette p1 p2 p3
#> GSM876886 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876887 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876888 1 0.4605 0.736 0.796 0.000 0.204
#> GSM876889 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876890 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876891 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876862 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876863 1 0.4702 0.723 0.788 0.000 0.212
#> GSM876864 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876865 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876866 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876867 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876838 2 0.0000 0.972 0.000 1.000 0.000
#> GSM876839 2 0.0000 0.972 0.000 1.000 0.000
#> GSM876840 3 0.6225 0.245 0.000 0.432 0.568
#> GSM876841 2 0.0000 0.972 0.000 1.000 0.000
#> GSM876842 2 0.0000 0.972 0.000 1.000 0.000
#> GSM876843 3 0.1031 0.944 0.000 0.024 0.976
#> GSM876892 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876893 3 0.5733 0.520 0.324 0.000 0.676
#> GSM876894 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876895 3 0.0747 0.950 0.000 0.016 0.984
#> GSM876896 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876897 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876868 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876869 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876870 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876871 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876872 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876873 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876844 2 0.0000 0.972 0.000 1.000 0.000
#> GSM876845 2 0.0000 0.972 0.000 1.000 0.000
#> GSM876846 3 0.4452 0.754 0.000 0.192 0.808
#> GSM876847 2 0.0000 0.972 0.000 1.000 0.000
#> GSM876848 3 0.0424 0.954 0.000 0.008 0.992
#> GSM876849 3 0.0424 0.954 0.000 0.008 0.992
#> GSM876898 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876899 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876900 3 0.1163 0.941 0.028 0.000 0.972
#> GSM876901 1 0.0424 0.950 0.992 0.008 0.000
#> GSM876902 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876903 3 0.0892 0.947 0.000 0.020 0.980
#> GSM876904 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876874 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876875 3 0.2261 0.906 0.068 0.000 0.932
#> GSM876876 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876877 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876878 1 0.0592 0.947 0.988 0.000 0.012
#> GSM876879 3 0.0747 0.949 0.016 0.000 0.984
#> GSM876880 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876850 2 0.0000 0.972 0.000 1.000 0.000
#> GSM876851 2 0.0000 0.972 0.000 1.000 0.000
#> GSM876852 2 0.0000 0.972 0.000 1.000 0.000
#> GSM876853 2 0.0000 0.972 0.000 1.000 0.000
#> GSM876854 2 0.1643 0.932 0.000 0.956 0.044
#> GSM876855 2 0.0237 0.969 0.000 0.996 0.004
#> GSM876856 2 0.1163 0.948 0.000 0.972 0.028
#> GSM876905 1 0.0592 0.947 0.988 0.000 0.012
#> GSM876906 3 0.0592 0.952 0.000 0.012 0.988
#> GSM876907 3 0.3669 0.890 0.064 0.040 0.896
#> GSM876908 3 0.0892 0.947 0.020 0.000 0.980
#> GSM876909 2 0.0000 0.972 0.000 1.000 0.000
#> GSM876881 1 0.6180 0.270 0.584 0.416 0.000
#> GSM876882 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876883 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876884 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876885 3 0.0000 0.957 0.000 0.000 1.000
#> GSM876857 1 0.0000 0.955 1.000 0.000 0.000
#> GSM876858 2 0.0000 0.972 0.000 1.000 0.000
#> GSM876859 2 0.0000 0.972 0.000 1.000 0.000
#> GSM876860 2 0.0000 0.972 0.000 1.000 0.000
#> GSM876861 2 0.6008 0.379 0.000 0.628 0.372
cbind(get_classes(res, k = 4), get_membership(res, k = 4))
#> class entropy silhouette p1 p2 p3 p4
#> GSM876886 4 0.5755 0.1057 0.028 0.000 0.444 0.528
#> GSM876887 4 0.4933 0.2001 0.000 0.000 0.432 0.568
#> GSM876888 1 0.5070 0.4634 0.580 0.000 0.416 0.004
#> GSM876889 4 0.3266 0.6678 0.000 0.000 0.168 0.832
#> GSM876890 4 0.4331 0.5248 0.000 0.000 0.288 0.712
#> GSM876891 4 0.4989 -0.0407 0.000 0.000 0.472 0.528
#> GSM876862 1 0.0000 0.8672 1.000 0.000 0.000 0.000
#> GSM876863 1 0.2999 0.7841 0.864 0.000 0.004 0.132
#> GSM876864 1 0.0000 0.8672 1.000 0.000 0.000 0.000
#> GSM876865 1 0.0188 0.8663 0.996 0.000 0.000 0.004
#> GSM876866 4 0.1792 0.6891 0.000 0.000 0.068 0.932
#> GSM876867 1 0.0000 0.8672 1.000 0.000 0.000 0.000
#> GSM876838 2 0.0188 0.8941 0.000 0.996 0.000 0.004
#> GSM876839 2 0.0524 0.8944 0.000 0.988 0.008 0.004
#> GSM876840 4 0.4464 0.5141 0.000 0.208 0.024 0.768
#> GSM876841 2 0.0336 0.8937 0.000 0.992 0.008 0.000
#> GSM876842 2 0.0336 0.8939 0.000 0.992 0.000 0.008
#> GSM876843 4 0.1022 0.6801 0.000 0.000 0.032 0.968
#> GSM876892 4 0.5427 0.1384 0.016 0.000 0.416 0.568
#> GSM876893 3 0.6637 0.5478 0.132 0.000 0.608 0.260
#> GSM876894 3 0.3668 0.7324 0.004 0.000 0.808 0.188
#> GSM876895 3 0.4375 0.7268 0.008 0.036 0.812 0.144
#> GSM876896 4 0.3172 0.6758 0.000 0.000 0.160 0.840
#> GSM876897 4 0.3024 0.6802 0.000 0.000 0.148 0.852
#> GSM876868 1 0.0000 0.8672 1.000 0.000 0.000 0.000
#> GSM876869 1 0.0000 0.8672 1.000 0.000 0.000 0.000
#> GSM876870 1 0.0000 0.8672 1.000 0.000 0.000 0.000
#> GSM876871 1 0.0188 0.8669 0.996 0.000 0.004 0.000
#> GSM876872 4 0.3172 0.6725 0.000 0.000 0.160 0.840
#> GSM876873 4 0.4331 0.5417 0.000 0.000 0.288 0.712
#> GSM876844 2 0.1151 0.8877 0.000 0.968 0.008 0.024
#> GSM876845 2 0.0592 0.8923 0.000 0.984 0.016 0.000
#> GSM876846 4 0.2411 0.6368 0.000 0.040 0.040 0.920
#> GSM876847 2 0.0817 0.8897 0.000 0.976 0.024 0.000
#> GSM876848 4 0.1302 0.6848 0.000 0.000 0.044 0.956
#> GSM876849 4 0.1302 0.6862 0.000 0.000 0.044 0.956
#> GSM876898 1 0.4010 0.8014 0.816 0.028 0.156 0.000
#> GSM876899 3 0.3113 0.7344 0.004 0.012 0.876 0.108
#> GSM876900 3 0.5708 0.3246 0.028 0.000 0.556 0.416
#> GSM876901 1 0.7344 0.2480 0.476 0.112 0.400 0.012
#> GSM876902 4 0.2868 0.6827 0.000 0.000 0.136 0.864
#> GSM876903 3 0.5770 0.6543 0.000 0.140 0.712 0.148
#> GSM876904 1 0.6198 0.4313 0.560 0.040 0.392 0.008
#> GSM876874 1 0.2408 0.8455 0.896 0.000 0.104 0.000
#> GSM876875 3 0.3900 0.7029 0.020 0.000 0.816 0.164
#> GSM876876 1 0.3024 0.8224 0.852 0.000 0.148 0.000
#> GSM876877 1 0.1637 0.8588 0.940 0.000 0.060 0.000
#> GSM876878 1 0.4277 0.7061 0.720 0.000 0.280 0.000
#> GSM876879 3 0.3681 0.7031 0.008 0.000 0.816 0.176
#> GSM876880 1 0.1389 0.8611 0.952 0.000 0.048 0.000
#> GSM876850 2 0.0921 0.8879 0.000 0.972 0.028 0.000
#> GSM876851 2 0.0336 0.8937 0.000 0.992 0.008 0.000
#> GSM876852 2 0.1820 0.8786 0.000 0.944 0.020 0.036
#> GSM876853 2 0.0336 0.8939 0.000 0.992 0.000 0.008
#> GSM876854 4 0.5723 0.1210 0.000 0.388 0.032 0.580
#> GSM876855 2 0.5010 0.6359 0.000 0.700 0.024 0.276
#> GSM876856 2 0.5466 0.3019 0.000 0.548 0.016 0.436
#> GSM876905 1 0.5672 0.5499 0.648 0.004 0.312 0.036
#> GSM876906 3 0.5206 0.5770 0.000 0.024 0.668 0.308
#> GSM876907 3 0.6215 0.4939 0.024 0.256 0.668 0.052
#> GSM876908 3 0.4060 0.7295 0.020 0.012 0.828 0.140
#> GSM876909 2 0.3443 0.7947 0.016 0.848 0.136 0.000
#> GSM876881 2 0.5653 0.6256 0.192 0.712 0.096 0.000
#> GSM876882 3 0.3873 0.6851 0.000 0.000 0.772 0.228
#> GSM876883 3 0.4277 0.6230 0.000 0.000 0.720 0.280
#> GSM876884 1 0.1940 0.8555 0.924 0.000 0.076 0.000
#> GSM876885 3 0.4040 0.6569 0.000 0.000 0.752 0.248
#> GSM876857 1 0.0188 0.8664 0.996 0.000 0.000 0.004
#> GSM876858 2 0.3820 0.8265 0.028 0.856 0.016 0.100
#> GSM876859 2 0.1584 0.8813 0.036 0.952 0.012 0.000
#> GSM876860 2 0.4928 0.7371 0.028 0.768 0.016 0.188
#> GSM876861 4 0.5005 0.4797 0.004 0.264 0.020 0.712
cbind(get_classes(res, k = 5), get_membership(res, k = 5))
#> class entropy silhouette p1 p2 p3 p4 p5
#> GSM876886 3 0.5547 0.5931 0.068 0.000 0.676 0.224 0.032
#> GSM876887 3 0.5185 0.1394 0.000 0.000 0.568 0.384 0.048
#> GSM876888 3 0.5496 -0.2299 0.468 0.000 0.476 0.004 0.052
#> GSM876889 4 0.4803 0.2442 0.000 0.000 0.020 0.536 0.444
#> GSM876890 5 0.4477 0.5166 0.000 0.000 0.040 0.252 0.708
#> GSM876891 5 0.3772 0.6547 0.000 0.000 0.036 0.172 0.792
#> GSM876862 1 0.0290 0.8608 0.992 0.000 0.008 0.000 0.000
#> GSM876863 1 0.3370 0.7494 0.824 0.000 0.028 0.148 0.000
#> GSM876864 1 0.0324 0.8614 0.992 0.000 0.000 0.004 0.004
#> GSM876865 1 0.0912 0.8562 0.972 0.000 0.016 0.012 0.000
#> GSM876866 4 0.3002 0.7093 0.008 0.000 0.048 0.876 0.068
#> GSM876867 1 0.0613 0.8602 0.984 0.000 0.008 0.004 0.004
#> GSM876838 2 0.0703 0.8713 0.000 0.976 0.000 0.000 0.024
#> GSM876839 2 0.1251 0.8713 0.000 0.956 0.000 0.008 0.036
#> GSM876840 4 0.4754 0.3933 0.000 0.304 0.012 0.664 0.020
#> GSM876841 2 0.1043 0.8696 0.000 0.960 0.000 0.000 0.040
#> GSM876842 2 0.0609 0.8649 0.000 0.980 0.000 0.020 0.000
#> GSM876843 4 0.2208 0.7105 0.000 0.000 0.020 0.908 0.072
#> GSM876892 5 0.2462 0.7119 0.000 0.000 0.008 0.112 0.880
#> GSM876893 5 0.3022 0.7622 0.064 0.000 0.020 0.036 0.880
#> GSM876894 5 0.4402 0.5744 0.000 0.000 0.352 0.012 0.636
#> GSM876895 5 0.4184 0.7395 0.000 0.048 0.176 0.004 0.772
#> GSM876896 4 0.4168 0.6510 0.000 0.000 0.200 0.756 0.044
#> GSM876897 4 0.4395 0.6626 0.000 0.000 0.188 0.748 0.064
#> GSM876868 1 0.0324 0.8614 0.992 0.000 0.000 0.004 0.004
#> GSM876869 1 0.0613 0.8602 0.984 0.000 0.008 0.004 0.004
#> GSM876870 1 0.0290 0.8610 0.992 0.000 0.000 0.008 0.000
#> GSM876871 1 0.0404 0.8599 0.988 0.000 0.012 0.000 0.000
#> GSM876872 4 0.3807 0.5991 0.000 0.000 0.240 0.748 0.012
#> GSM876873 4 0.4848 0.2697 0.000 0.000 0.420 0.556 0.024
#> GSM876844 2 0.0963 0.8615 0.000 0.964 0.000 0.036 0.000
#> GSM876845 2 0.1197 0.8672 0.000 0.952 0.000 0.000 0.048
#> GSM876846 4 0.3285 0.6699 0.000 0.044 0.008 0.856 0.092
#> GSM876847 2 0.1430 0.8647 0.000 0.944 0.004 0.000 0.052
#> GSM876848 4 0.2769 0.7124 0.000 0.000 0.032 0.876 0.092
#> GSM876849 4 0.2903 0.7141 0.000 0.000 0.048 0.872 0.080
#> GSM876898 1 0.5956 0.1715 0.544 0.028 0.044 0.004 0.380
#> GSM876899 5 0.4688 0.6279 0.000 0.020 0.312 0.008 0.660
#> GSM876900 5 0.2069 0.7580 0.012 0.000 0.012 0.052 0.924
#> GSM876901 5 0.3783 0.7179 0.152 0.020 0.012 0.004 0.812
#> GSM876902 4 0.4720 0.6792 0.000 0.000 0.124 0.736 0.140
#> GSM876903 5 0.3849 0.7607 0.000 0.052 0.116 0.012 0.820
#> GSM876904 5 0.4724 0.6348 0.236 0.008 0.036 0.004 0.716
#> GSM876874 1 0.3421 0.7735 0.816 0.000 0.164 0.004 0.016
#> GSM876875 3 0.2599 0.7255 0.028 0.000 0.904 0.024 0.044
#> GSM876876 1 0.4468 0.6241 0.696 0.000 0.276 0.004 0.024
#> GSM876877 1 0.2511 0.8276 0.892 0.000 0.088 0.004 0.016
#> GSM876878 1 0.5246 0.2182 0.512 0.000 0.448 0.004 0.036
#> GSM876879 3 0.2362 0.7338 0.024 0.000 0.916 0.028 0.032
#> GSM876880 1 0.2102 0.8371 0.916 0.000 0.068 0.004 0.012
#> GSM876850 2 0.1571 0.8605 0.000 0.936 0.004 0.000 0.060
#> GSM876851 2 0.1121 0.8686 0.000 0.956 0.000 0.000 0.044
#> GSM876852 2 0.1205 0.8588 0.000 0.956 0.000 0.040 0.004
#> GSM876853 2 0.0794 0.8711 0.000 0.972 0.000 0.000 0.028
#> GSM876854 4 0.4899 -0.0484 0.000 0.456 0.008 0.524 0.012
#> GSM876855 2 0.3875 0.6865 0.000 0.756 0.004 0.228 0.012
#> GSM876856 2 0.4919 0.4060 0.000 0.604 0.016 0.368 0.012
#> GSM876905 5 0.3449 0.7140 0.164 0.000 0.000 0.024 0.812
#> GSM876906 5 0.2060 0.7681 0.000 0.008 0.052 0.016 0.924
#> GSM876907 5 0.4179 0.7362 0.000 0.072 0.152 0.000 0.776
#> GSM876908 5 0.3773 0.7509 0.000 0.032 0.164 0.004 0.800
#> GSM876909 5 0.5335 0.2685 0.004 0.416 0.044 0.000 0.536
#> GSM876881 2 0.6007 0.5353 0.188 0.648 0.136 0.000 0.028
#> GSM876882 3 0.2189 0.7427 0.000 0.000 0.904 0.084 0.012
#> GSM876883 3 0.2448 0.7371 0.000 0.000 0.892 0.088 0.020
#> GSM876884 1 0.2984 0.8051 0.856 0.000 0.124 0.004 0.016
#> GSM876885 3 0.2189 0.7427 0.000 0.000 0.904 0.084 0.012
#> GSM876857 1 0.0451 0.8613 0.988 0.000 0.000 0.008 0.004
#> GSM876858 2 0.3003 0.8405 0.016 0.884 0.032 0.064 0.004
#> GSM876859 2 0.2680 0.8480 0.040 0.904 0.036 0.012 0.008
#> GSM876860 2 0.3436 0.8264 0.020 0.856 0.028 0.092 0.004
#> GSM876861 2 0.5856 0.3105 0.004 0.544 0.068 0.376 0.008
cbind(get_classes(res, k = 6), get_membership(res, k = 6))
#> class entropy silhouette p1 p2 p3 p4 p5 p6
#> GSM876886 6 0.6713 0.4667 0.064 0.000 0.036 0.252 NA 0.548
#> GSM876887 6 0.6225 0.0880 0.000 0.000 0.060 0.408 NA 0.440
#> GSM876888 1 0.5995 0.5037 0.500 0.000 0.024 0.000 NA 0.340
#> GSM876889 4 0.5801 0.2234 0.000 0.000 0.416 0.472 NA 0.044
#> GSM876890 3 0.4222 0.4894 0.000 0.000 0.692 0.268 NA 0.008
#> GSM876891 3 0.2739 0.7488 0.000 0.000 0.872 0.084 NA 0.012
#> GSM876862 1 0.0146 0.8053 0.996 0.000 0.000 0.000 NA 0.000
#> GSM876863 1 0.4844 0.6164 0.692 0.000 0.004 0.032 NA 0.048
#> GSM876864 1 0.0363 0.8062 0.988 0.000 0.000 0.000 NA 0.000
#> GSM876865 1 0.3274 0.7088 0.804 0.000 0.004 0.000 NA 0.024
#> GSM876866 4 0.5338 0.4885 0.024 0.000 0.080 0.676 NA 0.020
#> GSM876867 1 0.0260 0.8056 0.992 0.000 0.000 0.000 NA 0.000
#> GSM876838 2 0.2375 0.7062 0.000 0.896 0.016 0.020 NA 0.000
#> GSM876839 2 0.3997 0.6563 0.000 0.784 0.008 0.092 NA 0.004
#> GSM876840 4 0.5231 0.3091 0.000 0.216 0.004 0.624 NA 0.000
#> GSM876841 2 0.2369 0.7083 0.000 0.900 0.028 0.004 NA 0.008
#> GSM876842 2 0.2647 0.6924 0.000 0.868 0.000 0.044 NA 0.000
#> GSM876843 4 0.1743 0.5487 0.000 0.024 0.008 0.936 NA 0.004
#> GSM876892 3 0.2864 0.7392 0.000 0.000 0.860 0.100 NA 0.012
#> GSM876893 3 0.2454 0.7881 0.032 0.000 0.904 0.032 NA 0.008
#> GSM876894 3 0.4282 0.6865 0.000 0.000 0.720 0.000 NA 0.192
#> GSM876895 3 0.4026 0.7789 0.000 0.112 0.792 0.000 NA 0.048
#> GSM876896 4 0.5671 0.4265 0.000 0.000 0.052 0.636 NA 0.184
#> GSM876897 4 0.5905 0.4320 0.000 0.000 0.080 0.624 NA 0.172
#> GSM876868 1 0.0790 0.8030 0.968 0.000 0.000 0.000 NA 0.000
#> GSM876869 1 0.0790 0.8025 0.968 0.000 0.000 0.000 NA 0.000
#> GSM876870 1 0.0937 0.8002 0.960 0.000 0.000 0.000 NA 0.000
#> GSM876871 1 0.0458 0.8040 0.984 0.000 0.000 0.000 NA 0.000
#> GSM876872 4 0.6404 0.1518 0.000 0.000 0.024 0.456 NA 0.248
#> GSM876873 4 0.5861 -0.0423 0.000 0.000 0.016 0.448 NA 0.412
#> GSM876844 2 0.4343 0.6190 0.000 0.736 0.000 0.128 NA 0.004
#> GSM876845 2 0.1937 0.7128 0.000 0.924 0.032 0.004 NA 0.004
#> GSM876846 4 0.4301 0.4610 0.000 0.136 0.004 0.740 NA 0.000
#> GSM876847 2 0.2209 0.7084 0.000 0.904 0.040 0.000 NA 0.004
#> GSM876848 4 0.2024 0.5601 0.000 0.008 0.036 0.924 NA 0.012
#> GSM876849 4 0.1923 0.5603 0.000 0.008 0.036 0.928 NA 0.020
#> GSM876898 3 0.6831 0.3730 0.308 0.028 0.504 0.004 NA 0.060
#> GSM876899 3 0.4324 0.7414 0.000 0.036 0.756 0.000 NA 0.156
#> GSM876900 3 0.1963 0.7767 0.004 0.000 0.924 0.044 NA 0.012
#> GSM876901 3 0.3547 0.7961 0.060 0.040 0.844 0.000 NA 0.016
#> GSM876902 4 0.5730 0.4700 0.000 0.000 0.128 0.652 NA 0.120
#> GSM876903 3 0.4064 0.7681 0.000 0.128 0.776 0.000 NA 0.016
#> GSM876904 3 0.3929 0.7794 0.076 0.028 0.816 0.000 NA 0.016
#> GSM876874 1 0.4836 0.6951 0.664 0.000 0.000 0.000 NA 0.196
#> GSM876875 6 0.2681 0.7213 0.004 0.000 0.020 0.040 NA 0.888
#> GSM876876 1 0.5224 0.6554 0.616 0.000 0.004 0.000 NA 0.244
#> GSM876877 1 0.4354 0.7368 0.724 0.000 0.000 0.000 NA 0.132
#> GSM876878 1 0.5555 0.5713 0.548 0.000 0.008 0.000 NA 0.316
#> GSM876879 6 0.1881 0.7423 0.004 0.000 0.008 0.040 NA 0.928
#> GSM876880 1 0.4125 0.7458 0.748 0.000 0.000 0.000 NA 0.124
#> GSM876850 2 0.2583 0.7025 0.000 0.884 0.052 0.000 NA 0.008
#> GSM876851 2 0.1476 0.7148 0.000 0.948 0.028 0.008 NA 0.004
#> GSM876852 2 0.4381 0.6172 0.000 0.732 0.000 0.132 NA 0.004
#> GSM876853 2 0.2136 0.7078 0.000 0.908 0.012 0.016 NA 0.000
#> GSM876854 4 0.5403 0.2461 0.000 0.248 0.004 0.592 NA 0.000
#> GSM876855 2 0.5900 0.2812 0.000 0.480 0.004 0.352 NA 0.004
#> GSM876856 2 0.5828 0.1543 0.000 0.428 0.004 0.408 NA 0.000
#> GSM876905 3 0.3348 0.7666 0.112 0.000 0.836 0.016 NA 0.008
#> GSM876906 3 0.1307 0.7987 0.000 0.032 0.952 0.000 NA 0.008
#> GSM876907 3 0.4176 0.7601 0.000 0.136 0.768 0.000 NA 0.020
#> GSM876908 3 0.3649 0.7898 0.000 0.068 0.824 0.000 NA 0.068
#> GSM876909 3 0.5816 0.5275 0.012 0.284 0.580 0.004 NA 0.012
#> GSM876881 2 0.7247 0.3164 0.096 0.484 0.016 0.004 NA 0.156
#> GSM876882 6 0.2213 0.7492 0.000 0.000 0.004 0.100 NA 0.888
#> GSM876883 6 0.3726 0.7247 0.000 0.000 0.024 0.092 NA 0.812
#> GSM876884 1 0.4387 0.7323 0.720 0.000 0.000 0.000 NA 0.152
#> GSM876885 6 0.3469 0.7226 0.000 0.000 0.012 0.072 NA 0.824
#> GSM876857 1 0.0935 0.8028 0.964 0.000 0.000 0.004 NA 0.000
#> GSM876858 2 0.5336 0.5575 0.020 0.584 0.004 0.000 NA 0.064
#> GSM876859 2 0.5412 0.5756 0.036 0.620 0.000 0.000 NA 0.080
#> GSM876860 2 0.5432 0.5426 0.020 0.564 0.004 0.000 NA 0.068
#> GSM876861 2 0.6214 0.4040 0.016 0.444 0.000 0.016 NA 0.120
Heatmaps for the consensus matrix. It visualizes the probability of two samples to be in a same group.
consensus_heatmap(res, k = 2)
consensus_heatmap(res, k = 3)
consensus_heatmap(res, k = 4)
consensus_heatmap(res, k = 5)
consensus_heatmap(res, k = 6)
Heatmaps for the membership of samples in all partitions to see how consistent they are:
membership_heatmap(res, k = 2)
membership_heatmap(res, k = 3)
membership_heatmap(res, k = 4)
membership_heatmap(res, k = 5)
membership_heatmap(res, k = 6)
As soon as we have had the classes for columns, we can look for signatures which are significantly different between classes which can be candidate marks for certain classes. Following are the heatmaps for signatures.
Signature heatmaps where rows are scaled:
get_signatures(res, k = 2)
get_signatures(res, k = 3)
get_signatures(res, k = 4)
get_signatures(res, k = 5)
get_signatures(res, k = 6)
Signature heatmaps where rows are not scaled:
get_signatures(res, k = 2, scale_rows = FALSE)
get_signatures(res, k = 3, scale_rows = FALSE)
get_signatures(res, k = 4, scale_rows = FALSE)
get_signatures(res, k = 5, scale_rows = FALSE)
get_signatures(res, k = 6, scale_rows = FALSE)
Compare the overlap of signatures from different k:
compare_signatures(res)
get_signature() returns a data frame invisibly. TO get the list of signatures, the function
call should be assigned to a variable explicitly. In following code, if plot argument is set
to FALSE, no heatmap is plotted while only the differential analysis is performed.
# code only for demonstration
tb = get_signature(res, k = ..., plot = FALSE)
An example of the output of tb is:
#> which_row fdr mean_1 mean_2 scaled_mean_1 scaled_mean_2 km
#> 1 38 0.042760348 8.373488 9.131774 -0.5533452 0.5164555 1
#> 2 40 0.018707592 7.106213 8.469186 -0.6173731 0.5762149 1
#> 3 55 0.019134737 10.221463 11.207825 -0.6159697 0.5749050 1
#> 4 59 0.006059896 5.921854 7.869574 -0.6899429 0.6439467 1
#> 5 60 0.018055526 8.928898 10.211722 -0.6204761 0.5791110 1
#> 6 98 0.009384629 15.714769 14.887706 0.6635654 -0.6193277 2
...
The columns in tb are:
which_row: row indices corresponding to the input matrix.fdr: FDR for the differential test. mean_x: The mean value in group x.scaled_mean_x: The mean value in group x after rows are scaled.km: Row groups if k-means clustering is applied to rows.UMAP plot which shows how samples are separated.
dimension_reduction(res, k = 2, method = "UMAP")
dimension_reduction(res, k = 3, method = "UMAP")
dimension_reduction(res, k = 4, method = "UMAP")
dimension_reduction(res, k = 5, method = "UMAP")
dimension_reduction(res, k = 6, method = "UMAP")
Following heatmap shows how subgroups are split when increasing k:
collect_classes(res)
Test correlation between subgroups and known annotations. If the known annotation is numeric, one-way ANOVA test is applied, and if the known annotation is discrete, chi-squared contingency table test is applied.
test_to_known_factors(res)
#> n disease.state(p) tissue(p) k
#> ATC:NMF 69 0.7600 6.14e-05 2
#> ATC:NMF 69 0.5754 1.69e-11 3
#> ATC:NMF 60 0.0629 1.91e-08 4
#> ATC:NMF 61 0.2604 8.91e-16 5
#> ATC:NMF 54 0.2872 1.57e-17 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